Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1152,2,Mod(1151,1152)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1152, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1152.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1152 = 2^{7} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1152.c (of order \(2\), degree \(1\), 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: | \(9.19876631285\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.2 | ||
Root | \(0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1152.1151 |
Dual form | 1152.2.c.d.1151.3 |
$q$-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 \(\left(\mathbb{Z}/1152\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(641\) | \(901\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | − 0.585786i | − 0.261972i | −0.991384 | − | 0.130986i | \(-0.958186\pi\) | ||||
0.991384 | − | 0.130986i | \(-0.0418142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 0.828427i | − 0.313116i | −0.987669 | − | 0.156558i | \(-0.949960\pi\) | ||||
0.987669 | − | 0.156558i | \(-0.0500398\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.82843 | 0.852803 | 0.426401 | − | 0.904534i | \(-0.359781\pi\) | ||||
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.82843 | −0.784465 | −0.392232 | − | 0.919866i | \(-0.628297\pi\) | ||||
−0.392232 | + | 0.919866i | \(0.628297\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.58579i | 0.627145i | 0.949564 | + | 0.313573i | \(0.101526\pi\) | ||||
−0.949564 | + | 0.313573i | \(0.898474\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 5.65685i | − 1.29777i | −0.760886 | − | 0.648886i | \(-0.775235\pi\) | ||||
0.760886 | − | 0.648886i | \(-0.224765\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.82843 | 1.42383 | 0.711913 | − | 0.702268i | \(-0.247829\pi\) | ||||
0.711913 | + | 0.702268i | \(0.247829\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.65685 | 0.931371 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 3.41421i | − 0.634004i | −0.948425 | − | 0.317002i | \(-0.897324\pi\) | ||||
0.948425 | − | 0.317002i | \(-0.102676\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.82843i | − 1.58563i | −0.609461 | − | 0.792816i | \(-0.708614\pi\) | ||||
0.609461 | − | 0.792816i | \(-0.291386\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.485281 | −0.0820275 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.65685 | −1.25878 | −0.629390 | − | 0.777090i | \(-0.716695\pi\) | ||||
−0.629390 | + | 0.777090i | \(0.716695\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.41421i | 0.845558i | 0.906233 | + | 0.422779i | \(0.138945\pi\) | ||||
−0.906233 | + | 0.422779i | \(0.861055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.65685i | − 0.252668i | −0.991988 | − | 0.126334i | \(-0.959679\pi\) | ||||
0.991988 | − | 0.126334i | \(-0.0403211\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.48528 | −0.654246 | −0.327123 | − | 0.944982i | \(-0.606079\pi\) | ||||
−0.327123 | + | 0.944982i | \(0.606079\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.31371 | 0.901958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.07107i | − 1.24601i | −0.782219 | − | 0.623003i | \(-0.785912\pi\) | ||||
0.782219 | − | 0.623003i | \(-0.214088\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 1.65685i | − 0.223410i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.6569 | 1.77797 | 0.888985 | − | 0.457935i | \(-0.151411\pi\) | ||||
0.888985 | + | 0.457935i | \(0.151411\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.65685 | −0.468212 | −0.234106 | − | 0.972211i | \(-0.575216\pi\) | ||||
−0.234106 | + | 0.972211i | \(0.575216\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.65685i | 0.205507i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 12.0000i | − 1.46603i | −0.680211 | − | 0.733017i | \(-0.738112\pi\) | ||||
0.680211 | − | 0.733017i | \(-0.261888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.4853 | 1.48173 | 0.740865 | − | 0.671654i | \(-0.234416\pi\) | ||||
0.740865 | + | 0.671654i | \(0.234416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.00000 | 0.468165 | 0.234082 | − | 0.972217i | \(-0.424791\pi\) | ||||
0.234082 | + | 0.972217i | \(0.424791\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 2.34315i | − 0.267026i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 10.4853i | − 1.17969i | −0.807518 | − | 0.589843i | \(-0.799190\pi\) | ||||
0.807518 | − | 0.589843i | \(-0.200810\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.8284 | −1.18857 | −0.594287 | − | 0.804253i | \(-0.702566\pi\) | ||||
−0.594287 | + | 0.804253i | \(0.702566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.51472 | 0.164294 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.75736i | 0.398279i | 0.979971 | + | 0.199140i | \(0.0638147\pi\) | ||||
−0.979971 | + | 0.199140i | \(0.936185\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.34315i | 0.245628i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.31371 | −0.339979 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.34315 | 0.237910 | 0.118955 | − | 0.992900i | \(-0.462046\pi\) | ||||
0.118955 | + | 0.992900i | \(0.462046\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 14.7279i | 1.46548i | 0.680507 | + | 0.732742i | \(0.261760\pi\) | ||||
