Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4017,2,Mod(1,4017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4017 = 3 \cdot 13 \cdot 103 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4017.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: | \(32.0759064919\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 4017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.27578 | −0.902115 | −0.451057 | − | 0.892495i | \(-0.648953\pi\) | ||||
−0.451057 | + | 0.892495i | \(0.648953\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.372378 | −0.186189 | ||||||||
\(5\) | −0.506188 | −0.226374 | −0.113187 | − | 0.993574i | \(-0.536106\pi\) | ||||
−0.113187 | + | 0.993574i | \(0.536106\pi\) | |||||||
\(6\) | 1.27578 | 0.520836 | ||||||||
\(7\) | −3.05259 | −1.15377 | −0.576885 | − | 0.816825i | \(-0.695732\pi\) | ||||
−0.576885 | + | 0.816825i | \(0.695732\pi\) | |||||||
\(8\) | 3.02664 | 1.07008 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0.645786 | 0.204215 | ||||||||
\(11\) | −1.77709 | −0.535814 | −0.267907 | − | 0.963445i | \(-0.586332\pi\) | ||||
−0.267907 | + | 0.963445i | \(0.586332\pi\) | |||||||
\(12\) | 0.372378 | 0.107496 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 3.89444 | 1.04083 | ||||||||
\(15\) | 0.506188 | 0.130697 | ||||||||
\(16\) | −3.11658 | −0.779145 | ||||||||
\(17\) | −3.59426 | −0.871737 | −0.435869 | − | 0.900010i | \(-0.643559\pi\) | ||||
−0.435869 | + | 0.900010i | \(0.643559\pi\) | |||||||
\(18\) | −1.27578 | −0.300705 | ||||||||
\(19\) | −0.715310 | −0.164103 | −0.0820517 | − | 0.996628i | \(-0.526147\pi\) | ||||
−0.0820517 | + | 0.996628i | \(0.526147\pi\) | |||||||
\(20\) | 0.188493 | 0.0421483 | ||||||||
\(21\) | 3.05259 | 0.666129 | ||||||||
\(22\) | 2.26719 | 0.483365 | ||||||||
\(23\) | −0.238375 | −0.0497047 | −0.0248523 | − | 0.999691i | \(-0.507912\pi\) | ||||
−0.0248523 | + | 0.999691i | \(0.507912\pi\) | |||||||
\(24\) | −3.02664 | −0.617810 | ||||||||
\(25\) | −4.74377 | −0.948755 | ||||||||
\(26\) | −1.27578 | −0.250202 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.13672 | 0.214819 | ||||||||
\(29\) | 2.95446 | 0.548630 | 0.274315 | − | 0.961640i | \(-0.411549\pi\) | ||||
0.274315 | + | 0.961640i | \(0.411549\pi\) | |||||||
\(30\) | −0.645786 | −0.117904 | ||||||||
\(31\) | 0.136135 | 0.0244506 | 0.0122253 | − | 0.999925i | \(-0.496108\pi\) | ||||
0.0122253 | + | 0.999925i | \(0.496108\pi\) | |||||||
\(32\) | −2.07720 | −0.367200 | ||||||||
\(33\) | 1.77709 | 0.309352 | ||||||||
\(34\) | 4.58550 | 0.786407 | ||||||||
\(35\) | 1.54518 | 0.261184 | ||||||||
\(36\) | −0.372378 | −0.0620629 | ||||||||
\(37\) | 5.90568 | 0.970887 | 0.485444 | − | 0.874268i | \(-0.338658\pi\) | ||||
0.485444 | + | 0.874268i | \(0.338658\pi\) | |||||||
\(38\) | 0.912581 | 0.148040 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | −1.53205 | −0.242238 | ||||||||
\(41\) | −5.81439 | −0.908056 | −0.454028 | − | 0.890987i | \(-0.650013\pi\) | ||||
−0.454028 | + | 0.890987i | \(0.650013\pi\) | |||||||
\(42\) | −3.89444 | −0.600925 | ||||||||
\(43\) | −2.36383 | −0.360481 | −0.180241 | − | 0.983623i | \(-0.557688\pi\) | ||||
−0.180241 | + | 0.983623i | \(0.557688\pi\) | |||||||
\(44\) | 0.661750 | 0.0997625 | ||||||||
\(45\) | −0.506188 | −0.0754580 | ||||||||
\(46\) | 0.304115 | 0.0448393 | ||||||||
\(47\) | −7.27479 | −1.06114 | −0.530568 | − | 0.847642i | \(-0.678022\pi\) | ||||
−0.530568 | + | 0.847642i | \(0.678022\pi\) | |||||||
\(48\) | 3.11658 | 0.449840 | ||||||||
\(49\) | 2.31830 | 0.331185 | ||||||||
\(50\) | 6.05203 | 0.855886 | ||||||||
\(51\) | 3.59426 | 0.503298 | ||||||||
\(52\) | −0.372378 | −0.0516395 | ||||||||
\(53\) | −4.12441 | −0.566531 | −0.283266 | − | 0.959041i | \(-0.591418\pi\) | ||||
−0.283266 | + | 0.959041i | \(0.591418\pi\) | |||||||
\(54\) | 1.27578 | 0.173612 | ||||||||
\(55\) | 0.899543 | 0.121294 | ||||||||
\(56\) | −9.23908 | −1.23462 | ||||||||
\(57\) | 0.715310 | 0.0947452 | ||||||||
\(58\) | −3.76926 | −0.494927 | ||||||||
\(59\) | −4.06634 | −0.529392 | −0.264696 | − | 0.964332i | \(-0.585272\pi\) | ||||
−0.264696 | + | 0.964332i | \(0.585272\pi\) | |||||||
\(60\) | −0.188493 | −0.0243343 | ||||||||
\(61\) | −3.05264 | −0.390850 | −0.195425 | − | 0.980719i | \(-0.562609\pi\) | ||||
−0.195425 | + | 0.980719i | \(0.562609\pi\) | |||||||
\(62\) | −0.173679 | −0.0220573 | ||||||||
\(63\) | −3.05259 | −0.384590 | ||||||||
\(64\) | 8.88321 | 1.11040 | ||||||||
\(65\) | −0.506188 | −0.0627849 | ||||||||
\(66\) | −2.26719 | −0.279071 | ||||||||
\(67\) | 12.3054 | 1.50335 | 0.751673 | − | 0.659536i | \(-0.229247\pi\) | ||||
0.751673 | + | 0.659536i | \(0.229247\pi\) | |||||||
\(68\) | 1.33842 | 0.162308 | ||||||||
\(69\) | 0.238375 | 0.0286970 | ||||||||
\(70\) | −1.97132 | −0.235618 | ||||||||
\(71\) | 6.06837 | 0.720183 | 0.360091 | − | 0.932917i | \(-0.382746\pi\) | ||||
0.360091 | + | 0.932917i | \(0.382746\pi\) | |||||||
\(72\) | 3.02664 | 0.356693 | ||||||||
\(73\) | −13.9094 | −1.62797 | −0.813984 | − | 0.580888i | \(-0.802705\pi\) | ||||
−0.813984 | + | 0.580888i | \(0.802705\pi\) | |||||||
\(74\) | −7.53436 | −0.875852 | ||||||||
\(75\) | 4.74377 | 0.547764 | ||||||||
\(76\) | 0.266366 | 0.0305542 | ||||||||
\(77\) | 5.42473 | 0.618206 | ||||||||
\(78\) | 1.27578 | 0.144454 | ||||||||
\(79\) | −10.1863 | −1.14605 | −0.573027 | − | 0.819537i | \(-0.694231\pi\) | ||||
−0.573027 | + | 0.819537i | \(0.694231\pi\) | |||||||
\(80\) | 1.57758 | 0.176378 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.41791 | 0.819171 | ||||||||
\(83\) | 1.65318 | 0.181460 | 0.0907298 | − | 0.995876i | \(-0.471080\pi\) | ||||
0.0907298 | + | 0.995876i | \(0.471080\pi\) | |||||||
\(84\) | −1.13672 | −0.124026 | ||||||||
\(85\) | 1.81937 | 0.197339 | ||||||||
\(86\) | 3.01574 | 0.325196 | ||||||||
\(87\) | −2.95446 | −0.316752 | ||||||||
\(88\) | −5.37862 | −0.573363 | ||||||||
\(89\) | −12.4282 | −1.31739 | −0.658693 | − | 0.752412i | \(-0.728890\pi\) | ||||
−0.658693 | + | 0.752412i | \(0.728890\pi\) | |||||||
\(90\) | 0.645786 | 0.0680718 | ||||||||
\(91\) | −3.05259 | −0.319998 | ||||||||
\(92\) | 0.0887656 | 0.00925445 | ||||||||
\(93\) | −0.136135 | −0.0141166 | ||||||||
\(94\) | 9.28105 | 0.957267 | ||||||||
\(95\) | 0.362082 | 0.0371488 | ||||||||
\(96\) | 2.07720 | 0.212003 | ||||||||
\(97\) | −15.8471 | −1.60903 | −0.804515 | − | 0.593933i | \(-0.797575\pi\) | ||||
−0.804515 | + | 0.593933i | \(0.797575\pi\) | |||||||
\(98\) | −2.95764 | −0.298767 | ||||||||
\(99\) | −1.77709 | −0.178605 | ||||||||
\(100\) | 1.76648 | 0.176648 | ||||||||
\(101\) | −3.35478 | −0.333814 | −0.166907 | − | 0.985973i | \(-0.553378\pi\) | ||||
−0.166907 | + | 0.985973i | \(0.553378\pi\) | |||||||
\(102\) | −4.58550 | −0.454032 | ||||||||
\(103\) | −1.00000 | −0.0985329 | ||||||||
\(104\) | 3.02664 | 0.296786 | ||||||||
\(105\) | −1.54518 | −0.150794 | ||||||||
\(106\) | 5.26185 | 0.511076 | ||||||||
\(107\) | 17.7894 | 1.71977 | 0.859883 | − | 0.510492i | \(-0.170537\pi\) | ||||
0.859883 | + | 0.510492i | \(0.170537\pi\) | |||||||
\(108\) | 0.372378 | 0.0358321 | ||||||||
\(109\) | −16.2712 | −1.55849 | −0.779247 | − | 0.626717i | \(-0.784398\pi\) | ||||
−0.779247 | + | 0.626717i | \(0.784398\pi\) | |||||||
