Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3332,2,Mod(2549,3332)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3332, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3332.2549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3332 = 2^{2} \cdot 7^{2} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3332.b (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: | \(26.6061539535\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.980441344.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 8x^{6} + 18x^{4} + 9x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 476) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2549.5 | ||
Root | \(2.06150i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3332.2549 |
Dual form | 3332.2.b.b.2549.4 |
$q$-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 \(\left(\mathbb{Z}/3332\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(885\) | \(1667\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0.811721i | 0.468648i | 0.972159 | + | 0.234324i | \(0.0752876\pi\) | ||||
−0.972159 | + | 0.234324i | \(0.924712\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.15845i | 0.518073i | 0.965868 | + | 0.259037i | \(0.0834050\pi\) | ||||
−0.965868 | + | 0.259037i | \(0.916595\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.34111 | 0.780369 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.12300i | − | 0.640108i | −0.947399 | − | 0.320054i | \(-0.896299\pi\) | ||
0.947399 | − | 0.320054i | \(-0.103701\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.15283 | 0.319737 | 0.159869 | − | 0.987138i | \(-0.448893\pi\) | ||||
0.159869 | + | 0.987138i | \(0.448893\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.940336 | −0.242794 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.12300 | − | 0.0298321i | 0.999974 | − | 0.00723535i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.653275 | −0.149872 | −0.0749358 | − | 0.997188i | \(-0.523875\pi\) | ||||
−0.0749358 | + | 0.997188i | \(0.523875\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.65238i | − | 1.59563i | −0.602901 | − | 0.797816i | \(-0.705988\pi\) | ||
0.602901 | − | 0.797816i | \(-0.294012\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.65800 | 0.731600 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.33549i | 0.834366i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.49956i | − | 0.464156i | −0.972697 | − | 0.232078i | \(-0.925448\pi\) | ||
0.972697 | − | 0.232078i | \(-0.0745524\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.841553i | 0.151147i | 0.997140 | + | 0.0755737i | \(0.0240788\pi\) | ||||
−0.997140 | + | 0.0755737i | \(0.975921\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.72328 | 0.299985 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.97017i | − | 0.488293i | −0.969738 | − | 0.244146i | \(-0.921492\pi\) | ||
0.969738 | − | 0.244146i | \(-0.0785077\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0.935777i | 0.149844i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.81083i | − | 1.53219i | −0.642725 | − | 0.766097i | \(-0.722196\pi\) | ||
0.642725 | − | 0.766097i | \(-0.277804\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.03456 | −1.07276 | −0.536380 | − | 0.843977i | \(-0.680209\pi\) | ||||
−0.536380 | + | 0.843977i | \(0.680209\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.71205i | 0.404288i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.55922 | −0.956760 | −0.478380 | − | 0.878153i | \(-0.658776\pi\) | ||||
−0.478380 | + | 0.878153i | \(0.658776\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.0242154 | + | 3.34673i | 0.00339083 | + | 0.468635i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 6.90489 | 0.948459 | 0.474230 | − | 0.880401i | \(-0.342727\pi\) | ||||
0.474230 | + | 0.880401i | \(0.342727\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.45938 | 0.331623 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.530277i | − | 0.0702369i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.929992 | 0.121075 | 0.0605373 | − | 0.998166i | \(-0.480719\pi\) | ||||
0.0605373 | + | 0.998166i | \(0.480719\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.49394i | − | 0.703427i | −0.936108 | − | 0.351713i | \(-0.885599\pi\) | ||
0.936108 | − | 0.351713i | \(-0.114401\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.33549i | 0.165647i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.5871 | 1.41559 | 0.707795 | − | 0.706418i | \(-0.249690\pi\) | ||||
0.707795 | + | 0.706418i | \(0.249690\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.21160 | 0.747789 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.72328i | − | 0.679229i | −0.940565 | − | 0.339614i | \(-0.889703\pi\) | ||
0.940565 | − | 0.339614i | \(-0.110297\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.99805i | − | 0.819060i | −0.912297 | − | 0.409530i | \(-0.865693\pi\) | ||
0.912297 | − | 0.409530i | \(-0.134307\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.96928i | 0.342863i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 12.4883i | 1.40505i | 0.711661 | + | 0.702523i | \(0.247943\pi\) | ||||
−0.711661 | + | 0.702523i | \(0.752057\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3.50411 | 0.389346 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.3988 | 1.25118 | 0.625592 | − | 0.780151i | \(-0.284858\pi\) | ||||
0.625592 | + | 0.780151i | \(0.284858\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.0345589 | + | 4.77627i | 0.00374844 | + | 0.518059i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.02894 | 0.217525 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.75678 | −0.716218 | −0.358109 | − | 0.933680i | \(-0.616578\pi\) | ||||
−0.358109 | + | 0.933680i | \(0.616578\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −0.683107 | −0.0708349 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.756784i | − | 0.0776444i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 13.7810i | − | 1.39925i | −0.714511 | − | 0.699624i | \(-0.753351\pi\) | ||
0.714511 | − | 0.699624i | \(-0.246649\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 4.97017i | − | 0.499521i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 3.28706 | 0.327075 | 0.163537 | − | 0.986537i | \(-0.447710\pi\) | ||||
