Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(41,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.x (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.5 | ||
Root | \(-1.71965 - 0.206851i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.41 |
Dual form | 252.2.x.a.209.5 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.680689 | + | 1.59269i | 0.392996 | + | 0.919540i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.09336 | + | 3.62580i | −0.936177 | + | 1.62151i | −0.163656 | + | 0.986518i | \(0.552329\pi\) |
−0.772521 | + | 0.634989i | \(0.781005\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.36869 | − | 2.26422i | 0.517317 | − | 0.855794i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.07332 | + | 2.16825i | −0.691108 | + | 0.722751i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23222 | + | 0.711425i | −0.371529 | + | 0.214503i | −0.674126 | − | 0.738616i | \(-0.735480\pi\) |
0.302597 | + | 0.953119i | \(0.402146\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.850739 | − | 0.491174i | −0.235952 | − | 0.136227i | 0.377363 | − | 0.926066i | \(-0.376831\pi\) |
−0.613315 | + | 0.789838i | \(0.710164\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.19970 | − | 0.866025i | −1.85895 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.370947 | 0.0899679 | 0.0449840 | − | 0.998988i | \(-0.485676\pi\) | ||||
0.0449840 | + | 0.998988i | \(0.485676\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.97471i | 1.14128i | 0.821201 | + | 0.570638i | \(0.193304\pi\) | ||||
−0.821201 | + | 0.570638i | \(0.806696\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.53785 | + | 0.638674i | 0.990240 | + | 0.139370i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.98775 | + | 2.87968i | 1.04002 | + | 0.600455i | 0.919838 | − | 0.392298i | \(-0.128320\pi\) |
0.120179 | + | 0.992752i | \(0.461653\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.26427 | − | 10.8500i | −1.25285 | − | 2.17001i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.86465 | − | 1.82626i | −0.936202 | − | 0.351463i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.31732 | − | 4.22466i | 1.35879 | − | 0.784499i | 0.369332 | − | 0.929298i | \(-0.379587\pi\) |
0.989461 | + | 0.144798i | \(0.0462534\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.28007 | + | 3.62580i | 1.12793 | + | 0.651213i | 0.943414 | − | 0.331616i | \(-0.107594\pi\) |
0.184519 | + | 0.982829i | \(0.440927\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.97184 | − | 1.47829i | −0.343253 | − | 0.257338i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.34444 | + | 9.70241i | 0.903375 | + | 1.64001i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.46445 | 0.569552 | 0.284776 | − | 0.958594i | \(-0.408081\pi\) | ||||
0.284776 | + | 0.958594i | \(0.408081\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.203200 | − | 1.68930i | 0.0325380 | − | 0.270504i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.06981 | + | 1.85297i | −0.167077 | + | 0.289386i | −0.937391 | − | 0.348279i | \(-0.886766\pi\) |
0.770314 | + | 0.637665i | \(0.220099\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00875 | + | 5.21130i | 0.458830 | + | 0.794716i | 0.998899 | − | 0.0469039i | \(-0.0149354\pi\) |
−0.540070 | + | 0.841620i | \(0.681602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.52145 | − | 12.0564i | −0.524946 | − | 1.79726i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.13542 | − | 7.16276i | −0.603213 | − | 1.04480i | −0.992331 | − | 0.123608i | \(-0.960553\pi\) |
0.389118 | − | 0.921188i | \(-0.372780\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.25337 | − | 6.19803i | −0.464766 | − | 0.885433i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.252500 | + | 0.590804i | 0.0353570 | + | 0.0827291i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.97245i | 0.683019i | 0.939878 | + | 0.341509i | \(0.110938\pi\) | ||||
−0.939878 | + | 0.341509i | \(0.889062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 5.95706i | − | 0.803250i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.92317 | + | 3.38623i | −1.04945 | + | 0.448517i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.27883 | + | 3.94705i | −0.296678 | + | 0.513862i | −0.975374 | − | 0.220558i | \(-0.929212\pi\) |
0.678696 | + | 0.734420i | \(0.262546\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50416 | − | 3.75518i | 0.832772 | − | 0.480801i | −0.0220288 | − | 0.999757i | \(-0.507013\pi\) |
0.854801 | + | 0.518956i | \(0.173679\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.07166 | + | 7.66213i | 0.261004 | + | 0.965338i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.56180 | − | 2.05640i | 0.441786 | − | 0.255066i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.03205 | − | 8.71577i | 0.614763 | − | 1.06480i | −0.375663 | − | 0.926756i | \(-0.622585\pi\) |
0.990426 | − | 0.138044i | \(-0.0440816\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.19133 | + | 9.90411i | −0.143419 | + | 1.19231i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.9555i | − | 1.30018i | −0.759857 | − | 0.650090i | \(-0.774731\pi\) | ||
0.759857 | − | 0.650090i | \(-0.225269\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 9.52848i | − | 1.11522i | −0.830102 | − | 0.557612i | \(-0.811718\pi\) | ||
0.830102 | − | 0.557612i | \(-0.188282\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 13.0167 | − | 17.3626i | 1.50304 | − | 2.00486i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.0757141 | + | 3.76374i | −0.00862842 | + | 0.428918i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.25553 | + | 7.37079i | 0.478784 | + | 0.829278i | 0.999704 | − | 0.0243272i | \(-0.00774434\pi\) |
−0.520920 | + | 0.853606i | \(0.674411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.402651 | − | 8.99099i | −0.0447390 | − | 0.998999i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.972254 | + | 1.68399i | 0.106719 | + | 0.184842i | 0.914439 | − | 0.404724i | \(-0.132632\pi\) |
−0.807720 | + | 0.589566i | \(0.799299\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.776524 | + | 1.34498i | −0.0842259 | + | 0.145884i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.7094 | + | 8.77855i | 1.25538 | + | 0.941159i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −7.80735 | −0.827578 | −0.413789 | − | 0.910373i | \(-0.635795\pi\) | ||||
−0.413789 | + | 0.910373i | \(0.635795\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.27652 | + | 1.25399i | −0.238645 | + | 0.131454i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | + | 12.4702i | −0.155543 | + | 1.29310i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.0373 | − | 10.4138i | −1.85059 | − | 1.06844i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.34099 | + | 1.92892i | −0.339226 | + | 0.195852i | −0.659930 | − | 0.751327i | \(-0.729414\pi\) |
0.320704 | + | 0.947180i | \(0.396081\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.01225 | − | 4.14679i | 0.101735 | − | 0.416768i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.50637 | − | 7.80526i | −0.448401 | − | 0.776653i | 0.549882 | − | 0.835243i | \(-0.314673\pi\) |
−0.998282 | + | 0.0585901i | \(0.981340\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.96343 | + | 3.44299i | 0.587594 | + | 0.339248i | 0.764146 | − | 0.645044i | \(-0.223161\pi\) |
−0.176551 | + | 0.984291i | \(0.556494\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −11.8150 | + | 15.1164i | −1.15303 | + | 1.47521i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3630i | 1.09850i | 0.835658 | + | 0.549250i | \(0.185087\pi\) | ||||
−0.835658 | + | 0.549250i | \(0.814913\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.9930 | −1.53185 | −0.765926 | − | 0.642929i | \(-0.777719\pi\) | ||||
