Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8002,2,Mod(1,8002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8002, 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("8002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8002 = 2 \cdot 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8002.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: | \(63.8962916974\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.33 | ||
Character | \(\chi\) | \(=\) | 8002.1 |
$q$-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 | ||||||||
\(3\) | −0.671966 | −0.387960 | −0.193980 | − | 0.981006i | \(-0.562140\pi\) | ||||
−0.193980 | + | 0.981006i | \(0.562140\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.60256 | −1.61111 | −0.805557 | − | 0.592518i | \(-0.798134\pi\) | ||||
−0.805557 | + | 0.592518i | \(0.798134\pi\) | |||||||
\(6\) | −0.671966 | −0.274329 | ||||||||
\(7\) | 0.00320310 | 0.00121066 | 0.000605330 | − | 1.00000i | \(-0.499807\pi\) | ||||
0.000605330 | 1.00000i | \(0.499807\pi\) | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.54846 | −0.849487 | ||||||||
\(10\) | −3.60256 | −1.13923 | ||||||||
\(11\) | 2.35705 | 0.710677 | 0.355339 | − | 0.934738i | \(-0.384366\pi\) | ||||
0.355339 | + | 0.934738i | \(0.384366\pi\) | |||||||
\(12\) | −0.671966 | −0.193980 | ||||||||
\(13\) | −5.53956 | −1.53640 | −0.768199 | − | 0.640211i | \(-0.778847\pi\) | ||||
−0.768199 | + | 0.640211i | \(0.778847\pi\) | |||||||
\(14\) | 0.00320310 | 0.000856066 0 | ||||||||
\(15\) | 2.42080 | 0.625048 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.517979 | 0.125628 | 0.0628142 | − | 0.998025i | \(-0.479992\pi\) | ||||
0.0628142 | + | 0.998025i | \(0.479992\pi\) | |||||||
\(18\) | −2.54846 | −0.600678 | ||||||||
\(19\) | 6.37915 | 1.46348 | 0.731739 | − | 0.681585i | \(-0.238709\pi\) | ||||
0.731739 | + | 0.681585i | \(0.238709\pi\) | |||||||
\(20\) | −3.60256 | −0.805557 | ||||||||
\(21\) | −0.00215238 | −0.000469687 0 | ||||||||
\(22\) | 2.35705 | 0.502525 | ||||||||
\(23\) | 0.165673 | 0.0345451 | 0.0172726 | − | 0.999851i | \(-0.494502\pi\) | ||||
0.0172726 | + | 0.999851i | \(0.494502\pi\) | |||||||
\(24\) | −0.671966 | −0.137165 | ||||||||
\(25\) | 7.97845 | 1.59569 | ||||||||
\(26\) | −5.53956 | −1.08640 | ||||||||
\(27\) | 3.72838 | 0.717527 | ||||||||
\(28\) | 0.00320310 | 0.000605330 0 | ||||||||
\(29\) | −0.662984 | −0.123113 | −0.0615565 | − | 0.998104i | \(-0.519606\pi\) | ||||
−0.0615565 | + | 0.998104i | \(0.519606\pi\) | |||||||
\(30\) | 2.42080 | 0.441975 | ||||||||
\(31\) | 9.38043 | 1.68477 | 0.842387 | − | 0.538873i | \(-0.181150\pi\) | ||||
0.842387 | + | 0.538873i | \(0.181150\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.58386 | −0.275714 | ||||||||
\(34\) | 0.517979 | 0.0888326 | ||||||||
\(35\) | −0.0115394 | −0.00195051 | ||||||||
\(36\) | −2.54846 | −0.424744 | ||||||||
\(37\) | 10.4690 | 1.72109 | 0.860547 | − | 0.509371i | \(-0.170122\pi\) | ||||
0.860547 | + | 0.509371i | \(0.170122\pi\) | |||||||
\(38\) | 6.37915 | 1.03483 | ||||||||
\(39\) | 3.72240 | 0.596061 | ||||||||
\(40\) | −3.60256 | −0.569615 | ||||||||
\(41\) | −10.1097 | −1.57888 | −0.789438 | − | 0.613830i | \(-0.789628\pi\) | ||||
−0.789438 | + | 0.613830i | \(0.789628\pi\) | |||||||
\(42\) | −0.00215238 | −0.000332119 0 | ||||||||
\(43\) | 5.22363 | 0.796596 | 0.398298 | − | 0.917256i | \(-0.369601\pi\) | ||||
0.398298 | + | 0.917256i | \(0.369601\pi\) | |||||||
\(44\) | 2.35705 | 0.355339 | ||||||||
\(45\) | 9.18099 | 1.36862 | ||||||||
\(46\) | 0.165673 | 0.0244271 | ||||||||
\(47\) | −8.34349 | −1.21702 | −0.608511 | − | 0.793545i | \(-0.708233\pi\) | ||||
−0.608511 | + | 0.793545i | \(0.708233\pi\) | |||||||
\(48\) | −0.671966 | −0.0969900 | ||||||||
\(49\) | −6.99999 | −0.999999 | ||||||||
\(50\) | 7.97845 | 1.12832 | ||||||||
\(51\) | −0.348064 | −0.0487387 | ||||||||
\(52\) | −5.53956 | −0.768199 | ||||||||
\(53\) | −3.30773 | −0.454352 | −0.227176 | − | 0.973854i | \(-0.572949\pi\) | ||||
−0.227176 | + | 0.973854i | \(0.572949\pi\) | |||||||
\(54\) | 3.72838 | 0.507368 | ||||||||
\(55\) | −8.49142 | −1.14498 | ||||||||
\(56\) | 0.00320310 | 0.000428033 0 | ||||||||
\(57\) | −4.28657 | −0.567770 | ||||||||
\(58\) | −0.662984 | −0.0870540 | ||||||||
\(59\) | −12.7440 | −1.65913 | −0.829565 | − | 0.558410i | \(-0.811412\pi\) | ||||
−0.829565 | + | 0.558410i | \(0.811412\pi\) | |||||||
\(60\) | 2.42080 | 0.312524 | ||||||||
\(61\) | 8.70514 | 1.11458 | 0.557290 | − | 0.830318i | \(-0.311841\pi\) | ||||
0.557290 | + | 0.830318i | \(0.311841\pi\) | |||||||
\(62\) | 9.38043 | 1.19132 | ||||||||
\(63\) | −0.00816299 | −0.00102844 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 19.9566 | 2.47531 | ||||||||
\(66\) | −1.58386 | −0.194959 | ||||||||
\(67\) | 6.01503 | 0.734852 | 0.367426 | − | 0.930053i | \(-0.380239\pi\) | ||||
0.367426 | + | 0.930053i | \(0.380239\pi\) | |||||||
\(68\) | 0.517979 | 0.0628142 | ||||||||
\(69\) | −0.111326 | −0.0134021 | ||||||||
\(70\) | −0.0115394 | −0.00137922 | ||||||||
\(71\) | 9.69955 | 1.15112 | 0.575562 | − | 0.817758i | \(-0.304783\pi\) | ||||
0.575562 | + | 0.817758i | \(0.304783\pi\) | |||||||
\(72\) | −2.54846 | −0.300339 | ||||||||
\(73\) | −6.96842 | −0.815592 | −0.407796 | − | 0.913073i | \(-0.633703\pi\) | ||||
−0.407796 | + | 0.913073i | \(0.633703\pi\) | |||||||
\(74\) | 10.4690 | 1.21700 | ||||||||
\(75\) | −5.36125 | −0.619063 | ||||||||
\(76\) | 6.37915 | 0.731739 | ||||||||
\(77\) | 0.00754988 | 0.000860388 0 | ||||||||
\(78\) | 3.72240 | 0.421479 | ||||||||
\(79\) | 0.137198 | 0.0154360 | 0.00771802 | − | 0.999970i | \(-0.497543\pi\) | ||||
0.00771802 | + | 0.999970i | \(0.497543\pi\) | |||||||
\(80\) | −3.60256 | −0.402779 | ||||||||
\(81\) | 5.14004 | 0.571116 | ||||||||
\(82\) | −10.1097 | −1.11643 | ||||||||
\(83\) | −9.96639 | −1.09395 | −0.546977 | − | 0.837148i | \(-0.684221\pi\) | ||||
−0.546977 | + | 0.837148i | \(0.684221\pi\) | |||||||
\(84\) | −0.00215238 | −0.000234844 0 | ||||||||
\(85\) | −1.86605 | −0.202402 | ||||||||
\(86\) | 5.22363 | 0.563278 | ||||||||
\(87\) | 0.445503 | 0.0477629 | ||||||||
\(88\) | 2.35705 | 0.251262 | ||||||||
\(89\) | −8.65440 | −0.917365 | −0.458682 | − | 0.888600i | \(-0.651678\pi\) | ||||
−0.458682 | + | 0.888600i | \(0.651678\pi\) | |||||||
\(90\) | 9.18099 | 0.967761 | ||||||||
\(91\) | −0.0177438 | −0.00186006 | ||||||||
\(92\) | 0.165673 | 0.0172726 | ||||||||
\(93\) | −6.30333 | −0.653625 | ||||||||
\(94\) | −8.34349 | −0.860565 | ||||||||
\(95\) | −22.9813 | −2.35783 | ||||||||
\(96\) | −0.671966 | −0.0685823 | ||||||||
\(97\) | 17.4819 | 1.77502 | 0.887510 | − | 0.460789i | \(-0.152434\pi\) | ||||
0.887510 | + | 0.460789i | \(0.152434\pi\) | |||||||
\(98\) | −6.99999 | −0.707106 | ||||||||
\(99\) | −6.00685 | −0.603711 | ||||||||
\(100\) | 7.97845 | 0.797845 | ||||||||
\(101\) | 14.1088 | 1.40388 | 0.701941 | − | 0.712235i | \(-0.252317\pi\) | ||||
0.701941 | + | 0.712235i | \(0.252317\pi\) | |||||||
\(102\) | −0.348064 | −0.0344635 | ||||||||
\(103\) | −10.7738 | −1.06158 | −0.530789 | − | 0.847504i | \(-0.678104\pi\) | ||||
−0.530789 | + | 0.847504i | \(0.678104\pi\) | |||||||
\(104\) | −5.53956 | −0.543199 | ||||||||
\(105\) | 0.00775407 | 0.000756720 0 | ||||||||
\(106\) | −3.30773 | −0.321276 | ||||||||
