Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3680,2,Mod(1841,3680)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3680, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3680.1841");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3680 = 2^{5} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3680.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: | \(29.3849479438\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1871773696.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 31x^{4} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 920) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1841.4 | ||
Root | \(0.921201 + 0.921201i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3680.1841 |
Dual form | 3680.2.f.b.1841.5 |
$q$-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 \(\left(\mathbb{Z}/3680\mathbb{Z}\right)^\times\).
\(n\) | \(737\) | \(1151\) | \(1381\) | \(3041\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | − 1.30278i | − 0.752158i | −0.926588 | − | 0.376079i | \(-0.877272\pi\) | ||||
0.926588 | − | 0.376079i | \(-0.122728\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.30278 | −0.870367 | −0.435184 | − | 0.900342i | \(-0.643317\pi\) | ||||
−0.435184 | + | 0.900342i | \(0.643317\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.30278 | 0.434259 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.97361i | 1.80111i | 0.434742 | + | 0.900555i | \(0.356839\pi\) | ||||
−0.434742 | + | 0.900555i | \(0.643161\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.87459i | 1.07462i | 0.843386 | + | 0.537308i | \(0.180559\pi\) | ||||
−0.843386 | + | 0.537308i | \(0.819441\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.30278 | 0.336375 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.53963 | −0.615950 | −0.307975 | − | 0.951394i | \(-0.599651\pi\) | ||||
−0.307975 | + | 0.951394i | \(0.599651\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.95384i | − 1.13649i | −0.822860 | − | 0.568245i | \(-0.807623\pi\) | ||||
0.822860 | − | 0.568245i | \(-0.192377\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.00000i | 0.654654i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 5.60555i | − 1.07879i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.222876i | 0.0413870i | 0.999786 | + | 0.0206935i | \(0.00658742\pi\) | ||||
−0.999786 | + | 0.0206935i | \(0.993413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.9934 | −1.97447 | −0.987234 | − | 0.159278i | \(-0.949083\pi\) | ||||
−0.987234 | + | 0.159278i | \(0.949083\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.78227 | 1.35472 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 2.30278i | − 0.389240i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.77712i | 0.949753i | 0.880052 | + | 0.474877i | \(0.157507\pi\) | ||||
−0.880052 | + | 0.474877i | \(0.842493\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.04772 | 0.808282 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.98758 | 1.09128 | 0.545638 | − | 0.838021i | \(-0.316287\pi\) | ||||
0.545638 | + | 0.838021i | \(0.316287\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.07925i | − 0.164585i | −0.996608 | − | 0.0822924i | \(-0.973776\pi\) | ||||
0.996608 | − | 0.0822924i | \(-0.0262241\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.30278i | 0.194206i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −13.0908 | −1.90949 | −0.954747 | − | 0.297419i | \(-0.903874\pi\) | ||||
−0.954747 | + | 0.297419i | \(0.903874\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.69722 | −0.242461 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.30856i | 0.463292i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 9.46193i | − 1.29970i | −0.760064 | − | 0.649848i | \(-0.774833\pi\) | ||||
0.760064 | − | 0.649848i | \(-0.225167\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.97361 | −0.805481 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −6.45374 | −0.854819 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.51323i | − 0.847951i | −0.905674 | − | 0.423975i | \(-0.860634\pi\) | ||||
0.905674 | − | 0.423975i | \(-0.139366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 4.98758i | − 0.638594i | −0.947655 | − | 0.319297i | \(-0.896553\pi\) | ||||
0.947655 | − | 0.319297i | \(-0.103447\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.00000 | −0.377964 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.87459 | −0.480583 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 6.51323i | − 0.795718i | −0.917447 | − | 0.397859i | \(-0.869753\pi\) | ||||
0.917447 | − | 0.397859i | \(-0.130247\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 1.30278i | − 0.156836i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53963 | 0.301398 | 0.150699 | − | 0.988580i | \(-0.451848\pi\) | ||||
0.150699 | + | 0.988580i | \(0.451848\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.52630 | 0.412722 | 0.206361 | − | 0.978476i | \(-0.433838\pi\) | ||||
0.206361 | + | 0.978476i | \(0.433838\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.30278i | 0.150432i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 13.7559i | − 1.56763i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.87973 | −0.211486 | −0.105743 | − | 0.994393i | \(-0.533722\pi\) | ||||
−0.105743 | + | 0.994393i | \(0.533722\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.39445 | −0.377161 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 15.3417i | − 1.68397i | −0.539504 | − | 0.841983i | \(-0.681388\pi\) | ||||
0.539504 | − | 0.841983i | \(-0.318612\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 2.53963i | − 0.275461i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.290357 | 0.0311296 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.80048 | −0.508849 | −0.254425 | − | 0.967093i | \(-0.581886\pi\) | ||||
−0.254425 | + | 0.967093i | \(0.581886\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 8.92230i | − 0.935311i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 14.3219i | 1.48511i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.95384 | 0.508253 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −2.22443 | −0.225857 | −0.112928 | − | 0.993603i | \(-0.536023\pi\) | ||||
−0.112928 | + | 0.993603i | \(0.536023\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.78227i | 0.782147i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 5.14362i | − 0.511809i | −0.966702 | − | 0.255905i | \(-0.917627\pi\) | ||||
0.966702 | − | 0.255905i | \(-0.0823733\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.90833 | 0.582165 | 0.291082 | − | 0.956698i | \(-0.405985\pi\) | ||||
