Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [675,2,Mod(46,675)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(675, base_ring=CyclotomicField(30))
chi = DirichletCharacter(H, H._module([20, 18]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("675.46");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 675 = 3^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 675.r (of order \(15\), degree \(8\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.38990213644\) |
Analytic rank: | \(0\) |
Dimension: | \(224\) |
Relative dimension: | \(28\) over \(\Q(\zeta_{15})\) |
Twist minimal: | no (minimal twist has level 225) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{15}]$ |
Embedding invariants
Embedding label | 46.3 | ||
Character | \(\chi\) | \(=\) | 675.46 |
Dual form | 675.2.r.a.631.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/675\mathbb{Z}\right)^\times\).
\(n\) | \(326\) | \(352\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.64688 | − | 1.82905i | −1.16452 | − | 1.29333i | −0.948440 | − | 0.316956i | \(-0.897339\pi\) |
−0.216081 | − | 0.976376i | \(-0.569327\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.424138 | + | 4.03540i | −0.212069 | + | 2.01770i | ||||
\(5\) | −0.681844 | − | 2.12957i | −0.304930 | − | 0.952375i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.55879 | − | 4.43196i | 0.967132 | − | 1.67512i | 0.263357 | − | 0.964698i | \(-0.415170\pi\) |
0.703775 | − | 0.710423i | \(-0.251496\pi\) | |||||||
\(8\) | 4.09710 | − | 2.97672i | 1.44854 | − | 1.05243i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.77218 | + | 4.75428i | −0.876639 | + | 1.50344i | ||||
\(11\) | 1.05935 | + | 1.17653i | 0.319406 | + | 0.354737i | 0.881371 | − | 0.472424i | \(-0.156621\pi\) |
−0.561965 | + | 0.827161i | \(0.689954\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.596899 | − | 0.662924i | 0.165550 | − | 0.183862i | −0.654662 | − | 0.755922i | \(-0.727189\pi\) |
0.820212 | + | 0.572060i | \(0.193856\pi\) | |||||||
\(14\) | −12.3203 | + | 2.61876i | −3.29273 | + | 0.699892i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.25406 | − | 0.904229i | −1.06352 | − | 0.226057i | ||||
\(17\) | 3.04259 | − | 2.21057i | 0.737936 | − | 0.536142i | −0.154128 | − | 0.988051i | \(-0.549257\pi\) |
0.892064 | + | 0.451909i | \(0.149257\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.69404 | − | 2.68388i | 0.847472 | − | 0.615724i | −0.0769761 | − | 0.997033i | \(-0.524527\pi\) |
0.924448 | + | 0.381309i | \(0.124527\pi\) | |||||||
\(20\) | 8.88289 | − | 1.84828i | 1.98627 | − | 0.413288i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.407301 | − | 3.87521i | 0.0868368 | − | 0.826197i | ||||
\(23\) | 5.36085 | − | 1.13948i | 1.11781 | − | 0.237599i | 0.388279 | − | 0.921542i | \(-0.373070\pi\) |
0.729536 | + | 0.683943i | \(0.239736\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.07018 | + | 2.90407i | −0.814036 | + | 0.580815i | ||||
\(26\) | −2.19554 | −0.430581 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 16.7994 | + | 12.2055i | 3.17480 | + | 2.30662i | ||||
\(29\) | 0.0385420 | − | 0.0171600i | 0.00715708 | − | 0.00318654i | −0.403155 | − | 0.915132i | \(-0.632086\pi\) |
0.410312 | + | 0.911945i | \(0.365420\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.79980 | + | 0.801323i | 0.323254 | + | 0.143922i | 0.561947 | − | 0.827173i | \(-0.310052\pi\) |
−0.238693 | + | 0.971095i | \(0.576719\pi\) | |||||||
\(32\) | 0.287768 | + | 0.498429i | 0.0508707 | + | 0.0881106i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −9.05401 | − | 1.92449i | −1.55275 | − | 0.330047i | ||||
\(35\) | −11.1829 | − | 2.42724i | −1.89025 | − | 0.410278i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.43995 | − | 4.43171i | −0.236726 | − | 0.728569i | −0.996888 | − | 0.0788345i | \(-0.974880\pi\) |
0.760161 | − | 0.649734i | \(-0.225120\pi\) | |||||||
\(38\) | −10.9926 | − | 2.33655i | −1.78323 | − | 0.379038i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9.13272 | − | 6.69542i | −1.44401 | − | 1.05864i | ||||
\(41\) | −0.511798 | + | 0.568409i | −0.0799294 | + | 0.0887706i | −0.781783 | − | 0.623551i | \(-0.785689\pi\) |
0.701853 | + | 0.712321i | \(0.252356\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.11709 | + | 7.13101i | −0.627850 | + | 1.08747i | 0.360132 | + | 0.932901i | \(0.382732\pi\) |
−0.987982 | + | 0.154567i | \(0.950602\pi\) | |||||||
\(44\) | −5.19708 | + | 3.77590i | −0.783489 | + | 0.569238i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.9129 | − | 7.92865i | −1.60901 | − | 1.16902i | ||||
\(47\) | −3.72722 | + | 1.65947i | −0.543671 | + | 0.242058i | −0.660148 | − | 0.751135i | \(-0.729507\pi\) |
0.116477 | + | 0.993193i | \(0.462840\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.59482 | − | 16.6187i | −1.37069 | − | 2.37410i | ||||
\(50\) | 12.0148 | + | 2.66188i | 1.69915 | + | 0.376447i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.42200 | + | 2.68990i | 0.335870 | + | 0.373022i | ||||
\(53\) | 2.00012 | + | 1.45317i | 0.274737 | + | 0.199608i | 0.716619 | − | 0.697465i | \(-0.245689\pi\) |
−0.441882 | + | 0.897073i | \(0.645689\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.78319 | − | 3.05818i | 0.240446 | − | 0.412364i | ||||
\(56\) | −2.70906 | − | 25.7749i | −0.362013 | − | 3.44432i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.0948606 | − | 0.0422347i | −0.0124558 | − | 0.00554568i | ||||
\(59\) | −6.37293 | + | 7.07785i | −0.829684 | + | 0.921458i | −0.997931 | − | 0.0642869i | \(-0.979523\pi\) |
0.168247 | + | 0.985745i | \(0.446189\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.84864 | − | 5.38496i | −0.620805 | − | 0.689474i | 0.347944 | − | 0.937515i | \(-0.386880\pi\) |
−0.968749 | + | 0.248041i | \(0.920213\pi\) | |||||||
\(62\) | −1.49840 | − | 4.61160i | −0.190297 | − | 0.585674i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.25016 | + | 6.92529i | −0.281270 | + | 0.865661i | ||||
\(65\) | −1.81874 | − | 0.819131i | −0.225587 | − | 0.101601i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.28565 | + | 1.46287i | 0.401406 | + | 0.178717i | 0.597502 | − | 0.801867i | \(-0.296160\pi\) |
−0.196096 | + | 0.980585i | \(0.562827\pi\) | |||||||
\(68\) | 7.63006 | + | 13.2156i | 0.925280 | + | 1.60263i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 13.9773 | + | 24.4514i | 1.67061 | + | 2.92250i | ||||
\(71\) | 1.57130 | + | 1.14162i | 0.186479 | + | 0.135485i | 0.677108 | − | 0.735884i | \(-0.263233\pi\) |
−0.490629 | + | 0.871369i | \(0.663233\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.42033 | + | 13.6044i | −0.517361 | + | 1.59227i | 0.261584 | + | 0.965181i | \(0.415755\pi\) |
−0.778945 | + | 0.627093i | \(0.784245\pi\) | |||||||
\(74\) | −5.73438 | + | 9.93224i | −0.666608 | + | 1.15460i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.26375 | + | 16.0453i | 1.06262 | + | 1.84052i | ||||
\(77\) | 7.92498 | − | 1.68451i | 0.903135 | − | 0.191967i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.10949 | − | 1.38443i | 0.349844 | − | 0.155761i | −0.224289 | − | 0.974523i | \(-0.572006\pi\) |
0.574133 | + | 0.818762i | \(0.305339\pi\) | |||||||
\(80\) | 0.974982 | + | 9.67589i | 0.109006 | + | 1.08180i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.88252 | 0.207889 | ||||||||
\(83\) | −0.405949 | − | 3.86235i | −0.0445587 | − | 0.423948i | −0.993948 | − | 0.109847i | \(-0.964964\pi\) |
0.949390 | − | 0.314100i | \(-0.101703\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.78214 | − | 4.97215i | −0.735626 | − | 0.539306i | ||||
\(86\) | 19.8233 | − | 4.21357i | 2.13760 | − | 0.454361i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.84246 | + | 1.66697i | 0.836009 | + | 0.177699i | ||||
\(89\) | 0.935601 | − | 2.87948i | 0.0991735 | − | 0.305225i | −0.889145 | − | 0.457625i | \(-0.848700\pi\) |
0.988319 | + | 0.152400i | \(0.0487002\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.41071 | − | 4.34171i | −0.147882 | − | 0.455135i | ||||
\(92\) | 2.32454 | + | 22.1165i | 0.242350 | + | 2.30580i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 9.17353 | + | 4.08432i | 0.946178 | + | 0.421265i | ||||
\(95\) | −8.23428 | − | 6.03676i | −0.844819 | − | 0.619358i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.75481 | + | 2.11698i | −0.482777 | + | 0.214946i | −0.633669 | − | 0.773604i | \(-0.718452\pi\) |
0.150892 | + | 0.988550i | \(0.451785\pi\) | |||||||
\(98\) | −14.5949 | + | 44.9184i | −1.47431 | + | 4.53744i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −9.99279 | − | 17.6565i | −0.999279 | − | 1.76565i | ||||
\(101\) | −7.78401 | + | 13.4823i | −0.774538 | + | 1.34154i | 0.160516 | + | 0.987033i | \(0.448684\pi\) |
−0.935054 | + | 0.354506i | \(0.884649\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.66359 | − | 15.8280i | 0.163918 | − | 1.55958i | −0.535295 | − | 0.844665i | \(-0.679800\pi\) |
0.699213 | − | 0.714913i | \(-0.253534\pi\) | |||||||
\(104\) | 0.472219 | − | 4.49286i | 0.0463049 | − | 0.440561i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.636039 | − | 6.05150i | −0.0617775 | − | 0.587774i | ||||