\(107\) | −9.25256 | −0.894479 | −0.447239 | − | 0.894414i | \(-0.647593\pi\) | ||||
−0.447239 | + | 0.894414i | \(0.647593\pi\) | |||||||
\(108\) | 3.72838 | 0.358763 | ||||||||
\(109\) | 7.66927 | 0.734583 | 0.367291 | − | 0.930106i | \(-0.380285\pi\) | ||||
0.367291 | + | 0.930106i | \(0.380285\pi\) | |||||||
\(110\) | −8.49142 | −0.809625 | ||||||||
\(111\) | −7.03482 | −0.667715 | ||||||||
\(112\) | 0.00320310 | 0.000302665 0 | ||||||||
\(113\) | 6.17042 | 0.580464 | 0.290232 | − | 0.956956i | \(-0.406268\pi\) | ||||
0.290232 | + | 0.956956i | \(0.406268\pi\) | |||||||
\(114\) | −4.28657 | −0.401474 | ||||||||
\(115\) | −0.596845 | −0.0556561 | ||||||||
\(116\) | −0.662984 | −0.0615565 | ||||||||
\(117\) | 14.1174 | 1.30515 | ||||||||
\(118\) | −12.7440 | −1.17318 | ||||||||
\(119\) | 0.00165914 | 0.000152093 0 | ||||||||
\(120\) | 2.42080 | 0.220988 | ||||||||
\(121\) | −5.44431 | −0.494938 | ||||||||
\(122\) | 8.70514 | 0.788126 | ||||||||
\(123\) | 6.79341 | 0.612541 | ||||||||
\(124\) | 9.38043 | 0.842387 | ||||||||
\(125\) | −10.7300 | −0.959723 | ||||||||
\(126\) | −0.00816299 | −0.000727217 0 | ||||||||
\(127\) | −15.6138 | −1.38550 | −0.692750 | − | 0.721178i | \(-0.743601\pi\) | ||||
−0.692750 | + | 0.721178i | \(0.743601\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −3.51010 | −0.309047 | ||||||||
\(130\) | 19.9566 | 1.75031 | ||||||||
\(131\) | −9.21171 | −0.804831 | −0.402415 | − | 0.915457i | \(-0.631829\pi\) | ||||
−0.402415 | + | 0.915457i | \(0.631829\pi\) | |||||||
\(132\) | −1.58386 | −0.137857 | ||||||||
\(133\) | 0.0204331 | 0.00177177 | ||||||||
\(134\) | 6.01503 | 0.519619 | ||||||||
\(135\) | −13.4317 | −1.15602 | ||||||||
\(136\) | 0.517979 | 0.0444163 | ||||||||
\(137\) | −14.8483 | −1.26857 | −0.634286 | − | 0.773098i | \(-0.718706\pi\) | ||||
−0.634286 | + | 0.773098i | \(0.718706\pi\) | |||||||
\(138\) | −0.111326 | −0.00947673 | ||||||||
\(139\) | −8.10001 | −0.687034 | −0.343517 | − | 0.939146i | \(-0.611618\pi\) | ||||
−0.343517 | + | 0.939146i | \(0.611618\pi\) | |||||||
\(140\) | −0.0115394 | −0.000975255 0 | ||||||||
\(141\) | 5.60654 | 0.472156 | ||||||||
\(142\) | 9.69955 | 0.813968 | ||||||||
\(143\) | −13.0570 | −1.09188 | ||||||||
\(144\) | −2.54846 | −0.212372 | ||||||||
\(145\) | 2.38844 | 0.198349 | ||||||||
\(146\) | −6.96842 | −0.576711 | ||||||||
\(147\) | 4.70376 | 0.387959 | ||||||||
\(148\) | 10.4690 | 0.860547 | ||||||||
\(149\) | −7.99537 | −0.655007 | −0.327503 | − | 0.944850i | \(-0.606207\pi\) | ||||
−0.327503 | + | 0.944850i | \(0.606207\pi\) | |||||||
\(150\) | −5.36125 | −0.437744 | ||||||||
\(151\) | −20.5151 | −1.66949 | −0.834747 | − | 0.550633i | \(-0.814386\pi\) | ||||
−0.834747 | + | 0.550633i | \(0.814386\pi\) | |||||||
\(152\) | 6.37915 | 0.517417 | ||||||||
\(153\) | −1.32005 | −0.106720 | ||||||||
\(154\) | 0.00754988 | 0.000608386 0 | ||||||||
\(155\) | −33.7936 | −2.71436 | ||||||||
\(156\) | 3.72240 | 0.298031 | ||||||||
\(157\) | −22.6547 | −1.80804 | −0.904020 | − | 0.427491i | \(-0.859398\pi\) | ||||
−0.904020 | + | 0.427491i | \(0.859398\pi\) | |||||||
\(158\) | 0.137198 | 0.0109149 | ||||||||
\(159\) | 2.22269 | 0.176270 | ||||||||
\(160\) | −3.60256 | −0.284807 | ||||||||
\(161\) | 0.000530666 0 | 4.18224e−5 0 | ||||||||
\(162\) | 5.14004 | 0.403840 | ||||||||
\(163\) | −22.1106 | −1.73184 | −0.865919 | − | 0.500183i | \(-0.833266\pi\) | ||||
−0.865919 | + | 0.500183i | \(0.833266\pi\) | |||||||
\(164\) | −10.1097 | −0.789438 | ||||||||
\(165\) | 5.70594 | 0.444207 | ||||||||
\(166\) | −9.96639 | −0.773542 | ||||||||
\(167\) | 19.4887 | 1.50808 | 0.754042 | − | 0.656826i | \(-0.228101\pi\) | ||||
0.754042 | + | 0.656826i | \(0.228101\pi\) | |||||||
\(168\) | −0.00215238 | −0.000166060 0 | ||||||||
\(169\) | 17.6868 | 1.36052 | ||||||||
\(170\) | −1.86605 | −0.143120 | ||||||||
\(171\) | −16.2570 | −1.24321 | ||||||||
\(172\) | 5.22363 | 0.398298 | ||||||||
\(173\) | 9.37562 | 0.712815 | 0.356407 | − | 0.934331i | \(-0.384002\pi\) | ||||
0.356407 | + | 0.934331i | \(0.384002\pi\) | |||||||
\(174\) | 0.445503 | 0.0337735 | ||||||||
\(175\) | 0.0255558 | 0.00193184 | ||||||||
\(176\) | 2.35705 | 0.177669 | ||||||||
\(177\) | 8.56355 | 0.643676 | ||||||||
\(178\) | −8.65440 | −0.648675 | ||||||||
\(179\) | 0.360173 | 0.0269206 | 0.0134603 | − | 0.999909i | \(-0.495715\pi\) | ||||
0.0134603 | + | 0.999909i | \(0.495715\pi\) | |||||||
\(180\) | 9.18099 | 0.684310 | ||||||||
\(181\) | −14.0808 | −1.04662 | −0.523309 | − | 0.852143i | \(-0.675303\pi\) | ||||
−0.523309 | + | 0.852143i | \(0.675303\pi\) | |||||||
\(182\) | −0.0177438 | −0.00131526 | ||||||||
\(183\) | −5.84956 | −0.432412 | ||||||||
\(184\) | 0.165673 | 0.0122135 | ||||||||
\(185\) | −37.7152 | −2.77288 | ||||||||
\(186\) | −6.30333 | −0.462182 | ||||||||
\(187\) | 1.22090 | 0.0892812 | ||||||||
\(188\) | −8.34349 | −0.608511 | ||||||||
\(189\) | 0.0119424 | 0.000868681 0 | ||||||||
\(190\) | −22.9813 | −1.66724 | ||||||||
\(191\) | −9.96640 | −0.721143 | −0.360572 | − | 0.932732i | \(-0.617418\pi\) | ||||
−0.360572 | + | 0.932732i | \(0.617418\pi\) | |||||||
\(192\) | −0.671966 | −0.0484950 | ||||||||
\(193\) | 18.3471 | 1.32065 | 0.660327 | − | 0.750978i | \(-0.270418\pi\) | ||||
0.660327 | + | 0.750978i | \(0.270418\pi\) | |||||||
\(194\) | 17.4819 | 1.25513 | ||||||||
\(195\) | −13.4102 | −0.960322 | ||||||||
\(196\) | −6.99999 | −0.499999 | ||||||||
\(197\) | −18.8320 | −1.34172 | −0.670861 | − | 0.741583i | \(-0.734075\pi\) | ||||
−0.670861 | + | 0.741583i | \(0.734075\pi\) | |||||||
\(198\) | −6.00685 | −0.426888 | ||||||||
\(199\) | −17.7025 | −1.25490 | −0.627450 | − | 0.778657i | \(-0.715901\pi\) | ||||
−0.627450 | + | 0.778657i | \(0.715901\pi\) | |||||||
\(200\) | 7.97845 | 0.564161 | ||||||||
\(201\) | −4.04189 | −0.285093 | ||||||||
\(202\) | 14.1088 | 0.992694 | ||||||||
\(203\) | −0.00212361 | −0.000149048 0 | ||||||||
\(204\) | −0.348064 | −0.0243694 | ||||||||
\(205\) | 36.4210 | 2.54375 | ||||||||
\(206\) | −10.7738 | −0.750650 | ||||||||
\(207\) | −0.422210 | −0.0293456 | ||||||||
\(208\) | −5.53956 | −0.384100 | ||||||||
\(209\) | 15.0360 | 1.04006 | ||||||||
\(210\) | 0.00775407 | 0.000535082 0 | ||||||||
\(211\) | 19.3268 | 1.33051 | 0.665257 | − | 0.746615i | \(-0.268322\pi\) | ||||
0.665257 | + | 0.746615i | \(0.268322\pi\) | |||||||
\(212\) | −3.30773 | −0.227176 | ||||||||
\(213\) | −6.51777 | −0.446590 | ||||||||
\(214\) | −9.25256 | −0.632492 | ||||||||
\(215\) | −18.8184 | −1.28341 | ||||||||
\(216\) | 3.72838 | 0.253684 | ||||||||
\(217\) | 0.0300465 | 0.00203969 | ||||||||
\(218\) | 7.66927 | 0.519429 | ||||||||
\(219\) | 4.68254 | 0.316417 | ||||||||
\(220\) | −8.49142 | −0.572491 | ||||||||
\(221\) | −2.86938 | −0.193015 | ||||||||
\(222\) | −7.03482 | −0.472146 | ||||||||
\(223\) | 14.7486 | 0.987642 | 0.493821 | − | 0.869563i | \(-0.335600\pi\) | ||||
0.493821 | + | 0.869563i | \(0.335600\pi\) | |||||||
\(224\) | 0.00320310 | 0.000214016 0 | ||||||||
\(225\) | −20.3328 | −1.35552 | ||||||||
\(226\) | 6.17042 | 0.410450 | ||||||||
\(227\) | 7.54663 | 0.500887 | 0.250444 | − | 0.968131i | \(-0.419424\pi\) | ||||
0.250444 | + | 0.968131i | \(0.419424\pi\) | |||||||
\(228\) | −4.28657 | −0.283885 | ||||||||
\(229\) | −15.2598 | −1.00839 | −0.504197 | − | 0.863589i | \(-0.668212\pi\) | ||||