−0.680507 | + | 0.732742i | \(0.738240\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.82843i | 0.869891i | 0.900457 | + | 0.434945i | \(0.143232\pi\) | ||||
−0.900457 | + | 0.434945i | \(0.856768\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.3137 | 1.09374 | 0.546869 | − | 0.837218i | \(-0.315820\pi\) | ||||
0.546869 | + | 0.837218i | \(0.315820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.17157 | −0.495347 | −0.247673 | − | 0.968844i | \(-0.579666\pi\) | ||||
−0.247673 | + | 0.968844i | \(0.579666\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.75736i | 0.353463i | 0.984259 | + | 0.176731i | \(0.0565524\pi\) | ||||
−0.984259 | + | 0.176731i | \(0.943448\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 4.00000i | − 0.373002i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.14214 | 0.196369 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 5.65685i | − 0.505964i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 0.828427i | − 0.0735110i | −0.999324 | − | 0.0367555i | \(-0.988298\pi\) | ||||
0.999324 | − | 0.0367555i | \(-0.0117023\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −5.65685 | −0.494242 | −0.247121 | − | 0.968985i | \(-0.579484\pi\) | ||||
−0.247121 | + | 0.968985i | \(0.579484\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.68629 | −0.406353 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 13.4142i | − 1.14605i | −0.819537 | − | 0.573027i | \(-0.805769\pi\) | ||||
0.819537 | − | 0.573027i | \(-0.194231\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.0000i | 1.01783i | 0.860818 | + | 0.508913i | \(0.169953\pi\) | ||||
−0.860818 | + | 0.508913i | \(0.830047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −8.00000 | −0.668994 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2.00000 | −0.166091 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 18.7279i | − 1.53425i | −0.641497 | − | 0.767126i | \(-0.721686\pi\) | ||||
0.641497 | − | 0.767126i | \(-0.278314\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4853i | 0.853280i | 0.904422 | + | 0.426640i | \(0.140303\pi\) | ||||
−0.904422 | + | 0.426640i | \(0.859697\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −5.17157 | −0.415391 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6569 | 0.930318 | 0.465159 | − | 0.885227i | \(-0.345997\pi\) | ||||
0.465159 | + | 0.885227i | \(0.345997\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 5.65685i | − 0.445823i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.65685i | 0.756383i | 0.925727 | + | 0.378192i | \(0.123454\pi\) | ||||
−0.925727 | + | 0.378192i | \(0.876546\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.65685 | 0.437741 | 0.218870 | − | 0.975754i | \(-0.429763\pi\) | ||||
0.218870 | + | 0.975754i | \(0.429763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.00000 | −0.384615 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.4142i | 1.78015i | 0.455814 | + | 0.890075i | \(0.349348\pi\) | ||||
−0.455814 | + | 0.890075i | \(0.650652\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 3.85786i | − 0.291627i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.31371 | −0.247678 | −0.123839 | − | 0.992302i | \(-0.539521\pi\) | ||||
−0.123839 | + | 0.992302i | \(0.539521\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.1421 | 1.64581 | 0.822906 | − | 0.568178i | \(-0.192351\pi\) | ||||
0.822906 | + | 0.568178i | \(0.192351\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.48528i | 0.329764i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.31371i | 0.534831i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.6569 | −1.56703 | −0.783517 | − | 0.621370i | \(-0.786577\pi\) | ||||
−0.783517 | + | 0.621370i | \(0.786577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.3137 | −1.24627 | −0.623134 | − | 0.782115i | \(-0.714141\pi\) | ||||
−0.623134 | + | 0.782115i | \(0.714141\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 20.3848i | 1.45236i | 0.687507 | + | 0.726178i | \(0.258705\pi\) | ||||
−0.687507 | + | 0.726178i | \(0.741295\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.828427i | 0.0587256i | 0.999569 | + | 0.0293628i | \(0.00934782\pi\) | ||||
−0.999569 | + | 0.0293628i | \(0.990652\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −2.82843 | −0.198517 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.17157 | 0.221512 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 16.0000i | − 1.10674i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 0.686292i | − 0.0472463i | −0.999721 | − | 0.0236231i | \(-0.992480\pi\) | ||||
0.999721 | − | 0.0236231i | \(-0.00752017\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.970563 | −0.0661918 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7.31371 | −0.496487 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 7.31371i | − 0.491973i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7990i | 1.45977i | 0.683571 | + | 0.729884i | \(0.260426\pi\) | ||||
−0.683571 | + | 0.729884i | \(0.739574\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.1716 | −1.40521 | −0.702603 | − | 0.711582i | \(-0.747979\pi\) | ||||
