Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [896,2,Mod(449,896)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(896, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("896.449");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 896 = 2^{7} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 896.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: | \(7.15459602111\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 449.4 | ||
Root | \(1.61803i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 896.449 |
Dual form | 896.2.b.e.449.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/896\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(645\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 3.23607i | 1.86834i | 0.356822 | + | 0.934172i | \(0.383860\pi\) | ||||
−0.356822 | + | 0.934172i | \(0.616140\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.23607i | 1.44721i | 0.690212 | + | 0.723607i | \(0.257517\pi\) | ||||
−0.690212 | + | 0.723607i | \(0.742483\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −7.47214 | −2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 4.00000i | − 1.20605i | −0.797724 | − | 0.603023i | \(-0.793963\pi\) | ||||
0.797724 | − | 0.603023i | \(-0.206037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.23607i | 0.897524i | 0.893651 | + | 0.448762i | \(0.148135\pi\) | ||||
−0.893651 | + | 0.448762i | \(0.851865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.4721 | −2.70389 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 3.23607i | − 0.742405i | −0.928552 | − | 0.371202i | \(-0.878946\pi\) | ||||
0.928552 | − | 0.371202i | \(-0.121054\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 3.23607i | − 0.706168i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.47214 | 0.515476 | 0.257738 | − | 0.966215i | \(-0.417023\pi\) | ||||
0.257738 | + | 0.966215i | \(0.417023\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.47214 | −1.09443 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 14.4721i | − 2.78516i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 10.4721i | 1.94463i | 0.233681 | + | 0.972313i | \(0.424923\pi\) | ||||
−0.233681 | + | 0.972313i | \(0.575077\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 12.9443 | 2.25331 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 3.23607i | − 0.546995i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.47214i | 0.406417i | 0.979136 | + | 0.203208i | \(0.0651369\pi\) | ||||
−0.979136 | + | 0.203208i | \(0.934863\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −10.4721 | −1.67688 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.94427i | 1.36399i | 0.731357 | + | 0.681994i | \(0.238887\pi\) | ||||
−0.731357 | + | 0.681994i | \(0.761113\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 24.1803i | − 3.60459i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.94427 | 0.721196 | 0.360598 | − | 0.932721i | \(-0.382573\pi\) | ||||
0.360598 | + | 0.932721i | \(0.382573\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 6.47214i | − 0.906280i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 8.94427i | − 1.22859i | −0.789076 | − | 0.614295i | \(-0.789440\pi\) | ||||
0.789076 | − | 0.614295i | \(-0.210560\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 12.9443 | 1.74541 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.4721 | 1.38707 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 4.76393i | − 0.620211i | −0.950702 | − | 0.310106i | \(-0.899636\pi\) | ||||
0.950702 | − | 0.310106i | \(-0.100364\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 3.23607i | − 0.414336i | −0.978305 | − | 0.207168i | \(-0.933575\pi\) | ||||
0.978305 | − | 0.207168i | \(-0.0664247\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.47214 | 0.941401 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.4721 | −1.29891 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.4721i | 1.27938i | 0.768635 | + | 0.639688i | \(0.220936\pi\) | ||||
−0.768635 | + | 0.639688i | \(0.779064\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000i | 0.963087i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.9443 | −1.53620 | −0.768101 | − | 0.640328i | \(-0.778798\pi\) | ||||
−0.768101 | + | 0.640328i | \(0.778798\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.94427 | 0.344601 | 0.172300 | − | 0.985044i | \(-0.444880\pi\) | ||||
0.172300 | + | 0.985044i | \(0.444880\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 17.7082i | − 2.04477i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.00000i | 0.455842i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.9443 | −1.45634 | −0.728172 | − | 0.685394i | \(-0.759630\pi\) | ||||
−0.728172 | + | 0.685394i | \(0.759630\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.76393i | 0.522909i | 0.965216 | + | 0.261455i | \(0.0842022\pi\) | ||||
−0.965216 | + | 0.261455i | \(0.915798\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 6.47214i | − 0.702002i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −33.8885 | −3.63323 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2.00000 | −0.212000 | −0.106000 | − | 0.994366i | \(-0.533804\pi\) | ||||
−0.106000 | + | 0.994366i | \(0.533804\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 3.23607i | − 0.339232i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.4721 | 1.07442 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.94427 | −0.705084 | −0.352542 | − | 0.935796i | \(-0.614683\pi\) | ||||
−0.352542 | + | 0.935796i | \(0.614683\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 29.8885i | 3.00391i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.18034i | 0.813974i | 0.913434 | + | 0.406987i | \(0.133421\pi\) | ||||
−0.913434 | + | 0.406987i | \(0.866579\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 10.4721 | 1.02198 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 18.4721i | − 1.78577i | −0.450286 | − | 0.892884i | \(-0.648678\pi\) | ||||
0.450286 | − | 0.892884i | \(-0.351322\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.4721i | 1.00305i | 0.865144 | + | 0.501524i | \(0.167227\pi\) | ||||
−0.865144 | + | 0.501524i | \(0.832773\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.00000 | −0.759326 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.4164 | −1.26211 | −0.631055 | − | 0.775738i | \(-0.717378\pi\) | ||||
