Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(325,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
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("1764.325");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.z (of order \(6\), degree \(2\), 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: | \(48.0655186332\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.339738624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{6} + 14x^{4} - 8x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 7^{2} \) |
Twist minimal: | no (minimal twist has level 588) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 325.2 | ||
Root | \(1.60021 + 0.923880i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.325 |
Dual form | 1764.3.z.l.901.2 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.804540 | + | 0.464502i | −0.160908 | + | 0.0929003i | −0.578292 | − | 0.815830i | \(-0.696280\pi\) |
0.417384 | + | 0.908730i | \(0.362947\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.84490 | − | 8.39161i | 0.440445 | − | 0.762874i | −0.557277 | − | 0.830327i | \(-0.688154\pi\) |
0.997722 | + | 0.0674529i | \(0.0214872\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 15.9753i | 1.22887i | 0.788968 | + | 0.614434i | \(0.210616\pi\) | ||||
−0.788968 | + | 0.614434i | \(0.789384\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.14154 | + | 5.27787i | 0.537738 | + | 0.310463i | 0.744162 | − | 0.668000i | \(-0.232849\pi\) |
−0.206424 | + | 0.978463i | \(0.566183\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.25313 | + | 3.61025i | −0.329112 | + | 0.190013i | −0.655447 | − | 0.755241i | \(-0.727520\pi\) |
0.326335 | + | 0.945254i | \(0.394186\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.65003 | − | 9.78614i | −0.245654 | − | 0.425484i | 0.716662 | − | 0.697421i | \(-0.245669\pi\) |
−0.962315 | + | 0.271937i | \(0.912336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.0685 | + | 20.9032i | −0.482739 | + | 0.836129i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −46.3148 | −1.59706 | −0.798532 | − | 0.601953i | \(-0.794390\pi\) | ||||
−0.798532 | + | 0.601953i | \(0.794390\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.418333 | + | 0.241525i | 0.0134946 | + | 0.00779111i | 0.506732 | − | 0.862104i | \(-0.330853\pi\) |
−0.493238 | + | 0.869895i | \(0.664187\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.24065 | − | 2.14887i | −0.0335312 | − | 0.0580777i | 0.848773 | − | 0.528758i | \(-0.177342\pi\) |
−0.882304 | + | 0.470680i | \(0.844009\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 55.8520i | − | 1.36224i | −0.732170 | − | 0.681122i | \(-0.761492\pi\) | ||
0.732170 | − | 0.681122i | \(-0.238508\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 60.6786 | 1.41113 | 0.705566 | − | 0.708645i | \(-0.250693\pi\) | ||||
0.705566 | + | 0.708645i | \(0.250693\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 31.6850 | − | 18.2933i | 0.674149 | − | 0.389220i | −0.123498 | − | 0.992345i | \(-0.539411\pi\) |
0.797647 | + | 0.603125i | \(0.206078\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −14.2615 | + | 24.7016i | −0.269084 | + | 0.466068i | −0.968626 | − | 0.248524i | \(-0.920054\pi\) |
0.699541 | + | 0.714592i | \(0.253388\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00185i | 0.163670i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 81.4683 | + | 47.0358i | 1.38082 | + | 0.797216i | 0.992256 | − | 0.124206i | \(-0.0396383\pi\) |
0.388563 | + | 0.921422i | \(0.372972\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −95.4301 | + | 55.0966i | −1.56443 | + | 0.903223i | −0.567628 | + | 0.823285i | \(0.692139\pi\) |
−0.996800 | + | 0.0799382i | \(0.974528\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −7.42055 | − | 12.8528i | −0.114162 | − | 0.197735i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −41.0155 | + | 71.0409i | −0.612171 | + | 1.06031i | 0.378702 | + | 0.925518i | \(0.376370\pi\) |
−0.990874 | + | 0.134793i | \(0.956963\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −127.349 | −1.79365 | −0.896827 | − | 0.442382i | \(-0.854133\pi\) | ||||
−0.896827 | + | 0.442382i | \(0.854133\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 40.0577 | + | 23.1273i | 0.548735 | + | 0.316812i | 0.748612 | − | 0.663009i | \(-0.230721\pi\) |
−0.199877 | + | 0.979821i | \(0.564054\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −9.35016 | − | 16.1949i | −0.118356 | − | 0.204999i | 0.800760 | − | 0.598985i | \(-0.204429\pi\) |
−0.919116 | + | 0.393986i | \(0.871096\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 59.6357i | 0.718502i | 0.933241 | + | 0.359251i | \(0.116968\pi\) | ||||
−0.933241 | + | 0.359251i | \(0.883032\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.80632 | −0.115368 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −61.5988 | + | 35.5641i | −0.692121 | + | 0.399596i | −0.804406 | − | 0.594080i | \(-0.797516\pi\) |
0.112285 | + | 0.993676i | \(0.464183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.35393 | − | 5.80917i | 0.0353045 | − | 0.0611492i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 102.239i | 1.05401i | 0.849861 | + | 0.527007i | \(0.176686\pi\) | ||||
−0.849861 | + | 0.527007i | \(0.823314\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 94.3357 | + | 54.4647i | 0.934017 | + | 0.539255i | 0.888080 | − | 0.459690i | \(-0.152039\pi\) |
