Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,3,Mod(161,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.161");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.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: | \(8.82836056527\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 4x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 161.4 | ||
Root | \(1.93185i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.161 |
Dual form | 324.3.c.a.161.1 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(5\) | 5.79555i | 1.15911i | 0.814933 | + | 0.579555i | \(0.196774\pi\) | ||||
−0.814933 | + | 0.579555i | \(0.803226\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.19615 | −0.885165 | −0.442582 | − | 0.896728i | \(-0.645938\pi\) | ||||
−0.442582 | + | 0.896728i | \(0.645938\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.13681i | 0.103347i | 0.998664 | + | 0.0516733i | \(0.0164554\pi\) | ||||
−0.998664 | + | 0.0516733i | \(0.983545\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.3923 | −0.876331 | −0.438166 | − | 0.898894i | \(-0.644372\pi\) | ||||
−0.438166 | + | 0.898894i | \(0.644372\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 31.2514i | − 1.83832i | −0.393887 | − | 0.919159i | \(-0.628870\pi\) | ||||
0.393887 | − | 0.919159i | \(-0.371130\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −32.9808 | −1.73583 | −0.867915 | − | 0.496713i | \(-0.834540\pi\) | ||||
−0.867915 | + | 0.496713i | \(0.834540\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 33.6365i | 1.46246i | 0.682132 | + | 0.731229i | \(0.261053\pi\) | ||||
−0.682132 | + | 0.731229i | \(0.738947\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.58846 | −0.343538 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 25.5673i | − 0.881632i | −0.897597 | − | 0.440816i | \(-0.854689\pi\) | ||||
0.897597 | − | 0.440816i | \(-0.145311\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −23.1769 | −0.747642 | −0.373821 | − | 0.927501i | \(-0.621953\pi\) | ||||
−0.373821 | + | 0.927501i | \(0.621953\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 35.9101i | − 1.02600i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 8.80385 | 0.237942 | 0.118971 | − | 0.992898i | \(-0.462040\pi\) | ||||
0.118971 | + | 0.992898i | \(0.462040\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 70.6835i | 1.72399i | 0.506919 | + | 0.861994i | \(0.330784\pi\) | ||||
−0.506919 | + | 0.861994i | \(0.669216\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −59.7654 | −1.38989 | −0.694946 | − | 0.719062i | \(-0.744572\pi\) | ||||
−0.694946 | + | 0.719062i | \(0.744572\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 60.2292i | 1.28147i | 0.767761 | + | 0.640736i | \(0.221371\pi\) | ||||
−0.767761 | + | 0.640736i | \(0.778629\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.6077 | −0.216484 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 19.7718i | 0.373053i | 0.982450 | + | 0.186526i | \(0.0597229\pi\) | ||||
−0.982450 | + | 0.186526i | \(0.940277\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.58846 | −0.119790 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 83.4114i | − 1.41375i | −0.707337 | − | 0.706876i | \(-0.750104\pi\) | ||||
0.707337 | − | 0.706876i | \(-0.249896\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 30.7654 | 0.504350 | 0.252175 | − | 0.967682i | \(-0.418854\pi\) | ||||
0.252175 | + | 0.967682i | \(0.418854\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 66.0247i | − 1.01577i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.5885 | −0.158037 | −0.0790183 | − | 0.996873i | \(-0.525179\pi\) | ||||
−0.0790183 | + | 0.996873i | \(0.525179\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 3.63342i | − 0.0511750i | −0.999673 | − | 0.0255875i | \(-0.991854\pi\) | ||||
0.999673 | − | 0.0255875i | \(-0.00814564\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −17.2346 | −0.236091 | −0.118045 | − | 0.993008i | \(-0.537663\pi\) | ||||
−0.118045 | + | 0.993008i | \(0.537663\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 7.04386i | − 0.0914787i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 113.373 | 1.43510 | 0.717551 | − | 0.696506i | \(-0.245263\pi\) | ||||
0.717551 | + | 0.696506i | \(0.245263\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.8141i | 0.142339i | 0.997464 | + | 0.0711693i | \(0.0226730\pi\) | ||||
−0.997464 | + | 0.0711693i | \(0.977327\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 181.119 | 2.13081 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 111.252i | 1.25003i | 0.780614 | + | 0.625013i | \(0.214906\pi\) | ||||
−0.780614 | + | 0.625013i | \(0.785094\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 70.5885 | 0.775697 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − 191.142i | − 2.01202i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 74.3154 | 0.766138 | 0.383069 | − | 0.923720i | \(-0.374867\pi\) | ||||
0.383069 | + | 0.923720i | \(0.374867\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 17.2752i | − 0.171041i | −0.996336 | − | 0.0855206i | \(-0.972745\pi\) | ||||
0.996336 | − | 0.0855206i | \(-0.0272554\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −112.000 | −1.08738 | −0.543689 | − | 0.839287i | \(-0.682973\pi\) | ||||
