Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5610,2,Mod(1,5610)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5610, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5610.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5610 = 2 \cdot 3 \cdot 5 \cdot 11 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5610.a (trivial) |
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: | yes |
Analytic conductor: | \(44.7960755339\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{33}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 8 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(3.37228\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5610.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.37228 | 1.27460 | 0.637301 | − | 0.770615i | \(-0.280051\pi\) | ||||
0.637301 | + | 0.770615i | \(0.280051\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 4.74456 | 1.31590 | 0.657952 | − | 0.753059i | \(-0.271423\pi\) | ||||
0.657952 | + | 0.753059i | \(0.271423\pi\) | |||||||
\(14\) | 3.37228 | 0.901280 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 3.37228 | 0.735892 | ||||||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | −3.37228 | −0.703169 | −0.351585 | − | 0.936156i | \(-0.614357\pi\) | ||||
−0.351585 | + | 0.936156i | \(0.614357\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.74456 | 0.930485 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.37228 | 0.637301 | ||||||||
\(29\) | 2.62772 | 0.487955 | 0.243978 | − | 0.969781i | \(-0.421548\pi\) | ||||
0.243978 | + | 0.969781i | \(0.421548\pi\) | |||||||
\(30\) | 1.00000 | 0.182574 | ||||||||
\(31\) | 4.62772 | 0.831163 | 0.415581 | − | 0.909556i | \(-0.363578\pi\) | ||||
0.415581 | + | 0.909556i | \(0.363578\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 1.00000 | 0.174078 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 3.37228 | 0.570020 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −10.0000 | −1.64399 | −0.821995 | − | 0.569495i | \(-0.807139\pi\) | ||||
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 4.00000 | 0.648886 | ||||||||
\(39\) | 4.74456 | 0.759738 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −12.7446 | −1.99037 | −0.995183 | − | 0.0980332i | \(-0.968745\pi\) | ||||
−0.995183 | + | 0.0980332i | \(0.968745\pi\) | |||||||
\(42\) | 3.37228 | 0.520354 | ||||||||
\(43\) | 7.37228 | 1.12426 | 0.562131 | − | 0.827048i | \(-0.309982\pi\) | ||||
0.562131 | + | 0.827048i | \(0.309982\pi\) | |||||||
\(44\) | 1.00000 | 0.150756 | ||||||||
\(45\) | 1.00000 | 0.149071 | ||||||||
\(46\) | −3.37228 | −0.497216 | ||||||||
\(47\) | −13.4891 | −1.96759 | −0.983796 | − | 0.179294i | \(-0.942619\pi\) | ||||
−0.983796 | + | 0.179294i | \(0.942619\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 4.37228 | 0.624612 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 1.00000 | 0.140028 | ||||||||
\(52\) | 4.74456 | 0.657952 | ||||||||
\(53\) | −0.744563 | −0.102274 | −0.0511368 | − | 0.998692i | \(-0.516284\pi\) | ||||
−0.0511368 | + | 0.998692i | \(0.516284\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 1.00000 | 0.134840 | ||||||||
\(56\) | 3.37228 | 0.450640 | ||||||||
\(57\) | 4.00000 | 0.529813 | ||||||||
\(58\) | 2.62772 | 0.345036 | ||||||||
\(59\) | −10.7446 | −1.39882 | −0.699411 | − | 0.714719i | \(-0.746554\pi\) | ||||
−0.699411 | + | 0.714719i | \(0.746554\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −2.00000 | −0.256074 | −0.128037 | − | 0.991769i | \(-0.540868\pi\) | ||||
−0.128037 | + | 0.991769i | \(0.540868\pi\) | |||||||
\(62\) | 4.62772 | 0.587721 | ||||||||
\(63\) | 3.37228 | 0.424868 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.74456 | 0.588491 | ||||||||
\(66\) | 1.00000 | 0.123091 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 1.00000 | 0.121268 | ||||||||
\(69\) | −3.37228 | −0.405975 | ||||||||
\(70\) | 3.37228 | 0.403065 | ||||||||
\(71\) | 1.25544 | 0.148993 | 0.0744965 | − | 0.997221i | \(-0.476265\pi\) | ||||
0.0744965 | + | 0.997221i | \(0.476265\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −10.0000 | −1.16248 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | 3.37228 | 0.384307 | ||||||||
\(78\) | 4.74456 | 0.537216 | ||||||||
\(79\) | −13.4891 | −1.51765 | −0.758823 | − | 0.651297i | \(-0.774225\pi\) | ||||
−0.758823 | + | 0.651297i | \(0.774225\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −12.7446 | −1.40740 | ||||||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 3.37228 | 0.367946 | ||||||||
\(85\) | 1.00000 | 0.108465 | ||||||||
\(86\) | 7.37228 | 0.794974 | ||||||||
\(87\) | 2.62772 | 0.281721 | ||||||||
\(88\) | 1.00000 | 0.106600 | ||||||||
\(89\) | 16.7446 | 1.77492 | 0.887460 | − | 0.460885i | \(-0.152468\pi\) | ||||
0.887460 | + | 0.460885i | \(0.152468\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 16.0000 | 1.67726 | ||||||||
\(92\) | −3.37228 | −0.351585 | ||||||||
\(93\) | 4.62772 | 0.479872 | ||||||||
\(94\) | −13.4891 | −1.39130 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −9.37228 | −0.951611 | −0.475805 | − | 0.879551i | \(-0.657843\pi\) | ||||
−0.475805 | + | 0.879551i | \(0.657843\pi\) | |||||||
\(98\) | 4.37228 | 0.441667 | ||||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 6.00000 | 0.597022 | 0.298511 | − | 0.954406i | \(-0.403510\pi\) | ||||
0.298511 | + | 0.954406i | \(0.403510\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | −3.37228 | −0.332281 | −0.166140 | − | 0.986102i | \(-0.553130\pi\) | ||||
−0.166140 | + | 0.986102i | \(0.553130\pi\) | |||||||
\(104\) | 4.74456 | 0.465243 | ||||||||
\(105\) | 3.37228 | 0.329101 | ||||||||
\(106\) | −0.744563 | −0.0723183 | ||||||||
\(107\) | 14.1168 | 1.36473 | 0.682363 | − | 0.731013i | \(-0.260952\pi\) | ||||
0.682363 | + | 0.731013i | \(0.260952\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −8.74456 | −0.837577 | −0.418789 | − | 0.908084i | \(-0.637545\pi\) | ||||
−0.418789 | + | 0.908084i | \(0.637545\pi\) | |||||||
\(110\) | 1.00000 | 0.0953463 | ||||||||
\(111\) | −10.0000 | −0.949158 | ||||||||
\(112\) | 3.37228 | 0.318651 | ||||||||
\(113\) | −11.4891 | −1.08081 | −0.540403 | − | 0.841406i | \(-0.681728\pi\) | ||||
−0.540403 | + | 0.841406i | \(0.681728\pi\) | |||||||
\(114\) | 4.00000 | 0.374634 | ||||||||
\(115\) | −3.37228 | −0.314467 | ||||||||
\(116\) | 2.62772 | 0.243978 | ||||||||
\(117\) | 4.74456 | 0.438635 | ||||||||
\(118\) | −10.7446 | −0.989117 | ||||||||
\(119\) | 3.37228 | 0.309137 | ||||||||
\(120\) | 1.00000 | 0.0912871 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −2.00000 | −0.181071 | ||||||||
\(123\) | −12.7446 | −1.14914 | ||||||||
\(124\) | 4.62772 | 0.415581 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 3.37228 | 0.300427 | ||||||||
\(127\) | 20.2337 | 1.79545 | 0.897725 | − | 0.440557i | \(-0.145219\pi\) | ||||
0.897725 | + | 0.440557i | \(0.145219\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 7.37228 | 0.649093 | ||||||||
