Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6034,2,Mod(1,6034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6034, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("6034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6034 = 2 \cdot 7 \cdot 431 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6034.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: | \(48.1817325796\) |
Analytic rank: | \(0\) |
Dimension: | \(27\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6034.1 |
$q$-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 | ||||||||
\(3\) | 0.482352 | 0.278486 | 0.139243 | − | 0.990258i | \(-0.455533\pi\) | ||||
0.139243 | + | 0.990258i | \(0.455533\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.96654 | 1.32668 | 0.663338 | − | 0.748320i | \(-0.269139\pi\) | ||||
0.663338 | + | 0.748320i | \(0.269139\pi\) | |||||||
\(6\) | −0.482352 | −0.196919 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −2.76734 | −0.922446 | ||||||||
\(10\) | −2.96654 | −0.938102 | ||||||||
\(11\) | 2.13961 | 0.645117 | 0.322559 | − | 0.946549i | \(-0.395457\pi\) | ||||
0.322559 | + | 0.946549i | \(0.395457\pi\) | |||||||
\(12\) | 0.482352 | 0.139243 | ||||||||
\(13\) | 3.23107 | 0.896137 | 0.448068 | − | 0.893999i | \(-0.352112\pi\) | ||||
0.448068 | + | 0.893999i | \(0.352112\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 1.43092 | 0.369461 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.239086 | 0.0579868 | 0.0289934 | − | 0.999580i | \(-0.490770\pi\) | ||||
0.0289934 | + | 0.999580i | \(0.490770\pi\) | |||||||
\(18\) | 2.76734 | 0.652267 | ||||||||
\(19\) | −1.99134 | −0.456845 | −0.228423 | − | 0.973562i | \(-0.573357\pi\) | ||||
−0.228423 | + | 0.973562i | \(0.573357\pi\) | |||||||
\(20\) | 2.96654 | 0.663338 | ||||||||
\(21\) | 0.482352 | 0.105258 | ||||||||
\(22\) | −2.13961 | −0.456167 | ||||||||
\(23\) | −0.0927620 | −0.0193422 | −0.00967110 | − | 0.999953i | \(-0.503078\pi\) | ||||
−0.00967110 | + | 0.999953i | \(0.503078\pi\) | |||||||
\(24\) | −0.482352 | −0.0984597 | ||||||||
\(25\) | 3.80035 | 0.760070 | ||||||||
\(26\) | −3.23107 | −0.633664 | ||||||||
\(27\) | −2.78189 | −0.535374 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 5.49601 | 1.02058 | 0.510292 | − | 0.860001i | \(-0.329537\pi\) | ||||
0.510292 | + | 0.860001i | \(0.329537\pi\) | |||||||
\(30\) | −1.43092 | −0.261248 | ||||||||
\(31\) | −1.27192 | −0.228443 | −0.114222 | − | 0.993455i | \(-0.536437\pi\) | ||||
−0.114222 | + | 0.993455i | \(0.536437\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 1.03205 | 0.179656 | ||||||||
\(34\) | −0.239086 | −0.0410028 | ||||||||
\(35\) | 2.96654 | 0.501436 | ||||||||
\(36\) | −2.76734 | −0.461223 | ||||||||
\(37\) | 2.61566 | 0.430012 | 0.215006 | − | 0.976613i | \(-0.431023\pi\) | ||||
0.215006 | + | 0.976613i | \(0.431023\pi\) | |||||||
\(38\) | 1.99134 | 0.323038 | ||||||||
\(39\) | 1.55851 | 0.249562 | ||||||||
\(40\) | −2.96654 | −0.469051 | ||||||||
\(41\) | −8.16295 | −1.27484 | −0.637420 | − | 0.770517i | \(-0.719998\pi\) | ||||
−0.637420 | + | 0.770517i | \(0.719998\pi\) | |||||||
\(42\) | −0.482352 | −0.0744285 | ||||||||
\(43\) | 8.50523 | 1.29704 | 0.648518 | − | 0.761200i | \(-0.275389\pi\) | ||||
0.648518 | + | 0.761200i | \(0.275389\pi\) | |||||||
\(44\) | 2.13961 | 0.322559 | ||||||||
\(45\) | −8.20941 | −1.22379 | ||||||||
\(46\) | 0.0927620 | 0.0136770 | ||||||||
\(47\) | 9.39850 | 1.37091 | 0.685456 | − | 0.728114i | \(-0.259603\pi\) | ||||
0.685456 | + | 0.728114i | \(0.259603\pi\) | |||||||
\(48\) | 0.482352 | 0.0696215 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −3.80035 | −0.537451 | ||||||||
\(51\) | 0.115323 | 0.0161485 | ||||||||
\(52\) | 3.23107 | 0.448068 | ||||||||
\(53\) | 12.5678 | 1.72633 | 0.863163 | − | 0.504925i | \(-0.168480\pi\) | ||||
0.863163 | + | 0.504925i | \(0.168480\pi\) | |||||||
\(54\) | 2.78189 | 0.378567 | ||||||||
\(55\) | 6.34724 | 0.855862 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −0.960528 | −0.127225 | ||||||||
\(58\) | −5.49601 | −0.721662 | ||||||||
\(59\) | −11.2092 | −1.45931 | −0.729656 | − | 0.683814i | \(-0.760320\pi\) | ||||
−0.729656 | + | 0.683814i | \(0.760320\pi\) | |||||||
\(60\) | 1.43092 | 0.184730 | ||||||||
\(61\) | −13.1502 | −1.68371 | −0.841854 | − | 0.539705i | \(-0.818536\pi\) | ||||
−0.841854 | + | 0.539705i | \(0.818536\pi\) | |||||||
\(62\) | 1.27192 | 0.161534 | ||||||||
\(63\) | −2.76734 | −0.348652 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.58508 | 1.18888 | ||||||||
\(66\) | −1.03205 | −0.127036 | ||||||||
\(67\) | 9.29161 | 1.13515 | 0.567575 | − | 0.823321i | \(-0.307882\pi\) | ||||
0.567575 | + | 0.823321i | \(0.307882\pi\) | |||||||
\(68\) | 0.239086 | 0.0289934 | ||||||||
\(69\) | −0.0447439 | −0.00538654 | ||||||||
\(70\) | −2.96654 | −0.354569 | ||||||||
\(71\) | 0.681386 | 0.0808656 | 0.0404328 | − | 0.999182i | \(-0.487126\pi\) | ||||
0.0404328 | + | 0.999182i | \(0.487126\pi\) | |||||||
\(72\) | 2.76734 | 0.326134 | ||||||||
\(73\) | −0.776701 | −0.0909059 | −0.0454530 | − | 0.998966i | \(-0.514473\pi\) | ||||
−0.0454530 | + | 0.998966i | \(0.514473\pi\) | |||||||
\(74\) | −2.61566 | −0.304064 | ||||||||
\(75\) | 1.83311 | 0.211669 | ||||||||
\(76\) | −1.99134 | −0.228423 | ||||||||
\(77\) | 2.13961 | 0.243831 | ||||||||
\(78\) | −1.55851 | −0.176467 | ||||||||
\(79\) | 2.65766 | 0.299010 | 0.149505 | − | 0.988761i | \(-0.452232\pi\) | ||||
0.149505 | + | 0.988761i | \(0.452232\pi\) | |||||||
\(80\) | 2.96654 | 0.331669 | ||||||||
\(81\) | 6.96016 | 0.773351 | ||||||||
\(82\) | 8.16295 | 0.901447 | ||||||||
\(83\) | 0.462264 | 0.0507401 | 0.0253700 | − | 0.999678i | \(-0.491924\pi\) | ||||
0.0253700 | + | 0.999678i | \(0.491924\pi\) | |||||||
\(84\) | 0.482352 | 0.0526289 | ||||||||
\(85\) | 0.709257 | 0.0769297 | ||||||||
\(86\) | −8.50523 | −0.917142 | ||||||||
\(87\) | 2.65101 | 0.284218 | ||||||||
\(88\) | −2.13961 | −0.228083 | ||||||||
\(89\) | −8.66555 | −0.918547 | −0.459273 | − | 0.888295i | \(-0.651890\pi\) | ||||
−0.459273 | + | 0.888295i | \(0.651890\pi\) | |||||||
\(90\) | 8.20941 | 0.865348 | ||||||||
\(91\) | 3.23107 | 0.338708 | ||||||||
\(92\) | −0.0927620 | −0.00967110 | ||||||||
\(93\) | −0.613512 | −0.0636182 | ||||||||
\(94\) | −9.39850 | −0.969381 | ||||||||
\(95\) | −5.90739 | −0.606086 | ||||||||
\(96\) | −0.482352 | −0.0492298 | ||||||||
\(97\) | 8.48519 | 0.861541 | 0.430770 | − | 0.902462i | \(-0.358242\pi\) | ||||
0.430770 | + | 0.902462i | \(0.358242\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | −5.92103 | −0.595086 | ||||||||
\(100\) | 3.80035 | 0.380035 | ||||||||
\(101\) | 2.08371 | 0.207337 | 0.103668 | − | 0.994612i | \(-0.466942\pi\) | ||||
0.103668 | + | 0.994612i | \(0.466942\pi\) | |||||||
\(102\) | −0.115323 | −0.0114187 | ||||||||
\(103\) | 4.69630 | 0.462741 | 0.231370 | − | 0.972866i | \(-0.425679\pi\) | ||||
0.231370 | + | 0.972866i | \(0.425679\pi\) | |||||||
\(104\) | −3.23107 | −0.316832 | ||||||||
\(105\) | 1.43092 | 0.139643 | ||||||||
\(106\) | −12.5678 | −1.22070 | ||||||||
\(107\) | −4.74890 | −0.459094 | −0.229547 | − | 0.973298i | \(-0.573724\pi\) | ||||
−0.229547 | + | 0.973298i | \(0.573724\pi\) | |||||||
