Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6026,2,Mod(1,6026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6026, 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("6026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6026 = 2 \cdot 23 \cdot 131 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6026.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: | \(48.1178522580\) |
Analytic rank: | \(1\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.48980 | 0.860135 | 0.430068 | − | 0.902797i | \(-0.358490\pi\) | ||||
0.430068 | + | 0.902797i | \(0.358490\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.56615 | 1.59483 | 0.797415 | − | 0.603431i | \(-0.206200\pi\) | ||||
0.797415 | + | 0.603431i | \(0.206200\pi\) | |||||||
\(6\) | −1.48980 | −0.608207 | ||||||||
\(7\) | −2.69745 | −1.01954 | −0.509771 | − | 0.860310i | \(-0.670270\pi\) | ||||
−0.509771 | + | 0.860310i | \(0.670270\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.780502 | −0.260167 | ||||||||
\(10\) | −3.56615 | −1.12772 | ||||||||
\(11\) | −4.79381 | −1.44539 | −0.722694 | − | 0.691169i | \(-0.757096\pi\) | ||||
−0.722694 | + | 0.691169i | \(0.757096\pi\) | |||||||
\(12\) | 1.48980 | 0.430068 | ||||||||
\(13\) | 0.746865 | 0.207143 | 0.103572 | − | 0.994622i | \(-0.466973\pi\) | ||||
0.103572 | + | 0.994622i | \(0.466973\pi\) | |||||||
\(14\) | 2.69745 | 0.720925 | ||||||||
\(15\) | 5.31284 | 1.37177 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.10189 | 0.994854 | 0.497427 | − | 0.867506i | \(-0.334278\pi\) | ||||
0.497427 | + | 0.867506i | \(0.334278\pi\) | |||||||
\(18\) | 0.780502 | 0.183966 | ||||||||
\(19\) | 4.65428 | 1.06776 | 0.533882 | − | 0.845559i | \(-0.320733\pi\) | ||||
0.533882 | + | 0.845559i | \(0.320733\pi\) | |||||||
\(20\) | 3.56615 | 0.797415 | ||||||||
\(21\) | −4.01866 | −0.876944 | ||||||||
\(22\) | 4.79381 | 1.02204 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −1.48980 | −0.304104 | ||||||||
\(25\) | 7.71742 | 1.54348 | ||||||||
\(26\) | −0.746865 | −0.146472 | ||||||||
\(27\) | −5.63218 | −1.08391 | ||||||||
\(28\) | −2.69745 | −0.509771 | ||||||||
\(29\) | −6.16822 | −1.14541 | −0.572705 | − | 0.819762i | \(-0.694106\pi\) | ||||
−0.572705 | + | 0.819762i | \(0.694106\pi\) | |||||||
\(30\) | −5.31284 | −0.969988 | ||||||||
\(31\) | −8.26320 | −1.48411 | −0.742057 | − | 0.670337i | \(-0.766150\pi\) | ||||
−0.742057 | + | 0.670337i | \(0.766150\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −7.14180 | −1.24323 | ||||||||
\(34\) | −4.10189 | −0.703468 | ||||||||
\(35\) | −9.61952 | −1.62600 | ||||||||
\(36\) | −0.780502 | −0.130084 | ||||||||
\(37\) | −2.87867 | −0.473251 | −0.236625 | − | 0.971601i | \(-0.576041\pi\) | ||||
−0.236625 | + | 0.971601i | \(0.576041\pi\) | |||||||
\(38\) | −4.65428 | −0.755024 | ||||||||
\(39\) | 1.11268 | 0.178171 | ||||||||
\(40\) | −3.56615 | −0.563858 | ||||||||
\(41\) | −5.19872 | −0.811903 | −0.405951 | − | 0.913895i | \(-0.633060\pi\) | ||||
−0.405951 | + | 0.913895i | \(0.633060\pi\) | |||||||
\(42\) | 4.01866 | 0.620093 | ||||||||
\(43\) | 1.25728 | 0.191734 | 0.0958668 | − | 0.995394i | \(-0.469438\pi\) | ||||
0.0958668 | + | 0.995394i | \(0.469438\pi\) | |||||||
\(44\) | −4.79381 | −0.722694 | ||||||||
\(45\) | −2.78339 | −0.414923 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −6.72119 | −0.980387 | −0.490193 | − | 0.871614i | \(-0.663074\pi\) | ||||
−0.490193 | + | 0.871614i | \(0.663074\pi\) | |||||||
\(48\) | 1.48980 | 0.215034 | ||||||||
\(49\) | 0.276254 | 0.0394649 | ||||||||
\(50\) | −7.71742 | −1.09141 | ||||||||
\(51\) | 6.11098 | 0.855709 | ||||||||
\(52\) | 0.746865 | 0.103572 | ||||||||
\(53\) | 2.81932 | 0.387264 | 0.193632 | − | 0.981074i | \(-0.437973\pi\) | ||||
0.193632 | + | 0.981074i | \(0.437973\pi\) | |||||||
\(54\) | 5.63218 | 0.766443 | ||||||||
\(55\) | −17.0954 | −2.30515 | ||||||||
\(56\) | 2.69745 | 0.360462 | ||||||||
\(57\) | 6.93393 | 0.918422 | ||||||||
\(58\) | 6.16822 | 0.809927 | ||||||||
\(59\) | 5.55324 | 0.722971 | 0.361485 | − | 0.932378i | \(-0.382270\pi\) | ||||
0.361485 | + | 0.932378i | \(0.382270\pi\) | |||||||
\(60\) | 5.31284 | 0.685885 | ||||||||
\(61\) | −3.81590 | −0.488576 | −0.244288 | − | 0.969703i | \(-0.578554\pi\) | ||||
−0.244288 | + | 0.969703i | \(0.578554\pi\) | |||||||
\(62\) | 8.26320 | 1.04943 | ||||||||
\(63\) | 2.10537 | 0.265252 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.66343 | 0.330358 | ||||||||
\(66\) | 7.14180 | 0.879095 | ||||||||
\(67\) | −10.3918 | −1.26956 | −0.634778 | − | 0.772694i | \(-0.718909\pi\) | ||||
−0.634778 | + | 0.772694i | \(0.718909\pi\) | |||||||
\(68\) | 4.10189 | 0.497427 | ||||||||
\(69\) | −1.48980 | −0.179351 | ||||||||
\(70\) | 9.61952 | 1.14975 | ||||||||
\(71\) | 9.37733 | 1.11288 | 0.556442 | − | 0.830886i | \(-0.312166\pi\) | ||||
0.556442 | + | 0.830886i | \(0.312166\pi\) | |||||||
\(72\) | 0.780502 | 0.0919831 | ||||||||
\(73\) | −2.73400 | −0.319991 | −0.159995 | − | 0.987118i | \(-0.551148\pi\) | ||||
−0.159995 | + | 0.987118i | \(0.551148\pi\) | |||||||
\(74\) | 2.87867 | 0.334639 | ||||||||
\(75\) | 11.4974 | 1.32761 | ||||||||
\(76\) | 4.65428 | 0.533882 | ||||||||
\(77\) | 12.9311 | 1.47363 | ||||||||
\(78\) | −1.11268 | −0.125986 | ||||||||
\(79\) | −5.86082 | −0.659394 | −0.329697 | − | 0.944087i | \(-0.606947\pi\) | ||||
−0.329697 | + | 0.944087i | \(0.606947\pi\) | |||||||
\(80\) | 3.56615 | 0.398708 | ||||||||
\(81\) | −6.04931 | −0.672145 | ||||||||
\(82\) | 5.19872 | 0.574102 | ||||||||
\(83\) | −2.35445 | −0.258434 | −0.129217 | − | 0.991616i | \(-0.541246\pi\) | ||||
−0.129217 | + | 0.991616i | \(0.541246\pi\) | |||||||
\(84\) | −4.01866 | −0.438472 | ||||||||
\(85\) | 14.6279 | 1.58662 | ||||||||
\(86\) | −1.25728 | −0.135576 | ||||||||
\(87\) | −9.18940 | −0.985208 | ||||||||
\(88\) | 4.79381 | 0.511022 | ||||||||
\(89\) | −2.14139 | −0.226987 | −0.113494 | − | 0.993539i | \(-0.536204\pi\) | ||||
−0.113494 | + | 0.993539i | \(0.536204\pi\) | |||||||
\(90\) | 2.78339 | 0.293395 | ||||||||
\(91\) | −2.01463 | −0.211191 | ||||||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | −12.3105 | −1.27654 | ||||||||
\(94\) | 6.72119 | 0.693238 | ||||||||
\(95\) | 16.5979 | 1.70290 | ||||||||
\(96\) | −1.48980 | −0.152052 | ||||||||
\(97\) | −5.78968 | −0.587853 | −0.293927 | − | 0.955828i | \(-0.594962\pi\) | ||||
−0.293927 | + | 0.955828i | \(0.594962\pi\) | |||||||
\(98\) | −0.276254 | −0.0279059 | ||||||||
\(99\) | 3.74158 | 0.376043 | ||||||||
\(100\) | 7.71742 | 0.771742 | ||||||||
\(101\) | 4.56806 | 0.454539 | 0.227269 | − | 0.973832i | \(-0.427020\pi\) | ||||
0.227269 | + | 0.973832i | \(0.427020\pi\) | |||||||
\(102\) | −6.11098 | −0.605077 | ||||||||
\(103\) | 7.62144 | 0.750963 | 0.375481 | − | 0.926830i | \(-0.377477\pi\) | ||||
0.375481 | + | 0.926830i | \(0.377477\pi\) | |||||||
\(104\) | −0.746865 | −0.0732362 | ||||||||
\(105\) | −14.3311 | −1.39858 | ||||||||
\(106\) | −2.81932 | −0.273837 | ||||||||
\(107\) | −10.1233 | −0.978661 | −0.489330 | − | 0.872099i | \(-0.662759\pi\) | ||||
−0.489330 | + | 0.872099i | \(0.662759\pi\) | |||||||
\(108\) | −5.63218 | −0.541957 | ||||||||