−0.702603 | + | 0.711582i | \(0.747979\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −10.8284 | −0.715563 | −0.357781 | − | 0.933805i | \(-0.616467\pi\) | ||||
−0.357781 | + | 0.933805i | \(0.616467\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.89949i | 0.124440i | 0.998062 | + | 0.0622200i | \(0.0198181\pi\) | ||||
−0.998062 | + | 0.0622200i | \(0.980182\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.62742i | 0.171394i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.00000 | 0.517477 | 0.258738 | − | 0.965947i | \(-0.416693\pi\) | ||||
0.258738 | + | 0.965947i | \(0.416693\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.9706 | −0.835507 | −0.417754 | − | 0.908560i | \(-0.637183\pi\) | ||||
−0.417754 | + | 0.908560i | \(0.637183\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 3.69848i | − 0.236288i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 16.0000i | 1.01806i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.51472 | −0.474325 | −0.237162 | − | 0.971470i | \(-0.576217\pi\) | ||||
−0.237162 | + | 0.971470i | \(0.576217\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 19.3137 | 1.21424 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 9.89949i | 0.617514i | 0.951141 | + | 0.308757i | \(0.0999129\pi\) | ||||
−0.951141 | + | 0.308757i | \(0.900087\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.34315i | 0.394144i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −29.6569 | −1.82872 | −0.914360 | − | 0.404902i | \(-0.867306\pi\) | ||||
−0.914360 | + | 0.404902i | \(0.867306\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.31371 | −0.326419 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.38478i | 0.267345i | 0.991026 | + | 0.133672i | \(0.0426769\pi\) | ||||
−0.991026 | + | 0.133672i | \(0.957323\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.4853i | 1.12290i | 0.827510 | + | 0.561450i | \(0.189756\pi\) | ||||
−0.827510 | + | 0.561450i | \(0.810244\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 13.1716 | 0.794276 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 26.8284 | 1.61196 | 0.805982 | − | 0.591940i | \(-0.201638\pi\) | ||||
0.805982 | + | 0.591940i | \(0.201638\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 25.8995i | − 1.54503i | −0.634994 | − | 0.772517i | \(-0.718997\pi\) | ||||
0.634994 | − | 0.772517i | \(-0.281003\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.3137i | 1.14808i | 0.818827 | + | 0.574040i | \(0.194625\pi\) | ||||
−0.818827 | + | 0.574040i | \(0.805375\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.48528 | 0.264758 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.3137 | 0.606689 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 24.8701i | 1.45292i | 0.687206 | + | 0.726462i | \(0.258837\pi\) | ||||
−0.687206 | + | 0.726462i | \(0.741163\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 8.00000i | − 0.465778i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −19.3137 | −1.11694 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.37258 | −0.0791144 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.14214i | 0.122658i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.3137i | 1.33058i | 0.746583 | + | 0.665292i | \(0.231693\pi\) | ||||
−0.746583 | + | 0.665292i | \(0.768307\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.34315 | −0.132868 | −0.0664338 | − | 0.997791i | \(-0.521162\pi\) | ||||
−0.0664338 | + | 0.997791i | \(0.521162\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.3137 | −0.752535 | −0.376268 | − | 0.926511i | \(-0.622793\pi\) | ||||
−0.376268 | + | 0.926511i | \(0.622793\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.75736i | 0.323366i | 0.986843 | + | 0.161683i | \(0.0516921\pi\) | ||||
−0.986843 | + | 0.161683i | \(0.948308\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 9.65685i | − 0.540680i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.6274 | 0.813891 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.1716 | −0.730627 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.71573i | 0.204855i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.00000i | − 0.219860i | −0.993939 | − | 0.109930i | \(-0.964937\pi\) | ||||
0.993939 | − | 0.109930i | \(-0.0350627\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −7.02944 | −0.384059 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.686292 | 0.0373847 | 0.0186923 | − | 0.999825i | \(-0.494050\pi\) | ||||
0.0186923 | + | 0.999825i | \(0.494050\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 24.9706i | − 1.35223i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 11.0294i | − 0.595534i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −0.485281 | −0.0260513 | −0.0130256 | − | 0.999915i | \(-0.504146\pi\) | ||||
−0.0130256 | + | 0.999915i | \(0.504146\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −0.343146 | −0.0183682 | −0.00918409 | − | 0.999958i | \(-0.502923\pi\) | ||||
−0.00918409 | + | 0.999958i | \(0.502923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 34.8701i | − 1.85595i | −0.372648 | − | 0.927973i | \(-0.621550\pi\) | ||||
0.372648 | − | 0.927973i | \(-0.378450\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 7.31371i | − 0.388171i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.51472 | 0.185500 | 0.0927499 | − | 0.995689i | \(-0.470434\pi\) | ||||
