Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8006,2,Mod(1,8006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8006, 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("8006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8006 = 2 \cdot 4003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8006.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: | \(63.9282318582\) |
Analytic rank: | \(1\) |
Dimension: | \(75\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 8006.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.72100 | −0.993618 | −0.496809 | − | 0.867860i | \(-0.665495\pi\) | ||||
−0.496809 | + | 0.867860i | \(0.665495\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.49175 | 0.667129 | 0.333565 | − | 0.942727i | \(-0.391748\pi\) | ||||
0.333565 | + | 0.942727i | \(0.391748\pi\) | |||||||
\(6\) | 1.72100 | 0.702594 | ||||||||
\(7\) | −1.07018 | −0.404490 | −0.202245 | − | 0.979335i | \(-0.564824\pi\) | ||||
−0.202245 | + | 0.979335i | \(0.564824\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.0381718 | −0.0127239 | ||||||||
\(10\) | −1.49175 | −0.471732 | ||||||||
\(11\) | 1.68870 | 0.509162 | 0.254581 | − | 0.967051i | \(-0.418062\pi\) | ||||
0.254581 | + | 0.967051i | \(0.418062\pi\) | |||||||
\(12\) | −1.72100 | −0.496809 | ||||||||
\(13\) | 3.00150 | 0.832467 | 0.416233 | − | 0.909258i | \(-0.363350\pi\) | ||||
0.416233 | + | 0.909258i | \(0.363350\pi\) | |||||||
\(14\) | 1.07018 | 0.286018 | ||||||||
\(15\) | −2.56729 | −0.662871 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.629551 | −0.152689 | −0.0763443 | − | 0.997082i | \(-0.524325\pi\) | ||||
−0.0763443 | + | 0.997082i | \(0.524325\pi\) | |||||||
\(18\) | 0.0381718 | 0.00899718 | ||||||||
\(19\) | −0.905993 | −0.207849 | −0.103925 | − | 0.994585i | \(-0.533140\pi\) | ||||
−0.103925 | + | 0.994585i | \(0.533140\pi\) | |||||||
\(20\) | 1.49175 | 0.333565 | ||||||||
\(21\) | 1.84178 | 0.401909 | ||||||||
\(22\) | −1.68870 | −0.360032 | ||||||||
\(23\) | −0.523921 | −0.109245 | −0.0546225 | − | 0.998507i | \(-0.517396\pi\) | ||||
−0.0546225 | + | 0.998507i | \(0.517396\pi\) | |||||||
\(24\) | 1.72100 | 0.351297 | ||||||||
\(25\) | −2.77469 | −0.554939 | ||||||||
\(26\) | −3.00150 | −0.588643 | ||||||||
\(27\) | 5.22868 | 1.00626 | ||||||||
\(28\) | −1.07018 | −0.202245 | ||||||||
\(29\) | 0.474981 | 0.0882017 | 0.0441008 | − | 0.999027i | \(-0.485958\pi\) | ||||
0.0441008 | + | 0.999027i | \(0.485958\pi\) | |||||||
\(30\) | 2.56729 | 0.468721 | ||||||||
\(31\) | −0.660364 | −0.118605 | −0.0593025 | − | 0.998240i | \(-0.518888\pi\) | ||||
−0.0593025 | + | 0.998240i | \(0.518888\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −2.90625 | −0.505913 | ||||||||
\(34\) | 0.629551 | 0.107967 | ||||||||
\(35\) | −1.59644 | −0.269847 | ||||||||
\(36\) | −0.0381718 | −0.00636196 | ||||||||
\(37\) | 1.31640 | 0.216415 | 0.108207 | − | 0.994128i | \(-0.465489\pi\) | ||||
0.108207 | + | 0.994128i | \(0.465489\pi\) | |||||||
\(38\) | 0.905993 | 0.146971 | ||||||||
\(39\) | −5.16557 | −0.827154 | ||||||||
\(40\) | −1.49175 | −0.235866 | ||||||||
\(41\) | 1.65916 | 0.259117 | 0.129558 | − | 0.991572i | \(-0.458644\pi\) | ||||
0.129558 | + | 0.991572i | \(0.458644\pi\) | |||||||
\(42\) | −1.84178 | −0.284192 | ||||||||
\(43\) | −3.20887 | −0.489348 | −0.244674 | − | 0.969605i | \(-0.578681\pi\) | ||||
−0.244674 | + | 0.969605i | \(0.578681\pi\) | |||||||
\(44\) | 1.68870 | 0.254581 | ||||||||
\(45\) | −0.0569426 | −0.00848850 | ||||||||
\(46\) | 0.523921 | 0.0772479 | ||||||||
\(47\) | 3.81130 | 0.555935 | 0.277967 | − | 0.960590i | \(-0.410339\pi\) | ||||
0.277967 | + | 0.960590i | \(0.410339\pi\) | |||||||
\(48\) | −1.72100 | −0.248404 | ||||||||
\(49\) | −5.85471 | −0.836388 | ||||||||
\(50\) | 2.77469 | 0.392401 | ||||||||
\(51\) | 1.08346 | 0.151714 | ||||||||
\(52\) | 3.00150 | 0.416233 | ||||||||
\(53\) | −7.66072 | −1.05228 | −0.526141 | − | 0.850398i | \(-0.676361\pi\) | ||||
−0.526141 | + | 0.850398i | \(0.676361\pi\) | |||||||
\(54\) | −5.22868 | −0.711534 | ||||||||
\(55\) | 2.51911 | 0.339677 | ||||||||
\(56\) | 1.07018 | 0.143009 | ||||||||
\(57\) | 1.55921 | 0.206522 | ||||||||
\(58\) | −0.474981 | −0.0623680 | ||||||||
\(59\) | −8.83103 | −1.14970 | −0.574851 | − | 0.818258i | \(-0.694940\pi\) | ||||
−0.574851 | + | 0.818258i | \(0.694940\pi\) | |||||||
\(60\) | −2.56729 | −0.331436 | ||||||||
\(61\) | 0.188979 | 0.0241963 | 0.0120981 | − | 0.999927i | \(-0.496149\pi\) | ||||
0.0120981 | + | 0.999927i | \(0.496149\pi\) | |||||||
\(62\) | 0.660364 | 0.0838663 | ||||||||
\(63\) | 0.0408507 | 0.00514671 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.47748 | 0.555363 | ||||||||
\(66\) | 2.90625 | 0.357734 | ||||||||
\(67\) | 12.0430 | 1.47128 | 0.735642 | − | 0.677370i | \(-0.236880\pi\) | ||||
0.735642 | + | 0.677370i | \(0.236880\pi\) | |||||||
\(68\) | −0.629551 | −0.0763443 | ||||||||
\(69\) | 0.901666 | 0.108548 | ||||||||
\(70\) | 1.59644 | 0.190811 | ||||||||
\(71\) | 2.26035 | 0.268254 | 0.134127 | − | 0.990964i | \(-0.457177\pi\) | ||||
0.134127 | + | 0.990964i | \(0.457177\pi\) | |||||||
\(72\) | 0.0381718 | 0.00449859 | ||||||||
\(73\) | −2.11853 | −0.247955 | −0.123978 | − | 0.992285i | \(-0.539565\pi\) | ||||
−0.123978 | + | 0.992285i | \(0.539565\pi\) | |||||||
\(74\) | −1.31640 | −0.153028 | ||||||||
\(75\) | 4.77524 | 0.551397 | ||||||||
\(76\) | −0.905993 | −0.103925 | ||||||||
\(77\) | −1.80722 | −0.205951 | ||||||||
\(78\) | 5.16557 | 0.584886 | ||||||||
\(79\) | 5.32571 | 0.599189 | 0.299594 | − | 0.954067i | \(-0.403149\pi\) | ||||
0.299594 | + | 0.954067i | \(0.403149\pi\) | |||||||
\(80\) | 1.49175 | 0.166782 | ||||||||
\(81\) | −8.88403 | −0.987114 | ||||||||
\(82\) | −1.65916 | −0.183223 | ||||||||
\(83\) | −7.15493 | −0.785355 | −0.392678 | − | 0.919676i | \(-0.628451\pi\) | ||||
−0.392678 | + | 0.919676i | \(0.628451\pi\) | |||||||
\(84\) | 1.84178 | 0.200954 | ||||||||
\(85\) | −0.939131 | −0.101863 | ||||||||
\(86\) | 3.20887 | 0.346021 | ||||||||
\(87\) | −0.817440 | −0.0876387 | ||||||||
\(88\) | −1.68870 | −0.180016 | ||||||||
\(89\) | −10.0856 | −1.06907 | −0.534534 | − | 0.845147i | \(-0.679513\pi\) | ||||
−0.534534 | + | 0.845147i | \(0.679513\pi\) | |||||||
\(90\) | 0.0569426 | 0.00600228 | ||||||||
\(91\) | −3.21215 | −0.336725 | ||||||||
\(92\) | −0.523921 | −0.0546225 | ||||||||
\(93\) | 1.13648 | 0.117848 | ||||||||
\(94\) | −3.81130 | −0.393105 | ||||||||
\(95\) | −1.35151 | −0.138662 | ||||||||
\(96\) | 1.72100 | 0.175648 | ||||||||
\(97\) | −8.68119 | −0.881442 | −0.440721 | − | 0.897644i | \(-0.645277\pi\) | ||||
−0.440721 | + | 0.897644i | \(0.645277\pi\) | |||||||
\(98\) | 5.85471 | 0.591415 | ||||||||
\(99\) | −0.0644607 | −0.00647855 | ||||||||
\(100\) | −2.77469 | −0.277469 | ||||||||
\(101\) | 19.4422 | 1.93458 | 0.967288 | − | 0.253682i | \(-0.0816416\pi\) | ||||
0.967288 | + | 0.253682i | \(0.0816416\pi\) | |||||||
\(102\) | −1.08346 | −0.107278 | ||||||||
\(103\) | −4.58818 | −0.452086 | −0.226043 | − | 0.974117i | \(-0.572579\pi\) | ||||
−0.226043 | + | 0.974117i | \(0.572579\pi\) | |||||||
\(104\) | −3.00150 | −0.294321 | ||||||||
\(105\) | 2.74746 | 0.268125 | ||||||||
\(106\) | 7.66072 | 0.744075 | ||||||||
