Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(1,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, 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("920.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.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: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{17}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.56155\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.56155 | 1.47891 | 0.739457 | − | 0.673204i | \(-0.235083\pi\) | ||||
0.739457 | + | 0.673204i | \(0.235083\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.12311 | 1.93635 | 0.968176 | − | 0.250270i | \(-0.0805195\pi\) | ||||
0.968176 | + | 0.250270i | \(0.0805195\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.00000 | −1.20605 | −0.603023 | − | 0.797724i | \(-0.706037\pi\) | ||||
−0.603023 | + | 0.797724i | \(0.706037\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.561553 | −0.155747 | −0.0778734 | − | 0.996963i | \(-0.524813\pi\) | ||||
−0.0778734 | + | 0.996963i | \(0.524813\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.56155 | 0.661390 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.12311 | −0.757464 | −0.378732 | − | 0.925506i | \(-0.623640\pi\) | ||||
−0.378732 | + | 0.925506i | \(0.623640\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | 0.917663 | 0.458831 | − | 0.888523i | \(-0.348268\pi\) | ||||
0.458831 | + | 0.888523i | \(0.348268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.1231 | 2.86370 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.43845 | 0.276829 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.56155 | −1.58984 | −0.794920 | − | 0.606714i | \(-0.792487\pi\) | ||||
−0.794920 | + | 0.606714i | \(0.792487\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.43845 | 0.258353 | 0.129176 | − | 0.991622i | \(-0.458767\pi\) | ||||
0.129176 | + | 0.991622i | \(0.458767\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.2462 | −1.78364 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.12311 | 0.865963 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.12311 | −1.17103 | −0.585516 | − | 0.810661i | \(-0.699108\pi\) | ||||
−0.585516 | + | 0.810661i | \(0.699108\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.43845 | −0.230336 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.561553 | 0.0876998 | 0.0438499 | − | 0.999038i | \(-0.486038\pi\) | ||||
0.0438499 | + | 0.999038i | \(0.486038\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.12311 | −1.39126 | −0.695630 | − | 0.718400i | \(-0.744875\pi\) | ||||
−0.695630 | + | 0.718400i | \(0.744875\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.56155 | 0.530925 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.68466 | −0.537463 | −0.268731 | − | 0.963215i | \(-0.586604\pi\) | ||||
−0.268731 | + | 0.963215i | \(0.586604\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 19.2462 | 2.74946 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.00000 | −1.12022 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.24621 | −0.583262 | −0.291631 | − | 0.956531i | \(-0.594198\pi\) | ||||
−0.291631 | + | 0.956531i | \(0.594198\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.2462 | 1.35714 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.24621 | −0.813187 | −0.406594 | − | 0.913609i | \(-0.633284\pi\) | ||||
−0.406594 | + | 0.913609i | \(0.633284\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.1231 | 1.42417 | 0.712084 | − | 0.702094i | \(-0.247752\pi\) | ||||
0.712084 | + | 0.702094i | \(0.247752\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 18.2462 | 2.29881 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.561553 | −0.0696521 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.24621 | 0.763096 | 0.381548 | − | 0.924349i | \(-0.375391\pi\) | ||||
0.381548 | + | 0.924349i | \(0.375391\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.56155 | 0.308375 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.68466 | 0.437289 | 0.218644 | − | 0.975805i | \(-0.429837\pi\) | ||||
0.218644 | + | 0.975805i | \(0.429837\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 16.5616 | 1.93838 | 0.969192 | − | 0.246308i | \(-0.0792175\pi\) | ||||
0.969192 | + | 0.246308i | \(0.0792175\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.56155 | 0.295783 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −20.4924 | −2.33533 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.2462 | −1.15279 | −0.576394 | − | 0.817172i | \(-0.695541\pi\) | ||||
−0.576394 | + | 0.817172i | \(0.695541\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.12311 | −0.338748 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −21.9309 | −2.35124 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.0000 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.87689 | −0.301580 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.68466 | 0.382081 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.00000 | 0.410391 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −16.2462 | −1.64955 | −0.824776 | − | 0.565459i | \(-0.808699\pi\) | ||||
−0.824776 | + | 0.565459i | \(0.808699\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −14.2462 | −1.43180 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.246211 | 0.0244989 | 0.0122495 | − | 0.999925i | \(-0.496101\pi\) | ||||
0.0122495 | + | 0.999925i | \(0.496101\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.24621 | −0.221326 | −0.110663 | − | 0.993858i | \(-0.535297\pi\) | ||||
−0.110663 | + | 0.993858i | \(0.535297\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 13.1231 | 1.28068 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.24621 | 0.789844 | 0.394922 | − | 0.918715i | \(-0.370772\pi\) | ||||
0.394922 | + | 0.918715i | \(0.370772\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −18.2462 | −1.73185 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 20.2462 | 1.90460 | 0.952302 | − | 0.305158i | \(-0.0987093\pi\) | ||||
0.952302 | + | 0.305158i | \(0.0987093\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.00000 | 0.0932505 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.00000 | −0.184900 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −16.0000 | −1.46672 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | 0.454545 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.43845 | 0.129700 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −16.8078 | −1.49145 | −0.745724 | − | 0.666255i | \(-0.767896\pi\) | ||||
