Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,3,Mod(557,1764)]
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, 3, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.557");
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.bk (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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 16.0.329365073333488765586374656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 199x^{12} + 24960x^{8} - 2913559x^{4} + 214358881 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1745.1 | ||
Root | \(-0.365632 - 3.29641i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1745 |
Dual form | 1764.3.bk.g.557.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(5\) | −8.27698 | − | 4.77872i | −1.65540 | − | 0.955744i | −0.974798 | − | 0.223087i | \(-0.928387\pi\) |
−0.680598 | − | 0.732657i | \(-0.738280\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8.03119 | + | 4.63681i | −0.730108 | + | 0.421528i | −0.818462 | − | 0.574561i | \(-0.805173\pi\) |
0.0883536 | + | 0.996089i | \(0.471839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.24264 | 0.326357 | 0.163178 | − | 0.986597i | \(-0.447825\pi\) | ||||
0.163178 | + | 0.986597i | \(0.447825\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 13.4731 | − | 7.77872i | 0.792537 | − | 0.457572i | −0.0483176 | − | 0.998832i | \(-0.515386\pi\) |
0.840855 | + | 0.541260i | \(0.182053\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −17.4460 | + | 30.2173i | −0.918209 | + | 1.59038i | −0.116074 | + | 0.993241i | \(0.537031\pi\) |
−0.802135 | + | 0.597143i | \(0.796302\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −15.3797 | − | 8.87945i | −0.668681 | − | 0.386063i | 0.126896 | − | 0.991916i | \(-0.459499\pi\) |
−0.795577 | + | 0.605853i | \(0.792832\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 33.1723 | + | 57.4561i | 1.32689 | + | 2.29825i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26.2442i | 0.904972i | 0.891772 | + | 0.452486i | \(0.149463\pi\) | ||||
−0.891772 | + | 0.452486i | \(0.850537\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −16.0317 | − | 27.7678i | −0.517153 | − | 0.895736i | −0.999802 | − | 0.0199213i | \(-0.993658\pi\) |
0.482648 | − | 0.875814i | \(-0.339675\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −27.6723 | + | 47.9299i | −0.747900 | + | 1.29540i | 0.200927 | + | 0.979606i | \(0.435605\pi\) |
−0.948827 | + | 0.315795i | \(0.897729\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 38.4426i | − | 0.937623i | −0.883298 | − | 0.468812i | \(-0.844682\pi\) | ||
0.883298 | − | 0.468812i | \(-0.155318\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 29.3446 | 0.682433 | 0.341217 | − | 0.939985i | \(-0.389161\pi\) | ||||
0.341217 | + | 0.939985i | \(0.389161\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −59.0887 | − | 34.1149i | −1.25721 | − | 0.725848i | −0.284676 | − | 0.958624i | \(-0.591886\pi\) |
−0.972531 | + | 0.232775i | \(0.925219\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.943355 | − | 0.544646i | 0.0177991 | − | 0.0102763i | −0.491074 | − | 0.871118i | \(-0.663396\pi\) |
0.508873 | + | 0.860842i | \(0.330062\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 88.6320 | 1.61149 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 59.0887 | − | 34.1149i | 1.00150 | − | 0.578218i | 0.0928106 | − | 0.995684i | \(-0.470415\pi\) |
0.908693 | + | 0.417466i | \(0.137082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 23.8099 | − | 41.2400i | 0.390327 | − | 0.676066i | −0.602166 | − | 0.798371i | \(-0.705695\pi\) |
0.992493 | + | 0.122305i | \(0.0390288\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −35.1163 | − | 20.2744i | −0.540250 | − | 0.311914i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.32768 | + | 7.49577i | 0.0645923 | + | 0.111877i | 0.896513 | − | 0.443017i | \(-0.146092\pi\) |
−0.831921 | + | 0.554894i | \(0.812759\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 95.7031i | 1.34793i | 0.738763 | + | 0.673966i | \(0.235410\pi\) | ||||
−0.738763 | + | 0.673966i | \(0.764590\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 45.0231 | + | 77.9823i | 0.616755 | + | 1.06825i | 0.990074 | + | 0.140548i | \(0.0448865\pi\) |
−0.373319 | + | 0.927703i | \(0.621780\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74.3446 | − | 128.769i | 0.941071 | − | 1.62998i | 0.177639 | − | 0.984096i | \(-0.443154\pi\) |
0.763433 | − | 0.645887i | \(-0.223512\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 88.8851i | − | 1.07091i | −0.844565 | − | 0.535453i | \(-0.820141\pi\) | ||
0.844565 | − | 0.535453i | \(-0.179859\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −148.689 | −1.74929 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 66.0316 | + | 38.1234i | 0.741928 | + | 0.428352i | 0.822770 | − | 0.568375i | \(-0.192428\pi\) |
−0.0808420 | + | 0.996727i | \(0.525761\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 288.800 | − | 166.739i | 3.04000 | − | 1.75514i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.7519 | −0.131463 | −0.0657314 | − | 0.997837i | \(-0.520938\pi\) | ||||
−0.0657314 | + | 0.997837i | \(0.520938\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.64326 | + | 2.68079i | −0.0459729 | + | 0.0265425i | −0.522810 | − | 0.852449i | \(-0.675116\pi\) |
0.476837 | + | 0.878992i | \(0.341783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 68.3576 | − | 118.399i | 0.663667 | − | 1.14950i | −0.315979 | − | 0.948766i | \(-0.602333\pi\) |
