Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(2305,3024)]
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, 2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.2305");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.q (of order \(3\), 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: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{7} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2881.7 | ||
Root | \(-0.674693 - 1.59524i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2881 |
Dual form | 3024.2.q.j.2305.7 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.07260 | − | 3.58985i | 0.926894 | − | 1.60543i | 0.138409 | − | 0.990375i | \(-0.455801\pi\) |
0.788486 | − | 0.615053i | \(-0.210865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.19013 | + | 1.48437i | −0.827790 | + | 0.561038i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.434429 | − | 0.752453i | −0.130985 | − | 0.226873i | 0.793071 | − | 0.609129i | \(-0.208481\pi\) |
−0.924057 | + | 0.382256i | \(0.875147\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.86231 | + | 4.95766i | 0.793861 | + | 1.37501i | 0.923560 | + | 0.383455i | \(0.125266\pi\) |
−0.129698 | + | 0.991554i | \(0.541401\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.44613 | − | 2.50478i | 0.350739 | − | 0.607498i | −0.635640 | − | 0.771986i | \(-0.719264\pi\) |
0.986379 | + | 0.164488i | \(0.0525971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00703 | + | 3.47627i | 0.460444 | + | 0.797512i | 0.998983 | − | 0.0450884i | \(-0.0143570\pi\) |
−0.538539 | + | 0.842600i | \(0.681024\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.91488 | − | 5.04873i | 0.607795 | − | 1.05273i | −0.383808 | − | 0.923413i | \(-0.625387\pi\) |
0.991603 | − | 0.129319i | \(-0.0412792\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.09133 | − | 10.5505i | −1.21827 | − | 2.11010i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.900417 | − | 1.55957i | 0.167203 | − | 0.289604i | −0.770232 | − | 0.637763i | \(-0.779860\pi\) |
0.937435 | + | 0.348159i | \(0.113193\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.96091 | 0.531795 | 0.265898 | − | 0.964001i | \(-0.414332\pi\) | ||||
0.265898 | + | 0.964001i | \(0.414332\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.789399 | + | 10.9387i | 0.133433 | + | 1.84898i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.64925 | − | 4.58864i | −0.435535 | − | 0.754368i | 0.561804 | − | 0.827270i | \(-0.310107\pi\) |
−0.997339 | + | 0.0729017i | \(0.976774\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.89325 | + | 10.2074i | 0.920371 | + | 1.59413i | 0.798842 | + | 0.601541i | \(0.205446\pi\) |
0.121528 | + | 0.992588i | \(0.461220\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00703 | − | 3.47627i | 0.306069 | − | 0.530127i | −0.671430 | − | 0.741068i | \(-0.734320\pi\) |
0.977499 | + | 0.210941i | \(0.0676529\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.34436 | 0.341961 | 0.170980 | − | 0.985274i | \(-0.445307\pi\) | ||||
0.170980 | + | 0.985274i | \(0.445307\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.59331 | − | 6.50190i | 0.370472 | − | 0.928844i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.09116 | − | 1.88995i | 0.149883 | − | 0.259605i | −0.781301 | − | 0.624154i | \(-0.785444\pi\) |
0.931184 | + | 0.364549i | \(0.118777\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −3.60159 | −0.485638 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.05430 | −0.397636 | −0.198818 | − | 0.980036i | \(-0.563710\pi\) | ||||
−0.198818 | + | 0.980036i | \(0.563710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.63318 | 0.721255 | 0.360628 | − | 0.932710i | \(-0.382563\pi\) | ||||
0.360628 | + | 0.932710i | \(0.382563\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 23.7297 | 2.94330 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.51078 | 0.306740 | 0.153370 | − | 0.988169i | \(-0.450987\pi\) | ||||
0.153370 | + | 0.988169i | \(0.450987\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.09143 | −0.129529 | −0.0647647 | − | 0.997901i | \(-0.520630\pi\) | ||||
−0.0647647 | + | 0.997901i | \(0.520630\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.723285 | − | 1.25277i | 0.0846541 | − | 0.146625i | −0.820590 | − | 0.571518i | \(-0.806355\pi\) |
0.905244 | + | 0.424893i | \(0.139688\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.06837 | + | 1.00312i | 0.235713 | + | 0.114316i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.12928 | 0.239563 | 0.119781 | − | 0.992800i | \(-0.461781\pi\) | ||||
0.119781 | + | 0.992800i | \(0.461781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.18784 | − | 3.78946i | 0.240147 | − | 0.415947i | −0.720609 | − | 0.693342i | \(-0.756138\pi\) |
0.960756 | + | 0.277395i | \(0.0894710\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.99451 | − | 10.3828i | −0.650196 | − | 1.12617i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.83373 | − | 10.1043i | −0.618374 | − | 1.07105i | −0.989783 | − | 0.142585i | \(-0.954459\pi\) |
0.371409 | − | 0.928469i | \(-0.378875\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −13.6278 | − | 6.60919i | −1.42858 | − | 0.692831i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.6391 | 1.70713 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.98779 | + | 6.90706i | −0.404899 | + | 0.701306i | −0.994310 | − | 0.106528i | \(-0.966027\pi\) |
0.589411 | + | 0.807834i | \(0.299360\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.88185 | − | 3.25946i | −0.187251 | − | 0.324329i | 0.757082 | − | 0.653320i | \(-0.226624\pi\) |
−0.944333 | + | 0.328992i | \(0.893291\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.42778 | − | 9.40119i | 0.534815 | − | 0.926327i | −0.464357 | − | 0.885648i | \(-0.653715\pi\) |
