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 | 257.6 | ||
Root | \(-2.98985i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.257 |
Dual form | 384.3.e.a.257.5 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | \(0.230990\pi\) | ||||
−0.748051 | + | 0.663641i | \(0.769010\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.578158 | −0.0825940 | −0.0412970 | − | 0.999147i | \(-0.513149\pi\) | ||||
−0.0412970 | + | 0.999147i | \(0.513149\pi\) | |||||||
\(8\) | 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 | \(0.188871\pi\) | ||||
−0.829068 | + | 0.559147i | \(0.811129\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −32.1769 | −1.69352 | −0.846760 | − | 0.531976i | \(-0.821450\pi\) | ||||
−0.846760 | + | 0.531976i | \(0.821450\pi\) | |||||||
\(20\) | 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 | \(-0.875977\pi\) | ||
0.925050 | − | 0.379845i | \(-0.124023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −26.2344 | −0.846270 | −0.423135 | − | 0.906067i | \(-0.639070\pi\) | ||||
−0.423135 | + | 0.906067i | \(0.639070\pi\) | |||||||
\(32\) | 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 | \(-0.856647\pi\) | ||
0.900292 | − | 0.435287i | \(-0.143353\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −50.4895 | −1.17417 | −0.587087 | − | 0.809524i | \(-0.699725\pi\) | ||||
−0.587087 | + | 0.809524i | \(0.699725\pi\) | |||||||
\(44\) | 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 | \(0.316651\pi\) | ||||
−0.544681 | + | 0.838644i | \(0.683349\pi\) | |||||||
\(54\) | 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 | \(-0.199379\pi\) | ||||
0.810162 | + | 0.586206i | \(0.199379\pi\) | |||||||
\(68\) | 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 | \(-0.333344\pi\) | ||||
0.499971 | + | 0.866042i | \(0.333344\pi\) | |||||||
\(80\) | 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 | \(0.106994\pi\) | ||||
−0.944038 | + | 0.329836i | \(0.893006\pi\) | |||||||
\(90\) | 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 | \(0.191184\pi\) | ||||
−0.824985 | + | 0.565155i | \(0.808816\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −70.0355 | −0.679956 | −0.339978 | − | 0.940433i | \(-0.610420\pi\) | ||||
−0.339978 | + | 0.940433i | \(0.610420\pi\) | |||||||
\(104\) | 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 | \(0.0898460\pi\) | ||||
−0.960429 | + | 0.278527i | \(0.910154\pi\) | |||||||
\(114\) | 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 | \(-0.118302\pi\) | ||||
0.931727 | + | 0.363160i | \(0.118302\pi\) | |||||||
\(128\) | 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 | \(-0.833766\pi\) | ||
0.866704 | − | 0.498822i | \(-0.166234\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 29.5616 | 0.212673 | 0.106337 | − | 0.994330i | \(-0.466088\pi\) | ||||
0.106337 | + | 0.994330i | \(0.466088\pi\) | |||||||
\(140\) | 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 | \(0.0187133\pi\) | ||||
−0.998272 | + | 0.0587556i | \(0.981287\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 119.607 | 0.792099 | 0.396050 | − | 0.918229i | \(-0.370381\pi\) | ||||
0.396050 | + | 0.918229i | \(0.370381\pi\) | |||||||
\(152\) | 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 | \(-0.604028\pi\) | ||||
−0.321026 | + | 0.947071i | \(0.604028\pi\) | |||||||
\(164\) | 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 | \(0.0107283\pi\) | ||||
−0.999432 | + | 0.0336976i | \(0.989272\pi\) | |||||||
\(174\) | 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 | \(-0.855953\pi\) | ||
0.899341 | − | 0.437248i | \(-0.144047\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.598837 | −0.00300923 | −0.00150461 | − | 0.999999i | \(-0.500479\pi\) | ||||
