Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8004,2,Mod(1,8004)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8004, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8004.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8004.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(63.9122617778\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} - 8x^{6} + 19x^{5} + 19x^{4} - 35x^{3} - 10x^{2} + 18x - 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.03502\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8004.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.84132 | −0.823462 | −0.411731 | − | 0.911305i | \(-0.635076\pi\) | ||||
−0.411731 | + | 0.911305i | \(0.635076\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.79101 | −1.05490 | −0.527451 | − | 0.849585i | \(-0.676852\pi\) | ||||
−0.527451 | + | 0.849585i | \(0.676852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.31068 | 0.395184 | 0.197592 | − | 0.980284i | \(-0.436688\pi\) | ||||
0.197592 | + | 0.980284i | \(0.436688\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.49588 | 0.692233 | 0.346116 | − | 0.938192i | \(-0.387500\pi\) | ||||
0.346116 | + | 0.938192i | \(0.387500\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.84132 | −0.475426 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.40296 | −0.825339 | −0.412669 | − | 0.910881i | \(-0.635404\pi\) | ||||
−0.412669 | + | 0.910881i | \(0.635404\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.66867 | 0.612234 | 0.306117 | − | 0.951994i | \(-0.400970\pi\) | ||||
0.306117 | + | 0.951994i | \(0.400970\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.79101 | −0.609048 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.60955 | −0.321910 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.42965 | −1.33441 | −0.667203 | − | 0.744876i | \(-0.732508\pi\) | ||||
−0.667203 | + | 0.744876i | \(0.732508\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.31068 | 0.228160 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.13914 | 0.868673 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.47047 | 0.406143 | 0.203071 | − | 0.979164i | \(-0.434908\pi\) | ||||
0.203071 | + | 0.979164i | \(0.434908\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.49588 | 0.399661 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.01330 | 0.782945 | 0.391473 | − | 0.920190i | \(-0.371966\pi\) | ||||
0.391473 | + | 0.920190i | \(0.371966\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.20204 | 0.335808 | 0.167904 | − | 0.985803i | \(-0.446300\pi\) | ||||
0.167904 | + | 0.985803i | \(0.446300\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.84132 | −0.274487 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 10.0789 | 1.47015 | 0.735077 | − | 0.677984i | \(-0.237146\pi\) | ||||
0.735077 | + | 0.677984i | \(0.237146\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.789737 | 0.112820 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.40296 | −0.476510 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.225258 | −0.0309415 | −0.0154708 | − | 0.999880i | \(-0.504925\pi\) | ||||
−0.0154708 | + | 0.999880i | \(0.504925\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.41337 | −0.325419 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.66867 | 0.353474 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.31872 | −0.692439 | −0.346219 | − | 0.938154i | \(-0.612535\pi\) | ||||
−0.346219 | + | 0.938154i | \(0.612535\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.3322 | 1.45094 | 0.725468 | − | 0.688256i | \(-0.241623\pi\) | ||||
0.725468 | + | 0.688256i | \(0.241623\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.79101 | −0.351634 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −4.59571 | −0.570028 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.47132 | 0.546258 | 0.273129 | − | 0.961977i | \(-0.411941\pi\) | ||||
0.273129 | + | 0.961977i | \(0.411941\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.68684 | −0.437547 | −0.218774 | − | 0.975776i | \(-0.570206\pi\) | ||||
−0.218774 | + | 0.975776i | \(0.570206\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.11674 | −1.06703 | −0.533517 | − | 0.845789i | \(-0.679130\pi\) | ||||
−0.533517 | + | 0.845789i | \(0.679130\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.60955 | −0.185855 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.65812 | −0.416881 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.28120 | −0.144146 | −0.0720732 | − | 0.997399i | \(-0.522962\pi\) | ||||
−0.0720732 | + | 0.997399i | \(0.522962\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.6844 | −1.50206 | −0.751028 | − | 0.660271i | \(-0.770442\pi\) | ||||
−0.751028 | + | 0.660271i | \(0.770442\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.26593 | 0.679635 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.00000 | 0.107211 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.0027 | −1.69629 | −0.848143 | − | 0.529767i | \(-0.822280\pi\) | ||||
−0.848143 | + | 0.529767i | \(0.822280\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.96603 | −0.730238 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.42965 | −0.770419 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.91386 | −0.504152 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.382051 | −0.0387914 | −0.0193957 | − | 0.999812i | \(-0.506174\pi\) | ||||
−0.0193957 | + | 0.999812i | \(0.506174\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.31068 | 0.131728 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.91275 | −0.886852 | −0.443426 | − | 0.896311i | \(-0.646237\pi\) | ||||
−0.443426 | + | 0.896311i | \(0.646237\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.72402 | −0.169873 | −0.0849365 | − | 0.996386i | \(-0.527069\pi\) | ||||
−0.0849365 | + | 0.996386i | \(0.527069\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.13914 | 0.501528 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.98490 | 0.868603 | 0.434302 | − | 0.900767i | \(-0.356995\pi\) | ||||
0.434302 | + | 0.900767i | \(0.356995\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.52065 | −0.241434 | −0.120717 | − | 0.992687i | \(-0.538519\pi\) | ||||
−0.120717 | + | 0.992687i | \(0.538519\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.47047 | 0.234487 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.730972 | 0.0687641 | 0.0343820 | − | 0.999409i | \(-0.489054\pi\) | ||||