−0.543689 | + | 0.839287i | \(0.682973\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 141.144i | 1.31910i | 0.751660 | + | 0.659551i | \(0.229254\pi\) | ||||
−0.751660 | + | 0.659551i | \(0.770746\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 171.708 | 1.57530 | 0.787650 | − | 0.616123i | \(-0.211298\pi\) | ||||
0.787650 | + | 0.616123i | \(0.211298\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.57257i | 0.0493147i | 0.999696 | + | 0.0246574i | \(0.00784948\pi\) | ||||
−0.999696 | + | 0.0246574i | \(0.992151\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −194.942 | −1.69515 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 193.638i | 1.62721i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 119.708 | 0.989319 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 95.1140i | 0.760912i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −68.2346 | −0.537281 | −0.268640 | − | 0.963241i | \(-0.586574\pi\) | ||||
−0.268640 | + | 0.963241i | \(0.586574\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 154.095i | − 1.17630i | −0.808753 | − | 0.588148i | \(-0.799857\pi\) | ||||
0.808753 | − | 0.588148i | \(-0.200143\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 204.354 | 1.53649 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 76.4790i | − 0.558241i | −0.960256 | − | 0.279121i | \(-0.909957\pi\) | ||||
0.960256 | − | 0.279121i | \(-0.0900429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 94.0385 | 0.676536 | 0.338268 | − | 0.941050i | \(-0.390159\pi\) | ||||
0.338268 | + | 0.941050i | \(0.390159\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 12.9509i | − 0.0905658i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 148.177 | 1.02191 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 67.1615i | 0.450749i | 0.974272 | + | 0.225374i | \(0.0723605\pi\) | ||||
−0.974272 | + | 0.225374i | \(0.927640\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 46.3538 | 0.306979 | 0.153490 | − | 0.988150i | \(-0.450949\pi\) | ||||
0.153490 | + | 0.988150i | \(0.450949\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 134.323i | − 0.866601i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −169.588 | −1.08018 | −0.540091 | − | 0.841607i | \(-0.681610\pi\) | ||||
−0.540091 | + | 0.841607i | \(0.681610\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 208.417i | − 1.29452i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −243.023 | −1.49094 | −0.745469 | − | 0.666540i | \(-0.767775\pi\) | ||||
−0.745469 | + | 0.666540i | \(0.767775\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 112.724i | 0.674992i | 0.941327 | + | 0.337496i | \(0.109580\pi\) | ||||
−0.941327 | + | 0.337496i | \(0.890420\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −39.2154 | −0.232044 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 187.843i | − 1.08580i | −0.839798 | − | 0.542898i | \(-0.817327\pi\) | ||||
0.839798 | − | 0.542898i | \(-0.182673\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 53.2154 | 0.304088 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 16.3613i | 0.0914042i | 0.998955 | + | 0.0457021i | \(0.0145525\pi\) | ||||
−0.998955 | + | 0.0457021i | \(0.985448\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −227.608 | −1.25750 | −0.628751 | − | 0.777607i | \(-0.716433\pi\) | ||||
−0.628751 | + | 0.777607i | \(0.716433\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 51.0232i | 0.275801i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 35.5270 | 0.189984 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 364.562i | 1.90870i | 0.298684 | + | 0.954352i | \(0.403452\pi\) | ||||
−0.298684 | + | 0.954352i | \(0.596548\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −24.8846 | −0.128936 | −0.0644678 | − | 0.997920i | \(-0.520535\pi\) | ||||
−0.0644678 | + | 0.997920i | \(0.520535\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 171.259i | − 0.869333i | −0.900592 | − | 0.434666i | \(-0.856866\pi\) | ||||
0.900592 | − | 0.434666i | \(-0.143134\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 122.431 | 0.615230 | 0.307615 | − | 0.951511i | \(-0.400469\pi\) | ||||
0.307615 | + | 0.951511i | \(0.400469\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 158.419i | 0.780390i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −409.650 | −1.99829 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 37.4929i | − 0.179392i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −372.512 | −1.76546 | −0.882729 | − | 0.469883i | \(-0.844296\pi\) | ||||
−0.882729 | + | 0.469883i | \(0.844296\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 346.373i | − 1.61104i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 143.608 | 0.661787 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 356.025i | 1.61097i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −320.119 | −1.43551 | −0.717756 | − | 0.696295i | \(-0.754831\pi\) | ||||
−0.717756 | + | 0.696295i | \(0.754831\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 15.2245i | − 0.0670684i | −0.999438 | − | 0.0335342i | \(-0.989324\pi\) | ||||
