Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(881,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("3024.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.cc (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 2897.8 | ||
Root | \(-1.71965 + 0.206851i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2897 |
Dual form | 3024.2.cc.c.881.8 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.09336 | + | 3.62580i | 0.936177 | + | 1.62151i | 0.772521 | + | 0.634989i | \(0.218995\pi\) |
0.163656 | + | 0.986518i | \(0.447671\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.36869 | − | 2.26422i | −0.517317 | − | 0.855794i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23222 | − | 0.711425i | −0.371529 | − | 0.214503i | 0.302597 | − | 0.953119i | \(-0.402146\pi\) |
−0.674126 | + | 0.738616i | \(0.735480\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.850739 | + | 0.491174i | −0.235952 | + | 0.136227i | −0.613315 | − | 0.789838i | \(-0.710164\pi\) |
0.377363 | + | 0.926066i | \(0.376831\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.370947 | −0.0899679 | −0.0449840 | − | 0.998988i | \(-0.514324\pi\) | ||||
−0.0449840 | + | 0.998988i | \(0.514324\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.97471i | 1.14128i | 0.821201 | + | 0.570638i | \(0.193304\pi\) | ||||
−0.821201 | + | 0.570638i | \(0.806696\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.98775 | − | 2.87968i | 1.04002 | − | 0.600455i | 0.120179 | − | 0.992752i | \(-0.461653\pi\) |
0.919838 | + | 0.392298i | \(0.128320\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.26427 | + | 10.8500i | −1.25285 | + | 2.17001i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.31732 | − | 4.22466i | −1.35879 | − | 0.784499i | −0.369332 | − | 0.929298i | \(-0.620413\pi\) |
−0.989461 | + | 0.144798i | \(0.953747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.28007 | + | 3.62580i | −1.12793 | + | 0.651213i | −0.943414 | − | 0.331616i | \(-0.892406\pi\) |
−0.184519 | + | 0.982829i | \(0.559073\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 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 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.06981 | + | 1.85297i | 0.167077 | + | 0.289386i | 0.937391 | − | 0.348279i | \(-0.113234\pi\) |
−0.770314 | + | 0.637665i | \(0.779901\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.00875 | + | 5.21130i | −0.458830 | + | 0.794716i | −0.998899 | − | 0.0469039i | \(-0.985065\pi\) |
0.540070 | + | 0.841620i | \(0.318398\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.13542 | + | 7.16276i | −0.603213 | + | 1.04480i | 0.389118 | + | 0.921188i | \(0.372780\pi\) |
−0.992331 | + | 0.123608i | \(0.960553\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.25337 | + | 6.19803i | −0.464766 | + | 0.885433i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 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 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.27883 | − | 3.94705i | −0.296678 | − | 0.513862i | 0.678696 | − | 0.734420i | \(-0.262546\pi\) |
−0.975374 | + | 0.220558i | \(0.929212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.50416 | + | 3.75518i | 0.832772 | + | 0.480801i | 0.854801 | − | 0.518956i | \(-0.173679\pi\) |
−0.0220288 | + | 0.999757i | \(0.507013\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.56180 | − | 2.05640i | −0.441786 | − | 0.255066i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.03205 | − | 8.71577i | −0.614763 | − | 1.06480i | −0.990426 | − | 0.138044i | \(-0.955918\pi\) |
0.375663 | − | 0.926756i | \(-0.377415\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 10.9555i | 1.30018i | 0.759857 | + | 0.650090i | \(0.225269\pi\) | ||||
−0.759857 | + | 0.650090i | \(0.774731\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.52848i | 1.11522i | 0.830102 | + | 0.557612i | \(0.188282\pi\) | ||||
−0.830102 | + | 0.557612i | \(0.811718\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 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 | \(-0.992256\pi\) |
0.520920 | + | 0.853606i | \(0.325589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0.972254 | − | 1.68399i | 0.106719 | − | 0.184842i | −0.807720 | − | 0.589566i | \(-0.799299\pi\) |
0.914439 | + | 0.404724i | \(0.132632\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.776524 | − | 1.34498i | −0.0842259 | − | 0.145884i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.80735 | 0.827578 | 0.413789 | − | 0.910373i | \(-0.364205\pi\) | ||||
0.413789 | + | 0.910373i | \(0.364205\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.27652 | + | 1.25399i | 0.238645 | + | 0.131454i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −18.0373 | + | 10.4138i | −1.85059 | + | 1.06844i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.34099 | − | 1.92892i | −0.339226 | − | 0.195852i | 0.320704 | − | 0.947180i | \(-0.396081\pi\) |
