Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(305,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.305");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.e (of order \(2\), degree \(1\), 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: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 156x^{10} + 8721x^{8} + 208784x^{6} + 2024760x^{4} + 7117056x^{2} + 6533136 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 305.8 | ||
Root | \(2.16068i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.305 |
Dual form | 684.3.e.a.305.5 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.16068i | 0.432136i | 0.976378 | + | 0.216068i | \(0.0693232\pi\) | ||||
−0.976378 | + | 0.216068i | \(0.930677\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.11429 | −1.30204 | −0.651021 | − | 0.759060i | \(-0.725659\pi\) | ||||
−0.651021 | + | 0.759060i | \(0.725659\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.10046i | 0.100041i | 0.998748 | + | 0.0500207i | \(0.0159287\pi\) | ||||
−0.998748 | + | 0.0500207i | \(0.984071\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.28570 | 0.175823 | 0.0879116 | − | 0.996128i | \(-0.471981\pi\) | ||||
0.0879116 | + | 0.996128i | \(0.471981\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 19.2684i | − 1.13343i | −0.823913 | − | 0.566717i | \(-0.808213\pi\) | ||||
0.823913 | − | 0.566717i | \(-0.191787\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.35890 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 1.28620i | − 0.0559216i | −0.999609 | − | 0.0279608i | \(-0.991099\pi\) | ||||
0.999609 | − | 0.0279608i | \(-0.00890136\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 20.3315 | 0.813259 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 37.0190i | − 1.27652i | −0.769821 | − | 0.638259i | \(-0.779655\pi\) | ||||
0.769821 | − | 0.638259i | \(-0.220345\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 31.3785 | 1.01221 | 0.506104 | − | 0.862472i | \(-0.331085\pi\) | ||||
0.506104 | + | 0.862472i | \(0.331085\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 19.6930i | − 0.562659i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 34.9511 | 0.944625 | 0.472312 | − | 0.881431i | \(-0.343419\pi\) | ||||
0.472312 | + | 0.881431i | \(0.343419\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 43.5088i | − 1.06119i | −0.847626 | − | 0.530595i | \(-0.821969\pi\) | ||||
0.847626 | − | 0.530595i | \(-0.178031\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.553740 | 0.0128777 | 0.00643884 | − | 0.999979i | \(-0.497950\pi\) | ||||
0.00643884 | + | 0.999979i | \(0.497950\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.35139i | 0.198966i | 0.995039 | + | 0.0994828i | \(0.0317188\pi\) | ||||
−0.995039 | + | 0.0994828i | \(0.968281\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 34.0703 | 0.695312 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 75.0713i | − 1.41644i | −0.705992 | − | 0.708220i | \(-0.749499\pi\) | ||||
0.705992 | − | 0.708220i | \(-0.250501\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.37773 | −0.0432315 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 38.1174i | 0.646057i | 0.946389 | + | 0.323028i | \(0.104701\pi\) | ||||
−0.946389 | + | 0.323028i | \(0.895299\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −62.4816 | −1.02429 | −0.512145 | − | 0.858899i | \(-0.671149\pi\) | ||||
−0.512145 | + | 0.858899i | \(0.671149\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.93866i | 0.0759794i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 85.6623 | 1.27854 | 0.639271 | − | 0.768982i | \(-0.279236\pi\) | ||||
0.639271 | + | 0.768982i | \(0.279236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 15.9252i | 0.224298i | 0.993691 | + | 0.112149i | \(0.0357734\pi\) | ||||
−0.993691 | + | 0.112149i | \(0.964227\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 67.1233 | 0.919497 | 0.459748 | − | 0.888049i | \(-0.347940\pi\) | ||||
0.459748 | + | 0.888049i | \(0.347940\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 10.0299i | − 0.130258i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −58.5499 | −0.741138 | −0.370569 | − | 0.928805i | \(-0.620837\pi\) | ||||
−0.370569 | + | 0.928805i | \(0.620837\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 115.564i | − 1.39233i | −0.717881 | − | 0.696166i | \(-0.754888\pi\) | ||||
0.717881 | − | 0.696166i | \(-0.245112\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 41.6328 | 0.489797 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.59543i | 0.0741060i | 0.999313 | + | 0.0370530i | \(0.0117970\pi\) | ||||
−0.999313 | + | 0.0370530i | \(0.988203\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.8325 | −0.228929 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 9.41818i | 0.0991387i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.0228 | −0.144565 | −0.0722825 | − | 0.997384i | \(-0.523028\pi\) | ||||
−0.0722825 | + | 0.997384i | \(0.523028\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 99.4086i | − 0.984243i | −0.870526 | − | 0.492122i | \(-0.836221\pi\) | ||||
