Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2352,3,Mod(1471,2352)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2352, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2352.1471");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2352 = 2^{4} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2352.m (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: | \(64.0873581775\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{37})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 10x^{2} + 9x + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.4 | ||
Root | \(1.77069 + 3.06693i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2352.1471 |
Dual form | 2352.3.m.e.1471.2 |
$q$-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 \(\left(\mathbb{Z}/2352\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1471\) | \(1765\) | \(2257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.08276 | 0.616553 | 0.308276 | − | 0.951297i | \(-0.400248\pi\) | ||||
0.308276 | + | 0.951297i | \(0.400248\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 12.2677i | 1.11525i | 0.830094 | + | 0.557623i | \(0.188286\pi\) | ||||
−0.830094 | + | 0.557623i | \(0.811714\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.33950i | 0.355967i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 15.0828 | 0.887221 | 0.443611 | − | 0.896220i | \(-0.353697\pi\) | ||||
0.443611 | + | 0.896220i | \(0.353697\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 24.5354i | 1.29134i | 0.763618 | + | 0.645669i | \(0.223421\pi\) | ||||
−0.763618 | + | 0.645669i | \(0.776579\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.51691i | 0.370300i | 0.982710 | + | 0.185150i | \(0.0592771\pi\) | ||||
−0.982710 | + | 0.185150i | \(0.940723\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15.4966 | −0.619863 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.19615i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −24.4966 | −0.844709 | −0.422355 | − | 0.906431i | \(-0.638796\pi\) | ||||
−0.422355 | + | 0.906431i | \(0.638796\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.75080i | 0.120994i | 0.998168 | + | 0.0604968i | \(0.0192685\pi\) | ||||
−0.998168 | + | 0.0604968i | \(0.980732\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −21.2483 | −0.643888 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 52.4966 | 1.41883 | 0.709413 | − | 0.704793i | \(-0.248960\pi\) | ||||
0.709413 | + | 0.704793i | \(0.248960\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −39.0828 | −0.953238 | −0.476619 | − | 0.879110i | \(-0.658138\pi\) | ||||
−0.476619 | + | 0.879110i | \(0.658138\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 27.7128i | − 0.644484i | −0.946657 | − | 0.322242i | \(-0.895564\pi\) | ||||
0.946657 | − | 0.322242i | \(-0.104436\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9.24829 | −0.205518 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 21.3580i | − 0.454426i | −0.973845 | − | 0.227213i | \(-0.927039\pi\) | ||||
0.973845 | − | 0.227213i | \(-0.0729613\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 26.1241i | 0.512237i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11.5034 | 0.217046 | 0.108523 | − | 0.994094i | \(-0.465388\pi\) | ||||
0.108523 | + | 0.994094i | \(0.465388\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 37.8184i | 0.687608i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −42.4966 | −0.745554 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 42.1426i | − 0.714282i | −0.934051 | − | 0.357141i | \(-0.883752\pi\) | ||||
0.934051 | − | 0.357141i | \(-0.116248\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −29.5034 | −0.483663 | −0.241831 | − | 0.970318i | \(-0.577748\pi\) | ||||
−0.241831 | + | 0.970318i | \(0.577748\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 73.6062i | 1.09860i | 0.835625 | + | 0.549300i | \(0.185106\pi\) | ||||
−0.835625 | + | 0.549300i | \(0.814894\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −14.7517 | −0.213793 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 40.5539i | 0.571182i | 0.958352 | + | 0.285591i | \(0.0921899\pi\) | ||||
−0.958352 | + | 0.285591i | \(0.907810\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 42.4966 | 0.582145 | 0.291072 | − | 0.956701i | \(-0.405988\pi\) | ||||
0.291072 | + | 0.956701i | \(0.405988\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 26.8409i | − 0.357878i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 23.3886i | 0.296058i | 0.988983 | + | 0.148029i | \(0.0472930\pi\) | ||||
−0.988983 | + | 0.148029i | \(0.952707\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 83.7118i | 1.00858i | 0.863535 | + | 0.504288i | \(0.168245\pi\) | ||||
−0.863535 | + | 0.504288i | \(0.831755\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 46.4966 | 0.547019 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 42.4293i | − 0.487693i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −148.076 | −1.66377 | −0.831887 | − | 0.554945i | \(-0.812739\pi\) | ||||
−0.831887 | + | 0.554945i | \(0.812739\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.49658 | −0.0698556 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 75.6368i | 0.796177i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −186.497 | −1.92265 | −0.961323 | − | 0.275425i | \(-0.911181\pi\) | ||||
−0.961323 | + | 0.275425i | \(0.911181\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 36.8031i | − 0.371749i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.0759 | −0.159167 | −0.0795837 | − | 0.996828i | \(-0.525359\pi\) | ||||
−0.0795837 | + | 0.996828i | \(0.525359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 109.394i | 1.06208i | 0.847347 | + | 0.531039i | \(0.178198\pi\) | ||||
