Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5700,2,Mod(3649,5700)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5700, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5700.3649");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5700 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5700.f (of order \(2\), degree \(1\), not 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: | \(45.5147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 1140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3649.4 | ||
Root | \(2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5700.3649 |
Dual form | 5700.2.f.n.3649.1 |
$q$-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 \(\left(\mathbb{Z}/5700\mathbb{Z}\right)^\times\).
\(n\) | \(1901\) | \(2851\) | \(3877\) | \(4201\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.60555i | 1.74073i | 0.492403 | + | 0.870367i | \(0.336119\pi\) | ||||
−0.492403 | + | 0.870367i | \(0.663881\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.60555 | 0.785603 | 0.392802 | − | 0.919623i | \(-0.371506\pi\) | ||||
0.392802 | + | 0.919623i | \(0.371506\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.60555i | 0.722650i | 0.932440 | + | 0.361325i | \(0.117675\pi\) | ||||
−0.932440 | + | 0.361325i | \(0.882325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000i | 0.485071i | 0.970143 | + | 0.242536i | \(0.0779791\pi\) | ||||
−0.970143 | + | 0.242536i | \(0.922021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.60555 | −1.00501 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.00000i | 0.417029i | 0.978019 | + | 0.208514i | \(0.0668628\pi\) | ||||
−0.978019 | + | 0.208514i | \(0.933137\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.60555 | 0.855229 | 0.427615 | − | 0.903961i | \(-0.359354\pi\) | ||||
0.427615 | + | 0.903961i | \(0.359354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.00000 | 0.718421 | 0.359211 | − | 0.933257i | \(-0.383046\pi\) | ||||
0.359211 | + | 0.933257i | \(0.383046\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.60555i | 0.453568i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10.6056i | 1.74354i | 0.489914 | + | 0.871771i | \(0.337028\pi\) | ||||
−0.489914 | + | 0.871771i | \(0.662972\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.60555 | −0.417222 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.605551 | −0.0945712 | −0.0472856 | − | 0.998881i | \(-0.515057\pi\) | ||||
−0.0472856 | + | 0.998881i | \(0.515057\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 3.39445i | − 0.517649i | −0.965924 | − | 0.258824i | \(-0.916665\pi\) | ||||
0.965924 | − | 0.258824i | \(-0.0833351\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.00000i | 0.875190i | 0.899172 | + | 0.437595i | \(0.144170\pi\) | ||||
−0.899172 | + | 0.437595i | \(0.855830\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.2111 | −2.03016 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.00000 | −0.280056 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.00000i | 0.132453i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 9.21110 | 1.19918 | 0.599592 | − | 0.800306i | \(-0.295330\pi\) | ||||
0.599592 | + | 0.800306i | \(0.295330\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.21110 | 0.923287 | 0.461644 | − | 0.887066i | \(-0.347260\pi\) | ||||
0.461644 | + | 0.887066i | \(0.347260\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 4.60555i | − 0.580245i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.21110 | 0.618444 | 0.309222 | − | 0.950990i | \(-0.399931\pi\) | ||||
0.309222 | + | 0.950990i | \(0.399931\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 6.00000i | − 0.702247i | −0.936329 | − | 0.351123i | \(-0.885800\pi\) | ||||
0.936329 | − | 0.351123i | \(-0.114200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.0000i | 1.36753i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.00000 | −0.900070 | −0.450035 | − | 0.893011i | \(-0.648589\pi\) | ||||
−0.450035 | + | 0.893011i | \(0.648589\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 3.21110i | − 0.352464i | −0.984349 | − | 0.176232i | \(-0.943609\pi\) | ||||
0.984349 | − | 0.176232i | \(-0.0563909\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.60555i | 0.493767i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.605551 | 0.0641883 | 0.0320942 | − | 0.999485i | \(-0.489782\pi\) | ||||
0.0320942 | + | 0.999485i | \(0.489782\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −12.0000 | −1.25794 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.00000i | 0.414781i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.39445i | 0.953862i | 0.878941 | + | 0.476931i | \(0.158251\pi\) | ||||
−0.878941 | + | 0.476931i | \(0.841749\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.60555 | −0.261868 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.21110 | 0.717532 | 0.358766 | − | 0.933428i | \(-0.383198\pi\) | ||||
0.358766 | + | 0.933428i | \(0.383198\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.4222i | 1.02693i | 0.858110 | + | 0.513465i | \(0.171638\pi\) | ||||
−0.858110 | + | 0.513465i | \(0.828362\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 10.4222i | − 1.00755i | −0.863834 | − | 0.503776i | \(-0.831944\pi\) | ||||
0.863834 | − | 0.503776i | \(-0.168056\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.21110 | −0.307568 | −0.153784 | − | 0.988105i | \(-0.549146\pi\) | ||||