−0.504197 | + | 0.863589i | \(0.668212\pi\) | |||||||
\(230\) | −0.596845 | −0.0393548 | ||||||||
\(231\) | −0.00507326 | −0.000333796 0 | ||||||||
\(232\) | −0.662984 | −0.0435270 | ||||||||
\(233\) | 4.01000 | 0.262704 | 0.131352 | − | 0.991336i | \(-0.458068\pi\) | ||||
0.131352 | + | 0.991336i | \(0.458068\pi\) | |||||||
\(234\) | 14.1174 | 0.922881 | ||||||||
\(235\) | 30.0579 | 1.96076 | ||||||||
\(236\) | −12.7440 | −0.829565 | ||||||||
\(237\) | −0.0921927 | −0.00598856 | ||||||||
\(238\) | 0.00165914 | 0.000107546 0 | ||||||||
\(239\) | 7.17759 | 0.464280 | 0.232140 | − | 0.972682i | \(-0.425427\pi\) | ||||
0.232140 | + | 0.972682i | \(0.425427\pi\) | |||||||
\(240\) | 2.42080 | 0.156262 | ||||||||
\(241\) | 13.8399 | 0.891506 | 0.445753 | − | 0.895156i | \(-0.352936\pi\) | ||||
0.445753 | + | 0.895156i | \(0.352936\pi\) | |||||||
\(242\) | −5.44431 | −0.349974 | ||||||||
\(243\) | −14.6391 | −0.939097 | ||||||||
\(244\) | 8.70514 | 0.557290 | ||||||||
\(245\) | 25.2179 | 1.61111 | ||||||||
\(246\) | 6.79341 | 0.433132 | ||||||||
\(247\) | −35.3377 | −2.24848 | ||||||||
\(248\) | 9.38043 | 0.595658 | ||||||||
\(249\) | 6.69707 | 0.424410 | ||||||||
\(250\) | −10.7300 | −0.678627 | ||||||||
\(251\) | 1.00600 | 0.0634984 | 0.0317492 | − | 0.999496i | \(-0.489892\pi\) | ||||
0.0317492 | + | 0.999496i | \(0.489892\pi\) | |||||||
\(252\) | −0.00816299 | −0.000514220 0 | ||||||||
\(253\) | 0.390498 | 0.0245504 | ||||||||
\(254\) | −15.6138 | −0.979697 | ||||||||
\(255\) | 1.25392 | 0.0785237 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.2690 | −0.952454 | −0.476227 | − | 0.879322i | \(-0.657996\pi\) | ||||
−0.476227 | + | 0.879322i | \(0.657996\pi\) | |||||||
\(258\) | −3.51010 | −0.218529 | ||||||||
\(259\) | 0.0335333 | 0.00208366 | ||||||||
\(260\) | 19.9566 | 1.23766 | ||||||||
\(261\) | 1.68959 | 0.104583 | ||||||||
\(262\) | −9.21171 | −0.569101 | ||||||||
\(263\) | −2.79277 | −0.172210 | −0.0861048 | − | 0.996286i | \(-0.527442\pi\) | ||||
−0.0861048 | + | 0.996286i | \(0.527442\pi\) | |||||||
\(264\) | −1.58386 | −0.0974797 | ||||||||
\(265\) | 11.9163 | 0.732013 | ||||||||
\(266\) | 0.0204331 | 0.00125283 | ||||||||
\(267\) | 5.81547 | 0.355901 | ||||||||
\(268\) | 6.01503 | 0.367426 | ||||||||
\(269\) | 2.65737 | 0.162023 | 0.0810114 | − | 0.996713i | \(-0.474185\pi\) | ||||
0.0810114 | + | 0.996713i | \(0.474185\pi\) | |||||||
\(270\) | −13.4317 | −0.817428 | ||||||||
\(271\) | 20.1846 | 1.22612 | 0.613062 | − | 0.790034i | \(-0.289937\pi\) | ||||
0.613062 | + | 0.790034i | \(0.289937\pi\) | |||||||
\(272\) | 0.517979 | 0.0314071 | ||||||||
\(273\) | 0.0119232 | 0.000721627 0 | ||||||||
\(274\) | −14.8483 | −0.897016 | ||||||||
\(275\) | 18.8056 | 1.13402 | ||||||||
\(276\) | −0.111326 | −0.00670106 | ||||||||
\(277\) | 16.4138 | 0.986212 | 0.493106 | − | 0.869969i | \(-0.335861\pi\) | ||||
0.493106 | + | 0.869969i | \(0.335861\pi\) | |||||||
\(278\) | −8.10001 | −0.485807 | ||||||||
\(279\) | −23.9057 | −1.43119 | ||||||||
\(280\) | −0.0115394 | −0.000689610 0 | ||||||||
\(281\) | 8.03318 | 0.479219 | 0.239610 | − | 0.970869i | \(-0.422981\pi\) | ||||
0.239610 | + | 0.970869i | \(0.422981\pi\) | |||||||
\(282\) | 5.60654 | 0.333865 | ||||||||
\(283\) | −3.61553 | −0.214921 | −0.107460 | − | 0.994209i | \(-0.534272\pi\) | ||||
−0.107460 | + | 0.994209i | \(0.534272\pi\) | |||||||
\(284\) | 9.69955 | 0.575562 | ||||||||
\(285\) | 15.4426 | 0.914743 | ||||||||
\(286\) | −13.0570 | −0.772078 | ||||||||
\(287\) | −0.0323826 | −0.00191148 | ||||||||
\(288\) | −2.54846 | −0.150170 | ||||||||
\(289\) | −16.7317 | −0.984218 | ||||||||
\(290\) | 2.38844 | 0.140254 | ||||||||
\(291\) | −11.7473 | −0.688636 | ||||||||
\(292\) | −6.96842 | −0.407796 | ||||||||
\(293\) | −30.8642 | −1.80311 | −0.901553 | − | 0.432669i | \(-0.857572\pi\) | ||||
−0.901553 | + | 0.432669i | \(0.857572\pi\) | |||||||
\(294\) | 4.70376 | 0.274329 | ||||||||
\(295\) | 45.9111 | 2.67305 | ||||||||
\(296\) | 10.4690 | 0.608499 | ||||||||
\(297\) | 8.78797 | 0.509930 | ||||||||
\(298\) | −7.99537 | −0.463160 | ||||||||
\(299\) | −0.917754 | −0.0530751 | ||||||||
\(300\) | −5.36125 | −0.309532 | ||||||||
\(301\) | 0.0167318 | 0.000964406 0 | ||||||||
\(302\) | −20.5151 | −1.18051 | ||||||||
\(303\) | −9.48066 | −0.544650 | ||||||||
\(304\) | 6.37915 | 0.365869 | ||||||||
\(305\) | −31.3608 | −1.79571 | ||||||||
\(306\) | −1.32005 | −0.0754622 | ||||||||
\(307\) | 19.0538 | 1.08746 | 0.543728 | − | 0.839261i | \(-0.317012\pi\) | ||||
0.543728 | + | 0.839261i | \(0.317012\pi\) | |||||||
\(308\) | 0.00754988 | 0.000430194 0 | ||||||||
\(309\) | 7.23966 | 0.411850 | ||||||||
\(310\) | −33.7936 | −1.91934 | ||||||||
\(311\) | 11.8968 | 0.674604 | 0.337302 | − | 0.941396i | \(-0.390486\pi\) | ||||
0.337302 | + | 0.941396i | \(0.390486\pi\) | |||||||
\(312\) | 3.72240 | 0.210739 | ||||||||
\(313\) | −32.2628 | −1.82360 | −0.911800 | − | 0.410636i | \(-0.865307\pi\) | ||||
−0.911800 | + | 0.410636i | \(0.865307\pi\) | |||||||
\(314\) | −22.6547 | −1.27848 | ||||||||
\(315\) | 0.0294077 | 0.00165693 | ||||||||
\(316\) | 0.137198 | 0.00771802 | ||||||||
\(317\) | 11.4805 | 0.644807 | 0.322404 | − | 0.946602i | \(-0.395509\pi\) | ||||
0.322404 | + | 0.946602i | \(0.395509\pi\) | |||||||
\(318\) | 2.22269 | 0.124642 | ||||||||
\(319\) | −1.56269 | −0.0874936 | ||||||||
\(320\) | −3.60256 | −0.201389 | ||||||||
\(321\) | 6.21741 | 0.347022 | ||||||||
\(322\) | 0.000530666 0 | 2.95729e−5 0 | ||||||||
\(323\) | 3.30426 | 0.183854 | ||||||||
\(324\) | 5.14004 | 0.285558 | ||||||||
\(325\) | −44.1971 | −2.45161 | ||||||||
\(326\) | −22.1106 | −1.22460 | ||||||||
\(327\) | −5.15349 | −0.284989 | ||||||||
\(328\) | −10.1097 | −0.558217 | ||||||||
\(329\) | −0.0267251 | −0.00147340 | ||||||||
\(330\) | 5.70594 | 0.314102 | ||||||||
\(331\) | −18.9411 | −1.04110 | −0.520549 | − | 0.853832i | \(-0.674273\pi\) | ||||
−0.520549 | + | 0.853832i | \(0.674273\pi\) | |||||||
\(332\) | −9.96639 | −0.546977 | ||||||||
\(333\) | −26.6799 | −1.46205 | ||||||||
\(334\) | 19.4887 | 1.06638 | ||||||||
\(335\) | −21.6695 | −1.18393 | ||||||||
\(336\) | −0.00215238 | −0.000117422 0 | ||||||||
\(337\) | 21.7910 | 1.18703 | 0.593515 | − | 0.804823i | \(-0.297740\pi\) | ||||
0.593515 | + | 0.804823i | \(0.297740\pi\) | |||||||
\(338\) | 17.6868 | 0.962034 | ||||||||
\(339\) | −4.14631 | −0.225197 | ||||||||
\(340\) | −1.86605 | −0.101201 | ||||||||
\(341\) | 22.1101 | 1.19733 | ||||||||
\(342\) | −16.2570 | −0.879079 | ||||||||
\(343\) | −0.0448434 | −0.00242132 | ||||||||
\(344\) | 5.22363 | 0.281639 | ||||||||
\(345\) | 0.401060 | 0.0215923 | ||||||||
\(346\) | 9.37562 | 0.504036 | ||||||||
\(347\) | −20.6062 | −1.10620 | −0.553099 | − | 0.833115i | \(-0.686555\pi\) | ||||
−0.553099 | + | 0.833115i | \(0.686555\pi\) | |||||||
\(348\) | 0.445503 | 0.0238814 | ||||||||
\(349\) | −2.04297 | −0.109358 | −0.0546788 | − | 0.998504i | \(-0.517414\pi\) | ||||
−0.0546788 | + | 0.998504i | \(0.517414\pi\) | |||||||
\(350\) | 0.0255558 | 0.00136601 | ||||||||
\(351\) | −20.6536 | −1.10241 | ||||||||
\(352\) | 2.35705 | 0.125631 | ||||||||
\(353\) | −6.25826 | −0.333094 | −0.166547 | − | 0.986034i | \(-0.553262\pi\) | ||||
−0.166547 | + | 0.986034i | \(0.553262\pi\) | |||||||
\(354\) | 8.56355 | 0.455148 | ||||||||
