Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6048,2,Mod(3025,6048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6048.3025");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6048 = 2^{5} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6048.c (of order \(2\), degree \(1\), 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: | \(48.2935231425\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.3317760000.5 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 7x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 1512) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3025.4 | ||
Root | \(-0.178197 - 1.40294i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6048.3025 |
Dual form | 6048.2.c.c.3025.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/6048\mathbb{Z}\right)^\times\).
\(n\) | \(2593\) | \(3781\) | \(3809\) | \(4159\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(5\) | − 0.356394i | − 0.159384i | −0.996820 | − | 0.0796921i | \(-0.974606\pi\) | ||||
0.996820 | − | 0.0796921i | \(-0.0253937\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 5.96816i | − 1.79947i | −0.436438 | − | 0.899734i | \(-0.643760\pi\) | ||||
0.436438 | − | 0.899734i | \(-0.356240\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.87298i | 0.796822i | 0.917207 | + | 0.398411i | \(0.130438\pi\) | ||||
−0.917207 | + | 0.398411i | \(0.869562\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.16228 | −0.766965 | −0.383482 | − | 0.923548i | \(-0.625275\pi\) | ||||
−0.383482 | + | 0.923548i | \(0.625275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 0.127017i | − 0.0291396i | −0.999894 | − | 0.0145698i | \(-0.995362\pi\) | ||||
0.999894 | − | 0.0145698i | \(-0.00463788\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.80588 | −0.585067 | −0.292534 | − | 0.956255i | \(-0.594498\pi\) | ||||
−0.292534 | + | 0.956255i | \(0.594498\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.87298 | 0.974597 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.44949i | 0.454859i | 0.973795 | + | 0.227429i | \(0.0730321\pi\) | ||||
−0.973795 | + | 0.227429i | \(0.926968\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.00000 | 1.25724 | 0.628619 | − | 0.777714i | \(-0.283621\pi\) | ||||
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 0.356394i | − 0.0602416i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 1.87298i | − 0.307917i | −0.988077 | − | 0.153958i | \(-0.950798\pi\) | ||||
0.988077 | − | 0.153958i | \(-0.0492021\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.99208 | 1.09198 | 0.545989 | − | 0.837792i | \(-0.316154\pi\) | ||||
0.545989 | + | 0.837792i | \(0.316154\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.12702i | − 0.171868i | −0.996301 | − | 0.0859342i | \(-0.972613\pi\) | ||||
0.996301 | − | 0.0859342i | \(-0.0273875\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −7.34847 | −1.07188 | −0.535942 | − | 0.844255i | \(-0.680044\pi\) | ||||
−0.535942 | + | 0.844255i | \(0.680044\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.12702 | −0.286807 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.63568i | − 0.863892i | −0.901899 | − | 0.431946i | \(-0.857827\pi\) | ||||
0.901899 | − | 0.431946i | \(-0.142173\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 13.7460i | − 1.75999i | −0.474982 | − | 0.879995i | \(-0.657546\pi\) | ||||
0.474982 | − | 0.879995i | \(-0.342454\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.02391 | 0.127001 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.61895i | 1.05297i | 0.850184 | + | 0.526486i | \(0.176491\pi\) | ||||
−0.850184 | + | 0.526486i | \(0.823509\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.96816 | 0.708290 | 0.354145 | − | 0.935190i | \(-0.384772\pi\) | ||||
0.354145 | + | 0.935190i | \(0.384772\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.872983 | 0.102175 | 0.0510875 | − | 0.998694i | \(-0.483731\pi\) | ||||
0.0510875 | + | 0.998694i | \(0.483731\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 5.96816i | − 0.680135i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.6190 | −1.41974 | −0.709871 | − | 0.704331i | \(-0.751247\pi\) | ||||
−0.709871 | + | 0.704331i | \(0.751247\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 6.63568i | − 0.728361i | −0.931328 | − | 0.364180i | \(-0.881349\pi\) | ||||
0.931328 | − | 0.364180i | \(-0.118651\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.12702i | 0.122242i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.99208 | 0.741158 | 0.370579 | − | 0.928801i | \(-0.379159\pi\) | ||||
0.370579 | + | 0.928801i | \(0.379159\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.87298i | 0.301170i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0452680 | −0.00464440 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.74597 | −0.989553 | −0.494776 | − | 0.869020i | \(-0.664750\pi\) | ||||
−0.494776 | + | 0.869020i | \(0.664750\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 11.5347i | − 1.14774i | −0.818946 | − | 0.573871i | \(-0.805441\pi\) | ||||