−0.153784 | + | 0.988105i | \(0.549146\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.6056 | −1.00663 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 13.2111i | − 1.24280i | −0.783495 | − | 0.621398i | \(-0.786565\pi\) | ||||
0.783495 | − | 0.621398i | \(-0.213435\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 2.60555i | − 0.240883i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.21110 | −0.844380 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.21110 | −0.382828 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 0.605551i | − 0.0546007i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 10.4222i | − 0.924821i | −0.886666 | − | 0.462411i | \(-0.846985\pi\) | ||||
0.886666 | − | 0.462411i | \(-0.153015\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.39445 | 0.298865 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.6056 | −1.97506 | −0.987528 | − | 0.157443i | \(-0.949675\pi\) | ||||
−0.987528 | + | 0.157443i | \(0.949675\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.60555i | 0.399352i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 16.4222i | 1.40304i | 0.712648 | + | 0.701522i | \(0.247496\pi\) | ||||
−0.712648 | + | 0.701522i | \(0.752504\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.21110 | 0.442000 | 0.221000 | − | 0.975274i | \(-0.429068\pi\) | ||||
0.221000 | + | 0.975274i | \(0.429068\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.00000 | −0.505291 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.78890i | 0.567716i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − 14.2111i | − 1.17211i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.4222 | 1.01767 | 0.508833 | − | 0.860865i | \(-0.330077\pi\) | ||||
0.508833 | + | 0.860865i | \(0.330077\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.0000 | −0.976546 | −0.488273 | − | 0.872691i | \(-0.662373\pi\) | ||||
−0.488273 | + | 0.872691i | \(0.662373\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − 2.00000i | − 0.161690i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.788897i | 0.0629609i | 0.999504 | + | 0.0314804i | \(0.0100222\pi\) | ||||
−0.999504 | + | 0.0314804i | \(0.989978\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.21110 | −0.725937 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 19.0278i | − 1.49037i | −0.666858 | − | 0.745184i | \(-0.732361\pi\) | ||||
0.666858 | − | 0.745184i | \(-0.267639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 21.2111i | − 1.64136i | −0.571385 | − | 0.820682i | \(-0.693594\pi\) | ||||
0.571385 | − | 0.820682i | \(-0.306406\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.21110 | 0.477777 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 5.21110i | − 0.396193i | −0.980183 | − | 0.198096i | \(-0.936524\pi\) | ||||
0.980183 | − | 0.198096i | \(-0.0634759\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 9.21110i | 0.692349i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.78890 | 0.507426 | 0.253713 | − | 0.967280i | \(-0.418348\pi\) | ||||
0.253713 | + | 0.967280i | \(0.418348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.2111 | −1.13063 | −0.565316 | − | 0.824874i | \(-0.691246\pi\) | ||||
−0.565316 | + | 0.824874i | \(0.691246\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.21110i | 0.533060i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.21110i | 0.381074i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.60555 | 0.335005 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 15.8167 | 1.14445 | 0.572226 | − | 0.820096i | \(-0.306080\pi\) | ||||
0.572226 | + | 0.820096i | \(0.306080\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 6.60555i | − 0.475478i | −0.971329 | − | 0.237739i | \(-0.923594\pi\) | ||||
0.971329 | − | 0.237739i | \(-0.0764063\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.0000i | 0.997459i | 0.866758 | + | 0.498729i | \(0.166200\pi\) | ||||
−0.866758 | + | 0.498729i | \(0.833800\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.78890 | −0.197700 | −0.0988498 | − | 0.995102i | \(-0.531516\pi\) | ||||
−0.0988498 | + | 0.995102i | \(0.531516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.00000 | −0.282138 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 21.2111i | 1.48873i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 2.00000i | − 0.139010i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.60555 | 0.180230 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.00000 | −0.275371 | −0.137686 | − | 0.990476i | \(-0.543966\pi\) | ||||
−0.137686 | + | 0.990476i | \(0.543966\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.21110i | 0.357059i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 18.4222i | 1.25058i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 6.00000 | 0.405442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.21110 | −0.350537 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 18.4222i | − 1.23364i | −0.787103 | − | 0.616821i | \(-0.788420\pi\) | ||||
0.787103 | − | 0.616821i | \(-0.211580\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1.21110i | 0.0803837i | 0.999192 | + | 0.0401918i | \(0.0127969\pi\) | ||||
−0.999192 | + | 0.0401918i | \(0.987203\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.2111 | −0.740851 | −0.370425 | − | 0.928862i | \(-0.620788\pi\) | ||||
−0.370425 | + | 0.928862i | \(0.620788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.0000 | −0.789542 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 12.4222i | − 0.813806i | −0.913471 | − | 0.406903i | \(-0.866609\pi\) | ||||
