Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9450,2,Mod(1,9450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9450.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: | \(75.4586299101\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1890) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9450.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.73205 | −0.522233 | −0.261116 | − | 0.965307i | \(-0.584091\pi\) | ||||
−0.261116 | + | 0.965307i | \(0.584091\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.46410 | −1.51547 | −0.757735 | − | 0.652563i | \(-0.773694\pi\) | ||||
−0.757735 | + | 0.652563i | \(0.773694\pi\) | |||||||
\(14\) | 1.00000 | 0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.73205 | 1.31502 | 0.657511 | − | 0.753445i | \(-0.271609\pi\) | ||||
0.657511 | + | 0.753445i | \(0.271609\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.73205 | −0.369274 | ||||||||
\(23\) | 2.46410 | 0.513801 | 0.256900 | − | 0.966438i | \(-0.417299\pi\) | ||||
0.256900 | + | 0.966438i | \(0.417299\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.46410 | −1.07160 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.46410 | −0.271877 | −0.135938 | − | 0.990717i | \(-0.543405\pi\) | ||||
−0.135938 | + | 0.990717i | \(0.543405\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.267949 | −0.0481251 | −0.0240625 | − | 0.999710i | \(-0.507660\pi\) | ||||
−0.0240625 | + | 0.999710i | \(0.507660\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.19615 | 0.525444 | 0.262722 | − | 0.964872i | \(-0.415380\pi\) | ||||
0.262722 | + | 0.964872i | \(0.415380\pi\) | |||||||
\(38\) | 5.73205 | 0.929861 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.92820 | 0.613482 | 0.306741 | − | 0.951793i | \(-0.400761\pi\) | ||||
0.306741 | + | 0.951793i | \(0.400761\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.53590 | 0.691718 | 0.345859 | − | 0.938286i | \(-0.387588\pi\) | ||||
0.345859 | + | 0.938286i | \(0.387588\pi\) | |||||||
\(44\) | −1.73205 | −0.261116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.46410 | 0.363312 | ||||||||
\(47\) | 11.4641 | 1.67221 | 0.836106 | − | 0.548569i | \(-0.184827\pi\) | ||||
0.836106 | + | 0.548569i | \(0.184827\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.46410 | −0.757735 | ||||||||
\(53\) | −13.8564 | −1.90332 | −0.951662 | − | 0.307148i | \(-0.900625\pi\) | ||||
−0.951662 | + | 0.307148i | \(0.900625\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.46410 | −0.192246 | ||||||||
\(59\) | −4.92820 | −0.641597 | −0.320799 | − | 0.947147i | \(-0.603951\pi\) | ||||
−0.320799 | + | 0.947147i | \(0.603951\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −13.8564 | −1.77413 | −0.887066 | − | 0.461644i | \(-0.847260\pi\) | ||||
−0.887066 | + | 0.461644i | \(0.847260\pi\) | |||||||
\(62\) | −0.267949 | −0.0340296 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3923 | 1.51396 | 0.756980 | − | 0.653437i | \(-0.226674\pi\) | ||||
0.756980 | + | 0.653437i | \(0.226674\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.26795 | −0.506512 | −0.253256 | − | 0.967399i | \(-0.581502\pi\) | ||||
−0.253256 | + | 0.967399i | \(0.581502\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −16.9282 | −1.98130 | −0.990648 | − | 0.136441i | \(-0.956434\pi\) | ||||
−0.990648 | + | 0.136441i | \(0.956434\pi\) | |||||||
\(74\) | 3.19615 | 0.371545 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.73205 | 0.657511 | ||||||||
\(77\) | −1.73205 | −0.197386 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.92820 | 1.00450 | 0.502251 | − | 0.864722i | \(-0.332505\pi\) | ||||
0.502251 | + | 0.864722i | \(0.332505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.92820 | 0.433797 | ||||||||
\(83\) | 9.46410 | 1.03882 | 0.519410 | − | 0.854525i | \(-0.326152\pi\) | ||||
0.519410 | + | 0.854525i | \(0.326152\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.53590 | 0.489119 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.73205 | −0.184637 | ||||||||
\(89\) | −1.00000 | −0.106000 | −0.0529999 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529999 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.46410 | −0.572793 | ||||||||
\(92\) | 2.46410 | 0.256900 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 11.4641 | 1.18243 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.92820 | 0.703452 | 0.351726 | − | 0.936103i | \(-0.385595\pi\) | ||||
0.351726 | + | 0.936103i | \(0.385595\pi\) | |||||||
\(98\) | 1.00000 | 0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.9282 | 1.28640 | 0.643202 | − | 0.765696i | \(-0.277605\pi\) | ||||
0.643202 | + | 0.765696i | \(0.277605\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.4641 | 1.03106 | 0.515529 | − | 0.856872i | \(-0.327595\pi\) | ||||
0.515529 | + | 0.856872i | \(0.327595\pi\) | |||||||
\(104\) | −5.46410 | −0.535799 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −13.8564 | −1.34585 | ||||||||
\(107\) | −4.00000 | −0.386695 | −0.193347 | − | 0.981130i | \(-0.561934\pi\) | ||||
−0.193347 | + | 0.981130i | \(0.561934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.53590 | 0.721808 | 0.360904 | − | 0.932603i | \(-0.382468\pi\) | ||||
0.360904 | + | 0.932603i | \(0.382468\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 4.53590 | 0.426701 | 0.213351 | − | 0.976976i | \(-0.431562\pi\) | ||||
0.213351 | + | 0.976976i | \(0.431562\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.46410 | −0.135938 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.92820 | −0.453678 | ||||||||
\(119\) | 4.00000 | 0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.00000 | −0.727273 | ||||||||
\(122\) | −13.8564 | −1.25450 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.267949 | −0.0240625 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.46410 | −0.484861 | −0.242430 | − | 0.970169i | \(-0.577945\pi\) | ||||
