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 | 1.1 | ||
Root | \(-1.84776\) 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 | ||||||||
\(3\) | −2.61313 | −1.50869 | −0.754344 | − | 0.656479i | \(-0.772045\pi\) | ||||
−0.754344 | + | 0.656479i | \(0.772045\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.69552 | −1.39677 | −0.698387 | − | 0.715720i | \(-0.746099\pi\) | ||||
−0.698387 | + | 0.715720i | \(0.746099\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.82843 | 1.27614 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.08239 | −0.326354 | −0.163177 | − | 0.986597i | \(-0.552174\pi\) | ||||
−0.163177 | + | 0.986597i | \(0.552174\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.61313 | −0.674706 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −7.65685 | −1.85706 | −0.928530 | − | 0.371257i | \(-0.878927\pi\) | ||||
−0.928530 | + | 0.371257i | \(0.878927\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.08239 | −0.248318 | −0.124159 | − | 0.992262i | \(-0.539623\pi\) | ||||
−0.124159 | + | 0.992262i | \(0.539623\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.65685 | 2.10730 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.67459 | −1.18323 | −0.591617 | − | 0.806219i | \(-0.701510\pi\) | ||||
−0.591617 | + | 0.806219i | \(0.701510\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.16478 | −0.416613 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.82843 | 1.63940 | 0.819699 | − | 0.572795i | \(-0.194141\pi\) | ||||
0.819699 | + | 0.572795i | \(0.194141\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.47343 | −1.52187 | −0.760936 | − | 0.648827i | \(-0.775260\pi\) | ||||
−0.760936 | + | 0.648827i | \(0.775260\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.82843 | 0.492366 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.69552 | −0.624657 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −10.4853 | −1.72377 | −0.861885 | − | 0.507104i | \(-0.830716\pi\) | ||||
−0.861885 | + | 0.507104i | \(0.830716\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.61313 | −0.418435 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | −0.312348 | −0.156174 | − | 0.987730i | \(-0.549916\pi\) | ||||
−0.156174 | + | 0.987730i | \(0.549916\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.94269 | 1.05875 | 0.529376 | − | 0.848388i | \(-0.322426\pi\) | ||||
0.529376 | + | 0.848388i | \(0.322426\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.82843 | 0.570708 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 11.0866 | 1.61714 | 0.808570 | − | 0.588400i | \(-0.200242\pi\) | ||||
0.808570 | + | 0.588400i | \(0.200242\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65685 | 0.950979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 20.0083 | 2.80173 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.31371 | −1.27934 | −0.639668 | − | 0.768651i | \(-0.720928\pi\) | ||||
−0.639668 | + | 0.768651i | \(0.720928\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.08239 | −0.145950 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.82843 | 0.374634 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.37011 | −1.21988 | −0.609942 | − | 0.792446i | \(-0.708807\pi\) | ||||
−0.609942 | + | 0.792446i | \(0.708807\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.82843 | 1.13036 | 0.565182 | − | 0.824966i | \(-0.308806\pi\) | ||||
0.565182 | + | 0.824966i | \(0.308806\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −14.1480 | −1.78248 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.2513 | −1.61891 | −0.809454 | − | 0.587183i | \(-0.800237\pi\) | ||||
−0.809454 | + | 0.587183i | \(0.800237\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 14.8284 | 1.78513 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.5349 | −1.36894 | −0.684470 | − | 0.729041i | \(-0.739966\pi\) | ||||
−0.684470 | + | 0.729041i | \(0.739966\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.828427 | 0.0969601 | 0.0484800 | − | 0.998824i | \(-0.484562\pi\) | ||||
0.0484800 | + | 0.998824i | \(0.484562\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.61313 | −0.301738 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000 | 0.455842 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.28772 | 0.932441 | 0.466221 | − | 0.884668i | \(-0.345615\pi\) | ||||
0.466221 | + | 0.884668i | \(0.345615\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −5.82843 | −0.647603 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.69552 | −0.405636 | −0.202818 | − | 0.979216i | \(-0.565010\pi\) | ||||
−0.202818 | + | 0.979216i | \(0.565010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.65685 | −0.830502 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −23.0698 | −2.47334 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −11.6569 | −1.23562 | −0.617812 | − | 0.786326i | \(-0.711981\pi\) | ||||
−0.617812 | + | 0.786326i | \(0.711981\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.69552 | −0.387396 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.1421 | 2.29603 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.08239 | −0.111051 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.31371 | −0.539525 | −0.269763 | − | 0.962927i | \(-0.586945\pi\) | ||||
−0.269763 | + | 0.962927i | \(0.586945\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −4.14386 | −0.416474 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.0000 | 0.995037 | 0.497519 | − | 0.867453i | \(-0.334245\pi\) | ||||
0.497519 | + | 0.867453i | \(0.334245\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.71644 | 0.169126 | 0.0845631 | − | 0.996418i | \(-0.473051\pi\) | ||||
0.0845631 | + | 0.996418i | \(0.473051\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.65685 | 0.942412 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.88123 | 0.375212 | 0.187606 | − | 0.982244i | \(-0.439927\pi\) | ||||
0.187606 | + | 0.982244i | \(0.439927\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 27.3994 | 2.60063 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.00000 | −0.188144 | −0.0940721 | − | 0.995565i | \(-0.529988\pi\) | ||||
