Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(25,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.bk (of order \(6\), degree \(2\), 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: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 15x^{10} + 90x^{8} - 247x^{6} + 270x^{4} + 21x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 415.4 | ||
Root | \(2.23871 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.415 |
Dual form | 546.2.bk.b.25.4 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | −1.95878 | − | 1.13090i | −0.875992 | − | 0.505754i | −0.00665735 | − | 0.999978i | \(-0.502119\pi\) |
−0.869335 | + | 0.494223i | \(0.835452\pi\) | |||||||
\(6\) | − | 1.00000i | − | 0.408248i | ||||||
\(7\) | −2.41839 | + | 1.07303i | −0.914066 | + | 0.405566i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | −1.13090 | − | 1.95878i | −0.357622 | − | 0.619420i | ||||
\(11\) | −1.09275 | + | 0.630901i | −0.329477 | + | 0.190224i | −0.655609 | − | 0.755101i | \(-0.727588\pi\) |
0.326132 | + | 0.945324i | \(0.394255\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −1.26180 | − | 3.37755i | −0.349961 | − | 0.936764i | ||||
\(14\) | −2.63090 | − | 0.279927i | −0.703138 | − | 0.0748137i | ||||
\(15\) | 2.26180i | 0.583995i | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −0.188776 | − | 0.326969i | −0.0457849 | − | 0.0793017i | 0.842225 | − | 0.539127i | \(-0.181246\pi\) |
−0.888010 | + | 0.459825i | \(0.847912\pi\) | |||||||
\(18\) | −0.866025 | + | 0.500000i | −0.204124 | + | 0.117851i | ||||
\(19\) | −6.71612 | − | 3.87755i | −1.54078 | − | 0.889571i | −0.998790 | − | 0.0491885i | \(-0.984336\pi\) |
−0.541993 | − | 0.840383i | \(-0.682330\pi\) | |||||||
\(20\) | − | 2.26180i | − | 0.505754i | ||||||
\(21\) | 2.13846 | + | 1.55787i | 0.466651 | + | 0.339956i | ||||
\(22\) | −1.26180 | −0.269017 | ||||||||
\(23\) | −2.24665 | + | 3.89131i | −0.468459 | + | 0.811395i | −0.999350 | − | 0.0360452i | \(-0.988524\pi\) |
0.530891 | + | 0.847440i | \(0.321857\pi\) | |||||||
\(24\) | 0.866025 | − | 0.500000i | 0.176777 | − | 0.102062i | ||||
\(25\) | 0.0578747 | + | 0.100242i | 0.0115749 | + | 0.0200484i | ||||
\(26\) | 0.596023 | − | 3.55595i | 0.116890 | − | 0.697379i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.13846 | − | 1.55787i | −0.404132 | − | 0.294411i | ||||
\(29\) | −2.40786 | −0.447127 | −0.223564 | − | 0.974689i | \(-0.571769\pi\) | ||||
−0.223564 | + | 0.974689i | \(0.571769\pi\) | |||||||
\(30\) | −1.13090 | + | 1.95878i | −0.206473 | + | 0.357622i | ||||
\(31\) | −3.46410 | + | 2.00000i | −0.622171 | + | 0.359211i | −0.777714 | − | 0.628619i | \(-0.783621\pi\) |
0.155543 | + | 0.987829i | \(0.450287\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 1.09275 | + | 0.630901i | 0.190224 | + | 0.109826i | ||||
\(34\) | − | 0.377552i | − | 0.0647496i | ||||||
\(35\) | 5.95058 | + | 0.633140i | 1.00583 | + | 0.107020i | ||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | −2.92505 | − | 1.68878i | −0.480875 | − | 0.277633i | 0.239906 | − | 0.970796i | \(-0.422883\pi\) |
−0.720781 | + | 0.693163i | \(0.756217\pi\) | |||||||
\(38\) | −3.87755 | − | 6.71612i | −0.629022 | − | 1.08950i | ||||
\(39\) | −2.29414 | + | 2.78153i | −0.367357 | + | 0.445401i | ||||
\(40\) | 1.13090 | − | 1.95878i | 0.178811 | − | 0.309710i | ||||
\(41\) | 9.90116i | 1.54630i | 0.634223 | + | 0.773150i | \(0.281320\pi\) | ||||
−0.634223 | + | 0.773150i | \(0.718680\pi\) | |||||||
\(42\) | 1.07303 | + | 2.41839i | 0.165572 | + | 0.373166i | ||||
\(43\) | 8.75510 | 1.33514 | 0.667570 | − | 0.744547i | \(-0.267334\pi\) | ||||
0.667570 | + | 0.744547i | \(0.267334\pi\) | |||||||
\(44\) | −1.09275 | − | 0.630901i | −0.164739 | − | 0.0951119i | ||||
\(45\) | 1.95878 | − | 1.13090i | 0.291997 | − | 0.168585i | ||||
\(46\) | −3.89131 | + | 2.24665i | −0.573743 | + | 0.331251i | ||||
\(47\) | 2.85105 | + | 1.64605i | 0.415868 | + | 0.240101i | 0.693308 | − | 0.720642i | \(-0.256153\pi\) |
−0.277440 | + | 0.960743i | \(0.589486\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 4.69723 | − | 5.18999i | 0.671033 | − | 0.741428i | ||||
\(50\) | 0.115749i | 0.0163694i | ||||||||
\(51\) | −0.188776 | + | 0.326969i | −0.0264339 | + | 0.0457849i | ||||
\(52\) | 2.29414 | − | 2.78153i | 0.318141 | − | 0.385729i | ||||
\(53\) | −1.50000 | − | 2.59808i | −0.206041 | − | 0.356873i | 0.744423 | − | 0.667708i | \(-0.232725\pi\) |
−0.950464 | + | 0.310835i | \(0.899391\pi\) | |||||||
\(54\) | 0.866025 | + | 0.500000i | 0.117851 | + | 0.0680414i | ||||
\(55\) | 2.85395 | 0.384826 | ||||||||
\(56\) | −1.07303 | − | 2.41839i | −0.143389 | − | 0.323171i | ||||
\(57\) | 7.75510i | 1.02719i | ||||||||
\(58\) | −2.08526 | − | 1.20393i | −0.273809 | − | 0.158083i | ||||
\(59\) | 4.04404 | − | 2.33483i | 0.526489 | − | 0.303969i | −0.213096 | − | 0.977031i | \(-0.568355\pi\) |
0.739586 | + | 0.673062i | \(0.235021\pi\) | |||||||
\(60\) | −1.95878 | + | 1.13090i | −0.252877 | + | 0.145999i | ||||
\(61\) | 4.45058 | − | 7.70863i | 0.569838 | − | 0.986989i | −0.426743 | − | 0.904373i | \(-0.640339\pi\) |
0.996581 | − | 0.0826158i | \(-0.0263274\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0.279927 | − | 2.63090i | 0.0352675 | − | 0.331462i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −1.34809 | + | 8.04285i | −0.167210 | + | 0.997593i | ||||
\(66\) | 0.630901 | + | 1.09275i | 0.0776586 | + | 0.134509i | ||||
\(67\) | −1.11900 | + | 0.646053i | −0.136707 | + | 0.0789279i | −0.566794 | − | 0.823860i | \(-0.691816\pi\) |
0.430087 | + | 0.902788i | \(0.358483\pi\) | |||||||
\(68\) | 0.188776 | − | 0.326969i | 0.0228924 | − | 0.0396509i | ||||
\(69\) | 4.49330 | 0.540930 | ||||||||
\(70\) | 4.83678 | + | 3.52360i | 0.578106 | + | 0.421151i | ||||
\(71\) | − | 4.11575i | − | 0.488450i | −0.969719 | − | 0.244225i | \(-0.921467\pi\) | ||
0.969719 | − | 0.244225i | \(-0.0785335\pi\) | |||||||
\(72\) | −0.866025 | − | 0.500000i | −0.102062 | − | 0.0589256i | ||||
\(73\) | 8.26232 | − | 4.77026i | 0.967032 | − | 0.558316i | 0.0687018 | − | 0.997637i | \(-0.478114\pi\) |
0.898330 | + | 0.439321i | \(0.144781\pi\) | |||||||
\(74\) | −1.68878 | − | 2.92505i | −0.196316 | − | 0.340030i | ||||
\(75\) | 0.0578747 | − | 0.100242i | 0.00668279 | − | 0.0115749i | ||||
\(76\) | − | 7.75510i | − | 0.889571i | ||||||
\(77\) | 1.96573 | − | 2.69832i | 0.224016 | − | 0.307502i | ||||
\(78\) | −3.37755 | + | 1.26180i | −0.382432 | + | 0.142871i | ||||
\(79\) | 3.14605 | − | 5.44912i | 0.353959 | − | 0.613074i | −0.632981 | − | 0.774168i | \(-0.718169\pi\) |
0.986939 | + | 0.161093i | \(0.0515020\pi\) | |||||||
\(80\) | 1.95878 | − | 1.13090i | 0.218998 | − | 0.126439i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −4.95058 | + | 8.57465i | −0.546700 | + | 0.946912i | ||||
\(83\) | 6.39446i | 0.701883i | 0.936397 | + | 0.350941i | \(0.114138\pi\) | ||||
−0.936397 | + | 0.350941i | \(0.885862\pi\) | |||||||
\(84\) | −0.279927 | + | 2.63090i | −0.0305426 | + | 0.287055i | ||||
\(85\) | 0.853947i | 0.0926236i | ||||||||
\(86\) | 7.58214 | + | 4.37755i | 0.817603 | + | 0.472044i | ||||
\(87\) | 1.20393 | + | 2.08526i | 0.129075 | + | 0.223564i | ||||
\(88\) | −0.630901 | − | 1.09275i | −0.0672543 | − | 0.116488i | ||||
\(89\) | −9.85325 | − | 5.68878i | −1.04444 | − | 0.603009i | −0.123354 | − | 0.992363i | \(-0.539365\pi\) |
−0.921088 | + | 0.389354i | \(0.872698\pi\) | |||||||
\(90\) | 2.26180 | 0.238415 | ||||||||
\(91\) | 6.67573 | + | 6.81429i | 0.699807 | + | 0.714332i | ||||
\(92\) | −4.49330 | −0.468459 | ||||||||
\(93\) | 3.46410 | + | 2.00000i | 0.359211 | + | 0.207390i | ||||
\(94\) | 1.64605 | + | 2.85105i | 0.169777 | + | 0.294063i | ||||
\(95\) | 8.77026 | + | 15.1905i | 0.899809 | + | 1.55852i | ||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | − | 8.03030i | − | 0.815354i | −0.913126 | − | 0.407677i | \(-0.866339\pi\) | ||
0.913126 | − | 0.407677i | \(-0.133661\pi\) | |||||||
\(98\) | 6.66292 | − | 2.14605i | 0.673056 | − | 0.216784i | ||||
\(99\) | − | 1.26180i | − | 0.126816i | ||||||
\(100\) | −0.0578747 | + | 0.100242i | −0.00578747 | + | 0.0100242i | ||||
\(101\) | −5.81968 | − | 10.0800i | −0.579079 | − | 1.00300i | −0.995585 | − | 0.0938620i | \(-0.970079\pi\) |
0.416506 | − | 0.909133i | \(-0.363255\pi\) | |||||||
\(102\) | −0.326969 | + | 0.188776i | −0.0323748 | + | 0.0186916i | ||||
\(103\) | −6.23150 | + | 10.7933i | −0.614008 | + | 1.06349i | 0.376550 | + | 0.926396i | \(0.377110\pi\) |
−0.990558 | + | 0.137096i | \(0.956223\pi\) | |||||||
\(104\) | 3.37755 | − | 1.26180i | 0.331196 | − | 0.123730i | ||||
\(105\) | −2.42697 | − | 5.46992i | −0.236848 | − | 0.533810i | ||||
\(106\) | − | 3.00000i | − | 0.291386i | ||||||
\(107\) | −8.90116 | + | 15.4173i | −0.860507 | + | 1.49044i | 0.0109328 | + | 0.999940i | \(0.496520\pi\) |
−0.871440 | + | 0.490502i | \(0.836813\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 2.83944 | − | 1.63935i | 0.271969 | − | 0.157022i | −0.357813 | − | 0.933793i | \(-0.616477\pi\) |
0.629782 | + | 0.776772i | \(0.283144\pi\) | |||||||
\(110\) | 2.47159 | + | 1.42697i | 0.235657 | + | 0.136057i | ||||
\(111\) | 3.37755i | 0.320583i | ||||||||
\(112\) | 0.279927 | − | 2.63090i | 0.0264506 | − | 0.248597i | ||||
\(113\) | 1.32241 | 0.124402 | 0.0622009 | − | 0.998064i | \(-0.480188\pi\) | ||||
0.0622009 | + | 0.998064i | \(0.480188\pi\) | |||||||
\(114\) | −3.87755 | + | 6.71612i | −0.363166 | + | 0.629022i | ||||
\(115\) | 8.80138 | − | 5.08148i | 0.820733 | − | 0.473850i | ||||
\(116\) | −1.20393 | − | 2.08526i | −0.111782 | − | 0.193612i | ||||
\(117\) | 3.55595 | + | 0.596023i | 0.328747 | + | 0.0551023i | ||||
\(118\) | 4.66966 | 0.429877 | ||||||||
\(119\) | 0.807380 | + | 0.588178i | 0.0740124 | + | 0.0539182i | ||||
\(120\) | −2.26180 | −0.206473 | ||||||||