0.818946 | − | 0.573871i | \(-0.194559\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7460 | 1.05883 | 0.529416 | − | 0.848363i | \(-0.322411\pi\) | ||||
0.529416 | + | 0.848363i | \(0.322411\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 14.3858i | − 1.39073i | −0.718657 | − | 0.695364i | \(-0.755243\pi\) | ||||
0.718657 | − | 0.695364i | \(-0.244757\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 12.7460i | − 1.22084i | −0.792077 | − | 0.610421i | \(-0.791000\pi\) | ||||
0.792077 | − | 0.610421i | \(-0.209000\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.8353 | −1.58373 | −0.791866 | − | 0.610695i | \(-0.790890\pi\) | ||||
−0.791866 | + | 0.610695i | \(0.790890\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000i | 0.0932505i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.16228 | −0.289886 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.6190 | −2.23809 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 3.51867i | − 0.314720i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −10.8730 | −0.964821 | −0.482411 | − | 0.875945i | \(-0.660239\pi\) | ||||
−0.482411 | + | 0.875945i | \(0.660239\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 8.77405i | − 0.766592i | −0.923626 | − | 0.383296i | \(-0.874789\pi\) | ||||
0.923626 | − | 0.383296i | \(-0.125211\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 0.127017i | − 0.0110137i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.58785 | 0.391967 | 0.195983 | − | 0.980607i | \(-0.437210\pi\) | ||||
0.195983 | + | 0.980607i | \(0.437210\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.0000i | 1.18746i | 0.804663 | + | 0.593732i | \(0.202346\pi\) | ||||
−0.804663 | + | 0.593732i | \(0.797654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 17.1464 | 1.43386 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.872983 | 0.0724973 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.79796i | 0.802680i | 0.915929 | + | 0.401340i | \(0.131455\pi\) | ||||
−0.915929 | + | 0.401340i | \(0.868545\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000 | 0.976546 | 0.488273 | − | 0.872691i | \(-0.337627\pi\) | ||||
0.488273 | + | 0.872691i | \(0.337627\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 2.49476i | − 0.200384i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.12702i | 0.568798i | 0.958706 | + | 0.284399i | \(0.0917940\pi\) | ||||
−0.958706 | + | 0.284399i | \(0.908206\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.80588 | −0.221135 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 22.8730i | 1.79155i | 0.444507 | + | 0.895775i | \(0.353379\pi\) | ||||
−0.444507 | + | 0.895775i | \(0.646621\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.42558 | 0.110314 | 0.0551572 | − | 0.998478i | \(-0.482434\pi\) | ||||
0.0551572 | + | 0.998478i | \(0.482434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.74597 | 0.365074 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 18.2156i | − 1.38491i | −0.721462 | − | 0.692454i | \(-0.756530\pi\) | ||||
0.721462 | − | 0.692454i | \(-0.243470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 4.87298 | 0.368363 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 8.77405i | − 0.655803i | −0.944712 | − | 0.327901i | \(-0.893659\pi\) | ||||
0.944712 | − | 0.327901i | \(-0.106341\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 21.7460i | − 1.61636i | −0.588932 | − | 0.808182i | \(-0.700451\pi\) | ||||
0.588932 | − | 0.808182i | \(-0.299549\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.667520 | −0.0490770 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 18.8730i | 1.38013i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.7795 | −1.57591 | −0.787956 | − | 0.615731i | \(-0.788861\pi\) | ||||
−0.787956 | + | 0.615731i | \(0.788861\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.49193 | −0.683244 | −0.341622 | − | 0.939837i | \(-0.610976\pi\) | ||||
−0.341622 | + | 0.939837i | \(0.610976\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.04783i | 0.145902i | 0.997336 | + | 0.0729508i | \(0.0232416\pi\) | ||||
−0.997336 | + | 0.0729508i | \(0.976758\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.127017 | −0.00900397 | −0.00450199 | − | 0.999990i | \(-0.501433\pi\) | ||||
−0.00450199 | + | 0.999990i | \(0.501433\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.44949i | 0.171920i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 2.49193i | − 0.174044i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.758056 | −0.0524358 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 20.0000i | − 1.37686i | −0.725304 | − | 0.688428i | \(-0.758301\pi\) | ||||
0.725304 | − | 0.688428i | \(-0.241699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.401662 | −0.0273931 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.00000 | 0.475191 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 9.08517i | − 0.611135i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.61895 | −0.510203 | −0.255101 | − | 0.966914i | \(-0.582109\pi\) | ||||
