Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,3,Mod(415,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.415");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.m (of order \(4\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(31.3897264543\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6x^{14} + 10x^{12} + 88x^{10} - 752x^{8} + 1408x^{6} + 2560x^{4} - 24576x^{2} + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 144) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 415.1 | ||
Root | \(-1.99750 + 0.0999235i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.415 |
Dual form | 1152.3.m.d.991.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.01265 | − | 6.01265i | −1.20253 | − | 1.20253i | −0.973394 | − | 0.229136i | \(-0.926410\pi\) |
−0.229136 | − | 0.973394i | \(-0.573590\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.23187 | −1.17598 | −0.587990 | − | 0.808868i | \(-0.700081\pi\) | ||||
−0.587990 | + | 0.808868i | \(0.700081\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −6.51529 | + | 6.51529i | −0.592299 | + | 0.592299i | −0.938252 | − | 0.345953i | \(-0.887556\pi\) |
0.345953 | + | 0.938252i | \(0.387556\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −8.82865 | + | 8.82865i | −0.679127 | + | 0.679127i | −0.959803 | − | 0.280676i | \(-0.909441\pi\) |
0.280676 | + | 0.959803i | \(0.409441\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 14.1753 | 0.833844 | 0.416922 | − | 0.908942i | \(-0.363109\pi\) | ||||
0.416922 | + | 0.908942i | \(0.363109\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −23.7488 | − | 23.7488i | −1.24994 | − | 1.24994i | −0.955748 | − | 0.294187i | \(-0.904951\pi\) |
−0.294187 | − | 0.955748i | \(-0.595049\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −9.42125 | −0.409619 | −0.204810 | − | 0.978802i | \(-0.565658\pi\) | ||||
−0.204810 | + | 0.978802i | \(0.565658\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 47.3040i | 1.89216i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 23.7973 | − | 23.7973i | 0.820598 | − | 0.820598i | −0.165596 | − | 0.986194i | \(-0.552955\pi\) |
0.986194 | + | 0.165596i | \(0.0529547\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 24.4148i | 0.787575i | 0.919202 | + | 0.393787i | \(0.128835\pi\) | ||||
−0.919202 | + | 0.393787i | \(0.871165\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 49.4954 | + | 49.4954i | 1.41415 | + | 1.41415i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −24.2052 | − | 24.2052i | −0.654193 | − | 0.654193i | 0.299807 | − | 0.954000i | \(-0.403078\pi\) |
−0.954000 | + | 0.299807i | \(0.903078\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.67771i | 0.162871i | 0.996679 | + | 0.0814355i | \(0.0259505\pi\) | ||||
−0.996679 | + | 0.0814355i | \(0.974050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.897918 | − | 0.897918i | 0.0208818 | − | 0.0208818i | −0.696589 | − | 0.717471i | \(-0.745300\pi\) |
0.717471 | + | 0.696589i | \(0.245300\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 25.2401i | 0.537023i | 0.963276 | + | 0.268512i | \(0.0865318\pi\) | ||||
−0.963276 | + | 0.268512i | \(0.913468\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 18.7636 | 0.382931 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 32.6251 | + | 32.6251i | 0.615568 | + | 0.615568i | 0.944391 | − | 0.328824i | \(-0.106652\pi\) |
−0.328824 | + | 0.944391i | \(0.606652\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 78.3484 | 1.42452 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 8.31871 | − | 8.31871i | 0.140995 | − | 0.140995i | −0.633086 | − | 0.774081i | \(-0.718212\pi\) |
0.774081 | + | 0.633086i | \(0.218212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 68.4028 | − | 68.4028i | 1.12136 | − | 1.12136i | 0.129820 | − | 0.991538i | \(-0.458560\pi\) |
0.991538 | − | 0.129820i | \(-0.0414399\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 106.167 | 1.63334 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.71922 | − | 7.71922i | −0.115212 | − | 0.115212i | 0.647150 | − | 0.762362i | \(-0.275961\pi\) |
−0.762362 | + | 0.647150i | \(0.775961\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 137.259 | 1.93322 | 0.966612 | − | 0.256245i | \(-0.0824853\pi\) | ||||
0.966612 | + | 0.256245i | \(0.0824853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 52.8655i | − | 0.724185i | −0.932142 | − | 0.362093i | \(-0.882062\pi\) | ||
0.932142 | − | 0.362093i | \(-0.117938\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 53.6330 | − | 53.6330i | 0.696533 | − | 0.696533i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 87.2269i | 1.10414i | 0.833798 | + | 0.552069i | \(0.186162\pi\) | ||||
−0.833798 | + | 0.552069i | \(0.813838\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −9.53893 | − | 9.53893i | −0.114927 | − | 0.114927i | 0.647305 | − | 0.762231i | \(-0.275896\pi\) |
−0.762231 | + | 0.647305i | \(0.775896\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −85.2314 | − | 85.2314i | −1.00272 | − | 1.00272i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 146.488i | − | 1.64593i | −0.568089 | − | 0.822967i | \(-0.692317\pi\) | ||
0.568089 | − | 0.822967i | \(-0.307683\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 72.6762 | − | 72.6762i | 0.798640 | − | 0.798640i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 285.586i | 3.00617i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 101.170 | 1.04298 | 0.521492 | − | 0.853256i | \(-0.325376\pi\) | ||||
0.521492 | + | 0.853256i | \(0.325376\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 47.4912 | + | 47.4912i | 0.470210 | + | 0.470210i | 0.901982 | − | 0.431773i | \(-0.142112\pi\) |
−0.431773 | + | 0.901982i | \(0.642112\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.58518 | −0.0736425 | −0.0368213 | − | 0.999322i | \(-0.511723\pi\) | ||||