\(130\) | 4.74456 | 0.416126 | ||||||||
\(131\) | −9.48913 | −0.829069 | −0.414534 | − | 0.910034i | \(-0.636056\pi\) | ||||
−0.414534 | + | 0.910034i | \(0.636056\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 13.4891 | 1.16966 | ||||||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | −14.8614 | −1.26970 | −0.634848 | − | 0.772637i | \(-0.718937\pi\) | ||||
−0.634848 | + | 0.772637i | \(0.718937\pi\) | |||||||
\(138\) | −3.37228 | −0.287068 | ||||||||
\(139\) | 14.1168 | 1.19738 | 0.598688 | − | 0.800983i | \(-0.295689\pi\) | ||||
0.598688 | + | 0.800983i | \(0.295689\pi\) | |||||||
\(140\) | 3.37228 | 0.285010 | ||||||||
\(141\) | −13.4891 | −1.13599 | ||||||||
\(142\) | 1.25544 | 0.105354 | ||||||||
\(143\) | 4.74456 | 0.396760 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 2.62772 | 0.218220 | ||||||||
\(146\) | −6.00000 | −0.496564 | ||||||||
\(147\) | 4.37228 | 0.360620 | ||||||||
\(148\) | −10.0000 | −0.821995 | ||||||||
\(149\) | −0.744563 | −0.0609969 | −0.0304985 | − | 0.999535i | \(-0.509709\pi\) | ||||
−0.0304985 | + | 0.999535i | \(0.509709\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | 21.4891 | 1.74876 | 0.874380 | − | 0.485242i | \(-0.161268\pi\) | ||||
0.874380 | + | 0.485242i | \(0.161268\pi\) | |||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | 1.00000 | 0.0808452 | ||||||||
\(154\) | 3.37228 | 0.271746 | ||||||||
\(155\) | 4.62772 | 0.371707 | ||||||||
\(156\) | 4.74456 | 0.379869 | ||||||||
\(157\) | 11.4891 | 0.916932 | 0.458466 | − | 0.888712i | \(-0.348399\pi\) | ||||
0.458466 | + | 0.888712i | \(0.348399\pi\) | |||||||
\(158\) | −13.4891 | −1.07314 | ||||||||
\(159\) | −0.744563 | −0.0590477 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −11.3723 | −0.896261 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −7.37228 | −0.577442 | −0.288721 | − | 0.957413i | \(-0.593230\pi\) | ||||
−0.288721 | + | 0.957413i | \(0.593230\pi\) | |||||||
\(164\) | −12.7446 | −0.995183 | ||||||||
\(165\) | 1.00000 | 0.0778499 | ||||||||
\(166\) | −12.0000 | −0.931381 | ||||||||
\(167\) | −12.2337 | −0.946671 | −0.473336 | − | 0.880882i | \(-0.656950\pi\) | ||||
−0.473336 | + | 0.880882i | \(0.656950\pi\) | |||||||
\(168\) | 3.37228 | 0.260177 | ||||||||
\(169\) | 9.51087 | 0.731606 | ||||||||
\(170\) | 1.00000 | 0.0766965 | ||||||||
\(171\) | 4.00000 | 0.305888 | ||||||||
\(172\) | 7.37228 | 0.562131 | ||||||||
\(173\) | 11.4891 | 0.873502 | 0.436751 | − | 0.899582i | \(-0.356129\pi\) | ||||
0.436751 | + | 0.899582i | \(0.356129\pi\) | |||||||
\(174\) | 2.62772 | 0.199207 | ||||||||
\(175\) | 3.37228 | 0.254921 | ||||||||
\(176\) | 1.00000 | 0.0753778 | ||||||||
\(177\) | −10.7446 | −0.807611 | ||||||||
\(178\) | 16.7446 | 1.25506 | ||||||||
\(179\) | −18.7446 | −1.40103 | −0.700517 | − | 0.713636i | \(-0.747047\pi\) | ||||
−0.700517 | + | 0.713636i | \(0.747047\pi\) | |||||||
\(180\) | 1.00000 | 0.0745356 | ||||||||
\(181\) | −14.6277 | −1.08727 | −0.543635 | − | 0.839322i | \(-0.682952\pi\) | ||||
−0.543635 | + | 0.839322i | \(0.682952\pi\) | |||||||
\(182\) | 16.0000 | 1.18600 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | −3.37228 | −0.248608 | ||||||||
\(185\) | −10.0000 | −0.735215 | ||||||||
\(186\) | 4.62772 | 0.339321 | ||||||||
\(187\) | 1.00000 | 0.0731272 | ||||||||
\(188\) | −13.4891 | −0.983796 | ||||||||
\(189\) | 3.37228 | 0.245297 | ||||||||
\(190\) | 4.00000 | 0.290191 | ||||||||
\(191\) | −4.62772 | −0.334850 | −0.167425 | − | 0.985885i | \(-0.553545\pi\) | ||||
−0.167425 | + | 0.985885i | \(0.553545\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −0.510875 | −0.0367736 | −0.0183868 | − | 0.999831i | \(-0.505853\pi\) | ||||
−0.0183868 | + | 0.999831i | \(0.505853\pi\) | |||||||
\(194\) | −9.37228 | −0.672891 | ||||||||
\(195\) | 4.74456 | 0.339765 | ||||||||
\(196\) | 4.37228 | 0.312306 | ||||||||
\(197\) | 26.2337 | 1.86907 | 0.934536 | − | 0.355867i | \(-0.115815\pi\) | ||||
0.934536 | + | 0.355867i | \(0.115815\pi\) | |||||||
\(198\) | 1.00000 | 0.0710669 | ||||||||
\(199\) | −8.00000 | −0.567105 | −0.283552 | − | 0.958957i | \(-0.591513\pi\) | ||||
−0.283552 | + | 0.958957i | \(0.591513\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 4.00000 | 0.282138 | ||||||||
\(202\) | 6.00000 | 0.422159 | ||||||||
\(203\) | 8.86141 | 0.621949 | ||||||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | −12.7446 | −0.890119 | ||||||||
\(206\) | −3.37228 | −0.234958 | ||||||||
\(207\) | −3.37228 | −0.234390 | ||||||||
\(208\) | 4.74456 | 0.328976 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 3.37228 | 0.232710 | ||||||||
\(211\) | −14.1168 | −0.971844 | −0.485922 | − | 0.874002i | \(-0.661516\pi\) | ||||
−0.485922 | + | 0.874002i | \(0.661516\pi\) | |||||||
\(212\) | −0.744563 | −0.0511368 | ||||||||
\(213\) | 1.25544 | 0.0860212 | ||||||||
\(214\) | 14.1168 | 0.965008 | ||||||||
\(215\) | 7.37228 | 0.502785 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 15.6060 | 1.05940 | ||||||||
\(218\) | −8.74456 | −0.592257 | ||||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | 1.00000 | 0.0674200 | ||||||||
\(221\) | 4.74456 | 0.319154 | ||||||||
\(222\) | −10.0000 | −0.671156 | ||||||||
\(223\) | −11.3723 | −0.761544 | −0.380772 | − | 0.924669i | \(-0.624342\pi\) | ||||
−0.380772 | + | 0.924669i | \(0.624342\pi\) | |||||||
\(224\) | 3.37228 | 0.225320 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −11.4891 | −0.764245 | ||||||||
\(227\) | 6.11684 | 0.405989 | 0.202995 | − | 0.979180i | \(-0.434933\pi\) | ||||
0.202995 | + | 0.979180i | \(0.434933\pi\) | |||||||
\(228\) | 4.00000 | 0.264906 | ||||||||
\(229\) | −3.25544 | −0.215125 | −0.107563 | − | 0.994198i | \(-0.534305\pi\) | ||||
−0.107563 | + | 0.994198i | \(0.534305\pi\) | |||||||
\(230\) | −3.37228 | −0.222362 | ||||||||
\(231\) | 3.37228 | 0.221880 | ||||||||
\(232\) | 2.62772 | 0.172518 | ||||||||
\(233\) | −14.8614 | −0.973603 | −0.486802 | − | 0.873513i | \(-0.661837\pi\) | ||||
−0.486802 | + | 0.873513i | \(0.661837\pi\) | |||||||
\(234\) | 4.74456 | 0.310162 | ||||||||
\(235\) | −13.4891 | −0.879934 | ||||||||
\(236\) | −10.7446 | −0.699411 | ||||||||
\(237\) | −13.4891 | −0.876213 | ||||||||
\(238\) | 3.37228 | 0.218593 | ||||||||
\(239\) | 20.2337 | 1.30881 | 0.654404 | − | 0.756145i | \(-0.272919\pi\) | ||||
0.654404 | + | 0.756145i | \(0.272919\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | −9.37228 | −0.603722 | −0.301861 | − | 0.953352i | \(-0.597608\pi\) | ||||
−0.301861 | + | 0.953352i | \(0.597608\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 4.37228 | 0.279335 | ||||||||
\(246\) | −12.7446 | −0.812564 | ||||||||
\(247\) | 18.9783 | 1.20756 | ||||||||
\(248\) | 4.62772 | 0.293860 | ||||||||
\(249\) | −12.0000 | −0.760469 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −6.51087 | −0.410963 | −0.205481 | − | 0.978661i | \(-0.565876\pi\) | ||||