0.870526 | − | 0.492122i | \(-0.163779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8374 | 0.105217 | 0.0526087 | − | 0.998615i | \(-0.483246\pi\) | ||||
0.0526087 | + | 0.998615i | \(0.483246\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 133.136i | − 1.24426i | −0.782913 | − | 0.622131i | \(-0.786267\pi\) | ||||
0.782913 | − | 0.622131i | \(-0.213733\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.56068 | 0.0785384 | 0.0392692 | − | 0.999229i | \(-0.487497\pi\) | ||||
0.0392692 | + | 0.999229i | \(0.487497\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 190.600i | − 1.68672i | −0.537345 | − | 0.843362i | \(-0.680573\pi\) | ||||
0.537345 | − | 0.843362i | \(-0.319427\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.77906 | 0.0241657 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 175.618i | 1.47578i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 119.789 | 0.989992 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 97.9467i | 0.783574i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −66.8407 | −0.526305 | −0.263153 | − | 0.964754i | \(-0.584762\pi\) | ||||
−0.263153 | + | 0.964754i | \(0.584762\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 75.5187i | − 0.576479i | −0.957558 | − | 0.288239i | \(-0.906930\pi\) | ||||
0.957558 | − | 0.288239i | \(-0.0930699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −39.7283 | −0.298709 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 169.943i | 1.24046i | 0.784420 | + | 0.620230i | \(0.212961\pi\) | ||||
−0.784420 | + | 0.620230i | \(0.787039\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 130.111 | 0.936052 | 0.468026 | − | 0.883715i | \(-0.344965\pi\) | ||||
0.468026 | + | 0.883715i | \(0.344965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.51531i | 0.0175896i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 79.9863 | 0.551629 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 63.5185i | 0.426298i | 0.977020 | + | 0.213149i | \(0.0683720\pi\) | ||||
−0.977020 | + | 0.213149i | \(0.931628\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.44525 | −0.0360613 | −0.0180306 | − | 0.999837i | \(-0.505740\pi\) | ||||
−0.0180306 | + | 0.999837i | \(0.505740\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 67.7988i | 0.437412i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −111.650 | −0.711143 | −0.355572 | − | 0.934649i | \(-0.615714\pi\) | ||||
−0.355572 | + | 0.934649i | \(0.615714\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.7228i | 0.0728122i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −234.008 | −1.43563 | −0.717817 | − | 0.696232i | \(-0.754858\pi\) | ||||
−0.717817 | + | 0.696232i | \(0.754858\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 146.835i | 0.879253i | 0.898181 | + | 0.439627i | \(0.144889\pi\) | ||||
−0.898181 | + | 0.439627i | \(0.855111\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −163.776 | −0.969086 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 41.9823i | 0.242672i | 0.992611 | + | 0.121336i | \(0.0387179\pi\) | ||||
−0.992611 | + | 0.121336i | \(0.961282\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −185.307 | −1.05890 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 234.866i | 1.31210i | 0.754717 | + | 0.656051i | \(0.227774\pi\) | ||||
−0.754717 | + | 0.656051i | \(0.772226\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 95.8804 | 0.529726 | 0.264863 | − | 0.964286i | \(-0.414673\pi\) | ||||
0.264863 | + | 0.964286i | \(0.414673\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 75.5181i | 0.408206i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 21.2040 | 0.113390 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 164.583i | 0.861691i | 0.902426 | + | 0.430845i | \(0.141785\pi\) | ||||
−0.902426 | + | 0.430845i | \(0.858215\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 185.715 | 0.962255 | 0.481128 | − | 0.876651i | \(-0.340227\pi\) | ||||
0.481128 | + | 0.876651i | \(0.340227\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 159.624i | − 0.810275i | −0.914256 | − | 0.405137i | \(-0.867224\pi\) | ||||
0.914256 | − | 0.405137i | \(-0.132776\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −291.623 | −1.46544 | −0.732721 | − | 0.680529i | \(-0.761750\pi\) | ||||
−0.732721 | + | 0.680529i | \(0.761750\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 337.402i | 1.66208i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 94.0084 | 0.458578 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.79678i | 0.0229511i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −139.147 | −0.659464 | −0.329732 | − | 0.944075i | \(-0.606958\pi\) | ||||
−0.329732 | + | 0.944075i | \(0.606958\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.19645i | 0.00556490i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −285.993 | −1.31794 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 44.0417i | − 0.199284i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 98.6258 | 0.442268 | 0.221134 | − | 0.975243i | \(-0.429024\pi\) | ||||