\(121\) | −4.70393 | + | 8.14744i | −0.427630 | + | 0.740677i | ||||
\(122\) | 7.70863 | − | 4.45058i | 0.697906 | − | 0.402936i | ||||
\(123\) | 8.57465 | − | 4.95058i | 0.773150 | − | 0.446379i | ||||
\(124\) | −3.46410 | − | 2.00000i | −0.311086 | − | 0.179605i | ||||
\(125\) | 11.0472i | 0.988092i | ||||||||
\(126\) | 1.55787 | − | 2.13846i | 0.138787 | − | 0.190509i | ||||
\(127\) | −16.3642 | −1.45208 | −0.726042 | − | 0.687650i | \(-0.758642\pi\) | ||||
−0.726042 | + | 0.687650i | \(0.758642\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −4.37755 | − | 7.58214i | −0.385422 | − | 0.667570i | ||||
\(130\) | −5.18890 | + | 6.29127i | −0.455097 | + | 0.551781i | ||||
\(131\) | 5.71908 | − | 9.90574i | 0.499678 | − | 0.865468i | −0.500322 | − | 0.865840i | \(-0.666785\pi\) |
1.00000 | 0.000371455i | \(0.000118238\pi\) | ||||||||
\(132\) | 1.26180i | 0.109826i | ||||||||
\(133\) | 20.4029 | + | 2.17086i | 1.76916 | + | 0.188238i | ||||
\(134\) | −1.29211 | −0.111621 | ||||||||
\(135\) | −1.95878 | − | 1.13090i | −0.168585 | − | 0.0973325i | ||||
\(136\) | 0.326969 | − | 0.188776i | 0.0280374 | − | 0.0161874i | ||||
\(137\) | 9.65276 | − | 5.57303i | 0.824691 | − | 0.476136i | −0.0273402 | − | 0.999626i | \(-0.508704\pi\) |
0.852032 | + | 0.523490i | \(0.175370\pi\) | |||||||
\(138\) | 3.89131 | + | 2.24665i | 0.331251 | + | 0.191248i | ||||
\(139\) | −2.49330 | −0.211479 | −0.105740 | − | 0.994394i | \(-0.533721\pi\) | ||||
−0.105740 | + | 0.994394i | \(0.533721\pi\) | |||||||
\(140\) | 2.42697 | + | 5.46992i | 0.205117 | + | 0.462293i | ||||
\(141\) | − | 3.29211i | − | 0.277245i | ||||||
\(142\) | 2.05787 | − | 3.56434i | 0.172693 | − | 0.299113i | ||||
\(143\) | 3.50974 | + | 2.89476i | 0.293499 | + | 0.242072i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 4.71645 | + | 2.72305i | 0.391680 | + | 0.226137i | ||||
\(146\) | 9.54051 | 0.789578 | ||||||||
\(147\) | −6.84328 | − | 1.47292i | −0.564424 | − | 0.121485i | ||||
\(148\) | − | 3.37755i | − | 0.277633i | ||||||
\(149\) | −0.0262436 | − | 0.0151517i | −0.00214996 | − | 0.00124128i | 0.498925 | − | 0.866645i | \(-0.333728\pi\) |
−0.501075 | + | 0.865404i | \(0.667062\pi\) | |||||||
\(150\) | 0.100242 | − | 0.0578747i | 0.00818472 | − | 0.00472545i | ||||
\(151\) | −3.73171 | + | 2.15451i | −0.303683 | + | 0.175331i | −0.644096 | − | 0.764945i | \(-0.722766\pi\) |
0.340413 | + | 0.940276i | \(0.389433\pi\) | |||||||
\(152\) | 3.87755 | − | 6.71612i | 0.314511 | − | 0.544749i | ||||
\(153\) | 0.377552 | 0.0305232 | ||||||||
\(154\) | 3.05153 | − | 1.35395i | 0.245899 | − | 0.109104i | ||||
\(155\) | 9.04721 | 0.726689 | ||||||||
\(156\) | −3.55595 | − | 0.596023i | −0.284704 | − | 0.0477200i | ||||
\(157\) | −11.3557 | − | 19.6687i | −0.906284 | − | 1.56973i | −0.819185 | − | 0.573530i | \(-0.805574\pi\) |
−0.0870987 | − | 0.996200i | \(-0.527760\pi\) | |||||||
\(158\) | 5.44912 | − | 3.14605i | 0.433509 | − | 0.250287i | ||||
\(159\) | −1.50000 | + | 2.59808i | −0.118958 | + | 0.206041i | ||||
\(160\) | 2.26180 | 0.178811 | ||||||||
\(161\) | 1.25780 | − | 11.8214i | 0.0991283 | − | 0.931659i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −10.7455 | − | 6.20393i | −0.841654 | − | 0.485929i | 0.0161722 | − | 0.999869i | \(-0.494852\pi\) |
−0.857826 | + | 0.513940i | \(0.828185\pi\) | |||||||
\(164\) | −8.57465 | + | 4.95058i | −0.669568 | + | 0.386575i | ||||
\(165\) | −1.42697 | − | 2.47159i | −0.111090 | − | 0.192413i | ||||
\(166\) | −3.19723 | + | 5.53776i | −0.248153 | + | 0.429814i | ||||
\(167\) | 24.6732i | 1.90927i | 0.297784 | + | 0.954633i | \(0.403753\pi\) | ||||
−0.297784 | + | 0.954633i | \(0.596247\pi\) | |||||||
\(168\) | −1.55787 | + | 2.13846i | −0.120193 | + | 0.164986i | ||||
\(169\) | −9.81571 | + | 8.52360i | −0.755055 | + | 0.655662i | ||||
\(170\) | −0.426974 | + | 0.739540i | −0.0327474 | + | 0.0567201i | ||||
\(171\) | 6.71612 | − | 3.87755i | 0.513594 | − | 0.296524i | ||||
\(172\) | 4.37755 | + | 7.58214i | 0.333785 | + | 0.578133i | ||||
\(173\) | −11.9893 | + | 20.7661i | −0.911532 | + | 1.57882i | −0.0996316 | + | 0.995024i | \(0.531766\pi\) |
−0.811901 | + | 0.583796i | \(0.801567\pi\) | |||||||
\(174\) | 2.40786i | 0.182539i | ||||||||
\(175\) | −0.247526 | − | 0.180323i | −0.0187112 | − | 0.0136311i | ||||
\(176\) | − | 1.26180i | − | 0.0951119i | ||||||
\(177\) | −4.04404 | − | 2.33483i | −0.303969 | − | 0.175496i | ||||
\(178\) | −5.68878 | − | 9.85325i | −0.426392 | − | 0.738532i | ||||
\(179\) | 2.85395 | + | 4.94318i | 0.213314 | + | 0.369471i | 0.952750 | − | 0.303756i | \(-0.0982409\pi\) |
−0.739436 | + | 0.673227i | \(0.764908\pi\) | |||||||
\(180\) | 1.95878 | + | 1.13090i | 0.145999 | + | 0.0842924i | ||||
\(181\) | −16.6697 | −1.23905 | −0.619523 | − | 0.784979i | \(-0.712674\pi\) | ||||
−0.619523 | + | 0.784979i | \(0.712674\pi\) | |||||||
\(182\) | 2.37421 | + | 9.23922i | 0.175988 | + | 0.684856i | ||||
\(183\) | −8.90116 | −0.657992 | ||||||||
\(184\) | −3.89131 | − | 2.24665i | −0.286871 | − | 0.165625i | ||||
\(185\) | 3.81968 | + | 6.61587i | 0.280828 | + | 0.486409i | ||||
\(186\) | 2.00000 | + | 3.46410i | 0.146647 | + | 0.254000i | ||||
\(187\) | 0.412571 | + | 0.238198i | 0.0301702 | + | 0.0174187i | ||||
\(188\) | 3.29211i | 0.240101i | ||||||||
\(189\) | −2.41839 | + | 1.07303i | −0.175912 | + | 0.0780512i | ||||
\(190\) | 17.5405i | 1.27252i | ||||||||
\(191\) | −3.63935 | + | 6.30355i | −0.263334 | + | 0.456109i | −0.967126 | − | 0.254298i | \(-0.918156\pi\) |
0.703791 | + | 0.710407i | \(0.251489\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 14.9900 | − | 8.65451i | 1.07901 | − | 0.622965i | 0.148379 | − | 0.988931i | \(-0.452595\pi\) |
0.930628 | + | 0.365966i | \(0.119261\pi\) | |||||||
\(194\) | 4.01515 | − | 6.95445i | 0.288271 | − | 0.499300i | ||||
\(195\) | 7.63935 | − | 2.85395i | 0.547065 | − | 0.204375i | ||||
\(196\) | 6.84328 | + | 1.47292i | 0.488806 | + | 0.105209i | ||||
\(197\) | 3.21459i | 0.229030i | 0.993422 | + | 0.114515i | \(0.0365314\pi\) | ||||
−0.993422 | + | 0.114515i | \(0.963469\pi\) | |||||||
\(198\) | 0.630901 | − | 1.09275i | 0.0448362 | − | 0.0776586i | ||||
\(199\) | −5.85173 | − | 10.1355i | −0.414818 | − | 0.718487i | 0.580591 | − | 0.814195i | \(-0.302822\pi\) |
−0.995409 | + | 0.0957088i | \(0.969488\pi\) | |||||||
\(200\) | −0.100242 | + | 0.0578747i | −0.00708817 | + | 0.00409236i | ||||
\(201\) | 1.11900 | + | 0.646053i | 0.0789279 | + | 0.0455691i | ||||
\(202\) | − | 11.6394i | − | 0.818942i | ||||||
\(203\) | 5.82313 | − | 2.58369i | 0.408704 | − | 0.181340i | ||||
\(204\) | −0.377552 | −0.0264339 | ||||||||
\(205\) | 11.1972 | − | 19.3942i | 0.782048 | − | 1.35455i | ||||
\(206\) | −10.7933 | + | 6.23150i | −0.752003 | + | 0.434169i | ||||
\(207\) | −2.24665 | − | 3.89131i | −0.156153 | − | 0.270465i | ||||
\(208\) | 3.55595 | + | 0.596023i | 0.246561 | + | 0.0413268i | ||||
\(209\) | 9.78541 | 0.676871 | ||||||||
\(210\) | 0.633140 | − | 5.95058i | 0.0436908 | − | 0.410629i | ||||
\(211\) | −8.06411 | −0.555157 | −0.277578 | − | 0.960703i | \(-0.589532\pi\) | ||||
−0.277578 | + | 0.960703i | \(0.589532\pi\) | |||||||
\(212\) | 1.50000 | − | 2.59808i | 0.103020 | − | 0.178437i | ||||
\(213\) | −3.56434 | + | 2.05787i | −0.244225 | + | 0.141003i | ||||
\(214\) | −15.4173 | + | 8.90116i | −1.05390 | + | 0.608471i | ||||
\(215\) | −17.1493 | − | 9.90116i | −1.16957 | − | 0.675253i | ||||
\(216\) | 1.00000i | 0.0680414i | ||||||||
\(217\) | 6.23150 | − | 8.55385i | 0.423022 | − | 0.580673i | ||||
\(218\) | 3.27871 | 0.222062 | ||||||||
\(219\) | −8.26232 | − | 4.77026i | −0.558316 | − | 0.322344i | ||||
\(220\) | 1.42697 | + | 2.47159i | 0.0962065 | + | 0.166635i | ||||
\(221\) | −0.866158 | + | 1.05017i | −0.0582641 | + | 0.0706421i | ||||
\(222\) | −1.68878 | + | 2.92505i | −0.113343 | + | 0.196316i | ||||
\(223\) | 23.7854i | 1.59279i | 0.604778 | + | 0.796394i | \(0.293262\pi\) | ||||
−0.604778 | + | 0.796394i | \(0.706738\pi\) | |||||||
\(224\) | 1.55787 | − | 2.13846i | 0.104090 | − | 0.142882i | ||||
\(225\) | −0.115749 | −0.00771663 | ||||||||
\(226\) | 1.14524 | + | 0.661205i | 0.0761802 | + | 0.0439827i | ||||
\(227\) | −8.86074 | + | 5.11575i | −0.588108 | + | 0.339544i | −0.764349 | − | 0.644803i | \(-0.776939\pi\) |
0.176241 | + | 0.984347i | \(0.443606\pi\) | |||||||
\(228\) | −6.71612 | + | 3.87755i | −0.444786 | + | 0.256797i | ||||
\(229\) | −0.906910 | − | 0.523604i | −0.0599303 | − | 0.0346008i | 0.469735 | − | 0.882807i | \(-0.344349\pi\) |
−0.529666 | + | 0.848206i | \(0.677683\pi\) | |||||||
\(230\) | 10.1630 | 0.670126 | ||||||||
\(231\) | −3.31968 | − | 0.353213i | −0.218419 | − | 0.0232397i | ||||
\(232\) | − | 2.40786i | − | 0.158083i | ||||||
\(233\) | 1.87580 | − | 3.24898i | 0.122888 | − | 0.212848i | −0.798018 | − | 0.602634i | \(-0.794118\pi\) |
0.920905 | + | 0.389787i | \(0.127451\pi\) | |||||||
\(234\) | 2.78153 | + | 2.29414i | 0.181834 | + | 0.149973i | ||||
\(235\) | −3.72305 | − | 6.44850i | −0.242865 | − | 0.420654i | ||||
\(236\) | 4.04404 | + | 2.33483i | 0.263245 | + | 0.151984i | ||||
\(237\) | −6.29211 | −0.408716 | ||||||||
\(238\) | 0.405123 | + | 0.913067i | 0.0262602 | + | 0.0591854i | ||||
\(239\) | − | 29.1968i | − | 1.88858i | −0.329112 | − | 0.944291i | \(-0.606749\pi\) | ||
0.329112 | − | 0.944291i | \(-0.393251\pi\) | |||||||
\(240\) | −1.95878 | − | 1.13090i | −0.126439 | − | 0.0729994i | ||||
\(241\) | −1.47908 | + | 0.853947i | −0.0952759 | + | 0.0550076i | −0.546881 | − | 0.837210i | \(-0.684185\pi\) |
0.451605 | + | 0.892218i | \(0.350852\pi\) | |||||||
\(242\) | −8.14744 | + | 4.70393i | −0.523737 | + | 0.302380i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 8.90116 | 0.569838 | ||||||||
\(245\) | −15.0702 | + | 4.85395i | −0.962800 | + | 0.310107i | ||||
\(246\) | 9.90116 | 0.631275 | ||||||||