−0.205481 | + | 0.978661i | \(0.565876\pi\) | |||||||
\(252\) | 3.37228 | 0.212434 | ||||||||
\(253\) | −3.37228 | −0.212014 | ||||||||
\(254\) | 20.2337 | 1.26957 | ||||||||
\(255\) | 1.00000 | 0.0626224 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 13.3723 | 0.834140 | 0.417070 | − | 0.908874i | \(-0.363057\pi\) | ||||
0.417070 | + | 0.908874i | \(0.363057\pi\) | |||||||
\(258\) | 7.37228 | 0.458978 | ||||||||
\(259\) | −33.7228 | −2.09543 | ||||||||
\(260\) | 4.74456 | 0.294245 | ||||||||
\(261\) | 2.62772 | 0.162652 | ||||||||
\(262\) | −9.48913 | −0.586240 | ||||||||
\(263\) | 0.861407 | 0.0531166 | 0.0265583 | − | 0.999647i | \(-0.491545\pi\) | ||||
0.0265583 | + | 0.999647i | \(0.491545\pi\) | |||||||
\(264\) | 1.00000 | 0.0615457 | ||||||||
\(265\) | −0.744563 | −0.0457381 | ||||||||
\(266\) | 13.4891 | 0.827071 | ||||||||
\(267\) | 16.7446 | 1.02475 | ||||||||
\(268\) | 4.00000 | 0.244339 | ||||||||
\(269\) | 14.0000 | 0.853595 | 0.426798 | − | 0.904347i | \(-0.359642\pi\) | ||||
0.426798 | + | 0.904347i | \(0.359642\pi\) | |||||||
\(270\) | 1.00000 | 0.0608581 | ||||||||
\(271\) | −2.11684 | −0.128589 | −0.0642946 | − | 0.997931i | \(-0.520480\pi\) | ||||
−0.0642946 | + | 0.997931i | \(0.520480\pi\) | |||||||
\(272\) | 1.00000 | 0.0606339 | ||||||||
\(273\) | 16.0000 | 0.968364 | ||||||||
\(274\) | −14.8614 | −0.897810 | ||||||||
\(275\) | 1.00000 | 0.0603023 | ||||||||
\(276\) | −3.37228 | −0.202987 | ||||||||
\(277\) | 22.0000 | 1.32185 | 0.660926 | − | 0.750451i | \(-0.270164\pi\) | ||||
0.660926 | + | 0.750451i | \(0.270164\pi\) | |||||||
\(278\) | 14.1168 | 0.846672 | ||||||||
\(279\) | 4.62772 | 0.277054 | ||||||||
\(280\) | 3.37228 | 0.201532 | ||||||||
\(281\) | 18.8614 | 1.12518 | 0.562589 | − | 0.826737i | \(-0.309806\pi\) | ||||
0.562589 | + | 0.826737i | \(0.309806\pi\) | |||||||
\(282\) | −13.4891 | −0.803266 | ||||||||
\(283\) | 18.7446 | 1.11425 | 0.557124 | − | 0.830429i | \(-0.311905\pi\) | ||||
0.557124 | + | 0.830429i | \(0.311905\pi\) | |||||||
\(284\) | 1.25544 | 0.0744965 | ||||||||
\(285\) | 4.00000 | 0.236940 | ||||||||
\(286\) | 4.74456 | 0.280552 | ||||||||
\(287\) | −42.9783 | −2.53693 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 2.62772 | 0.154305 | ||||||||
\(291\) | −9.37228 | −0.549413 | ||||||||
\(292\) | −6.00000 | −0.351123 | ||||||||
\(293\) | 30.8614 | 1.80294 | 0.901471 | − | 0.432839i | \(-0.142488\pi\) | ||||
0.901471 | + | 0.432839i | \(0.142488\pi\) | |||||||
\(294\) | 4.37228 | 0.254997 | ||||||||
\(295\) | −10.7446 | −0.625573 | ||||||||
\(296\) | −10.0000 | −0.581238 | ||||||||
\(297\) | 1.00000 | 0.0580259 | ||||||||
\(298\) | −0.744563 | −0.0431314 | ||||||||
\(299\) | −16.0000 | −0.925304 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 24.8614 | 1.43299 | ||||||||
\(302\) | 21.4891 | 1.23656 | ||||||||
\(303\) | 6.00000 | 0.344691 | ||||||||
\(304\) | 4.00000 | 0.229416 | ||||||||
\(305\) | −2.00000 | −0.114520 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 3.37228 | 0.192154 | ||||||||
\(309\) | −3.37228 | −0.191842 | ||||||||
\(310\) | 4.62772 | 0.262837 | ||||||||
\(311\) | −5.48913 | −0.311260 | −0.155630 | − | 0.987815i | \(-0.549741\pi\) | ||||
−0.155630 | + | 0.987815i | \(0.549741\pi\) | |||||||
\(312\) | 4.74456 | 0.268608 | ||||||||
\(313\) | 18.8614 | 1.06611 | 0.533055 | − | 0.846081i | \(-0.321044\pi\) | ||||
0.533055 | + | 0.846081i | \(0.321044\pi\) | |||||||
\(314\) | 11.4891 | 0.648369 | ||||||||
\(315\) | 3.37228 | 0.190007 | ||||||||
\(316\) | −13.4891 | −0.758823 | ||||||||
\(317\) | 0.116844 | 0.00656261 | 0.00328131 | − | 0.999995i | \(-0.498956\pi\) | ||||
0.00328131 | + | 0.999995i | \(0.498956\pi\) | |||||||
\(318\) | −0.744563 | −0.0417530 | ||||||||
\(319\) | 2.62772 | 0.147124 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 14.1168 | 0.787925 | ||||||||
\(322\) | −11.3723 | −0.633752 | ||||||||
\(323\) | 4.00000 | 0.222566 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 4.74456 | 0.263181 | ||||||||
\(326\) | −7.37228 | −0.408313 | ||||||||
\(327\) | −8.74456 | −0.483575 | ||||||||
\(328\) | −12.7446 | −0.703701 | ||||||||
\(329\) | −45.4891 | −2.50790 | ||||||||
\(330\) | 1.00000 | 0.0550482 | ||||||||
\(331\) | 18.3505 | 1.00864 | 0.504318 | − | 0.863518i | \(-0.331744\pi\) | ||||
0.504318 | + | 0.863518i | \(0.331744\pi\) | |||||||
\(332\) | −12.0000 | −0.658586 | ||||||||
\(333\) | −10.0000 | −0.547997 | ||||||||
\(334\) | −12.2337 | −0.669398 | ||||||||
\(335\) | 4.00000 | 0.218543 | ||||||||
\(336\) | 3.37228 | 0.183973 | ||||||||
\(337\) | −24.9783 | −1.36065 | −0.680326 | − | 0.732910i | \(-0.738162\pi\) | ||||
−0.680326 | + | 0.732910i | \(0.738162\pi\) | |||||||
\(338\) | 9.51087 | 0.517323 | ||||||||
\(339\) | −11.4891 | −0.624004 | ||||||||
\(340\) | 1.00000 | 0.0542326 | ||||||||
\(341\) | 4.62772 | 0.250605 | ||||||||
\(342\) | 4.00000 | 0.216295 | ||||||||
\(343\) | −8.86141 | −0.478471 | ||||||||
\(344\) | 7.37228 | 0.397487 | ||||||||
\(345\) | −3.37228 | −0.181558 | ||||||||
\(346\) | 11.4891 | 0.617659 | ||||||||
\(347\) | 22.9783 | 1.23354 | 0.616769 | − | 0.787145i | \(-0.288441\pi\) | ||||
0.616769 | + | 0.787145i | \(0.288441\pi\) | |||||||
\(348\) | 2.62772 | 0.140861 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 3.37228 | 0.180256 | ||||||||
\(351\) | 4.74456 | 0.253246 | ||||||||
\(352\) | 1.00000 | 0.0533002 | ||||||||
\(353\) | −22.8614 | −1.21679 | −0.608395 | − | 0.793634i | \(-0.708186\pi\) | ||||
−0.608395 | + | 0.793634i | \(0.708186\pi\) | |||||||
\(354\) | −10.7446 | −0.571067 | ||||||||
\(355\) | 1.25544 | 0.0666317 | ||||||||
\(356\) | 16.7446 | 0.887460 | ||||||||
\(357\) | 3.37228 | 0.178480 | ||||||||
\(358\) | −18.7446 | −0.990681 | ||||||||
\(359\) | −28.2337 | −1.49012 | −0.745059 | − | 0.666999i | \(-0.767578\pi\) | ||||
−0.745059 | + | 0.666999i | \(0.767578\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | −14.6277 | −0.768816 | ||||||||
\(363\) | 1.00000 | 0.0524864 | ||||||||
\(364\) | 16.0000 | 0.838628 | ||||||||
\(365\) | −6.00000 | −0.314054 | ||||||||
\(366\) | −2.00000 | −0.104542 | ||||||||
\(367\) | −22.7446 | −1.18726 | −0.593628 | − | 0.804739i | \(-0.702305\pi\) | ||||
−0.593628 | + | 0.804739i | \(0.702305\pi\) | |||||||
\(368\) | −3.37228 | −0.175792 | ||||||||
\(369\) | −12.7446 | −0.663455 | ||||||||
\(370\) | −10.0000 | −0.519875 | ||||||||
\(371\) | −2.51087 | −0.130358 | ||||||||
\(372\) | 4.62772 | 0.239936 | ||||||||
\(373\) | −23.4891 | −1.21622 | −0.608110 | − | 0.793852i | \(-0.708072\pi\) | ||||
−0.608110 | + | 0.793852i | \(0.708072\pi\) | |||||||
\(374\) | 1.00000 | 0.0517088 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | −13.4891 | −0.695649 | ||||||||
\(377\) | 12.4674 | 0.642103 | ||||||||
\(378\) | 3.37228 | 0.173451 | ||||||||