0.221134 | + | 0.975243i | \(0.429024\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 103.162i | − 0.454460i | −0.973841 | − | 0.227230i | \(-0.927033\pi\) | ||||
0.973841 | − | 0.227230i | \(-0.0729669\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.27807 | −0.0361488 | −0.0180744 | − | 0.999837i | \(-0.505754\pi\) | ||||
−0.0180744 | + | 0.999837i | \(0.505754\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 164.236i | − 0.704874i | −0.935835 | − | 0.352437i | \(-0.885353\pi\) | ||||
0.935835 | − | 0.352437i | \(-0.114647\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.2053 | −0.0859802 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 306.024i | 1.28044i | 0.768194 | + | 0.640218i | \(0.221156\pi\) | ||||
−0.768194 | + | 0.640218i | \(0.778844\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 159.742 | 0.662829 | 0.331414 | − | 0.943485i | \(-0.392474\pi\) | ||||
0.331414 | + | 0.943485i | \(0.392474\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 73.6149i | 0.300469i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 9.96314 | 0.0403366 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 311.540i | 1.24120i | 0.784129 | + | 0.620598i | \(0.213110\pi\) | ||||
−0.784129 | + | 0.620598i | \(0.786890\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.41540 | 0.00559448 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 299.046i | − 1.16360i | −0.813331 | − | 0.581802i | \(-0.802348\pi\) | ||||
0.813331 | − | 0.581802i | \(-0.197652\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −318.555 | −1.22994 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 256.742i | − 0.976207i | −0.872786 | − | 0.488104i | \(-0.837689\pi\) | ||||
0.872786 | − | 0.488104i | \(-0.162311\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 162.205 | 0.612094 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 101.739i | 0.378212i | 0.981957 | + | 0.189106i | \(0.0605589\pi\) | ||||
−0.981957 | + | 0.189106i | \(0.939441\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −413.450 | −1.52565 | −0.762823 | − | 0.646608i | \(-0.776187\pi\) | ||||
−0.762823 | + | 0.646608i | \(0.776187\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 22.3739i | 0.0813596i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −52.8385 | −0.190753 | −0.0953764 | − | 0.995441i | \(-0.530405\pi\) | ||||
−0.0953764 | + | 0.995441i | \(0.530405\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 249.276i | − 0.887102i | −0.896249 | − | 0.443551i | \(-0.853719\pi\) | ||||
0.896249 | − | 0.443551i | \(-0.146281\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 264.801 | 0.935691 | 0.467846 | − | 0.883810i | \(-0.345030\pi\) | ||||
0.467846 | + | 0.883810i | \(0.345030\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 396.551i | 1.38171i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −82.2702 | −0.284672 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 140.716i | 0.480261i | 0.970741 | + | 0.240130i | \(0.0771902\pi\) | ||||
−0.970741 | + | 0.240130i | \(0.922810\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −82.3594 | −0.279184 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − 2.93986i | − 0.00983231i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.04695 | −0.0167673 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 135.003i | − 0.442632i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −224.226 | −0.730379 | −0.365189 | − | 0.930933i | \(-0.618996\pi\) | ||||
−0.365189 | + | 0.930933i | \(0.618996\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 190.561i | 0.612737i | 0.951913 | + | 0.306369i | \(0.0991140\pi\) | ||||
−0.951913 | + | 0.306369i | \(0.900886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 346.633 | 1.10745 | 0.553727 | − | 0.832698i | \(-0.313205\pi\) | ||||
0.553727 | + | 0.832698i | \(0.313205\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 394.319i | 1.24391i | 0.783054 | + | 0.621954i | \(0.213661\pi\) | ||||
−0.783054 | + | 0.621954i | \(0.786339\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 40.7378 | 0.127705 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 83.9889i | − 0.260028i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 46.4716 | 0.142990 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 85.2313i | − 0.259062i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −207.167 | −0.625882 | −0.312941 | − | 0.949773i | \(-0.601314\pi\) | ||||
−0.312941 | + | 0.949773i | \(0.601314\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 185.089i | 0.552504i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 288.916 | 0.857319 | 0.428659 | − | 0.903466i | \(-0.358986\pi\) | ||||
0.428659 | + | 0.903466i | \(0.358986\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 34.5306i | 0.101263i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 136.074 | 0.396717 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 111.771i | 0.322106i | 0.986946 | + | 0.161053i | \(0.0514891\pi\) | ||||
−0.986946 | + | 0.161053i | \(0.948511\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −364.709 | −1.04501 | −0.522505 | − | 0.852636i | \(-0.675003\pi\) | ||||