0.999172 | − | 0.0406786i | \(-0.0129520\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.82343 | − | 8.35442i | −0.466298 | − | 0.807653i | 0.532961 | − | 0.846140i | \(-0.321079\pi\) |
−0.999259 | + | 0.0384875i | \(0.987746\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.86131 | + | 10.1521i | −0.561412 | + | 0.972394i | 0.435962 | + | 0.899965i | \(0.356408\pi\) |
−0.997374 | + | 0.0724288i | \(0.976925\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.88981 | − | 5.00530i | −0.271851 | − | 0.470859i | 0.697485 | − | 0.716599i | \(-0.254302\pi\) |
−0.969336 | + | 0.245740i | \(0.920969\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.0828 | − | 20.9280i | −1.12672 | − | 1.95154i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.550795 | + | 7.63237i | 0.0504913 | + | 0.699659i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.12254 | − | 8.87250i | 0.465686 | − | 0.806591i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −29.7736 | −2.66303 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.47468 | −0.574535 | −0.287268 | − | 0.957850i | \(-0.592747\pi\) | ||||
−0.287268 | + | 0.957850i | \(0.592747\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.86514 | − | 15.3549i | 0.774551 | − | 1.34156i | −0.160495 | − | 0.987037i | \(-0.551309\pi\) |
0.935046 | − | 0.354525i | \(-0.115357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.55571 | − | 4.63431i | −0.828585 | − | 0.401846i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.36116 | + | 2.35760i | 0.116292 | + | 0.201423i | 0.918295 | − | 0.395896i | \(-0.129566\pi\) |
−0.802004 | + | 0.597319i | \(0.796233\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.65431 | − | 14.9897i | −0.734049 | − | 1.27141i | −0.955139 | − | 0.296157i | \(-0.904295\pi\) |
0.221090 | − | 0.975253i | \(-0.429038\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.48694 | − | 4.30751i | 0.207968 | − | 0.360212i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.73241 | − | 6.46472i | −0.309959 | − | 0.536865i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.42343 | + | 5.92955i | −0.280458 | + | 0.485767i | −0.971498 | − | 0.237049i | \(-0.923820\pi\) |
0.691040 | + | 0.722817i | \(0.257153\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.64083 | + | 8.03816i | 0.377666 | + | 0.654136i | 0.990722 | − | 0.135903i | \(-0.0433936\pi\) |
−0.613057 | + | 0.790039i | \(0.710060\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.13678 | − | 10.6292i | 0.492918 | − | 0.853759i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.6768 | 1.09153 | 0.545764 | − | 0.837939i | \(-0.316240\pi\) | ||||
0.545764 | + | 0.837939i | \(0.316240\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.11020 | + | 15.3841i | 0.0874963 | + | 1.21244i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1.65003 | + | 2.85793i | 0.129240 | + | 0.223850i | 0.923382 | − | 0.383882i | \(-0.125413\pi\) |
−0.794142 | + | 0.607732i | \(0.792080\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.96228 | + | 10.3270i | 0.461375 | + | 0.799125i | 0.999030 | − | 0.0440399i | \(-0.0140229\pi\) |
−0.537655 | + | 0.843165i | \(0.680690\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.88562 | + | 17.1224i | −0.760432 | + | 1.31711i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.63389 | 0.732451 | 0.366225 | − | 0.930526i | \(-0.380650\pi\) | ||||
0.366225 | + | 0.930526i | \(0.380650\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 29.0016 | + | 14.0651i | 2.19231 | + | 1.06322i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.5285 | + | 19.9680i | −0.861682 | + | 1.49248i | 0.00862183 | + | 0.999963i | \(0.497256\pi\) |
−0.870304 | + | 0.492515i | \(0.836078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8325 | −0.879504 | −0.439752 | − | 0.898119i | \(-0.644934\pi\) | ||||
−0.439752 | + | 0.898119i | \(0.644934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −21.9634 | −1.61478 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.51297 | −0.183767 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.28508 | −0.454772 | −0.227386 | − | 0.973805i | \(-0.573018\pi\) | ||||
−0.227386 | + | 0.973805i | \(0.573018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.7312 | 0.988392 | 0.494196 | − | 0.869351i | \(-0.335463\pi\) | ||||
0.494196 | + | 0.869351i | \(0.335463\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 0.161495 | 0.0115061 | 0.00575303 | − | 0.999983i | \(-0.498169\pi\) | ||||
0.00575303 | + | 0.999983i | \(0.498169\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.4140 | − | 21.5016i | 0.880003 | − | 1.52421i | 0.0286672 | − | 0.999589i | \(-0.490874\pi\) |
0.851336 | − | 0.524621i | \(-0.175793\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.342945 | + | 4.75220i | 0.0240700 | + | 0.333539i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 48.8573 | 3.41235 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.74382 | − | 3.02039i | 0.120623 | − | 0.208925i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.44607 | − | 16.3611i | −0.650295 | − | 1.12634i | −0.983051 | − | 0.183331i | \(-0.941312\pi\) |
0.332757 | − | 0.943013i | \(-0.392021\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.31953 | − | 14.4098i | −0.567387 | − | 0.982743i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.48477 | + | 4.39508i | −0.440215 | + | 0.298357i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.5571 | 1.11375 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.04717 | + | 12.2061i | −0.471914 | + | 0.817378i | −0.999484 | − | 0.0321333i | \(-0.989770\pi\) |
0.527570 | + | 0.849512i | \(0.323103\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −12.9891 | − | 22.4978i | −0.862118 | − | 1.49323i | −0.869881 | − | 0.493262i | \(-0.835804\pi\) |
