Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,2,Mod(161,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([5, 7]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.161");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.f (of order \(10\), degree \(4\), 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: | \(2.89856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 16.0.6879707136000000000000.7 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4x^{14} + 15x^{12} - 56x^{10} + 209x^{8} - 56x^{6} + 15x^{4} - 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 11^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{10}]$ |
Embedding invariants
Embedding label | 239.1 | ||
Root | \(-0.304260 - 0.418778i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.239 |
Dual form | 363.2.f.g.161.1 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{10}\right)\) |
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 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(3\) | −0.535233 | − | 1.64728i | −0.309017 | − | 0.951057i | ||||
\(4\) | −0.618034 | + | 1.90211i | −0.309017 | + | 0.951057i | ||||
\(5\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.19769 | − | 0.714073i | −0.830649 | − | 0.269894i | −0.137330 | − | 0.990525i | \(-0.543852\pi\) |
−0.693319 | + | 0.720631i | \(0.743852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.42705 | + | 1.76336i | −0.809017 | + | 0.587785i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 3.46410 | 1.00000 | ||||||||
\(13\) | −3.71080 | − | 5.10748i | −1.02919 | − | 1.41656i | −0.905553 | − | 0.424233i | \(-0.860544\pi\) |
−0.123638 | − | 0.992327i | \(-0.539456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.23607 | − | 2.35114i | −0.809017 | − | 0.587785i | ||||
\(17\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −8.20189 | + | 2.66496i | −1.88164 | + | 0.611383i | −0.895609 | + | 0.444842i | \(0.853260\pi\) |
−0.986035 | + | 0.166541i | \(0.946740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.00240i | 0.873396i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.54508 | + | 4.75528i | 0.309017 | + | 0.951057i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.20378 | + | 3.05422i | 0.809017 | + | 0.587785i | ||||
\(28\) | 2.71650 | − | 3.73894i | 0.513369 | − | 0.706592i | ||||
\(29\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.40126 | + | 1.01807i | −0.251673 | + | 0.182851i | −0.706468 | − | 0.707745i | \(-0.749713\pi\) |
0.454795 | + | 0.890596i | \(0.349713\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.85410 | − | 5.70634i | −0.309017 | − | 0.951057i | ||||
\(37\) | 1.60570 | − | 4.94183i | 0.263975 | − | 0.812433i | −0.727952 | − | 0.685628i | \(-0.759528\pi\) |
0.991928 | − | 0.126805i | \(-0.0404722\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.42730 | + | 8.84642i | −1.02919 | + | 1.41656i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.69161i | − | 0.257969i | −0.991647 | − | 0.128984i | \(-0.958828\pi\) | ||
0.991647 | − | 0.128984i | \(-0.0411717\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(48\) | −2.14093 | + | 6.58911i | −0.309017 | + | 0.951057i | ||||
\(49\) | −1.34317 | − | 0.975873i | −0.191882 | − | 0.139410i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 12.0084 | − | 3.90177i | 1.66527 | − | 0.541078i | ||||
\(53\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.77985 | + | 12.0844i | 1.16292 | + | 1.60062i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.06336 | − | 8.34549i | 0.776333 | − | 1.06853i | −0.219344 | − | 0.975648i | \(-0.570392\pi\) |
0.995677 | − | 0.0928833i | \(-0.0296084\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 6.59307 | − | 2.14222i | 0.830649 | − | 0.269894i | ||||
\(64\) | 6.47214 | − | 4.70228i | 0.809017 | − | 0.587785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.1244 | −1.48123 | −0.740613 | − | 0.671932i | \(-0.765465\pi\) | ||||
−0.740613 | + | 0.671932i | \(0.765465\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.5973 | + | 4.09310i | 1.47440 | + | 0.479061i | 0.932434 | − | 0.361339i | \(-0.117680\pi\) |
0.541965 | + | 0.840401i | \(0.317680\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 7.00629 | − | 5.09037i | 0.809017 | − | 0.587785i | ||||
\(76\) | − | 17.2480i | − | 1.97848i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.363941 | − | 0.500922i | −0.0409466 | − | 0.0563582i | 0.788053 | − | 0.615608i | \(-0.211089\pi\) |