0.291082 | + | 0.956698i | \(0.405985\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.00000 | −0.292770 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 7.81665i | − 0.755664i | −0.925874 | − | 0.377832i | \(-0.876670\pi\) | ||||
0.925874 | − | 0.377832i | \(-0.123330\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.78954i | 0.362972i | 0.983393 | + | 0.181486i | \(0.0580908\pi\) | ||||
−0.983393 | + | 0.181486i | \(0.941909\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.52630 | 0.714364 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −17.0660 | −1.60543 | −0.802717 | − | 0.596360i | \(-0.796613\pi\) | ||||
−0.802717 | + | 0.596360i | \(0.796613\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000i | 0.0932505i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.04772i | 0.466662i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.84819 | 0.536103 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −24.6840 | −2.24400 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 9.10325i | − 0.820813i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −18.5807 | −1.64877 | −0.824386 | − | 0.566028i | \(-0.808479\pi\) | ||||
−0.824386 | + | 0.566028i | \(0.808479\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.40603 | −0.123794 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.5925i | 1.18758i | 0.804620 | + | 0.593791i | \(0.202369\pi\) | ||||
−0.804620 | + | 0.593791i | \(0.797631\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 11.4076i | 0.989163i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 5.60555 | 0.482449 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.703013 | −0.0600625 | −0.0300312 | − | 0.999549i | \(-0.509561\pi\) | ||||
−0.0300312 | + | 0.999549i | \(0.509561\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.8944i | 1.51779i | 0.651216 | + | 0.758893i | \(0.274259\pi\) | ||||
−0.651216 | + | 0.758893i | \(0.725741\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 17.0544i | 1.43624i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −23.1453 | −1.93550 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.222876 | −0.0185088 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.21110i | 0.182369i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 2.10785i | − 0.172682i | −0.996266 | − | 0.0863410i | \(-0.972483\pi\) | ||||
0.996266 | − | 0.0863410i | \(-0.0275174\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.98667 | 0.243052 | 0.121526 | − | 0.992588i | \(-0.461221\pi\) | ||||
0.121526 | + | 0.992588i | \(0.461221\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.30856 | −0.267482 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 10.9934i | − 0.883009i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 19.0265i | − 1.51848i | −0.650812 | − | 0.759239i | \(-0.725572\pi\) | ||||
0.650812 | − | 0.759239i | \(-0.274428\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.3268 | −0.977577 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.30278 | −0.181484 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 16.0271i | 1.25534i | 0.778479 | + | 0.627670i | \(0.215991\pi\) | ||||
−0.778479 | + | 0.627670i | \(0.784009\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.78227i | 0.605849i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.89591 | 0.224092 | 0.112046 | − | 0.993703i | \(-0.464260\pi\) | ||||
0.112046 | + | 0.993703i | \(0.464260\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.01242 | −0.154801 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 6.45374i | − 0.493530i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 0.950254i | − 0.0722465i | −0.999347 | − | 0.0361233i | \(-0.988499\pi\) | ||||
0.999347 | − | 0.0361233i | \(-0.0115009\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.30278 | 0.174073 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −8.48528 | −0.637793 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 19.8167i | 1.48117i | 0.671965 | + | 0.740583i | \(0.265451\pi\) | ||||
−0.671965 | + | 0.740583i | \(0.734549\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.5139i | 1.15314i | 0.817049 | + | 0.576569i | \(0.195609\pi\) | ||||
−0.817049 | + | 0.576569i | \(0.804391\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −6.49770 | −0.480324 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −5.77712 | −0.424743 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 15.1707i | − 1.10939i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 12.9083i | 0.938943i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.09083 | −0.513075 | −0.256537 | − | 0.966534i | \(-0.582582\pi\) | ||||
−0.256537 | + | 0.966534i | \(0.582582\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.48528 | −0.322858 | −0.161429 | − | 0.986884i | \(-0.551610\pi\) | ||||
−0.161429 | + | 0.986884i | \(0.551610\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 5.04772i | 0.361474i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 13.1555i | − 0.937288i | −0.883387 | − | 0.468644i | \(-0.844743\pi\) | ||||
0.883387 | − | 0.468644i | \(-0.155257\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.8549 | 1.69103 | 0.845514 | − | 0.533953i | \(-0.179294\pi\) | ||||
0.845514 | + | 0.533953i | \(0.179294\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.48528 | −0.598506 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 0.513233i | − 0.0360219i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.98758i | 0.488034i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.30278 | 0.0905492 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 29.5923 | 2.04694 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2655i | 1.11976i | 0.828572 | + | 0.559882i | \(0.189154\pi\) | ||||
−0.828572 | + | 0.559882i | \(0.810846\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 3.30856i | − 0.226699i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.07925 | 0.0736046 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 25.3153 | 1.71851 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 4.59397i | − 0.310432i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 9.84001i | − 0.661910i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.33137 | −0.357015 | −0.178508 | − | 0.983939i | \(-0.557127\pi\) | ||||
−0.178508 | + | 0.983939i | \(0.557127\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −1.30278 | −0.0868517 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.01306i | 0.465473i | 0.972540 | + | 0.232737i | \(0.0747680\pi\) | ||||
