Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4410,2,Mod(881,4410)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4410, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4410.881");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4410 = 2 \cdot 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4410.b (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: | \(35.2140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.8 | ||
Root | \(0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4410.881 |
Dual form | 4410.2.b.b.881.1 |
$q$-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 \(\left(\mathbb{Z}/4410\mathbb{Z}\right)^\times\).
\(n\) | \(1081\) | \(2647\) | \(3431\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 1.00000i | − 0.316228i | ||||||||
\(11\) | 5.39595i | 1.62694i | 0.581606 | + | 0.813471i | \(0.302425\pi\) | ||||
−0.581606 | + | 0.813471i | \(0.697575\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51764i | 0.698267i | 0.937073 | + | 0.349134i | \(0.113524\pi\) | ||||
−0.937073 | + | 0.349134i | \(0.886476\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.49938 | 1.09126 | 0.545630 | − | 0.838026i | \(-0.316291\pi\) | ||||
0.545630 | + | 0.838026i | \(0.316291\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.86370i | 0.656979i | 0.944508 | + | 0.328489i | \(0.106539\pi\) | ||||
−0.944508 | + | 0.328489i | \(0.893461\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.39595 | −1.15042 | ||||||||
\(23\) | 0.267949i | 0.0558713i | 0.999610 | + | 0.0279356i | \(0.00889335\pi\) | ||||
−0.999610 | + | 0.0279356i | \(0.991107\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −2.51764 | −0.493749 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.89898i | − 1.65250i | −0.563304 | − | 0.826250i | \(-0.690470\pi\) | ||||
0.563304 | − | 0.826250i | \(-0.309530\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.82843i | 0.867211i | 0.901103 | + | 0.433606i | \(0.142759\pi\) | ||||
−0.901103 | + | 0.433606i | \(0.857241\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.49938i | 0.771637i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.51764 | −1.07149 | −0.535747 | − | 0.844379i | \(-0.679970\pi\) | ||||
−0.535747 | + | 0.844379i | \(0.679970\pi\) | |||||||
\(38\) | −2.86370 | −0.464554 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | −0.760279 | −0.118736 | −0.0593678 | − | 0.998236i | \(-0.518908\pi\) | ||||
−0.0593678 | + | 0.998236i | \(0.518908\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.86370 | −0.894206 | −0.447103 | − | 0.894482i | \(-0.647544\pi\) | ||||
−0.447103 | + | 0.894482i | \(0.647544\pi\) | |||||||
\(44\) | − 5.39595i | − 0.813471i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.267949 | −0.0395070 | ||||||||
\(47\) | 7.99536 | 1.16624 | 0.583121 | − | 0.812385i | \(-0.301831\pi\) | ||||
0.583121 | + | 0.812385i | \(0.301831\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.51764i | − 0.349134i | ||||||||
\(53\) | 8.39836i | 1.15360i | 0.816884 | + | 0.576802i | \(0.195699\pi\) | ||||
−0.816884 | + | 0.576802i | \(0.804301\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 5.39595i | − 0.727590i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 8.89898 | 1.16849 | ||||||||
\(59\) | 12.6715 | 1.64968 | 0.824842 | − | 0.565363i | \(-0.191264\pi\) | ||||
0.824842 | + | 0.565363i | \(0.191264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.62158i | 0.335659i | 0.985816 | + | 0.167829i | \(0.0536758\pi\) | ||||
−0.985816 | + | 0.167829i | \(0.946324\pi\) | |||||||
\(62\) | −4.82843 | −0.613211 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − 2.51764i | − 0.312275i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.82237 | 1.19999 | 0.599997 | − | 0.800002i | \(-0.295168\pi\) | ||||
0.599997 | + | 0.800002i | \(0.295168\pi\) | |||||||
\(68\) | −4.49938 | −0.545630 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 4.76268i | − 0.565226i | −0.959234 | − | 0.282613i | \(-0.908799\pi\) | ||||
0.959234 | − | 0.282613i | \(-0.0912013\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 11.6569i | 1.36433i | 0.731198 | + | 0.682166i | \(0.238962\pi\) | ||||
−0.731198 | + | 0.682166i | \(0.761038\pi\) | |||||||
\(74\) | − 6.51764i | − 0.757660i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − 2.86370i | − 0.328489i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.59235 | 0.966715 | 0.483358 | − | 0.875423i | \(-0.339417\pi\) | ||||
0.483358 | + | 0.875423i | \(0.339417\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − 0.760279i | − 0.0839587i | ||||||||
\(83\) | −9.45001 | −1.03727 | −0.518636 | − | 0.854995i | \(-0.673560\pi\) | ||||
−0.518636 | + | 0.854995i | \(0.673560\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.49938 | −0.488026 | ||||||||
\(86\) | − 5.86370i | − 0.632299i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.39595 | 0.575211 | ||||||||
\(89\) | −7.97005 | −0.844823 | −0.422412 | − | 0.906404i | \(-0.638816\pi\) | ||||
−0.422412 | + | 0.906404i | \(0.638816\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 0.267949i | − 0.0279356i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.99536i | 0.824658i | ||||||||
\(95\) | − 2.86370i | − 0.293810i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.16353i | 0.625812i | 0.949784 | + | 0.312906i | \(0.101302\pi\) | ||||
−0.949784 | + | 0.312906i | \(0.898698\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −14.0492 | −1.39794 | −0.698972 | − | 0.715149i | \(-0.746359\pi\) | ||||
−0.698972 | + | 0.715149i | \(0.746359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 14.1769i | − 1.39689i | −0.715663 | − | 0.698446i | \(-0.753875\pi\) | ||||
0.715663 | − | 0.698446i | \(-0.246125\pi\) | |||||||
\(104\) | 2.51764 | 0.246875 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.39836 | −0.815721 | ||||||||
\(107\) | − 1.64173i | − 0.158712i | −0.996846 | − | 0.0793559i | \(-0.974714\pi\) | ||||
0.996846 | − | 0.0793559i | \(-0.0252863\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −19.8977 | −1.90586 | −0.952929 | − | 0.303195i | \(-0.901947\pi\) | ||||
−0.952929 | + | 0.303195i | \(0.901947\pi\) | |||||||
\(110\) | 5.39595 | 0.514484 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.95867i | 0.560545i | 0.959921 | + | 0.280272i | \(0.0904248\pi\) | ||||
−0.959921 | + | 0.280272i | \(0.909575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.267949i | − 0.0249864i | ||||||||