−0.242430 | + | 0.970169i | \(0.577945\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.9282 | 1.82851 | 0.914253 | − | 0.405144i | \(-0.132779\pi\) | ||||
0.914253 | + | 0.405144i | \(0.132779\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 5.73205 | 0.497032 | ||||||||
\(134\) | 12.3923 | 1.07053 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.00000 | 0.342997 | ||||||||
\(137\) | 13.4641 | 1.15032 | 0.575158 | − | 0.818042i | \(-0.304941\pi\) | ||||
0.575158 | + | 0.818042i | \(0.304941\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.535898 | 0.0454543 | 0.0227272 | − | 0.999742i | \(-0.492765\pi\) | ||||
0.0227272 | + | 0.999742i | \(0.492765\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.26795 | −0.358158 | ||||||||
\(143\) | 9.46410 | 0.791428 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −16.9282 | −1.40099 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.19615 | 0.262722 | ||||||||
\(149\) | 12.9282 | 1.05912 | 0.529560 | − | 0.848273i | \(-0.322357\pi\) | ||||
0.529560 | + | 0.848273i | \(0.322357\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.3205 | 1.40952 | 0.704761 | − | 0.709444i | \(-0.251054\pi\) | ||||
0.704761 | + | 0.709444i | \(0.251054\pi\) | |||||||
\(152\) | 5.73205 | 0.464931 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.73205 | −0.139573 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.53590 | −0.202387 | −0.101193 | − | 0.994867i | \(-0.532266\pi\) | ||||
−0.101193 | + | 0.994867i | \(0.532266\pi\) | |||||||
\(158\) | 8.92820 | 0.710290 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.46410 | 0.194198 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.53590 | −0.198627 | −0.0993134 | − | 0.995056i | \(-0.531665\pi\) | ||||
−0.0993134 | + | 0.995056i | \(0.531665\pi\) | |||||||
\(164\) | 3.92820 | 0.306741 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.46410 | 0.734557 | ||||||||
\(167\) | 12.9282 | 1.00041 | 0.500207 | − | 0.865906i | \(-0.333257\pi\) | ||||
0.500207 | + | 0.865906i | \(0.333257\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 16.8564 | 1.29665 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.53590 | 0.345859 | ||||||||
\(173\) | 18.1244 | 1.37797 | 0.688985 | − | 0.724776i | \(-0.258057\pi\) | ||||
0.688985 | + | 0.724776i | \(0.258057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.73205 | −0.130558 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.00000 | −0.0749532 | ||||||||
\(179\) | −4.53590 | −0.339029 | −0.169514 | − | 0.985528i | \(-0.554220\pi\) | ||||
−0.169514 | + | 0.985528i | \(0.554220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.85641 | 0.286644 | 0.143322 | − | 0.989676i | \(-0.454221\pi\) | ||||
0.143322 | + | 0.989676i | \(0.454221\pi\) | |||||||
\(182\) | −5.46410 | −0.405026 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.46410 | 0.181656 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.92820 | −0.506640 | ||||||||
\(188\) | 11.4641 | 0.836106 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.80385 | −0.637024 | −0.318512 | − | 0.947919i | \(-0.603183\pi\) | ||||
−0.318512 | + | 0.947919i | \(0.603183\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.8564 | −1.28533 | −0.642666 | − | 0.766146i | \(-0.722172\pi\) | ||||
−0.642666 | + | 0.766146i | \(0.722172\pi\) | |||||||
\(194\) | 6.92820 | 0.497416 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 19.4641 | 1.38676 | 0.693380 | − | 0.720572i | \(-0.256121\pi\) | ||||
0.693380 | + | 0.720572i | \(0.256121\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.0526 | −0.925271 | −0.462636 | − | 0.886548i | \(-0.653096\pi\) | ||||
−0.462636 | + | 0.886548i | \(0.653096\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.9282 | 0.909625 | ||||||||
\(203\) | −1.46410 | −0.102760 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 10.4641 | 0.729069 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.46410 | −0.378867 | ||||||||
\(209\) | −9.92820 | −0.686748 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.3923 | −0.715436 | −0.357718 | − | 0.933830i | \(-0.616445\pi\) | ||||
−0.357718 | + | 0.933830i | \(0.616445\pi\) | |||||||
\(212\) | −13.8564 | −0.951662 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.00000 | −0.273434 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.267949 | −0.0181896 | ||||||||
\(218\) | 7.53590 | 0.510395 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21.8564 | −1.47022 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.3923 | 1.16467 | 0.582337 | − | 0.812947i | \(-0.302138\pi\) | ||||
0.582337 | + | 0.812947i | \(0.302138\pi\) | |||||||
\(224\) | 1.00000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.53590 | 0.301723 | ||||||||
\(227\) | −26.7846 | −1.77776 | −0.888878 | − | 0.458143i | \(-0.848515\pi\) | ||||
−0.888878 | + | 0.458143i | \(0.848515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.9282 | 0.722156 | 0.361078 | − | 0.932536i | \(-0.382409\pi\) | ||||
0.361078 | + | 0.932536i | \(0.382409\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.46410 | −0.0961230 | ||||||||
\(233\) | 12.5359 | 0.821254 | 0.410627 | − | 0.911803i | \(-0.365310\pi\) | ||||
0.410627 | + | 0.911803i | \(0.365310\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.92820 | −0.320799 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.00000 | 0.259281 | ||||||||
\(239\) | 11.4641 | 0.741551 | 0.370776 | − | 0.928723i | \(-0.379092\pi\) | ||||
0.370776 | + | 0.928723i | \(0.379092\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.3923 | −0.669427 | −0.334714 | − | 0.942320i | \(-0.608640\pi\) | ||||
−0.334714 | + | 0.942320i | \(0.608640\pi\) | |||||||
\(242\) | −8.00000 | −0.514259 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −13.8564 | −0.887066 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −31.3205 | −1.99288 | ||||||||
