Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1176,2,Mod(589,1176)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1176, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1176.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1176 = 2^{3} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1176.c (of order \(2\), degree \(1\), 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: | \(9.39040727770\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + x^{14} - 2 x^{13} - 2 x^{12} - 4 x^{11} - 2 x^{10} + 16 x^{9} + 8 x^{8} + 32 x^{7} - 8 x^{6} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | no (minimal twist has level 168) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 589.15 | ||
Root | \(0.284419 - 1.38532i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1176.589 |
Dual form | 1176.2.c.f.589.16 |
$q$-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 \(\left(\mathbb{Z}/1176\mathbb{Z}\right)^\times\).
\(n\) | \(295\) | \(589\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38532 | − | 0.284419i | 0.979568 | − | 0.201115i | ||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 1.83821 | − | 0.788022i | 0.919106 | − | 0.394011i | ||||
\(5\) | − | 2.29465i | − | 1.02620i | −0.858329 | − | 0.513099i | \(-0.828497\pi\) | ||
0.858329 | − | 0.513099i | \(-0.171503\pi\) | |||||||
\(6\) | 0.284419 | + | 1.38532i | 0.116114 | + | 0.565554i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.32238 | − | 1.61448i | 0.821085 | − | 0.570806i | ||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.652642 | − | 3.17882i | −0.206384 | − | 1.00523i | ||||
\(11\) | − | 3.88667i | − | 1.17188i | −0.810356 | − | 0.585938i | \(-0.800726\pi\) | ||
0.810356 | − | 0.585938i | \(-0.199274\pi\) | |||||||
\(12\) | 0.788022 | + | 1.83821i | 0.227482 | + | 0.530646i | ||||
\(13\) | 3.33413i | 0.924721i | 0.886692 | + | 0.462361i | \(0.152997\pi\) | ||||
−0.886692 | + | 0.462361i | \(0.847003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.29465 | 0.592476 | ||||||||
\(16\) | 2.75804 | − | 2.89710i | 0.689511 | − | 0.724275i | ||||
\(17\) | −0.287121 | −0.0696370 | −0.0348185 | − | 0.999394i | \(-0.511085\pi\) | ||||
−0.0348185 | + | 0.999394i | \(0.511085\pi\) | |||||||
\(18\) | −1.38532 | + | 0.284419i | −0.326523 | + | 0.0670382i | ||||
\(19\) | − | 2.78525i | − | 0.638981i | −0.947589 | − | 0.319491i | \(-0.896488\pi\) | ||
0.947589 | − | 0.319491i | \(-0.103512\pi\) | |||||||
\(20\) | −1.80823 | − | 4.21805i | −0.404333 | − | 0.943185i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.10544 | − | 5.38428i | −0.235681 | − | 1.14793i | ||||
\(23\) | 6.53425 | 1.36249 | 0.681243 | − | 0.732058i | \(-0.261440\pi\) | ||||
0.681243 | + | 0.732058i | \(0.261440\pi\) | |||||||
\(24\) | 1.61448 | + | 2.32238i | 0.329555 | + | 0.474054i | ||||
\(25\) | −0.265415 | −0.0530829 | ||||||||
\(26\) | 0.948290 | + | 4.61883i | 0.185975 | + | 0.905827i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 5.53374i | − | 1.02759i | −0.857913 | − | 0.513795i | \(-0.828239\pi\) | ||
0.857913 | − | 0.513795i | \(-0.171761\pi\) | |||||||
\(30\) | 3.17882 | − | 0.652642i | 0.580370 | − | 0.119156i | ||||
\(31\) | −7.44308 | −1.33682 | −0.668408 | − | 0.743795i | \(-0.733024\pi\) | ||||
−0.668408 | + | 0.743795i | \(0.733024\pi\) | |||||||
\(32\) | 2.99678 | − | 4.79785i | 0.529760 | − | 0.848147i | ||||
\(33\) | 3.88667 | 0.676583 | ||||||||
\(34\) | −0.397754 | + | 0.0816627i | −0.0682142 | + | 0.0140050i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.83821 | + | 0.788022i | −0.306369 | + | 0.131337i | ||||
\(37\) | − | 5.95539i | − | 0.979060i | −0.871987 | − | 0.489530i | \(-0.837168\pi\) | ||
0.871987 | − | 0.489530i | \(-0.162832\pi\) | |||||||
\(38\) | −0.792179 | − | 3.85846i | −0.128508 | − | 0.625925i | ||||
\(39\) | −3.33413 | −0.533888 | ||||||||
\(40\) | −3.70467 | − | 5.32905i | −0.585760 | − | 0.842596i | ||||
\(41\) | 3.51617 | 0.549134 | 0.274567 | − | 0.961568i | \(-0.411466\pi\) | ||||
0.274567 | + | 0.961568i | \(0.411466\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2465i | 1.71508i | 0.514416 | + | 0.857541i | \(0.328009\pi\) | ||||
−0.514416 | + | 0.857541i | \(0.671991\pi\) | |||||||
\(44\) | −3.06278 | − | 7.14453i | −0.461732 | − | 1.07708i | ||||
\(45\) | 2.29465i | 0.342066i | ||||||||
\(46\) | 9.05201 | − | 1.85847i | 1.33465 | − | 0.274016i | ||||
\(47\) | −0.0870075 | −0.0126913 | −0.00634567 | − | 0.999980i | \(-0.502020\pi\) | ||||
−0.00634567 | + | 0.999980i | \(0.502020\pi\) | |||||||
\(48\) | 2.89710 | + | 2.75804i | 0.418161 | + | 0.398089i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −0.367684 | + | 0.0754890i | −0.0519983 | + | 0.0106758i | ||||
\(51\) | − | 0.287121i | − | 0.0402050i | ||||||
\(52\) | 2.62737 | + | 6.12883i | 0.364350 | + | 0.849916i | ||||
\(53\) | 7.05820i | 0.969518i | 0.874648 | + | 0.484759i | \(0.161093\pi\) | ||||
−0.874648 | + | 0.484759i | \(0.838907\pi\) | |||||||
\(54\) | −0.284419 | − | 1.38532i | −0.0387045 | − | 0.188518i | ||||
\(55\) | −8.91855 | −1.20258 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2.78525 | 0.368916 | ||||||||
\(58\) | −1.57390 | − | 7.66599i | −0.206663 | − | 1.00659i | ||||
\(59\) | − | 4.35217i | − | 0.566605i | −0.959031 | − | 0.283302i | \(-0.908570\pi\) | ||
0.959031 | − | 0.283302i | \(-0.0914300\pi\) | |||||||
\(60\) | 4.21805 | − | 1.80823i | 0.544548 | − | 0.233442i | ||||
\(61\) | − | 7.16714i | − | 0.917659i | −0.888524 | − | 0.458829i | \(-0.848269\pi\) | ||
0.888524 | − | 0.458829i | \(-0.151731\pi\) | |||||||
\(62\) | −10.3110 | + | 2.11695i | −1.30950 | + | 0.268853i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.78689 | − | 7.49888i | 0.348361 | − | 0.937360i | ||||
\(65\) | 7.65066 | 0.948947 | ||||||||
\(66\) | 5.38428 | − | 1.10544i | 0.662759 | − | 0.136071i | ||||
\(67\) | 13.0255i | 1.59132i | 0.605743 | + | 0.795661i | \(0.292876\pi\) | ||||
−0.605743 | + | 0.795661i | \(0.707124\pi\) | |||||||
\(68\) | −0.527789 | + | 0.226257i | −0.0640038 | + | 0.0274378i | ||||
\(69\) | 6.53425i | 0.786631i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.18835 | −0.734421 | −0.367211 | − | 0.930138i | \(-0.619687\pi\) | ||||
−0.367211 | + | 0.930138i | \(0.619687\pi\) | |||||||
\(72\) | −2.32238 | + | 1.61448i | −0.273695 | + | 0.190269i | ||||
\(73\) | 13.8796 | 1.62448 | 0.812240 | − | 0.583323i | \(-0.198248\pi\) | ||||
0.812240 | + | 0.583323i | \(0.198248\pi\) | |||||||
\(74\) | −1.69383 | − | 8.25010i | −0.196903 | − | 0.959055i | ||||
\(75\) | − | 0.265415i | − | 0.0306474i | ||||||
\(76\) | −2.19484 | − | 5.11989i | −0.251766 | − | 0.587291i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.61883 | + | 0.948290i | −0.522979 | + | 0.107373i | ||||
\(79\) | −8.99853 | −1.01241 | −0.506207 | − | 0.862412i | \(-0.668953\pi\) | ||||
−0.506207 | + | 0.862412i | \(0.668953\pi\) | |||||||
\(80\) | −6.64783 | − | 6.32874i | −0.743250 | − | 0.707575i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 4.87102 | − | 1.00007i | 0.537914 | − | 0.110439i | ||||
\(83\) | 17.6313i | 1.93529i | 0.252312 | + | 0.967646i | \(0.418809\pi\) | ||||
−0.252312 | + | 0.967646i | \(0.581191\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.658842i | 0.0714614i | ||||||||
\(86\) | 3.19873 | + | 15.5800i | 0.344928 | + | 1.68004i | ||||
\(87\) | 5.53374 | 0.593280 | ||||||||
\(88\) | −6.27497 | − | 9.02633i | −0.668914 | − | 0.962210i | ||||
\(89\) | 17.1839 | 1.82149 | 0.910744 | − | 0.412972i | \(-0.135509\pi\) | ||||
0.910744 | + | 0.412972i | \(0.135509\pi\) | |||||||
\(90\) | 0.652642 | + | 3.17882i | 0.0687945 | + | 0.335077i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 12.0113 | − | 5.14913i | 1.25227 | − | 0.536834i | ||||
\(93\) | − | 7.44308i | − | 0.771811i | ||||||
\(94\) | −0.120533 | + | 0.0247466i | −0.0124320 | + | 0.00255242i | ||||
\(95\) | −6.39118 | −0.655721 | ||||||||
\(96\) | 4.79785 | + | 2.99678i | 0.489678 | + | 0.305857i | ||||
\(97\) | −6.46528 | −0.656450 | −0.328225 | − | 0.944600i | \(-0.606450\pi\) | ||||
−0.328225 | + | 0.944600i | \(0.606450\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.88667i | 0.390625i | ||||||||
\(100\) | −0.487888 | + | 0.209152i | −0.0487888 | + | 0.0209152i | ||||
\(101\) | 11.8461i | 1.17873i | 0.807867 | + | 0.589365i | \(0.200622\pi\) | ||||
−0.807867 | + | 0.589365i | \(0.799378\pi\) | |||||||
\(102\) | −0.0816627 | − | 0.397754i | −0.00808581 | − | 0.0393835i | ||||
\(103\) | −1.62190 | −0.159810 | −0.0799051 | − | 0.996802i | \(-0.525462\pi\) | ||||
−0.0799051 | + | 0.996802i | \(0.525462\pi\) | |||||||
\(104\) | 5.38290 | + | 7.74311i | 0.527836 | + | 0.759275i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.00749 | + | 9.77785i | 0.194984 | + | 0.949708i | ||||
\(107\) | 5.02926i | 0.486197i | 0.970002 | + | 0.243098i | \(0.0781638\pi\) | ||||
−0.970002 | + | 0.243098i | \(0.921836\pi\) | |||||||
\(108\) | −0.788022 | − | 1.83821i | −0.0758274 | − | 0.176882i | ||||