0.00776306 | − | 0.999970i | \(-0.497529\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.4579 | + | 21.5777i | −0.823239 | + | 1.42589i | 0.0800190 | + | 0.996793i | \(0.474502\pi\) |
−0.903258 | + | 0.429098i | \(0.858831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.05923 | + | 5.29874i | 0.200417 | + | 0.347132i | 0.948663 | − | 0.316289i | \(-0.102437\pi\) |
−0.748246 | + | 0.663421i | \(0.769104\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.85893 | − | 8.41591i | 0.316961 | − | 0.548993i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.71988 | − | 13.3712i | −0.499357 | − | 0.864912i | 0.500643 | − | 0.865654i | \(-0.333097\pi\) |
−1.00000 | 0.000742080i | \(0.999764\pi\) | ||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.92259 | − | 8.52617i | −0.317092 | − | 0.549219i | 0.662788 | − | 0.748807i | \(-0.269373\pi\) |
−0.979880 | + | 0.199588i | \(0.936040\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −17.9660 | − | 22.7854i | −1.14780 | − | 1.45571i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.4895 | + | 19.9003i | −0.731057 | + | 1.26623i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.8843 | 1.69692 | 0.848461 | − | 0.529258i | \(-0.177530\pi\) | ||||
0.848461 | + | 0.529258i | \(0.177530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.06524 | −0.318449 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.50636 | − | 9.53729i | 0.343477 | − | 0.594920i | −0.641599 | − | 0.767040i | \(-0.721729\pi\) |
0.985076 | + | 0.172121i | \(0.0550619\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 12.6134 | + | 6.11724i | 0.783761 | + | 0.380107i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.65547 | + | 6.33146i | 0.225406 | + | 0.390415i | 0.956441 | − | 0.291925i | \(-0.0942958\pi\) |
−0.731035 | + | 0.682340i | \(0.760962\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.52309 | − | 7.83423i | −0.277851 | − | 0.481253i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 2.08048 | − | 3.60349i | 0.126849 | − | 0.219709i | −0.795605 | − | 0.605815i | \(-0.792847\pi\) |
0.922454 | + | 0.386107i | \(0.126180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.18300 | + | 7.24516i | 0.254099 | + | 0.440112i | 0.964650 | − | 0.263533i | \(-0.0848878\pi\) |
−0.710551 | + | 0.703645i | \(0.751554\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.29250 | + | 9.16689i | −0.319150 | + | 0.552784i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.39928 | + | 2.42362i | 0.0840745 | + | 0.145621i | 0.904996 | − | 0.425419i | \(-0.139873\pi\) |
−0.820922 | + | 0.571040i | \(0.806540\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.44314 | − | 9.42779i | 0.324710 | − | 0.562415i | −0.656743 | − | 0.754114i | \(-0.728067\pi\) |
0.981454 | + | 0.191699i | \(0.0613998\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.02424 | 0.120328 | 0.0601642 | − | 0.998188i | \(-0.480838\pi\) | ||||
0.0601642 | + | 0.998188i | \(0.480838\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.0585 | − | 13.6078i | −1.65624 | − | 0.803241i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.31739 | + | 7.47794i | 0.253964 | + | 0.439879i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 9.65448 | + | 16.7220i | 0.564021 | + | 0.976912i | 0.997140 | + | 0.0755757i | \(0.0240795\pi\) |
−0.433120 | + | 0.901336i | \(0.642587\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.33035 | + | 10.9645i | −0.368567 | + | 0.638377i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 33.3732 | 1.93002 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0.764425 | + | 10.5926i | 0.0440607 | + | 0.610550i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.6753 | − | 20.2223i | 0.668527 | − | 1.15792i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 13.1378 | 0.749813 | 0.374907 | − | 0.927063i | \(-0.377675\pi\) | ||||
0.374907 | + | 0.927063i | \(0.377675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −13.5321 | −0.767336 | −0.383668 | − | 0.923471i | \(-0.625339\pi\) | ||||
−0.383668 | + | 0.923471i | \(0.625339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −25.2000 | −1.42439 | −0.712194 | − | 0.701983i | \(-0.752298\pi\) | ||||
−0.712194 | + | 0.701983i | \(0.752298\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.2978 | 0.690711 | 0.345356 | − | 0.938472i | \(-0.387758\pi\) | ||||
0.345356 | + | 0.938472i | \(0.387758\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.56467 | −0.0876047 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.6097 | 0.645982 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.8705 | − | 60.3975i | 1.93427 | − | 3.35025i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.13445 | + | 3.47990i | −0.283072 | + | 0.191853i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.9257 | 1.09522 | 0.547608 | − | 0.836735i | \(-0.315539\pi\) | ||||
0.547608 | + | 0.836735i | \(0.315539\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.20383 | − | 9.01330i | 0.284316 | − | 0.492449i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.966380 | − | 1.67382i | −0.0526421 | − | 0.0911788i | 0.838504 | − | 0.544896i | \(-0.183431\pi\) |
−0.891146 | + | 0.453717i | \(0.850098\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.28631 | − | 2.22795i | −0.0696574 | − | 0.120650i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.97155 | + | 18.0894i | 0.214444 | + | 0.976736i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.9648 | 0.910720 | 0.455360 | − | 0.890307i | \(-0.349511\pi\) | ||||
0.455360 | + | 0.890307i | \(0.349511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.25767 | + | 10.8386i | −0.334966 | + | 0.580177i | −0.983478 | − | 0.181027i | \(-0.942058\pi\) |
0.648513 | + | 0.761204i | \(0.275391\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.1929 | + | 28.0468i | 0.861859 | + | 1.49278i | 0.870133 | + | 0.492817i | \(0.164033\pi\) |
