Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(17,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(20))
chi = DirichletCharacter(H, H._module([10, 13]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.s (of order \(20\), degree \(8\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{20})\) |
Coefficient field: | \(\Q(\zeta_{40})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{12} + x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{20}]$ |
Embedding invariants
Embedding label | 197.1 | ||
Root | \(-0.891007 + 0.453990i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.197 |
Dual form | 450.2.s.b.233.1 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{17}{20}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.453990 | − | 0.891007i | −0.321020 | − | 0.630037i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.587785 | + | 0.809017i | −0.293893 | + | 0.404508i | ||||
\(5\) | −0.349798 | + | 2.20854i | −0.156434 | + | 0.987688i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.28408 | − | 1.28408i | −0.485336 | − | 0.485336i | 0.421495 | − | 0.906831i | \(-0.361506\pi\) |
−0.906831 | + | 0.421495i | \(0.861506\pi\) | |||||||
\(8\) | 0.987688 | + | 0.156434i | 0.349201 | + | 0.0553079i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.12663 | − | 0.690983i | 0.672499 | − | 0.218508i | ||||
\(11\) | −3.75739 | − | 1.22085i | −1.13290 | − | 0.368100i | −0.318220 | − | 0.948017i | \(-0.603085\pi\) |
−0.814676 | + | 0.579917i | \(0.803085\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.45434 | + | 2.26960i | 1.23541 | + | 0.629473i | 0.944888 | − | 0.327394i | \(-0.106171\pi\) |
0.290524 | + | 0.956868i | \(0.406171\pi\) | |||||||
\(14\) | −0.561163 | + | 1.72708i | −0.149977 | + | 0.461582i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.309017 | − | 0.951057i | −0.0772542 | − | 0.237764i | ||||
\(17\) | −1.17159 | + | 7.39712i | −0.284152 | + | 1.79406i | 0.271278 | + | 0.962501i | \(0.412554\pi\) |
−0.555430 | + | 0.831563i | \(0.687446\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.22358 | + | 3.06050i | 0.510125 | + | 0.702126i | 0.983940 | − | 0.178498i | \(-0.0571237\pi\) |
−0.473816 | + | 0.880624i | \(0.657124\pi\) | |||||||
\(20\) | −1.58114 | − | 1.58114i | −0.353553 | − | 0.353553i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.618034 | + | 3.90211i | 0.131765 | + | 0.831933i | ||||
\(23\) | −8.36783 | + | 4.26362i | −1.74481 | + | 0.889027i | −0.780128 | + | 0.625619i | \(0.784846\pi\) |
−0.964685 | + | 0.263407i | \(0.915154\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.75528 | − | 1.54508i | −0.951057 | − | 0.309017i | ||||
\(26\) | − | 4.99922i | − | 0.980428i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.79360 | − | 0.284079i | 0.338959 | − | 0.0536859i | ||||
\(29\) | 4.12416 | + | 2.99638i | 0.765838 | + | 0.556414i | 0.900695 | − | 0.434451i | \(-0.143058\pi\) |
−0.134858 | + | 0.990865i | \(0.543058\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.17557 | + | 1.58064i | −0.390744 | + | 0.283892i | −0.765760 | − | 0.643126i | \(-0.777637\pi\) |
0.375016 | + | 0.927018i | \(0.377637\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.12277 | − | 2.31433i | 1.22154 | − | 0.396904i | ||||
\(35\) | 3.28511 | − | 2.38677i | 0.555284 | − | 0.403438i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.85588 | + | 7.56758i | −0.633902 | + | 1.24410i | 0.320971 | + | 0.947089i | \(0.395991\pi\) |
−0.954873 | + | 0.297014i | \(0.904009\pi\) | |||||||
\(38\) | 1.71744 | − | 3.37066i | 0.278605 | − | 0.546794i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.690983 | + | 2.12663i | −0.109254 | + | 0.336249i | ||||
\(41\) | 8.02285 | − | 2.60678i | 1.25296 | − | 0.407111i | 0.393979 | − | 0.919120i | \(-0.371098\pi\) |
0.858980 | + | 0.512008i | \(0.171098\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.0913225 | − | 0.0913225i | 0.0139265 | − | 0.0139265i | −0.700109 | − | 0.714036i | \(-0.746865\pi\) |
0.714036 | + | 0.700109i | \(0.246865\pi\) | |||||||
\(44\) | 3.19623 | − | 2.32219i | 0.481849 | − | 0.350084i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.59783 | + | 5.52015i | 1.12024 | + | 0.813901i | ||||
\(47\) | 0.407709 | − | 0.0645747i | 0.0594705 | − | 0.00941919i | −0.126628 | − | 0.991950i | \(-0.540416\pi\) |
0.186099 | + | 0.982531i | \(0.440416\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 3.70228i | − | 0.528897i | ||||||
\(50\) | 0.782172 | + | 4.93844i | 0.110616 | + | 0.698401i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −4.45434 | + | 2.26960i | −0.617706 | + | 0.314737i | ||||
\(53\) | −1.22699 | − | 7.74691i | −0.168540 | − | 1.06412i | −0.916400 | − | 0.400264i | \(-0.868918\pi\) |
0.747860 | − | 0.663857i | \(-0.231082\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.01062 | − | 7.87129i | 0.540792 | − | 1.06136i | ||||
\(56\) | −1.06740 | − | 1.46914i | −0.142637 | − | 0.196323i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.797463 | − | 5.03498i | 0.104712 | − | 0.661126i | ||||
\(59\) | 0.625738 | + | 1.92582i | 0.0814641 | + | 0.250721i | 0.983490 | − | 0.180960i | \(-0.0579206\pi\) |
−0.902026 | + | 0.431681i | \(0.857921\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.33245 | − | 4.10085i | 0.170602 | − | 0.525060i | −0.828803 | − | 0.559540i | \(-0.810978\pi\) |
0.999405 | + | 0.0344806i | \(0.0109777\pi\) | |||||||
\(62\) | 2.39605 | + | 1.22085i | 0.304299 | + | 0.155048i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.951057 | + | 0.309017i | 0.118882 | + | 0.0386271i | ||||
\(65\) | −6.57062 | + | 9.04368i | −0.814985 | + | 1.12173i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.64771 | + | 0.260971i | 0.201299 | + | 0.0318827i | 0.256270 | − | 0.966605i | \(-0.417506\pi\) |
−0.0549704 | + | 0.998488i | \(0.517506\pi\) | |||||||
\(68\) | −5.29575 | − | 5.29575i | −0.642204 | − | 0.642204i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.61803 | − | 1.84348i | −0.432438 | − | 0.220338i | ||||
\(71\) | 6.41138 | − | 8.82451i | 0.760891 | − | 1.04728i | −0.236249 | − | 0.971693i | \(-0.575918\pi\) |
0.997139 | − | 0.0755839i | \(-0.0240821\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.183899 | − | 0.360921i | −0.0215237 | − | 0.0422427i | 0.879994 | − | 0.474984i | \(-0.157546\pi\) |
−0.901518 | + | 0.432742i | \(0.857546\pi\) | |||||||
\(74\) | 8.49330 | 0.987326 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.78298 | −0.433938 | ||||||||
\(77\) | 3.25712 | + | 6.39245i | 0.371183 | + | 0.728488i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.18504 | + | 11.2657i | −0.920889 | + | 1.26749i | 0.0424201 | + | 0.999100i | \(0.486493\pi\) |
−0.963309 | + | 0.268395i | \(0.913507\pi\) | |||||||
\(80\) | 2.20854 | − | 0.349798i | 0.246922 | − | 0.0391086i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.96496 | − | 5.96496i | −0.658720 | − | 0.658720i | ||||
\(83\) | −0.680668 | − | 0.107807i | −0.0747131 | − | 0.0118334i | 0.118966 | − | 0.992898i | \(-0.462042\pi\) |
−0.193679 | + | 0.981065i | \(0.562042\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −15.9270 | − | 5.17499i | −1.72753 | − | 0.561307i | ||||
\(86\) | −0.122828 | − | 0.0399094i | −0.0132449 | − | 0.00430354i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.52015 | − | 1.79360i | −0.375249 | − | 0.191199i | ||||
\(89\) | 1.03224 | − | 3.17691i | 0.109417 | − | 0.336751i | −0.881325 | − | 0.472511i | \(-0.843348\pi\) |
0.990742 | + | 0.135760i | \(0.0433476\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.80538 | − | 8.63407i | −0.294084 | − | 0.905096i | ||||
\(92\) | 1.46914 | − | 9.27581i | 0.153169 | − | 0.967070i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.242632 | − | 0.333955i | −0.0250256 | − | 0.0344448i | ||||
\(95\) | −7.53703 | + | 3.84031i | −0.773283 | + | 0.394007i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.426119 | − | 2.69041i | −0.0432658 | − | 0.273169i | 0.956566 | − | 0.291516i | \(-0.0941597\pi\) |
−0.999832 | + | 0.0183468i | \(0.994160\pi\) | |||||||
\(98\) | −3.29876 | + | 1.68080i | −0.333225 | + | 0.169787i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.04508 | − | 2.93893i | 0.404508 | − | 0.293893i | ||||
\(101\) | − | 4.20442i | − | 0.418356i | −0.977878 | − | 0.209178i | \(-0.932921\pi\) | ||
0.977878 | − | 0.209178i | \(-0.0670788\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.4999 | − | 2.13818i | 1.33019 | − | 0.210681i | 0.549444 | − | 0.835531i | \(-0.314840\pi\) |
0.780745 | + | 0.624849i | \(0.214840\pi\) | |||||||
\(104\) | 4.04445 | + | 2.93847i | 0.396591 | + | 0.288141i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.34551 | + | 4.61028i | −0.616330 | + | 0.447790i | ||||
\(107\) | 0.309546 | − | 0.309546i | 0.0299249 | − | 0.0299249i | −0.691986 | − | 0.721911i | \(-0.743264\pi\) |
