Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4008,2,Mod(1,4008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4008, 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("4008.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4008 = 2^{3} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4008.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0040411301\) |
Analytic rank: | \(0\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 33 x^{9} + 22 x^{8} + 417 x^{7} - 151 x^{6} - 2470 x^{5} + 272 x^{4} + 6584 x^{3} + 292 x^{2} - 5687 x + 242 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.38119\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4008.1 |
$q$-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 | ||||||||
\(5\) | −1.38119 | −0.617687 | −0.308843 | − | 0.951113i | \(-0.599942\pi\) | ||||
−0.308843 | + | 0.951113i | \(0.599942\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.260099 | −0.0983081 | −0.0491540 | − | 0.998791i | \(-0.515653\pi\) | ||||
−0.0491540 | + | 0.998791i | \(0.515653\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.57901 | −1.07911 | −0.539556 | − | 0.841950i | \(-0.681408\pi\) | ||||
−0.539556 | + | 0.841950i | \(0.681408\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.29974 | −0.360482 | −0.180241 | − | 0.983622i | \(-0.557688\pi\) | ||||
−0.180241 | + | 0.983622i | \(0.557688\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.38119 | 0.356621 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.24502 | −1.02957 | −0.514784 | − | 0.857320i | \(-0.672128\pi\) | ||||
−0.514784 | + | 0.857320i | \(0.672128\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.37321 | 1.23270 | 0.616350 | − | 0.787473i | \(-0.288611\pi\) | ||||
0.616350 | + | 0.787473i | \(0.288611\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.260099 | 0.0567582 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.60388 | 1.16849 | 0.584245 | − | 0.811578i | \(-0.301391\pi\) | ||||
0.584245 | + | 0.811578i | \(0.301391\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.09232 | −0.618463 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.23067 | 0.414224 | 0.207112 | − | 0.978317i | \(-0.433594\pi\) | ||||
0.207112 | + | 0.978317i | \(0.433594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.62228 | −1.72821 | −0.864106 | − | 0.503309i | \(-0.832116\pi\) | ||||
−0.864106 | + | 0.503309i | \(0.832116\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.57901 | 0.623025 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.359246 | 0.0607236 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.0808905 | 0.0132983 | 0.00664916 | − | 0.999978i | \(-0.497883\pi\) | ||||
0.00664916 | + | 0.999978i | \(0.497883\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.29974 | 0.208125 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.29012 | 0.670005 | 0.335002 | − | 0.942217i | \(-0.391263\pi\) | ||||
0.335002 | + | 0.942217i | \(0.391263\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.5096 | −1.60270 | −0.801352 | − | 0.598193i | \(-0.795886\pi\) | ||||
−0.801352 | + | 0.598193i | \(0.795886\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.38119 | −0.205896 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.20376 | −0.904911 | −0.452455 | − | 0.891787i | \(-0.649452\pi\) | ||||
−0.452455 | + | 0.891787i | \(0.649452\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.93235 | −0.990336 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.24502 | 0.594421 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.3984 | 1.70305 | 0.851524 | − | 0.524316i | \(-0.175679\pi\) | ||||
0.851524 | + | 0.524316i | \(0.175679\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.94329 | 0.666553 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5.37321 | −0.711699 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.18358 | 0.414467 | 0.207234 | − | 0.978292i | \(-0.433554\pi\) | ||||
0.207234 | + | 0.978292i | \(0.433554\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.40971 | −0.820679 | −0.410339 | − | 0.911933i | \(-0.634590\pi\) | ||||
−0.410339 | + | 0.911933i | \(0.634590\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.260099 | −0.0327694 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.79518 | 0.222665 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.58992 | 0.316409 | 0.158204 | − | 0.987406i | \(-0.449430\pi\) | ||||
0.158204 | + | 0.987406i | \(0.449430\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −5.60388 | −0.674627 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9927 | 1.30460 | 0.652298 | − | 0.757963i | \(-0.273805\pi\) | ||||
0.652298 | + | 0.757963i | \(0.273805\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.2300 | 1.31437 | 0.657185 | − | 0.753729i | \(-0.271747\pi\) | ||||
0.657185 | + | 0.753729i | \(0.271747\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.09232 | 0.357070 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.930895 | 0.106085 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −11.9509 | −1.34458 | −0.672290 | − | 0.740288i | \(-0.734689\pi\) | ||||
−0.672290 | + | 0.740288i | \(0.734689\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.33550 | 0.475883 | 0.237941 | − | 0.971280i | \(-0.423527\pi\) | ||||
0.237941 | + | 0.971280i | \(0.423527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.86317 | 0.635950 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.23067 | −0.239152 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.61186 | 0.912855 | 0.456428 | − | 0.889760i | \(-0.349129\pi\) | ||||
0.456428 | + | 0.889760i | \(0.349129\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.338060 | 0.0354383 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.62228 | 0.997784 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.42142 | −0.761422 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.0718231 | 0.00729253 | 0.00364627 | − | 0.999993i | \(-0.498839\pi\) | ||||
0.00364627 | + | 0.999993i | \(0.498839\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.57901 | −0.359704 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 17.9592 | 1.78700 | 0.893501 | − | 0.449061i | \(-0.148241\pi\) | ||||
0.893501 | + | 0.449061i | \(0.148241\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.277767 | 0.0273692 | 0.0136846 | − | 0.999906i | \(-0.495644\pi\) | ||||