−0.0940721 | + | 0.995565i | \(0.529988\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.67459 | −0.529159 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.82843 | 0.353938 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 28.2960 | 2.59389 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.82843 | −0.893493 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.22625 | 0.471235 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.94269 | 0.616065 | 0.308032 | − | 0.951376i | \(-0.400330\pi\) | ||||
0.308032 | + | 0.951376i | \(0.400330\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −18.1421 | −1.59733 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.8435 | 1.55900 | 0.779499 | − | 0.626404i | \(-0.215474\pi\) | ||||
0.779499 | + | 0.626404i | \(0.215474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | 0.346844 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.16478 | −0.186315 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.95815 | −0.335726 | −0.167863 | − | 0.985810i | \(-0.553687\pi\) | ||||
−0.167863 | + | 0.985810i | \(0.553687\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −28.9706 | −2.43976 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.08239 | −0.0905142 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.82843 | 0.733161 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −17.3952 | −1.43473 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.343146 | 0.0281116 | 0.0140558 | − | 0.999901i | \(-0.495526\pi\) | ||||
0.0140558 | + | 0.999901i | \(0.495526\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.24718 | −0.264251 | −0.132126 | − | 0.991233i | \(-0.542180\pi\) | ||||
−0.132126 | + | 0.991233i | \(0.542180\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −29.3137 | −2.36987 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.47343 | −0.680602 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 24.3379 | 1.93012 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 20.9706 | 1.65271 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.59220 | 0.359689 | 0.179844 | − | 0.983695i | \(-0.442441\pi\) | ||||
0.179844 | + | 0.983695i | \(0.442441\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.82843 | 0.220193 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 23.3324 | 1.80552 | 0.902759 | − | 0.430148i | \(-0.141538\pi\) | ||||
0.902759 | + | 0.430148i | \(0.141538\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.14386 | −0.316889 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −14.9706 | −1.13819 | −0.569095 | − | 0.822272i | \(-0.692706\pi\) | ||||
−0.569095 | + | 0.822272i | \(0.692706\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.69552 | −0.279355 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 24.4853 | 1.84043 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.65914 | −0.647214 | −0.323607 | − | 0.946192i | \(-0.604896\pi\) | ||||
−0.323607 | + | 0.946192i | \(0.604896\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1421 | 1.49715 | 0.748577 | − | 0.663048i | \(-0.230738\pi\) | ||||
0.748577 | + | 0.663048i | \(0.230738\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.0698 | −1.70537 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.4853 | −0.770893 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.28772 | 0.606058 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 8.00000 | 0.581914 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.7206 | 0.848073 | 0.424037 | − | 0.905645i | \(-0.360613\pi\) | ||||
0.424037 | + | 0.905645i | \(0.360613\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.31371 | −0.382489 | −0.191245 | − | 0.981542i | \(-0.561252\pi\) | ||||
−0.191245 | + | 0.981542i | \(0.561252\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.61313 | −0.187130 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 9.31371 | 0.663574 | 0.331787 | − | 0.943354i | \(-0.392348\pi\) | ||||
0.331787 | + | 0.943354i | \(0.392348\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34.6274 | 2.44243 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −32.6256 | −2.28987 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −21.7248 | −1.50998 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.17157 | 0.0810394 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7206 | −0.806880 | −0.403440 | − | 0.915006i | \(-0.632186\pi\) | ||||
−0.403440 | + | 0.915006i | \(0.632186\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 30.1421 | 2.06531 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.94269 | 0.473488 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 31.3137 | 2.12571 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.16478 | −0.146283 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.65685 | −0.515056 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.48888 | 0.367563 | 0.183781 | − | 0.982967i | \(-0.441166\pi\) | ||||
0.183781 | + | 0.982967i | \(0.441166\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.82843 | 0.255228 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 20.6424 | 1.37008 | 0.685041 | − | 0.728504i | \(-0.259784\pi\) | ||||
0.685041 | + | 0.728504i | \(0.259784\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −20.6274 | −1.36310 | −0.681549 | − | 0.731772i | \(-0.738693\pi\) | ||||
−0.681549 | + | 0.731772i | \(0.738693\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.4525 | −0.687724 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.31371 | 0.348113 | 0.174056 | − | 0.984736i | \(-0.444313\pi\) | ||||
0.174056 | + | 0.984736i | \(0.444313\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 11.0866 | 0.723207 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −21.6569 | −1.40676 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.6578 | 1.14219 | 0.571095 | − | 0.820884i | \(-0.306519\pi\) | ||||
0.571095 | + | 0.820884i | \(0.306519\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.00000 | 0.386494 | 0.193247 | − | 0.981150i | \(-0.438098\pi\) | ||||
0.193247 | + | 0.981150i | \(0.438098\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 21.7248 | 1.39364 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.65685 | 0.425291 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.08239 | −0.0688710 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.65685 | 0.611978 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.22625 | 0.329878 | 0.164939 | − | 0.986304i | \(-0.447257\pi\) | ||||