\(107\) | −2.75485 | −0.266322 | −0.133161 | − | 0.991094i | \(-0.542513\pi\) | ||||
−0.133161 | + | 0.991094i | \(0.542513\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.89734 | + | 11.9948i | 0.373297 | + | 1.14889i | 0.944620 | + | 0.328166i | \(0.106430\pi\) |
−0.571323 | + | 0.820726i | \(0.693570\pi\) | |||||||
\(110\) | −8.53026 | + | 1.77491i | −0.813328 | + | 0.169231i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −14.8928 | + | 16.5401i | −1.40723 | + | 1.56289i | ||||
\(113\) | 8.54130 | − | 9.48607i | 0.803498 | − | 0.892375i | −0.192541 | − | 0.981289i | \(-0.561673\pi\) |
0.996039 | + | 0.0889141i | \(0.0283396\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.08188 | − | 10.6394i | −0.567138 | − | 0.992128i | ||||
\(116\) | 0.0529004 | + | 0.162811i | 0.00491168 | + | 0.0151166i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 23.4412 | 2.15794 | ||||||||
\(119\) | −2.01180 | − | 19.1410i | −0.184421 | − | 1.75465i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.887818 | − | 8.44703i | 0.0807107 | − | 0.767911i | ||||
\(122\) | −1.86421 | + | 17.7368i | −0.168778 | + | 1.60581i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.99702 | + | 6.92305i | −0.358943 | + | 0.621708i | ||||
\(125\) | 8.95967 | + | 6.68763i | 0.801377 | + | 0.598160i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.35801 | + | 7.25722i | −0.209240 | + | 0.643974i | 0.790273 | + | 0.612755i | \(0.209939\pi\) |
−0.999513 | + | 0.0312188i | \(0.990061\pi\) | |||||||
\(128\) | 17.4240 | − | 7.75766i | 1.54008 | − | 0.685686i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 1.49702 | + | 4.67557i | 0.131297 | + | 0.410074i | ||||
\(131\) | −2.37476 | − | 1.05731i | −0.207484 | − | 0.0923778i | 0.300364 | − | 0.953825i | \(-0.402892\pi\) |
−0.507847 | + | 0.861447i | \(0.669559\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.44255 | − | 23.2393i | −0.211796 | − | 2.01510i | ||||
\(134\) | −2.73542 | − | 8.41877i | −0.236305 | − | 0.727271i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 5.88554 | − | 18.1138i | 0.504681 | − | 1.55325i | ||||
\(137\) | 5.49049 | + | 1.16704i | 0.469085 | + | 0.0997070i | 0.436389 | − | 0.899758i | \(-0.356257\pi\) |
0.0326961 | + | 0.999465i | \(0.489591\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.68680 | − | 0.358539i | 0.143072 | − | 0.0304109i | −0.135819 | − | 0.990734i | \(-0.543367\pi\) |
0.278891 | + | 0.960323i | \(0.410033\pi\) | |||||||
\(140\) | 14.5380 | − | 44.0979i | 1.22868 | − | 3.72695i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.499675 | − | 4.75409i | −0.0419318 | − | 0.398955i | ||||
\(143\) | 1.41227 | 0.118100 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.0628232 | − | 0.0703777i | −0.00521718 | − | 0.00584455i | ||||
\(146\) | 32.1628 | − | 14.3198i | 2.66182 | − | 1.18512i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 18.4945 | − | 3.93112i | 1.52024 | − | 0.323136i | ||||
\(149\) | 6.23532 | + | 10.7999i | 0.510817 | + | 0.884761i | 0.999921 | + | 0.0125357i | \(0.00399034\pi\) |
−0.489104 | + | 0.872225i | \(0.662676\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −3.71371 | + | 6.43234i | −0.302218 | + | 0.523457i | −0.976638 | − | 0.214891i | \(-0.931060\pi\) |
0.674420 | + | 0.738348i | \(0.264394\pi\) | |||||||
\(152\) | 7.14571 | − | 21.9922i | 0.579594 | − | 1.78381i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −16.1325 | − | 11.7210i | −1.30000 | − | 0.944503i | ||||
\(155\) | 0.479295 | − | 4.37919i | 0.0384979 | − | 0.351745i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.70564 | + | 8.15040i | 0.375551 | + | 0.650473i | 0.990409 | − | 0.138164i | \(-0.0441202\pi\) |
−0.614859 | + | 0.788637i | \(0.710787\pi\) | |||||||
\(158\) | −7.65314 | − | 3.40740i | −0.608852 | − | 0.271078i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.865229 | − | 0.952675i | 0.0684024 | − | 0.0753155i | ||||
\(161\) | 8.66715 | − | 26.6748i | 0.683067 | − | 2.10227i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.969935 | − | 2.98515i | −0.0759712 | − | 0.233815i | 0.905858 | − | 0.423581i | \(-0.139227\pi\) |
−0.981829 | + | 0.189766i | \(0.939227\pi\) | |||||||
\(164\) | −2.07669 | − | 2.30639i | −0.162162 | − | 0.180099i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.39587 | + | 7.10333i | −0.496416 | + | 0.551325i | ||||
\(167\) | −2.62097 | − | 1.16693i | −0.202816 | − | 0.0902997i | 0.302815 | − | 0.953049i | \(-0.402074\pi\) |
−0.505631 | + | 0.862750i | \(0.668740\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.27569 | + | 12.1374i | 0.0981301 | + | 0.933645i | ||||
\(170\) | 2.07507 | + | 20.5934i | 0.159151 | + | 1.57944i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −27.0303 | − | 19.6386i | −2.06104 | − | 1.49743i | ||||
\(173\) | −10.6348 | − | 11.8112i | −0.808550 | − | 0.897986i | 0.187899 | − | 0.982188i | \(-0.439832\pi\) |
−0.996449 | + | 0.0842025i | \(0.973166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.45599 | + | 25.4698i | 0.185655 | + | 1.92533i | ||||
\(176\) | −3.44270 | − | 5.96292i | −0.259503 | − | 0.449472i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.80754 | + | 3.03091i | −0.510246 | + | 0.227176i | ||||
\(179\) | −14.4077 | − | 10.4678i | −1.07688 | − | 0.782399i | −0.0997433 | − | 0.995013i | \(-0.531802\pi\) |
−0.977136 | + | 0.212614i | \(0.931802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 14.8249 | − | 10.7709i | 1.10192 | − | 0.800594i | 0.120550 | − | 0.992707i | \(-0.461534\pi\) |
0.981373 | + | 0.192114i | \(0.0615342\pi\) | |||||||
\(182\) | −5.61793 | + | 9.73054i | −0.416429 | + | 0.721275i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 18.5720 | − | 20.6263i | 1.36915 | − | 1.52059i | ||||
\(185\) | −8.45584 | + | 6.08822i | −0.621686 | + | 0.447615i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.82397 | + | 1.23792i | 0.425891 | + | 0.0905258i | ||||
\(188\) | −5.11576 | − | 15.7447i | −0.373105 | − | 1.14830i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.51937 | + | 25.0027i | 0.182775 | + | 1.81389i | ||||
\(191\) | 10.7709 | + | 2.28943i | 0.779356 | + | 0.165657i | 0.580379 | − | 0.814347i | \(-0.302905\pi\) |
0.198978 | + | 0.980004i | \(0.436238\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3.22947 | − | 5.59361i | −0.232463 | − | 0.402637i | 0.726070 | − | 0.687621i | \(-0.241345\pi\) |
−0.958532 | + | 0.284984i | \(0.908012\pi\) | |||||||
\(194\) | 11.7026 | + | 5.21035i | 0.840201 | + | 0.374082i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 71.1327 | − | 31.6703i | 5.08091 | − | 2.26217i | ||||
\(197\) | 20.4081 | + | 14.8274i | 1.45402 | + | 1.05641i | 0.984872 | + | 0.173284i | \(0.0554379\pi\) |
0.469145 | + | 0.883121i | \(0.344562\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.48202 | 0.175946 | 0.0879729 | − | 0.996123i | \(-0.471961\pi\) | ||||
0.0879729 | + | 0.996123i | \(0.471961\pi\) | |||||||
\(200\) | −8.03132 | + | 24.0140i | −0.567900 | + | 1.69805i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 37.4791 | − | 7.96643i | 2.63702 | − | 0.560516i | ||||
\(203\) | 0.0225686 | − | 0.214725i | 0.00158400 | − | 0.0150708i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.55944 | + | 0.702346i | 0.108916 | + | 0.0490540i | ||||
\(206\) | −31.6899 | + | 23.0240i | −2.20794 | + | 1.60416i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −3.13868 | + | 2.28039i | −0.217628 | + | 0.158116i | ||||
\(209\) | 7.07095 | + | 1.50298i | 0.489108 | + | 0.103963i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.74542 | − | 1.43378i | 0.464374 | − | 0.0987057i | 0.0302177 | − | 0.999543i | \(-0.490380\pi\) |
0.434156 | + | 0.900838i | \(0.357047\pi\) | |||||||
\(212\) | −6.71245 | + | 7.45493i | −0.461013 | + | 0.512007i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.53692 | + | 5.03876i | 0.310137 | + | 0.344442i | ||||
\(215\) | 17.9932 | + | 3.90542i | 1.22713 | + | 0.266347i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.15674 | − | 5.92622i | 0.553716 | − | 0.402298i | ||||
\(218\) | 15.5206 | − | 26.8824i | 1.05118 | − | 1.82071i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 11.5847 | + | 8.49299i | 0.781037 | + | 0.572598i | ||||
\(221\) | 0.350679 | − | 3.33649i | 0.0235892 | − | 0.224437i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.82544 | − | 9.80164i | −0.590995 | − | 0.656366i | 0.371256 | − | 0.928531i | \(-0.378927\pi\) |
−0.962251 | + | 0.272164i | \(0.912261\pi\) | |||||||
\(224\) | 2.94535 | 0.196795 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31.4170 | −2.08983 | ||||||||
\(227\) | 11.7306 | + | 13.0281i | 0.778586 | + | 0.864707i | 0.993722 | − | 0.111877i | \(-0.0356863\pi\) |
−0.215136 | + | 0.976584i | \(0.569020\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.69849 | + | 16.1600i | −0.112239 | + | 1.06788i | 0.782915 | + | 0.622128i | \(0.213732\pi\) |
−0.895154 | + | 0.445756i | \(0.852935\pi\) | |||||||
\(230\) | −9.44380 | + | 28.6458i | −0.622706 | + | 1.88885i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.106830 | − | 0.185035i | 0.00701373 | − | 0.0121481i | ||||