0.0136846 | + | 0.999906i | \(0.495644\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.359246 | −0.0350588 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.01695 | −0.485007 | −0.242504 | − | 0.970150i | \(-0.577969\pi\) | ||||
−0.242504 | + | 0.970150i | \(0.577969\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0343 | 1.44002 | 0.720012 | − | 0.693962i | \(-0.244136\pi\) | ||||
0.720012 | + | 0.693962i | \(0.244136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.0808905 | −0.00767779 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.2708 | 0.966198 | 0.483099 | − | 0.875566i | \(-0.339511\pi\) | ||||
0.483099 | + | 0.875566i | \(0.339511\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.74001 | −0.721760 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.29974 | −0.120161 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.10412 | 0.101215 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.80930 | 0.164481 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −4.29012 | −0.386827 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1770 | 0.999703 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.02975 | −0.268847 | −0.134423 | − | 0.990924i | \(-0.542918\pi\) | ||||
−0.134423 | + | 0.990924i | \(0.542918\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.5096 | 0.925322 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.2097 | −1.50361 | −0.751807 | − | 0.659383i | \(-0.770818\pi\) | ||||
−0.751807 | + | 0.659383i | \(0.770818\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.39757 | −0.121184 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.38119 | 0.118874 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.36980 | −0.629645 | −0.314822 | − | 0.949151i | \(-0.601945\pi\) | ||||
−0.314822 | + | 0.949151i | \(0.601945\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.4085 | 1.30693 | 0.653465 | − | 0.756957i | \(-0.273315\pi\) | ||||
0.653465 | + | 0.756957i | \(0.273315\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.20376 | 0.522450 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 4.65177 | 0.389001 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.08097 | −0.255861 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.93235 | 0.571770 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19.7078 | −1.61452 | −0.807261 | − | 0.590194i | \(-0.799051\pi\) | ||||
−0.807261 | + | 0.590194i | \(0.799051\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.39372 | −0.520314 | −0.260157 | − | 0.965566i | \(-0.583774\pi\) | ||||
−0.260157 | + | 0.965566i | \(0.583774\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.24502 | −0.343189 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 13.2902 | 1.06749 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6913 | 0.933070 | 0.466535 | − | 0.884503i | \(-0.345502\pi\) | ||||
0.466535 | + | 0.884503i | \(0.345502\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.3984 | −0.983255 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.45756 | −0.114872 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.58622 | 0.750851 | 0.375425 | − | 0.926853i | \(-0.377497\pi\) | ||||
0.375425 | + | 0.926853i | \(0.377497\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.94329 | −0.384834 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.00000 | 0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.3107 | −0.870052 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.37321 | 0.410900 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.1843 | 1.91472 | 0.957362 | − | 0.288890i | \(-0.0932860\pi\) | ||||
0.957362 | + | 0.288890i | \(0.0932860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.804308 | 0.0607999 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.18358 | −0.239293 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.125279 | −0.00936380 | −0.00468190 | − | 0.999989i | \(-0.501490\pi\) | ||||
−0.00468190 | + | 0.999989i | \(0.501490\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0014 | −1.11504 | −0.557522 | − | 0.830162i | \(-0.688248\pi\) | ||||
−0.557522 | + | 0.830162i | \(0.688248\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.40971 | 0.473819 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.111725 | −0.00821419 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.1929 | 1.11102 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.260099 | 0.0189194 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.07344 | −0.294744 | −0.147372 | − | 0.989081i | \(-0.547081\pi\) | ||||
−0.147372 | + | 0.989081i | \(0.547081\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.2459 | 0.809496 | 0.404748 | − | 0.914428i | \(-0.367359\pi\) | ||||
0.404748 | + | 0.914428i | \(0.367359\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.79518 | −0.128556 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.88075 | −0.418986 | −0.209493 | − | 0.977810i | \(-0.567181\pi\) | ||||
−0.209493 | + | 0.977810i | \(0.567181\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.8895 | 1.40993 | 0.704963 | − | 0.709244i | \(-0.250963\pi\) | ||||
0.704963 | + | 0.709244i | \(0.250963\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.58992 | −0.182679 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.580193 | −0.0407216 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −5.92547 | −0.413853 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.60388 | 0.389496 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −19.2308 | −1.33022 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.3807 | 0.990008 | 0.495004 | − | 0.868891i | \(-0.335167\pi\) | ||||
0.495004 | + | 0.868891i | \(0.335167\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −10.9927 | −0.753209 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.5158 | 0.989969 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.50274 | 0.169897 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −11.2300 | −0.758852 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.51741 | 0.371141 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −28.9444 | −1.93826 | −0.969131 | − | 0.246546i | \(-0.920704\pi\) | ||||
−0.969131 | + | 0.246546i | \(0.920704\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.09232 | −0.206154 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.1056 | 1.33445 | 0.667227 | − | 0.744855i | \(-0.267481\pi\) | ||||
0.667227 | + | 0.744855i | \(0.267481\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.3261 | 1.73968 | 0.869838 | − | 0.493337i | \(-0.164223\pi\) | ||||