\(379\) | 28.0000 | 1.43826 | 0.719132 | − | 0.694874i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694874i | \(0.244540\pi\) | |||||||
\(380\) | 4.00000 | 0.205196 | ||||||||
\(381\) | 20.2337 | 1.03660 | ||||||||
\(382\) | −4.62772 | −0.236775 | ||||||||
\(383\) | 2.51087 | 0.128300 | 0.0641499 | − | 0.997940i | \(-0.479566\pi\) | ||||
0.0641499 | + | 0.997940i | \(0.479566\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 3.37228 | 0.171867 | ||||||||
\(386\) | −0.510875 | −0.0260028 | ||||||||
\(387\) | 7.37228 | 0.374754 | ||||||||
\(388\) | −9.37228 | −0.475805 | ||||||||
\(389\) | −34.4674 | −1.74757 | −0.873783 | − | 0.486317i | \(-0.838340\pi\) | ||||
−0.873783 | + | 0.486317i | \(0.838340\pi\) | |||||||
\(390\) | 4.74456 | 0.240250 | ||||||||
\(391\) | −3.37228 | −0.170544 | ||||||||
\(392\) | 4.37228 | 0.220834 | ||||||||
\(393\) | −9.48913 | −0.478663 | ||||||||
\(394\) | 26.2337 | 1.32163 | ||||||||
\(395\) | −13.4891 | −0.678712 | ||||||||
\(396\) | 1.00000 | 0.0502519 | ||||||||
\(397\) | −2.00000 | −0.100377 | −0.0501886 | − | 0.998740i | \(-0.515982\pi\) | ||||
−0.0501886 | + | 0.998740i | \(0.515982\pi\) | |||||||
\(398\) | −8.00000 | −0.401004 | ||||||||
\(399\) | 13.4891 | 0.675301 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −9.37228 | −0.468029 | −0.234015 | − | 0.972233i | \(-0.575186\pi\) | ||||
−0.234015 | + | 0.972233i | \(0.575186\pi\) | |||||||
\(402\) | 4.00000 | 0.199502 | ||||||||
\(403\) | 21.9565 | 1.09373 | ||||||||
\(404\) | 6.00000 | 0.298511 | ||||||||
\(405\) | 1.00000 | 0.0496904 | ||||||||
\(406\) | 8.86141 | 0.439784 | ||||||||
\(407\) | −10.0000 | −0.495682 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | 30.2337 | 1.49496 | 0.747480 | − | 0.664285i | \(-0.231264\pi\) | ||||
0.747480 | + | 0.664285i | \(0.231264\pi\) | |||||||
\(410\) | −12.7446 | −0.629409 | ||||||||
\(411\) | −14.8614 | −0.733059 | ||||||||
\(412\) | −3.37228 | −0.166140 | ||||||||
\(413\) | −36.2337 | −1.78294 | ||||||||
\(414\) | −3.37228 | −0.165739 | ||||||||
\(415\) | −12.0000 | −0.589057 | ||||||||
\(416\) | 4.74456 | 0.232621 | ||||||||
\(417\) | 14.1168 | 0.691305 | ||||||||
\(418\) | 4.00000 | 0.195646 | ||||||||
\(419\) | 24.6277 | 1.20314 | 0.601571 | − | 0.798819i | \(-0.294542\pi\) | ||||
0.601571 | + | 0.798819i | \(0.294542\pi\) | |||||||
\(420\) | 3.37228 | 0.164550 | ||||||||
\(421\) | −16.7446 | −0.816080 | −0.408040 | − | 0.912964i | \(-0.633788\pi\) | ||||
−0.408040 | + | 0.912964i | \(0.633788\pi\) | |||||||
\(422\) | −14.1168 | −0.687197 | ||||||||
\(423\) | −13.4891 | −0.655864 | ||||||||
\(424\) | −0.744563 | −0.0361592 | ||||||||
\(425\) | 1.00000 | 0.0485071 | ||||||||
\(426\) | 1.25544 | 0.0608261 | ||||||||
\(427\) | −6.74456 | −0.326392 | ||||||||
\(428\) | 14.1168 | 0.682363 | ||||||||
\(429\) | 4.74456 | 0.229070 | ||||||||
\(430\) | 7.37228 | 0.355523 | ||||||||
\(431\) | 2.11684 | 0.101965 | 0.0509824 | − | 0.998700i | \(-0.483765\pi\) | ||||
0.0509824 | + | 0.998700i | \(0.483765\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 27.2554 | 1.30981 | 0.654906 | − | 0.755710i | \(-0.272708\pi\) | ||||
0.654906 | + | 0.755710i | \(0.272708\pi\) | |||||||
\(434\) | 15.6060 | 0.749110 | ||||||||
\(435\) | 2.62772 | 0.125989 | ||||||||
\(436\) | −8.74456 | −0.418789 | ||||||||
\(437\) | −13.4891 | −0.645272 | ||||||||
\(438\) | −6.00000 | −0.286691 | ||||||||
\(439\) | −28.2337 | −1.34752 | −0.673760 | − | 0.738950i | \(-0.735322\pi\) | ||||
−0.673760 | + | 0.738950i | \(0.735322\pi\) | |||||||
\(440\) | 1.00000 | 0.0476731 | ||||||||
\(441\) | 4.37228 | 0.208204 | ||||||||
\(442\) | 4.74456 | 0.225676 | ||||||||
\(443\) | −22.1168 | −1.05080 | −0.525401 | − | 0.850854i | \(-0.676085\pi\) | ||||
−0.525401 | + | 0.850854i | \(0.676085\pi\) | |||||||
\(444\) | −10.0000 | −0.474579 | ||||||||
\(445\) | 16.7446 | 0.793768 | ||||||||
\(446\) | −11.3723 | −0.538493 | ||||||||
\(447\) | −0.744563 | −0.0352166 | ||||||||
\(448\) | 3.37228 | 0.159325 | ||||||||
\(449\) | 29.3723 | 1.38616 | 0.693082 | − | 0.720859i | \(-0.256252\pi\) | ||||
0.693082 | + | 0.720859i | \(0.256252\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | −12.7446 | −0.600118 | ||||||||
\(452\) | −11.4891 | −0.540403 | ||||||||
\(453\) | 21.4891 | 1.00965 | ||||||||
\(454\) | 6.11684 | 0.287078 | ||||||||
\(455\) | 16.0000 | 0.750092 | ||||||||
\(456\) | 4.00000 | 0.187317 | ||||||||
\(457\) | 10.0000 | 0.467780 | 0.233890 | − | 0.972263i | \(-0.424854\pi\) | ||||
0.233890 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(458\) | −3.25544 | −0.152117 | ||||||||
\(459\) | 1.00000 | 0.0466760 | ||||||||
\(460\) | −3.37228 | −0.157233 | ||||||||
\(461\) | 0.510875 | 0.0237938 | 0.0118969 | − | 0.999929i | \(-0.496213\pi\) | ||||
0.0118969 | + | 0.999929i | \(0.496213\pi\) | |||||||
\(462\) | 3.37228 | 0.156893 | ||||||||
\(463\) | 16.0000 | 0.743583 | 0.371792 | − | 0.928316i | \(-0.378744\pi\) | ||||
0.371792 | + | 0.928316i | \(0.378744\pi\) | |||||||
\(464\) | 2.62772 | 0.121989 | ||||||||
\(465\) | 4.62772 | 0.214605 | ||||||||
\(466\) | −14.8614 | −0.688441 | ||||||||
\(467\) | 30.9783 | 1.43350 | 0.716751 | − | 0.697329i | \(-0.245628\pi\) | ||||
0.716751 | + | 0.697329i | \(0.245628\pi\) | |||||||
\(468\) | 4.74456 | 0.219317 | ||||||||
\(469\) | 13.4891 | 0.622870 | ||||||||
\(470\) | −13.4891 | −0.622207 | ||||||||
\(471\) | 11.4891 | 0.529391 | ||||||||
\(472\) | −10.7446 | −0.494559 | ||||||||
\(473\) | 7.37228 | 0.338978 | ||||||||
\(474\) | −13.4891 | −0.619576 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 3.37228 | 0.154568 | ||||||||
\(477\) | −0.744563 | −0.0340912 | ||||||||
\(478\) | 20.2337 | 0.925467 | ||||||||
\(479\) | 35.8397 | 1.63756 | 0.818778 | − | 0.574110i | \(-0.194652\pi\) | ||||
0.818778 | + | 0.574110i | \(0.194652\pi\) | |||||||
\(480\) | 1.00000 | 0.0456435 | ||||||||
\(481\) | −47.4456 | −2.16333 | ||||||||
\(482\) | −9.37228 | −0.426896 | ||||||||
\(483\) | −11.3723 | −0.517457 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −9.37228 | −0.425573 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 1.25544 | 0.0568893 | 0.0284446 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284446 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(488\) | −2.00000 | −0.0905357 | ||||||||
\(489\) | −7.37228 | −0.333386 | ||||||||
\(490\) | 4.37228 | 0.197520 | ||||||||
\(491\) | −6.51087 | −0.293832 | −0.146916 | − | 0.989149i | \(-0.546935\pi\) | ||||
−0.146916 | + | 0.989149i | \(0.546935\pi\) | |||||||
\(492\) | −12.7446 | −0.574569 | ||||||||
\(493\) | 2.62772 | 0.118346 | ||||||||
\(494\) | 18.9783 | 0.853872 | ||||||||
\(495\) | 1.00000 | 0.0449467 | ||||||||
\(496\) | 4.62772 | 0.207791 | ||||||||
\(497\) | 4.23369 | 0.189907 | ||||||||
\(498\) | −12.0000 | −0.537733 | ||||||||
\(499\) | 1.48913 | 0.0666624 | 0.0333312 | − | 0.999444i | \(-0.489388\pi\) | ||||