−0.659930 | + | 0.751327i | \(0.729414\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50637 | − | 7.80526i | 0.448401 | − | 0.776653i | −0.549882 | − | 0.835243i | \(-0.685327\pi\) |
0.998282 | + | 0.0585901i | \(0.0186605\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.96343 | + | 3.44299i | −0.587594 | + | 0.339248i | −0.764146 | − | 0.645044i | \(-0.776839\pi\) |
0.176551 | + | 0.984291i | \(0.443506\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 11.3630i | − | 1.09850i | −0.835658 | − | 0.549250i | \(-0.814913\pi\) | ||
0.835658 | − | 0.549250i | \(-0.185087\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.9930 | −1.53185 | −0.765926 | − | 0.642929i | \(-0.777719\pi\) | ||||
−0.765926 | + | 0.642929i | \(0.777719\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.17043 | + | 1.25310i | −0.204177 | + | 0.117881i | −0.598602 | − | 0.801046i | \(-0.704277\pi\) |
0.394426 | + | 0.918928i | \(0.370944\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20.8823 | + | 12.0564i | 1.94728 | + | 1.12426i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −31.5199 | −2.81922 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.91140 | 0.169609 | 0.0848046 | − | 0.996398i | \(-0.472973\pi\) | ||||
0.0848046 | + | 0.996398i | \(0.472973\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.32591 | − | 7.49270i | −0.377957 | − | 0.654640i | 0.612808 | − | 0.790232i | \(-0.290040\pi\) |
−0.990765 | + | 0.135592i | \(0.956707\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.2638 | − | 6.80885i | 0.976698 | − | 0.590402i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0973 | − | 5.82971i | −0.862675 | − | 0.498065i | 0.00223233 | − | 0.999998i | \(-0.499289\pi\) |
−0.864907 | + | 0.501932i | \(0.832623\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.82663 | − | 2.78666i | 0.409390 | − | 0.236361i | −0.281138 | − | 0.959667i | \(-0.590712\pi\) |
0.690528 | + | 0.723306i | \(0.257378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.39773 | 0.116884 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 35.3748i | − | 2.93772i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.4024 | − | 7.73789i | 1.09797 | − | 0.633913i | 0.162282 | − | 0.986744i | \(-0.448114\pi\) |
0.935687 | + | 0.352832i | \(0.114781\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.31732 | + | 14.4060i | −0.676854 | + | 1.17235i | 0.299069 | + | 0.954231i | \(0.403324\pi\) |
−0.975923 | + | 0.218114i | \(0.930009\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −26.2928 | − | 15.1802i | −2.11189 | − | 1.21930i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.5559 | − | 8.40387i | 1.16169 | − | 0.670702i | 0.209981 | − | 0.977705i | \(-0.432660\pi\) |
0.951708 | + | 0.307004i | \(0.0993264\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.3469 | − | 7.35196i | −1.05188 | − | 0.579416i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.51105 | −0.275007 | −0.137503 | − | 0.990501i | \(-0.543908\pi\) | ||||
−0.137503 | + | 0.990501i | \(0.543908\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 4.05253 | + | 7.01918i | 0.313594 | + | 0.543160i | 0.979138 | − | 0.203198i | \(-0.0651336\pi\) |
−0.665544 | + | 0.746359i | \(0.731800\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.01750 | + | 10.4226i | −0.462884 | + | 0.801739i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.54844 | − | 11.3422i | 0.497868 | − | 0.862334i | −0.502128 | − | 0.864793i | \(-0.667450\pi\) |
0.999997 | + | 0.00245951i | \(0.000782886\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 33.1407 | − | 0.666682i | 2.50520 | − | 0.0503964i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.7179i | 0.950578i | 0.879830 | + | 0.475289i | \(0.157656\pi\) | ||||
−0.879830 | + | 0.475289i | \(0.842344\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.5518i | 1.97358i | 0.161998 | + | 0.986791i | \(0.448206\pi\) | ||||
−0.161998 | + | 0.986791i | \(0.551794\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 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 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.09735 | − | 0.633555i | −0.0794014 | − | 0.0458424i | 0.459774 | − | 0.888036i | \(-0.347931\pi\) |
−0.539175 | + | 0.842194i | \(0.681264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.31732 | − | 16.1381i | −0.670676 | − | 1.16164i | −0.977713 | − | 0.209947i | \(-0.932671\pi\) |
0.307037 | − | 0.951697i | \(-0.400662\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 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 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 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 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 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 | \(-0.189763\pi\) |