0.0927499 | + | 0.995689i | \(0.470434\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.0000 | −0.684211 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 2.34315i | − 0.122646i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1716i | 0.791950i | 0.918261 | + | 0.395975i | \(0.129593\pi\) | ||||
−0.918261 | + | 0.395975i | \(0.870407\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.51472 | −0.390145 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 18.9706 | 0.982259 | 0.491129 | − | 0.871087i | \(-0.336584\pi\) | ||||
0.491129 | + | 0.871087i | \(0.336584\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 9.65685i | 0.497353i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 36.2843i | − 1.86380i | −0.362718 | − | 0.931899i | \(-0.618151\pi\) | ||||
0.362718 | − | 0.931899i | \(-0.381849\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 30.6274 | 1.56499 | 0.782494 | − | 0.622658i | \(-0.213947\pi\) | ||||
0.782494 | + | 0.622658i | \(0.213947\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.37258 | −0.0699533 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 33.5563i | 1.70137i | 0.525672 | + | 0.850687i | \(0.323814\pi\) | ||||
−0.525672 | + | 0.850687i | \(0.676186\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 17.6569i | 0.892946i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −6.14214 | −0.309044 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.9706 | −0.751351 | −0.375676 | − | 0.926751i | \(-0.622589\pi\) | ||||
−0.375676 | + | 0.926751i | \(0.622589\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.5858i | 0.528629i | 0.964437 | + | 0.264314i | \(0.0851457\pi\) | ||||
−0.964437 | + | 0.264314i | \(0.914854\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 24.9706i | 1.24387i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −21.6569 | −1.07349 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 21.6569 | 1.07086 | 0.535431 | − | 0.844579i | \(-0.320149\pi\) | ||||
0.535431 | + | 0.844579i | \(0.320149\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 11.3137i | − 0.556711i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.34315i | 0.311373i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.7990 | 1.35807 | 0.679035 | − | 0.734106i | \(-0.262399\pi\) | ||||
0.679035 | + | 0.734106i | \(0.262399\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.4853 | −1.19334 | −0.596670 | − | 0.802487i | \(-0.703510\pi\) | ||||
−0.596670 | + | 0.802487i | \(0.703510\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0416i | 0.584105i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.02944i | 0.146605i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.5147 | 0.554644 | 0.277322 | − | 0.960777i | \(-0.410553\pi\) | ||||
0.277322 | + | 0.960777i | \(0.410553\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −16.6274 | −0.799063 | −0.399531 | − | 0.916720i | \(-0.630827\pi\) | ||||
−0.399531 | + | 0.916720i | \(0.630827\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 38.6274i | − 1.84780i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 36.1421i | − 1.72497i | −0.506083 | − | 0.862485i | \(-0.668907\pi\) | ||||
0.506083 | − | 0.862485i | \(-0.331093\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −33.4558 | −1.58954 | −0.794768 | − | 0.606914i | \(-0.792407\pi\) | ||||
−0.794768 | + | 0.606914i | \(0.792407\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.20101 | 0.104338 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 40.7279i | 1.92207i | 0.276428 | + | 0.961035i | \(0.410849\pi\) | ||||
−0.276428 | + | 0.961035i | \(0.589151\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 15.3137i | 0.721094i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.37258 | 0.0643477 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 24.9706 | 1.16807 | 0.584037 | − | 0.811727i | \(-0.301472\pi\) | ||||
0.584037 | + | 0.811727i | \(0.301472\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.8995i | 1.29941i | 0.760187 | + | 0.649705i | \(0.225107\pi\) | ||||
−0.760187 | + | 0.649705i | \(0.774893\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 5.79899i | − 0.269502i | −0.990879 | − | 0.134751i | \(-0.956977\pi\) | ||||
0.990879 | − | 0.134751i | \(-0.0430234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 22.1421 | 1.02462 | 0.512308 | − | 0.858802i | \(-0.328791\pi\) | ||||
0.512308 | + | 0.858802i | \(0.328791\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.94113 | −0.459039 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 4.68629i | − 0.215476i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 26.3431i | − 1.20871i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 14.8284 | 0.677528 | 0.338764 | − | 0.940871i | \(-0.389991\pi\) | ||||
0.338764 | + | 0.940871i | \(0.389991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21.6569 | 0.987468 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 1.37258i | − 0.0623258i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 23.1716i | − 1.05000i | −0.851101 | − | 0.525002i | \(-0.824065\pi\) | ||||
0.851101 | − | 0.525002i | \(-0.175935\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.6863 | 0.572524 | 0.286262 | − | 0.958151i | \(-0.407587\pi\) | ||||
