Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4160,2,Mod(1,4160)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4160, 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("4160.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4160 = 2^{6} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4160.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: | \(33.2177672409\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{16})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 4x^{2} + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 2080) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.765367\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4160.1 |
$q$-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 | ||||||||
\(3\) | −1.08239 | −0.624919 | −0.312460 | − | 0.949931i | \(-0.601153\pi\) | ||||
−0.312460 | + | 0.949931i | \(0.601153\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.53073 | 0.578563 | 0.289281 | − | 0.957244i | \(-0.406584\pi\) | ||||
0.289281 | + | 0.957244i | \(0.406584\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.82843 | −0.609476 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.61313 | 0.787887 | 0.393944 | − | 0.919135i | \(-0.371111\pi\) | ||||
0.393944 | + | 0.919135i | \(0.371111\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.08239 | −0.279472 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.65685 | 0.886917 | 0.443459 | − | 0.896295i | \(-0.353751\pi\) | ||||
0.443459 | + | 0.896295i | \(0.353751\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.61313 | 0.599492 | 0.299746 | − | 0.954019i | \(-0.403098\pi\) | ||||
0.299746 | + | 0.954019i | \(0.403098\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.65685 | −0.361555 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.47343 | −1.76683 | −0.883416 | − | 0.468590i | \(-0.844762\pi\) | ||||
−0.883416 | + | 0.468590i | \(0.844762\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.22625 | 1.00579 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.17157 | 0.588946 | 0.294473 | − | 0.955660i | \(-0.404856\pi\) | ||||
0.294473 | + | 0.955660i | \(0.404856\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.67459 | 1.01919 | 0.509594 | − | 0.860415i | \(-0.329796\pi\) | ||||
0.509594 | + | 0.860415i | \(0.329796\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.82843 | −0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.53073 | 0.258741 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.48528 | 1.06617 | 0.533087 | − | 0.846061i | \(-0.321032\pi\) | ||||
0.533087 | + | 0.846061i | \(0.321032\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.08239 | −0.173321 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.37011 | −1.42893 | −0.714464 | − | 0.699672i | \(-0.753330\pi\) | ||||
−0.714464 | + | 0.699672i | \(0.753330\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.82843 | −0.272566 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.59220 | −0.669841 | −0.334921 | − | 0.942246i | \(-0.608710\pi\) | ||||
−0.334921 | + | 0.942246i | \(0.608710\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.65685 | −0.665265 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.95815 | −0.554252 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3137 | 1.82878 | 0.914389 | − | 0.404836i | \(-0.132671\pi\) | ||||
0.914389 | + | 0.404836i | \(0.132671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.61313 | 0.352354 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.82843 | −0.374634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.94269 | −0.903862 | −0.451931 | − | 0.892053i | \(-0.649265\pi\) | ||||
−0.451931 | + | 0.892053i | \(0.649265\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.17157 | 0.406078 | 0.203039 | − | 0.979171i | \(-0.434918\pi\) | ||||
0.203039 | + | 0.979171i | \(0.434918\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.79884 | −0.352620 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.81845 | 1.19951 | 0.599757 | − | 0.800182i | \(-0.295264\pi\) | ||||
0.599757 | + | 0.800182i | \(0.295264\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 9.17157 | 1.10413 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.71644 | −0.203704 | −0.101852 | − | 0.994800i | \(-0.532477\pi\) | ||||
−0.101852 | + | 0.994800i | \(0.532477\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.82843 | −0.565125 | −0.282562 | − | 0.959249i | \(-0.591184\pi\) | ||||
−0.282562 | + | 0.959249i | \(0.591184\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.08239 | −0.124984 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.55582 | 1.07511 | 0.537557 | − | 0.843227i | \(-0.319347\pi\) | ||||
0.537557 | + | 0.843227i | \(0.319347\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.171573 | −0.0190637 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.53073 | 0.168020 | 0.0840099 | − | 0.996465i | \(-0.473227\pi\) | ||||
0.0840099 | + | 0.996465i | \(0.473227\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.65685 | 0.396642 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.43289 | −0.368044 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.343146 | −0.0363734 | −0.0181867 | − | 0.999835i | \(-0.505789\pi\) | ||||
−0.0181867 | + | 0.999835i | \(0.505789\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.53073 | 0.160464 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.14214 | −0.636910 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.61313 | 0.268101 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.3137 | 1.75794 | 0.878970 | − | 0.476876i | \(-0.158231\pi\) | ||||
0.878970 | + | 0.476876i | \(0.158231\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.77791 | −0.480198 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.5349 | −1.13657 | −0.568284 | − | 0.822833i | \(-0.692392\pi\) | ||||
−0.568284 | + | 0.822833i | \(0.692392\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.65685 | −0.161692 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −16.7611 | −1.62036 | −0.810181 | − | 0.586180i | \(-0.800631\pi\) | ||||
