Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(341,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.be (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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 341.1 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.341 |
Dual form | 630.2.be.b.521.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | − | 0.500000i | −0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0.500000 | − | 0.866025i | 0.223607 | − | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.63896 | − | 0.189469i | −0.997433 | − | 0.0716124i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.866025 | + | 0.500000i | −0.273861 | + | 0.158114i | ||||
\(11\) | 4.67303 | − | 2.69798i | 1.40897 | − | 0.813471i | 0.413683 | − | 0.910421i | \(-0.364242\pi\) |
0.995289 | + | 0.0969504i | \(0.0309088\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51764i | 0.698267i | 0.937073 | + | 0.349134i | \(0.113524\pi\) | ||||
−0.937073 | + | 0.349134i | \(0.886476\pi\) | |||||||
\(14\) | 2.19067 | + | 1.48356i | 0.585481 | + | 0.396499i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −2.24969 | − | 3.89658i | −0.545630 | − | 0.945058i | −0.998567 | − | 0.0535160i | \(-0.982957\pi\) |
0.452937 | − | 0.891542i | \(-0.350376\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.48004 | − | 1.43185i | −0.568960 | − | 0.328489i | 0.187774 | − | 0.982212i | \(-0.439873\pi\) |
−0.756734 | + | 0.653723i | \(0.773206\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.39595 | −1.15042 | ||||||||
\(23\) | −0.232051 | − | 0.133975i | −0.0483859 | − | 0.0279356i | 0.475612 | − | 0.879655i | \(-0.342227\pi\) |
−0.523998 | + | 0.851720i | \(0.675560\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 1.25882 | − | 2.18034i | 0.246875 | − | 0.427600i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.15539 | − | 2.38014i | −0.218349 | − | 0.449804i | ||||
\(29\) | − | 8.89898i | − | 1.65250i | −0.563304 | − | 0.826250i | \(-0.690470\pi\) | ||
0.563304 | − | 0.826250i | \(-0.309530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.18154 | − | 2.41421i | 0.751027 | − | 0.433606i | −0.0750380 | − | 0.997181i | \(-0.523908\pi\) |
0.826065 | + | 0.563575i | \(0.190574\pi\) | |||||||
\(32\) | 0.866025 | − | 0.500000i | 0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.49938i | 0.771637i | ||||||||
\(35\) | −1.48356 | + | 2.19067i | −0.250768 | + | 0.370291i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.25882 | − | 5.64444i | 0.535747 | − | 0.927940i | −0.463380 | − | 0.886160i | \(-0.653364\pi\) |
0.999127 | − | 0.0417807i | \(-0.0133031\pi\) | |||||||
\(38\) | 1.43185 | + | 2.48004i | 0.232277 | + | 0.402316i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.866025 | − | 0.500000i | −0.136931 | − | 0.0790569i | ||||
\(41\) | −0.760279 | −0.118736 | −0.0593678 | − | 0.998236i | \(-0.518908\pi\) | ||||
−0.0593678 | + | 0.998236i | \(0.518908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.86370 | −0.894206 | −0.447103 | − | 0.894482i | \(-0.647544\pi\) | ||||
−0.447103 | + | 0.894482i | \(0.647544\pi\) | |||||||
\(44\) | 4.67303 | + | 2.69798i | 0.704486 | + | 0.406735i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.133975 | + | 0.232051i | 0.0197535 | + | 0.0342140i | ||||
\(47\) | −3.99768 | + | 6.92418i | −0.583121 | + | 1.01000i | 0.411986 | + | 0.911190i | \(0.364835\pi\) |
−0.995107 | + | 0.0988053i | \(0.968498\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.92820 | + | 1.00000i | 0.989743 | + | 0.142857i | ||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.18034 | + | 1.25882i | −0.302359 | + | 0.174567i | ||||
\(53\) | 7.27319 | − | 4.19918i | 0.999050 | − | 0.576802i | 0.0910826 | − | 0.995843i | \(-0.470967\pi\) |
0.907967 | + | 0.419042i | \(0.137634\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.39595i | − | 0.727590i | ||||||
\(56\) | −0.189469 | + | 2.63896i | −0.0253188 | + | 0.352646i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −4.44949 | + | 7.70674i | −0.584247 | + | 1.01194i | ||||
\(59\) | −6.33573 | − | 10.9738i | −0.824842 | − | 1.42867i | −0.902040 | − | 0.431653i | \(-0.857931\pi\) |
0.0771977 | − | 0.997016i | \(-0.475403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.27035 | − | 1.31079i | −0.290689 | − | 0.167829i | 0.347564 | − | 0.937656i | \(-0.387009\pi\) |
−0.638253 | + | 0.769827i | \(0.720342\pi\) | |||||||
\(62\) | −4.82843 | −0.613211 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 2.18034 | + | 1.25882i | 0.270438 | + | 0.156137i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.91119 | − | 8.50643i | −0.599997 | − | 1.03923i | −0.992821 | − | 0.119612i | \(-0.961835\pi\) |
0.392824 | − | 0.919614i | \(-0.371498\pi\) | |||||||
\(68\) | 2.24969 | − | 3.89658i | 0.272815 | − | 0.472529i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.38014 | − | 1.15539i | 0.284481 | − | 0.138096i | ||||
\(71\) | − | 4.76268i | − | 0.565226i | −0.959234 | − | 0.282613i | \(-0.908799\pi\) | ||
0.959234 | − | 0.282613i | \(-0.0912013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.0951 | − | 5.82843i | 1.18155 | − | 0.682166i | 0.225174 | − | 0.974319i | \(-0.427705\pi\) |
0.956372 | + | 0.292153i | \(0.0943716\pi\) | |||||||
\(74\) | −5.64444 | + | 3.25882i | −0.656153 | + | 0.378830i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 2.86370i | − | 0.328489i | ||||||
\(77\) | −12.8431 | + | 6.23445i | −1.46361 | + | 0.710482i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.29618 | + | 7.44120i | −0.483358 | + | 0.837200i | −0.999817 | − | 0.0191114i | \(-0.993916\pi\) |
0.516460 | + | 0.856312i | \(0.327250\pi\) | |||||||
\(80\) | 0.500000 | + | 0.866025i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.658421 | + | 0.380139i | 0.0727104 | + | 0.0419794i | ||||
\(83\) | −9.45001 | −1.03727 | −0.518636 | − | 0.854995i | \(-0.673560\pi\) | ||||
−0.518636 | + | 0.854995i | \(0.673560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.49938 | −0.488026 | ||||||||
\(86\) | 5.07812 | + | 2.93185i | 0.547587 | + | 0.316150i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.69798 | − | 4.67303i | −0.287605 | − | 0.498147i | ||||
\(89\) | 3.98502 | − | 6.90226i | 0.422412 | − | 0.731638i | −0.573763 | − | 0.819021i | \(-0.694517\pi\) |
0.996175 | + | 0.0873828i | \(0.0278503\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.477014 | − | 6.64394i | 0.0500046 | − | 0.696474i | ||||
\(92\) | − | 0.267949i | − | 0.0279356i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.92418 | − | 3.99768i | 0.714175 | − | 0.412329i | ||||
\(95\) | −2.48004 | + | 1.43185i | −0.254447 | + | 0.146905i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.16353i | 0.625812i | 0.949784 | + | 0.312906i | \(0.101302\pi\) | ||||
−0.949784 | + | 0.312906i | \(0.898698\pi\) | |||||||
\(98\) | −5.50000 | − | 4.33013i | −0.555584 | − | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | − | 0.866025i | 0.0500000 | − | 0.0866025i | ||||
\(101\) | 7.02458 | + | 12.1669i | 0.698972 | + | 1.21065i | 0.968823 | + | 0.247753i | \(0.0796920\pi\) |
−0.269852 | + | 0.962902i | \(0.586975\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 12.2776 | + | 7.08845i | 1.20974 | + | 0.698446i | 0.962703 | − | 0.270560i | \(-0.0872088\pi\) |
0.247040 | + | 0.969005i | \(0.420542\pi\) | |||||||
\(104\) | 2.51764 | 0.246875 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.39836 | −0.815721 | ||||||||
\(107\) | 1.42178 | + | 0.820863i | 0.137448 | + | 0.0793559i | 0.567147 | − | 0.823616i | \(-0.308047\pi\) |
−0.429699 | + | 0.902972i | \(0.641380\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.94887 | + | 17.2319i | 0.952929 | + | 1.65052i | 0.739039 | + | 0.673663i | \(0.235280\pi\) |
0.213890 | + | 0.976858i | \(0.431387\pi\) | |||||||
\(110\) | −2.69798 | + | 4.67303i | −0.257242 | + | 0.445556i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.48356 | − | 2.19067i | 0.140184 | − | 0.206999i | ||||
\(113\) | 5.95867i | 0.560545i | 0.959921 | + | 0.280272i | \(0.0904248\pi\) | ||||
−0.959921 | + | 0.280272i | \(0.909575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.232051 | + | 0.133975i | −0.0216388 | + | 0.0124932i | ||||
\(116\) | 7.70674 | − | 4.44949i | 0.715553 | − | 0.413125i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.6715i | 1.16650i | ||||||||
\(119\) | 5.19856 | + | 10.7091i | 0.476551 | + | 0.981706i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.05816 | − | 15.6892i | 0.823469 | − | 1.42629i | ||||