\(109\) | 0.204420i | 0.0195799i | 0.999952 | + | 0.00978994i | \(0.00311628\pi\) | ||||
−0.999952 | + | 0.00978994i | \(0.996884\pi\) | |||||||
\(110\) | −12.3550 | + | 2.53661i | −1.17801 | + | 0.241856i | ||||
\(111\) | 5.95539 | 0.565260 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.9203 | −1.40358 | −0.701792 | − | 0.712382i | \(-0.747616\pi\) | ||||
−0.701792 | + | 0.712382i | \(0.747616\pi\) | |||||||
\(114\) | 3.85846 | − | 0.792179i | 0.361378 | − | 0.0741944i | ||||
\(115\) | − | 14.9938i | − | 1.39818i | ||||||
\(116\) | −4.36071 | − | 10.1722i | −0.404882 | − | 0.944464i | ||||
\(117\) | − | 3.33413i | − | 0.308240i | ||||||
\(118\) | −1.23784 | − | 6.02915i | −0.113953 | − | 0.555028i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 5.32905 | − | 3.70467i | 0.486473 | − | 0.338189i | ||||
\(121\) | −4.10622 | −0.373293 | ||||||||
\(122\) | −2.03847 | − | 9.92877i | −0.184555 | − | 0.898909i | ||||
\(123\) | 3.51617i | 0.317043i | ||||||||
\(124\) | −13.6819 | + | 5.86531i | −1.22868 | + | 0.526720i | ||||
\(125\) | − | 10.8642i | − | 0.971725i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.29267 | −0.558384 | −0.279192 | − | 0.960235i | \(-0.590067\pi\) | ||||
−0.279192 | + | 0.960235i | \(0.590067\pi\) | |||||||
\(128\) | 1.72790 | − | 11.1810i | 0.152726 | − | 0.988269i | ||||
\(129\) | −11.2465 | −0.990203 | ||||||||
\(130\) | 10.5986 | − | 2.17599i | 0.929558 | − | 0.190847i | ||||
\(131\) | − | 1.24096i | − | 0.108423i | −0.998529 | − | 0.0542116i | \(-0.982735\pi\) | ||
0.998529 | − | 0.0542116i | \(-0.0172646\pi\) | |||||||
\(132\) | 7.14453 | − | 3.06278i | 0.621851 | − | 0.266581i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.70471 | + | 18.0445i | 0.320038 | + | 1.55881i | ||||
\(135\) | −2.29465 | −0.197492 | ||||||||
\(136\) | −0.666804 | + | 0.463552i | −0.0571779 | + | 0.0397492i | ||||
\(137\) | 1.59019 | 0.135859 | 0.0679296 | − | 0.997690i | \(-0.478361\pi\) | ||||
0.0679296 | + | 0.997690i | \(0.478361\pi\) | |||||||
\(138\) | 1.85847 | + | 9.05201i | 0.158203 | + | 0.770559i | ||||
\(139\) | 1.02981i | 0.0873470i | 0.999046 | + | 0.0436735i | \(0.0139061\pi\) | ||||
−0.999046 | + | 0.0436735i | \(0.986094\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 0.0870075i | − | 0.00732735i | ||||||
\(142\) | −8.57283 | + | 1.76008i | −0.719416 | + | 0.147703i | ||||
\(143\) | 12.9587 | 1.08366 | ||||||||
\(144\) | −2.75804 | + | 2.89710i | −0.229837 | + | 0.241425i | ||||
\(145\) | −12.6980 | −1.05451 | ||||||||
\(146\) | 19.2276 | − | 3.94761i | 1.59129 | − | 0.326707i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.69297 | − | 10.9473i | −0.385760 | − | 0.899859i | ||||
\(149\) | 9.59178i | 0.785789i | 0.919584 | + | 0.392895i | \(0.128526\pi\) | ||||
−0.919584 | + | 0.392895i | \(0.871474\pi\) | |||||||
\(150\) | −0.0754890 | − | 0.367684i | −0.00616365 | − | 0.0300212i | ||||
\(151\) | 6.99222 | 0.569019 | 0.284510 | − | 0.958673i | \(-0.408169\pi\) | ||||
0.284510 | + | 0.958673i | \(0.408169\pi\) | |||||||
\(152\) | −4.49675 | − | 6.46842i | −0.364734 | − | 0.524658i | ||||
\(153\) | 0.287121 | 0.0232123 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.0792i | 1.37184i | ||||||||
\(156\) | −6.12883 | + | 2.62737i | −0.490700 | + | 0.210358i | ||||
\(157\) | 17.3579i | 1.38531i | 0.721269 | + | 0.692655i | \(0.243559\pi\) | ||||
−0.721269 | + | 0.692655i | \(0.756441\pi\) | |||||||
\(158\) | −12.4658 | + | 2.55935i | −0.991728 | + | 0.203611i | ||||
\(159\) | −7.05820 | −0.559751 | ||||||||
\(160\) | −11.0094 | − | 6.87655i | −0.870367 | − | 0.543639i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.38532 | − | 0.284419i | 0.108841 | − | 0.0223461i | ||||
\(163\) | 15.7220i | 1.23144i | 0.787965 | + | 0.615720i | \(0.211135\pi\) | ||||
−0.787965 | + | 0.615720i | \(0.788865\pi\) | |||||||
\(164\) | 6.46347 | − | 2.77082i | 0.504712 | − | 0.216365i | ||||
\(165\) | − | 8.91855i | − | 0.694308i | ||||||
\(166\) | 5.01469 | + | 24.4250i | 0.389216 | + | 1.89575i | ||||
\(167\) | 0.102064 | 0.00789795 | 0.00394897 | − | 0.999992i | \(-0.498743\pi\) | ||||
0.00394897 | + | 0.999992i | \(0.498743\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.88358 | 0.144891 | ||||||||
\(170\) | 0.187387 | + | 0.912705i | 0.0143719 | + | 0.0700013i | ||||
\(171\) | 2.78525i | 0.212994i | ||||||||
\(172\) | 8.86252 | + | 20.6735i | 0.675761 | + | 1.57634i | ||||
\(173\) | − | 2.28777i | − | 0.173936i | −0.996211 | − | 0.0869678i | \(-0.972282\pi\) | ||
0.996211 | − | 0.0869678i | \(-0.0277177\pi\) | |||||||
\(174\) | 7.66599 | − | 1.57390i | 0.581158 | − | 0.119317i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −11.2601 | − | 10.7196i | −0.848761 | − | 0.808021i | ||||
\(177\) | 4.35217 | 0.327130 | ||||||||
\(178\) | 23.8051 | − | 4.88742i | 1.78427 | − | 0.366328i | ||||
\(179\) | 18.6231i | 1.39196i | 0.718064 | + | 0.695978i | \(0.245029\pi\) | ||||
−0.718064 | + | 0.695978i | \(0.754971\pi\) | |||||||
\(180\) | 1.80823 | + | 4.21805i | 0.134778 | + | 0.314395i | ||||
\(181\) | − | 13.6786i | − | 1.01672i | −0.861144 | − | 0.508361i | \(-0.830252\pi\) | ||
0.861144 | − | 0.508361i | \(-0.169748\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.16714 | 0.529810 | ||||||||
\(184\) | 15.1750 | − | 10.5494i | 1.11872 | − | 0.777715i | ||||
\(185\) | −13.6655 | −1.00471 | ||||||||
\(186\) | −2.11695 | − | 10.3110i | −0.155223 | − | 0.756041i | ||||
\(187\) | 1.11594i | 0.0816060i | ||||||||
\(188\) | −0.159938 | + | 0.0685638i | −0.0116647 | + | 0.00500053i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −8.85382 | + | 1.81777i | −0.642323 | + | 0.131875i | ||||
\(191\) | −12.6346 | −0.914207 | −0.457103 | − | 0.889414i | \(-0.651113\pi\) | ||||
−0.457103 | + | 0.889414i | \(0.651113\pi\) | |||||||
\(192\) | 7.49888 | + | 2.78689i | 0.541185 | + | 0.201126i | ||||
\(193\) | 2.60582 | 0.187571 | 0.0937856 | − | 0.995592i | \(-0.470103\pi\) | ||||
0.0937856 | + | 0.995592i | \(0.470103\pi\) | |||||||
\(194\) | −8.95647 | + | 1.83885i | −0.643037 | + | 0.132022i | ||||
\(195\) | 7.65066i | 0.547875i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 0.794777i | − | 0.0566255i | −0.999599 | − | 0.0283127i | \(-0.990987\pi\) | ||
0.999599 | − | 0.0283127i | \(-0.00901343\pi\) | |||||||
\(198\) | 1.10544 | + | 5.38428i | 0.0785605 | + | 0.382644i | ||||
\(199\) | −10.7343 | −0.760933 | −0.380466 | − | 0.924795i | \(-0.624237\pi\) | ||||
−0.380466 | + | 0.924795i | \(0.624237\pi\) | |||||||
\(200\) | −0.616393 | + | 0.428507i | −0.0435856 | + | 0.0303001i | ||||
\(201\) | −13.0255 | −0.918750 | ||||||||
\(202\) | 3.36925 | + | 16.4106i | 0.237060 | + | 1.15465i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −0.226257 | − | 0.527789i | −0.0158412 | − | 0.0369526i | ||||
\(205\) | − | 8.06838i | − | 0.563520i | ||||||
\(206\) | −2.24684 | + | 0.461298i | −0.156545 | + | 0.0321402i | ||||
\(207\) | −6.53425 | −0.454162 | ||||||||
\(208\) | 9.65931 | + | 9.19567i | 0.669753 | + | 0.637605i | ||||
\(209\) | −10.8254 | −0.748807 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 0.556345i | − | 0.0383004i | −0.999817 | − | 0.0191502i | \(-0.993904\pi\) | ||
0.999817 | − | 0.0191502i | \(-0.00609607\pi\) | |||||||
\(212\) | 5.56201 | + | 12.9745i | 0.382001 | + | 0.891090i | ||||
\(213\) | − | 6.18835i | − | 0.424018i | ||||||
\(214\) | 1.43042 | + | 6.96712i | 0.0977813 | + | 0.476263i | ||||
\(215\) | 25.8069 | 1.76001 | ||||||||
\(216\) | −1.61448 | − | 2.32238i | −0.109852 | − | 0.158018i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.0581409 | + | 0.283187i | 0.00393780 | + | 0.0191798i | ||||
\(219\) | 13.8796i | 0.937894i | ||||||||
\(220\) | −16.3942 | + | 7.02801i | −1.10530 | + | 0.473828i | ||||
\(221\) | − | 0.957298i | − | 0.0643948i | ||||||
\(222\) | 8.25010 | − | 1.69383i | 0.553711 | − | 0.113682i | ||||
\(223\) | −11.1076 | −0.743820 | −0.371910 | − | 0.928269i | \(-0.621297\pi\) | ||||
−0.371910 | + | 0.928269i | \(0.621297\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.265415 | 0.0176943 | ||||||||
\(226\) | −20.6694 | + | 4.24362i | −1.37491 | + | 0.282281i | ||||
\(227\) | − | 8.76788i | − | 0.581945i | −0.956731 | − | 0.290972i | \(-0.906021\pi\) | ||
0.956731 | − | 0.290972i | \(-0.0939788\pi\) | |||||||
\(228\) | 5.11989 | − | 2.19484i | 0.339073 | − | 0.145357i | ||||
\(229\) | − | 20.6962i | − | 1.36764i | −0.729648 | − | 0.683822i | \(-0.760316\pi\) | ||
0.729648 | − | 0.683822i | \(-0.239684\pi\) | |||||||
\(230\) | −4.26453 | − | 20.7712i | −0.281195 | − | 1.36961i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.93414 | − | 12.8514i | −0.586555 | − | 0.843739i | ||||
\(233\) | −5.72853 | −0.375288 | −0.187644 | − | 0.982237i | \(-0.560085\pi\) | ||||
−0.187644 | + | 0.982237i | \(0.560085\pi\) | |||||||
\(234\) | −0.948290 | − | 4.61883i | −0.0619917 | − | 0.301942i | ||||
\(235\) | 0.199652i | 0.0130238i | ||||||||
\(236\) | −3.42961 | − | 8.00022i | −0.223248 | − | 0.520770i | ||||