\(109\) | −0.727196 | −0.0696527 | −0.0348264 | − | 0.999393i | \(-0.511088\pi\) | ||||
−0.0348264 | + | 0.999393i | \(0.511088\pi\) | |||||||
\(110\) | 17.0954 | 1.62999 | ||||||||
\(111\) | −4.28864 | −0.407060 | ||||||||
\(112\) | −2.69745 | −0.254885 | ||||||||
\(113\) | 13.1529 | 1.23732 | 0.618659 | − | 0.785660i | \(-0.287676\pi\) | ||||
0.618659 | + | 0.785660i | \(0.287676\pi\) | |||||||
\(114\) | −6.93393 | −0.649422 | ||||||||
\(115\) | −3.56615 | −0.332545 | ||||||||
\(116\) | −6.16822 | −0.572705 | ||||||||
\(117\) | −0.582930 | −0.0538919 | ||||||||
\(118\) | −5.55324 | −0.511217 | ||||||||
\(119\) | −11.0646 | −1.01429 | ||||||||
\(120\) | −5.31284 | −0.484994 | ||||||||
\(121\) | 11.9806 | 1.08914 | ||||||||
\(122\) | 3.81590 | 0.345476 | ||||||||
\(123\) | −7.74503 | −0.698346 | ||||||||
\(124\) | −8.26320 | −0.742057 | ||||||||
\(125\) | 9.69074 | 0.866766 | ||||||||
\(126\) | −2.10537 | −0.187561 | ||||||||
\(127\) | −9.25234 | −0.821012 | −0.410506 | − | 0.911858i | \(-0.634648\pi\) | ||||
−0.410506 | + | 0.911858i | \(0.634648\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.87310 | 0.164917 | ||||||||
\(130\) | −2.66343 | −0.233599 | ||||||||
\(131\) | −1.00000 | −0.0873704 | ||||||||
\(132\) | −7.14180 | −0.621614 | ||||||||
\(133\) | −12.5547 | −1.08863 | ||||||||
\(134\) | 10.3918 | 0.897712 | ||||||||
\(135\) | −20.0852 | −1.72866 | ||||||||
\(136\) | −4.10189 | −0.351734 | ||||||||
\(137\) | −16.9974 | −1.45219 | −0.726093 | − | 0.687597i | \(-0.758666\pi\) | ||||
−0.726093 | + | 0.687597i | \(0.758666\pi\) | |||||||
\(138\) | 1.48980 | 0.126820 | ||||||||
\(139\) | −1.64747 | −0.139737 | −0.0698683 | − | 0.997556i | \(-0.522258\pi\) | ||||
−0.0698683 | + | 0.997556i | \(0.522258\pi\) | |||||||
\(140\) | −9.61952 | −0.812998 | ||||||||
\(141\) | −10.0132 | −0.843265 | ||||||||
\(142\) | −9.37733 | −0.786928 | ||||||||
\(143\) | −3.58033 | −0.299402 | ||||||||
\(144\) | −0.780502 | −0.0650419 | ||||||||
\(145\) | −21.9968 | −1.82674 | ||||||||
\(146\) | 2.73400 | 0.226268 | ||||||||
\(147\) | 0.411563 | 0.0339451 | ||||||||
\(148\) | −2.87867 | −0.236625 | ||||||||
\(149\) | 5.21941 | 0.427591 | 0.213795 | − | 0.976878i | \(-0.431417\pi\) | ||||
0.213795 | + | 0.976878i | \(0.431417\pi\) | |||||||
\(150\) | −11.4974 | −0.938759 | ||||||||
\(151\) | −0.660230 | −0.0537288 | −0.0268644 | − | 0.999639i | \(-0.508552\pi\) | ||||
−0.0268644 | + | 0.999639i | \(0.508552\pi\) | |||||||
\(152\) | −4.65428 | −0.377512 | ||||||||
\(153\) | −3.20153 | −0.258828 | ||||||||
\(154\) | −12.9311 | −1.04202 | ||||||||
\(155\) | −29.4678 | −2.36691 | ||||||||
\(156\) | 1.11268 | 0.0890856 | ||||||||
\(157\) | 9.01181 | 0.719221 | 0.359610 | − | 0.933103i | \(-0.382910\pi\) | ||||
0.359610 | + | 0.933103i | \(0.382910\pi\) | |||||||
\(158\) | 5.86082 | 0.466262 | ||||||||
\(159\) | 4.20022 | 0.333099 | ||||||||
\(160\) | −3.56615 | −0.281929 | ||||||||
\(161\) | 2.69745 | 0.212589 | ||||||||
\(162\) | 6.04931 | 0.475279 | ||||||||
\(163\) | 6.96678 | 0.545681 | 0.272840 | − | 0.962059i | \(-0.412037\pi\) | ||||
0.272840 | + | 0.962059i | \(0.412037\pi\) | |||||||
\(164\) | −5.19872 | −0.405951 | ||||||||
\(165\) | −25.4687 | −1.98274 | ||||||||
\(166\) | 2.35445 | 0.182740 | ||||||||
\(167\) | −12.9286 | −1.00045 | −0.500224 | − | 0.865896i | \(-0.666749\pi\) | ||||
−0.500224 | + | 0.865896i | \(0.666749\pi\) | |||||||
\(168\) | 4.01866 | 0.310046 | ||||||||
\(169\) | −12.4422 | −0.957092 | ||||||||
\(170\) | −14.6279 | −1.12191 | ||||||||
\(171\) | −3.63268 | −0.277798 | ||||||||
\(172\) | 1.25728 | 0.0958668 | ||||||||
\(173\) | −2.74653 | −0.208815 | −0.104407 | − | 0.994535i | \(-0.533295\pi\) | ||||
−0.104407 | + | 0.994535i | \(0.533295\pi\) | |||||||
\(174\) | 9.18940 | 0.696647 | ||||||||
\(175\) | −20.8174 | −1.57365 | ||||||||
\(176\) | −4.79381 | −0.361347 | ||||||||
\(177\) | 8.27321 | 0.621853 | ||||||||
\(178\) | 2.14139 | 0.160504 | ||||||||
\(179\) | −15.4429 | −1.15425 | −0.577127 | − | 0.816654i | \(-0.695826\pi\) | ||||
−0.577127 | + | 0.816654i | \(0.695826\pi\) | |||||||
\(180\) | −2.78339 | −0.207462 | ||||||||
\(181\) | 18.1904 | 1.35208 | 0.676040 | − | 0.736865i | \(-0.263694\pi\) | ||||
0.676040 | + | 0.736865i | \(0.263694\pi\) | |||||||
\(182\) | 2.01463 | 0.149335 | ||||||||
\(183\) | −5.68492 | −0.420242 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −10.2658 | −0.754755 | ||||||||
\(186\) | 12.3105 | 0.902649 | ||||||||
\(187\) | −19.6636 | −1.43795 | ||||||||
\(188\) | −6.72119 | −0.490193 | ||||||||
\(189\) | 15.1926 | 1.10510 | ||||||||
\(190\) | −16.5979 | −1.20413 | ||||||||
\(191\) | 2.00049 | 0.144750 | 0.0723751 | − | 0.997377i | \(-0.476942\pi\) | ||||
0.0723751 | + | 0.997377i | \(0.476942\pi\) | |||||||
\(192\) | 1.48980 | 0.107517 | ||||||||
\(193\) | −1.38564 | −0.0997404 | −0.0498702 | − | 0.998756i | \(-0.515881\pi\) | ||||
−0.0498702 | + | 0.998756i | \(0.515881\pi\) | |||||||
\(194\) | 5.78968 | 0.415675 | ||||||||
\(195\) | 3.96798 | 0.284153 | ||||||||
\(196\) | 0.276254 | 0.0197324 | ||||||||
\(197\) | 0.933591 | 0.0665156 | 0.0332578 | − | 0.999447i | \(-0.489412\pi\) | ||||
0.0332578 | + | 0.999447i | \(0.489412\pi\) | |||||||
\(198\) | −3.74158 | −0.265902 | ||||||||
\(199\) | 0.0385265 | 0.00273107 | 0.00136554 | − | 0.999999i | \(-0.499565\pi\) | ||||
0.00136554 | + | 0.999999i | \(0.499565\pi\) | |||||||
\(200\) | −7.71742 | −0.545704 | ||||||||
\(201\) | −15.4816 | −1.09199 | ||||||||
\(202\) | −4.56806 | −0.321407 | ||||||||
\(203\) | 16.6385 | 1.16779 | ||||||||
\(204\) | 6.11098 | 0.427854 | ||||||||
\(205\) | −18.5394 | −1.29485 | ||||||||
\(206\) | −7.62144 | −0.531011 | ||||||||
\(207\) | 0.780502 | 0.0542487 | ||||||||
\(208\) | 0.746865 | 0.0517858 | ||||||||
\(209\) | −22.3117 | −1.54333 | ||||||||
\(210\) | 14.3311 | 0.988943 | ||||||||
\(211\) | −1.69707 | −0.116831 | −0.0584155 | − | 0.998292i | \(-0.518605\pi\) | ||||
−0.0584155 | + | 0.998292i | \(0.518605\pi\) | |||||||
\(212\) | 2.81932 | 0.193632 | ||||||||
\(213\) | 13.9703 | 0.957231 | ||||||||
\(214\) | 10.1233 | 0.692018 | ||||||||
\(215\) | 4.48365 | 0.305783 | ||||||||
\(216\) | 5.63218 | 0.383222 | ||||||||
\(217\) | 22.2896 | 1.51312 | ||||||||
\(218\) | 0.727196 | 0.0492519 | ||||||||
\(219\) | −4.07311 | −0.275235 | ||||||||
\(220\) | −17.0954 | −1.15257 | ||||||||
\(221\) | 3.06356 | 0.206077 | ||||||||
\(222\) | 4.28864 | 0.287835 | ||||||||
\(223\) | 13.8360 | 0.926529 | 0.463265 | − | 0.886220i | \(-0.346678\pi\) | ||||
0.463265 | + | 0.886220i | \(0.346678\pi\) | |||||||
\(224\) | 2.69745 | 0.180231 | ||||||||
\(225\) | −6.02347 | −0.401565 | ||||||||
\(226\) | −13.1529 | −0.874915 | ||||||||
\(227\) | −10.5000 | −0.696910 | −0.348455 | − | 0.937326i | \(-0.613294\pi\) | ||||
−0.348455 | + | 0.937326i | \(0.613294\pi\) | |||||||
\(228\) | 6.93393 | 0.459211 | ||||||||
\(229\) | 12.3635 | 0.817005 | 0.408503 | − | 0.912757i | \(-0.366051\pi\) | ||||
0.408503 | + | 0.912757i | \(0.366051\pi\) | |||||||
\(230\) | 3.56615 | 0.235145 | ||||||||
\(231\) | 19.2647 | 1.26752 | ||||||||
\(232\) | 6.16822 | 0.404964 | ||||||||
\(233\) | 7.47482 | 0.489692 | 0.244846 | − | 0.969562i | \(-0.421263\pi\) | ||||