\(248\) | −0.267949 | −0.0170148 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.85641 | −0.369653 | −0.184827 | − | 0.982771i | \(-0.559172\pi\) | ||||
−0.184827 | + | 0.982771i | \(0.559172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.26795 | −0.268324 | ||||||||
\(254\) | −5.46410 | −0.342848 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.5885 | 1.72092 | 0.860460 | − | 0.509517i | \(-0.170176\pi\) | ||||
0.860460 | + | 0.509517i | \(0.170176\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.19615 | 0.198599 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.9282 | 1.29295 | ||||||||
\(263\) | 17.5359 | 1.08131 | 0.540655 | − | 0.841244i | \(-0.318176\pi\) | ||||
0.540655 | + | 0.841244i | \(0.318176\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 5.73205 | 0.351455 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.3923 | 0.756980 | ||||||||
\(269\) | −18.3205 | −1.11702 | −0.558511 | − | 0.829497i | \(-0.688627\pi\) | ||||
−0.558511 | + | 0.829497i | \(0.688627\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3923 | 0.631288 | 0.315644 | − | 0.948878i | \(-0.397780\pi\) | ||||
0.315644 | + | 0.948878i | \(0.397780\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 13.4641 | 0.813396 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.05256 | −0.543916 | −0.271958 | − | 0.962309i | \(-0.587671\pi\) | ||||
−0.271958 | + | 0.962309i | \(0.587671\pi\) | |||||||
\(278\) | 0.535898 | 0.0321410 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.3923 | 0.619953 | 0.309976 | − | 0.950744i | \(-0.399679\pi\) | ||||
0.309976 | + | 0.950744i | \(0.399679\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.07180 | −0.539262 | −0.269631 | − | 0.962964i | \(-0.586902\pi\) | ||||
−0.269631 | + | 0.962964i | \(0.586902\pi\) | |||||||
\(284\) | −4.26795 | −0.253256 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.46410 | 0.559624 | ||||||||
\(287\) | 3.92820 | 0.231875 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.9282 | −0.990648 | ||||||||
\(293\) | 5.07180 | 0.296298 | 0.148149 | − | 0.988965i | \(-0.452669\pi\) | ||||
0.148149 | + | 0.988965i | \(0.452669\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.19615 | 0.185773 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.9282 | 0.748911 | ||||||||
\(299\) | −13.4641 | −0.778649 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.53590 | 0.261445 | ||||||||
\(302\) | 17.3205 | 0.996683 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 5.73205 | 0.328756 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.9282 | 1.36565 | 0.682827 | − | 0.730580i | \(-0.260750\pi\) | ||||
0.682827 | + | 0.730580i | \(0.260750\pi\) | |||||||
\(308\) | −1.73205 | −0.0986928 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.39230 | −0.249065 | −0.124532 | − | 0.992216i | \(-0.539743\pi\) | ||||
−0.124532 | + | 0.992216i | \(0.539743\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 31.3205 | 1.77034 | 0.885170 | − | 0.465268i | \(-0.154042\pi\) | ||||
0.885170 | + | 0.465268i | \(0.154042\pi\) | |||||||
\(314\) | −2.53590 | −0.143109 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.92820 | 0.502251 | ||||||||
\(317\) | 15.0718 | 0.846516 | 0.423258 | − | 0.906009i | \(-0.360886\pi\) | ||||
0.423258 | + | 0.906009i | \(0.360886\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.53590 | 0.141983 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.46410 | 0.137319 | ||||||||
\(323\) | 22.9282 | 1.27576 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.53590 | −0.140450 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.92820 | 0.216899 | ||||||||
\(329\) | 11.4641 | 0.632036 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −12.7846 | −0.702706 | −0.351353 | − | 0.936243i | \(-0.614278\pi\) | ||||
−0.351353 | + | 0.936243i | \(0.614278\pi\) | |||||||
\(332\) | 9.46410 | 0.519410 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.9282 | 0.707400 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −21.7321 | −1.18382 | −0.591910 | − | 0.806004i | \(-0.701626\pi\) | ||||
−0.591910 | + | 0.806004i | \(0.701626\pi\) | |||||||
\(338\) | 16.8564 | 0.916868 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.464102 | 0.0251325 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 4.53590 | 0.244559 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.1244 | 0.974371 | ||||||||
\(347\) | −21.9282 | −1.17717 | −0.588584 | − | 0.808436i | \(-0.700314\pi\) | ||||
−0.588584 | + | 0.808436i | \(0.700314\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.14359 | 0.221801 | 0.110901 | − | 0.993831i | \(-0.464626\pi\) | ||||
0.110901 | + | 0.993831i | \(0.464626\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.73205 | −0.0923186 | ||||||||
\(353\) | 8.66025 | 0.460939 | 0.230469 | − | 0.973080i | \(-0.425974\pi\) | ||||
0.230469 | + | 0.973080i | \(0.425974\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.00000 | −0.0529999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.53590 | −0.239730 | ||||||||
\(359\) | −28.5359 | −1.50607 | −0.753034 | − | 0.657982i | \(-0.771410\pi\) | ||||
−0.753034 | + | 0.657982i | \(0.771410\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.8564 | 0.729285 | ||||||||
\(362\) | 3.85641 | 0.202688 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.46410 | −0.286397 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 23.3923 | 1.22107 | 0.610534 | − | 0.791990i | \(-0.290955\pi\) | ||||
0.610534 | + | 0.791990i | \(0.290955\pi\) | |||||||
\(368\) | 2.46410 | 0.128450 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8564 | −0.719389 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.19615 | 0.372603 | 0.186301 | − | 0.982493i | \(-0.440350\pi\) | ||||
0.186301 | + | 0.982493i | \(0.440350\pi\) | |||||||
\(374\) | −6.92820 | −0.358249 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.4641 | 0.591216 | ||||||||
