Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [936,2,Mod(361,936)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(936, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("936.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 936 = 2^{3} \cdot 3^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 936.bi (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.47399762919\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.649638144.4 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} + 75x^{4} - 170x^{2} + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 312) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 433.4 | ||
Root | \(-2.34138 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 936.433 |
Dual form | 936.2.bi.c.361.1 |
$q$-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 \(\left(\mathbb{Z}/936\mathbb{Z}\right)^\times\).
\(n\) | \(145\) | \(209\) | \(469\) | \(703\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | 4.20740i | 1.88161i | 0.338951 | + | 0.940804i | \(0.389928\pi\) | ||||
−0.338951 | + | 0.940804i | \(0.610072\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.07905 | + | 1.77769i | −1.16377 | + | 0.671905i | −0.952205 | − | 0.305459i | \(-0.901190\pi\) |
−0.211568 | + | 0.977363i | \(0.567857\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.39944 | + | 2.54002i | 1.32648 | + | 0.765844i | 0.984754 | − | 0.173956i | \(-0.0556549\pi\) |
0.341727 | + | 0.939799i | \(0.388988\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.51537 | − | 0.801361i | −0.974988 | − | 0.222258i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.62835 | − | 2.82038i | −0.394933 | − | 0.684043i | 0.598160 | − | 0.801377i | \(-0.295899\pi\) |
−0.993093 | + | 0.117333i | \(0.962565\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.88800 | − | 1.66739i | 0.662552 | − | 0.382525i | −0.130696 | − | 0.991422i | \(-0.541721\pi\) |
0.793249 | + | 0.608898i | \(0.208388\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.192034 | + | 0.332613i | −0.0400419 | + | 0.0693546i | −0.885352 | − | 0.464922i | \(-0.846082\pi\) |
0.845310 | + | 0.534276i | \(0.179416\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.7022 | −2.54045 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.64372 | + | 6.31111i | −0.676621 | + | 1.17194i | 0.299371 | + | 0.954137i | \(0.403223\pi\) |
−0.975992 | + | 0.217806i | \(0.930110\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.47535i | − | 1.16301i | −0.813544 | − | 0.581504i | \(-0.802465\pi\) | ||
0.813544 | − | 0.581504i | \(-0.197535\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.47947 | − | 12.9548i | −1.26426 | − | 2.18976i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.70838 | − | 1.56369i | −0.445255 | − | 0.257068i | 0.260569 | − | 0.965455i | \(-0.416090\pi\) |
−0.705824 | + | 0.708387i | \(0.749423\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.86649 | − | 3.38702i | −0.916192 | − | 0.528964i | −0.0337737 | − | 0.999430i | \(-0.510753\pi\) |
−0.882418 | + | 0.470466i | \(0.844086\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.07905 | + | 3.60103i | 0.317053 | + | 0.549152i | 0.979872 | − | 0.199628i | \(-0.0639734\pi\) |
−0.662819 | + | 0.748780i | \(0.730640\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.49484i | 0.801505i | 0.916186 | + | 0.400752i | \(0.131251\pi\) | ||||
−0.916186 | + | 0.400752i | \(0.868749\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.82038 | − | 4.88505i | 0.402912 | − | 0.697864i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.613974 | −0.0843358 | −0.0421679 | − | 0.999111i | \(-0.513426\pi\) | ||||
−0.0421679 | + | 0.999111i | \(0.513426\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.6869 | + | 18.5102i | −1.44102 | + | 2.49592i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.82333 | − | 3.93945i | 0.888323 | − | 0.512873i | 0.0149291 | − | 0.999889i | \(-0.495248\pi\) |
0.873393 | + | 0.487015i | \(0.161914\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.15614 | + | 7.19864i | 0.532139 | + | 0.921691i | 0.999296 | + | 0.0375170i | \(0.0119448\pi\) |
−0.467157 | + | 0.884174i | \(0.654722\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.37165 | − | 14.7906i | 0.418202 | − | 1.83455i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.79162 | + | 1.03439i | 0.218881 | + | 0.126371i | 0.605432 | − | 0.795897i | \(-0.293000\pi\) |
−0.386551 | + | 0.922268i | \(0.626334\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.44677 | + | 1.41265i | −0.290379 | + | 0.167650i | −0.638113 | − | 0.769943i | \(-0.720285\pi\) |
0.347734 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.21865i | 0.376715i | 0.982101 | + | 0.188357i | \(0.0603164\pi\) | ||||
−0.982101 | + | 0.188357i | \(0.939684\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −18.0615 | −2.05830 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.64077 | −0.297109 | −0.148555 | − | 0.988904i | \(-0.547462\pi\) | ||||
−0.148555 | + | 0.988904i | \(0.547462\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.96926i | 0.216155i | 0.994142 | + | 0.108077i | \(0.0344694\pi\) | ||||
−0.994142 | + | 0.108077i | \(0.965531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.8665 | − | 6.85112i | 1.28710 | − | 0.743108i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 12.2630 | + | 7.08003i | 1.29987 | + | 0.750482i | 0.980382 | − | 0.197107i | \(-0.0631547\pi\) |
0.319491 | + | 0.947589i | \(0.396488\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.2486 | − | 3.78181i | 1.28400 | − | 0.396442i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 7.01537 | + | 12.1510i | 0.719762 | + | 1.24666i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.67962 | + | 4.43383i | −0.779747 | + | 0.450187i | −0.836341 | − | 0.548210i | \(-0.815309\pi\) |
0.0565937 | + | 0.998397i | \(0.481976\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.72375 | + | 8.18178i | −0.470031 | + | 0.814117i | −0.999413 | − | 0.0342664i | \(-0.989091\pi\) |