0.0459371 | + | 0.998944i | \(0.485373\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.647083 | − | 0.373594i | 0.00628236 | − | 0.00362712i | −0.496856 | − | 0.867833i | \(-0.665512\pi\) |
0.503138 | + | 0.864206i | \(0.332179\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 7.64630 | + | 13.2438i | 0.0714608 | + | 0.123774i | 0.899542 | − | 0.436835i | \(-0.143901\pi\) |
−0.828081 | + | 0.560609i | \(0.810567\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 27.1116 | − | 46.9587i | 0.248730 | − | 0.430814i | −0.714443 | − | 0.699693i | \(-0.753320\pi\) |
0.963174 | + | 0.268879i | \(0.0866533\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −65.2511 | −0.577444 | −0.288722 | − | 0.957413i | \(-0.593230\pi\) | ||||
−0.288722 | + | 0.957413i | \(0.593230\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.09136 | + | 5.24890i | 0.0790553 | + | 0.0456426i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 13.5539 | + | 23.4761i | 0.112016 | + | 0.194017i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 45.6484i | − | 0.365187i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −235.761 | −1.85639 | −0.928193 | − | 0.372098i | \(-0.878639\pi\) | ||||
−0.928193 | + | 0.372098i | \(0.878639\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −196.180 | + | 113.265i | −1.49756 | + | 0.864616i | −0.999996 | − | 0.00281117i | \(-0.999105\pi\) |
−0.497563 | + | 0.867428i | \(0.665772\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −126.872 | + | 219.748i | −0.926070 | + | 1.60400i | −0.136238 | + | 0.990676i | \(0.543501\pi\) |
−0.789832 | + | 0.613323i | \(0.789832\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 148.040i | − | 1.06503i | −0.846419 | − | 0.532517i | \(-0.821246\pi\) | ||
0.846419 | − | 0.532517i | \(-0.178754\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 134.058 | + | 77.3986i | 0.937471 | + | 0.541249i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 37.2622 | − | 21.5133i | 0.256980 | − | 0.148368i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −122.732 | − | 212.579i | −0.823708 | − | 1.42670i | −0.902903 | − | 0.429845i | \(-0.858568\pi\) |
0.0791950 | − | 0.996859i | \(-0.474765\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −88.1270 | + | 152.640i | −0.583623 | + | 1.01086i | 0.411423 | + | 0.911445i | \(0.365032\pi\) |
−0.995046 | + | 0.0994194i | \(0.968301\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.448754 | −0.00289519 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 179.836 | + | 103.828i | 1.14545 | + | 0.661326i | 0.947774 | − | 0.318942i | \(-0.103327\pi\) |
0.197675 | + | 0.980268i | \(0.436661\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −47.5121 | − | 82.2933i | −0.291485 | − | 0.504867i | 0.682676 | − | 0.730721i | \(-0.260816\pi\) |
−0.974161 | + | 0.225854i | \(0.927483\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 158.478i | 0.948972i | 0.880263 | + | 0.474486i | \(0.157366\pi\) | ||||
−0.880263 | + | 0.474486i | \(0.842634\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −86.2098 | −0.510117 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −187.054 | + | 107.995i | −1.08123 | + | 0.624251i | −0.931229 | − | 0.364434i | \(-0.881262\pi\) |
−0.150005 | + | 0.988685i | \(0.547929\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −131.029 | + | 226.950i | −0.732008 | + | 1.26787i | 0.224016 | + | 0.974585i | \(0.428083\pi\) |
−0.956024 | + | 0.293289i | \(0.905250\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 83.8554i | − | 0.463290i | −0.972800 | − | 0.231645i | \(-0.925589\pi\) | ||
0.972800 | − | 0.231645i | \(-0.0744107\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.99631 | + | 1.15257i | 0.0107909 | + | 0.00623011i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 88.5797 | − | 51.1415i | 0.473688 | − | 0.273484i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 116.846 | + | 202.384i | 0.611760 | + | 1.05960i | 0.990944 | + | 0.134278i | \(0.0428716\pi\) |
−0.379183 | + | 0.925322i | \(0.623795\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 111.819 | − | 193.677i | 0.579375 | − | 1.00351i | −0.416176 | − | 0.909284i | \(-0.636630\pi\) |
0.995551 | − | 0.0942227i | \(-0.0300366\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 133.006 | 0.675158 | 0.337579 | − | 0.941297i | \(-0.390392\pi\) | ||||
0.337579 | + | 0.941297i | \(0.390392\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 52.5277 | + | 30.3269i | 0.263959 | + | 0.152397i | 0.626139 | − | 0.779711i | \(-0.284634\pi\) |
−0.362180 | + | 0.932108i | \(0.617968\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 25.9433 | + | 44.9352i | 0.126553 | + | 0.219196i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 69.9651i | 0.334761i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −169.145 | −0.801637 | −0.400819 | − | 0.916157i | \(-0.631274\pi\) | ||||
−0.400819 | + | 0.916157i | \(0.631274\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −48.8184 | + | 28.1853i | −0.227062 | + | 0.131095i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −84.3155 | + | 146.039i | −0.381518 | + | 0.660809i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 162.093i | − | 0.726874i | −0.931619 | − | 0.363437i | \(-0.881603\pi\) | ||
0.931619 | − | 0.363437i | \(-0.118397\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 306.755 | + | 177.105i | 1.35134 | + | 0.780198i | 0.988438 | − | 0.151628i | \(-0.0484517\pi\) |