\(108\) | −2.78189 | −0.267687 | ||||||||
\(109\) | 13.9853 | 1.33955 | 0.669775 | − | 0.742565i | \(-0.266391\pi\) | ||||
0.669775 | + | 0.742565i | \(0.266391\pi\) | |||||||
\(110\) | −6.34724 | −0.605186 | ||||||||
\(111\) | 1.26167 | 0.119752 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 18.6168 | 1.75132 | 0.875661 | − | 0.482926i | \(-0.160426\pi\) | ||||
0.875661 | + | 0.482926i | \(0.160426\pi\) | |||||||
\(114\) | 0.960528 | 0.0899617 | ||||||||
\(115\) | −0.275182 | −0.0256608 | ||||||||
\(116\) | 5.49601 | 0.510292 | ||||||||
\(117\) | −8.94145 | −0.826637 | ||||||||
\(118\) | 11.2092 | 1.03189 | ||||||||
\(119\) | 0.239086 | 0.0219169 | ||||||||
\(120\) | −1.43092 | −0.130624 | ||||||||
\(121\) | −6.42206 | −0.583824 | ||||||||
\(122\) | 13.1502 | 1.19056 | ||||||||
\(123\) | −3.93742 | −0.355025 | ||||||||
\(124\) | −1.27192 | −0.114222 | ||||||||
\(125\) | −3.55881 | −0.318310 | ||||||||
\(126\) | 2.76734 | 0.246534 | ||||||||
\(127\) | −0.713567 | −0.0633188 | −0.0316594 | − | 0.999499i | \(-0.510079\pi\) | ||||
−0.0316594 | + | 0.999499i | \(0.510079\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 4.10251 | 0.361206 | ||||||||
\(130\) | −9.58508 | −0.840667 | ||||||||
\(131\) | 12.8879 | 1.12602 | 0.563012 | − | 0.826448i | \(-0.309642\pi\) | ||||
0.563012 | + | 0.826448i | \(0.309642\pi\) | |||||||
\(132\) | 1.03205 | 0.0898281 | ||||||||
\(133\) | −1.99134 | −0.172671 | ||||||||
\(134\) | −9.29161 | −0.802673 | ||||||||
\(135\) | −8.25257 | −0.710268 | ||||||||
\(136\) | −0.239086 | −0.0205014 | ||||||||
\(137\) | −3.85098 | −0.329012 | −0.164506 | − | 0.986376i | \(-0.552603\pi\) | ||||
−0.164506 | + | 0.986376i | \(0.552603\pi\) | |||||||
\(138\) | 0.0447439 | 0.00380886 | ||||||||
\(139\) | 14.2324 | 1.20718 | 0.603590 | − | 0.797295i | \(-0.293736\pi\) | ||||
0.603590 | + | 0.797295i | \(0.293736\pi\) | |||||||
\(140\) | 2.96654 | 0.250718 | ||||||||
\(141\) | 4.53339 | 0.381780 | ||||||||
\(142\) | −0.681386 | −0.0571806 | ||||||||
\(143\) | 6.91323 | 0.578113 | ||||||||
\(144\) | −2.76734 | −0.230611 | ||||||||
\(145\) | 16.3041 | 1.35398 | ||||||||
\(146\) | 0.776701 | 0.0642802 | ||||||||
\(147\) | 0.482352 | 0.0397837 | ||||||||
\(148\) | 2.61566 | 0.215006 | ||||||||
\(149\) | 3.30358 | 0.270640 | 0.135320 | − | 0.990802i | \(-0.456794\pi\) | ||||
0.135320 | + | 0.990802i | \(0.456794\pi\) | |||||||
\(150\) | −1.83311 | −0.149673 | ||||||||
\(151\) | −6.56285 | −0.534077 | −0.267039 | − | 0.963686i | \(-0.586045\pi\) | ||||
−0.267039 | + | 0.963686i | \(0.586045\pi\) | |||||||
\(152\) | 1.99134 | 0.161519 | ||||||||
\(153\) | −0.661630 | −0.0534896 | ||||||||
\(154\) | −2.13961 | −0.172415 | ||||||||
\(155\) | −3.77319 | −0.303070 | ||||||||
\(156\) | 1.55851 | 0.124781 | ||||||||
\(157\) | −9.37570 | −0.748262 | −0.374131 | − | 0.927376i | \(-0.622059\pi\) | ||||
−0.374131 | + | 0.927376i | \(0.622059\pi\) | |||||||
\(158\) | −2.65766 | −0.211432 | ||||||||
\(159\) | 6.06213 | 0.480758 | ||||||||
\(160\) | −2.96654 | −0.234525 | ||||||||
\(161\) | −0.0927620 | −0.00731067 | ||||||||
\(162\) | −6.96016 | −0.546842 | ||||||||
\(163\) | 14.2718 | 1.11786 | 0.558928 | − | 0.829216i | \(-0.311213\pi\) | ||||
0.558928 | + | 0.829216i | \(0.311213\pi\) | |||||||
\(164\) | −8.16295 | −0.637420 | ||||||||
\(165\) | 3.06161 | 0.238346 | ||||||||
\(166\) | −0.462264 | −0.0358786 | ||||||||
\(167\) | 13.5331 | 1.04722 | 0.523612 | − | 0.851957i | \(-0.324584\pi\) | ||||
0.523612 | + | 0.851957i | \(0.324584\pi\) | |||||||
\(168\) | −0.482352 | −0.0372143 | ||||||||
\(169\) | −2.56021 | −0.196939 | ||||||||
\(170\) | −0.709257 | −0.0543975 | ||||||||
\(171\) | 5.51071 | 0.421415 | ||||||||
\(172\) | 8.50523 | 0.648518 | ||||||||
\(173\) | −10.7610 | −0.818145 | −0.409073 | − | 0.912502i | \(-0.634148\pi\) | ||||
−0.409073 | + | 0.912502i | \(0.634148\pi\) | |||||||
\(174\) | −2.65101 | −0.200973 | ||||||||
\(175\) | 3.80035 | 0.287279 | ||||||||
\(176\) | 2.13961 | 0.161279 | ||||||||
\(177\) | −5.40678 | −0.406398 | ||||||||
\(178\) | 8.66555 | 0.649511 | ||||||||
\(179\) | 2.13053 | 0.159243 | 0.0796216 | − | 0.996825i | \(-0.474629\pi\) | ||||
0.0796216 | + | 0.996825i | \(0.474629\pi\) | |||||||
\(180\) | −8.20941 | −0.611893 | ||||||||
\(181\) | −0.133121 | −0.00989477 | −0.00494738 | − | 0.999988i | \(-0.501575\pi\) | ||||
−0.00494738 | + | 0.999988i | \(0.501575\pi\) | |||||||
\(182\) | −3.23107 | −0.239503 | ||||||||
\(183\) | −6.34302 | −0.468889 | ||||||||
\(184\) | 0.0927620 | 0.00683850 | ||||||||
\(185\) | 7.75946 | 0.570487 | ||||||||
\(186\) | 0.613512 | 0.0449849 | ||||||||
\(187\) | 0.511550 | 0.0374083 | ||||||||
\(188\) | 9.39850 | 0.685456 | ||||||||
\(189\) | −2.78189 | −0.202352 | ||||||||
\(190\) | 5.90739 | 0.428567 | ||||||||
\(191\) | −3.11563 | −0.225439 | −0.112720 | − | 0.993627i | \(-0.535956\pi\) | ||||
−0.112720 | + | 0.993627i | \(0.535956\pi\) | |||||||
\(192\) | 0.482352 | 0.0348108 | ||||||||
\(193\) | 16.5168 | 1.18891 | 0.594453 | − | 0.804131i | \(-0.297369\pi\) | ||||
0.594453 | + | 0.804131i | \(0.297369\pi\) | |||||||
\(194\) | −8.48519 | −0.609201 | ||||||||
\(195\) | 4.62338 | 0.331087 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 2.22701 | 0.158668 | 0.0793338 | − | 0.996848i | \(-0.474721\pi\) | ||||
0.0793338 | + | 0.996848i | \(0.474721\pi\) | |||||||
\(198\) | 5.92103 | 0.420789 | ||||||||
\(199\) | 15.1913 | 1.07688 | 0.538442 | − | 0.842663i | \(-0.319013\pi\) | ||||
0.538442 | + | 0.842663i | \(0.319013\pi\) | |||||||
\(200\) | −3.80035 | −0.268725 | ||||||||
\(201\) | 4.48183 | 0.316124 | ||||||||
\(202\) | −2.08371 | −0.146609 | ||||||||
\(203\) | 5.49601 | 0.385745 | ||||||||
\(204\) | 0.115323 | 0.00807425 | ||||||||
\(205\) | −24.2157 | −1.69130 | ||||||||
\(206\) | −4.69630 | −0.327207 | ||||||||
\(207\) | 0.256704 | 0.0178421 | ||||||||
\(208\) | 3.23107 | 0.224034 | ||||||||
\(209\) | −4.26070 | −0.294719 | ||||||||
\(210\) | −1.43092 | −0.0987426 | ||||||||
\(211\) | −26.0216 | −1.79140 | −0.895699 | − | 0.444661i | \(-0.853324\pi\) | ||||
−0.895699 | + | 0.444661i | \(0.853324\pi\) | |||||||
\(212\) | 12.5678 | 0.863163 | ||||||||
\(213\) | 0.328668 | 0.0225199 | ||||||||
\(214\) | 4.74890 | 0.324628 | ||||||||
\(215\) | 25.2311 | 1.72075 | ||||||||
\(216\) | 2.78189 | 0.189283 | ||||||||
\(217\) | −1.27192 | −0.0863434 | ||||||||
\(218\) | −13.9853 | −0.947204 | ||||||||
\(219\) | −0.374643 | −0.0253160 | ||||||||
\(220\) | 6.34724 | 0.427931 | ||||||||
\(221\) | 0.772501 | 0.0519641 | ||||||||
\(222\) | −1.26167 | −0.0846777 | ||||||||
\(223\) | −23.9130 | −1.60133 | −0.800665 | − | 0.599112i | \(-0.795520\pi\) | ||||
−0.800665 | + | 0.599112i | \(0.795520\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −10.5168 | −0.701123 | ||||||||
\(226\) | −18.6168 | −1.23837 | ||||||||
\(227\) | 23.4759 | 1.55815 | 0.779075 | − | 0.626931i | \(-0.215689\pi\) | ||||
0.779075 | + | 0.626931i | \(0.215689\pi\) | |||||||
\(228\) | −0.960528 | −0.0636125 | ||||||||
\(229\) | 16.6106 | 1.09766 | 0.548830 | − | 0.835934i | \(-0.315073\pi\) | ||||
0.548830 | + | 0.835934i | \(0.315073\pi\) | |||||||
\(230\) | 0.275182 | 0.0181450 | ||||||||
\(231\) | 1.03205 | 0.0679037 | ||||||||