0.244846 | + | 0.969562i | \(0.421263\pi\) | |||||||
\(234\) | 0.582930 | 0.0381073 | ||||||||
\(235\) | −23.9688 | −1.56355 | ||||||||
\(236\) | 5.55324 | 0.361485 | ||||||||
\(237\) | −8.73144 | −0.567168 | ||||||||
\(238\) | 11.0646 | 0.717214 | ||||||||
\(239\) | 2.73435 | 0.176870 | 0.0884350 | − | 0.996082i | \(-0.471813\pi\) | ||||
0.0884350 | + | 0.996082i | \(0.471813\pi\) | |||||||
\(240\) | 5.31284 | 0.342942 | ||||||||
\(241\) | 25.7983 | 1.66181 | 0.830907 | − | 0.556412i | \(-0.187822\pi\) | ||||
0.830907 | + | 0.556412i | \(0.187822\pi\) | |||||||
\(242\) | −11.9806 | −0.770141 | ||||||||
\(243\) | 7.88431 | 0.505778 | ||||||||
\(244\) | −3.81590 | −0.244288 | ||||||||
\(245\) | 0.985164 | 0.0629398 | ||||||||
\(246\) | 7.74503 | 0.493805 | ||||||||
\(247\) | 3.47612 | 0.221180 | ||||||||
\(248\) | 8.26320 | 0.524714 | ||||||||
\(249\) | −3.50765 | −0.222288 | ||||||||
\(250\) | −9.69074 | −0.612896 | ||||||||
\(251\) | −16.1788 | −1.02120 | −0.510599 | − | 0.859819i | \(-0.670577\pi\) | ||||
−0.510599 | + | 0.859819i | \(0.670577\pi\) | |||||||
\(252\) | 2.10537 | 0.132626 | ||||||||
\(253\) | 4.79381 | 0.301384 | ||||||||
\(254\) | 9.25234 | 0.580543 | ||||||||
\(255\) | 21.7927 | 1.36471 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −20.7693 | −1.29555 | −0.647777 | − | 0.761830i | \(-0.724301\pi\) | ||||
−0.647777 | + | 0.761830i | \(0.724301\pi\) | |||||||
\(258\) | −1.87310 | −0.116614 | ||||||||
\(259\) | 7.76509 | 0.482499 | ||||||||
\(260\) | 2.66343 | 0.165179 | ||||||||
\(261\) | 4.81431 | 0.297998 | ||||||||
\(262\) | 1.00000 | 0.0617802 | ||||||||
\(263\) | −11.5028 | −0.709296 | −0.354648 | − | 0.935000i | \(-0.615399\pi\) | ||||
−0.354648 | + | 0.935000i | \(0.615399\pi\) | |||||||
\(264\) | 7.14180 | 0.439548 | ||||||||
\(265\) | 10.0541 | 0.617620 | ||||||||
\(266\) | 12.5547 | 0.769778 | ||||||||
\(267\) | −3.19024 | −0.195240 | ||||||||
\(268\) | −10.3918 | −0.634778 | ||||||||
\(269\) | 16.5846 | 1.01118 | 0.505590 | − | 0.862774i | \(-0.331275\pi\) | ||||
0.505590 | + | 0.862774i | \(0.331275\pi\) | |||||||
\(270\) | 20.0852 | 1.22235 | ||||||||
\(271\) | −7.01482 | −0.426120 | −0.213060 | − | 0.977039i | \(-0.568343\pi\) | ||||
−0.213060 | + | 0.977039i | \(0.568343\pi\) | |||||||
\(272\) | 4.10189 | 0.248713 | ||||||||
\(273\) | −3.00140 | −0.181653 | ||||||||
\(274\) | 16.9974 | 1.02685 | ||||||||
\(275\) | −36.9958 | −2.23093 | ||||||||
\(276\) | −1.48980 | −0.0896753 | ||||||||
\(277\) | −28.5911 | −1.71787 | −0.858936 | − | 0.512083i | \(-0.828874\pi\) | ||||
−0.858936 | + | 0.512083i | \(0.828874\pi\) | |||||||
\(278\) | 1.64747 | 0.0988086 | ||||||||
\(279\) | 6.44945 | 0.386118 | ||||||||
\(280\) | 9.61952 | 0.574876 | ||||||||
\(281\) | −3.76526 | −0.224617 | −0.112308 | − | 0.993673i | \(-0.535824\pi\) | ||||
−0.112308 | + | 0.993673i | \(0.535824\pi\) | |||||||
\(282\) | 10.0132 | 0.596278 | ||||||||
\(283\) | 21.7158 | 1.29087 | 0.645436 | − | 0.763814i | \(-0.276676\pi\) | ||||
0.645436 | + | 0.763814i | \(0.276676\pi\) | |||||||
\(284\) | 9.37733 | 0.556442 | ||||||||
\(285\) | 24.7274 | 1.46473 | ||||||||
\(286\) | 3.58033 | 0.211709 | ||||||||
\(287\) | 14.0233 | 0.827769 | ||||||||
\(288\) | 0.780502 | 0.0459915 | ||||||||
\(289\) | −0.174531 | −0.0102665 | ||||||||
\(290\) | 21.9968 | 1.29170 | ||||||||
\(291\) | −8.62545 | −0.505633 | ||||||||
\(292\) | −2.73400 | −0.159995 | ||||||||
\(293\) | −9.75958 | −0.570161 | −0.285080 | − | 0.958504i | \(-0.592020\pi\) | ||||
−0.285080 | + | 0.958504i | \(0.592020\pi\) | |||||||
\(294\) | −0.411563 | −0.0240028 | ||||||||
\(295\) | 19.8037 | 1.15302 | ||||||||
\(296\) | 2.87867 | 0.167319 | ||||||||
\(297\) | 26.9996 | 1.56668 | ||||||||
\(298\) | −5.21941 | −0.302352 | ||||||||
\(299\) | −0.746865 | −0.0431923 | ||||||||
\(300\) | 11.4974 | 0.663803 | ||||||||
\(301\) | −3.39146 | −0.195480 | ||||||||
\(302\) | 0.660230 | 0.0379920 | ||||||||
\(303\) | 6.80548 | 0.390965 | ||||||||
\(304\) | 4.65428 | 0.266941 | ||||||||
\(305\) | −13.6081 | −0.779196 | ||||||||
\(306\) | 3.20153 | 0.183019 | ||||||||
\(307\) | −19.3190 | −1.10259 | −0.551297 | − | 0.834309i | \(-0.685867\pi\) | ||||
−0.551297 | + | 0.834309i | \(0.685867\pi\) | |||||||
\(308\) | 12.9311 | 0.736816 | ||||||||
\(309\) | 11.3544 | 0.645929 | ||||||||
\(310\) | 29.4678 | 1.67366 | ||||||||
\(311\) | 10.5007 | 0.595440 | 0.297720 | − | 0.954653i | \(-0.403774\pi\) | ||||
0.297720 | + | 0.954653i | \(0.403774\pi\) | |||||||
\(312\) | −1.11268 | −0.0629930 | ||||||||
\(313\) | 6.56310 | 0.370968 | 0.185484 | − | 0.982647i | \(-0.440615\pi\) | ||||
0.185484 | + | 0.982647i | \(0.440615\pi\) | |||||||
\(314\) | −9.01181 | −0.508566 | ||||||||
\(315\) | 7.50806 | 0.423031 | ||||||||
\(316\) | −5.86082 | −0.329697 | ||||||||
\(317\) | −1.15264 | −0.0647385 | −0.0323693 | − | 0.999476i | \(-0.510305\pi\) | ||||
−0.0323693 | + | 0.999476i | \(0.510305\pi\) | |||||||
\(318\) | −4.20022 | −0.235537 | ||||||||
\(319\) | 29.5693 | 1.65556 | ||||||||
\(320\) | 3.56615 | 0.199354 | ||||||||
\(321\) | −15.0817 | −0.841781 | ||||||||
\(322\) | −2.69745 | −0.150323 | ||||||||
\(323\) | 19.0913 | 1.06227 | ||||||||
\(324\) | −6.04931 | −0.336073 | ||||||||
\(325\) | 5.76388 | 0.319722 | ||||||||
\(326\) | −6.96678 | −0.385855 | ||||||||
\(327\) | −1.08337 | −0.0599107 | ||||||||
\(328\) | 5.19872 | 0.287051 | ||||||||
\(329\) | 18.1301 | 0.999545 | ||||||||
\(330\) | 25.4687 | 1.40201 | ||||||||
\(331\) | −21.0778 | −1.15854 | −0.579271 | − | 0.815135i | \(-0.696663\pi\) | ||||
−0.579271 | + | 0.815135i | \(0.696663\pi\) | |||||||
\(332\) | −2.35445 | −0.129217 | ||||||||
\(333\) | 2.24681 | 0.123124 | ||||||||
\(334\) | 12.9286 | 0.707424 | ||||||||
\(335\) | −37.0586 | −2.02473 | ||||||||
\(336\) | −4.01866 | −0.219236 | ||||||||
\(337\) | 17.8366 | 0.971622 | 0.485811 | − | 0.874064i | \(-0.338524\pi\) | ||||
0.485811 | + | 0.874064i | \(0.338524\pi\) | |||||||
\(338\) | 12.4422 | 0.676766 | ||||||||
\(339\) | 19.5951 | 1.06426 | ||||||||
\(340\) | 14.6279 | 0.793311 | ||||||||
\(341\) | 39.6122 | 2.14512 | ||||||||
\(342\) | 3.63268 | 0.196433 | ||||||||
\(343\) | 18.1370 | 0.979305 | ||||||||
\(344\) | −1.25728 | −0.0677881 | ||||||||
\(345\) | −5.31284 | −0.286034 | ||||||||
\(346\) | 2.74653 | 0.147654 | ||||||||
\(347\) | −30.1746 | −1.61986 | −0.809929 | − | 0.586529i | \(-0.800494\pi\) | ||||
−0.809929 | + | 0.586529i | \(0.800494\pi\) | |||||||
\(348\) | −9.18940 | −0.492604 | ||||||||
\(349\) | −19.9201 | −1.06630 | −0.533148 | − | 0.846022i | \(-0.678991\pi\) | ||||
−0.533148 | + | 0.846022i | \(0.678991\pi\) | |||||||
\(350\) | 20.8174 | 1.11274 | ||||||||
\(351\) | −4.20648 | −0.224525 | ||||||||
\(352\) | 4.79381 | 0.255511 | ||||||||
\(353\) | −3.43107 | −0.182617 | −0.0913087 | − | 0.995823i | \(-0.529105\pi\) | ||||
−0.0913087 | + | 0.995823i | \(0.529105\pi\) | |||||||
\(354\) | −8.27321 | −0.439716 | ||||||||
\(355\) | 33.4410 | 1.77486 | ||||||||
\(356\) | −2.14139 | −0.113494 | ||||||||
\(357\) | −16.4841 | −0.872430 | ||||||||
\(358\) | 15.4429 | 0.816181 | ||||||||