−0.0368213 | + | 0.999322i | \(0.511723\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −119.757 | + | 119.757i | −1.11922 | + | 1.11922i | −0.127367 | + | 0.991856i | \(0.540653\pi\) |
−0.991856 | + | 0.127367i | \(0.959347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −61.0263 | + | 61.0263i | −0.559874 | + | 0.559874i | −0.929272 | − | 0.369397i | \(-0.879564\pi\) |
0.369397 | + | 0.929272i | \(0.379564\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 31.6377 | 0.279980 | 0.139990 | − | 0.990153i | \(-0.455293\pi\) | ||||
0.139990 | + | 0.990153i | \(0.455293\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 56.6467 | + | 56.6467i | 0.492580 | + | 0.492580i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −116.690 | −0.980585 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 36.1019i | 0.298363i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 134.106 | − | 134.106i | 1.07285 | − | 1.07285i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 87.8736i | − | 0.691918i | −0.938250 | − | 0.345959i | \(-0.887554\pi\) | ||
0.938250 | − | 0.345959i | \(-0.112446\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 176.351 | + | 176.351i | 1.34619 | + | 1.34619i | 0.889761 | + | 0.456428i | \(0.150871\pi\) |
0.456428 | + | 0.889761i | \(0.349129\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 195.497 | + | 195.497i | 1.46990 | + | 1.46990i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 97.0224i | − | 0.708192i | −0.935209 | − | 0.354096i | \(-0.884789\pi\) | ||
0.935209 | − | 0.354096i | \(-0.115211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −130.221 | + | 130.221i | −0.936841 | + | 0.936841i | −0.998121 | − | 0.0612800i | \(-0.980482\pi\) |
0.0612800 | + | 0.998121i | \(0.480482\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 115.042i | − | 0.804493i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −286.170 | −1.97359 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 26.3592 | + | 26.3592i | 0.176907 | + | 0.176907i | 0.790006 | − | 0.613099i | \(-0.210077\pi\) |
−0.613099 | + | 0.790006i | \(0.710077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −196.107 | −1.29872 | −0.649360 | − | 0.760481i | \(-0.724963\pi\) | ||||
−0.649360 | + | 0.760481i | \(0.724963\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 146.798 | − | 146.798i | 0.947083 | − | 0.947083i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −98.5323 | + | 98.5323i | −0.627594 | + | 0.627594i | −0.947462 | − | 0.319868i | \(-0.896362\pi\) |
0.319868 | + | 0.947462i | \(0.396362\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 77.5545 | 0.481705 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −90.6677 | − | 90.6677i | −0.556244 | − | 0.556244i | 0.371992 | − | 0.928236i | \(-0.378675\pi\) |
−0.928236 | + | 0.371992i | \(0.878675\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 181.602 | 1.08744 | 0.543719 | − | 0.839267i | \(-0.317016\pi\) | ||||
0.543719 | + | 0.839267i | \(0.317016\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.1100i | 0.0775741i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.66532 | − | 2.66532i | 0.0154065 | − | 0.0154065i | −0.699362 | − | 0.714768i | \(-0.746532\pi\) |
0.714768 | + | 0.699362i | \(0.246532\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 389.400i | − | 2.22514i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.7491 | − | 12.7491i | −0.0712241 | − | 0.0712241i | 0.670597 | − | 0.741822i | \(-0.266038\pi\) |
−0.741822 | + | 0.670597i | \(0.766038\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 61.3009 | + | 61.3009i | 0.338679 | + | 0.338679i | 0.855870 | − | 0.517191i | \(-0.173022\pi\) |
−0.517191 | + | 0.855870i | \(0.673022\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 291.074i | 1.57338i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −92.3566 | + | 92.3566i | −0.493885 | + | 0.493885i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 80.1204i | 0.419479i | 0.977757 | + | 0.209739i | \(0.0672615\pi\) | ||||
−0.977757 | + | 0.209739i | \(0.932738\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 28.7555 | 0.148992 | 0.0744961 | − | 0.997221i | \(-0.476265\pi\) | ||||
0.0744961 | + | 0.997221i | \(0.476265\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −92.8030 | − | 92.8030i | −0.471081 | − | 0.471081i | 0.431183 | − | 0.902264i | \(-0.358096\pi\) |
−0.902264 | + | 0.431183i | \(0.858096\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −165.555 | −0.831934 | −0.415967 | − | 0.909380i | \(-0.636557\pi\) | ||||
−0.415967 | + | 0.909380i | \(0.636557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −195.897 | + | 195.897i | −0.965008 | + | 0.965008i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 40.1507 | − | 40.1507i | 0.195857 | − | 0.195857i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 309.460 | 1.48067 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 187.769 | + | 187.769i | 0.889902 | + | 0.889902i | 0.994513 | − | 0.104611i | \(-0.0333598\pi\) |
−0.104611 | + | 0.994513i | \(0.533360\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −10.7977 | −0.0502220 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 200.980i | − | 0.926173i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −125.149 | + | 125.149i | −0.566286 | + | 0.566286i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 307.192i | 1.37754i | 0.724979 | + | 0.688771i | \(0.241849\pi\) | ||||
−0.724979 | + | 0.688771i | \(0.758151\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 112.960 | + | 112.960i | 0.497621 | + | 0.497621i | 0.910697 | − | 0.413075i | \(-0.135545\pi\) |
−0.413075 | + | 0.910697i | \(0.635545\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.32210 | + | 7.32210i | 0.0319742 | + | 0.0319742i | 0.722913 | − | 0.690939i | \(-0.242803\pi\) |