0.0333312 | + | 0.999444i | \(0.489388\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −12.2337 | −0.546561 | ||||||||
\(502\) | −6.51087 | −0.290595 | ||||||||
\(503\) | 2.97825 | 0.132794 | 0.0663968 | − | 0.997793i | \(-0.478850\pi\) | ||||
0.0663968 | + | 0.997793i | \(0.478850\pi\) | |||||||
\(504\) | 3.37228 | 0.150213 | ||||||||
\(505\) | 6.00000 | 0.266996 | ||||||||
\(506\) | −3.37228 | −0.149916 | ||||||||
\(507\) | 9.51087 | 0.422393 | ||||||||
\(508\) | 20.2337 | 0.897725 | ||||||||
\(509\) | 11.4891 | 0.509247 | 0.254623 | − | 0.967040i | \(-0.418049\pi\) | ||||
0.254623 | + | 0.967040i | \(0.418049\pi\) | |||||||
\(510\) | 1.00000 | 0.0442807 | ||||||||
\(511\) | −20.2337 | −0.895086 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.00000 | 0.176604 | ||||||||
\(514\) | 13.3723 | 0.589826 | ||||||||
\(515\) | −3.37228 | −0.148600 | ||||||||
\(516\) | 7.37228 | 0.324547 | ||||||||
\(517\) | −13.4891 | −0.593251 | ||||||||
\(518\) | −33.7228 | −1.48170 | ||||||||
\(519\) | 11.4891 | 0.504317 | ||||||||
\(520\) | 4.74456 | 0.208063 | ||||||||
\(521\) | 20.9783 | 0.919074 | 0.459537 | − | 0.888159i | \(-0.348015\pi\) | ||||
0.459537 | + | 0.888159i | \(0.348015\pi\) | |||||||
\(522\) | 2.62772 | 0.115012 | ||||||||
\(523\) | −24.6277 | −1.07689 | −0.538447 | − | 0.842659i | \(-0.680989\pi\) | ||||
−0.538447 | + | 0.842659i | \(0.680989\pi\) | |||||||
\(524\) | −9.48913 | −0.414534 | ||||||||
\(525\) | 3.37228 | 0.147178 | ||||||||
\(526\) | 0.861407 | 0.0375591 | ||||||||
\(527\) | 4.62772 | 0.201587 | ||||||||
\(528\) | 1.00000 | 0.0435194 | ||||||||
\(529\) | −11.6277 | −0.505553 | ||||||||
\(530\) | −0.744563 | −0.0323417 | ||||||||
\(531\) | −10.7446 | −0.466274 | ||||||||
\(532\) | 13.4891 | 0.584828 | ||||||||
\(533\) | −60.4674 | −2.61913 | ||||||||
\(534\) | 16.7446 | 0.724608 | ||||||||
\(535\) | 14.1168 | 0.610324 | ||||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | −18.7446 | −0.808888 | ||||||||
\(538\) | 14.0000 | 0.603583 | ||||||||
\(539\) | 4.37228 | 0.188327 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | −6.23369 | −0.268007 | −0.134004 | − | 0.990981i | \(-0.542783\pi\) | ||||
−0.134004 | + | 0.990981i | \(0.542783\pi\) | |||||||
\(542\) | −2.11684 | −0.0909262 | ||||||||
\(543\) | −14.6277 | −0.627735 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | −8.74456 | −0.374576 | ||||||||
\(546\) | 16.0000 | 0.684737 | ||||||||
\(547\) | 8.23369 | 0.352047 | 0.176024 | − | 0.984386i | \(-0.443677\pi\) | ||||
0.176024 | + | 0.984386i | \(0.443677\pi\) | |||||||
\(548\) | −14.8614 | −0.634848 | ||||||||
\(549\) | −2.00000 | −0.0853579 | ||||||||
\(550\) | 1.00000 | 0.0426401 | ||||||||
\(551\) | 10.5109 | 0.447778 | ||||||||
\(552\) | −3.37228 | −0.143534 | ||||||||
\(553\) | −45.4891 | −1.93439 | ||||||||
\(554\) | 22.0000 | 0.934690 | ||||||||
\(555\) | −10.0000 | −0.424476 | ||||||||
\(556\) | 14.1168 | 0.598688 | ||||||||
\(557\) | −24.3505 | −1.03177 | −0.515883 | − | 0.856659i | \(-0.672536\pi\) | ||||
−0.515883 | + | 0.856659i | \(0.672536\pi\) | |||||||
\(558\) | 4.62772 | 0.195907 | ||||||||
\(559\) | 34.9783 | 1.47942 | ||||||||
\(560\) | 3.37228 | 0.142505 | ||||||||
\(561\) | 1.00000 | 0.0422200 | ||||||||
\(562\) | 18.8614 | 0.795620 | ||||||||
\(563\) | −12.0000 | −0.505740 | −0.252870 | − | 0.967500i | \(-0.581374\pi\) | ||||
−0.252870 | + | 0.967500i | \(0.581374\pi\) | |||||||
\(564\) | −13.4891 | −0.567995 | ||||||||
\(565\) | −11.4891 | −0.483351 | ||||||||
\(566\) | 18.7446 | 0.787893 | ||||||||
\(567\) | 3.37228 | 0.141623 | ||||||||
\(568\) | 1.25544 | 0.0526770 | ||||||||
\(569\) | 20.9783 | 0.879454 | 0.439727 | − | 0.898131i | \(-0.355075\pi\) | ||||
0.439727 | + | 0.898131i | \(0.355075\pi\) | |||||||
\(570\) | 4.00000 | 0.167542 | ||||||||
\(571\) | 22.9783 | 0.961610 | 0.480805 | − | 0.876828i | \(-0.340345\pi\) | ||||
0.480805 | + | 0.876828i | \(0.340345\pi\) | |||||||
\(572\) | 4.74456 | 0.198380 | ||||||||
\(573\) | −4.62772 | −0.193326 | ||||||||
\(574\) | −42.9783 | −1.79388 | ||||||||
\(575\) | −3.37228 | −0.140634 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 47.4891 | 1.97700 | 0.988499 | − | 0.151227i | \(-0.0483224\pi\) | ||||
0.988499 | + | 0.151227i | \(0.0483224\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | −0.510875 | −0.0212312 | ||||||||
\(580\) | 2.62772 | 0.109110 | ||||||||
\(581\) | −40.4674 | −1.67887 | ||||||||
\(582\) | −9.37228 | −0.388494 | ||||||||
\(583\) | −0.744563 | −0.0308366 | ||||||||
\(584\) | −6.00000 | −0.248282 | ||||||||
\(585\) | 4.74456 | 0.196164 | ||||||||
\(586\) | 30.8614 | 1.27487 | ||||||||
\(587\) | 25.0951 | 1.03579 | 0.517893 | − | 0.855446i | \(-0.326717\pi\) | ||||
0.517893 | + | 0.855446i | \(0.326717\pi\) | |||||||
\(588\) | 4.37228 | 0.180310 | ||||||||
\(589\) | 18.5109 | 0.762727 | ||||||||
\(590\) | −10.7446 | −0.442347 | ||||||||
\(591\) | 26.2337 | 1.07911 | ||||||||
\(592\) | −10.0000 | −0.410997 | ||||||||
\(593\) | −0.510875 | −0.0209791 | −0.0104896 | − | 0.999945i | \(-0.503339\pi\) | ||||
−0.0104896 | + | 0.999945i | \(0.503339\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 3.37228 | 0.138250 | ||||||||
\(596\) | −0.744563 | −0.0304985 | ||||||||
\(597\) | −8.00000 | −0.327418 | ||||||||
\(598\) | −16.0000 | −0.654289 | ||||||||
\(599\) | −30.3505 | −1.24009 | −0.620045 | − | 0.784567i | \(-0.712885\pi\) | ||||
−0.620045 | + | 0.784567i | \(0.712885\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −8.51087 | −0.347166 | −0.173583 | − | 0.984819i | \(-0.555534\pi\) | ||||
−0.173583 | + | 0.984819i | \(0.555534\pi\) | |||||||
\(602\) | 24.8614 | 1.01328 | ||||||||
\(603\) | 4.00000 | 0.162893 | ||||||||
\(604\) | 21.4891 | 0.874380 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | 6.00000 | 0.243733 | ||||||||
\(607\) | 16.0000 | 0.649420 | 0.324710 | − | 0.945814i | \(-0.394733\pi\) | ||||
0.324710 | + | 0.945814i | \(0.394733\pi\) | |||||||
\(608\) | 4.00000 | 0.162221 | ||||||||
\(609\) | 8.86141 | 0.359082 | ||||||||
\(610\) | −2.00000 | −0.0809776 | ||||||||
\(611\) | −64.0000 | −2.58916 | ||||||||
\(612\) | 1.00000 | 0.0404226 | ||||||||
\(613\) | −47.9565 | −1.93694 | −0.968472 | − | 0.249121i | \(-0.919858\pi\) | ||||
−0.968472 | + | 0.249121i | \(0.919858\pi\) | |||||||
\(614\) | 4.00000 | 0.161427 | ||||||||
\(615\) | −12.7446 | −0.513910 | ||||||||
\(616\) | 3.37228 | 0.135873 | ||||||||
\(617\) | 12.5109 | 0.503669 | 0.251834 | − | 0.967770i | \(-0.418966\pi\) | ||||
0.251834 | + | 0.967770i | \(0.418966\pi\) | |||||||
\(618\) | −3.37228 | −0.135653 | ||||||||
\(619\) | 16.2337 | 0.652487 | 0.326244 | − | 0.945286i | \(-0.394217\pi\) | ||||
0.326244 | + | 0.945286i | \(0.394217\pi\) | |||||||
\(620\) | 4.62772 | 0.185854 | ||||||||
\(621\) | −3.37228 | −0.135325 | ||||||||
\(622\) | −5.48913 | −0.220094 | ||||||||
\(623\) | 56.4674 | 2.26232 | ||||||||