\(107\) | 8.88578 | 0.859020 | 0.429510 | − | 0.903062i | \(-0.358686\pi\) | ||||
0.429510 | + | 0.903062i | \(0.358686\pi\) | |||||||
\(108\) | 5.22868 | 0.503130 | ||||||||
\(109\) | 12.5508 | 1.20215 | 0.601073 | − | 0.799194i | \(-0.294740\pi\) | ||||
0.601073 | + | 0.799194i | \(0.294740\pi\) | |||||||
\(110\) | −2.51911 | −0.240188 | ||||||||
\(111\) | −2.26552 | −0.215034 | ||||||||
\(112\) | −1.07018 | −0.101123 | ||||||||
\(113\) | 6.53956 | 0.615190 | 0.307595 | − | 0.951517i | \(-0.400476\pi\) | ||||
0.307595 | + | 0.951517i | \(0.400476\pi\) | |||||||
\(114\) | −1.55921 | −0.146033 | ||||||||
\(115\) | −0.781557 | −0.0728806 | ||||||||
\(116\) | 0.474981 | 0.0441008 | ||||||||
\(117\) | −0.114573 | −0.0105922 | ||||||||
\(118\) | 8.83103 | 0.812962 | ||||||||
\(119\) | 0.673734 | 0.0617611 | ||||||||
\(120\) | 2.56729 | 0.234360 | ||||||||
\(121\) | −8.14829 | −0.740754 | ||||||||
\(122\) | −0.188979 | −0.0171093 | ||||||||
\(123\) | −2.85540 | −0.257463 | ||||||||
\(124\) | −0.660364 | −0.0593025 | ||||||||
\(125\) | −11.5979 | −1.03734 | ||||||||
\(126\) | −0.0408507 | −0.00363927 | ||||||||
\(127\) | 5.39811 | 0.479005 | 0.239502 | − | 0.970896i | \(-0.423016\pi\) | ||||
0.239502 | + | 0.970896i | \(0.423016\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 5.52245 | 0.486224 | ||||||||
\(130\) | −4.47748 | −0.392701 | ||||||||
\(131\) | 2.39765 | 0.209484 | 0.104742 | − | 0.994499i | \(-0.466598\pi\) | ||||
0.104742 | + | 0.994499i | \(0.466598\pi\) | |||||||
\(132\) | −2.90625 | −0.252956 | ||||||||
\(133\) | 0.969576 | 0.0840729 | ||||||||
\(134\) | −12.0430 | −1.04036 | ||||||||
\(135\) | 7.79987 | 0.671306 | ||||||||
\(136\) | 0.629551 | 0.0539836 | ||||||||
\(137\) | −21.9377 | −1.87426 | −0.937131 | − | 0.348977i | \(-0.886529\pi\) | ||||
−0.937131 | + | 0.348977i | \(0.886529\pi\) | |||||||
\(138\) | −0.901666 | −0.0767549 | ||||||||
\(139\) | −8.36040 | −0.709119 | −0.354560 | − | 0.935033i | \(-0.615369\pi\) | ||||
−0.354560 | + | 0.935033i | \(0.615369\pi\) | |||||||
\(140\) | −1.59644 | −0.134924 | ||||||||
\(141\) | −6.55923 | −0.552387 | ||||||||
\(142\) | −2.26035 | −0.189684 | ||||||||
\(143\) | 5.06864 | 0.423861 | ||||||||
\(144\) | −0.0381718 | −0.00318098 | ||||||||
\(145\) | 0.708550 | 0.0588419 | ||||||||
\(146\) | 2.11853 | 0.175331 | ||||||||
\(147\) | 10.0759 | 0.831049 | ||||||||
\(148\) | 1.31640 | 0.108207 | ||||||||
\(149\) | −22.2698 | −1.82441 | −0.912206 | − | 0.409731i | \(-0.865622\pi\) | ||||
−0.912206 | + | 0.409731i | \(0.865622\pi\) | |||||||
\(150\) | −4.77524 | −0.389896 | ||||||||
\(151\) | 4.25695 | 0.346426 | 0.173213 | − | 0.984884i | \(-0.444585\pi\) | ||||
0.173213 | + | 0.984884i | \(0.444585\pi\) | |||||||
\(152\) | 0.905993 | 0.0734857 | ||||||||
\(153\) | 0.0240311 | 0.00194280 | ||||||||
\(154\) | 1.80722 | 0.145630 | ||||||||
\(155\) | −0.985096 | −0.0791248 | ||||||||
\(156\) | −5.16557 | −0.413577 | ||||||||
\(157\) | 4.51315 | 0.360189 | 0.180094 | − | 0.983649i | \(-0.442360\pi\) | ||||
0.180094 | + | 0.983649i | \(0.442360\pi\) | |||||||
\(158\) | −5.32571 | −0.423691 | ||||||||
\(159\) | 13.1841 | 1.04557 | ||||||||
\(160\) | −1.49175 | −0.117933 | ||||||||
\(161\) | 0.560690 | 0.0441886 | ||||||||
\(162\) | 8.88403 | 0.697995 | ||||||||
\(163\) | −10.2065 | −0.799432 | −0.399716 | − | 0.916639i | \(-0.630891\pi\) | ||||
−0.399716 | + | 0.916639i | \(0.630891\pi\) | |||||||
\(164\) | 1.65916 | 0.129558 | ||||||||
\(165\) | −4.33538 | −0.337509 | ||||||||
\(166\) | 7.15493 | 0.555330 | ||||||||
\(167\) | 6.46771 | 0.500486 | 0.250243 | − | 0.968183i | \(-0.419489\pi\) | ||||
0.250243 | + | 0.968183i | \(0.419489\pi\) | |||||||
\(168\) | −1.84178 | −0.142096 | ||||||||
\(169\) | −3.99099 | −0.306999 | ||||||||
\(170\) | 0.939131 | 0.0720281 | ||||||||
\(171\) | 0.0345834 | 0.00264466 | ||||||||
\(172\) | −3.20887 | −0.244674 | ||||||||
\(173\) | 10.4767 | 0.796530 | 0.398265 | − | 0.917270i | \(-0.369612\pi\) | ||||
0.398265 | + | 0.917270i | \(0.369612\pi\) | |||||||
\(174\) | 0.817440 | 0.0619699 | ||||||||
\(175\) | 2.96942 | 0.224467 | ||||||||
\(176\) | 1.68870 | 0.127291 | ||||||||
\(177\) | 15.1982 | 1.14236 | ||||||||
\(178\) | 10.0856 | 0.755945 | ||||||||
\(179\) | 6.70309 | 0.501012 | 0.250506 | − | 0.968115i | \(-0.419403\pi\) | ||||
0.250506 | + | 0.968115i | \(0.419403\pi\) | |||||||
\(180\) | −0.0569426 | −0.00424425 | ||||||||
\(181\) | 3.66864 | 0.272688 | 0.136344 | − | 0.990662i | \(-0.456465\pi\) | ||||
0.136344 | + | 0.990662i | \(0.456465\pi\) | |||||||
\(182\) | 3.21215 | 0.238100 | ||||||||
\(183\) | −0.325232 | −0.0240418 | ||||||||
\(184\) | 0.523921 | 0.0386240 | ||||||||
\(185\) | 1.96373 | 0.144377 | ||||||||
\(186\) | −1.13648 | −0.0833311 | ||||||||
\(187\) | −1.06312 | −0.0777433 | ||||||||
\(188\) | 3.81130 | 0.277967 | ||||||||
\(189\) | −5.59564 | −0.407023 | ||||||||
\(190\) | 1.35151 | 0.0980489 | ||||||||
\(191\) | 3.49506 | 0.252894 | 0.126447 | − | 0.991973i | \(-0.459643\pi\) | ||||
0.126447 | + | 0.991973i | \(0.459643\pi\) | |||||||
\(192\) | −1.72100 | −0.124202 | ||||||||
\(193\) | −25.3685 | −1.82607 | −0.913034 | − | 0.407885i | \(-0.866267\pi\) | ||||
−0.913034 | + | 0.407885i | \(0.866267\pi\) | |||||||
\(194\) | 8.68119 | 0.623273 | ||||||||
\(195\) | −7.70573 | −0.551818 | ||||||||
\(196\) | −5.85471 | −0.418194 | ||||||||
\(197\) | 24.2370 | 1.72681 | 0.863406 | − | 0.504509i | \(-0.168327\pi\) | ||||
0.863406 | + | 0.504509i | \(0.168327\pi\) | |||||||
\(198\) | 0.0644607 | 0.00458102 | ||||||||
\(199\) | −8.57145 | −0.607614 | −0.303807 | − | 0.952734i | \(-0.598258\pi\) | ||||
−0.303807 | + | 0.952734i | \(0.598258\pi\) | |||||||
\(200\) | 2.77469 | 0.196200 | ||||||||
\(201\) | −20.7259 | −1.46189 | ||||||||
\(202\) | −19.4422 | −1.36795 | ||||||||
\(203\) | −0.508315 | −0.0356767 | ||||||||
\(204\) | 1.08346 | 0.0758571 | ||||||||
\(205\) | 2.47504 | 0.172864 | ||||||||
\(206\) | 4.58818 | 0.319673 | ||||||||
\(207\) | 0.0199990 | 0.00139003 | ||||||||
\(208\) | 3.00150 | 0.208117 | ||||||||
\(209\) | −1.52995 | −0.105829 | ||||||||
\(210\) | −2.74746 | −0.189593 | ||||||||
\(211\) | 5.44236 | 0.374667 | 0.187334 | − | 0.982296i | \(-0.440015\pi\) | ||||
0.187334 | + | 0.982296i | \(0.440015\pi\) | |||||||
\(212\) | −7.66072 | −0.526141 | ||||||||
\(213\) | −3.89005 | −0.266542 | ||||||||
\(214\) | −8.88578 | −0.607419 | ||||||||
\(215\) | −4.78682 | −0.326458 | ||||||||
\(216\) | −5.22868 | −0.355767 | ||||||||
\(217\) | 0.706709 | 0.0479745 | ||||||||
\(218\) | −12.5508 | −0.850046 | ||||||||
\(219\) | 3.64598 | 0.246373 | ||||||||
\(220\) | 2.51911 | 0.169839 | ||||||||
\(221\) | −1.88960 | −0.127108 | ||||||||
\(222\) | 2.26552 | 0.152052 | ||||||||
\(223\) | 7.72095 | 0.517033 | 0.258517 | − | 0.966007i | \(-0.416766\pi\) | ||||
0.258517 | + | 0.966007i | \(0.416766\pi\) | |||||||
\(224\) | 1.07018 | 0.0715045 | ||||||||
\(225\) | 0.105915 | 0.00706100 | ||||||||
\(226\) | −6.53956 | −0.435005 | ||||||||
\(227\) | −22.1025 | −1.46699 | −0.733497 | − | 0.679692i | \(-0.762113\pi\) | ||||
−0.733497 | + | 0.679692i | \(0.762113\pi\) | |||||||
\(228\) | 1.55921 | 0.103261 | ||||||||
\(229\) | 2.43523 | 0.160924 | 0.0804622 | − | 0.996758i | \(-0.474360\pi\) | ||||
0.0804622 | + | 0.996758i | \(0.474360\pi\) | |||||||