\(232\) | −5.49601 | −0.360831 | ||||||||
\(233\) | −9.15714 | −0.599904 | −0.299952 | − | 0.953954i | \(-0.596971\pi\) | ||||
−0.299952 | + | 0.953954i | \(0.596971\pi\) | |||||||
\(234\) | 8.94145 | 0.584521 | ||||||||
\(235\) | 27.8810 | 1.81876 | ||||||||
\(236\) | −11.2092 | −0.729656 | ||||||||
\(237\) | 1.28193 | 0.0832701 | ||||||||
\(238\) | −0.239086 | −0.0154976 | ||||||||
\(239\) | 9.43344 | 0.610198 | 0.305099 | − | 0.952321i | \(-0.401310\pi\) | ||||
0.305099 | + | 0.952321i | \(0.401310\pi\) | |||||||
\(240\) | 1.43092 | 0.0923652 | ||||||||
\(241\) | −19.6860 | −1.26808 | −0.634042 | − | 0.773298i | \(-0.718605\pi\) | ||||
−0.634042 | + | 0.773298i | \(0.718605\pi\) | |||||||
\(242\) | 6.42206 | 0.412826 | ||||||||
\(243\) | 11.7029 | 0.750742 | ||||||||
\(244\) | −13.1502 | −0.841854 | ||||||||
\(245\) | 2.96654 | 0.189525 | ||||||||
\(246\) | 3.93742 | 0.251041 | ||||||||
\(247\) | −6.43416 | −0.409396 | ||||||||
\(248\) | 1.27192 | 0.0807669 | ||||||||
\(249\) | 0.222974 | 0.0141304 | ||||||||
\(250\) | 3.55881 | 0.225079 | ||||||||
\(251\) | 29.2174 | 1.84419 | 0.922094 | − | 0.386966i | \(-0.126477\pi\) | ||||
0.922094 | + | 0.386966i | \(0.126477\pi\) | |||||||
\(252\) | −2.76734 | −0.174326 | ||||||||
\(253\) | −0.198475 | −0.0124780 | ||||||||
\(254\) | 0.713567 | 0.0447732 | ||||||||
\(255\) | 0.342111 | 0.0214238 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.5388 | −1.28118 | −0.640588 | − | 0.767885i | \(-0.721309\pi\) | ||||
−0.640588 | + | 0.767885i | \(0.721309\pi\) | |||||||
\(258\) | −4.10251 | −0.255411 | ||||||||
\(259\) | 2.61566 | 0.162529 | ||||||||
\(260\) | 9.58508 | 0.594442 | ||||||||
\(261\) | −15.2093 | −0.941433 | ||||||||
\(262\) | −12.8879 | −0.796220 | ||||||||
\(263\) | −16.6882 | −1.02904 | −0.514519 | − | 0.857479i | \(-0.672029\pi\) | ||||
−0.514519 | + | 0.857479i | \(0.672029\pi\) | |||||||
\(264\) | −1.03205 | −0.0635181 | ||||||||
\(265\) | 37.2830 | 2.29028 | ||||||||
\(266\) | 1.99134 | 0.122097 | ||||||||
\(267\) | −4.17985 | −0.255802 | ||||||||
\(268\) | 9.29161 | 0.567575 | ||||||||
\(269\) | −22.0360 | −1.34356 | −0.671778 | − | 0.740752i | \(-0.734469\pi\) | ||||
−0.671778 | + | 0.740752i | \(0.734469\pi\) | |||||||
\(270\) | 8.25257 | 0.502236 | ||||||||
\(271\) | −11.9667 | −0.726924 | −0.363462 | − | 0.931609i | \(-0.618405\pi\) | ||||
−0.363462 | + | 0.931609i | \(0.618405\pi\) | |||||||
\(272\) | 0.239086 | 0.0144967 | ||||||||
\(273\) | 1.55851 | 0.0943254 | ||||||||
\(274\) | 3.85098 | 0.232646 | ||||||||
\(275\) | 8.13127 | 0.490334 | ||||||||
\(276\) | −0.0447439 | −0.00269327 | ||||||||
\(277\) | 4.88474 | 0.293495 | 0.146748 | − | 0.989174i | \(-0.453119\pi\) | ||||
0.146748 | + | 0.989174i | \(0.453119\pi\) | |||||||
\(278\) | −14.2324 | −0.853606 | ||||||||
\(279\) | 3.51982 | 0.210726 | ||||||||
\(280\) | −2.96654 | −0.177285 | ||||||||
\(281\) | 16.4054 | 0.978663 | 0.489331 | − | 0.872098i | \(-0.337241\pi\) | ||||
0.489331 | + | 0.872098i | \(0.337241\pi\) | |||||||
\(282\) | −4.53339 | −0.269959 | ||||||||
\(283\) | −30.2586 | −1.79869 | −0.899344 | − | 0.437242i | \(-0.855955\pi\) | ||||
−0.899344 | + | 0.437242i | \(0.855955\pi\) | |||||||
\(284\) | 0.681386 | 0.0404328 | ||||||||
\(285\) | −2.84944 | −0.168786 | ||||||||
\(286\) | −6.91323 | −0.408788 | ||||||||
\(287\) | −8.16295 | −0.481844 | ||||||||
\(288\) | 2.76734 | 0.163067 | ||||||||
\(289\) | −16.9428 | −0.996638 | ||||||||
\(290\) | −16.3041 | −0.957412 | ||||||||
\(291\) | 4.09285 | 0.239927 | ||||||||
\(292\) | −0.776701 | −0.0454530 | ||||||||
\(293\) | 11.3651 | 0.663958 | 0.331979 | − | 0.943287i | \(-0.392284\pi\) | ||||
0.331979 | + | 0.943287i | \(0.392284\pi\) | |||||||
\(294\) | −0.482352 | −0.0281313 | ||||||||
\(295\) | −33.2525 | −1.93604 | ||||||||
\(296\) | −2.61566 | −0.152032 | ||||||||
\(297\) | −5.95216 | −0.345379 | ||||||||
\(298\) | −3.30358 | −0.191371 | ||||||||
\(299\) | −0.299720 | −0.0173333 | ||||||||
\(300\) | 1.83311 | 0.105834 | ||||||||
\(301\) | 8.50523 | 0.490233 | ||||||||
\(302\) | 6.56285 | 0.377650 | ||||||||
\(303\) | 1.00508 | 0.0577404 | ||||||||
\(304\) | −1.99134 | −0.114211 | ||||||||
\(305\) | −39.0105 | −2.23374 | ||||||||
\(306\) | 0.661630 | 0.0378229 | ||||||||
\(307\) | −17.4281 | −0.994676 | −0.497338 | − | 0.867557i | \(-0.665689\pi\) | ||||
−0.497338 | + | 0.867557i | \(0.665689\pi\) | |||||||
\(308\) | 2.13961 | 0.121916 | ||||||||
\(309\) | 2.26527 | 0.128867 | ||||||||
\(310\) | 3.77319 | 0.214303 | ||||||||
\(311\) | −12.7887 | −0.725183 | −0.362592 | − | 0.931948i | \(-0.618108\pi\) | ||||
−0.362592 | + | 0.931948i | \(0.618108\pi\) | |||||||
\(312\) | −1.55851 | −0.0882333 | ||||||||
\(313\) | 22.2518 | 1.25775 | 0.628874 | − | 0.777507i | \(-0.283516\pi\) | ||||
0.628874 | + | 0.777507i | \(0.283516\pi\) | |||||||
\(314\) | 9.37570 | 0.529101 | ||||||||
\(315\) | −8.20941 | −0.462548 | ||||||||
\(316\) | 2.65766 | 0.149505 | ||||||||
\(317\) | 6.60862 | 0.371177 | 0.185589 | − | 0.982628i | \(-0.440581\pi\) | ||||
0.185589 | + | 0.982628i | \(0.440581\pi\) | |||||||
\(318\) | −6.06213 | −0.339947 | ||||||||
\(319\) | 11.7593 | 0.658397 | ||||||||
\(320\) | 2.96654 | 0.165835 | ||||||||
\(321\) | −2.29064 | −0.127851 | ||||||||
\(322\) | 0.0927620 | 0.00516942 | ||||||||
\(323\) | −0.476101 | −0.0264910 | ||||||||
\(324\) | 6.96016 | 0.386676 | ||||||||
\(325\) | 12.2792 | 0.681126 | ||||||||
\(326\) | −14.2718 | −0.790444 | ||||||||
\(327\) | 6.74584 | 0.373046 | ||||||||
\(328\) | 8.16295 | 0.450724 | ||||||||
\(329\) | 9.39850 | 0.518156 | ||||||||
\(330\) | −3.06161 | −0.168536 | ||||||||
\(331\) | 12.0841 | 0.664202 | 0.332101 | − | 0.943244i | \(-0.392242\pi\) | ||||
0.332101 | + | 0.943244i | \(0.392242\pi\) | |||||||
\(332\) | 0.462264 | 0.0253700 | ||||||||
\(333\) | −7.23842 | −0.396663 | ||||||||
\(334\) | −13.5331 | −0.740499 | ||||||||
\(335\) | 27.5639 | 1.50598 | ||||||||
\(336\) | 0.482352 | 0.0263145 | ||||||||
\(337\) | −17.3674 | −0.946065 | −0.473033 | − | 0.881045i | \(-0.656841\pi\) | ||||
−0.473033 | + | 0.881045i | \(0.656841\pi\) | |||||||
\(338\) | 2.56021 | 0.139257 | ||||||||
\(339\) | 8.97986 | 0.487719 | ||||||||
\(340\) | 0.709257 | 0.0384648 | ||||||||
\(341\) | −2.72141 | −0.147373 | ||||||||
\(342\) | −5.51071 | −0.297985 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −8.50523 | −0.458571 | ||||||||
\(345\) | −0.132735 | −0.00714619 | ||||||||
\(346\) | 10.7610 | 0.578516 | ||||||||
\(347\) | 28.9006 | 1.55147 | 0.775734 | − | 0.631060i | \(-0.217380\pi\) | ||||
0.775734 | + | 0.631060i | \(0.217380\pi\) | |||||||
\(348\) | 2.65101 | 0.142109 | ||||||||
\(349\) | −12.0905 | −0.647192 | −0.323596 | − | 0.946195i | \(-0.604892\pi\) | ||||
−0.323596 | + | 0.946195i | \(0.604892\pi\) | |||||||
\(350\) | −3.80035 | −0.203137 | ||||||||
\(351\) | −8.98846 | −0.479768 | ||||||||
\(352\) | −2.13961 | −0.114042 | ||||||||
\(353\) | −27.7700 | −1.47805 | −0.739024 | − | 0.673679i | \(-0.764713\pi\) | ||||
−0.739024 | + | 0.673679i | \(0.764713\pi\) | |||||||
\(354\) | 5.40678 | 0.287367 | ||||||||
\(355\) | 2.02136 | 0.107282 | ||||||||
\(356\) | −8.66555 | −0.459273 | ||||||||
