Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8020,2,Mod(1,8020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8020, 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("8020.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8020 = 2^{2} \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8020.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0400224211\) |
Analytic rank: | \(1\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8020.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.910150 | 0.525476 | 0.262738 | − | 0.964867i | \(-0.415375\pi\) | ||||
0.262738 | + | 0.964867i | \(0.415375\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.40834 | 0.532302 | 0.266151 | − | 0.963931i | \(-0.414248\pi\) | ||||
0.266151 | + | 0.963931i | \(0.414248\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.17163 | −0.723875 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.72560 | −0.821798 | −0.410899 | − | 0.911681i | \(-0.634785\pi\) | ||||
−0.410899 | + | 0.911681i | \(0.634785\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.96710 | 1.37763 | 0.688813 | − | 0.724939i | \(-0.258132\pi\) | ||||
0.688813 | + | 0.724939i | \(0.258132\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.910150 | −0.235000 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.31929 | 0.319976 | 0.159988 | − | 0.987119i | \(-0.448855\pi\) | ||||
0.159988 | + | 0.987119i | \(0.448855\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.68185 | −0.385844 | −0.192922 | − | 0.981214i | \(-0.561796\pi\) | ||||
−0.192922 | + | 0.981214i | \(0.561796\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.28180 | 0.279711 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.30276 | 0.897188 | 0.448594 | − | 0.893736i | \(-0.351925\pi\) | ||||
0.448594 | + | 0.893736i | \(0.351925\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.70696 | −0.905854 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.98564 | −1.11151 | −0.555753 | − | 0.831347i | \(-0.687570\pi\) | ||||
−0.555753 | + | 0.831347i | \(0.687570\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.173134 | 0.0310957 | 0.0155479 | − | 0.999879i | \(-0.495051\pi\) | ||||
0.0155479 | + | 0.999879i | \(0.495051\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.48070 | −0.431835 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.40834 | −0.238052 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.08751 | −0.343185 | −0.171592 | − | 0.985168i | \(-0.554891\pi\) | ||||
−0.171592 | + | 0.985168i | \(0.554891\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.52081 | 0.723909 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.57854 | −0.246526 | −0.123263 | − | 0.992374i | \(-0.539336\pi\) | ||||
−0.123263 | + | 0.992374i | \(0.539336\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.3754 | −1.58223 | −0.791116 | − | 0.611666i | \(-0.790500\pi\) | ||||
−0.791116 | + | 0.611666i | \(0.790500\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.17163 | 0.323727 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.61807 | −0.381885 | −0.190942 | − | 0.981601i | \(-0.561154\pi\) | ||||
−0.190942 | + | 0.981601i | \(0.561154\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.01659 | −0.716655 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.20075 | 0.168139 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.01074 | 0.276196 | 0.138098 | − | 0.990419i | \(-0.455901\pi\) | ||||
0.138098 | + | 0.990419i | \(0.455901\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.72560 | 0.367519 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.53074 | −0.202751 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.37023 | 0.438767 | 0.219383 | − | 0.975639i | \(-0.429595\pi\) | ||||
0.219383 | + | 0.975639i | \(0.429595\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.01769 | 0.386375 | 0.193188 | − | 0.981162i | \(-0.438117\pi\) | ||||
0.193188 | + | 0.981162i | \(0.438117\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.05838 | −0.385320 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.96710 | −0.616093 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.07701 | −0.131578 | −0.0657891 | − | 0.997834i | \(-0.520956\pi\) | ||||
−0.0657891 | + | 0.997834i | \(0.520956\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.91616 | 0.471450 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.238719 | 0.0283307 | 0.0141654 | − | 0.999900i | \(-0.495491\pi\) | ||||
0.0141654 | + | 0.999900i | \(0.495491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −11.9587 | −1.39967 | −0.699833 | − | 0.714307i | \(-0.746742\pi\) | ||||
−0.699833 | + | 0.714307i | \(0.746742\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.910150 | 0.105095 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.83856 | −0.437444 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.59577 | 0.517064 | 0.258532 | − | 0.966003i | \(-0.416761\pi\) | ||||
0.258532 | + | 0.966003i | \(0.416761\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.23084 | 0.247871 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.18072 | 0.129601 | 0.0648004 | − | 0.997898i | \(-0.479359\pi\) | ||||
0.0648004 | + | 0.997898i | \(0.479359\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.31929 | −0.143097 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −5.44784 | −0.584069 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.48814 | 0.157743 | 0.0788715 | − | 0.996885i | \(-0.474868\pi\) | ||||
0.0788715 | + | 0.996885i | \(0.474868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.99536 | 0.733313 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.157578 | 0.0163400 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.68185 | 0.172555 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.7986 | −1.50257 | −0.751287 | − | 0.659976i | \(-0.770567\pi\) | ||||
−0.751287 | + | 0.659976i | \(0.770567\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.91898 | 0.594880 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.09561 | 0.606536 | 0.303268 | − | 0.952905i | \(-0.401922\pi\) | ||||
0.303268 | + | 0.952905i | \(0.401922\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.0756 | 1.87957 | 0.939785 | − | 0.341766i | \(-0.111025\pi\) | ||||
0.939785 | + | 0.341766i | \(0.111025\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.28180 | −0.125091 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3.44412 | −0.332956 | −0.166478 | − | 0.986045i | \(-0.553239\pi\) | ||||
