Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(671,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.671");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.h (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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 671.3 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.671 |
Dual form | 2240.2.h.d.671.1 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | 0.957427 | + | 0.288675i | \(0.0932147\pi\) | ||||
−0.957427 | + | 0.288675i | \(0.906785\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | − | 2.00000i | −0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.19615 | −1.56670 | −0.783349 | − | 0.621582i | \(-0.786490\pi\) | ||||
−0.783349 | + | 0.621582i | \(0.786490\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000 | 0.277350 | 0.138675 | − | 0.990338i | \(-0.455716\pi\) | ||||
0.138675 | + | 0.990338i | \(0.455716\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.00000i | 0.258199i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.73205i | 0.420084i | 0.977692 | + | 0.210042i | \(0.0673601\pi\) | ||||
−0.977692 | + | 0.210042i | \(0.932640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.00000i | 0.458831i | 0.973329 | + | 0.229416i | \(0.0736815\pi\) | ||||
−0.973329 | + | 0.229416i | \(0.926318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | − | 1.73205i | 0.436436 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.00000i | 0.962250i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.73205i | 0.321634i | 0.986984 | + | 0.160817i | \(0.0514129\pi\) | ||||
−0.986984 | + | 0.160817i | \(0.948587\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.46410 | 0.622171 | 0.311086 | − | 0.950382i | \(-0.399307\pi\) | ||||
0.311086 | + | 0.950382i | \(0.399307\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 5.19615i | − | 0.904534i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.73205 | − | 2.00000i | −0.292770 | − | 0.338062i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.92820i | 1.13899i | 0.821995 | + | 0.569495i | \(0.192861\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000i | 0.160128i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.3923i | 1.62301i | 0.584349 | + | 0.811503i | \(0.301350\pi\) | ||||
−0.584349 | + | 0.811503i | \(0.698650\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.46410 | −0.528271 | −0.264135 | − | 0.964486i | \(-0.585087\pi\) | ||||
−0.264135 | + | 0.964486i | \(0.585087\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.1244 | 1.76852 | 0.884260 | − | 0.466996i | \(-0.154664\pi\) | ||||
0.884260 | + | 0.466996i | \(0.154664\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | + | 6.92820i | −0.142857 | + | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.73205 | −0.242536 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.46410i | 0.475831i | 0.971286 | + | 0.237915i | \(0.0764641\pi\) | ||||
−0.971286 | + | 0.237915i | \(0.923536\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.19615 | −0.700649 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −2.00000 | −0.264906 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 6.00000i | 0.781133i | 0.920575 | + | 0.390567i | \(0.127721\pi\) | ||||
−0.920575 | + | 0.390567i | \(0.872279\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.46410 | − | 4.00000i | −0.436436 | − | 0.503953i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.00000 | 0.124035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.3923 | 1.26962 | 0.634811 | − | 0.772667i | \(-0.281078\pi\) | ||||
0.634811 | + | 0.772667i | \(0.281078\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.00000i | 0.115470i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.00000 | + | 10.3923i | 1.02565 | + | 1.18431i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 1.00000i | − | 0.112509i | −0.998416 | − | 0.0562544i | \(-0.982084\pi\) | ||
0.998416 | − | 0.0562544i | \(-0.0179158\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.73205i | 0.187867i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.73205 | −0.185695 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 6.92820i | − | 0.734388i | −0.930144 | − | 0.367194i | \(-0.880318\pi\) | ||
0.930144 | − | 0.367194i | \(-0.119682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.73205 | − | 2.00000i | −0.181568 | − | 0.209657i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.46410i | 0.359211i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000i | 0.205196i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.66025i | − | 0.879316i | −0.898165 | − | 0.439658i | \(-0.855100\pi\) | ||
0.898165 | − | 0.439658i | \(-0.144900\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −10.3923 | −1.04447 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.73205 | −0.170664 | −0.0853320 | − | 0.996353i | \(-0.527195\pi\) | ||||
−0.0853320 | + | 0.996353i | \(0.527195\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.00000 | − | 1.73205i | 0.195180 | − | 0.169031i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.3923 | −1.00466 | −0.502331 | − | 0.864675i | \(-0.667524\pi\) | ||||
−0.502331 | + | 0.864675i | \(0.667524\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1244i | 1.16130i | 0.814152 | + | 0.580651i | \(0.197202\pi\) | ||||
−0.814152 | + | 0.580651i | \(0.802798\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.92820 | −0.657596 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | 0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3.46410 | − | 3.00000i | 0.317554 | − | 0.275010i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.0000 | 1.45455 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.3923 | −0.937043 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.0000i | − | 1.24230i | −0.783692 | − | 0.621150i | \(-0.786666\pi\) | ||
0.783692 | − | 0.621150i | \(-0.213334\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 3.46410i | − | 0.304997i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.0000i | 1.04844i | 0.851581 | + | 0.524222i | \(0.175644\pi\) | ||||