0.979645 | − | 0.200738i | \(-0.0643339\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 129.182 | + | 74.5831i | 1.20731 | + | 0.697038i | 0.962170 | − | 0.272450i | \(-0.0878340\pi\) |
0.245136 | + | 0.969489i | \(0.421167\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −14.3446 | − | 24.8456i | −0.131602 | − | 0.227942i | 0.792692 | − | 0.609622i | \(-0.208679\pi\) |
−0.924294 | + | 0.381681i | \(0.875345\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 145.712i | − | 1.28949i | −0.764399 | − | 0.644743i | \(-0.776964\pi\) | ||
0.764399 | − | 0.644743i | \(-0.223036\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 84.8648 | + | 146.990i | 0.737955 | + | 1.27818i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.5000 | + | 30.3109i | −0.144628 | + | 0.250503i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 395.149i | − | 3.16119i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −119.345 | −0.939722 | −0.469861 | − | 0.882741i | \(-0.655696\pi\) | ||||
−0.469861 | + | 0.882741i | \(0.655696\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −83.1384 | − | 48.0000i | −0.634645 | − | 0.366412i | 0.147904 | − | 0.989002i | \(-0.452747\pi\) |
−0.782549 | + | 0.622590i | \(0.786081\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 149.018 | − | 86.0353i | 1.08772 | − | 0.627995i | 0.154751 | − | 0.987954i | \(-0.450542\pi\) |
0.932968 | + | 0.359958i | \(0.117209\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 211.205 | 1.51946 | 0.759731 | − | 0.650238i | \(-0.225331\pi\) | ||||
0.759731 | + | 0.650238i | \(0.225331\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −34.0735 | + | 19.6723i | −0.238276 | + | 0.137569i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 125.414 | − | 217.223i | 0.864921 | − | 1.49809i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −130.808 | − | 75.5219i | −0.877905 | − | 0.506859i | −0.00793782 | − | 0.999968i | \(-0.502527\pi\) |
−0.869967 | + | 0.493110i | \(0.835860\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.01695 | − | 10.4217i | −0.0398473 | − | 0.0690176i | 0.845414 | − | 0.534112i | \(-0.179354\pi\) |
−0.885261 | + | 0.465094i | \(0.846020\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 306.445i | 1.97706i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 80.3785 | + | 139.220i | 0.511965 | + | 0.886749i | 0.999904 | + | 0.0138712i | \(0.00441550\pi\) |
−0.487939 | + | 0.872878i | \(0.662251\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 129.017 | − | 223.464i | 0.791515 | − | 1.37094i | −0.133514 | − | 0.991047i | \(-0.542626\pi\) |
0.925029 | − | 0.379897i | \(-0.124041\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 107.838i | 0.645737i | 0.946444 | + | 0.322868i | \(0.104647\pi\) | ||||
−0.946444 | + | 0.322868i | \(0.895353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −151.000 | −0.893491 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −21.9344 | − | 12.6638i | −0.126789 | − | 0.0732014i | 0.435264 | − | 0.900303i | \(-0.356655\pi\) |
−0.562053 | + | 0.827101i | \(0.689988\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 48.5470 | − | 28.0286i | 0.271212 | − | 0.156584i | −0.358226 | − | 0.933635i | \(-0.616618\pi\) |
0.629438 | + | 0.777050i | \(0.283285\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 118.307 | 0.653627 | 0.326814 | − | 0.945089i | \(-0.394025\pi\) | ||||
0.326814 | + | 0.945089i | \(0.394025\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 458.087 | − | 264.476i | 2.47614 | − | 1.42960i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −72.1369 | + | 124.945i | −0.385759 | + | 0.668154i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −81.5159 | − | 47.0632i | −0.426785 | − | 0.246404i | 0.271191 | − | 0.962525i | \(-0.412582\pi\) |
−0.697976 | + | 0.716121i | \(0.745916\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 152.689 | + | 264.466i | 0.791136 | + | 1.37029i | 0.925264 | + | 0.379324i | \(0.123843\pi\) |
−0.134128 | + | 0.990964i | \(0.542823\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 369.483i | 1.87555i | 0.347249 | + | 0.937773i | \(0.387116\pi\) | ||||
−0.347249 | + | 0.937773i | \(0.612884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −134.374 | − | 232.743i | −0.675248 | − | 1.16956i | −0.976396 | − | 0.215986i | \(-0.930703\pi\) |
0.301149 | − | 0.953577i | \(-0.402630\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −183.706 | + | 318.188i | −0.896128 | + | 1.55214i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 323.574i | − | 1.54820i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 296.068 | 1.40316 | 0.701582 | − | 0.712588i | \(-0.252477\pi\) | ||||
0.701582 | + | 0.712588i | \(0.252477\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −242.885 | − | 140.230i | −1.12970 | − | 0.652231i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 57.1617 | − | 33.0023i | 0.258650 | − | 0.149332i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 298.934 | 1.34051 | 0.670256 | − | 0.742130i | \(-0.266184\pi\) | ||||
0.670256 | + | 0.742130i | \(0.266184\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −114.912 | + | 66.3446i | −0.506221 | + | 0.292267i | −0.731279 | − | 0.682078i | \(-0.761076\pi\) |
0.225058 | + | 0.974345i | \(0.427743\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −117.647 | + | 203.771i | −0.513744 | + | 0.889831i | 0.486129 | + | 0.873887i | \(0.338409\pi\) |