−0.899994 | + | 0.435902i | \(0.856429\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −25.1935 | −1.71818 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 16.8051 | + | 9.25684i | 1.14080 | + | 0.628395i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 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 | \(-0.401836\pi\) |
−0.673407 | + | 0.739272i | \(0.735170\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.72365 | + | 9.91365i | −0.379892 | + | 0.657992i | −0.991046 | − | 0.133520i | \(-0.957372\pi\) |
0.611154 | + | 0.791511i | \(0.290705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.88696 | + | 2.82149i | −0.322940 | + | 0.186449i | −0.652702 | − | 0.757615i | \(-0.726365\pi\) |
0.329762 | + | 0.944064i | \(0.393031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 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 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.52450 | − | 2.03487i | 0.227981 | − | 0.131625i | −0.381659 | − | 0.924303i | \(-0.624647\pi\) |
0.609640 | + | 0.792678i | \(0.291314\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.26195 | + | 2.46064i | 0.274537 | + | 0.158504i | 0.630947 | − | 0.775826i | \(-0.282666\pi\) |
−0.356411 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 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 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 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 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.44701 | + | 9.43450i | 0.339775 | + | 0.588508i | 0.984390 | − | 0.175999i | \(-0.0563156\pi\) |
−0.644615 | + | 0.764507i | \(0.722982\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.74176 | − | 7.84426i | −0.294639 | − | 0.487419i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.6489 | + | 9.03488i | 0.964951 | + | 0.557114i | 0.897693 | − | 0.440621i | \(-0.145242\pi\) |
0.0672574 | + | 0.997736i | \(0.478575\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.0291 | + | 10.4091i | −1.10752 | + | 0.639427i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.98410 | −0.181944 | −0.0909718 | − | 0.995853i | \(-0.528997\pi\) | ||||
−0.0909718 | + | 0.995853i | \(0.528997\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.3608i | 0.629375i | 0.949195 | + | 0.314688i | \(0.101900\pi\) | ||||
−0.949195 | + | 0.314688i | \(0.898100\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 15.4380 | − | 8.91312i | 0.930945 | − | 0.537481i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.94345 | − | 10.2944i | 0.357107 | − | 0.618528i | −0.630369 | − | 0.776296i | \(-0.717096\pi\) |
0.987476 | + | 0.157768i | \(0.0504297\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.0740 | + | 6.97095i | 0.720277 | + | 0.415852i | 0.814855 | − | 0.579665i | \(-0.196817\pi\) |
−0.0945775 | + | 0.995518i | \(0.530150\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.19593 | + | 1.26782i | −0.130535 | + | 0.0753642i | −0.563845 | − | 0.825880i | \(-0.690679\pi\) |
0.433311 | + | 0.901245i | \(0.357345\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.73129 | − | 4.95844i | 0.161223 | − | 0.292687i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.8624 | −0.991906 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.95496 | − | 6.85020i | −0.231052 | − | 0.400193i | 0.727066 | − | 0.686567i | \(-0.240883\pi\) |
−0.958118 | + | 0.286374i | \(0.907550\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.54080 | − | 16.5251i | 0.555487 | − | 0.962131i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 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 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 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 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 16.3163 | + | 28.2607i | 0.925215 | + | 1.60252i | 0.791215 | + | 0.611539i | \(0.209449\pi\) |
0.134001 | + | 0.990981i | \(0.457218\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.6110 | + | 7.85832i | 0.769340 | + | 0.444178i | 0.832639 | − | 0.553816i | \(-0.186829\pi\) |
−0.0632994 | + | 0.997995i | \(0.520162\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 25.1366 | + | 14.5126i | 1.41181 | + | 0.815111i | 0.995559 | − | 0.0941377i | \(-0.0300094\pi\) |
0.416254 | + | 0.909248i | \(0.363343\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.01105 | + | 10.4114i | 0.336554 | + | 0.582929i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 1.84535i | − | 0.102678i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 12.3074i | − | 0.682692i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 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 | \(-0.715445\pi\) |
0.988282 | + | 0.152641i | \(0.0487779\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 21.0677 | − | 36.4904i | 1.15105 | − | 1.99368i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.31732 | + | 14.4060i | 0.453073 | + | 0.784746i | 0.998575 | − | 0.0533635i | \(-0.0169942\pi\) |
