Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(257,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.257");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 99x^{4} + 170x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 257.4 | ||
Root | \(2.98985i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.257 |
Dual form | 384.3.e.d.257.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.246559 | + | 2.98985i | 0.0821862 | + | 0.996617i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 6.63641i | − | 1.32728i | −0.748051 | − | 0.663641i | \(-0.769010\pi\) | ||
0.748051 | − | 0.663641i | \(-0.230990\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.578158 | 0.0825940 | 0.0412970 | − | 0.999147i | \(-0.486851\pi\) | ||||
0.0412970 | + | 0.999147i | \(0.486851\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.87842 | + | 1.47435i | −0.986491 | + | 0.163816i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.68786i | 0.789806i | 0.918723 | + | 0.394903i | \(0.129222\pi\) | ||||
−0.918723 | + | 0.394903i | \(0.870778\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 17.9269 | 1.37899 | 0.689497 | − | 0.724289i | \(-0.257832\pi\) | ||||
0.689497 | + | 0.724289i | \(0.257832\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 19.8419 | − | 1.63626i | 1.32279 | − | 0.109084i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 19.0110i | − | 1.11829i | −0.829068 | − | 0.559147i | \(-0.811129\pi\) | ||
0.829068 | − | 0.559147i | \(-0.188871\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 32.1769 | 1.69352 | 0.846760 | − | 0.531976i | \(-0.178550\pi\) | ||||
0.846760 | + | 0.531976i | \(0.178550\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.142550 | + | 1.72861i | 0.00678808 | + | 0.0823146i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 20.4836i | − | 0.890592i | −0.895383 | − | 0.445296i | \(-0.853098\pi\) | ||
0.895383 | − | 0.445296i | \(-0.146902\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −19.0419 | −0.761677 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −6.59713 | − | 26.1816i | −0.244338 | − | 0.969690i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.0310i | 0.759690i | 0.925050 | + | 0.379845i | \(0.124023\pi\) | ||||
−0.925050 | + | 0.379845i | \(0.875977\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 26.2344 | 0.846270 | 0.423135 | − | 0.906067i | \(-0.360930\pi\) | ||||
0.423135 | + | 0.906067i | \(0.360930\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −25.9754 | + | 2.14207i | −0.787134 | + | 0.0649111i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 3.83689i | − | 0.109625i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 53.3855 | 1.44285 | 0.721426 | − | 0.692492i | \(-0.243487\pi\) | ||||
0.721426 | + | 0.692492i | \(0.243487\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.42003 | + | 53.5988i | 0.113334 | + | 1.37433i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 35.6935i | 0.870574i | 0.900292 | + | 0.435287i | \(0.143353\pi\) | ||||
−0.900292 | + | 0.435287i | \(0.856647\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 50.4895 | 1.17417 | 0.587087 | − | 0.809524i | \(-0.300275\pi\) | ||||
0.587087 | + | 0.809524i | \(0.300275\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 9.78437 | + | 58.9208i | 0.217430 | + | 1.30935i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 30.6265i | 0.651628i | 0.945434 | + | 0.325814i | \(0.105638\pi\) | ||||
−0.945434 | + | 0.325814i | \(0.894362\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.6657 | −0.993178 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 56.8401 | − | 4.68732i | 1.11451 | − | 0.0919083i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 88.8962i | − | 1.67729i | −0.544681 | − | 0.838644i | \(-0.683349\pi\) | ||
0.544681 | − | 0.838644i | \(-0.316651\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 57.6562 | 1.04829 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 7.93348 | + | 96.2040i | 0.139184 | + | 1.68779i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 63.1939i | 1.07108i | 0.844509 | + | 0.535542i | \(0.179893\pi\) | ||||
−0.844509 | + | 0.535542i | \(0.820107\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −33.5317 | −0.549700 | −0.274850 | − | 0.961487i | \(-0.588628\pi\) | ||||
−0.274850 | + | 0.961487i | \(0.588628\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.13313 | + | 0.852405i | −0.0814782 | + | 0.0135302i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 118.970i | − | 1.83031i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −108.562 | −1.62032 | −0.810162 | − | 0.586206i | \(-0.800621\pi\) | ||||
−0.810162 | + | 0.586206i | \(0.800621\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 61.2430 | − | 5.05041i | 0.887579 | − | 0.0731944i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 59.3600i | − | 0.836056i | −0.908434 | − | 0.418028i | \(-0.862721\pi\) | ||
0.908434 | − | 0.418028i | \(-0.137279\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −5.60477 | −0.0767777 | −0.0383889 | − | 0.999263i | \(-0.512223\pi\) | ||||
−0.0383889 | + | 0.999263i | \(0.512223\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.69495 | − | 56.9325i | −0.0625994 | − | 0.759101i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.02296i | 0.0652332i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −78.9955 | −0.999943 | −0.499971 | − | 0.866042i | \(-0.666656\pi\) | ||||
−0.499971 | + | 0.866042i | \(0.666656\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 76.6526 | − | 26.1797i | 0.946328 | − | 0.323207i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 48.5283i | 0.584679i | 0.956315 | + | 0.292339i | \(0.0944337\pi\) | ||||
−0.956315 | + | 0.292339i | \(0.905566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −126.165 | −1.48429 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −65.8694 | + | 5.43193i | −0.757120 | + | 0.0624360i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 58.7109i | − | 0.659672i | −0.944038 | − | 0.329836i | \(-0.893006\pi\) | ||
0.944038 | − | 0.329836i | \(-0.106994\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3646 | 0.113897 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.46831 | + | 78.4369i | 0.0695517 | + | 0.843407i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 213.539i | − | 2.24778i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 93.3544 | 0.962416 | 0.481208 | − | 0.876606i | \(-0.340198\pi\) | ||||
0.481208 | + | 0.876606i | \(0.340198\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12.8089 | − | 77.1345i | −0.129383 | − | 0.779136i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 114.161i | − | 1.13031i | −0.824985 | − | 0.565155i | \(-0.808816\pi\) | ||
0.824985 | − | 0.565155i | \(-0.191184\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 70.0355 | 0.679956 | 0.339978 | − | 0.940433i | \(-0.389580\pi\) | ||||
0.339978 | + | 0.940433i | \(0.389580\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 11.4717 | − | 0.946018i | 0.109255 | − | 0.00900970i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 50.9072i | 0.475769i | 0.971293 | + | 0.237884i | \(0.0764539\pi\) | ||||
−0.971293 | + | 0.237884i | \(0.923546\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.2178 | 0.121264 | 0.0606320 | − | 0.998160i | \(-0.480688\pi\) | ||||