\(624\) | 4.74456 | 0.189935 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 18.8614 | 0.753853 | ||||||||
\(627\) | 4.00000 | 0.159745 | ||||||||
\(628\) | 11.4891 | 0.458466 | ||||||||
\(629\) | −10.0000 | −0.398726 | ||||||||
\(630\) | 3.37228 | 0.134355 | ||||||||
\(631\) | −12.2337 | −0.487015 | −0.243508 | − | 0.969899i | \(-0.578298\pi\) | ||||
−0.243508 | + | 0.969899i | \(0.578298\pi\) | |||||||
\(632\) | −13.4891 | −0.536569 | ||||||||
\(633\) | −14.1168 | −0.561094 | ||||||||
\(634\) | 0.116844 | 0.00464047 | ||||||||
\(635\) | 20.2337 | 0.802949 | ||||||||
\(636\) | −0.744563 | −0.0295238 | ||||||||
\(637\) | 20.7446 | 0.821929 | ||||||||
\(638\) | 2.62772 | 0.104032 | ||||||||
\(639\) | 1.25544 | 0.0496643 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −21.1386 | −0.834924 | −0.417462 | − | 0.908694i | \(-0.637080\pi\) | ||||
−0.417462 | + | 0.908694i | \(0.637080\pi\) | |||||||
\(642\) | 14.1168 | 0.557147 | ||||||||
\(643\) | 10.3505 | 0.408185 | 0.204093 | − | 0.978952i | \(-0.434576\pi\) | ||||
0.204093 | + | 0.978952i | \(0.434576\pi\) | |||||||
\(644\) | −11.3723 | −0.448131 | ||||||||
\(645\) | 7.37228 | 0.290283 | ||||||||
\(646\) | 4.00000 | 0.157378 | ||||||||
\(647\) | −25.7228 | −1.01127 | −0.505634 | − | 0.862748i | \(-0.668741\pi\) | ||||
−0.505634 | + | 0.862748i | \(0.668741\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −10.7446 | −0.421761 | ||||||||
\(650\) | 4.74456 | 0.186097 | ||||||||
\(651\) | 15.6060 | 0.611646 | ||||||||
\(652\) | −7.37228 | −0.288721 | ||||||||
\(653\) | 16.1168 | 0.630701 | 0.315350 | − | 0.948975i | \(-0.397878\pi\) | ||||
0.315350 | + | 0.948975i | \(0.397878\pi\) | |||||||
\(654\) | −8.74456 | −0.341939 | ||||||||
\(655\) | −9.48913 | −0.370771 | ||||||||
\(656\) | −12.7446 | −0.497592 | ||||||||
\(657\) | −6.00000 | −0.234082 | ||||||||
\(658\) | −45.4891 | −1.77335 | ||||||||
\(659\) | 31.3723 | 1.22209 | 0.611045 | − | 0.791596i | \(-0.290749\pi\) | ||||
0.611045 | + | 0.791596i | \(0.290749\pi\) | |||||||
\(660\) | 1.00000 | 0.0389249 | ||||||||
\(661\) | −5.76631 | −0.224284 | −0.112142 | − | 0.993692i | \(-0.535771\pi\) | ||||
−0.112142 | + | 0.993692i | \(0.535771\pi\) | |||||||
\(662\) | 18.3505 | 0.713214 | ||||||||
\(663\) | 4.74456 | 0.184264 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 13.4891 | 0.523086 | ||||||||
\(666\) | −10.0000 | −0.387492 | ||||||||
\(667\) | −8.86141 | −0.343115 | ||||||||
\(668\) | −12.2337 | −0.473336 | ||||||||
\(669\) | −11.3723 | −0.439678 | ||||||||
\(670\) | 4.00000 | 0.154533 | ||||||||
\(671\) | −2.00000 | −0.0772091 | ||||||||
\(672\) | 3.37228 | 0.130089 | ||||||||
\(673\) | −18.2337 | −0.702857 | −0.351429 | − | 0.936215i | \(-0.614304\pi\) | ||||
−0.351429 | + | 0.936215i | \(0.614304\pi\) | |||||||
\(674\) | −24.9783 | −0.962126 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 9.51087 | 0.365803 | ||||||||
\(677\) | −10.0000 | −0.384331 | −0.192166 | − | 0.981363i | \(-0.561551\pi\) | ||||
−0.192166 | + | 0.981363i | \(0.561551\pi\) | |||||||
\(678\) | −11.4891 | −0.441237 | ||||||||
\(679\) | −31.6060 | −1.21293 | ||||||||
\(680\) | 1.00000 | 0.0383482 | ||||||||
\(681\) | 6.11684 | 0.234398 | ||||||||
\(682\) | 4.62772 | 0.177205 | ||||||||
\(683\) | −6.51087 | −0.249132 | −0.124566 | − | 0.992211i | \(-0.539754\pi\) | ||||
−0.124566 | + | 0.992211i | \(0.539754\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | −14.8614 | −0.567825 | ||||||||
\(686\) | −8.86141 | −0.338330 | ||||||||
\(687\) | −3.25544 | −0.124203 | ||||||||
\(688\) | 7.37228 | 0.281066 | ||||||||
\(689\) | −3.53262 | −0.134582 | ||||||||
\(690\) | −3.37228 | −0.128381 | ||||||||
\(691\) | 46.9783 | 1.78714 | 0.893568 | − | 0.448927i | \(-0.148194\pi\) | ||||
0.893568 | + | 0.448927i | \(0.148194\pi\) | |||||||
\(692\) | 11.4891 | 0.436751 | ||||||||
\(693\) | 3.37228 | 0.128102 | ||||||||
\(694\) | 22.9783 | 0.872242 | ||||||||
\(695\) | 14.1168 | 0.535482 | ||||||||
\(696\) | 2.62772 | 0.0996034 | ||||||||
\(697\) | −12.7446 | −0.482735 | ||||||||
\(698\) | −2.00000 | −0.0757011 | ||||||||
\(699\) | −14.8614 | −0.562110 | ||||||||
\(700\) | 3.37228 | 0.127460 | ||||||||
\(701\) | 11.4891 | 0.433938 | 0.216969 | − | 0.976178i | \(-0.430383\pi\) | ||||
0.216969 | + | 0.976178i | \(0.430383\pi\) | |||||||
\(702\) | 4.74456 | 0.179072 | ||||||||
\(703\) | −40.0000 | −1.50863 | ||||||||
\(704\) | 1.00000 | 0.0376889 | ||||||||
\(705\) | −13.4891 | −0.508030 | ||||||||
\(706\) | −22.8614 | −0.860400 | ||||||||
\(707\) | 20.2337 | 0.760966 | ||||||||
\(708\) | −10.7446 | −0.403805 | ||||||||
\(709\) | 30.4674 | 1.14423 | 0.572113 | − | 0.820175i | \(-0.306124\pi\) | ||||
0.572113 | + | 0.820175i | \(0.306124\pi\) | |||||||
\(710\) | 1.25544 | 0.0471157 | ||||||||
\(711\) | −13.4891 | −0.505882 | ||||||||
\(712\) | 16.7446 | 0.627529 | ||||||||
\(713\) | −15.6060 | −0.584448 | ||||||||
\(714\) | 3.37228 | 0.126204 | ||||||||
\(715\) | 4.74456 | 0.177437 | ||||||||
\(716\) | −18.7446 | −0.700517 | ||||||||
\(717\) | 20.2337 | 0.755641 | ||||||||
\(718\) | −28.2337 | −1.05367 | ||||||||
\(719\) | −49.7228 | −1.85435 | −0.927174 | − | 0.374631i | \(-0.877769\pi\) | ||||
−0.927174 | + | 0.374631i | \(0.877769\pi\) | |||||||
\(720\) | 1.00000 | 0.0372678 | ||||||||
\(721\) | −11.3723 | −0.423526 | ||||||||
\(722\) | −3.00000 | −0.111648 | ||||||||
\(723\) | −9.37228 | −0.348559 | ||||||||
\(724\) | −14.6277 | −0.543635 | ||||||||
\(725\) | 2.62772 | 0.0975910 | ||||||||
\(726\) | 1.00000 | 0.0371135 | ||||||||
\(727\) | −14.3505 | −0.532232 | −0.266116 | − | 0.963941i | \(-0.585740\pi\) | ||||
−0.266116 | + | 0.963941i | \(0.585740\pi\) | |||||||
\(728\) | 16.0000 | 0.592999 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.00000 | −0.222070 | ||||||||
\(731\) | 7.37228 | 0.272674 | ||||||||
\(732\) | −2.00000 | −0.0739221 | ||||||||
\(733\) | 2.23369 | 0.0825031 | 0.0412516 | − | 0.999149i | \(-0.486865\pi\) | ||||
0.0412516 | + | 0.999149i | \(0.486865\pi\) | |||||||
\(734\) | −22.7446 | −0.839517 | ||||||||
\(735\) | 4.37228 | 0.161274 | ||||||||
\(736\) | −3.37228 | −0.124304 | ||||||||
\(737\) | 4.00000 | 0.147342 | ||||||||
\(738\) | −12.7446 | −0.469134 | ||||||||
\(739\) | 10.7446 | 0.395245 | 0.197623 | − | 0.980278i | \(-0.436678\pi\) | ||||
0.197623 | + | 0.980278i | \(0.436678\pi\) | |||||||
\(740\) | −10.0000 | −0.367607 | ||||||||
\(741\) | 18.9783 | 0.697183 | ||||||||
\(742\) | −2.51087 | −0.0921771 | ||||||||
\(743\) | 5.48913 | 0.201376 | 0.100688 | − | 0.994918i | \(-0.467896\pi\) | ||||
0.100688 | + | 0.994918i | \(0.467896\pi\) | |||||||
\(744\) | 4.62772 | 0.169660 | ||||||||
\(745\) | −0.744563 | −0.0272787 | ||||||||
\(746\) | −23.4891 | −0.859998 | ||||||||
\(747\) | −12.0000 | −0.439057 | ||||||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | 47.6060 | 1.73948 | ||||||||
\(750\) | 1.00000 | 0.0365148 | ||||||||