−0.851581 | + | 0.524222i | \(0.824356\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.00000 | − | 3.46410i | 0.346844 | − | 0.300376i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.00000i | 0.430331i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.0000 | −1.02523 | −0.512615 | − | 0.858619i | \(-0.671323\pi\) | ||||
−0.512615 | + | 0.858619i | \(0.671323\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 16.0000i | 1.35710i | 0.734553 | + | 0.678551i | \(0.237392\pi\) | ||||
−0.734553 | + | 0.678551i | \(0.762608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 12.1244i | 1.02105i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.19615 | −0.434524 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.73205i | 0.143839i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.92820 | − | 1.00000i | −0.571429 | − | 0.0824786i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 13.8564i | − | 1.13516i | −0.823318 | − | 0.567581i | \(-0.807880\pi\) | ||
0.823318 | − | 0.567581i | \(-0.192120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.0000i | 1.38344i | 0.722166 | + | 0.691720i | \(0.243147\pi\) | ||||
−0.722166 | + | 0.691720i | \(0.756853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 3.46410i | 0.280056i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.46410 | 0.278243 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.0000 | 1.11732 | 0.558661 | − | 0.829396i | \(-0.311315\pi\) | ||||
0.558661 | + | 0.829396i | \(0.311315\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.46410 | −0.274721 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 5.19615i | − | 0.404520i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.19615 | 0.402090 | 0.201045 | − | 0.979582i | \(-0.435566\pi\) | ||||
0.201045 | + | 0.979582i | \(0.435566\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0000 | −0.923077 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.00000i | 0.305888i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.00000 | 0.684257 | 0.342129 | − | 0.939653i | \(-0.388852\pi\) | ||||
0.342129 | + | 0.939653i | \(0.388852\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.73205 | − | 2.00000i | −0.130931 | − | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −6.00000 | −0.450988 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.2487 | −1.81243 | −0.906217 | − | 0.422813i | \(-0.861043\pi\) | ||||
−0.906217 | + | 0.422813i | \(0.861043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.00000i | 0.591377i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 6.92820i | 0.509372i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 9.00000i | − | 0.658145i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.0000 | − | 8.66025i | 0.727393 | − | 0.629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.0000i | 1.08536i | 0.839939 | + | 0.542681i | \(0.182591\pi\) | ||||
−0.839939 | + | 0.542681i | \(0.817409\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.00000 | 0.287926 | 0.143963 | − | 0.989583i | \(-0.454015\pi\) | ||||
0.143963 | + | 0.989583i | \(0.454015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.00000i | 0.0716115i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.46410i | − | 0.246807i | −0.992357 | − | 0.123404i | \(-0.960619\pi\) | ||
0.992357 | − | 0.123404i | \(-0.0393809\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3923 | 0.736691 | 0.368345 | − | 0.929689i | \(-0.379924\pi\) | ||||
0.368345 | + | 0.929689i | \(0.379924\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.3923i | 0.733017i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.46410 | − | 3.00000i | 0.243132 | − | 0.210559i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.3923i | 0.725830i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 10.3923i | − | 0.718851i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.19615 | 0.357718 | 0.178859 | − | 0.983875i | \(-0.442759\pi\) | ||||
0.178859 | + | 0.983875i | \(0.442759\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.46410 | −0.236250 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | − | 6.92820i | −0.407307 | − | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.92820 | 0.468165 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.73205i | 0.116510i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.66025 | 0.579934 | 0.289967 | − | 0.957037i | \(-0.406356\pi\) | ||||
0.289967 | + | 0.957037i | \(0.406356\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.00000 | 0.133333 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 15.0000i | − | 0.995585i | −0.867296 | − | 0.497792i | \(-0.834144\pi\) | ||
0.867296 | − | 0.497792i | \(-0.165856\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.0000 | −1.45380 | −0.726900 | − | 0.686743i | \(-0.759040\pi\) | ||||
−0.726900 | + | 0.686743i | \(0.759040\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.3923 | + | 9.00000i | −0.683763 | + | 0.592157i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12.0000 | 0.786146 | 0.393073 | − | 0.919507i | \(-0.371412\pi\) | ||||
0.393073 | + | 0.919507i | \(0.371412\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 12.1244 | 0.790906 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.00000 | 0.0649570 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 9.00000i | − | 0.582162i | −0.956698 | − | 0.291081i | \(-0.905985\pi\) | ||
0.956698 | − | 0.291081i | \(-0.0940149\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.7846i | 1.33885i | 0.742878 | + | 0.669427i | \(0.233460\pi\) | ||||
−0.742878 | + | 0.669427i | \(0.766540\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.0000i | 1.02640i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.00000 | + | 6.92820i | −0.0638877 | + | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.00000i | 0.127257i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.0000i | 0.757433i | 0.925513 | + | 0.378717i | \(0.123635\pi\) | ||||
−0.925513 | + | 0.378717i | \(0.876365\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.73205 | −0.108465 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 6.92820i | − | 0.432169i | −0.976375 | − | 0.216085i | \(-0.930671\pi\) | ||