−0.166478 | + | 0.986045i | \(0.553239\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.5293 | 1.67900 | 0.839499 | − | 0.543361i | \(-0.182848\pi\) | ||||
0.839499 | + | 0.543361i | \(0.182848\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.89995 | −0.180335 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.663647 | −0.0624306 | −0.0312153 | − | 0.999513i | \(-0.509938\pi\) | ||||
−0.0312153 | + | 0.999513i | \(0.509938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.30276 | −0.401235 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.7867 | −0.997230 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.85801 | 0.170323 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.57112 | −0.324648 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.43670 | −0.129543 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.2684 | −1.26612 | −0.633058 | − | 0.774104i | \(-0.718201\pi\) | ||||
−0.633058 | + | 0.774104i | \(0.718201\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −9.44317 | −0.831425 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.18673 | −0.453166 | −0.226583 | − | 0.973992i | \(-0.572756\pi\) | ||||
−0.226583 | + | 0.973992i | \(0.572756\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.36862 | −0.205385 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.70696 | 0.405110 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.96049 | −0.252932 | −0.126466 | − | 0.991971i | \(-0.540363\pi\) | ||||
−0.126466 | + | 0.991971i | \(0.540363\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.0029 | −1.10289 | −0.551444 | − | 0.834212i | \(-0.685923\pi\) | ||||
−0.551444 | + | 0.834212i | \(0.685923\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.38284 | −0.200671 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.5383 | −1.13213 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.98564 | 0.497081 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.56585 | −0.376585 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −8.13362 | −0.666332 | −0.333166 | − | 0.942868i | \(-0.608117\pi\) | ||||
−0.333166 | + | 0.942868i | \(0.608117\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.42500 | 0.441481 | 0.220740 | − | 0.975333i | \(-0.429153\pi\) | ||||
0.220740 | + | 0.975333i | \(0.429153\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.86501 | −0.231622 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.173134 | −0.0139064 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.6459 | 1.00925 | 0.504627 | − | 0.863338i | \(-0.331630\pi\) | ||||
0.504627 | + | 0.863338i | \(0.331630\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.83007 | 0.145134 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.05974 | 0.477575 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.36001 | 0.733133 | 0.366566 | − | 0.930392i | \(-0.380533\pi\) | ||||
0.366566 | + | 0.930392i | \(0.380533\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.48070 | 0.193122 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.29438 | −0.487073 | −0.243537 | − | 0.969892i | \(-0.578308\pi\) | ||||
−0.243537 | + | 0.969892i | \(0.578308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.6721 | 0.897855 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.65236 | 0.279303 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.9019 | −1.28503 | −0.642513 | − | 0.766275i | \(-0.722108\pi\) | ||||
−0.642513 | + | 0.766275i | \(0.722108\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.40834 | 0.106460 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.06742 | 0.230561 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.58148 | −0.267692 | −0.133846 | − | 0.991002i | \(-0.542733\pi\) | ||||
−0.133846 | + | 0.991002i | \(0.542733\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1076 | 0.974280 | 0.487140 | − | 0.873324i | \(-0.338040\pi\) | ||||
0.487140 | + | 0.873324i | \(0.338040\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.74655 | 0.203031 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.08751 | 0.153477 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.59586 | −0.262955 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −6.62898 | −0.482188 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 13.5106 | 0.977590 | 0.488795 | − | 0.872399i | \(-0.337437\pi\) | ||||
0.488795 | + | 0.872399i | \(0.337437\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.0813 | −1.73341 | −0.866704 | − | 0.498824i | \(-0.833766\pi\) | ||||
−0.866704 | + | 0.498824i | \(0.833766\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.52081 | −0.323742 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.0530 | −1.42872 | −0.714359 | − | 0.699780i | \(-0.753281\pi\) | ||||
−0.714359 | + | 0.699780i | \(0.753281\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.9413 | −1.41360 | −0.706801 | − | 0.707413i | \(-0.749862\pi\) | ||||
−0.706801 | + | 0.707413i | \(0.749862\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.980245 | −0.0691411 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.42981 | −0.591656 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.57854 | 0.110250 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −9.34399 | −0.649452 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.58405 | 0.317086 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.1730 | −0.700337 | −0.350169 | − | 0.936687i | \(-0.613876\pi\) | ||||
−0.350169 | + | 0.936687i | \(0.613876\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.217270 | 0.0148871 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.3754 | 0.707596 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.243830 | 0.0165523 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10.8843 | −0.735490 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.55306 | 0.440807 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.14739 | 0.344695 | 0.172347 | − | 0.985036i | \(-0.444865\pi\) | ||||
0.172347 | + | 0.985036i | \(0.444865\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.17163 | −0.144775 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −22.8204 | −1.51465 | −0.757323 | − | 0.653041i | \(-0.773493\pi\) | ||||
−0.757323 | + | 0.653041i | \(0.773493\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.05583 | −0.268017 | −0.134008 | − | 0.990980i | \(-0.542785\pi\) | ||||