\(247\) | −4.62222 | + | 27.5767i | −0.294105 | + | 1.75467i | ||||
\(248\) | −2.00000 | − | 3.46410i | −0.127000 | − | 0.219971i | ||||
\(249\) | 5.53776 | − | 3.19723i | 0.350941 | − | 0.202616i | ||||
\(250\) | −5.52360 | + | 9.56716i | −0.349343 | + | 0.605081i | ||||
\(251\) | 19.4496 | 1.22765 | 0.613824 | − | 0.789443i | \(-0.289630\pi\) | ||||
0.613824 | + | 0.789443i | \(0.289630\pi\) | |||||||
\(252\) | 2.41839 | − | 1.07303i | 0.152344 | − | 0.0675943i | ||||
\(253\) | − | 5.66966i | − | 0.356448i | ||||||
\(254\) | −14.1718 | − | 8.18208i | −0.889216 | − | 0.513389i | ||||
\(255\) | 0.739540 | − | 0.426974i | 0.0463118 | − | 0.0267381i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.14605 | + | 10.6453i | −0.383380 | + | 0.664034i | −0.991543 | − | 0.129778i | \(-0.958573\pi\) |
0.608163 | + | 0.793812i | \(0.291907\pi\) | |||||||
\(258\) | − | 8.75510i | − | 0.545069i | ||||||
\(259\) | 8.88600 | + | 0.945469i | 0.552149 | + | 0.0587486i | ||||
\(260\) | −7.63935 | + | 2.85395i | −0.473773 | + | 0.176994i | ||||
\(261\) | 1.20393 | − | 2.08526i | 0.0745212 | − | 0.129075i | ||||
\(262\) | 9.90574 | − | 5.71908i | 0.611978 | − | 0.353326i | ||||
\(263\) | −1.65451 | − | 2.86569i | −0.102021 | − | 0.176706i | 0.810496 | − | 0.585744i | \(-0.199198\pi\) |
−0.912517 | + | 0.409038i | \(0.865864\pi\) | |||||||
\(264\) | −0.630901 | + | 1.09275i | −0.0388293 | + | 0.0672543i | ||||
\(265\) | 6.78541i | 0.416824i | ||||||||
\(266\) | 16.5840 | + | 12.0815i | 1.01683 | + | 0.740763i | ||||
\(267\) | 11.3776i | 0.696295i | ||||||||
\(268\) | −1.11900 | − | 0.646053i | −0.0683536 | − | 0.0394640i | ||||
\(269\) | −16.0062 | − | 27.7236i | −0.975918 | − | 1.69034i | −0.676873 | − | 0.736100i | \(-0.736665\pi\) |
−0.299045 | − | 0.954239i | \(-0.596668\pi\) | |||||||
\(270\) | −1.13090 | − | 1.95878i | −0.0688245 | − | 0.119207i | ||||
\(271\) | −19.3202 | − | 11.1545i | −1.17362 | − | 0.677588i | −0.219088 | − | 0.975705i | \(-0.570308\pi\) |
−0.954529 | + | 0.298117i | \(0.903641\pi\) | |||||||
\(272\) | 0.377552 | 0.0228924 | ||||||||
\(273\) | 2.56348 | − | 9.18850i | 0.155149 | − | 0.556113i | ||||
\(274\) | 11.1461 | 0.673358 | ||||||||
\(275\) | −0.126485 | − | 0.0730264i | −0.00762736 | − | 0.00440366i | ||||
\(276\) | 2.24665 | + | 3.89131i | 0.135232 | + | 0.234230i | ||||
\(277\) | 5.20568 | + | 9.01650i | 0.312779 | + | 0.541749i | 0.978963 | − | 0.204038i | \(-0.0654067\pi\) |
−0.666184 | + | 0.745788i | \(0.732073\pi\) | |||||||
\(278\) | −2.15926 | − | 1.24665i | −0.129504 | − | 0.0747691i | ||||
\(279\) | − | 4.00000i | − | 0.239474i | ||||||
\(280\) | −0.633140 | + | 5.95058i | −0.0378374 | + | 0.355615i | ||||
\(281\) | − | 29.5102i | − | 1.76043i | −0.474574 | − | 0.880216i | \(-0.657398\pi\) | ||
0.474574 | − | 0.880216i | \(-0.342602\pi\) | |||||||
\(282\) | 1.64605 | − | 2.85105i | 0.0980210 | − | 0.169777i | ||||
\(283\) | −1.60730 | − | 2.78392i | −0.0955439 | − | 0.165487i | 0.814292 | − | 0.580456i | \(-0.197126\pi\) |
−0.909835 | + | 0.414969i | \(0.863792\pi\) | |||||||
\(284\) | 3.56434 | − | 2.05787i | 0.211505 | − | 0.122112i | ||||
\(285\) | 8.77026 | − | 15.1905i | 0.519505 | − | 0.899809i | ||||
\(286\) | 1.59214 | + | 4.26180i | 0.0941455 | + | 0.252006i | ||||
\(287\) | −10.6242 | − | 23.9449i | −0.627127 | − | 1.41342i | ||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | 8.42873 | − | 14.5990i | 0.495807 | − | 0.858764i | ||||
\(290\) | 2.72305 | + | 4.71645i | 0.159903 | + | 0.276960i | ||||
\(291\) | −6.95445 | + | 4.01515i | −0.407677 | + | 0.235372i | ||||
\(292\) | 8.26232 | + | 4.77026i | 0.483516 | + | 0.279158i | ||||
\(293\) | − | 24.7248i | − | 1.44444i | −0.691664 | − | 0.722219i | \(-0.743122\pi\) | ||
0.691664 | − | 0.722219i | \(-0.256878\pi\) | |||||||
\(294\) | −5.18999 | − | 4.69723i | −0.302687 | − | 0.273948i | ||||
\(295\) | −10.5618 | −0.614934 | ||||||||
\(296\) | 1.68878 | − | 2.92505i | 0.0981581 | − | 0.170015i | ||||
\(297\) | −1.09275 | + | 0.630901i | −0.0634079 | + | 0.0366086i | ||||
\(298\) | −0.0151517 | − | 0.0262436i | −0.000877716 | − | 0.00152025i | ||||
\(299\) | 15.9779 | + | 2.67811i | 0.924028 | + | 0.154879i | ||||
\(300\) | 0.115749 | 0.00668279 | ||||||||
\(301\) | −21.1733 | + | 9.39446i | −1.22041 | + | 0.541488i | ||||
\(302\) | −4.30901 | −0.247956 | ||||||||
\(303\) | −5.81968 | + | 10.0800i | −0.334332 | + | 0.579079i | ||||
\(304\) | 6.71612 | − | 3.87755i | 0.385196 | − | 0.222393i | ||||
\(305\) | −17.4354 | + | 10.0663i | −0.998348 | + | 0.576396i | ||||
\(306\) | 0.326969 | + | 0.188776i | 0.0186916 | + | 0.0107916i | ||||
\(307\) | 6.93939i | 0.396052i | 0.980197 | + | 0.198026i | \(0.0634531\pi\) | ||||
−0.980197 | + | 0.198026i | \(0.936547\pi\) | |||||||
\(308\) | 3.31968 | + | 0.353213i | 0.189156 | + | 0.0201262i | ||||
\(309\) | 12.4630 | 0.708995 | ||||||||
\(310\) | 7.83511 | + | 4.52360i | 0.445005 | + | 0.256923i | ||||
\(311\) | 5.53876 | + | 9.59341i | 0.314074 | + | 0.543992i | 0.979240 | − | 0.202703i | \(-0.0649726\pi\) |
−0.665166 | + | 0.746695i | \(0.731639\pi\) | |||||||
\(312\) | −2.78153 | − | 2.29414i | −0.157473 | − | 0.129880i | ||||
\(313\) | 10.7039 | − | 18.5397i | 0.605022 | − | 1.04793i | −0.387026 | − | 0.922069i | \(-0.626498\pi\) |
0.992048 | − | 0.125860i | \(-0.0401689\pi\) | |||||||
\(314\) | − | 22.7114i | − | 1.28168i | ||||||
\(315\) | −3.52360 | + | 4.83678i | −0.198533 | + | 0.272522i | ||||
\(316\) | 6.29211 | 0.353959 | ||||||||
\(317\) | 18.3754 | + | 10.6091i | 1.03207 | + | 0.595864i | 0.917576 | − | 0.397561i | \(-0.130143\pi\) |
0.114490 | + | 0.993424i | \(0.463477\pi\) | |||||||
\(318\) | −2.59808 | + | 1.50000i | −0.145693 | + | 0.0841158i | ||||
\(319\) | 2.63119 | − | 1.51912i | 0.147318 | − | 0.0850543i | ||||
\(320\) | 1.95878 | + | 1.13090i | 0.109499 | + | 0.0632193i | ||||
\(321\) | 17.8023 | 0.993628 | ||||||||
\(322\) | 7.00000 | − | 9.60876i | 0.390095 | − | 0.535475i | ||||
\(323\) | 2.92795i | 0.162916i | ||||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0.265546 | − | 0.321960i | 0.0147298 | − | 0.0178591i | ||||
\(326\) | −6.20393 | − | 10.7455i | −0.343604 | − | 0.595139i | ||||
\(327\) | −2.83944 | − | 1.63935i | −0.157022 | − | 0.0906565i | ||||
\(328\) | −9.90116 | −0.546700 | ||||||||
\(329\) | −8.66120 | − | 0.921550i | −0.477508 | − | 0.0508067i | ||||
\(330\) | − | 2.85395i | − | 0.157105i | ||||||
\(331\) | 18.2205 | + | 10.5196i | 1.00149 | + | 0.578212i | 0.908689 | − | 0.417473i | \(-0.137084\pi\) |
0.0928025 | + | 0.995685i | \(0.470417\pi\) | |||||||
\(332\) | −5.53776 | + | 3.19723i | −0.303924 | + | 0.175471i | ||||
\(333\) | 2.92505 | − | 1.68878i | 0.160292 | − | 0.0925443i | ||||
\(334\) | −12.3366 | + | 21.3676i | −0.675028 | + | 1.16918i | ||||
\(335\) | 2.92249 | 0.159673 | ||||||||
\(336\) | −2.41839 | + | 1.07303i | −0.131934 | + | 0.0585384i | ||||
\(337\) | −25.5574 | −1.39220 | −0.696101 | − | 0.717944i | \(-0.745083\pi\) | ||||
−0.696101 | + | 0.717944i | \(0.745083\pi\) | |||||||
\(338\) | −12.7625 | + | 2.47380i | −0.694186 | + | 0.134557i | ||||
\(339\) | −0.661205 | − | 1.14524i | −0.0359117 | − | 0.0622009i | ||||
\(340\) | −0.739540 | + | 0.426974i | −0.0401072 | + | 0.0231559i | ||||
\(341\) | 2.52360 | − | 4.37101i | 0.136661 | − | 0.236704i | ||||
\(342\) | 7.75510 | 0.419348 | ||||||||
\(343\) | −5.79073 | + | 17.5917i | −0.312670 | + | 0.949862i | ||||
\(344\) | 8.75510i | 0.472044i | ||||||||
\(345\) | −8.80138 | − | 5.08148i | −0.473850 | − | 0.273578i | ||||
\(346\) | −20.7661 | + | 11.9893i | −1.11639 | + | 0.644551i | ||||
\(347\) | −9.16517 | − | 15.8745i | −0.492012 | − | 0.852190i | 0.507946 | − | 0.861389i | \(-0.330405\pi\) |
−0.999958 | + | 0.00919912i | \(0.997072\pi\) | |||||||
\(348\) | −1.20393 | + | 2.08526i | −0.0645373 | + | 0.111782i | ||||
\(349\) | − | 4.19326i | − | 0.224460i | −0.993682 | − | 0.112230i | \(-0.964201\pi\) | ||
0.993682 | − | 0.112230i | \(-0.0357994\pi\) | |||||||
\(350\) | −0.124202 | − | 0.279927i | −0.00663888 | − | 0.0149627i | ||||
\(351\) | −1.26180 | − | 3.37755i | −0.0673500 | − | 0.180280i | ||||
\(352\) | 0.630901 | − | 1.09275i | 0.0336271 | − | 0.0582439i | ||||
\(353\) | −18.9338 | + | 10.9315i | −1.00775 | + | 0.581823i | −0.910531 | − | 0.413440i | \(-0.864327\pi\) |
−0.0972156 | + | 0.995263i | \(0.530994\pi\) | |||||||
\(354\) | −2.33483 | − | 4.04404i | −0.124095 | − | 0.214938i | ||||
\(355\) | −4.65451 | + | 8.06184i | −0.247036 | + | 0.427878i | ||||
\(356\) | − | 11.3776i | − | 0.603009i | ||||||
\(357\) | 0.105687 | − | 0.993301i | 0.00559355 | − | 0.0525711i | ||||
\(358\) | 5.70789i | 0.301672i | ||||||||
\(359\) | −22.4341 | − | 12.9523i | −1.18403 | − | 0.683598i | −0.227084 | − | 0.973875i | \(-0.572919\pi\) |
−0.956943 | + | 0.290277i | \(0.906252\pi\) | |||||||
\(360\) | 1.13090 | + | 1.95878i | 0.0596037 | + | 0.103237i | ||||
\(361\) | 20.5708 | + | 35.6297i | 1.08267 | + | 1.87525i | ||||
\(362\) | −14.4363 | − | 8.33483i | −0.758758 | − | 0.438069i | ||||
\(363\) | 9.40786 | 0.493784 | ||||||||
\(364\) | −2.56348 | + | 9.18850i | −0.134363 | + | 0.481608i | ||||
\(365\) | −21.5787 | −1.12948 | ||||||||
\(366\) | −7.70863 | − | 4.45058i | −0.402936 | − | 0.232635i | ||||
\(367\) | 8.93146 | + | 15.4697i | 0.466218 | + | 0.807514i | 0.999256 | − | 0.0385779i | \(-0.0122828\pi\) |
−0.533037 | + | 0.846092i | \(0.678949\pi\) | |||||||
\(368\) | −2.24665 | − | 3.89131i | −0.117115 | − | 0.202849i | ||||
\(369\) | −8.57465 | − | 4.95058i | −0.446379 | − | 0.257717i | ||||
\(370\) | 7.63935i | 0.397151i | ||||||||
\(371\) | 6.41539 | + | 4.67362i | 0.333070 | + | 0.242642i | ||||
\(372\) | 4.00000i | 0.207390i | ||||||||
\(373\) | 7.56236 | − | 13.0984i | 0.391564 | − | 0.678209i | −0.601092 | − | 0.799180i | \(-0.705267\pi\) |