−0.690939 | + | 0.722913i | \(0.742803\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 115.408i | 0.495315i | 0.968848 | + | 0.247657i | \(0.0796607\pi\) | ||||
−0.968848 | + | 0.247657i | \(0.920339\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 151.760 | − | 151.760i | 0.645787 | − | 0.645787i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 323.271i | − | 1.35260i | −0.736627 | − | 0.676300i | \(-0.763583\pi\) | ||
0.736627 | − | 0.676300i | \(-0.236417\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 118.056 | 0.489860 | 0.244930 | − | 0.969541i | \(-0.421235\pi\) | ||||
0.244930 | + | 0.969541i | \(0.421235\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −112.819 | − | 112.819i | −0.460486 | − | 0.460486i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 419.339 | 1.69773 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 166.229 | − | 166.229i | 0.662265 | − | 0.662265i | −0.293648 | − | 0.955913i | \(-0.594870\pi\) |
0.955913 | + | 0.293648i | \(0.0948695\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 61.3822 | − | 61.3822i | 0.242617 | − | 0.242617i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −342.745 | −1.33364 | −0.666820 | − | 0.745219i | \(-0.732345\pi\) | ||||
−0.666820 | + | 0.745219i | \(0.732345\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 199.254 | + | 199.254i | 0.769319 | + | 0.769319i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −219.637 | −0.835123 | −0.417562 | − | 0.908649i | \(-0.637115\pi\) | ||||
−0.417562 | + | 0.908649i | \(0.637115\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 392.327i | − | 1.48048i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 77.9061 | − | 77.9061i | 0.289614 | − | 0.289614i | −0.547314 | − | 0.836928i | \(-0.684350\pi\) |
0.836928 | + | 0.547314i | \(0.184350\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 155.092i | − | 0.572294i | −0.958186 | − | 0.286147i | \(-0.907625\pi\) | ||
0.958186 | − | 0.286147i | \(-0.0923746\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −308.199 | − | 308.199i | −1.12072 | − | 1.12072i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.0601 | + | 30.0601i | 0.108520 | + | 0.108520i | 0.759282 | − | 0.650762i | \(-0.225550\pi\) |
−0.650762 | + | 0.759282i | \(0.725550\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 265.590i | − | 0.945162i | −0.881287 | − | 0.472581i | \(-0.843323\pi\) | ||
0.881287 | − | 0.472581i | \(-0.156677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 160.221 | − | 160.221i | 0.566153 | − | 0.566153i | −0.364895 | − | 0.931049i | \(-0.618895\pi\) |
0.931049 | + | 0.364895i | \(0.118895\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 54.9700i | − | 0.191533i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −88.0595 | −0.304704 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 173.762 | + | 173.762i | 0.593044 | + | 0.593044i | 0.938453 | − | 0.345408i | \(-0.112260\pi\) |
−0.345408 | + | 0.938453i | \(0.612260\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −100.035 | −0.339102 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 83.1769 | − | 83.1769i | 0.278183 | − | 0.278183i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.39154 | + | 7.39154i | −0.0245566 | + | 0.0245566i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −822.565 | −2.69693 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 136.842 | + | 136.842i | 0.445741 | + | 0.445741i | 0.893936 | − | 0.448195i | \(-0.147933\pi\) |
−0.448195 | + | 0.893936i | \(0.647933\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −458.117 | −1.47305 | −0.736523 | − | 0.676412i | \(-0.763534\pi\) | ||||
−0.736523 | + | 0.676412i | \(0.763534\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 170.865i | 0.545893i | 0.962029 | + | 0.272947i | \(0.0879982\pi\) | ||||
−0.962029 | + | 0.272947i | \(0.912002\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −372.560 | + | 372.560i | −1.17527 | + | 1.17527i | −0.194334 | + | 0.980935i | \(0.562254\pi\) |
−0.980935 | + | 0.194334i | \(0.937746\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 310.093i | 0.972079i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −336.647 | − | 336.647i | −1.04225 | − | 1.04225i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −417.630 | − | 417.630i | −1.28502 | − | 1.28502i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 207.773i | − | 0.631529i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −177.685 | + | 177.685i | −0.536812 | + | 0.536812i | −0.922591 | − | 0.385779i | \(-0.873933\pi\) |
0.385779 | + | 0.922591i | \(0.373933\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 92.8260i | 0.277092i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 491.680 | 1.45899 | 0.729496 | − | 0.683985i | \(-0.239755\pi\) | ||||
0.729496 | + | 0.683985i | \(0.239755\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −159.070 | − | 159.070i | −0.466480 | − | 0.466480i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 248.902 | 0.725661 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −176.788 | + | 176.788i | −0.509477 | + | 0.509477i | −0.914366 | − | 0.404889i | \(-0.867310\pi\) |
0.404889 | + | 0.914366i | \(0.367310\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 272.298 | − | 272.298i | 0.780223 | − | 0.780223i | −0.199645 | − | 0.979868i | \(-0.563979\pi\) |
0.979868 | + | 0.199645i | \(0.0639789\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −168.099 | −0.476200 | −0.238100 | − | 0.971241i | \(-0.576525\pi\) | ||||
−0.238100 | + | 0.971241i | \(0.576525\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −825.290 | − | 825.290i | −2.32476 | − | 2.32476i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 476.009 | 1.32593 | 0.662965 | − | 0.748651i | \(-0.269298\pi\) | ||||