0.163537 | + | 0.986537i | \(0.447710\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −13.2795 | −1.30847 | −0.654234 | − | 0.756292i | \(-0.727009\pi\) | ||||
−0.654234 | + | 0.756292i | \(0.727009\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.52939i | − | 0.727893i | −0.931420 | − | 0.363947i | \(-0.881429\pi\) | ||
0.931420 | − | 0.363947i | \(-0.118571\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.9291i | 1.52573i | 0.646557 | + | 0.762866i | \(0.276208\pi\) | ||||
−0.646557 | + | 0.762866i | \(0.723792\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.41095 | 0.228837 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.4390i | 1.64052i | 0.571989 | + | 0.820262i | \(0.306172\pi\) | ||||
−0.571989 | + | 0.820262i | \(0.693828\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.86488 | 0.826654 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.69890 | 0.249513 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.49288 | 0.590262 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.96366 | 0.718059 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.0298i | 0.897095i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.51710 | −0.755770 | −0.377885 | − | 0.925853i | \(-0.623349\pi\) | ||||
−0.377885 | + | 0.925853i | \(0.623349\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 5.71010i | − | 0.502746i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.69345i | − | 0.235328i | −0.993053 | − | 0.117664i | \(-0.962459\pi\) | ||
0.993053 | − | 0.117664i | \(-0.0375406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.02244 | −0.432262 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4.89454 | 0.418169 | 0.209085 | − | 0.977898i | \(-0.432952\pi\) | ||||
0.209085 | + | 0.977898i | \(0.432952\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.34478i | − | 0.114063i | −0.998372 | − | 0.0570313i | \(-0.981837\pi\) | ||
0.998372 | − | 0.0570313i | \(-0.0181635\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 5.32426i | − | 0.448383i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 2.44746i | − | 0.204666i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.89560 | 0.240467 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 12.8331 | 1.05133 | 0.525664 | − | 0.850692i | \(-0.323817\pi\) | ||||
0.525664 | + | 0.850692i | \(0.323817\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.1509 | 0.988825 | 0.494412 | − | 0.869227i | \(-0.335383\pi\) | ||||
0.494412 | + | 0.869227i | \(0.335383\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.65238 | − | 0.0698402i | 0.780349 | − | 0.00564625i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.974895 | −0.0783054 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.3793 | 1.22740 | 0.613702 | − | 0.789537i | \(-0.289679\pi\) | ||||
0.613702 | + | 0.789537i | \(0.289679\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.60484i | 0.444493i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.41006i | 0.580401i | 0.956966 | + | 0.290200i | \(0.0937219\pi\) | ||||
−0.956966 | + | 0.290200i | \(0.906278\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.99633i | 0.155414i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 15.1174i | 1.16982i | 0.811099 | + | 0.584909i | \(0.198870\pi\) | ||||
−0.811099 | + | 0.584909i | \(0.801130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −11.6710 | −0.897768 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.52939 | −0.116955 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.0474i | 0.763888i | 0.924186 | + | 0.381944i | \(0.124745\pi\) | ||||
−0.924186 | + | 0.381944i | \(0.875255\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0.754895i | 0.0567413i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.9533 | 1.19241 | 0.596203 | − | 0.802833i | \(-0.296675\pi\) | ||||
0.596203 | + | 0.802833i | \(0.296675\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.69256i | 0.423125i | 0.977365 | + | 0.211562i | \(0.0678551\pi\) | ||||
−0.977365 | + | 0.211562i | \(0.932145\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.45955 | 0.329659 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.44078 | 0.252971 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.0633335 | − | 8.75311i | −0.00463140 | − | 0.640091i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.15177 | −0.589842 | −0.294921 | − | 0.955522i | \(-0.595293\pi\) | ||||
−0.294921 | + | 0.955522i | \(0.595293\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 2.91807i | − | 0.210047i | −0.994470 | − | 0.105024i | \(-0.966508\pi\) | ||
0.994470 | − | 0.105024i | \(-0.0334918\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.08405 | −0.0776302 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 9.33916i | − | 0.665388i | −0.943035 | − | 0.332694i | \(-0.892042\pi\) | ||
0.943035 | − | 0.332694i | \(-0.107958\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 12.9868i | − | 0.920611i | −0.887761 | − | 0.460306i | \(-0.847740\pi\) | ||
0.887761 | − | 0.460306i | \(-0.152260\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.40550i | 0.663413i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3653 | 0.793789 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 17.9151i | − | 1.24518i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.38690i | 0.0959339i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 8.57412i | 0.590267i | 0.955456 | + | 0.295133i | \(0.0953641\pi\) | ||||
−0.955456 | + | 0.295133i | \(0.904636\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.64571 | 0.318319 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 8.14916i | − | 0.555768i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.68047 | 0.383850 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.75311 | − | 0.0343913i | 0.319729 | − | 0.00231341i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.981401 | 0.0657195 | 0.0328597 | − | 0.999460i | \(-0.489539\pi\) | ||||
0.0328597 | + | 0.999460i | \(0.489539\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.56378 | 0.570919 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 27.2626i | 1.80949i | 0.425958 | + | 0.904743i | \(0.359937\pi\) | ||||