\(237\) | − | 8.99853i | − | 0.584517i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2.27651 | 0.147255 | 0.0736276 | − | 0.997286i | \(-0.476542\pi\) | ||||
0.0736276 | + | 0.997286i | \(0.476542\pi\) | |||||||
\(240\) | 6.32874 | − | 6.64783i | 0.408519 | − | 0.429116i | ||||
\(241\) | −23.5850 | −1.51925 | −0.759623 | − | 0.650364i | \(-0.774616\pi\) | ||||
−0.759623 | + | 0.650364i | \(0.774616\pi\) | |||||||
\(242\) | −5.68842 | + | 1.16789i | −0.365666 | + | 0.0750747i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −5.64786 | − | 13.1747i | −0.361567 | − | 0.843425i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.00007 | + | 4.87102i | 0.0637619 | + | 0.310565i | ||||
\(247\) | 9.28640 | 0.590879 | ||||||||
\(248\) | −17.2856 | + | 12.0167i | −1.09764 | + | 0.763062i | ||||
\(249\) | −17.6313 | −1.11734 | ||||||||
\(250\) | −3.08999 | − | 15.0504i | −0.195428 | − | 0.951870i | ||||
\(251\) | − | 12.4322i | − | 0.784716i | −0.919813 | − | 0.392358i | \(-0.871659\pi\) | ||
0.919813 | − | 0.392358i | \(-0.128341\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 25.3965i | − | 1.59666i | ||||||
\(254\) | −8.71735 | + | 1.78976i | −0.546975 | + | 0.112299i | ||||
\(255\) | −0.658842 | −0.0412583 | ||||||||
\(256\) | −0.786392 | − | 15.9807i | −0.0491495 | − | 0.998791i | ||||
\(257\) | −0.282984 | −0.0176521 | −0.00882604 | − | 0.999961i | \(-0.502809\pi\) | ||||
−0.00882604 | + | 0.999961i | \(0.502809\pi\) | |||||||
\(258\) | −15.5800 | + | 3.19873i | −0.969971 | + | 0.199144i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 14.0635 | − | 6.02888i | 0.872183 | − | 0.373895i | ||||
\(261\) | 5.53374i | 0.342530i | ||||||||
\(262\) | −0.352953 | − | 1.71912i | −0.0218055 | − | 0.106208i | ||||
\(263\) | 14.3192 | 0.882962 | 0.441481 | − | 0.897271i | \(-0.354453\pi\) | ||||
0.441481 | + | 0.897271i | \(0.354453\pi\) | |||||||
\(264\) | 9.02633 | − | 6.27497i | 0.555532 | − | 0.386197i | ||||
\(265\) | 16.1961 | 0.994918 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.1839i | 1.05164i | ||||||||
\(268\) | 10.2644 | + | 23.9437i | 0.626998 | + | 1.46259i | ||||
\(269\) | 16.8141i | 1.02517i | 0.858636 | + | 0.512586i | \(0.171312\pi\) | ||||
−0.858636 | + | 0.512586i | \(0.828688\pi\) | |||||||
\(270\) | −3.17882 | + | 0.652642i | −0.193457 | + | 0.0397185i | ||||
\(271\) | −26.8456 | −1.63076 | −0.815378 | − | 0.578929i | \(-0.803471\pi\) | ||||
−0.815378 | + | 0.578929i | \(0.803471\pi\) | |||||||
\(272\) | −0.791892 | + | 0.831818i | −0.0480155 | + | 0.0504364i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.20292 | − | 0.452281i | 0.133083 | − | 0.0273233i | ||||
\(275\) | 1.03158i | 0.0622066i | ||||||||
\(276\) | 5.14913 | + | 12.0113i | 0.309941 | + | 0.722997i | ||||
\(277\) | 22.5030i | 1.35207i | 0.736868 | + | 0.676036i | \(0.236304\pi\) | ||||
−0.736868 | + | 0.676036i | \(0.763696\pi\) | |||||||
\(278\) | 0.292897 | + | 1.42661i | 0.0175668 | + | 0.0855623i | ||||
\(279\) | 7.44308 | 0.445605 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.8375 | 0.765824 | 0.382912 | − | 0.923785i | \(-0.374921\pi\) | ||||
0.382912 | + | 0.923785i | \(0.374921\pi\) | |||||||
\(282\) | −0.0247466 | − | 0.120533i | −0.00147364 | − | 0.00717764i | ||||
\(283\) | 7.29790i | 0.433815i | 0.976192 | + | 0.216908i | \(0.0695971\pi\) | ||||
−0.976192 | + | 0.216908i | \(0.930403\pi\) | |||||||
\(284\) | −11.3755 | + | 4.87655i | −0.675011 | + | 0.289370i | ||||
\(285\) | − | 6.39118i | − | 0.378581i | ||||||
\(286\) | 17.9519 | − | 3.68569i | 1.06152 | − | 0.217940i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.99678 | + | 4.79785i | −0.176587 | + | 0.282716i | ||||
\(289\) | −16.9176 | −0.995151 | ||||||||
\(290\) | −17.5908 | + | 3.61155i | −1.03297 | + | 0.212078i | ||||
\(291\) | − | 6.46528i | − | 0.379001i | ||||||
\(292\) | 25.5136 | − | 10.9374i | 1.49307 | − | 0.640063i | ||||
\(293\) | 9.95674i | 0.581679i | 0.956772 | + | 0.290840i | \(0.0939346\pi\) | ||||
−0.956772 | + | 0.290840i | \(0.906065\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.98671 | −0.581449 | ||||||||
\(296\) | −9.61487 | − | 13.8307i | −0.558853 | − | 0.803891i | ||||
\(297\) | −3.88667 | −0.225528 | ||||||||
\(298\) | 2.72808 | + | 13.2877i | 0.158034 | + | 0.769734i | ||||
\(299\) | 21.7860i | 1.25992i | ||||||||
\(300\) | −0.209152 | − | 0.487888i | −0.0120754 | − | 0.0281682i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 9.68645 | − | 1.98872i | 0.557393 | − | 0.114438i | ||||
\(303\) | −11.8461 | −0.680540 | ||||||||
\(304\) | −8.06916 | − | 7.68185i | −0.462798 | − | 0.440584i | ||||
\(305\) | −16.4461 | −0.941700 | ||||||||
\(306\) | 0.397754 | − | 0.0816627i | 0.0227381 | − | 0.00466834i | ||||
\(307\) | − | 14.9479i | − | 0.853122i | −0.904459 | − | 0.426561i | \(-0.859725\pi\) | ||
0.904459 | − | 0.426561i | \(-0.140275\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.62190i | − | 0.0922664i | ||||||
\(310\) | 4.85766 | + | 23.6602i | 0.275897 | + | 1.34381i | ||||
\(311\) | 31.2591 | 1.77254 | 0.886270 | − | 0.463169i | \(-0.153288\pi\) | ||||
0.886270 | + | 0.463169i | \(0.153288\pi\) | |||||||
\(312\) | −7.74311 | + | 5.38290i | −0.438367 | + | 0.304746i | ||||
\(313\) | 3.06468 | 0.173226 | 0.0866130 | − | 0.996242i | \(-0.472396\pi\) | ||||
0.0866130 | + | 0.996242i | \(0.472396\pi\) | |||||||
\(314\) | 4.93692 | + | 24.0462i | 0.278606 | + | 1.35701i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −16.5412 | + | 7.09104i | −0.930515 | + | 0.398902i | ||||
\(317\) | − | 16.2981i | − | 0.915391i | −0.889109 | − | 0.457695i | \(-0.848675\pi\) | ||
0.889109 | − | 0.457695i | \(-0.151325\pi\) | |||||||
\(318\) | −9.77785 | + | 2.00749i | −0.548314 | + | 0.112574i | ||||
\(319\) | −21.5078 | −1.20421 | ||||||||
\(320\) | −17.2073 | − | 6.39493i | −0.961918 | − | 0.357488i | ||||
\(321\) | −5.02926 | −0.280706 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.799705i | 0.0444968i | ||||||||
\(324\) | 1.83821 | − | 0.788022i | 0.102123 | − | 0.0437790i | ||||
\(325\) | − | 0.884927i | − | 0.0490869i | ||||||
\(326\) | 4.47163 | + | 21.7799i | 0.247661 | + | 1.20628i | ||||
\(327\) | −0.204420 | −0.0113044 | ||||||||
\(328\) | 8.16588 | − | 5.67680i | 0.450885 | − | 0.313449i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −2.53661 | − | 12.3550i | −0.139636 | − | 0.680122i | ||||
\(331\) | − | 2.76307i | − | 0.151872i | −0.997113 | − | 0.0759359i | \(-0.975806\pi\) | ||
0.997113 | − | 0.0759359i | \(-0.0241945\pi\) | |||||||
\(332\) | 13.8939 | + | 32.4101i | 0.762526 | + | 1.77874i | ||||
\(333\) | 5.95539i | 0.326353i | ||||||||
\(334\) | 0.141391 | − | 0.0290289i | 0.00773657 | − | 0.00158839i | ||||
\(335\) | 29.8890 | 1.63301 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.8259 | 1.40682 | 0.703412 | − | 0.710782i | \(-0.251659\pi\) | ||||
0.703412 | + | 0.710782i | \(0.251659\pi\) | |||||||
\(338\) | 2.60936 | − | 0.535727i | 0.141930 | − | 0.0291397i | ||||
\(339\) | − | 14.9203i | − | 0.810359i | ||||||
\(340\) | 0.519182 | + | 1.21109i | 0.0281566 | + | 0.0656806i | ||||
\(341\) | 28.9288i | 1.56658i | ||||||||
\(342\) | 0.792179 | + | 3.85846i | 0.0428362 | + | 0.208642i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 18.1573 | + | 26.1187i | 0.978979 | + | 1.40823i | ||||
\(345\) | 14.9938 | 0.807240 | ||||||||
\(346\) | −0.650685 | − | 3.16928i | −0.0349810 | − | 0.170382i | ||||
\(347\) | − | 12.2755i | − | 0.658984i | −0.944158 | − | 0.329492i | \(-0.893123\pi\) | ||
0.944158 | − | 0.329492i | \(-0.106877\pi\) | |||||||
\(348\) | 10.1722 | − | 4.36071i | 0.545287 | − | 0.233759i | ||||
\(349\) | − | 0.209753i | − | 0.0112278i | −0.999984 | − | 0.00561390i | \(-0.998213\pi\) | ||
0.999984 | − | 0.00561390i | \(-0.00178697\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.33413 | 0.177963 | ||||||||
\(352\) | −18.6477 | − | 11.6475i | −0.993923 | − | 0.620813i | ||||
\(353\) | 19.5985 | 1.04312 | 0.521561 | − | 0.853214i | \(-0.325350\pi\) | ||||
0.521561 | + | 0.853214i | \(0.325350\pi\) | |||||||
\(354\) | 6.02915 | − | 1.23784i | 0.320445 | − | 0.0657905i | ||||
\(355\) | 14.2001i | 0.753662i | ||||||||
\(356\) | 31.5876 | − | 13.5413i | 1.67414 | − | 0.717686i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 5.29676 | + | 25.7989i | 0.279943 | + | 1.36351i | ||||
\(359\) | −5.71112 | −0.301422 | −0.150711 | − | 0.988578i | \(-0.548156\pi\) | ||||
−0.150711 | + | 0.988578i | \(0.548156\pi\) | |||||||
\(360\) | 3.70467 | + | 5.32905i | 0.195253 | + | 0.280865i | ||||
\(361\) | 11.2424 | 0.591703 | ||||||||
\(362\) | −3.89045 | − | 18.9492i | −0.204478 | − | 0.995948i | ||||
\(363\) | − | 4.10622i | − | 0.215521i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 31.8487i | − | 1.66704i | ||||||
\(366\) | 9.92877 | − | 2.03847i | 0.518985 | − | 0.106553i | ||||
\(367\) | −28.1275 | −1.46824 | −0.734122 | − | 0.679017i | \(-0.762406\pi\) | ||||
−0.734122 | + | 0.679017i | \(0.762406\pi\) | |||||||