−0.631055 | + | 0.775738i | \(0.717378\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.00000i | 0.746004i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 24.1803i | − 2.23547i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | −0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.47214i | 0.583573i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.52786i | − 0.136656i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −7.41641 | −0.658100 | −0.329050 | − | 0.944313i | \(-0.606728\pi\) | ||||
−0.329050 | + | 0.944313i | \(0.606728\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −28.9443 | −2.54840 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 8.18034i | − 0.714720i | −0.933967 | − | 0.357360i | \(-0.883677\pi\) | ||||
0.933967 | − | 0.357360i | \(-0.116323\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.23607i | 0.280603i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 46.8328 | 4.03073 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.0000 | 0.854358 | 0.427179 | − | 0.904167i | \(-0.359507\pi\) | ||||
0.427179 | + | 0.904167i | \(0.359507\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.7639i | 1.08262i | 0.840822 | + | 0.541311i | \(0.182072\pi\) | ||||
−0.840822 | + | 0.541311i | \(0.817928\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.0000i | 1.34744i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 12.9443 | 1.08245 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −33.8885 | −2.81429 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.23607i | 0.266906i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.944272i | 0.0773578i | 0.999252 | + | 0.0386789i | \(0.0123149\pi\) | ||||
−0.999252 | + | 0.0386789i | \(0.987685\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.47214 | −0.201180 | −0.100590 | − | 0.994928i | \(-0.532073\pi\) | ||||
−0.100590 | + | 0.994928i | \(0.532073\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 14.9443 | 1.20817 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.180340i | 0.0143927i | 0.999974 | + | 0.00719634i | \(0.00229069\pi\) | ||||
−0.999974 | + | 0.00719634i | \(0.997709\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 28.9443 | 2.29543 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.47214 | −0.194832 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.0000i | 0.939913i | 0.882690 | + | 0.469956i | \(0.155730\pi\) | ||||
−0.882690 | + | 0.469956i | \(0.844270\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 41.8885i | 3.26102i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.9443 | 1.00166 | 0.500829 | − | 0.865546i | \(-0.333029\pi\) | ||||
0.500829 | + | 0.865546i | \(0.333029\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.52786 | 0.194451 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 24.1803i | 1.84912i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 9.70820i | − 0.738101i | −0.929409 | − | 0.369051i | \(-0.879683\pi\) | ||||
0.929409 | − | 0.369051i | \(-0.120317\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.47214 | 0.413655 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 15.4164 | 1.15877 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 2.47214i | − 0.184776i | −0.995723 | − | 0.0923881i | \(-0.970550\pi\) | ||||
0.995723 | − | 0.0923881i | \(-0.0294500\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.7639i | 1.54337i | 0.636004 | + | 0.771685i | \(0.280586\pi\) | ||||
−0.636004 | + | 0.771685i | \(0.719414\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.4721 | 0.774123 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.00000 | −0.588172 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.00000i | 0.585018i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.4721i | 1.05269i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.8885 | −1.29437 | −0.647185 | − | 0.762333i | \(-0.724054\pi\) | ||||
−0.647185 | + | 0.762333i | \(0.724054\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.52786 | 0.253941 | 0.126971 | − | 0.991906i | \(-0.459475\pi\) | ||||
0.126971 | + | 0.991906i | \(0.459475\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 33.8885i | − 2.42681i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.00000i | 0.284988i | 0.989796 | + | 0.142494i | \(0.0455122\pi\) | ||||
−0.989796 | + | 0.142494i | \(0.954488\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −33.8885 | −2.39031 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 10.4721i | − 0.735000i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6.47214i | 0.452034i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −18.4721 | −1.28390 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −12.9443 | −0.895374 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 15.4164i | − 1.06131i | −0.847588 | − | 0.530655i | \(-0.821946\pi\) | ||||
0.847588 | − | 0.530655i | \(-0.178054\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 41.8885i | − 2.87016i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −28.9443 | −1.97398 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.52786i | 0.643833i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 6.47214i | − 0.435363i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 11.0557 | 0.740346 | 0.370173 | − | 0.928963i | \(-0.379298\pi\) | ||||
0.370173 | + | 0.928963i | \(0.379298\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 40.8885 | 2.72590 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.70820i | 0.644356i | 0.946679 | + | 0.322178i | \(0.104415\pi\) | ||||
−0.946679 | + | 0.322178i | \(0.895585\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.65248i | 0.439608i | 0.975544 | + | 0.219804i | \(0.0705418\pi\) | ||||
−0.975544 | + | 0.219804i | \(0.929458\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −12.9443 | −0.851671 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.8885 | 1.04089 | 0.520447 | − | 0.853894i | \(-0.325765\pi\) | ||||
0.520447 | + | 0.853894i | \(0.325765\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.0000i | 1.04372i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 41.8885i | − 2.72095i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.4721 | −1.19486 | −0.597432 | − | 0.801920i | \(-0.703812\pi\) | ||||