0.999438 | − | 0.0335342i | \(-0.0106763\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −179.708 | −0.784750 | −0.392375 | − | 0.919805i | \(-0.628346\pi\) | ||||
−0.392375 | + | 0.919805i | \(0.628346\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 150.796i | 0.647193i | 0.946195 | + | 0.323596i | \(0.104892\pi\) | ||||
−0.946195 | + | 0.323596i | \(0.895108\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −349.061 | −1.48537 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 264.545i | 1.10688i | 0.832888 | + | 0.553441i | \(0.186686\pi\) | ||||
−0.832888 | + | 0.553441i | \(0.813314\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 228.450 | 0.947925 | 0.473963 | − | 0.880545i | \(-0.342823\pi\) | ||||
0.473963 | + | 0.880545i | \(0.342823\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 61.4775i | − 0.250928i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 375.727 | 1.52116 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 47.2783i | − 0.188360i | −0.995555 | − | 0.0941798i | \(-0.969977\pi\) | ||||
0.995555 | − | 0.0941798i | \(-0.0300229\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −38.2384 | −0.151140 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.7903i | 0.100351i | 0.998740 | + | 0.0501757i | \(0.0159781\pi\) | ||||
−0.998740 | + | 0.0501757i | \(0.984022\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −54.5500 | −0.210618 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 285.230i | − 1.08453i | −0.840209 | − | 0.542263i | \(-0.817568\pi\) | ||||
0.840209 | − | 0.542263i | \(-0.182432\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −114.588 | −0.432409 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 205.341i | − 0.763350i | −0.924297 | − | 0.381675i | \(-0.875347\pi\) | ||||
0.924297 | − | 0.381675i | \(-0.124653\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 282.004 | 1.04060 | 0.520302 | − | 0.853982i | \(-0.325819\pi\) | ||||
0.520302 | + | 0.853982i | \(0.325819\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 9.76346i | − 0.0355035i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 48.7077 | 0.175840 | 0.0879200 | − | 0.996128i | \(-0.471978\pi\) | ||||
0.0879200 | + | 0.996128i | \(0.471978\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 246.712i | 0.877980i | 0.898492 | + | 0.438990i | \(0.144664\pi\) | ||||
−0.898492 | + | 0.438990i | \(0.855336\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −352.946 | −1.24716 | −0.623580 | − | 0.781760i | \(-0.714322\pi\) | ||||
−0.623580 | + | 0.781760i | \(0.714322\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 437.966i | − 1.52601i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −687.650 | −2.37941 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 279.658i | − 0.954464i | −0.878777 | − | 0.477232i | \(-0.841640\pi\) | ||||
0.878777 | − | 0.477232i | \(-0.158360\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 483.415 | 1.63870 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 383.197i | − 1.28160i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 370.315 | 1.23028 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 178.302i | 0.584598i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 234.708 | 0.764520 | 0.382260 | − | 0.924055i | \(-0.375146\pi\) | ||||
0.382260 | + | 0.924055i | \(0.375146\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 235.700i | − 0.757879i | −0.925421 | − | 0.378940i | \(-0.876289\pi\) | ||||
0.925421 | − | 0.378940i | \(-0.123711\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −357.669 | −1.14271 | −0.571357 | − | 0.820702i | \(-0.693583\pi\) | ||||
−0.571357 | + | 0.820702i | \(0.693583\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 603.986i | 1.90532i | 0.304040 | + | 0.952659i | \(0.401664\pi\) | ||||
−0.304040 | + | 0.952659i | \(0.598336\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 29.0653 | 0.0911137 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1030.69i | 3.19101i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 97.8423 | 0.301053 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 373.189i | − 1.13431i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −36.7424 | −0.111004 | −0.0555021 | − | 0.998459i | \(-0.517676\pi\) | ||||
−0.0555021 | + | 0.998459i | \(0.517676\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 61.3660i | − 0.183182i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 168.277 | 0.499338 | 0.249669 | − | 0.968331i | \(-0.419678\pi\) | ||||
0.249669 | + | 0.968331i | \(0.419678\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 26.3478i | − 0.0772663i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 369.338 | 1.07679 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 176.608i | 0.508957i | 0.967078 | + | 0.254479i | \(0.0819038\pi\) | ||||
−0.967078 | + | 0.254479i | \(0.918096\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 131.215 | 0.375975 | 0.187988 | − | 0.982171i | \(-0.439804\pi\) | ||||
0.187988 | + | 0.982171i | \(0.439804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.6199i | 0.0385832i | 0.999814 | + | 0.0192916i | \(0.00614109\pi\) | ||||
