Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,3,Mod(721,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("912.721");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.o (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.8502001097\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.219615408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 22x^{4} - 39x^{3} + 112x^{2} - 93x + 39 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 228) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 721.3 | ||
Root | \(0.500000 - 0.460304i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.721 |
Dual form | 912.3.o.c.721.6 |
$q$-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 \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.83539 | 1.16708 | 0.583539 | − | 0.812085i | \(-0.301668\pi\) | ||||
0.583539 | + | 0.812085i | \(0.301668\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.24085 | −0.748693 | −0.374347 | − | 0.927289i | \(-0.622133\pi\) | ||||
−0.374347 | + | 0.927289i | \(0.622133\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.24085 | −0.112805 | −0.0564023 | − | 0.998408i | \(-0.517963\pi\) | ||||
−0.0564023 | + | 0.998408i | \(0.517963\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 5.89843i | − | 0.453726i | −0.973927 | − | 0.226863i | \(-0.927153\pi\) | ||
0.973927 | − | 0.226863i | \(-0.0728469\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 10.1072i | − | 0.673813i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.57007 | −0.0923572 | −0.0461786 | − | 0.998933i | \(-0.514704\pi\) | ||||
−0.0461786 | + | 0.998933i | \(0.514704\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −10.6708 | − | 15.7205i | −0.561620 | − | 0.827395i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.07742i | 0.432258i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −27.5579 | −1.19817 | −0.599086 | − | 0.800685i | \(-0.704469\pi\) | ||||
−0.599086 | + | 0.800685i | \(0.704469\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.05177 | 0.362071 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 15.9159i | 0.548826i | 0.961612 | + | 0.274413i | \(0.0884835\pi\) | ||||
−0.961612 | + | 0.274413i | \(0.911517\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 53.2554i | − | 1.71792i | −0.512046 | − | 0.858958i | \(-0.671112\pi\) | ||
0.512046 | − | 0.858958i | \(-0.328888\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.14922i | 0.0651278i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −30.5824 | −0.873783 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.0175i | − | 0.270744i | −0.990795 | − | 0.135372i | \(-0.956777\pi\) | ||
0.990795 | − | 0.135372i | \(-0.0432229\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.2164 | −0.261959 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 69.8102i | − | 1.70269i | −0.524607 | − | 0.851344i | \(-0.675788\pi\) | ||
0.524607 | − | 0.851344i | \(-0.324212\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 52.9116 | 1.23050 | 0.615252 | − | 0.788331i | \(-0.289054\pi\) | ||||
0.615252 | + | 0.788331i | \(0.289054\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −17.5062 | −0.389026 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12.2135 | −0.259863 | −0.129931 | − | 0.991523i | \(-0.541476\pi\) | ||||
−0.129931 | + | 0.991523i | \(0.541476\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −21.5335 | −0.439459 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.71944i | 0.0533224i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 40.4288i | − | 0.762807i | −0.924409 | − | 0.381403i | \(-0.875441\pi\) | ||
0.924409 | − | 0.381403i | \(-0.124559\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.24085 | −0.131652 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −27.2287 | + | 18.4823i | −0.477697 | + | 0.324251i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 75.8194i | 1.28507i | 0.766255 | + | 0.642537i | \(0.222118\pi\) | ||||
−0.766255 | + | 0.642537i | \(0.777882\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −28.0275 | −0.459468 | −0.229734 | − | 0.973254i | \(-0.573786\pi\) | ||||
−0.229734 | + | 0.973254i | \(0.573786\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 15.7226 | 0.249564 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 34.4197i | − | 0.529533i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 47.3570i | − | 0.706820i | −0.935468 | − | 0.353410i | \(-0.885022\pi\) | ||
0.935468 | − | 0.353410i | \(-0.114978\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 47.7318i | 0.691765i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 56.3447i | 0.793588i | 0.917908 | + | 0.396794i | \(0.129877\pi\) | ||||
−0.917908 | + | 0.396794i | \(0.870123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −74.9363 | −1.02652 | −0.513262 | − | 0.858232i | \(-0.671563\pi\) | ||||
−0.513262 | + | 0.858232i | \(0.671563\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 15.6781i | − | 0.209042i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.50312 | 0.0844561 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 38.2585i | 0.484285i | 0.970241 | + | 0.242143i | \(0.0778502\pi\) | ||||
−0.970241 | + | 0.242143i | \(0.922150\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 42.6584 | 0.513957 | 0.256979 | − | 0.966417i | \(-0.417273\pi\) | ||||
0.256979 | + | 0.966417i | \(0.417273\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.16198 | −0.107788 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 27.5672 | 0.316865 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 24.5128i | − | 0.275425i | −0.990472 | − | 0.137712i | \(-0.956025\pi\) | ||
0.990472 | − | 0.137712i | \(-0.0439750\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 30.9128i | 0.339701i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −92.2411 | −0.991839 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −62.2682 | − | 91.7353i | −0.655454 | − | 0.965635i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.19999i | − | 0.0329896i | −0.999864 | − | 0.0164948i | \(-0.994749\pi\) | ||
0.999864 | − | 0.0164948i | \(-0.00525070\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.72255 | 0.0376016 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −67.7650 | −0.670941 | −0.335471 | − | 0.942051i | \(-0.608895\pi\) | ||||
−0.335471 | + | 0.942051i | \(0.608895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 50.0554i | 0.485975i | 0.970029 | + | 0.242987i | \(0.0781274\pi\) | ||||
−0.970029 | + | 0.242987i | \(0.921873\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 52.9703i | 0.504479i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 128.605i | − | 1.20192i | −0.799279 | − | 0.600960i | \(-0.794785\pi\) | ||
