Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8042,2,Mod(1,8042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8042, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8042 = 2 \cdot 4021 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8042.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2156933055\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8042.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.49912 | −1.44287 | −0.721433 | − | 0.692485i | \(-0.756516\pi\) | ||||
−0.721433 | + | 0.692485i | \(0.756516\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.77840 | −1.68975 | −0.844876 | − | 0.534962i | \(-0.820326\pi\) | ||||
−0.844876 | + | 0.534962i | \(0.820326\pi\) | |||||||
\(6\) | 2.49912 | 1.02026 | ||||||||
\(7\) | −0.508744 | −0.192287 | −0.0961436 | − | 0.995367i | \(-0.530651\pi\) | ||||
−0.0961436 | + | 0.995367i | \(0.530651\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.24558 | 1.08186 | ||||||||
\(10\) | 3.77840 | 1.19483 | ||||||||
\(11\) | 4.72877 | 1.42578 | 0.712889 | − | 0.701277i | \(-0.247386\pi\) | ||||
0.712889 | + | 0.701277i | \(0.247386\pi\) | |||||||
\(12\) | −2.49912 | −0.721433 | ||||||||
\(13\) | −1.56616 | −0.434375 | −0.217187 | − | 0.976130i | \(-0.569688\pi\) | ||||
−0.217187 | + | 0.976130i | \(0.569688\pi\) | |||||||
\(14\) | 0.508744 | 0.135968 | ||||||||
\(15\) | 9.44266 | 2.43808 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.70941 | −0.414592 | −0.207296 | − | 0.978278i | \(-0.566466\pi\) | ||||
−0.207296 | + | 0.978278i | \(0.566466\pi\) | |||||||
\(18\) | −3.24558 | −0.764990 | ||||||||
\(19\) | −7.33030 | −1.68169 | −0.840843 | − | 0.541278i | \(-0.817941\pi\) | ||||
−0.840843 | + | 0.541278i | \(0.817941\pi\) | |||||||
\(20\) | −3.77840 | −0.844876 | ||||||||
\(21\) | 1.27141 | 0.277444 | ||||||||
\(22\) | −4.72877 | −1.00818 | ||||||||
\(23\) | 6.82278 | 1.42265 | 0.711324 | − | 0.702865i | \(-0.248096\pi\) | ||||
0.711324 | + | 0.702865i | \(0.248096\pi\) | |||||||
\(24\) | 2.49912 | 0.510130 | ||||||||
\(25\) | 9.27631 | 1.85526 | ||||||||
\(26\) | 1.56616 | 0.307149 | ||||||||
\(27\) | −0.613729 | −0.118112 | ||||||||
\(28\) | −0.508744 | −0.0961436 | ||||||||
\(29\) | 6.46138 | 1.19985 | 0.599924 | − | 0.800057i | \(-0.295197\pi\) | ||||
0.599924 | + | 0.800057i | \(0.295197\pi\) | |||||||
\(30\) | −9.44266 | −1.72399 | ||||||||
\(31\) | −0.0712862 | −0.0128034 | −0.00640169 | − | 0.999980i | \(-0.502038\pi\) | ||||
−0.00640169 | + | 0.999980i | \(0.502038\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −11.8177 | −2.05720 | ||||||||
\(34\) | 1.70941 | 0.293161 | ||||||||
\(35\) | 1.92224 | 0.324917 | ||||||||
\(36\) | 3.24558 | 0.540930 | ||||||||
\(37\) | 9.42635 | 1.54968 | 0.774841 | − | 0.632156i | \(-0.217830\pi\) | ||||
0.774841 | + | 0.632156i | \(0.217830\pi\) | |||||||
\(38\) | 7.33030 | 1.18913 | ||||||||
\(39\) | 3.91402 | 0.626744 | ||||||||
\(40\) | 3.77840 | 0.597417 | ||||||||
\(41\) | −5.14690 | −0.803810 | −0.401905 | − | 0.915681i | \(-0.631652\pi\) | ||||
−0.401905 | + | 0.915681i | \(0.631652\pi\) | |||||||
\(42\) | −1.27141 | −0.196183 | ||||||||
\(43\) | 1.98166 | 0.302200 | 0.151100 | − | 0.988518i | \(-0.451718\pi\) | ||||
0.151100 | + | 0.988518i | \(0.451718\pi\) | |||||||
\(44\) | 4.72877 | 0.712889 | ||||||||
\(45\) | −12.2631 | −1.82807 | ||||||||
\(46\) | −6.82278 | −1.00596 | ||||||||
\(47\) | 5.36150 | 0.782055 | 0.391028 | − | 0.920379i | \(-0.372120\pi\) | ||||
0.391028 | + | 0.920379i | \(0.372120\pi\) | |||||||
\(48\) | −2.49912 | −0.360716 | ||||||||
\(49\) | −6.74118 | −0.963026 | ||||||||
\(50\) | −9.27631 | −1.31187 | ||||||||
\(51\) | 4.27200 | 0.598200 | ||||||||
\(52\) | −1.56616 | −0.217187 | ||||||||
\(53\) | 0.630655 | 0.0866271 | 0.0433136 | − | 0.999062i | \(-0.486209\pi\) | ||||
0.0433136 | + | 0.999062i | \(0.486209\pi\) | |||||||
\(54\) | 0.613729 | 0.0835179 | ||||||||
\(55\) | −17.8672 | −2.40921 | ||||||||
\(56\) | 0.508744 | 0.0679838 | ||||||||
\(57\) | 18.3193 | 2.42645 | ||||||||
\(58\) | −6.46138 | −0.848421 | ||||||||
\(59\) | −3.96183 | −0.515787 | −0.257893 | − | 0.966173i | \(-0.583028\pi\) | ||||
−0.257893 | + | 0.966173i | \(0.583028\pi\) | |||||||
\(60\) | 9.44266 | 1.21904 | ||||||||
\(61\) | 10.9418 | 1.40095 | 0.700477 | − | 0.713675i | \(-0.252971\pi\) | ||||
0.700477 | + | 0.713675i | \(0.252971\pi\) | |||||||
\(62\) | 0.0712862 | 0.00905335 | ||||||||
\(63\) | −1.65117 | −0.208028 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.91758 | 0.733986 | ||||||||
\(66\) | 11.8177 | 1.45466 | ||||||||
\(67\) | −0.192213 | −0.0234825 | −0.0117412 | − | 0.999931i | \(-0.503737\pi\) | ||||
−0.0117412 | + | 0.999931i | \(0.503737\pi\) | |||||||
\(68\) | −1.70941 | −0.207296 | ||||||||
\(69\) | −17.0509 | −2.05269 | ||||||||
\(70\) | −1.92224 | −0.229751 | ||||||||
\(71\) | 4.53092 | 0.537721 | 0.268861 | − | 0.963179i | \(-0.413353\pi\) | ||||
0.268861 | + | 0.963179i | \(0.413353\pi\) | |||||||
\(72\) | −3.24558 | −0.382495 | ||||||||
\(73\) | 0.588797 | 0.0689134 | 0.0344567 | − | 0.999406i | \(-0.489030\pi\) | ||||
0.0344567 | + | 0.999406i | \(0.489030\pi\) | |||||||
\(74\) | −9.42635 | −1.09579 | ||||||||
\(75\) | −23.1826 | −2.67689 | ||||||||
\(76\) | −7.33030 | −0.840843 | ||||||||
\(77\) | −2.40573 | −0.274159 | ||||||||
\(78\) | −3.91402 | −0.443175 | ||||||||
\(79\) | −16.1449 | −1.81644 | −0.908221 | − | 0.418492i | \(-0.862559\pi\) | ||||
−0.908221 | + | 0.418492i | \(0.862559\pi\) | |||||||
\(80\) | −3.77840 | −0.422438 | ||||||||
\(81\) | −8.20296 | −0.911440 | ||||||||
\(82\) | 5.14690 | 0.568380 | ||||||||
\(83\) | 6.65631 | 0.730625 | 0.365312 | − | 0.930885i | \(-0.380962\pi\) | ||||
0.365312 | + | 0.930885i | \(0.380962\pi\) | |||||||
\(84\) | 1.27141 | 0.138722 | ||||||||
\(85\) | 6.45882 | 0.700558 | ||||||||
\(86\) | −1.98166 | −0.213688 | ||||||||
\(87\) | −16.1477 | −1.73122 | ||||||||
\(88\) | −4.72877 | −0.504089 | ||||||||
\(89\) | −0.667289 | −0.0707325 | −0.0353662 | − | 0.999374i | \(-0.511260\pi\) | ||||
−0.0353662 | + | 0.999374i | \(0.511260\pi\) | |||||||
\(90\) | 12.2631 | 1.29264 | ||||||||
\(91\) | 0.796775 | 0.0835247 | ||||||||
\(92\) | 6.82278 | 0.711324 | ||||||||
\(93\) | 0.178152 | 0.0184735 | ||||||||
\(94\) | −5.36150 | −0.552997 | ||||||||
\(95\) | 27.6968 | 2.84163 | ||||||||
\(96\) | 2.49912 | 0.255065 | ||||||||
\(97\) | 2.10060 | 0.213284 | 0.106642 | − | 0.994297i | \(-0.465990\pi\) | ||||
0.106642 | + | 0.994297i | \(0.465990\pi\) | |||||||
\(98\) | 6.74118 | 0.680962 | ||||||||
\(99\) | 15.3476 | 1.54249 | ||||||||
\(100\) | 9.27631 | 0.927631 | ||||||||
\(101\) | 2.07226 | 0.206198 | 0.103099 | − | 0.994671i | \(-0.467124\pi\) | ||||
0.103099 | + | 0.994671i | \(0.467124\pi\) | |||||||
\(102\) | −4.27200 | −0.422992 | ||||||||
\(103\) | 14.2849 | 1.40753 | 0.703764 | − | 0.710434i | \(-0.251501\pi\) | ||||
0.703764 | + | 0.710434i | \(0.251501\pi\) | |||||||
\(104\) | 1.56616 | 0.153575 | ||||||||
\(105\) | −4.80389 | −0.468812 | ||||||||
\(106\) | −0.630655 | −0.0612546 | ||||||||
\(107\) | −10.1314 | −0.979437 | −0.489718 | − | 0.871881i | \(-0.662900\pi\) | ||||
−0.489718 | + | 0.871881i | \(0.662900\pi\) | |||||||
