Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(73,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 9, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.73");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.bv (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 10x^{14} + 61x^{12} + 266x^{10} + 852x^{8} + 1438x^{6} + 1933x^{4} + 3038x^{2} + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 70) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 397.2 | ||
Root | \(1.45333 + 1.51725i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.397 |
Dual form | 630.2.bv.c.73.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.965926 | + | 0.258819i | −0.683013 | + | 0.183013i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.866025 | − | 0.500000i | 0.433013 | − | 0.250000i | ||||
\(5\) | 1.79038 | − | 1.33961i | 0.800681 | − | 0.599091i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.55176 | + | 0.698943i | −0.964475 | + | 0.264175i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.38266 | + | 1.75735i | −0.437234 | + | 0.555722i | ||||
\(11\) | 0.371536 | + | 0.643519i | 0.112022 | + | 0.194028i | 0.916586 | − | 0.399839i | \(-0.130934\pi\) |
−0.804563 | + | 0.593867i | \(0.797601\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.05532 | + | 2.05532i | 0.570044 | + | 0.570044i | 0.932141 | − | 0.362097i | \(-0.117939\pi\) |
−0.362097 | + | 0.932141i | \(0.617939\pi\) | |||||||
\(14\) | 2.28391 | − | 1.33557i | 0.610401 | − | 0.356946i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | 6.33660 | + | 1.69789i | 1.53685 | + | 0.411798i | 0.925247 | − | 0.379365i | \(-0.123857\pi\) |
0.611605 | + | 0.791163i | \(0.290524\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.946027 | − | 1.63857i | 0.217033 | − | 0.375913i | −0.736866 | − | 0.676039i | \(-0.763695\pi\) |
0.953900 | + | 0.300126i | \(0.0970286\pi\) | |||||||
\(20\) | 0.880708 | − | 2.05532i | 0.196932 | − | 0.459584i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.525431 | − | 0.525431i | −0.112022 | − | 0.112022i | ||||
\(23\) | 1.36952 | + | 5.11112i | 0.285565 | + | 1.06574i | 0.948426 | + | 0.317000i | \(0.102675\pi\) |
−0.662861 | + | 0.748743i | \(0.730658\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.41090 | − | 4.79681i | 0.282180 | − | 0.959361i | ||||
\(26\) | −2.51725 | − | 1.45333i | −0.493673 | − | 0.285022i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.86042 | + | 1.88118i | −0.351586 | + | 0.355510i | ||||
\(29\) | − | 9.69135i | − | 1.79964i | −0.436263 | − | 0.899819i | \(-0.643698\pi\) | ||
0.436263 | − | 0.899819i | \(-0.356302\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.96403 | − | 1.71129i | 0.532356 | − | 0.307356i | −0.209619 | − | 0.977783i | \(-0.567222\pi\) |
0.741975 | + | 0.670427i | \(0.233889\pi\) | |||||||
\(32\) | −0.258819 | + | 0.965926i | −0.0457532 | + | 0.170753i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −6.56014 | −1.12505 | ||||||||
\(35\) | −3.63230 | + | 4.66973i | −0.613971 | + | 0.789328i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.58012 | − | 0.691342i | 0.424170 | − | 0.113656i | −0.0404183 | − | 0.999183i | \(-0.512869\pi\) |
0.464588 | + | 0.885527i | \(0.346202\pi\) | |||||||
\(38\) | −0.489700 | + | 1.82758i | −0.0794398 | + | 0.296473i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.318742 | + | 2.21323i | −0.0503975 | + | 0.349943i | ||||
\(41\) | 0.817699i | 0.127703i | 0.997959 | + | 0.0638515i | \(0.0203384\pi\) | ||||
−0.997959 | + | 0.0638515i | \(0.979662\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.59589 | − | 1.59589i | 0.243371 | − | 0.243371i | −0.574872 | − | 0.818243i | \(-0.694948\pi\) |
0.818243 | + | 0.574872i | \(0.194948\pi\) | |||||||
\(44\) | 0.643519 | + | 0.371536i | 0.0970142 | + | 0.0560111i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.64571 | − | 4.58251i | −0.390089 | − | 0.675654i | ||||
\(47\) | −1.21894 | − | 4.54913i | −0.177800 | − | 0.663560i | −0.996058 | − | 0.0887076i | \(-0.971726\pi\) |
0.818257 | − | 0.574852i | \(-0.194940\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.02296 | − | 3.56707i | 0.860423 | − | 0.509581i | ||||
\(50\) | −0.121320 | + | 4.99853i | −0.0171573 | + | 0.706899i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.80762 | + | 0.752300i | 0.389347 | + | 0.104325i | ||||
\(53\) | 4.81583 | + | 1.29040i | 0.661505 | + | 0.177250i | 0.573925 | − | 0.818908i | \(-0.305420\pi\) |
0.0875798 | + | 0.996158i | \(0.472087\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.52725 | + | 0.654429i | 0.205935 | + | 0.0882432i | ||||
\(56\) | 1.31014 | − | 2.29859i | 0.175075 | − | 0.307163i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50831 | + | 9.36112i | 0.329357 | + | 1.22918i | ||||
\(59\) | 1.27487 | + | 2.20815i | 0.165975 | + | 0.287476i | 0.937001 | − | 0.349327i | \(-0.113590\pi\) |
−0.771026 | + | 0.636803i | \(0.780256\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.25989 | + | 3.03680i | 0.673460 | + | 0.388822i | 0.797386 | − | 0.603469i | \(-0.206215\pi\) |
−0.123927 | + | 0.992291i | \(0.539549\pi\) | |||||||
\(62\) | −2.42012 | + | 2.42012i | −0.307356 | + | 0.307356i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 6.43313 | + | 0.926476i | 0.797932 | + | 0.114915i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.54358 | + | 13.2248i | −0.432917 | + | 1.61567i | 0.313084 | + | 0.949725i | \(0.398638\pi\) |
−0.746002 | + | 0.665944i | \(0.768029\pi\) | |||||||
\(68\) | 6.33660 | − | 1.69789i | 0.768426 | − | 0.205899i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.29992 | − | 5.45072i | 0.274893 | − | 0.651486i | ||||
\(71\) | 16.0173 | 1.90090 | 0.950450 | − | 0.310879i | \(-0.100623\pi\) | ||||
0.950450 | + | 0.310879i | \(0.100623\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.29071 | + | 8.54906i | −0.268108 | + | 1.00059i | 0.692213 | + | 0.721693i | \(0.256636\pi\) |
−0.960321 | + | 0.278898i | \(0.910031\pi\) | |||||||
\(74\) | −2.31328 | + | 1.33557i | −0.268913 | + | 0.155257i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 1.89205i | − | 0.217033i | ||||||
\(77\) | −1.39785 | − | 1.38242i | −0.159300 | − | 0.157542i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.70091 | − | 3.29142i | −0.641402 | − | 0.370314i | 0.143752 | − | 0.989614i | \(-0.454083\pi\) |
−0.785155 | + | 0.619300i | \(0.787417\pi\) | |||||||
\(80\) | −0.264946 | − | 2.22032i | −0.0296219 | − | 0.248239i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.211636 | − | 0.789836i | −0.0233713 | − | 0.0872228i | ||||
\(83\) | −9.23519 | − | 9.23519i | −1.01369 | − | 1.01369i | −0.999905 | − | 0.0137887i | \(-0.995611\pi\) |
−0.0137887 | − | 0.999905i | \(-0.504389\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.6194 | − | 5.44871i | 1.47723 | − | 0.590995i | ||||
\(86\) | −1.12846 | + | 1.95456i | −0.121685 | + | 0.210765i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.717752 | − | 0.192321i | −0.0765127 | − | 0.0205015i | ||||
\(89\) | −3.01603 | + | 5.22392i | −0.319699 | + | 0.553735i | −0.980425 | − | 0.196892i | \(-0.936915\pi\) |
0.660726 | + | 0.750627i | \(0.270248\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.68124 | − | 3.80814i | −0.700385 | − | 0.399201i | ||||
\(92\) | 3.74160 | + | 3.74160i | 0.390089 | + | 0.390089i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.35481 | + | 4.07864i | 0.242880 | + | 0.420680i | ||||
\(95\) | −0.501292 | − | 4.20096i | −0.0514315 | − | 0.431009i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.16693 | − | 3.16693i | 0.321553 | − | 0.321553i | −0.527810 | − | 0.849363i | \(-0.676987\pi\) |
0.849363 | + | 0.527810i | \(0.176987\pi\) | |||||||
\(98\) | −4.89451 | + | 5.00438i | −0.494420 | + | 0.505519i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.17653 | − | 4.85961i | −0.117653 | − | 0.485961i | ||||
\(101\) | −9.68359 | + | 5.59083i | −0.963554 | + | 0.556308i | −0.897265 | − | 0.441493i | \(-0.854449\pi\) |
−0.0662887 | + | 0.997800i | \(0.521116\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.34351 | − | 0.627940i | 0.230912 | − | 0.0618728i | −0.141507 | − | 0.989937i | \(-0.545195\pi\) |
0.372420 | + | 0.928064i | \(0.378528\pi\) | |||||||
\(104\) | −2.90667 | −0.285022 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.98571 | −0.484255 | ||||||||
\(107\) | −6.41422 | + | 1.71868i | −0.620086 | + | 0.166151i | −0.555167 | − | 0.831739i | \(-0.687346\pi\) |
−0.0649189 | + | 0.997891i | \(0.520679\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.76000 | + | 4.48024i | −0.743274 | + | 0.429129i | −0.823258 | − | 0.567667i | \(-0.807846\pi\) |
0.0799848 | + | 0.996796i | \(0.474513\pi\) | |||||||
\(110\) | −1.64459 | − | 0.236848i | −0.156806 | − | 0.0225826i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.670578 | + | 2.55936i | −0.0633637 | + | 0.241837i | ||||
\(113\) | −0.307790 | + | 0.307790i | −0.0289545 | + | 0.0289545i | −0.721436 | − | 0.692481i | \(-0.756518\pi\) |
0.692481 | + | 0.721436i | \(0.256518\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.29886 | + | 7.31621i | 0.867123 | + | 0.682240i | ||||