\(751\) | −20.6277 | −0.752716 | −0.376358 | − | 0.926474i | \(-0.622824\pi\) | ||||
−0.376358 | + | 0.926474i | \(0.622824\pi\) | |||||||
\(752\) | −13.4891 | −0.491898 | ||||||||
\(753\) | −6.51087 | −0.237269 | ||||||||
\(754\) | 12.4674 | 0.454035 | ||||||||
\(755\) | 21.4891 | 0.782069 | ||||||||
\(756\) | 3.37228 | 0.122649 | ||||||||
\(757\) | 19.8832 | 0.722666 | 0.361333 | − | 0.932437i | \(-0.382322\pi\) | ||||
0.361333 | + | 0.932437i | \(0.382322\pi\) | |||||||
\(758\) | 28.0000 | 1.01701 | ||||||||
\(759\) | −3.37228 | −0.122406 | ||||||||
\(760\) | 4.00000 | 0.145095 | ||||||||
\(761\) | −44.3505 | −1.60771 | −0.803853 | − | 0.594828i | \(-0.797220\pi\) | ||||
−0.803853 | + | 0.594828i | \(0.797220\pi\) | |||||||
\(762\) | 20.2337 | 0.732989 | ||||||||
\(763\) | −29.4891 | −1.06758 | ||||||||
\(764\) | −4.62772 | −0.167425 | ||||||||
\(765\) | 1.00000 | 0.0361551 | ||||||||
\(766\) | 2.51087 | 0.0907216 | ||||||||
\(767\) | −50.9783 | −1.84072 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 15.4891 | 0.558552 | 0.279276 | − | 0.960211i | \(-0.409906\pi\) | ||||
0.279276 | + | 0.960211i | \(0.409906\pi\) | |||||||
\(770\) | 3.37228 | 0.121529 | ||||||||
\(771\) | 13.3723 | 0.481591 | ||||||||
\(772\) | −0.510875 | −0.0183868 | ||||||||
\(773\) | 15.2554 | 0.548700 | 0.274350 | − | 0.961630i | \(-0.411537\pi\) | ||||
0.274350 | + | 0.961630i | \(0.411537\pi\) | |||||||
\(774\) | 7.37228 | 0.264991 | ||||||||
\(775\) | 4.62772 | 0.166233 | ||||||||
\(776\) | −9.37228 | −0.336445 | ||||||||
\(777\) | −33.7228 | −1.20980 | ||||||||
\(778\) | −34.4674 | −1.23572 | ||||||||
\(779\) | −50.9783 | −1.82649 | ||||||||
\(780\) | 4.74456 | 0.169883 | ||||||||
\(781\) | 1.25544 | 0.0449231 | ||||||||
\(782\) | −3.37228 | −0.120593 | ||||||||
\(783\) | 2.62772 | 0.0939070 | ||||||||
\(784\) | 4.37228 | 0.156153 | ||||||||
\(785\) | 11.4891 | 0.410064 | ||||||||
\(786\) | −9.48913 | −0.338466 | ||||||||
\(787\) | −25.4891 | −0.908589 | −0.454295 | − | 0.890852i | \(-0.650109\pi\) | ||||
−0.454295 | + | 0.890852i | \(0.650109\pi\) | |||||||
\(788\) | 26.2337 | 0.934536 | ||||||||
\(789\) | 0.861407 | 0.0306669 | ||||||||
\(790\) | −13.4891 | −0.479922 | ||||||||
\(791\) | −38.7446 | −1.37760 | ||||||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −9.48913 | −0.336969 | ||||||||
\(794\) | −2.00000 | −0.0709773 | ||||||||
\(795\) | −0.744563 | −0.0264069 | ||||||||
\(796\) | −8.00000 | −0.283552 | ||||||||
\(797\) | 39.2554 | 1.39050 | 0.695249 | − | 0.718769i | \(-0.255294\pi\) | ||||
0.695249 | + | 0.718769i | \(0.255294\pi\) | |||||||
\(798\) | 13.4891 | 0.477510 | ||||||||
\(799\) | −13.4891 | −0.477211 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 16.7446 | 0.591640 | ||||||||
\(802\) | −9.37228 | −0.330947 | ||||||||
\(803\) | −6.00000 | −0.211735 | ||||||||
\(804\) | 4.00000 | 0.141069 | ||||||||
\(805\) | −11.3723 | −0.400820 | ||||||||
\(806\) | 21.9565 | 0.773385 | ||||||||
\(807\) | 14.0000 | 0.492823 | ||||||||
\(808\) | 6.00000 | 0.211079 | ||||||||
\(809\) | −48.9783 | −1.72198 | −0.860992 | − | 0.508619i | \(-0.830156\pi\) | ||||
−0.860992 | + | 0.508619i | \(0.830156\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −1.48913 | −0.0522903 | −0.0261451 | − | 0.999658i | \(-0.508323\pi\) | ||||
−0.0261451 | + | 0.999658i | \(0.508323\pi\) | |||||||
\(812\) | 8.86141 | 0.310974 | ||||||||
\(813\) | −2.11684 | −0.0742410 | ||||||||
\(814\) | −10.0000 | −0.350500 | ||||||||
\(815\) | −7.37228 | −0.258240 | ||||||||
\(816\) | 1.00000 | 0.0350070 | ||||||||
\(817\) | 29.4891 | 1.03169 | ||||||||
\(818\) | 30.2337 | 1.05710 | ||||||||
\(819\) | 16.0000 | 0.559085 | ||||||||
\(820\) | −12.7446 | −0.445059 | ||||||||
\(821\) | 17.3723 | 0.606297 | 0.303148 | − | 0.952943i | \(-0.401962\pi\) | ||||
0.303148 | + | 0.952943i | \(0.401962\pi\) | |||||||
\(822\) | −14.8614 | −0.518351 | ||||||||
\(823\) | 17.2554 | 0.601487 | 0.300743 | − | 0.953705i | \(-0.402765\pi\) | ||||
0.300743 | + | 0.953705i | \(0.402765\pi\) | |||||||
\(824\) | −3.37228 | −0.117479 | ||||||||
\(825\) | 1.00000 | 0.0348155 | ||||||||
\(826\) | −36.2337 | −1.26073 | ||||||||
\(827\) | −6.11684 | −0.212704 | −0.106352 | − | 0.994329i | \(-0.533917\pi\) | ||||
−0.106352 | + | 0.994329i | \(0.533917\pi\) | |||||||
\(828\) | −3.37228 | −0.117195 | ||||||||
\(829\) | 24.9783 | 0.867531 | 0.433765 | − | 0.901026i | \(-0.357185\pi\) | ||||
0.433765 | + | 0.901026i | \(0.357185\pi\) | |||||||
\(830\) | −12.0000 | −0.416526 | ||||||||
\(831\) | 22.0000 | 0.763172 | ||||||||
\(832\) | 4.74456 | 0.164488 | ||||||||
\(833\) | 4.37228 | 0.151491 | ||||||||
\(834\) | 14.1168 | 0.488826 | ||||||||
\(835\) | −12.2337 | −0.423364 | ||||||||
\(836\) | 4.00000 | 0.138343 | ||||||||
\(837\) | 4.62772 | 0.159957 | ||||||||
\(838\) | 24.6277 | 0.850750 | ||||||||
\(839\) | 14.7446 | 0.509039 | 0.254519 | − | 0.967068i | \(-0.418083\pi\) | ||||
0.254519 | + | 0.967068i | \(0.418083\pi\) | |||||||
\(840\) | 3.37228 | 0.116355 | ||||||||
\(841\) | −22.0951 | −0.761900 | ||||||||
\(842\) | −16.7446 | −0.577056 | ||||||||
\(843\) | 18.8614 | 0.649621 | ||||||||
\(844\) | −14.1168 | −0.485922 | ||||||||
\(845\) | 9.51087 | 0.327184 | ||||||||
\(846\) | −13.4891 | −0.463766 | ||||||||
\(847\) | 3.37228 | 0.115873 | ||||||||
\(848\) | −0.744563 | −0.0255684 | ||||||||
\(849\) | 18.7446 | 0.643312 | ||||||||
\(850\) | 1.00000 | 0.0342997 | ||||||||
\(851\) | 33.7228 | 1.15600 | ||||||||
\(852\) | 1.25544 | 0.0430106 | ||||||||
\(853\) | −34.8614 | −1.19363 | −0.596816 | − | 0.802378i | \(-0.703568\pi\) | ||||
−0.596816 | + | 0.802378i | \(0.703568\pi\) | |||||||
\(854\) | −6.74456 | −0.230794 | ||||||||
\(855\) | 4.00000 | 0.136797 | ||||||||
\(856\) | 14.1168 | 0.482504 | ||||||||
\(857\) | 10.3940 | 0.355053 | 0.177527 | − | 0.984116i | \(-0.443190\pi\) | ||||
0.177527 | + | 0.984116i | \(0.443190\pi\) | |||||||
\(858\) | 4.74456 | 0.161977 | ||||||||
\(859\) | −15.3723 | −0.524495 | −0.262248 | − | 0.965001i | \(-0.584464\pi\) | ||||
−0.262248 | + | 0.965001i | \(0.584464\pi\) | |||||||
\(860\) | 7.37228 | 0.251393 | ||||||||
\(861\) | −42.9783 | −1.46469 | ||||||||
\(862\) | 2.11684 | 0.0721000 | ||||||||
\(863\) | −10.9783 | −0.373704 | −0.186852 | − | 0.982388i | \(-0.559828\pi\) | ||||
−0.186852 | + | 0.982388i | \(0.559828\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 11.4891 | 0.390642 | ||||||||
\(866\) | 27.2554 | 0.926177 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | 15.6060 | 0.529701 | ||||||||
\(869\) | −13.4891 | −0.457587 | ||||||||
\(870\) | 2.62772 | 0.0890880 | ||||||||
\(871\) | 18.9783 | 0.643053 | ||||||||
\(872\) | −8.74456 | −0.296128 | ||||||||
\(873\) | −9.37228 | −0.317204 | ||||||||
\(874\) | −13.4891 | −0.456276 | ||||||||
\(875\) | 3.37228 | 0.114004 | ||||||||
\(876\) | −6.00000 | −0.202721 | ||||||||
\(877\) | −42.8614 | −1.44733 | −0.723663 | − | 0.690153i | \(-0.757543\pi\) | ||||