\(377\) | 8.00000 | 0.412021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0000 | −0.719132 | −0.359566 | − | 0.933120i | \(-0.617075\pi\) | ||||
−0.359566 | + | 0.933120i | \(0.617075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.80385 | −0.450444 | ||||||||
\(383\) | 11.0718 | 0.565742 | 0.282871 | − | 0.959158i | \(-0.408713\pi\) | ||||
0.282871 | + | 0.959158i | \(0.408713\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −17.8564 | −0.908867 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.92820 | 0.351726 | ||||||||
\(389\) | −6.92820 | −0.351274 | −0.175637 | − | 0.984455i | \(-0.556198\pi\) | ||||
−0.175637 | + | 0.984455i | \(0.556198\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.85641 | 0.498460 | ||||||||
\(392\) | 1.00000 | 0.0505076 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 19.4641 | 0.980587 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.60770 | 0.281442 | 0.140721 | − | 0.990049i | \(-0.455058\pi\) | ||||
0.140721 | + | 0.990049i | \(0.455058\pi\) | |||||||
\(398\) | −13.0526 | −0.654266 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.60770 | −0.379910 | −0.189955 | − | 0.981793i | \(-0.560834\pi\) | ||||
−0.189955 | + | 0.981793i | \(0.560834\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.46410 | 0.0729321 | ||||||||
\(404\) | 12.9282 | 0.643202 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.46410 | −0.0726621 | ||||||||
\(407\) | −5.53590 | −0.274404 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −37.3205 | −1.84538 | −0.922690 | − | 0.385542i | \(-0.874014\pi\) | ||||
−0.922690 | + | 0.385542i | \(0.874014\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 10.4641 | 0.515529 | ||||||||
\(413\) | −4.92820 | −0.242501 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −5.46410 | −0.267900 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.92820 | −0.485604 | ||||||||
\(419\) | 23.4641 | 1.14630 | 0.573148 | − | 0.819452i | \(-0.305722\pi\) | ||||
0.573148 | + | 0.819452i | \(0.305722\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.46410 | 0.217567 | 0.108784 | − | 0.994065i | \(-0.465304\pi\) | ||||
0.108784 | + | 0.994065i | \(0.465304\pi\) | |||||||
\(422\) | −10.3923 | −0.505889 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −13.8564 | −0.672927 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8564 | −0.670559 | ||||||||
\(428\) | −4.00000 | −0.193347 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.5167 | 1.18093 | 0.590463 | − | 0.807065i | \(-0.298945\pi\) | ||||
0.590463 | + | 0.807065i | \(0.298945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −38.2487 | −1.83812 | −0.919058 | − | 0.394123i | \(-0.871049\pi\) | ||||
−0.919058 | + | 0.394123i | \(0.871049\pi\) | |||||||
\(434\) | −0.267949 | −0.0128620 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.53590 | 0.360904 | ||||||||
\(437\) | 14.1244 | 0.675660 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.6077 | −0.840369 | −0.420185 | − | 0.907439i | \(-0.638035\pi\) | ||||
−0.420185 | + | 0.907439i | \(0.638035\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −21.8564 | −1.03960 | ||||||||
\(443\) | −10.8564 | −0.515803 | −0.257902 | − | 0.966171i | \(-0.583031\pi\) | ||||
−0.257902 | + | 0.966171i | \(0.583031\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 17.3923 | 0.823550 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −10.0000 | −0.471929 | −0.235965 | − | 0.971762i | \(-0.575825\pi\) | ||||
−0.235965 | + | 0.971762i | \(0.575825\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.80385 | −0.320381 | ||||||||
\(452\) | 4.53590 | 0.213351 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −26.7846 | −1.25706 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.5167 | −0.679061 | −0.339530 | − | 0.940595i | \(-0.610268\pi\) | ||||
−0.339530 | + | 0.940595i | \(0.610268\pi\) | |||||||
\(458\) | 10.9282 | 0.510641 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5.39230 | 0.251145 | 0.125572 | − | 0.992084i | \(-0.459923\pi\) | ||||
0.125572 | + | 0.992084i | \(0.459923\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.143594 | −0.00667336 | −0.00333668 | − | 0.999994i | \(-0.501062\pi\) | ||||
−0.00333668 | + | 0.999994i | \(0.501062\pi\) | |||||||
\(464\) | −1.46410 | −0.0679692 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.5359 | 0.580714 | ||||||||
\(467\) | −20.2487 | −0.936999 | −0.468499 | − | 0.883464i | \(-0.655205\pi\) | ||||
−0.468499 | + | 0.883464i | \(0.655205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.3923 | 0.572223 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.92820 | −0.226839 | ||||||||
\(473\) | −7.85641 | −0.361238 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.00000 | 0.183340 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.4641 | 0.524356 | ||||||||
\(479\) | 20.7846 | 0.949673 | 0.474837 | − | 0.880074i | \(-0.342507\pi\) | ||||
0.474837 | + | 0.880074i | \(0.342507\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.4641 | −0.796294 | ||||||||
\(482\) | −10.3923 | −0.473357 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.00000 | −0.363636 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.3923 | 1.19595 | 0.597975 | − | 0.801515i | \(-0.295972\pi\) | ||||
0.597975 | + | 0.801515i | \(0.295972\pi\) | |||||||
\(488\) | −13.8564 | −0.627250 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −41.4449 | −1.87038 | −0.935190 | − | 0.354146i | \(-0.884772\pi\) | ||||
−0.935190 | + | 0.354146i | \(0.884772\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.85641 | −0.263759 | ||||||||
\(494\) | −31.3205 | −1.40918 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.267949 | −0.0120313 | ||||||||
\(497\) | −4.26795 | −0.191444 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −7.07180 | −0.316577 | −0.158289 | − | 0.987393i | \(-0.550598\pi\) | ||||