0.721911 | + | 0.691986i | \(0.243264\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −8.68806 | + | 2.82292i | −0.832165 | + | 0.270387i | −0.693957 | − | 0.720016i | \(-0.744134\pi\) |
−0.138208 | + | 0.990403i | \(0.544134\pi\) | |||||||
\(110\) | −8.83415 | −0.842303 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.824429 | + | 1.61803i | −0.0779013 | + | 0.152890i | ||||
\(113\) | −5.88788 | + | 11.5556i | −0.553885 | + | 1.08706i | 0.429079 | + | 0.903267i | \(0.358838\pi\) |
−0.982965 | + | 0.183794i | \(0.941162\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.48932 | − | 19.9721i | −0.605132 | − | 1.86241i | ||||
\(116\) | −4.84824 | + | 1.57529i | −0.450148 | + | 0.146262i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.43184 | − | 1.43184i | 0.131812 | − | 0.131812i | ||||
\(119\) | 11.0029 | − | 7.99407i | 1.00863 | − | 0.732815i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.72832 | + | 2.70878i | 0.338938 | + | 0.246253i | ||||
\(122\) | −4.25880 | + | 0.674528i | −0.385574 | + | 0.0610689i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 2.68915i | − | 0.241493i | ||||||
\(125\) | 5.07577 | − | 9.96176i | 0.453990 | − | 0.891007i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.15537 | + | 3.64584i | −0.634936 | + | 0.323516i | −0.741663 | − | 0.670772i | \(-0.765963\pi\) |
0.106727 | + | 0.994288i | \(0.465963\pi\) | |||||||
\(128\) | −0.156434 | − | 0.987688i | −0.0138270 | − | 0.0873001i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 11.0410 | + | 1.74872i | 0.968357 | + | 0.153373i | ||||
\(131\) | −8.66900 | − | 11.9319i | −0.757414 | − | 1.04249i | −0.997425 | − | 0.0717208i | \(-0.977151\pi\) |
0.240011 | − | 0.970770i | \(-0.422849\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.07467 | − | 6.78518i | 0.0931854 | − | 0.588349i | ||||
\(134\) | −0.515516 | − | 1.58660i | −0.0445338 | − | 0.137061i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.31433 | + | 7.12277i | −0.198452 | + | 0.610772i | ||||
\(137\) | 9.99117 | + | 5.09076i | 0.853604 | + | 0.434933i | 0.825319 | − | 0.564667i | \(-0.190995\pi\) |
0.0282849 | + | 0.999600i | \(0.490995\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8137 | + | 3.51358i | 0.917206 | + | 0.298018i | 0.729320 | − | 0.684173i | \(-0.239837\pi\) |
0.187886 | + | 0.982191i | \(0.439837\pi\) | |||||||
\(140\) | 4.06061i | 0.343185i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.7734 | − | 1.70634i | −0.904084 | − | 0.143193i | ||||
\(143\) | −13.9658 | − | 13.9658i | −1.16788 | − | 1.16788i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.06024 | + | 8.06024i | −0.669367 | + | 0.669367i | ||||
\(146\) | −0.238095 | + | 0.327710i | −0.0197049 | + | 0.0271215i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.85588 | − | 7.56758i | −0.316951 | − | 0.622051i | ||||
\(149\) | 10.8708 | 0.890569 | 0.445285 | − | 0.895389i | \(-0.353103\pi\) | ||||
0.445285 | + | 0.895389i | \(0.353103\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.0865 | 1.71600 | 0.857998 | − | 0.513653i | \(-0.171708\pi\) | ||||
0.857998 | + | 0.513653i | \(0.171708\pi\) | |||||||
\(152\) | 1.71744 | + | 3.37066i | 0.139303 | + | 0.273397i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.21702 | − | 5.80423i | 0.339817 | − | 0.467718i | ||||
\(155\) | −2.72990 | − | 5.35774i | −0.219271 | − | 0.430344i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.50271 | + | 6.50271i | 0.518972 | + | 0.518972i | 0.917260 | − | 0.398288i | \(-0.130396\pi\) |
−0.398288 | + | 0.917260i | \(0.630396\pi\) | |||||||
\(158\) | 13.7538 | + | 2.17838i | 1.09419 | + | 0.173303i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.31433 | − | 1.80902i | −0.103907 | − | 0.143015i | ||||
\(161\) | 16.2198 | + | 5.27013i | 1.27830 | + | 0.415344i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −14.3203 | − | 7.29657i | −1.12165 | − | 0.571511i | −0.208051 | − | 0.978118i | \(-0.566712\pi\) |
−0.913603 | + | 0.406607i | \(0.866712\pi\) | |||||||
\(164\) | −2.60678 | + | 8.02285i | −0.203556 | + | 0.626480i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.212960 | + | 0.655423i | 0.0165289 | + | 0.0508707i | ||||
\(167\) | −2.52299 | + | 15.9295i | −0.195235 | + | 1.23266i | 0.674175 | + | 0.738572i | \(0.264499\pi\) |
−0.869410 | + | 0.494092i | \(0.835501\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.04885 | + | 9.70190i | 0.542219 | + | 0.746300i | ||||
\(170\) | 2.61975 | + | 16.5405i | 0.200926 | + | 1.26859i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.0202034 | + | 0.127559i | 0.00154050 | + | 0.00972632i | ||||
\(173\) | −5.33223 | + | 2.71690i | −0.405402 | + | 0.206562i | −0.644787 | − | 0.764362i | \(-0.723054\pi\) |
0.239386 | + | 0.970925i | \(0.423054\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.12215 | + | 8.09017i | 0.311605 | + | 0.611559i | ||||
\(176\) | 3.95075i | 0.297799i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.29927 | + | 0.522553i | −0.247291 | + | 0.0391670i | ||||
\(179\) | −8.10451 | − | 5.88827i | −0.605760 | − | 0.440110i | 0.242159 | − | 0.970237i | \(-0.422144\pi\) |
−0.847919 | + | 0.530126i | \(0.822144\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.84011 | + | 2.79000i | −0.285433 | + | 0.207379i | −0.721284 | − | 0.692640i | \(-0.756448\pi\) |
0.435851 | + | 0.900019i | \(0.356448\pi\) | |||||||
\(182\) | −6.41940 | + | 6.41940i | −0.475837 | + | 0.475837i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.93179 | + | 2.90211i | −0.658460 | + | 0.213947i | ||||
\(185\) | −15.3645 | − | 11.1630i | −1.12962 | − | 0.820718i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 13.4329 | − | 26.3635i | 0.982310 | − | 1.92789i | ||||
\(188\) | −0.187403 | + | 0.367799i | −0.0136678 | + | 0.0268245i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.84348 | + | 4.97208i | 0.496478 | + | 0.360713i | ||||
\(191\) | 23.6587 | − | 7.68716i | 1.71188 | − | 0.556223i | 0.721235 | − | 0.692690i | \(-0.243575\pi\) |
0.990645 | + | 0.136467i | \(0.0435747\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.55217 | + | 9.55217i | −0.687580 | + | 0.687580i | −0.961697 | − | 0.274116i | \(-0.911615\pi\) |
0.274116 | + | 0.961697i | \(0.411615\pi\) | |||||||
\(194\) | −2.20372 | + | 1.60109i | −0.158218 | + | 0.114952i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 2.99521 | + | 2.17615i | 0.213944 | + | 0.155439i | ||||
\(197\) | 3.51260 | − | 0.556341i | 0.250262 | − | 0.0396377i | −0.0300428 | − | 0.999549i | \(-0.509564\pi\) |
0.280305 | + | 0.959911i | \(0.409564\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.7236i | 0.831067i | 0.909578 | + | 0.415533i | \(0.136405\pi\) | ||||
−0.909578 | + | 0.415533i | \(0.863595\pi\) | |||||||
\(200\) | −4.45503 | − | 2.26995i | −0.315018 | − | 0.160510i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.74617 | + | 1.90877i | −0.263580 | + | 0.134301i | ||||
\(203\) | −1.44816 | − | 9.14334i | −0.101641 | − | 0.641737i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.95080 | + | 18.6306i | 0.206093 | + | 1.30122i | ||||
\(206\) | −8.03398 | − | 11.0578i | −0.559754 | − | 0.770435i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.782051 | − | 4.93767i | 0.0542254 | − | 0.342366i | ||||
\(209\) | −4.61845 | − | 14.2141i | −0.319465 | − | 0.983213i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.13703 | − | 25.0432i | 0.560176 | − | 1.72404i | −0.121690 | − | 0.992568i | \(-0.538831\pi\) |
0.681866 | − | 0.731477i | \(-0.261169\pi\) | |||||||
\(212\) | 6.98859 | + | 3.56087i | 0.479978 | + | 0.244561i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.416338 | − | 0.135276i | −0.0284603 | − | 0.00924731i | ||||
\(215\) | 0.169745 | + | 0.233634i | 0.0115765 | + | 0.0159337i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.82328 | + | 0.763932i | 0.327425 | + | 0.0518591i | ||||
\(218\) | 6.45954 | + | 6.45954i | 0.437495 | + | 0.437495i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.01062 | + | 7.87129i | 0.270396 | + | 0.530682i | ||||
\(221\) | −22.0071 | + | 30.2902i | −1.48036 | + | 2.03754i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.7063 | + | 22.9750i | 0.783914 | + | 1.53852i | 0.841549 | + | 0.540181i | \(0.181644\pi\) |
−0.0576344 | + | 0.998338i | \(0.518356\pi\) | |||||||
\(224\) | 1.81596 | 0.121334 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 12.9692 | 0.862697 | ||||||||
\(227\) | 0.0662680 | + | 0.130058i | 0.00439836 | + | 0.00863227i | 0.893195 | − | 0.449669i | \(-0.148458\pi\) |
−0.888797 | + | 0.458301i | \(0.848458\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.1985 | + | 15.4134i | −0.740015 | + | 1.01854i | 0.258603 | + | 0.965984i | \(0.416738\pi\) |
−0.998618 | + | 0.0525595i | \(0.983262\pi\) | |||||||
\(230\) | −14.8492 | + | 14.8492i | −0.979125 | + | 0.979125i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.60465 | + | 3.60465i | 0.236657 | + | 0.236657i | ||||
\(233\) | 8.40064 | + | 1.33053i | 0.550344 | + | 0.0871660i | 0.425413 | − | 0.904999i | \(-0.360129\pi\) |