−0.828999 | + | 0.559250i | \(0.811089\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.78115 | − | 8.55951i | 0.309017 | − | 0.951057i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(84\) | −7.61302 | − | 2.47362i | −0.830649 | − | 0.269894i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.50808 | + | 13.8744i | 0.472575 | + | 1.45444i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.42705 | + | 1.76336i | 0.251673 | + | 0.182851i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.04508 | − | 2.93893i | 0.410716 | − | 0.298403i | −0.363176 | − | 0.931721i | \(-0.618307\pi\) |
0.773892 | + | 0.633318i | \(0.218307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −10.0000 | −1.00000 | ||||||||
\(101\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.16312 | − | 6.65740i | 0.213138 | − | 0.655973i | −0.786142 | − | 0.618046i | \(-0.787925\pi\) |
0.999281 | − | 0.0379269i | \(-0.0120754\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(108\) | −8.40755 | + | 6.10844i | −0.809017 | + | 0.587785i | ||||
\(109\) | 19.5588i | 1.87339i | 0.350148 | + | 0.936694i | \(0.386131\pi\) | ||||
−0.350148 | + | 0.936694i | \(0.613869\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.00000 | −0.854242 | ||||||||
\(112\) | 5.43299 | + | 7.47787i | 0.513369 | + | 0.706592i | ||||
\(113\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 18.0126 | + | 5.85265i | 1.66527 | + | 0.541078i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.07047 | − | 3.29456i | −0.0961307 | − | 0.295860i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.77416 | + | 13.4530i | −0.867316 | + | 1.19376i | 0.112459 | + | 0.993656i | \(0.464127\pi\) |
−0.979775 | + | 0.200102i | \(0.935873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.78656 | + | 0.905408i | −0.245343 | + | 0.0797168i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 19.9282 | 1.72799 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.4080 | − | 7.28080i | −1.90062 | − | 0.617549i | −0.962547 | − | 0.271113i | \(-0.912608\pi\) |
−0.938074 | − | 0.346436i | \(-0.887392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0000 | 1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.888623 | + | 2.73490i | −0.0732924 | + | 0.225571i | ||||
\(148\) | 8.40755 | + | 6.10844i | 0.691096 | + | 0.502111i | ||||
\(149\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −13.6172 | + | 4.42451i | −1.10815 | + | 0.360061i | −0.805235 | − | 0.592955i | \(-0.797961\pi\) |
−0.302919 | + | 0.953016i | \(0.597961\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −12.8546 | − | 17.6928i | −1.02919 | − | 1.41656i | ||||
\(157\) | −6.95803 | − | 21.4146i | −0.555311 | − | 1.70907i | −0.695120 | − | 0.718894i | \(-0.744649\pi\) |
0.139808 | − | 0.990179i | \(-0.455351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −13.7533 | + | 9.99235i | −1.07724 | + | 0.782661i | −0.977200 | − | 0.212322i | \(-0.931897\pi\) |
−0.100041 | + | 0.994983i | \(0.531897\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.29909 | + | 25.5420i | −0.638391 | + | 1.96477i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 15.2071 | − | 20.9308i | 1.16292 | − | 1.60062i | ||||
\(172\) | 3.21764 | + | 1.04548i | 0.245343 | + | 0.0797168i | ||||
\(173\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 11.5539i | − | 0.873396i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.3713 | − | 11.1679i | −1.14254 | − | 0.830105i | −0.155070 | − | 0.987903i | \(-0.549560\pi\) |
−0.987471 | + | 0.157799i | \(0.949560\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −16.9927 | − | 5.52125i | −1.25613 | − | 0.408142i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.05766 | − | 9.71404i | −0.513369 | − | 0.706592i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(192\) | −11.2101 | − | 8.14459i | −0.809017 | − | 0.587785i | ||||
\(193\) | −3.08044 | + | 4.23986i | −0.221735 | + | 0.305192i | −0.905363 | − | 0.424639i | \(-0.860401\pi\) |
0.683628 | + | 0.729831i | \(0.260401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.68635 | − | 1.95175i | 0.191882 | − | 0.139410i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 25.9808 | 1.84173 | 0.920864 | − | 0.389885i | \(-0.127485\pi\) | ||||