−0.999873 | + | 0.0159436i | \(0.994925\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 82.8813 | + | 47.8516i | 0.355714 | + | 0.205371i | 0.667199 | − | 0.744880i | \(-0.267493\pi\) |
−0.311485 | + | 0.950251i | \(0.600826\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 326.051 | + | 564.737i | 1.38745 | + | 2.40313i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 382.397i | − | 1.59999i | −0.600009 | − | 0.799994i | \(-0.704836\pi\) | ||
0.600009 | − | 0.799994i | \(-0.295164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.03490 | − | 6.98865i | −0.0167423 | − | 0.0289985i | 0.857533 | − | 0.514429i | \(-0.171996\pi\) |
−0.874275 | + | 0.485431i | \(0.838663\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −74.0169 | + | 128.201i | −0.299664 | + | 0.519033i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 216.264i | − | 0.861608i | −0.902445 | − | 0.430804i | \(-0.858230\pi\) | ||
0.902445 | − | 0.430804i | \(-0.141770\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 164.689 | 0.650946 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −250.056 | − | 144.370i | −0.972982 | − | 0.561751i | −0.0728377 | − | 0.997344i | \(-0.523205\pi\) |
−0.900144 | + | 0.435593i | \(0.856539\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −58.4279 | + | 33.7334i | −0.222159 | + | 0.128264i | −0.606950 | − | 0.794740i | \(-0.707607\pi\) |
0.384790 | + | 0.923004i | \(0.374274\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.4108 | −0.0392862 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 50.5834 | − | 29.2043i | 0.188042 | − | 0.108566i | −0.403023 | − | 0.915190i | \(-0.632041\pi\) |
0.591066 | + | 0.806623i | \(0.298707\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −69.3324 | + | 120.087i | −0.255839 | + | 0.443126i | −0.965123 | − | 0.261796i | \(-0.915685\pi\) |
0.709284 | + | 0.704923i | \(0.249018\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −532.826 | − | 307.627i | −1.93755 | − | 1.11865i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 64.3446 | + | 111.448i | 0.232291 | + | 0.402340i | 0.958482 | − | 0.285153i | \(-0.0920445\pi\) |
−0.726191 | + | 0.687493i | \(0.758711\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 225.534i | 0.802611i | 0.915944 | + | 0.401306i | \(0.131443\pi\) | ||||
−0.915944 | + | 0.401306i | \(0.868557\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.7651 | − | 20.3778i | −0.0415729 | − | 0.0720064i | 0.844490 | − | 0.535571i | \(-0.179904\pi\) |
−0.886063 | + | 0.463565i | \(0.846570\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −23.4831 | + | 40.6738i | −0.0812562 | + | 0.140740i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 301.855i | 1.03022i | 0.857124 | + | 0.515111i | \(0.172249\pi\) | ||||
−0.857124 | + | 0.515111i | \(0.827751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −652.102 | −2.21051 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −65.2504 | − | 37.6723i | −0.218229 | − | 0.125994i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −394.149 | + | 227.562i | −1.29229 | + | 0.746104i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −320.611 | −1.04434 | −0.522168 | − | 0.852843i | \(-0.674877\pi\) | ||||
−0.522168 | + | 0.852843i | \(0.674877\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 339.400 | − | 195.953i | 1.09132 | − | 0.630074i | 0.157392 | − | 0.987536i | \(-0.449691\pi\) |
0.933927 | + | 0.357463i | \(0.116358\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −199.648 | + | 345.800i | −0.637852 | + | 1.10479i | 0.348051 | + | 0.937476i | \(0.386844\pi\) |
−0.985903 | + | 0.167317i | \(0.946490\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 496.345 | + | 286.565i | 1.56576 | + | 0.903990i | 0.996655 | + | 0.0817216i | \(0.0260418\pi\) |
0.569101 | + | 0.822268i | \(0.307292\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −121.689 | − | 210.772i | −0.381471 | − | 0.660727i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 542.829i | 1.68058i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 140.738 | + | 243.766i | 0.433041 | + | 0.750048i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 211.345 | − | 366.060i | 0.638503 | − | 1.10592i | −0.347258 | − | 0.937770i | \(-0.612887\pi\) |
0.985761 | − | 0.168151i | \(-0.0537795\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 82.7232i | − | 0.246935i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 299.345 | 0.888263 | 0.444132 | − | 0.895962i | \(-0.353512\pi\) | ||||
0.444132 | + | 0.895962i | \(0.353512\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 257.508 | + | 148.672i | 0.755155 | + | 0.435989i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 367.908 | − | 212.412i | 1.06025 | − | 0.612137i | 0.134751 | − | 0.990880i | \(-0.456977\pi\) |
0.925502 | + | 0.378742i | \(0.123643\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 182.505 | 0.522938 | 0.261469 | − | 0.965212i | \(-0.415793\pi\) | ||||
0.261469 | + | 0.965212i | \(0.415793\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −182.875 | + | 105.583i | −0.518059 | + | 0.299102i | −0.736140 | − | 0.676829i | \(-0.763354\pi\) |
0.218081 | + | 0.975931i | \(0.430020\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 457.338 | − | 792.133i | 1.28828 | − | 2.23136i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −80.1504 | − | 46.2749i | −0.223260 | − | 0.128899i | 0.384199 | − | 0.923250i | \(-0.374478\pi\) |