0.913471 | − | 0.406903i | \(-0.133391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 8.00000i | − 0.519656i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.18335 | −0.270598 | −0.135299 | − | 0.990805i | \(-0.543200\pi\) | ||||
−0.135299 | + | 0.990805i | \(0.543200\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.0000 | −0.644157 | −0.322078 | − | 0.946713i | \(-0.604381\pi\) | ||||
−0.322078 | + | 0.946713i | \(0.604381\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.60555i | 0.165787i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.21110 | 0.203495 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −27.8167 | −1.75577 | −0.877886 | − | 0.478870i | \(-0.841047\pi\) | ||||
−0.877886 | + | 0.478870i | \(0.841047\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.21110i | 0.327619i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.2111i | 1.07360i | 0.843710 | + | 0.536800i | \(0.180367\pi\) | ||||
−0.843710 | + | 0.536800i | \(0.819633\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −48.8444 | −3.03504 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.60555 | −0.285076 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 7.21110i | 0.444656i | 0.974972 | + | 0.222328i | \(0.0713655\pi\) | ||||
−0.974972 | + | 0.222328i | \(0.928634\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0.605551i | 0.0370591i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 24.6056 | 1.50023 | 0.750113 | − | 0.661309i | \(-0.229999\pi\) | ||||
0.750113 | + | 0.661309i | \(0.229999\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.6333 | −1.92159 | −0.960793 | − | 0.277266i | \(-0.910572\pi\) | ||||
−0.960793 | + | 0.277266i | \(0.910572\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − 12.0000i | − 0.726273i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.00000i | − 0.120168i | −0.998193 | − | 0.0600842i | \(-0.980863\pi\) | ||||
0.998193 | − | 0.0600842i | \(-0.0191369\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | −0.239474 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −32.2389 | −1.92321 | −0.961605 | − | 0.274439i | \(-0.911508\pi\) | ||||
−0.961605 | + | 0.274439i | \(0.911508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.3944i | 0.677330i | 0.940907 | + | 0.338665i | \(0.109975\pi\) | ||||
−0.940907 | + | 0.338665i | \(0.890025\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2.78890i | − 0.164623i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0000 | 0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −9.39445 | −0.550712 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 23.6333i | 1.38067i | 0.723489 | + | 0.690336i | \(0.242537\pi\) | ||||
−0.723489 | + | 0.690336i | \(0.757463\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 2.60555i | − 0.151189i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.21110 | −0.301366 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 15.6333 | 0.901089 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 7.21110i | 0.414267i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.6333i | 1.80541i | 0.430262 | + | 0.902704i | \(0.358421\pi\) | ||||
−0.430262 | + | 0.902704i | \(0.641579\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.4222 | −0.592899 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.39445 | 0.532710 | 0.266355 | − | 0.963875i | \(-0.414181\pi\) | ||||
0.266355 | + | 0.963875i | \(0.414181\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 15.2111i | − 0.859782i | −0.902881 | − | 0.429891i | \(-0.858552\pi\) | ||||
0.902881 | − | 0.429891i | \(-0.141448\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 22.4222i | 1.25936i | 0.776856 | + | 0.629678i | \(0.216813\pi\) | ||||
−0.776856 | + | 0.629678i | \(0.783187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0000 | 0.671871 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 10.4222 | 0.581711 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.00000i | 0.111283i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 3.21110i | − 0.177574i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.6333 | −1.52347 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.00000 | −0.439720 | −0.219860 | − | 0.975531i | \(-0.570560\pi\) | ||||
−0.219860 | + | 0.975531i | \(0.570560\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 10.6056i | − 0.581181i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 33.0278i | − 1.79914i | −0.436780 | − | 0.899568i | \(-0.643881\pi\) | ||||
0.436780 | − | 0.899568i | \(-0.356119\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.2111 | 0.717529 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4222 | 0.564394 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 33.2111i | − 1.79323i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 21.6333i | − 1.16134i | −0.814140 | − | 0.580668i | \(-0.802791\pi\) | ||||
0.814140 | − | 0.580668i | \(-0.197209\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.8444 | 1.22283 | 0.611417 | − | 0.791309i | \(-0.290600\pi\) | ||||
0.611417 | + | 0.791309i | \(0.290600\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.60555 | 0.139074 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.4222i | 1.51276i | 0.654132 | + | 0.756381i | \(0.273034\pi\) | ||||