−0.522505 | + | 0.852636i | \(0.675003\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 227.805i | − 0.645341i | −0.946511 | − | 0.322671i | \(-0.895419\pi\) | ||||
0.946511 | − | 0.322671i | \(-0.104581\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.4091 | −0.0969272 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 125.832i | − 0.350506i | −0.984523 | − | 0.175253i | \(-0.943926\pi\) | ||||
0.984523 | − | 0.175253i | \(-0.0560744\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 145.032i | 0.397347i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 372.047 | 1.01375 | 0.506876 | − | 0.862019i | \(-0.330800\pi\) | ||||
0.506876 | + | 0.862019i | \(0.330800\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 684.221i | 1.84426i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 122.215 | 0.327655 | 0.163828 | − | 0.986489i | \(-0.447616\pi\) | ||||
0.163828 | + | 0.986489i | \(0.447616\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 84.6144i | − 0.224442i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −76.5257 | −0.201915 | −0.100957 | − | 0.994891i | \(-0.532191\pi\) | ||||
−0.100957 | + | 0.994891i | \(0.532191\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 494.820i | − 1.29196i | −0.763355 | − | 0.645979i | \(-0.776449\pi\) | ||||
0.763355 | − | 0.645979i | \(-0.223551\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 21.6713 | 0.0562892 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 685.225i | − 1.76150i | −0.473578 | − | 0.880752i | \(-0.657038\pi\) | ||||
0.473578 | − | 0.880752i | \(-0.342962\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.7829 | −0.0633834 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 126.508i | − 0.320272i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −171.558 | −0.432136 | −0.216068 | − | 0.976378i | \(-0.569323\pi\) | ||||
−0.216068 | + | 0.976378i | \(0.569323\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 704.126i | − 1.75593i | −0.478729 | − | 0.877963i | \(-0.658902\pi\) | ||||
0.478729 | − | 0.877963i | \(-0.341098\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 71.7218 | 0.177970 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 38.4622i | 0.0945016i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 223.677 | 0.546889 | 0.273444 | − | 0.961888i | \(-0.411837\pi\) | ||||
0.273444 | + | 0.961888i | \(0.411837\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 347.413i | − 0.841193i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 249.696 | 0.601676 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 527.562i | − 1.25910i | −0.776961 | − | 0.629549i | \(-0.783240\pi\) | ||||
0.776961 | − | 0.629549i | \(-0.216760\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 239.059 | 0.567836 | 0.283918 | − | 0.958849i | \(-0.408366\pi\) | ||||
0.283918 | + | 0.958849i | \(0.408366\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 391.754i | − 0.921775i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 569.476 | 1.33367 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − 165.894i | − 0.384905i | −0.981306 | − | 0.192452i | \(-0.938356\pi\) | ||||
0.981306 | − | 0.192452i | \(-0.0616441\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 266.348 | 0.615123 | 0.307561 | − | 0.951528i | \(-0.400487\pi\) | ||||
0.307561 | + | 0.951528i | \(0.400487\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 5.60640i | − 0.0128293i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 216.344 | 0.492811 | 0.246406 | − | 0.969167i | \(-0.420750\pi\) | ||||
0.246406 | + | 0.969167i | \(0.420750\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 307.303i | − 0.693686i | −0.937923 | − | 0.346843i | \(-0.887254\pi\) | ||||
0.937923 | − | 0.346843i | \(-0.112746\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.2506 | −0.0320238 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 652.614i | 1.45348i | 0.686911 | + | 0.726741i | \(0.258966\pi\) | ||||
−0.686911 | + | 0.726741i | \(0.741034\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 47.8795 | 0.106163 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 45.0124i | − 0.0989284i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 141.214 | 0.309002 | 0.154501 | − | 0.987993i | \(-0.450623\pi\) | ||||
0.154501 | + | 0.987993i | \(0.450623\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 43.3889i | 0.0941190i | 0.998892 | + | 0.0470595i | \(0.0149850\pi\) | ||||
−0.998892 | + | 0.0470595i | \(0.985015\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 640.051 | 1.38240 | 0.691199 | − | 0.722664i | \(-0.257083\pi\) | ||||
0.691199 | + | 0.722664i | \(0.257083\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 80.7873i | 0.172992i | 0.996252 | + | 0.0864961i | \(0.0275670\pi\) | ||||
−0.996252 | + | 0.0864961i | \(0.972433\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −780.751 | −1.66471 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0.609367i | 0.00128830i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 88.6228 | 0.186574 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 585.566i | − 1.22248i | −0.791447 | − | 0.611238i | \(-0.790672\pi\) | ||||