\(116\) | −4.84567 | − | 8.39295i | −0.449910 | − | 0.779266i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.80295 | − | 1.80295i | −0.165975 | − | 0.165975i | ||||
\(119\) | −17.3562 | + | 0.0963204i | −1.59104 | + | 0.00882967i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.22392 | − | 9.04810i | 0.474902 | − | 0.822554i | ||||
\(122\) | −5.86664 | − | 1.57196i | −0.531141 | − | 0.142319i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.71129 | − | 2.96403i | 0.153678 | − | 0.266178i | ||||
\(125\) | −3.89980 | − | 10.4781i | −0.348808 | − | 0.937194i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.1823 | − | 11.1823i | −0.992267 | − | 0.992267i | 0.00770296 | − | 0.999970i | \(-0.497548\pi\) |
−0.999970 | + | 0.00770296i | \(0.997548\pi\) | |||||||
\(128\) | 0.258819 | + | 0.965926i | 0.0228766 | + | 0.0853766i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.45372 | + | 0.770110i | −0.566028 | + | 0.0675431i | ||||
\(131\) | 8.30763 | + | 4.79641i | 0.725841 | + | 0.419064i | 0.816899 | − | 0.576781i | \(-0.195692\pi\) |
−0.0910579 | + | 0.995846i | \(0.529025\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.26877 | + | 4.84245i | −0.110016 | + | 0.419893i | ||||
\(134\) | − | 13.6913i | − | 1.18275i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.68124 | + | 3.28007i | −0.487163 | + | 0.281264i | ||||
\(137\) | −2.40949 | + | 8.99233i | −0.205856 | + | 0.768267i | 0.783330 | + | 0.621606i | \(0.213519\pi\) |
−0.989187 | + | 0.146661i | \(0.953147\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.1714 | −1.88056 | −0.940278 | − | 0.340408i | \(-0.889435\pi\) | ||||
−0.940278 | + | 0.340408i | \(0.889435\pi\) | |||||||
\(140\) | −0.810803 | + | 5.86026i | −0.0685253 | + | 0.495282i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −15.4715 | + | 4.14557i | −1.29834 | + | 0.347889i | ||||
\(143\) | −0.559013 | + | 2.08627i | −0.0467470 | + | 0.174462i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.9826 | − | 17.3512i | −1.07815 | − | 1.44094i | ||||
\(146\) | − | 8.85064i | − | 0.732484i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.88878 | − | 1.88878i | 0.155257 | − | 0.155257i | ||||
\(149\) | −3.41418 | − | 1.97118i | −0.279701 | − | 0.161485i | 0.353587 | − | 0.935402i | \(-0.384962\pi\) |
−0.633288 | + | 0.773916i | \(0.718295\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.97267 | + | 17.2732i | 0.811564 | + | 1.40567i | 0.911769 | + | 0.410703i | \(0.134717\pi\) |
−0.100205 | + | 0.994967i | \(0.531950\pi\) | |||||||
\(152\) | 0.489700 | + | 1.82758i | 0.0397199 | + | 0.148237i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.70802 | + | 0.973528i | 0.137636 | + | 0.0784491i | ||||
\(155\) | 3.01429 | − | 7.03449i | 0.242113 | − | 0.565024i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.20903 | − | 1.93165i | −0.575343 | − | 0.154163i | −0.0405972 | − | 0.999176i | \(-0.512926\pi\) |
−0.534746 | + | 0.845013i | \(0.679593\pi\) | |||||||
\(158\) | 6.35854 | + | 1.70376i | 0.505858 | + | 0.135544i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.830578 | + | 2.07609i | 0.0656630 | + | 0.164129i | ||||
\(161\) | −7.06707 | − | 12.0851i | −0.556963 | − | 0.952442i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.14893 | + | 11.7520i | 0.246644 | + | 0.920486i | 0.972550 | + | 0.232693i | \(0.0747537\pi\) |
−0.725907 | + | 0.687793i | \(0.758580\pi\) | |||||||
\(164\) | 0.408849 | + | 0.708148i | 0.0319258 | + | 0.0552970i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.3107 | + | 6.53026i | 0.877884 | + | 0.506847i | ||||
\(167\) | −1.45564 | + | 1.45564i | −0.112641 | + | 0.112641i | −0.761181 | − | 0.648540i | \(-0.775380\pi\) |
0.648540 | + | 0.761181i | \(0.275380\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 4.55129i | − | 0.350099i | ||||||
\(170\) | −11.7451 | + | 8.78801i | −0.900809 | + | 0.674010i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.584136 | − | 2.18003i | 0.0445400 | − | 0.166225i | ||||
\(173\) | −9.08750 | + | 2.43499i | −0.690910 | + | 0.185129i | −0.587155 | − | 0.809474i | \(-0.699752\pi\) |
−0.103754 | + | 0.994603i | \(0.533086\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.247587 | + | 13.2264i | −0.0187158 | + | 0.999825i | ||||
\(176\) | 0.743072 | 0.0560111 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.56121 | − | 5.82653i | 0.117018 | − | 0.436717i | ||||
\(179\) | −3.89494 | + | 2.24874i | −0.291121 | + | 0.168079i | −0.638447 | − | 0.769665i | \(-0.720423\pi\) |
0.347326 | + | 0.937744i | \(0.387090\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 17.8850i | − | 1.32938i | −0.747118 | − | 0.664691i | \(-0.768563\pi\) | ||
0.747118 | − | 0.664691i | \(-0.231437\pi\) | |||||||
\(182\) | 7.43921 | + | 1.94915i | 0.551431 | + | 0.144480i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.58251 | − | 2.64571i | −0.337827 | − | 0.195044i | ||||
\(185\) | 3.69327 | − | 4.69412i | 0.271535 | − | 0.345119i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.26165 | + | 4.70855i | 0.0922612 | + | 0.344323i | ||||
\(188\) | −3.33020 | − | 3.33020i | −0.242880 | − | 0.242880i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.57150 | + | 3.92807i | 0.114009 | + | 0.284972i | ||||
\(191\) | −1.38774 | + | 2.40364i | −0.100413 | + | 0.173921i | −0.911855 | − | 0.410512i | \(-0.865350\pi\) |
0.811442 | + | 0.584433i | \(0.198683\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.96491 | + | 1.33034i | 0.357382 | + | 0.0957602i | 0.433043 | − | 0.901373i | \(-0.357440\pi\) |
−0.0756607 | + | 0.997134i | \(0.524107\pi\) | |||||||
\(194\) | −2.23936 | + | 3.87868i | −0.160776 | + | 0.278473i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.43250 | − | 6.10065i | 0.245179 | − | 0.435761i | ||||
\(197\) | −1.34043 | − | 1.34043i | −0.0955019 | − | 0.0955019i | 0.657742 | − | 0.753244i | \(-0.271512\pi\) |
−0.753244 | + | 0.657742i | \(0.771512\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.25148 | − | 12.5599i | −0.514043 | − | 0.890349i | −0.999867 | − | 0.0162926i | \(-0.994814\pi\) |
0.485824 | − | 0.874057i | \(-0.338520\pi\) | |||||||
\(200\) | 2.39420 | + | 4.38951i | 0.169295 | + | 0.310385i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.90662 | − | 7.90662i | 0.556308 | − | 0.556308i | ||||
\(203\) | 6.77370 | + | 24.7300i | 0.475420 | + | 1.73571i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.09540 | + | 1.46399i | 0.0765057 | + | 0.102249i | ||||
\(206\) | −2.10113 | + | 1.21309i | −0.146393 | + | 0.0845198i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.80762 | − | 0.752300i | 0.194674 | − | 0.0521627i | ||||
\(209\) | 1.40593 | 0.0972504 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0324 | 0.690660 | 0.345330 | − | 0.938481i | \(-0.387767\pi\) | ||||
0.345330 | + | 0.938481i | \(0.387767\pi\) | |||||||
\(212\) | 4.81583 | − | 1.29040i | 0.330752 | − | 0.0886249i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.75083 | − | 3.32024i | 0.393119 | − | 0.226967i | ||||
\(215\) | 0.719378 | − | 4.99511i | 0.0490611 | − | 0.340664i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.36741 | + | 6.43848i | −0.432248 | + | 0.437073i | ||||
\(218\) | 6.33602 | − | 6.33602i | 0.429129 | − | 0.429129i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.64985 | − | 0.196874i | 0.111233 | − | 0.0132732i | ||||
\(221\) | 9.53406 | + | 16.5135i | 0.641330 | + | 1.11082i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.13756 | − | 3.13756i | −0.210107 | − | 0.210107i | 0.594206 | − | 0.804313i | \(-0.297466\pi\) |
−0.804313 | + | 0.594206i | \(0.797466\pi\) | |||||||
\(224\) | −0.0146827 | − | 2.64571i | −0.000981028 | − | 0.176774i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.217641 | − | 0.376965i | 0.0144772 | − | 0.0250753i | ||||
\(227\) | −0.648012 | − | 0.173634i | −0.0430101 | − | 0.0115245i | 0.237250 | − | 0.971449i | \(-0.423754\pi\) |
−0.280260 | + | 0.959924i | \(0.590421\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −6.60166 | + | 11.4344i | −0.436250 | + | 0.755608i | −0.997397 | − | 0.0721088i | \(-0.977027\pi\) |
0.561146 | + | 0.827717i | \(0.310360\pi\) | |||||||
\(230\) | −10.8756 | − | 4.66020i | −0.717115 | − | 0.307284i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.85282 | + | 6.85282i | 0.449910 | + | 0.449910i | ||||
\(233\) | 2.24110 | + | 8.36389i | 0.146819 | + | 0.547937i | 0.999668 | + | 0.0257782i | \(0.00820637\pi\) |
−0.852849 | + | 0.522158i | \(0.825127\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −8.27641 | − | 6.51177i | −0.539894 | − | 0.424781i | ||||
\(236\) | 2.20815 | + | 1.27487i | 0.143738 | + | 0.0829873i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 16.7399 | − | 4.58516i | 1.08509 | − | 0.297212i | ||||
\(239\) | − | 4.00294i | − | 0.258929i | −0.991584 | − | 0.129464i | \(-0.958674\pi\) | ||
0.991584 | − | 0.129464i | \(-0.0413258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −15.0040 | + | 8.66256i | −0.966493 | + | 0.558005i | −0.898165 | − | 0.439658i | \(-0.855100\pi\) |