−0.597432 | + | 0.801920i | \(0.703812\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.94427 | 0.189657 | 0.0948286 | − | 0.995494i | \(-0.469770\pi\) | ||||
0.0948286 | + | 0.995494i | \(0.469770\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 35.5967i | 2.28353i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 3.23607i | 0.206745i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.4721 | 0.666326 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.4164 | −0.976975 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6525i | 0.924856i | 0.886657 | + | 0.462428i | \(0.153022\pi\) | ||||
−0.886657 | + | 0.462428i | \(0.846978\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 9.88854i | − 0.621687i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.9443 | 1.31158 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 27.8885 | 1.73964 | 0.869820 | − | 0.493370i | \(-0.164235\pi\) | ||||
0.869820 | + | 0.493370i | \(0.164235\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.47214i | − 0.153611i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 78.2492i | − 4.84351i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.05573 | 0.188424 | 0.0942121 | − | 0.995552i | \(-0.469967\pi\) | ||||
0.0942121 | + | 0.995552i | \(0.469967\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 28.9443 | 1.77803 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 6.47214i | − 0.396088i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1246i | 0.800222i | 0.916467 | + | 0.400111i | \(0.131028\pi\) | ||||
−0.916467 | + | 0.400111i | \(0.868972\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.9443 | 1.27227 | 0.636137 | − | 0.771576i | \(-0.280531\pi\) | ||||
0.636137 | + | 0.771576i | \(0.280531\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 10.4721 | 0.633803 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 21.8885i | 1.31993i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.0000i | 1.20168i | 0.799368 | + | 0.600842i | \(0.205168\pi\) | ||||
−0.799368 | + | 0.600842i | \(0.794832\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 6.65248i | − 0.395449i | −0.980258 | − | 0.197724i | \(-0.936645\pi\) | ||||
0.980258 | − | 0.197724i | \(-0.0633551\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 33.8885i | 2.00738i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.00000 | −0.118056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 22.4721i | − 1.31734i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.2918i | 0.834936i | 0.908692 | + | 0.417468i | \(0.137082\pi\) | ||||
−0.908692 | + | 0.417468i | \(0.862918\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.4164 | 0.897578 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −57.8885 | −3.35903 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.00000i | 0.462652i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 8.94427i | − 0.515539i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −26.4721 | −1.52078 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 10.4721 | 0.599633 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 27.5967i | 1.57503i | 0.616296 | + | 0.787515i | \(0.288633\pi\) | ||||
−0.616296 | + | 0.787515i | \(0.711367\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 25.8885i | 1.47275i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | −0.453638 | −0.226819 | − | 0.973937i | \(-0.572833\pi\) | ||||
−0.226819 | + | 0.973937i | \(0.572833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.8885 | 1.57635 | 0.788177 | − | 0.615449i | \(-0.211025\pi\) | ||||
0.788177 | + | 0.615449i | \(0.211025\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 24.1803i | 1.36241i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 13.8885i | − 0.780058i | −0.920803 | − | 0.390029i | \(-0.872465\pi\) | ||||
0.920803 | − | 0.390029i | \(-0.127535\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 41.8885 | 2.34531 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 59.7771 | 3.33643 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.47214i | 0.360119i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 17.7082i | − 0.982274i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −33.8885 | −1.87404 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.94427 | −0.272587 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.9443i | 1.37106i | 0.728044 | + | 0.685531i | \(0.240430\pi\) | ||||
−0.728044 | + | 0.685531i | \(0.759570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 18.4721i | − 1.01227i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −33.8885 | −1.85153 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.4164 | 0.948732 | 0.474366 | − | 0.880328i | \(-0.342677\pi\) | ||||
0.474366 | + | 0.880328i | \(0.342677\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 43.4164i | − 2.35806i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −25.8885 | −1.39379 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 32.9443i | − 1.76854i | −0.466975 | − | 0.884271i | \(-0.654656\pi\) | ||||
0.466975 | − | 0.884271i | \(-0.345344\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 17.7082i | − 0.947898i | −0.880552 | − | 0.473949i | \(-0.842828\pi\) | ||||
0.880552 | − | 0.473949i | \(-0.157172\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 46.8328 | 2.49975 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −34.9443 | −1.85990 | −0.929948 | − | 0.367691i | \(-0.880148\pi\) | ||||
−0.929948 | + | 0.367691i | \(0.880148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 41.8885i | − 2.22321i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.47214i | 0.342542i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.4164 | −1.23587 | −0.617935 | − | 0.786229i | \(-0.712031\pi\) | ||||
−0.617935 | + | 0.786229i | \(0.712031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.52786 | 0.448835 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 16.1803i | − 0.849248i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.52786i | 0.498711i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.0557 | −0.577104 | −0.288552 | − | 0.957464i | \(-0.593174\pi\) | ||||