0.662965 | + | 0.748651i | \(0.269298\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 767.008i | 2.12468i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −317.862 | + | 317.862i | −0.870855 | + | 0.870855i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 104.894i | 0.285814i | 0.989736 | + | 0.142907i | \(0.0456450\pi\) | ||||
−0.989736 | + | 0.142907i | \(0.954355\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −268.565 | − | 268.565i | −0.723896 | − | 0.723896i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 122.301 | + | 122.301i | 0.327884 | + | 0.327884i | 0.851781 | − | 0.523898i | \(-0.175523\pi\) |
−0.523898 | + | 0.851781i | \(0.675523\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 420.197i | 1.11458i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 75.5625 | − | 75.5625i | 0.199373 | − | 0.199373i | −0.600358 | − | 0.799731i | \(-0.704975\pi\) |
0.799731 | + | 0.600358i | \(0.204975\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 501.509i | − | 1.30942i | −0.755878 | − | 0.654712i | \(-0.772790\pi\) | ||
0.755878 | − | 0.654712i | \(-0.227210\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −644.953 | −1.67520 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.6053 | + | 22.6053i | 0.0581114 | + | 0.0581114i | 0.735565 | − | 0.677454i | \(-0.236917\pi\) |
−0.677454 | + | 0.735565i | \(0.736917\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −133.549 | −0.341559 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 524.465 | − | 524.465i | 1.32776 | − | 1.32776i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.09563 | − | 6.09563i | 0.0153542 | − | 0.0153542i | −0.699388 | − | 0.714742i | \(-0.746544\pi\) |
0.714742 | + | 0.699388i | \(0.246544\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 598.130 | 1.49160 | 0.745798 | − | 0.666172i | \(-0.232068\pi\) | ||||
0.745798 | + | 0.666172i | \(0.232068\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −215.550 | − | 215.550i | −0.534863 | − | 0.534863i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 315.407 | 0.774957 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 271.241i | 0.663181i | 0.943423 | + | 0.331591i | \(0.107585\pi\) | ||||
−0.943423 | + | 0.331591i | \(0.892415\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −68.4785 | + | 68.4785i | −0.165808 | + | 0.165808i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 114.709i | 0.276406i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −412.163 | − | 412.163i | −0.983681 | − | 0.983681i | 0.0161876 | − | 0.999869i | \(-0.494847\pi\) |
−0.999869 | + | 0.0161876i | \(0.994847\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −135.609 | − | 135.609i | −0.322111 | − | 0.322111i | 0.527466 | − | 0.849576i | \(-0.323142\pi\) |
−0.849576 | + | 0.527466i | \(0.823142\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 670.550i | 1.57777i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −563.083 | + | 563.083i | −1.31869 | + | 1.31869i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 204.169i | − | 0.473710i | −0.971545 | − | 0.236855i | \(-0.923883\pi\) | ||
0.971545 | − | 0.236855i | \(-0.0761166\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 317.530 | 0.733325 | 0.366663 | − | 0.930354i | \(-0.380500\pi\) | ||||
0.366663 | + | 0.930354i | \(0.380500\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 223.743 | + | 223.743i | 0.511998 | + | 0.511998i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −226.050 | −0.514921 | −0.257461 | − | 0.966289i | \(-0.582886\pi\) | ||||
−0.257461 | + | 0.966289i | \(0.582886\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −157.388 | + | 157.388i | −0.355278 | + | 0.355278i | −0.862069 | − | 0.506791i | \(-0.830831\pi\) |
0.506791 | + | 0.862069i | \(0.330831\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −880.782 | + | 880.782i | −1.97929 | + | 1.97929i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −458.567 | −1.02131 | −0.510653 | − | 0.859787i | \(-0.670596\pi\) | ||||
−0.510653 | + | 0.859787i | \(0.670596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −43.5072 | − | 43.5072i | −0.0964684 | − | 0.0964684i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −873.954 | −1.92078 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 548.682i | 1.20062i | 0.799768 | + | 0.600309i | \(0.204956\pi\) | ||||
−0.799768 | + | 0.600309i | \(0.795044\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −359.058 | + | 359.058i | −0.778868 | + | 0.778868i | −0.979638 | − | 0.200770i | \(-0.935656\pi\) |
0.200770 | + | 0.979638i | \(0.435656\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 126.697i | − | 0.273643i | −0.990596 | − | 0.136822i | \(-0.956311\pi\) | ||
0.990596 | − | 0.136822i | \(-0.0436887\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 526.834 | + | 526.834i | 1.12812 | + | 1.12812i | 0.990482 | + | 0.137643i | \(0.0439527\pi\) |
0.137643 | + | 0.990482i | \(0.456047\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 63.5436 | + | 63.5436i | 0.135487 | + | 0.135487i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.7004i | 0.0247366i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1123.41 | − | 1123.41i | 2.36508 | − | 2.36508i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 712.831i | − | 1.48817i | −0.668087 | − | 0.744083i | \(-0.732887\pi\) | ||
0.668087 | − | 0.744083i | \(-0.267113\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 427.398 | 0.888560 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −608.297 | − | 608.297i | −1.25422 | − | 1.25422i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −579.851 | −1.19066 | −0.595330 | − | 0.803481i | \(-0.702979\pi\) | ||||
−0.595330 | + | 0.803481i | \(0.702979\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 131.309 | − | 131.309i | 0.267432 | − | 0.267432i | −0.560632 | − | 0.828065i | \(-0.689442\pi\) |