0.791447 | − | 0.611238i | \(-0.209328\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 79.8878 | 0.166087 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 30.2988i | − 0.0624717i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −314.449 | −0.645686 | −0.322843 | − | 0.946453i | \(-0.604639\pi\) | ||||
−0.322843 | + | 0.946453i | \(0.604639\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 422.460i | − 0.860408i | −0.902732 | − | 0.430204i | \(-0.858442\pi\) | ||||
0.902732 | − | 0.430204i | \(-0.141558\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −713.297 | −1.44685 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 145.147i | − 0.292045i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 975.125 | 1.95416 | 0.977079 | − | 0.212877i | \(-0.0682833\pi\) | ||||
0.977079 | + | 0.212877i | \(0.0682833\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 675.102i | − 1.34215i | −0.741389 | − | 0.671076i | \(-0.765832\pi\) | ||||
0.741389 | − | 0.671076i | \(-0.234168\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 214.790 | 0.425327 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.87656i | 0.00761603i | 0.999993 | + | 0.00380801i | \(0.00121213\pi\) | ||||
−0.999993 | + | 0.00380801i | \(0.998788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −611.781 | −1.19722 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23.4161i | 0.0454682i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.2908 | −0.0199048 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 890.215i | 1.70867i | 0.519726 | + | 0.854333i | \(0.326034\pi\) | ||||
−0.519726 | + | 0.854333i | \(0.673966\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −786.449 | −1.50373 | −0.751864 | − | 0.659319i | \(-0.770845\pi\) | ||||
−0.751864 | + | 0.659319i | \(0.770845\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 604.612i | − 1.14727i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 527.346 | 0.996873 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 99.4480i | − 0.186582i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 287.664 | 0.537690 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 37.4928i | 0.0695600i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 462.603 | 0.855088 | 0.427544 | − | 0.903995i | \(-0.359379\pi\) | ||||
0.427544 | + | 0.903995i | \(0.359379\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 18.4969i | 0.0339392i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −980.369 | −1.79227 | −0.896133 | − | 0.443786i | \(-0.853635\pi\) | ||||
−0.896133 | + | 0.443786i | \(0.853635\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 161.362i | − 0.292853i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 533.641 | 0.964993 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.4835i | 0.0403654i | 0.999796 | + | 0.0201827i | \(0.00642479\pi\) | ||||
−0.999796 | + | 0.0201827i | \(0.993575\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.26568 | 0.00226419 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 620.228i | 1.10165i | 0.834621 | + | 0.550824i | \(0.185687\pi\) | ||||
−0.834621 | + | 0.550824i | \(0.814313\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 411.825 | 0.728894 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 160.563i | 0.282184i | 0.989997 | + | 0.141092i | \(0.0450613\pi\) | ||||
−0.989997 | + | 0.141092i | \(0.954939\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 541.216 | 0.947840 | 0.473920 | − | 0.880568i | \(-0.342839\pi\) | ||||
0.473920 | + | 0.880568i | \(0.342839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 26.1503i | − 0.0454787i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −43.5123 | −0.0754112 | −0.0377056 | − | 0.999289i | \(-0.512005\pi\) | ||||
−0.0377056 | + | 0.999289i | \(0.512005\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1053.28i | 1.81287i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 82.6126 | 0.141703 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 64.7751i | 0.110349i | 0.998477 | + | 0.0551747i | \(0.0175716\pi\) | ||||
−0.998477 | + | 0.0551747i | \(0.982428\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 136.776 | 0.232217 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 702.719i | − 1.18502i | −0.805562 | − | 0.592512i | \(-0.798136\pi\) | ||||
0.805562 | − | 0.592512i | \(-0.201864\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −379.453 | −0.637736 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 858.099i | 1.43255i | 0.697817 | + | 0.716276i | \(0.254155\pi\) | ||||
−0.697817 | + | 0.716276i | \(0.745845\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1116.90 | −1.85840 | −0.929200 | − | 0.369577i | \(-0.879502\pi\) | ||||
−0.929200 | + | 0.369577i | \(0.879502\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 258.825i | 0.427811i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1135.10 | 1.87002 | 0.935012 | − | 0.354616i | \(-0.115388\pi\) | ||||