\(233\) | 15.4281 | − | 11.2092i | 1.01073 | − | 0.734339i | 0.0463684 | − | 0.998924i | \(-0.485235\pi\) |
0.964362 | + | 0.264586i | \(0.0852352\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.07534 | + | 6.80590i | 0.396311 | + | 0.443968i | ||||
\(236\) | −25.8590 | − | 28.7193i | −1.68328 | − | 1.86947i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −31.6966 | + | 35.2026i | −2.05458 | + | 2.28185i | ||||
\(239\) | −6.81591 | + | 1.44877i | −0.440884 | + | 0.0937129i | −0.423005 | − | 0.906127i | \(-0.639025\pi\) |
−0.0178793 | + | 0.999840i | \(0.505691\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.96735 | + | 0.630730i | 0.191144 | + | 0.0406289i | 0.302489 | − | 0.953153i | \(-0.402183\pi\) |
−0.111345 | + | 0.993782i | \(0.535516\pi\) | |||||||
\(242\) | −16.9121 | + | 12.2874i | −1.08715 | + | 0.789863i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 23.7870 | − | 17.2823i | 1.52281 | − | 1.10638i | ||||
\(245\) | −28.8486 | + | 31.7642i | −1.84307 | + | 2.02934i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.425764 | − | 4.05087i | 0.0270907 | − | 0.257751i | ||||
\(248\) | 9.75927 | − | 2.07440i | 0.619714 | − | 0.131724i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.52353 | − | 27.4014i | −0.159602 | − | 1.73302i | ||||
\(251\) | −14.6208 | −0.922854 | −0.461427 | − | 0.887178i | \(-0.652662\pi\) | ||||
−0.461427 | + | 0.887178i | \(0.652662\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.01966 | + | 5.10008i | 0.441322 | + | 0.320639i | ||||
\(254\) | 17.1572 | − | 7.63886i | 1.07654 | − | 0.479305i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.5801 | − | 13.1699i | −1.84875 | − | 0.823118i | ||||
\(257\) | −8.94002 | − | 15.4846i | −0.557663 | − | 0.965900i | −0.997691 | − | 0.0679164i | \(-0.978365\pi\) |
0.440028 | − | 0.897984i | \(-0.354968\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −23.3257 | − | 4.95803i | −1.44939 | − | 0.308077i | ||||
\(260\) | 4.07692 | − | 6.99191i | 0.252840 | − | 0.433620i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.97708 | + | 6.08482i | 0.122144 | + | 0.375921i | ||||
\(263\) | 12.0007 | + | 2.55082i | 0.739993 | + | 0.157290i | 0.562460 | − | 0.826824i | \(-0.309855\pi\) |
0.177533 | + | 0.984115i | \(0.443188\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.73087 | − | 5.25023i | 0.106326 | − | 0.322519i | ||||
\(266\) | −38.4832 | + | 42.7399i | −2.35956 | + | 2.62055i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.29682 | + | 12.6385i | −0.445724 | + | 0.772017i | ||||
\(269\) | 18.8007 | − | 13.6595i | 1.14630 | − | 0.832835i | 0.158314 | − | 0.987389i | \(-0.449394\pi\) |
0.987984 | + | 0.154554i | \(0.0493941\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.0116 | + | 15.9923i | 1.33711 | + | 0.971466i | 0.999545 | + | 0.0301632i | \(0.00960270\pi\) |
0.337563 | + | 0.941303i | \(0.390397\pi\) | |||||||
\(272\) | −14.9422 | + | 6.65270i | −0.906005 | + | 0.403379i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.90762 | − | 11.9643i | −0.417305 | − | 0.722793i | ||||
\(275\) | −7.72848 | − | 1.71225i | −0.466045 | − | 0.103252i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.7830 | + | 13.0863i | 0.707972 | + | 0.786282i | 0.984624 | − | 0.174688i | \(-0.0558917\pi\) |
−0.276652 | + | 0.960970i | \(0.589225\pi\) | |||||||
\(278\) | −3.43374 | − | 2.49476i | −0.205942 | − | 0.149626i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −53.0425 | + | 23.3436i | −3.16990 | + | 1.39505i | ||||
\(281\) | 1.50810 | + | 14.3486i | 0.0899657 | + | 0.855967i | 0.942704 | + | 0.333629i | \(0.108273\pi\) |
−0.852739 | + | 0.522338i | \(0.825060\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.3496 | − | 5.05317i | −0.674663 | − | 0.300379i | 0.0406600 | − | 0.999173i | \(-0.487054\pi\) |
−0.715323 | + | 0.698794i | \(0.753721\pi\) | |||||||
\(284\) | −5.27333 | + | 5.85663i | −0.312915 | + | 0.347527i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.32585 | − | 2.58312i | −0.137530 | − | 0.152743i | ||||
\(287\) | 1.20958 | + | 3.72271i | 0.0713993 | + | 0.219744i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.882569 | + | 2.71627i | −0.0519158 | + | 0.159781i | ||||
\(290\) | −0.0252618 | + | 0.230810i | −0.00148342 | + | 0.0135536i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −53.0244 | − | 23.6080i | −3.10302 | − | 1.38155i | ||||
\(293\) | −11.2824 | − | 19.5417i | −0.659125 | − | 1.14164i | −0.980843 | − | 0.194802i | \(-0.937594\pi\) |
0.321718 | − | 0.946836i | \(-0.395740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.4182 | + | 8.74564i | 1.13057 | + | 0.509191i | ||||
\(296\) | −19.0916 | − | 13.8708i | −1.10967 | − | 0.806226i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.48467 | − | 29.1908i | 0.549432 | − | 1.69098i | ||||
\(299\) | 2.44450 | − | 4.23399i | 0.141369 | − | 0.244858i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 21.0695 | + | 36.4935i | 1.21443 | + | 2.10345i | ||||
\(302\) | 17.8811 | − | 3.80074i | 1.02894 | − | 0.218708i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −18.1415 | + | 8.07713i | −1.04049 | + | 0.463255i | ||||
\(305\) | −8.16167 | + | 13.9973i | −0.467336 | + | 0.801480i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −27.5455 | −1.57211 | −0.786054 | − | 0.618158i | \(-0.787879\pi\) | ||||
−0.786054 | + | 0.618158i | \(0.787879\pi\) | |||||||
\(308\) | 3.43638 | + | 32.6949i | 0.195806 | + | 1.86297i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.79908 | + | 6.33535i | −0.499754 | + | 0.359824i | ||||
\(311\) | 0.496015 | − | 0.105431i | 0.0281264 | − | 0.00597846i | −0.193827 | − | 0.981036i | \(-0.562090\pi\) |
0.221953 | + | 0.975057i | \(0.428757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.9331 | + | 2.74901i | 0.731021 | + | 0.155383i | 0.558361 | − | 0.829598i | \(-0.311430\pi\) |
0.172660 | + | 0.984981i | \(0.444764\pi\) | |||||||
\(314\) | 7.15784 | − | 22.0296i | 0.403941 | − | 1.24320i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.26789 | + | 13.1352i | 0.240088 | + | 0.738914i | ||||
\(317\) | −1.09655 | − | 10.4330i | −0.0615883 | − | 0.585973i | −0.981180 | − | 0.193097i | \(-0.938147\pi\) |
0.919591 | − | 0.392876i | \(-0.128520\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.0610188 | + | 0.0271673i | 0.00341640 | + | 0.00152108i | ||||
\(320\) | 16.2822 | + | 0.0699267i | 0.910201 | + | 0.00390902i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −63.0631 | + | 28.0775i | −3.51437 | + | 1.56470i | ||||
\(323\) | 5.30655 | − | 16.3319i | 0.295264 | − | 0.908730i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.504307 | + | 4.43166i | −0.0279739 | + | 0.245824i | ||||
\(326\) | −3.86262 | + | 6.69025i | −0.213931 | + | 0.370539i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.404894 | + | 3.85231i | −0.0223565 | + | 0.212708i | ||||
\(329\) | −2.18250 | + | 20.7651i | −0.120325 | + | 1.14482i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.255661 | + | 2.43245i | 0.0140524 | + | 0.133700i | 0.999299 | − | 0.0374422i | \(-0.0119210\pi\) |
−0.985246 | + | 0.171142i | \(0.945254\pi\) | |||||||
\(332\) | 15.7583 | 0.864850 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.18205 | + | 6.71566i | 0.119397 | + | 0.367465i | ||||
\(335\) | 0.874982 | − | 7.99448i | 0.0478054 | − | 0.436785i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.22740 | − | 1.36317i | 0.0668607 | − | 0.0742564i | −0.708786 | − | 0.705423i | \(-0.750757\pi\) |
0.775647 | + | 0.631167i | \(0.217424\pi\) | |||||||
\(338\) | 20.0989 | − | 22.3221i | 1.09324 | − | 1.21416i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 22.9412 | − | 25.2598i | 1.24416 | − | 1.36990i | ||||
\(341\) | 0.963842 | + | 2.96640i | 0.0521950 | + | 0.160640i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −62.3814 | −3.36828 | ||||||||
\(344\) | 4.35887 | + | 41.4718i | 0.235014 | + | 2.23601i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.08889 | + | 38.9032i | −0.219820 | + | 2.09145i | ||||
\(347\) | −0.0311880 | + | 0.296734i | −0.00167426 | + | 0.0159295i | −0.995327 | − | 0.0965604i | \(-0.969216\pi\) |
0.993653 | + | 0.112490i | \(0.0358826\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.44783 | + | 14.6321i | −0.452202 | + | 0.783237i | −0.998523 | − | 0.0543395i | \(-0.982695\pi\) |
0.546321 | + | 0.837576i | \(0.316028\pi\) | |||||||
\(350\) | 42.5407 | − | 46.4378i | 2.27389 | − | 2.48220i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.281569 | + | 0.866579i | −0.0150077 | + | 0.0461888i | ||||
\(353\) | −6.64968 | + | 2.96063i | −0.353927 | + | 0.157578i | −0.575996 | − | 0.817453i | \(-0.695386\pi\) |
0.222069 | + | 0.975031i | \(0.428719\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.35978 | − | 4.12461i | 0.0721695 | − | 0.218912i | ||||
\(356\) | 11.2231 | + | 4.99683i | 0.594821 | + | 0.264831i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.58165 | + | 43.5915i | 0.242148 | + | 2.30388i | ||||
\(359\) | 8.36007 | + | 25.7297i | 0.441228 | + | 1.35796i | 0.886568 | + | 0.462598i | \(0.153083\pi\) |