\(122\) | 1.31079 | + | 2.27035i | 0.118673 | + | 0.205548i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.18154 | + | 2.41421i | 0.375513 | + | 0.216803i | ||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5103 | −1.28758 | −0.643792 | − | 0.765200i | \(-0.722640\pi\) | ||||
−0.643792 | + | 0.765200i | \(0.722640\pi\) | |||||||
\(128\) | 0.866025 | + | 0.500000i | 0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.25882 | − | 2.18034i | −0.110406 | − | 0.191228i | ||||
\(131\) | −7.73325 | + | 13.3944i | −0.675657 | + | 1.17027i | 0.300619 | + | 0.953744i | \(0.402807\pi\) |
−0.976276 | + | 0.216529i | \(0.930527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.27343 | + | 4.24849i | 0.543975 | + | 0.368391i | ||||
\(134\) | 9.82237i | 0.848524i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.89658 | + | 2.24969i | −0.334129 | + | 0.192909i | ||||
\(137\) | −7.46651 | + | 4.31079i | −0.637907 | + | 0.368296i | −0.783808 | − | 0.621004i | \(-0.786725\pi\) |
0.145901 | + | 0.989299i | \(0.453392\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.2512i | 0.869495i | 0.900552 | + | 0.434748i | \(0.143162\pi\) | ||||
−0.900552 | + | 0.434748i | \(0.856838\pi\) | |||||||
\(140\) | −2.63896 | − | 0.189469i | −0.223033 | − | 0.0160130i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.38134 | + | 4.12460i | −0.199838 | + | 0.346129i | ||||
\(143\) | 6.79253 | + | 11.7650i | 0.568020 | + | 0.983839i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.70674 | − | 4.44949i | −0.640010 | − | 0.369510i | ||||
\(146\) | −11.6569 | −0.964728 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.51764 | 0.535747 | ||||||||
\(149\) | 7.96640 | + | 4.59940i | 0.652633 | + | 0.376798i | 0.789464 | − | 0.613797i | \(-0.210359\pi\) |
−0.136831 | + | 0.990594i | \(0.543692\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.37429 | + | 11.0406i | 0.518733 | + | 0.898471i | 0.999763 | + | 0.0217674i | \(0.00692931\pi\) |
−0.481030 | + | 0.876704i | \(0.659737\pi\) | |||||||
\(152\) | −1.43185 | + | 2.48004i | −0.116139 | + | 0.201158i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 14.2397 | + | 1.02236i | 1.14747 | + | 0.0823845i | ||||
\(155\) | − | 4.82843i | − | 0.387829i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.9899 | − | 6.92236i | 0.956896 | − | 0.552464i | 0.0616798 | − | 0.998096i | \(-0.480354\pi\) |
0.895216 | + | 0.445632i | \(0.147021\pi\) | |||||||
\(158\) | 7.44120 | − | 4.29618i | 0.591990 | − | 0.341786i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | 0.586988 | + | 0.397520i | 0.0462612 | + | 0.0313289i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3025 | − | 17.8444i | 0.806954 | − | 1.39768i | −0.108010 | − | 0.994150i | \(-0.534448\pi\) |
0.914964 | − | 0.403535i | \(-0.132219\pi\) | |||||||
\(164\) | −0.380139 | − | 0.658421i | −0.0296839 | − | 0.0514140i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.18394 | + | 4.72500i | 0.635197 | + | 0.366731i | ||||
\(167\) | −6.84961 | −0.530038 | −0.265019 | − | 0.964243i | \(-0.585378\pi\) | ||||
−0.265019 | + | 0.964243i | \(0.585378\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.66150 | 0.512423 | ||||||||
\(170\) | 3.89658 | + | 2.24969i | 0.298854 | + | 0.172543i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.93185 | − | 5.07812i | −0.223552 | − | 0.387203i | ||||
\(173\) | 6.37902 | − | 11.0488i | 0.484988 | − | 0.840024i | −0.514863 | − | 0.857272i | \(-0.672157\pi\) |
0.999851 | + | 0.0172486i | \(0.00549068\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.15539 | + | 2.38014i | 0.0873396 | + | 0.179922i | ||||
\(176\) | 5.39595i | 0.406735i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.90226 | + | 3.98502i | −0.517347 | + | 0.298690i | ||||
\(179\) | 16.3390 | − | 9.43331i | 1.22123 | − | 0.705079i | 0.256052 | − | 0.966663i | \(-0.417578\pi\) |
0.965181 | + | 0.261584i | \(0.0842449\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.5498i | 1.89910i | 0.313615 | + | 0.949550i | \(0.398460\pi\) | ||||
−0.313615 | + | 0.949550i | \(0.601540\pi\) | |||||||
\(182\) | −3.73508 | + | 5.51532i | −0.276862 | + | 0.408822i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.133975 | + | 0.232051i | −0.00987674 | + | 0.0171070i | ||||
\(185\) | −3.25882 | − | 5.64444i | −0.239593 | − | 0.414987i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.0257 | − | 12.1392i | −1.53755 | − | 0.887707i | ||||
\(188\) | −7.99536 | −0.583121 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.86370 | 0.207755 | ||||||||
\(191\) | 7.00657 | + | 4.04524i | 0.506977 | + | 0.292704i | 0.731590 | − | 0.681745i | \(-0.238778\pi\) |
−0.224613 | + | 0.974448i | \(0.572112\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.06350 | + | 12.2343i | 0.508442 | + | 0.880648i | 0.999952 | + | 0.00977575i | \(0.00311177\pi\) |
−0.491510 | + | 0.870872i | \(0.663555\pi\) | |||||||
\(194\) | 3.08176 | − | 5.33777i | 0.221258 | − | 0.383230i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.59808 | + | 6.50000i | 0.185577 | + | 0.464286i | ||||
\(197\) | − | 14.2738i | − | 1.01697i | −0.861072 | − | 0.508483i | \(-0.830207\pi\) | ||
0.861072 | − | 0.508483i | \(-0.169793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.06742 | − | 1.77098i | 0.217444 | − | 0.125541i | −0.387322 | − | 0.921944i | \(-0.626600\pi\) |
0.604766 | + | 0.796403i | \(0.293267\pi\) | |||||||
\(200\) | −0.866025 | + | 0.500000i | −0.0612372 | + | 0.0353553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 14.0492i | − | 0.988495i | ||||||
\(203\) | −1.68608 | + | 23.4840i | −0.118339 | + | 1.64826i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.380139 | + | 0.658421i | −0.0265501 | + | 0.0459861i | ||||
\(206\) | −7.08845 | − | 12.2776i | −0.493876 | − | 0.855418i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.18034 | − | 1.25882i | −0.151179 | − | 0.0872834i | ||||
\(209\) | −15.4524 | −1.06887 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.92340 | −0.270098 | −0.135049 | − | 0.990839i | \(-0.543119\pi\) | ||||
−0.135049 | + | 0.990839i | \(0.543119\pi\) | |||||||
\(212\) | 7.27319 | + | 4.19918i | 0.499525 | + | 0.288401i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.820863 | − | 1.42178i | −0.0561131 | − | 0.0971907i | ||||
\(215\) | −2.93185 | + | 5.07812i | −0.199951 | + | 0.346325i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.4923 | + | 5.57874i | −0.780150 | + | 0.378709i | ||||
\(218\) | − | 19.8977i | − | 1.34764i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.67303 | − | 2.69798i | 0.315056 | − | 0.181898i | ||||
\(221\) | 9.81017 | − | 5.66390i | 0.659903 | − | 0.380995i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6904i | 0.983740i | 0.870669 | + | 0.491870i | \(0.163686\pi\) | ||||
−0.870669 | + | 0.491870i | \(0.836314\pi\) | |||||||
\(224\) | −2.38014 | + | 1.15539i | −0.159030 | + | 0.0771980i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.97934 | − | 5.16036i | 0.198182 | − | 0.343262i | ||||
\(227\) | 11.3913 | + | 19.7303i | 0.756068 | + | 1.30955i | 0.944842 | + | 0.327527i | \(0.106215\pi\) |
−0.188774 | + | 0.982021i | \(0.560451\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.5089 | − | 10.1087i | −1.15702 | − | 0.668005i | −0.206431 | − | 0.978461i | \(-0.566185\pi\) |
−0.950588 | + | 0.310456i | \(0.899518\pi\) | |||||||
\(230\) | 0.267949 | 0.0176680 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.89898 | −0.584247 | ||||||||
\(233\) | −2.27840 | − | 1.31543i | −0.149263 | − | 0.0861769i | 0.423509 | − | 0.905892i | \(-0.360798\pi\) |
−0.572771 | + | 0.819715i | \(0.694132\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.99768 | + | 6.92418i | 0.260780 | + | 0.451684i | ||||
\(236\) | 6.33573 | − | 10.9738i | 0.412421 | − | 0.714334i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.852491 | − | 11.8737i | 0.0552588 | − | 0.769656i | ||||
\(239\) | − | 16.8766i | − | 1.09165i | −0.837898 | − | 0.545827i | \(-0.816216\pi\) | ||
0.837898 | − | 0.545827i | \(-0.183784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.5793 | + | 7.26268i | −0.810306 | + | 0.467831i | −0.847062 | − | 0.531494i | \(-0.821631\pi\) |
0.0367560 | + | 0.999324i | \(0.488298\pi\) | |||||||
\(242\) | −15.6892 | + | 9.05816i | −1.00854 | + | 0.582280i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 2.62158i | − | 0.167829i | ||||||
\(245\) | 4.33013 | − | 5.50000i | 0.276642 | − | 0.351382i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.60488 | − | 6.24384i | 0.229373 | − | 0.397286i | ||||