−0.810181 | + | 0.586180i | \(0.800631\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.01962 | −0.666273 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.47343 | −0.790151 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.82843 | −0.169038 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.59767 | 0.513138 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.17157 | −0.379234 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.16478 | 0.195192 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.37011 | −0.831463 | −0.415731 | − | 0.909487i | \(-0.636474\pi\) | ||||
−0.415731 | + | 0.909487i | \(0.636474\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 10.1421 | 0.892965 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.26810 | 0.110795 | 0.0553973 | − | 0.998464i | \(-0.482357\pi\) | ||||
0.0553973 | + | 0.998464i | \(0.482357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.22625 | 0.449804 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −20.0083 | −1.69708 | −0.848542 | − | 0.529128i | \(-0.822519\pi\) | ||||
−0.848542 | + | 0.529128i | \(0.822519\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.97056 | 0.418597 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.61313 | 0.218521 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.17157 | 0.263385 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.04054 | 0.415737 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.6569 | 0.954967 | 0.477483 | − | 0.878641i | \(-0.341549\pi\) | ||||
0.477483 | + | 0.878641i | \(0.341549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.83938 | 0.637960 | 0.318980 | − | 0.947762i | \(-0.396660\pi\) | ||||
0.318980 | + | 0.947762i | \(0.396660\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.68629 | −0.540555 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.67459 | 0.455794 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −14.4107 | −1.14284 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −12.9706 | −1.02222 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.0866 | 0.868366 | 0.434183 | − | 0.900825i | \(-0.357037\pi\) | ||||
0.434183 | + | 0.900825i | \(0.357037\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.82843 | −0.220193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 24.9719 | 1.93239 | 0.966194 | − | 0.257818i | \(-0.0830035\pi\) | ||||
0.966194 | + | 0.257818i | \(0.0830035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.77791 | −0.365376 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.9706 | 1.44231 | 0.721153 | − | 0.692776i | \(-0.243613\pi\) | ||||
0.721153 | + | 0.692776i | \(0.243613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.53073 | 0.115713 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.51472 | 0.564841 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.9050 | 1.56251 | 0.781257 | − | 0.624210i | \(-0.214579\pi\) | ||||
0.781257 | + | 0.624210i | \(0.214579\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.14214 | −0.605200 | −0.302600 | − | 0.953118i | \(-0.597855\pi\) | ||||
−0.302600 | + | 0.953118i | \(0.597855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.43289 | −0.253766 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.48528 | 0.476807 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.55582 | 0.698791 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.00000 | 0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.5140 | −0.977837 | −0.488918 | − | 0.872330i | \(-0.662608\pi\) | ||||
−0.488918 | + | 0.872330i | \(0.662608\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.3137 | 1.24627 | 0.623134 | − | 0.782115i | \(-0.285859\pi\) | ||||
0.623134 | + | 0.782115i | \(0.285859\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.08239 | −0.0775117 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −13.3137 | −0.948562 | −0.474281 | − | 0.880373i | \(-0.657292\pi\) | ||||
−0.474281 | + | 0.880373i | \(0.657292\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.6274 | −0.749600 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.85483 | 0.340743 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 15.4930 | 1.07684 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.82843 | 0.472332 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 13.5140 | 0.930340 | 0.465170 | − | 0.885221i | \(-0.345993\pi\) | ||||
0.465170 | + | 0.885221i | \(0.345993\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.85786 | 0.127299 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.37011 | −0.639036 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.68629 | 0.589664 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.22625 | 0.353157 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.65685 | 0.245987 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.7038 | 1.58733 | 0.793663 | − | 0.608357i | \(-0.208171\pi\) | ||||
0.793663 | + | 0.608357i | \(0.208171\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.82843 | −0.121895 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.8799 | −0.854870 | −0.427435 | − | 0.904046i | \(-0.640583\pi\) | ||||
−0.427435 | + | 0.904046i | \(0.640583\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.6274 | 1.62743 | 0.813713 | − | 0.581267i | \(-0.197443\pi\) | ||||
0.813713 | + | 0.581267i | \(0.197443\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.32957 | −0.284865 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.3137 | −1.13426 | −0.567129 | − | 0.823629i | \(-0.691946\pi\) | ||||
−0.567129 | + | 0.823629i | \(0.691946\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.59220 | −0.299562 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.3431 | −0.671860 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 16.4985 | 1.06720 | 0.533600 | − | 0.845737i | \(-0.320839\pi\) | ||||
0.533600 | + | 0.845737i | \(0.320839\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.4930 | −0.993879 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −4.65685 | −0.297516 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.61313 | 0.166269 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.65685 | −0.104999 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.16478 | 0.136640 | 0.0683200 | − | 0.997663i | \(-0.478236\pi\) | ||||