0.0343820 | + | 0.999409i | \(0.489054\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.84132 | −0.171704 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.49588 | 0.230744 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.49769 | 0.870652 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.28212 | −0.843829 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.01330 | 0.452034 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1703 | 1.08854 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.3161 | −1.53655 | −0.768277 | − | 0.640118i | \(-0.778885\pi\) | ||||
−0.768277 | + | 0.640118i | \(0.778885\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.20204 | 0.193879 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.66794 | 0.407840 | 0.203920 | − | 0.978988i | \(-0.434632\pi\) | ||||
0.203920 | + | 0.978988i | \(0.434632\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.44828 | −0.645848 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.84132 | −0.158475 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.70740 | −0.145873 | −0.0729366 | − | 0.997337i | \(-0.523237\pi\) | ||||
−0.0729366 | + | 0.997337i | \(0.523237\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.2410 | −1.12309 | −0.561544 | − | 0.827447i | \(-0.689792\pi\) | ||||
−0.561544 | + | 0.827447i | \(0.689792\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.0789 | 0.848793 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.27130 | 0.273560 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.84132 | −0.152913 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.789737 | 0.0651364 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 21.2448 | 1.74044 | 0.870219 | − | 0.492665i | \(-0.163977\pi\) | ||||
0.870219 | + | 0.492665i | \(0.163977\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.89935 | −0.561461 | −0.280730 | − | 0.959787i | \(-0.590577\pi\) | ||||
−0.280730 | + | 0.959787i | \(0.590577\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.40296 | −0.275113 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.6804 | 1.09883 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.10423 | −0.327553 | −0.163777 | − | 0.986497i | \(-0.552368\pi\) | ||||
−0.163777 | + | 0.986497i | \(0.552368\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −0.225258 | −0.0178641 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.79101 | −0.219962 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.13570 | −0.558911 | −0.279455 | − | 0.960159i | \(-0.590154\pi\) | ||||
−0.279455 | + | 0.960159i | \(0.590154\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.41337 | −0.187881 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.57124 | −0.198968 | −0.0994842 | − | 0.995039i | \(-0.531719\pi\) | ||||
−0.0994842 | + | 0.995039i | \(0.531719\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.77058 | −0.520813 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.66867 | 0.204078 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.34813 | 0.482639 | 0.241320 | − | 0.970446i | \(-0.422420\pi\) | ||||
0.241320 | + | 0.970446i | \(0.422420\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.49227 | 0.339584 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −5.31872 | −0.399780 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.2017 | 0.986739 | 0.493369 | − | 0.869820i | \(-0.335765\pi\) | ||||
0.493369 | + | 0.869820i | \(0.335765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.44048 | −0.255729 | −0.127864 | − | 0.991792i | \(-0.540812\pi\) | ||||
−0.127864 | + | 0.991792i | \(0.540812\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.3322 | 0.837698 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −4.54892 | −0.334443 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.46018 | −0.326161 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.79101 | −0.203016 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.0228 | −0.942298 | −0.471149 | − | 0.882054i | \(-0.656161\pi\) | ||||
−0.471149 | + | 0.882054i | \(0.656161\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.25619 | −0.234386 | −0.117193 | − | 0.993109i | \(-0.537390\pi\) | ||||
−0.117193 | + | 0.993109i | \(0.537390\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.59571 | −0.329106 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −12.8117 | −0.912794 | −0.456397 | − | 0.889776i | \(-0.650860\pi\) | ||||
−0.456397 | + | 0.889776i | \(0.650860\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.641529 | −0.0454768 | −0.0227384 | − | 0.999741i | \(-0.507238\pi\) | ||||
−0.0227384 | + | 0.999741i | \(0.507238\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.47132 | 0.315382 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.79101 | −0.195891 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.23107 | −0.644726 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.49776 | 0.241945 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.1764 | −1.45785 | −0.728923 | − | 0.684596i | \(-0.759979\pi\) | ||||
−0.728923 | + | 0.684596i | \(0.759979\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.68684 | −0.252618 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.05466 | −0.276525 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 20.7362 | 1.40767 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −9.11674 | −0.616052 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.49338 | −0.571327 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.964487 | 0.0645868 | 0.0322934 | − | 0.999478i | \(-0.489719\pi\) | ||||
0.0322934 | + | 0.999478i | \(0.489719\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.60955 | −0.107303 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.721082 | 0.0478599 | 0.0239299 | − | 0.999714i | \(-0.492382\pi\) | ||||
0.0239299 | + | 0.999714i | \(0.492382\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.60402 | 0.304242 | 0.152121 | − | 0.988362i | \(-0.451390\pi\) | ||||
0.152121 | + | 0.988362i | \(0.451390\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.65812 | −0.240686 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −23.2612 | −1.52389 | −0.761947 | − | 0.647640i | \(-0.775756\pi\) | ||||