\(116\) | 8.89898i | 0.826250i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 12.6715i | 1.16650i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −18.1163 | −1.64694 | ||||||||
\(122\) | −2.62158 | −0.237347 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 4.82843i | − 0.433606i | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.5103 | −1.28758 | −0.643792 | − | 0.765200i | \(-0.722640\pi\) | ||||
−0.643792 | + | 0.765200i | \(0.722640\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.51764 | 0.220811 | ||||||||
\(131\) | 15.4665 | 1.35131 | 0.675657 | − | 0.737216i | \(-0.263860\pi\) | ||||
0.675657 | + | 0.737216i | \(0.263860\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.82237i | 0.848524i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − 4.49938i | − 0.385818i | ||||||||
\(137\) | − 8.62158i | − 0.736591i | −0.929709 | − | 0.368296i | \(-0.879941\pi\) | ||||
0.929709 | − | 0.368296i | \(-0.120059\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.2512i | 0.869495i | 0.900552 | + | 0.434748i | \(0.143162\pi\) | ||||
−0.900552 | + | 0.434748i | \(0.856838\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.76268 | 0.399675 | ||||||||
\(143\) | −13.5851 | −1.13604 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.89898i | 0.739020i | ||||||||
\(146\) | −11.6569 | −0.964728 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.51764 | 0.535747 | ||||||||
\(149\) | − 9.19881i | − 0.753595i | −0.926296 | − | 0.376798i | \(-0.877025\pi\) | ||||
0.926296 | − | 0.376798i | \(-0.122975\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7486 | −1.03747 | −0.518733 | − | 0.854937i | \(-0.673596\pi\) | ||||
−0.518733 | + | 0.854937i | \(0.673596\pi\) | |||||||
\(152\) | 2.86370 | 0.232277 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 4.82843i | − 0.387829i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 13.8447i | 1.10493i | 0.833537 | + | 0.552464i | \(0.186312\pi\) | ||||
−0.833537 | + | 0.552464i | \(0.813688\pi\) | |||||||
\(158\) | 8.59235i | 0.683571i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 1.00000i | − 0.0790569i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20.6050 | −1.61391 | −0.806954 | − | 0.590615i | \(-0.798885\pi\) | ||||
−0.806954 | + | 0.590615i | \(0.798885\pi\) | |||||||
\(164\) | 0.760279 | 0.0593678 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − 9.45001i | − 0.733463i | ||||||||
\(167\) | −6.84961 | −0.530038 | −0.265019 | − | 0.964243i | \(-0.585378\pi\) | ||||
−0.265019 | + | 0.964243i | \(0.585378\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.66150 | 0.512423 | ||||||||
\(170\) | − 4.49938i | − 0.345087i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 5.86370 | 0.447103 | ||||||||
\(173\) | −12.7580 | −0.969976 | −0.484988 | − | 0.874521i | \(-0.661176\pi\) | ||||
−0.484988 | + | 0.874521i | \(0.661176\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.39595i | 0.406735i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 7.97005i | − 0.597380i | ||||||||
\(179\) | 18.8666i | 1.41016i | 0.709129 | + | 0.705079i | \(0.249088\pi\) | ||||
−0.709129 | + | 0.705079i | \(0.750912\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 25.5498i | 1.89910i | 0.313615 | + | 0.949550i | \(0.398460\pi\) | ||||
−0.313615 | + | 0.949550i | \(0.601540\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.267949 | 0.0197535 | ||||||||
\(185\) | 6.51764 | 0.479186 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.2784i | 1.77541i | ||||||||
\(188\) | −7.99536 | −0.583121 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.86370 | 0.207755 | ||||||||
\(191\) | − 8.09049i | − 0.585407i | −0.956203 | − | 0.292704i | \(-0.905445\pi\) | ||||
0.956203 | − | 0.292704i | \(-0.0945549\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.1270 | −1.01688 | −0.508442 | − | 0.861096i | \(-0.669778\pi\) | ||||
−0.508442 | + | 0.861096i | \(0.669778\pi\) | |||||||
\(194\) | −6.16353 | −0.442516 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 14.2738i | − 1.01697i | −0.861072 | − | 0.508483i | \(-0.830207\pi\) | ||||
0.861072 | − | 0.508483i | \(-0.169793\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.54195i | 0.251082i | 0.992088 | + | 0.125541i | \(0.0400667\pi\) | ||||
−0.992088 | + | 0.125541i | \(0.959933\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 14.0492i | − 0.988495i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.760279 | 0.0531002 | ||||||||
\(206\) | 14.1769 | 0.987751 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.51764i | 0.174567i | ||||||||
\(209\) | −15.4524 | −1.06887 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.92340 | −0.270098 | −0.135049 | − | 0.990839i | \(-0.543119\pi\) | ||||
−0.135049 | + | 0.990839i | \(0.543119\pi\) | |||||||
\(212\) | − 8.39836i | − 0.576802i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.64173 | 0.112226 | ||||||||
\(215\) | 5.86370 | 0.399901 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − 19.8977i | − 1.34764i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.39595i | 0.363795i | ||||||||
\(221\) | 11.3278i | 0.761991i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.6904i | 0.983740i | 0.870669 | + | 0.491870i | \(0.163686\pi\) | ||||
−0.870669 | + | 0.491870i | \(0.836314\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.95867 | −0.396365 | ||||||||
\(227\) | −22.7826 | −1.51214 | −0.756068 | − | 0.654493i | \(-0.772882\pi\) | ||||
−0.756068 | + | 0.654493i | \(0.772882\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 20.2175i | 1.33601i | 0.744157 | + | 0.668005i | \(0.232851\pi\) | ||||
−0.744157 | + | 0.668005i | \(0.767149\pi\) | |||||||
\(230\) | 0.267949 | 0.0176680 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.89898 | −0.584247 | ||||||||
\(233\) | 2.63087i | 0.172354i | 0.996280 | + | 0.0861769i | \(0.0274650\pi\) | ||||
−0.996280 | + | 0.0861769i | \(0.972535\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.99536 | −0.521560 | ||||||||
\(236\) | −12.6715 | −0.824842 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − 16.8766i | − 1.09165i | −0.837898 | − | 0.545827i | \(-0.816216\pi\) | ||||
0.837898 | − | 0.545827i | \(-0.183784\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 14.5254i | − 0.935661i | −0.883818 | − | 0.467831i | \(-0.845036\pi\) | ||||
0.883818 | − | 0.467831i | \(-0.154964\pi\) | |||||||