\(110\) | −1.14762 | −0.109421 | ||||||||
\(111\) | −5.90568 | −0.560542 | ||||||||
\(112\) | 9.51363 | 0.898954 | ||||||||
\(113\) | −0.902316 | −0.0848827 | −0.0424414 | − | 0.999099i | \(-0.513514\pi\) | ||||
−0.0424414 | + | 0.999099i | \(0.513514\pi\) | |||||||
\(114\) | −0.912581 | −0.0854710 | ||||||||
\(115\) | 0.120663 | 0.0112519 | ||||||||
\(116\) | −1.10018 | −0.102149 | ||||||||
\(117\) | 1.00000 | 0.0924500 | ||||||||
\(118\) | 5.18777 | 0.477573 | ||||||||
\(119\) | 10.9718 | 1.00578 | ||||||||
\(120\) | 1.53205 | 0.139856 | ||||||||
\(121\) | −7.84194 | −0.712904 | ||||||||
\(122\) | 3.89450 | 0.352592 | ||||||||
\(123\) | 5.81439 | 0.524266 | ||||||||
\(124\) | −0.0506938 | −0.00455243 | ||||||||
\(125\) | 4.93218 | 0.441148 | ||||||||
\(126\) | 3.89444 | 0.346944 | ||||||||
\(127\) | −18.5786 | −1.64858 | −0.824290 | − | 0.566168i | \(-0.808425\pi\) | ||||
−0.824290 | + | 0.566168i | \(0.808425\pi\) | |||||||
\(128\) | −7.17866 | −0.634510 | ||||||||
\(129\) | 2.36383 | 0.208124 | ||||||||
\(130\) | 0.645786 | 0.0566392 | ||||||||
\(131\) | −7.85737 | −0.686501 | −0.343251 | − | 0.939244i | \(-0.611528\pi\) | ||||
−0.343251 | + | 0.939244i | \(0.611528\pi\) | |||||||
\(132\) | −0.661750 | −0.0575979 | ||||||||
\(133\) | 2.18355 | 0.189338 | ||||||||
\(134\) | −15.6990 | −1.35619 | ||||||||
\(135\) | 0.506188 | 0.0435657 | ||||||||
\(136\) | −10.8785 | −0.932827 | ||||||||
\(137\) | 14.1353 | 1.20766 | 0.603829 | − | 0.797114i | \(-0.293641\pi\) | ||||
0.603829 | + | 0.797114i | \(0.293641\pi\) | |||||||
\(138\) | −0.304115 | −0.0258880 | ||||||||
\(139\) | 16.7119 | 1.41748 | 0.708742 | − | 0.705468i | \(-0.249263\pi\) | ||||
0.708742 | + | 0.705468i | \(0.249263\pi\) | |||||||
\(140\) | −0.575392 | −0.0486295 | ||||||||
\(141\) | 7.27479 | 0.612648 | ||||||||
\(142\) | −7.74192 | −0.649687 | ||||||||
\(143\) | −1.77709 | −0.148608 | ||||||||
\(144\) | −3.11658 | −0.259715 | ||||||||
\(145\) | −1.49551 | −0.124196 | ||||||||
\(146\) | 17.7453 | 1.46861 | ||||||||
\(147\) | −2.31830 | −0.191210 | ||||||||
\(148\) | −2.19914 | −0.180768 | ||||||||
\(149\) | 1.64008 | 0.134361 | 0.0671803 | − | 0.997741i | \(-0.478600\pi\) | ||||
0.0671803 | + | 0.997741i | \(0.478600\pi\) | |||||||
\(150\) | −6.05203 | −0.494146 | ||||||||
\(151\) | −3.05639 | −0.248726 | −0.124363 | − | 0.992237i | \(-0.539689\pi\) | ||||
−0.124363 | + | 0.992237i | \(0.539689\pi\) | |||||||
\(152\) | −2.16499 | −0.175604 | ||||||||
\(153\) | −3.59426 | −0.290579 | ||||||||
\(154\) | −6.92078 | −0.557693 | ||||||||
\(155\) | −0.0689101 | −0.00553499 | ||||||||
\(156\) | 0.372378 | 0.0298141 | ||||||||
\(157\) | 8.64949 | 0.690304 | 0.345152 | − | 0.938547i | \(-0.387827\pi\) | ||||
0.345152 | + | 0.938547i | \(0.387827\pi\) | |||||||
\(158\) | 12.9956 | 1.03387 | ||||||||
\(159\) | 4.12441 | 0.327087 | ||||||||
\(160\) | 1.05145 | 0.0831247 | ||||||||
\(161\) | 0.727661 | 0.0573477 | ||||||||
\(162\) | −1.27578 | −0.100235 | ||||||||
\(163\) | 16.6605 | 1.30495 | 0.652474 | − | 0.757811i | \(-0.273731\pi\) | ||||
0.652474 | + | 0.757811i | \(0.273731\pi\) | |||||||
\(164\) | 2.16515 | 0.169070 | ||||||||
\(165\) | −0.899543 | −0.0700293 | ||||||||
\(166\) | −2.10909 | −0.163697 | ||||||||
\(167\) | 18.1176 | 1.40198 | 0.700989 | − | 0.713172i | \(-0.252742\pi\) | ||||
0.700989 | + | 0.713172i | \(0.252742\pi\) | |||||||
\(168\) | 9.23908 | 0.712811 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.32113 | −0.178022 | ||||||||
\(171\) | −0.715310 | −0.0547012 | ||||||||
\(172\) | 0.880239 | 0.0671176 | ||||||||
\(173\) | −7.61457 | −0.578925 | −0.289462 | − | 0.957189i | \(-0.593477\pi\) | ||||
−0.289462 | + | 0.957189i | \(0.593477\pi\) | |||||||
\(174\) | 3.76926 | 0.285746 | ||||||||
\(175\) | 14.4808 | 1.09464 | ||||||||
\(176\) | 5.53845 | 0.417477 | ||||||||
\(177\) | 4.06634 | 0.305645 | ||||||||
\(178\) | 15.8557 | 1.18843 | ||||||||
\(179\) | 20.9646 | 1.56696 | 0.783482 | − | 0.621414i | \(-0.213442\pi\) | ||||
0.783482 | + | 0.621414i | \(0.213442\pi\) | |||||||
\(180\) | 0.188493 | 0.0140494 | ||||||||
\(181\) | −14.2964 | −1.06264 | −0.531321 | − | 0.847171i | \(-0.678304\pi\) | ||||
−0.531321 | + | 0.847171i | \(0.678304\pi\) | |||||||
\(182\) | 3.89444 | 0.288675 | ||||||||
\(183\) | 3.05264 | 0.225657 | ||||||||
\(184\) | −0.721476 | −0.0531879 | ||||||||
\(185\) | −2.98938 | −0.219784 | ||||||||
\(186\) | 0.173679 | 0.0127348 | ||||||||
\(187\) | 6.38734 | 0.467089 | ||||||||
\(188\) | 2.70897 | 0.197572 | ||||||||
\(189\) | 3.05259 | 0.222043 | ||||||||
\(190\) | −0.461937 | −0.0335125 | ||||||||
\(191\) | 2.42083 | 0.175165 | 0.0875824 | − | 0.996157i | \(-0.472086\pi\) | ||||
0.0875824 | + | 0.996157i | \(0.472086\pi\) | |||||||
\(192\) | −8.88321 | −0.641091 | ||||||||
\(193\) | −5.40273 | −0.388897 | −0.194449 | − | 0.980913i | \(-0.562292\pi\) | ||||
−0.194449 | + | 0.980913i | \(0.562292\pi\) | |||||||
\(194\) | 20.2175 | 1.45153 | ||||||||
\(195\) | 0.506188 | 0.0362489 | ||||||||
\(196\) | −0.863281 | −0.0616629 | ||||||||
\(197\) | 19.6801 | 1.40215 | 0.701073 | − | 0.713089i | \(-0.252705\pi\) | ||||
0.701073 | + | 0.713089i | \(0.252705\pi\) | |||||||
\(198\) | 2.26719 | 0.161122 | ||||||||
\(199\) | −17.2785 | −1.22484 | −0.612422 | − | 0.790531i | \(-0.709805\pi\) | ||||
−0.612422 | + | 0.790531i | \(0.709805\pi\) | |||||||
\(200\) | −14.3577 | −1.01524 | ||||||||
\(201\) | −12.3054 | −0.867957 | ||||||||
\(202\) | 4.27998 | 0.301138 | ||||||||
\(203\) | −9.01876 | −0.632993 | ||||||||
\(204\) | −1.33842 | −0.0937084 | ||||||||
\(205\) | 2.94318 | 0.205560 | ||||||||
\(206\) | 1.27578 | 0.0888880 | ||||||||
\(207\) | −0.238375 | −0.0165682 | ||||||||
\(208\) | −3.11658 | −0.216096 | ||||||||
\(209\) | 1.27117 | 0.0879289 | ||||||||
\(210\) | 1.97132 | 0.136034 | ||||||||
\(211\) | 15.3626 | 1.05760 | 0.528802 | − | 0.848745i | \(-0.322641\pi\) | ||||
0.528802 | + | 0.848745i | \(0.322641\pi\) | |||||||
\(212\) | 1.53584 | 0.105482 | ||||||||
\(213\) | −6.06837 | −0.415798 | ||||||||
\(214\) | −22.6954 | −1.55143 | ||||||||
\(215\) | 1.19654 | 0.0816037 | ||||||||
\(216\) | −3.02664 | −0.205937 | ||||||||
\(217\) | −0.415565 | −0.0282104 | ||||||||
\(218\) | 20.7585 | 1.40594 | ||||||||
\(219\) | 13.9094 | 0.939907 | ||||||||
\(220\) | −0.334970 | −0.0225837 | ||||||||
\(221\) | −3.59426 | −0.241776 | ||||||||
\(222\) | 7.53436 | 0.505673 | ||||||||
\(223\) | 17.5213 | 1.17332 | 0.586658 | − | 0.809835i | \(-0.300443\pi\) | ||||
0.586658 | + | 0.809835i | \(0.300443\pi\) | |||||||
\(224\) | 6.34083 | 0.423665 | ||||||||
\(225\) | −4.74377 | −0.316252 | ||||||||
\(226\) | 1.15116 | 0.0765740 | ||||||||
\(227\) | −24.0192 | −1.59421 | −0.797104 | − | 0.603842i | \(-0.793636\pi\) | ||||
−0.797104 | + | 0.603842i | \(0.793636\pi\) | |||||||
\(228\) | −0.266366 | −0.0176405 | ||||||||
\(229\) | −2.09099 | −0.138177 | −0.0690884 | − | 0.997611i | \(-0.522009\pi\) | ||||
−0.0690884 | + | 0.997611i | \(0.522009\pi\) | |||||||
\(230\) | −0.153939 | −0.0101505 | ||||||||
\(231\) | −5.42473 | −0.356921 | ||||||||
\(232\) | 8.94210 | 0.587077 | ||||||||
\(233\) | −9.15311 | −0.599640 | −0.299820 | − | 0.953996i | \(-0.596927\pi\) | ||||