−0.255101 | + | 0.966914i | \(0.582109\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.9205i | 1.72040i | 0.509955 | + | 0.860201i | \(0.329662\pi\) | ||||
−0.509955 | + | 0.860201i | \(0.670338\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 15.7460i | − 1.04052i | −0.854007 | − | 0.520261i | \(-0.825835\pi\) | ||||
0.854007 | − | 0.520261i | \(-0.174165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.61177 | 0.367639 | 0.183820 | − | 0.982960i | \(-0.441154\pi\) | ||||
0.183820 | + | 0.982960i | \(0.441154\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.61895i | 0.170841i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.2474 | −0.792222 | −0.396111 | − | 0.918203i | \(-0.629640\pi\) | ||||
−0.396111 | + | 0.918203i | \(0.629640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 28.6190 | 1.84351 | 0.921754 | − | 0.387774i | \(-0.126756\pi\) | ||||
0.921754 | + | 0.387774i | \(0.126756\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 0.356394i | − 0.0227692i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.364917 | 0.0232191 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 16.8353i | − 1.06263i | −0.847173 | − | 0.531317i | \(-0.821697\pi\) | ||||
0.847173 | − | 0.531317i | \(-0.178303\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 16.7460i | 1.05281i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −20.0428 | −1.25024 | −0.625119 | − | 0.780529i | \(-0.714950\pi\) | ||||
−0.625119 | + | 0.780529i | \(0.714950\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 1.87298i | − 0.116382i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2.80588 | 0.173018 | 0.0865091 | − | 0.996251i | \(-0.472429\pi\) | ||||
0.0865091 | + | 0.996251i | \(0.472429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 10.5560i | − 0.643612i | −0.946806 | − | 0.321806i | \(-0.895710\pi\) | ||||
0.946806 | − | 0.321806i | \(-0.104290\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 19.7460 | 1.19948 | 0.599741 | − | 0.800194i | \(-0.295270\pi\) | ||||
0.599741 | + | 0.800194i | \(0.295270\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 29.0828i | − 1.75376i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 5.87298i | − 0.352873i | −0.984312 | − | 0.176437i | \(-0.943543\pi\) | ||||
0.984312 | − | 0.176437i | \(-0.0564571\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.0454 | 1.31512 | 0.657559 | − | 0.753403i | \(-0.271589\pi\) | ||||
0.657559 | + | 0.753403i | \(0.271589\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 11.4919i | − 0.683125i | −0.939859 | − | 0.341562i | \(-0.889044\pi\) | ||||
0.939859 | − | 0.341562i | \(-0.110956\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.99208 | 0.412729 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 31.8434i | − 1.86031i | −0.367168 | − | 0.930155i | \(-0.619673\pi\) | ||||
0.367168 | − | 0.930155i | \(-0.380327\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.36492 | −0.137691 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 8.06126i | − 0.466195i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.12702i | − 0.0649602i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.89898 | −0.280515 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 29.6190i | − 1.69044i | −0.534416 | − | 0.845221i | \(-0.679469\pi\) | ||||
0.534416 | − | 0.845221i | \(-0.320531\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −20.7104 | −1.17438 | −0.587189 | − | 0.809450i | \(-0.699765\pi\) | ||||
−0.587189 | + | 0.809450i | \(0.699765\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.87298 | 0.162391 | 0.0811953 | − | 0.996698i | \(-0.474126\pi\) | ||||
0.0811953 | + | 0.996698i | \(0.474126\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 13.6730i | − 0.767954i | −0.923343 | − | 0.383977i | \(-0.874554\pi\) | ||||
0.923343 | − | 0.383977i | \(-0.125446\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.6190 | 0.818504 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.401662i | 0.0223491i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 14.0000i | 0.776580i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.34847 | −0.405134 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000i | 0.549650i | 0.961494 | + | 0.274825i | \(0.0886199\pi\) | ||||
−0.961494 | + | 0.274825i | \(0.911380\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.07174 | 0.167827 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.25403 | −0.177258 | −0.0886292 | − | 0.996065i | \(-0.528249\pi\) | ||||
−0.0886292 | + | 0.996065i | \(0.528249\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 41.7771i | − 2.26236i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 36.4765i | 1.95816i | 0.203475 | + | 0.979080i | \(0.434777\pi\) | ||||
−0.203475 | + | 0.979080i | \(0.565223\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.4919i | 1.25749i | 0.777610 | + | 0.628747i | \(0.216432\pi\) | ||||
−0.777610 | + | 0.628747i | \(0.783568\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −13.3166 | −0.708773 | −0.354386 | − | 0.935099i | \(-0.615310\pi\) | ||||