−0.158289 | + | 0.987393i | \(0.550598\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −5.85641 | −0.261384 | ||||||||
\(503\) | 8.39230 | 0.374194 | 0.187097 | − | 0.982341i | \(-0.440092\pi\) | ||||
0.187097 | + | 0.982341i | \(0.440092\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.26795 | −0.189733 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −5.46410 | −0.242430 | ||||||||
\(509\) | −13.7128 | −0.607810 | −0.303905 | − | 0.952702i | \(-0.598291\pi\) | ||||
−0.303905 | + | 0.952702i | \(0.598291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.9282 | −0.748860 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 27.5885 | 1.21687 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.8564 | −0.873284 | ||||||||
\(518\) | 3.19615 | 0.140431 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 41.7846 | 1.83062 | 0.915308 | − | 0.402753i | \(-0.131947\pi\) | ||||
0.915308 | + | 0.402753i | \(0.131947\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 18.0718 | 0.790224 | 0.395112 | − | 0.918633i | \(-0.370706\pi\) | ||||
0.395112 | + | 0.918633i | \(0.370706\pi\) | |||||||
\(524\) | 20.9282 | 0.914253 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.5359 | 0.764602 | ||||||||
\(527\) | −1.07180 | −0.0466882 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.9282 | −0.736009 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 5.73205 | 0.248516 | ||||||||
\(533\) | −21.4641 | −0.929713 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 12.3923 | 0.535266 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −18.3205 | −0.789853 | ||||||||
\(539\) | −1.73205 | −0.0746047 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.46410 | −0.191927 | −0.0959634 | − | 0.995385i | \(-0.530593\pi\) | ||||
−0.0959634 | + | 0.995385i | \(0.530593\pi\) | |||||||
\(542\) | 10.3923 | 0.446388 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.00000 | 0.171499 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −20.0000 | −0.855138 | −0.427569 | − | 0.903983i | \(-0.640630\pi\) | ||||
−0.427569 | + | 0.903983i | \(0.640630\pi\) | |||||||
\(548\) | 13.4641 | 0.575158 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −8.39230 | −0.357524 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.92820 | 0.379666 | ||||||||
\(554\) | −9.05256 | −0.384606 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.535898 | 0.0227272 | ||||||||
\(557\) | −5.60770 | −0.237606 | −0.118803 | − | 0.992918i | \(-0.537906\pi\) | ||||
−0.118803 | + | 0.992918i | \(0.537906\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.7846 | −1.04828 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.3923 | 0.438373 | ||||||||
\(563\) | 24.3923 | 1.02801 | 0.514007 | − | 0.857786i | \(-0.328161\pi\) | ||||
0.514007 | + | 0.857786i | \(0.328161\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −9.07180 | −0.381316 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.26795 | −0.179079 | ||||||||
\(569\) | −33.7128 | −1.41331 | −0.706657 | − | 0.707556i | \(-0.749798\pi\) | ||||
−0.706657 | + | 0.707556i | \(0.749798\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −31.4641 | −1.31673 | −0.658366 | − | 0.752698i | \(-0.728752\pi\) | ||||
−0.658366 | + | 0.752698i | \(0.728752\pi\) | |||||||
\(572\) | 9.46410 | 0.395714 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.92820 | 0.163960 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −33.3205 | −1.38715 | −0.693575 | − | 0.720384i | \(-0.743966\pi\) | ||||
−0.693575 | + | 0.720384i | \(0.743966\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 9.46410 | 0.392637 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.0000 | 0.993978 | ||||||||
\(584\) | −16.9282 | −0.700494 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.07180 | 0.209514 | ||||||||
\(587\) | 4.92820 | 0.203409 | 0.101704 | − | 0.994815i | \(-0.467570\pi\) | ||||
0.101704 | + | 0.994815i | \(0.467570\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.53590 | −0.0632856 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.19615 | 0.131361 | ||||||||
\(593\) | 43.3013 | 1.77817 | 0.889085 | − | 0.457742i | \(-0.151342\pi\) | ||||
0.889085 | + | 0.457742i | \(0.151342\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 12.9282 | 0.529560 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −13.4641 | −0.550588 | ||||||||
\(599\) | 42.1244 | 1.72115 | 0.860577 | − | 0.509320i | \(-0.170103\pi\) | ||||
0.860577 | + | 0.509320i | \(0.170103\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.392305 | 0.0160024 | 0.00800122 | − | 0.999968i | \(-0.497453\pi\) | ||||
0.00800122 | + | 0.999968i | \(0.497453\pi\) | |||||||
\(602\) | 4.53590 | 0.184869 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.3205 | 0.704761 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.7846 | 1.16833 | 0.584166 | − | 0.811634i | \(-0.301422\pi\) | ||||
0.584166 | + | 0.811634i | \(0.301422\pi\) | |||||||
\(608\) | 5.73205 | 0.232465 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −62.6410 | −2.53418 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.9474 | −0.442163 | −0.221081 | − | 0.975255i | \(-0.570959\pi\) | ||||
−0.221081 | + | 0.975255i | \(0.570959\pi\) | |||||||
\(614\) | 23.9282 | 0.965664 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.73205 | −0.0697863 | ||||||||
\(617\) | −4.92820 | −0.198402 | −0.0992010 | − | 0.995067i | \(-0.531629\pi\) | ||||
−0.0992010 | + | 0.995067i | \(0.531629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.3397 | −0.455783 | −0.227891 | − | 0.973687i | \(-0.573183\pi\) | ||||
−0.227891 | + | 0.973687i | \(0.573183\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.39230 | −0.176115 | ||||||||
\(623\) | −1.00000 | −0.0400642 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 31.3205 | 1.25182 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.53590 | −0.101193 | ||||||||