−0.0683274 | + | 0.997663i | \(0.521766\pi\) | |||||||
\(242\) | −2.70410 | + | 10.0918i | −0.173826 | + | 0.648728i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 6.07359 | 0.388822 | ||||||||
\(245\) | 6.00489 | − | 14.4548i | 0.383639 | − | 0.923483i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.31218 | − | 1.42339i | 0.338006 | − | 0.0905683i | ||||
\(248\) | −0.885827 | + | 3.30595i | −0.0562501 | + | 0.209928i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.47886 | + | 9.11177i | 0.409759 | + | 0.576279i | ||||
\(251\) | − | 5.49938i | − | 0.347118i | −0.984824 | − | 0.173559i | \(-0.944473\pi\) | ||
0.984824 | − | 0.173559i | \(-0.0555267\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.78028 | + | 2.78028i | −0.174795 | + | 0.174795i | ||||
\(254\) | 13.6954 | + | 7.90707i | 0.859329 | + | 0.496134i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −4.27307 | − | 15.9473i | −0.266547 | − | 0.994766i | −0.961297 | − | 0.275515i | \(-0.911152\pi\) |
0.694750 | − | 0.719251i | \(-0.255515\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.10065 | + | 3.56750i | −0.379076 | + | 0.221674i | ||||
\(260\) | 6.03449 | − | 2.41421i | 0.374243 | − | 0.149723i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.26595 | − | 2.48280i | −0.572453 | − | 0.153388i | ||||
\(263\) | −9.52484 | − | 2.55217i | −0.587327 | − | 0.157374i | −0.0470956 | − | 0.998890i | \(-0.514997\pi\) |
−0.540231 | + | 0.841517i | \(0.681663\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 10.3508 | − | 4.14102i | 0.635843 | − | 0.254381i | ||||
\(266\) | −0.0277804 | − | 5.00583i | −0.00170333 | − | 0.306927i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.54358 | + | 13.2248i | 0.216459 | + | 0.807835i | ||||
\(269\) | 4.47922 | + | 7.75824i | 0.273103 | + | 0.473028i | 0.969655 | − | 0.244478i | \(-0.0786167\pi\) |
−0.696552 | + | 0.717506i | \(0.745283\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −19.7889 | − | 11.4251i | −1.20209 | − | 0.694027i | −0.241071 | − | 0.970507i | \(-0.577499\pi\) |
−0.961020 | + | 0.276480i | \(0.910832\pi\) | |||||||
\(272\) | 4.63872 | − | 4.63872i | 0.281264 | − | 0.281264i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 9.30954i | − | 0.562410i | ||||||
\(275\) | 3.61104 | − | 0.874245i | 0.217754 | − | 0.0527189i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.57320 | − | 20.7995i | 0.334861 | − | 1.24972i | −0.569158 | − | 0.822228i | \(-0.692731\pi\) |
0.904019 | − | 0.427491i | \(-0.140603\pi\) | |||||||
\(278\) | 21.4160 | − | 5.73839i | 1.28444 | − | 0.344166i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.733571 | − | 5.87042i | −0.0438392 | − | 0.350825i | ||||
\(281\) | 5.64885 | 0.336982 | 0.168491 | − | 0.985703i | \(-0.446111\pi\) | ||||
0.168491 | + | 0.985703i | \(0.446111\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.757948 | + | 2.82870i | −0.0450553 | + | 0.168149i | −0.984788 | − | 0.173762i | \(-0.944408\pi\) |
0.939732 | + | 0.341911i | \(0.111074\pi\) | |||||||
\(284\) | 13.8714 | − | 8.00863i | 0.823113 | − | 0.475225i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 2.15986i | − | 0.127715i | ||||||
\(287\) | −0.571524 | − | 2.08657i | −0.0337360 | − | 0.123166i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 22.5473 | + | 13.0177i | 1.32631 | + | 0.765747i | ||||
\(290\) | 17.0310 | + | 13.3998i | 1.00010 | + | 0.786863i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.29071 | + | 8.54906i | 0.134054 | + | 0.500296i | ||||
\(293\) | −10.7875 | − | 10.7875i | −0.630212 | − | 0.630212i | 0.317909 | − | 0.948121i | \(-0.397019\pi\) |
−0.948121 | + | 0.317909i | \(0.897019\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 5.24056 | + | 2.24558i | 0.305117 | + | 0.130743i | ||||
\(296\) | −1.33557 | + | 2.31328i | −0.0776285 | + | 0.134456i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.80802 | + | 1.02036i | 0.220593 | + | 0.0591077i | ||||
\(299\) | −7.69020 | + | 13.3198i | −0.444736 | + | 0.770305i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.95689 | + | 5.18776i | −0.170432 | + | 0.299018i | ||||
\(302\) | −14.1035 | − | 14.1035i | −0.811564 | − | 0.811564i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.946027 | − | 1.63857i | −0.0542584 | − | 0.0939783i | ||||
\(305\) | 13.4853 | − | 1.60917i | 0.772166 | − | 0.0921411i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.89201 | + | 6.89201i | −0.393348 | + | 0.393348i | −0.875879 | − | 0.482531i | \(-0.839718\pi\) |
0.482531 | + | 0.875879i | \(0.339718\pi\) | |||||||
\(308\) | −1.90179 | − | 0.498288i | −0.108364 | − | 0.0283926i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.09092 | + | 7.57495i | −0.0619599 | + | 0.430228i | ||||
\(311\) | 0.109136 | − | 0.0630096i | 0.00618852 | − | 0.00357294i | −0.496903 | − | 0.867806i | \(-0.665529\pi\) |
0.503091 | + | 0.864233i | \(0.332196\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.2955 | + | 3.02662i | −0.638459 | + | 0.171075i | −0.563505 | − | 0.826112i | \(-0.690548\pi\) |
−0.0749536 | + | 0.997187i | \(0.523881\pi\) | |||||||
\(314\) | 7.46334 | 0.421181 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.58284 | −0.370314 | ||||||||
\(317\) | −10.5732 | + | 2.83308i | −0.593851 | + | 0.159122i | −0.543212 | − | 0.839595i | \(-0.682792\pi\) |
−0.0506382 | + | 0.998717i | \(0.516126\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.23657 | − | 3.60068i | 0.349181 | − | 0.201600i | ||||
\(320\) | −1.33961 | − | 1.79038i | −0.0748864 | − | 0.100085i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9.95413 | + | 9.84425i | 0.554722 | + | 0.548599i | ||||
\(323\) | 8.77670 | − | 8.77670i | 0.488349 | − | 0.488349i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.7588 | − | 6.95913i | 0.707733 | − | 0.386023i | ||||
\(326\) | −6.08327 | − | 10.5365i | −0.336921 | − | 0.583565i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.578200 | − | 0.578200i | −0.0319258 | − | 0.0319258i | ||||
\(329\) | 6.29002 | + | 10.7563i | 0.346780 | + | 0.593016i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.73019 | − | 4.72883i | 0.150065 | − | 0.259920i | −0.781186 | − | 0.624298i | \(-0.785385\pi\) |
0.931251 | + | 0.364378i | \(0.118718\pi\) | |||||||
\(332\) | −12.6155 | − | 3.38031i | −0.692366 | − | 0.185519i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.02929 | − | 1.78279i | 0.0563205 | − | 0.0975500i | ||||
\(335\) | 11.3717 | + | 28.4244i | 0.621304 | + | 1.55299i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.4823 | + | 20.4823i | 1.11574 | + | 1.11574i | 0.992359 | + | 0.123385i | \(0.0393751\pi\) |
0.123385 | + | 0.992359i | \(0.460625\pi\) | |||||||
\(338\) | 1.17796 | + | 4.39621i | 0.0640727 | + | 0.239122i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.07041 | − | 11.5284i | 0.491912 | − | 0.625217i | ||||
\(341\) | 2.20249 | + | 1.27161i | 0.119272 | + | 0.0688615i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.8760 | + | 13.3120i | −0.695237 | + | 0.718781i | ||||
\(344\) | 2.25693i | 0.121685i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 8.14763 | − | 4.70404i | 0.438019 | − | 0.252891i | ||||
\(347\) | 5.57442 | − | 20.8040i | 0.299250 | − | 1.11682i | −0.638532 | − | 0.769595i | \(-0.720458\pi\) |
0.937783 | − | 0.347223i | \(-0.112875\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.5744 | 0.673093 | 0.336546 | − | 0.941667i | \(-0.390741\pi\) | ||||
0.336546 | + | 0.941667i | \(0.390741\pi\) | |||||||
\(350\) | −3.18410 | − | 12.8398i | −0.170198 | − | 0.686318i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.717752 | + | 0.192321i | −0.0382563 | + | 0.0102508i | ||||
\(353\) | −0.178457 | + | 0.666012i | −0.00949832 | + | 0.0354482i | −0.970512 | − | 0.241051i | \(-0.922508\pi\) |
0.961014 | + | 0.276500i | \(0.0891744\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 28.6769 | − | 21.4569i | 1.52201 | − | 1.13881i | ||||
\(356\) | 6.03207i | 0.319699i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.18020 | − | 3.18020i | 0.168079 | − | 0.168079i | ||||
\(359\) | 19.1381 | + | 11.0494i | 1.01007 | + | 0.583165i | 0.911212 | − | 0.411937i | \(-0.135148\pi\) |
0.0988582 | + | 0.995102i | \(0.468481\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 7.71007 | + | 13.3542i | 0.405793 | + | 0.702854i | ||||
\(362\) | 4.62898 | + | 17.2756i | 0.243294 | + | 0.907985i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −7.69020 | + | 0.0426776i | −0.403076 | + | 0.00223692i | ||||
\(365\) | 7.35115 | + | 18.3747i | 0.384777 | + | 0.961775i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.9539 | + | 3.47100i | 0.676191 | + | 0.181185i | 0.580542 | − | 0.814230i | \(-0.302841\pi\) |
0.0956487 | + | 0.995415i | \(0.469507\pi\) | |||||||
\(368\) | 5.11112 | + | 1.36952i | 0.266436 | + | 0.0713912i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.35250 | + | 5.49006i | −0.122300 | + | 0.285415i | ||||
\(371\) | −13.1908 | + | 0.0732036i | −0.684830 | + | 0.00380054i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.87359 | − | 14.4564i | −0.200567 | − | 0.748526i | −0.990755 | − | 0.135662i | \(-0.956684\pi\) |