0.828065 | + | 0.560632i | \(0.189442\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 337.336 | − | 337.336i | 0.684251 | − | 0.684251i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1129.90 | −2.27343 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 329.208 | + | 329.208i | 0.659736 | + | 0.659736i | 0.955318 | − | 0.295582i | \(-0.0955134\pi\) |
−0.295582 | + | 0.955318i | \(0.595513\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 254.299 | 0.505564 | 0.252782 | − | 0.967523i | \(-0.418654\pi\) | ||||
0.252782 | + | 0.967523i | \(0.418654\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 571.096i | − | 1.13088i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 326.512 | − | 326.512i | 0.641477 | − | 0.641477i | −0.309442 | − | 0.950918i | \(-0.600142\pi\) |
0.950918 | + | 0.309442i | \(0.100142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 435.182i | 0.851628i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 45.6071 | + | 45.6071i | 0.0885574 | + | 0.0885574i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −164.447 | − | 164.447i | −0.318079 | − | 0.318079i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 775.042i | − | 1.48760i | −0.668400 | − | 0.743802i | \(-0.733020\pi\) | ||
0.668400 | − | 0.743802i | \(-0.266980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −461.875 | + | 461.875i | −0.883126 | + | 0.883126i | −0.993851 | − | 0.110725i | \(-0.964683\pi\) |
0.110725 | + | 0.993851i | \(0.464683\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 346.089i | 0.656715i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −440.240 | −0.832212 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −58.9551 | − | 58.9551i | −0.110610 | − | 0.110610i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1440.11 | 2.69180 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −122.251 | + | 122.251i | −0.226810 | + | 0.226810i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 426.071 | − | 426.071i | 0.787563 | − | 0.787563i | −0.193531 | − | 0.981094i | \(-0.561994\pi\) |
0.981094 | + | 0.193531i | \(0.0619941\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 733.860 | 1.34653 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −111.138 | − | 111.138i | −0.203178 | − | 0.203178i | 0.598182 | − | 0.801360i | \(-0.295890\pi\) |
−0.801360 | + | 0.598182i | \(0.795890\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1130.32 | −2.05139 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 718.041i | − | 1.29845i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 233.731 | − | 233.731i | 0.419625 | − | 0.419625i | −0.465449 | − | 0.885075i | \(-0.654107\pi\) |
0.885075 | + | 0.465449i | \(0.154107\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 15.8548i | 0.0283628i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 261.362 | + | 261.362i | 0.464231 | + | 0.464231i | 0.900039 | − | 0.435809i | \(-0.143538\pi\) |
−0.435809 | + | 0.900039i | \(0.643538\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −190.227 | − | 190.227i | −0.336684 | − | 0.336684i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 453.881i | 0.797682i | 0.917020 | + | 0.398841i | \(0.130587\pi\) | ||||
−0.917020 | + | 0.398841i | \(0.869413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −289.009 | + | 289.009i | −0.506146 | + | 0.506146i | −0.913341 | − | 0.407195i | \(-0.866507\pi\) |
0.407195 | + | 0.913341i | \(0.366507\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 445.662i | − | 0.775065i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 588.041 | 1.01913 | 0.509567 | − | 0.860431i | \(-0.329806\pi\) | ||||
0.509567 | + | 0.860431i | \(0.329806\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 78.5232 | + | 78.5232i | 0.135152 | + | 0.135152i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −425.124 | −0.729201 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −392.596 | + | 392.596i | −0.668818 | + | 0.668818i | −0.957442 | − | 0.288624i | \(-0.906802\pi\) |
0.288624 | + | 0.957442i | \(0.406802\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 579.822 | − | 579.822i | 0.984417 | − | 0.984417i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 1008.70 | 1.70101 | 0.850505 | − | 0.525967i | \(-0.176297\pi\) | ||||
0.850505 | + | 0.525967i | \(0.176297\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 701.614 | + | 701.614i | 1.17918 | + | 1.17918i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 526.819 | 0.879498 | 0.439749 | − | 0.898121i | \(-0.355067\pi\) | ||||
0.439749 | + | 0.898121i | \(0.355067\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 867.891i | − | 1.44408i | −0.691853 | − | 0.722039i | \(-0.743205\pi\) | ||
0.691853 | − | 0.722039i | \(-0.256795\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 217.068 | − | 217.068i | 0.358790 | − | 0.358790i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 98.8497i | − | 0.162850i | −0.996679 | − | 0.0814248i | \(-0.974053\pi\) | ||
0.996679 | − | 0.0814248i | \(-0.0259470\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −222.836 | − | 222.836i | −0.364707 | − | 0.364707i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 616.976 | + | 616.976i | 1.00649 | + | 1.00649i | 0.999979 | + | 0.00650651i | \(0.00207110\pi\) |
0.00650651 | + | 0.999979i | \(0.497929\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1073.62i | 1.74007i | 0.492993 | + | 0.870033i | \(0.335903\pi\) | ||||
−0.492993 | + | 0.870033i | \(0.664097\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 397.119 | − | 397.119i | 0.641549 | − | 0.641549i | −0.309387 | − | 0.950936i | \(-0.600124\pi\) |