\(629\) | 12.7846 | 0.509756 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.85641 | −0.312759 | −0.156379 | − | 0.987697i | \(-0.549982\pi\) | ||||
−0.156379 | + | 0.987697i | \(0.549982\pi\) | |||||||
\(632\) | 8.92820 | 0.355145 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 15.0718 | 0.598578 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −5.46410 | −0.216496 | ||||||||
\(638\) | 2.53590 | 0.100397 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.07180 | 0.121329 | 0.0606643 | − | 0.998158i | \(-0.480678\pi\) | ||||
0.0606643 | + | 0.998158i | \(0.480678\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.0718 | −0.633810 | −0.316905 | − | 0.948457i | \(-0.602644\pi\) | ||||
−0.316905 | + | 0.948457i | \(0.602644\pi\) | |||||||
\(644\) | 2.46410 | 0.0970992 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.9282 | 0.902098 | ||||||||
\(647\) | 20.5359 | 0.807349 | 0.403675 | − | 0.914903i | \(-0.367733\pi\) | ||||
0.403675 | + | 0.914903i | \(0.367733\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.53590 | 0.335063 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.53590 | −0.0993134 | ||||||||
\(653\) | −7.85641 | −0.307445 | −0.153722 | − | 0.988114i | \(-0.549126\pi\) | ||||
−0.153722 | + | 0.988114i | \(0.549126\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.92820 | 0.153371 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 11.4641 | 0.446917 | ||||||||
\(659\) | 22.5167 | 0.877125 | 0.438562 | − | 0.898701i | \(-0.355488\pi\) | ||||
0.438562 | + | 0.898701i | \(0.355488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.2487 | 0.865375 | 0.432687 | − | 0.901544i | \(-0.357565\pi\) | ||||
0.432687 | + | 0.901544i | \(0.357565\pi\) | |||||||
\(662\) | −12.7846 | −0.496888 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.46410 | 0.367278 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.60770 | −0.139691 | ||||||||
\(668\) | 12.9282 | 0.500207 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 24.0000 | 0.926510 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.85641 | 0.379937 | 0.189968 | − | 0.981790i | \(-0.439161\pi\) | ||||
0.189968 | + | 0.981790i | \(0.439161\pi\) | |||||||
\(674\) | −21.7321 | −0.837087 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 16.8564 | 0.648323 | ||||||||
\(677\) | −46.9090 | −1.80286 | −0.901429 | − | 0.432927i | \(-0.857481\pi\) | ||||
−0.901429 | + | 0.432927i | \(0.857481\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.92820 | 0.265880 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.464102 | 0.0177714 | ||||||||
\(683\) | 20.8564 | 0.798048 | 0.399024 | − | 0.916940i | \(-0.369349\pi\) | ||||
0.399024 | + | 0.916940i | \(0.369349\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4.53590 | 0.172930 | ||||||||
\(689\) | 75.7128 | 2.88443 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 16.2487 | 0.618130 | 0.309065 | − | 0.951041i | \(-0.399984\pi\) | ||||
0.309065 | + | 0.951041i | \(0.399984\pi\) | |||||||
\(692\) | 18.1244 | 0.688985 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −21.9282 | −0.832383 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15.7128 | 0.595165 | ||||||||
\(698\) | 4.14359 | 0.156837 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.3923 | 0.468051 | 0.234025 | − | 0.972230i | \(-0.424810\pi\) | ||||
0.234025 | + | 0.972230i | \(0.424810\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.3205 | 0.690971 | ||||||||
\(704\) | −1.73205 | −0.0652791 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.66025 | 0.325933 | ||||||||
\(707\) | 12.9282 | 0.486215 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.53590 | −0.207905 | −0.103953 | − | 0.994582i | \(-0.533149\pi\) | ||||
−0.103953 | + | 0.994582i | \(0.533149\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.00000 | −0.0374766 | ||||||||
\(713\) | −0.660254 | −0.0247267 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.53590 | −0.169514 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −28.5359 | −1.06495 | ||||||||
\(719\) | −47.8564 | −1.78474 | −0.892371 | − | 0.451302i | \(-0.850960\pi\) | ||||
−0.892371 | + | 0.451302i | \(0.850960\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.4641 | 0.389704 | ||||||||
\(722\) | 13.8564 | 0.515682 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.85641 | 0.143322 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 48.7846 | 1.80932 | 0.904661 | − | 0.426133i | \(-0.140124\pi\) | ||||
0.904661 | + | 0.426133i | \(0.140124\pi\) | |||||||
\(728\) | −5.46410 | −0.202513 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.1436 | 0.671065 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.8564 | 1.02890 | 0.514450 | − | 0.857520i | \(-0.327996\pi\) | ||||
0.514450 | + | 0.857520i | \(0.327996\pi\) | |||||||
\(734\) | 23.3923 | 0.863426 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.46410 | 0.0908280 | ||||||||
\(737\) | −21.4641 | −0.790640 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −40.5359 | −1.49114 | −0.745569 | − | 0.666429i | \(-0.767822\pi\) | ||||
−0.745569 | + | 0.666429i | \(0.767822\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −13.8564 | −0.508685 | ||||||||
\(743\) | 22.6077 | 0.829396 | 0.414698 | − | 0.909959i | \(-0.363887\pi\) | ||||
0.414698 | + | 0.909959i | \(0.363887\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.19615 | 0.263470 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −6.92820 | −0.253320 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.8564 | −0.578608 | −0.289304 | − | 0.957237i | \(-0.593424\pi\) | ||||
−0.289304 | + | 0.957237i | \(0.593424\pi\) | |||||||
\(752\) | 11.4641 | 0.418053 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00000 | 0.291343 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.8564 | 0.503620 | 0.251810 | − | 0.967777i | \(-0.418974\pi\) | ||||