0.799279 | − | 0.600960i | \(-0.205215\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 40.9303i | − | 0.375508i | −0.982216 | − | 0.187754i | \(-0.939879\pi\) | ||
0.982216 | − | 0.187754i | \(-0.0601207\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.3508 | −0.156314 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 161.546i | − | 1.42961i | −0.699326 | − | 0.714803i | \(-0.746516\pi\) | ||
0.699326 | − | 0.714803i | \(-0.253484\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −160.811 | −1.39836 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 17.6953i | 0.151242i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.22851 | 0.0691472 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119.460 | −0.987275 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −120.915 | −0.983048 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −93.0641 | −0.744513 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 26.4617i | − | 0.208360i | −0.994558 | − | 0.104180i | \(-0.966778\pi\) | ||
0.994558 | − | 0.104180i | \(-0.0332218\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 91.6456i | − | 0.710431i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −23.7282 | −0.181132 | −0.0905658 | − | 0.995890i | \(-0.528868\pi\) | ||||
−0.0905658 | + | 0.995890i | \(0.528868\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 55.9240 | + | 82.3889i | 0.420481 | + | 0.619465i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 30.3216i | 0.224604i | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 127.778 | 0.932683 | 0.466342 | − | 0.884605i | \(-0.345572\pi\) | ||||
0.466342 | + | 0.884605i | \(0.345572\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −104.967 | −0.755156 | −0.377578 | − | 0.925978i | \(-0.623243\pi\) | ||||
−0.377578 | + | 0.925978i | \(0.623243\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 21.1545i | 0.150032i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.31908i | 0.0511824i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 92.8758i | 0.640522i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 37.2971i | 0.253722i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 144.372 | 0.968940 | 0.484470 | − | 0.874808i | \(-0.339012\pi\) | ||||
0.484470 | + | 0.874808i | \(0.339012\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 34.0021i | − | 0.225180i | −0.993642 | − | 0.112590i | \(-0.964085\pi\) | ||
0.993642 | − | 0.112590i | \(-0.0359146\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.71022 | 0.0307857 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 310.766i | − | 2.00494i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −167.385 | −1.06615 | −0.533073 | − | 0.846069i | \(-0.678963\pi\) | ||||
−0.533073 | + | 0.846069i | \(0.678963\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −70.0247 | −0.440407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 144.427 | 0.897063 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −212.281 | −1.30234 | −0.651169 | − | 0.758933i | \(-0.725721\pi\) | ||||
−0.651169 | + | 0.758933i | \(0.725721\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 12.5415i | 0.0760092i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 52.3097i | 0.313231i | 0.987660 | + | 0.156616i | \(0.0500584\pi\) | ||||
−0.987660 | + | 0.156616i | \(0.949942\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 134.208 | 0.794133 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 32.0123 | + | 47.1615i | 0.187207 | + | 0.275798i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.9128i | 0.0862014i | 0.999071 | + | 0.0431007i | \(0.0137236\pi\) | ||||
−0.999071 | + | 0.0431007i | \(0.986276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −47.4390 | −0.271080 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 131.323 | 0.741938 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 183.640i | − | 1.02592i | −0.858412 | − | 0.512961i | \(-0.828548\pi\) | ||
0.858412 | − | 0.512961i | \(-0.171452\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 87.8964i | 0.485616i | 0.970074 | + | 0.242808i | \(0.0780684\pi\) | ||||
−0.970074 | + | 0.242808i | \(0.921932\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 48.5451i | 0.265274i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 58.4561i | − | 0.315979i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.94823 | 0.0104183 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 27.2323i | − | 0.144086i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 269.940 | 1.41330 | 0.706649 | − | 0.707565i | \(-0.250206\pi\) | ||||
0.706649 | + | 0.707565i | \(0.250206\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 361.323i | 1.87214i | 0.351814 | + | 0.936070i | \(0.385565\pi\) | ||||
−0.351814 | + | 0.936070i | \(0.614435\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −59.6166 | −0.305726 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.6863 | −0.125311 | −0.0626556 | − | 0.998035i | \(-0.519957\pi\) | ||||
−0.0626556 | + | 0.998035i | \(0.519957\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 339.851 | 1.70779 | 0.853897 | − | 0.520441i | \(-0.174233\pi\) | ||||
0.853897 | + | 0.520441i | \(0.174233\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −82.0247 | −0.408083 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 83.4131i | − | 0.410902i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 407.370i | − | 1.98717i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 82.6738 | 0.399390 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.2409 | + | 19.5068i | 0.0633534 | + | 0.0933341i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 376.489i | 1.78431i | 0.451730 | + | 0.892155i | \(0.350807\pi\) | ||||
−0.451730 | + | 0.892155i | \(0.649193\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 97.5919 | 0.458178 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 308.760 | 1.43609 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 279.104i | 1.28619i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 129.793i | 0.592664i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.26096i | 0.0419048i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 370.168i | 1.65995i | 0.557804 | + | 0.829973i | \(0.311644\pi\) | ||||
−0.557804 | + | 0.829973i | \(0.688356\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.1553 | −0.120690 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 341.595i | − | 1.50482i | −0.658693 | − | 0.752411i | \(-0.728891\pi\) | ||
0.658693 | − | 0.752411i | \(-0.271109\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 369.046 | 1.61155 | 0.805777 | − | 0.592219i | \(-0.201748\pi\) | ||||
0.805777 | + | 0.592219i | \(0.201748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 11.2637i | − | 0.0487607i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 75.5098 | 0.324076 | 0.162038 | − | 0.986784i | \(-0.448193\pi\) | ||||