−0.745724 | + | 0.666255i | \(0.767896\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −23.3693 | −2.05755 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.93087 | 0.867664 | 0.433832 | − | 0.900994i | \(-0.357161\pi\) | ||||
0.433832 | + | 0.900994i | \(0.357161\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.4924 | 1.77692 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.43845 | 0.123802 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.1231 | 1.29205 | 0.646027 | − | 0.763315i | \(-0.276429\pi\) | ||||
0.646027 | + | 0.763315i | \(0.276429\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.315342 | 0.0267469 | 0.0133735 | − | 0.999911i | \(-0.495743\pi\) | ||||
0.0133735 | + | 0.999911i | \(0.495743\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.43845 | −0.794861 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.24621 | 0.187838 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −8.56155 | −0.710998 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 49.3002 | 4.06621 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.24621 | −0.347863 | −0.173932 | − | 0.984758i | \(-0.555647\pi\) | ||||
−0.173932 | + | 0.984758i | \(0.555647\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.8078 | −1.36780 | −0.683898 | − | 0.729577i | \(-0.739717\pi\) | ||||
−0.683898 | + | 0.729577i | \(0.739717\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.1231 | −0.899250 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.43845 | 0.115539 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.00000 | −0.159617 | −0.0798087 | − | 0.996810i | \(-0.525431\pi\) | ||||
−0.0798087 | + | 0.996810i | \(0.525431\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.8769 | −0.862594 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.12311 | 0.403757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.315342 | −0.0246995 | −0.0123497 | − | 0.999924i | \(-0.503931\pi\) | ||||
−0.0123497 | + | 0.999924i | \(0.503931\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −10.2462 | −0.797666 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6847 | −0.975743 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 14.2462 | 1.08944 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.4924 | 0.797724 | 0.398862 | − | 0.917011i | \(-0.369405\pi\) | ||||
0.398862 | + | 0.917011i | \(0.369405\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.12311 | 0.387270 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −16.0000 | −1.20263 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.68466 | −0.574378 | −0.287189 | − | 0.957874i | \(-0.592721\pi\) | ||||
−0.287189 | + | 0.957874i | \(0.592721\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.12311 | 0.232139 | 0.116069 | − | 0.993241i | \(-0.462971\pi\) | ||||
0.116069 | + | 0.993241i | \(0.462971\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 28.4924 | 2.10622 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.12311 | −0.523701 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 12.4924 | 0.913536 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 7.36932 | 0.536039 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.87689 | −0.208165 | −0.104082 | − | 0.994569i | \(-0.533191\pi\) | ||||
−0.104082 | + | 0.994569i | \(0.533191\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 24.5616 | 1.76798 | 0.883990 | − | 0.467507i | \(-0.154848\pi\) | ||||
0.883990 | + | 0.467507i | \(0.154848\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1.43845 | −0.103009 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.4384 | −0.814956 | −0.407478 | − | 0.913215i | \(-0.633592\pi\) | ||||
−0.407478 | + | 0.913215i | \(0.633592\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 24.0000 | 1.70131 | 0.850657 | − | 0.525720i | \(-0.176204\pi\) | ||||
0.850657 | + | 0.525720i | \(0.176204\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 16.0000 | 1.12855 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −43.8617 | −3.07849 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.561553 | 0.0392205 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.56155 | 0.247545 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −16.0000 | −1.10674 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.2462 | −0.980750 | −0.490375 | − | 0.871512i | \(-0.663140\pi\) | ||||
−0.490375 | + | 0.871512i | \(0.663140\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.43845 | 0.646712 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.12311 | −0.622191 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.36932 | 0.500262 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 42.4233 | 2.86670 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.75379 | 0.117973 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −20.4924 | −1.37227 | −0.686137 | − | 0.727472i | \(-0.740695\pi\) | ||||
−0.686137 | + | 0.727472i | \(0.740695\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 3.56155 | 0.237437 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.12311 | 0.605522 | 0.302761 | − | 0.953067i | \(-0.402092\pi\) | ||||
0.302761 | + | 0.953067i | \(0.402092\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.246211 | 0.0162701 | 0.00813505 | − | 0.999967i | \(-0.497411\pi\) | ||||
0.00813505 | + | 0.999967i | \(0.497411\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −52.4924 | −3.45375 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.5616 | −0.822935 | −0.411467 | − | 0.911425i | \(-0.634984\pi\) | ||||
−0.411467 | + | 0.911425i | \(0.634984\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.68466 | −0.240361 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −26.2462 | −1.70487 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.80776 | −0.569727 | −0.284863 | − | 0.958568i | \(-0.591948\pi\) | ||||
−0.284863 | + | 0.958568i | \(0.591948\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.4924 | −1.19120 | −0.595601 | − | 0.803281i | \(-0.703086\pi\) | ||||