0.0606320 | + | 0.998160i | \(0.480688\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 13.1627 | + | 159.615i | 0.118582 | + | 1.43797i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 62.9470i | − | 0.557053i | −0.960429 | − | 0.278527i | \(-0.910154\pi\) | ||
0.960429 | − | 0.278527i | \(-0.0898460\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −135.938 | −1.18207 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −159.163 | + | 26.4305i | −1.36036 | + | 0.225902i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 10.9914i | − | 0.0923644i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 45.5210 | 0.376207 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −106.718 | + | 8.80054i | −0.867629 | + | 0.0715491i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 39.5402i | − | 0.316321i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −236.659 | −1.86345 | −0.931727 | − | 0.363160i | \(-0.881698\pi\) | ||||
−0.931727 | + | 0.363160i | \(0.881698\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.4486 | + | 150.956i | 0.0965009 | + | 1.17020i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 121.212i | 0.925279i | 0.886546 | + | 0.462640i | \(0.153098\pi\) | ||||
−0.886546 | + | 0.462640i | \(0.846902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.6033 | 0.139875 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −173.752 | + | 43.7812i | −1.28705 | + | 0.324305i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 136.677i | 0.997645i | 0.866704 | + | 0.498822i | \(0.166234\pi\) | ||||
−0.866704 | + | 0.498822i | \(0.833766\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −29.5616 | −0.212673 | −0.106337 | − | 0.994330i | \(-0.533912\pi\) | ||||
−0.106337 | + | 0.994330i | \(0.533912\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −91.5687 | + | 7.55123i | −0.649424 | + | 0.0535548i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 155.747i | 1.08914i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 146.207 | 1.00832 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.9990 | − | 145.503i | −0.0816255 | − | 0.989818i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 17.5092i | − | 0.117511i | −0.998272 | − | 0.0587556i | \(-0.981287\pi\) | ||
0.998272 | − | 0.0587556i | \(-0.0187133\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −119.607 | −0.792099 | −0.396050 | − | 0.918229i | \(-0.629619\pi\) | ||||
−0.396050 | + | 0.918229i | \(0.629619\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 28.0288 | + | 168.788i | 0.183195 | + | 1.10319i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 174.102i | − | 1.12324i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −189.488 | −1.20693 | −0.603466 | − | 0.797388i | \(-0.706214\pi\) | ||||
−0.603466 | + | 0.797388i | \(0.706214\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 265.786 | − | 21.9181i | 1.67161 | − | 0.137850i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.8428i | − | 0.0735576i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 104.654 | 0.642051 | 0.321026 | − | 0.947071i | \(-0.395972\pi\) | ||||
0.321026 | + | 0.947071i | \(0.395972\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 14.2156 | + | 172.384i | 0.0861553 | + | 1.04475i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 142.664i | 0.854278i | 0.904186 | + | 0.427139i | \(0.140478\pi\) | ||||
−0.904186 | + | 0.427139i | \(0.859522\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 152.374 | 0.901623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −285.680 | + | 47.4399i | −1.67064 | + | 0.277426i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 11.6594i | − | 0.0673952i | −0.999432 | − | 0.0336976i | \(-0.989272\pi\) | ||
0.999432 | − | 0.0336976i | \(-0.0107283\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.0092 | −0.0629100 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −188.940 | + | 15.5810i | −1.06746 | + | 0.0880283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 40.3979i | 0.225687i | 0.993613 | + | 0.112843i | \(0.0359958\pi\) | ||||
−0.993613 | + | 0.112843i | \(0.964004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 121.175 | 0.669472 | 0.334736 | − | 0.942312i | \(-0.391353\pi\) | ||||
0.334736 | + | 0.942312i | \(0.391353\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.26752 | − | 100.255i | −0.0451777 | − | 0.547840i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 354.288i | − | 1.91507i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 165.165 | 0.883235 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −3.81418 | − | 15.1371i | −0.0201808 | − | 0.0800906i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 337.287i | − | 1.76590i | −0.469465 | − | 0.882951i | \(-0.655553\pi\) | ||
0.469465 | − | 0.882951i | \(-0.344447\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −227.937 | −1.18102 | −0.590511 | − | 0.807029i | \(-0.701074\pi\) | ||||
−0.590511 | + | 0.807029i | \(0.701074\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 355.704 | − | 29.3332i | 1.82412 | − | 0.150426i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 172.276i | 0.874495i | 0.899341 | + | 0.437248i | \(0.144047\pi\) | ||||
−0.899341 | + | 0.437248i | \(0.855953\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.598837 | 0.00300923 | 0.00150461 | − | 0.999999i | \(-0.499521\pi\) | ||||
0.00150461 | + | 0.999999i | \(0.499521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −26.7668 | − | 324.583i | −0.133168 | − | 1.61484i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 12.7374i | 0.0627458i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 236.877 | 1.15550 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 30.2000 | + | 181.862i | 0.145894 | + | 0.878561i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 279.548i | 1.33755i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −243.040 | −1.15185 | −0.575923 | − | 0.817504i | \(-0.695357\pi\) | ||||
−0.575923 | + | 0.817504i | \(0.695357\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 177.478 | − | 14.6357i | 0.833228 | − | 0.0687123i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 335.069i | − | 1.55846i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.1676 | 0.0698968 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.38190 | − | 16.7574i | −0.00631007 | − | 0.0765180i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 340.809i | − | 1.54212i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 191.174 | 0.857284 | 0.428642 | − | 0.903474i | \(-0.358992\pi\) | ||||
0.428642 | + | 0.903474i | \(0.358992\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 169.062 | − | 28.0744i | 0.751388 | − | 0.124775i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 8.76834i | 0.0386271i | 0.999813 | + | 0.0193135i | \(0.00614807\pi\) | ||||
−0.999813 | + | 0.0193135i | \(0.993852\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −131.740 | −0.575283 | −0.287641 | − | 0.957738i | \(-0.592871\pi\) | ||||
−0.287641 | + | 0.957738i | \(0.592871\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.0179 | + | 1.23845i | −0.0650125 | + | 0.00536127i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 96.0149i | − | 0.412081i | −0.978543 | − | 0.206040i | \(-0.933942\pi\) | ||
0.978543 | − | 0.206040i | \(-0.0660579\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 203.250 | 0.864894 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −19.4770 | − | 236.185i | −0.0821815 | − | 0.996560i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 317.978i | 1.33045i | 0.746643 | + | 0.665225i | \(0.231664\pi\) | ||||