−0.354386 | + | 0.935099i | \(0.615310\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 2.12702i | − 0.112890i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 29.1733 | 1.53971 | 0.769854 | − | 0.638221i | \(-0.220329\pi\) | ||||
0.769854 | + | 0.638221i | \(0.220329\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 18.9839 | 0.999151 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 0.311126i | − 0.0162851i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −21.8730 | −1.14176 | −0.570880 | − | 0.821033i | \(-0.693398\pi\) | ||||
−0.570880 | + | 0.821033i | \(0.693398\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 28.2379i | − 1.46210i | −0.682322 | − | 0.731052i | \(-0.739030\pi\) | ||||
0.682322 | − | 0.731052i | \(-0.260970\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −7.03734 | −0.362442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.87298i | 0.455775i | 0.973688 | + | 0.227887i | \(0.0731818\pi\) | ||||
−0.973688 | + | 0.227887i | \(0.926818\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 17.4576 | 0.892039 | 0.446020 | − | 0.895023i | \(-0.352841\pi\) | ||||
0.446020 | + | 0.895023i | \(0.352841\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.12702 | −0.108403 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 15.4097i | − 0.781304i | −0.920538 | − | 0.390652i | \(-0.872250\pi\) | ||||
0.920538 | − | 0.390652i | \(-0.127750\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.87298 | 0.448726 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.49732i | 0.226285i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0000i | 0.501886i | 0.968002 | + | 0.250943i | \(0.0807406\pi\) | ||||
−0.968002 | + | 0.250943i | \(0.919259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.5242 | −0.825178 | −0.412589 | − | 0.910917i | \(-0.635375\pi\) | ||||
−0.412589 | + | 0.910917i | \(0.635375\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20.1109i | 1.00179i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −11.1783 | −0.554086 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −12.3649 | −0.611406 | −0.305703 | − | 0.952127i | \(-0.598891\pi\) | ||||
−0.305703 | + | 0.952127i | \(0.598891\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 6.63568i | − 0.326521i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.36492 | −0.116089 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 28.7716i | − 1.40559i | −0.711394 | − | 0.702793i | \(-0.751936\pi\) | ||||
0.711394 | − | 0.702793i | \(-0.248064\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.1109i | 0.931407i | 0.884941 | + | 0.465704i | \(0.154199\pi\) | ||||
−0.884941 | + | 0.465704i | \(0.845801\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −15.4097 | −0.747482 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 13.7460i | − 0.665214i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 23.1146 | 1.11339 | 0.556695 | − | 0.830717i | \(-0.312069\pi\) | ||||
0.556695 | + | 0.830717i | \(0.312069\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.87298 | −0.234181 | −0.117090 | − | 0.993121i | \(-0.537357\pi\) | ||||
−0.117090 | + | 0.993121i | \(0.537357\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.356394i | 0.0170486i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.7460 | −1.22879 | −0.614394 | − | 0.788999i | \(-0.710599\pi\) | ||||
−0.614394 | + | 0.788999i | \(0.710599\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 27.7024i | − 1.31618i | −0.752938 | − | 0.658091i | \(-0.771364\pi\) | ||||
0.752938 | − | 0.658091i | \(-0.228636\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 2.49193i | − 0.118129i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.9100 | 1.45873 | 0.729366 | − | 0.684123i | \(-0.239815\pi\) | ||||
0.729366 | + | 0.684123i | \(0.239815\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 41.7298i | − 1.96498i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.02391 | 0.0480018 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.25403 | 0.432885 | 0.216443 | − | 0.976295i | \(-0.430555\pi\) | ||||
0.216443 | + | 0.976295i | \(0.430555\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 13.9389i | 0.649198i | 0.945852 | + | 0.324599i | \(0.105229\pi\) | ||||
−0.945852 | + | 0.324599i | \(0.894771\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.508067 | −0.0236119 | −0.0118059 | − | 0.999930i | \(-0.503758\pi\) | ||||
−0.0118059 | + | 0.999930i | \(0.503758\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 0.401662i | − 0.0185867i | −0.999957 | − | 0.00929335i | \(-0.997042\pi\) | ||||
0.999957 | − | 0.00929335i | \(-0.00295821\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.61895i | 0.397986i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.72622 | −0.309272 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 0.618950i | − 0.0283994i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.712788 | −0.0325681 | −0.0162841 | − | 0.999867i | \(-0.505184\pi\) | ||||
−0.0162841 | + | 0.999867i | \(0.505184\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.38105 | 0.245355 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.47340i | 0.157719i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.1109 | −1.18320 | −0.591599 | − | 0.806233i | \(-0.701503\pi\) | ||||