\(355\) | −34.9432 | −1.85459 | ||||||||
\(356\) | −8.65440 | −0.458682 | ||||||||
\(357\) | −0.00111489 | −5.90060e−5 0 | ||||||||
\(358\) | 0.360173 | 0.0190357 | ||||||||
\(359\) | −2.32159 | −0.122529 | −0.0612643 | − | 0.998122i | \(-0.519513\pi\) | ||||
−0.0612643 | + | 0.998122i | \(0.519513\pi\) | |||||||
\(360\) | 9.18099 | 0.483881 | ||||||||
\(361\) | 21.6936 | 1.14177 | ||||||||
\(362\) | −14.0808 | −0.740071 | ||||||||
\(363\) | 3.65840 | 0.192016 | ||||||||
\(364\) | −0.0177438 | −0.000930028 0 | ||||||||
\(365\) | 25.1042 | 1.31401 | ||||||||
\(366\) | −5.84956 | −0.305761 | ||||||||
\(367\) | 34.7000 | 1.81133 | 0.905663 | − | 0.423999i | \(-0.139374\pi\) | ||||
0.905663 | + | 0.423999i | \(0.139374\pi\) | |||||||
\(368\) | 0.165673 | 0.00863628 | ||||||||
\(369\) | 25.7643 | 1.34124 | ||||||||
\(370\) | −37.7152 | −1.96072 | ||||||||
\(371\) | −0.0105950 | −0.000550066 0 | ||||||||
\(372\) | −6.30333 | −0.326812 | ||||||||
\(373\) | 10.0646 | 0.521125 | 0.260562 | − | 0.965457i | \(-0.416092\pi\) | ||||
0.260562 | + | 0.965457i | \(0.416092\pi\) | |||||||
\(374\) | 1.22090 | 0.0631313 | ||||||||
\(375\) | 7.21022 | 0.372334 | ||||||||
\(376\) | −8.34349 | −0.430283 | ||||||||
\(377\) | 3.67264 | 0.189151 | ||||||||
\(378\) | 0.0119424 | 0.000614250 0 | ||||||||
\(379\) | −1.70743 | −0.0877048 | −0.0438524 | − | 0.999038i | \(-0.513963\pi\) | ||||
−0.0438524 | + | 0.999038i | \(0.513963\pi\) | |||||||
\(380\) | −22.9813 | −1.17891 | ||||||||
\(381\) | 10.4919 | 0.537519 | ||||||||
\(382\) | −9.96640 | −0.509925 | ||||||||
\(383\) | −25.8225 | −1.31947 | −0.659734 | − | 0.751499i | \(-0.729331\pi\) | ||||
−0.659734 | + | 0.751499i | \(0.729331\pi\) | |||||||
\(384\) | −0.671966 | −0.0342911 | ||||||||
\(385\) | −0.0271989 | −0.00138618 | ||||||||
\(386\) | 18.3471 | 0.933843 | ||||||||
\(387\) | −13.3122 | −0.676698 | ||||||||
\(388\) | 17.4819 | 0.887510 | ||||||||
\(389\) | −21.7658 | −1.10357 | −0.551786 | − | 0.833986i | \(-0.686053\pi\) | ||||
−0.551786 | + | 0.833986i | \(0.686053\pi\) | |||||||
\(390\) | −13.4102 | −0.679050 | ||||||||
\(391\) | 0.0858148 | 0.00433984 | ||||||||
\(392\) | −6.99999 | −0.353553 | ||||||||
\(393\) | 6.18996 | 0.312242 | ||||||||
\(394\) | −18.8320 | −0.948741 | ||||||||
\(395\) | −0.494266 | −0.0248692 | ||||||||
\(396\) | −6.00685 | −0.301856 | ||||||||
\(397\) | −15.9100 | −0.798502 | −0.399251 | − | 0.916842i | \(-0.630730\pi\) | ||||
−0.399251 | + | 0.916842i | \(0.630730\pi\) | |||||||
\(398\) | −17.7025 | −0.887348 | ||||||||
\(399\) | −0.0137303 | −0.000687377 0 | ||||||||
\(400\) | 7.97845 | 0.398922 | ||||||||
\(401\) | 27.3375 | 1.36517 | 0.682586 | − | 0.730806i | \(-0.260855\pi\) | ||||
0.682586 | + | 0.730806i | \(0.260855\pi\) | |||||||
\(402\) | −4.04189 | −0.201591 | ||||||||
\(403\) | −51.9635 | −2.58848 | ||||||||
\(404\) | 14.1088 | 0.701941 | ||||||||
\(405\) | −18.5173 | −0.920132 | ||||||||
\(406\) | −0.00212361 | −0.000105393 0 | ||||||||
\(407\) | 24.6760 | 1.22314 | ||||||||
\(408\) | −0.348064 | −0.0172317 | ||||||||
\(409\) | −1.77857 | −0.0879444 | −0.0439722 | − | 0.999033i | \(-0.514001\pi\) | ||||
−0.0439722 | + | 0.999033i | \(0.514001\pi\) | |||||||
\(410\) | 36.4210 | 1.79870 | ||||||||
\(411\) | 9.97753 | 0.492155 | ||||||||
\(412\) | −10.7738 | −0.530789 | ||||||||
\(413\) | −0.0408204 | −0.00200864 | ||||||||
\(414\) | −0.422210 | −0.0207505 | ||||||||
\(415\) | 35.9045 | 1.76248 | ||||||||
\(416\) | −5.53956 | −0.271599 | ||||||||
\(417\) | 5.44293 | 0.266542 | ||||||||
\(418\) | 15.0360 | 0.735434 | ||||||||
\(419\) | 33.0783 | 1.61598 | 0.807990 | − | 0.589196i | \(-0.200555\pi\) | ||||
0.807990 | + | 0.589196i | \(0.200555\pi\) | |||||||
\(420\) | 0.00775407 | 0.000378360 0 | ||||||||
\(421\) | 8.69390 | 0.423715 | 0.211857 | − | 0.977301i | \(-0.432049\pi\) | ||||
0.211857 | + | 0.977301i | \(0.432049\pi\) | |||||||
\(422\) | 19.3268 | 0.940815 | ||||||||
\(423\) | 21.2631 | 1.03385 | ||||||||
\(424\) | −3.30773 | −0.160638 | ||||||||
\(425\) | 4.13267 | 0.200464 | ||||||||
\(426\) | −6.51777 | −0.315787 | ||||||||
\(427\) | 0.0278835 | 0.00134938 | ||||||||
\(428\) | −9.25256 | −0.447239 | ||||||||
\(429\) | 8.77388 | 0.423607 | ||||||||
\(430\) | −18.8184 | −0.907506 | ||||||||
\(431\) | −9.39970 | −0.452768 | −0.226384 | − | 0.974038i | \(-0.572690\pi\) | ||||
−0.226384 | + | 0.974038i | \(0.572690\pi\) | |||||||
\(432\) | 3.72838 | 0.179382 | ||||||||
\(433\) | −10.4032 | −0.499947 | −0.249974 | − | 0.968253i | \(-0.580422\pi\) | ||||
−0.249974 | + | 0.968253i | \(0.580422\pi\) | |||||||
\(434\) | 0.0300465 | 0.00144228 | ||||||||
\(435\) | −1.60495 | −0.0769515 | ||||||||
\(436\) | 7.66927 | 0.367291 | ||||||||
\(437\) | 1.05685 | 0.0505560 | ||||||||
\(438\) | 4.68254 | 0.223741 | ||||||||
\(439\) | −22.4008 | −1.06913 | −0.534566 | − | 0.845127i | \(-0.679525\pi\) | ||||
−0.534566 | + | 0.845127i | \(0.679525\pi\) | |||||||
\(440\) | −8.49142 | −0.404812 | ||||||||
\(441\) | 17.8392 | 0.849486 | ||||||||
\(442\) | −2.86938 | −0.136482 | ||||||||
\(443\) | 37.0228 | 1.75901 | 0.879504 | − | 0.475892i | \(-0.157875\pi\) | ||||
0.879504 | + | 0.475892i | \(0.157875\pi\) | |||||||
\(444\) | −7.03482 | −0.333858 | ||||||||
\(445\) | 31.1780 | 1.47798 | ||||||||
\(446\) | 14.7486 | 0.698369 | ||||||||
\(447\) | 5.37262 | 0.254116 | ||||||||
\(448\) | 0.00320310 | 0.000151332 0 | ||||||||
\(449\) | −23.0335 | −1.08702 | −0.543509 | − | 0.839404i | \(-0.682905\pi\) | ||||
−0.543509 | + | 0.839404i | \(0.682905\pi\) | |||||||
\(450\) | −20.3328 | −0.958496 | ||||||||
\(451\) | −23.8292 | −1.12207 | ||||||||
\(452\) | 6.17042 | 0.290232 | ||||||||
\(453\) | 13.7855 | 0.647697 | ||||||||
\(454\) | 7.54663 | 0.354181 | ||||||||
\(455\) | 0.0639231 | 0.00299676 | ||||||||
\(456\) | −4.28657 | −0.200737 | ||||||||
\(457\) | 15.5058 | 0.725333 | 0.362666 | − | 0.931919i | \(-0.381866\pi\) | ||||
0.362666 | + | 0.931919i | \(0.381866\pi\) | |||||||
\(458\) | −15.2598 | −0.713043 | ||||||||
\(459\) | 1.93122 | 0.0901417 | ||||||||
\(460\) | −0.596845 | −0.0278281 | ||||||||
\(461\) | 4.71579 | 0.219636 | 0.109818 | − | 0.993952i | \(-0.464973\pi\) | ||||
0.109818 | + | 0.993952i | \(0.464973\pi\) | |||||||
\(462\) | −0.00507326 | −0.000236029 0 | ||||||||
\(463\) | 2.51673 | 0.116962 | 0.0584812 | − | 0.998289i | \(-0.481374\pi\) | ||||
0.0584812 | + | 0.998289i | \(0.481374\pi\) | |||||||
\(464\) | −0.662984 | −0.0307782 | ||||||||
\(465\) | 22.7081 | 1.05306 | ||||||||
\(466\) | 4.01000 | 0.185760 | ||||||||
\(467\) | −23.6562 | −1.09468 | −0.547339 | − | 0.836911i | \(-0.684359\pi\) | ||||
−0.547339 | + | 0.836911i | \(0.684359\pi\) | |||||||
\(468\) | 14.1174 | 0.652576 | ||||||||
\(469\) | 0.0192668 | 0.000889656 0 | ||||||||
\(470\) | 30.0579 | 1.38647 | ||||||||
\(471\) | 15.2232 | 0.701447 | ||||||||
\(472\) | −12.7440 | −0.586591 | ||||||||
\(473\) | 12.3124 | 0.566123 | ||||||||
\(474\) | −0.0921927 | −0.00423455 | ||||||||
\(475\) | 50.8957 | 2.33525 | ||||||||
\(476\) | 0.00165914 | 7.60465e−5 0 | ||||||||
\(477\) | 8.42963 | 0.385966 | ||||||||
\(478\) | 7.17759 | 0.328296 | ||||||||
\(479\) | 5.55788 | 0.253946 | 0.126973 | − | 0.991906i | \(-0.459474\pi\) | ||||
0.126973 | + | 0.991906i | \(0.459474\pi\) | |||||||
\(480\) | 2.42080 | 0.110494 | ||||||||
