Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,1,Mod(59,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, base_ring=CyclotomicField(156))
chi = DirichletCharacter(H, H._module([78, 26, 35]))
N = Newforms(chi, 1, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3549.59");
S:= CuspForms(chi, 1);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 1 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.ep (of order \(156\), degree \(48\), 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: | \(1.77118172983\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Coefficient field: | \(\Q(\zeta_{156})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{48} + x^{46} - x^{42} - x^{40} + x^{36} + x^{34} - x^{30} - x^{28} + x^{24} - x^{20} - x^{18} + \cdots + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Projective image: | \(D_{156}\) |
Projective field: | Galois closure of \(\mathbb{Q}[x]/(x^{156} - \cdots)\) |
Embedding invariants
Embedding label | 2147.1 | ||
Root | \(-0.960518 - 0.278217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.2147 |
Dual form | 3549.1.ep.a.605.1 |
$q$-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 \(\left(\mathbb{Z}/3549\mathbb{Z}\right)^\times\).
\(n\) | \(1184\) | \(1522\) | \(3382\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{97}{156}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.616719 | − | 0.787183i | \(-0.711538\pi\) | ||||
0.616719 | + | 0.787183i | \(0.288462\pi\) | |||||||
\(3\) | −0.979791 | + | 0.200026i | −0.979791 | + | 0.200026i | ||||
\(4\) | −0.239316 | + | 0.970942i | −0.239316 | + | 0.970942i | ||||
\(5\) | 0 | 0 | 0.735006 | − | 0.678061i | \(-0.237179\pi\) | ||||
−0.735006 | + | 0.678061i | \(0.762821\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.999189 | − | 0.0402659i | −0.999189 | − | 0.0402659i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.919979 | − | 0.391967i | 0.919979 | − | 0.391967i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.373361 | − | 0.927686i | \(-0.621795\pi\) | ||||
0.373361 | + | 0.927686i | \(0.378205\pi\) | |||||||
\(12\) | 0.0402659 | − | 0.999189i | 0.0402659 | − | 0.999189i | ||||
\(13\) | −0.866025 | + | 0.500000i | −0.866025 | + | 0.500000i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.885456 | − | 0.464723i | −0.885456 | − | 0.464723i | ||||
\(17\) | 0 | 0 | 0.354605 | − | 0.935016i | \(-0.384615\pi\) | ||||
−0.354605 | + | 0.935016i | \(0.615385\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0727294 | − | 0.271430i | 0.0727294 | − | 0.271430i | −0.919979 | − | 0.391967i | \(-0.871795\pi\) |
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.987050 | − | 0.160411i | 0.987050 | − | 0.160411i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0804666 | − | 0.996757i | 0.0804666 | − | 0.996757i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.822984 | + | 0.568065i | −0.822984 | + | 0.568065i | ||||
\(28\) | 0.278217 | − | 0.960518i | 0.278217 | − | 0.960518i | ||||
\(29\) | 0 | 0 | 0.919979 | − | 0.391967i | \(-0.128205\pi\) | ||||
−0.919979 | + | 0.391967i | \(0.871795\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.974631 | + | 0.347345i | −0.974631 | + | 0.347345i | −0.774605 | − | 0.632445i | \(-0.782051\pi\) |
−0.200026 | + | 0.979791i | \(0.564103\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.160411 | + | 0.987050i | 0.160411 | + | 0.987050i | ||||
\(37\) | 0.292510 | − | 1.59617i | 0.292510 | − | 1.59617i | −0.428693 | − | 0.903450i | \(-0.641026\pi\) |
0.721202 | − | 0.692724i | \(-0.243590\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.748511 | − | 0.663123i | 0.748511 | − | 0.663123i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | −0.446798 | − | 0.894635i | \(-0.647436\pi\) | ||||
0.446798 | + | 0.894635i | \(0.352564\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.289847 | + | 0.137534i | −0.289847 | + | 0.137534i | −0.568065 | − | 0.822984i | \(-0.692308\pi\) |
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.482459 | − | 0.875918i | \(-0.660256\pi\) | ||||
0.482459 | + | 0.875918i | \(0.339744\pi\) | |||||||
\(48\) | 0.960518 | + | 0.278217i | 0.960518 | + | 0.278217i | ||||
\(49\) | 0.996757 | + | 0.0804666i | 0.996757 | + | 0.0804666i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.278217 | − | 0.960518i | −0.278217 | − | 0.960518i | ||||
\(53\) | 0 | 0 | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) | ||||
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0169667 | + | 0.280492i | −0.0169667 | + | 0.280492i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.297503 | − | 0.954721i | \(-0.403846\pi\) | ||||
−0.297503 | + | 0.954721i | \(0.596154\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.431017 | + | 0.351915i | 0.431017 | + | 0.351915i | 0.822984 | − | 0.568065i | \(-0.192308\pi\) |
−0.391967 | + | 0.919979i | \(0.628205\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.935016 | + | 0.354605i | −0.935016 | + | 0.354605i | ||||
\(64\) | 0.663123 | − | 0.748511i | 0.663123 | − | 0.748511i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.173931 | − | 0.315777i | −0.173931 | − | 0.315777i | 0.774605 | − | 0.632445i | \(-0.217949\pi\) |
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | −0.834256 | − | 0.551377i | \(-0.814103\pi\) | ||||
0.834256 | + | 0.551377i | \(0.185897\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.0617411 | − | 0.435071i | 0.0617411 | − | 0.435071i | −0.935016 | − | 0.354605i | \(-0.884615\pi\) |
0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.120537 | + | 0.992709i | 0.120537 | + | 0.992709i | ||||