−0.972540 | + | 0.232737i | \(0.925232\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 9.05259i | − 0.598212i | −0.954220 | − | 0.299106i | \(-0.903312\pi\) | ||||
0.954220 | − | 0.299106i | \(-0.0966885\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −17.9208 | −1.17910 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.6438 | −0.828322 | −0.414161 | − | 0.910204i | \(-0.635925\pi\) | ||||
−0.414161 | + | 0.910204i | \(0.635925\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 13.0908i | − 0.853952i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.44887i | 0.159071i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.158509 | 0.0102531 | 0.00512656 | − | 0.999987i | \(-0.498368\pi\) | ||||
0.00512656 | + | 0.999987i | \(0.498368\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −16.6438 | −1.07212 | −0.536060 | − | 0.844180i | \(-0.680088\pi\) | ||||
−0.536060 | + | 0.844180i | \(0.680088\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 12.3944i | − 0.795104i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1.69722i | − 0.108432i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 19.1941 | 1.22129 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −19.9867 | −1.26661 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.35987i | 0.401431i | 0.979650 | + | 0.200716i | \(0.0643267\pi\) | ||||
−0.979650 | + | 0.200716i | \(0.935673\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.97361i | 0.375557i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.30856 | −0.207190 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.24934 | −0.452202 | −0.226101 | − | 0.974104i | \(-0.572598\pi\) | ||||
−0.226101 | + | 0.974104i | \(0.572598\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 13.3034i | − 0.826634i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.290357i | 0.0179727i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −23.8263 | −1.46919 | −0.734596 | − | 0.678505i | \(-0.762628\pi\) | ||||
−0.734596 | + | 0.678505i | \(0.762628\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 9.46193 | 0.581242 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.25394i | 0.382735i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.32989i | 0.507882i | 0.967220 | + | 0.253941i | \(0.0817269\pi\) | ||||
−0.967220 | + | 0.253941i | \(0.918273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.9524 | 1.33351 | 0.666755 | − | 0.745277i | \(-0.267683\pi\) | ||||
0.666755 | + | 0.745277i | \(0.267683\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −11.6238 | −0.703502 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 5.97361i | − 0.360222i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 25.6964i | 1.54395i | 0.635655 | + | 0.771973i | \(0.280730\pi\) | ||||
−0.635655 | + | 0.771973i | \(0.719270\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −14.3219 | −0.857429 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −3.48988 | −0.208189 | −0.104094 | − | 0.994567i | \(-0.533194\pi\) | ||||
−0.104094 | + | 0.994567i | \(0.533194\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.4853i | 1.21772i | 0.793276 | + | 0.608862i | \(0.208374\pi\) | ||||
−0.793276 | + | 0.608862i | \(0.791626\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 6.45374i | − 0.382287i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.0908 | −0.949812 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.5503 | −0.620605 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.89794i | 0.169880i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 9.29184i | − 0.542835i | −0.962462 | − | 0.271418i | \(-0.912508\pi\) | ||||
0.962462 | − | 0.271418i | \(-0.0874925\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.51323 | 0.379215 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 33.4854 | 1.94302 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.87459i | 0.224073i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.48528i | 0.143249i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −6.70098 | −0.384961 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.98758 | 0.285588 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 33.9581i | − 1.93809i | −0.246877 | − | 0.969047i | \(-0.579404\pi\) | ||||
0.246877 | − | 0.969047i | \(-0.420596\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 7.69722i | − 0.437880i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 25.3696 | 1.43858 | 0.719289 | − | 0.694711i | \(-0.244468\pi\) | ||||
0.719289 | + | 0.694711i | \(0.244468\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −32.2427 | −1.82247 | −0.911233 | − | 0.411891i | \(-0.864868\pi\) | ||||
−0.911233 | + | 0.411891i | \(0.864868\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 3.00000i | − 0.169031i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 9.91100i | − 0.556657i | −0.960486 | − | 0.278329i | \(-0.910220\pi\) | ||||
0.960486 | − | 0.278329i | \(-0.0897804\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.33137 | −0.0745425 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.1833 | −0.568379 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.5809i | 0.700021i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 3.87459i | − 0.214923i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.93692 | 0.273013 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 30.1453 | 1.66196 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 27.0660i | − 1.48768i | −0.668357 | − | 0.743841i | \(-0.733002\pi\) | ||||
0.668357 | − | 0.743841i | \(-0.266998\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.52630i | 0.412439i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.51323 | 0.355856 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.292386 | −0.0159273 | −0.00796365 | − | 0.999968i | \(-0.502535\pi\) | ||||
−0.00796365 | + | 0.999968i | \(0.502535\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 22.2332i | 1.20754i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 65.6701i | − 3.55623i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0278 | 1.08140 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.30278 | 0.0701391 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 25.2500i | 1.35549i | 0.735297 | + | 0.677745i | \(0.237043\pi\) | ||||
−0.735297 | + | 0.677745i | \(0.762957\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 25.7639i | − 1.37911i | −0.724234 | − | 0.689554i | \(-0.757807\pi\) | ||||
0.724234 | − | 0.689554i | \(-0.242193\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 21.7192 | 1.15928 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 28.4720 | 1.51541 | 0.757706 | − | 0.652596i | \(-0.226320\pi\) | ||||