0.164939 | + | 0.986304i | \(0.447257\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.14214 | 0.386153 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.0083 | 1.25297 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.65685 | 0.477621 | 0.238811 | − | 0.971066i | \(-0.423242\pi\) | ||||
0.238811 | + | 0.971066i | \(0.423242\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.7485 | 2.40772 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 33.7990 | 2.09210 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.448342 | −0.0276459 | −0.0138230 | − | 0.999904i | \(-0.504400\pi\) | ||||
−0.0138230 | + | 0.999904i | \(0.504400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.31371 | −0.572137 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 30.4608 | 1.86417 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 15.6569 | 0.954615 | 0.477308 | − | 0.878736i | \(-0.341613\pi\) | ||||
0.477308 | + | 0.878736i | \(0.341613\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 17.6578 | 1.07264 | 0.536318 | − | 0.844016i | \(-0.319815\pi\) | ||||
0.536318 | + | 0.844016i | \(0.319815\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 9.65685 | 0.584459 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.08239 | −0.0652707 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.9706 | 1.13983 | 0.569915 | − | 0.821703i | \(-0.306976\pi\) | ||||
0.569915 | + | 0.821703i | \(0.306976\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −32.4399 | −1.94213 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.6274 | −1.94639 | −0.973194 | − | 0.229985i | \(-0.926132\pi\) | ||||
−0.973194 | + | 0.229985i | \(0.926132\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −7.83938 | −0.466003 | −0.233001 | − | 0.972476i | \(-0.574855\pi\) | ||||
−0.233001 | + | 0.972476i | \(0.574855\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2.82843 | 0.167542 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.39104 | 0.436279 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 41.6274 | 2.44867 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 13.8854 | 0.813976 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.4853 | 0.846239 | 0.423120 | − | 0.906074i | \(-0.360935\pi\) | ||||
0.423120 | + | 0.906074i | \(0.360935\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.37011 | −0.545549 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 2.34315 | 0.135963 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.67459 | −0.328170 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.6569 | −1.47884 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.1313 | −1.50120 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.82843 | 0.505514 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.42742 | −0.138540 | −0.0692700 | − | 0.997598i | \(-0.522067\pi\) | ||||
−0.0692700 | + | 0.997598i | \(0.522067\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.48528 | −0.255159 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.896683 | 0.0508462 | 0.0254231 | − | 0.999677i | \(-0.491907\pi\) | ||||
0.0254231 | + | 0.999677i | \(0.491907\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 11.6569 | 0.658884 | 0.329442 | − | 0.944176i | \(-0.393139\pi\) | ||||
0.329442 | + | 0.944176i | \(0.393139\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −14.1480 | −0.797151 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −8.14214 | −0.457308 | −0.228654 | − | 0.973508i | \(-0.573432\pi\) | ||||
−0.228654 | + | 0.973508i | \(0.573432\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.55582 | −0.535023 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.1421 | −0.566079 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.28772 | 0.461141 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −36.5838 | −2.02309 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −40.9706 | −2.25878 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.45381 | −0.0799087 | −0.0399543 | − | 0.999202i | \(-0.512721\pi\) | ||||
−0.0399543 | + | 0.999202i | \(0.512721\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −40.1421 | −2.19978 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.2513 | −0.723998 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.0000 | 1.19842 | 0.599208 | − | 0.800593i | \(-0.295482\pi\) | ||||
0.599208 | + | 0.800593i | \(0.295482\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.22625 | 0.283851 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9.17157 | 0.496669 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.26810 | 0.0684710 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 14.8284 | 0.798336 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.0769232 | 0.00412946 | 0.00206473 | − | 0.999998i | \(-0.499343\pi\) | ||||
0.00206473 | + | 0.999998i | \(0.499343\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.9706 | 1.87193 | 0.935966 | − | 0.352091i | \(-0.114529\pi\) | ||||
0.935966 | + | 0.352091i | \(0.114529\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.16478 | −0.115548 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.48528 | 0.345177 | 0.172588 | − | 0.984994i | \(-0.444787\pi\) | ||||
0.172588 | + | 0.984994i | \(0.444787\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −11.5349 | −0.612209 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −73.9411 | −3.91338 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.97908 | 0.104452 | 0.0522258 | − | 0.998635i | \(-0.483368\pi\) | ||||
0.0522258 | + | 0.998635i | \(0.483368\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.8284 | −0.938338 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 25.6829 | 1.34800 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.828427 | 0.0433619 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 21.3533 | 1.11464 | 0.557318 | − | 0.830299i | \(-0.311830\pi\) | ||||
0.557318 | + | 0.830299i | \(0.311830\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7.65685 | −0.398600 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.4190 | 1.78694 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −29.3137 | −1.51781 | −0.758903 | − | 0.651204i | \(-0.774264\pi\) | ||||