−0.134008 | + | 0.990980i | \(0.542785\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.49367 | −0.229866 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.6247 | −1.67873 | −0.839364 | − | 0.543570i | \(-0.817072\pi\) | ||||
−0.839364 | + | 0.543570i | \(0.817072\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.61807 | 0.170784 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.18284 | 0.271705 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −23.0528 | −1.49116 | −0.745582 | − | 0.666414i | \(-0.767828\pi\) | ||||
−0.745582 | + | 0.666414i | \(0.767828\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.59104 | 0.102488 | 0.0512440 | − | 0.998686i | \(-0.483681\pi\) | ||||
0.0512440 | + | 0.998686i | \(0.483681\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.1513 | 1.03610 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 5.01659 | 0.320498 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.35394 | −0.531548 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.07463 | 0.0681020 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.9822 | −1.13502 | −0.567512 | − | 0.823365i | \(-0.692094\pi\) | ||||
−0.567512 | + | 0.823365i | \(0.692094\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.7276 | −0.737308 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.20075 | −0.0751942 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −27.1656 | −1.69454 | −0.847272 | − | 0.531159i | \(-0.821757\pi\) | ||||
−0.847272 | + | 0.531159i | \(0.821757\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.93992 | −0.182678 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 12.9986 | 0.804592 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.50076 | −0.585842 | −0.292921 | − | 0.956137i | \(-0.594627\pi\) | ||||
−0.292921 | + | 0.956137i | \(0.594627\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.01074 | −0.123519 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.35444 | 0.0828901 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.25679 | 0.137599 | 0.0687995 | − | 0.997631i | \(-0.478083\pi\) | ||||
0.0687995 | + | 0.997631i | \(0.478083\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.67960 | −0.223520 | −0.111760 | − | 0.993735i | \(-0.535649\pi\) | ||||
−0.111760 | + | 0.993735i | \(0.535649\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.36683 | 0.385338 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.72560 | −0.164360 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 19.2379 | 1.15589 | 0.577947 | − | 0.816075i | \(-0.303854\pi\) | ||||
0.577947 | + | 0.816075i | \(0.303854\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.375981 | −0.0225094 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.1217 | −1.14071 | −0.570353 | − | 0.821400i | \(-0.693193\pi\) | ||||
−0.570353 | + | 0.821400i | \(0.693193\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.3929 | 1.15279 | 0.576394 | − | 0.817172i | \(-0.304459\pi\) | ||||
0.576394 | + | 0.817172i | \(0.304459\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.53074 | 0.0906732 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.22311 | −0.131226 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.2595 | −0.897616 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.4690 | −0.789566 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.20722 | 0.479471 | 0.239735 | − | 0.970838i | \(-0.422939\pi\) | ||||
0.239735 | + | 0.970838i | \(0.422939\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.37023 | −0.196222 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 12.8293 | 0.744430 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.3723 | 1.23599 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.6121 | −0.842225 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 5.54792 | 0.318720 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.01769 | −0.172792 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.1911 | 0.981150 | 0.490575 | − | 0.871399i | \(-0.336787\pi\) | ||||
0.490575 | + | 0.871399i | \(0.336787\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.3616 | 0.987668 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.02356 | −0.228155 | −0.114077 | − | 0.993472i | \(-0.536391\pi\) | ||||
−0.114077 | + | 0.993472i | \(0.536391\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 29.9299 | 1.69174 | 0.845869 | − | 0.533390i | \(-0.179082\pi\) | ||||
0.845869 | + | 0.533390i | \(0.179082\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.05838 | 0.172320 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.09734 | 0.173964 | 0.0869821 | − | 0.996210i | \(-0.472278\pi\) | ||||
0.0869821 | + | 0.996210i | \(0.472278\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.3144 | 0.913434 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.13467 | −0.174960 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.21886 | −0.123461 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.96710 | 0.275525 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.9543 | 0.882273 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.68712 | −0.203278 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.27948 | −0.455082 | −0.227541 | − | 0.973769i | \(-0.573069\pi\) | ||||
−0.227541 | + | 0.973769i | \(0.573069\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.53329 | 0.248423 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.07701 | 0.0588436 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.2680 | 0.940650 | 0.470325 | − | 0.882493i | \(-0.344137\pi\) | ||||
0.470325 | + | 0.882493i | \(0.344137\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.604018 | −0.0328058 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −0.471892 | −0.0255544 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.9234 | −0.913778 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.91616 | −0.210839 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −23.5763 | −1.26564 | −0.632820 | − | 0.774299i | \(-0.718103\pi\) | ||||
−0.632820 | + | 0.774299i | \(0.718103\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −29.7277 | −1.59129 | −0.795644 | − | 0.605765i | \(-0.792867\pi\) | ||||
−0.795644 | + | 0.605765i | \(0.792867\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.3799 | −1.24793 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −32.9290 | −1.75264 | −0.876318 | − | 0.481734i | \(-0.840007\pi\) | ||||