0.976375 | − | 0.216085i | \(-0.0693287\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.8564 | − | 12.0000i | 0.860995 | − | 0.745644i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.46410i | 0.214423i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 6.00000i | − | 0.369976i | −0.982741 | − | 0.184988i | \(-0.940775\pi\) | ||
0.982741 | − | 0.184988i | \(-0.0592246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.46410i | 0.212798i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.92820 | 0.423999 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.0000 | 1.46331 | 0.731653 | − | 0.681677i | \(-0.238749\pi\) | ||||
0.731653 | + | 0.681677i | \(0.238749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −27.7128 | −1.68343 | −0.841717 | − | 0.539919i | \(-0.818455\pi\) | ||||
−0.841717 | + | 0.539919i | \(0.818455\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.00000 | − | 1.73205i | 0.121046 | − | 0.104828i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −5.19615 | −0.313340 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 27.7128i | − | 1.66510i | −0.553949 | − | 0.832551i | \(-0.686880\pi\) | ||
0.553949 | − | 0.832551i | \(-0.313120\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 6.92820 | 0.414781 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 27.0000 | 1.61068 | 0.805342 | − | 0.592810i | \(-0.201981\pi\) | ||||
0.805342 | + | 0.592810i | \(0.201981\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 31.0000i | − | 1.84276i | −0.388664 | − | 0.921379i | \(-0.627063\pi\) | ||
0.388664 | − | 0.921379i | \(-0.372937\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.00000 | −0.118470 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.7846 | − | 18.0000i | 1.22688 | − | 1.06251i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.0000 | 0.823529 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.66025 | 0.507673 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −27.0000 | −1.57736 | −0.788678 | − | 0.614806i | \(-0.789234\pi\) | ||||
−0.788678 | + | 0.614806i | \(0.789234\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000i | 0.349334i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 25.9808i | − | 1.50756i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.00000 | + | 6.92820i | 0.345834 | + | 0.399335i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.00000i | 0.344691i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 8.00000 | 0.458079 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.00000i | 0.0570730i | 0.999593 | + | 0.0285365i | \(0.00908469\pi\) | ||||
−0.999593 | + | 0.0285365i | \(0.990915\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 1.73205i | − | 0.0985329i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.1769 | −1.76788 | −0.883940 | − | 0.467600i | \(-0.845119\pi\) | ||||
−0.883940 | + | 0.467600i | \(0.845119\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.9808i | 1.46852i | 0.678869 | + | 0.734260i | \(0.262471\pi\) | ||||
−0.678869 | + | 0.734260i | \(0.737529\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.46410 | − | 4.00000i | −0.195180 | − | 0.225374i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 17.3205i | 0.972817i | 0.873732 | + | 0.486408i | \(0.161693\pi\) | ||||
−0.873732 | + | 0.486408i | \(0.838307\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9.00000i | − | 0.503903i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 10.3923i | − | 0.580042i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3.46410 | −0.192748 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.00000 | 0.0554700 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.1244 | −0.670478 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −21.0000 | − | 24.2487i | −1.15777 | − | 1.33687i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.46410 | 0.190404 | 0.0952021 | − | 0.995458i | \(-0.469650\pi\) | ||||
0.0952021 | + | 0.995458i | \(0.469650\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.8564i | 0.759326i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.3923 | 0.567792 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | −0.435788 | −0.217894 | − | 0.975972i | \(-0.569919\pi\) | ||||
−0.217894 | + | 0.975972i | \(0.569919\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − | 12.0000i | − | 0.651751i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −18.0000 | −0.974755 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | − | 10.0000i | 0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.7128 | 1.48770 | 0.743851 | − | 0.668346i | \(-0.232997\pi\) | ||||
0.743851 | + | 0.668346i | \(0.232997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0000 | −1.39175 | −0.695874 | − | 0.718164i | \(-0.744983\pi\) | ||||
−0.695874 | + | 0.718164i | \(0.744983\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00000i | 0.266880i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 15.5885i | 0.829690i | 0.909892 | + | 0.414845i | \(0.136164\pi\) | ||||
−0.909892 | + | 0.414845i | \(0.863836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.00000 | + | 3.46410i | 0.158777 | + | 0.183340i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 24.0000i | − | 1.26667i | −0.773877 | − | 0.633336i | \(-0.781685\pi\) | ||
0.773877 | − | 0.633336i | \(-0.218315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.0000 | 0.789474 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 16.0000i | 0.839782i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 6.92820i | − | 0.362639i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.5885 | 0.813711 | 0.406855 | − | 0.913493i | \(-0.366625\pi\) | ||||
0.406855 | + | 0.913493i | \(0.366625\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 20.7846i | 1.08200i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.92820 | − | 6.00000i | 0.359694 | − | 0.311504i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 34.6410i | − | 1.79364i | −0.442392 | − | 0.896822i | \(-0.645870\pi\) | ||
0.442392 | − | 0.896822i | \(-0.354130\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000i | 0.0516398i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.73205i | 0.0892052i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.3923 | 0.533817 | 0.266908 | − | 0.963722i | \(-0.413998\pi\) | ||||
