Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4006,2,Mod(1,4006)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4006, 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("4006.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4006 = 2 \cdot 2003 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4006.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: | \(31.9880710497\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 4006.1 |
$q$-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 | ||||||||
\(3\) | 0.0490190 | 0.0283011 | 0.0141506 | − | 0.999900i | \(-0.495496\pi\) | ||||
0.0141506 | + | 0.999900i | \(0.495496\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.547018 | 0.244634 | 0.122317 | − | 0.992491i | \(-0.460968\pi\) | ||||
0.122317 | + | 0.992491i | \(0.460968\pi\) | |||||||
\(6\) | 0.0490190 | 0.0200119 | ||||||||
\(7\) | −4.51424 | −1.70622 | −0.853112 | − | 0.521728i | \(-0.825288\pi\) | ||||
−0.853112 | + | 0.521728i | \(0.825288\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.99760 | −0.999199 | ||||||||
\(10\) | 0.547018 | 0.172982 | ||||||||
\(11\) | 0.850349 | 0.256390 | 0.128195 | − | 0.991749i | \(-0.459082\pi\) | ||||
0.128195 | + | 0.991749i | \(0.459082\pi\) | |||||||
\(12\) | 0.0490190 | 0.0141506 | ||||||||
\(13\) | 5.33838 | 1.48060 | 0.740300 | − | 0.672277i | \(-0.234683\pi\) | ||||
0.740300 | + | 0.672277i | \(0.234683\pi\) | |||||||
\(14\) | −4.51424 | −1.20648 | ||||||||
\(15\) | 0.0268143 | 0.00692342 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.19834 | −0.533175 | −0.266587 | − | 0.963811i | \(-0.585896\pi\) | ||||
−0.266587 | + | 0.963811i | \(0.585896\pi\) | |||||||
\(18\) | −2.99760 | −0.706540 | ||||||||
\(19\) | −0.355291 | −0.0815094 | −0.0407547 | − | 0.999169i | \(-0.512976\pi\) | ||||
−0.0407547 | + | 0.999169i | \(0.512976\pi\) | |||||||
\(20\) | 0.547018 | 0.122317 | ||||||||
\(21\) | −0.221284 | −0.0482880 | ||||||||
\(22\) | 0.850349 | 0.181295 | ||||||||
\(23\) | 4.91805 | 1.02548 | 0.512742 | − | 0.858542i | \(-0.328630\pi\) | ||||
0.512742 | + | 0.858542i | \(0.328630\pi\) | |||||||
\(24\) | 0.0490190 | 0.0100060 | ||||||||
\(25\) | −4.70077 | −0.940154 | ||||||||
\(26\) | 5.33838 | 1.04694 | ||||||||
\(27\) | −0.293996 | −0.0565796 | ||||||||
\(28\) | −4.51424 | −0.853112 | ||||||||
\(29\) | −1.79123 | −0.332623 | −0.166311 | − | 0.986073i | \(-0.553186\pi\) | ||||
−0.166311 | + | 0.986073i | \(0.553186\pi\) | |||||||
\(30\) | 0.0268143 | 0.00489559 | ||||||||
\(31\) | 10.6418 | 1.91133 | 0.955663 | − | 0.294464i | \(-0.0951411\pi\) | ||||
0.955663 | + | 0.294464i | \(0.0951411\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.0416832 | 0.00725612 | ||||||||
\(34\) | −2.19834 | −0.377011 | ||||||||
\(35\) | −2.46937 | −0.417400 | ||||||||
\(36\) | −2.99760 | −0.499600 | ||||||||
\(37\) | 3.67532 | 0.604218 | 0.302109 | − | 0.953273i | \(-0.402309\pi\) | ||||
0.302109 | + | 0.953273i | \(0.402309\pi\) | |||||||
\(38\) | −0.355291 | −0.0576359 | ||||||||
\(39\) | 0.261682 | 0.0419026 | ||||||||
\(40\) | 0.547018 | 0.0864912 | ||||||||
\(41\) | 5.45355 | 0.851702 | 0.425851 | − | 0.904793i | \(-0.359975\pi\) | ||||
0.425851 | + | 0.904793i | \(0.359975\pi\) | |||||||
\(42\) | −0.221284 | −0.0341448 | ||||||||
\(43\) | −4.54506 | −0.693114 | −0.346557 | − | 0.938029i | \(-0.612649\pi\) | ||||
−0.346557 | + | 0.938029i | \(0.612649\pi\) | |||||||
\(44\) | 0.850349 | 0.128195 | ||||||||
\(45\) | −1.63974 | −0.244438 | ||||||||
\(46\) | 4.91805 | 0.725127 | ||||||||
\(47\) | 5.16120 | 0.752838 | 0.376419 | − | 0.926450i | \(-0.377155\pi\) | ||||
0.376419 | + | 0.926450i | \(0.377155\pi\) | |||||||
\(48\) | 0.0490190 | 0.00707528 | ||||||||
\(49\) | 13.3784 | 1.91120 | ||||||||
\(50\) | −4.70077 | −0.664789 | ||||||||
\(51\) | −0.107760 | −0.0150894 | ||||||||
\(52\) | 5.33838 | 0.740300 | ||||||||
\(53\) | 3.22422 | 0.442881 | 0.221441 | − | 0.975174i | \(-0.428924\pi\) | ||||
0.221441 | + | 0.975174i | \(0.428924\pi\) | |||||||
\(54\) | −0.293996 | −0.0400078 | ||||||||
\(55\) | 0.465156 | 0.0627217 | ||||||||
\(56\) | −4.51424 | −0.603241 | ||||||||
\(57\) | −0.0174160 | −0.00230681 | ||||||||
\(58\) | −1.79123 | −0.235200 | ||||||||
\(59\) | −1.10040 | −0.143261 | −0.0716303 | − | 0.997431i | \(-0.522820\pi\) | ||||
−0.0716303 | + | 0.997431i | \(0.522820\pi\) | |||||||
\(60\) | 0.0268143 | 0.00346171 | ||||||||
\(61\) | −5.65294 | −0.723785 | −0.361892 | − | 0.932220i | \(-0.617869\pi\) | ||||
−0.361892 | + | 0.932220i | \(0.617869\pi\) | |||||||
\(62\) | 10.6418 | 1.35151 | ||||||||
\(63\) | 13.5319 | 1.70486 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.92019 | 0.362205 | ||||||||
\(66\) | 0.0416832 | 0.00513085 | ||||||||
\(67\) | 7.10303 | 0.867773 | 0.433886 | − | 0.900968i | \(-0.357142\pi\) | ||||
0.433886 | + | 0.900968i | \(0.357142\pi\) | |||||||
\(68\) | −2.19834 | −0.266587 | ||||||||
\(69\) | 0.241078 | 0.0290224 | ||||||||
\(70\) | −2.46937 | −0.295147 | ||||||||
\(71\) | 1.00310 | 0.119047 | 0.0595233 | − | 0.998227i | \(-0.481042\pi\) | ||||
0.0595233 | + | 0.998227i | \(0.481042\pi\) | |||||||
\(72\) | −2.99760 | −0.353270 | ||||||||
\(73\) | −6.80012 | −0.795894 | −0.397947 | − | 0.917408i | \(-0.630277\pi\) | ||||
−0.397947 | + | 0.917408i | \(0.630277\pi\) | |||||||
\(74\) | 3.67532 | 0.427247 | ||||||||
\(75\) | −0.230427 | −0.0266074 | ||||||||
\(76\) | −0.355291 | −0.0407547 | ||||||||
\(77\) | −3.83868 | −0.437458 | ||||||||
\(78\) | 0.261682 | 0.0296296 | ||||||||
\(79\) | 5.87430 | 0.660910 | 0.330455 | − | 0.943822i | \(-0.392798\pi\) | ||||
0.330455 | + | 0.943822i | \(0.392798\pi\) | |||||||
\(80\) | 0.547018 | 0.0611585 | ||||||||
\(81\) | 8.97838 | 0.997598 | ||||||||
\(82\) | 5.45355 | 0.602244 | ||||||||
\(83\) | −10.5420 | −1.15713 | −0.578565 | − | 0.815636i | \(-0.696387\pi\) | ||||
−0.578565 | + | 0.815636i | \(0.696387\pi\) | |||||||
\(84\) | −0.221284 | −0.0241440 | ||||||||
\(85\) | −1.20253 | −0.130433 | ||||||||
\(86\) | −4.54506 | −0.490106 | ||||||||
\(87\) | −0.0878042 | −0.00941360 | ||||||||
\(88\) | 0.850349 | 0.0906475 | ||||||||
\(89\) | 8.57054 | 0.908475 | 0.454238 | − | 0.890881i | \(-0.349912\pi\) | ||||
0.454238 | + | 0.890881i | \(0.349912\pi\) | |||||||
\(90\) | −1.63974 | −0.172844 | ||||||||
\(91\) | −24.0987 | −2.52623 | ||||||||
\(92\) | 4.91805 | 0.512742 | ||||||||
\(93\) | 0.521651 | 0.0540926 | ||||||||
\(94\) | 5.16120 | 0.532337 | ||||||||
\(95\) | −0.194351 | −0.0199400 | ||||||||
\(96\) | 0.0490190 | 0.00500298 | ||||||||
\(97\) | 1.16982 | 0.118777 | 0.0593885 | − | 0.998235i | \(-0.481085\pi\) | ||||
0.0593885 | + | 0.998235i | \(0.481085\pi\) | |||||||
\(98\) | 13.3784 | 1.35142 | ||||||||
\(99\) | −2.54900 | −0.256184 | ||||||||
\(100\) | −4.70077 | −0.470077 | ||||||||
\(101\) | 18.0610 | 1.79714 | 0.898568 | − | 0.438833i | \(-0.144608\pi\) | ||||
0.898568 | + | 0.438833i | \(0.144608\pi\) | |||||||
\(102\) | −0.107760 | −0.0106698 | ||||||||
\(103\) | 14.5396 | 1.43263 | 0.716314 | − | 0.697778i | \(-0.245828\pi\) | ||||
0.716314 | + | 0.697778i | \(0.245828\pi\) | |||||||
\(104\) | 5.33838 | 0.523471 | ||||||||
\(105\) | −0.121046 | −0.0118129 | ||||||||
\(106\) | 3.22422 | 0.313164 | ||||||||
\(107\) | 15.7386 | 1.52151 | 0.760756 | − | 0.649038i | \(-0.224828\pi\) | ||||
