Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.138917.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 6x^{3} - 2x^{2} + 3x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 502) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-0.779397\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | 1.14049 | 0.658462 | 0.329231 | − | 0.944249i | \(-0.393211\pi\) | ||||
0.329231 | + | 0.944249i | \(0.393211\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.02938 | −0.907568 | −0.453784 | − | 0.891112i | \(-0.649926\pi\) | ||||
−0.453784 | + | 0.891112i | \(0.649926\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.81607 | 1.44234 | 0.721170 | − | 0.692758i | \(-0.243605\pi\) | ||||
0.721170 | + | 0.692758i | \(0.243605\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.69928 | −0.566428 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.49635 | −0.451168 | −0.225584 | − | 0.974224i | \(-0.572429\pi\) | ||||
−0.225584 | + | 0.974224i | \(0.572429\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.70658 | 1.02802 | 0.514010 | − | 0.857784i | \(-0.328160\pi\) | ||||
0.514010 | + | 0.857784i | \(0.328160\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.31449 | −0.597599 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.98233 | 1.20839 | 0.604196 | − | 0.796836i | \(-0.293494\pi\) | ||||
0.604196 | + | 0.796836i | \(0.293494\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.85745 | 0.655543 | 0.327772 | − | 0.944757i | \(-0.393702\pi\) | ||||
0.327772 | + | 0.944757i | \(0.393702\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.35219 | 0.949726 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.43753 | −1.34232 | −0.671159 | − | 0.741313i | \(-0.734203\pi\) | ||||
−0.671159 | + | 0.741313i | \(0.734203\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.881602 | −0.176320 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.35948 | −1.03143 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.64253 | −0.676400 | −0.338200 | − | 0.941074i | \(-0.609818\pi\) | ||||
−0.338200 | + | 0.941074i | \(0.609818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.05435 | 0.368972 | 0.184486 | − | 0.982835i | \(-0.440938\pi\) | ||||
0.184486 | + | 0.982835i | \(0.440938\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.70658 | −0.297077 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.74428 | −1.30902 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.4344 | 1.71541 | 0.857706 | − | 0.514140i | \(-0.171889\pi\) | ||||
0.857706 | + | 0.514140i | \(0.171889\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.22731 | 0.676912 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.36551 | 1.46265 | 0.731324 | − | 0.682031i | \(-0.238903\pi\) | ||||
0.731324 | + | 0.682031i | \(0.238903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.0717 | 1.68843 | 0.844213 | − | 0.536009i | \(-0.180069\pi\) | ||||
0.844213 | + | 0.536009i | \(0.180069\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.44850 | 0.514072 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.32281 | −0.922276 | −0.461138 | − | 0.887328i | \(-0.652559\pi\) | ||||
−0.461138 | + | 0.887328i | \(0.652559\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.56241 | 1.08034 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.68229 | 0.795680 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.92195 | 0.676082 | 0.338041 | − | 0.941131i | \(-0.390236\pi\) | ||||
0.338041 | + | 0.941131i | \(0.390236\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.03668 | 0.409465 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.25889 | 0.431650 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.897795 | −0.116883 | −0.0584415 | − | 0.998291i | \(-0.518613\pi\) | ||||
−0.0584415 | + | 0.998291i | \(0.518613\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.628527 | −0.0804746 | −0.0402373 | − | 0.999190i | \(-0.512811\pi\) | ||||
−0.0402373 | + | 0.999190i | \(0.512811\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.48459 | −0.816982 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.52206 | −0.932997 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.6372 | −1.42172 | −0.710858 | − | 0.703336i | \(-0.751693\pi\) | ||||
−0.710858 | + | 0.703336i | \(0.751693\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.34194 | −0.883866 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.48517 | −0.532292 | −0.266146 | − | 0.963933i | \(-0.585750\pi\) | ||||
−0.266146 | + | 0.963933i | \(0.585750\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.44517 | 0.403227 | 0.201613 | − | 0.979465i | \(-0.435382\pi\) | ||||
0.201613 | + | 0.979465i | \(0.435382\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.00546 | −0.116100 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −5.71020 | −0.650737 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 13.5066 | 1.51961 | 0.759805 | − | 0.650151i | \(-0.225295\pi\) | ||||
0.759805 | + | 0.650151i | \(0.225295\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.01458 | −0.112732 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.59547 | 0.723947 | 0.361973 | − | 0.932188i | \(-0.382103\pi\) | ||||
0.361973 | + | 0.932188i | \(0.382103\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10.1111 | −1.09670 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.15426 | −0.445384 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.0236 | −1.38050 | −0.690252 | − | 0.723569i | \(-0.742500\pi\) | ||||
−0.690252 | + | 0.723569i | \(0.742500\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.1446 | 1.48275 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.34296 | 0.242954 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.79886 | −0.594950 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.00831686 | −0.000844449 0 | −0.000422224 | − | 1.00000i | \(-0.500134\pi\) | ||||
−0.000422224 | 1.00000i | \(0.500134\pi\) | ||||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.54273 | 0.255554 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.3535 | 1.32873 | 0.664363 | − | 0.747411i | \(-0.268703\pi\) | ||||
0.664363 | + | 0.747411i | \(0.268703\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.93777 | 0.585066 | 0.292533 | − | 0.956255i | \(-0.405502\pi\) | ||||
0.292533 | + | 0.956255i | \(0.405502\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8.83227 | −0.861941 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.9211 | −1.24913 | −0.624565 | − | 0.780973i | \(-0.714724\pi\) | ||||