\(357\) | 0.115323 | 0.00610356 | ||||||||
\(358\) | −2.13053 | −0.112602 | ||||||||
\(359\) | −32.5443 | −1.71762 | −0.858812 | − | 0.512290i | \(-0.828797\pi\) | ||||
−0.858812 | + | 0.512290i | \(0.828797\pi\) | |||||||
\(360\) | 8.20941 | 0.432674 | ||||||||
\(361\) | −15.0346 | −0.791292 | ||||||||
\(362\) | 0.133121 | 0.00699666 | ||||||||
\(363\) | −3.09769 | −0.162587 | ||||||||
\(364\) | 3.23107 | 0.169354 | ||||||||
\(365\) | −2.30411 | −0.120603 | ||||||||
\(366\) | 6.34302 | 0.331555 | ||||||||
\(367\) | 1.36993 | 0.0715097 | 0.0357548 | − | 0.999361i | \(-0.488616\pi\) | ||||
0.0357548 | + | 0.999361i | \(0.488616\pi\) | |||||||
\(368\) | −0.0927620 | −0.00483555 | ||||||||
\(369\) | 22.5896 | 1.17597 | ||||||||
\(370\) | −7.75946 | −0.403395 | ||||||||
\(371\) | 12.5678 | 0.652490 | ||||||||
\(372\) | −0.613512 | −0.0318091 | ||||||||
\(373\) | 27.5413 | 1.42603 | 0.713016 | − | 0.701147i | \(-0.247328\pi\) | ||||
0.713016 | + | 0.701147i | \(0.247328\pi\) | |||||||
\(374\) | −0.511550 | −0.0264516 | ||||||||
\(375\) | −1.71660 | −0.0886448 | ||||||||
\(376\) | −9.39850 | −0.484691 | ||||||||
\(377\) | 17.7580 | 0.914583 | ||||||||
\(378\) | 2.78189 | 0.143085 | ||||||||
\(379\) | −2.55245 | −0.131110 | −0.0655552 | − | 0.997849i | \(-0.520882\pi\) | ||||
−0.0655552 | + | 0.997849i | \(0.520882\pi\) | |||||||
\(380\) | −5.90739 | −0.303043 | ||||||||
\(381\) | −0.344190 | −0.0176334 | ||||||||
\(382\) | 3.11563 | 0.159409 | ||||||||
\(383\) | −33.6175 | −1.71777 | −0.858887 | − | 0.512165i | \(-0.828844\pi\) | ||||
−0.858887 | + | 0.512165i | \(0.828844\pi\) | |||||||
\(384\) | −0.482352 | −0.0246149 | ||||||||
\(385\) | 6.34724 | 0.323485 | ||||||||
\(386\) | −16.5168 | −0.840683 | ||||||||
\(387\) | −23.5368 | −1.19644 | ||||||||
\(388\) | 8.48519 | 0.430770 | ||||||||
\(389\) | 8.37623 | 0.424692 | 0.212346 | − | 0.977195i | \(-0.431890\pi\) | ||||
0.212346 | + | 0.977195i | \(0.431890\pi\) | |||||||
\(390\) | −4.62338 | −0.234114 | ||||||||
\(391\) | −0.0221780 | −0.00112159 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 6.21653 | 0.313582 | ||||||||
\(394\) | −2.22701 | −0.112195 | ||||||||
\(395\) | 7.88405 | 0.396690 | ||||||||
\(396\) | −5.92103 | −0.297543 | ||||||||
\(397\) | 7.71781 | 0.387346 | 0.193673 | − | 0.981066i | \(-0.437960\pi\) | ||||
0.193673 | + | 0.981066i | \(0.437960\pi\) | |||||||
\(398\) | −15.1913 | −0.761472 | ||||||||
\(399\) | −0.960528 | −0.0480865 | ||||||||
\(400\) | 3.80035 | 0.190017 | ||||||||
\(401\) | 10.3982 | 0.519260 | 0.259630 | − | 0.965708i | \(-0.416399\pi\) | ||||
0.259630 | + | 0.965708i | \(0.416399\pi\) | |||||||
\(402\) | −4.48183 | −0.223533 | ||||||||
\(403\) | −4.10965 | −0.204716 | ||||||||
\(404\) | 2.08371 | 0.103668 | ||||||||
\(405\) | 20.6476 | 1.02599 | ||||||||
\(406\) | −5.49601 | −0.272763 | ||||||||
\(407\) | 5.59650 | 0.277408 | ||||||||
\(408\) | −0.115323 | −0.00570936 | ||||||||
\(409\) | 39.0810 | 1.93243 | 0.966215 | − | 0.257737i | \(-0.0829768\pi\) | ||||
0.966215 | + | 0.257737i | \(0.0829768\pi\) | |||||||
\(410\) | 24.2157 | 1.19593 | ||||||||
\(411\) | −1.85753 | −0.0916252 | ||||||||
\(412\) | 4.69630 | 0.231370 | ||||||||
\(413\) | −11.2092 | −0.551568 | ||||||||
\(414\) | −0.256704 | −0.0126163 | ||||||||
\(415\) | 1.37132 | 0.0673156 | ||||||||
\(416\) | −3.23107 | −0.158416 | ||||||||
\(417\) | 6.86505 | 0.336183 | ||||||||
\(418\) | 4.26070 | 0.208398 | ||||||||
\(419\) | 25.0634 | 1.22443 | 0.612213 | − | 0.790693i | \(-0.290279\pi\) | ||||
0.612213 | + | 0.790693i | \(0.290279\pi\) | |||||||
\(420\) | 1.43092 | 0.0698215 | ||||||||
\(421\) | −15.6053 | −0.760558 | −0.380279 | − | 0.924872i | \(-0.624172\pi\) | ||||
−0.380279 | + | 0.924872i | \(0.624172\pi\) | |||||||
\(422\) | 26.0216 | 1.26671 | ||||||||
\(423\) | −26.0088 | −1.26459 | ||||||||
\(424\) | −12.5678 | −0.610349 | ||||||||
\(425\) | 0.908609 | 0.0440740 | ||||||||
\(426\) | −0.328668 | −0.0159240 | ||||||||
\(427\) | −13.1502 | −0.636382 | ||||||||
\(428\) | −4.74890 | −0.229547 | ||||||||
\(429\) | 3.33461 | 0.160997 | ||||||||
\(430\) | −25.2311 | −1.21675 | ||||||||
\(431\) | −1.00000 | −0.0481683 | ||||||||
\(432\) | −2.78189 | −0.133844 | ||||||||
\(433\) | −18.6033 | −0.894017 | −0.447008 | − | 0.894530i | \(-0.647511\pi\) | ||||
−0.447008 | + | 0.894530i | \(0.647511\pi\) | |||||||
\(434\) | 1.27192 | 0.0610540 | ||||||||
\(435\) | 7.86433 | 0.377066 | ||||||||
\(436\) | 13.9853 | 0.669775 | ||||||||
\(437\) | 0.184721 | 0.00883639 | ||||||||
\(438\) | 0.374643 | 0.0179011 | ||||||||
\(439\) | 21.8233 | 1.04157 | 0.520785 | − | 0.853688i | \(-0.325639\pi\) | ||||
0.520785 | + | 0.853688i | \(0.325639\pi\) | |||||||
\(440\) | −6.34724 | −0.302593 | ||||||||
\(441\) | −2.76734 | −0.131778 | ||||||||
\(442\) | −0.772501 | −0.0367441 | ||||||||
\(443\) | 17.6938 | 0.840656 | 0.420328 | − | 0.907372i | \(-0.361915\pi\) | ||||
0.420328 | + | 0.907372i | \(0.361915\pi\) | |||||||
\(444\) | 1.26167 | 0.0598762 | ||||||||
\(445\) | −25.7067 | −1.21861 | ||||||||
\(446\) | 23.9130 | 1.13231 | ||||||||
\(447\) | 1.59349 | 0.0753694 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −16.6261 | −0.784636 | −0.392318 | − | 0.919830i | \(-0.628327\pi\) | ||||
−0.392318 | + | 0.919830i | \(0.628327\pi\) | |||||||
\(450\) | 10.5168 | 0.495769 | ||||||||
\(451\) | −17.4656 | −0.822421 | ||||||||
\(452\) | 18.6168 | 0.875661 | ||||||||
\(453\) | −3.16560 | −0.148733 | ||||||||
\(454\) | −23.4759 | −1.10178 | ||||||||
\(455\) | 9.58508 | 0.449356 | ||||||||
\(456\) | 0.960528 | 0.0449808 | ||||||||
\(457\) | 1.44455 | 0.0675730 | 0.0337865 | − | 0.999429i | \(-0.489243\pi\) | ||||
0.0337865 | + | 0.999429i | \(0.489243\pi\) | |||||||
\(458\) | −16.6106 | −0.776163 | ||||||||
\(459\) | −0.665109 | −0.0310446 | ||||||||
\(460\) | −0.275182 | −0.0128304 | ||||||||
\(461\) | −3.80273 | −0.177111 | −0.0885554 | − | 0.996071i | \(-0.528225\pi\) | ||||
−0.0885554 | + | 0.996071i | \(0.528225\pi\) | |||||||
\(462\) | −1.03205 | −0.0480151 | ||||||||
\(463\) | −11.8740 | −0.551831 | −0.275916 | − | 0.961182i | \(-0.588981\pi\) | ||||
−0.275916 | + | 0.961182i | \(0.588981\pi\) | |||||||
\(464\) | 5.49601 | 0.255146 | ||||||||
\(465\) | −1.82001 | −0.0844008 | ||||||||
\(466\) | 9.15714 | 0.424196 | ||||||||
\(467\) | −23.2619 | −1.07643 | −0.538217 | − | 0.842806i | \(-0.680902\pi\) | ||||
−0.538217 | + | 0.842806i | \(0.680902\pi\) | |||||||
\(468\) | −8.94145 | −0.413319 | ||||||||
\(469\) | 9.29161 | 0.429047 | ||||||||
\(470\) | −27.8810 | −1.28606 | ||||||||
\(471\) | −4.52239 | −0.208381 | ||||||||
\(472\) | 11.2092 | 0.515945 | ||||||||
\(473\) | 18.1979 | 0.836740 | ||||||||
\(474\) | −1.28193 | −0.0588809 | ||||||||
\(475\) | −7.56780 | −0.347234 | ||||||||
\(476\) | 0.239086 | 0.0109585 | ||||||||
\(477\) | −34.7795 | −1.59244 | ||||||||
\(478\) | −9.43344 | −0.431475 | ||||||||
\(479\) | 1.74403 | 0.0796870 | 0.0398435 | − | 0.999206i | \(-0.487314\pi\) | ||||
0.0398435 | + | 0.999206i | \(0.487314\pi\) | |||||||
\(480\) | −1.43092 | −0.0653121 | ||||||||
\(481\) | 8.45138 | 0.385350 | ||||||||
\(482\) | 19.6860 | 0.896671 | ||||||||
\(483\) | −0.0447439 | −0.00203592 | ||||||||
\(484\) | −6.42206 | −0.291912 | ||||||||