0.760756 | + | 0.649038i | \(0.224828\pi\) | |||||||
\(108\) | −0.293996 | −0.0282898 | ||||||||
\(109\) | 16.9779 | 1.62619 | 0.813094 | − | 0.582132i | \(-0.197782\pi\) | ||||
0.813094 | + | 0.582132i | \(0.197782\pi\) | |||||||
\(110\) | 0.465156 | 0.0443509 | ||||||||
\(111\) | 0.180160 | 0.0171001 | ||||||||
\(112\) | −4.51424 | −0.426556 | ||||||||
\(113\) | 13.4910 | 1.26912 | 0.634561 | − | 0.772873i | \(-0.281181\pi\) | ||||
0.634561 | + | 0.772873i | \(0.281181\pi\) | |||||||
\(114\) | −0.0174160 | −0.00163116 | ||||||||
\(115\) | 2.69026 | 0.250868 | ||||||||
\(116\) | −1.79123 | −0.166311 | ||||||||
\(117\) | −16.0023 | −1.47941 | ||||||||
\(118\) | −1.10040 | −0.101300 | ||||||||
\(119\) | 9.92382 | 0.909715 | ||||||||
\(120\) | 0.0268143 | 0.00244780 | ||||||||
\(121\) | −10.2769 | −0.934264 | ||||||||
\(122\) | −5.65294 | −0.511793 | ||||||||
\(123\) | 0.267327 | 0.0241041 | ||||||||
\(124\) | 10.6418 | 0.955663 | ||||||||
\(125\) | −5.30650 | −0.474628 | ||||||||
\(126\) | 13.5319 | 1.20552 | ||||||||
\(127\) | 3.46526 | 0.307492 | 0.153746 | − | 0.988110i | \(-0.450866\pi\) | ||||
0.153746 | + | 0.988110i | \(0.450866\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −0.222794 | −0.0196159 | ||||||||
\(130\) | 2.92019 | 0.256118 | ||||||||
\(131\) | −14.4600 | −1.26338 | −0.631688 | − | 0.775222i | \(-0.717638\pi\) | ||||
−0.631688 | + | 0.775222i | \(0.717638\pi\) | |||||||
\(132\) | 0.0416832 | 0.00362806 | ||||||||
\(133\) | 1.60387 | 0.139073 | ||||||||
\(134\) | 7.10303 | 0.613608 | ||||||||
\(135\) | −0.160821 | −0.0138413 | ||||||||
\(136\) | −2.19834 | −0.188506 | ||||||||
\(137\) | −0.325206 | −0.0277842 | −0.0138921 | − | 0.999903i | \(-0.504422\pi\) | ||||
−0.0138921 | + | 0.999903i | \(0.504422\pi\) | |||||||
\(138\) | 0.241078 | 0.0205219 | ||||||||
\(139\) | −1.59207 | −0.135038 | −0.0675190 | − | 0.997718i | \(-0.521508\pi\) | ||||
−0.0675190 | + | 0.997718i | \(0.521508\pi\) | |||||||
\(140\) | −2.46937 | −0.208700 | ||||||||
\(141\) | 0.252997 | 0.0213062 | ||||||||
\(142\) | 1.00310 | 0.0841787 | ||||||||
\(143\) | 4.53948 | 0.379611 | ||||||||
\(144\) | −2.99760 | −0.249800 | ||||||||
\(145\) | −0.979835 | −0.0813709 | ||||||||
\(146\) | −6.80012 | −0.562782 | ||||||||
\(147\) | 0.655795 | 0.0540891 | ||||||||
\(148\) | 3.67532 | 0.302109 | ||||||||
\(149\) | −15.9572 | −1.30726 | −0.653630 | − | 0.756814i | \(-0.726755\pi\) | ||||
−0.653630 | + | 0.756814i | \(0.726755\pi\) | |||||||
\(150\) | −0.230427 | −0.0188143 | ||||||||
\(151\) | 9.08255 | 0.739127 | 0.369564 | − | 0.929205i | \(-0.379507\pi\) | ||||
0.369564 | + | 0.929205i | \(0.379507\pi\) | |||||||
\(152\) | −0.355291 | −0.0288179 | ||||||||
\(153\) | 6.58972 | 0.532748 | ||||||||
\(154\) | −3.83868 | −0.309330 | ||||||||
\(155\) | 5.82126 | 0.467575 | ||||||||
\(156\) | 0.261682 | 0.0209513 | ||||||||
\(157\) | −18.4756 | −1.47451 | −0.737257 | − | 0.675613i | \(-0.763879\pi\) | ||||
−0.737257 | + | 0.675613i | \(0.763879\pi\) | |||||||
\(158\) | 5.87430 | 0.467334 | ||||||||
\(159\) | 0.158048 | 0.0125340 | ||||||||
\(160\) | 0.547018 | 0.0432456 | ||||||||
\(161\) | −22.2013 | −1.74971 | ||||||||
\(162\) | 8.97838 | 0.705408 | ||||||||
\(163\) | 19.2850 | 1.51052 | 0.755260 | − | 0.655426i | \(-0.227511\pi\) | ||||
0.755260 | + | 0.655426i | \(0.227511\pi\) | |||||||
\(164\) | 5.45355 | 0.425851 | ||||||||
\(165\) | 0.0228015 | 0.00177509 | ||||||||
\(166\) | −10.5420 | −0.818214 | ||||||||
\(167\) | −1.56342 | −0.120981 | −0.0604904 | − | 0.998169i | \(-0.519266\pi\) | ||||
−0.0604904 | + | 0.998169i | \(0.519266\pi\) | |||||||
\(168\) | −0.221284 | −0.0170724 | ||||||||
\(169\) | 15.4983 | 1.19218 | ||||||||
\(170\) | −1.20253 | −0.0922298 | ||||||||
\(171\) | 1.06502 | 0.0814441 | ||||||||
\(172\) | −4.54506 | −0.346557 | ||||||||
\(173\) | 5.22013 | 0.396879 | 0.198440 | − | 0.980113i | \(-0.436413\pi\) | ||||
0.198440 | + | 0.980113i | \(0.436413\pi\) | |||||||
\(174\) | −0.0878042 | −0.00665642 | ||||||||
\(175\) | 21.2204 | 1.60411 | ||||||||
\(176\) | 0.850349 | 0.0640974 | ||||||||
\(177\) | −0.0539407 | −0.00405443 | ||||||||
\(178\) | 8.57054 | 0.642389 | ||||||||
\(179\) | 14.1956 | 1.06103 | 0.530515 | − | 0.847675i | \(-0.321999\pi\) | ||||
0.530515 | + | 0.847675i | \(0.321999\pi\) | |||||||
\(180\) | −1.63974 | −0.122219 | ||||||||
\(181\) | 17.6045 | 1.30853 | 0.654266 | − | 0.756265i | \(-0.272978\pi\) | ||||
0.654266 | + | 0.756265i | \(0.272978\pi\) | |||||||
\(182\) | −24.0987 | −1.78632 | ||||||||
\(183\) | −0.277101 | −0.0204839 | ||||||||
\(184\) | 4.91805 | 0.362564 | ||||||||
\(185\) | 2.01047 | 0.147812 | ||||||||
\(186\) | 0.521651 | 0.0382493 | ||||||||
\(187\) | −1.86935 | −0.136700 | ||||||||
\(188\) | 5.16120 | 0.376419 | ||||||||
\(189\) | 1.32717 | 0.0965374 | ||||||||
\(190\) | −0.194351 | −0.0140997 | ||||||||
\(191\) | 0.544050 | 0.0393661 | 0.0196830 | − | 0.999806i | \(-0.493734\pi\) | ||||
0.0196830 | + | 0.999806i | \(0.493734\pi\) | |||||||
\(192\) | 0.0490190 | 0.00353764 | ||||||||
\(193\) | −18.0871 | −1.30194 | −0.650969 | − | 0.759105i | \(-0.725637\pi\) | ||||
−0.650969 | + | 0.759105i | \(0.725637\pi\) | |||||||
\(194\) | 1.16982 | 0.0839881 | ||||||||
\(195\) | 0.143145 | 0.0102508 | ||||||||
\(196\) | 13.3784 | 0.955599 | ||||||||
\(197\) | −8.52995 | −0.607734 | −0.303867 | − | 0.952715i | \(-0.598278\pi\) | ||||
−0.303867 | + | 0.952715i | \(0.598278\pi\) | |||||||
\(198\) | −2.54900 | −0.181150 | ||||||||
\(199\) | −18.0997 | −1.28305 | −0.641525 | − | 0.767102i | \(-0.721698\pi\) | ||||
−0.641525 | + | 0.767102i | \(0.721698\pi\) | |||||||
\(200\) | −4.70077 | −0.332395 | ||||||||
\(201\) | 0.348183 | 0.0245589 | ||||||||
\(202\) | 18.0610 | 1.27077 | ||||||||
\(203\) | 8.08604 | 0.567529 | ||||||||
\(204\) | −0.107760 | −0.00754472 | ||||||||
\(205\) | 2.98319 | 0.208355 | ||||||||
\(206\) | 14.5396 | 1.01302 | ||||||||
\(207\) | −14.7423 | −1.02466 | ||||||||
\(208\) | 5.33838 | 0.370150 | ||||||||
\(209\) | −0.302122 | −0.0208982 | ||||||||
\(210\) | −0.121046 | −0.00835298 | ||||||||
\(211\) | 1.60334 | 0.110379 | 0.0551894 | − | 0.998476i | \(-0.482424\pi\) | ||||
0.0551894 | + | 0.998476i | \(0.482424\pi\) | |||||||
\(212\) | 3.22422 | 0.221441 | ||||||||
\(213\) | 0.0491712 | 0.00336915 | ||||||||
\(214\) | 15.7386 | 1.07587 | ||||||||
\(215\) | −2.48623 | −0.169559 | ||||||||
\(216\) | −0.293996 | −0.0200039 | ||||||||
\(217\) | −48.0397 | −3.26115 | ||||||||
\(218\) | 16.9779 | 1.14989 | ||||||||
\(219\) | −0.333335 | −0.0225247 | ||||||||
\(220\) | 0.465156 | 0.0313608 | ||||||||
\(221\) | −11.7355 | −0.789418 | ||||||||
\(222\) | 0.180160 | 0.0120916 | ||||||||
\(223\) | 16.8365 | 1.12746 | 0.563728 | − | 0.825960i | \(-0.309367\pi\) | ||||
0.563728 | + | 0.825960i | \(0.309367\pi\) | |||||||
\(224\) | −4.51424 | −0.301621 | ||||||||
\(225\) | 14.0910 | 0.939401 | ||||||||
\(226\) | 13.4910 | 0.897405 | ||||||||
\(227\) | −18.7675 | −1.24564 | −0.622821 | − | 0.782365i | \(-0.714013\pi\) | ||||
−0.622821 | + | 0.782365i | \(0.714013\pi\) | |||||||
\(228\) | −0.0174160 | −0.00115340 | ||||||||
\(229\) | 9.78439 | 0.646571 | 0.323285 | − | 0.946302i | \(-0.395213\pi\) | ||||
0.323285 | + | 0.946302i | \(0.395213\pi\) | |||||||
\(230\) | 2.69026 | 0.177391 | ||||||||