−0.545502 | + | 0.838110i | \(0.683661\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.3179 | 0.558747 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.4866 | − | 1.11687i | 0.998180 | − | 0.0603053i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 21.4012 | − | 12.3560i | 1.14888 | − | 0.663305i | 0.200264 | − | 0.979742i | \(-0.435820\pi\) |
0.948614 | + | 0.316437i | \(0.102487\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.7994 | − | 15.4727i | −1.43454 | − | 0.828232i | −0.437078 | − | 0.899424i | \(-0.643987\pi\) |
−0.997463 | + | 0.0711915i | \(0.977320\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.6758 | + | 20.2231i | −0.621440 | + | 1.07637i | 0.367778 | + | 0.929914i | \(0.380119\pi\) |
−0.989218 | + | 0.146452i | \(0.953215\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −39.7225 | + | 22.9338i | −2.10825 | + | 1.21720i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 21.2351i | 1.12075i | 0.828240 | + | 0.560374i | \(0.189343\pi\) | ||||
−0.828240 | + | 0.560374i | \(0.810657\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.74775 | −0.302513 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 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 | \(-0.451302\pi\) |
−0.779714 | + | 0.626135i | \(0.784636\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 11.2587 | − | 6.80576i | 0.584523 | − | 0.353337i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0728 | + | 27.8390i | 0.832221 | + | 1.44145i | 0.896273 | + | 0.443502i | \(0.146264\pi\) |
−0.0640529 | + | 0.997947i | \(0.520403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.30017 | 0.427481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.95340 | −0.100339 | −0.0501696 | − | 0.998741i | \(-0.515976\pi\) | ||||
−0.0501696 | + | 0.998741i | \(0.515976\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0.788167 | + | 1.36514i | 0.0402734 | + | 0.0697557i | 0.885460 | − | 0.464717i | \(-0.153844\pi\) |
−0.845186 | + | 0.534472i | \(0.820510\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −13.4881 | + | 8.15338i | −0.687416 | + | 0.415535i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.74447 | − | 5.62597i | −0.494064 | − | 0.285248i | 0.232195 | − | 0.972669i | \(-0.425409\pi\) |
−0.726259 | + | 0.687421i | \(0.758743\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.85019 | + | 1.06821i | −0.0935682 | + | 0.0540216i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −35.6333 | −1.79291 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.632961i | 0.0317674i | 0.999874 | + | 0.0158837i | \(0.00505615\pi\) | ||||
−0.999874 | + | 0.0158837i | \(0.994944\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.38032 | + | 4.26103i | −0.368555 | + | 0.212786i | −0.672827 | − | 0.739800i | \(-0.734920\pi\) |
0.304272 | + | 0.952585i | \(0.401587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.56180 | − | 6.16921i | 0.177426 | − | 0.307310i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.26897 | − | 2.46469i | −0.211605 | − | 0.122170i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12.1822 | − | 7.03338i | 0.602370 | − | 0.347778i | −0.167603 | − | 0.985855i | \(-0.553603\pi\) |
0.769973 | + | 0.638076i | \(0.220269\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5.81796 | + | 10.5621i | −0.286283 | + | 0.519725i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.14109 | 0.399630 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.9339 | − | 18.9381i | −0.534156 | − | 0.925185i | −0.999204 | − | 0.0398995i | \(-0.987296\pi\) |
0.465048 | − | 0.885286i | \(-0.346037\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.3616 | − | 23.1430i | 0.651206 | − | 1.12792i | −0.331625 | − | 0.943411i | \(-0.607597\pi\) |
0.982831 | − | 0.184510i | \(-0.0590698\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 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 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 19.9400i | − | 0.960476i | −0.877138 | − | 0.480238i | \(-0.840550\pi\) | ||
0.877138 | − | 0.480238i | \(-0.159450\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2826i | 0.974719i | 0.873201 | + | 0.487359i | \(0.162040\pi\) | ||||
−0.873201 | + | 0.487359i | \(0.837960\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 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 | \(-0.0963158\pi\) |
0.219219 | + | 0.975676i | \(0.429649\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 10.6570 | + | 6.15281i | 0.506328 | + | 0.292329i | 0.731323 | − | 0.682031i | \(-0.238903\pi\) |
−0.224995 | + | 0.974360i | \(0.572236\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 16.3436 | + | 28.3079i | 0.774759 | + | 1.34192i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 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 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.218855 | + | 10.8793i | 0.0102601 | + | 0.510028i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.20892 | − | 7.29007i | 0.196885 | − | 0.341015i | −0.750632 | − | 0.660721i | \(-0.770251\pi\) |