−0.591599 | + | 0.806233i | \(0.701503\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.4072i | 0.605057i | 0.953140 | + | 0.302528i | \(0.0978307\pi\) | ||||
−0.953140 | + | 0.302528i | \(0.902169\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 7.74597i | − 0.348861i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.96816 | 0.267709 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 34.3649i | − 1.53838i | −0.639017 | − | 0.769192i | \(-0.720659\pi\) | ||||
0.639017 | − | 0.769192i | \(-0.279341\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 7.34847 | 0.327652 | 0.163826 | − | 0.986489i | \(-0.447616\pi\) | ||||
0.163826 | + | 0.986489i | \(0.447616\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.11088 | −0.182932 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 0.311126i | − 0.0137904i | −0.999976 | − | 0.00689521i | \(-0.997805\pi\) | ||||
0.999976 | − | 0.00689521i | \(-0.00219483\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0.872983 | 0.0386185 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3.82980i | − 0.168761i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.8569i | 1.92882i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 29.8408 | 1.30735 | 0.653675 | − | 0.756776i | \(-0.273226\pi\) | ||||
0.653675 | + | 0.756776i | \(0.273226\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.7460i | 1.51934i | 0.650312 | + | 0.759668i | \(0.274638\pi\) | ||||
−0.650312 | + | 0.759668i | \(0.725362\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.1359 | −0.964257 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.1270 | −0.657696 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 20.0881i | 0.870113i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.12702 | −0.221660 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.96816i | − 0.257067i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.8569i | 1.32664i | 0.748336 | + | 0.663320i | \(0.230853\pi\) | ||||
−0.748336 | + | 0.663320i | \(0.769147\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.54259 | −0.194583 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 39.2379i | − 1.67769i | −0.544369 | − | 0.838846i | \(-0.683231\pi\) | ||||
0.544369 | − | 0.838846i | \(-0.316769\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.311126 | 0.0132544 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.6190 | −0.536612 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 9.17571i | − 0.388787i | −0.980924 | − | 0.194394i | \(-0.937726\pi\) | ||||
0.980924 | − | 0.194394i | \(-0.0622739\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.23790 | 0.136949 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.34847i | 0.309701i | 0.987938 | + | 0.154851i | \(0.0494896\pi\) | ||||
−0.987938 | + | 0.154851i | \(0.950510\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.00000i | 0.252422i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.52123 | 0.231462 | 0.115731 | − | 0.993281i | \(-0.463079\pi\) | ||||
0.115731 | + | 0.993281i | \(0.463079\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.9839i | 1.38033i | 0.723651 | + | 0.690166i | \(0.242462\pi\) | ||||
−0.723651 | + | 0.690166i | \(0.757538\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.6730 | −0.570205 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.2540 | −0.926448 | −0.463224 | − | 0.886241i | \(-0.653307\pi\) | ||||
−0.463224 | + | 0.886241i | \(0.653307\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 6.63568i | − 0.275294i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 37.8568i | − 1.56252i | −0.624208 | − | 0.781259i | \(-0.714578\pi\) | ||||
0.624208 | − | 0.781259i | \(-0.285422\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − 0.889117i | − 0.0366354i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.8035 | 0.936426 | 0.468213 | − | 0.883616i | \(-0.344898\pi\) | ||||
0.468213 | + | 0.883616i | \(0.344898\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.12702i | 0.0462032i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −41.3755 | −1.69056 | −0.845278 | − | 0.534327i | \(-0.820565\pi\) | ||||
−0.845278 | + | 0.534327i | \(0.820565\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 32.1109 | 1.30983 | 0.654915 | − | 0.755702i | \(-0.272704\pi\) | ||||
0.654915 | + | 0.755702i | \(0.272704\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.77405i | 0.356716i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −15.2379 | −0.618487 | −0.309244 | − | 0.950983i | \(-0.600076\pi\) | ||||
−0.309244 | + | 0.950983i | \(0.600076\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 21.1120i | − 0.854101i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 40.2379i | − 1.62519i | −0.582826 | − | 0.812597i | \(-0.698053\pi\) | ||||
0.582826 | − | 0.812597i | \(-0.301947\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.7209 | −0.632898 | −0.316449 | − | 0.948610i | \(-0.602491\pi\) | ||||