−0.999814 | + | 0.0192916i | \(0.993859\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.0577 | 0.0593175 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 96.5853i | − 0.269040i | −0.990911 | − | 0.134520i | \(-0.957051\pi\) | ||||
0.990911 | − | 0.134520i | \(-0.0429492\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 726.731 | 2.01310 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 99.8842i | − 0.273655i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 254.946 | 0.694676 | 0.347338 | − | 0.937740i | \(-0.387086\pi\) | ||||
0.347338 | + | 0.937740i | \(0.387086\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 122.509i | − 0.330213i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −91.1000 | −0.244236 | −0.122118 | − | 0.992516i | \(-0.538969\pi\) | ||||
−0.122118 | + | 0.992516i | \(0.538969\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 291.271i | 0.772602i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 193.454 | 0.510432 | 0.255216 | − | 0.966884i | \(-0.417853\pi\) | ||||
0.255216 | + | 0.966884i | \(0.417853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 332.955i | − 0.869334i | −0.900591 | − | 0.434667i | \(-0.856866\pi\) | ||||
0.900591 | − | 0.434667i | \(-0.143134\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 40.8231 | 0.106034 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 41.1264i | 0.105723i | 0.998602 | + | 0.0528616i | \(0.0168342\pi\) | ||||
−0.998602 | + | 0.0528616i | \(0.983166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1051.19 | 2.68846 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 657.060i | 1.66344i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −176.881 | −0.445544 | −0.222772 | − | 0.974871i | \(-0.571510\pi\) | ||||
−0.222772 | + | 0.974871i | \(0.571510\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 437.185i | − 1.09024i | −0.838359 | − | 0.545119i | \(-0.816485\pi\) | ||||
0.838359 | − | 0.545119i | \(-0.183515\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 264.038 | 0.655182 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.0083i | 0.0245905i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −145.904 | −0.356733 | −0.178367 | − | 0.983964i | \(-0.557081\pi\) | ||||
−0.178367 | + | 0.983964i | \(0.557081\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 516.830i | 1.25140i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −68.4693 | −0.164986 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 133.431i | 0.318451i | 0.987242 | + | 0.159226i | \(0.0508998\pi\) | ||||
−0.987242 | + | 0.159226i | \(0.949100\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 288.692 | 0.685730 | 0.342865 | − | 0.939385i | \(-0.388603\pi\) | ||||
0.342865 | + | 0.939385i | \(0.388603\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 268.401i | 0.631532i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −190.627 | −0.446433 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 669.565i | − 1.55351i | −0.629800 | − | 0.776757i | \(-0.716863\pi\) | ||||
0.629800 | − | 0.776757i | \(-0.283137\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −510.654 | −1.17934 | −0.589669 | − | 0.807645i | \(-0.700742\pi\) | ||||
−0.589669 | + | 0.807645i | \(0.700742\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 1109.36i | − 2.53858i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 77.2999 | 0.176082 | 0.0880409 | − | 0.996117i | \(-0.471939\pi\) | ||||
0.0880409 | + | 0.996117i | \(0.471939\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 759.351i | − 1.71411i | −0.515224 | − | 0.857055i | \(-0.672291\pi\) | ||||
0.515224 | − | 0.857055i | \(-0.327709\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −644.769 | −1.44892 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 541.149i | − 1.20523i | −0.798032 | − | 0.602616i | \(-0.794125\pi\) | ||||
0.798032 | − | 0.602616i | \(-0.205875\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −80.3538 | −0.178168 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 409.099i | 0.899119i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −55.5885 | −0.121638 | −0.0608189 | − | 0.998149i | \(-0.519371\pi\) | ||||
−0.0608189 | + | 0.998149i | \(0.519371\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 250.702i | 0.543822i | 0.962322 | + | 0.271911i | \(0.0876557\pi\) | ||||
−0.962322 | + | 0.271911i | \(0.912344\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 571.023 | 1.23331 | 0.616656 | − | 0.787233i | \(-0.288487\pi\) | ||||
0.616656 | + | 0.787233i | \(0.288487\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 72.2663i | 0.154746i | 0.997002 | + | 0.0773729i | \(0.0246532\pi\) | ||||
−0.997002 | + | 0.0773729i | \(0.975347\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 65.6077 | 0.139888 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 67.9420i | − 0.143641i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 283.254 | 0.596324 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 707.526i | 1.47709i | 0.674205 | + | 0.738544i | \(0.264486\pi\) | ||||
−0.674205 | + | 0.738544i | \(0.735514\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −100.296 | −0.208516 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 430.699i | 0.888039i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 360.908 | 0.741083 | 0.370542 | − | 0.928816i | \(-0.379172\pi\) | ||||