−0.765926 | + | 0.642929i | \(0.777719\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.35821 | + | 5.51779i | 0.223832 | + | 0.523726i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.17043 | + | 1.25310i | 0.204177 | + | 0.117881i | 0.598602 | − | 0.801046i | \(-0.295723\pi\) |
−0.394426 | + | 0.918928i | \(0.629056\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.8823 | + | 12.0564i | −1.94728 | + | 1.12426i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.82885 | − | 0.826254i | 0.261527 | − | 0.0763872i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.507712 | − | 0.839905i | 0.0465419 | − | 0.0769940i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.48775 | + | 7.77301i | −0.407977 | + | 0.706637i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.67942 | − | 0.442584i | −0.331762 | − | 0.0399065i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 31.5199 | 2.81922 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.91140 | −0.169609 | −0.0848046 | − | 0.996398i | \(-0.527027\pi\) | ||||
−0.0848046 | + | 0.996398i | \(0.527027\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.25197 | + | 8.33928i | −0.550455 | + | 0.734233i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.32591 | + | 7.49270i | −0.377957 | + | 0.654640i | −0.990765 | − | 0.135592i | \(-0.956707\pi\) |
0.612808 | + | 0.790232i | \(0.290040\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.2638 | + | 6.80885i | 0.976698 | + | 0.590402i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.8051 | − | 13.8152i | 1.44635 | − | 1.18902i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0973 | − | 5.82971i | 0.862675 | − | 0.498065i | −0.00223233 | − | 0.999998i | \(-0.500711\pi\) |
0.864907 | + | 0.501932i | \(0.167377\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.82663 | − | 2.78666i | −0.409390 | − | 0.236361i | 0.281138 | − | 0.959667i | \(-0.409288\pi\) |
−0.690528 | + | 0.723306i | \(0.742622\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.59312 | − | 11.4621i | 0.723672 | − | 0.965280i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.39773 | 0.116884 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 35.3748i | 2.93772i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 7.65702 | − | 9.40054i | 0.631540 | − | 0.775343i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.4024 | − | 7.73789i | −1.09797 | − | 0.633913i | −0.162282 | − | 0.986744i | \(-0.551886\pi\) |
−0.935687 | + | 0.352832i | \(0.885219\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.31732 | + | 14.4060i | 0.676854 | + | 1.17235i | 0.975923 | + | 0.218114i | \(0.0699905\pi\) |
−0.299069 | + | 0.954231i | \(0.596676\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.769094 | + | 0.804308i | −0.0621776 | + | 0.0650244i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −26.2928 | + | 15.1802i | −2.11189 | + | 1.21930i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.5559 | + | 8.40387i | 1.16169 | + | 0.670702i | 0.951708 | − | 0.307004i | \(-0.0993264\pi\) |
0.209981 | + | 0.977705i | \(0.432660\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.91958 | + | 3.38469i | −0.628063 | + | 0.268424i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 13.3469 | − | 7.35196i | 1.05188 | − | 0.579416i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.51105 | 0.275007 | 0.137503 | − | 0.990501i | \(-0.456092\pi\) | ||||
0.137503 | + | 0.990501i | \(0.456092\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.48775 | − | 4.05491i | 0.738620 | − | 0.315674i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.05253 | − | 7.01918i | 0.313594 | − | 0.543160i | −0.665544 | − | 0.746359i | \(-0.731800\pi\) |
0.979138 | + | 0.203198i | \(0.0651336\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.01750 | − | 10.4226i | −0.462884 | − | 0.801739i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −10.7864 | − | 10.3142i | −0.824859 | − | 0.788746i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.54844 | − | 11.3422i | −0.497868 | − | 0.862334i | 0.502128 | − | 0.864793i | \(-0.332550\pi\) |
−0.999997 | + | 0.00245951i | \(0.999217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −33.1407 | − | 0.666682i | −2.50520 | − | 0.0503964i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.83760 | − | 0.942756i | −0.589110 | − | 0.0708619i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 12.7179i | − | 0.950578i | −0.879830 | − | 0.475289i | \(-0.842344\pi\) | ||
0.879830 | − | 0.475289i | \(-0.157656\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 26.5518i | − | 1.97358i | −0.161998 | − | 0.986791i | \(-0.551794\pi\) | ||
0.161998 | − | 0.986791i | \(-0.448206\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.4081 | + | 7.80300i | 0.769392 | + | 0.576814i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.25232 | + | 12.5614i | −0.533201 | + | 0.923532i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.457090 | + | 0.263901i | −0.0334257 | + | 0.0192983i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −10.7932 | + | 8.51504i | −0.785093 | + | 0.619378i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.09735 | + | 0.633555i | −0.0794014 | + | 0.0458424i | −0.539175 | − | 0.842194i | \(-0.681264\pi\) |
0.459774 | + | 0.888036i | \(0.347931\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.31732 | + | 16.1381i | −0.670676 | + | 1.16164i | 0.307037 | + | 0.951697i | \(0.400662\pi\) |
−0.977713 | + | 0.209947i | \(0.932671\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.69969 | + | 4.27307i | 0.408163 | + | 0.306001i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.94312i | 0.423430i | 0.977331 | + | 0.211715i | \(0.0679049\pi\) | ||||
−0.977331 | + | 0.211715i | \(0.932095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 5.62675i | − | 0.398870i | −0.979911 | − | 0.199435i | \(-0.936089\pi\) | ||
0.979911 | − | 0.199435i | \(-0.0639106\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.3068 | + | 2.08177i | 1.22073 | + | 0.146837i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.449613 | − | 22.3503i | 0.0315567 | − | 1.56868i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.47900 | − | 7.75786i | −0.312827 | − | 0.541832i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −16.5851 | + | 4.84420i | −1.15274 | + | 0.336695i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.53913 | − | 6.12996i | −0.244807 | − | 0.424018i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.05305 | − | 1.82393i | 0.0724948 | − | 0.125565i | −0.827499 | − | 0.561467i | \(-0.810237\pi\) |
0.899994 | + | 0.435902i | \(0.143571\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 17.4487 | − | 7.45730i | 1.19557 | − | 0.510966i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.1935 | −1.71818 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.8051 | − | 9.25684i | 1.14080 | − | 0.628395i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 15.1759 | − | 6.48593i | 1.02549 | − | 0.438279i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.315579 | − | 0.182200i | −0.0212281 | − | 0.0122561i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.52351 | − | 3.18900i | 0.369882 | − | 0.213551i | −0.303525 | − | 0.952823i | \(-0.598164\pi\) |
0.673407 | + | 0.739272i | \(0.264830\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 36.5135 | + | 8.91312i | 2.43423 | + | 0.594208i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.72365 | − | 9.91365i | −0.379892 | − | 0.657992i | 0.611154 | − | 0.791511i | \(-0.290705\pi\) |
−0.991046 | + | 0.133520i | \(0.957372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.88696 | − | 2.82149i | −0.322940 | − | 0.186449i | 0.329762 | − | 0.944064i | \(-0.393031\pi\) |
−0.652702 | + | 0.757615i | \(0.726365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.04602 | + | 2.44135i | −0.397799 | + | 0.160629i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 12.4463i | − | 0.815385i | −0.913119 | − | 0.407693i | \(-0.866333\pi\) | ||