−0.00827416 | + | 0.999966i | \(0.502634\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.26211 | + | 3.91808i | −0.120060 | + | 0.207950i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.98559 | + | 15.5635i | 0.474242 | + | 0.821410i | 0.999565 | − | 0.0294922i | \(-0.00938902\pi\) |
−0.525323 | + | 0.850903i | \(0.676056\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44368 | − | 2.50052i | 0.0759830 | − | 0.131606i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.99816 | − | 5.19297i | −0.156931 | − | 0.271812i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.08420 | + | 7.07404i | 0.213194 | + | 0.369262i | 0.952712 | − | 0.303874i | \(-0.0982802\pi\) |
−0.739519 | + | 0.673136i | \(0.764947\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.415596 | + | 5.75892i | 0.0215767 | + | 0.298988i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.58080 | − | 4.47008i | 0.133629 | − | 0.231452i | −0.791444 | − | 0.611242i | \(-0.790670\pi\) |
0.925073 | + | 0.379790i | \(0.124004\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.3091 | 0.530945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.0017 | −1.07878 | −0.539392 | − | 0.842055i | \(-0.681346\pi\) | ||||
−0.539392 | + | 0.842055i | \(0.681346\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14.7794 | + | 25.5988i | −0.755194 | + | 1.30804i | 0.190083 | + | 0.981768i | \(0.439124\pi\) |
−0.945278 | + | 0.326267i | \(0.894209\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.88794 | − | 5.34608i | 0.402006 | − | 0.272462i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.26895 | − | 14.3222i | −0.419252 | − | 0.726166i | 0.576612 | − | 0.817018i | \(-0.304374\pi\) |
−0.995864 | + | 0.0908518i | \(0.971041\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.43063 | − | 14.6023i | −0.426355 | − | 0.738469i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.41315 | − | 7.64379i | 0.222049 | − | 0.384601i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4394 | + | 26.7418i | 0.774881 | + | 1.34213i | 0.934861 | + | 0.355014i | \(0.115524\pi\) |
−0.159980 | + | 0.987120i | \(0.551143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5.31614 | − | 9.20782i | 0.265475 | − | 0.459817i | −0.702213 | − | 0.711967i | \(-0.747804\pi\) |
0.967688 | + | 0.252150i | \(0.0811378\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 8.47504 | + | 14.6792i | 0.422172 | + | 0.731223i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.30183 | + | 3.98688i | −0.114097 | + | 0.197622i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.7956 | −0.731598 | −0.365799 | − | 0.930694i | \(-0.619204\pi\) | ||||
−0.365799 | + | 0.930694i | \(0.619204\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.68931 | − | 4.53371i | 0.329159 | − | 0.223089i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.06904 | − | 15.7080i | −0.445182 | − | 0.771078i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.56134 | − | 2.70432i | −0.0762765 | − | 0.132115i | 0.825364 | − | 0.564601i | \(-0.190970\pi\) |
−0.901641 | + | 0.432486i | \(0.857637\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.644580 | + | 1.11645i | −0.0314149 | + | 0.0544122i | −0.881305 | − | 0.472547i | \(-0.843335\pi\) |
0.849891 | + | 0.526959i | \(0.176668\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −35.2355 | −1.70917 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −12.3374 | + | 8.36171i | −0.597048 | + | 0.404652i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.5916 | + | 20.0773i | −0.558350 | + | 0.967090i | 0.439285 | + | 0.898348i | \(0.355232\pi\) |
−0.997634 | + | 0.0687421i | \(0.978101\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.6437 | 1.71293 | 0.856464 | − | 0.516207i | \(-0.172657\pi\) | ||||
0.856464 | + | 0.516207i | \(0.172657\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 23.4010 | 1.11942 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.0124 | −0.764230 | −0.382115 | − | 0.924115i | \(-0.624804\pi\) | ||||
−0.382115 | + | 0.924115i | \(0.624804\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.3556 | 0.682054 | 0.341027 | − | 0.940054i | \(-0.389225\pi\) | ||||
0.341027 | + | 0.940054i | \(0.389225\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.3639 | −2.29267 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.72475 | −0.270168 | −0.135084 | − | 0.990834i | \(-0.543130\pi\) | ||||
−0.135084 | + | 0.990834i | \(0.543130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.12040 | − | 8.86879i | 0.241110 | − | 0.417615i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −51.9710 | + | 35.2235i | −2.43644 | + | 1.65131i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 14.6635 | 0.685930 | 0.342965 | − | 0.939348i | \(-0.388569\pi\) | ||||
0.342965 | + | 0.939348i | \(0.388569\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 12.9720 | − | 22.4681i | 0.604164 | − | 1.04644i | −0.388018 | − | 0.921652i | \(-0.626840\pi\) |
0.992183 | − | 0.124792i | \(-0.0398263\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.46277 | + | 11.1939i | 0.300351 | + | 0.520223i | 0.976215 | − | 0.216803i | \(-0.0695630\pi\) |
−0.675865 | + | 0.737026i | \(0.736230\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.3104 | − | 28.2504i | −0.754755 | − | 1.30727i | −0.945496 | − | 0.325633i | \(-0.894423\pi\) |
0.190741 | − | 0.981640i | \(-0.438911\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.49892 | + | 3.72692i | −0.253916 | + | 0.172093i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.48765 | −0.160362 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 24.4509 | − | 42.3503i | 1.12189 | − | 1.94316i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 12.6739 | + | 21.9518i | 0.579084 | + | 1.00300i | 0.995585 | + | 0.0938679i | \(0.0299231\pi\) |