−0.654132 | + | 0.756381i | \(0.726966\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 9.21110i | − 0.487503i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.81665 | −0.412547 | −0.206274 | − | 0.978494i | \(-0.566134\pi\) | ||||
−0.206274 | + | 0.978494i | \(0.566134\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 4.21110i | − 0.221026i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 11.0278i | − 0.575644i | −0.957684 | − | 0.287822i | \(-0.907069\pi\) | ||||
0.957684 | − | 0.287822i | \(-0.0929312\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.605551 | 0.0315237 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 9.39445i | − 0.486426i | −0.969973 | − | 0.243213i | \(-0.921799\pi\) | ||||
0.969973 | − | 0.243213i | \(-0.0782014\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0000i | 0.618031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.42221 | 0.124420 | 0.0622102 | − | 0.998063i | \(-0.480185\pi\) | ||||
0.0622102 | + | 0.998063i | \(0.480185\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.4222 | 0.533946 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.0000i | 0.613171i | 0.951843 | + | 0.306586i | \(0.0991866\pi\) | ||||
−0.951843 | + | 0.306586i | \(0.900813\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.39445i | 0.172550i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −7.57779 | −0.384209 | −0.192105 | − | 0.981374i | \(-0.561531\pi\) | ||||
−0.192105 | + | 0.981374i | \(0.561531\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 22.6056i | − 1.14030i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 36.4222i | − 1.82798i | −0.405739 | − | 0.913989i | \(-0.632986\pi\) | ||||
0.405739 | − | 0.913989i | \(-0.367014\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.60555 | −0.230566 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 32.6056 | 1.62824 | 0.814122 | − | 0.580694i | \(-0.197219\pi\) | ||||
0.814122 | + | 0.580694i | \(0.197219\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 10.4222i | 0.519167i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.6333i | 1.36973i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.2111 | 1.34550 | 0.672751 | − | 0.739869i | \(-0.265112\pi\) | ||||
0.672751 | + | 0.739869i | \(0.265112\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.4222 | −0.810048 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 42.4222i | 2.08746i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.21110i | 0.255189i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −29.0278 | −1.41810 | −0.709049 | − | 0.705159i | \(-0.750876\pi\) | ||||
−0.709049 | + | 0.705159i | \(0.750876\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.4222 | 0.995317 | 0.497659 | − | 0.867373i | \(-0.334193\pi\) | ||||
0.497659 | + | 0.867373i | \(0.334193\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 6.00000i | − 0.291730i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.2111i | 1.60720i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.78890 | −0.327771 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5.21110 | 0.251010 | 0.125505 | − | 0.992093i | \(-0.459945\pi\) | ||||
0.125505 | + | 0.992093i | \(0.459945\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.39445i | 0.451468i | 0.974189 | + | 0.225734i | \(0.0724781\pi\) | ||||
−0.974189 | + | 0.225734i | \(0.927522\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000i | 0.0956730i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.57779 | −0.266214 | −0.133107 | − | 0.991102i | \(-0.542495\pi\) | ||||
−0.133107 | + | 0.991102i | \(0.542495\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.2111 | 0.676719 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 38.8444i | 1.84555i | 0.385335 | + | 0.922777i | \(0.374086\pi\) | ||||
−0.385335 | + | 0.922777i | \(0.625914\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.4222i | 0.587550i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.2389 | −1.52145 | −0.760723 | − | 0.649077i | \(-0.775155\pi\) | ||||
−0.760723 | + | 0.649077i | \(0.775155\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.57779 | −0.0742955 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 12.0000i | − 0.563809i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 40.0555i | − 1.87372i | −0.349708 | − | 0.936859i | \(-0.613719\pi\) | ||||
0.349708 | − | 0.936859i | \(-0.386281\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.00000 | 0.0933520 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 34.8444 | 1.62287 | 0.811433 | − | 0.584445i | \(-0.198688\pi\) | ||||
0.811433 | + | 0.584445i | \(0.198688\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.02776i | 0.140712i | 0.997522 | + | 0.0703559i | \(0.0224135\pi\) | ||||
−0.997522 | + | 0.0703559i | \(0.977587\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 34.8444i | − 1.61241i | −0.591638 | − | 0.806204i | \(-0.701519\pi\) | ||||
0.591638 | − | 0.806204i | \(-0.298481\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −18.4222 | −0.850658 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.788897 | −0.0363505 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 8.84441i | − 0.406666i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −21.3944 | −0.977537 | −0.488769 | − | 0.872413i | \(-0.662554\pi\) | ||||
−0.488769 | + | 0.872413i | \(0.662554\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −27.6333 | −1.25997 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 9.21110i | − 0.419120i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 43.6333i | 1.97721i | 0.150520 | + | 0.988607i | \(0.451905\pi\) | ||||