0.251810 | + | 0.967777i | \(0.418974\pi\) | |||||||
\(758\) | −14.0000 | −0.508503 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 49.7128 | 1.80209 | 0.901044 | − | 0.433728i | \(-0.142802\pi\) | ||||
0.901044 | + | 0.433728i | \(0.142802\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.53590 | 0.272818 | ||||||||
\(764\) | −8.80385 | −0.318512 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 11.0718 | 0.400040 | ||||||||
\(767\) | 26.9282 | 0.972321 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −53.9615 | −1.94590 | −0.972951 | − | 0.231011i | \(-0.925797\pi\) | ||||
−0.972951 | + | 0.231011i | \(0.925797\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −17.8564 | −0.642666 | ||||||||
\(773\) | −30.3731 | −1.09244 | −0.546222 | − | 0.837641i | \(-0.683934\pi\) | ||||
−0.546222 | + | 0.837641i | \(0.683934\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.92820 | 0.248708 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.92820 | −0.248388 | ||||||||
\(779\) | 22.5167 | 0.806743 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.39230 | 0.264517 | ||||||||
\(782\) | 9.85641 | 0.352464 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −13.8564 | −0.493928 | −0.246964 | − | 0.969025i | \(-0.579433\pi\) | ||||
−0.246964 | + | 0.969025i | \(0.579433\pi\) | |||||||
\(788\) | 19.4641 | 0.693380 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.53590 | 0.161278 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 75.7128 | 2.68864 | ||||||||
\(794\) | 5.60770 | 0.199010 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.0526 | −0.462636 | ||||||||
\(797\) | 20.5167 | 0.726737 | 0.363369 | − | 0.931645i | \(-0.381627\pi\) | ||||
0.363369 | + | 0.931645i | \(0.381627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.8564 | 1.62228 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.60770 | −0.268637 | ||||||||
\(803\) | 29.3205 | 1.03470 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.46410 | 0.0515708 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.9282 | 0.454813 | ||||||||
\(809\) | −29.4641 | −1.03590 | −0.517951 | − | 0.855410i | \(-0.673305\pi\) | ||||
−0.517951 | + | 0.855410i | \(0.673305\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.2679 | −1.20331 | −0.601655 | − | 0.798756i | \(-0.705492\pi\) | ||||
−0.601655 | + | 0.798756i | \(0.705492\pi\) | |||||||
\(812\) | −1.46410 | −0.0513799 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −5.53590 | −0.194033 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 26.0000 | 0.909625 | ||||||||
\(818\) | −37.3205 | −1.30488 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −18.6795 | −0.651919 | −0.325959 | − | 0.945384i | \(-0.605687\pi\) | ||||
−0.325959 | + | 0.945384i | \(0.605687\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −42.4974 | −1.48137 | −0.740684 | − | 0.671854i | \(-0.765498\pi\) | ||||
−0.740684 | + | 0.671854i | \(0.765498\pi\) | |||||||
\(824\) | 10.4641 | 0.364534 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.92820 | −0.171474 | ||||||||
\(827\) | −20.8564 | −0.725248 | −0.362624 | − | 0.931935i | \(-0.618119\pi\) | ||||
−0.362624 | + | 0.931935i | \(0.618119\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.4641 | 1.50957 | 0.754785 | − | 0.655972i | \(-0.227741\pi\) | ||||
0.754785 | + | 0.655972i | \(0.227741\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.46410 | −0.189434 | ||||||||
\(833\) | 4.00000 | 0.138592 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.92820 | −0.343374 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 23.4641 | 0.810554 | ||||||||
\(839\) | 10.5359 | 0.363740 | 0.181870 | − | 0.983323i | \(-0.441785\pi\) | ||||
0.181870 | + | 0.983323i | \(0.441785\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.8564 | −0.926083 | ||||||||
\(842\) | 4.46410 | 0.153843 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −10.3923 | −0.357718 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −8.00000 | −0.274883 | ||||||||
\(848\) | −13.8564 | −0.475831 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.87564 | 0.269974 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.4974 | −1.38661 | −0.693303 | − | 0.720647i | \(-0.743845\pi\) | ||||
−0.693303 | + | 0.720647i | \(0.743845\pi\) | |||||||
\(854\) | −13.8564 | −0.474156 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.00000 | −0.136717 | ||||||||
\(857\) | −5.73205 | −0.195803 | −0.0979016 | − | 0.995196i | \(-0.531213\pi\) | ||||
−0.0979016 | + | 0.995196i | \(0.531213\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.124356 | 0.00424296 | 0.00212148 | − | 0.999998i | \(-0.499325\pi\) | ||||
0.00212148 | + | 0.999998i | \(0.499325\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 24.5167 | 0.835041 | ||||||||
\(863\) | 48.7846 | 1.66065 | 0.830324 | − | 0.557281i | \(-0.188156\pi\) | ||||
0.830324 | + | 0.557281i | \(0.188156\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −38.2487 | −1.29974 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.267949 | −0.00909479 | ||||||||
\(869\) | −15.4641 | −0.524584 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −67.7128 | −2.29436 | ||||||||
\(872\) | 7.53590 | 0.255198 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 14.1244 | 0.477763 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.784610 | 0.0264944 | 0.0132472 | − | 0.999912i | \(-0.495783\pi\) | ||||
0.0132472 | + | 0.999912i | \(0.495783\pi\) | |||||||
\(878\) | −17.6077 | −0.594231 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −52.8564 | −1.78078 | −0.890389 | − | 0.455201i | \(-0.849567\pi\) | ||||
−0.890389 | + | 0.455201i | \(0.849567\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −50.9282 | −1.71387 | −0.856935 | − | 0.515424i | \(-0.827634\pi\) | ||||
−0.856935 | + | 0.515424i | \(0.827634\pi\) | |||||||