0.920864 | + | 0.389885i | \(0.127485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.48936 | + | 19.9722i | 0.457724 | + | 1.40873i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 25.2528i | 1.75096i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.2015 | − | 22.2994i | −1.11535 | − | 1.53515i | −0.813283 | − | 0.581868i | \(-0.802322\pi\) |
−0.302071 | − | 0.953286i | \(-0.597678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.80651 | − | 1.23681i | 0.258403 | − | 0.0839602i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 22.9420i | − | 1.55028i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.10739 | − | 21.8743i | −0.475946 | − | 1.46481i | −0.844678 | − | 0.535275i | \(-0.820208\pi\) |
0.368731 | − | 0.929536i | \(-0.379792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −12.1353 | − | 8.81678i | −0.809017 | − | 0.587785i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(228\) | −28.4122 | + | 9.23168i | −1.88164 | + | 0.611383i | ||||
\(229\) | −16.8151 | + | 12.2169i | −1.11117 | + | 0.807315i | −0.982848 | − | 0.184418i | \(-0.940960\pi\) |
−0.128325 | + | 0.991732i | \(0.540960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.630365 | + | 0.867623i | −0.0409466 | + | 0.0563582i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.69642i | 0.624602i | 0.949983 | + | 0.312301i | \(0.101100\pi\) | ||||
−0.949983 | + | 0.312301i | \(0.898900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | 12.1267 | + | 16.6910i | 0.776333 | + | 1.06853i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44.0468 | + | 32.0019i | 2.80263 | + | 2.03623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(252\) | 13.8647i | 0.873396i | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.94427 | + | 15.2169i | 0.309017 | + | 0.951057i | ||||
\(257\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.05766 | + | 9.71404i | −0.438542 | + | 0.603601i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.49326 | − | 23.0619i | 0.457724 | − | 1.40873i | ||||
\(269\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.18194 | + | 2.33355i | 0.436272 | + | 0.141753i | 0.518915 | − | 0.854826i | \(-0.326336\pi\) |
−0.0826430 | + | 0.996579i | \(0.526336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 20.4422 | − | 14.8521i | 1.23722 | − | 0.898892i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.9236 | + | 24.6698i | 1.07693 | + | 1.48226i | 0.862859 | + | 0.505445i | \(0.168672\pi\) |
0.214068 | + | 0.976819i | \(0.431328\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.60570 | − | 4.94183i | 0.0961307 | − | 0.295860i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 17.4237 | − | 5.66132i | 1.03573 | − | 0.336530i | 0.258679 | − | 0.965963i | \(-0.416713\pi\) |
0.777055 | + | 0.629433i | \(0.216713\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −5.25329 | − | 16.1680i | −0.309017 | − | 0.951057i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.00629 | − | 5.09037i | −0.410716 | − | 0.298403i | ||||
\(292\) | −15.5711 | + | 21.4318i | −0.911229 | + | 1.25420i | ||||
\(293\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.35233 | + | 16.4728i | 0.309017 | + | 0.951057i | ||||
\(301\) | −1.20794 | + | 3.71765i | −0.0696243 | + | 0.214282i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 32.8076 | + | 10.6598i | 1.88164 | + | 0.611383i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7.38563i | − | 0.421520i | −0.977538 | − | 0.210760i | \(-0.932406\pi\) | ||
0.977538 | − | 0.210760i | \(-0.0675939\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −12.1244 | −0.689730 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −22.4201 | − | 16.2892i | −1.26726 | − | 0.920719i | −0.268171 | − | 0.963371i | \(-0.586419\pi\) |
−0.999090 | + | 0.0426523i | \(0.986419\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.17774 | − | 0.382671i | 0.0662530 | − | 0.0215269i | ||||
\(317\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 14.5623 | + | 10.5801i | 0.809017 | + | 0.587785i | ||||
\(325\) | 18.5540 | − | 25.5374i | 1.02919 | − | 1.41656i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 32.2187 | − | 10.4685i | 1.78170 | − | 0.578909i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −31.0000 | −1.70391 | −0.851957 | − | 0.523612i | \(-0.824584\pi\) | ||||
−0.851957 | + | 0.523612i | \(0.824584\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.81710 | + | 14.8255i | 0.263975 | + | 0.812433i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 9.41022 | − | 12.9521i | 0.513369 | − | 0.706592i | ||||