0.286262 | + | 0.958151i | \(0.407587\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.82843 | 0.397612 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 10.3431i | − 0.463953i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 38.6274i | − 1.72920i | −0.502460 | − | 0.864600i | \(-0.667572\pi\) | ||||
0.502460 | − | 0.864600i | \(-0.332428\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −23.7990 | −1.06114 | −0.530572 | − | 0.847640i | \(-0.678023\pi\) | ||||
−0.530572 | + | 0.847640i | \(0.678023\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.62742 | 0.383915 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 38.7279i | − 1.71658i | −0.513161 | − | 0.858292i | \(-0.671526\pi\) | ||||
0.513161 | − | 0.858292i | \(-0.328474\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − 3.31371i | − 0.146590i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.17157 | 0.227887 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −12.6863 | −0.557942 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 11.0711i | − 0.485032i | −0.970147 | − | 0.242516i | \(-0.922027\pi\) | ||||
0.970147 | − | 0.242516i | \(-0.0779727\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 34.3431i | − 1.50172i | −0.660461 | − | 0.750860i | \(-0.729639\pi\) | ||||
0.660461 | − | 0.750860i | \(-0.270361\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 22.8284 | 0.994422 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.6274 | 1.02728 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 15.3137i | − 0.663310i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 6.62742i | − 0.286528i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.8579 | 0.769193 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.79899 | −0.163331 | −0.0816657 | − | 0.996660i | \(-0.526024\pi\) | ||||
−0.0816657 | + | 0.996660i | \(0.526024\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.02944i | 0.129767i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 1.65685i | − 0.0708420i | −0.999372 | − | 0.0354210i | \(-0.988723\pi\) | ||||
0.999372 | − | 0.0354210i | \(-0.0112772\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −19.3137 | −0.822792 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.68629 | −0.369379 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 5.07107i | − 0.214868i | −0.994212 | − | 0.107434i | \(-0.965737\pi\) | ||||
0.994212 | − | 0.107434i | \(-0.0342634\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.68629i | 0.198209i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 25.4558 | 1.07284 | 0.536418 | − | 0.843952i | \(-0.319777\pi\) | ||||
0.536418 | + | 0.843952i | \(0.319777\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.20101 | 0.0925972 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.8995i | 0.918075i | 0.888417 | + | 0.459037i | \(0.151806\pi\) | ||||
−0.888417 | + | 0.459037i | \(0.848194\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0000i | 1.00437i | 0.864761 | + | 0.502184i | \(0.167470\pi\) | ||||
−0.864761 | + | 0.502184i | \(0.832530\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.7990 | 1.32611 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.68629 | −0.278354 | −0.139177 | − | 0.990268i | \(-0.544446\pi\) | ||||
−0.139177 | + | 0.990268i | \(0.544446\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8.97056i | 0.372162i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − 25.6569i | − 1.06260i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −18.3431 | −0.757103 | −0.378551 | − | 0.925580i | \(-0.623578\pi\) | ||||
−0.378551 | + | 0.925580i | \(0.623578\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −49.9411 | −2.05779 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 0.928932i | 0.0381467i | 0.999818 | + | 0.0190733i | \(0.00607160\pi\) | ||||
−0.999818 | + | 0.0190733i | \(0.993928\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 1.25483i | − 0.0514432i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 27.5147 | 1.12422 | 0.562110 | − | 0.827062i | \(-0.309990\pi\) | ||||
0.562110 | + | 0.827062i | \(0.309990\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.31371 | −0.0535873 | −0.0267936 | − | 0.999641i | \(-0.508530\pi\) | ||||
−0.0267936 | + | 0.999641i | \(0.508530\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.75736i | 0.0714468i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 24.8284i | − 1.00775i | −0.863775 | − | 0.503877i | \(-0.831906\pi\) | ||||
0.863775 | − | 0.503877i | \(-0.168094\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.6863 | 0.513232 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.343146 | −0.0138595 | −0.00692976 | − | 0.999976i | \(-0.502206\pi\) | ||||
−0.00692976 | + | 0.999976i | \(0.502206\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4142i | 1.34521i | 0.740004 | + | 0.672603i | \(0.234824\pi\) | ||||
−0.740004 | + | 0.672603i | \(0.765176\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 33.9411i | − 1.36421i | −0.731255 | − | 0.682105i | \(-0.761065\pi\) | ||||