−0.624565 | + | 0.780973i | \(0.714724\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.6838 | 1.11911 | 0.559555 | − | 0.828793i | \(-0.310972\pi\) | ||||
0.559555 | + | 0.828793i | \(0.310972\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.9004 | 1.12953 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.88626 | −0.271517 | −0.135758 | − | 0.990742i | \(-0.543347\pi\) | ||||
−0.135758 | + | 0.990742i | \(0.543347\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.0642 | 1.21825 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.29852 | −0.582299 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 19.0129 | 1.74291 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.76093 | −0.796448 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 10.6813 | 0.963097 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.9360 | 1.06759 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.94904 | −0.439157 | −0.219578 | − | 0.975595i | \(-0.570468\pi\) | ||||
−0.219578 | + | 0.975595i | \(0.570468\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.6272 | 1.11176 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 15.1764 | 1.32596 | 0.662982 | − | 0.748635i | \(-0.269291\pi\) | ||||
0.662982 | + | 0.748635i | \(0.269291\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 10.9042 | 0.945516 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 10.8764 | 0.936096 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.0367 | 1.11380 | 0.556899 | − | 0.830580i | \(-0.311991\pi\) | ||||
0.556899 | + | 0.830580i | \(0.311991\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.63891 | 0.647924 | 0.323962 | − | 0.946070i | \(-0.394985\pi\) | ||||
0.323962 | + | 0.946070i | \(0.394985\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.21110 | −0.607284 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.54635 | −0.463809 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.39208 | 0.613879 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.62485 | 0.711366 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.7367 | 0.961509 | 0.480755 | − | 0.876855i | \(-0.340363\pi\) | ||||
0.480755 | + | 0.876855i | \(0.340363\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.7106 | −1.44127 | −0.720634 | − | 0.693316i | \(-0.756149\pi\) | ||||
−0.720634 | + | 0.693316i | \(0.756149\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −8.46639 | −0.684467 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.16906 | −0.334867 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.93777 | 0.314269 | 0.157134 | − | 0.987577i | \(-0.449774\pi\) | ||||
0.157134 | + | 0.987577i | \(0.449774\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.61343 | 0.445174 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −24.5661 | −1.93608 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5452 | 0.904290 | 0.452145 | − | 0.891945i | \(-0.350659\pi\) | ||||
0.452145 | + | 0.891945i | \(0.350659\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.46330 | 0.269617 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.4435 | 1.81411 | 0.907057 | − | 0.421009i | \(-0.138324\pi\) | ||||
0.907057 | + | 0.421009i | \(0.138324\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.738705 | 0.0568235 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.85561 | −0.371318 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 21.8265 | 1.65944 | 0.829718 | − | 0.558183i | \(-0.188501\pi\) | ||||
0.829718 | + | 0.558183i | \(0.188501\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.36426 | −0.254314 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.02393 | −0.0769630 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −13.0480 | −0.975257 | −0.487628 | − | 0.873051i | \(-0.662138\pi\) | ||||
−0.487628 | + | 0.873051i | \(0.662138\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.2566 | −1.13402 | −0.567009 | − | 0.823712i | \(-0.691899\pi\) | ||||
−0.567009 | + | 0.823712i | \(0.691899\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.716828 | −0.0529894 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.1755 | −1.55685 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.45532 | −0.545187 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −20.4522 | −1.48768 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −9.41734 | −0.681415 | −0.340707 | − | 0.940169i | \(-0.610667\pi\) | ||||
−0.340707 | + | 0.940169i | \(0.610667\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 21.1899 | 1.52528 | 0.762640 | − | 0.646823i | \(-0.223903\pi\) | ||||
0.762640 | + | 0.646823i | \(0.223903\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −8.57884 | −0.614343 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 11.4445 | 0.815389 | 0.407694 | − | 0.913118i | \(-0.366333\pi\) | ||||
0.407694 | + | 0.913118i | \(0.366333\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.06949 | 0.642919 | 0.321460 | − | 0.946923i | \(-0.395827\pi\) | ||||
0.321460 | + | 0.946923i | \(0.395827\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.2722 | −0.936146 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −13.9001 | −0.975599 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −19.0062 | −1.32745 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.9392 | 0.760327 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.27575 | −0.295760 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4721 | −0.927460 | −0.463730 | − | 0.885977i | \(-0.653489\pi\) | ||||
−0.463730 | + | 0.885977i | \(0.653489\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.11529 | −0.350494 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −22.4688 | −1.53236 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.83955 | 0.532183 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3.92918 | 0.265509 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 18.4674 | 1.24225 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.05994 | 0.137944 | 0.0689718 | − | 0.997619i | \(-0.478028\pi\) | ||||
0.0689718 | + | 0.997619i | \(0.478028\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.49809 | 0.0998728 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.76947 | 0.648423 | 0.324211 | − | 0.945985i | \(-0.394901\pi\) | ||||
0.324211 | + | 0.945985i | \(0.394901\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0709 | 1.45849 | 0.729244 | − | 0.684254i | \(-0.239872\pi\) | ||||