\(230\) | 0.781557 | 0.0515343 | ||||||||
\(231\) | 3.11021 | 0.204637 | ||||||||
\(232\) | −0.474981 | −0.0311840 | ||||||||
\(233\) | −28.6314 | −1.87571 | −0.937853 | − | 0.347033i | \(-0.887189\pi\) | ||||
−0.937853 | + | 0.347033i | \(0.887189\pi\) | |||||||
\(234\) | 0.114573 | 0.00748985 | ||||||||
\(235\) | 5.68549 | 0.370880 | ||||||||
\(236\) | −8.83103 | −0.574851 | ||||||||
\(237\) | −9.16552 | −0.595365 | ||||||||
\(238\) | −0.673734 | −0.0436717 | ||||||||
\(239\) | −3.85355 | −0.249265 | −0.124633 | − | 0.992203i | \(-0.539775\pi\) | ||||
−0.124633 | + | 0.992203i | \(0.539775\pi\) | |||||||
\(240\) | −2.56729 | −0.165718 | ||||||||
\(241\) | 22.0678 | 1.42151 | 0.710756 | − | 0.703438i | \(-0.248353\pi\) | ||||
0.710756 | + | 0.703438i | \(0.248353\pi\) | |||||||
\(242\) | 8.14829 | 0.523792 | ||||||||
\(243\) | −0.396669 | −0.0254463 | ||||||||
\(244\) | 0.188979 | 0.0120981 | ||||||||
\(245\) | −8.73375 | −0.557979 | ||||||||
\(246\) | 2.85540 | 0.182054 | ||||||||
\(247\) | −2.71934 | −0.173027 | ||||||||
\(248\) | 0.660364 | 0.0419332 | ||||||||
\(249\) | 12.3136 | 0.780343 | ||||||||
\(250\) | 11.5979 | 0.733514 | ||||||||
\(251\) | 10.4314 | 0.658423 | 0.329211 | − | 0.944256i | \(-0.393217\pi\) | ||||
0.329211 | + | 0.944256i | \(0.393217\pi\) | |||||||
\(252\) | 0.0408507 | 0.00257335 | ||||||||
\(253\) | −0.884746 | −0.0556235 | ||||||||
\(254\) | −5.39811 | −0.338707 | ||||||||
\(255\) | 1.61624 | 0.101213 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.8546 | 0.988986 | 0.494493 | − | 0.869182i | \(-0.335354\pi\) | ||||
0.494493 | + | 0.869182i | \(0.335354\pi\) | |||||||
\(258\) | −5.52245 | −0.343813 | ||||||||
\(259\) | −1.40879 | −0.0875377 | ||||||||
\(260\) | 4.47748 | 0.277681 | ||||||||
\(261\) | −0.0181309 | −0.00112227 | ||||||||
\(262\) | −2.39765 | −0.148127 | ||||||||
\(263\) | 28.5821 | 1.76245 | 0.881224 | − | 0.472700i | \(-0.156720\pi\) | ||||
0.881224 | + | 0.472700i | \(0.156720\pi\) | |||||||
\(264\) | 2.90625 | 0.178867 | ||||||||
\(265\) | −11.4279 | −0.702008 | ||||||||
\(266\) | −0.969576 | −0.0594485 | ||||||||
\(267\) | 17.3572 | 1.06224 | ||||||||
\(268\) | 12.0430 | 0.735642 | ||||||||
\(269\) | 0.791621 | 0.0482660 | 0.0241330 | − | 0.999709i | \(-0.492317\pi\) | ||||
0.0241330 | + | 0.999709i | \(0.492317\pi\) | |||||||
\(270\) | −7.79987 | −0.474685 | ||||||||
\(271\) | 6.60941 | 0.401493 | 0.200747 | − | 0.979643i | \(-0.435663\pi\) | ||||
0.200747 | + | 0.979643i | \(0.435663\pi\) | |||||||
\(272\) | −0.629551 | −0.0381722 | ||||||||
\(273\) | 5.52810 | 0.334576 | ||||||||
\(274\) | 21.9377 | 1.32530 | ||||||||
\(275\) | −4.68563 | −0.282554 | ||||||||
\(276\) | 0.901666 | 0.0542739 | ||||||||
\(277\) | 7.34257 | 0.441172 | 0.220586 | − | 0.975367i | \(-0.429203\pi\) | ||||
0.220586 | + | 0.975367i | \(0.429203\pi\) | |||||||
\(278\) | 8.36040 | 0.501423 | ||||||||
\(279\) | 0.0252073 | 0.00150912 | ||||||||
\(280\) | 1.59644 | 0.0954054 | ||||||||
\(281\) | 5.23271 | 0.312157 | 0.156079 | − | 0.987745i | \(-0.450115\pi\) | ||||
0.156079 | + | 0.987745i | \(0.450115\pi\) | |||||||
\(282\) | 6.55923 | 0.390596 | ||||||||
\(283\) | 22.4417 | 1.33402 | 0.667010 | − | 0.745048i | \(-0.267574\pi\) | ||||
0.667010 | + | 0.745048i | \(0.267574\pi\) | |||||||
\(284\) | 2.26035 | 0.134127 | ||||||||
\(285\) | 2.32595 | 0.137777 | ||||||||
\(286\) | −5.06864 | −0.299715 | ||||||||
\(287\) | −1.77560 | −0.104810 | ||||||||
\(288\) | 0.0381718 | 0.00224929 | ||||||||
\(289\) | −16.6037 | −0.976686 | ||||||||
\(290\) | −0.708550 | −0.0416075 | ||||||||
\(291\) | 14.9403 | 0.875816 | ||||||||
\(292\) | −2.11853 | −0.123978 | ||||||||
\(293\) | −18.2607 | −1.06680 | −0.533399 | − | 0.845864i | \(-0.679086\pi\) | ||||
−0.533399 | + | 0.845864i | \(0.679086\pi\) | |||||||
\(294\) | −10.0759 | −0.587641 | ||||||||
\(295\) | −13.1736 | −0.767000 | ||||||||
\(296\) | −1.31640 | −0.0765142 | ||||||||
\(297\) | 8.82968 | 0.512350 | ||||||||
\(298\) | 22.2698 | 1.29005 | ||||||||
\(299\) | −1.57255 | −0.0909429 | ||||||||
\(300\) | 4.77524 | 0.275698 | ||||||||
\(301\) | 3.43407 | 0.197936 | ||||||||
\(302\) | −4.25695 | −0.244960 | ||||||||
\(303\) | −33.4600 | −1.92223 | ||||||||
\(304\) | −0.905993 | −0.0519623 | ||||||||
\(305\) | 0.281909 | 0.0161420 | ||||||||
\(306\) | −0.0240311 | −0.00137377 | ||||||||
\(307\) | 19.9080 | 1.13621 | 0.568104 | − | 0.822957i | \(-0.307677\pi\) | ||||
0.568104 | + | 0.822957i | \(0.307677\pi\) | |||||||
\(308\) | −1.80722 | −0.102976 | ||||||||
\(309\) | 7.89623 | 0.449201 | ||||||||
\(310\) | 0.985096 | 0.0559497 | ||||||||
\(311\) | −32.6917 | −1.85377 | −0.926887 | − | 0.375341i | \(-0.877526\pi\) | ||||
−0.926887 | + | 0.375341i | \(0.877526\pi\) | |||||||
\(312\) | 5.16557 | 0.292443 | ||||||||
\(313\) | 5.08826 | 0.287605 | 0.143803 | − | 0.989606i | \(-0.454067\pi\) | ||||
0.143803 | + | 0.989606i | \(0.454067\pi\) | |||||||
\(314\) | −4.51315 | −0.254692 | ||||||||
\(315\) | 0.0609389 | 0.00343352 | ||||||||
\(316\) | 5.32571 | 0.299594 | ||||||||
\(317\) | 0.0528738 | 0.00296969 | 0.00148484 | − | 0.999999i | \(-0.499527\pi\) | ||||
0.00148484 | + | 0.999999i | \(0.499527\pi\) | |||||||
\(318\) | −13.1841 | −0.739326 | ||||||||
\(319\) | 0.802100 | 0.0449090 | ||||||||
\(320\) | 1.49175 | 0.0833911 | ||||||||
\(321\) | −15.2924 | −0.853538 | ||||||||
\(322\) | −0.560690 | −0.0312460 | ||||||||
\(323\) | 0.570369 | 0.0317362 | ||||||||
\(324\) | −8.88403 | −0.493557 | ||||||||
\(325\) | −8.32825 | −0.461968 | ||||||||
\(326\) | 10.2065 | 0.565284 | ||||||||
\(327\) | −21.5998 | −1.19447 | ||||||||
\(328\) | −1.65916 | −0.0916116 | ||||||||
\(329\) | −4.07878 | −0.224870 | ||||||||
\(330\) | 4.33538 | 0.238655 | ||||||||
\(331\) | −12.8595 | −0.706821 | −0.353410 | − | 0.935468i | \(-0.614978\pi\) | ||||
−0.353410 | + | 0.935468i | \(0.614978\pi\) | |||||||
\(332\) | −7.15493 | −0.392678 | ||||||||
\(333\) | −0.0502493 | −0.00275365 | ||||||||
\(334\) | −6.46771 | −0.353897 | ||||||||
\(335\) | 17.9651 | 0.981537 | ||||||||
\(336\) | 1.84178 | 0.100477 | ||||||||
\(337\) | −17.2499 | −0.939662 | −0.469831 | − | 0.882756i | \(-0.655685\pi\) | ||||
−0.469831 | + | 0.882756i | \(0.655685\pi\) | |||||||
\(338\) | 3.99099 | 0.217081 | ||||||||
\(339\) | −11.2546 | −0.611264 | ||||||||
\(340\) | −0.939131 | −0.0509315 | ||||||||
\(341\) | −1.11516 | −0.0603892 | ||||||||
\(342\) | −0.0345834 | −0.00187005 | ||||||||
\(343\) | 13.7569 | 0.742801 | ||||||||
\(344\) | 3.20887 | 0.173011 | ||||||||
\(345\) | 1.34506 | 0.0724154 | ||||||||
\(346\) | −10.4767 | −0.563232 | ||||||||
\(347\) | 27.2330 | 1.46194 | 0.730971 | − | 0.682409i | \(-0.239068\pi\) | ||||
0.730971 | + | 0.682409i | \(0.239068\pi\) | |||||||
\(348\) | −0.817440 | −0.0438194 | ||||||||
\(349\) | −22.2712 | −1.19215 | −0.596074 | − | 0.802929i | \(-0.703274\pi\) | ||||
−0.596074 | + | 0.802929i | \(0.703274\pi\) | |||||||
\(350\) | −2.96942 | −0.158722 | ||||||||
\(351\) | 15.6939 | 0.837678 | ||||||||
\(352\) | −1.68870 | −0.0900081 | ||||||||
\(353\) | −7.04399 | −0.374914 | −0.187457 | − | 0.982273i | \(-0.560025\pi\) | ||||
−0.187457 | + | 0.982273i | \(0.560025\pi\) | |||||||
\(354\) | −15.1982 | −0.807773 | ||||||||
\(355\) | 3.37187 | 0.178960 | ||||||||