−0.150520 | + | 0.988607i | \(0.548095\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 19.0278 | 0.860465 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 38.2389 | 1.72570 | 0.862848 | − | 0.505464i | \(-0.168679\pi\) | ||||
0.862848 | + | 0.505464i | \(0.168679\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.21110i | 0.414847i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 24.0000i | 1.07655i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.6333 | −0.699843 | −0.349921 | − | 0.936779i | \(-0.613792\pi\) | ||||
−0.349921 | + | 0.936779i | \(0.613792\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.2111 | 0.947642 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 27.2111i | − 1.21328i | −0.794975 | − | 0.606642i | \(-0.792516\pi\) | ||||
0.794975 | − | 0.606642i | \(-0.207484\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 6.21110i | 0.275845i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −29.4500 | −1.30535 | −0.652673 | − | 0.757639i | \(-0.726353\pi\) | ||||
−0.652673 | + | 0.757639i | \(0.726353\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 27.6333 | 1.22243 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 1.00000i | − 0.0441511i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.6333i | 0.687552i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 5.21110 | 0.228742 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −25.8167 | −1.13105 | −0.565524 | − | 0.824732i | \(-0.691326\pi\) | ||||
−0.565524 | + | 0.824732i | \(0.691326\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7889i | 0.471766i | 0.971782 | + | 0.235883i | \(0.0757981\pi\) | ||||
−0.971782 | + | 0.235883i | \(0.924202\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 8.00000i | 0.348485i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.0000 | 0.826087 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9.21110 | −0.399728 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.57779i | − 0.0683419i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6.78890i | 0.292963i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −37.0278 | −1.59490 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 15.2111i | − 0.652771i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 37.2111i | − 1.59103i | −0.605933 | − | 0.795516i | \(-0.707200\pi\) | ||||
0.605933 | − | 0.795516i | \(-0.292800\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.21110 | −0.307762 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.60555 | 0.196203 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − 36.8444i | − 1.56678i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 24.4222i | 1.03480i | 0.855743 | + | 0.517401i | \(0.173100\pi\) | ||||
−0.855743 | + | 0.517401i | \(0.826900\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.84441 | 0.374079 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.21110 | −0.220013 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.6333i | 0.490285i | 0.969487 | + | 0.245143i | \(0.0788348\pi\) | ||||
−0.969487 | + | 0.245143i | \(0.921165\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.60555i | 0.193415i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 25.4500 | 1.06692 | 0.533459 | − | 0.845826i | \(-0.320892\pi\) | ||||
0.533459 | + | 0.845826i | \(0.320892\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −35.6333 | −1.49121 | −0.745604 | − | 0.666390i | \(-0.767839\pi\) | ||||
−0.745604 | + | 0.666390i | \(0.767839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 15.8167i | 0.660750i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 8.78890i | − 0.365887i | −0.983123 | − | 0.182943i | \(-0.941438\pi\) | ||||
0.983123 | − | 0.182943i | \(-0.0585625\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.60555 | 0.274517 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 14.7889 | 0.613547 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 16.4222i | − 0.677817i | −0.940819 | − | 0.338908i | \(-0.889942\pi\) | ||||
0.940819 | − | 0.338908i | \(-0.110058\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.00000 | 0.164817 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.0000 | −0.575883 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 32.4222i | 1.33142i | 0.746210 | + | 0.665710i | \(0.231871\pi\) | ||||
−0.746210 | + | 0.665710i | \(0.768129\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 2.78890i | − 0.114142i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 20.8444 | 0.851680 | 0.425840 | − | 0.904799i | \(-0.359979\pi\) | ||||
0.425840 | + | 0.904799i | \(0.359979\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.2111 | 0.783637 | 0.391819 | − | 0.920042i | \(-0.371846\pi\) | ||||
0.391819 | + | 0.920042i | \(0.371846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 4.00000i | − 0.162893i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 19.6333i | 0.796891i | 0.917192 | + | 0.398446i | \(0.130450\pi\) | ||||
−0.917192 | + | 0.398446i | \(0.869550\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −21.2111 | −0.859517 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −15.6333 | −0.632456 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 19.2111i | − 0.775929i | −0.921674 | − | 0.387965i | \(-0.873178\pi\) | ||||
0.921674 | − | 0.387965i | \(-0.126822\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000i | 1.36879i | 0.729112 | + | 0.684394i | \(0.239933\pi\) | ||||