0.529382 | + | 0.848384i | \(0.322424\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.15811 | 0.212645 | 0.106322 | − | 0.994332i | \(-0.466092\pi\) | ||||
0.106322 | + | 0.994332i | \(0.466092\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.35014 | + | 16.1949i | −0.903912 | + | 1.56562i | −0.0815419 | + | 0.996670i | \(0.525984\pi\) |
−0.822371 | + | 0.568952i | \(0.807349\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 14.4754i | − | 1.38649i | −0.720703 | − | 0.693244i | \(-0.756181\pi\) | ||
0.720703 | − | 0.693244i | \(-0.243819\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.37165 | + | 2.37577i | 0.129034 | + | 0.223494i | 0.923303 | − | 0.384073i | \(-0.125479\pi\) |
−0.794269 | + | 0.607567i | \(0.792146\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.39944 | − | 0.807966i | −0.130498 | − | 0.0753432i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.0276 | + | 5.78941i | 0.919224 | + | 0.530714i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.40337 | + | 12.8230i | 0.673033 | + | 1.16573i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 32.4064i | − | 2.89852i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.06369 | + | 8.77056i | −0.449329 | + | 0.778261i | −0.998342 | − | 0.0575524i | \(-0.981670\pi\) |
0.549013 | + | 0.835814i | \(0.315004\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.3430 | 1.16578 | 0.582892 | − | 0.812550i | \(-0.301921\pi\) | ||||
0.582892 | + | 0.812550i | \(0.301921\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.92820 | + | 10.2679i | −0.514040 | + | 0.890344i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.3018 | + | 5.94775i | −0.880143 | + | 0.508151i | −0.870706 | − | 0.491805i | \(-0.836337\pi\) |
−0.00943756 | + | 0.999955i | \(0.503004\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.71035 | − | 11.6227i | −0.569165 | − | 0.985822i | −0.996649 | − | 0.0817995i | \(-0.973933\pi\) |
0.427484 | − | 0.904023i | \(-0.359400\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −13.4302 | − | 12.4546i | −1.12309 | − | 1.04151i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −26.5534 | − | 15.3306i | −2.20514 | − | 1.27314i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.77305 | + | 2.75572i | −0.391023 | + | 0.225757i | −0.682603 | − | 0.730789i | \(-0.739152\pi\) |
0.291580 | + | 0.956546i | \(0.405819\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.08003i | − | 0.413407i | −0.978404 | − | 0.206704i | \(-0.933726\pi\) | ||
0.978404 | − | 0.206704i | \(-0.0662736\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.2444 | 2.18832 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −12.5670 | −1.00296 | −0.501478 | − | 0.865170i | \(-0.667210\pi\) | ||||
−0.501478 | + | 0.865170i | \(0.667210\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1.36551i | − | 0.107617i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.63660 | − | 4.40899i | 0.598145 | − | 0.345339i | −0.170167 | − | 0.985415i | \(-0.554431\pi\) |
0.768311 | + | 0.640076i | \(0.221097\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.7042 | + | 7.33477i | 0.983081 | + | 0.567582i | 0.903199 | − | 0.429223i | \(-0.141212\pi\) |
0.0798818 | + | 0.996804i | \(0.474546\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.7156 | + | 5.63416i | 0.901203 | + | 0.433397i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.20740 | + | 2.09128i | 0.0917972 | + | 0.158997i | 0.908267 | − | 0.418390i | \(-0.137406\pi\) |
−0.816470 | + | 0.577388i | \(0.804072\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 39.1109 | − | 22.5807i | 2.95651 | − | 1.70694i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2.67864 | − | 4.63954i | 0.200211 | − | 0.346775i | −0.748385 | − | 0.663264i | \(-0.769171\pi\) |
0.948596 | + | 0.316489i | \(0.102504\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.6715 | 1.31351 | 0.656756 | − | 0.754103i | \(-0.271928\pi\) | ||||
0.656756 | + | 0.754103i | \(0.271928\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.57905 | − | 11.3953i | 0.483702 | − | 0.837796i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 16.5441i | − | 1.20983i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.28744 | + | 3.96196i | 0.165513 | + | 0.286677i | 0.936837 | − | 0.349765i | \(-0.113739\pi\) |
−0.771324 | + | 0.636442i | \(0.780405\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.5863 | + | 8.42141i | 1.04995 | + | 0.606186i | 0.922634 | − | 0.385676i | \(-0.126032\pi\) |
0.127312 | + | 0.991863i | \(0.459365\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.60770 | + | 0.928203i | 0.114544 | + | 0.0661317i | 0.556177 | − | 0.831064i | \(-0.312268\pi\) |
−0.441634 | + | 0.897195i | \(0.645601\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.49386 | − | 16.4438i | −0.673002 | − | 1.16567i | −0.977049 | − | 0.213016i | \(-0.931671\pi\) |
0.304047 | − | 0.952657i | \(-0.401662\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 25.9096i | − | 1.81850i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 14.2506 | − | 24.6827i | 0.995302 | − | 1.72391i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 16.9408 | 1.17182 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.12122 | + | 10.6023i | −0.421402 | + | 0.729890i | −0.996077 | − | 0.0884922i | \(-0.971795\pi\) |
0.574675 | + | 0.818382i | \(0.305128\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.1510 | + | 8.74742i | −1.03329 | + | 0.596569i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.5112 | + | 19.9380i | 0.781430 | + | 1.35348i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.46410 | + | 11.2196i | 0.233021 | + | 0.754711i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.9341 | + | 10.3543i | 1.20096 | + | 0.693373i | 0.960768 | − | 0.277354i | \(-0.0894574\pi\) |
0.240189 | + | 0.970726i | \(0.422791\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −7.48143 | + | 4.31940i | −0.496560 | + | 0.286689i | −0.727292 | − | 0.686328i | \(-0.759221\pi\) |