0.162038 | + | 0.986784i | \(0.448193\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −71.2708 | −0.303280 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 66.2657 | 0.279602 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 399.287 | 1.67066 | 0.835329 | − | 0.549750i | \(-0.185277\pi\) | ||||
0.835329 | + | 0.549750i | \(0.185277\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 228.357i | − | 0.947541i | −0.880648 | − | 0.473771i | \(-0.842893\pi\) | ||
0.880648 | − | 0.473771i | \(-0.157107\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −125.656 | −0.512883 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −92.7264 | + | 62.9409i | −0.375410 | + | 0.254821i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 73.8866i | − | 0.296733i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 15.0827 | 0.0600904 | 0.0300452 | − | 0.999549i | \(-0.490435\pi\) | ||||
0.0300452 | + | 0.999549i | \(0.490435\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 34.1953 | 0.135159 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 15.8690i | 0.0622314i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 223.762i | 0.870669i | 0.900269 | + | 0.435335i | \(0.143370\pi\) | ||||
−0.900269 | + | 0.435335i | \(0.856630\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 52.5003i | 0.202704i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 47.7478i | − | 0.182942i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 50.2140 | 0.190928 | 0.0954638 | − | 0.995433i | \(-0.469567\pi\) | ||||
0.0954638 | + | 0.995433i | \(0.469567\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 235.918i | − | 0.890255i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −42.4574 | −0.159017 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 329.132i | 1.22354i | 0.791035 | + | 0.611770i | \(0.209542\pi\) | ||||
−0.791035 | + | 0.611770i | \(0.790458\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 283.879 | 1.04752 | 0.523762 | − | 0.851864i | \(-0.324528\pi\) | ||||
0.523762 | + | 0.851864i | \(0.324528\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 53.5426 | 0.196127 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −11.2319 | −0.0408433 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 167.315 | 0.604025 | 0.302012 | − | 0.953304i | \(-0.402342\pi\) | ||||
0.302012 | + | 0.953304i | \(0.402342\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 159.766i | 0.572639i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 491.818i | − | 1.75024i | −0.483903 | − | 0.875122i | \(-0.660781\pi\) | ||
0.483903 | − | 0.875122i | \(-0.339219\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 41.3743 | 0.146199 | 0.0730995 | − | 0.997325i | \(-0.476711\pi\) | ||||
0.0730995 | + | 0.997325i | \(0.476711\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −158.890 | + | 107.852i | −0.557510 | + | 0.378427i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 365.865i | 1.27479i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −286.535 | −0.991470 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.54255 | −0.0190466 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 416.306i | 1.42084i | 0.703778 | + | 0.710420i | \(0.251495\pi\) | ||||
−0.703778 | + | 0.710420i | \(0.748505\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 442.436i | 1.49978i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 6.44765i | − | 0.0217093i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 162.549i | 0.543641i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −277.302 | −0.921269 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 117.372i | 0.387368i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −163.551 | −0.536234 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 536.008i | − | 1.74595i | −0.487762 | − | 0.872976i | \(-0.662187\pi\) | ||
0.487762 | − | 0.872976i | \(-0.337813\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 86.6985 | 0.280578 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 405.293 | 1.30319 | 0.651596 | − | 0.758566i | \(-0.274100\pi\) | ||||
0.651596 | + | 0.758566i | \(0.274100\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −64.9274 | −0.207436 | −0.103718 | − | 0.994607i | \(-0.533074\pi\) | ||||
−0.103718 | + | 0.994607i | \(0.533074\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 91.7472 | 0.291261 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 466.133i | − | 1.47045i | −0.677823 | − | 0.735225i | \(-0.737076\pi\) | ||
0.677823 | − | 0.735225i | \(-0.262924\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 19.7493i | − | 0.0619101i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −222.751 | −0.693928 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 16.7539 | + | 24.6823i | 0.0518696 | + | 0.0764159i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 53.3913i | − | 0.164281i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −70.8934 | −0.216799 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 64.0094 | 0.194557 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 423.761i | − | 1.28024i | −0.768273 | − | 0.640122i | \(-0.778884\pi\) | ||
0.768273 | − | 0.640122i | \(-0.221116\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 30.0525i | 0.0902479i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 276.346i | − | 0.824915i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 204.478i | 0.606760i | 0.952870 | + | 0.303380i | \(0.0981151\pi\) | ||||
−0.952870 | + | 0.303380i | \(0.901885\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −279.805 | −0.825384 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 66.0820i | 0.193789i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 369.655 | 1.07771 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 278.533i | 0.807343i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −384.045 | −1.10676 | −0.553380 | − | 0.832929i | \(-0.686662\pi\) | ||||
−0.553380 | + | 0.832929i | \(0.686662\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 376.053 | 1.07751 | 0.538757 | − | 0.842461i | \(-0.318894\pi\) | ||||
0.538757 | + | 0.842461i | \(0.318894\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 30.6492 | 0.0873195 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 695.360 | 1.96986 | 0.984929 | − | 0.172959i | \(-0.0553329\pi\) | ||||
0.984929 | + | 0.172959i | \(0.0553329\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 328.793i | 0.926179i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 14.2522i | − | 0.0399221i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −456.970 | −1.27290 | −0.636448 | − | 0.771319i | \(-0.719597\pi\) | ||||