−0.761947 | + | 0.647640i | \(0.775756\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18.5584 | −1.21062 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.28120 | −0.0832229 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.82598 | 0.635590 | 0.317795 | − | 0.948159i | \(-0.397058\pi\) | ||||
0.317795 | + | 0.948159i | \(0.397058\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.446152 | −0.0287392 | −0.0143696 | − | 0.999897i | \(-0.504574\pi\) | ||||
−0.0143696 | + | 0.999897i | \(0.504574\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.45416 | −0.0929027 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.66068 | 0.423809 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.6844 | −0.867212 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.8713 | 1.56987 | 0.784933 | − | 0.619581i | \(-0.212698\pi\) | ||||
0.784933 | + | 0.619581i | \(0.212698\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.31068 | 0.0824016 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.26593 | 0.392388 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −18.7469 | −1.16940 | −0.584699 | − | 0.811251i | \(-0.698787\pi\) | ||||
−0.584699 | + | 0.811251i | \(0.698787\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.89510 | −0.428441 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.00000 | 0.0618984 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.0245 | −1.78973 | −0.894863 | − | 0.446341i | \(-0.852727\pi\) | ||||
−0.894863 | + | 0.446341i | \(0.852727\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.414771 | 0.0254792 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.0027 | −0.979352 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −30.8162 | −1.87890 | −0.939450 | − | 0.342686i | \(-0.888663\pi\) | ||||
−0.939450 | + | 0.342686i | \(0.888663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.3061 | 1.84096 | 0.920482 | − | 0.390784i | \(-0.127796\pi\) | ||||
0.920482 | + | 0.390784i | \(0.127796\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.96603 | −0.421603 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.10960 | −0.127214 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.1153 | 0.607767 | 0.303883 | − | 0.952709i | \(-0.401717\pi\) | ||||
0.303883 | + | 0.952709i | \(0.401717\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.42965 | −0.444802 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.35616 | −0.319521 | −0.159761 | − | 0.987156i | \(-0.551072\pi\) | ||||
−0.159761 | + | 0.987156i | \(0.551072\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3122 | 0.910216 | 0.455108 | − | 0.890436i | \(-0.349601\pi\) | ||||
0.455108 | + | 0.890436i | \(0.349601\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.91386 | −0.291072 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −13.9922 | −0.825931 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.41987 | −0.318816 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.382051 | −0.0223962 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.0293 | 1.17012 | 0.585062 | − | 0.810989i | \(-0.301070\pi\) | ||||
0.585062 | + | 0.810989i | \(0.301070\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.79346 | 0.570197 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.31068 | 0.0760533 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.49588 | 0.144341 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.14592 | −0.354245 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.91275 | −0.512024 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −20.8661 | −1.19479 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.9678 | −1.71035 | −0.855176 | − | 0.518337i | \(-0.826551\pi\) | ||||
−0.855176 | + | 0.518337i | \(0.826551\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.72402 | −0.0980762 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.1613 | 1.14324 | 0.571620 | − | 0.820518i | \(-0.306315\pi\) | ||||
0.571620 | + | 0.820518i | \(0.306315\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.24273 | −0.522430 | −0.261215 | − | 0.965281i | \(-0.584123\pi\) | ||||
−0.261215 | + | 0.965281i | \(0.584123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.13914 | 0.289558 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.91035 | 0.163462 | 0.0817308 | − | 0.996654i | \(-0.473955\pi\) | ||||
0.0817308 | + | 0.996654i | \(0.473955\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.31068 | 0.0733839 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 8.98490 | 0.501488 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.08136 | −0.505301 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.01724 | −0.222837 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.52065 | −0.139392 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −28.1302 | −1.55087 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.1303 | −1.27135 | −0.635677 | − | 0.771955i | \(-0.719279\pi\) | ||||
−0.635677 | + | 0.771955i | \(0.719279\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.47047 | 0.135381 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −8.23312 | −0.449823 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.73470 | −0.148969 | −0.0744843 | − | 0.997222i | \(-0.523731\pi\) | ||||
−0.0744843 | + | 0.997222i | \(0.523731\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0.730972 | 0.0397010 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.73788 | −0.527336 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.3329 | 0.935889 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.84132 | −0.0991332 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.6496 | −0.732747 | −0.366374 | − | 0.930468i | \(-0.619401\pi\) | ||||
−0.366374 | + | 0.930468i | \(0.619401\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.3981 | −0.877771 | −0.438886 | − | 0.898543i | \(-0.644627\pi\) | ||||
−0.438886 | + | 0.898543i | \(0.644627\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.49588 | 0.133220 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.1416 | −0.593008 | −0.296504 | − | 0.955032i | \(-0.595821\pi\) | ||||
−0.296504 | + | 0.955032i | \(0.595821\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.78864 | 0.360304 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.49769 | 0.502671 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −15.2834 | −0.806626 | −0.403313 | − | 0.915062i | \(-0.632141\pi\) | ||||