\(248\) | −2.41421 | − | 4.18154i | −0.153303 | − | 0.265528i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0.866025 | + | 0.500000i | 0.0547723 | + | 0.0316228i | ||||
\(251\) | −15.7243 | −0.992507 | −0.496254 | − | 0.868178i | \(-0.665291\pi\) | ||||
−0.496254 | + | 0.868178i | \(0.665291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.44584 | −0.0908993 | ||||||||
\(254\) | 12.5663 | + | 7.25517i | 0.788481 | + | 0.455230i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −9.83083 | + | 17.0275i | −0.613230 | + | 1.06215i | 0.377462 | + | 0.926025i | \(0.376797\pi\) |
−0.990692 | + | 0.136121i | \(0.956536\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.66933 | + | 14.2780i | −0.600823 | + | 0.887192i | ||||
\(260\) | 2.51764i | 0.156137i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.3944 | − | 7.73325i | 0.827508 | − | 0.477762i | ||||
\(263\) | 3.74275 | − | 2.16088i | 0.230788 | − | 0.133245i | −0.380148 | − | 0.924926i | \(-0.624127\pi\) |
0.610935 | + | 0.791680i | \(0.290794\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 8.39836i | − | 0.515907i | ||||||
\(266\) | −3.30871 | − | 6.81601i | −0.202870 | − | 0.417917i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.91119 | − | 8.50643i | 0.299999 | − | 0.519613i | ||||
\(269\) | −8.79895 | − | 15.2402i | −0.536482 | − | 0.929214i | −0.999090 | − | 0.0426509i | \(-0.986420\pi\) |
0.462608 | − | 0.886563i | \(-0.346914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.12436 | − | 5.26795i | −0.554265 | − | 0.320005i | 0.196575 | − | 0.980489i | \(-0.437018\pi\) |
−0.750840 | + | 0.660484i | \(0.770351\pi\) | |||||||
\(272\) | 4.49938 | 0.272815 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.62158 | 0.520849 | ||||||||
\(275\) | −4.67303 | − | 2.69798i | −0.281794 | − | 0.162694i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.50971 | − | 2.61489i | −0.0907097 | − | 0.157114i | 0.817100 | − | 0.576496i | \(-0.195580\pi\) |
−0.907810 | + | 0.419382i | \(0.862247\pi\) | |||||||
\(278\) | 5.12560 | − | 8.87780i | 0.307413 | − | 0.532455i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.19067 | + | 1.48356i | 0.130918 | + | 0.0886599i | ||||
\(281\) | − | 10.6880i | − | 0.637591i | −0.947824 | − | 0.318795i | \(-0.896722\pi\) | ||
0.947824 | − | 0.318795i | \(-0.103278\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.2149 | + | 8.78434i | −0.904434 | + | 0.522175i | −0.878636 | − | 0.477492i | \(-0.841546\pi\) |
−0.0257976 | + | 0.999667i | \(0.508213\pi\) | |||||||
\(284\) | 4.12460 | − | 2.38134i | 0.244750 | − | 0.141307i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 13.5851i | − | 0.803301i | ||||||
\(287\) | 2.00634 | + | 0.144049i | 0.118431 | + | 0.00850295i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.62220 | + | 2.80973i | −0.0954235 | + | 0.165278i | ||||
\(290\) | 4.44949 | + | 7.70674i | 0.261283 | + | 0.452555i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 10.0951 | + | 5.82843i | 0.590773 | + | 0.341083i | ||||
\(293\) | 14.6710 | 0.857086 | 0.428543 | − | 0.903521i | \(-0.359027\pi\) | ||||
0.428543 | + | 0.903521i | \(0.359027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.6715 | −0.737761 | ||||||||
\(296\) | −5.64444 | − | 3.25882i | −0.328076 | − | 0.189415i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.59940 | − | 7.96640i | −0.266436 | − | 0.461481i | ||||
\(299\) | 0.337300 | − | 0.584220i | 0.0195065 | − | 0.0337863i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.4741 | + | 1.11099i | 0.891911 | + | 0.0640363i | ||||
\(302\) | − | 12.7486i | − | 0.733599i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.48004 | − | 1.43185i | 0.142240 | − | 0.0821223i | ||||
\(305\) | −2.27035 | + | 1.31079i | −0.130000 | + | 0.0750556i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.2772i | − | 1.21435i | −0.794567 | − | 0.607177i | \(-0.792302\pi\) | ||
0.794567 | − | 0.607177i | \(-0.207698\pi\) | |||||||
\(308\) | −11.8208 | − | 8.00524i | −0.673550 | − | 0.456141i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.41421 | + | 4.18154i | −0.137118 | + | 0.237496i | ||||
\(311\) | 5.91724 | + | 10.2490i | 0.335536 | + | 0.581165i | 0.983588 | − | 0.180431i | \(-0.0577493\pi\) |
−0.648052 | + | 0.761596i | \(0.724416\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.90551 | − | 2.25485i | −0.220753 | − | 0.127452i | 0.385546 | − | 0.922689i | \(-0.374013\pi\) |
−0.606299 | + | 0.795237i | \(0.707346\pi\) | |||||||
\(314\) | −13.8447 | −0.781302 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.59235 | −0.483358 | ||||||||
\(317\) | 15.9202 | + | 9.19151i | 0.894165 | + | 0.516247i | 0.875303 | − | 0.483576i | \(-0.160662\pi\) |
0.0188626 | + | 0.999822i | \(0.493995\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −24.0092 | − | 41.5852i | −1.34426 | − | 2.32833i | ||||
\(320\) | −0.500000 | + | 0.866025i | −0.0279508 | + | 0.0484123i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.309587 | − | 0.637756i | −0.0172526 | − | 0.0355408i | ||||
\(323\) | 12.8849i | 0.716934i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.18034 | − | 1.25882i | 0.120943 | − | 0.0698267i | ||||
\(326\) | −17.8444 | + | 10.3025i | −0.988313 | + | 0.570603i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.760279i | 0.0419794i | ||||||||
\(329\) | 11.8616 | − | 17.5152i | 0.653952 | − | 0.965644i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.98066 | + | 6.89471i | −0.218797 | + | 0.378967i | −0.954440 | − | 0.298401i | \(-0.903547\pi\) |
0.735643 | + | 0.677369i | \(0.236880\pi\) | |||||||
\(332\) | −4.72500 | − | 8.18394i | −0.259318 | − | 0.449152i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.93193 | + | 3.42480i | 0.324581 | + | 0.187397i | ||||
\(335\) | −9.82237 | −0.536654 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.89417 | −0.375549 | −0.187775 | − | 0.982212i | \(-0.560127\pi\) | ||||
−0.187775 | + | 0.982212i | \(0.560127\pi\) | |||||||
\(338\) | −5.76903 | − | 3.33075i | −0.313794 | − | 0.181169i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.24969 | − | 3.89658i | −0.122007 | − | 0.211321i | ||||
\(341\) | 13.0270 | − | 22.5634i | 0.705451 | − | 1.22188i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.0938 | − | 3.95164i | −0.976972 | − | 0.213368i | ||||
\(344\) | 5.86370i | 0.316150i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.0488 | + | 6.37902i | −0.593986 | + | 0.342938i | ||||
\(347\) | 14.1645 | − | 8.17789i | 0.760392 | − | 0.439012i | −0.0690448 | − | 0.997614i | \(-0.521995\pi\) |
0.829436 | + | 0.558601i | \(0.188662\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.5851i | 1.31601i | 0.753014 | + | 0.658004i | \(0.228599\pi\) | ||||
−0.753014 | + | 0.658004i | \(0.771401\pi\) | |||||||
\(350\) | 0.189469 | − | 2.63896i | 0.0101275 | − | 0.141058i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.69798 | − | 4.67303i | 0.143803 | − | 0.249073i | ||||
\(353\) | −6.85906 | − | 11.8802i | −0.365071 | − | 0.632321i | 0.623717 | − | 0.781651i | \(-0.285622\pi\) |
−0.988788 | + | 0.149329i | \(0.952289\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.12460 | − | 2.38134i | −0.218911 | − | 0.126388i | ||||
\(356\) | 7.97005 | 0.422412 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.8666 | −0.997132 | ||||||||
\(359\) | 10.3059 | + | 5.95011i | 0.543924 | + | 0.314035i | 0.746668 | − | 0.665197i | \(-0.231652\pi\) |
−0.202744 | + | 0.979232i | \(0.564986\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.39960 | − | 9.35238i | −0.284190 | − | 0.492231i | ||||
\(362\) | 12.7749 | − | 22.1268i | 0.671433 | − | 1.16296i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 5.99233 | − | 2.90887i | 0.314083 | − | 0.152466i | ||||
\(365\) | − | 11.6569i | − | 0.610148i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.9026 | + | 6.29461i | −0.569110 | + | 0.328576i | −0.756794 | − | 0.653654i | \(-0.773235\pi\) |
0.187684 | + | 0.982230i | \(0.439902\pi\) | |||||||
\(368\) | 0.232051 | − | 0.133975i | 0.0120965 | − | 0.00698391i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.51764i | 0.338836i | ||||||||
\(371\) | −19.9893 | + | 9.70342i | −1.03779 | + | 0.503776i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.5868 | − | 23.5331i | 0.703499 | − | 1.21850i | −0.263731 | − | 0.964596i | \(-0.584953\pi\) |
0.967230 | − | 0.253900i | \(-0.0817136\pi\) | |||||||
\(374\) | 12.1392 | + | 21.0257i | 0.627704 | + | 1.08722i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.92418 | + | 3.99768i | 0.357087 | + | 0.206164i | ||||