−0.607459 | + | 0.794351i | \(0.707811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −428.223 | − | 741.704i | −1.18621 | − | 2.05458i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 860.612i | − | 2.35784i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −151.808 | − | 262.940i | −0.413646 | − | 0.716457i | 0.581639 | − | 0.813447i | \(-0.302412\pi\) |
−0.995285 | + | 0.0969905i | \(0.969078\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 173.723 | − | 300.897i | 0.465746 | − | 0.806695i | −0.533489 | − | 0.845807i | \(-0.679119\pi\) |
0.999235 | + | 0.0391117i | \(0.0124528\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 111.345i | 0.295344i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 233.379 | 0.615774 | 0.307887 | − | 0.951423i | \(-0.400378\pi\) | ||||
0.307887 | + | 0.951423i | \(0.400378\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 191.380 | + | 110.493i | 0.499687 | + | 0.288495i | 0.728584 | − | 0.684956i | \(-0.240179\pi\) |
−0.228897 | + | 0.973451i | \(0.573512\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 113.442 | − | 65.4959i | 0.291625 | − | 0.168370i | −0.347049 | − | 0.937847i | \(-0.612816\pi\) |
0.638675 | + | 0.769477i | \(0.279483\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −276.283 | −0.706606 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1230.70 | + | 710.544i | −3.11569 | + | 1.79885i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 98.3238 | − | 170.302i | 0.247667 | − | 0.428972i | −0.715211 | − | 0.698909i | \(-0.753669\pi\) |
0.962878 | + | 0.269937i | \(0.0870028\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 550.775 | + | 317.990i | 1.37350 | + | 0.792993i | 0.991368 | − | 0.131112i | \(-0.0418549\pi\) |
0.382137 | + | 0.924106i | \(0.375188\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −68.0169 | − | 117.809i | −0.168777 | − | 0.292330i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 513.245i | − | 1.26104i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.1236 | + | 60.8359i | 0.0858768 | + | 0.148743i | 0.905765 | − | 0.423781i | \(-0.139298\pi\) |
−0.819888 | + | 0.572524i | \(0.805964\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −424.757 | + | 735.701i | −1.02351 | + | 1.77277i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 436.196i | 1.04104i | 0.853849 | + | 0.520520i | \(0.174262\pi\) | ||||
−0.853849 | + | 0.520520i | \(0.825738\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.37852 | 0.0175262 | 0.00876309 | − | 0.999962i | \(-0.497211\pi\) | ||||
0.00876309 | + | 0.999962i | \(0.497211\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 893.870 | + | 516.076i | 2.10322 | + | 1.21430i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 173.595 | − | 100.225i | 0.402774 | − | 0.232542i | −0.284906 | − | 0.958555i | \(-0.591963\pi\) |
0.687680 | + | 0.726014i | \(0.258629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 454.106 | 1.04874 | 0.524372 | − | 0.851489i | \(-0.324300\pi\) | ||||
0.524372 | + | 0.851489i | \(0.324300\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 536.626 | − | 309.821i | 1.22798 | − | 0.708973i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 131.106 | − | 227.083i | 0.298648 | − | 0.517273i | −0.677179 | − | 0.735818i | \(-0.736798\pi\) |
0.975827 | + | 0.218545i | \(0.0701311\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −201.499 | − | 116.336i | −0.454852 | − | 0.262609i | 0.255025 | − | 0.966934i | \(-0.417916\pi\) |
−0.709877 | + | 0.704326i | \(0.751250\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −364.362 | − | 631.093i | −0.818790 | − | 1.41819i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 92.0197i | 0.204944i | 0.994736 | + | 0.102472i | \(0.0326752\pi\) | ||||
−0.994736 | + | 0.102472i | \(0.967325\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 178.251 | + | 308.739i | 0.395235 | + | 0.684566i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 347.412 | − | 601.736i | 0.760202 | − | 1.31671i | −0.182544 | − | 0.983198i | \(-0.558433\pi\) |
0.942746 | − | 0.333511i | \(-0.108233\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 432.476i | 0.938127i | 0.883164 | + | 0.469063i | \(0.155408\pi\) | ||||
−0.883164 | + | 0.469063i | \(0.844592\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −310.169 | −0.669912 | −0.334956 | − | 0.942234i | \(-0.608722\pi\) | ||||
−0.334956 | + | 0.942234i | \(0.608722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 360.097 | + | 207.902i | 0.771086 | + | 0.445186i | 0.833262 | − | 0.552879i | \(-0.186471\pi\) |
−0.0621762 | + | 0.998065i | \(0.519804\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −235.672 | + | 136.065i | −0.498250 | + | 0.287665i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2314.89 | −4.87346 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −247.993 | + | 143.179i | −0.517731 | + | 0.298912i | −0.736006 | − | 0.676975i | \(-0.763290\pi\) |
0.218275 | + | 0.975887i | \(0.429957\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −117.404 | + | 203.349i | −0.244083 | + | 0.422763i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 105.547 | + | 60.9377i | 0.217623 | + | 0.125645i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −242.706 | − | 420.379i | −0.498370 | − | 0.863202i | 0.501628 | − | 0.865083i | \(-0.332735\pi\) |