\(242\) | − 18.1163i | − 1.16456i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 2.62158i | − 0.167829i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −7.20977 | −0.458747 | ||||||||
\(248\) | 4.82843 | 0.306605 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 1.00000i | − 0.0632456i | ||||||||
\(251\) | −15.7243 | −0.992507 | −0.496254 | − | 0.868178i | \(-0.665291\pi\) | ||||
−0.496254 | + | 0.868178i | \(0.665291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.44584 | −0.0908993 | ||||||||
\(254\) | − 14.5103i | − 0.910460i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.6617 | 1.22646 | 0.613230 | − | 0.789904i | \(-0.289870\pi\) | ||||
0.613230 | + | 0.789904i | \(0.289870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 2.51764i | 0.156137i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 15.4665i | 0.955524i | ||||||||
\(263\) | 4.32175i | 0.266491i | 0.991083 | + | 0.133245i | \(0.0425398\pi\) | ||||
−0.991083 | + | 0.133245i | \(0.957460\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 8.39836i | − 0.515907i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.82237 | −0.599997 | ||||||||
\(269\) | 17.5979 | 1.07296 | 0.536482 | − | 0.843912i | \(-0.319753\pi\) | ||||
0.536482 | + | 0.843912i | \(0.319753\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.5359i | 0.640010i | 0.947416 | + | 0.320005i | \(0.103685\pi\) | ||||
−0.947416 | + | 0.320005i | \(0.896315\pi\) | |||||||
\(272\) | 4.49938 | 0.272815 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.62158 | 0.520849 | ||||||||
\(275\) | 5.39595i | 0.325388i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.01942 | 0.181419 | 0.0907097 | − | 0.995877i | \(-0.471086\pi\) | ||||
0.0907097 | + | 0.995877i | \(0.471086\pi\) | |||||||
\(278\) | −10.2512 | −0.614826 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 10.6880i | − 0.637591i | −0.947824 | − | 0.318795i | \(-0.896722\pi\) | ||||
0.947824 | − | 0.318795i | \(-0.103278\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 17.5687i | − 1.04435i | −0.852838 | − | 0.522175i | \(-0.825121\pi\) | ||||
0.852838 | − | 0.522175i | \(-0.174879\pi\) | |||||||
\(284\) | 4.76268i | 0.282613i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − 13.5851i | − 0.803301i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.24440 | 0.190847 | ||||||||
\(290\) | −8.89898 | −0.522566 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 11.6569i | − 0.682166i | ||||||||
\(293\) | 14.6710 | 0.857086 | 0.428543 | − | 0.903521i | \(-0.359027\pi\) | ||||
0.428543 | + | 0.903521i | \(0.359027\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.6715 | −0.737761 | ||||||||
\(296\) | 6.51764i | 0.378830i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.19881 | 0.532872 | ||||||||
\(299\) | −0.674599 | −0.0390131 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 12.7486i | − 0.733599i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.86370i | 0.164245i | ||||||||
\(305\) | − 2.62158i | − 0.150111i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 21.2772i | − 1.21435i | −0.794567 | − | 0.607177i | \(-0.792302\pi\) | ||||
0.794567 | − | 0.607177i | \(-0.207698\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.82843 | 0.274236 | ||||||||
\(311\) | −11.8345 | −0.671072 | −0.335536 | − | 0.942027i | \(-0.608917\pi\) | ||||
−0.335536 | + | 0.942027i | \(0.608917\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.50970i | 0.254903i | 0.991845 | + | 0.127452i | \(0.0406797\pi\) | ||||
−0.991845 | + | 0.127452i | \(0.959320\pi\) | |||||||
\(314\) | −13.8447 | −0.781302 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.59235 | −0.483358 | ||||||||
\(317\) | − 18.3830i | − 1.03249i | −0.856440 | − | 0.516247i | \(-0.827329\pi\) | ||||
0.856440 | − | 0.516247i | \(-0.172671\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 48.0185 | 2.68852 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.8849i | 0.716934i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.51764i | 0.139653i | ||||||||
\(326\) | − 20.6050i | − 1.14121i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0.760279i | 0.0419794i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.96132 | 0.437594 | 0.218797 | − | 0.975770i | \(-0.429787\pi\) | ||||
0.218797 | + | 0.975770i | \(0.429787\pi\) | |||||||
\(332\) | 9.45001 | 0.518636 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 6.84961i | − 0.374794i | ||||||||
\(335\) | −9.82237 | −0.536654 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.89417 | −0.375549 | −0.187775 | − | 0.982212i | \(-0.560127\pi\) | ||||
−0.187775 | + | 0.982212i | \(0.560127\pi\) | |||||||
\(338\) | 6.66150i | 0.362338i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.49938 | 0.244013 | ||||||||
\(341\) | −26.0540 | −1.41090 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 5.86370i | 0.316150i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 12.7580i | − 0.685876i | ||||||||
\(347\) | 16.3558i | 0.878025i | 0.898481 | + | 0.439012i | \(0.144672\pi\) | ||||
−0.898481 | + | 0.439012i | \(0.855328\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.5851i | 1.31601i | 0.753014 | + | 0.658004i | \(0.228599\pi\) | ||||
−0.753014 | + | 0.658004i | \(0.771401\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.39595 | −0.287605 | ||||||||
\(353\) | 13.7181 | 0.730142 | 0.365071 | − | 0.930980i | \(-0.381045\pi\) | ||||
0.365071 | + | 0.930980i | \(0.381045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.76268i | 0.252777i | ||||||||
\(356\) | 7.97005 | 0.422412 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.8666 | −0.997132 | ||||||||
\(359\) | − 11.9002i | − 0.628070i | −0.949411 | − | 0.314035i | \(-0.898319\pi\) | ||||
0.949411 | − | 0.314035i | \(-0.101681\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.7992 | 0.568379 | ||||||||
\(362\) | −25.5498 | −1.34287 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 11.6569i | − 0.610148i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 12.5892i | − 0.657152i | −0.944478 | − | 0.328576i | \(-0.893431\pi\) | ||||
0.944478 | − | 0.328576i | \(-0.106569\pi\) | |||||||
\(368\) | 0.267949i | 0.0139678i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.51764i | 0.338836i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −27.1737 | −1.40700 | −0.703499 | − | 0.710696i | \(-0.748380\pi\) | ||||
−0.703499 | + | 0.710696i | \(0.748380\pi\) | |||||||