−0.758903 | + | 0.651204i | \(0.774264\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.61313 | −0.134941 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.82843 | 0.454687 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −35.5014 | −1.82358 | −0.911791 | − | 0.410654i | \(-0.865301\pi\) | ||||
−0.911791 | + | 0.410654i | \(0.865301\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −18.1421 | −0.929450 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −27.6620 | −1.41346 | −0.706731 | − | 0.707482i | \(-0.749831\pi\) | ||||
−0.706731 | + | 0.707482i | \(0.749831\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.00000 | 0.203859 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.5796 | 1.35112 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.3431 | 0.625822 | 0.312911 | − | 0.949782i | \(-0.398696\pi\) | ||||
0.312911 | + | 0.949782i | \(0.398696\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.4495 | 2.19734 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −46.6274 | −2.35204 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.28772 | 0.417000 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.4558 | 1.17722 | 0.588608 | − | 0.808419i | \(-0.299676\pi\) | ||||
0.588608 | + | 0.808419i | \(0.299676\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.4525 | −0.523280 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6.97056 | −0.348093 | −0.174047 | − | 0.984737i | \(-0.555684\pi\) | ||||
−0.174047 | + | 0.984737i | \(0.555684\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −8.47343 | −0.422092 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −5.82843 | −0.289617 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 11.3492 | 0.562558 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 10.6863 | 0.528403 | 0.264202 | − | 0.964467i | \(-0.414892\pi\) | ||||
0.264202 | + | 0.964467i | \(0.414892\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.22625 | 0.257792 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 34.6274 | 1.70390 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.69552 | −0.181406 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.3431 | 0.506506 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.2764 | 1.03942 | 0.519711 | − | 0.854342i | \(-0.326040\pi\) | ||||
0.519711 | + | 0.854342i | \(0.326040\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.62742 | −0.420475 | −0.210237 | − | 0.977650i | \(-0.567424\pi\) | ||||
−0.210237 | + | 0.977650i | \(0.567424\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 42.4441 | 2.06370 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.65685 | −0.371412 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −32.6256 | −1.57886 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.82843 | 0.136558 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.3366 | 1.60577 | 0.802883 | − | 0.596136i | \(-0.203298\pi\) | ||||
0.802883 | + | 0.596136i | \(0.203298\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −23.0698 | −1.10611 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.14214 | 0.293818 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.65914 | −0.413278 | −0.206639 | − | 0.978417i | \(-0.566253\pi\) | ||||
−0.206639 | + | 0.978417i | \(0.566253\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25.4853 | 1.21358 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6.04601 | 0.287255 | 0.143627 | − | 0.989632i | \(-0.454123\pi\) | ||||
0.143627 | + | 0.989632i | \(0.454123\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −11.6569 | −0.552588 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.896683 | −0.0424117 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 22.9706 | 1.08405 | 0.542024 | − | 0.840363i | \(-0.317658\pi\) | ||||
0.542024 | + | 0.840363i | \(0.317658\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.16478 | 0.101936 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.48528 | 0.398673 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.69552 | −0.173249 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.00000 | 0.280668 | 0.140334 | − | 0.990104i | \(-0.455182\pi\) | ||||
0.140334 | + | 0.990104i | \(0.455182\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 16.5754 | 0.773675 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.34315 | −0.388579 | −0.194290 | − | 0.980944i | \(-0.562240\pi\) | ||||
−0.194290 | + | 0.980944i | \(0.562240\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.262632 | −0.0122056 | −0.00610278 | − | 0.999981i | \(-0.501943\pi\) | ||||
−0.00610278 | + | 0.999981i | \(0.501943\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 22.1421 | 1.02682 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15.2304 | 0.704780 | 0.352390 | − | 0.935853i | \(-0.385369\pi\) | ||||
0.352390 | + | 0.935853i | \(0.385369\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 48.9706 | 2.26125 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.22625 | 0.240813 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.51472 | −0.345527 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.08239 | −0.0496636 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −35.6569 | −1.63262 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.3897 | −0.748866 | −0.374433 | − | 0.927254i | \(-0.622163\pi\) | ||||
−0.374433 | + | 0.927254i | \(0.622163\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.4853 | −0.478088 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −54.7987 | −2.49343 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5.31371 | −0.241283 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.7766 | −0.624277 | −0.312139 | − | 0.950037i | \(-0.601045\pi\) | ||||
−0.312139 | + | 0.950037i | \(0.601045\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.0000 | −0.542659 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.55582 | 0.431248 | 0.215624 | − | 0.976476i | \(-0.430821\pi\) | ||||