−0.847347 | + | 0.531039i | \(0.821802\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 68.8401i | 0.643366i | 0.946847 | + | 0.321683i | \(0.104248\pi\) | ||||
−0.946847 | + | 0.321683i | \(0.895752\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.99315 | 0.0274601 | 0.0137300 | − | 0.999906i | \(-0.495629\pi\) | ||||
0.0137300 | + | 0.999906i | \(0.495629\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 90.9267i | 0.819160i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 30.9932 | 0.274276 | 0.137138 | − | 0.990552i | \(-0.456210\pi\) | ||||
0.137138 | + | 0.990552i | \(0.456210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.2556i | 0.228310i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −29.4966 | −0.243773 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 67.6933i | − 0.550352i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −124.841 | −0.998731 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 87.4626i | − 0.688682i | −0.938845 | − | 0.344341i | \(-0.888102\pi\) | ||||
0.938845 | − | 0.344341i | \(-0.111898\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 48.0000 | 0.372093 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 187.061i | 1.42795i | 0.700171 | + | 0.713975i | \(0.253107\pi\) | ||||
−0.700171 | + | 0.713975i | \(0.746893\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − 16.0185i | − 0.118656i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 151.986 | 1.10939 | 0.554695 | − | 0.832054i | \(-0.312835\pi\) | ||||
0.554695 | + | 0.832054i | \(0.312835\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 43.2894i | − 0.311435i | −0.987802 | − | 0.155717i | \(-0.950231\pi\) | ||||
0.987802 | − | 0.155717i | \(-0.0497689\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 36.9932 | 0.262363 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −75.5171 | −0.520808 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11.5034 | 0.0772042 | 0.0386021 | − | 0.999255i | \(-0.487710\pi\) | ||||
0.0386021 | + | 0.999255i | \(0.487710\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 266.712i | − 1.76631i | −0.469086 | − | 0.883153i | \(-0.655416\pi\) | ||||
0.469086 | − | 0.883153i | \(-0.344584\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −45.2483 | −0.295740 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 11.5628i | 0.0745989i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 284.483 | 1.81199 | 0.905996 | − | 0.423285i | \(-0.139123\pi\) | ||||
0.905996 | + | 0.423285i | \(0.139123\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 19.9245i | 0.125311i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 82.2546i | 0.504630i | 0.967645 | + | 0.252315i | \(0.0811918\pi\) | ||||
−0.967645 | + | 0.252315i | \(0.918808\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −65.5034 | −0.396990 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 144.919i | 0.867778i | 0.900966 | + | 0.433889i | \(0.142859\pi\) | ||||
−0.900966 | + | 0.433889i | \(0.857141\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −169.000 | −1.00000 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 73.6062i | − 0.430446i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −219.083 | −1.26637 | −0.633187 | − | 0.773999i | \(-0.718254\pi\) | ||||
−0.633187 | + | 0.773999i | \(0.718254\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 72.9932 | 0.412391 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 119.942i | 0.670065i | 0.942207 | + | 0.335032i | \(0.108747\pi\) | ||||
−0.942207 | + | 0.335032i | \(0.891253\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −313.986 | −1.73473 | −0.867365 | − | 0.497672i | \(-0.834188\pi\) | ||||
−0.867365 | + | 0.497672i | \(0.834188\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 51.1014i | − 0.279243i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 161.834 | 0.874781 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 185.031i | 0.989470i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 344.511i | − 1.80372i | −0.432026 | − | 0.901861i | \(-0.642201\pi\) | ||||
0.432026 | − | 0.901861i | \(-0.357799\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 69.4897 | 0.360050 | 0.180025 | − | 0.983662i | \(-0.442382\pi\) | ||||
0.180025 | + | 0.983662i | \(0.442382\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 325.490 | 1.65223 | 0.826116 | − | 0.563500i | \(-0.190546\pi\) | ||||
0.826116 | + | 0.563500i | \(0.190546\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 56.5724i | 0.284284i | 0.989846 | + | 0.142142i | \(0.0453989\pi\) | ||||
−0.989846 | + | 0.142142i | \(0.954601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −127.490 | −0.634277 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −120.483 | −0.587721 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 25.5507i | − 0.123433i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −300.993 | −1.44016 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 147.212i | 0.697689i | 0.937181 | + | 0.348845i | \(0.113426\pi\) | ||||
−0.937181 | + | 0.348845i | \(0.886574\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −70.2414 | −0.329772 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 85.4320i | − 0.397358i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 73.6062i | 0.336101i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 340.055i | 1.52491i | 0.647040 | + | 0.762456i | \(0.276007\pi\) | ||||
−0.647040 | + | 0.762456i | \(0.723993\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 46.4897 | 0.206621 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 334.274i | − 1.47257i | −0.676670 | − | 0.736286i | \(-0.736578\pi\) | ||||