\(368\) | 18.0217 | − | 18.9304i | 0.939448 | − | 0.986815i | ||||
\(369\) | −3.51617 | −0.183045 | ||||||||
\(370\) | −18.9311 | + | 3.88674i | −0.984181 | + | 0.202062i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −5.86531 | − | 13.6819i | −0.304102 | − | 0.709376i | ||||
\(373\) | − | 17.2035i | − | 0.890764i | −0.895341 | − | 0.445382i | \(-0.853068\pi\) | ||
0.895341 | − | 0.445382i | \(-0.146932\pi\) | |||||||
\(374\) | 0.317396 | + | 1.54594i | 0.0164122 | + | 0.0799386i | ||||
\(375\) | 10.8642 | 0.561026 | ||||||||
\(376\) | −0.202064 | + | 0.140472i | −0.0104207 | + | 0.00724429i | ||||
\(377\) | 18.4502 | 0.950234 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.1872i | 0.523281i | 0.965165 | + | 0.261640i | \(0.0842635\pi\) | ||||
−0.965165 | + | 0.261640i | \(0.915737\pi\) | |||||||
\(380\) | −11.7483 | + | 5.03639i | −0.602677 | + | 0.258361i | ||||
\(381\) | − | 6.29267i | − | 0.322383i | ||||||
\(382\) | −17.5029 | + | 3.59352i | −0.895527 | + | 0.183860i | ||||
\(383\) | 19.8433 | 1.01394 | 0.506972 | − | 0.861962i | \(-0.330765\pi\) | ||||
0.506972 | + | 0.861962i | \(0.330765\pi\) | |||||||
\(384\) | 11.1810 | + | 1.72790i | 0.570577 | + | 0.0881766i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.60989 | − | 0.741145i | 0.183739 | − | 0.0377233i | ||||
\(387\) | − | 11.2465i | − | 0.571694i | ||||||
\(388\) | −11.8846 | + | 5.09478i | −0.603347 | + | 0.258648i | ||||
\(389\) | − | 18.5333i | − | 0.939677i | −0.882752 | − | 0.469838i | \(-0.844312\pi\) | ||
0.882752 | − | 0.469838i | \(-0.155688\pi\) | |||||||
\(390\) | 2.17599 | + | 10.5986i | 0.110186 | + | 0.536681i | ||||
\(391\) | −1.87612 | −0.0948794 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1.24096 | 0.0625982 | ||||||||
\(394\) | −0.226050 | − | 1.10102i | −0.0113882 | − | 0.0554685i | ||||
\(395\) | 20.6485i | 1.03894i | ||||||||
\(396\) | 3.06278 | + | 7.14453i | 0.153911 | + | 0.359026i | ||||
\(397\) | 7.98137i | 0.400573i | 0.979737 | + | 0.200287i | \(0.0641874\pi\) | ||||
−0.979737 | + | 0.200287i | \(0.935813\pi\) | |||||||
\(398\) | −14.8704 | + | 3.05303i | −0.745385 | + | 0.153035i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −0.732025 | + | 0.768933i | −0.0366013 | + | 0.0384467i | ||||
\(401\) | 36.0420 | 1.79985 | 0.899925 | − | 0.436045i | \(-0.143621\pi\) | ||||
0.899925 | + | 0.436045i | \(0.143621\pi\) | |||||||
\(402\) | −18.0445 | + | 3.70471i | −0.899977 | + | 0.184774i | ||||
\(403\) | − | 24.8162i | − | 1.23618i | ||||||
\(404\) | 9.33498 | + | 21.7756i | 0.464432 | + | 1.08338i | ||||
\(405\) | − | 2.29465i | − | 0.114022i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −23.1466 | −1.14734 | ||||||||
\(408\) | −0.463552 | − | 0.666804i | −0.0229492 | − | 0.0330117i | ||||
\(409\) | 29.5666 | 1.46197 | 0.730987 | − | 0.682391i | \(-0.239060\pi\) | ||||
0.730987 | + | 0.682391i | \(0.239060\pi\) | |||||||
\(410\) | −2.29480 | − | 11.1773i | −0.113332 | − | 0.552006i | ||||
\(411\) | 1.59019i | 0.0784384i | ||||||||
\(412\) | −2.98139 | + | 1.27809i | −0.146882 | + | 0.0629669i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −9.05201 | + | 1.85847i | −0.444882 | + | 0.0913386i | ||||
\(415\) | 40.4578 | 1.98599 | ||||||||
\(416\) | 15.9966 | + | 9.99164i | 0.784300 | + | 0.489880i | ||||
\(417\) | −1.02981 | −0.0504298 | ||||||||
\(418\) | −14.9966 | + | 3.07894i | −0.733507 | + | 0.150596i | ||||
\(419\) | 8.73304i | 0.426637i | 0.976983 | + | 0.213318i | \(0.0684271\pi\) | ||||
−0.976983 | + | 0.213318i | \(0.931573\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.77349i | 0.0864344i | 0.999066 | + | 0.0432172i | \(0.0137607\pi\) | ||||
−0.999066 | + | 0.0432172i | \(0.986239\pi\) | |||||||
\(422\) | −0.158235 | − | 0.770715i | −0.00770277 | − | 0.0375178i | ||||
\(423\) | 0.0870075 | 0.00423045 | ||||||||
\(424\) | 11.3953 | + | 16.3918i | 0.553407 | + | 0.796057i | ||||
\(425\) | 0.0762061 | 0.00369654 | ||||||||
\(426\) | −1.76008 | − | 8.57283i | −0.0852763 | − | 0.415355i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.96316 | + | 9.24484i | 0.191567 | + | 0.446866i | ||||
\(429\) | 12.9587i | 0.625650i | ||||||||
\(430\) | 35.7507 | − | 7.33996i | 1.72405 | − | 0.353965i | ||||
\(431\) | 28.3672 | 1.36640 | 0.683200 | − | 0.730231i | \(-0.260588\pi\) | ||||
0.683200 | + | 0.730231i | \(0.260588\pi\) | |||||||
\(432\) | −2.89710 | − | 2.75804i | −0.139387 | − | 0.132696i | ||||
\(433\) | 6.53217 | 0.313916 | 0.156958 | − | 0.987605i | \(-0.449831\pi\) | ||||
0.156958 | + | 0.987605i | \(0.449831\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 12.6980i | − | 0.608822i | ||||||
\(436\) | 0.161087 | + | 0.375767i | 0.00771468 | + | 0.0179960i | ||||
\(437\) | − | 18.1995i | − | 0.870602i | ||||||
\(438\) | 3.94761 | + | 19.2276i | 0.188624 | + | 0.918731i | ||||
\(439\) | −0.532322 | −0.0254063 | −0.0127032 | − | 0.999919i | \(-0.504044\pi\) | ||||
−0.0127032 | + | 0.999919i | \(0.504044\pi\) | |||||||
\(440\) | −20.7123 | + | 14.3988i | −0.987418 | + | 0.686438i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.272274 | − | 1.32616i | −0.0129507 | − | 0.0630791i | ||||
\(443\) | 8.51970i | 0.404783i | 0.979305 | + | 0.202392i | \(0.0648714\pi\) | ||||
−0.979305 | + | 0.202392i | \(0.935129\pi\) | |||||||
\(444\) | 10.9473 | − | 4.69297i | 0.519534 | − | 0.222719i | ||||
\(445\) | − | 39.4310i | − | 1.86921i | ||||||
\(446\) | −15.3876 | + | 3.15922i | −0.728622 | + | 0.149593i | ||||
\(447\) | −9.59178 | −0.453676 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0180 | −0.708745 | −0.354373 | − | 0.935104i | \(-0.615306\pi\) | ||||
−0.354373 | + | 0.935104i | \(0.615306\pi\) | |||||||
\(450\) | 0.367684 | − | 0.0754890i | 0.0173328 | − | 0.00355858i | ||||
\(451\) | − | 13.6662i | − | 0.643517i | ||||||
\(452\) | −27.4267 | + | 11.7575i | −1.29004 | + | 0.553027i | ||||
\(453\) | 6.99222i | 0.328523i | ||||||||
\(454\) | −2.49375 | − | 12.1463i | −0.117038 | − | 0.570054i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6.46842 | − | 4.49675i | 0.302911 | − | 0.210579i | ||||
\(457\) | −31.4552 | −1.47141 | −0.735705 | − | 0.677302i | \(-0.763149\pi\) | ||||
−0.735705 | + | 0.677302i | \(0.763149\pi\) | |||||||
\(458\) | −5.88640 | − | 28.6708i | −0.275053 | − | 1.33970i | ||||
\(459\) | 0.287121i | 0.0134017i | ||||||||
\(460\) | −11.8154 | − | 27.5618i | −0.550898 | − | 1.28508i | ||||
\(461\) | 4.36281i | 0.203196i | 0.994826 | + | 0.101598i | \(0.0323956\pi\) | ||||
−0.994826 | + | 0.101598i | \(0.967604\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.9787 | 0.649646 | 0.324823 | − | 0.945775i | \(-0.394695\pi\) | ||||
0.324823 | + | 0.945775i | \(0.394695\pi\) | |||||||
\(464\) | −16.0318 | − | 15.2623i | −0.744258 | − | 0.708535i | ||||
\(465\) | −17.0792 | −0.792031 | ||||||||
\(466\) | −7.93584 | + | 1.62930i | −0.367620 | + | 0.0754760i | ||||
\(467\) | 16.5383i | 0.765302i | 0.923893 | + | 0.382651i | \(0.124989\pi\) | ||||
−0.923893 | + | 0.382651i | \(0.875011\pi\) | |||||||
\(468\) | −2.62737 | − | 6.12883i | −0.121450 | − | 0.283305i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0.0567847 | + | 0.276581i | 0.00261928 | + | 0.0127577i | ||||
\(471\) | −17.3579 | −0.799810 | ||||||||
\(472\) | −7.02651 | − | 10.1074i | −0.323421 | − | 0.465231i | ||||
\(473\) | 43.7116 | 2.00986 | ||||||||
\(474\) | −2.55935 | − | 12.4658i | −0.117555 | − | 0.572574i | ||||
\(475\) | 0.739247i | 0.0339190i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 7.05820i | − | 0.323173i | ||||||
\(478\) | 3.15369 | − | 0.647483i | 0.144247 | − | 0.0296152i | ||||
\(479\) | 1.18401 | 0.0540990 | 0.0270495 | − | 0.999634i | \(-0.491389\pi\) | ||||
0.0270495 | + | 0.999634i | \(0.491389\pi\) | |||||||
\(480\) | 6.87655 | − | 11.0094i | 0.313870 | − | 0.502507i | ||||
\(481\) | 19.8560 | 0.905357 | ||||||||
\(482\) | −32.6728 | + | 6.70803i | −1.48820 | + | 0.305542i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.54810 | + | 3.23579i | −0.343096 | + | 0.147081i | ||||
\(485\) | 14.8356i | 0.673648i | ||||||||
\(486\) | 0.284419 | + | 1.38532i | 0.0129015 | + | 0.0628393i | ||||
\(487\) | −24.0896 | −1.09160 | −0.545801 | − | 0.837915i | \(-0.683775\pi\) | ||||
−0.545801 | + | 0.837915i | \(0.683775\pi\) | |||||||
\(488\) | −11.5712 | − | 16.6448i | −0.523805 | − | 0.753476i | ||||
\(489\) | −15.7220 | −0.710973 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 18.4971i | − | 0.834761i | −0.908732 | − | 0.417381i | \(-0.862948\pi\) | ||
0.908732 | − | 0.417381i | \(-0.137052\pi\) | |||||||
\(492\) | 2.77082 | + | 6.46347i | 0.124918 | + | 0.291396i | ||||
\(493\) | 1.58885i | 0.0715584i | ||||||||
\(494\) | 12.8646 | − | 2.64123i | 0.578806 | − | 0.118834i | ||||
\(495\) | 8.91855 | 0.400859 | ||||||||
\(496\) | −20.5283 | + | 21.5633i | −0.921749 | + | 0.968223i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −24.4250 | + | 5.01469i | −1.09451 | + | 0.224714i | ||||