0.757706 | + | 0.652596i | \(0.226320\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.53963i | 0.134789i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 7.61888i | − 0.403234i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.5807 | −1.50843 | −0.754216 | − | 0.656626i | \(-0.771983\pi\) | ||||
−0.754216 | + | 0.656626i | \(0.771983\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.54054 | −0.291607 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.1577i | 1.68784i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.52630i | 0.184575i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.42221 | −0.126438 | −0.0632190 | − | 0.998000i | \(-0.520137\pi\) | ||||
−0.0632190 | + | 0.998000i | \(0.520137\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.10325 | 0.473896 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 21.7887i | 1.13121i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.3448i | 0.898078i | 0.893512 | + | 0.449039i | \(0.148234\pi\) | ||||
−0.893512 | + | 0.449039i | \(0.851766\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.30278 | −0.0672750 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −0.863552 | −0.0444752 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6845i | 0.600194i | 0.953909 | + | 0.300097i | \(0.0970191\pi\) | ||||
−0.953909 | + | 0.300097i | \(0.902981\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 24.2065i | 1.24014i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.0526 | −1.17793 | −0.588966 | − | 0.808158i | \(-0.700465\pi\) | ||||
−0.588966 | + | 0.808158i | \(0.700465\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 13.7559 | 0.701064 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 1.40603i | − 0.0714724i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.1972i | 0.669125i | 0.942374 | + | 0.334562i | \(0.108588\pi\) | ||||
−0.942374 | + | 0.334562i | \(0.891412\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.53963 | −0.128434 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 17.7080 | 0.893249 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 1.87973i | − 0.0945795i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0264i | 0.904719i | 0.891836 | + | 0.452359i | \(0.149418\pi\) | ||||
−0.891836 | + | 0.452359i | \(0.850582\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 14.8615 | 0.744007 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.5015 | −1.47323 | −0.736616 | − | 0.676311i | \(-0.763578\pi\) | ||||
−0.736616 | + | 0.676311i | \(0.763578\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 42.5948i | − 2.12180i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − 3.39445i | − 0.168672i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −34.5103 | −1.71061 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.25018 | 0.259605 | 0.129802 | − | 0.991540i | \(-0.458566\pi\) | ||||
0.129802 | + | 0.991540i | \(0.458566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.915869i | 0.0451765i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 14.9985i | 0.738029i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 15.3417 | 0.753092 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 23.3124 | 1.14161 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 0.923860i | − 0.0451335i | −0.999745 | − | 0.0225668i | \(-0.992816\pi\) | ||||
0.999745 | − | 0.0225668i | \(-0.00718383\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 27.2382i | − 1.32751i | −0.747950 | − | 0.663755i | \(-0.768962\pi\) | ||||
0.747950 | − | 0.663755i | \(-0.231038\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −17.0544 | −0.829214 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.53963 | 0.123190 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 11.4853i | 0.555812i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 30.1531i | 1.45580i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.7756 | 1.28974 | 0.644869 | − | 0.764293i | \(-0.276912\pi\) | ||||
0.644869 | + | 0.764293i | \(0.276912\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5.33340 | 0.256307 | 0.128153 | − | 0.991754i | \(-0.459095\pi\) | ||||
0.128153 | + | 0.991754i | \(0.459095\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.290357i | 0.0139216i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 4.95384i | − 0.236974i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −14.8233 | −0.707477 | −0.353738 | − | 0.935344i | \(-0.615090\pi\) | ||||
−0.353738 | + | 0.935344i | \(0.615090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2.21110 | −0.105291 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.09330i | 0.194479i | 0.995261 | + | 0.0972393i | \(0.0310012\pi\) | ||||
−0.995261 | + | 0.0972393i | \(0.968999\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 4.80048i | − 0.227564i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −2.74606 | −0.129884 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0622 | 0.758024 | 0.379012 | − | 0.925392i | \(-0.376264\pi\) | ||||
0.379012 | + | 0.925392i | \(0.376264\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.7411i | 1.96551i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 3.89096i | − 0.182813i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8.92230 | 0.418284 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −21.3830 | −1.00026 | −0.500128 | − | 0.865952i | \(-0.666714\pi\) | ||||
−0.500128 | + | 0.865952i | \(0.666714\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 14.2360i | 0.664480i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 12.9737i | − 0.604244i | −0.953269 | − | 0.302122i | \(-0.902305\pi\) | ||||
0.953269 | − | 0.302122i | \(-0.0976951\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.2361 | −0.801029 | −0.400514 | − | 0.916290i | \(-0.631169\pi\) | ||||
−0.400514 | + | 0.916290i | \(0.631169\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.3219 | −0.664162 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 13.3532i | − 0.617914i | −0.951076 | − | 0.308957i | \(-0.900020\pi\) | ||||
0.951076 | − | 0.308957i | \(-0.0999799\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.9985i | 0.692567i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −24.7872 | −1.14213 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.44704 | 0.296435 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.95384i | 0.227298i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 12.3268i | − 0.564404i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −30.0498 | −1.37301 | −0.686506 | − | 0.727125i | \(-0.740856\pi\) | ||||