−0.403313 | + | 0.915062i | \(0.632141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −11.8782 | −0.625169 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.28212 | −0.487185 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.7868 | 0.878662 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −34.4019 | −1.79576 | −0.897882 | − | 0.440237i | \(-0.854895\pi\) | ||||
−0.897882 | + | 0.440237i | \(0.854895\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.01330 | 0.260982 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.628697 | 0.0326403 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.0848 | −0.936393 | −0.468197 | − | 0.883624i | \(-0.655096\pi\) | ||||
−0.468197 | + | 0.883624i | \(0.655096\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.1703 | 0.628471 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.49588 | 0.128544 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.85047 | 0.351885 | 0.175943 | − | 0.984400i | \(-0.443703\pi\) | ||||
0.175943 | + | 0.984400i | \(0.443703\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.3161 | −0.887130 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.08057 | 0.361800 | 0.180900 | − | 0.983501i | \(-0.442099\pi\) | ||||
0.180900 | + | 0.983501i | \(0.442099\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.73575 | 0.343286 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.20204 | 0.111936 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.4254 | 0.680693 | 0.340347 | − | 0.940300i | \(-0.389456\pi\) | ||||
0.340347 | + | 0.940300i | \(0.389456\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.40296 | −0.172095 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.66794 | 0.235467 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.35910 | 0.118699 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 34.0450 | 1.70867 | 0.854335 | − | 0.519723i | \(-0.173965\pi\) | ||||
0.854335 | + | 0.519723i | \(0.173965\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.44828 | −0.372880 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −34.5040 | −1.72305 | −0.861524 | − | 0.507717i | \(-0.830490\pi\) | ||||
−0.861524 | + | 0.507717i | \(0.830490\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.5435 | −0.923719 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.84132 | −0.0914958 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.23799 | 0.160501 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −34.8839 | −1.72490 | −0.862449 | − | 0.506145i | \(-0.831070\pi\) | ||||
−0.862449 | + | 0.506145i | \(0.831070\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.70740 | −0.0842199 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.8446 | 0.730455 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 25.1973 | 1.23689 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.2410 | −0.648415 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.38156 | −0.0674937 | −0.0337468 | − | 0.999430i | \(-0.510744\pi\) | ||||
−0.0337468 | + | 0.999430i | \(0.510744\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.2379 | 0.840125 | 0.420062 | − | 0.907495i | \(-0.362008\pi\) | ||||
0.420062 | + | 0.907495i | \(0.362008\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.0789 | 0.490051 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5.47723 | 0.265685 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −31.6282 | −1.53060 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.27130 | 0.157940 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.1235 | 0.728474 | 0.364237 | − | 0.931306i | \(-0.381330\pi\) | ||||
0.364237 | + | 0.931306i | \(0.381330\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.90927 | 0.283981 | 0.141991 | − | 0.989868i | \(-0.454650\pi\) | ||||
0.141991 | + | 0.989868i | \(0.454650\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.84132 | −0.0882844 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.66867 | 0.127660 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.02290 | −0.287457 | −0.143729 | − | 0.989617i | \(-0.545909\pi\) | ||||
−0.143729 | + | 0.989617i | \(0.545909\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.789737 | 0.0376065 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 40.0603 | 1.90332 | 0.951660 | − | 0.307154i | \(-0.0993765\pi\) | ||||
0.951660 | + | 0.307154i | \(0.0993765\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 29.4661 | 1.39683 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 21.2448 | 1.00484 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.37150 | −0.0647252 | −0.0323626 | − | 0.999476i | \(-0.510303\pi\) | ||||
−0.0323626 | + | 0.999476i | \(0.510303\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.57082 | 0.309408 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.89935 | −0.324160 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 12.8267 | 0.601324 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −39.6704 | −1.85570 | −0.927851 | − | 0.372952i | \(-0.878346\pi\) | ||||
−0.927851 | + | 0.372952i | \(0.878346\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.40296 | −0.158837 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.9461 | 0.742686 | 0.371343 | − | 0.928496i | \(-0.378897\pi\) | ||||
0.371343 | + | 0.928496i | \(0.378897\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −23.4418 | −1.08943 | −0.544716 | − | 0.838621i | \(-0.683363\pi\) | ||||
−0.544716 | + | 0.838621i | \(0.683363\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 13.6804 | 0.634411 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 23.4489 | 1.08508 | 0.542542 | − | 0.840029i | \(-0.317462\pi\) | ||||
0.542542 | + | 0.840029i | \(0.317462\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.4795 | −0.576249 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.10423 | −0.189113 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.88617 | 0.132706 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4.29535 | −0.197084 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.225258 | −0.0103138 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −39.7274 | −1.81519 | −0.907595 | − | 0.419847i | \(-0.862084\pi\) | ||||
−0.907595 | + | 0.419847i | \(0.862084\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.16600 | 0.281145 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −2.79101 | −0.126995 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.703477 | 0.0319432 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −24.2376 | −1.09831 | −0.549156 | − | 0.835720i | \(-0.685051\pi\) | ||||