\(499\) | 12.1283i | 0.542937i | 0.962447 | + | 0.271468i | \(0.0875092\pi\) | ||||
−0.962447 | + | 0.271468i | \(0.912491\pi\) | |||||||
\(500\) | −8.56124 | − | 19.9707i | −0.382870 | − | 0.893118i | ||||
\(501\) | 0.102064i | 0.00455988i | ||||||||
\(502\) | −3.53597 | − | 17.2226i | −0.157818 | − | 0.768683i | ||||
\(503\) | 7.61078 | 0.339348 | 0.169674 | − | 0.985500i | \(-0.445729\pi\) | ||||
0.169674 | + | 0.985500i | \(0.445729\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 27.1826 | 1.20961 | ||||||||
\(506\) | −7.22325 | − | 35.1822i | −0.321112 | − | 1.56404i | ||||
\(507\) | 1.88358i | 0.0836528i | ||||||||
\(508\) | −11.5673 | + | 4.95876i | −0.513214 | + | 0.220009i | ||||
\(509\) | − | 16.0956i | − | 0.713424i | −0.934214 | − | 0.356712i | \(-0.883898\pi\) | ||
0.934214 | − | 0.356712i | \(-0.116102\pi\) | |||||||
\(510\) | −0.912705 | + | 0.187387i | −0.0404153 | + | 0.00829764i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −5.63461 | − | 21.9146i | −0.249017 | − | 0.968499i | ||||
\(513\) | −2.78525 | −0.122972 | ||||||||
\(514\) | −0.392023 | + | 0.0804861i | −0.0172914 | + | 0.00355009i | ||||
\(515\) | 3.72168i | 0.163997i | ||||||||
\(516\) | −20.6735 | + | 8.86252i | −0.910101 | + | 0.390151i | ||||
\(517\) | 0.338169i | 0.0148727i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.28777 | 0.100422 | ||||||||
\(520\) | 17.7677 | − | 12.3519i | 0.779166 | − | 0.541665i | ||||
\(521\) | 19.2934 | 0.845258 | 0.422629 | − | 0.906303i | \(-0.361107\pi\) | ||||
0.422629 | + | 0.906303i | \(0.361107\pi\) | |||||||
\(522\) | 1.57390 | + | 7.66599i | 0.0688878 | + | 0.335531i | ||||
\(523\) | − | 32.2551i | − | 1.41042i | −0.709001 | − | 0.705208i | \(-0.750854\pi\) | ||
0.709001 | − | 0.705208i | \(-0.249146\pi\) | |||||||
\(524\) | −0.977904 | − | 2.28115i | −0.0427199 | − | 0.0996524i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.8367 | − | 4.07266i | 0.864921 | − | 0.177577i | ||||
\(527\) | 2.13706 | 0.0930919 | ||||||||
\(528\) | 10.7196 | − | 11.2601i | 0.466511 | − | 0.490032i | ||||
\(529\) | 19.6964 | 0.856366 | ||||||||
\(530\) | 22.4367 | − | 4.60648i | 0.974589 | − | 0.200093i | ||||
\(531\) | 4.35217i | 0.188868i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.7234i | 0.507796i | ||||||||
\(534\) | 4.88742 | + | 23.8051i | 0.211500 | + | 1.03015i | ||||
\(535\) | 11.5404 | 0.498934 | ||||||||
\(536\) | 21.0295 | + | 30.2502i | 0.908336 | + | 1.30661i | ||||
\(537\) | −18.6231 | −0.803646 | ||||||||
\(538\) | 4.78224 | + | 23.2928i | 0.206177 | + | 1.00423i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.21805 | + | 1.80823i | −0.181516 | + | 0.0778140i | ||||
\(541\) | − | 3.98877i | − | 0.171491i | −0.996317 | − | 0.0857454i | \(-0.972673\pi\) | ||
0.996317 | − | 0.0857454i | \(-0.0273272\pi\) | |||||||
\(542\) | −37.1897 | + | 7.63541i | −1.59744 | + | 0.327969i | ||||
\(543\) | 13.6786 | 0.587005 | ||||||||
\(544\) | −0.860437 | + | 1.37756i | −0.0368909 | + | 0.0590625i | ||||
\(545\) | 0.469072 | 0.0200928 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 12.1824i | − | 0.520882i | −0.965490 | − | 0.260441i | \(-0.916132\pi\) | ||
0.965490 | − | 0.260441i | \(-0.0838679\pi\) | |||||||
\(548\) | 2.92311 | − | 1.25311i | 0.124869 | − | 0.0535300i | ||||
\(549\) | 7.16714i | 0.305886i | ||||||||
\(550\) | 0.293401 | + | 1.42907i | 0.0125107 | + | 0.0609356i | ||||
\(551\) | −15.4129 | −0.656611 | ||||||||
\(552\) | 10.5494 | + | 15.1750i | 0.449014 | + | 0.645891i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 6.40027 | + | 31.1738i | 0.271922 | + | 1.32445i | ||||
\(555\) | − | 13.6655i | − | 0.580069i | ||||||
\(556\) | 0.811510 | + | 1.89300i | 0.0344157 | + | 0.0802812i | ||||
\(557\) | − | 2.98826i | − | 0.126617i | −0.997994 | − | 0.0633084i | \(-0.979835\pi\) | ||
0.997994 | − | 0.0633084i | \(-0.0201652\pi\) | |||||||
\(558\) | 10.3110 | − | 2.11695i | 0.436501 | − | 0.0896178i | ||||
\(559\) | −37.4974 | −1.58597 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.11594 | −0.0471152 | ||||||||
\(562\) | 17.7841 | − | 3.65124i | 0.750176 | − | 0.154018i | ||||
\(563\) | − | 4.41292i | − | 0.185982i | −0.995667 | − | 0.0929911i | \(-0.970357\pi\) | ||
0.995667 | − | 0.0929911i | \(-0.0296428\pi\) | |||||||
\(564\) | −0.0685638 | − | 0.159938i | −0.00288706 | − | 0.00673461i | ||||
\(565\) | 34.2368i | 1.44035i | ||||||||
\(566\) | 2.07566 | + | 10.1099i | 0.0872466 | + | 0.424952i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −14.3717 | + | 9.99098i | −0.603022 | + | 0.419212i | ||||
\(569\) | −12.3086 | −0.516005 | −0.258002 | − | 0.966144i | \(-0.583064\pi\) | ||||
−0.258002 | + | 0.966144i | \(0.583064\pi\) | |||||||
\(570\) | −1.81777 | − | 8.85382i | −0.0761382 | − | 0.370846i | ||||
\(571\) | − | 30.3416i | − | 1.26975i | −0.772613 | − | 0.634877i | \(-0.781051\pi\) | ||
0.772613 | − | 0.634877i | \(-0.218949\pi\) | |||||||
\(572\) | 23.8208 | − | 10.2117i | 0.995997 | − | 0.426973i | ||||
\(573\) | − | 12.6346i | − | 0.527818i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.73429 | −0.0723247 | ||||||||
\(576\) | −2.78689 | + | 7.49888i | −0.116120 | + | 0.312453i | ||||
\(577\) | 12.0512 | 0.501697 | 0.250848 | − | 0.968026i | \(-0.419290\pi\) | ||||
0.250848 | + | 0.968026i | \(0.419290\pi\) | |||||||
\(578\) | −23.4362 | + | 4.81168i | −0.974817 | + | 0.200139i | ||||
\(579\) | 2.60582i | 0.108294i | ||||||||
\(580\) | −23.3416 | + | 10.0063i | −0.969208 | + | 0.415489i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.83885 | − | 8.95647i | −0.0762228 | − | 0.371258i | ||||
\(583\) | 27.4329 | 1.13615 | ||||||||
\(584\) | 32.2336 | − | 22.4083i | 1.33384 | − | 0.927263i | ||||
\(585\) | −7.65066 | −0.316316 | ||||||||
\(586\) | 2.83189 | + | 13.7933i | 0.116984 | + | 0.569794i | ||||
\(587\) | − | 5.34331i | − | 0.220542i | −0.993902 | − | 0.110271i | \(-0.964828\pi\) | ||
0.993902 | − | 0.110271i | \(-0.0351719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.7309i | 0.854200i | ||||||||
\(590\) | −13.8348 | + | 2.84041i | −0.569569 | + | 0.116938i | ||||
\(591\) | 0.794777 | 0.0326927 | ||||||||
\(592\) | −17.2534 | − | 16.4252i | −0.709109 | − | 0.675072i | ||||
\(593\) | −9.49060 | −0.389732 | −0.194866 | − | 0.980830i | \(-0.562427\pi\) | ||||
−0.194866 | + | 0.980830i | \(0.562427\pi\) | |||||||
\(594\) | −5.38428 | + | 1.10544i | −0.220920 | + | 0.0453569i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 7.55853 | + | 17.6317i | 0.309609 | + | 0.722223i | ||||
\(597\) | − | 10.7343i | − | 0.439325i | ||||||
\(598\) | 6.19636 | + | 30.1806i | 0.253388 | + | 1.23418i | ||||
\(599\) | −7.73951 | −0.316228 | −0.158114 | − | 0.987421i | \(-0.550541\pi\) | ||||
−0.158114 | + | 0.987421i | \(0.550541\pi\) | |||||||
\(600\) | −0.428507 | − | 0.616393i | −0.0174937 | − | 0.0251642i | ||||
\(601\) | 19.0198 | 0.775835 | 0.387917 | − | 0.921694i | \(-0.373195\pi\) | ||||
0.387917 | + | 0.921694i | \(0.373195\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 13.0255i | − | 0.530440i | ||||||
\(604\) | 12.8532 | − | 5.51002i | 0.522989 | − | 0.224200i | ||||
\(605\) | 9.42234i | 0.383072i | ||||||||
\(606\) | −16.4106 | + | 3.36925i | −0.666635 | + | 0.136867i | ||||
\(607\) | −9.19581 | −0.373247 | −0.186623 | − | 0.982432i | \(-0.559754\pi\) | ||||
−0.186623 | + | 0.982432i | \(0.559754\pi\) | |||||||
\(608\) | −13.3632 | − | 8.34678i | −0.541950 | − | 0.338507i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −22.7830 | + | 4.67758i | −0.922459 | + | 0.189390i | ||||
\(611\) | − | 0.290094i | − | 0.0117360i | ||||||
\(612\) | 0.527789 | − | 0.226257i | 0.0213346 | − | 0.00914592i | ||||
\(613\) | − | 26.4067i | − | 1.06655i | −0.845940 | − | 0.533277i | \(-0.820960\pi\) | ||
0.845940 | − | 0.533277i | \(-0.179040\pi\) | |||||||
\(614\) | −4.25147 | − | 20.7076i | −0.171575 | − | 0.835691i | ||||
\(615\) | 8.06838 | 0.325348 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −45.5837 | −1.83513 | −0.917565 | − | 0.397585i | \(-0.869848\pi\) | ||||
−0.917565 | + | 0.397585i | \(0.869848\pi\) | |||||||
\(618\) | −0.461298 | − | 2.24684i | −0.0185561 | − | 0.0903812i | ||||
\(619\) | − | 49.0337i | − | 1.97083i | −0.170169 | − | 0.985415i | \(-0.554431\pi\) | ||
0.170169 | − | 0.985415i | \(-0.445569\pi\) | |||||||
\(620\) | 13.4588 | + | 31.3953i | 0.540519 | + | 1.26086i | ||||
\(621\) | − | 6.53425i | − | 0.262210i | ||||||
\(622\) | 43.3038 | − | 8.89068i | 1.73632 | − | 0.356484i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −9.19567 | + | 9.65931i | −0.368122 | + | 0.386682i | ||||
\(625\) | −26.2566 | −1.05027 | ||||||||
\(626\) | 4.24556 | − | 0.871654i | 0.169687 | − | 0.0348383i | ||||
\(627\) | − | 10.8254i | − | 0.432324i | ||||||
\(628\) | 13.6784 | + | 31.9075i | 0.545828 | + | 1.27325i | ||||
\(629\) | 1.70992i | 0.0681788i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.5801 | −0.500804 | −0.250402 | − | 0.968142i | \(-0.580563\pi\) | ||||