−0.686506 | + | 0.727125i | \(0.740856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.3840 | −1.02062 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.00000i | 0.136505i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 2.22443i | − 0.101006i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.8843 | −0.855731 | −0.427865 | − | 0.903842i | \(-0.640734\pi\) | ||||
−0.427865 | + | 0.903842i | \(0.640734\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 20.8797 | 0.944214 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.4735i | 1.42038i | 0.704010 | + | 0.710190i | \(0.251391\pi\) | ||||
−0.704010 | + | 0.710190i | \(0.748609\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 0.566022i | − 0.0254923i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.78227 | −0.349787 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.84819 | −0.262327 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.0895i | 1.30223i | 0.758980 | + | 0.651113i | \(0.225698\pi\) | ||||
−0.758980 | + | 0.651113i | \(0.774302\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 3.77272i | − 0.168553i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.1033 | 1.20847 | 0.604237 | − | 0.796805i | \(-0.293478\pi\) | ||||
0.604237 | + | 0.796805i | \(0.293478\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.14362 | 0.228888 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2.62173i | 0.116435i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.9836i | 0.797110i | 0.917144 | + | 0.398555i | \(0.130488\pi\) | ||||
−0.917144 | + | 0.398555i | \(0.869512\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.12027 | −0.359220 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −27.7690 | −1.22603 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.90833i | 0.260352i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 78.1995i | − 3.43921i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.23797 | −0.0543408 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.5149 | 1.03020 | 0.515102 | − | 0.857129i | \(-0.327754\pi\) | ||||
0.515102 | + | 0.857129i | \(0.327754\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.3284i | 1.28244i | 0.767356 | + | 0.641221i | \(0.221572\pi\) | ||||
−0.767356 | + | 0.641221i | \(0.778428\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 3.00000i | − 0.130931i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 27.9191 | 1.21617 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 8.48528i | − 0.368230i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 27.0740i | 1.17270i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.81665 | 0.337943 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.8167 | 1.11407 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 10.1385i | − 0.436698i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 13.6072i | − 0.585018i | −0.956263 | − | 0.292509i | \(-0.905510\pi\) | ||||
0.956263 | − | 0.292509i | \(-0.0944902\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 20.2111 | 0.867341 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.78954 | −0.162326 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 7.45668i | − 0.318825i | −0.987212 | − | 0.159412i | \(-0.949040\pi\) | ||||
0.987212 | − | 0.159412i | \(-0.0509600\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 6.49770i | − 0.277315i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.10409 | 0.0470359 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.32860 | 0.184071 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.52630i | 0.319473i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 12.4294i | − 0.526650i | −0.964707 | − | 0.263325i | \(-0.915181\pi\) | ||||
0.964707 | − | 0.263325i | \(-0.0848191\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.18167 | 0.176866 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.7641 | −0.834439 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 14.6407i | 0.617031i | 0.951219 | + | 0.308515i | \(0.0998322\pi\) | ||||
−0.951219 | + | 0.308515i | \(0.900168\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 17.0660i | − 0.717972i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 7.81665 | 0.328269 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.0412 | −1.30131 | −0.650657 | − | 0.759372i | \(-0.725506\pi\) | ||||
−0.650657 | + | 0.759372i | \(0.725506\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 34.8186i | − 1.45711i | −0.684987 | − | 0.728555i | \(-0.740192\pi\) | ||||
0.684987 | − | 0.728555i | \(-0.259808\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9.23776i | 0.385913i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.2992 | 1.38626 | 0.693131 | − | 0.720812i | \(-0.256231\pi\) | ||||
0.693131 | + | 0.720812i | \(0.256231\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.84332i | 0.242840i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.3284i | 1.46567i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 56.5218 | 2.34090 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.04772 | −0.208697 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 20.1726i | − 0.832611i | −0.909225 | − | 0.416305i | \(-0.863325\pi\) | ||||
0.909225 | − | 0.416305i | \(-0.136675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 54.4594i | 2.24396i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −17.1386 | −0.704989 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.6217 | −0.723638 | −0.361819 | − | 0.932248i | \(-0.617844\pi\) | ||||
−0.361819 | + | 0.932248i | \(0.617844\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.84819i | 0.239752i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 31.0776i | − 1.27192i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 34.3048 | 1.40166 | 0.700828 | − | 0.713331i | \(-0.252814\pi\) | ||||
0.700828 | + | 0.713331i | \(0.252814\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.2601 | 1.76462 | 0.882308 | − | 0.470673i | \(-0.155989\pi\) | ||||
0.882308 | + | 0.470673i | \(0.155989\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 8.48528i | − 0.345547i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 24.6840i | − 1.00355i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.66863 | 0.351849 | 0.175924 | − | 0.984404i | \(-0.443709\pi\) | ||||
0.175924 | + | 0.984404i | \(0.443709\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.668628 | −0.0270942 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 50.7216i | − 2.05197i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 41.9091i | − 1.69269i | −0.532633 | − | 0.846347i | \(-0.678797\pi\) | ||||