0.362905 | + | 0.931826i | \(0.381785\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −113.844 | + | 65.7279i | −0.497136 | + | 0.287021i | −0.727530 | − | 0.686076i | \(-0.759332\pi\) |
0.230394 | + | 0.973097i | \(0.425998\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −71.4744 | − | 123.797i | −0.306757 | − | 0.531319i | 0.670894 | − | 0.741553i | \(-0.265911\pi\) |
−0.977651 | + | 0.210234i | \(0.932577\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −16.9946 | + | 29.4354i | −0.0723173 | + | 0.125257i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −47.5259 | −0.198853 | −0.0994266 | − | 0.995045i | \(-0.531701\pi\) | ||||
−0.0994266 | + | 0.995045i | \(0.531701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 205.380 | + | 118.576i | 0.852198 | + | 0.492017i | 0.861392 | − | 0.507941i | \(-0.169593\pi\) |
−0.00919389 | + | 0.999958i | \(0.502927\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −57.6747 | − | 99.8955i | −0.233501 | − | 0.404435i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 309.248i | 1.23206i | 0.787722 | + | 0.616031i | \(0.211261\pi\) | ||||
−0.787722 | + | 0.616031i | \(0.788739\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −109.495 | −0.432788 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −155.317 | + | 89.6724i | −0.604347 | + | 0.348920i | −0.770750 | − | 0.637138i | \(-0.780118\pi\) |
0.166403 | + | 0.986058i | \(0.446785\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 37.3848 | − | 64.7523i | 0.142147 | − | 0.246206i | −0.786158 | − | 0.618026i | \(-0.787933\pi\) |
0.928305 | + | 0.371820i | \(0.121266\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 26.4979i | − | 0.0999921i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −49.2164 | − | 28.4151i | −0.182961 | − | 0.105632i | 0.405722 | − | 0.913996i | \(-0.367020\pi\) |
−0.588683 | + | 0.808364i | \(0.700353\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.6951 | − | 6.75218i | 0.0431554 | − | 0.0249158i | −0.478267 | − | 0.878214i | \(-0.658735\pi\) |
0.521422 | + | 0.853299i | \(0.325402\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 116.941 | + | 202.548i | 0.425240 | + | 0.736538i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 124.726 | − | 216.032i | 0.450274 | − | 0.779897i | −0.548129 | − | 0.836394i | \(-0.684660\pi\) |
0.998403 | + | 0.0564965i | \(0.0179930\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −200.268 | −0.712696 | −0.356348 | − | 0.934353i | \(-0.615978\pi\) | ||||
−0.356348 | + | 0.934353i | \(0.615978\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −59.5549 | − | 34.3840i | −0.210441 | − | 0.121498i | 0.391075 | − | 0.920359i | \(-0.372103\pi\) |
−0.601516 | + | 0.798860i | \(0.705437\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −88.7881 | − | 153.786i | −0.307225 | − | 0.532130i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 253.164i | − | 0.864040i | −0.901864 | − | 0.432020i | \(-0.857801\pi\) | ||
0.901864 | − | 0.432020i | \(-0.142199\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −87.3927 | −0.296247 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 156.336 | − | 90.2609i | 0.522864 | − | 0.301876i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 51.1849 | − | 88.6549i | 0.167819 | − | 0.290672i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 529.913i | 1.72610i | 0.505116 | + | 0.863051i | \(0.331450\pi\) | ||||
−0.505116 | + | 0.863051i | \(0.668550\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.4186 | + | 15.2528i | 0.0849473 | + | 0.0490444i | 0.541872 | − | 0.840461i | \(-0.317716\pi\) |
−0.456925 | + | 0.889505i | \(0.651049\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.44956 | − | 4.30101i | 0.0238005 | − | 0.0137412i | −0.488053 | − | 0.872814i | \(-0.662293\pi\) |
0.511853 | + | 0.859073i | \(0.328959\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −240.076 | − | 415.824i | −0.757337 | − | 1.31175i | −0.944204 | − | 0.329362i | \(-0.893167\pi\) |
0.186866 | − | 0.982385i | \(-0.440167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −224.391 | + | 388.656i | −0.703419 | + | 1.21836i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −76.2176 | −0.235968 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −333.935 | − | 192.797i | −1.02749 | − | 0.593223i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 44.5098 | + | 77.0932i | 0.134471 | + | 0.232910i | 0.925395 | − | 0.379004i | \(-0.123733\pi\) |
−0.790924 | + | 0.611914i | \(0.790400\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 76.2070i | − | 0.227484i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 495.701 | 1.47092 | 0.735461 | − | 0.677567i | \(-0.236966\pi\) | ||||
0.735461 | + | 0.677567i | \(0.236966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.05356 | − | 2.34032i | 0.0118873 | − | 0.00686312i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −30.1767 | + | 52.2676i | −0.0869645 | + | 0.150627i | −0.906227 | − | 0.422792i | \(-0.861050\pi\) |
0.819262 | + | 0.573419i | \(0.194383\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 72.2171i | − | 0.206926i | −0.994633 | − | 0.103463i | \(-0.967008\pi\) | ||
0.994633 | − | 0.103463i | \(-0.0329923\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −332.000 | − | 191.680i | −0.940510 | − | 0.543004i | −0.0503901 | − | 0.998730i | \(-0.516046\pi\) |
−0.890120 | + | 0.455726i | \(0.849380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 102.458 | − | 59.1540i | 0.288613 | − | 0.166631i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −40.0224 | − | 69.3209i | −0.111483 | − | 0.193094i | 0.804885 | − | 0.593430i | \(-0.202227\pi\) |