0.370542 | + | 0.928816i | \(0.379172\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 680.019i | 1.38497i | 0.721433 | + | 0.692484i | \(0.243484\pi\) | ||||
−0.721433 | + | 0.692484i | \(0.756516\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −799.015 | −1.62072 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 22.5133i | 0.0452983i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 236.704 | 0.474356 | 0.237178 | − | 0.971466i | \(-0.423777\pi\) | ||||
0.237178 | + | 0.971466i | \(0.423777\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 95.6715i | 0.190202i | 0.995468 | + | 0.0951009i | \(0.0303174\pi\) | ||||
−0.995468 | + | 0.0951009i | \(0.969683\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 100.119 | 0.198256 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 435.224i | 0.855057i | 0.904002 | + | 0.427529i | \(0.140616\pi\) | ||||
−0.904002 | + | 0.427529i | \(0.859384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 106.788 | 0.208979 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 649.102i | − 1.26039i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −68.4693 | −0.132436 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 794.771i | − 1.52547i | −0.646709 | − | 0.762737i | \(-0.723855\pi\) | ||||
0.646709 | − | 0.762737i | \(-0.276145\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −594.481 | −1.13667 | −0.568337 | − | 0.822796i | \(-0.692413\pi\) | ||||
−0.568337 | + | 0.822796i | \(0.692413\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 724.311i | 1.37440i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −602.415 | −1.13878 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 805.248i | − 1.51078i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −818.008 | −1.52899 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 12.0590i | − 0.0223728i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 219.508 | 0.405744 | 0.202872 | − | 0.979205i | \(-0.434972\pi\) | ||||
0.202872 | + | 0.979205i | \(0.434972\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 995.141i | 1.82595i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −584.592 | −1.06872 | −0.534362 | − | 0.845256i | \(-0.679448\pi\) | ||||
−0.534362 | + | 0.845256i | \(0.679448\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 843.230i | 1.53036i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −702.477 | −1.27030 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 597.187i | − 1.07215i | −0.844171 | − | 0.536075i | \(-0.819907\pi\) | ||||
0.844171 | − | 0.536075i | \(-0.180093\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 680.865 | 1.21801 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 360.216i | − 0.639816i | −0.947449 | − | 0.319908i | \(-0.896348\pi\) | ||||
0.947449 | − | 0.319908i | \(-0.103652\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.2961 | −0.0571613 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 561.723i | 0.987211i | 0.869686 | + | 0.493605i | \(0.164321\pi\) | ||||
−0.869686 | + | 0.493605i | \(0.835679\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.0770 | −0.0666847 | −0.0333423 | − | 0.999444i | \(-0.510615\pi\) | ||||
−0.0333423 | + | 0.999444i | \(0.510615\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 288.886i | − 0.502410i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −747.008 | −1.29464 | −0.647320 | − | 0.762218i | \(-0.724110\pi\) | ||||
−0.647320 | + | 0.762218i | \(0.724110\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 73.2020i | − 0.125993i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.4768 | −0.0385537 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 599.773i | − 1.02176i | −0.859652 | − | 0.510880i | \(-0.829320\pi\) | ||||
0.859652 | − | 0.510880i | \(-0.170680\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 764.392 | 1.29778 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 212.184i | − 0.357814i | −0.983866 | − | 0.178907i | \(-0.942744\pi\) | ||||
0.983866 | − | 0.178907i | \(-0.0572561\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1122.24 | −1.88612 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 325.220i | 0.542938i | 0.962447 | + | 0.271469i | \(0.0875095\pi\) | ||||
−0.962447 | + | 0.271469i | \(0.912491\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 747.477 | 1.24372 | 0.621861 | − | 0.783128i | \(-0.286377\pi\) | ||||
0.621861 | + | 0.783128i | \(0.286377\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 693.772i | 1.14673i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −123.727 | −0.203833 | −0.101917 | − | 0.994793i | \(-0.532498\pi\) | ||||
−0.101917 | + | 0.994793i | \(0.532498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 686.149i | − 1.12299i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −954.008 | −1.55629 | −0.778146 | − | 0.628083i | \(-0.783840\pi\) | ||||
−0.778146 | + | 0.628083i | \(0.783840\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 250.123i | 0.405385i | 0.979242 | + | 0.202693i | \(0.0649692\pi\) | ||||
−0.979242 | + | 0.202693i | \(0.935031\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1017.54 | −1.64384 | −0.821921 | − | 0.569601i | \(-0.807098\pi\) | ||||