\(374\) | −24.2784 | −1.25541 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 7.99536i | − 0.412329i | ||||||||
\(377\) | 22.4044 | 1.15389 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 15.7335 | 0.808174 | 0.404087 | − | 0.914721i | \(-0.367589\pi\) | ||||
0.404087 | + | 0.914721i | \(0.367589\pi\) | |||||||
\(380\) | 2.86370i | 0.146905i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 8.09049 | 0.413945 | ||||||||
\(383\) | −15.7812 | −0.806382 | −0.403191 | − | 0.915116i | \(-0.632099\pi\) | ||||
−0.403191 | + | 0.915116i | \(0.632099\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 14.1270i | − 0.719046i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 6.16353i | − 0.312906i | ||||||||
\(389\) | 15.8836i | 0.805332i | 0.915347 | + | 0.402666i | \(0.131916\pi\) | ||||
−0.915347 | + | 0.402666i | \(0.868084\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.20560i | 0.0609700i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 14.2738 | 0.719103 | ||||||||
\(395\) | −8.59235 | −0.432328 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 37.3611i | − 1.87510i | −0.347850 | − | 0.937550i | \(-0.613088\pi\) | ||||
0.347850 | − | 0.937550i | \(-0.386912\pi\) | |||||||
\(398\) | −3.54195 | −0.177542 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 28.2735i | 1.41191i | 0.708255 | + | 0.705957i | \(0.249483\pi\) | ||||
−0.708255 | + | 0.705957i | \(0.750517\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.1562 | −0.605545 | ||||||||
\(404\) | 14.0492 | 0.698972 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 35.1689i | − 1.74326i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 16.0096i | 0.791625i | 0.918331 | + | 0.395812i | \(0.129537\pi\) | ||||
−0.918331 | + | 0.395812i | \(0.870463\pi\) | |||||||
\(410\) | 0.760279i | 0.0375475i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.1769i | 0.698446i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.45001 | 0.463883 | ||||||||
\(416\) | −2.51764 | −0.123437 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − 15.4524i | − 0.755802i | ||||||||
\(419\) | −29.5137 | −1.44184 | −0.720919 | − | 0.693020i | \(-0.756280\pi\) | ||||
−0.720919 | + | 0.693020i | \(0.756280\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 0.309114 | 0.0150653 | 0.00753265 | − | 0.999972i | \(-0.497602\pi\) | ||||
0.00753265 | + | 0.999972i | \(0.497602\pi\) | |||||||
\(422\) | − 3.92340i | − 0.190988i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.39836 | 0.407860 | ||||||||
\(425\) | 4.49938 | 0.218252 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 1.64173i | 0.0793559i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.86370i | 0.282773i | ||||||||
\(431\) | − 8.82010i | − 0.424849i | −0.977177 | − | 0.212425i | \(-0.931864\pi\) | ||||
0.977177 | − | 0.212425i | \(-0.0681360\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 9.56388i | − 0.459611i | −0.973237 | − | 0.229805i | \(-0.926191\pi\) | ||||
0.973237 | − | 0.229805i | \(-0.0738089\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.8977 | 0.952929 | ||||||||
\(437\) | −0.767327 | −0.0367062 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.1810i | 1.72682i | 0.504500 | + | 0.863412i | \(0.331677\pi\) | ||||
−0.504500 | + | 0.863412i | \(0.668323\pi\) | |||||||
\(440\) | −5.39595 | −0.257242 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −11.3278 | −0.538809 | ||||||||
\(443\) | − 4.08568i | − 0.194116i | −0.995279 | − | 0.0970582i | \(-0.969057\pi\) | ||||
0.995279 | − | 0.0970582i | \(-0.0309433\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.97005 | 0.377816 | ||||||||
\(446\) | −14.6904 | −0.695609 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9377i | 0.940918i | 0.882422 | + | 0.470459i | \(0.155912\pi\) | ||||
−0.882422 | + | 0.470459i | \(0.844088\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 4.10243i | − 0.193176i | ||||||||
\(452\) | − 5.95867i | − 0.280272i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − 22.7826i | − 1.06924i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.1245 | −0.941385 | −0.470693 | − | 0.882297i | \(-0.655996\pi\) | ||||
−0.470693 | + | 0.882297i | \(0.655996\pi\) | |||||||
\(458\) | −20.2175 | −0.944702 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.267949i | 0.0124932i | ||||||||
\(461\) | 0.909299 | 0.0423503 | 0.0211751 | − | 0.999776i | \(-0.493259\pi\) | ||||
0.0211751 | + | 0.999776i | \(0.493259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.4280 | 0.995843 | 0.497922 | − | 0.867222i | \(-0.334097\pi\) | ||||
0.497922 | + | 0.867222i | \(0.334097\pi\) | |||||||
\(464\) | − 8.89898i | − 0.413125i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.63087 | −0.121873 | ||||||||
\(467\) | −12.6921 | −0.587322 | −0.293661 | − | 0.955910i | \(-0.594874\pi\) | ||||
−0.293661 | + | 0.955910i | \(0.594874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 7.99536i | − 0.368798i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 12.6715i | − 0.583252i | ||||||||
\(473\) | − 31.6403i | − 1.45482i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.86370i | 0.131396i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 16.8766 | 0.771916 | ||||||||
\(479\) | 12.8766 | 0.588345 | 0.294172 | − | 0.955752i | \(-0.404956\pi\) | ||||
0.294172 | + | 0.955752i | \(0.404956\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 16.4091i | − 0.748188i | ||||||||
\(482\) | 14.5254 | 0.661612 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 18.1163 | 0.823469 | ||||||||
\(485\) | − 6.16353i | − 0.279871i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.8194 | −0.943416 | −0.471708 | − | 0.881755i | \(-0.656362\pi\) | ||||
−0.471708 | + | 0.881755i | \(0.656362\pi\) | |||||||
\(488\) | 2.62158 | 0.118673 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 27.3271i | 1.23325i | 0.787256 | + | 0.616627i | \(0.211501\pi\) | ||||
−0.787256 | + | 0.616627i | \(0.788499\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 40.0399i | − 1.80331i | ||||||||
\(494\) | − 7.20977i | − 0.324383i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.82843i | 0.216803i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.3604 | 1.49342 | 0.746708 | − | 0.665152i | \(-0.231633\pi\) | ||||
0.746708 | + | 0.665152i | \(0.231633\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 15.7243i | − 0.701809i | ||||||||
\(503\) | 16.2936 | 0.726494 | 0.363247 | − | 0.931693i | \(-0.381668\pi\) | ||||