−0.595601 | + | 0.803281i | \(0.703086\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −22.2462 | −1.42710 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 19.2462 | 1.22960 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.24621 | −0.142923 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 30.7386 | 1.94798 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.24621 | 0.394257 | 0.197129 | − | 0.980378i | \(-0.436838\pi\) | ||||
0.197129 | + | 0.980378i | \(0.436838\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.00000 | −0.251478 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −8.00000 | −0.500979 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.05398 | −0.564771 | −0.282386 | − | 0.959301i | \(-0.591126\pi\) | ||||
−0.282386 | + | 0.959301i | \(0.591126\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −36.4924 | −2.26753 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −30.4924 | −1.88743 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.00000 | −0.493301 | −0.246651 | − | 0.969104i | \(-0.579330\pi\) | ||||
−0.246651 | + | 0.969104i | \(0.579330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.24621 | −0.260843 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 25.6155 | 1.56764 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −23.3002 | −1.42064 | −0.710319 | − | 0.703880i | \(-0.751449\pi\) | ||||
−0.710319 | + | 0.703880i | \(0.751449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.24621 | −0.136448 | −0.0682238 | − | 0.997670i | \(-0.521733\pi\) | ||||
−0.0682238 | + | 0.997670i | \(0.521733\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.36932 | −0.446011 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.00000 | −0.241209 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.4384 | −0.687270 | −0.343635 | − | 0.939103i | \(-0.611658\pi\) | ||||
−0.343635 | + | 0.939103i | \(0.611658\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.12311 | 0.306712 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 30.4924 | 1.81903 | 0.909513 | − | 0.415676i | \(-0.136455\pi\) | ||||
0.909513 | + | 0.415676i | \(0.136455\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 22.8769 | 1.35989 | 0.679945 | − | 0.733263i | \(-0.262004\pi\) | ||||
0.679945 | + | 0.733263i | \(0.262004\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.2462 | 0.606933 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.87689 | 0.169818 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.24621 | −0.426248 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −41.6155 | −2.43955 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.8769 | −0.752276 | −0.376138 | − | 0.926564i | \(-0.622748\pi\) | ||||
−0.376138 | + | 0.926564i | \(0.622748\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.24621 | −0.363668 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.75379 | −0.333869 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.561553 | −0.0324754 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −46.7386 | −2.69397 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0.630683 | 0.0362318 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 11.1231 | 0.636907 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5.75379 | −0.327322 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.9309 | 0.789947 | 0.394974 | − | 0.918692i | \(-0.370754\pi\) | ||||
0.394974 | + | 0.918692i | \(0.370754\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.1231 | 0.854808 | 0.427404 | − | 0.904061i | \(-0.359428\pi\) | ||||
0.427404 | + | 0.904061i | \(0.359428\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 18.2462 | 1.02806 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 20.7386 | 1.16480 | 0.582399 | − | 0.812903i | \(-0.302114\pi\) | ||||
0.582399 | + | 0.812903i | \(0.302114\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 34.2462 | 1.91742 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.7386 | −1.71566 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.4924 | −0.695097 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.561553 | −0.0311493 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 21.1231 | 1.16811 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −18.8769 | −1.04072 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.5616 | 0.580515 | 0.290258 | − | 0.956949i | \(-0.406259\pi\) | ||||
0.290258 | + | 0.956949i | \(0.406259\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −25.3693 | −1.39023 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.24621 | 0.341267 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.7538 | 0.858164 | 0.429082 | − | 0.903266i | \(-0.358837\pi\) | ||||
0.429082 | + | 0.903266i | \(0.358837\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 51.8617 | 2.81674 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.75379 | −0.311585 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 62.7386 | 3.38757 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.56155 | 0.137909 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −16.4924 | −0.885360 | −0.442680 | − | 0.896680i | \(-0.645972\pi\) | ||||
−0.442680 | + | 0.896680i | \(0.645972\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.80776 | −0.150296 | −0.0751481 | − | 0.997172i | \(-0.523943\pi\) | ||||
−0.0751481 | + | 0.997172i | \(0.523943\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.807764 | −0.0431153 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 34.8078 | 1.85263 | 0.926315 | − | 0.376750i | \(-0.122958\pi\) | ||||
0.926315 | + | 0.376750i | \(0.122958\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.68466 | 0.195561 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −40.9848 | −2.16915 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.7538 | −0.725897 | −0.362949 | − | 0.931809i | \(-0.618230\pi\) | ||||
−0.362949 | + | 0.931809i | \(0.618230\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.00000 | −0.157895 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 12.8078 | 0.672233 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.5616 | 0.866871 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 20.4924 | 1.06970 | 0.534848 | − | 0.844948i | \(-0.320369\pi\) | ||||
0.534848 | + | 0.844948i | \(0.320369\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −21.7538 | −1.12940 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −24.7386 | −1.28092 | −0.640459 | − | 0.767992i | \(-0.721256\pi\) | ||||