\(108\) | −0.613729 | −0.0590561 | ||||||||
\(109\) | 13.6923 | 1.31148 | 0.655742 | − | 0.754985i | \(-0.272356\pi\) | ||||
0.655742 | + | 0.754985i | \(0.272356\pi\) | |||||||
\(110\) | 17.8672 | 1.70357 | ||||||||
\(111\) | −23.5575 | −2.23598 | ||||||||
\(112\) | −0.508744 | −0.0480718 | ||||||||
\(113\) | −8.47807 | −0.797550 | −0.398775 | − | 0.917049i | \(-0.630565\pi\) | ||||
−0.398775 | + | 0.917049i | \(0.630565\pi\) | |||||||
\(114\) | −18.3193 | −1.71576 | ||||||||
\(115\) | −25.7792 | −2.40392 | ||||||||
\(116\) | 6.46138 | 0.599924 | ||||||||
\(117\) | −5.08310 | −0.469933 | ||||||||
\(118\) | 3.96183 | 0.364716 | ||||||||
\(119\) | 0.869650 | 0.0797207 | ||||||||
\(120\) | −9.44266 | −0.861993 | ||||||||
\(121\) | 11.3613 | 1.03284 | ||||||||
\(122\) | −10.9418 | −0.990624 | ||||||||
\(123\) | 12.8627 | 1.15979 | ||||||||
\(124\) | −0.0712862 | −0.00640169 | ||||||||
\(125\) | −16.1576 | −1.44518 | ||||||||
\(126\) | 1.65117 | 0.147098 | ||||||||
\(127\) | −14.9791 | −1.32918 | −0.664590 | − | 0.747208i | \(-0.731394\pi\) | ||||
−0.664590 | + | 0.747208i | \(0.731394\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −4.95240 | −0.436034 | ||||||||
\(130\) | −5.91758 | −0.519006 | ||||||||
\(131\) | −10.5654 | −0.923106 | −0.461553 | − | 0.887113i | \(-0.652708\pi\) | ||||
−0.461553 | + | 0.887113i | \(0.652708\pi\) | |||||||
\(132\) | −11.8177 | −1.02860 | ||||||||
\(133\) | 3.72925 | 0.323367 | ||||||||
\(134\) | 0.192213 | 0.0166046 | ||||||||
\(135\) | 2.31891 | 0.199580 | ||||||||
\(136\) | 1.70941 | 0.146580 | ||||||||
\(137\) | −11.8114 | −1.00912 | −0.504559 | − | 0.863377i | \(-0.668345\pi\) | ||||
−0.504559 | + | 0.863377i | \(0.668345\pi\) | |||||||
\(138\) | 17.0509 | 1.45147 | ||||||||
\(139\) | −2.76617 | −0.234624 | −0.117312 | − | 0.993095i | \(-0.537428\pi\) | ||||
−0.117312 | + | 0.993095i | \(0.537428\pi\) | |||||||
\(140\) | 1.92224 | 0.162459 | ||||||||
\(141\) | −13.3990 | −1.12840 | ||||||||
\(142\) | −4.53092 | −0.380226 | ||||||||
\(143\) | −7.40602 | −0.619322 | ||||||||
\(144\) | 3.24558 | 0.270465 | ||||||||
\(145\) | −24.4137 | −2.02745 | ||||||||
\(146\) | −0.588797 | −0.0487291 | ||||||||
\(147\) | 16.8470 | 1.38952 | ||||||||
\(148\) | 9.42635 | 0.774841 | ||||||||
\(149\) | 0.0224216 | 0.00183685 | 0.000918426 | − | 1.00000i | \(-0.499708\pi\) | ||||
0.000918426 | 1.00000i | \(0.499708\pi\) | ||||||||
\(150\) | 23.1826 | 1.89285 | ||||||||
\(151\) | 15.8603 | 1.29070 | 0.645348 | − | 0.763888i | \(-0.276712\pi\) | ||||
0.645348 | + | 0.763888i | \(0.276712\pi\) | |||||||
\(152\) | 7.33030 | 0.594566 | ||||||||
\(153\) | −5.54801 | −0.448530 | ||||||||
\(154\) | 2.40573 | 0.193859 | ||||||||
\(155\) | 0.269348 | 0.0216345 | ||||||||
\(156\) | 3.91402 | 0.313372 | ||||||||
\(157\) | 5.68936 | 0.454061 | 0.227030 | − | 0.973888i | \(-0.427098\pi\) | ||||
0.227030 | + | 0.973888i | \(0.427098\pi\) | |||||||
\(158\) | 16.1449 | 1.28442 | ||||||||
\(159\) | −1.57608 | −0.124991 | ||||||||
\(160\) | 3.77840 | 0.298709 | ||||||||
\(161\) | −3.47105 | −0.273557 | ||||||||
\(162\) | 8.20296 | 0.644485 | ||||||||
\(163\) | 4.12095 | 0.322777 | 0.161389 | − | 0.986891i | \(-0.448403\pi\) | ||||
0.161389 | + | 0.986891i | \(0.448403\pi\) | |||||||
\(164\) | −5.14690 | −0.401905 | ||||||||
\(165\) | 44.6522 | 3.47617 | ||||||||
\(166\) | −6.65631 | −0.516630 | ||||||||
\(167\) | 2.34577 | 0.181521 | 0.0907607 | − | 0.995873i | \(-0.471070\pi\) | ||||
0.0907607 | + | 0.995873i | \(0.471070\pi\) | |||||||
\(168\) | −1.27141 | −0.0980914 | ||||||||
\(169\) | −10.5471 | −0.811318 | ||||||||
\(170\) | −6.45882 | −0.495369 | ||||||||
\(171\) | −23.7911 | −1.81935 | ||||||||
\(172\) | 1.98166 | 0.151100 | ||||||||
\(173\) | −16.9073 | −1.28544 | −0.642718 | − | 0.766103i | \(-0.722193\pi\) | ||||
−0.642718 | + | 0.766103i | \(0.722193\pi\) | |||||||
\(174\) | 16.1477 | 1.22416 | ||||||||
\(175\) | −4.71926 | −0.356743 | ||||||||
\(176\) | 4.72877 | 0.356444 | ||||||||
\(177\) | 9.90108 | 0.744211 | ||||||||
\(178\) | 0.667289 | 0.0500154 | ||||||||
\(179\) | −25.4604 | −1.90300 | −0.951498 | − | 0.307654i | \(-0.900456\pi\) | ||||
−0.951498 | + | 0.307654i | \(0.900456\pi\) | |||||||
\(180\) | −12.2631 | −0.914037 | ||||||||
\(181\) | −1.99371 | −0.148191 | −0.0740957 | − | 0.997251i | \(-0.523607\pi\) | ||||
−0.0740957 | + | 0.997251i | \(0.523607\pi\) | |||||||
\(182\) | −0.796775 | −0.0590609 | ||||||||
\(183\) | −27.3448 | −2.02139 | ||||||||
\(184\) | −6.82278 | −0.502982 | ||||||||
\(185\) | −35.6165 | −2.61858 | ||||||||
\(186\) | −0.178152 | −0.0130628 | ||||||||
\(187\) | −8.08339 | −0.591116 | ||||||||
\(188\) | 5.36150 | 0.391028 | ||||||||
\(189\) | 0.312231 | 0.0227114 | ||||||||
\(190\) | −27.6968 | −2.00934 | ||||||||
\(191\) | −14.4859 | −1.04816 | −0.524081 | − | 0.851669i | \(-0.675591\pi\) | ||||
−0.524081 | + | 0.851669i | \(0.675591\pi\) | |||||||
\(192\) | −2.49912 | −0.180358 | ||||||||
\(193\) | 21.0958 | 1.51851 | 0.759254 | − | 0.650794i | \(-0.225564\pi\) | ||||
0.759254 | + | 0.650794i | \(0.225564\pi\) | |||||||
\(194\) | −2.10060 | −0.150815 | ||||||||
\(195\) | −14.7887 | −1.05904 | ||||||||
\(196\) | −6.74118 | −0.481513 | ||||||||
\(197\) | −24.1967 | −1.72394 | −0.861970 | − | 0.506959i | \(-0.830770\pi\) | ||||
−0.861970 | + | 0.506959i | \(0.830770\pi\) | |||||||
\(198\) | −15.3476 | −1.09071 | ||||||||
\(199\) | 16.5051 | 1.17002 | 0.585008 | − | 0.811028i | \(-0.301091\pi\) | ||||
0.585008 | + | 0.811028i | \(0.301091\pi\) | |||||||
\(200\) | −9.27631 | −0.655934 | ||||||||
\(201\) | 0.480361 | 0.0338821 | ||||||||
\(202\) | −2.07226 | −0.145804 | ||||||||
\(203\) | −3.28719 | −0.230715 | ||||||||
\(204\) | 4.27200 | 0.299100 | ||||||||
\(205\) | 19.4470 | 1.35824 | ||||||||
\(206\) | −14.2849 | −0.995273 | ||||||||
\(207\) | 22.1439 | 1.53910 | ||||||||
\(208\) | −1.56616 | −0.108594 | ||||||||
\(209\) | −34.6633 | −2.39771 | ||||||||
\(210\) | 4.80389 | 0.331500 | ||||||||
\(211\) | 12.4250 | 0.855375 | 0.427688 | − | 0.903927i | \(-0.359328\pi\) | ||||
0.427688 | + | 0.903927i | \(0.359328\pi\) | |||||||
\(212\) | 0.630655 | 0.0433136 | ||||||||
\(213\) | −11.3233 | −0.775859 | ||||||||
\(214\) | 10.1314 | 0.692566 | ||||||||
\(215\) | −7.48751 | −0.510644 | ||||||||
\(216\) | 0.613729 | 0.0417589 | ||||||||
\(217\) | 0.0362664 | 0.00246192 | ||||||||
\(218\) | −13.6923 | −0.927360 | ||||||||
\(219\) | −1.47147 | −0.0994328 | ||||||||
\(220\) | −17.8672 | −1.20461 | ||||||||
\(221\) | 2.67721 | 0.180088 | ||||||||
\(222\) | 23.5575 | 1.58108 | ||||||||
\(223\) | −13.1348 | −0.879569 | −0.439784 | − | 0.898103i | \(-0.644945\pi\) | ||||
−0.439784 | + | 0.898103i | \(0.644945\pi\) | |||||||
\(224\) | 0.508744 | 0.0339919 | ||||||||
\(225\) | 30.1070 | 2.00713 | ||||||||
\(226\) | 8.47807 | 0.563953 | ||||||||
\(227\) | −8.32519 | −0.552562 | −0.276281 | − | 0.961077i | \(-0.589102\pi\) | ||||
−0.276281 | + | 0.961077i | \(0.589102\pi\) | |||||||
\(228\) | 18.3193 | 1.21322 | ||||||||
\(229\) | −10.2884 | −0.679875 | −0.339937 | − | 0.940448i | \(-0.610406\pi\) | ||||
−0.339937 | + | 0.940448i | \(0.610406\pi\) | |||||||
\(230\) | 25.7792 | 1.69983 | ||||||||