−0.729112 | + | 0.684394i | \(0.760067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 47.6333 | 1.91454 | 0.957272 | − | 0.289189i | \(-0.0933855\pi\) | ||||
0.957272 | + | 0.289189i | \(0.0933855\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.00000 | 0.0802572 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.78890i | 0.111735i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.60555i | 0.104056i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21.2111 | −0.845742 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.8444 | −0.829803 | −0.414901 | − | 0.909866i | \(-0.636184\pi\) | ||||
−0.414901 | + | 0.909866i | \(0.636184\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 4.00000i | − 0.158986i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 37.0278i | − 1.46709i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.21110 | −0.206148 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −29.4500 | −1.16320 | −0.581602 | − | 0.813474i | \(-0.697574\pi\) | ||||
−0.581602 | + | 0.813474i | \(0.697574\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 12.6056i | − 0.497114i | −0.968617 | − | 0.248557i | \(-0.920044\pi\) | ||||
0.968617 | − | 0.248557i | \(-0.0799564\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 45.6333i | − 1.79403i | −0.442000 | − | 0.897015i | \(-0.645731\pi\) | ||||
0.442000 | − | 0.897015i | \(-0.354269\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.0000 | 0.942082 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.4222 | −0.722023 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 42.0000i | − 1.64359i | −0.569785 | − | 0.821794i | \(-0.692974\pi\) | ||||
0.569785 | − | 0.821794i | \(-0.307026\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.00000i | 0.234082i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −36.0000 | −1.40236 | −0.701180 | − | 0.712984i | \(-0.747343\pi\) | ||||
−0.701180 | + | 0.712984i | \(0.747343\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.7889 | −0.653012 | −0.326506 | − | 0.945195i | \(-0.605871\pi\) | ||||
−0.326506 | + | 0.945195i | \(0.605871\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 5.21110i | − 0.202382i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.21110i | 0.356655i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 18.4222 | 0.712244 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18.7889 | 0.725337 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 29.3944i | − 1.13307i | −0.824037 | − | 0.566536i | \(-0.808283\pi\) | ||||
0.824037 | − | 0.566536i | \(-0.191717\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 18.4222i | − 0.708023i | −0.935241 | − | 0.354011i | \(-0.884817\pi\) | ||||
0.935241 | − | 0.354011i | \(-0.115183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43.2666 | −1.66042 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.21110 | −0.0464096 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 48.0000i | 1.83667i | 0.395805 | + | 0.918334i | \(0.370466\pi\) | ||||
−0.395805 | + | 0.918334i | \(0.629534\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 11.2111i | − 0.427730i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.0555 | 1.14337 | 0.571683 | − | 0.820475i | \(-0.306291\pi\) | ||||
0.571683 | + | 0.820475i | \(0.306291\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 12.0000i | − 0.455842i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 1.21110i | − 0.0458738i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.4222 | 0.469851 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.6056i | 0.399996i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 33.2111i | 1.24903i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −17.6333 | −0.662233 | −0.331116 | − | 0.943590i | \(-0.607425\pi\) | ||||
−0.331116 | + | 0.943590i | \(0.607425\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 8.00000 | 0.300023 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.00000i | 0.299602i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 4.18335i | − 0.156230i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 34.2389 | 1.27689 | 0.638447 | − | 0.769666i | \(-0.279577\pi\) | ||||
0.638447 | + | 0.769666i | \(0.279577\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −48.0000 | −1.78761 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 10.0000i | − 0.371904i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 24.6056i | − 0.912569i | −0.889834 | − | 0.456285i | \(-0.849180\pi\) | ||||
0.889834 | − | 0.456285i | \(-0.150820\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.78890 | 0.251096 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 4.42221i | − 0.163338i | −0.996660 | − | 0.0816689i | \(-0.973975\pi\) | ||||
0.996660 | − | 0.0816689i | \(-0.0260250\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 10.4222i | 0.383907i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.57779 | −0.352325 | −0.176162 | − | 0.984361i | \(-0.556368\pi\) | ||||
−0.176162 | + | 0.984361i | \(0.556368\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.60555 | −0.0957173 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 20.0000i | 0.733729i | 0.930274 | + | 0.366864i | \(0.119569\pi\) | ||||
−0.930274 | + | 0.366864i | \(0.880431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.21110i | 0.117488i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 48.0000 | 1.75388 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.8444 | −0.614661 | −0.307331 | − | 0.951603i | \(-0.599436\pi\) | ||||