0.869838 | + | 0.493337i | \(0.164223\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −0.930895 | −0.0612484 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.10123 | 0.530729 | 0.265365 | − | 0.964148i | \(-0.414508\pi\) | ||||
0.265365 | + | 0.964148i | \(0.414508\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.56856 | 0.558951 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 11.9509 | 0.776294 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.5900 | −0.879062 | −0.439531 | − | 0.898227i | \(-0.644855\pi\) | ||||
−0.439531 | + | 0.898227i | \(0.644855\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 25.7782 | 1.66052 | 0.830261 | − | 0.557375i | \(-0.188191\pi\) | ||||
0.830261 | + | 0.557375i | \(0.188191\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.57488 | 0.611717 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6.98377 | −0.444366 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.33550 | −0.274751 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4113 | 0.720274 | 0.360137 | − | 0.932899i | \(-0.382730\pi\) | ||||
0.360137 | + | 0.932899i | \(0.382730\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.0563 | −1.26093 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5.86317 | −0.367166 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.63267 | 0.476113 | 0.238056 | − | 0.971251i | \(-0.423490\pi\) | ||||
0.238056 | + | 0.971251i | \(0.423490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.0210395 | −0.00130733 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.23067 | 0.138075 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.6577 | 0.780510 | 0.390255 | − | 0.920707i | \(-0.372387\pi\) | ||||
0.390255 | + | 0.920707i | \(0.372387\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −17.1245 | −1.05195 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −8.61186 | −0.527037 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −0.272939 | −0.0166414 | −0.00832070 | − | 0.999965i | \(-0.502649\pi\) | ||||
−0.00832070 | + | 0.999965i | \(0.502649\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.48099 | 0.211455 | 0.105727 | − | 0.994395i | \(-0.466283\pi\) | ||||
0.105727 | + | 0.994395i | \(0.466283\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.338060 | −0.0204603 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.0674 | 0.667391 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 9.17422 | 0.551225 | 0.275613 | − | 0.961269i | \(-0.411119\pi\) | ||||
0.275613 | + | 0.961269i | \(0.411119\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.62228 | −0.576071 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.2804 | 1.62741 | 0.813706 | − | 0.581277i | \(-0.197447\pi\) | ||||
0.813706 | + | 0.581277i | \(0.197447\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.4054 | 0.915759 | 0.457879 | − | 0.889014i | \(-0.348609\pi\) | ||||
0.457879 | + | 0.889014i | \(0.348609\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.42142 | 0.439607 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.11586 | −0.0658669 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.02017 | 0.0600100 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.0718231 | −0.00421034 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.4315 | 0.901519 | 0.450759 | − | 0.892645i | \(-0.351153\pi\) | ||||
0.450759 | + | 0.892645i | \(0.351153\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.39713 | −0.256011 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.57901 | 0.207675 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −7.28357 | −0.421220 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.73354 | 0.157559 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −17.9592 | −1.03173 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.85302 | 0.506922 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8.51510 | 0.485982 | 0.242991 | − | 0.970029i | \(-0.421871\pi\) | ||||
0.242991 | + | 0.970029i | \(0.421871\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.277767 | −0.0158016 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.1383 | 1.31205 | 0.656026 | − | 0.754739i | \(-0.272236\pi\) | ||||
0.656026 | + | 0.754739i | \(0.272236\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.5786 | 0.937079 | 0.468539 | − | 0.883443i | \(-0.344780\pi\) | ||||
0.468539 | + | 0.883443i | \(0.344780\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.359246 | 0.0202412 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 15.1097 | 0.848645 | 0.424322 | − | 0.905511i | \(-0.360512\pi\) | ||||
0.424322 | + | 0.905511i | \(0.360512\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.98357 | −0.446994 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.01695 | 0.280019 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.8094 | −1.26915 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.01920 | 0.222945 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.0343 | −0.831398 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.61359 | 0.0889600 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.7163 | 1.19364 | 0.596818 | − | 0.802377i | \(-0.296432\pi\) | ||||
0.596818 | + | 0.802377i | \(0.296432\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0.0808905 | 0.00443277 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −3.57716 | −0.195441 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −31.3088 | −1.70550 | −0.852750 | − | 0.522319i | \(-0.825067\pi\) | ||||
−0.852750 | + | 0.522319i | \(0.825067\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.2708 | −0.557835 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 34.4382 | 1.86493 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.62379 | 0.195666 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.74001 | 0.416708 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.35131 | −0.0725419 | −0.0362710 | − | 0.999342i | \(-0.511548\pi\) | ||||
−0.0362710 | + | 0.999342i | \(0.511548\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.0510230 | −0.00273120 | −0.00136560 | − | 0.999999i | \(-0.500435\pi\) | ||||
−0.00136560 | + | 0.999999i | \(0.500435\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.29974 | 0.0693749 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.0639 | 1.01467 | 0.507334 | − | 0.861749i | \(-0.330631\pi\) | ||||
0.507334 | + | 0.861749i | \(0.330631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.1830 | −0.805831 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.10412 | −0.0584364 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.9791 | −1.10724 | −0.553618 | − | 0.832771i | \(-0.686753\pi\) | ||||