−0.821921 | + | 0.569601i | \(0.807098\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 689.337i | − 1.10648i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −765.950 | −1.22552 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 275.133i | − 0.437413i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −75.6001 | −0.119810 | −0.0599050 | − | 0.998204i | \(-0.519080\pi\) | ||||
−0.0599050 | + | 0.998204i | \(0.519080\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 395.458i | − 0.622768i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 120.846 | 0.189711 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 242.366i | − 0.378106i | −0.981967 | − | 0.189053i | \(-0.939458\pi\) | ||||
0.981967 | − | 0.189053i | \(-0.0605418\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −733.184 | −1.14026 | −0.570128 | − | 0.821556i | \(-0.693106\pi\) | ||||
−0.570128 | + | 0.821556i | \(0.693106\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 1177.72i | − 1.82028i | −0.414296 | − | 0.910142i | \(-0.635972\pi\) | ||||
0.414296 | − | 0.910142i | \(-0.364028\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 94.8231 | 0.146106 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 635.259i | 0.972832i | 0.873727 | + | 0.486416i | \(0.161696\pi\) | ||||
−0.873727 | + | 0.486416i | \(0.838304\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 893.065 | 1.36346 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 916.389i | − 1.39057i | −0.718732 | − | 0.695287i | \(-0.755277\pi\) | ||||
0.718732 | − | 0.695287i | \(-0.244723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 413.358 | 0.625352 | 0.312676 | − | 0.949860i | \(-0.398775\pi\) | ||||
0.312676 | + | 0.949860i | \(0.398775\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1184.34i | 1.78097i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 859.996 | 1.28935 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.9744i | 0.0521229i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −732.454 | −1.08834 | −0.544171 | − | 0.838975i | \(-0.683156\pi\) | ||||
−0.544171 | + | 0.838975i | \(0.683156\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 585.686i | 0.865119i | 0.901605 | + | 0.432559i | \(0.142389\pi\) | ||||
−0.901605 | + | 0.432559i | \(0.857611\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −460.469 | −0.678158 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1082.97i | 1.58560i | 0.609480 | + | 0.792801i | \(0.291378\pi\) | ||||
−0.609480 | + | 0.792801i | \(0.708622\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 443.238 | 0.647063 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 225.246i | − 0.326918i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −178.358 | −0.258115 | −0.129058 | − | 0.991637i | \(-0.541195\pi\) | ||||
−0.129058 | + | 0.991637i | \(0.541195\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 545.005i | 0.784180i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2208.96 | 3.16924 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 638.090i | − 0.910257i | −0.890426 | − | 0.455129i | \(-0.849593\pi\) | ||||
0.890426 | − | 0.455129i | \(-0.150407\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −290.358 | −0.413026 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 107.040i | 0.151400i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 824.846 | 1.16339 | 0.581697 | − | 0.813406i | \(-0.302389\pi\) | ||||
0.581697 | + | 0.813406i | \(0.302389\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 779.591i | − 1.09340i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 75.0577 | 0.104976 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 748.451i | 1.04096i | 0.853874 | + | 0.520480i | \(0.174247\pi\) | ||||
−0.853874 | + | 0.520480i | \(0.825753\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 693.969 | 0.962509 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 219.584i | 0.302874i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.3576 | 0.0362553 | 0.0181276 | − | 0.999836i | \(-0.494229\pi\) | ||||
0.0181276 | + | 0.999836i | \(0.494229\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1867.75i | 2.55506i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1072.95 | −1.46377 | −0.731887 | − | 0.681426i | \(-0.761360\pi\) | ||||
−0.731887 | + | 0.681426i | \(0.761360\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 12.0371i | − 0.0163325i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 158.831 | 0.214926 | 0.107463 | − | 0.994209i | \(-0.465727\pi\) | ||||
0.107463 | + | 0.994209i | \(0.465727\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 164.059i | − 0.220807i | −0.993887 | − | 0.110403i | \(-0.964786\pi\) | ||||
0.993887 | − | 0.110403i | \(-0.0352143\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −389.238 | −0.522468 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 874.549i | − 1.16762i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 232.396 | 0.309449 | 0.154724 | − | 0.987958i | \(-0.450551\pi\) | ||||
0.154724 | + | 0.987958i | \(0.450551\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 268.646i | 0.355823i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1012.72 | 1.33781 | 0.668905 | − | 0.743348i | \(-0.266763\pi\) | ||||