\(485\) | 25.1716 | 1.14299 | ||||||||
\(486\) | −11.7029 | −0.530855 | ||||||||
\(487\) | 17.9150 | 0.811808 | 0.405904 | − | 0.913916i | \(-0.366957\pi\) | ||||
0.405904 | + | 0.913916i | \(0.366957\pi\) | |||||||
\(488\) | 13.1502 | 0.595281 | ||||||||
\(489\) | 6.88405 | 0.311307 | ||||||||
\(490\) | −2.96654 | −0.134015 | ||||||||
\(491\) | 15.3446 | 0.692491 | 0.346246 | − | 0.938144i | \(-0.387456\pi\) | ||||
0.346246 | + | 0.938144i | \(0.387456\pi\) | |||||||
\(492\) | −3.93742 | −0.177512 | ||||||||
\(493\) | 1.31402 | 0.0591804 | ||||||||
\(494\) | 6.43416 | 0.289486 | ||||||||
\(495\) | −17.5650 | −0.789486 | ||||||||
\(496\) | −1.27192 | −0.0571108 | ||||||||
\(497\) | 0.681386 | 0.0305643 | ||||||||
\(498\) | −0.222974 | −0.00999170 | ||||||||
\(499\) | 25.0219 | 1.12014 | 0.560068 | − | 0.828447i | \(-0.310775\pi\) | ||||
0.560068 | + | 0.828447i | \(0.310775\pi\) | |||||||
\(500\) | −3.55881 | −0.159155 | ||||||||
\(501\) | 6.52772 | 0.291637 | ||||||||
\(502\) | −29.2174 | −1.30404 | ||||||||
\(503\) | −8.07209 | −0.359917 | −0.179958 | − | 0.983674i | \(-0.557596\pi\) | ||||
−0.179958 | + | 0.983674i | \(0.557596\pi\) | |||||||
\(504\) | 2.76734 | 0.123267 | ||||||||
\(505\) | 6.18140 | 0.275069 | ||||||||
\(506\) | 0.198475 | 0.00882327 | ||||||||
\(507\) | −1.23492 | −0.0548449 | ||||||||
\(508\) | −0.713567 | −0.0316594 | ||||||||
\(509\) | 12.2895 | 0.544721 | 0.272361 | − | 0.962195i | \(-0.412196\pi\) | ||||
0.272361 | + | 0.962195i | \(0.412196\pi\) | |||||||
\(510\) | −0.342111 | −0.0151489 | ||||||||
\(511\) | −0.776701 | −0.0343592 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.53969 | 0.244583 | ||||||||
\(514\) | 20.5388 | 0.905928 | ||||||||
\(515\) | 13.9318 | 0.613907 | ||||||||
\(516\) | 4.10251 | 0.180603 | ||||||||
\(517\) | 20.1091 | 0.884399 | ||||||||
\(518\) | −2.61566 | −0.114926 | ||||||||
\(519\) | −5.19060 | −0.227842 | ||||||||
\(520\) | −9.58508 | −0.420334 | ||||||||
\(521\) | 14.2891 | 0.626016 | 0.313008 | − | 0.949750i | \(-0.398663\pi\) | ||||
0.313008 | + | 0.949750i | \(0.398663\pi\) | |||||||
\(522\) | 15.2093 | 0.665694 | ||||||||
\(523\) | −33.4009 | −1.46052 | −0.730259 | − | 0.683170i | \(-0.760601\pi\) | ||||
−0.730259 | + | 0.683170i | \(0.760601\pi\) | |||||||
\(524\) | 12.8879 | 0.563012 | ||||||||
\(525\) | 1.83311 | 0.0800033 | ||||||||
\(526\) | 16.6882 | 0.727639 | ||||||||
\(527\) | −0.304097 | −0.0132467 | ||||||||
\(528\) | 1.03205 | 0.0449141 | ||||||||
\(529\) | −22.9914 | −0.999626 | ||||||||
\(530\) | −37.2830 | −1.61947 | ||||||||
\(531\) | 31.0196 | 1.34614 | ||||||||
\(532\) | −1.99134 | −0.0863356 | ||||||||
\(533\) | −26.3750 | −1.14243 | ||||||||
\(534\) | 4.17985 | 0.180880 | ||||||||
\(535\) | −14.0878 | −0.609069 | ||||||||
\(536\) | −9.29161 | −0.401336 | ||||||||
\(537\) | 1.02767 | 0.0443470 | ||||||||
\(538\) | 22.0360 | 0.950038 | ||||||||
\(539\) | 2.13961 | 0.0921596 | ||||||||
\(540\) | −8.25257 | −0.355134 | ||||||||
\(541\) | 12.6938 | 0.545751 | 0.272875 | − | 0.962049i | \(-0.412025\pi\) | ||||
0.272875 | + | 0.962049i | \(0.412025\pi\) | |||||||
\(542\) | 11.9667 | 0.514013 | ||||||||
\(543\) | −0.0642110 | −0.00275556 | ||||||||
\(544\) | −0.239086 | −0.0102507 | ||||||||
\(545\) | 41.4879 | 1.77715 | ||||||||
\(546\) | −1.55851 | −0.0666981 | ||||||||
\(547\) | 32.6253 | 1.39496 | 0.697478 | − | 0.716606i | \(-0.254305\pi\) | ||||
0.697478 | + | 0.716606i | \(0.254305\pi\) | |||||||
\(548\) | −3.85098 | −0.164506 | ||||||||
\(549\) | 36.3910 | 1.55313 | ||||||||
\(550\) | −8.13127 | −0.346719 | ||||||||
\(551\) | −10.9444 | −0.466249 | ||||||||
\(552\) | 0.0447439 | 0.00190443 | ||||||||
\(553\) | 2.65766 | 0.113015 | ||||||||
\(554\) | −4.88474 | −0.207533 | ||||||||
\(555\) | 3.74279 | 0.158873 | ||||||||
\(556\) | 14.2324 | 0.603590 | ||||||||
\(557\) | −4.81152 | −0.203871 | −0.101935 | − | 0.994791i | \(-0.532503\pi\) | ||||
−0.101935 | + | 0.994791i | \(0.532503\pi\) | |||||||
\(558\) | −3.51982 | −0.149006 | ||||||||
\(559\) | 27.4810 | 1.16232 | ||||||||
\(560\) | 2.96654 | 0.125359 | ||||||||
\(561\) | 0.246747 | 0.0104177 | ||||||||
\(562\) | −16.4054 | −0.692019 | ||||||||
\(563\) | 37.7250 | 1.58992 | 0.794959 | − | 0.606663i | \(-0.207492\pi\) | ||||
0.794959 | + | 0.606663i | \(0.207492\pi\) | |||||||
\(564\) | 4.53339 | 0.190890 | ||||||||
\(565\) | 55.2275 | 2.32344 | ||||||||
\(566\) | 30.2586 | 1.27186 | ||||||||
\(567\) | 6.96016 | 0.292299 | ||||||||
\(568\) | −0.681386 | −0.0285903 | ||||||||
\(569\) | −10.3231 | −0.432767 | −0.216384 | − | 0.976308i | \(-0.569426\pi\) | ||||
−0.216384 | + | 0.976308i | \(0.569426\pi\) | |||||||
\(570\) | 2.84944 | 0.119350 | ||||||||
\(571\) | −17.7888 | −0.744438 | −0.372219 | − | 0.928145i | \(-0.621403\pi\) | ||||
−0.372219 | + | 0.928145i | \(0.621403\pi\) | |||||||
\(572\) | 6.91323 | 0.289057 | ||||||||
\(573\) | −1.50283 | −0.0627816 | ||||||||
\(574\) | 8.16295 | 0.340715 | ||||||||
\(575\) | −0.352528 | −0.0147014 | ||||||||
\(576\) | −2.76734 | −0.115306 | ||||||||
\(577\) | −1.19926 | −0.0499259 | −0.0249630 | − | 0.999688i | \(-0.507947\pi\) | ||||
−0.0249630 | + | 0.999688i | \(0.507947\pi\) | |||||||
\(578\) | 16.9428 | 0.704729 | ||||||||
\(579\) | 7.96691 | 0.331094 | ||||||||
\(580\) | 16.3041 | 0.676992 | ||||||||
\(581\) | 0.462264 | 0.0191779 | ||||||||
\(582\) | −4.09285 | −0.169654 | ||||||||
\(583\) | 26.8903 | 1.11368 | ||||||||
\(584\) | 0.776701 | 0.0321401 | ||||||||
\(585\) | −26.5251 | −1.09668 | ||||||||
\(586\) | −11.3651 | −0.469489 | ||||||||
\(587\) | 28.2652 | 1.16663 | 0.583316 | − | 0.812246i | \(-0.301755\pi\) | ||||
0.583316 | + | 0.812246i | \(0.301755\pi\) | |||||||
\(588\) | 0.482352 | 0.0198919 | ||||||||
\(589\) | 2.53282 | 0.104363 | ||||||||
\(590\) | 33.2525 | 1.36898 | ||||||||
\(591\) | 1.07420 | 0.0441867 | ||||||||
\(592\) | 2.61566 | 0.107503 | ||||||||
\(593\) | −27.6786 | −1.13663 | −0.568313 | − | 0.822813i | \(-0.692404\pi\) | ||||
−0.568313 | + | 0.822813i | \(0.692404\pi\) | |||||||
\(594\) | 5.95216 | 0.244220 | ||||||||
\(595\) | 0.709257 | 0.0290767 | ||||||||
\(596\) | 3.30358 | 0.135320 | ||||||||
\(597\) | 7.32756 | 0.299897 | ||||||||
\(598\) | 0.299720 | 0.0122565 | ||||||||
\(599\) | −39.0073 | −1.59380 | −0.796898 | − | 0.604113i | \(-0.793527\pi\) | ||||
−0.796898 | + | 0.604113i | \(0.793527\pi\) | |||||||
\(600\) | −1.83311 | −0.0748363 | ||||||||
\(601\) | 17.1496 | 0.699547 | 0.349773 | − | 0.936834i | \(-0.386259\pi\) | ||||
0.349773 | + | 0.936834i | \(0.386259\pi\) | |||||||
\(602\) | −8.50523 | −0.346647 | ||||||||
\(603\) | −25.7130 | −1.04711 | ||||||||
\(604\) | −6.56285 | −0.267039 | ||||||||
\(605\) | −19.0513 | −0.774545 | ||||||||
\(606\) | −1.00508 | −0.0408286 | ||||||||
\(607\) | 31.1658 | 1.26498 | 0.632490 | − | 0.774569i | \(-0.282033\pi\) | ||||
0.632490 | + | 0.774569i | \(0.282033\pi\) | |||||||
\(608\) | 1.99134 | 0.0807596 | ||||||||
\(609\) | 2.65101 | 0.107424 | ||||||||
\(610\) | 39.0105 | 1.57949 | ||||||||
\(611\) | 30.3672 | 1.22852 | ||||||||
\(612\) | −0.661630 | −0.0267448 | ||||||||
\(613\) | 25.6400 | 1.03559 | 0.517794 | − | 0.855505i | \(-0.326753\pi\) | ||||