\(356\) | −10.0856 | −0.534534 | ||||||||
\(357\) | −1.15949 | −0.0613669 | ||||||||
\(358\) | −6.70309 | −0.354269 | ||||||||
\(359\) | −19.4730 | −1.02775 | −0.513874 | − | 0.857866i | \(-0.671790\pi\) | ||||
−0.513874 | + | 0.857866i | \(0.671790\pi\) | |||||||
\(360\) | 0.0569426 | 0.00300114 | ||||||||
\(361\) | −18.1792 | −0.956799 | ||||||||
\(362\) | −3.66864 | −0.192820 | ||||||||
\(363\) | 14.0232 | 0.736026 | ||||||||
\(364\) | −3.21215 | −0.168362 | ||||||||
\(365\) | −3.16031 | −0.165418 | ||||||||
\(366\) | 0.325232 | 0.0170001 | ||||||||
\(367\) | −24.0895 | −1.25746 | −0.628730 | − | 0.777624i | \(-0.716425\pi\) | ||||
−0.628730 | + | 0.777624i | \(0.716425\pi\) | |||||||
\(368\) | −0.523921 | −0.0273113 | ||||||||
\(369\) | −0.0633330 | −0.00329698 | ||||||||
\(370\) | −1.96373 | −0.102090 | ||||||||
\(371\) | 8.19836 | 0.425638 | ||||||||
\(372\) | 1.13648 | 0.0589240 | ||||||||
\(373\) | −7.50688 | −0.388691 | −0.194346 | − | 0.980933i | \(-0.562258\pi\) | ||||
−0.194346 | + | 0.980933i | \(0.562258\pi\) | |||||||
\(374\) | 1.06312 | 0.0549728 | ||||||||
\(375\) | 19.9599 | 1.03072 | ||||||||
\(376\) | −3.81130 | −0.196553 | ||||||||
\(377\) | 1.42566 | 0.0734250 | ||||||||
\(378\) | 5.59564 | 0.287808 | ||||||||
\(379\) | 4.26329 | 0.218990 | 0.109495 | − | 0.993987i | \(-0.465077\pi\) | ||||
0.109495 | + | 0.993987i | \(0.465077\pi\) | |||||||
\(380\) | −1.35151 | −0.0693311 | ||||||||
\(381\) | −9.29012 | −0.475947 | ||||||||
\(382\) | −3.49506 | −0.178823 | ||||||||
\(383\) | 2.04896 | 0.104697 | 0.0523484 | − | 0.998629i | \(-0.483329\pi\) | ||||
0.0523484 | + | 0.998629i | \(0.483329\pi\) | |||||||
\(384\) | 1.72100 | 0.0878242 | ||||||||
\(385\) | −2.69591 | −0.137396 | ||||||||
\(386\) | 25.3685 | 1.29122 | ||||||||
\(387\) | 0.122488 | 0.00622642 | ||||||||
\(388\) | −8.68119 | −0.440721 | ||||||||
\(389\) | 21.7457 | 1.10255 | 0.551276 | − | 0.834323i | \(-0.314141\pi\) | ||||
0.551276 | + | 0.834323i | \(0.314141\pi\) | |||||||
\(390\) | 7.70573 | 0.390195 | ||||||||
\(391\) | 0.329835 | 0.0166805 | ||||||||
\(392\) | 5.85471 | 0.295708 | ||||||||
\(393\) | −4.12635 | −0.208147 | ||||||||
\(394\) | −24.2370 | −1.22104 | ||||||||
\(395\) | 7.94460 | 0.399736 | ||||||||
\(396\) | −0.0644607 | −0.00323927 | ||||||||
\(397\) | −19.7781 | −0.992635 | −0.496318 | − | 0.868141i | \(-0.665315\pi\) | ||||
−0.496318 | + | 0.868141i | \(0.665315\pi\) | |||||||
\(398\) | 8.57145 | 0.429648 | ||||||||
\(399\) | −1.66864 | −0.0835363 | ||||||||
\(400\) | −2.77469 | −0.138735 | ||||||||
\(401\) | −30.2560 | −1.51091 | −0.755456 | − | 0.655200i | \(-0.772584\pi\) | ||||
−0.755456 | + | 0.655200i | \(0.772584\pi\) | |||||||
\(402\) | 20.7259 | 1.03372 | ||||||||
\(403\) | −1.98208 | −0.0987347 | ||||||||
\(404\) | 19.4422 | 0.967288 | ||||||||
\(405\) | −13.2527 | −0.658533 | ||||||||
\(406\) | 0.508315 | 0.0252273 | ||||||||
\(407\) | 2.22301 | 0.110190 | ||||||||
\(408\) | −1.08346 | −0.0536390 | ||||||||
\(409\) | −3.90825 | −0.193251 | −0.0966253 | − | 0.995321i | \(-0.530805\pi\) | ||||
−0.0966253 | + | 0.995321i | \(0.530805\pi\) | |||||||
\(410\) | −2.47504 | −0.122234 | ||||||||
\(411\) | 37.7547 | 1.86230 | ||||||||
\(412\) | −4.58818 | −0.226043 | ||||||||
\(413\) | 9.45079 | 0.465043 | ||||||||
\(414\) | −0.0199990 | −0.000982897 0 | ||||||||
\(415\) | −10.6733 | −0.523934 | ||||||||
\(416\) | −3.00150 | −0.147161 | ||||||||
\(417\) | 14.3882 | 0.704594 | ||||||||
\(418\) | 1.52995 | 0.0748324 | ||||||||
\(419\) | 3.60625 | 0.176177 | 0.0880885 | − | 0.996113i | \(-0.471924\pi\) | ||||
0.0880885 | + | 0.996113i | \(0.471924\pi\) | |||||||
\(420\) | 2.74746 | 0.134063 | ||||||||
\(421\) | −11.7802 | −0.574134 | −0.287067 | − | 0.957911i | \(-0.592680\pi\) | ||||
−0.287067 | + | 0.957911i | \(0.592680\pi\) | |||||||
\(422\) | −5.44236 | −0.264930 | ||||||||
\(423\) | −0.145484 | −0.00707368 | ||||||||
\(424\) | 7.66072 | 0.372038 | ||||||||
\(425\) | 1.74681 | 0.0847328 | ||||||||
\(426\) | 3.89005 | 0.188474 | ||||||||
\(427\) | −0.202242 | −0.00978716 | ||||||||
\(428\) | 8.88578 | 0.429510 | ||||||||
\(429\) | −8.72311 | −0.421156 | ||||||||
\(430\) | 4.78682 | 0.230841 | ||||||||
\(431\) | −12.9393 | −0.623262 | −0.311631 | − | 0.950203i | \(-0.600875\pi\) | ||||
−0.311631 | + | 0.950203i | \(0.600875\pi\) | |||||||
\(432\) | 5.22868 | 0.251565 | ||||||||
\(433\) | 1.56045 | 0.0749906 | 0.0374953 | − | 0.999297i | \(-0.488062\pi\) | ||||
0.0374953 | + | 0.999297i | \(0.488062\pi\) | |||||||
\(434\) | −0.706709 | −0.0339231 | ||||||||
\(435\) | −1.21941 | −0.0584664 | ||||||||
\(436\) | 12.5508 | 0.601073 | ||||||||
\(437\) | 0.474669 | 0.0227065 | ||||||||
\(438\) | −3.64598 | −0.174212 | ||||||||
\(439\) | −29.9307 | −1.42852 | −0.714258 | − | 0.699883i | \(-0.753236\pi\) | ||||
−0.714258 | + | 0.699883i | \(0.753236\pi\) | |||||||
\(440\) | −2.51911 | −0.120094 | ||||||||
\(441\) | 0.223485 | 0.0106421 | ||||||||
\(442\) | 1.88960 | 0.0898791 | ||||||||
\(443\) | 29.5035 | 1.40175 | 0.700877 | − | 0.713282i | \(-0.252792\pi\) | ||||
0.700877 | + | 0.713282i | \(0.252792\pi\) | |||||||
\(444\) | −2.26552 | −0.107517 | ||||||||
\(445\) | −15.0451 | −0.713206 | ||||||||
\(446\) | −7.72095 | −0.365598 | ||||||||
\(447\) | 38.3262 | 1.81277 | ||||||||
\(448\) | −1.07018 | −0.0505613 | ||||||||
\(449\) | 16.6803 | 0.787190 | 0.393595 | − | 0.919284i | \(-0.371231\pi\) | ||||
0.393595 | + | 0.919284i | \(0.371231\pi\) | |||||||
\(450\) | −0.105915 | −0.00499288 | ||||||||
\(451\) | 2.80182 | 0.131933 | ||||||||
\(452\) | 6.53956 | 0.307595 | ||||||||
\(453\) | −7.32620 | −0.344215 | ||||||||
\(454\) | 22.1025 | 1.03732 | ||||||||
\(455\) | −4.79171 | −0.224639 | ||||||||
\(456\) | −1.55921 | −0.0730167 | ||||||||
\(457\) | 12.9587 | 0.606185 | 0.303092 | − | 0.952961i | \(-0.401981\pi\) | ||||
0.303092 | + | 0.952961i | \(0.401981\pi\) | |||||||
\(458\) | −2.43523 | −0.113791 | ||||||||
\(459\) | −3.29172 | −0.153645 | ||||||||
\(460\) | −0.781557 | −0.0364403 | ||||||||
\(461\) | −3.45467 | −0.160900 | −0.0804500 | − | 0.996759i | \(-0.525636\pi\) | ||||
−0.0804500 | + | 0.996759i | \(0.525636\pi\) | |||||||
\(462\) | −3.11021 | −0.144700 | ||||||||
\(463\) | 7.47857 | 0.347559 | 0.173779 | − | 0.984785i | \(-0.444402\pi\) | ||||
0.173779 | + | 0.984785i | \(0.444402\pi\) | |||||||
\(464\) | 0.474981 | 0.0220504 | ||||||||
\(465\) | 1.69535 | 0.0786198 | ||||||||
\(466\) | 28.6314 | 1.32632 | ||||||||
\(467\) | −27.1896 | −1.25818 | −0.629091 | − | 0.777331i | \(-0.716573\pi\) | ||||
−0.629091 | + | 0.777331i | \(0.716573\pi\) | |||||||
\(468\) | −0.114573 | −0.00529612 | ||||||||
\(469\) | −12.8882 | −0.595120 | ||||||||
\(470\) | −5.68549 | −0.262252 | ||||||||
\(471\) | −7.76712 | −0.357890 | ||||||||
\(472\) | 8.83103 | 0.406481 | ||||||||
\(473\) | −5.41882 | −0.249157 | ||||||||
\(474\) | 9.16552 | 0.420986 | ||||||||
\(475\) | 2.51385 | 0.115343 | ||||||||
\(476\) | 0.673734 | 0.0308805 | ||||||||
\(477\) | 0.292424 | 0.0133892 | ||||||||
\(478\) | 3.85355 | 0.176257 | ||||||||
\(479\) | −11.4309 | −0.522291 | −0.261145 | − | 0.965299i | \(-0.584100\pi\) | ||||
−0.261145 | + | 0.965299i | \(0.584100\pi\) | |||||||
\(480\) | 2.56729 | 0.117180 | ||||||||
\(481\) | 3.95118 | 0.180158 | ||||||||