0.363247 | + | 0.931693i | \(0.381668\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.0492 | 0.625179 | ||||||||
\(506\) | − 1.44584i | − 0.0642755i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.5103 | 0.643792 | ||||||||
\(509\) | 24.6800 | 1.09392 | 0.546961 | − | 0.837158i | \(-0.315784\pi\) | ||||
0.546961 | + | 0.837158i | \(0.315784\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 19.6617i | 0.867239i | ||||||||
\(515\) | 14.1769i | 0.624709i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 43.1426i | 1.89741i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.51764 | −0.110406 | ||||||||
\(521\) | 0.283325 | 0.0124127 | 0.00620635 | − | 0.999981i | \(-0.498024\pi\) | ||||
0.00620635 | + | 0.999981i | \(0.498024\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.2817i | 0.493313i | 0.969103 | + | 0.246656i | \(0.0793319\pi\) | ||||
−0.969103 | + | 0.246656i | \(0.920668\pi\) | |||||||
\(524\) | −15.4665 | −0.675657 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.32175 | −0.188437 | ||||||||
\(527\) | 21.7249i | 0.946352i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.9282 | 0.996878 | ||||||||
\(530\) | 8.39836 | 0.364801 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.91411i | − 0.0829092i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.64173i | 0.0709780i | ||||||||
\(536\) | − 9.82237i | − 0.424262i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.5979i | 0.758700i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.8250 | −1.49724 | −0.748621 | − | 0.662998i | \(-0.769284\pi\) | ||||
−0.748621 | + | 0.662998i | \(0.769284\pi\) | |||||||
\(542\) | −10.5359 | −0.452556 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.49938i | 0.192909i | ||||||||
\(545\) | 19.8977 | 0.852325 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.4261 | 1.51471 | 0.757356 | − | 0.653002i | \(-0.226491\pi\) | ||||
0.757356 | + | 0.653002i | \(0.226491\pi\) | |||||||
\(548\) | 8.62158i | 0.368296i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.39595 | −0.230084 | ||||||||
\(551\) | 25.4840 | 1.08566 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.01942i | 0.128283i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 10.2512i | − 0.434748i | ||||||||
\(557\) | − 8.14185i | − 0.344981i | −0.985011 | − | 0.172491i | \(-0.944819\pi\) | ||||
0.985011 | − | 0.172491i | \(-0.0551815\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 14.7627i | − 0.624395i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 10.6880 | 0.450845 | ||||||||
\(563\) | 20.4175 | 0.860497 | 0.430248 | − | 0.902711i | \(-0.358426\pi\) | ||||
0.430248 | + | 0.902711i | \(0.358426\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 5.95867i | − 0.250683i | ||||||||
\(566\) | 17.5687 | 0.738467 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.76268 | −0.199838 | ||||||||
\(569\) | 26.0433i | 1.09179i | 0.837853 | + | 0.545896i | \(0.183811\pi\) | ||||
−0.837853 | + | 0.545896i | \(0.816189\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −12.3762 | −0.517929 | −0.258964 | − | 0.965887i | \(-0.583381\pi\) | ||||
−0.258964 | + | 0.965887i | \(0.583381\pi\) | |||||||
\(572\) | 13.5851 | 0.568020 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.267949i | 0.0111743i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 26.9506i | 1.12197i | 0.827826 | + | 0.560985i | \(0.189577\pi\) | ||||
−0.827826 | + | 0.560985i | \(0.810423\pi\) | |||||||
\(578\) | 3.24440i | 0.134949i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 8.89898i | − 0.369510i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −45.3171 | −1.87684 | ||||||||
\(584\) | 11.6569 | 0.482364 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 14.6710i | 0.606051i | ||||||||
\(587\) | 35.3511 | 1.45910 | 0.729548 | − | 0.683930i | \(-0.239731\pi\) | ||||
0.729548 | + | 0.683930i | \(0.239731\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −13.8272 | −0.569739 | ||||||||
\(590\) | − 12.6715i | − 0.521676i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −6.51764 | −0.267873 | ||||||||
\(593\) | 29.4115 | 1.20779 | 0.603893 | − | 0.797066i | \(-0.293616\pi\) | ||||
0.603893 | + | 0.797066i | \(0.293616\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.19881i | 0.376798i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 0.674599i | − 0.0275864i | ||||||||
\(599\) | − 30.6566i | − 1.25260i | −0.779584 | − | 0.626298i | \(-0.784569\pi\) | ||||
0.779584 | − | 0.626298i | \(-0.215431\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 34.3407i | − 1.40078i | −0.713758 | − | 0.700392i | \(-0.753008\pi\) | ||||
0.713758 | − | 0.700392i | \(-0.246992\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.7486 | 0.518733 | ||||||||
\(605\) | 18.1163 | 0.736533 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 32.6174i | − 1.32390i | −0.749548 | − | 0.661950i | \(-0.769729\pi\) | ||||
0.749548 | − | 0.661950i | \(-0.230271\pi\) | |||||||
\(608\) | −2.86370 | −0.116139 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.62158 | 0.106145 | ||||||||
\(611\) | 20.1294i | 0.814349i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.9969 | −0.646107 | −0.323054 | − | 0.946381i | \(-0.604709\pi\) | ||||
−0.323054 | + | 0.946381i | \(0.604709\pi\) | |||||||
\(614\) | 21.2772 | 0.858677 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.1429i | 1.01221i | 0.862471 | + | 0.506107i | \(0.168916\pi\) | ||||
−0.862471 | + | 0.506107i | \(0.831084\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.3406i | 1.50085i | 0.660958 | + | 0.750423i | \(0.270150\pi\) | ||||
−0.660958 | + | 0.750423i | \(0.729850\pi\) | |||||||
\(620\) | 4.82843i | 0.193914i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 11.8345i | − 0.474519i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −4.50970 | −0.180244 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 13.8447i | − 0.552464i | ||||||||
\(629\) | −29.3253 | −1.16928 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 49.5015 | 1.97062 | 0.985311 | − | 0.170767i | \(-0.0546245\pi\) | ||||
0.985311 | + | 0.170767i | \(0.0546245\pi\) | |||||||
\(632\) | − 8.59235i | − 0.341786i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.3830 | 0.730083 | ||||||||
\(635\) | 14.5103 | 0.575825 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 48.0185i | 1.90107i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 36.3083i | 1.43409i | 0.697026 | + | 0.717046i | \(0.254506\pi\) | ||||