−0.299820 | + | 0.953996i | \(0.596927\pi\) | |||||||
\(234\) | −1.27578 | −0.0834005 | ||||||||
\(235\) | 3.68241 | 0.240214 | ||||||||
\(236\) | 1.51421 | 0.0985669 | ||||||||
\(237\) | 10.1863 | 0.661674 | ||||||||
\(238\) | −13.9976 | −0.907333 | ||||||||
\(239\) | 6.93850 | 0.448814 | 0.224407 | − | 0.974495i | \(-0.427955\pi\) | ||||
0.224407 | + | 0.974495i | \(0.427955\pi\) | |||||||
\(240\) | −1.57758 | −0.101832 | ||||||||
\(241\) | 26.6620 | 1.71745 | 0.858724 | − | 0.512438i | \(-0.171258\pi\) | ||||
0.858724 | + | 0.512438i | \(0.171258\pi\) | |||||||
\(242\) | 10.0046 | 0.643121 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 1.13673 | 0.0727719 | ||||||||
\(245\) | −1.17349 | −0.0749717 | ||||||||
\(246\) | −7.41791 | −0.472948 | ||||||||
\(247\) | −0.715310 | −0.0455141 | ||||||||
\(248\) | 0.412033 | 0.0261641 | ||||||||
\(249\) | −1.65318 | −0.104766 | ||||||||
\(250\) | −6.29239 | −0.397966 | ||||||||
\(251\) | 13.4503 | 0.848978 | 0.424489 | − | 0.905433i | \(-0.360454\pi\) | ||||
0.424489 | + | 0.905433i | \(0.360454\pi\) | |||||||
\(252\) | 1.13672 | 0.0716063 | ||||||||
\(253\) | 0.423615 | 0.0266324 | ||||||||
\(254\) | 23.7022 | 1.48721 | ||||||||
\(255\) | −1.81937 | −0.113934 | ||||||||
\(256\) | −8.60802 | −0.538001 | ||||||||
\(257\) | 26.9808 | 1.68302 | 0.841509 | − | 0.540243i | \(-0.181668\pi\) | ||||
0.841509 | + | 0.540243i | \(0.181668\pi\) | |||||||
\(258\) | −3.01574 | −0.187752 | ||||||||
\(259\) | −18.0276 | −1.12018 | ||||||||
\(260\) | 0.188493 | 0.0116898 | ||||||||
\(261\) | 2.95446 | 0.182877 | ||||||||
\(262\) | 10.0243 | 0.619303 | ||||||||
\(263\) | −5.11106 | −0.315161 | −0.157581 | − | 0.987506i | \(-0.550369\pi\) | ||||
−0.157581 | + | 0.987506i | \(0.550369\pi\) | |||||||
\(264\) | 5.37862 | 0.331031 | ||||||||
\(265\) | 2.08773 | 0.128248 | ||||||||
\(266\) | −2.78573 | −0.170804 | ||||||||
\(267\) | 12.4282 | 0.760593 | ||||||||
\(268\) | −4.58226 | −0.279906 | ||||||||
\(269\) | −5.04937 | −0.307865 | −0.153933 | − | 0.988081i | \(-0.549194\pi\) | ||||
−0.153933 | + | 0.988081i | \(0.549194\pi\) | |||||||
\(270\) | −0.645786 | −0.0393013 | ||||||||
\(271\) | −10.8978 | −0.661996 | −0.330998 | − | 0.943632i | \(-0.607385\pi\) | ||||
−0.330998 | + | 0.943632i | \(0.607385\pi\) | |||||||
\(272\) | 11.2018 | 0.679209 | ||||||||
\(273\) | 3.05259 | 0.184751 | ||||||||
\(274\) | −18.0335 | −1.08945 | ||||||||
\(275\) | 8.43013 | 0.508356 | ||||||||
\(276\) | −0.0887656 | −0.00534306 | ||||||||
\(277\) | −3.91725 | −0.235365 | −0.117682 | − | 0.993051i | \(-0.537546\pi\) | ||||
−0.117682 | + | 0.993051i | \(0.537546\pi\) | |||||||
\(278\) | −21.3207 | −1.27873 | ||||||||
\(279\) | 0.136135 | 0.00815021 | ||||||||
\(280\) | 4.67671 | 0.279487 | ||||||||
\(281\) | 6.75296 | 0.402848 | 0.201424 | − | 0.979504i | \(-0.435443\pi\) | ||||
0.201424 | + | 0.979504i | \(0.435443\pi\) | |||||||
\(282\) | −9.28105 | −0.552679 | ||||||||
\(283\) | −6.30052 | −0.374527 | −0.187263 | − | 0.982310i | \(-0.559962\pi\) | ||||
−0.187263 | + | 0.982310i | \(0.559962\pi\) | |||||||
\(284\) | −2.25972 | −0.134090 | ||||||||
\(285\) | −0.362082 | −0.0214479 | ||||||||
\(286\) | 2.26719 | 0.134061 | ||||||||
\(287\) | 17.7490 | 1.04769 | ||||||||
\(288\) | −2.07720 | −0.122400 | ||||||||
\(289\) | −4.08127 | −0.240075 | ||||||||
\(290\) | 1.90795 | 0.112039 | ||||||||
\(291\) | 15.8471 | 0.928974 | ||||||||
\(292\) | 5.17953 | 0.303109 | ||||||||
\(293\) | −14.8568 | −0.867943 | −0.433971 | − | 0.900927i | \(-0.642888\pi\) | ||||
−0.433971 | + | 0.900927i | \(0.642888\pi\) | |||||||
\(294\) | 2.95764 | 0.172493 | ||||||||
\(295\) | 2.05833 | 0.119841 | ||||||||
\(296\) | 17.8744 | 1.03893 | ||||||||
\(297\) | 1.77709 | 0.103117 | ||||||||
\(298\) | −2.09239 | −0.121209 | ||||||||
\(299\) | −0.238375 | −0.0137856 | ||||||||
\(300\) | −1.76648 | −0.101987 | ||||||||
\(301\) | 7.21581 | 0.415913 | ||||||||
\(302\) | 3.89929 | 0.224379 | ||||||||
\(303\) | 3.35478 | 0.192727 | ||||||||
\(304\) | 2.22932 | 0.127860 | ||||||||
\(305\) | 1.54521 | 0.0884784 | ||||||||
\(306\) | 4.58550 | 0.262136 | ||||||||
\(307\) | 2.47596 | 0.141310 | 0.0706552 | − | 0.997501i | \(-0.477491\pi\) | ||||
0.0706552 | + | 0.997501i | \(0.477491\pi\) | |||||||
\(308\) | −2.02005 | −0.115103 | ||||||||
\(309\) | 1.00000 | 0.0568880 | ||||||||
\(310\) | 0.0879143 | 0.00499320 | ||||||||
\(311\) | 4.91918 | 0.278941 | 0.139471 | − | 0.990226i | \(-0.455460\pi\) | ||||
0.139471 | + | 0.990226i | \(0.455460\pi\) | |||||||
\(312\) | −3.02664 | −0.171350 | ||||||||
\(313\) | −22.5452 | −1.27433 | −0.637166 | − | 0.770727i | \(-0.719893\pi\) | ||||
−0.637166 | + | 0.770727i | \(0.719893\pi\) | |||||||
\(314\) | −11.0349 | −0.622734 | ||||||||
\(315\) | 1.54518 | 0.0870612 | ||||||||
\(316\) | 3.79317 | 0.213382 | ||||||||
\(317\) | 26.6686 | 1.49786 | 0.748930 | − | 0.662649i | \(-0.230568\pi\) | ||||
0.748930 | + | 0.662649i | \(0.230568\pi\) | |||||||
\(318\) | −5.26185 | −0.295070 | ||||||||
\(319\) | −5.25036 | −0.293964 | ||||||||
\(320\) | −4.49658 | −0.251366 | ||||||||
\(321\) | −17.7894 | −0.992907 | ||||||||
\(322\) | −0.928338 | −0.0517343 | ||||||||
\(323\) | 2.57101 | 0.143055 | ||||||||
\(324\) | −0.372378 | −0.0206876 | ||||||||
\(325\) | −4.74377 | −0.263137 | ||||||||
\(326\) | −21.2551 | −1.17721 | ||||||||
\(327\) | 16.2712 | 0.899797 | ||||||||
\(328\) | −17.5981 | −0.971691 | ||||||||
\(329\) | 22.2069 | 1.22431 | ||||||||
\(330\) | 1.14762 | 0.0631745 | ||||||||
\(331\) | 27.3313 | 1.50226 | 0.751131 | − | 0.660153i | \(-0.229509\pi\) | ||||
0.751131 | + | 0.660153i | \(0.229509\pi\) | |||||||
\(332\) | −0.615606 | −0.0337858 | ||||||||
\(333\) | 5.90568 | 0.323629 | ||||||||
\(334\) | −23.1141 | −1.26475 | ||||||||
\(335\) | −6.22885 | −0.340319 | ||||||||
\(336\) | −9.51363 | −0.519011 | ||||||||
\(337\) | 30.3518 | 1.65337 | 0.826683 | − | 0.562668i | \(-0.190225\pi\) | ||||
0.826683 | + | 0.562668i | \(0.190225\pi\) | |||||||
\(338\) | −1.27578 | −0.0693934 | ||||||||
\(339\) | 0.902316 | 0.0490071 | ||||||||
\(340\) | −0.677494 | −0.0367423 | ||||||||
\(341\) | −0.241925 | −0.0131010 | ||||||||
\(342\) | 0.912581 | 0.0493467 | ||||||||
\(343\) | 14.2913 | 0.771659 | ||||||||
\(344\) | −7.15448 | −0.385743 | ||||||||
\(345\) | −0.120663 | −0.00649626 | ||||||||
\(346\) | 9.71454 | 0.522257 | ||||||||
\(347\) | 25.3945 | 1.36325 | 0.681625 | − | 0.731702i | \(-0.261274\pi\) | ||||
0.681625 | + | 0.731702i | \(0.261274\pi\) | |||||||
\(348\) | 1.10018 | 0.0589756 | ||||||||
\(349\) | 13.8170 | 0.739607 | 0.369804 | − | 0.929110i | \(-0.379425\pi\) | ||||
0.369804 | + | 0.929110i | \(0.379425\pi\) | |||||||
\(350\) | −18.4743 | −0.987495 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 3.69138 | 0.196751 | ||||||||
\(353\) | 10.9712 | 0.583941 | 0.291970 | − | 0.956427i | \(-0.405689\pi\) | ||||
0.291970 | + | 0.956427i | \(0.405689\pi\) | |||||||
\(354\) | −5.18777 | −0.275727 | ||||||||
\(355\) | −3.07173 | −0.163031 | ||||||||
\(356\) | 4.62798 | 0.245282 | ||||||||
\(357\) | −10.9718 | −0.580690 | ||||||||
\(358\) | −26.7462 | −1.41358 | ||||||||
\(359\) | 22.8471 | 1.20583 | 0.602913 | − | 0.797807i | \(-0.294007\pi\) | ||||
0.602913 | + | 0.797807i | \(0.294007\pi\) | |||||||
\(360\) | −1.53205 | −0.0807460 | ||||||||
\(361\) | −18.4883 | −0.973070 | ||||||||
\(362\) | 18.2391 | 0.958625 | ||||||||
\(363\) | 7.84194 | 0.411595 | ||||||||
\(364\) | 1.13672 | 0.0595801 | ||||||||
\(365\) | 7.04075 | 0.368530 | ||||||||
\(366\) | −3.89450 | −0.203569 | ||||||||
\(367\) | −11.2060 | −0.584947 | −0.292474 | − | 0.956274i | \(-0.594478\pi\) | ||||
−0.292474 | + | 0.956274i | \(0.594478\pi\) | |||||||
\(368\) | 0.742915 | 0.0387271 | ||||||||
\(369\) | −5.81439 | −0.302685 | ||||||||
\(370\) | 3.81380 | 0.198270 | ||||||||
\(371\) | 12.5901 | 0.653647 | ||||||||
\(372\) | 0.0506938 | 0.00262835 | ||||||||
\(373\) | −6.17534 | −0.319747 | −0.159874 | − | 0.987138i | \(-0.551109\pi\) | ||||
−0.159874 | + | 0.987138i | \(0.551109\pi\) | |||||||
\(374\) | −8.14886 | −0.421368 | ||||||||
\(375\) | −4.93218 | −0.254697 | ||||||||
\(376\) | −22.0182 | −1.13550 | ||||||||
\(377\) | 2.95446 | 0.152163 | ||||||||
\(378\) | −3.89444 | −0.200308 | ||||||||
\(379\) | 17.3821 | 0.892857 | 0.446428 | − | 0.894819i | \(-0.352696\pi\) | ||||
0.446428 | + | 0.894819i | \(0.352696\pi\) | |||||||
\(380\) | −0.134831 | −0.00691669 | ||||||||
\(381\) | 18.5786 | 0.951808 | ||||||||
\(382\) | −3.08845 | −0.158019 | ||||||||
\(383\) | 9.86224 | 0.503937 | 0.251969 | − | 0.967735i | \(-0.418922\pi\) | ||||
0.251969 | + | 0.967735i | \(0.418922\pi\) | |||||||
\(384\) | 7.17866 | 0.366334 | ||||||||
\(385\) | −2.74593 | −0.139946 | ||||||||
\(386\) | 6.89271 | 0.350830 | ||||||||
\(387\) | −2.36383 | −0.120160 | ||||||||
\(388\) | 5.90111 | 0.299583 | ||||||||
\(389\) | 14.5318 | 0.736791 | 0.368396 | − | 0.929669i | \(-0.379907\pi\) | ||||
0.368396 | + | 0.929669i | \(0.379907\pi\) | |||||||
\(390\) | −0.645786 | −0.0327006 | ||||||||
\(391\) | 0.856783 | 0.0433294 | ||||||||
\(392\) | 7.01664 | 0.354394 | ||||||||
\(393\) | 7.85737 | 0.396352 | ||||||||
\(394\) | −25.1075 | −1.26490 | ||||||||
\(395\) | 5.15621 | 0.259437 | ||||||||
\(396\) | 0.661750 | 0.0332542 | ||||||||
\(397\) | −21.6455 | −1.08635 | −0.543177 | − | 0.839618i | \(-0.682779\pi\) | ||||
−0.543177 | + | 0.839618i | \(0.682779\pi\) | |||||||
\(398\) | 22.0437 | 1.10495 | ||||||||
\(399\) | −2.18355 | −0.109314 | ||||||||
\(400\) | 14.7843 | 0.739217 | ||||||||
\(401\) | 8.98126 | 0.448503 | 0.224251 | − | 0.974531i | \(-0.428006\pi\) | ||||
0.224251 | + | 0.974531i | \(0.428006\pi\) | |||||||
\(402\) | 15.6990 | 0.782997 | ||||||||
\(403\) | 0.136135 | 0.00678139 | ||||||||
\(404\) | 1.24925 | 0.0621523 | ||||||||
\(405\) | −0.506188 | −0.0251527 | ||||||||
\(406\) | 11.5060 | 0.571032 | ||||||||
\(407\) | −10.4949 | −0.520215 | ||||||||
\(408\) | 10.8785 | 0.538568 | ||||||||
\(409\) | −30.4957 | −1.50791 | −0.753957 | − | 0.656923i | \(-0.771857\pi\) | ||||
−0.753957 | + | 0.656923i | \(0.771857\pi\) | |||||||
\(410\) | −3.75485 | −0.185439 | ||||||||
\(411\) | −14.1353 | −0.697242 | ||||||||
\(412\) | 0.372378 | 0.0183457 | ||||||||
\(413\) | 12.4129 | 0.610797 | ||||||||
\(414\) | 0.304115 | 0.0149464 | ||||||||
\(415\) | −0.836818 | −0.0410778 | ||||||||
\(416\) | −2.07720 | −0.101843 | ||||||||
\(417\) | −16.7119 | −0.818385 | ||||||||
\(418\) | −1.62174 | −0.0793220 | ||||||||
\(419\) | −4.37964 | −0.213959 | −0.106980 | − | 0.994261i | \(-0.534118\pi\) | ||||
−0.106980 | + | 0.994261i | \(0.534118\pi\) | |||||||
\(420\) | 0.575392 | 0.0280762 | ||||||||
\(421\) | 5.87184 | 0.286176 | 0.143088 | − | 0.989710i | \(-0.454297\pi\) | ||||
0.143088 | + | 0.989710i | \(0.454297\pi\) | |||||||
\(422\) | −19.5993 | −0.954080 | ||||||||
\(423\) | −7.27479 | −0.353712 | ||||||||
\(424\) | −12.4831 | −0.606233 | ||||||||
\(425\) | 17.0504 | 0.827065 | ||||||||
\(426\) | 7.74192 | 0.375097 | ||||||||
\(427\) | 9.31845 | 0.450951 | ||||||||
\(428\) | −6.62437 | −0.320201 | ||||||||
\(429\) | 1.77709 | 0.0857989 | ||||||||
\(430\) | −1.52653 | −0.0736159 | ||||||||
\(431\) | −18.9790 | −0.914187 | −0.457094 | − | 0.889419i | \(-0.651110\pi\) | ||||
−0.457094 | + | 0.889419i | \(0.651110\pi\) | |||||||
\(432\) | 3.11658 | 0.149947 | ||||||||
\(433\) | 31.1549 | 1.49721 | 0.748604 | − | 0.663017i | \(-0.230724\pi\) | ||||
0.748604 | + | 0.663017i | \(0.230724\pi\) | |||||||
\(434\) | 0.530171 | 0.0254490 | ||||||||
\(435\) | 1.49551 | 0.0717044 | ||||||||
\(436\) | 6.05901 | 0.290174 | ||||||||
\(437\) | 0.170512 | 0.00815671 | ||||||||
\(438\) | −17.7453 | −0.847904 | ||||||||
\(439\) | −16.0983 | −0.768332 | −0.384166 | − | 0.923264i | \(-0.625511\pi\) | ||||
−0.384166 | + | 0.923264i | \(0.625511\pi\) | |||||||
\(440\) | 2.72259 | 0.129794 | ||||||||
\(441\) | 2.31830 | 0.110395 | ||||||||
\(442\) | 4.58550 | 0.218110 | ||||||||
\(443\) | −21.9726 | −1.04395 | −0.521975 | − | 0.852961i | \(-0.674805\pi\) | ||||
−0.521975 | + | 0.852961i | \(0.674805\pi\) | |||||||
\(444\) | 2.19914 | 0.104367 | ||||||||
\(445\) | 6.29100 | 0.298222 | ||||||||
\(446\) | −22.3534 | −1.05847 | ||||||||
\(447\) | −1.64008 | −0.0775732 | ||||||||
\(448\) | −27.1168 | −1.28115 | ||||||||
\(449\) | 20.9980 | 0.990956 | 0.495478 | − | 0.868621i | \(-0.334993\pi\) | ||||
0.495478 | + | 0.868621i | \(0.334993\pi\) | |||||||
\(450\) | 6.05203 | 0.285295 | ||||||||
\(451\) | 10.3327 | 0.486549 | ||||||||
\(452\) | 0.336002 | 0.0158042 | ||||||||
\(453\) | 3.05639 | 0.143602 | ||||||||
\(454\) | 30.6432 | 1.43816 | ||||||||
\(455\) | 1.54518 | 0.0724393 | ||||||||
\(456\) | 2.16499 | 0.101385 | ||||||||
\(457\) | −7.24415 | −0.338867 | −0.169433 | − | 0.985542i | \(-0.554194\pi\) | ||||
−0.169433 | + | 0.985542i | \(0.554194\pi\) | |||||||
\(458\) | 2.66765 | 0.124651 | ||||||||
\(459\) | 3.59426 | 0.167766 | ||||||||
\(460\) | −0.0449321 | −0.00209497 | ||||||||
\(461\) | 10.9642 | 0.510652 | 0.255326 | − | 0.966855i | \(-0.417817\pi\) | ||||
0.255326 | + | 0.966855i | \(0.417817\pi\) | |||||||
\(462\) | 6.92078 | 0.321984 | ||||||||
\(463\) | −29.2865 | −1.36106 | −0.680529 | − | 0.732721i | \(-0.738250\pi\) | ||||
−0.680529 | + | 0.732721i | \(0.738250\pi\) | |||||||
\(464\) | −9.20782 | −0.427462 | ||||||||
\(465\) | 0.0689101 | 0.00319563 | ||||||||
\(466\) | 11.6774 | 0.540944 | ||||||||
\(467\) | 41.8942 | 1.93863 | 0.969317 | − | 0.245813i | \(-0.0790548\pi\) | ||||
0.969317 | + | 0.245813i | \(0.0790548\pi\) | |||||||
\(468\) | −0.372378 | −0.0172132 | ||||||||
\(469\) | −37.5634 | −1.73452 | ||||||||
\(470\) | −4.69796 | −0.216701 | ||||||||
\(471\) | −8.64949 | −0.398547 | ||||||||
\(472\) | −12.3073 | −0.566491 | ||||||||
\(473\) | 4.20075 | 0.193151 | ||||||||
\(474\) | −12.9956 | −0.596906 | ||||||||
\(475\) | 3.39327 | 0.155694 | ||||||||
\(476\) | −4.08566 | −0.187266 | ||||||||
\(477\) | −4.12441 | −0.188844 | ||||||||
\(478\) | −8.85202 | −0.404882 | ||||||||
\(479\) | 1.31516 | 0.0600912 | 0.0300456 | − | 0.999549i | \(-0.490435\pi\) | ||||
0.0300456 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(480\) | −1.05145 | −0.0479920 | ||||||||
\(481\) | 5.90568 | 0.269276 | ||||||||
\(482\) | −34.0149 | −1.54934 | ||||||||
\(483\) | −0.727661 | −0.0331097 | ||||||||
\(484\) | 2.92016 | 0.132735 | ||||||||
\(485\) | 8.02161 | 0.364243 | ||||||||
\(486\) | 1.27578 | 0.0578707 | ||||||||
\(487\) | 29.8662 | 1.35337 | 0.676683 | − | 0.736274i | \(-0.263417\pi\) | ||||
0.676683 | + | 0.736274i | \(0.263417\pi\) | |||||||
\(488\) | −9.23923 | −0.418240 | ||||||||
\(489\) | −16.6605 | −0.753412 | ||||||||
\(490\) | 1.49712 | 0.0676331 | ||||||||
\(491\) | −8.17232 | −0.368811 | −0.184406 | − | 0.982850i | \(-0.559036\pi\) | ||||
−0.184406 | + | 0.982850i | \(0.559036\pi\) | |||||||
\(492\) | −2.16515 | −0.0976125 | ||||||||
\(493\) | −10.6191 | −0.478261 | ||||||||
\(494\) | 0.912581 | 0.0410590 | ||||||||
\(495\) | 0.899543 | 0.0404315 | ||||||||
\(496\) | −0.424277 | −0.0190506 | ||||||||
\(497\) | −18.5242 | −0.830925 | ||||||||
\(498\) | 2.10909 | 0.0945108 | ||||||||
\(499\) | 5.99482 | 0.268365 | 0.134183 | − | 0.990957i | \(-0.457159\pi\) | ||||
0.134183 | + | 0.990957i | \(0.457159\pi\) | |||||||
\(500\) | −1.83663 | −0.0821368 | ||||||||
\(501\) | −18.1176 | −0.809433 | ||||||||
\(502\) | −17.1597 | −0.765876 | ||||||||
\(503\) | 36.3423 | 1.62042 | 0.810212 | − | 0.586137i | \(-0.199352\pi\) | ||||
0.810212 | + | 0.586137i | \(0.199352\pi\) | |||||||
\(504\) | −9.23908 | −0.411541 | ||||||||
\(505\) | 1.69815 | 0.0755667 | ||||||||
\(506\) | −0.540441 | −0.0240255 | ||||||||
\(507\) | −1.00000 | −0.0444116 | ||||||||
\(508\) | 6.91824 | 0.306947 | ||||||||
\(509\) | 13.6721 | 0.606007 | 0.303003 | − | 0.952989i | \(-0.402011\pi\) | ||||
0.303003 | + | 0.952989i | \(0.402011\pi\) | |||||||
\(510\) | 2.32113 | 0.102781 | ||||||||
\(511\) | 42.4595 | 1.87830 | ||||||||
\(512\) | 25.3393 | 1.11985 | ||||||||
\(513\) | 0.715310 | 0.0315817 | ||||||||
\(514\) | −34.4217 | −1.51828 | ||||||||
\(515\) | 0.506188 | 0.0223053 | ||||||||
\(516\) | −0.880239 | −0.0387504 | ||||||||
\(517\) | 12.9280 | 0.568572 | ||||||||
\(518\) | 22.9993 | 1.01053 | ||||||||
\(519\) | 7.61457 | 0.334242 | ||||||||
\(520\) | −1.53205 | −0.0671848 | ||||||||
\(521\) | −5.96539 | −0.261348 | −0.130674 | − | 0.991425i | \(-0.541714\pi\) | ||||
−0.130674 | + | 0.991425i | \(0.541714\pi\) | |||||||
\(522\) | −3.76926 | −0.164976 | ||||||||
\(523\) | 18.0919 | 0.791106 | 0.395553 | − | 0.918443i | \(-0.370553\pi\) | ||||
0.395553 | + | 0.918443i | \(0.370553\pi\) | |||||||
\(524\) | 2.92591 | 0.127819 | ||||||||
\(525\) | −14.4808 | −0.631993 | ||||||||
\(526\) | 6.52060 | 0.284312 | ||||||||
\(527\) | −0.489307 | −0.0213145 | ||||||||
\(528\) | −5.53845 | −0.241030 | ||||||||
\(529\) | −22.9432 | −0.997529 | ||||||||
\(530\) | −2.66349 | −0.115694 | ||||||||
\(531\) | −4.06634 | −0.176464 | ||||||||
\(532\) | −0.813104 | −0.0352525 | ||||||||
\(533\) | −5.81439 | −0.251849 | ||||||||
\(534\) | −15.8557 | −0.686142 | ||||||||
\(535\) | −9.00478 | −0.389310 | ||||||||
\(536\) | 37.2441 | 1.60870 | ||||||||
\(537\) | −20.9646 | −0.904687 | ||||||||
\(538\) | 6.44190 | 0.277730 | ||||||||
\(539\) | −4.11983 | −0.177453 | ||||||||
\(540\) | −0.188493 | −0.00811145 | ||||||||
\(541\) | −10.5646 | −0.454208 | −0.227104 | − | 0.973871i | \(-0.572926\pi\) | ||||
−0.227104 | + | 0.973871i | \(0.572926\pi\) | |||||||
\(542\) | 13.9033 | 0.597196 | ||||||||
\(543\) | 14.2964 | 0.613517 | ||||||||
\(544\) | 7.46600 | 0.320102 | ||||||||
\(545\) | 8.23626 | 0.352803 | ||||||||
\(546\) | −3.89444 | −0.166667 | ||||||||
\(547\) | −23.2951 | −0.996027 | −0.498013 | − | 0.867169i | \(-0.665937\pi\) | ||||
−0.498013 | + | 0.867169i | \(0.665937\pi\) | |||||||
\(548\) | −5.26366 | −0.224852 | ||||||||
\(549\) | −3.05264 | −0.130283 | ||||||||
\(550\) | −10.7550 | −0.458595 | ||||||||
\(551\) | −2.11336 | −0.0900321 | ||||||||
\(552\) | 0.721476 | 0.0307080 | ||||||||
\(553\) | 31.0947 | 1.32228 | ||||||||
\(554\) | 4.99757 | 0.212326 | ||||||||
\(555\) | 2.98938 | 0.126892 | ||||||||
\(556\) | −6.22313 | −0.263920 | ||||||||
\(557\) | −4.54236 | −0.192466 | −0.0962331 | − | 0.995359i | \(-0.530679\pi\) | ||||
−0.0962331 | + | 0.995359i | \(0.530679\pi\) | |||||||
\(558\) | −0.173679 | −0.00735243 | ||||||||
\(559\) | −2.36383 | −0.0999796 | ||||||||
\(560\) | −4.81569 | −0.203500 | ||||||||
\(561\) | −6.38734 | −0.269674 | ||||||||
\(562\) | −8.61531 | −0.363415 | ||||||||
\(563\) | −11.5640 | −0.487364 | −0.243682 | − | 0.969855i | \(-0.578355\pi\) | ||||
−0.243682 | + | 0.969855i | \(0.578355\pi\) | |||||||
\(564\) | −2.70897 | −0.114068 | ||||||||
\(565\) | 0.456741 | 0.0192153 | ||||||||
\(566\) | 8.03809 | 0.337866 | ||||||||
\(567\) | −3.05259 | −0.128197 | ||||||||
\(568\) | 18.3668 | 0.770652 | ||||||||
\(569\) | 25.6662 | 1.07598 | 0.537991 | − | 0.842950i | \(-0.319183\pi\) | ||||
0.537991 | + | 0.842950i | \(0.319183\pi\) | |||||||
\(570\) | 0.461937 | 0.0193484 | ||||||||
\(571\) | −31.6651 | −1.32514 | −0.662572 | − | 0.748998i | \(-0.730535\pi\) | ||||
−0.662572 | + | 0.748998i | \(0.730535\pi\) | |||||||
\(572\) | 0.661750 | 0.0276691 | ||||||||
\(573\) | −2.42083 | −0.101131 | ||||||||
\(574\) | −22.6438 | −0.945134 | ||||||||
\(575\) | 1.13080 | 0.0471575 | ||||||||
\(576\) | 8.88321 | 0.370134 | ||||||||
\(577\) | 3.75953 | 0.156511 | 0.0782556 | − | 0.996933i | \(-0.475065\pi\) | ||||
0.0782556 | + | 0.996933i | \(0.475065\pi\) | |||||||
\(578\) | 5.20681 | 0.216575 | ||||||||
\(579\) | 5.40273 | 0.224530 | ||||||||
\(580\) | 0.556896 | 0.0231238 | ||||||||
\(581\) | −5.04647 | −0.209363 | ||||||||
\(582\) | −20.2175 | −0.838041 | ||||||||
\(583\) | 7.32946 | 0.303555 | ||||||||
\(584\) | −42.0986 | −1.74205 | ||||||||
\(585\) | −0.506188 | −0.0209283 | ||||||||
\(586\) | 18.9540 | 0.782984 | ||||||||
\(587\) | −9.25750 | −0.382098 | −0.191049 | − | 0.981580i | \(-0.561189\pi\) | ||||
−0.191049 | + | 0.981580i | \(0.561189\pi\) | |||||||
\(588\) | 0.863281 | 0.0356011 | ||||||||
\(589\) | −0.0973791 | −0.00401243 | ||||||||
\(590\) | −2.62599 | −0.108110 | ||||||||
\(591\) | −19.6801 | −0.809530 | ||||||||
\(592\) | −18.4055 | −0.756462 | ||||||||
\(593\) | 23.2842 | 0.956168 | 0.478084 | − | 0.878314i | \(-0.341331\pi\) | ||||
0.478084 | + | 0.878314i | \(0.341331\pi\) | |||||||
\(594\) | −2.26719 | −0.0930237 | ||||||||
\(595\) | −5.55380 | −0.227683 | ||||||||
\(596\) | −0.610729 | −0.0250165 | ||||||||
\(597\) | 17.2785 | 0.707164 | ||||||||
\(598\) | 0.304115 | 0.0124362 | ||||||||
\(599\) | 31.4527 | 1.28512 | 0.642561 | − | 0.766235i | \(-0.277872\pi\) | ||||
0.642561 | + | 0.766235i | \(0.277872\pi\) | |||||||
\(600\) | 14.3577 | 0.586150 | ||||||||
\(601\) | 40.8070 | 1.66455 | 0.832275 | − | 0.554362i | \(-0.187038\pi\) | ||||
0.832275 | + | 0.554362i | \(0.187038\pi\) | |||||||
\(602\) | −9.20581 | −0.375201 | ||||||||
\(603\) | 12.3054 | 0.501115 | ||||||||
\(604\) | 1.13813 | 0.0463099 | ||||||||
\(605\) | 3.96950 | 0.161383 | ||||||||
\(606\) | −4.27998 | −0.173862 | ||||||||
\(607\) | 35.9070 | 1.45742 | 0.728709 | − | 0.684823i | \(-0.240121\pi\) | ||||
0.728709 | + | 0.684823i | \(0.240121\pi\) | |||||||
\(608\) | 1.48584 | 0.0602588 | ||||||||
\(609\) | 9.01876 | 0.365459 | ||||||||
\(610\) | −1.97135 | −0.0798177 | ||||||||
\(611\) | −7.27479 | −0.294306 | ||||||||
\(612\) | 1.33842 | 0.0541026 | ||||||||
\(613\) | 6.01339 | 0.242879 | 0.121439 | − | 0.992599i | \(-0.461249\pi\) | ||||