\(231\) | −0.188168 | −0.0123806 | ||||||||
\(232\) | −1.79123 | −0.117600 | ||||||||
\(233\) | −29.9794 | −1.96402 | −0.982008 | − | 0.188841i | \(-0.939527\pi\) | ||||
−0.982008 | + | 0.188841i | \(0.939527\pi\) | |||||||
\(234\) | −16.0023 | −1.04610 | ||||||||
\(235\) | 2.82327 | 0.184170 | ||||||||
\(236\) | −1.10040 | −0.0716303 | ||||||||
\(237\) | 0.287952 | 0.0187045 | ||||||||
\(238\) | 9.92382 | 0.643266 | ||||||||
\(239\) | −2.66434 | −0.172342 | −0.0861709 | − | 0.996280i | \(-0.527463\pi\) | ||||
−0.0861709 | + | 0.996280i | \(0.527463\pi\) | |||||||
\(240\) | 0.0268143 | 0.00173085 | ||||||||
\(241\) | −27.4438 | −1.76781 | −0.883907 | − | 0.467663i | \(-0.845096\pi\) | ||||
−0.883907 | + | 0.467663i | \(0.845096\pi\) | |||||||
\(242\) | −10.2769 | −0.660625 | ||||||||
\(243\) | 1.32210 | 0.0848127 | ||||||||
\(244\) | −5.65294 | −0.361892 | ||||||||
\(245\) | 7.31822 | 0.467544 | ||||||||
\(246\) | 0.267327 | 0.0170442 | ||||||||
\(247\) | −1.89668 | −0.120683 | ||||||||
\(248\) | 10.6418 | 0.675756 | ||||||||
\(249\) | −0.516756 | −0.0327481 | ||||||||
\(250\) | −5.30650 | −0.335612 | ||||||||
\(251\) | 26.0953 | 1.64712 | 0.823560 | − | 0.567230i | \(-0.191985\pi\) | ||||
0.823560 | + | 0.567230i | \(0.191985\pi\) | |||||||
\(252\) | 13.5319 | 0.852428 | ||||||||
\(253\) | 4.18206 | 0.262924 | ||||||||
\(254\) | 3.46526 | 0.217430 | ||||||||
\(255\) | −0.0589468 | −0.00369139 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.5155 | −0.843074 | −0.421537 | − | 0.906811i | \(-0.638509\pi\) | ||||
−0.421537 | + | 0.906811i | \(0.638509\pi\) | |||||||
\(258\) | −0.222794 | −0.0138705 | ||||||||
\(259\) | −16.5913 | −1.03093 | ||||||||
\(260\) | 2.92019 | 0.181103 | ||||||||
\(261\) | 5.36938 | 0.332356 | ||||||||
\(262\) | −14.4600 | −0.893342 | ||||||||
\(263\) | 18.1005 | 1.11612 | 0.558061 | − | 0.829800i | \(-0.311545\pi\) | ||||
0.558061 | + | 0.829800i | \(0.311545\pi\) | |||||||
\(264\) | 0.0416832 | 0.00256542 | ||||||||
\(265\) | 1.76371 | 0.108344 | ||||||||
\(266\) | 1.60387 | 0.0983397 | ||||||||
\(267\) | 0.420119 | 0.0257109 | ||||||||
\(268\) | 7.10303 | 0.433886 | ||||||||
\(269\) | 2.39550 | 0.146056 | 0.0730282 | − | 0.997330i | \(-0.476734\pi\) | ||||
0.0730282 | + | 0.997330i | \(0.476734\pi\) | |||||||
\(270\) | −0.160821 | −0.00978727 | ||||||||
\(271\) | −23.5917 | −1.43309 | −0.716546 | − | 0.697540i | \(-0.754278\pi\) | ||||
−0.716546 | + | 0.697540i | \(0.754278\pi\) | |||||||
\(272\) | −2.19834 | −0.133294 | ||||||||
\(273\) | −1.18130 | −0.0714953 | ||||||||
\(274\) | −0.325206 | −0.0196464 | ||||||||
\(275\) | −3.99729 | −0.241046 | ||||||||
\(276\) | 0.241078 | 0.0145112 | ||||||||
\(277\) | 22.1683 | 1.33196 | 0.665982 | − | 0.745968i | \(-0.268013\pi\) | ||||
0.665982 | + | 0.745968i | \(0.268013\pi\) | |||||||
\(278\) | −1.59207 | −0.0954863 | ||||||||
\(279\) | −31.8999 | −1.90979 | ||||||||
\(280\) | −2.46937 | −0.147573 | ||||||||
\(281\) | 9.29990 | 0.554785 | 0.277393 | − | 0.960757i | \(-0.410530\pi\) | ||||
0.277393 | + | 0.960757i | \(0.410530\pi\) | |||||||
\(282\) | 0.252997 | 0.0150657 | ||||||||
\(283\) | 23.5009 | 1.39698 | 0.698490 | − | 0.715620i | \(-0.253856\pi\) | ||||
0.698490 | + | 0.715620i | \(0.253856\pi\) | |||||||
\(284\) | 1.00310 | 0.0595233 | ||||||||
\(285\) | −0.00952688 | −0.000564324 0 | ||||||||
\(286\) | 4.53948 | 0.268425 | ||||||||
\(287\) | −24.6187 | −1.45319 | ||||||||
\(288\) | −2.99760 | −0.176635 | ||||||||
\(289\) | −12.1673 | −0.715725 | ||||||||
\(290\) | −0.979835 | −0.0575379 | ||||||||
\(291\) | 0.0573433 | 0.00336152 | ||||||||
\(292\) | −6.80012 | −0.397947 | ||||||||
\(293\) | −11.1623 | −0.652106 | −0.326053 | − | 0.945351i | \(-0.605719\pi\) | ||||
−0.326053 | + | 0.945351i | \(0.605719\pi\) | |||||||
\(294\) | 0.655795 | 0.0382467 | ||||||||
\(295\) | −0.601942 | −0.0350464 | ||||||||
\(296\) | 3.67532 | 0.213623 | ||||||||
\(297\) | −0.249999 | −0.0145064 | ||||||||
\(298\) | −15.9572 | −0.924373 | ||||||||
\(299\) | 26.2544 | 1.51833 | ||||||||
\(300\) | −0.230427 | −0.0133037 | ||||||||
\(301\) | 20.5175 | 1.18261 | ||||||||
\(302\) | 9.08255 | 0.522642 | ||||||||
\(303\) | 0.885332 | 0.0508610 | ||||||||
\(304\) | −0.355291 | −0.0203774 | ||||||||
\(305\) | −3.09226 | −0.177062 | ||||||||
\(306\) | 6.58972 | 0.376709 | ||||||||
\(307\) | 3.01939 | 0.172326 | 0.0861629 | − | 0.996281i | \(-0.472539\pi\) | ||||
0.0861629 | + | 0.996281i | \(0.472539\pi\) | |||||||
\(308\) | −3.83868 | −0.218729 | ||||||||
\(309\) | 0.712716 | 0.0405450 | ||||||||
\(310\) | 5.82126 | 0.330626 | ||||||||
\(311\) | −20.1603 | −1.14319 | −0.571593 | − | 0.820537i | \(-0.693674\pi\) | ||||
−0.571593 | + | 0.820537i | \(0.693674\pi\) | |||||||
\(312\) | 0.261682 | 0.0148148 | ||||||||
\(313\) | 0.175370 | 0.00991250 | 0.00495625 | − | 0.999988i | \(-0.498422\pi\) | ||||
0.00495625 | + | 0.999988i | \(0.498422\pi\) | |||||||
\(314\) | −18.4756 | −1.04264 | ||||||||
\(315\) | 7.40219 | 0.417066 | ||||||||
\(316\) | 5.87430 | 0.330455 | ||||||||
\(317\) | −23.9922 | −1.34754 | −0.673769 | − | 0.738942i | \(-0.735326\pi\) | ||||
−0.673769 | + | 0.738942i | \(0.735326\pi\) | |||||||
\(318\) | 0.158048 | 0.00886290 | ||||||||
\(319\) | −1.52317 | −0.0852811 | ||||||||
\(320\) | 0.547018 | 0.0305793 | ||||||||
\(321\) | 0.771492 | 0.0430605 | ||||||||
\(322\) | −22.2013 | −1.23723 | ||||||||
\(323\) | 0.781050 | 0.0434588 | ||||||||
\(324\) | 8.97838 | 0.498799 | ||||||||
\(325\) | −25.0945 | −1.39199 | ||||||||
\(326\) | 19.2850 | 1.06810 | ||||||||
\(327\) | 0.832239 | 0.0460229 | ||||||||
\(328\) | 5.45355 | 0.301122 | ||||||||
\(329\) | −23.2989 | −1.28451 | ||||||||
\(330\) | 0.0228015 | 0.00125518 | ||||||||
\(331\) | −2.13517 | −0.117359 | −0.0586797 | − | 0.998277i | \(-0.518689\pi\) | ||||
−0.0586797 | + | 0.998277i | \(0.518689\pi\) | |||||||
\(332\) | −10.5420 | −0.578565 | ||||||||
\(333\) | −11.0171 | −0.603735 | ||||||||
\(334\) | −1.56342 | −0.0855463 | ||||||||
\(335\) | 3.88549 | 0.212287 | ||||||||
\(336\) | −0.221284 | −0.0120720 | ||||||||
\(337\) | −25.4435 | −1.38600 | −0.692999 | − | 0.720939i | \(-0.743711\pi\) | ||||
−0.692999 | + | 0.720939i | \(0.743711\pi\) | |||||||
\(338\) | 15.4983 | 0.842996 | ||||||||
\(339\) | 0.661313 | 0.0359176 | ||||||||
\(340\) | −1.20253 | −0.0652163 | ||||||||
\(341\) | 9.04925 | 0.490044 | ||||||||
\(342\) | 1.06502 | 0.0575897 | ||||||||
\(343\) | −28.7936 | −1.55471 | ||||||||
\(344\) | −4.54506 | −0.245053 | ||||||||
\(345\) | 0.131874 | 0.00709986 | ||||||||
\(346\) | 5.22013 | 0.280636 | ||||||||
\(347\) | −23.1490 | −1.24270 | −0.621352 | − | 0.783531i | \(-0.713416\pi\) | ||||
−0.621352 | + | 0.783531i | \(0.713416\pi\) | |||||||
\(348\) | −0.0878042 | −0.00470680 | ||||||||
\(349\) | −13.4485 | −0.719884 | −0.359942 | − | 0.932975i | \(-0.617204\pi\) | ||||
−0.359942 | + | 0.932975i | \(0.617204\pi\) | |||||||
\(350\) | 21.2204 | 1.13428 | ||||||||
\(351\) | −1.56946 | −0.0837717 | ||||||||
\(352\) | 0.850349 | 0.0453237 | ||||||||
\(353\) | −2.93296 | −0.156106 | −0.0780529 | − | 0.996949i | \(-0.524870\pi\) | ||||
−0.0780529 | + | 0.996949i | \(0.524870\pi\) | |||||||
\(354\) | −0.0539407 | −0.00286692 | ||||||||
\(355\) | 0.548717 | 0.0291229 | ||||||||
\(356\) | 8.57054 | 0.454238 | ||||||||
