Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4022,2,Mod(1,4022)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4022, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4022.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4022 = 2 \cdot 2011 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4022.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: | \(32.1158316930\) |
Analytic rank: | \(1\) |
Dimension: | \(31\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Character | \(\chi\) | \(=\) | 4022.1 |
$q$-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 | ||||||||
\(3\) | −2.62663 | −1.51649 | −0.758243 | − | 0.651972i | \(-0.773942\pi\) | ||||
−0.758243 | + | 0.651972i | \(0.773942\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −2.01799 | −0.902473 | −0.451236 | − | 0.892404i | \(-0.649017\pi\) | ||||
−0.451236 | + | 0.892404i | \(0.649017\pi\) | |||||||
\(6\) | −2.62663 | −1.07232 | ||||||||
\(7\) | 0.869262 | 0.328550 | 0.164275 | − | 0.986415i | \(-0.447472\pi\) | ||||
0.164275 | + | 0.986415i | \(0.447472\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.89919 | 1.29973 | ||||||||
\(10\) | −2.01799 | −0.638145 | ||||||||
\(11\) | −3.06749 | −0.924882 | −0.462441 | − | 0.886650i | \(-0.653026\pi\) | ||||
−0.462441 | + | 0.886650i | \(0.653026\pi\) | |||||||
\(12\) | −2.62663 | −0.758243 | ||||||||
\(13\) | 4.63284 | 1.28492 | 0.642460 | − | 0.766319i | \(-0.277914\pi\) | ||||
0.642460 | + | 0.766319i | \(0.277914\pi\) | |||||||
\(14\) | 0.869262 | 0.232320 | ||||||||
\(15\) | 5.30052 | 1.36859 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.775089 | −0.187987 | −0.0939933 | − | 0.995573i | \(-0.529963\pi\) | ||||
−0.0939933 | + | 0.995573i | \(0.529963\pi\) | |||||||
\(18\) | 3.89919 | 0.919049 | ||||||||
\(19\) | −4.44299 | −1.01929 | −0.509646 | − | 0.860384i | \(-0.670224\pi\) | ||||
−0.509646 | + | 0.860384i | \(0.670224\pi\) | |||||||
\(20\) | −2.01799 | −0.451236 | ||||||||
\(21\) | −2.28323 | −0.498242 | ||||||||
\(22\) | −3.06749 | −0.653991 | ||||||||
\(23\) | −0.835104 | −0.174131 | −0.0870656 | − | 0.996203i | \(-0.527749\pi\) | ||||
−0.0870656 | + | 0.996203i | \(0.527749\pi\) | |||||||
\(24\) | −2.62663 | −0.536159 | ||||||||
\(25\) | −0.927713 | −0.185543 | ||||||||
\(26\) | 4.63284 | 0.908575 | ||||||||
\(27\) | −2.36185 | −0.454539 | ||||||||
\(28\) | 0.869262 | 0.164275 | ||||||||
\(29\) | 7.31632 | 1.35861 | 0.679303 | − | 0.733858i | \(-0.262282\pi\) | ||||
0.679303 | + | 0.733858i | \(0.262282\pi\) | |||||||
\(30\) | 5.30052 | 0.967738 | ||||||||
\(31\) | −1.45586 | −0.261480 | −0.130740 | − | 0.991417i | \(-0.541735\pi\) | ||||
−0.130740 | + | 0.991417i | \(0.541735\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 8.05716 | 1.40257 | ||||||||
\(34\) | −0.775089 | −0.132927 | ||||||||
\(35\) | −1.75416 | −0.296508 | ||||||||
\(36\) | 3.89919 | 0.649866 | ||||||||
\(37\) | 9.35814 | 1.53847 | 0.769234 | − | 0.638967i | \(-0.220638\pi\) | ||||
0.769234 | + | 0.638967i | \(0.220638\pi\) | |||||||
\(38\) | −4.44299 | −0.720748 | ||||||||
\(39\) | −12.1688 | −1.94856 | ||||||||
\(40\) | −2.01799 | −0.319072 | ||||||||
\(41\) | 1.66167 | 0.259509 | 0.129754 | − | 0.991546i | \(-0.458581\pi\) | ||||
0.129754 | + | 0.991546i | \(0.458581\pi\) | |||||||
\(42\) | −2.28323 | −0.352310 | ||||||||
\(43\) | −9.08328 | −1.38519 | −0.692593 | − | 0.721328i | \(-0.743532\pi\) | ||||
−0.692593 | + | 0.721328i | \(0.743532\pi\) | |||||||
\(44\) | −3.06749 | −0.462441 | ||||||||
\(45\) | −7.86854 | −1.17297 | ||||||||
\(46\) | −0.835104 | −0.123129 | ||||||||
\(47\) | −1.03325 | −0.150715 | −0.0753576 | − | 0.997157i | \(-0.524010\pi\) | ||||
−0.0753576 | + | 0.997157i | \(0.524010\pi\) | |||||||
\(48\) | −2.62663 | −0.379122 | ||||||||
\(49\) | −6.24438 | −0.892055 | ||||||||
\(50\) | −0.927713 | −0.131198 | ||||||||
\(51\) | 2.03587 | 0.285079 | ||||||||
\(52\) | 4.63284 | 0.642460 | ||||||||
\(53\) | 4.38682 | 0.602576 | 0.301288 | − | 0.953533i | \(-0.402583\pi\) | ||||
0.301288 | + | 0.953533i | \(0.402583\pi\) | |||||||
\(54\) | −2.36185 | −0.321408 | ||||||||
\(55\) | 6.19016 | 0.834681 | ||||||||
\(56\) | 0.869262 | 0.116160 | ||||||||
\(57\) | 11.6701 | 1.54574 | ||||||||
\(58\) | 7.31632 | 0.960680 | ||||||||
\(59\) | 11.3418 | 1.47657 | 0.738287 | − | 0.674487i | \(-0.235635\pi\) | ||||
0.738287 | + | 0.674487i | \(0.235635\pi\) | |||||||
\(60\) | 5.30052 | 0.684294 | ||||||||
\(61\) | −0.898436 | −0.115033 | −0.0575165 | − | 0.998345i | \(-0.518318\pi\) | ||||
−0.0575165 | + | 0.998345i | \(0.518318\pi\) | |||||||
\(62\) | −1.45586 | −0.184894 | ||||||||
\(63\) | 3.38942 | 0.427027 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.34903 | −1.15960 | ||||||||
\(66\) | 8.05716 | 0.991768 | ||||||||
\(67\) | 4.69714 | 0.573847 | 0.286923 | − | 0.957954i | \(-0.407368\pi\) | ||||
0.286923 | + | 0.957954i | \(0.407368\pi\) | |||||||
\(68\) | −0.775089 | −0.0939933 | ||||||||
\(69\) | 2.19351 | 0.264068 | ||||||||
\(70\) | −1.75416 | −0.209662 | ||||||||
\(71\) | 5.82527 | 0.691332 | 0.345666 | − | 0.938358i | \(-0.387653\pi\) | ||||
0.345666 | + | 0.938358i | \(0.387653\pi\) | |||||||
\(72\) | 3.89919 | 0.459525 | ||||||||
\(73\) | 0.985216 | 0.115311 | 0.0576554 | − | 0.998337i | \(-0.481638\pi\) | ||||
0.0576554 | + | 0.998337i | \(0.481638\pi\) | |||||||
\(74\) | 9.35814 | 1.08786 | ||||||||
\(75\) | 2.43676 | 0.281373 | ||||||||
\(76\) | −4.44299 | −0.509646 | ||||||||
\(77\) | −2.66645 | −0.303870 | ||||||||
\(78\) | −12.1688 | −1.37784 | ||||||||
\(79\) | −8.32160 | −0.936254 | −0.468127 | − | 0.883661i | \(-0.655071\pi\) | ||||
−0.468127 | + | 0.883661i | \(0.655071\pi\) | |||||||
\(80\) | −2.01799 | −0.225618 | ||||||||
\(81\) | −5.49386 | −0.610429 | ||||||||
\(82\) | 1.66167 | 0.183501 | ||||||||
\(83\) | −6.68708 | −0.734002 | −0.367001 | − | 0.930220i | \(-0.619616\pi\) | ||||
−0.367001 | + | 0.930220i | \(0.619616\pi\) | |||||||
\(84\) | −2.28323 | −0.249121 | ||||||||
\(85\) | 1.56412 | 0.169653 | ||||||||
\(86\) | −9.08328 | −0.979475 | ||||||||
\(87\) | −19.2173 | −2.06031 | ||||||||
\(88\) | −3.06749 | −0.326995 | ||||||||
\(89\) | −5.26768 | −0.558373 | −0.279186 | − | 0.960237i | \(-0.590065\pi\) | ||||
−0.279186 | + | 0.960237i | \(0.590065\pi\) | |||||||
\(90\) | −7.86854 | −0.829417 | ||||||||
\(91\) | 4.02715 | 0.422160 | ||||||||
\(92\) | −0.835104 | −0.0870656 | ||||||||
\(93\) | 3.82400 | 0.396530 | ||||||||
\(94\) | −1.03325 | −0.106572 | ||||||||
\(95\) | 8.96591 | 0.919883 | ||||||||
\(96\) | −2.62663 | −0.268079 | ||||||||
\(97\) | −6.27376 | −0.637004 | −0.318502 | − | 0.947922i | \(-0.603180\pi\) | ||||
−0.318502 | + | 0.947922i | \(0.603180\pi\) | |||||||
\(98\) | −6.24438 | −0.630778 | ||||||||
\(99\) | −11.9607 | −1.20210 | ||||||||
\(100\) | −0.927713 | −0.0927713 | ||||||||
\(101\) | −12.2375 | −1.21768 | −0.608840 | − | 0.793293i | \(-0.708365\pi\) | ||||
−0.608840 | + | 0.793293i | \(0.708365\pi\) | |||||||
\(102\) | 2.03587 | 0.201582 | ||||||||
\(103\) | −0.130840 | −0.0128921 | −0.00644603 | − | 0.999979i | \(-0.502052\pi\) | ||||
−0.00644603 | + | 0.999979i | \(0.502052\pi\) | |||||||
\(104\) | 4.63284 | 0.454288 | ||||||||
\(105\) | 4.60754 | 0.449650 | ||||||||