\(337\) | −27.8233 | − | 9.04035i | −1.51563 | − | 0.492459i | −0.571101 | − | 0.820879i | \(-0.693484\pi\) |
−0.944532 | + | 0.328420i | \(0.893484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.7628 | + | 16.1901i | 0.635130 | + | 0.874181i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.3880 | − | 6.94940i | 1.14488 | − | 0.371993i | 0.325665 | − | 0.945485i | \(-0.394412\pi\) |
0.819211 | + | 0.573493i | \(0.194412\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 32.8043i | − | 1.75096i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 44.7978 | − | 32.5475i | 2.35778 | − | 1.71302i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −29.1769 | −1.52929 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.23607 | + | 3.80423i | −0.0645222 | + | 0.198579i | −0.978121 | − | 0.208039i | \(-0.933292\pi\) |
0.913598 | + | 0.406618i | \(0.133292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −4.85410 | + | 3.52671i | −0.251673 | + | 0.182851i | ||||
\(373\) | − | 38.4983i | − | 1.99337i | −0.0813690 | − | 0.996684i | \(-0.525929\pi\) | ||
0.0813690 | − | 0.996684i | \(-0.474071\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.47214 | − | 4.70228i | −0.332451 | − | 0.241540i | 0.409019 | − | 0.912526i | \(-0.365871\pi\) |
−0.741470 | + | 0.670986i | \(0.765871\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 27.3922 | + | 8.90028i | 1.40335 | + | 0.455975i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.98292 | + | 4.10564i | 0.151630 | + | 0.208701i | ||||
\(388\) | 3.09017 | + | 9.51057i | 0.156880 | + | 0.482826i | ||||
\(389\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 35.0000 | 1.75660 | 0.878300 | − | 0.478110i | \(-0.158678\pi\) | ||||
0.878300 | + | 0.478110i | \(0.158678\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.6662 | − | 32.8273i | −0.533980 | − | 1.64342i | ||||
\(400\) | 6.18034 | − | 19.0211i | 0.309017 | − | 0.951057i | ||||
\(401\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.3996 | + | 3.37903i | 0.518040 | + | 0.168321i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.08613 | + | 2.87131i | 0.103153 | + | 0.141977i | 0.857473 | − | 0.514529i | \(-0.172033\pi\) |
−0.754320 | + | 0.656507i | \(0.772033\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 11.3262 | + | 8.22899i | 0.558004 | + | 0.405413i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 40.8091i | 1.99843i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.7047 | + | 32.9456i | 0.521713 | + | 1.60567i | 0.770725 | + | 0.637168i | \(0.219894\pi\) |
−0.249012 | + | 0.968501i | \(0.580106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.2847 | + | 14.0111i | −0.933251 | + | 0.678046i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(432\) | −6.42280 | − | 19.7673i | −0.309017 | − | 0.951057i | ||||
\(433\) | −11.4336 | + | 35.1891i | −0.549465 | + | 1.69108i | 0.160665 | + | 0.987009i | \(0.448636\pi\) |
−0.710130 | + | 0.704071i | \(0.751364\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −37.2030 | − | 12.0880i | −1.78170 | − | 0.578909i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 35.1151i | 1.67595i | 0.545707 | + | 0.837976i | \(0.316261\pi\) | ||||
−0.545707 | + | 0.837976i | \(0.683739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.98076 | 0.237179 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(444\) | 5.56231 | − | 17.1190i | 0.263975 | − | 0.812433i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −17.5815 | + | 5.71258i | −0.830649 | + | 0.269894i | ||||
\(449\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 14.5768 | + | 20.0632i | 0.684877 | + | 0.942652i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −13.1210 | + | 18.0595i | −0.613775 | + | 0.844789i | −0.996881 | − | 0.0789151i | \(-0.974854\pi\) |
0.383106 | + | 0.923704i | \(0.374854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(468\) | −22.2648 | + | 30.6449i | −1.02919 | + | 1.41656i | ||||
\(469\) | 26.6456 | + | 8.65768i | 1.23038 | + | 0.399774i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.5517 | + | 22.9236i | −1.45382 | + | 1.05626i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −25.3452 | − | 34.8847i | −1.16292 | − | 1.60062i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.1988 | + | 10.1371i | −1.42254 | + | 0.462212i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.07047 | − | 3.29456i | −0.0485075 | − | 0.149291i | 0.923869 | − | 0.382709i | \(-0.125009\pi\) |
−0.972376 | + | 0.233418i | \(0.925009\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 23.8214 | + | 17.3073i | 1.07724 | + | 0.782661i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.92820 | 0.311086 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13.3808 | − | 41.1820i | 0.599008 | − | 1.84356i | 0.0653408 | − | 0.997863i | \(-0.479187\pi\) |
0.533667 | − | 0.845694i | \(-0.320813\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 46.5167 | 2.06588 | ||||||||
\(508\) | −19.5483 | − | 26.9059i | −0.867316 | − | 1.19376i | ||||
\(509\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −24.7621 | − | 17.9908i | −1.09541 | − | 0.795864i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −42.6183 | − | 13.8475i | −1.88164 | − | 0.611383i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 5.85993i | − | 0.257969i | ||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.3509 | − | 33.5162i | 1.06479 | − | 1.46556i | 0.189553 | − | 0.981870i | \(-0.439296\pi\) |
0.875239 | − | 0.483690i | \(-0.160704\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −19.0326 | + | 6.18405i | −0.830649 | + | 0.269894i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.3163 | + | 37.9057i | −0.533980 | + | 1.64342i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −21.9984 | − | 30.2782i | −0.945785 | − | 1.30176i | −0.953375 | − | 0.301790i | \(-0.902416\pi\) |
0.00759004 | − | 0.999971i | \(-0.497584\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −10.1694 | + | 31.2983i | −0.436412 | + | 1.34314i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −43.2072 | + | 14.0389i | −1.84740 | + | 0.600258i | −0.850122 | + | 0.526585i | \(0.823472\pi\) |
−0.997282 | + | 0.0736732i | \(0.976528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.9468i | 1.32078i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.442136 | + | 1.36075i | 0.0188015 | + | 0.0578651i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 27.6978 | − | 38.1228i | 1.17465 | − | 1.61676i | ||||
\(557\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.63989 | + | 6.27725i | −0.365428 | + | 0.265499i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −12.2242 | + | 16.8252i | −0.513369 | + | 0.706592i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 27.1103i | − | 1.13453i | −0.823535 | − | 0.567265i | \(-0.808001\pi\) | ||
0.823535 | − | 0.567265i | \(-0.191999\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −7.41641 | + | 22.8254i | −0.309017 | + | 0.951057i | ||||
\(577\) | −37.8340 | − | 27.4880i | −1.57505 | − | 1.14434i | −0.922109 | − | 0.386931i | \(-0.873535\pi\) |
−0.652941 | − | 0.757409i | \(-0.726465\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.63298 | + | 2.80502i | 0.358774 | + | 0.116573i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(588\) | −4.65289 | − | 3.38052i | −0.191882 | − | 0.139410i | ||||
\(589\) | 8.77985 | − | 12.0844i | 0.361767 | − | 0.497930i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −16.8151 | + | 12.2169i | −0.691096 | + | 0.502111i | ||||
\(593\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.9058 | − | 42.7975i | −0.569125 | − | 1.75159i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.7876 | − | 10.3284i | −1.29664 | − | 0.421305i | −0.422232 | − | 0.906488i | \(-0.638753\pi\) |
−0.874413 | + | 0.485183i | \(0.838753\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 29.4264 | − | 21.3796i | 1.19834 | − | 0.870643i | ||||
\(604\) | − | 28.6360i | − | 1.16518i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.4045 | − | 14.3206i | −0.422307 | − | 0.581255i | 0.543859 | − | 0.839176i | \(-0.316962\pi\) |
−0.966166 | + | 0.257921i | \(0.916962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.0137 | − | 15.2757i | 1.89886 | − | 0.616978i | 0.931380 | − | 0.364049i | \(-0.118606\pi\) |
0.967485 | − | 0.252929i | \(-0.0813939\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.88854 | + | 30.4338i | 0.397454 | + | 1.22324i | 0.927034 | + | 0.374978i | \(0.122350\pi\) |
−0.529580 | + | 0.848260i | \(0.677650\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 41.5983 | − | 13.5161i | 1.66527 | − | 0.541078i | ||||
\(625\) | −20.2254 | + | 14.6946i | −0.809017 | + | 0.587785i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 45.0333 | 1.79703 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.49326 | − | 23.0619i | 0.298302 | − | 0.918080i | −0.683790 | − | 0.729679i | \(-0.739670\pi\) |
0.982092 | − | 0.188401i | \(-0.0603304\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −28.0617 | + | 38.6237i | −1.11535 | + | 1.53515i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.4815i | 0.415292i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 38.0238 | + | 27.6259i | 1.49951 | + | 1.08946i | 0.970575 | + | 0.240798i | \(0.0774093\pi\) |
0.528937 | + | 0.848661i | \(0.322591\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.07474 | − | 5.60840i | −0.159702 | − | 0.219811i | ||||
\(652\) | −10.5066 | − | 32.3359i | −0.411469 | − | 1.26637i | ||||
\(653\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −37.7918 | + | 12.2793i | −1.47440 | + | 0.479061i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −50.2295 | −1.95370 | −0.976850 | − | 0.213925i | \(-0.931375\pi\) | ||||
−0.976850 | + | 0.213925i | \(0.931375\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −32.2289 | + | 23.4157i | −1.24604 | + | 0.905303i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.4736 | + | 21.2975i | 0.596462 | + | 0.820960i | 0.995379 | − | 0.0960273i | \(-0.0306136\pi\) |
−0.398916 | + | 0.916987i | \(0.630614\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −8.02850 | + | 24.7092i | −0.309017 | + | 0.951057i | ||||
\(676\) | −43.4546 | − | 31.5716i | −1.67133 | − | 1.21429i | ||||
\(677\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10.9885 | + | 3.57037i | −0.421698 | + | 0.137018i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 30.4143 | + | 41.8617i | 1.16292 | + | 1.60062i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.1246 | + | 21.1603i | 1.11117 | + | 0.807315i | ||||
\(688\) | −3.97723 | + | 5.47418i | −0.151630 | + | 0.208701i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.6418 | − | 28.8015i | 1.50805 | − | 1.09566i | 0.541012 | − | 0.841015i | \(-0.318041\pi\) |
0.967035 | − | 0.254645i | \(-0.0819585\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.9769 | + | 7.14073i | 0.830649 | + | 0.269894i | ||||
\(701\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.8115i | 1.69010i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 39.2352 | + | 28.5061i | 1.47351 | + | 1.07057i | 0.979577 | + | 0.201068i | \(0.0644412\pi\) |
0.493933 | + | 0.869500i | \(0.335559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.76661 | + | 0.574006i | 0.0662530 | + | 0.0215269i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.50773 | + | 13.0863i | −0.354087 | + | 0.487358i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 15.9727 | − | 5.18985i | 0.594031 | − | 0.193012i | ||||
\(724\) | 30.7426 | − | 22.3358i | 1.14254 | − | 0.830105i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −31.1769 | −1.15629 | −0.578144 | − | 0.815935i | \(-0.696223\pi\) | ||||
−0.578144 | + | 0.815935i | \(0.696223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.34346 | + | 25.6785i | 0.309017 | + | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 21.0041 | − | 28.9096i | 0.776333 | − | 1.06853i | ||||
\(733\) | 47.6025 | + | 15.4670i | 1.75824 | + | 0.571287i | 0.997016 | − | 0.0772015i | \(-0.0245985\pi\) |
0.761225 | + | 0.648488i | \(0.224598\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.0674 | + | 37.2551i | 0.995692 | + | 1.37045i | 0.927932 | + | 0.372750i | \(0.121585\pi\) |
0.0677601 | + | 0.997702i | \(0.478415\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 29.1407 | − | 89.6858i | 1.07051 | − | 3.29469i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 16.5922 | + | 51.0656i | 0.605459 | + | 1.86341i | 0.493604 | + | 0.869687i | \(0.335679\pi\) |
0.111854 | + | 0.993725i | \(0.464321\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 22.8391 | − | 7.42087i | 0.830649 | − | 0.269894i | ||||
\(757\) | −1.40126 | + | 1.01807i | −0.0509296 | + | 0.0370025i | −0.612959 | − | 0.790115i | \(-0.710021\pi\) |
0.562029 | + | 0.827117i | \(0.310021\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.9664 | − | 42.9841i | 0.505617 | − | 1.55613i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 22.4201 | − | 16.2892i | 0.809017 | − | 0.587785i | ||||
\(769\) | − | 54.0547i | − | 1.94926i | −0.223819 | − | 0.974631i | \(-0.571852\pi\) | ||
0.223819 | − | 0.974631i | \(-0.428148\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.16087 | − | 8.47972i | −0.221735 | − | 0.305192i | ||||