−0.00150461 | + | 0.999999i | \(0.500479\pi\) | |||||||
\(200\) | 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 | \(-0.304643\pi\) | ||||
0.575923 | + | 0.817504i | \(0.304643\pi\) | |||||||
\(212\) | 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 | \(-0.641008\pi\) | ||||
−0.428642 | + | 0.903474i | \(0.641008\pi\) | |||||||
\(224\) | 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 | \(0.0660579\pi\) | ||||
−0.978543 | + | 0.206040i | \(0.933942\pi\) | |||||||
\(234\) | 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 | \(-0.904414\pi\) | ||
0.955250 | − | 0.295800i | \(-0.0955861\pi\) | |||||||
\(258\) | 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 | \(0.104555\pi\) | ||||
−0.946537 | + | 0.322595i | \(0.895445\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 125.415 | 0.462784 | 0.231392 | − | 0.972861i | \(-0.425672\pi\) | ||||
0.231392 | + | 0.972861i | \(0.425672\pi\) | |||||||
\(272\) | 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 | \(0.00786421\pi\) | ||||
−0.999695 | + | 0.0247036i | \(0.992136\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −306.461 | −1.08290 | −0.541450 | − | 0.840733i | \(-0.682125\pi\) | ||||
−0.541450 | + | 0.840733i | \(0.682125\pi\) | |||||||
\(284\) | 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 | \(-0.933315\pi\) | ||
0.978136 | − | 0.207968i | \(-0.0666848\pi\) | |||||||
\(294\) | 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 | \(-0.490126\pi\) | ||||
0.0310149 | + | 0.999519i | \(0.490126\pi\) | |||||||
\(308\) | 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 | \(-0.682895\pi\) | ||
0.543483 | − | 0.839420i | \(-0.317105\pi\) | |||||||
\(318\) | 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 | \(-0.544248\pi\) | ||||
−0.138561 | + | 0.990354i | \(0.544248\pi\) | |||||||
\(332\) | 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 | \(-0.837828\pi\) | ||
0.872999 | − | 0.487722i | \(-0.162172\pi\) | |||||||
\(354\) | 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 | \(-0.317204\pi\) | ||||
0.543223 | + | 0.839589i | \(0.317204\pi\) | |||||||
\(368\) | 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 | \(-0.385647\pi\) | ||||
0.351573 | + | 0.936161i | \(0.385647\pi\) | |||||||
\(380\) | 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 | \(-0.909705\pi\) | ||
0.960035 | − | 0.279881i | \(-0.0902951\pi\) | |||||||
\(390\) | 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 | \(0.119597\pi\) | ||||
−0.930242 | + | 0.366946i | \(0.880403\pi\) | |||||||
\(402\) | 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 | \(-0.183803\pi\) | ||||
0.837867 | + | 0.545875i | \(0.183803\pi\) | |||||||
\(440\) | 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 | \(0.145560\pi\) | ||||
−0.897252 | + | 0.441520i | \(0.854440\pi\) | |||||||
\(450\) | 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 | \(-0.885684\pi\) | ||
0.936201 | − | 0.351464i | \(-0.114316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.33727 | −0.0136874 | −0.00684371 | − | 0.999977i | \(-0.502178\pi\) | ||||
−0.00684371 | + | 0.999977i | \(0.502178\pi\) | |||||||
\(464\) | 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 | \(-0.276731\pi\) | ||||
0.645304 | + | 0.763926i | \(0.276731\pi\) | |||||||
\(488\) | 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 | \(-0.577494\pi\) | ||||
−0.241058 | + | 0.970511i | \(0.577494\pi\) | |||||||
\(500\) | 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 | \(-0.847683\pi\) | ||
0.887679 | − | 0.460464i | \(-0.152317\pi\) | |||||||
\(510\) | 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 | \(0.144354\pi\) | ||||