0.215624 | + | 0.976476i | \(0.430821\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −67.5980 | −3.04446 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.14386 | −0.186253 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 42.6274 | 1.91210 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.37011 | 0.419464 | 0.209732 | − | 0.977759i | \(-0.432741\pi\) | ||||
0.209732 | + | 0.977759i | \(0.432741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −60.9706 | −2.72396 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −41.7331 | −1.86079 | −0.930393 | − | 0.366563i | \(-0.880534\pi\) | ||||
−0.930393 | + | 0.366563i | \(0.880534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.0000 | 0.444994 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.61313 | −0.116053 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.65685 | −0.162087 | −0.0810436 | − | 0.996711i | \(-0.525825\pi\) | ||||
−0.0810436 | + | 0.996711i | \(0.525825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.06147 | −0.135431 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.34315 | 0.103452 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.71644 | 0.0756355 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.0000 | −0.527759 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 39.1200 | 1.71718 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 20.1421 | 0.882443 | 0.441221 | − | 0.897398i | \(-0.354545\pi\) | ||||
0.441221 | + | 0.897398i | \(0.354545\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −40.0936 | −1.75317 | −0.876585 | − | 0.481248i | \(-0.840184\pi\) | ||||
−0.876585 | + | 0.481248i | \(0.840184\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.65685 | 0.421460 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 64.8798 | 2.82621 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.20101 | 0.400044 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −35.8728 | −1.55675 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.00000 | −0.0866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.88123 | 0.167800 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.6274 | 0.976445 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −7.20533 | −0.310355 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.31371 | 0.228454 | 0.114227 | − | 0.993455i | \(-0.463561\pi\) | ||||
0.114227 | + | 0.993455i | \(0.463561\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −52.6339 | −2.25874 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 14.0000 | 0.599694 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 33.4454 | 1.43002 | 0.715010 | − | 0.699114i | \(-0.246422\pi\) | ||||
0.715010 | + | 0.699114i | \(0.246422\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 33.7990 | 1.44251 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −9.55582 | −0.407092 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −30.6274 | −1.30241 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 27.3994 | 1.16304 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.8579 | −0.502434 | −0.251217 | − | 0.967931i | \(-0.580831\pi\) | ||||
−0.251217 | + | 0.967931i | \(0.580831\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.94269 | 0.293645 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21.6569 | −0.914353 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −24.4148 | −1.02896 | −0.514481 | − | 0.857502i | \(-0.672015\pi\) | ||||
−0.514481 | + | 0.857502i | \(0.672015\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.00000 | −0.0841406 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 21.5391 | 0.904555 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.79899 | 0.0754176 | 0.0377088 | − | 0.999289i | \(-0.487994\pi\) | ||||
0.0377088 | + | 0.999289i | \(0.487994\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.8017 | 0.912372 | 0.456186 | − | 0.889884i | \(-0.349215\pi\) | ||||
0.456186 | + | 0.889884i | \(0.349215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −30.6274 | −1.27948 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −5.67459 | −0.236647 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −13.7990 | −0.574459 | −0.287230 | − | 0.957862i | \(-0.592734\pi\) | ||||
−0.287230 | + | 0.957862i | \(0.592734\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 13.8854 | 0.577057 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 13.6569 | 0.566582 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.0811 | 0.417516 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.82843 | 0.158286 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 41.5474 | 1.71484 | 0.857422 | − | 0.514614i | \(-0.172065\pi\) | ||||
0.857422 | + | 0.514614i | \(0.172065\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.17157 | 0.377908 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.3379 | −1.00113 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −45.3137 | −1.86081 | −0.930405 | − | 0.366532i | \(-0.880545\pi\) | ||||
−0.930405 | + | 0.366532i | \(0.880545\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.2960 | 1.16002 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.9469 | −0.692430 | −0.346215 | − | 0.938155i | \(-0.612533\pi\) | ||||
−0.346215 | + | 0.938155i | \(0.612533\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.9706 | 0.447499 | 0.223749 | − | 0.974647i | \(-0.428170\pi\) | ||||
0.223749 | + | 0.974647i | \(0.428170\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −50.7318 | −2.06596 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.82843 | −0.399582 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.50981 | 0.142459 | 0.0712294 | − | 0.997460i | \(-0.477308\pi\) | ||||
0.0712294 | + | 0.997460i | \(0.477308\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 85.2548 | 3.45470 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.0866 | 0.448514 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −37.3137 | −1.50709 | −0.753543 | − | 0.657398i | \(-0.771657\pi\) | ||||
−0.753543 | + | 0.657398i | \(0.771657\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.22625 | 0.210743 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −35.9411 | −1.44694 | −0.723468 | − | 0.690358i | \(-0.757453\pi\) | ||||
−0.723468 | + | 0.690358i | \(0.757453\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 13.3283 | 0.535708 | 0.267854 | − | 0.963460i | \(-0.413686\pi\) | ||||