−0.640459 | + | 0.767992i | \(0.721256\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 2.56155 | 0.132278 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.80776 | 0.247612 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.2462 | −0.731779 | −0.365889 | − | 0.930658i | \(-0.619235\pi\) | ||||
−0.365889 | + | 0.930658i | \(0.619235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.0540 | −2.20572 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 33.6155 | 1.71767 | 0.858837 | − | 0.512250i | \(-0.171188\pi\) | ||||
0.858837 | + | 0.512250i | \(0.171188\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −20.4924 | −1.04439 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −32.4924 | −1.65168 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.61553 | 0.386123 | 0.193061 | − | 0.981187i | \(-0.438158\pi\) | ||||
0.193061 | + | 0.981187i | \(0.438158\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.12311 | −0.157942 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 25.4384 | 1.28320 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.2462 | −0.515543 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.93087 | 0.197285 | 0.0986423 | − | 0.995123i | \(-0.468550\pi\) | ||||
0.0986423 | + | 0.995123i | \(0.468550\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 52.4924 | 2.62791 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.7386 | −1.43514 | −0.717569 | − | 0.696487i | \(-0.754745\pi\) | ||||
−0.717569 | + | 0.696487i | \(0.754745\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.807764 | −0.0402376 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 28.4924 | 1.41232 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.31534 | −0.114486 | −0.0572431 | − | 0.998360i | \(-0.518231\pi\) | ||||
−0.0572431 | + | 0.998360i | \(0.518231\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 38.7386 | 1.91084 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −32.0000 | −1.57462 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.0000 | 0.589057 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.807764 | 0.0395564 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.12311 | −0.445693 | −0.222846 | − | 0.974854i | \(-0.571535\pi\) | ||||
−0.222846 | + | 0.974854i | \(0.571535\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.4924 | 1.29116 | 0.645581 | − | 0.763692i | \(-0.276615\pi\) | ||||
0.645581 | + | 0.763692i | \(0.276615\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −13.1231 | −0.638067 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3.12311 | −0.151493 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 56.9848 | 2.75769 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.75379 | 0.277796 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.6155 | −1.61920 | −0.809602 | − | 0.586980i | \(-0.800317\pi\) | ||||
−0.809602 | + | 0.586980i | \(0.800317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 24.7386 | 1.18886 | 0.594431 | − | 0.804146i | \(-0.297377\pi\) | ||||
0.594431 | + | 0.804146i | \(0.297377\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −21.9309 | −1.05150 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.00000 | 0.191346 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.3002 | 1.01660 | 0.508301 | − | 0.861179i | \(-0.330274\pi\) | ||||
0.508301 | + | 0.861179i | \(0.330274\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 68.5464 | 3.26411 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.6847 | −0.745201 | −0.372600 | − | 0.927992i | \(-0.621534\pi\) | ||||
−0.372600 | + | 0.927992i | \(0.621534\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.0000 | 0.474045 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.8769 | −0.514459 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.7386 | 0.789945 | 0.394972 | − | 0.918693i | \(-0.370754\pi\) | ||||
0.394972 | + | 0.918693i | \(0.370754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.24621 | −0.105770 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −43.0540 | −2.02285 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −2.87689 | −0.134871 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.876894 | −0.0410194 | −0.0205097 | − | 0.999790i | \(-0.506529\pi\) | ||||
−0.0205097 | + | 0.999790i | \(0.506529\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.49242 | −0.209688 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 23.4384 | 1.09164 | 0.545819 | − | 0.837903i | \(-0.316219\pi\) | ||||
0.545819 | + | 0.837903i | \(0.316219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.2462 | 0.476182 | 0.238091 | − | 0.971243i | \(-0.423478\pi\) | ||||
0.238091 | + | 0.971243i | \(0.423478\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.68466 | 0.170872 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 35.3693 | 1.63670 | 0.818348 | − | 0.574722i | \(-0.194890\pi\) | ||||
0.818348 | + | 0.574722i | \(0.194890\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0000 | 1.47762 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.12311 | −0.236060 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 36.4924 | 1.67792 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.00000 | 0.183533 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −15.1231 | −0.692439 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 16.0000 | 0.731059 | 0.365529 | − | 0.930800i | \(-0.380888\pi\) | ||||
0.365529 | + | 0.930800i | \(0.380888\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.00000 | 0.182384 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 13.1231 | 0.597122 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.2462 | −0.737702 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.05398 | −0.138389 | −0.0691944 | − | 0.997603i | \(-0.522043\pi\) | ||||
−0.0691944 | + | 0.997603i | \(0.522043\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.807764 | −0.0365284 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.5616 | 0.476636 | 0.238318 | − | 0.971187i | \(-0.423404\pi\) | ||||
0.238318 | + | 0.971187i | \(0.423404\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 26.7386 | 1.20425 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.2462 | −0.640320 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 18.8769 | 0.846744 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.946025 | 0.0423499 | 0.0211749 | − | 0.999776i | \(-0.493259\pi\) | ||||