−0.316449 | + | 0.948610i | \(0.602491\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 0.491933i | − 0.0197725i | −0.999951 | − | 0.00988624i | \(-0.996853\pi\) | ||||
0.999951 | − | 0.00988624i | \(-0.00314694\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.99208 | 0.280132 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.1109 | 0.924435 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.92289i | 0.236161i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.87298 | 0.353228 | 0.176614 | − | 0.984280i | \(-0.443486\pi\) | ||||
0.176614 | + | 0.984280i | \(0.443486\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.87507i | 0.153777i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 2.87298i | 0.113832i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.1703 | −0.717685 | −0.358843 | − | 0.933398i | \(-0.616829\pi\) | ||||
−0.358843 | + | 0.933398i | \(0.616829\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 8.38105i | − 0.330516i | −0.986250 | − | 0.165258i | \(-0.947154\pi\) | ||||
0.986250 | − | 0.165258i | \(-0.0528457\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.4232 | 0.842231 | 0.421116 | − | 0.907007i | \(-0.361639\pi\) | ||||
0.421116 | + | 0.907007i | \(0.361639\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −39.6028 | −1.55455 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 0.311126i | 0.0121753i | 0.999981 | + | 0.00608765i | \(0.00193777\pi\) | ||||
−0.999981 | + | 0.00608765i | \(0.998062\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.12702 | −0.122183 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 35.3620i | 1.37751i | 0.724994 | + | 0.688755i | \(0.241842\pi\) | ||||
−0.724994 | + | 0.688755i | \(0.758158\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 45.8569i | 1.78362i | 0.452405 | + | 0.891812i | \(0.350566\pi\) | ||||
−0.452405 | + | 0.891812i | \(0.649434\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.0452680 | −0.00175542 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 6.87298i | − 0.266123i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −82.0381 | −3.16705 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.4919 | 1.13683 | 0.568415 | − | 0.822742i | \(-0.307557\pi\) | ||||
0.568415 | + | 0.822742i | \(0.307557\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 17.9045i | − 0.688125i | −0.938947 | − | 0.344063i | \(-0.888197\pi\) | ||||
0.938947 | − | 0.344063i | \(-0.111803\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −9.74597 | −0.374016 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 9.44157i | 0.361271i | 0.983550 | + | 0.180636i | \(0.0578155\pi\) | ||||
−0.983550 | + | 0.180636i | \(0.942184\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 1.63508i | − 0.0624733i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 22.0000i | − 0.836919i | −0.908235 | − | 0.418460i | \(-0.862570\pi\) | ||||
0.908235 | − | 0.418460i | \(-0.137430\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.98952 | 0.189263 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.1109 | −0.837509 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.7692i | 1.84199i | 0.389577 | + | 0.920994i | \(0.372621\pi\) | ||||
−0.389577 | + | 0.920994i | \(0.627379\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.237900 | −0.00897257 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 11.5347i | − 0.433806i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 21.2540i | − 0.798212i | −0.916905 | − | 0.399106i | \(-0.869321\pi\) | ||||
0.916905 | − | 0.399106i | \(-0.130679\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19.6412 | −0.735568 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 6.11088i | − 0.228534i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.8329 | 1.37363 | 0.686817 | − | 0.726830i | \(-0.259007\pi\) | ||||
0.686817 | + | 0.726830i | \(0.259007\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10.7460 | 0.400201 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11.9363i | 0.443304i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.49193 | −0.129509 | −0.0647543 | − | 0.997901i | \(-0.520626\pi\) | ||||
−0.0647543 | + | 0.997901i | \(0.520626\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.56394i | 0.131817i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 8.36492i | − 0.308965i | −0.987996 | − | 0.154483i | \(-0.950629\pi\) | ||||
0.987996 | − | 0.154483i | \(-0.0493711\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 51.4393 | 1.89479 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 0.254033i | − 0.00934477i | −0.999989 | − | 0.00467238i | \(-0.998513\pi\) | ||||
0.999989 | − | 0.00467238i | \(-0.00148727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 38.3037 | 1.40523 | 0.702614 | − | 0.711571i | \(-0.252016\pi\) | ||||
0.702614 | + | 0.711571i | \(0.252016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.49193 | 0.127935 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 14.3858i | − 0.525646i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.3488 | 1.87374 | 0.936872 | − | 0.349673i | \(-0.113707\pi\) | ||||