0.230732 | + | 0.973017i | \(0.425888\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.1111i | 1.32898i | 0.747296 | + | 0.664491i | \(0.231352\pi\) | ||||
−0.747296 | + | 0.664491i | \(0.768648\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.41089 | −0.288967 | −0.144484 | − | 0.989507i | \(-0.546152\pi\) | ||||
−0.144484 | + | 0.989507i | \(0.546152\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −23.1190 | −1.50812 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.51734i | 0.227518i | 0.993508 | + | 0.113759i | \(0.0362892\pi\) | ||||
−0.993508 | + | 0.113759i | \(0.963711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.10782 | + | 2.37165i | −0.264608 | + | 0.152771i | −0.626435 | − | 0.779474i | \(-0.715487\pi\) |
0.361827 | + | 0.932245i | \(0.382153\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 20.5534 | + | 11.8665i | 1.31311 | + | 0.758122i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.4886 | + | 3.54715i | −0.731000 | + | 0.225700i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.49484 | − | 6.05324i | −0.220592 | − | 0.382077i | 0.734396 | − | 0.678722i | \(-0.237466\pi\) |
−0.954988 | + | 0.296644i | \(0.904132\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.68969 | + | 0.975541i | −0.106230 | + | 0.0613317i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.35505 | − | 4.07907i | 0.146904 | − | 0.254445i | −0.783178 | − | 0.621798i | \(-0.786402\pi\) |
0.930082 | + | 0.367353i | \(0.119736\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.1190 | 0.690902 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.06466 | + | 3.57610i | −0.127313 | + | 0.220512i | −0.922635 | − | 0.385675i | \(-0.873968\pi\) |
0.795322 | + | 0.606187i | \(0.207302\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.58324i | − | 0.158687i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.12933 | + | 14.0804i | 0.495654 | + | 0.858498i | 0.999987 | − | 0.00501123i | \(-0.00159513\pi\) |
−0.504334 | + | 0.863509i | \(0.668262\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 27.9875 | + | 16.1586i | 1.70012 | + | 0.981563i | 0.945627 | + | 0.325253i | \(0.105449\pi\) |
0.754491 | + | 0.656311i | \(0.227884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −55.8827 | − | 32.2639i | −3.36986 | − | 1.94559i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.8684 | − | 20.5568i | −0.713106 | − | 1.23514i | −0.963686 | − | 0.267040i | \(-0.913955\pi\) |
0.250580 | − | 0.968096i | \(-0.419379\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 25.5812i | 1.52604i | 0.646373 | + | 0.763022i | \(0.276285\pi\) | ||||
−0.646373 | + | 0.763022i | \(0.723715\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.82431 | + | 10.0880i | −0.346220 | + | 0.599670i | −0.985575 | − | 0.169242i | \(-0.945868\pi\) |
0.639355 | + | 0.768912i | \(0.279201\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 24.0843 | 1.42165 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.19696 | − | 5.53729i | 0.188056 | − | 0.325723i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.53049 | − | 4.92508i | 0.498356 | − | 0.287726i | −0.229678 | − | 0.973267i | \(-0.573767\pi\) |
0.728035 | + | 0.685540i | \(0.240434\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.5749 | + | 28.7085i | 0.965026 | + | 1.67147i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.941615 | − | 1.01537i | 0.0544550 | − | 0.0587203i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −12.8030 | − | 7.39184i | −0.737955 | − | 0.426059i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −30.2876 | + | 17.4865i | −1.73426 | + | 1.00128i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 12.4182i | − | 0.708744i | −0.935105 | − | 0.354372i | \(-0.884695\pi\) | ||
0.935105 | − | 0.354372i | \(-0.115305\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.42267 | 0.420901 | 0.210450 | − | 0.977605i | \(-0.432507\pi\) | ||||
0.210450 | + | 0.977605i | \(0.432507\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.9799 | 1.58152 | 0.790758 | − | 0.612129i | \(-0.209687\pi\) | ||||
0.790758 | + | 0.612129i | \(0.209687\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 8.02484i | − | 0.450720i | −0.974276 | − | 0.225360i | \(-0.927644\pi\) | ||
0.974276 | − | 0.225360i | \(-0.0723558\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −32.0606 | + | 18.5102i | −1.79505 | + | 1.03637i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −9.40534 | − | 5.43018i | −0.523327 | − | 0.302143i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 44.6531 | + | 10.1791i | 2.47691 | + | 0.564634i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −9.76814 | − | 16.9189i | −0.538535 | − | 0.932770i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.3897 | + | 9.46261i | −0.900860 | + | 0.520112i | −0.877479 | − | 0.479615i | \(-0.840776\pi\) |
−0.0233812 | + | 0.999727i | \(0.507443\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.35210 | + | 7.53806i | −0.237781 | + | 0.411848i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −13.8296 | −0.753347 | −0.376674 | − | 0.926346i | \(-0.622932\pi\) | ||||
−0.376674 | + | 0.926346i | \(0.622932\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.4475 | − | 28.4879i | 0.890682 | − | 1.54271i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 4.83260i | − | 0.260936i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.45464 | − | 14.6439i | −0.453869 | − | 0.786123i | 0.544754 | − | 0.838596i | \(-0.316623\pi\) |
−0.998622 | + | 0.0524726i | \(0.983290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −13.6366 | − | 7.87309i | −0.729950 | − | 0.421437i | 0.0884536 | − | 0.996080i | \(-0.471808\pi\) |
−0.818404 | + | 0.574643i | \(0.805141\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 19.0491 | + | 10.9980i | 1.01388 | + | 0.585363i | 0.912325 | − | 0.409467i | \(-0.134285\pi\) |
0.101554 | + | 0.994830i | \(0.467619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.94357 | − | 10.2946i | −0.315452 | − | 0.546379i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.5606i | 1.29626i | 0.761530 | + | 0.648130i | \(0.224449\pi\) | ||||