−0.697026 | + | 0.717046i | \(0.745494\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 10.2653i | − 0.404824i | −0.979300 | − | 0.202412i | \(-0.935122\pi\) | ||||
0.979300 | − | 0.202412i | \(-0.0648780\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.8849 | −0.506949 | ||||||||
\(647\) | −21.8215 | −0.857892 | −0.428946 | − | 0.903330i | \(-0.641115\pi\) | ||||
−0.428946 | + | 0.903330i | \(0.641115\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 68.3746i | 2.68394i | ||||||||
\(650\) | −2.51764 | −0.0987499 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 20.6050 | 0.806954 | ||||||||
\(653\) | 47.2914i | 1.85066i | 0.379166 | + | 0.925329i | \(0.376211\pi\) | ||||
−0.379166 | + | 0.925329i | \(0.623789\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.4665 | −0.604326 | ||||||||
\(656\) | −0.760279 | −0.0296839 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.58255i | 0.139556i | 0.997563 | + | 0.0697782i | \(0.0222291\pi\) | ||||
−0.997563 | + | 0.0697782i | \(0.977771\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1.63692i | − 0.0636688i | −0.999493 | − | 0.0318344i | \(-0.989865\pi\) | ||||
0.999493 | − | 0.0318344i | \(-0.0101349\pi\) | |||||||
\(662\) | 7.96132i | 0.309426i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.45001i | 0.366731i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.38447 | 0.0923272 | ||||||||
\(668\) | 6.84961 | 0.265019 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 9.82237i | − 0.379471i | ||||||||
\(671\) | −14.1459 | −0.546097 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.02242 | −0.0779587 | −0.0389794 | − | 0.999240i | \(-0.512411\pi\) | ||||
−0.0389794 | + | 0.999240i | \(0.512411\pi\) | |||||||
\(674\) | − 6.89417i | − 0.265554i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.66150 | −0.256211 | ||||||||
\(677\) | 22.8826 | 0.879450 | 0.439725 | − | 0.898132i | \(-0.355076\pi\) | ||||
0.439725 | + | 0.898132i | \(0.355076\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.49938i | 0.172543i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 26.0540i | − 0.997658i | ||||||||
\(683\) | − 31.4052i | − 1.20169i | −0.799366 | − | 0.600844i | \(-0.794831\pi\) | ||||
0.799366 | − | 0.600844i | \(-0.205169\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.62158i | 0.329414i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.86370 | −0.223552 | ||||||||
\(689\) | −21.1440 | −0.805523 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 33.9109i | − 1.29003i | −0.764170 | − | 0.645015i | \(-0.776851\pi\) | ||||
0.764170 | − | 0.645015i | \(-0.223149\pi\) | |||||||
\(692\) | 12.7580 | 0.484988 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.3558 | −0.620857 | ||||||||
\(695\) | − 10.2512i | − 0.388850i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.42078 | −0.129571 | ||||||||
\(698\) | −24.5851 | −0.930558 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 10.5296i | − 0.397699i | −0.980030 | − | 0.198849i | \(-0.936280\pi\) | ||||
0.980030 | − | 0.198849i | \(-0.0637205\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 18.6646i | − 0.703948i | ||||||||
\(704\) | − 5.39595i | − 0.203368i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 13.7181i | 0.516288i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.0514 | 0.565268 | 0.282634 | − | 0.959228i | \(-0.408792\pi\) | ||||
0.282634 | + | 0.959228i | \(0.408792\pi\) | |||||||
\(710\) | −4.76268 | −0.178740 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.97005i | 0.298690i | ||||||||
\(713\) | −1.29377 | −0.0484522 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.5851 | 0.508052 | ||||||||
\(716\) | − 18.8666i | − 0.705079i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11.9002 | 0.444112 | ||||||||
\(719\) | 24.4274 | 0.910987 | 0.455494 | − | 0.890239i | \(-0.349463\pi\) | ||||
0.455494 | + | 0.890239i | \(0.349463\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 10.7992i | 0.401905i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − 25.5498i | − 0.949550i | ||||||||
\(725\) | − 8.89898i | − 0.330500i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 43.7349i | − 1.62204i | −0.585020 | − | 0.811019i | \(-0.698913\pi\) | ||||
0.585020 | − | 0.811019i | \(-0.301087\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 11.6569 | 0.431440 | ||||||||
\(731\) | −26.3830 | −0.975811 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 44.7193i | − 1.65174i | −0.563857 | − | 0.825872i | \(-0.690683\pi\) | ||||
0.563857 | − | 0.825872i | \(-0.309317\pi\) | |||||||
\(734\) | 12.5892 | 0.464677 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.267949 | −0.00987674 | ||||||||
\(737\) | 53.0011i | 1.95232i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.4721 | −0.789864 | −0.394932 | − | 0.918710i | \(-0.629232\pi\) | ||||
−0.394932 | + | 0.918710i | \(0.629232\pi\) | |||||||
\(740\) | −6.51764 | −0.239593 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 29.5637i | − 1.08459i | −0.840190 | − | 0.542293i | \(-0.817556\pi\) | ||||
0.840190 | − | 0.542293i | \(-0.182444\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.19881i | 0.337018i | ||||||||
\(746\) | − 27.1737i | − 0.994898i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 24.2784i | − 0.887707i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.19350 | 0.0435514 | 0.0217757 | − | 0.999763i | \(-0.493068\pi\) | ||||
0.0217757 | + | 0.999763i | \(0.493068\pi\) | |||||||
\(752\) | 7.99536 | 0.291561 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 22.4044i | 0.815920i | ||||||||
\(755\) | 12.7486 | 0.463969 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −26.8915 | −0.977386 | −0.488693 | − | 0.872456i | \(-0.662526\pi\) | ||||
−0.488693 | + | 0.872456i | \(0.662526\pi\) | |||||||
\(758\) | 15.7335i | 0.571465i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.86370 | −0.103877 | ||||||||
\(761\) | −1.87915 | −0.0681190 | −0.0340595 | − | 0.999420i | \(-0.510844\pi\) | ||||
−0.0340595 | + | 0.999420i | \(0.510844\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 8.09049i | 0.292704i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 15.7812i | − 0.570198i | ||||||||
\(767\) | 31.9022i | 1.15192i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 50.6544i | − 1.82664i | −0.407239 | − | 0.913322i | \(-0.633508\pi\) | ||||