0.947517 | + | 0.319706i | \(0.103584\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.07730 | − | 15.7224i | 0.422772 | − | 0.732263i | −0.573437 | − | 0.819249i | \(-0.694390\pi\) |
0.996209 | + | 0.0869865i | \(0.0277237\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.64690 | + | 13.2448i | 0.355381 | + | 0.615539i | 0.987183 | − | 0.159591i | \(-0.0510177\pi\) |
−0.631802 | + | 0.775130i | \(0.717684\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 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 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.2775 | − | 24.7294i | 0.652357 | − | 1.12992i | −0.330193 | − | 0.943914i | \(-0.607114\pi\) |
0.982549 | − | 0.186002i | \(-0.0595529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.94734 | + | 1.70165i | −0.134387 | + | 0.0775884i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 16.1517i | − | 0.733409i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.1527 | 0.596006 | 0.298003 | − | 0.954565i | \(-0.403679\pi\) | ||||
0.298003 | + | 0.954565i | \(0.403679\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.6854 | − | 16.5615i | 1.29455 | − | 0.747411i | 0.315096 | − | 0.949060i | \(-0.397963\pi\) |
0.979458 | + | 0.201649i | \(0.0646301\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.71434 | + | 1.56712i | 0.122248 | + | 0.0705798i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 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 | \(-0.213525\pi\) |
−0.929997 | + | 0.367566i | \(0.880191\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 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 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.30237 | − | 5.71987i | −0.146375 | − | 0.253529i | 0.783510 | − | 0.621379i | \(-0.213427\pi\) |
−0.929885 | + | 0.367850i | \(0.880094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.5746 | − | 13.0416i | 0.954402 | − | 0.576924i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 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 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.9784 | 0.700026 | 0.350013 | − | 0.936745i | \(-0.386177\pi\) | ||||
0.350013 | + | 0.936745i | \(0.386177\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 11.7615i | − | 0.514293i | −0.966372 | − | 0.257147i | \(-0.917218\pi\) | ||
0.966372 | − | 0.257147i | \(-0.0827824\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 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 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 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 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.4790 | − | 57.9874i | −1.43408 | − | 2.48391i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.9166 | + | 20.6402i | −0.509519 | + | 0.882513i | 0.490420 | + | 0.871486i | \(0.336843\pi\) |
−0.999939 | + | 0.0110266i | \(0.996490\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 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 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 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 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 15.9454 | + | 27.6182i | 0.672019 | + | 1.16397i | 0.977331 | + | 0.211718i | \(0.0679058\pi\) |
−0.305312 | + | 0.952252i | \(0.598761\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.08695 | − | 5.24635i | −0.382291 | − | 0.220716i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.428895 | − | 0.247623i | −0.0179802 | − | 0.0103809i | 0.490983 | − | 0.871169i | \(-0.336638\pi\) |
−0.508963 | + | 0.860788i | \(0.669971\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.34182 | + | 2.32411i | 0.0561535 | + | 0.0972608i | 0.892736 | − | 0.450581i | \(-0.148783\pi\) |
−0.836582 | + | 0.547841i | \(0.815450\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 72.1564i | 3.00913i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 42.0259i | − | 1.74956i | −0.484518 | − | 0.874781i | \(-0.661005\pi\) | ||
0.484518 | − | 0.874781i | \(-0.338995\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 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 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.71916 | − | 2.97768i | 0.0709575 | − | 0.122902i | −0.828364 | − | 0.560191i | \(-0.810728\pi\) |
0.899321 | + | 0.437289i | \(0.144061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.0373 | − | 31.2415i | −0.743214 | − | 1.28728i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −9.10251 | −0.373795 | −0.186898 | − | 0.982379i | \(-0.559843\pi\) | ||||
−0.186898 | + | 0.982379i | \(0.559843\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.98250 | + | 3.59908i | −0.0812747 | + | 0.147548i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.71186 | − | 3.87510i | 0.274239 | − | 0.158332i | −0.356573 | − | 0.934267i | \(-0.616055\pi\) |