−0.425958 | + | 0.904743i | \(0.640063\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8770 | −0.784854 | −0.392427 | − | 0.919783i | \(-0.628365\pi\) | ||||
−0.392427 | + | 0.919783i | \(0.628365\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.97017i | 0.456631i | 0.973587 | + | 0.228315i | \(0.0733217\pi\) | ||||
−0.973587 | + | 0.228315i | \(0.926678\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 7.59850i | − | 0.495672i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −10.1370 | −0.658471 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −0.777330 | −0.0502813 | −0.0251406 | − | 0.999684i | \(-0.508003\pi\) | ||||
−0.0251406 | + | 0.999684i | \(0.508003\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.9098i | 1.54016i | 0.637945 | + | 0.770082i | \(0.279785\pi\) | ||||
−0.637945 | + | 0.770082i | \(0.720215\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 15.8508i | 1.01683i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.753115 | −0.0479195 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 9.25267i | 0.586364i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 21.9675 | 1.38658 | 0.693288 | − | 0.720661i | \(-0.256161\pi\) | ||||
0.693288 | + | 0.720661i | \(0.256161\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.2460 | −1.02138 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3.87700 | + | 0.0280522i | −0.242787 | + | 0.00175670i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.58238 | 0.161084 | 0.0805421 | − | 0.996751i | \(-0.474335\pi\) | ||||
0.0805421 | + | 0.996751i | \(0.474335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 5.85173i | − | 0.362213i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −2.08213 | −0.128390 | −0.0641949 | − | 0.997937i | \(-0.520448\pi\) | ||||
−0.0641949 | + | 0.997937i | \(0.520448\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.99894i | 0.491371i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.48463i | − | 0.335654i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.3065i | 1.17714i | 0.808446 | + | 0.588571i | \(0.200309\pi\) | ||||
−0.808446 | + | 0.588571i | \(0.799691\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.90961 | −0.601966 | −0.300983 | − | 0.953629i | \(-0.597315\pi\) | ||||
−0.300983 | + | 0.953629i | \(0.597315\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 7.76593i | − | 0.468303i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 20.7575i | − | 1.24720i | −0.781745 | − | 0.623598i | \(-0.785670\pi\) | ||
0.781745 | − | 0.623598i | \(-0.214330\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.97017i | 0.117951i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.42235 | 0.263815 | 0.131908 | − | 0.991262i | \(-0.457890\pi\) | ||||
0.131908 | + | 0.991262i | \(0.457890\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 29.1567i | − | 1.73318i | −0.499017 | − | 0.866592i | \(-0.666306\pi\) | ||
0.499017 | − | 0.866592i | \(-0.333694\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.614298 | 0.0363879 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.9982 | − | 0.245995i | 0.999895 | − | 0.0144703i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.1863 | 0.655754 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.0194886 | −0.00113853 | −0.000569267 | − | 1.00000i | \(-0.500181\pi\) | ||||
−0.000569267 | 1.00000i | \(0.500181\pi\) | ||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.07735i | 0.0627255i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 9.20424 | 0.534084 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 8.82190i | − | 0.510183i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.66818i | 0.153283i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 6.36443 | 0.364426 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3979 | 0.707588 | 0.353794 | − | 0.935323i | \(-0.384891\pi\) | ||||
0.353794 | + | 0.935323i | \(0.384891\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 10.7793i | − | 0.613210i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 8.02699i | − | 0.455169i | −0.973758 | − | 0.227585i | \(-0.926917\pi\) | ||
0.973758 | − | 0.227585i | \(-0.0730828\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 31.7101i | − | 1.79236i | −0.443690 | − | 0.896180i | \(-0.646331\pi\) | ||
0.443690 | − | 0.896180i | \(-0.353669\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 19.7678i | − | 1.11027i | −0.831760 | − | 0.555136i | \(-0.812666\pi\) | ||
0.831760 | − | 0.555136i | \(-0.187334\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.30655 | −0.297110 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.11176 | 0.341125 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −2.69345 | + | 0.0194886i | −0.149868 | + | 0.00108437i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.21705 | 0.233920 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.9300 | −0.715030 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.0224 | −1.48529 | −0.742644 | − | 0.669687i | \(-0.766428\pi\) | ||||
−0.742644 | + | 0.669687i | \(0.766428\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.95349i | − | 0.381049i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 13.4230i | 0.733379i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 6.55343i | − | 0.356988i | −0.983941 | − | 0.178494i | \(-0.942877\pi\) | ||
0.983941 | − | 0.178494i | \(-0.0571226\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −14.1556 | −0.768827 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.78662 | 0.0967507 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 7.19581i | 0.387409i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.0463i | 0.968777i | 0.874853 | + | 0.484388i | \(0.160958\pi\) | ||||
−0.874853 | + | 0.484388i | \(0.839042\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.6439 | −0.676814 | −0.338407 | − | 0.941000i | \(-0.609888\pi\) | ||||
−0.338407 | + | 0.941000i | \(0.609888\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.99808i | 0.266778i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.25267 | −0.173122 | −0.0865611 | − | 0.996247i | \(-0.527588\pi\) | ||||