−0.746643 | + | 0.665225i | \(0.768336\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −114.189 | −0.473812 | −0.236906 | − | 0.971533i | \(-0.576133\pi\) | ||||
−0.236906 | + | 0.971533i | \(0.576133\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 97.1728 | + | 222.725i | 0.399888 | + | 0.916564i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 322.966i | 1.31823i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 576.832 | 2.33535 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −145.093 | + | 11.9651i | −0.582701 | + | 0.0480525i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 376.853i | 1.50140i | 0.660641 | + | 0.750702i | \(0.270285\pi\) | ||||
−0.660641 | + | 0.750702i | \(0.729715\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 177.959 | 0.703395 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −31.1070 | − | 377.214i | −0.121988 | − | 1.47927i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 152.041i | 0.591599i | 0.955250 | + | 0.295800i | \(0.0955861\pi\) | ||||
−0.955250 | + | 0.295800i | \(0.904414\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 30.8653 | 0.119171 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −32.4813 | − | 195.600i | −0.124450 | − | 0.749427i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 495.013i | 1.88218i | 0.338158 | + | 0.941089i | \(0.390196\pi\) | ||||
−0.338158 | + | 0.941089i | \(0.609804\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −589.952 | −2.22623 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 175.537 | − | 14.4757i | 0.657441 | − | 0.0542160i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 173.556i | − | 0.645190i | −0.946537 | − | 0.322595i | \(-0.895445\pi\) | ||
0.946537 | − | 0.322595i | \(-0.104555\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −125.415 | −0.462784 | −0.231392 | − | 0.972861i | \(-0.574328\pi\) | ||||
−0.231392 | + | 0.972861i | \(0.574328\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.55548 | + | 30.9886i | 0.00936072 | + | 0.113511i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 165.434i | − | 0.601577i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 226.300 | 0.816967 | 0.408483 | − | 0.912766i | \(-0.366058\pi\) | ||||
0.408483 | + | 0.912766i | \(0.366058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −232.920 | + | 38.6786i | −0.834838 | + | 0.138633i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 13.8834i | − | 0.0494073i | −0.999695 | − | 0.0247036i | \(-0.992136\pi\) | ||
0.999695 | − | 0.0247036i | \(-0.00786421\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 306.461 | 1.08290 | 0.541450 | − | 0.840733i | \(-0.317875\pi\) | ||||
0.541450 | + | 0.840733i | \(0.317875\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 638.449 | − | 52.6498i | 2.24017 | − | 0.184736i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.6365i | 0.0719042i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −72.4183 | −0.250582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.0173 | + | 279.116i | 0.0790973 | + | 0.959160i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 121.869i | 0.415935i | 0.978136 | + | 0.207968i | \(0.0666848\pi\) | ||||
−0.978136 | + | 0.207968i | \(0.933315\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 419.381 | 1.42163 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 227.462 | − | 57.3149i | 0.765867 | − | 0.192980i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 367.208i | − | 1.22812i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.1909 | 0.0969797 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 341.325 | − | 28.1474i | 1.12649 | − | 0.0928959i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 222.530i | 0.729607i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −19.0431 | −0.0620298 | −0.0310149 | − | 0.999519i | \(-0.509874\pi\) | ||||
−0.0310149 | + | 0.999519i | \(0.509874\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 17.2678 | + | 209.396i | 0.0558830 | + | 0.677656i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 223.159i | − | 0.717552i | −0.933424 | − | 0.358776i | \(-0.883194\pi\) | ||
0.933424 | − | 0.358776i | \(-0.116806\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −194.708 | −0.622070 | −0.311035 | − | 0.950399i | \(-0.600676\pi\) | ||||
−0.311035 | + | 0.950399i | \(0.600676\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.65691 | + | 34.0655i | 0.0179584 | + | 0.108145i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 532.192i | 1.67884i | 0.543483 | + | 0.839420i | \(0.317105\pi\) | ||||
−0.543483 | + | 0.839420i | \(0.682895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −191.402 | −0.600007 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −152.205 | + | 12.5516i | −0.474159 | + | 0.0391016i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 611.715i | − | 1.89385i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −341.363 | −1.05035 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.25896 | + | 39.5192i | 0.00996623 | + | 0.120854i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.7070i | 0.0538206i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 91.7273 | 0.277122 | 0.138561 | − | 0.990354i | \(-0.455752\pi\) | ||||
0.138561 | + | 0.990354i | \(0.455752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −473.979 | + | 78.7088i | −1.42336 | + | 0.236363i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 720.460i | 2.15063i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 82.1658 | 0.243815 | 0.121908 | − | 0.992541i | \(-0.461099\pi\) | ||||
0.121908 | + | 0.992541i | \(0.461099\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 188.202 | − | 15.5201i | 0.555169 | − | 0.0457821i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 227.921i | 0.668389i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −56.4662 | −0.164625 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −33.5166 | − | 406.433i | −0.0971496 | − | 1.17807i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 323.122i | − | 0.931189i | −0.884998 | − | 0.465594i | \(-0.845841\pi\) | ||
0.884998 | − | 0.465594i | \(-0.154159\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −255.324 | −0.731586 | −0.365793 | − | 0.930696i | \(-0.619202\pi\) | ||||
−0.365793 | + | 0.930696i | \(0.619202\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −118.266 | − | 469.356i | −0.336941 | − | 1.33720i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 344.332i | 0.975444i | 0.872999 | + | 0.487722i | \(0.162172\pi\) | ||||
−0.872999 | + | 0.487722i | \(0.837828\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −393.937 | −1.10968 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 32.8625 | − | 2.71001i | 0.0920519 | − | 0.00759107i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 119.962i | − | 0.334157i | −0.985944 | − | 0.167079i | \(-0.946567\pi\) | ||
0.985944 | − | 0.167079i | \(-0.0534334\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 674.351 | 1.86801 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 11.2236 | + | 136.101i | 0.0309190 | + | 0.374934i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.1956i | 0.101906i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −398.726 | −1.08645 | −0.543223 | − | 0.839589i | \(-0.682796\pi\) | ||||