0.676670 | − | 0.736286i | \(-0.263422\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −398.979 | −1.74227 | −0.871134 | − | 0.491045i | \(-0.836615\pi\) | ||||
−0.871134 | + | 0.491045i | \(0.836615\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −306.000 | −1.31330 | −0.656652 | − | 0.754193i | \(-0.728028\pi\) | ||||
−0.656652 | + | 0.754193i | \(0.728028\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 65.8417i | − 0.280177i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −40.5103 | −0.170929 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 307.003i | 1.28453i | 0.766482 | + | 0.642266i | \(0.222005\pi\) | ||||
−0.766482 | + | 0.642266i | \(0.777995\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −153.476 | −0.636830 | −0.318415 | − | 0.947951i | \(-0.603151\pi\) | ||||
−0.318415 | + | 0.947951i | \(0.603151\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −144.993 | −0.582302 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 147.786i | 0.588788i | 0.955684 | + | 0.294394i | \(0.0951178\pi\) | ||||
−0.955684 | + | 0.294394i | \(0.904882\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −104.483 | −0.412976 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 80.5344i | 0.315821i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −74.0896 | −0.288286 | −0.144143 | − | 0.989557i | \(-0.546043\pi\) | ||||
−0.144143 | + | 0.989557i | \(0.546043\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 73.4897 | 0.281570 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 216.363i | 0.822673i | 0.911484 | + | 0.411337i | \(0.134938\pi\) | ||||
−0.911484 | + | 0.411337i | \(0.865062\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 35.4623 | 0.133820 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 256.475i | − 0.960581i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 221.069 | 0.821818 | 0.410909 | − | 0.911676i | \(-0.365211\pi\) | ||||
0.410909 | + | 0.911676i | \(0.365211\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 113.455i | 0.418654i | 0.977846 | + | 0.209327i | \(0.0671273\pi\) | ||||
−0.977846 | + | 0.209327i | \(0.932873\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 190.107i | − 0.691300i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −286.483 | −1.03423 | −0.517117 | − | 0.855915i | \(-0.672995\pi\) | ||||
−0.517117 | + | 0.855915i | \(0.672995\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − 11.2524i | − 0.0403312i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −56.9795 | −0.202774 | −0.101387 | − | 0.994847i | \(-0.532328\pi\) | ||||
−0.101387 | + | 0.994847i | \(0.532328\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 428.665i | − 1.51472i | −0.653000 | − | 0.757358i | \(-0.726490\pi\) | ||||
0.653000 | − | 0.757358i | \(-0.273510\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −131.007 | −0.459673 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −61.5103 | −0.212838 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 323.022i | − 1.11004i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −376.076 | −1.28354 | −0.641768 | − | 0.766899i | \(-0.721799\pi\) | ||||
−0.641768 | + | 0.766899i | \(0.721799\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 129.916i | − 0.440392i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 63.7449 | 0.214629 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 27.8443i | − 0.0918954i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −90.9521 | −0.298203 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 130.179i | 0.424035i | 0.977266 | + | 0.212017i | \(0.0680033\pi\) | ||||
−0.977266 | + | 0.212017i | \(0.931997\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −189.476 | −0.613191 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 269.627i | 0.866966i | 0.901162 | + | 0.433483i | \(0.142716\pi\) | ||||
−0.901162 | + | 0.433483i | \(0.857284\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.9863 | 0.0830233 | 0.0415117 | − | 0.999138i | \(-0.486783\pi\) | ||||
0.0415117 | + | 0.999138i | \(0.486783\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 364.469 | 1.14975 | 0.574873 | − | 0.818243i | \(-0.305052\pi\) | ||||
0.574873 | + | 0.818243i | \(0.305052\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − 300.517i | − 0.942059i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −119.235 | −0.371447 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 370.062i | 1.14570i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.18429i | 0.0158541i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 219.935i | − 0.664456i | −0.943199 | − | 0.332228i | \(-0.892200\pi\) | ||||
0.943199 | − | 0.332228i | \(-0.107800\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −157.490 | −0.472942 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 226.911i | 0.677345i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −155.986 | −0.462867 | −0.231434 | − | 0.972851i | \(-0.574342\pi\) | ||||
−0.231434 | + | 0.972851i | \(0.574342\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 53.6817i | 0.158353i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −46.0137 | −0.134938 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −45.4760 | −0.131815 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 459.997i | 1.32564i | 0.748779 | + | 0.662820i | \(0.230640\pi\) | ||||
−0.748779 | + | 0.662820i | \(0.769360\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −395.462 | −1.13313 | −0.566565 | − | 0.824017i | \(-0.691728\pi\) | ||||
−0.566565 | + | 0.824017i | \(0.691728\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.07591 | 0.0115465 | 0.00577325 | − | 0.999983i | \(-0.498162\pi\) | ||||