−0.636448 | + | 0.771319i | \(0.719597\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −133.269 | + | 335.500i | −0.369166 | + | 0.929363i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 206.911i | 0.570004i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −437.283 | −1.19803 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −337.233 | −0.918891 | −0.459446 | − | 0.888206i | \(-0.651952\pi\) | ||||
−0.459446 | + | 0.888206i | \(0.651952\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 209.431i | 0.567563i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 211.881i | 0.571108i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 343.151i | 0.919977i | 0.887925 | + | 0.459988i | \(0.152146\pi\) | ||||
−0.887925 | + | 0.459988i | \(0.847854\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 161.192i | 0.429845i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 93.8791 | 0.249016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 397.158i | − | 1.04791i | −0.851746 | − | 0.523955i | \(-0.824456\pi\) | ||
0.851746 | − | 0.523955i | \(-0.175544\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −45.8330 | −0.120297 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 474.318i | − | 1.23843i | −0.785222 | − | 0.619214i | \(-0.787451\pi\) | ||
0.785222 | − | 0.619214i | \(-0.212549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 37.9482 | 0.0985668 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −158.735 | −0.410168 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 539.232 | 1.38620 | 0.693101 | − | 0.720841i | \(-0.256244\pi\) | ||||
0.693101 | + | 0.720841i | \(0.256244\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 43.2679 | 0.110660 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 41.0985i | 0.104576i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 223.254i | 0.565199i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 421.186 | 1.06092 | 0.530461 | − | 0.847709i | \(-0.322019\pi\) | ||||
0.530461 | + | 0.847709i | \(0.322019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 142.702 | − | 96.8632i | 0.357648 | − | 0.242765i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 433.330i | − | 1.08062i | −0.841465 | − | 0.540312i | \(-0.818306\pi\) | ||
0.841465 | − | 0.540312i | \(-0.181694\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −314.123 | −0.779463 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 52.5185 | 0.129675 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 12.4302i | 0.0305411i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 569.984i | 1.39361i | 0.717263 | + | 0.696803i | \(0.245395\pi\) | ||||
−0.717263 | + | 0.696803i | \(0.754605\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 221.317i | − | 0.538485i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 397.358i | − | 0.962126i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 248.929 | 0.599828 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 181.808i | 0.435989i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −156.568 | −0.373672 | −0.186836 | − | 0.982391i | \(-0.559823\pi\) | ||||
−0.186836 | + | 0.982391i | \(0.559823\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 367.275i | − | 0.872387i | −0.899853 | − | 0.436193i | \(-0.856326\pi\) | ||
0.899853 | − | 0.436193i | \(-0.143674\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 36.6406 | 0.0866209 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −14.2119 | −0.0334398 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 146.888 | 0.344000 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.6770 | 0.0295502 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 289.780i | 0.672343i | 0.941801 | + | 0.336171i | \(0.109132\pi\) | ||||
−0.941801 | + | 0.336171i | \(0.890868\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 284.531i | − | 0.657116i | −0.944484 | − | 0.328558i | \(-0.893437\pi\) | ||
0.944484 | − | 0.328558i | \(-0.106563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 160.866 | 0.369806 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 294.065 | + | 433.225i | 0.672917 | + | 0.991361i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 628.180i | 1.43093i | 0.698646 | + | 0.715467i | \(0.253786\pi\) | ||||
−0.698646 | + | 0.715467i | \(0.746214\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 64.6004 | 0.146486 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 416.332 | 0.939801 | 0.469900 | − | 0.882720i | \(-0.344290\pi\) | ||||
0.469900 | + | 0.882720i | \(0.344290\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 143.042i | − | 0.321442i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 250.060i | − | 0.559418i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 499.834i | 1.11322i | 0.830775 | + | 0.556608i | \(0.187897\pi\) | ||||
−0.830775 | + | 0.556608i | \(0.812103\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 86.6241i | 0.192071i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −58.8934 | −0.130008 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 180.388i | 0.396458i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 143.028 | 0.312973 | 0.156486 | − | 0.987680i | \(-0.449983\pi\) | ||||
0.156486 | + | 0.987680i | \(0.449983\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 8.15833i | − | 0.0177741i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 562.915 | 1.22107 | 0.610537 | − | 0.791988i | \(-0.290954\pi\) | ||||
0.610537 | + | 0.791988i | \(0.290954\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −253.173 | −0.546810 | −0.273405 | − | 0.961899i | \(-0.588150\pi\) | ||||
−0.273405 | + | 0.961899i | \(0.588150\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −538.263 | −1.15755 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −246.479 | −0.527793 | −0.263896 | − | 0.964551i | \(-0.585008\pi\) | ||||
−0.263896 | + | 0.964551i | \(0.585008\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 248.191i | 0.529192i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 289.919i | 0.615539i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −65.6555 | −0.138806 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −96.5895 | − | 142.299i | −0.203346 | − | 0.299576i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 121.286i | 0.254269i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 223.144 | 0.465853 | 0.232927 | − | 0.972494i | \(-0.425170\pi\) | ||||
0.232927 | + | 0.972494i | \(0.425170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −59.0876 | −0.122843 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 250.155i | − | 0.517919i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 18.6732i | − | 0.0385015i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 674.619i | − | 1.38526i | −0.721295 | − | 0.692628i | \(-0.756453\pi\) | ||