−0.999998 | + | 0.00188110i | \(0.999401\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 138.130i | − | 0.281323i | −0.990058 | − | 0.140661i | \(-0.955077\pi\) | ||
0.990058 | − | 0.140661i | \(-0.0449229\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 204.146 | + | 353.591i | 0.414089 | + | 0.717224i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 72.6723 | − | 125.872i | 0.145636 | − | 0.252249i | −0.783974 | − | 0.620794i | \(-0.786811\pi\) |
0.929610 | + | 0.368545i | \(0.120144\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 619.115i | 1.23084i | 0.788198 | + | 0.615422i | \(0.211015\pi\) | ||||
−0.788198 | + | 0.615422i | \(0.788985\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 51.2430 | 0.101471 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −200.851 | − | 115.961i | −0.394599 | − | 0.227822i | 0.289552 | − | 0.957162i | \(-0.406494\pi\) |
−0.684151 | + | 0.729340i | \(0.739827\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1131.59 | + | 653.324i | −2.19726 | + | 1.26859i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 632.737 | 1.22386 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 45.7558 | − | 26.4171i | 0.0878231 | − | 0.0507047i | −0.455445 | − | 0.890264i | \(-0.650520\pi\) |
0.543268 | + | 0.839559i | \(0.317187\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −28.3082 | + | 49.0313i | −0.0541266 | + | 0.0937501i | −0.891819 | − | 0.452392i | \(-0.850571\pi\) |
0.837693 | + | 0.546142i | \(0.183904\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −431.996 | − | 249.413i | −0.819727 | − | 0.473269i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −106.811 | − | 185.002i | −0.201911 | − | 0.349720i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 163.098i | − | 0.306000i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −712.824 | − | 1234.65i | −1.33238 | − | 2.30775i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −45.6215 | + | 79.0187i | −0.0843281 | + | 0.146060i | −0.905105 | − | 0.425189i | \(-0.860208\pi\) |
0.820777 | + | 0.571249i | \(0.193541\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 274.196i | 0.503112i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 356.825 | 0.652331 | 0.326165 | − | 0.945313i | \(-0.394243\pi\) | ||||
0.326165 | + | 0.945313i | \(0.394243\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −793.028 | − | 457.855i | −1.43925 | − | 0.830953i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −812.850 | + | 469.299i | −1.45934 | + | 0.842548i | −0.998979 | − | 0.0451859i | \(-0.985612\pi\) |
−0.460357 | + | 0.887734i | \(0.652279\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 124.499 | 0.222717 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −877.413 | + | 506.574i | −1.55846 | + | 0.899777i | −0.561055 | + | 0.827779i | \(0.689604\pi\) |
−0.997405 | + | 0.0719980i | \(0.977062\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −696.316 | + | 1206.06i | −1.23242 | + | 2.13461i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 837.689 | + | 483.640i | 1.47221 | + | 0.849982i | 0.999512 | − | 0.0312415i | \(-0.00994608\pi\) |
0.472700 | + | 0.881223i | \(0.343279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 315.757 | + | 546.907i | 0.552990 | + | 0.957806i | 0.998057 | + | 0.0623089i | \(0.0198464\pi\) |
−0.445067 | + | 0.895497i | \(0.646820\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1178.21i | − | 2.04906i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −307.176 | − | 532.044i | −0.532367 | − | 0.922087i | −0.999286 | − | 0.0377869i | \(-0.987969\pi\) |
0.466918 | − | 0.884300i | \(-0.345364\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.05084 | + | 8.74831i | −0.00866353 | + | 0.0150057i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 411.243i | 0.700584i | 0.936641 | + | 0.350292i | \(0.113918\pi\) | ||||
−0.936641 | + | 0.350292i | \(0.886082\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1118.76 | 1.89942 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −330.755 | − | 190.961i | −0.557765 | − | 0.322026i | 0.194483 | − | 0.980906i | \(-0.437697\pi\) |
−0.752248 | + | 0.658880i | \(0.771030\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −212.423 | + | 122.642i | −0.354629 | + | 0.204745i | −0.666722 | − | 0.745306i | \(-0.732303\pi\) |
0.312093 | + | 0.950052i | \(0.398970\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −168.243 | −0.279939 | −0.139970 | − | 0.990156i | \(-0.544700\pi\) | ||||
−0.139970 | + | 0.990156i | \(0.544700\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 289.694 | − | 167.255i | 0.478834 | − | 0.276455i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −279.183 | + | 483.560i | −0.459940 | + | 0.796639i | −0.998957 | − | 0.0456558i | \(-0.985462\pi\) |
0.539018 | + | 0.842294i | \(0.318796\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −250.692 | − | 144.737i | −0.410298 | − | 0.236886i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 130.085 | + | 225.313i | 0.212210 | + | 0.367559i | 0.952406 | − | 0.304833i | \(-0.0986006\pi\) |
−0.740196 | + | 0.672391i | \(0.765267\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 351.007i | 0.568893i | 0.958692 | + | 0.284447i | \(0.0918099\pi\) | ||||
−0.958692 | + | 0.284447i | \(0.908190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 158.903 | + | 275.229i | 0.256710 | + | 0.444634i | 0.965358 | − | 0.260927i | \(-0.0840283\pi\) |
−0.708649 | + | 0.705561i | \(0.750695\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1059.00 | + | 1834.24i | −1.69440 | + | 2.93478i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 861.021i | 1.36887i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 297.966 | 0.472213 | 0.236106 | − | 0.971727i | \(-0.424129\pi\) | ||||
0.236106 | + | 0.971727i | \(0.424129\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 987.814 | + | 570.314i | 1.55561 | + | 0.898133i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −659.835 | + | 380.956i | −1.02938 | + | 0.594315i | −0.916808 | − | 0.399328i | \(-0.869244\pi\) |
−0.112576 | + | 0.993643i | \(0.535910\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −21.5808 | −0.0335626 | −0.0167813 | − | 0.999859i | \(-0.505342\pi\) | ||||
−0.0167813 | + | 0.999859i | \(0.505342\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −90.5462 | + | 52.2768i | −0.139948 | + | 0.0807988i | −0.568339 | − | 0.822794i | \(-0.692414\pi\) |
0.428391 | + | 0.903593i | \(0.359080\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −316.368 | + | 547.966i | −0.487471 | + | 0.844324i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 311.528 | + | 179.861i | 0.477072 | + | 0.275438i | 0.719195 | − | 0.694808i | \(-0.244511\pi\) |
−0.242123 | + | 0.970245i | \(0.577844\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 458.757 | + | 794.591i | 0.700392 | + | 1.21312i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 983.046i | 1.49172i | 0.666100 | + | 0.745862i | \(0.267962\pi\) | ||||
−0.666100 | + | 0.745862i | \(0.732038\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −255.813 | − | 443.081i | −0.387009 | − | 0.670319i | 0.605037 | − | 0.796197i | \(-0.293158\pi\) |
−0.992046 | + | 0.125879i | \(0.959825\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 233.034 | − | 403.627i | 0.349376 | − | 0.605137i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 441.608i | 0.658135i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −49.8644 | −0.0740928 | −0.0370464 | − | 0.999314i | \(-0.511795\pi\) | ||||
−0.0370464 | + | 0.999314i | \(0.511795\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 488.482 | + | 282.025i | 0.721540 | + | 0.416581i | 0.815319 | − | 0.579012i | \(-0.196562\pi\) |
−0.0937794 | + | 0.995593i | \(0.529895\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 114.683 | − | 66.2124i | 0.167911 | − | 0.0969434i | −0.413689 | − | 0.910418i | \(-0.635760\pi\) |
0.581600 | + | 0.813475i | \(0.302427\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1644.55 | −2.40081 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.00232 | − | 2.31074i | 0.00580888 | − | 0.00335376i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −551.056 | + | 954.457i | −0.797476 | + | 1.38127i | 0.123779 | + | 0.992310i | \(0.460499\pi\) |
−0.921255 | + | 0.388959i | \(0.872835\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1748.14 | − | 1009.29i | −2.51531 | − | 1.45222i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −299.034 | − | 517.942i | −0.429030 | − | 0.743102i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 302.130i | − | 0.430999i | −0.976504 | − | 0.215500i | \(-0.930862\pi\) | ||
0.976504 | − | 0.215500i | \(-0.0691380\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −965.540 | − | 1672.36i | −1.37346 | − | 2.37890i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.31074 | − | 10.9305i | 0.00890090 | − | 0.0154168i | −0.861541 | − | 0.507689i | \(-0.830500\pi\) |
0.870442 | + | 0.492272i | \(0.163833\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 569.412i | 0.798615i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 376.034 | 0.525922 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −657.840 | − | 379.804i | −0.914938 | − | 0.528239i | −0.0329210 | − | 0.999458i | \(-0.510481\pi\) |
−0.882016 | + | 0.471219i | \(0.843814\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1507.89 | + | 870.580i | −2.07985 | + | 1.20080i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 829.041 | 1.14036 | 0.570179 | − | 0.821520i | \(-0.306874\pi\) | ||||
0.570179 | + | 0.821520i | \(0.306874\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 395.364 | − | 228.264i | 0.540854 | − | 0.312262i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 677.260 | − | 1173.05i | 0.923957 | − | 1.60034i | 0.130727 | − | 0.991418i | \(-0.458269\pi\) |
0.793230 | − | 0.608922i | \(-0.208398\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −69.5129 | − | 40.1333i | −0.0943187 | − | 0.0544549i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −17.0169 | − | 29.4742i | −0.0230270 | − | 0.0398839i | 0.854282 | − | 0.519809i | \(-0.173997\pi\) |
−0.877309 | + | 0.479925i | \(0.840664\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 61.0163i | − | 0.0821215i | −0.999157 | − | 0.0410607i | \(-0.986926\pi\) | ||
0.999157 | − | 0.0410607i | \(-0.0130737\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 721.796 | + | 1250.19i | 0.968854 | + | 1.67810i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 70.0678 | − | 121.361i | 0.0932993 | − | 0.161599i | −0.815598 | − | 0.578619i | \(-0.803592\pi\) |
0.908898 | + | 0.417019i | \(0.136925\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 115.013i | 0.152335i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 518.000 | 0.684280 | 0.342140 | − | 0.939649i | \(-0.388848\pi\) | ||||