0.532633 | − | 0.846347i | \(-0.321203\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.10325 | 0.367079 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.51757 | −0.0610949 | −0.0305475 | − | 0.999533i | \(-0.509725\pi\) | ||||
−0.0305475 | + | 0.999533i | \(0.509725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 6.83669i | 0.274790i | 0.990516 | + | 0.137395i | \(0.0438729\pi\) | ||||
−0.990516 | + | 0.137395i | \(0.956127\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 5.60555i | − 0.224943i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 11.0544 | 0.442886 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 38.5521i | − 1.53962i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 14.6717i | − 0.585001i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.39445 | −0.214750 | −0.107375 | − | 0.994219i | \(-0.534244\pi\) | ||||
−0.107375 | + | 0.994219i | \(0.534244\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 21.1903 | 0.842240 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 18.5807i | − 0.737353i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 6.57604i | − 0.260552i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.30856 | 0.130885 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.17009 | −0.243704 | −0.121852 | − | 0.992548i | \(-0.538883\pi\) | ||||
−0.121852 | + | 0.992548i | \(0.538883\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 49.5016i | − 1.95215i | −0.217428 | − | 0.976076i | \(-0.569767\pi\) | ||||
0.217428 | − | 0.976076i | \(-0.430233\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 1.40603i | − 0.0553622i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −37.0642 | −1.45714 | −0.728571 | − | 0.684970i | \(-0.759815\pi\) | ||||
−0.728571 | + | 0.684970i | \(0.759815\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 38.9075 | 1.52725 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 32.9801i | − 1.29259i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.1664i | 0.515242i | 0.966246 | + | 0.257621i | \(0.0829386\pi\) | ||||
−0.966246 | + | 0.257621i | \(0.917061\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.5925 | −0.531102 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 4.59397 | 0.179228 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 36.6833i | − 1.42898i | −0.699646 | − | 0.714490i | \(-0.746659\pi\) | ||||
0.699646 | − | 0.714490i | \(-0.253341\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 37.8495i | 1.47217i | 0.676887 | + | 0.736087i | \(0.263328\pi\) | ||||
−0.676887 | + | 0.736087i | \(0.736672\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −12.8193 | −0.497861 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −11.4076 | −0.442367 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.222876i | 0.00862979i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.94558i | 0.268532i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.7938 | 1.15018 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.6028 | 0.524348 | 0.262174 | − | 0.965021i | \(-0.415560\pi\) | ||||
0.262174 | + | 0.965021i | \(0.415560\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.60555i | 0.215758i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 43.5908i | − 1.67533i | −0.546184 | − | 0.837665i | \(-0.683920\pi\) | ||||
0.546184 | − | 0.837665i | \(-0.316080\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.12237 | 0.196579 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 9.13645 | 0.350109 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 7.35537i | 0.281445i | 0.990049 | + | 0.140723i | \(0.0449426\pi\) | ||||
−0.990049 | + | 0.140723i | \(0.955057\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 0.703013i | − 0.0268608i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.7935 | −0.449950 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 36.6611 | 1.39668 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 23.8974i | − 0.909100i | −0.890721 | − | 0.454550i | \(-0.849800\pi\) | ||||
0.890721 | − | 0.454550i | \(-0.150200\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 17.9208i | − 0.680756i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −17.8944 | −0.678774 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.7459 | −0.672172 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 16.4720i | 0.623029i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0151i | 1.58689i | 0.608642 | + | 0.793445i | \(0.291715\pi\) | ||||
−0.608642 | + | 0.793445i | \(0.708285\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.6190 | 1.07938 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.0544 | −0.642307 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 11.8446i | 0.445462i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 5.17533i | − 0.194364i | −0.995267 | − | 0.0971819i | \(-0.969017\pi\) | ||||
0.995267 | − | 0.0971819i | \(-0.0309828\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.44887 | −0.0918397 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.9934 | −0.411705 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 23.1453i | − 0.865583i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 0.206502i | − 0.00771196i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −4.95696 | −0.184863 | −0.0924316 | − | 0.995719i | \(-0.529464\pi\) | ||||
−0.0924316 | + | 0.995719i | \(0.529464\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.6056 | −0.506697 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 21.6831i | 0.806404i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 0.222876i | − 0.00827740i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.69445 | 0.285371 | 0.142686 | − | 0.989768i | \(-0.454426\pi\) | ||||
0.142686 | + | 0.989768i | \(0.454426\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −26.3305 | −0.975205 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.74090i | 0.101376i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.03641i | 0.222960i | 0.993767 | + | 0.111480i | \(0.0355591\pi\) | ||||
−0.993767 | + | 0.111480i | \(0.964441\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.21110 | −0.0815577 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 38.9075 | 1.43318 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 16.1629i | − 0.594562i | −0.954790 | − | 0.297281i | \(-0.903920\pi\) | ||||
0.954790 | − | 0.297281i | \(-0.0960799\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 25.0056i | − 0.918603i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0.486122 | 0.0178341 | 0.00891704 | − | 0.999960i | \(-0.497162\pi\) | ||||