−0.445340 | + | 0.895361i | \(0.646917\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.571423 | − | 1.75866i | 0.0300749 | − | 0.0925610i | ||||
\(362\) | −44.1152 | − | 9.37698i | −2.31864 | − | 0.492843i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 18.1189 | − | 3.85129i | 0.949688 | − | 0.201862i | ||||
\(365\) | 31.9855 | + | 0.137368i | 1.67420 | + | 0.00719014i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.804907 | − | 7.65818i | −0.0420158 | − | 0.399754i | −0.995237 | − | 0.0974811i | \(-0.968921\pi\) |
0.953222 | − | 0.302272i | \(-0.0977452\pi\) | |||||||
\(368\) | −23.8358 | −1.24252 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 25.0614 | + | 5.43956i | 1.30288 | + | 0.282789i | ||||
\(371\) | 11.5583 | − | 5.14607i | 0.600075 | − | 0.267171i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.9033 | − | 4.86824i | 1.18589 | − | 0.252068i | 0.427587 | − | 0.903974i | \(-0.359364\pi\) |
0.758300 | + | 0.651906i | \(0.226030\pi\) | |||||||
\(374\) | −7.32716 | − | 12.6910i | −0.378879 | − | 0.656237i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −10.3310 | + | 17.8939i | −0.532782 | + | 0.922806i | ||||
\(377\) | 0.0116299 | − | 0.0357932i | 0.000598972 | − | 0.00184345i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5.93052 | − | 4.30878i | −0.304630 | − | 0.221327i | 0.424959 | − | 0.905213i | \(-0.360289\pi\) |
−0.729589 | + | 0.683886i | \(0.760289\pi\) | |||||||
\(380\) | 27.8532 | − | 30.6682i | 1.42884 | − | 1.57325i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −13.5509 | − | 23.4709i | −0.693327 | − | 1.20088i | ||||
\(383\) | −16.0311 | − | 7.13749i | −0.819149 | − | 0.364709i | −0.0460067 | − | 0.998941i | \(-0.514650\pi\) |
−0.773142 | + | 0.634232i | \(0.781316\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.99088 | − | 15.7283i | −0.458218 | − | 0.801587i | ||||
\(386\) | −4.91242 | + | 15.1189i | −0.250035 | + | 0.769530i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.52616 | − | 20.0854i | −0.331315 | − | 1.01968i | ||||
\(389\) | −0.222858 | − | 0.247509i | −0.0112993 | − | 0.0125492i | 0.737469 | − | 0.675381i | \(-0.236021\pi\) |
−0.748768 | + | 0.662832i | \(0.769354\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7919 | − | 15.3175i | 0.697489 | − | 0.774640i | ||||
\(392\) | −88.7801 | − | 39.5274i | −4.48407 | − | 1.99644i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6.48979 | − | 61.7463i | −0.326951 | − | 3.11073i | ||||
\(395\) | −5.06843 | − | 5.67792i | −0.255021 | − | 0.285687i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.6674 | + | 14.2892i | 0.987079 | + | 0.717155i | 0.959279 | − | 0.282459i | \(-0.0911501\pi\) |
0.0277993 | + | 0.999614i | \(0.491150\pi\) | |||||||
\(398\) | −4.08759 | − | 4.53973i | −0.204892 | − | 0.227556i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.9407 | − | 8.67374i | 0.997037 | − | 0.433687i | ||||
\(401\) | 10.6053 | + | 18.3689i | 0.529604 | + | 0.917301i | 0.999404 | + | 0.0345279i | \(0.0109927\pi\) |
−0.469800 | + | 0.882773i | \(0.655674\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.60552 | − | 0.714822i | 0.0799764 | − | 0.0356078i | ||||
\(404\) | −51.1050 | − | 37.1300i | −2.54257 | − | 1.84729i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.429911 | + | 0.312348i | −0.0213361 | + | 0.0155016i | ||||
\(407\) | 3.68862 | − | 6.38888i | 0.182838 | − | 0.316685i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.8116 | + | 12.0075i | −0.534601 | + | 0.593734i | −0.948574 | − | 0.316555i | \(-0.897474\pi\) |
0.413974 | + | 0.910289i | \(0.364141\pi\) | |||||||
\(410\) | −1.28358 | − | 4.00896i | −0.0633916 | − | 0.197989i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 63.1667 | + | 13.4265i | 3.11200 | + | 0.661476i | ||||
\(413\) | 15.0617 | + | 46.3553i | 0.741140 | + | 2.28099i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7.94837 | + | 3.49802i | −0.390170 | + | 0.171711i | ||||
\(416\) | 0.502189 | + | 0.106744i | 0.0246218 | + | 0.00523353i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −8.89600 | − | 15.4083i | −0.435118 | − | 0.753646i | ||||
\(419\) | −12.9294 | − | 5.75655i | −0.631644 | − | 0.281226i | 0.0658358 | − | 0.997830i | \(-0.479029\pi\) |
−0.697480 | + | 0.716604i | \(0.745695\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.8321 | + | 10.1655i | −1.11277 | + | 0.495436i | −0.878983 | − | 0.476852i | \(-0.841778\pi\) |
−0.233784 | + | 0.972288i | \(0.575111\pi\) | |||||||
\(422\) | −13.7314 | − | 9.97642i | −0.668432 | − | 0.485644i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.5203 | 0.608042 | ||||||||
\(425\) | −5.96422 | + | 17.8333i | −0.289307 | + | 0.865042i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −36.2726 | + | 7.70998i | −1.75535 | + | 0.373112i | ||||
\(428\) | 1.16844 | − | 11.1169i | 0.0564786 | − | 0.537358i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −22.4895 | − | 39.3422i | −1.08454 | − | 1.89725i | ||||
\(431\) | −4.09020 | + | 2.97170i | −0.197018 | + | 0.143142i | −0.681921 | − | 0.731426i | \(-0.738855\pi\) |
0.484903 | + | 0.874568i | \(0.338855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 16.2872 | − | 11.8334i | 0.782715 | − | 0.568676i | −0.123078 | − | 0.992397i | \(-0.539276\pi\) |
0.905793 | + | 0.423721i | \(0.139276\pi\) | |||||||
\(434\) | −24.2725 | − | 5.15928i | −1.16512 | − | 0.247654i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −50.0568 | + | 10.6399i | −2.39728 | + | 0.509558i | ||||
\(437\) | 16.7450 | − | 18.5972i | 0.801021 | − | 0.889624i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −26.5647 | − | 29.5031i | −1.26787 | − | 1.40811i | −0.871783 | − | 0.489892i | \(-0.837036\pi\) |
−0.396083 | − | 0.918215i | \(-0.629631\pi\) | |||||||
\(440\) | −1.79740 | − | 17.8377i | −0.0856877 | − | 0.850380i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.68012 | + | 4.85339i | −0.317741 | + | 0.230852i | ||||
\(443\) | −14.2137 | + | 24.6188i | −0.675313 | + | 1.16968i | 0.301065 | + | 0.953604i | \(0.402658\pi\) |
−0.976377 | + | 0.216072i | \(0.930675\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.77001 | − | 0.0290750i | −0.320929 | − | 0.00137829i | ||||
\(446\) | −3.39321 | + | 32.2843i | −0.160673 | + | 1.52870i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 24.9349 | + | 27.6930i | 1.17806 | + | 1.30837i | ||||
\(449\) | 32.9656 | 1.55574 | 0.777871 | − | 0.628424i | \(-0.216300\pi\) | ||||
0.777871 | + | 0.628424i | \(0.216300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.21092 | −0.0570202 | ||||||||
\(452\) | 34.6574 | + | 38.4910i | 1.63015 | + | 1.81046i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.51018 | − | 42.9115i | 0.211673 | − | 2.01394i | ||||
\(455\) | −8.28412 | + | 5.96458i | −0.388366 | + | 0.279624i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.1520 | − | 24.5120i | 0.662004 | − | 1.14663i | −0.318084 | − | 0.948063i | \(-0.603039\pi\) |
0.980088 | − | 0.198563i | \(-0.0636273\pi\) | |||||||
\(458\) | 32.3547 | − | 23.5070i | 1.51183 | − | 1.09841i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 45.5137 | − | 20.0303i | 2.12209 | − | 0.933916i | ||||
\(461\) | −11.1242 | − | 12.3547i | −0.518107 | − | 0.575416i | 0.426139 | − | 0.904658i | \(-0.359874\pi\) |
−0.944246 | + | 0.329242i | \(0.893207\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.28894 | − | 8.09519i | 0.338746 | − | 0.376216i | −0.549570 | − | 0.835447i | \(-0.685209\pi\) |
0.888316 | + | 0.459232i | \(0.151875\pi\) | |||||||
\(464\) | −0.179477 | + | 0.0381490i | −0.00833200 | + | 0.00177102i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −45.9104 | − | 9.75857i | −2.12676 | − | 0.452057i | ||||
\(467\) | −19.9438 | + | 14.4900i | −0.922888 | + | 0.670517i | −0.944241 | − | 0.329255i | \(-0.893203\pi\) |
0.0213532 | + | 0.999772i | \(0.493203\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.8906 | − | 10.8187i | 0.687586 | − | 0.499560i | ||||
\(470\) | 2.44295 | − | 22.3206i | 0.112685 | − | 1.02957i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.04175 | + | 47.9690i | −0.232065 | + | 2.20795i | ||||
\(473\) | −12.7513 | + | 2.71037i | −0.586304 | + | 0.124623i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.24123 | + | 21.6516i | −0.332250 | + | 0.993446i | ||||
\(476\) | 78.0949 | 3.57947 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.8749 | + | 10.0807i | 0.634621 | + | 0.461079i | ||||
\(479\) | 35.3981 | − | 15.7603i | 1.61738 | − | 0.720105i | 0.619490 | − | 0.785004i | \(-0.287339\pi\) |
0.997892 | + | 0.0648994i | \(0.0206727\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.79739 | − | 1.69071i | −0.173146 | − | 0.0770896i | ||||
\(482\) | −3.73324 | − | 6.46616i | −0.170044 | − | 0.294526i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 33.7106 | + | 7.16541i | 1.53230 | + | 0.325700i | ||||
\(485\) | 7.75029 | + | 8.68227i | 0.351923 | + | 0.394242i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.280386 | − | 0.862940i | −0.0127055 | − | 0.0391036i | 0.944503 | − | 0.328503i | \(-0.106544\pi\) |
−0.957208 | + | 0.289400i | \(0.906544\pi\) | |||||||