−0.876318 | + | 0.481734i | \(0.840007\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.238719 | −0.0126699 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.69107 | 0.0895008 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 17.3352 | 0.914915 | 0.457458 | − | 0.889231i | \(-0.348760\pi\) | ||||
0.457458 | + | 0.889231i | \(0.348760\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.1714 | −0.851125 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −3.25026 | −0.170594 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 11.9587 | 0.625949 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −30.1011 | −1.57127 | −0.785634 | − | 0.618692i | \(-0.787663\pi\) | ||||
−0.785634 | + | 0.618692i | \(0.787663\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.42799 | 0.178454 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.83180 | 0.147020 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.5408 | −0.701115 | −0.350558 | − | 0.936541i | \(-0.614008\pi\) | ||||
−0.350558 | + | 0.936541i | \(0.614008\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −0.910150 | −0.0470000 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −29.7313 | −1.53124 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 28.6588 | 1.47210 | 0.736052 | − | 0.676925i | \(-0.236688\pi\) | ||||
0.736052 | + | 0.676925i | \(0.236688\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −12.9864 | −0.665313 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −10.9371 | −0.558861 | −0.279431 | − | 0.960166i | \(-0.590146\pi\) | ||||
−0.279431 | + | 0.960166i | \(0.590146\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.83856 | 0.195631 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.5315 | 1.14534 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.4862 | 0.633076 | 0.316538 | − | 0.948580i | \(-0.397479\pi\) | ||||
0.316538 | + | 0.948580i | \(0.397479\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.67660 | 0.287078 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.72070 | −0.238128 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.59577 | −0.231238 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 21.1365 | 1.06081 | 0.530406 | − | 0.847744i | \(-0.322039\pi\) | ||||
0.530406 | + | 0.847744i | \(0.322039\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.15580 | −0.107925 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.00000 | 0.0499376 | ||||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.859972 | 0.0428383 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.23084 | −0.110851 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.68971 | 0.282029 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.1784 | 0.799973 | 0.399986 | − | 0.916521i | \(-0.369015\pi\) | ||||
0.399986 | + | 0.916521i | \(0.369015\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.69449 | −0.132910 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.74642 | 0.233556 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.18072 | −0.0579592 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −11.8346 | −0.579540 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.50376 | 0.122317 | 0.0611583 | − | 0.998128i | \(-0.480521\pi\) | ||||
0.0611583 | + | 0.998128i | \(0.480521\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.1000 | 1.02835 | 0.514175 | − | 0.857685i | \(-0.328098\pi\) | ||||
0.514175 | + | 0.857685i | \(0.328098\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.68547 | 0.276437 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.31929 | 0.0639951 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.24992 | 0.205668 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12.3219 | −0.594907 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.25772 | −0.397760 | −0.198880 | − | 0.980024i | \(-0.563730\pi\) | ||||
−0.198880 | + | 0.980024i | \(0.563730\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.1255 | 1.25551 | 0.627756 | − | 0.778410i | \(-0.283973\pi\) | ||||
0.627756 | + | 0.778410i | \(0.283973\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.44784 | 0.261204 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −7.23662 | −0.346174 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.5302 | −0.932124 | −0.466062 | − | 0.884752i | \(-0.654328\pi\) | ||||
−0.466062 | + | 0.884752i | \(0.654328\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 10.8941 | 0.518769 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.8710 | −1.60926 | −0.804629 | − | 0.593778i | \(-0.797636\pi\) | ||||
−0.804629 | + | 0.593778i | \(0.797636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.48814 | −0.0705448 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7.40282 | −0.350141 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.4004 | 0.490827 | 0.245414 | − | 0.969418i | \(-0.421076\pi\) | ||||
0.245414 | + | 0.969418i | \(0.421076\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.30245 | 0.202595 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.93757 | 0.231987 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −6.99536 | −0.327947 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.74839 | 0.456011 | 0.228005 | − | 0.973660i | \(-0.426780\pi\) | ||||
0.228005 | + | 0.973660i | \(0.426780\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.20986 | −0.289851 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2.69522 | −0.125529 | −0.0627644 | − | 0.998028i | \(-0.519992\pi\) | ||||
−0.0627644 | + | 0.998028i | \(0.519992\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.80445 | 0.130334 | 0.0651669 | − | 0.997874i | \(-0.479242\pi\) | ||||
0.0651669 | + | 0.997874i | \(0.479242\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.157578 | −0.00730748 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 14.1427 | 0.654448 | 0.327224 | − | 0.944947i | \(-0.393887\pi\) | ||||
0.327224 | + | 0.944947i | \(0.393887\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.51680 | −0.0700393 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.5097 | 0.530338 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 28.2791 | 1.30028 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.68185 | −0.0771687 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.36657 | −0.199931 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.4348 | −1.02507 | −0.512536 | − | 0.858666i | \(-0.671294\pi\) | ||||