−0.553618 | + | 0.832771i | \(0.686753\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.87140 | 0.519547 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.80930 | −0.0949634 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −15.5107 | −0.811869 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.3923 | −1.11667 | −0.558335 | − | 0.829616i | \(-0.688560\pi\) | ||||
−0.558335 | + | 0.829616i | \(0.688560\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.29012 | 0.223335 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.22480 | −0.167423 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 35.6765 | 1.84726 | 0.923628 | − | 0.383289i | \(-0.125209\pi\) | ||||
0.923628 | + | 0.383289i | \(0.125209\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.1770 | −0.577179 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.89928 | −0.149321 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.77234 | 0.142405 | 0.0712027 | − | 0.997462i | \(-0.477316\pi\) | ||||
0.0712027 | + | 0.997462i | \(0.477316\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.02975 | 0.155219 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.0347 | 1.12592 | 0.562960 | − | 0.826484i | \(-0.309663\pi\) | ||||
0.562960 | + | 0.826484i | \(0.309663\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.28574 | −0.0655275 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −10.5096 | −0.534235 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 17.7239 | 0.898635 | 0.449318 | − | 0.893372i | \(-0.351667\pi\) | ||||
0.449318 | + | 0.893372i | \(0.351667\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −23.7886 | −1.20304 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.2097 | 0.868112 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.5064 | 0.830529 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.1866 | −1.21389 | −0.606944 | − | 0.794744i | \(-0.707605\pi\) | ||||
−0.606944 | + | 0.794744i | \(0.707605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.39757 | 0.0699658 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.3128 | −0.714748 | −0.357374 | − | 0.933961i | \(-0.616328\pi\) | ||||
−0.357374 | + | 0.933961i | \(0.616328\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 12.5064 | 0.622990 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.38119 | −0.0686318 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.289508 | −0.0143504 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −21.1631 | −1.04645 | −0.523223 | − | 0.852196i | \(-0.675271\pi\) | ||||
−0.523223 | + | 0.852196i | \(0.675271\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7.36980 | 0.363526 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.828046 | −0.0407455 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.98814 | −0.293946 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −15.4085 | −0.754556 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.8760 | −0.971004 | −0.485502 | − | 0.874235i | \(-0.661363\pi\) | ||||
−0.485502 | + | 0.874235i | \(0.661363\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.1319 | −1.51728 | −0.758639 | − | 0.651511i | \(-0.774135\pi\) | ||||
−0.758639 | + | 0.651511i | \(0.774135\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −6.20376 | −0.301637 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 13.1269 | 0.636750 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.66716 | 0.0806794 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.65177 | −0.224590 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.1346 | −1.01802 | −0.509008 | − | 0.860762i | \(-0.669988\pi\) | ||||
−0.509008 | + | 0.860762i | \(0.669988\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −28.1322 | −1.35195 | −0.675974 | − | 0.736926i | \(-0.736277\pi\) | ||||
−0.675974 | + | 0.736926i | \(0.736277\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3.08097 | 0.147721 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 30.1108 | 1.44040 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −29.5191 | −1.40887 | −0.704435 | − | 0.709769i | \(-0.748799\pi\) | ||||
−0.704435 | + | 0.709769i | \(0.748799\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.93235 | −0.330112 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −29.2445 | −1.38945 | −0.694724 | − | 0.719276i | \(-0.744474\pi\) | ||||
−0.694724 | + | 0.719276i | \(0.744474\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.8946 | −0.563859 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.7078 | 0.932145 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.0316 | 1.46447 | 0.732236 | − | 0.681051i | \(-0.238477\pi\) | ||||
0.732236 | + | 0.681051i | \(0.238477\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.3544 | −0.723010 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.39372 | 0.300403 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.466925 | −0.0218898 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.48784 | −0.0695981 | −0.0347991 | − | 0.999394i | \(-0.511079\pi\) | ||||
−0.0347991 | + | 0.999394i | \(0.511079\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4.24502 | 0.198140 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.65328 | −0.263299 | −0.131650 | − | 0.991296i | \(-0.542027\pi\) | ||||
−0.131650 | + | 0.991296i | \(0.542027\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.1653 | 0.472421 | 0.236210 | − | 0.971702i | \(-0.424095\pi\) | ||||
0.236210 | + | 0.971702i | \(0.424095\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −13.2902 | −0.616318 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −17.3327 | −0.802062 | −0.401031 | − | 0.916064i | \(-0.631348\pi\) | ||||
−0.401031 | + | 0.916064i | \(0.631348\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.673634 | −0.0311055 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −11.6913 | −0.538708 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 37.6141 | 1.72950 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −16.6157 | −0.762379 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.3984 | 0.567683 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −32.5368 | −1.48664 | −0.743322 | − | 0.668934i | \(-0.766751\pi\) | ||||