0.790188 | − | 0.612864i | \(-0.209983\pi\) | |||||||
\(374\) | −2.43733 | − | 4.22157i | −0.126031 | − | 0.218292i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.07864 | + | 2.35481i | 0.210340 | + | 0.121440i | ||||
\(377\) | 19.9189 | − | 19.9189i | 1.02587 | − | 1.02587i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.71784i | 0.0882395i | 0.999026 | + | 0.0441198i | \(0.0140483\pi\) | ||||
−0.999026 | + | 0.0441198i | \(0.985952\pi\) | |||||||
\(380\) | −2.53461 | − | 3.38749i | −0.130023 | − | 0.173775i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.718348 | − | 2.68091i | 0.0367539 | − | 0.137167i | ||||
\(383\) | 10.1017 | − | 2.70676i | 0.516175 | − | 0.138309i | 0.00867837 | − | 0.999962i | \(-0.497238\pi\) |
0.507497 | + | 0.861654i | \(0.330571\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.35459 | − | 0.602485i | −0.221931 | − | 0.0307055i | ||||
\(386\) | −5.14005 | −0.261622 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.15918 | − | 4.32611i | 0.0588483 | − | 0.219625i | ||||
\(389\) | 18.8548 | − | 10.8858i | 0.955978 | − | 0.551934i | 0.0610449 | − | 0.998135i | \(-0.480557\pi\) |
0.894933 | + | 0.446201i | \(0.147223\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 34.7124i | 1.75548i | ||||||||
\(392\) | −1.73658 | + | 6.78117i | −0.0877104 | + | 0.342501i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.64169 | + | 0.947829i | 0.0827071 | + | 0.0477510i | ||||
\(395\) | −14.6160 | + | 1.74410i | −0.735410 | + | 0.0877551i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8.20427 | − | 30.6188i | −0.411761 | − | 1.53671i | −0.791237 | − | 0.611510i | \(-0.790562\pi\) |
0.379476 | − | 0.925202i | \(-0.376104\pi\) | |||||||
\(398\) | 10.2551 | + | 10.2551i | 0.514043 | + | 0.514043i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.44871 | − | 3.62028i | −0.172435 | − | 0.181014i | ||||
\(401\) | 6.98528 | − | 12.0989i | 0.348828 | − | 0.604188i | −0.637213 | − | 0.770687i | \(-0.719913\pi\) |
0.986042 | + | 0.166499i | \(0.0532463\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.60930 | + | 2.57480i | 0.478673 | + | 0.128260i | ||||
\(404\) | −5.59083 | + | 9.68359i | −0.278154 | + | 0.481777i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.9435 | − | 22.1342i | −0.642374 | − | 1.09850i | ||||
\(407\) | 1.40350 | + | 1.40350i | 0.0695690 | + | 0.0695690i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.36960 | + | 16.2286i | 0.463297 | + | 0.802454i | 0.999123 | − | 0.0418748i | \(-0.0133330\pi\) |
−0.535826 | + | 0.844328i | \(0.680000\pi\) | |||||||
\(410\) | −1.43698 | − | 1.13060i | −0.0709673 | − | 0.0558361i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.71557 | − | 1.71557i | 0.0845198 | − | 0.0845198i | ||||
\(413\) | −4.79654 | − | 4.74360i | −0.236022 | − | 0.233417i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −28.9060 | − | 4.16294i | −1.41894 | − | 0.204351i | ||||
\(416\) | −2.51725 | + | 1.45333i | −0.123418 | + | 0.0712555i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.35803 | + | 0.363882i | −0.0664232 | + | 0.0177981i | ||||
\(419\) | −31.5744 | −1.54251 | −0.771255 | − | 0.636526i | \(-0.780371\pi\) | ||||
−0.771255 | + | 0.636526i | \(0.780371\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5569 | −0.660722 | −0.330361 | − | 0.943855i | \(-0.607171\pi\) | ||||
−0.330361 | + | 0.943855i | \(0.607171\pi\) | |||||||
\(422\) | −9.69057 | + | 2.59658i | −0.471729 | + | 0.126399i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.31775 | + | 2.49286i | −0.209689 | + | 0.121064i | ||||
\(425\) | 17.0848 | − | 27.9999i | 0.828733 | − | 1.35820i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −15.5445 | − | 4.07282i | −0.752252 | − | 0.197097i | ||||
\(428\) | −4.69553 | + | 4.69553i | −0.226967 | + | 0.226967i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.597964 | + | 5.01109i | 0.0288364 | + | 0.241656i | ||||
\(431\) | 6.63518 | + | 11.4925i | 0.319605 | + | 0.553572i | 0.980406 | − | 0.196989i | \(-0.0631164\pi\) |
−0.660800 | + | 0.750562i | \(0.729783\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.0535 | − | 12.0535i | −0.579252 | − | 0.579252i | 0.355445 | − | 0.934697i | \(-0.384329\pi\) |
−0.934697 | + | 0.355445i | \(0.884329\pi\) | |||||||
\(434\) | 4.48405 | − | 7.86710i | 0.215241 | − | 0.377633i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.48024 | + | 7.76000i | −0.214565 | + | 0.371637i | ||||
\(437\) | 9.67052 | + | 2.59121i | 0.462604 | + | 0.123954i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.5238 | + | 30.3521i | −0.836366 | + | 1.44863i | 0.0565475 | + | 0.998400i | \(0.481991\pi\) |
−0.892913 | + | 0.450228i | \(0.851343\pi\) | |||||||
\(440\) | −1.54268 | + | 0.617179i | −0.0735445 | + | 0.0294229i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −13.4832 | − | 13.4832i | −0.641330 | − | 0.641330i | ||||
\(443\) | 0.0163232 | + | 0.0609189i | 0.000775538 | + | 0.00289435i | 0.966313 | − | 0.257372i | \(-0.0828564\pi\) |
−0.965537 | + | 0.260266i | \(0.916190\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.59817 | + | 13.3931i | 0.0757606 | + | 0.634893i | ||||
\(446\) | 3.84271 | + | 2.21859i | 0.181958 | + | 0.105053i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.698943 | + | 2.55176i | 0.0330219 | + | 0.120559i | ||||
\(449\) | 24.5207i | 1.15720i | 0.815611 | + | 0.578601i | \(0.196401\pi\) | ||||
−0.815611 | + | 0.578601i | \(0.803599\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.526205 | + | 0.303804i | −0.0247780 | + | 0.0143056i | ||||
\(452\) | −0.112659 | + | 0.420450i | −0.00529904 | + | 0.0197763i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.670872 | 0.0314856 | ||||||||
\(455\) | −17.0634 | + | 2.13224i | −0.799943 | + | 0.0999612i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19.3892 | + | 5.19531i | −0.906987 | + | 0.243027i | −0.682015 | − | 0.731339i | \(-0.738896\pi\) |
−0.224973 | + | 0.974365i | \(0.572229\pi\) | |||||||
\(458\) | 3.41727 | − | 12.7534i | 0.159679 | − | 0.595929i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 11.7112 | + | 1.68660i | 0.546035 | + | 0.0786380i | ||||
\(461\) | 11.6940i | 0.544642i | 0.962207 | + | 0.272321i | \(0.0877912\pi\) | ||||
−0.962207 | + | 0.272321i | \(0.912209\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.77226 | − | 2.77226i | 0.128838 | − | 0.128838i | −0.639747 | − | 0.768585i | \(-0.720961\pi\) |
0.768585 | + | 0.639747i | \(0.220961\pi\) | |||||||
\(464\) | −8.39295 | − | 4.84567i | −0.389633 | − | 0.224955i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.32947 | − | 7.49886i | −0.200559 | − | 0.347378i | ||||
\(467\) | 5.41472 | + | 20.2080i | 0.250563 | + | 0.935116i | 0.970505 | + | 0.241081i | \(0.0775019\pi\) |
−0.719942 | + | 0.694035i | \(0.755831\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.201026 | − | 36.2233i | −0.00928250 | − | 1.67264i | ||||
\(470\) | 9.67977 | + | 4.14779i | 0.446495 | + | 0.191323i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.46287 | − | 0.659924i | −0.113363 | − | 0.0303754i | ||||
\(473\) | 1.61992 | + | 0.434055i | 0.0744838 | + | 0.0199579i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.52514 | − | 6.84976i | −0.299394 | − | 0.314289i | ||||
\(476\) | −14.9828 | + | 8.76153i | −0.686734 | + | 0.401584i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.03604 | + | 3.86655i | 0.0473873 | + | 0.176852i | ||||
\(479\) | −12.1419 | − | 21.0303i | −0.554775 | − | 0.960899i | −0.997921 | − | 0.0644496i | \(-0.979471\pi\) |
0.443145 | − | 0.896450i | \(-0.353863\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.72392 | + | 3.88206i | 0.306584 | + | 0.177007i | ||||
\(482\) | 12.2507 | − | 12.2507i | 0.558005 | − | 0.558005i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 10.4478i | − | 0.474902i | ||||||
\(485\) | 1.42755 | − | 9.91244i | 0.0648219 | − | 0.450101i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.661539 | − | 2.46890i | 0.0299772 | − | 0.111876i | −0.949316 | − | 0.314323i | \(-0.898223\pi\) |
0.979293 | + | 0.202446i | \(0.0648892\pi\) | |||||||
\(488\) | −5.86664 | + | 1.57196i | −0.265570 | + | 0.0711594i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.05910 | + | 15.5164i | −0.0930209 | + | 0.700962i | ||||
\(491\) | −14.5668 | −0.657391 | −0.328695 | − | 0.944436i | \(-0.606609\pi\) | ||||
−0.328695 | + | 0.944436i | \(0.606609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 16.4548 | − | 61.4102i | 0.741088 | − | 2.76578i | ||||
\(494\) | −4.76277 | + | 2.74978i | −0.214287 | + | 0.123719i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 3.42257i | − | 0.153678i | ||||||
\(497\) | −40.8722 | + | 11.1951i | −1.83337 | + | 0.502171i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.0565 | + | 15.0437i | 1.16645 | + | 0.673450i | 0.952841 | − | 0.303469i | \(-0.0981450\pi\) |
0.213608 | + | 0.976919i | \(0.431478\pi\) | |||||||
\(500\) | −8.61640 | − | 7.12444i | −0.385337 | − | 0.318615i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.42334 | + | 5.31199i | 0.0635269 | + | 0.237086i | ||||