0.124931 | + | 0.992165i | \(0.460129\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.923029i | 0.0602118i | ||||||||
\(236\) | −1.92582 | − | 0.625738i | −0.125360 | − | 0.0407321i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −12.1180 | − | 6.17442i | −0.785492 | − | 0.400228i | ||||
\(239\) | −4.16282 | + | 12.8118i | −0.269271 | + | 0.828730i | 0.721408 | + | 0.692510i | \(0.243495\pi\) |
−0.990679 | + | 0.136219i | \(0.956505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.14111 | + | 9.66733i | 0.202336 | + | 0.622728i | 0.999812 | + | 0.0193767i | \(0.00616819\pi\) |
−0.797476 | + | 0.603351i | \(0.793832\pi\) | |||||||
\(242\) | 0.720921 | − | 4.55171i | 0.0463425 | − | 0.292595i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2.53446 | + | 3.48839i | 0.162252 | + | 0.223321i | ||||
\(245\) | 8.17663 | + | 1.29505i | 0.522386 | + | 0.0827378i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.95848 | + | 18.6791i | 0.188244 | + | 1.18852i | ||||
\(248\) | −2.39605 | + | 1.22085i | −0.152150 | + | 0.0775240i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.1803 | −0.707107 | ||||||||
\(251\) | 9.38052i | 0.592093i | 0.955174 | + | 0.296047i | \(0.0956683\pi\) | ||||
−0.955174 | + | 0.296047i | \(0.904332\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 36.6464 | − | 5.80423i | 2.30394 | − | 0.364909i | ||||
\(254\) | 6.49694 | + | 4.72030i | 0.407654 | + | 0.296178i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | 2.22859 | − | 2.22859i | 0.139016 | − | 0.139016i | −0.634174 | − | 0.773190i | \(-0.718660\pi\) |
0.773190 | + | 0.634174i | \(0.218660\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.6686 | − | 4.76612i | 0.911464 | − | 0.296153i | ||||
\(260\) | −3.45438 | − | 10.6315i | −0.214231 | − | 0.659336i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.69572 | + | 13.1411i | −0.413663 | + | 0.811859i | ||||
\(263\) | 10.5219 | − | 20.6504i | 0.648809 | − | 1.27336i | −0.298919 | − | 0.954279i | \(-0.596626\pi\) |
0.947728 | − | 0.319080i | \(-0.103374\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.5386 | 1.07738 | ||||||||
\(266\) | −6.53352 | + | 2.12287i | −0.400596 | + | 0.130162i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.17963 | + | 1.17963i | −0.0720572 | + | 0.0720572i | ||||
\(269\) | 5.69732 | − | 4.13934i | 0.347372 | − | 0.252380i | −0.400394 | − | 0.916343i | \(-0.631127\pi\) |
0.747766 | + | 0.663963i | \(0.231127\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6553 | + | 8.46808i | 0.708010 | + | 0.514399i | 0.882531 | − | 0.470254i | \(-0.155838\pi\) |
−0.174521 | + | 0.984653i | \(0.555838\pi\) | |||||||
\(272\) | 7.39712 | − | 1.17159i | 0.448516 | − | 0.0710380i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 11.2134i | − | 0.677424i | ||||||
\(275\) | 15.9811 | + | 11.6110i | 0.963699 | + | 0.700168i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 16.5331 | − | 8.42403i | 0.993378 | − | 0.506151i | 0.119780 | − | 0.992800i | \(-0.461781\pi\) |
0.873597 | + | 0.486649i | \(0.161781\pi\) | |||||||
\(278\) | −1.77869 | − | 11.2302i | −0.106679 | − | 0.673543i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.61803 | − | 1.84348i | 0.216219 | − | 0.110169i | ||||
\(281\) | −11.5453 | − | 15.8908i | −0.688735 | − | 0.947963i | 0.311262 | − | 0.950324i | \(-0.399248\pi\) |
−0.999997 | + | 0.00236125i | \(0.999248\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.11102 | + | 7.01468i | −0.0660430 | + | 0.416979i | 0.932411 | + | 0.361399i | \(0.117701\pi\) |
−0.998454 | + | 0.0555802i | \(0.982299\pi\) | |||||||
\(284\) | 3.37066 | + | 10.3738i | 0.200012 | + | 0.615574i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.10330 | + | 18.7840i | −0.360896 | + | 1.11072i | ||||
\(287\) | −13.6493 | − | 6.95466i | −0.805692 | − | 0.410521i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −37.1767 | − | 12.0795i | −2.18687 | − | 0.710556i | ||||
\(290\) | 10.8410 | + | 3.52246i | 0.636606 | + | 0.206846i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0.400084 | + | 0.0633672i | 0.0234132 | + | 0.00370828i | ||||
\(293\) | 15.5402 | + | 15.5402i | 0.907869 | + | 0.907869i | 0.996100 | − | 0.0882312i | \(-0.0281214\pi\) |
−0.0882312 | + | 0.996100i | \(0.528121\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.47214 | + | 0.708317i | −0.260378 | + | 0.0412398i | ||||
\(296\) | −4.99223 | + | 6.87122i | −0.290168 | + | 0.399382i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.93523 | − | 9.68594i | −0.285890 | − | 0.561091i | ||||
\(299\) | −46.9499 | −2.71518 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.234531 | −0.0135181 | ||||||||
\(302\) | −9.57308 | − | 18.7882i | −0.550869 | − | 1.08114i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.22358 | − | 3.06050i | 0.127531 | − | 0.175532i | ||||
\(305\) | 8.59079 | + | 4.37723i | 0.491907 | + | 0.250639i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.79953 | − | 1.79953i | −0.102704 | − | 0.102704i | 0.653887 | − | 0.756592i | \(-0.273137\pi\) |
−0.756592 | + | 0.653887i | \(0.773137\pi\) | |||||||
\(308\) | −7.08609 | − | 1.12233i | −0.403767 | − | 0.0639505i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −3.53443 | + | 4.86472i | −0.200742 | + | 0.276298i | ||||
\(311\) | 2.94129 | + | 0.955682i | 0.166785 | + | 0.0541917i | 0.391219 | − | 0.920297i | \(-0.372053\pi\) |
−0.224434 | + | 0.974489i | \(0.572053\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.9683 | − | 6.60767i | −0.733010 | − | 0.373487i | 0.0472993 | − | 0.998881i | \(-0.484939\pi\) |
−0.780310 | + | 0.625393i | \(0.784939\pi\) | |||||||
\(314\) | 2.84179 | − | 8.74612i | 0.160371 | − | 0.493572i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.30313 | − | 13.2437i | −0.242070 | − | 0.745015i | ||||
\(317\) | −0.731491 | + | 4.61845i | −0.0410846 | + | 0.259398i | −0.999678 | − | 0.0253807i | \(-0.991920\pi\) |
0.958593 | + | 0.284779i | \(0.0919202\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −11.8380 | − | 16.2935i | −0.662798 | − | 0.912264i | ||||
\(320\) | −1.01515 | + | 1.99235i | −0.0567488 | + | 0.111376i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.66791 | − | 16.8445i | −0.148677 | − | 0.938708i | ||||
\(323\) | −25.2440 | + | 12.8624i | −1.40461 | + | 0.715686i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.6749 | − | 17.6749i | −0.980428 | − | 0.980428i | ||||
\(326\) | 16.0721i | 0.890149i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.33187 | − | 1.31964i | 0.460051 | − | 0.0728649i | ||||
\(329\) | −0.606449 | − | 0.440611i | −0.0334346 | − | 0.0242917i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.4424 | + | 16.3053i | −1.23354 | + | 0.896222i | −0.997151 | − | 0.0754361i | \(-0.975965\pi\) |
−0.236393 | + | 0.971658i | \(0.575965\pi\) | |||||||
\(332\) | 0.487305 | − | 0.487305i | 0.0267443 | − | 0.0267443i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.3387 | − | 4.98385i | 0.839298 | − | 0.272704i | ||||
\(335\) | −1.15273 | + | 3.54774i | −0.0629803 | + | 0.193834i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.66328 | − | 17.0026i | 0.471919 | − | 0.926193i | −0.525246 | − | 0.850950i | \(-0.676027\pi\) |
0.997165 | − | 0.0752430i | \(-0.0239732\pi\) | |||||||
\(338\) | 5.44435 | − | 10.6851i | 0.296134 | − | 0.581195i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 13.5483 | − | 9.84342i | 0.734760 | − | 0.533835i | ||||
\(341\) | 10.1042 | − | 3.28305i | 0.547173 | − | 0.177787i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.7426 | + | 13.7426i | −0.742029 | + | 0.742029i | ||||
\(344\) | 0.104484 | − | 0.0759122i | 0.00563341 | − | 0.00409291i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.84156 | + | 3.51760i | 0.260284 | + | 0.189107i | ||||
\(347\) | 8.05268 | − | 1.27542i | 0.432291 | − | 0.0684681i | 0.0635027 | − | 0.997982i | \(-0.479773\pi\) |
0.368788 | + | 0.929514i | \(0.379773\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.60220i | − | 0.299879i | −0.988695 | − | 0.149940i | \(-0.952092\pi\) | ||
0.988695 | − | 0.149940i | \(-0.0479079\pi\) | |||||||
\(350\) | 5.33698 | − | 7.34572i | 0.285273 | − | 0.392645i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.52015 | − | 1.79360i | 0.187624 | − | 0.0955994i | ||||
\(353\) | 2.15819 | + | 13.6263i | 0.114869 | + | 0.725253i | 0.976146 | + | 0.217117i | \(0.0696652\pi\) |
−0.861277 | + | 0.508136i | \(0.830335\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.2466 | + | 17.2466i | 0.915353 | + | 0.915353i | ||||
\(356\) | 1.96344 | + | 2.70244i | 0.104062 | + | 0.143229i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.56712 | + | 9.89440i | −0.0828248 | + | 0.522935i | ||||
\(359\) | −8.04326 | − | 24.7546i | −0.424507 | − | 1.30650i | −0.903465 | − | 0.428661i | \(-0.858985\pi\) |
0.478958 | − | 0.877838i | \(-0.341015\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44899 | − | 4.45954i | 0.0762628 | − | 0.234713i | ||||