−0.723663 | + | 0.690153i | \(0.757543\pi\) | |||||||
\(878\) | −28.2337 | −0.952841 | ||||||||
\(879\) | 30.8614 | 1.04093 | ||||||||
\(880\) | 1.00000 | 0.0337100 | ||||||||
\(881\) | 17.6060 | 0.593160 | 0.296580 | − | 0.955008i | \(-0.404154\pi\) | ||||
0.296580 | + | 0.955008i | \(0.404154\pi\) | |||||||
\(882\) | 4.37228 | 0.147222 | ||||||||
\(883\) | −33.9565 | −1.14273 | −0.571364 | − | 0.820697i | \(-0.693585\pi\) | ||||
−0.571364 | + | 0.820697i | \(0.693585\pi\) | |||||||
\(884\) | 4.74456 | 0.159577 | ||||||||
\(885\) | −10.7446 | −0.361175 | ||||||||
\(886\) | −22.1168 | −0.743030 | ||||||||
\(887\) | −59.4456 | −1.99599 | −0.997994 | − | 0.0633023i | \(-0.979837\pi\) | ||||
−0.997994 | + | 0.0633023i | \(0.979837\pi\) | |||||||
\(888\) | −10.0000 | −0.335578 | ||||||||
\(889\) | 68.2337 | 2.28848 | ||||||||
\(890\) | 16.7446 | 0.561279 | ||||||||
\(891\) | 1.00000 | 0.0335013 | ||||||||
\(892\) | −11.3723 | −0.380772 | ||||||||
\(893\) | −53.9565 | −1.80559 | ||||||||
\(894\) | −0.744563 | −0.0249019 | ||||||||
\(895\) | −18.7446 | −0.626562 | ||||||||
\(896\) | 3.37228 | 0.112660 | ||||||||
\(897\) | −16.0000 | −0.534224 | ||||||||
\(898\) | 29.3723 | 0.980166 | ||||||||
\(899\) | 12.1603 | 0.405570 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | −0.744563 | −0.0248050 | ||||||||
\(902\) | −12.7446 | −0.424348 | ||||||||
\(903\) | 24.8614 | 0.827336 | ||||||||
\(904\) | −11.4891 | −0.382123 | ||||||||
\(905\) | −14.6277 | −0.486242 | ||||||||
\(906\) | 21.4891 | 0.713928 | ||||||||
\(907\) | −30.5842 | −1.01553 | −0.507766 | − | 0.861495i | \(-0.669529\pi\) | ||||
−0.507766 | + | 0.861495i | \(0.669529\pi\) | |||||||
\(908\) | 6.11684 | 0.202995 | ||||||||
\(909\) | 6.00000 | 0.199007 | ||||||||
\(910\) | 16.0000 | 0.530395 | ||||||||
\(911\) | −5.02175 | −0.166378 | −0.0831890 | − | 0.996534i | \(-0.526511\pi\) | ||||
−0.0831890 | + | 0.996534i | \(0.526511\pi\) | |||||||
\(912\) | 4.00000 | 0.132453 | ||||||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | 10.0000 | 0.330771 | ||||||||
\(915\) | −2.00000 | −0.0661180 | ||||||||
\(916\) | −3.25544 | −0.107563 | ||||||||
\(917\) | −32.0000 | −1.05673 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | 15.1386 | 0.499376 | 0.249688 | − | 0.968326i | \(-0.419672\pi\) | ||||
0.249688 | + | 0.968326i | \(0.419672\pi\) | |||||||
\(920\) | −3.37228 | −0.111181 | ||||||||
\(921\) | 4.00000 | 0.131804 | ||||||||
\(922\) | 0.510875 | 0.0168248 | ||||||||
\(923\) | 5.95650 | 0.196061 | ||||||||
\(924\) | 3.37228 | 0.110940 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 16.0000 | 0.525793 | ||||||||
\(927\) | −3.37228 | −0.110760 | ||||||||
\(928\) | 2.62772 | 0.0862591 | ||||||||
\(929\) | −2.62772 | −0.0862127 | −0.0431063 | − | 0.999070i | \(-0.513725\pi\) | ||||
−0.0431063 | + | 0.999070i | \(0.513725\pi\) | |||||||
\(930\) | 4.62772 | 0.151749 | ||||||||
\(931\) | 17.4891 | 0.573183 | ||||||||
\(932\) | −14.8614 | −0.486802 | ||||||||
\(933\) | −5.48913 | −0.179706 | ||||||||
\(934\) | 30.9783 | 1.01364 | ||||||||
\(935\) | 1.00000 | 0.0327035 | ||||||||
\(936\) | 4.74456 | 0.155081 | ||||||||
\(937\) | 10.0000 | 0.326686 | 0.163343 | − | 0.986569i | \(-0.447772\pi\) | ||||
0.163343 | + | 0.986569i | \(0.447772\pi\) | |||||||
\(938\) | 13.4891 | 0.440436 | ||||||||
\(939\) | 18.8614 | 0.615519 | ||||||||
\(940\) | −13.4891 | −0.439967 | ||||||||
\(941\) | −2.00000 | −0.0651981 | −0.0325991 | − | 0.999469i | \(-0.510378\pi\) | ||||
−0.0325991 | + | 0.999469i | \(0.510378\pi\) | |||||||
\(942\) | 11.4891 | 0.374336 | ||||||||
\(943\) | 42.9783 | 1.39956 | ||||||||
\(944\) | −10.7446 | −0.349706 | ||||||||
\(945\) | 3.37228 | 0.109700 | ||||||||
\(946\) | 7.37228 | 0.239694 | ||||||||
\(947\) | 29.2554 | 0.950674 | 0.475337 | − | 0.879804i | \(-0.342326\pi\) | ||||
0.475337 | + | 0.879804i | \(0.342326\pi\) | |||||||
\(948\) | −13.4891 | −0.438106 | ||||||||
\(949\) | −28.4674 | −0.924090 | ||||||||
\(950\) | 4.00000 | 0.129777 | ||||||||
\(951\) | 0.116844 | 0.00378893 | ||||||||
\(952\) | 3.37228 | 0.109296 | ||||||||
\(953\) | −24.5109 | −0.793985 | −0.396993 | − | 0.917822i | \(-0.629946\pi\) | ||||
−0.396993 | + | 0.917822i | \(0.629946\pi\) | |||||||
\(954\) | −0.744563 | −0.0241061 | ||||||||
\(955\) | −4.62772 | −0.149749 | ||||||||
\(956\) | 20.2337 | 0.654404 | ||||||||
\(957\) | 2.62772 | 0.0849421 | ||||||||
\(958\) | 35.8397 | 1.15793 | ||||||||
\(959\) | −50.1168 | −1.61836 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −9.58422 | −0.309168 | ||||||||
\(962\) | −47.4456 | −1.52971 | ||||||||
\(963\) | 14.1168 | 0.454909 | ||||||||
\(964\) | −9.37228 | −0.301861 | ||||||||
\(965\) | −0.510875 | −0.0164456 | ||||||||
\(966\) | −11.3723 | −0.365897 | ||||||||
\(967\) | −30.7446 | −0.988678 | −0.494339 | − | 0.869269i | \(-0.664590\pi\) | ||||
−0.494339 | + | 0.869269i | \(0.664590\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | 4.00000 | 0.128499 | ||||||||
\(970\) | −9.37228 | −0.300926 | ||||||||
\(971\) | −44.4674 | −1.42703 | −0.713513 | − | 0.700642i | \(-0.752897\pi\) | ||||
−0.713513 | + | 0.700642i | \(0.752897\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 47.6060 | 1.52618 | ||||||||
\(974\) | 1.25544 | 0.0402268 | ||||||||
\(975\) | 4.74456 | 0.151948 | ||||||||
\(976\) | −2.00000 | −0.0640184 | ||||||||
\(977\) | −14.0000 | −0.447900 | −0.223950 | − | 0.974601i | \(-0.571895\pi\) | ||||
−0.223950 | + | 0.974601i | \(0.571895\pi\) | |||||||
\(978\) | −7.37228 | −0.235740 | ||||||||
\(979\) | 16.7446 | 0.535159 | ||||||||
\(980\) | 4.37228 | 0.139667 | ||||||||
\(981\) | −8.74456 | −0.279192 | ||||||||
\(982\) | −6.51087 | −0.207770 | ||||||||
\(983\) | −8.39403 | −0.267728 | −0.133864 | − | 0.991000i | \(-0.542739\pi\) | ||||
−0.133864 | + | 0.991000i | \(0.542739\pi\) | |||||||
\(984\) | −12.7446 | −0.406282 | ||||||||
\(985\) | 26.2337 | 0.835875 | ||||||||
\(986\) | 2.62772 | 0.0836836 | ||||||||
\(987\) | −45.4891 | −1.44793 | ||||||||
\(988\) | 18.9783 | 0.603779 | ||||||||
\(989\) | −24.8614 | −0.790547 | ||||||||
\(990\) | 1.00000 | 0.0317821 | ||||||||
\(991\) | 35.8397 | 1.13848 | 0.569242 | − | 0.822170i | \(-0.307237\pi\) | ||||
0.569242 | + | 0.822170i | \(0.307237\pi\) | |||||||
\(992\) | 4.62772 | 0.146930 | ||||||||
\(993\) | 18.3505 | 0.582337 | ||||||||
\(994\) | 4.23369 | 0.134284 | ||||||||
\(995\) | −8.00000 | −0.253617 | ||||||||
\(996\) | −12.0000 | −0.380235 | ||||||||
\(997\) | −28.1168 | −0.890469 | −0.445235 | − | 0.895414i | \(-0.646880\pi\) | ||||
−0.445235 | + | 0.895414i | \(0.646880\pi\) | |||||||
\(998\) | 1.48913 | 0.0471374 | ||||||||
\(999\) | −10.0000 | −0.316386 |
(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 | 5610.2.a.bx.1.2 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5610.2.a.bx.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial |