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 | 239.3 | ||
Root | \(1.13551 + 1.56290i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.239 |
Dual form | 363.2.f.g.161.3 |
$q$-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 | ||||||||
\(7\) | −4.52729 | − | 1.47101i | −1.71116 | − | 0.555988i | −0.720631 | − | 0.693319i | \(-0.756148\pi\) |
−0.990525 | + | 0.137330i | \(0.956148\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.42705 | + | 1.76336i | −0.809017 | + | 0.587785i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.46410 | −1.00000 | ||||||||
\(13\) | 2.04829 | + | 2.81923i | 0.568095 | + | 0.781915i | 0.992327 | − | 0.123638i | \(-0.0394562\pi\) |
−0.424233 | + | 0.905553i | \(0.639456\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | −1.21308 | + | 0.394155i | −0.278301 | + | 0.0904254i | −0.444842 | − | 0.895609i | \(-0.646740\pi\) |
0.166541 | + | 0.986035i | \(0.446740\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 8.24504i | − | 1.79922i | ||||||
\(22\) | 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 | ||||
\(28\) | 5.59604 | − | 7.70229i | 1.05755 | − | 1.45560i | ||||
\(29\) | 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 | −0.454795 | − | 0.890596i | \(-0.650287\pi\) |
0.706468 | + | 0.707745i | \(0.250287\pi\) | |||||||
\(32\) | 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 | \(0.240472\pi\) |
−0.991928 | + | 0.126805i | \(0.959528\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.54775 | + | 4.88306i | −0.568095 | + | 0.781915i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 13.0053i | 1.98329i | 0.128984 | + | 0.991647i | \(0.458828\pi\) | ||||
−0.128984 | + | 0.991647i | \(0.541172\pi\) | |||||||
\(44\) | 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 | ||||
\(49\) | 12.6694 | + | 9.20487i | 1.80992 | + | 1.31498i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.62842 | + | 2.15370i | −0.919196 | + | 0.298665i | ||||
\(53\) | 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 | ||||||||
\(57\) | −1.29857 | − | 1.78732i | −0.171999 | − | 0.236737i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.309017 | − | 0.951057i | \(-0.400000\pi\) | ||||
−0.309017 | + | 0.951057i | \(0.600000\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.89461 | + | 9.48962i | −0.882764 | + | 1.21502i | 0.0928833 | + | 0.995677i | \(0.470392\pi\) |
−0.975648 | + | 0.219344i | \(0.929608\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.5819 | − | 4.41302i | 1.71116 | − | 0.555988i | ||||
\(64\) | 6.47214 | − | 4.70228i | 0.809017 | − | 0.587785i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.1244 | 1.48123 | 0.740613 | − | 0.671932i | \(-0.234535\pi\) | ||||
0.740613 | + | 0.671932i | \(0.234535\pi\) | |||||||
\(68\) | 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 | ||||||||
\(73\) | 10.2677 | + | 3.33617i | 1.20174 | + | 0.390469i | 0.840401 | − | 0.541965i | \(-0.182320\pi\) |
0.361339 | + | 0.932434i | \(0.382320\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −7.00629 | + | 5.09037i | −0.809017 | + | 0.587785i | ||||
\(76\) | − | 2.55103i | − | 0.292623i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.4424 | − | 14.3727i | −1.17486 | − | 1.61705i | −0.615608 | − | 0.788053i | \(-0.711089\pi\) |
−0.559250 | − | 0.828999i | \(-0.688911\pi\) | |||||||
\(80\) | 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 | \(0.700000\pi\) | |||||||
\(84\) | 15.6830 | + | 5.09572i | 1.71116 | + | 0.555988i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.12612 | − | 15.7766i | −0.537363 | − | 1.65383i | ||||
\(92\) | 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 | ||||
\(109\) | 7.31130i | 0.700296i | 0.936694 | + | 0.350148i | \(0.113869\pi\) | ||||
−0.936694 | + | 0.350148i | \(0.886131\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −9.00000 | −0.854242 | ||||||||
\(112\) | 11.1921 | + | 15.4046i | 1.05755 | + | 1.45560i | ||||
\(113\) | 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 | ||||||||
\(117\) | −9.94263 | − | 3.23056i | −0.919196 | − | 0.298665i | ||||
\(118\) | 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 | ||||||||
\(127\) | 8.94290 | − | 12.3089i | 0.793554 | − | 1.09223i | −0.200102 | − | 0.979775i | \(-0.564127\pi\) |
0.993656 | − | 0.112459i | \(-0.0358726\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −21.4234 | + | 6.96088i | −1.88622 | + | 0.612871i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.07180 | 0.526492 | ||||||||
\(134\) | 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 | ||||||||
\(139\) | 0.888040 | + | 0.288542i | 0.0753225 | + | 0.0244738i | 0.346436 | − | 0.938074i | \(-0.387392\pi\) |
−0.271113 | + | 0.962547i | \(0.587392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 12.0000 | 1.00000 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.38189 | + | 25.7968i | −0.691326 | + | 2.12768i | ||||
\(148\) | −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 | ||||||||
\(151\) | 18.9972 | − | 6.17257i | 1.54597 | − | 0.502317i | 0.592955 | − | 0.805235i | \(-0.297961\pi\) |
0.953016 | + | 0.302919i | \(0.0979611\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7.09550 | − | 9.76612i | −0.568095 | − | 0.781915i | ||||
\(157\) | 6.95803 | + | 21.4146i | 0.555311 | + | 1.70907i | 0.695120 | + | 0.718894i | \(0.255351\pi\) |
−0.139808 | + | 0.990179i | \(0.544649\pi\) | |||||||
\(158\) | 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 | ||||||||
\(169\) | 0.264644 | − | 0.814491i | 0.0203572 | − | 0.0626531i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.24918 | − | 3.09573i | 0.171999 | − | 0.236737i | ||||
\(172\) | −24.7376 | − | 8.03773i | −1.88622 | − | 0.612871i | ||||
\(173\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 23.8014i | − | 1.79922i | ||||||
\(176\) | 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 | ||||||||
\(183\) | −19.3223 | − | 6.27818i | −1.42834 | − | 0.464097i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.5389 | + | 20.0111i | 1.05755 | + | 1.45560i | ||||
\(190\) | 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 | ||||
\(193\) | −16.0384 | + | 22.0750i | −1.15447 | + | 1.58899i | −0.424639 | + | 0.905363i | \(0.639599\pi\) |
−0.729831 | + | 0.683628i | \(0.760401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −25.3388 | + | 18.4097i | −1.80992 | + | 1.31498i | ||||
\(197\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.9808 | −1.84173 | −0.920864 | − | 0.389885i | \(-0.872515\pi\) | ||||
−0.920864 | + | 0.389885i | \(0.872515\pi\) | |||||||
\(200\) | 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 | ||||||||
\(208\) | − | 13.9391i | − | 0.966500i | ||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.39515 | + | 7.42579i | 0.371418 | + | 0.511213i | 0.953286 | − | 0.302071i | \(-0.0976779\pi\) |
−0.581868 | + | 0.813283i | \(0.697678\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.84150 | + | 2.54786i | −0.532316 | + | 0.172960i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 18.6993i | 1.26358i | ||||||||
\(220\) | 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 | \(0.100000\pi\) | |||||||
\(228\) | 4.20225 | − | 1.36539i | 0.278301 | − | 0.0904254i | ||||
\(229\) | 16.8151 | − | 12.2169i | 1.11117 | − | 0.807315i | 0.128325 | − | 0.991732i | \(-0.459040\pi\) |
0.982848 | + | 0.184418i | \(0.0590399\pi\) | |||||||
\(230\) | 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 | ||||||||
\(237\) | 18.0867 | − | 24.8942i | 1.17486 | − | 1.61705i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 29.4954i | − | 1.89997i | −0.312301 | − | 0.949983i | \(-0.601100\pi\) | ||
0.312301 | − | 0.949983i | \(-0.398900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885 | 1.00000 | ||||||||
\(244\) | −13.7892 | − | 18.9792i | −0.882764 | − | 1.21502i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.59597 | − | 2.61263i | −0.228806 | − | 0.166237i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.809017 | − | 0.587785i | \(-0.200000\pi\) | ||||
−0.809017 | + | 0.587785i | \(0.800000\pi\) | |||||||
\(252\) | 28.5617i | 1.79922i | ||||||||
\(253\) | 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 | ||||||||
\(259\) | 14.5389 | − | 20.0111i | 0.903406 | − | 1.24343i | ||||
\(260\) | 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 | ||||||||
\(271\) | 30.4780 | + | 9.90289i | 1.85141 | + | 0.601558i | 0.996579 | + | 0.0826430i | \(0.0263361\pi\) |
0.854826 | + | 0.518915i | \(0.173664\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 23.2447 | − | 16.8883i | 1.40683 | − | 1.02212i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.84523 | + | 10.7980i | 0.471374 | + | 0.648791i | 0.976819 | − | 0.214068i | \(-0.0686715\pi\) |
−0.505445 | + | 0.862859i | \(0.668672\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | −26.8387 | + | 8.72043i | −1.59540 | + | 0.518376i | −0.965963 | − | 0.258679i | \(-0.916713\pi\) |
−0.629433 | + | 0.777055i | \(0.716713\pi\) | |||||||
\(284\) | 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 | ||||
\(292\) | −12.6915 | + | 17.4684i | −0.742716 | + | 1.02226i | ||||
\(293\) | 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 | ||||
\(301\) | 19.1309 | − | 58.8789i | 1.10269 | − | 3.39372i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 4.85234 | + | 1.57662i | 0.278301 | + | 0.0904254i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 34.2557i | 1.95508i | 0.210760 | + | 0.977538i | \(0.432406\pi\) | ||||
−0.210760 | + | 0.977538i | \(0.567594\pi\) | |||||||
\(308\) | 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 | 0.999090 | − | 0.0426523i | \(-0.0135808\pi\) |
0.268171 | + | 0.963371i | \(0.413581\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 33.7922 | − | 10.9797i | 1.90096 | − | 0.617659i | ||||
\(317\) | 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 | ||||
\(325\) | −10.2415 | + | 14.0962i | −0.568095 | + | 0.781915i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.0438 | + | 3.91325i | −0.666021 | + | 0.216403i | ||||
\(328\) | 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 | ||||||||
\(336\) | −19.3853 | + | 26.6815i | −1.05755 | + | 1.45560i | ||||
\(337\) | 21.0983 | + | 6.85527i | 1.14930 | + | 0.373430i | 0.820879 | − | 0.571101i | \(-0.193484\pi\) |
0.328420 | + | 0.944532i | \(0.393484\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −24.2316 | − | 33.3519i | −1.30838 | − | 1.80083i | ||||
\(344\) | 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 | ||||||||
\(349\) | 28.3768 | − | 9.22020i | 1.51898 | − | 0.493546i | 0.573493 | − | 0.819211i | \(-0.305588\pi\) |
0.945485 | + | 0.325665i | \(0.105588\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 18.1074i | − | 0.966500i | ||||||
\(352\) | 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 | ||||||||
\(361\) | −14.0551 | + | 10.2116i | −0.739742 | + | 0.537454i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 33.1769 | 1.73894 | ||||||||
\(365\) | 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 | ||||
\(373\) | 3.14299i | 0.162738i | 0.996684 | + | 0.0813690i | \(0.0259292\pi\) | ||||
−0.996684 | + | 0.0813690i | \(0.974071\pi\) | |||||||
\(374\) | 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 | ||||||||
\(381\) | 25.0626 | + | 8.14335i | 1.28400 | + | 0.417196i | ||||
\(382\) | 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 | ||||||||
\(387\) | −22.9330 | − | 31.5646i | −1.16575 | − | 1.60452i | ||||
\(388\) | 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 | ||||||||
\(399\) | 3.24983 | + | 10.0019i | 0.162695 | + | 0.500723i | ||||
\(400\) | 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 | ||||||||
\(403\) | 5.74038 | + | 1.86516i | 0.285949 | + | 0.0929103i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 23.6827 | + | 32.5965i | 1.17104 | + | 1.61179i | 0.656507 | + | 0.754320i | \(0.272033\pi\) |
0.514529 | + | 0.857473i | \(0.327967\pi\) | |||||||
\(410\) | 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 | ||||||||
\(417\) | 1.61729i | 0.0791988i | ||||||||
\(418\) | 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 | \(-0.780106\pi\) |
0.249012 | − | 0.968501i | \(-0.419894\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 45.1732 | − | 32.8203i | 2.18609 | − | 1.58828i | ||||
\(428\) | 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 | ||||||||
\(436\) | −13.9069 | − | 4.51863i | −0.666021 | − | 0.216403i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.8677i | 1.09141i | 0.837976 | + | 0.545707i | \(0.183739\pi\) | ||||
−0.837976 | + | 0.545707i | \(0.816261\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −46.9808 | −2.23718 | ||||||||
\(442\) | 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 | ||||||||
\(448\) | −36.2184 | + | 11.7681i | −1.71116 | + | 0.555988i | ||||
\(449\) | 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 | ||||||||
\(453\) | 20.3359 | + | 27.9899i | 0.955463 | + | 1.31508i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.4336 | − | 29.5008i | 1.00262 | − | 1.37999i | 0.0789151 | − | 0.996881i | \(-0.474854\pi\) |
0.923704 | − | 0.383106i | \(-0.125146\pi\) | |||||||
\(458\) | 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 | \(0.200000\pi\) | |||||||
\(468\) | 12.2898 | − | 16.9154i | 0.568095 | − | 0.781915i | ||||
\(469\) | −54.8905 | − | 17.8350i | −2.53461 | − | 0.823544i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −31.5517 | + | 22.9236i | −1.45382 | + | 1.05626i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.74864 | − | 5.15956i | −0.171999 | − | 0.236737i | ||||
\(476\) | 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 | ||||||||
\(481\) | −17.2211 | + | 5.59549i | −0.785216 | + | 0.255132i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.07047 | + | 3.29456i | 0.0485075 | + | 0.149291i | 0.972376 | − | 0.233418i | \(-0.0749912\pi\) |
−0.923869 | + | 0.382709i | \(0.874991\pi\) | |||||||
\(488\) | 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 | \(0.520813\pi\) |
−0.533667 | + | 0.845694i | \(0.679187\pi\) | |||||||
\(500\) | 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 | ||||||||
\(507\) | 1.48334 | 0.0658774 | ||||||||
\(508\) | 17.8858 | + | 24.6177i | 0.793554 | + | 1.09223i | ||||
\(509\) | 0 | 0 | −0.309017 | − | 0.951057i | \(-0.600000\pi\) | ||||
0.309017 | + | 0.951057i | \(0.400000\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −41.5772 | − | 30.2076i | −1.83927 | − | 1.33631i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.30337 | + | 2.04809i | 0.278301 | + | 0.0904254i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 45.0518i | − | 1.98329i | ||||||
\(517\) | 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 | ||||||||
\(523\) | 11.3930 | − | 15.6811i | 0.498180 | − | 0.685686i | −0.483690 | − | 0.875239i | \(-0.660704\pi\) |
0.981870 | + | 0.189553i | \(0.0607039\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 39.2075 | − | 12.7393i | 1.71116 | − | 0.555988i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.75258 | + | 11.5492i | −0.162695 | + | 0.500723i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.2393 | − | 22.3515i | −0.698182 | − | 0.960965i | −0.999971 | − | 0.00759004i | \(-0.997584\pi\) |
0.301790 | − | 0.953375i | \(-0.402416\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.1694 | − | 31.2983i | 0.436412 | − | 1.34314i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.5927 | + | 3.44178i | −0.452912 | + | 0.147160i | −0.526585 | − | 0.850122i | \(-0.676528\pi\) |
0.0736732 | + | 0.997282i | \(0.476528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 35.1894i | − | 1.50185i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 26.1333 | + | 80.4301i | 1.11130 | + | 3.42024i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.09768 | + | 1.51082i | −0.0465519 | + | 0.0640732i | ||||
\(557\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −36.6651 | + | 26.6387i | −1.55077 | + | 1.12670i | ||||
\(560\) | 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 | ||||||||
\(567\) | −25.1822 | + | 34.6603i | −1.05755 | + | 1.45560i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 39.3577i | − | 1.64707i | −0.567265 | − | 0.823535i | \(-0.691999\pi\) | ||
0.567265 | − | 0.823535i | \(-0.308001\pi\) | |||||||
\(572\) | 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 | \(0.126465\pi\) |
0.652941 | + | 0.757409i | \(0.273535\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −44.9479 | − | 14.6045i | −1.86797 | − | 0.606941i | ||||
\(580\) | 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 | \(0.600000\pi\) | |||||||
\(588\) | −43.8881 | − | 31.8866i | −1.80992 | − | 1.31498i | ||||
\(589\) | −1.29857 | + | 1.78732i | −0.0535065 | + | 0.0736454i | ||||
\(590\) | 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 | ||||||||
\(601\) | −34.1172 | − | 11.0854i | −1.39167 | − | 0.452181i | −0.485183 | − | 0.874413i | \(-0.661247\pi\) |
−0.906488 | + | 0.422232i | \(0.861247\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29.4264 | + | 21.3796i | −1.19834 | + | 0.870643i | ||||
\(604\) | 39.9497i | 1.62553i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.0296 | + | 37.2031i | 1.09710 | + | 1.51003i | 0.839176 | + | 0.543859i | \(0.183038\pi\) |
0.257921 | + | 0.966166i | \(0.416962\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.75121 | − | 0.893924i | 0.111121 | − | 0.0361052i | −0.252929 | − | 0.967485i | \(-0.581394\pi\) |
0.364049 | + | 0.931380i | \(0.381394\pi\) | |||||||
\(614\) | 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 | ||||||||
\(624\) | 22.9615 | − | 7.46065i | 0.919196 | − | 0.298665i | ||||
\(625\) | −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 | \(0.260330\pi\) |
−0.982092 | + | 0.188401i | \(0.939670\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −9.34468 | + | 12.8619i | −0.371418 | + | 0.511213i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 54.5723i | 2.16223i | ||||||||
\(638\) | 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 | ||||||||
\(651\) | −8.39406 | − | 11.5534i | −0.328989 | − | 0.452815i | ||||
\(652\) | −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 | ||||||||
\(657\) | −30.8030 | + | 10.0085i | −1.20174 | + | 0.390469i | ||||
\(658\) | 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 | \(-0.0686249\pi\) | ||||
0.976850 | + | 0.213925i | \(0.0686249\pi\) | |||||||
\(662\) | 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 | ||||||||
\(673\) | −26.2799 | − | 36.1711i | −1.01301 | − | 1.39430i | −0.916987 | − | 0.398916i | \(-0.869386\pi\) |
−0.0960273 | − | 0.995379i | \(-0.530614\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8.02850 | − | 24.7092i | 0.309017 | − | 0.951057i | ||||
\(676\) | 1.38569 | + | 1.00677i | 0.0532960 | + | 0.0387218i | ||||
\(677\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.6365 | + | 7.35504i | −0.868708 | + | 0.282260i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(684\) | 4.49837 | + | 6.19147i | 0.171999 | + | 0.236737i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 29.1246 | + | 21.1603i | 1.11117 | + | 0.807315i | ||||
\(688\) | 30.5773 | − | 42.0861i | 1.16575 | − | 1.60452i | ||||
\(689\) | 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 | ||||||||
\(700\) | 45.2729 | + | 14.7101i | 1.71116 | + | 0.555988i | ||||
\(701\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.62776i | − | 0.249971i | ||||||
\(704\) | 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 | \(-0.935559\pi\) |
−0.493933 | − | 0.869500i | \(-0.664441\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 50.6883 | + | 16.4696i | 1.90096 | + | 0.617659i | ||||
\(712\) | 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 | ||||||||
\(721\) | −19.5862 | + | 26.9580i | −0.729426 | + | 1.00397i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 48.5872 | − | 15.7869i | 1.80698 | − | 0.587122i | ||||
\(724\) | 30.7426 | − | 22.3358i | 1.14254 | − | 0.830105i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.1769 | 1.15629 | 0.578144 | − | 0.815935i | \(-0.303777\pi\) | ||||
0.578144 | + | 0.815935i | \(0.303777\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 8.34346 | + | 25.6785i | 0.309017 | + | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 23.8836 | − | 32.8730i | 0.882764 | − | 1.21502i | ||||
\(733\) | 19.6473 | + | 6.38380i | 0.725690 | + | 0.235791i | 0.648488 | − | 0.761225i | \(-0.275402\pi\) |
0.0772015 | + | 0.997016i | \(0.475402\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.9890 | + | 23.3834i | 0.624951 | + | 0.860171i | 0.997702 | − | 0.0677601i | \(-0.0215853\pi\) |
−0.372750 | + | 0.927932i | \(0.621585\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.37904 | − | 7.32193i | 0.0873962 | − | 0.268978i | ||||
\(742\) | 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 | \(-0.664321\pi\) |
−0.111854 | − | 0.993725i | \(-0.535679\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −47.0490 | + | 15.2872i | −1.71116 | + | 0.555988i | ||||
\(757\) | 1.40126 | − | 1.01807i | 0.0509296 | − | 0.0370025i | −0.562029 | − | 0.827117i | \(-0.689979\pi\) |
0.612959 | + | 0.790115i | \(0.289979\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 10.7550 | − | 33.1004i | 0.389356 | − | 1.19832i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −22.4201 | + | 16.2892i | −0.809017 | + | 0.587785i | ||||
\(769\) | − | 12.4134i | − | 0.447637i | −0.974631 | − | 0.223819i | \(-0.928148\pi\) | ||
0.974631 | − | 0.223819i | \(-0.0718523\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −32.0768 | − | 44.1499i | −1.15447 | − | 1.58899i | ||||
\(773\) | 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 | ||||||||
\(777\) | 40.7456 | + | 13.2391i | 1.46174 | + | 0.474949i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −19.3571 | − | 59.5751i | −0.691326 | − | 2.12768i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.8353 | + | 30.0538i | −0.778346 | + | 1.07130i | 0.217117 | + | 0.976146i | \(0.430335\pi\) |
−0.995462 | + | 0.0951552i | \(0.969665\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −40.8756 | −1.45154 | ||||||||
\(794\) | 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 | ||||||||
\(811\) | 54.0025 | − | 17.5465i | 1.89628 | − | 0.616140i | 0.923967 | − | 0.382471i | \(-0.124927\pi\) |
0.972316 | − | 0.233669i | \(-0.0750732\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 55.5061i | 1.94668i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.12612 | − | 15.7766i | −0.179340 | − | 0.551952i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 40.2610 | + | 29.2514i | 1.40683 | + | 1.02212i | ||||
\(820\) | 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 | ||||||||
\(831\) | −13.5883 | + | 18.7027i | −0.471374 | + | 0.648791i | ||||
\(832\) | 26.5137 | + | 8.61482i | 0.919196 | + | 0.298665i | ||||
\(833\) | 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 | ||||||||
\(844\) | −17.4591 | + | 5.67280i | −0.600967 | + | 0.195266i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −28.7299 | − | 39.5434i | −0.986009 | − | 1.35713i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −31.8759 | + | 43.8734i | −1.09141 | + | 1.50220i | −0.245108 | + | 0.969496i | \(0.578823\pi\) |
−0.846303 | + | 0.532702i | \(0.821177\pi\) | |||||||
\(854\) | 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 | ||||
\(868\) | − | 16.4901i | − | 0.559710i | ||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.8342 | + | 34.1814i | 0.841476 | + | 1.15819i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.63525 | + | 14.2658i | −0.156880 | + | 0.482826i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −35.5683 | − | 11.5568i | −1.20174 | − | 0.390469i | ||||
\(877\) | 43.1718 | − | 14.0274i | 1.45781 | − | 0.473671i | 0.530409 | − | 0.847742i | \(-0.322038\pi\) |
0.927400 | + | 0.374071i | \(0.122038\pi\) | |||||||
\(878\) | 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 | \(0.0236883\pi\) |
−0.763076 | + | 0.646309i | \(0.776312\pi\) | |||||||
\(884\) | 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 | ||||||||
\(889\) | −58.5936 | + | 42.5707i | −1.96517 | + | 1.42778i | ||||
\(890\) | 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 | ||||||||
\(903\) | 107.229 | 3.56837 | ||||||||
\(904\) | 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 | \(0.800000\pi\) | |||||||
\(912\) | 8.83701i | 0.292623i | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.8456 | + | 39.5347i | 0.424430 | + | 1.30626i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.7804 | − | 34.1073i | 0.817431 | − | 1.12510i | −0.172704 | − | 0.984974i | \(-0.555250\pi\) |
0.990134 | − | 0.140123i | \(-0.0447497\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −56.4287 | + | 18.3348i | −1.85939 | + | 0.604152i | ||||
\(922\) | 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 | ||||||||
\(931\) | −18.9972 | − | 6.17257i | −0.622609 | − | 0.202298i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −35.4237 | − | 48.7565i | −1.15724 | − | 1.59281i | −0.720928 | − | 0.693010i | \(-0.756284\pi\) |
−0.436313 | − | 0.899795i | \(-0.643716\pi\) | |||||||
\(938\) | 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 | \(\pi\) | |||||||||
\(948\) | 36.1734 | + | 49.7884i | 1.17486 | + | 1.61705i | ||||
\(949\) | 11.6258 | + | 35.7804i | 0.377388 | + | 1.16148i | ||||
\(950\) | 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 | ||||||||
\(964\) | 56.1036 | + | 18.2292i | 1.80698 | + | 0.587122i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 4.07673i | − | 0.131099i | −0.997849 | − | 0.0655495i | \(-0.979120\pi\) | ||
0.997849 | − | 0.0655495i | \(-0.0208800\pi\) | |||||||
\(968\) | 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 | ||||
\(973\) | −3.59597 | − | 2.61263i | −0.115282 | − | 0.0837569i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −28.7019 | − | 9.32581i | −0.919196 | − | 0.298665i | ||||
\(976\) | 44.6229 | − | 14.4988i | 1.42834 | − | 0.464097i | ||||
\(977\) | 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 | ||||||||
\(981\) | −12.8924 | − | 17.7449i | −0.411624 | − | 0.566551i | ||||
\(982\) | 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 | ||||||||
\(988\) | 7.19194 | − | 5.22525i | 0.228806 | − | 0.166237i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −45.0333 | −1.43053 | −0.715265 | − | 0.698853i | \(-0.753694\pi\) | ||||
−0.715265 | + | 0.698853i | \(0.753694\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −16.5922 | − | 51.0656i | −0.526538 | − | 1.62052i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −59.7429 | − | 19.4116i | −1.89208 | − | 0.614773i | −0.977742 | − | 0.209810i | \(-0.932715\pi\) |
−0.914333 | − | 0.404962i | \(-0.867285\pi\) | |||||||
\(998\) | 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.239.3 | 16 | ||
3.2 | odd | 2 | CM | 363.2.f.g.239.3 | 16 | ||
11.2 | odd | 10 | 363.2.d.d.362.4 | yes | 4 | ||
11.3 | even | 5 | inner | 363.2.f.g.215.2 | 16 | ||
11.4 | even | 5 | inner | 363.2.f.g.161.4 | 16 | ||
11.5 | even | 5 | inner | 363.2.f.g.233.1 | 16 | ||
11.6 | odd | 10 | inner | 363.2.f.g.233.2 | 16 | ||
11.7 | odd | 10 | inner | 363.2.f.g.161.3 | 16 | ||
11.8 | odd | 10 | inner | 363.2.f.g.215.1 | 16 | ||
11.9 | even | 5 | 363.2.d.d.362.3 | ✓ | 4 | ||
11.10 | odd | 2 | inner | 363.2.f.g.239.4 | 16 | ||
33.2 | even | 10 | 363.2.d.d.362.4 | yes | 4 | ||
33.5 | odd | 10 | inner | 363.2.f.g.233.1 | 16 | ||
33.8 | even | 10 | inner | 363.2.f.g.215.1 | 16 | ||
33.14 | odd | 10 | inner | 363.2.f.g.215.2 | 16 | ||
33.17 | even | 10 | inner | 363.2.f.g.233.2 | 16 | ||
33.20 | odd | 10 | 363.2.d.d.362.3 | ✓ | 4 | ||
33.26 | odd | 10 | inner | 363.2.f.g.161.4 | 16 | ||
33.29 | even | 10 | inner | 363.2.f.g.161.3 | 16 | ||
33.32 | even | 2 | inner | 363.2.f.g.239.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
363.2.d.d.362.3 | ✓ | 4 | 11.9 | even | 5 | ||
363.2.d.d.362.3 | ✓ | 4 | 33.20 | odd | 10 | ||
363.2.d.d.362.4 | yes | 4 | 11.2 | odd | 10 | ||
363.2.d.d.362.4 | yes | 4 | 33.2 | even | 10 | ||
363.2.f.g.161.3 | 16 | 11.7 | odd | 10 | inner | ||
363.2.f.g.161.3 | 16 | 33.29 | even | 10 | inner | ||
363.2.f.g.161.4 | 16 | 11.4 | even | 5 | inner | ||
363.2.f.g.161.4 | 16 | 33.26 | odd | 10 | inner | ||
363.2.f.g.215.1 | 16 | 11.8 | odd | 10 | inner | ||
363.2.f.g.215.1 | 16 | 33.8 | even | 10 | inner | ||
363.2.f.g.215.2 | 16 | 11.3 | even | 5 | inner | ||
363.2.f.g.215.2 | 16 | 33.14 | odd | 10 | inner | ||
363.2.f.g.233.1 | 16 | 11.5 | even | 5 | inner | ||
363.2.f.g.233.1 | 16 | 33.5 | odd | 10 | inner | ||
363.2.f.g.233.2 | 16 | 11.6 | odd | 10 | inner | ||
363.2.f.g.233.2 | 16 | 33.17 | even | 10 | inner | ||
363.2.f.g.239.3 | 16 | 1.1 | even | 1 | trivial | ||
363.2.f.g.239.3 | 16 | 3.2 | odd | 2 | CM | ||
363.2.f.g.239.4 | 16 | 11.10 | odd | 2 | inner | ||
363.2.f.g.239.4 | 16 | 33.32 | even | 2 | inner |