−0.288552 | + | 0.957464i | \(0.593174\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −14.9443 | −0.777968 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.94427i | 0.464363i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 15.0557i | − 0.779556i | −0.920909 | − | 0.389778i | \(-0.872552\pi\) | ||||
0.920909 | − | 0.389778i | \(-0.127448\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 4.94427 | 0.255321 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −33.8885 | −1.74535 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.11146i | 0.108458i | 0.998529 | + | 0.0542291i | \(0.0172701\pi\) | ||||
−0.998529 | + | 0.0542291i | \(0.982730\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 24.0000i | − 1.22956i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.9443 | −1.07020 | −0.535101 | − | 0.844788i | \(-0.679727\pi\) | ||||
−0.535101 | + | 0.844788i | \(0.679727\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.9443 | −0.659701 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 66.8328i | − 3.39730i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 7.41641i | − 0.376027i | −0.982166 | − | 0.188013i | \(-0.939795\pi\) | ||||
0.982166 | − | 0.188013i | \(-0.0602048\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.94427 | −0.250043 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 26.4721 | 1.33534 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − 41.8885i | − 2.10764i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 37.1246i | 1.86323i | 0.363446 | + | 0.931615i | \(0.381600\pi\) | ||||
−0.363446 | + | 0.931615i | \(0.618400\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −10.4721 | −0.524263 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.47214 | 0.423078 | 0.211539 | − | 0.977370i | \(-0.432152\pi\) | ||||
0.211539 | + | 0.977370i | \(0.432152\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 79.0132i | 3.92620i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9.88854 | 0.490157 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.94427 | −0.145585 | −0.0727924 | − | 0.997347i | \(-0.523191\pi\) | ||||
−0.0727924 | + | 0.997347i | \(0.523191\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 32.3607i | 1.59623i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.76393i | 0.234418i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −15.4164 | −0.756762 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −41.3050 | −2.02271 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 16.1803i | 0.790461i | 0.918582 | + | 0.395231i | \(0.129335\pi\) | ||||
−0.918582 | + | 0.395231i | \(0.870665\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 12.0000i | − 0.584844i | −0.956289 | − | 0.292422i | \(-0.905539\pi\) | ||||
0.956289 | − | 0.292422i | \(-0.0944612\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −36.9443 | −1.79629 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 10.9443 | 0.530875 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.23607i | 0.156604i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 41.8885i | 2.02240i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.3607 | 0.595393 | 0.297696 | − | 0.954661i | \(-0.403782\pi\) | ||||
0.297696 | + | 0.954661i | \(0.403782\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 109.666i | − 5.25806i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 8.00000i | − 0.382692i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.05573 | 0.145842 | 0.0729210 | − | 0.997338i | \(-0.476768\pi\) | ||||
0.0729210 | + | 0.997338i | \(0.476768\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −7.47214 | −0.355816 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 20.3607i | 0.967365i | 0.875244 | + | 0.483683i | \(0.160701\pi\) | ||||
−0.875244 | + | 0.483683i | \(0.839299\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 6.47214i | − 0.306809i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.05573 | −0.144531 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −11.8885 | −0.561055 | −0.280528 | − | 0.959846i | \(-0.590509\pi\) | ||||
−0.280528 | + | 0.959846i | \(0.590509\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 8.00000i | − 0.376705i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 8.00000i | − 0.375873i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 10.4721 | 0.490941 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.5279 | −0.539251 | −0.269625 | − | 0.962965i | \(-0.586900\pi\) | ||||
−0.269625 | + | 0.962965i | \(0.586900\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 28.9443i | 1.35100i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.0689i | 0.841552i | 0.907165 | + | 0.420776i | \(0.138242\pi\) | ||||
−0.907165 | + | 0.420776i | \(0.861758\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 33.8885 | 1.57493 | 0.787467 | − | 0.616357i | \(-0.211392\pi\) | ||||
0.787467 | + | 0.616357i | \(0.211392\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.65248i | 0.307840i | 0.988083 | + | 0.153920i | \(0.0491898\pi\) | ||||
−0.988083 | + | 0.153920i | \(0.950810\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 10.4721i | − 0.483558i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −0.583592 | −0.0268905 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 35.7771 | 1.64503 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 17.7082i | 0.812508i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 66.8328i | 3.06006i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0000 | 0.731059 | 0.365529 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365529 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.00000 | −0.364769 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 8.00000i | − 0.364013i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 22.4721i | − 1.02041i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.5279 | −0.613006 | −0.306503 | − | 0.951870i | \(-0.599159\pi\) | ||||
−0.306503 | + | 0.951870i | \(0.599159\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −38.8328 | −1.75608 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 5.52786i | − 0.249469i | −0.992190 | − | 0.124735i | \(-0.960192\pi\) | ||||
0.992190 | − | 0.124735i | \(-0.0398079\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 20.9443i | − 0.943283i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −96.7214 | −4.34730 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.9443 | 0.580630 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.3607i | 0.911469i | 0.890116 | + | 0.455735i | \(0.150623\pi\) | ||||