\(106\) | 4.38682 | 0.426086 | ||||||||
\(107\) | −13.7200 | −1.32636 | −0.663182 | − | 0.748458i | \(-0.730794\pi\) | ||||
−0.663182 | + | 0.748458i | \(0.730794\pi\) | |||||||
\(108\) | −2.36185 | −0.227269 | ||||||||
\(109\) | −16.3980 | −1.57065 | −0.785323 | − | 0.619086i | \(-0.787503\pi\) | ||||
−0.785323 | + | 0.619086i | \(0.787503\pi\) | |||||||
\(110\) | 6.19016 | 0.590209 | ||||||||
\(111\) | −24.5804 | −2.33307 | ||||||||
\(112\) | 0.869262 | 0.0821375 | ||||||||
\(113\) | 16.7815 | 1.57867 | 0.789337 | − | 0.613960i | \(-0.210424\pi\) | ||||
0.789337 | + | 0.613960i | \(0.210424\pi\) | |||||||
\(114\) | 11.6701 | 1.09300 | ||||||||
\(115\) | 1.68523 | 0.157149 | ||||||||
\(116\) | 7.31632 | 0.679303 | ||||||||
\(117\) | 18.0644 | 1.67005 | ||||||||
\(118\) | 11.3418 | 1.04410 | ||||||||
\(119\) | −0.673755 | −0.0617630 | ||||||||
\(120\) | 5.30052 | 0.483869 | ||||||||
\(121\) | −1.59052 | −0.144592 | ||||||||
\(122\) | −0.898436 | −0.0813406 | ||||||||
\(123\) | −4.36459 | −0.393542 | ||||||||
\(124\) | −1.45586 | −0.130740 | ||||||||
\(125\) | 11.9621 | 1.06992 | ||||||||
\(126\) | 3.38942 | 0.301954 | ||||||||
\(127\) | −18.7825 | −1.66667 | −0.833337 | − | 0.552765i | \(-0.813573\pi\) | ||||
−0.833337 | + | 0.552765i | \(0.813573\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 23.8584 | 2.10062 | ||||||||
\(130\) | −9.34903 | −0.819965 | ||||||||
\(131\) | −7.58408 | −0.662624 | −0.331312 | − | 0.943521i | \(-0.607491\pi\) | ||||
−0.331312 | + | 0.943521i | \(0.607491\pi\) | |||||||
\(132\) | 8.05716 | 0.701286 | ||||||||
\(133\) | −3.86212 | −0.334888 | ||||||||
\(134\) | 4.69714 | 0.405771 | ||||||||
\(135\) | 4.76620 | 0.410209 | ||||||||
\(136\) | −0.775089 | −0.0664633 | ||||||||
\(137\) | 5.47271 | 0.467565 | 0.233783 | − | 0.972289i | \(-0.424890\pi\) | ||||
0.233783 | + | 0.972289i | \(0.424890\pi\) | |||||||
\(138\) | 2.19351 | 0.186724 | ||||||||
\(139\) | −12.4032 | −1.05202 | −0.526012 | − | 0.850477i | \(-0.676313\pi\) | ||||
−0.526012 | + | 0.850477i | \(0.676313\pi\) | |||||||
\(140\) | −1.75416 | −0.148254 | ||||||||
\(141\) | 2.71397 | 0.228558 | ||||||||
\(142\) | 5.82527 | 0.488845 | ||||||||
\(143\) | −14.2112 | −1.18840 | ||||||||
\(144\) | 3.89919 | 0.324933 | ||||||||
\(145\) | −14.7643 | −1.22611 | ||||||||
\(146\) | 0.985216 | 0.0815371 | ||||||||
\(147\) | 16.4017 | 1.35279 | ||||||||
\(148\) | 9.35814 | 0.769234 | ||||||||
\(149\) | 5.67473 | 0.464892 | 0.232446 | − | 0.972609i | \(-0.425327\pi\) | ||||
0.232446 | + | 0.972609i | \(0.425327\pi\) | |||||||
\(150\) | 2.43676 | 0.198961 | ||||||||
\(151\) | −2.77842 | −0.226104 | −0.113052 | − | 0.993589i | \(-0.536063\pi\) | ||||
−0.113052 | + | 0.993589i | \(0.536063\pi\) | |||||||
\(152\) | −4.44299 | −0.360374 | ||||||||
\(153\) | −3.02222 | −0.244332 | ||||||||
\(154\) | −2.66645 | −0.214869 | ||||||||
\(155\) | 2.93791 | 0.235978 | ||||||||
\(156\) | −12.1688 | −0.974282 | ||||||||
\(157\) | 7.38851 | 0.589668 | 0.294834 | − | 0.955549i | \(-0.404736\pi\) | ||||
0.294834 | + | 0.955549i | \(0.404736\pi\) | |||||||
\(158\) | −8.32160 | −0.662031 | ||||||||
\(159\) | −11.5226 | −0.913799 | ||||||||
\(160\) | −2.01799 | −0.159536 | ||||||||
\(161\) | −0.725924 | −0.0572108 | ||||||||
\(162\) | −5.49386 | −0.431639 | ||||||||
\(163\) | 19.6105 | 1.53601 | 0.768007 | − | 0.640441i | \(-0.221248\pi\) | ||||
0.768007 | + | 0.640441i | \(0.221248\pi\) | |||||||
\(164\) | 1.66167 | 0.129754 | ||||||||
\(165\) | −16.2593 | −1.26578 | ||||||||
\(166\) | −6.68708 | −0.519018 | ||||||||
\(167\) | −15.9501 | −1.23425 | −0.617127 | − | 0.786863i | \(-0.711704\pi\) | ||||
−0.617127 | + | 0.786863i | \(0.711704\pi\) | |||||||
\(168\) | −2.28323 | −0.176155 | ||||||||
\(169\) | 8.46323 | 0.651018 | ||||||||
\(170\) | 1.56412 | 0.119963 | ||||||||
\(171\) | −17.3241 | −1.32481 | ||||||||
\(172\) | −9.08328 | −0.692593 | ||||||||
\(173\) | −21.5598 | −1.63916 | −0.819581 | − | 0.572963i | \(-0.805794\pi\) | ||||
−0.819581 | + | 0.572963i | \(0.805794\pi\) | |||||||
\(174\) | −19.2173 | −1.45686 | ||||||||
\(175\) | −0.806426 | −0.0609600 | ||||||||
\(176\) | −3.06749 | −0.231221 | ||||||||
\(177\) | −29.7907 | −2.23920 | ||||||||
\(178\) | −5.26768 | −0.394829 | ||||||||
\(179\) | 4.17437 | 0.312007 | 0.156003 | − | 0.987757i | \(-0.450139\pi\) | ||||
0.156003 | + | 0.987757i | \(0.450139\pi\) | |||||||
\(180\) | −7.86854 | −0.586486 | ||||||||
\(181\) | −10.1009 | −0.750797 | −0.375399 | − | 0.926863i | \(-0.622494\pi\) | ||||
−0.375399 | + | 0.926863i | \(0.622494\pi\) | |||||||
\(182\) | 4.02715 | 0.298512 | ||||||||
\(183\) | 2.35986 | 0.174446 | ||||||||
\(184\) | −0.835104 | −0.0615647 | ||||||||
\(185\) | −18.8846 | −1.38843 | ||||||||
\(186\) | 3.82400 | 0.280389 | ||||||||
\(187\) | 2.37758 | 0.173866 | ||||||||
\(188\) | −1.03325 | −0.0753576 | ||||||||
\(189\) | −2.05307 | −0.149339 | ||||||||
\(190\) | 8.96591 | 0.650456 | ||||||||
\(191\) | −11.6898 | −0.845843 | −0.422922 | − | 0.906166i | \(-0.638995\pi\) | ||||
−0.422922 | + | 0.906166i | \(0.638995\pi\) | |||||||
\(192\) | −2.62663 | −0.189561 | ||||||||
\(193\) | −20.8039 | −1.49750 | −0.748750 | − | 0.662852i | \(-0.769346\pi\) | ||||
−0.748750 | + | 0.662852i | \(0.769346\pi\) | |||||||
\(194\) | −6.27376 | −0.450430 | ||||||||
\(195\) | 24.5565 | 1.75853 | ||||||||
\(196\) | −6.24438 | −0.446027 | ||||||||
\(197\) | 4.24154 | 0.302197 | 0.151099 | − | 0.988519i | \(-0.451719\pi\) | ||||
0.151099 | + | 0.988519i | \(0.451719\pi\) | |||||||
\(198\) | −11.9607 | −0.850012 | ||||||||
\(199\) | −26.0230 | −1.84472 | −0.922362 | − | 0.386326i | \(-0.873744\pi\) | ||||
−0.922362 | + | 0.386326i | \(0.873744\pi\) | |||||||
\(200\) | −0.927713 | −0.0655992 | ||||||||
\(201\) | −12.3376 | −0.870231 | ||||||||
\(202\) | −12.2375 | −0.861030 | ||||||||
\(203\) | 6.35980 | 0.446370 | ||||||||
\(204\) | 2.03587 | 0.142540 | ||||||||
\(205\) | −3.35323 | −0.234200 | ||||||||
\(206\) | −0.130840 | −0.00911606 | ||||||||
\(207\) | −3.25623 | −0.226324 | ||||||||
\(208\) | 4.63284 | 0.321230 | ||||||||
\(209\) | 13.6288 | 0.942725 | ||||||||
\(210\) | 4.60754 | 0.317950 | ||||||||
\(211\) | −3.43432 | −0.236429 | −0.118214 | − | 0.992988i | \(-0.537717\pi\) | ||||
−0.118214 | + | 0.992988i | \(0.537717\pi\) | |||||||
\(212\) | 4.38682 | 0.301288 | ||||||||
\(213\) | −15.3008 | −1.04840 | ||||||||
\(214\) | −13.7200 | −0.937881 | ||||||||
\(215\) | 18.3300 | 1.25009 | ||||||||
\(216\) | −2.36185 | −0.160704 | ||||||||
\(217\) | −1.26552 | −0.0859092 | ||||||||
\(218\) | −16.3980 | −1.11061 | ||||||||
\(219\) | −2.58780 | −0.174867 | ||||||||
\(220\) | 6.19016 | 0.417341 | ||||||||
\(221\) | −3.59087 | −0.241548 | ||||||||
\(222\) | −24.5804 | −1.64973 | ||||||||
\(223\) | −24.7701 | −1.65873 | −0.829363 | − | 0.558710i | \(-0.811297\pi\) | ||||
−0.829363 | + | 0.558710i | \(0.811297\pi\) | |||||||
\(224\) | 0.869262 | 0.0580800 | ||||||||
\(225\) | −3.61733 | −0.241156 | ||||||||
\(226\) | 16.7815 | 1.11629 | ||||||||
\(227\) | −15.3499 | −1.01881 | −0.509405 | − | 0.860527i | \(-0.670134\pi\) | ||||
−0.509405 | + | 0.860527i | \(0.670134\pi\) | |||||||
\(228\) | 11.6701 | 0.772871 | ||||||||