0.721295 | − | 0.692628i | \(-0.243547\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 367.682i | 0.751905i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −31.6662 | −0.0644933 | −0.0322466 | − | 0.999480i | \(-0.510266\pi\) | ||||
−0.0322466 | + | 0.999480i | \(0.510266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 24.9892i | − | 0.0506880i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 21.7226 | 0.0438839 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 295.294i | − | 0.594153i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −151.589 | −0.303786 | −0.151893 | − | 0.988397i | \(-0.548537\pi\) | ||||
−0.151893 | + | 0.988397i | \(0.548537\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 90.6030 | 0.180844 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −355.069 | −0.705903 | −0.352952 | − | 0.935642i | \(-0.614822\pi\) | ||||
−0.352952 | + | 0.935642i | \(0.614822\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −395.435 | −0.783040 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 232.456i | − | 0.458493i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 411.332i | − | 0.808118i | −0.914733 | − | 0.404059i | \(-0.867599\pi\) | ||
0.914733 | − | 0.404059i | \(-0.132401\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 392.730 | 0.768552 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 81.6862 | − | 55.4470i | 0.159232 | − | 0.108084i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 292.093i | 0.567171i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 15.1552 | 0.0293137 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 25.8298 | 0.0497684 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 538.069i | − | 1.03276i | −0.856359 | − | 0.516381i | \(-0.827279\pi\) | ||
0.856359 | − | 0.516381i | \(-0.172721\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 367.164i | − | 0.702035i | −0.936369 | − | 0.351017i | \(-0.885836\pi\) | ||
0.936369 | − | 0.351017i | \(-0.114164\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 82.1668i | 0.156508i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 83.6148i | 0.158662i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 230.440 | 0.435615 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 227.458i | − | 0.428358i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −411.771 | −0.772554 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 750.463i | − | 1.40273i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −318.074 | −0.592317 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.7198 | 0.0495730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −873.057 | −1.61378 | −0.806892 | − | 0.590699i | \(-0.798852\pi\) | ||||
−0.806892 | + | 0.590699i | \(0.798852\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 152.241 | 0.280370 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 238.844i | − | 0.438247i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 855.495i | 1.56398i | 0.623293 | + | 0.781988i | \(0.285794\pi\) | ||||
−0.623293 | + | 0.781988i | \(0.714206\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 84.0826 | 0.153156 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 250.207 | − | 169.836i | 0.454096 | − | 0.308232i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 200.507i | − | 0.362581i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −101.249 | −0.182431 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −140.061 | −0.251455 | −0.125728 | − | 0.992065i | \(-0.540127\pi\) | ||||
−0.125728 | + | 0.992065i | \(0.540127\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 312.096i | − | 0.558311i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 3.37443i | − | 0.00601502i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 10.5527i | − | 0.0187437i | −0.999956 | − | 0.00937185i | \(-0.997017\pi\) | ||
0.999956 | − | 0.00937185i | \(-0.00298320\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 942.681i | − | 1.66846i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −47.1677 | −0.0831881 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 971.756i | − | 1.70783i | −0.520412 | − | 0.853916i | \(-0.674221\pi\) | ||
0.520412 | − | 0.853916i | \(-0.325779\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 895.734 | 1.56871 | 0.784355 | − | 0.620312i | \(-0.212994\pi\) | ||||
0.784355 | + | 0.620312i | \(0.212994\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 467.549i | − | 0.815968i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −249.448 | −0.433823 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 209.918 | 0.363809 | 0.181905 | − | 0.983316i | \(-0.441774\pi\) | ||||
0.181905 | + | 0.983316i | \(0.441774\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 625.830 | 1.08088 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −223.567 | −0.384796 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.1661i | 0.0860482i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 103.259i | 0.176511i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1032.25 | −1.75852 | −0.879258 | − | 0.476345i | \(-0.841961\pi\) | ||||
−0.879258 | + | 0.476345i | \(0.841961\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −837.202 | + | 568.277i | −1.42140 | + | 0.964816i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 42.7579i | 0.0723484i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1030.88 | −1.73842 | −0.869210 | − | 0.494442i | \(-0.835372\pi\) | ||||
−0.869210 | + | 0.494442i | \(0.835372\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 48.0166 | 0.0807001 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 588.640i | − | 0.985996i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 83.7382i | 0.139797i | 0.997554 | + | 0.0698983i | \(0.0222675\pi\) | ||||
−0.997554 | + | 0.0698983i | \(0.977733\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 293.467i | 0.488298i | 0.969738 | + | 0.244149i | \(0.0785086\pi\) | ||||
−0.969738 | + | 0.244149i | \(0.921491\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 142.071i | 0.235607i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −697.097 | −1.15223 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 418.633i | 0.689676i | 0.938662 | + | 0.344838i | \(0.112066\pi\) | ||||
−0.938662 | + | 0.344838i | \(0.887934\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −144.476 | −0.237234 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 72.0408i | 0.117906i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −377.709 | −0.616165 | −0.308083 | − | 0.951360i | \(-0.599687\pi\) | ||||
−0.308083 | + | 0.951360i | \(0.599687\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −705.586 | −1.14729 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 845.723 | 1.37070 | 0.685351 | − | 0.728213i | \(-0.259649\pi\) | ||||