−0.0865611 | + | 0.996247i | \(0.527588\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.63012 | 0.351890 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.2114 | −0.538939 | −0.269470 | − | 0.963009i | \(-0.586848\pi\) | ||||
−0.269470 | + | 0.963009i | \(0.586848\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.5732 | −0.977539 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.27041i | 0.276625i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.10687 | 0.424333 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.18828i | 0.166427i | 0.996532 | + | 0.0832134i | \(0.0265183\pi\) | ||||
−0.996532 | + | 0.0832134i | \(0.973482\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 22.9682i | − | 1.19568i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.23301 | 0.115621 | 0.0578105 | − | 0.998328i | \(-0.481588\pi\) | ||||
0.0578105 | + | 0.998328i | \(0.481588\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −8.14143 | −0.420422 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 2.88156i | − | 0.148408i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.5657i | 1.31322i | 0.754230 | + | 0.656610i | \(0.228010\pi\) | ||||
−0.754230 | + | 0.656610i | \(0.771990\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 6.91351i | − | 0.354190i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 15.9946 | 0.817283 | 0.408642 | − | 0.912695i | \(-0.366003\pi\) | ||||
0.408642 | + | 0.912695i | \(0.366003\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −16.4687 | −0.837149 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.04668 | 0.357281 | 0.178640 | − | 0.983914i | \(-0.442830\pi\) | ||||
0.178640 | + | 0.983914i | \(0.442830\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.228287 | − | 31.5508i | −0.0115450 | − | 1.59559i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.18633 | 0.110286 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −14.4671 | −0.727916 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 39.0840i | 1.96157i | 0.195094 | + | 0.980785i | \(0.437499\pi\) | ||||
−0.195094 | + | 0.980785i | \(0.562501\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.5115i | 0.524918i | 0.964943 | + | 0.262459i | \(0.0845335\pi\) | ||||
−0.964943 | + | 0.262459i | \(0.915467\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.970168i | 0.0483275i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 4.05933i | 0.201710i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −6.30566 | −0.312560 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 24.6208 | 1.21742 | 0.608709 | − | 0.793393i | \(-0.291688\pi\) | ||||
0.608709 | + | 0.793393i | \(0.291688\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.97301i | 0.195974i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 13.2049i | 0.648205i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.09158 | 0.0534551 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 27.9579i | − | 1.36583i | −0.730497 | − | 0.682916i | \(-0.760712\pi\) | ||
0.730497 | − | 0.682916i | \(-0.239288\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.41290 | 0.166334 | 0.0831672 | − | 0.996536i | \(-0.473496\pi\) | ||||
0.0831672 | + | 0.996536i | \(0.473496\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.3558 | −0.746627 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.0819 | − | 0.109126i | 0.731581 | − | 0.00529338i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.98665 | 0.0959164 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 7.27216i | − | 0.350288i | −0.984543 | − | 0.175144i | \(-0.943961\pi\) | ||
0.984543 | − | 0.175144i | \(-0.0560390\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −29.4853 | −1.41697 | −0.708487 | − | 0.705724i | \(-0.750622\pi\) | ||||
−0.708487 | + | 0.705724i | \(0.750622\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.35042i | 0.112694i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.99911i | 0.239140i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 26.6681i | − | 1.27280i | −0.771359 | − | 0.636401i | \(-0.780423\pi\) | ||
0.771359 | − | 0.636401i | \(-0.219577\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.7994 | −0.798165 | −0.399083 | − | 0.916915i | \(-0.630671\pi\) | ||||
−0.399083 | + | 0.916915i | \(0.630671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 7.82737i | − | 0.371053i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.4169i | 0.492702i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.8938i | 1.45797i | 0.684530 | + | 0.728985i | \(0.260008\pi\) | ||||
−0.684530 | + | 0.728985i | \(0.739992\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −20.8284 | −0.980770 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.86313i | 0.463410i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.3186 | 0.997244 | 0.498622 | − | 0.866820i | \(-0.333840\pi\) | ||||
0.498622 | + | 0.866820i | \(0.333840\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.129337 | + | 17.8752i | 0.00603693 | + | 0.834344i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.63957 | −0.309236 | −0.154618 | − | 0.987974i | \(-0.549415\pi\) | ||||
−0.154618 | + | 0.987974i | \(0.549415\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.0316 | −0.559154 | −0.279577 | − | 0.960123i | \(-0.590194\pi\) | ||||
−0.279577 | + | 0.960123i | \(0.590194\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 0.791343i | − | 0.0366976i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.1230 | −0.931181 | −0.465591 | − | 0.885000i | \(-0.654158\pi\) | ||||
−0.465591 | + | 0.885000i | \(0.654158\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.4837i | 0.575220i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14.9344i | 0.686682i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.38968 | −0.109646 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 16.1651 | 0.740149 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 7.79014i | − | 0.355941i | −0.984036 | − | 0.177970i | \(-0.943047\pi\) | ||
0.984036 | − | 0.177970i | \(-0.0569531\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3.42410i | − | 0.156125i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.9646 | 0.724913 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.5388i | 0.885389i | 0.896672 | + | 0.442695i | \(0.145977\pi\) | ||||