−0.416500 | + | 0.909136i | \(0.636744\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 15.1660 | − | 26.2682i | 0.691509 | − | 1.19773i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 16.5302 | + | 28.6311i | 0.750597 | + | 1.30007i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −17.7383 | + | 30.7236i | −0.803799 | + | 1.39222i | 0.113299 | + | 0.993561i | \(0.463858\pi\) |
−0.917099 | + | 0.398660i | \(0.869475\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.2554 | + | 22.9590i | 0.598208 | + | 1.03613i | 0.993085 | + | 0.117393i | \(0.0374538\pi\) |
−0.394877 | + | 0.918734i | \(0.629213\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.60425 | − | 4.51069i | −0.117289 | − | 0.203151i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.39038 | − | 1.62009i | 0.107223 | − | 0.0726710i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.00130 | + | 5.19841i | −0.134357 | + | 0.232713i | −0.925352 | − | 0.379110i | \(-0.876230\pi\) |
0.790995 | + | 0.611823i | \(0.209563\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.9460 | −1.02311 | −0.511556 | − | 0.859250i | \(-0.670931\pi\) | ||||
−0.511556 | + | 0.859250i | \(0.670931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6013 | −0.694248 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.9348 | − | 25.8679i | 0.661975 | − | 1.14657i | −0.318121 | − | 0.948050i | \(-0.603052\pi\) |
0.980096 | − | 0.198524i | \(-0.0636147\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.275480 | + | 3.81734i | 0.0121865 | + | 0.168869i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −22.4992 | − | 38.9698i | −0.991434 | − | 1.71721i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.01846 | − | 1.76402i | −0.0447918 | − | 0.0775817i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.5980 | + | 27.0166i | −0.683362 | + | 1.18362i | 0.290587 | + | 0.956849i | \(0.406149\pi\) |
−0.973949 | + | 0.226769i | \(0.927184\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.07911 | + | 5.33318i | 0.134640 | + | 0.233203i | 0.925460 | − | 0.378846i | \(-0.123679\pi\) |
−0.790820 | + | 0.612049i | \(0.790346\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.28187 | − | 7.41642i | 0.186521 | − | 0.323064i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.49310 | − | 9.51433i | −0.238830 | − | 0.413666i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −33.7366 | + | 58.4335i | −1.46129 | + | 2.53103i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39.9881 | −1.72884 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.01899 | + | 0.873275i | −0.259256 | + | 0.0376146i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5137 | − | 23.4064i | −0.580999 | − | 1.00632i | −0.995361 | − | 0.0962083i | \(-0.969329\pi\) |
0.414362 | − | 0.910112i | \(-0.364005\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 24.2963 | + | 42.0824i | 1.04074 | + | 1.80261i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.9426 | + | 25.8814i | −0.638900 | + | 1.10661i | 0.346775 | + | 0.937948i | \(0.387277\pi\) |
−0.985675 | + | 0.168658i | \(0.946057\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 7.22865 | 0.307951 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.66339 | + | 3.16064i | −0.198308 | + | 0.134404i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10.6650 | + | 18.4722i | −0.451889 | + | 0.782694i | −0.998503 | − | 0.0546900i | \(-0.982583\pi\) |
0.546615 | + | 0.837384i | \(0.315916\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 22.9789 | 0.971905 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.4635 | 1.32603 | 0.663014 | − | 0.748607i | \(-0.269277\pi\) | ||||
0.663014 | + | 0.748607i | \(0.269277\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −23.9577 | −1.00791 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.3391 | −1.22996 | −0.614980 | − | 0.788543i | \(-0.710836\pi\) | ||||
−0.614980 | + | 0.788543i | \(0.710836\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.4947 | 1.15062 | 0.575308 | − | 0.817937i | \(-0.304882\pi\) | ||||
0.575308 | + | 0.817937i | \(0.304882\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −71.0221 | −2.96183 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.2293 | + | 35.0381i | −0.842156 | + | 1.45866i | 0.0459122 | + | 0.998945i | \(0.485381\pi\) |
−0.888068 | + | 0.459712i | \(0.847953\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.833292 | + | 11.5470i | 0.0345708 | + | 0.479048i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.89613 | −0.0785299 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.6559 | + | 23.6528i | −0.563641 | + | 0.976255i | 0.433533 | + | 0.901137i | \(0.357267\pi\) |
−0.997175 | + | 0.0751177i | \(0.976067\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.94263 | + | 10.2929i | 0.244862 | + | 0.424113i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.2898 | − | 24.7507i | −0.586813 | − | 1.01639i | −0.994647 | − | 0.103334i | \(-0.967049\pi\) |
0.407833 | − | 0.913056i | \(-0.366284\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 28.5406 | + | 13.8416i | 1.17005 | + | 0.567449i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 39.9838 | 1.63370 | 0.816848 | − | 0.576854i | \(-0.195720\pi\) | ||||
0.816848 | + | 0.576854i | \(0.195720\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.6948 | + | 21.9880i | −0.517831 | + | 0.896910i | 0.481954 | + | 0.876196i | \(0.339927\pi\) |
−0.999785 | + | 0.0207133i | \(0.993406\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.2340 | − | 36.7783i | −0.863283 | − | 1.49525i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −18.6469 | + | 32.2975i | −0.756856 | + | 1.31091i | 0.187590 | + | 0.982247i | \(0.439932\pi\) |