−0.890116 | + | 0.455735i | \(0.849377\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 41.8885i | 1.87144i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −28.9443 | −1.29056 | −0.645281 | − | 0.763946i | \(-0.723260\pi\) | ||||
−0.645281 | + | 0.763946i | \(0.723260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.4721 | −1.17799 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 8.18034i | 0.363302i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 30.6525i | − 1.35865i | −0.733839 | − | 0.679324i | \(-0.762273\pi\) | ||||
0.733839 | − | 0.679324i | \(-0.237727\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.94427 | −0.130247 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −46.8328 | −2.06772 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.8885i | 1.14079i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 19.7771i | − 0.869795i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 31.4164 | 1.37903 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.05573 | −0.396739 | −0.198369 | − | 0.980127i | \(-0.563565\pi\) | ||||
−0.198369 | + | 0.980127i | \(0.563565\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.1803i | 1.05733i | 0.848830 | + | 0.528666i | \(0.177308\pi\) | ||||
−0.848830 | + | 0.528666i | \(0.822692\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 17.7082i | 0.772849i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8885 | −0.734285 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 35.5967i | 1.54477i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.47214i | 0.280339i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 59.7771 | 2.58439 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 8.00000 | 0.345225 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 4.00000i | − 0.172292i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 16.9443i | − 0.728491i | −0.931303 | − | 0.364246i | \(-0.881327\pi\) | ||||
0.931303 | − | 0.364246i | \(-0.118673\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −67.1935 | −2.88355 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.8885 | −1.45163 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.8328i | 0.805233i | 0.915369 | + | 0.402617i | \(0.131899\pi\) | ||||
−0.915369 | + | 0.402617i | \(0.868101\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 24.1803i | 1.03199i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 33.8885 | 1.44370 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 12.9443 | 0.550446 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − 25.8885i | − 1.09891i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 29.8885i | − 1.26642i | −0.773981 | − | 0.633209i | \(-0.781737\pi\) | ||||
0.773981 | − | 0.633209i | \(-0.218263\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −28.9443 | −1.22421 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −25.8885 | −1.09302 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 24.5410i | − 1.03428i | −0.855901 | − | 0.517140i | \(-0.826997\pi\) | ||||
0.855901 | − | 0.517140i | \(-0.173003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 43.4164i | − 1.82654i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −24.4164 | −1.02539 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 41.4164 | 1.73627 | 0.868133 | − | 0.496332i | \(-0.165320\pi\) | ||||
0.868133 | + | 0.496332i | \(0.165320\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 39.7771i | − 1.66462i | −0.554311 | − | 0.832310i | \(-0.687018\pi\) | ||||
0.554311 | − | 0.832310i | \(-0.312982\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 57.8885i | − 2.41833i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.5279 | −0.564151 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 32.8328 | 1.36685 | 0.683424 | − | 0.730022i | \(-0.260490\pi\) | ||||
0.683424 | + | 0.730022i | \(0.260490\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 11.4164i | 0.474450i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 4.76393i | − 0.197641i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −35.7771 | −1.48174 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 78.2492 | 3.23521 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 19.2361i | − 0.793957i | −0.917828 | − | 0.396979i | \(-0.870059\pi\) | ||||
0.917828 | − | 0.396979i | \(-0.129941\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.9443 | −0.532456 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.00000 | 0.0821302 | 0.0410651 | − | 0.999156i | \(-0.486925\pi\) | ||||
0.0410651 | + | 0.999156i | \(0.486925\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.47214i | 0.265332i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 77.6656i | 3.17864i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.8885 | 1.62709 | 0.813544 | − | 0.581504i | \(-0.197535\pi\) | ||||
0.813544 | + | 0.581504i | \(0.197535\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 78.2492i | − 3.18655i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 16.1803i | − 0.657824i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 25.8885 | 1.05078 | 0.525392 | − | 0.850860i | \(-0.323919\pi\) | ||||
0.525392 | + | 0.850860i | \(0.323919\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 33.8885 | 1.37323 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 16.0000i | 0.647291i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.52786i | 0.223268i | 0.993749 | + | 0.111634i | \(0.0356085\pi\) | ||||
−0.993749 | + | 0.111634i | \(0.964392\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −20.9443 | −0.844555 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 32.4721 | 1.30728 | 0.653639 | − | 0.756806i | \(-0.273241\pi\) | ||||
0.653639 | + | 0.756806i | \(0.273241\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.1803i | 1.29344i | 0.762729 | + | 0.646719i | \(0.223859\pi\) | ||||