0.731255 | − | 0.682105i | \(-0.238935\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 3.11270 | 0.124708 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 19.9706 | 0.798823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 19.7990i | − 0.789437i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − 18.4853i | − 0.735887i | −0.929848 | − | 0.367944i | \(-0.880062\pi\) | ||||
0.929848 | − | 0.367944i | \(-0.119938\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.485281 | −0.0192578 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −17.8579 | −0.707554 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.8701i | 0.587332i | 0.955908 | + | 0.293666i | \(0.0948753\pi\) | ||||
−0.955908 | + | 0.293666i | \(0.905125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.65685i | 0.380829i | 0.981704 | + | 0.190415i | \(0.0609832\pi\) | ||||
−0.981704 | + | 0.190415i | \(0.939017\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.7990 | 0.621122 | 0.310561 | − | 0.950553i | \(-0.399483\pi\) | ||||
0.310561 | + | 0.950553i | \(0.399483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.6274 | 1.51626 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 5.27208i | − 0.206312i | −0.994665 | − | 0.103156i | \(-0.967106\pi\) | ||||
0.994665 | − | 0.103156i | \(-0.0328941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.31371i | 0.129477i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.97056 | 0.349444 | 0.174722 | − | 0.984618i | \(-0.444097\pi\) | ||||
0.174722 | + | 0.984618i | \(0.444097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.65685 | 0.142235 | 0.0711176 | − | 0.997468i | \(-0.477343\pi\) | ||||
0.0711176 | + | 0.997468i | \(0.477343\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 2.74517i | 0.106453i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 23.3137i | − 0.902710i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.3431 | −0.399293 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0000 | 0.693849 | 0.346925 | − | 0.937893i | \(-0.387226\pi\) | ||||
0.346925 | + | 0.937893i | \(0.387226\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.7279i | 0.719773i | 0.932996 | + | 0.359886i | \(0.117185\pi\) | ||||
−0.932996 | + | 0.359886i | \(0.882815\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 1.94113i | − 0.0744936i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −22.1421 | −0.847245 | −0.423623 | − | 0.905839i | \(-0.639242\pi\) | ||||
−0.423623 | + | 0.905839i | \(0.639242\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.85786 | −0.300234 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 25.6569i | 0.977448i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.02944i | 0.115245i | 0.998338 | + | 0.0576226i | \(0.0183520\pi\) | ||||
−0.998338 | + | 0.0576226i | \(0.981648\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.02944 | 0.266642 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −14.0000 | −0.530288 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 13.7574i | − 0.519608i | −0.965661 | − | 0.259804i | \(-0.916342\pi\) | ||||
0.965661 | − | 0.259804i | \(-0.0836580\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 43.3137i | 1.63361i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 12.2010 | 0.458866 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.0833 | −1.80580 | −0.902902 | − | 0.429846i | \(-0.858568\pi\) | ||||
−0.902902 | + | 0.429846i | \(0.858568\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 60.2843i | − 2.25766i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.68629i | 0.175257i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 28.4853 | 1.06232 | 0.531161 | − | 0.847271i | \(-0.321756\pi\) | ||||
0.531161 | + | 0.847271i | \(0.321756\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.31371 | 0.272377 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 15.8995i | − 0.590492i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.82843i | 0.327428i | 0.986508 | + | 0.163714i | \(0.0523475\pi\) | ||||
−0.986508 | + | 0.163714i | \(0.947653\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.28427 | 0.158459 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 24.4853 | 0.904385 | 0.452192 | − | 0.891920i | \(-0.350642\pi\) | ||||
0.452192 | + | 0.891920i | \(0.350642\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 33.9411i | − 1.25024i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 8.00000i | − 0.294285i | −0.989115 | − | 0.147142i | \(-0.952992\pi\) | ||||
0.989115 | − | 0.147142i | \(-0.0470076\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −16.9706 | −0.622590 | −0.311295 | − | 0.950313i | \(-0.600763\pi\) | ||||
−0.311295 | + | 0.950313i | \(0.600763\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.9706 | −0.401930 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 9.37258i | − 0.342467i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − 40.8284i | − 1.48985i | −0.667148 | − | 0.744925i | \(-0.732485\pi\) | ||||
0.667148 | − | 0.744925i | \(-0.267515\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.14214 | 0.223535 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.485281 | 0.0176379 | 0.00881893 | − | 0.999961i | \(-0.497193\pi\) | ||||
0.00881893 | + | 0.999961i | \(0.497193\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.6985i | 0.931569i | 0.884898 | + | 0.465785i | \(0.154228\pi\) | ||||