\(76\) | 0.246137 | + | 0.135573i | 0.246137 | + | 0.135573i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.368985 | − | 1.27388i | 0.368985 | − | 1.27388i | −0.534466 | − | 0.845190i | \(-0.679487\pi\) |
0.903450 | − | 0.428693i | \(-0.141026\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.692724 | − | 0.721202i | 0.692724 | − | 0.721202i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | −0.0603785 | − | 0.998176i | \(-0.519231\pi\) | ||||
0.0603785 | + | 0.998176i | \(0.480769\pi\) | |||||||
\(84\) | −0.0804666 | + | 0.996757i | −0.0804666 | + | 0.996757i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.885456 | − | 0.464723i | 0.885456 | − | 0.464723i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.885456 | − | 0.535277i | 0.885456 | − | 0.535277i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.504989 | + | 0.113733i | 0.504989 | + | 0.113733i | 0.464723 | − | 0.885456i | \(-0.346154\pi\) |
0.0402659 | + | 0.999189i | \(0.487179\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.948536 | + | 0.316668i | 0.948536 | + | 0.316668i | ||||
\(101\) | 0 | 0 | −0.428693 | − | 0.903450i | \(-0.641026\pi\) | ||||
0.428693 | + | 0.903450i | \(0.358974\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.338119 | − | 1.65622i | −0.338119 | − | 1.65622i | −0.692724 | − | 0.721202i | \(-0.743590\pi\) |
0.354605 | − | 0.935016i | \(-0.384615\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.885456 | − | 0.464723i | \(-0.153846\pi\) | ||||
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(108\) | −0.354605 | − | 0.935016i | −0.354605 | − | 0.935016i | ||||
\(109\) | 1.11973 | − | 0.952443i | 1.11973 | − | 0.952443i | 0.120537 | − | 0.992709i | \(-0.461538\pi\) |
0.999189 | + | 0.0402659i | \(0.0128205\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.0326775 | + | 1.62243i | 0.0326775 | + | 1.62243i | ||||
\(112\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(113\) | 0 | 0 | 0.948536 | − | 0.316668i | \(-0.102564\pi\) | ||||
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.600742 | + | 0.799443i | −0.600742 | + | 0.799443i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.721202 | + | 0.692724i | −0.721202 | + | 0.692724i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.104008 | − | 1.02943i | −0.104008 | − | 1.02943i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.0580798 | + | 0.0557864i | −0.0580798 | + | 0.0557864i | −0.721202 | − | 0.692724i | \(-0.756410\pi\) |
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.256479 | − | 0.192732i | 0.256479 | − | 0.192732i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | 0.600742 | − | 0.799443i | \(-0.294872\pi\) | ||||
−0.600742 | + | 0.799443i | \(0.705128\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.0835998 | + | 0.268281i | −0.0835998 | + | 0.268281i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | 0.983620 | − | 0.180255i | \(-0.0576923\pi\) | ||||
−0.983620 | + | 0.180255i | \(0.942308\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.879714 | + | 1.39116i | 0.879714 | + | 1.39116i | 0.919979 | + | 0.391967i | \(0.128205\pi\) |
−0.0402659 | + | 0.999189i | \(0.512821\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.996757 | − | 0.0804666i | −0.996757 | − | 0.0804666i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.992709 | + | 0.120537i | −0.992709 | + | 0.120537i | ||||
\(148\) | 1.47979 | + | 0.666000i | 1.47979 | + | 0.666000i | ||||
\(149\) | 0 | 0 | −0.999797 | − | 0.0201371i | \(-0.993590\pi\) | ||||
0.999797 | + | 0.0201371i | \(0.00641026\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.949113 | − | 1.72314i | 0.949113 | − | 1.72314i | 0.316668 | − | 0.948536i | \(-0.397436\pi\) |
0.632445 | − | 0.774605i | \(-0.282051\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0.464723 | + | 0.885456i | 0.464723 | + | 0.885456i | ||||
\(157\) | 0.770916 | − | 1.21911i | 0.770916 | − | 1.21911i | −0.200026 | − | 0.979791i | \(-0.564103\pi\) |
0.970942 | − | 0.239316i | \(-0.0769231\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.632445 | + | 0.225395i | −0.632445 | + | 0.225395i | −0.632445 | − | 0.774605i | \(-0.717949\pi\) |
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 0.373361 | − | 0.927686i | \(-0.378205\pi\) | ||||
−0.373361 | + | 0.927686i | \(0.621795\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.500000 | − | 0.866025i | 0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0394819 | − | 0.278217i | −0.0394819 | − | 0.278217i | ||||
\(172\) | −0.0641728 | − | 0.314339i | −0.0641728 | − | 0.314339i | ||||
\(173\) | 0 | 0 | −0.278217 | − | 0.960518i | \(-0.589744\pi\) | ||||
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.120537 | + | 0.992709i | −0.120537 | + | 0.992709i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
−0.160411 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0.759177 | − | 0.398447i | 0.759177 | − | 0.398447i | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) |
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.492699 | − | 0.258588i | −0.492699 | − | 0.258588i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0.845190 | − | 0.534466i | 0.845190 | − | 0.534466i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(192\) | −0.500000 | + | 0.866025i | −0.500000 | + | 0.866025i | ||||
\(193\) | −1.16312 | − | 1.61454i | −1.16312 | − | 1.61454i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
−0.500000 | − | 0.866025i | \(-0.666667\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.316668 | + | 0.948536i | −0.316668 | + | 0.948536i | ||||
\(197\) | 0 | 0 | 0.761712 | − | 0.647915i | \(-0.224359\pi\) | ||||