0.407239 | − | 0.913322i | \(-0.366492\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.1270 | 0.508442 | ||||||||
\(773\) | −48.6705 | −1.75056 | −0.875279 | − | 0.483619i | \(-0.839322\pi\) | ||||
−0.875279 | + | 0.483619i | \(0.839322\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.82843i | 0.173442i | ||||||||
\(776\) | 6.16353 | 0.221258 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.8836 | −0.569456 | ||||||||
\(779\) | − 2.17721i | − 0.0780067i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.6992 | 0.919590 | ||||||||
\(782\) | −1.20560 | −0.0431123 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 13.8447i | − 0.494139i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 14.9461i | − 0.532773i | −0.963866 | − | 0.266386i | \(-0.914170\pi\) | ||||
0.963866 | − | 0.266386i | \(-0.0858297\pi\) | |||||||
\(788\) | 14.2738i | 0.508483i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 8.59235i | − 0.305702i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.60018 | −0.234379 | ||||||||
\(794\) | 37.3611 | 1.32590 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 3.54195i | − 0.125541i | ||||||||
\(797\) | 15.0557 | 0.533301 | 0.266650 | − | 0.963793i | \(-0.414083\pi\) | ||||
0.266650 | + | 0.963793i | \(0.414083\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.9741 | 1.27267 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −28.2735 | −0.998373 | ||||||||
\(803\) | −62.8998 | −2.21969 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 12.1562i | − 0.428185i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 14.0492i | 0.494248i | ||||||||
\(809\) | − 35.4985i | − 1.24806i | −0.781399 | − | 0.624031i | \(-0.785494\pi\) | ||||
0.781399 | − | 0.624031i | \(-0.214506\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 24.5935i | 0.863594i | 0.901971 | + | 0.431797i | \(0.142120\pi\) | ||||
−0.901971 | + | 0.431797i | \(0.857880\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 35.1689 | 1.23267 | ||||||||
\(815\) | 20.6050 | 0.721761 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 16.7919i | − 0.587474i | ||||||||
\(818\) | −16.0096 | −0.559763 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.760279 | −0.0265501 | ||||||||
\(821\) | − 14.2068i | − 0.495822i | −0.968783 | − | 0.247911i | \(-0.920256\pi\) | ||||
0.968783 | − | 0.247911i | \(-0.0797441\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.89117 | 0.0659219 | 0.0329610 | − | 0.999457i | \(-0.489506\pi\) | ||||
0.0329610 | + | 0.999457i | \(0.489506\pi\) | |||||||
\(824\) | −14.1769 | −0.493876 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 31.9280i | − 1.11024i | −0.831769 | − | 0.555122i | \(-0.812671\pi\) | ||||
0.831769 | − | 0.555122i | \(-0.187329\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.91286i | 0.135899i | 0.997689 | + | 0.0679497i | \(0.0216457\pi\) | ||||
−0.997689 | + | 0.0679497i | \(0.978354\pi\) | |||||||
\(830\) | 9.45001i | 0.328014i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 2.51764i | − 0.0872834i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.84961 | 0.237040 | ||||||||
\(836\) | 15.4524 | 0.534433 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 29.5137i | − 1.01953i | ||||||||
\(839\) | 15.3513 | 0.529984 | 0.264992 | − | 0.964251i | \(-0.414631\pi\) | ||||
0.264992 | + | 0.964251i | \(0.414631\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −50.1918 | −1.73075 | ||||||||
\(842\) | 0.309114i | 0.0106528i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.92340 | 0.135049 | ||||||||
\(845\) | −6.66150 | −0.229163 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 8.39836i | 0.288401i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.49938i | 0.154327i | ||||||||
\(851\) | − 1.74640i | − 0.0598657i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.2302i | 0.761148i | 0.924750 | + | 0.380574i | \(0.124274\pi\) | ||||
−0.924750 | + | 0.380574i | \(0.875726\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.64173 | −0.0561131 | ||||||||
\(857\) | 52.8197 | 1.80429 | 0.902143 | − | 0.431438i | \(-0.141993\pi\) | ||||
0.902143 | + | 0.431438i | \(0.141993\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.6572i | 0.602455i | 0.953552 | + | 0.301228i | \(0.0973964\pi\) | ||||
−0.953552 | + | 0.301228i | \(0.902604\pi\) | |||||||
\(860\) | −5.86370 | −0.199951 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.82010 | 0.300414 | ||||||||
\(863\) | − 16.4489i | − 0.559928i | −0.960011 | − | 0.279964i | \(-0.909677\pi\) | ||||
0.960011 | − | 0.279964i | \(-0.0903225\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.7580 | 0.433786 | ||||||||
\(866\) | 9.56388 | 0.324994 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 46.3639i | 1.57279i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24.7292i | 0.837916i | ||||||||
\(872\) | 19.8977i | 0.673822i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 0.767327i | − 0.0259552i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54.2156 | 1.83073 | 0.915366 | − | 0.402623i | \(-0.131902\pi\) | ||||
0.915366 | + | 0.402623i | \(0.131902\pi\) | |||||||
\(878\) | −36.1810 | −1.22105 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 5.39595i | − 0.181898i | ||||||||
\(881\) | 50.1647 | 1.69009 | 0.845046 | − | 0.534694i | \(-0.179573\pi\) | ||||
0.845046 | + | 0.534694i | \(0.179573\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.841563 | −0.0283208 | −0.0141604 | − | 0.999900i | \(-0.504508\pi\) | ||||
−0.0141604 | + | 0.999900i | \(0.504508\pi\) | |||||||
\(884\) | − 11.3278i | − 0.380995i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.08568 | 0.137261 | ||||||||
\(887\) | −40.0983 | −1.34637 | −0.673185 | − | 0.739474i | \(-0.735074\pi\) | ||||
−0.673185 | + | 0.739474i | \(0.735074\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 7.97005i | 0.267157i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 14.6904i | − 0.491870i | ||||||||
\(893\) | 22.8963i | 0.766196i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 18.8666i | − 0.630642i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −19.9377 | −0.665329 | ||||||||
\(899\) | 42.9681 | 1.43307 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37.7874i | 1.25888i | ||||||||
\(902\) | 4.10243 | 0.136596 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.95867 | 0.198182 | ||||||||
\(905\) | − 25.5498i | − 0.849303i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −45.1890 | −1.50048 | −0.750238 | − | 0.661167i | \(-0.770061\pi\) | ||||