0.267854 | + | 0.963460i | \(0.413686\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 12.2843 | 0.492951 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 43.0781 | 1.72589 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.06147 | −0.122263 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 80.2843 | 3.20114 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.2974 | −0.768215 | −0.384108 | − | 0.923288i | \(-0.625491\pi\) | ||||
−0.384108 | + | 0.923288i | \(0.625491\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 30.6274 | 1.21733 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.94269 | 0.275512 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.65685 | 0.263754 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −44.1605 | −1.74696 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −43.6569 | −1.72434 | −0.862171 | − | 0.506617i | \(-0.830896\pi\) | ||||
−0.862171 | + | 0.506617i | \(0.830896\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.02509 | −0.316479 | −0.158239 | − | 0.987401i | \(-0.550582\pi\) | ||||
−0.158239 | + | 0.987401i | \(0.550582\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18.1421 | −0.714346 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.1969 | −1.54099 | −0.770494 | − | 0.637447i | \(-0.779991\pi\) | ||||
−0.770494 | + | 0.637447i | \(0.779991\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.1421 | 0.398114 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −81.8267 | −3.20704 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 18.2843 | 0.715519 | 0.357759 | − | 0.933814i | \(-0.383541\pi\) | ||||
0.357759 | + | 0.933814i | \(0.383541\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 17.8435 | 0.697205 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.17157 | 0.123735 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.2764 | −0.828812 | −0.414406 | − | 0.910092i | \(-0.636011\pi\) | ||||
−0.414406 | + | 0.910092i | \(0.636011\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.3137 | −1.14017 | −0.570086 | − | 0.821585i | \(-0.693090\pi\) | ||||
−0.570086 | + | 0.821585i | \(0.693090\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.0083 | 0.777059 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.00000 | 0.155113 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −50.0977 | −1.93979 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −14.3431 | −0.554538 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.55582 | −0.368898 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 6.97056 | 0.268695 | 0.134348 | − | 0.990934i | \(-0.457106\pi\) | ||||
0.134348 | + | 0.990934i | \(0.457106\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.16478 | −0.0833226 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 40.6274 | 1.56144 | 0.780719 | − | 0.624882i | \(-0.214853\pi\) | ||||
0.780719 | + | 0.624882i | \(0.214853\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 19.6369 | 0.753595 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −53.9411 | −2.06703 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.8268 | 1.14129 | 0.570645 | − | 0.821197i | \(-0.306693\pi\) | ||||
0.570645 | + | 0.821197i | \(0.306693\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 53.9020 | 2.05649 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −9.31371 | −0.354824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 24.5236 | 0.932922 | 0.466461 | − | 0.884542i | \(-0.345529\pi\) | ||||
0.466461 | + | 0.884542i | \(0.345529\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 15.3137 | 0.581720 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.95815 | −0.150141 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.3137 | 0.580048 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.8854 | −0.525194 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.6569 | −1.04458 | −0.522292 | − | 0.852766i | \(-0.674923\pi\) | ||||
−0.522292 | + | 0.852766i | \(0.674923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 11.3492 | 0.428043 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −28.9706 | −1.09109 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −36.9552 | −1.38984 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.3137 | −0.650230 | −0.325115 | − | 0.945674i | \(-0.605403\pi\) | ||||
−0.325115 | + | 0.945674i | \(0.605403\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.7289 | 1.18993 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 48.0833 | 1.80073 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.08239 | −0.0404792 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −46.1421 | −1.72321 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −47.9329 | −1.78760 | −0.893799 | − | 0.448468i | \(-0.851970\pi\) | ||||
−0.893799 | + | 0.448468i | \(0.851970\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.34315 | −0.236231 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15.6788 | −0.583099 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 8.82843 | 0.327880 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.5683 | 1.46751 | 0.733754 | − | 0.679416i | \(-0.237767\pi\) | ||||
0.733754 | + | 0.679416i | \(0.237767\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −39.2843 | −1.45497 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −53.1592 | −1.96616 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.68629 | 0.0992204 | 0.0496102 | − | 0.998769i | \(-0.484202\pi\) | ||||
0.0496102 | + | 0.998769i | \(0.484202\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −17.3952 | −0.641632 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.3431 | 0.528337 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 50.2834 | 1.84971 | 0.924853 | − | 0.380324i | \(-0.124188\pi\) | ||||
0.924853 | + | 0.380324i | \(0.124188\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.82843 | 0.103905 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.2710 | 0.743669 | 0.371835 | − | 0.928299i | \(-0.378729\pi\) | ||||
0.371835 | + | 0.928299i | \(0.378729\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0.343146 | 0.0125719 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −14.1480 | −0.517649 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −14.3431 | −0.524087 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.0083 | −0.730114 | −0.365057 | − | 0.930985i | \(-0.618951\pi\) | ||||