−0.761712 | + | 0.647915i | \(0.775641\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.06386 | − | 0.558358i | −1.06386 | − | 0.558358i | −0.160411 | − | 0.987050i | \(-0.551282\pi\) |
−0.903450 | + | 0.428693i | \(0.858974\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.233580 | + | 0.274605i | 0.233580 | + | 0.274605i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.999189 | − | 0.0402659i | 0.999189 | − | 0.0402659i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.25168 | + | 1.30314i | 1.25168 | + | 1.30314i | 0.935016 | + | 0.354605i | \(0.115385\pi\) |
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.987826 | − | 0.307819i | 0.987826 | − | 0.307819i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0.0265322 | + | 0.438629i | 0.0265322 | + | 0.438629i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.310724 | − | 1.37966i | −0.310724 | − | 1.37966i | −0.845190 | − | 0.534466i | \(-0.820513\pi\) |
0.534466 | − | 0.845190i | \(-0.320513\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.316668 | − | 0.948536i | −0.316668 | − | 0.948536i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | −0.517338 | − | 0.855781i | \(-0.673077\pi\) | ||||
0.517338 | + | 0.855781i | \(0.326923\pi\) | |||||||
\(228\) | −0.268281 | − | 0.0835998i | −0.268281 | − | 0.0835998i | ||||
\(229\) | −1.27742 | − | 0.455256i | −1.27742 | − | 0.455256i | −0.391967 | − | 0.919979i | \(-0.628205\pi\) |
−0.885456 | + | 0.464723i | \(0.846154\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −0.106718 | + | 1.32194i | −0.106718 | + | 1.32194i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.63406 | + | 0.509195i | −1.63406 | + | 0.509195i | −0.970942 | − | 0.239316i | \(-0.923077\pi\) |
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.534466 | + | 0.845190i | −0.534466 | + | 0.845190i | ||||
\(244\) | −0.444838 | + | 0.334274i | −0.444838 | + | 0.334274i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.0727294 | + | 0.271430i | 0.0727294 | + | 0.271430i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | 0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | ||||
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(252\) | −0.120537 | − | 0.992709i | −0.120537 | − | 0.992709i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.568065 | + | 0.822984i | 0.568065 | + | 0.822984i | ||||
\(257\) | 0 | 0 | −0.970942 | − | 0.239316i | \(-0.923077\pi\) | ||||
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.356544 | + | 1.58310i | −0.356544 | + | 1.58310i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.919979 | − | 0.391967i | \(-0.871795\pi\) | ||||
0.919979 | + | 0.391967i | \(0.128205\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.348226 | − | 0.0933069i | 0.348226 | − | 0.0933069i | ||||
\(269\) | 0 | 0 | −0.663123 | − | 0.748511i | \(-0.730769\pi\) | ||||
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.0208353 | + | 0.0344658i | −0.0208353 | + | 0.0344658i | −0.866025 | − | 0.500000i | \(-0.833333\pi\) |
0.845190 | + | 0.534466i | \(0.179487\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −0.774605 | + | 0.632445i | −0.774605 | + | 0.632445i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.83224 | + | 0.694877i | −1.83224 | + | 0.694877i | −0.845190 | + | 0.534466i | \(0.820513\pi\) |
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.760492 | + | 0.701573i | −0.760492 | + | 0.701573i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | −0.998176 | − | 0.0603785i | \(-0.980769\pi\) | ||||
0.998176 | + | 0.0603785i | \(0.0192308\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.06547 | + | 0.0860133i | −1.06547 | + | 0.0860133i | −0.600742 | − | 0.799443i | \(-0.705128\pi\) |
−0.464723 | + | 0.885456i | \(0.653846\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.748511 | − | 0.663123i | −0.748511 | − | 0.663123i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.517533 | − | 0.0104237i | −0.517533 | − | 0.0104237i | ||||
\(292\) | 0.407653 | + | 0.164066i | 0.407653 | + | 0.164066i | ||||
\(293\) | 0 | 0 | 0.811378 | − | 0.584522i | \(-0.198718\pi\) | ||||
−0.811378 | + | 0.584522i | \(0.801282\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −0.992709 | − | 0.120537i | −0.992709 | − | 0.120537i | ||||
\(301\) | 0.295150 | − | 0.125752i | 0.295150 | − | 0.125752i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.190538 | + | 0.206540i | −0.190538 | + | 0.206540i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.79393 | − | 0.328749i | −1.79393 | − | 0.328749i | −0.822984 | − | 0.568065i | \(-0.807692\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0.662573 | + | 1.55512i | 0.662573 | + | 1.55512i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.428693 | − | 0.903450i | \(-0.358974\pi\) | ||||
−0.428693 | + | 0.903450i | \(0.641026\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.361427 | + | 0.171499i | −0.361427 | + | 0.171499i | −0.600742 | − | 0.799443i | \(-0.705128\pi\) |
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.14856 | + | 0.663123i | 1.14856 | + | 0.663123i | ||||
\(317\) | 0 | 0 | 0.811378 | − | 0.584522i | \(-0.198718\pi\) | ||||
−0.811378 | + | 0.584522i | \(0.801282\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.534466 | + | 0.845190i | 0.534466 | + | 0.845190i | ||||
\(325\) | 0.428693 | + | 0.903450i | 0.428693 | + | 0.903450i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.906584 | + | 1.15717i | −0.906584 | + | 1.15717i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.890475 | + | 1.23607i | −0.890475 | + | 1.23607i | 0.0804666 | + | 0.996757i | \(0.474359\pi\) |