−0.896672 | + | 0.442695i | \(0.854023\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −6.01490 | −0.272003 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.0903 | 0.906664 | 0.453332 | − | 0.891342i | \(-0.350235\pi\) | ||||
0.453332 | + | 0.891342i | \(0.350235\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.0745670 | − | 10.3057i | −0.00335833 | − | 0.464144i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.75767 | 0.258788 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 4.29374i | − | 0.192214i | −0.995371 | − | 0.0961070i | \(-0.969361\pi\) | ||
0.995371 | − | 0.0961070i | \(-0.0306391\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −12.2711 | −0.548232 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 30.2863i | − | 1.35040i | −0.737634 | − | 0.675201i | \(-0.764057\pi\) | ||
0.737634 | − | 0.675201i | \(-0.235943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.80788i | 0.169449i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 9.47359i | − | 0.420737i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 41.6448 | 1.84587 | 0.922937 | − | 0.384951i | \(-0.125782\pi\) | ||||
0.922937 | + | 0.384951i | \(0.125782\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 2.83227i | − | 0.125048i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 15.3836i | − | 0.677882i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.9252i | 0.612430i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −8.15567 | −0.357994 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 7.74171i | − | 0.339171i | −0.985516 | − | 0.169585i | \(-0.945757\pi\) | ||
0.985516 | − | 0.169585i | \(-0.0542428\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −21.6134 | −0.945088 | −0.472544 | − | 0.881307i | \(-0.656664\pi\) | ||||
−0.472544 | + | 0.881307i | \(0.656664\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.0251053 | + | 3.46972i | 0.00109360 | + | 0.151144i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −35.5590 | −1.54604 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.17721 | 0.0944830 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 11.3102i | − | 0.489900i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 8.72239 | 0.377102 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12.9496i | 0.558819i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 34.9666i | − | 1.50333i | −0.659544 | − | 0.751666i | \(-0.729251\pi\) | ||
0.659544 | − | 0.751666i | \(-0.270749\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −4.62077 | −0.198296 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −18.4530 | −0.790440 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 26.8856i | − | 1.14954i | −0.818314 | − | 0.574772i | \(-0.805091\pi\) | ||
0.818314 | − | 0.574772i | \(-0.194909\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 12.8619i | − | 0.548933i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.63290i | 0.0695637i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.79296i | 0.118554i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −39.4297 | −1.67069 | −0.835344 | − | 0.549727i | \(-0.814732\pi\) | ||||
−0.835344 | + | 0.549727i | \(0.814732\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.10965 | −0.343002 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.10509 | − | 0.0514091i | 0.299977 | − | 0.00217050i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −13.3197 | −0.561357 | −0.280679 | − | 0.959802i | \(-0.590560\pi\) | ||||
−0.280679 | + | 0.959802i | \(0.590560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −20.2022 | −0.849911 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.88420 | 0.0789898 | 0.0394949 | − | 0.999220i | \(-0.487425\pi\) | ||||
0.0394949 | + | 0.999220i | \(0.487425\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.6866i | 1.36789i | 0.729533 | + | 0.683945i | \(0.239737\pi\) | ||||
−0.729533 | + | 0.683945i | \(0.760263\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6.61697i | − | 0.276428i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 27.9924i | − | 1.16737i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.84840 | −0.326733 | −0.163366 | − | 0.986565i | \(-0.552235\pi\) | ||||
−0.163366 | + | 0.986565i | \(0.552235\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.36866 | 0.0984381 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 14.6591i | − | 0.607116i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 3.12653i | 0.129266i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 1.68500 | 0.0695472 | 0.0347736 | − | 0.999395i | \(-0.488929\pi\) | ||||
0.0347736 | + | 0.999395i | \(0.488929\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 0.549766i | − | 0.0226527i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.58080 | 0.311832 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 40.0065 | 1.64287 | 0.821435 | − | 0.570303i | \(-0.193174\pi\) | ||||
0.821435 | + | 0.570303i | \(0.193174\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 10.5417 | 0.431442 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.3774 | −1.44548 | −0.722741 | − | 0.691119i | \(-0.757118\pi\) | ||||
−0.722741 | + | 0.691119i | \(0.757118\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 20.8664i | 0.851160i | 0.904921 | + | 0.425580i | \(0.139930\pi\) | ||||
−0.904921 | + | 0.425580i | \(0.860070\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 27.1267 | 1.10468 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.52166i | 0.305799i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13.3223i | 0.540736i | 0.962757 | + | 0.270368i | \(0.0871454\pi\) | ||||
−0.962757 | + | 0.270368i | \(0.912855\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.56166 | −0.305912 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −21.3299 | −0.861506 | −0.430753 | − | 0.902470i | \(-0.641752\pi\) | ||||
−0.430753 | + | 0.902470i | \(0.641752\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.22548i | 0.372007i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10.8277i | 0.435906i | 0.975959 | + | 0.217953i | \(0.0699380\pi\) | ||||