−0.762729 | + | 0.646719i | \(0.776141\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 35.7771i | − 1.43569i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.00000 | 0.0801283 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −22.4164 | −0.896656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 41.8885i | − 1.67287i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 4.94427i | − 0.197141i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8885 | −0.712132 | −0.356066 | − | 0.934461i | \(-0.615882\pi\) | ||||
−0.356066 | + | 0.934461i | \(0.615882\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 49.8885 | 1.98289 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 24.0000i | − 0.952411i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.23607i | 0.128218i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 96.7214 | 3.82624 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 34.3607 | 1.35717 | 0.678583 | − | 0.734524i | \(-0.262595\pi\) | ||||
0.678583 | + | 0.734524i | \(0.262595\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 40.5410i | − 1.59878i | −0.600811 | − | 0.799391i | \(-0.705156\pi\) | ||||
0.600811 | − | 0.799391i | \(-0.294844\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 93.6656i | − 3.68808i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.8885 | 0.703271 | 0.351636 | − | 0.936137i | \(-0.385626\pi\) | ||||
0.351636 | + | 0.936137i | \(0.385626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.0557 | −0.748003 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 39.4164i | 1.54248i | 0.636543 | + | 0.771242i | \(0.280364\pi\) | ||||
−0.636543 | + | 0.771242i | \(0.719636\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 26.4721 | 1.03435 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.0000 | −0.858302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 10.8328i | − 0.421987i | −0.977488 | − | 0.210993i | \(-0.932330\pi\) | ||||
0.977488 | − | 0.210993i | \(-0.0676698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.2361i | 1.05936i | 0.848197 | + | 0.529680i | \(0.177688\pi\) | ||||
−0.848197 | + | 0.529680i | \(0.822312\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20.9443 | 0.813408 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −10.4721 | −0.406092 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.8885i | 1.00241i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 35.7771i | 1.38322i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −12.9443 | −0.499708 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.8885 | 0.920836 | 0.460418 | − | 0.887702i | \(-0.347700\pi\) | ||||
0.460418 | + | 0.887702i | \(0.347700\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 79.1935i | 3.04816i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 21.1246i | − 0.811885i | −0.913899 | − | 0.405942i | \(-0.866943\pi\) | ||||
0.913899 | − | 0.405942i | \(-0.133057\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.94427 | 0.266497 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −31.4164 | −1.20388 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 21.5279i | − 0.823741i | −0.911242 | − | 0.411870i | \(-0.864876\pi\) | ||||
0.911242 | − | 0.411870i | \(-0.135124\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.3607i | 1.23644i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −21.5279 | −0.821339 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 28.9443 | 1.10269 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 33.7082i | 1.28232i | 0.767407 | + | 0.641160i | \(0.221547\pi\) | ||||
−0.767407 | + | 0.641160i | \(0.778453\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 29.8885i | − 1.13537i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −41.3050 | −1.56679 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4.00000 | −0.151511 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 51.4164i | 1.94475i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 28.3607i | − 1.07117i | −0.844482 | − | 0.535584i | \(-0.820092\pi\) | ||||
0.844482 | − | 0.535584i | \(-0.179908\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.00000 | 0.301726 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −51.7771 | −1.95004 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 8.18034i | − 0.307653i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.47214i | 0.0928430i | 0.998922 | + | 0.0464215i | \(0.0147817\pi\) | ||||
−0.998922 | + | 0.0464215i | \(0.985218\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 96.7214 | 3.62733 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 41.8885i | 1.56654i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 59.7771i | − 2.23242i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 36.9443 | 1.37779 | 0.688894 | − | 0.724862i | \(-0.258096\pi\) | ||||
0.688894 | + | 0.724862i | \(0.258096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.00000 | −0.297936 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.52786i | 0.354345i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 57.3050i | − 2.12825i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.8328 | −1.44023 | −0.720115 | − | 0.693855i | \(-0.755911\pi\) | ||||
−0.720115 | + | 0.693855i | \(0.755911\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −41.9443 | −1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 17.8885i | − 0.661632i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 26.0689i | − 0.962876i | −0.876480 | − | 0.481438i | \(-0.840115\pi\) | ||||
0.876480 | − | 0.481438i | \(-0.159885\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.4721 | −0.386271 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 41.8885 | 1.54298 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 13.8885i | − 0.510898i | −0.966822 | − | 0.255449i | \(-0.917777\pi\) | ||||
0.966822 | − | 0.255449i | \(-0.0822233\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.8885i | 1.24493i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.4721 | 1.26466 | 0.632330 | − | 0.774699i | \(-0.282099\pi\) | ||||
0.632330 | + | 0.774699i | \(0.282099\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.05573 | −0.111953 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 35.5967i | − 1.30242i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18.4721i | 0.674957i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.3607 | 1.03490 | 0.517448 | − | 0.855715i | \(-0.326882\pi\) | ||||