−0.307331 | + | 0.951603i | \(0.599436\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 27.8167i | − 1.01370i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.0555i | 1.31046i | 0.755429 | + | 0.655230i | \(0.227428\pi\) | ||||
−0.755429 | + | 0.655230i | \(0.772572\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5.21110 | −0.189151 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 14.7889i | − 0.535394i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.0000i | 0.866590i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.42221 | −0.303712 | −0.151856 | − | 0.988403i | \(-0.548525\pi\) | ||||
−0.151856 | + | 0.988403i | \(0.548525\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.2111 | −0.619843 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 43.2666i | − 1.55619i | −0.628145 | − | 0.778096i | \(-0.716186\pi\) | ||||
0.628145 | − | 0.778096i | \(-0.283814\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − 48.8444i | − 1.75228i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.605551 | −0.0216961 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 13.5778 | 0.485852 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 4.60555i | − 0.164589i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.6333i | 0.842436i | 0.906959 | + | 0.421218i | \(0.138397\pi\) | ||||
−0.906959 | + | 0.421218i | \(0.861603\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.21110 | −0.256722 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 60.8444 | 2.16338 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 18.7889i | 0.667213i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.78890i | 0.0987878i | 0.998779 | + | 0.0493939i | \(0.0157290\pi\) | ||||
−0.998779 | + | 0.0493939i | \(0.984271\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.605551 | −0.0213961 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 15.6333i | − 0.551687i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 24.6056i | 0.866156i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 19.5778 | 0.688319 | 0.344159 | − | 0.938911i | \(-0.388164\pi\) | ||||
0.344159 | + | 0.938911i | \(0.388164\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 16.8444 | 0.591487 | 0.295744 | − | 0.955267i | \(-0.404433\pi\) | ||||
0.295744 | + | 0.955267i | \(0.404433\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 31.6333i | − 1.10943i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 3.39445i | − 0.118757i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 12.0000 | 0.419314 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 28.7889 | 1.00474 | 0.502370 | − | 0.864653i | \(-0.332462\pi\) | ||||
0.502370 | + | 0.864653i | \(0.332462\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.1833i | 0.912694i | 0.889802 | + | 0.456347i | \(0.150842\pi\) | ||||
−0.889802 | + | 0.456347i | \(0.849158\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 15.6333i | 0.543623i | 0.962350 | + | 0.271812i | \(0.0876228\pi\) | ||||
−0.962350 | + | 0.271812i | \(0.912377\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.788897 | −0.0273995 | −0.0136998 | − | 0.999906i | \(-0.504361\pi\) | ||||
−0.0136998 | + | 0.999906i | \(0.504361\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000 | 0.0693792 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 28.4222i | − 0.984771i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 4.00000i | − 0.138260i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.6333 | 0.539722 | 0.269861 | − | 0.962899i | \(-0.413022\pi\) | ||||
0.269861 | + | 0.962899i | \(0.413022\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 32.2389i | − 1.11037i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 19.3944i | − 0.666401i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −11.3944 | −0.391056 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −21.2111 | −0.727107 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.6333i | 0.466796i | 0.972381 | + | 0.233398i | \(0.0749844\pi\) | ||||
−0.972381 | + | 0.233398i | \(0.925016\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 22.4222i | − 0.765928i | −0.923763 | − | 0.382964i | \(-0.874903\pi\) | ||||
0.923763 | − | 0.382964i | \(-0.125097\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.8444 | 1.66655 | 0.833275 | − | 0.552859i | \(-0.186463\pi\) | ||||
0.833275 | + | 0.552859i | \(0.186463\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.78890 | 0.0950454 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.4222i | 0.763261i | 0.924315 | + | 0.381630i | \(0.124637\pi\) | ||||
−0.924315 | + | 0.381630i | \(0.875363\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.0000i | 0.441503i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −20.8444 | −0.707098 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.4222 | −0.353143 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 9.39445i | − 0.317954i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 9.02776i | − 0.304846i | −0.988315 | − | 0.152423i | \(-0.951292\pi\) | ||||
0.988315 | − | 0.152423i | \(-0.0487076\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −23.6333 | −0.797132 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.7889 | 1.50898 | 0.754488 | − | 0.656314i | \(-0.227885\pi\) | ||||