−0.975959 | + | 0.217953i | \(0.930062\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.5534i | 0.665339i | 0.943044 | + | 0.332669i | \(0.107949\pi\) | ||||
−0.943044 | + | 0.332669i | \(0.892051\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 33.1769 | 1.33134 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.67098 | 0.266839 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.12578 | −0.0449592 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −0.0886064 | − | 12.2460i | −0.00353297 | − | 0.488280i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.6334 | −1.25931 | −0.629653 | − | 0.776876i | \(-0.716803\pi\) | ||||
−0.629653 | + | 0.776876i | \(0.716803\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −6.95980 | −0.276627 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 9.86660i | − | 0.391544i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 13.3988i | − | 0.530049i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 9.84628i | − | 0.388905i | −0.980912 | − | 0.194452i | \(-0.937707\pi\) | ||
0.980912 | − | 0.194452i | \(-0.0622930\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 2.31795i | − | 0.0914110i | −0.998955 | − | 0.0457055i | \(-0.985446\pi\) | ||
0.998955 | − | 0.0457055i | \(-0.0145536\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.61485 | 0.260459 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18.7231 | −0.736080 | −0.368040 | − | 0.929810i | \(-0.619971\pi\) | ||||
−0.368040 | + | 0.929810i | \(0.619971\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.97437i | − | 0.0775009i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.9282i | 1.52338i | 0.647942 | + | 0.761689i | \(0.275630\pi\) | ||||
−0.647942 | + | 0.761689i | \(0.724370\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 3.12022 | 0.121917 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 16.3832i | − | 0.639170i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 32.6904 | 1.27344 | 0.636719 | − | 0.771096i | \(-0.280291\pi\) | ||||
0.636719 | + | 0.771096i | \(0.280291\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −17.9507 | −0.698202 | −0.349101 | − | 0.937085i | \(-0.613513\pi\) | ||||
−0.349101 | + | 0.937085i | \(0.613513\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0.0279162 | + | 3.85820i | 0.00108417 | + | 0.149840i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −19.1276 | −0.740622 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.796624i | 0.0307993i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −11.6636 | −0.450269 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 42.8631i | − | 1.65225i | −0.563486 | − | 0.826126i | \(-0.690540\pi\) | ||
0.563486 | − | 0.826126i | \(-0.309460\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15.8592i | 0.610422i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 22.8110i | 0.876698i | 0.898805 | + | 0.438349i | \(0.144437\pi\) | ||||
−0.898805 | + | 0.438349i | \(0.855563\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −22.1297 | −0.848011 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 37.2068i | − | 1.42368i | −0.702342 | − | 0.711840i | \(-0.747862\pi\) | ||
0.702342 | − | 0.711840i | \(-0.252138\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.67007i | 0.216642i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 9.64082i | − | 0.367820i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.96016 | 0.303258 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 15.9263i | 0.605864i | 0.953012 | + | 0.302932i | \(0.0979655\pi\) | ||||
−0.953012 | + | 0.302932i | \(0.902035\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.55785 | 0.0590927 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.292678 | − | 40.4500i | −0.0110860 | − | 1.53215i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.65783 | −0.213999 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.1249 | 1.36442 | 0.682209 | − | 0.731157i | \(-0.261019\pi\) | ||||
0.682209 | + | 0.731157i | \(0.261019\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.94034i | 0.0731812i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.16787 | 0.232295 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.3906i | 0.916008i | 0.888950 | + | 0.458004i | \(0.151435\pi\) | ||||
−0.888950 | + | 0.458004i | \(0.848565\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 29.2365i | 1.09645i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.43989 | 0.241176 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.83525 | 0.106032 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 0.630975i | − | 0.0235642i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 26.6103i | 0.992395i | 0.868210 | + | 0.496198i | \(0.165271\pi\) | ||||
−0.868210 | + | 0.496198i | \(0.834729\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −19.4081 | −0.721794 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 9.14338i | − | 0.339576i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.7943 | −1.69842 | −0.849208 | − | 0.528058i | \(-0.822920\pi\) | ||||
−0.849208 | + | 0.528058i | \(0.822920\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.35412 | −0.0871897 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −29.0035 | + | 0.209856i | −1.07273 | + | 0.00776179i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.380227 | −0.0140440 | −0.00702199 | − | 0.999975i | \(-0.502235\pi\) | ||||
−0.00702199 | + | 0.999975i | \(0.502235\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 24.5994i | − | 0.906130i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.7613 | −1.09479 | −0.547394 | − | 0.836875i | \(-0.684380\pi\) | ||||
−0.547394 | + | 0.836875i | \(0.684380\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 0.611319i | − | 0.0224574i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 8.09336i | − | 0.296917i | −0.988919 | − | 0.148458i | \(-0.952569\pi\) | ||
0.988919 | − | 0.148458i | \(-0.0474311\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14.8665i | 0.544665i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 26.6859 | 0.976386 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 32.2728i | − | 1.17765i | −0.808260 | − | 0.588826i | \(-0.799590\pi\) | ||