0.950936 | + | 0.309387i | \(0.100124\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1205.87i | 1.93559i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −430.067 | −0.688107 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −343.117 | − | 343.117i | −0.545495 | − | 0.545495i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 381.081 | 0.603931 | 0.301966 | − | 0.953319i | \(-0.402357\pi\) | ||||
0.301966 | + | 0.953319i | \(0.402357\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −528.354 | + | 528.354i | −0.832053 | + | 0.832053i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −165.657 | + | 165.657i | −0.260059 | + | 0.260059i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 485.443 | 0.757321 | 0.378661 | − | 0.925536i | \(-0.376385\pi\) | ||||
0.378661 | + | 0.925536i | \(0.376385\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 457.641 | + | 457.641i | 0.711728 | + | 0.711728i | 0.966897 | − | 0.255168i | \(-0.0821308\pi\) |
−0.255168 | + | 0.966897i | \(0.582131\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 845.780 | 1.30723 | 0.653617 | − | 0.756826i | \(-0.273251\pi\) | ||||
0.653617 | + | 0.756826i | \(0.273251\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 108.398i | 0.167023i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.1039 | + | 11.1039i | −0.0170044 | + | 0.0170044i | −0.715558 | − | 0.698553i | \(-0.753827\pi\) |
0.698553 | + | 0.715558i | \(0.253827\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 2120.67i | − | 3.23766i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 296.711 | + | 296.711i | 0.450245 | + | 0.450245i | 0.895436 | − | 0.445191i | \(-0.146864\pi\) |
−0.445191 | + | 0.895436i | \(0.646864\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.564899 | + | 0.564899i | 0.000854613 | + | 0.000854613i | 0.707534 | − | 0.706679i | \(-0.249808\pi\) |
−0.706679 | + | 0.707534i | \(0.749808\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 2350.91i | − | 3.53520i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −224.201 | + | 224.201i | −0.336133 | + | 0.336133i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 891.329i | 1.32836i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1091.24 | −1.62146 | −0.810731 | − | 0.585419i | \(-0.800930\pi\) | ||||
−0.810731 | + | 0.585419i | \(0.800930\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 494.409 | + | 494.409i | 0.730294 | + | 0.730294i | 0.970678 | − | 0.240384i | \(-0.0772733\pi\) |
−0.240384 | + | 0.970678i | \(0.577273\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −832.814 | −1.22653 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 845.268 | − | 845.268i | 1.23758 | − | 1.23758i | 0.276594 | − | 0.960987i | \(-0.410794\pi\) |
0.960987 | − | 0.276594i | \(-0.0892057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −583.362 | + | 583.362i | −0.851623 | + | 0.851623i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −576.071 | −0.836097 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 457.715 | + | 457.715i | 0.662395 | + | 0.662395i | 0.955944 | − | 0.293549i | \(-0.0948364\pi\) |
−0.293549 | + | 0.955944i | \(0.594836\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1565.95 | 2.25316 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 94.6589i | 0.135809i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −199.252 | + | 199.252i | −0.284239 | + | 0.284239i | −0.834797 | − | 0.550558i | \(-0.814415\pi\) |
0.550558 | + | 0.834797i | \(0.314415\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1149.69i | 1.63540i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −390.941 | − | 390.941i | −0.552958 | − | 0.552958i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 547.374 | + | 547.374i | 0.772036 | + | 0.772036i | 0.978462 | − | 0.206426i | \(-0.0661832\pi\) |
−0.206426 | + | 0.978462i | \(0.566183\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 230.018i | − | 0.322606i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −691.710 | + | 691.710i | −0.967427 | + | 0.967427i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 90.5082i | 0.125881i | 0.998017 | + | 0.0629403i | \(0.0200478\pi\) | ||||
−0.998017 | + | 0.0629403i | \(0.979952\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 62.4402 | 0.0866022 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1125.71 | + | 1125.71i | 1.55270 | + | 1.55270i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 222.068 | 0.305459 | 0.152729 | − | 0.988268i | \(-0.451194\pi\) | ||||
0.152729 | + | 0.988268i | \(0.451194\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 12.7283 | − | 12.7283i | 0.0174122 | − | 0.0174122i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −201.142 | + | 201.142i | −0.274410 | + | 0.274410i | −0.830873 | − | 0.556463i | \(-0.812158\pi\) |
0.556463 | + | 0.830873i | \(0.312158\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 100.586 | 0.136480 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −771.595 | − | 771.595i | −1.04411 | − | 1.04411i | −0.998981 | − | 0.0451261i | \(-0.985631\pi\) |
−0.0451261 | − | 0.998981i | \(-0.514369\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −754.171 | −1.01503 | −0.507517 | − | 0.861641i | \(-0.669437\pi\) | ||||
−0.507517 | + | 0.861641i | \(0.669437\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 316.977i | − | 0.425473i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 985.822 | − | 985.822i | 1.31618 | − | 1.31618i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 606.477i | − | 0.807559i | −0.914856 | − | 0.403780i | \(-0.867696\pi\) | ||
0.914856 | − | 0.403780i | \(-0.132304\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1179.12 | + | 1179.12i | 1.56175 | + | 1.56175i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 852.254 | + | 852.254i | 1.12583 | + | 1.12583i | 0.990848 | + | 0.134983i | \(0.0430981\pi\) |
0.134983 | + | 0.990848i | \(0.456902\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1373.25i | 1.80453i | 0.431180 | + | 0.902266i | \(0.358097\pi\) | ||||
−0.431180 | + | 0.902266i | \(0.641903\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 502.360 | − | 502.360i | 0.658401 | − | 0.658401i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 146.886i | 0.191507i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 515.727 | 0.670647 | 0.335323 | − | 0.942103i | \(-0.391154\pi\) | ||||
0.335323 | + | 0.942103i | \(0.391154\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 448.985 | + | 448.985i | 0.580834 | + | 0.580834i | 0.935132 | − | 0.354299i | \(-0.115280\pi\) |
−0.354299 | + | 0.935132i | \(0.615280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1154.92 | −1.49022 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 158.587 | − | 158.587i | 0.203578 | − | 0.203578i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −894.282 | + | 894.282i | −1.14505 | + | 1.14505i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1184.88 | 1.50940 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 70.0485 | + | 70.0485i | 0.0890070 | + | 0.0890070i | 0.750208 | − | 0.661201i | \(-0.229953\pi\) |
−0.661201 | + | 0.750208i | \(0.729953\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −260.437 | −0.329251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1207.81i | 1.52309i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 584.026 | − | 584.026i | 0.732780 | − | 0.732780i | −0.238390 | − | 0.971170i | \(-0.576620\pi\) |
0.971170 | + | 0.238390i | \(0.0766195\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 357.787i | 0.447794i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 344.434 | + | 344.434i | 0.428935 | + | 0.428935i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −466.308 | − | 466.308i | −0.579265 | − | 0.579265i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1252.15i | − | 1.54778i | −0.633321 | − | 0.773889i | \(-0.718309\pi\) | ||
0.633321 | − | 0.773889i | \(-0.281691\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −255.775 | + | 255.775i | −0.315382 | + | 0.315382i | −0.846990 | − | 0.531608i | \(-0.821588\pi\) |
0.531608 | + | 0.846990i | \(0.321588\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1090.31i | 1.33780i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.6489 | −0.0522018 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 228.380 | + | 228.380i | 0.278173 | + | 0.278173i | 0.832379 | − | 0.554206i | \(-0.186978\pi\) |
−0.554206 | + | 0.832379i | \(0.686978\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1050.55 | −1.27649 | −0.638246 | − | 0.769832i | \(-0.720340\pi\) | ||||
−0.638246 | + | 0.769832i | \(0.720340\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −78.0300 | + | 78.0300i | −0.0943531 | + | 0.0943531i | −0.752708 | − | 0.658355i | \(-0.771253\pi\) |
0.658355 | + | 0.752708i | \(0.271253\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 517.848 | − | 517.848i | 0.624665 | − | 0.624665i | −0.322056 | − | 0.946721i | \(-0.604374\pi\) |
0.946721 | + | 0.322056i | \(0.104374\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 265.981 | 0.319305 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1091.91 | − | 1091.91i | −1.30768 | − | 1.30768i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 649.581 | 0.774232 | 0.387116 | − | 0.922031i | \(-0.373471\pi\) | ||||
0.387116 | + | 0.922031i | \(0.373471\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | − | 291.627i | − | 0.346762i | ||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 78.8260 | − | 78.8260i | 0.0932852 | − | 0.0932852i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 297.186i | − | 0.350869i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 228.043 | + | 228.043i | 0.267970 | + | 0.267970i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1124.04 | − | 1124.04i | −1.31775 | − | 1.31775i | −0.915551 | − | 0.402202i | \(-0.868245\pi\) |
−0.402202 | − | 0.915551i | \(-0.631755\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 596.973i | − | 0.696585i | −0.937386 | − | 0.348292i | \(-0.886762\pi\) | ||
0.937386 | − | 0.348292i | \(-0.113238\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 701.595 | − | 701.595i | 0.816758 | − | 0.816758i | −0.168879 | − | 0.985637i | \(-0.554015\pi\) |
0.985637 | + | 0.168879i | \(0.0540147\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 437.703i | 0.507187i | 0.967311 | + | 0.253594i | \(0.0816126\pi\) | ||||
−0.967311 | + | 0.253594i | \(0.918387\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −32.0513 | −0.0370535 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −568.309 | − | 568.309i | −0.653981 | − | 0.653981i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 136.301 | 0.156487 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1103.94 | + | 1103.94i | −1.26165 | + | 1.26165i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −769.110 | + | 769.110i | −0.876978 | + | 0.876978i | −0.993221 | − | 0.116243i | \(-0.962915\pi\) |
0.116243 | + | 0.993221i | \(0.462915\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 351.923 | 0.399459 | 0.199729 | − | 0.979851i | \(-0.435994\pi\) | ||||
0.199729 | + | 0.979851i | \(0.435994\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 661.014 | + | 661.014i | 0.748601 | + | 0.748601i | 0.974216 | − | 0.225616i | \(-0.0724394\pi\) |
−0.225616 | + | 0.974216i | \(0.572439\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −794.853 | −0.896114 | −0.448057 | − | 0.894005i | \(-0.647884\pi\) | ||||