−0.898918 | + | 0.438116i | \(0.855646\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 287.095 | 0.548939 | 0.274469 | − | 0.961596i | \(-0.411498\pi\) | ||||
0.274469 | + | 0.961596i | \(0.411498\pi\) | |||||||
\(524\) | 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 | \(-0.477781\pi\) | ||||
0.0697471 | + | 0.997565i | \(0.477781\pi\) | |||||||
\(548\) | 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 | \(-0.838737\pi\) | ||
0.874388 | − | 0.485228i | \(-0.161263\pi\) | |||||||
\(558\) | 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 | \(-0.681173\pi\) | ||
0.538933 | − | 0.842348i | \(-0.318827\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −118.951 | −0.208321 | −0.104161 | − | 0.994560i | \(-0.533216\pi\) | ||||
−0.104161 | + | 0.994560i | \(0.533216\pi\) | |||||||
\(572\) | 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 | \(0.101106\pi\) | ||||
−0.949977 | + | 0.312320i | \(0.898894\pi\) | |||||||
\(594\) | 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 | \(-0.159485\pi\) | ||||
0.877085 | + | 0.480336i | \(0.159485\pi\) | |||||||
\(608\) | 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 | \(0.0379623\pi\) | ||||
−0.992897 | + | 0.118980i | \(0.962038\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 596.307 | 0.963340 | 0.481670 | − | 0.876353i | \(-0.340030\pi\) | ||||
0.481670 | + | 0.876353i | \(0.340030\pi\) | |||||||
\(620\) | 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 | \(-0.480401\pi\) | ||||
0.0615337 | + | 0.998105i | \(0.480401\pi\) | |||||||
\(632\) | 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 | \(-0.852123\pi\) | ||
0.894014 | − | 0.448039i | \(-0.147877\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1217.20 | −1.89299 | −0.946497 | − | 0.322712i | \(-0.895406\pi\) | ||||
−0.946497 | + | 0.322712i | \(0.895406\pi\) | |||||||
\(644\) | 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 | \(0.0529581\pi\) | ||||
−0.986192 | + | 0.165606i | \(0.947042\pi\) | |||||||
\(654\) | 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 | \(0.0765063\pi\) | ||||
−0.971254 | + | 0.238044i | \(0.923494\pi\) | |||||||
\(678\) | 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 | \(-0.439767\pi\) | ||||
0.188100 | + | 0.982150i | \(0.439767\pi\) | |||||||
\(692\) | 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 | \(0.100370\pi\) | ||||
−0.950696 | + | 0.310123i | \(0.899630\pi\) | |||||||
\(702\) | 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 | \(-0.506931\pi\) | ||||
−0.0217718 | + | 0.999763i | \(0.506931\pi\) | |||||||
\(728\) | 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 | \(-0.782484\pi\) | ||||
−0.775464 | + | 0.631391i | \(0.782484\pi\) | |||||||
\(740\) | 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 | \(-0.321759\pi\) | ||||
0.531154 | + | 0.847275i | \(0.321759\pi\) | |||||||
\(752\) | 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 | \(0.224359\pi\) | ||||
−0.761713 | + | 0.647914i | \(0.775641\pi\) | |||||||
\(762\) | 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 | \(-0.875311\pi\) | ||
0.924253 | − | 0.381780i | \(-0.124689\pi\) | |||||||
\(774\) | 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 | \(-0.382964\pi\) | ||||
0.359451 | + | 0.933164i | \(0.382964\pi\) | |||||||
\(788\) | 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 | \(0.250251\pi\) | ||||
−0.706549 | + | 0.707664i | \(0.749749\pi\) | |||||||
\(798\) | 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 | \(0.163376\pi\) | ||||
−0.871148 | + | 0.491021i | \(0.836624\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1430.50 | 1.76387 | 0.881937 | − | 0.471367i | \(-0.156239\pi\) | ||||
0.881937 | + | 0.471367i | \(0.156239\pi\) | |||||||
\(812\) | 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 | \(-0.712459\pi\) | ||
0.618992 | − | 0.785397i | \(-0.287541\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1064.14 | 1.29300 | 0.646502 | − | 0.762913i | \(-0.276231\pi\) | ||||
0.646502 | + | 0.762913i | \(0.276231\pi\) | |||||||
\(824\) | 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 | \(-0.940978\pi\) | ||
0.982859 | − | 0.184361i | \(-0.0590215\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.3157 | 0.0480975 | 0.0240487 | − | 0.999711i | \(-0.492344\pi\) | ||||
0.0240487 | + | 0.999711i | \(0.492344\pi\) | |||||||
\(860\) | 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 | \(-0.607495\pi\) | ||
0.331322 | − | 0.943518i | \(-0.392505\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1258.25 | −1.42497 | −0.712486 | − | 0.701686i | \(-0.752431\pi\) | ||||
−0.712486 | + | 0.701686i | \(0.752431\pi\) | |||||||
\(884\) | 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 | \(-0.288510\pi\) | ||||
0.616599 | + | 0.787277i | \(0.288510\pi\) | |||||||
\(908\) | 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 | \(-0.466022\pi\) | ||||
0.106544 | + | 0.994308i | \(0.466022\pi\) | |||||||
\(920\) | 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 | \(0.0137709\pi\) | ||||
−0.999064 | + | 0.0432491i | \(0.986229\pi\) | |||||||
\(930\) | 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 | \(0.381020\pi\) | ||||
−0.365144 | + | 0.930951i | \(0.618980\pi\) | |||||||
\(942\) | 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 | \(0.100343\pi\) | ||||
−0.950723 | + | 0.310040i | \(0.899657\pi\) | |||||||
\(954\) | 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 | \(-0.711806\pi\) | ||||
−0.617381 | + | 0.786665i | \(0.711806\pi\) | |||||||
\(968\) | 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 | \(0.361126\pi\) | ||||
−0.422576 | + | 0.906328i | \(0.638874\pi\) | |||||||
\(978\) | 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 | \(-0.258225\pi\) | ||||
0.688602 | + | 0.725140i | \(0.258225\pi\) | |||||||
\(992\) | 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.a.257.6 | yes | 8 | |
3.2 | odd | 2 | inner | 384.3.e.a.257.5 | ✓ | 8 | |
4.3 | odd | 2 | 384.3.e.d.257.3 | yes | 8 | ||
8.3 | odd | 2 | 384.3.e.b.257.6 | yes | 8 | ||
8.5 | even | 2 | 384.3.e.c.257.3 | yes | 8 | ||
12.11 | even | 2 | 384.3.e.d.257.4 | yes | 8 | ||
16.3 | odd | 4 | 768.3.h.g.641.16 | 16 | |||
16.5 | even | 4 | 768.3.h.h.641.16 | 16 | |||
16.11 | odd | 4 | 768.3.h.g.641.1 | 16 | |||
16.13 | even | 4 | 768.3.h.h.641.1 | 16 | |||
24.5 | odd | 2 | 384.3.e.c.257.4 | yes | 8 | ||
24.11 | even | 2 | 384.3.e.b.257.5 | yes | 8 | ||
48.5 | odd | 4 | 768.3.h.h.641.2 | 16 | |||
48.11 | even | 4 | 768.3.h.g.641.15 | 16 | |||
48.29 | odd | 4 | 768.3.h.h.641.15 | 16 | |||
48.35 | even | 4 | 768.3.h.g.641.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.e.a.257.5 | ✓ | 8 | 3.2 | odd | 2 | inner | |
384.3.e.a.257.6 | yes | 8 | 1.1 | even | 1 | trivial | |
384.3.e.b.257.5 | yes | 8 | 24.11 | even | 2 | ||
384.3.e.b.257.6 | yes | 8 | 8.3 | odd | 2 | ||
384.3.e.c.257.3 | yes | 8 | 8.5 | even | 2 | ||
384.3.e.c.257.4 | yes | 8 | 24.5 | odd | 2 | ||
384.3.e.d.257.3 | yes | 8 | 4.3 | odd | 2 | ||
384.3.e.d.257.4 | yes | 8 | 12.11 | even | 2 | ||
768.3.h.g.641.1 | 16 | 16.11 | odd | 4 | |||
768.3.h.g.641.2 | 16 | 48.35 | even | 4 | |||
768.3.h.g.641.15 | 16 | 48.11 | even | 4 | |||
768.3.h.g.641.16 | 16 | 16.3 | odd | 4 | |||
768.3.h.h.641.1 | 16 | 16.13 | even | 4 | |||
768.3.h.h.641.2 | 16 | 48.5 | odd | 4 | |||
768.3.h.h.641.15 | 16 | 48.29 | odd | 4 | |||
768.3.h.h.641.16 | 16 | 16.5 | even | 4 |