−0.365057 | + | 0.930985i | \(0.618951\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13.6569 | −0.497683 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.24718 | −0.118177 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.6569 | −0.423676 | −0.211838 | − | 0.977305i | \(-0.567945\pi\) | ||||
−0.211838 | + | 0.977305i | \(0.567945\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −16.0502 | −0.582584 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6.00000 | −0.217500 | −0.108750 | − | 0.994069i | \(-0.534685\pi\) | ||||
−0.108750 | + | 0.994069i | \(0.534685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −51.7373 | −1.87301 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −29.3137 | −1.05984 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.37011 | −0.338335 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −25.3137 | −0.912836 | −0.456418 | − | 0.889766i | \(-0.650868\pi\) | ||||
−0.456418 | + | 0.889766i | \(0.650868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.0083 | −0.720582 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.82843 | 0.317536 | 0.158768 | − | 0.987316i | \(-0.449248\pi\) | ||||
0.158768 | + | 0.987316i | \(0.449248\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.47343 | −0.304375 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −101.255 | −3.63250 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.16478 | 0.0775615 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.4853 | 0.446758 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.1116 | −0.682994 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.4776 | 0.658655 | 0.329327 | − | 0.944216i | \(-0.393178\pi\) | ||||
0.329327 | + | 0.944216i | \(0.393178\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.17157 | 0.0417091 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.39104 | 0.262795 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.82843 | 0.313507 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.3379 | 0.863176 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −13.3137 | −0.471596 | −0.235798 | − | 0.971802i | \(-0.575770\pi\) | ||||
−0.235798 | + | 0.971802i | \(0.575770\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −84.8881 | −3.00313 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −44.6274 | −1.57683 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −0.896683 | −0.0316433 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 20.9706 | 0.739115 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −40.9133 | −1.44022 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.51472 | −0.0532547 | −0.0266273 | − | 0.999645i | \(-0.508477\pi\) | ||||
−0.0266273 | + | 0.999645i | \(0.508477\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.3283 | 0.468019 | 0.234009 | − | 0.972234i | \(-0.424815\pi\) | ||||
0.234009 | + | 0.972234i | \(0.424815\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −46.1421 | −1.61828 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4.59220 | 0.160858 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −7.51472 | −0.262907 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −14.1480 | −0.494372 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.2843 | −1.33613 | −0.668065 | − | 0.744103i | \(-0.732877\pi\) | ||||
−0.668065 | + | 0.744103i | \(0.732877\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.4872 | 1.02786 | 0.513930 | − | 0.857832i | \(-0.328189\pi\) | ||||
0.513930 | + | 0.857832i | \(0.328189\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.82843 | 0.0984732 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.55035 | −0.297325 | −0.148662 | − | 0.988888i | \(-0.547497\pi\) | ||||
−0.148662 | + | 0.988888i | \(0.547497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −17.1127 | −0.594349 | −0.297174 | − | 0.954823i | \(-0.596044\pi\) | ||||
−0.297174 | + | 0.954823i | \(0.596044\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −49.5725 | −1.71965 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −50.9706 | −1.76603 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 23.3324 | 0.807452 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 18.3431 | 0.634032 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.9063 | 0.411052 | 0.205526 | − | 0.978652i | \(-0.434110\pi\) | ||||
0.205526 | + | 0.978652i | \(0.434110\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 48.9411 | 1.68763 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 85.2595 | 2.93649 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.3211 | 1.24801 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 20.4853 | 0.703053 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 59.4997 | 2.03962 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 29.1127 | 0.996800 | 0.498400 | − | 0.866947i | \(-0.333921\pi\) | ||||
0.498400 | + | 0.866947i | \(0.333921\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −4.14386 | −0.141717 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −35.6569 | −1.21801 | −0.609007 | − | 0.793164i | \(-0.708432\pi\) | ||||
−0.609007 | + | 0.793164i | \(0.708432\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −31.7289 | −1.08258 | −0.541289 | − | 0.840837i | \(-0.682063\pi\) | ||||
−0.541289 | + | 0.840837i | \(0.682063\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.3137 | −0.658209 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.3547 | 0.420557 | 0.210279 | − | 0.977641i | \(-0.432563\pi\) | ||||
0.210279 | + | 0.977641i | \(0.432563\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −14.9706 | −0.509014 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −108.778 | −3.69428 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.97056 | −0.304305 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.2513 | −0.449004 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −20.3431 | −0.688511 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.69552 | −0.124931 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.0000 | −0.607817 | −0.303908 | − | 0.952701i | \(-0.598292\pi\) | ||||