0.517448 | + | 0.855715i | \(0.326882\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −47.4164 | −1.72795 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 8.00000i | − 0.291150i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 16.5836i | − 0.602741i | −0.953507 | − | 0.301370i | \(-0.902556\pi\) | ||||
0.953507 | − | 0.301370i | \(-0.0974441\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 32.0000 | 1.16153 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.88854 | −0.285959 | −0.142980 | − | 0.989726i | \(-0.545668\pi\) | ||||
−0.142980 | + | 0.989726i | \(0.545668\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 10.4721i | − 0.379117i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 48.3607i | 1.74848i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.4164 | 0.556654 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.9443 | 1.26012 | 0.630061 | − | 0.776545i | \(-0.283030\pi\) | ||||
0.630061 | + | 0.776545i | \(0.283030\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 90.2492i | 3.25025i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 29.1246i | 1.04754i | 0.851860 | + | 0.523770i | \(0.175475\pi\) | ||||
−0.851860 | + | 0.523770i | \(0.824525\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 8.00000 | 0.286998 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 6.47214i | − 0.231888i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 51.7771i | 1.85273i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 151.554 | 5.41610 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.583592 | −0.0208293 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 45.1246i | − 1.60852i | −0.594278 | − | 0.804259i | \(-0.702562\pi\) | ||||
0.594278 | − | 0.804259i | \(-0.297438\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9.88854i | 0.352041i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.4164 | 0.477033 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.4721 | 0.371876 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 93.6656i | 3.32198i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 28.7639i | − 1.01887i | −0.860509 | − | 0.509435i | \(-0.829854\pi\) | ||||
0.860509 | − | 0.509435i | \(-0.170146\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.88854 | −0.349832 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.9443 | 0.528030 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 11.7771i | − 0.415604i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 8.00000i | − 0.281963i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −42.4721 | −1.49509 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.4164 | −0.752961 | −0.376480 | − | 0.926425i | \(-0.622866\pi\) | ||||
−0.376480 | + | 0.926425i | \(0.622866\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.1246i | 0.460867i | 0.973088 | + | 0.230434i | \(0.0740145\pi\) | ||||
−0.973088 | + | 0.230434i | \(0.925986\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 67.7771i | 2.37705i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −38.8328 | −1.36025 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.9443 | 1.01263 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 24.1803i | 0.844929i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.00000i | 0.139601i | 0.997561 | + | 0.0698005i | \(0.0222363\pi\) | ||||
−0.997561 | + | 0.0698005i | \(0.977764\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.8328 | −0.795902 | −0.397951 | − | 0.917407i | \(-0.630279\pi\) | ||||
−0.397951 | + | 0.917407i | \(0.630279\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −70.8328 | −2.46608 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 8.58359i | − 0.298481i | −0.988801 | − | 0.149240i | \(-0.952317\pi\) | ||||
0.988801 | − | 0.149240i | \(-0.0476828\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 13.1246i | − 0.455837i | −0.973680 | − | 0.227918i | \(-0.926808\pi\) | ||||
0.973680 | − | 0.227918i | \(-0.0731919\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −64.7214 | −2.24516 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 41.8885i | 1.44961i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 40.0000 | 1.38095 | 0.690477 | − | 0.723355i | \(-0.257401\pi\) | ||||
0.690477 | + | 0.723355i | \(0.257401\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −80.6656 | −2.78157 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.4164i | 0.668737i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.18034i | 0.281412i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.00000 | 0.171802 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 21.5279 | 0.738834 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 6.11146i | 0.209498i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.7639i | 0.984858i | 0.870353 | + | 0.492429i | \(0.163891\pi\) | ||||
−0.870353 | + | 0.492429i | \(0.836109\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −78.2492 | −2.67607 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.16718 | 0.108189 | 0.0540945 | − | 0.998536i | \(-0.482773\pi\) | ||||
0.0540945 | + | 0.998536i | \(0.482773\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.81966i | 0.266803i | 0.991062 | + | 0.133402i | \(0.0425900\pi\) | ||||
−0.991062 | + | 0.133402i | \(0.957410\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − 6.47214i | − 0.220570i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1.88854 | 0.0642868 | 0.0321434 | − | 0.999483i | \(-0.489767\pi\) | ||||
0.0321434 | + | 0.999483i | \(0.489767\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.4164 | 1.06819 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 42.0689i | − 1.42873i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 51.7771i | 1.75642i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −33.8885 | −1.14827 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 51.8885 | 1.75616 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.52786i | 0.0516512i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 44.3607i | − 1.49795i | −0.662596 | − | 0.748977i | \(-0.730545\pi\) | ||||
0.662596 | − | 0.748977i | \(-0.269455\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −46.2492 | −1.55995 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.8328 | 1.10617 | 0.553083 | − | 0.833126i | \(-0.313451\pi\) | ||||