0.936872 | + | 0.349673i | \(0.113707\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 4.27673i | − 0.155646i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 25.7460i | 0.935753i | 0.883794 | + | 0.467877i | \(0.154981\pi\) | ||||
−0.883794 | + | 0.467877i | \(0.845019\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.6945 | −1.25768 | −0.628838 | − | 0.777537i | \(-0.716469\pi\) | ||||
−0.628838 | + | 0.777537i | \(0.716469\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 12.7460i | − 0.461435i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 19.0642 | 0.688368 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.6351 | 0.419572 | 0.209786 | − | 0.977747i | \(-0.432723\pi\) | ||||
0.209786 | + | 0.977747i | \(0.432723\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.0001i | 0.791290i | 0.918404 | + | 0.395645i | \(0.129479\pi\) | ||||
−0.918404 | + | 0.395645i | \(0.870521\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 34.1109 | 1.22530 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 0.888110i | − 0.0318198i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 35.6190i | − 1.27455i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.54003 | 0.0906574 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.25403i | 0.151640i | 0.997122 | + | 0.0758200i | \(0.0241574\pi\) | ||||
−0.997122 | + | 0.0758200i | \(0.975843\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.8353 | −0.598594 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 39.4919 | 1.40240 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 31.2664i | 1.10751i | 0.832679 | + | 0.553756i | \(0.186806\pi\) | ||||
−0.832679 | + | 0.553756i | \(0.813194\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.2379 | 0.822098 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 5.21011i | − 0.183861i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.00000i | 0.0352454i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.58785 | −0.161300 | −0.0806502 | − | 0.996742i | \(-0.525700\pi\) | ||||
−0.0806502 | + | 0.996742i | \(0.525700\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 41.9839i | − 1.47425i | −0.675755 | − | 0.737126i | \(-0.736182\pi\) | ||||
0.675755 | − | 0.737126i | \(-0.263818\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 8.15179 | 0.285545 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.143150 | −0.00500818 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.1359i | 0.772550i | 0.922384 | + | 0.386275i | \(0.126238\pi\) | ||||
−0.922384 | + | 0.386275i | \(0.873762\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 37.4919 | 1.30689 | 0.653443 | − | 0.756975i | \(-0.273324\pi\) | ||||
0.653443 | + | 0.756975i | \(0.273324\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.1519i | 1.04849i | 0.851569 | + | 0.524243i | \(0.175652\pi\) | ||||
−0.851569 | + | 0.524243i | \(0.824348\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.36492i | 0.0821370i | 0.999156 | + | 0.0410685i | \(0.0130762\pi\) | ||||
−0.999156 | + | 0.0410685i | \(0.986924\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.16228 | −0.109566 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 0.508067i | − 0.0175824i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 37.5457 | 1.29622 | 0.648110 | − | 0.761547i | \(-0.275560\pi\) | ||||
0.648110 | + | 0.761547i | \(0.275560\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0000 | 0.793103 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 1.69143i | − 0.0581871i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −24.6190 | −0.845917 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.25537i | 0.180152i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.23790i | 0.179342i | 0.995971 | + | 0.0896711i | \(0.0285816\pi\) | ||||
−0.995971 | + | 0.0896711i | \(0.971418\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −47.6095 | −1.62631 | −0.813155 | − | 0.582048i | \(-0.802252\pi\) | ||||
−0.813155 | + | 0.582048i | \(0.802252\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 31.8730i | 1.08749i | 0.839250 | + | 0.543746i | \(0.182995\pi\) | ||||
−0.839250 | + | 0.543746i | \(0.817005\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −26.3221 | −0.896016 | −0.448008 | − | 0.894030i | \(-0.647866\pi\) | ||||
−0.448008 | + | 0.894030i | \(0.647866\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −6.49193 | −0.220732 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 75.3119i | 2.55478i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −24.7621 | −0.839032 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 3.51867i | − 0.118953i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.4919i | 0.455590i | 0.973709 | + | 0.227795i | \(0.0731516\pi\) | ||||
−0.973709 | + | 0.227795i | \(0.926848\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43.4233 | 1.46297 | 0.731484 | − | 0.681859i | \(-0.238828\pi\) | ||||
0.731484 | + | 0.681859i | \(0.238828\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15.2379i | 0.512796i | 0.966571 | + | 0.256398i | \(0.0825358\pi\) | ||||