−0.743322 | + | 0.668934i | \(0.766751\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.105136 | −0.00479381 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 1.45756 | 0.0663213 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.0992013 | −0.00450450 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.4665 | 0.927426 | 0.463713 | − | 0.885985i | \(-0.346517\pi\) | ||||
0.463713 | + | 0.885985i | \(0.346517\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.58622 | −0.433504 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.2008 | −1.54346 | −0.771730 | − | 0.635951i | \(-0.780608\pi\) | ||||
−0.771730 | + | 0.635951i | \(0.780608\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.46921 | −0.426472 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.94329 | 0.222184 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.85919 | −0.128252 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.6637 | 0.880269 | 0.440134 | − | 0.897932i | \(-0.354931\pi\) | ||||
0.440134 | + | 0.897932i | \(0.354931\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −38.2959 | −1.70753 | −0.853764 | − | 0.520660i | \(-0.825686\pi\) | ||||
−0.853764 | + | 0.520660i | \(0.825686\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.8050 | −1.10381 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 11.3107 | 0.502325 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 27.9600 | 1.23931 | 0.619653 | − | 0.784876i | \(-0.287273\pi\) | ||||
0.619653 | + | 0.784876i | \(0.287273\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.92091 | −0.129213 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.37321 | −0.237233 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.383648 | −0.0169056 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.2033 | 0.976499 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.1843 | −1.10547 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.32725 | −0.189580 | −0.0947900 | − | 0.995497i | \(-0.530218\pi\) | ||||
−0.0947900 | + | 0.995497i | \(0.530218\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.71291 | 0.206081 | 0.103041 | − | 0.994677i | \(-0.467143\pi\) | ||||
0.103041 | + | 0.994677i | \(0.467143\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.804308 | −0.0351029 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 40.8467 | 1.77931 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.40344 | 0.365367 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.18358 | 0.138156 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.57604 | −0.241525 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.92936 | 0.299582 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.125279 | 0.00540619 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.8109 | 1.06868 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −24.6119 | −1.05815 | −0.529075 | − | 0.848575i | \(-0.677461\pi\) | ||||
−0.529075 | + | 0.848575i | \(0.677461\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 15.0014 | 0.643771 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.7652 | −0.889483 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.3102 | 1.25321 | 0.626607 | − | 0.779335i | \(-0.284443\pi\) | ||||
0.626607 | + | 0.779335i | \(0.284443\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.40971 | −0.273560 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11.9858 | 0.510614 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.10841 | 0.132183 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0.111725 | 0.00474247 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.1370 | −1.36169 | −0.680844 | − | 0.732428i | \(-0.738387\pi\) | ||||
−0.680844 | + | 0.732428i | \(0.738387\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13.6598 | 0.577747 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.1929 | −0.641447 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 36.8692 | 1.55385 | 0.776926 | − | 0.629591i | \(-0.216778\pi\) | ||||
0.776926 | + | 0.629591i | \(0.216778\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −14.1860 | −0.596808 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.260099 | −0.0109231 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 39.4146 | 1.65234 | 0.826172 | − | 0.563418i | \(-0.190514\pi\) | ||||
0.826172 | + | 0.563418i | \(0.190514\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.3581 | 0.893809 | 0.446905 | − | 0.894582i | \(-0.352526\pi\) | ||||
0.446905 | + | 0.894582i | \(0.352526\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.07344 | 0.170170 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −17.3290 | −0.722668 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.0651 | 1.50141 | 0.750704 | − | 0.660639i | \(-0.229714\pi\) | ||||
0.750704 | + | 0.660639i | \(0.229714\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −11.2459 | −0.467363 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.12766 | −0.0467831 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −44.3739 | −1.83778 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.79518 | 0.0742217 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6.65047 | 0.274494 | 0.137247 | − | 0.990537i | \(-0.456175\pi\) | ||||
0.137247 | + | 0.990537i | \(0.456175\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −51.7025 | −2.13037 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.88075 | 0.241902 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.0351096 | 0.00144178 | 0.000720889 | − | 1.00000i | \(-0.499771\pi\) | ||||
0.000720889 | 1.00000i | \(0.499771\pi\) | ||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.52500 | −0.0625190 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.8895 | −0.814022 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.1516 | −1.19110 | −0.595550 | − | 0.803318i | \(-0.703066\pi\) | ||||
−0.595550 | + | 0.803318i | \(0.703066\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 41.1130 | 1.67703 | 0.838517 | − | 0.544876i | \(-0.183423\pi\) | ||||
0.838517 | + | 0.544876i | \(0.183423\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.58992 | 0.105470 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.49898 | −0.101598 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.72077 | 0.232199 | 0.116099 | − | 0.993238i | \(-0.462961\pi\) | ||||
0.116099 | + | 0.993238i | \(0.462961\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.580193 | 0.0235106 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.06326 | 0.326204 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.16466 | 0.208599 | 0.104299 | − | 0.994546i | \(-0.466740\pi\) | ||||