−0.970942 | + | 0.239316i | \(0.923077\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.356544 | − | 1.58310i | −0.356544 | − | 1.58310i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.948536 | − | 0.316668i | −0.948536 | − | 0.316668i | ||||
\(337\) | 1.26489i | 1.26489i | 0.774605 | + | 0.632445i | \(0.217949\pi\) | ||||
−0.774605 | + | 0.632445i | \(0.782051\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.992709 | − | 0.120537i | −0.992709 | − | 0.120537i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.120537 | − | 0.992709i | \(-0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.271430 | − | 1.91269i | 0.271430 | − | 1.91269i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.391967 | − | 0.919979i | \(-0.371795\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.428693 | − | 0.903450i | 0.428693 | − | 0.903450i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.100522 | − | 0.994935i | \(-0.467949\pi\) | ||||
−0.100522 | + | 0.994935i | \(0.532051\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | −0.584522 | − | 0.811378i | \(-0.698718\pi\) | ||||
0.584522 | + | 0.811378i | \(0.301282\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.797641 | + | 0.460518i | 0.797641 | + | 0.460518i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.568065 | − | 0.822984i | 0.568065 | − | 0.822984i | ||||
\(364\) | 0.239316 | + | 0.970942i | 0.239316 | + | 0.970942i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.380472 | + | 0.506316i | −0.380472 | + | 0.506316i | −0.948536 | − | 0.316668i | \(-0.897436\pi\) |
0.568065 | + | 0.822984i | \(0.307692\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0.307819 | + | 0.987826i | 0.307819 | + | 0.987826i | ||||
\(373\) | 0.382638 | − | 0.287534i | 0.382638 | − | 0.287534i | −0.391967 | − | 0.919979i | \(-0.628205\pi\) |
0.774605 | + | 0.632445i | \(0.217949\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.40848 | + | 0.703425i | −1.40848 | + | 0.703425i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) |
−0.428693 | + | 0.903450i | \(0.641026\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.0457473 | − | 0.0662764i | 0.0457473 | − | 0.0662764i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | 0.994935 | − | 0.100522i | \(-0.0320513\pi\) | ||||
−0.994935 | + | 0.100522i | \(0.967949\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −0.212745 | + | 0.240139i | −0.212745 | + | 0.240139i | ||||
\(388\) | −0.231280 | + | 0.463097i | −0.231280 | + | 0.463097i | ||||
\(389\) | 0 | 0 | −0.774605 | − | 0.632445i | \(-0.782051\pi\) | ||||
0.774605 | + | 0.632445i | \(0.217949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.70903 | + | 0.384905i | −1.70903 | + | 0.384905i | −0.960518 | − | 0.278217i | \(-0.910256\pi\) |
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.0282472 | − | 0.279582i | 0.0282472 | − | 0.279582i | ||||
\(400\) | −0.534466 | + | 0.845190i | −0.534466 | + | 0.845190i | ||||
\(401\) | 0 | 0 | −0.297503 | − | 0.954721i | \(-0.596154\pi\) | ||||
0.297503 | + | 0.954721i | \(0.403846\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.670382 | − | 0.788125i | 0.670382 | − | 0.788125i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.745361 | + | 0.0450860i | 0.745361 | + | 0.0450860i | 0.428693 | − | 0.903450i | \(-0.358974\pi\) |
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.68901 | + | 0.0680647i | 1.68901 | + | 0.0680647i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.14020 | − | 1.18708i | −1.14020 | − | 1.18708i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | 0.960518 | − | 0.278217i | \(-0.0897436\pi\) | ||||
−0.960518 | + | 0.278217i | \(0.910256\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.593921 | − | 0.0359256i | 0.593921 | − | 0.0359256i | 0.239316 | − | 0.970942i | \(-0.423077\pi\) |
0.354605 | + | 0.935016i | \(0.384615\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.416498 | − | 0.368985i | −0.416498 | − | 0.368985i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.0201371 | − | 0.999797i | \(-0.506410\pi\) | ||||
0.0201371 | + | 0.999797i | \(0.493590\pi\) | |||||||
\(432\) | 0.992709 | − | 0.120537i | 0.992709 | − | 0.120537i | ||||
\(433\) | 0.0799447 | − | 1.98381i | 0.0799447 | − | 1.98381i | −0.0804666 | − | 0.996757i | \(-0.525641\pi\) |
0.160411 | − | 0.987050i | \(-0.448718\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.656799 | + | 1.31512i | 0.656799 | + | 1.31512i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.908271 | − | 1.31586i | 0.908271 | − | 1.31586i | −0.0402659 | − | 0.999189i | \(-0.512821\pi\) |
0.948536 | − | 0.316668i | \(-0.102564\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0.948536 | − | 0.316668i | 0.948536 | − | 0.316668i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.948536 | − | 0.316668i | \(-0.102564\pi\) | ||||
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(444\) | −1.58310 | − | 0.356544i | −1.58310 | − | 0.356544i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.692724 | + | 0.721202i | −0.692724 | + | 0.721202i | ||||
\(449\) | 0 | 0 | 0.999797 | − | 0.0201371i | \(-0.00641026\pi\) | ||||
−0.999797 | + | 0.0201371i | \(0.993590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −0.585260 | + | 1.87816i | −0.585260 | + | 1.87816i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.90596 | − | 0.115289i | 1.90596 | − | 0.115289i | 0.935016 | − | 0.354605i | \(-0.115385\pi\) |
0.970942 | + | 0.239316i | \(0.0769231\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | −0.140502 | − | 0.990080i | \(-0.544872\pi\) | ||||
0.140502 | + | 0.990080i | \(0.455128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.46052 | + | 1.14424i | −1.46052 | + | 1.14424i | −0.500000 | + | 0.866025i | \(0.666667\pi\) |