\(359\) | −0.142270 | −0.00750874 | −0.00375437 | − | 0.999993i | \(-0.501195\pi\) | ||||
−0.00375437 | + | 0.999993i | \(0.501195\pi\) | |||||||
\(360\) | 2.78339 | 0.146697 | ||||||||
\(361\) | 2.66231 | 0.140121 | ||||||||
\(362\) | −18.1904 | −0.956065 | ||||||||
\(363\) | 17.8486 | 0.936811 | ||||||||
\(364\) | −2.01463 | −0.105596 | ||||||||
\(365\) | −9.74986 | −0.510331 | ||||||||
\(366\) | 5.68492 | 0.297156 | ||||||||
\(367\) | −12.4235 | −0.648500 | −0.324250 | − | 0.945971i | \(-0.605112\pi\) | ||||
−0.324250 | + | 0.945971i | \(0.605112\pi\) | |||||||
\(368\) | −1.00000 | −0.0521286 | ||||||||
\(369\) | 4.05761 | 0.211231 | ||||||||
\(370\) | 10.2658 | 0.533692 | ||||||||
\(371\) | −7.60499 | −0.394831 | ||||||||
\(372\) | −12.3105 | −0.638270 | ||||||||
\(373\) | −34.9365 | −1.80894 | −0.904470 | − | 0.426536i | \(-0.859734\pi\) | ||||
−0.904470 | + | 0.426536i | \(0.859734\pi\) | |||||||
\(374\) | 19.6636 | 1.01678 | ||||||||
\(375\) | 14.4372 | 0.745536 | ||||||||
\(376\) | 6.72119 | 0.346619 | ||||||||
\(377\) | −4.60683 | −0.237264 | ||||||||
\(378\) | −15.1926 | −0.781421 | ||||||||
\(379\) | −21.9430 | −1.12714 | −0.563569 | − | 0.826069i | \(-0.690572\pi\) | ||||
−0.563569 | + | 0.826069i | \(0.690572\pi\) | |||||||
\(380\) | 16.5979 | 0.851452 | ||||||||
\(381\) | −13.7841 | −0.706181 | ||||||||
\(382\) | −2.00049 | −0.102354 | ||||||||
\(383\) | −25.5463 | −1.30535 | −0.652676 | − | 0.757637i | \(-0.726354\pi\) | ||||
−0.652676 | + | 0.757637i | \(0.726354\pi\) | |||||||
\(384\) | −1.48980 | −0.0760259 | ||||||||
\(385\) | 46.1141 | 2.35019 | ||||||||
\(386\) | 1.38564 | 0.0705271 | ||||||||
\(387\) | −0.981311 | −0.0498829 | ||||||||
\(388\) | −5.78968 | −0.293927 | ||||||||
\(389\) | 1.15731 | 0.0586779 | 0.0293389 | − | 0.999570i | \(-0.490660\pi\) | ||||
0.0293389 | + | 0.999570i | \(0.490660\pi\) | |||||||
\(390\) | −3.96798 | −0.200926 | ||||||||
\(391\) | −4.10189 | −0.207441 | ||||||||
\(392\) | −0.276254 | −0.0139529 | ||||||||
\(393\) | −1.48980 | −0.0751504 | ||||||||
\(394\) | −0.933591 | −0.0470336 | ||||||||
\(395\) | −20.9006 | −1.05162 | ||||||||
\(396\) | 3.74158 | 0.188021 | ||||||||
\(397\) | 21.3912 | 1.07360 | 0.536798 | − | 0.843711i | \(-0.319634\pi\) | ||||
0.536798 | + | 0.843711i | \(0.319634\pi\) | |||||||
\(398\) | −0.0385265 | −0.00193116 | ||||||||
\(399\) | −18.7040 | −0.936369 | ||||||||
\(400\) | 7.71742 | 0.385871 | ||||||||
\(401\) | 32.6522 | 1.63057 | 0.815286 | − | 0.579059i | \(-0.196580\pi\) | ||||
0.815286 | + | 0.579059i | \(0.196580\pi\) | |||||||
\(402\) | 15.4816 | 0.772154 | ||||||||
\(403\) | −6.17150 | −0.307424 | ||||||||
\(404\) | 4.56806 | 0.227269 | ||||||||
\(405\) | −21.5727 | −1.07196 | ||||||||
\(406\) | −16.6385 | −0.825754 | ||||||||
\(407\) | 13.7998 | 0.684031 | ||||||||
\(408\) | −6.11098 | −0.302539 | ||||||||
\(409\) | −9.95033 | −0.492012 | −0.246006 | − | 0.969268i | \(-0.579118\pi\) | ||||
−0.246006 | + | 0.969268i | \(0.579118\pi\) | |||||||
\(410\) | 18.5394 | 0.915596 | ||||||||
\(411\) | −25.3227 | −1.24908 | ||||||||
\(412\) | 7.62144 | 0.375481 | ||||||||
\(413\) | −14.9796 | −0.737099 | ||||||||
\(414\) | −0.780502 | −0.0383596 | ||||||||
\(415\) | −8.39630 | −0.412158 | ||||||||
\(416\) | −0.746865 | −0.0366181 | ||||||||
\(417\) | −2.45440 | −0.120192 | ||||||||
\(418\) | 22.3117 | 1.09130 | ||||||||
\(419\) | −13.7916 | −0.673763 | −0.336881 | − | 0.941547i | \(-0.609372\pi\) | ||||
−0.336881 | + | 0.941547i | \(0.609372\pi\) | |||||||
\(420\) | −14.3311 | −0.699288 | ||||||||
\(421\) | 8.50368 | 0.414444 | 0.207222 | − | 0.978294i | \(-0.433558\pi\) | ||||
0.207222 | + | 0.978294i | \(0.433558\pi\) | |||||||
\(422\) | 1.69707 | 0.0826121 | ||||||||
\(423\) | 5.24591 | 0.255065 | ||||||||
\(424\) | −2.81932 | −0.136918 | ||||||||
\(425\) | 31.6560 | 1.53554 | ||||||||
\(426\) | −13.9703 | −0.676864 | ||||||||
\(427\) | 10.2932 | 0.498124 | ||||||||
\(428\) | −10.1233 | −0.489330 | ||||||||
\(429\) | −5.33396 | −0.257526 | ||||||||
\(430\) | −4.48365 | −0.216221 | ||||||||
\(431\) | −22.1517 | −1.06701 | −0.533505 | − | 0.845797i | \(-0.679126\pi\) | ||||
−0.533505 | + | 0.845797i | \(0.679126\pi\) | |||||||
\(432\) | −5.63218 | −0.270979 | ||||||||
\(433\) | 33.6565 | 1.61743 | 0.808714 | − | 0.588202i | \(-0.200164\pi\) | ||||
0.808714 | + | 0.588202i | \(0.200164\pi\) | |||||||
\(434\) | −22.2896 | −1.06993 | ||||||||
\(435\) | −32.7708 | −1.57124 | ||||||||
\(436\) | −0.727196 | −0.0348264 | ||||||||
\(437\) | −4.65428 | −0.222644 | ||||||||
\(438\) | 4.07311 | 0.194621 | ||||||||
\(439\) | −15.3656 | −0.733360 | −0.366680 | − | 0.930347i | \(-0.619506\pi\) | ||||
−0.366680 | + | 0.930347i | \(0.619506\pi\) | |||||||
\(440\) | 17.0954 | 0.814993 | ||||||||
\(441\) | −0.215617 | −0.0102675 | ||||||||
\(442\) | −3.06356 | −0.145719 | ||||||||
\(443\) | 22.7407 | 1.08044 | 0.540222 | − | 0.841523i | \(-0.318340\pi\) | ||||
0.540222 | + | 0.841523i | \(0.318340\pi\) | |||||||
\(444\) | −4.28864 | −0.203530 | ||||||||
\(445\) | −7.63653 | −0.362006 | ||||||||
\(446\) | −13.8360 | −0.655155 | ||||||||
\(447\) | 7.77587 | 0.367786 | ||||||||
\(448\) | −2.69745 | −0.127443 | ||||||||
\(449\) | 14.9135 | 0.703813 | 0.351907 | − | 0.936035i | \(-0.385533\pi\) | ||||
0.351907 | + | 0.936035i | \(0.385533\pi\) | |||||||
\(450\) | 6.02347 | 0.283949 | ||||||||
\(451\) | 24.9216 | 1.17351 | ||||||||
\(452\) | 13.1529 | 0.618659 | ||||||||
\(453\) | −0.983610 | −0.0462140 | ||||||||
\(454\) | 10.5000 | 0.492790 | ||||||||
\(455\) | −7.18449 | −0.336814 | ||||||||
\(456\) | −6.93393 | −0.324711 | ||||||||
\(457\) | −22.3010 | −1.04320 | −0.521599 | − | 0.853191i | \(-0.674664\pi\) | ||||
−0.521599 | + | 0.853191i | \(0.674664\pi\) | |||||||
\(458\) | −12.3635 | −0.577710 | ||||||||
\(459\) | −23.1026 | −1.07834 | ||||||||
\(460\) | −3.56615 | −0.166273 | ||||||||
\(461\) | 1.90159 | 0.0885657 | 0.0442829 | − | 0.999019i | \(-0.485900\pi\) | ||||
0.0442829 | + | 0.999019i | \(0.485900\pi\) | |||||||
\(462\) | −19.2647 | −0.896274 | ||||||||
\(463\) | −29.3617 | −1.36455 | −0.682277 | − | 0.731094i | \(-0.739010\pi\) | ||||
−0.682277 | + | 0.731094i | \(0.739010\pi\) | |||||||
\(464\) | −6.16822 | −0.286353 | ||||||||
\(465\) | −43.9011 | −2.03586 | ||||||||
\(466\) | −7.47482 | −0.346264 | ||||||||
\(467\) | 24.7902 | 1.14715 | 0.573577 | − | 0.819152i | \(-0.305556\pi\) | ||||
0.573577 | + | 0.819152i | \(0.305556\pi\) | |||||||
\(468\) | −0.582930 | −0.0269460 | ||||||||
\(469\) | 28.0313 | 1.29437 | ||||||||
\(470\) | 23.9688 | 1.10560 | ||||||||
\(471\) | 13.4258 | 0.618627 | ||||||||
\(472\) | −5.55324 | −0.255609 | ||||||||
\(473\) | −6.02716 | −0.277129 | ||||||||
\(474\) | 8.73144 | 0.401048 | ||||||||
\(475\) | 35.9190 | 1.64808 | ||||||||
\(476\) | −11.0646 | −0.507147 | ||||||||
\(477\) | −2.20049 | −0.100753 | ||||||||
\(478\) | −2.73435 | −0.125066 | ||||||||
\(479\) | −15.1463 | −0.692052 | −0.346026 | − | 0.938225i | \(-0.612469\pi\) | ||||
−0.346026 | + | 0.938225i | \(0.612469\pi\) | |||||||
\(480\) | −5.31284 | −0.242497 | ||||||||
\(481\) | −2.14998 | −0.0980307 | ||||||||
\(482\) | −25.7983 | −1.17508 | ||||||||
\(483\) | 4.01866 | 0.182855 | ||||||||