0.0683200 | + | 0.997663i | \(0.478236\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.1421 | −1.39206 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.95815 | −0.247869 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.65685 | −0.228108 | −0.114054 | − | 0.993475i | \(-0.536384\pi\) | ||||
−0.114054 | + | 0.993475i | \(0.536384\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.92724 | 0.616849 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.79899 | −0.358948 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.30864 | −0.389008 | −0.194504 | − | 0.980902i | \(-0.562310\pi\) | ||||
−0.194504 | + | 0.980902i | \(0.562310\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 13.3137 | 0.817855 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.371418 | 0.0227304 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.34315 | 0.264806 | 0.132403 | − | 0.991196i | \(-0.457731\pi\) | ||||
0.132403 | + | 0.991196i | \(0.457731\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 16.4985 | 1.00221 | 0.501107 | − | 0.865385i | \(-0.332926\pi\) | ||||
0.501107 | + | 0.865385i | \(0.332926\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.65685 | −0.100277 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.61313 | 0.157577 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −14.9706 | −0.899494 | −0.449747 | − | 0.893156i | \(-0.648486\pi\) | ||||
−0.449747 | + | 0.893156i | \(0.648486\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −10.3756 | −0.621170 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.6274 | 0.753289 | 0.376644 | − | 0.926358i | \(-0.377078\pi\) | ||||
0.376644 | + | 0.926358i | \(0.377078\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.24718 | −0.193025 | −0.0965123 | − | 0.995332i | \(-0.530769\pi\) | ||||
−0.0965123 | + | 0.995332i | \(0.530769\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.82843 | −0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.06147 | −0.180713 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.7402 | −1.09857 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.48528 | −0.145192 | −0.0725958 | − | 0.997361i | \(-0.523128\pi\) | ||||
−0.0725958 | + | 0.997361i | \(0.523128\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.94269 | −0.404219 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 13.6569 | 0.792451 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.47343 | −0.490031 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.3431 | −0.826725 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.8239 | −0.621818 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.17157 | 0.181604 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −16.3128 | −0.931021 | −0.465511 | − | 0.885042i | \(-0.654129\pi\) | ||||
−0.465511 | + | 0.885042i | \(0.654129\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.4853 | 0.710263 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.6173 | 0.715461 | 0.357730 | − | 0.933825i | \(-0.383551\pi\) | ||||
0.357730 | + | 0.933825i | \(0.383551\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.343146 | 0.0193957 | 0.00969787 | − | 0.999953i | \(-0.496913\pi\) | ||||
0.00969787 | + | 0.999953i | \(0.496913\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.79884 | −0.157696 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.1421 | 1.13130 | 0.565648 | − | 0.824647i | \(-0.308626\pi\) | ||||
0.565648 | + | 0.824647i | \(0.308626\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.28772 | 0.464023 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.1421 | 1.01260 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.55582 | 0.531700 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.1535 | −0.837990 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.02944 | −0.387545 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 33.0740 | 1.81791 | 0.908954 | − | 0.416895i | \(-0.136882\pi\) | ||||
0.908954 | + | 0.416895i | \(0.136882\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −11.8579 | −0.649807 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 9.81845 | 0.536439 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.16478 | 0.117575 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 14.8284 | 0.803004 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.8435 | −0.963461 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.17157 | 0.493781 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 36.7695 | 1.97389 | 0.986944 | − | 0.161062i | \(-0.0514918\pi\) | ||||
0.986944 | + | 0.161062i | \(0.0514918\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.02944 | 0.0551045 | 0.0275523 | − | 0.999620i | \(-0.491229\pi\) | ||||
0.0275523 | + | 0.999620i | \(0.491229\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.22625 | 0.278957 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.4853 | −0.558075 | −0.279038 | − | 0.960280i | \(-0.590015\pi\) | ||||
−0.279038 | + | 0.960280i | \(0.590015\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.71644 | −0.0910993 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.05887 | −0.320670 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0042 | 0.527999 | 0.264000 | − | 0.964523i | \(-0.414958\pi\) | ||||
0.264000 | + | 0.964523i | \(0.414958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.1716 | −0.640609 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4.51528 | 0.236991 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −4.82843 | −0.252731 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 14.9678 | 0.781312 | 0.390656 | − | 0.920537i | \(-0.372248\pi\) | ||||
0.390656 | + | 0.920537i | \(0.372248\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.65685 | 0.190368 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.3797 | 1.05806 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.68629 | −0.346203 | −0.173102 | − | 0.984904i | \(-0.555379\pi\) | ||||