−0.543223 | + | 0.839589i | \(0.682796\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −52.6246 | − | 316.902i | −0.142614 | − | 0.858813i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 51.3960i | − | 0.138534i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 606.592 | 1.62625 | 0.813126 | − | 0.582088i | \(-0.197764\pi\) | ||||
0.813126 | + | 0.582088i | \(0.197764\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 118.219 | − | 9.74896i | 0.315251 | − | 0.0259972i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 394.948i | 1.04761i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −266.492 | −0.703146 | −0.351573 | − | 0.936161i | \(-0.614353\pi\) | ||||
−0.351573 | + | 0.936161i | \(0.614353\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −58.3502 | − | 707.574i | −0.153150 | − | 1.85715i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 406.790i | − | 1.06212i | −0.847336 | − | 0.531058i | \(-0.821795\pi\) | ||
0.847336 | − | 0.531058i | \(-0.178205\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 33.3344 | 0.0865828 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −448.267 | + | 74.4390i | −1.15831 | + | 0.192349i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 217.748i | 0.559763i | 0.960035 | + | 0.279881i | \(0.0902951\pi\) | ||||
−0.960035 | + | 0.279881i | \(0.909705\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −389.414 | −0.995944 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −362.405 | + | 29.8858i | −0.922149 | + | 0.0760452i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 524.246i | 1.32721i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 53.9651 | 0.135932 | 0.0679661 | − | 0.997688i | \(-0.478349\pi\) | ||||
0.0679661 | + | 0.997688i | \(0.478349\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.58680 | + | 55.6211i | 0.0114958 | + | 0.139401i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 294.291i | − | 0.733893i | −0.930242 | − | 0.366946i | \(-0.880403\pi\) | ||
0.930242 | − | 0.366946i | \(-0.119597\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 470.302 | 1.16700 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −173.739 | − | 508.698i | −0.428986 | − | 1.25604i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 463.806i | 1.13957i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 569.204 | 1.39170 | 0.695849 | − | 0.718188i | \(-0.255028\pi\) | ||||
0.695849 | + | 0.718188i | \(0.255028\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −408.645 | + | 33.6990i | −0.994270 | + | 0.0819926i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.5361i | 0.0884651i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 322.054 | 0.776034 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.28866 | − | 88.3847i | −0.0174788 | − | 0.211954i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 590.728i | 1.40985i | 0.709281 | + | 0.704926i | \(0.249020\pi\) | ||||
−0.709281 | + | 0.704926i | \(0.750980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −475.989 | −1.13061 | −0.565307 | − | 0.824880i | \(-0.691242\pi\) | ||||
−0.565307 | + | 0.824880i | \(0.691242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −45.1541 | − | 271.915i | −0.106747 | − | 0.642825i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 362.006i | 0.851780i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.3866 | −0.0454019 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −465.659 | + | 38.4007i | −1.08545 | + | 0.0895120i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 341.539i | 0.792435i | 0.918157 | + | 0.396217i | \(0.129677\pi\) | ||||
−0.918157 | + | 0.396217i | \(0.870323\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −88.2258 | −0.203755 | −0.101877 | − | 0.994797i | \(-0.532485\pi\) | ||||
−0.101877 | + | 0.994797i | \(0.532485\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 36.0485 | + | 437.136i | 0.0828702 | + | 1.00491i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 659.099i | − | 1.50824i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −735.647 | −1.67573 | −0.837867 | − | 0.545875i | \(-0.816197\pi\) | ||||
−0.837867 | + | 0.545875i | \(0.816197\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 432.075 | − | 71.7502i | 0.979761 | − | 0.162699i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 333.798i | − | 0.753494i | −0.926316 | − | 0.376747i | \(-0.877043\pi\) | ||
0.926316 | − | 0.376747i | \(-0.122957\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −389.629 | −0.875571 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 52.3498 | − | 4.31703i | 0.117114 | − | 0.00965779i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 396.485i | − | 0.883039i | −0.897252 | − | 0.441520i | \(-0.854440\pi\) | ||
0.897252 | − | 0.441520i | \(-0.145560\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −310.100 | −0.687584 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −29.4901 | − | 357.607i | −0.0650996 | − | 0.789419i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 68.7836i | − | 0.151173i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 34.5362 | 0.0755715 | 0.0377857 | − | 0.999286i | \(-0.487970\pi\) | ||||
0.0377857 | + | 0.999286i | \(0.487970\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −497.739 | + | 125.418i | −1.08440 | + | 0.273242i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 324.050i | 0.702929i | 0.936201 | + | 0.351464i | \(0.114316\pi\) | ||||
−0.936201 | + | 0.351464i | \(0.885684\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.33727 | 0.0136874 | 0.00684371 | − | 0.999977i | \(-0.497822\pi\) | ||||
0.00684371 | + | 0.999977i | \(0.497822\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 520.539 | − | 42.9264i | 1.11944 | − | 0.0923147i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 450.706i | − | 0.965109i | −0.875866 | − | 0.482554i | \(-0.839709\pi\) | ||
0.875866 | − | 0.482554i | \(-0.160291\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −62.7658 | −0.133829 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −46.7200 | − | 566.542i | −0.0991932 | − | 1.20285i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 438.646i | 0.927370i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −612.710 | −1.28992 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 131.064 | + | 789.258i | 0.274767 | + | 1.65463i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 259.094i | − | 0.540906i | −0.962733 | − | 0.270453i | \(-0.912827\pi\) | ||
0.962733 | − | 0.270453i | \(-0.0871735\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 957.038 | 1.98968 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 35.4081 | − | 2.91993i | 0.0733087 | − | 0.00604541i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 619.538i | − | 1.27740i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −628.526 | −1.29061 | −0.645304 | − | 0.763926i | \(-0.723269\pi\) | ||||
−0.645304 | + | 0.763926i | \(0.723269\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.8034 | + | 312.901i | 0.0527677 | + | 0.639879i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 352.334i | − | 0.717585i | −0.933417 | − | 0.358792i | \(-0.883189\pi\) | ||
0.933417 | − | 0.358792i | \(-0.116811\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 418.831 | 0.849557 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −511.896 | + | 85.0052i | −1.03413 | + | 0.171728i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 34.3195i | − | 0.0690532i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 240.576 | 0.482116 | 0.241058 | − | 0.970511i | \(-0.422506\pi\) | ||||