0.266908 | + | 0.963722i | \(0.413998\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 14.0000 | 0.717242 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 10.3923 | 0.531022 | 0.265511 | − | 0.964108i | \(-0.414459\pi\) | ||||
0.265511 | + | 0.964108i | \(0.414459\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.00000 | + | 10.3923i | 0.458682 | + | 0.529641i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.92820 | −0.352180 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8.66025i | 0.439092i | 0.975602 | + | 0.219546i | \(0.0704577\pi\) | ||||
−0.975602 | + | 0.219546i | \(0.929542\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −12.0000 | −0.605320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 1.00000i | − | 0.0503155i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.0000 | −0.552074 | −0.276037 | − | 0.961147i | \(-0.589021\pi\) | ||||
−0.276037 | + | 0.961147i | \(0.589021\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.46410 | + | 4.00000i | 0.173422 | + | 0.200250i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.0000 | 1.04869 | 0.524345 | − | 0.851506i | \(-0.324310\pi\) | ||||
0.524345 | + | 0.851506i | \(0.324310\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.46410 | 0.172559 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 36.0000i | − | 1.78445i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 10.3923i | − | 0.513866i | −0.966429 | − | 0.256933i | \(-0.917288\pi\) | ||
0.966429 | − | 0.256933i | \(-0.0827120\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 12.0000i | − | 0.591916i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 12.0000 | − | 10.3923i | 0.590481 | − | 0.511372i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000i | 0.589057i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −16.0000 | −0.783523 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.00000i | 0.293119i | 0.989202 | + | 0.146560i | \(0.0468200\pi\) | ||||
−0.989202 | + | 0.146560i | \(0.953180\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 39.8372i | − | 1.94154i | −0.240002 | − | 0.970772i | \(-0.577148\pi\) | ||
0.240002 | − | 0.970772i | \(-0.422852\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 24.2487 | 1.17901 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.73205i | 0.0840168i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.8564 | − | 16.0000i | −0.670559 | − | 0.774294i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 5.19615i | − | 0.250873i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 27.0000i | 1.30054i | 0.759701 | + | 0.650272i | \(0.225345\pi\) | ||||
−0.759701 | + | 0.650272i | \(0.774655\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.8564i | − | 0.665896i | −0.942945 | − | 0.332948i | \(-0.891957\pi\) | ||
0.942945 | − | 0.332948i | \(-0.108043\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.73205 | −0.0830455 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 27.7128 | 1.32266 | 0.661330 | − | 0.750095i | \(-0.269992\pi\) | ||||
0.661330 | + | 0.750095i | \(0.269992\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.00000 | + | 13.8564i | −0.0952381 | + | 0.659829i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 24.2487 | 1.15209 | 0.576046 | − | 0.817418i | \(-0.304595\pi\) | ||||
0.576046 | + | 0.817418i | \(0.304595\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 6.92820i | − | 0.328428i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 13.8564 | 0.655386 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.0000 | −0.707894 | −0.353947 | − | 0.935266i | \(-0.615161\pi\) | ||||
−0.353947 | + | 0.935266i | \(0.615161\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 54.0000i | − | 2.54276i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.0000 | −0.798730 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.73205 | − | 2.00000i | −0.0811998 | − | 0.0937614i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.0000 | −1.59045 | −0.795226 | − | 0.606313i | \(-0.792648\pi\) | ||||
−0.795226 | + | 0.606313i | \(0.792648\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.66025 | −0.404226 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000i | 0.185896i | 0.995671 | + | 0.0929479i | \(0.0296290\pi\) | ||||
−0.995671 | + | 0.0929479i | \(0.970371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.46410i | 0.160644i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 21.0000i | 0.971764i | 0.874024 | + | 0.485882i | \(0.161502\pi\) | ||||
−0.874024 | + | 0.485882i | \(0.838498\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.0000 | − | 20.7846i | −0.831163 | − | 0.959744i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 14.0000i | 0.645086i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 18.0000 | 0.827641 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000i | 0.0917663i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 6.92820i | 0.317221i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.8564 | −0.633115 | −0.316558 | − | 0.948573i | \(-0.602527\pi\) | ||||
−0.316558 | + | 0.948573i | \(0.602527\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.92820i | 0.315899i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 8.66025i | − | 0.393242i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 16.0000i | − | 0.725029i | −0.931978 | − | 0.362515i | \(-0.881918\pi\) | ||
0.931978 | − | 0.362515i | \(-0.118082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.5167 | −1.01616 | −0.508081 | − | 0.861309i | \(-0.669645\pi\) | ||||
−0.508081 | + | 0.861309i | \(0.669645\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.00000 | −0.135113 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.3923 | −0.467099 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.4449 | 1.31813 | 0.659067 | − | 0.752085i | \(-0.270952\pi\) | ||||
0.659067 | + | 0.752085i | \(0.270952\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.19615i | 0.232147i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.5885 | −0.695055 | −0.347527 | − | 0.937670i | \(-0.612979\pi\) | ||||
−0.347527 | + | 0.937670i | \(0.612979\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 12.0000i | − | 0.532939i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −12.0000 | −0.531891 | −0.265945 | − | 0.963988i | \(-0.585684\pi\) | ||||