0.517794 | + | 0.855505i | \(0.326753\pi\) | |||||||
\(614\) | 17.4281 | 0.703342 | ||||||||
\(615\) | −11.6805 | −0.471003 | ||||||||
\(616\) | −2.13961 | −0.0862074 | ||||||||
\(617\) | 40.9546 | 1.64877 | 0.824385 | − | 0.566029i | \(-0.191521\pi\) | ||||
0.824385 | + | 0.566029i | \(0.191521\pi\) | |||||||
\(618\) | −2.26527 | −0.0911226 | ||||||||
\(619\) | 14.6410 | 0.588471 | 0.294235 | − | 0.955733i | \(-0.404935\pi\) | ||||
0.294235 | + | 0.955733i | \(0.404935\pi\) | |||||||
\(620\) | −3.77319 | −0.151535 | ||||||||
\(621\) | 0.258053 | 0.0103553 | ||||||||
\(622\) | 12.7887 | 0.512782 | ||||||||
\(623\) | −8.66555 | −0.347178 | ||||||||
\(624\) | 1.55851 | 0.0623904 | ||||||||
\(625\) | −29.5591 | −1.18236 | ||||||||
\(626\) | −22.2518 | −0.889362 | ||||||||
\(627\) | −2.05516 | −0.0820751 | ||||||||
\(628\) | −9.37570 | −0.374131 | ||||||||
\(629\) | 0.625367 | 0.0249350 | ||||||||
\(630\) | 8.20941 | 0.327071 | ||||||||
\(631\) | 20.1195 | 0.800946 | 0.400473 | − | 0.916309i | \(-0.368846\pi\) | ||||
0.400473 | + | 0.916309i | \(0.368846\pi\) | |||||||
\(632\) | −2.65766 | −0.105716 | ||||||||
\(633\) | −12.5516 | −0.498879 | ||||||||
\(634\) | −6.60862 | −0.262462 | ||||||||
\(635\) | −2.11682 | −0.0840036 | ||||||||
\(636\) | 6.06213 | 0.240379 | ||||||||
\(637\) | 3.23107 | 0.128020 | ||||||||
\(638\) | −11.7593 | −0.465557 | ||||||||
\(639\) | −1.88562 | −0.0745941 | ||||||||
\(640\) | −2.96654 | −0.117263 | ||||||||
\(641\) | 39.1696 | 1.54710 | 0.773552 | − | 0.633732i | \(-0.218478\pi\) | ||||
0.773552 | + | 0.633732i | \(0.218478\pi\) | |||||||
\(642\) | 2.29064 | 0.0904045 | ||||||||
\(643\) | −2.87102 | −0.113222 | −0.0566109 | − | 0.998396i | \(-0.518029\pi\) | ||||
−0.0566109 | + | 0.998396i | \(0.518029\pi\) | |||||||
\(644\) | −0.0927620 | −0.00365533 | ||||||||
\(645\) | 12.1703 | 0.479204 | ||||||||
\(646\) | 0.476101 | 0.0187319 | ||||||||
\(647\) | 12.2329 | 0.480927 | 0.240463 | − | 0.970658i | \(-0.422701\pi\) | ||||
0.240463 | + | 0.970658i | \(0.422701\pi\) | |||||||
\(648\) | −6.96016 | −0.273421 | ||||||||
\(649\) | −23.9833 | −0.941428 | ||||||||
\(650\) | −12.2792 | −0.481629 | ||||||||
\(651\) | −0.613512 | −0.0240454 | ||||||||
\(652\) | 14.2718 | 0.558928 | ||||||||
\(653\) | 31.5162 | 1.23332 | 0.616662 | − | 0.787228i | \(-0.288485\pi\) | ||||
0.616662 | + | 0.787228i | \(0.288485\pi\) | |||||||
\(654\) | −6.74584 | −0.263783 | ||||||||
\(655\) | 38.2326 | 1.49387 | ||||||||
\(656\) | −8.16295 | −0.318710 | ||||||||
\(657\) | 2.14939 | 0.0838558 | ||||||||
\(658\) | −9.39850 | −0.366392 | ||||||||
\(659\) | 15.0682 | 0.586974 | 0.293487 | − | 0.955963i | \(-0.405184\pi\) | ||||
0.293487 | + | 0.955963i | \(0.405184\pi\) | |||||||
\(660\) | 3.06161 | 0.119173 | ||||||||
\(661\) | 11.3999 | 0.443405 | 0.221703 | − | 0.975114i | \(-0.428839\pi\) | ||||
0.221703 | + | 0.975114i | \(0.428839\pi\) | |||||||
\(662\) | −12.0841 | −0.469662 | ||||||||
\(663\) | 0.372618 | 0.0144713 | ||||||||
\(664\) | −0.462264 | −0.0179393 | ||||||||
\(665\) | −5.90739 | −0.229079 | ||||||||
\(666\) | 7.23842 | 0.280483 | ||||||||
\(667\) | −0.509821 | −0.0197403 | ||||||||
\(668\) | 13.5331 | 0.523612 | ||||||||
\(669\) | −11.5345 | −0.445948 | ||||||||
\(670\) | −27.5639 | −1.06489 | ||||||||
\(671\) | −28.1363 | −1.08619 | ||||||||
\(672\) | −0.482352 | −0.0186071 | ||||||||
\(673\) | −46.2126 | −1.78137 | −0.890683 | − | 0.454625i | \(-0.849773\pi\) | ||||
−0.890683 | + | 0.454625i | \(0.849773\pi\) | |||||||
\(674\) | 17.3674 | 0.668969 | ||||||||
\(675\) | −10.5721 | −0.406922 | ||||||||
\(676\) | −2.56021 | −0.0984696 | ||||||||
\(677\) | −16.8944 | −0.649303 | −0.324652 | − | 0.945834i | \(-0.605247\pi\) | ||||
−0.324652 | + | 0.945834i | \(0.605247\pi\) | |||||||
\(678\) | −8.97986 | −0.344869 | ||||||||
\(679\) | 8.48519 | 0.325632 | ||||||||
\(680\) | −0.709257 | −0.0271987 | ||||||||
\(681\) | 11.3236 | 0.433923 | ||||||||
\(682\) | 2.72141 | 0.104208 | ||||||||
\(683\) | −24.9338 | −0.954063 | −0.477032 | − | 0.878886i | \(-0.658287\pi\) | ||||
−0.477032 | + | 0.878886i | \(0.658287\pi\) | |||||||
\(684\) | 5.51071 | 0.210707 | ||||||||
\(685\) | −11.4241 | −0.436492 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | 8.01216 | 0.305683 | ||||||||
\(688\) | 8.50523 | 0.324259 | ||||||||
\(689\) | 40.6076 | 1.54702 | ||||||||
\(690\) | 0.132735 | 0.00505312 | ||||||||
\(691\) | −21.5010 | −0.817935 | −0.408968 | − | 0.912549i | \(-0.634111\pi\) | ||||
−0.408968 | + | 0.912549i | \(0.634111\pi\) | |||||||
\(692\) | −10.7610 | −0.409073 | ||||||||
\(693\) | −5.92103 | −0.224921 | ||||||||
\(694\) | −28.9006 | −1.09705 | ||||||||
\(695\) | 42.2211 | 1.60154 | ||||||||
\(696\) | −2.65101 | −0.100486 | ||||||||
\(697\) | −1.95164 | −0.0739238 | ||||||||
\(698\) | 12.0905 | 0.457634 | ||||||||
\(699\) | −4.41697 | −0.167065 | ||||||||
\(700\) | 3.80035 | 0.143640 | ||||||||
\(701\) | −18.6725 | −0.705251 | −0.352625 | − | 0.935765i | \(-0.614711\pi\) | ||||
−0.352625 | + | 0.935765i | \(0.614711\pi\) | |||||||
\(702\) | 8.98846 | 0.339248 | ||||||||
\(703\) | −5.20868 | −0.196449 | ||||||||
\(704\) | 2.13961 | 0.0806397 | ||||||||
\(705\) | 13.4485 | 0.506498 | ||||||||
\(706\) | 27.7700 | 1.04514 | ||||||||
\(707\) | 2.08371 | 0.0783659 | ||||||||
\(708\) | −5.40678 | −0.203199 | ||||||||
\(709\) | −1.31186 | −0.0492679 | −0.0246339 | − | 0.999697i | \(-0.507842\pi\) | ||||
−0.0246339 | + | 0.999697i | \(0.507842\pi\) | |||||||
\(710\) | −2.02136 | −0.0758602 | ||||||||
\(711\) | −7.35464 | −0.275820 | ||||||||
\(712\) | 8.66555 | 0.324755 | ||||||||
\(713\) | 0.117986 | 0.00441860 | ||||||||
\(714\) | −0.115323 | −0.00431587 | ||||||||
\(715\) | 20.5084 | 0.766969 | ||||||||
\(716\) | 2.13053 | 0.0796216 | ||||||||
\(717\) | 4.55024 | 0.169932 | ||||||||
\(718\) | 32.5443 | 1.21454 | ||||||||
\(719\) | 12.0334 | 0.448770 | 0.224385 | − | 0.974501i | \(-0.427963\pi\) | ||||
0.224385 | + | 0.974501i | \(0.427963\pi\) | |||||||
\(720\) | −8.20941 | −0.305947 | ||||||||
\(721\) | 4.69630 | 0.174899 | ||||||||
\(722\) | 15.0346 | 0.559528 | ||||||||
\(723\) | −9.49557 | −0.353144 | ||||||||
\(724\) | −0.133121 | −0.00494738 | ||||||||
\(725\) | 20.8868 | 0.775715 | ||||||||
\(726\) | 3.09769 | 0.114966 | ||||||||
\(727\) | 32.5309 | 1.20650 | 0.603251 | − | 0.797551i | \(-0.293872\pi\) | ||||
0.603251 | + | 0.797551i | \(0.293872\pi\) | |||||||
\(728\) | −3.23107 | −0.119751 | ||||||||
\(729\) | −15.2356 | −0.564280 | ||||||||
\(730\) | 2.30411 | 0.0852790 | ||||||||
\(731\) | 2.03348 | 0.0752109 | ||||||||
\(732\) | −6.34302 | −0.234445 | ||||||||
\(733\) | −38.9318 | −1.43798 | −0.718989 | − | 0.695022i | \(-0.755395\pi\) | ||||
−0.718989 | + | 0.695022i | \(0.755395\pi\) | |||||||
\(734\) | −1.36993 | −0.0505650 | ||||||||
\(735\) | 1.43092 | 0.0527801 | ||||||||
\(736\) | 0.0927620 | 0.00341925 | ||||||||
\(737\) | 19.8804 | 0.732305 | ||||||||
\(738\) | −22.5896 | −0.831536 | ||||||||
\(739\) | 11.4812 | 0.422344 | 0.211172 | − | 0.977449i | \(-0.432272\pi\) | ||||
0.211172 | + | 0.977449i | \(0.432272\pi\) | |||||||
\(740\) | 7.75946 | 0.285243 | ||||||||
\(741\) | −3.10353 | −0.114011 | ||||||||
\(742\) | −12.5678 | −0.461380 | ||||||||