−0.250402 | + | 0.968142i | \(0.580563\pi\) | |||||||
\(632\) | −20.8980 | + | 14.5280i | −0.831277 | + | 0.577892i | ||||
\(633\) | 0.556345 | 0.0221127 | ||||||||
\(634\) | −4.63548 | − | 22.5780i | −0.184099 | − | 0.896687i | ||||
\(635\) | 14.4395i | 0.573013i | ||||||||
\(636\) | −12.9745 | + | 5.56201i | −0.514471 | + | 0.220548i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −29.7952 | + | 6.11724i | −1.17960 | + | 0.242184i | ||||
\(639\) | 6.18835 | 0.244807 | ||||||||
\(640\) | −25.6564 | − | 3.96493i | −1.01416 | − | 0.156728i | ||||
\(641\) | −34.2258 | −1.35184 | −0.675920 | − | 0.736975i | \(-0.736253\pi\) | ||||
−0.675920 | + | 0.736975i | \(0.736253\pi\) | |||||||
\(642\) | −6.96712 | + | 1.43042i | −0.274970 | + | 0.0564540i | ||||
\(643\) | 23.0442i | 0.908776i | 0.890804 | + | 0.454388i | \(0.150142\pi\) | ||||
−0.890804 | + | 0.454388i | \(0.849858\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 25.8069i | 1.01614i | ||||||||
\(646\) | 0.227451 | + | 1.10785i | 0.00894895 | + | 0.0435876i | ||||
\(647\) | −15.5820 | −0.612590 | −0.306295 | − | 0.951937i | \(-0.599089\pi\) | ||||
−0.306295 | + | 0.951937i | \(0.599089\pi\) | |||||||
\(648\) | 2.32238 | − | 1.61448i | 0.0912317 | − | 0.0634229i | ||||
\(649\) | −16.9155 | −0.663991 | ||||||||
\(650\) | −0.251690 | − | 1.22590i | −0.00987210 | − | 0.0480839i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.3893 | + | 28.9003i | 0.485201 | + | 1.13182i | ||||
\(653\) | − | 49.2269i | − | 1.92640i | −0.268789 | − | 0.963199i | \(-0.586623\pi\) | ||
0.268789 | − | 0.963199i | \(-0.413377\pi\) | |||||||
\(654\) | −0.283187 | + | 0.0581409i | −0.0110735 | + | 0.00227349i | ||||
\(655\) | −2.84757 | −0.111264 | ||||||||
\(656\) | 9.69775 | − | 10.1867i | 0.378634 | − | 0.397724i | ||||
\(657\) | −13.8796 | −0.541493 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.33204i | − | 0.207707i | −0.994593 | − | 0.103853i | \(-0.966883\pi\) | ||
0.994593 | − | 0.103853i | \(-0.0331173\pi\) | |||||||
\(660\) | −7.02801 | − | 16.3942i | −0.273565 | − | 0.638143i | ||||
\(661\) | − | 38.6891i | − | 1.50483i | −0.658689 | − | 0.752416i | \(-0.728889\pi\) | ||
0.658689 | − | 0.752416i | \(-0.271111\pi\) | |||||||
\(662\) | −0.785869 | − | 3.82773i | −0.0305437 | − | 0.148769i | ||||
\(663\) | 0.957298 | 0.0371784 | ||||||||
\(664\) | 28.4655 | + | 40.9467i | 1.10468 | + | 1.58904i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.69383 | + | 8.25010i | 0.0656344 | + | 0.319685i | ||||
\(667\) | − | 36.1589i | − | 1.40008i | ||||||
\(668\) | 0.187615 | − | 0.0804286i | 0.00725905 | − | 0.00311188i | ||||
\(669\) | − | 11.1076i | − | 0.429445i | ||||||
\(670\) | 41.4058 | − | 8.50100i | 1.59964 | − | 0.328422i | ||||
\(671\) | −27.8563 | −1.07538 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.56678 | −0.368772 | −0.184386 | − | 0.982854i | \(-0.559030\pi\) | ||||
−0.184386 | + | 0.982854i | \(0.559030\pi\) | |||||||
\(674\) | 35.7770 | − | 7.34537i | 1.37808 | − | 0.282933i | ||||
\(675\) | 0.265415i | 0.0102158i | ||||||||
\(676\) | 3.46242 | − | 1.48430i | 0.133170 | − | 0.0570886i | ||||
\(677\) | − | 17.7288i | − | 0.681372i | −0.940177 | − | 0.340686i | \(-0.889341\pi\) | ||
0.940177 | − | 0.340686i | \(-0.110659\pi\) | |||||||
\(678\) | −4.24362 | − | 20.6694i | −0.162975 | − | 0.793802i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1.06369 | + | 1.53008i | 0.0407906 | + | 0.0586759i | ||||
\(681\) | 8.76788 | 0.335986 | ||||||||
\(682\) | 8.22790 | + | 40.0756i | 0.315063 | + | 1.53457i | ||||
\(683\) | 8.77302i | 0.335690i | 0.985813 | + | 0.167845i | \(0.0536808\pi\) | ||||
−0.985813 | + | 0.167845i | \(0.946319\pi\) | |||||||
\(684\) | 2.19484 | + | 5.11989i | 0.0839218 | + | 0.195764i | ||||
\(685\) | − | 3.64893i | − | 0.139418i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 20.6962 | 0.789610 | ||||||||
\(688\) | 32.5824 | + | 31.0184i | 1.24219 | + | 1.18257i | ||||
\(689\) | −23.5329 | −0.896534 | ||||||||
\(690\) | 20.7712 | − | 4.26453i | 0.790746 | − | 0.162348i | ||||
\(691\) | 21.3823i | 0.813421i | 0.913557 | + | 0.406710i | \(0.133324\pi\) | ||||
−0.913557 | + | 0.406710i | \(0.866676\pi\) | |||||||
\(692\) | −1.80281 | − | 4.20540i | −0.0685326 | − | 0.159865i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.49139 | − | 17.0055i | −0.132531 | − | 0.645519i | ||||
\(695\) | 2.36304 | 0.0896354 | ||||||||
\(696\) | 12.8514 | − | 8.93414i | 0.487133 | − | 0.338648i | ||||
\(697\) | −1.00957 | −0.0382400 | ||||||||
\(698\) | −0.0596576 | − | 0.290574i | −0.00225807 | − | 0.0109984i | ||||
\(699\) | − | 5.72853i | − | 0.216673i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.4233i | − | 0.506990i | −0.967337 | − | 0.253495i | \(-0.918420\pi\) | ||
0.967337 | − | 0.253495i | \(-0.0815802\pi\) | |||||||
\(702\) | 4.61883 | − | 0.948290i | 0.174326 | − | 0.0357909i | ||||
\(703\) | −16.5873 | −0.625601 | ||||||||
\(704\) | −29.1457 | − | 10.8317i | −1.09847 | − | 0.408236i | ||||
\(705\) | −0.199652 | −0.00751931 | ||||||||
\(706\) | 27.1501 | − | 5.57418i | 1.02181 | − | 0.209787i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 8.00022 | − | 3.42961i | 0.300667 | − | 0.128893i | ||||
\(709\) | 50.6521i | 1.90228i | 0.308762 | + | 0.951139i | \(0.400085\pi\) | ||||
−0.308762 | + | 0.951139i | \(0.599915\pi\) | |||||||
\(710\) | 4.03877 | + | 19.6716i | 0.151572 | + | 0.738263i | ||||
\(711\) | 8.99853 | 0.337471 | ||||||||
\(712\) | 39.9075 | − | 27.7431i | 1.49560 | − | 1.03972i | ||||
\(713\) | −48.6349 | −1.82139 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 29.7356i | − | 1.11205i | ||||||
\(716\) | 14.6754 | + | 34.2332i | 0.548445 | + | 1.27935i | ||||
\(717\) | 2.27651i | 0.0850179i | ||||||||
\(718\) | −7.91172 | + | 1.62435i | −0.295263 | + | 0.0606203i | ||||
\(719\) | −28.9600 | −1.08003 | −0.540013 | − | 0.841657i | \(-0.681581\pi\) | ||||
−0.540013 | + | 0.841657i | \(0.681581\pi\) | |||||||
\(720\) | 6.64783 | + | 6.32874i | 0.247750 | + | 0.235858i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 15.5742 | − | 3.19754i | 0.579613 | − | 0.119000i | ||||
\(723\) | − | 23.5850i | − | 0.877137i | ||||||
\(724\) | −10.7790 | − | 25.1441i | −0.400599 | − | 0.934475i | ||||
\(725\) | 1.46874i | 0.0545475i | ||||||||
\(726\) | −1.16789 | − | 5.68842i | −0.0433444 | − | 0.211117i | ||||
\(727\) | 10.5092 | 0.389766 | 0.194883 | − | 0.980827i | \(-0.437567\pi\) | ||||
0.194883 | + | 0.980827i | \(0.437567\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −9.05839 | − | 44.1206i | −0.335266 | − | 1.63298i | ||||
\(731\) | − | 3.22912i | − | 0.119433i | ||||||
\(732\) | 13.1747 | − | 5.64786i | 0.486952 | − | 0.208751i | ||||
\(733\) | 28.1008i | 1.03793i | 0.854797 | + | 0.518963i | \(0.173682\pi\) | ||||
−0.854797 | + | 0.518963i | \(0.826318\pi\) | |||||||
\(734\) | −38.9655 | + | 8.00000i | −1.43824 | + | 0.295285i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 19.5817 | − | 31.3503i | 0.721791 | − | 1.15559i | ||||
\(737\) | 50.6259 | 1.86483 | ||||||||
\(738\) | −4.87102 | + | 1.00007i | −0.179305 | + | 0.0368129i | ||||
\(739\) | 34.8553i | 1.28217i | 0.767469 | + | 0.641086i | \(0.221516\pi\) | ||||
−0.767469 | + | 0.641086i | \(0.778484\pi\) | |||||||
\(740\) | −25.1201 | + | 10.7687i | −0.923434 | + | 0.395866i | ||||
\(741\) | 9.28640i | 0.341144i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.4805 | 1.41171 | 0.705857 | − | 0.708354i | \(-0.250562\pi\) | ||||
0.705857 | + | 0.708354i | \(0.250562\pi\) | |||||||
\(744\) | −12.0167 | − | 17.2856i | −0.440554 | − | 0.633722i | ||||
\(745\) | 22.0098 | 0.806375 | ||||||||
\(746\) | −4.89301 | − | 23.8323i | −0.179146 | − | 0.872564i | ||||
\(747\) | − | 17.6313i | − | 0.645097i | ||||||
\(748\) | 0.879389 | + | 2.05134i | 0.0321536 | + | 0.0750045i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15.0504 | − | 3.08999i | 0.549562 | − | 0.112830i | ||||
\(751\) | 0.0225322 | 0.000822212 | 0.000411106 | − | 1.00000i | \(-0.499869\pi\) | ||||
0.000411106 | 1.00000i | \(0.499869\pi\) | ||||||||
\(752\) | −0.239970 | + | 0.252069i | −0.00875082 | + | 0.00919203i | ||||
\(753\) | 12.4322 | 0.453056 | ||||||||
\(754\) | 25.5594 | − | 5.24759i | 0.930819 | − | 0.191106i | ||||
\(755\) | − | 16.0447i | − | 0.583926i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 30.0479i | 1.09211i | 0.837749 | + | 0.546055i | \(0.183871\pi\) | ||||
−0.837749 | + | 0.546055i | \(0.816129\pi\) | |||||||
\(758\) | 2.89743 | + | 14.1125i | 0.105239 | + | 0.512589i | ||||
\(759\) | 25.3965 | 0.921834 | ||||||||
\(760\) | −14.8427 | + | 10.3185i | −0.538403 | + | 0.374290i | ||||
\(761\) | 17.1613 | 0.622096 | 0.311048 | − | 0.950394i | \(-0.399320\pi\) | ||||
0.311048 | + | 0.950394i | \(0.399320\pi\) | |||||||
\(762\) | −1.78976 | − | 8.71735i | −0.0648360 | − | 0.315796i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −23.2250 | + | 9.95633i | −0.840253 | + | 0.360207i | ||||