−0.884898 | + | 0.465785i | \(0.845772\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.28427i | 0.155101i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −38.6274 | −1.39476 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.3137 | −0.768592 | −0.384296 | − | 0.923210i | \(-0.625556\pi\) | ||||
−0.384296 | + | 0.923210i | \(0.625556\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.5858i | 0.452679i | 0.974048 | + | 0.226340i | \(0.0726759\pi\) | ||||
−0.974048 | + | 0.226340i | \(0.927324\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 41.1127i | − 1.47681i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.6274 | 1.09734 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 35.3137 | 1.26362 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 6.82843i | − 0.243717i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 26.3431i | − 0.939032i | −0.882924 | − | 0.469516i | \(-0.844428\pi\) | ||||
0.882924 | − | 0.469516i | \(-0.155572\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.11270 | 0.110675 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.3431 | 0.367296 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.0711i | 0.463001i | 0.972835 | + | 0.231500i | \(0.0743635\pi\) | ||||
−0.972835 | + | 0.231500i | \(0.925637\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 11.5980i | − 0.410307i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 11.3137 | 0.399252 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.31371 | −0.116793 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 42.6690i | 1.50016i | 0.661345 | + | 0.750082i | \(0.269986\pi\) | ||||
−0.661345 | + | 0.750082i | \(0.730014\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.5980i | 1.10956i | 0.831999 | + | 0.554778i | \(0.187197\pi\) | ||||
−0.831999 | + | 0.554778i | \(0.812803\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.65685 | 0.198151 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.37258 | −0.327905 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.4142i | 0.398359i | 0.979963 | + | 0.199179i | \(0.0638276\pi\) | ||||
−0.979963 | + | 0.199179i | \(0.936172\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 52.4264i | 1.82747i | 0.406311 | + | 0.913735i | \(0.366815\pi\) | ||||
−0.406311 | + | 0.913735i | \(0.633185\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.0294 | 0.522625 | 0.261312 | − | 0.965254i | \(-0.415845\pi\) | ||||
0.261312 | + | 0.965254i | \(0.415845\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.20101 | 0.145907 | 0.0729536 | − | 0.997335i | \(-0.476758\pi\) | ||||
0.0729536 | + | 0.997335i | \(0.476758\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 16.3259i | 0.565659i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 3.31371i | − 0.114676i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 3.51472 | 0.121342 | 0.0606708 | − | 0.998158i | \(-0.480676\pi\) | ||||
0.0606708 | + | 0.998158i | \(0.480676\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.3431 | 0.598040 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.92893i | 0.100758i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.48528i | 0.0853953i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −52.2843 | −1.79228 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.2843 | 1.44779 | 0.723893 | − | 0.689912i | \(-0.242351\pi\) | ||||
0.723893 | + | 0.689912i | \(0.242351\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 21.8995i | − 0.748072i | −0.927414 | − | 0.374036i | \(-0.877974\pi\) | ||||
0.927414 | − | 0.374036i | \(-0.122026\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.65685i | − 0.0565311i | −0.999600 | − | 0.0282656i | \(-0.991002\pi\) | ||||
0.999600 | − | 0.0282656i | \(-0.00899841\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.970563 | −0.0330383 | −0.0165192 | − | 0.999864i | \(-0.505258\pi\) | ||||
−0.0165192 | + | 0.999864i | \(0.505258\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 13.7157 | 0.466349 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 29.6569i | − 1.00604i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 33.9411i | 1.15005i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.68629 | −0.158426 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.97056 | −0.235379 | −0.117690 | − | 0.993050i | \(-0.537549\pi\) | ||||
−0.117690 | + | 0.993050i | \(0.537549\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 12.7279i | − 0.428815i | −0.976744 | − | 0.214407i | \(-0.931218\pi\) | ||||
0.976744 | − | 0.214407i | \(-0.0687820\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 40.2843i | 1.35567i | 0.735212 | + | 0.677837i | \(0.237082\pi\) | ||||
−0.735212 | + | 0.677837i | \(0.762918\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 2.34315 | 0.0786751 | 0.0393376 | − | 0.999226i | \(-0.487475\pi\) | ||||
0.0393376 | + | 0.999226i | \(0.487475\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −0.686292 | −0.0230175 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.3726i | 0.849061i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.94113i | 0.0648847i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.1421 | −1.00530 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 23.4558 | 0.781427 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 12.9706i | − 0.431156i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.3431i | 0.476256i | 0.971234 | + | 0.238128i | \(0.0765338\pi\) | ||||