\(743\) | 33.0620 | 1.21293 | 0.606463 | − | 0.795112i | \(-0.292588\pi\) | ||||
0.606463 | + | 0.795112i | \(0.292588\pi\) | |||||||
\(744\) | 0.613512 | 0.0224924 | ||||||||
\(745\) | 9.80019 | 0.359051 | ||||||||
\(746\) | −27.5413 | −1.00836 | ||||||||
\(747\) | −1.27924 | −0.0468049 | ||||||||
\(748\) | 0.511550 | 0.0187041 | ||||||||
\(749\) | −4.74890 | −0.173521 | ||||||||
\(750\) | 1.71660 | 0.0626813 | ||||||||
\(751\) | −25.2421 | −0.921098 | −0.460549 | − | 0.887634i | \(-0.652347\pi\) | ||||
−0.460549 | + | 0.887634i | \(0.652347\pi\) | |||||||
\(752\) | 9.39850 | 0.342728 | ||||||||
\(753\) | 14.0931 | 0.513581 | ||||||||
\(754\) | −17.7580 | −0.646708 | ||||||||
\(755\) | −19.4689 | −0.708548 | ||||||||
\(756\) | −2.78189 | −0.101176 | ||||||||
\(757\) | −31.7867 | −1.15531 | −0.577653 | − | 0.816282i | \(-0.696031\pi\) | ||||
−0.577653 | + | 0.816282i | \(0.696031\pi\) | |||||||
\(758\) | 2.55245 | 0.0927091 | ||||||||
\(759\) | −0.0957346 | −0.00347495 | ||||||||
\(760\) | 5.90739 | 0.214284 | ||||||||
\(761\) | 15.1575 | 0.549460 | 0.274730 | − | 0.961521i | \(-0.411412\pi\) | ||||
0.274730 | + | 0.961521i | \(0.411412\pi\) | |||||||
\(762\) | 0.344190 | 0.0124687 | ||||||||
\(763\) | 13.9853 | 0.506302 | ||||||||
\(764\) | −3.11563 | −0.112720 | ||||||||
\(765\) | −1.96275 | −0.0709634 | ||||||||
\(766\) | 33.6175 | 1.21465 | ||||||||
\(767\) | −36.2176 | −1.30774 | ||||||||
\(768\) | 0.482352 | 0.0174054 | ||||||||
\(769\) | −47.5970 | −1.71639 | −0.858195 | − | 0.513324i | \(-0.828414\pi\) | ||||
−0.858195 | + | 0.513324i | \(0.828414\pi\) | |||||||
\(770\) | −6.34724 | −0.228739 | ||||||||
\(771\) | −9.90693 | −0.356789 | ||||||||
\(772\) | 16.5168 | 0.594453 | ||||||||
\(773\) | −11.0673 | −0.398064 | −0.199032 | − | 0.979993i | \(-0.563780\pi\) | ||||
−0.199032 | + | 0.979993i | \(0.563780\pi\) | |||||||
\(774\) | 23.5368 | 0.846014 | ||||||||
\(775\) | −4.83373 | −0.173633 | ||||||||
\(776\) | −8.48519 | −0.304601 | ||||||||
\(777\) | 1.26167 | 0.0452621 | ||||||||
\(778\) | −8.37623 | −0.300302 | ||||||||
\(779\) | 16.2552 | 0.582404 | ||||||||
\(780\) | 4.62338 | 0.165544 | ||||||||
\(781\) | 1.45790 | 0.0521678 | ||||||||
\(782\) | 0.0221780 | 0.000793085 0 | ||||||||
\(783\) | −15.2893 | −0.546394 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −27.8134 | −0.992702 | ||||||||
\(786\) | −6.21653 | −0.221736 | ||||||||
\(787\) | 21.1935 | 0.755466 | 0.377733 | − | 0.925915i | \(-0.376704\pi\) | ||||
0.377733 | + | 0.925915i | \(0.376704\pi\) | |||||||
\(788\) | 2.22701 | 0.0793338 | ||||||||
\(789\) | −8.04958 | −0.286573 | ||||||||
\(790\) | −7.88405 | −0.280502 | ||||||||
\(791\) | 18.6168 | 0.661938 | ||||||||
\(792\) | 5.92103 | 0.210395 | ||||||||
\(793\) | −42.4891 | −1.50883 | ||||||||
\(794\) | −7.71781 | −0.273895 | ||||||||
\(795\) | 17.9835 | 0.637810 | ||||||||
\(796\) | 15.1913 | 0.538442 | ||||||||
\(797\) | −2.94749 | −0.104406 | −0.0522028 | − | 0.998637i | \(-0.516624\pi\) | ||||
−0.0522028 | + | 0.998637i | \(0.516624\pi\) | |||||||
\(798\) | 0.960528 | 0.0340023 | ||||||||
\(799\) | 2.24705 | 0.0794948 | ||||||||
\(800\) | −3.80035 | −0.134363 | ||||||||
\(801\) | 23.9805 | 0.847309 | ||||||||
\(802\) | −10.3982 | −0.367173 | ||||||||
\(803\) | −1.66184 | −0.0586450 | ||||||||
\(804\) | 4.48183 | 0.158062 | ||||||||
\(805\) | −0.275182 | −0.00969889 | ||||||||
\(806\) | 4.10965 | 0.144756 | ||||||||
\(807\) | −10.6291 | −0.374162 | ||||||||
\(808\) | −2.08371 | −0.0733046 | ||||||||
\(809\) | 51.4707 | 1.80961 | 0.904807 | − | 0.425821i | \(-0.140015\pi\) | ||||
0.904807 | + | 0.425821i | \(0.140015\pi\) | |||||||
\(810\) | −20.6476 | −0.725482 | ||||||||
\(811\) | 6.07227 | 0.213226 | 0.106613 | − | 0.994301i | \(-0.465999\pi\) | ||||
0.106613 | + | 0.994301i | \(0.465999\pi\) | |||||||
\(812\) | 5.49601 | 0.192872 | ||||||||
\(813\) | −5.77215 | −0.202438 | ||||||||
\(814\) | −5.59650 | −0.196157 | ||||||||
\(815\) | 42.3379 | 1.48303 | ||||||||
\(816\) | 0.115323 | 0.00403713 | ||||||||
\(817\) | −16.9368 | −0.592544 | ||||||||
\(818\) | −39.0810 | −1.36643 | ||||||||
\(819\) | −8.94145 | −0.312439 | ||||||||
\(820\) | −24.2157 | −0.845649 | ||||||||
\(821\) | −25.4579 | −0.888487 | −0.444243 | − | 0.895906i | \(-0.646527\pi\) | ||||
−0.444243 | + | 0.895906i | \(0.646527\pi\) | |||||||
\(822\) | 1.85753 | 0.0647888 | ||||||||
\(823\) | −5.89889 | −0.205623 | −0.102811 | − | 0.994701i | \(-0.532784\pi\) | ||||
−0.102811 | + | 0.994701i | \(0.532784\pi\) | |||||||
\(824\) | −4.69630 | −0.163603 | ||||||||
\(825\) | 3.92214 | 0.136551 | ||||||||
\(826\) | 11.2092 | 0.390018 | ||||||||
\(827\) | 48.7745 | 1.69606 | 0.848028 | − | 0.529952i | \(-0.177790\pi\) | ||||
0.848028 | + | 0.529952i | \(0.177790\pi\) | |||||||
\(828\) | 0.256704 | 0.00892107 | ||||||||
\(829\) | −3.12935 | −0.108687 | −0.0543434 | − | 0.998522i | \(-0.517307\pi\) | ||||
−0.0543434 | + | 0.998522i | \(0.517307\pi\) | |||||||
\(830\) | −1.37132 | −0.0475993 | ||||||||
\(831\) | 2.35616 | 0.0817344 | ||||||||
\(832\) | 3.23107 | 0.112017 | ||||||||
\(833\) | 0.239086 | 0.00828382 | ||||||||
\(834\) | −6.86505 | −0.237717 | ||||||||
\(835\) | 40.1465 | 1.38933 | ||||||||
\(836\) | −4.26070 | −0.147359 | ||||||||
\(837\) | 3.53833 | 0.122303 | ||||||||
\(838\) | −25.0634 | −0.865800 | ||||||||
\(839\) | −7.40192 | −0.255543 | −0.127771 | − | 0.991804i | \(-0.540782\pi\) | ||||
−0.127771 | + | 0.991804i | \(0.540782\pi\) | |||||||
\(840\) | −1.43092 | −0.0493713 | ||||||||
\(841\) | 1.20616 | 0.0415918 | ||||||||
\(842\) | 15.6053 | 0.537796 | ||||||||
\(843\) | 7.91317 | 0.272544 | ||||||||
\(844\) | −26.0216 | −0.895699 | ||||||||
\(845\) | −7.59496 | −0.261275 | ||||||||
\(846\) | 26.0088 | 0.894201 | ||||||||
\(847\) | −6.42206 | −0.220665 | ||||||||
\(848\) | 12.5678 | 0.431582 | ||||||||
\(849\) | −14.5953 | −0.500910 | ||||||||
\(850\) | −0.908609 | −0.0311650 | ||||||||
\(851\) | −0.242634 | −0.00831738 | ||||||||
\(852\) | 0.328668 | 0.0112600 | ||||||||
\(853\) | 16.3931 | 0.561288 | 0.280644 | − | 0.959812i | \(-0.409452\pi\) | ||||
0.280644 | + | 0.959812i | \(0.409452\pi\) | |||||||
\(854\) | 13.1502 | 0.449990 | ||||||||
\(855\) | 16.3477 | 0.559081 | ||||||||
\(856\) | 4.74890 | 0.162314 | ||||||||
\(857\) | 5.74407 | 0.196214 | 0.0981068 | − | 0.995176i | \(-0.468721\pi\) | ||||
0.0981068 | + | 0.995176i | \(0.468721\pi\) | |||||||
\(858\) | −3.33461 | −0.113842 | ||||||||
\(859\) | −24.8230 | −0.846951 | −0.423476 | − | 0.905907i | \(-0.639190\pi\) | ||||
−0.423476 | + | 0.905907i | \(0.639190\pi\) | |||||||
\(860\) | 25.2311 | 0.860373 | ||||||||
\(861\) | −3.93742 | −0.134187 | ||||||||
\(862\) | 1.00000 | 0.0340601 | ||||||||
\(863\) | −19.1481 | −0.651809 | −0.325905 | − | 0.945403i | \(-0.605669\pi\) | ||||
−0.325905 | + | 0.945403i | \(0.605669\pi\) | |||||||
\(864\) | 2.78189 | 0.0946417 | ||||||||
\(865\) | −31.9230 | −1.08541 | ||||||||
\(866\) | 18.6033 | 0.632165 | ||||||||
\(867\) | −8.17241 | −0.277550 | ||||||||
\(868\) | −1.27192 | −0.0431717 | ||||||||
\(869\) | 5.68636 | 0.192897 | ||||||||
\(870\) | −7.86433 | −0.266626 | ||||||||
\(871\) | 30.0218 | 1.01725 | ||||||||