0.729244 | + | 0.684254i | \(0.239872\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.51242 | −0.428486 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.1694 | −1.05929 | −0.529645 | − | 0.848219i | \(-0.677675\pi\) | ||||
−0.529645 | + | 0.848219i | \(0.677675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.8314 | 0.837028 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.4041 | 1.00061 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.6213 | −1.39857 | −0.699283 | − | 0.714845i | \(-0.746497\pi\) | ||||
−0.699283 | + | 0.714845i | \(0.746497\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.8537 | 1.27889 | 0.639446 | − | 0.768836i | \(-0.279164\pi\) | ||||
0.639446 | + | 0.768836i | \(0.279164\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.9213 | 0.957204 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −15.3470 | −0.980486 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.5913 | 0.673911 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 7.52206 | 0.476691 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00000 | −0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.63283 | 0.605611 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −11.5316 | −0.722134 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.49666 | −0.0933588 | −0.0466794 | − | 0.998910i | \(-0.514864\pi\) | ||||
−0.0466794 | + | 0.998910i | \(0.514864\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 39.8186 | 2.47421 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.18969 | 0.383132 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.639363 | −0.0394248 | −0.0197124 | − | 0.999806i | \(-0.506275\pi\) | ||||
−0.0197124 | + | 0.999806i | \(0.506275\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.98853 | −0.613590 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −14.8533 | −0.909009 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.15667 | 0.314408 | 0.157204 | − | 0.987566i | \(-0.449752\pi\) | ||||
0.157204 | + | 0.987566i | \(0.449752\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.1081 | −1.09999 | −0.549994 | − | 0.835169i | \(-0.685370\pi\) | ||||
−0.549994 | + | 0.835169i | \(0.685370\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 16.1317 | 0.976337 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.31919 | 0.0795500 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −22.7214 | −1.36520 | −0.682598 | − | 0.730794i | \(-0.739150\pi\) | ||||
−0.682598 | + | 0.730794i | \(0.739150\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −3.49092 | −0.208996 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4504 | −0.802384 | −0.401192 | − | 0.915994i | \(-0.631404\pi\) | ||||
−0.401192 | + | 0.915994i | \(0.631404\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.4980 | −1.21848 | −0.609239 | − | 0.792986i | \(-0.708525\pi\) | ||||
−0.609239 | + | 0.792986i | \(0.708525\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.61353 | −0.391752 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 35.7395 | 2.10963 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.82358 | 0.460211 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.00948529 | −0.000556037 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.4624 | 0.611219 | 0.305610 | − | 0.952157i | \(-0.401140\pi\) | ||||
0.305610 | + | 0.952157i | \(0.401140\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.82197 | 0.106079 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 8.01968 | 0.465349 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.8612 | −1.37993 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 42.2506 | 2.43528 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 15.2296 | 0.874915 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.27552 | 0.0730361 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.32266 | 0.246707 | 0.123354 | − | 0.992363i | \(-0.460635\pi\) | ||||
0.123354 | + | 0.992363i | \(0.460635\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.77197 | 0.385244 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.55444 | 0.144849 | 0.0724245 | − | 0.997374i | \(-0.476926\pi\) | ||||
0.0724245 | + | 0.997374i | \(0.476926\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.5974 | −1.16424 | −0.582118 | − | 0.813104i | \(-0.697776\pi\) | ||||
−0.582118 | + | 0.813104i | \(0.697776\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 13.1597 | 0.741466 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 28.4867 | 1.59997 | 0.799985 | − | 0.600020i | \(-0.204841\pi\) | ||||
0.799985 | + | 0.600020i | \(0.204841\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 5.45051 | 0.305170 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.7364 | −0.822504 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.2367 | 0.792153 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.26772 | −0.181261 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.3253 | 0.736891 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.1283 | −1.33024 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −29.7471 | −1.63505 | −0.817526 | − | 0.575892i | \(-0.804655\pi\) | ||||
−0.817526 | + | 0.575892i | \(0.804655\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −17.7311 | −0.971657 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 23.6164 | 1.29030 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.39501 | 0.348358 | 0.174179 | − | 0.984714i | \(-0.444273\pi\) | ||||
0.174179 | + | 0.984714i | \(0.444273\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.29175 | −0.178783 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −3.07403 | −0.166468 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.14621 | 0.115885 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.8996 | 0.802168 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2.73435 | 0.146788 | 0.0733938 | − | 0.997303i | \(-0.476617\pi\) | ||||
0.0733938 | + | 0.997303i | \(0.476617\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.63841 | 0.408875 | 0.204437 | − | 0.978880i | \(-0.434463\pi\) | ||||
0.204437 | + | 0.978880i | \(0.434463\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −19.8653 | −1.06033 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.8175 | 0.575758 | 0.287879 | − | 0.957667i | \(-0.407050\pi\) | ||||
0.287879 | + | 0.957667i | \(0.407050\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.10214 | 0.483091 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 21.6840 | 1.14764 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 7.26766 | 0.383572 | 0.191786 | − | 0.981437i | \(-0.438572\pi\) | ||||