−0.549156 | + | 0.835720i | \(0.685051\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.13570 | −0.322687 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.61956 | 0.298737 | 0.149368 | − | 0.988782i | \(-0.452276\pi\) | ||||
0.149368 | + | 0.988782i | \(0.452276\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.40296 | −0.153262 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.41337 | −0.108473 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.2900 | 0.461570 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.22263 | −0.0994986 | −0.0497493 | − | 0.998762i | \(-0.515842\pi\) | ||||
−0.0497493 | + | 0.998762i | \(0.515842\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.57124 | −0.114874 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −35.3252 | −1.57507 | −0.787536 | − | 0.616269i | \(-0.788643\pi\) | ||||
−0.787536 | + | 0.616269i | \(0.788643\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.4112 | 0.730289 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.77058 | −0.300692 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.24953 | −0.365654 | −0.182827 | − | 0.983145i | \(-0.558525\pi\) | ||||
−0.182827 | + | 0.983145i | \(0.558525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.4449 | 1.12562 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.66867 | 0.117825 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.17447 | 0.139884 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.2101 | 0.580982 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.34813 | 0.278652 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.3404 | −0.453020 | −0.226510 | − | 0.974009i | \(-0.572732\pi\) | ||||
−0.226510 | + | 0.974009i | \(0.572732\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.8697 | 0.562754 | 0.281377 | − | 0.959597i | \(-0.409209\pi\) | ||||
0.281377 | + | 0.959597i | \(0.409209\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 4.49227 | 0.196059 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 25.2828 | 1.10134 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.31872 | −0.230813 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.5126 | 0.541981 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.5441 | −0.715262 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.2017 | 0.569694 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.03509 | 0.0445846 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −26.5276 | −1.14051 | −0.570255 | − | 0.821468i | \(-0.693156\pi\) | ||||
−0.570255 | + | 0.821468i | \(0.693156\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.44048 | −0.147645 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.64131 | 0.198812 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.7253 | −1.18545 | −0.592724 | − | 0.805406i | \(-0.701947\pi\) | ||||
−0.592724 | + | 0.805406i | \(0.701947\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 11.3322 | 0.483645 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.66867 | 0.113689 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.57584 | 0.152060 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −4.54892 | −0.193091 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.61863 | −0.280440 | −0.140220 | − | 0.990120i | \(-0.544781\pi\) | ||||
−0.140220 | + | 0.990120i | \(0.544781\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.49603 | 0.232457 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.46018 | −0.188309 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −4.44737 | −0.187434 | −0.0937172 | − | 0.995599i | \(-0.529875\pi\) | ||||
−0.0937172 | + | 0.995599i | \(0.529875\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.34595 | −0.0566246 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.79101 | −0.117211 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −27.7708 | −1.16421 | −0.582106 | − | 0.813113i | \(-0.697771\pi\) | ||||
−0.582106 | + | 0.813113i | \(0.697771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.7301 | 0.825679 | 0.412839 | − | 0.910804i | \(-0.364537\pi\) | ||||
0.412839 | + | 0.910804i | \(0.364537\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −13.0228 | −0.544036 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.60955 | −0.0671229 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.1301 | 1.04618 | 0.523091 | − | 0.852277i | \(-0.324779\pi\) | ||||
0.523091 | + | 0.852277i | \(0.324779\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.25619 | −0.135323 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 38.1932 | 1.58452 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.295240 | −0.0122276 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.59571 | −0.190009 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0.444202 | 0.0183342 | 0.00916710 | − | 0.999958i | \(-0.497082\pi\) | ||||
0.00916710 | + | 0.999958i | \(0.497082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.8273 | −0.816969 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.8117 | −0.527002 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.18109 | 0.0895666 | 0.0447833 | − | 0.998997i | \(-0.485740\pi\) | ||||
0.0447833 | + | 0.998997i | \(0.485740\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −17.4883 | −0.716949 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.641529 | −0.0262560 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.5022 | −0.469969 | −0.234984 | − | 0.971999i | \(-0.575504\pi\) | ||||
−0.234984 | + | 0.971999i | \(0.575504\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.5290 | 0.918979 | 0.459489 | − | 0.888183i | \(-0.348032\pi\) | ||||
0.459489 | + | 0.888183i | \(0.348032\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.47132 | 0.182086 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.0913 | 0.694862 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −28.5352 | −1.15821 | −0.579104 | − | 0.815254i | \(-0.696597\pi\) | ||||
−0.579104 | + | 0.815254i | \(0.696597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.79101 | −0.113097 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.1557 | 1.01769 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.67998 | 0.108243 | 0.0541217 | − | 0.998534i | \(-0.482764\pi\) | ||||