0.00577325 | + | 0.999983i | \(0.498162\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 125.018i | 0.352164i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 28.9911i | 0.0807551i | 0.999184 | + | 0.0403776i | \(0.0128561\pi\) | ||||
−0.999184 | + | 0.0403776i | \(0.987144\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −240.986 | −0.667552 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 51.0896i | − 0.140743i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 131.007 | 0.358923 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 302.547i | 0.824380i | 0.911098 | + | 0.412190i | \(0.135236\pi\) | ||||
−0.911098 | + | 0.412190i | \(0.864764\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 117.248 | 0.317746 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 317.973 | 0.852473 | 0.426237 | − | 0.904612i | \(-0.359839\pi\) | ||||
0.426237 | + | 0.904612i | \(0.359839\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − 216.232i | − 0.576617i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 285.777i | − 0.754028i | −0.926208 | − | 0.377014i | \(-0.876951\pi\) | ||||
0.926208 | − | 0.377014i | \(-0.123049\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 151.490 | 0.397611 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 506.858i | 1.32339i | 0.749773 | + | 0.661695i | \(0.230163\pi\) | ||||
−0.749773 | + | 0.661695i | \(0.769837\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 83.1384i | 0.214828i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 747.476 | 1.92153 | 0.960766 | − | 0.277360i | \(-0.0894594\pi\) | ||||
0.960766 | + | 0.277360i | \(0.0894594\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 128.458i | 0.328538i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −324.000 | −0.824427 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 72.1016i | 0.182536i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −107.462 | −0.270686 | −0.135343 | − | 0.990799i | \(-0.543214\pi\) | ||||
−0.135343 | + | 0.990799i | \(0.543214\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −475.986 | −1.18700 | −0.593499 | − | 0.804835i | \(-0.702254\pi\) | ||||
−0.593499 | + | 0.804835i | \(0.702254\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 27.7449 | 0.0685058 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 644.012i | 1.58234i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 330.497 | 0.808060 | 0.404030 | − | 0.914746i | \(-0.367609\pi\) | ||||
0.404030 | + | 0.914746i | \(0.367609\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 263.248i | 0.640506i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 258.064i | 0.621840i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 74.9795 | 0.179807 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 818.627i | − 1.95376i | −0.213778 | − | 0.976882i | \(-0.568577\pi\) | ||||
0.213778 | − | 0.976882i | \(-0.431423\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 319.476 | 0.758850 | 0.379425 | − | 0.925222i | \(-0.376122\pi\) | ||||
0.379425 | + | 0.925222i | \(0.376122\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 64.0740i | 0.151475i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −233.731 | −0.549956 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 826.308i | 1.91719i | 0.284777 | + | 0.958594i | \(0.408080\pi\) | ||||
−0.284777 | + | 0.958594i | \(0.591920\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 280.966 | 0.648882 | 0.324441 | − | 0.945906i | \(-0.394824\pi\) | ||||
0.324441 | + | 0.945906i | \(0.394824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 130.799i | − 0.300688i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −208.966 | −0.478182 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 777.631i | − 1.77137i | −0.464286 | − | 0.885685i | \(-0.653689\pi\) | ||||
0.464286 | − | 0.885685i | \(-0.346311\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 412.336i | − 0.930781i | −0.885106 | − | 0.465390i | \(-0.845914\pi\) | ||||
0.885106 | − | 0.465390i | \(-0.154086\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −456.483 | −1.02580 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.9245i | 0.0445739i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 306.000 | 0.681514 | 0.340757 | − | 0.940151i | \(-0.389317\pi\) | ||||
0.340757 | + | 0.940151i | \(0.389317\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 479.456i | − 1.06309i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 461.959 | 1.01978 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 443.986 | 0.971524 | 0.485762 | − | 0.874091i | \(-0.338542\pi\) | ||||
0.485762 | + | 0.874091i | \(0.338542\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 78.3723i | − 0.170746i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 613.883 | 1.33163 | 0.665817 | − | 0.746115i | \(-0.268083\pi\) | ||||
0.665817 | + | 0.746115i | \(0.268083\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 695.377i | − 1.50189i | −0.660363 | − | 0.750947i | \(-0.729597\pi\) | ||||
0.660363 | − | 0.750947i | \(-0.270403\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −20.0274 | −0.0430697 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 187.061i | 0.400560i | 0.979739 | + | 0.200280i | \(0.0641852\pi\) | ||||
−0.979739 | + | 0.200280i | \(0.935815\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 492.739i | 1.04615i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 339.973 | 0.718758 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 380.215i | − 0.800452i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −34.5103 | −0.0723486 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 248.269i | 0.518306i | 0.965836 | + | 0.259153i | \(0.0834434\pi\) | ||||