−0.173102 | + | 0.984904i | \(0.555379\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.08239 | −0.0558945 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.17157 | 0.163344 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.7666 | −0.912610 | −0.456305 | − | 0.889823i | \(-0.650827\pi\) | ||||
−0.456305 | + | 0.889823i | \(0.650827\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.1421 | 0.519597 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.5194 | −0.741909 | −0.370954 | − | 0.928651i | \(-0.620969\pi\) | ||||
−0.370954 | + | 0.928651i | \(0.620969\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 17.1326 | 0.870897 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.6569 | 1.19945 | 0.599725 | − | 0.800206i | \(-0.295277\pi\) | ||||
0.599725 | + | 0.800206i | \(0.295277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −30.9861 | −1.56703 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.37258 | −0.0692377 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 9.55582 | 0.480806 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −27.4558 | −1.37797 | −0.688985 | − | 0.724776i | \(-0.741943\pi\) | ||||
−0.688985 | + | 0.724776i | \(0.741943\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.32957 | −0.216750 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.9706 | 1.34685 | 0.673423 | − | 0.739258i | \(-0.264823\pi\) | ||||
0.673423 | + | 0.739258i | \(0.264823\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.67459 | 0.282672 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.171573 | −0.00852552 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9469 | 0.840025 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.3137 | 1.64726 | 0.823628 | − | 0.567130i | \(-0.191946\pi\) | ||||
0.823628 | + | 0.567130i | \(0.191946\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.16478 | 0.106781 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −10.6274 | −0.522941 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.53073 | 0.0751408 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.6569 | 1.06054 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −21.8017 | −1.06508 | −0.532541 | − | 0.846404i | \(-0.678763\pi\) | ||||
−0.532541 | + | 0.846404i | \(0.678763\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.6274 | 1.78511 | 0.892556 | − | 0.450937i | \(-0.148910\pi\) | ||||
0.892556 | + | 0.450937i | \(0.148910\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.39651 | 0.408252 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.65685 | 0.177383 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.85483 | 0.234942 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.82843 | −0.136558 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 22.9929 | 1.10753 | 0.553764 | − | 0.832674i | \(-0.313191\pi\) | ||||
0.553764 | + | 0.832674i | \(0.313191\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.43289 | −0.164594 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.1421 | −1.05920 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.9050 | 0.997742 | 0.498871 | − | 0.866676i | \(-0.333748\pi\) | ||||
0.498871 | + | 0.866676i | \(0.333748\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.51472 | 0.405463 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −21.9874 | −1.04465 | −0.522326 | − | 0.852746i | \(-0.674936\pi\) | ||||
−0.522326 | + | 0.852746i | \(0.674936\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.343146 | −0.0162667 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.6173 | −0.596777 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.9706 | −0.517733 | −0.258866 | − | 0.965913i | \(-0.583349\pi\) | ||||
−0.258866 | + | 0.965913i | \(0.583349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.22625 | −0.246095 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.48528 | −0.398673 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.53073 | 0.0717619 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.00000 | 0.280668 | 0.140334 | − | 0.990104i | \(-0.455182\pi\) | ||||
0.140334 | + | 0.990104i | \(0.455182\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 19.1116 | 0.892055 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −19.6569 | −0.915511 | −0.457755 | − | 0.889078i | \(-0.651346\pi\) | ||||
−0.457755 | + | 0.889078i | \(0.651346\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −21.5391 | −1.00100 | −0.500502 | − | 0.865735i | \(-0.666851\pi\) | ||||
−0.500502 | + | 0.865735i | \(0.666851\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.14214 | −0.284835 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.185709 | 0.00859359 | 0.00429680 | − | 0.999991i | \(-0.498632\pi\) | ||||
0.00429680 | + | 0.999991i | \(0.498632\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.0294 | 0.693995 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.16478 | 0.0997480 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −24.4853 | −1.12583 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.61313 | 0.119898 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.3431 | −1.11460 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.3421 | −1.56913 | −0.784564 | − | 0.620047i | \(-0.787113\pi\) | ||||
−0.784564 | + | 0.620047i | \(0.787113\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.48528 | 0.295703 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 14.0392 | 0.638807 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 17.3137 | 0.786175 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.2597 | −1.50714 | −0.753570 | − | 0.657368i | \(-0.771670\pi\) | ||||
−0.753570 | + | 0.657368i | \(0.771670\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.28772 | −0.374020 | −0.187010 | − | 0.982358i | \(-0.559880\pi\) | ||||
−0.187010 | + | 0.982358i | \(0.559880\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5980 | 0.522347 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.77791 | −0.214751 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.62742 | −0.117856 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.94269 | 0.310798 | 0.155399 | − | 0.987852i | \(-0.450334\pi\) | ||||