\(482\) | −22.0678 | −1.00516 | ||||||||
\(483\) | −0.964946 | −0.0439065 | ||||||||
\(484\) | −8.14829 | −0.370377 | ||||||||
\(485\) | −12.9501 | −0.588035 | ||||||||
\(486\) | 0.396669 | 0.0179933 | ||||||||
\(487\) | −3.06882 | −0.139062 | −0.0695309 | − | 0.997580i | \(-0.522150\pi\) | ||||
−0.0695309 | + | 0.997580i | \(0.522150\pi\) | |||||||
\(488\) | −0.188979 | −0.00855467 | ||||||||
\(489\) | 17.5653 | 0.794330 | ||||||||
\(490\) | 8.73375 | 0.394550 | ||||||||
\(491\) | −27.2157 | −1.22823 | −0.614113 | − | 0.789218i | \(-0.710486\pi\) | ||||
−0.614113 | + | 0.789218i | \(0.710486\pi\) | |||||||
\(492\) | −2.85540 | −0.128732 | ||||||||
\(493\) | −0.299025 | −0.0134674 | ||||||||
\(494\) | 2.71934 | 0.122349 | ||||||||
\(495\) | −0.0961591 | −0.00432203 | ||||||||
\(496\) | −0.660364 | −0.0296512 | ||||||||
\(497\) | −2.41898 | −0.108506 | ||||||||
\(498\) | −12.3136 | −0.551786 | ||||||||
\(499\) | 2.40788 | 0.107792 | 0.0538959 | − | 0.998547i | \(-0.482836\pi\) | ||||
0.0538959 | + | 0.998547i | \(0.482836\pi\) | |||||||
\(500\) | −11.5979 | −0.518672 | ||||||||
\(501\) | −11.1309 | −0.497292 | ||||||||
\(502\) | −10.4314 | −0.465575 | ||||||||
\(503\) | 17.8861 | 0.797501 | 0.398751 | − | 0.917059i | \(-0.369444\pi\) | ||||
0.398751 | + | 0.917059i | \(0.369444\pi\) | |||||||
\(504\) | −0.0408507 | −0.00181964 | ||||||||
\(505\) | 29.0029 | 1.29061 | ||||||||
\(506\) | 0.884746 | 0.0393317 | ||||||||
\(507\) | 6.86847 | 0.305039 | ||||||||
\(508\) | 5.39811 | 0.239502 | ||||||||
\(509\) | 29.7716 | 1.31960 | 0.659802 | − | 0.751439i | \(-0.270640\pi\) | ||||
0.659802 | + | 0.751439i | \(0.270640\pi\) | |||||||
\(510\) | −1.61624 | −0.0715683 | ||||||||
\(511\) | 2.26721 | 0.100295 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −4.73715 | −0.209150 | ||||||||
\(514\) | −15.8546 | −0.699319 | ||||||||
\(515\) | −6.84439 | −0.301600 | ||||||||
\(516\) | 5.52245 | 0.243112 | ||||||||
\(517\) | 6.43614 | 0.283061 | ||||||||
\(518\) | 1.40879 | 0.0618985 | ||||||||
\(519\) | −18.0304 | −0.791446 | ||||||||
\(520\) | −4.47748 | −0.196350 | ||||||||
\(521\) | −35.4047 | −1.55111 | −0.775554 | − | 0.631282i | \(-0.782529\pi\) | ||||
−0.775554 | + | 0.631282i | \(0.782529\pi\) | |||||||
\(522\) | 0.0181309 | 0.000793566 0 | ||||||||
\(523\) | −26.0379 | −1.13856 | −0.569280 | − | 0.822144i | \(-0.692778\pi\) | ||||
−0.569280 | + | 0.822144i | \(0.692778\pi\) | |||||||
\(524\) | 2.39765 | 0.104742 | ||||||||
\(525\) | −5.11037 | −0.223035 | ||||||||
\(526\) | −28.5821 | −1.24624 | ||||||||
\(527\) | 0.415733 | 0.0181096 | ||||||||
\(528\) | −2.90625 | −0.126478 | ||||||||
\(529\) | −22.7255 | −0.988066 | ||||||||
\(530\) | 11.4279 | 0.496394 | ||||||||
\(531\) | 0.337096 | 0.0146287 | ||||||||
\(532\) | 0.969576 | 0.0420365 | ||||||||
\(533\) | 4.97996 | 0.215706 | ||||||||
\(534\) | −17.3572 | −0.751121 | ||||||||
\(535\) | 13.2553 | 0.573078 | ||||||||
\(536\) | −12.0430 | −0.520178 | ||||||||
\(537\) | −11.5360 | −0.497815 | ||||||||
\(538\) | −0.791621 | −0.0341292 | ||||||||
\(539\) | −9.88686 | −0.425857 | ||||||||
\(540\) | 7.79987 | 0.335653 | ||||||||
\(541\) | 11.8680 | 0.510243 | 0.255122 | − | 0.966909i | \(-0.417884\pi\) | ||||
0.255122 | + | 0.966909i | \(0.417884\pi\) | |||||||
\(542\) | −6.60941 | −0.283899 | ||||||||
\(543\) | −6.31372 | −0.270948 | ||||||||
\(544\) | 0.629551 | 0.0269918 | ||||||||
\(545\) | 18.7226 | 0.801987 | ||||||||
\(546\) | −5.52810 | −0.236581 | ||||||||
\(547\) | −16.1838 | −0.691971 | −0.345986 | − | 0.938240i | \(-0.612455\pi\) | ||||
−0.345986 | + | 0.938240i | \(0.612455\pi\) | |||||||
\(548\) | −21.9377 | −0.937131 | ||||||||
\(549\) | −0.00721366 | −0.000307872 0 | ||||||||
\(550\) | 4.68563 | 0.199796 | ||||||||
\(551\) | −0.430329 | −0.0183326 | ||||||||
\(552\) | −0.901666 | −0.0383775 | ||||||||
\(553\) | −5.69947 | −0.242366 | ||||||||
\(554\) | −7.34257 | −0.311956 | ||||||||
\(555\) | −3.37958 | −0.143455 | ||||||||
\(556\) | −8.36040 | −0.354560 | ||||||||
\(557\) | −8.64260 | −0.366199 | −0.183099 | − | 0.983094i | \(-0.558613\pi\) | ||||
−0.183099 | + | 0.983094i | \(0.558613\pi\) | |||||||
\(558\) | −0.0252073 | −0.00106711 | ||||||||
\(559\) | −9.63142 | −0.407366 | ||||||||
\(560\) | −1.59644 | −0.0674618 | ||||||||
\(561\) | 1.82963 | 0.0772471 | ||||||||
\(562\) | −5.23271 | −0.220728 | ||||||||
\(563\) | 42.2887 | 1.78226 | 0.891128 | − | 0.453751i | \(-0.149915\pi\) | ||||
0.891128 | + | 0.453751i | \(0.149915\pi\) | |||||||
\(564\) | −6.55923 | −0.276193 | ||||||||
\(565\) | 9.75536 | 0.410411 | ||||||||
\(566\) | −22.4417 | −0.943295 | ||||||||
\(567\) | 9.50752 | 0.399278 | ||||||||
\(568\) | −2.26035 | −0.0948422 | ||||||||
\(569\) | −22.5679 | −0.946094 | −0.473047 | − | 0.881037i | \(-0.656846\pi\) | ||||
−0.473047 | + | 0.881037i | \(0.656846\pi\) | |||||||
\(570\) | −2.32595 | −0.0974232 | ||||||||
\(571\) | −37.8283 | −1.58307 | −0.791534 | − | 0.611126i | \(-0.790717\pi\) | ||||
−0.791534 | + | 0.611126i | \(0.790717\pi\) | |||||||
\(572\) | 5.06864 | 0.211930 | ||||||||
\(573\) | −6.01499 | −0.251280 | ||||||||
\(574\) | 1.77560 | 0.0741120 | ||||||||
\(575\) | 1.45372 | 0.0606243 | ||||||||
\(576\) | −0.0381718 | −0.00159049 | ||||||||
\(577\) | 3.15010 | 0.131140 | 0.0655701 | − | 0.997848i | \(-0.479113\pi\) | ||||
0.0655701 | + | 0.997848i | \(0.479113\pi\) | |||||||
\(578\) | 16.6037 | 0.690621 | ||||||||
\(579\) | 43.6592 | 1.81441 | ||||||||
\(580\) | 0.708550 | 0.0294210 | ||||||||
\(581\) | 7.65707 | 0.317669 | ||||||||
\(582\) | −14.9403 | −0.619295 | ||||||||
\(583\) | −12.9367 | −0.535782 | ||||||||
\(584\) | 2.11853 | 0.0876654 | ||||||||
\(585\) | −0.170913 | −0.00706640 | ||||||||
\(586\) | 18.2607 | 0.754341 | ||||||||
\(587\) | −8.57414 | −0.353893 | −0.176946 | − | 0.984221i | \(-0.556622\pi\) | ||||
−0.176946 | + | 0.984221i | \(0.556622\pi\) | |||||||
\(588\) | 10.0759 | 0.415525 | ||||||||
\(589\) | 0.598285 | 0.0246519 | ||||||||
\(590\) | 13.1736 | 0.542351 | ||||||||
\(591\) | −41.7117 | −1.71579 | ||||||||
\(592\) | 1.31640 | 0.0541037 | ||||||||
\(593\) | −37.8596 | −1.55471 | −0.777354 | − | 0.629063i | \(-0.783439\pi\) | ||||
−0.777354 | + | 0.629063i | \(0.783439\pi\) | |||||||
\(594\) | −8.82968 | −0.362286 | ||||||||
\(595\) | 1.00504 | 0.0412026 | ||||||||
\(596\) | −22.2698 | −0.912206 | ||||||||
\(597\) | 14.7514 | 0.603736 | ||||||||
\(598\) | 1.57255 | 0.0643063 | ||||||||
\(599\) | 14.6887 | 0.600166 | 0.300083 | − | 0.953913i | \(-0.402986\pi\) | ||||
0.300083 | + | 0.953913i | \(0.402986\pi\) | |||||||
\(600\) | −4.77524 | −0.194948 | ||||||||
\(601\) | −6.03798 | −0.246294 | −0.123147 | − | 0.992388i | \(-0.539299\pi\) | ||||
−0.123147 | + | 0.992388i | \(0.539299\pi\) | |||||||
\(602\) | −3.43407 | −0.139962 | ||||||||
\(603\) | −0.459702 | −0.0187205 | ||||||||
\(604\) | 4.25695 | 0.173213 | ||||||||
\(605\) | −12.1552 | −0.494178 | ||||||||
\(606\) | 33.4600 | 1.35922 | ||||||||
\(607\) | 35.8038 | 1.45323 | 0.726616 | − | 0.687044i | \(-0.241092\pi\) | ||||
0.726616 | + | 0.687044i | \(0.241092\pi\) | |||||||
\(608\) | 0.905993 | 0.0367429 | ||||||||
\(609\) | 0.874808 | 0.0354490 | ||||||||
\(610\) | −0.281909 | −0.0114141 | ||||||||
\(611\) | 11.4396 | 0.462797 | ||||||||