\(488\) | −35.8949 | − | 7.62969i | −1.62488 | − | 0.345380i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 105.609 | + | 0.453554i | 4.77091 | + | 0.0204895i | ||||
\(491\) | −3.13305 | + | 3.47961i | −0.141393 | + | 0.157032i | −0.809682 | − | 0.586869i | \(-0.800360\pi\) |
0.668289 | + | 0.743902i | \(0.267027\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.0793341 | − | 0.137411i | 0.00357303 | − | 0.00618866i | ||||
\(494\) | −8.11042 | + | 5.89257i | −0.364905 | + | 0.265119i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.93189 | − | 5.03631i | −0.311251 | − | 0.226137i | ||||
\(497\) | 9.08023 | − | 4.04278i | 0.407304 | − | 0.181343i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 7.00291 | + | 12.1294i | 0.313493 | + | 0.542986i | 0.979116 | − | 0.203302i | \(-0.0651673\pi\) |
−0.665623 | + | 0.746288i | \(0.731834\pi\) | |||||||
\(500\) | −30.7874 | + | 33.3194i | −1.37685 | + | 1.49009i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 24.0787 | + | 26.7421i | 1.07468 | + | 1.19356i | ||||
\(503\) | −23.8114 | − | 17.3000i | −1.06170 | − | 0.771370i | −0.0872979 | − | 0.996182i | \(-0.527823\pi\) |
−0.974402 | + | 0.224812i | \(0.927823\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 34.0191 | + | 7.38381i | 1.51383 | + | 0.328575i | ||||
\(506\) | −2.23226 | − | 21.2385i | −0.0992360 | − | 0.944167i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −28.2857 | − | 12.5936i | −1.25497 | − | 0.558750i | ||||
\(509\) | −3.82486 | + | 4.24793i | −0.169534 | + | 0.188286i | −0.821924 | − | 0.569596i | \(-0.807099\pi\) |
0.652391 | + | 0.757883i | \(0.273766\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 48.9833 | + | 54.4015i | 2.16690 | + | 2.40658i | ||||
\(512\) | 12.8388 | + | 39.5137i | 0.567399 | + | 1.74628i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.5988 | + | 41.8529i | −0.599819 | + | 1.84605i | ||||
\(515\) | −34.8412 | + | 7.24948i | −1.53529 | + | 0.319450i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −5.90085 | − | 2.62723i | −0.259519 | − | 0.115545i | ||||
\(518\) | 29.3462 | + | 50.8290i | 1.28940 | + | 2.23330i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9.88987 | + | 2.05780i | −0.433699 | + | 0.0902407i | ||||
\(521\) | 6.83148 | + | 4.96336i | 0.299293 | + | 0.217449i | 0.727288 | − | 0.686332i | \(-0.240780\pi\) |
−0.427996 | + | 0.903781i | \(0.640780\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.335514 | + | 1.03260i | −0.0146710 | + | 0.0451527i | −0.958124 | − | 0.286354i | \(-0.907557\pi\) |
0.943453 | + | 0.331506i | \(0.107557\pi\) | |||||||
\(524\) | 5.27390 | − | 9.13467i | 0.230392 | − | 0.399050i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.0981 | − | 26.1507i | −0.658309 | − | 1.14022i | ||||
\(527\) | 7.24743 | − | 1.54049i | 0.315703 | − | 0.0671047i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.42876 | − | 2.86227i | 0.279511 | − | 0.124446i | ||||
\(530\) | −12.4535 | + | 5.48067i | −0.540943 | + | 0.238065i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 94.8160 | 4.11079 | ||||||||
\(533\) | 0.0713202 | + | 0.678566i | 0.00308922 | + | 0.0293920i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.87838 | + | 5.86667i | 0.0812094 | + | 0.253638i | ||||
\(536\) | 17.8162 | − | 3.78694i | 0.769541 | − | 0.163571i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −55.9464 | − | 11.8918i | −2.41202 | − | 0.512691i | ||||
\(539\) | 9.38811 | − | 28.8936i | 0.404375 | − | 1.24454i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.62252 | + | 11.1490i | 0.155744 | + | 0.479331i | 0.998236 | − | 0.0593787i | \(-0.0189120\pi\) |
−0.842491 | + | 0.538710i | \(0.818912\pi\) | |||||||
\(542\) | −6.99970 | − | 66.5977i | −0.300663 | − | 2.86062i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.97737 | + | 0.880382i | 0.0847791 | + | 0.0377461i | ||||
\(545\) | 22.8864 | − | 16.4782i | 0.980346 | − | 0.705850i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −17.4993 | + | 7.79121i | −0.748217 | + | 0.333128i | −0.745176 | − | 0.666867i | \(-0.767635\pi\) |
−0.00304116 | + | 0.999995i | \(0.500968\pi\) | |||||||
\(548\) | −7.03820 | + | 21.6614i | −0.300657 | + | 0.925328i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.59610 | + | 16.9556i | 0.409179 | + | 0.722990i | ||||
\(551\) | 0.0963205 | − | 0.166832i | 0.00410339 | − | 0.00710728i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.82078 | − | 17.3236i | 0.0774275 | − | 0.736673i | ||||
\(554\) | 4.53034 | − | 43.1033i | 0.192476 | − | 1.83128i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.731417 | + | 6.95897i | 0.0310190 | + | 0.295126i | ||||
\(557\) | −18.2151 | −0.771799 | −0.385899 | − | 0.922541i | \(-0.626109\pi\) | ||||
−0.385899 | + | 0.922541i | \(0.626109\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.26983 | + | 6.98581i | 0.0960034 | + | 0.295468i | ||||
\(560\) | 45.3779 | + | 20.4375i | 1.91757 | + | 0.863642i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 23.7606 | − | 26.3889i | 1.00228 | − | 1.11315i | ||||
\(563\) | 9.06124 | − | 10.0635i | 0.381886 | − | 0.424127i | −0.521302 | − | 0.853372i | \(-0.674554\pi\) |
0.903188 | + | 0.429245i | \(0.141220\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −26.0251 | − | 11.7213i | −1.09489 | − | 0.493120i | ||||
\(566\) | 9.44896 | + | 29.0809i | 0.397169 | + | 1.22236i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.83605 | 0.412711 | ||||||||
\(569\) | 2.47240 | + | 23.5233i | 0.103648 | + | 0.986150i | 0.915509 | + | 0.402298i | \(0.131788\pi\) |
−0.811860 | + | 0.583852i | \(0.801545\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.79953 | − | 36.1501i | 0.159006 | − | 1.51284i | −0.566179 | − | 0.824282i | \(-0.691579\pi\) |
0.725185 | − | 0.688554i | \(-0.241754\pi\) | |||||||
\(572\) | −0.598999 | + | 5.69910i | −0.0250454 | + | 0.238291i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.81697 | − | 8.34323i | 0.201056 | − | 0.348240i | ||||
\(575\) | −18.5105 | + | 20.2062i | −0.771940 | + | 0.842657i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 10.9221 | − | 33.6148i | 0.454694 | − | 1.39940i | −0.416801 | − | 0.908998i | \(-0.636849\pi\) |
0.871494 | − | 0.490406i | \(-0.163151\pi\) | |||||||
\(578\) | 6.42167 | − | 2.85911i | 0.267106 | − | 0.118923i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.310648 | − | 0.223667i | 0.0128990 | − | 0.00928726i | ||||
\(581\) | −18.1565 | − | 8.08379i | −0.753258 | − | 0.335372i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.409130 | + | 3.89261i | 0.0169444 | + | 0.161215i | ||||
\(584\) | 22.3859 | + | 68.8966i | 0.926334 | + | 2.85096i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17.1619 | + | 52.8189i | −0.708951 | + | 2.18193i | ||||
\(587\) | 37.0299 | + | 7.87095i | 1.52839 | + | 0.324869i | 0.893972 | − | 0.448123i | \(-0.147907\pi\) |
0.634416 | + | 0.772992i | \(0.281240\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.79920 | − | 1.87033i | 0.362565 | − | 0.0770655i | ||||
\(590\) | −15.9832 | − | 49.9197i | −0.658019 | − | 2.05516i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.11836 | + | 20.1548i | 0.0870640 | + | 0.828358i | ||||
\(593\) | −33.1095 | −1.35964 | −0.679822 | − | 0.733377i | \(-0.737943\pi\) | ||||
−0.679822 | + | 0.733377i | \(0.737943\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −39.3904 | + | 17.3354i | −1.61485 | + | 0.710684i | ||||
\(596\) | −46.2265 | + | 20.5814i | −1.89351 | + | 0.843046i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −11.7700 | + | 2.50178i | −0.481310 | + | 0.102306i | ||||
\(599\) | −16.9563 | − | 29.3692i | −0.692816 | − | 1.19999i | −0.970912 | − | 0.239439i | \(-0.923037\pi\) |
0.278096 | − | 0.960553i | \(-0.410297\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.45268 | − | 12.9084i | 0.304001 | − | 0.526545i | −0.673037 | − | 0.739608i | \(-0.735011\pi\) |
0.977038 | + | 0.213063i | \(0.0683441\pi\) | |||||||
\(602\) | 32.0493 | − | 98.6376i | 1.30623 | − | 4.02017i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.3820 | − | 17.7145i | −0.992088 | − | 0.720794i | ||||
\(605\) | −18.5939 | + | 3.86887i | −0.755951 | + | 0.157292i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1.90528 | − | 3.30004i | −0.0773328 | − | 0.133944i | 0.824766 | − | 0.565475i | \(-0.191307\pi\) |
−0.902098 | + | 0.431530i | \(0.857974\pi\) | |||||||
\(608\) | 2.40075 | + | 1.06888i | 0.0973633 | + | 0.0433490i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 39.0429 | − | 8.12374i | 1.58080 | − | 0.328921i | ||||
\(611\) | −1.12468 | + | 3.46140i | −0.0454995 | + | 0.140033i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.301134 | + | 0.926794i | 0.0121627 | + | 0.0374329i | 0.956954 | − | 0.290241i | \(-0.0937354\pi\) |
−0.944791 | + | 0.327674i | \(0.893735\pi\) | |||||||
\(614\) | 45.3642 | + | 50.3821i | 1.83075 | + | 2.03326i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 27.4551 | − | 30.4920i | 1.10620 | − | 1.22856i | ||||
\(617\) | −26.9664 | − | 12.0062i | −1.08563 | − | 0.483352i | −0.215663 | − | 0.976468i | \(-0.569191\pi\) |