0.0541217 | + | 0.998534i | \(0.482764\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.23107 | −0.372233 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.8179 | 0.596546 | 0.298273 | − | 0.954481i | \(-0.403589\pi\) | ||||
0.298273 | + | 0.954481i | \(0.403589\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −29.8951 | −1.20159 | −0.600793 | − | 0.799404i | \(-0.705149\pi\) | ||||
−0.600793 | + | 0.799404i | \(0.705149\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 44.6638 | 1.78942 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −14.3616 | −0.574464 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.49776 | 0.139687 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8.40690 | −0.335205 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 21.3013 | 0.847993 | 0.423996 | − | 0.905664i | \(-0.360627\pi\) | ||||
0.423996 | + | 0.905664i | \(0.360627\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −21.1764 | −0.841688 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 31.8844 | 1.26529 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.97109 | 0.0780975 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.68684 | −0.145849 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.5956 | −0.418502 | −0.209251 | − | 0.977862i | \(-0.567103\pi\) | ||||
−0.209251 | + | 0.977862i | \(0.567103\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.99622 | 0.236468 | 0.118234 | − | 0.992986i | \(-0.462277\pi\) | ||||
0.118234 | + | 0.992986i | \(0.462277\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.05466 | −0.159652 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 39.5310 | 1.55412 | 0.777062 | − | 0.629424i | \(-0.216709\pi\) | ||||
0.777062 | + | 0.629424i | \(0.216709\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6.97113 | −0.273641 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 20.7362 | 0.812717 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.01241 | 0.196151 | 0.0980754 | − | 0.995179i | \(-0.468731\pi\) | ||||
0.0980754 | + | 0.995179i | \(0.468731\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.59517 | −0.335841 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.11674 | −0.355678 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.0968 | 0.471225 | 0.235612 | − | 0.971847i | \(-0.424290\pi\) | ||||
0.235612 | + | 0.971847i | \(0.424290\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 44.6828 | 1.73796 | 0.868980 | − | 0.494847i | \(-0.164776\pi\) | ||||
0.868980 | + | 0.494847i | \(0.164776\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.49338 | −0.329856 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 13.7146 | 0.531831 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.964487 | 0.0372892 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.8528 | 0.573387 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.38496 | 0.361764 | 0.180882 | − | 0.983505i | \(-0.442105\pi\) | ||||
0.180882 | + | 0.983505i | \(0.442105\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.60955 | −0.0619516 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 41.0590 | 1.57802 | 0.789012 | − | 0.614378i | \(-0.210593\pi\) | ||||
0.789012 | + | 0.614378i | \(0.210593\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.06631 | 0.0409211 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.721082 | 0.0276319 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −0.237475 | −0.00908675 | −0.00454337 | − | 0.999990i | \(-0.501446\pi\) | ||||
−0.00454337 | + | 0.999990i | \(0.501446\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.14387 | 0.120121 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.60402 | 0.175654 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.562217 | −0.0214187 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.1078 | −0.688852 | −0.344426 | − | 0.938813i | \(-0.611926\pi\) | ||||
−0.344426 | + | 0.938813i | \(0.611926\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −3.65812 | −0.138960 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 24.3809 | 0.924821 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.0600 | −0.646195 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −23.2612 | −0.879820 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.16563 | 0.119564 | 0.0597821 | − | 0.998211i | \(-0.480959\pi\) | ||||
0.0597821 | + | 0.998211i | \(0.480959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.59286 | 0.248654 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −18.5584 | −0.698949 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 24.8756 | 0.935542 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −31.0905 | −1.16763 | −0.583814 | − | 0.811887i | \(-0.698440\pi\) | ||||
−0.583814 | + | 0.811887i | \(0.698440\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.28120 | −0.0480488 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.42965 | −0.278243 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.02350 | −0.225266 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.82598 | 0.366958 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.6141 | 0.582309 | 0.291154 | − | 0.956676i | \(-0.405961\pi\) | ||||
0.291154 | + | 0.956676i | \(0.405961\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.81176 | 0.179199 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −0.446152 | −0.0165926 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.60955 | −0.0597772 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.95160 | 0.294909 | 0.147454 | − | 0.989069i | \(-0.452892\pi\) | ||||
0.147454 | + | 0.989069i | \(0.452892\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.49346 | −0.277156 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.71166 | −0.210965 | −0.105482 | − | 0.994421i | \(-0.533639\pi\) | ||||
−0.105482 | + | 0.994421i | \(0.533639\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.45416 | −0.0536374 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.86046 | 0.215873 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.90655 | 0.290847 | 0.145424 | − | 0.989369i | \(-0.453546\pi\) | ||||
0.145424 | + | 0.989369i | \(0.453546\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.66068 | 0.244686 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 40.3623 | 1.48075 | 0.740375 | − | 0.672194i | \(-0.234648\pi\) | ||||