0.104299 | + | 0.994546i | \(0.466740\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.92547 | 0.238938 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.1409 | −1.41472 | −0.707360 | − | 0.706854i | \(-0.750114\pi\) | ||||
−0.707360 | + | 0.706854i | \(0.750114\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.6982 | −0.912318 | −0.456159 | − | 0.889898i | \(-0.650775\pi\) | ||||
−0.456159 | + | 0.889898i | \(0.650775\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.60388 | −0.224876 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.23993 | −0.0897411 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0.0240062 | 0.000960247 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 19.2308 | 0.768003 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.343382 | −0.0136915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −35.0964 | −1.39717 | −0.698583 | − | 0.715529i | \(-0.746186\pi\) | ||||
−0.698583 | + | 0.715529i | \(0.746186\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.3807 | −0.571581 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.18465 | 0.166063 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.01024 | 0.356999 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 10.9927 | 0.434865 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.49562 | 0.217064 | 0.108532 | − | 0.994093i | \(-0.465385\pi\) | ||||
0.108532 | + | 0.994093i | \(0.465385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −30.9837 | −1.22188 | −0.610940 | − | 0.791677i | \(-0.709208\pi\) | ||||
−0.610940 | + | 0.791677i | \(0.709208\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −14.5158 | −0.571559 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.3651 | 0.604065 | 0.302033 | − | 0.953298i | \(-0.402335\pi\) | ||||
0.302033 | + | 0.953298i | \(0.402335\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −11.3941 | −0.447256 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.50274 | −0.0980902 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −49.3594 | −1.93158 | −0.965791 | − | 0.259321i | \(-0.916501\pi\) | ||||
−0.965791 | + | 0.259321i | \(0.916501\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.7698 | 0.928762 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 11.2300 | 0.438124 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −18.8524 | −0.734385 | −0.367192 | − | 0.930145i | \(-0.619681\pi\) | ||||
−0.367192 | + | 0.930145i | \(0.619681\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −36.9080 | −1.43556 | −0.717778 | − | 0.696272i | \(-0.754841\pi\) | ||||
−0.717778 | + | 0.696272i | \(0.754841\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.51741 | −0.214278 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.93030 | 0.0748539 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.5004 | 0.484017 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 28.9444 | 1.11906 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.9404 | 0.885604 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.15105 | −0.160011 | −0.0800057 | − | 0.996794i | \(-0.525494\pi\) | ||||
−0.0800057 | + | 0.996794i | \(0.525494\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 3.09232 | 0.119023 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −45.6659 | −1.75508 | −0.877541 | − | 0.479502i | \(-0.840817\pi\) | ||||
−0.877541 | + | 0.479502i | \(0.840817\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0186811 | −0.000716915 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.1056 | −0.770447 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.4197 | 1.31704 | 0.658518 | − | 0.752565i | \(-0.271184\pi\) | ||||
0.658518 | + | 0.752565i | \(0.271184\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.1791 | 0.388923 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.3261 | −1.00440 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −16.1146 | −0.613919 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −28.3874 | −1.07991 | −0.539954 | − | 0.841694i | \(-0.681559\pi\) | ||||
−0.539954 | + | 0.841694i | \(0.681559\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.930895 | 0.0353618 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −21.2820 | −0.807273 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.2117 | −0.689815 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −8.10123 | −0.306417 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20.7096 | 0.782189 | 0.391095 | − | 0.920350i | \(-0.372096\pi\) | ||||
0.391095 | + | 0.920350i | \(0.372096\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.434642 | 0.0163928 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −8.56856 | −0.322711 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.67115 | −0.175677 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.3505 | 0.463833 | 0.231917 | − | 0.972736i | \(-0.425500\pi\) | ||||
0.231917 | + | 0.972736i | \(0.425500\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −11.9509 | −0.448193 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −53.9221 | −2.01940 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.42498 | −0.240281 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 13.5900 | 0.507527 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −40.7997 | −1.52157 | −0.760786 | − | 0.649003i | \(-0.775186\pi\) | ||||
−0.760786 | + | 0.649003i | \(0.775186\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −0.0722468 | −0.00269061 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −25.7782 | −0.958703 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.89793 | −0.256183 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.3456 | 0.940015 | 0.470007 | − | 0.882662i | \(-0.344251\pi\) | ||||
0.470007 | + | 0.882662i | \(0.344251\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 44.6136 | 1.65009 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.51219 | −0.0927899 | −0.0463949 | − | 0.998923i | \(-0.514773\pi\) | ||||
−0.0463949 | + | 0.998923i | \(0.514773\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −9.57488 | −0.353175 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −9.26933 | −0.341440 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 35.0409 | 1.28900 | 0.644499 | − | 0.764605i | \(-0.277066\pi\) | ||||
0.644499 | + | 0.764605i | \(0.277066\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.98377 | 0.256555 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.5421 | 0.423440 | 0.211720 | − | 0.977330i | \(-0.432094\pi\) | ||||