\(377\) | 22.4044 | 1.15389 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7335 | 0.808174 | 0.404087 | − | 0.914721i | \(-0.367589\pi\) | ||||
0.404087 | + | 0.914721i | \(0.367589\pi\) | |||||||
\(380\) | −2.48004 | − | 1.43185i | −0.127223 | − | 0.0734524i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.04524 | − | 7.00657i | −0.206973 | − | 0.358487i | ||||
\(383\) | 7.89060 | − | 13.6669i | 0.403191 | − | 0.698347i | −0.590918 | − | 0.806732i | \(-0.701234\pi\) |
0.994109 | + | 0.108384i | \(0.0345677\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.02236 | + | 14.2397i | −0.0521045 | + | 0.725722i | ||||
\(386\) | − | 14.1270i | − | 0.719046i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.33777 | + | 3.08176i | −0.270984 | + | 0.156453i | ||||
\(389\) | 13.7556 | − | 7.94182i | 0.697438 | − | 0.402666i | −0.108954 | − | 0.994047i | \(-0.534750\pi\) |
0.806393 | + | 0.591381i | \(0.201417\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.20560i | 0.0609700i | ||||||||
\(392\) | 1.00000 | − | 6.92820i | 0.0505076 | − | 0.349927i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.13689 | + | 12.3615i | −0.359552 | + | 0.622762i | ||||
\(395\) | 4.29618 | + | 7.44120i | 0.216164 | + | 0.374407i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 32.3557 | + | 18.6806i | 1.62388 | + | 0.937550i | 0.985867 | + | 0.167528i | \(0.0535784\pi\) |
0.638017 | + | 0.770022i | \(0.279755\pi\) | |||||||
\(398\) | −3.54195 | −0.177542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −24.4856 | − | 14.1368i | −1.22275 | − | 0.705957i | −0.257249 | − | 0.966345i | \(-0.582816\pi\) |
−0.965504 | + | 0.260389i | \(0.916149\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.07812 | + | 10.5276i | 0.302773 | + | 0.524417i | ||||
\(404\) | −7.02458 | + | 12.1669i | −0.349486 | + | 0.605327i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 13.2022 | − | 19.4947i | 0.655214 | − | 0.967507i | ||||
\(407\) | − | 35.1689i | − | 1.74326i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.8647 | − | 8.00481i | 0.685567 | − | 0.395812i | −0.116382 | − | 0.993204i | \(-0.537130\pi\) |
0.801949 | + | 0.597392i | \(0.203796\pi\) | |||||||
\(410\) | 0.658421 | − | 0.380139i | 0.0325171 | − | 0.0187737i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.1769i | 0.698446i | ||||||||
\(413\) | 14.6405 | + | 30.1599i | 0.720414 | + | 1.48407i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.72500 | + | 8.18394i | −0.231941 | + | 0.401734i | ||||
\(416\) | 1.25882 | + | 2.18034i | 0.0617187 | + | 0.106900i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 13.3822 | + | 7.72620i | 0.654544 | + | 0.377901i | ||||
\(419\) | −29.5137 | −1.44184 | −0.720919 | − | 0.693020i | \(-0.756280\pi\) | ||||
−0.720919 | + | 0.693020i | \(0.756280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.309114 | 0.0150653 | 0.00753265 | − | 0.999972i | \(-0.497602\pi\) | ||||
0.00753265 | + | 0.999972i | \(0.497602\pi\) | |||||||
\(422\) | 3.39776 | + | 1.96170i | 0.165400 | + | 0.0954939i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.19918 | − | 7.27319i | −0.203930 | − | 0.353217i | ||||
\(425\) | −2.24969 | + | 3.89658i | −0.109126 | + | 0.189012i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.74301 | + | 3.88928i | 0.277924 | + | 0.188215i | ||||
\(428\) | 1.64173i | 0.0793559i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.07812 | − | 2.93185i | 0.244889 | − | 0.141386i | ||||
\(431\) | −7.63843 | + | 4.41005i | −0.367930 | + | 0.212425i | −0.672554 | − | 0.740048i | \(-0.734803\pi\) |
0.304624 | + | 0.952473i | \(0.401469\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 9.56388i | − | 0.459611i | −0.973237 | − | 0.229805i | \(-0.926191\pi\) | ||
0.973237 | − | 0.229805i | \(-0.0738089\pi\) | |||||||
\(434\) | 12.7420 | + | 0.914836i | 0.611636 | + | 0.0439135i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.94887 | + | 17.2319i | −0.476464 | + | 0.825260i | ||||
\(437\) | 0.383663 | + | 0.664525i | 0.0183531 | + | 0.0317885i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −31.3336 | − | 18.0905i | −1.49547 | − | 0.863412i | −0.495487 | − | 0.868615i | \(-0.665010\pi\) |
−0.999986 | + | 0.00520362i | \(0.998344\pi\) | |||||||
\(440\) | −5.39595 | −0.257242 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.3278 | −0.538809 | ||||||||
\(443\) | 3.53830 | + | 2.04284i | 0.168110 | + | 0.0970582i | 0.581694 | − | 0.813408i | \(-0.302390\pi\) |
−0.413584 | + | 0.910466i | \(0.635723\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.98502 | − | 6.90226i | −0.188908 | − | 0.327199i | ||||
\(446\) | 7.34519 | − | 12.7222i | 0.347805 | − | 0.602415i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.63896 | + | 0.189469i | 0.124679 | + | 0.00895155i | ||||
\(449\) | 19.9377i | 0.940918i | 0.882422 | + | 0.470459i | \(0.155912\pi\) | ||||
−0.882422 | + | 0.470459i | \(0.844088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.55281 | + | 2.05121i | −0.167295 | + | 0.0965879i | ||||
\(452\) | −5.16036 | + | 2.97934i | −0.242723 | + | 0.140136i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 22.7826i | − | 1.06924i | ||||||
\(455\) | −5.51532 | − | 3.73508i | −0.258562 | − | 0.175103i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0623 | − | 17.4283i | 0.470693 | − | 0.815264i | −0.528745 | − | 0.848780i | \(-0.677337\pi\) |
0.999438 | + | 0.0335168i | \(0.0106707\pi\) | |||||||
\(458\) | 10.1087 | + | 17.5089i | 0.472351 | + | 0.818136i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.232051 | − | 0.133975i | −0.0108194 | − | 0.00624660i | ||||
\(461\) | 0.909299 | 0.0423503 | 0.0211751 | − | 0.999776i | \(-0.493259\pi\) | ||||
0.0211751 | + | 0.999776i | \(0.493259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.4280 | 0.995843 | 0.497922 | − | 0.867222i | \(-0.334097\pi\) | ||||
0.497922 | + | 0.867222i | \(0.334097\pi\) | |||||||
\(464\) | 7.70674 | + | 4.44949i | 0.357777 | + | 0.206562i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.31543 | + | 2.27840i | 0.0609363 | + | 0.105545i | ||||
\(467\) | 6.34607 | − | 10.9917i | 0.293661 | − | 0.508636i | −0.681012 | − | 0.732273i | \(-0.738460\pi\) |
0.974672 | + | 0.223637i | \(0.0717930\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.3487 | + | 23.3786i | 0.524035 | + | 1.07952i | ||||
\(470\) | − | 7.99536i | − | 0.368798i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −10.9738 | + | 6.33573i | −0.505111 | + | 0.291626i | ||||
\(473\) | −27.4013 | + | 15.8201i | −1.25991 | + | 0.727411i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.86370i | 0.131396i | ||||||||
\(476\) | −6.67511 | + | 9.85666i | −0.305953 | + | 0.451779i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.43828 | + | 14.6155i | −0.385958 | + | 0.668499i | ||||
\(479\) | −6.43828 | − | 11.1514i | −0.294172 | − | 0.509522i | 0.680620 | − | 0.732637i | \(-0.261711\pi\) |
−0.974792 | + | 0.223115i | \(0.928377\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.2107 | + | 8.20453i | 0.647950 | + | 0.374094i | ||||
\(482\) | 14.5254 | 0.661612 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.1163 | 0.823469 | ||||||||
\(485\) | 5.33777 | + | 3.08176i | 0.242376 | + | 0.139936i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.4097 | + | 18.0301i | 0.471708 | + | 0.817022i | 0.999476 | − | 0.0323665i | \(-0.0103044\pi\) |
−0.527768 | + | 0.849388i | \(0.676971\pi\) | |||||||
\(488\) | −1.31079 | + | 2.27035i | −0.0593366 | + | 0.102774i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.50000 | + | 2.59808i | −0.293640 | + | 0.117369i | ||||
\(491\) | 27.3271i | 1.23325i | 0.787256 | + | 0.616627i | \(0.211501\pi\) | ||||
−0.787256 | + | 0.616627i | \(0.788499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −34.6755 | + | 20.0199i | −1.56171 | + | 0.901653i | ||||
\(494\) | −6.24384 | + | 3.60488i | −0.280924 | + | 0.162191i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.82843i | 0.216803i | ||||||||
\(497\) | −0.902379 | + | 12.5685i | −0.0404772 | + | 0.563775i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6802 | + | 28.8909i | −0.746708 | + | 1.29334i | 0.202685 | + | 0.979244i | \(0.435033\pi\) |
−0.949393 | + | 0.314092i | \(0.898300\pi\) | |||||||
\(500\) | −0.500000 | − | 0.866025i | −0.0223607 | − | 0.0387298i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 13.6176 | + | 7.86214i | 0.607784 | + | 0.350904i | ||||
\(503\) | 16.2936 | 0.726494 | 0.363247 | − | 0.931693i | \(-0.381668\pi\) | ||||