−0.869964 | + | 0.493115i | \(0.835858\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.456050 | + | 4.33902i | 0.0183302 | + | 0.174400i | 0.999857 | − | 0.0169259i | \(-0.00538792\pi\) |
−0.981527 | + | 0.191326i | \(0.938721\pi\) | |||||||
\(620\) | 17.4685 | + | 3.79153i | 0.701552 | + | 0.152271i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.00972 | − | 0.733602i | −0.0404859 | − | 0.0294148i | ||||
\(623\) | −10.3677 | − | 11.5145i | −0.415375 | − | 0.461320i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 8.13271 | − | 23.6402i | 0.325308 | − | 0.945608i | ||||
\(626\) | −16.2712 | − | 28.1825i | −0.650327 | − | 1.12640i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −34.8860 | + | 15.5322i | −1.39210 | + | 0.619804i | ||||
\(629\) | −14.1778 | − | 10.3008i | −0.565305 | − | 0.410718i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 39.3657 | − | 28.6008i | 1.56712 | − | 1.13858i | 0.637274 | − | 0.770637i | \(-0.280062\pi\) |
0.929848 | − | 0.367944i | \(-0.119938\pi\) | |||||||
\(632\) | 8.61881 | − | 14.9282i | 0.342838 | − | 0.593812i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −17.2765 | + | 19.1875i | −0.686137 | + | 0.762032i | ||||
\(635\) | 17.0626 | + | 0.0732783i | 0.677108 | + | 0.00290796i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16.7441 | − | 3.55906i | −0.663424 | − | 0.141015i | ||||
\(638\) | −0.0508004 | − | 0.156348i | −0.00201121 | − | 0.00618986i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −28.4009 | − | 31.8162i | −1.12265 | − | 1.25764i | ||||
\(641\) | 4.86398 | + | 1.03387i | 0.192116 | + | 0.0408354i | 0.302965 | − | 0.953002i | \(-0.402024\pi\) |
−0.110849 | + | 0.993837i | \(0.535357\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.30748 | + | 2.26463i | 0.0515621 | + | 0.0893081i | 0.890654 | − | 0.454681i | \(-0.150247\pi\) |
−0.839092 | + | 0.543989i | \(0.816913\pi\) | |||||||
\(644\) | 103.967 | + | 46.2892i | 4.09688 | + | 1.82405i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −38.6110 | + | 17.1907i | −1.51913 | + | 0.676360i | ||||
\(647\) | −13.0683 | − | 9.49465i | −0.513767 | − | 0.373273i | 0.300484 | − | 0.953787i | \(-0.402852\pi\) |
−0.814251 | + | 0.580514i | \(0.802852\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.0785 | −0.591882 | ||||||||
\(650\) | 8.93624 | − | 6.37601i | 0.350508 | − | 0.250088i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 12.4577 | − | 2.64796i | 0.487880 | − | 0.103702i | ||||
\(653\) | −1.81745 | + | 17.2919i | −0.0711222 | + | 0.676683i | 0.899639 | + | 0.436635i | \(0.143830\pi\) |
−0.970761 | + | 0.240048i | \(0.922837\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.632409 | + | 5.77815i | −0.0247103 | + | 0.225771i | ||||
\(656\) | 2.69119 | − | 1.95527i | 0.105073 | − | 0.0763403i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 41.5747 | − | 30.2058i | 1.62075 | − | 1.17754i | ||||
\(659\) | −44.0854 | − | 9.37064i | −1.71732 | − | 0.365028i | −0.759083 | − | 0.650993i | \(-0.774353\pi\) |
−0.958240 | + | 0.285965i | \(0.907686\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 29.8878 | − | 6.35285i | 1.16250 | − | 0.247097i | 0.414029 | − | 0.910263i | \(-0.364121\pi\) |
0.748472 | + | 0.663166i | \(0.230788\pi\) | |||||||
\(662\) | 4.02803 | − | 4.47358i | 0.156554 | − | 0.173871i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −13.1603 | − | 14.6160i | −0.510720 | − | 0.567212i | ||||
\(665\) | −47.8244 | + | 21.0472i | −1.85455 | + | 0.816174i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.187065 | − | 0.135910i | 0.00724317 | − | 0.00526247i | ||||
\(668\) | 5.82068 | − | 10.0817i | 0.225209 | − | 0.390073i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −16.0633 | + | 11.5656i | −0.620578 | + | 0.446817i | ||||
\(671\) | 1.19915 | − | 11.4091i | 0.0462926 | − | 0.440445i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −9.69457 | − | 10.7669i | −0.373698 | − | 0.415034i | 0.526734 | − | 0.850030i | \(-0.323416\pi\) |
−0.900432 | + | 0.434996i | \(0.856750\pi\) | |||||||
\(674\) | −4.51468 | −0.173899 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −49.5203 | −1.90463 | ||||||||
\(677\) | 7.87728 | + | 8.74860i | 0.302748 | + | 0.336236i | 0.875253 | − | 0.483665i | \(-0.160695\pi\) |
−0.572505 | + | 0.819901i | \(0.694028\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.78421 | + | 26.4900i | −0.106848 | + | 1.01659i | ||||
\(680\) | −42.5878 | − | 0.182901i | −1.63317 | − | 0.00701392i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.83835 | − | 6.64822i | 0.146978 | − | 0.254574i | ||||
\(683\) | 7.80859 | − | 5.67327i | 0.298787 | − | 0.217082i | −0.428283 | − | 0.903645i | \(-0.640881\pi\) |
0.727070 | + | 0.686563i | \(0.240881\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.25836 | − | 12.4882i | −0.0480794 | − | 0.477148i | ||||
\(686\) | 102.735 | + | 114.099i | 3.92243 | + | 4.35630i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 23.9624 | − | 26.6130i | 0.913559 | − | 1.01461i | ||||
\(689\) | 2.15721 | − | 0.458529i | 0.0821831 | − | 0.0174686i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.843717 | − | 0.179338i | −0.0320965 | − | 0.00682233i | 0.191835 | − | 0.981427i | \(-0.438556\pi\) |
−0.223932 | + | 0.974605i | \(0.571889\pi\) | |||||||
\(692\) | 52.1734 | − | 37.9062i | 1.98334 | − | 1.44098i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0.594103 | − | 0.431641i | 0.0225518 | − | 0.0163849i | ||||
\(695\) | −1.91367 | − | 3.34769i | −0.0725895 | − | 0.126985i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.300682 | + | 2.86080i | −0.0113891 | + | 0.108360i | ||||
\(698\) | 40.6753 | − | 8.64580i | 1.53958 | − | 0.327248i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −103.822 | − | 0.891783i | −3.92412 | − | 0.0337062i | ||||
\(701\) | 9.06128 | 0.342240 | 0.171120 | − | 0.985250i | \(-0.445261\pi\) | ||||
0.171120 | + | 0.985250i | \(0.445261\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.2134 | − | 12.5063i | −0.649216 | − | 0.471683i | ||||
\(704\) | −10.5315 | + | 4.68893i | −0.396921 | + | 0.176721i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.3664 | + | 7.28677i | 0.615956 | + | 0.274241i | ||||
\(707\) | 39.8353 | + | 68.9968i | 1.49816 | + | 2.59489i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.1213 | + | 8.95316i | 1.58190 | + | 0.336243i | 0.913270 | − | 0.407354i | \(-0.133548\pi\) |
0.668628 | + | 0.743597i | \(0.266882\pi\) | |||||||
\(710\) | −9.78350 | + | 4.30564i | −0.367168 | + | 0.161588i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.73816 | − | 14.5825i | −0.177570 | − | 0.546504i | ||||
\(713\) | 10.5616 | + | 2.24493i | 0.395534 | + | 0.0840733i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.962950 | − | 3.00754i | −0.0360123 | − | 0.112476i | ||||
\(716\) | 48.3525 | − | 53.7009i | 1.80702 | − | 2.00690i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 33.2927 | − | 57.6647i | 1.24247 | − | 2.15203i | ||||
\(719\) | −22.4736 | + | 16.3280i | −0.838124 | + | 0.608933i | −0.921846 | − | 0.387556i | \(-0.873319\pi\) |
0.0837219 | + | 0.996489i | \(0.473319\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −65.8922 | − | 47.8735i | −2.45395 | − | 1.78290i | ||||
\(722\) | −4.15773 | + | 1.85114i | −0.154735 | + | 0.0688924i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 37.1771 | + | 64.3926i | 1.38167 | + | 2.39313i | ||||
\(725\) | −0.107039 | + | 0.181773i | −0.00397533 | + | 0.00675089i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.2729 | + | 21.4047i | 0.714792 | + | 0.793857i | 0.985657 | − | 0.168761i | \(-0.0539765\pi\) |
−0.270865 | + | 0.962617i | \(0.587310\pi\) | |||||||
\(728\) | −18.7039 | − | 13.5891i | −0.693211 | − | 0.503647i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −52.4251 | − | 58.7293i | −1.94034 | − | 2.17367i | ||||
\(731\) | 3.23698 | + | 30.7978i | 0.119724 | + | 1.13910i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4914 | + | 5.11632i | 0.424446 | + | 0.188976i | 0.607832 | − | 0.794065i | \(-0.292039\pi\) |
−0.183386 | + | 0.983041i | \(0.558706\pi\) | |||||||
\(734\) | −12.6816 | + | 14.0843i | −0.468086 | + | 0.519862i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.11063 | + | 2.34410i | 0.0777990 | + | 0.0864046i | ||||
\(737\) | 1.75955 | + | 5.41535i | 0.0648140 | + | 0.199477i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −14.5062 | + | 44.6456i | −0.533620 | + | 1.64231i | 0.212992 | + | 0.977054i | \(0.431679\pi\) |
−0.746612 | + | 0.665259i | \(0.768321\pi\) | |||||||
\(740\) | −20.9820 | − | 36.7050i | −0.771312 | − | 1.34930i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −28.4475 | − | 12.6656i | −1.04434 | − | 0.464970i | ||||
\(743\) | −3.97180 | − | 6.87937i | −0.145711 | − | 0.252379i | 0.783927 | − | 0.620853i | \(-0.213214\pi\) |
−0.929638 | + | 0.368474i | \(0.879880\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 18.7477 | − | 20.6424i | 0.686861 | − | 0.756279i | ||||
\(746\) | −46.6232 | − | 33.8738i | −1.70700 | − | 1.24021i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −7.46568 | + | 22.9770i | −0.272972 | + | 0.840122i | ||||