−0.960518 | + | 0.278217i | \(0.910256\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.919979 | − | 0.391967i | \(-0.871795\pi\) | ||||
0.919979 | + | 0.391967i | \(0.128205\pi\) | |||||||
\(468\) | −0.632445 | − | 0.774605i | −0.632445 | − | 0.774605i | ||||
\(469\) | 0.161075 | + | 0.322525i | 0.161075 | + | 0.322525i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.511484 | + | 1.34867i | −0.511484 | + | 1.34867i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.264697 | − | 0.0943346i | −0.264697 | − | 0.0943346i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | −0.941967 | − | 0.335705i | \(-0.891026\pi\) | ||||
0.941967 | + | 0.335705i | \(0.108974\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.544766 | + | 1.52858i | 0.544766 | + | 1.52858i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.03447 | − | 1.71122i | 1.03447 | − | 1.71122i | 0.500000 | − | 0.866025i | \(-0.333333\pi\) |
0.534466 | − | 0.845190i | \(-0.320513\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.574579 | − | 0.347345i | 0.574579 | − | 0.347345i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 0.999189 | − | 0.0402659i | \(-0.0128205\pi\) | ||||
−0.999189 | + | 0.0402659i | \(0.987179\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.02441 | + | 0.145374i | 1.02441 | + | 0.145374i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.94125 | − | 0.196131i | −1.94125 | − | 0.196131i | −0.948536 | − | 0.316668i | \(-0.897436\pi\) |
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | −0.721202 | − | 0.692724i | \(-0.756410\pi\) | ||||
0.721202 | + | 0.692724i | \(0.243590\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.316668 | + | 0.948536i | −0.316668 | + | 0.948536i | ||||
\(508\) | −0.0402659 | − | 0.0697427i | −0.0402659 | − | 0.0697427i | ||||
\(509\) | 0 | 0 | 0.787183 | − | 0.616719i | \(-0.211538\pi\) | ||||
−0.787183 | + | 0.616719i | \(0.788462\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.0792096 | + | 0.432233i | −0.0792096 | + | 0.432233i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.0943346 | + | 0.264697i | 0.0943346 | + | 0.264697i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.125752 | + | 0.295150i | 0.125752 | + | 0.295150i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.999189 | − | 0.0402659i | \(-0.0128205\pi\) | ||||
−0.999189 | + | 0.0402659i | \(0.987179\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.364312 | + | 0.694138i | −0.364312 | + | 0.694138i | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) |
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.0804666 | − | 0.996757i | −0.0804666 | − | 0.996757i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −0.240479 | − | 0.145374i | −0.240479 | − | 0.145374i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.26417 | − | 0.284714i | −1.26417 | − | 0.284714i | −0.464723 | − | 0.885456i | \(-0.653846\pi\) |
−0.799443 | + | 0.600742i | \(0.794872\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −0.664135 | + | 0.542249i | −0.664135 | + | 0.542249i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.166997 | + | 1.37535i | 0.166997 | + | 1.37535i | 0.799443 | + | 0.600742i | \(0.205128\pi\) |
−0.632445 | + | 0.774605i | \(0.717949\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.534466 | + | 0.154810i | 0.534466 | + | 0.154810i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.419979 | + | 1.25799i | −0.419979 | + | 1.25799i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.56126 | + | 0.521225i | −1.56126 | + | 0.521225i | ||||
\(557\) | 0 | 0 | −0.894635 | − | 0.446798i | \(-0.852564\pi\) | ||||
0.894635 | + | 0.446798i | \(0.147436\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.182248 | − | 0.264032i | 0.182248 | − | 0.264032i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | −0.748511 | − | 0.663123i | \(-0.769231\pi\) | ||||
0.748511 | + | 0.663123i | \(0.230769\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −0.721202 | + | 0.692724i | −0.721202 | + | 0.692724i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | −0.464723 | − | 0.885456i | \(-0.653846\pi\) | ||||
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.85873 | + | 0.379463i | 1.85873 | + | 0.379463i | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) |
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0.316668 | − | 0.948536i | 0.316668 | − | 0.948536i | ||||
\(577\) | −0.487598 | + | 1.81974i | −0.487598 | + | 1.81974i | 0.0804666 | + | 0.996757i | \(0.474359\pi\) |
−0.568065 | + | 0.822984i | \(0.692308\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.46257 | + | 1.34925i | 1.46257 | + | 1.34925i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(588\) | 0.120537 | − | 0.992709i | 0.120537 | − | 0.992709i | ||||
\(589\) | 0.0233956 | + | 0.289806i | 0.0233956 | + | 0.289806i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.00078 | + | 1.27741i | −1.00078 | + | 1.27741i | ||||
\(593\) | 0 | 0 | 0.446798 | − | 0.894635i | \(-0.352564\pi\) | ||||
−0.446798 | + | 0.894635i | \(0.647436\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.15405 | + | 0.334274i | 1.15405 | + | 0.334274i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.278217 | − | 0.960518i | \(-0.589744\pi\) | ||||
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.18593 | + | 1.57818i | 1.18593 | + | 1.57818i | 0.721202 | + | 0.692724i | \(0.243590\pi\) |
0.464723 | + | 0.885456i | \(0.346154\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.283788 | − | 0.222333i | −0.283788 | − | 0.222333i | ||||