0.363247 | + | 0.931693i | \(0.381668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0492 | 0.625179 | ||||||||
\(506\) | 1.25214 | + | 0.722921i | 0.0556642 | + | 0.0321377i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.25517 | − | 12.5663i | −0.321896 | − | 0.557540i | ||||
\(509\) | −12.3400 | + | 21.3735i | −0.546961 | + | 0.947365i | 0.451519 | + | 0.892261i | \(0.350882\pi\) |
−0.998481 | + | 0.0551036i | \(0.982451\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.7449 | + | 13.4683i | −1.22736 | + | 0.595801i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.0275 | − | 9.83083i | 0.751051 | − | 0.433619i | ||||
\(515\) | 12.2776 | − | 7.08845i | 0.541014 | − | 0.312354i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.1426i | 1.89741i | ||||||||
\(518\) | 15.5129 | − | 7.53044i | 0.681597 | − | 0.330869i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.25882 | − | 2.18034i | 0.0552029 | − | 0.0956142i | ||||
\(521\) | −0.141663 | − | 0.245367i | −0.00620635 | − | 0.0107497i | 0.862906 | − | 0.505365i | \(-0.168642\pi\) |
−0.869112 | + | 0.494616i | \(0.835309\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.77021 | − | 5.64083i | −0.427222 | − | 0.246656i | 0.270941 | − | 0.962596i | \(-0.412665\pi\) |
−0.698162 | + | 0.715940i | \(0.745999\pi\) | |||||||
\(524\) | −15.4665 | −0.675657 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.32175 | −0.188437 | ||||||||
\(527\) | −18.8143 | − | 10.8625i | −0.819565 | − | 0.473176i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.4641 | − | 19.8564i | −0.498439 | − | 0.863322i | ||||
\(530\) | −4.19918 | + | 7.27319i | −0.182401 | + | 0.315927i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.542582 | + | 7.55719i | −0.0235239 | + | 0.327646i | ||||
\(533\) | − | 1.91411i | − | 0.0829092i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.42178 | − | 0.820863i | 0.0614688 | − | 0.0354890i | ||||
\(536\) | −8.50643 | + | 4.91119i | −0.367422 | + | 0.212131i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.5979i | 0.758700i | ||||||||
\(539\) | 35.0737 | − | 14.0191i | 1.51073 | − | 0.603845i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.4125 | − | 30.1593i | 0.748621 | − | 1.29665i | −0.199862 | − | 0.979824i | \(-0.564049\pi\) |
0.948484 | − | 0.316826i | \(-0.102617\pi\) | |||||||
\(542\) | 5.26795 | + | 9.12436i | 0.226278 | + | 0.391925i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.89658 | − | 2.24969i | −0.167064 | − | 0.0964546i | ||||
\(545\) | 19.8977 | 0.852325 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.4261 | 1.51471 | 0.757356 | − | 0.653002i | \(-0.226491\pi\) | ||||
0.757356 | + | 0.653002i | \(0.226491\pi\) | |||||||
\(548\) | −7.46651 | − | 4.31079i | −0.318953 | − | 0.184148i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.69798 | + | 4.67303i | 0.115042 | + | 0.199259i | ||||
\(551\) | −12.7420 | + | 22.0698i | −0.542828 | + | 0.940206i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.7473 | − | 18.8230i | 0.542071 | − | 0.800436i | ||||
\(554\) | 3.01942i | 0.128283i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.87780 | + | 5.12560i | −0.376503 | + | 0.217374i | ||||
\(557\) | −7.05105 | + | 4.07093i | −0.298763 | + | 0.172491i | −0.641887 | − | 0.766799i | \(-0.721848\pi\) |
0.343124 | + | 0.939290i | \(0.388515\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 14.7627i | − | 0.624395i | ||||||
\(560\) | −1.15539 | − | 2.38014i | −0.0488243 | − | 0.100579i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.34398 | + | 9.25605i | −0.225422 | + | 0.390443i | ||||
\(563\) | −10.2088 | − | 17.6821i | −0.430248 | − | 0.745212i | 0.566646 | − | 0.823961i | \(-0.308241\pi\) |
−0.996894 | + | 0.0787491i | \(0.974907\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.16036 | + | 2.97934i | 0.217098 | + | 0.125342i | ||||
\(566\) | 17.5687 | 0.738467 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.76268 | −0.199838 | ||||||||
\(569\) | −22.5542 | − | 13.0217i | −0.945520 | − | 0.545896i | −0.0538334 | − | 0.998550i | \(-0.517144\pi\) |
−0.891686 | + | 0.452654i | \(0.850477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.18811 | + | 10.7181i | 0.258964 | + | 0.448539i | 0.965965 | − | 0.258674i | \(-0.0832855\pi\) |
−0.707000 | + | 0.707213i | \(0.749952\pi\) | |||||||
\(572\) | −6.79253 | + | 11.7650i | −0.284010 | + | 0.491920i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.66552 | − | 1.12792i | −0.0695175 | − | 0.0470786i | ||||
\(575\) | 0.267949i | 0.0111743i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 23.3399 | − | 13.4753i | 0.971654 | − | 0.560985i | 0.0719139 | − | 0.997411i | \(-0.477089\pi\) |
0.899740 | + | 0.436426i | \(0.143756\pi\) | |||||||
\(578\) | 2.80973 | − | 1.62220i | 0.116869 | − | 0.0674746i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 8.89898i | − | 0.369510i | ||||||
\(581\) | 24.9382 | + | 1.79048i | 1.03461 | + | 0.0742816i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.6586 | − | 39.2458i | 0.938422 | − | 1.62539i | ||||
\(584\) | −5.82843 | − | 10.0951i | −0.241182 | − | 0.417740i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.7054 | − | 7.33548i | −0.524856 | − | 0.303026i | ||||
\(587\) | 35.3511 | 1.45910 | 0.729548 | − | 0.683930i | \(-0.239731\pi\) | ||||
0.729548 | + | 0.683930i | \(0.239731\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.8272 | −0.569739 | ||||||||
\(590\) | 10.9738 | + | 6.33573i | 0.451785 | + | 0.260838i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.25882 | + | 5.64444i | 0.133937 | + | 0.231985i | ||||
\(593\) | −14.7057 | + | 25.4711i | −0.603893 | + | 1.04597i | 0.388333 | + | 0.921519i | \(0.373051\pi\) |
−0.992225 | + | 0.124454i | \(0.960282\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 11.8737 | + | 0.852491i | 0.486773 | + | 0.0349487i | ||||
\(596\) | 9.19881i | 0.376798i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.584220 | + | 0.337300i | −0.0238905 | + | 0.0137932i | ||||
\(599\) | −26.5494 | + | 15.3283i | −1.08478 | + | 0.626298i | −0.932182 | − | 0.361990i | \(-0.882097\pi\) |
−0.152598 | + | 0.988288i | \(0.548764\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 34.3407i | − | 1.40078i | −0.713758 | − | 0.700392i | \(-0.753008\pi\) | ||
0.713758 | − | 0.700392i | \(-0.246992\pi\) | |||||||
\(602\) | −12.8454 | − | 8.69918i | −0.523541 | − | 0.354552i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.37429 | + | 11.0406i | −0.259366 | + | 0.449236i | ||||
\(605\) | −9.05816 | − | 15.6892i | −0.368266 | − | 0.637856i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 28.2475 | + | 16.3087i | 1.14653 | + | 0.661950i | 0.948040 | − | 0.318153i | \(-0.103062\pi\) |
0.198492 | + | 0.980103i | \(0.436396\pi\) | |||||||
\(608\) | −2.86370 | −0.116139 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.62158 | 0.106145 | ||||||||
\(611\) | −17.4326 | − | 10.0647i | −0.705247 | − | 0.407174i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.99843 | + | 13.8537i | 0.323054 | + | 0.559545i | 0.981117 | − | 0.193418i | \(-0.0619572\pi\) |
−0.658063 | + | 0.752963i | \(0.728624\pi\) | |||||||
\(614\) | −10.6386 | + | 18.4266i | −0.429339 | + | 0.743636i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 6.23445 | + | 12.8431i | 0.251193 | + | 0.517464i | ||||
\(617\) | 25.1429i | 1.01221i | 0.862471 | + | 0.506107i | \(0.168916\pi\) | ||||
−0.862471 | + | 0.506107i | \(0.831084\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.3379 | − | 18.6703i | 1.29977 | − | 0.750423i | 0.319406 | − | 0.947618i | \(-0.396517\pi\) |
0.980364 | + | 0.197195i | \(0.0631832\pi\) | |||||||
\(620\) | 4.18154 | − | 2.41421i | 0.167935 | − | 0.0969571i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 11.8345i | − | 0.474519i | ||||||
\(623\) | −11.8241 | + | 17.4597i | −0.473722 | + | 0.699510i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 2.25485 | + | 3.90551i | 0.0901219 | + | 0.156096i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.9899 | + | 6.92236i | 0.478448 | + | 0.276232i | ||||
\(629\) | −29.3253 | −1.16928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.5015 | 1.97062 | 0.985311 | − | 0.170767i | \(-0.0546245\pi\) | ||||
0.985311 | + | 0.170767i | \(0.0546245\pi\) | |||||||
\(632\) | 7.44120 | + | 4.29618i | 0.295995 | + | 0.170893i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −9.19151 | − | 15.9202i | −0.365041 | − | 0.632270i | ||||
\(635\) | −7.25517 | + | 12.5663i | −0.287913 | + | 0.498679i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.51764 | + | 17.4427i | −0.0997525 | + | 0.691105i | ||||