−0.512536 | + | 0.858666i | \(0.671294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.3689 | −0.472780 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.51528 | 0.250954 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 14.7986 | 0.671971 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.55046 | −0.432773 | −0.216386 | − | 0.976308i | \(-0.569427\pi\) | ||||
−0.216386 | + | 0.976308i | \(0.569427\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8.51902 | 0.385243 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.4807 | −1.01454 | −0.507270 | − | 0.861787i | \(-0.669345\pi\) | ||||
−0.507270 | + | 0.861787i | \(0.669345\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −7.89682 | −0.355655 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.91898 | −0.266038 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.336197 | 0.0150805 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.2833 | 1.40043 | 0.700217 | − | 0.713930i | \(-0.253086\pi\) | ||||
0.700217 | + | 0.713930i | \(0.253086\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.72883 | −0.255945 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 34.9055 | 1.55636 | 0.778180 | − | 0.628042i | \(-0.216143\pi\) | ||||
0.778180 | + | 0.628042i | \(0.216143\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.09561 | −0.271251 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.6234 | 0.471801 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.70394 | −0.252823 | −0.126411 | − | 0.991978i | \(-0.540346\pi\) | ||||
−0.126411 | + | 0.991978i | \(0.540346\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.8420 | −0.745044 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.91641 | 0.349518 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.0756 | −0.840569 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.13580 | 0.313832 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.3832 | −0.675249 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.4893 | −0.810032 | −0.405016 | − | 0.914310i | \(-0.632734\pi\) | ||||
−0.405016 | + | 0.914310i | \(0.632734\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.185716 | 0.00812078 | 0.00406039 | − | 0.999992i | \(-0.498708\pi\) | ||||
0.00406039 | + | 0.999992i | \(0.498708\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.28180 | 0.0559423 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.228414 | 0.00994986 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.48623 | −0.195054 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.31888 | −0.317612 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.84075 | −0.339621 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.44412 | 0.148902 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.25969 | −0.140666 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 13.6732 | 0.588946 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.6216 | 1.40251 | 0.701256 | − | 0.712909i | \(-0.252623\pi\) | ||||
0.701256 | + | 0.712909i | \(0.252623\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 11.9299 | 0.511960 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −17.5293 | −0.750871 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.7955 | −1.01742 | −0.508710 | − | 0.860938i | \(-0.669878\pi\) | ||||
−0.508710 | + | 0.860938i | \(0.669878\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.55328 | −0.279687 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.0670 | 0.428868 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.47239 | 0.275234 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1.89995 | 0.0806483 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 23.7350 | 1.00568 | 0.502842 | − | 0.864378i | \(-0.332288\pi\) | ||||
0.502842 | + | 0.864378i | \(0.332288\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −51.5356 | −2.17973 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.27277 | −0.138177 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.3811 | 0.648235 | 0.324117 | − | 0.946017i | \(-0.394933\pi\) | ||||
0.324117 | + | 0.946017i | \(0.394933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.663647 | 0.0279198 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 3.14178 | 0.131942 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −41.8330 | −1.75373 | −0.876865 | − | 0.480737i | \(-0.840369\pi\) | ||||
−0.876865 | + | 0.480737i | \(0.840369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.80060 | 0.159050 | 0.0795251 | − | 0.996833i | \(-0.474660\pi\) | ||||
0.0795251 | + | 0.996833i | \(0.474660\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.2966 | 0.513700 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.30276 | 0.179438 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.5594 | 1.14731 | 0.573657 | − | 0.819095i | \(-0.305524\pi\) | ||||
0.573657 | + | 0.819095i | \(0.305524\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −21.9176 | −0.910863 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.66285 | 0.0689867 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.48046 | −0.226977 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 10.7867 | 0.445975 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.4787 | −1.29926 | −0.649632 | − | 0.760249i | \(-0.725077\pi\) | ||||
−0.649632 | + | 0.760249i | \(0.725077\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.291185 | −0.0119981 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −18.2512 | −0.750756 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.54584 | 0.186675 | 0.0933376 | − | 0.995635i | \(-0.470246\pi\) | ||||
0.0933376 | + | 0.995635i | \(0.470246\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.85801 | −0.0761710 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.1496 | −0.742813 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 32.3791 | 1.32297 | 0.661486 | − | 0.749957i | \(-0.269926\pi\) | ||||
0.661486 | + | 0.749957i | \(0.269926\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.98405 | 0.162513 | 0.0812563 | − | 0.996693i | \(-0.474107\pi\) | ||||
0.0812563 | + | 0.996693i | \(0.474107\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.33887 | 0.0952462 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.57112 | 0.145187 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.788641 | −0.0320100 | −0.0160050 | − | 0.999872i | \(-0.505095\pi\) | ||||
−0.0160050 | + | 0.999872i | \(0.505095\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.67239 | −0.310901 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −13.0042 | −0.526094 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.3260 | 0.901740 | 0.450870 | − | 0.892590i | \(-0.351114\pi\) | ||||