\(612\) | 0.0240311 | 0.000971400 0 | ||||||||
\(613\) | 7.44892 | 0.300859 | 0.150429 | − | 0.988621i | \(-0.451934\pi\) | ||||
0.150429 | + | 0.988621i | \(0.451934\pi\) | |||||||
\(614\) | −19.9080 | −0.803420 | ||||||||
\(615\) | −4.25954 | −0.171761 | ||||||||
\(616\) | 1.80722 | 0.0728148 | ||||||||
\(617\) | −30.1387 | −1.21334 | −0.606670 | − | 0.794954i | \(-0.707495\pi\) | ||||
−0.606670 | + | 0.794954i | \(0.707495\pi\) | |||||||
\(618\) | −7.89623 | −0.317633 | ||||||||
\(619\) | −44.4650 | −1.78720 | −0.893599 | − | 0.448866i | \(-0.851828\pi\) | ||||
−0.893599 | + | 0.448866i | \(0.851828\pi\) | |||||||
\(620\) | −0.985096 | −0.0395624 | ||||||||
\(621\) | −2.73942 | −0.109929 | ||||||||
\(622\) | 32.6917 | 1.31082 | ||||||||
\(623\) | 10.7934 | 0.432428 | ||||||||
\(624\) | −5.16557 | −0.206788 | ||||||||
\(625\) | −3.42761 | −0.137104 | ||||||||
\(626\) | −5.08826 | −0.203368 | ||||||||
\(627\) | 2.63304 | 0.105153 | ||||||||
\(628\) | 4.51315 | 0.180094 | ||||||||
\(629\) | −0.828741 | −0.0330441 | ||||||||
\(630\) | −0.0609389 | −0.00242786 | ||||||||
\(631\) | −3.42615 | −0.136393 | −0.0681964 | − | 0.997672i | \(-0.521724\pi\) | ||||
−0.0681964 | + | 0.997672i | \(0.521724\pi\) | |||||||
\(632\) | −5.32571 | −0.211845 | ||||||||
\(633\) | −9.36627 | −0.372276 | ||||||||
\(634\) | −0.0528738 | −0.00209988 | ||||||||
\(635\) | 8.05261 | 0.319558 | ||||||||
\(636\) | 13.1841 | 0.522783 | ||||||||
\(637\) | −17.5729 | −0.696265 | ||||||||
\(638\) | −0.802100 | −0.0317554 | ||||||||
\(639\) | −0.0862816 | −0.00341325 | ||||||||
\(640\) | −1.49175 | −0.0589664 | ||||||||
\(641\) | −48.4663 | −1.91430 | −0.957152 | − | 0.289585i | \(-0.906483\pi\) | ||||
−0.957152 | + | 0.289585i | \(0.906483\pi\) | |||||||
\(642\) | 15.2924 | 0.603542 | ||||||||
\(643\) | 19.4529 | 0.767149 | 0.383575 | − | 0.923510i | \(-0.374693\pi\) | ||||
0.383575 | + | 0.923510i | \(0.374693\pi\) | |||||||
\(644\) | 0.560690 | 0.0220943 | ||||||||
\(645\) | 8.23809 | 0.324375 | ||||||||
\(646\) | −0.570369 | −0.0224409 | ||||||||
\(647\) | −9.69744 | −0.381246 | −0.190623 | − | 0.981663i | \(-0.561051\pi\) | ||||
−0.190623 | + | 0.981663i | \(0.561051\pi\) | |||||||
\(648\) | 8.88403 | 0.348998 | ||||||||
\(649\) | −14.9130 | −0.585385 | ||||||||
\(650\) | 8.32825 | 0.326661 | ||||||||
\(651\) | −1.21624 | −0.0476683 | ||||||||
\(652\) | −10.2065 | −0.399716 | ||||||||
\(653\) | 46.3487 | 1.81377 | 0.906883 | − | 0.421384i | \(-0.138455\pi\) | ||||
0.906883 | + | 0.421384i | \(0.138455\pi\) | |||||||
\(654\) | 21.5998 | 0.844621 | ||||||||
\(655\) | 3.57669 | 0.139753 | ||||||||
\(656\) | 1.65916 | 0.0647792 | ||||||||
\(657\) | 0.0808681 | 0.00315496 | ||||||||
\(658\) | 4.07878 | 0.159007 | ||||||||
\(659\) | 14.3452 | 0.558811 | 0.279405 | − | 0.960173i | \(-0.409863\pi\) | ||||
0.279405 | + | 0.960173i | \(0.409863\pi\) | |||||||
\(660\) | −4.33538 | −0.168755 | ||||||||
\(661\) | −32.0420 | −1.24629 | −0.623146 | − | 0.782106i | \(-0.714146\pi\) | ||||
−0.623146 | + | 0.782106i | \(0.714146\pi\) | |||||||
\(662\) | 12.8595 | 0.499798 | ||||||||
\(663\) | 3.25199 | 0.126297 | ||||||||
\(664\) | 7.15493 | 0.277665 | ||||||||
\(665\) | 1.44636 | 0.0560875 | ||||||||
\(666\) | 0.0502493 | 0.00194712 | ||||||||
\(667\) | −0.248852 | −0.00963560 | ||||||||
\(668\) | 6.46771 | 0.250243 | ||||||||
\(669\) | −13.2877 | −0.513733 | ||||||||
\(670\) | −17.9651 | −0.694051 | ||||||||
\(671\) | 0.319129 | 0.0123198 | ||||||||
\(672\) | −1.84178 | −0.0710481 | ||||||||
\(673\) | −25.3822 | −0.978411 | −0.489206 | − | 0.872169i | \(-0.662713\pi\) | ||||
−0.489206 | + | 0.872169i | \(0.662713\pi\) | |||||||
\(674\) | 17.2499 | 0.664442 | ||||||||
\(675\) | −14.5080 | −0.558413 | ||||||||
\(676\) | −3.99099 | −0.153499 | ||||||||
\(677\) | 2.61878 | 0.100648 | 0.0503240 | − | 0.998733i | \(-0.483975\pi\) | ||||
0.0503240 | + | 0.998733i | \(0.483975\pi\) | |||||||
\(678\) | 11.2546 | 0.432229 | ||||||||
\(679\) | 9.29045 | 0.356535 | ||||||||
\(680\) | 0.939131 | 0.0360140 | ||||||||
\(681\) | 38.0383 | 1.45763 | ||||||||
\(682\) | 1.11516 | 0.0427016 | ||||||||
\(683\) | −19.3856 | −0.741770 | −0.370885 | − | 0.928679i | \(-0.620946\pi\) | ||||
−0.370885 | + | 0.928679i | \(0.620946\pi\) | |||||||
\(684\) | 0.0345834 | 0.00132233 | ||||||||
\(685\) | −32.7255 | −1.25038 | ||||||||
\(686\) | −13.7569 | −0.525240 | ||||||||
\(687\) | −4.19102 | −0.159897 | ||||||||
\(688\) | −3.20887 | −0.122337 | ||||||||
\(689\) | −22.9937 | −0.875989 | ||||||||
\(690\) | −1.34506 | −0.0512054 | ||||||||
\(691\) | −33.2680 | −1.26558 | −0.632788 | − | 0.774325i | \(-0.718089\pi\) | ||||
−0.632788 | + | 0.774325i | \(0.718089\pi\) | |||||||
\(692\) | 10.4767 | 0.398265 | ||||||||
\(693\) | 0.0689846 | 0.00262051 | ||||||||
\(694\) | −27.2330 | −1.03375 | ||||||||
\(695\) | −12.4716 | −0.473074 | ||||||||
\(696\) | 0.817440 | 0.0309850 | ||||||||
\(697\) | −1.04452 | −0.0395642 | ||||||||
\(698\) | 22.2712 | 0.842976 | ||||||||
\(699\) | 49.2746 | 1.86373 | ||||||||
\(700\) | 2.96942 | 0.112234 | ||||||||
\(701\) | 19.8226 | 0.748689 | 0.374345 | − | 0.927290i | \(-0.377868\pi\) | ||||
0.374345 | + | 0.927290i | \(0.377868\pi\) | |||||||
\(702\) | −15.6939 | −0.592328 | ||||||||
\(703\) | −1.19265 | −0.0449816 | ||||||||
\(704\) | 1.68870 | 0.0636453 | ||||||||
\(705\) | −9.78471 | −0.368513 | ||||||||
\(706\) | 7.04399 | 0.265104 | ||||||||
\(707\) | −20.8067 | −0.782517 | ||||||||
\(708\) | 15.1982 | 0.571182 | ||||||||
\(709\) | −16.1748 | −0.607456 | −0.303728 | − | 0.952759i | \(-0.598231\pi\) | ||||
−0.303728 | + | 0.952759i | \(0.598231\pi\) | |||||||
\(710\) | −3.37187 | −0.126544 | ||||||||
\(711\) | −0.203292 | −0.00762404 | ||||||||
\(712\) | 10.0856 | 0.377973 | ||||||||
\(713\) | 0.345979 | 0.0129570 | ||||||||
\(714\) | 1.15949 | 0.0433930 | ||||||||
\(715\) | 7.56112 | 0.282770 | ||||||||
\(716\) | 6.70309 | 0.250506 | ||||||||
\(717\) | 6.63194 | 0.247674 | ||||||||
\(718\) | 19.4730 | 0.726728 | ||||||||
\(719\) | 3.02187 | 0.112697 | 0.0563484 | − | 0.998411i | \(-0.482054\pi\) | ||||
0.0563484 | + | 0.998411i | \(0.482054\pi\) | |||||||
\(720\) | −0.0569426 | −0.00212213 | ||||||||
\(721\) | 4.91018 | 0.182865 | ||||||||
\(722\) | 18.1792 | 0.676559 | ||||||||
\(723\) | −37.9786 | −1.41244 | ||||||||
\(724\) | 3.66864 | 0.136344 | ||||||||
\(725\) | −1.31793 | −0.0489465 | ||||||||
\(726\) | −14.0232 | −0.520449 | ||||||||
\(727\) | 27.4998 | 1.01991 | 0.509956 | − | 0.860201i | \(-0.329662\pi\) | ||||
0.509956 | + | 0.860201i | \(0.329662\pi\) | |||||||
\(728\) | 3.21215 | 0.119050 | ||||||||
\(729\) | 27.3347 | 1.01240 | ||||||||
\(730\) | 3.16031 | 0.116968 | ||||||||
\(731\) | 2.02015 | 0.0747178 | ||||||||
\(732\) | −0.325232 | −0.0120209 | ||||||||
\(733\) | −49.2084 | −1.81755 | −0.908776 | − | 0.417284i | \(-0.862982\pi\) | ||||
−0.908776 | + | 0.417284i | \(0.862982\pi\) | |||||||
\(734\) | 24.0895 | 0.889158 | ||||||||
\(735\) | 15.0307 | 0.554417 | ||||||||
\(736\) | 0.523921 | 0.0193120 | ||||||||
\(737\) | 20.3370 | 0.749123 | ||||||||
\(738\) | 0.0633330 | 0.00233132 | ||||||||
\(739\) | −7.21843 | −0.265534 | −0.132767 | − | 0.991147i | \(-0.542386\pi\) | ||||
−0.132767 | + | 0.991147i | \(0.542386\pi\) | |||||||
\(740\) | 1.96373 | 0.0721883 | ||||||||