−0.944446 | + | 0.328666i | \(0.893401\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.71029 | + | 11.6226i | 0.271469 | + | 0.470199i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.7319 | + | 20.3203i | −0.473848 | + | 0.820729i | −0.999552 | − | 0.0299390i | \(-0.990469\pi\) |
0.525704 | + | 0.850668i | \(0.323802\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.56888 | − | 11.3776i | −0.264453 | − | 0.458047i | 0.702967 | − | 0.711223i | \(-0.251858\pi\) |
−0.967420 | + | 0.253176i | \(0.918525\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.7776 | + | 18.6674i | 0.433190 | + | 0.750308i | 0.997146 | − | 0.0754975i | \(-0.0240545\pi\) |
−0.563956 | + | 0.825805i | \(0.690721\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.7751 | + | 13.4703i | 1.11279 | + | 0.539677i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.2520 | + | 54.1300i | −1.25008 | + | 2.16520i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.3247 | −0.611036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.15223 | 0.244916 | 0.122458 | − | 0.992474i | \(-0.460922\pi\) | ||||
0.122458 | + | 0.992474i | \(0.460922\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −13.4194 | + | 23.2431i | −0.532533 | + | 0.922375i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.6571 | − | 5.75372i | 1.57127 | − | 0.227971i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.23682 | − | 3.87429i | −0.0883491 | − | 0.153025i | 0.818464 | − | 0.574557i | \(-0.194826\pi\) |
−0.906813 | + | 0.421532i | \(0.861492\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.98009 | − | 15.5540i | −0.354140 | − | 0.613389i | 0.632830 | − | 0.774291i | \(-0.281893\pi\) |
−0.986970 | + | 0.160902i | \(0.948560\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.02992 | − | 10.4441i | 0.237061 | − | 0.410601i | −0.722809 | − | 0.691048i | \(-0.757149\pi\) |
0.959870 | + | 0.280447i | \(0.0904826\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.32688 | + | 2.29822i | 0.0520845 | + | 0.0902131i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −24.1366 | + | 41.8059i | −0.944540 | + | 1.63599i | −0.187870 | + | 0.982194i | \(0.560158\pi\) |
−0.756670 | + | 0.653797i | \(0.773175\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −36.7478 | − | 63.6490i | −1.43585 | − | 2.48697i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.5795 | − | 25.2525i | 0.567937 | − | 0.983696i | −0.428832 | − | 0.903384i | \(-0.641075\pi\) |
0.996770 | − | 0.0803122i | \(-0.0255917\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −14.5486 | −0.565873 | −0.282937 | − | 0.959139i | \(-0.591309\pi\) | ||||
−0.282937 | + | 0.959139i | \(0.591309\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −36.4416 | + | 24.6985i | −1.41315 | + | 0.957766i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.24922 | − | 9.09192i | −0.203251 | − | 0.352040i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.44722 | − | 4.23871i | −0.0944738 | − | 0.163633i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6825 | − | 20.2348i | 0.450329 | − | 0.779993i | −0.548077 | − | 0.836428i | \(-0.684640\pi\) |
0.998406 | + | 0.0564349i | \(0.0179733\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.7175 | 0.680939 | 0.340469 | − | 0.940256i | \(-0.389414\pi\) | ||||
0.340469 | + | 0.940256i | \(0.389414\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.51885 | − | 21.0467i | −0.0582880 | − | 0.807698i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.7769 | − | 37.7186i | 0.833269 | − | 1.44326i | −0.0621637 | − | 0.998066i | \(-0.519800\pi\) |
0.895432 | − | 0.445198i | \(-0.146867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2846 | 0.431161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.4930 | 0.475945 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.5344 | −0.895291 | −0.447645 | − | 0.894211i | \(-0.647737\pi\) | ||||
−0.447645 | + | 0.894211i | \(0.647737\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −71.7476 | −2.72154 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.0897 | 1.29124 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −45.1804 | −1.70644 | −0.853219 | − | 0.521552i | \(-0.825353\pi\) | ||||
−0.853219 | + | 0.521552i | \(0.825353\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6343 | − | 18.4191i | 0.401079 | − | 0.694689i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 8.95973 | + | 4.34527i | 0.336965 | + | 0.163421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.0127 | −1.01448 | −0.507242 | − | 0.861804i | \(-0.669335\pi\) | ||||
−0.507242 | + | 0.861804i | \(0.669335\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.63071 | − | 14.9488i | 0.323223 | − | 0.559838i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −10.3089 | − | 17.8555i | −0.385529 | − | 0.667757i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.2096 | − | 19.4156i | −0.418048 | − | 0.724080i | 0.577695 | − | 0.816253i | \(-0.303952\pi\) |
−0.995743 | + | 0.0921724i | \(0.970619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.06730 | + | 28.6466i | 0.0769902 | + | 1.06686i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −21.9389 | −0.814792 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −21.9820 | + | 38.0740i | −0.815268 | + | 1.41208i | 0.0938680 | + | 0.995585i | \(0.470077\pi\) |
−0.909136 | + | 0.416500i | \(0.863256\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.80486 | − | 10.0543i | −0.214701 | − | 0.371872i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.433386 | + | 0.750646i | −0.0160075 | + | 0.0277257i | −0.873918 | − | 0.486073i | \(-0.838429\pi\) |
0.857911 | + | 0.513799i | \(0.171762\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.09075 | − | 1.88924i | −0.0401785 | − | 0.0695911i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.0442 | + | 22.5932i | −0.479838 | + | 0.831103i | −0.999733 | − | 0.0231270i | \(-0.992638\pi\) |