0.685351 | + | 0.728213i | \(0.259649\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −410.355 | −0.662932 | −0.331466 | − | 0.943467i | \(-0.607543\pi\) | ||||
−0.331466 | + | 0.943467i | \(0.607543\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 143.195i | − | 0.230588i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 128.468i | 0.206209i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −769.360 | −1.23098 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 33.7868 | − | 22.9338i | 0.0538864 | − | 0.0365771i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.7282i | 0.0250051i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −313.898 | −0.497462 | −0.248731 | − | 0.968573i | \(-0.580013\pi\) | ||||
−0.248731 | + | 0.968573i | \(0.580013\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 652.099 | 1.03017 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 154.414i | − | 0.243172i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 127.014i | 0.199394i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 169.034i | − | 0.264529i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 425.842i | − | 0.664339i | −0.943220 | − | 0.332170i | \(-0.892219\pi\) | ||
0.943220 | − | 0.332170i | \(-0.107781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1038.06 | −1.61441 | −0.807204 | − | 0.590272i | \(-0.799020\pi\) | ||||
−0.807204 | + | 0.590272i | \(0.799020\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 534.788i | − | 0.829129i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −174.684 | −0.269991 | −0.134995 | − | 0.990846i | \(-0.543102\pi\) | ||||
−0.134995 | + | 0.990846i | \(0.543102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 94.0806i | − | 0.144962i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 483.422 | 0.742583 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1247.54 | −1.91048 | −0.955238 | − | 0.295839i | \(-0.904401\pi\) | ||||
−0.955238 | + | 0.295839i | \(0.904401\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −138.464 | −0.211395 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 224.809 | 0.342175 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 746.281i | − | 1.13244i | −0.824253 | − | 0.566222i | \(-0.808405\pi\) | ||
0.824253 | − | 0.566222i | \(-0.191595\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 73.1406i | 0.110651i | 0.998468 | + | 0.0553257i | \(0.0176197\pi\) | ||||
−0.998468 | + | 0.0553257i | \(0.982380\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 16.0405 | 0.0241938 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 326.338 | + | 480.771i | 0.490734 | + | 0.722964i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 438.611i | − | 0.657587i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 641.150 | 0.958370 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.7780 | 0.0518301 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 939.481i | − | 1.39596i | −0.716117 | − | 0.697980i | \(-0.754082\pi\) | ||
0.716117 | − | 0.697980i | \(-0.245918\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 47.0344i | 0.0696806i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 666.060i | 0.983841i | 0.870640 | + | 0.491920i | \(0.163705\pi\) | ||||
−0.870640 | + | 0.491920i | \(0.836295\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.7707i | 0.0246991i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −591.660 | −0.868810 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 79.9509i | − | 0.117058i | −0.998286 | − | 0.0585292i | \(-0.981359\pi\) | ||
0.998286 | − | 0.0585292i | \(-0.0186411\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 745.632 | 1.08851 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 639.206i | − | 0.930431i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −238.466 | −0.346105 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −208.333 | −0.301495 | −0.150748 | − | 0.988572i | \(-0.548168\pi\) | ||||
−0.150748 | + | 0.988572i | \(0.548168\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −19.5094 | −0.0281520 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −612.521 | −0.881326 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 109.607i | 0.157256i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 130.787i | − | 0.187106i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.0082 | 0.0299688 | 0.0149844 | − | 0.999888i | \(-0.495230\pi\) | ||||
0.0149844 | + | 0.999888i | \(0.495230\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −157.480 | + | 106.895i | −0.224012 | + | 0.152055i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 123.445i | 0.175099i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 355.147 | 0.502329 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 230.915 | 0.325691 | 0.162845 | − | 0.986652i | \(-0.447933\pi\) | ||||
0.162845 | + | 0.986652i | \(0.447933\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 114.776i | − | 0.161428i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1467.61i | 2.05836i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.7097i | 0.0597338i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 691.586i | − | 0.964555i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 846.640 | 1.17752 | 0.588762 | − | 0.808306i | \(-0.299615\pi\) | ||||
0.588762 | + | 0.808306i | \(0.299615\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 262.333i | − | 0.363846i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −395.527 | −0.547063 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 144.068i | 0.198714i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1078.59 | −1.48362 | −0.741810 | − | 0.670610i | \(-0.766032\pi\) | ||||
−0.741810 | + | 0.670610i | \(0.766032\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −83.0751 | −0.113646 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −648.893 | −0.885256 | −0.442628 | − | 0.896705i | \(-0.645954\pi\) | ||||
−0.442628 | + | 0.896705i | \(0.645954\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 217.643i | 0.296113i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 58.7630i | 0.0797326i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1022.09 | 1.38307 | 0.691534 | − | 0.722344i | \(-0.256935\pi\) | ||||
0.691534 | + | 0.722344i | \(0.256935\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 109.017 | + | 160.607i | 0.147121 | + | 0.216743i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 257.760i | − | 0.346918i | −0.984841 | − | 0.173459i | \(-0.944506\pi\) | ||
0.984841 | − | 0.173459i | \(-0.0554944\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 842.468 | 1.13083 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −127.975 | −0.171319 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 674.002i | 0.899869i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 553.605i | 0.737157i | 0.929597 | + | 0.368578i | \(0.120155\pi\) | ||||