−0.916368 | + | 0.400336i | \(0.868893\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −154.432 | + | 267.485i | −0.427790 | + | 0.740954i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −42.9707 | −0.117728 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −70.5218 | − | 40.7158i | −0.192157 | − | 0.110942i | 0.400835 | − | 0.916150i | \(-0.368720\pi\) |
−0.592992 | + | 0.805208i | \(0.702054\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 266.126 | + | 460.944i | 0.713475 | + | 1.23577i | 0.963545 | + | 0.267547i | \(0.0862131\pi\) |
−0.250070 | + | 0.968228i | \(0.580454\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 739.893i | − | 1.96258i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 440.518 | 1.16232 | 0.581159 | − | 0.813790i | \(-0.302600\pi\) | ||||
0.581159 | + | 0.813790i | \(0.302600\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 605.603 | − | 349.645i | 1.58121 | − | 0.912911i | 0.586525 | − | 0.809931i | \(-0.300496\pi\) |
0.994683 | − | 0.102980i | \(-0.0328377\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 312.231 | − | 540.800i | 0.802650 | − | 1.39023i | −0.115216 | − | 0.993340i | \(-0.536756\pi\) |
0.917866 | − | 0.396891i | \(-0.129911\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 119.281i | − | 0.305065i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 15.0452 | + | 8.68632i | 0.0380890 | + | 0.0219907i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −547.801 | + | 316.273i | −1.37985 | + | 0.796658i | −0.992141 | − | 0.125123i | \(-0.960067\pi\) |
−0.387711 | + | 0.921781i | \(0.626734\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 233.671 | + | 404.731i | 0.582721 | + | 1.00930i | 0.995155 | + | 0.0983156i | \(0.0313455\pi\) |
−0.412434 | + | 0.910988i | \(0.635321\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.85842 | + | 6.68298i | −0.00957425 | + | 0.0165831i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −24.0434 | −0.0590746 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 280.848 | + | 162.148i | 0.686671 | + | 0.396450i | 0.802364 | − | 0.596835i | \(-0.203575\pi\) |
−0.115693 | + | 0.993285i | \(0.536909\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −27.7009 | − | 47.9793i | −0.0667491 | − | 0.115613i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.8211i | 0.0687854i | 0.999408 | + | 0.0343927i | \(0.0109497\pi\) | ||||
−0.999408 | + | 0.0343927i | \(0.989050\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.326830 | −0.000776319 | −0.000388160 | − | 1.00000i | \(-0.500124\pi\) | ||||
−0.000388160 | 1.00000i | \(0.500124\pi\) | ||||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −220.649 | + | 127.392i | −0.519174 | + | 0.299745i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 195.669 | − | 338.908i | 0.453988 | − | 0.786329i | −0.544642 | − | 0.838669i | \(-0.683334\pi\) |
0.998629 | + | 0.0523393i | \(0.0166677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 470.579i | 1.08679i | 0.839478 | + | 0.543394i | \(0.182861\pi\) | ||||
−0.839478 | + | 0.543394i | \(0.817139\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 70.6607 | + | 40.7960i | 0.161695 | + | 0.0933547i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 116.395 | − | 67.2006i | 0.265136 | − | 0.153077i | −0.361539 | − | 0.932357i | \(-0.617749\pi\) |
0.626675 | + | 0.779280i | \(0.284415\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 164.528 | + | 284.971i | 0.371395 | + | 0.643275i | 0.989780 | − | 0.142600i | \(-0.0455462\pi\) |
−0.618385 | + | 0.785875i | \(0.712213\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 33.0391 | − | 57.2254i | 0.0742452 | − | 0.128596i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −130.592 | −0.290851 | −0.145426 | − | 0.989369i | \(-0.546455\pi\) | ||||
−0.145426 | + | 0.989369i | \(0.546455\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −468.688 | − | 270.597i | −1.03922 | − | 0.599994i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −158.141 | − | 273.908i | −0.346041 | − | 0.599361i | 0.639501 | − | 0.768790i | \(-0.279141\pi\) |
−0.985542 | + | 0.169429i | \(0.945808\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.4853i | 0.0682979i | 0.999417 | + | 0.0341490i | \(0.0108721\pi\) | ||||
−0.999417 | + | 0.0341490i | \(0.989128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 667.424 | 1.44152 | 0.720761 | − | 0.693184i | \(-0.243793\pi\) | ||||
0.720761 | + | 0.693184i | \(0.243793\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 748.502 | − | 432.148i | 1.60279 | − | 0.925370i | 0.611861 | − | 0.790965i | \(-0.290421\pi\) |
0.990927 | − | 0.134405i | \(-0.0429122\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 293.982 | − | 509.192i | 0.621526 | − | 1.07651i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 174.281i | − | 0.366907i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −542.476 | − | 313.198i | −1.13252 | − | 0.653859i | −0.187950 | − | 0.982179i | \(-0.560184\pi\) |
−0.944567 | + | 0.328320i | \(0.893518\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 34.3289 | − | 19.8198i | 0.0713698 | − | 0.0412054i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −47.4904 | − | 82.2557i | −0.0979183 | − | 0.169599i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 242.924 | − | 420.756i | 0.498817 | − | 0.863976i | −0.501182 | − | 0.865342i | \(-0.667101\pi\) |