0.241058 | + | 0.970511i | \(0.422506\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −426.545 | + | 35.1751i | −0.851388 | + | 0.0702098i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.1648i | 0.0261725i | 0.999914 | + | 0.0130862i | \(0.00416560\pi\) | ||||
−0.999914 | + | 0.0130862i | \(0.995834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −757.621 | −1.50024 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 37.5692 | + | 455.577i | 0.0741010 | + | 0.898573i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 468.752i | 0.920927i | 0.887679 | + | 0.460464i | \(0.152317\pi\) | ||||
−0.887679 | + | 0.460464i | \(0.847683\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.24044 | −0.00634138 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −212.275 | − | 842.443i | −0.413791 | − | 1.64219i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 464.784i | − | 0.902494i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −266.079 | −0.514660 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 34.8598 | − | 2.87472i | 0.0671672 | − | 0.00553895i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 456.517i | − | 0.876232i | −0.898918 | − | 0.438116i | \(-0.855646\pi\) | ||
0.898918 | − | 0.438116i | \(-0.144354\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −287.095 | −0.548939 | −0.274469 | − | 0.961596i | \(-0.588502\pi\) | ||||
−0.274469 | + | 0.961596i | \(0.588502\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −2.71442 | − | 32.9160i | −0.00517033 | − | 0.0626971i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 498.742i | − | 0.946379i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 109.421 | 0.206845 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −93.1698 | − | 561.062i | −0.175461 | − | 1.05661i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 639.875i | 1.20052i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 337.841 | 0.631479 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −120.784 | + | 9.96046i | −0.224923 | + | 0.0185483i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 422.801i | − | 0.784418i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −804.779 | −1.48758 | −0.743788 | − | 0.668416i | \(-0.766973\pi\) | ||||
−0.743788 | + | 0.668416i | \(0.766973\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.8766 | + | 362.294i | 0.0550214 | + | 0.667208i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 87.7186i | − | 0.160952i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −76.3034 | −0.139494 | −0.0697471 | − | 0.997565i | \(-0.522219\pi\) | ||||
−0.0697471 | + | 0.997565i | \(0.522219\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 297.708 | − | 49.4373i | 0.542274 | − | 0.0900498i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 708.889i | 1.28655i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −45.6718 | −0.0825892 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1059.27 | − | 87.3528i | 1.90859 | − | 0.157392i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 540.544i | 0.970455i | 0.874388 | + | 0.485228i | \(0.161263\pi\) | ||||
−0.874388 | + | 0.485228i | \(0.838737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 905.121 | 1.61918 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.7228 | + | 493.819i | 0.0725897 | + | 0.880247i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1047.65i | 1.86084i | 0.366491 | + | 0.930422i | \(0.380559\pi\) | ||||
−0.366491 | + | 0.930422i | \(0.619441\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −417.742 | −0.739366 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 44.3173 | − | 15.1360i | 0.0781610 | − | 0.0266949i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 958.593i | 1.68470i | 0.538933 | + | 0.842348i | \(0.318827\pi\) | ||||
−0.538933 | + | 0.842348i | \(0.681173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 118.951 | 0.208321 | 0.104161 | − | 0.994560i | \(-0.466784\pi\) | ||||
0.104161 | + | 0.994560i | \(0.466784\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1008.44 | − | 83.1611i | 1.75993 | − | 0.145133i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 390.048i | 0.678344i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −355.825 | −0.616681 | −0.308340 | − | 0.951276i | \(-0.599774\pi\) | ||||
−0.308340 | + | 0.951276i | \(0.599774\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −56.1999 | − | 681.499i | −0.0970637 | − | 1.17703i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 28.0570i | 0.0482910i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 772.318 | 1.32473 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 175.404 | + | 1056.27i | 0.299835 | + | 1.80559i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 571.017i | − | 0.972771i | −0.873744 | − | 0.486386i | \(-0.838315\pi\) | ||
0.873744 | − | 0.486386i | \(-0.161685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 844.140 | 1.43318 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −515.078 | + | 42.4760i | −0.871537 | + | 0.0718714i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 370.411i | − | 0.624640i | −0.949977 | − | 0.312320i | \(-0.898894\pi\) | ||
0.949977 | − | 0.312320i | \(-0.101106\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −72.9432 | −0.122594 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.147648 | + | 1.79043i | 0.000247317 | + | 0.00299905i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 68.6579i | − | 0.114621i | −0.998356 | − | 0.0573104i | \(-0.981748\pi\) | ||
0.998356 | − | 0.0573104i | \(-0.0182525\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.39898 | 0.0156389 | 0.00781945 | − | 0.999969i | \(-0.497511\pi\) | ||||
0.00781945 | + | 0.999969i | \(0.497511\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 963.857 | − | 160.058i | 1.59844 | − | 0.265436i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 302.096i | − | 0.499333i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1064.78 | −1.75417 | −0.877085 | − | 0.480336i | \(-0.840515\pi\) | ||||
−0.877085 | + | 0.480336i | \(0.840515\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −38.0829 | + | 3.14051i | −0.0625335 | + | 0.00515684i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 549.039i | 0.898591i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 651.884 | 1.06343 | 0.531716 | − | 0.846922i | \(-0.321547\pi\) | ||||
0.531716 | + | 0.846922i | \(0.321547\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 58.4040 | + | 708.227i | 0.0949659 | + | 1.15159i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 146.821i | − | 0.237959i | −0.992897 | − | 0.118980i | \(-0.962038\pi\) | ||
0.992897 | − | 0.118980i | \(-0.0379623\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −596.307 | −0.963340 | −0.481670 | − | 0.876353i | \(-0.659970\pi\) | ||||
−0.481670 | + | 0.876353i | \(0.659970\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −536.295 | + | 135.133i | −0.863598 | + | 0.217606i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 33.9441i | − | 0.0544850i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −738.453 | −1.18152 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −835.808 | + | 68.9250i | −1.33303 | + | 0.109928i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 1014.91i | − | 1.61353i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −77.6556 | −0.123067 | −0.0615337 | − | 0.998105i | \(-0.519599\pi\) | ||||