0.191786 | + | 0.981437i | \(0.438572\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.8350 | −0.570263 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.99174 | −0.524431 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.99157 | −0.365955 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.7296 | 1.34307 | 0.671537 | − | 0.740971i | \(-0.265635\pi\) | ||||
0.671537 | + | 0.740971i | \(0.265635\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.9147 | −0.828484 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.7825 | 0.975140 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.2892 | 1.30943 | 0.654714 | − | 0.755877i | \(-0.272789\pi\) | ||||
0.654714 | + | 0.755877i | \(0.272789\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 13.6129 | 0.702968 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −13.5013 | −0.695352 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.2568 | −1.50282 | −0.751410 | − | 0.659835i | \(-0.770626\pi\) | ||||
−0.751410 | + | 0.659835i | \(0.770626\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.64433 | −0.289168 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −17.1697 | −0.877331 | −0.438666 | − | 0.898650i | \(-0.644549\pi\) | ||||
−0.438666 | + | 0.898650i | \(0.644549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.5882 | 0.590588 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −18.8140 | −0.956371 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 1.28895 | 0.0653525 | 0.0326763 | − | 0.999466i | \(-0.489597\pi\) | ||||
0.0326763 | + | 0.999466i | \(0.489597\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −32.0739 | −1.62205 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.3085 | 0.873097 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −27.4100 | −1.37915 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.194786 | −0.00977601 | −0.00488801 | − | 0.999988i | \(-0.501556\pi\) | ||||
−0.00488801 | + | 0.999988i | \(0.501556\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 12.4362 | 0.622586 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.4677 | −1.12198 | −0.560991 | − | 0.827822i | \(-0.689580\pi\) | ||||
−0.560991 | + | 0.827822i | \(0.689580\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.61460 | 0.379310 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.05898 | 0.102312 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.6136 | −0.773938 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.5990 | −0.721873 | −0.360936 | − | 0.932590i | \(-0.617543\pi\) | ||||
−0.360936 | + | 0.932590i | \(0.617543\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 14.8682 | 0.733394 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3.42605 | −0.168585 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.3847 | −0.657031 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 8.71209 | 0.426633 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 26.0017 | 1.27027 | 0.635134 | − | 0.772402i | \(-0.280945\pi\) | ||||
0.635134 | + | 0.772402i | \(0.280945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7755 | 0.671377 | 0.335689 | − | 0.941973i | \(-0.391031\pi\) | ||||
0.335689 | + | 0.941973i | \(0.391031\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.7442 | 0.522403 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.39243 | −0.213064 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.39850 | −0.116072 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.32555 | −0.305401 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.41827 | 0.405494 | 0.202747 | − | 0.979231i | \(-0.435013\pi\) | ||||
0.202747 | + | 0.979231i | \(0.435013\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.0471 | −0.819233 | −0.409616 | − | 0.912258i | \(-0.634337\pi\) | ||||
−0.409616 | + | 0.912258i | \(0.634337\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.43060 | 0.404216 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −18.3949 | −0.879948 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 24.7138 | 1.17952 | 0.589762 | − | 0.807577i | \(-0.299222\pi\) | ||||
0.589762 | + | 0.807577i | \(0.299222\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −12.8507 | −0.611937 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −30.4345 | −1.44599 | −0.722993 | − | 0.690856i | \(-0.757234\pi\) | ||||
−0.722993 | + | 0.690856i | \(0.757234\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.4300 | 1.25290 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.3856 | 0.633117 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.6290 | −0.879155 | −0.439578 | − | 0.898205i | \(-0.644872\pi\) | ||||
−0.439578 | + | 0.898205i | \(0.644872\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −14.0141 | −0.659899 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.1988 | −0.949020 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −28.7047 | −1.34570 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.74271 | −0.221855 | −0.110927 | − | 0.993829i | \(-0.535382\pi\) | ||||
−0.110927 | + | 0.993829i | \(0.535382\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −26.7027 | −1.24638 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −27.7318 | −1.29160 | −0.645800 | − | 0.763506i | \(-0.723476\pi\) | ||||
−0.645800 | + | 0.763506i | \(0.723476\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.5182 | 1.23240 | 0.616202 | − | 0.787588i | \(-0.288670\pi\) | ||||
0.616202 | + | 0.787588i | \(0.288670\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.75477 | −0.220497 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.5357 | −0.904005 | −0.452002 | − | 0.892017i | \(-0.649290\pi\) | ||||
−0.452002 | + | 0.892017i | \(0.649290\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −44.4086 | −2.05060 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.49099 | 0.206934 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −16.5672 | −0.761763 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.51913 | −0.115586 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.36379 | −0.382952 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.9921 | 0.685007 | 0.342503 | − | 0.939517i | \(-0.388725\pi\) | ||||
0.342503 | + | 0.939517i | \(0.388725\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 38.6761 | 1.76348 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −28.0174 | −1.27483 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.0168781 | 0.000766395 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.27755 | 0.284463 | 0.142231 | − | 0.989833i | \(-0.454572\pi\) | ||||
0.142231 | + | 0.989833i | \(0.454572\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.1672 | 0.595440 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −17.3489 | −0.782946 | −0.391473 | − | 0.920190i | \(-0.628034\pi\) | ||||
−0.391473 | + | 0.920190i | \(0.628034\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −18.1483 | −0.817357 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −5.16017 | −0.231933 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −17.1158 | −0.767746 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.3577 | −0.553209 | −0.276604 | − | 0.960984i | \(-0.589209\pi\) | ||||
−0.276604 | + | 0.960984i | \(0.589209\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 26.7371 | 1.19452 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 26.5532 | 1.18395 | 0.591975 | − | 0.805956i | \(-0.298348\pi\) | ||||
0.591975 | + | 0.805956i | \(0.298348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −27.0994 | −1.20591 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.842485 | 0.0374161 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.23099 | 0.276184 | 0.138092 | − | 0.990419i | \(-0.455903\pi\) | ||||
0.138092 | + | 0.990419i | \(0.455903\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.1470 | 0.581590 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −15.3144 | −0.676149 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.0500 | −0.530987 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 9.46116 | 0.416101 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.8929 | 1.09268 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.6417 | 1.12338 | 0.561692 | − | 0.827346i | \(-0.310150\pi\) | ||||
0.561692 | + | 0.827346i | \(0.310150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 21.9192 | 0.958460 | 0.479230 | − | 0.877689i | \(-0.340916\pi\) | ||||
0.479230 | + | 0.877689i | \(0.340916\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.83690 | −0.167456 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 10.2354 | 0.445863 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.4418 | 0.801819 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.52561 | 0.0662058 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 34.7140 | 1.50363 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 26.2219 | 1.13367 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −14.8812 | −0.642169 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.3160 | −0.487417 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20.5507 | −0.883545 | −0.441772 | − | 0.897127i | \(-0.645650\pi\) | ||||
−0.441772 | + | 0.897127i | \(0.645650\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.4000 | −0.746707 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.7110 | −1.01567 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −19.1703 | −0.819665 | −0.409832 | − | 0.912161i | \(-0.634413\pi\) | ||||
−0.409832 | + | 0.912161i | \(0.634413\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.06804 | 0.0455830 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.4083 | −0.443410 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 51.5421 | 2.19179 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.1504 | −1.02513 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −32.5259 | −1.37817 | −0.689083 | − | 0.724682i | \(-0.741986\pi\) | ||||
−0.689083 | + | 0.724682i | \(0.741986\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41.0383 | 1.73573 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.50272 | −0.358985 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.87879 | 0.416341 | 0.208171 | − | 0.978093i | \(-0.433249\pi\) | ||||
0.208171 | + | 0.978093i | \(0.433249\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.85733 | 0.246420 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.87173 | −0.162597 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −46.9242 | −1.96717 | −0.983583 | − | 0.180455i | \(-0.942243\pi\) | ||||
−0.983583 | + | 0.180455i | \(0.942243\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.80202 | 0.117261 | 0.0586304 | − | 0.998280i | \(-0.481327\pi\) | ||||
0.0586304 | + | 0.998280i | \(0.481327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.7404 | −0.448686 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.67534 | 0.236678 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4.53373 | 0.188741 | 0.0943707 | − | 0.995537i | \(-0.469916\pi\) | ||||
0.0943707 | + | 0.995537i | \(0.469916\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.1668 | 1.00434 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.1688 | 1.04418 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.36498 | −0.305026 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 12.7821 | 0.528476 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −20.8948 | −0.862422 | −0.431211 | − | 0.902251i | \(-0.641914\pi\) | ||||
−0.431211 | + | 0.902251i | \(0.641914\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.87019 | 0.241877 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.0524 | 0.536902 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.93943 | 0.367098 | 0.183549 | − | 0.983011i | \(-0.441241\pi\) | ||||
0.183549 | + | 0.983011i | \(0.441241\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −38.5845 | −1.58181 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.3437 | 0.423338 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.0894 | −1.55629 | −0.778146 | − | 0.628084i | \(-0.783840\pi\) | ||||
−0.778146 | + | 0.628084i | \(0.783840\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −48.0421 | −1.95968 | −0.979839 | − | 0.199790i | \(-0.935974\pi\) | ||||
−0.979839 | + | 0.199790i | \(0.935974\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 19.7750 | 0.805299 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 17.7793 | 0.722830 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −34.7009 | −1.40846 | −0.704232 | − | 0.709970i | \(-0.748709\pi\) | ||||
−0.704232 | + | 0.709970i | \(0.748709\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.8530 | −0.642395 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −23.4360 | −0.948118 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.07375 | −0.124148 | −0.0620739 | − | 0.998072i | \(-0.519771\pi\) | ||||