0.992656 | + | 0.120971i | \(0.0386008\pi\) | |||||||
\(374\) | 0.238198 | + | 0.412571i | 0.0123169 | + | 0.0213335i | ||||
\(375\) | 9.56716 | − | 5.52360i | 0.494046 | − | 0.285238i | ||||
\(376\) | −1.64605 | + | 2.85105i | −0.0848887 | + | 0.147032i | ||||
\(377\) | 3.03824 | + | 8.13265i | 0.156477 | + | 0.418853i | ||||
\(378\) | −2.63090 | − | 0.279927i | −0.135319 | − | 0.0143979i | ||||
\(379\) | − | 12.5236i | − | 0.643294i | −0.946860 | − | 0.321647i | \(-0.895764\pi\) | ||
0.946860 | − | 0.321647i | \(-0.104236\pi\) | |||||||
\(380\) | −8.77026 | + | 15.1905i | −0.449905 | + | 0.779258i | ||||
\(381\) | 8.18208 | + | 14.1718i | 0.419180 | + | 0.726042i | ||||
\(382\) | −6.30355 | + | 3.63935i | −0.322517 | + | 0.186206i | ||||
\(383\) | 1.36723 | + | 0.789373i | 0.0698624 | + | 0.0403351i | 0.534524 | − | 0.845153i | \(-0.320491\pi\) |
−0.464662 | + | 0.885488i | \(0.653824\pi\) | |||||||
\(384\) | 1.00000i | 0.0510310i | ||||||||
\(385\) | −6.90196 | + | 3.06236i | −0.351756 | + | 0.156072i | ||||
\(386\) | 17.3090 | 0.881005 | ||||||||
\(387\) | −4.37755 | + | 7.58214i | −0.222523 | + | 0.385422i | ||||
\(388\) | 6.95445 | − | 4.01515i | 0.353059 | − | 0.203838i | ||||
\(389\) | −2.40512 | − | 4.16580i | −0.121945 | − | 0.211214i | 0.798590 | − | 0.601876i | \(-0.205580\pi\) |
−0.920534 | + | 0.390661i | \(0.872246\pi\) | |||||||
\(390\) | 8.04285 | + | 1.34809i | 0.407265 | + | 0.0682630i | ||||
\(391\) | 1.69645 | 0.0857933 | ||||||||
\(392\) | 5.18999 | + | 4.69723i | 0.262134 | + | 0.237246i | ||||
\(393\) | −11.4382 | −0.576979 | ||||||||
\(394\) | −1.60730 | + | 2.78392i | −0.0809744 | + | 0.140252i | ||||
\(395\) | −12.3248 | + | 7.11575i | −0.620130 | + | 0.358032i | ||||
\(396\) | 1.09275 | − | 0.630901i | 0.0549129 | − | 0.0317040i | ||||
\(397\) | 23.3380 | + | 13.4742i | 1.17130 | + | 0.676250i | 0.953986 | − | 0.299852i | \(-0.0969373\pi\) |
0.217313 | + | 0.976102i | \(0.430271\pi\) | |||||||
\(398\) | − | 11.7035i | − | 0.586642i | ||||||
\(399\) | −8.32143 | − | 18.7549i | −0.416593 | − | 0.938918i | ||||
\(400\) | −0.115749 | −0.00578747 | ||||||||
\(401\) | 17.8364 | + | 10.2978i | 0.890705 | + | 0.514249i | 0.874173 | − | 0.485614i | \(-0.161404\pi\) |
0.0165321 | + | 0.999863i | \(0.494737\pi\) | |||||||
\(402\) | 0.646053 | + | 1.11900i | 0.0322222 | + | 0.0558105i | ||||
\(403\) | 11.1261 | + | 9.17658i | 0.554231 | + | 0.457118i | ||||
\(404\) | 5.81968 | − | 10.0800i | 0.289540 | − | 0.501498i | ||||
\(405\) | 2.26180i | 0.112390i | ||||||||
\(406\) | 6.33483 | + | 0.674024i | 0.314392 | + | 0.0334513i | ||||
\(407\) | 4.26180 | 0.211250 | ||||||||
\(408\) | −0.326969 | − | 0.188776i | −0.0161874 | − | 0.00934580i | ||||
\(409\) | 4.59774 | − | 2.65451i | 0.227344 | − | 0.131257i | −0.382002 | − | 0.924161i | \(-0.624765\pi\) |
0.609346 | + | 0.792904i | \(0.291432\pi\) | |||||||
\(410\) | 19.3942 | − | 11.1972i | 0.957810 | − | 0.552992i | ||||
\(411\) | −9.65276 | − | 5.57303i | −0.476136 | − | 0.274897i | ||||
\(412\) | −12.4630 | −0.614008 | ||||||||
\(413\) | −7.27474 | + | 9.98589i | −0.357967 | + | 0.491374i | ||||
\(414\) | − | 4.49330i | − | 0.220834i | ||||||
\(415\) | 7.23150 | − | 12.5253i | 0.354980 | − | 0.614844i | ||||
\(416\) | 2.78153 | + | 2.29414i | 0.136376 | + | 0.112480i | ||||
\(417\) | 1.24665 | + | 2.15926i | 0.0610487 | + | 0.105740i | ||||
\(418\) | 8.47441 | + | 4.89270i | 0.414497 | + | 0.239310i | ||||
\(419\) | −20.5842 | −1.00560 | −0.502802 | − | 0.864401i | \(-0.667698\pi\) | ||||
−0.502802 | + | 0.864401i | \(0.667698\pi\) | |||||||
\(420\) | 3.52360 | − | 4.83678i | 0.171934 | − | 0.236011i | ||||
\(421\) | 12.8878i | 0.628111i | 0.949405 | + | 0.314055i | \(0.101688\pi\) | ||||
−0.949405 | + | 0.314055i | \(0.898312\pi\) | |||||||
\(422\) | −6.98373 | − | 4.03206i | −0.339963 | − | 0.196277i | ||||
\(423\) | −2.85105 | + | 1.64605i | −0.138623 | + | 0.0800338i | ||||
\(424\) | 2.59808 | − | 1.50000i | 0.126174 | − | 0.0728464i | ||||
\(425\) | 0.0218507 | − | 0.0378465i | 0.00105991 | − | 0.00183582i | ||||
\(426\) | −4.11575 | −0.199409 | ||||||||
\(427\) | −2.49168 | + | 23.4181i | −0.120581 | + | 1.13328i | ||||
\(428\) | −17.8023 | −0.860507 | ||||||||
\(429\) | 0.752063 | − | 4.48690i | 0.0363100 | − | 0.216630i | ||||
\(430\) | −9.90116 | − | 17.1493i | −0.477476 | − | 0.827013i | ||||
\(431\) | −23.0588 | + | 13.3130i | −1.11070 | + | 0.641264i | −0.939011 | − | 0.343887i | \(-0.888256\pi\) |
−0.171690 | + | 0.985151i | \(0.554923\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −28.0810 | −1.34949 | −0.674744 | − | 0.738052i | \(-0.735746\pi\) | ||||
−0.674744 | + | 0.738052i | \(0.735746\pi\) | |||||||
\(434\) | 9.67356 | − | 4.29211i | 0.464346 | − | 0.206028i | ||||
\(435\) | − | 5.44609i | − | 0.261120i | ||||||
\(436\) | 2.83944 | + | 1.63935i | 0.135985 | + | 0.0785108i | ||||
\(437\) | 30.1775 | − | 17.4230i | 1.44359 | − | 0.833455i | ||||
\(438\) | −4.77026 | − | 8.26232i | −0.227932 | − | 0.394789i | ||||
\(439\) | −13.8820 | + | 24.0444i | −0.662554 | + | 1.14758i | 0.317389 | + | 0.948295i | \(0.397194\pi\) |
−0.979942 | + | 0.199281i | \(0.936139\pi\) | |||||||
\(440\) | 2.85395i | 0.136057i | ||||||||
\(441\) | 2.14605 | + | 6.66292i | 0.102193 | + | 0.317282i | ||||
\(442\) | −1.27520 | + | 0.476396i | −0.0606551 | + | 0.0226598i | ||||
\(443\) | −2.28092 | + | 3.95067i | −0.108370 | + | 0.187702i | −0.915110 | − | 0.403204i | \(-0.867896\pi\) |
0.806740 | + | 0.590906i | \(0.201230\pi\) | |||||||
\(444\) | −2.92505 | + | 1.68878i | −0.138817 | + | 0.0801458i | ||||
\(445\) | 12.8669 | + | 22.2861i | 0.609949 | + | 1.05646i | ||||
\(446\) | −11.8927 | + | 20.5988i | −0.563136 | + | 0.975380i | ||||
\(447\) | 0.0303035i | 0.00143330i | ||||||||
\(448\) | 2.41839 | − | 1.07303i | 0.114258 | − | 0.0506957i | ||||
\(449\) | 2.78190i | 0.131286i | 0.997843 | + | 0.0656430i | \(0.0209098\pi\) | ||||
−0.997843 | + | 0.0656430i | \(0.979090\pi\) | |||||||
\(450\) | −0.100242 | − | 0.0578747i | −0.00472545 | − | 0.00272824i | ||||
\(451\) | −6.24665 | − | 10.8195i | −0.294143 | − | 0.509471i | ||||
\(452\) | 0.661205 | + | 1.14524i | 0.0311004 | + | 0.0538676i | ||||
\(453\) | 3.73171 | + | 2.15451i | 0.175331 | + | 0.101228i | ||||
\(454\) | −10.2315 | −0.480188 | ||||||||
\(455\) | −5.36999 | − | 20.8973i | −0.251749 | − | 0.979680i | ||||
\(456\) | −7.75510 | −0.363166 | ||||||||
\(457\) | 25.8126 | + | 14.9029i | 1.20746 | + | 0.697129i | 0.962204 | − | 0.272329i | \(-0.0877939\pi\) |
0.245258 | + | 0.969458i | \(0.421127\pi\) | |||||||
\(458\) | −0.523604 | − | 0.906910i | −0.0244664 | − | 0.0423771i | ||||
\(459\) | −0.188776 | − | 0.326969i | −0.00881130 | − | 0.0152616i | ||||
\(460\) | 8.80138 | + | 5.08148i | 0.410366 | + | 0.236925i | ||||
\(461\) | − | 18.6180i | − | 0.867128i | −0.901123 | − | 0.433564i | \(-0.857256\pi\) | ||
0.901123 | − | 0.433564i | \(-0.142744\pi\) | |||||||
\(462\) | −2.69832 | − | 1.96573i | −0.125537 | − | 0.0914540i | ||||
\(463\) | − | 42.0338i | − | 1.95348i | −0.214434 | − | 0.976738i | \(-0.568791\pi\) | ||
0.214434 | − | 0.976738i | \(-0.431209\pi\) | |||||||
\(464\) | 1.20393 | − | 2.08526i | 0.0558909 | − | 0.0968059i | ||||
\(465\) | −4.52360 | − | 7.83511i | −0.209777 | − | 0.363345i | ||||
\(466\) | 3.24898 | − | 1.87580i | 0.150506 | − | 0.0868947i | ||||
\(467\) | 19.4608 | − | 33.7071i | 0.900538 | − | 1.55978i | 0.0737402 | − | 0.997277i | \(-0.476506\pi\) |
0.826798 | − | 0.562500i | \(-0.190160\pi\) | |||||||
\(468\) | 1.26180 | + | 3.37755i | 0.0583268 | + | 0.156127i | ||||
\(469\) | 2.01294 | − | 2.76312i | 0.0929489 | − | 0.127589i | ||||
\(470\) | − | 7.44609i | − | 0.343463i | ||||||
\(471\) | −11.3557 | + | 19.6687i | −0.523243 | + | 0.906284i | ||||
\(472\) | 2.33483 | + | 4.04404i | 0.107469 | + | 0.186142i | ||||
\(473\) | −9.56716 | + | 5.52360i | −0.439899 | + | 0.253976i | ||||
\(474\) | −5.44912 | − | 3.14605i | −0.250287 | − | 0.144503i | ||||
\(475\) | − | 0.897649i | − | 0.0411869i | ||||||
\(476\) | −0.105687 | + | 0.993301i | −0.00484416 | + | 0.0455279i | ||||
\(477\) | 3.00000 | 0.137361 | ||||||||
\(478\) | 14.5984 | − | 25.2851i | 0.667715 | − | 1.15652i | ||||
\(479\) | 1.98029 | − | 1.14332i | 0.0904817 | − | 0.0522397i | −0.454076 | − | 0.890963i | \(-0.650031\pi\) |
0.544558 | + | 0.838723i | \(0.316697\pi\) | |||||||
\(480\) | −1.13090 | − | 1.95878i | −0.0516183 | − | 0.0894056i | ||||
\(481\) | −2.01310 | + | 12.0104i | −0.0917894 | + | 0.547627i | ||||
\(482\) | −1.70789 | −0.0777925 | ||||||||
\(483\) | −10.8666 | + | 4.82143i | −0.494446 | + | 0.219383i | ||||
\(484\) | −9.40786 | −0.427630 | ||||||||
\(485\) | −9.08148 | + | 15.7296i | −0.412369 | + | 0.714244i | ||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | 26.7087 | − | 15.4203i | 1.21029 | − | 0.698759i | 0.247465 | − | 0.968897i | \(-0.420402\pi\) |
0.962822 | + | 0.270138i | \(0.0870692\pi\) | |||||||
\(488\) | 7.70863 | + | 4.45058i | 0.348953 | + | 0.201468i | ||||
\(489\) | 12.4079i | 0.561103i | ||||||||
\(490\) | −15.4781 | − | 3.33146i | −0.699232 | − | 0.150500i | ||||
\(491\) | 41.1754 | 1.85822 | 0.929111 | − | 0.369802i | \(-0.120574\pi\) | ||||
0.929111 | + | 0.369802i | \(0.120574\pi\) | |||||||
\(492\) | 8.57465 | + | 4.95058i | 0.386575 | + | 0.223189i | ||||
\(493\) | 0.454545 | + | 0.787295i | 0.0204717 | + | 0.0354580i | ||||
\(494\) | −17.7913 | + | 21.5710i | −0.800470 | + | 0.970527i | ||||
\(495\) | −1.42697 | + | 2.47159i | −0.0641377 | + | 0.111090i | ||||
\(496\) | − | 4.00000i | − | 0.179605i | ||||||
\(497\) | 4.41631 | + | 9.95349i | 0.198098 | + | 0.446475i | ||||
\(498\) | 6.39446 | 0.286542 | ||||||||
\(499\) | −13.3961 | − | 7.73423i | −0.599691 | − | 0.346232i | 0.169229 | − | 0.985577i | \(-0.445872\pi\) |
