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 | 721.6 | ||
Root | \(0.500000 + 0.460304i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.721 |
Dual form | 912.3.o.c.721.3 |
$q$-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 | \(0.0728469\pi\) | ||||
−0.973927 | + | 0.226863i | \(0.927153\pi\) | |||||||
\(14\) | 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 | \(-0.911517\pi\) | ||
0.961612 | − | 0.274413i | \(-0.0884835\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 53.2554i | 1.71792i | 0.512046 | + | 0.858958i | \(0.328888\pi\) | ||||
−0.512046 | + | 0.858958i | \(0.671112\pi\) | |||||||
\(32\) | 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 | \(0.0432229\pi\) | ||||
−0.990795 | + | 0.135372i | \(0.956777\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.2164 | −0.261959 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 69.8102i | 1.70269i | 0.524607 | + | 0.851344i | \(0.324212\pi\) | ||||
−0.524607 | + | 0.851344i | \(0.675788\pi\) | |||||||
\(42\) | 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 | \(0.124559\pi\) | ||||
−0.924409 | + | 0.381403i | \(0.875441\pi\) | |||||||
\(54\) | 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 | \(-0.777882\pi\) | ||
0.766255 | − | 0.642537i | \(-0.222118\pi\) | |||||||
\(60\) | 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 | \(0.114978\pi\) | ||||
−0.935468 | + | 0.353410i | \(0.885022\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 47.7318i | − | 0.691765i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 56.3447i | − | 0.793588i | −0.917908 | − | 0.396794i | \(-0.870123\pi\) | ||
0.917908 | − | 0.396794i | \(-0.129877\pi\) | |||||||
\(72\) | 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 | \(-0.922150\pi\) | ||
0.970241 | − | 0.242143i | \(-0.0778502\pi\) | |||||||
\(80\) | 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 | \(0.0439750\pi\) | ||||
−0.990472 | + | 0.137712i | \(0.956025\pi\) | |||||||
\(90\) | 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 | \(0.00525070\pi\) | ||||
−0.999864 | + | 0.0164948i | \(0.994749\pi\) | |||||||
\(98\) | 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 | \(-0.921873\pi\) | ||
0.970029 | − | 0.242987i | \(-0.0781274\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 52.9703i | − | 0.504479i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 128.605i | 1.20192i | 0.799279 | + | 0.600960i | \(0.205215\pi\) | ||||
−0.799279 | + | 0.600960i | \(0.794785\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 40.9303i | 0.375508i | 0.982216 | + | 0.187754i | \(0.0601207\pi\) | ||||
−0.982216 | + | 0.187754i | \(0.939879\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −17.3508 | −0.156314 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 161.546i | 1.42961i | 0.699326 | + | 0.714803i | \(0.253484\pi\) | ||||
−0.699326 | + | 0.714803i | \(0.746516\pi\) | |||||||
\(114\) | 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 | \(0.0332218\pi\) | ||||
−0.994558 | + | 0.104180i | \(0.966778\pi\) | |||||||
\(128\) | 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 | \(0.0359146\pi\) | ||||
−0.993642 | + | 0.112590i | \(0.964085\pi\) | |||||||
\(152\) | 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 | \(-0.949942\pi\) | ||
0.987660 | − | 0.156616i | \(-0.0500584\pi\) | |||||||
\(168\) | 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 | \(-0.986276\pi\) | ||
0.999071 | − | 0.0431007i | \(-0.0137236\pi\) | |||||||
\(174\) | 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 | \(0.171452\pi\) | ||||
−0.858412 | + | 0.512961i | \(0.828548\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 87.8964i | − | 0.485616i | −0.970074 | − | 0.242808i | \(-0.921932\pi\) | ||
0.970074 | − | 0.242808i | \(-0.0780684\pi\) | |||||||
\(182\) | 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 | \(-0.614435\pi\) | ||
0.351814 | − | 0.936070i | \(-0.385565\pi\) | |||||||
\(194\) | 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 | \(-0.649193\pi\) | ||
0.451730 | − | 0.892155i | \(-0.350807\pi\) | |||||||
\(212\) | 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 | \(-0.688356\pi\) | ||
0.557804 | − | 0.829973i | \(-0.311644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −27.1553 | −0.120690 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 341.595i | 1.50482i | 0.658693 | + | 0.752411i | \(0.271109\pi\) | ||||
−0.658693 | + | 0.752411i | \(0.728891\pi\) | |||||||
\(228\) | 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 | \(0.157107\pi\) | ||||