0.0211749 | + | 0.999776i | \(0.493259\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.4924 | −0.915534 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.6155 | 1.14214 | 0.571070 | − | 0.820901i | \(-0.306528\pi\) | ||||
0.571070 | + | 0.820901i | \(0.306528\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.246211 | 0.0109563 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −32.4924 | −1.44304 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.56155 | −0.379484 | −0.189742 | − | 0.981834i | \(-0.560765\pi\) | ||||
−0.189742 | + | 0.981834i | \(0.560765\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 84.8466 | 3.75339 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.75379 | 0.254036 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.24621 | −0.0989799 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 14.7386 | 0.648204 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 26.8769 | 1.17976 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.8617 | −0.782537 | −0.391269 | − | 0.920277i | \(-0.627964\pi\) | ||||
−0.391269 | + | 0.920277i | \(0.627964\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −23.8617 | −1.04340 | −0.521701 | − | 0.853129i | \(-0.674702\pi\) | ||||
−0.521701 | + | 0.853129i | \(0.674702\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.1231 | 0.572739 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.49242 | −0.195693 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −22.2462 | −0.965403 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.315342 | −0.0136590 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.0000 | −0.518805 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −19.6847 | −0.849456 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −76.9848 | −3.31597 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.6847 | 1.44822 | 0.724108 | − | 0.689686i | \(-0.242252\pi\) | ||||
0.724108 | + | 0.689686i | \(0.242252\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8.00000 | 0.343313 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.24621 | 0.353229 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.946025 | 0.0404491 | 0.0202245 | − | 0.999795i | \(-0.493562\pi\) | ||||
0.0202245 | + | 0.999795i | \(0.493562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 39.6155 | 1.69075 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −34.2462 | −1.45894 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −52.4924 | −2.23220 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.2462 | −0.774509 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −7.75379 | −0.328539 | −0.164269 | − | 0.986416i | \(-0.552527\pi\) | ||||
−0.164269 | + | 0.986416i | \(0.552527\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.12311 | 0.216684 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 32.0000 | 1.35104 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −39.2311 | −1.65339 | −0.826696 | − | 0.562649i | \(-0.809782\pi\) | ||||
−0.826696 | + | 0.562649i | \(0.809782\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 20.2462 | 0.851765 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −35.8617 | −1.50605 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.7386 | −0.869409 | −0.434704 | − | 0.900573i | \(-0.643147\pi\) | ||||
−0.434704 | + | 0.900573i | \(0.643147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.0000 | 0.502184 | 0.251092 | − | 0.967963i | \(-0.419210\pi\) | ||||
0.251092 | + | 0.967963i | \(0.419210\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −7.36932 | −0.307858 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.00000 | 0.0417029 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −32.4233 | −1.34980 | −0.674900 | − | 0.737910i | \(-0.735813\pi\) | ||||
−0.674900 | + | 0.737910i | \(0.735813\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 62.9157 | 2.61469 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 61.4773 | 2.55051 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 16.9848 | 0.703440 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.00000 | −0.0826898 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −36.1771 | −1.49319 | −0.746594 | − | 0.665280i | \(-0.768312\pi\) | ||||
−0.746594 | + | 0.665280i | \(0.768312\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.75379 | 0.237081 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −29.3002 | −1.20525 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 26.9848 | 1.10813 | 0.554067 | − | 0.832472i | \(-0.313075\pi\) | ||||
0.554067 | + | 0.832472i | \(0.313075\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0000 | −0.655936 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 61.4773 | 2.51610 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −32.0000 | −1.30748 | −0.653742 | − | 0.756717i | \(-0.726802\pi\) | ||||
−0.653742 | + | 0.756717i | \(0.726802\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.1771 | 0.741459 | 0.370729 | − | 0.928741i | \(-0.379108\pi\) | ||||
0.370729 | + | 0.928741i | \(0.379108\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 22.2462 | 0.905936 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.00000 | 0.203279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −112.354 | −4.55282 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.06913 | 0.0837081 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.12311 | 0.126141 | 0.0630705 | − | 0.998009i | \(-0.479911\pi\) | ||||
0.0630705 | + | 0.998009i | \(0.479911\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1.43845 | 0.0580038 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.6155 | 1.43383 | 0.716914 | − | 0.697162i | \(-0.245554\pi\) | ||||
0.716914 | + | 0.697162i | \(0.245554\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.9848 | −1.16500 | −0.582500 | − | 0.812831i | \(-0.697925\pi\) | ||||
−0.582500 | + | 0.812831i | \(0.697925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.43845 | 0.0577229 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 51.2311 | 2.05253 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −40.9848 | −1.63678 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.2462 | 0.887015 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.3693 | −1.24879 | −0.624396 | − | 0.781108i | \(-0.714655\pi\) | ||||
−0.624396 | + | 0.781108i | \(0.714655\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −36.4924 | −1.45044 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −16.8078 | −0.666996 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.8078 | −0.428219 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 13.1231 | 0.519142 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.7538 | 0.938218 | 0.469109 | − | 0.883140i | \(-0.344575\pi\) | ||||
0.469109 | + | 0.883140i | \(0.344575\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.3542 | 1.74916 | 0.874579 | − | 0.484884i | \(-0.161138\pi\) | ||||
0.874579 | + | 0.484884i | \(0.161138\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −23.3693 | −0.920166 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.43845 | −0.0565512 | −0.0282756 | − | 0.999600i | \(-0.509002\pi\) | ||||
−0.0282756 | + | 0.999600i | \(0.509002\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.9848 | 0.980741 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 18.8769 | 0.739844 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −35.7926 | −1.40067 | −0.700337 | − | 0.713813i | \(-0.746967\pi\) | ||||
−0.700337 | + | 0.713813i | \(0.746967\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.93087 | 0.388031 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 58.9848 | 2.30122 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.2462 | 0.554954 | 0.277477 | − | 0.960732i | \(-0.410502\pi\) | ||||
0.277477 | + | 0.960732i | \(0.410502\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.4924 | 0.408108 | 0.204054 | − | 0.978960i | \(-0.434588\pi\) | ||||
0.204054 | + | 0.978960i | \(0.434588\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.49242 | 0.174471 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 20.4924 | 0.794662 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.56155 | −0.331505 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −52.4924 | −2.02947 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −44.4924 | −1.71761 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.56155 | −0.175835 | −0.0879175 | − | 0.996128i | \(-0.528021\pi\) | ||||
−0.0879175 | + | 0.996128i | \(0.528021\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.43845 | 0.0553659 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.7386 | 0.797050 | 0.398525 | − | 0.917157i | \(-0.369522\pi\) | ||||
0.398525 | + | 0.917157i | \(0.369522\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −83.2311 | −3.19411 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.3693 | 0.895514 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −18.5616 | −0.710238 | −0.355119 | − | 0.934821i | \(-0.615560\pi\) | ||||
−0.355119 | + | 0.934821i | \(0.615560\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.1231 | 0.577824 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.630683 | 0.0240621 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.38447 | 0.0908411 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.24621 | 0.237617 | 0.118809 | − | 0.992917i | \(-0.462093\pi\) | ||||
0.118809 | + | 0.992917i | \(0.462093\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −72.9848 | −2.77247 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.315342 | 0.0119616 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.75379 | −0.0664295 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −32.1771 | −1.21705 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.9848 | 1.47244 | 0.736219 | − | 0.676744i | \(-0.236610\pi\) | ||||
0.736219 | + | 0.676744i | \(0.236610\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −28.4924 | −1.07461 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.43845 | −0.355472 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.26137 | 0.0474386 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.7386 | −1.52997 | −0.764986 | − | 0.644047i | \(-0.777254\pi\) | ||||
−0.764986 | + | 0.644047i | \(0.777254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.4924 | −1.36857 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.43845 | 0.0538703 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.24621 | 0.0840035 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −22.5616 | −0.842577 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 38.7386 | 1.44471 | 0.722354 | − | 0.691524i | \(-0.243060\pi\) | ||||
0.722354 | + | 0.691524i | \(0.243060\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −11.5076 | −0.428565 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −47.3693 | −1.76168 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.56155 | −0.317968 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 37.1231 | 1.37682 | 0.688410 | − | 0.725322i | \(-0.258309\pi\) | ||||
0.688410 | + | 0.725322i | \(0.258309\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 28.4924 | 1.05383 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.1231 | 0.410841 | 0.205421 | − | 0.978674i | \(-0.434144\pi\) | ||||
0.205421 | + | 0.978674i | \(0.434144\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 49.3002 | 1.81846 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.9848 | −0.920329 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.5464 | 1.01331 | 0.506655 | − | 0.862149i | \(-0.330882\pi\) | ||||
0.506655 | + | 0.862149i | \(0.330882\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.75379 | −0.211371 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −13.7538 | −0.504578 | −0.252289 | − | 0.967652i | \(-0.581183\pi\) | ||||
−0.252289 | + | 0.967652i | \(0.581183\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.24621 | −0.155569 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 42.7386 | 1.56372 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −61.4773 | −2.24633 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 49.6155 | 1.81050 | 0.905248 | − | 0.424883i | \(-0.139685\pi\) | ||||
0.905248 | + | 0.424883i | \(0.139685\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 16.0000 | 0.583072 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.8078 | −0.611697 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 24.8769 | 0.904166 | 0.452083 | − | 0.891976i | \(-0.350681\pi\) | ||||
0.452083 | + | 0.891976i | \(0.350681\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.2462 | −0.371914 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −11.3002 | −0.409631 | −0.204816 | − | 0.978801i | \(-0.565660\pi\) | ||||