\(362\) | 4.22928 | + | 2.15493i | 0.222286 | + | 0.113260i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 8.63407 | + | 2.80538i | 0.452548 | + | 0.147042i | ||||
\(365\) | 0.861436 | − | 0.279898i | 0.0450896 | − | 0.0146505i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.07768 | − | 0.804226i | −0.265053 | − | 0.0419803i | 0.0224934 | − | 0.999747i | \(-0.492840\pi\) |
−0.287546 | + | 0.957767i | \(0.592840\pi\) | |||||||
\(368\) | 6.64075 | + | 6.64075i | 0.346173 | + | 0.346173i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.97094 | + | 18.7578i | −0.154452 | + | 0.975170i | ||||
\(371\) | −8.37210 | + | 11.5232i | −0.434658 | + | 0.598255i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −6.25519 | − | 12.2765i | −0.323882 | − | 0.635653i | 0.670453 | − | 0.741952i | \(-0.266100\pi\) |
−0.994334 | + | 0.106299i | \(0.966100\pi\) | |||||||
\(374\) | −29.5885 | −1.52998 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0.412791 | 0.0212881 | ||||||||
\(377\) | 11.5698 | + | 22.7071i | 0.595877 | + | 1.16947i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.60074 | − | 3.57960i | 0.133591 | − | 0.183872i | −0.736981 | − | 0.675914i | \(-0.763749\pi\) |
0.870572 | + | 0.492042i | \(0.163749\pi\) | |||||||
\(380\) | 1.32328 | − | 8.35486i | 0.0678828 | − | 0.428595i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −17.5901 | − | 17.5901i | −0.899989 | − | 0.899989i | ||||
\(383\) | 23.2779 | + | 3.68685i | 1.18944 | + | 0.188389i | 0.719618 | − | 0.694370i | \(-0.244317\pi\) |
0.469826 | + | 0.882759i | \(0.344317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15.2573 | + | 4.95740i | −0.777585 | + | 0.252653i | ||||
\(386\) | 12.8476 | + | 4.17445i | 0.653928 | + | 0.212474i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.42705 | + | 1.23664i | 0.123215 | + | 0.0627811i | ||||
\(389\) | −3.51895 | + | 10.8302i | −0.178418 | + | 0.549114i | −0.999773 | − | 0.0213032i | \(-0.993218\pi\) |
0.821355 | + | 0.570417i | \(0.193218\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.7349 | − | 66.8930i | −1.09918 | − | 3.38293i | ||||
\(392\) | 0.579165 | − | 3.65670i | 0.0292522 | − | 0.184691i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.09039 | − | 2.87718i | −0.105312 | − | 0.144950i | ||||
\(395\) | −22.0177 | − | 22.0177i | −1.10783 | − | 1.10783i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.77709 | − | 17.5338i | −0.139378 | − | 0.879998i | −0.953957 | − | 0.299945i | \(-0.903032\pi\) |
0.814579 | − | 0.580053i | \(-0.196968\pi\) | |||||||
\(398\) | 10.4458 | − | 5.32242i | 0.523603 | − | 0.266789i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000i | 0.250000i | ||||||||
\(401\) | − | 4.48497i | − | 0.223969i | −0.993710 | − | 0.111984i | \(-0.964279\pi\) | ||
0.993710 | − | 0.111984i | \(-0.0357207\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.2782 | + | 2.10305i | −0.661432 | + | 0.104761i | ||||
\(404\) | 3.40145 | + | 2.47130i | 0.169229 | + | 0.122952i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −7.48932 | + | 5.44131i | −0.371689 | + | 0.270048i | ||||
\(407\) | 23.7269 | − | 23.7269i | 1.17610 | − | 1.17610i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −13.9740 | + | 4.54042i | −0.690968 | + | 0.224509i | −0.633391 | − | 0.773832i | \(-0.718338\pi\) |
−0.0575771 | + | 0.998341i | \(0.518338\pi\) | |||||||
\(410\) | 15.2604 | − | 11.0873i | 0.753656 | − | 0.547563i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −6.20524 | + | 12.1785i | −0.305710 | + | 0.599990i | ||||
\(413\) | 1.66941 | − | 3.27641i | 0.0821464 | − | 0.161221i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.476193 | − | 1.46557i | 0.0233754 | − | 0.0719421i | ||||
\(416\) | −4.75454 | + | 1.54484i | −0.233111 | + | 0.0757422i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −10.5682 | + | 10.5682i | −0.516906 | + | 0.516906i | ||||
\(419\) | −11.7751 | + | 8.55510i | −0.575250 | + | 0.417944i | −0.837009 | − | 0.547190i | \(-0.815698\pi\) |
0.261758 | + | 0.965133i | \(0.415698\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.4271 | + | 14.1146i | 0.946818 | + | 0.687904i | 0.950052 | − | 0.312091i | \(-0.101029\pi\) |
−0.00323396 | + | 0.999995i | \(0.501029\pi\) | |||||||
\(422\) | −26.0078 | + | 4.11923i | −1.26604 | + | 0.200521i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 7.84348i | − | 0.380913i | ||||||
\(425\) | 17.0004 | − | 33.3652i | 0.824641 | − | 1.61845i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.97678 | + | 3.55485i | −0.337630 | + | 0.172031i | ||||
\(428\) | 0.0684814 | + | 0.432374i | 0.00331017 | + | 0.0208996i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.131107 | − | 0.257311i | 0.00632252 | − | 0.0124086i | ||||
\(431\) | 20.6224 | + | 28.3843i | 0.993347 | + | 1.36723i | 0.929319 | + | 0.369277i | \(0.120395\pi\) |
0.0640277 | + | 0.997948i | \(0.479605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.494242 | − | 3.12052i | 0.0237517 | − | 0.149963i | −0.972962 | − | 0.230964i | \(-0.925812\pi\) |
0.996714 | + | 0.0810017i | \(0.0258119\pi\) | |||||||
\(434\) | −1.50905 | − | 4.64439i | −0.0724369 | − | 0.222938i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.82292 | − | 8.68806i | 0.135193 | − | 0.416082i | ||||
\(437\) | −31.6554 | − | 16.1292i | −1.51428 | − | 0.771565i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.5487 | + | 5.05207i | 0.742097 | + | 0.241122i | 0.655577 | − | 0.755128i | \(-0.272425\pi\) |
0.0865201 | + | 0.996250i | \(0.472425\pi\) | |||||||
\(440\) | 5.19258 | − | 7.14698i | 0.247547 | − | 0.340719i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 36.9798 | + | 5.85703i | 1.75895 | + | 0.278590i | ||||
\(443\) | 0.530898 | + | 0.530898i | 0.0252237 | + | 0.0252237i | 0.719606 | − | 0.694382i | \(-0.244322\pi\) |
−0.694382 | + | 0.719606i | \(0.744322\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.65524 | + | 3.39102i | 0.315489 | + | 0.160750i | ||||
\(446\) | 15.1563 | − | 20.8608i | 0.717671 | − | 0.987790i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.824429 | − | 1.61803i | −0.0389506 | − | 0.0764449i | ||||
\(449\) | 13.4807 | 0.636192 | 0.318096 | − | 0.948059i | \(-0.396957\pi\) | ||||
0.318096 | + | 0.948059i | \(0.396957\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −33.3275 | −1.56933 | ||||||||
\(452\) | −5.88788 | − | 11.5556i | −0.276943 | − | 0.543531i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.0857977 | − | 0.118090i | 0.00402669 | − | 0.00554226i | ||||
\(455\) | 20.0500 | − | 3.17561i | 0.939958 | − | 0.148875i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.7163 | + | 18.7163i | 0.875512 | + | 0.875512i | 0.993066 | − | 0.117554i | \(-0.0375053\pi\) |
−0.117554 | + | 0.993066i | \(0.537505\pi\) | |||||||
\(458\) | 18.8174 | + | 2.98038i | 0.879279 | + | 0.139264i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 19.9721 | + | 6.48932i | 0.931203 | + | 0.302566i | ||||
\(461\) | −22.2113 | − | 7.21690i | −1.03448 | − | 0.336125i | −0.257923 | − | 0.966165i | \(-0.583038\pi\) |
−0.776562 | + | 0.630041i | \(0.783038\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9.41860 | − | 4.79902i | −0.437719 | − | 0.223029i | 0.221222 | − | 0.975223i | \(-0.428995\pi\) |
−0.658941 | + | 0.752194i | \(0.728995\pi\) | |||||||
\(464\) | 1.57529 | − | 4.84824i | 0.0731310 | − | 0.225074i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.62830 | − | 8.08907i | −0.121754 | − | 0.374719i | ||||
\(467\) | 5.31450 | − | 33.5545i | 0.245926 | − | 1.55272i | −0.487608 | − | 0.873063i | \(-0.662131\pi\) |
0.733534 | − | 0.679653i | \(-0.237869\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.78068 | − | 2.45089i | −0.0822241 | − | 0.113172i | ||||
\(470\) | 0.822425 | − | 0.419046i | 0.0379356 | − | 0.0193292i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.316769 | + | 2.00000i | 0.0145805 | + | 0.0920575i | ||||
\(473\) | −0.454625 | + | 0.231643i | −0.0209037 | + | 0.0106510i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −5.84503 | − | 17.9892i | −0.268188 | − | 0.825399i | ||||
\(476\) | 13.6003i | 0.623370i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.3053 | − | 2.10736i | 0.608571 | − | 0.0963882i | ||||
\(479\) | 31.2773 | + | 22.7243i | 1.42910 | + | 1.03830i | 0.990184 | + | 0.139771i | \(0.0446367\pi\) |
0.438914 | + | 0.898529i | \(0.355363\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −34.3508 | + | 24.9573i | −1.56626 | + | 1.13795i | ||||
\(482\) | 7.18762 | − | 7.18762i | 0.327387 | − | 0.327387i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.38290 | + | 1.42409i | −0.199223 | + | 0.0647314i | ||||
\(485\) | 6.09092 | 0.276575 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.91273 | + | 17.4922i | −0.403875 | + | 0.792648i | −0.999947 | − | 0.0102821i | \(-0.996727\pi\) |
0.596073 | + | 0.802931i | \(0.296727\pi\) | |||||||