\(638\) | 48.0185i | 1.90107i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0.866025 | − | 0.500000i | 0.0342327 | − | 0.0197642i | ||||
\(641\) | 31.4439 | − | 18.1542i | 1.24196 | − | 0.717046i | 0.272467 | − | 0.962165i | \(-0.412160\pi\) |
0.969493 | + | 0.245119i | \(0.0788271\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 10.2653i | − | 0.404824i | −0.979300 | − | 0.202412i | \(-0.935122\pi\) | ||
0.979300 | − | 0.202412i | \(-0.0648780\pi\) | |||||||
\(644\) | −0.0507680 | + | 0.707107i | −0.00200054 | + | 0.0278639i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.44244 | − | 11.1586i | 0.253474 | − | 0.439031i | ||||
\(647\) | 10.9108 | + | 18.8980i | 0.428946 | + | 0.742956i | 0.996780 | − | 0.0801869i | \(-0.0255517\pi\) |
−0.567834 | + | 0.823143i | \(0.692218\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −59.2142 | − | 34.1873i | −2.32436 | − | 1.34197i | ||||
\(650\) | −2.51764 | −0.0987499 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.6050 | 0.806954 | ||||||||
\(653\) | −40.9556 | − | 23.6457i | −1.60272 | − | 0.925329i | −0.990941 | − | 0.134297i | \(-0.957122\pi\) |
−0.611775 | − | 0.791032i | \(-0.709544\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.73325 | + | 13.3944i | 0.302163 | + | 0.523362i | ||||
\(656\) | 0.380139 | − | 0.658421i | 0.0148419 | − | 0.0257070i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.0301 | + | 9.23779i | −0.741869 | + | 0.360127i | ||||
\(659\) | 3.58255i | 0.139556i | 0.997563 | + | 0.0697782i | \(0.0222291\pi\) | ||||
−0.997563 | + | 0.0697782i | \(0.977771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.41761 | + | 0.818459i | −0.0551388 | + | 0.0318344i | −0.527316 | − | 0.849669i | \(-0.676802\pi\) |
0.472177 | + | 0.881504i | \(0.343468\pi\) | |||||||
\(662\) | 6.89471 | − | 3.98066i | 0.267970 | − | 0.154713i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.45001i | 0.366731i | ||||||||
\(665\) | 6.81601 | − | 3.30871i | 0.264314 | − | 0.128306i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.19224 | + | 2.06502i | −0.0461636 | + | 0.0799577i | ||||
\(668\) | −3.42480 | − | 5.93193i | −0.132510 | − | 0.229513i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.50643 | + | 4.91119i | 0.328632 | + | 0.189736i | ||||
\(671\) | −14.1459 | −0.546097 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.02242 | −0.0779587 | −0.0389794 | − | 0.999240i | \(-0.512411\pi\) | ||||
−0.0389794 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(674\) | 5.97053 | + | 3.44709i | 0.229976 | + | 0.132777i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.33075 | + | 5.76903i | 0.128106 | + | 0.221886i | ||||
\(677\) | −11.4413 | + | 19.8169i | −0.439725 | + | 0.761626i | −0.997668 | − | 0.0682532i | \(-0.978257\pi\) |
0.557943 | + | 0.829879i | \(0.311591\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.16780 | − | 16.2653i | 0.0448159 | − | 0.624205i | ||||
\(680\) | 4.49938i | 0.172543i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −22.5634 | + | 13.0270i | −0.863997 | + | 0.498829i | ||||
\(683\) | −27.1977 | + | 15.7026i | −1.04069 | + | 0.600844i | −0.920029 | − | 0.391850i | \(-0.871835\pi\) |
−0.120663 | + | 0.992694i | \(0.538502\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.62158i | 0.329414i | ||||||||
\(686\) | 13.6938 | + | 12.4691i | 0.522834 | + | 0.476073i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.93185 | − | 5.07812i | 0.111776 | − | 0.193601i | ||||
\(689\) | 10.5720 | + | 18.3113i | 0.402762 | + | 0.697604i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 29.3677 | + | 16.9554i | 1.11720 | + | 0.645015i | 0.940684 | − | 0.339283i | \(-0.110184\pi\) |
0.176515 | + | 0.984298i | \(0.443518\pi\) | |||||||
\(692\) | 12.7580 | 0.484988 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.3558 | −0.620857 | ||||||||
\(695\) | 8.87780 | + | 5.12560i | 0.336754 | + | 0.194425i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.71039 | + | 2.96248i | 0.0647857 | + | 0.112212i | ||||
\(698\) | 12.2925 | − | 21.2913i | 0.465279 | − | 0.805887i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.48356 | + | 2.19067i | −0.0560734 | + | 0.0827996i | ||||
\(701\) | − | 10.5296i | − | 0.397699i | −0.980030 | − | 0.198849i | \(-0.936280\pi\) | ||
0.980030 | − | 0.198849i | \(-0.0637205\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −16.1640 | + | 9.33229i | −0.609637 | + | 0.351974i | ||||
\(704\) | −4.67303 | + | 2.69798i | −0.176122 | + | 0.101684i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.7181i | 0.516288i | ||||||||
\(707\) | −16.2323 | − | 33.4390i | −0.610479 | − | 1.25760i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.52572 | + | 13.0349i | −0.282634 | + | 0.489537i | −0.972033 | − | 0.234845i | \(-0.924542\pi\) |
0.689398 | + | 0.724382i | \(0.257875\pi\) | |||||||
\(710\) | 2.38134 | + | 4.12460i | 0.0893702 | + | 0.154794i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.90226 | − | 3.98502i | −0.258673 | − | 0.149345i | ||||
\(713\) | −1.29377 | −0.0484522 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.5851 | 0.508052 | ||||||||
\(716\) | 16.3390 | + | 9.43331i | 0.610616 | + | 0.352539i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.95011 | − | 10.3059i | −0.222056 | − | 0.384613i | ||||
\(719\) | −12.2137 | + | 21.1547i | −0.455494 | + | 0.788938i | −0.998716 | − | 0.0506506i | \(-0.983871\pi\) |
0.543223 | + | 0.839589i | \(0.317204\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −31.0569 | − | 21.0323i | −1.15662 | − | 0.783285i | ||||
\(722\) | 10.7992i | 0.401905i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −22.1268 | + | 12.7749i | −0.822335 | + | 0.474775i | ||||
\(725\) | −7.70674 | + | 4.44949i | −0.286221 | + | 0.165250i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 43.7349i | − | 1.62204i | −0.585020 | − | 0.811019i | \(-0.698913\pi\) | ||
0.585020 | − | 0.811019i | \(-0.301087\pi\) | |||||||
\(728\) | −6.64394 | − | 0.477014i | −0.246241 | − | 0.0176793i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.82843 | + | 10.0951i | −0.215720 | + | 0.373638i | ||||
\(731\) | 13.1915 | + | 22.8484i | 0.487906 | + | 0.845077i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 38.7280 | + | 22.3596i | 1.43045 | + | 0.825872i | 0.997155 | − | 0.0753789i | \(-0.0240166\pi\) |
0.433297 | + | 0.901251i | \(0.357350\pi\) | |||||||
\(734\) | 12.5892 | 0.464677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.267949 | −0.00987674 | ||||||||
\(737\) | −45.9003 | − | 26.5005i | −1.69076 | − | 0.976160i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 10.7360 | + | 18.5954i | 0.394932 | + | 0.684042i | 0.993092 | − | 0.117334i | \(-0.0374348\pi\) |
−0.598161 | + | 0.801376i | \(0.704102\pi\) | |||||||
\(740\) | 3.25882 | − | 5.64444i | 0.119797 | − | 0.207494i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.1629 | + | 1.59123i | 0.813626 | + | 0.0584157i | ||||
\(743\) | − | 29.5637i | − | 1.08459i | −0.840190 | − | 0.542293i | \(-0.817556\pi\) | ||
0.840190 | − | 0.542293i | \(-0.182444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 7.96640 | − | 4.59940i | 0.291866 | − | 0.168509i | ||||
\(746\) | −23.5331 | + | 13.5868i | −0.861607 | + | 0.497449i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 24.2784i | − | 0.887707i | ||||||
\(749\) | −3.59648 | − | 2.43561i | −0.131413 | − | 0.0889951i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.596750 | + | 1.03360i | −0.0217757 | + | 0.0377166i | −0.876708 | − | 0.481023i | \(-0.840265\pi\) |
0.854932 | + | 0.518740i | \(0.173599\pi\) | |||||||
\(752\) | −3.99768 | − | 6.92418i | −0.145780 | − | 0.252499i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.4028 | − | 11.2022i | −0.706608 | − | 0.407960i | ||||
\(755\) | 12.7486 | 0.463969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.8915 | −0.977386 | −0.488693 | − | 0.872456i | \(-0.662526\pi\) | ||||
−0.488693 | + | 0.872456i | \(0.662526\pi\) | |||||||
\(758\) | −13.6256 | − | 7.86673i | −0.494903 | − | 0.285732i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.43185 | + | 2.48004i | 0.0519387 | + | 0.0899605i | ||||
\(761\) | 0.939574 | − | 1.62739i | 0.0340595 | − | 0.0589928i | −0.848493 | − | 0.529206i | \(-0.822490\pi\) |
0.882553 | + | 0.470213i | \(0.155823\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.9897 | − | 47.3594i | −0.832284 | − | 1.71452i | ||||
\(764\) | 8.09049i | 0.292704i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.6669 | + | 7.89060i | −0.493806 | + | 0.285099i | ||||