−0.761530 | + | 0.648130i | \(0.775551\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.93964 | + | 6.82366i | −0.207350 | + | 0.359140i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −13.5422 | −0.708830 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.10389 | + | 7.10815i | −0.214221 | + | 0.371042i | −0.953031 | − | 0.302871i | \(-0.902055\pi\) |
0.738810 | + | 0.673914i | \(0.235388\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.89046 | − | 1.09146i | 0.0981477 | − | 0.0566656i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.05950 | + | 8.76332i | 0.261971 | + | 0.453747i | 0.966766 | − | 0.255664i | \(-0.0822941\pi\) |
−0.704794 | + | 0.709412i | \(0.748961\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.8665 | − | 19.2659i | 0.920171 | − | 0.992246i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.3263 | + | 10.5807i | 0.941358 | + | 0.543493i | 0.890386 | − | 0.455207i | \(-0.150435\pi\) |
0.0509723 | + | 0.998700i | \(0.483768\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 22.6163 | − | 13.0575i | 1.15564 | − | 0.667209i | 0.205384 | − | 0.978681i | \(-0.434156\pi\) |
0.950255 | + | 0.311473i | \(0.100822\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 75.9919i | − | 3.87291i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9.18493 | 0.465695 | 0.232847 | − | 0.972513i | \(-0.425196\pi\) | ||||
0.232847 | + | 0.972513i | \(0.425196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.25080 | 0.0632554 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 11.1108i | − | 0.559044i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2115 | + | 5.89560i | −0.512499 | + | 0.295892i | −0.733860 | − | 0.679300i | \(-0.762283\pi\) |
0.221361 | + | 0.975192i | \(0.428950\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −26.3983 | − | 15.2411i | −1.31827 | − | 0.761104i | −0.334820 | − | 0.942282i | \(-0.608676\pi\) |
−0.983450 | + | 0.181178i | \(0.942009\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.18910 | + | 22.7633i | −0.258487 | + | 1.13392i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.94357 | − | 13.7587i | −0.393748 | − | 0.681992i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.5576 | + | 8.40481i | −0.719825 | + | 0.415591i | −0.814688 | − | 0.579899i | \(-0.803092\pi\) |
0.0948632 | + | 0.995490i | \(0.469759\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −14.0063 | + | 24.2596i | −0.689204 | + | 1.19374i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.28548 | −0.406718 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.2894 | + | 21.2859i | −0.600376 | + | 1.03988i | 0.392388 | + | 0.919800i | \(0.371649\pi\) |
−0.992764 | + | 0.120082i | \(0.961684\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 11.1157i | − | 0.541748i | −0.962615 | − | 0.270874i | \(-0.912687\pi\) | ||
0.962615 | − | 0.270874i | \(-0.0873127\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 20.6837 | + | 35.8252i | 1.00331 | + | 1.73778i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.5939 | − | 14.7767i | −1.23858 | − | 0.715093i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −31.6624 | − | 18.2803i | −1.52512 | − | 0.880531i | −0.999556 | − | 0.0297799i | \(-0.990519\pi\) |
−0.525568 | − | 0.850751i | \(-0.676147\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.58827 | − | 16.6074i | −0.460783 | − | 0.798099i | 0.538217 | − | 0.842806i | \(-0.319098\pi\) |
−0.999000 | + | 0.0447068i | \(0.985765\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.28078i | 0.0612681i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.9106 | − | 20.6298i | 0.568463 | − | 0.984607i | −0.428255 | − | 0.903658i | \(-0.640872\pi\) |
0.996718 | − | 0.0809491i | \(-0.0257951\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.48020 | −0.307884 | −0.153942 | − | 0.988080i | \(-0.549197\pi\) | ||||
−0.153942 | + | 0.988080i | \(0.549197\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −29.7886 | + | 51.5953i | −1.41211 | + | 2.44585i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.15811 | + | 3.55539i | −0.290619 | + | 0.167789i | −0.638221 | − | 0.769853i | \(-0.720329\pi\) |
0.347602 | + | 0.937642i | \(0.386996\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.2062 | − | 29.8020i | −0.810207 | − | 1.40332i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.9116 | + | 51.5347i | 0.745948 | + | 2.41599i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.48573 | − | 0.857789i | −0.0694997 | − | 0.0401257i | 0.464847 | − | 0.885391i | \(-0.346109\pi\) |
−0.534347 | + | 0.845265i | \(0.679442\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.1570 | − | 16.2565i | 1.31140 | − | 0.757139i | 0.329075 | − | 0.944304i | \(-0.393263\pi\) |
0.982328 | + | 0.187165i | \(0.0599299\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.37282i | 0.156748i | 0.996924 | + | 0.0783741i | \(0.0249728\pi\) | ||||
−0.996924 | + | 0.0783741i | \(0.975027\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −19.3241 | −0.894212 | −0.447106 | − | 0.894481i | \(-0.647545\pi\) | ||||
−0.447106 | + | 0.894481i | \(0.647545\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.35532 | −0.339637 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 21.1233i | 0.971252i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −36.6841 | + | 21.1796i | −1.68318 | + | 0.971785i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −7.55446 | − | 4.36157i | −0.345172 | − | 0.199285i | 0.317385 | − | 0.948297i | \(-0.397195\pi\) |
−0.662557 | + | 0.749012i | \(0.730529\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8.26789 | + | 7.66732i | 0.376983 | + | 0.349600i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −18.6549 | − | 32.3112i | −0.847076 | − | 1.46718i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10.0832 | − | 5.82155i | 0.456914 | − | 0.263800i | −0.253832 | − | 0.967248i | \(-0.581691\pi\) |