\(749\) | −7.04910 | + | 12.2094i | −0.257568 | + | 0.446121i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.40667 | + | 11.0967i | 0.233783 | + | 0.404923i | 0.958918 | − | 0.283683i | \(-0.0915563\pi\) |
−0.725136 | + | 0.688606i | \(0.758223\pi\) | |||||||
\(752\) | 17.3564 | − | 3.68921i | 0.632922 | − | 0.134532i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.0846206 | + | 0.0376755i | −0.00308170 | + | 0.00137206i | ||||
\(755\) | 16.2303 | + | 3.52278i | 0.590682 | + | 0.128207i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 4.66915 | 0.169703 | 0.0848516 | − | 0.996394i | \(-0.472958\pi\) | ||||
0.0848516 | + | 0.996394i | \(0.472958\pi\) | |||||||
\(758\) | 1.88591 | + | 17.9432i | 0.0684994 | + | 0.651728i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −51.7064 | − | 0.222062i | −1.87559 | − | 0.00805504i | ||||
\(761\) | −0.470836 | + | 0.100079i | −0.0170678 | + | 0.00362787i | −0.216438 | − | 0.976296i | \(-0.569444\pi\) |
0.199370 | + | 0.979924i | \(0.436110\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 63.1328 | + | 13.4193i | 2.28556 | + | 0.485811i | ||||
\(764\) | −13.8071 | + | 42.4939i | −0.499524 | + | 1.53738i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 13.3465 | + | 41.0762i | 0.482227 | + | 1.48414i | ||||
\(767\) | 0.888081 | + | 8.44953i | 0.0320668 | + | 0.305095i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.7723 | + | 4.79612i | 0.388458 | + | 0.172952i | 0.591666 | − | 0.806183i | \(-0.298470\pi\) |
−0.203209 | + | 0.979135i | \(0.565137\pi\) | |||||||
\(770\) | −13.9608 | + | 42.3473i | −0.503113 | + | 1.52609i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.9422 | − | 10.6598i | 0.861699 | − | 0.383653i | ||||
\(773\) | 9.94328 | − | 30.6023i | 0.357635 | − | 1.10069i | −0.596831 | − | 0.802367i | \(-0.703574\pi\) |
0.954466 | − | 0.298320i | \(-0.0964262\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9.65261 | + | 1.96523i | −0.346732 | + | 0.0705930i | ||||
\(776\) | −13.1793 | + | 22.8272i | −0.473108 | + | 0.819447i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −0.0856846 | + | 0.815235i | −0.00307194 | + | 0.0292276i | ||||
\(779\) | −0.365062 | + | 3.47333i | −0.0130797 | + | 0.124445i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.321415 | + | 3.05806i | 0.0115011 | + | 0.109426i | ||||
\(782\) | −50.7301 | −1.81411 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 25.7898 | + | 79.3730i | 0.921066 | + | 2.83475i | ||||
\(785\) | 14.1484 | − | 15.5783i | 0.504978 | − | 0.556014i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.5391 | + | 17.2580i | −0.553911 | + | 0.615180i | −0.953456 | − | 0.301533i | \(-0.902502\pi\) |
0.399545 | + | 0.916714i | \(0.369168\pi\) | |||||||
\(788\) | −68.4902 | + | 76.0661i | −2.43986 | + | 2.70974i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.03807 | + | 18.6213i | −0.0725111 | + | 0.662515i | ||||
\(791\) | −20.1865 | − | 62.1275i | −0.717748 | − | 2.20900i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.46397 | −0.229542 | ||||||||
\(794\) | −6.25425 | − | 59.5052i | −0.221955 | − | 2.11176i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.05272 | + | 10.0159i | −0.0373126 | + | 0.355006i | ||||
\(797\) | −4.96592 | + | 47.2475i | −0.175902 | + | 1.67359i | 0.449492 | + | 0.893285i | \(0.351605\pi\) |
−0.625394 | + | 0.780310i | \(0.715062\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7.67203 | + | 13.2883i | −0.271417 | + | 0.470108i | ||||
\(800\) | −2.61874 | − | 1.19300i | −0.0925865 | − | 0.0421788i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 16.1320 | − | 49.6491i | 0.569639 | − | 1.75317i | ||||
\(803\) | −20.6886 | + | 9.21118i | −0.730087 | + | 0.325055i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −62.7155 | − | 0.269343i | −2.21043 | − | 0.00949309i | ||||
\(806\) | −3.95154 | − | 1.75934i | −0.139187 | − | 0.0619700i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 8.24113 | + | 78.4091i | 0.289922 | + | 2.75842i | ||||
\(809\) | −8.12369 | − | 25.0022i | −0.285614 | − | 0.879029i | −0.986214 | − | 0.165475i | \(-0.947084\pi\) |
0.700600 | − | 0.713554i | \(-0.252916\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.66526 | + | 14.3582i | −0.163819 | + | 0.504184i | −0.998947 | − | 0.0458715i | \(-0.985394\pi\) |
0.835128 | + | 0.550056i | \(0.185394\pi\) | |||||||
\(812\) | 0.856931 | + | 0.182146i | 0.0300724 | + | 0.00639208i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −17.7603 | + | 3.77507i | −0.622498 | + | 0.132316i | ||||
\(815\) | −5.69576 | + | 4.10096i | −0.199514 | + | 0.143650i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.93006 | + | 37.3920i | 0.137495 | + | 1.30818i | ||||
\(818\) | 39.7678 | 1.39045 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.49566 | + | 5.99506i | −0.122074 | + | 0.209357i | ||||
\(821\) | −3.68804 | + | 1.64202i | −0.128714 | + | 0.0573070i | −0.470083 | − | 0.882622i | \(-0.655776\pi\) |
0.341369 | + | 0.939929i | \(0.389109\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −38.8703 | + | 8.26213i | −1.35493 | + | 0.288000i | −0.827437 | − | 0.561558i | \(-0.810202\pi\) |
−0.527495 | + | 0.849558i | \(0.676869\pi\) | |||||||
\(824\) | −40.2995 | − | 69.8009i | −1.40390 | − | 2.43163i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 59.9811 | − | 103.890i | 2.08701 | − | 3.61480i | ||||
\(827\) | −11.8321 | + | 36.4154i | −0.411441 | + | 1.26629i | 0.503954 | + | 0.863730i | \(0.331878\pi\) |
−0.915396 | + | 0.402556i | \(0.868122\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.2683 | + | 22.7178i | 1.08599 | + | 0.789020i | 0.978718 | − | 0.205209i | \(-0.0657874\pi\) |
0.107275 | + | 0.994229i | \(0.465787\pi\) | |||||||
\(830\) | 19.4881 | + | 8.77712i | 0.676440 | + | 0.304658i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.24782 | + | 5.62538i | 0.112598 | + | 0.195025i | ||||
\(833\) | −65.9299 | − | 29.3539i | −2.28433 | − | 1.01705i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.697975 | + | 6.37721i | −0.0241544 | + | 0.220692i | ||||
\(836\) | −9.06417 | + | 27.8967i | −0.313491 | + | 0.964826i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.7642 | + | 33.1289i | 0.371844 | + | 1.14442i | ||||
\(839\) | 22.1018 | + | 24.5466i | 0.763039 | + | 0.847441i | 0.992032 | − | 0.125987i | \(-0.0402098\pi\) |
−0.228993 | + | 0.973428i | \(0.573543\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −19.4036 | + | 21.5499i | −0.669090 | + | 0.743099i | ||||
\(842\) | 56.1949 | + | 25.0196i | 1.93660 | + | 0.862232i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.92490 | + | 27.8286i | 0.100679 | + | 0.957900i | ||||
\(845\) | 24.9777 | − | 10.9925i | 0.859257 | − | 0.378153i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −35.1651 | − | 25.5489i | −1.20829 | − | 0.877872i | ||||
\(848\) | −7.19462 | − | 7.99044i | −0.247064 | − | 0.274393i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 42.4403 | − | 18.4605i | 1.45569 | − | 0.633190i | ||||
\(851\) | −12.7692 | − | 22.1169i | −0.437723 | − | 0.758159i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.4168 | − | 6.41879i | 0.493623 | − | 0.219775i | −0.144800 | − | 0.989461i | \(-0.546254\pi\) |
0.638423 | + | 0.769686i | \(0.279587\pi\) | |||||||
\(854\) | 73.8385 | + | 53.6468i | 2.52670 | + | 1.83576i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −11.2869 | + | 8.20042i | −0.385779 | + | 0.280285i | ||||
\(857\) | 19.9971 | − | 34.6359i | 0.683086 | − | 1.18314i | −0.290948 | − | 0.956739i | \(-0.593971\pi\) |
0.974034 | − | 0.226401i | \(-0.0726961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.3537 | − | 41.4854i | 1.27449 | − | 1.41547i | 0.410576 | − | 0.911826i | \(-0.365328\pi\) |
0.863914 | − | 0.503639i | \(-0.168006\pi\) | |||||||
\(860\) | −23.3915 | + | 70.9535i | −0.797645 | + | 2.41949i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 12.1715 | + | 2.58712i | 0.414562 | + | 0.0881178i | ||||
\(863\) | −2.37722 | − | 7.31633i | −0.0809215 | − | 0.249051i | 0.902408 | − | 0.430882i | \(-0.141797\pi\) |
−0.983330 | + | 0.181831i | \(0.941797\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.9015 | + | 30.7010i | −0.608668 | + | 1.04387i | ||||
\(866\) | −48.4670 | − | 10.3020i | −1.64697 | − | 0.350075i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 20.4551 | + | 35.4293i | 0.694291 | + | 1.20255i | ||||
\(869\) | 4.92286 | + | 2.19180i | 0.166997 | + | 0.0743517i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.93097 | − | 1.30495i | 0.0993121 | − | 0.0442166i | ||||
\(872\) | 51.6728 | + | 37.5425i | 1.74986 | + | 1.27135i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −61.5921 | −2.08338 | ||||||||
\(875\) | 52.5652 | − | 22.5966i | 1.77703 | − | 0.763905i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5.86040 | − | 1.24567i | 0.197892 | − | 0.0420632i | −0.107899 | − | 0.994162i | \(-0.534412\pi\) |
0.305791 | + | 0.952099i | \(0.401079\pi\) | |||||||
\(878\) | −10.2136 | + | 97.1763i | −0.344694 | + | 3.27954i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10.3511 | + | 11.3973i | −0.348936 | + | 0.384202i | ||||