0.630813 | + | 0.775935i | \(0.282722\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −22.0034 | − | 12.7037i | −0.897536 | − | 0.518193i | −0.0211361 | − | 0.999777i | \(-0.506728\pi\) |
−0.876400 | + | 0.481584i | \(0.840062\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 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 | \(-0.755145\pi\) |
0.243173 | + | 0.969983i | \(0.421812\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.30333 | + | 3.06188i | −0.213504 | + | 0.123267i | −0.602939 | − | 0.797787i | \(-0.706004\pi\) |
0.389435 | + | 0.921054i | \(0.372670\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.94313 | − | 2.85392i | −0.198681 | − | 0.114709i | 0.397359 | − | 0.917663i | \(-0.369927\pi\) |
−0.596040 | + | 0.802955i | \(0.703260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 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 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.28513 | −0.0512414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.0525 | 0.758468 | 0.379234 | − | 0.925301i | \(-0.376188\pi\) | ||||
0.379234 | + | 0.925301i | \(0.376188\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 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 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2820 | − | 7.66837i | −0.524607 | − | 0.302882i | 0.214210 | − | 0.976788i | \(-0.431282\pi\) |
−0.738818 | + | 0.673905i | \(0.764616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.3209 | − | 6.53612i | 0.446453 | − | 0.257759i | −0.259878 | − | 0.965641i | \(-0.583682\pi\) |
0.706331 | + | 0.707882i | \(0.250349\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 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 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.6131 | − | 13.6330i | 0.924051 | − | 0.533501i | 0.0391261 | − | 0.999234i | \(-0.487543\pi\) |
0.884925 | + | 0.465733i | \(0.154209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.1113 | − | 31.3698i | 0.707669 | − | 1.22572i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.7911 | − | 8.53963i | −0.576179 | − | 0.332657i | 0.183435 | − | 0.983032i | \(-0.441278\pi\) |
−0.759613 | + | 0.650375i | \(0.774612\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −40.6657 | + | 23.4784i | −1.58171 | + | 0.913203i | −0.587105 | + | 0.809511i | \(0.699732\pi\) |
−0.994609 | + | 0.103692i | \(0.966934\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 48.2667 | + | 26.5870i | 1.87170 | + | 1.03100i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −48.6626 | −1.88422 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.34305 | − | 9.25444i | −0.206266 | − | 0.357264i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.76077 | − | 13.4421i | 0.299156 | − | 0.518153i | −0.676787 | − | 0.736179i | \(-0.736628\pi\) |
0.975943 | + | 0.218026i | \(0.0699616\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.07869 | − | 15.7248i | 0.348922 | − | 0.604351i | −0.637136 | − | 0.770751i | \(-0.719881\pi\) |
0.986058 | + | 0.166400i | \(0.0532143\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.205287 | + | 10.2048i | 0.00787820 | + | 0.391625i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.1917i | 0.772615i | 0.922370 | + | 0.386308i | \(0.126250\pi\) | ||||
−0.922370 | + | 0.386308i | \(0.873750\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 48.8146i | − | 1.86511i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | \(-0.332847\pi\) |
−0.498676 | + | 0.866788i | \(0.666180\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 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 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 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 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −23.8406 | + | 0.479595i | −0.896620 | + | 0.0180370i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.782968 | + | 1.35614i | −0.0294050 | + | 0.0509309i | −0.880353 | − | 0.474318i | \(-0.842695\pi\) |
0.850948 | + | 0.525249i | \(0.176028\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 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 | 0 | ||||||||
\(718\) | 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 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 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 | \(-0.340085\pi\) |
−0.518256 | + | 0.855225i | \(0.673419\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.11609 | − | 1.93312i | 0.0412800 | − | 0.0714990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.1408 | + | 11.6283i | −0.743916 | + | 0.429500i | −0.823491 | − | 0.567329i | \(-0.807977\pi\) |
0.0795755 | + | 0.996829i | \(0.474644\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 14.3197i | 0.527473i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.1516 | 1.32986 | 0.664929 | − | 0.746907i | \(-0.268462\pi\) | ||||