\(767\) | 27.6281 | − | 15.9511i | 0.997592 | − | 0.575960i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 50.6544i | − | 1.82664i | −0.407239 | − | 0.913322i | \(-0.633508\pi\) | ||
0.407239 | − | 0.913322i | \(-0.366492\pi\) | |||||||
\(770\) | 8.00524 | − | 11.8208i | 0.288489 | − | 0.425991i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.06350 | + | 12.2343i | −0.254221 | + | 0.440324i | ||||
\(773\) | 24.3353 | + | 42.1499i | 0.875279 | + | 1.51603i | 0.856466 | + | 0.516204i | \(0.172655\pi\) |
0.0188128 | + | 0.999823i | \(0.494011\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.18154 | − | 2.41421i | −0.150205 | − | 0.0867211i | ||||
\(776\) | 6.16353 | 0.221258 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.8836 | −0.569456 | ||||||||
\(779\) | 1.88552 | + | 1.08861i | 0.0675558 | + | 0.0390034i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.8496 | − | 22.2562i | −0.459795 | − | 0.796388i | ||||
\(782\) | 0.602802 | − | 1.04408i | 0.0215562 | − | 0.0373364i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.33013 | + | 5.50000i | −0.154647 | + | 0.196429i | ||||
\(785\) | − | 13.8447i | − | 0.494139i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.9437 | + | 7.47307i | −0.461395 | + | 0.266386i | −0.712630 | − | 0.701540i | \(-0.752496\pi\) |
0.251236 | + | 0.967926i | \(0.419163\pi\) | |||||||
\(788\) | 12.3615 | − | 7.13689i | 0.440359 | − | 0.254241i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 8.59235i | − | 0.305702i | ||||||
\(791\) | 1.12898 | − | 15.7247i | 0.0401420 | − | 0.559105i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.30009 | − | 5.71593i | 0.117190 | − | 0.202979i | ||||
\(794\) | −18.6806 | − | 32.3557i | −0.662948 | − | 1.14826i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.06742 | + | 1.77098i | 0.108722 | + | 0.0627706i | ||||
\(797\) | 15.0557 | 0.533301 | 0.266650 | − | 0.963793i | \(-0.414083\pi\) | ||||
0.266650 | + | 0.963793i | \(0.414083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.9741 | 1.27267 | ||||||||
\(800\) | −0.866025 | − | 0.500000i | −0.0306186 | − | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 14.1368 | + | 24.4856i | 0.499187 | + | 0.864617i | ||||
\(803\) | 31.4499 | − | 54.4729i | 1.10984 | − | 1.92231i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.637756 | − | 0.309587i | 0.0224780 | − | 0.0109115i | ||||
\(806\) | − | 12.1562i | − | 0.428185i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 12.1669 | − | 7.02458i | 0.428031 | − | 0.247124i | ||||
\(809\) | −30.7426 | + | 17.7493i | −1.08085 | + | 0.624031i | −0.931127 | − | 0.364696i | \(-0.881173\pi\) |
−0.149727 | + | 0.988727i | \(0.547840\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.5935i | 0.863594i | 0.901971 | + | 0.431797i | \(0.142120\pi\) | ||||
−0.901971 | + | 0.431797i | \(0.857880\pi\) | |||||||
\(812\) | −21.1808 | + | 10.2818i | −0.743301 | + | 0.360822i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.5844 | + | 30.4571i | −0.616334 | + | 1.06752i | ||||
\(815\) | −10.3025 | − | 17.8444i | −0.360881 | − | 0.625064i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 14.5422 | + | 8.39595i | 0.508768 | + | 0.293737i | ||||
\(818\) | −16.0096 | −0.559763 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.760279 | −0.0265501 | ||||||||
\(821\) | 12.3035 | + | 7.10342i | 0.429395 | + | 0.247911i | 0.699089 | − | 0.715035i | \(-0.253589\pi\) |
−0.269694 | + | 0.962946i | \(0.586923\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.945584 | − | 1.63780i | −0.0329610 | − | 0.0570901i | 0.849074 | − | 0.528273i | \(-0.177160\pi\) |
−0.882035 | + | 0.471183i | \(0.843827\pi\) | |||||||
\(824\) | 7.08845 | − | 12.2776i | 0.246938 | − | 0.427709i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.40085 | − | 33.4395i | 0.0835361 | − | 1.16351i | ||||
\(827\) | − | 31.9280i | − | 1.11024i | −0.831769 | − | 0.555122i | \(-0.812671\pi\) | ||
0.831769 | − | 0.555122i | \(-0.187329\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.38864 | − | 1.95643i | 0.117692 | − | 0.0679497i | −0.439998 | − | 0.897999i | \(-0.645021\pi\) |
0.557691 | + | 0.830049i | \(0.311688\pi\) | |||||||
\(830\) | 8.18394 | − | 4.72500i | 0.284069 | − | 0.164007i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.51764i | − | 0.0872834i | ||||||
\(833\) | −11.6897 | − | 29.2460i | −0.405025 | − | 1.01331i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.42480 | + | 5.93193i | −0.118520 | + | 0.205283i | ||||
\(836\) | −7.72620 | − | 13.3822i | −0.267216 | − | 0.462832i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 25.5596 | + | 14.7568i | 0.882941 | + | 0.509766i | ||||
\(839\) | 15.3513 | 0.529984 | 0.264992 | − | 0.964251i | \(-0.414631\pi\) | ||||
0.264992 | + | 0.964251i | \(0.414631\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.1918 | −1.73075 | ||||||||
\(842\) | −0.267701 | − | 0.154557i | −0.00922557 | − | 0.00532639i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.96170 | − | 3.39776i | −0.0675244 | − | 0.116956i | ||||
\(845\) | 3.33075 | − | 5.76903i | 0.114581 | − | 0.198461i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −26.8767 | + | 39.6869i | −0.923495 | + | 1.36366i | ||||
\(848\) | 8.39836i | 0.288401i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.89658 | − | 2.24969i | 0.133651 | − | 0.0771637i | ||||
\(851\) | −1.51242 | + | 0.873198i | −0.0518452 | + | 0.0299328i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2302i | 0.761148i | 0.924750 | + | 0.380574i | \(0.124274\pi\) | ||||
−0.924750 | + | 0.380574i | \(0.875726\pi\) | |||||||
\(854\) | −3.02896 | − | 6.23972i | −0.103649 | − | 0.213519i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.820863 | − | 1.42178i | 0.0280565 | − | 0.0485953i | ||||
\(857\) | −26.4098 | − | 45.7432i | −0.902143 | − | 1.56256i | −0.824707 | − | 0.565560i | \(-0.808660\pi\) |
−0.0774356 | − | 0.996997i | \(-0.524673\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.2916 | − | 8.82859i | −0.521742 | − | 0.301228i | 0.215905 | − | 0.976414i | \(-0.430730\pi\) |
−0.737647 | + | 0.675187i | \(0.764063\pi\) | |||||||
\(860\) | −5.86370 | −0.199951 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.82010 | 0.300414 | ||||||||
\(863\) | 14.2452 | + | 8.22446i | 0.484912 | + | 0.279964i | 0.722461 | − | 0.691412i | \(-0.243011\pi\) |
−0.237549 | + | 0.971375i | \(0.576344\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.37902 | − | 11.0488i | −0.216893 | − | 0.375670i | ||||
\(866\) | −4.78194 | + | 8.28256i | −0.162497 | + | 0.281453i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −10.5775 | − | 7.16328i | −0.359024 | − | 0.243138i | ||||
\(869\) | 46.3639i | 1.57279i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.4161 | − | 12.3646i | 0.725657 | − | 0.418958i | ||||
\(872\) | 17.2319 | − | 9.94887i | 0.583547 | − | 0.336911i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 0.767327i | − | 0.0259552i | ||||||
\(875\) | 2.63896 | + | 0.189469i | 0.0892131 | + | 0.00640521i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.1078 | + | 46.9521i | −0.915366 | + | 1.58546i | −0.109001 | + | 0.994042i | \(0.534765\pi\) |
−0.806365 | + | 0.591418i | \(0.798568\pi\) | |||||||
\(878\) | 18.0905 | + | 31.3336i | 0.610524 | + | 1.05746i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 4.67303 | + | 2.69798i | 0.157528 | + | 0.0909488i | ||||
\(881\) | 50.1647 | 1.69009 | 0.845046 | − | 0.534694i | \(-0.179573\pi\) | ||||
0.845046 | + | 0.534694i | \(0.179573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.841563 | −0.0283208 | −0.0141604 | − | 0.999900i | \(-0.504508\pi\) | ||||
−0.0141604 | + | 0.999900i | \(0.504508\pi\) | |||||||
\(884\) | 9.81017 | + | 5.66390i | 0.329952 | + | 0.190498i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.04284 | − | 3.53830i | −0.0686305 | − | 0.118872i | ||||
\(887\) | 20.0492 | − | 34.7262i | 0.673185 | − | 1.16599i | −0.303811 | − | 0.952732i | \(-0.598259\pi\) |
0.976996 | − | 0.213258i | \(-0.0684075\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 38.2922 | + | 2.74926i | 1.28428 | + | 0.0922071i | ||||
\(890\) | 7.97005i | 0.267157i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −12.7222 | + | 7.34519i | −0.425972 | + | 0.245935i | ||||
\(893\) | 19.8288 | − | 11.4482i | 0.663546 | − | 0.383098i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 18.8666i | − | 0.630642i | ||||||