0.710746 | + | 0.703449i | \(0.248358\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.88604 | + | 6.73082i | −0.175375 | + | 0.303758i | −0.940291 | − | 0.340372i | \(-0.889447\pi\) |
0.764916 | + | 0.644130i | \(0.222780\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.7330 | 1.06888 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.02250 | − | 8.69923i | 0.225290 | − | 0.390214i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 20.3434i | − | 0.910695i | −0.890314 | − | 0.455348i | \(-0.849515\pi\) | ||
0.890314 | − | 0.455348i | \(-0.150485\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −10.5761 | − | 18.3183i | −0.471565 | − | 0.816775i | 0.527906 | − | 0.849303i | \(-0.322977\pi\) |
−0.999471 | + | 0.0325282i | \(0.989644\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −34.4240 | − | 19.8747i | −1.53185 | − | 0.884414i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 32.9785 | + | 19.0401i | 1.46175 | + | 0.843939i | 0.999092 | − | 0.0425997i | \(-0.0135640\pi\) |
0.462654 | + | 0.886539i | \(0.346897\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.72178 | − | 9.91041i | −0.253117 | − | 0.438411i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.08003i | 0.400114i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −13.9570 | + | 24.1742i | −0.613827 | + | 1.06318i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −20.7433 | −0.908781 | −0.454390 | − | 0.890803i | \(-0.650143\pi\) | ||||
−0.454390 | + | 0.890803i | \(0.650143\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.47123 | − | 4.28030i | 0.108060 | − | 0.187165i | −0.806925 | − | 0.590655i | \(-0.798870\pi\) |
0.914984 | + | 0.403490i | \(0.132203\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.2630 | + | 10.5441i | −0.795548 | + | 0.459310i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.4262 | + | 19.7908i | 0.496793 | + | 0.860471i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.9087 | + | 16.6078i | 0.775710 | + | 0.719364i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −68.1386 | − | 39.3398i | −2.94589 | − | 1.70081i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 24.8162 | − | 14.3276i | 1.06891 | − | 0.617135i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 43.7196i | 1.87965i | 0.341650 | + | 0.939827i | \(0.389014\pi\) | ||||
−0.341650 | + | 0.939827i | \(0.610986\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 60.9036 | 2.60883 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 39.1028 | 1.67191 | 0.835957 | − | 0.548795i | \(-0.184913\pi\) | ||||
0.835957 | + | 0.548795i | \(0.184913\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 24.3020i | 1.03530i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.13106 | − | 4.69447i | 0.345768 | − | 0.199629i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −20.7774 | − | 11.9958i | −0.880365 | − | 0.508279i | −0.00958646 | − | 0.999954i | \(-0.503052\pi\) |
−0.870779 | + | 0.491675i | \(0.836385\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.42292 | − | 14.3250i | −0.187070 | − | 0.605884i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −5.23814 | − | 9.07273i | −0.220761 | − | 0.382370i | 0.734278 | − | 0.678849i | \(-0.237521\pi\) |
−0.955039 | + | 0.296479i | \(0.904188\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.99582 | + | 5.77109i | −0.420527 | + | 0.242792i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15.3982 | + | 26.6705i | −0.645526 | + | 1.11808i | 0.338653 | + | 0.940911i | \(0.390029\pi\) |
−0.984180 | + | 0.177173i | \(0.943305\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.52126 | −0.398452 | −0.199226 | − | 0.979954i | \(-0.563843\pi\) | ||||
−0.199226 | + | 0.979954i | \(0.563843\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.43927 | − | 4.22493i | 0.101724 | − | 0.176192i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 47.7495i | 1.98784i | 0.110124 | + | 0.993918i | \(0.464875\pi\) | ||||
−0.110124 | + | 0.993918i | \(0.535125\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.50074 | − | 6.06346i | −0.145235 | − | 0.251555i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.70114 | − | 1.55950i | −0.111870 | − | 0.0645880i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 34.1946 | + | 19.7423i | 1.41136 | + | 0.814851i | 0.995517 | − | 0.0945840i | \(-0.0301521\pi\) |
0.415846 | + | 0.909435i | \(0.363485\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.7969 | − | 18.7008i | −0.444879 | − | 0.770553i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 20.0166i | − | 0.821983i | −0.911639 | − | 0.410992i | \(-0.865183\pi\) | ||
0.911639 | − | 0.410992i | \(-0.134817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −24.3584 | + | 42.1900i | −0.998596 | + | 1.72962i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 19.8517 | 0.811120 | 0.405560 | − | 0.914068i | \(-0.367077\pi\) | ||||
0.405560 | + | 0.914068i | \(0.367077\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.85112 | + | 10.1344i | −0.238672 | + | 0.413392i | −0.960334 | − | 0.278854i | \(-0.910045\pi\) |
0.721661 | + | 0.692246i | \(0.243379\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −53.9516 | + | 31.1490i | −2.19344 | + | 1.26639i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.5978 | + | 37.4084i | 0.876626 | + | 1.51836i | 0.855021 | + | 0.518594i | \(0.173544\pi\) |
0.0216048 | + | 0.999767i | \(0.493122\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.40335 | − | 19.3164i | 0.178141 | − | 0.781457i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.4025 | − | 15.8208i | −1.10678 | − | 0.638998i | −0.168784 | − | 0.985653i | \(-0.553984\pi\) |
−0.937993 | + | 0.346655i | \(0.887317\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.6855 | + | 7.90135i | −0.550959 | + | 0.318096i | −0.749509 | − | 0.661995i | \(-0.769710\pi\) |
0.198550 | + | 0.980091i | \(0.436377\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 36.0663i | − | 1.44963i | −0.688945 | − | 0.724814i | \(-0.741926\pi\) | ||