\(229\) | −17.2681 | −1.14111 | −0.570555 | − | 0.821259i | \(-0.693272\pi\) | ||||
−0.570555 | + | 0.821259i | \(0.693272\pi\) | |||||||
\(230\) | 1.68523 | 0.111121 | ||||||||
\(231\) | 7.00378 | 0.460815 | ||||||||
\(232\) | 7.31632 | 0.480340 | ||||||||
\(233\) | −7.61184 | −0.498668 | −0.249334 | − | 0.968417i | \(-0.580212\pi\) | ||||
−0.249334 | + | 0.968417i | \(0.580212\pi\) | |||||||
\(234\) | 18.0644 | 1.18090 | ||||||||
\(235\) | 2.08509 | 0.136016 | ||||||||
\(236\) | 11.3418 | 0.738287 | ||||||||
\(237\) | 21.8578 | 1.41982 | ||||||||
\(238\) | −0.673755 | −0.0436731 | ||||||||
\(239\) | 20.7851 | 1.34448 | 0.672239 | − | 0.740334i | \(-0.265333\pi\) | ||||
0.672239 | + | 0.740334i | \(0.265333\pi\) | |||||||
\(240\) | 5.30052 | 0.342147 | ||||||||
\(241\) | −6.31856 | −0.407014 | −0.203507 | − | 0.979073i | \(-0.565234\pi\) | ||||
−0.203507 | + | 0.979073i | \(0.565234\pi\) | |||||||
\(242\) | −1.59052 | −0.102242 | ||||||||
\(243\) | 21.5159 | 1.38025 | ||||||||
\(244\) | −0.898436 | −0.0575165 | ||||||||
\(245\) | 12.6011 | 0.805055 | ||||||||
\(246\) | −4.36459 | −0.278276 | ||||||||
\(247\) | −20.5837 | −1.30971 | ||||||||
\(248\) | −1.45586 | −0.0924470 | ||||||||
\(249\) | 17.5645 | 1.11310 | ||||||||
\(250\) | 11.9621 | 0.756548 | ||||||||
\(251\) | 1.19661 | 0.0755295 | 0.0377648 | − | 0.999287i | \(-0.487976\pi\) | ||||
0.0377648 | + | 0.999287i | \(0.487976\pi\) | |||||||
\(252\) | 3.38942 | 0.213513 | ||||||||
\(253\) | 2.56167 | 0.161051 | ||||||||
\(254\) | −18.7825 | −1.17852 | ||||||||
\(255\) | −4.10837 | −0.257276 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 0.713759 | 0.0445230 | 0.0222615 | − | 0.999752i | \(-0.492913\pi\) | ||||
0.0222615 | + | 0.999752i | \(0.492913\pi\) | |||||||
\(258\) | 23.8584 | 1.48536 | ||||||||
\(259\) | 8.13467 | 0.505464 | ||||||||
\(260\) | −9.34903 | −0.579802 | ||||||||
\(261\) | 28.5278 | 1.76582 | ||||||||
\(262\) | −7.58408 | −0.468546 | ||||||||
\(263\) | 30.3768 | 1.87312 | 0.936558 | − | 0.350513i | \(-0.113993\pi\) | ||||
0.936558 | + | 0.350513i | \(0.113993\pi\) | |||||||
\(264\) | 8.05716 | 0.495884 | ||||||||
\(265\) | −8.85257 | −0.543809 | ||||||||
\(266\) | −3.86212 | −0.236802 | ||||||||
\(267\) | 13.8363 | 0.846765 | ||||||||
\(268\) | 4.69714 | 0.286923 | ||||||||
\(269\) | −0.769870 | −0.0469398 | −0.0234699 | − | 0.999725i | \(-0.507471\pi\) | ||||
−0.0234699 | + | 0.999725i | \(0.507471\pi\) | |||||||
\(270\) | 4.76620 | 0.290062 | ||||||||
\(271\) | 6.50686 | 0.395264 | 0.197632 | − | 0.980276i | \(-0.436675\pi\) | ||||
0.197632 | + | 0.980276i | \(0.436675\pi\) | |||||||
\(272\) | −0.775089 | −0.0469967 | ||||||||
\(273\) | −10.5778 | −0.640201 | ||||||||
\(274\) | 5.47271 | 0.330619 | ||||||||
\(275\) | 2.84575 | 0.171605 | ||||||||
\(276\) | 2.19351 | 0.132034 | ||||||||
\(277\) | −19.1652 | −1.15153 | −0.575763 | − | 0.817617i | \(-0.695295\pi\) | ||||
−0.575763 | + | 0.817617i | \(0.695295\pi\) | |||||||
\(278\) | −12.4032 | −0.743893 | ||||||||
\(279\) | −5.67667 | −0.339853 | ||||||||
\(280\) | −1.75416 | −0.104831 | ||||||||
\(281\) | 19.9604 | 1.19074 | 0.595370 | − | 0.803452i | \(-0.297005\pi\) | ||||
0.595370 | + | 0.803452i | \(0.297005\pi\) | |||||||
\(282\) | 2.71397 | 0.161615 | ||||||||
\(283\) | 21.5655 | 1.28193 | 0.640967 | − | 0.767569i | \(-0.278534\pi\) | ||||
0.640967 | + | 0.767569i | \(0.278534\pi\) | |||||||
\(284\) | 5.82527 | 0.345666 | ||||||||
\(285\) | −23.5501 | −1.39499 | ||||||||
\(286\) | −14.2112 | −0.840325 | ||||||||
\(287\) | 1.44442 | 0.0852617 | ||||||||
\(288\) | 3.89919 | 0.229762 | ||||||||
\(289\) | −16.3992 | −0.964661 | ||||||||
\(290\) | −14.7643 | −0.866987 | ||||||||
\(291\) | 16.4789 | 0.966009 | ||||||||
\(292\) | 0.985216 | 0.0576554 | ||||||||
\(293\) | 9.51601 | 0.555931 | 0.277966 | − | 0.960591i | \(-0.410340\pi\) | ||||
0.277966 | + | 0.960591i | \(0.410340\pi\) | |||||||
\(294\) | 16.4017 | 0.956566 | ||||||||
\(295\) | −22.8876 | −1.33257 | ||||||||
\(296\) | 9.35814 | 0.543931 | ||||||||
\(297\) | 7.24496 | 0.420395 | ||||||||
\(298\) | 5.67473 | 0.328728 | ||||||||
\(299\) | −3.86890 | −0.223745 | ||||||||
\(300\) | 2.43676 | 0.140686 | ||||||||
\(301\) | −7.89575 | −0.455103 | ||||||||
\(302\) | −2.77842 | −0.159880 | ||||||||
\(303\) | 32.1435 | 1.84660 | ||||||||
\(304\) | −4.44299 | −0.254823 | ||||||||
\(305\) | 1.81304 | 0.103814 | ||||||||
\(306\) | −3.02222 | −0.172769 | ||||||||
\(307\) | 26.7324 | 1.52570 | 0.762848 | − | 0.646577i | \(-0.223800\pi\) | ||||
0.762848 | + | 0.646577i | \(0.223800\pi\) | |||||||
\(308\) | −2.66645 | −0.151935 | ||||||||
\(309\) | 0.343669 | 0.0195506 | ||||||||
\(310\) | 2.93791 | 0.166862 | ||||||||
\(311\) | −3.78382 | −0.214561 | −0.107280 | − | 0.994229i | \(-0.534214\pi\) | ||||
−0.107280 | + | 0.994229i | \(0.534214\pi\) | |||||||
\(312\) | −12.1688 | −0.688921 | ||||||||
\(313\) | −6.50925 | −0.367925 | −0.183962 | − | 0.982933i | \(-0.558892\pi\) | ||||
−0.183962 | + | 0.982933i | \(0.558892\pi\) | |||||||
\(314\) | 7.38851 | 0.416958 | ||||||||
\(315\) | −6.83982 | −0.385380 | ||||||||
\(316\) | −8.32160 | −0.468127 | ||||||||
\(317\) | −18.8198 | −1.05703 | −0.528513 | − | 0.848925i | \(-0.677250\pi\) | ||||
−0.528513 | + | 0.848925i | \(0.677250\pi\) | |||||||
\(318\) | −11.5226 | −0.646153 | ||||||||
\(319\) | −22.4427 | −1.25655 | ||||||||
\(320\) | −2.01799 | −0.112809 | ||||||||
\(321\) | 36.0374 | 2.01141 | ||||||||
\(322\) | −0.725924 | −0.0404542 | ||||||||
\(323\) | 3.44371 | 0.191613 | ||||||||
\(324\) | −5.49386 | −0.305215 | ||||||||
\(325\) | −4.29795 | −0.238407 | ||||||||
\(326\) | 19.6105 | 1.08613 | ||||||||
\(327\) | 43.0716 | 2.38186 | ||||||||
\(328\) | 1.66167 | 0.0917503 | ||||||||
\(329\) | −0.898166 | −0.0495175 | ||||||||
\(330\) | −16.2593 | −0.895044 | ||||||||
\(331\) | 16.9172 | 0.929854 | 0.464927 | − | 0.885349i | \(-0.346081\pi\) | ||||
0.464927 | + | 0.885349i | \(0.346081\pi\) | |||||||
\(332\) | −6.68708 | −0.367001 | ||||||||
\(333\) | 36.4892 | 1.99960 | ||||||||
\(334\) | −15.9501 | −0.872750 | ||||||||
\(335\) | −9.47878 | −0.517881 | ||||||||
\(336\) | −2.28323 | −0.124560 | ||||||||
\(337\) | 5.19508 | 0.282994 | 0.141497 | − | 0.989939i | \(-0.454808\pi\) | ||||
0.141497 | + | 0.989939i | \(0.454808\pi\) | |||||||
\(338\) | 8.46323 | 0.460339 | ||||||||
\(339\) | −44.0789 | −2.39404 | ||||||||
\(340\) | 1.56412 | 0.0848265 | ||||||||
\(341\) | 4.46582 | 0.241838 | ||||||||
\(342\) | −17.3241 | −0.936779 | ||||||||
\(343\) | −11.5128 | −0.621635 | ||||||||
\(344\) | −9.08328 | −0.489737 | ||||||||
\(345\) | −4.42648 | −0.238314 | ||||||||
\(346\) | −21.5598 | −1.15906 | ||||||||
\(347\) | −16.9331 | −0.909016 | −0.454508 | − | 0.890743i | \(-0.650185\pi\) | ||||
−0.454508 | + | 0.890743i | \(0.650185\pi\) | |||||||
\(348\) | −19.2173 | −1.03015 | ||||||||
\(349\) | −22.8937 | −1.22547 | −0.612735 | − | 0.790288i | \(-0.709931\pi\) | ||||
−0.612735 | + | 0.790288i | \(0.709931\pi\) | |||||||
\(350\) | −0.806426 | −0.0431053 | ||||||||
\(351\) | −10.9421 | −0.584046 | ||||||||
\(352\) | −3.06749 | −0.163498 | ||||||||
\(353\) | −8.90369 | −0.473896 | −0.236948 | − | 0.971522i | \(-0.576147\pi\) | ||||
−0.236948 | + | 0.971522i | \(0.576147\pi\) | |||||||
\(354\) | −29.7907 | −1.58336 | ||||||||
\(355\) | −11.7553 | −0.623908 | ||||||||
\(356\) | −5.26768 | −0.279186 | ||||||||
\(357\) | 1.76971 | 0.0936628 | ||||||||
\(358\) | 4.17437 | 0.220622 | ||||||||
\(359\) | 11.3467 | 0.598856 | 0.299428 | − | 0.954119i | \(-0.403204\pi\) | ||||
0.299428 | + | 0.954119i | \(0.403204\pi\) | |||||||
\(360\) | −7.86854 | −0.414708 | ||||||||
\(361\) | 0.740152 | 0.0389554 | ||||||||
\(362\) | −10.1009 | −0.530894 | ||||||||
\(363\) | 4.17770 | 0.219272 | ||||||||
\(364\) | 4.02715 | 0.211080 | ||||||||
\(365\) | −1.98816 | −0.104065 | ||||||||
\(366\) | 2.35986 | 0.123352 | ||||||||
\(367\) | −29.6837 | −1.54948 | −0.774738 | − | 0.632282i | \(-0.782118\pi\) | ||||
−0.774738 | + | 0.632282i | \(0.782118\pi\) | |||||||
\(368\) | −0.835104 | −0.0435328 | ||||||||
\(369\) | 6.47917 | 0.337292 | ||||||||
\(370\) | −18.8846 | −0.981765 | ||||||||
\(371\) | 3.81330 | 0.197976 | ||||||||
\(372\) | 3.82400 | 0.198265 | ||||||||
\(373\) | 19.6595 | 1.01793 | 0.508964 | − | 0.860788i | \(-0.330029\pi\) | ||||
0.508964 | + | 0.860788i | \(0.330029\pi\) | |||||||
\(374\) | 2.37758 | 0.122942 | ||||||||
\(375\) | −31.4200 | −1.62252 | ||||||||
\(376\) | −1.03325 | −0.0532859 | ||||||||
\(377\) | 33.8954 | 1.74570 | ||||||||
\(378\) | −2.05307 | −0.105598 | ||||||||
\(379\) | −6.66140 | −0.342173 | −0.171087 | − | 0.985256i | \(-0.554728\pi\) | ||||
−0.171087 | + | 0.985256i | \(0.554728\pi\) | |||||||
\(380\) | 8.96591 | 0.459942 | ||||||||
\(381\) | 49.3346 | 2.52749 | ||||||||
\(382\) | −11.6898 | −0.598101 | ||||||||
\(383\) | −18.8105 | −0.961170 | −0.480585 | − | 0.876948i | \(-0.659576\pi\) | ||||
−0.480585 | + | 0.876948i | \(0.659576\pi\) | |||||||
\(384\) | −2.62663 | −0.134040 | ||||||||
\(385\) | 5.38087 | 0.274235 | ||||||||
\(386\) | −20.8039 | −1.05889 | ||||||||
\(387\) | −35.4175 | −1.80037 | ||||||||
\(388\) | −6.27376 | −0.318502 | ||||||||
\(389\) | 19.2467 | 0.975849 | 0.487924 | − | 0.872886i | \(-0.337754\pi\) | ||||
0.487924 | + | 0.872886i | \(0.337754\pi\) | |||||||
\(390\) | 24.5565 | 1.24347 | ||||||||
\(391\) | 0.647280 | 0.0327343 | ||||||||
\(392\) | −6.24438 | −0.315389 | ||||||||
\(393\) | 19.9206 | 1.00486 | ||||||||
\(394\) | 4.24154 | 0.213686 | ||||||||
\(395\) | 16.7929 | 0.844943 | ||||||||
\(396\) | −11.9607 | −0.601049 | ||||||||
\(397\) | 3.92053 | 0.196766 | 0.0983829 | − | 0.995149i | \(-0.468633\pi\) | ||||
0.0983829 | + | 0.995149i | \(0.468633\pi\) | |||||||
\(398\) | −26.0230 | −1.30442 | ||||||||
\(399\) | 10.1444 | 0.507854 | ||||||||
\(400\) | −0.927713 | −0.0463857 | ||||||||
\(401\) | 14.4986 | 0.724023 | 0.362012 | − | 0.932174i | \(-0.382090\pi\) | ||||
0.362012 | + | 0.932174i | \(0.382090\pi\) | |||||||
\(402\) | −12.3376 | −0.615346 | ||||||||
\(403\) | −6.74476 | −0.335980 | ||||||||
\(404\) | −12.2375 | −0.608840 | ||||||||
\(405\) | 11.0866 | 0.550896 | ||||||||
\(406\) | 6.35980 | 0.315631 | ||||||||
\(407\) | −28.7060 | −1.42290 | ||||||||
\(408\) | 2.03587 | 0.100791 | ||||||||
\(409\) | −23.4191 | −1.15800 | −0.579001 | − | 0.815327i | \(-0.696557\pi\) | ||||
−0.579001 | + | 0.815327i | \(0.696557\pi\) | |||||||
\(410\) | −3.35323 | −0.165604 | ||||||||
\(411\) | −14.3748 | −0.709056 | ||||||||
\(412\) | −0.130840 | −0.00644603 | ||||||||
\(413\) | 9.85897 | 0.485128 | ||||||||
\(414\) | −3.25623 | −0.160035 | ||||||||
\(415\) | 13.4945 | 0.662417 | ||||||||
\(416\) | 4.63284 | 0.227144 | ||||||||
\(417\) | 32.5786 | 1.59538 | ||||||||
\(418\) | 13.6288 | 0.666607 | ||||||||
\(419\) | 11.8966 | 0.581187 | 0.290593 | − | 0.956847i | \(-0.406147\pi\) | ||||
0.290593 | + | 0.956847i | \(0.406147\pi\) | |||||||
\(420\) | 4.60754 | 0.224825 | ||||||||
\(421\) | 6.94450 | 0.338454 | 0.169227 | − | 0.985577i | \(-0.445873\pi\) | ||||
0.169227 | + | 0.985577i | \(0.445873\pi\) | |||||||
\(422\) | −3.43432 | −0.167180 | ||||||||
\(423\) | −4.02885 | −0.195889 | ||||||||
\(424\) | 4.38682 | 0.213043 | ||||||||
\(425\) | 0.719060 | 0.0348795 | ||||||||
\(426\) | −15.3008 | −0.741327 | ||||||||
\(427\) | −0.780976 | −0.0377941 | ||||||||
\(428\) | −13.7200 | −0.663182 | ||||||||
\(429\) | 37.3276 | 1.80219 | ||||||||
\(430\) | 18.3300 | 0.883950 | ||||||||
\(431\) | 15.5617 | 0.749580 | 0.374790 | − | 0.927110i | \(-0.377715\pi\) | ||||
0.374790 | + | 0.927110i | \(0.377715\pi\) | |||||||
\(432\) | −2.36185 | −0.113635 | ||||||||
\(433\) | 21.6943 | 1.04256 | 0.521280 | − | 0.853386i | \(-0.325455\pi\) | ||||
0.521280 | + | 0.853386i | \(0.325455\pi\) | |||||||
\(434\) | −1.26552 | −0.0607469 | ||||||||
\(435\) | 38.7803 | 1.85937 | ||||||||
\(436\) | −16.3980 | −0.785323 | ||||||||
\(437\) | 3.71036 | 0.177490 | ||||||||
\(438\) | −2.58780 | −0.123650 | ||||||||
\(439\) | 20.4553 | 0.976276 | 0.488138 | − | 0.872766i | \(-0.337676\pi\) | ||||
0.488138 | + | 0.872766i | \(0.337676\pi\) | |||||||
\(440\) | 6.19016 | 0.295104 | ||||||||
\(441\) | −24.3481 | −1.15943 | ||||||||
\(442\) | −3.59087 | −0.170800 | ||||||||
\(443\) | −2.10477 | −0.100001 | −0.0500004 | − | 0.998749i | \(-0.515922\pi\) | ||||
−0.0500004 | + | 0.998749i | \(0.515922\pi\) | |||||||
\(444\) | −24.5804 | −1.16653 | ||||||||
\(445\) | 10.6301 | 0.503916 | ||||||||
\(446\) | −24.7701 | −1.17290 | ||||||||
\(447\) | −14.9054 | −0.705003 | ||||||||
\(448\) | 0.869262 | 0.0410688 | ||||||||
\(449\) | 14.3330 | 0.676416 | 0.338208 | − | 0.941071i | \(-0.390179\pi\) | ||||
0.338208 | + | 0.941071i | \(0.390179\pi\) | |||||||
\(450\) | −3.61733 | −0.170523 | ||||||||
\(451\) | −5.09715 | −0.240015 | ||||||||
\(452\) | 16.7815 | 0.789337 | ||||||||
\(453\) | 7.29788 | 0.342884 | ||||||||
\(454\) | −15.3499 | −0.720407 | ||||||||
\(455\) | −8.12676 | −0.380988 | ||||||||
\(456\) | 11.6701 | 0.546502 | ||||||||
\(457\) | 12.3206 | 0.576332 | 0.288166 | − | 0.957581i | \(-0.406955\pi\) | ||||
0.288166 | + | 0.957581i | \(0.406955\pi\) | |||||||
\(458\) | −17.2681 | −0.806887 | ||||||||
\(459\) | 1.83065 | 0.0854473 | ||||||||
\(460\) | 1.68523 | 0.0785743 | ||||||||
\(461\) | 4.23570 | 0.197276 | 0.0986381 | − | 0.995123i | \(-0.468551\pi\) | ||||
0.0986381 | + | 0.995123i | \(0.468551\pi\) | |||||||
\(462\) | 7.00378 | 0.325845 | ||||||||
\(463\) | 2.85761 | 0.132804 | 0.0664022 | − | 0.997793i | \(-0.478848\pi\) | ||||
0.0664022 | + | 0.997793i | \(0.478848\pi\) | |||||||
\(464\) | 7.31632 | 0.339652 | ||||||||
\(465\) | −7.71680 | −0.357858 | ||||||||
\(466\) | −7.61184 | −0.352612 | ||||||||
\(467\) | −2.96500 | −0.137204 | −0.0686019 | − | 0.997644i | \(-0.521854\pi\) | ||||
−0.0686019 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(468\) | 18.0644 | 0.835025 | ||||||||
\(469\) | 4.08304 | 0.188537 | ||||||||
\(470\) | 2.08509 | 0.0961781 | ||||||||
\(471\) | −19.4069 | −0.894223 | ||||||||
\(472\) | 11.3418 | 0.522048 | ||||||||
\(473\) | 27.8628 | 1.28114 | ||||||||
\(474\) | 21.8578 | 1.00396 | ||||||||
\(475\) | 4.12182 | 0.189122 | ||||||||
\(476\) | −0.673755 | −0.0308815 | ||||||||
\(477\) | 17.1051 | 0.783187 | ||||||||
\(478\) | 20.7851 | 0.950689 | ||||||||
\(479\) | −29.9074 | −1.36650 | −0.683251 | − | 0.730183i | \(-0.739435\pi\) | ||||
−0.683251 | + | 0.730183i | \(0.739435\pi\) | |||||||
\(480\) | 5.30052 | 0.241934 | ||||||||
\(481\) | 43.3548 | 1.97681 | ||||||||
\(482\) | −6.31856 | −0.287802 | ||||||||
\(483\) | 1.90673 | 0.0867594 | ||||||||
\(484\) | −1.59052 | −0.0722962 | ||||||||
\(485\) | 12.6604 | 0.574879 | ||||||||
\(486\) | 21.5159 | 0.975982 | ||||||||
\(487\) | −33.0113 | −1.49588 | −0.747941 | − | 0.663765i | \(-0.768958\pi\) | ||||
−0.747941 | + | 0.663765i | \(0.768958\pi\) | |||||||
\(488\) | −0.898436 | −0.0406703 | ||||||||
\(489\) | −51.5096 | −2.32935 | ||||||||
\(490\) | 12.6011 | 0.569260 | ||||||||
\(491\) | 15.9388 | 0.719308 | 0.359654 | − | 0.933086i | \(-0.382895\pi\) | ||||
0.359654 | + | 0.933086i | \(0.382895\pi\) | |||||||
\(492\) | −4.36459 | −0.196771 | ||||||||
\(493\) | −5.67080 | −0.255400 | ||||||||
\(494\) | −20.5837 | −0.926103 | ||||||||
\(495\) | 24.1367 | 1.08486 | ||||||||
\(496\) | −1.45586 | −0.0653699 | ||||||||
\(497\) | 5.06368 | 0.227137 | ||||||||
\(498\) | 17.5645 | 0.787084 | ||||||||
\(499\) | 30.3075 | 1.35675 | 0.678375 | − | 0.734716i | \(-0.262685\pi\) | ||||
0.678375 | + | 0.734716i | \(0.262685\pi\) | |||||||
\(500\) | 11.9621 | 0.534960 | ||||||||
\(501\) | 41.8950 | 1.87173 | ||||||||
\(502\) | 1.19661 | 0.0534074 | ||||||||
\(503\) | −21.0148 | −0.937006 | −0.468503 | − | 0.883462i | \(-0.655206\pi\) | ||||
−0.468503 | + | 0.883462i | \(0.655206\pi\) | |||||||
\(504\) | 3.38942 | 0.150977 | ||||||||
\(505\) | 24.6952 | 1.09892 | ||||||||
\(506\) | 2.56167 | 0.113880 | ||||||||
\(507\) | −22.2298 | −0.987260 | ||||||||
\(508\) | −18.7825 | −0.833337 | ||||||||
\(509\) | 8.40933 | 0.372737 | 0.186368 | − | 0.982480i | \(-0.440328\pi\) | ||||
0.186368 | + | 0.982480i | \(0.440328\pi\) | |||||||
\(510\) | −4.10837 | −0.181922 | ||||||||
\(511\) | 0.856411 | 0.0378854 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 10.4937 | 0.463308 | ||||||||
\(514\) | 0.713759 | 0.0314825 | ||||||||
\(515\) | 0.264034 | 0.0116347 | ||||||||
\(516\) | 23.8584 | 1.05031 | ||||||||
\(517\) | 3.16949 | 0.139394 | ||||||||
\(518\) | 8.13467 | 0.357417 | ||||||||
\(519\) | 56.6297 | 2.48577 | ||||||||
\(520\) | −9.34903 | −0.409982 | ||||||||
\(521\) | −30.4088 | −1.33223 | −0.666116 | − | 0.745848i | \(-0.732045\pi\) | ||||
−0.666116 | + | 0.745848i | \(0.732045\pi\) | |||||||
\(522\) | 28.5278 | 1.24863 | ||||||||
\(523\) | 14.4158 | 0.630359 | 0.315179 | − | 0.949032i | \(-0.397935\pi\) | ||||
0.315179 | + | 0.949032i | \(0.397935\pi\) | |||||||
\(524\) | −7.58408 | −0.331312 | ||||||||
\(525\) | 2.11818 | 0.0924451 | ||||||||
\(526\) | 30.3768 | 1.32449 | ||||||||
\(527\) | 1.12842 | 0.0491547 | ||||||||
\(528\) | 8.05716 | 0.350643 | ||||||||
\(529\) | −22.3026 | −0.969678 | ||||||||
\(530\) | −8.85257 | −0.384531 | ||||||||
\(531\) | 44.2238 | 1.91915 | ||||||||
\(532\) | −3.86212 | −0.167444 | ||||||||
\(533\) | 7.69825 | 0.333448 | ||||||||
\(534\) | 13.8363 | 0.598753 | ||||||||
\(535\) | 27.6869 | 1.19701 | ||||||||
\(536\) | 4.69714 | 0.202885 | ||||||||
\(537\) | −10.9645 | −0.473154 | ||||||||
\(538\) | −0.769870 | −0.0331915 | ||||||||
\(539\) | 19.1546 | 0.825046 | ||||||||
\(540\) | 4.76620 | 0.205105 | ||||||||
\(541\) | −25.8777 | −1.11257 | −0.556284 | − | 0.830992i | \(-0.687773\pi\) | ||||
−0.556284 | + | 0.830992i | \(0.687773\pi\) | |||||||
\(542\) | 6.50686 | 0.279494 | ||||||||
\(543\) | 26.5315 | 1.13857 | ||||||||
\(544\) | −0.775089 | −0.0332317 | ||||||||
\(545\) | 33.0911 | 1.41747 | ||||||||
\(546\) | −10.5778 | −0.452690 | ||||||||
\(547\) | −23.5624 | −1.00745 | −0.503727 | − | 0.863863i | \(-0.668038\pi\) | ||||
−0.503727 | + | 0.863863i | \(0.668038\pi\) | |||||||
\(548\) | 5.47271 | 0.233783 | ||||||||
\(549\) | −3.50318 | −0.149512 | ||||||||
\(550\) | 2.84575 | 0.121343 | ||||||||
\(551\) | −32.5063 | −1.38482 | ||||||||
\(552\) | 2.19351 | 0.0933620 | ||||||||
\(553\) | −7.23365 | −0.307606 | ||||||||
\(554\) | −19.1652 | −0.814252 | ||||||||
\(555\) | 49.6030 | 2.10553 | ||||||||
\(556\) | −12.4032 | −0.526012 | ||||||||
\(557\) | −3.83761 | −0.162605 | −0.0813023 | − | 0.996689i | \(-0.525908\pi\) | ||||
−0.0813023 | + | 0.996689i | \(0.525908\pi\) | |||||||
\(558\) | −5.67667 | −0.240313 | ||||||||
\(559\) | −42.0814 | −1.77985 | ||||||||
\(560\) | −1.75416 | −0.0741269 | ||||||||
\(561\) | −6.24502 | −0.263665 | ||||||||
\(562\) | 19.9604 | 0.841980 | ||||||||
\(563\) | −2.79561 | −0.117821 | −0.0589105 | − | 0.998263i | \(-0.518763\pi\) | ||||
−0.0589105 | + | 0.998263i | \(0.518763\pi\) | |||||||
\(564\) | 2.71397 | 0.114279 | ||||||||
\(565\) | −33.8650 | −1.42471 | ||||||||
\(566\) | 21.5655 | 0.906464 | ||||||||
\(567\) | −4.77561 | −0.200557 | ||||||||
\(568\) | 5.82527 | 0.244423 | ||||||||
\(569\) | −23.4932 | −0.984886 | −0.492443 | − | 0.870345i | \(-0.663896\pi\) | ||||
−0.492443 | + | 0.870345i | \(0.663896\pi\) | |||||||
\(570\) | −23.5501 | −0.986407 | ||||||||
\(571\) | −15.6974 | −0.656916 | −0.328458 | − | 0.944519i | \(-0.606529\pi\) | ||||
−0.328458 | + | 0.944519i | \(0.606529\pi\) | |||||||
\(572\) | −14.2112 | −0.594200 | ||||||||
\(573\) | 30.7048 | 1.28271 | ||||||||
\(574\) | 1.44442 | 0.0602891 | ||||||||
\(575\) | 0.774737 | 0.0323088 | ||||||||
\(576\) | 3.89919 | 0.162466 | ||||||||
\(577\) | −24.7883 | −1.03195 | −0.515976 | − | 0.856603i | \(-0.672571\pi\) | ||||
−0.515976 | + | 0.856603i | \(0.672571\pi\) | |||||||
\(578\) | −16.3992 | −0.682118 | ||||||||
\(579\) | 54.6443 | 2.27094 | ||||||||
\(580\) | −14.7643 | −0.613053 | ||||||||
\(581\) | −5.81282 | −0.241157 | ||||||||
\(582\) | 16.4789 | 0.683071 | ||||||||
\(583\) | −13.4565 | −0.557312 | ||||||||
\(584\) | 0.985216 | 0.0407685 | ||||||||
\(585\) | −36.4537 | −1.50718 | ||||||||
\(586\) | 9.51601 | 0.393103 | ||||||||
\(587\) | 3.28898 | 0.135751 | 0.0678753 | − | 0.997694i | \(-0.478378\pi\) | ||||
0.0678753 | + | 0.997694i | \(0.478378\pi\) | |||||||
\(588\) | 16.4017 | 0.676395 | ||||||||
\(589\) | 6.46836 | 0.266524 | ||||||||
\(590\) | −22.8876 | −0.942268 | ||||||||
\(591\) | −11.1410 | −0.458278 | ||||||||
\(592\) | 9.35814 | 0.384617 | ||||||||
\(593\) | 33.8030 | 1.38812 | 0.694062 | − | 0.719915i | \(-0.255819\pi\) | ||||
0.694062 | + | 0.719915i | \(0.255819\pi\) | |||||||
\(594\) | 7.24496 | 0.297264 | ||||||||
\(595\) | 1.35963 | 0.0557395 | ||||||||
\(596\) | 5.67473 | 0.232446 | ||||||||
\(597\) | 68.3530 | 2.79750 | ||||||||
\(598\) | −3.86890 | −0.158211 | ||||||||
\(599\) | −26.9428 | −1.10085 | −0.550427 | − | 0.834883i | \(-0.685535\pi\) | ||||
−0.550427 | + | 0.834883i | \(0.685535\pi\) | |||||||
\(600\) | 2.43676 | 0.0994804 | ||||||||
\(601\) | 15.9044 | 0.648756 | 0.324378 | − | 0.945928i | \(-0.394845\pi\) | ||||
0.324378 | + | 0.945928i | \(0.394845\pi\) | |||||||
\(602\) | −7.89575 | −0.321807 | ||||||||
\(603\) | 18.3151 | 0.745847 | ||||||||
\(604\) | −2.77842 | −0.113052 | ||||||||
\(605\) | 3.20965 | 0.130491 | ||||||||
\(606\) | 32.1435 | 1.30574 | ||||||||
\(607\) | −31.7959 | −1.29055 | −0.645277 | − | 0.763948i | \(-0.723258\pi\) | ||||
−0.645277 | + | 0.763948i | \(0.723258\pi\) | |||||||
\(608\) | −4.44299 | −0.180187 | ||||||||
\(609\) | −16.7048 | −0.676914 | ||||||||
\(610\) | 1.81304 | 0.0734077 | ||||||||
\(611\) | −4.78689 | −0.193657 | ||||||||
\(612\) | −3.02222 | −0.122166 | ||||||||
\(613\) | 37.7191 | 1.52346 | 0.761730 | − | 0.647895i | \(-0.224350\pi\) | ||||
0.761730 | + | 0.647895i | \(0.224350\pi\) | |||||||
\(614\) | 26.7324 | 1.07883 | ||||||||
\(615\) | 8.80770 | 0.355161 | ||||||||
\(616\) | −2.66645 | −0.107434 | ||||||||
\(617\) | 19.4220 | 0.781900 | 0.390950 | − | 0.920412i | \(-0.372147\pi\) | ||||
0.390950 | + | 0.920412i | \(0.372147\pi\) | |||||||
\(618\) | 0.343669 | 0.0138244 | ||||||||
\(619\) | −10.2017 | −0.410041 | −0.205021 | − | 0.978758i | \(-0.565726\pi\) | ||||
−0.205021 | + | 0.978758i | \(0.565726\pi\) | |||||||
\(620\) | 2.93791 | 0.117989 | ||||||||
\(621\) | 1.97239 | 0.0791494 | ||||||||
\(622\) | −3.78382 | −0.151717 | ||||||||
\(623\) | −4.57899 | −0.183453 | ||||||||
\(624\) | −12.1688 | −0.487141 | ||||||||
\(625\) | −19.5008 | −0.780031 | ||||||||
\(626\) | −6.50925 | −0.260162 | ||||||||
\(627\) | −35.7979 | −1.42963 | ||||||||
\(628\) | 7.38851 | 0.294834 | ||||||||
\(629\) | −7.25339 | −0.289212 | ||||||||
\(630\) | −6.83982 | −0.272505 | ||||||||
\(631\) | 38.8917 | 1.54825 | 0.774127 | − | 0.633031i | \(-0.218189\pi\) | ||||
0.774127 | + | 0.633031i | \(0.218189\pi\) | |||||||
\(632\) | −8.32160 | −0.331016 | ||||||||
\(633\) | 9.02071 | 0.358541 | ||||||||
\(634\) | −18.8198 | −0.747430 | ||||||||
\(635\) | 37.9028 | 1.50413 | ||||||||
\(636\) | −11.5226 | −0.456899 | ||||||||
\(637\) | −28.9292 | −1.14622 | ||||||||
\(638\) | −22.4427 | −0.888516 | ||||||||
\(639\) | 22.7138 | 0.898546 | ||||||||
\(640\) | −2.01799 | −0.0797681 | ||||||||
\(641\) | 25.4677 | 1.00591 | 0.502956 | − | 0.864312i | \(-0.332246\pi\) | ||||
0.502956 | + | 0.864312i | \(0.332246\pi\) | |||||||
\(642\) | 36.0374 | 1.42228 | ||||||||
\(643\) | −37.3387 | −1.47250 | −0.736248 | − | 0.676712i | \(-0.763404\pi\) | ||||
−0.736248 | + | 0.676712i | \(0.763404\pi\) | |||||||
\(644\) | −0.725924 | −0.0286054 | ||||||||
\(645\) | −48.1461 | −1.89575 | ||||||||
\(646\) | 3.44371 | 0.135491 | ||||||||
\(647\) | −27.3563 | −1.07549 | −0.537744 | − | 0.843108i | \(-0.680723\pi\) | ||||
−0.537744 | + | 0.843108i | \(0.680723\pi\) | |||||||
\(648\) | −5.49386 | −0.215819 | ||||||||
\(649\) | −34.7908 | −1.36566 | ||||||||
\(650\) | −4.29795 | −0.168579 | ||||||||
\(651\) | 3.32406 | 0.130280 | ||||||||
\(652\) | 19.6105 | 0.768007 | ||||||||
\(653\) | 15.4388 | 0.604169 | 0.302084 | − | 0.953281i | \(-0.402318\pi\) | ||||
0.302084 | + | 0.953281i | \(0.402318\pi\) | |||||||
\(654\) | 43.0716 | 1.68423 | ||||||||
\(655\) | 15.3046 | 0.598000 | ||||||||
\(656\) | 1.66167 | 0.0648772 | ||||||||
\(657\) | 3.84155 | 0.149873 | ||||||||
\(658\) | −0.898166 | −0.0350142 | ||||||||
\(659\) | 22.7415 | 0.885883 | 0.442942 | − | 0.896550i | \(-0.353935\pi\) | ||||
0.442942 | + | 0.896550i | \(0.353935\pi\) | |||||||
\(660\) | −16.2593 | −0.632892 | ||||||||
\(661\) | 39.1052 | 1.52102 | 0.760508 | − | 0.649329i | \(-0.224950\pi\) | ||||
0.760508 | + | 0.649329i | \(0.224950\pi\) | |||||||
\(662\) | 16.9172 | 0.657506 | ||||||||
\(663\) | 9.43188 | 0.366304 | ||||||||
\(664\) | −6.68708 | −0.259509 | ||||||||
\(665\) | 7.79372 | 0.302228 | ||||||||
\(666\) | 36.4892 | 1.41393 | ||||||||
\(667\) | −6.10989 | −0.236576 | ||||||||
\(668\) | −15.9501 | −0.617127 | ||||||||
\(669\) | 65.0618 | 2.51544 | ||||||||
\(670\) | −9.47878 | −0.366197 | ||||||||
\(671\) | 2.75594 | 0.106392 | ||||||||
\(672\) | −2.28323 | −0.0880775 | ||||||||
\(673\) | 0.167066 | 0.00643992 | 0.00321996 | − | 0.999995i | \(-0.498975\pi\) | ||||
0.00321996 | + | 0.999995i | \(0.498975\pi\) | |||||||
\(674\) | 5.19508 | 0.200107 | ||||||||
\(675\) | 2.19112 | 0.0843364 | ||||||||
\(676\) | 8.46323 | 0.325509 | ||||||||
\(677\) | 14.2245 | 0.546693 | 0.273346 | − | 0.961916i | \(-0.411870\pi\) | ||||
0.273346 | + | 0.961916i | \(0.411870\pi\) | |||||||
\(678\) | −44.0789 | −1.69284 | ||||||||
\(679\) | −5.45354 | −0.209288 | ||||||||
\(680\) | 1.56412 | 0.0599814 | ||||||||
\(681\) | 40.3186 | 1.54501 | ||||||||
\(682\) | 4.46582 | 0.171005 | ||||||||
\(683\) | −23.4179 | −0.896060 | −0.448030 | − | 0.894019i | \(-0.647874\pi\) | ||||
−0.448030 | + | 0.894019i | \(0.647874\pi\) | |||||||
\(684\) | −17.3241 | −0.662403 | ||||||||
\(685\) | −11.0439 | −0.421965 | ||||||||
\(686\) | −11.5128 | −0.439562 | ||||||||
\(687\) | 45.3570 | 1.73048 | ||||||||
\(688\) | −9.08328 | −0.346297 | ||||||||
\(689\) | 20.3235 | 0.774262 | ||||||||
\(690\) | −4.42648 | −0.168513 | ||||||||
\(691\) | 48.6733 | 1.85162 | 0.925809 | − | 0.377991i | \(-0.123385\pi\) | ||||
0.925809 | + | 0.377991i | \(0.123385\pi\) | |||||||
\(692\) | −21.5598 | −0.819581 | ||||||||
\(693\) | −10.3970 | −0.394950 | ||||||||
\(694\) | −16.9331 | −0.642771 | ||||||||
\(695\) | 25.0295 | 0.949423 | ||||||||
\(696\) | −19.2173 | −0.728429 | ||||||||
\(697\) | −1.28794 | −0.0487842 | ||||||||
\(698\) | −22.8937 | −0.866539 | ||||||||
\(699\) | 19.9935 | 0.756224 | ||||||||
\(700\) | −0.806426 | −0.0304800 | ||||||||
\(701\) | 50.1979 | 1.89595 | 0.947975 | − | 0.318344i | \(-0.103127\pi\) | ||||
0.947975 | + | 0.318344i | \(0.103127\pi\) | |||||||
\(702\) | −10.9421 | −0.412983 | ||||||||
\(703\) | −41.5781 | −1.56815 | ||||||||
\(704\) | −3.06749 | −0.115610 | ||||||||
\(705\) | −5.47677 | −0.206267 | ||||||||
\(706\) | −8.90369 | −0.335095 | ||||||||
\(707\) | −10.6376 | −0.400069 | ||||||||
\(708\) | −29.7907 | −1.11960 | ||||||||
\(709\) | 21.5133 | 0.807951 | 0.403975 | − | 0.914770i | \(-0.367628\pi\) | ||||
0.403975 | + | 0.914770i | \(0.367628\pi\) | |||||||
\(710\) | −11.7553 | −0.441170 | ||||||||
\(711\) | −32.4476 | −1.21688 | ||||||||
\(712\) | −5.26768 | −0.197415 | ||||||||
\(713\) | 1.21579 | 0.0455318 | ||||||||
\(714\) | 1.76971 | 0.0662296 | ||||||||
\(715\) | 28.6781 | 1.07250 | ||||||||
\(716\) | 4.17437 | 0.156003 | ||||||||
\(717\) | −54.5949 | −2.03888 | ||||||||
\(718\) | 11.3467 | 0.423455 | ||||||||
\(719\) | −26.1358 | −0.974701 | −0.487350 | − | 0.873206i | \(-0.662037\pi\) | ||||
−0.487350 | + | 0.873206i | \(0.662037\pi\) | |||||||
\(720\) | −7.86854 | −0.293243 | ||||||||
\(721\) | −0.113734 | −0.00423569 | ||||||||
\(722\) | 0.740152 | 0.0275456 | ||||||||
\(723\) | 16.5965 | 0.617231 | ||||||||
\(724\) | −10.1009 | −0.375399 | ||||||||
\(725\) | −6.78745 | −0.252079 | ||||||||
\(726\) | 4.17770 | 0.155049 | ||||||||
\(727\) | −3.28252 | −0.121742 | −0.0608709 | − | 0.998146i | \(-0.519388\pi\) | ||||
−0.0608709 | + | 0.998146i | \(0.519388\pi\) | |||||||
\(728\) | 4.02715 | 0.149256 | ||||||||
\(729\) | −40.0328 | −1.48270 | ||||||||
\(730\) | −1.98816 | −0.0735850 | ||||||||
\(731\) | 7.04035 | 0.260397 | ||||||||
\(732\) | 2.35986 | 0.0872230 | ||||||||
\(733\) | 11.8125 | 0.436306 | 0.218153 | − | 0.975915i | \(-0.429997\pi\) | ||||
0.218153 | + | 0.975915i | \(0.429997\pi\) | |||||||
\(734\) | −29.6837 | −1.09564 | ||||||||
\(735\) | −33.0985 | −1.22086 | ||||||||
\(736\) | −0.835104 | −0.0307823 | ||||||||
\(737\) | −14.4084 | −0.530741 | ||||||||
\(738\) | 6.47917 | 0.238501 | ||||||||
\(739\) | −17.3528 | −0.638332 | −0.319166 | − | 0.947699i | \(-0.603403\pi\) | ||||
−0.319166 | + | 0.947699i | \(0.603403\pi\) | |||||||
\(740\) | −18.8846 | −0.694213 | ||||||||
\(741\) | 54.0657 | 1.98615 | ||||||||
\(742\) | 3.81330 | 0.139991 | ||||||||
\(743\) | −52.0966 | −1.91124 | −0.955619 | − | 0.294606i | \(-0.904812\pi\) | ||||
−0.955619 | + | 0.294606i | \(0.904812\pi\) | |||||||
\(744\) | 3.82400 | 0.140195 | ||||||||
\(745\) | −11.4516 | −0.419553 | ||||||||
\(746\) | 19.6595 | 0.719784 | ||||||||
\(747\) | −26.0742 | −0.954006 | ||||||||
\(748\) | 2.37758 | 0.0869328 | ||||||||
\(749\) | −11.9263 | −0.435777 | ||||||||
\(750\) | −31.4200 | −1.14729 | ||||||||
\(751\) | −11.5572 | −0.421730 | −0.210865 | − | 0.977515i | \(-0.567628\pi\) | ||||
−0.210865 | + | 0.977515i | \(0.567628\pi\) | |||||||
\(752\) | −1.03325 | −0.0376788 | ||||||||
\(753\) | −3.14306 | −0.114539 | ||||||||
\(754\) | 33.8954 | 1.23440 | ||||||||
\(755\) | 5.60682 | 0.204053 | ||||||||
\(756\) | −2.05307 | −0.0746694 | ||||||||
\(757\) | 4.04044 | 0.146852 | 0.0734262 | − | 0.997301i | \(-0.476607\pi\) | ||||
0.0734262 | + | 0.997301i | \(0.476607\pi\) | |||||||
\(758\) | −6.66140 | −0.241953 | ||||||||
\(759\) | −6.72857 | −0.244231 | ||||||||
\(760\) | 8.96591 | 0.325228 | ||||||||
\(761\) | −25.4419 | −0.922268 | −0.461134 | − | 0.887330i | \(-0.652557\pi\) | ||||
−0.461134 | + | 0.887330i | \(0.652557\pi\) | |||||||
\(762\) | 49.3346 | 1.78721 | ||||||||
\(763\) | −14.2542 | −0.516036 | ||||||||
\(764\) | −11.6898 | −0.422922 | ||||||||
\(765\) | 6.09882 | 0.220503 | ||||||||
\(766\) | −18.8105 | −0.679650 | ||||||||
\(767\) | 52.5447 | 1.89728 | ||||||||
\(768\) | −2.62663 | −0.0947804 | ||||||||
\(769\) | 8.44581 | 0.304564 | 0.152282 | − | 0.988337i | \(-0.451338\pi\) | ||||
0.152282 | + | 0.988337i | \(0.451338\pi\) | |||||||
\(770\) | 5.38087 | 0.193913 | ||||||||
\(771\) | −1.87478 | −0.0675186 | ||||||||
\(772\) | −20.8039 | −0.748750 | ||||||||
\(773\) | −21.1247 | −0.759801 | −0.379900 | − | 0.925027i | \(-0.624042\pi\) | ||||
−0.379900 | + | 0.925027i | \(0.624042\pi\) | |||||||
\(774\) | −35.4175 | −1.27305 | ||||||||
\(775\) | 1.35062 | 0.0485156 | ||||||||
\(776\) | −6.27376 | −0.225215 | ||||||||
\(777\) | −21.3668 | −0.766529 | ||||||||
\(778\) | 19.2467 | 0.690029 | ||||||||
\(779\) | −7.38277 | −0.264515 | ||||||||
\(780\) | 24.5565 | 0.879263 | ||||||||
\(781\) | −17.8689 | −0.639401 | ||||||||
\(782\) | 0.647280 | 0.0231467 | ||||||||
\(783\) | −17.2801 | −0.617539 | ||||||||
\(784\) | −6.24438 | −0.223014 | ||||||||
\(785\) | −14.9100 | −0.532159 | ||||||||
\(786\) | 19.9206 | 0.710543 | ||||||||
\(787\) | 17.2896 | 0.616308 | 0.308154 | − | 0.951336i | \(-0.400289\pi\) | ||||
0.308154 | + | 0.951336i | \(0.400289\pi\) | |||||||
\(788\) | 4.24154 | 0.151099 | ||||||||
\(789\) | −79.7888 | −2.84055 | ||||||||
\(790\) | 16.7929 | 0.597465 | ||||||||
\(791\) | 14.5876 | 0.518674 | ||||||||
\(792\) | −11.9607 | −0.425006 | ||||||||
\(793\) | −4.16231 | −0.147808 | ||||||||
\(794\) | 3.92053 | 0.139134 | ||||||||
\(795\) | 23.2524 | 0.824679 | ||||||||
\(796\) | −26.0230 | −0.922362 | ||||||||
\(797\) | −12.0918 | −0.428312 | −0.214156 | − | 0.976799i | \(-0.568700\pi\) | ||||
−0.214156 | + | 0.976799i | \(0.568700\pi\) | |||||||
\(798\) | 10.1444 | 0.359107 | ||||||||
\(799\) | 0.800862 | 0.0283325 | ||||||||
\(800\) | −0.927713 | −0.0327996 | ||||||||
\(801\) | −20.5397 | −0.725735 | ||||||||
\(802\) | 14.4986 | 0.511962 | ||||||||
\(803\) | −3.02214 | −0.106649 | ||||||||
\(804\) | −12.3376 | −0.435115 | ||||||||
\(805\) | 1.46491 | 0.0516312 | ||||||||
\(806\) | −6.74476 | −0.237574 | ||||||||
\(807\) | 2.02217 | 0.0711836 | ||||||||
\(808\) | −12.2375 | −0.430515 | ||||||||
\(809\) | 8.28065 | 0.291132 | 0.145566 | − | 0.989349i | \(-0.453500\pi\) | ||||
0.145566 | + | 0.989349i | \(0.453500\pi\) | |||||||
\(810\) | 11.0866 | 0.389542 | ||||||||
\(811\) | −17.0409 | −0.598388 | −0.299194 | − | 0.954192i | \(-0.596718\pi\) | ||||
−0.299194 | + | 0.954192i | \(0.596718\pi\) | |||||||
\(812\) | 6.35980 | 0.223185 | ||||||||
\(813\) | −17.0911 | −0.599412 | ||||||||
\(814\) | −28.7060 | −1.00614 | ||||||||
\(815\) | −39.5739 | −1.38621 | ||||||||
\(816\) | 2.03587 | 0.0712698 | ||||||||
\(817\) | 40.3569 | 1.41191 | ||||||||
\(818\) | −23.4191 | −0.818831 | ||||||||
\(819\) | 15.7027 | 0.548695 | ||||||||
\(820\) | −3.35323 | −0.117100 | ||||||||
\(821\) | −23.2456 | −0.811277 | −0.405638 | − | 0.914034i | \(-0.632951\pi\) | ||||
−0.405638 | + | 0.914034i | \(0.632951\pi\) | |||||||
\(822\) | −14.3748 | −0.501379 | ||||||||
\(823\) | 31.2422 | 1.08904 | 0.544518 | − | 0.838749i | \(-0.316713\pi\) | ||||
0.544518 | + | 0.838749i | \(0.316713\pi\) | |||||||
\(824\) | −0.130840 | −0.00455803 | ||||||||
\(825\) | −7.47474 | −0.260237 | ||||||||
\(826\) | 9.85897 | 0.343038 | ||||||||
\(827\) | 31.8831 | 1.10869 | 0.554343 | − | 0.832288i | \(-0.312970\pi\) | ||||
0.554343 | + | 0.832288i | \(0.312970\pi\) | |||||||
\(828\) | −3.25623 | −0.113162 | ||||||||
\(829\) | 41.9577 | 1.45725 | 0.728626 | − | 0.684912i | \(-0.240159\pi\) | ||||
0.728626 | + | 0.684912i | \(0.240159\pi\) | |||||||
\(830\) | 13.4945 | 0.468400 | ||||||||
\(831\) | 50.3399 | 1.74627 | ||||||||
\(832\) | 4.63284 | 0.160615 | ||||||||
\(833\) | 4.83995 | 0.167694 | ||||||||
\(834\) | 32.5786 | 1.12810 | ||||||||
\(835\) | 32.1871 | 1.11388 | ||||||||
\(836\) | 13.6288 | 0.471362 | ||||||||
\(837\) | 3.43852 | 0.118853 | ||||||||
\(838\) | 11.8966 | 0.410961 | ||||||||
\(839\) | 24.1542 | 0.833895 | 0.416947 | − | 0.908931i | \(-0.363100\pi\) | ||||
0.416947 | + | 0.908931i | \(0.363100\pi\) | |||||||
\(840\) | 4.60754 | 0.158975 | ||||||||
\(841\) | 24.5285 | 0.845811 | ||||||||
\(842\) | 6.94450 | 0.239323 | ||||||||
\(843\) | −52.4287 | −1.80574 | ||||||||
\(844\) | −3.43432 | −0.118214 | ||||||||
\(845\) | −17.0787 | −0.587526 | ||||||||
\(846\) | −4.02885 | −0.138515 | ||||||||
\(847\) | −1.38258 | −0.0475058 | ||||||||
\(848\) | 4.38682 | 0.150644 | ||||||||
\(849\) | −56.6445 | −1.94403 | ||||||||
\(850\) | 0.719060 | 0.0246636 | ||||||||
\(851\) | −7.81501 | −0.267895 | ||||||||
\(852\) | −15.3008 | −0.524198 | ||||||||
\(853\) | −14.0040 | −0.479487 | −0.239743 | − | 0.970836i | \(-0.577063\pi\) | ||||
−0.239743 | + | 0.970836i | \(0.577063\pi\) | |||||||
\(854\) | −0.780976 | −0.0267245 | ||||||||
\(855\) | 34.9598 | 1.19560 | ||||||||
\(856\) | −13.7200 | −0.468940 | ||||||||
\(857\) | −44.2853 | −1.51276 | −0.756378 | − | 0.654135i | \(-0.773033\pi\) | ||||
−0.756378 | + | 0.654135i | \(0.773033\pi\) | |||||||
\(858\) | 37.3276 | 1.27434 | ||||||||
\(859\) | 39.4789 | 1.34700 | 0.673501 | − | 0.739187i | \(-0.264790\pi\) | ||||
0.673501 | + | 0.739187i | \(0.264790\pi\) | |||||||
\(860\) | 18.3300 | 0.625047 | ||||||||
\(861\) | −3.79397 | −0.129298 | ||||||||
\(862\) | 15.5617 | 0.530033 | ||||||||
\(863\) | −41.8207 | −1.42359 | −0.711796 | − | 0.702386i | \(-0.752118\pi\) | ||||
−0.711796 | + | 0.702386i | \(0.752118\pi\) | |||||||
\(864\) | −2.36185 | −0.0803519 | ||||||||
\(865\) | 43.5075 | 1.47930 | ||||||||
\(866\) | 21.6943 | 0.737202 | ||||||||
\(867\) | 43.0748 | 1.46290 | ||||||||
\(868\) | −1.26552 | −0.0429546 | ||||||||
\(869\) | 25.5264 | 0.865925 | ||||||||
\(870\) | 38.7803 | 1.31477 | ||||||||
\(871\) | 21.7611 | 0.737347 | ||||||||
\(872\) | −16.3980 | −0.555307 | ||||||||
\(873\) | −24.4626 | −0.827935 | ||||||||
\(874\) | 3.71036 | 0.125505 | ||||||||
\(875\) | 10.3982 | 0.351522 | ||||||||
\(876\) | −2.58780 | −0.0874337 | ||||||||
\(877\) | 40.8081 | 1.37799 | 0.688996 | − | 0.724766i | \(-0.258052\pi\) | ||||
0.688996 | + | 0.724766i | \(0.258052\pi\) | |||||||
\(878\) | 20.4553 | 0.690331 | ||||||||
\(879\) | −24.9950 | −0.843062 | ||||||||
\(880\) | 6.19016 | 0.208670 | ||||||||
\(881\) | 39.4179 | 1.32802 | 0.664011 | − | 0.747723i | \(-0.268853\pi\) | ||||
0.664011 | + | 0.747723i | \(0.268853\pi\) | |||||||
\(882\) | −24.3481 | −0.819842 | ||||||||
\(883\) | −32.1634 | −1.08238 | −0.541192 | − | 0.840899i | \(-0.682027\pi\) | ||||
−0.541192 | + | 0.840899i | \(0.682027\pi\) | |||||||
\(884\) | −3.59087 | −0.120774 | ||||||||
\(885\) | 60.1173 | 2.02082 | ||||||||
\(886\) | −2.10477 | −0.0707112 | ||||||||
\(887\) | 6.25831 | 0.210133 | 0.105067 | − | 0.994465i | \(-0.466494\pi\) | ||||
0.105067 | + | 0.994465i | \(0.466494\pi\) | |||||||
\(888\) | −24.5804 | −0.824863 | ||||||||
\(889\) | −16.3269 | −0.547586 | ||||||||
\(890\) | 10.6301 | 0.356323 | ||||||||
\(891\) | 16.8524 | 0.564575 | ||||||||
\(892\) | −24.7701 | −0.829363 | ||||||||
\(893\) | 4.59073 | 0.153623 | ||||||||
\(894\) | −14.9054 | −0.498512 | ||||||||
\(895\) | −8.42383 | −0.281578 | ||||||||
\(896\) | 0.869262 | 0.0290400 | ||||||||
\(897\) | 10.1622 | 0.339306 | ||||||||
\(898\) | 14.3330 | 0.478298 | ||||||||
\(899\) | −10.6515 | −0.355248 | ||||||||
\(900\) | −3.61733 | −0.120578 | ||||||||
\(901\) | −3.40018 | −0.113276 | ||||||||
\(902\) | −5.09715 | −0.169716 | ||||||||
\(903\) | 20.7392 | 0.690158 | ||||||||
\(904\) | 16.7815 | 0.558146 | ||||||||
\(905\) | 20.3836 | 0.677574 | ||||||||
\(906\) | 7.29788 | 0.242456 | ||||||||
\(907\) | 5.58079 | 0.185307 | 0.0926535 | − | 0.995698i | \(-0.470465\pi\) | ||||
0.0926535 | + | 0.995698i | \(0.470465\pi\) | |||||||
\(908\) | −15.3499 | −0.509405 | ||||||||
\(909\) | −47.7166 | −1.58266 | ||||||||
\(910\) | −8.12676 | −0.269399 | ||||||||
\(911\) | −18.1293 | −0.600650 | −0.300325 | − | 0.953837i | \(-0.597095\pi\) | ||||
−0.300325 | + | 0.953837i | \(0.597095\pi\) | |||||||
\(912\) | 11.6701 | 0.386436 | ||||||||
\(913\) | 20.5125 | 0.678866 | ||||||||
\(914\) | 12.3206 | 0.407528 | ||||||||
\(915\) | −4.76218 | −0.157433 | ||||||||
\(916\) | −17.2681 | −0.570555 | ||||||||
\(917\) | −6.59255 | −0.217705 | ||||||||
\(918\) | 1.83065 | 0.0604204 | ||||||||
\(919\) | −18.3856 | −0.606485 | −0.303242 | − | 0.952913i | \(-0.598069\pi\) | ||||
−0.303242 | + | 0.952913i | \(0.598069\pi\) | |||||||
\(920\) | 1.68523 | 0.0555604 | ||||||||
\(921\) | −70.2161 | −2.31370 | ||||||||
\(922\) | 4.23570 | 0.139495 | ||||||||
\(923\) | 26.9875 | 0.888306 | ||||||||
\(924\) | 7.00378 | 0.230408 | ||||||||
\(925\) | −8.68167 | −0.285451 | ||||||||
\(926\) | 2.85761 | 0.0939068 | ||||||||
\(927\) | −0.510171 | −0.0167562 | ||||||||
\(928\) | 7.31632 | 0.240170 | ||||||||
\(929\) | 5.84001 | 0.191605 | 0.0958023 | − | 0.995400i | \(-0.469458\pi\) | ||||
0.0958023 | + | 0.995400i | \(0.469458\pi\) | |||||||
\(930\) | −7.71680 | −0.253044 | ||||||||
\(931\) | 27.7437 | 0.909264 | ||||||||
\(932\) | −7.61184 | −0.249334 | ||||||||
\(933\) | 9.93870 | 0.325378 | ||||||||
\(934\) | −2.96500 | −0.0970177 | ||||||||
\(935\) | −4.79793 | −0.156909 | ||||||||
\(936\) | 18.0644 | 0.590452 | ||||||||
\(937\) | 42.9149 | 1.40197 | 0.700985 | − | 0.713176i | \(-0.252744\pi\) | ||||
0.700985 | + | 0.713176i | \(0.252744\pi\) | |||||||
\(938\) | 4.08304 | 0.133316 | ||||||||
\(939\) | 17.0974 | 0.557953 | ||||||||
\(940\) | 2.08509 | 0.0680082 | ||||||||
\(941\) | −52.2286 | −1.70260 | −0.851302 | − | 0.524675i | \(-0.824187\pi\) | ||||
−0.851302 | + | 0.524675i | \(0.824187\pi\) | |||||||
\(942\) | −19.4069 | −0.632311 | ||||||||
\(943\) | −1.38767 | −0.0451886 | ||||||||
\(944\) | 11.3418 | 0.369143 | ||||||||
\(945\) | 4.14307 | 0.134774 | ||||||||
\(946\) | 27.8628 | 0.905899 | ||||||||
\(947\) | −46.7622 | −1.51957 | −0.759784 | − | 0.650176i | \(-0.774695\pi\) | ||||
−0.759784 | + | 0.650176i | \(0.774695\pi\) | |||||||
\(948\) | 21.8578 | 0.709908 | ||||||||
\(949\) | 4.56435 | 0.148165 | ||||||||
\(950\) | 4.12182 | 0.133729 | ||||||||
\(951\) | 49.4327 | 1.60296 | ||||||||
\(952\) | −0.673755 | −0.0218365 | ||||||||
\(953\) | 28.3752 | 0.919162 | 0.459581 | − | 0.888136i | \(-0.348000\pi\) | ||||
0.459581 | + | 0.888136i | \(0.348000\pi\) | |||||||
\(954\) | 17.1051 | 0.553797 | ||||||||
\(955\) | 23.5899 | 0.763351 | ||||||||
\(956\) | 20.7851 | 0.672239 | ||||||||
\(957\) | 58.9488 | 1.90554 | ||||||||
\(958\) | −29.9074 | −0.966263 | ||||||||
\(959\) | 4.75722 | 0.153619 | ||||||||
\(960\) | 5.30052 | 0.171074 | ||||||||
\(961\) | −28.8805 | −0.931628 | ||||||||
\(962\) | 43.3548 | 1.39781 | ||||||||
\(963\) | −53.4970 | −1.72392 | ||||||||
\(964\) | −6.31856 | −0.203507 | ||||||||
\(965\) | 41.9822 | 1.35145 | ||||||||
\(966\) | 1.90673 | 0.0613482 | ||||||||
\(967\) | −2.41319 | −0.0776029 | −0.0388015 | − | 0.999247i | \(-0.512354\pi\) | ||||
−0.0388015 | + | 0.999247i | \(0.512354\pi\) | |||||||
\(968\) | −1.59052 | −0.0511211 | ||||||||
\(969\) | −9.04536 | −0.290579 | ||||||||
\(970\) | 12.6604 | 0.406501 | ||||||||
\(971\) | −52.8134 | −1.69486 | −0.847432 | − | 0.530904i | \(-0.821852\pi\) | ||||
−0.847432 | + | 0.530904i | \(0.821852\pi\) | |||||||
\(972\) | 21.5159 | 0.690123 | ||||||||
\(973\) | −10.7816 | −0.345642 | ||||||||
\(974\) | −33.0113 | −1.05775 | ||||||||
\(975\) | 11.2891 | 0.361542 | ||||||||
\(976\) | −0.898436 | −0.0287582 | ||||||||
\(977\) | 19.3440 | 0.618870 | 0.309435 | − | 0.950921i | \(-0.399860\pi\) | ||||
0.309435 | + | 0.950921i | \(0.399860\pi\) | |||||||
\(978\) | −51.5096 | −1.64710 | ||||||||
\(979\) | 16.1585 | 0.516429 | ||||||||
\(980\) | 12.6011 | 0.402528 | ||||||||
\(981\) | −63.9391 | −2.04142 | ||||||||
\(982\) | 15.9388 | 0.508628 | ||||||||
\(983\) | −43.6044 | −1.39077 | −0.695383 | − | 0.718639i | \(-0.744765\pi\) | ||||
−0.695383 | + | 0.718639i | \(0.744765\pi\) | |||||||
\(984\) | −4.36459 | −0.139138 | ||||||||
\(985\) | −8.55939 | −0.272725 | ||||||||
\(986\) | −5.67080 | −0.180595 | ||||||||
\(987\) | 2.35915 | 0.0750926 | ||||||||
\(988\) | −20.5837 | −0.654854 | ||||||||
\(989\) | 7.58548 | 0.241204 | ||||||||
\(990\) | 24.1367 | 0.767113 | ||||||||
\(991\) | 1.06141 | 0.0337167 | 0.0168583 | − | 0.999858i | \(-0.494634\pi\) | ||||
0.0168583 | + | 0.999858i | \(0.494634\pi\) | |||||||
\(992\) | −1.45586 | −0.0462235 | ||||||||
\(993\) | −44.4353 | −1.41011 | ||||||||
\(994\) | 5.06368 | 0.160610 | ||||||||
\(995\) | 52.5143 | 1.66481 | ||||||||
\(996\) | 17.5645 | 0.556552 | ||||||||
\(997\) | 25.6535 | 0.812455 | 0.406227 | − | 0.913772i | \(-0.366844\pi\) | ||||
0.406227 | + | 0.913772i | \(0.366844\pi\) | |||||||
\(998\) | 30.3075 | 0.959367 | ||||||||
\(999\) | −22.1025 | −0.699294 |
(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 | 4022.2.a.c.1.6 | ✓ | 31 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4022.2.a.c.1.6 | ✓ | 31 | 1.1 | even | 1 | trivial |