\(488\) | 1.95756 | − | 3.84192i | 0.0886144 | − | 0.173916i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.55821 | − | 7.87337i | −0.115568 | − | 0.355683i | ||||
\(491\) | 7.53071 | − | 2.44688i | 0.339856 | − | 0.110426i | −0.134116 | − | 0.990966i | \(-0.542820\pi\) |
0.473973 | + | 0.880540i | \(0.342820\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −26.9964 | + | 26.9964i | −1.21586 | + | 1.21586i | ||||
\(494\) | 15.3001 | − | 11.1162i | 0.688384 | − | 0.500140i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.17557 | + | 1.58064i | 0.0976860 | + | 0.0709730i | ||||
\(497\) | −19.5641 | + | 3.09865i | −0.877569 | + | 0.138993i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6.96924i | − | 0.311986i | −0.987758 | − | 0.155993i | \(-0.950142\pi\) | ||
0.987758 | − | 0.155993i | \(-0.0498578\pi\) | |||||||
\(500\) | 5.07577 | + | 9.96176i | 0.226995 | + | 0.445503i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 8.35810 | − | 4.25867i | 0.373040 | − | 0.190074i | ||||
\(503\) | 6.03430 | + | 38.0991i | 0.269056 | + | 1.69875i | 0.638599 | + | 0.769539i | \(0.279514\pi\) |
−0.369543 | + | 0.929214i | \(0.620486\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.28563 | + | 1.47070i | 0.413205 | + | 0.0654453i | ||||
\(506\) | −21.8087 | − | 30.0172i | −0.969517 | − | 1.33443i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.25627 | − | 7.93179i | 0.0557380 | − | 0.351916i | ||||
\(509\) | −0.608017 | − | 1.87128i | −0.0269499 | − | 0.0829432i | 0.936677 | − | 0.350195i | \(-0.113885\pi\) |
−0.963627 | + | 0.267251i | \(0.913885\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.227311 | + | 0.699592i | −0.0100557 | + | 0.0309481i | ||||
\(512\) | 0.891007 | + | 0.453990i | 0.0393773 | + | 0.0200637i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −2.99745 | − | 0.973931i | −0.132212 | − | 0.0429583i | ||||
\(515\) | 30.5631i | 1.34677i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.61076 | − | 0.255119i | −0.0708410 | − | 0.0112201i | ||||
\(518\) | −10.9061 | − | 10.9061i | −0.479185 | − | 0.479185i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −7.90446 | + | 7.90446i | −0.346634 | + | 0.346634i | ||||
\(521\) | −18.4841 | + | 25.4412i | −0.809804 | + | 1.11460i | 0.181549 | + | 0.983382i | \(0.441889\pi\) |
−0.991354 | + | 0.131218i | \(0.958111\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 13.8578 | + | 27.1975i | 0.605961 | + | 1.18926i | 0.966535 | + | 0.256534i | \(0.0825807\pi\) |
−0.360574 | + | 0.932730i | \(0.617419\pi\) | |||||||
\(524\) | 14.7486 | 0.644295 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.1765 | −1.01054 | ||||||||
\(527\) | −9.14334 | − | 17.9448i | −0.398290 | − | 0.781688i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 38.3230 | − | 52.7471i | 1.66622 | − | 2.29335i | ||||
\(530\) | −7.96234 | − | 15.6270i | −0.345862 | − | 0.678792i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.85765 | + | 4.85765i | 0.210606 | + | 0.210606i | ||||
\(533\) | 41.6529 | + | 6.59717i | 1.80419 | + | 0.285755i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.575365 | + | 0.791922i | 0.0248752 | + | 0.0342378i | ||||
\(536\) | 1.58660 | + | 0.515516i | 0.0685305 | + | 0.0222669i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.27471 | − | 3.19713i | −0.270522 | − | 0.137838i | ||||
\(539\) | −4.51993 | + | 13.9109i | −0.194687 | + | 0.599186i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.72668 | − | 20.7026i | −0.289202 | − | 0.890074i | −0.985107 | − | 0.171940i | \(-0.944997\pi\) |
0.695905 | − | 0.718134i | \(-0.255003\pi\) | |||||||
\(542\) | 2.25371 | − | 14.2294i | 0.0968053 | − | 0.611204i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −4.40211 | − | 6.05899i | −0.188739 | − | 0.259777i | ||||
\(545\) | −3.19546 | − | 20.1754i | −0.136879 | − | 0.864217i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.54680 | − | 16.0799i | −0.108893 | − | 0.687526i | −0.980382 | − | 0.197109i | \(-0.936845\pi\) |
0.871488 | − | 0.490417i | \(-0.163155\pi\) | |||||||
\(548\) | −9.99117 | + | 5.09076i | −0.426802 | + | 0.217466i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.09017 | − | 19.5106i | 0.131765 | − | 0.831933i | ||||
\(551\) | 19.2847i | 0.821555i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 24.9763 | − | 3.95586i | 1.06210 | − | 0.168220i | ||||
\(554\) | −15.0117 | − | 10.9067i | −0.637788 | − | 0.463380i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.19868 | + | 6.68323i | −0.390111 | + | 0.283432i | ||||
\(557\) | −12.0707 | + | 12.0707i | −0.511450 | + | 0.511450i | −0.914971 | − | 0.403520i | \(-0.867786\pi\) |
0.403520 | + | 0.914971i | \(0.367786\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.614047 | − | 0.199516i | 0.0259714 | − | 0.00843862i | ||||
\(560\) | −3.28511 | − | 2.38677i | −0.138821 | − | 0.100859i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.91731 | + | 17.5012i | −0.376154 | + | 0.738243i | ||||
\(563\) | −7.27841 | + | 14.2847i | −0.306748 | + | 0.602027i | −0.991994 | − | 0.126285i | \(-0.959695\pi\) |
0.685246 | + | 0.728312i | \(0.259695\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.4615 | − | 17.0457i | −0.987031 | − | 0.717120i | ||||
\(566\) | 6.75452 | − | 2.19468i | 0.283913 | − | 0.0922491i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.71290 | − | 7.71290i | 0.323626 | − | 0.323626i | ||||
\(569\) | −28.1494 | + | 20.4518i | −1.18009 | + | 0.857382i | −0.992181 | − | 0.124805i | \(-0.960169\pi\) |
−0.187904 | + | 0.982187i | \(0.560169\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.17087 | − | 0.850687i | −0.0489994 | − | 0.0356002i | 0.563016 | − | 0.826446i | \(-0.309641\pi\) |
−0.612015 | + | 0.790846i | \(0.709641\pi\) | |||||||
\(572\) | 19.5075 | − | 3.08969i | 0.815651 | − | 0.129186i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.3190i | 0.639401i | ||||||||
\(575\) | 46.3791 | − | 7.34572i | 1.93414 | − | 0.306338i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.9356 | − | 9.13864i | 0.746668 | − | 0.380446i | −0.0388824 | − | 0.999244i | \(-0.512380\pi\) |
0.785551 | + | 0.618797i | \(0.212380\pi\) | |||||||
\(578\) | 6.11501 | + | 38.6087i | 0.254351 | + | 1.60591i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.78318 | − | 11.2586i | −0.0740426 | − | 0.467486i | ||||
\(581\) | 0.735599 | + | 1.01247i | 0.0305178 | + | 0.0420041i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.84754 | + | 30.6061i | −0.200764 | + | 1.26758i | ||||
\(584\) | −0.125174 | − | 0.385246i | −0.00517974 | − | 0.0159416i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.79132 | − | 20.9015i | 0.280547 | − | 0.863435i | ||||
\(587\) | −29.3326 | − | 14.9457i | −1.21069 | − | 0.616875i | −0.272215 | − | 0.962236i | \(-0.587756\pi\) |
−0.938470 | + | 0.345361i | \(0.887756\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.67512 | − | 3.14364i | −0.398656 | − | 0.129531i | ||||
\(590\) | 2.66142 | + | 3.66313i | 0.109569 | + | 0.150809i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.38873 | + | 1.32864i | 0.344775 | + | 0.0546069i | ||||
\(593\) | −13.2453 | − | 13.2453i | −0.543920 | − | 0.543920i | 0.380756 | − | 0.924676i | \(-0.375664\pi\) |
−0.924676 | + | 0.380756i | \(0.875664\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 13.8064 | + | 27.0966i | 0.566008 | + | 1.11085i | ||||
\(596\) | −6.38968 | + | 8.79465i | −0.261732 | + | 0.360243i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.3148 | + | 41.8326i | 0.871627 | + | 1.71066i | ||||
\(599\) | 5.34213 | 0.218274 | 0.109137 | − | 0.994027i | \(-0.465191\pi\) | ||||
0.109137 | + | 0.994027i | \(0.465191\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 30.5114 | 1.24459 | 0.622293 | − | 0.782785i | \(-0.286201\pi\) | ||||
0.622293 | + | 0.782785i | \(0.286201\pi\) | |||||||
\(602\) | 0.106475 | + | 0.208968i | 0.00433958 | + | 0.00851691i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12.3943 | + | 17.0593i | −0.504319 | + | 0.694135i | ||||
\(605\) | −7.28660 | + | 7.28660i | −0.296243 | + | 0.296243i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.27295 | + | 2.27295i | 0.0922561 | + | 0.0922561i | 0.751729 | − | 0.659473i | \(-0.229220\pi\) |
−0.659473 | + | 0.751729i | \(0.729220\pi\) | |||||||
\(608\) | −3.73641 | − | 0.591789i | −0.151531 | − | 0.0240002i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 9.64167i | − | 0.390380i | ||||||
\(611\) | 1.96263 | + | 0.637698i | 0.0793996 | + | 0.0257985i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.99219 | − | 3.56270i | −0.282412 | − | 0.143896i | 0.307047 | − | 0.951694i | \(-0.400659\pi\) |
−0.589459 | + | 0.807798i | \(0.700659\pi\) | |||||||
\(614\) | −0.786422 | + | 2.42036i | −0.0317374 | + | 0.0976777i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.21702 | + | 6.82328i | 0.0893262 | + | 0.274918i | ||||