\(484\) | 11.9806 | 0.544572 | ||||||||
\(485\) | −20.6469 | −0.937526 | ||||||||
\(486\) | −7.88431 | −0.357639 | ||||||||
\(487\) | −21.9472 | −0.994522 | −0.497261 | − | 0.867601i | \(-0.665661\pi\) | ||||
−0.497261 | + | 0.867601i | \(0.665661\pi\) | |||||||
\(488\) | 3.81590 | 0.172738 | ||||||||
\(489\) | 10.3791 | 0.469359 | ||||||||
\(490\) | −0.985164 | −0.0445052 | ||||||||
\(491\) | −2.23531 | −0.100878 | −0.0504390 | − | 0.998727i | \(-0.516062\pi\) | ||||
−0.0504390 | + | 0.998727i | \(0.516062\pi\) | |||||||
\(492\) | −7.74503 | −0.349173 | ||||||||
\(493\) | −25.3013 | −1.13952 | ||||||||
\(494\) | −3.47612 | −0.156398 | ||||||||
\(495\) | 13.3430 | 0.599724 | ||||||||
\(496\) | −8.26320 | −0.371029 | ||||||||
\(497\) | −25.2949 | −1.13463 | ||||||||
\(498\) | 3.50765 | 0.157181 | ||||||||
\(499\) | −10.8109 | −0.483961 | −0.241980 | − | 0.970281i | \(-0.577797\pi\) | ||||
−0.241980 | + | 0.970281i | \(0.577797\pi\) | |||||||
\(500\) | 9.69074 | 0.433383 | ||||||||
\(501\) | −19.2611 | −0.860521 | ||||||||
\(502\) | 16.1788 | 0.722097 | ||||||||
\(503\) | 37.7272 | 1.68217 | 0.841086 | − | 0.540901i | \(-0.181917\pi\) | ||||
0.841086 | + | 0.540901i | \(0.181917\pi\) | |||||||
\(504\) | −2.10537 | −0.0937806 | ||||||||
\(505\) | 16.2904 | 0.724912 | ||||||||
\(506\) | −4.79381 | −0.213111 | ||||||||
\(507\) | −18.5364 | −0.823228 | ||||||||
\(508\) | −9.25234 | −0.410506 | ||||||||
\(509\) | −1.72412 | −0.0764205 | −0.0382102 | − | 0.999270i | \(-0.512166\pi\) | ||||
−0.0382102 | + | 0.999270i | \(0.512166\pi\) | |||||||
\(510\) | −21.7927 | −0.964996 | ||||||||
\(511\) | 7.37484 | 0.326244 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −26.2138 | −1.15737 | ||||||||
\(514\) | 20.7693 | 0.916096 | ||||||||
\(515\) | 27.1792 | 1.19766 | ||||||||
\(516\) | 1.87310 | 0.0824584 | ||||||||
\(517\) | 32.2201 | 1.41704 | ||||||||
\(518\) | −7.76509 | −0.341178 | ||||||||
\(519\) | −4.09178 | −0.179609 | ||||||||
\(520\) | −2.66343 | −0.116799 | ||||||||
\(521\) | 44.3691 | 1.94384 | 0.971922 | − | 0.235302i | \(-0.0756080\pi\) | ||||
0.971922 | + | 0.235302i | \(0.0756080\pi\) | |||||||
\(522\) | −4.81431 | −0.210717 | ||||||||
\(523\) | 2.24719 | 0.0982626 | 0.0491313 | − | 0.998792i | \(-0.484355\pi\) | ||||
0.0491313 | + | 0.998792i | \(0.484355\pi\) | |||||||
\(524\) | −1.00000 | −0.0436852 | ||||||||
\(525\) | −31.0137 | −1.35355 | ||||||||
\(526\) | 11.5028 | 0.501548 | ||||||||
\(527\) | −33.8947 | −1.47648 | ||||||||
\(528\) | −7.14180 | −0.310807 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −10.0541 | −0.436723 | ||||||||
\(531\) | −4.33432 | −0.188093 | ||||||||
\(532\) | −12.5547 | −0.544315 | ||||||||
\(533\) | −3.88274 | −0.168180 | ||||||||
\(534\) | 3.19024 | 0.138055 | ||||||||
\(535\) | −36.1014 | −1.56080 | ||||||||
\(536\) | 10.3918 | 0.448856 | ||||||||
\(537\) | −23.0068 | −0.992815 | ||||||||
\(538\) | −16.5846 | −0.715013 | ||||||||
\(539\) | −1.32431 | −0.0570420 | ||||||||
\(540\) | −20.0852 | −0.864330 | ||||||||
\(541\) | 29.7587 | 1.27943 | 0.639714 | − | 0.768613i | \(-0.279053\pi\) | ||||
0.639714 | + | 0.768613i | \(0.279053\pi\) | |||||||
\(542\) | 7.01482 | 0.301312 | ||||||||
\(543\) | 27.1000 | 1.16297 | ||||||||
\(544\) | −4.10189 | −0.175867 | ||||||||
\(545\) | −2.59329 | −0.111084 | ||||||||
\(546\) | 3.00140 | 0.128448 | ||||||||
\(547\) | 23.6462 | 1.01104 | 0.505520 | − | 0.862815i | \(-0.331301\pi\) | ||||
0.505520 | + | 0.862815i | \(0.331301\pi\) | |||||||
\(548\) | −16.9974 | −0.726093 | ||||||||
\(549\) | 2.97832 | 0.127112 | ||||||||
\(550\) | 36.9958 | 1.57751 | ||||||||
\(551\) | −28.7086 | −1.22303 | ||||||||
\(552\) | 1.48980 | 0.0634100 | ||||||||
\(553\) | 15.8093 | 0.672279 | ||||||||
\(554\) | 28.5911 | 1.21472 | ||||||||
\(555\) | −15.2939 | −0.649191 | ||||||||
\(556\) | −1.64747 | −0.0698683 | ||||||||
\(557\) | 35.2034 | 1.49162 | 0.745808 | − | 0.666161i | \(-0.232064\pi\) | ||||
0.745808 | + | 0.666161i | \(0.232064\pi\) | |||||||
\(558\) | −6.44945 | −0.273027 | ||||||||
\(559\) | 0.939020 | 0.0397163 | ||||||||
\(560\) | −9.61952 | −0.406499 | ||||||||
\(561\) | −29.2949 | −1.23683 | ||||||||
\(562\) | 3.76526 | 0.158828 | ||||||||
\(563\) | −9.43221 | −0.397520 | −0.198760 | − | 0.980048i | \(-0.563691\pi\) | ||||
−0.198760 | + | 0.980048i | \(0.563691\pi\) | |||||||
\(564\) | −10.0132 | −0.421633 | ||||||||
\(565\) | 46.9051 | 1.97331 | ||||||||
\(566\) | −21.7158 | −0.912784 | ||||||||
\(567\) | 16.3177 | 0.685280 | ||||||||
\(568\) | −9.37733 | −0.393464 | ||||||||
\(569\) | 1.53518 | 0.0643581 | 0.0321791 | − | 0.999482i | \(-0.489755\pi\) | ||||
0.0321791 | + | 0.999482i | \(0.489755\pi\) | |||||||
\(570\) | −24.7274 | −1.03572 | ||||||||
\(571\) | −33.2809 | −1.39276 | −0.696382 | − | 0.717671i | \(-0.745208\pi\) | ||||
−0.696382 | + | 0.717671i | \(0.745208\pi\) | |||||||
\(572\) | −3.58033 | −0.149701 | ||||||||
\(573\) | 2.98032 | 0.124505 | ||||||||
\(574\) | −14.0233 | −0.585321 | ||||||||
\(575\) | −7.71742 | −0.321839 | ||||||||
\(576\) | −0.780502 | −0.0325209 | ||||||||
\(577\) | −20.4334 | −0.850652 | −0.425326 | − | 0.905040i | \(-0.639840\pi\) | ||||
−0.425326 | + | 0.905040i | \(0.639840\pi\) | |||||||
\(578\) | 0.174531 | 0.00725951 | ||||||||
\(579\) | −2.06432 | −0.0857902 | ||||||||
\(580\) | −21.9968 | −0.913368 | ||||||||
\(581\) | 6.35101 | 0.263484 | ||||||||
\(582\) | 8.62545 | 0.357537 | ||||||||
\(583\) | −13.5153 | −0.559746 | ||||||||
\(584\) | 2.73400 | 0.113134 | ||||||||
\(585\) | −2.07882 | −0.0859485 | ||||||||
\(586\) | 9.75958 | 0.403165 | ||||||||
\(587\) | −6.44000 | −0.265807 | −0.132904 | − | 0.991129i | \(-0.542430\pi\) | ||||
−0.132904 | + | 0.991129i | \(0.542430\pi\) | |||||||
\(588\) | 0.411563 | 0.0169726 | ||||||||
\(589\) | −38.4592 | −1.58468 | ||||||||
\(590\) | −19.8037 | −0.815305 | ||||||||
\(591\) | 1.39086 | 0.0572124 | ||||||||
\(592\) | −2.87867 | −0.118313 | ||||||||
\(593\) | 43.3150 | 1.77873 | 0.889367 | − | 0.457194i | \(-0.151146\pi\) | ||||
0.889367 | + | 0.457194i | \(0.151146\pi\) | |||||||
\(594\) | −26.9996 | −1.10781 | ||||||||
\(595\) | −39.4582 | −1.61763 | ||||||||
\(596\) | 5.21941 | 0.213795 | ||||||||
\(597\) | 0.0573967 | 0.00234909 | ||||||||
\(598\) | 0.746865 | 0.0305416 | ||||||||
\(599\) | 40.6066 | 1.65914 | 0.829571 | − | 0.558401i | \(-0.188585\pi\) | ||||
0.829571 | + | 0.558401i | \(0.188585\pi\) | |||||||
\(600\) | −11.4974 | −0.469379 | ||||||||
\(601\) | 42.2059 | 1.72162 | 0.860808 | − | 0.508929i | \(-0.169959\pi\) | ||||
0.860808 | + | 0.508929i | \(0.169959\pi\) | |||||||
\(602\) | 3.39146 | 0.138226 | ||||||||
\(603\) | 8.11080 | 0.330297 | ||||||||
\(604\) | −0.660230 | −0.0268644 | ||||||||
\(605\) | 42.7246 | 1.73700 | ||||||||
\(606\) | −6.80548 | −0.276454 | ||||||||
\(607\) | −26.3401 | −1.06911 | −0.534556 | − | 0.845133i | \(-0.679521\pi\) | ||||
−0.534556 | + | 0.845133i | \(0.679521\pi\) | |||||||
\(608\) | −4.65428 | −0.188756 | ||||||||
\(609\) | 24.7880 | 1.00446 | ||||||||
\(610\) | 13.6081 | 0.550975 | ||||||||
\(611\) | −5.01983 | −0.203080 | ||||||||
\(612\) | −3.20153 | −0.129414 | ||||||||