\(231\) | 6.01220 | 0.395574 | ||||||||
\(232\) | −6.46138 | −0.424210 | ||||||||
\(233\) | 29.6620 | 1.94322 | 0.971611 | − | 0.236582i | \(-0.0760273\pi\) | ||||
0.971611 | + | 0.236582i | \(0.0760273\pi\) | |||||||
\(234\) | 5.08310 | 0.332293 | ||||||||
\(235\) | −20.2579 | −1.32148 | ||||||||
\(236\) | −3.96183 | −0.257893 | ||||||||
\(237\) | 40.3479 | 2.62088 | ||||||||
\(238\) | −0.869650 | −0.0563710 | ||||||||
\(239\) | −27.9429 | −1.80748 | −0.903738 | − | 0.428086i | \(-0.859188\pi\) | ||||
−0.903738 | + | 0.428086i | \(0.859188\pi\) | |||||||
\(240\) | 9.44266 | 0.609521 | ||||||||
\(241\) | 8.10538 | 0.522113 | 0.261057 | − | 0.965323i | \(-0.415929\pi\) | ||||
0.261057 | + | 0.965323i | \(0.415929\pi\) | |||||||
\(242\) | −11.3613 | −0.730330 | ||||||||
\(243\) | 22.3413 | 1.43320 | ||||||||
\(244\) | 10.9418 | 0.700477 | ||||||||
\(245\) | 25.4709 | 1.62727 | ||||||||
\(246\) | −12.8627 | −0.820095 | ||||||||
\(247\) | 11.4804 | 0.730483 | ||||||||
\(248\) | 0.0712862 | 0.00452668 | ||||||||
\(249\) | −16.6349 | −1.05419 | ||||||||
\(250\) | 16.1576 | 1.02190 | ||||||||
\(251\) | 22.2154 | 1.40223 | 0.701113 | − | 0.713050i | \(-0.252687\pi\) | ||||
0.701113 | + | 0.713050i | \(0.252687\pi\) | |||||||
\(252\) | −1.65117 | −0.104014 | ||||||||
\(253\) | 32.2633 | 2.02838 | ||||||||
\(254\) | 14.9791 | 0.939873 | ||||||||
\(255\) | −16.1413 | −1.01081 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −11.3368 | −0.707168 | −0.353584 | − | 0.935403i | \(-0.615037\pi\) | ||||
−0.353584 | + | 0.935403i | \(0.615037\pi\) | |||||||
\(258\) | 4.95240 | 0.308323 | ||||||||
\(259\) | −4.79560 | −0.297984 | ||||||||
\(260\) | 5.91758 | 0.366993 | ||||||||
\(261\) | 20.9709 | 1.29807 | ||||||||
\(262\) | 10.5654 | 0.652735 | ||||||||
\(263\) | −14.7510 | −0.909589 | −0.454794 | − | 0.890596i | \(-0.650287\pi\) | ||||
−0.454794 | + | 0.890596i | \(0.650287\pi\) | |||||||
\(264\) | 11.8177 | 0.727332 | ||||||||
\(265\) | −2.38287 | −0.146378 | ||||||||
\(266\) | −3.72925 | −0.228655 | ||||||||
\(267\) | 1.66763 | 0.102057 | ||||||||
\(268\) | −0.192213 | −0.0117412 | ||||||||
\(269\) | 20.7231 | 1.26351 | 0.631753 | − | 0.775169i | \(-0.282336\pi\) | ||||
0.631753 | + | 0.775169i | \(0.282336\pi\) | |||||||
\(270\) | −2.31891 | −0.141124 | ||||||||
\(271\) | −28.7047 | −1.74369 | −0.871844 | − | 0.489784i | \(-0.837076\pi\) | ||||
−0.871844 | + | 0.489784i | \(0.837076\pi\) | |||||||
\(272\) | −1.70941 | −0.103648 | ||||||||
\(273\) | −1.99123 | −0.120515 | ||||||||
\(274\) | 11.8114 | 0.713554 | ||||||||
\(275\) | 43.8655 | 2.64519 | ||||||||
\(276\) | −17.0509 | −1.02634 | ||||||||
\(277\) | −18.6874 | −1.12282 | −0.561409 | − | 0.827539i | \(-0.689740\pi\) | ||||
−0.561409 | + | 0.827539i | \(0.689740\pi\) | |||||||
\(278\) | 2.76617 | 0.165904 | ||||||||
\(279\) | −0.231365 | −0.0138515 | ||||||||
\(280\) | −1.92224 | −0.114876 | ||||||||
\(281\) | −21.3536 | −1.27385 | −0.636924 | − | 0.770926i | \(-0.719794\pi\) | ||||
−0.636924 | + | 0.770926i | \(0.719794\pi\) | |||||||
\(282\) | 13.3990 | 0.797899 | ||||||||
\(283\) | 22.4804 | 1.33632 | 0.668160 | − | 0.744018i | \(-0.267082\pi\) | ||||
0.668160 | + | 0.744018i | \(0.267082\pi\) | |||||||
\(284\) | 4.53092 | 0.268861 | ||||||||
\(285\) | −69.2175 | −4.10009 | ||||||||
\(286\) | 7.40602 | 0.437927 | ||||||||
\(287\) | 2.61845 | 0.154562 | ||||||||
\(288\) | −3.24558 | −0.191248 | ||||||||
\(289\) | −14.0779 | −0.828113 | ||||||||
\(290\) | 24.4137 | 1.43362 | ||||||||
\(291\) | −5.24965 | −0.307740 | ||||||||
\(292\) | 0.588797 | 0.0344567 | ||||||||
\(293\) | 14.4598 | 0.844752 | 0.422376 | − | 0.906421i | \(-0.361196\pi\) | ||||
0.422376 | + | 0.906421i | \(0.361196\pi\) | |||||||
\(294\) | −16.8470 | −0.982536 | ||||||||
\(295\) | 14.9694 | 0.871552 | ||||||||
\(296\) | −9.42635 | −0.547896 | ||||||||
\(297\) | −2.90218 | −0.168402 | ||||||||
\(298\) | −0.0224216 | −0.00129885 | ||||||||
\(299\) | −10.6856 | −0.617962 | ||||||||
\(300\) | −23.1826 | −1.33845 | ||||||||
\(301\) | −1.00816 | −0.0581093 | ||||||||
\(302\) | −15.8603 | −0.912660 | ||||||||
\(303\) | −5.17882 | −0.297516 | ||||||||
\(304\) | −7.33030 | −0.420422 | ||||||||
\(305\) | −41.3425 | −2.36726 | ||||||||
\(306\) | 5.54801 | 0.317159 | ||||||||
\(307\) | −8.08162 | −0.461242 | −0.230621 | − | 0.973044i | \(-0.574076\pi\) | ||||
−0.230621 | + | 0.973044i | \(0.574076\pi\) | |||||||
\(308\) | −2.40573 | −0.137079 | ||||||||
\(309\) | −35.6995 | −2.03087 | ||||||||
\(310\) | −0.269348 | −0.0152979 | ||||||||
\(311\) | −21.1984 | −1.20205 | −0.601027 | − | 0.799229i | \(-0.705242\pi\) | ||||
−0.601027 | + | 0.799229i | \(0.705242\pi\) | |||||||
\(312\) | −3.91402 | −0.221588 | ||||||||
\(313\) | 16.5817 | 0.937252 | 0.468626 | − | 0.883397i | \(-0.344749\pi\) | ||||
0.468626 | + | 0.883397i | \(0.344749\pi\) | |||||||
\(314\) | −5.68936 | −0.321069 | ||||||||
\(315\) | 6.23877 | 0.351515 | ||||||||
\(316\) | −16.1449 | −0.908221 | ||||||||
\(317\) | 20.8454 | 1.17079 | 0.585397 | − | 0.810747i | \(-0.300939\pi\) | ||||
0.585397 | + | 0.810747i | \(0.300939\pi\) | |||||||
\(318\) | 1.57608 | 0.0883822 | ||||||||
\(319\) | 30.5544 | 1.71072 | ||||||||
\(320\) | −3.77840 | −0.211219 | ||||||||
\(321\) | 25.3195 | 1.41320 | ||||||||
\(322\) | 3.47105 | 0.193434 | ||||||||
\(323\) | 12.5305 | 0.697214 | ||||||||
\(324\) | −8.20296 | −0.455720 | ||||||||
\(325\) | −14.5282 | −0.805879 | ||||||||
\(326\) | −4.12095 | −0.228238 | ||||||||
\(327\) | −34.2186 | −1.89229 | ||||||||
\(328\) | 5.14690 | 0.284190 | ||||||||
\(329\) | −2.72763 | −0.150379 | ||||||||
\(330\) | −44.6522 | −2.45802 | ||||||||
\(331\) | −3.40899 | −0.187375 | −0.0936875 | − | 0.995602i | \(-0.529865\pi\) | ||||
−0.0936875 | + | 0.995602i | \(0.529865\pi\) | |||||||
\(332\) | 6.65631 | 0.365312 | ||||||||
\(333\) | 30.5940 | 1.67654 | ||||||||
\(334\) | −2.34577 | −0.128355 | ||||||||
\(335\) | 0.726256 | 0.0396796 | ||||||||
\(336\) | 1.27141 | 0.0693611 | ||||||||
\(337\) | 13.2438 | 0.721434 | 0.360717 | − | 0.932675i | \(-0.382532\pi\) | ||||
0.360717 | + | 0.932675i | \(0.382532\pi\) | |||||||
\(338\) | 10.5471 | 0.573689 | ||||||||
\(339\) | 21.1877 | 1.15076 | ||||||||
\(340\) | 6.45882 | 0.350279 | ||||||||
\(341\) | −0.337096 | −0.0182548 | ||||||||
\(342\) | 23.7911 | 1.28647 | ||||||||
\(343\) | 6.99074 | 0.377465 | ||||||||
\(344\) | −1.98166 | −0.106844 | ||||||||
\(345\) | 64.4252 | 3.46853 | ||||||||
\(346\) | 16.9073 | 0.908940 | ||||||||
\(347\) | 16.4422 | 0.882664 | 0.441332 | − | 0.897344i | \(-0.354506\pi\) | ||||
0.441332 | + | 0.897344i | \(0.354506\pi\) | |||||||
\(348\) | −16.1477 | −0.865610 | ||||||||
\(349\) | 4.96654 | 0.265853 | 0.132926 | − | 0.991126i | \(-0.457563\pi\) | ||||
0.132926 | + | 0.991126i | \(0.457563\pi\) | |||||||
\(350\) | 4.71926 | 0.252255 | ||||||||
\(351\) | 0.961198 | 0.0513049 | ||||||||
\(352\) | −4.72877 | −0.252044 | ||||||||
\(353\) | −12.8929 | −0.686217 | −0.343109 | − | 0.939296i | \(-0.611480\pi\) | ||||
−0.343109 | + | 0.939296i | \(0.611480\pi\) | |||||||
\(354\) | −9.90108 | −0.526236 | ||||||||
\(355\) | −17.1196 | −0.908616 | ||||||||
\(356\) | −0.667289 | −0.0353662 | ||||||||
