Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [768,3,Mod(641,768)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(768, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("768.641");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 768 = 2^{8} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 768.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(20.9264843029\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 14 x^{14} - 28 x^{13} + 50 x^{12} - 104 x^{11} - 66 x^{10} + 640 x^{9} + 555 x^{8} + \cdots + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{34}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 384) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 641.15 | ||
Root | \(1.20927 - 2.91944i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 768.641 |
Dual form | 768.3.h.g.641.16 |
$q$-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 \(\left(\mathbb{Z}/768\mathbb{Z}\right)^\times\).
\(n\) | \(257\) | \(511\) | \(517\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 2.98985 | − | 0.246559i | 0.996617 | − | 0.0821862i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 6.63641 | 1.32728 | 0.663641 | − | 0.748051i | \(-0.269010\pi\) | ||||
0.663641 | + | 0.748051i | \(0.269010\pi\) | |||||||
\(6\) | 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 | ||||||||
\(11\) | −8.68786 | −0.789806 | −0.394903 | − | 0.918723i | \(-0.629222\pi\) | ||||
−0.394903 | + | 0.918723i | \(0.629222\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 17.9269i | − | 1.37899i | −0.724289 | − | 0.689497i | \(-0.757832\pi\) | ||
0.724289 | − | 0.689497i | \(-0.242168\pi\) | |||||||
\(14\) | 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 | ||||||||
\(19\) | − | 32.1769i | − | 1.69352i | −0.531976 | − | 0.846760i | \(-0.678550\pi\) | ||
0.531976 | − | 0.846760i | \(-0.321450\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.72861 | + | 0.142550i | −0.0823146 | + | 0.00678808i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.4836i | 0.890592i | 0.895383 | + | 0.445296i | \(0.146902\pi\) | ||||
−0.895383 | + | 0.445296i | \(0.853098\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 19.0419 | 0.761677 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.1816 | − | 6.59713i | 0.969690 | − | 0.244338i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.0310 | 0.759690 | 0.379845 | − | 0.925050i | \(-0.375977\pi\) | ||||
0.379845 | + | 0.925050i | \(0.375977\pi\) | |||||||
\(30\) | 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 | ||||||||
\(35\) | −3.83689 | −0.109625 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 53.3855i | 1.44285i | 0.692492 | + | 0.721426i | \(0.256513\pi\) | ||||
−0.692492 | + | 0.721426i | \(0.743487\pi\) | |||||||
\(38\) | 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 | ||||||||
\(43\) | 50.4895i | 1.17417i | 0.809524 | + | 0.587087i | \(0.199725\pi\) | ||||
−0.809524 | + | 0.587087i | \(0.800275\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 58.9208 | − | 9.78437i | 1.30935 | − | 0.217430i | ||||
\(46\) | 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 | ||||||||
\(51\) | −4.68732 | − | 56.8401i | −0.0919083 | − | 1.11451i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 88.8962 | 1.67729 | 0.838644 | − | 0.544681i | \(-0.183349\pi\) | ||||
0.838644 | + | 0.544681i | \(0.183349\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −57.6562 | −1.04829 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.93348 | − | 96.2040i | −0.139184 | − | 1.68779i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −63.1939 | −1.07108 | −0.535542 | − | 0.844509i | \(-0.679893\pi\) | ||||
−0.535542 | + | 0.844509i | \(0.679893\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 33.5317i | 0.549700i | 0.961487 | + | 0.274850i | \(0.0886282\pi\) | ||||
−0.961487 | + | 0.274850i | \(0.911372\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5.13313 | + | 0.852405i | −0.0814782 | + | 0.0135302i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 118.970i | − | 1.83031i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 108.562i | 1.62032i | 0.586206 | + | 0.810162i | \(0.300621\pi\) | ||||
−0.586206 | + | 0.810162i | \(0.699379\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.05041 | + | 61.2430i | 0.0731944 | + | 0.887579i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 59.3600i | 0.836056i | 0.908434 | + | 0.418028i | \(0.137279\pi\) | ||||
−0.908434 | + | 0.418028i | \(0.862721\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.60477 | 0.0767777 | 0.0383889 | − | 0.999263i | \(-0.487777\pi\) | ||||
0.0383889 | + | 0.999263i | \(0.487777\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 56.9325 | − | 4.69495i | 0.759101 | − | 0.0625994i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.02296 | 0.0652332 | ||||||||
\(78\) | 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 | ||||||||
\(83\) | 48.5283 | 0.584679 | 0.292339 | − | 0.956315i | \(-0.405566\pi\) | ||||
0.292339 | + | 0.956315i | \(0.405566\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 126.165i | − | 1.48429i | ||||||
\(86\) | 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 | ||||||||
\(91\) | 10.3646i | 0.113897i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 78.4369 | − | 6.46831i | 0.843407 | − | 0.0695517i | ||||
\(94\) | 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 | ||||||||
\(99\) | −77.1345 | + | 12.8089i | −0.779136 | + | 0.129383i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 114.161 | 1.13031 | 0.565155 | − | 0.824985i | \(-0.308816\pi\) | ||||
0.565155 | + | 0.824985i | \(0.308816\pi\) | |||||||
\(102\) | 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 | ||||||||
\(107\) | −50.9072 | −0.475769 | −0.237884 | − | 0.971293i | \(-0.576454\pi\) | ||||
−0.237884 | + | 0.971293i | \(0.576454\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.2178i | − | 0.121264i | −0.998160 | − | 0.0606320i | \(-0.980688\pi\) | ||
0.998160 | − | 0.0606320i | \(-0.0193116\pi\) | |||||||
\(110\) | 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 | ||||||||
\(115\) | 135.938i | 1.18207i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −26.4305 | − | 159.163i | −0.225902 | − | 1.36036i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.9914i | 0.0923644i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −45.5210 | −0.376207 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −8.80054 | − | 106.718i | −0.0715491 | − | 0.867629i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −39.5402 | −0.316321 | ||||||||
\(126\) | 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 | ||||||||
\(131\) | 121.212 | 0.925279 | 0.462640 | − | 0.886546i | \(-0.346902\pi\) | ||||
0.462640 | + | 0.886546i | \(0.346902\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.6033i | 0.139875i | ||||||||
\(134\) | 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 | ||||||||
\(139\) | − | 29.5616i | − | 0.212673i | −0.994330 | − | 0.106337i | \(-0.966088\pi\) | ||
0.994330 | − | 0.106337i | \(-0.0339121\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.55123 | + | 91.5687i | 0.0535548 | + | 0.649424i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 155.747i | 1.08914i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 146.207 | 1.00832 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −145.503 | + | 11.9990i | −0.989818 | + | 0.0816255i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 17.5092 | 0.117511 | 0.0587556 | − | 0.998272i | \(-0.481287\pi\) | ||||
0.0587556 | + | 0.998272i | \(0.481287\pi\) | |||||||
\(150\) | 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 | ||||||||
\(155\) | 174.102 | 1.12324 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 189.488i | 1.20693i | 0.797388 | + | 0.603466i | \(0.206214\pi\) | ||||
−0.797388 | + | 0.603466i | \(0.793786\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 265.786 | − | 21.9181i | 1.67161 | − | 0.137850i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 11.8428i | − | 0.0735576i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 104.654i | − | 0.642051i | −0.947071 | − | 0.321026i | \(-0.895972\pi\) | ||
0.947071 | − | 0.321026i | \(-0.104028\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −172.384 | + | 14.2156i | −1.04475 | + | 0.0861553i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 142.664i | − | 0.854278i | −0.904186 | − | 0.427139i | \(-0.859522\pi\) | ||
0.904186 | − | 0.427139i | \(-0.140478\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −152.374 | −0.901623 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −47.4399 | − | 285.680i | −0.277426 | − | 1.67064i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.6594 | −0.0673952 | −0.0336976 | − | 0.999432i | \(-0.510728\pi\) | ||||
−0.0336976 | + | 0.999432i | \(0.510728\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.0092 | −0.0629100 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −188.940 | + | 15.5810i | −1.06746 | + | 0.0880283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 40.3979 | 0.225687 | 0.112843 | − | 0.993613i | \(-0.464004\pi\) | ||||
0.112843 | + | 0.993613i | \(0.464004\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 121.175i | 0.669472i | 0.942312 | + | 0.334736i | \(0.108647\pi\) | ||||
−0.942312 | + | 0.334736i | \(0.891353\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 8.26752 | + | 100.255i | 0.0451777 | + | 0.547840i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 354.288i | 1.91507i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 165.165i | 0.883235i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −15.1371 | + | 3.81418i | −0.0800906 | + | 0.0201808i | ||||
\(190\) | 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 | ||||||||
\(195\) | −29.3332 | − | 355.704i | −0.150426 | − | 1.82412i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −172.276 | −0.874495 | −0.437248 | − | 0.899341i | \(-0.644047\pi\) | ||||
−0.437248 | + | 0.899341i | \(0.644047\pi\) | |||||||
\(198\) | 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 | ||||||||
\(203\) | −12.7374 | −0.0627458 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 236.877i | − | 1.15550i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 30.2000 | + | 181.862i | 0.145894 | + | 0.878561i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 279.548i | 1.33755i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 243.040i | 1.15185i | 0.817504 | + | 0.575923i | \(0.195357\pi\) | ||||
−0.817504 | + | 0.575923i | \(0.804643\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 14.6357 | + | 177.478i | 0.0687123 | + | 0.833228i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 335.069i | 1.55846i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.1676 | −0.0698968 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 16.7574 | − | 1.38190i | 0.0765180 | − | 0.00631007i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −340.809 | −1.54212 | ||||||||
\(222\) | 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 | ||||||||
\(227\) | 8.76834 | 0.0386271 | 0.0193135 | − | 0.999813i | \(-0.493852\pi\) | ||||
0.0193135 | + | 0.999813i | \(0.493852\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 131.740i | − | 0.575283i | −0.957738 | − | 0.287641i | \(-0.907129\pi\) | ||
0.957738 | − | 0.287641i | \(-0.0928711\pi\) | |||||||
\(230\) | 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 | ||||||||
\(235\) | 203.250i | 0.864894i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −236.185 | + | 19.4770i | −0.996560 | + | 0.0821815i | ||||
\(238\) | 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 | ||||||||
\(243\) | 222.725 | − | 97.1728i | 0.916564 | − | 0.399888i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −322.966 | −1.31823 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −576.832 | −2.33535 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 145.093 | − | 11.9651i | 0.582701 | − | 0.0480525i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −376.853 | −1.50140 | −0.750702 | − | 0.660641i | \(-0.770285\pi\) | ||||
−0.750702 | + | 0.660641i | \(0.770285\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 177.959i | − | 0.703395i | ||||||
\(254\) | 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 | ||||||||
\(259\) | − | 30.8653i | − | 0.119171i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 195.600 | − | 32.4813i | 0.749427 | − | 0.124450i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 495.013i | − | 1.88218i | −0.338158 | − | 0.941089i | \(-0.609804\pi\) | ||
0.338158 | − | 0.941089i | \(-0.390196\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 589.952 | 2.22623 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 14.4757 | + | 175.537i | 0.0542160 | + | 0.657441i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −173.556 | −0.645190 | −0.322595 | − | 0.946537i | \(-0.604555\pi\) | ||||
−0.322595 | + | 0.946537i | \(0.604555\pi\) | |||||||
\(270\) | 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 | ||||||||
\(275\) | −165.434 | −0.601577 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 226.300i | 0.816967i | 0.912766 | + | 0.408483i | \(0.133942\pi\) | ||||
−0.912766 | + | 0.408483i | \(0.866058\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | 306.461i | 1.08290i | 0.840733 | + | 0.541450i | \(0.182125\pi\) | ||||
−0.840733 | + | 0.541450i | \(0.817875\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −52.6498 | − | 638.449i | −0.184736 | − | 2.24017i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 20.6365i | 0.0719042i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −72.4183 | −0.250582 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 279.116 | − | 23.0173i | 0.959160 | − | 0.0790973i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −121.869 | −0.415935 | −0.207968 | − | 0.978136i | \(-0.566685\pi\) | ||||
−0.207968 | + | 0.978136i | \(0.566685\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −419.381 | −1.42163 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −227.462 | + | 57.3149i | −0.765867 | + | 0.192980i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 367.208 | 1.22812 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 29.1909i | − | 0.0969797i | ||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 341.325 | − | 28.1474i | 1.12649 | − | 0.0928959i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 222.530i | 0.729607i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 19.0431i | 0.0620298i | 0.999519 | + | 0.0310149i | \(0.00987393\pi\) | ||||
−0.999519 | + | 0.0310149i | \(0.990126\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −209.396 | + | 17.2678i | −0.677656 | + | 0.0558830i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 223.159i | 0.717552i | 0.933424 | + | 0.358776i | \(0.116806\pi\) | ||||
−0.933424 | + | 0.358776i | \(0.883194\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 194.708 | 0.622070 | 0.311035 | − | 0.950399i | \(-0.399324\pi\) | ||||
0.311035 | + | 0.950399i | \(0.399324\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −34.0655 | + | 5.65691i | −0.108145 | + | 0.0179584i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 532.192 | 1.67884 | 0.839420 | − | 0.543483i | \(-0.182895\pi\) | ||||
0.839420 | + | 0.543483i | \(0.182895\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −191.402 | −0.600007 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −152.205 | + | 12.5516i | −0.474159 | + | 0.0391016i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −611.715 | −1.89385 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 341.363i | − | 1.05035i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.25896 | − | 39.5192i | −0.00996623 | − | 0.120854i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 17.7070i | − | 0.0538206i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 91.7273i | 0.277122i | 0.990354 | + | 0.138561i | \(0.0442476\pi\) | ||||
−0.990354 | + | 0.138561i | \(0.955752\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 78.7088 | + | 473.979i | 0.236363 | + | 1.42336i | ||||
\(334\) | 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 | ||||||||
\(339\) | −15.5201 | − | 188.202i | −0.0457821 | − | 0.555169i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −227.921 | −0.668389 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 56.4662 | 0.164625 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 33.5166 | + | 406.433i | 0.0971496 | + | 1.17807i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 323.122 | 0.931189 | 0.465594 | − | 0.884998i | \(-0.345841\pi\) | ||||
0.465594 | + | 0.884998i | \(0.345841\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 255.324i | 0.731586i | 0.930696 | + | 0.365793i | \(0.119202\pi\) | ||||
−0.930696 | + | 0.365793i | \(0.880798\pi\) | |||||||
\(350\) | 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 | ||||||||
\(355\) | 393.937i | 1.10968i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.71001 | + | 32.8625i | 0.00759107 | + | 0.0920519i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 119.962i | 0.334157i | 0.985944 | + | 0.167079i | \(0.0534334\pi\) | ||||
−0.985944 | + | 0.167079i | \(0.946567\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −674.351 | −1.86801 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −136.101 | + | 11.2236i | −0.374934 | + | 0.0309190i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.1956 | 0.101906 | ||||||||
\(366\) | 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 | ||||||||
\(371\) | −51.3960 | −0.138534 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 606.592i | 1.62625i | 0.582088 | + | 0.813126i | \(0.302236\pi\) | ||||
−0.582088 | + | 0.813126i | \(0.697764\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −118.219 | + | 9.74896i | −0.315251 | + | 0.0259972i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 394.948i | − | 1.04761i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 266.492i | − | 0.703146i | −0.936161 | − | 0.351573i | \(-0.885647\pi\) | ||
0.936161 | − | 0.351573i | \(-0.114353\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −707.574 | + | 58.3502i | −1.85715 | + | 0.153150i | ||||
\(382\) | 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 | ||||||||
\(387\) | 74.4390 | + | 448.267i | 0.192349 | + | 1.15831i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −217.748 | −0.559763 | −0.279881 | − | 0.960035i | \(-0.590295\pi\) | ||||
−0.279881 | + | 0.960035i | \(0.590295\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 389.414 | 0.995944 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 362.405 | − | 29.8858i | 0.922149 | − | 0.0760452i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −524.246 | −1.32721 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 53.9651i | − | 0.135932i | −0.997688 | − | 0.0679661i | \(-0.978349\pi\) | ||
0.997688 | − | 0.0679661i | \(-0.0216510\pi\) | |||||||
\(398\) | 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 | ||||||||
\(403\) | − | 470.302i | − | 1.16700i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 508.698 | − | 173.739i | 1.25604 | − | 0.428986i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 463.806i | − | 1.13957i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −569.204 | −1.39170 | −0.695849 | − | 0.718188i | \(-0.744972\pi\) | ||||
−0.695849 | + | 0.718188i | \(0.744972\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −33.6990 | − | 408.645i | −0.0819926 | − | 0.994270i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.5361 | 0.0884651 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 322.054 | 0.776034 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −7.28866 | − | 88.3847i | −0.0174788 | − | 0.211954i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 590.728 | 1.40985 | 0.704926 | − | 0.709281i | \(-0.250980\pi\) | ||||
0.704926 | + | 0.709281i | \(0.250980\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 475.989i | − | 1.13061i | −0.824880 | − | 0.565307i | \(-0.808758\pi\) | ||
0.824880 | − | 0.565307i | \(-0.191242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 45.1541 | + | 271.915i | 0.106747 | + | 0.642825i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 362.006i | − | 0.851780i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 19.3866i | − | 0.0454019i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 38.4007 | + | 465.659i | 0.0895120 | + | 1.08545i | ||||
\(430\) | 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 | ||||||||
\(435\) | 437.136 | − | 36.0485i | 1.00491 | − | 0.0828702i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 659.099 | 1.50824 | ||||||||
\(438\) | 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 | ||||||||
\(443\) | 333.798 | 0.753494 | 0.376747 | − | 0.926316i | \(-0.377043\pi\) | ||||
0.376747 | + | 0.926316i | \(0.377043\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 389.629i | 0.875571i | ||||||||
\(446\) | 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 | ||||||||
\(451\) | 310.100i | 0.687584i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 357.607 | − | 29.4901i | 0.789419 | − | 0.0650996i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 68.7836i | 0.151173i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.5362 | −0.0755715 | −0.0377857 | − | 0.999286i | \(-0.512030\pi\) | ||||
−0.0377857 | + | 0.999286i | \(0.512030\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −125.418 | − | 497.739i | −0.273242 | − | 1.08440i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 324.050 | 0.702929 | 0.351464 | − | 0.936201i | \(-0.385684\pi\) | ||||
0.351464 | + | 0.936201i | \(0.385684\pi\) | |||||||
\(462\) | 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 | ||||||||
\(467\) | −450.706 | −0.965109 | −0.482554 | − | 0.875866i | \(-0.660291\pi\) | ||||
−0.482554 | + | 0.875866i | \(0.660291\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 62.7658i | − | 0.133829i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 46.7200 | + | 566.542i | 0.0991932 | + | 1.20285i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 438.646i | − | 0.927370i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 612.710i | − | 1.28992i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 789.258 | − | 131.064i | 1.65463 | − | 0.274767i | ||||
\(478\) | 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 | ||||||||
\(483\) | −2.91993 | − | 35.4081i | −0.00604541 | − | 0.0733087i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 619.538 | 1.27740 | ||||||||
\(486\) | 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 | ||||||||
\(491\) | 352.334 | 0.717585 | 0.358792 | − | 0.933417i | \(-0.383189\pi\) | ||||
0.358792 | + | 0.933417i | \(0.383189\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 418.831i | − | 0.849557i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −511.896 | + | 85.0052i | −1.03413 | + | 0.171728i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 34.3195i | − | 0.0690532i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 240.576i | − | 0.482116i | −0.970511 | − | 0.241058i | \(-0.922506\pi\) | ||
0.970511 | − | 0.241058i | \(-0.0774943\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −35.1751 | − | 426.545i | −0.0702098 | − | 0.851388i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 13.1648i | − | 0.0261725i | −0.999914 | − | 0.0130862i | \(-0.995834\pi\) | ||
0.999914 | − | 0.0130862i | \(-0.00416560\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 757.621 | 1.50024 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −455.577 | + | 37.5692i | −0.898573 | + | 0.0741010i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 468.752 | 0.920927 | 0.460464 | − | 0.887679i | \(-0.347683\pi\) | ||||
0.460464 | + | 0.887679i | \(0.347683\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.24044 | −0.00634138 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −212.275 | − | 842.443i | −0.413791 | − | 1.64219i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −464.784 | −0.902494 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 266.079i | − | 0.514660i | ||||||
\(518\) | 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 | ||||||||
\(523\) | − | 287.095i | − | 0.548939i | −0.961596 | − | 0.274469i | \(-0.911498\pi\) | ||
0.961596 | − | 0.274469i | \(-0.0885022\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −32.9160 | + | 2.71442i | −0.0626971 | + | 0.00517033i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 498.742i | − | 0.946379i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 109.421 | 0.206845 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −561.062 | + | 93.1698i | −1.05661 | + | 0.175461i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −639.875 | −1.20052 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −337.841 | −0.631479 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 120.784 | − | 9.96046i | 0.224923 | − | 0.0185483i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 422.801 | 0.784418 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 804.779i | 1.48758i | 0.668416 | + | 0.743788i | \(0.266973\pi\) | ||||
−0.668416 | + | 0.743788i | \(0.733027\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.8766 | + | 362.294i | 0.0550214 | + | 0.667208i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 87.7186i | − | 0.160952i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 76.3034i | 0.139494i | 0.997565 | + | 0.0697471i | \(0.0222192\pi\) | ||||
−0.997565 | + | 0.0697471i | \(0.977781\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 49.4373 | + | 297.708i | 0.0900498 | + | 0.542274i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 708.889i | − | 1.28655i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 45.6718 | 0.0825892 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 87.3528 | + | 1059.27i | 0.157392 | + | 1.90859i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 540.544 | 0.970455 | 0.485228 | − | 0.874388i | \(-0.338737\pi\) | ||||
0.485228 | + | 0.874388i | \(0.338737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 905.121 | 1.61918 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 40.7228 | + | 493.819i | 0.0725897 | + | 0.880247i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1047.65 | 1.86084 | 0.930422 | − | 0.366491i | \(-0.119441\pi\) | ||||
0.930422 | + | 0.366491i | \(0.119441\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 417.742i | − | 0.739366i | ||||||
\(566\) | 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 | ||||||||
\(571\) | 118.951i | 0.208321i | 0.994560 | + | 0.104161i | \(0.0332156\pi\) | ||||
−0.994560 | + | 0.104161i | \(0.966784\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −83.1611 | − | 1008.44i | −0.145133 | − | 1.75993i | ||||
\(574\) | 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 | ||||||||
\(579\) | −681.499 | + | 56.1999i | −1.17703 | + | 0.0970637i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.0570 | −0.0482910 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −772.318 | −1.32473 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −175.404 | − | 1056.27i | −0.299835 | − | 1.80559i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 571.017 | 0.972771 | 0.486386 | − | 0.873744i | \(-0.338315\pi\) | ||||
0.486386 | + | 0.873744i | \(0.338315\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 844.140i | − | 1.43318i | ||||||
\(590\) | 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 | ||||||||
\(595\) | 72.9432i | 0.122594i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.79043 | + | 0.147648i | −0.00299905 | + | 0.000247317i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 68.6579i | 0.114621i | 0.998356 | + | 0.0573104i | \(0.0182525\pi\) | ||||
−0.998356 | + | 0.0573104i | \(0.981748\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −9.39898 | −0.0156389 | −0.00781945 | − | 0.999969i | \(-0.502489\pi\) | ||||
−0.00781945 | + | 0.999969i | \(0.502489\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 160.058 | + | 963.857i | 0.265436 | + | 1.59844i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −302.096 | −0.499333 | ||||||||
\(606\) | 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 | ||||||||
\(611\) | 549.039 | 0.898591 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 651.884i | 1.06343i | 0.846922 | + | 0.531716i | \(0.178453\pi\) | ||||
−0.846922 | + | 0.531716i | \(0.821547\pi\) | |||||||
\(614\) | 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 | ||||||||
\(619\) | − | 596.307i | − | 0.963340i | −0.876353 | − | 0.481670i | \(-0.840030\pi\) | ||
0.876353 | − | 0.481670i | \(-0.159970\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 135.133 | + | 536.295i | 0.217606 | + | 0.863598i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 33.9441i | − | 0.0544850i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −738.453 | −1.18152 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 68.9250 | + | 835.808i | 0.109928 | + | 1.33303i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1014.91 | 1.61353 | ||||||||
\(630\) | 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 | ||||||||
\(635\) | −1570.56 | −2.47333 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 872.427i | 1.36959i | ||||||||
\(638\) | 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 | ||||||||
\(643\) | − | 1217.20i | − | 1.89299i | −0.322712 | − | 0.946497i | \(-0.604594\pi\) | ||
0.322712 | − | 0.946497i | \(-0.395406\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 82.6141 | + | 1001.81i | 0.128084 | + | 1.55319i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 802.675i | 1.24061i | 0.784360 | + | 0.620305i | \(0.212991\pi\) | ||||
−0.784360 | + | 0.620305i | \(0.787009\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 549.020 | 0.845948 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −45.3489 | + | 3.73970i | −0.0696604 | + | 0.00574455i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −216.282 | −0.331212 | −0.165606 | − | 0.986192i | \(-0.552958\pi\) | ||||
−0.165606 | + | 0.986192i | \(0.552958\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 804.410 | 1.22811 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 49.7615 | − | 8.26338i | 0.0757405 | − | 0.0125774i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −611.696 | −0.928218 | −0.464109 | − | 0.885778i | \(-0.653625\pi\) | ||||
−0.464109 | + | 0.885778i | \(0.653625\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 214.961i | 0.325206i | 0.986692 | + | 0.162603i | \(0.0519890\pi\) | ||||
−0.986692 | + | 0.162603i | \(0.948011\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1018.97 | + | 84.0293i | −1.53690 | + | 0.126741i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 123.459i | 0.185653i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 451.275i | 0.676574i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 571.583 | − | 47.1357i | 0.854384 | − | 0.0704569i | ||||
\(670\) | 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 | ||||||||
\(675\) | 498.549 | − | 125.622i | 0.738591 | − | 0.186107i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 322.312 | 0.476088 | 0.238044 | − | 0.971254i | \(-0.423494\pi\) | ||||
0.238044 | + | 0.971254i | \(0.423494\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −53.9736 | −0.0794898 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.2160 | − | 2.16191i | 0.0384964 | − | 0.00317461i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −451.564 | −0.661148 | −0.330574 | − | 0.943780i | \(-0.607242\pi\) | ||||
−0.330574 | + | 0.943780i | \(0.607242\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 907.047i | − | 1.32416i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −32.4816 | − | 393.882i | −0.0472803 | − | 0.573337i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1593.64i | − | 2.31297i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 259.954i | 0.376199i | 0.982150 | + | 0.188100i | \(0.0602328\pi\) | ||||
−0.982150 | + | 0.188100i | \(0.939767\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 44.5959 | − | 7.40558i | 0.0643520 | − | 0.0106863i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 196.183i | − | 0.282277i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −678.570 | −0.973558 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 23.6733 | + | 287.070i | 0.0338674 | + | 0.410687i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −434.792 | −0.620246 | −0.310123 | − | 0.950696i | \(-0.600370\pi\) | ||||
−0.310123 | + | 0.950696i | \(0.600370\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1717.78 | 2.44350 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 50.1131 | + | 607.688i | 0.0710823 | + | 0.861968i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −66.0033 | −0.0933568 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1136.05i | 1.60232i | 0.598448 | + | 0.801162i | \(0.295784\pi\) | ||||
−0.598448 | + | 0.801162i | \(0.704216\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −701.355 | + | 116.467i | −0.986434 | + | 0.163807i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 537.375i | 0.753682i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1033.60i | 1.44559i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 78.4001 | + | 950.705i | 0.109345 | + | 1.32595i | ||||
\(718\) | 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 | ||||||||
\(723\) | −341.407 | + | 28.1542i | −0.472209 | + | 0.0389408i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 419.513 | 0.578638 | ||||||||
\(726\) | 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 | ||||||||
\(731\) | 959.856 | 1.31307 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 596.421i | − | 0.813671i | −0.913501 | − | 0.406836i | \(-0.866632\pi\) | ||
0.913501 | − | 0.406836i | \(-0.133368\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −965.619 | + | 79.6300i | −1.31377 | + | 0.108340i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 943.170i | − | 1.27974i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 1146.14i | − | 1.55093i | −0.631391 | − | 0.775464i | \(-0.717516\pi\) | ||
0.631391 | − | 0.775464i | \(-0.282484\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1724.64 | + | 142.223i | −2.32745 | + | 0.191934i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 842.850i | 1.13439i | 0.823584 | + | 0.567194i | \(0.191971\pi\) | ||||
−0.823584 | + | 0.567194i | \(0.808029\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 116.198 | 0.155970 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 430.855 | − | 71.5476i | 0.576780 | − | 0.0957799i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.4324 | 0.0392956 | ||||||||
\(750\) | 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 | ||||||||
\(755\) | 793.761 | 1.05134 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 278.402i | − | 0.367770i | −0.982948 | − | 0.183885i | \(-0.941133\pi\) | ||
0.982948 | − | 0.183885i | \(-0.0588674\pi\) | |||||||
\(758\) | 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 | ||||||||
\(763\) | 7.64197i | 0.0100157i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −186.011 | − | 1120.14i | −0.243151 | − | 1.46424i | ||||
\(766\) | 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 | ||||||||
\(771\) | 37.4870 | + | 454.580i | 0.0486213 | + | 0.589598i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −590.233 | −0.763561 | −0.381780 | − | 0.924253i | \(-0.624689\pi\) | ||||
−0.381780 | + | 0.924253i | \(0.624689\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 499.553 | 0.644585 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.61009 | − | 92.2825i | −0.00979420 | − | 0.118768i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1148.51 | −1.47433 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 515.712i | − | 0.660322i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 576.808 | − | 145.341i | 0.736664 | − | 0.185621i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1257.52i | 1.60194i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 565.777i | 0.718903i | 0.933164 | + | 0.359451i | \(0.117036\pi\) | ||||
−0.933164 | + | 0.359451i | \(0.882964\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −122.050 | − | 1480.02i | −0.154689 | − | 1.87581i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 36.3933i | 0.0460092i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 601.120 | 0.758033 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1763.87 | − | 145.458i | 2.21870 | − | 0.182966i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −1128.02 | −1.41533 | −0.707664 | − | 0.706549i | \(-0.750251\pi\) | ||||
−0.707664 | + | 0.706549i | \(0.750251\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 582.241 | 0.728712 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 86.5601 | + | 521.259i | 0.108065 | + | 0.650761i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −48.6935 | −0.0606395 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 78.5934i | − | 0.0976316i | ||||||
\(806\) | 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 | ||||||||
\(811\) | − | 1430.50i | − | 1.76387i | −0.471367 | − | 0.881937i | \(-0.656239\pi\) | ||
0.471367 | − | 0.881937i | \(-0.343761\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −374.971 | + | 30.9220i | −0.461219 | + | 0.0380345i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 694.529i | − | 0.852183i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1624.59 | 1.98849 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.2810 | + | 92.0211i | 0.0186581 | + | 0.112358i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1289.62 | −1.57079 | −0.785397 | − | 0.618992i | \(-0.787541\pi\) | ||||
−0.785397 | + | 0.618992i | \(0.787541\pi\) | |||||||
\(822\) | 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 | ||||||||
\(827\) | −1258.48 | −1.52174 | −0.760868 | − | 0.648907i | \(-0.775227\pi\) | ||||
−0.760868 | + | 0.648907i | \(0.775227\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1197.65i | 1.44469i | 0.691531 | + | 0.722347i | \(0.256936\pi\) | ||||
−0.691531 | + | 0.722347i | \(0.743064\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 55.7961 | + | 676.603i | 0.0671434 | + | 0.814203i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 925.184i | 1.11067i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 946.779i | − | 1.13387i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 686.859 | − | 173.071i | 0.820620 | − | 0.206776i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 423.903i | 0.505248i | 0.967565 | + | 0.252624i | \(0.0812936\pi\) | ||||
−0.967565 | + | 0.252624i | \(0.918706\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −355.635 | −0.422872 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.42308 | + | 41.5094i | 0.00406059 | + | 0.0492401i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1011.22 | −1.19671 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 26.3183 | 0.0310724 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 75.5605 | + | 916.272i | 0.0889995 | + | 1.07924i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1093.53 | −1.28499 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.0080i | 0.0386964i | 0.999813 | + | 0.0193482i | \(0.00615911\pi\) | ||||
−0.999813 | + | 0.0193482i | \(0.993841\pi\) | |||||||
\(854\) | 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 | ||||||||
\(859\) | − | 41.3157i | − | 0.0480975i | −0.999711 | − | 0.0240487i | \(-0.992344\pi\) | ||
0.999711 | − | 0.0240487i | \(-0.00765569\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.08810 | + | 61.7000i | 0.00590953 | + | 0.0716609i | ||||
\(862\) | 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 | ||||||||
\(867\) | −216.520 | + | 17.8553i | −0.249735 | + | 0.0205944i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 686.302 | 0.789760 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1946.18 | 2.23442 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 828.839 | − | 137.637i | 0.949415 | − | 0.157659i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.8605 | 0.0261262 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 917.504i | − | 1.04618i | −0.852276 | − | 0.523092i | \(-0.824778\pi\) | ||
0.852276 | − | 0.523092i | \(-0.175222\pi\) | |||||||
\(878\) | 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 | ||||||||
\(883\) | − | 1258.25i | − | 1.42497i | −0.701686 | − | 0.712486i | \(-0.747569\pi\) | ||
0.701686 | − | 0.712486i | \(-0.252431\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1253.89 | + | 103.402i | −1.41682 | + | 0.116838i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 237.781i | 0.268073i | 0.990976 | + | 0.134037i | \(0.0427940\pi\) | ||||
−0.990976 | + | 0.134037i | \(0.957206\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 136.826 | 0.153910 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −665.947 | + | 227.446i | −0.747416 | + | 0.255270i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 985.466 | 1.10354 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 268.097 | 0.299550 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1097.90 | − | 90.5383i | 1.22397 | − | 0.100935i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 577.970 | 0.642903 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1690.01i | − | 1.87570i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −7.19727 | − | 87.2764i | −0.00797039 | − | 0.0966517i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 804.164i | 0.888579i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1118.51i | − | 1.23320i | −0.787277 | − | 0.616599i | \(-0.788510\pi\) | ||
0.787277 | − | 0.616599i | \(-0.211490\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1013.57 | − | 168.313i | 1.11504 | − | 0.185163i | ||||
\(910\) | 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 | ||||||||
\(915\) | 54.8667 | + | 665.332i | 0.0599636 | + | 0.727138i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −70.0794 | −0.0764225 | ||||||||
\(918\) | 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 | ||||||||
\(923\) | 1064.14 | 1.15292 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1016.56i | 1.09899i | ||||||||
\(926\) | 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 | ||||||||
\(931\) | 1565.91i | 1.68197i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 55.0217 | + | 667.211i | 0.0589728 | + | 0.715124i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1096.10i | 1.17230i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −502.272 | −0.536043 | −0.268021 | − | 0.963413i | \(-0.586370\pi\) | ||||
−0.268021 | + | 0.963413i | \(0.586370\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 582.147 | − | 48.0069i | 0.619965 | − | 0.0511255i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1752.05 | −1.86190 | −0.930951 | − | 0.365144i | \(-0.881020\pi\) | ||||
−0.930951 | + | 0.365144i | \(0.881020\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 731.133 | 0.775326 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −100.456 | + | 25.3125i | −0.106303 | + | 0.0267857i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 634.493 | 0.670003 | 0.335001 | − | 0.942218i | \(-0.391263\pi\) | ||||
0.335001 | + | 0.942218i | \(0.391263\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 100.476i | − | 0.105876i | ||||||
\(950\) | 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 | ||||||||
\(955\) | − | 2238.38i | − | 2.34385i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −572.264 | + | 47.1919i | −0.597977 | + | 0.0493123i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 79.0211i | 0.0823994i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −272.757 | −0.283827 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −451.976 | + | 75.0549i | −0.469341 | + | 0.0779386i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1512.69 | −1.56755 | ||||||||
\(966\) | 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 | ||||||||
\(971\) | 827.456 | 0.852169 | 0.426084 | − | 0.904683i | \(-0.359893\pi\) | ||||
0.426084 | + | 0.904683i | \(0.359893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.0913i | 0.0175655i | ||||||||
\(974\) | 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 | ||||||||
\(979\) | − | 510.072i | − | 0.521013i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −19.4876 | − | 117.353i | −0.0198650 | − | 0.119626i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 406.666i | − | 0.413699i | −0.978373 | − | 0.206850i | \(-0.933679\pi\) | ||
0.978373 | − | 0.206850i | \(-0.0663211\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1143.29 | −1.16070 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.36580 | − | 52.9412i | −0.00442331 | − | 0.0536385i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1034.21 | −1.04571 | ||||||||
\(990\) | 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 | ||||||||
\(995\) | −3.97413 | −0.00399410 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1201.02i | − | 1.20463i | −0.798257 | − | 0.602317i | \(-0.794244\pi\) | ||
0.798257 | − | 0.602317i | \(-0.205756\pi\) | |||||||
\(998\) | 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 | 768.3.h.g.641.15 | 16 | ||
3.2 | odd | 2 | inner | 768.3.h.g.641.1 | 16 | ||
4.3 | odd | 2 | 768.3.h.h.641.2 | 16 | |||
8.3 | odd | 2 | 768.3.h.h.641.15 | 16 | |||
8.5 | even | 2 | inner | 768.3.h.g.641.2 | 16 | ||
12.11 | even | 2 | 768.3.h.h.641.16 | 16 | |||
16.3 | odd | 4 | 384.3.e.a.257.5 | ✓ | 8 | ||
16.5 | even | 4 | 384.3.e.b.257.5 | yes | 8 | ||
16.11 | odd | 4 | 384.3.e.c.257.4 | yes | 8 | ||
16.13 | even | 4 | 384.3.e.d.257.4 | yes | 8 | ||
24.5 | odd | 2 | inner | 768.3.h.g.641.16 | 16 | ||
24.11 | even | 2 | 768.3.h.h.641.1 | 16 | |||
48.5 | odd | 4 | 384.3.e.b.257.6 | yes | 8 | ||
48.11 | even | 4 | 384.3.e.c.257.3 | yes | 8 | ||
48.29 | odd | 4 | 384.3.e.d.257.3 | yes | 8 | ||
48.35 | even | 4 | 384.3.e.a.257.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.3.e.a.257.5 | ✓ | 8 | 16.3 | odd | 4 | ||
384.3.e.a.257.6 | yes | 8 | 48.35 | even | 4 | ||
384.3.e.b.257.5 | yes | 8 | 16.5 | even | 4 | ||
384.3.e.b.257.6 | yes | 8 | 48.5 | odd | 4 | ||
384.3.e.c.257.3 | yes | 8 | 48.11 | even | 4 | ||
384.3.e.c.257.4 | yes | 8 | 16.11 | odd | 4 | ||
384.3.e.d.257.3 | yes | 8 | 48.29 | odd | 4 | ||
384.3.e.d.257.4 | yes | 8 | 16.13 | even | 4 | ||
768.3.h.g.641.1 | 16 | 3.2 | odd | 2 | inner | ||
768.3.h.g.641.2 | 16 | 8.5 | even | 2 | inner | ||
768.3.h.g.641.15 | 16 | 1.1 | even | 1 | trivial | ||
768.3.h.g.641.16 | 16 | 24.5 | odd | 2 | inner | ||
768.3.h.h.641.1 | 16 | 24.11 | even | 2 | |||
768.3.h.h.641.2 | 16 | 4.3 | odd | 2 | |||
768.3.h.h.641.15 | 16 | 8.3 | odd | 2 | |||
768.3.h.h.641.16 | 16 | 12.11 | even | 2 |