\(613\) | 18.7395 | 0.756883 | 0.378442 | − | 0.925625i | \(-0.376460\pi\) | ||||
0.378442 | + | 0.925625i | \(0.376460\pi\) | |||||||
\(614\) | 19.3190 | 0.779652 | ||||||||
\(615\) | −27.6200 | −1.11374 | ||||||||
\(616\) | −12.9311 | −0.521008 | ||||||||
\(617\) | −0.893218 | −0.0359596 | −0.0179798 | − | 0.999838i | \(-0.505723\pi\) | ||||
−0.0179798 | + | 0.999838i | \(0.505723\pi\) | |||||||
\(618\) | −11.3544 | −0.456741 | ||||||||
\(619\) | 16.3533 | 0.657295 | 0.328647 | − | 0.944453i | \(-0.393407\pi\) | ||||
0.328647 | + | 0.944453i | \(0.393407\pi\) | |||||||
\(620\) | −29.4678 | −1.18346 | ||||||||
\(621\) | 5.63218 | 0.226012 | ||||||||
\(622\) | −10.5007 | −0.421040 | ||||||||
\(623\) | 5.77631 | 0.231423 | ||||||||
\(624\) | 1.11268 | 0.0445428 | ||||||||
\(625\) | −4.02848 | −0.161139 | ||||||||
\(626\) | −6.56310 | −0.262314 | ||||||||
\(627\) | −33.2399 | −1.32748 | ||||||||
\(628\) | 9.01181 | 0.359610 | ||||||||
\(629\) | −11.8080 | −0.470815 | ||||||||
\(630\) | −7.50806 | −0.299128 | ||||||||
\(631\) | −8.13369 | −0.323797 | −0.161899 | − | 0.986807i | \(-0.551762\pi\) | ||||
−0.161899 | + | 0.986807i | \(0.551762\pi\) | |||||||
\(632\) | 5.86082 | 0.233131 | ||||||||
\(633\) | −2.52829 | −0.100491 | ||||||||
\(634\) | 1.15264 | 0.0457770 | ||||||||
\(635\) | −32.9952 | −1.30938 | ||||||||
\(636\) | 4.20022 | 0.166549 | ||||||||
\(637\) | 0.206325 | 0.00817488 | ||||||||
\(638\) | −29.5693 | −1.17066 | ||||||||
\(639\) | −7.31903 | −0.289536 | ||||||||
\(640\) | −3.56615 | −0.140964 | ||||||||
\(641\) | −40.5643 | −1.60219 | −0.801096 | − | 0.598535i | \(-0.795750\pi\) | ||||
−0.801096 | + | 0.598535i | \(0.795750\pi\) | |||||||
\(642\) | 15.0817 | 0.595229 | ||||||||
\(643\) | 30.9504 | 1.22056 | 0.610282 | − | 0.792184i | \(-0.291056\pi\) | ||||
0.610282 | + | 0.792184i | \(0.291056\pi\) | |||||||
\(644\) | 2.69745 | 0.106295 | ||||||||
\(645\) | 6.67974 | 0.263014 | ||||||||
\(646\) | −19.0913 | −0.751138 | ||||||||
\(647\) | 25.9875 | 1.02167 | 0.510837 | − | 0.859678i | \(-0.329336\pi\) | ||||
0.510837 | + | 0.859678i | \(0.329336\pi\) | |||||||
\(648\) | 6.04931 | 0.237639 | ||||||||
\(649\) | −26.6212 | −1.04497 | ||||||||
\(650\) | −5.76388 | −0.226078 | ||||||||
\(651\) | 33.2070 | 1.30148 | ||||||||
\(652\) | 6.96678 | 0.272840 | ||||||||
\(653\) | 5.55371 | 0.217334 | 0.108667 | − | 0.994078i | \(-0.465342\pi\) | ||||
0.108667 | + | 0.994078i | \(0.465342\pi\) | |||||||
\(654\) | 1.08337 | 0.0423633 | ||||||||
\(655\) | −3.56615 | −0.139341 | ||||||||
\(656\) | −5.19872 | −0.202976 | ||||||||
\(657\) | 2.13389 | 0.0832511 | ||||||||
\(658\) | −18.1301 | −0.706785 | ||||||||
\(659\) | −1.49785 | −0.0583480 | −0.0291740 | − | 0.999574i | \(-0.509288\pi\) | ||||
−0.0291740 | + | 0.999574i | \(0.509288\pi\) | |||||||
\(660\) | −25.4687 | −0.991369 | ||||||||
\(661\) | 10.6508 | 0.414269 | 0.207135 | − | 0.978312i | \(-0.433586\pi\) | ||||
0.207135 | + | 0.978312i | \(0.433586\pi\) | |||||||
\(662\) | 21.0778 | 0.819213 | ||||||||
\(663\) | 4.56408 | 0.177254 | ||||||||
\(664\) | 2.35445 | 0.0913702 | ||||||||
\(665\) | −44.7719 | −1.73618 | ||||||||
\(666\) | −2.24681 | −0.0870622 | ||||||||
\(667\) | 6.16822 | 0.238835 | ||||||||
\(668\) | −12.9286 | −0.500224 | ||||||||
\(669\) | 20.6129 | 0.796940 | ||||||||
\(670\) | 37.0586 | 1.43170 | ||||||||
\(671\) | 18.2927 | 0.706182 | ||||||||
\(672\) | 4.01866 | 0.155023 | ||||||||
\(673\) | 19.9996 | 0.770928 | 0.385464 | − | 0.922723i | \(-0.374041\pi\) | ||||
0.385464 | + | 0.922723i | \(0.374041\pi\) | |||||||
\(674\) | −17.8366 | −0.687040 | ||||||||
\(675\) | −43.4660 | −1.67301 | ||||||||
\(676\) | −12.4422 | −0.478546 | ||||||||
\(677\) | −10.3796 | −0.398921 | −0.199460 | − | 0.979906i | \(-0.563919\pi\) | ||||
−0.199460 | + | 0.979906i | \(0.563919\pi\) | |||||||
\(678\) | −19.5951 | −0.752546 | ||||||||
\(679\) | 15.6174 | 0.599341 | ||||||||
\(680\) | −14.6279 | −0.560956 | ||||||||
\(681\) | −15.6429 | −0.599436 | ||||||||
\(682\) | −39.6122 | −1.51683 | ||||||||
\(683\) | 25.7090 | 0.983729 | 0.491864 | − | 0.870672i | \(-0.336316\pi\) | ||||
0.491864 | + | 0.870672i | \(0.336316\pi\) | |||||||
\(684\) | −3.63268 | −0.138899 | ||||||||
\(685\) | −60.6152 | −2.31599 | ||||||||
\(686\) | −18.1370 | −0.692474 | ||||||||
\(687\) | 18.4192 | 0.702735 | ||||||||
\(688\) | 1.25728 | 0.0479334 | ||||||||
\(689\) | 2.10565 | 0.0802190 | ||||||||
\(690\) | 5.31284 | 0.202256 | ||||||||
\(691\) | −40.2532 | −1.53130 | −0.765651 | − | 0.643256i | \(-0.777583\pi\) | ||||
−0.765651 | + | 0.643256i | \(0.777583\pi\) | |||||||
\(692\) | −2.74653 | −0.104407 | ||||||||
\(693\) | −10.0927 | −0.383391 | ||||||||
\(694\) | 30.1746 | 1.14541 | ||||||||
\(695\) | −5.87512 | −0.222856 | ||||||||
\(696\) | 9.18940 | 0.348323 | ||||||||
\(697\) | −21.3245 | −0.807724 | ||||||||
\(698\) | 19.9201 | 0.753986 | ||||||||
\(699\) | 11.1360 | 0.421201 | ||||||||
\(700\) | −20.8174 | −0.786823 | ||||||||
\(701\) | 13.1463 | 0.496528 | 0.248264 | − | 0.968692i | \(-0.420140\pi\) | ||||
0.248264 | + | 0.968692i | \(0.420140\pi\) | |||||||
\(702\) | 4.20648 | 0.158763 | ||||||||
\(703\) | −13.3981 | −0.505321 | ||||||||
\(704\) | −4.79381 | −0.180673 | ||||||||
\(705\) | −35.7086 | −1.34487 | ||||||||
\(706\) | 3.43107 | 0.129130 | ||||||||
\(707\) | −12.3221 | −0.463421 | ||||||||
\(708\) | 8.27321 | 0.310926 | ||||||||
\(709\) | −14.6856 | −0.551529 | −0.275765 | − | 0.961225i | \(-0.588931\pi\) | ||||
−0.275765 | + | 0.961225i | \(0.588931\pi\) | |||||||
\(710\) | −33.4410 | −1.25502 | ||||||||
\(711\) | 4.57438 | 0.171553 | ||||||||
\(712\) | 2.14139 | 0.0802521 | ||||||||
\(713\) | 8.26320 | 0.309459 | ||||||||
\(714\) | 16.4841 | 0.616901 | ||||||||
\(715\) | −12.7680 | −0.477496 | ||||||||
\(716\) | −15.4429 | −0.577127 | ||||||||
\(717\) | 4.07362 | 0.152132 | ||||||||
\(718\) | 0.142270 | 0.00530948 | ||||||||
\(719\) | 21.4588 | 0.800279 | 0.400139 | − | 0.916454i | \(-0.368962\pi\) | ||||
0.400139 | + | 0.916454i | \(0.368962\pi\) | |||||||
\(720\) | −2.78339 | −0.103731 | ||||||||
\(721\) | −20.5585 | −0.765638 | ||||||||
\(722\) | −2.66231 | −0.0990808 | ||||||||
\(723\) | 38.4342 | 1.42938 | ||||||||
\(724\) | 18.1904 | 0.676040 | ||||||||
\(725\) | −47.6028 | −1.76792 | ||||||||
\(726\) | −17.8486 | −0.662425 | ||||||||
\(727\) | −11.1963 | −0.415248 | −0.207624 | − | 0.978209i | \(-0.566573\pi\) | ||||
−0.207624 | + | 0.978209i | \(0.566573\pi\) | |||||||
\(728\) | 2.01463 | 0.0746673 | ||||||||
\(729\) | 29.8939 | 1.10718 | ||||||||
\(730\) | 9.74986 | 0.360858 | ||||||||
\(731\) | 5.15723 | 0.190747 | ||||||||
\(732\) | −5.68492 | −0.210121 | ||||||||
\(733\) | −7.95722 | −0.293906 | −0.146953 | − | 0.989143i | \(-0.546947\pi\) | ||||
−0.146953 | + | 0.989143i | \(0.546947\pi\) | |||||||
\(734\) | 12.4235 | 0.458559 | ||||||||
\(735\) | 1.46769 | 0.0541367 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 49.8161 | 1.83500 | ||||||||
\(738\) | −4.05761 | −0.149363 | ||||||||
\(739\) | −11.5665 | −0.425481 | −0.212741 | − | 0.977109i | \(-0.568239\pi\) | ||||
−0.212741 | + | 0.977109i | \(0.568239\pi\) | |||||||
\(740\) | −10.2658 | −0.377378 | ||||||||
