Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1232,2,Mod(1,1232)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1232, 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("1232.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1232 = 2^{4} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1232.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: | \(9.83756952902\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11348.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 5x^{2} + x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 616) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.77571\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1232.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.12631 | −0.650274 | −0.325137 | − | 0.945667i | \(-0.605410\pi\) | ||||
−0.325137 | + | 0.945667i | \(0.605410\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.42512 | 1.97897 | 0.989486 | − | 0.144626i | \(-0.0461980\pi\) | ||||
0.989486 | + | 0.144626i | \(0.0461980\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.73143 | −0.577143 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.85774 | 1.62464 | 0.812322 | − | 0.583209i | \(-0.198203\pi\) | ||||
0.812322 | + | 0.583209i | \(0.198203\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −4.98405 | −1.28688 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.55143 | −0.376276 | −0.188138 | − | 0.982143i | \(-0.560245\pi\) | ||||
−0.188138 | + | 0.982143i | \(0.560245\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 7.40916 | 1.69978 | 0.849889 | − | 0.526961i | \(-0.176669\pi\) | ||||
0.849889 | + | 0.526961i | \(0.176669\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.12631 | −0.245781 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.98405 | −1.03925 | −0.519623 | − | 0.854396i | \(-0.673927\pi\) | ||||
−0.519623 | + | 0.854396i | \(0.673927\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 14.5817 | 2.91633 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.32905 | 1.02558 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.10285 | −1.69036 | −0.845179 | − | 0.534484i | \(-0.820506\pi\) | ||||
−0.845179 | + | 0.534484i | \(0.820506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.43262 | 0.257306 | 0.128653 | − | 0.991690i | \(-0.458935\pi\) | ||||
0.128653 | + | 0.991690i | \(0.458935\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.12631 | 0.196065 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.42512 | 0.747981 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.731430 | −0.120246 | −0.0601232 | − | 0.998191i | \(-0.519149\pi\) | ||||
−0.0601232 | + | 0.998191i | \(0.519149\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.59762 | −1.05646 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.55143 | −0.242292 | −0.121146 | − | 0.992635i | \(-0.538657\pi\) | ||||
−0.121146 | + | 0.992635i | \(0.538657\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.59762 | −0.396133 | −0.198067 | − | 0.980189i | \(-0.563466\pi\) | ||||
−0.198067 | + | 0.980189i | \(0.563466\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.66178 | −1.14215 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.953807 | 0.139127 | 0.0695635 | − | 0.997578i | \(-0.477839\pi\) | ||||
0.0695635 | + | 0.997578i | \(0.477839\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.74738 | 0.244683 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.42512 | −0.596683 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.34500 | −1.10532 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.22916 | 1.07135 | 0.535673 | − | 0.844426i | \(-0.320058\pi\) | ||||
0.535673 | + | 0.844426i | \(0.320058\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.60512 | 0.461589 | 0.230794 | − | 0.973003i | \(-0.425868\pi\) | ||||
0.230794 | + | 0.973003i | \(0.425868\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73143 | −0.218140 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 25.9212 | 3.21513 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.32905 | −1.13972 | −0.569862 | − | 0.821740i | \(-0.693003\pi\) | ||||
−0.569862 | + | 0.821740i | \(0.693003\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.61357 | 0.675795 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.478813 | 0.0568247 | 0.0284123 | − | 0.999596i | \(-0.490955\pi\) | ||||
0.0284123 | + | 0.999596i | \(0.490955\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.16405 | 0.721448 | 0.360724 | − | 0.932673i | \(-0.382530\pi\) | ||||
0.360724 | + | 0.932673i | \(0.382530\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −16.4234 | −1.89642 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.00000 | −0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.74738 | 1.09667 | 0.548333 | − | 0.836260i | \(-0.315263\pi\) | ||||
0.548333 | + | 0.836260i | \(0.315263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.807862 | −0.0897624 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.5589 | −1.15899 | −0.579497 | − | 0.814975i | \(-0.696751\pi\) | ||||
−0.579497 | + | 0.814975i | \(0.696751\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.86524 | −0.744640 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.2526 | 1.09920 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.11881 | 0.436592 | 0.218296 | − | 0.975883i | \(-0.429950\pi\) | ||||
0.218296 | + | 0.975883i | \(0.429950\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.85774 | 0.614058 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.61357 | −0.167320 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 32.7864 | 3.36382 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −11.3290 | −1.15029 | −0.575145 | − | 0.818051i | \(-0.695054\pi\) | ||||
−0.575145 | + | 0.818051i | \(0.695054\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.73143 | 0.174015 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.24511 | 0.521908 | 0.260954 | − | 0.965351i | \(-0.415963\pi\) | ||||
0.260954 | + | 0.965351i | \(0.415963\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.6543 | 1.83806 | 0.919030 | − | 0.394187i | \(-0.128974\pi\) | ||||
0.919030 | + | 0.394187i | \(0.128974\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.98405 | −0.486393 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.3555 | 1.29112 | 0.645561 | − | 0.763709i | \(-0.276624\pi\) | ||||
0.645561 | + | 0.763709i | \(0.276624\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.44785 | −0.904940 | −0.452470 | − | 0.891780i | \(-0.649457\pi\) | ||||
−0.452470 | + | 0.891780i | \(0.649457\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.823815 | 0.0781931 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.5817 | −1.27766 | −0.638828 | − | 0.769350i | \(-0.720580\pi\) | ||||
−0.638828 | + | 0.769350i | \(0.720580\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −22.0550 | −2.05664 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −10.1423 | −0.937652 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.55143 | −0.142219 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.74738 | 0.157556 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 42.4000 | 3.79237 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.35547 | −0.120278 | −0.0601392 | − | 0.998190i | \(-0.519154\pi\) | ||||
−0.0601392 | + | 0.998190i | \(0.519154\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.92572 | 0.257595 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.0068 | 0.874297 | 0.437148 | − | 0.899389i | \(-0.355988\pi\) | ||||
0.437148 | + | 0.899389i | \(0.355988\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.40916 | 0.642456 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 23.5817 | 2.02959 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 18.4319 | 1.57474 | 0.787372 | − | 0.616479i | \(-0.211441\pi\) | ||||
0.787372 | + | 0.616479i | \(0.211441\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.90393 | −0.246308 | −0.123154 | − | 0.992388i | \(-0.539301\pi\) | ||||
−0.123154 | + | 0.992388i | \(0.539301\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.07428 | −0.0904708 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.85774 | −0.489849 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −40.2812 | −3.34517 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.12631 | −0.0928963 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.2057 | −1.32762 | −0.663811 | − | 0.747900i | \(-0.731062\pi\) | ||||
−0.663811 | + | 0.747900i | \(0.731062\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.63999 | 0.458976 | 0.229488 | − | 0.973311i | \(-0.426295\pi\) | ||||
0.229488 | + | 0.973311i | \(0.426295\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.68618 | 0.217165 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.33951 | 0.509202 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.692740 | −0.0552867 | −0.0276433 | − | 0.999618i | \(-0.508800\pi\) | ||||
−0.0276433 | + | 0.999618i | \(0.508800\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.25262 | −0.178644 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.98405 | −0.392798 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.2207 | 1.27050 | 0.635252 | − | 0.772305i | \(-0.280896\pi\) | ||||
0.635252 | + | 0.772305i | \(0.280896\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.98405 | 0.388007 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −12.8502 | −0.994381 | −0.497191 | − | 0.867641i | \(-0.665635\pi\) | ||||
−0.497191 | + | 0.867641i | \(0.665635\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 21.3131 | 1.63947 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −12.8284 | −0.981016 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0680 | −0.993540 | −0.496770 | − | 0.867882i | \(-0.665481\pi\) | ||||
−0.496770 | + | 0.867882i | \(0.665481\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 14.5817 | 1.10227 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −9.26857 | −0.696668 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.8493 | −0.885657 | −0.442829 | − | 0.896606i | \(-0.646025\pi\) | ||||
−0.442829 | + | 0.896606i | \(0.646025\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −7.52797 | −0.559550 | −0.279775 | − | 0.960066i | \(-0.590260\pi\) | ||||
−0.279775 | + | 0.960066i | \(0.590260\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −4.06048 | −0.300159 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.23666 | −0.237964 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.55143 | 0.113451 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 5.32905 | 0.387631 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.3245 | −1.76006 | −0.880030 | − | 0.474918i | \(-0.842478\pi\) | ||||
−0.880030 | + | 0.474918i | \(0.842478\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.31309 | −0.598390 | −0.299195 | − | 0.954192i | \(-0.596718\pi\) | ||||
−0.299195 | + | 0.954192i | \(0.596718\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −29.1952 | −2.09071 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.6126 | −0.756118 | −0.378059 | − | 0.925781i | \(-0.623408\pi\) | ||||
−0.378059 | + | 0.925781i | \(0.623408\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.04619 | −0.499491 | −0.249746 | − | 0.968311i | \(-0.580347\pi\) | ||||
−0.249746 | + | 0.968311i | \(0.580347\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.5074 | 0.741134 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −9.10285 | −0.638895 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.86524 | −0.479489 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.62953 | 0.599794 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7.40916 | −0.512503 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.86070 | −0.678839 | −0.339419 | − | 0.940635i | \(-0.610231\pi\) | ||||
−0.339419 | + | 0.940635i | \(0.610231\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.539291 | −0.0369516 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −11.4948 | −0.783937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.43262 | 0.0972526 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.94262 | −0.469139 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −9.08785 | −0.611315 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.4176 | 0.764580 | 0.382290 | − | 0.924042i | \(-0.375136\pi\) | ||||
0.382290 | + | 0.924042i | \(0.375136\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.2471 | −1.68314 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −14.1670 | −0.940298 | −0.470149 | − | 0.882587i | \(-0.655800\pi\) | ||||
−0.470149 | + | 0.882587i | \(0.655800\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.0227 | −1.25706 | −0.628529 | − | 0.777786i | \(-0.716343\pi\) | ||||
−0.628529 | + | 0.777786i | \(0.716343\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.12631 | 0.0741056 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.1029 | −0.858396 | −0.429198 | − | 0.903210i | \(-0.641204\pi\) | ||||
−0.429198 | + | 0.903210i | \(0.641204\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.22071 | 0.275329 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.9786 | −0.713134 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −21.1179 | −1.36600 | −0.683000 | − | 0.730418i | \(-0.739325\pi\) | ||||
−0.683000 | + | 0.730418i | \(0.739325\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −24.7148 | −1.59202 | −0.796009 | − | 0.605285i | \(-0.793059\pi\) | ||||
−0.796009 | + | 0.605285i | \(0.793059\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.0772 | −0.967206 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.42512 | 0.282710 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 43.4009 | 2.76154 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.8926 | 0.753663 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −17.1868 | −1.08482 | −0.542410 | − | 0.840114i | \(-0.682488\pi\) | ||||
−0.542410 | + | 0.840114i | \(0.682488\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.98405 | 0.313344 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.73238 | 0.484220 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.4310 | 1.58634 | 0.793170 | − | 0.609001i | \(-0.208429\pi\) | ||||
0.793170 | + | 0.609001i | \(0.208429\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.731430 | −0.0454488 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.7609 | 0.975578 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.957627 | −0.0590498 | −0.0295249 | − | 0.999564i | \(-0.509399\pi\) | ||||
−0.0295249 | + | 0.999564i | \(0.509399\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.85023 | 0.543666 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.63904 | −0.283905 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6.82845 | 0.416338 | 0.208169 | − | 0.978093i | \(-0.433250\pi\) | ||||
0.208169 | + | 0.978093i | \(0.433250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −18.0286 | −1.09516 | −0.547579 | − | 0.836754i | \(-0.684450\pi\) | ||||
−0.547579 | + | 0.836754i | \(0.684450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −6.59762 | −0.399306 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −14.5817 | −0.879307 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.53714 | −0.272610 | −0.136305 | − | 0.990667i | \(-0.543523\pi\) | ||||
−0.136305 | + | 0.990667i | \(0.543523\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.48048 | −0.148503 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.37047 | 0.558996 | 0.279498 | − | 0.960146i | \(-0.409832\pi\) | ||||
0.279498 | + | 0.960146i | \(0.409832\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.23083 | −0.132609 | −0.0663045 | − | 0.997799i | \(-0.521121\pi\) | ||||
−0.0663045 | + | 0.997799i | \(0.521121\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −36.9276 | −2.18740 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.55143 | −0.0915778 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.5931 | −0.858416 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.7600 | 0.748004 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 20.6156 | 1.20438 | 0.602188 | − | 0.798355i | \(-0.294296\pi\) | ||||
0.602188 | + | 0.798355i | \(0.294296\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 36.4150 | 2.12016 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.32905 | −0.309223 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −29.1952 | −1.68840 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.59762 | −0.149724 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.90761 | −0.339384 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.9531 | 0.913471 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.6618 | −1.46460 | −0.732298 | − | 0.680985i | \(-0.761552\pi\) | ||||
−0.732298 | + | 0.680985i | \(0.761552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.0105 | −1.19524 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.2564 | 1.03523 | 0.517614 | − | 0.855614i | \(-0.326820\pi\) | ||||
0.517614 | + | 0.855614i | \(0.326820\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 23.4424 | 1.32504 | 0.662520 | − | 0.749044i | \(-0.269487\pi\) | ||||
0.662520 | + | 0.749044i | \(0.269487\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −7.66178 | −0.431692 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −5.07643 | −0.285121 | −0.142560 | − | 0.989786i | \(-0.545534\pi\) | ||||
−0.142560 | + | 0.989786i | \(0.545534\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.10285 | 0.509662 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −15.0424 | −0.839583 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −11.4948 | −0.639586 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 85.4156 | 4.73800 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.6412 | 0.588459 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0.953807 | 0.0525851 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.81928 | 0.429786 | 0.214893 | − | 0.976638i | \(-0.431060\pi\) | ||||
0.214893 | + | 0.976638i | \(0.431060\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.26642 | 0.0693993 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −41.2821 | −2.25548 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.01501 | −0.218711 | −0.109356 | − | 0.994003i | \(-0.534879\pi\) | ||||
−0.109356 | + | 0.994003i | \(0.534879\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 15.2971 | 0.830827 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.43262 | −0.0775808 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 24.8407 | 1.33738 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.0709 | −1.34588 | −0.672939 | − | 0.739698i | \(-0.734969\pi\) | ||||
−0.672939 | + | 0.739698i | \(0.734969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5.69751 | −0.304981 | −0.152490 | − | 0.988305i | \(-0.548729\pi\) | ||||
−0.152490 | + | 0.988305i | \(0.548729\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 31.2162 | 1.66620 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.7450 | 1.74284 | 0.871420 | − | 0.490537i | \(-0.163200\pi\) | ||||
0.871420 | + | 0.490537i | \(0.163200\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.11881 | 0.112455 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.74738 | 0.0924813 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −2.09239 | −0.110432 | −0.0552159 | − | 0.998474i | \(-0.517585\pi\) | ||||
−0.0552159 | + | 0.998474i | \(0.517585\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 35.8957 | 1.88925 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.12631 | −0.0591159 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 27.2766 | 1.42772 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.71714 | 0.0896342 | 0.0448171 | − | 0.998995i | \(-0.485729\pi\) | ||||
0.0448171 | + | 0.998995i | \(0.485729\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.68618 | 0.139837 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | 0.103835 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.35547 | 0.380852 | 0.190426 | − | 0.981702i | \(-0.439013\pi\) | ||||
0.190426 | + | 0.981702i | \(0.439013\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −47.7555 | −2.46608 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −53.3221 | −2.74623 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.0914 | −0.672462 | −0.336231 | − | 0.941780i | \(-0.609152\pi\) | ||||
−0.336231 | + | 0.941780i | \(0.609152\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.52667 | 0.0782139 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.62786 | 0.338668 | 0.169334 | − | 0.985559i | \(-0.445838\pi\) | ||||
0.169334 | + | 0.985559i | \(0.445838\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.42512 | −0.225525 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.49759 | 0.228626 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.2262 | 0.619893 | 0.309946 | − | 0.950754i | \(-0.399689\pi\) | ||||
0.309946 | + | 0.950754i | \(0.399689\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7.73238 | 0.391043 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −11.2707 | −0.568533 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 43.1333 | 2.17027 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.9644 | −1.25293 | −0.626464 | − | 0.779450i | \(-0.715498\pi\) | ||||
−0.626464 | + | 0.779450i | \(0.715498\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −8.34500 | −0.417773 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −35.6367 | −1.77961 | −0.889805 | − | 0.456341i | \(-0.849160\pi\) | ||||
−0.889805 | + | 0.456341i | \(0.849160\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.39192 | 0.418031 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.57488 | −0.177637 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.731430 | 0.0362556 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.44857 | −0.121074 | −0.0605371 | − | 0.998166i | \(-0.519281\pi\) | ||||
−0.0605371 | + | 0.998166i | \(0.519281\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −20.7600 | −1.02402 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.22916 | 0.404930 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −46.7245 | −2.29362 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.27072 | 0.160168 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.5023 | −0.513069 | −0.256535 | − | 0.966535i | \(-0.582581\pi\) | ||||
−0.256535 | + | 0.966535i | \(0.582581\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.7109 | 1.39929 | 0.699643 | − | 0.714493i | \(-0.253343\pi\) | ||||
0.699643 | + | 0.714493i | \(0.253343\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.65145 | −0.0802963 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −22.6224 | −1.09735 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.60512 | 0.174464 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.59762 | 0.318536 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −9.87760 | −0.475787 | −0.237894 | − | 0.971291i | \(-0.576457\pi\) | ||||
−0.237894 | + | 0.971291i | \(0.576457\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.5967 | 0.749528 | 0.374764 | − | 0.927120i | \(-0.377724\pi\) | ||||
0.374764 | + | 0.927120i | \(0.377724\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 45.3690 | 2.17528 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −36.9276 | −1.76649 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.2662 | −1.06271 | −0.531353 | − | 0.847150i | \(-0.678316\pi\) | ||||
−0.531353 | + | 0.847150i | \(0.678316\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.73143 | −0.0824490 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 29.8174 | 1.41667 | 0.708333 | − | 0.705878i | \(-0.249447\pi\) | ||||
0.708333 | + | 0.705878i | \(0.249447\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.2262 | 0.864005 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 18.2526 | 0.863319 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.23666 | −0.435905 | −0.217953 | − | 0.975959i | \(-0.569938\pi\) | ||||
−0.217953 | + | 0.975959i | \(0.569938\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.55143 | 0.0730538 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.35237 | −0.298460 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 25.9212 | 1.21520 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.13930 | 0.193628 | 0.0968141 | − | 0.995302i | \(-0.469135\pi\) | ||||
0.0968141 | + | 0.995302i | \(0.469135\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.26762 | −0.385900 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.1982 | 0.801000 | 0.400500 | − | 0.916297i | \(-0.368836\pi\) | ||||
0.400500 | + | 0.916297i | \(0.368836\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.1897 | 0.891823 | 0.445912 | − | 0.895077i | \(-0.352880\pi\) | ||||
0.445912 | + | 0.895077i | \(0.352880\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.14025 | −0.331121 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −21.0794 | −0.975438 | −0.487719 | − | 0.873001i | \(-0.662171\pi\) | ||||
−0.487719 | + | 0.873001i | \(0.662171\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.32905 | −0.430775 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.780239 | 0.0359515 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.59762 | 0.119439 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 108.038 | 4.95712 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.46286 | −0.158553 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.41595 | 0.0646962 | 0.0323481 | − | 0.999477i | \(-0.489701\pi\) | ||||
0.0323481 | + | 0.999477i | \(0.489701\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.28452 | −0.195357 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.61357 | 0.255426 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −50.1324 | −2.27639 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.24120 | 0.192187 | 0.0960936 | − | 0.995372i | \(-0.469365\pi\) | ||||
0.0960936 | + | 0.995372i | \(0.469365\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −18.2695 | −0.826176 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.4479 | 1.05819 | 0.529093 | − | 0.848564i | \(-0.322532\pi\) | ||||
0.529093 | + | 0.848564i | \(0.322532\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 14.1224 | 0.636041 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.66178 | 0.344371 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.478813 | 0.0214777 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.4159 | −0.600580 | −0.300290 | − | 0.953848i | \(-0.597083\pi\) | ||||
−0.300290 | + | 0.953848i | \(0.597083\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.4733 | 0.646620 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4.17713 | −0.186249 | −0.0931246 | − | 0.995654i | \(-0.529685\pi\) | ||||
−0.0931246 | + | 0.995654i | \(0.529685\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 23.2102 | 1.03284 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −24.0051 | −1.06610 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 10.1725 | 0.450888 | 0.225444 | − | 0.974256i | \(-0.427617\pi\) | ||||
0.225444 | + | 0.974256i | \(0.427617\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.16405 | 0.272682 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 39.4838 | 1.74325 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 82.5474 | 3.63747 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.953807 | −0.0419484 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.7186 | 0.646074 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.17618 | 0.0515296 | 0.0257648 | − | 0.999668i | \(-0.491798\pi\) | ||||
0.0257648 | + | 0.999668i | \(0.491798\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −35.3623 | −1.54628 | −0.773142 | − | 0.634233i | \(-0.781316\pi\) | ||||
−0.773142 | + | 0.634233i | \(0.781316\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −16.4234 | −0.716778 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.22260 | −0.0968182 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.84072 | 0.0800312 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −14.2482 | −0.618320 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9.08785 | −0.393638 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.0995 | 2.55509 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.3459 | 0.575920 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.00000 | −0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.2812 | −0.957943 | −0.478972 | − | 0.877830i | \(-0.658990\pi\) | ||||
−0.478972 | + | 0.877830i | \(0.658990\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.47881 | 0.363861 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −41.8079 | −1.79085 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.3371 | −1.85296 | −0.926481 | − | 0.376342i | \(-0.877182\pi\) | ||||
−0.926481 | + | 0.376342i | \(0.877182\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.24201 | −0.266403 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −67.4445 | −2.87323 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.74738 | 0.414501 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.64548 | 0.154742 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 27.2388 | 1.15415 | 0.577073 | − | 0.816693i | \(-0.304195\pi\) | ||||
0.577073 | + | 0.816693i | \(0.304195\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −15.2162 | −0.643575 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.74738 | −0.0737746 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.37726 | −0.395204 | −0.197602 | − | 0.980282i | \(-0.563315\pi\) | ||||
−0.197602 | + | 0.980282i | \(0.563315\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −60.1005 | −2.52845 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.807862 | −0.0339270 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.0150061 | 0.000629087 0 | 0.000314544 | − | 1.00000i | \(-0.499900\pi\) | ||||
0.000314544 | 1.00000i | \(0.499900\pi\) | ||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −32.4114 | −1.35638 | −0.678188 | − | 0.734889i | \(-0.737234\pi\) | ||||
−0.678188 | + | 0.734889i | \(0.737234\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.3969 | 1.14452 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −72.6757 | −3.03079 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.3831 | −1.84769 | −0.923846 | − | 0.382764i | \(-0.874972\pi\) | ||||
−0.923846 | + | 0.382764i | \(0.874972\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.36311 | 0.389117 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.5589 | −0.438058 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.00000 | −0.0828315 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −44.8807 | −1.85559 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.11489 | 0.128565 | 0.0642827 | − | 0.997932i | \(-0.479524\pi\) | ||||
0.0642827 | + | 0.997932i | \(0.479524\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10.6145 | 0.437364 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.9531 | 0.491684 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.26690 | −0.380546 | −0.190273 | − | 0.981731i | \(-0.560937\pi\) | ||||
−0.190273 | + | 0.981731i | \(0.560937\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.86524 | −0.281447 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.93618 | 0.324806 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.5233 | −0.879420 | −0.439710 | − | 0.898140i | \(-0.644919\pi\) | ||||
−0.439710 | + | 0.898140i | \(0.644919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.70119 | −0.191766 | −0.0958828 | − | 0.995393i | \(-0.530567\pi\) | ||||
−0.0958828 | + | 0.995393i | \(0.530567\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.1526 | 0.657784 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.42512 | 0.179907 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.2376 | 1.14613 | 0.573065 | − | 0.819510i | \(-0.305754\pi\) | ||||
0.573065 | + | 0.819510i | \(0.305754\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 10.2526 | 0.415457 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.58715 | 0.226032 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.37047 | −0.0553529 | −0.0276765 | − | 0.999617i | \(-0.508811\pi\) | ||||
−0.0276765 | + | 0.999617i | \(0.508811\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 7.73238 | 0.311800 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −27.6231 | −1.11206 | −0.556032 | − | 0.831161i | \(-0.687677\pi\) | ||||
−0.556032 | + | 0.831161i | \(0.687677\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −21.8222 | −0.877110 | −0.438555 | − | 0.898704i | \(-0.644510\pi\) | ||||
−0.438555 | + | 0.898704i | \(0.644510\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −26.5602 | −1.06583 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.11881 | 0.165016 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 114.717 | 4.58866 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 8.34500 | 0.333267 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.13476 | 0.0452458 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.0974 | −0.521398 | −0.260699 | − | 0.965420i | \(-0.583953\pi\) | ||||
−0.260699 | + | 0.965420i | \(0.583953\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.1062 | 0.441431 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.99810 | −0.238028 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.85774 | 0.232092 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.829032 | −0.0327960 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.04143 | −0.159627 | −0.0798134 | − | 0.996810i | \(-0.525432\pi\) | ||||
−0.0798134 | + | 0.996810i | \(0.525432\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.6346 | 1.28698 | 0.643492 | − | 0.765453i | \(-0.277485\pi\) | ||||
0.643492 | + | 0.765453i | \(0.277485\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 12.9467 | 0.509774 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −46.8621 | −1.84234 | −0.921170 | − | 0.389160i | \(-0.872765\pi\) | ||||
−0.921170 | + | 0.389160i | \(0.872765\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −8.22916 | −0.323023 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.61357 | −0.0632409 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.8948 | 0.935074 | 0.467537 | − | 0.883973i | \(-0.345141\pi\) | ||||
0.467537 | + | 0.883973i | \(0.345141\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 44.2812 | 1.73021 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −10.6726 | −0.416379 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.6400 | −0.687157 | −0.343578 | − | 0.939124i | \(-0.611639\pi\) | ||||
−0.343578 | + | 0.939124i | \(0.611639\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.1256 | 0.860586 | 0.430293 | − | 0.902689i | \(-0.358410\pi\) | ||||
0.430293 | + | 0.902689i | \(0.358410\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.2357 | 0.397522 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 32.7864 | 1.27140 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.3690 | 1.75670 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −12.8598 | −0.497187 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.60512 | −0.139174 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.63999 | −0.294500 | −0.147250 | − | 0.989099i | \(-0.547042\pi\) | ||||
−0.147250 | + | 0.989099i | \(0.547042\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 77.7064 | 2.99092 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.6006 | 0.868611 | 0.434305 | − | 0.900766i | \(-0.356994\pi\) | ||||
0.434305 | + | 0.900766i | \(0.356994\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.3290 | −0.434769 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.9564 | 0.611451 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.4414 | 1.70050 | 0.850252 | − | 0.526376i | \(-0.176450\pi\) | ||||
0.850252 | + | 0.526376i | \(0.176450\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 81.5633 | 3.11637 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 21.4255 | 0.817432 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 11.7155 | 0.446324 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 47.1249 | 1.79271 | 0.896357 | − | 0.443333i | \(-0.146204\pi\) | ||||
0.896357 | + | 0.443333i | \(0.146204\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.73143 | 0.0657716 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −12.8502 | −0.487437 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.40692 | 0.0911687 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 14.7578 | 0.558193 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −23.6536 | −0.893382 | −0.446691 | − | 0.894688i | \(-0.647398\pi\) | ||||
−0.446691 | + | 0.894688i | \(0.647398\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −5.41928 | −0.204392 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.75382 | −0.179039 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.24511 | 0.197263 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.73143 | −0.177693 | −0.0888463 | − | 0.996045i | \(-0.528318\pi\) | ||||
−0.0888463 | + | 0.996045i | \(0.528318\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.8769 | −0.632934 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.14025 | −0.267404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.9212 | −0.969397 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 23.7852 | 0.888275 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4.14356 | 0.154529 | 0.0772643 | − | 0.997011i | \(-0.475381\pi\) | ||||
0.0772643 | + | 0.997011i | \(0.475381\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.6543 | 0.694722 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 27.8364 | 1.03525 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −132.735 | −4.92964 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 51.1331 | 1.89642 | 0.948211 | − | 0.317642i | \(-0.102891\pi\) | ||||
0.948211 | + | 0.317642i | \(0.102891\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.4052 | 0.718711 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.03001 | 0.149055 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.7685 | 1.28420 | 0.642101 | − | 0.766620i | \(-0.278063\pi\) | ||||
0.642101 | + | 0.766620i | \(0.278063\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.98405 | −0.183839 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.32905 | 0.343640 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −47.0995 | −1.73258 | −0.866292 | − | 0.499538i | \(-0.833503\pi\) | ||||
−0.866292 | + | 0.499538i | \(0.833503\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −48.8828 | −1.79576 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.12832 | −0.224826 | −0.112413 | − | 0.993662i | \(-0.535858\pi\) | ||||
−0.112413 | + | 0.993662i | \(0.535858\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −71.7121 | −2.62733 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 18.2820 | 0.668905 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 13.3555 | 0.487998 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.8902 | 1.05422 | 0.527110 | − | 0.849797i | \(-0.323276\pi\) | ||||
0.527110 | + | 0.849797i | \(0.323276\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 19.3576 | 0.705431 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 24.9576 | 0.908301 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.7140 | −1.15267 | −0.576333 | − | 0.817215i | \(-0.695517\pi\) | ||||
−0.576333 | + | 0.817215i | \(0.695517\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.61357 | −0.203760 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.7981 | 0.427681 | 0.213841 | − | 0.976869i | \(-0.431403\pi\) | ||||
0.213841 | + | 0.976869i | \(0.431403\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.44785 | −0.342035 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 11.8867 | 0.429764 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 48.2043 | 1.74055 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 42.2305 | 1.52287 | 0.761435 | − | 0.648242i | \(-0.224495\pi\) | ||||
0.761435 | + | 0.648242i | \(0.224495\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.6431 | −1.03156 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 5.86156 | 0.210826 | 0.105413 | − | 0.994429i | \(-0.466384\pi\) | ||||
0.105413 | + | 0.994429i | \(0.466384\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.8900 | 0.750391 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.823815 | 0.0295542 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −11.4948 | −0.411843 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.478813 | −0.0171333 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −48.5095 | −1.73359 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.06546 | −0.109411 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.32132 | −0.225331 | −0.112665 | − | 0.993633i | \(-0.535939\pi\) | ||||
−0.112665 | + | 0.993633i | \(0.535939\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.07858 | 0.0383986 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.5817 | −0.482908 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 21.1179 | 0.749917 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −9.96809 | −0.353532 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 18.5534 | 0.657197 | 0.328598 | − | 0.944470i | \(-0.393424\pi\) | ||||
0.328598 | + | 0.944470i | \(0.393424\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.47976 | −0.0523502 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.13142 | −0.251976 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.16405 | −0.217525 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −22.0550 | −0.777336 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −7.69094 | −0.270734 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.1817 | −0.815024 | −0.407512 | − | 0.913200i | \(-0.633604\pi\) | ||||
−0.407512 | + | 0.913200i | \(0.633604\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.5451 | −1.31839 | −0.659194 | − | 0.751973i | \(-0.729102\pi\) | ||||
−0.659194 | + | 0.751973i | \(0.729102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 20.3057 | 0.712153 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 71.7785 | 2.51429 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.2462 | −0.673339 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.1423 | −0.354399 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −20.7109 | −0.722817 | −0.361408 | − | 0.932408i | \(-0.617704\pi\) | ||||
−0.361408 | + | 0.932408i | \(0.617704\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.3988 | 0.467052 | 0.233526 | − | 0.972351i | \(-0.424974\pi\) | ||||
0.233526 | + | 0.972351i | \(0.424974\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 16.4234 | 0.571791 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.8364 | 1.10706 | 0.553531 | − | 0.832829i | \(-0.313280\pi\) | ||||
0.553531 | + | 0.832829i | \(0.313280\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −13.8444 | −0.480836 | −0.240418 | − | 0.970669i | \(-0.577284\pi\) | ||||
−0.240418 | + | 0.970669i | \(0.577284\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.11022 | 0.177272 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.55143 | −0.0537537 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −56.8638 | −1.96785 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.63450 | 0.263887 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.9078 | 0.618247 | 0.309124 | − | 0.951022i | \(-0.399964\pi\) | ||||
0.309124 | + | 0.951022i | \(0.399964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 53.8619 | 1.85731 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.5540 | −0.363501 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 94.3129 | 3.24446 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.00000 | 0.0343604 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.51260 | 0.0862322 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.64548 | 0.124965 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 11.1058 | 0.380256 | 0.190128 | − | 0.981759i | \(-0.439110\pi\) | ||||
0.190128 | + | 0.981759i | \(0.439110\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −56.7674 | −1.94140 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.4048 | 1.55100 | 0.775499 | − | 0.631349i | \(-0.217499\pi\) | ||||
0.775499 | + | 0.631349i | \(0.217499\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.6711 | −0.671169 | −0.335584 | − | 0.942010i | \(-0.608934\pi\) | ||||
−0.335584 | + | 0.942010i | \(0.608934\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.74738 | 0.0595507 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.92572 | −0.0995926 | −0.0497963 | − | 0.998759i | \(-0.515857\pi\) | ||||
−0.0497963 | + | 0.998759i | \(0.515857\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −57.8274 | −1.96619 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.4363 | 0.558206 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.74738 | −0.330657 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −54.6471 | −1.85165 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 19.6155 | 0.663882 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 42.4000 | 1.43338 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.3521 | 0.923616 | 0.461808 | − | 0.886980i | \(-0.347201\pi\) | ||||
0.461808 | + | 0.886980i | \(0.347201\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.2195 | −0.783174 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.6722 | −0.864917 | −0.432458 | − | 0.901654i | \(-0.642354\pi\) | ||||
−0.432458 | + | 0.901654i | \(0.642354\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.63665 | 0.324299 | 0.162150 | − | 0.986766i | \(-0.448157\pi\) | ||||
0.162150 | + | 0.986766i | \(0.448157\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −41.0145 | −1.37869 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 43.2902 | 1.45354 | 0.726772 | − | 0.686879i | \(-0.241020\pi\) | ||||
0.726772 | + | 0.686879i | \(0.241020\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.35547 | −0.0454609 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.807862 | 0.0270644 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.06691 | 0.236485 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −52.4345 | −1.75269 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.8828 | 1.09793 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.0409 | −0.434939 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.10285 | −0.103371 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.92572 | 0.0973618 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.3121 | −1.10733 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.9107 | 1.09278 | 0.546391 | − | 0.837530i | \(-0.316001\pi\) | ||||
0.546391 | + | 0.837530i | \(0.316001\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −9.08155 | −0.301216 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.3086 | −0.971036 | −0.485518 | − | 0.874227i | \(-0.661369\pi\) | ||||
−0.485518 | + | 0.874227i | \(0.661369\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.5589 | 0.349450 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −17.9681 | −0.594007 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.0068 | 0.330453 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 25.1314 | 0.829009 | 0.414505 | − | 0.910047i | \(-0.363955\pi\) | ||||
0.414505 | + | 0.910047i | \(0.363955\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 28.9031 | 0.952389 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 2.80476 | 0.0923199 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.6655 | −0.350678 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −32.2986 | −1.06082 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 37.4369 | 1.22826 | 0.614132 | − | 0.789203i | \(-0.289506\pi\) | ||||
0.614132 | + | 0.789203i | \(0.289506\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.40916 | 0.242826 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −20.5624 | −0.673182 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.86524 | 0.224517 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.17641 | 0.0384317 | 0.0192158 | − | 0.999815i | \(-0.493883\pi\) | ||||
0.0192158 | + | 0.999815i | \(0.493883\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.4033 | −0.861640 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.0361 | 1.14214 | 0.571072 | − | 0.820900i | \(-0.306528\pi\) | ||||
0.571072 | + | 0.820900i | \(0.306528\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.73238 | 0.251801 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 23.5817 | 0.767112 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46.1459 | −1.49954 | −0.749771 | − | 0.661698i | \(-0.769836\pi\) | ||||
−0.749771 | + | 0.661698i | \(0.769836\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.1074 | 1.17210 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.71763 | 0.185407 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.52667 | 0.114240 | 0.0571201 | − | 0.998367i | \(-0.481808\pi\) | ||||
0.0571201 | + | 0.998367i | \(0.481808\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −107.639 | −3.48311 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10.2526 | −0.331420 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 18.4319 | 0.595197 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9476 | −0.933793 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −23.1241 | −0.745162 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −36.7864 | −1.18420 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.34046 | 0.236053 | 0.118027 | − | 0.993010i | \(-0.462343\pi\) | ||||
0.118027 | + | 0.993010i | \(0.462343\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 12.9467 | 0.415906 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.5254 | 1.36470 | 0.682352 | − | 0.731024i | \(-0.260957\pi\) | ||||
0.682352 | + | 0.731024i | \(0.260957\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.90393 | −0.0930957 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −96.2043 | −3.08100 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −43.8812 | −1.40388 | −0.701942 | − | 0.712234i | \(-0.747683\pi\) | ||||
−0.701942 | + | 0.712234i | \(0.747683\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.11881 | −0.131638 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.3583 | 0.522280 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.5993 | 0.401855 | 0.200927 | − | 0.979606i | \(-0.435604\pi\) | ||||
0.200927 | + | 0.979606i | \(0.435604\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −46.9621 | −1.49634 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −1.07428 | −0.0341947 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.9467 | 0.411680 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 23.5443 | 0.747908 | 0.373954 | − | 0.927447i | \(-0.378002\pi\) | ||||
0.373954 | + | 0.927447i | \(0.378002\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.80691 | −0.279479 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −31.1802 | −0.988480 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −11.7654 | −0.372612 | −0.186306 | − | 0.982492i | \(-0.559652\pi\) | ||||
−0.186306 | + | 0.982492i | \(0.559652\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −3.89782 | −0.123322 |
(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 | 1232.2.a.s.1.2 | 4 | ||
4.3 | odd | 2 | 616.2.a.h.1.3 | ✓ | 4 | ||
7.6 | odd | 2 | 8624.2.a.cy.1.3 | 4 | |||
8.3 | odd | 2 | 4928.2.a.cc.1.2 | 4 | |||
8.5 | even | 2 | 4928.2.a.ch.1.3 | 4 | |||
12.11 | even | 2 | 5544.2.a.bm.1.1 | 4 | |||
28.27 | even | 2 | 4312.2.a.z.1.2 | 4 | |||
44.43 | even | 2 | 6776.2.a.bb.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
616.2.a.h.1.3 | ✓ | 4 | 4.3 | odd | 2 | ||
1232.2.a.s.1.2 | 4 | 1.1 | even | 1 | trivial | ||
4312.2.a.z.1.2 | 4 | 28.27 | even | 2 | |||
4928.2.a.cc.1.2 | 4 | 8.3 | odd | 2 | |||
4928.2.a.ch.1.3 | 4 | 8.5 | even | 2 | |||
5544.2.a.bm.1.1 | 4 | 12.11 | even | 2 | |||
6776.2.a.bb.1.3 | 4 | 44.43 | even | 2 | |||
8624.2.a.cy.1.3 | 4 | 7.6 | odd | 2 |