−0.768920 | + | 0.639345i | \(0.779206\pi\) | |||||||
\(500\) | −9.56716 | + | 5.52360i | −0.427857 | + | 0.247023i | ||||
\(501\) | 21.3676 | − | 12.3366i | 0.954633 | − | 0.551158i | ||||
\(502\) | 16.8438 | + | 9.72480i | 0.751778 | + | 0.434039i | ||||
\(503\) | −0.986602 | −0.0439904 | −0.0219952 | − | 0.999758i | \(-0.507002\pi\) | ||||
−0.0219952 | + | 0.999758i | \(0.507002\pi\) | |||||||
\(504\) | 2.63090 | + | 0.279927i | 0.117190 | + | 0.0124690i | ||||
\(505\) | 26.3259i | 1.17149i | ||||||||
\(506\) | 2.83483 | − | 4.91007i | 0.126024 | − | 0.218279i | ||||
\(507\) | 12.2895 | + | 4.23885i | 0.545796 | + | 0.188254i | ||||
\(508\) | −8.18208 | − | 14.1718i | −0.363021 | − | 0.628771i | ||||
\(509\) | 14.8588 | + | 8.57875i | 0.658606 | + | 0.380246i | 0.791746 | − | 0.610851i | \(-0.209173\pi\) |
−0.133140 | + | 0.991097i | \(0.542506\pi\) | |||||||
\(510\) | 0.853947 | 0.0378134 | ||||||||
\(511\) | −14.8629 | + | 20.4020i | −0.657497 | + | 0.902533i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −6.71612 | − | 3.87755i | −0.296524 | − | 0.171198i | ||||
\(514\) | −10.6453 | + | 6.14605i | −0.469543 | + | 0.271091i | ||||
\(515\) | 24.4122 | − | 14.0944i | 1.07573 | − | 0.621074i | ||||
\(516\) | 4.37755 | − | 7.58214i | 0.192711 | − | 0.333785i | ||||
\(517\) | −4.15399 | −0.182692 | ||||||||
\(518\) | 7.22277 | + | 5.26180i | 0.317350 | + | 0.231190i | ||||
\(519\) | 23.9787 | 1.05255 | ||||||||
\(520\) | −8.04285 | − | 1.34809i | −0.352702 | − | 0.0591175i | ||||
\(521\) | 16.2787 | + | 28.1955i | 0.713183 | + | 1.23527i | 0.963656 | + | 0.267146i | \(0.0860805\pi\) |
−0.250473 | + | 0.968124i | \(0.580586\pi\) | |||||||
\(522\) | 2.08526 | − | 1.20393i | 0.0912695 | − | 0.0526945i | ||||
\(523\) | 17.4248 | − | 30.1806i | 0.761932 | − | 1.31970i | −0.179922 | − | 0.983681i | \(-0.557585\pi\) |
0.941854 | − | 0.336023i | \(-0.109082\pi\) | |||||||
\(524\) | 11.4382 | 0.499678 | ||||||||
\(525\) | −0.0324014 | + | 0.304525i | −0.00141411 | + | 0.0132906i | ||||
\(526\) | − | 3.30901i | − | 0.144280i | ||||||
\(527\) | 1.30788 | + | 0.755103i | 0.0569720 | + | 0.0328928i | ||||
\(528\) | −1.09275 | + | 0.630901i | −0.0475560 | + | 0.0274564i | ||||
\(529\) | 1.40512 | + | 2.43374i | 0.0610923 | + | 0.105815i | ||||
\(530\) | −3.39270 | + | 5.87633i | −0.147370 | + | 0.255252i | ||||
\(531\) | 4.66966i | 0.202646i | ||||||||
\(532\) | 8.32143 | + | 18.7549i | 0.360780 | + | 0.813127i | ||||
\(533\) | 33.4417 | − | 12.4933i | 1.44852 | − | 0.541145i | ||||
\(534\) | −5.68878 | + | 9.85325i | −0.246177 | + | 0.426392i | ||||
\(535\) | 34.8708 | − | 20.1327i | 1.50760 | − | 0.870411i | ||||
\(536\) | −0.646053 | − | 1.11900i | −0.0279052 | − | 0.0483333i | ||||
\(537\) | 2.85395 | − | 4.94318i | 0.123157 | − | 0.213314i | ||||
\(538\) | − | 32.0125i | − | 1.38016i | ||||||
\(539\) | −1.85854 | + | 8.63487i | −0.0800528 | + | 0.371930i | ||||
\(540\) | − | 2.26180i | − | 0.0973325i | ||||||
\(541\) | 23.3905 | + | 13.5045i | 1.00563 | + | 0.580603i | 0.909910 | − | 0.414805i | \(-0.136150\pi\) |
0.0957238 | + | 0.995408i | \(0.469483\pi\) | |||||||
\(542\) | −11.1545 | − | 19.3202i | −0.479127 | − | 0.829872i | ||||
\(543\) | 8.33483 | + | 14.4363i | 0.357682 | + | 0.619523i | ||||
\(544\) | 0.326969 | + | 0.188776i | 0.0140187 | + | 0.00809370i | ||||
\(545\) | −7.41579 | −0.317657 | ||||||||
\(546\) | 6.81429 | − | 6.67573i | 0.291625 | − | 0.285695i | ||||
\(547\) | 33.1719 | 1.41833 | 0.709165 | − | 0.705043i | \(-0.249072\pi\) | ||||
0.709165 | + | 0.705043i | \(0.249072\pi\) | |||||||
\(548\) | 9.65276 | + | 5.57303i | 0.412346 | + | 0.238068i | ||||
\(549\) | 4.45058 | + | 7.70863i | 0.189946 | + | 0.328996i | ||||
\(550\) | −0.0730264 | − | 0.126485i | −0.00311386 | − | 0.00539336i | ||||
\(551\) | 16.1714 | + | 9.33658i | 0.688926 | + | 0.397752i | ||||
\(552\) | 4.49330i | 0.191248i | ||||||||
\(553\) | −1.76133 | + | 16.5539i | −0.0748995 | + | 0.703944i | ||||
\(554\) | 10.4114i | 0.442336i | ||||||||
\(555\) | 3.81968 | − | 6.61587i | 0.162136 | − | 0.280828i | ||||
\(556\) | −1.24665 | − | 2.15926i | −0.0528698 | − | 0.0915731i | ||||
\(557\) | 16.4136 | − | 9.47640i | 0.695466 | − | 0.401528i | −0.110190 | − | 0.993911i | \(-0.535146\pi\) |
0.805657 | + | 0.592383i | \(0.201813\pi\) | |||||||
\(558\) | 2.00000 | − | 3.46410i | 0.0846668 | − | 0.146647i | ||||
\(559\) | −11.0472 | − | 29.5708i | −0.467247 | − | 1.25071i | ||||
\(560\) | −3.52360 | + | 4.83678i | −0.148899 | + | 0.204391i | ||||
\(561\) | − | 0.476396i | − | 0.0201134i | ||||||
\(562\) | 14.7551 | − | 25.5566i | 0.622406 | − | 1.07804i | ||||
\(563\) | 15.7720 | + | 27.3179i | 0.664711 | + | 1.15131i | 0.979364 | + | 0.202106i | \(0.0647786\pi\) |
−0.314653 | + | 0.949207i | \(0.601888\pi\) | |||||||
\(564\) | 2.85105 | − | 1.64605i | 0.120051 | − | 0.0693113i | ||||
\(565\) | −2.59031 | − | 1.49551i | −0.108975 | − | 0.0629167i | ||||
\(566\) | − | 3.21459i | − | 0.135119i | ||||||
\(567\) | 2.13846 | + | 1.55787i | 0.0898070 | + | 0.0654246i | ||||
\(568\) | 4.11575 | 0.172693 | ||||||||
\(569\) | −1.53206 | + | 2.65360i | −0.0642272 | + | 0.111245i | −0.896351 | − | 0.443345i | \(-0.853792\pi\) |
0.832124 | + | 0.554590i | \(0.187125\pi\) | |||||||
\(570\) | 15.1905 | − | 8.77026i | 0.636261 | − | 0.367346i | ||||
\(571\) | 2.05514 | + | 3.55961i | 0.0860050 | + | 0.148965i | 0.905819 | − | 0.423665i | \(-0.139257\pi\) |
−0.819814 | + | 0.572630i | \(0.805923\pi\) | |||||||
\(572\) | −0.752063 | + | 4.48690i | −0.0314453 | + | 0.187607i | ||||
\(573\) | 7.27871 | 0.304072 | ||||||||
\(574\) | 2.77160 | − | 26.0490i | 0.115685 | − | 1.08726i | ||||
\(575\) | −0.520097 | −0.0216895 | ||||||||
\(576\) | 0.500000 | − | 0.866025i | 0.0208333 | − | 0.0360844i | ||||
\(577\) | −16.4954 | + | 9.52360i | −0.686711 | + | 0.396473i | −0.802379 | − | 0.596815i | \(-0.796433\pi\) |
0.115668 | + | 0.993288i | \(0.463099\pi\) | |||||||
\(578\) | 14.5990 | − | 8.42873i | 0.607238 | − | 0.350589i | ||||
\(579\) | −14.9900 | − | 8.65451i | −0.622965 | − | 0.359669i | ||||
\(580\) | 5.44609i | 0.226137i | ||||||||
\(581\) | −6.86142 | − | 15.4643i | −0.284660 | − | 0.641567i | ||||
\(582\) | −8.03030 | −0.332867 | ||||||||
\(583\) | 3.27826 | + | 1.89270i | 0.135772 | + | 0.0783878i | ||||
\(584\) | 4.77026 | + | 8.26232i | 0.197395 | + | 0.341897i | ||||
\(585\) | −6.29127 | − | 5.18890i | −0.260112 | − | 0.214535i | ||||
\(586\) | 12.3624 | − | 21.4123i | 0.510686 | − | 0.884534i | ||||
\(587\) | 36.2216i | 1.49503i | 0.664247 | + | 0.747513i | \(0.268752\pi\) | ||||
−0.664247 | + | 0.747513i | \(0.731248\pi\) | |||||||
\(588\) | −2.14605 | − | 6.66292i | −0.0885017 | − | 0.274774i | ||||
\(589\) | 31.0204 | 1.27817 | ||||||||
\(590\) | −9.14682 | − | 5.28092i | −0.376569 | − | 0.217412i | ||||
\(591\) | 2.78392 | − | 1.60730i | 0.114515 | − | 0.0661153i | ||||
\(592\) | 2.92505 | − | 1.68878i | 0.120219 | − | 0.0694083i | ||||
\(593\) | −4.35164 | − | 2.51242i | −0.178700 | − | 0.103173i | 0.407982 | − | 0.912990i | \(-0.366233\pi\) |
−0.586682 | + | 0.809817i | \(0.699566\pi\) | |||||||
\(594\) | −1.26180 | −0.0517724 | ||||||||
\(595\) | −0.916308 | − | 2.06518i | −0.0375650 | − | 0.0846640i | ||||
\(596\) | − | 0.0303035i | − | 0.00124128i | ||||||
\(597\) | −5.85173 | + | 10.1355i | −0.239496 | + | 0.414818i | ||||
\(598\) | 12.4982 | + | 10.3083i | 0.511091 | + | 0.421537i | ||||
\(599\) | −15.4096 | − | 26.6902i | −0.629620 | − | 1.09053i | −0.987628 | − | 0.156815i | \(-0.949877\pi\) |
0.358008 | − | 0.933718i | \(-0.383456\pi\) | |||||||
\(600\) | 0.100242 | + | 0.0578747i | 0.00409236 | + | 0.00236272i | ||||
\(601\) | 9.12121 | 0.372062 | 0.186031 | − | 0.982544i | \(-0.440438\pi\) | ||||
0.186031 | + | 0.982544i | \(0.440438\pi\) | |||||||
\(602\) | −23.0338 | − | 2.45079i | −0.938788 | − | 0.0998868i | ||||
\(603\) | − | 1.29211i | − | 0.0526186i | ||||||
\(604\) | −3.73171 | − | 2.15451i | −0.151841 | − | 0.0876656i | ||||
\(605\) | 18.4279 | − | 10.6394i | 0.749201 | − | 0.432551i | ||||
\(606\) | −10.0800 | + | 5.81968i | −0.409471 | + | 0.236408i | ||||
\(607\) | −11.1821 | + | 19.3679i | −0.453866 | + | 0.786120i | −0.998622 | − | 0.0524749i | \(-0.983289\pi\) |
0.544756 | + | 0.838595i | \(0.316622\pi\) | |||||||
\(608\) | 7.75510 | 0.314511 | ||||||||
\(609\) | −5.14911 | − | 3.75114i | −0.208652 | − | 0.152004i | ||||
\(610\) | −20.1327 | −0.815147 | ||||||||
\(611\) | 1.96217 | − | 11.7066i | 0.0793809 | − | 0.473596i | ||||
\(612\) | 0.188776 | + | 0.326969i | 0.00763081 | + | 0.0132170i | ||||
\(613\) | −29.9508 | + | 17.2921i | −1.20970 | + | 0.698422i | −0.962694 | − | 0.270592i | \(-0.912781\pi\) |
−0.247008 | + | 0.969014i | \(0.579447\pi\) | |||||||
\(614\) | −3.46970 | + | 6.00969i | −0.140026 | + | 0.242531i | ||||
\(615\) | −22.3945 | −0.903032 | ||||||||
\(616\) | 2.69832 | + | 1.96573i | 0.108718 | + | 0.0792015i | ||||
\(617\) | 1.21810i | 0.0490389i | 0.999699 | + | 0.0245194i | \(0.00780556\pi\) | ||||
−0.999699 | + | 0.0245194i | \(0.992194\pi\) | |||||||
\(618\) | 10.7933 | + | 6.23150i | 0.434169 | + | 0.250668i | ||||
\(619\) | −6.93507 | + | 4.00397i | −0.278744 | + | 0.160933i | −0.632855 | − | 0.774271i | \(-0.718117\pi\) |
0.354111 | + | 0.935204i | \(0.384784\pi\) | |||||||
\(620\) | 4.52360 | + | 7.83511i | 0.181672 | + | 0.314666i | ||||
\(621\) | −2.24665 | + | 3.89131i | −0.0901550 | + | 0.156153i | ||||
\(622\) | 11.0775i | 0.444168i | ||||||||
\(623\) | 29.9332 | + | 3.18489i | 1.19925 | + | 0.127600i | ||||
\(624\) | −1.26180 | − | 3.37755i | −0.0505125 | − | 0.135210i | ||||
\(625\) | 12.7827 | − | 22.1402i | 0.511307 | − | 0.885610i | ||||
\(626\) | 18.5397 | − | 10.7039i | 0.740997 | − | 0.427815i | ||||
\(627\) | −4.89270 | − | 8.47441i | −0.195396 | − | 0.338435i | ||||