0.519895 | + | 0.854230i | \(0.325971\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5842 | + | 39.1170i | 0.828533 | + | 1.43506i | 0.899189 | + | 0.437561i | \(0.144158\pi\) |
−0.0706551 | + | 0.997501i | \(0.522509\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.1908 | + | 24.5791i | 0.519910 | + | 0.900510i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.9650 | + | 11.1375i | 0.839121 | + | 0.406955i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.2994 | + | 17.8391i | −0.375831 | + | 0.650958i | −0.990451 | − | 0.137865i | \(-0.955976\pi\) |
0.614620 | + | 0.788823i | \(0.289309\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.4743 | 1.40022 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.0856 | −1.42059 | −0.710294 | − | 0.703905i | \(-0.751438\pi\) | ||||
−0.710294 | + | 0.703905i | \(0.751438\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.4436 | + | 25.0171i | −0.523581 | + | 0.906868i | 0.476043 | + | 0.879422i | \(0.342071\pi\) |
−0.999623 | + | 0.0274459i | \(0.991263\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.23242 | − | 30.9347i | −0.0808191 | − | 1.11991i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −8.74236 | − | 15.1422i | −0.315668 | − | 0.546753i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.1407 | − | 19.2962i | −0.401742 | − | 0.695838i | 0.592194 | − | 0.805796i | \(-0.298262\pi\) |
−0.993936 | + | 0.109957i | \(0.964929\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 21.3593 | − | 36.9955i | 0.768242 | − | 1.33063i | −0.170273 | − | 0.985397i | \(-0.554465\pi\) |
0.938515 | − | 0.345238i | \(-0.112202\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.0359 | − | 31.2391i | −0.647868 | − | 1.12214i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −23.6558 | + | 40.9731i | −0.847558 | + | 1.46801i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.474151 | + | 0.821254i | 0.0169665 | + | 0.0293868i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.3465 | − | 49.0976i | 1.01173 | − | 1.75237i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.286769 | 0.0102222 | 0.00511110 | − | 0.999987i | \(-0.498373\pi\) | ||||
0.00511110 | + | 0.999987i | \(0.498373\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.7588 | + | 6.67270i | 0.489205 | + | 0.237254i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1239 | + | 27.9274i | 0.572577 | + | 0.991732i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.457746 | + | 0.792840i | 0.0162142 | + | 0.0280838i | 0.874019 | − | 0.485892i | \(-0.161505\pi\) |
−0.857804 | + | 0.513976i | \(0.828172\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.39026 | − | 5.87211i | 0.119939 | − | 0.207740i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.25687 | −0.0443538 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 57.5276 | + | 27.8996i | 2.02758 | + | 0.983333i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.3721 | − | 24.8932i | 0.505297 | − | 0.875199i | −0.494685 | − | 0.869073i | \(-0.664716\pi\) |
0.999981 | − | 0.00612685i | \(-0.00195025\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.3005 | −0.502157 | −0.251079 | − | 0.967967i | \(-0.580785\pi\) | ||||
−0.251079 | + | 0.967967i | \(0.580785\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 13.6794 | 0.479167 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.1126 | 0.563710 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −35.6250 | −1.24332 | −0.621660 | − | 0.783287i | \(-0.713542\pi\) | ||||
−0.621660 | + | 0.783287i | \(0.713542\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.4313 | 0.781907 | 0.390953 | − | 0.920411i | \(-0.372145\pi\) | ||||
0.390953 | + | 0.920411i | \(0.372145\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.6728 | −0.927505 | −0.463753 | − | 0.885965i | \(-0.653497\pi\) | ||||
−0.463753 | + | 0.885965i | \(0.653497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0078 | + | 27.7263i | −0.555973 | + | 0.962973i | 0.441854 | + | 0.897087i | \(0.354321\pi\) |
−0.997827 | + | 0.0658866i | \(0.979012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.5356 | − | 15.8983i | −0.434331 | − | 0.550843i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.4297 | 1.71058 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.10375 | − | 15.7682i | 0.314296 | − | 0.544377i | −0.664991 | − | 0.746851i | \(-0.731565\pi\) |
0.979288 | + | 0.202474i | \(0.0648982\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8785 | + | 22.3062i | 0.444086 | + | 0.769180i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 40.9778 | + | 70.9757i | 1.40968 | + | 2.44164i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.95104 | + | 27.0356i | 0.0670386 | + | 0.928956i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −30.8891 | −1.05886 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.9242 | − | 36.2419i | 0.716432 | − | 1.24090i | −0.245972 | − | 0.969277i | \(-0.579107\pi\) |
0.962404 | − | 0.271621i | \(-0.0875596\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 7.85704 | + | 13.6088i | 0.268391 | + | 0.464867i | 0.968447 | − | 0.249221i | \(-0.0801746\pi\) |
−0.700055 | + | 0.714089i | \(0.746841\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12.1023 | − | 20.9618i | 0.412924 | − | 0.715206i | −0.582284 | − | 0.812986i | \(-0.697841\pi\) |
0.995208 | + | 0.0977797i | \(0.0311741\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.0542 | + | 45.1272i | 0.886896 | + | 1.53615i | 0.843525 | + | 0.537090i | \(0.180477\pi\) |