0.00891704 | + | 0.999960i | \(0.497162\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.10785 | 0.0772257 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 19.9867i | − 0.731277i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.0000i | 0.657706i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.82254 | 0.0665053 | 0.0332527 | − | 0.999447i | \(-0.489413\pi\) | ||||
0.0332527 | + | 0.999447i | \(0.489413\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.28548 | 0.301940 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.98667i | 0.108696i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.8698i | 0.903908i | 0.892041 | + | 0.451954i | \(0.149273\pi\) | ||||
−0.892041 | + | 0.451954i | \(0.850727\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 7.78227 | 0.282478 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.4480 | 0.741240 | 0.370620 | − | 0.928785i | \(-0.379145\pi\) | ||||
0.370620 | + | 0.928785i | \(0.379145\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 8.72647i | − 0.315919i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 3.30856i | − 0.119621i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 25.2361 | 0.911222 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.2407 | −0.874141 | −0.437071 | − | 0.899427i | \(-0.643984\pi\) | ||||
−0.437071 | + | 0.899427i | \(0.643984\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.44427i | 0.340127i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.06619i | 0.218186i | 0.994032 | + | 0.109093i | \(0.0347946\pi\) | ||||
−0.994032 | + | 0.109093i | \(0.965205\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.9934 | 0.394894 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −17.3314 | −0.621760 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 34.6154i | − 1.24022i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.1707i | 0.542851i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.24934 | 0.0446478 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19.0265 | 0.679084 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.8446i | 0.422215i | 0.977463 | + | 0.211107i | \(0.0677069\pi\) | ||||
−0.977463 | + | 0.211107i | \(0.932293\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 31.0403i | 1.10506i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 39.2992 | 1.39732 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.3248 | 0.686244 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 12.3268i | − 0.437186i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 17.0016i | − 0.602229i | −0.953588 | − | 0.301114i | \(-0.902641\pi\) | ||||
0.953588 | − | 0.301114i | \(-0.0973586\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 33.2458 | 1.17615 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.25394 | −0.220972 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 21.0647i | 0.743357i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 2.30278i | − 0.0811622i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 10.8520 | 0.382008 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.4595 | −0.754474 | −0.377237 | − | 0.926117i | \(-0.623126\pi\) | ||||
−0.377237 | + | 0.926117i | \(0.623126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 38.2083i | − 1.34168i | −0.741604 | − | 0.670838i | \(-0.765935\pi\) | ||||
0.741604 | − | 0.670838i | \(-0.234065\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 28.5990i | − 1.00301i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.0271 | −0.561405 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.34646 | −0.187049 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − 11.6238i | − 0.406167i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 22.4235i | − 0.782585i | −0.920266 | − | 0.391293i | \(-0.872028\pi\) | ||||
0.920266 | − | 0.391293i | \(-0.127972\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 39.3199 | 1.37061 | 0.685303 | − | 0.728258i | \(-0.259670\pi\) | ||||
0.685303 | + | 0.728258i | \(0.259670\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.78227 | −0.270944 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 21.3564i | 0.742633i | 0.928506 | + | 0.371317i | \(0.121094\pi\) | ||||
−0.928506 | + | 0.371317i | \(0.878906\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.3930i | 0.847203i | 0.905849 | + | 0.423601i | \(0.139234\pi\) | ||||
−0.905849 | + | 0.423601i | \(0.860766\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 33.4766 | 1.16129 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.31032 | 0.149344 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.89591i | 0.100217i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 61.6239i | 2.13003i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −10.6669 | −0.368264 | −0.184132 | − | 0.982902i | \(-0.558947\pi\) | ||||
−0.184132 | + | 0.982902i | \(0.558947\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.9503 | 0.998287 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.54653i | 0.156591i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 2.01242i | − 0.0692293i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 56.8416 | 1.95310 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 26.6877 | 0.915920 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 5.77712i | 0.198037i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 7.33523i | − 0.251153i | −0.992084 | − | 0.125577i | \(-0.959922\pi\) | ||||
0.992084 | − | 0.125577i | \(-0.0400781\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.45374 | 0.220713 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −38.9075 | −1.32905 | −0.664527 | − | 0.747264i | \(-0.731367\pi\) | ||||
−0.664527 | + | 0.747264i | \(0.731367\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.4179i | 1.58376i | 0.610677 | + | 0.791880i | \(0.290897\pi\) | ||||
−0.610677 | + | 0.791880i | \(0.709103\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.9627i | 0.714408i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9.86647 | 0.335859 | 0.167929 | − | 0.985799i | \(-0.446292\pi\) | ||||
0.167929 | + | 0.985799i | \(0.446292\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.950254 | 0.0323096 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.7447i | 0.466793i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 11.2288i | − 0.380910i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.2361 | 0.855092 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.89794 | −0.0980803 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.30278i | 0.0778480i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.86918i | 0.130653i | 0.997864 | + | 0.0653264i | \(0.0208089\pi\) | ||||