\(503\) | −24.6819 | − | 24.6819i | −1.10051 | − | 1.10051i | −0.994349 | − | 0.106161i | \(-0.966144\pi\) |
−0.106161 | − | 0.994349i | \(-0.533856\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.84777 | + | 22.9819i | −0.438220 | + | 1.02268i | ||||
\(506\) | 1.96595 | − | 3.40513i | 0.0873973 | − | 0.151377i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −15.2753 | − | 4.09300i | −0.677731 | − | 0.181598i | ||||
\(509\) | 6.22521 | − | 10.7824i | 0.275927 | − | 0.477920i | −0.694441 | − | 0.719549i | \(-0.744348\pi\) |
0.970369 | + | 0.241629i | \(0.0776817\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.129951 | − | 23.4162i | −0.00574869 | − | 1.03587i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.25494 | + | 14.2980i | 0.364110 | + | 0.630656i | ||||
\(515\) | 3.35456 | − | 4.26363i | 0.147820 | − | 0.187878i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.47458 | − | 2.47458i | 0.108832 | − | 0.108832i | ||||
\(518\) | 4.96944 | − | 5.02490i | 0.218345 | − | 0.220782i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.20403 | + | 3.89379i | −0.228212 | + | 0.170754i | ||||
\(521\) | −30.6011 | + | 17.6676i | −1.34066 | + | 0.774030i | −0.986904 | − | 0.161308i | \(-0.948429\pi\) |
−0.353756 | + | 0.935338i | \(0.615096\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −15.8804 | + | 4.25513i | −0.694400 | + | 0.186064i | −0.588721 | − | 0.808336i | \(-0.700368\pi\) |
−0.105679 | + | 0.994400i | \(0.533702\pi\) | |||||||
\(524\) | 9.59282 | 0.419064 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.86084 | 0.429953 | ||||||||
\(527\) | 21.6875 | − | 5.81115i | 0.944722 | − | 0.253137i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.32938 | + | 2.49957i | −0.188234 | + | 0.108677i | ||||
\(530\) | −8.92631 | + | 6.67890i | −0.387734 | + | 0.290113i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.32244 | + | 4.82807i | 0.0573349 | + | 0.209323i | ||||
\(533\) | −1.68063 | + | 1.68063i | −0.0727964 | + | 0.0727964i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.18150 | + | 11.6696i | −0.396951 | + | 0.504522i | ||||
\(536\) | −6.84567 | − | 11.8571i | −0.295688 | − | 0.512147i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −6.33457 | − | 6.33457i | −0.273103 | − | 0.273103i | ||||
\(539\) | 4.53322 | + | 2.55059i | 0.195260 | + | 0.109862i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.2572 | − | 22.9621i | 0.569970 | − | 0.987218i | −0.426598 | − | 0.904441i | \(-0.640288\pi\) |
0.996568 | − | 0.0827763i | \(-0.0263787\pi\) | |||||||
\(542\) | 22.0717 | + | 5.91408i | 0.948059 | + | 0.254032i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.28007 | + | 5.68124i | −0.140632 | + | 0.243581i | ||||
\(545\) | −7.89157 | + | 18.4167i | −0.338038 | + | 0.788884i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.07403 | − | 1.07403i | −0.0459223 | − | 0.0459223i | 0.683773 | − | 0.729695i | \(-0.260338\pi\) |
−0.729695 | + | 0.683773i | \(0.760338\pi\) | |||||||
\(548\) | 2.40949 | + | 8.99233i | 0.102928 | + | 0.384133i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.26172 | + | 1.77906i | −0.139080 | + | 0.0758594i | ||||
\(551\) | −15.8799 | − | 9.16828i | −0.676507 | − | 0.390582i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.8479 | + | 4.41431i | 0.716444 | + | 0.187715i | ||||
\(554\) | 21.5332i | 0.914858i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.2010 | + | 11.0857i | −0.814305 | + | 0.470139i | ||||
\(557\) | −4.02313 | + | 15.0145i | −0.170466 | + | 0.636186i | 0.826814 | + | 0.562475i | \(0.190151\pi\) |
−0.997280 | + | 0.0737108i | \(0.976516\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.56014 | 0.277464 | ||||||||
\(560\) | 2.22795 | + | 5.48053i | 0.0941482 | + | 0.231595i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.45637 | + | 1.46203i | −0.230163 | + | 0.0616721i | ||||
\(563\) | 7.10355 | − | 26.5108i | 0.299379 | − | 1.11730i | −0.638298 | − | 0.769789i | \(-0.720361\pi\) |
0.937677 | − | 0.347508i | \(-0.112972\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.138742 | + | 0.963380i | −0.00583694 | + | 0.0405297i | ||||
\(566\) | − | 2.92849i | − | 0.123093i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −11.3259 | + | 11.3259i | −0.475225 | + | 0.475225i | ||||
\(569\) | 5.85207 | + | 3.37869i | 0.245332 | + | 0.141642i | 0.617625 | − | 0.786473i | \(-0.288095\pi\) |
−0.372293 | + | 0.928115i | \(0.621428\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.87721 | − | 10.1796i | −0.245953 | − | 0.426004i | 0.716446 | − | 0.697643i | \(-0.245768\pi\) |
−0.962399 | + | 0.271639i | \(0.912434\pi\) | |||||||
\(572\) | 0.559013 | + | 2.08627i | 0.0233735 | + | 0.0872312i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.09209 | + | 1.86755i | 0.0455831 | + | 0.0779501i | ||||
\(575\) | 26.4493 | + | 0.641957i | 1.10301 | + | 0.0267715i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.17865 | + | 0.583767i | 0.0906983 | + | 0.0243025i | 0.303883 | − | 0.952709i | \(-0.401717\pi\) |
−0.213184 | + | 0.977012i | \(0.568384\pi\) | |||||||
\(578\) | −25.1483 | − | 6.73845i | −1.04603 | − | 0.280283i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −19.9189 | − | 8.53525i | −0.827085 | − | 0.354407i | ||||
\(581\) | 30.0209 | + | 17.1111i | 1.24547 | + | 0.709889i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.958858 | + | 3.57851i | 0.0397118 | + | 0.148207i | ||||
\(584\) | −4.42532 | − | 7.66488i | −0.183121 | − | 0.317175i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.2119 | + | 7.62790i | 0.545779 | + | 0.315106i | ||||
\(587\) | −12.8372 | + | 12.8372i | −0.529847 | + | 0.529847i | −0.920527 | − | 0.390680i | \(-0.872240\pi\) |
0.390680 | + | 0.920527i | \(0.372240\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 6.47569i | − | 0.266826i | ||||||
\(590\) | −5.64319 | − | 0.812712i | −0.232327 | − | 0.0334588i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.691342 | − | 2.58012i | 0.0284140 | − | 0.106042i | ||||
\(593\) | −35.1170 | + | 9.40957i | −1.44208 | + | 0.386405i | −0.893262 | − | 0.449535i | \(-0.851590\pi\) |
−0.548820 | + | 0.835940i | \(0.684923\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −30.9452 | + | 23.4230i | −1.26863 | + | 0.960249i | ||||
\(596\) | −3.94236 | −0.161485 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.98074 | − | 14.8563i | 0.162785 | − | 0.607520i | ||||
\(599\) | −30.9792 | + | 17.8858i | −1.26578 | + | 0.730796i | −0.974186 | − | 0.225748i | \(-0.927517\pi\) |
−0.291589 | + | 0.956544i | \(0.594184\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 45.6631i | 1.86264i | 0.364204 | + | 0.931319i | \(0.381341\pi\) | ||||
−0.364204 | + | 0.931319i | \(0.618659\pi\) | |||||||
\(602\) | 1.51345 | − | 5.77629i | 0.0616835 | − | 0.235424i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 17.2732 | + | 9.97267i | 0.702835 | + | 0.405782i | ||||
\(605\) | −2.76811 | − | 23.1975i | −0.112540 | − | 0.943113i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.303188 | − | 1.13151i | −0.0123060 | − | 0.0459267i | 0.959500 | − | 0.281709i | \(-0.0909014\pi\) |
−0.971806 | + | 0.235783i | \(0.924235\pi\) | |||||||
\(608\) | 1.33788 | + | 1.33788i | 0.0542584 | + | 0.0542584i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.6093 | + | 5.04460i | −0.510536 | + | 0.204250i | ||||
\(611\) | 6.84463 | − | 11.8553i | 0.276904 | − | 0.479612i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.4629 | + | 3.60737i | 0.543760 | + | 0.145700i | 0.520235 | − | 0.854023i | \(-0.325844\pi\) |
0.0235253 | + | 0.999723i | \(0.492511\pi\) | |||||||
\(614\) | 4.87339 | − | 8.44095i | 0.196674 | − | 0.340649i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.96595 | − | 0.0109103i | 0.0792105 | − | 0.000439588i | ||||
\(617\) | −22.7725 | − | 22.7725i | −0.916788 | − | 0.916788i | 0.0800065 | − | 0.996794i | \(-0.474506\pi\) |
−0.996794 | + | 0.0800065i | \(0.974506\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11.3386 | − | 19.6391i | −0.455738 | − | 0.789361i | 0.542992 | − | 0.839738i | \(-0.317291\pi\) |
−0.998730 | + | 0.0503763i | \(0.983958\pi\) | |||||||
\(620\) | −0.906797 | − | 7.59919i | −0.0364178 | − | 0.305191i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.0891090 | + | 0.0891090i | −0.00357294 | + | 0.00357294i | ||||
\(623\) | 4.04497 | − | 15.4382i | 0.162058 | − | 0.618520i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.0187 | − | 13.5356i | −0.840749 | − | 0.541425i | ||||
\(626\) | 10.1273 | − | 5.84698i | 0.404767 | − | 0.233692i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −7.20903 | + | 1.93165i | −0.287672 | + | 0.0770814i | ||||
\(629\) | 17.5231 | 0.698690 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4210 | 1.29066 | 0.645330 | − | 0.763904i | \(-0.276720\pi\) | ||||
0.645330 | + | 0.763904i | \(0.276720\pi\) | |||||||
\(632\) | 6.35854 | − | 1.70376i | 0.252929 | − | 0.0677721i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 9.47968 | − | 5.47310i | 0.376486 | − | 0.217364i | ||||
\(635\) | −35.0004 | − | 5.04063i | −1.38895 | − | 0.200031i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 19.7106 | + | 5.04765i | 0.780963 | + | 0.199995i | ||||
\(638\) | −5.09214 | + | 5.09214i | −0.201600 | + | 0.201600i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.75735 | + | 1.38266i | 0.0694652 | + | 0.0546543i | ||||
\(641\) | −0.428070 | − | 0.741439i | −0.0169077 | − | 0.0292851i | 0.857448 | − | 0.514571i | \(-0.172049\pi\) |
−0.874355 | + | 0.485286i | \(0.838715\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.4254 | − | 16.4254i | −0.647754 | − | 0.647754i | 0.304696 | − | 0.952450i | \(-0.401445\pi\) |
−0.952450 | + | 0.304696i | \(0.901445\pi\) | |||||||
\(644\) | −12.1628 | − | 6.93250i | −0.479283 | − | 0.273179i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.20607 | + | 10.7492i | −0.244174 | + | 0.422922i | ||||
\(647\) | 45.8316 | + | 12.2805i | 1.80183 | + | 0.482798i | 0.994261 | − | 0.106982i | \(-0.0341186\pi\) |
0.807564 | + | 0.589779i | \(0.200785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.947323 | + | 1.64081i | −0.0371857 | + | 0.0644075i | ||||
\(650\) | −10.5229 | + | 10.0242i | −0.412744 | + | 0.393183i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.60305 | + | 8.60305i | 0.336921 | + | 0.336921i | ||||
\(653\) | −6.80004 | − | 25.3781i | −0.266106 | − | 0.993121i | −0.961570 | − | 0.274560i | \(-0.911468\pi\) |
0.695464 | − | 0.718561i | \(-0.255199\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.2991 | − | 2.54158i | 0.832225 | − | 0.0993077i | ||||
\(656\) | 0.708148 | + | 0.408849i | 0.0276485 | + | 0.0159629i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.85964 | − | 8.76184i | −0.345385 | − | 0.341572i | ||||
\(659\) | − | 26.2355i | − | 1.02199i | −0.859583 | − | 0.510996i | \(-0.829277\pi\) | ||
0.859583 | − | 0.510996i | \(-0.170723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −12.6197 | + | 7.28597i | −0.490848 | + | 0.283391i | −0.724926 | − | 0.688827i | \(-0.758126\pi\) |
0.234078 | + | 0.972218i | \(0.424793\pi\) | |||||||
\(662\) | −1.41325 | + | 5.27432i | −0.0549275 | + | 0.204992i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.0605 | 0.506847 | ||||||||
\(665\) | 4.21541 | + | 10.3695i | 0.163466 | + | 0.402110i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 49.5336 | − | 13.2725i | 1.91795 | − | 0.513913i | ||||
\(668\) | −0.532802 | + | 1.98844i | −0.0206147 | + | 0.0769352i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −18.3410 | − | 24.5127i | −0.708576 | − | 0.947007i | ||||
\(671\) | 4.51312i | 0.174227i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.4201 | + | 16.4201i | −0.632950 | + | 0.632950i | −0.948807 | − | 0.315857i | \(-0.897708\pi\) |
0.315857 | + | 0.948807i | \(0.397708\pi\) | |||||||
\(674\) | −25.0856 | − | 14.4832i | −0.966263 | − | 0.557872i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.27565 | − | 3.94154i | −0.0875249 | − | 0.151598i | ||||
\(677\) | 5.89172 | + | 21.9882i | 0.226437 | + | 0.845075i | 0.981824 | + | 0.189796i | \(0.0607825\pi\) |
−0.755386 | + | 0.655280i | \(0.772551\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.86774 | + | 10.2947i | −0.225183 | + | 0.395076i | ||||
\(680\) | −5.77756 | + | 13.4832i | −0.221559 | + | 0.517057i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.45656 | − | 0.658233i | −0.0940665 | − | 0.0252050i | ||||
\(683\) | 29.5964 | + | 7.93034i | 1.13248 | + | 0.303446i | 0.775922 | − | 0.630829i | \(-0.217285\pi\) |
0.356554 | + | 0.934275i | \(0.383952\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 7.73231 | + | 19.3274i | 0.295436 | + | 0.738463i | ||||
\(686\) | 8.99183 | − | 16.1910i | 0.343310 | − | 0.618173i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.584136 | − | 2.18003i | −0.0222700 | − | 0.0831127i | ||||
\(689\) | 7.24590 | + | 12.5503i | 0.276047 | + | 0.478127i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.7284 | + | 16.0090i | 1.05484 | + | 0.609012i | 0.924000 | − | 0.382392i | \(-0.124900\pi\) |
0.130839 | + | 0.991404i | \(0.458233\pi\) | |||||||
\(692\) | −6.65251 | + | 6.65251i | −0.252891 | + | 0.252891i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.5379i | 0.817567i | ||||||||
\(695\) | −39.6952 | + | 29.7010i | −1.50573 | + | 1.12662i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.38836 | + | 5.18143i | −0.0525879 | + | 0.196261i | ||||
\(698\) | −12.1459 | + | 3.25450i | −0.459731 | + | 0.123184i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 6.39880 | + | 11.5782i | 0.241852 | + | 0.437616i | ||||
\(701\) | 18.5294 | 0.699844 | 0.349922 | − | 0.936779i | \(-0.386208\pi\) | ||||
0.349922 | + | 0.936779i | \(0.386208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.30806 | − | 4.88174i | 0.0493343 | − | 0.184118i | ||||
\(704\) | 0.643519 | − | 0.371536i | 0.0242535 | − | 0.0140028i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 0.689506i | − | 0.0259499i | ||||||
\(707\) | 20.8025 | − | 21.0347i | 0.782360 | − | 0.791092i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.1074 | − | 13.3411i | −0.867818 | − | 0.501035i | −0.00119522 | − | 0.999999i | \(-0.500380\pi\) |
−0.866622 | + | 0.498965i | \(0.833714\pi\) | |||||||
\(710\) | −22.1464 | + | 28.1479i | −0.831138 | + | 1.05637i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.56121 | − | 5.82653i | −0.0585089 | − | 0.218358i | ||||
\(713\) | 12.8059 | + | 12.8059i | 0.479585 | + | 0.479585i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.79393 | + | 4.48406i | 0.0670893 | + | 0.167694i | ||||
\(716\) | −2.24874 | + | 3.89494i | −0.0840395 | + | 0.145561i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −21.3458 | − | 5.71959i | −0.796618 | − | 0.213453i | ||||
\(719\) | 15.9890 | − | 27.6937i | 0.596288 | − | 1.03280i | −0.397076 | − | 0.917786i | \(-0.629975\pi\) |
0.993364 | − | 0.115015i | \(-0.0366917\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.54117 | + | 3.24033i | −0.206364 | + | 0.120676i | ||||
\(722\) | −10.9037 | − | 10.9037i | −0.405793 | − | 0.405793i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.94250 | − | 15.4889i | −0.332346 | − | 0.575639i | ||||
\(725\) | −46.4875 | − | 13.6735i | −1.72650 | − | 0.507822i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.4539 | − | 21.4539i | 0.795683 | − | 0.795683i | −0.186729 | − | 0.982412i | \(-0.559789\pi\) |
0.982412 | + | 0.186729i | \(0.0597885\pi\) | |||||||
\(728\) | 7.41711 | − | 2.03159i | 0.274897 | − | 0.0752958i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −11.8564 | − | 15.8460i | −0.438824 | − | 0.586486i | ||||
\(731\) | 12.8222 | − | 7.40288i | 0.474245 | − | 0.273805i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −12.5691 | + | 3.36789i | −0.464252 | + | 0.124396i | −0.483360 | − | 0.875422i | \(-0.660584\pi\) |
0.0191085 | + | 0.999817i | \(0.493917\pi\) | |||||||
\(734\) | −13.4109 | −0.495006 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.29142 | −0.195044 | ||||||||
\(737\) | −9.82700 | + | 2.63314i | −0.361982 | + | 0.0969928i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.12136 | + | 1.80212i | −0.114821 | + | 0.0662920i | −0.556311 | − | 0.830974i | \(-0.687784\pi\) |
0.441490 | + | 0.897266i | \(0.354450\pi\) | |||||||
\(740\) | 0.851405 | − | 5.91186i | 0.0312983 | − | 0.217324i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 12.7223 | − | 3.48473i | 0.467052 | − | 0.127928i | ||||
\(743\) | −31.1070 | + | 31.1070i | −1.14121 | + | 1.14121i | −0.152977 | + | 0.988230i | \(0.548886\pi\) |
−0.988230 | + | 0.152977i | \(0.951114\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.75328 | + | 1.04451i | −0.320695 | + | 0.0382680i | ||||
\(746\) | 7.48320 | + | 12.9613i | 0.273979 | + | 0.474546i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.44690 | + | 3.44690i | 0.126031 | + | 0.126031i | ||||
\(749\) | 15.1663 | − | 8.86884i | 0.554164 | − | 0.324060i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.5141 | − | 44.1917i | 0.931023 | − | 1.61258i | 0.149447 | − | 0.988770i | \(-0.452251\pi\) |
0.781576 | − | 0.623810i | \(-0.214416\pi\) | |||||||
\(752\) | −4.54913 | − | 1.21894i | −0.165890 | − | 0.0444501i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −14.0848 | + | 24.3955i | −0.512936 | + | 0.888432i | ||||
\(755\) | 40.9941 | + | 17.5660i | 1.49193 | + | 0.639293i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 26.8141 | + | 26.8141i | 0.974576 | + | 0.974576i | 0.999685 | − | 0.0251083i | \(-0.00799305\pi\) |
−0.0251083 | + | 0.999685i | \(0.507993\pi\) | |||||||
\(758\) | −0.444610 | − | 1.65931i | −0.0161490 | − | 0.0602687i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.32499 | + | 2.61606i | 0.120610 | + | 0.0948944i | ||||
\(761\) | 25.8753 | + | 14.9391i | 0.937980 | + | 0.541543i | 0.889326 | − | 0.457273i | \(-0.151174\pi\) |
0.0486532 | + | 0.998816i | \(0.484507\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 16.6702 | − | 16.8563i | 0.603503 | − | 0.610239i | ||||
\(764\) | 2.77548i | 0.100413i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.05698 | + | 5.22905i | −0.327242 | + | 0.188933i | ||||
\(767\) | −1.91818 | + | 7.15874i | −0.0692614 | + | 0.258487i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 44.7341 | 1.61315 | 0.806576 | − | 0.591130i | \(-0.201318\pi\) | ||||
0.806576 | + | 0.591130i | \(0.201318\pi\) | |||||||
\(770\) | 4.36215 | − | 0.545096i | 0.157201 | − | 0.0196439i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.96491 | − | 1.33034i | 0.178691 | − | 0.0478801i | ||||
\(773\) | 6.25202 | − | 23.3328i | 0.224869 | − | 0.839224i | −0.757587 | − | 0.652734i | \(-0.773622\pi\) |
0.982457 | − | 0.186490i | \(-0.0597113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.02675 | − | 16.6324i | −0.144645 | − | 0.597452i | ||||
\(776\) | 4.47871i | 0.160776i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.3949 | + | 15.3949i | −0.551934 | + | 0.551934i | ||||
\(779\) | 1.33985 | + | 0.773565i | 0.0480052 | + | 0.0277158i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.95099 | + | 10.3074i | 0.212943 | + | 0.368828i | ||||
\(782\) | −8.98424 | − | 33.5296i | −0.321276 | − | 1.19902i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.0776922 | − | 6.99957i | −0.00277472 | − | 0.249985i | ||||
\(785\) | −15.4945 | + | 6.19889i | −0.553024 | + | 0.221248i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.2669 | + | 3.28689i | 0.437266 | + | 0.117165i | 0.470735 | − | 0.882275i | \(-0.343989\pi\) |
−0.0334688 | + | 0.999440i | \(0.510655\pi\) | |||||||
\(788\) | −1.83107 | − | 0.490633i | −0.0652290 | − | 0.0174781i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.6666 | − | 5.46757i | 0.486234 | − | 0.194527i | ||||
\(791\) | 0.570279 | − | 1.00054i | 0.0202768 | − | 0.0355749i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.56917 | + | 17.0524i | 0.162256 | + | 0.605547i | ||||
\(794\) | 15.8494 | + | 27.4520i | 0.562475 | + | 0.974236i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.5599 | − | 7.25148i | −0.445175 | − | 0.257022i | ||||
\(797\) | 8.99183 | − | 8.99183i | 0.318507 | − | 0.318507i | −0.529687 | − | 0.848193i | \(-0.677690\pi\) |
0.848193 | + | 0.529687i | \(0.177690\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 30.8957i | − | 1.09301i | ||||||
\(800\) | 4.26819 | + | 2.60433i | 0.150903 | + | 0.0920770i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.61585 | + | 13.4945i | −0.127680 | + | 0.476508i | ||||
\(803\) | −6.35256 | + | 1.70216i | −0.224177 | + | 0.0600681i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −28.8421 | − | 12.1699i | −1.01655 | − | 0.428931i | ||||
\(806\) | −9.94828 | −0.350413 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.89402 | − | 10.8006i | 0.101811 | − | 0.379965i | ||||
\(809\) | −23.7782 | + | 13.7284i | −0.835997 | + | 0.482663i | −0.855902 | − | 0.517139i | \(-0.826997\pi\) |
0.0199044 | + | 0.999802i | \(0.493664\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.7335i | 0.447132i | 0.974689 | + | 0.223566i | \(0.0717699\pi\) | ||||
−0.974689 | + | 0.223566i | \(0.928230\pi\) | |||||||
\(812\) | 18.2312 | + | 18.0300i | 0.639789 | + | 0.632727i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.71893 | − | 0.992425i | −0.0602485 | − | 0.0347845i | ||||
\(815\) | 21.3808 | + | 16.8221i | 0.748938 | + | 0.589254i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.10522 | − | 4.12473i | −0.0386666 | − | 0.144306i | ||||
\(818\) | −13.2506 | − | 13.2506i | −0.463297 | − | 0.463297i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.68063 | + | 0.720154i | 0.0586903 | + | 0.0251489i | ||||
\(821\) | 15.1707 | − | 26.2764i | 0.529461 | − | 0.917054i | −0.469948 | − | 0.882694i | \(-0.655727\pi\) |
0.999410 | − | 0.0343601i | \(-0.0109393\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.82702 | − | 2.63314i | −0.342549 | − | 0.0917856i | 0.0834435 | − | 0.996513i | \(-0.473408\pi\) |
−0.425992 | + | 0.904727i | \(0.640075\pi\) | |||||||
\(824\) | −1.21309 | + | 2.10113i | −0.0422599 | + | 0.0731963i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.86084 | + | 3.34053i | 0.203925 | + | 0.116232i | ||||
\(827\) | 15.9794 | + | 15.9794i | 0.555660 | + | 0.555660i | 0.928069 | − | 0.372409i | \(-0.121468\pi\) |
−0.372409 | + | 0.928069i | \(0.621468\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.17447 | + | 5.49835i | 0.110254 | + | 0.190966i | 0.915873 | − | 0.401469i | \(-0.131500\pi\) |
−0.805619 | + | 0.592435i | \(0.798167\pi\) | |||||||
\(830\) | 28.9985 | − | 3.46033i | 1.00655 | − | 0.120110i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.05532 | − | 2.05532i | 0.0712555 | − | 0.0712555i | ||||
\(833\) | 44.2216 | − | 12.3768i | 1.53219 | − | 0.428830i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.656159 | + | 4.55614i | −0.0227073 | + | 0.157672i | ||||
\(836\) | 1.21757 | − | 0.702966i | 0.0421106 | − | 0.0243126i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 30.4985 | − | 8.17206i | 1.05355 | − | 0.282299i | ||||
\(839\) | 39.7411 | 1.37202 | 0.686008 | − | 0.727594i | \(-0.259362\pi\) | ||||
0.686008 | + | 0.727594i | \(0.259362\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −64.9222 | −2.23870 | ||||||||
\(842\) | 13.0949 | − | 3.50878i | 0.451282 | − | 0.120921i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 8.68832 | − | 5.01621i | 0.299064 | − | 0.172665i | ||||
\(845\) | −6.09695 | − | 8.14853i | −0.209741 | − | 0.280318i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.00609 | + | 26.7398i | −0.240732 | + | 0.918790i | ||||
\(848\) | 3.52543 | − | 3.52543i | 0.121064 | − | 0.121064i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.25570 | + | 31.4677i | −0.317468 | + | 1.07933i | ||||
\(851\) | 7.06707 | + | 12.2405i | 0.242256 | + | 0.419600i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −17.1451 | − | 17.1451i | −0.587036 | − | 0.587036i | 0.349791 | − | 0.936828i | \(-0.386252\pi\) |
−0.936828 | + | 0.349791i | \(0.886252\pi\) | |||||||
\(854\) | 16.0690 | − | 0.0891766i | 0.549869 | − | 0.00305156i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.32024 | − | 5.75083i | 0.113484 | − | 0.196559i | ||||
\(857\) | −16.2677 | − | 4.35890i | −0.555692 | − | 0.148897i | −0.0299658 | − | 0.999551i | \(-0.509540\pi\) |
−0.525727 | + | 0.850654i | \(0.676206\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.4345 | − | 26.7333i | 0.526619 | − | 0.912130i | −0.472900 | − | 0.881116i | \(-0.656793\pi\) |
0.999519 | − | 0.0310142i | \(-0.00987370\pi\) | |||||||
\(860\) | −1.87456 | − | 4.68558i | −0.0639218 | − | 0.159777i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −9.38356 | − | 9.38356i | −0.319605 | − | 0.319605i | ||||
\(863\) | 0.334691 | + | 1.24908i | 0.0113930 | + | 0.0425193i | 0.971388 | − | 0.237497i | \(-0.0763269\pi\) |
−0.959995 | + | 0.280016i | \(0.909660\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −13.0081 | + | 16.5332i | −0.442289 | + | 0.562147i | ||||
\(866\) | 14.7624 | + | 8.52308i | 0.501647 | + | 0.289626i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.29510 | + | 8.75960i | −0.0779008 | + | 0.297320i | ||||
\(869\) | − | 4.89152i | − | 0.165934i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34.4645 | + | 19.8981i | −1.16778 | + | 0.674221i | ||||
\(872\) | 2.31914 | − | 8.65516i | 0.0785361 | − | 0.293101i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −10.0117 | −0.338649 | ||||||||
\(875\) | 17.2750 | + | 24.0120i | 0.584001 | + | 0.811753i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.37406 | + | 2.51177i | −0.316540 | + | 0.0848165i | −0.413591 | − | 0.910463i | \(-0.635726\pi\) |
0.0970513 | + | 0.995279i | \(0.469059\pi\) | |||||||
\(878\) | 9.07099 | − | 33.8534i | 0.306131 | − | 1.14250i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.33038 | − | 0.995425i | 0.0448471 | − | 0.0335558i | ||||
\(881\) | 18.3500i | 0.618227i | 0.951025 | + | 0.309113i | \(0.100032\pi\) | ||||
−0.951025 | + | 0.309113i | \(0.899968\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 23.7527 | − | 23.7527i | 0.799342 | − | 0.799342i | −0.183650 | − | 0.982992i | \(-0.558791\pi\) |
0.982992 | + | 0.183650i | \(0.0587913\pi\) | |||||||
\(884\) | 16.5135 | + | 9.53406i | 0.555408 | + | 0.320665i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.0315340 | − | 0.0546184i | −0.00105940 | − | 0.00183494i | ||||
\(887\) | −10.0547 | − | 37.5247i | −0.337604 | − | 1.25996i | −0.901018 | − | 0.433781i | \(-0.857179\pi\) |
0.563414 | − | 0.826175i | \(-0.309488\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 36.3503 | + | 20.7187i | 1.21915 | + | 0.694884i | ||||
\(890\) | −5.01010 | − | 12.5231i | −0.167939 | − | 0.419775i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −4.28599 | − | 1.14843i | −0.143506 | − | 0.0384522i | ||||
\(893\) | −8.60721 | − | 2.30629i | −0.288029 | − | 0.0771772i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.96097 | + | 9.24379i | −0.132401 | + | 0.308986i | ||||
\(896\) | −1.33557 | − | 2.28391i | −0.0446183 | − | 0.0763001i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −6.34642 | − | 23.6851i | −0.211783 | − | 0.790384i | ||||
\(899\) | −16.5847 | − | 28.7255i | −0.553130 | − | 0.958049i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.3251 | + | 16.3535i | 0.943644 | + | 0.544813i | ||||
\(902\) | 0.429644 | − | 0.429644i | 0.0143056 | − | 0.0143056i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 0.435281i | − | 0.0144772i | ||||||
\(905\) | −23.9589 | − | 32.0209i | −0.796421 | − | 1.06441i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.97748 | − | 33.5044i | 0.298092 | − | 1.11250i | −0.640638 | − | 0.767843i | \(-0.721330\pi\) |
0.938730 | − | 0.344653i | \(-0.112003\pi\) | |||||||
\(908\) | −0.648012 | + | 0.173634i | −0.0215050 | + | 0.00576226i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 15.9301 | − | 6.47591i | 0.528077 | − | 0.214674i | ||||
\(911\) | −48.1523 | −1.59536 | −0.797678 | − | 0.603083i | \(-0.793939\pi\) | ||||
−0.797678 | + | 0.603083i | \(0.793939\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.51182 | − | 9.37422i | 0.0831290 | − | 0.310242i | ||||
\(914\) | 17.3839 | − | 10.0366i | 0.575007 | − | 0.331980i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 13.2033i | 0.436250i | ||||||||
\(917\) | −24.5515 | − | 6.43273i | −0.810761 | − | 0.212428i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.4242 | + | 8.90515i | 0.508797 | + | 0.293754i | 0.732339 | − | 0.680940i | \(-0.238429\pi\) |
−0.223542 | + | 0.974694i | \(0.571762\pi\) | |||||||
\(920\) | −11.7486 | + | 1.40194i | −0.387341 | + | 0.0462206i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −3.02662 | − | 11.2955i | −0.0996763 | − | 0.371997i | ||||
\(923\) | 32.9206 | + | 32.9206i | 1.08360 | + | 1.08360i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.324064 | − | 13.3518i | 0.0106552 | − | 0.439004i | ||||
\(926\) | −1.96028 | + | 3.39531i | −0.0644188 | + | 0.111577i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.36112 | + | 2.50831i | 0.307294 | + | 0.0823392i | ||||
\(929\) | −16.1326 | + | 27.9424i | −0.529292 | + | 0.916761i | 0.470124 | + | 0.882600i | \(0.344209\pi\) |
−0.999416 | + | 0.0341607i | \(0.989124\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.146998 | − | 13.2436i | −0.00481766 | − | 0.434040i | ||||
\(932\) | 6.12279 | + | 6.12279i | 0.200559 | + | 0.200559i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.4604 | − | 18.1180i | −0.342276 | − | 0.592839i | ||||
\(935\) | 8.56645 | + | 6.73996i | 0.280153 | + | 0.220420i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.9650 | + | 28.9650i | −0.946244 | + | 0.946244i | −0.998627 | − | 0.0523829i | \(-0.983318\pi\) |
0.0523829 | + | 0.998627i | \(0.483318\pi\) | |||||||
\(938\) | 9.56947 | + | 34.9370i | 0.312454 | + | 1.14073i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −10.4235 | − | 1.50115i | −0.339976 | − | 0.0489621i | ||||
\(941\) | −30.8629 | + | 17.8187i | −1.00610 | + | 0.580874i | −0.910048 | − | 0.414502i | \(-0.863956\pi\) |
−0.0960550 | + | 0.995376i | \(0.530622\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.17936 | + | 1.11985i | −0.136099 | + | 0.0364675i | ||||
\(944\) | 2.54975 | 0.0829873 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.67706 | −0.0545259 | ||||||||
\(947\) | 13.4783 | − | 3.61149i | 0.437985 | − | 0.117358i | −0.0330871 | − | 0.999452i | \(-0.510534\pi\) |
0.471072 | + | 0.882095i | \(0.343867\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −22.2792 | + | 12.8629i | −0.723214 | + | 0.417548i | ||||
\(950\) | 8.07565 | + | 4.92753i | 0.262009 | + | 0.159870i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.2046 | − | 12.3408i | 0.395553 | − | 0.399968i | ||||
\(953\) | −25.4475 | + | 25.4475i | −0.824326 | + | 0.824326i | −0.986725 | − | 0.162399i | \(-0.948077\pi\) |
0.162399 | + | 0.986725i | \(0.448077\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.735353 | + | 6.16245i | 0.0237955 | + | 0.199412i | ||||
\(956\) | −2.00147 | − | 3.46665i | −0.0647322 | − | 0.112120i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.1712 | + | 17.1712i | 0.554775 | + | 0.554775i | ||||
\(959\) | −0.136689 | − | 24.6304i | −0.00441392 | − | 0.795356i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.64300 | + | 16.7022i | −0.311064 | + | 0.538779i | ||||
\(962\) | −7.49956 | − | 2.00950i | −0.241796 | − | 0.0647889i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.66256 | + | 15.0040i | −0.279002 | + | 0.483246i | ||||
\(965\) | 10.6712 | − | 4.26922i | 0.343518 | − | 0.137431i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −34.0735 | − | 34.0735i | −1.09573 | − | 1.09573i | −0.994904 | − | 0.100827i | \(-0.967851\pi\) |
−0.100827 | − | 0.994904i | \(-0.532149\pi\) | |||||||
\(968\) | 2.70410 | + | 10.0918i | 0.0869131 | + | 0.324364i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.18662 | + | 9.94416i | 0.0381000 | + | 0.319288i | ||||
\(971\) | −4.07547 | − | 2.35297i | −0.130788 | − | 0.0755105i | 0.433179 | − | 0.901308i | \(-0.357392\pi\) |
−0.563966 | + | 0.825798i | \(0.690725\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 56.5762 | − | 15.4966i | 1.81375 | − | 0.496797i | ||||
\(974\) | 2.55599i | 0.0818993i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.25989 | − | 3.03680i | 0.168365 | − | 0.0972055i | ||||
\(977\) | 7.12351 | − | 26.5853i | 0.227901 | − | 0.850540i | −0.753320 | − | 0.657654i | \(-0.771549\pi\) |
0.981221 | − | 0.192885i | \(-0.0617846\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.48226 | −0.143254 | ||||||||
\(980\) | −2.02701 | − | 15.5207i | −0.0647504 | − | 0.495790i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.0704 | − | 3.77017i | 0.449006 | − | 0.120311i | ||||
\(983\) | −11.6256 | + | 43.3874i | −0.370799 | + | 1.38384i | 0.488587 | + | 0.872515i | \(0.337513\pi\) |
−0.859386 | + | 0.511327i | \(0.829154\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.19554 | − | 0.604226i | −0.133681 | − | 0.0192522i | ||||
\(986\) | 63.5766i | 2.02469i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.88878 | − | 3.88878i | 0.123719 | − | 0.123719i | ||||
\(989\) | 10.3424 | + | 5.97118i | 0.328869 | + | 0.189872i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.08498 | + | 5.34334i | 0.0979975 | + | 0.169737i | 0.910856 | − | 0.412725i | \(-0.135423\pi\) |
−0.812858 | + | 0.582462i | \(0.802090\pi\) | |||||||
\(992\) | 0.885827 | + | 3.30595i | 0.0281250 | + | 0.104964i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 36.5820 | − | 21.3922i | 1.16031 | − | 0.678519i | ||||
\(995\) | −29.8083 | − | 12.7729i | −0.944985 | − | 0.404927i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.1820 | + | 4.87184i | 0.575829 | + | 0.154293i | 0.534968 | − | 0.844872i | \(-0.320324\pi\) |
0.0408602 | + | 0.999165i | \(0.486990\pi\) | |||||||
\(998\) | −29.0623 | − | 7.78721i | −0.919950 | − | 0.246500i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 630.2.bv.c.397.2 | 16 | ||
3.2 | odd | 2 | 70.2.k.a.47.4 | yes | 16 | ||
5.3 | odd | 4 | inner | 630.2.bv.c.523.3 | 16 | ||
7.3 | odd | 6 | inner | 630.2.bv.c.577.3 | 16 | ||
12.11 | even | 2 | 560.2.ci.c.257.2 | 16 | |||
15.2 | even | 4 | 350.2.o.c.243.3 | 16 | |||
15.8 | even | 4 | 70.2.k.a.33.2 | yes | 16 | ||
15.14 | odd | 2 | 350.2.o.c.257.1 | 16 | |||
21.2 | odd | 6 | 490.2.g.c.97.3 | 16 | |||
21.5 | even | 6 | 490.2.g.c.97.2 | 16 | |||
21.11 | odd | 6 | 490.2.l.c.227.1 | 16 | |||
21.17 | even | 6 | 70.2.k.a.17.2 | yes | 16 | ||
21.20 | even | 2 | 490.2.l.c.117.3 | 16 | |||
35.3 | even | 12 | inner | 630.2.bv.c.73.2 | 16 | ||
60.23 | odd | 4 | 560.2.ci.c.33.2 | 16 | |||
84.59 | odd | 6 | 560.2.ci.c.17.2 | 16 | |||
105.17 | odd | 12 | 350.2.o.c.143.1 | 16 | |||
105.23 | even | 12 | 490.2.g.c.293.2 | 16 | |||
105.38 | odd | 12 | 70.2.k.a.3.4 | ✓ | 16 | ||
105.53 | even | 12 | 490.2.l.c.423.3 | 16 | |||
105.59 | even | 6 | 350.2.o.c.157.3 | 16 | |||
105.68 | odd | 12 | 490.2.g.c.293.3 | 16 | |||
105.83 | odd | 4 | 490.2.l.c.313.1 | 16 | |||
420.143 | even | 12 | 560.2.ci.c.353.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.k.a.3.4 | ✓ | 16 | 105.38 | odd | 12 | ||
70.2.k.a.17.2 | yes | 16 | 21.17 | even | 6 | ||
70.2.k.a.33.2 | yes | 16 | 15.8 | even | 4 | ||
70.2.k.a.47.4 | yes | 16 | 3.2 | odd | 2 | ||
350.2.o.c.143.1 | 16 | 105.17 | odd | 12 | |||
350.2.o.c.157.3 | 16 | 105.59 | even | 6 | |||
350.2.o.c.243.3 | 16 | 15.2 | even | 4 | |||
350.2.o.c.257.1 | 16 | 15.14 | odd | 2 | |||
490.2.g.c.97.2 | 16 | 21.5 | even | 6 | |||
490.2.g.c.97.3 | 16 | 21.2 | odd | 6 | |||
490.2.g.c.293.2 | 16 | 105.23 | even | 12 | |||
490.2.g.c.293.3 | 16 | 105.68 | odd | 12 | |||
490.2.l.c.117.3 | 16 | 21.20 | even | 2 | |||
490.2.l.c.227.1 | 16 | 21.11 | odd | 6 | |||
490.2.l.c.313.1 | 16 | 105.83 | odd | 4 | |||
490.2.l.c.423.3 | 16 | 105.53 | even | 12 | |||
560.2.ci.c.17.2 | 16 | 84.59 | odd | 6 | |||
560.2.ci.c.33.2 | 16 | 60.23 | odd | 4 | |||
560.2.ci.c.257.2 | 16 | 12.11 | even | 2 | |||
560.2.ci.c.353.2 | 16 | 420.143 | even | 12 | |||
630.2.bv.c.73.2 | 16 | 35.3 | even | 12 | inner | ||
630.2.bv.c.397.2 | 16 | 1.1 | even | 1 | trivial | ||
630.2.bv.c.523.3 | 16 | 5.3 | odd | 4 | inner | ||
630.2.bv.c.577.3 | 16 | 7.3 | odd | 6 | inner |