\(357\) | 0.486455 | 0.0257460 | ||||||||
\(358\) | 14.1956 | 0.750262 | ||||||||
\(359\) | 13.6695 | 0.721449 | 0.360725 | − | 0.932672i | \(-0.382529\pi\) | ||||
0.360725 | + | 0.932672i | \(0.382529\pi\) | |||||||
\(360\) | −1.63974 | −0.0864219 | ||||||||
\(361\) | −18.8738 | −0.993356 | ||||||||
\(362\) | 17.6045 | 0.925272 | ||||||||
\(363\) | −0.503763 | −0.0264407 | ||||||||
\(364\) | −24.0987 | −1.26312 | ||||||||
\(365\) | −3.71979 | −0.194703 | ||||||||
\(366\) | −0.277101 | −0.0144843 | ||||||||
\(367\) | 11.5125 | 0.600949 | 0.300474 | − | 0.953790i | \(-0.402855\pi\) | ||||
0.300474 | + | 0.953790i | \(0.402855\pi\) | |||||||
\(368\) | 4.91805 | 0.256371 | ||||||||
\(369\) | −16.3476 | −0.851019 | ||||||||
\(370\) | 2.01047 | 0.104519 | ||||||||
\(371\) | −14.5549 | −0.755654 | ||||||||
\(372\) | 0.521651 | 0.0270463 | ||||||||
\(373\) | −1.32606 | −0.0686607 | −0.0343303 | − | 0.999411i | \(-0.510930\pi\) | ||||
−0.0343303 | + | 0.999411i | \(0.510930\pi\) | |||||||
\(374\) | −1.86935 | −0.0966618 | ||||||||
\(375\) | −0.260119 | −0.0134325 | ||||||||
\(376\) | 5.16120 | 0.266168 | ||||||||
\(377\) | −9.56226 | −0.492481 | ||||||||
\(378\) | 1.32717 | 0.0682622 | ||||||||
\(379\) | −19.0090 | −0.976426 | −0.488213 | − | 0.872724i | \(-0.662351\pi\) | ||||
−0.488213 | + | 0.872724i | \(0.662351\pi\) | |||||||
\(380\) | −0.194351 | −0.00996999 | ||||||||
\(381\) | 0.169864 | 0.00870237 | ||||||||
\(382\) | 0.544050 | 0.0278360 | ||||||||
\(383\) | 11.7329 | 0.599521 | 0.299760 | − | 0.954015i | \(-0.403093\pi\) | ||||
0.299760 | + | 0.954015i | \(0.403093\pi\) | |||||||
\(384\) | 0.0490190 | 0.00250149 | ||||||||
\(385\) | −2.09983 | −0.107017 | ||||||||
\(386\) | −18.0871 | −0.920609 | ||||||||
\(387\) | 13.6242 | 0.692559 | ||||||||
\(388\) | 1.16982 | 0.0593885 | ||||||||
\(389\) | 24.3102 | 1.23257 | 0.616287 | − | 0.787522i | \(-0.288636\pi\) | ||||
0.616287 | + | 0.787522i | \(0.288636\pi\) | |||||||
\(390\) | 0.143145 | 0.00724842 | ||||||||
\(391\) | −10.8115 | −0.546762 | ||||||||
\(392\) | 13.3784 | 0.675711 | ||||||||
\(393\) | −0.708815 | −0.0357550 | ||||||||
\(394\) | −8.52995 | −0.429732 | ||||||||
\(395\) | 3.21335 | 0.161681 | ||||||||
\(396\) | −2.54900 | −0.128092 | ||||||||
\(397\) | 2.85651 | 0.143364 | 0.0716822 | − | 0.997428i | \(-0.477163\pi\) | ||||
0.0716822 | + | 0.997428i | \(0.477163\pi\) | |||||||
\(398\) | −18.0997 | −0.907254 | ||||||||
\(399\) | 0.0786201 | 0.00393593 | ||||||||
\(400\) | −4.70077 | −0.235039 | ||||||||
\(401\) | 12.4445 | 0.621448 | 0.310724 | − | 0.950500i | \(-0.399428\pi\) | ||||
0.310724 | + | 0.950500i | \(0.399428\pi\) | |||||||
\(402\) | 0.348183 | 0.0173658 | ||||||||
\(403\) | 56.8100 | 2.82991 | ||||||||
\(404\) | 18.0610 | 0.898568 | ||||||||
\(405\) | 4.91134 | 0.244046 | ||||||||
\(406\) | 8.08604 | 0.401304 | ||||||||
\(407\) | 3.12530 | 0.154915 | ||||||||
\(408\) | −0.107760 | −0.00533492 | ||||||||
\(409\) | −13.0403 | −0.644804 | −0.322402 | − | 0.946603i | \(-0.604490\pi\) | ||||
−0.322402 | + | 0.946603i | \(0.604490\pi\) | |||||||
\(410\) | 2.98319 | 0.147329 | ||||||||
\(411\) | −0.0159413 | −0.000786325 0 | ||||||||
\(412\) | 14.5396 | 0.716314 | ||||||||
\(413\) | 4.96750 | 0.244434 | ||||||||
\(414\) | −14.7423 | −0.724546 | ||||||||
\(415\) | −5.76664 | −0.283073 | ||||||||
\(416\) | 5.33838 | 0.261736 | ||||||||
\(417\) | −0.0780419 | −0.00382173 | ||||||||
\(418\) | −0.302122 | −0.0147772 | ||||||||
\(419\) | −7.28880 | −0.356081 | −0.178041 | − | 0.984023i | \(-0.556976\pi\) | ||||
−0.178041 | + | 0.984023i | \(0.556976\pi\) | |||||||
\(420\) | −0.121046 | −0.00590645 | ||||||||
\(421\) | 29.7670 | 1.45075 | 0.725377 | − | 0.688351i | \(-0.241665\pi\) | ||||
0.725377 | + | 0.688351i | \(0.241665\pi\) | |||||||
\(422\) | 1.60334 | 0.0780496 | ||||||||
\(423\) | −15.4712 | −0.752235 | ||||||||
\(424\) | 3.22422 | 0.156582 | ||||||||
\(425\) | 10.3339 | 0.501266 | ||||||||
\(426\) | 0.0491712 | 0.00238235 | ||||||||
\(427\) | 25.5187 | 1.23494 | ||||||||
\(428\) | 15.7386 | 0.760756 | ||||||||
\(429\) | 0.222521 | 0.0107434 | ||||||||
\(430\) | −2.48623 | −0.119897 | ||||||||
\(431\) | 14.2404 | 0.685935 | 0.342968 | − | 0.939347i | \(-0.388568\pi\) | ||||
0.342968 | + | 0.939347i | \(0.388568\pi\) | |||||||
\(432\) | −0.293996 | −0.0141449 | ||||||||
\(433\) | −0.908372 | −0.0436536 | −0.0218268 | − | 0.999762i | \(-0.506948\pi\) | ||||
−0.0218268 | + | 0.999762i | \(0.506948\pi\) | |||||||
\(434\) | −48.0397 | −2.30598 | ||||||||
\(435\) | −0.0480305 | −0.00230289 | ||||||||
\(436\) | 16.9779 | 0.813094 | ||||||||
\(437\) | −1.74734 | −0.0835867 | ||||||||
\(438\) | −0.333335 | −0.0159274 | ||||||||
\(439\) | 24.0351 | 1.14713 | 0.573567 | − | 0.819159i | \(-0.305559\pi\) | ||||
0.573567 | + | 0.819159i | \(0.305559\pi\) | |||||||
\(440\) | 0.465156 | 0.0221755 | ||||||||
\(441\) | −40.1030 | −1.90967 | ||||||||
\(442\) | −11.7355 | −0.558203 | ||||||||
\(443\) | 7.12066 | 0.338313 | 0.169156 | − | 0.985589i | \(-0.445896\pi\) | ||||
0.169156 | + | 0.985589i | \(0.445896\pi\) | |||||||
\(444\) | 0.180160 | 0.00855003 | ||||||||
\(445\) | 4.68824 | 0.222244 | ||||||||
\(446\) | 16.8365 | 0.797232 | ||||||||
\(447\) | −0.782203 | −0.0369969 | ||||||||
\(448\) | −4.51424 | −0.213278 | ||||||||
\(449\) | 12.7532 | 0.601862 | 0.300931 | − | 0.953646i | \(-0.402703\pi\) | ||||
0.300931 | + | 0.953646i | \(0.402703\pi\) | |||||||
\(450\) | 14.0910 | 0.664257 | ||||||||
\(451\) | 4.63742 | 0.218368 | ||||||||
\(452\) | 13.4910 | 0.634561 | ||||||||
\(453\) | 0.445217 | 0.0209181 | ||||||||
\(454\) | −18.7675 | −0.880801 | ||||||||
\(455\) | −13.1825 | −0.618003 | ||||||||
\(456\) | −0.0174160 | −0.000815580 0 | ||||||||
\(457\) | 24.8661 | 1.16319 | 0.581593 | − | 0.813480i | \(-0.302430\pi\) | ||||
0.581593 | + | 0.813480i | \(0.302430\pi\) | |||||||
\(458\) | 9.78439 | 0.457194 | ||||||||
\(459\) | 0.646302 | 0.0301668 | ||||||||
\(460\) | 2.69026 | 0.125434 | ||||||||
\(461\) | −32.8411 | −1.52956 | −0.764781 | − | 0.644291i | \(-0.777153\pi\) | ||||
−0.764781 | + | 0.644291i | \(0.777153\pi\) | |||||||
\(462\) | −0.188168 | −0.00875438 | ||||||||
\(463\) | 21.3501 | 0.992225 | 0.496113 | − | 0.868258i | \(-0.334760\pi\) | ||||
0.496113 | + | 0.868258i | \(0.334760\pi\) | |||||||
\(464\) | −1.79123 | −0.0831557 | ||||||||
\(465\) | 0.285352 | 0.0132329 | ||||||||
\(466\) | −29.9794 | −1.38877 | ||||||||
\(467\) | −31.2761 | −1.44728 | −0.723641 | − | 0.690176i | \(-0.757533\pi\) | ||||
−0.723641 | + | 0.690176i | \(0.757533\pi\) | |||||||
\(468\) | −16.0023 | −0.739707 | ||||||||
\(469\) | −32.0648 | −1.48061 | ||||||||
\(470\) | 2.82327 | 0.130228 | ||||||||
\(471\) | −0.905655 | −0.0417304 | ||||||||
\(472\) | −1.10040 | −0.0506502 | ||||||||
\(473\) | −3.86488 | −0.177707 | ||||||||
\(474\) | 0.287952 | 0.0132261 | ||||||||
\(475\) | 1.67014 | 0.0766314 | ||||||||
\(476\) | 9.92382 | 0.454857 | ||||||||
\(477\) | −9.66493 | −0.442527 | ||||||||
\(478\) | −2.66434 | −0.121864 | ||||||||
\(479\) | 30.3216 | 1.38543 | 0.692715 | − | 0.721211i | \(-0.256414\pi\) | ||||
0.692715 | + | 0.721211i | \(0.256414\pi\) | |||||||
\(480\) | 0.0268143 | 0.00122390 | ||||||||
\(481\) | 19.6202 | 0.894606 | ||||||||
\(482\) | −27.4438 | −1.25003 | ||||||||