0.999999 | + | 0.00136550i | \(0.000434653\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6.00051 | 0.0122210 | 0.00611049 | − | 0.999981i | \(-0.498055\pi\) | ||||
0.00611049 | + | 0.999981i | \(0.498055\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −423.389 | − | 244.444i | −0.858801 | − | 0.495829i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 343.775 | + | 595.437i | 0.688929 | + | 1.19326i | 0.972185 | + | 0.234215i | \(0.0752520\pi\) |
−0.283256 | + | 0.959044i | \(0.591415\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 435.270i | 0.865348i | 0.901550 | + | 0.432674i | \(0.142430\pi\) | ||||
−0.901550 | + | 0.432674i | \(0.857570\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −101.196 | −0.200388 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 418.381 | − | 241.553i | 0.821967 | − | 0.474563i | −0.0291272 | − | 0.999576i | \(-0.509273\pi\) |
0.851094 | + | 0.525013i | \(0.175939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −0.347070 | + | 0.601142i | −0.000673921 | + | 0.00116727i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 354.517i | − | 0.685720i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −272.425 | − | 157.285i | −0.522888 | − | 0.301890i | 0.215227 | − | 0.976564i | \(-0.430951\pi\) |
−0.738116 | + | 0.674674i | \(0.764284\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 135.591 | − | 78.2835i | 0.259256 | − | 0.149682i | −0.364739 | − | 0.931110i | \(-0.618842\pi\) |
0.623995 | + | 0.781428i | \(0.285508\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.54947 | + | 4.41581i | 0.00483771 | + | 0.00837915i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 200.654 | − | 347.543i | 0.379309 | − | 0.656982i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 892.251 | 1.67402 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.3035 | − | 7.10344i | −0.0229972 | − | 0.0132775i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −386.033 | − | 668.628i | −0.713554 | − | 1.23591i | −0.963515 | − | 0.267656i | \(-0.913751\pi\) |
0.249960 | − | 0.968256i | \(-0.419582\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 50.3736i | 0.0924285i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 48.0113 | 0.0877721 | 0.0438860 | − | 0.999037i | \(-0.486026\pi\) | ||||
0.0438860 | + | 0.999037i | \(0.486026\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 289.613 | − | 167.208i | 0.525613 | − | 0.303463i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 75.7027 | − | 131.121i | 0.135911 | − | 0.235406i | −0.790034 | − | 0.613063i | \(-0.789937\pi\) |
0.925945 | + | 0.377658i | \(0.123270\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 969.359i | 1.73409i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −732.918 | − | 423.150i | −1.30181 | − | 0.751599i | −0.321094 | − | 0.947047i | \(-0.604051\pi\) |
−0.980714 | + | 0.195448i | \(0.937384\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 52.4972 | − | 30.3093i | 0.0929153 | − | 0.0536447i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −10.7887 | − | 18.6865i | −0.0189608 | − | 0.0328410i | 0.856389 | − | 0.516331i | \(-0.172702\pi\) |
−0.875350 | + | 0.483490i | \(0.839369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −141.623 | + | 245.298i | −0.248026 | + | 0.429593i | −0.962978 | − | 0.269580i | \(-0.913115\pi\) |
0.714952 | + | 0.699173i | \(0.246448\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 272.749 | 0.474346 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −406.431 | − | 234.653i | −0.704387 | − | 0.406678i | 0.104593 | − | 0.994515i | \(-0.466646\pi\) |
−0.808979 | + | 0.587837i | \(0.799979\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 138.191 | + | 239.353i | 0.237034 | + | 0.410555i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 554.500i | − | 0.944634i | −0.881429 | − | 0.472317i | \(-0.843418\pi\) | ||
0.881429 | − | 0.472317i | \(-0.156582\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.48785 | −0.00592165 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −707.094 | + | 408.241i | −1.19240 | + | 0.688433i | −0.958850 | − | 0.283912i | \(-0.908368\pi\) |
−0.233550 | + | 0.972345i | \(0.575034\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −434.341 | + | 752.301i | −0.725111 | + | 1.25593i | 0.233818 | + | 0.972280i | \(0.424878\pi\) |
−0.958928 | + | 0.283648i | \(0.908455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 705.861i | − | 1.17448i | −0.809413 | − | 0.587239i | \(-0.800215\pi\) | ||
0.809413 | − | 0.587239i | \(-0.199785\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.8093 | − | 12.5916i | −0.0360485 | − | 0.0208126i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 464.026 | − | 267.906i | 0.764458 | − | 0.441360i | −0.0664361 | − | 0.997791i | \(-0.521163\pi\) |
0.830894 | + | 0.556431i | \(0.187830\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 292.241 | + | 506.177i | 0.478300 | + | 0.828440i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 142.247 | − | 246.379i | 0.232050 | − | 0.401923i | −0.726361 | − | 0.687313i | \(-0.758790\pi\) |
0.958411 | + | 0.285390i | \(0.0921232\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 766.565 | 1.24241 | 0.621203 | − | 0.783650i | \(-0.286644\pi\) | ||||
0.621203 | + | 0.783650i | \(0.286644\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 470.257 | + | 271.503i | 0.759705 | + | 0.438616i | 0.829190 | − | 0.558967i | \(-0.188802\pi\) |
−0.0694849 | + | 0.997583i | \(0.522136\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −280.508 | − | 485.854i | −0.448813 | − | 0.777367i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 26.1920i | − | 0.0416408i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −967.080 | −1.53261 | −0.766307 | − | 0.642474i | \(-0.777908\pi\) | ||||
−0.766307 | + | 0.642474i | \(0.777908\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 189.679 | − | 109.511i | 0.298708 | − | 0.172459i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 489.512 | − | 847.860i | 0.763669 | − | 1.32271i | −0.177278 | − | 0.984161i | \(-0.556729\pi\) |
0.940947 | − | 0.338553i | \(-0.109937\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 991.244i | − | 1.54159i | −0.637081 | − | 0.770797i | \(-0.719858\pi\) | ||
0.637081 | − | 0.770797i | \(-0.280142\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1067.31 | − | 616.209i | −1.64962 | − | 0.952409i | −0.977222 | − | 0.212222i | \(-0.931930\pi\) |
−0.672400 | − | 0.740188i | \(-0.734736\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 789.412 | − | 455.767i | 1.21635 | − | 0.702260i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −390.535 | − | 676.426i | −0.598062 | − | 1.03587i | −0.993107 | − | 0.117212i | \(-0.962604\pi\) |
0.395045 | − | 0.918662i | \(-0.370729\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 105.223 | − | 182.252i | 0.160646 | − | 0.278247i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 549.328 | 0.833578 | 0.416789 | − | 0.909003i | \(-0.363155\pi\) | ||||
0.416789 | + | 0.909003i | \(0.363155\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −358.214 | − | 206.815i | −0.541927 | − | 0.312882i | 0.203932 | − | 0.978985i | \(-0.434628\pi\) |
−0.745860 | + | 0.666103i | \(0.767961\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 261.680 | + | 453.244i | 0.392324 | + | 0.679526i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1067.75i | 1.59128i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 553.924 | 0.823067 | 0.411533 | − | 0.911395i | \(-0.364993\pi\) | ||||
0.411533 | + | 0.911395i | \(0.364993\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 95.5972 | − | 55.1930i | 0.141207 | − | 0.0815259i | −0.427732 | − | 0.903906i | \(-0.640687\pi\) |
0.568939 | + | 0.822380i | \(0.307354\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −97.8156 | + | 169.422i | −0.143215 | + | 0.248055i | −0.928705 | − | 0.370818i | \(-0.879077\pi\) |
0.785491 | + | 0.618873i | \(0.212411\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 235.728i | − | 0.344129i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −394.615 | − | 227.831i | −0.572736 | − | 0.330669i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 574.132 | − | 331.475i | 0.830871 | − | 0.479703i | −0.0232799 | − | 0.999729i | \(-0.507411\pi\) |
0.854151 | + | 0.520025i | \(0.174078\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 68.7647 | + | 119.104i | 0.0989421 | + | 0.171373i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 294.780 | − | 510.573i | 0.422926 | − | 0.732530i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1236.29 | 1.76361 | 0.881807 | − | 0.471610i | \(-0.156327\pi\) | ||||
0.881807 | + | 0.471610i | \(0.156327\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.5159 | + | 8.95812i | 0.0220710 | + | 0.0127427i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 450.250 | + | 779.856i | 0.635050 | + | 1.09994i | 0.986505 | + | 0.163734i | \(0.0523537\pi\) |
−0.351455 | + | 0.936205i | \(0.614313\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 5.45848i | − | 0.00765566i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −143.807 | −0.201129 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −103.145 | + | 59.5509i | −0.143456 | + | 0.0828246i | −0.570010 | − | 0.821638i | \(-0.693061\pi\) |
0.426554 | + | 0.904462i | \(0.359727\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 558.950 | − | 968.129i | 0.770965 | − | 1.33535i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 815.672i | 1.12197i | 0.827826 | + | 0.560985i | \(0.189577\pi\) | ||||
−0.827826 | + | 0.560985i | \(0.810423\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 554.696 | + | 320.254i | 0.758819 | + | 0.438104i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 193.766 | − | 111.871i | 0.264346 | − | 0.152620i | −0.361969 | − | 0.932190i | \(-0.617896\pi\) |
0.626316 | + | 0.779570i | \(0.284562\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 397.432 | + | 688.372i | 0.539256 | + | 0.934019i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 636.897 | − | 1103.14i | 0.861836 | − | 1.49274i | −0.00831892 | − | 0.999965i | \(-0.502648\pi\) |
0.870155 | − | 0.492778i | \(-0.164019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 204.339 | 0.275019 | 0.137510 | − | 0.990500i | \(-0.456090\pi\) | ||||
0.137510 | + | 0.990500i | \(0.456090\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 197.486 | + | 114.019i | 0.265082 | + | 0.153045i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 193.280 | + | 334.770i | 0.257363 | + | 0.445766i | 0.965535 | − | 0.260275i | \(-0.0838131\pi\) |
−0.708172 | + | 0.706040i | \(0.750480\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 163.741i | − | 0.216875i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1254.03 | −1.65658 | −0.828290 | − | 0.560300i | \(-0.810686\pi\) | ||||
−0.828290 | + | 0.560300i | \(0.810686\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −702.009 | + | 405.305i | −0.922483 | + | 0.532596i | −0.884426 | − | 0.466680i | \(-0.845450\pi\) |
−0.0380564 | + | 0.999276i | \(0.512117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −751.410 | + | 1301.48i | −0.979674 | + | 1.69684i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1338.07i | − | 1.74002i | −0.493036 | − | 0.870009i | \(-0.664113\pi\) | ||
0.493036 | − | 0.870009i | \(-0.335887\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 446.977 | + | 258.062i | 0.578236 | + | 0.333845i | 0.760432 | − | 0.649417i | \(-0.224987\pi\) |
−0.182196 | + | 0.983262i | \(0.558320\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −10.0973 | + | 5.82967i | −0.0130287 | + | 0.00752215i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 201.639 | + | 349.250i | 0.258844 | + | 0.448331i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −616.995 | + | 1068.67i | −0.790006 | + | 1.36833i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −192.913 | −0.245749 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1302.69 | + | 752.107i | 1.65526 | + | 0.955663i | 0.974860 | + | 0.222819i | \(0.0715257\pi\) |
0.680396 | + | 0.732844i | \(0.261808\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −880.184 | − | 1524.52i | −1.10994 | − | 1.92248i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 147.647i | 0.185254i | 0.995701 | + | 0.0926268i | \(0.0295263\pi\) | ||||
−0.995701 | + | 0.0926268i | \(0.970474\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 386.200 | 0.483354 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 388.151 | − | 224.099i | 0.483375 | − | 0.279077i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 85.5922 | − | 148.250i | 0.105800 | − | 0.183251i | −0.808265 | − | 0.588819i | \(-0.799593\pi\) |
0.914065 | + | 0.405568i | \(0.132926\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 668.261i | 0.823997i | 0.911185 | + | 0.411998i | \(0.135169\pi\) | ||||
−0.911185 | + | 0.411998i | \(0.864831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 76.4507 | + | 44.1388i | 0.0938046 | + | 0.0541581i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −379.431 | + | 219.065i | −0.464420 | + | 0.268133i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −8.32054 | − | 14.4116i | −0.0101346 | − | 0.0175537i | 0.860914 | − | 0.508751i | \(-0.169893\pi\) |
−0.871048 | + | 0.491197i | \(0.836559\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 155.347 | − | 269.070i | 0.188758 | − | 0.326938i | −0.756079 | − | 0.654481i | \(-0.772887\pi\) |
0.944836 | + | 0.327543i | \(0.106221\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −139.891 | −0.169155 | −0.0845777 | − | 0.996417i | \(-0.526954\pi\) | ||||
−0.0845777 | + | 0.996417i | \(0.526954\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1249.13 | − | 721.184i | −1.50679 | − | 0.869944i | −0.999969 | − | 0.00789201i | \(-0.997488\pi\) |
−0.506819 | − | 0.862052i | \(-0.669179\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −73.6134 | − | 127.502i | −0.0881598 | − | 0.152697i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 657.634i | 0.783831i | 0.920001 | + | 0.391915i | \(0.128187\pi\) | ||||
−0.920001 | + | 0.391915i | \(0.871813\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1304.06 | 1.55061 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 69.3592 | − | 40.0446i | 0.0820819 | − | 0.0473900i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.0195 | + | 24.2824i | −0.0164741 | + | 0.0285340i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 121.230i | − | 0.142122i | −0.997472 | − | 0.0710609i | \(-0.977362\pi\) | ||
0.997472 | − | 0.0710609i | \(-0.0226385\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1078.70 | − | 622.790i | −1.25870 | − | 0.726710i | −0.285876 | − | 0.958266i | \(-0.592285\pi\) |
−0.972821 | + | 0.231557i | \(0.925618\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −675.130 | + | 389.787i | −0.785949 | + | 0.453768i | −0.838534 | − | 0.544849i | \(-0.816587\pi\) |
0.0525855 | + | 0.998616i | \(0.483254\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −420.375 | − | 728.111i | −0.487109 | − | 0.843697i | 0.512781 | − | 0.858519i | \(-0.328615\pi\) |
−0.999890 | + | 0.0148220i | \(0.995282\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 100.328 | − | 173.773i | 0.115986 | − | 0.200894i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −181.202 | −0.208518 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1134.90 | − | 655.234i | −1.30298 | − | 0.752278i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 737.122 | + | 1276.73i | 0.840504 | + | 1.45580i | 0.889469 | + | 0.456995i | \(0.151074\pi\) |
−0.0489658 | + | 0.998800i | \(0.515593\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 583.982i | 0.662863i | 0.943479 | + | 0.331431i | \(0.107532\pi\) | ||||
−0.943479 | + | 0.331431i | \(0.892468\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1226.32 | −1.38882 | −0.694408 | − | 0.719581i | \(-0.744334\pi\) | ||||
−0.694408 | + | 0.719581i | \(0.744334\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 431.607 | − | 249.188i | 0.486591 | − | 0.280934i | −0.236568 | − | 0.971615i | \(-0.576023\pi\) |