\(741\) | 4.67997 | 0.171923 | ||||||||
\(742\) | −8.19836 | −0.300971 | ||||||||
\(743\) | −32.8917 | −1.20668 | −0.603340 | − | 0.797484i | \(-0.706164\pi\) | ||||
−0.603340 | + | 0.797484i | \(0.706164\pi\) | |||||||
\(744\) | −1.13648 | −0.0416655 | ||||||||
\(745\) | −33.2209 | −1.21712 | ||||||||
\(746\) | 7.50688 | 0.274846 | ||||||||
\(747\) | 0.273116 | 0.00999281 | ||||||||
\(748\) | −1.06312 | −0.0388717 | ||||||||
\(749\) | −9.50939 | −0.347465 | ||||||||
\(750\) | −19.9599 | −0.728832 | ||||||||
\(751\) | −47.9278 | −1.74891 | −0.874455 | − | 0.485106i | \(-0.838781\pi\) | ||||
−0.874455 | + | 0.485106i | \(0.838781\pi\) | |||||||
\(752\) | 3.81130 | 0.138984 | ||||||||
\(753\) | −17.9524 | −0.654221 | ||||||||
\(754\) | −1.42566 | −0.0519193 | ||||||||
\(755\) | 6.35029 | 0.231111 | ||||||||
\(756\) | −5.59564 | −0.203511 | ||||||||
\(757\) | 41.9225 | 1.52370 | 0.761850 | − | 0.647753i | \(-0.224291\pi\) | ||||
0.761850 | + | 0.647753i | \(0.224291\pi\) | |||||||
\(758\) | −4.26329 | −0.154850 | ||||||||
\(759\) | 1.52264 | 0.0552685 | ||||||||
\(760\) | 1.35151 | 0.0490245 | ||||||||
\(761\) | 16.0830 | 0.583009 | 0.291505 | − | 0.956569i | \(-0.405844\pi\) | ||||
0.291505 | + | 0.956569i | \(0.405844\pi\) | |||||||
\(762\) | 9.29012 | 0.336546 | ||||||||
\(763\) | −13.4316 | −0.486257 | ||||||||
\(764\) | 3.49506 | 0.126447 | ||||||||
\(765\) | 0.0358483 | 0.00129610 | ||||||||
\(766\) | −2.04896 | −0.0740318 | ||||||||
\(767\) | −26.5063 | −0.957089 | ||||||||
\(768\) | −1.72100 | −0.0621011 | ||||||||
\(769\) | −23.8882 | −0.861429 | −0.430715 | − | 0.902488i | \(-0.641738\pi\) | ||||
−0.430715 | + | 0.902488i | \(0.641738\pi\) | |||||||
\(770\) | 2.69591 | 0.0971537 | ||||||||
\(771\) | −27.2858 | −0.982674 | ||||||||
\(772\) | −25.3685 | −0.913034 | ||||||||
\(773\) | −15.1586 | −0.545217 | −0.272608 | − | 0.962125i | \(-0.587886\pi\) | ||||
−0.272608 | + | 0.962125i | \(0.587886\pi\) | |||||||
\(774\) | −0.122488 | −0.00440275 | ||||||||
\(775\) | 1.83231 | 0.0658184 | ||||||||
\(776\) | 8.68119 | 0.311637 | ||||||||
\(777\) | 2.42451 | 0.0869790 | ||||||||
\(778\) | −21.7457 | −0.779622 | ||||||||
\(779\) | −1.50318 | −0.0538572 | ||||||||
\(780\) | −7.70573 | −0.275909 | ||||||||
\(781\) | 3.81705 | 0.136585 | ||||||||
\(782\) | −0.329835 | −0.0117949 | ||||||||
\(783\) | 2.48352 | 0.0887539 | ||||||||
\(784\) | −5.85471 | −0.209097 | ||||||||
\(785\) | 6.73248 | 0.240292 | ||||||||
\(786\) | 4.12635 | 0.147182 | ||||||||
\(787\) | −22.6897 | −0.808802 | −0.404401 | − | 0.914582i | \(-0.632520\pi\) | ||||
−0.404401 | + | 0.914582i | \(0.632520\pi\) | |||||||
\(788\) | 24.2370 | 0.863406 | ||||||||
\(789\) | −49.1897 | −1.75120 | ||||||||
\(790\) | −7.94460 | −0.282656 | ||||||||
\(791\) | −6.99851 | −0.248838 | ||||||||
\(792\) | 0.0644607 | 0.00229051 | ||||||||
\(793\) | 0.567221 | 0.0201426 | ||||||||
\(794\) | 19.7781 | 0.701899 | ||||||||
\(795\) | 19.6673 | 0.697527 | ||||||||
\(796\) | −8.57145 | −0.303807 | ||||||||
\(797\) | 17.3969 | 0.616230 | 0.308115 | − | 0.951349i | \(-0.400302\pi\) | ||||
0.308115 | + | 0.951349i | \(0.400302\pi\) | |||||||
\(798\) | 1.66864 | 0.0590691 | ||||||||
\(799\) | −2.39941 | −0.0848850 | ||||||||
\(800\) | 2.77469 | 0.0981002 | ||||||||
\(801\) | 0.384984 | 0.0136027 | ||||||||
\(802\) | 30.2560 | 1.06838 | ||||||||
\(803\) | −3.57756 | −0.126249 | ||||||||
\(804\) | −20.7259 | −0.730947 | ||||||||
\(805\) | 0.836407 | 0.0294795 | ||||||||
\(806\) | 1.98208 | 0.0698159 | ||||||||
\(807\) | −1.36238 | −0.0479580 | ||||||||
\(808\) | −19.4422 | −0.683976 | ||||||||
\(809\) | 9.85310 | 0.346416 | 0.173208 | − | 0.984885i | \(-0.444587\pi\) | ||||
0.173208 | + | 0.984885i | \(0.444587\pi\) | |||||||
\(810\) | 13.2527 | 0.465653 | ||||||||
\(811\) | −40.5571 | −1.42415 | −0.712077 | − | 0.702101i | \(-0.752245\pi\) | ||||
−0.712077 | + | 0.702101i | \(0.752245\pi\) | |||||||
\(812\) | −0.508315 | −0.0178384 | ||||||||
\(813\) | −11.3748 | −0.398931 | ||||||||
\(814\) | −2.22301 | −0.0779163 | ||||||||
\(815\) | −15.2255 | −0.533324 | ||||||||
\(816\) | 1.08346 | 0.0379285 | ||||||||
\(817\) | 2.90721 | 0.101710 | ||||||||
\(818\) | 3.90825 | 0.136649 | ||||||||
\(819\) | 0.122614 | 0.00428446 | ||||||||
\(820\) | 2.47504 | 0.0864322 | ||||||||
\(821\) | −27.5773 | −0.962453 | −0.481226 | − | 0.876596i | \(-0.659809\pi\) | ||||
−0.481226 | + | 0.876596i | \(0.659809\pi\) | |||||||
\(822\) | −37.7547 | −1.31685 | ||||||||
\(823\) | −17.5605 | −0.612122 | −0.306061 | − | 0.952012i | \(-0.599011\pi\) | ||||
−0.306061 | + | 0.952012i | \(0.599011\pi\) | |||||||
\(824\) | 4.58818 | 0.159837 | ||||||||
\(825\) | 8.06395 | 0.280751 | ||||||||
\(826\) | −9.45079 | −0.328835 | ||||||||
\(827\) | −14.2749 | −0.496388 | −0.248194 | − | 0.968710i | \(-0.579837\pi\) | ||||
−0.248194 | + | 0.968710i | \(0.579837\pi\) | |||||||
\(828\) | 0.0199990 | 0.000695013 0 | ||||||||
\(829\) | −43.2830 | −1.50328 | −0.751640 | − | 0.659573i | \(-0.770737\pi\) | ||||
−0.751640 | + | 0.659573i | \(0.770737\pi\) | |||||||
\(830\) | 10.6733 | 0.370477 | ||||||||
\(831\) | −12.6365 | −0.438357 | ||||||||
\(832\) | 3.00150 | 0.104058 | ||||||||
\(833\) | 3.68584 | 0.127707 | ||||||||
\(834\) | −14.3882 | −0.498223 | ||||||||
\(835\) | 9.64818 | 0.333889 | ||||||||
\(836\) | −1.52995 | −0.0529145 | ||||||||
\(837\) | −3.45283 | −0.119347 | ||||||||
\(838\) | −3.60625 | −0.124576 | ||||||||
\(839\) | 30.2971 | 1.04597 | 0.522986 | − | 0.852342i | \(-0.324818\pi\) | ||||
0.522986 | + | 0.852342i | \(0.324818\pi\) | |||||||
\(840\) | −2.74746 | −0.0947965 | ||||||||
\(841\) | −28.7744 | −0.992220 | ||||||||
\(842\) | 11.7802 | 0.405974 | ||||||||
\(843\) | −9.00547 | −0.310165 | ||||||||
\(844\) | 5.44236 | 0.187334 | ||||||||
\(845\) | −5.95354 | −0.204808 | ||||||||
\(846\) | 0.145484 | 0.00500184 | ||||||||
\(847\) | 8.72014 | 0.299628 | ||||||||
\(848\) | −7.66072 | −0.263070 | ||||||||
\(849\) | −38.6221 | −1.32551 | ||||||||
\(850\) | −1.74681 | −0.0599152 | ||||||||
\(851\) | −0.689689 | −0.0236422 | ||||||||
\(852\) | −3.89005 | −0.133271 | ||||||||
\(853\) | −40.2436 | −1.37792 | −0.688958 | − | 0.724802i | \(-0.741931\pi\) | ||||
−0.688958 | + | 0.724802i | \(0.741931\pi\) | |||||||
\(854\) | 0.202242 | 0.00692057 | ||||||||
\(855\) | 0.0515896 | 0.00176433 | ||||||||
\(856\) | −8.88578 | −0.303710 | ||||||||
\(857\) | −33.2032 | −1.13420 | −0.567099 | − | 0.823650i | \(-0.691934\pi\) | ||||
−0.567099 | + | 0.823650i | \(0.691934\pi\) | |||||||
\(858\) | 8.72311 | 0.297802 | ||||||||
\(859\) | −10.7462 | −0.366654 | −0.183327 | − | 0.983052i | \(-0.558687\pi\) | ||||
−0.183327 | + | 0.983052i | \(0.558687\pi\) | |||||||
\(860\) | −4.78682 | −0.163229 | ||||||||
\(861\) | 3.05580 | 0.104141 | ||||||||
\(862\) | 12.9393 | 0.440713 | ||||||||
\(863\) | −9.17913 | −0.312461 | −0.156231 | − | 0.987721i | \(-0.549934\pi\) | ||||
−0.156231 | + | 0.987721i | \(0.549934\pi\) | |||||||
\(864\) | −5.22868 | −0.177883 | ||||||||
\(865\) | 15.6286 | 0.531388 | ||||||||
\(866\) | −1.56045 | −0.0530263 | ||||||||
\(867\) | 28.5748 | 0.970453 | ||||||||
\(868\) | 0.706709 | 0.0239873 | ||||||||
\(869\) | 8.99353 | 0.305085 | ||||||||
\(870\) | 1.21941 | 0.0413420 | ||||||||