−0.929597 | + | 0.368578i | \(0.879845\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 26.1240i | − | 0.0346932i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 198.416i | − | 0.262802i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 456.061 | 0.602458 | 0.301229 | − | 0.953552i | \(-0.402603\pi\) | ||||
0.301229 | + | 0.953552i | \(0.402603\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 59.2280i | − | 0.0780343i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 536.682 | 0.705233 | 0.352616 | − | 0.935768i | \(-0.385292\pi\) | ||||
0.352616 | + | 0.935768i | \(0.385292\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 214.510i | 0.281140i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 27.4859 | 0.0359293 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 447.215 | 0.583071 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 814.347 | 1.05897 | 0.529484 | − | 0.848320i | \(-0.322385\pi\) | ||||
0.529484 | + | 0.848320i | \(0.322385\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 387.567 | 0.502681 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1451.94i | 1.87831i | 0.343490 | + | 0.939156i | \(0.388391\pi\) | ||||
−0.343490 | + | 0.939156i | \(0.611609\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 482.056i | − | 0.622008i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 90.9332 | 0.117031 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1097.45 | + | 744.930i | −1.40880 | + | 0.956264i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 69.9154i | − | 0.0895204i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −82.7017 | −0.105622 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −976.756 | −1.24427 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 389.048i | − | 0.494343i | −0.968972 | − | 0.247172i | \(-0.920499\pi\) | ||
0.968972 | − | 0.247172i | \(-0.0795012\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 86.9731i | − | 0.110232i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 846.636i | 1.07034i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 165.318i | 0.208472i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −408.621 | −0.513989 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1243.63i | 1.56039i | 0.625539 | + | 0.780193i | \(0.284879\pi\) | ||||
−0.625539 | + | 0.780193i | \(0.715121\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.1761 | 0.0240002 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 73.5385i | 0.0918083i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 92.9848 | 0.115797 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 842.788 | 1.04694 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 570.074 | 0.706411 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 683.371 | 0.844711 | 0.422355 | − | 0.906430i | \(-0.361203\pi\) | ||||
0.422355 | + | 0.906430i | \(0.361203\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 68.3221i | 0.0842443i | 0.999112 | + | 0.0421221i | \(0.0134119\pi\) | ||||
−0.999112 | + | 0.0421221i | \(0.986588\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 491.693i | − | 0.604789i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1238.74 | −1.51993 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −564.608 | − | 831.798i | −0.691075 | − | 1.01811i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 92.7384i | − | 0.113234i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1353.27 | −1.64832 | −0.824161 | − | 0.566356i | \(-0.808353\pi\) | ||||
−0.824161 | + | 0.566356i | \(0.808353\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −239.439 | −0.290935 | −0.145467 | − | 0.989363i | \(-0.546469\pi\) | ||||
−0.145467 | + | 0.989363i | \(0.546469\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 19.4542i | 0.0235809i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 31.7267i | 0.0383636i | 0.999816 | + | 0.0191818i | \(0.00610614\pi\) | ||||
−0.999816 | + | 0.0191818i | \(0.993894\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 37.0436i | 0.0446847i | 0.999750 | + | 0.0223424i | \(0.00711239\pi\) | ||||
−0.999750 | + | 0.0223424i | \(0.992888\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 289.798i | − | 0.348734i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 33.8091 | 0.0405872 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 305.247i | 0.365566i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 276.723 | 0.330613 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 526.714i | − | 0.627788i | −0.949458 | − | 0.313894i | \(-0.898366\pi\) | ||
0.949458 | − | 0.313894i | \(-0.101634\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 587.683 | 0.698790 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −851.854 | −1.01050 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 783.159 | 0.926815 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 626.074 | 0.739166 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 71.6625i | − | 0.0844081i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 276.062i | 0.324397i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 104.843 | 0.122911 | 0.0614557 | − | 0.998110i | \(-0.480426\pi\) | ||||
0.0614557 | + | 0.998110i | \(0.480426\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 186.804 | + | 275.206i | 0.218485 | + | 0.321878i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 192.081i | − | 0.224132i | −0.993701 | − | 0.112066i | \(-0.964253\pi\) | ||
0.993701 | − | 0.112066i | \(-0.0357469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −653.580 | −0.760861 | −0.380431 | − | 0.924809i | \(-0.624224\pi\) | ||||
−0.380431 | + | 0.924809i | \(0.624224\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 633.697 | 0.736001 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 1166.58i | − | 1.35177i | −0.737005 | − | 0.675887i | \(-0.763761\pi\) | ||
0.737005 | − | 0.675887i | \(-0.236239\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 87.0222i | 0.100604i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 496.293i | 0.572426i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 47.4732i | − | 0.0546296i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −279.332 | −0.320703 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9.59998i | 0.0109965i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 487.735 | 0.557412 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 596.868i | − | 0.680579i | −0.940321 | − | 0.340289i | \(-0.889475\pi\) | ||
0.940321 | − | 0.340289i | \(-0.110525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 721.063 | 0.820322 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1397.14 | −1.58585 | −0.792927 | − | 0.609317i | \(-0.791444\pi\) | ||||