0.668905 | + | 0.743348i | \(0.266763\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − 578.998i | − 0.760838i | −0.924814 | − | 0.380419i | \(-0.875780\pi\) | ||||
0.924814 | − | 0.380419i | \(-0.124220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1063.93 | −1.39440 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 950.248i | 1.23892i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −267.269 | −0.347554 | −0.173777 | − | 0.984785i | \(-0.555597\pi\) | ||||
−0.173777 | + | 0.984785i | \(0.555597\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1356.98i | 1.75548i | 0.479140 | + | 0.877739i | \(0.340949\pi\) | ||||
−0.479140 | + | 0.877739i | \(0.659051\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 199.054 | 0.256844 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 2331.19i | − 2.99255i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.13052 | 0.00528876 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 982.859i | − 1.25205i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 57.8808 | 0.0735461 | 0.0367731 | − | 0.999324i | \(-0.488292\pi\) | ||||
0.0367731 | + | 0.999324i | \(0.488292\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 34.5285i | − 0.0436517i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −350.488 | −0.441978 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 164.884i | − 0.206880i | −0.994636 | − | 0.103440i | \(-0.967015\pi\) | ||||
0.994636 | − | 0.103440i | \(-0.0329850\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1882.25 | 2.35575 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 19.5925i | − 0.0243992i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1207.89 | 1.50049 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 981.255i | 1.21292i | 0.795113 | + | 0.606461i | \(0.207412\pi\) | ||||
−0.795113 | + | 0.606461i | \(0.792588\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −289.877 | −0.357432 | −0.178716 | − | 0.983901i | \(-0.557194\pi\) | ||||
−0.178716 | + | 0.983901i | \(0.557194\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1408.45i | − 1.72816i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1971.11 | 2.41262 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 132.139i | 0.160949i | 0.996757 | + | 0.0804745i | \(0.0256435\pi\) | ||||
−0.996757 | + | 0.0804745i | \(0.974356\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 486.192 | 0.590756 | 0.295378 | − | 0.955380i | \(-0.404554\pi\) | ||||
0.295378 | + | 0.955380i | \(0.404554\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 258.192i | − 0.312203i | −0.987741 | − | 0.156101i | \(-0.950107\pi\) | ||||
0.987741 | − | 0.156101i | \(-0.0498927\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −376.400 | −0.454041 | −0.227020 | − | 0.973890i | \(-0.572898\pi\) | ||||
−0.227020 | + | 0.973890i | \(0.572898\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 331.505i | 0.397966i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −653.296 | −0.782391 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 291.584i | 0.347537i | 0.984787 | + | 0.173768i | \(0.0555944\pi\) | ||||
−0.984787 | + | 0.173768i | \(0.944406\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 187.311 | 0.222724 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 227.275i | − 0.268964i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −741.727 | −0.875711 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 296.131i | 0.347980i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 193.538 | 0.226891 | 0.113446 | − | 0.993544i | \(-0.463811\pi\) | ||||
0.113446 | + | 0.993544i | \(0.463811\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 191.677i | 0.223661i | 0.993727 | + | 0.111830i | \(0.0356714\pi\) | ||||
−0.993727 | + | 0.111830i | \(0.964329\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1196.52 | 1.39292 | 0.696458 | − | 0.717597i | \(-0.254758\pi\) | ||||
0.696458 | + | 0.717597i | \(0.254758\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 692.323i | 0.802228i | 0.916028 | + | 0.401114i | \(0.131377\pi\) | ||||
−0.916028 | + | 0.401114i | \(0.868623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1088.65 | 1.25856 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 128.884i | 0.148313i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 120.627 | 0.138492 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 589.341i | − 0.673532i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1026.61 | −1.17059 | −0.585297 | − | 0.810819i | \(-0.699022\pi\) | ||||
−0.585297 | + | 0.810819i | \(0.699022\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 984.820i | − 1.11784i | −0.829220 | − | 0.558922i | \(-0.811215\pi\) | ||||
0.829220 | − | 0.558922i | \(-0.188785\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1038.19 | 1.17576 | 0.587878 | − | 0.808950i | \(-0.299964\pi\) | ||||
0.587878 | + | 0.808950i | \(0.299964\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 169.564i | − 0.191166i | −0.995421 | − | 0.0955830i | \(-0.969528\pi\) | ||||