0.155399 | + | 0.987852i | \(0.450334\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −27.0294 | −1.20759 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 19.4512 | 0.867286 | 0.433643 | − | 0.901085i | \(-0.357228\pi\) | ||||
0.433643 | + | 0.901085i | \(0.357228\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −1.08239 | −0.0480707 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.65685 | 0.339384 | 0.169692 | − | 0.985497i | \(-0.445723\pi\) | ||||
0.169692 | + | 0.985497i | \(0.445723\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.39104 | −0.326960 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 13.6569 | 0.602965 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −11.5349 | −0.508288 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | −0.527759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −20.5336 | −0.901325 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −8.14214 | −0.356713 | −0.178357 | − | 0.983966i | \(-0.557078\pi\) | ||||
−0.178357 | + | 0.983966i | \(0.557078\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.8532 | −1.26166 | −0.630831 | − | 0.775921i | \(-0.717286\pi\) | ||||
−0.630831 | + | 0.775921i | \(0.717286\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.65685 | −0.0723110 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.7512 | 0.903935 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.7990 | 2.12170 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.6942 | 0.550882 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.00000 | −0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.7611 | −0.724648 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22.6274 | −0.976445 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −12.1689 | −0.524154 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.3137 | −0.744374 | −0.372187 | − | 0.928158i | \(-0.621392\pi\) | ||||
−0.372187 | + | 0.928158i | \(0.621392\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.81298 | 0.378201 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0000 | 0.599694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −29.0070 | −1.24025 | −0.620125 | − | 0.784503i | \(-0.712918\pi\) | ||||
−0.620125 | + | 0.784503i | \(0.712918\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.79899 | −0.247495 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.28772 | 0.353069 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.6274 | 0.622021 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.01962 | −0.297966 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −40.1421 | −1.70088 | −0.850438 | − | 0.526075i | \(-0.823663\pi\) | ||||
−0.850438 | + | 0.526075i | \(0.823663\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −9.37011 | −0.396313 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.3431 | −0.436688 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −22.3588 | −0.942312 | −0.471156 | − | 0.882050i | \(-0.656163\pi\) | ||||
−0.471156 | + | 0.882050i | \(0.656163\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.262632 | −0.0110295 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.7990 | −1.58462 | −0.792308 | − | 0.610121i | \(-0.791121\pi\) | ||||
−0.792308 | + | 0.610121i | \(0.791121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.2764 | 0.890391 | 0.445195 | − | 0.895433i | \(-0.353134\pi\) | ||||
0.445195 | + | 0.895433i | \(0.353134\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.6274 | 0.611069 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.47343 | −0.353366 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 25.7990 | 1.07403 | 0.537013 | − | 0.843574i | \(-0.319553\pi\) | ||||
0.537013 | + | 0.843574i | \(0.319553\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.7402 | −0.778817 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.34315 | 0.0972101 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 34.7904 | 1.44087 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.82843 | −0.0755962 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.22078 | −0.174210 | −0.0871052 | − | 0.996199i | \(-0.527762\pi\) | ||||
−0.0871052 | + | 0.996199i | \(0.527762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.8284 | 0.610995 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.4107 | 0.592775 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −22.6863 | −0.931614 | −0.465807 | − | 0.884886i | \(-0.654236\pi\) | ||||
−0.465807 | + | 0.884886i | \(0.654236\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.59767 | 0.229482 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.3492 | 0.463715 | 0.231858 | − | 0.972750i | \(-0.425520\pi\) | ||||
0.231858 | + | 0.972750i | \(0.425520\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.9706 | −0.936989 | −0.468494 | − | 0.883466i | \(-0.655203\pi\) | ||||
−0.468494 | + | 0.883466i | \(0.655203\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −17.9523 | −0.731075 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.17157 | −0.169599 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.6997 | 0.556053 | 0.278026 | − | 0.960573i | \(-0.410320\pi\) | ||||
0.278026 | + | 0.960573i | \(0.410320\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.25483 | −0.212937 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.59220 | −0.185781 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.6863 | −0.593174 | −0.296587 | − | 0.955006i | \(-0.595848\pi\) | ||||
−0.296587 | + | 0.955006i | \(0.595848\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 2.16478 | 0.0872925 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 31.9411 | 1.28590 | 0.642951 | − | 0.765908i | \(-0.277710\pi\) | ||||
0.642951 | + | 0.765908i | \(0.277710\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.9510 | 1.08325 | 0.541626 | − | 0.840619i | \(-0.317809\pi\) | ||||
0.541626 | + | 0.840619i | \(0.317809\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −44.2843 | −1.77707 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −0.525265 | −0.0210443 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.39104 | −0.295170 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 23.7157 | 0.945608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.8059 | 1.26617 | 0.633086 | − | 0.774082i | \(-0.281788\pi\) | ||||