\(357\) | −2.17336 | −0.115026 | ||||||||
\(358\) | 25.4604 | 1.34562 | ||||||||
\(359\) | −0.764622 | −0.0403552 | −0.0201776 | − | 0.999796i | \(-0.506423\pi\) | ||||
−0.0201776 | + | 0.999796i | \(0.506423\pi\) | |||||||
\(360\) | 12.2631 | 0.646322 | ||||||||
\(361\) | 34.7333 | 1.82807 | ||||||||
\(362\) | 1.99371 | 0.104787 | ||||||||
\(363\) | −28.3931 | −1.49025 | ||||||||
\(364\) | 0.796775 | 0.0417623 | ||||||||
\(365\) | −2.22471 | −0.116447 | ||||||||
\(366\) | 27.3448 | 1.42934 | ||||||||
\(367\) | −20.4308 | −1.06648 | −0.533239 | − | 0.845964i | \(-0.679025\pi\) | ||||
−0.533239 | + | 0.845964i | \(0.679025\pi\) | |||||||
\(368\) | 6.82278 | 0.355662 | ||||||||
\(369\) | −16.7047 | −0.869610 | ||||||||
\(370\) | 35.6165 | 1.85162 | ||||||||
\(371\) | −0.320842 | −0.0166573 | ||||||||
\(372\) | 0.178152 | 0.00923677 | ||||||||
\(373\) | 12.5231 | 0.648422 | 0.324211 | − | 0.945985i | \(-0.394901\pi\) | ||||
0.324211 | + | 0.945985i | \(0.394901\pi\) | |||||||
\(374\) | 8.08339 | 0.417982 | ||||||||
\(375\) | 40.3797 | 2.08520 | ||||||||
\(376\) | −5.36150 | −0.276498 | ||||||||
\(377\) | −10.1196 | −0.521184 | ||||||||
\(378\) | −0.312231 | −0.0160594 | ||||||||
\(379\) | 32.1780 | 1.65287 | 0.826436 | − | 0.563031i | \(-0.190365\pi\) | ||||
0.826436 | + | 0.563031i | \(0.190365\pi\) | |||||||
\(380\) | 27.6968 | 1.42082 | ||||||||
\(381\) | 37.4345 | 1.91783 | ||||||||
\(382\) | 14.4859 | 0.741162 | ||||||||
\(383\) | 37.0698 | 1.89418 | 0.947089 | − | 0.320971i | \(-0.104009\pi\) | ||||
0.947089 | + | 0.320971i | \(0.104009\pi\) | |||||||
\(384\) | 2.49912 | 0.127532 | ||||||||
\(385\) | 9.08982 | 0.463260 | ||||||||
\(386\) | −21.0958 | −1.07375 | ||||||||
\(387\) | 6.43164 | 0.326938 | ||||||||
\(388\) | 2.10060 | 0.106642 | ||||||||
\(389\) | −10.0922 | −0.511697 | −0.255849 | − | 0.966717i | \(-0.582355\pi\) | ||||
−0.255849 | + | 0.966717i | \(0.582355\pi\) | |||||||
\(390\) | 14.7887 | 0.748856 | ||||||||
\(391\) | −11.6629 | −0.589818 | ||||||||
\(392\) | 6.74118 | 0.340481 | ||||||||
\(393\) | 26.4042 | 1.33192 | ||||||||
\(394\) | 24.1967 | 1.21901 | ||||||||
\(395\) | 61.0018 | 3.06933 | ||||||||
\(396\) | 15.3476 | 0.771246 | ||||||||
\(397\) | 19.5206 | 0.979713 | 0.489856 | − | 0.871803i | \(-0.337049\pi\) | ||||
0.489856 | + | 0.871803i | \(0.337049\pi\) | |||||||
\(398\) | −16.5051 | −0.827326 | ||||||||
\(399\) | −9.31982 | −0.466575 | ||||||||
\(400\) | 9.27631 | 0.463815 | ||||||||
\(401\) | 23.5426 | 1.17566 | 0.587829 | − | 0.808985i | \(-0.299983\pi\) | ||||
0.587829 | + | 0.808985i | \(0.299983\pi\) | |||||||
\(402\) | −0.480361 | −0.0239582 | ||||||||
\(403\) | 0.111646 | 0.00556147 | ||||||||
\(404\) | 2.07226 | 0.103099 | ||||||||
\(405\) | 30.9940 | 1.54011 | ||||||||
\(406\) | 3.28719 | 0.163140 | ||||||||
\(407\) | 44.5751 | 2.20950 | ||||||||
\(408\) | −4.27200 | −0.211496 | ||||||||
\(409\) | −36.4807 | −1.80385 | −0.901927 | − | 0.431889i | \(-0.857847\pi\) | ||||
−0.901927 | + | 0.431889i | \(0.857847\pi\) | |||||||
\(410\) | −19.4470 | −0.960421 | ||||||||
\(411\) | 29.5181 | 1.45602 | ||||||||
\(412\) | 14.2849 | 0.703764 | ||||||||
\(413\) | 2.01556 | 0.0991792 | ||||||||
\(414\) | −22.1439 | −1.08831 | ||||||||
\(415\) | −25.1502 | −1.23457 | ||||||||
\(416\) | 1.56616 | 0.0767874 | ||||||||
\(417\) | 6.91299 | 0.338531 | ||||||||
\(418\) | 34.6633 | 1.69544 | ||||||||
\(419\) | 5.85624 | 0.286096 | 0.143048 | − | 0.989716i | \(-0.454310\pi\) | ||||
0.143048 | + | 0.989716i | \(0.454310\pi\) | |||||||
\(420\) | −4.80389 | −0.234406 | ||||||||
\(421\) | 14.3591 | 0.699819 | 0.349909 | − | 0.936784i | \(-0.386212\pi\) | ||||
0.349909 | + | 0.936784i | \(0.386212\pi\) | |||||||
\(422\) | −12.4250 | −0.604842 | ||||||||
\(423\) | 17.4012 | 0.846074 | ||||||||
\(424\) | −0.630655 | −0.0306273 | ||||||||
\(425\) | −15.8570 | −0.769177 | ||||||||
\(426\) | 11.3233 | 0.548615 | ||||||||
\(427\) | −5.56657 | −0.269385 | ||||||||
\(428\) | −10.1314 | −0.489718 | ||||||||
\(429\) | 18.5085 | 0.893598 | ||||||||
\(430\) | 7.48751 | 0.361080 | ||||||||
\(431\) | −10.4899 | −0.505280 | −0.252640 | − | 0.967560i | \(-0.581299\pi\) | ||||
−0.252640 | + | 0.967560i | \(0.581299\pi\) | |||||||
\(432\) | −0.613729 | −0.0295280 | ||||||||
\(433\) | −36.7641 | −1.76677 | −0.883384 | − | 0.468650i | \(-0.844741\pi\) | ||||
−0.883384 | + | 0.468650i | \(0.844741\pi\) | |||||||
\(434\) | −0.0362664 | −0.00174084 | ||||||||
\(435\) | 61.0126 | 2.92533 | ||||||||
\(436\) | 13.6923 | 0.655742 | ||||||||
\(437\) | −50.0130 | −2.39245 | ||||||||
\(438\) | 1.47147 | 0.0703096 | ||||||||
\(439\) | 38.0471 | 1.81589 | 0.907943 | − | 0.419093i | \(-0.137652\pi\) | ||||
0.907943 | + | 0.419093i | \(0.137652\pi\) | |||||||
\(440\) | 17.8672 | 0.851785 | ||||||||
\(441\) | −21.8790 | −1.04186 | ||||||||
\(442\) | −2.67721 | −0.127342 | ||||||||
\(443\) | 38.1362 | 1.81190 | 0.905952 | − | 0.423381i | \(-0.139157\pi\) | ||||
0.905952 | + | 0.423381i | \(0.139157\pi\) | |||||||
\(444\) | −23.5575 | −1.11799 | ||||||||
\(445\) | 2.52128 | 0.119520 | ||||||||
\(446\) | 13.1348 | 0.621949 | ||||||||
\(447\) | −0.0560342 | −0.00265033 | ||||||||
\(448\) | −0.508744 | −0.0240359 | ||||||||
\(449\) | 9.26607 | 0.437293 | 0.218646 | − | 0.975804i | \(-0.429836\pi\) | ||||
0.218646 | + | 0.975804i | \(0.429836\pi\) | |||||||
\(450\) | −30.1070 | −1.41926 | ||||||||
\(451\) | −24.3385 | −1.14605 | ||||||||
\(452\) | −8.47807 | −0.398775 | ||||||||
\(453\) | −39.6368 | −1.86230 | ||||||||
\(454\) | 8.32519 | 0.390720 | ||||||||
\(455\) | −3.01053 | −0.141136 | ||||||||
\(456\) | −18.3193 | −0.857879 | ||||||||
\(457\) | 40.9023 | 1.91333 | 0.956665 | − | 0.291189i | \(-0.0940509\pi\) | ||||
0.956665 | + | 0.291189i | \(0.0940509\pi\) | |||||||
\(458\) | 10.2884 | 0.480744 | ||||||||
\(459\) | 1.04911 | 0.0489683 | ||||||||
\(460\) | −25.7792 | −1.20196 | ||||||||
\(461\) | 4.97150 | 0.231546 | 0.115773 | − | 0.993276i | \(-0.463065\pi\) | ||||
0.115773 | + | 0.993276i | \(0.463065\pi\) | |||||||
\(462\) | −6.01220 | −0.279713 | ||||||||
\(463\) | 26.8750 | 1.24899 | 0.624494 | − | 0.781030i | \(-0.285305\pi\) | ||||
0.624494 | + | 0.781030i | \(0.285305\pi\) | |||||||
\(464\) | 6.46138 | 0.299962 | ||||||||
\(465\) | −0.673131 | −0.0312157 | ||||||||
\(466\) | −29.6620 | −1.37407 | ||||||||
\(467\) | 3.24381 | 0.150105 | 0.0750527 | − | 0.997180i | \(-0.476087\pi\) | ||||
0.0750527 | + | 0.997180i | \(0.476087\pi\) | |||||||
\(468\) | −5.08310 | −0.234966 | ||||||||
\(469\) | 0.0977869 | 0.00451538 | ||||||||
\(470\) | 20.2579 | 0.934427 | ||||||||
\(471\) | −14.2184 | −0.655148 | ||||||||
\(472\) | 3.96183 | 0.182358 | ||||||||
\(473\) | 9.37082 | 0.430871 | ||||||||
\(474\) | −40.3479 | −1.85324 | ||||||||
\(475\) | −67.9981 | −3.11997 | ||||||||
\(476\) | 0.869650 | 0.0398604 | ||||||||
\(477\) | 2.04684 | 0.0937184 | ||||||||
\(478\) | 27.9429 | 1.27808 | ||||||||
\(479\) | 28.9709 | 1.32371 | 0.661856 | − | 0.749631i | \(-0.269769\pi\) | ||||
0.661856 | + | 0.749631i | \(0.269769\pi\) | |||||||
\(480\) | −9.44266 | −0.430996 | ||||||||
\(481\) | −14.7632 | −0.673143 | ||||||||
\(482\) | −8.10538 | −0.369190 | ||||||||