−0.971234 | + | 0.238128i | \(0.923466\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.5980 | −0.781836 | −0.390918 | − | 0.920426i | \(-0.627842\pi\) | ||||
−0.390918 | + | 0.920426i | \(0.627842\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −30.6274 | −1.01362 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.68629i | 0.154755i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 23.4558i | − 0.773737i | −0.922135 | − | 0.386868i | \(-0.873557\pi\) | ||||
0.922135 | − | 0.386868i | \(-0.126443\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −35.3137 | −1.16236 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −35.6569 | −1.17239 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 16.7279i | − 0.548825i | −0.961612 | − | 0.274413i | \(-0.911517\pi\) | ||||
0.961612 | − | 0.274413i | \(-0.0884834\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 35.7157i | − 1.17054i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.28427 | 0.140111 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −56.6274 | −1.84994 | −0.924969 | − | 0.380044i | \(-0.875909\pi\) | ||||
−0.924969 | + | 0.380044i | \(0.875909\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.2721i | 0.693450i | 0.937967 | + | 0.346725i | \(0.112706\pi\) | ||||
−0.937967 | + | 0.346725i | \(0.887294\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 36.9706i | 1.20393i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −31.5980 | −1.02680 | −0.513398 | − | 0.858151i | \(-0.671614\pi\) | ||||
−0.513398 | + | 0.858151i | \(0.671614\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.3137 | −0.367259 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 4.44365i | − 0.143944i | −0.997407 | − | 0.0719720i | \(-0.977071\pi\) | ||||
0.997407 | − | 0.0719720i | \(-0.0229292\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.6863i | 0.410519i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.1127 | −0.358848 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −46.9411 | −1.51423 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 10.1421i | 0.326487i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 46.0833i | 1.48194i | 0.671539 | + | 0.740969i | \(0.265633\pi\) | ||||
−0.671539 | + | 0.740969i | \(0.734367\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.1716 | 0.679428 | 0.339714 | − | 0.940529i | \(-0.389670\pi\) | ||||
0.339714 | + | 0.940529i | \(0.389670\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.94113 | 0.318698 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 12.5269i | − 0.400771i | −0.979717 | − | 0.200386i | \(-0.935780\pi\) | ||||
0.979717 | − | 0.200386i | \(-0.0642195\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 10.6274i | 0.339654i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −34.3431 | −1.09538 | −0.547688 | − | 0.836683i | \(-0.684492\pi\) | ||||
−0.547688 | + | 0.836683i | \(0.684492\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 11.9411 | 0.380476 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 11.3137i | − 0.359755i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 13.7990i | 0.438339i | 0.975687 | + | 0.219170i | \(0.0703348\pi\) | ||||
−0.975687 | + | 0.219170i | \(0.929665\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.485281 | 0.0153845 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.5980 | 0.557334 | 0.278667 | − | 0.960388i | \(-0.410107\pi\) | ||||
0.278667 | + | 0.960388i | \(0.410107\pi\) | |||||||
\(998\) | 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 | 1152.2.c.d.1151.2 | yes | 4 | |
3.2 | odd | 2 | 1152.2.c.a.1151.3 | yes | 4 | ||
4.3 | odd | 2 | 1152.2.c.a.1151.2 | ✓ | 4 | ||
8.3 | odd | 2 | 1152.2.c.b.1151.3 | yes | 4 | ||
8.5 | even | 2 | 1152.2.c.c.1151.3 | yes | 4 | ||
12.11 | even | 2 | inner | 1152.2.c.d.1151.3 | yes | 4 | |
16.3 | odd | 4 | 2304.2.f.b.1151.3 | 4 | |||
16.5 | even | 4 | 2304.2.f.g.1151.2 | 4 | |||
16.11 | odd | 4 | 2304.2.f.h.1151.1 | 4 | |||
16.13 | even | 4 | 2304.2.f.a.1151.4 | 4 | |||
24.5 | odd | 2 | 1152.2.c.b.1151.2 | yes | 4 | ||
24.11 | even | 2 | 1152.2.c.c.1151.2 | yes | 4 | ||
48.5 | odd | 4 | 2304.2.f.b.1151.4 | 4 | |||
48.11 | even | 4 | 2304.2.f.a.1151.3 | 4 | |||
48.29 | odd | 4 | 2304.2.f.h.1151.2 | 4 | |||
48.35 | even | 4 | 2304.2.f.g.1151.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1152.2.c.a.1151.2 | ✓ | 4 | 4.3 | odd | 2 | ||
1152.2.c.a.1151.3 | yes | 4 | 3.2 | odd | 2 | ||
1152.2.c.b.1151.2 | yes | 4 | 24.5 | odd | 2 | ||
1152.2.c.b.1151.3 | yes | 4 | 8.3 | odd | 2 | ||
1152.2.c.c.1151.2 | yes | 4 | 24.11 | even | 2 | ||
1152.2.c.c.1151.3 | yes | 4 | 8.5 | even | 2 | ||
1152.2.c.d.1151.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1152.2.c.d.1151.3 | yes | 4 | 12.11 | even | 2 | inner | |
2304.2.f.a.1151.3 | 4 | 48.11 | even | 4 | |||
2304.2.f.a.1151.4 | 4 | 16.13 | even | 4 | |||
2304.2.f.b.1151.3 | 4 | 16.3 | odd | 4 | |||
2304.2.f.b.1151.4 | 4 | 48.5 | odd | 4 | |||
2304.2.f.g.1151.1 | 4 | 48.35 | even | 4 | |||
2304.2.f.g.1151.2 | 4 | 16.5 | even | 4 | |||
2304.2.f.h.1151.1 | 4 | 16.11 | odd | 4 | |||
2304.2.f.h.1151.2 | 4 | 48.29 | odd | 4 |