\(481\) | −57.9937 | −2.64429 | ||||||||
\(482\) | 13.8399 | 0.630390 | ||||||||
\(483\) | −0.000356590 0 | −1.62254e−5 0 | ||||||||
\(484\) | −5.44431 | −0.247469 | ||||||||
\(485\) | −62.9796 | −2.85976 | ||||||||
\(486\) | −14.6391 | −0.664042 | ||||||||
\(487\) | −33.0410 | −1.49723 | −0.748616 | − | 0.663004i | \(-0.769281\pi\) | ||||
−0.748616 | + | 0.663004i | \(0.769281\pi\) | |||||||
\(488\) | 8.70514 | 0.394063 | ||||||||
\(489\) | 14.8576 | 0.671884 | ||||||||
\(490\) | 25.2179 | 1.13923 | ||||||||
\(491\) | 9.44418 | 0.426210 | 0.213105 | − | 0.977029i | \(-0.431642\pi\) | ||||
0.213105 | + | 0.977029i | \(0.431642\pi\) | |||||||
\(492\) | 6.79341 | 0.306270 | ||||||||
\(493\) | −0.343412 | −0.0154665 | ||||||||
\(494\) | −35.3377 | −1.58992 | ||||||||
\(495\) | 21.6400 | 0.972648 | ||||||||
\(496\) | 9.38043 | 0.421194 | ||||||||
\(497\) | 0.0310687 | 0.00139362 | ||||||||
\(498\) | 6.69707 | 0.300103 | ||||||||
\(499\) | −31.4323 | −1.40710 | −0.703551 | − | 0.710644i | \(-0.748404\pi\) | ||||
−0.703551 | + | 0.710644i | \(0.748404\pi\) | |||||||
\(500\) | −10.7300 | −0.479862 | ||||||||
\(501\) | −13.0958 | −0.585076 | ||||||||
\(502\) | 1.00600 | 0.0449001 | ||||||||
\(503\) | 22.7101 | 1.01260 | 0.506298 | − | 0.862359i | \(-0.331014\pi\) | ||||
0.506298 | + | 0.862359i | \(0.331014\pi\) | |||||||
\(504\) | −0.00816299 | −0.000363608 0 | ||||||||
\(505\) | −50.8279 | −2.26181 | ||||||||
\(506\) | 0.390498 | 0.0173598 | ||||||||
\(507\) | −11.8849 | −0.527828 | ||||||||
\(508\) | −15.6138 | −0.692750 | ||||||||
\(509\) | −42.2922 | −1.87457 | −0.937283 | − | 0.348568i | \(-0.886668\pi\) | ||||
−0.937283 | + | 0.348568i | \(0.886668\pi\) | |||||||
\(510\) | 1.25392 | 0.0555246 | ||||||||
\(511\) | −0.0223206 | −0.000987404 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 23.7839 | 1.05008 | ||||||||
\(514\) | −15.2690 | −0.673487 | ||||||||
\(515\) | 38.8134 | 1.71032 | ||||||||
\(516\) | −3.51010 | −0.154524 | ||||||||
\(517\) | −19.6660 | −0.864910 | ||||||||
\(518\) | 0.0335333 | 0.00147337 | ||||||||
\(519\) | −6.30010 | −0.276544 | ||||||||
\(520\) | 19.9566 | 0.875156 | ||||||||
\(521\) | −7.63690 | −0.334579 | −0.167289 | − | 0.985908i | \(-0.553501\pi\) | ||||
−0.167289 | + | 0.985908i | \(0.553501\pi\) | |||||||
\(522\) | 1.68959 | 0.0739513 | ||||||||
\(523\) | −30.3552 | −1.32734 | −0.663670 | − | 0.748025i | \(-0.731002\pi\) | ||||
−0.663670 | + | 0.748025i | \(0.731002\pi\) | |||||||
\(524\) | −9.21171 | −0.402415 | ||||||||
\(525\) | −0.0171726 | −0.000749475 0 | ||||||||
\(526\) | −2.79277 | −0.121771 | ||||||||
\(527\) | 4.85886 | 0.211655 | ||||||||
\(528\) | −1.58386 | −0.0689286 | ||||||||
\(529\) | −22.9726 | −0.998807 | ||||||||
\(530\) | 11.9163 | 0.517612 | ||||||||
\(531\) | 32.4777 | 1.40941 | ||||||||
\(532\) | 0.0204331 | 0.000885886 0 | ||||||||
\(533\) | 56.0036 | 2.42578 | ||||||||
\(534\) | 5.81547 | 0.251660 | ||||||||
\(535\) | 33.3329 | 1.44111 | ||||||||
\(536\) | 6.01503 | 0.259810 | ||||||||
\(537\) | −0.242024 | −0.0104441 | ||||||||
\(538\) | 2.65737 | 0.114567 | ||||||||
\(539\) | −16.4993 | −0.710676 | ||||||||
\(540\) | −13.4317 | −0.578009 | ||||||||
\(541\) | 41.1438 | 1.76891 | 0.884456 | − | 0.466624i | \(-0.154530\pi\) | ||||
0.884456 | + | 0.466624i | \(0.154530\pi\) | |||||||
\(542\) | 20.1846 | 0.867001 | ||||||||
\(543\) | 9.46183 | 0.406046 | ||||||||
\(544\) | 0.517979 | 0.0222082 | ||||||||
\(545\) | −27.6290 | −1.18350 | ||||||||
\(546\) | 0.0119232 | 0.000510267 0 | ||||||||
\(547\) | −22.0474 | −0.942677 | −0.471338 | − | 0.881952i | \(-0.656229\pi\) | ||||
−0.471338 | + | 0.881952i | \(0.656229\pi\) | |||||||
\(548\) | −14.8483 | −0.634286 | ||||||||
\(549\) | −22.1847 | −0.946821 | ||||||||
\(550\) | 18.8056 | 0.801873 | ||||||||
\(551\) | −4.22927 | −0.180173 | ||||||||
\(552\) | −0.111326 | −0.00473836 | ||||||||
\(553\) | 0.000439461 0 | 1.86878e−5 0 | ||||||||
\(554\) | 16.4138 | 0.697357 | ||||||||
\(555\) | 25.3434 | 1.07577 | ||||||||
\(556\) | −8.10001 | −0.343517 | ||||||||
\(557\) | 12.8761 | 0.545578 | 0.272789 | − | 0.962074i | \(-0.412054\pi\) | ||||
0.272789 | + | 0.962074i | \(0.412054\pi\) | |||||||
\(558\) | −23.9057 | −1.01201 | ||||||||
\(559\) | −28.9366 | −1.22389 | ||||||||
\(560\) | −0.0115394 | −0.000487628 0 | ||||||||
\(561\) | −0.820405 | −0.0346375 | ||||||||
\(562\) | 8.03318 | 0.338859 | ||||||||
\(563\) | −21.6422 | −0.912110 | −0.456055 | − | 0.889952i | \(-0.650738\pi\) | ||||
−0.456055 | + | 0.889952i | \(0.650738\pi\) | |||||||
\(564\) | 5.60654 | 0.236078 | ||||||||
\(565\) | −22.2293 | −0.935194 | ||||||||
\(566\) | −3.61553 | −0.151972 | ||||||||
\(567\) | 0.0164641 | 0.000691427 0 | ||||||||
\(568\) | 9.69955 | 0.406984 | ||||||||
\(569\) | 3.87671 | 0.162520 | 0.0812600 | − | 0.996693i | \(-0.474106\pi\) | ||||
0.0812600 | + | 0.996693i | \(0.474106\pi\) | |||||||
\(570\) | 15.4426 | 0.646821 | ||||||||
\(571\) | 13.8813 | 0.580913 | 0.290456 | − | 0.956888i | \(-0.406193\pi\) | ||||
0.290456 | + | 0.956888i | \(0.406193\pi\) | |||||||
\(572\) | −13.0570 | −0.545942 | ||||||||
\(573\) | 6.69708 | 0.279775 | ||||||||
\(574\) | −0.0323826 | −0.00135162 | ||||||||
\(575\) | 1.32181 | 0.0551232 | ||||||||
\(576\) | −2.54846 | −0.106186 | ||||||||
\(577\) | 3.99826 | 0.166450 | 0.0832249 | − | 0.996531i | \(-0.473478\pi\) | ||||
0.0832249 | + | 0.996531i | \(0.473478\pi\) | |||||||
\(578\) | −16.7317 | −0.695947 | ||||||||
\(579\) | −12.3286 | −0.512361 | ||||||||
\(580\) | 2.38844 | 0.0991745 | ||||||||
\(581\) | −0.0319234 | −0.00132440 | ||||||||
\(582\) | −11.7473 | −0.486939 | ||||||||
\(583\) | −7.79650 | −0.322898 | ||||||||
\(584\) | −6.96842 | −0.288355 | ||||||||
\(585\) | −50.8587 | −2.10275 | ||||||||
\(586\) | −30.8642 | −1.27499 | ||||||||
\(587\) | −33.3117 | −1.37492 | −0.687460 | − | 0.726223i | \(-0.741274\pi\) | ||||
−0.687460 | + | 0.726223i | \(0.741274\pi\) | |||||||
\(588\) | 4.70376 | 0.193980 | ||||||||
\(589\) | 59.8391 | 2.46563 | ||||||||
\(590\) | 45.9111 | 1.89013 | ||||||||
\(591\) | 12.6544 | 0.520534 | ||||||||
\(592\) | 10.4690 | 0.430273 | ||||||||
\(593\) | 26.2795 | 1.07917 | 0.539584 | − | 0.841931i | \(-0.318581\pi\) | ||||
0.539584 | + | 0.841931i | \(0.318581\pi\) | |||||||
\(594\) | 8.78797 | 0.360575 | ||||||||
\(595\) | −0.00597715 | −0.000245039 0 | ||||||||
\(596\) | −7.99537 | −0.327503 | ||||||||
\(597\) | 11.8955 | 0.486851 | ||||||||
\(598\) | −0.917754 | −0.0375297 | ||||||||
\(599\) | 15.7522 | 0.643617 | 0.321808 | − | 0.946805i | \(-0.395709\pi\) | ||||
0.321808 | + | 0.946805i | \(0.395709\pi\) | |||||||
\(600\) | −5.36125 | −0.218872 | ||||||||
\(601\) | −36.9363 | −1.50666 | −0.753331 | − | 0.657641i | \(-0.771554\pi\) | ||||
−0.753331 | + | 0.657641i | \(0.771554\pi\) | |||||||
\(602\) | 0.0167318 | 0.000681938 0 | ||||||||
\(603\) | −15.3291 | −0.624248 | ||||||||
\(604\) | −20.5151 | −0.834747 | ||||||||
\(605\) | 19.6135 | 0.797401 | ||||||||
\(606\) | −9.48066 | −0.385126 | ||||||||
\(607\) | −32.3173 | −1.31172 | −0.655859 | − | 0.754883i | \(-0.727693\pi\) | ||||
−0.655859 | + | 0.754883i | \(0.727693\pi\) | |||||||
\(608\) | 6.37915 | 0.258709 | ||||||||
\(609\) | 0.00142699 | 5.78246e−5 0 | ||||||||
\(610\) | −31.3608 | −1.26976 | ||||||||
\(611\) | 46.2193 | 1.86983 | ||||||||
\(612\) | −1.32005 | −0.0533598 | ||||||||
\(613\) | −30.4679 | −1.23059 | −0.615294 | − | 0.788298i | \(-0.710963\pi\) | ||||
−0.615294 | + | 0.788298i | \(0.710963\pi\) | |||||||
\(614\) | 19.0538 | 0.768948 | ||||||||
\(615\) | −24.4737 | −0.986873 | ||||||||
\(616\) | 0.00754988 | 0.000304193 0 | ||||||||
\(617\) | 33.2509 | 1.33863 | 0.669316 | − | 0.742978i | \(-0.266587\pi\) | ||||
0.669316 | + | 0.742978i | \(0.266587\pi\) | |||||||
\(618\) | 7.23966 | 0.291222 | ||||||||
\(619\) | −17.3282 | −0.696479 | −0.348240 | − | 0.937406i | \(-0.613220\pi\) | ||||
−0.348240 | + | 0.937406i | \(0.613220\pi\) | |||||||
\(620\) | −33.7936 | −1.35718 | ||||||||
\(621\) | 0.617690 | 0.0247870 | ||||||||
\(622\) | 11.8968 | 0.477017 | ||||||||
\(623\) | −0.0277210 | −0.00111062 | ||||||||
\(624\) | 3.72240 | 0.149015 | ||||||||
\(625\) | −1.23664 | −0.0494656 | ||||||||
\(626\) | −32.2628 | −1.28948 | ||||||||
\(627\) | −10.1037 | −0.403502 | ||||||||
\(628\) | −22.6547 | −0.904020 | ||||||||
\(629\) | 5.42272 | 0.216218 | ||||||||
\(630\) | 0.0294077 | 0.00117163 | ||||||||
\(631\) | −21.7063 | −0.864114 | −0.432057 | − | 0.901846i | \(-0.642212\pi\) | ||||
−0.432057 | + | 0.901846i | \(0.642212\pi\) | |||||||
\(632\) | 0.137198 | 0.00545746 | ||||||||
\(633\) | −12.9870 | −0.516186 | ||||||||
\(634\) | 11.4805 | 0.455948 | ||||||||
\(635\) | 56.2497 | 2.23220 | ||||||||
\(636\) | 2.22269 | 0.0881352 | ||||||||
\(637\) | 38.7769 | 1.53640 | ||||||||
\(638\) | −1.56269 | −0.0618673 | ||||||||
\(639\) | −24.7189 | −0.977866 | ||||||||
\(640\) | −3.60256 | −0.142404 | ||||||||
\(641\) | 16.3099 | 0.644201 | 0.322101 | − | 0.946705i | \(-0.395611\pi\) | ||||
0.322101 | + | 0.946705i | \(0.395611\pi\) | |||||||
\(642\) | 6.21741 | 0.245381 | ||||||||
\(643\) | −25.8929 | −1.02112 | −0.510558 | − | 0.859843i | \(-0.670561\pi\) | ||||
−0.510558 | + | 0.859843i | \(0.670561\pi\) | |||||||
\(644\) | 0.000530666 0 | 2.09112e−5 0 | ||||||||
\(645\) | 12.6454 | 0.497910 | ||||||||
\(646\) | 3.30426 | 0.130005 | ||||||||
\(647\) | −28.8063 | −1.13249 | −0.566245 | − | 0.824237i | \(-0.691605\pi\) | ||||
−0.566245 | + | 0.824237i | \(0.691605\pi\) | |||||||
\(648\) | 5.14004 | 0.201920 | ||||||||
\(649\) | −30.0383 | −1.17911 | ||||||||
\(650\) | −44.1971 | −1.73355 | ||||||||
\(651\) | −0.0201902 | −0.000791317 0 | ||||||||
\(652\) | −22.1106 | −0.865919 | ||||||||
\(653\) | −6.45010 | −0.252412 | −0.126206 | − | 0.992004i | \(-0.540280\pi\) | ||||
−0.126206 | + | 0.992004i | \(0.540280\pi\) | |||||||
\(654\) | −5.15349 | −0.201517 | ||||||||
\(655\) | 33.1857 | 1.29667 | ||||||||
\(656\) | −10.1097 | −0.394719 | ||||||||
\(657\) | 17.7588 | 0.692835 | ||||||||
\(658\) | −0.0267251 | −0.00104185 | ||||||||
\(659\) | 3.70233 | 0.144222 | 0.0721112 | − | 0.997397i | \(-0.477026\pi\) | ||||
0.0721112 | + | 0.997397i | \(0.477026\pi\) | |||||||
\(660\) | 5.70594 | 0.222104 | ||||||||
\(661\) | 18.7570 | 0.729562 | 0.364781 | − | 0.931093i | \(-0.381144\pi\) | ||||
0.364781 | + | 0.931093i | \(0.381144\pi\) | |||||||
\(662\) | −18.9411 | −0.736168 | ||||||||
\(663\) | 1.92812 | 0.0748821 | ||||||||
\(664\) | −9.96639 | −0.386771 | ||||||||
\(665\) | −0.0736114 | −0.00285453 | ||||||||
\(666\) | −26.6799 | −1.03382 | ||||||||
\(667\) | −0.109838 | −0.00425295 | ||||||||
\(668\) | 19.4887 | 0.754042 | ||||||||
\(669\) | −9.91059 | −0.383166 | ||||||||
\(670\) | −21.6695 | −0.837166 | ||||||||
\(671\) | 20.5185 | 0.792106 | ||||||||
\(672\) | −0.00215238 | −8.30298e−5 0 | ||||||||
\(673\) | 3.54194 | 0.136532 | 0.0682659 | − | 0.997667i | \(-0.478253\pi\) | ||||
0.0682659 | + | 0.997667i | \(0.478253\pi\) | |||||||
\(674\) | 21.7910 | 0.839357 | ||||||||
\(675\) | 29.7467 | 1.14495 | ||||||||
\(676\) | 17.6868 | 0.680261 | ||||||||
\(677\) | −31.0465 | −1.19321 | −0.596606 | − | 0.802534i | \(-0.703485\pi\) | ||||
−0.596606 | + | 0.802534i | \(0.703485\pi\) | |||||||
\(678\) | −4.14631 | −0.159238 | ||||||||
\(679\) | 0.0559964 | 0.00214894 | ||||||||
\(680\) | −1.86605 | −0.0715598 | ||||||||
\(681\) | −5.07108 | −0.194324 | ||||||||
\(682\) | 22.1101 | 0.846641 | ||||||||
\(683\) | −21.0820 | −0.806680 | −0.403340 | − | 0.915050i | \(-0.632151\pi\) | ||||
−0.403340 | + | 0.915050i | \(0.632151\pi\) | |||||||
\(684\) | −16.2570 | −0.621603 | ||||||||
\(685\) | 53.4918 | 2.04382 | ||||||||
\(686\) | −0.0448434 | −0.00171213 | ||||||||
\(687\) | 10.2541 | 0.391217 | ||||||||
\(688\) | 5.22363 | 0.199149 | ||||||||
\(689\) | 18.3234 | 0.698066 | ||||||||
\(690\) | 0.401060 | 0.0152681 | ||||||||
\(691\) | 2.52267 | 0.0959671 | 0.0479835 | − | 0.998848i | \(-0.484721\pi\) | ||||
0.0479835 | + | 0.998848i | \(0.484721\pi\) | |||||||
\(692\) | 9.37562 | 0.356407 | ||||||||
\(693\) | −0.0192406 | −0.000730889 0 | ||||||||
\(694\) | −20.6062 | −0.782201 | ||||||||
\(695\) | 29.1808 | 1.10689 | ||||||||
\(696\) | 0.445503 | 0.0168867 | ||||||||
\(697\) | −5.23663 | −0.198352 | ||||||||
\(698\) | −2.04297 | −0.0773276 | ||||||||
\(699\) | −2.69459 | −0.101919 | ||||||||
\(700\) | 0.0255558 | 0.000965918 0 | ||||||||
\(701\) | 26.7602 | 1.01072 | 0.505359 | − | 0.862909i | \(-0.331360\pi\) | ||||
0.505359 | + | 0.862909i | \(0.331360\pi\) | |||||||
\(702\) | −20.6536 | −0.779520 | ||||||||
\(703\) | 66.7833 | 2.51878 | ||||||||
\(704\) | 2.35705 | 0.0888347 | ||||||||
\(705\) | −20.1979 | −0.760697 | ||||||||
\(706\) | −6.25826 | −0.235533 | ||||||||
\(707\) | 0.0451921 | 0.00169962 | ||||||||
\(708\) | 8.56355 | 0.321838 | ||||||||
\(709\) | −4.06287 | −0.152584 | −0.0762921 | − | 0.997086i | \(-0.524308\pi\) | ||||
−0.0762921 | + | 0.997086i | \(0.524308\pi\) | |||||||
\(710\) | −34.9432 | −1.31140 | ||||||||
\(711\) | −0.349645 | −0.0131127 | ||||||||
\(712\) | −8.65440 | −0.324337 | ||||||||
\(713\) | 1.55408 | 0.0582007 | ||||||||
\(714\) | −0.00111489 | −4.17236e−5 0 | ||||||||
\(715\) | 47.0387 | 1.75915 | ||||||||
\(716\) | 0.360173 | 0.0134603 | ||||||||
\(717\) | −4.82310 | −0.180122 | ||||||||
\(718\) | −2.32159 | −0.0866408 | ||||||||
\(719\) | −20.3585 | −0.759244 | −0.379622 | − | 0.925142i | \(-0.623946\pi\) | ||||
−0.379622 | + | 0.925142i | \(0.623946\pi\) | |||||||
\(720\) | 9.18099 | 0.342155 | ||||||||
\(721\) | −0.0345098 | −0.00128521 | ||||||||
\(722\) | 21.6936 | 0.807350 | ||||||||
\(723\) | −9.29994 | −0.345868 | ||||||||
\(724\) | −14.0808 | −0.523309 | ||||||||
\(725\) | −5.28958 | −0.196450 | ||||||||
\(726\) | 3.65840 | 0.135776 | ||||||||
\(727\) | 10.6501 | 0.394989 | 0.197495 | − | 0.980304i | \(-0.436719\pi\) | ||||
0.197495 | + | 0.980304i | \(0.436719\pi\) | |||||||
\(728\) | −0.0177438 | −0.000657629 0 | ||||||||
\(729\) | −5.58316 | −0.206784 | ||||||||
\(730\) | 25.1042 | 0.929147 | ||||||||
\(731\) | 2.70573 | 0.100075 | ||||||||
\(732\) | −5.84956 | −0.216206 | ||||||||
\(733\) | −12.9808 | −0.479456 | −0.239728 | − | 0.970840i | \(-0.577058\pi\) | ||||
−0.239728 | + | 0.970840i | \(0.577058\pi\) | |||||||
\(734\) | 34.7000 | 1.28080 | ||||||||
\(735\) | −16.9456 | −0.625047 | ||||||||
\(736\) | 0.165673 | 0.00610677 | ||||||||
\(737\) | 14.1777 | 0.522243 | ||||||||
\(738\) | 25.7643 | 0.948397 | ||||||||
\(739\) | 1.18608 | 0.0436308 | 0.0218154 | − | 0.999762i | \(-0.493055\pi\) | ||||
0.0218154 | + | 0.999762i | \(0.493055\pi\) | |||||||