−0.0615337 | + | 0.998105i | \(0.519599\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −59.9235 | − | 726.652i | −0.0946658 | − | 1.14795i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1570.56i | 2.47333i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −872.427 | −1.36959 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 87.5172 | + | 527.023i | 0.136960 | + | 0.824762i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 574.386i | 0.896078i | 0.894014 | + | 0.448039i | \(0.147877\pi\) | ||||
−0.894014 | + | 0.448039i | \(0.852123\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1217.20 | 1.89299 | 0.946497 | − | 0.322712i | \(-0.104594\pi\) | ||||
0.946497 | + | 0.322712i | \(0.104594\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1001.81 | − | 82.6141i | 1.55319 | − | 0.128084i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 802.675i | − | 1.24061i | −0.784360 | − | 0.620305i | \(-0.787009\pi\) | ||
0.784360 | − | 0.620305i | \(-0.212991\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −549.020 | −0.845948 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.73970 | + | 45.3489i | 0.00574455 | + | 0.0696604i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 216.282i | − | 0.331212i | −0.986192 | − | 0.165606i | \(-0.947042\pi\) | ||
0.986192 | − | 0.165606i | \(-0.0529581\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 804.410 | 1.22811 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 49.7615 | − | 8.26338i | 0.0757405 | − | 0.0125774i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 611.696i | − | 0.928218i | −0.885778 | − | 0.464109i | \(-0.846375\pi\) | ||
0.885778 | − | 0.464109i | \(-0.153625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 214.961 | 0.325206 | 0.162603 | − | 0.986692i | \(-0.448011\pi\) | ||||
0.162603 | + | 0.986692i | \(0.448011\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1018.97 | − | 84.0293i | 1.53690 | − | 0.126741i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 123.459i | − | 0.185653i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 451.275 | 0.676574 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 47.1357 | + | 571.583i | 0.0704569 | + | 0.854384i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 291.319i | − | 0.434156i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −900.809 | −1.33850 | −0.669249 | − | 0.743038i | \(-0.733384\pi\) | ||||
−0.669249 | + | 0.743038i | \(0.733384\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 125.622 | + | 498.549i | 0.186107 | + | 0.738591i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 322.312i | − | 0.476088i | −0.971254 | − | 0.238044i | \(-0.923494\pi\) | ||
0.971254 | − | 0.238044i | \(-0.0765063\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 53.9736 | 0.0794898 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.2160 | + | 2.16191i | −0.0384964 | + | 0.00317461i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 451.564i | 0.661148i | 0.943780 | + | 0.330574i | \(0.107242\pi\) | ||||
−0.943780 | + | 0.330574i | \(0.892758\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 907.047 | 1.32416 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.4816 | − | 393.882i | −0.0472803 | − | 0.573337i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1593.64i | − | 2.31297i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −259.954 | −0.376199 | −0.188100 | − | 0.982150i | \(-0.560233\pi\) | ||||
−0.188100 | + | 0.982150i | \(0.560233\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.40558 | − | 44.5959i | −0.0106863 | − | 0.0643520i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 196.183i | 0.282277i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 678.570 | 0.973558 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 287.070 | − | 23.6733i | 0.410687 | − | 0.0338674i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 434.792i | − | 0.620246i | −0.950696 | − | 0.310123i | \(-0.899630\pi\) | ||
0.950696 | − | 0.310123i | \(-0.100370\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1717.78 | 2.44350 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 50.1131 | + | 607.688i | 0.0710823 | + | 0.861968i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 66.0033i | − | 0.0933568i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1136.05 | 1.60232 | 0.801162 | − | 0.598448i | \(-0.204216\pi\) | ||||
0.801162 | + | 0.598448i | \(0.204216\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 701.355 | − | 116.467i | 0.986434 | − | 0.163807i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 537.375i | − | 0.753682i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1033.60 | 1.44559 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −950.705 | + | 78.4001i | −1.32595 | + | 0.109345i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1284.33i | − | 1.78627i | −0.449792 | − | 0.893133i | \(-0.648502\pi\) | ||
0.449792 | − | 0.893133i | \(-0.351498\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 40.4916 | 0.0561603 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −28.1542 | − | 341.407i | −0.0389408 | − | 0.472209i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 419.513i | − | 0.578638i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 31.6562 | 0.0435437 | 0.0217718 | − | 0.999763i | \(-0.493069\pi\) | ||||
0.0217718 | + | 0.999763i | \(0.493069\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −641.956 | + | 345.447i | −0.880598 | + | 0.473864i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 959.856i | − | 1.31307i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 596.421 | 0.813671 | 0.406836 | − | 0.913501i | \(-0.366632\pi\) | ||||
0.406836 | + | 0.913501i | \(0.366632\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −965.619 | + | 79.6300i | −1.31377 | + | 0.108340i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 943.170i | − | 1.27974i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1146.14 | 1.55093 | 0.775464 | − | 0.631391i | \(-0.217516\pi\) | ||||
0.775464 | + | 0.631391i | \(0.217516\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 142.223 | + | 1724.64i | 0.191934 | + | 2.32745i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 842.850i | − | 1.13439i | −0.823584 | − | 0.567194i | \(-0.808029\pi\) | ||
0.823584 | − | 0.567194i | \(-0.191971\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −116.198 | −0.155970 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −71.5476 | − | 430.855i | −0.0957799 | − | 0.576780i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.4324i | 0.0392956i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −797.793 | −1.06231 | −0.531154 | − | 0.847275i | \(-0.678241\pi\) | ||||
−0.531154 | + | 0.847275i | \(0.678241\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1126.73 | + | 92.9162i | −1.49633 | + | 0.123395i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 793.761i | 1.05134i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −278.402 | −0.367770 | −0.183885 | − | 0.982948i | \(-0.558867\pi\) | ||||
−0.183885 | + | 0.982948i | \(0.558867\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 43.8773 | + | 532.071i | 0.0578093 | + | 0.701015i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 986.126i | − | 1.29583i | −0.761713 | − | 0.647914i | \(-0.775641\pi\) | ||