\(483\) | −1.08828 | −0.0495186 | ||||||||
\(484\) | −10.2769 | −0.467132 | ||||||||
\(485\) | 0.639912 | 0.0290569 | ||||||||
\(486\) | 1.32210 | 0.0599716 | ||||||||
\(487\) | 23.4994 | 1.06486 | 0.532429 | − | 0.846474i | \(-0.321279\pi\) | ||||
0.532429 | + | 0.846474i | \(0.321279\pi\) | |||||||
\(488\) | −5.65294 | −0.255897 | ||||||||
\(489\) | 0.945332 | 0.0427494 | ||||||||
\(490\) | 7.31822 | 0.330604 | ||||||||
\(491\) | −16.6852 | −0.752994 | −0.376497 | − | 0.926418i | \(-0.622871\pi\) | ||||
−0.376497 | + | 0.926418i | \(0.622871\pi\) | |||||||
\(492\) | 0.267327 | 0.0120521 | ||||||||
\(493\) | 3.93772 | 0.177346 | ||||||||
\(494\) | −1.89668 | −0.0853357 | ||||||||
\(495\) | −1.39435 | −0.0626714 | ||||||||
\(496\) | 10.6418 | 0.477831 | ||||||||
\(497\) | −4.52826 | −0.203120 | ||||||||
\(498\) | −0.516756 | −0.0231564 | ||||||||
\(499\) | 20.2918 | 0.908386 | 0.454193 | − | 0.890903i | \(-0.349928\pi\) | ||||
0.454193 | + | 0.890903i | \(0.349928\pi\) | |||||||
\(500\) | −5.30650 | −0.237314 | ||||||||
\(501\) | −0.0766370 | −0.00342389 | ||||||||
\(502\) | 26.0953 | 1.16469 | ||||||||
\(503\) | −3.68169 | −0.164159 | −0.0820793 | − | 0.996626i | \(-0.526156\pi\) | ||||
−0.0820793 | + | 0.996626i | \(0.526156\pi\) | |||||||
\(504\) | 13.5319 | 0.602758 | ||||||||
\(505\) | 9.87970 | 0.439641 | ||||||||
\(506\) | 4.18206 | 0.185915 | ||||||||
\(507\) | 0.759711 | 0.0337399 | ||||||||
\(508\) | 3.46526 | 0.153746 | ||||||||
\(509\) | 22.8932 | 1.01473 | 0.507363 | − | 0.861733i | \(-0.330620\pi\) | ||||
0.507363 | + | 0.861733i | \(0.330620\pi\) | |||||||
\(510\) | −0.0589468 | −0.00261021 | ||||||||
\(511\) | 30.6974 | 1.35797 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0.104454 | 0.00461177 | ||||||||
\(514\) | −13.5155 | −0.596143 | ||||||||
\(515\) | 7.95342 | 0.350470 | ||||||||
\(516\) | −0.222794 | −0.00980796 | ||||||||
\(517\) | 4.38882 | 0.193020 | ||||||||
\(518\) | −16.5913 | −0.728979 | ||||||||
\(519\) | 0.255885 | 0.0112321 | ||||||||
\(520\) | 2.92019 | 0.128059 | ||||||||
\(521\) | −2.33914 | −0.102480 | −0.0512398 | − | 0.998686i | \(-0.516317\pi\) | ||||
−0.0512398 | + | 0.998686i | \(0.516317\pi\) | |||||||
\(522\) | 5.36938 | 0.235011 | ||||||||
\(523\) | 31.1293 | 1.36119 | 0.680596 | − | 0.732659i | \(-0.261721\pi\) | ||||
0.680596 | + | 0.732659i | \(0.261721\pi\) | |||||||
\(524\) | −14.4600 | −0.631688 | ||||||||
\(525\) | 1.04020 | 0.0453982 | ||||||||
\(526\) | 18.1005 | 0.789218 | ||||||||
\(527\) | −23.3943 | −1.01907 | ||||||||
\(528\) | 0.0416832 | 0.00181403 | ||||||||
\(529\) | 1.18724 | 0.0516191 | ||||||||
\(530\) | 1.76371 | 0.0766107 | ||||||||
\(531\) | 3.29857 | 0.143146 | ||||||||
\(532\) | 1.60387 | 0.0695367 | ||||||||
\(533\) | 29.1131 | 1.26103 | ||||||||
\(534\) | 0.420119 | 0.0181803 | ||||||||
\(535\) | 8.60932 | 0.372214 | ||||||||
\(536\) | 7.10303 | 0.306804 | ||||||||
\(537\) | 0.695855 | 0.0300283 | ||||||||
\(538\) | 2.39550 | 0.103278 | ||||||||
\(539\) | 11.3763 | 0.490012 | ||||||||
\(540\) | −0.160821 | −0.00692064 | ||||||||
\(541\) | −9.67810 | −0.416094 | −0.208047 | − | 0.978119i | \(-0.566711\pi\) | ||||
−0.208047 | + | 0.978119i | \(0.566711\pi\) | |||||||
\(542\) | −23.5917 | −1.01335 | ||||||||
\(543\) | 0.862954 | 0.0370329 | ||||||||
\(544\) | −2.19834 | −0.0942528 | ||||||||
\(545\) | 9.28722 | 0.397821 | ||||||||
\(546\) | −1.18130 | −0.0505548 | ||||||||
\(547\) | −29.3785 | −1.25614 | −0.628068 | − | 0.778159i | \(-0.716154\pi\) | ||||
−0.628068 | + | 0.778159i | \(0.716154\pi\) | |||||||
\(548\) | −0.325206 | −0.0138921 | ||||||||
\(549\) | 16.9452 | 0.723205 | ||||||||
\(550\) | −3.99729 | −0.170445 | ||||||||
\(551\) | 0.636408 | 0.0271119 | ||||||||
\(552\) | 0.241078 | 0.0102610 | ||||||||
\(553\) | −26.5180 | −1.12766 | ||||||||
\(554\) | 22.1683 | 0.941841 | ||||||||
\(555\) | 0.0985510 | 0.00418326 | ||||||||
\(556\) | −1.59207 | −0.0675190 | ||||||||
\(557\) | −31.4834 | −1.33400 | −0.666998 | − | 0.745060i | \(-0.732421\pi\) | ||||
−0.666998 | + | 0.745060i | \(0.732421\pi\) | |||||||
\(558\) | −31.8999 | −1.35043 | ||||||||
\(559\) | −24.2632 | −1.02623 | ||||||||
\(560\) | −2.46937 | −0.104350 | ||||||||
\(561\) | −0.0916337 | −0.00386878 | ||||||||
\(562\) | 9.29990 | 0.392292 | ||||||||
\(563\) | 33.2445 | 1.40109 | 0.700543 | − | 0.713610i | \(-0.252941\pi\) | ||||
0.700543 | + | 0.713610i | \(0.252941\pi\) | |||||||
\(564\) | 0.252997 | 0.0106531 | ||||||||
\(565\) | 7.37980 | 0.310470 | ||||||||
\(566\) | 23.5009 | 0.987814 | ||||||||
\(567\) | −40.5306 | −1.70212 | ||||||||
\(568\) | 1.00310 | 0.0420893 | ||||||||
\(569\) | 3.44296 | 0.144336 | 0.0721681 | − | 0.997392i | \(-0.477008\pi\) | ||||
0.0721681 | + | 0.997392i | \(0.477008\pi\) | |||||||
\(570\) | −0.00952688 | −0.000399037 0 | ||||||||
\(571\) | 28.2755 | 1.18329 | 0.591646 | − | 0.806198i | \(-0.298478\pi\) | ||||
0.591646 | + | 0.806198i | \(0.298478\pi\) | |||||||
\(572\) | 4.53948 | 0.189805 | ||||||||
\(573\) | 0.0266688 | 0.00111410 | ||||||||
\(574\) | −24.6187 | −1.02756 | ||||||||
\(575\) | −23.1186 | −0.964114 | ||||||||
\(576\) | −2.99760 | −0.124900 | ||||||||
\(577\) | −28.0531 | −1.16786 | −0.583932 | − | 0.811802i | \(-0.698487\pi\) | ||||
−0.583932 | + | 0.811802i | \(0.698487\pi\) | |||||||
\(578\) | −12.1673 | −0.506094 | ||||||||
\(579\) | −0.886611 | −0.0368463 | ||||||||
\(580\) | −0.979835 | −0.0406854 | ||||||||
\(581\) | 47.5889 | 1.97432 | ||||||||
\(582\) | 0.0573433 | 0.00237696 | ||||||||
\(583\) | 2.74171 | 0.113550 | ||||||||
\(584\) | −6.80012 | −0.281391 | ||||||||
\(585\) | −8.75356 | −0.361915 | ||||||||
\(586\) | −11.1623 | −0.461109 | ||||||||
\(587\) | 6.14993 | 0.253835 | 0.126917 | − | 0.991913i | \(-0.459492\pi\) | ||||
0.126917 | + | 0.991913i | \(0.459492\pi\) | |||||||
\(588\) | 0.655795 | 0.0270445 | ||||||||
\(589\) | −3.78094 | −0.155791 | ||||||||
\(590\) | −0.601942 | −0.0247815 | ||||||||
\(591\) | −0.418129 | −0.0171995 | ||||||||
\(592\) | 3.67532 | 0.151055 | ||||||||
\(593\) | −8.74886 | −0.359273 | −0.179636 | − | 0.983733i | \(-0.557492\pi\) | ||||
−0.179636 | + | 0.983733i | \(0.557492\pi\) | |||||||
\(594\) | −0.249999 | −0.0102576 | ||||||||
\(595\) | 5.42851 | 0.222547 | ||||||||
\(596\) | −15.9572 | −0.653630 | ||||||||
\(597\) | −0.887227 | −0.0363118 | ||||||||
\(598\) | 26.2544 | 1.07362 | ||||||||
\(599\) | −24.5956 | −1.00495 | −0.502475 | − | 0.864592i | \(-0.667577\pi\) | ||||
−0.502475 | + | 0.864592i | \(0.667577\pi\) | |||||||
\(600\) | −0.230427 | −0.00940714 | ||||||||
\(601\) | −0.679717 | −0.0277262 | −0.0138631 | − | 0.999904i | \(-0.504413\pi\) | ||||
−0.0138631 | + | 0.999904i | \(0.504413\pi\) | |||||||
\(602\) | 20.5175 | 0.836230 | ||||||||
\(603\) | −21.2920 | −0.867078 | ||||||||
\(604\) | 9.08255 | 0.369564 | ||||||||
\(605\) | −5.62166 | −0.228553 | ||||||||
\(606\) | 0.885332 | 0.0359641 | ||||||||
\(607\) | 34.1855 | 1.38755 | 0.693773 | − | 0.720193i | \(-0.255947\pi\) | ||||
0.693773 | + | 0.720193i | \(0.255947\pi\) | |||||||
\(608\) | −0.355291 | −0.0144090 | ||||||||
\(609\) | 0.396369 | 0.0160617 | ||||||||
\(610\) | −3.09226 | −0.125202 | ||||||||
\(611\) | 27.5524 | 1.11465 | ||||||||
\(612\) | 6.58972 | 0.266374 | ||||||||