−0.965836 | + | 0.259153i | \(0.916557\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −574.925 | −1.18541 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 147.212i | − 0.302284i | −0.988512 | − | 0.151142i | \(-0.951705\pi\) | ||||
0.988512 | − | 0.151142i | \(-0.0482951\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −142.469 | −0.291348 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 309.344i | 0.630029i | 0.949087 | + | 0.315014i | \(0.102009\pi\) | ||||
−0.949087 | + | 0.315014i | \(0.897991\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −369.476 | −0.749444 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − 113.455i | − 0.229203i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 590.617i | 1.18360i | 0.806084 | + | 0.591801i | \(0.201583\pi\) | ||||
−0.806084 | + | 0.591801i | \(0.798417\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −251.007 | −0.501012 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 820.348i | 1.63091i | 0.578821 | + | 0.815455i | \(0.303513\pi\) | ||||
−0.578821 | + | 0.815455i | \(0.696487\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −49.5582 | −0.0981351 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 292.717i | − 0.577350i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 415.055 | 0.815433 | 0.407716 | − | 0.913109i | \(-0.366325\pi\) | ||||
0.407716 | + | 0.913109i | \(0.366325\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 127.490 | 0.248518 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 337.236i | 0.654827i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 262.014 | 0.506796 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − 379.462i | − 0.731142i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −135.951 | −0.260943 | −0.130472 | − | 0.991452i | \(-0.541649\pi\) | ||||
−0.130472 | + | 0.991452i | \(0.541649\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 386.785i | − 0.739551i | −0.929121 | − | 0.369775i | \(-0.879435\pi\) | ||||
0.929121 | − | 0.369775i | \(-0.120565\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 56.5724i | 0.107348i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 456.462 | 0.862878 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 126.428i | 0.238094i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 212.218i | 0.396669i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −207.745 | −0.386862 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 193.517 | 0.357703 | 0.178851 | − | 0.983876i | \(-0.442762\pi\) | ||||
0.178851 | + | 0.983876i | \(0.442762\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 543.840i | − 1.00155i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 9.22717 | 0.0169306 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 452.937i | − 0.828039i | −0.910268 | − | 0.414019i | \(-0.864125\pi\) | ||||
0.910268 | − | 0.414019i | \(-0.135875\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 88.5103 | 0.161221 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 601.033i | − 1.09080i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 280.306i | 0.505055i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 495.476 | 0.889544 | 0.444772 | − | 0.895644i | \(-0.353285\pi\) | ||||
0.444772 | + | 0.895644i | \(0.353285\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −320.483 | −0.571271 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 549.001i | − 0.975135i | −0.873085 | − | 0.487567i | \(-0.837884\pi\) | ||||
0.873085 | − | 0.487567i | \(-0.162116\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 95.5445 | 0.169105 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 360.952 | 0.634362 | 0.317181 | − | 0.948365i | \(-0.397264\pi\) | ||||
0.317181 | + | 0.948365i | \(0.397264\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 856.446i | − 1.49990i | −0.661492 | − | 0.749952i | \(-0.730076\pi\) | ||||
0.661492 | − | 0.749952i | \(-0.269924\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 596.711 | 1.04138 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 131.983i | − 0.229535i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −450.952 | −0.781546 | −0.390773 | − | 0.920487i | \(-0.627792\pi\) | ||||
−0.390773 | + | 0.920487i | \(0.627792\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 120.360i | 0.207875i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 141.121i | 0.242059i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 708.397i | − 1.20681i | −0.797435 | − | 0.603405i | \(-0.793810\pi\) | ||||
0.797435 | − | 0.603405i | \(-0.206190\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −92.0274 | −0.156243 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 563.765i | 0.953917i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 467.110 | 0.787707 | 0.393853 | − | 0.919173i | \(-0.371142\pi\) | ||||
0.393853 | + | 0.919173i | \(0.371142\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −97.9863 | −0.164131 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 906.006i | 1.51253i | 0.654265 | + | 0.756265i | \(0.272978\pi\) | ||||
−0.654265 | + | 0.756265i | \(0.727022\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 738.952 | 1.22954 | 0.614769 | − | 0.788707i | \(-0.289249\pi\) | ||||
0.614769 | + | 0.788707i | \(0.289249\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 220.819i | − 0.366200i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −90.9309 | −0.150299 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 438.197i | − 0.721906i | −0.932584 | − | 0.360953i | \(-0.882451\pi\) | ||||
0.932584 | − | 0.360953i | \(-0.117549\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 317.945 | 0.518671 | 0.259335 | − | 0.965787i | \(-0.416496\pi\) | ||||