\(483\) | 8.67455 | 0.394705 | ||||||||
\(484\) | 11.3613 | 0.516421 | ||||||||
\(485\) | −7.93692 | −0.360397 | ||||||||
\(486\) | −22.3413 | −1.01342 | ||||||||
\(487\) | −5.33853 | −0.241912 | −0.120956 | − | 0.992658i | \(-0.538596\pi\) | ||||
−0.120956 | + | 0.992658i | \(0.538596\pi\) | |||||||
\(488\) | −10.9418 | −0.495312 | ||||||||
\(489\) | −10.2987 | −0.465724 | ||||||||
\(490\) | −25.4709 | −1.15066 | ||||||||
\(491\) | 26.8776 | 1.21297 | 0.606484 | − | 0.795096i | \(-0.292580\pi\) | ||||
0.606484 | + | 0.795096i | \(0.292580\pi\) | |||||||
\(492\) | 12.8627 | 0.579895 | ||||||||
\(493\) | −11.0451 | −0.497448 | ||||||||
\(494\) | −11.4804 | −0.516529 | ||||||||
\(495\) | −57.9893 | −2.60643 | ||||||||
\(496\) | −0.0712862 | −0.00320084 | ||||||||
\(497\) | −2.30508 | −0.103397 | ||||||||
\(498\) | 16.6349 | 0.745427 | ||||||||
\(499\) | 25.8270 | 1.15618 | 0.578088 | − | 0.815975i | \(-0.303799\pi\) | ||||
0.578088 | + | 0.815975i | \(0.303799\pi\) | |||||||
\(500\) | −16.1576 | −0.722590 | ||||||||
\(501\) | −5.86236 | −0.261911 | ||||||||
\(502\) | −22.2154 | −0.991524 | ||||||||
\(503\) | 27.8491 | 1.24173 | 0.620866 | − | 0.783917i | \(-0.286781\pi\) | ||||
0.620866 | + | 0.783917i | \(0.286781\pi\) | |||||||
\(504\) | 1.65117 | 0.0735489 | ||||||||
\(505\) | −7.82983 | −0.348423 | ||||||||
\(506\) | −32.2633 | −1.43428 | ||||||||
\(507\) | 26.3585 | 1.17062 | ||||||||
\(508\) | −14.9791 | −0.664590 | ||||||||
\(509\) | 7.29862 | 0.323505 | 0.161753 | − | 0.986831i | \(-0.448285\pi\) | ||||
0.161753 | + | 0.986831i | \(0.448285\pi\) | |||||||
\(510\) | 16.1413 | 0.714751 | ||||||||
\(511\) | −0.299547 | −0.0132512 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.49882 | 0.198628 | ||||||||
\(514\) | 11.3368 | 0.500043 | ||||||||
\(515\) | −53.9739 | −2.37837 | ||||||||
\(516\) | −4.95240 | −0.218017 | ||||||||
\(517\) | 25.3533 | 1.11504 | ||||||||
\(518\) | 4.79560 | 0.210707 | ||||||||
\(519\) | 42.2532 | 1.85471 | ||||||||
\(520\) | −5.91758 | −0.259503 | ||||||||
\(521\) | −29.9555 | −1.31237 | −0.656187 | − | 0.754598i | \(-0.727832\pi\) | ||||
−0.656187 | + | 0.754598i | \(0.727832\pi\) | |||||||
\(522\) | −20.9709 | −0.917872 | ||||||||
\(523\) | 29.8986 | 1.30737 | 0.653686 | − | 0.756766i | \(-0.273222\pi\) | ||||
0.653686 | + | 0.756766i | \(0.273222\pi\) | |||||||
\(524\) | −10.5654 | −0.461553 | ||||||||
\(525\) | 11.7940 | 0.514732 | ||||||||
\(526\) | 14.7510 | 0.643176 | ||||||||
\(527\) | 0.121857 | 0.00530818 | ||||||||
\(528\) | −11.8177 | −0.514301 | ||||||||
\(529\) | 23.5503 | 1.02393 | ||||||||
\(530\) | 2.38287 | 0.103505 | ||||||||
\(531\) | −12.8584 | −0.558009 | ||||||||
\(532\) | 3.72925 | 0.161683 | ||||||||
\(533\) | 8.06087 | 0.349155 | ||||||||
\(534\) | −1.66763 | −0.0721655 | ||||||||
\(535\) | 38.2804 | 1.65501 | ||||||||
\(536\) | 0.192213 | 0.00830232 | ||||||||
\(537\) | 63.6284 | 2.74577 | ||||||||
\(538\) | −20.7231 | −0.893434 | ||||||||
\(539\) | −31.8775 | −1.37306 | ||||||||
\(540\) | 2.31891 | 0.0997901 | ||||||||
\(541\) | −11.9125 | −0.512158 | −0.256079 | − | 0.966656i | \(-0.582431\pi\) | ||||
−0.256079 | + | 0.966656i | \(0.582431\pi\) | |||||||
\(542\) | 28.7047 | 1.23297 | ||||||||
\(543\) | 4.98251 | 0.213820 | ||||||||
\(544\) | 1.70941 | 0.0732902 | ||||||||
\(545\) | −51.7350 | −2.21608 | ||||||||
\(546\) | 1.99123 | 0.0852169 | ||||||||
\(547\) | −20.9557 | −0.896001 | −0.448001 | − | 0.894033i | \(-0.647864\pi\) | ||||
−0.448001 | + | 0.894033i | \(0.647864\pi\) | |||||||
\(548\) | −11.8114 | −0.504559 | ||||||||
\(549\) | 35.5125 | 1.51563 | ||||||||
\(550\) | −43.8655 | −1.87043 | ||||||||
\(551\) | −47.3639 | −2.01777 | ||||||||
\(552\) | 17.0509 | 0.725735 | ||||||||
\(553\) | 8.21361 | 0.349278 | ||||||||
\(554\) | 18.6874 | 0.793952 | ||||||||
\(555\) | 89.0098 | 3.77826 | ||||||||
\(556\) | −2.76617 | −0.117312 | ||||||||
\(557\) | −40.3513 | −1.70974 | −0.854869 | − | 0.518843i | \(-0.826363\pi\) | ||||
−0.854869 | + | 0.518843i | \(0.826363\pi\) | |||||||
\(558\) | 0.231365 | 0.00979446 | ||||||||
\(559\) | −3.10360 | −0.131268 | ||||||||
\(560\) | 1.92224 | 0.0812294 | ||||||||
\(561\) | 20.2013 | 0.852901 | ||||||||
\(562\) | 21.3536 | 0.900747 | ||||||||
\(563\) | −30.5264 | −1.28653 | −0.643266 | − | 0.765643i | \(-0.722421\pi\) | ||||
−0.643266 | + | 0.765643i | \(0.722421\pi\) | |||||||
\(564\) | −13.3990 | −0.564200 | ||||||||
\(565\) | 32.0335 | 1.34766 | ||||||||
\(566\) | −22.4804 | −0.944920 | ||||||||
\(567\) | 4.17320 | 0.175258 | ||||||||
\(568\) | −4.53092 | −0.190113 | ||||||||
\(569\) | −5.77079 | −0.241924 | −0.120962 | − | 0.992657i | \(-0.538598\pi\) | ||||
−0.120962 | + | 0.992657i | \(0.538598\pi\) | |||||||
\(570\) | 69.2175 | 2.89920 | ||||||||
\(571\) | 1.36888 | 0.0572859 | 0.0286429 | − | 0.999590i | \(-0.490881\pi\) | ||||
0.0286429 | + | 0.999590i | \(0.490881\pi\) | |||||||
\(572\) | −7.40602 | −0.309661 | ||||||||
\(573\) | 36.2019 | 1.51235 | ||||||||
\(574\) | −2.61845 | −0.109292 | ||||||||
\(575\) | 63.2902 | 2.63938 | ||||||||
\(576\) | 3.24558 | 0.135232 | ||||||||
\(577\) | 8.91467 | 0.371123 | 0.185561 | − | 0.982633i | \(-0.440590\pi\) | ||||
0.185561 | + | 0.982633i | \(0.440590\pi\) | |||||||
\(578\) | 14.0779 | 0.585565 | ||||||||
\(579\) | −52.7208 | −2.19100 | ||||||||
\(580\) | −24.4137 | −1.01372 | ||||||||
\(581\) | −3.38636 | −0.140490 | ||||||||
\(582\) | 5.24965 | 0.217605 | ||||||||
\(583\) | 2.98222 | 0.123511 | ||||||||
\(584\) | −0.588797 | −0.0243646 | ||||||||
\(585\) | 19.2060 | 0.794069 | ||||||||
\(586\) | −14.4598 | −0.597330 | ||||||||
\(587\) | −40.2858 | −1.66277 | −0.831386 | − | 0.555695i | \(-0.812452\pi\) | ||||
−0.831386 | + | 0.555695i | \(0.812452\pi\) | |||||||
\(588\) | 16.8470 | 0.694758 | ||||||||
\(589\) | 0.522549 | 0.0215313 | ||||||||
\(590\) | −14.9694 | −0.616280 | ||||||||
\(591\) | 60.4702 | 2.48741 | ||||||||
\(592\) | 9.42635 | 0.387421 | ||||||||
\(593\) | −11.7372 | −0.481990 | −0.240995 | − | 0.970526i | \(-0.577474\pi\) | ||||
−0.240995 | + | 0.970526i | \(0.577474\pi\) | |||||||
\(594\) | 2.90218 | 0.119078 | ||||||||
\(595\) | −3.28589 | −0.134708 | ||||||||
\(596\) | 0.0224216 | 0.000918426 0 | ||||||||
\(597\) | −41.2482 | −1.68817 | ||||||||
\(598\) | 10.6856 | 0.436965 | ||||||||
\(599\) | −24.5752 | −1.00411 | −0.502057 | − | 0.864835i | \(-0.667423\pi\) | ||||
−0.502057 | + | 0.864835i | \(0.667423\pi\) | |||||||
\(600\) | 23.1826 | 0.946424 | ||||||||
\(601\) | −1.53950 | −0.0627973 | −0.0313987 | − | 0.999507i | \(-0.509996\pi\) | ||||
−0.0313987 | + | 0.999507i | \(0.509996\pi\) | |||||||
\(602\) | 1.00816 | 0.0410894 | ||||||||
\(603\) | −0.623841 | −0.0254048 | ||||||||
\(604\) | 15.8603 | 0.645348 | ||||||||
\(605\) | −42.9274 | −1.74525 | ||||||||
\(606\) | 5.17882 | 0.210375 | ||||||||
\(607\) | 16.9070 | 0.686232 | 0.343116 | − | 0.939293i | \(-0.388518\pi\) | ||||
0.343116 | + | 0.939293i | \(0.388518\pi\) | |||||||
\(608\) | 7.33030 | 0.297283 | ||||||||
\(609\) | 8.21506 | 0.332891 | ||||||||
\(610\) | 41.3425 | 1.67391 | ||||||||
\(611\) | −8.39697 | −0.339705 | ||||||||
\(612\) | −5.54801 | −0.224265 | ||||||||