\(872\) | −13.9853 | −0.473602 | ||||||||
\(873\) | −23.4814 | −0.794724 | ||||||||
\(874\) | −0.184721 | −0.00624827 | ||||||||
\(875\) | −3.55881 | −0.120310 | ||||||||
\(876\) | −0.374643 | −0.0126580 | ||||||||
\(877\) | −13.6165 | −0.459796 | −0.229898 | − | 0.973215i | \(-0.573839\pi\) | ||||
−0.229898 | + | 0.973215i | \(0.573839\pi\) | |||||||
\(878\) | −21.8233 | −0.736501 | ||||||||
\(879\) | 5.48199 | 0.184903 | ||||||||
\(880\) | 6.34724 | 0.213965 | ||||||||
\(881\) | 40.1314 | 1.35206 | 0.676031 | − | 0.736873i | \(-0.263699\pi\) | ||||
0.676031 | + | 0.736873i | \(0.263699\pi\) | |||||||
\(882\) | 2.76734 | 0.0931811 | ||||||||
\(883\) | −7.47828 | −0.251664 | −0.125832 | − | 0.992052i | \(-0.540160\pi\) | ||||
−0.125832 | + | 0.992052i | \(0.540160\pi\) | |||||||
\(884\) | 0.772501 | 0.0259820 | ||||||||
\(885\) | −16.0394 | −0.539159 | ||||||||
\(886\) | −17.6938 | −0.594434 | ||||||||
\(887\) | −31.9660 | −1.07331 | −0.536657 | − | 0.843800i | \(-0.680313\pi\) | ||||
−0.536657 | + | 0.843800i | \(0.680313\pi\) | |||||||
\(888\) | −1.26167 | −0.0423389 | ||||||||
\(889\) | −0.713567 | −0.0239323 | ||||||||
\(890\) | 25.7067 | 0.861690 | ||||||||
\(891\) | 14.8920 | 0.498902 | ||||||||
\(892\) | −23.9130 | −0.800665 | ||||||||
\(893\) | −18.7156 | −0.626295 | ||||||||
\(894\) | −1.59349 | −0.0532942 | ||||||||
\(895\) | 6.32030 | 0.211264 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −0.144571 | −0.00482707 | ||||||||
\(898\) | 16.6261 | 0.554822 | ||||||||
\(899\) | −6.99048 | −0.233145 | ||||||||
\(900\) | −10.5168 | −0.350562 | ||||||||
\(901\) | 3.00479 | 0.100104 | ||||||||
\(902\) | 17.4656 | 0.581539 | ||||||||
\(903\) | 4.10251 | 0.136523 | ||||||||
\(904\) | −18.6168 | −0.619186 | ||||||||
\(905\) | −0.394907 | −0.0131272 | ||||||||
\(906\) | 3.16560 | 0.105170 | ||||||||
\(907\) | 30.3328 | 1.00718 | 0.503591 | − | 0.863942i | \(-0.332012\pi\) | ||||
0.503591 | + | 0.863942i | \(0.332012\pi\) | |||||||
\(908\) | 23.4759 | 0.779075 | ||||||||
\(909\) | −5.76632 | −0.191257 | ||||||||
\(910\) | −9.58508 | −0.317742 | ||||||||
\(911\) | 21.3856 | 0.708537 | 0.354268 | − | 0.935144i | \(-0.384730\pi\) | ||||
0.354268 | + | 0.935144i | \(0.384730\pi\) | |||||||
\(912\) | −0.960528 | −0.0318063 | ||||||||
\(913\) | 0.989066 | 0.0327333 | ||||||||
\(914\) | −1.44455 | −0.0477813 | ||||||||
\(915\) | −18.8168 | −0.622064 | ||||||||
\(916\) | 16.6106 | 0.548830 | ||||||||
\(917\) | 12.8879 | 0.425597 | ||||||||
\(918\) | 0.665109 | 0.0219519 | ||||||||
\(919\) | −27.2282 | −0.898176 | −0.449088 | − | 0.893487i | \(-0.648251\pi\) | ||||
−0.449088 | + | 0.893487i | \(0.648251\pi\) | |||||||
\(920\) | 0.275182 | 0.00907248 | ||||||||
\(921\) | −8.40650 | −0.277004 | ||||||||
\(922\) | 3.80273 | 0.125236 | ||||||||
\(923\) | 2.20160 | 0.0724666 | ||||||||
\(924\) | 1.03205 | 0.0339518 | ||||||||
\(925\) | 9.94043 | 0.326839 | ||||||||
\(926\) | 11.8740 | 0.390204 | ||||||||
\(927\) | −12.9963 | −0.426853 | ||||||||
\(928\) | −5.49601 | −0.180415 | ||||||||
\(929\) | −59.9752 | −1.96772 | −0.983861 | − | 0.178934i | \(-0.942735\pi\) | ||||
−0.983861 | + | 0.178934i | \(0.942735\pi\) | |||||||
\(930\) | 1.82001 | 0.0596804 | ||||||||
\(931\) | −1.99134 | −0.0652636 | ||||||||
\(932\) | −9.15714 | −0.299952 | ||||||||
\(933\) | −6.16868 | −0.201953 | ||||||||
\(934\) | 23.2619 | 0.761154 | ||||||||
\(935\) | 1.51753 | 0.0496287 | ||||||||
\(936\) | 8.94145 | 0.292260 | ||||||||
\(937\) | −40.9136 | −1.33659 | −0.668295 | − | 0.743896i | \(-0.732976\pi\) | ||||
−0.668295 | + | 0.743896i | \(0.732976\pi\) | |||||||
\(938\) | −9.29161 | −0.303382 | ||||||||
\(939\) | 10.7332 | 0.350265 | ||||||||
\(940\) | 27.8810 | 0.909378 | ||||||||
\(941\) | −45.0824 | −1.46965 | −0.734823 | − | 0.678259i | \(-0.762735\pi\) | ||||
−0.734823 | + | 0.678259i | \(0.762735\pi\) | |||||||
\(942\) | 4.52239 | 0.147347 | ||||||||
\(943\) | 0.757212 | 0.0246582 | ||||||||
\(944\) | −11.2092 | −0.364828 | ||||||||
\(945\) | −8.25257 | −0.268456 | ||||||||
\(946\) | −18.1979 | −0.591665 | ||||||||
\(947\) | 16.1246 | 0.523977 | 0.261989 | − | 0.965071i | \(-0.415622\pi\) | ||||
0.261989 | + | 0.965071i | \(0.415622\pi\) | |||||||
\(948\) | 1.28193 | 0.0416351 | ||||||||
\(949\) | −2.50957 | −0.0814641 | ||||||||
\(950\) | 7.56780 | 0.245532 | ||||||||
\(951\) | 3.18768 | 0.103368 | ||||||||
\(952\) | −0.239086 | −0.00774881 | ||||||||
\(953\) | −12.4513 | −0.403336 | −0.201668 | − | 0.979454i | \(-0.564636\pi\) | ||||
−0.201668 | + | 0.979454i | \(0.564636\pi\) | |||||||
\(954\) | 34.7795 | 1.12603 | ||||||||
\(955\) | −9.24264 | −0.299085 | ||||||||
\(956\) | 9.43344 | 0.305099 | ||||||||
\(957\) | 5.67214 | 0.183354 | ||||||||
\(958\) | −1.74403 | −0.0563472 | ||||||||
\(959\) | −3.85098 | −0.124355 | ||||||||
\(960\) | 1.43092 | 0.0461826 | ||||||||
\(961\) | −29.3822 | −0.947814 | ||||||||
\(962\) | −8.45138 | −0.272483 | ||||||||
\(963\) | 13.1418 | 0.423489 | ||||||||
\(964\) | −19.6860 | −0.634042 | ||||||||
\(965\) | 48.9977 | 1.57729 | ||||||||
\(966\) | 0.0447439 | 0.00143961 | ||||||||
\(967\) | −11.3303 | −0.364358 | −0.182179 | − | 0.983265i | \(-0.558315\pi\) | ||||
−0.182179 | + | 0.983265i | \(0.558315\pi\) | |||||||
\(968\) | 6.42206 | 0.206413 | ||||||||
\(969\) | −0.229648 | −0.00737737 | ||||||||
\(970\) | −25.1716 | −0.808213 | ||||||||
\(971\) | 28.5218 | 0.915308 | 0.457654 | − | 0.889130i | \(-0.348690\pi\) | ||||
0.457654 | + | 0.889130i | \(0.348690\pi\) | |||||||
\(972\) | 11.7029 | 0.375371 | ||||||||
\(973\) | 14.2324 | 0.456271 | ||||||||
\(974\) | −17.9150 | −0.574035 | ||||||||
\(975\) | 5.92289 | 0.189684 | ||||||||
\(976\) | −13.1502 | −0.420927 | ||||||||
\(977\) | 18.0110 | 0.576222 | 0.288111 | − | 0.957597i | \(-0.406973\pi\) | ||||
0.288111 | + | 0.957597i | \(0.406973\pi\) | |||||||
\(978\) | −6.88405 | −0.220128 | ||||||||
\(979\) | −18.5409 | −0.592570 | ||||||||
\(980\) | 2.96654 | 0.0947626 | ||||||||
\(981\) | −38.7020 | −1.23566 | ||||||||
\(982\) | −15.3446 | −0.489665 | ||||||||
\(983\) | 22.1089 | 0.705164 | 0.352582 | − | 0.935781i | \(-0.385304\pi\) | ||||
0.352582 | + | 0.935781i | \(0.385304\pi\) | |||||||
\(984\) | 3.93742 | 0.125520 | ||||||||
\(985\) | 6.60650 | 0.210501 | ||||||||
\(986\) | −1.31402 | −0.0418468 | ||||||||
\(987\) | 4.53339 | 0.144299 | ||||||||
\(988\) | −6.43416 | −0.204698 | ||||||||
\(989\) | −0.788962 | −0.0250875 | ||||||||
\(990\) | 17.5650 | 0.558251 | ||||||||
\(991\) | −53.2704 | −1.69219 | −0.846094 | − | 0.533033i | \(-0.821052\pi\) | ||||
−0.846094 | + | 0.533033i | \(0.821052\pi\) | |||||||
\(992\) | 1.27192 | 0.0403834 | ||||||||
\(993\) | 5.82879 | 0.184971 | ||||||||
\(994\) | −0.681386 | −0.0216122 | ||||||||
\(995\) | 45.0656 | 1.42868 | ||||||||
\(996\) | 0.222974 | 0.00706520 | ||||||||
\(997\) | −43.5453 | −1.37909 | −0.689547 | − | 0.724241i | \(-0.742190\pi\) | ||||
−0.689547 | + | 0.724241i | \(0.742190\pi\) | |||||||
\(998\) | −25.0219 | −0.792056 | ||||||||
\(999\) | −7.27647 | −0.230217 |
(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 | 6034.2.a.p.1.16 | ✓ | 27 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6034.2.a.p.1.16 | ✓ | 27 | 1.1 | even | 1 | trivial |