\(741\) | 5.17871 | 0.190245 | ||||||||
\(742\) | 7.60499 | 0.279188 | ||||||||
\(743\) | −7.81447 | −0.286685 | −0.143343 | − | 0.989673i | \(-0.545785\pi\) | ||||
−0.143343 | + | 0.989673i | \(0.545785\pi\) | |||||||
\(744\) | 12.3105 | 0.451325 | ||||||||
\(745\) | 18.6132 | 0.681935 | ||||||||
\(746\) | 34.9365 | 1.27911 | ||||||||
\(747\) | 1.83765 | 0.0672361 | ||||||||
\(748\) | −19.6636 | −0.718974 | ||||||||
\(749\) | 27.3072 | 0.997785 | ||||||||
\(750\) | −14.4372 | −0.527174 | ||||||||
\(751\) | 11.0866 | 0.404555 | 0.202277 | − | 0.979328i | \(-0.435166\pi\) | ||||
0.202277 | + | 0.979328i | \(0.435166\pi\) | |||||||
\(752\) | −6.72119 | −0.245097 | ||||||||
\(753\) | −24.1032 | −0.878369 | ||||||||
\(754\) | 4.60683 | 0.167771 | ||||||||
\(755\) | −2.35448 | −0.0856883 | ||||||||
\(756\) | 15.1926 | 0.552548 | ||||||||
\(757\) | −27.4416 | −0.997381 | −0.498690 | − | 0.866780i | \(-0.666186\pi\) | ||||
−0.498690 | + | 0.866780i | \(0.666186\pi\) | |||||||
\(758\) | 21.9430 | 0.797007 | ||||||||
\(759\) | 7.14180 | 0.259231 | ||||||||
\(760\) | −16.5979 | −0.602067 | ||||||||
\(761\) | −27.3015 | −0.989680 | −0.494840 | − | 0.868984i | \(-0.664773\pi\) | ||||
−0.494840 | + | 0.868984i | \(0.664773\pi\) | |||||||
\(762\) | 13.7841 | 0.499346 | ||||||||
\(763\) | 1.96158 | 0.0710138 | ||||||||
\(764\) | 2.00049 | 0.0723751 | ||||||||
\(765\) | −11.4171 | −0.412788 | ||||||||
\(766\) | 25.5463 | 0.923024 | ||||||||
\(767\) | 4.14752 | 0.149758 | ||||||||
\(768\) | 1.48980 | 0.0537584 | ||||||||
\(769\) | −36.1673 | −1.30423 | −0.652113 | − | 0.758122i | \(-0.726117\pi\) | ||||
−0.652113 | + | 0.758122i | \(0.726117\pi\) | |||||||
\(770\) | −46.1141 | −1.66184 | ||||||||
\(771\) | −30.9421 | −1.11435 | ||||||||
\(772\) | −1.38564 | −0.0498702 | ||||||||
\(773\) | 28.7322 | 1.03343 | 0.516713 | − | 0.856159i | \(-0.327155\pi\) | ||||
0.516713 | + | 0.856159i | \(0.327155\pi\) | |||||||
\(774\) | 0.981311 | 0.0352725 | ||||||||
\(775\) | −63.7706 | −2.29071 | ||||||||
\(776\) | 5.78968 | 0.207837 | ||||||||
\(777\) | 11.5684 | 0.415014 | ||||||||
\(778\) | −1.15731 | −0.0414915 | ||||||||
\(779\) | −24.1963 | −0.866921 | ||||||||
\(780\) | 3.96798 | 0.142076 | ||||||||
\(781\) | −44.9531 | −1.60855 | ||||||||
\(782\) | 4.10189 | 0.146683 | ||||||||
\(783\) | 34.7406 | 1.24153 | ||||||||
\(784\) | 0.276254 | 0.00986622 | ||||||||
\(785\) | 32.1375 | 1.14704 | ||||||||
\(786\) | 1.48980 | 0.0531393 | ||||||||
\(787\) | 46.7334 | 1.66587 | 0.832934 | − | 0.553373i | \(-0.186660\pi\) | ||||
0.832934 | + | 0.553373i | \(0.186660\pi\) | |||||||
\(788\) | 0.933591 | 0.0332578 | ||||||||
\(789\) | −17.1369 | −0.610090 | ||||||||
\(790\) | 20.9006 | 0.743609 | ||||||||
\(791\) | −35.4792 | −1.26150 | ||||||||
\(792\) | −3.74158 | −0.132951 | ||||||||
\(793\) | −2.84997 | −0.101205 | ||||||||
\(794\) | −21.3912 | −0.759147 | ||||||||
\(795\) | 14.9786 | 0.531236 | ||||||||
\(796\) | 0.0385265 | 0.00136554 | ||||||||
\(797\) | 12.0369 | 0.426369 | 0.213185 | − | 0.977012i | \(-0.431616\pi\) | ||||
0.213185 | + | 0.977012i | \(0.431616\pi\) | |||||||
\(798\) | 18.7040 | 0.662113 | ||||||||
\(799\) | −27.5696 | −0.975341 | ||||||||
\(800\) | −7.71742 | −0.272852 | ||||||||
\(801\) | 1.67136 | 0.0590547 | ||||||||
\(802\) | −32.6522 | −1.15299 | ||||||||
\(803\) | 13.1063 | 0.462510 | ||||||||
\(804\) | −15.4816 | −0.545995 | ||||||||
\(805\) | 9.61952 | 0.339044 | ||||||||
\(806\) | 6.17150 | 0.217382 | ||||||||
\(807\) | 24.7077 | 0.869752 | ||||||||
\(808\) | −4.56806 | −0.160704 | ||||||||
\(809\) | 49.6868 | 1.74690 | 0.873448 | − | 0.486918i | \(-0.161879\pi\) | ||||
0.873448 | + | 0.486918i | \(0.161879\pi\) | |||||||
\(810\) | 21.5727 | 0.757989 | ||||||||
\(811\) | −26.9745 | −0.947204 | −0.473602 | − | 0.880739i | \(-0.657046\pi\) | ||||
−0.473602 | + | 0.880739i | \(0.657046\pi\) | |||||||
\(812\) | 16.6385 | 0.583897 | ||||||||
\(813\) | −10.4507 | −0.366521 | ||||||||
\(814\) | −13.7998 | −0.483683 | ||||||||
\(815\) | 24.8446 | 0.870268 | ||||||||
\(816\) | 6.11098 | 0.213927 | ||||||||
\(817\) | 5.85174 | 0.204726 | ||||||||
\(818\) | 9.95033 | 0.347905 | ||||||||
\(819\) | 1.57243 | 0.0549450 | ||||||||
\(820\) | −18.5394 | −0.647424 | ||||||||
\(821\) | 17.6996 | 0.617720 | 0.308860 | − | 0.951107i | \(-0.400053\pi\) | ||||
0.308860 | + | 0.951107i | \(0.400053\pi\) | |||||||
\(822\) | 25.3227 | 0.883230 | ||||||||
\(823\) | 49.8018 | 1.73598 | 0.867991 | − | 0.496580i | \(-0.165411\pi\) | ||||
0.867991 | + | 0.496580i | \(0.165411\pi\) | |||||||
\(824\) | −7.62144 | −0.265505 | ||||||||
\(825\) | −55.1163 | −1.91890 | ||||||||
\(826\) | 14.9796 | 0.521207 | ||||||||
\(827\) | −4.66362 | −0.162170 | −0.0810850 | − | 0.996707i | \(-0.525839\pi\) | ||||
−0.0810850 | + | 0.996707i | \(0.525839\pi\) | |||||||
\(828\) | 0.780502 | 0.0271243 | ||||||||
\(829\) | −8.20300 | −0.284902 | −0.142451 | − | 0.989802i | \(-0.545498\pi\) | ||||
−0.142451 | + | 0.989802i | \(0.545498\pi\) | |||||||
\(830\) | 8.39630 | 0.291440 | ||||||||
\(831\) | −42.5949 | −1.47760 | ||||||||
\(832\) | 0.746865 | 0.0258929 | ||||||||
\(833\) | 1.13316 | 0.0392618 | ||||||||
\(834\) | 2.45440 | 0.0849888 | ||||||||
\(835\) | −46.1055 | −1.59555 | ||||||||
\(836\) | −22.3117 | −0.771667 | ||||||||
\(837\) | 46.5399 | 1.60865 | ||||||||
\(838\) | 13.7916 | 0.476422 | ||||||||
\(839\) | 27.2736 | 0.941589 | 0.470795 | − | 0.882243i | \(-0.343967\pi\) | ||||
0.470795 | + | 0.882243i | \(0.343967\pi\) | |||||||
\(840\) | 14.3311 | 0.494471 | ||||||||
\(841\) | 9.04696 | 0.311964 | ||||||||
\(842\) | −8.50368 | −0.293056 | ||||||||
\(843\) | −5.60948 | −0.193201 | ||||||||
\(844\) | −1.69707 | −0.0584155 | ||||||||
\(845\) | −44.3707 | −1.52640 | ||||||||
\(846\) | −5.24591 | −0.180358 | ||||||||
\(847\) | −32.3171 | −1.11043 | ||||||||
\(848\) | 2.81932 | 0.0968159 | ||||||||
\(849\) | 32.3522 | 1.11032 | ||||||||
\(850\) | −31.6560 | −1.08579 | ||||||||
\(851\) | 2.87867 | 0.0986796 | ||||||||
\(852\) | 13.9703 | 0.478615 | ||||||||
\(853\) | −53.4894 | −1.83144 | −0.915722 | − | 0.401813i | \(-0.868380\pi\) | ||||
−0.915722 | + | 0.401813i | \(0.868380\pi\) | |||||||
\(854\) | −10.2932 | −0.352227 | ||||||||
\(855\) | −12.9547 | −0.443040 | ||||||||
\(856\) | 10.1233 | 0.346009 | ||||||||
\(857\) | −45.9350 | −1.56911 | −0.784554 | − | 0.620060i | \(-0.787108\pi\) | ||||
−0.784554 | + | 0.620060i | \(0.787108\pi\) | |||||||
\(858\) | 5.33396 | 0.182099 | ||||||||
\(859\) | 3.53685 | 0.120676 | 0.0603379 | − | 0.998178i | \(-0.480782\pi\) | ||||
0.0603379 | + | 0.998178i | \(0.480782\pi\) | |||||||
\(860\) | 4.48365 | 0.152891 | ||||||||
\(861\) | 20.8919 | 0.711993 | ||||||||
\(862\) | 22.1517 | 0.754491 | ||||||||
\(863\) | 50.0558 | 1.70392 | 0.851959 | − | 0.523608i | \(-0.175414\pi\) | ||||
0.851959 | + | 0.523608i | \(0.175414\pi\) | |||||||
\(864\) | 5.63218 | 0.191611 | ||||||||
\(865\) | −9.79454 | −0.333025 | ||||||||
\(866\) | −33.6565 | −1.14369 | ||||||||
\(867\) | −0.260015 | −0.00883058 | ||||||||
\(868\) | 22.2896 | 0.756558 | ||||||||
\(869\) | 28.0956 | 0.953079 | ||||||||
\(870\) | 32.7708 | 1.11103 | ||||||||