−0.0620739 | + | 0.998072i | \(0.519771\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.6764 | −0.874076 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −7.75817 | −0.312332 | −0.156166 | − | 0.987731i | \(-0.549913\pi\) | ||||
−0.156166 | + | 0.987731i | \(0.549913\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.20212 | −0.329671 | −0.164835 | − | 0.986321i | \(-0.552709\pi\) | ||||
−0.164835 | + | 0.986321i | \(0.552709\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 34.5019 | 1.38451 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −49.6992 | −1.99116 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.8148 | −0.792591 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.87645 | −0.194747 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 51.9878 | 2.07289 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −36.5135 | −1.45358 | −0.726790 | − | 0.686860i | \(-0.758989\pi\) | ||||
−0.726790 | + | 0.686860i | \(0.758989\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −15.3648 | −0.610697 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10.0435 | 0.398565 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.0307 | 1.11062 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.62158 | 0.301505 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 48.4002 | 1.91169 | 0.955846 | − | 0.293869i | \(-0.0949430\pi\) | ||||
0.955846 | + | 0.293869i | \(0.0949430\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 17.1467 | 0.676198 | 0.338099 | − | 0.941111i | \(-0.390216\pi\) | ||||
0.338099 | + | 0.941111i | \(0.390216\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.6254 | −1.00900 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.9336 | −1.29475 | −0.647377 | − | 0.762170i | \(-0.724134\pi\) | ||||
−0.647377 | + | 0.762170i | \(0.724134\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.34342 | 0.0527338 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.94092 | 0.350422 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.23931 | 0.205030 | 0.102515 | − | 0.994731i | \(-0.467311\pi\) | ||||
0.102515 | + | 0.994731i | \(0.467311\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −30.7986 | −1.20340 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5.85432 | −0.228399 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −10.1470 | −0.395271 | −0.197635 | − | 0.980276i | \(-0.563326\pi\) | ||||
−0.197635 | + | 0.980276i | \(0.563326\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.5201 | 0.681453 | 0.340727 | − | 0.940162i | \(-0.389327\pi\) | ||||
0.340727 | + | 0.940162i | \(0.389327\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 21.0618 | 0.817974 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.1289 | −0.858120 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 23.4489 | 0.907945 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.34934 | 0.0908306 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.940498 | 0.0363075 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.1182 | 1.85482 | 0.927410 | − | 0.374046i | \(-0.122030\pi\) | ||||
0.927410 | + | 0.374046i | \(0.122030\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.72493 | 0.181863 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −11.8423 | −0.455137 | −0.227568 | − | 0.973762i | \(-0.573078\pi\) | ||||
−0.227568 | + | 0.973762i | \(0.573078\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.0317377 | −0.00121798 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.1420 | 0.426962 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −28.2604 | −1.08136 | −0.540678 | − | 0.841230i | \(-0.681832\pi\) | ||||
−0.540678 | + | 0.841230i | \(0.681832\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.4564 | −1.01085 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 25.1717 | 0.960359 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 18.2436 | 0.695025 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.4838 | 0.627073 | 0.313536 | − | 0.949576i | \(-0.398486\pi\) | ||||
0.313536 | + | 0.949576i | \(0.398486\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 9.70324 | 0.368596 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −15.5023 | −0.588035 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 46.6620 | 1.76745 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −18.4410 | −0.697502 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −50.3831 | −1.90294 | −0.951471 | − | 0.307738i | \(-0.900428\pi\) | ||||
−0.951471 | + | 0.307738i | \(0.900428\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 29.8159 | 1.12453 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 14.6341 | 0.551151 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 50.9580 | 1.91647 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −33.2434 | −1.24848 | −0.624241 | − | 0.781231i | \(-0.714592\pi\) | ||||
−0.624241 | + | 0.781231i | \(0.714592\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.9515 | −0.860749 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −13.2249 | −0.495278 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 11.2557 | 0.420938 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −24.6589 | −0.920902 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 10.4707 | 0.390492 | 0.195246 | − | 0.980754i | \(-0.437449\pi\) | ||||
0.195246 | + | 0.980754i | \(0.437449\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.6590 | 0.843865 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.6430 | 0.842101 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.21126 | 0.119263 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −28.5204 | −1.05776 | −0.528881 | − | 0.848696i | \(-0.677388\pi\) | ||||
−0.528881 | + | 0.848696i | \(0.677388\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.0614 | 0.743014 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 55.1630 | 2.04028 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 3.63254 | 0.134171 | 0.0670855 | − | 0.997747i | \(-0.478630\pi\) | ||||
0.0670855 | + | 0.997747i | \(0.478630\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.5031 | −0.645613 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 17.4134 | 0.641432 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24.0059 | 0.883072 | 0.441536 | − | 0.897244i | \(-0.354434\pi\) | ||||
0.441536 | + | 0.897244i | \(0.354434\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0793 | 0.443745 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.4194 | 0.749113 | 0.374557 | − | 0.927204i | \(-0.377795\pi\) | ||||