−0.750238 | + | 0.661167i | \(0.770061\pi\) | |||||||
\(908\) | 22.7826 | 0.756068 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 58.2281i | 1.92918i | 0.263746 | + | 0.964592i | \(0.415042\pi\) | ||||
−0.263746 | + | 0.964592i | \(0.584958\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 50.9918i | − 1.68758i | ||||||||
\(914\) | − 20.1245i | − 0.665660i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − 20.2175i | − 0.668005i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 13.2349 | 0.436579 | 0.218290 | − | 0.975884i | \(-0.429952\pi\) | ||||
0.218290 | + | 0.975884i | \(0.429952\pi\) | |||||||
\(920\) | −0.267949 | −0.00883402 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0.909299i | 0.0299462i | ||||||||
\(923\) | 11.9907 | 0.394679 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.51764 | −0.214299 | ||||||||
\(926\) | 21.4280i | 0.704168i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 8.89898 | 0.292123 | ||||||||
\(929\) | 20.8868 | 0.685273 | 0.342637 | − | 0.939468i | \(-0.388680\pi\) | ||||
0.342637 | + | 0.939468i | \(0.388680\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 2.63087i | − 0.0861769i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 12.6921i | − 0.415299i | ||||||||
\(935\) | − 24.2784i | − 0.793990i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.2465i | 0.759430i | 0.925103 | + | 0.379715i | \(0.123978\pi\) | ||||
−0.925103 | + | 0.379715i | \(0.876022\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.99536 | 0.260780 | ||||||||
\(941\) | 1.50510 | 0.0490649 | 0.0245325 | − | 0.999699i | \(-0.492190\pi\) | ||||
0.0245325 | + | 0.999699i | \(0.492190\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 0.203716i | − 0.00663391i | ||||||||
\(944\) | 12.6715 | 0.412421 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 31.6403 | 1.02871 | ||||||||
\(947\) | − 24.2628i | − 0.788435i | −0.919017 | − | 0.394218i | \(-0.871016\pi\) | ||||
0.919017 | − | 0.394218i | \(-0.128984\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −29.3477 | −0.952668 | ||||||||
\(950\) | −2.86370 | −0.0929108 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 56.7061i | 1.83689i | 0.395547 | + | 0.918446i | \(0.370555\pi\) | ||||
−0.395547 | + | 0.918446i | \(0.629445\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 8.09049i | 0.261802i | ||||||||
\(956\) | 16.8766i | 0.545827i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.8766i | 0.416023i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.68629 | 0.247945 | ||||||||
\(962\) | 16.4091 | 0.529049 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 14.5254i | 0.467831i | ||||||||
\(965\) | 14.1270 | 0.454764 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.23556 | 0.232680 | 0.116340 | − | 0.993209i | \(-0.462884\pi\) | ||||
0.116340 | + | 0.993209i | \(0.462884\pi\) | |||||||
\(968\) | 18.1163i | 0.582280i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.16353 | 0.197899 | ||||||||
\(971\) | −38.7120 | −1.24233 | −0.621163 | − | 0.783681i | \(-0.713340\pi\) | ||||
−0.621163 | + | 0.783681i | \(0.713340\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 20.8194i | − 0.667096i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.62158i | 0.0839147i | ||||||||
\(977\) | − 18.1610i | − 0.581023i | −0.956871 | − | 0.290512i | \(-0.906175\pi\) | ||||
0.956871 | − | 0.290512i | \(-0.0938255\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 43.0060i | − 1.37448i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.3271 | −0.872042 | ||||||||
\(983\) | 16.3998 | 0.523071 | 0.261536 | − | 0.965194i | \(-0.415771\pi\) | ||||
0.261536 | + | 0.965194i | \(0.415771\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.2738i | 0.454801i | ||||||||
\(986\) | 40.0399 | 1.27513 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 7.20977 | 0.229373 | ||||||||
\(989\) | − 1.57117i | − 0.0499604i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −10.8917 | −0.345986 | −0.172993 | − | 0.984923i | \(-0.555344\pi\) | ||||
−0.172993 | + | 0.984923i | \(0.555344\pi\) | |||||||
\(992\) | −4.82843 | −0.153303 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 3.54195i | − 0.112287i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.5481i | 1.12582i | 0.826518 | + | 0.562910i | \(0.190318\pi\) | ||||
−0.826518 | + | 0.562910i | \(0.809682\pi\) | |||||||
\(998\) | 33.3604i | 1.05600i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4410.2.b.b.881.8 | 8 | ||
3.2 | odd | 2 | 4410.2.b.e.881.1 | 8 | |||
7.4 | even | 3 | 630.2.be.b.341.1 | yes | 8 | ||
7.5 | odd | 6 | 630.2.be.a.521.3 | yes | 8 | ||
7.6 | odd | 2 | 4410.2.b.e.881.8 | 8 | |||
21.5 | even | 6 | 630.2.be.b.521.1 | yes | 8 | ||
21.11 | odd | 6 | 630.2.be.a.341.3 | ✓ | 8 | ||
21.20 | even | 2 | inner | 4410.2.b.b.881.1 | 8 | ||
35.4 | even | 6 | 3150.2.bf.c.1601.4 | 8 | |||
35.12 | even | 12 | 3150.2.bp.d.899.2 | 8 | |||
35.18 | odd | 12 | 3150.2.bp.c.1349.2 | 8 | |||
35.19 | odd | 6 | 3150.2.bf.b.1151.2 | 8 | |||
35.32 | odd | 12 | 3150.2.bp.f.1349.3 | 8 | |||
35.33 | even | 12 | 3150.2.bp.a.899.3 | 8 | |||
105.32 | even | 12 | 3150.2.bp.a.1349.3 | 8 | |||
105.47 | odd | 12 | 3150.2.bp.c.899.2 | 8 | |||
105.53 | even | 12 | 3150.2.bp.d.1349.2 | 8 | |||
105.68 | odd | 12 | 3150.2.bp.f.899.3 | 8 | |||
105.74 | odd | 6 | 3150.2.bf.b.1601.2 | 8 | |||
105.89 | even | 6 | 3150.2.bf.c.1151.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.be.a.341.3 | ✓ | 8 | 21.11 | odd | 6 | ||
630.2.be.a.521.3 | yes | 8 | 7.5 | odd | 6 | ||
630.2.be.b.341.1 | yes | 8 | 7.4 | even | 3 | ||
630.2.be.b.521.1 | yes | 8 | 21.5 | even | 6 | ||
3150.2.bf.b.1151.2 | 8 | 35.19 | odd | 6 | |||
3150.2.bf.b.1601.2 | 8 | 105.74 | odd | 6 | |||
3150.2.bf.c.1151.4 | 8 | 105.89 | even | 6 | |||
3150.2.bf.c.1601.4 | 8 | 35.4 | even | 6 | |||
3150.2.bp.a.899.3 | 8 | 35.33 | even | 12 | |||
3150.2.bp.a.1349.3 | 8 | 105.32 | even | 12 | |||
3150.2.bp.c.899.2 | 8 | 105.47 | odd | 12 | |||
3150.2.bp.c.1349.2 | 8 | 35.18 | odd | 12 | |||
3150.2.bp.d.899.2 | 8 | 35.12 | even | 12 | |||
3150.2.bp.d.1349.2 | 8 | 105.53 | even | 12 | |||
3150.2.bp.f.899.3 | 8 | 105.68 | odd | 12 | |||
3150.2.bp.f.1349.3 | 8 | 35.32 | odd | 12 | |||
4410.2.b.b.881.1 | 8 | 21.20 | even | 2 | inner | ||
4410.2.b.b.881.8 | 8 | 1.1 | even | 1 | trivial | ||
4410.2.b.e.881.1 | 8 | 3.2 | odd | 2 | |||
4410.2.b.e.881.8 | 8 | 7.6 | odd | 2 |