\(613\) | 29.9590 | 1.21003 | 0.605017 | − | 0.796212i | \(-0.293166\pi\) | ||||
0.605017 | + | 0.796212i | \(0.293166\pi\) | |||||||
\(614\) | 8.08162 | 0.326148 | ||||||||
\(615\) | −48.6004 | −1.95976 | ||||||||
\(616\) | 2.40573 | 0.0969297 | ||||||||
\(617\) | −23.8586 | −0.960510 | −0.480255 | − | 0.877129i | \(-0.659456\pi\) | ||||
−0.480255 | + | 0.877129i | \(0.659456\pi\) | |||||||
\(618\) | 35.6995 | 1.43604 | ||||||||
\(619\) | −22.9469 | −0.922316 | −0.461158 | − | 0.887318i | \(-0.652566\pi\) | ||||
−0.461158 | + | 0.887318i | \(0.652566\pi\) | |||||||
\(620\) | 0.269348 | 0.0108173 | ||||||||
\(621\) | −4.18733 | −0.168032 | ||||||||
\(622\) | 21.1984 | 0.849980 | ||||||||
\(623\) | 0.339479 | 0.0136009 | ||||||||
\(624\) | 3.91402 | 0.156686 | ||||||||
\(625\) | 14.6683 | 0.586733 | ||||||||
\(626\) | −16.5817 | −0.662737 | ||||||||
\(627\) | 86.6276 | 3.45957 | ||||||||
\(628\) | 5.68936 | 0.227030 | ||||||||
\(629\) | −16.1135 | −0.642486 | ||||||||
\(630\) | −6.23877 | −0.248559 | ||||||||
\(631\) | −30.4685 | −1.21293 | −0.606467 | − | 0.795109i | \(-0.707414\pi\) | ||||
−0.606467 | + | 0.795109i | \(0.707414\pi\) | |||||||
\(632\) | 16.1449 | 0.642209 | ||||||||
\(633\) | −31.0516 | −1.23419 | ||||||||
\(634\) | −20.8454 | −0.827876 | ||||||||
\(635\) | 56.5971 | 2.24599 | ||||||||
\(636\) | −1.57608 | −0.0624956 | ||||||||
\(637\) | 10.5578 | 0.418314 | ||||||||
\(638\) | −30.5544 | −1.20966 | ||||||||
\(639\) | 14.7055 | 0.581739 | ||||||||
\(640\) | 3.77840 | 0.149354 | ||||||||
\(641\) | −26.6974 | −1.05448 | −0.527241 | − | 0.849716i | \(-0.676774\pi\) | ||||
−0.527241 | + | 0.849716i | \(0.676774\pi\) | |||||||
\(642\) | −25.3195 | −0.999280 | ||||||||
\(643\) | 22.7392 | 0.896748 | 0.448374 | − | 0.893846i | \(-0.352003\pi\) | ||||
0.448374 | + | 0.893846i | \(0.352003\pi\) | |||||||
\(644\) | −3.47105 | −0.136778 | ||||||||
\(645\) | 18.7121 | 0.736790 | ||||||||
\(646\) | −12.5305 | −0.493005 | ||||||||
\(647\) | 7.31694 | 0.287659 | 0.143829 | − | 0.989603i | \(-0.454058\pi\) | ||||
0.143829 | + | 0.989603i | \(0.454058\pi\) | |||||||
\(648\) | 8.20296 | 0.322243 | ||||||||
\(649\) | −18.7346 | −0.735397 | ||||||||
\(650\) | 14.5282 | 0.569842 | ||||||||
\(651\) | −0.0906339 | −0.00355222 | ||||||||
\(652\) | 4.12095 | 0.161389 | ||||||||
\(653\) | −17.8937 | −0.700236 | −0.350118 | − | 0.936706i | \(-0.613858\pi\) | ||||
−0.350118 | + | 0.936706i | \(0.613858\pi\) | |||||||
\(654\) | 34.2186 | 1.33805 | ||||||||
\(655\) | 39.9204 | 1.55982 | ||||||||
\(656\) | −5.14690 | −0.200953 | ||||||||
\(657\) | 1.91099 | 0.0745546 | ||||||||
\(658\) | 2.72763 | 0.106334 | ||||||||
\(659\) | 23.3582 | 0.909905 | 0.454952 | − | 0.890516i | \(-0.349656\pi\) | ||||
0.454952 | + | 0.890516i | \(0.349656\pi\) | |||||||
\(660\) | 44.6522 | 1.73808 | ||||||||
\(661\) | 22.6576 | 0.881280 | 0.440640 | − | 0.897684i | \(-0.354752\pi\) | ||||
0.440640 | + | 0.897684i | \(0.354752\pi\) | |||||||
\(662\) | 3.40899 | 0.132494 | ||||||||
\(663\) | −6.69065 | −0.259843 | ||||||||
\(664\) | −6.65631 | −0.258315 | ||||||||
\(665\) | −14.0906 | −0.546409 | ||||||||
\(666\) | −30.5940 | −1.18549 | ||||||||
\(667\) | 44.0846 | 1.70696 | ||||||||
\(668\) | 2.34577 | 0.0907607 | ||||||||
\(669\) | 32.8253 | 1.26910 | ||||||||
\(670\) | −0.726256 | −0.0280577 | ||||||||
\(671\) | 51.7412 | 1.99745 | ||||||||
\(672\) | −1.27141 | −0.0490457 | ||||||||
\(673\) | −7.86813 | −0.303294 | −0.151647 | − | 0.988435i | \(-0.548458\pi\) | ||||
−0.151647 | + | 0.988435i | \(0.548458\pi\) | |||||||
\(674\) | −13.2438 | −0.510131 | ||||||||
\(675\) | −5.69313 | −0.219129 | ||||||||
\(676\) | −10.5471 | −0.405659 | ||||||||
\(677\) | 36.0153 | 1.38418 | 0.692090 | − | 0.721811i | \(-0.256690\pi\) | ||||
0.692090 | + | 0.721811i | \(0.256690\pi\) | |||||||
\(678\) | −21.1877 | −0.813708 | ||||||||
\(679\) | −1.06867 | −0.0410118 | ||||||||
\(680\) | −6.45882 | −0.247685 | ||||||||
\(681\) | 20.8056 | 0.797273 | ||||||||
\(682\) | 0.337096 | 0.0129081 | ||||||||
\(683\) | −26.3791 | −1.00937 | −0.504685 | − | 0.863304i | \(-0.668391\pi\) | ||||
−0.504685 | + | 0.863304i | \(0.668391\pi\) | |||||||
\(684\) | −23.7911 | −0.909674 | ||||||||
\(685\) | 44.6283 | 1.70516 | ||||||||
\(686\) | −6.99074 | −0.266908 | ||||||||
\(687\) | 25.7118 | 0.980968 | ||||||||
\(688\) | 1.98166 | 0.0755501 | ||||||||
\(689\) | −0.987707 | −0.0376287 | ||||||||
\(690\) | −64.4252 | −2.45262 | ||||||||
\(691\) | −1.26320 | −0.0480543 | −0.0240271 | − | 0.999711i | \(-0.507649\pi\) | ||||
−0.0240271 | + | 0.999711i | \(0.507649\pi\) | |||||||
\(692\) | −16.9073 | −0.642718 | ||||||||
\(693\) | −7.80799 | −0.296601 | ||||||||
\(694\) | −16.4422 | −0.624138 | ||||||||
\(695\) | 10.4517 | 0.396456 | ||||||||
\(696\) | 16.1477 | 0.612078 | ||||||||
\(697\) | 8.79814 | 0.333253 | ||||||||
\(698\) | −4.96654 | −0.187986 | ||||||||
\(699\) | −74.1288 | −2.80381 | ||||||||
\(700\) | −4.71926 | −0.178371 | ||||||||
\(701\) | −21.1907 | −0.800362 | −0.400181 | − | 0.916436i | \(-0.631053\pi\) | ||||
−0.400181 | + | 0.916436i | \(0.631053\pi\) | |||||||
\(702\) | −0.961198 | −0.0362781 | ||||||||
\(703\) | −69.0980 | −2.60608 | ||||||||
\(704\) | 4.72877 | 0.178222 | ||||||||
\(705\) | 50.6268 | 1.90672 | ||||||||
\(706\) | 12.8929 | 0.485229 | ||||||||
\(707\) | −1.05425 | −0.0396492 | ||||||||
\(708\) | 9.90108 | 0.372105 | ||||||||
\(709\) | −35.9556 | −1.35034 | −0.675171 | − | 0.737661i | \(-0.735930\pi\) | ||||
−0.675171 | + | 0.737661i | \(0.735930\pi\) | |||||||
\(710\) | 17.1196 | 0.642488 | ||||||||
\(711\) | −52.3995 | −1.96513 | ||||||||
\(712\) | 0.667289 | 0.0250077 | ||||||||
\(713\) | −0.486370 | −0.0182147 | ||||||||
\(714\) | 2.17336 | 0.0813358 | ||||||||
\(715\) | 27.9829 | 1.04650 | ||||||||
\(716\) | −25.4604 | −0.951498 | ||||||||
\(717\) | 69.8325 | 2.60794 | ||||||||
\(718\) | 0.764622 | 0.0285354 | ||||||||
\(719\) | −24.7782 | −0.924070 | −0.462035 | − | 0.886862i | \(-0.652881\pi\) | ||||
−0.462035 | + | 0.886862i | \(0.652881\pi\) | |||||||
\(720\) | −12.2631 | −0.457018 | ||||||||
\(721\) | −7.26733 | −0.270650 | ||||||||
\(722\) | −34.7333 | −1.29264 | ||||||||
\(723\) | −20.2563 | −0.753339 | ||||||||
\(724\) | −1.99371 | −0.0740957 | ||||||||
\(725\) | 59.9378 | 2.22603 | ||||||||
\(726\) | 28.3931 | 1.05377 | ||||||||
\(727\) | 10.8869 | 0.403775 | 0.201887 | − | 0.979409i | \(-0.435293\pi\) | ||||
0.201887 | + | 0.979409i | \(0.435293\pi\) | |||||||
\(728\) | −0.796775 | −0.0295304 | ||||||||
\(729\) | −31.2247 | −1.15647 | ||||||||
\(730\) | 2.22471 | 0.0823402 | ||||||||
\(731\) | −3.38746 | −0.125290 | ||||||||
\(732\) | −27.3448 | −1.01069 | ||||||||
\(733\) | 32.3175 | 1.19368 | 0.596838 | − | 0.802362i | \(-0.296424\pi\) | ||||
0.596838 | + | 0.802362i | \(0.296424\pi\) | |||||||
\(734\) | 20.4308 | 0.754114 | ||||||||
\(735\) | −63.6547 | −2.34794 | ||||||||
\(736\) | −6.82278 | −0.251491 | ||||||||
\(737\) | −0.908929 | −0.0334808 | ||||||||
\(738\) | 16.7047 | 0.614907 | ||||||||
\(739\) | −20.6425 | −0.759346 | −0.379673 | − | 0.925121i | \(-0.623963\pi\) | ||||
−0.379673 | + | 0.925121i | \(0.623963\pi\) | |||||||
\(740\) | −35.6165 | −1.30929 | ||||||||