0.688945 | − | 0.724814i | \(-0.258074\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −50.3445 | −2.01701 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 72.8358 | 2.91343 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.1849i | 0.406099i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.5073 | − | 8.95313i | 0.617335 | − | 0.356418i | −0.158496 | − | 0.987360i | \(-0.550664\pi\) |
0.775831 | + | 0.630941i | \(0.217331\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −36.9013 | − | 21.3050i | −1.46438 | − | 0.845462i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.8294 | + | 14.9126i | −0.547940 | + | 0.590859i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.3551 | − | 30.0598i | −0.685483 | − | 1.18729i | −0.973285 | − | 0.229602i | \(-0.926258\pi\) |
0.287801 | − | 0.957690i | \(-0.407076\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.4414 | − | 22.7715i | 1.55542 | − | 0.898020i | 0.557731 | − | 0.830022i | \(-0.311672\pi\) |
0.997685 | − | 0.0679979i | \(-0.0216611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 8.93016 | − | 15.4675i | 0.351081 | − | 0.608090i | −0.635358 | − | 0.772218i | \(-0.719148\pi\) |
0.986439 | + | 0.164128i | \(0.0524809\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 40.0251 | 1.57112 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.8378 | + | 32.6281i | −0.737182 | + | 1.27684i | 0.216577 | + | 0.976265i | \(0.430511\pi\) |
−0.953759 | + | 0.300571i | \(0.902823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 56.1394i | 2.19355i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.3737 | + | 30.0922i | 0.676785 | + | 1.17223i | 0.975944 | + | 0.218023i | \(0.0699607\pi\) |
−0.299159 | + | 0.954203i | \(0.596706\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.0551 | + | 19.6617i | 1.32459 | + | 0.764752i | 0.984457 | − | 0.175626i | \(-0.0561948\pi\) |
0.340132 | + | 0.940378i | \(0.389528\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −43.2014 | − | 24.9423i | −1.67528 | − | 0.967223i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.39944 | − | 2.42390i | −0.0541864 | − | 0.0938537i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.2266i | 1.63014i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.57180 | − | 9.65064i | 0.214777 | − | 0.372005i | −0.738427 | − | 0.674334i | \(-0.764431\pi\) |
0.953204 | + | 0.302329i | \(0.0977642\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.3037 | 0.472868 | 0.236434 | − | 0.971648i | \(-0.424021\pi\) | ||||
0.236434 | + | 0.971648i | \(0.424021\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 15.7640 | − | 27.3040i | 0.604966 | − | 1.04783i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 15.1885 | − | 8.76907i | 0.581171 | − | 0.335539i | −0.180428 | − | 0.983588i | \(-0.557748\pi\) |
0.761598 | + | 0.648049i | \(0.224415\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −25.0246 | − | 43.3439i | −0.956141 | − | 1.65608i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.15834 | + | 0.492015i | 0.0822264 | + | 0.0187443i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.3606 | − | 6.55904i | −0.432177 | − | 0.249518i | 0.268097 | − | 0.963392i | \(-0.413605\pi\) |
−0.700274 | + | 0.713874i | \(0.746939\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 48.9013 | − | 28.2332i | 1.85493 | − | 1.07095i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 22.0610i | 0.835620i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −0.768137 | −0.0290121 | −0.0145061 | − | 0.999895i | \(-0.504618\pi\) | ||||
−0.0145061 | + | 0.999895i | \(0.504618\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.4291 | −0.393340 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 33.5895i | − | 1.26326i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.7905 | + | 16.0449i | −1.04369 | + | 0.602577i | −0.920877 | − | 0.389852i | \(-0.872526\pi\) |
−0.122817 | + | 0.992429i | \(0.539193\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.15379 | + | 1.24349i | 0.0806600 | + | 0.0465691i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 52.4017 | − | 56.5062i | 1.95971 | − | 2.11321i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 5.48856 | + | 9.50647i | 0.204689 | + | 0.354531i | 0.950034 | − | 0.312148i | \(-0.101048\pi\) |
−0.745345 | + | 0.666679i | \(0.767715\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.64493 | + | 3.83645i | −0.247470 | + | 0.142877i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 46.2834 | − | 80.1652i | 1.71892 | − | 2.97726i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −40.9056 | −1.51710 | −0.758552 | − | 0.651612i | \(-0.774093\pi\) | ||||
−0.758552 | + | 0.651612i | \(0.774093\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.77085 | − | 11.7275i | 0.250429 | − | 0.433756i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.18829i | 0.228570i | 0.993448 | + | 0.114285i | \(0.0364577\pi\) | ||||
−0.993448 | + | 0.114285i | \(0.963542\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.25474 | + | 9.10148i | 0.193561 | + | 0.335257i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.2014 | + | 26.6744i | 1.69955 | + | 0.981233i | 0.946185 | + | 0.323626i | \(0.104902\pi\) |
0.753361 | + | 0.657607i | \(0.228431\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −38.6012 | − | 22.2864i | −1.41614 | − | 0.817609i | −0.420183 | − | 0.907439i | \(-0.638034\pi\) |
−0.995957 | + | 0.0898302i | \(0.971368\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −11.5944 | − | 20.0821i | −0.424787 | − | 0.735752i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 66.4867i | − | 2.42937i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.754726 | + | 1.30722i | −0.0275403 | + | 0.0477012i | −0.879467 | − | 0.475960i | \(-0.842101\pi\) |
0.851927 | + | 0.523661i | \(0.175434\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.3737 | 0.777870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.9897 | − | 45.0154i | 0.944611 | − | 1.63611i | 0.188083 | − | 0.982153i | \(-0.439773\pi\) |