0.808260 | − | 0.588826i | \(-0.200410\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.8315i | 0.649816i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 14.0761i | 0.512283i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.1707 | −1.13292 | −0.566459 | − | 0.824090i | \(-0.691687\pi\) | ||||
−0.566459 | + | 0.824090i | \(0.691687\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 13.1872i | − | 0.478666i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −30.2779 | −1.09757 | −0.548787 | − | 0.835962i | \(-0.684910\pi\) | ||||
−0.548787 | + | 0.835962i | \(0.684910\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0809061 | + | 11.1818i | 0.00292517 | + | 0.404278i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.07212 | 0.0387121 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −44.7810 | −1.61484 | −0.807421 | − | 0.589975i | \(-0.799138\pi\) | ||||
−0.807421 | + | 0.589975i | \(0.799138\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.09617i | 0.0754917i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.2600 | −0.764669 | −0.382335 | − | 0.924024i | \(-0.624880\pi\) | ||||
−0.382335 | + | 0.924024i | \(0.624880\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.07840i | 0.110580i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.40917i | 0.229632i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −12.1505 | −0.434780 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 10.8368 | 0.387276 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.8161i | 0.635885i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 30.1828i | 1.07590i | 0.842977 | + | 0.537950i | \(0.180801\pi\) | ||||
−0.842977 | + | 0.537950i | \(0.819199\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 1.69011i | − | 0.0601695i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 6.33358i | − | 0.224912i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.49291 | −0.230280 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −12.8320 | −0.454534 | −0.227267 | − | 0.973832i | \(-0.572979\pi\) | ||||
−0.227267 | + | 0.973832i | \(0.572979\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27.0436 | + | 0.195675i | −0.956735 | + | 0.00692250i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −15.8184 | −0.558914 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.8568 | −0.524287 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.6715 | −0.551664 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.4667i | 0.367990i | 0.982927 | + | 0.183995i | \(0.0589031\pi\) | ||||
−0.982927 | + | 0.183995i | \(0.941097\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.42304i | − | 0.0499697i | −0.999688 | − | 0.0249849i | \(-0.992046\pi\) | ||
0.999688 | − | 0.0249849i | \(-0.00795375\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 8.04384i | − | 0.282110i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8.58416 | −0.300690 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.59550 | 0.160776 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 8.39215i | − | 0.292888i | −0.989219 | − | 0.146444i | \(-0.953217\pi\) | ||
0.989219 | − | 0.146444i | \(-0.0467828\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 9.64624i | − | 0.336247i | −0.985766 | − | 0.168123i | \(-0.946229\pi\) | ||
0.985766 | − | 0.168123i | \(-0.0537707\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.30377 | 0.219469 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 30.0944i | 1.04648i | 0.852184 | + | 0.523242i | \(0.175278\pi\) | ||||
−0.852184 | + | 0.523242i | \(0.824722\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.1537 | 0.352653 | 0.176327 | − | 0.984332i | \(-0.443579\pi\) | ||||
0.176327 | + | 0.984332i | \(0.443579\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 16.8493 | 0.584495 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.5127 | −0.606051 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.64855 | −0.126112 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.57501i | 0.0543755i | 0.999630 | + | 0.0271877i | \(0.00865519\pi\) | ||||
−0.999630 | + | 0.0271877i | \(0.991345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22.7522 | 0.784559 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3.58972i | 0.123636i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 13.5202i | − | 0.465109i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 23.6671 | 0.812252 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −22.7289 | −0.779136 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.14407i | − | 0.0391721i | −0.999808 | − | 0.0195861i | \(-0.993765\pi\) | ||
0.999808 | − | 0.0195861i | \(-0.00623483\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 1.77171i | − | 0.0605913i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 15.0875i | − | 0.515381i | −0.966228 | − | 0.257690i | \(-0.917039\pi\) | ||
0.966228 | − | 0.257690i | \(-0.0829615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 19.5808 | 0.668088 | 0.334044 | − | 0.942557i | \(-0.391587\pi\) | ||||
0.334044 | + | 0.942557i | \(0.391587\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −54.6083 | −1.85889 | −0.929444 | − | 0.368964i | \(-0.879713\pi\) | ||||
−0.929444 | + | 0.368964i | \(0.879713\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −11.6393 | −0.395750 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.199680 | + | 13.7978i | 0.00678148 | + | 0.468598i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 26.5127 | 0.899381 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 13.3580 | 0.452617 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 32.2628i | − | 1.09193i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 0.753805i | − | 0.0254542i | −0.999919 | − | 0.0127271i | \(-0.995949\pi\) | ||
0.999919 | − | 0.0127271i | \(-0.00405127\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 0.0158193i | − | 0.000533571i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 17.7585i | 0.598300i | 0.954206 | + | 0.299150i | \(0.0967031\pi\) | ||||
−0.954206 | + | 0.299150i | \(0.903297\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6.97578 | −0.234754 | −0.117377 | − | 0.993087i | \(-0.537449\pi\) | ||||