0.342140 | + | 0.939649i | \(0.388848\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 117.905 | + | 68.0725i | 0.154934 | + | 0.0894514i | 0.575463 | − | 0.817828i | \(-0.304822\pi\) |
−0.420528 | + | 0.907279i | \(0.638155\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 250.692 | − | 144.737i | 0.326848 | − | 0.188706i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −237.244 | −0.308510 | −0.154255 | − | 0.988031i | \(-0.549298\pi\) | ||||
−0.154255 | + | 0.988031i | \(0.549298\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 747.641 | − | 431.651i | 0.967194 | − | 0.558410i | 0.0688142 | − | 0.997629i | \(-0.478078\pi\) |
0.898380 | + | 0.439220i | \(0.144745\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1063.62 | − | 1842.24i | 1.37241 | − | 2.37709i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1161.63 | + | 670.667i | 1.49118 | + | 0.860934i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −443.757 | − | 768.610i | −0.568191 | − | 0.984135i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 1536.42i | − | 1.95723i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 382.421 | + | 662.372i | 0.485922 | + | 0.841642i | 0.999869 | − | 0.0161799i | \(-0.00515044\pi\) |
−0.513947 | + | 0.857822i | \(0.671817\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 101.017 | − | 174.966i | 0.127386 | − | 0.220639i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1413.60i | − | 1.77365i | −0.462106 | − | 0.886825i | \(-0.652906\pi\) | ||
0.462106 | − | 0.886825i | \(-0.347094\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1061.48 | −1.32851 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −723.178 | − | 417.527i | −0.900596 | − | 0.519959i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 624.645 | − | 360.639i | 0.772120 | − | 0.445784i | −0.0615102 | − | 0.998106i | \(-0.519592\pi\) |
0.833630 | + | 0.552323i | \(0.186258\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 928.795 | 1.14525 | 0.572623 | − | 0.819819i | \(-0.305926\pi\) | ||||
0.572623 | + | 0.819819i | \(0.305926\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −2135.74 | + | 1233.07i | −2.62054 | + | 1.51297i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −511.945 | + | 886.715i | −0.626616 | + | 1.08533i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 876.578 | + | 506.093i | 1.06770 | + | 0.616434i | 0.927551 | − | 0.373697i | \(-0.121910\pi\) |
0.140145 | + | 0.990131i | \(0.455243\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −665.791 | − | 1153.18i | −0.808980 | − | 1.40120i | −0.913571 | − | 0.406680i | \(-0.866686\pi\) |
0.104590 | − | 0.994515i | \(-0.466647\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 96.8217i | − | 0.117076i | −0.998285 | − | 0.0585379i | \(-0.981356\pi\) | ||
0.998285 | − | 0.0585379i | \(-0.0186438\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 137.422 | + | 238.023i | 0.165769 | + | 0.287120i | 0.936928 | − | 0.349522i | \(-0.113656\pi\) |
−0.771159 | + | 0.636642i | \(0.780323\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 515.328 | − | 892.574i | 0.617159 | − | 1.06895i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1196.53i | 1.42614i | 0.701091 | + | 0.713072i | \(0.252697\pi\) | ||||
−0.701091 | + | 0.713072i | \(0.747303\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 152.243 | 0.181026 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1249.82 | + | 721.587i | 1.47908 | + | 0.853949i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 851.182 | − | 491.430i | 1.00021 | − | 0.577473i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −761.454 | −0.892678 | −0.446339 | − | 0.894864i | \(-0.647272\pi\) | ||||
−0.446339 | + | 0.894864i | \(0.647272\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −177.030 | + | 102.208i | −0.206569 | + | 0.119263i | −0.599716 | − | 0.800213i | \(-0.704720\pi\) |
0.393147 | + | 0.919476i | \(0.371386\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.2244 | − | 48.8860i | 0.0328572 | − | 0.0569104i | −0.849129 | − | 0.528185i | \(-0.822873\pi\) |
0.881986 | + | 0.471275i | \(0.156206\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 768.748 | + | 443.837i | 0.890785 | + | 0.514295i | 0.874199 | − | 0.485567i | \(-0.161387\pi\) |
0.0165860 | + | 0.999862i | \(0.494720\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 121.034 | + | 209.637i | 0.139924 | + | 0.242355i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1378.89i | 1.58675i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18.3608 | + | 31.8019i | 0.0210801 | + | 0.0365119i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −38.5706 | + | 66.8063i | −0.0439802 | + | 0.0761759i | −0.887178 | − | 0.461428i | \(-0.847337\pi\) |
0.843197 | + | 0.537604i | \(0.180671\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 918.740i | − | 1.04284i | −0.853301 | − | 0.521419i | \(-0.825403\pi\) | ||
0.853301 | − | 0.521419i | \(-0.174597\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.72316 | 0.00761399 | 0.00380700 | − | 0.999993i | \(-0.498788\pi\) | ||||
0.00380700 | + | 0.999993i | \(0.498788\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 136.610 | + | 78.8719i | 0.154014 | + | 0.0889199i | 0.575026 | − | 0.818135i | \(-0.304992\pi\) |