0.121439 | + | 0.992599i | \(0.461249\pi\) | |||||||
\(614\) | −3.15879 | −0.127478 | ||||||||
\(615\) | −2.94318 | −0.118680 | ||||||||
\(616\) | 16.4187 | 0.661529 | ||||||||
\(617\) | 42.9411 | 1.72874 | 0.864372 | − | 0.502852i | \(-0.167716\pi\) | ||||
0.864372 | + | 0.502852i | \(0.167716\pi\) | |||||||
\(618\) | −1.27578 | −0.0513195 | ||||||||
\(619\) | 5.03275 | 0.202283 | 0.101142 | − | 0.994872i | \(-0.467750\pi\) | ||||
0.101142 | + | 0.994872i | \(0.467750\pi\) | |||||||
\(620\) | 0.0256606 | 0.00103055 | ||||||||
\(621\) | 0.238375 | 0.00956567 | ||||||||
\(622\) | −6.27581 | −0.251637 | ||||||||
\(623\) | 37.9382 | 1.51996 | ||||||||
\(624\) | 3.11658 | 0.124763 | ||||||||
\(625\) | 21.2223 | 0.848890 | ||||||||
\(626\) | 28.7628 | 1.14959 | ||||||||
\(627\) | −1.27117 | −0.0507658 | ||||||||
\(628\) | −3.22088 | −0.128527 | ||||||||
\(629\) | −21.2266 | −0.846358 | ||||||||
\(630\) | −1.97132 | −0.0785392 | ||||||||
\(631\) | −29.7510 | −1.18437 | −0.592185 | − | 0.805802i | \(-0.701734\pi\) | ||||
−0.592185 | + | 0.805802i | \(0.701734\pi\) | |||||||
\(632\) | −30.8304 | −1.22637 | ||||||||
\(633\) | −15.3626 | −0.610608 | ||||||||
\(634\) | −34.0234 | −1.35124 | ||||||||
\(635\) | 9.40424 | 0.373196 | ||||||||
\(636\) | −1.53584 | −0.0608999 | ||||||||
\(637\) | 2.31830 | 0.0918542 | ||||||||
\(638\) | 6.69832 | 0.265189 | ||||||||
\(639\) | 6.06837 | 0.240061 | ||||||||
\(640\) | 3.63375 | 0.143637 | ||||||||
\(641\) | −38.8127 | −1.53301 | −0.766505 | − | 0.642238i | \(-0.778006\pi\) | ||||
−0.766505 | + | 0.642238i | \(0.778006\pi\) | |||||||
\(642\) | 22.6954 | 0.895716 | ||||||||
\(643\) | −34.5045 | −1.36073 | −0.680363 | − | 0.732875i | \(-0.738178\pi\) | ||||
−0.680363 | + | 0.732875i | \(0.738178\pi\) | |||||||
\(644\) | −0.270965 | −0.0106775 | ||||||||
\(645\) | −1.19654 | −0.0471139 | ||||||||
\(646\) | −3.28006 | −0.129052 | ||||||||
\(647\) | −21.0735 | −0.828483 | −0.414241 | − | 0.910167i | \(-0.635953\pi\) | ||||
−0.414241 | + | 0.910167i | \(0.635953\pi\) | |||||||
\(648\) | 3.02664 | 0.118898 | ||||||||
\(649\) | 7.22626 | 0.283656 | ||||||||
\(650\) | 6.05203 | 0.237380 | ||||||||
\(651\) | 0.415565 | 0.0162873 | ||||||||
\(652\) | −6.20398 | −0.242967 | ||||||||
\(653\) | 8.74814 | 0.342341 | 0.171171 | − | 0.985241i | \(-0.445245\pi\) | ||||
0.171171 | + | 0.985241i | \(0.445245\pi\) | |||||||
\(654\) | −20.7585 | −0.811720 | ||||||||
\(655\) | 3.97730 | 0.155406 | ||||||||
\(656\) | 18.1210 | 0.707507 | ||||||||
\(657\) | −13.9094 | −0.542656 | ||||||||
\(658\) | −28.3312 | −1.10447 | ||||||||
\(659\) | −4.59733 | −0.179087 | −0.0895433 | − | 0.995983i | \(-0.528541\pi\) | ||||
−0.0895433 | + | 0.995983i | \(0.528541\pi\) | |||||||
\(660\) | 0.334970 | 0.0130387 | ||||||||
\(661\) | −7.30213 | −0.284020 | −0.142010 | − | 0.989865i | \(-0.545357\pi\) | ||||
−0.142010 | + | 0.989865i | \(0.545357\pi\) | |||||||
\(662\) | −34.8688 | −1.35521 | ||||||||
\(663\) | 3.59426 | 0.139590 | ||||||||
\(664\) | 5.00357 | 0.194176 | ||||||||
\(665\) | −1.10529 | −0.0428611 | ||||||||
\(666\) | −7.53436 | −0.291951 | ||||||||
\(667\) | −0.704271 | −0.0272695 | ||||||||
\(668\) | −6.74657 | −0.261033 | ||||||||
\(669\) | −17.5213 | −0.677414 | ||||||||
\(670\) | 7.94667 | 0.307006 | ||||||||
\(671\) | 5.42482 | 0.209423 | ||||||||
\(672\) | −6.34083 | −0.244603 | ||||||||
\(673\) | −51.1172 | −1.97042 | −0.985211 | − | 0.171344i | \(-0.945189\pi\) | ||||
−0.985211 | + | 0.171344i | \(0.945189\pi\) | |||||||
\(674\) | −38.7223 | −1.49153 | ||||||||
\(675\) | 4.74377 | 0.182588 | ||||||||
\(676\) | −0.372378 | −0.0143222 | ||||||||
\(677\) | −12.0934 | −0.464788 | −0.232394 | − | 0.972622i | \(-0.574656\pi\) | ||||
−0.232394 | + | 0.972622i | \(0.574656\pi\) | |||||||
\(678\) | −1.15116 | −0.0442100 | ||||||||
\(679\) | 48.3747 | 1.85645 | ||||||||
\(680\) | 5.50659 | 0.211168 | ||||||||
\(681\) | 24.0192 | 0.920417 | ||||||||
\(682\) | 0.308644 | 0.0118186 | ||||||||
\(683\) | 25.9836 | 0.994234 | 0.497117 | − | 0.867684i | \(-0.334392\pi\) | ||||
0.497117 | + | 0.867684i | \(0.334392\pi\) | |||||||
\(684\) | 0.266366 | 0.0101847 | ||||||||
\(685\) | −7.15510 | −0.273382 | ||||||||
\(686\) | −18.2326 | −0.696125 | ||||||||
\(687\) | 2.09099 | 0.0797764 | ||||||||
\(688\) | 7.36708 | 0.280867 | ||||||||
\(689\) | −4.12441 | −0.157127 | ||||||||
\(690\) | 0.153939 | 0.00586037 | ||||||||
\(691\) | 30.7103 | 1.16828 | 0.584138 | − | 0.811654i | \(-0.301433\pi\) | ||||
0.584138 | + | 0.811654i | \(0.301433\pi\) | |||||||
\(692\) | 2.83549 | 0.107789 | ||||||||
\(693\) | 5.42473 | 0.206069 | ||||||||
\(694\) | −32.3979 | −1.22981 | ||||||||
\(695\) | −8.45936 | −0.320882 | ||||||||
\(696\) | −8.94210 | −0.338949 | ||||||||
\(697\) | 20.8985 | 0.791586 | ||||||||
\(698\) | −17.6275 | −0.667211 | ||||||||
\(699\) | 9.15311 | 0.346202 | ||||||||
\(700\) | −5.39232 | −0.203811 | ||||||||
\(701\) | −51.8192 | −1.95719 | −0.978593 | − | 0.205806i | \(-0.934018\pi\) | ||||
−0.978593 | + | 0.205806i | \(0.934018\pi\) | |||||||
\(702\) | 1.27578 | 0.0481513 | ||||||||
\(703\) | −4.22439 | −0.159326 | ||||||||
\(704\) | −15.7863 | −0.594968 | ||||||||
\(705\) | −3.68241 | −0.138688 | ||||||||
\(706\) | −13.9969 | −0.526782 | ||||||||
\(707\) | 10.2408 | 0.385144 | ||||||||
\(708\) | −1.51421 | −0.0569076 | ||||||||
\(709\) | −31.7882 | −1.19383 | −0.596915 | − | 0.802305i | \(-0.703607\pi\) | ||||
−0.596915 | + | 0.802305i | \(0.703607\pi\) | |||||||
\(710\) | 3.91887 | 0.147072 | ||||||||
\(711\) | −10.1863 | −0.382018 | ||||||||
\(712\) | −37.6157 | −1.40971 | ||||||||
\(713\) | −0.0324513 | −0.00121531 | ||||||||
\(714\) | 13.9976 | 0.523849 | ||||||||
\(715\) | 0.899543 | 0.0336410 | ||||||||
\(716\) | −7.80673 | −0.291751 | ||||||||
\(717\) | −6.93850 | −0.259123 | ||||||||
\(718\) | −29.1480 | −1.08779 | ||||||||
\(719\) | −33.9686 | −1.26681 | −0.633407 | − | 0.773819i | \(-0.718344\pi\) | ||||
−0.633407 | + | 0.773819i | \(0.718344\pi\) | |||||||
\(720\) | 1.57758 | 0.0587928 | ||||||||
\(721\) | 3.05259 | 0.113684 | ||||||||
\(722\) | 23.5871 | 0.877821 | ||||||||
\(723\) | −26.6620 | −0.991569 | ||||||||
\(724\) | 5.32365 | 0.197852 | ||||||||
\(725\) | −14.0153 | −0.520515 | ||||||||
\(726\) | −10.0046 | −0.371306 | ||||||||
\(727\) | −16.9776 | −0.629663 | −0.314832 | − | 0.949148i | \(-0.601948\pi\) | ||||
−0.314832 | + | 0.949148i | \(0.601948\pi\) | |||||||
\(728\) | −9.23908 | −0.342423 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −8.98247 | −0.332456 | ||||||||
\(731\) | 8.49625 | 0.314245 | ||||||||
\(732\) | −1.13673 | −0.0420149 | ||||||||
\(733\) | −20.9167 | −0.772576 | −0.386288 | − | 0.922378i | \(-0.626243\pi\) | ||||
−0.386288 | + | 0.922378i | \(0.626243\pi\) | |||||||
\(734\) | 14.2964 | 0.527690 | ||||||||
\(735\) | 1.17349 | 0.0432849 | ||||||||
\(736\) | 0.495153 | 0.0182516 | ||||||||
\(737\) | −21.8679 | −0.805513 | ||||||||
\(738\) | 7.41791 | 0.273057 | ||||||||
\(739\) | 12.0997 | 0.445095 | 0.222548 | − | 0.974922i | \(-0.428563\pi\) | ||||
0.222548 | + | 0.974922i | \(0.428563\pi\) | |||||||
\(740\) | 1.11318 | 0.0409213 | ||||||||
\(741\) | 0.715310 | 0.0262776 | ||||||||
\(742\) | −16.0623 | −0.589664 | ||||||||