0.761713 | − | 0.647914i | \(-0.224359\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.64197 | 0.0100157 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1120.14 | − | 186.011i | 1.46424 | − | 0.243151i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1132.87i | 1.47702i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 242.053 | 0.314764 | 0.157382 | − | 0.987538i | \(-0.449695\pi\) | ||||
0.157382 | + | 0.987538i | \(0.449695\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −454.580 | + | 37.4870i | −0.589598 | + | 0.0486213i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 590.233i | 0.763561i | 0.924253 | + | 0.381780i | \(0.124689\pi\) | ||||
−0.924253 | + | 0.381780i | \(0.875311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −499.553 | −0.644585 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.61009 | + | 92.2825i | 0.00979420 | + | 0.118768i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1148.51i | 1.47433i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 515.712 | 0.660322 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 576.808 | − | 145.341i | 0.736664 | − | 0.185621i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1257.52i | 1.60194i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −565.777 | −0.718903 | −0.359451 | − | 0.933164i | \(-0.617036\pi\) | ||||
−0.359451 | + | 0.933164i | \(0.617036\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1480.02 | + | 122.050i | −1.87581 | + | 0.154689i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 36.3933i | − | 0.0460092i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −601.120 | −0.758033 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −145.458 | − | 1763.87i | −0.182966 | − | 2.21870i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1128.02i | − | 1.41533i | −0.706549 | − | 0.707664i | \(-0.749749\pi\) | ||
0.706549 | − | 0.707664i | \(-0.250251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 582.241 | 0.728712 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 86.5601 | + | 521.259i | 0.108065 | + | 0.650761i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 48.6935i | − | 0.0606395i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −78.5934 | −0.0976316 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 518.907 | − | 42.7917i | 0.643007 | − | 0.0530257i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 794.472i | − | 0.982042i | −0.871148 | − | 0.491021i | \(-0.836624\pi\) | ||
0.871148 | − | 0.491021i | \(-0.163376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1430.50 | −1.76387 | −0.881937 | − | 0.471367i | \(-0.843761\pi\) | ||||
−0.881937 | + | 0.471367i | \(0.843761\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.9220 | − | 374.971i | −0.0380345 | − | 0.461219i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 694.529i | − | 0.852183i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1624.59 | 1.98849 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −92.0211 | + | 15.2810i | −0.112358 | + | 0.0186581i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1289.62i | 1.57079i | 0.618992 | + | 0.785397i | \(0.287541\pi\) | ||||
−0.618992 | + | 0.785397i | \(0.712459\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1064.14 | −1.29300 | −0.646502 | − | 0.762913i | \(-0.723769\pi\) | ||||
−0.646502 | + | 0.762913i | \(0.723769\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 494.622 | − | 40.7891i | 0.599542 | − | 0.0494413i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1258.48i | 1.52174i | 0.648907 | + | 0.760868i | \(0.275227\pi\) | ||||
−0.648907 | + | 0.760868i | \(0.724773\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1197.65 | −1.44469 | −0.722347 | − | 0.691531i | \(-0.756936\pi\) | ||||
−0.722347 | + | 0.691531i | \(0.756936\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 55.7961 | + | 676.603i | 0.0671434 | + | 0.814203i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 925.184i | 1.11067i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 946.779 | 1.13387 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −173.071 | − | 686.859i | −0.206776 | − | 0.820620i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 423.903i | − | 0.505248i | −0.967565 | − | 0.252624i | \(-0.918706\pi\) | ||
0.967565 | − | 0.252624i | \(-0.0812936\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 355.635 | 0.422872 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 41.5094 | − | 3.42308i | 0.0492401 | − | 0.00406059i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1011.22i | − | 1.19671i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.3183 | 0.0310724 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 75.5605 | + | 916.272i | 0.0889995 | + | 1.07924i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1093.53i | − | 1.28499i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.0080 | 0.0386964 | 0.0193482 | − | 0.999813i | \(-0.493841\pi\) | ||||
0.0193482 | + | 0.999813i | \(0.493841\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 314.830 | + | 1895.89i | 0.368223 | + | 2.21741i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 315.995i | 0.368722i | 0.982859 | + | 0.184361i | \(0.0590215\pi\) | ||||
−0.982859 | + | 0.184361i | \(0.940978\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −41.3157 | −0.0480975 | −0.0240487 | − | 0.999711i | \(-0.507656\pi\) | ||||
−0.0240487 | + | 0.999711i | \(0.507656\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −61.7000 | + | 5.08810i | −0.0716609 | + | 0.00590953i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1173.36i | 1.35963i | 0.733382 | + | 0.679817i | \(0.237941\pi\) | ||||
−0.733382 | + | 0.679817i | \(0.762059\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −77.3763 | −0.0894524 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.8553 | − | 216.520i | −0.0205944 | − | 0.249735i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 686.302i | − | 0.789760i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1946.18 | −2.23442 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −828.839 | + | 137.637i | −0.949415 | + | 0.157659i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 22.8605i | − | 0.0261262i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 917.504 | 1.04618 | 0.523092 | − | 0.852276i | \(-0.324778\pi\) | ||||
0.523092 | + | 0.852276i | \(0.324778\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −364.370 | + | 30.0478i | −0.414528 | + | 0.0341841i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1662.48i | 1.88704i | 0.331322 | + | 0.943518i | \(0.392505\pi\) | ||||
−0.331322 | + | 0.943518i | \(0.607495\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1258.25 | 1.42497 | 0.712486 | − | 0.701686i | \(-0.247569\pi\) | ||||
0.712486 | + | 0.701686i | \(0.247569\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 103.402 | + | 1253.89i | 0.116838 | + | 1.41682i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 237.781i | − | 0.268073i | −0.990976 | − | 0.134037i | \(-0.957206\pi\) | ||