0.211720 | + | 0.977330i | \(0.432094\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.2201 | 0.997269 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.33550 | 0.158628 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.30490 | 0.0476801 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −37.9598 | −1.38517 | −0.692586 | − | 0.721336i | \(-0.743529\pi\) | ||||
−0.692586 | + | 0.721336i | \(0.743529\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.4113 | −0.415851 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.83094 | 0.321391 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 8.58630 | 0.312074 | 0.156037 | − | 0.987751i | \(-0.450128\pi\) | ||||
0.156037 | + | 0.987751i | \(0.450128\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.0563 | 0.727998 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.05601 | −0.0382802 | −0.0191401 | − | 0.999817i | \(-0.506093\pi\) | ||||
−0.0191401 | + | 0.999817i | \(0.506093\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.91040 | −0.141566 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 5.86317 | 0.211983 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.13782 | −0.149408 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.6410 | 1.53767 | 0.768836 | − | 0.639446i | \(-0.220836\pi\) | ||||
0.768836 | + | 0.639446i | \(0.220836\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.63267 | −0.274884 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 32.7347 | 1.17738 | 0.588692 | − | 0.808357i | \(-0.299643\pi\) | ||||
0.588692 | + | 0.808357i | \(0.299643\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.7551 | 1.06884 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0210395 | 0.000754789 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 23.0517 | 0.825914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −39.3430 | −1.40780 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.23067 | −0.0797175 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −16.1479 | −0.576345 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.4271 | 1.36978 | 0.684890 | − | 0.728647i | \(-0.259850\pi\) | ||||
0.684890 | + | 0.728647i | \(0.259850\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.6577 | −0.450627 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.67143 | −0.0949851 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.33094 | 0.295840 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 17.1245 | 0.607344 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 46.5485 | 1.64883 | 0.824416 | − | 0.565985i | \(-0.191504\pi\) | ||||
0.824416 | + | 0.565985i | \(0.191504\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 26.3350 | 0.931667 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.61186 | 0.304285 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −40.1922 | −1.41835 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.01317 | 0.0709548 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0.272939 | 0.00960791 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 38.3586 | 1.34862 | 0.674308 | − | 0.738450i | \(-0.264442\pi\) | ||||
0.674308 | + | 0.738450i | \(0.264442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35.3307 | −1.24063 | −0.620314 | − | 0.784354i | \(-0.712995\pi\) | ||||
−0.620314 | + | 0.784354i | \(0.712995\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3.48099 | −0.122084 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −13.2404 | −0.463790 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −56.4705 | −1.97565 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.338060 | 0.0118128 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.32816 | −0.220854 | −0.110427 | − | 0.993884i | \(-0.535222\pi\) | ||||
−0.110427 | + | 0.993884i | \(0.535222\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.5763 | 0.473239 | 0.236620 | − | 0.971602i | \(-0.423960\pi\) | ||||
0.236620 | + | 0.971602i | \(0.423960\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.0674 | −0.385318 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −9.00252 | −0.313048 | −0.156524 | − | 0.987674i | \(-0.550029\pi\) | ||||
−0.156524 | + | 0.987674i | \(0.550029\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26.7081 | 0.927610 | 0.463805 | − | 0.885937i | \(-0.346484\pi\) | ||||
0.463805 | + | 0.885937i | \(0.346484\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9.17422 | −0.318250 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 29.4279 | 1.01962 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.38119 | −0.0477980 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 9.62228 | 0.332595 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.2297 | 1.31983 | 0.659917 | − | 0.751338i | \(-0.270591\pi\) | ||||
0.659917 | + | 0.751338i | \(0.270591\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.0241 | −0.828418 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −27.2804 | −0.939587 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 15.6222 | 0.537420 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.470595 | −0.0161699 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.4054 | −0.528713 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0.453301 | 0.0155389 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.6328 | −0.946129 | −0.473065 | − | 0.881028i | \(-0.656852\pi\) | ||||
−0.473065 | + | 0.881028i | \(0.656852\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −7.42142 | −0.253807 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.1251 | −1.60976 | −0.804882 | − | 0.593436i | \(-0.797771\pi\) | ||||
−0.804882 | + | 0.593436i | \(0.797771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −49.2154 | −1.67921 | −0.839604 | − | 0.543199i | \(-0.817213\pi\) | ||||
−0.839604 | + | 0.543199i | \(0.817213\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.11586 | 0.0380283 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 23.9655 | 0.815795 | 0.407897 | − | 0.913028i | \(-0.366262\pi\) | ||||
0.407897 | + | 0.913028i | \(0.366262\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.7842 | −1.18270 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.02017 | −0.0346468 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.7723 | 1.45095 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.36621 | −0.114060 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.0718231 | 0.00243084 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.90713 | −0.0982789 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.72694 | 0.227152 | 0.113576 | − | 0.993529i | \(-0.463769\pi\) | ||||