−0.204816 | + | 0.978801i | \(0.565660\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 42.2462 | 1.52942 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.1231 | −0.402157 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.50758 | 0.126651 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 38.4924 | 1.38807 | 0.694036 | − | 0.719940i | \(-0.255831\pi\) | ||||
0.694036 | + | 0.719940i | \(0.255831\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −23.1922 | −0.835248 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.24621 | −0.152726 | −0.0763628 | − | 0.997080i | \(-0.524331\pi\) | ||||
−0.0763628 | + | 0.997080i | \(0.524331\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.43845 | 0.0516705 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −93.4773 | −3.35348 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.24621 | 0.0804789 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.7386 | −0.527390 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −12.3153 | −0.440114 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.00000 | −0.0713831 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −46.2462 | −1.64850 | −0.824250 | − | 0.566226i | \(-0.808403\pi\) | ||||
−0.824250 | + | 0.566226i | \(0.808403\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −20.4924 | −0.729550 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 103.723 | 3.68798 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.24621 | −0.221809 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −10.8769 | −0.385764 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 27.1231 | 0.960750 | 0.480375 | − | 0.877063i | \(-0.340501\pi\) | ||||
0.480375 | + | 0.877063i | \(0.340501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.5076 | 0.407109 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 35.6155 | 1.25841 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −66.2462 | −2.33778 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 5.12311 | 0.180566 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −59.6847 | −2.10100 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −10.4924 | −0.368894 | −0.184447 | − | 0.982842i | \(-0.559049\pi\) | ||||
−0.184447 | + | 0.982842i | \(0.559049\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.31534 | −0.291991 | −0.145996 | − | 0.989285i | \(-0.546639\pi\) | ||||
−0.145996 | + | 0.989285i | \(0.546639\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −5.75379 | −0.201794 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.315342 | −0.0110459 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −36.4924 | −1.27671 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.2462 | −0.358032 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −31.7538 | −1.10821 | −0.554107 | − | 0.832445i | \(-0.686940\pi\) | ||||
−0.554107 | + | 0.832445i | \(0.686940\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.4384 | −0.607866 | −0.303933 | − | 0.952693i | \(-0.598300\pi\) | ||||
−0.303933 | + | 0.952693i | \(0.598300\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −10.2462 | −0.356727 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.0000 | −0.417281 | −0.208640 | − | 0.977992i | \(-0.566904\pi\) | ||||
−0.208640 | + | 0.977992i | \(0.566904\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 50.4924 | 1.75367 | 0.876837 | − | 0.480787i | \(-0.159649\pi\) | ||||
0.876837 | + | 0.480787i | \(0.159649\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −29.3002 | −1.01641 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −60.1080 | −2.08262 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.00000 | −0.276851 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.06913 | 0.0715196 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.61553 | 0.331965 | 0.165982 | − | 0.986129i | \(-0.446920\pi\) | ||||
0.165982 | + | 0.986129i | \(0.446920\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 44.3002 | 1.52759 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 78.1080 | 2.69018 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −12.6847 | −0.436366 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 25.6155 | 0.880160 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 58.6004 | 2.01116 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −7.12311 | −0.244177 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 22.9848 | 0.786986 | 0.393493 | − | 0.919328i | \(-0.371267\pi\) | ||||
0.393493 | + | 0.919328i | \(0.371267\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.2462 | 0.487210 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 34.1771 | 1.16747 | 0.583733 | − | 0.811945i | \(-0.301591\pi\) | ||||
0.583733 | + | 0.811945i | \(0.301591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 38.4233 | 1.31099 | 0.655493 | − | 0.755201i | \(-0.272461\pi\) | ||||
0.655493 | + | 0.755201i | \(0.272461\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.36932 | 0.251146 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 18.4233 | 0.627136 | 0.313568 | − | 0.949566i | \(-0.398476\pi\) | ||||
0.313568 | + | 0.949566i | \(0.398476\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.4924 | 0.356753 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −18.5616 | −0.630383 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 40.9848 | 1.39032 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.50758 | −0.118850 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −57.8617 | −1.95832 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.12311 | 0.173193 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −40.7386 | −1.37565 | −0.687823 | − | 0.725878i | \(-0.741433\pi\) | ||||
−0.687823 | + | 0.725878i | \(0.741433\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.9848 | −1.11255 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 24.1080 | 0.812217 | 0.406109 | − | 0.913825i | \(-0.366885\pi\) | ||||
0.406109 | + | 0.913825i | \(0.366885\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.4924 | −1.36268 | −0.681339 | − | 0.731968i | \(-0.738602\pi\) | ||||
−0.681339 | + | 0.731968i | \(0.738602\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.0000 | −0.537834 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.4384 | −1.12275 | −0.561377 | − | 0.827560i | \(-0.689728\pi\) | ||||