0.0433714 | + | 0.999059i | \(0.486190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.9672 | − | 34.5842i | 0.678904 | − | 1.17590i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.925022 | − | 1.60219i | −0.0313792 | − | 0.0543504i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.18662 | + | 12.4476i | 0.243509 | + | 0.421770i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 65.2078 | − | 44.1949i | 2.20443 | − | 1.49406i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 6.98841 | − | 12.1043i | 0.235982 | − | 0.408733i | −0.723576 | − | 0.690245i | \(-0.757503\pi\) |
0.959558 | + | 0.281512i | \(0.0908360\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −28.1210 | −0.947421 | −0.473710 | − | 0.880681i | \(-0.657086\pi\) | ||||
−0.473710 | + | 0.880681i | \(0.657086\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.1633 | 1.18334 | 0.591670 | − | 0.806180i | \(-0.298469\pi\) | ||||
0.591670 | + | 0.806180i | \(0.298469\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 13.4610 | − | 23.3151i | 0.451975 | − | 0.782844i | −0.546533 | − | 0.837437i | \(-0.684053\pi\) |
0.998509 | + | 0.0545932i | \(0.0173862\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 14.1804 | − | 9.61081i | 0.475594 | − | 0.322336i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.70520 | + | 8.14965i | 0.157454 | + | 0.272718i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 47.7880 | + | 82.7713i | 1.59738 | + | 2.76674i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.66605 | − | 4.61774i | 0.0889179 | − | 0.154010i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.15594 | − | 5.46625i | −0.105140 | − | 0.182107i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −24.5241 | + | 42.4769i | −0.815207 | + | 1.41198i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.3571 | − | 38.7236i | −0.742355 | − | 1.28580i | −0.951420 | − | 0.307895i | \(-0.900375\pi\) |
0.209065 | − | 0.977902i | \(-0.432958\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.7822 | + | 23.8715i | −0.456626 | + | 0.790899i | −0.998780 | − | 0.0493800i | \(-0.984275\pi\) |
0.542154 | + | 0.840279i | \(0.317609\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.80185 | −0.125823 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.37650 | + | 46.7882i | 0.111502 | + | 1.54508i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 21.3836 | + | 37.0376i | 0.705381 | + | 1.22176i | 0.966554 | + | 0.256464i | \(0.0825575\pi\) |
−0.261173 | + | 0.965292i | \(0.584109\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.12402 | − | 5.41096i | −0.102828 | − | 0.178104i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.2750 | + | 55.9019i | −1.06119 | + | 1.83804i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −47.9497 | −1.57318 | −0.786589 | − | 0.617477i | \(-0.788155\pi\) | ||||
−0.786589 | + | 0.617477i | \(0.788155\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 27.8072 | − | 4.03446i | 0.911346 | − | 0.132224i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.20838 | + | 9.02118i | −0.170332 | + | 0.295024i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.9136 | 1.10791 | 0.553955 | − | 0.832547i | \(-0.313118\pi\) | ||||
0.553955 | + | 0.832547i | \(0.313118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.54790 | 0.278654 | 0.139327 | − | 0.990246i | \(-0.455506\pi\) | ||||
0.139327 | + | 0.990246i | \(0.455506\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 68.7125 | 2.23759 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0.823127 | 0.0267480 | 0.0133740 | − | 0.999911i | \(-0.495743\pi\) | ||||
0.0133740 | + | 0.999911i | \(0.495743\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.28106 | 0.268815 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.6726 | 1.44709 | 0.723544 | − | 0.690278i | \(-0.242512\pi\) | ||||
0.723544 | + | 0.690278i | \(0.242512\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13.0264 | + | 22.5625i | −0.421526 | + | 0.730104i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.48065 | − | 3.14298i | −0.209271 | − | 0.101492i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2330 | −0.717194 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 28.4592 | − | 49.2928i | 0.916135 | − | 1.58679i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.2289 | + | 31.5735i | 0.586203 | + | 1.01533i | 0.994724 | + | 0.102585i | \(0.0327114\pi\) |
−0.408521 | + | 0.912749i | \(0.633955\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.63674 | + | 14.9593i | 0.277166 | + | 0.480066i | 0.970679 | − | 0.240378i | \(-0.0772714\pi\) |
−0.693513 | + | 0.720444i | \(0.743938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.2043 | + | 19.9832i | 1.32095 | + | 0.640631i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.03550 | −0.289071 | −0.144536 | − | 0.989500i | \(-0.546169\pi\) | ||||
−0.144536 | + | 0.989500i | \(0.546169\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.06868 | + | 8.77921i | −0.161996 | + | 0.280585i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.4286 | + | 19.7950i | 0.364517 | + | 0.631362i | 0.988698 | − | 0.149918i | \(-0.0479008\pi\) |
−0.624182 | + | 0.781279i | \(0.714568\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.334715 | − | 0.579743i | 0.0106649 | − | 0.0184722i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −11.7005 | − | 20.2659i | −0.372055 | − | 0.644417i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.37884 | − | 7.58437i | 0.139098 | − | 0.240925i | −0.788057 | − | 0.615602i | \(-0.788913\pi\) |
0.927156 | + | 0.374677i | \(0.122246\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.4584 | − | 89.1285i | −1.63134 | − | 2.82556i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.46535 | − | 6.00216i | −0.109749 | − | 0.190090i | 0.805920 | − | 0.592025i | \(-0.201671\pi\) |
−0.915668 | + | 0.401934i | \(0.868338\pi\) | |||||||
\(998\) | 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 \(a_p\))