0.935012 | + | 0.354616i | \(0.115388\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 21.3745i | 0.0349828i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 228.738 | 0.373145 | 0.186573 | − | 0.982441i | \(-0.440262\pi\) | ||||
0.186573 | + | 0.982441i | \(0.440262\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 1084.17i | − 1.75716i | −0.477591 | − | 0.878582i | \(-0.658490\pi\) | ||||
0.477591 | − | 0.878582i | \(-0.341510\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −479.659 | −0.774893 | −0.387446 | − | 0.921892i | \(-0.626643\pi\) | ||||
−0.387446 | + | 0.921892i | \(0.626643\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 60.1127i | − 0.0964890i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 296.655 | 0.474649 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 673.451i | − 1.07067i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −39.9974 | −0.0633873 | −0.0316937 | − | 0.999498i | \(-0.510090\pi\) | ||||
−0.0316937 | + | 0.999498i | \(0.510090\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 144.421i | − 0.227435i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 77.8745 | 0.122252 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 1121.58i | − 1.74973i | −0.484364 | − | 0.874866i | \(-0.660949\pi\) | ||||
0.484364 | − | 0.874866i | \(-0.339051\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 653.314 | 1.01604 | 0.508020 | − | 0.861345i | \(-0.330378\pi\) | ||||
0.508020 | + | 0.861345i | \(0.330378\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 475.997i | − 0.735698i | −0.929885 | − | 0.367849i | \(-0.880094\pi\) | ||||
0.929885 | − | 0.367849i | \(-0.119906\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.9465 | −0.0646325 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 949.403i | 1.45391i | 0.686685 | + | 0.726955i | \(0.259065\pi\) | ||||
−0.686685 | + | 0.726955i | \(0.740935\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 163.172 | 0.249117 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 462.803i | 0.702281i | 0.936323 | + | 0.351140i | \(0.114206\pi\) | ||||
−0.936323 | + | 0.351140i | \(0.885794\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 395.105 | 0.597738 | 0.298869 | − | 0.954294i | \(-0.403391\pi\) | ||||
0.298869 | + | 0.954294i | \(0.403391\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − 85.8400i | − 0.129083i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −47.6138 | −0.0713849 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 68.7583i | − 0.102471i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −718.411 | −1.06748 | −0.533738 | − | 0.845650i | \(-0.679213\pi\) | ||||
−0.533738 | + | 0.845650i | \(0.679213\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1162.70i | 1.71743i | 0.512457 | + | 0.858713i | \(0.328735\pi\) | ||||
−0.512457 | + | 0.858713i | \(0.671265\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 127.808 | 0.188230 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 419.297i | − 0.613905i | −0.951725 | − | 0.306952i | \(-0.900691\pi\) | ||||
0.951725 | − | 0.306952i | \(-0.0993092\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −367.192 | −0.536047 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 171.590i | − 0.249043i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −767.513 | −1.11073 | −0.555364 | − | 0.831607i | \(-0.687421\pi\) | ||||
−0.555364 | + | 0.831607i | \(0.687421\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 281.129i | 0.404502i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −838.343 | −1.20279 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1227.38i | 1.75089i | 0.483314 | + | 0.875447i | \(0.339433\pi\) | ||||
−0.483314 | + | 0.875447i | \(0.660567\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 152.348 | 0.216712 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 906.039i | 1.28153i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 302.852 | 0.427154 | 0.213577 | − | 0.976926i | \(-0.431489\pi\) | ||||
0.213577 | + | 0.976926i | \(0.431489\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 40.3589i | − 0.0566043i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.43478 | −0.00760109 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 834.235i | − 1.16027i | −0.814520 | − | 0.580136i | \(-0.802999\pi\) | ||||
0.814520 | − | 0.580136i | \(-0.197001\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −98.7751 | −0.136997 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 752.652i | − 1.03814i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −760.433 | −1.04599 | −0.522994 | − | 0.852336i | \(-0.675185\pi\) | ||||
−0.522994 | + | 0.852336i | \(0.675185\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 10.6697i | − 0.0145960i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −486.420 | −0.663602 | −0.331801 | − | 0.943349i | \(-0.607656\pi\) | ||||
−0.331801 | + | 0.943349i | \(0.607656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 94.2676i | 0.127907i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 542.728 | 0.734408 | 0.367204 | − | 0.930140i | \(-0.380315\pi\) | ||||
0.367204 | + | 0.930140i | \(0.380315\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 250.265i | − 0.336830i | −0.985716 | − | 0.168415i | \(-0.946135\pi\) | ||||