0.664929 | + | 0.746907i | \(0.268462\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.43940 | − | 3.71779i | 0.236239 | − | 0.136392i | −0.377208 | − | 0.926129i | \(-0.623116\pi\) |
0.613447 | + | 0.789736i | \(0.289783\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 56.1121 | + | 32.3963i | 2.05579 | + | 1.18691i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 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 | \(-0.123817\pi\) |
−0.791085 | + | 0.611707i | \(0.790483\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 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 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.7203 | − | 37.6207i | −0.787362 | − | 1.36375i | −0.927578 | − | 0.373629i | \(-0.878113\pi\) |
0.140217 | − | 0.990121i | \(-0.455220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 21.8895 | + | 36.2116i | 0.792452 | + | 1.31095i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.87738 | + | 2.23860i | 0.140004 | + | 0.0808313i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.8491 | + | 10.8825i | −0.679716 | + | 0.392434i | −0.799748 | − | 0.600336i | \(-0.795034\pi\) |
0.120032 | + | 0.992770i | \(0.461700\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 14.5147 | 0.522056 | 0.261028 | − | 0.965331i | \(-0.415938\pi\) | ||||
0.261028 | + | 0.965331i | \(0.415938\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 90.8520i | − | 3.26350i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 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 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 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 | \(-0.742246\pi\) |
0.282269 | + | 0.959335i | \(0.408913\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.80793 | + | 3.19922i | 0.206506 | + | 0.113751i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.37778 | −0.261993 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.8899 | + | 43.1106i | 0.881646 | + | 1.52706i | 0.849511 | + | 0.527572i | \(0.176897\pi\) |
0.0321352 | + | 0.999484i | \(0.489769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.53402 | − | 2.65701i | 0.0542698 | − | 0.0939981i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 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 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 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 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 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 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46.9123 | + | 27.0848i | 1.63725 | + | 0.945267i | 0.981774 | + | 0.190050i | \(0.0608650\pi\) |
0.655475 | + | 0.755217i | \(0.272468\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.2695 | + | 24.7155i | 0.497404 | + | 0.861529i | 0.999996 | − | 0.00299479i | \(-0.000953273\pi\) |
−0.502591 | + | 0.864524i | \(0.667620\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 37.2062i | − | 1.29379i | −0.762581 | − | 0.646893i | \(-0.776068\pi\) | ||
0.762581 | − | 0.646893i | \(-0.223932\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 2.22345i | − | 0.0772238i | −0.999254 | − | 0.0386119i | \(-0.987706\pi\) | ||
0.999254 | − | 0.0386119i | \(-0.0122936\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 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 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −27.8383 | + | 48.2173i | −0.961084 | + | 1.66465i | −0.241297 | + | 0.970451i | \(0.577573\pi\) |
−0.719787 | + | 0.694195i | \(0.755760\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1955 | + | 36.7116i | 0.730878 | + | 1.26592i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −50.3870 | −1.73337 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11.4574 | + | 20.8001i | −0.393682 | + | 0.714700i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 17.2798 | − | 9.97650i | 0.592344 | − | 0.341990i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.2574 | − | 9.38622i | −0.556643 | − | 0.321378i | 0.195154 | − | 0.980773i | \(-0.437479\pi\) |
−0.751797 | + | 0.659395i | \(0.770813\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.8516 | + | 20.5276i | −0.404844 | + | 0.701210i | −0.994303 | − | 0.106588i | \(-0.966007\pi\) |
0.589460 | + | 0.807798i | \(0.299341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.5237 | − | 8.38527i | 0.495543 | − | 0.286102i | −0.231328 | − | 0.972876i | \(-0.574307\pi\) |
0.726871 | + | 0.686774i | \(0.240974\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 33.7443i | 1.14867i | 0.818620 | + | 0.574335i | \(0.194739\pi\) | ||||
−0.818620 | + | 0.574335i | \(0.805261\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 54.8328 | 1.86437 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 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 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 43.1410 | + | 71.3678i | 1.45843 | + | 2.41267i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.7087 | + | 34.1365i | 0.665515 | + | 1.15271i | 0.979145 | + | 0.203161i | \(0.0651215\pi\) |