\(740\) | −37.7152 | −1.38644 | ||||||||
\(741\) | 23.7457 | 0.872322 | ||||||||
\(742\) | −0.0105950 | −0.000388955 0 | ||||||||
\(743\) | −32.8493 | −1.20512 | −0.602562 | − | 0.798072i | \(-0.705853\pi\) | ||||
−0.602562 | + | 0.798072i | \(0.705853\pi\) | |||||||
\(744\) | −6.30333 | −0.231091 | ||||||||
\(745\) | 28.8038 | 1.05529 | ||||||||
\(746\) | 10.0646 | 0.368491 | ||||||||
\(747\) | 25.3990 | 0.929299 | ||||||||
\(748\) | 1.22090 | 0.0446406 | ||||||||
\(749\) | −0.0296369 | −0.00108291 | ||||||||
\(750\) | 7.21022 | 0.263280 | ||||||||
\(751\) | −4.04124 | −0.147467 | −0.0737335 | − | 0.997278i | \(-0.523491\pi\) | ||||
−0.0737335 | + | 0.997278i | \(0.523491\pi\) | |||||||
\(752\) | −8.34349 | −0.304256 | ||||||||
\(753\) | −0.676000 | −0.0246348 | ||||||||
\(754\) | 3.67264 | 0.133750 | ||||||||
\(755\) | 73.9069 | 2.68975 | ||||||||
\(756\) | 0.0119424 | 0.000434340 0 | ||||||||
\(757\) | −33.6150 | −1.22176 | −0.610879 | − | 0.791724i | \(-0.709184\pi\) | ||||
−0.610879 | + | 0.791724i | \(0.709184\pi\) | |||||||
\(758\) | −1.70743 | −0.0620166 | ||||||||
\(759\) | −0.262402 | −0.00952458 | ||||||||
\(760\) | −22.9813 | −0.833618 | ||||||||
\(761\) | 5.80307 | 0.210361 | 0.105181 | − | 0.994453i | \(-0.466458\pi\) | ||||
0.105181 | + | 0.994453i | \(0.466458\pi\) | |||||||
\(762\) | 10.4919 | 0.380083 | ||||||||
\(763\) | 0.0245655 | 0.000889330 0 | ||||||||
\(764\) | −9.96640 | −0.360572 | ||||||||
\(765\) | 4.75556 | 0.171938 | ||||||||
\(766\) | −25.8225 | −0.933005 | ||||||||
\(767\) | 70.5963 | 2.54909 | ||||||||
\(768\) | −0.671966 | −0.0242475 | ||||||||
\(769\) | −9.59462 | −0.345991 | −0.172995 | − | 0.984923i | \(-0.555345\pi\) | ||||
−0.172995 | + | 0.984923i | \(0.555345\pi\) | |||||||
\(770\) | −0.0271989 | −0.000980180 0 | ||||||||
\(771\) | 10.2603 | 0.369514 | ||||||||
\(772\) | 18.3471 | 0.660327 | ||||||||
\(773\) | 6.48372 | 0.233203 | 0.116602 | − | 0.993179i | \(-0.462800\pi\) | ||||
0.116602 | + | 0.993179i | \(0.462800\pi\) | |||||||
\(774\) | −13.3122 | −0.478498 | ||||||||
\(775\) | 74.8412 | 2.68838 | ||||||||
\(776\) | 17.4819 | 0.627564 | ||||||||
\(777\) | −0.0225332 | −0.000808376 0 | ||||||||
\(778\) | −21.7658 | −0.780343 | ||||||||
\(779\) | −64.4916 | −2.31065 | ||||||||
\(780\) | −13.4102 | −0.480161 | ||||||||
\(781\) | 22.8623 | 0.818078 | ||||||||
\(782\) | 0.0858148 | 0.00306873 | ||||||||
\(783\) | −2.47185 | −0.0883369 | ||||||||
\(784\) | −6.99999 | −0.250000 | ||||||||
\(785\) | 81.6148 | 2.91296 | ||||||||
\(786\) | 6.18996 | 0.220788 | ||||||||
\(787\) | −28.7497 | −1.02481 | −0.512407 | − | 0.858742i | \(-0.671246\pi\) | ||||
−0.512407 | + | 0.858742i | \(0.671246\pi\) | |||||||
\(788\) | −18.8320 | −0.670861 | ||||||||
\(789\) | 1.87665 | 0.0668104 | ||||||||
\(790\) | −0.494266 | −0.0175852 | ||||||||
\(791\) | 0.0197645 | 0.000702744 0 | ||||||||
\(792\) | −6.00685 | −0.213444 | ||||||||
\(793\) | −48.2227 | −1.71244 | ||||||||
\(794\) | −15.9100 | −0.564627 | ||||||||
\(795\) | −8.00736 | −0.283992 | ||||||||
\(796\) | −17.7025 | −0.627450 | ||||||||
\(797\) | −33.1793 | −1.17527 | −0.587635 | − | 0.809126i | \(-0.699941\pi\) | ||||
−0.587635 | + | 0.809126i | \(0.699941\pi\) | |||||||
\(798\) | −0.0137303 | −0.000486049 0 | ||||||||
\(799\) | −4.32175 | −0.152893 | ||||||||
\(800\) | 7.97845 | 0.282081 | ||||||||
\(801\) | 22.0554 | 0.779290 | ||||||||
\(802\) | 27.3375 | 0.965322 | ||||||||
\(803\) | −16.4249 | −0.579623 | ||||||||
\(804\) | −4.04189 | −0.142547 | ||||||||
\(805\) | −0.00191176 | −6.73806e−5 0 | ||||||||
\(806\) | −51.9635 | −1.83034 | ||||||||
\(807\) | −1.78566 | −0.0628584 | ||||||||
\(808\) | 14.1088 | 0.496347 | ||||||||
\(809\) | −21.5104 | −0.756265 | −0.378132 | − | 0.925752i | \(-0.623434\pi\) | ||||
−0.378132 | + | 0.925752i | \(0.623434\pi\) | |||||||
\(810\) | −18.5173 | −0.650632 | ||||||||
\(811\) | 26.4504 | 0.928800 | 0.464400 | − | 0.885626i | \(-0.346270\pi\) | ||||
0.464400 | + | 0.885626i | \(0.346270\pi\) | |||||||
\(812\) | −0.00212361 | −7.45240e−5 0 | ||||||||
\(813\) | −13.5633 | −0.475687 | ||||||||
\(814\) | 24.6760 | 0.864892 | ||||||||
\(815\) | 79.6549 | 2.79019 | ||||||||
\(816\) | −0.348064 | −0.0121847 | ||||||||
\(817\) | 33.3223 | 1.16580 | ||||||||
\(818\) | −1.77857 | −0.0621861 | ||||||||
\(819\) | 0.0452194 | 0.00158009 | ||||||||
\(820\) | 36.4210 | 1.27188 | ||||||||
\(821\) | −33.5884 | −1.17224 | −0.586122 | − | 0.810223i | \(-0.699346\pi\) | ||||
−0.586122 | + | 0.810223i | \(0.699346\pi\) | |||||||
\(822\) | 9.97753 | 0.348006 | ||||||||
\(823\) | 35.2370 | 1.22829 | 0.614143 | − | 0.789195i | \(-0.289502\pi\) | ||||
0.614143 | + | 0.789195i | \(0.289502\pi\) | |||||||
\(824\) | −10.7738 | −0.375325 | ||||||||
\(825\) | −12.6367 | −0.439954 | ||||||||
\(826\) | −0.0408204 | −0.00142032 | ||||||||
\(827\) | −10.8491 | −0.377260 | −0.188630 | − | 0.982048i | \(-0.560405\pi\) | ||||
−0.188630 | + | 0.982048i | \(0.560405\pi\) | |||||||
\(828\) | −0.422210 | −0.0146728 | ||||||||
\(829\) | −7.26722 | −0.252401 | −0.126201 | − | 0.992005i | \(-0.540278\pi\) | ||||
−0.126201 | + | 0.992005i | \(0.540278\pi\) | |||||||
\(830\) | 35.9045 | 1.24626 | ||||||||
\(831\) | −11.0295 | −0.382611 | ||||||||
\(832\) | −5.53956 | −0.192050 | ||||||||
\(833\) | −3.62585 | −0.125628 | ||||||||
\(834\) | 5.44293 | 0.188473 | ||||||||
\(835\) | −70.2094 | −2.42970 | ||||||||
\(836\) | 15.0360 | 0.520030 | ||||||||
\(837\) | 34.9738 | 1.20887 | ||||||||
\(838\) | 33.0783 | 1.14267 | ||||||||
\(839\) | 14.2921 | 0.493417 | 0.246709 | − | 0.969090i | \(-0.420651\pi\) | ||||
0.246709 | + | 0.969090i | \(0.420651\pi\) | |||||||
\(840\) | 0.00775407 | 0.000267541 0 | ||||||||
\(841\) | −28.5605 | −0.984843 | ||||||||
\(842\) | 8.69390 | 0.299611 | ||||||||
\(843\) | −5.39803 | −0.185918 | ||||||||
\(844\) | 19.3268 | 0.665257 | ||||||||
\(845\) | −63.7177 | −2.19195 | ||||||||
\(846\) | 21.2631 | 0.731039 | ||||||||
\(847\) | −0.0174387 | −0.000599201 0 | ||||||||
\(848\) | −3.30773 | −0.113588 | ||||||||
\(849\) | 2.42951 | 0.0833806 | ||||||||
\(850\) | 4.13267 | 0.141749 | ||||||||
\(851\) | 1.73443 | 0.0594554 | ||||||||
\(852\) | −6.51777 | −0.223295 | ||||||||
\(853\) | 1.05162 | 0.0360069 | 0.0180034 | − | 0.999838i | \(-0.494269\pi\) | ||||
0.0180034 | + | 0.999838i | \(0.494269\pi\) | |||||||
\(854\) | 0.0278835 | 0.000954153 0 | ||||||||
\(855\) | 58.5669 | 2.00295 | ||||||||
\(856\) | −9.25256 | −0.316246 | ||||||||
\(857\) | −51.9264 | −1.77377 | −0.886886 | − | 0.461988i | \(-0.847136\pi\) | ||||
−0.886886 | + | 0.461988i | \(0.847136\pi\) | |||||||
\(858\) | 8.77388 | 0.299535 | ||||||||
\(859\) | 8.23630 | 0.281019 | 0.140510 | − | 0.990079i | \(-0.455126\pi\) | ||||
0.140510 | + | 0.990079i | \(0.455126\pi\) | |||||||
\(860\) | −18.8184 | −0.641703 | ||||||||
\(861\) | 0.0217600 | 0.000741578 0 | ||||||||
\(862\) | −9.39970 | −0.320155 | ||||||||
\(863\) | −9.17787 | −0.312418 | −0.156209 | − | 0.987724i | \(-0.549927\pi\) | ||||
−0.156209 | + | 0.987724i | \(0.549927\pi\) | |||||||
\(864\) | 3.72838 | 0.126842 | ||||||||
\(865\) | −33.7762 | −1.14843 | ||||||||
\(866\) | −10.4032 | −0.353516 | ||||||||
\(867\) | 11.2431 | 0.381837 | ||||||||
\(868\) | 0.0300465 | 0.00101984 | ||||||||
\(869\) | 0.323384 | 0.0109700 | ||||||||
\(870\) | −1.60495 | −0.0544129 | ||||||||