0.740375 | + | 0.672194i | \(0.234648\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −39.1183 | −1.43318 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −13.6844 | −0.500685 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.0770 | −0.916292 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 54.5012 | 1.98878 | 0.994389 | − | 0.105783i | \(-0.0337350\pi\) | ||||
0.994389 | + | 0.105783i | \(0.0337350\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 24.8713 | 0.906362 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.7039 | 0.462342 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 43.2504 | 1.57196 | 0.785980 | − | 0.618251i | \(-0.212159\pi\) | ||||
0.785980 | + | 0.618251i | \(0.212159\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.31068 | 0.0475746 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.9295 | 1.26619 | 0.633096 | − | 0.774073i | \(-0.281784\pi\) | ||||
0.633096 | + | 0.774073i | \(0.281784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.03515 | 0.254690 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.26593 | 0.226545 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −13.2749 | −0.479329 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 0.322606 | 0.0116335 | 0.00581673 | − | 0.999983i | \(-0.498148\pi\) | ||||
0.00581673 | + | 0.999983i | \(0.498148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.7469 | −0.675152 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.7294 | −0.421878 | −0.210939 | − | 0.977499i | \(-0.567652\pi\) | ||||
−0.210939 | + | 0.977499i | \(0.567652\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 11.9584 | 0.429558 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6.89510 | −0.247360 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 13.3788 | 0.479346 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.83226 | −0.172912 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.55719 | 0.269728 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29.7868 | −1.06179 | −0.530893 | − | 0.847439i | \(-0.678143\pi\) | ||||
−0.530893 | + | 0.847439i | \(0.678143\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −29.0245 | −1.03330 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.04015 | −0.0725394 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.2838 | 1.00439 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.414771 | 0.0147104 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −14.1416 | −0.500921 | −0.250460 | − | 0.968127i | \(-0.580582\pi\) | ||||
−0.250460 | + | 0.968127i | \(0.580582\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −34.2980 | −1.21337 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −16.0027 | −0.565429 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11.9491 | −0.421675 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.13914 | 0.181131 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −30.8162 | −1.08478 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 24.6028 | 0.864989 | 0.432495 | − | 0.901637i | \(-0.357633\pi\) | ||||
0.432495 | + | 0.901637i | \(0.357633\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 45.8185 | 1.60890 | 0.804452 | − | 0.594018i | \(-0.202459\pi\) | ||||
0.804452 | + | 0.594018i | \(0.202459\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 30.3061 | 1.06288 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.1391 | 0.460242 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.87652 | 0.205593 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.96603 | −0.243413 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 30.1401 | 1.05190 | 0.525948 | − | 0.850517i | \(-0.323711\pi\) | ||||
0.525948 | + | 0.850517i | \(0.323711\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.8868 | −0.867499 | −0.433749 | − | 0.901034i | \(-0.642810\pi\) | ||||
−0.433749 | + | 0.901034i | \(0.642810\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.10960 | −0.0734469 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 16.4625 | 0.572459 | 0.286229 | − | 0.958161i | \(-0.407598\pi\) | ||||
0.286229 | + | 0.958161i | \(0.407598\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.1519 | −0.352589 | −0.176295 | − | 0.984337i | \(-0.556411\pi\) | ||||
−0.176295 | + | 0.984337i | \(0.556411\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.1153 | 0.350894 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.68744 | −0.0931144 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 4.73447 | 0.163843 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.42965 | −0.256806 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 7.98039 | 0.275514 | 0.137757 | − | 0.990466i | \(-0.456011\pi\) | ||||
0.137757 | + | 0.990466i | \(0.456011\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −5.35616 | −0.184476 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 12.4668 | 0.428870 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.9065 | 0.890158 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 15.3122 | 0.525514 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.47047 | 0.0846866 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −18.3786 | −0.629270 | −0.314635 | − | 0.949213i | \(-0.601882\pi\) | ||||
−0.314635 | + | 0.949213i | \(0.601882\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.91386 | −0.168051 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.3869 | 1.17464 | 0.587318 | − | 0.809357i | \(-0.300184\pi\) | ||||
0.587318 | + | 0.809357i | \(0.300184\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.1092 | −1.23203 | −0.616014 | − | 0.787735i | \(-0.711254\pi\) | ||||
−0.616014 | + | 0.787735i | \(0.711254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −13.9922 | −0.476852 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 24.6333 | 0.838528 | 0.419264 | − | 0.907864i | \(-0.362288\pi\) | ||||
0.419264 | + | 0.907864i | \(0.362288\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.6889 | −0.397435 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.41987 | −0.184068 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.67924 | −0.0569644 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.1599 | 0.378138 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.382051 | −0.0129305 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −33.9674 | −1.14831 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −0.299645 | −0.0101183 | −0.00505914 | − | 0.999987i | \(-0.501610\pi\) | ||||