−0.421013 | + | 0.907055i | \(0.638325\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2061.72 | − | 1190.33i | 2.30876 | − | 1.33296i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −535.763 | −0.598618 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 728.743 | − | 420.740i | 0.810615 | − | 0.468009i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.47330 | − | 14.6762i | 0.00940433 | − | 0.0162888i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −979.222 | − | 565.354i | −1.08201 | − | 0.624700i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −306.085 | − | 530.154i | −0.337469 | − | 0.584514i | 0.646487 | − | 0.762925i | \(-0.276238\pi\) |
−0.983956 | + | 0.178411i | \(0.942904\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 570.650i | − | 0.626399i | −0.949687 | − | 0.313200i | \(-0.898599\pi\) | ||
0.949687 | − | 0.313200i | \(-0.101401\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 412.143 | + | 713.853i | 0.451417 | + | 0.781876i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 633.463 | − | 1097.19i | 0.689296 | − | 1.19390i | −0.282770 | − | 0.959188i | \(-0.591253\pi\) |
0.972066 | − | 0.234708i | \(-0.0754135\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 406.034i | 0.439907i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3671.82 | −3.96953 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1192.81 | + | 688.668i | 1.28397 | + | 0.741300i | 0.977572 | − | 0.210604i | \(-0.0675430\pi\) |
0.306398 | + | 0.951904i | \(0.400876\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1194.15 | − | 689.444i | 1.27717 | − | 0.737373i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 754.751 | 0.805497 | 0.402748 | − | 0.915311i | \(-0.368055\pi\) | ||||
0.402748 | + | 0.915311i | \(0.368055\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −658.289 | + | 380.063i | −0.699563 | + | 0.403893i | −0.807185 | − | 0.590299i | \(-0.799010\pi\) |
0.107622 | + | 0.994192i | \(0.465676\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −341.349 | + | 591.233i | −0.361982 | + | 0.626971i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.0058 | − | 19.0559i | −0.0348531 | − | 0.0201224i | 0.482472 | − | 0.875911i | \(-0.339739\pi\) |
−0.517325 | + | 0.855789i | \(0.673072\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 191.017 | + | 330.851i | 0.201282 | + | 0.348631i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 1140.96i | − | 1.19723i | −0.801039 | − | 0.598613i | \(-0.795719\pi\) | ||
0.801039 | − | 0.598613i | \(-0.204281\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 449.804 | + | 779.083i | 0.470999 | + | 0.815794i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −33.5339 | + | 58.0824i | −0.0348948 | + | 0.0604395i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2918.64i | − | 3.02449i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1212.79 | 1.25418 | 0.627089 | − | 0.778947i | \(-0.284246\pi\) | ||||
0.627089 | + | 0.778947i | \(0.284246\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 411.462 | + | 237.557i | 0.423750 | + | 0.244652i | 0.696681 | − | 0.717381i | \(-0.254659\pi\) |
−0.272930 | + | 0.962034i | \(0.587993\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1156.85 | + | 667.908i | −1.18409 | + | 0.683632i | −0.956956 | − | 0.290233i | \(-0.906267\pi\) |
−0.227129 | + | 0.973865i | \(0.572934\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −707.083 | −0.722250 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −94.1799 | + | 54.3748i | −0.0958086 | + | 0.0553151i | −0.547139 | − | 0.837042i | \(-0.684283\pi\) |
0.451330 | + | 0.892357i | \(0.350950\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1765.65 | − | 3058.20i | 1.79254 | − | 3.10477i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −451.310 | − | 260.564i | −0.456330 | − | 0.263462i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −275.429 | − | 477.058i | −0.277931 | − | 0.481390i | 0.692940 | − | 0.720996i | \(-0.256315\pi\) |
−0.970870 | + | 0.239605i | \(0.922982\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2568.55i | 2.58145i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −35.7308 | − | 61.8876i | −0.0358384 | − | 0.0620739i | 0.847550 | − | 0.530716i | \(-0.178077\pi\) |
−0.883388 | + | 0.468642i | \(0.844743\pi\) | |||||||
\(998\) | 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.bk.g.1745.1 | 16 | ||
3.2 | odd | 2 | inner | 1764.3.bk.g.1745.8 | 16 | ||
7.2 | even | 3 | 1764.3.c.h.197.7 | yes | 8 | ||
7.3 | odd | 6 | inner | 1764.3.bk.g.557.2 | 16 | ||
7.4 | even | 3 | inner | 1764.3.bk.g.557.8 | 16 | ||
7.5 | odd | 6 | 1764.3.c.h.197.1 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 1764.3.bk.g.1745.7 | 16 | ||
21.2 | odd | 6 | 1764.3.c.h.197.2 | yes | 8 | ||
21.5 | even | 6 | 1764.3.c.h.197.8 | yes | 8 | ||
21.11 | odd | 6 | inner | 1764.3.bk.g.557.1 | 16 | ||
21.17 | even | 6 | inner | 1764.3.bk.g.557.7 | 16 | ||
21.20 | even | 2 | inner | 1764.3.bk.g.1745.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1764.3.c.h.197.1 | ✓ | 8 | 7.5 | odd | 6 | ||
1764.3.c.h.197.2 | yes | 8 | 21.2 | odd | 6 | ||
1764.3.c.h.197.7 | yes | 8 | 7.2 | even | 3 | ||
1764.3.c.h.197.8 | yes | 8 | 21.5 | even | 6 | ||
1764.3.bk.g.557.1 | 16 | 21.11 | odd | 6 | inner | ||
1764.3.bk.g.557.2 | 16 | 7.3 | odd | 6 | inner | ||
1764.3.bk.g.557.7 | 16 | 21.17 | even | 6 | inner | ||
1764.3.bk.g.557.8 | 16 | 7.4 | even | 3 | inner | ||
1764.3.bk.g.1745.1 | 16 | 1.1 | even | 1 | trivial | ||
1764.3.bk.g.1745.2 | 16 | 21.20 | even | 2 | inner | ||
1764.3.bk.g.1745.7 | 16 | 7.6 | odd | 2 | inner | ||
1764.3.bk.g.1745.8 | 16 | 3.2 | odd | 2 | inner |