\(871\) | −33.3206 | −1.12903 | ||||||||
\(872\) | 7.66927 | 0.259714 | ||||||||
\(873\) | −44.5520 | −1.50786 | ||||||||
\(874\) | 1.05685 | 0.0357485 | ||||||||
\(875\) | −0.0343694 | −0.00116190 | ||||||||
\(876\) | 4.68254 | 0.158208 | ||||||||
\(877\) | −10.7179 | −0.361918 | −0.180959 | − | 0.983491i | \(-0.557920\pi\) | ||||
−0.180959 | + | 0.983491i | \(0.557920\pi\) | |||||||
\(878\) | −22.4008 | −0.755990 | ||||||||
\(879\) | 20.7397 | 0.699533 | ||||||||
\(880\) | −8.49142 | −0.286246 | ||||||||
\(881\) | 34.6970 | 1.16897 | 0.584487 | − | 0.811403i | \(-0.301296\pi\) | ||||
0.584487 | + | 0.811403i | \(0.301296\pi\) | |||||||
\(882\) | 17.8392 | 0.600677 | ||||||||
\(883\) | −30.8117 | −1.03690 | −0.518448 | − | 0.855109i | \(-0.673490\pi\) | ||||
−0.518448 | + | 0.855109i | \(0.673490\pi\) | |||||||
\(884\) | −2.86938 | −0.0965076 | ||||||||
\(885\) | −30.8507 | −1.03704 | ||||||||
\(886\) | 37.0228 | 1.24381 | ||||||||
\(887\) | −4.14407 | −0.139144 | −0.0695721 | − | 0.997577i | \(-0.522163\pi\) | ||||
−0.0695721 | + | 0.997577i | \(0.522163\pi\) | |||||||
\(888\) | −7.03482 | −0.236073 | ||||||||
\(889\) | −0.0500126 | −0.00167737 | ||||||||
\(890\) | 31.1780 | 1.04509 | ||||||||
\(891\) | 12.1153 | 0.405879 | ||||||||
\(892\) | 14.7486 | 0.493821 | ||||||||
\(893\) | −53.2244 | −1.78109 | ||||||||
\(894\) | 5.37262 | 0.179687 | ||||||||
\(895\) | −1.29754 | −0.0433721 | ||||||||
\(896\) | 0.00320310 | 0.000107008 0 | ||||||||
\(897\) | 0.616699 | 0.0205910 | ||||||||
\(898\) | −23.0335 | −0.768637 | ||||||||
\(899\) | −6.21907 | −0.207418 | ||||||||
\(900\) | −20.3328 | −0.677759 | ||||||||
\(901\) | −1.71334 | −0.0570795 | ||||||||
\(902\) | −23.8292 | −0.793425 | ||||||||
\(903\) | −0.0112432 | −0.000374151 0 | ||||||||
\(904\) | 6.17042 | 0.205225 | ||||||||
\(905\) | 50.7270 | 1.68622 | ||||||||
\(906\) | 13.7855 | 0.457991 | ||||||||
\(907\) | −40.2684 | −1.33709 | −0.668545 | − | 0.743672i | \(-0.733083\pi\) | ||||
−0.668545 | + | 0.743672i | \(0.733083\pi\) | |||||||
\(908\) | 7.54663 | 0.250444 | ||||||||
\(909\) | −35.9558 | −1.19258 | ||||||||
\(910\) | 0.0639231 | 0.00211903 | ||||||||
\(911\) | 9.19510 | 0.304647 | 0.152324 | − | 0.988331i | \(-0.451324\pi\) | ||||
0.152324 | + | 0.988331i | \(0.451324\pi\) | |||||||
\(912\) | −4.28657 | −0.141943 | ||||||||
\(913\) | −23.4913 | −0.777448 | ||||||||
\(914\) | 15.5058 | 0.512888 | ||||||||
\(915\) | 21.0734 | 0.696665 | ||||||||
\(916\) | −15.2598 | −0.504197 | ||||||||
\(917\) | −0.0295061 | −0.000974376 0 | ||||||||
\(918\) | 1.93122 | 0.0637398 | ||||||||
\(919\) | 55.5879 | 1.83368 | 0.916838 | − | 0.399260i | \(-0.130733\pi\) | ||||
0.916838 | + | 0.399260i | \(0.130733\pi\) | |||||||
\(920\) | −0.596845 | −0.0196774 | ||||||||
\(921\) | −12.8035 | −0.421890 | ||||||||
\(922\) | 4.71579 | 0.155306 | ||||||||
\(923\) | −53.7313 | −1.76859 | ||||||||
\(924\) | −0.00507326 | −0.000166898 0 | ||||||||
\(925\) | 83.5264 | 2.74633 | ||||||||
\(926\) | 2.51673 | 0.0827048 | ||||||||
\(927\) | 27.4567 | 0.901798 | ||||||||
\(928\) | −0.662984 | −0.0217635 | ||||||||
\(929\) | 46.2577 | 1.51767 | 0.758833 | − | 0.651285i | \(-0.225770\pi\) | ||||
0.758833 | + | 0.651285i | \(0.225770\pi\) | |||||||
\(930\) | 22.7081 | 0.744629 | ||||||||
\(931\) | −44.6540 | −1.46348 | ||||||||
\(932\) | 4.01000 | 0.131352 | ||||||||
\(933\) | −7.99423 | −0.261719 | ||||||||
\(934\) | −23.6562 | −0.774055 | ||||||||
\(935\) | −4.39837 | −0.143842 | ||||||||
\(936\) | 14.1174 | 0.461441 | ||||||||
\(937\) | 52.3222 | 1.70929 | 0.854646 | − | 0.519211i | \(-0.173774\pi\) | ||||
0.854646 | + | 0.519211i | \(0.173774\pi\) | |||||||
\(938\) | 0.0192668 | 0.000629082 0 | ||||||||
\(939\) | 21.6795 | 0.707483 | ||||||||
\(940\) | 30.0579 | 0.980381 | ||||||||
\(941\) | 20.8204 | 0.678727 | 0.339363 | − | 0.940655i | \(-0.389788\pi\) | ||||
0.339363 | + | 0.940655i | \(0.389788\pi\) | |||||||
\(942\) | 15.2232 | 0.495998 | ||||||||
\(943\) | −1.67491 | −0.0545425 | ||||||||
\(944\) | −12.7440 | −0.414783 | ||||||||
\(945\) | −0.0430232 | −0.00139954 | ||||||||
\(946\) | 12.3124 | 0.400309 | ||||||||
\(947\) | 4.95633 | 0.161059 | 0.0805296 | − | 0.996752i | \(-0.474339\pi\) | ||||
0.0805296 | + | 0.996752i | \(0.474339\pi\) | |||||||
\(948\) | −0.0921927 | −0.00299428 | ||||||||
\(949\) | 38.6020 | 1.25307 | ||||||||
\(950\) | 50.8957 | 1.65127 | ||||||||
\(951\) | −7.71448 | −0.250159 | ||||||||
\(952\) | 0.00165914 | 5.37730e−5 0 | ||||||||
\(953\) | 12.1823 | 0.394622 | 0.197311 | − | 0.980341i | \(-0.436779\pi\) | ||||
0.197311 | + | 0.980341i | \(0.436779\pi\) | |||||||
\(954\) | 8.42963 | 0.272919 | ||||||||
\(955\) | 35.9046 | 1.16184 | ||||||||
\(956\) | 7.17759 | 0.232140 | ||||||||
\(957\) | 1.05007 | 0.0339440 | ||||||||
\(958\) | 5.55788 | 0.179567 | ||||||||
\(959\) | −0.0475605 | −0.00153581 | ||||||||
\(960\) | 2.42080 | 0.0781310 | ||||||||
\(961\) | 56.9924 | 1.83846 | ||||||||
\(962\) | −57.9937 | −1.86979 | ||||||||
\(963\) | 23.5798 | 0.759848 | ||||||||
\(964\) | 13.8399 | 0.445753 | ||||||||
\(965\) | −66.0966 | −2.12772 | ||||||||
\(966\) | −0.000356590 0 | −1.14731e−5 0 | ||||||||
\(967\) | 45.0624 | 1.44911 | 0.724555 | − | 0.689217i | \(-0.242045\pi\) | ||||
0.724555 | + | 0.689217i | \(0.242045\pi\) | |||||||
\(968\) | −5.44431 | −0.174987 | ||||||||
\(969\) | −2.22035 | −0.0713280 | ||||||||
\(970\) | −62.9796 | −2.02215 | ||||||||
\(971\) | −53.5674 | −1.71906 | −0.859530 | − | 0.511085i | \(-0.829244\pi\) | ||||
−0.859530 | + | 0.511085i | \(0.829244\pi\) | |||||||
\(972\) | −14.6391 | −0.469548 | ||||||||
\(973\) | −0.0259452 | −0.000831764 0 | ||||||||
\(974\) | −33.0410 | −1.05870 | ||||||||
\(975\) | 29.6990 | 0.951128 | ||||||||
\(976\) | 8.70514 | 0.278645 | ||||||||
\(977\) | −40.9825 | −1.31115 | −0.655573 | − | 0.755132i | \(-0.727573\pi\) | ||||
−0.655573 | + | 0.755132i | \(0.727573\pi\) | |||||||
\(978\) | 14.8576 | 0.475094 | ||||||||
\(979\) | −20.3989 | −0.651951 | ||||||||
\(980\) | 25.2179 | 0.805556 | ||||||||
\(981\) | −19.5448 | −0.624019 | ||||||||
\(982\) | 9.44418 | 0.301376 | ||||||||
\(983\) | −12.6994 | −0.405047 | −0.202524 | − | 0.979277i | \(-0.564914\pi\) | ||||
−0.202524 | + | 0.979277i | \(0.564914\pi\) | |||||||
\(984\) | 6.79341 | 0.216566 | ||||||||
\(985\) | 67.8433 | 2.16167 | ||||||||
\(986\) | −0.343412 | −0.0109365 | ||||||||
\(987\) | 0.0179583 | 0.000571620 0 | ||||||||
\(988\) | −35.3377 | −1.12424 | ||||||||
\(989\) | 0.865412 | 0.0275185 | ||||||||
\(990\) | 21.6400 | 0.687766 | ||||||||
\(991\) | −3.69875 | −0.117495 | −0.0587473 | − | 0.998273i | \(-0.518711\pi\) | ||||
−0.0587473 | + | 0.998273i | \(0.518711\pi\) | |||||||
\(992\) | 9.38043 | 0.297829 | ||||||||
\(993\) | 12.7278 | 0.403905 | ||||||||
\(994\) | 0.0310687 | 0.000985438 0 | ||||||||
\(995\) | 63.7745 | 2.02179 | ||||||||
\(996\) | 6.69707 | 0.212205 | ||||||||
\(997\) | 1.55814 | 0.0493468 | 0.0246734 | − | 0.999696i | \(-0.492145\pi\) | ||||
0.0246734 | + | 0.999696i | \(0.492145\pi\) | |||||||
\(998\) | −31.4323 | −0.994972 | ||||||||
\(999\) | 39.0324 | 1.23493 |
(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 | 8002.2.a.d.1.33 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8002.2.a.d.1.33 | ✓ | 69 | 1.1 | even | 1 | trivial |