\(604\) | 1.44593 | + | 1.33391i | 1.44593 | + | 1.33391i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0.490585 | − | 1.46948i | 0.490585 | − | 1.46948i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
0.845190 | − | 0.534466i | \(-0.179487\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.0441724 | + | 0.196131i | −0.0441724 | + | 0.196131i | −0.992709 | − | 0.120537i | \(-0.961538\pi\) |
0.948536 | + | 0.316668i | \(0.102564\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | −0.678061 | − | 0.735006i | \(-0.737179\pi\) | ||||
0.678061 | + | 0.735006i | \(0.262821\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.04587 | − | 0.522327i | 1.04587 | − | 0.522327i | 0.160411 | − | 0.987050i | \(-0.448718\pi\) |
0.885456 | + | 0.464723i | \(0.153846\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −0.970942 | + | 0.239316i | −0.970942 | + | 0.239316i | ||||
\(625\) | −0.987050 | − | 0.160411i | −0.987050 | − | 0.160411i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0.999189 | + | 1.04027i | 0.999189 | + | 1.04027i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −0.683332 | − | 0.948536i | −0.683332 | − | 0.948536i | 0.316668 | − | 0.948536i | \(-0.397436\pi\) |
−1.00000 | \(\pi\) | |||||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.48705 | − | 1.02644i | −1.48705 | − | 1.02644i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.903450 | + | 0.428693i | −0.903450 | + | 0.428693i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | 0.992709 | − | 0.120537i | \(-0.0384615\pi\) | ||||
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −0.179861 | − | 0.0898262i | −0.179861 | − | 0.0898262i | 0.354605 | − | 0.935016i | \(-0.384615\pi\) |
−0.534466 | + | 0.845190i | \(0.679487\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | −0.799443 | − | 0.600742i | \(-0.794872\pi\) | ||||
0.799443 | + | 0.600742i | \(0.205128\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.906291 | + | 0.499189i | −0.906291 | + | 0.499189i | ||||
\(652\) | −0.0674914 | − | 0.668008i | −0.0674914 | − | 0.668008i | ||||
\(653\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −0.113733 | − | 0.424457i | −0.113733 | − | 0.424457i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | −0.632445 | − | 0.774605i | \(-0.717949\pi\) | ||||
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.22719 | + | 0.123988i | 1.22719 | + | 0.123988i | 0.692724 | − | 0.721202i | \(-0.256410\pi\) |
0.534466 | + | 0.845190i | \(0.320513\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.580411 | + | 1.28962i | 0.580411 | + | 1.28962i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.248247 | − | 0.743589i | 0.248247 | − | 0.743589i | −0.748511 | − | 0.663123i | \(-0.769231\pi\) |
0.996757 | − | 0.0804666i | \(-0.0256410\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.500000 | + | 0.866025i | 0.500000 | + | 0.866025i | ||||
\(676\) | 0.721202 | + | 0.692724i | 0.721202 | + | 0.692724i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.500000 | − | 0.133975i | −0.500000 | − | 0.133975i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | 0.911900 | − | 0.410413i | \(-0.134615\pi\) | ||||
−0.911900 | + | 0.410413i | \(0.865385\pi\) | |||||||
\(684\) | 0.279582 | + | 0.0282472i | 0.279582 | + | 0.0282472i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.34267 | + | 0.190538i | 1.34267 | + | 0.190538i | ||||
\(688\) | 0.320562 | + | 0.0129182i | 0.320562 | + | 0.0129182i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −0.879909 | + | 0.396015i | −0.879909 | + | 0.396015i | −0.799443 | − | 0.600742i | \(-0.794872\pi\) |
−0.0804666 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −0.935016 | − | 0.354605i | −0.935016 | − | 0.354605i | ||||
\(701\) | 0 | 0 | −0.822984 | − | 0.568065i | \(-0.807692\pi\) | ||||
0.822984 | + | 0.568065i | \(0.192308\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.411976 | − | 0.195485i | −0.411976 | − | 0.195485i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.57168 | − | 1.03876i | 1.57168 | − | 1.03876i | 0.600742 | − | 0.799443i | \(-0.294872\pi\) |
0.970942 | − | 0.239316i | \(-0.0769231\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.159861 | − | 1.31658i | −0.159861 | − | 1.31658i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.996757 | − | 0.0804666i | \(-0.974359\pi\) | ||||
0.996757 | + | 0.0804666i | \(0.0256410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.271156 | + | 1.66849i | 0.271156 | + | 1.66849i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.49919 | − | 0.825759i | 1.49919 | − | 0.825759i | ||||
\(724\) | 0.205186 | + | 0.832471i | 0.205186 | + | 0.832471i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.663123 | − | 1.74851i | −0.663123 | − | 1.74851i | −0.663123 | − | 0.748511i | \(-0.730769\pi\) |
− | 1.00000i | \(-0.5\pi\) | ||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.354605 | − | 0.935016i | 0.354605 | − | 0.935016i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0.368985 | − | 0.416498i | 0.368985 | − | 0.416498i | ||||
\(733\) | 0.452584 | − | 0.684779i | 0.452584 | − | 0.684779i | −0.534466 | − | 0.845190i | \(-0.679487\pi\) |
0.987050 | + | 0.160411i | \(0.0512821\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −0.941340 | − | 0.212007i | −0.941340 | − | 0.212007i | −0.278217 | − | 0.960518i | \(-0.589744\pi\) |
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.125553 | − | 0.251397i | −0.125553 | − | 0.251397i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | −0.999797 | − | 0.0201371i | \(-0.993590\pi\) | ||||
0.999797 | + | 0.0201371i | \(0.00641026\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.98381 | + | 0.240878i | −1.98381 | + | 0.240878i | −0.987050 | + | 0.160411i | \(0.948718\pi\) |