\(765\) | − | 0.658842i | − | 0.0238205i | ||||||
\(766\) | 27.4893 | − | 5.64381i | 0.993227 | − | 0.203919i | ||||
\(767\) | 14.5107 | 0.523952 | ||||||||
\(768\) | 15.9807 | − | 0.786392i | 0.576653 | − | 0.0283765i | ||||
\(769\) | 47.2945 | 1.70548 | 0.852742 | − | 0.522332i | \(-0.174938\pi\) | ||||
0.852742 | + | 0.522332i | \(0.174938\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 0.282984i | − | 0.0101914i | ||||||
\(772\) | 4.79005 | − | 2.05344i | 0.172398 | − | 0.0739051i | ||||
\(773\) | − | 42.7753i | − | 1.53852i | −0.638935 | − | 0.769260i | \(-0.720625\pi\) | ||
0.638935 | − | 0.769260i | \(-0.279375\pi\) | |||||||
\(774\) | −3.19873 | − | 15.5800i | −0.114976 | − | 0.560013i | ||||
\(775\) | 1.97550 | 0.0709621 | ||||||||
\(776\) | −15.0148 | + | 10.4381i | −0.539001 | + | 0.374705i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.27123 | − | 25.6745i | −0.188983 | − | 0.920477i | ||||
\(779\) | − | 9.79343i | − | 0.350886i | ||||||
\(780\) | 6.02888 | + | 14.0635i | 0.215869 | + | 0.503555i | ||||
\(781\) | 24.0521i | 0.860651i | ||||||||
\(782\) | −2.59902 | + | 0.533604i | −0.0929408 | + | 0.0190816i | ||||
\(783\) | −5.53374 | −0.197760 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.8303 | 1.42160 | ||||||||
\(786\) | 1.71912 | − | 0.352953i | 0.0613191 | − | 0.0125894i | ||||
\(787\) | 49.4625i | 1.76315i | 0.472046 | + | 0.881574i | \(0.343515\pi\) | ||||
−0.472046 | + | 0.881574i | \(0.656485\pi\) | |||||||
\(788\) | −0.626301 | − | 1.46097i | −0.0223111 | − | 0.0520448i | ||||
\(789\) | 14.3192i | 0.509778i | ||||||||
\(790\) | 5.87282 | + | 28.6047i | 0.208945 | + | 1.01771i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.27497 | + | 9.02633i | 0.222971 | + | 0.320737i | ||||
\(793\) | 23.8962 | 0.848578 | ||||||||
\(794\) | 2.27005 | + | 11.0567i | 0.0805612 | + | 0.392389i | ||||
\(795\) | 16.1961i | 0.574416i | ||||||||
\(796\) | −19.7319 | + | 8.45884i | −0.699378 | + | 0.299816i | ||||
\(797\) | − | 13.3755i | − | 0.473783i | −0.971536 | − | 0.236892i | \(-0.923871\pi\) | ||
0.971536 | − | 0.236892i | \(-0.0761286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.0249817 | 0.000883788 | ||||||||
\(800\) | −0.795388 | + | 1.27342i | −0.0281212 | + | 0.0450221i | ||||
\(801\) | −17.1839 | −0.607163 | ||||||||
\(802\) | 49.9296 | − | 10.2510i | 1.76307 | − | 0.361976i | ||||
\(803\) | − | 53.9453i | − | 1.90369i | ||||||
\(804\) | −23.9437 | + | 10.2644i | −0.844428 | + | 0.361997i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −7.05819 | − | 34.3783i | −0.248614 | − | 1.21092i | ||||
\(807\) | −16.8141 | −0.591883 | ||||||||
\(808\) | 19.1253 | + | 27.5111i | 0.672826 | + | 0.967838i | ||||
\(809\) | 14.2253 | 0.500136 | 0.250068 | − | 0.968228i | \(-0.419547\pi\) | ||||
0.250068 | + | 0.968228i | \(0.419547\pi\) | |||||||
\(810\) | −0.652642 | − | 3.17882i | −0.0229315 | − | 0.111692i | ||||
\(811\) | 20.7849i | 0.729855i | 0.931036 | + | 0.364928i | \(0.118906\pi\) | ||||
−0.931036 | + | 0.364928i | \(0.881094\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 26.8456i | − | 0.941518i | ||||||
\(814\) | −32.0655 | + | 6.58335i | −1.12389 | + | 0.230746i | ||||
\(815\) | 36.0764 | 1.26370 | ||||||||
\(816\) | −0.831818 | − | 0.791892i | −0.0291195 | − | 0.0277218i | ||||
\(817\) | 31.3245 | 1.09590 | ||||||||
\(818\) | 40.9591 | − | 8.40931i | 1.43210 | − | 0.294025i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.35806 | − | 14.8314i | −0.222033 | − | 0.517935i | ||||
\(821\) | − | 4.96410i | − | 0.173248i | −0.996241 | − | 0.0866241i | \(-0.972392\pi\) | ||
0.996241 | − | 0.0866241i | \(-0.0276079\pi\) | |||||||
\(822\) | 0.452281 | + | 2.20292i | 0.0157751 | + | 0.0768357i | ||||
\(823\) | 9.83498 | 0.342826 | 0.171413 | − | 0.985199i | \(-0.445167\pi\) | ||||
0.171413 | + | 0.985199i | \(0.445167\pi\) | |||||||
\(824\) | −3.76666 | + | 2.61852i | −0.131218 | + | 0.0912206i | ||||
\(825\) | −1.03158 | −0.0359150 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 41.4331i | − | 1.44077i | −0.693574 | − | 0.720385i | \(-0.743965\pi\) | ||
0.693574 | − | 0.720385i | \(-0.256035\pi\) | |||||||
\(828\) | −12.0113 | + | 5.14913i | −0.417423 | + | 0.178945i | ||||
\(829\) | 25.0029i | 0.868386i | 0.900820 | + | 0.434193i | \(0.142966\pi\) | ||||
−0.900820 | + | 0.434193i | \(0.857034\pi\) | |||||||
\(830\) | 56.0468 | − | 11.5070i | 1.94541 | − | 0.399412i | ||||
\(831\) | −22.5030 | −0.780619 | ||||||||
\(832\) | 25.0022 | + | 9.29185i | 0.866797 | + | 0.322137i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1.42661 | + | 0.292897i | −0.0493994 | + | 0.0101422i | ||||
\(835\) | − | 0.234201i | − | 0.00810486i | ||||||
\(836\) | −19.8993 | + | 8.53063i | −0.688232 | + | 0.295038i | ||||
\(837\) | 7.44308i | 0.257270i | ||||||||
\(838\) | 2.48384 | + | 12.0980i | 0.0858029 | + | 0.417920i | ||||
\(839\) | −2.43551 | −0.0840833 | −0.0420416 | − | 0.999116i | \(-0.513386\pi\) | ||||
−0.0420416 | + | 0.999116i | \(0.513386\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.62232 | −0.0559420 | ||||||||
\(842\) | 0.504413 | + | 2.45684i | 0.0173832 | + | 0.0846683i | ||||
\(843\) | 12.8375i | 0.442148i | ||||||||
\(844\) | −0.438412 | − | 1.02268i | −0.0150908 | − | 0.0352021i | ||||
\(845\) | − | 4.32216i | − | 0.148687i | ||||||
\(846\) | 0.120533 | − | 0.0247466i | 0.00414401 | − | 0.000850805i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 20.4483 | + | 19.4668i | 0.702198 | + | 0.668493i | ||||
\(849\) | −7.29790 | −0.250463 | ||||||||
\(850\) | 0.105570 | − | 0.0216745i | 0.00362101 | − | 0.000743428i | ||||
\(851\) | − | 38.9140i | − | 1.33395i | ||||||
\(852\) | −4.87655 | − | 11.3755i | −0.167068 | − | 0.389718i | ||||
\(853\) | 51.1404i | 1.75101i | 0.483206 | + | 0.875507i | \(0.339472\pi\) | ||||
−0.483206 | + | 0.875507i | \(0.660528\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.39118 | 0.218574 | ||||||||
\(856\) | 8.11965 | + | 11.6798i | 0.277524 | + | 0.399209i | ||||
\(857\) | −53.4628 | −1.82625 | −0.913127 | − | 0.407675i | \(-0.866340\pi\) | ||||
−0.913127 | + | 0.407675i | \(0.866340\pi\) | |||||||
\(858\) | 3.68569 | + | 17.9519i | 0.125827 | + | 0.612867i | ||||
\(859\) | 16.5958i | 0.566242i | 0.959084 | + | 0.283121i | \(0.0913697\pi\) | ||||
−0.959084 | + | 0.283121i | \(0.908630\pi\) | |||||||
\(860\) | 47.4385 | − | 20.3364i | 1.61764 | − | 0.693464i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 39.2976 | − | 8.06817i | 1.33848 | − | 0.274803i | ||||
\(863\) | −40.8512 | −1.39059 | −0.695296 | − | 0.718724i | \(-0.744727\pi\) | ||||
−0.695296 | + | 0.718724i | \(0.744727\pi\) | |||||||
\(864\) | −4.79785 | − | 2.99678i | −0.163226 | − | 0.101952i | ||||
\(865\) | −5.24962 | −0.178493 | ||||||||
\(866\) | 9.04914 | − | 1.85787i | 0.307502 | − | 0.0631332i | ||||
\(867\) | − | 16.9176i | − | 0.574551i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 34.9743i | 1.18642i | ||||||||
\(870\) | −3.61155 | − | 17.5908i | −0.122443 | − | 0.596383i | ||||
\(871\) | −43.4288 | −1.47153 | ||||||||
\(872\) | 0.330032 | + | 0.474740i | 0.0111763 | + | 0.0160767i | ||||
\(873\) | 6.46528 | 0.218817 | ||||||||
\(874\) | −5.17630 | − | 25.2122i | −0.175091 | − | 0.852814i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.9374 | + | 25.5136i | 0.369540 | + | 0.862024i | ||||
\(877\) | − | 1.51953i | − | 0.0513107i | −0.999671 | − | 0.0256554i | \(-0.991833\pi\) | ||
0.999671 | − | 0.0256554i | \(-0.00816725\pi\) | |||||||
\(878\) | −0.737435 | + | 0.151402i | −0.0248872 | + | 0.00510959i | ||||
\(879\) | −9.95674 | −0.335833 | ||||||||
\(880\) | −24.5977 | + | 25.8379i | −0.829190 | + | 0.870997i | ||||
\(881\) | −12.3299 | −0.415406 | −0.207703 | − | 0.978192i | \(-0.566599\pi\) | ||||
−0.207703 | + | 0.978192i | \(0.566599\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.0145i | 0.404319i | 0.979353 | + | 0.202159i | \(0.0647959\pi\) | ||||
−0.979353 | + | 0.202159i | \(0.935204\pi\) | |||||||
\(884\) | −0.754372 | − | 1.75972i | −0.0253723 | − | 0.0591857i | ||||
\(885\) | − | 9.98671i | − | 0.335700i | ||||||
\(886\) | 2.42316 | + | 11.8025i | 0.0814078 | + | 0.396512i | ||||
\(887\) | 23.0480 | 0.773875 | 0.386938 | − | 0.922106i | \(-0.373533\pi\) | ||||
0.386938 | + | 0.922106i | \(0.373533\pi\) | |||||||
\(888\) | 13.8307 | − | 9.61487i | 0.464127 | − | 0.322654i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −11.2149 | − | 54.6244i | −0.375925 | − | 1.83102i | ||||
\(891\) | − | 3.88667i | − | 0.130208i | ||||||
\(892\) | −20.4181 | + | 8.75303i | −0.683650 | + | 0.293073i | ||||
\(893\) | 0.242338i | 0.00810953i | ||||||||
\(894\) | −13.2877 | + | 2.72808i | −0.444406 | + | 0.0912408i | ||||
\(895\) | 42.7335 | 1.42842 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −21.7860 | −0.727415 | ||||||||
\(898\) | −20.8048 | + | 4.27142i | −0.694264 | + | 0.142539i | ||||
\(899\) | 41.1881i | 1.37370i | ||||||||
\(900\) | 0.487888 | − | 0.209152i | 0.0162629 | − | 0.00697175i | ||||