0.450870 | + | 0.892590i | \(0.351114\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.43670 | 0.0579335 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 42.9781 | 1.73023 | 0.865116 | − | 0.501572i | \(-0.167245\pi\) | ||||
0.865116 | + | 0.501572i | \(0.167245\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.8889 | 1.28172 | 0.640861 | − | 0.767657i | \(-0.278577\pi\) | ||||
0.640861 | + | 0.767657i | \(0.278577\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −20.2529 | −0.812722 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.09581 | 0.0839668 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.17218 | 0.166621 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.75404 | −0.109811 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 46.1653 | 1.83781 | 0.918905 | − | 0.394479i | \(-0.129075\pi\) | ||||
0.918905 | + | 0.394479i | \(0.129075\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.25895 | −0.368010 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.2684 | 0.566224 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.9179 | −0.987283 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.518408 | −0.0205079 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −38.8169 | −1.53318 | −0.766588 | − | 0.642140i | \(-0.778047\pi\) | ||||
−0.766588 | + | 0.642140i | \(0.778047\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −22.2086 | −0.875820 | −0.437910 | − | 0.899019i | \(-0.644281\pi\) | ||||
−0.437910 | + | 0.899019i | \(0.644281\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 9.44317 | 0.371824 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −0.631871 | −0.0248414 | −0.0124207 | − | 0.999923i | \(-0.503954\pi\) | ||||
−0.0124207 | + | 0.999923i | \(0.503954\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.18589 | −0.360578 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.221922 | 0.00869782 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −16.2224 | −0.634830 | −0.317415 | − | 0.948287i | \(-0.602815\pi\) | ||||
−0.317415 | + | 0.948287i | \(0.602815\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 5.18673 | 0.202662 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 25.9699 | 1.01318 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −45.6183 | −1.77704 | −0.888518 | − | 0.458841i | \(-0.848265\pi\) | ||||
−0.888518 | + | 0.458841i | \(0.848265\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.6362 | −1.15272 | −0.576358 | − | 0.817197i | \(-0.695527\pi\) | ||||
−0.576358 | + | 0.817197i | \(0.695527\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.96427 | 0.231633 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.36862 | 0.0918510 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −25.7548 | −0.997230 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.68490 | 0.181129 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.22499 | −0.317522 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.6613 | 1.10481 | 0.552407 | − | 0.833575i | \(-0.313710\pi\) | ||||
0.552407 | + | 0.833575i | \(0.313710\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −4.70696 | −0.181171 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.6801 | −1.75563 | −0.877815 | − | 0.479000i | \(-0.840999\pi\) | ||||
−0.877815 | + | 0.479000i | \(0.840999\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −20.8415 | −0.799822 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.7700 | −0.795909 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.0350 | 0.766616 | 0.383308 | − | 0.923621i | \(-0.374785\pi\) | ||||
0.383308 | + | 0.923621i | \(0.374785\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.96049 | 0.113115 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −3.69141 | −0.140836 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.98754 | 0.380495 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.54348 | 0.0587166 | 0.0293583 | − | 0.999569i | \(-0.490654\pi\) | ||||
0.0293583 | + | 0.999569i | \(0.490654\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.33592 | 0.316655 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 13.0029 | 0.493226 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.08255 | −0.0788822 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.3223 | −0.882130 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 10.4916 | 0.396264 | 0.198132 | − | 0.980175i | \(-0.436513\pi\) | ||||
0.198132 | + | 0.980175i | \(0.436513\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.51089 | 0.132416 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.38284 | 0.0897428 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.58467 | 0.322860 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.08650 | −0.115916 | −0.0579579 | − | 0.998319i | \(-0.518459\pi\) | ||||
−0.0579579 | + | 0.998319i | \(0.518459\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9.98029 | −0.374290 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0.744953 | 0.0278987 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.5383 | 0.506304 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −20.9815 | −0.783570 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 43.5852 | 1.62545 | 0.812727 | − | 0.582645i | \(-0.197982\pi\) | ||||
0.812727 | + | 0.582645i | \(0.197982\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.8648 | 1.00050 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.44809 | 0.0538550 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.98564 | −0.222301 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.9249 | 0.553532 | 0.276766 | − | 0.960937i | \(-0.410737\pi\) | ||||
0.276766 | + | 0.960937i | \(0.410737\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.00757 | 0.296577 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.6882 | −0.506276 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.0259 | −0.739673 | −0.369837 | − | 0.929097i | \(-0.620586\pi\) | ||||
−0.369837 | + | 0.929097i | \(0.620586\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.56585 | 0.168414 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 2.93551 | 0.108131 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 22.2677 | 0.819130 | 0.409565 | − | 0.912281i | \(-0.365680\pi\) | ||||
0.409565 | + | 0.912281i | \(0.365680\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −7.60334 | −0.279316 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 35.6037 | 1.30617 | 0.653086 | − | 0.757284i | \(-0.273474\pi\) | ||||