\(613\) | −32.7836 | −1.32412 | −0.662058 | − | 0.749452i | \(-0.730317\pi\) | ||||
−0.662058 | + | 0.749452i | \(0.730317\pi\) | |||||||
\(614\) | 3.01939 | 0.121853 | ||||||||
\(615\) | 0.146233 | 0.00589669 | ||||||||
\(616\) | −3.83868 | −0.154665 | ||||||||
\(617\) | 16.5536 | 0.666423 | 0.333212 | − | 0.942852i | \(-0.391868\pi\) | ||||
0.333212 | + | 0.942852i | \(0.391868\pi\) | |||||||
\(618\) | 0.712716 | 0.0286696 | ||||||||
\(619\) | 25.7728 | 1.03590 | 0.517948 | − | 0.855412i | \(-0.326696\pi\) | ||||
0.517948 | + | 0.855412i | \(0.326696\pi\) | |||||||
\(620\) | 5.82126 | 0.233788 | ||||||||
\(621\) | −1.44589 | −0.0580215 | ||||||||
\(622\) | −20.1603 | −0.808355 | ||||||||
\(623\) | −38.6895 | −1.55006 | ||||||||
\(624\) | 0.261682 | 0.0104757 | ||||||||
\(625\) | 20.6011 | 0.824044 | ||||||||
\(626\) | 0.175370 | 0.00700919 | ||||||||
\(627\) | −0.0148097 | −0.000591442 0 | ||||||||
\(628\) | −18.4756 | −0.737257 | ||||||||
\(629\) | −8.07958 | −0.322154 | ||||||||
\(630\) | 7.40219 | 0.294910 | ||||||||
\(631\) | −14.1508 | −0.563334 | −0.281667 | − | 0.959512i | \(-0.590887\pi\) | ||||
−0.281667 | + | 0.959512i | \(0.590887\pi\) | |||||||
\(632\) | 5.87430 | 0.233667 | ||||||||
\(633\) | 0.0785943 | 0.00312384 | ||||||||
\(634\) | −23.9922 | −0.952854 | ||||||||
\(635\) | 1.89556 | 0.0752230 | ||||||||
\(636\) | 0.158048 | 0.00626702 | ||||||||
\(637\) | 71.4189 | 2.82972 | ||||||||
\(638\) | −1.52317 | −0.0603028 | ||||||||
\(639\) | −3.00690 | −0.118951 | ||||||||
\(640\) | 0.547018 | 0.0216228 | ||||||||
\(641\) | −34.8017 | −1.37458 | −0.687292 | − | 0.726381i | \(-0.741201\pi\) | ||||
−0.687292 | + | 0.726381i | \(0.741201\pi\) | |||||||
\(642\) | 0.771492 | 0.0304484 | ||||||||
\(643\) | −28.4031 | −1.12011 | −0.560054 | − | 0.828456i | \(-0.689219\pi\) | ||||
−0.560054 | + | 0.828456i | \(0.689219\pi\) | |||||||
\(644\) | −22.2013 | −0.874853 | ||||||||
\(645\) | −0.121872 | −0.00479872 | ||||||||
\(646\) | 0.781050 | 0.0307300 | ||||||||
\(647\) | −37.8389 | −1.48760 | −0.743801 | − | 0.668401i | \(-0.766979\pi\) | ||||
−0.743801 | + | 0.668401i | \(0.766979\pi\) | |||||||
\(648\) | 8.97838 | 0.352704 | ||||||||
\(649\) | −0.935728 | −0.0367305 | ||||||||
\(650\) | −25.0945 | −0.984287 | ||||||||
\(651\) | −2.35486 | −0.0922941 | ||||||||
\(652\) | 19.2850 | 0.755260 | ||||||||
\(653\) | 33.0285 | 1.29250 | 0.646252 | − | 0.763124i | \(-0.276335\pi\) | ||||
0.646252 | + | 0.763124i | \(0.276335\pi\) | |||||||
\(654\) | 0.832239 | 0.0325431 | ||||||||
\(655\) | −7.90989 | −0.309065 | ||||||||
\(656\) | 5.45355 | 0.212925 | ||||||||
\(657\) | 20.3840 | 0.795257 | ||||||||
\(658\) | −23.2989 | −0.908286 | ||||||||
\(659\) | −1.72785 | −0.0673075 | −0.0336537 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336537 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(660\) | 0.0228015 | 0.000887547 0 | ||||||||
\(661\) | 7.06851 | 0.274933 | 0.137467 | − | 0.990506i | \(-0.456104\pi\) | ||||
0.137467 | + | 0.990506i | \(0.456104\pi\) | |||||||
\(662\) | −2.13517 | −0.0829856 | ||||||||
\(663\) | −0.575264 | −0.0223414 | ||||||||
\(664\) | −10.5420 | −0.409107 | ||||||||
\(665\) | 0.877347 | 0.0340221 | ||||||||
\(666\) | −11.0171 | −0.426905 | ||||||||
\(667\) | −8.80936 | −0.341100 | ||||||||
\(668\) | −1.56342 | −0.0604904 | ||||||||
\(669\) | 0.825309 | 0.0319083 | ||||||||
\(670\) | 3.88549 | 0.150109 | ||||||||
\(671\) | −4.80697 | −0.185571 | ||||||||
\(672\) | −0.221284 | −0.00853620 | ||||||||
\(673\) | 29.5820 | 1.14030 | 0.570151 | − | 0.821540i | \(-0.306885\pi\) | ||||
0.570151 | + | 0.821540i | \(0.306885\pi\) | |||||||
\(674\) | −25.4435 | −0.980048 | ||||||||
\(675\) | 1.38201 | 0.0531935 | ||||||||
\(676\) | 15.4983 | 0.596088 | ||||||||
\(677\) | 38.0283 | 1.46154 | 0.730772 | − | 0.682621i | \(-0.239160\pi\) | ||||
0.730772 | + | 0.682621i | \(0.239160\pi\) | |||||||
\(678\) | 0.661313 | 0.0253976 | ||||||||
\(679\) | −5.28084 | −0.202660 | ||||||||
\(680\) | −1.20253 | −0.0461149 | ||||||||
\(681\) | −0.919963 | −0.0352530 | ||||||||
\(682\) | 9.04925 | 0.346514 | ||||||||
\(683\) | 20.0533 | 0.767318 | 0.383659 | − | 0.923475i | \(-0.374664\pi\) | ||||
0.383659 | + | 0.923475i | \(0.374664\pi\) | |||||||
\(684\) | 1.06502 | 0.0407221 | ||||||||
\(685\) | −0.177894 | −0.00679697 | ||||||||
\(686\) | −28.7936 | −1.09934 | ||||||||
\(687\) | 0.479621 | 0.0182987 | ||||||||
\(688\) | −4.54506 | −0.173279 | ||||||||
\(689\) | 17.2121 | 0.655730 | ||||||||
\(690\) | 0.131874 | 0.00502036 | ||||||||
\(691\) | −20.1682 | −0.767235 | −0.383618 | − | 0.923492i | \(-0.625322\pi\) | ||||
−0.383618 | + | 0.923492i | \(0.625322\pi\) | |||||||
\(692\) | 5.22013 | 0.198440 | ||||||||
\(693\) | 11.5068 | 0.437108 | ||||||||
\(694\) | −23.1490 | −0.878725 | ||||||||
\(695\) | −0.870894 | −0.0330349 | ||||||||
\(696\) | −0.0878042 | −0.00332821 | ||||||||
\(697\) | −11.9887 | −0.454106 | ||||||||
\(698\) | −13.4485 | −0.509035 | ||||||||
\(699\) | −1.46956 | −0.0555838 | ||||||||
\(700\) | 21.2204 | 0.802057 | ||||||||
\(701\) | −12.5956 | −0.475728 | −0.237864 | − | 0.971298i | \(-0.576447\pi\) | ||||
−0.237864 | + | 0.971298i | \(0.576447\pi\) | |||||||
\(702\) | −1.56946 | −0.0592355 | ||||||||
\(703\) | −1.30581 | −0.0492495 | ||||||||
\(704\) | 0.850349 | 0.0320487 | ||||||||
\(705\) | 0.138394 | 0.00521221 | ||||||||
\(706\) | −2.93296 | −0.110384 | ||||||||
\(707\) | −81.5318 | −3.06632 | ||||||||
\(708\) | −0.0539407 | −0.00202722 | ||||||||
\(709\) | −13.0028 | −0.488332 | −0.244166 | − | 0.969733i | \(-0.578514\pi\) | ||||
−0.244166 | + | 0.969733i | \(0.578514\pi\) | |||||||
\(710\) | 0.548717 | 0.0205930 | ||||||||
\(711\) | −17.6088 | −0.660381 | ||||||||
\(712\) | 8.57054 | 0.321195 | ||||||||
\(713\) | 52.3370 | 1.96003 | ||||||||
\(714\) | 0.486455 | 0.0182051 | ||||||||
\(715\) | 2.48318 | 0.0928657 | ||||||||
\(716\) | 14.1956 | 0.530515 | ||||||||
\(717\) | −0.130603 | −0.00487746 | ||||||||
\(718\) | 13.6695 | 0.510142 | ||||||||
\(719\) | −52.2726 | −1.94944 | −0.974719 | − | 0.223435i | \(-0.928273\pi\) | ||||
−0.974719 | + | 0.223435i | \(0.928273\pi\) | |||||||
\(720\) | −1.63974 | −0.0611095 | ||||||||
\(721\) | −65.6352 | −2.44438 | ||||||||
\(722\) | −18.8738 | −0.702409 | ||||||||
\(723\) | −1.34527 | −0.0500311 | ||||||||
\(724\) | 17.6045 | 0.654266 | ||||||||
\(725\) | 8.42016 | 0.312717 | ||||||||
\(726\) | −0.503763 | −0.0186964 | ||||||||
\(727\) | 12.3230 | 0.457033 | 0.228517 | − | 0.973540i | \(-0.426612\pi\) | ||||
0.228517 | + | 0.973540i | \(0.426612\pi\) | |||||||
\(728\) | −24.0987 | −0.893159 | ||||||||
\(729\) | −26.8703 | −0.995197 | ||||||||
\(730\) | −3.71979 | −0.137676 | ||||||||
\(731\) | 9.99155 | 0.369551 | ||||||||
\(732\) | −0.277101 | −0.0102420 | ||||||||
\(733\) | −6.57385 | −0.242811 | −0.121405 | − | 0.992603i | \(-0.538740\pi\) | ||||
−0.121405 | + | 0.992603i | \(0.538740\pi\) | |||||||
\(734\) | 11.5125 | 0.424935 | ||||||||
\(735\) | 0.358732 | 0.0132320 | ||||||||
\(736\) | 4.91805 | 0.181282 | ||||||||
\(737\) | 6.04005 | 0.222488 | ||||||||
\(738\) | −16.3476 | −0.601762 | ||||||||
\(739\) | −15.3370 | −0.564180 | −0.282090 | − | 0.959388i | \(-0.591028\pi\) | ||||
−0.282090 | + | 0.959388i | \(0.591028\pi\) | |||||||
\(740\) | 2.01047 | 0.0739062 | ||||||||