−0.792927 | + | 0.609317i | \(0.791444\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −148.675 | −0.168375 | −0.0841876 | − | 0.996450i | \(-0.526829\pi\) | ||||
−0.0841876 | + | 0.996450i | \(0.526829\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 766.321 | 0.865899 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1414.59i | 1.59480i | 0.603450 | + | 0.797401i | \(0.293792\pi\) | ||||
−0.603450 | + | 0.797401i | \(0.706208\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 138.682i | 0.155997i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.1677 | −0.0125339 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 130.328 | + | 192.003i | 0.145944 | + | 0.215009i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1071.61i | − | 1.19733i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 281.543 | 0.313871 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 847.610 | 0.942837 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 63.4761i | 0.0704507i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 480.301i | 0.531895i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 512.910i | 0.566751i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 906.084i | − | 0.998991i | −0.866317 | − | 0.499495i | \(-0.833519\pi\) | ||
0.866317 | − | 0.499495i | \(-0.166481\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 203.295 | 0.223647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 132.618i | − | 0.145574i | −0.997348 | − | 0.0727870i | \(-0.976811\pi\) | ||
0.997348 | − | 0.0727870i | \(-0.0231893\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −52.9328 | −0.0579768 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 283.280i | 0.309595i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 124.356 | 0.135612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 860.497 | 0.936341 | 0.468170 | − | 0.883638i | \(-0.344913\pi\) | ||||
0.468170 | + | 0.883638i | \(0.344913\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −928.392 | −1.00803 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 332.345 | 0.360071 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 90.6763i | − | 0.0980284i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 150.166i | − | 0.161992i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 403.521 | 0.434360 | 0.217180 | − | 0.976132i | \(-0.430314\pi\) | ||||
0.217180 | + | 0.976132i | \(0.430314\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 229.779 | + | 338.517i | 0.246809 | + | 0.363606i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 701.988i | − | 0.752398i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 11.3687 | 0.0121590 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 559.112 | 0.596704 | 0.298352 | − | 0.954456i | \(-0.403563\pi\) | ||||
0.298352 | + | 0.954456i | \(0.403563\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 112.457i | 0.119763i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 824.556i | − | 0.876255i | −0.898913 | − | 0.438127i | \(-0.855642\pi\) | ||
0.898913 | − | 0.438127i | \(-0.144358\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1923.83i | 2.04011i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 158.911i | − | 0.168160i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −79.0790 | −0.0835048 | −0.0417524 | − | 0.999128i | \(-0.513294\pi\) | ||||
−0.0417524 | + | 0.999128i | \(0.513294\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 442.007i | 0.465761i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −807.366 | −0.848965 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 230.825i | − | 0.242208i | −0.992640 | − | 0.121104i | \(-0.961356\pi\) | ||
0.992640 | − | 0.121104i | \(-0.0386435\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1575.20 | 1.64943 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −34.2068 | −0.0357438 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −669.663 | −0.698293 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1875.14 | −1.95124 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 385.816i | 0.400640i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 2108.46i | 2.18493i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1527.67 | 1.57980 | 0.789901 | − | 0.613235i | \(-0.210132\pi\) | ||||
0.789901 | + | 0.613235i | \(0.210132\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 42.7510 | − | 29.0186i | 0.0441187 | − | 0.0299469i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 285.090i | − | 0.293605i | −0.989166 | − | 0.146802i | \(-0.953102\pi\) | ||
0.989166 | − | 0.146802i | \(-0.0468981\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 550.115 | 0.565380 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −92.4764 | −0.0948476 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1833.67i | − | 1.87684i | −0.345499 | − | 0.938419i | \(-0.612290\pi\) | ||
0.345499 | − | 0.938419i | \(-0.387710\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.4168i | 0.0310692i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 122.791i | 0.125169i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1140.39i | − | 1.16011i | −0.814578 | − | 0.580054i | \(-0.803031\pi\) | ||
0.814578 | − | 0.580054i | \(-0.196969\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −144.054 | −0.146248 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 110.867i | − | 0.112328i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1458.14 | −1.47435 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 579.463i | − | 0.584725i | −0.956308 | − | 0.292363i | \(-0.905559\pi\) | ||
0.956308 | − | 0.292363i | \(-0.0944414\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −733.975 | −0.739149 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1983.16 | 1.99313 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 59.6215 | 0.0598009 | 0.0299005 | − | 0.999553i | \(-0.490481\pi\) | ||||
0.0299005 | + | 0.999553i | \(0.490481\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 52.0525 | 0.0521046 |
(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 | 912.3.o.c.721.3 | 6 | ||
3.2 | odd | 2 | 2736.3.o.m.721.1 | 6 | |||
4.3 | odd | 2 | 228.3.h.a.37.6 | yes | 6 | ||
12.11 | even | 2 | 684.3.h.e.37.1 | 6 | |||
19.18 | odd | 2 | inner | 912.3.o.c.721.6 | 6 | ||
57.56 | even | 2 | 2736.3.o.m.721.2 | 6 | |||
76.75 | even | 2 | 228.3.h.a.37.3 | ✓ | 6 | ||
228.227 | odd | 2 | 684.3.h.e.37.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.3.h.a.37.3 | ✓ | 6 | 76.75 | even | 2 | ||
228.3.h.a.37.6 | yes | 6 | 4.3 | odd | 2 | ||
684.3.h.e.37.1 | 6 | 12.11 | even | 2 | |||
684.3.h.e.37.2 | 6 | 228.227 | odd | 2 | |||
912.3.o.c.721.3 | 6 | 1.1 | even | 1 | trivial | ||
912.3.o.c.721.6 | 6 | 19.18 | odd | 2 | inner | ||
2736.3.o.m.721.1 | 6 | 3.2 | odd | 2 | |||
2736.3.o.m.721.2 | 6 | 57.56 | even | 2 |