0.633086 | + | 0.774082i | \(0.281788\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −14.6274 | −0.581388 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.37011 | −0.371842 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.65685 | −0.184511 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.13839 | 0.124153 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −32.3431 | −1.27748 | −0.638739 | − | 0.769424i | \(-0.720544\pi\) | ||||
−0.638739 | + | 0.769424i | \(0.720544\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.9832 | 0.472573 | 0.236286 | − | 0.971683i | \(-0.424070\pi\) | ||||
0.236286 | + | 0.971683i | \(0.424070\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.1421 | 0.399346 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.2359 | −0.638298 | −0.319149 | − | 0.947704i | \(-0.603397\pi\) | ||||
−0.319149 | + | 0.947704i | \(0.603397\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −18.1421 | −0.712141 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −9.40197 | −0.368492 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −38.2843 | −1.49818 | −0.749090 | − | 0.662469i | \(-0.769509\pi\) | ||||
−0.749090 | + | 0.662469i | \(0.769509\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.26810 | 0.0495488 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.82843 | 0.344430 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 21.8017 | 0.849273 | 0.424637 | − | 0.905364i | \(-0.360402\pi\) | ||||
0.424637 | + | 0.905364i | \(0.360402\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.68629 | −0.260067 | −0.130033 | − | 0.991510i | \(-0.541508\pi\) | ||||
−0.130033 | + | 0.991510i | \(0.541508\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.95815 | −0.153722 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.00000 | 0.155113 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −26.8741 | −1.04057 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −25.6569 | −0.991951 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.28772 | 0.319944 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −26.9706 | −1.03964 | −0.519819 | − | 0.854276i | \(-0.674001\pi\) | ||||
−0.519819 | + | 0.854276i | \(0.674001\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.22625 | 0.201159 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.62742 | −0.177846 | −0.0889230 | − | 0.996038i | \(-0.528343\pi\) | ||||
−0.0889230 | + | 0.996038i | \(0.528343\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 26.5027 | 1.01708 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.9411 | 0.534225 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.29319 | 0.355594 | 0.177797 | − | 0.984067i | \(-0.443103\pi\) | ||||
0.177797 | + | 0.984067i | \(0.443103\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −26.6565 | −1.01701 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 13.3137 | 0.507212 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.6411 | −1.12760 | −0.563800 | − | 0.825912i | \(-0.690661\pi\) | ||||
−0.563800 | + | 0.825912i | \(0.690661\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.31371 | −0.277825 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −20.0083 | −0.758959 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.31371 | −0.277026 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 18.7402 | 0.708820 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.3431 | −0.617272 | −0.308636 | − | 0.951180i | \(-0.599873\pi\) | ||||
−0.308636 | + | 0.951180i | \(0.599873\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 16.9469 | 0.639163 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 4.97056 | 0.187202 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 15.3073 | 0.575692 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.31371 | 0.199561 | 0.0997803 | − | 0.995009i | \(-0.468186\pi\) | ||||
0.0997803 | + | 0.995009i | \(0.468186\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −17.4721 | −0.655256 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −48.0833 | −1.80073 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.61313 | 0.0977254 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.8579 | −0.666914 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −32.1003 | −1.19714 | −0.598570 | − | 0.801070i | \(-0.704264\pi\) | ||||
−0.598570 | + | 0.801070i | \(0.704264\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −17.6569 | −0.657576 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.49435 | −0.241528 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.17157 | 0.117789 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.2249 | −0.527574 | −0.263787 | − | 0.964581i | \(-0.584972\pi\) | ||||
−0.263787 | + | 0.964581i | \(0.584972\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.2843 | 0.640158 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.2651 | −1.26734 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.3137 | 0.934983 | 0.467492 | − | 0.883998i | \(-0.345158\pi\) | ||||
0.467492 | + | 0.883998i | \(0.345158\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.04054 | 0.185923 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 25.6569 | 0.945082 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.6437 | 0.428320 | 0.214160 | − | 0.976799i | \(-0.431299\pi\) | ||||
0.214160 | + | 0.976799i | \(0.431299\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.82843 | −0.103905 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.5809 | 0.644981 | 0.322490 | − | 0.946573i | \(-0.395480\pi\) | ||||
0.322490 | + | 0.946573i | \(0.395480\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.6569 | 0.427074 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.79884 | −0.102404 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −25.6569 | −0.937481 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.95815 | 0.144435 | 0.0722175 | − | 0.997389i | \(-0.476992\pi\) | ||||