\(741\) | −0.0929733 | −0.00341546 | ||||||||
\(742\) | −14.5549 | −0.534328 | ||||||||
\(743\) | −11.8513 | −0.434781 | −0.217390 | − | 0.976085i | \(-0.569754\pi\) | ||||
−0.217390 | + | 0.976085i | \(0.569754\pi\) | |||||||
\(744\) | 0.521651 | 0.0191246 | ||||||||
\(745\) | −8.72886 | −0.319801 | ||||||||
\(746\) | −1.32606 | −0.0485504 | ||||||||
\(747\) | 31.6005 | 1.15620 | ||||||||
\(748\) | −1.86935 | −0.0683502 | ||||||||
\(749\) | −71.0480 | −2.59604 | ||||||||
\(750\) | −0.260119 | −0.00949821 | ||||||||
\(751\) | −16.9962 | −0.620200 | −0.310100 | − | 0.950704i | \(-0.600363\pi\) | ||||
−0.310100 | + | 0.950704i | \(0.600363\pi\) | |||||||
\(752\) | 5.16120 | 0.188209 | ||||||||
\(753\) | 1.27916 | 0.0466153 | ||||||||
\(754\) | −9.56226 | −0.348237 | ||||||||
\(755\) | 4.96832 | 0.180816 | ||||||||
\(756\) | 1.32717 | 0.0482687 | ||||||||
\(757\) | −35.2526 | −1.28128 | −0.640639 | − | 0.767842i | \(-0.721331\pi\) | ||||
−0.640639 | + | 0.767842i | \(0.721331\pi\) | |||||||
\(758\) | −19.0090 | −0.690437 | ||||||||
\(759\) | 0.205000 | 0.00744104 | ||||||||
\(760\) | −0.194351 | −0.00704985 | ||||||||
\(761\) | 8.11829 | 0.294288 | 0.147144 | − | 0.989115i | \(-0.452992\pi\) | ||||
0.147144 | + | 0.989115i | \(0.452992\pi\) | |||||||
\(762\) | 0.169864 | 0.00615351 | ||||||||
\(763\) | −76.6424 | −2.77464 | ||||||||
\(764\) | 0.544050 | 0.0196830 | ||||||||
\(765\) | 3.60470 | 0.130328 | ||||||||
\(766\) | 11.7329 | 0.423925 | ||||||||
\(767\) | −5.87438 | −0.212112 | ||||||||
\(768\) | 0.0490190 | 0.00176882 | ||||||||
\(769\) | 29.6433 | 1.06896 | 0.534482 | − | 0.845180i | \(-0.320507\pi\) | ||||
0.534482 | + | 0.845180i | \(0.320507\pi\) | |||||||
\(770\) | −2.09983 | −0.0756726 | ||||||||
\(771\) | −0.662516 | −0.0238599 | ||||||||
\(772\) | −18.0871 | −0.650969 | ||||||||
\(773\) | 45.5742 | 1.63919 | 0.819595 | − | 0.572944i | \(-0.194199\pi\) | ||||
0.819595 | + | 0.572944i | \(0.194199\pi\) | |||||||
\(774\) | 13.6242 | 0.489713 | ||||||||
\(775\) | −50.0247 | −1.79694 | ||||||||
\(776\) | 1.16982 | 0.0419940 | ||||||||
\(777\) | −0.813287 | −0.0291765 | ||||||||
\(778\) | 24.3102 | 0.871561 | ||||||||
\(779\) | −1.93760 | −0.0694217 | ||||||||
\(780\) | 0.143145 | 0.00512541 | ||||||||
\(781\) | 0.852989 | 0.0305223 | ||||||||
\(782\) | −10.8115 | −0.386619 | ||||||||
\(783\) | 0.526614 | 0.0188197 | ||||||||
\(784\) | 13.3784 | 0.477800 | ||||||||
\(785\) | −10.1065 | −0.360716 | ||||||||
\(786\) | −0.708815 | −0.0252826 | ||||||||
\(787\) | −26.8828 | −0.958267 | −0.479133 | − | 0.877742i | \(-0.659049\pi\) | ||||
−0.479133 | + | 0.877742i | \(0.659049\pi\) | |||||||
\(788\) | −8.52995 | −0.303867 | ||||||||
\(789\) | 0.887266 | 0.0315875 | ||||||||
\(790\) | 3.21335 | 0.114326 | ||||||||
\(791\) | −60.9014 | −2.16541 | ||||||||
\(792\) | −2.54900 | −0.0905749 | ||||||||
\(793\) | −30.1775 | −1.07164 | ||||||||
\(794\) | 2.85651 | 0.101374 | ||||||||
\(795\) | 0.0864552 | 0.00306625 | ||||||||
\(796\) | −18.0997 | −0.641525 | ||||||||
\(797\) | −24.0564 | −0.852123 | −0.426061 | − | 0.904694i | \(-0.640099\pi\) | ||||
−0.426061 | + | 0.904694i | \(0.640099\pi\) | |||||||
\(798\) | 0.0786201 | 0.00278312 | ||||||||
\(799\) | −11.3460 | −0.401394 | ||||||||
\(800\) | −4.70077 | −0.166197 | ||||||||
\(801\) | −25.6910 | −0.907748 | ||||||||
\(802\) | 12.4445 | 0.439430 | ||||||||
\(803\) | −5.78247 | −0.204059 | ||||||||
\(804\) | 0.348183 | 0.0122795 | ||||||||
\(805\) | −12.1445 | −0.428038 | ||||||||
\(806\) | 56.8100 | 2.00105 | ||||||||
\(807\) | 0.117425 | 0.00413356 | ||||||||
\(808\) | 18.0610 | 0.635384 | ||||||||
\(809\) | −36.0928 | −1.26896 | −0.634478 | − | 0.772941i | \(-0.718785\pi\) | ||||
−0.634478 | + | 0.772941i | \(0.718785\pi\) | |||||||
\(810\) | 4.91134 | 0.172567 | ||||||||
\(811\) | −30.4154 | −1.06803 | −0.534015 | − | 0.845475i | \(-0.679317\pi\) | ||||
−0.534015 | + | 0.845475i | \(0.679317\pi\) | |||||||
\(812\) | 8.08604 | 0.283764 | ||||||||
\(813\) | −1.15644 | −0.0405581 | ||||||||
\(814\) | 3.12530 | 0.109542 | ||||||||
\(815\) | 10.5493 | 0.369524 | ||||||||
\(816\) | −0.107760 | −0.00377236 | ||||||||
\(817\) | 1.61482 | 0.0564954 | ||||||||
\(818\) | −13.0403 | −0.455945 | ||||||||
\(819\) | 72.2383 | 2.52421 | ||||||||
\(820\) | 2.98319 | 0.104178 | ||||||||
\(821\) | 12.8725 | 0.449253 | 0.224626 | − | 0.974445i | \(-0.427884\pi\) | ||||
0.224626 | + | 0.974445i | \(0.427884\pi\) | |||||||
\(822\) | −0.0159413 | −0.000556015 0 | ||||||||
\(823\) | −3.25035 | −0.113300 | −0.0566501 | − | 0.998394i | \(-0.518042\pi\) | ||||
−0.0566501 | + | 0.998394i | \(0.518042\pi\) | |||||||
\(824\) | 14.5396 | 0.506510 | ||||||||
\(825\) | −0.195943 | −0.00682187 | ||||||||
\(826\) | 4.96750 | 0.172841 | ||||||||
\(827\) | −17.6675 | −0.614359 | −0.307180 | − | 0.951652i | \(-0.599385\pi\) | ||||
−0.307180 | + | 0.951652i | \(0.599385\pi\) | |||||||
\(828\) | −14.7423 | −0.512332 | ||||||||
\(829\) | 31.1367 | 1.08142 | 0.540711 | − | 0.841209i | \(-0.318155\pi\) | ||||
0.540711 | + | 0.841209i | \(0.318155\pi\) | |||||||
\(830\) | −5.76664 | −0.200163 | ||||||||
\(831\) | 1.08667 | 0.0376961 | ||||||||
\(832\) | 5.33838 | 0.185075 | ||||||||
\(833\) | −29.4102 | −1.01900 | ||||||||
\(834\) | −0.0780419 | −0.00270237 | ||||||||
\(835\) | −0.855217 | −0.0295960 | ||||||||
\(836\) | −0.302122 | −0.0104491 | ||||||||
\(837\) | −3.12865 | −0.108142 | ||||||||
\(838\) | −7.28880 | −0.251788 | ||||||||
\(839\) | 23.1978 | 0.800878 | 0.400439 | − | 0.916323i | \(-0.368858\pi\) | ||||
0.400439 | + | 0.916323i | \(0.368858\pi\) | |||||||
\(840\) | −0.121046 | −0.00417649 | ||||||||
\(841\) | −25.7915 | −0.889362 | ||||||||
\(842\) | 29.7670 | 1.02584 | ||||||||
\(843\) | 0.455871 | 0.0157010 | ||||||||
\(844\) | 1.60334 | 0.0551894 | ||||||||
\(845\) | 8.47785 | 0.291647 | ||||||||
\(846\) | −15.4712 | −0.531910 | ||||||||
\(847\) | 46.3925 | 1.59406 | ||||||||
\(848\) | 3.22422 | 0.110720 | ||||||||
\(849\) | 1.15199 | 0.0395361 | ||||||||
\(850\) | 10.3339 | 0.354449 | ||||||||
\(851\) | 18.0754 | 0.619617 | ||||||||
\(852\) | 0.0491712 | 0.00168458 | ||||||||
\(853\) | −0.972998 | −0.0333148 | −0.0166574 | − | 0.999861i | \(-0.505302\pi\) | ||||
−0.0166574 | + | 0.999861i | \(0.505302\pi\) | |||||||
\(854\) | 25.5187 | 0.873233 | ||||||||
\(855\) | 0.582586 | 0.0199240 | ||||||||
\(856\) | 15.7386 | 0.537936 | ||||||||
\(857\) | −2.17457 | −0.0742820 | −0.0371410 | − | 0.999310i | \(-0.511825\pi\) | ||||
−0.0371410 | + | 0.999310i | \(0.511825\pi\) | |||||||
\(858\) | 0.222521 | 0.00759674 | ||||||||
\(859\) | 24.5912 | 0.839041 | 0.419521 | − | 0.907746i | \(-0.362198\pi\) | ||||
0.419521 | + | 0.907746i | \(0.362198\pi\) | |||||||
\(860\) | −2.48623 | −0.0847797 | ||||||||
\(861\) | −1.20678 | −0.0411270 | ||||||||
\(862\) | 14.2404 | 0.485029 | ||||||||
\(863\) | 4.24342 | 0.144448 | 0.0722239 | − | 0.997388i | \(-0.476990\pi\) | ||||
0.0722239 | + | 0.997388i | \(0.476990\pi\) | |||||||
\(864\) | −0.293996 | −0.0100019 | ||||||||
\(865\) | 2.85551 | 0.0970902 | ||||||||
\(866\) | −0.908372 | −0.0308677 | ||||||||
\(867\) | −0.596430 | −0.0202558 | ||||||||
\(868\) | −48.0397 | −1.63057 | ||||||||
\(869\) | 4.99520 | 0.169451 | ||||||||
\(870\) | −0.0480305 | −0.00162839 | ||||||||
\(871\) | 37.9186 | 1.28482 | ||||||||