−0.00505914 | + | 0.999987i | \(0.501610\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 20.0293 | 0.675571 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.4170 | 0.586792 | 0.293396 | − | 0.955991i | \(-0.405215\pi\) | ||||
0.293396 | + | 0.955991i | \(0.405215\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 58.5341 | 1.96983 | 0.984915 | − | 0.173038i | \(-0.0553583\pi\) | ||||
0.984915 | + | 0.173038i | \(0.0553583\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.79346 | 0.329203 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.9826 | 0.402337 | 0.201169 | − | 0.979557i | \(-0.435526\pi\) | ||||
0.201169 | + | 0.979557i | \(0.435526\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.3293 | 1.62091 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.31068 | 0.0439094 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 26.8971 | 0.900078 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.3085 | −0.812542 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.49588 | 0.0833351 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.42965 | −0.247793 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.766543 | 0.0255372 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.14592 | −0.204523 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.33501 | 0.210583 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −28.4906 | −0.946016 | −0.473008 | − | 0.881058i | \(-0.656832\pi\) | ||||
−0.473008 | + | 0.881058i | \(0.656832\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.91275 | −0.295617 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.1639 | −1.52948 | −0.764739 | − | 0.644340i | \(-0.777132\pi\) | ||||
−0.764739 | + | 0.644340i | \(0.777132\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −17.9358 | −0.593589 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −20.8661 | −0.689813 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13.0283 | −0.430232 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.8727 | −0.952421 | −0.476211 | − | 0.879331i | \(-0.657990\pi\) | ||||
−0.476211 | + | 0.879331i | \(0.657990\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29.9678 | −0.987473 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −9.20191 | −0.302885 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.97634 | −0.130741 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.72402 | −0.0566243 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −8.26220 | −0.271074 | −0.135537 | − | 0.990772i | \(-0.543276\pi\) | ||||
−0.135537 | + | 0.990772i | \(0.543276\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.10755 | 0.0690720 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 20.1613 | 0.660050 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.21262 | 0.268581 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −42.0102 | −1.37241 | −0.686207 | − | 0.727406i | \(-0.740726\pi\) | ||||
−0.686207 | + | 0.727406i | \(0.740726\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −9.24273 | −0.301625 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.2044 | −0.658646 | −0.329323 | − | 0.944217i | \(-0.606820\pi\) | ||||
−0.329323 | + | 0.944217i | \(0.606820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.01330 | 0.163255 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 5.13914 | 0.167176 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.8025 | −0.578503 | −0.289251 | − | 0.957253i | \(-0.593406\pi\) | ||||
−0.289251 | + | 0.957253i | \(0.593406\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.7543 | −0.738636 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.91035 | 0.0943745 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 7.84427 | 0.254101 | 0.127050 | − | 0.991896i | \(-0.459449\pi\) | ||||
0.127050 | + | 0.991896i | \(0.459449\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.9791 | 0.775947 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.31068 | 0.0423682 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.76537 | 0.153882 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.1998 | 0.780637 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.98490 | 0.289534 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.99568 | 0.193008 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.66288 | −0.310737 | −0.155369 | − | 0.987857i | \(-0.549657\pi\) | ||||
−0.155369 | + | 0.987857i | \(0.549657\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.08136 | −0.291735 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.3599 | −0.589196 | −0.294598 | − | 0.955621i | \(-0.595186\pi\) | ||||
−0.294598 | + | 0.955621i | \(0.595186\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.9558 | 1.18475 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.01724 | −0.128655 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.09208 | 0.130917 | 0.0654586 | − | 0.997855i | \(-0.479149\pi\) | ||||
0.0654586 | + | 0.997855i | \(0.479149\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.9744 | −0.670346 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.52065 | −0.0804781 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.24113 | −0.135271 | −0.0676356 | − | 0.997710i | \(-0.521546\pi\) | ||||
−0.0676356 | + | 0.997710i | \(0.521546\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 23.5904 | 0.751652 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −28.1302 | −0.895394 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.20204 | 0.0700208 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −58.6987 | −1.86463 | −0.932313 | − | 0.361654i | \(-0.882212\pi\) | ||||
−0.932313 | + | 0.361654i | \(0.882212\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −23.1303 | −0.734017 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.18126 | 0.0374484 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 21.2189 | 0.672009 | 0.336005 | − | 0.941860i | \(-0.390924\pi\) | ||||
0.336005 | + | 0.941860i | \(0.390924\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.47047 | 0.0781622 |
(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 | 8004.2.a.d.1.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8004.2.a.d.1.3 | ✓ | 8 | 1.1 | even | 1 | trivial |