\(871\) | 36.1470 | 1.22480 | ||||||||
\(872\) | −12.5508 | −0.425023 | ||||||||
\(873\) | 0.331377 | 0.0112154 | ||||||||
\(874\) | −0.474669 | −0.0160559 | ||||||||
\(875\) | 12.4118 | 0.419596 | ||||||||
\(876\) | 3.64598 | 0.123186 | ||||||||
\(877\) | −22.2087 | −0.749936 | −0.374968 | − | 0.927038i | \(-0.622346\pi\) | ||||
−0.374968 | + | 0.927038i | \(0.622346\pi\) | |||||||
\(878\) | 29.9307 | 1.01011 | ||||||||
\(879\) | 31.4265 | 1.05999 | ||||||||
\(880\) | 2.51911 | 0.0849193 | ||||||||
\(881\) | −19.7013 | −0.663755 | −0.331877 | − | 0.943322i | \(-0.607682\pi\) | ||||
−0.331877 | + | 0.943322i | \(0.607682\pi\) | |||||||
\(882\) | −0.223485 | −0.00752513 | ||||||||
\(883\) | 33.5175 | 1.12795 | 0.563977 | − | 0.825791i | \(-0.309271\pi\) | ||||
0.563977 | + | 0.825791i | \(0.309271\pi\) | |||||||
\(884\) | −1.88960 | −0.0635541 | ||||||||
\(885\) | 22.6718 | 0.762104 | ||||||||
\(886\) | −29.5035 | −0.991190 | ||||||||
\(887\) | 51.1726 | 1.71821 | 0.859103 | − | 0.511803i | \(-0.171022\pi\) | ||||
0.859103 | + | 0.511803i | \(0.171022\pi\) | |||||||
\(888\) | 2.26552 | 0.0760258 | ||||||||
\(889\) | −5.77695 | −0.193753 | ||||||||
\(890\) | 15.0451 | 0.504313 | ||||||||
\(891\) | −15.0025 | −0.502602 | ||||||||
\(892\) | 7.72095 | 0.258517 | ||||||||
\(893\) | −3.45301 | −0.115551 | ||||||||
\(894\) | −38.3262 | −1.28182 | ||||||||
\(895\) | 9.99930 | 0.334240 | ||||||||
\(896\) | 1.07018 | 0.0357522 | ||||||||
\(897\) | 2.70635 | 0.0903625 | ||||||||
\(898\) | −16.6803 | −0.556628 | ||||||||
\(899\) | −0.313660 | −0.0104612 | ||||||||
\(900\) | 0.105915 | 0.00353050 | ||||||||
\(901\) | 4.82282 | 0.160671 | ||||||||
\(902\) | −2.80182 | −0.0932904 | ||||||||
\(903\) | −5.91002 | −0.196673 | ||||||||
\(904\) | −6.53956 | −0.217502 | ||||||||
\(905\) | 5.47268 | 0.181918 | ||||||||
\(906\) | 7.32620 | 0.243397 | ||||||||
\(907\) | 17.6063 | 0.584606 | 0.292303 | − | 0.956326i | \(-0.405578\pi\) | ||||
0.292303 | + | 0.956326i | \(0.405578\pi\) | |||||||
\(908\) | −22.1025 | −0.733497 | ||||||||
\(909\) | −0.742145 | −0.0246154 | ||||||||
\(910\) | 4.79171 | 0.158844 | ||||||||
\(911\) | −26.5176 | −0.878566 | −0.439283 | − | 0.898349i | \(-0.644767\pi\) | ||||
−0.439283 | + | 0.898349i | \(0.644767\pi\) | |||||||
\(912\) | 1.55921 | 0.0516306 | ||||||||
\(913\) | −12.0825 | −0.399874 | ||||||||
\(914\) | −12.9587 | −0.428637 | ||||||||
\(915\) | −0.485164 | −0.0160390 | ||||||||
\(916\) | 2.43523 | 0.0804622 | ||||||||
\(917\) | −2.56592 | −0.0847342 | ||||||||
\(918\) | 3.29172 | 0.108643 | ||||||||
\(919\) | 46.5952 | 1.53704 | 0.768518 | − | 0.639829i | \(-0.220995\pi\) | ||||
0.768518 | + | 0.639829i | \(0.220995\pi\) | |||||||
\(920\) | 0.781557 | 0.0257672 | ||||||||
\(921\) | −34.2615 | −1.12896 | ||||||||
\(922\) | 3.45467 | 0.113773 | ||||||||
\(923\) | 6.78444 | 0.223313 | ||||||||
\(924\) | 3.11021 | 0.102318 | ||||||||
\(925\) | −3.65261 | −0.120097 | ||||||||
\(926\) | −7.47857 | −0.245761 | ||||||||
\(927\) | 0.175139 | 0.00575232 | ||||||||
\(928\) | −0.474981 | −0.0155920 | ||||||||
\(929\) | −36.1551 | −1.18621 | −0.593105 | − | 0.805125i | \(-0.702098\pi\) | ||||
−0.593105 | + | 0.805125i | \(0.702098\pi\) | |||||||
\(930\) | −1.69535 | −0.0555926 | ||||||||
\(931\) | 5.30433 | 0.173842 | ||||||||
\(932\) | −28.6314 | −0.937853 | ||||||||
\(933\) | 56.2622 | 1.84194 | ||||||||
\(934\) | 27.1896 | 0.889670 | ||||||||
\(935\) | −1.58591 | −0.0518648 | ||||||||
\(936\) | 0.114573 | 0.00374493 | ||||||||
\(937\) | −26.6691 | −0.871241 | −0.435620 | − | 0.900131i | \(-0.643471\pi\) | ||||
−0.435620 | + | 0.900131i | \(0.643471\pi\) | |||||||
\(938\) | 12.8882 | 0.420814 | ||||||||
\(939\) | −8.75687 | −0.285770 | ||||||||
\(940\) | 5.68549 | 0.185440 | ||||||||
\(941\) | −25.1301 | −0.819217 | −0.409608 | − | 0.912261i | \(-0.634335\pi\) | ||||
−0.409608 | + | 0.912261i | \(0.634335\pi\) | |||||||
\(942\) | 7.76712 | 0.253066 | ||||||||
\(943\) | −0.869267 | −0.0283072 | ||||||||
\(944\) | −8.83103 | −0.287425 | ||||||||
\(945\) | −8.34727 | −0.271537 | ||||||||
\(946\) | 5.41882 | 0.176181 | ||||||||
\(947\) | −36.6343 | −1.19046 | −0.595228 | − | 0.803557i | \(-0.702938\pi\) | ||||
−0.595228 | + | 0.803557i | \(0.702938\pi\) | |||||||
\(948\) | −9.16552 | −0.297682 | ||||||||
\(949\) | −6.35877 | −0.206415 | ||||||||
\(950\) | −2.51385 | −0.0815601 | ||||||||
\(951\) | −0.0909955 | −0.00295073 | ||||||||
\(952\) | −0.673734 | −0.0218358 | ||||||||
\(953\) | −0.651456 | −0.0211027 | −0.0105514 | − | 0.999944i | \(-0.503359\pi\) | ||||
−0.0105514 | + | 0.999944i | \(0.503359\pi\) | |||||||
\(954\) | −0.292424 | −0.00946756 | ||||||||
\(955\) | 5.21375 | 0.168713 | ||||||||
\(956\) | −3.85355 | −0.124633 | ||||||||
\(957\) | −1.38041 | −0.0446224 | ||||||||
\(958\) | 11.4309 | 0.369315 | ||||||||
\(959\) | 23.4773 | 0.758121 | ||||||||
\(960\) | −2.56729 | −0.0828589 | ||||||||
\(961\) | −30.5639 | −0.985933 | ||||||||
\(962\) | −3.95118 | −0.127391 | ||||||||
\(963\) | −0.339186 | −0.0109301 | ||||||||
\(964\) | 22.0678 | 0.710756 | ||||||||
\(965\) | −37.8434 | −1.21822 | ||||||||
\(966\) | 0.964946 | 0.0310466 | ||||||||
\(967\) | −1.48564 | −0.0477751 | −0.0238875 | − | 0.999715i | \(-0.507604\pi\) | ||||
−0.0238875 | + | 0.999715i | \(0.507604\pi\) | |||||||
\(968\) | 8.14829 | 0.261896 | ||||||||
\(969\) | −0.981603 | −0.0315336 | ||||||||
\(970\) | 12.9501 | 0.415804 | ||||||||
\(971\) | −10.2557 | −0.329121 | −0.164561 | − | 0.986367i | \(-0.552621\pi\) | ||||
−0.164561 | + | 0.986367i | \(0.552621\pi\) | |||||||
\(972\) | −0.396669 | −0.0127232 | ||||||||
\(973\) | 8.94713 | 0.286832 | ||||||||
\(974\) | 3.06882 | 0.0983315 | ||||||||
\(975\) | 14.3329 | 0.459020 | ||||||||
\(976\) | 0.188979 | 0.00604907 | ||||||||
\(977\) | 43.6001 | 1.39489 | 0.697446 | − | 0.716637i | \(-0.254320\pi\) | ||||
0.697446 | + | 0.716637i | \(0.254320\pi\) | |||||||
\(978\) | −17.5653 | −0.561676 | ||||||||
\(979\) | −17.0315 | −0.544329 | ||||||||
\(980\) | −8.73375 | −0.278989 | ||||||||
\(981\) | −0.479086 | −0.0152960 | ||||||||
\(982\) | 27.2157 | 0.868487 | ||||||||
\(983\) | −16.7535 | −0.534354 | −0.267177 | − | 0.963648i | \(-0.586091\pi\) | ||||
−0.267177 | + | 0.963648i | \(0.586091\pi\) | |||||||
\(984\) | 2.85540 | 0.0910269 | ||||||||
\(985\) | 36.1554 | 1.15201 | ||||||||
\(986\) | 0.299025 | 0.00952289 | ||||||||
\(987\) | 7.01956 | 0.223435 | ||||||||
\(988\) | −2.71934 | −0.0865137 | ||||||||
\(989\) | 1.68119 | 0.0534588 | ||||||||
\(990\) | 0.0961591 | 0.00305614 | ||||||||
\(991\) | 3.97479 | 0.126263 | 0.0631317 | − | 0.998005i | \(-0.479891\pi\) | ||||
0.0631317 | + | 0.998005i | \(0.479891\pi\) | |||||||
\(992\) | 0.660364 | 0.0209666 | ||||||||
\(993\) | 22.1311 | 0.702309 | ||||||||
\(994\) | 2.41898 | 0.0767255 | ||||||||
\(995\) | −12.7864 | −0.405357 | ||||||||
\(996\) | 12.3136 | 0.390172 | ||||||||
\(997\) | 10.9747 | 0.347571 | 0.173785 | − | 0.984784i | \(-0.444400\pi\) | ||||
0.173785 | + | 0.984784i | \(0.444400\pi\) | |||||||
\(998\) | −2.40788 | −0.0762203 | ||||||||
\(999\) | 6.88304 | 0.217770 |
(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 | 8006.2.a.b.1.19 | ✓ | 75 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8006.2.a.b.1.19 | ✓ | 75 | 1.1 | even | 1 | trivial |