\(617\) | −2.34372 | + | 14.7976i | −0.0943545 | + | 0.595731i | 0.894526 | + | 0.447017i | \(0.147513\pi\) |
−0.988880 | + | 0.148714i | \(0.952487\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.8199 | + | 23.1506i | 0.676047 | + | 0.930499i | 0.999878 | − | 0.0156157i | \(-0.00497083\pi\) |
−0.323831 | + | 0.946115i | \(0.604971\pi\) | |||||||
\(620\) | 5.93910 | + | 0.940661i | 0.238520 | + | 0.0377778i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.483797 | − | 3.05458i | −0.0193985 | − | 0.122477i | ||||
\(623\) | −5.40488 | + | 2.75392i | −0.216542 | + | 0.110334i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 20.2254 | + | 14.6946i | 0.809017 | + | 0.587785i | ||||
\(626\) | 14.5546i | 0.581720i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.08299 | + | 1.43860i | −0.362451 | + | 0.0574066i | ||||
\(629\) | −51.4608 | − | 37.3884i | −2.05188 | − | 1.49078i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.6803 | + | 19.3844i | −1.06213 | + | 0.771679i | −0.974480 | − | 0.224473i | \(-0.927934\pi\) |
−0.0876449 | + | 0.996152i | \(0.527934\pi\) | |||||||
\(632\) | −9.84662 | + | 9.84662i | −0.391677 | + | 0.391677i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.44716 | − | 1.44497i | 0.176619 | − | 0.0573871i | ||||
\(635\) | −5.54905 | − | 17.0782i | −0.220207 | − | 0.677728i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.40270 | − | 16.4912i | 0.332927 | − | 0.653406i | ||||
\(638\) | −9.14334 | + | 17.9448i | −0.361988 | + | 0.710442i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.23607 | 0.0883883 | ||||||||
\(641\) | 3.70952 | − | 1.20529i | 0.146517 | − | 0.0476063i | −0.234840 | − | 0.972034i | \(-0.575457\pi\) |
0.381357 | + | 0.924428i | \(0.375457\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.3761 | − | 24.3761i | 0.961300 | − | 0.961300i | −0.0379785 | − | 0.999279i | \(-0.512092\pi\) |
0.999279 | + | 0.0379785i | \(0.0120918\pi\) | |||||||
\(644\) | −13.7974 | + | 10.0244i | −0.543693 | + | 0.395016i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 22.9211 | + | 16.6531i | 0.901817 | + | 0.655208i | ||||
\(647\) | 16.2504 | − | 2.57381i | 0.638869 | − | 0.101187i | 0.171408 | − | 0.985200i | \(-0.445169\pi\) |
0.467462 | + | 0.884013i | \(0.345169\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 8.00000i | − | 0.314027i | ||||||
\(650\) | −7.72422 | + | 23.7727i | −0.302969 | + | 0.932442i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 14.3203 | − | 7.29657i | 0.560827 | − | 0.285756i | ||||
\(653\) | 0.0431419 | + | 0.272387i | 0.00168827 | + | 0.0106593i | 0.988518 | − | 0.151103i | \(-0.0482824\pi\) |
−0.986830 | + | 0.161762i | \(0.948282\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 29.3844 | − | 14.9721i | 1.14814 | − | 0.585008i | ||||
\(656\) | −4.95840 | − | 6.82465i | −0.193593 | − | 0.266458i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −0.117265 | + | 0.740384i | −0.00457148 | + | 0.0288632i | ||||
\(659\) | 12.8571 | + | 39.5702i | 0.500843 | + | 1.54144i | 0.807649 | + | 0.589664i | \(0.200740\pi\) |
−0.306806 | + | 0.951772i | \(0.599260\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.76974 | + | 26.9905i | −0.341103 | + | 1.04981i | 0.622533 | + | 0.782593i | \(0.286103\pi\) |
−0.963637 | + | 0.267215i | \(0.913897\pi\) | |||||||
\(662\) | 24.7168 | + | 12.5938i | 0.960644 | + | 0.489473i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.655423 | − | 0.212960i | −0.0254354 | − | 0.00826445i | ||||
\(665\) | 14.6094 | + | 4.74688i | 0.566528 | + | 0.184076i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −47.2857 | − | 7.48932i | −1.83091 | − | 0.289988i | ||||
\(668\) | −11.4043 | − | 11.4043i | −0.441245 | − | 0.441245i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.68438 | − | 0.583549i | 0.142340 | − | 0.0225445i | ||||
\(671\) | −10.0130 | + | 13.7818i | −0.386549 | + | 0.532039i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.83026 | − | 9.47992i | −0.186193 | − | 0.365424i | 0.778975 | − | 0.627055i | \(-0.215740\pi\) |
−0.965168 | + | 0.261631i | \(0.915740\pi\) | |||||||
\(674\) | −19.0825 | −0.735031 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.9922 | −0.461239 | ||||||||
\(677\) | −15.3677 | − | 30.1608i | −0.590628 | − | 1.15917i | −0.972051 | − | 0.234772i | \(-0.924566\pi\) |
0.381423 | − | 0.924401i | \(-0.375434\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.90752 | + | 4.00186i | −0.111581 | + | 0.153577i | ||||
\(680\) | −14.9214 | − | 7.60281i | −0.572208 | − | 0.291555i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.51243 | − | 7.51243i | −0.287666 | − | 0.287666i | ||||
\(683\) | −21.0295 | − | 3.33075i | −0.804673 | − | 0.127448i | −0.259470 | − | 0.965751i | \(-0.583548\pi\) |
−0.545204 | + | 0.838304i | \(0.683548\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −14.7380 | + | 20.2852i | −0.563111 | + | 0.775056i | ||||
\(686\) | 18.4837 | + | 6.00573i | 0.705712 | + | 0.229300i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.115073 | − | 0.0586326i | −0.00438712 | − | 0.00223535i | ||||
\(689\) | 12.1170 | − | 37.2922i | 0.461619 | − | 1.42072i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.82212 | + | 30.2294i | 0.373651 | + | 1.14998i | 0.944384 | + | 0.328844i | \(0.106659\pi\) |
−0.570733 | + | 0.821136i | \(0.693341\pi\) | |||||||
\(692\) | 0.936181 | − | 5.91082i | 0.0355883 | − | 0.224696i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.79225 | − | 6.59597i | −0.181911 | − | 0.250379i | ||||
\(695\) | −11.5425 | + | 22.6534i | −0.437832 | + | 0.859293i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.88320 | + | 62.4001i | 0.374353 | + | 2.36357i | ||||
\(698\) | −4.99160 | + | 2.54335i | −0.188935 | + | 0.0962671i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.96802 | − | 1.42040i | −0.338959 | − | 0.0536859i | ||||
\(701\) | 6.45719i | 0.243885i | 0.992537 | + | 0.121942i | \(0.0389123\pi\) | ||||
−0.992537 | + | 0.121942i | \(0.961088\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −31.7344 | + | 5.02624i | −1.19689 | + | 0.189568i | ||||
\(704\) | −3.19623 | − | 2.32219i | −0.120462 | − | 0.0875210i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.1613 | − | 8.10915i | 0.420061 | − | 0.305192i | ||||
\(707\) | −5.39881 | + | 5.39881i | −0.203043 | + | 0.203043i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.9374 | − | 13.9512i | 1.61255 | − | 0.523949i | 0.642382 | − | 0.766385i | \(-0.277946\pi\) |
0.970168 | + | 0.242436i | \(0.0779463\pi\) | |||||||
\(710\) | 7.53703 | − | 23.1966i | 0.282860 | − | 0.870553i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.51651 | − | 2.97632i | 0.0568336 | − | 0.111542i | ||||
\(713\) | 11.4655 | − | 22.5024i | 0.429388 | − | 0.842721i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 35.7293 | − | 25.9589i | 1.33620 | − | 0.970807i | ||||
\(716\) | 9.52743 | − | 3.09565i | 0.356057 | − | 0.115690i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −18.4050 | + | 18.4050i | −0.686867 | + | 0.686867i | ||||
\(719\) | −11.5028 | + | 8.35728i | −0.428982 | + | 0.311674i | −0.781242 | − | 0.624228i | \(-0.785413\pi\) |
0.352260 | + | 0.935902i | \(0.385413\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.0806 | − | 14.5894i | −0.747840 | − | 0.543338i | ||||
\(722\) | −4.63131 | + | 0.733527i | −0.172360 | + | 0.0272991i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 4.74663i | − | 0.176407i | ||||||
\(725\) | −14.9819 | − | 20.6208i | −0.556414 | − | 0.765838i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.44311 | + | 4.81150i | −0.350225 | + | 0.178449i | −0.620249 | − | 0.784405i | \(-0.712968\pi\) |
0.270024 | + | 0.962854i | \(0.412968\pi\) | |||||||
\(728\) | −1.42017 | − | 8.96663i | −0.0526352 | − | 0.332325i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −0.640474 | − | 0.640474i | −0.0237050 | − | 0.0237050i | ||||
\(731\) | 0.568531 | + | 0.782515i | 0.0210279 | + | 0.0289424i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7.86115 | − | 49.6334i | 0.290358 | − | 1.83325i | −0.222689 | − | 0.974890i | \(-0.571483\pi\) |
0.513047 | − | 0.858360i | \(-0.328517\pi\) | |||||||
\(734\) | 1.58865 | + | 4.88936i | 0.0586381 | + | 0.180470i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.90211 | − | 8.93179i | 0.106973 | − | 0.329230i | ||||
\(737\) | −5.87247 | − | 2.99217i | −0.216315 | − | 0.110218i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.51035 | + | 1.46550i | 0.165916 | + | 0.0539094i | 0.390797 | − | 0.920477i | \(-0.372199\pi\) |
−0.224881 | + | 0.974386i | \(0.572199\pi\) | |||||||
\(740\) | 18.0621 | − | 5.86872i | 0.663975 | − | 0.215739i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 14.0681 | + | 2.22817i | 0.516456 | + | 0.0817986i | ||||
\(743\) | −5.38309 | − | 5.38309i | −0.197486 | − | 0.197486i | 0.601435 | − | 0.798922i | \(-0.294596\pi\) |
−0.798922 | + | 0.601435i | \(0.794596\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.80258 | + | 24.0085i | −0.139316 | + | 0.879605i | ||||