\(872\) | 16.9779 | 0.574944 | ||||||||
\(873\) | −3.50664 | −0.118682 | ||||||||
\(874\) | −1.74734 | −0.0591047 | ||||||||
\(875\) | 23.9548 | 0.809821 | ||||||||
\(876\) | −0.333335 | −0.0112623 | ||||||||
\(877\) | −7.86293 | −0.265512 | −0.132756 | − | 0.991149i | \(-0.542383\pi\) | ||||
−0.132756 | + | 0.991149i | \(0.542383\pi\) | |||||||
\(878\) | 24.0351 | 0.811146 | ||||||||
\(879\) | −0.547162 | −0.0184553 | ||||||||
\(880\) | 0.465156 | 0.0156804 | ||||||||
\(881\) | 7.18705 | 0.242138 | 0.121069 | − | 0.992644i | \(-0.461368\pi\) | ||||
0.121069 | + | 0.992644i | \(0.461368\pi\) | |||||||
\(882\) | −40.1030 | −1.35034 | ||||||||
\(883\) | 20.9108 | 0.703705 | 0.351852 | − | 0.936055i | \(-0.385552\pi\) | ||||
0.351852 | + | 0.936055i | \(0.385552\pi\) | |||||||
\(884\) | −11.7355 | −0.394709 | ||||||||
\(885\) | −0.0295066 | −0.000991852 0 | ||||||||
\(886\) | 7.12066 | 0.239223 | ||||||||
\(887\) | −2.21558 | −0.0743920 | −0.0371960 | − | 0.999308i | \(-0.511843\pi\) | ||||
−0.0371960 | + | 0.999308i | \(0.511843\pi\) | |||||||
\(888\) | 0.180160 | 0.00604578 | ||||||||
\(889\) | −15.6430 | −0.524650 | ||||||||
\(890\) | 4.68824 | 0.157150 | ||||||||
\(891\) | 7.63475 | 0.255774 | ||||||||
\(892\) | 16.8365 | 0.563728 | ||||||||
\(893\) | −1.83373 | −0.0613634 | ||||||||
\(894\) | −0.782203 | −0.0261608 | ||||||||
\(895\) | 7.76526 | 0.259564 | ||||||||
\(896\) | −4.51424 | −0.150810 | ||||||||
\(897\) | 1.28697 | 0.0429705 | ||||||||
\(898\) | 12.7532 | 0.425580 | ||||||||
\(899\) | −19.0619 | −0.635750 | ||||||||
\(900\) | 14.0910 | 0.469701 | ||||||||
\(901\) | −7.08793 | −0.236133 | ||||||||
\(902\) | 4.63742 | 0.154409 | ||||||||
\(903\) | 1.00575 | 0.0334691 | ||||||||
\(904\) | 13.4910 | 0.448702 | ||||||||
\(905\) | 9.62998 | 0.320111 | ||||||||
\(906\) | 0.445217 | 0.0147914 | ||||||||
\(907\) | 29.7125 | 0.986587 | 0.493294 | − | 0.869863i | \(-0.335793\pi\) | ||||
0.493294 | + | 0.869863i | \(0.335793\pi\) | |||||||
\(908\) | −18.7675 | −0.622821 | ||||||||
\(909\) | −54.1396 | −1.79570 | ||||||||
\(910\) | −13.1825 | −0.436994 | ||||||||
\(911\) | 29.8920 | 0.990367 | 0.495183 | − | 0.868789i | \(-0.335101\pi\) | ||||
0.495183 | + | 0.868789i | \(0.335101\pi\) | |||||||
\(912\) | −0.0174160 | −0.000576702 0 | ||||||||
\(913\) | −8.96434 | −0.296676 | ||||||||
\(914\) | 24.8661 | 0.822497 | ||||||||
\(915\) | −0.151579 | −0.00501106 | ||||||||
\(916\) | 9.78439 | 0.323285 | ||||||||
\(917\) | 65.2760 | 2.15560 | ||||||||
\(918\) | 0.646302 | 0.0213311 | ||||||||
\(919\) | −9.64806 | −0.318260 | −0.159130 | − | 0.987258i | \(-0.550869\pi\) | ||||
−0.159130 | + | 0.987258i | \(0.550869\pi\) | |||||||
\(920\) | 2.69026 | 0.0886954 | ||||||||
\(921\) | 0.148007 | 0.00487701 | ||||||||
\(922\) | −32.8411 | −1.08156 | ||||||||
\(923\) | 5.35495 | 0.176260 | ||||||||
\(924\) | −0.188168 | −0.00619028 | ||||||||
\(925\) | −17.2768 | −0.568059 | ||||||||
\(926\) | 21.3501 | 0.701609 | ||||||||
\(927\) | −43.5838 | −1.43148 | ||||||||
\(928\) | −1.79123 | −0.0588000 | ||||||||
\(929\) | 33.5306 | 1.10010 | 0.550051 | − | 0.835131i | \(-0.314608\pi\) | ||||
0.550051 | + | 0.835131i | \(0.314608\pi\) | |||||||
\(930\) | 0.285352 | 0.00935707 | ||||||||
\(931\) | −4.75323 | −0.155781 | ||||||||
\(932\) | −29.9794 | −0.982008 | ||||||||
\(933\) | −0.988238 | −0.0323534 | ||||||||
\(934\) | −31.2761 | −1.02338 | ||||||||
\(935\) | −1.02257 | −0.0334416 | ||||||||
\(936\) | −16.0023 | −0.523052 | ||||||||
\(937\) | −31.5401 | −1.03037 | −0.515185 | − | 0.857079i | \(-0.672277\pi\) | ||||
−0.515185 | + | 0.857079i | \(0.672277\pi\) | |||||||
\(938\) | −32.0648 | −1.04695 | ||||||||
\(939\) | 0.00859646 | 0.000280535 0 | ||||||||
\(940\) | 2.82327 | 0.0920849 | ||||||||
\(941\) | 2.60195 | 0.0848212 | 0.0424106 | − | 0.999100i | \(-0.486496\pi\) | ||||
0.0424106 | + | 0.999100i | \(0.486496\pi\) | |||||||
\(942\) | −0.905655 | −0.0295078 | ||||||||
\(943\) | 26.8209 | 0.873407 | ||||||||
\(944\) | −1.10040 | −0.0358151 | ||||||||
\(945\) | 0.725986 | 0.0236163 | ||||||||
\(946\) | −3.86488 | −0.125658 | ||||||||
\(947\) | 11.9055 | 0.386876 | 0.193438 | − | 0.981113i | \(-0.438036\pi\) | ||||
0.193438 | + | 0.981113i | \(0.438036\pi\) | |||||||
\(948\) | 0.287952 | 0.00935225 | ||||||||
\(949\) | −36.3016 | −1.17840 | ||||||||
\(950\) | 1.67014 | 0.0541866 | ||||||||
\(951\) | −1.17608 | −0.0381368 | ||||||||
\(952\) | 9.92382 | 0.321633 | ||||||||
\(953\) | −24.3663 | −0.789303 | −0.394652 | − | 0.918831i | \(-0.629135\pi\) | ||||
−0.394652 | + | 0.918831i | \(0.629135\pi\) | |||||||
\(954\) | −9.66493 | −0.312914 | ||||||||
\(955\) | 0.297605 | 0.00963028 | ||||||||
\(956\) | −2.66434 | −0.0861709 | ||||||||
\(957\) | −0.0746642 | −0.00241355 | ||||||||
\(958\) | 30.3216 | 0.979647 | ||||||||
\(959\) | 1.46806 | 0.0474061 | ||||||||
\(960\) | 0.0268143 | 0.000865427 0 | ||||||||
\(961\) | 82.2481 | 2.65316 | ||||||||
\(962\) | 19.6202 | 0.632582 | ||||||||
\(963\) | −47.1781 | −1.52029 | ||||||||
\(964\) | −27.4438 | −0.883907 | ||||||||
\(965\) | −9.89397 | −0.318498 | ||||||||
\(966\) | −1.08828 | −0.0350150 | ||||||||
\(967\) | 1.54217 | 0.0495928 | 0.0247964 | − | 0.999693i | \(-0.492106\pi\) | ||||
0.0247964 | + | 0.999693i | \(0.492106\pi\) | |||||||
\(968\) | −10.2769 | −0.330312 | ||||||||
\(969\) | 0.0382862 | 0.00122993 | ||||||||
\(970\) | 0.639912 | 0.0205463 | ||||||||
\(971\) | 20.9905 | 0.673616 | 0.336808 | − | 0.941573i | \(-0.390653\pi\) | ||||
0.336808 | + | 0.941573i | \(0.390653\pi\) | |||||||
\(972\) | 1.32210 | 0.0424064 | ||||||||
\(973\) | 7.18701 | 0.230405 | ||||||||
\(974\) | 23.4994 | 0.752969 | ||||||||
\(975\) | −1.23011 | −0.0393949 | ||||||||
\(976\) | −5.65294 | −0.180946 | ||||||||
\(977\) | −20.6989 | −0.662217 | −0.331109 | − | 0.943593i | \(-0.607423\pi\) | ||||
−0.331109 | + | 0.943593i | \(0.607423\pi\) | |||||||
\(978\) | 0.945332 | 0.0302284 | ||||||||
\(979\) | 7.28795 | 0.232924 | ||||||||
\(980\) | 7.31822 | 0.233772 | ||||||||
\(981\) | −50.8929 | −1.62489 | ||||||||
\(982\) | −16.6852 | −0.532447 | ||||||||
\(983\) | −48.6672 | −1.55224 | −0.776122 | − | 0.630583i | \(-0.782816\pi\) | ||||
−0.776122 | + | 0.630583i | \(0.782816\pi\) | |||||||
\(984\) | 0.267327 | 0.00852209 | ||||||||
\(985\) | −4.66604 | −0.148672 | ||||||||
\(986\) | 3.93772 | 0.125403 | ||||||||
\(987\) | −1.14209 | −0.0363531 | ||||||||
\(988\) | −1.89668 | −0.0603414 | ||||||||
\(989\) | −22.3528 | −0.710778 | ||||||||
\(990\) | −1.39435 | −0.0443154 | ||||||||
\(991\) | −43.1229 | −1.36984 | −0.684922 | − | 0.728616i | \(-0.740164\pi\) | ||||
−0.684922 | + | 0.728616i | \(0.740164\pi\) | |||||||
\(992\) | 10.6418 | 0.337878 | ||||||||
\(993\) | −0.104664 | −0.00332140 | ||||||||
\(994\) | −4.52826 | −0.143628 | ||||||||
\(995\) | −9.90085 | −0.313878 | ||||||||
\(996\) | −0.516756 | −0.0163740 | ||||||||
\(997\) | −4.15228 | −0.131504 | −0.0657520 | − | 0.997836i | \(-0.520945\pi\) | ||||
−0.0657520 | + | 0.997836i | \(0.520945\pi\) | |||||||
\(998\) | 20.2918 | 0.642326 | ||||||||
\(999\) | −1.08053 | −0.0341864 |
(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 | 4006.2.a.i.1.20 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4006.2.a.i.1.20 | ✓ | 46 | 1.1 | even | 1 | trivial |