\(743\) | 15.0790 | 0.553194 | 0.276597 | − | 0.960986i | \(-0.410793\pi\) | ||||
0.276597 | + | 0.960986i | \(0.410793\pi\) | |||||||
\(744\) | −0.412033 | −0.0151059 | ||||||||
\(745\) | −0.830189 | −0.0304158 | ||||||||
\(746\) | 7.87840 | 0.288449 | ||||||||
\(747\) | 1.65318 | 0.0604866 | ||||||||
\(748\) | −2.37850 | −0.0869667 | ||||||||
\(749\) | −54.3037 | −1.98421 | ||||||||
\(750\) | 6.29239 | 0.229766 | ||||||||
\(751\) | 21.9237 | 0.800009 | 0.400004 | − | 0.916513i | \(-0.369009\pi\) | ||||
0.400004 | + | 0.916513i | \(0.369009\pi\) | |||||||
\(752\) | 22.6725 | 0.826779 | ||||||||
\(753\) | −13.4503 | −0.490158 | ||||||||
\(754\) | −3.76926 | −0.137268 | ||||||||
\(755\) | 1.54711 | 0.0563050 | ||||||||
\(756\) | −1.13672 | −0.0413419 | ||||||||
\(757\) | −2.99591 | −0.108888 | −0.0544440 | − | 0.998517i | \(-0.517339\pi\) | ||||
−0.0544440 | + | 0.998517i | \(0.517339\pi\) | |||||||
\(758\) | −22.1757 | −0.805459 | ||||||||
\(759\) | −0.423615 | −0.0153762 | ||||||||
\(760\) | 1.09589 | 0.0397521 | ||||||||
\(761\) | 4.79728 | 0.173901 | 0.0869506 | − | 0.996213i | \(-0.472288\pi\) | ||||
0.0869506 | + | 0.996213i | \(0.472288\pi\) | |||||||
\(762\) | −23.7022 | −0.858640 | ||||||||
\(763\) | 49.6691 | 1.79814 | ||||||||
\(764\) | −0.901461 | −0.0326137 | ||||||||
\(765\) | 1.81937 | 0.0657796 | ||||||||
\(766\) | −12.5821 | −0.454609 | ||||||||
\(767\) | −4.06634 | −0.146827 | ||||||||
\(768\) | 8.60802 | 0.310615 | ||||||||
\(769\) | −31.6564 | −1.14156 | −0.570779 | − | 0.821103i | \(-0.693359\pi\) | ||||
−0.570779 | + | 0.821103i | \(0.693359\pi\) | |||||||
\(770\) | 3.50322 | 0.126247 | ||||||||
\(771\) | −26.9808 | −0.971691 | ||||||||
\(772\) | 2.01186 | 0.0724083 | ||||||||
\(773\) | −38.0532 | −1.36868 | −0.684340 | − | 0.729163i | \(-0.739910\pi\) | ||||
−0.684340 | + | 0.729163i | \(0.739910\pi\) | |||||||
\(774\) | 3.01574 | 0.108399 | ||||||||
\(775\) | −0.645795 | −0.0231977 | ||||||||
\(776\) | −47.9635 | −1.72179 | ||||||||
\(777\) | 18.0276 | 0.646736 | ||||||||
\(778\) | −18.5394 | −0.664671 | ||||||||
\(779\) | 4.15910 | 0.149015 | ||||||||
\(780\) | −0.188493 | −0.00674913 | ||||||||
\(781\) | −10.7841 | −0.385884 | ||||||||
\(782\) | −1.09307 | −0.0390881 | ||||||||
\(783\) | −2.95446 | −0.105584 | ||||||||
\(784\) | −7.22515 | −0.258041 | ||||||||
\(785\) | −4.37827 | −0.156267 | ||||||||
\(786\) | −10.0243 | −0.357555 | ||||||||
\(787\) | 38.5758 | 1.37508 | 0.687539 | − | 0.726148i | \(-0.258691\pi\) | ||||
0.687539 | + | 0.726148i | \(0.258691\pi\) | |||||||
\(788\) | −7.32842 | −0.261064 | ||||||||
\(789\) | 5.11106 | 0.181959 | ||||||||
\(790\) | −6.57820 | −0.234042 | ||||||||
\(791\) | 2.75440 | 0.0979351 | ||||||||
\(792\) | −5.37862 | −0.191121 | ||||||||
\(793\) | −3.05264 | −0.108402 | ||||||||
\(794\) | 27.6149 | 0.980017 | ||||||||
\(795\) | −2.08773 | −0.0740440 | ||||||||
\(796\) | 6.43414 | 0.228052 | ||||||||
\(797\) | 35.8686 | 1.27053 | 0.635266 | − | 0.772294i | \(-0.280891\pi\) | ||||
0.635266 | + | 0.772294i | \(0.280891\pi\) | |||||||
\(798\) | 2.78573 | 0.0986139 | ||||||||
\(799\) | 26.1475 | 0.925032 | ||||||||
\(800\) | 9.85376 | 0.348383 | ||||||||
\(801\) | −12.4282 | −0.439129 | ||||||||
\(802\) | −11.4581 | −0.404601 | ||||||||
\(803\) | 24.7182 | 0.872287 | ||||||||
\(804\) | 4.58226 | 0.161604 | ||||||||
\(805\) | −0.368333 | −0.0129820 | ||||||||
\(806\) | −0.173679 | −0.00611759 | ||||||||
\(807\) | 5.04937 | 0.177746 | ||||||||
\(808\) | −10.1537 | −0.357207 | ||||||||
\(809\) | −43.6710 | −1.53539 | −0.767696 | − | 0.640814i | \(-0.778597\pi\) | ||||
−0.767696 | + | 0.640814i | \(0.778597\pi\) | |||||||
\(810\) | 0.645786 | 0.0226906 | ||||||||
\(811\) | 42.7642 | 1.50166 | 0.750828 | − | 0.660498i | \(-0.229655\pi\) | ||||
0.750828 | + | 0.660498i | \(0.229655\pi\) | |||||||
\(812\) | 3.35838 | 0.117856 | ||||||||
\(813\) | 10.8978 | 0.382203 | ||||||||
\(814\) | 13.3893 | 0.469293 | ||||||||
\(815\) | −8.43332 | −0.295406 | ||||||||
\(816\) | −11.2018 | −0.392142 | ||||||||
\(817\) | 1.69088 | 0.0591563 | ||||||||
\(818\) | 38.9059 | 1.36031 | ||||||||
\(819\) | −3.05259 | −0.106666 | ||||||||
\(820\) | −1.09597 | −0.0382730 | ||||||||
\(821\) | −2.57276 | −0.0897898 | −0.0448949 | − | 0.998992i | \(-0.514295\pi\) | ||||
−0.0448949 | + | 0.998992i | \(0.514295\pi\) | |||||||
\(822\) | 18.0335 | 0.628992 | ||||||||
\(823\) | 44.5744 | 1.55377 | 0.776883 | − | 0.629645i | \(-0.216800\pi\) | ||||
0.776883 | + | 0.629645i | \(0.216800\pi\) | |||||||
\(824\) | −3.02664 | −0.105438 | ||||||||
\(825\) | −8.43013 | −0.293499 | ||||||||
\(826\) | −15.8361 | −0.551009 | ||||||||
\(827\) | 9.11085 | 0.316815 | 0.158408 | − | 0.987374i | \(-0.449364\pi\) | ||||
0.158408 | + | 0.987374i | \(0.449364\pi\) | |||||||
\(828\) | 0.0887656 | 0.00308482 | ||||||||
\(829\) | 12.1320 | 0.421361 | 0.210680 | − | 0.977555i | \(-0.432432\pi\) | ||||
0.210680 | + | 0.977555i | \(0.432432\pi\) | |||||||
\(830\) | 1.06760 | 0.0370569 | ||||||||
\(831\) | 3.91725 | 0.135888 | ||||||||
\(832\) | 8.88321 | 0.307970 | ||||||||
\(833\) | −8.33256 | −0.288706 | ||||||||
\(834\) | 21.3207 | 0.738277 | ||||||||
\(835\) | −9.17089 | −0.317372 | ||||||||
\(836\) | −0.473356 | −0.0163714 | ||||||||
\(837\) | −0.136135 | −0.00470553 | ||||||||
\(838\) | 5.58747 | 0.193016 | ||||||||
\(839\) | −53.8711 | −1.85984 | −0.929918 | − | 0.367767i | \(-0.880122\pi\) | ||||
−0.929918 | + | 0.367767i | \(0.880122\pi\) | |||||||
\(840\) | −4.67671 | −0.161362 | ||||||||
\(841\) | −20.2711 | −0.699005 | ||||||||
\(842\) | −7.49119 | −0.258164 | ||||||||
\(843\) | −6.75296 | −0.232584 | ||||||||
\(844\) | −5.72068 | −0.196914 | ||||||||
\(845\) | −0.506188 | −0.0174134 | ||||||||
\(846\) | 9.28105 | 0.319089 | ||||||||
\(847\) | 23.9382 | 0.822527 | ||||||||
\(848\) | 12.8541 | 0.441410 | ||||||||
\(849\) | 6.30052 | 0.216233 | ||||||||
\(850\) | −21.7526 | −0.746107 | ||||||||
\(851\) | −1.40777 | −0.0482576 | ||||||||
\(852\) | 2.25972 | 0.0774169 | ||||||||
\(853\) | 1.06628 | 0.0365089 | 0.0182544 | − | 0.999833i | \(-0.494189\pi\) | ||||
0.0182544 | + | 0.999833i | \(0.494189\pi\) | |||||||
\(854\) | −11.8883 | −0.406810 | ||||||||
\(855\) | 0.362082 | 0.0123829 | ||||||||
\(856\) | 53.8421 | 1.84028 | ||||||||
\(857\) | −16.6961 | −0.570328 | −0.285164 | − | 0.958479i | \(-0.592048\pi\) | ||||
−0.285164 | + | 0.958479i | \(0.592048\pi\) | |||||||
\(858\) | −2.26719 | −0.0774004 | ||||||||
\(859\) | −1.34068 | −0.0457434 | −0.0228717 | − | 0.999738i | \(-0.507281\pi\) | ||||
−0.0228717 | + | 0.999738i | \(0.507281\pi\) | |||||||
\(860\) | −0.445566 | −0.0151937 | ||||||||
\(861\) | −17.7490 | −0.604883 | ||||||||
\(862\) | 24.2131 | 0.824702 | ||||||||
\(863\) | −7.94115 | −0.270320 | −0.135160 | − | 0.990824i | \(-0.543155\pi\) | ||||
−0.135160 | + | 0.990824i | \(0.543155\pi\) | |||||||
\(864\) | 2.07720 | 0.0706677 | ||||||||
\(865\) | 3.85440 | 0.131054 | ||||||||
\(866\) | −39.7469 | −1.35065 | ||||||||
\(867\) | 4.08127 | 0.138607 | ||||||||
\(868\) | 0.154747 | 0.00525246 | ||||||||
\(869\) | 18.1021 | 0.614071 | ||||||||
\(870\) | −1.90795 | −0.0646856 | ||||||||
\(871\) | 12.3054 | 0.416953 | ||||||||