0.653086 | + | 0.757284i | \(0.273474\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 8.13362 | 0.297993 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.56408 | −0.0938148 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.85049 | −0.177233 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.72066 | −0.135769 | −0.0678844 | − | 0.997693i | \(-0.521625\pi\) | ||||
−0.0678844 | + | 0.997693i | \(0.521625\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −16.3665 | −0.596427 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.42500 | −0.197436 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.80917 | 0.174792 | 0.0873962 | − | 0.996174i | \(-0.472145\pi\) | ||||
0.0873962 | + | 0.996174i | \(0.472145\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.6739 | −0.387437 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −41.8969 | −1.51876 | −0.759381 | − | 0.650647i | \(-0.774498\pi\) | ||||
−0.759381 | + | 0.650647i | \(0.774498\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.6871 | 0.893734 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.86501 | 0.103585 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.7403 | 0.604456 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.5554 | −0.452761 | −0.226381 | − | 0.974039i | \(-0.572689\pi\) | ||||
−0.226381 | + | 0.974039i | \(0.572689\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.7248 | −0.890442 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.05283 | 0.145770 | 0.0728850 | − | 0.997340i | \(-0.476779\pi\) | ||||
0.0728850 | + | 0.997340i | \(0.476779\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.173134 | 0.00621914 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.67577 | −0.0959927 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.65487 | 0.0951204 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.650651 | −0.0232821 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.1742 | 1.00686 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.6459 | −0.451352 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.18545 | −0.291780 | −0.145890 | − | 0.989301i | \(-0.546605\pi\) | ||||
−0.145890 | + | 0.989301i | \(0.546605\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.64712 | −0.307846 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −0.934638 | −0.0332319 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 14.9892 | 0.532280 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.83007 | −0.0649060 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.0042 | −0.602320 | −0.301160 | − | 0.953574i | \(-0.597374\pi\) | ||||
−0.301160 | + | 0.953574i | \(0.597374\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.45400 | −0.122194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.23169 | −0.114186 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 32.5947 | 1.15024 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.05974 | −0.213578 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.05402 | 0.0723049 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −13.6213 | −0.478900 | −0.239450 | − | 0.970909i | \(-0.576967\pi\) | ||||
−0.239450 | + | 0.970909i | \(0.576967\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −9.23919 | −0.324432 | −0.162216 | − | 0.986755i | \(-0.551864\pi\) | ||||
−0.162216 | + | 0.986755i | \(0.551864\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.34899 | −0.117454 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.36001 | −0.327867 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 17.4499 | 0.610495 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.1913 | −0.530827 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 21.2747 | 0.742493 | 0.371246 | − | 0.928534i | \(-0.378931\pi\) | ||||
0.371246 | + | 0.928534i | \(0.378931\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.1633 | −0.423984 | −0.211992 | − | 0.977271i | \(-0.567995\pi\) | ||||
−0.211992 | + | 0.977271i | \(0.567995\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.48070 | −0.0863670 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 8.71185 | 0.302941 | 0.151470 | − | 0.988462i | \(-0.451599\pi\) | ||||
0.151470 | + | 0.988462i | \(0.451599\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 19.2545 | 0.668736 | 0.334368 | − | 0.942443i | \(-0.391477\pi\) | ||||
0.334368 | + | 0.942443i | \(0.391477\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 17.5094 | 0.607394 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −6.61835 | −0.229312 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.29438 | 0.217826 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.814932 | −0.0281682 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.7907 | 0.855869 | 0.427934 | − | 0.903810i | \(-0.359241\pi\) | ||||
0.427934 | + | 0.903810i | \(0.359241\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.82793 | 0.235446 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.4036 | −0.599413 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −11.6721 | −0.401533 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.02935 | −0.172810 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 17.6505 | 0.605762 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.98206 | −0.307901 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.640816 | 0.0219411 | 0.0109706 | − | 0.999940i | \(-0.496508\pi\) | ||||
0.0109706 | + | 0.999940i | \(0.496508\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.65236 | −0.124908 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.2067 | −1.30512 | −0.652558 | − | 0.757738i | \(-0.726304\pi\) | ||||
−0.652558 | + | 0.757738i | \(0.726304\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.38812 | 0.286199 | 0.143099 | − | 0.989708i | \(-0.454293\pi\) | ||||
0.143099 | + | 0.989708i | \(0.454293\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.02337 | −0.0689561 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.70332 | 0.0579818 | 0.0289909 | − | 0.999580i | \(-0.490771\pi\) | ||||
0.0289909 | + | 0.999580i | \(0.490771\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.9019 | 0.574681 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13.8884 | −0.471675 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.5262 | −0.424923 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.34964 | −0.181266 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 32.1371 | 1.08768 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.40834 | −0.0476105 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 52.0454 | 1.75745 | 0.878725 | − | 0.477329i | \(-0.158395\pi\) | ||||