0.754488 | + | 0.656314i | \(0.227885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 6.18335i | − 0.208086i | −0.994573 | − | 0.104043i | \(-0.966822\pi\) | ||||
0.994573 | − | 0.104043i | \(-0.0331780\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 36.8444i | 1.23711i | 0.785740 | + | 0.618557i | \(0.212282\pi\) | ||||
−0.785740 | + | 0.618557i | \(0.787718\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.0000 | 1.60987 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.60555 | 0.0872893 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.00000i | 0.200782i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − 5.21110i | − 0.173994i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 18.4222 | 0.614415 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15.6333i | 0.520244i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 42.0555i | − 1.39643i | −0.715888 | − | 0.698215i | \(-0.753978\pi\) | ||||
0.715888 | − | 0.698215i | \(-0.246022\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.21110 | −0.239177 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −18.4222 | −0.610355 | −0.305177 | − | 0.952296i | \(-0.598716\pi\) | ||||
−0.305177 | + | 0.952296i | \(0.598716\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 8.36669i | − 0.276897i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 104.111i | − 3.43805i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 16.0000 | 0.527791 | 0.263896 | − | 0.964551i | \(-0.414993\pi\) | ||||
0.263896 | + | 0.964551i | \(0.414993\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.6333 | −1.04235 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.5778i | 0.446919i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 10.4222i | − 0.342310i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.36669 | 0.0776487 | 0.0388243 | − | 0.999246i | \(-0.487639\pi\) | ||||
0.0388243 | + | 0.999246i | \(0.487639\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −14.2111 | −0.465750 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 9.39445i | 0.307560i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 4.78890i | − 0.156446i | −0.996936 | − | 0.0782232i | \(-0.975075\pi\) | ||||
0.996936 | − | 0.0782232i | \(-0.0249247\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 15.2111 | 0.496396 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 20.2389 | 0.659768 | 0.329884 | − | 0.944021i | \(-0.392990\pi\) | ||||
0.329884 | + | 0.944021i | \(0.392990\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 1.21110i | − 0.0394389i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 7.21110i | 0.234329i | 0.993113 | + | 0.117165i | \(0.0373805\pi\) | ||||
−0.993113 | + | 0.117165i | \(0.962619\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.6333 | 0.507479 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22.4222 | −0.727090 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.21110i | 0.298377i | 0.988809 | + | 0.149188i | \(0.0476661\pi\) | ||||
−0.988809 | + | 0.149188i | \(0.952334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 12.0000i | 0.387905i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −75.6333 | −2.44233 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.4222i | 0.335851i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 24.2389i | 0.779469i | 0.920927 | + | 0.389735i | \(0.127433\pi\) | ||||
−0.920927 | + | 0.389735i | \(0.872567\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.00000 | −0.0642493 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.0000 | −0.385098 | −0.192549 | − | 0.981287i | \(-0.561675\pi\) | ||||
−0.192549 | + | 0.981287i | \(0.561675\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.0000i | 0.769405i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 22.4222i | − 0.717350i | −0.933463 | − | 0.358675i | \(-0.883229\pi\) | ||||
0.933463 | − | 0.358675i | \(-0.116771\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.57779 | 0.0504265 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.21110 | 0.102523 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 5.21110i | − 0.166208i | −0.996541 | − | 0.0831042i | \(-0.973517\pi\) | ||||
0.996541 | − | 0.0831042i | \(-0.0264834\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 27.6333i | − 0.879578i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.78890 | 0.215874 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.5778 | 0.685441 | 0.342721 | − | 0.939437i | \(-0.388652\pi\) | ||||
0.342721 | + | 0.939437i | \(0.388652\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 8.00000i | − 0.253872i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 18.3667i | − 0.581679i | −0.956772 | − | 0.290839i | \(-0.906065\pi\) | ||||
0.956772 | − | 0.290839i | \(-0.0939346\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.6056 | 0.335545 |
(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 | 5700.2.f.n.3649.4 | 4 | ||
5.2 | odd | 4 | 5700.2.a.u.1.1 | 2 | |||
5.3 | odd | 4 | 1140.2.a.e.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 5700.2.f.n.3649.1 | 4 | ||
15.8 | even | 4 | 3420.2.a.i.1.2 | 2 | |||
20.3 | even | 4 | 4560.2.a.bl.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1140.2.a.e.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
3420.2.a.i.1.2 | 2 | 15.8 | even | 4 | |||
4560.2.a.bl.1.1 | 2 | 20.3 | even | 4 | |||
5700.2.a.u.1.1 | 2 | 5.2 | odd | 4 | |||
5700.2.f.n.3649.1 | 4 | 5.4 | even | 2 | inner | ||
5700.2.f.n.3649.4 | 4 | 1.1 | even | 1 | trivial |