−0.996757 | + | 0.0804666i | \(0.974359\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.316668 | + | 0.948536i | 0.316668 | + | 0.948536i | ||||
\(757\) | 0.520276 | + | 1.79620i | 0.520276 | + | 1.79620i | 0.600742 | + | 0.799443i | \(0.294872\pi\) |
−0.0804666 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.140502 | − | 0.990080i | \(-0.455128\pi\) | ||||
−0.140502 | + | 0.990080i | \(0.544872\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.15717 | + | 0.906584i | −1.15717 | + | 0.906584i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.721202 | − | 0.692724i | −0.721202 | − | 0.692724i | ||||
\(769\) | 0.625186 | − | 1.13504i | 0.625186 | − | 1.13504i | −0.354605 | − | 0.935016i | \(-0.615385\pi\) |
0.979791 | − | 0.200026i | \(-0.0641026\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.84597 | − | 0.742941i | 1.84597 | − | 0.742941i | ||||
\(773\) | 0 | 0 | −0.297503 | − | 0.954721i | \(-0.596154\pi\) | ||||
0.297503 | + | 0.954721i | \(0.403846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0.267794 | + | 0.999420i | 0.267794 | + | 0.999420i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.0326775 | − | 1.62243i | 0.0326775 | − | 1.62243i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −0.845190 | − | 0.534466i | −0.845190 | − | 0.534466i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.66974 | + | 1.00939i | −1.66974 | + | 1.00939i | −0.721202 | + | 0.692724i | \(0.756410\pi\) |
−0.948536 | + | 0.316668i | \(0.897436\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.549229 | − | 0.0892584i | −0.549229 | − | 0.0892584i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0.796732 | − | 0.899324i | 0.796732 | − | 0.899324i | ||||
\(797\) | 0 | 0 | 0.278217 | − | 0.960518i | \(-0.410256\pi\) | ||||
−0.278217 | + | 0.960518i | \(0.589744\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −0.322525 | + | 0.161075i | −0.322525 | + | 0.161075i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.632445 | − | 0.774605i | \(-0.717949\pi\) | ||||
0.632445 | + | 0.774605i | \(0.282051\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.589104 | − | 1.89050i | −0.589104 | − | 1.89050i | −0.428693 | − | 0.903450i | \(-0.641026\pi\) |
−0.160411 | − | 0.987050i | \(-0.551282\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.0135202 | − | 0.0379369i | 0.0135202 | − | 0.0379369i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0162505 | + | 0.0886760i | 0.0162505 | + | 0.0886760i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.632445 | − | 0.774605i | 0.632445 | − | 0.774605i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | −0.911900 | − | 0.410413i | \(-0.865385\pi\) | ||||
0.911900 | + | 0.410413i | \(0.134615\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.98542i | 1.98542i | 0.120537 | + | 0.992709i | \(0.461538\pi\) | ||||
−0.120537 | + | 0.992709i | \(0.538462\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | −0.517338 | − | 0.855781i | \(-0.673077\pi\) | ||||
0.517338 | + | 0.855781i | \(0.326923\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.68901 | − | 1.06806i | 1.68901 | − | 1.06806i | 0.822984 | − | 0.568065i | \(-0.192308\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.65622 | − | 1.04733i | 1.65622 | − | 1.04733i | ||||
\(832\) | −0.200026 | + | 0.979791i | −0.200026 | + | 0.979791i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0.604791 | − | 0.839513i | 0.604791 | − | 0.839513i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.647915 | − | 0.761712i | \(-0.275641\pi\) | ||||
−0.647915 | + | 0.761712i | \(0.724359\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.692724 | − | 0.721202i | 0.692724 | − | 0.721202i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.56482 | + | 0.903450i | −1.56482 | + | 0.903450i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.748511 | − | 0.663123i | 0.748511 | − | 0.663123i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.02673 | − | 0.297395i | 1.02673 | − | 0.297395i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −0.244198 | − | 0.542586i | −0.244198 | − | 0.542586i | 0.748511 | − | 0.663123i | \(-0.230769\pi\) |
−0.992709 | + | 0.120537i | \(0.961538\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | −0.845190 | − | 0.534466i | \(-0.820513\pi\) | ||||
0.845190 | + | 0.534466i | \(0.179487\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.01392 | − | 1.60339i | −1.01392 | − | 1.60339i | −0.774605 | − | 0.632445i | \(-0.782051\pi\) |
−0.239316 | − | 0.970942i | \(-0.576923\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | −0.0201371 | − | 0.999797i | \(-0.506410\pi\) | ||||
0.0201371 | + | 0.999797i | \(0.493590\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.866025 | + | 0.500000i | 0.866025 | + | 0.500000i | ||||
\(868\) | 0.0624722 | + | 1.03279i | 0.0624722 | + | 1.03279i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.308518 | + | 0.186505i | 0.308518 | + | 0.186505i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0.509159 | − | 0.0933069i | 0.509159 | − | 0.0933069i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −0.432233 | − | 0.0792096i | −0.432233 | − | 0.0792096i | ||||
\(877\) | −0.625233 | + | 0.531826i | −0.625233 | + | 0.531826i | −0.903450 | − | 0.428693i | \(-0.858974\pi\) |
0.278217 | + | 0.960518i | \(0.410256\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | 0.987050 | − | 0.160411i | \(-0.0512821\pi\) | ||||
−0.987050 | + | 0.160411i | \(0.948718\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.95971 | + | 0.237952i | 1.95971 | + | 0.237952i | 0.999189 | − | 0.0402659i | \(-0.0128205\pi\) |