0.995421 | − | 0.0955830i | \(-0.0304715\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 422.792 | 0.475582 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 1986.40i | − 2.22442i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −94.8231 | −0.105948 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 592.572i | 0.659146i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 617.896 | 0.685789 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 1319.11i | − 1.45758i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 731.962 | 0.807014 | 0.403507 | − | 0.914977i | \(-0.367791\pi\) | ||||
0.403507 | + | 0.914977i | \(0.367791\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 985.712i | 1.08201i | 0.841019 | + | 0.541006i | \(0.181956\pi\) | ||||
−0.841019 | + | 0.541006i | \(0.818044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.4304 | −0.0147102 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 954.795i | 1.04122i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −839.650 | −0.913656 | −0.456828 | − | 0.889555i | \(-0.651015\pi\) | ||||
−0.456828 | + | 0.889555i | \(0.651015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 41.3931i | 0.0448462i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −75.6115 | −0.0817421 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 599.706i | 0.645539i | 0.946478 | + | 0.322769i | \(0.104614\pi\) | ||||
−0.946478 | + | 0.322769i | \(0.895386\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 349.850 | 0.375779 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 205.899i | 0.220212i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1610.24 | 1.71850 | 0.859252 | − | 0.511553i | \(-0.170930\pi\) | ||||
0.859252 | + | 0.511553i | \(0.170930\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 880.100i | 0.935282i | 0.883919 | + | 0.467641i | \(0.154896\pi\) | ||||
−0.883919 | + | 0.467641i | \(0.845104\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2377.55 | −2.52126 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 985.043i | 1.04017i | 0.854114 | + | 0.520086i | \(0.174100\pi\) | ||||
−0.854114 | + | 0.520086i | \(0.825900\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 196.342 | 0.206894 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 845.550i | 0.887251i | 0.896212 | + | 0.443625i | \(0.146308\pi\) | ||||
−0.896212 | + | 0.443625i | \(0.853692\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2112.84 | −2.21240 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 473.876i | 0.494135i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −423.831 | −0.441031 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 144.220i | − 0.149451i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1026.94 | −1.06199 | −0.530994 | − | 0.847376i | \(-0.678181\pi\) | ||||
−0.530994 | + | 0.847376i | \(0.678181\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 338.171i | − 0.348271i | −0.984722 | − | 0.174135i | \(-0.944287\pi\) | ||||
0.984722 | − | 0.174135i | \(-0.0557130\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −582.677 | −0.598846 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 911.618i | 0.933079i | 0.884500 | + | 0.466540i | \(0.154499\pi\) | ||||
−0.884500 | + | 0.466540i | \(0.845501\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −126.473 | −0.129186 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 957.961i | 0.974528i | 0.873255 | + | 0.487264i | \(0.162005\pi\) | ||||
−0.873255 | + | 0.487264i | \(0.837995\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 992.538 | 1.00765 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 2010.30i | − 2.03266i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1771.18 | 1.78727 | 0.893633 | − | 0.448798i | \(-0.148148\pi\) | ||||
0.893633 | + | 0.448798i | \(0.148148\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 709.554i | 0.713120i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1088.65 | −1.09193 | −0.545963 | − | 0.837809i | \(-0.683836\pi\) | ||||
−0.545963 | + | 0.837809i | \(0.683836\pi\) | |||||||
\(998\) | 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 | 324.3.c.a.161.4 | yes | 4 | |
3.2 | odd | 2 | inner | 324.3.c.a.161.1 | ✓ | 4 | |
4.3 | odd | 2 | 1296.3.e.f.161.4 | 4 | |||
9.2 | odd | 6 | 324.3.g.d.53.4 | 8 | |||
9.4 | even | 3 | 324.3.g.d.269.4 | 8 | |||
9.5 | odd | 6 | 324.3.g.d.269.1 | 8 | |||
9.7 | even | 3 | 324.3.g.d.53.1 | 8 | |||
12.11 | even | 2 | 1296.3.e.f.161.1 | 4 | |||
36.7 | odd | 6 | 1296.3.q.n.1025.1 | 8 | |||
36.11 | even | 6 | 1296.3.q.n.1025.4 | 8 | |||
36.23 | even | 6 | 1296.3.q.n.593.1 | 8 | |||
36.31 | odd | 6 | 1296.3.q.n.593.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.3.c.a.161.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
324.3.c.a.161.4 | yes | 4 | 1.1 | even | 1 | trivial | |
324.3.g.d.53.1 | 8 | 9.7 | even | 3 | |||
324.3.g.d.53.4 | 8 | 9.2 | odd | 6 | |||
324.3.g.d.269.1 | 8 | 9.5 | odd | 6 | |||
324.3.g.d.269.4 | 8 | 9.4 | even | 3 | |||
1296.3.e.f.161.1 | 4 | 12.11 | even | 2 | |||
1296.3.e.f.161.4 | 4 | 4.3 | odd | 2 | |||
1296.3.q.n.593.1 | 8 | 36.23 | even | 6 | |||
1296.3.q.n.593.4 | 8 | 36.31 | odd | 6 | |||
1296.3.q.n.1025.1 | 8 | 36.7 | odd | 6 | |||
1296.3.q.n.1025.4 | 8 | 36.11 | even | 6 |