\(628\) | 11.3557 | − | 19.6687i | 0.453142 | − | 0.784865i | ||||
\(629\) | 1.27520i | 0.0508456i | ||||||||
\(630\) | −5.46992 | + | 2.42697i | −0.217927 | + | 0.0966929i | ||||
\(631\) | 36.8843i | 1.46834i | 0.678966 | + | 0.734169i | \(0.262428\pi\) | ||||
−0.678966 | + | 0.734169i | \(0.737572\pi\) | |||||||
\(632\) | 5.44912 | + | 3.14605i | 0.216754 | + | 0.125143i | ||||
\(633\) | 4.03206 | + | 6.98373i | 0.160260 | + | 0.277578i | ||||
\(634\) | 10.6091 | + | 18.3754i | 0.421339 | + | 0.729781i | ||||
\(635\) | 32.0537 | + | 18.5062i | 1.27201 | + | 0.734398i | ||||
\(636\) | −3.00000 | −0.118958 | ||||||||
\(637\) | −23.4564 | − | 9.31639i | −0.929378 | − | 0.369129i | ||||
\(638\) | 3.03824 | 0.120285 | ||||||||
\(639\) | 3.56434 | + | 2.05787i | 0.141003 | + | 0.0814083i | ||||
\(640\) | 1.13090 | + | 1.95878i | 0.0447028 | + | 0.0774275i | ||||
\(641\) | −21.5748 | − | 37.3686i | −0.852153 | − | 1.47597i | −0.879262 | − | 0.476339i | \(-0.841963\pi\) |
0.0271091 | − | 0.999632i | \(-0.491370\pi\) | |||||||
\(642\) | 15.4173 | + | 8.90116i | 0.608471 | + | 0.351301i | ||||
\(643\) | − | 5.10235i | − | 0.201217i | −0.994926 | − | 0.100609i | \(-0.967921\pi\) | ||
0.994926 | − | 0.100609i | \(-0.0320790\pi\) | |||||||
\(644\) | 10.8666 | − | 4.82143i | 0.428202 | − | 0.189991i | ||||
\(645\) | 19.8023i | 0.779715i | ||||||||
\(646\) | −1.46398 | + | 2.53568i | −0.0575994 | + | 0.0997650i | ||||
\(647\) | −18.4079 | − | 31.8833i | −0.723687 | − | 1.25346i | −0.959512 | − | 0.281668i | \(-0.909112\pi\) |
0.235825 | − | 0.971796i | \(-0.424221\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −2.94609 | + | 5.10278i | −0.115644 | + | 0.200302i | ||||
\(650\) | 0.390950 | − | 0.146053i | 0.0153343 | − | 0.00572866i | ||||
\(651\) | −10.5236 | − | 1.11971i | −0.412453 | − | 0.0438849i | ||||
\(652\) | − | 12.4079i | − | 0.485929i | ||||||
\(653\) | −14.8669 | + | 25.7502i | −0.581786 | + | 1.00768i | 0.413482 | + | 0.910513i | \(0.364313\pi\) |
−0.995268 | + | 0.0971708i | \(0.969021\pi\) | |||||||
\(654\) | −1.63935 | − | 2.83944i | −0.0641038 | − | 0.111031i | ||||
\(655\) | −22.4048 | + | 12.9354i | −0.875429 | + | 0.505429i | ||||
\(656\) | −8.57465 | − | 4.95058i | −0.334784 | − | 0.193288i | ||||
\(657\) | 9.54051i | 0.372211i | ||||||||
\(658\) | −7.04005 | − | 5.12869i | −0.274450 | − | 0.199937i | ||||
\(659\) | 16.9216 | 0.659171 | 0.329585 | − | 0.944126i | \(-0.393091\pi\) | ||||
0.329585 | + | 0.944126i | \(0.393091\pi\) | |||||||
\(660\) | 1.42697 | − | 2.47159i | 0.0555449 | − | 0.0962065i | ||||
\(661\) | −35.9451 | + | 20.7529i | −1.39810 | + | 0.807194i | −0.994194 | − | 0.107606i | \(-0.965681\pi\) |
−0.403907 | + | 0.914800i | \(0.632348\pi\) | |||||||
\(662\) | 10.5196 | + | 18.2205i | 0.408857 | + | 0.708162i | ||||
\(663\) | 1.34255 | + | 0.225029i | 0.0521405 | + | 0.00873942i | ||||
\(664\) | −6.39446 | −0.248153 | ||||||||
\(665\) | −37.5097 | − | 27.3259i | −1.45457 | − | 1.05965i | ||||
\(666\) | 3.37755 | 0.130877 | ||||||||
\(667\) | 5.40961 | − | 9.36972i | 0.209461 | − | 0.362797i | ||||
\(668\) | −21.3676 | + | 12.3366i | −0.826737 | + | 0.477317i | ||||
\(669\) | 20.5988 | − | 11.8927i | 0.796394 | − | 0.459798i | ||||
\(670\) | 2.53095 | + | 1.46124i | 0.0977791 | + | 0.0564528i | ||||
\(671\) | 11.2315i | 0.433587i | ||||||||
\(672\) | −2.63090 | − | 0.279927i | −0.101489 | − | 0.0107984i | ||||
\(673\) | 15.6394 | 0.602853 | 0.301426 | − | 0.953489i | \(-0.402537\pi\) | ||||
0.301426 | + | 0.953489i | \(0.402537\pi\) | |||||||
\(674\) | −22.1334 | − | 12.7787i | −0.852546 | − | 0.492217i | ||||
\(675\) | 0.0578747 | + | 0.100242i | 0.00222760 | + | 0.00385831i | ||||
\(676\) | −12.2895 | − | 4.23885i | −0.472674 | − | 0.163033i | ||||
\(677\) | −6.61178 | + | 11.4519i | −0.254111 | + | 0.440134i | −0.964654 | − | 0.263521i | \(-0.915116\pi\) |
0.710542 | + | 0.703654i | \(0.248450\pi\) | |||||||
\(678\) | − | 1.32241i | − | 0.0507868i | ||||||
\(679\) | 8.61673 | + | 19.4204i | 0.330680 | + | 0.745287i | ||||
\(680\) | −0.853947 | −0.0327474 | ||||||||
\(681\) | 8.86074 | + | 5.11575i | 0.339544 | + | 0.196036i | ||||
\(682\) | 4.37101 | − | 2.52360i | 0.167375 | − | 0.0966338i | ||||
\(683\) | −22.4935 | + | 12.9866i | −0.860688 | + | 0.496919i | −0.864243 | − | 0.503075i | \(-0.832202\pi\) |
0.00355454 | + | 0.999994i | \(0.498869\pi\) | |||||||
\(684\) | 6.71612 | + | 3.87755i | 0.256797 | + | 0.148262i | ||||
\(685\) | −25.2102 | −0.963231 | ||||||||
\(686\) | −13.8108 | + | 12.3395i | −0.527297 | + | 0.471124i | ||||
\(687\) | 1.04721i | 0.0399535i | ||||||||
\(688\) | −4.37755 | + | 7.58214i | −0.166893 | + | 0.289066i | ||||
\(689\) | −6.88243 | + | 8.34459i | −0.262200 | + | 0.317903i | ||||
\(690\) | −5.08148 | − | 8.80138i | −0.193449 | − | 0.335063i | ||||
\(691\) | −14.6467 | − | 8.45630i | −0.557188 | − | 0.321693i | 0.194828 | − | 0.980837i | \(-0.437585\pi\) |
−0.752016 | + | 0.659145i | \(0.770918\pi\) | |||||||
\(692\) | −23.9787 | −0.911532 | ||||||||
\(693\) | 1.35395 | + | 3.05153i | 0.0514322 | + | 0.115918i | ||||
\(694\) | − | 18.3303i | − | 0.695810i | ||||||
\(695\) | 4.88382 | + | 2.81968i | 0.185254 | + | 0.106956i | ||||
\(696\) | −2.08526 | + | 1.20393i | −0.0790417 | + | 0.0456348i | ||||
\(697\) | 3.23737 | − | 1.86910i | 0.122624 | − | 0.0707972i | ||||
\(698\) | 2.09663 | − | 3.63147i | 0.0793587 | − | 0.137453i | ||||
\(699\) | −3.75160 | −0.141898 | ||||||||
\(700\) | 0.0324014 | − | 0.304525i | 0.00122466 | − | 0.0115100i | ||||
\(701\) | −33.0731 | −1.24915 | −0.624577 | − | 0.780964i | \(-0.714728\pi\) | ||||
−0.624577 | + | 0.780964i | \(0.714728\pi\) | |||||||
\(702\) | 0.596023 | − | 3.55595i | 0.0224954 | − | 0.134211i | ||||
\(703\) | 13.0966 | + | 22.6840i | 0.493949 | + | 0.855544i | ||||
\(704\) | 1.09275 | − | 0.630901i | 0.0411847 | − | 0.0237780i | ||||
\(705\) | −3.72305 | + | 6.44850i | −0.140218 | + | 0.242865i | ||||
\(706\) | −21.8629 | −0.822822 | ||||||||
\(707\) | 24.8903 | + | 18.1327i | 0.936097 | + | 0.681949i | ||||
\(708\) | − | 4.66966i | − | 0.175496i | ||||||
\(709\) | −10.4254 | − | 6.01912i | −0.391535 | − | 0.226053i | 0.291290 | − | 0.956635i | \(-0.405916\pi\) |
−0.682825 | + | 0.730582i | \(0.739249\pi\) | |||||||
\(710\) | −8.06184 | + | 4.65451i | −0.302555 | + | 0.174680i | ||||
\(711\) | 3.14605 | + | 5.44912i | 0.117986 | + | 0.204358i | ||||
\(712\) | 5.68878 | − | 9.85325i | 0.213196 | − | 0.369266i | ||||
\(713\) | − | 17.9732i | − | 0.673102i | ||||||
\(714\) | 0.588178 | − | 0.807380i | 0.0220120 | − | 0.0302155i | ||||
\(715\) | −3.60112 | − | 9.63935i | −0.134674 | − | 0.360491i | ||||
\(716\) | −2.85395 | + | 4.94318i | −0.106657 | + | 0.184735i | ||||
\(717\) | −25.2851 | + | 14.5984i | −0.944291 | + | 0.545187i | ||||
\(718\) | −12.9523 | − | 22.4341i | −0.483377 | − | 0.837233i | ||||
\(719\) | 3.59214 | − | 6.22178i | 0.133964 | − | 0.232033i | −0.791237 | − | 0.611510i | \(-0.790563\pi\) |
0.925201 | + | 0.379476i | \(0.123896\pi\) | |||||||
\(720\) | 2.26180i | 0.0842924i | ||||||||
\(721\) | 3.48873 | − | 32.7889i | 0.129927 | − | 1.22112i | ||||
\(722\) | 41.1416i | 1.53113i | ||||||||
\(723\) | 1.47908 | + | 0.853947i | 0.0550076 | + | 0.0317586i | ||||
\(724\) | −8.33483 | − | 14.4363i | −0.309761 | − | 0.536523i | ||||
\(725\) | −0.139354 | − | 0.241368i | −0.00517547 | − | 0.00896418i | ||||
\(726\) | 8.14744 | + | 4.70393i | 0.302380 | + | 0.174579i | ||||
\(727\) | −41.8967 | −1.55386 | −0.776932 | − | 0.629585i | \(-0.783225\pi\) | ||||
−0.776932 | + | 0.629585i | \(0.783225\pi\) | |||||||
\(728\) | −6.81429 | + | 6.67573i | −0.252554 | + | 0.247419i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −18.6877 | − | 10.7894i | −0.691664 | − | 0.399333i | ||||
\(731\) | −1.65275 | − | 2.86265i | −0.0611292 | − | 0.105879i | ||||
\(732\) | −4.45058 | − | 7.70863i | −0.164498 | − | 0.284919i | ||||
\(733\) | −19.5022 | − | 11.2596i | −0.720329 | − | 0.415882i | 0.0945445 | − | 0.995521i | \(-0.469861\pi\) |
−0.814874 | + | 0.579638i | \(0.803194\pi\) | |||||||
\(734\) | 17.8629i | 0.659332i | ||||||||
\(735\) | 11.7387 | + | 10.6242i | 0.432990 | + | 0.391880i | ||||
\(736\) | − | 4.49330i | − | 0.165625i | ||||||
\(737\) | 0.815191 | − | 1.41195i | 0.0300279 | − | 0.0520099i | ||||
\(738\) | −4.95058 | − | 8.57465i | −0.182233 | − | 0.315637i | ||||
\(739\) | 10.3992 | − | 6.00397i | 0.382540 | − | 0.220859i | −0.296383 | − | 0.955069i | \(-0.595780\pi\) |
0.678923 | + | 0.734210i | \(0.262447\pi\) | |||||||
\(740\) | −3.81968 | + | 6.61587i | −0.140414 | + | 0.243204i | ||||
\(741\) | 26.1933 | − | 9.78541i | 0.962234 | − | 0.359476i | ||||
\(742\) | 3.21908 | + | 7.25517i | 0.118176 | + | 0.266346i | ||||
\(743\) | − | 9.52360i | − | 0.349387i | −0.984623 | − | 0.174694i | \(-0.944107\pi\) | ||
0.984623 | − | 0.174694i | \(-0.0558935\pi\) | |||||||
\(744\) | −2.00000 | + | 3.46410i | −0.0733236 | + | 0.127000i | ||||
\(745\) | 0.0342702 | + | 0.0593577i | 0.00125556 | + | 0.00217470i | ||||
\(746\) | 13.0984 | − | 7.56236i | 0.479566 | − | 0.276878i | ||||
\(747\) | −5.53776 | − | 3.19723i | −0.202616 | − | 0.116980i | ||||
\(748\) | 0.476396i | 0.0174187i | ||||||||
\(749\) | 4.98335 | − | 46.8361i | 0.182088 | − | 1.71135i | ||||
\(750\) | 11.0472 | 0.403387 | ||||||||
\(751\) | 19.7248 | − | 34.1644i | 0.719768 | − | 1.24668i | −0.241323 | − | 0.970445i | \(-0.577581\pi\) |
0.961091 | − | 0.276230i | \(-0.0890852\pi\) | |||||||
\(752\) | −2.85105 | + | 1.64605i | −0.103967 | + | 0.0600254i | ||||
\(753\) | −9.72480 | − | 16.8438i | −0.354391 | − | 0.613824i | ||||
\(754\) | −1.43514 | + | 8.56220i | −0.0522646 | + | 0.311817i | ||||
\(755\) | 9.74613 | 0.354698 | ||||||||
\(756\) | −2.13846 | − | 1.55787i | −0.0777752 | − | 0.0566594i | ||||
\(757\) | 19.4854 | 0.708208 | 0.354104 | − | 0.935206i | \(-0.384786\pi\) | ||||