0.374557 | + | 0.927204i | \(0.377795\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −23.8183 | −0.872635 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −11.2076 | −0.410064 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −49.3079 | −1.80167 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.8862 | −1.63792 | −0.818961 | − | 0.573849i | \(-0.805450\pi\) | ||||
−0.818961 | + | 0.573849i | \(0.805450\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.14049 | −0.0415618 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 35.9416 | 1.30805 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −29.9782 | −1.08957 | −0.544787 | − | 0.838574i | \(-0.683390\pi\) | ||||
−0.544787 | + | 0.838574i | \(0.683390\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 10.9861 | 0.398772 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −36.1087 | −1.30894 | −0.654469 | − | 0.756089i | \(-0.727108\pi\) | ||||
−0.654469 | + | 0.756089i | \(0.727108\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 44.5864 | 1.61414 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17.1815 | 0.621200 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.32775 | −0.120158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −48.6196 | −1.75327 | −0.876633 | − | 0.481160i | \(-0.840216\pi\) | ||||
−0.876633 | + | 0.481160i | \(0.840216\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.70692 | −0.0614732 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.0205 | 0.648151 | 0.324075 | − | 0.946031i | \(-0.394947\pi\) | ||||
0.324075 | + | 0.946031i | \(0.394947\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.81112 | −0.0650573 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 45.4127 | 1.62917 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.7614 | 0.958828 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.71141 | 0.240153 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 19.5221 | 0.697662 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.99125 | −0.285220 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 37.4092 | 1.33350 | 0.666748 | − | 0.745283i | \(-0.267686\pi\) | ||||
0.666748 | + | 0.745283i | \(0.267686\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.729187 | −0.0259597 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.0142 | −0.391619 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.32968 | −0.0827294 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.3918 | −0.404026 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 38.7582 | 1.37288 | 0.686442 | − | 0.727184i | \(-0.259171\pi\) | ||||
0.686442 | + | 0.727184i | \(0.259171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −31.5023 | −1.11447 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.1309 | 0.781956 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −5.15519 | −0.181923 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 49.8540 | 1.75712 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.88113 | 0.207026 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 5.29507 | 0.186165 | 0.0930824 | − | 0.995658i | \(-0.470328\pi\) | ||||
0.0930824 | + | 0.995658i | \(0.470328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.7038 | −0.727009 | −0.363504 | − | 0.931592i | \(-0.618420\pi\) | ||||
−0.363504 | + | 0.931592i | \(0.618420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.6521 | −0.724300 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −23.4296 | −0.820704 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.6369 | 1.10684 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −24.0356 | −0.839873 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −43.1154 | −1.50474 | −0.752369 | − | 0.658741i | \(-0.771089\pi\) | ||||
−0.752369 | + | 0.658741i | \(0.771089\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26.6434 | −0.928729 | −0.464365 | − | 0.885644i | \(-0.653717\pi\) | ||||
−0.464365 | + | 0.885644i | \(0.653717\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.50452 | 0.0523807 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.3708 | 0.499722 | 0.249861 | − | 0.968282i | \(-0.419615\pi\) | ||||
0.249861 | + | 0.968282i | \(0.419615\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −33.9001 | −1.17740 | −0.588700 | − | 0.808351i | \(-0.700360\pi\) | ||||
−0.588700 | + | 0.808351i | \(0.700360\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −25.9135 | −0.898930 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37.6784 | 1.30548 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −47.5759 | −1.64643 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −11.0103 | −0.380570 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 52.1634 | 1.80088 | 0.900441 | − | 0.434978i | \(-0.143244\pi\) | ||||
0.900441 | + | 0.434978i | \(0.143244\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15.7320 | −0.542483 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −15.3400 | −0.528339 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1.49912 | −0.0515712 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −33.4323 | −1.14875 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −23.3777 | −0.802322 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −67.1721 | −2.30263 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 35.3930 | 1.21183 | 0.605917 | − | 0.795528i | \(-0.292806\pi\) | ||||
0.605917 | + | 0.795528i | \(0.292806\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.85390 | 0.336996 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −50.1472 | −1.71300 | −0.856498 | − | 0.516151i | \(-0.827364\pi\) | ||||
−0.856498 | + | 0.516151i | \(0.827364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.2759 | −1.40832 | −0.704158 | − | 0.710043i | \(-0.748675\pi\) | ||||
−0.704158 | + | 0.710043i | \(0.748675\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.7605 | 1.38911 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 13.8787 | 0.472436 | 0.236218 | − | 0.971700i | \(-0.424092\pi\) | ||||
0.236218 | + | 0.971700i | \(0.424092\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.2943 | −1.50605 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 8.92271 | 0.303031 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.2106 | −0.685599 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −43.1343 | −1.46155 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.0141327 | 0.000478319 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 45.5488 | 1.53983 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 10.1481 | 0.342676 | 0.171338 | − | 0.985212i | \(-0.445191\pi\) | ||||