\(746\) | −8.09865 | + | 11.1468i | −0.296513 | + | 0.408115i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 13.4329 | + | 26.3635i | 0.491155 | + | 0.963946i | ||||
\(749\) | −0.794962 | −0.0290473 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 33.6368 | 1.22742 | 0.613712 | − | 0.789530i | \(-0.289676\pi\) | ||||
0.613712 | + | 0.789530i | \(0.289676\pi\) | |||||||
\(752\) | −0.187403 | − | 0.367799i | −0.00683389 | − | 0.0134123i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14.9796 | − | 20.6176i | 0.545524 | − | 0.750849i | ||||
\(755\) | −7.37602 | + | 46.5704i | −0.268441 | + | 1.69487i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35.2101 | + | 35.2101i | 1.27973 | + | 1.27973i | 0.940817 | + | 0.338914i | \(0.110060\pi\) |
0.338914 | + | 0.940817i | \(0.389940\pi\) | |||||||
\(758\) | −4.37016 | − | 0.692165i | −0.158731 | − | 0.0251406i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −8.04499 | + | 2.61398i | −0.291823 | + | 0.0948189i | ||||
\(761\) | −32.5920 | − | 10.5898i | −1.18146 | − | 0.383880i | −0.348552 | − | 0.937290i | \(-0.613326\pi\) |
−0.832909 | + | 0.553410i | \(0.813326\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 14.7810 | + | 7.53130i | 0.535108 | + | 0.272651i | ||||
\(764\) | −7.68716 | + | 23.6587i | −0.278112 | + | 0.855940i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.28293 | − | 22.4145i | −0.263143 | − | 0.809870i | ||||
\(767\) | −1.58360 | + | 9.99844i | −0.0571804 | + | 0.361023i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.9362 | − | 23.3106i | −0.610733 | − | 0.840603i | 0.385904 | − | 0.922539i | \(-0.373890\pi\) |
−0.996638 | + | 0.0819364i | \(0.973890\pi\) | |||||||
\(770\) | 11.3438 | + | 11.3438i | 0.408800 | + | 0.408800i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.11324 | − | 13.3425i | −0.0760573 | − | 0.480207i | ||||
\(773\) | 4.95291 | − | 2.52363i | 0.178144 | − | 0.0907688i | −0.362644 | − | 0.931928i | \(-0.618126\pi\) |
0.540788 | + | 0.841159i | \(0.318126\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 12.7877 | − | 4.15497i | 0.459347 | − | 0.149251i | ||||
\(776\) | − | 2.72394i | − | 0.0977839i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 11.2474 | − | 1.78141i | 0.403238 | − | 0.0638666i | ||||
\(779\) | 25.8175 | + | 18.7575i | 0.925009 | + | 0.672058i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −34.8635 | + | 25.3298i | −1.24751 | + | 0.906371i | ||||
\(782\) | −49.7347 | + | 49.7347i | −1.77851 | + | 1.77851i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.52108 | + | 1.14407i | −0.125753 | + | 0.0408596i | ||||
\(785\) | −16.6361 | + | 12.0868i | −0.593768 | + | 0.431398i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −5.09132 | + | 9.99228i | −0.181486 | + | 0.356186i | −0.963770 | − | 0.266736i | \(-0.914055\pi\) |
0.782284 | + | 0.622922i | \(0.214055\pi\) | |||||||
\(788\) | −1.61456 | + | 3.16876i | −0.0575165 | + | 0.112882i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −9.62209 | + | 29.6138i | −0.342339 | + | 1.05361i | ||||
\(791\) | 22.3988 | − | 7.27782i | 0.796411 | − | 0.258770i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.2424 | − | 15.2424i | 0.541275 | − | 0.541275i | ||||
\(794\) | −14.3620 | + | 10.4346i | −0.509688 | + | 0.370310i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.48462 | − | 6.89098i | −0.336174 | − | 0.244244i | ||||
\(797\) | 21.6471 | − | 3.42856i | 0.766779 | − | 0.121446i | 0.239221 | − | 0.970965i | \(-0.423108\pi\) |
0.527558 | + | 0.849519i | \(0.323108\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.09152i | 0.109370i | ||||||||
\(800\) | 4.45503 | − | 2.26995i | 0.157509 | − | 0.0802549i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.99614 | + | 2.03614i | −0.141109 | + | 0.0718985i | ||||
\(803\) | 0.250348 | + | 1.58064i | 0.00883459 | + | 0.0557794i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −17.3129 | + | 33.9785i | −0.610200 | + | 1.19759i | ||||
\(806\) | 7.90199 | + | 10.8762i | 0.278336 | + | 0.383096i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0.657717 | − | 4.15266i | 0.0231384 | − | 0.146090i | ||||
\(809\) | 13.4672 | + | 41.4479i | 0.473483 | + | 1.45723i | 0.847993 | + | 0.530007i | \(0.177811\pi\) |
−0.374510 | + | 0.927223i | \(0.622189\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.3078 | − | 53.2679i | 0.607759 | − | 1.87049i | 0.131175 | − | 0.991359i | \(-0.458125\pi\) |
0.476583 | − | 0.879129i | \(-0.341875\pi\) | |||||||
\(812\) | 8.24832 | + | 4.20273i | 0.289459 | + | 0.147487i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −31.9126 | − | 10.3690i | −1.11854 | − | 0.363435i | ||||
\(815\) | 21.1240 | − | 29.0746i | 0.739940 | − | 1.01844i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.482555 | + | 0.0764292i | 0.0168825 | + | 0.00267392i | ||||
\(818\) | 10.3896 | + | 10.3896i | 0.363263 | + | 0.363263i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.8069 | − | 8.56356i | −0.586924 | − | 0.299052i | ||||
\(821\) | 8.72276 | − | 12.0058i | 0.304426 | − | 0.419007i | −0.629207 | − | 0.777238i | \(-0.716620\pi\) |
0.933633 | + | 0.358231i | \(0.116620\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.74444 | + | 19.1245i | 0.339670 | + | 0.666640i | 0.996146 | − | 0.0877069i | \(-0.0279539\pi\) |
−0.656476 | + | 0.754347i | \(0.727954\pi\) | |||||||
\(824\) | 13.6682 | 0.476155 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.67720 | −0.127946 | ||||||||
\(827\) | 10.2597 | + | 20.1358i | 0.356765 | + | 0.700190i | 0.997727 | − | 0.0673818i | \(-0.0214646\pi\) |
−0.640962 | + | 0.767572i | \(0.721465\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.34963 | + | 10.1159i | −0.255263 | + | 0.351339i | −0.917346 | − | 0.398091i | \(-0.869673\pi\) |
0.662083 | + | 0.749431i | \(0.269673\pi\) | |||||||
\(830\) | −1.52202 | + | 0.241064i | −0.0528301 | + | 0.00836747i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.53498 | + | 3.53498i | 0.122553 | + | 0.122553i | ||||
\(833\) | 27.3862 | + | 4.33755i | 0.948876 | + | 0.150287i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −34.2984 | − | 11.1442i | −1.18695 | − | 0.385662i | ||||
\(836\) | 14.2141 | + | 4.61845i | 0.491606 | + | 0.159733i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.9684 | + | 6.60774i | 0.447987 | + | 0.228261i | ||||
\(839\) | 7.81986 | − | 24.0670i | 0.269971 | − | 0.830887i | −0.720535 | − | 0.693419i | \(-0.756104\pi\) |
0.990506 | − | 0.137468i | \(-0.0438964\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.931067 | − | 2.86553i | −0.0321058 | − | 0.0988114i | ||||
\(842\) | 3.75649 | − | 23.7176i | 0.129457 | − | 0.817361i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.4775 | + | 21.3030i | 0.532759 | + | 0.733280i | ||||
\(845\) | −23.8927 | + | 12.1739i | −0.821934 | + | 0.418796i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.30916 | − | 8.26574i | −0.0449834 | − | 0.284014i | ||||
\(848\) | −6.98859 | + | 3.56087i | −0.239989 | + | 0.122281i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −37.4466 | −1.28441 | ||||||||
\(851\) | − | 79.7642i | − | 2.73428i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.11601 | − | 0.335142i | 0.0724506 | − | 0.0114751i | −0.120104 | − | 0.992761i | \(-0.538323\pi\) |
0.192555 | + | 0.981286i | \(0.438323\pi\) | |||||||
\(854\) | 6.33478 | + | 4.60249i | 0.216772 | + | 0.157494i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0.354158 | − | 0.257311i | 0.0121049 | − | 0.00879471i | ||||
\(857\) | 36.7477 | − | 36.7477i | 1.25528 | − | 1.25528i | 0.301957 | − | 0.953322i | \(-0.402360\pi\) |
0.953322 | − | 0.301957i | \(-0.0976398\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.24700 | + | 2.67961i | −0.281384 | + | 0.0914273i | −0.446309 | − | 0.894879i | \(-0.647262\pi\) |
0.164925 | + | 0.986306i | \(0.447262\pi\) | |||||||
\(860\) | −0.288787 | −0.00984756 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.9282 | − | 31.2609i | 0.542518 | − | 1.06475i | ||||
\(863\) | 8.01248 | − | 15.7254i | 0.272748 | − | 0.535298i | −0.713483 | − | 0.700673i | \(-0.752883\pi\) |
0.986231 | + | 0.165375i | \(0.0528834\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.13519 | − | 12.7268i | −0.140601 | − | 0.432724i | ||||
\(866\) | −3.00478 | + | 0.976314i | −0.102107 | + | 0.0331765i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.45309 | + | 3.45309i | −0.117205 | + | 0.117205i | ||||
\(869\) | 44.5082 | − | 32.3371i | 1.50984 | − | 1.09696i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.74714 | + | 4.90209i | 0.228618 | + | 0.166101i | ||||
\(872\) | −9.02269 | + | 1.42905i | −0.305547 | + | 0.0483939i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 35.5276i | 1.20174i | ||||||||
\(875\) | −19.3094 | + | 6.27399i | −0.652776 | + | 0.212100i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −15.9099 | + | 8.10651i | −0.537240 | + | 0.273738i | −0.701488 | − | 0.712682i | \(-0.747480\pi\) |