−0.561377 | + | 0.827560i | \(0.689728\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −86.1080 | −2.88797 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 28.0000 | 0.938035 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −14.7386 | −0.493210 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.68466 | −0.256870 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.43845 | −0.0480284 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −12.3153 | −0.410740 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.2614 | 0.441800 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −119.723 | −3.98415 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 3.12311 | 0.103816 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.0000 | 0.664089 | 0.332045 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332045 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.876894 | 0.0290848 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −20.4924 | −0.678944 | −0.339472 | − | 0.940616i | \(-0.610248\pi\) | ||||
−0.339472 | + | 0.940616i | \(0.610248\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −48.0000 | −1.58857 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 28.4924 | 0.941930 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 50.8769 | 1.68010 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.8617 | −1.18297 | −0.591485 | − | 0.806316i | \(-0.701458\pi\) | ||||
−0.591485 | + | 0.806316i | \(0.701458\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.7386 | 1.01287 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −2.06913 | −0.0681063 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.12311 | −0.234206 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −8.00000 | −0.262754 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.0540 | 0.428287 | 0.214144 | − | 0.976802i | \(-0.431304\pi\) | ||||
0.214144 | + | 0.976802i | \(0.431304\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 76.9848 | 2.52308 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 35.6847 | 1.16826 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 12.4924 | 0.408546 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 41.3693 | 1.35148 | 0.675738 | − | 0.737142i | \(-0.263825\pi\) | ||||
0.675738 | + | 0.737142i | \(0.263825\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 38.7386 | 1.26419 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −60.6004 | −1.97552 | −0.987758 | − | 0.155995i | \(-0.950142\pi\) | ||||
−0.987758 | + | 0.155995i | \(0.950142\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.561553 | 0.0182867 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.36932 | 0.239724 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.1922 | −1.14359 | −0.571797 | − | 0.820395i | \(-0.693754\pi\) | ||||
−0.571797 | + | 0.820395i | \(0.693754\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −9.30019 | −0.301897 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 53.1231 | 1.72263 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.5076 | 0.437553 | 0.218777 | − | 0.975775i | \(-0.429793\pi\) | ||||
0.218777 | + | 0.975775i | \(0.429793\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.87689 | −0.0930941 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 87.7235 | 2.83570 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 77.4773 | 2.50187 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.9309 | −0.933254 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −42.7386 | −1.37723 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 24.5616 | 0.790664 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 0.177081 | 0.00569454 | 0.00284727 | − | 0.999996i | \(-0.499094\pi\) | ||||
0.00284727 | + | 0.999996i | \(0.499094\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.0000 | −1.02799 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.36932 | 0.108127 | 0.0540633 | − | 0.998538i | \(-0.482783\pi\) | ||||
0.0540633 | + | 0.998538i | \(0.482783\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.61553 | 0.0517915 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.43845 | −0.0460672 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 48.1080 | 1.53911 | 0.769555 | − | 0.638581i | \(-0.220478\pi\) | ||||
0.769555 | + | 0.638581i | \(0.220478\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.0000 | −1.27841 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 29.3693 | 0.937690 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 37.1231 | 1.18404 | 0.592022 | − | 0.805922i | \(-0.298330\pi\) | ||||
0.592022 | + | 0.805922i | \(0.298330\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −11.4384 | −0.364459 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −48.3542 | −1.53913 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.12311 | −0.290098 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.4924 | −0.396835 | −0.198417 | − | 0.980118i | \(-0.563580\pi\) | ||||
−0.198417 | + | 0.980118i | \(0.563580\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 27.0540 | 0.858532 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.0000 | 0.760851 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −48.7386 | −1.54357 | −0.771784 | − | 0.635885i | \(-0.780635\pi\) | ||||
−0.771784 | + | 0.635885i | \(0.780635\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.2462 | −0.324176 |
(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 | 920.2.a.f.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 8280.2.a.bb.1.2 | 2 | |||
4.3 | odd | 2 | 1840.2.a.k.1.1 | 2 | |||
5.2 | odd | 4 | 4600.2.e.m.4049.1 | 4 | |||
5.3 | odd | 4 | 4600.2.e.m.4049.4 | 4 | |||
5.4 | even | 2 | 4600.2.a.r.1.1 | 2 | |||
8.3 | odd | 2 | 7360.2.a.bm.1.2 | 2 | |||
8.5 | even | 2 | 7360.2.a.bj.1.1 | 2 | |||
20.19 | odd | 2 | 9200.2.a.bx.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.a.f.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
1840.2.a.k.1.1 | 2 | 4.3 | odd | 2 | |||
4600.2.a.r.1.1 | 2 | 5.4 | even | 2 | |||
4600.2.e.m.4049.1 | 4 | 5.2 | odd | 4 | |||
4600.2.e.m.4049.4 | 4 | 5.3 | odd | 4 | |||
7360.2.a.bj.1.1 | 2 | 8.5 | even | 2 | |||
7360.2.a.bm.1.2 | 2 | 8.3 | odd | 2 | |||
8280.2.a.bb.1.2 | 2 | 3.2 | odd | 2 | |||
9200.2.a.bx.1.2 | 2 | 20.19 | odd | 2 |