0.171338 | + | 0.985212i | \(0.445191\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.9322 | 0.402464 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.3824 | 0.551937 | 0.275968 | − | 0.961167i | \(-0.411001\pi\) | ||||
0.275968 | + | 0.961167i | \(0.411001\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.7048 | −0.528508 | −0.264254 | − | 0.964453i | \(-0.585126\pi\) | ||||
−0.264254 | + | 0.964453i | \(0.585126\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 2.07794 | 0.0698492 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.68720 | 0.190957 | 0.0954787 | − | 0.995431i | \(-0.469562\pi\) | ||||
0.0954787 | + | 0.995431i | \(0.469562\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.8859 | −0.633413 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.51818 | 0.0508609 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −18.0671 | −0.604592 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 26.4795 | 0.885112 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −27.2135 | −0.908631 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.48302 | −0.249573 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.5228 | 0.816972 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 48.1863 | 1.60354 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 30.9616 | 1.02920 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.7121 | 1.45144 | 0.725718 | − | 0.687992i | \(-0.241508\pi\) | ||||
0.725718 | + | 0.687992i | \(0.241508\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −22.6914 | −0.752627 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −8.68438 | −0.287726 | −0.143863 | − | 0.989598i | \(-0.545953\pi\) | ||||
−0.143863 | + | 0.989598i | \(0.545953\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −9.86916 | −0.326621 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.45472 | 0.0480915 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 57.9141 | 1.91249 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.65811 | −0.219631 | −0.109815 | − | 0.993952i | \(-0.535026\pi\) | ||||
−0.109815 | + | 0.993952i | \(0.535026\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4.92995 | 0.162447 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −16.6246 | −0.547207 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.19903 | −0.302462 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −10.0900 | −0.331398 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −27.5701 | −0.904544 | −0.452272 | − | 0.891880i | \(-0.649386\pi\) | ||||
−0.452272 | + | 0.891880i | \(0.649386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 21.6092 | 0.708213 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 2.91331 | 0.0953776 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.1297 | 0.494795 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.4470 | 1.32135 | 0.660673 | − | 0.750674i | \(-0.270271\pi\) | ||||
0.660673 | + | 0.750674i | \(0.270271\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.4912 | −0.766605 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.6692 | 0.934588 | 0.467294 | − | 0.884102i | \(-0.345229\pi\) | ||||
0.467294 | + | 0.884102i | \(0.345229\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −60.2908 | −1.96334 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 41.5053 | 1.35017 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 15.0634 | 0.489496 | 0.244748 | − | 0.969587i | \(-0.421295\pi\) | ||||
0.244748 | + | 0.969587i | \(0.421295\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.7698 | 0.414525 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 32.4887 | 1.05352 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.82793 | 0.123999 | 0.0619995 | − | 0.998076i | \(-0.480252\pi\) | ||||
0.0619995 | + | 0.998076i | \(0.480252\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.1114 | 0.618430 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.21625 | 0.200943 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 49.7489 | 1.60648 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.7796 | −0.863860 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.9566 | 0.707542 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −43.0024 | −1.38429 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.660265 | 0.0212327 | 0.0106163 | − | 0.999944i | \(-0.496621\pi\) | ||||
0.0106163 | + | 0.999944i | \(0.496621\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.2368 | 0.521603 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 25.2503 | 0.810320 | 0.405160 | − | 0.914246i | \(-0.367216\pi\) | ||||
0.405160 | + | 0.914246i | \(0.367216\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 29.1506 | 0.934526 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.72681 | −0.119353 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.3327 | 0.458544 | 0.229272 | − | 0.973362i | \(-0.426365\pi\) | ||||
0.229272 | + | 0.973362i | \(0.426365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 19.4880 | 0.622839 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.8542 | −0.633895 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 54.6511 | 1.74310 | 0.871550 | − | 0.490306i | \(-0.163115\pi\) | ||||
0.871550 | + | 0.490306i | \(0.163115\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −23.2253 | −0.740021 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.5181 | −0.875910 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −71.2747 | −2.26640 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −50.0085 | −1.58857 | −0.794285 | − | 0.607545i | \(-0.792155\pi\) | ||||
−0.794285 | + | 0.607545i | \(0.792155\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −33.9263 | −1.07662 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −18.4055 | −0.583493 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.7296 | −0.909876 | −0.454938 | − | 0.890523i | \(-0.650339\pi\) | ||||
−0.454938 | + | 0.890523i | \(0.650339\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −55.9232 | −1.76933 |
(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 | 4016.2.a.d.1.4 | 5 | ||
4.3 | odd | 2 | 502.2.a.d.1.2 | ✓ | 5 | ||
12.11 | even | 2 | 4518.2.a.t.1.5 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
502.2.a.d.1.2 | ✓ | 5 | 4.3 | odd | 2 | ||
4016.2.a.d.1.4 | 5 | 1.1 | even | 1 | trivial | ||
4518.2.a.t.1.5 | 5 | 12.11 | even | 2 |