\(884\) | −21.8564 | −0.735111 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.8564 | −0.364728 | ||||||||
\(887\) | −25.1769 | −0.845358 | −0.422679 | − | 0.906279i | \(-0.638910\pi\) | ||||
−0.422679 | + | 0.906279i | \(0.638910\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.46410 | −0.183260 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 17.3923 | 0.582337 | ||||||||
\(893\) | 65.7128 | 2.19900 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −10.0000 | −0.333704 | ||||||||
\(899\) | 0.392305 | 0.0130841 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −55.4256 | −1.84650 | ||||||||
\(902\) | −6.80385 | −0.226543 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.53590 | 0.150862 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.0718 | 1.03172 | 0.515861 | − | 0.856672i | \(-0.327472\pi\) | ||||
0.515861 | + | 0.856672i | \(0.327472\pi\) | |||||||
\(908\) | −26.7846 | −0.888878 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.2487 | 1.06845 | 0.534224 | − | 0.845343i | \(-0.320604\pi\) | ||||
0.534224 | + | 0.845343i | \(0.320604\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −16.3923 | −0.542506 | ||||||||
\(914\) | −14.5167 | −0.480168 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 10.9282 | 0.361078 | ||||||||
\(917\) | 20.9282 | 0.691110 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −14.1436 | −0.466554 | −0.233277 | − | 0.972410i | \(-0.574945\pi\) | ||||
−0.233277 | + | 0.972410i | \(0.574945\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 5.39230 | 0.177586 | ||||||||
\(923\) | 23.3205 | 0.767604 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −0.143594 | −0.00471878 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.46410 | −0.0480615 | ||||||||
\(929\) | −16.1436 | −0.529654 | −0.264827 | − | 0.964296i | \(-0.585315\pi\) | ||||
−0.264827 | + | 0.964296i | \(0.585315\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.73205 | 0.187860 | ||||||||
\(932\) | 12.5359 | 0.410627 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.2487 | −0.662558 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.6410 | 0.870324 | 0.435162 | − | 0.900352i | \(-0.356691\pi\) | ||||
0.435162 | + | 0.900352i | \(0.356691\pi\) | |||||||
\(938\) | 12.3923 | 0.404623 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −21.1051 | −0.688007 | −0.344004 | − | 0.938968i | \(-0.611783\pi\) | ||||
−0.344004 | + | 0.938968i | \(0.611783\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.67949 | 0.315208 | ||||||||
\(944\) | −4.92820 | −0.160399 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.85641 | −0.255434 | ||||||||
\(947\) | 32.5692 | 1.05836 | 0.529179 | − | 0.848510i | \(-0.322500\pi\) | ||||
0.529179 | + | 0.848510i | \(0.322500\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 92.4974 | 3.00259 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.00000 | 0.129641 | ||||||||
\(953\) | −2.53590 | −0.0821458 | −0.0410729 | − | 0.999156i | \(-0.513078\pi\) | ||||
−0.0410729 | + | 0.999156i | \(0.513078\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.4641 | 0.370776 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.7846 | 0.671520 | ||||||||
\(959\) | 13.4641 | 0.434779 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.9282 | −0.997684 | ||||||||
\(962\) | −17.4641 | −0.563065 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −10.3923 | −0.334714 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −35.8564 | −1.15306 | −0.576532 | − | 0.817074i | \(-0.695594\pi\) | ||||
−0.576532 | + | 0.817074i | \(0.695594\pi\) | |||||||
\(968\) | −8.00000 | −0.257130 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.679492 | 0.0218059 | 0.0109030 | − | 0.999941i | \(-0.496529\pi\) | ||||
0.0109030 | + | 0.999941i | \(0.496529\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.535898 | 0.0171801 | ||||||||
\(974\) | 26.3923 | 0.845664 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −13.8564 | −0.443533 | ||||||||
\(977\) | 41.5692 | 1.32992 | 0.664959 | − | 0.746880i | \(-0.268449\pi\) | ||||
0.664959 | + | 0.746880i | \(0.268449\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.73205 | 0.0553566 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.4449 | −1.32256 | ||||||||
\(983\) | 17.6077 | 0.561598 | 0.280799 | − | 0.959767i | \(-0.409401\pi\) | ||||
0.280799 | + | 0.959767i | \(0.409401\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −5.85641 | −0.186506 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −31.3205 | −0.996438 | ||||||||
\(989\) | 11.1769 | 0.355405 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.3923 | −1.15604 | −0.578020 | − | 0.816023i | \(-0.696174\pi\) | ||||
−0.578020 | + | 0.816023i | \(0.696174\pi\) | |||||||
\(992\) | −0.267949 | −0.00850740 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.26795 | −0.135371 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 55.9615 | 1.77232 | 0.886160 | − | 0.463380i | \(-0.153364\pi\) | ||||
0.886160 | + | 0.463380i | \(0.153364\pi\) | |||||||
\(998\) | −7.07180 | −0.223854 | ||||||||
\(999\) | 0 | 0 |
(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 | 9450.2.a.eu.1.1 | 2 | ||
3.2 | odd | 2 | 9450.2.a.ei.1.2 | 2 | |||
5.2 | odd | 4 | 1890.2.g.n.379.4 | yes | 4 | ||
5.3 | odd | 4 | 1890.2.g.n.379.2 | ✓ | 4 | ||
5.4 | even | 2 | 9450.2.a.eb.1.1 | 2 | |||
15.2 | even | 4 | 1890.2.g.q.379.1 | yes | 4 | ||
15.8 | even | 4 | 1890.2.g.q.379.3 | yes | 4 | ||
15.14 | odd | 2 | 9450.2.a.er.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1890.2.g.n.379.2 | ✓ | 4 | 5.3 | odd | 4 | ||
1890.2.g.n.379.4 | yes | 4 | 5.2 | odd | 4 | ||
1890.2.g.q.379.1 | yes | 4 | 15.2 | even | 4 | ||
1890.2.g.q.379.3 | yes | 4 | 15.8 | even | 4 | ||
9450.2.a.eb.1.1 | 2 | 5.4 | even | 2 | |||
9450.2.a.ei.1.2 | 2 | 3.2 | odd | 2 | |||
9450.2.a.er.1.2 | 2 | 15.14 | odd | 2 | |||
9450.2.a.eu.1.1 | 2 | 1.1 | even | 1 | trivial |