−0.313630 | + | 0.949545i | \(0.601545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.2496 | −0.884372 | −0.442186 | − | 0.896923i | \(-0.645797\pi\) | ||||
−0.442186 | + | 0.896923i | \(0.645797\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43.5087 | 1.46418 | 0.732091 | − | 0.681206i | \(-0.238544\pi\) | ||||
0.732091 | + | 0.681206i | \(0.238544\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.83888 | + | 4.91708i | 0.0953202 | + | 0.165099i | 0.909742 | − | 0.415174i | \(-0.136279\pi\) |
−0.814422 | + | 0.580273i | \(0.802946\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.61612 | − | 4.32782i | −0.0877417 | − | 0.145151i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 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 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 61.2710 | 2.04350 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1.84452i | − | 0.0614498i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 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 | \(-0.755103\pi\) |
0.961653 | + | 0.274269i | \(0.0884359\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.19133 | + | 4.15192i | 0.238260 | + | 0.137559i | 0.614377 | − | 0.789013i | \(-0.289408\pi\) |
−0.376117 | + | 0.926572i | \(0.622741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.39607 | + | 1.38337i | −0.0792983 | + | 0.0457829i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −11.0443 | + | 20.0500i | −0.364714 | + | 0.662109i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.1107 | 1.22417 | 0.612085 | − | 0.790792i | \(-0.290331\pi\) | ||||
0.612085 | + | 0.790792i | \(0.290331\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 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 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.94493 | + | 6.83283i | −0.129429 | + | 0.224178i | −0.923456 | − | 0.383705i | \(-0.874648\pi\) |
0.794026 | + | 0.607883i | \(0.207981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −30.8334 | − | 16.1846i | −1.01052 | − | 0.530427i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.20975i | 0.0722667i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.2688i | 0.433472i | 0.976230 | + | 0.216736i | \(0.0695411\pi\) | ||||
−0.976230 | + | 0.216736i | \(0.930459\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.96461 | + | 6.86691i | 0.129243 | + | 0.223855i | 0.923383 | − | 0.383879i | \(-0.125412\pi\) |
−0.794141 | + | 0.607734i | \(0.792079\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 10.6719 | + | 6.16144i | 0.347526 | + | 0.200644i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −26.8152 | − | 15.4817i | −0.871375 | − | 0.503089i | −0.00357041 | − | 0.999994i | \(-0.501136\pi\) |
−0.867805 | + | 0.496905i | \(0.834470\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.68014 | − | 8.10625i | −0.151924 | − | 0.263140i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 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 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 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 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.0089 | − | 67.5655i | 1.25574 | − | 2.17501i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −29.1066 | − | 50.4142i | −0.936007 | − | 1.62121i | −0.772829 | − | 0.634614i | \(-0.781159\pi\) |
−0.163177 | − | 0.986597i | \(-0.552174\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 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 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 29.0356 | − | 16.7637i | 0.928930 | − | 0.536318i | 0.0424567 | − | 0.999098i | \(-0.486482\pi\) |
0.886473 | + | 0.462781i | \(0.153148\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.62041 | − | 5.55434i | −0.307470 | − | 0.177518i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.2359 | + | 41.9779i | −0.773006 | + | 1.33889i | 0.162902 | + | 0.986642i | \(0.447914\pi\) |
−0.935908 | + | 0.352243i | \(0.885419\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.5486 | + | 12.4411i | −0.686594 | + | 0.396405i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 34.6569i | 1.10203i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 53.0011 | 1.68364 | 0.841818 | − | 0.539762i | \(-0.181486\pi\) | ||||
0.841818 | + | 0.539762i | \(0.181486\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.4015 | − | 11.7788i | 0.646770 | − | 0.373413i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.57384 | − | 4.37276i | −0.239866 | − | 0.138487i | 0.375249 | − | 0.926924i | \(-0.377557\pi\) |
−0.615115 | + | 0.788437i | \(0.710890\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))