0.756528 | − | 0.653961i | \(-0.226894\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.24010 | − | 5.33477i | 0.334953 | − | 0.193385i | −0.323085 | − | 0.946370i | \(-0.604720\pi\) |
0.658038 | + | 0.752985i | \(0.271387\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.7327 | + | 44.5704i | 0.931587 | + | 1.61356i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.1435 | + | 8.38068i | −0.980094 | + | 0.302609i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.20703 | + | 3.00628i | 0.187770 | + | 0.108409i | 0.590938 | − | 0.806717i | \(-0.298758\pi\) |
−0.403168 | + | 0.915126i | \(0.632091\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 34.5464 | − | 19.9454i | 1.24255 | − | 0.717385i | 0.272935 | − | 0.962033i | \(-0.412006\pi\) |
0.969612 | + | 0.244648i | \(0.0786724\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 82.2515i | 2.95456i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.5899 | −0.809367 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.3526 | −0.513576 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 52.8745i | − | 1.88717i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3.03295 | − | 1.75107i | 0.108113 | − | 0.0624190i | −0.444969 | − | 0.895546i | \(-0.646785\pi\) |
0.553081 | + | 0.833127i | \(0.313452\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.44677 | − | 4.87675i | −0.300333 | − | 0.173397i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.84164 | − | 28.6364i | −0.313976 | − | 1.01691i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12.1435 | + | 21.0331i | 0.430144 | + | 0.745031i | 0.996885 | − | 0.0788649i | \(-0.0251296\pi\) |
−0.566742 | + | 0.823896i | \(0.691796\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.4976 | − | 8.94752i | 0.548264 | − | 0.316540i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.17544 | + | 14.1603i | −0.288505 | + | 0.499705i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.74526 | 0.202494 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −9.56441 | + | 16.5660i | −0.336267 | + | 0.582431i | −0.983727 | − | 0.179668i | \(-0.942498\pi\) |
0.647461 | + | 0.762099i | \(0.275831\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 55.1857i | − | 1.93783i | −0.247387 | − | 0.968917i | \(-0.579572\pi\) | ||
0.247387 | − | 0.968917i | \(-0.420428\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.5504 | + | 32.1303i | 0.649793 | + | 1.12547i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0086 | + | 6.93318i | 0.420128 | + | 0.242561i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.2098 | + | 11.6681i | 0.705326 | + | 0.407220i | 0.809328 | − | 0.587357i | \(-0.199832\pi\) |
−0.104002 | + | 0.994577i | \(0.533165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.02679 | − | 1.77846i | −0.0357918 | − | 0.0619931i | 0.847575 | − | 0.530676i | \(-0.178062\pi\) |
−0.883366 | + | 0.468683i | \(0.844729\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.96289i | − | 0.207350i | −0.994611 | − | 0.103675i | \(-0.966940\pi\) | ||
0.994611 | − | 0.103675i | \(-0.0330602\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.28155 | − | 12.6120i | 0.252899 | − | 0.438033i | −0.711424 | − | 0.702763i | \(-0.751949\pi\) |
0.964323 | + | 0.264730i | \(0.0852827\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.3703 | −0.636492 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −30.8604 | + | 53.4517i | −1.06797 | + | 1.84977i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.4990 | − | 24.5368i | 1.46723 | − | 0.847105i | 0.467902 | − | 0.883780i | \(-0.345010\pi\) |
0.999327 | + | 0.0366748i | \(0.0116766\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −12.0534 | − | 20.8770i | −0.415633 | − | 0.719898i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23.7052 | + | 49.2924i | −0.815483 | + | 1.69571i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −45.5907 | − | 26.3218i | −1.56652 | − | 0.904429i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.04020 | − | 0.600562i | 0.0356578 | − | 0.0205870i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 54.6929i | − | 1.87265i | −0.351138 | − | 0.936324i | \(-0.614205\pi\) | ||
0.351138 | − | 0.936324i | \(-0.385795\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −23.2811 | −0.795266 | −0.397633 | − | 0.917545i | \(-0.630168\pi\) | ||||
−0.397633 | + | 0.917545i | \(0.630168\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 43.4229 | 1.48157 | 0.740785 | − | 0.671742i | \(-0.234454\pi\) | ||||
0.740785 | + | 0.671742i | \(0.234454\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7.28977i | − | 0.248147i | −0.992273 | − | 0.124073i | \(-0.960404\pi\) | ||
0.992273 | − | 0.124073i | \(-0.0395958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.79888 | + | 5.08003i | −0.299171 | + | 0.172726i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −11.6179 | − | 6.70759i | −0.394110 | − | 0.227539i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.46928 | − | 5.07200i | −0.185319 | − | 0.171858i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 57.6087 | + | 99.7812i | 1.94753 | + | 3.37322i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 28.7922 | − | 16.6232i | 0.972245 | − | 0.561326i | 0.0723248 | − | 0.997381i | \(-0.476958\pi\) |
0.899920 | + | 0.436055i | \(0.143625\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.09441 | + | 14.0199i | −0.272708 | + | 0.472343i | −0.969554 | − | 0.244877i | \(-0.921252\pi\) |
0.696847 | + | 0.717220i | \(0.254586\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.0492 | 0.674708 | 0.337354 | − | 0.941378i | \(-0.390468\pi\) | ||||
0.337354 | + | 0.941378i | \(0.390468\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −27.1560 | + | 47.0356i | −0.911810 | + | 1.57930i | −0.100304 | + | 0.994957i | \(0.531982\pi\) |