\(871\) | −7.76125 | −0.262980 | ||||||||
\(872\) | 0.727196 | 0.0246260 | ||||||||
\(873\) | 4.51886 | 0.152940 | ||||||||
\(874\) | 4.65428 | 0.157433 | ||||||||
\(875\) | −26.1403 | −0.883704 | ||||||||
\(876\) | −4.07311 | −0.137618 | ||||||||
\(877\) | 20.8561 | 0.704261 | 0.352131 | − | 0.935951i | \(-0.385457\pi\) | ||||
0.352131 | + | 0.935951i | \(0.385457\pi\) | |||||||
\(878\) | 15.3656 | 0.518564 | ||||||||
\(879\) | −14.5398 | −0.490415 | ||||||||
\(880\) | −17.0954 | −0.576287 | ||||||||
\(881\) | 9.62865 | 0.324398 | 0.162199 | − | 0.986758i | \(-0.448141\pi\) | ||||
0.162199 | + | 0.986758i | \(0.448141\pi\) | |||||||
\(882\) | 0.215617 | 0.00726020 | ||||||||
\(883\) | 16.4198 | 0.552570 | 0.276285 | − | 0.961076i | \(-0.410897\pi\) | ||||
0.276285 | + | 0.961076i | \(0.410897\pi\) | |||||||
\(884\) | 3.06356 | 0.103039 | ||||||||
\(885\) | 29.5035 | 0.991749 | ||||||||
\(886\) | −22.7407 | −0.763989 | ||||||||
\(887\) | 48.5468 | 1.63004 | 0.815022 | − | 0.579431i | \(-0.196725\pi\) | ||||
0.815022 | + | 0.579431i | \(0.196725\pi\) | |||||||
\(888\) | 4.28864 | 0.143917 | ||||||||
\(889\) | 24.9577 | 0.837056 | ||||||||
\(890\) | 7.63653 | 0.255977 | ||||||||
\(891\) | 28.9992 | 0.971510 | ||||||||
\(892\) | 13.8360 | 0.463265 | ||||||||
\(893\) | −31.2823 | −1.04682 | ||||||||
\(894\) | −7.77587 | −0.260064 | ||||||||
\(895\) | −55.0716 | −1.84084 | ||||||||
\(896\) | 2.69745 | 0.0901156 | ||||||||
\(897\) | −1.11268 | −0.0371512 | ||||||||
\(898\) | −14.9135 | −0.497671 | ||||||||
\(899\) | 50.9692 | 1.69992 | ||||||||
\(900\) | −6.02347 | −0.200782 | ||||||||
\(901\) | 11.5645 | 0.385270 | ||||||||
\(902\) | −24.9216 | −0.829800 | ||||||||
\(903\) | −5.05259 | −0.168140 | ||||||||
\(904\) | −13.1529 | −0.437458 | ||||||||
\(905\) | 64.8696 | 2.15634 | ||||||||
\(906\) | 0.983610 | 0.0326783 | ||||||||
\(907\) | −23.4932 | −0.780079 | −0.390040 | − | 0.920798i | \(-0.627539\pi\) | ||||
−0.390040 | + | 0.920798i | \(0.627539\pi\) | |||||||
\(908\) | −10.5000 | −0.348455 | ||||||||
\(909\) | −3.56538 | −0.118256 | ||||||||
\(910\) | 7.18449 | 0.238163 | ||||||||
\(911\) | −0.163661 | −0.00542232 | −0.00271116 | − | 0.999996i | \(-0.500863\pi\) | ||||
−0.00271116 | + | 0.999996i | \(0.500863\pi\) | |||||||
\(912\) | 6.93393 | 0.229605 | ||||||||
\(913\) | 11.2868 | 0.373537 | ||||||||
\(914\) | 22.3010 | 0.737653 | ||||||||
\(915\) | −20.2733 | −0.670214 | ||||||||
\(916\) | 12.3635 | 0.408503 | ||||||||
\(917\) | 2.69745 | 0.0890778 | ||||||||
\(918\) | 23.1026 | 0.762499 | ||||||||
\(919\) | −13.7266 | −0.452799 | −0.226400 | − | 0.974034i | \(-0.572696\pi\) | ||||
−0.226400 | + | 0.974034i | \(0.572696\pi\) | |||||||
\(920\) | 3.56615 | 0.117572 | ||||||||
\(921\) | −28.7814 | −0.948381 | ||||||||
\(922\) | −1.90159 | −0.0626254 | ||||||||
\(923\) | 7.00360 | 0.230526 | ||||||||
\(924\) | 19.2647 | 0.633761 | ||||||||
\(925\) | −22.2159 | −0.730456 | ||||||||
\(926\) | 29.3617 | 0.964885 | ||||||||
\(927\) | −5.94855 | −0.195376 | ||||||||
\(928\) | 6.16822 | 0.202482 | ||||||||
\(929\) | −0.724085 | −0.0237565 | −0.0118782 | − | 0.999929i | \(-0.503781\pi\) | ||||
−0.0118782 | + | 0.999929i | \(0.503781\pi\) | |||||||
\(930\) | 43.9011 | 1.43957 | ||||||||
\(931\) | 1.28576 | 0.0421392 | ||||||||
\(932\) | 7.47482 | 0.244846 | ||||||||
\(933\) | 15.6439 | 0.512159 | ||||||||
\(934\) | −24.7902 | −0.811160 | ||||||||
\(935\) | −70.1235 | −2.29328 | ||||||||
\(936\) | 0.582930 | 0.0190537 | ||||||||
\(937\) | 14.3312 | 0.468181 | 0.234091 | − | 0.972215i | \(-0.424789\pi\) | ||||
0.234091 | + | 0.972215i | \(0.424789\pi\) | |||||||
\(938\) | −28.0313 | −0.915255 | ||||||||
\(939\) | 9.77769 | 0.319083 | ||||||||
\(940\) | −23.9688 | −0.781775 | ||||||||
\(941\) | 45.7456 | 1.49126 | 0.745632 | − | 0.666358i | \(-0.232148\pi\) | ||||
0.745632 | + | 0.666358i | \(0.232148\pi\) | |||||||
\(942\) | −13.4258 | −0.437435 | ||||||||
\(943\) | 5.19872 | 0.169293 | ||||||||
\(944\) | 5.55324 | 0.180743 | ||||||||
\(945\) | 54.1789 | 1.76244 | ||||||||
\(946\) | 6.02716 | 0.195960 | ||||||||
\(947\) | 34.3980 | 1.11778 | 0.558892 | − | 0.829240i | \(-0.311227\pi\) | ||||
0.558892 | + | 0.829240i | \(0.311227\pi\) | |||||||
\(948\) | −8.73144 | −0.283584 | ||||||||
\(949\) | −2.04193 | −0.0662839 | ||||||||
\(950\) | −35.9190 | −1.16537 | ||||||||
\(951\) | −1.71720 | −0.0556839 | ||||||||
\(952\) | 11.0646 | 0.358607 | ||||||||
\(953\) | −47.9522 | −1.55333 | −0.776663 | − | 0.629917i | \(-0.783089\pi\) | ||||
−0.776663 | + | 0.629917i | \(0.783089\pi\) | |||||||
\(954\) | 2.20049 | 0.0712434 | ||||||||
\(955\) | 7.13404 | 0.230852 | ||||||||
\(956\) | 2.73435 | 0.0884350 | ||||||||
\(957\) | 44.0522 | 1.42401 | ||||||||
\(958\) | 15.1463 | 0.489354 | ||||||||
\(959\) | 45.8497 | 1.48056 | ||||||||
\(960\) | 5.31284 | 0.171471 | ||||||||
\(961\) | 37.2805 | 1.20260 | ||||||||
\(962\) | 2.14998 | 0.0693182 | ||||||||
\(963\) | 7.90129 | 0.254616 | ||||||||
\(964\) | 25.7983 | 0.830907 | ||||||||
\(965\) | −4.94139 | −0.159069 | ||||||||
\(966\) | −4.01866 | −0.129298 | ||||||||
\(967\) | −53.9920 | −1.73627 | −0.868133 | − | 0.496332i | \(-0.834680\pi\) | ||||
−0.868133 | + | 0.496332i | \(0.834680\pi\) | |||||||
\(968\) | −11.9806 | −0.385071 | ||||||||
\(969\) | 28.4422 | 0.913695 | ||||||||
\(970\) | 20.6469 | 0.662931 | ||||||||
\(971\) | 31.6232 | 1.01484 | 0.507418 | − | 0.861700i | \(-0.330600\pi\) | ||||
0.507418 | + | 0.861700i | \(0.330600\pi\) | |||||||
\(972\) | 7.88431 | 0.252889 | ||||||||
\(973\) | 4.44397 | 0.142467 | ||||||||
\(974\) | 21.9472 | 0.703234 | ||||||||
\(975\) | 8.58701 | 0.275004 | ||||||||
\(976\) | −3.81590 | −0.122144 | ||||||||
\(977\) | 33.5811 | 1.07435 | 0.537177 | − | 0.843469i | \(-0.319491\pi\) | ||||
0.537177 | + | 0.843469i | \(0.319491\pi\) | |||||||
\(978\) | −10.3791 | −0.331887 | ||||||||
\(979\) | 10.2654 | 0.328084 | ||||||||
\(980\) | 0.985164 | 0.0314699 | ||||||||
\(981\) | 0.567578 | 0.0181214 | ||||||||
\(982\) | 2.23531 | 0.0713315 | ||||||||
\(983\) | −14.6335 | −0.466735 | −0.233368 | − | 0.972389i | \(-0.574975\pi\) | ||||
−0.233368 | + | 0.972389i | \(0.574975\pi\) | |||||||
\(984\) | 7.74503 | 0.246903 | ||||||||
\(985\) | 3.32933 | 0.106081 | ||||||||
\(986\) | 25.3013 | 0.805759 | ||||||||
\(987\) | 27.0102 | 0.859744 | ||||||||
\(988\) | 3.47612 | 0.110590 | ||||||||
\(989\) | −1.25728 | −0.0399792 | ||||||||
\(990\) | −13.3430 | −0.424069 | ||||||||
\(991\) | 54.6984 | 1.73755 | 0.868777 | − | 0.495204i | \(-0.164907\pi\) | ||||
0.868777 | + | 0.495204i | \(0.164907\pi\) | |||||||
\(992\) | 8.26320 | 0.262357 | ||||||||
\(993\) | −31.4017 | −0.996503 | ||||||||
\(994\) | 25.2949 | 0.802306 | ||||||||
\(995\) | 0.137391 | 0.00435560 | ||||||||
\(996\) | −3.50765 | −0.111144 | ||||||||
\(997\) | 3.56303 | 0.112842 | 0.0564212 | − | 0.998407i | \(-0.482031\pi\) | ||||
0.0564212 | + | 0.998407i | \(0.482031\pi\) | |||||||
\(998\) | 10.8109 | 0.342212 | ||||||||
\(999\) | 16.2132 | 0.512964 |
(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 | 6026.2.a.h.1.17 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6026.2.a.h.1.17 | ✓ | 24 | 1.1 | even | 1 | trivial |