−0.265945 | + | 0.963988i | \(0.585684\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.8564 | + | 12.0000i | −0.612971 | + | 0.530849i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.0000 | −0.441511 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.73205 | −0.0763233 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −63.0000 | −2.77074 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 9.00000i | 0.395056i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.3205i | 0.758825i | 0.925228 | + | 0.379413i | \(0.123874\pi\) | ||||
−0.925228 | + | 0.379413i | \(0.876126\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 16.0000i | − | 0.699631i | −0.936819 | − | 0.349816i | \(-0.886244\pi\) | ||
0.936819 | − | 0.349816i | \(-0.113756\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.00000 | − | 1.73205i | 0.0872872 | − | 0.0755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000i | 0.261364i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 23.0000 | 1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000i | 0.520756i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 10.3923i | 0.450141i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −10.3923 | −0.449299 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 24.2487i | − | 1.04641i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.19615 | − | 36.0000i | 0.223814 | − | 1.55063i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 32.9090i | − | 1.41487i | −0.706780 | − | 0.707433i | \(-0.749853\pi\) | ||
0.706780 | − | 0.707433i | \(-0.250147\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 22.0000i | − | 0.944110i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.1244i | 0.519350i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 27.7128 | 1.18491 | 0.592457 | − | 0.805602i | \(-0.298158\pi\) | ||||
0.592457 | + | 0.805602i | \(0.298158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 16.0000 | 0.682863 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.46410 | −0.147576 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.00000 | + | 1.73205i | −0.0850487 | + | 0.0736543i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.92820 | −0.294086 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 27.7128i | − | 1.17423i | −0.809504 | − | 0.587115i | \(-0.800264\pi\) | ||
0.809504 | − | 0.587115i | \(-0.199736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.46410 | −0.146516 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | 0.379980 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 36.0000i | − | 1.51722i | −0.651546 | − | 0.758610i | \(-0.725879\pi\) | ||
0.651546 | − | 0.758610i | \(-0.274121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.0000 | −0.504844 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.73205 | − | 2.00000i | −0.0727393 | − | 0.0839921i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.46410 | −0.144968 | −0.0724841 | − | 0.997370i | \(-0.523093\pi\) | ||||
−0.0724841 | + | 0.997370i | \(0.523093\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.0000 | −0.626634 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 19.0526i | − | 0.793168i | −0.917998 | − | 0.396584i | \(-0.870195\pi\) | ||
0.917998 | − | 0.396584i | \(-0.129805\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 4.00000i | 0.166234i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | − | 20.7846i | 0.995688 | − | 0.862291i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.0000i | − | 0.745484i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2.00000 | 0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.0000i | 1.48588i | 0.669359 | + | 0.742940i | \(0.266569\pi\) | ||||
−0.669359 | + | 0.742940i | \(0.733431\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.92820i | 0.285472i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.46410 | 0.142494 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 39.8372i | − | 1.63592i | −0.575278 | − | 0.817958i | \(-0.695106\pi\) | ||
0.575278 | − | 0.817958i | \(-0.304894\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.46410 | − | 3.00000i | 0.142014 | − | 0.122988i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.3923i | 0.425329i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 9.00000i | − | 0.367730i | −0.982952 | − | 0.183865i | \(-0.941139\pi\) | ||
0.982952 | − | 0.183865i | \(-0.0588609\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.2487i | 0.989126i | 0.869142 | + | 0.494563i | \(0.164672\pi\) | ||||
−0.869142 | + | 0.494563i | \(0.835328\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 20.7846 | 0.846415 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 16.0000 | 0.650493 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.66025 | 0.351509 | 0.175754 | − | 0.984434i | \(-0.443764\pi\) | ||||
0.175754 | + | 0.984434i | \(0.443764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.00000 | + | 3.46410i | 0.121566 | + | 0.140372i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.1244 | 0.490499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24.2487i | − | 0.979396i | −0.871892 | − | 0.489698i | \(-0.837107\pi\) | ||
0.871892 | − | 0.489698i | \(-0.162893\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10.3923 | −0.419058 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 24.0000 | 0.966204 | 0.483102 | − | 0.875564i | \(-0.339510\pi\) | ||||
0.483102 | + | 0.875564i | \(0.339510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.00000i | 0.160774i | 0.996764 | + | 0.0803868i | \(0.0256155\pi\) | ||||
−0.996764 | + | 0.0803868i | \(0.974384\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.8564 | + | 12.0000i | −0.555145 | + | 0.480770i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 10.3923 | 0.415029 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.0000i | 0.517522i | 0.965941 | + | 0.258761i | \(0.0833142\pi\) | ||||
−0.965941 | + | 0.258761i | \(0.916686\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.19615i | 0.206529i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 14.0000i | − | 0.555573i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.00000 | + | 6.92820i | −0.0396214 | + | 0.274505i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | 0.710957 | 0.355479 | − | 0.934684i | \(-0.384318\pi\) | ||||