0.0722175 | + | 0.997389i | \(0.476992\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.34315 | −0.0853890 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.83938 | 0.285304 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.343146 | −0.0124718 | −0.00623592 | − | 0.999981i | \(-0.501985\pi\) | ||||
−0.00623592 | + | 0.999981i | \(0.501985\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 23.9665 | 0.869928 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.4303 | 0.775828 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −6.68629 | −0.241743 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −6.94269 | −0.250686 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2.68629 | −0.0968701 | −0.0484351 | − | 0.998826i | \(-0.515423\pi\) | ||||
−0.0484351 | + | 0.998826i | \(0.515423\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.95815 | 0.142549 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.17157 | 0.114074 | 0.0570368 | − | 0.998372i | \(-0.481835\pi\) | ||||
0.0570368 | + | 0.998372i | \(0.481835\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.67459 | 0.203837 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.7452 | −0.385481 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.22625 | −0.187250 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.48528 | −0.160496 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 16.5754 | 0.592358 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −7.65367 | −0.272824 | −0.136412 | − | 0.990652i | \(-0.543557\pi\) | ||||
−0.136412 | + | 0.990652i | \(0.543557\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.82843 | 0.243098 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.06147 | −0.108853 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.17157 | 0.112626 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −14.4107 | −0.511093 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.31371 | 0.329908 | 0.164954 | − | 0.986301i | \(-0.447252\pi\) | ||||
0.164954 | + | 0.986301i | \(0.447252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −16.7930 | −0.594094 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.627417 | 0.0221687 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.6173 | −0.445254 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −12.9706 | −0.457152 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.70099 | −0.165483 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −18.4853 | −0.649908 | −0.324954 | − | 0.945730i | \(-0.605349\pi\) | ||||
−0.324954 | + | 0.945730i | \(0.605349\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 26.9510 | 0.946378 | 0.473189 | − | 0.880961i | \(-0.343103\pi\) | ||||
0.473189 | + | 0.880961i | \(0.343103\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −17.8579 | −0.626303 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.0866 | 0.388345 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −24.4853 | −0.856632 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.79884 | −0.0977992 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.2843 | 0.638125 | 0.319063 | − | 0.947734i | \(-0.396632\pi\) | ||||
0.319063 | + | 0.947734i | \(0.396632\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −49.0153 | −1.70857 | −0.854284 | − | 0.519807i | \(-0.826004\pi\) | ||||
−0.854284 | + | 0.519807i | \(0.826004\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.82843 | −0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −31.0949 | −1.08127 | −0.540637 | − | 0.841256i | \(-0.681817\pi\) | ||||
−0.540637 | + | 0.841256i | \(0.681817\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.1127 | 1.56683 | 0.783414 | − | 0.621500i | \(-0.213476\pi\) | ||||
0.783414 | + | 0.621500i | \(0.213476\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.2040 | 0.562111 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −17.0294 | −0.590035 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.9719 | 0.864190 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.6569 | 1.02509 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −28.7444 | −0.992366 | −0.496183 | − | 0.868218i | \(-0.665266\pi\) | ||||
−0.496183 | + | 0.868218i | \(0.665266\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −18.9411 | −0.653142 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −13.6678 | −0.470745 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.38557 | −0.219411 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.51472 | 0.120625 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54.9526 | −1.88375 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −33.1127 | −1.13376 | −0.566879 | − | 0.823801i | \(-0.691849\pi\) | ||||
−0.566879 | + | 0.823801i | \(0.691849\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.77791 | −0.163401 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −24.3431 | −0.831546 | −0.415773 | − | 0.909468i | \(-0.636489\pi\) | ||||
−0.415773 | + | 0.909468i | \(0.636489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.4721 | 0.596141 | 0.298071 | − | 0.954544i | \(-0.403657\pi\) | ||||
0.298071 | + | 0.954544i | \(0.403657\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.31371 | 0.112931 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.4357 | −0.763722 | −0.381861 | − | 0.924220i | \(-0.624717\pi\) | ||||
−0.381861 | + | 0.924220i | \(0.624717\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 18.9706 | 0.645018 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.92629 | 0.133344 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 24.9706 | 0.847068 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.81845 | 0.332686 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −31.6569 | −1.07142 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.53073 | 0.0517482 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.0000 | −0.607817 | −0.303908 | − | 0.952701i | \(-0.598292\pi\) | ||||
−0.303908 | + | 0.952701i | \(0.598292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.69005 | 0.0907331 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.8284 | −1.77983 | −0.889917 | − | 0.456122i | \(-0.849238\pi\) | ||||