0.960518 | + | 0.278217i | \(0.0897436\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.239316 | − | 0.970942i | \(-0.576923\pi\) | ||||
0.239316 | + | 0.970942i | \(0.423077\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.0602790 | − | 0.0534025i | 0.0602790 | − | 0.0534025i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.41393 | + | 0.0284781i | 1.41393 | + | 0.0284781i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0.996757 | − | 0.0804666i | 0.996757 | − | 0.0804666i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.264032 | + | 0.182248i | −0.264032 | + | 0.182248i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.99190 | + | 0.0802707i | 1.99190 | + | 0.0802707i | 0.999189 | − | 0.0402659i | \(-0.0128205\pi\) |
0.992709 | + | 0.120537i | \(0.0384615\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 0.748511 | − | 0.663123i | \(-0.230769\pi\) | ||||
−0.748511 | + | 0.663123i | \(0.769231\pi\) | |||||||
\(912\) | 0.145374 | − | 0.240479i | 0.145374 | − | 0.240479i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.747735 | − | 1.13135i | 0.747735 | − | 1.13135i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.136019 | − | 0.0860133i | −0.136019 | − | 0.0860133i | 0.464723 | − | 0.885456i | \(-0.346154\pi\) |
−0.600742 | + | 0.799443i | \(0.705128\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.82343 | − | 0.0367260i | 1.82343 | − | 0.0367260i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.56746 | − | 0.420000i | −1.56746 | − | 0.420000i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.960245 | − | 1.39116i | −0.960245 | − | 1.39116i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.990080 | − | 0.140502i | \(-0.955128\pi\) | ||||
0.990080 | + | 0.140502i | \(0.0448718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.0943346 | − | 0.264697i | 0.0943346 | − | 0.264697i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −0.440331 | + | 1.78649i | −0.440331 | + | 1.78649i | 0.160411 | + | 0.987050i | \(0.448718\pi\) |
−0.600742 | + | 0.799443i | \(0.705128\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.319818 | − | 0.240328i | 0.319818 | − | 0.240328i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | −0.990080 | − | 0.140502i | \(-0.955128\pi\) | ||||
0.990080 | + | 0.140502i | \(0.0448718\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.855781 | − | 0.517338i | \(-0.826923\pi\) | ||||
0.855781 | + | 0.517338i | \(0.173077\pi\) | |||||||
\(948\) | −1.25799 | − | 0.419979i | −1.25799 | − | 0.419979i | ||||
\(949\) | 0.164066 | + | 0.407653i | 0.164066 | + | 0.407653i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 0.160411 | − | 0.987050i | \(-0.448718\pi\) | ||||
−0.160411 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.0546512 | − | 0.0446213i | 0.0546512 | − | 0.0446213i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −0.103342 | − | 1.70844i | −0.103342 | − | 1.70844i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.906291 | − | 1.49919i | 0.906291 | − | 1.49919i | 0.0402659 | − | 0.999189i | \(-0.487179\pi\) |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.0804666 | − | 0.996757i | \(-0.474359\pi\) | ||||
−0.0804666 | + | 0.996757i | \(0.525641\pi\) | |||||||
\(972\) | −0.692724 | − | 0.721202i | −0.692724 | − | 0.721202i | ||||
\(973\) | −0.822984 | − | 1.42545i | −0.822984 | − | 1.42545i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.600742 | − | 0.799443i | −0.600742 | − | 0.799443i | ||||
\(976\) | −0.218104 | − | 0.511909i | −0.218104 | − | 0.511909i | ||||
\(977\) | 0 | 0 | 0.647915 | − | 0.761712i | \(-0.275641\pi\) | ||||
−0.647915 | + | 0.761712i | \(0.724359\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.656799 | − | 1.31512i | 0.656799 | − | 1.31512i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | −0.335705 | − | 0.941967i | \(-0.608974\pi\) | ||||
0.335705 | + | 0.941967i | \(0.391026\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −0.280948 | + | 0.00565861i | −0.280948 | + | 0.00565861i | ||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.799443 | − | 1.38468i | 0.799443 | − | 1.38468i | −0.120537 | − | 0.992709i | \(-0.538462\pi\) |
0.919979 | − | 0.391967i | \(-0.128205\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.625233 | − | 1.38921i | 0.625233 | − | 1.38921i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.150475 | − | 0.0570677i | −0.150475 | − | 0.0570677i | 0.278217 | − | 0.960518i | \(-0.410256\pi\) |
−0.428693 | + | 0.903450i | \(0.641026\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.666000 | + | 1.47979i | 0.666000 | + | 1.47979i |
(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 | 3549.1.ep.a.2147.1 | yes | 48 | |
3.2 | odd | 2 | CM | 3549.1.ep.a.2147.1 | yes | 48 | |
7.3 | odd | 6 | 3549.1.ea.a.626.1 | ✓ | 48 | ||
21.17 | even | 6 | 3549.1.ea.a.626.1 | ✓ | 48 | ||
169.98 | odd | 156 | 3549.1.ea.a.2126.1 | yes | 48 | ||
507.98 | even | 156 | 3549.1.ea.a.2126.1 | yes | 48 | ||
1183.605 | even | 156 | inner | 3549.1.ep.a.605.1 | yes | 48 | |
3549.605 | odd | 156 | inner | 3549.1.ep.a.605.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.1.ea.a.626.1 | ✓ | 48 | 7.3 | odd | 6 | ||
3549.1.ea.a.626.1 | ✓ | 48 | 21.17 | even | 6 | ||
3549.1.ea.a.2126.1 | yes | 48 | 169.98 | odd | 156 | ||
3549.1.ea.a.2126.1 | yes | 48 | 507.98 | even | 156 | ||
3549.1.ep.a.605.1 | yes | 48 | 1183.605 | even | 156 | inner | |
3549.1.ep.a.605.1 | yes | 48 | 3549.605 | odd | 156 | inner | |
3549.1.ep.a.2147.1 | yes | 48 | 1.1 | even | 1 | trivial | |
3549.1.ep.a.2147.1 | yes | 48 | 3.2 | odd | 2 | CM |