−0.997864 | + | 0.0653264i | \(0.979191\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.1052 | −0.408298 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5.40603 | −0.182134 | −0.0910668 | − | 0.995845i | \(-0.529028\pi\) | ||||
−0.0910668 | + | 0.995845i | \(0.529028\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.3660i | 1.15651i | 0.815857 | + | 0.578254i | \(0.196266\pi\) | ||||
−0.815857 | + | 0.578254i | \(0.803734\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 8.48528i | − 0.285230i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.9867 | −0.805396 | −0.402698 | − | 0.915333i | \(-0.631928\pi\) | ||||
−0.402698 | + | 0.915333i | \(0.631928\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 42.7872 | 1.43504 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 20.2771i | − 0.679308i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 64.8499i | 2.17012i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −19.8167 | −0.662398 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.04772 | 0.168538 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 2.45016i | − 0.0817173i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24.0298i | 0.800548i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.23776 | 0.107746 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −15.5139 | −0.515699 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 7.11438i | − 0.236229i | −0.993000 | − | 0.118115i | \(-0.962315\pi\) | ||||
0.993000 | − | 0.118115i | \(-0.0376850\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 6.70098i | − 0.222258i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.8328 | 0.690223 | 0.345111 | − | 0.938562i | \(-0.387841\pi\) | ||||
0.345111 | + | 0.938562i | \(0.387841\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 91.6450 | 3.03301 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 6.49770i | − 0.214807i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 31.3004i | − 1.03363i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −47.0527 | −1.55213 | −0.776063 | − | 0.630655i | \(-0.782786\pi\) | ||||
−0.776063 | + | 0.630655i | \(0.782786\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −44.2398 | −1.45775 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9.84001i | 0.323888i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 5.77712i | − 0.189951i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 7.69722 | 0.252810 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −57.4924 | −1.88626 | −0.943132 | − | 0.332418i | \(-0.892136\pi\) | ||||
−0.943132 | + | 0.332418i | \(0.892136\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.40778i | 0.275554i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 33.0509i | − 1.08204i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 15.1707 | 0.496136 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −11.9713 | −0.391086 | −0.195543 | − | 0.980695i | \(-0.562647\pi\) | ||||
−0.195543 | + | 0.980695i | \(0.562647\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 42.0050i | 1.37078i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 3.22204i | − 0.105035i | −0.998620 | − | 0.0525177i | \(-0.983275\pi\) | ||||
0.998620 | − | 0.0525177i | \(-0.0167246\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.98758 | 0.227547 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −12.9083 | −0.419908 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.73527i | 0.218867i | 0.993994 | + | 0.109433i | \(0.0349036\pi\) | ||||
−0.993994 | + | 0.109433i | \(0.965096\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.6629i | 0.443518i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.9118 | −0.418694 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.1683 | −0.944855 | −0.472428 | − | 0.881370i | \(-0.656622\pi\) | ||||
−0.472428 | + | 0.881370i | \(0.656622\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 7.09083i | − 0.229454i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.73448i | 0.0560678i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.61888 | 0.0522764 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 89.8542 | 2.89852 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 10.1833i | − 0.328154i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 4.48528i | − 0.144386i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 48.0614 | 1.54555 | 0.772775 | − | 0.634680i | \(-0.218868\pi\) | ||||
0.772775 | + | 0.634680i | \(0.218868\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 16.3901 | 0.526526 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 10.9254i | 0.350613i | 0.984514 | + | 0.175307i | \(0.0560917\pi\) | ||||
−0.984514 | + | 0.175307i | \(0.943908\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 41.2068i | − 1.32103i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −5.04772 | −0.161656 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.7394 | 1.11141 | 0.555706 | − | 0.831379i | \(-0.312448\pi\) | ||||
0.555706 | + | 0.831379i | \(0.312448\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 28.6761i | − 0.916494i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 4.93692i | 0.157624i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −12.0419 | −0.384076 | −0.192038 | − | 0.981388i | \(-0.561510\pi\) | ||||
−0.192038 | + | 0.981388i | \(0.561510\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.1555 | 0.419168 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 39.2725i | − 1.25006i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 1.07925i | − 0.0343183i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −52.9868 | −1.68318 | −0.841591 | − | 0.540116i | \(-0.818380\pi\) | ||||
−0.841591 | + | 0.540116i | \(0.818380\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −35.2609 | −1.11897 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 23.8549i | 0.756251i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.5382i | 0.713792i | 0.934144 | + | 0.356896i | \(0.116165\pi\) | ||||
−0.934144 | + | 0.356896i | \(0.883835\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 32.3840 | 1.02458 |
(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 | 3680.2.f.b.1841.4 | 8 | ||
4.3 | odd | 2 | 920.2.f.b.461.3 | ✓ | 8 | ||
8.3 | odd | 2 | 920.2.f.b.461.6 | yes | 8 | ||
8.5 | even | 2 | inner | 3680.2.f.b.1841.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.f.b.461.3 | ✓ | 8 | 4.3 | odd | 2 | ||
920.2.f.b.461.6 | yes | 8 | 8.3 | odd | 2 | ||
3680.2.f.b.1841.4 | 8 | 1.1 | even | 1 | trivial | ||
3680.2.f.b.1841.5 | 8 | 8.5 | even | 2 | inner |