\(741\) | −28.6909 | −1.05399 | ||||||||
\(742\) | 0.320842 | 0.0117785 | ||||||||
\(743\) | 32.4736 | 1.19134 | 0.595670 | − | 0.803230i | \(-0.296887\pi\) | ||||
0.595670 | + | 0.803230i | \(0.296887\pi\) | |||||||
\(744\) | −0.178152 | −0.00653138 | ||||||||
\(745\) | −0.0847179 | −0.00310382 | ||||||||
\(746\) | −12.5231 | −0.458503 | ||||||||
\(747\) | 21.6036 | 0.790434 | ||||||||
\(748\) | −8.08339 | −0.295558 | ||||||||
\(749\) | 5.15427 | 0.188333 | ||||||||
\(750\) | −40.3797 | −1.47446 | ||||||||
\(751\) | 1.17709 | 0.0429525 | 0.0214763 | − | 0.999769i | \(-0.493163\pi\) | ||||
0.0214763 | + | 0.999769i | \(0.493163\pi\) | |||||||
\(752\) | 5.36150 | 0.195514 | ||||||||
\(753\) | −55.5189 | −2.02322 | ||||||||
\(754\) | 10.1196 | 0.368533 | ||||||||
\(755\) | −59.9267 | −2.18096 | ||||||||
\(756\) | 0.312231 | 0.0113557 | ||||||||
\(757\) | −6.43499 | −0.233884 | −0.116942 | − | 0.993139i | \(-0.537309\pi\) | ||||
−0.116942 | + | 0.993139i | \(0.537309\pi\) | |||||||
\(758\) | −32.1780 | −1.16876 | ||||||||
\(759\) | −80.6298 | −2.92668 | ||||||||
\(760\) | −27.6968 | −1.00467 | ||||||||
\(761\) | 21.5453 | 0.781015 | 0.390508 | − | 0.920600i | \(-0.372300\pi\) | ||||
0.390508 | + | 0.920600i | \(0.372300\pi\) | |||||||
\(762\) | −37.4345 | −1.35611 | ||||||||
\(763\) | −6.96587 | −0.252182 | ||||||||
\(764\) | −14.4859 | −0.524081 | ||||||||
\(765\) | 20.9626 | 0.757905 | ||||||||
\(766\) | −37.0698 | −1.33939 | ||||||||
\(767\) | 6.20487 | 0.224045 | ||||||||
\(768\) | −2.49912 | −0.0901791 | ||||||||
\(769\) | −23.3646 | −0.842550 | −0.421275 | − | 0.906933i | \(-0.638417\pi\) | ||||
−0.421275 | + | 0.906933i | \(0.638417\pi\) | |||||||
\(770\) | −9.08982 | −0.327574 | ||||||||
\(771\) | 28.3319 | 1.02035 | ||||||||
\(772\) | 21.0958 | 0.759254 | ||||||||
\(773\) | 12.0401 | 0.433052 | 0.216526 | − | 0.976277i | \(-0.430527\pi\) | ||||
0.216526 | + | 0.976277i | \(0.430527\pi\) | |||||||
\(774\) | −6.43164 | −0.231180 | ||||||||
\(775\) | −0.661272 | −0.0237536 | ||||||||
\(776\) | −2.10060 | −0.0754073 | ||||||||
\(777\) | 11.9848 | 0.429951 | ||||||||
\(778\) | 10.0922 | 0.361825 | ||||||||
\(779\) | 37.7283 | 1.35176 | ||||||||
\(780\) | −14.7887 | −0.529521 | ||||||||
\(781\) | 21.4257 | 0.766671 | ||||||||
\(782\) | 11.6629 | 0.417065 | ||||||||
\(783\) | −3.96553 | −0.141717 | ||||||||
\(784\) | −6.74118 | −0.240756 | ||||||||
\(785\) | −21.4967 | −0.767250 | ||||||||
\(786\) | −26.4042 | −0.941808 | ||||||||
\(787\) | 23.8812 | 0.851272 | 0.425636 | − | 0.904894i | \(-0.360050\pi\) | ||||
0.425636 | + | 0.904894i | \(0.360050\pi\) | |||||||
\(788\) | −24.1967 | −0.861970 | ||||||||
\(789\) | 36.8646 | 1.31241 | ||||||||
\(790\) | −61.0018 | −2.17035 | ||||||||
\(791\) | 4.31317 | 0.153359 | ||||||||
\(792\) | −15.3476 | −0.545353 | ||||||||
\(793\) | −17.1366 | −0.608539 | ||||||||
\(794\) | −19.5206 | −0.692761 | ||||||||
\(795\) | 5.95506 | 0.211204 | ||||||||
\(796\) | 16.5051 | 0.585008 | ||||||||
\(797\) | 22.4521 | 0.795295 | 0.397648 | − | 0.917538i | \(-0.369827\pi\) | ||||
0.397648 | + | 0.917538i | \(0.369827\pi\) | |||||||
\(798\) | 9.31982 | 0.329918 | ||||||||
\(799\) | −9.16498 | −0.324234 | ||||||||
\(800\) | −9.27631 | −0.327967 | ||||||||
\(801\) | −2.16574 | −0.0765226 | ||||||||
\(802\) | −23.5426 | −0.831316 | ||||||||
\(803\) | 2.78428 | 0.0982552 | ||||||||
\(804\) | 0.480361 | 0.0169410 | ||||||||
\(805\) | 13.1150 | 0.462243 | ||||||||
\(806\) | −0.111646 | −0.00393255 | ||||||||
\(807\) | −51.7893 | −1.82307 | ||||||||
\(808\) | −2.07226 | −0.0729019 | ||||||||
\(809\) | −19.8751 | −0.698772 | −0.349386 | − | 0.936979i | \(-0.613610\pi\) | ||||
−0.349386 | + | 0.936979i | \(0.613610\pi\) | |||||||
\(810\) | −30.9940 | −1.08902 | ||||||||
\(811\) | 6.78435 | 0.238231 | 0.119115 | − | 0.992880i | \(-0.461994\pi\) | ||||
0.119115 | + | 0.992880i | \(0.461994\pi\) | |||||||
\(812\) | −3.28719 | −0.115358 | ||||||||
\(813\) | 71.7364 | 2.51591 | ||||||||
\(814\) | −44.5751 | −1.56235 | ||||||||
\(815\) | −15.5706 | −0.545414 | ||||||||
\(816\) | 4.27200 | 0.149550 | ||||||||
\(817\) | −14.5262 | −0.508207 | ||||||||
\(818\) | 36.4807 | 1.27552 | ||||||||
\(819\) | 2.58600 | 0.0903620 | ||||||||
\(820\) | 19.4470 | 0.679120 | ||||||||
\(821\) | −31.2628 | −1.09108 | −0.545540 | − | 0.838085i | \(-0.683675\pi\) | ||||
−0.545540 | + | 0.838085i | \(0.683675\pi\) | |||||||
\(822\) | −29.5181 | −1.02956 | ||||||||
\(823\) | 42.3528 | 1.47632 | 0.738162 | − | 0.674623i | \(-0.235694\pi\) | ||||
0.738162 | + | 0.674623i | \(0.235694\pi\) | |||||||
\(824\) | −14.2849 | −0.497636 | ||||||||
\(825\) | −109.625 | −3.81665 | ||||||||
\(826\) | −2.01556 | −0.0701303 | ||||||||
\(827\) | 35.5451 | 1.23602 | 0.618011 | − | 0.786169i | \(-0.287939\pi\) | ||||
0.618011 | + | 0.786169i | \(0.287939\pi\) | |||||||
\(828\) | 22.1439 | 0.769552 | ||||||||
\(829\) | 4.59014 | 0.159422 | 0.0797111 | − | 0.996818i | \(-0.474600\pi\) | ||||
0.0797111 | + | 0.996818i | \(0.474600\pi\) | |||||||
\(830\) | 25.1502 | 0.872976 | ||||||||
\(831\) | 46.7020 | 1.62007 | ||||||||
\(832\) | −1.56616 | −0.0542969 | ||||||||
\(833\) | 11.5234 | 0.399263 | ||||||||
\(834\) | −6.91299 | −0.239377 | ||||||||
\(835\) | −8.86327 | −0.306726 | ||||||||
\(836\) | −34.6633 | −1.19886 | ||||||||
\(837\) | 0.0437504 | 0.00151223 | ||||||||
\(838\) | −5.85624 | −0.202300 | ||||||||
\(839\) | −1.67928 | −0.0579753 | −0.0289877 | − | 0.999580i | \(-0.509228\pi\) | ||||
−0.0289877 | + | 0.999580i | \(0.509228\pi\) | |||||||
\(840\) | 4.80389 | 0.165750 | ||||||||
\(841\) | 12.7495 | 0.439636 | ||||||||
\(842\) | −14.3591 | −0.494847 | ||||||||
\(843\) | 53.3651 | 1.83799 | ||||||||
\(844\) | 12.4250 | 0.427688 | ||||||||
\(845\) | 39.8513 | 1.37093 | ||||||||
\(846\) | −17.4012 | −0.598265 | ||||||||
\(847\) | −5.77997 | −0.198602 | ||||||||
\(848\) | 0.630655 | 0.0216568 | ||||||||
\(849\) | −56.1810 | −1.92813 | ||||||||
\(850\) | 15.8570 | 0.543890 | ||||||||
\(851\) | 64.3139 | 2.20465 | ||||||||
\(852\) | −11.3233 | −0.387930 | ||||||||
\(853\) | −20.2165 | −0.692201 | −0.346101 | − | 0.938197i | \(-0.612494\pi\) | ||||
−0.346101 | + | 0.938197i | \(0.612494\pi\) | |||||||
\(854\) | 5.56657 | 0.190484 | ||||||||
\(855\) | 89.8922 | 3.07425 | ||||||||
\(856\) | 10.1314 | 0.346283 | ||||||||
\(857\) | −7.18968 | −0.245595 | −0.122797 | − | 0.992432i | \(-0.539187\pi\) | ||||
−0.122797 | + | 0.992432i | \(0.539187\pi\) | |||||||
\(858\) | −18.5085 | −0.631869 | ||||||||
\(859\) | −31.0062 | −1.05792 | −0.528959 | − | 0.848647i | \(-0.677417\pi\) | ||||
−0.528959 | + | 0.848647i | \(0.677417\pi\) | |||||||
\(860\) | −7.48751 | −0.255322 | ||||||||
\(861\) | −6.54381 | −0.223013 | ||||||||
\(862\) | 10.4899 | 0.357287 | ||||||||
\(863\) | 19.8583 | 0.675986 | 0.337993 | − | 0.941149i | \(-0.390252\pi\) | ||||
0.337993 | + | 0.941149i | \(0.390252\pi\) | |||||||
\(864\) | 0.613729 | 0.0208795 | ||||||||
\(865\) | 63.8824 | 2.17207 | ||||||||
\(866\) | 36.7641 | 1.24929 | ||||||||
\(867\) | 35.1824 | 1.19486 | ||||||||
\(868\) | 0.0362664 | 0.00123096 | ||||||||
\(869\) | −76.3454 | −2.58984 | ||||||||
\(870\) | −61.0126 | −2.06852 | ||||||||