0.164247 | + | 0.986419i | \(0.447480\pi\) | |||||||
\(878\) | −2.55752 | − | 16.1476i | −0.0863122 | − | 0.544954i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −8.72539 | − | 1.38197i | −0.294133 | − | 0.0465861i | ||||
\(881\) | −31.2335 | − | 42.9892i | −1.05228 | − | 1.44834i | −0.886813 | − | 0.462129i | \(-0.847086\pi\) |
−0.165471 | − | 0.986215i | \(-0.552914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.81503 | − | 36.7147i | 0.195691 | − | 1.23555i | −0.672793 | − | 0.739830i | \(-0.734906\pi\) |
0.868485 | − | 0.495716i | \(-0.165094\pi\) | |||||||
\(884\) | −11.5698 | − | 35.6083i | −0.389136 | − | 1.19764i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0.232011 | − | 0.714056i | 0.00779456 | − | 0.0239892i | ||||
\(887\) | 4.03516 | + | 2.05602i | 0.135488 | + | 0.0690344i | 0.520420 | − | 0.853910i | \(-0.325775\pi\) |
−0.384933 | + | 0.922945i | \(0.625775\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13.8696 | + | 4.50651i | 0.465172 | + | 0.151143i | ||||
\(890\) | − | 7.46936i | − | 0.250373i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −25.4680 | − | 4.03373i | −0.852731 | − | 0.135059i | ||||
\(893\) | 1.10420 | + | 1.10420i | 0.0369508 | + | 0.0369508i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.8394 | − | 15.8394i | 0.529454 | − | 0.529454i | ||||
\(896\) | −1.06740 | + | 1.46914i | −0.0356592 | + | 0.0490807i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.12009 | − | 12.0114i | −0.204230 | − | 0.400824i | ||||
\(899\) | −13.7086 | −0.457208 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.7424 | 1.95699 | ||||||||
\(902\) | 15.1304 | + | 29.6950i | 0.503786 | + | 0.988735i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.62309 | + | 10.4923i | −0.253540 | + | 0.348968i | ||||
\(905\) | −4.81856 | − | 9.45696i | −0.160174 | − | 0.314360i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.8147 | − | 39.8147i | −1.32203 | − | 1.32203i | −0.912134 | − | 0.409893i | \(-0.865566\pi\) |
−0.409893 | − | 0.912134i | \(-0.634434\pi\) | |||||||
\(908\) | −0.144171 | − | 0.0228344i | −0.00478447 | − | 0.000757786i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −11.9320 | − | 16.4230i | −0.395542 | − | 0.544416i | ||||
\(911\) | 14.7757 | + | 4.80090i | 0.489540 | + | 0.159061i | 0.543377 | − | 0.839489i | \(-0.317145\pi\) |
−0.0538376 | + | 0.998550i | \(0.517145\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.42592 | + | 1.23607i | 0.0802862 | + | 0.0409079i | ||||
\(914\) | 8.17933 | − | 25.1734i | 0.270548 | − | 0.832662i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.88738 | − | 18.1195i | −0.194524 | − | 0.598685i | ||||
\(917\) | −4.18976 | + | 26.4531i | −0.138358 | + | 0.873559i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.4958 | + | 21.3281i | 0.511158 | + | 0.703549i | 0.984114 | − | 0.177537i | \(-0.0568129\pi\) |
−0.472956 | + | 0.881086i | \(0.656813\pi\) | |||||||
\(920\) | −3.28511 | − | 20.7413i | −0.108307 | − | 0.683822i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.65343 | + | 23.0668i | 0.120319 | + | 0.759666i | ||||
\(923\) | 48.5866 | − | 24.7561i | 1.59925 | − | 0.814857i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.0283 | − | 30.0283i | 0.987326 | − | 0.987326i | ||||
\(926\) | 10.5707i | 0.347376i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.03498 | + | 0.797463i | −0.165281 | + | 0.0261780i | ||||
\(929\) | 9.86752 | + | 7.16917i | 0.323743 | + | 0.235213i | 0.737771 | − | 0.675051i | \(-0.235878\pi\) |
−0.414028 | + | 0.910264i | \(0.635878\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 11.3308 | − | 8.23233i | 0.371353 | − | 0.269804i | ||||
\(932\) | −6.01419 | + | 6.01419i | −0.197001 | + | 0.197001i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.3100 | + | 10.4981i | −1.05721 | + | 0.343510i | ||||
\(935\) | 53.5260 | + | 38.8889i | 1.75049 | + | 1.27180i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.8820 | − | 37.0581i | 0.616850 | − | 1.21064i | −0.345397 | − | 0.938457i | \(-0.612256\pi\) |
0.962247 | − | 0.272179i | \(-0.0877442\pi\) | |||||||
\(938\) | −1.37535 | + | 2.69928i | −0.0449068 | + | 0.0881345i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.746746 | − | 0.542543i | −0.0243562 | − | 0.0176958i | ||||
\(941\) | −8.88126 | + | 2.88570i | −0.289521 | + | 0.0940710i | −0.450177 | − | 0.892939i | \(-0.648639\pi\) |
0.160656 | + | 0.987010i | \(0.448639\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −56.0195 | + | 56.0195i | −1.82425 | + | 1.82425i | ||||
\(944\) | 1.63820 | − | 1.19022i | 0.0533190 | − | 0.0387385i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.412791 | + | 0.299910i | 0.0134210 | + | 0.00975092i | ||||
\(947\) | −2.62415 | + | 0.415625i | −0.0852734 | + | 0.0135060i | −0.198925 | − | 0.980015i | \(-0.563745\pi\) |
0.113652 | + | 0.993521i | \(0.463745\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2.02504i | − | 0.0657357i | ||||||
\(950\) | −13.3749 | + | 13.3749i | −0.433938 | + | 0.433938i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.1180 | − | 6.17442i | 0.392746 | − | 0.200114i | ||||
\(953\) | −4.92811 | − | 31.1149i | −0.159637 | − | 1.00791i | −0.929264 | − | 0.369416i | \(-0.879558\pi\) |
0.769627 | − | 0.638494i | \(-0.220442\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.70164 | + | 54.9400i | 0.281578 | + | 1.77782i | ||||
\(956\) | −7.91816 | − | 10.8984i | −0.256092 | − | 0.352480i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6.04790 | − | 38.1849i | 0.195399 | − | 1.23370i | ||||
\(959\) | −6.29252 | − | 19.3664i | −0.203196 | − | 0.625373i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.34486 | + | 22.6051i | −0.236931 | + | 0.729198i | ||||
\(962\) | 37.8320 | + | 19.2764i | 1.21975 | + | 0.621495i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.66733 | − | 3.14111i | −0.311364 | − | 0.101168i | ||||
\(965\) | −17.7550 | − | 24.4377i | −0.571554 | − | 0.786676i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −27.9494 | − | 4.42675i | −0.898791 | − | 0.142355i | −0.310092 | − | 0.950707i | \(-0.600360\pi\) |
−0.588699 | + | 0.808352i | \(0.700360\pi\) | |||||||
\(968\) | 3.25867 | + | 3.25867i | 0.104738 | + | 0.104738i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.76522 | − | 5.42705i | −0.0887859 | − | 0.174252i | ||||
\(971\) | −10.9794 | + | 15.1119i | −0.352347 | + | 0.484964i | −0.947997 | − | 0.318280i | \(-0.896895\pi\) |
0.595650 | + | 0.803244i | \(0.296895\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.37392 | − | 18.3974i | −0.300514 | − | 0.589792i | ||||
\(974\) | 19.6320 | 0.629049 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.31189 | −0.138020 | ||||||||
\(977\) | −1.32908 | − | 2.60846i | −0.0425210 | − | 0.0834521i | 0.868768 | − | 0.495218i | \(-0.164912\pi\) |
−0.911289 | + | 0.411766i | \(0.864912\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.75705 | + | 10.6767i | −0.247916 | + | 0.341228i | ||||
\(980\) | −5.85382 | + | 5.85382i | −0.186993 | + | 0.186993i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.59905 | − | 5.59905i | −0.178673 | − | 0.178673i | ||||
\(983\) | −31.9014 | − | 5.05268i | −1.01750 | − | 0.161156i | −0.374662 | − | 0.927161i | \(-0.622241\pi\) |
−0.642834 | + | 0.766006i | \(0.722241\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.95232i | 0.253382i | ||||||||
\(986\) | 36.3101 | + | 11.7979i | 1.15635 | + | 0.375720i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −16.8507 | − | 8.58585i | −0.536092 | − | 0.273152i | ||||
\(989\) | −0.374806 | + | 1.15354i | −0.0119182 | + | 0.0366803i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.1116 | + | 37.2757i | 0.384738 | + | 1.18410i | 0.936670 | + | 0.350213i | \(0.113891\pi\) |
−0.551932 | + | 0.833889i | \(0.686109\pi\) | |||||||
\(992\) | 0.420676 | − | 2.65605i | 0.0133565 | − | 0.0843295i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.6428 | + | 16.0250i | 0.369288 | + | 0.508281i | ||||
\(995\) | −25.8921 | − | 4.10091i | −0.820835 | − | 0.130007i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.01914 | − | 50.6308i | −0.253969 | − | 1.60350i | −0.703811 | − | 0.710387i | \(-0.748520\pi\) |
0.449842 | − | 0.893108i | \(-0.351480\pi\) | |||||||
\(998\) | −6.20964 | + | 3.16397i | −0.196563 | + | 0.100154i | ||||
\(999\) | 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 | 450.2.s.b.197.1 | ✓ | 16 | |
3.2 | odd | 2 | inner | 450.2.s.b.197.2 | yes | 16 | |
25.8 | odd | 20 | inner | 450.2.s.b.233.2 | yes | 16 | |
75.8 | even | 20 | inner | 450.2.s.b.233.1 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.s.b.197.1 | ✓ | 16 | 1.1 | even | 1 | trivial | |
450.2.s.b.197.2 | yes | 16 | 3.2 | odd | 2 | inner | |
450.2.s.b.233.1 | yes | 16 | 75.8 | even | 20 | inner | |
450.2.s.b.233.2 | yes | 16 | 25.8 | odd | 20 | inner |