−0.880648 | + | 0.473771i | \(0.842893\pi\) | |||||||
\(242\) | 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 | \(-0.856630\pi\) | ||
0.900269 | − | 0.435335i | \(-0.143370\pi\) | |||||||
\(258\) | 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 | \(-0.790458\pi\) | ||
0.791035 | − | 0.611770i | \(-0.209542\pi\) | |||||||
\(270\) | 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 | \(0.339219\pi\) | ||||
−0.483903 | + | 0.875122i | \(0.660781\pi\) | |||||||
\(282\) | 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 | \(-0.748505\pi\) | ||
0.703778 | − | 0.710420i | \(-0.251495\pi\) | |||||||
\(294\) | 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 | \(0.337813\pi\) | ||||
−0.487762 | + | 0.872976i | \(0.662187\pi\) | |||||||
\(308\) | 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 | \(0.262924\pi\) | ||||
−0.677823 | + | 0.735225i | \(0.737076\pi\) | |||||||
\(318\) | 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 | \(0.221116\pi\) | ||||
−0.768273 | + | 0.640122i | \(0.778884\pi\) | |||||||
\(332\) | 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 | \(-0.901885\pi\) | ||
0.952870 | − | 0.303380i | \(-0.0981151\pi\) | |||||||
\(338\) | 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 | \(-0.847854\pi\) | ||
0.887925 | − | 0.459988i | \(-0.152146\pi\) | |||||||
\(374\) | 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 | \(0.175544\pi\) | ||||
−0.851746 | + | 0.523955i | \(0.824456\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −45.8330 | −0.120297 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 474.318i | 1.23843i | 0.785222 | + | 0.619214i | \(0.212549\pi\) | ||||
−0.785222 | + | 0.619214i | \(0.787451\pi\) | |||||||
\(384\) | 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 | \(0.181694\pi\) | ||||
−0.841465 | + | 0.540312i | \(0.818306\pi\) | |||||||
\(402\) | 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 | \(-0.754605\pi\) | ||
0.717263 | − | 0.696803i | \(-0.245395\pi\) | |||||||
\(410\) | 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 | \(0.143674\pi\) | ||||
−0.899853 | + | 0.436193i | \(0.856326\pi\) | |||||||
\(422\) | 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 | \(-0.890868\pi\) | ||
0.941801 | − | 0.336171i | \(-0.109132\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 284.531i | 0.657116i | 0.944484 | + | 0.328558i | \(0.106563\pi\) | ||||
−0.944484 | + | 0.328558i | \(0.893437\pi\) | |||||||
\(434\) | 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 | \(-0.746214\pi\) | ||
0.698646 | − | 0.715467i | \(-0.253786\pi\) | |||||||
\(440\) | 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 | \(-0.812103\pi\) | ||
0.830775 | − | 0.556608i | \(-0.187897\pi\) | |||||||
\(450\) | 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 | \(0.243547\pi\) | ||||
−0.721295 | + | 0.692628i | \(0.756453\pi\) | |||||||
\(488\) | 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 | \(0.132401\pi\) | ||||
−0.914733 | + | 0.404059i | \(0.867599\pi\) | |||||||
\(510\) | 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 | \(0.172721\pi\) | ||||
−0.856359 | + | 0.516381i | \(0.827279\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 367.164i | 0.702035i | 0.936369 | + | 0.351017i | \(0.114164\pi\) | ||||
−0.936369 | + | 0.351017i | \(0.885836\pi\) | |||||||
\(524\) | 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 | \(-0.714206\pi\) | ||
0.623293 | − | 0.781988i | \(-0.285794\pi\) | |||||||
\(548\) | 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 | \(0.00298320\pi\) | ||||
−0.999956 | + | 0.00937185i | \(0.997017\pi\) | |||||||
\(564\) | 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 | \(0.325779\pi\) | ||||
−0.520412 | + | 0.853916i | \(0.674221\pi\) | |||||||
\(570\) | 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 | \(-0.977733\pi\) | ||
0.997554 | − | 0.0698983i | \(-0.0222675\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 293.467i | − | 0.488298i | −0.969738 | − | 0.244149i | \(-0.921491\pi\) | ||
0.969738 | − | 0.244149i | \(-0.0785086\pi\) | |||||||
\(602\) | 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 | \(-0.887934\pi\) | ||
0.938662 | − | 0.344838i | \(-0.112066\pi\) | |||||||
\(608\) | 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 | \(0.107781\pi\) | ||||
−0.943220 | + | 0.332170i | \(0.892219\pi\) | |||||||
\(642\) | 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 | \(0.191595\pi\) | ||||
−0.824253 | + | 0.566222i | \(0.808405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 73.1406i | − | 0.110651i | −0.998468 | − | 0.0553257i | \(-0.982380\pi\) | ||