\(872\) | −49.2469 | −1.66771 | ||||||||
\(873\) | −15.8471 | −0.536343 | ||||||||
\(874\) | −0.217537 | −0.00735829 | ||||||||
\(875\) | −15.0559 | −0.508983 | ||||||||
\(876\) | −5.17953 | −0.175000 | ||||||||
\(877\) | 51.0387 | 1.72346 | 0.861728 | − | 0.507370i | \(-0.169382\pi\) | ||||
0.861728 | + | 0.507370i | \(0.169382\pi\) | |||||||
\(878\) | 20.5380 | 0.693124 | ||||||||
\(879\) | 14.8568 | 0.501107 | ||||||||
\(880\) | −2.80350 | −0.0945059 | ||||||||
\(881\) | 25.6095 | 0.862805 | 0.431403 | − | 0.902160i | \(-0.358019\pi\) | ||||
0.431403 | + | 0.902160i | \(0.358019\pi\) | |||||||
\(882\) | −2.95764 | −0.0995890 | ||||||||
\(883\) | −53.5333 | −1.80154 | −0.900769 | − | 0.434298i | \(-0.856997\pi\) | ||||
−0.900769 | + | 0.434298i | \(0.856997\pi\) | |||||||
\(884\) | 1.33842 | 0.0450160 | ||||||||
\(885\) | −2.05833 | −0.0691901 | ||||||||
\(886\) | 28.0323 | 0.941763 | ||||||||
\(887\) | 26.0123 | 0.873409 | 0.436704 | − | 0.899605i | \(-0.356146\pi\) | ||||
0.436704 | + | 0.899605i | \(0.356146\pi\) | |||||||
\(888\) | −17.8744 | −0.599824 | ||||||||
\(889\) | 56.7127 | 1.90208 | ||||||||
\(890\) | −8.02595 | −0.269031 | ||||||||
\(891\) | −1.77709 | −0.0595349 | ||||||||
\(892\) | −6.52456 | −0.218458 | ||||||||
\(893\) | 5.20373 | 0.174136 | ||||||||
\(894\) | 2.09239 | 0.0699799 | ||||||||
\(895\) | −10.6120 | −0.354720 | ||||||||
\(896\) | 21.9135 | 0.732078 | ||||||||
\(897\) | 0.238375 | 0.00795912 | ||||||||
\(898\) | −26.7889 | −0.893956 | ||||||||
\(899\) | 0.402207 | 0.0134144 | ||||||||
\(900\) | 1.76648 | 0.0588825 | ||||||||
\(901\) | 14.8242 | 0.493866 | ||||||||
\(902\) | −13.1823 | −0.438923 | ||||||||
\(903\) | −7.21581 | −0.240127 | ||||||||
\(904\) | −2.73098 | −0.0908312 | ||||||||
\(905\) | 7.23666 | 0.240555 | ||||||||
\(906\) | −3.89929 | −0.129545 | ||||||||
\(907\) | −14.1824 | −0.470918 | −0.235459 | − | 0.971884i | \(-0.575659\pi\) | ||||
−0.235459 | + | 0.971884i | \(0.575659\pi\) | |||||||
\(908\) | 8.94420 | 0.296824 | ||||||||
\(909\) | −3.35478 | −0.111271 | ||||||||
\(910\) | −1.97132 | −0.0653486 | ||||||||
\(911\) | −14.2700 | −0.472786 | −0.236393 | − | 0.971657i | \(-0.575965\pi\) | ||||
−0.236393 | + | 0.971657i | \(0.575965\pi\) | |||||||
\(912\) | −2.22932 | −0.0738202 | ||||||||
\(913\) | −2.93785 | −0.0972286 | ||||||||
\(914\) | 9.24196 | 0.305697 | ||||||||
\(915\) | −1.54521 | −0.0510830 | ||||||||
\(916\) | 0.778639 | 0.0257270 | ||||||||
\(917\) | 23.9853 | 0.792065 | ||||||||
\(918\) | −4.58550 | −0.151344 | ||||||||
\(919\) | −34.3479 | −1.13303 | −0.566517 | − | 0.824050i | \(-0.691709\pi\) | ||||
−0.566517 | + | 0.824050i | \(0.691709\pi\) | |||||||
\(920\) | 0.365202 | 0.0120404 | ||||||||
\(921\) | −2.47596 | −0.0815856 | ||||||||
\(922\) | −13.9879 | −0.460667 | ||||||||
\(923\) | 6.06837 | 0.199743 | ||||||||
\(924\) | 2.02005 | 0.0664547 | ||||||||
\(925\) | −28.0152 | −0.921134 | ||||||||
\(926\) | 37.3632 | 1.22783 | ||||||||
\(927\) | −1.00000 | −0.0328443 | ||||||||
\(928\) | −6.13701 | −0.201457 | ||||||||
\(929\) | 16.2958 | 0.534647 | 0.267324 | − | 0.963607i | \(-0.413861\pi\) | ||||
0.267324 | + | 0.963607i | \(0.413861\pi\) | |||||||
\(930\) | −0.0879143 | −0.00288282 | ||||||||
\(931\) | −1.65830 | −0.0543486 | ||||||||
\(932\) | 3.40841 | 0.111646 | ||||||||
\(933\) | −4.91918 | −0.161047 | ||||||||
\(934\) | −53.4480 | −1.74887 | ||||||||
\(935\) | −3.23320 | −0.105737 | ||||||||
\(936\) | 3.02664 | 0.0989288 | ||||||||
\(937\) | −33.8529 | −1.10593 | −0.552963 | − | 0.833206i | \(-0.686503\pi\) | ||||
−0.552963 | + | 0.833206i | \(0.686503\pi\) | |||||||
\(938\) | 47.9227 | 1.56473 | ||||||||
\(939\) | 22.5452 | 0.735736 | ||||||||
\(940\) | −1.37125 | −0.0447251 | ||||||||
\(941\) | 46.8092 | 1.52594 | 0.762969 | − | 0.646435i | \(-0.223741\pi\) | ||||
0.762969 | + | 0.646435i | \(0.223741\pi\) | |||||||
\(942\) | 11.0349 | 0.359536 | ||||||||
\(943\) | 1.38601 | 0.0451346 | ||||||||
\(944\) | 12.6731 | 0.412473 | ||||||||
\(945\) | −1.54518 | −0.0502648 | ||||||||
\(946\) | −5.35925 | −0.174244 | ||||||||
\(947\) | −52.0261 | −1.69062 | −0.845311 | − | 0.534275i | \(-0.820585\pi\) | ||||
−0.845311 | + | 0.534275i | \(0.820585\pi\) | |||||||
\(948\) | −3.79317 | −0.123196 | ||||||||
\(949\) | −13.9094 | −0.451517 | ||||||||
\(950\) | −4.32908 | −0.140454 | ||||||||
\(951\) | −26.6686 | −0.864790 | ||||||||
\(952\) | 33.2077 | 1.07627 | ||||||||
\(953\) | 9.23155 | 0.299039 | 0.149520 | − | 0.988759i | \(-0.452227\pi\) | ||||
0.149520 | + | 0.988759i | \(0.452227\pi\) | |||||||
\(954\) | 5.26185 | 0.170359 | ||||||||
\(955\) | −1.22539 | −0.0396528 | ||||||||
\(956\) | −2.58374 | −0.0835642 | ||||||||
\(957\) | 5.25036 | 0.169720 | ||||||||
\(958\) | −1.67786 | −0.0542092 | ||||||||
\(959\) | −43.1492 | −1.39336 | ||||||||
\(960\) | 4.49658 | 0.145126 | ||||||||
\(961\) | −30.9815 | −0.999402 | ||||||||
\(962\) | −7.53436 | −0.242918 | ||||||||
\(963\) | 17.7894 | 0.573255 | ||||||||
\(964\) | −9.92832 | −0.319770 | ||||||||
\(965\) | 2.73480 | 0.0880363 | ||||||||
\(966\) | 0.928338 | 0.0298688 | ||||||||
\(967\) | −36.9716 | −1.18893 | −0.594463 | − | 0.804123i | \(-0.702635\pi\) | ||||
−0.594463 | + | 0.804123i | \(0.702635\pi\) | |||||||
\(968\) | −23.7347 | −0.762863 | ||||||||
\(969\) | −2.57101 | −0.0825929 | ||||||||
\(970\) | −10.2338 | −0.328589 | ||||||||
\(971\) | −34.7886 | −1.11642 | −0.558210 | − | 0.829700i | \(-0.688512\pi\) | ||||
−0.558210 | + | 0.829700i | \(0.688512\pi\) | |||||||
\(972\) | 0.372378 | 0.0119440 | ||||||||
\(973\) | −51.0145 | −1.63545 | ||||||||
\(974\) | −38.1028 | −1.22089 | ||||||||
\(975\) | 4.74377 | 0.151922 | ||||||||
\(976\) | 9.51379 | 0.304529 | ||||||||
\(977\) | −9.71591 | −0.310839 | −0.155420 | − | 0.987849i | \(-0.549673\pi\) | ||||
−0.155420 | + | 0.987849i | \(0.549673\pi\) | |||||||
\(978\) | 21.2551 | 0.679664 | ||||||||
\(979\) | 22.0861 | 0.705873 | ||||||||
\(980\) | 0.436983 | 0.0139589 | ||||||||
\(981\) | −16.2712 | −0.519498 | ||||||||
\(982\) | 10.4261 | 0.332710 | ||||||||
\(983\) | 9.45583 | 0.301594 | 0.150797 | − | 0.988565i | \(-0.451816\pi\) | ||||
0.150797 | + | 0.988565i | \(0.451816\pi\) | |||||||
\(984\) | 17.5981 | 0.561006 | ||||||||
\(985\) | −9.96181 | −0.317410 | ||||||||
\(986\) | 13.5477 | 0.431447 | ||||||||
\(987\) | −22.2069 | −0.706854 | ||||||||
\(988\) | 0.266366 | 0.00847422 | ||||||||
\(989\) | 0.563480 | 0.0179176 | ||||||||
\(990\) | −1.14762 | −0.0364738 | ||||||||
\(991\) | −10.9428 | −0.347610 | −0.173805 | − | 0.984780i | \(-0.555606\pi\) | ||||
−0.173805 | + | 0.984780i | \(0.555606\pi\) | |||||||
\(992\) | −0.282780 | −0.00897828 | ||||||||
\(993\) | −27.3313 | −0.867332 | ||||||||
\(994\) | 23.6329 | 0.749590 | ||||||||
\(995\) | 8.74619 | 0.277273 | ||||||||
\(996\) | 0.615606 | 0.0195062 | ||||||||
\(997\) | 34.6737 | 1.09813 | 0.549063 | − | 0.835781i | \(-0.314985\pi\) | ||||
0.549063 | + | 0.835781i | \(0.314985\pi\) | |||||||
\(998\) | −7.64810 | −0.242096 | ||||||||
\(999\) | −5.90568 | −0.186847 |
(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 | 4017.2.a.j.1.7 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4017.2.a.j.1.7 | ✓ | 25 | 1.1 | even | 1 | trivial |