−0.889917 | + | 0.456122i | \(0.849238\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 25.5741 | 0.860638 | 0.430319 | − | 0.902677i | \(-0.358401\pi\) | ||||
0.430319 | + | 0.902677i | \(0.358401\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.51472 | 0.252605 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.4901 | −1.62814 | −0.814069 | − | 0.580769i | \(-0.802752\pi\) | ||||
−0.814069 | + | 0.580769i | \(0.802752\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.3431 | −0.481054 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.448342 | −0.0150200 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0000 | −0.401565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 20.9050 | 0.698777 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 9.17157 | 0.306230 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.9974 | 0.600246 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 48.6863 | 1.62198 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.5249 | 0.516637 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.14214 | −0.270654 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −5.93723 | −0.197142 | −0.0985712 | − | 0.995130i | \(-0.531427\pi\) | ||||
−0.0985712 | + | 0.995130i | \(0.531427\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −18.2843 | −0.606451 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −26.5027 | −0.878073 | −0.439036 | − | 0.898469i | \(-0.644680\pi\) | ||||
−0.439036 | + | 0.898469i | \(0.644680\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.43289 | −0.113488 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.94113 | 0.0641016 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.5838 | −1.20679 | −0.603393 | − | 0.797444i | \(-0.706185\pi\) | ||||
−0.603393 | + | 0.797444i | \(0.706185\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17.6569 | 0.581813 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.71644 | −0.0564974 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.48528 | 0.213235 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 21.0907 | 0.692710 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26.9706 | −0.884875 | −0.442438 | − | 0.896799i | \(-0.645886\pi\) | ||||
−0.442438 | + | 0.896799i | \(0.645886\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −12.1689 | −0.398821 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −13.6569 | −0.447105 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.55582 | 0.312509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −43.2548 | −1.41307 | −0.706537 | − | 0.707676i | \(-0.749744\pi\) | ||||
−0.706537 | + | 0.707676i | \(0.749744\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −0.371418 | −0.0121208 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.00000 | 0.0651981 | 0.0325991 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325991 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.9469 | 0.551866 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.00000 | 0.260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.7151 | 0.348195 | 0.174098 | − | 0.984728i | \(-0.444299\pi\) | ||||
0.174098 | + | 0.984728i | \(0.444299\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.82843 | −0.156737 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.8017 | −0.706968 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −59.6569 | −1.93248 | −0.966238 | − | 0.257653i | \(-0.917051\pi\) | ||||
−0.966238 | + | 0.257653i | \(0.917051\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.5140 | −0.437302 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.97056 | −0.289977 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −3.06147 | −0.0988599 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.20101 | 0.0387423 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.6465 | 0.987571 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.3137 | 0.557348 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.7849 | 1.08645 | 0.543225 | − | 0.839587i | \(-0.317203\pi\) | ||||
0.543225 | + | 0.839587i | \(0.317203\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −10.3431 | −0.332270 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −25.7598 | −0.826673 | −0.413336 | − | 0.910578i | \(-0.635637\pi\) | ||||
−0.413336 | + | 0.910578i | \(0.635637\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −30.6274 | −0.981870 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.08239 | −0.0346643 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.1421 | −0.772375 | −0.386188 | − | 0.922420i | \(-0.626208\pi\) | ||||
−0.386188 | + | 0.922420i | \(0.626208\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.896683 | −0.0286581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −25.5980 | −0.817281 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.15932 | 0.0369764 | 0.0184882 | − | 0.999829i | \(-0.494115\pi\) | ||||
0.0184882 | + | 0.999829i | \(0.494115\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.3137 | −0.424210 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.60861 | 0.242185 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 79.3970 | 2.52468 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −43.8210 | −1.39202 | −0.696009 | − | 0.718033i | \(-0.745043\pi\) | ||||
−0.696009 | + | 0.718033i | \(0.745043\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.7990 | −1.13605 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0000 | −0.696747 | −0.348373 | − | 0.937356i | \(-0.613266\pi\) | ||||
−0.348373 | + | 0.937356i | \(0.613266\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33.8937 | 1.07235 |
(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 | 4160.2.a.bu.1.2 | 4 | ||
4.3 | odd | 2 | inner | 4160.2.a.bu.1.3 | 4 | ||
8.3 | odd | 2 | 2080.2.a.q.1.2 | ✓ | 4 | ||
8.5 | even | 2 | 2080.2.a.q.1.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2080.2.a.q.1.2 | ✓ | 4 | 8.3 | odd | 2 | ||
2080.2.a.q.1.3 | yes | 4 | 8.5 | even | 2 | ||
4160.2.a.bu.1.2 | 4 | 1.1 | even | 1 | trivial | ||
4160.2.a.bu.1.3 | 4 | 4.3 | odd | 2 | inner |