0.553083 | + | 0.833126i | \(0.313451\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.5279i | 0.993692i | 0.867839 | + | 0.496846i | \(0.165509\pi\) | ||||
−0.867839 | + | 0.496846i | \(0.834491\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 49.8885i | 1.67699i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 38.8328 | 1.30388 | 0.651939 | − | 0.758271i | \(-0.273956\pi\) | ||||
0.651939 | + | 0.758271i | \(0.273956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.41641 | 0.248738 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 97.6656i | − 3.27192i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 16.0000i | − 0.535420i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −25.8885 | −0.864393 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.8885i | 0.595954i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 28.9443 | 0.963205 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −67.1935 | −2.23359 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 8.58359i | − 0.285013i | −0.989794 | − | 0.142507i | \(-0.954484\pi\) | ||||
0.989794 | − | 0.142507i | \(-0.0455163\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 61.1246i | − 2.02738i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.5279 | 1.50841 | 0.754203 | − | 0.656642i | \(-0.228024\pi\) | ||||
0.754203 | + | 0.656642i | \(0.228024\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.0557 | 0.630653 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 33.8885i | 1.12032i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.18034i | 0.270139i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −6.83282 | −0.225394 | −0.112697 | − | 0.993629i | \(-0.535949\pi\) | ||||
−0.112697 | + | 0.993629i | \(0.535949\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −89.3050 | −2.94270 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 41.8885i | − 1.37878i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 13.5279i | − 0.444793i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −59.7771 | −1.96334 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.88854 | 0.258815 | 0.129407 | − | 0.991592i | \(-0.458693\pi\) | ||||
0.129407 | + | 0.991592i | \(0.458693\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 3.23607i | − 0.106058i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 25.8885i | − 0.847553i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −25.8885 | −0.846646 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 9.05573 | 0.295838 | 0.147919 | − | 0.988999i | \(-0.452743\pi\) | ||||
0.147919 | + | 0.988999i | \(0.452743\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 90.2492i | 2.94517i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.6525i | 0.999242i | 0.866244 | + | 0.499621i | \(0.166527\pi\) | ||||
−0.866244 | + | 0.499621i | \(0.833473\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.94427 | 0.161008 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −46.8328 | −1.52347 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56.9443i | 1.85044i | 0.379431 | + | 0.925220i | \(0.376120\pi\) | ||||
−0.379431 | + | 0.925220i | \(0.623880\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.52786i | 0.309288i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 44.9443 | 1.45742 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 3.88854 | 0.125962 | 0.0629811 | − | 0.998015i | \(-0.479939\pi\) | ||||
0.0629811 | + | 0.998015i | \(0.479939\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 57.8885i | − 1.87323i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 135.554i | 4.38184i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.0000 | −0.322917 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.0000 | −1.00000 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 138.026i | 4.44784i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 11.4164i | 0.367507i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −39.4164 | −1.26755 | −0.633773 | − | 0.773519i | \(-0.718495\pi\) | ||||
−0.633773 | + | 0.773519i | \(0.718495\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −20.9443 | −0.672827 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 46.6525i | − 1.49715i | −0.663051 | − | 0.748575i | \(-0.730739\pi\) | ||||
0.663051 | − | 0.748575i | \(-0.269261\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 12.7639i | − 0.409193i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 57.3050 | 1.83523 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.00000i | 0.255681i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 78.2492i | − 2.49831i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 43.7771 | 1.39627 | 0.698136 | − | 0.715965i | \(-0.254013\pi\) | ||||
0.698136 | + | 0.715965i | \(0.254013\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.9443 | −0.412439 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 16.0000i | − 0.509286i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.1115i | 0.703103i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.8328 | 0.725308 | 0.362654 | − | 0.931924i | \(-0.381871\pi\) | ||||
0.362654 | + | 0.931924i | \(0.381871\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −80.7214 | −2.56161 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 77.6656i | 2.46217i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 35.2361i | 1.11594i | 0.829862 | + | 0.557969i | \(0.188419\pi\) | ||||
−0.829862 | + | 0.557969i | \(0.811581\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 35.7771 | 1.13194 |
(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 | 896.2.b.e.449.4 | yes | 4 | |
4.3 | odd | 2 | 896.2.b.g.449.1 | yes | 4 | ||
8.3 | odd | 2 | 896.2.b.g.449.4 | yes | 4 | ||
8.5 | even | 2 | inner | 896.2.b.e.449.1 | ✓ | 4 | |
16.3 | odd | 4 | 1792.2.a.t.1.2 | 2 | |||
16.5 | even | 4 | 1792.2.a.r.1.2 | 2 | |||
16.11 | odd | 4 | 1792.2.a.j.1.1 | 2 | |||
16.13 | even | 4 | 1792.2.a.l.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
896.2.b.e.449.1 | ✓ | 4 | 8.5 | even | 2 | inner | |
896.2.b.e.449.4 | yes | 4 | 1.1 | even | 1 | trivial | |
896.2.b.g.449.1 | yes | 4 | 4.3 | odd | 2 | ||
896.2.b.g.449.4 | yes | 4 | 8.3 | odd | 2 | ||
1792.2.a.j.1.1 | 2 | 16.11 | odd | 4 | |||
1792.2.a.l.1.1 | 2 | 16.13 | even | 4 | |||
1792.2.a.r.1.2 | 2 | 16.5 | even | 4 | |||
1792.2.a.t.1.2 | 2 | 16.3 | odd | 4 |