0.723159 | + | 0.690681i | \(0.242689\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −132.087 | + | 228.781i | −0.147914 | + | 0.256194i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 243.453i | − | 0.272015i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.3750 | − | 11.1862i | −0.0215517 | − | 0.0124429i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −260.744 | + | 150.540i | −0.289394 | + | 0.167081i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 38.9510 | + | 67.4651i | 0.0430398 | + | 0.0745470i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −36.9123 | + | 63.9339i | −0.0406971 | + | 0.0704895i | −0.885656 | − | 0.464341i | \(-0.846291\pi\) |
0.844959 | + | 0.534830i | \(0.179625\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1102.46 | −1.21017 | −0.605084 | − | 0.796162i | \(-0.706860\pi\) | ||||
−0.605084 | + | 0.796162i | \(0.706860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 500.439 | + | 288.929i | 0.548126 | + | 0.316461i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −491.086 | − | 850.586i | −0.534370 | − | 0.925556i | −0.999194 | − | 0.0401527i | \(-0.987216\pi\) |
0.464823 | − | 0.885403i | \(-0.346118\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2034.44i | − | 2.20416i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 59.8912 | 0.0647472 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −561.889 | + | 324.407i | −0.604832 | + | 0.349200i | −0.770940 | − | 0.636908i | \(-0.780213\pi\) |
0.166108 | + | 0.986108i | \(0.446880\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −47.5106 | + | 82.2908i | −0.0508135 | + | 0.0880116i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1348.17i | 1.43881i | 0.694590 | + | 0.719406i | \(0.255586\pi\) | ||||
−0.694590 | + | 0.719406i | \(0.744414\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1028.20 | + | 593.631i | 1.09267 | + | 0.630851i | 0.934285 | − | 0.356527i | \(-0.116039\pi\) |
0.158381 | + | 0.987378i | \(0.449373\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −546.575 | + | 315.565i | −0.579613 | + | 0.334640i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −66.2820 | − | 114.804i | −0.0699915 | − | 0.121229i | 0.828906 | − | 0.559388i | \(-0.188964\pi\) |
−0.898897 | + | 0.438159i | \(0.855631\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −369.465 | + | 639.932i | −0.389321 | + | 0.674323i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1521.99 | −1.59705 | −0.798524 | − | 0.601963i | \(-0.794385\pi\) | ||||
−0.798524 | + | 0.601963i | \(0.794385\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −188.015 | − | 108.550i | −0.196874 | − | 0.113665i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −480.383 | − | 832.048i | −0.499879 | − | 0.865815i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 207.761i | 0.215296i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 645.014 | 0.667026 | 0.333513 | − | 0.942746i | \(-0.391766\pi\) | ||||
0.333513 | + | 0.942746i | \(0.391766\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1394.17 | − | 804.924i | 1.43581 | − | 0.828964i | 0.438253 | − | 0.898851i | \(-0.355597\pi\) |
0.997555 | + | 0.0698871i | \(0.0222639\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −127.572 | + | 220.960i | −0.130575 | + | 0.226162i | −0.923898 | − | 0.382638i | \(-0.875016\pi\) |
0.793324 | + | 0.608800i | \(0.208349\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 689.217i | 0.704001i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 417.370 | + | 240.969i | 0.424588 | + | 0.245136i | 0.697038 | − | 0.717034i | \(-0.254501\pi\) |
−0.272450 | + | 0.962170i | \(0.587834\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −107.009 | + | 61.7815i | −0.108638 | + | 0.0627224i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −342.836 | − | 593.810i | −0.346649 | − | 0.600414i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −563.108 | + | 975.331i | −0.568222 | + | 0.984189i | 0.428520 | + | 0.903532i | \(0.359035\pi\) |
−0.996742 | + | 0.0806568i | \(0.974298\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −56.3476 | −0.0566307 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 918.605 | + | 530.357i | 0.921369 | + | 0.531953i | 0.884072 | − | 0.467351i | \(-0.154792\pi\) |
0.0372976 | + | 0.999304i | \(0.488125\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 1764.3.z.l.325.2 | 8 | ||
3.2 | odd | 2 | 588.3.m.f.325.3 | 8 | |||
7.2 | even | 3 | 1764.3.z.m.901.3 | 8 | |||
7.3 | odd | 6 | 1764.3.d.h.685.6 | 8 | |||
7.4 | even | 3 | 1764.3.d.h.685.3 | 8 | |||
7.5 | odd | 6 | inner | 1764.3.z.l.901.2 | 8 | ||
7.6 | odd | 2 | 1764.3.z.m.325.3 | 8 | |||
21.2 | odd | 6 | 588.3.m.e.313.2 | 8 | |||
21.5 | even | 6 | 588.3.m.f.313.3 | 8 | |||
21.11 | odd | 6 | 588.3.d.c.97.3 | ✓ | 8 | ||
21.17 | even | 6 | 588.3.d.c.97.6 | yes | 8 | ||
21.20 | even | 2 | 588.3.m.e.325.2 | 8 | |||
84.11 | even | 6 | 2352.3.f.j.97.7 | 8 | |||
84.59 | odd | 6 | 2352.3.f.j.97.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.d.c.97.3 | ✓ | 8 | 21.11 | odd | 6 | ||
588.3.d.c.97.6 | yes | 8 | 21.17 | even | 6 | ||
588.3.m.e.313.2 | 8 | 21.2 | odd | 6 | |||
588.3.m.e.325.2 | 8 | 21.20 | even | 2 | |||
588.3.m.f.313.3 | 8 | 21.5 | even | 6 | |||
588.3.m.f.325.3 | 8 | 3.2 | odd | 2 | |||
1764.3.d.h.685.3 | 8 | 7.4 | even | 3 | |||
1764.3.d.h.685.6 | 8 | 7.3 | odd | 6 | |||
1764.3.z.l.325.2 | 8 | 1.1 | even | 1 | trivial | ||
1764.3.z.l.901.2 | 8 | 7.5 | odd | 6 | inner | ||
1764.3.z.m.325.3 | 8 | 7.6 | odd | 2 | |||
1764.3.z.m.901.3 | 8 | 7.2 | even | 3 | |||
2352.3.f.j.97.2 | 8 | 84.59 | odd | 6 | |||
2352.3.f.j.97.7 | 8 | 84.11 | even | 6 |