\(773\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.00629 | − | 5.09037i | −0.251673 | − | 0.182851i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.7792 | + | 6.42666i | 0.709576 | + | 0.230555i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.05219 | + | 6.31598i | 0.0732924 | + | 0.225571i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24.7149 | + | 34.0171i | −0.880990 | + | 1.21258i | 0.0951552 | + | 0.995462i | \(0.469665\pi\) |
−0.976146 | + | 0.217117i | \(0.930335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −65.1244 | −2.31263 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16.0570 | + | 49.4183i | −0.569125 | + | 1.75159i | ||||
\(797\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −42.0000 | −1.48123 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.23759 | + | 1.37688i | −0.148802 | + | 0.0483487i | −0.382471 | − | 0.923967i | \(-0.624927\pi\) |
0.233669 | + | 0.972316i | \(0.424927\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 13.0797i | − | 0.458723i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.50808 | + | 13.8744i | 0.157718 | + | 0.485405i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −35.4069 | − | 25.7246i | −1.23722 | − | 0.898892i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 4.04508 | − | 2.93893i | 0.141003 | − | 0.102445i | −0.515048 | − | 0.857161i | \(-0.672226\pi\) |
0.656051 | + | 0.754717i | \(0.272226\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.16312 | − | 6.65740i | 0.0751282 | − | 0.231221i | −0.906439 | − | 0.422336i | \(-0.861210\pi\) |
0.981568 | + | 0.191115i | \(0.0612103\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 31.0447 | − | 42.7293i | 1.07693 | − | 1.48226i | ||||
\(832\) | −48.0336 | − | 15.6071i | −1.66527 | − | 0.541078i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.00000 | −0.311086 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.4615 | + | 17.0458i | 0.809017 | + | 0.587785i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 52.4290 | − | 17.0352i | 1.80468 | − | 0.586376i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.6515 | − | 25.6716i | −0.640119 | − | 0.881048i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.7571 | − | 17.5586i | 0.436794 | − | 0.601195i | −0.532702 | − | 0.846303i | \(-0.678823\pi\) |
0.969496 | + | 0.245108i | \(0.0788233\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.0000 | 0.443554 | 0.221777 | − | 0.975097i | \(-0.428814\pi\) | ||||
0.221777 | + | 0.975097i | \(0.428814\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −23.8214 | + | 17.3073i | −0.809017 | + | 0.587785i | ||||
\(868\) | 8.00481i | 0.271701i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 44.9911 | + | 61.9249i | 1.52446 | + | 2.09825i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.63525 | + | 14.2658i | −0.156880 | + | 0.482826i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 43.6382 | + | 14.1789i | 1.47440 | + | 0.479061i | ||||
\(877\) | 36.1830 | − | 11.7566i | 1.22181 | − | 0.396991i | 0.374071 | − | 0.927400i | \(-0.377962\pi\) |
0.847742 | + | 0.530409i | \(0.177962\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.95803 | − | 21.4146i | −0.234156 | − | 0.720659i | −0.997232 | − | 0.0743502i | \(-0.976312\pi\) |
0.763076 | − | 0.646309i | \(-0.223688\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 31.0870 | − | 22.5860i | 1.04262 | − | 0.757511i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 46.0000 | 1.54019 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 24.2705 | − | 17.6336i | 0.809017 | − | 0.587785i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.77053 | 0.225309 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.3713 | − | 11.1679i | −0.510396 | − | 0.370825i | 0.302578 | − | 0.953125i | \(-0.402153\pi\) |
−0.812974 | + | 0.582300i | \(0.802153\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(912\) | − | 59.7487i | − | 1.97848i | ||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.8456 | − | 39.5347i | −0.424430 | − | 1.30626i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.6117 | + | 35.2514i | −0.844851 | + | 1.16284i | 0.140123 | + | 0.990134i | \(0.455250\pi\) |
−0.984974 | + | 0.172704i | \(0.944750\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.1662 | + | 3.95304i | −0.400890 | + | 0.130257i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.9808 | 0.854242 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.48936 | + | 19.9722i | 0.213138 | + | 0.655973i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.809017 | − | 0.587785i | \(-0.800000\pi\) | ||||