0.990976 | − | 0.134037i | \(-0.0427940\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −136.826 | −0.153910 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 227.446 | + | 665.947i | 0.255270 | + | 0.747416i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 985.466i | 1.10354i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 268.097 | 0.299550 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1097.90 | − | 90.5383i | 1.22397 | − | 0.100935i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 577.970i | 0.642903i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1690.01 | −1.87570 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 7.19727 | + | 87.2764i | 0.00797039 | + | 0.0966517i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 804.164i | − | 0.888579i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1118.51 | −1.23320 | −0.616599 | − | 0.787277i | \(-0.711490\pi\) | ||||
−0.616599 | + | 0.787277i | \(0.711490\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 168.313 | + | 1013.57i | 0.185163 | + | 1.11504i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 307.830i | 0.337903i | 0.985624 | + | 0.168952i | \(0.0540382\pi\) | ||||
−0.985624 | + | 0.168952i | \(0.945962\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −421.608 | −0.461783 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −665.332 | + | 54.8667i | −0.727138 | + | 0.0599636i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 70.0794i | 0.0764225i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −195.828 | −0.213088 | −0.106544 | − | 0.994308i | \(-0.533978\pi\) | ||||
−0.106544 | + | 0.994308i | \(0.533978\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.69525 | − | 56.9362i | −0.00509799 | − | 0.0618199i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 1064.14i | − | 1.15292i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1016.56 | −1.09899 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −621.804 | + | 103.257i | −0.670771 | + | 0.111388i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 80.3569i | − | 0.0864982i | −0.999064 | − | 0.0432491i | \(-0.986229\pi\) | ||
0.999064 | − | 0.0432491i | \(-0.0137709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1565.91 | −1.68197 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 667.211 | − | 55.0217i | 0.715124 | − | 0.0589728i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1096.10i | − | 1.17230i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 502.272 | 0.536043 | 0.268021 | − | 0.963413i | \(-0.413630\pi\) | ||||
0.268021 | + | 0.963413i | \(0.413630\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −48.0069 | − | 582.147i | −0.0511255 | − | 0.619965i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 1752.05i | − | 1.86190i | −0.365144 | − | 0.930951i | \(-0.618980\pi\) | ||
0.365144 | − | 0.930951i | \(-0.381020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 731.133 | 0.775326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −100.456 | + | 25.3125i | −0.106303 | + | 0.0267857i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 634.493i | 0.670003i | 0.942218 | + | 0.335001i | \(0.108737\pi\) | ||||
−0.942218 | + | 0.335001i | \(0.891263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −100.476 | −0.105876 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1591.18 | + | 131.217i | −1.67316 | + | 0.137977i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 590.937i | − | 0.620081i | −0.950723 | − | 0.310040i | \(-0.899657\pi\) | ||
0.950723 | − | 0.310040i | \(-0.100343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2238.38 | −2.34385 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −47.1919 | − | 572.264i | −0.0493123 | − | 0.597977i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 79.0211i | 0.0823994i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −272.757 | −0.283827 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −75.0549 | − | 451.976i | −0.0779386 | − | 0.469341i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1512.69i | 1.56755i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1194.01 | 1.23476 | 0.617381 | − | 0.786665i | \(-0.288194\pi\) | ||||
0.617381 | + | 0.786665i | \(0.288194\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1828.94 | − | 150.823i | 1.88745 | − | 0.155649i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 827.456i | − | 0.852169i | −0.904683 | − | 0.426084i | \(-0.859893\pi\) | ||
0.904683 | − | 0.426084i | \(-0.140107\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −17.0913 | −0.0175655 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −84.1660 | − | 1020.63i | −0.0863241 | − | 1.04679i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1770.96i | − | 1.81266i | −0.422576 | − | 0.906328i | \(-0.638874\pi\) | ||
0.422576 | − | 0.906328i | \(-0.361126\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 510.072 | 0.521013 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −117.353 | + | 19.4876i | −0.119626 | + | 0.0198650i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 406.666i | 0.413699i | 0.978373 | + | 0.206850i | \(0.0663211\pi\) | ||||
−0.978373 | + | 0.206850i | \(0.933679\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1143.29 | 1.16070 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −52.9412 | + | 4.36580i | −0.0536385 | + | 0.00442331i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 1034.21i | − | 1.04571i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1364.81 | −1.37720 | −0.688602 | − | 0.725140i | \(-0.741775\pi\) | ||||
−0.688602 | + | 0.725140i | \(0.741775\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 22.6161 | + | 274.251i | 0.0227756 | + | 0.276184i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 3.97413i | − | 0.00399410i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1201.02 | −1.20463 | −0.602317 | − | 0.798257i | \(-0.705756\pi\) | ||||
−0.602317 | + | 0.798257i | \(0.705756\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −352.191 | − | 1397.72i | −0.352544 | − | 1.39912i |
(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 | 384.3.e.d.257.4 | yes | 8 | |
3.2 | odd | 2 | inner | 384.3.e.d.257.3 | yes | 8 | |
4.3 | odd | 2 | 384.3.e.a.257.5 | ✓ | 8 | ||
8.3 | odd | 2 | 384.3.e.c.257.4 | yes | 8 | ||
8.5 | even | 2 | 384.3.e.b.257.5 | yes | 8 | ||
12.11 | even | 2 | 384.3.e.a.257.6 | yes | 8 | ||
16.3 | odd | 4 | 768.3.h.h.641.15 | 16 | |||
16.5 | even | 4 | 768.3.h.g.641.15 | 16 | |||
16.11 | odd | 4 | 768.3.h.h.641.2 | 16 | |||
16.13 | even | 4 | 768.3.h.g.641.2 | 16 | |||
24.5 | odd | 2 | 384.3.e.b.257.6 | yes | 8 | ||
24.11 | even | 2 | 384.3.e.c.257.3 | yes | 8 | ||
48.5 | odd | 4 | 768.3.h.g.641.1 | 16 | |||
48.11 | even | 4 | 768.3.h.h.641.16 | 16 | |||
48.29 | odd | 4 | 768.3.h.g.641.16 | 16 | |||
48.35 | even | 4 | 768.3.h.h.641.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.e.a.257.5 | ✓ | 8 | 4.3 | odd | 2 | ||
384.3.e.a.257.6 | yes | 8 | 12.11 | even | 2 | ||
384.3.e.b.257.5 | yes | 8 | 8.5 | even | 2 | ||
384.3.e.b.257.6 | yes | 8 | 24.5 | odd | 2 | ||
384.3.e.c.257.3 | yes | 8 | 24.11 | even | 2 | ||
384.3.e.c.257.4 | yes | 8 | 8.3 | odd | 2 | ||
384.3.e.d.257.3 | yes | 8 | 3.2 | odd | 2 | inner | |
384.3.e.d.257.4 | yes | 8 | 1.1 | even | 1 | trivial | |
768.3.h.g.641.1 | 16 | 48.5 | odd | 4 | |||
768.3.h.g.641.2 | 16 | 16.13 | even | 4 | |||
768.3.h.g.641.15 | 16 | 16.5 | even | 4 | |||
768.3.h.g.641.16 | 16 | 48.29 | odd | 4 | |||
768.3.h.h.641.1 | 16 | 48.35 | even | 4 | |||
768.3.h.h.641.2 | 16 | 16.11 | odd | 4 | |||
768.3.h.h.641.15 | 16 | 16.3 | odd | 4 | |||
768.3.h.h.641.16 | 16 | 48.11 | even | 4 |