−0.448057 | + | 0.894005i | \(0.647884\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 723.364i | 0.813683i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 599.421 | − | 599.421i | 0.671244 | − | 0.671244i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 153.312i | 0.171298i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 581.008 | + | 581.008i | 0.646282 | + | 0.646282i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 462.472 | + | 462.472i | 0.513288 | + | 0.513288i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 737.162i | − | 0.814544i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −943.805 | + | 943.805i | −1.04058 | + | 1.04058i | −0.0414379 | + | 0.999141i | \(0.513194\pi\) |
−0.999141 | + | 0.0414379i | \(0.986806\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 190.842i | 0.209487i | 0.994499 | + | 0.104743i | \(0.0334021\pi\) | ||||
−0.994499 | + | 0.104743i | \(0.966598\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 124.298 | 0.136142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1451.70 | − | 1451.70i | −1.58309 | − | 1.58309i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 925.230 | 1.00678 | 0.503389 | − | 0.864060i | \(-0.332086\pi\) | ||||
0.503389 | + | 0.864060i | \(0.332086\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1211.81 | + | 1211.81i | −1.31290 | + | 1.31290i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1145.00 | − | 1145.00i | 1.23784 | − | 1.23784i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 91.8388 | 0.0988577 | 0.0494289 | − | 0.998778i | \(-0.484260\pi\) | ||||
0.0494289 | + | 0.998778i | \(0.484260\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −445.613 | − | 445.613i | −0.478639 | − | 0.478639i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1110.62 | 1.18782 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1615.44i | − | 1.72406i | −0.506857 | − | 0.862030i | \(-0.669193\pi\) | ||
0.506857 | − | 0.862030i | \(-0.330807\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −484.931 | + | 484.931i | −0.515336 | + | 0.515336i | −0.916157 | − | 0.400820i | \(-0.868725\pi\) |
0.400820 | + | 0.916157i | \(0.368725\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 62.9124i | − | 0.0667151i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1053.02 | − | 1053.02i | −1.11195 | − | 1.11195i | −0.992887 | − | 0.119064i | \(-0.962010\pi\) |
−0.119064 | − | 0.992887i | \(-0.537990\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 466.731 | + | 466.731i | 0.491814 | + | 0.491814i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1256.72i | 1.31870i | 0.751838 | + | 0.659348i | \(0.229168\pi\) | ||||
−0.751838 | + | 0.659348i | \(0.770832\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 481.736 | − | 481.736i | 0.504436 | − | 0.504436i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 798.675i | 0.832821i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 364.917 | 0.379726 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −172.897 | − | 172.897i | −0.179168 | − | 0.179168i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1842.43 | 1.90530 | 0.952651 | − | 0.304066i | \(-0.0983444\pi\) | ||||
0.952651 | + | 0.304066i | \(0.0983444\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 802.530 | − | 802.530i | 0.826498 | − | 0.826498i | −0.160532 | − | 0.987031i | \(-0.551321\pi\) |
0.987031 | + | 0.160532i | \(0.0513211\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1071.96 | − | 1071.96i | 1.10171 | − | 1.10171i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1505.64 | 1.54109 | 0.770544 | − | 0.637387i | \(-0.219985\pi\) | ||||
0.770544 | + | 0.637387i | \(0.219985\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 954.413 | + | 954.413i | 0.974886 | + | 0.974886i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −764.708 | −0.777933 | −0.388966 | − | 0.921252i | \(-0.627168\pi\) | ||||
−0.388966 | + | 0.921252i | \(0.627168\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1115.98i | 1.13298i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −8.45951 | + | 8.45951i | −0.00855360 | + | 0.00855360i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1683.22i | 1.69851i | 0.527984 | + | 0.849254i | \(0.322948\pi\) | ||||
−0.527984 | + | 0.849254i | \(0.677052\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 995.424 | + | 995.424i | 1.00043 | + | 1.00043i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −942.082 | − | 942.082i | −0.944917 | − | 0.944917i | 0.0536431 | − | 0.998560i | \(-0.482917\pi\) |
−0.998560 | + | 0.0536431i | \(0.982917\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 1152.3.m.d.415.1 | 16 | ||
3.2 | odd | 2 | inner | 1152.3.m.d.415.8 | 16 | ||
4.3 | odd | 2 | 1152.3.m.e.415.1 | 16 | |||
8.3 | odd | 2 | 144.3.m.b.91.5 | yes | 16 | ||
8.5 | even | 2 | 576.3.m.b.271.8 | 16 | |||
12.11 | even | 2 | 1152.3.m.e.415.8 | 16 | |||
16.3 | odd | 4 | inner | 1152.3.m.d.991.1 | 16 | ||
16.5 | even | 4 | 144.3.m.b.19.5 | yes | 16 | ||
16.11 | odd | 4 | 576.3.m.b.559.8 | 16 | |||
16.13 | even | 4 | 1152.3.m.e.991.1 | 16 | |||
24.5 | odd | 2 | 576.3.m.b.271.1 | 16 | |||
24.11 | even | 2 | 144.3.m.b.91.4 | yes | 16 | ||
48.5 | odd | 4 | 144.3.m.b.19.4 | ✓ | 16 | ||
48.11 | even | 4 | 576.3.m.b.559.1 | 16 | |||
48.29 | odd | 4 | 1152.3.m.e.991.8 | 16 | |||
48.35 | even | 4 | inner | 1152.3.m.d.991.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.m.b.19.4 | ✓ | 16 | 48.5 | odd | 4 | ||
144.3.m.b.19.5 | yes | 16 | 16.5 | even | 4 | ||
144.3.m.b.91.4 | yes | 16 | 24.11 | even | 2 | ||
144.3.m.b.91.5 | yes | 16 | 8.3 | odd | 2 | ||
576.3.m.b.271.1 | 16 | 24.5 | odd | 2 | |||
576.3.m.b.271.8 | 16 | 8.5 | even | 2 | |||
576.3.m.b.559.1 | 16 | 48.11 | even | 4 | |||
576.3.m.b.559.8 | 16 | 16.11 | odd | 4 | |||
1152.3.m.d.415.1 | 16 | 1.1 | even | 1 | trivial | ||
1152.3.m.d.415.8 | 16 | 3.2 | odd | 2 | inner | ||
1152.3.m.d.991.1 | 16 | 16.3 | odd | 4 | inner | ||
1152.3.m.d.991.8 | 16 | 48.35 | even | 4 | inner | ||
1152.3.m.e.415.1 | 16 | 4.3 | odd | 2 | |||
1152.3.m.e.415.8 | 16 | 12.11 | even | 2 | |||
1152.3.m.e.991.1 | 16 | 16.13 | even | 4 | |||
1152.3.m.e.991.8 | 16 | 48.29 | odd | 4 |