0.998468 | − | 0.0553257i | \(-0.0176197\pi\) | |||||||
\(662\) | 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 | \(0.245918\pi\) | ||||
−0.716117 | + | 0.697980i | \(0.754082\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 47.0344i | − | 0.0696806i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 666.060i | − | 0.983841i | −0.870640 | − | 0.491920i | \(-0.836295\pi\) | ||
0.870640 | − | 0.491920i | \(-0.163705\pi\) | |||||||
\(678\) | 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 | \(0.0186411\pi\) | ||||
−0.998286 | + | 0.0585292i | \(0.981359\pi\) | |||||||
\(684\) | 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 | \(0.0554944\pi\) | ||||
−0.984841 | + | 0.173459i | \(0.944506\pi\) | |||||||
\(744\) | 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 | \(-0.879845\pi\) | ||
0.929597 | − | 0.368578i | \(-0.120155\pi\) | |||||||
\(752\) | 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 | \(-0.611609\pi\) | ||
0.343490 | − | 0.939156i | \(-0.388391\pi\) | |||||||
\(774\) | 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 | \(0.0795012\pi\) | ||||
−0.968972 | + | 0.247172i | \(0.920499\pi\) | |||||||
\(788\) | 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 | \(-0.715121\pi\) | ||
0.625539 | − | 0.780193i | \(-0.284879\pi\) | |||||||
\(798\) | 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 | \(-0.986588\pi\) | ||
0.999112 | − | 0.0421221i | \(-0.0134119\pi\) | |||||||
\(812\) | 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 | \(-0.993894\pi\) | ||
0.999816 | − | 0.0191818i | \(-0.00610614\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.0436i | − | 0.0446847i | −0.999750 | − | 0.0223424i | \(-0.992888\pi\) | ||
0.999750 | − | 0.0223424i | \(-0.00711239\pi\) | |||||||
\(830\) | 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 | \(0.101634\pi\) | ||||
−0.949458 | + | 0.313894i | \(0.898366\pi\) | |||||||
\(840\) | 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 | \(0.0357469\pi\) | ||||
−0.993701 | + | 0.112066i | \(0.964253\pi\) | |||||||
\(858\) | 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 | \(0.236239\pi\) | ||||
−0.737005 | + | 0.675887i | \(0.763761\pi\) | |||||||
\(864\) | 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 | \(0.110525\pi\) | ||||
−0.940321 | + | 0.340289i | \(0.889475\pi\) | |||||||
\(878\) | 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 | \(-0.706208\pi\) | ||
0.603450 | − | 0.797401i | \(-0.293792\pi\) | |||||||
\(888\) | 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 | \(0.166481\pi\) | ||||
−0.866317 | + | 0.499495i | \(0.833519\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 203.295 | 0.223647 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 132.618i | 0.145574i | 0.997348 | + | 0.0727870i | \(0.0231893\pi\) | ||||
−0.997348 | + | 0.0727870i | \(0.976811\pi\) | |||||||
\(912\) | 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 | \(0.144358\pi\) | ||||
−0.898913 | + | 0.438127i | \(0.855642\pi\) | |||||||
\(942\) | 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 | \(0.0386435\pi\) | ||||
−0.992640 | + | 0.121104i | \(0.961356\pi\) | |||||||
\(954\) | 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 | \(0.0468981\pi\) | ||||
−0.989166 | + | 0.146802i | \(0.953102\pi\) | |||||||
\(972\) | 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 | \(0.387710\pi\) | ||||
−0.345499 | + | 0.938419i | \(0.612290\pi\) | |||||||
\(978\) | 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 | \(0.196969\pi\) | ||||
−0.814578 | + | 0.580054i | \(0.803031\pi\) | |||||||
\(984\) | 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 | \(0.0944414\pi\) | ||||
−0.956308 | + | 0.292363i | \(0.905559\pi\) | |||||||
\(992\) | 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.721.6 | 6 | ||
3.2 | odd | 2 | 2736.3.o.m.721.2 | 6 | |||
4.3 | odd | 2 | 228.3.h.a.37.3 | ✓ | 6 | ||
12.11 | even | 2 | 684.3.h.e.37.2 | 6 | |||
19.18 | odd | 2 | inner | 912.3.o.c.721.3 | 6 | ||
57.56 | even | 2 | 2736.3.o.m.721.1 | 6 | |||
76.75 | even | 2 | 228.3.h.a.37.6 | yes | 6 | ||
228.227 | odd | 2 | 684.3.h.e.37.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
228.3.h.a.37.3 | ✓ | 6 | 4.3 | odd | 2 | ||
228.3.h.a.37.6 | yes | 6 | 76.75 | even | 2 | ||
684.3.h.e.37.1 | 6 | 228.227 | odd | 2 | |||
684.3.h.e.37.2 | 6 | 12.11 | even | 2 | |||
912.3.o.c.721.3 | 6 | 19.18 | odd | 2 | inner | ||
912.3.o.c.721.6 | 6 | 1.1 | even | 1 | trivial | ||
2736.3.o.m.721.1 | 6 | 57.56 | even | 2 | |||
2736.3.o.m.721.2 | 6 | 3.2 | odd | 2 |