0.354104 | + | 0.935206i | \(0.384786\pi\) | |||||||
\(758\) | 6.26180 | − | 10.8458i | 0.227439 | − | 0.393936i | ||||
\(759\) | −4.91007 | + | 2.83483i | −0.178224 | + | 0.102898i | ||||
\(760\) | −15.1905 | + | 8.77026i | −0.551018 | + | 0.318131i | ||||
\(761\) | 5.73138 | + | 3.30901i | 0.207762 | + | 0.119952i | 0.600271 | − | 0.799797i | \(-0.295059\pi\) |
−0.392509 | + | 0.919748i | \(0.628393\pi\) | |||||||
\(762\) | 16.3642i | 0.592811i | ||||||||
\(763\) | −5.10782 | + | 7.01140i | −0.184915 | + | 0.253830i | ||||
\(764\) | −7.27871 | −0.263334 | ||||||||
\(765\) | −0.739540 | − | 0.426974i | −0.0267381 | − | 0.0154373i | ||||
\(766\) | 0.789373 | + | 1.36723i | 0.0285212 | + | 0.0494002i | ||||
\(767\) | −12.9888 | − | 10.7129i | −0.468998 | − | 0.386819i | ||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | − | 14.3900i | − | 0.518918i | −0.965754 | − | 0.259459i | \(-0.916456\pi\) | ||
0.965754 | − | 0.259459i | \(-0.0835442\pi\) | |||||||
\(770\) | −7.50845 | − | 0.798898i | −0.270586 | − | 0.0287903i | ||||
\(771\) | 12.2921 | 0.442689 | ||||||||
\(772\) | 14.9900 | + | 8.65451i | 0.539503 | + | 0.311482i | ||||
\(773\) | −47.8358 | + | 27.6180i | −1.72053 | + | 0.993351i | −0.802706 | + | 0.596375i | \(0.796607\pi\) |
−0.917829 | + | 0.396976i | \(0.870060\pi\) | |||||||
\(774\) | −7.58214 | + | 4.37755i | −0.272534 | + | 0.157348i | ||||
\(775\) | −0.400968 | − | 0.231499i | −0.0144032 | − | 0.00831568i | ||||
\(776\) | 8.03030 | 0.288271 | ||||||||
\(777\) | −3.62420 | − | 8.16824i | −0.130018 | − | 0.293034i | ||||
\(778\) | − | 4.81025i | − | 0.172456i | ||||||
\(779\) | 38.3922 | − | 66.4973i | 1.37554 | − | 2.38251i | ||||
\(780\) | 6.29127 | + | 5.18890i | 0.225264 | + | 0.185792i | ||||
\(781\) | 2.59663 | + | 4.49750i | 0.0929148 | + | 0.160933i | ||||
\(782\) | 1.46917 | + | 0.848227i | 0.0525375 | + | 0.0303325i | ||||
\(783\) | −2.40786 | −0.0860497 | ||||||||
\(784\) | 2.14605 | + | 6.66292i | 0.0766447 | + | 0.237961i | ||||
\(785\) | 51.3687i | 1.83343i | ||||||||
\(786\) | −9.90574 | − | 5.71908i | −0.353326 | − | 0.203993i | ||||
\(787\) | 0.642336 | − | 0.370853i | 0.0228968 | − | 0.0132195i | −0.488508 | − | 0.872559i | \(-0.662459\pi\) |
0.511405 | + | 0.859340i | \(0.329125\pi\) | |||||||
\(788\) | −2.78392 | + | 1.60730i | −0.0991730 | + | 0.0572576i | ||||
\(789\) | −1.65451 | + | 2.86569i | −0.0589020 | + | 0.102021i | ||||
\(790\) | −14.2315 | −0.506334 | ||||||||
\(791\) | −3.19810 | + | 1.41898i | −0.113711 | + | 0.0504531i | ||||
\(792\) | 1.26180 | 0.0448362 | ||||||||
\(793\) | −31.6520 | − | 5.30529i | −1.12400 | − | 0.188397i | ||||
\(794\) | 13.4742 | + | 23.3380i | 0.478181 | + | 0.828234i | ||||
\(795\) | 5.87633 | − | 3.39270i | 0.208412 | − | 0.120327i | ||||
\(796\) | 5.85173 | − | 10.1355i | 0.207409 | − | 0.359243i | ||||
\(797\) | 21.4685 | 0.760452 | 0.380226 | − | 0.924894i | \(-0.375846\pi\) | ||||
0.380226 | + | 0.924894i | \(0.375846\pi\) | |||||||
\(798\) | 2.17086 | − | 20.4029i | 0.0768478 | − | 0.722255i | ||||
\(799\) | − | 1.24294i | − | 0.0439721i | ||||||
\(800\) | −0.100242 | − | 0.0578747i | −0.00354409 | − | 0.00204618i | ||||
\(801\) | 9.85325 | − | 5.68878i | 0.348147 | − | 0.201003i | ||||
\(802\) | 10.2978 | + | 17.8364i | 0.363629 | + | 0.629824i | ||||
\(803\) | −6.01912 | + | 10.4254i | −0.212410 | + | 0.367905i | ||||
\(804\) | 1.29211i | 0.0455691i | ||||||||
\(805\) | −15.8326 | + | 21.7331i | −0.558026 | + | 0.765992i | ||||
\(806\) | 5.04721 | + | 13.5102i | 0.177780 | + | 0.475877i | ||||
\(807\) | −16.0062 | + | 27.7236i | −0.563446 | + | 0.975918i | ||||
\(808\) | 10.0800 | − | 5.81968i | 0.354612 | − | 0.204736i | ||||
\(809\) | 6.63487 | + | 11.4919i | 0.233270 | + | 0.404035i | 0.958768 | − | 0.284189i | \(-0.0917242\pi\) |
−0.725499 | + | 0.688223i | \(0.758391\pi\) | |||||||
\(810\) | −1.13090 | + | 1.95878i | −0.0397358 | + | 0.0688245i | ||||
\(811\) | 14.8236i | 0.520529i | 0.965537 | + | 0.260264i | \(0.0838097\pi\) | ||||
−0.965537 | + | 0.260264i | \(0.916190\pi\) | |||||||
\(812\) | 5.14911 | + | 3.75114i | 0.180698 | + | 0.131639i | ||||
\(813\) | 22.3090i | 0.782411i | ||||||||
\(814\) | 3.69083 | + | 2.13090i | 0.129363 | + | 0.0746880i | ||||
\(815\) | 14.0321 | + | 24.3042i | 0.491522 | + | 0.851340i | ||||
\(816\) | −0.188776 | − | 0.326969i | −0.00660848 | − | 0.0114462i | ||||
\(817\) | −58.8003 | − | 33.9484i | −2.05716 | − | 1.18770i | ||||
\(818\) | 5.30901 | 0.185625 | ||||||||
\(819\) | −9.23922 | + | 2.37421i | −0.322844 | + | 0.0829615i | ||||
\(820\) | 22.3945 | 0.782048 | ||||||||
\(821\) | −28.2743 | − | 16.3242i | −0.986779 | − | 0.569717i | −0.0824692 | − | 0.996594i | \(-0.526281\pi\) |
−0.904310 | + | 0.426876i | \(0.859614\pi\) | |||||||
\(822\) | −5.57303 | − | 9.65276i | −0.194382 | − | 0.336679i | ||||
\(823\) | 5.67187 | + | 9.82397i | 0.197709 | + | 0.342442i | 0.947785 | − | 0.318909i | \(-0.103317\pi\) |
−0.750076 | + | 0.661351i | \(0.769983\pi\) | |||||||
\(824\) | −10.7933 | − | 6.23150i | −0.376001 | − | 0.217085i | ||||
\(825\) | 0.146053i | 0.00508491i | ||||||||
\(826\) | −11.2931 | + | 5.01067i | −0.392936 | + | 0.174343i | ||||
\(827\) | − | 14.7988i | − | 0.514605i | −0.966331 | − | 0.257302i | \(-0.917166\pi\) | ||
0.966331 | − | 0.257302i | \(-0.0828337\pi\) | |||||||
\(828\) | 2.24665 | − | 3.89131i | 0.0780765 | − | 0.135232i | ||||
\(829\) | −6.23598 | − | 10.8010i | −0.216585 | − | 0.375136i | 0.737177 | − | 0.675700i | \(-0.236158\pi\) |
−0.953762 | + | 0.300564i | \(0.902825\pi\) | |||||||
\(830\) | 12.5253 | − | 7.23150i | 0.434760 | − | 0.251009i | ||||
\(831\) | 5.20568 | − | 9.01650i | 0.180583 | − | 0.312779i | ||||
\(832\) | 1.26180 | + | 3.37755i | 0.0437451 | + | 0.117096i | ||||
\(833\) | −2.58369 | − | 0.556104i | −0.0895196 | − | 0.0192679i | ||||
\(834\) | 2.49330i | 0.0863360i | ||||||||
\(835\) | 27.9029 | − | 48.3293i | 0.965620 | − | 1.67250i | ||||
\(836\) | 4.89270 | + | 8.47441i | 0.169218 | + | 0.293094i | ||||
\(837\) | −3.46410 | + | 2.00000i | −0.119737 | + | 0.0691301i | ||||
\(838\) | −17.8264 | − | 10.2921i | −0.615804 | − | 0.355535i | ||||
\(839\) | 10.0890i | 0.348309i | 0.984718 | + | 0.174155i | \(0.0557193\pi\) | ||||
−0.984718 | + | 0.174155i | \(0.944281\pi\) | |||||||
\(840\) | 5.46992 | − | 2.42697i | 0.188730 | − | 0.0837385i | ||||
\(841\) | −23.2022 | −0.800077 | ||||||||
\(842\) | −6.44388 | + | 11.1611i | −0.222071 | + | 0.384638i | ||||
\(843\) | −25.5566 | + | 14.7551i | −0.880216 | + | 0.508193i | ||||
\(844\) | −4.03206 | − | 6.98373i | −0.138789 | − | 0.240390i | ||||
\(845\) | 28.8662 | − | 5.59525i | 0.993026 | − | 0.192483i | ||||
\(846\) | −3.29211 | −0.113185 | ||||||||
\(847\) | 2.63352 | − | 24.7511i | 0.0904887 | − | 0.850459i | ||||
\(848\) | 3.00000 | 0.103020 | ||||||||
\(849\) | −1.60730 | + | 2.78392i | −0.0551623 | + | 0.0955439i | ||||
\(850\) | 0.0378465 | − | 0.0218507i | 0.00129812 | − | 0.000749472i | ||||
\(851\) | 13.1431 | − | 7.58818i | 0.450540 | − | 0.260119i | ||||
\(852\) | −3.56434 | − | 2.05787i | −0.122112 | − | 0.0705016i | ||||
\(853\) | − | 1.48784i | − | 0.0509426i | −0.999676 | − | 0.0254713i | \(-0.991891\pi\) | ||
0.999676 | − | 0.0254713i | \(-0.00810864\pi\) | |||||||
\(854\) | −13.8669 | + | 19.0348i | −0.474515 | + | 0.651357i | ||||
\(855\) | −17.5405 | −0.599873 | ||||||||
\(856\) | −15.4173 | − | 8.90116i | −0.526951 | − | 0.304235i | ||||
\(857\) | 22.2832 | + | 38.5956i | 0.761179 | + | 1.31840i | 0.942243 | + | 0.334930i | \(0.108713\pi\) |
−0.181064 | + | 0.983471i | \(0.557954\pi\) | |||||||
\(858\) | 2.89476 | − | 3.50974i | 0.0988254 | − | 0.119821i | ||||
\(859\) | 9.06411 | − | 15.6995i | 0.309264 | − | 0.535660i | −0.668938 | − | 0.743318i | \(-0.733251\pi\) |
0.978201 | + | 0.207658i | \(0.0665841\pi\) | |||||||
\(860\) | − | 19.8023i | − | 0.675253i | ||||||
\(861\) | −15.4248 | + | 21.1733i | −0.525674 | + | 0.721583i | ||||
\(862\) | −26.6260 | −0.906884 | ||||||||
\(863\) | −19.8838 | − | 11.4799i | −0.676852 | − | 0.390780i | 0.121816 | − | 0.992553i | \(-0.461128\pi\) |
−0.798668 | + | 0.601772i | \(0.794461\pi\) | |||||||
\(864\) | −0.866025 | + | 0.500000i | −0.0294628 | + | 0.0170103i | ||||
\(865\) | 46.9689 | − | 27.1175i | 1.59699 | − | 0.922023i | ||||
\(866\) | −24.3189 | − | 14.0405i | −0.826389 | − | 0.477116i | ||||
\(867\) | −16.8575 | −0.572509 | ||||||||
\(868\) | 10.5236 | + | 1.11971i | 0.357194 | + | 0.0380054i | ||||
\(869\) | 7.93939i | 0.269325i | ||||||||
\(870\) | 2.72305 | − | 4.71645i | 0.0923199 | − | 0.159903i | ||||
\(871\) | 3.59403 | + | 2.96428i | 0.121779 | + | 0.100441i | ||||
\(872\) | 1.63935 | + | 2.83944i | 0.0555155 | + | 0.0961557i | ||||
\(873\) | 6.95445 | + | 4.01515i | 0.235372 | + | 0.135892i | ||||
\(874\) | 34.8460 | 1.17868 | ||||||||
\(875\) | −11.8539 | − | 26.7165i | −0.400737 | − | 0.903182i | ||||
\(876\) | − | 9.54051i | − | 0.322344i | ||||||
\(877\) | 26.6309 | + | 15.3753i | 0.899261 | + | 0.519188i | 0.876960 | − | 0.480563i | \(-0.159568\pi\) |
0.0223003 | + | 0.999751i | \(0.492901\pi\) | |||||||
\(878\) | −24.0444 | + | 13.8820i | −0.811459 | + | 0.468496i | ||||
\(879\) | −21.4123 | + | 12.3624i | −0.722219 | + | 0.416973i | ||||
\(880\) | −1.42697 | + | 2.47159i | −0.0481033 | + | 0.0833173i | ||||
\(881\) | −28.7551 | −0.968784 | −0.484392 | − | 0.874851i | \(-0.660959\pi\) | ||||
−0.484392 | + | 0.874851i | \(0.660959\pi\) | |||||||
\(882\) | −1.47292 | + | 6.84328i | −0.0495959 | + | 0.230425i | ||||
\(883\) | −31.3696 | −1.05567 | −0.527836 | − | 0.849346i | \(-0.676996\pi\) | ||||
−0.527836 | + | 0.849346i | \(0.676996\pi\) | |||||||
\(884\) | −1.34255 | − | 0.225029i | −0.0451550 | − | 0.00756856i | ||||
\(885\) | 5.28092 | + | 9.14682i | 0.177516 | + | 0.307467i | ||||