0.985716 | − | 0.168415i | \(-0.0538649\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −137.243 | −0.184219 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1213.44i | 1.62008i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1194.76 | −1.59090 | −0.795448 | − | 0.606022i | \(-0.792764\pi\) | ||||
−0.795448 | + | 0.606022i | \(0.792764\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 11.7654i | − 0.0155834i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1179.94 | −1.55871 | −0.779355 | − | 0.626583i | \(-0.784453\pi\) | ||||
−0.779355 | + | 0.626583i | \(0.784453\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 523.434i | 0.687823i | 0.939002 | + | 0.343912i | \(0.111752\pi\) | ||||
−0.939002 | + | 0.343912i | \(0.888248\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −78.0246 | −0.102260 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 87.1249i | 0.113592i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1050.26 | 1.36574 | 0.682872 | − | 0.730538i | \(-0.260731\pi\) | ||||
0.682872 | + | 0.730538i | \(0.260731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1231.05i | 1.59256i | 0.604928 | + | 0.796280i | \(0.293202\pi\) | ||||
−0.604928 | + | 0.796280i | \(0.706798\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 637.970 | 0.823188 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 189.650i | − 0.243453i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −17.5249 | −0.0224391 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 241.239i | − 0.307310i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −151.612 | −0.192646 | −0.0963228 | − | 0.995350i | \(-0.530708\pi\) | ||||
−0.0963228 | + | 0.995350i | \(0.530708\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1737.18i | 2.19619i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −142.814 | −0.180094 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1199.06i | 1.50446i | 0.658899 | + | 0.752232i | \(0.271023\pi\) | ||||
−0.658899 | + | 0.752232i | \(0.728977\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 180.186 | 0.225514 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 73.8662i | 0.0919878i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −25.3291 | −0.0314648 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 21.7239i | 0.0268528i | 0.999910 | + | 0.0134264i | \(0.00427389\pi\) | ||||
−0.999910 | + | 0.0134264i | \(0.995726\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1050.05 | −1.29476 | −0.647381 | − | 0.762166i | \(-0.724136\pi\) | ||||
−0.647381 | + | 0.762166i | \(0.724136\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 505.617i | − 0.620388i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.41370 | 0.00295434 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1316.52i | 1.60355i | 0.597624 | + | 0.801776i | \(0.296111\pi\) | ||||
−0.597624 | + | 0.801776i | \(0.703889\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.71401 | −0.00572784 | −0.00286392 | − | 0.999996i | \(-0.500912\pi\) | ||||
−0.00286392 | + | 0.999996i | \(0.500912\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 107.497i | 0.129985i | 0.997886 | + | 0.0649924i | \(0.0207023\pi\) | ||||
−0.997886 | + | 0.0649924i | \(0.979298\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1234.04 | −1.48859 | −0.744293 | − | 0.667853i | \(-0.767213\pi\) | ||||
−0.744293 | + | 0.667853i | \(0.767213\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 656.479i | − 0.788090i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −317.264 | −0.379957 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 212.712i | 0.253530i | 0.991933 | + | 0.126765i | \(0.0404595\pi\) | ||||
−0.991933 | + | 0.126765i | \(0.959541\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −529.410 | −0.629500 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 353.866i | − 0.418777i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1091.79 | −1.28901 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 44.9540i | − 0.0528249i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −581.654 | −0.681892 | −0.340946 | − | 0.940083i | \(-0.610747\pi\) | ||||
−0.340946 | + | 0.940083i | \(0.610747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 452.387i | 0.527873i | 0.964540 | + | 0.263937i | \(0.0850209\pi\) | ||||
−0.964540 | + | 0.263937i | \(0.914979\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 880.415 | 1.02493 | 0.512465 | − | 0.858708i | \(-0.328732\pi\) | ||||
0.512465 | + | 0.858708i | \(0.328732\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 470.242i | 0.544892i | 0.962171 | + | 0.272446i | \(0.0878326\pi\) | ||||
−0.962171 | + | 0.272446i | \(0.912167\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −90.7103 | −0.104867 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 64.4316i | − 0.0741445i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 195.798 | 0.224797 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − 892.715i | − 1.02025i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 64.6856 | 0.0737579 | 0.0368789 | − | 0.999320i | \(-0.488258\pi\) | ||||