0.259335 | + | 0.965787i | \(0.416496\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 208.682i | − 0.339321i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 766.966 | 1.24306 | 0.621528 | − | 0.783392i | \(-0.286512\pi\) | ||||
0.621528 | + | 0.783392i | \(0.286512\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 470.544i | − 0.760169i | −0.924952 | − | 0.380084i | \(-0.875895\pi\) | ||||
0.924952 | − | 0.380084i | \(-0.124105\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 44.2551 | 0.0712643 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.55822 | 0.00409316 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 521.335i | − 0.831476i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 791.793 | 1.25881 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 251.972i | 0.399322i | 0.979865 | + | 0.199661i | \(0.0639840\pi\) | ||||
−0.979865 | + | 0.199661i | \(0.936016\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −254.979 | −0.402811 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 269.627i | − 0.424609i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − 121.662i | − 0.190394i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 792.952 | 1.23705 | 0.618527 | − | 0.785763i | \(-0.287730\pi\) | ||||
0.618527 | + | 0.785763i | \(0.287730\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 682.141i | − 1.06087i | −0.847725 | − | 0.530436i | \(-0.822028\pi\) | ||||
0.847725 | − | 0.530436i | \(-0.177972\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 147.973 | 0.229415 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1030.49i | 1.59272i | 0.604826 | + | 0.796358i | \(0.293243\pi\) | ||||
−0.604826 | + | 0.796358i | \(0.706757\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 516.993 | 0.796600 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 315.476 | 0.483118 | 0.241559 | − | 0.970386i | \(-0.422341\pi\) | ||||
0.241559 | + | 0.970386i | \(0.422341\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 576.666i | 0.880406i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −127.490 | −0.194048 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1084.32i | 1.64541i | 0.568470 | + | 0.822704i | \(0.307536\pi\) | ||||
−0.568470 | + | 0.822704i | \(0.692464\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −553.531 | −0.837414 | −0.418707 | − | 0.908121i | \(-0.637517\pi\) | ||||
−0.418707 | + | 0.908121i | \(0.637517\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 208.635i | − 0.312796i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −588.993 | −0.880408 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 361.939i | − 0.539403i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −579.449 | −0.860994 | −0.430497 | − | 0.902592i | \(-0.641662\pi\) | ||||
−0.430497 | + | 0.902592i | \(0.641662\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 80.5226i | 0.119293i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1121.86 | 1.65710 | 0.828549 | − | 0.559916i | \(-0.189167\pi\) | ||||
0.828549 | + | 0.559916i | \(0.189167\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 578.979 | 0.850190 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1238.25i | 1.81296i | 0.422253 | + | 0.906478i | \(0.361240\pi\) | ||||
−0.422253 | + | 0.906478i | \(0.638760\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 468.538 | 0.683997 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 691.053i | − 1.00590i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 775.911i | 1.12288i | 0.827517 | + | 0.561441i | \(0.189753\pi\) | ||||
−0.827517 | + | 0.561441i | \(0.810247\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − 133.451i | − 0.192016i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −589.476 | −0.845733 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 530.008i | − 0.758237i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 315.476 | 0.450037 | 0.225019 | − | 0.974354i | \(-0.427756\pi\) | ||||
0.225019 | + | 0.974354i | \(0.427756\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1288.02i | 1.83218i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 114.041 | 0.161760 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −813.007 | −1.14670 | −0.573348 | − | 0.819312i | \(-0.694356\pi\) | ||||
−0.573348 | + | 0.819312i | \(0.694356\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − 70.1659i | − 0.0986862i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −31.9452 | −0.0448039 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −531.745 | −0.741625 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 798.989i | − 1.11125i | −0.831433 | − | 0.555626i | \(-0.812479\pi\) | ||||
0.831433 | − | 0.555626i | \(-0.187521\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 265.828i | − 0.367674i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 379.613 | 0.523604 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 381.935i | 0.525358i | 0.964883 | + | 0.262679i | \(0.0846060\pi\) | ||||
−0.964883 | + | 0.262679i | \(0.915394\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 417.986i | − 0.571800i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1059.97 | 1.44607 | 0.723037 | − | 0.690809i | \(-0.242745\pi\) | ||||
0.723037 | + | 0.690809i | \(0.242745\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −902.979 | −1.22521 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 956.881i | − 1.29483i | −0.762137 | − | 0.647416i | \(-0.775850\pi\) | ||||
0.762137 | − | 0.647416i | \(-0.224150\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 440.622i | 0.593031i | 0.955028 | + | 0.296516i | \(0.0958246\pi\) | ||||