0.913119 | − | 0.407693i | \(-0.133667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 34.6276 | 2.25886 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −8.84269 | + | 11.7950i | −0.574394 | + | 0.766164i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.52450 | + | 2.03487i | 0.227981 | + | 0.131625i | 0.609640 | − | 0.792678i | \(-0.291314\pi\) |
−0.381659 | + | 0.924303i | \(0.624647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.26195 | − | 2.46064i | 0.274537 | − | 0.158504i | −0.356411 | − | 0.934329i | \(-0.616000\pi\) |
0.630947 | + | 0.775826i | \(0.282666\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.0458 | − | 6.76137i | 0.901037 | − | 0.433742i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 29.2833 | + | 1.17864i | 1.87084 | + | 0.0753007i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.44345 | − | 4.23218i | 0.155473 | − | 0.269287i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.02028 | + | 2.69477i | −0.128030 | + | 0.170774i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.65020 | −0.293518 | −0.146759 | − | 0.989172i | \(-0.546884\pi\) | ||||
−0.146759 | + | 0.989172i | \(0.546884\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.19470 | −0.515196 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.67071 | − | 0.321250i | −0.167246 | − | 0.0201174i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.44701 | + | 9.43450i | −0.339775 | + | 0.588508i | −0.984390 | − | 0.175999i | \(-0.943684\pi\) |
0.644615 | + | 0.764507i | \(0.277018\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.74176 | − | 7.84426i | 0.294639 | − | 0.487419i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.01105 | + | 24.6249i | −0.372075 | + | 1.52424i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.6489 | − | 9.03488i | 0.964951 | − | 0.557114i | 0.0672574 | − | 0.997736i | \(-0.478575\pi\) |
0.897693 | + | 0.440621i | \(0.145242\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.0291 | − | 10.4091i | −1.10752 | − | 0.639427i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.31438 | − | 12.4347i | −0.325235 | − | 0.760991i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.98410 | 0.181944 | 0.0909718 | − | 0.995853i | \(-0.471003\pi\) | ||||
0.0909718 | + | 0.995853i | \(0.471003\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3608i | 0.629375i | 0.949195 | + | 0.314688i | \(0.101900\pi\) | ||||
−0.949195 | + | 0.314688i | \(0.898100\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.54683 | − | 2.77222i | −0.214664 | − | 0.167782i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.4380 | + | 8.91312i | 0.930945 | + | 0.537481i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.94345 | + | 10.2944i | 0.357107 | + | 0.618528i | 0.987476 | − | 0.157768i | \(-0.0504297\pi\) |
−0.630369 | + | 0.776296i | \(0.717096\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −20.8823 | + | 6.09932i | −1.25019 | + | 0.365157i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0740 | + | 6.97095i | −0.720277 | + | 0.415852i | −0.814855 | − | 0.579665i | \(-0.803183\pi\) |
0.0945775 | + | 0.995518i | \(0.469850\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.19593 | + | 1.26782i | 0.130535 | + | 0.0753642i | 0.563845 | − | 0.825880i | \(-0.309321\pi\) |
−0.433311 | + | 0.901245i | \(0.642655\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.30823 | − | 35.8164i | 0.255197 | − | 2.12158i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.73129 | + | 4.95844i | 0.161223 | + | 0.292687i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8624 | −0.991906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.34635 | − | 4.00816i | −0.313408 | − | 0.234963i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.95496 | − | 6.85020i | 0.231052 | − | 0.400193i | −0.727066 | − | 0.686567i | \(-0.759117\pi\) |
0.958118 | + | 0.286374i | \(0.0924501\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.54080 | − | 16.5251i | −0.555487 | − | 0.962131i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.29358 | − | 1.21047i | 0.423216 | − | 0.0702388i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.82885 | − | 4.89971i | −0.163596 | − | 0.283357i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.9176 | + | 0.320209i | 0.917474 | + | 0.0184565i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 9.36393 | − | 12.4902i | 0.537944 | − | 0.717544i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 31.4437i | 1.80046i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.9676i | 0.797170i | 0.917131 | + | 0.398585i | \(0.130499\pi\) | ||||
−0.917131 | + | 0.398585i | \(0.869501\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.42437 | + | 11.8415i | −0.0810296 | + | 0.673640i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3163 | − | 28.2607i | 0.925215 | − | 1.60252i | 0.134001 | − | 0.990981i | \(-0.457218\pi\) |
0.791215 | − | 0.611539i | \(-0.209449\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.6110 | − | 7.85832i | 0.769340 | − | 0.444178i | −0.0632994 | − | 0.997995i | \(-0.520162\pi\) |
0.832639 | + | 0.553816i | \(0.186829\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −32.1181 | − | 8.52815i | −1.80965 | − | 0.480507i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −25.1366 | + | 14.5126i | −1.41181 | + | 0.815111i | −0.995559 | − | 0.0941377i | \(-0.969991\pi\) |
−0.416254 | + | 0.909248i | \(0.636657\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.01105 | + | 10.4114i | −0.336554 | + | 0.582929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0977 | + | 7.73465i | −1.01012 | + | 0.431706i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.84535i | 0.102678i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.3074i | 0.682692i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.8863 | − | 25.4719i | −0.602011 | − | 1.40860i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.8782 | − | 0.440117i | −1.20618 | − | 0.0242644i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.58510 | − | 11.4057i | −0.361950 | − | 0.626915i | 0.626332 | − | 0.779556i | \(-0.284555\pi\) |
−0.988282 | + | 0.152641i | \(0.951222\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −7.18292 | + | 7.51180i | −0.393622 | + | 0.411644i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.0677 | + | 36.4904i | 1.15105 | + | 1.99368i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.31732 | − | 14.4060i | 0.453073 | − | 0.784746i | −0.545502 | − | 0.838110i | \(-0.683661\pi\) |
0.998575 | + | 0.0533635i | \(0.0169942\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.518409 | + | 4.30979i | −0.0281561 | + | 0.234076i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.3179 | −0.558747 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.4866 | − | 1.11687i | −0.998180 | − | 0.0603053i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −33.4164 | − | 25.0523i | −1.79908 | − | 1.34877i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.4012 | + | 12.3560i | 1.14888 | + | 0.663305i | 0.948614 | − | 0.316437i | \(-0.102487\pi\) |
0.200264 | + | 0.979742i | \(0.435820\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.7994 | + | 15.4727i | −1.43454 | + | 0.828232i | −0.997463 | − | 0.0711915i | \(-0.977320\pi\) |
−0.437078 | + | 0.899424i | \(0.643987\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.24153 | + | 3.94306i | 0.173020 | + | 0.210465i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 11.6758 | + | 20.2231i | 0.621440 | + | 1.07637i | 0.989218 | + | 0.146452i | \(0.0467853\pi\) |
−0.367778 | + | 0.929914i | \(0.619881\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.7225 | + | 22.9338i | 2.10825 | + | 1.21720i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.68330 | + | 0.236914i | 0.0890898 | + | 0.0125388i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 21.2351i | − | 1.12075i | −0.828240 | − | 0.560374i | \(-0.810657\pi\) | ||
0.828240 | − | 0.560374i | \(-0.189343\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.74775 | −0.302513 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −15.4348 | − | 1.85659i | −0.810115 | − | 0.0974458i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.5483 | + | 19.9465i | 1.80834 | + | 1.04405i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0178 | − | 6.93846i | 0.627322 | − | 0.362185i | −0.152392 | − | 0.988320i | \(-0.548698\pi\) |
0.779714 | + | 0.626135i | \(0.215364\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.79964 | − | 6.16144i | −0.0936857 | − | 0.320752i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.2587 | + | 6.80576i | 0.584523 | + | 0.353337i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0728 | − | 27.8390i | 0.832221 | − | 1.44145i | −0.0640529 | − | 0.997947i | \(-0.520403\pi\) |
0.896273 | − | 0.443502i | \(-0.146264\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.4552 | + | 50.2014i | 1.10794 | + | 2.59239i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.30017 | −0.427481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.95340 | 0.100339 | 0.0501696 | − | 0.998741i | \(-0.484024\pi\) | ||||
0.0501696 | + | 0.998741i | \(0.484024\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.30107 | − | 3.04427i | −0.0666558 | − | 0.155962i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.788167 | − | 1.36514i | 0.0402734 | − | 0.0697557i | −0.845186 | − | 0.534472i | \(-0.820510\pi\) |
0.885460 | + | 0.464717i | \(0.153844\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.4881 | − | 8.15338i | −0.687416 | − | 0.415535i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −17.5375 | − | 4.28100i | −0.891483 | − | 0.217615i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.74447 | − | 5.62597i | 0.494064 | − | 0.285248i | −0.232195 | − | 0.972669i | \(-0.574591\pi\) |
0.726259 | + | 0.687421i | \(0.241257\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.85019 | + | 1.06821i | 0.0935682 | + | 0.0540216i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.8782 | − | 1.78964i | −0.750503 | − | 0.0902753i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −35.6333 | −1.79291 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 0.632961i | − | 0.0317674i | −0.999874 | − | 0.0158837i | \(-0.994944\pi\) | ||
0.999874 | − | 0.0158837i | \(-0.00505615\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.17722 | + | 22.5745i | −0.159060 | + | 1.13014i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.38032 | + | 4.26103i | 0.368555 | + | 0.212786i | 0.672827 | − | 0.739800i | \(-0.265080\pi\) |
−0.304272 | + | 0.952585i | \(0.598413\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.56180 | − | 6.16921i | −0.177426 | − | 0.307310i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 33.4424 | + | 17.3614i | 1.66177 | + | 0.862695i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.26897 | + | 2.46469i | −0.211605 | + | 0.122170i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.1822 | + | 7.03338i | 0.602370 | + | 0.347778i | 0.769973 | − | 0.638076i | \(-0.220269\pi\) |
−0.167603 | + | 0.985855i | \(0.553603\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 16.1581 | + | 12.1137i | 0.797019 | + | 0.597526i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.81796 | + | 10.5621i | 0.286283 | + | 0.519725i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.14109 | −0.399630 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.15285 | − | 9.58418i | 0.0564551 | − | 0.469339i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.9339 | + | 18.9381i | −0.534156 | + | 0.925185i | 0.465048 | + | 0.885286i | \(0.346037\pi\) |
−0.999204 | + | 0.0398995i | \(0.987296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.3616 | + | 23.1430i | 0.651206 | + | 1.12792i | 0.982831 | + | 0.184510i | \(0.0590698\pi\) |
−0.331625 | + | 0.943411i | \(0.607597\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.1048 | + | 5.88408i | 1.17201 | + | 0.286094i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.32371 | − | 4.02479i | −0.112717 | − | 0.195231i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.399648 | − | 19.8665i | 0.0193403 | − | 0.961408i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0.951422 | + | 2.22616i | 0.0459351 | + | 0.107480i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.9400i | 0.960476i | 0.877138 | + | 0.480238i | \(0.159450\pi\) | ||||
−0.877138 | + | 0.480238i | \(0.840550\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 20.2826i | − | 0.974719i | −0.873201 | − | 0.487359i | \(-0.837960\pi\) | ||
0.873201 | − | 0.487359i | \(-0.162040\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −56.3412 | + | 24.0793i | −2.70135 | + | 1.15451i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.3256 | + | 24.8126i | −0.685285 | + | 1.18695i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −24.5936 | + | 14.1991i | −1.17379 | + | 0.677687i | −0.954569 | − | 0.297989i | \(-0.903684\pi\) |
−0.219219 | + | 0.975676i | \(0.570351\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 20.1842 | + | 5.79641i | 0.961152 | + | 0.276020i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.6570 | − | 6.15281i | 0.506328 | − | 0.292329i | −0.224995 | − | 0.974360i | \(-0.572236\pi\) |
0.731323 | + | 0.682031i | \(0.238903\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.3436 | − | 28.3079i | 0.774759 | − | 1.34192i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 3.20118 | − | 26.6130i | 0.151411 | − | 1.25875i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 36.1924i | − | 1.70803i | −0.520251 | − | 0.854013i | \(-0.674162\pi\) | ||
0.520251 | − | 0.854013i | \(-0.325838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.04437i | − | 0.143354i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.2828 | + | 23.0529i | −0.812018 | + | 1.08312i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.218855 | − | 10.8793i | 0.0102601 | − | 0.510028i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.20892 | + | 7.29007i | 0.196885 | + | 0.341015i | 0.947517 | − | 0.319706i | \(-0.103584\pi\) |
−0.750632 | + | 0.660721i | \(0.770251\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.80453 | − | 0.677445i | −0.0842281 | − | 0.0316204i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −9.07730 | − | 15.7224i | −0.422772 | − | 0.732263i | 0.573437 | − | 0.819249i | \(-0.305610\pi\) |
−0.996209 | + | 0.0869865i | \(0.972276\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.64690 | + | 13.2448i | −0.355381 | + | 0.615539i | −0.987183 | − | 0.159591i | \(-0.948982\pi\) |
0.631802 | + | 0.775130i | \(0.282316\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −42.0745 | − | 31.5433i | −1.95116 | − | 1.46279i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −26.7864 | −1.23953 | −0.619763 | − | 0.784789i | \(-0.712771\pi\) | ||||
−0.619763 | + | 0.784789i | \(0.712771\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.8471 | − | 23.3229i | −0.593223 | − | 1.07695i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.47670 | + | 28.9035i | −0.160198 | + | 1.33180i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.41490 | − | 4.28100i | −0.340938 | − | 0.196840i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 53.9758 | − | 31.1630i | 2.47658 | − | 1.42985i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.7815 | − | 10.3095i | −0.493653 | − | 0.472040i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.2775 | + | 24.7294i | 0.652357 | + | 1.12992i | 0.982549 | + | 0.186002i | \(0.0595529\pi\) |
−0.330193 | + | 0.943914i | \(0.607114\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.94734 | − | 1.70165i | −0.134387 | − | 0.0775884i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.7945 | + | 16.2531i | 0.946182 | + | 0.739542i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 16.1517i | − | 0.733409i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.1527 | −0.596006 | −0.298003 | − | 0.954565i | \(-0.596321\pi\) | ||||
−0.298003 | + | 0.954565i | \(0.596321\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.38994 | + | 5.59202i | 0.108077 | + | 0.252880i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.6854 | + | 16.5615i | 1.29455 | + | 0.747411i | 0.979458 | − | 0.201649i | \(-0.0646301\pi\) |
0.315096 | + | 0.949060i | \(0.397963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.71434 | − | 1.56712i | 0.122248 | − | 0.0705798i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 12.9164 | + | 12.3509i | 0.580550 | + | 0.555132i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −24.8057 | − | 14.9947i | −1.11269 | − | 0.672605i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.27652 | − | 5.67511i | 0.146677 | − | 0.254053i | −0.783320 | − | 0.621619i | \(-0.786475\pi\) |
0.929997 | + | 0.367566i | \(0.119809\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 13.9379 | + | 1.67654i | 0.622699 | + | 0.0749022i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.4969 | 0.557210 | 0.278605 | − | 0.960406i | \(-0.410128\pi\) | ||||
0.278605 | + | 0.960406i | \(0.410128\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 37.7337 | 1.67913 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.5039 | − | 16.6786i | 0.555320 | − | 0.740721i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.30237 | − | 5.71987i | 0.146375 | − | 0.253529i | −0.783510 | − | 0.621379i | \(-0.786573\pi\) |
0.929885 | + | 0.367850i | \(0.119906\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.5746 | − | 13.0416i | −0.954402 | − | 0.576924i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 9.08510 | − | 24.2002i | 0.401117 | − | 1.06847i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −24.9672 | + | 14.4148i | −1.10018 | + | 0.635192i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 10.1915 | + | 5.88408i | 0.448223 | + | 0.258782i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.6072 | − | 18.1502i | 0.597290 | − | 0.796704i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.9784 | −0.700026 | −0.350013 | − | 0.936745i | \(-0.613823\pi\) | ||||
−0.350013 | + | 0.936745i | \(0.613823\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 11.7615i | − | 0.514293i | −0.966372 | − | 0.257147i | \(-0.917218\pi\) | ||
0.966372 | − | 0.257147i | \(-0.0827824\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −21.4967 | − | 53.2367i | −0.938193 | − | 2.32344i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.32957 | + | 1.34498i | 0.101478 | + | 0.0585882i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.08510 | + | 8.80765i | 0.221091 | + | 0.382941i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.83345 | − | 13.1246i | −0.166358 | − | 0.569559i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.82026 | − | 1.05093i | 0.0788444 | − | 0.0455208i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −41.1999 | − | 23.7867i | −1.78122 | − | 1.02839i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.2556 | − | 8.65691i | 0.874094 | − | 0.373573i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 8.41831 | + | 5.32284i | 0.362602 | + | 0.229271i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.411960 | −0.0177115 | −0.00885576 | − | 0.999961i | \(-0.502819\pi\) | ||||
−0.00885576 | + | 0.999961i | \(0.502819\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 42.2888 | − | 18.0735i | 1.81479 | − | 0.775610i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.4790 | − | 57.9874i | 1.43408 | − | 2.48391i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.9166 | + | 20.6402i | 0.509519 | + | 0.882513i | 0.999939 | + | 0.0110266i | \(0.00350995\pi\) |
−0.490420 | + | 0.871486i | \(0.663157\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.34305 | + | 21.8884i | −0.228036 | + | 0.934173i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.0165 | + | 36.4016i | 0.895331 | + | 1.55076i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 22.5136 | + | 0.452899i | 0.957374 | + | 0.0192592i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −24.9430 | − | 3.00030i | −1.05877 | − | 0.127356i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 42.9474i | 1.81974i | 0.414896 | + | 0.909869i | \(0.363818\pi\) | ||||
−0.414896 | + | 0.909869i | \(0.636182\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5.91128i | − | 0.250020i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.731449 | − | 0.548368i | −0.0308818 | − | 0.0231521i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.9454 | − | 27.6182i | 0.672019 | − | 1.16397i | −0.305312 | − | 0.952252i | \(-0.598761\pi\) |
0.977331 | − | 0.211718i | \(-0.0679058\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.08695 | + | 5.24635i | −0.382291 | + | 0.220716i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −20.9087 | − | 11.3942i | −0.878081 | − | 0.478512i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.428895 | − | 0.247623i | 0.0179802 | − | 0.0103809i | −0.490983 | − | 0.871169i | \(-0.663362\pi\) |
0.508963 | + | 0.860788i | \(0.330029\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.34182 | + | 2.32411i | −0.0561535 | + | 0.0972608i | −0.892736 | − | 0.450581i | \(-0.851217\pi\) |
0.836582 | + | 0.547841i | \(0.184550\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.75601 | − | 1.31648i | −0.0733584 | − | 0.0549969i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 72.1564i | − | 3.00913i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 42.0259i | 1.74956i | 0.484518 | + | 0.874781i | \(0.338995\pi\) | ||||
−0.484518 | + | 0.874781i | \(0.661005\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −32.0452 | − | 3.85460i | −1.33175 | − | 0.160192i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.14364 | + | 0.103473i | 0.213394 | + | 0.00429279i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.53753 | − | 6.12717i | −0.146509 | − | 0.253762i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.92595 | + | 11.9865i | −0.120973 | + | 0.495580i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.71916 | + | 2.97768i | 0.0709575 | + | 0.122902i | 0.899321 | − | 0.437289i | \(-0.144061\pi\) |
−0.828364 | + | 0.560191i | \(0.810728\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.0373 | + | 31.2415i | −0.743214 | + | 1.28728i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.46555 | + | 4.04542i | −0.389361 | + | 0.166406i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.10251 | 0.373795 | 0.186898 | − | 0.982379i | \(-0.440157\pi\) | ||||
0.186898 | + | 0.982379i | \(0.440157\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.98250 | + | 3.59908i | 0.0812747 | + | 0.147548i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8.96167 | − | 3.83007i | 0.366777 | − | 0.156754i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.71186 | + | 3.87510i | 0.274239 | + | 0.158332i | 0.630813 | − | 0.775935i | \(-0.282722\pi\) |
−0.356573 | + | 0.934267i | \(0.616055\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0034 | + | 12.7037i | −0.897536 | + | 0.518193i | −0.876400 | − | 0.481584i | \(-0.840062\pi\) |
−0.0211361 | + | 0.999777i | \(0.506728\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.46492 | + | 28.9814i | 0.344718 | + | 1.18021i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −18.7889 | − | 32.5433i | −0.763878 | − | 1.32308i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.7094 | + | 6.76042i | 0.475270 | + | 0.274397i | 0.718443 | − | 0.695586i | \(-0.244855\pi\) |
−0.243173 | + | 0.969983i | \(0.578188\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 35.9031 | − | 14.4975i | 1.45487 | − | 0.587468i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 8.12485i | 0.328696i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.83635 | 0.195338 | 0.0976691 | − | 0.995219i | \(-0.468861\pi\) | ||||
0.0976691 | + | 0.995219i | \(0.468861\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.30706 | − | 12.4144i | 0.375297 | − | 0.500595i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.30333 | + | 3.06188i | 0.213504 | + | 0.123267i | 0.602939 | − | 0.797787i | \(-0.293996\pi\) |
−0.389435 | + | 0.921054i | \(0.627330\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.94313 | − | 2.85392i | 0.198681 | − | 0.114709i | −0.397359 | − | 0.917663i | \(-0.630073\pi\) |
0.596040 | + | 0.802955i | \(0.296740\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −19.0046 | − | 23.1175i | −0.762629 | − | 0.927675i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.6859 | + | 17.6775i | −0.428120 | + | 0.708236i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −34.6609 | + | 60.0344i | −1.38644 | + | 2.40138i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 7.35407 | − | 9.80934i | 0.293693 | − | 0.391747i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.28513 | 0.0512414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0525 | −0.758468 | −0.379234 | − | 0.925301i | \(-0.623812\pi\) | ||||
−0.379234 | + | 0.925301i | \(0.623812\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3.62176 | + | 0.435648i | 0.143952 | + | 0.0173155i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.00124 | − | 6.93035i | 0.158784 | − | 0.275022i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.276550 | + | 6.87087i | −0.0109573 | + | 0.272234i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 23.7543 | + | 22.7143i | 0.939707 | + | 0.898565i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13.2820 | − | 7.66837i | 0.524607 | − | 0.302882i | −0.214210 | − | 0.976788i | \(-0.568718\pi\) |
0.738818 | + | 0.673905i | \(0.235384\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −11.3209 | − | 6.53612i | −0.446453 | − | 0.257759i | 0.259878 | − | 0.965641i | \(-0.416318\pi\) |
−0.706331 | + | 0.707882i | \(0.749651\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.1490 | − | 40.1255i | −0.675239 | − | 1.57994i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.7066 | 1.40377 | 0.701885 | − | 0.712290i | \(-0.252342\pi\) | ||||
0.701885 | + | 0.712290i | \(0.252342\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 6.48486i | − | 0.254553i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 26.1823 | + | 20.4642i | 1.02617 | + | 0.802057i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −23.6131 | − | 13.6330i | −0.924051 | − | 0.533501i | −0.0391261 | − | 0.999234i | \(-0.512457\pi\) |
−0.884925 | + | 0.465733i | \(0.845791\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.1113 | − | 31.3698i | −0.707669 | − | 1.22572i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.6602 | + | 19.7556i | 0.806030 | + | 0.770741i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.7911 | + | 8.53963i | −0.576179 | + | 0.332657i | −0.759613 | − | 0.650375i | \(-0.774612\pi\) |
0.183435 | + | 0.983032i | \(0.441278\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.6657 | − | 23.4784i | −1.58171 | − | 0.913203i | −0.994609 | − | 0.103692i | \(-0.966934\pi\) |
−0.587105 | − | 0.809511i | \(-0.699732\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0753764 | − | 0.626641i | 0.00292738 | − | 0.0243367i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −48.2667 | + | 26.5870i | −1.87170 | + | 1.03100i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 48.6626 | 1.88422 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.83888 | + | 6.62652i | 0.341731 | + | 0.256196i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.34305 | + | 9.25444i | −0.206266 | + | 0.357264i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.76077 | + | 13.4421i | 0.299156 | + | 0.518153i | 0.975943 | − | 0.218026i | \(-0.0699616\pi\) |
−0.676787 | + | 0.736179i | \(0.736628\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.6585 | + | 64.2218i | 0.410247 | + | 2.47190i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −9.07869 | − | 15.7248i | −0.348922 | − | 0.604351i | 0.637136 | − | 0.770751i | \(-0.280119\pi\) |
−0.986058 | + | 0.166400i | \(0.946786\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.205287 | + | 10.2048i | −0.00787820 | + | 0.391625i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 11.8933 | − | 15.8641i | 0.455754 | − | 0.607914i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.1917i | − | 0.772615i | −0.922370 | − | 0.386308i | \(-0.873750\pi\) | ||
0.922370 | − | 0.386308i | \(-0.126250\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 48.8146i | 1.86511i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.16726 | − | 9.70398i | 0.0445336 | − | 0.370230i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.44234 | − | 4.23026i | 0.0930458 | − | 0.161160i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.0695792 | + | 0.0401716i | −0.00264692 | + | 0.00152820i | −0.501323 | − | 0.865260i | \(-0.667153\pi\) |
0.498676 | + | 0.866788i | \(0.333820\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.00377 | − | 7.96763i | −0.304038 | − | 0.302665i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 20.2077 | − | 11.6669i | 0.766523 | − | 0.442552i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.396844 | + | 0.687355i | −0.0150316 | + | 0.0260354i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.8231 | − | 8.47207i | 0.749780 | − | 0.320443i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.1490i | − | 1.32756i | −0.747928 | − | 0.663780i | \(-0.768951\pi\) | ||
0.747928 | − | 0.663780i | \(-0.231049\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.2346i | 0.650016i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.5707 | + | 55.1511i | 0.887722 | + | 2.07711i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.8406 | − | 0.479595i | −0.896620 | − | 0.0180370i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.782968 | − | 1.35614i | −0.0294050 | − | 0.0509309i | 0.850948 | − | 0.525249i | \(-0.176028\pi\) |
−0.880353 | + | 0.474318i | \(0.842695\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24.8048 | − | 6.05497i | −0.930254 | − | 0.227079i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 20.8823 | + | 36.1691i | 0.782047 | + | 1.35455i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.92595 | + | 5.06790i | −0.109424 | + | 0.189529i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.841830 | + | 6.99855i | −0.0314387 | + | 0.261366i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 25.8787 | 0.965112 | 0.482556 | − | 0.875865i | \(-0.339709\pi\) | ||||
0.482556 | + | 0.875865i | \(0.339709\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9578 | − | 8.79012i | 0.594299 | − | 0.327361i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.82010 | + | 5.11304i | 0.253642 | + | 0.190156i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −91.6754 | − | 52.9288i | −3.40474 | − | 1.96573i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0.990545 | − | 0.571891i | 0.0367373 | − | 0.0212103i | −0.481519 | − | 0.876436i | \(-0.659915\pi\) |
0.518256 | + | 0.855225i | \(0.326581\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.3296 | + | 17.7682i | 0.752947 | + | 0.658081i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.11609 | + | 1.93312i | 0.0412800 | + | 0.0714990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.1408 | − | 11.6283i | −0.743916 | − | 0.429500i | 0.0795755 | − | 0.996829i | \(-0.474644\pi\) |
−0.823491 | + | 0.567329i | \(0.807977\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 18.0556 | + | 47.4415i | 0.665990 | + | 1.74990i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.3197i | 0.527473i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −36.1516 | −1.32986 | −0.664929 | − | 0.746907i | \(-0.731538\pi\) | ||||
−0.664929 | + | 0.746907i | \(0.731538\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.40378 | + | 1.01086i | 0.308721 | + | 0.0371349i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.43940 | + | 3.71779i | 0.236239 | + | 0.136392i | 0.613447 | − | 0.789736i | \(-0.289783\pi\) |
−0.377208 | + | 0.926129i | \(0.623116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 56.1121 | − | 32.3963i | 2.05579 | − | 1.18691i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −5.66712 | − | 1.38337i | −0.207349 | − | 0.0506149i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 25.7283 | + | 15.5524i | 0.940090 | + | 0.568273i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.67798 | + | 6.37044i | −0.134211 | + | 0.232461i | −0.925296 | − | 0.379246i | \(-0.876183\pi\) |
0.791085 | + | 0.611707i | \(0.209517\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.16534 | − | 7.40633i | −0.115352 | − | 0.269902i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −69.6445 | −2.53462 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.65326 | 0.278163 | 0.139081 | − | 0.990281i | \(-0.455585\pi\) | ||||
0.139081 | + | 0.990281i | \(0.455585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.57804 | − | 13.0516i | −0.202470 | − | 0.473744i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.7203 | − | 37.6207i | 0.787362 | − | 1.36375i | −0.140217 | − | 0.990121i | \(-0.544780\pi\) |
0.927578 | − | 0.373629i | \(-0.121887\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −21.8895 | + | 36.2116i | −0.792452 | + | 1.31095i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.30627 | − | 4.47228i | −0.0472283 | − | 0.161696i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.87738 | − | 2.23860i | 0.140004 | − | 0.0808313i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.8491 | − | 10.8825i | −0.679716 | − | 0.392434i | 0.120032 | − | 0.992770i | \(-0.461700\pi\) |
−0.799748 | + | 0.600336i | \(0.795034\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.7340 | − | 2.25344i | −0.674687 | − | 0.0811557i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14.5147 | −0.522056 | −0.261028 | − | 0.965331i | \(-0.584062\pi\) | ||||
−0.261028 | + | 0.965331i | \(0.584062\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 90.8520i | − | 3.26350i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 15.7211 | + | 2.21265i | 0.563993 | + | 0.0793784i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −9.21800 | − | 5.32202i | −0.330269 | − | 0.190681i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.79402 | + | 13.4996i | 0.278892 | + | 0.483055i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −43.3115 | + | 7.18816i | −1.54783 | + | 0.256884i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −60.9415 | + | 35.1846i | −2.17509 | + | 1.25579i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.4291 | + | 6.59861i | 0.407405 | + | 0.235215i | 0.689674 | − | 0.724120i | \(-0.257754\pi\) |
−0.282269 | + | 0.959335i | \(0.591087\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 25.0418 | + | 18.7739i | 0.891511 | + | 0.668367i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.80793 | − | 3.19922i | 0.206506 | − | 0.113751i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.37778 | −0.261993 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.30627 | − | 35.8002i | 0.152728 | − | 1.26970i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −24.8899 | + | 43.1106i | −0.881646 | + | 1.52706i | −0.0321352 | + | 0.999484i | \(0.510231\pi\) |
−0.849511 | + | 0.527572i | \(0.823103\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.53402 | − | 2.65701i | −0.0542698 | − | 0.0939981i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16.1872 | − | 16.9283i | 0.571946 | − | 0.598133i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.77880 | + | 11.7412i | 0.239219 | + | 0.414339i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.28311 | + | 63.7835i | −0.0452238 | + | 2.24807i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.03124 | + | 4.75274i | 0.0715032 | + | 0.167305i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 28.1889i | − | 0.991068i | −0.868589 | − | 0.495534i | \(-0.834972\pi\) | ||
0.868589 | − | 0.495534i | \(-0.165028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 33.5981i | 1.17979i | 0.807480 | + | 0.589894i | \(0.200831\pi\) | ||||
−0.807480 | + | 0.589894i | \(0.799169\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.5016 | + | 7.05250i | −0.578736 | + | 0.247342i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.34988 | + | 12.7304i | −0.257455 | + | 0.445925i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.9247 | + | 14.9677i | −0.906992 | + | 0.523652i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 2.00100 | − | 7.53601i | 0.0699207 | − | 0.263330i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −46.9123 | + | 27.0848i | −1.63725 | + | 0.945267i | −0.655475 | + | 0.755217i | \(0.727532\pi\) |
−0.981774 | + | 0.190050i | \(0.939135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.2695 | + | 24.7155i | −0.497404 | + | 0.861529i | −0.999996 | − | 0.00299479i | \(-0.999047\pi\) |
0.502591 | + | 0.864524i | \(0.332380\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.68738 | + | 30.6550i | −0.128378 | + | 1.06727i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.2062i | 1.29379i | 0.762581 | + | 0.646893i | \(0.223932\pi\) | ||||
−0.762581 | + | 0.646893i | \(0.776068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.22345i | 0.0772238i | 0.999254 | + | 0.0386119i | \(0.0122936\pi\) | ||||
−0.999254 | + | 0.0386119i | \(0.987706\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12.3501 | + | 16.4733i | −0.428419 | + | 0.571454i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.20683 | − | 2.29914i | −0.0418141 | − | 0.0796606i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.9668 | + | 29.3873i | 0.587159 | + | 1.01699i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −23.9287 | − | 29.1072i | −0.827096 | − | 1.00609i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.8383 | − | 48.2173i | −0.961084 | − | 1.66465i | −0.719787 | − | 0.694195i | \(-0.755760\pi\) |
−0.241297 | − | 0.970451i | \(-0.577573\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1955 | − | 36.7116i | 0.730878 | − | 1.26592i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −19.3212 | − | 14.4852i | −0.665459 | − | 0.498896i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 50.3870 | 1.73337 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.4574 | + | 20.8001i | 0.393682 | + | 0.714700i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.524500 | + | 4.36043i | −0.0180008 | + | 0.149650i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.2798 | + | 9.97650i | 0.592344 | + | 0.341990i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.2574 | + | 9.38622i | −0.556643 | + | 0.321378i | −0.751797 | − | 0.659395i | \(-0.770813\pi\) |
0.195154 | + | 0.980773i | \(0.437479\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 59.9770 | − | 17.5182i | 2.05117 | − | 0.599109i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.8516 | + | 20.5276i | 0.404844 | + | 0.701210i | 0.994303 | − | 0.106588i | \(-0.0339926\pi\) |
−0.589460 | + | 0.807798i | \(0.700659\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.5237 | − | 8.38527i | −0.495543 | − | 0.286102i | 0.231328 | − | 0.972876i | \(-0.425693\pi\) |
−0.726871 | + | 0.686774i | \(0.759026\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.03810 | + | 7.72525i | −0.205778 | + | 0.263276i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 33.7443i | − | 1.14867i | −0.818620 | − | 0.574335i | \(-0.805261\pi\) | ||
0.818620 | − | 0.574335i | \(-0.194739\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.8328 | 1.86437 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.4781 | − | 26.8566i | −0.389815 | − | 0.912097i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.4875 | − | 6.05497i | −0.355765 | − | 0.205401i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.56192 | + | 4.94323i | −0.290110 | + | 0.167495i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.74456 | − | 11.2434i | 0.0928894 | − | 0.380531i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 43.1410 | − | 71.3678i | 1.45843 | − | 2.41267i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.7087 | − | 34.1365i | 0.665515 | − | 1.15271i | −0.313630 | − | 0.949545i | \(-0.601545\pi\) |
0.979145 | − | 0.203161i | \(-0.0651215\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.6023 | + | 1.63618i | 0.458796 | + | 0.0551869i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.2496 | 0.884372 | 0.442186 | − | 0.896923i | \(-0.354203\pi\) | ||||
0.442186 | + | 0.896923i | \(0.354203\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.5087 | −1.46418 | −0.732091 | − | 0.681206i | \(-0.761456\pi\) | ||||
−0.732091 | + | 0.681206i | \(0.761456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 19.8251 | − | 26.4440i | 0.666414 | − | 0.888906i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.83888 | − | 4.91708i | 0.0953202 | − | 0.165099i | −0.814422 | − | 0.580273i | \(-0.802946\pi\) |
0.909742 | + | 0.415174i | \(0.136279\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.61612 | + | 4.32782i | −0.0877417 | + | 0.145151i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.89257 | + | 10.7925i | 0.230910 | + | 0.361561i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.6327 | − | 20.5725i | 1.19240 | − | 0.688434i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 46.1124 | + | 26.6230i | 1.54137 | + | 0.889909i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.87815 | − | 7.84066i | 0.196266 | − | 0.261792i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 61.2710 | 2.04350 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.84452i | 0.0614498i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.3249 | + | 25.5697i | 0.343592 | + | 0.850907i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 96.2716 | + | 55.5824i | 3.20018 | + | 1.84762i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.32741 | − | 12.6914i | −0.243303 | − | 0.421412i | 0.718350 | − | 0.695681i | \(-0.244897\pi\) |
−0.961653 | + | 0.274269i | \(0.911564\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.2670 | + | 6.41189i | 0.871220 | + | 0.212669i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.19133 | − | 4.15192i | 0.238260 | − | 0.137559i | −0.376117 | − | 0.926572i | \(-0.622741\pi\) |
0.614377 | + | 0.789013i | \(0.289408\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.39607 | − | 1.38337i | −0.0792983 | − | 0.0457829i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −50.0800 | + | 21.4034i | −1.65560 | + | 0.707574i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.0443 | + | 20.0500i | 0.364714 | + | 0.662109i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.1107 | −1.22417 | −0.612085 | − | 0.790792i | \(-0.709669\pi\) | ||||
−0.612085 | + | 0.790792i | \(0.709669\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −22.2460 | + | 9.50756i | −0.733030 | + | 0.313285i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −5.38106 | + | 9.32027i | −0.177120 | + | 0.306781i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.7022 | − | 37.5894i | −0.713566 | − | 1.23593i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.8294 | + | 5.79180i | −0.651283 | + | 0.190228i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.94493 | + | 6.83283i | 0.129429 | + | 0.224178i | 0.923456 | − | 0.383705i | \(-0.125352\pi\) |
−0.794026 | + | 0.607883i | \(0.792019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.8334 | − | 16.1846i | 1.01052 | − | 0.530427i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 56.1170 | + | 6.75011i | 1.83719 | + | 0.220989i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 2.20975i | − | 0.0722667i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 13.2688i | − | 0.433472i | −0.976230 | − | 0.216736i | \(-0.930459\pi\) | ||
0.976230 | − | 0.216736i | \(-0.0695411\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.7807 | + | 16.3290i | 0.710787 | + | 0.532878i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.96461 | + | 6.86691i | −0.129243 | + | 0.223855i | −0.923383 | − | 0.383879i | \(-0.874588\pi\) |
0.794141 | + | 0.607734i | \(0.207921\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −10.6719 | + | 6.16144i | −0.347526 | + | 0.200644i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.27970 | − | 56.9591i | −0.269339 | − | 1.85288i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.8152 | + | 15.4817i | −0.871375 | + | 0.503089i | −0.867805 | − | 0.496905i | \(-0.834470\pi\) |
−0.00357041 | + | 0.999994i | \(0.501136\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.68014 | + | 8.10625i | −0.151924 | + | 0.263140i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −40.2244 | − | 30.1563i | −1.30436 | − | 0.977884i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.1087i | 1.10489i | 0.833549 | + | 0.552445i | \(0.186305\pi\) | ||||
−0.833549 | + | 0.552445i | \(0.813695\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 5.30502i | − | 0.171666i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −20.6739 | − | 2.48678i | −0.668291 | − | 0.0803863i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.620432 | − | 30.8417i | 0.0200348 | − | 0.995929i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.7928 | + | 18.6937i | 0.348156 | + | 0.603023i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −24.6378 | − | 23.5591i | −0.793943 | − | 0.759183i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −39.0089 | − | 67.5655i | −1.25574 | − | 2.17501i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.1066 | − | 50.4142i | 0.936007 | − | 1.62121i | 0.163177 | − | 0.986597i | \(-0.447826\pi\) |
0.772829 | − | 0.634614i | \(-0.218841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.93908 | + | 1.25611i | −0.0944168 | + | 0.0403522i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9.83792 | 0.315714 | 0.157857 | − | 0.987462i | \(-0.449542\pi\) | ||||
0.157857 | + | 0.987462i | \(0.449542\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −12.9158 | + | 7.11447i | −0.414061 | + | 0.228080i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −19.6019 | + | 8.37751i | −0.627762 | + | 0.268295i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −29.0356 | − | 16.7637i | −0.928930 | − | 0.536318i | −0.0424567 | − | 0.999098i | \(-0.513518\pi\) |
−0.886473 | + | 0.462781i | \(0.846852\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.62041 | − | 5.55434i | 0.307470 | − | 0.177518i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.1587 | − | 34.6769i | 1.05867 | − | 1.10715i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.2359 | − | 41.9779i | −0.773006 | − | 1.33889i | −0.935908 | − | 0.352243i | \(-0.885419\pi\) |
0.162902 | − | 0.986642i | \(-0.447914\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.5486 | − | 12.4411i | −0.686594 | − | 0.396405i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −14.1913 | − | 35.1447i | −0.451713 | − | 1.11867i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.6569i | 1.10203i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −53.0011 | −1.68364 | −0.841818 | − | 0.539762i | \(-0.818514\pi\) | ||||
−0.841818 | + | 0.539762i | \(0.818514\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.6834 | − | 18.2518i | 0.434229 | − | 0.579203i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.4015 | + | 11.7788i | 0.646770 | + | 0.373413i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.57384 | + | 4.37276i | −0.239866 | + | 0.138487i | −0.615115 | − | 0.788437i | \(-0.710890\pi\) |
0.375249 | + | 0.926924i | \(0.377557\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −16.8533 | − | 6.32697i | −0.533215 | − | 0.200176i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))