\(896\) | −2.19067 | − | 1.48356i | −0.0731852 | − | 0.0495624i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.96885 | − | 17.2665i | 0.332665 | − | 0.576192i | ||||
\(899\) | −21.4840 | − | 37.2114i | −0.716533 | − | 1.24107i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.7248 | − | 18.8937i | −1.09022 | − | 0.629440i | ||||
\(902\) | 4.10243 | 0.136596 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.95867 | 0.198182 | ||||||||
\(905\) | 22.1268 | + | 12.7749i | 0.735518 | + | 0.424652i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 22.5945 | + | 39.1348i | 0.750238 | + | 1.29945i | 0.947707 | + | 0.319142i | \(0.103395\pi\) |
−0.197469 | + | 0.980309i | \(0.563272\pi\) | |||||||
\(908\) | −11.3913 | + | 19.7303i | −0.378034 | + | 0.654774i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.90887 | + | 5.99233i | 0.0964279 | + | 0.198644i | ||||
\(911\) | 58.2281i | 1.92918i | 0.263746 | + | 0.964592i | \(0.415042\pi\) | ||||
−0.263746 | + | 0.964592i | \(0.584958\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −44.1602 | + | 25.4959i | −1.46149 | + | 0.843791i | ||||
\(914\) | −17.4283 | + | 10.0623i | −0.576478 | + | 0.332830i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 20.2175i | − | 0.668005i | ||||||
\(917\) | 22.9455 | − | 33.8820i | 0.757729 | − | 1.11888i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.61745 | + | 11.4618i | −0.218290 | + | 0.378089i | −0.954285 | − | 0.298898i | \(-0.903381\pi\) |
0.735996 | + | 0.676986i | \(0.236714\pi\) | |||||||
\(920\) | 0.133975 | + | 0.232051i | 0.00441701 | + | 0.00765049i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.787476 | − | 0.454649i | −0.0259341 | − | 0.0149731i | ||||
\(923\) | 11.9907 | 0.394679 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.51764 | −0.214299 | ||||||||
\(926\) | −18.5572 | − | 10.7140i | −0.609827 | − | 0.352084i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.44949 | − | 7.70674i | −0.146062 | − | 0.252986i | ||||
\(929\) | −10.4434 | + | 18.0885i | −0.342637 | + | 0.593464i | −0.984921 | − | 0.173002i | \(-0.944653\pi\) |
0.642285 | + | 0.766466i | \(0.277987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.7504 | − | 12.4002i | −0.516197 | − | 0.406400i | ||||
\(932\) | − | 2.63087i | − | 0.0861769i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.9917 | + | 6.34607i | −0.359660 | + | 0.207650i | ||||
\(935\) | −21.0257 | + | 12.1392i | −0.687615 | + | 0.396995i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.2465i | 0.759430i | 0.925103 | + | 0.379715i | \(0.123978\pi\) | ||||
−0.925103 | + | 0.379715i | \(0.876022\pi\) | |||||||
\(938\) | 1.86103 | − | 25.9208i | 0.0607649 | − | 0.846345i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.99768 | + | 6.92418i | −0.130390 | + | 0.225842i | ||||
\(941\) | −0.752551 | − | 1.30346i | −0.0245325 | − | 0.0424915i | 0.853499 | − | 0.521095i | \(-0.174476\pi\) |
−0.878031 | + | 0.478604i | \(0.841143\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.176423 | + | 0.101858i | 0.00574513 | + | 0.00331695i | ||||
\(944\) | 12.6715 | 0.412421 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.6403 | 1.02871 | ||||||||
\(947\) | 21.0122 | + | 12.1314i | 0.682805 | + | 0.394218i | 0.800911 | − | 0.598783i | \(-0.204349\pi\) |
−0.118106 | + | 0.993001i | \(0.537682\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 14.6739 | + | 25.4159i | 0.476334 | + | 0.825035i | ||||
\(950\) | 1.43185 | − | 2.48004i | 0.0464554 | − | 0.0804631i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 10.7091 | − | 5.19856i | 0.347085 | − | 0.168486i | ||||
\(953\) | 56.7061i | 1.83689i | 0.395547 | + | 0.918446i | \(0.370555\pi\) | ||||
−0.395547 | + | 0.918446i | \(0.629445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.00657 | − | 4.04524i | 0.226727 | − | 0.130901i | ||||
\(956\) | 14.6155 | − | 8.43828i | 0.472700 | − | 0.272913i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.8766i | 0.416023i | ||||||||
\(959\) | 20.5206 | − | 9.96132i | 0.662643 | − | 0.321668i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −3.84315 | + | 6.65652i | −0.123972 | + | 0.214727i | ||||
\(962\) | −8.20453 | − | 14.2107i | −0.264525 | − | 0.458170i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −12.5793 | − | 7.26268i | −0.405153 | − | 0.233915i | ||||
\(965\) | 14.1270 | 0.454764 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.23556 | 0.232680 | 0.116340 | − | 0.993209i | \(-0.462884\pi\) | ||||
0.116340 | + | 0.993209i | \(0.462884\pi\) | |||||||
\(968\) | −15.6892 | − | 9.05816i | −0.504270 | − | 0.291140i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.08176 | − | 5.33777i | −0.0989495 | − | 0.171386i | ||||
\(971\) | 19.3560 | − | 33.5256i | 0.621163 | − | 1.07589i | −0.368106 | − | 0.929784i | \(-0.619994\pi\) |
0.989269 | − | 0.146103i | \(-0.0466730\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.94228 | − | 27.0525i | 0.0622667 | − | 0.867263i | ||||
\(974\) | − | 20.8194i | − | 0.667096i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.27035 | − | 1.31079i | 0.0726722 | − | 0.0419573i | ||||
\(977\) | −15.7279 | + | 9.08052i | −0.503181 | + | 0.290512i | −0.730026 | − | 0.683419i | \(-0.760492\pi\) |
0.226845 | + | 0.973931i | \(0.427159\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 43.0060i | − | 1.37448i | ||||||
\(980\) | 6.92820 | + | 1.00000i | 0.221313 | + | 0.0319438i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 13.6635 | − | 23.6659i | 0.436021 | − | 0.755211i | ||||
\(983\) | −8.19988 | − | 14.2026i | −0.261536 | − | 0.452993i | 0.705115 | − | 0.709093i | \(-0.250896\pi\) |
−0.966650 | + | 0.256100i | \(0.917562\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.3615 | − | 7.13689i | −0.393869 | − | 0.227400i | ||||
\(986\) | 40.0399 | 1.27513 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.20977 | 0.229373 | ||||||||
\(989\) | 1.36068 | + | 0.785587i | 0.0432670 | + | 0.0249802i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.44584 | + | 9.43247i | 0.172993 | + | 0.299632i | 0.939465 | − | 0.342645i | \(-0.111323\pi\) |
−0.766472 | + | 0.642278i | \(0.777990\pi\) | |||||||
\(992\) | 2.41421 | − | 4.18154i | 0.0766514 | − | 0.132764i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.06574 | − | 10.4335i | 0.224112 | − | 0.330930i | ||||
\(995\) | − | 3.54195i | − | 0.112287i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.7856 | − | 17.7740i | 0.974988 | − | 0.562910i | 0.0742349 | − | 0.997241i | \(-0.476349\pi\) |
0.900753 | + | 0.434331i | \(0.143015\pi\) | |||||||
\(998\) | 28.8909 | − | 16.6802i | 0.914527 | − | 0.528002i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 630.2.be.b.341.1 | yes | 8 | |
3.2 | odd | 2 | 630.2.be.a.341.3 | ✓ | 8 | ||
5.2 | odd | 4 | 3150.2.bp.f.1349.3 | 8 | |||
5.3 | odd | 4 | 3150.2.bp.c.1349.2 | 8 | |||
5.4 | even | 2 | 3150.2.bf.c.1601.4 | 8 | |||
7.2 | even | 3 | 4410.2.b.b.881.8 | 8 | |||
7.3 | odd | 6 | 630.2.be.a.521.3 | yes | 8 | ||
7.5 | odd | 6 | 4410.2.b.e.881.8 | 8 | |||
15.2 | even | 4 | 3150.2.bp.a.1349.3 | 8 | |||
15.8 | even | 4 | 3150.2.bp.d.1349.2 | 8 | |||
15.14 | odd | 2 | 3150.2.bf.b.1601.2 | 8 | |||
21.2 | odd | 6 | 4410.2.b.e.881.1 | 8 | |||
21.5 | even | 6 | 4410.2.b.b.881.1 | 8 | |||
21.17 | even | 6 | inner | 630.2.be.b.521.1 | yes | 8 | |
35.3 | even | 12 | 3150.2.bp.a.899.3 | 8 | |||
35.17 | even | 12 | 3150.2.bp.d.899.2 | 8 | |||
35.24 | odd | 6 | 3150.2.bf.b.1151.2 | 8 | |||
105.17 | odd | 12 | 3150.2.bp.c.899.2 | 8 | |||
105.38 | odd | 12 | 3150.2.bp.f.899.3 | 8 | |||
105.59 | even | 6 | 3150.2.bf.c.1151.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.3 | ✓ | 8 | 3.2 | odd | 2 | ||
630.2.be.a.521.3 | yes | 8 | 7.3 | odd | 6 | ||
630.2.be.b.341.1 | yes | 8 | 1.1 | even | 1 | trivial | |
630.2.be.b.521.1 | yes | 8 | 21.17 | even | 6 | inner | |
3150.2.bf.b.1151.2 | 8 | 35.24 | odd | 6 | |||
3150.2.bf.b.1601.2 | 8 | 15.14 | odd | 2 | |||
3150.2.bf.c.1151.4 | 8 | 105.59 | even | 6 | |||
3150.2.bf.c.1601.4 | 8 | 5.4 | even | 2 | |||
3150.2.bp.a.899.3 | 8 | 35.3 | even | 12 | |||
3150.2.bp.a.1349.3 | 8 | 15.2 | even | 4 | |||
3150.2.bp.c.899.2 | 8 | 105.17 | odd | 12 | |||
3150.2.bp.c.1349.2 | 8 | 5.3 | odd | 4 | |||
3150.2.bp.d.899.2 | 8 | 35.17 | even | 12 | |||
3150.2.bp.d.1349.2 | 8 | 15.8 | even | 4 | |||
3150.2.bp.f.899.3 | 8 | 105.38 | odd | 12 | |||
3150.2.bp.f.1349.3 | 8 | 5.2 | odd | 4 | |||
4410.2.b.b.881.1 | 8 | 21.5 | even | 6 | |||
4410.2.b.b.881.8 | 8 | 7.2 | even | 3 | |||
4410.2.b.e.881.1 | 8 | 21.2 | odd | 6 | |||
4410.2.b.e.881.8 | 8 | 7.5 | odd | 6 |