\(886\) | −3.95067 | + | 2.28092i | −0.132725 | + | 0.0766290i | ||||
\(887\) | −4.40786 | + | 7.63463i | −0.148001 | + | 0.256346i | −0.930489 | − | 0.366321i | \(-0.880617\pi\) |
0.782487 | + | 0.622666i | \(0.213951\pi\) | |||||||
\(888\) | −3.37755 | −0.113343 | ||||||||
\(889\) | 39.5749 | − | 17.5592i | 1.32730 | − | 0.588916i | ||||
\(890\) | 25.7338i | 0.862598i | ||||||||
\(891\) | 1.09275 | + | 0.630901i | 0.0366086 | + | 0.0211360i | ||||
\(892\) | −20.5988 | + | 11.8927i | −0.689698 | + | 0.398197i | ||||
\(893\) | −12.7653 | − | 22.1102i | −0.427175 | − | 0.739888i | ||||
\(894\) | −0.0151517 | + | 0.0262436i | −0.000506750 | + | 0.000877716i | ||||
\(895\) | − | 12.9101i | − | 0.431538i | ||||||
\(896\) | 2.63090 | + | 0.279927i | 0.0878922 | + | 0.00935171i | ||||
\(897\) | −5.66966 | − | 15.1764i | −0.189304 | − | 0.506724i | ||||
\(898\) | −1.39095 | + | 2.40920i | −0.0464166 | + | 0.0803959i | ||||
\(899\) | 8.34105 | − | 4.81571i | 0.278190 | − | 0.160613i | ||||
\(900\) | −0.0578747 | − | 0.100242i | −0.00192916 | − | 0.00334140i | ||||
\(901\) | −0.566327 | + | 0.980908i | −0.0188671 | + | 0.0326788i | ||||
\(902\) | − | 12.4933i | − | 0.415981i | ||||||
\(903\) | 18.7225 | + | 13.6394i | 0.623045 | + | 0.453889i | ||||
\(904\) | 1.32241i | 0.0439827i | ||||||||
\(905\) | 32.6522 | + | 18.8517i | 1.08539 | + | 0.626653i | ||||
\(906\) | 2.15451 | + | 3.73171i | 0.0715787 | + | 0.123978i | ||||
\(907\) | 2.01515 | + | 3.49035i | 0.0669120 | + | 0.115895i | 0.897541 | − | 0.440932i | \(-0.145352\pi\) |
−0.830629 | + | 0.556827i | \(0.812019\pi\) | |||||||
\(908\) | −8.86074 | − | 5.11575i | −0.294054 | − | 0.169772i | ||||
\(909\) | 11.6394 | 0.386053 | ||||||||
\(910\) | 5.79809 | − | 20.7826i | 0.192205 | − | 0.688936i | ||||
\(911\) | −14.1212 | −0.467857 | −0.233928 | − | 0.972254i | \(-0.575158\pi\) | ||||
−0.233928 | + | 0.972254i | \(0.575158\pi\) | |||||||
\(912\) | −6.71612 | − | 3.87755i | −0.222393 | − | 0.128399i | ||||
\(913\) | −4.03427 | − | 6.98756i | −0.133515 | − | 0.231255i | ||||
\(914\) | 14.9029 | + | 25.8126i | 0.492944 | + | 0.853805i | ||||
\(915\) | 17.4354 | + | 10.0663i | 0.576396 | + | 0.332783i | ||||
\(916\) | − | 1.04721i | − | 0.0346008i | ||||||
\(917\) | −3.20185 | + | 30.0927i | −0.105734 | + | 0.993747i | ||||
\(918\) | − | 0.377552i | − | 0.0124611i | ||||||
\(919\) | 5.06411 | − | 8.77130i | 0.167050 | − | 0.289339i | −0.770332 | − | 0.637644i | \(-0.779909\pi\) |
0.937381 | + | 0.348305i | \(0.113243\pi\) | |||||||
\(920\) | 5.08148 | + | 8.80138i | 0.167531 | + | 0.290173i | ||||
\(921\) | 6.00969 | − | 3.46970i | 0.198026 | − | 0.114330i | ||||
\(922\) | 9.30901 | − | 16.1237i | 0.306576 | − | 0.531005i | ||||
\(923\) | −13.9012 | + | 5.19326i | −0.457562 | + | 0.170938i | ||||
\(924\) | −1.35395 | − | 3.05153i | −0.0445416 | − | 0.100388i | ||||
\(925\) | − | 0.390950i | − | 0.0128543i | ||||||
\(926\) | 21.0169 | − | 36.4023i | 0.690658 | − | 1.19626i | ||||
\(927\) | −6.23150 | − | 10.7933i | −0.204669 | − | 0.354498i | ||||
\(928\) | 2.08526 | − | 1.20393i | 0.0684521 | − | 0.0395209i | ||||
\(929\) | −30.3811 | − | 17.5405i | −0.996770 | − | 0.575485i | −0.0894790 | − | 0.995989i | \(-0.528520\pi\) |
−0.907291 | + | 0.420503i | \(0.861854\pi\) | |||||||
\(930\) | − | 9.04721i | − | 0.296670i | ||||||
\(931\) | −51.6716 | + | 16.6429i | −1.69347 | + | 0.545448i | ||||
\(932\) | 3.75160 | 0.122888 | ||||||||
\(933\) | 5.53876 | − | 9.59341i | 0.181331 | − | 0.314074i | ||||
\(934\) | 33.7071 | − | 19.4608i | 1.10293 | − | 0.636776i | ||||
\(935\) | −0.538756 | − | 0.933153i | −0.0176192 | − | 0.0305174i | ||||
\(936\) | −0.596023 | + | 3.55595i | −0.0194816 | + | 0.116230i | ||||
\(937\) | 22.6055 | 0.738491 | 0.369245 | − | 0.929332i | \(-0.379616\pi\) | ||||
0.369245 | + | 0.929332i | \(0.379616\pi\) | |||||||
\(938\) | 3.12482 | − | 1.38646i | 0.102029 | − | 0.0452696i | ||||
\(939\) | −21.4079 | −0.698619 | ||||||||
\(940\) | 3.72305 | − | 6.44850i | 0.121432 | − | 0.210327i | ||||
\(941\) | 23.8013 | − | 13.7417i | 0.775901 | − | 0.447967i | −0.0590745 | − | 0.998254i | \(-0.518815\pi\) |
0.834976 | + | 0.550287i | \(0.185482\pi\) | |||||||
\(942\) | −19.6687 | + | 11.3557i | −0.640839 | + | 0.369989i | ||||
\(943\) | −38.5285 | − | 22.2444i | −1.25466 | − | 0.724379i | ||||
\(944\) | 4.66966i | 0.151984i | ||||||||
\(945\) | 5.95058 | + | 0.633140i | 0.193572 | + | 0.0205961i | ||||
\(946\) | −11.0472 | −0.359176 | ||||||||
\(947\) | 24.5757 | + | 14.1888i | 0.798602 | + | 0.461073i | 0.842982 | − | 0.537941i | \(-0.180798\pi\) |
−0.0443799 | + | 0.999015i | \(0.514131\pi\) | |||||||
\(948\) | −3.14605 | − | 5.44912i | −0.102179 | − | 0.176979i | ||||
\(949\) | −26.5372 | − | 21.8873i | −0.861434 | − | 0.710492i | ||||
\(950\) | 0.448824 | − | 0.777386i | 0.0145618 | − | 0.0252217i | ||||
\(951\) | − | 21.2181i | − | 0.688044i | ||||||
\(952\) | −0.588178 | + | 0.807380i | −0.0190630 | + | 0.0261674i | ||||
\(953\) | 9.58864 | 0.310606 | 0.155303 | − | 0.987867i | \(-0.450365\pi\) | ||||
0.155303 | + | 0.987867i | \(0.450365\pi\) | |||||||
\(954\) | 2.59808 | + | 1.50000i | 0.0841158 | + | 0.0485643i | ||||
\(955\) | 14.2574 | − | 8.23150i | 0.461358 | − | 0.266365i | ||||
\(956\) | 25.2851 | − | 14.5984i | 0.817780 | − | 0.472146i | ||||
\(957\) | −2.63119 | − | 1.51912i | −0.0850543 | − | 0.0491061i | ||||
\(958\) | 2.28664 | 0.0738780 | ||||||||
\(959\) | −17.3642 | + | 23.8354i | −0.560718 | + | 0.769686i | ||||
\(960\) | − | 2.26180i | − | 0.0729994i | ||||||
\(961\) | −7.50000 | + | 12.9904i | −0.241935 | + | 0.419045i | ||||
\(962\) | −7.74859 | + | 9.39476i | −0.249825 | + | 0.302899i | ||||
\(963\) | −8.90116 | − | 15.4173i | −0.286836 | − | 0.496814i | ||||
\(964\) | −1.47908 | − | 0.853947i | −0.0476380 | − | 0.0275038i | ||||
\(965\) | −39.1496 | −1.26027 | ||||||||
\(966\) | −11.8214 | − | 1.25780i | −0.380348 | − | 0.0404690i | ||||
\(967\) | − | 31.2271i | − | 1.00419i | −0.864811 | − | 0.502097i | \(-0.832562\pi\) | ||
0.864811 | − | 0.502097i | \(-0.167438\pi\) | |||||||
\(968\) | −8.14744 | − | 4.70393i | −0.261869 | − | 0.151190i | ||||
\(969\) | 2.53568 | − | 1.46398i | 0.0814578 | − | 0.0470297i | ||||
\(970\) | −15.7296 | + | 9.08148i | −0.505046 | + | 0.291589i | ||||
\(971\) | 18.3833 | − | 31.8408i | 0.589947 | − | 1.02182i | −0.404291 | − | 0.914630i | \(-0.632482\pi\) |
0.994239 | − | 0.107188i | \(-0.0341848\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 6.02978 | − | 2.67538i | 0.193306 | − | 0.0857687i | ||||
\(974\) | 30.8405 | 0.988195 | ||||||||
\(975\) | −0.411599 | − | 0.0689893i | −0.0131817 | − | 0.00220943i | ||||
\(976\) | 4.45058 | + | 7.70863i | 0.142460 | + | 0.246747i | ||||
\(977\) | −14.4811 | + | 8.36065i | −0.463290 | + | 0.267481i | −0.713427 | − | 0.700730i | \(-0.752858\pi\) |
0.250136 | + | 0.968211i | \(0.419525\pi\) | |||||||
\(978\) | −6.20393 | + | 10.7455i | −0.198380 | + | 0.343604i | ||||
\(979\) | 14.3562 | 0.458827 | ||||||||
\(980\) | −11.7387 | − | 10.6242i | −0.374980 | − | 0.339378i | ||||
\(981\) | 3.27871i | 0.104681i | ||||||||
\(982\) | 35.6590 | + | 20.5877i | 1.13792 | + | 0.656981i | ||||
\(983\) | 39.2534 | − | 22.6630i | 1.25199 | − | 0.722836i | 0.280485 | − | 0.959859i | \(-0.409505\pi\) |
0.971504 | + | 0.237022i | \(0.0761715\pi\) | |||||||
\(984\) | 4.95058 | + | 8.57465i | 0.157819 | + | 0.273350i | ||||
\(985\) | 3.63539 | − | 6.29668i | 0.115833 | − | 0.200629i | ||||
\(986\) | 0.909090i | 0.0289513i | ||||||||
\(987\) | 3.53252 | + | 7.96160i | 0.112441 | + | 0.253420i | ||||
\(988\) | −26.1933 | + | 9.78541i | −0.833319 | + | 0.311315i | ||||
\(989\) | −19.6697 | + | 34.0688i | −0.625459 | + | 1.08333i | ||||
\(990\) | −2.47159 | + | 1.42697i | −0.0785523 | + | 0.0453522i | ||||
\(991\) | −25.7417 | − | 44.5859i | −0.817712 | − | 1.41632i | −0.907364 | − | 0.420346i | \(-0.861909\pi\) |
0.0896517 | − | 0.995973i | \(-0.471425\pi\) | |||||||
\(992\) | 2.00000 | − | 3.46410i | 0.0635001 | − | 0.109985i | ||||
\(993\) | − | 21.0393i | − | 0.667661i | ||||||
\(994\) | −1.15211 | + | 10.8281i | −0.0365427 | + | 0.343447i | ||||
\(995\) | 26.4709i | 0.839185i | ||||||||
\(996\) | 5.53776 | + | 3.19723i | 0.175471 | + | 0.101308i | ||||
\(997\) | 26.7333 | + | 46.3034i | 0.846651 | + | 1.46644i | 0.884180 | + | 0.467146i | \(0.154718\pi\) |
−0.0375294 | + | 0.999296i | \(0.511949\pi\) | |||||||
\(998\) | −7.73423 | − | 13.3961i | −0.244823 | − | 0.424046i | ||||
\(999\) | −2.92505 | − | 1.68878i | −0.0925443 | − | 0.0534305i |
(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 | 546.2.bk.b.415.4 | yes | 12 | |
3.2 | odd | 2 | 1638.2.dm.c.415.3 | 12 | |||
7.2 | even | 3 | 3822.2.c.k.883.3 | 6 | |||
7.4 | even | 3 | inner | 546.2.bk.b.25.3 | ✓ | 12 | |
7.5 | odd | 6 | 3822.2.c.j.883.1 | 6 | |||
13.12 | even | 2 | inner | 546.2.bk.b.415.3 | yes | 12 | |
21.11 | odd | 6 | 1638.2.dm.c.1117.4 | 12 | |||
39.38 | odd | 2 | 1638.2.dm.c.415.4 | 12 | |||
91.12 | odd | 6 | 3822.2.c.j.883.6 | 6 | |||
91.25 | even | 6 | inner | 546.2.bk.b.25.4 | yes | 12 | |
91.51 | even | 6 | 3822.2.c.k.883.4 | 6 | |||
273.116 | odd | 6 | 1638.2.dm.c.1117.3 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.bk.b.25.3 | ✓ | 12 | 7.4 | even | 3 | inner | |
546.2.bk.b.25.4 | yes | 12 | 91.25 | even | 6 | inner | |
546.2.bk.b.415.3 | yes | 12 | 13.12 | even | 2 | inner | |
546.2.bk.b.415.4 | yes | 12 | 1.1 | even | 1 | trivial | |
1638.2.dm.c.415.3 | 12 | 3.2 | odd | 2 | |||
1638.2.dm.c.415.4 | 12 | 39.38 | odd | 2 | |||
1638.2.dm.c.1117.3 | 12 | 273.116 | odd | 6 | |||
1638.2.dm.c.1117.4 | 12 | 21.11 | odd | 6 | |||
3822.2.c.j.883.1 | 6 | 7.5 | odd | 6 | |||
3822.2.c.j.883.6 | 6 | 91.12 | odd | 6 | |||
3822.2.c.k.883.3 | 6 | 7.2 | even | 3 | |||
3822.2.c.k.883.4 | 6 | 91.51 | even | 6 |