−0.811506 | + | 0.584345i | \(0.801352\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 36.0067i | − | 1.20763i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.16202 | + | 15.8691i | 0.306595 | + | 0.531039i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 19.5204 | + | 11.2701i | 0.652495 | + | 0.376718i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 40.8666 | + | 23.5944i | 1.36298 | + | 0.786916i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.999764 | + | 1.73164i | 0.0333070 | + | 0.0576893i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 74.3511i | 2.47152i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −25.9486 | + | 44.9443i | −0.861610 | + | 1.49235i | 0.00876464 | + | 0.999962i | \(0.497210\pi\) |
−0.870374 | + | 0.492390i | \(0.836123\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.0433 | −0.564669 | −0.282334 | − | 0.959316i | \(-0.591109\pi\) | ||||
−0.282334 | + | 0.959316i | \(0.591109\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.00196 | + | 8.66364i | −0.165541 | + | 0.286725i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −41.0839 | + | 23.7198i | −1.35671 | + | 0.783296i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.03465 | + | 13.9164i | 0.265039 | + | 0.459061i | 0.967574 | − | 0.252589i | \(-0.0812819\pi\) |
−0.702535 | + | 0.711649i | \(0.747949\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.73336 | − | 3.00522i | 0.320377 | − | 0.0989181i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34.4025 | + | 19.8623i | 1.13115 | + | 0.653069i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.87485 | + | 5.70125i | −0.323983 | + | 0.187052i | −0.653167 | − | 0.757214i | \(-0.726560\pi\) |
0.329183 | + | 0.944266i | \(0.393227\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 18.8107i | − | 0.616495i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 69.6078 | 2.27642 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.8213 | −1.10489 | −0.552447 | − | 0.833548i | \(-0.686306\pi\) | ||||
−0.552447 | + | 0.833548i | \(0.686306\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 48.0429i | − | 1.56615i | −0.621925 | − | 0.783077i | \(-0.713649\pi\) | ||
0.621925 | − | 0.783077i | \(-0.286351\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.25313 | − | 1.30085i | 0.0733722 | − | 0.0423614i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.4598 | + | 6.03897i | 0.339898 | + | 0.196240i | 0.660227 | − | 0.751066i | \(-0.270460\pi\) |
−0.320329 | + | 0.947306i | \(0.603793\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.57931 | − | 11.3148i | 0.0837278 | − | 0.367293i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −7.71256 | − | 13.3586i | −0.249834 | − | 0.432726i | 0.713645 | − | 0.700507i | \(-0.247043\pi\) |
−0.963480 | + | 0.267781i | \(0.913710\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −16.6695 | + | 9.62417i | −0.539414 | + | 0.311431i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 21.1466 | − | 36.6269i | 0.682858 | − | 1.18274i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −10.9302 | −0.352587 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −35.4323 | + | 61.3705i | −1.14061 | + | 1.97559i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 49.7289i | − | 1.59917i | −0.600550 | − | 0.799587i | \(-0.705052\pi\) | ||
0.600550 | − | 0.799587i | \(-0.294948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −15.4948 | − | 26.8378i | −0.497253 | − | 0.861268i | 0.502742 | − | 0.864437i | \(-0.332325\pi\) |
−0.999995 | + | 0.00316898i | \(0.998991\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.3231 | + | 23.8579i | 1.32476 | + | 0.764849i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 19.8117 | + | 11.4383i | 0.633831 | + | 0.365943i | 0.782234 | − | 0.622984i | \(-0.214080\pi\) |
−0.148403 | + | 0.988927i | \(0.547413\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.9668 | + | 62.2963i | 1.14950 | + | 1.99100i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 28.0019i | − | 0.893121i | −0.894754 | − | 0.446560i | \(-0.852649\pi\) | ||
0.894754 | − | 0.446560i | \(-0.147351\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.90533 | + | 6.76422i | −0.124434 | + | 0.215526i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.59700 | −0.0507816 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.14274 | − | 14.1036i | 0.258663 | − | 0.448017i | −0.707221 | − | 0.706992i | \(-0.750052\pi\) |
0.965884 | + | 0.258975i | \(0.0833849\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 69.1859 | − | 39.9445i | 2.19334 | − | 1.26633i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −23.1517 | − | 40.1000i | −0.733222 | − | 1.26998i | −0.955499 | − | 0.294995i | \(-0.904682\pi\) |
0.222277 | − | 0.974984i | \(-0.428651\pi\) | |||||||
\(998\) | 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 \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 936.2.bi.c.433.4 | 8 | ||
3.2 | odd | 2 | 312.2.bf.b.121.1 | yes | 8 | ||
4.3 | odd | 2 | 1872.2.by.m.433.4 | 8 | |||
12.11 | even | 2 | 624.2.bv.g.433.1 | 8 | |||
13.10 | even | 6 | inner | 936.2.bi.c.361.1 | 8 | ||
39.17 | odd | 6 | 4056.2.c.p.337.8 | 8 | |||
39.20 | even | 12 | 4056.2.a.be.1.4 | 4 | |||
39.23 | odd | 6 | 312.2.bf.b.49.4 | ✓ | 8 | ||
39.32 | even | 12 | 4056.2.a.bd.1.1 | 4 | |||
39.35 | odd | 6 | 4056.2.c.p.337.1 | 8 | |||
52.23 | odd | 6 | 1872.2.by.m.1297.1 | 8 | |||
156.23 | even | 6 | 624.2.bv.g.49.4 | 8 | |||
156.59 | odd | 12 | 8112.2.a.cs.1.4 | 4 | |||
156.71 | odd | 12 | 8112.2.a.cq.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
312.2.bf.b.49.4 | ✓ | 8 | 39.23 | odd | 6 | ||
312.2.bf.b.121.1 | yes | 8 | 3.2 | odd | 2 | ||
624.2.bv.g.49.4 | 8 | 156.23 | even | 6 | |||
624.2.bv.g.433.1 | 8 | 12.11 | even | 2 | |||
936.2.bi.c.361.1 | 8 | 13.10 | even | 6 | inner | ||
936.2.bi.c.433.4 | 8 | 1.1 | even | 1 | trivial | ||
1872.2.by.m.433.4 | 8 | 4.3 | odd | 2 | |||
1872.2.by.m.1297.1 | 8 | 52.23 | odd | 6 | |||
4056.2.a.bd.1.1 | 4 | 39.32 | even | 12 | |||
4056.2.a.be.1.4 | 4 | 39.20 | even | 12 | |||
4056.2.c.p.337.1 | 8 | 39.35 | odd | 6 | |||
4056.2.c.p.337.8 | 8 | 39.17 | odd | 6 | |||
8112.2.a.cq.1.1 | 4 | 156.71 | odd | 12 | |||
8112.2.a.cs.1.4 | 4 | 156.59 | odd | 12 |