−0.117377 | + | 0.993087i | \(0.537449\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.874505 | −0.0293962 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 19.6504i | − | 0.659797i | −0.944016 | − | 0.329899i | \(-0.892985\pi\) | ||
0.944016 | − | 0.329899i | \(-0.107015\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 7.43923i | − | 0.249223i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.28497 | 0.143391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.4811i | 0.617754i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.16092 | 0.239096 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.10351 | 0.0701560 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 28.4688 | − | 0.205987i | 0.948434 | − | 0.00686243i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.59453 | −0.219209 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.8828i | 0.593788i | 0.954910 | + | 0.296894i | \(0.0959508\pi\) | ||||
−0.954910 | + | 0.296894i | \(0.904049\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.69537 | 0.255239 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 38.2247i | 1.26644i | 0.773971 | + | 0.633221i | \(0.218268\pi\) | ||||
−0.773971 | + | 0.633221i | \(0.781732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 24.1997i | − | 0.800893i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.16615i | 0.170788i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 28.6429 | 0.944841 | 0.472421 | − | 0.881373i | \(-0.343380\pi\) | ||||
0.472421 | + | 0.881373i | \(0.343380\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.0637i | 0.331609i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 6.59797i | − | 0.217175i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 10.8649i | − | 0.357235i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31.0887 | −1.02109 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 8.78923i | − | 0.288365i | −0.989551 | − | 0.144183i | \(-0.953945\pi\) | ||
0.989551 | − | 0.144183i | \(-0.0460553\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.51568 | 0.213314 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 10.1400 | − | 0.0733685i | 0.331614 | − | 0.00239941i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.4664 | 0.603270 | 0.301635 | − | 0.953424i | \(-0.402468\pi\) | ||||
0.301635 | + | 0.953424i | \(0.402468\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 25.7398 | 0.839986 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 45.0296i | − | 1.46792i | −0.679192 | − | 0.733961i | \(-0.737669\pi\) | ||
0.679192 | − | 0.733961i | \(-0.262331\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −75.0763 | −2.44482 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 34.7361i | − | 1.12877i | −0.825511 | − | 0.564386i | \(-0.809113\pi\) | ||
0.825511 | − | 0.564386i | \(-0.190887\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 8.06756i | − | 0.261884i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 16.0460 | 0.520326 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 11.2590 | 0.364714 | 0.182357 | − | 0.983232i | \(-0.441627\pi\) | ||||
0.182357 | + | 0.983232i | \(0.441627\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 9.44339i | − | 0.305581i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 4.30744i | − | 0.139240i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.2918 | 0.977154 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 17.6271i | − | 0.568026i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.38043 | 0.108820 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −47.7038 | −1.53405 | −0.767025 | − | 0.641617i | \(-0.778264\pi\) | ||||
−0.767025 | + | 0.641617i | \(0.778264\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.0158193 | − | 2.18633i | −0.000508189 | − | 0.0702351i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.7589 | 0.602002 | 0.301001 | − | 0.953624i | \(-0.402679\pi\) | ||||
0.301001 | + | 0.953624i | \(0.402679\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.42307i | 0.109626i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −42.4708 | −1.35876 | −0.679380 | − | 0.733786i | \(-0.737751\pi\) | ||||
−0.679380 | + | 0.733786i | \(0.737751\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.3446i | 0.458457i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 37.2918i | 1.19063i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 16.4611i | 0.525028i | 0.964928 | + | 0.262514i | \(0.0845515\pi\) | ||||
−0.964928 | + | 0.262514i | \(0.915448\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.8189 | 0.344719 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 53.8312i | 1.71173i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 38.2811i | − | 1.21604i | −0.793922 | − | 0.608019i | \(-0.791964\pi\) | ||
0.793922 | − | 0.608019i | \(-0.208036\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 21.9347i | − | 0.696076i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 15.0445 | 0.476944 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 32.7205i | 1.03627i | 0.855300 | + | 0.518134i | \(0.173373\pi\) | ||||
−0.855300 | + | 0.518134i | \(0.826627\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.8771 | 0.407415 |
(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 | 3332.2.b.b.2549.5 | 8 | ||
7.6 | odd | 2 | 476.2.b.a.169.4 | ✓ | 8 | ||
17.16 | even | 2 | inner | 3332.2.b.b.2549.4 | 8 | ||
21.20 | even | 2 | 4284.2.d.e.3025.5 | 8 | |||
28.27 | even | 2 | 1904.2.c.f.1121.5 | 8 | |||
119.13 | odd | 4 | 8092.2.a.r.1.2 | 4 | |||
119.55 | odd | 4 | 8092.2.a.q.1.3 | 4 | |||
119.118 | odd | 2 | 476.2.b.a.169.5 | yes | 8 | ||
357.356 | even | 2 | 4284.2.d.e.3025.4 | 8 | |||
476.475 | even | 2 | 1904.2.c.f.1121.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
476.2.b.a.169.4 | ✓ | 8 | 7.6 | odd | 2 | ||
476.2.b.a.169.5 | yes | 8 | 119.118 | odd | 2 | ||
1904.2.c.f.1121.4 | 8 | 476.475 | even | 2 | |||
1904.2.c.f.1121.5 | 8 | 28.27 | even | 2 | |||
3332.2.b.b.2549.4 | 8 | 17.16 | even | 2 | inner | ||
3332.2.b.b.2549.5 | 8 | 1.1 | even | 1 | trivial | ||
4284.2.d.e.3025.4 | 8 | 357.356 | even | 2 | |||
4284.2.d.e.3025.5 | 8 | 21.20 | even | 2 | |||
8092.2.a.q.1.3 | 4 | 119.55 | odd | 4 | |||
8092.2.a.r.1.2 | 4 | 119.13 | odd | 4 |