0.0368789 | + | 0.999320i | \(0.488258\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 804.020i | − 0.912622i | −0.889820 | − | 0.456311i | \(-0.849171\pi\) | ||||
0.889820 | − | 0.456311i | \(-0.150829\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 894.396 | 1.01291 | 0.506453 | − | 0.862267i | \(-0.330956\pi\) | ||||
0.506453 | + | 0.862267i | \(0.330956\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1450.55i | 1.63535i | 0.575682 | + | 0.817674i | \(0.304737\pi\) | ||||
−0.575682 | + | 0.817674i | \(0.695263\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 609.206 | 0.685271 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 40.7618i | 0.0456459i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −507.470 | −0.567006 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1161.60i | − 1.29210i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1446.50 | −1.60544 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 207.167i | 0.228914i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1663.35 | 1.83391 | 0.916954 | − | 0.398993i | \(-0.130640\pi\) | ||||
0.916954 | + | 0.398993i | \(0.130640\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 150.701i | − 0.165424i | −0.996574 | − | 0.0827118i | \(-0.973642\pi\) | ||||
0.996574 | − | 0.0827118i | \(-0.0263581\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 127.173 | 0.139291 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 688.300i | 0.750600i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 826.616 | 0.899473 | 0.449736 | − | 0.893161i | \(-0.351518\pi\) | ||||
0.449736 | + | 0.893161i | \(0.351518\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 36.4001i | 0.0394368i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 710.607 | 0.768224 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1130.62i | 1.21703i | 0.793541 | + | 0.608517i | \(0.208235\pi\) | ||||
−0.793541 | + | 0.608517i | \(0.791765\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 148.509 | 0.159515 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 45.8150i | 0.0490000i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.1269 | 0.0364214 | 0.0182107 | − | 0.999834i | \(-0.494203\pi\) | ||||
0.0182107 | + | 0.999834i | \(0.494203\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 424.451i | 0.451063i | 0.974236 | + | 0.225532i | \(0.0724119\pi\) | ||||
−0.974236 | + | 0.225532i | \(0.927588\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −55.9608 | −0.0593434 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1653.85i | − 1.74641i | −0.487356 | − | 0.873203i | \(-0.662039\pi\) | ||||
0.487356 | − | 0.873203i | \(-0.337961\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 153.424 | 0.161669 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 458.801i | 0.481428i | 0.970596 | + | 0.240714i | \(0.0773816\pi\) | ||||
−0.970596 | + | 0.240714i | \(0.922618\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −355.611 | −0.372367 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − 1548.91i | − 1.61513i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.6087 | 0.0245668 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 401.271i | 0.415825i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 953.711 | 0.986257 | 0.493129 | − | 0.869956i | \(-0.335853\pi\) | ||||
0.493129 | + | 0.869956i | \(0.335853\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 668.931i | 0.688909i | 0.938803 | + | 0.344454i | \(0.111936\pi\) | ||||
−0.938803 | + | 0.344454i | \(0.888064\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1185.87 | −1.21878 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1236.97i | 1.26609i | 0.774116 | + | 0.633044i | \(0.218195\pi\) | ||||
−0.774116 | + | 0.633044i | \(0.781805\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.25798 | −0.00741367 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 608.856i | − 0.619385i | −0.950837 | − | 0.309693i | \(-0.899774\pi\) | ||||
0.950837 | − | 0.309693i | \(-0.100226\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 344.896 | 0.350149 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 0.712219i | 0 0.000720140i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1705.01 | 1.72049 | 0.860246 | − | 0.509878i | \(-0.170310\pi\) | ||||
0.860246 | + | 0.509878i | \(0.170310\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 630.104i | − 0.633270i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 74.8450 | 0.0750702 | 0.0375351 | − | 0.999295i | \(-0.488049\pi\) | ||||
0.0375351 | + | 0.999295i | \(0.488049\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 684.3.e.a.305.8 | yes | 12 | |
3.2 | odd | 2 | inner | 684.3.e.a.305.5 | ✓ | 12 | |
4.3 | odd | 2 | 2736.3.h.c.305.8 | 12 | |||
12.11 | even | 2 | 2736.3.h.c.305.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.e.a.305.5 | ✓ | 12 | 3.2 | odd | 2 | inner | |
684.3.e.a.305.8 | yes | 12 | 1.1 | even | 1 | trivial | |
2736.3.h.c.305.5 | 12 | 12.11 | even | 2 | |||
2736.3.h.c.305.8 | 12 | 4.3 | odd | 2 |