−0.955028 | + | 0.296516i | \(0.904175\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 35.4623 | 0.0476004 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 251.136i | − 0.336192i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 748.246i | 0.996333i | 0.867081 | + | 0.498166i | \(0.165993\pi\) | ||||
−0.867081 | + | 0.498166i | \(0.834007\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −255.973 | −0.339937 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 822.210i | − 1.08902i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −924.897 | −1.22179 | −0.610896 | − | 0.791710i | \(-0.709191\pi\) | ||||
−0.610896 | + | 0.791710i | \(0.709191\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 180.970i | − 0.238432i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 745.883 | 0.980135 | 0.490068 | − | 0.871684i | \(-0.336972\pi\) | ||||
0.490068 | + | 0.871684i | \(0.336972\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −139.490 | −0.182340 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 897.021 | 1.16648 | 0.583238 | − | 0.812301i | \(-0.301785\pi\) | ||||
0.583238 | + | 0.812301i | \(0.301785\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 128.327i | − 0.166442i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 39.8693 | 0.0515773 | 0.0257887 | − | 0.999667i | \(-0.491790\pi\) | ||||
0.0257887 | + | 0.999667i | \(0.491790\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 58.1245i | − 0.0749994i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 958.912i | − 1.23095i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −497.503 | −0.637008 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 127.288i | 0.162564i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 876.993 | 1.11719 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 216.447i | 0.275028i | 0.990500 | + | 0.137514i | \(0.0439112\pi\) | ||||
−0.990500 | + | 0.137514i | \(0.956089\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −374.752 | −0.474970 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 61.4226i | 0.0772611i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 681.910 | 0.855596 | 0.427798 | − | 0.903874i | \(-0.359289\pi\) | ||||
0.427798 | + | 0.903874i | \(0.359289\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − 322.138i | − 0.403176i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 444.228 | 0.554591 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 521.335i | 0.649235i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 382.903i | 0.474477i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1224.95 | −1.51416 | −0.757078 | − | 0.653325i | \(-0.773374\pi\) | ||||
−0.757078 | + | 0.653325i | \(0.773374\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 953.751i | − 1.17602i | −0.808854 | − | 0.588009i | \(-0.799912\pi\) | ||||
0.808854 | − | 0.588009i | \(-0.200088\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −196.510 | −0.241710 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 253.571i | 0.311131i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 679.945 | 0.832246 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 769.408 | 0.937159 | 0.468579 | − | 0.883421i | \(-0.344766\pi\) | ||||
0.468579 | + | 0.883421i | \(0.344766\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 605.358i | − 0.735550i | −0.929915 | − | 0.367775i | \(-0.880120\pi\) | ||||
0.929915 | − | 0.367775i | \(-0.119880\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 329.276 | 0.399122 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 764.575i | 0.924516i | 0.886745 | + | 0.462258i | \(0.152961\pi\) | ||||
−0.886745 | + | 0.462258i | \(0.847039\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 313.986 | 0.378753 | 0.189377 | − | 0.981905i | \(-0.439353\pi\) | ||||
0.189377 | + | 0.981905i | \(0.439353\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 496.203i | − 0.597115i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 446.750i | 0.535031i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.4897 | 0.0232852 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 43.8628i | − 0.0522799i | −0.999658 | − | 0.0261399i | \(-0.991678\pi\) | ||||
0.999658 | − | 0.0261399i | \(-0.00832155\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −240.918 | −0.286466 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 98.6913i | − 0.117072i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −520.987 | −0.616553 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 742.469 | 0.874522 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 447.108i | 0.525392i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 860.483 | 1.00877 | 0.504386 | − | 0.863478i | \(-0.331719\pi\) | ||||
0.504386 | + | 0.863478i | \(0.331719\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − 226.911i | − 0.265392i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −879.994 | −1.02683 | −0.513415 | − | 0.858140i | \(-0.671620\pi\) | ||||
−0.513415 | + | 0.858140i | \(0.671620\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 221.440i | − 0.257788i | −0.991658 | − | 0.128894i | \(-0.958857\pi\) | ||||
0.991658 | − | 0.128894i | \(-0.0411426\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 1282.95i | − 1.48661i | −0.668950 | − | 0.743307i | \(-0.733256\pi\) | ||||
0.668950 | − | 0.743307i | \(-0.266744\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −675.380 | −0.780786 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 106.539i | − 0.122882i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −286.925 | −0.330178 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 559.490 | 0.640882 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.0411 | −0.0502179 | −0.0251089 | − | 0.999685i | \(-0.507993\pi\) | ||||