\(871\) | 0.301036 | 0.0102002 | ||||||||
\(872\) | −13.6923 | −0.463680 | ||||||||
\(873\) | 6.81767 | 0.230743 | ||||||||
\(874\) | 50.0130 | 1.69172 | ||||||||
\(875\) | 8.22008 | 0.277889 | ||||||||
\(876\) | −1.47147 | −0.0497164 | ||||||||
\(877\) | 23.8428 | 0.805114 | 0.402557 | − | 0.915395i | \(-0.368122\pi\) | ||||
0.402557 | + | 0.915395i | \(0.368122\pi\) | |||||||
\(878\) | −38.0471 | −1.28403 | ||||||||
\(879\) | −36.1368 | −1.21886 | ||||||||
\(880\) | −17.8672 | −0.602303 | ||||||||
\(881\) | −21.4631 | −0.723110 | −0.361555 | − | 0.932351i | \(-0.617754\pi\) | ||||
−0.361555 | + | 0.932351i | \(0.617754\pi\) | |||||||
\(882\) | 21.8790 | 0.736705 | ||||||||
\(883\) | −9.49777 | −0.319626 | −0.159813 | − | 0.987147i | \(-0.551089\pi\) | ||||
−0.159813 | + | 0.987147i | \(0.551089\pi\) | |||||||
\(884\) | 2.67721 | 0.0900442 | ||||||||
\(885\) | −37.4102 | −1.25753 | ||||||||
\(886\) | −38.1362 | −1.28121 | ||||||||
\(887\) | 16.9315 | 0.568504 | 0.284252 | − | 0.958750i | \(-0.408255\pi\) | ||||
0.284252 | + | 0.958750i | \(0.408255\pi\) | |||||||
\(888\) | 23.5575 | 0.790539 | ||||||||
\(889\) | 7.62053 | 0.255584 | ||||||||
\(890\) | −2.52128 | −0.0845136 | ||||||||
\(891\) | −38.7899 | −1.29951 | ||||||||
\(892\) | −13.1348 | −0.439784 | ||||||||
\(893\) | −39.3014 | −1.31517 | ||||||||
\(894\) | 0.0560342 | 0.00187407 | ||||||||
\(895\) | 96.1994 | 3.21559 | ||||||||
\(896\) | 0.508744 | 0.0169959 | ||||||||
\(897\) | 26.7045 | 0.891636 | ||||||||
\(898\) | −9.26607 | −0.309213 | ||||||||
\(899\) | −0.460607 | −0.0153621 | ||||||||
\(900\) | 30.1070 | 1.00357 | ||||||||
\(901\) | −1.07805 | −0.0359149 | ||||||||
\(902\) | 24.3385 | 0.810383 | ||||||||
\(903\) | 2.51950 | 0.0838438 | ||||||||
\(904\) | 8.47807 | 0.281976 | ||||||||
\(905\) | 7.53304 | 0.250407 | ||||||||
\(906\) | 39.6368 | 1.31685 | ||||||||
\(907\) | 45.8683 | 1.52303 | 0.761516 | − | 0.648146i | \(-0.224456\pi\) | ||||
0.761516 | + | 0.648146i | \(0.224456\pi\) | |||||||
\(908\) | −8.32519 | −0.276281 | ||||||||
\(909\) | 6.72569 | 0.223077 | ||||||||
\(910\) | 3.01053 | 0.0997982 | ||||||||
\(911\) | 49.6128 | 1.64375 | 0.821873 | − | 0.569671i | \(-0.192929\pi\) | ||||
0.821873 | + | 0.569671i | \(0.192929\pi\) | |||||||
\(912\) | 18.3193 | 0.606612 | ||||||||
\(913\) | 31.4762 | 1.04171 | ||||||||
\(914\) | −40.9023 | −1.35293 | ||||||||
\(915\) | 103.320 | 3.41564 | ||||||||
\(916\) | −10.2884 | −0.339937 | ||||||||
\(917\) | 5.37510 | 0.177501 | ||||||||
\(918\) | −1.04911 | −0.0346258 | ||||||||
\(919\) | 44.4103 | 1.46496 | 0.732481 | − | 0.680787i | \(-0.238362\pi\) | ||||
0.732481 | + | 0.680787i | \(0.238362\pi\) | |||||||
\(920\) | 25.7792 | 0.849914 | ||||||||
\(921\) | 20.1969 | 0.665510 | ||||||||
\(922\) | −4.97150 | −0.163728 | ||||||||
\(923\) | −7.09615 | −0.233573 | ||||||||
\(924\) | 6.01220 | 0.197787 | ||||||||
\(925\) | 87.4417 | 2.87507 | ||||||||
\(926\) | −26.8750 | −0.883167 | ||||||||
\(927\) | 46.3626 | 1.52275 | ||||||||
\(928\) | −6.46138 | −0.212105 | ||||||||
\(929\) | 11.7818 | 0.386549 | 0.193274 | − | 0.981145i | \(-0.438089\pi\) | ||||
0.193274 | + | 0.981145i | \(0.438089\pi\) | |||||||
\(930\) | 0.673131 | 0.0220728 | ||||||||
\(931\) | 49.4149 | 1.61951 | ||||||||
\(932\) | 29.6620 | 0.971611 | ||||||||
\(933\) | 52.9774 | 1.73440 | ||||||||
\(934\) | −3.24381 | −0.106141 | ||||||||
\(935\) | 30.5423 | 0.998840 | ||||||||
\(936\) | 5.08310 | 0.166146 | ||||||||
\(937\) | 1.07946 | 0.0352644 | 0.0176322 | − | 0.999845i | \(-0.494387\pi\) | ||||
0.0176322 | + | 0.999845i | \(0.494387\pi\) | |||||||
\(938\) | −0.0977869 | −0.00319286 | ||||||||
\(939\) | −41.4395 | −1.35233 | ||||||||
\(940\) | −20.2579 | −0.660740 | ||||||||
\(941\) | 42.9535 | 1.40024 | 0.700121 | − | 0.714024i | \(-0.253129\pi\) | ||||
0.700121 | + | 0.714024i | \(0.253129\pi\) | |||||||
\(942\) | 14.2184 | 0.463260 | ||||||||
\(943\) | −35.1161 | −1.14354 | ||||||||
\(944\) | −3.96183 | −0.128947 | ||||||||
\(945\) | −1.17973 | −0.0383767 | ||||||||
\(946\) | −9.37082 | −0.304672 | ||||||||
\(947\) | 9.97975 | 0.324298 | 0.162149 | − | 0.986766i | \(-0.448157\pi\) | ||||
0.162149 | + | 0.986766i | \(0.448157\pi\) | |||||||
\(948\) | 40.3479 | 1.31044 | ||||||||
\(949\) | −0.922150 | −0.0299343 | ||||||||
\(950\) | 67.9981 | 2.20615 | ||||||||
\(951\) | −52.0950 | −1.68930 | ||||||||
\(952\) | −0.869650 | −0.0281855 | ||||||||
\(953\) | −17.2418 | −0.558516 | −0.279258 | − | 0.960216i | \(-0.590089\pi\) | ||||
−0.279258 | + | 0.960216i | \(0.590089\pi\) | |||||||
\(954\) | −2.04684 | −0.0662689 | ||||||||
\(955\) | 54.7334 | 1.77113 | ||||||||
\(956\) | −27.9429 | −0.903738 | ||||||||
\(957\) | −76.3589 | −2.46833 | ||||||||
\(958\) | −28.9709 | −0.936006 | ||||||||
\(959\) | 6.00899 | 0.194040 | ||||||||
\(960\) | 9.44266 | 0.304760 | ||||||||
\(961\) | −30.9949 | −0.999836 | ||||||||
\(962\) | 14.7632 | 0.475984 | ||||||||
\(963\) | −32.8822 | −1.05961 | ||||||||
\(964\) | 8.10538 | 0.261057 | ||||||||
\(965\) | −79.7083 | −2.56590 | ||||||||
\(966\) | −8.67455 | −0.279099 | ||||||||
\(967\) | −2.59124 | −0.0833286 | −0.0416643 | − | 0.999132i | \(-0.513266\pi\) | ||||
−0.0416643 | + | 0.999132i | \(0.513266\pi\) | |||||||
\(968\) | −11.3613 | −0.365165 | ||||||||
\(969\) | −31.3151 | −1.00599 | ||||||||
\(970\) | 7.93692 | 0.254839 | ||||||||
\(971\) | −56.9588 | −1.82790 | −0.913948 | − | 0.405832i | \(-0.866982\pi\) | ||||
−0.913948 | + | 0.405832i | \(0.866982\pi\) | |||||||
\(972\) | 22.3413 | 0.716598 | ||||||||
\(973\) | 1.40727 | 0.0451151 | ||||||||
\(974\) | 5.33853 | 0.171058 | ||||||||
\(975\) | 36.3076 | 1.16277 | ||||||||
\(976\) | 10.9418 | 0.350238 | ||||||||
\(977\) | 14.5138 | 0.464338 | 0.232169 | − | 0.972676i | \(-0.425418\pi\) | ||||
0.232169 | + | 0.972676i | \(0.425418\pi\) | |||||||
\(978\) | 10.2987 | 0.329317 | ||||||||
\(979\) | −3.15546 | −0.100849 | ||||||||
\(980\) | 25.4709 | 0.813637 | ||||||||
\(981\) | 44.4394 | 1.41884 | ||||||||
\(982\) | −26.8776 | −0.857697 | ||||||||
\(983\) | −28.6998 | −0.915381 | −0.457691 | − | 0.889112i | \(-0.651323\pi\) | ||||
−0.457691 | + | 0.889112i | \(0.651323\pi\) | |||||||
\(984\) | −12.8627 | −0.410048 | ||||||||
\(985\) | 91.4246 | 2.91303 | ||||||||
\(986\) | 11.0451 | 0.351749 | ||||||||
\(987\) | 6.81666 | 0.216977 | ||||||||
\(988\) | 11.4804 | 0.365241 | ||||||||
\(989\) | 13.5204 | 0.429925 | ||||||||
\(990\) | 57.9893 | 1.84302 | ||||||||
\(991\) | −32.0748 | −1.01889 | −0.509444 | − | 0.860504i | \(-0.670149\pi\) | ||||
−0.509444 | + | 0.860504i | \(0.670149\pi\) | |||||||
\(992\) | 0.0712862 | 0.00226334 | ||||||||
\(993\) | 8.51946 | 0.270357 | ||||||||
\(994\) | 2.30508 | 0.0731126 | ||||||||
\(995\) | −62.3629 | −1.97704 | ||||||||
\(996\) | −16.6349 | −0.527097 | ||||||||
\(997\) | 17.8809 | 0.566295 | 0.283147 | − | 0.959076i | \(-0.408621\pi\) | ||||
0.283147 | + | 0.959076i | \(0.408621\pi\) | |||||||
\(998\) | −25.8270 | −0.817539 | ||||||||
\(999\) | −5.78522 | −0.183036 |
(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 | 8042.2.a.c.1.11 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8042.2.a.c.1.11 | ✓ | 86 | 1.1 | even | 1 | trivial |