0.113576 | + | 0.993529i | \(0.463769\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.4315 | −0.520492 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.21204 | −0.0745254 | −0.0372627 | − | 0.999306i | \(-0.511864\pi\) | ||||
−0.0372627 | + | 0.999306i | \(0.511864\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.9253 | 1.37725 | 0.688623 | − | 0.725119i | \(-0.258215\pi\) | ||||
0.688623 | + | 0.725119i | \(0.258215\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4.39713 | 0.147808 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.67010 | −0.0896532 | −0.0448266 | − | 0.998995i | \(-0.514274\pi\) | ||||
−0.0448266 | + | 0.998995i | \(0.514274\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.788033 | 0.0264298 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.57901 | −0.119901 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −33.3341 | −1.11548 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0.173034 | 0.00578389 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.28357 | 0.243191 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −21.4641 | −0.715868 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.6313 | −1.75340 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2.73354 | −0.0909666 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.7198 | 0.688748 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.5598 | −1.04793 | −0.523963 | − | 0.851741i | \(-0.675547\pi\) | ||||
−0.523963 | + | 0.851741i | \(0.675547\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 17.9592 | 0.595667 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.18983 | 0.0394210 | 0.0197105 | − | 0.999806i | \(-0.493726\pi\) | ||||
0.0197105 | + | 0.999806i | \(0.493726\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −15.5168 | −0.513530 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.85302 | −0.292672 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.47621 | 0.147817 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.7543 | −0.618648 | −0.309324 | − | 0.950957i | \(-0.600103\pi\) | ||||
−0.309324 | + | 0.950957i | \(0.600103\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.51510 | −0.280582 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −14.2877 | −0.470284 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.250139 | −0.00822452 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.277767 | 0.00912306 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.6507 | 0.579102 | 0.289551 | − | 0.957163i | \(-0.406494\pi\) | ||||
0.289551 | + | 0.957163i | \(0.406494\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −37.2490 | −1.22079 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.1383 | −0.757513 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −20.9843 | −0.686261 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −48.8423 | −1.59561 | −0.797805 | − | 0.602916i | \(-0.794005\pi\) | ||||
−0.797805 | + | 0.602916i | \(0.794005\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −16.5786 | −0.541023 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.14208 | −0.102429 | −0.0512145 | − | 0.998688i | \(-0.516309\pi\) | ||||
−0.0512145 | + | 0.998688i | \(0.516309\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 24.0413 | 0.782893 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.359246 | −0.0116863 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.0506 | 0.326602 | 0.163301 | − | 0.986576i | \(-0.447786\pi\) | ||||
0.163301 | + | 0.986576i | \(0.447786\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14.5960 | −0.473808 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −15.1097 | −0.489965 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.69926 | −0.249403 | −0.124702 | − | 0.992194i | \(-0.539797\pi\) | ||||
−0.124702 | + | 0.992194i | \(0.539797\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.62619 | 0.182059 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 7.98357 | 0.258072 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.91688 | 0.0618992 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 61.5883 | 1.98672 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −5.01695 | −0.161669 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15.5327 | −0.500015 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.5188 | 0.852789 | 0.426394 | − | 0.904537i | \(-0.359784\pi\) | ||||
0.426394 | + | 0.904537i | \(0.359784\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 22.8094 | 0.732743 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 47.1360 | 1.51267 | 0.756333 | − | 0.654187i | \(-0.226989\pi\) | ||||
0.756333 | + | 0.654187i | \(0.226989\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4.00773 | −0.128482 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.01920 | −0.128717 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.34004 | 0.0428718 | 0.0214359 | − | 0.999770i | \(-0.493176\pi\) | ||||
0.0214359 | + | 0.999770i | \(0.493176\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −30.8219 | −0.985073 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.0343 | 0.480008 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −18.9209 | −0.603485 | −0.301742 | − | 0.953390i | \(-0.597568\pi\) | ||||
−0.301742 | + | 0.953390i | \(0.597568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 8.12242 | 0.258802 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.61359 | −0.0513611 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −58.8947 | −1.87274 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.1851 | 1.68948 | 0.844740 | − | 0.535178i | \(-0.179755\pi\) | ||||
0.844740 | + | 0.535178i | \(0.179755\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.7163 | −0.689146 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −27.4711 | −0.870893 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 5.58170 | 0.176774 | 0.0883870 | − | 0.996086i | \(-0.471829\pi\) | ||||
0.0883870 | + | 0.996086i | \(0.471829\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −0.0808905 | −0.00255926 |
(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 | 4008.2.a.k.1.4 | ✓ | 11 | |
4.3 | odd | 2 | 8016.2.a.be.1.4 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.k.1.4 | ✓ | 11 | 1.1 | even | 1 | trivial | |
8016.2.a.be.1.4 | 11 | 4.3 | odd | 2 |