0.809017 | + | 0.587785i | \(0.200000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.6172 | + | 4.42451i | 0.446287 | + | 0.145007i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 6.32978 | + | 8.71219i | 0.206785 | + | 0.284615i | 0.899795 | − | 0.436313i | \(-0.143716\pi\) |
−0.693010 | + | 0.720928i | \(0.743716\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.8328 | + | 45.6507i | −0.484051 | + | 1.48975i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(948\) | −1.26073 | − | 1.73525i | −0.0409466 | − | 0.0563582i | ||||
\(949\) | −25.8406 | − | 79.5290i | −0.838820 | − | 2.58162i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.65248 | + | 26.6296i | −0.279112 | + | 0.859019i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −18.4437 | − | 5.99272i | −0.594031 | − | 0.193012i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 62.0595i | 1.99570i | 0.0655495 | + | 0.997849i | \(0.479120\pi\) | ||||
−0.0655495 | + | 0.997849i | \(0.520880\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(972\) | 9.63420 | − | 29.6510i | 0.309017 | − | 0.951057i | ||||
\(973\) | 44.0468 | + | 32.0019i | 1.41208 | + | 1.02593i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −51.9979 | − | 16.8952i | −1.66527 | − | 0.541078i | ||||
\(976\) | −39.2429 | + | 12.7508i | −1.25613 | + | 0.408142i | ||||
\(977\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.4890 | − | 47.4701i | −1.10115 | − | 1.51560i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −88.0936 | + | 64.0038i | −2.80263 | + | 2.03623i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 45.0333 | 1.43053 | 0.715265 | − | 0.698853i | \(-0.246306\pi\) | ||||
0.715265 | + | 0.698853i | \(0.246306\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 16.5922 | + | 51.0656i | 0.526538 | + | 1.62052i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −6.16199 | − | 2.00215i | −0.195152 | − | 0.0634088i | 0.209810 | − | 0.977742i | \(-0.432715\pi\) |
−0.404962 | + | 0.914333i | \(0.632715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 21.8435 | − | 15.8702i | 0.691096 | − | 0.502111i |
(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 | 363.2.f.g.239.1 | 16 | ||
3.2 | odd | 2 | CM | 363.2.f.g.239.1 | 16 | ||
11.2 | odd | 10 | 363.2.d.d.362.2 | yes | 4 | ||
11.3 | even | 5 | inner | 363.2.f.g.215.4 | 16 | ||
11.4 | even | 5 | inner | 363.2.f.g.161.2 | 16 | ||
11.5 | even | 5 | inner | 363.2.f.g.233.3 | 16 | ||
11.6 | odd | 10 | inner | 363.2.f.g.233.4 | 16 | ||
11.7 | odd | 10 | inner | 363.2.f.g.161.1 | 16 | ||
11.8 | odd | 10 | inner | 363.2.f.g.215.3 | 16 | ||
11.9 | even | 5 | 363.2.d.d.362.1 | ✓ | 4 | ||
11.10 | odd | 2 | inner | 363.2.f.g.239.2 | 16 | ||
33.2 | even | 10 | 363.2.d.d.362.2 | yes | 4 | ||
33.5 | odd | 10 | inner | 363.2.f.g.233.3 | 16 | ||
33.8 | even | 10 | inner | 363.2.f.g.215.3 | 16 | ||
33.14 | odd | 10 | inner | 363.2.f.g.215.4 | 16 | ||
33.17 | even | 10 | inner | 363.2.f.g.233.4 | 16 | ||
33.20 | odd | 10 | 363.2.d.d.362.1 | ✓ | 4 | ||
33.26 | odd | 10 | inner | 363.2.f.g.161.2 | 16 | ||
33.29 | even | 10 | inner | 363.2.f.g.161.1 | 16 | ||
33.32 | even | 2 | inner | 363.2.f.g.239.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.d.362.1 | ✓ | 4 | 11.9 | even | 5 | ||
363.2.d.d.362.1 | ✓ | 4 | 33.20 | odd | 10 | ||
363.2.d.d.362.2 | yes | 4 | 11.2 | odd | 10 | ||
363.2.d.d.362.2 | yes | 4 | 33.2 | even | 10 | ||
363.2.f.g.161.1 | 16 | 11.7 | odd | 10 | inner | ||
363.2.f.g.161.1 | 16 | 33.29 | even | 10 | inner | ||
363.2.f.g.161.2 | 16 | 11.4 | even | 5 | inner | ||
363.2.f.g.161.2 | 16 | 33.26 | odd | 10 | inner | ||
363.2.f.g.215.3 | 16 | 11.8 | odd | 10 | inner | ||
363.2.f.g.215.3 | 16 | 33.8 | even | 10 | inner | ||
363.2.f.g.215.4 | 16 | 11.3 | even | 5 | inner | ||
363.2.f.g.215.4 | 16 | 33.14 | odd | 10 | inner | ||
363.2.f.g.233.3 | 16 | 11.5 | even | 5 | inner | ||
363.2.f.g.233.3 | 16 | 33.5 | odd | 10 | inner | ||
363.2.f.g.233.4 | 16 | 11.6 | odd | 10 | inner | ||
363.2.f.g.233.4 | 16 | 33.17 | even | 10 | inner | ||
363.2.f.g.239.1 | 16 | 1.1 | even | 1 | trivial | ||
363.2.f.g.239.1 | 16 | 3.2 | odd | 2 | CM | ||
363.2.f.g.239.2 | 16 | 11.10 | odd | 2 | inner | ||
363.2.f.g.239.2 | 16 | 33.32 | even | 2 | inner |