\(901\) | − | 2.02656i | − | 0.0675144i | ||||||
\(902\) | −3.88693 | − | 18.9320i | −0.129421 | − | 0.630368i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −34.6506 | + | 24.0886i | −1.15246 | + | 0.801174i | ||||
\(905\) | −31.3876 | −1.04336 | ||||||||
\(906\) | 1.98872 | + | 9.68645i | 0.0660709 | + | 0.321811i | ||||
\(907\) | − | 32.7639i | − | 1.08791i | −0.839115 | − | 0.543954i | \(-0.816927\pi\) | ||
0.839115 | − | 0.543954i | \(-0.183073\pi\) | |||||||
\(908\) | −6.90928 | − | 16.1172i | −0.229293 | − | 0.534869i | ||||
\(909\) | − | 11.8461i | − | 0.392910i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.5607 | 1.17818 | 0.589090 | − | 0.808067i | \(-0.299486\pi\) | ||||
0.589090 | + | 0.808067i | \(0.299486\pi\) | |||||||
\(912\) | 7.68185 | − | 8.06916i | 0.254372 | − | 0.267197i | ||||
\(913\) | 68.5273 | 2.26792 | ||||||||
\(914\) | −43.5754 | + | 8.94645i | −1.44135 | + | 0.295922i | ||||
\(915\) | − | 16.4461i | − | 0.543691i | ||||||
\(916\) | −16.3091 | − | 38.0440i | −0.538867 | − | 1.25701i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.0816627 | + | 0.397754i | 0.00269527 | + | 0.0131278i | ||||
\(919\) | −27.5241 | −0.907937 | −0.453969 | − | 0.891018i | \(-0.649992\pi\) | ||||
−0.453969 | + | 0.891018i | \(0.649992\pi\) | |||||||
\(920\) | −24.2073 | − | 34.8213i | −0.798090 | − | 1.14802i | ||||
\(921\) | 14.9479 | 0.492550 | ||||||||
\(922\) | 1.24087 | + | 6.04388i | 0.0408658 | + | 0.199045i | ||||
\(923\) | − | 20.6327i | − | 0.679135i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.58065i | 0.0519713i | ||||||||
\(926\) | 19.3650 | − | 3.97581i | 0.636372 | − | 0.130653i | ||||
\(927\) | 1.62190 | 0.0532701 | ||||||||
\(928\) | −26.5501 | − | 16.5834i | −0.871548 | − | 0.544376i | ||||
\(929\) | −34.9480 | −1.14661 | −0.573303 | − | 0.819343i | \(-0.694338\pi\) | ||||
−0.573303 | + | 0.819343i | \(0.694338\pi\) | |||||||
\(930\) | −23.6602 | + | 4.85766i | −0.775848 | + | 0.159289i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −10.5303 | + | 4.51421i | −0.344930 | + | 0.147868i | ||||
\(933\) | 31.2591i | 1.02338i | ||||||||
\(934\) | 4.70381 | + | 22.9108i | 0.153913 | + | 0.749665i | ||||
\(935\) | 2.56070 | 0.0837439 | ||||||||
\(936\) | −5.38290 | − | 7.74311i | −0.175945 | − | 0.253092i | ||||
\(937\) | −17.7423 | −0.579615 | −0.289807 | − | 0.957085i | \(-0.593591\pi\) | ||||
−0.289807 | + | 0.957085i | \(0.593591\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.06468i | 0.100012i | ||||||||
\(940\) | 0.157330 | + | 0.367002i | 0.00513153 | + | 0.0119703i | ||||
\(941\) | − | 22.5728i | − | 0.735852i | −0.929855 | − | 0.367926i | \(-0.880068\pi\) | ||
0.929855 | − | 0.367926i | \(-0.119932\pi\) | |||||||
\(942\) | −24.0462 | + | 4.93692i | −0.783468 | + | 0.160853i | ||||
\(943\) | 22.9755 | 0.748187 | ||||||||
\(944\) | −12.6087 | − | 12.0035i | −0.410378 | − | 0.390680i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 60.5545 | − | 12.4324i | 1.96880 | − | 0.404213i | ||||
\(947\) | − | 27.2714i | − | 0.886203i | −0.896471 | − | 0.443102i | \(-0.853878\pi\) | ||
0.896471 | − | 0.443102i | \(-0.146122\pi\) | |||||||
\(948\) | −7.09104 | − | 16.5412i | −0.230306 | − | 0.537233i | ||||
\(949\) | 46.2763i | 1.50219i | ||||||||
\(950\) | 0.210256 | + | 1.02409i | 0.00682161 | + | 0.0332259i | ||||
\(951\) | 16.2981 | 0.528501 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −5.90986 | −0.191439 | −0.0957196 | − | 0.995408i | \(-0.530515\pi\) | ||||
−0.0957196 | + | 0.995408i | \(0.530515\pi\) | |||||||
\(954\) | −2.00749 | − | 9.77785i | −0.0649948 | − | 0.316569i | ||||
\(955\) | 28.9920i | 0.938157i | ||||||||
\(956\) | 4.18471 | − | 1.79394i | 0.135343 | − | 0.0580202i | ||||
\(957\) | − | 21.5078i | − | 0.695250i | ||||||
\(958\) | 1.64024 | − | 0.336756i | 0.0529936 | − | 0.0108801i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.39493 | − | 17.2073i | 0.206396 | − | 0.555363i | ||||
\(961\) | 24.3994 | 0.787077 | ||||||||
\(962\) | 27.5069 | − | 5.64743i | 0.886858 | − | 0.182081i | ||||
\(963\) | − | 5.02926i | − | 0.162066i | ||||||
\(964\) | −43.3543 | + | 18.5855i | −1.39635 | + | 0.598599i | ||||
\(965\) | − | 5.97945i | − | 0.192485i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.0032 | 0.450312 | 0.225156 | − | 0.974323i | \(-0.427711\pi\) | ||||
0.225156 | + | 0.974323i | \(0.427711\pi\) | |||||||
\(968\) | −9.53620 | + | 6.62942i | −0.306505 | + | 0.213078i | ||||
\(969\) | −0.799705 | −0.0256902 | ||||||||
\(970\) | 4.21951 | + | 20.5520i | 0.135480 | + | 0.659884i | ||||
\(971\) | − | 9.13650i | − | 0.293204i | −0.989196 | − | 0.146602i | \(-0.953166\pi\) | ||
0.989196 | − | 0.146602i | \(-0.0468337\pi\) | |||||||
\(972\) | 0.788022 | + | 1.83821i | 0.0252758 | + | 0.0589607i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −33.3717 | + | 6.85153i | −1.06930 | + | 0.219537i | ||||
\(975\) | 0.884927 | 0.0283403 | ||||||||
\(976\) | −20.7639 | − | 19.7673i | −0.664638 | − | 0.632736i | ||||
\(977\) | 21.1534 | 0.676758 | 0.338379 | − | 0.941010i | \(-0.390121\pi\) | ||||
0.338379 | + | 0.941010i | \(0.390121\pi\) | |||||||
\(978\) | −21.7799 | + | 4.47163i | −0.696446 | + | 0.142987i | ||||
\(979\) | − | 66.7881i | − | 2.13456i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 0.204420i | − | 0.00652662i | ||||||
\(982\) | −5.26092 | − | 25.6243i | −0.167883 | − | 0.817705i | ||||
\(983\) | −46.4009 | −1.47996 | −0.739979 | − | 0.672630i | \(-0.765164\pi\) | ||||
−0.739979 | + | 0.672630i | \(0.765164\pi\) | |||||||
\(984\) | 5.67680 | + | 8.16588i | 0.180970 | + | 0.260319i | ||||
\(985\) | −1.82373 | −0.0581090 | ||||||||
\(986\) | 0.451900 | + | 2.20107i | 0.0143914 | + | 0.0700963i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 17.0704 | − | 7.31788i | 0.543081 | − | 0.232813i | ||||
\(989\) | 73.4877i | 2.33677i | ||||||||
\(990\) | 12.3550 | − | 2.53661i | 0.392669 | − | 0.0806186i | ||||
\(991\) | 2.58561 | 0.0821345 | 0.0410672 | − | 0.999156i | \(-0.486924\pi\) | ||||
0.0410672 | + | 0.999156i | \(0.486924\pi\) | |||||||
\(992\) | −22.3052 | + | 35.7107i | −0.708192 | + | 1.13382i | ||||
\(993\) | 2.76307 | 0.0876833 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.6314i | 0.780868i | ||||||||
\(996\) | −32.4101 | + | 13.8939i | −1.02695 | + | 0.440245i | ||||
\(997\) | 20.7334i | 0.656635i | 0.944567 | + | 0.328317i | \(0.106482\pi\) | ||||
−0.944567 | + | 0.328317i | \(0.893518\pi\) | |||||||
\(998\) | 3.44952 | + | 16.8015i | 0.109193 | + | 0.531843i | ||||
\(999\) | −5.95539 | −0.188420 |
(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 | 1176.2.c.f.589.15 | 16 | ||
4.3 | odd | 2 | 4704.2.c.f.2353.2 | 16 | |||
7.3 | odd | 6 | 168.2.bc.a.37.6 | yes | 32 | ||
7.5 | odd | 6 | 168.2.bc.a.109.5 | yes | 32 | ||
7.6 | odd | 2 | 1176.2.c.e.589.15 | 16 | |||
8.3 | odd | 2 | 4704.2.c.f.2353.15 | 16 | |||
8.5 | even | 2 | inner | 1176.2.c.f.589.16 | 16 | ||
21.5 | even | 6 | 504.2.cj.e.109.12 | 32 | |||
21.17 | even | 6 | 504.2.cj.e.37.11 | 32 | |||
28.3 | even | 6 | 672.2.bk.a.625.10 | 32 | |||
28.19 | even | 6 | 672.2.bk.a.529.7 | 32 | |||
28.27 | even | 2 | 4704.2.c.e.2353.15 | 16 | |||
56.3 | even | 6 | 672.2.bk.a.625.7 | 32 | |||
56.5 | odd | 6 | 168.2.bc.a.109.6 | yes | 32 | ||
56.13 | odd | 2 | 1176.2.c.e.589.16 | 16 | |||
56.19 | even | 6 | 672.2.bk.a.529.10 | 32 | |||
56.27 | even | 2 | 4704.2.c.e.2353.2 | 16 | |||
56.45 | odd | 6 | 168.2.bc.a.37.5 | ✓ | 32 | ||
84.47 | odd | 6 | 2016.2.cr.e.1873.4 | 32 | |||
84.59 | odd | 6 | 2016.2.cr.e.1297.13 | 32 | |||
168.5 | even | 6 | 504.2.cj.e.109.11 | 32 | |||
168.59 | odd | 6 | 2016.2.cr.e.1297.4 | 32 | |||
168.101 | even | 6 | 504.2.cj.e.37.12 | 32 | |||
168.131 | odd | 6 | 2016.2.cr.e.1873.13 | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
168.2.bc.a.37.5 | ✓ | 32 | 56.45 | odd | 6 | ||
168.2.bc.a.37.6 | yes | 32 | 7.3 | odd | 6 | ||
168.2.bc.a.109.5 | yes | 32 | 7.5 | odd | 6 | ||
168.2.bc.a.109.6 | yes | 32 | 56.5 | odd | 6 | ||
504.2.cj.e.37.11 | 32 | 21.17 | even | 6 | |||
504.2.cj.e.37.12 | 32 | 168.101 | even | 6 | |||
504.2.cj.e.109.11 | 32 | 168.5 | even | 6 | |||
504.2.cj.e.109.12 | 32 | 21.5 | even | 6 | |||
672.2.bk.a.529.7 | 32 | 28.19 | even | 6 | |||
672.2.bk.a.529.10 | 32 | 56.19 | even | 6 | |||
672.2.bk.a.625.7 | 32 | 56.3 | even | 6 | |||
672.2.bk.a.625.10 | 32 | 28.3 | even | 6 | |||
1176.2.c.e.589.15 | 16 | 7.6 | odd | 2 | |||
1176.2.c.e.589.16 | 16 | 56.13 | odd | 2 | |||
1176.2.c.f.589.15 | 16 | 1.1 | even | 1 | trivial | ||
1176.2.c.f.589.16 | 16 | 8.5 | even | 2 | inner | ||
2016.2.cr.e.1297.4 | 32 | 168.59 | odd | 6 | |||
2016.2.cr.e.1297.13 | 32 | 84.59 | odd | 6 | |||
2016.2.cr.e.1873.4 | 32 | 84.47 | odd | 6 | |||
2016.2.cr.e.1873.13 | 32 | 168.131 | odd | 6 | |||
4704.2.c.e.2353.2 | 16 | 56.27 | even | 2 | |||
4704.2.c.e.2353.15 | 16 | 28.27 | even | 2 | |||
4704.2.c.f.2353.2 | 16 | 4.3 | odd | 2 | |||
4704.2.c.f.2353.15 | 16 | 8.3 | odd | 2 |