0.878725 | + | 0.477329i | \(0.158395\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.46980 | 0.251950 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.56874 | −0.254997 | −0.127499 | − | 0.991839i | \(-0.540695\pi\) | ||||
−0.127499 | + | 0.991839i | \(0.540695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 59.0344 | 1.98666 | 0.993332 | − | 0.115288i | \(-0.0367792\pi\) | ||||
0.993332 | + | 0.115288i | \(0.0367792\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −3.06742 | −0.103110 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −0.169272 | −0.00568361 | −0.00284180 | − | 0.999996i | \(-0.500905\pi\) | ||||
−0.00284180 | + | 0.999996i | \(0.500905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0947 | −0.673956 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.08037 | −0.203700 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.40321 | 0.147348 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.58148 | 0.119716 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 19.4520 | 0.649483 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.03632 | −0.0345631 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.65275 | 0.0883760 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −13.2992 | −0.442569 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −13.1076 | −0.435711 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.2540 | 0.672523 | 0.336262 | − | 0.941769i | \(-0.390837\pi\) | ||||
0.336262 | + | 0.941769i | \(0.390837\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.2374 | −0.439056 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.6549 | 1.34696 | 0.673478 | − | 0.739207i | \(-0.264800\pi\) | ||||
0.673478 | + | 0.739207i | \(0.264800\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.21816 | −0.106506 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.74655 | −0.0907981 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.30466 | −0.241221 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 58.0652 | 1.91539 | 0.957696 | − | 0.287780i | \(-0.0929173\pi\) | ||||
0.957696 | + | 0.287780i | \(0.0929173\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.6465 | 0.515571 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.18574 | 0.0390291 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.08751 | −0.0686369 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −41.4250 | −1.36057 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.8235 | 1.24095 | 0.620474 | − | 0.784227i | \(-0.286940\pi\) | ||||
0.620474 | + | 0.784227i | \(0.286940\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.43716 | 0.276517 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −3.66204 | −0.119890 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.59586 | 0.117597 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −18.6064 | −0.607844 | −0.303922 | − | 0.952697i | \(-0.598296\pi\) | ||||
−0.303922 | + | 0.952697i | \(0.598296\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 27.2407 | 0.888967 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −32.9383 | −1.07376 | −0.536879 | − | 0.843659i | \(-0.680397\pi\) | ||||
−0.536879 | + | 0.843659i | \(0.680397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.79206 | −0.221180 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.62898 | 0.215641 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −21.4528 | −0.697123 | −0.348561 | − | 0.937286i | \(-0.613330\pi\) | ||||
−0.348561 | + | 0.937286i | \(0.613330\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −59.4003 | −1.92822 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.81905 | 0.0914139 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 48.2736 | 1.56374 | 0.781868 | − | 0.623444i | \(-0.214267\pi\) | ||||
0.781868 | + | 0.623444i | \(0.214267\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.5106 | −0.437192 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.8486 | 0.479987 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.16937 | −0.134636 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9700 | −0.999033 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 7.47935 | 0.241019 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.0813 | 0.775203 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −40.8247 | −1.31283 | −0.656416 | − | 0.754399i | \(-0.727929\pi\) | ||||
−0.656416 | + | 0.754399i | \(0.727929\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.01949 | −0.0648755 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.4176 | 1.74634 | 0.873171 | − | 0.487413i | \(-0.162060\pi\) | ||||
0.873171 | + | 0.487413i | \(0.162060\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3124 | −0.587069 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.52081 | 0.144782 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.82295 | −0.186293 | −0.0931464 | − | 0.995652i | \(-0.529692\pi\) | ||||
−0.0931464 | + | 0.995652i | \(0.529692\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.05608 | −0.129633 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −38.0670 | −1.21539 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −26.3549 | −0.840590 | −0.420295 | − | 0.907388i | \(-0.638073\pi\) | ||||
−0.420295 | + | 0.907388i | \(0.638073\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 20.0530 | 0.638942 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.35584 | −0.106817 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.6429 | −1.41956 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.87927 | 0.0596969 | 0.0298485 | − | 0.999554i | \(-0.490498\pi\) | ||||
0.0298485 | + | 0.999554i | \(0.490498\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.53558 | −0.239134 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.9413 | 0.632182 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −50.5797 | −1.60188 | −0.800938 | − | 0.598748i | \(-0.795665\pi\) | ||||
−0.800938 | + | 0.598748i | \(0.795665\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 9.82582 | 0.310875 |
(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 | 8020.2.a.c.1.17 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8020.2.a.c.1.17 | ✓ | 28 | 1.1 | even | 1 | trivial |