0.355479 | + | 0.934684i | \(0.384318\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.00000i | − | 0.0394362i | −0.999806 | − | 0.0197181i | \(-0.993723\pi\) | ||
0.999806 | − | 0.0197181i | \(-0.00627687\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 3.46410i | − | 0.136399i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.2487 | 0.953315 | 0.476658 | − | 0.879089i | \(-0.341848\pi\) | ||||
0.476658 | + | 0.879089i | \(0.341848\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 31.1769i | − | 1.22380i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.92820 | − | 6.00000i | 0.271538 | − | 0.235159i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.1051i | 1.49117i | 0.666411 | + | 0.745584i | \(0.267829\pi\) | ||||
−0.666411 | + | 0.745584i | \(0.732171\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.0000i | 0.468879i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 13.8564i | − | 0.540590i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 12.1244 | 0.472298 | 0.236149 | − | 0.971717i | \(-0.424115\pi\) | ||||
0.236149 | + | 0.971717i | \(0.424115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −20.0000 | −0.777910 | −0.388955 | − | 0.921257i | \(-0.627164\pi\) | ||||
−0.388955 | + | 0.921257i | \(0.627164\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.73205 | −0.0672673 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.00000 | − | 3.46410i | 0.155113 | − | 0.134332i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8.66025i | 0.334825i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −41.5692 | −1.60476 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −40.0000 | −1.54189 | −0.770943 | − | 0.636904i | \(-0.780215\pi\) | ||||
−0.770943 | + | 0.636904i | \(0.780215\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.00000i | 0.192450i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.00000 | −0.115299 | −0.0576497 | − | 0.998337i | \(-0.518361\pi\) | ||||
−0.0576497 | + | 0.998337i | \(0.518361\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.3205 | + | 15.0000i | −0.664700 | + | 0.575647i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.0000 | 0.574801 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.0000 | −0.458496 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 22.0000i | − | 0.839352i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.46410i | 0.131972i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.00000i | − | 0.304334i | −0.988355 | − | 0.152167i | \(-0.951375\pi\) | ||
0.988355 | − | 0.152167i | \(-0.0486252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.0000 | + | 20.7846i | 0.683763 | + | 0.789542i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 16.0000i | 0.606915i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −18.0000 | −0.681799 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.0000i | 0.453882i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.9808i | 0.981280i | 0.871362 | + | 0.490640i | \(0.163237\pi\) | ||||
−0.871362 | + | 0.490640i | \(0.836763\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.8564 | −0.522604 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 12.1244i | 0.456630i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −10.3923 | − | 12.0000i | −0.390843 | − | 0.451306i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.73205i | 0.0650485i | 0.999471 | + | 0.0325243i | \(0.0103546\pi\) | ||||
−0.999471 | + | 0.0325243i | \(0.989645\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2.00000i | − | 0.0750059i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.19615 | −0.194325 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 9.00000 | 0.336111 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.92820 | 0.258378 | 0.129189 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129189 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.00000 | + | 3.46410i | 0.111726 | + | 0.129010i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.7846 | −0.772988 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.73205i | 0.0643268i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.3205 | 0.642382 | 0.321191 | − | 0.947014i | \(-0.395917\pi\) | ||||
0.321191 | + | 0.947014i | \(0.395917\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −13.0000 | −0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 6.00000i | − | 0.221918i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 19.0000 | 0.701781 | 0.350891 | − | 0.936416i | \(-0.385879\pi\) | ||||
0.350891 | + | 0.936416i | \(0.385879\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −6.92820 | − | 1.00000i | −0.255551 | − | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −54.0000 | −1.98912 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 25.9808 | 0.955718 | 0.477859 | − | 0.878437i | \(-0.341413\pi\) | ||||
0.477859 | + | 0.878437i | \(0.341413\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.00000 | −0.0734718 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 30.0000i | 1.10059i | 0.834969 | + | 0.550297i | \(0.185485\pi\) | ||||
−0.834969 | + | 0.550297i | \(0.814515\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 13.8564i | − | 0.507659i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 24.0000i | 0.878114i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000 | + | 20.7846i | 0.657706 | + | 0.759453i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.00000i | 0.255434i | 0.991811 | + | 0.127717i | \(0.0407649\pi\) | ||||
−0.991811 | + | 0.127717i | \(0.959235\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12.0000 | −0.437304 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 17.0000i | 0.618693i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34.6410i | − | 1.25905i | −0.776981 | − | 0.629525i | \(-0.783250\pi\) | ||
0.776981 | − | 0.629525i | \(-0.216750\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.8564i | 0.502294i | 0.967949 | + | 0.251147i | \(0.0808078\pi\) | ||||