−0.303908 | + | 0.952701i | \(0.598292\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −37.8519 | −1.27671 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −47.1716 | −1.58925 | −0.794625 | − | 0.607100i | \(-0.792333\pi\) | ||||
−0.794625 | + | 0.607100i | \(0.792333\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −56.5152 | −1.90189 | −0.950943 | − | 0.309365i | \(-0.899883\pi\) | ||||
−0.950943 | + | 0.309365i | \(0.899883\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 24.4853 | 0.823064 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −13.5909 | −0.456338 | −0.228169 | − | 0.973622i | \(-0.573274\pi\) | ||||
−0.228169 | + | 0.973622i | \(0.573274\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −25.6569 | −0.860503 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.30864 | 0.211348 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.0000 | −0.401565 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.65914 | −0.289443 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.8284 | 0.495107 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −74.8070 | −2.49495 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 71.3137 | 2.37580 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 67.0446 | 2.23110 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.1421 | 0.669547 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.0125 | 0.996548 | 0.498274 | − | 0.867020i | \(-0.333967\pi\) | ||||
0.498274 | + | 0.867020i | \(0.333967\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 38.2843 | 1.26981 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −19.6369 | −0.650600 | −0.325300 | − | 0.945611i | \(-0.605465\pi\) | ||||
−0.325300 | + | 0.945611i | \(0.605465\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.00000 | 0.132381 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −23.0698 | −0.762664 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −65.9411 | −2.17757 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.1535 | 0.499868 | 0.249934 | − | 0.968263i | \(-0.419591\pi\) | ||||
0.249934 | + | 0.968263i | \(0.419591\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.34315 | 0.209014 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.5349 | −0.379676 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.4853 | −0.344754 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.57128 | 0.215829 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.97056 | 0.228697 | 0.114348 | − | 0.993441i | \(-0.463522\pi\) | ||||
0.114348 | + | 0.993441i | \(0.463522\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −7.20533 | −0.236145 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.34315 | −0.0767111 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.28772 | 0.271037 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 47.2548 | 1.54375 | 0.771874 | − | 0.635775i | \(-0.219320\pi\) | ||||
0.771874 | + | 0.635775i | \(0.219320\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30.4608 | −0.994052 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.00000 | 0.0651981 | 0.0325991 | − | 0.999469i | \(-0.489622\pi\) | ||||
0.0325991 | + | 0.999469i | \(0.489622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.3492 | 0.369580 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.00000 | 0.260240 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.8686 | −0.840617 | −0.420309 | − | 0.907381i | \(-0.638078\pi\) | ||||
−0.420309 | + | 0.907381i | \(0.638078\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.828427 | 0.0268919 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 21.2764 | 0.689935 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −48.3431 | −1.56599 | −0.782994 | − | 0.622029i | \(-0.786309\pi\) | ||||
−0.782994 | + | 0.622029i | \(0.786309\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.7206 | 0.379270 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.9706 | 0.807184 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 7.39104 | 0.238669 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40.7990 | 1.31610 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 14.8590 | 0.478824 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.31371 | −0.171054 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.3015 | −0.942273 | −0.471137 | − | 0.882060i | \(-0.656156\pi\) | ||||
−0.471137 | + | 0.882060i | \(0.656156\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −21.6569 | −0.695718 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.2848 | 1.32489 | 0.662445 | − | 0.749110i | \(-0.269519\pi\) | ||||
0.662445 | + | 0.749110i | \(0.269519\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.6274 | 0.468933 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.61313 | −0.0836870 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.14214 | 0.132519 | 0.0662593 | − | 0.997802i | \(-0.478894\pi\) | ||||
0.0662593 | + | 0.997802i | \(0.478894\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 12.6173 | 0.403250 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 53.5980 | 1.71125 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.1563 | −1.08942 | −0.544709 | − | 0.838625i | \(-0.683360\pi\) | ||||
−0.544709 | + | 0.838625i | \(0.683360\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9.31371 | 0.296759 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 107.061 | 3.40780 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −39.3970 | −1.25275 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −61.4469 | −1.95193 | −0.975963 | − | 0.217937i | \(-0.930067\pi\) | ||||
−0.975963 | + | 0.217937i | \(0.930067\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.79899 | 0.120557 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | 22.6984 | 0.718145 |
(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.1.1 | 4 | ||
4.3 | odd | 2 | inner | 4160.2.a.bu.1.4 | 4 | ||
8.3 | odd | 2 | 2080.2.a.q.1.1 | ✓ | 4 | ||
8.5 | even | 2 | 2080.2.a.q.1.4 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2080.2.a.q.1.1 | ✓ | 4 | 8.3 | odd | 2 | ||
2080.2.a.q.1.4 | yes | 4 | 8.5 | even | 2 | ||
4160.2.a.bu.1.1 | 4 | 1.1 | even | 1 | trivial | ||
4160.2.a.bu.1.4 | 4 | 4.3 | odd | 2 | inner |