−0.0251089 | + | 0.999685i | \(0.507993\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − 651.383i | − 0.741050i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1605.95 | 1.82287 | 0.911437 | − | 0.411439i | \(-0.134974\pi\) | ||||
0.911437 | + | 0.411439i | \(0.134974\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 694.588i | − 0.786623i | −0.919405 | − | 0.393311i | \(-0.871329\pi\) | ||||
0.919405 | − | 0.393311i | \(-0.128671\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 225.021 | 0.254261 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 1102.16i | − 1.24257i | −0.783586 | − | 0.621284i | \(-0.786611\pi\) | ||||
0.783586 | − | 0.621284i | \(-0.213389\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 110.409i | 0.123916i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 524.027 | 0.586817 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 369.751i | 0.413130i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 91.8817i | − 0.102204i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 173.503 | 0.192568 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −967.945 | −1.06955 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 720.533i | − 0.794414i | −0.917729 | − | 0.397207i | \(-0.869980\pi\) | ||||
0.917729 | − | 0.397207i | \(-0.130020\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 48.2277 | 0.0530558 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 751.292i | 0.824689i | 0.911028 | + | 0.412345i | \(0.135290\pi\) | ||||
−0.911028 | + | 0.412345i | \(0.864710\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1026.95 | −1.12481 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 157.534i | − 0.172168i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − 874.626i | − 0.951715i | −0.879522 | − | 0.475858i | \(-0.842138\pi\) | ||||
0.879522 | − | 0.475858i | \(-0.157862\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −225.476 | −0.244817 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −813.517 | −0.879478 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 328.182i | − 0.354026i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −350.007 | −0.376757 | −0.188379 | − | 0.982096i | \(-0.560323\pi\) | ||||
−0.188379 | + | 0.982096i | \(0.560323\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −467.007 | −0.500543 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 570.406i | 0.610060i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 169.986 | 0.181415 | 0.0907077 | − | 0.995878i | \(-0.471087\pi\) | ||||
0.0907077 | + | 0.995878i | \(0.471087\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 45.0096i | 0.0479335i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1454.79 | −1.54601 | −0.773004 | − | 0.634401i | \(-0.781247\pi\) | ||||
−0.773004 | + | 0.634401i | \(0.781247\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 332.864i | − 0.352984i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 712.853i | − 0.752748i | −0.926468 | − | 0.376374i | \(-0.877171\pi\) | ||||
0.926468 | − | 0.376374i | \(-0.122829\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 631.279i | 0.663806i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 84.0411 | 0.0881858 | 0.0440929 | − | 0.999027i | \(-0.485960\pi\) | ||||
0.0440929 | + | 0.999027i | \(0.485960\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1062.05i | − 1.11209i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 520.510 | 0.543898 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 946.932 | 0.985361 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 206.520i | − 0.214455i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 214.220 | 0.221990 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1772.64i | 1.83313i | 0.399880 | + | 0.916567i | \(0.369052\pi\) | ||||
−0.399880 | + | 0.916567i | \(0.630948\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −640.966 | −0.661471 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 383.871i | − 0.395335i | −0.980269 | − | 0.197668i | \(-0.936663\pi\) | ||||
0.980269 | − | 0.197668i | \(-0.0633367\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 373.945 | 0.382748 | 0.191374 | − | 0.981517i | \(-0.438706\pi\) | ||||
0.191374 | + | 0.981517i | \(0.438706\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 1816.55i | − 1.85552i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.97945 | −0.00915337 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 681.878i | 0.693671i | 0.937926 | + | 0.346835i | \(0.112744\pi\) | ||||
−0.937926 | + | 0.346835i | \(0.887256\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1003.41 | 1.01869 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 236.027 | 0.238653 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 81.3708i | 0.0821098i | 0.999157 | + | 0.0410549i | \(0.0130719\pi\) | ||||
−0.999157 | + | 0.0410549i | \(0.986928\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 380.938 | 0.383624 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 174.399i | 0.175276i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1408.35 | 1.41258 | 0.706292 | − | 0.707921i | \(-0.250367\pi\) | ||||
0.706292 | + | 0.707921i | \(0.250367\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − 272.780i | − 0.273053i |
(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 | 2352.3.m.e.1471.4 | yes | 4 | |
4.3 | odd | 2 | inner | 2352.3.m.e.1471.2 | ✓ | 4 | |
7.6 | odd | 2 | 2352.3.m.j.1471.1 | yes | 4 | ||
28.27 | even | 2 | 2352.3.m.j.1471.3 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2352.3.m.e.1471.2 | ✓ | 4 | 4.3 | odd | 2 | inner | |
2352.3.m.e.1471.4 | yes | 4 | 1.1 | even | 1 | trivial | |
2352.3.m.j.1471.1 | yes | 4 | 7.6 | odd | 2 | ||
2352.3.m.j.1471.3 | yes | 4 | 28.27 | even | 2 |