−0.967949 | + | 0.251147i | \(0.919192\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 24.2487 | − | 21.0000i | 0.877862 | − | 0.760251i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.46410i | 0.125245i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.00000i | 0.216647i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.1769i | 1.12427i | 0.827046 | + | 0.562134i | \(0.190020\pi\) | ||||
−0.827046 | + | 0.562134i | \(0.809980\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.92820 | 0.249513 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 15.0000 | 0.539513 | 0.269756 | − | 0.962929i | \(-0.413057\pi\) | ||||
0.269756 | + | 0.962929i | \(0.413057\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.46410 | 0.124434 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 12.0000 | + | 13.8564i | 0.430498 | + | 0.497096i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.7846 | −0.744686 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.66025 | −0.309492 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0000 | 0.499681 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 29.0000i | − | 1.03374i | −0.856064 | − | 0.516869i | \(-0.827097\pi\) | ||
0.856064 | − | 0.516869i | \(-0.172903\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 6.00000 | 0.213606 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20.7846 | + | 24.0000i | 0.739016 | + | 0.853342i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.00000 | 0.284088 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.46410 | −0.122859 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −15.0000 | −0.531327 | −0.265664 | − | 0.964066i | \(-0.585591\pi\) | ||||
−0.265664 | + | 0.964066i | \(0.585591\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 21.0000i | 0.742927i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13.8564i | − | 0.489592i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 36.0000i | 1.27041i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.0000i | 0.844840i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.0000 | −0.949269 | −0.474635 | − | 0.880183i | \(-0.657420\pi\) | ||||
−0.474635 | + | 0.880183i | \(0.657420\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 44.0000i | 1.54505i | 0.634985 | + | 0.772524i | \(0.281006\pi\) | ||||
−0.634985 | + | 0.772524i | \(0.718994\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 27.7128i | − | 0.971931i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.92820i | − | 0.242387i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.46410 | − | 4.00000i | −0.121046 | − | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 39.8372i | 1.39033i | 0.718852 | + | 0.695163i | \(0.244668\pi\) | ||||
−0.718852 | + | 0.695163i | \(0.755332\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 14.0000i | − | 0.488009i | −0.969774 | − | 0.244005i | \(-0.921539\pi\) | ||
0.969774 | − | 0.244005i | \(-0.0784612\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 5.19615i | − | 0.180907i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.6410 | −1.20459 | −0.602293 | − | 0.798275i | \(-0.705746\pi\) | ||||
−0.602293 | + | 0.798275i | \(0.705746\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 38.0000 | 1.31979 | 0.659897 | − | 0.751356i | \(-0.270600\pi\) | ||||
0.659897 | + | 0.751356i | \(0.270600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 27.7128 | 0.961347 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.0000 | − | 1.73205i | −0.415775 | − | 0.0600120i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 5.19615 | 0.179820 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 17.3205i | 0.598684i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.8564 | 0.478376 | 0.239188 | − | 0.970973i | \(-0.423119\pi\) | ||||
0.239188 | + | 0.970973i | \(0.423119\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 26.0000 | 0.896552 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 27.0000i | 0.929929i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.0000 | −0.412813 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.7128 | − | 32.0000i | −0.952224 | − | 1.09953i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 31.0000 | 1.06392 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −46.0000 | −1.57501 | −0.787505 | − | 0.616308i | \(-0.788628\pi\) | ||||
−0.787505 | + | 0.616308i | \(0.788628\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.00000i | 0.136797i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.6410i | 1.18331i | 0.806190 | + | 0.591657i | \(0.201526\pi\) | ||||
−0.806190 | + | 0.591657i | \(0.798474\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 56.0000i | − | 1.91070i | −0.295484 | − | 0.955348i | \(-0.595481\pi\) | ||
0.295484 | − | 0.955348i | \(-0.404519\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18.0000 | + | 20.7846i | 0.613438 | + | 0.708338i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 6.00000i | − | 0.204242i | −0.994772 | − | 0.102121i | \(-0.967437\pi\) | ||
0.994772 | − | 0.102121i | \(-0.0325630\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 9.00000 | 0.306009 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.0000i | 0.475465i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.19615i | 0.176267i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.3923 | 0.352130 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 17.3205i | − | 0.586210i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.73205 | − | 2.00000i | −0.0585540 | − | 0.0676123i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 45.0333i | − | 1.52067i | −0.649533 | − | 0.760334i | \(-0.725035\pi\) | ||
0.649533 | − | 0.760334i | \(-0.274965\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 27.0000i | − | 0.910687i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.4974i | 1.63392i | 0.576695 | + | 0.816960i | \(0.304342\pi\) | ||||
−0.576695 | + | 0.816960i | \(0.695658\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −13.8564 | −0.466305 | −0.233153 | − | 0.972440i | \(-0.574904\pi\) | ||||
−0.233153 | + | 0.972440i | \(0.574904\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.00000 | −0.201688 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 51.9615 | 1.74470 | 0.872349 | − | 0.488884i | \(-0.162596\pi\) | ||||