−0.966571 | + | 0.256398i | \(0.917464\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −48.0564 | −1.61358 | −0.806788 | − | 0.590841i | \(-0.798796\pi\) | ||||
−0.806788 | + | 0.590841i | \(0.798796\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −10.8730 | −0.364668 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.933378i | 0.0312343i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.12702 | −0.104525 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.1464i | 0.571865i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.75013 | −0.257623 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.00000i | 0.265636i | 0.991140 | + | 0.132818i | \(0.0424025\pi\) | ||||
−0.991140 | + | 0.132818i | \(0.957597\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.3595 | 1.10525 | 0.552624 | − | 0.833430i | \(-0.313626\pi\) | ||||
0.552624 | + | 0.833430i | \(0.313626\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −39.6028 | −1.31066 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 8.77405i | − 0.289744i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 14.5081 | 0.478577 | 0.239288 | − | 0.970949i | \(-0.423086\pi\) | ||||
0.239288 | + | 0.970949i | \(0.423086\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 17.1464i | 0.564382i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 9.12702i | − 0.300094i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.4710 | 0.770058 | 0.385029 | − | 0.922904i | \(-0.374191\pi\) | ||||
0.385029 | + | 0.922904i | \(0.374191\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 0.127017i | − 0.00416280i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 6.72622 | 0.219971 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.4919 | 1.35548 | 0.677741 | − | 0.735301i | \(-0.262959\pi\) | ||||
0.677741 | + | 0.735301i | \(0.262959\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 11.4894i | − 0.374544i | −0.982308 | − | 0.187272i | \(-0.940036\pi\) | ||||
0.982308 | − | 0.187272i | \(-0.0599645\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −19.6190 | −0.638881 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 2.00256i | − 0.0650745i | −0.999471 | − | 0.0325372i | \(-0.989641\pi\) | ||||
0.999471 | − | 0.0325372i | \(-0.0103587\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.50807i | 0.0814153i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −0.311126 | −0.0100784 | −0.00503918 | − | 0.999987i | \(-0.501604\pi\) | ||||
−0.00503918 | + | 0.999987i | \(0.501604\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7.76210i | 0.251176i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.58785 | 0.148150 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18.0000 | 0.580645 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.38287i | 0.108898i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −25.2379 | −0.811596 | −0.405798 | − | 0.913963i | \(-0.633006\pi\) | ||||
−0.405798 | + | 0.913963i | \(0.633006\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 13.7636i | − 0.441694i | −0.975309 | − | 0.220847i | \(-0.929118\pi\) | ||||
0.975309 | − | 0.220847i | \(-0.0708821\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0000i | 0.448819i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.1599 | 0.740949 | 0.370475 | − | 0.928843i | \(-0.379195\pi\) | ||||
0.370475 | + | 0.928843i | \(0.379195\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 41.7298i | − 1.33369i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −53.6682 | −1.71175 | −0.855875 | − | 0.517183i | \(-0.826981\pi\) | ||||
−0.855875 | + | 0.517183i | \(0.826981\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.729833 | 0.0232544 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.16228i | 0.100555i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −17.3810 | −0.552127 | −0.276064 | − | 0.961139i | \(-0.589030\pi\) | ||||
−0.276064 | + | 0.961139i | \(0.589030\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.0452680i | 0.00143509i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 18.0000i | 0.570066i | 0.958518 | + | 0.285033i | \(0.0920045\pi\) | ||||
−0.958518 | + | 0.285033i | \(0.907995\pi\) | |||||||
\(998\) | 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 | 6048.2.c.c.3025.4 | 8 | ||
3.2 | odd | 2 | inner | 6048.2.c.c.3025.6 | 8 | ||
4.3 | odd | 2 | 1512.2.c.c.757.8 | yes | 8 | ||
8.3 | odd | 2 | 1512.2.c.c.757.7 | yes | 8 | ||
8.5 | even | 2 | inner | 6048.2.c.c.3025.5 | 8 | ||
12.11 | even | 2 | 1512.2.c.c.757.1 | ✓ | 8 | ||
24.5 | odd | 2 | inner | 6048.2.c.c.3025.3 | 8 | ||
24.11 | even | 2 | 1512.2.c.c.757.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.c.c.757.1 | ✓ | 8 | 12.11 | even | 2 | ||
1512.2.c.c.757.2 | yes | 8 | 24.11 | even | 2 | ||
1512.2.c.c.757.7 | yes | 8 | 8.3 | odd | 2 | ||
1512.2.c.c.757.8 | yes | 8 | 4.3 | odd | 2 | ||
6048.2.c.c.3025.3 | 8 | 24.5 | odd | 2 | inner | ||
6048.2.c.c.3025.4 | 8 | 1.1 | even | 1 | trivial | ||
6048.2.c.c.3025.5 | 8 | 8.5 | even | 2 | inner | ||
6048.2.c.c.3025.6 | 8 | 3.2 | odd | 2 | inner |