\(881\) | 35.8213 | − | 26.0257i | 1.20685 | − | 0.876829i | 0.211910 | − | 0.977289i | \(-0.432032\pi\) |
0.994941 | + | 0.100461i | \(0.0320317\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.8054 | − | 27.4673i | 1.27225 | − | 0.924347i | 0.272964 | − | 0.962024i | \(-0.411996\pi\) |
0.999290 | + | 0.0376774i | \(0.0119959\pi\) | |||||||
\(884\) | 13.3153 | + | 2.83026i | 0.447843 | + | 0.0951920i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 68.4372 | − | 14.5468i | 2.29919 | − | 0.488709i | ||||
\(887\) | −24.3581 | + | 27.0524i | −0.817865 | + | 0.908331i | −0.997148 | − | 0.0754668i | \(-0.975955\pi\) |
0.179284 | + | 0.983797i | \(0.442622\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 26.1300 | + | 29.0203i | 0.876372 | + | 0.973310i | ||||
\(890\) | 11.0962 | + | 12.4306i | 0.371946 | + | 0.416673i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 43.2968 | − | 31.4569i | 1.44968 | − | 1.05326i | ||||
\(893\) | −9.31471 | + | 16.1336i | −0.311705 | + | 0.539889i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.4682 | + | 37.8196i | −0.416764 | + | 1.26417i | ||||
\(896\) | 10.2027 | − | 97.0725i | 0.340849 | − | 3.24297i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −54.2904 | − | 60.2956i | −1.81169 | − | 2.01209i | ||||
\(899\) | 0.0831187 | 0.00277216 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.29786 | 0.309757 | ||||||||
\(902\) | 1.99425 | + | 2.21484i | 0.0664012 | + | 0.0737460i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.75719 | − | 64.2904i | 0.224741 | − | 2.13827i | ||||
\(905\) | −33.0456 | − | 24.2266i | −1.09847 | − | 0.805319i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.52629 | − | 13.0359i | 0.249906 | − | 0.432850i | −0.713593 | − | 0.700560i | \(-0.752934\pi\) |
0.963500 | + | 0.267710i | \(0.0862669\pi\) | |||||||
\(908\) | −57.5491 | + | 41.8119i | −1.90983 | + | 1.38758i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 24.5525 | + | 5.32909i | 0.813906 | + | 0.176658i | ||||
\(911\) | −39.2302 | − | 43.5696i | −1.29976 | − | 1.44352i | −0.826862 | − | 0.562405i | \(-0.809876\pi\) |
−0.472894 | − | 0.881120i | \(-0.656791\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.11412 | − | 4.56920i | 0.136158 | − | 0.151218i | ||||
\(914\) | −68.1404 | + | 14.4837i | −2.25388 | + | 0.479078i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −64.4918 | − | 13.7082i | −2.13087 | − | 0.452930i | ||||
\(917\) | −10.7625 | + | 7.81939i | −0.355408 | + | 0.258219i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.91856 | + | 4.30008i | −0.195235 | + | 0.141847i | −0.681108 | − | 0.732183i | \(-0.738502\pi\) |
0.485873 | + | 0.874029i | \(0.338502\pi\) | |||||||
\(920\) | −56.5885 | − | 25.4866i | −1.86567 | − | 0.840267i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.27706 | + | 40.6935i | −0.140857 | + | 1.34017i | ||||
\(923\) | 1.69471 | − | 0.360223i | 0.0557822 | − | 0.0118569i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.7309 | + | 13.8561i | 0.615867 | + | 0.455587i | ||||
\(926\) | −26.8105 | −0.881048 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.0196442 | + | 0.0142724i | 0.000644853 | + | 0.000468513i | ||||
\(929\) | 18.1828 | − | 8.09550i | 0.596558 | − | 0.265605i | −0.0861664 | − | 0.996281i | \(-0.527462\pi\) |
0.682724 | + | 0.730676i | \(0.260795\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −80.0463 | − | 35.6389i | −2.62341 | − | 1.16802i | ||||
\(932\) | 38.6899 | + | 67.0130i | 1.26733 | + | 2.19508i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 59.3479 | + | 12.6148i | 1.94192 | + | 0.412769i | ||||
\(935\) | −1.33479 | − | 13.2466i | −0.0436522 | − | 0.433211i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.65299 | + | 17.3981i | 0.184675 | + | 0.568371i | 0.999943 | − | 0.0107132i | \(-0.00341019\pi\) |
−0.815268 | + | 0.579084i | \(0.803410\pi\) | |||||||
\(938\) | −44.3110 | − | 9.41859i | −1.44681 | − | 0.307528i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30.0413 | + | 21.6298i | −0.979840 | + | 0.705486i | ||||
\(941\) | 12.6090 | − | 14.0037i | 0.411041 | − | 0.456507i | −0.501703 | − | 0.865040i | \(-0.667293\pi\) |
0.912743 | + | 0.408533i | \(0.133960\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.09598 | + | 3.63034i | −0.0682545 | + | 0.118220i | ||||
\(944\) | 33.5108 | − | 24.3470i | 1.09068 | − | 0.792429i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.9572 | + | 18.8590i | 0.843942 | + | 0.613160i | ||||
\(947\) | −27.7953 | + | 12.3753i | −0.903226 | + | 0.402142i | −0.805174 | − | 0.593039i | \(-0.797928\pi\) |
−0.0980527 | + | 0.995181i | \(0.531261\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.38018 | + | 11.0508i | 0.207109 | + | 0.358724i | ||||
\(950\) | 51.5273 | − | 22.4131i | 1.67177 | − | 0.727178i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −65.2198 | − | 72.4339i | −2.11379 | − | 2.34760i | ||||
\(953\) | 6.16233 | + | 4.47720i | 0.199617 | + | 0.145031i | 0.683104 | − | 0.730321i | \(-0.260630\pi\) |
−0.483486 | + | 0.875352i | \(0.660630\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.46857 | − | 24.4985i | −0.0798810 | − | 0.792753i | ||||
\(956\) | −2.95547 | − | 28.1194i | −0.0955867 | − | 0.909446i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −87.1228 | − | 38.7896i | −2.81481 | − | 1.25323i | ||||
\(959\) | 19.2213 | − | 21.3474i | 0.620688 | − | 0.689344i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18.1459 | − | 20.1530i | −0.585351 | − | 0.650098i | ||||
\(962\) | 3.16147 | + | 9.73000i | 0.101930 | + | 0.313708i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.80381 | + | 11.7069i | −0.122513 | + | 0.377055i | ||||
\(965\) | −9.71002 | + | 10.6914i | −0.312577 | + | 0.344167i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 45.3597 | + | 20.1955i | 1.45867 | + | 0.649442i | 0.974266 | − | 0.225402i | \(-0.0723695\pi\) |
0.484405 | + | 0.874844i | \(0.339036\pi\) | |||||||
\(968\) | −21.5069 | − | 37.2511i | −0.691258 | − | 1.19729i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.11647 | − | 28.4743i | 0.100064 | − | 0.914255i | ||||
\(971\) | 0.472976 | + | 0.343637i | 0.0151785 | + | 0.0110278i | 0.595349 | − | 0.803467i | \(-0.297014\pi\) |
−0.580170 | + | 0.814495i | \(0.697014\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.72713 | − | 8.39323i | 0.0874276 | − | 0.269075i | ||||
\(974\) | −1.11660 | + | 1.93400i | −0.0357780 | + | 0.0619693i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 15.7572 | + | 27.2923i | 0.504376 | + | 0.873604i | ||||
\(977\) | 53.8166 | − | 11.4391i | 1.72174 | − | 0.365968i | 0.762160 | − | 0.647389i | \(-0.224139\pi\) |
0.959585 | + | 0.281420i | \(0.0908055\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.37893 | − | 1.94962i | 0.139951 | − | 0.0623103i | ||||
\(980\) | −115.946 | − | 129.888i | −3.70375 | − | 4.14913i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.5241 | 0.367750 | ||||||||
\(983\) | 6.11179 | + | 58.1498i | 0.194936 | + | 1.85469i | 0.456778 | + | 0.889581i | \(0.349003\pi\) |
−0.261842 | + | 0.965111i | \(0.584330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 17.6608 | − | 53.5705i | 0.562721 | − | 1.70690i | ||||
\(986\) | −0.381984 | + | 0.0811933i | −0.0121649 | + | 0.00258572i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 16.1663 | + | 3.43626i | 0.514319 | + | 0.109322i | ||||
\(989\) | −13.9454 | + | 42.9196i | −0.443439 | + | 1.36476i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.9966 | − | 46.1549i | −0.476384 | − | 1.46616i | −0.844082 | − | 0.536213i | \(-0.819854\pi\) |
0.367699 | − | 0.929945i | \(-0.380146\pi\) | |||||||
\(992\) | 0.118523 | + | 1.12767i | 0.00376310 | + | 0.0358035i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.3485 | − | 9.95019i | −0.708851 | − | 0.315601i | ||||
\(995\) | −1.69235 | − | 5.28565i | −0.0536511 | − | 0.167566i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 42.4960 | − | 18.9204i | 1.34586 | − | 0.599216i | 0.397849 | − | 0.917451i | \(-0.369757\pi\) |
0.948012 | + | 0.318235i | \(0.103090\pi\) | |||||||
\(998\) | 10.6523 | − | 32.7843i | 0.337192 | − | 1.03777i | ||||
\(999\) | 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 | 675.2.r.a.46.3 | 224 | ||
3.2 | odd | 2 | 225.2.q.a.196.26 | yes | 224 | ||
9.4 | even | 3 | inner | 675.2.r.a.496.26 | 224 | ||
9.5 | odd | 6 | 225.2.q.a.121.3 | yes | 224 | ||
25.6 | even | 5 | inner | 675.2.r.a.181.26 | 224 | ||
75.56 | odd | 10 | 225.2.q.a.106.3 | yes | 224 | ||
225.31 | even | 15 | inner | 675.2.r.a.631.3 | 224 | ||
225.131 | odd | 30 | 225.2.q.a.31.26 | ✓ | 224 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.q.a.31.26 | ✓ | 224 | 225.131 | odd | 30 | ||
225.2.q.a.106.3 | yes | 224 | 75.56 | odd | 10 | ||
225.2.q.a.121.3 | yes | 224 | 9.5 | odd | 6 | ||
225.2.q.a.196.26 | yes | 224 | 3.2 | odd | 2 | ||
675.2.r.a.46.3 | 224 | 1.1 | even | 1 | trivial | ||
675.2.r.a.181.26 | 224 | 25.6 | even | 5 | inner | ||
675.2.r.a.496.26 | 224 | 9.4 | even | 3 | inner | ||
675.2.r.a.631.3 | 224 | 225.31 | even | 15 | inner |