0.872349 | + | 0.488884i | \(0.162596\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −28.0000 | + | 24.2487i | −0.939090 | + | 0.813276i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.19615 | −0.174078 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 24.2487i | 0.811452i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24.2487 | −0.810545 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.00000i | 0.200111i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.00000 | −0.199889 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.92820 | + | 6.00000i | −0.230556 | + | 0.199667i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.0000 | −0.731305 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −48.4974 | −1.61033 | −0.805165 | − | 0.593051i | \(-0.797923\pi\) | ||||
−0.805165 | + | 0.593051i | \(0.797923\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12.0000 | 0.398015 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.0000i | 0.795155i | 0.917568 | + | 0.397578i | \(0.130149\pi\) | ||||
−0.917568 | + | 0.397578i | \(0.869851\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 62.3538i | − | 2.06361i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.00000i | 0.264472i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 24.0000 | − | 20.7846i | 0.792550 | − | 0.686368i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 55.0000i | − | 1.81428i | −0.420826 | − | 0.907141i | \(-0.638260\pi\) | ||
0.420826 | − | 0.907141i | \(-0.361740\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.00000 | −0.0329511 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.92820i | 0.227798i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.46410 | −0.113776 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 24.2487i | − | 0.795574i | −0.917478 | − | 0.397787i | \(-0.869778\pi\) | ||
0.917478 | − | 0.397787i | \(-0.130222\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13.8564 | − | 2.00000i | −0.454125 | − | 0.0655474i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 31.1769i | − | 1.02069i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 9.00000i | − | 0.294331i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 29.4449i | − | 0.961922i | −0.876742 | − | 0.480961i | \(-0.840288\pi\) | ||
0.876742 | − | 0.480961i | \(-0.159712\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.9808 | −0.847850 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.0000 | − | 8.66025i | 0.325300 | − | 0.281718i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.3923 | −0.337705 | −0.168852 | − | 0.985641i | \(-0.554006\pi\) | ||||
−0.168852 | + | 0.985641i | \(0.554006\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 6.92820i | − | 0.224899i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.3205 | −0.561656 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.0000 | 1.74923 | 0.874616 | − | 0.484817i | \(-0.161114\pi\) | ||||
0.874616 | + | 0.484817i | \(0.161114\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0000i | 0.485389i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.00000 | 0.290929 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 20.7846 | + | 24.0000i | 0.671170 | + | 0.775000i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19.0000 | −0.612903 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −20.7846 | −0.669775 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.00000 | 0.128765 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 22.0000i | − | 0.707472i | −0.935345 | − | 0.353736i | \(-0.884911\pi\) | ||
0.935345 | − | 0.353736i | \(-0.115089\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 3.46410i | − | 0.111283i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.0000i | 1.34784i | 0.738802 | + | 0.673922i | \(0.235392\pi\) | ||||
−0.738802 | + | 0.673922i | \(0.764608\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 32.0000 | − | 27.7128i | 1.02587 | − | 0.888432i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.00000i | 0.0320256i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −6.00000 | −0.191957 | −0.0959785 | − | 0.995383i | \(-0.530598\pi\) | ||||
−0.0959785 | + | 0.995383i | \(0.530598\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 36.0000i | 1.15056i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 24.2487i | 0.774202i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −32.9090 | −1.04963 | −0.524816 | − | 0.851215i | \(-0.675866\pi\) | ||||
−0.524816 | + | 0.851215i | \(0.675866\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 3.46410i | − | 0.110375i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 24.2487 | − | 21.0000i | 0.771845 | − | 0.668437i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 20.0000i | − | 0.635321i | −0.948205 | − | 0.317660i | \(-0.897103\pi\) | ||
0.948205 | − | 0.317660i | \(-0.102897\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.46410i | 0.109930i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10.3923 | 0.329458 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.00000 | −0.0316703 | −0.0158352 | − | 0.999875i | \(-0.505041\pi\) | ||||
−0.0158352 | + | 0.999875i | \(0.505041\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −34.6410 | −1.09599 |
(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 | 2240.2.h.d.671.3 | yes | 4 | |
4.3 | odd | 2 | inner | 2240.2.h.d.671.2 | yes | 4 | |
7.6 | odd | 2 | 2240.2.h.b.671.2 | yes | 4 | ||
8.3 | odd | 2 | 2240.2.h.b.671.4 | yes | 4 | ||
8.5 | even | 2 | 2240.2.h.b.671.1 | ✓ | 4 | ||
28.27 | even | 2 | 2240.2.h.b.671.3 | yes | 4 | ||
56.13 | odd | 2 | inner | 2240.2.h.d.671.4 | yes | 4 | |
56.27 | even | 2 | inner | 2240.2.h.d.671.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2240.2.h.b.671.1 | ✓ | 4 | 8.5 | even | 2 | ||
2240.2.h.b.671.2 | yes | 4 | 7.6 | odd | 2 | ||
2240.2.h.b.671.3 | yes | 4 | 28.27 | even | 2 | ||
2240.2.h.b.671.4 | yes | 4 | 8.3 | odd | 2 | ||
2240.2.h.d.671.1 | yes | 4 | 56.27 | even | 2 | inner | |
2240.2.h.d.671.2 | yes | 4 | 4.3 | odd | 2 | inner | |
2240.2.h.d.671.3 | yes | 4 | 1.1 | even | 1 | trivial | |
2240.2.h.d.671.4 | yes | 4 | 56.13 | odd | 2 | inner |