Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8045,2,Mod(1,8045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8045, 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("8045.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8045 = 5 \cdot 1609 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8045.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: | \(64.2396484261\) |
Analytic rank: | \(1\) |
Dimension: | \(126\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Character | \(\chi\) | \(=\) | 8045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59235 | −1.83307 | −0.916534 | − | 0.399957i | \(-0.869025\pi\) | ||||
−0.916534 | + | 0.399957i | \(0.869025\pi\) | |||||||
\(3\) | −0.476573 | −0.275150 | −0.137575 | − | 0.990491i | \(-0.543931\pi\) | ||||
−0.137575 | + | 0.990491i | \(0.543931\pi\) | |||||||
\(4\) | 4.72028 | 2.36014 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.23544 | 0.504368 | ||||||||
\(7\) | −4.74079 | −1.79185 | −0.895925 | − | 0.444206i | \(-0.853486\pi\) | ||||
−0.895925 | + | 0.444206i | \(0.853486\pi\) | |||||||
\(8\) | −7.05191 | −2.49323 | ||||||||
\(9\) | −2.77288 | −0.924293 | ||||||||
\(10\) | 2.59235 | 0.819773 | ||||||||
\(11\) | −6.33301 | −1.90948 | −0.954738 | − | 0.297450i | \(-0.903864\pi\) | ||||
−0.954738 | + | 0.297450i | \(0.903864\pi\) | |||||||
\(12\) | −2.24956 | −0.649391 | ||||||||
\(13\) | −0.258183 | −0.0716071 | −0.0358036 | − | 0.999359i | \(-0.511399\pi\) | ||||
−0.0358036 | + | 0.999359i | \(0.511399\pi\) | |||||||
\(14\) | 12.2898 | 3.28458 | ||||||||
\(15\) | 0.476573 | 0.123051 | ||||||||
\(16\) | 8.84045 | 2.21011 | ||||||||
\(17\) | −5.75668 | −1.39620 | −0.698100 | − | 0.716001i | \(-0.745971\pi\) | ||||
−0.698100 | + | 0.716001i | \(0.745971\pi\) | |||||||
\(18\) | 7.18827 | 1.69429 | ||||||||
\(19\) | −5.13370 | −1.17775 | −0.588876 | − | 0.808223i | \(-0.700429\pi\) | ||||
−0.588876 | + | 0.808223i | \(0.700429\pi\) | |||||||
\(20\) | −4.72028 | −1.05549 | ||||||||
\(21\) | 2.25933 | 0.493027 | ||||||||
\(22\) | 16.4174 | 3.50020 | ||||||||
\(23\) | 8.08141 | 1.68509 | 0.842545 | − | 0.538626i | \(-0.181056\pi\) | ||||
0.842545 | + | 0.538626i | \(0.181056\pi\) | |||||||
\(24\) | 3.36075 | 0.686010 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0.669301 | 0.131261 | ||||||||
\(27\) | 2.75120 | 0.529469 | ||||||||
\(28\) | −22.3778 | −4.22901 | ||||||||
\(29\) | 1.19129 | 0.221218 | 0.110609 | − | 0.993864i | \(-0.464720\pi\) | ||||
0.110609 | + | 0.993864i | \(0.464720\pi\) | |||||||
\(30\) | −1.23544 | −0.225560 | ||||||||
\(31\) | −9.86768 | −1.77229 | −0.886143 | − | 0.463411i | \(-0.846625\pi\) | ||||
−0.886143 | + | 0.463411i | \(0.846625\pi\) | |||||||
\(32\) | −8.81373 | −1.55806 | ||||||||
\(33\) | 3.01814 | 0.525392 | ||||||||
\(34\) | 14.9233 | 2.55933 | ||||||||
\(35\) | 4.74079 | 0.801340 | ||||||||
\(36\) | −13.0887 | −2.18146 | ||||||||
\(37\) | 9.79477 | 1.61025 | 0.805125 | − | 0.593105i | \(-0.202098\pi\) | ||||
0.805125 | + | 0.593105i | \(0.202098\pi\) | |||||||
\(38\) | 13.3083 | 2.15890 | ||||||||
\(39\) | 0.123043 | 0.0197027 | ||||||||
\(40\) | 7.05191 | 1.11500 | ||||||||
\(41\) | 2.89622 | 0.452313 | 0.226157 | − | 0.974091i | \(-0.427384\pi\) | ||||
0.226157 | + | 0.974091i | \(0.427384\pi\) | |||||||
\(42\) | −5.85698 | −0.903752 | ||||||||
\(43\) | −9.66952 | −1.47459 | −0.737294 | − | 0.675572i | \(-0.763897\pi\) | ||||
−0.737294 | + | 0.675572i | \(0.763897\pi\) | |||||||
\(44\) | −29.8936 | −4.50662 | ||||||||
\(45\) | 2.77288 | 0.413356 | ||||||||
\(46\) | −20.9498 | −3.08888 | ||||||||
\(47\) | 1.79413 | 0.261701 | 0.130850 | − | 0.991402i | \(-0.458229\pi\) | ||||
0.130850 | + | 0.991402i | \(0.458229\pi\) | |||||||
\(48\) | −4.21312 | −0.608112 | ||||||||
\(49\) | 15.4751 | 2.21073 | ||||||||
\(50\) | −2.59235 | −0.366614 | ||||||||
\(51\) | 2.74348 | 0.384164 | ||||||||
\(52\) | −1.21870 | −0.169003 | ||||||||
\(53\) | 6.02549 | 0.827665 | 0.413832 | − | 0.910353i | \(-0.364190\pi\) | ||||
0.413832 | + | 0.910353i | \(0.364190\pi\) | |||||||
\(54\) | −7.13207 | −0.970552 | ||||||||
\(55\) | 6.33301 | 0.853943 | ||||||||
\(56\) | 33.4316 | 4.46749 | ||||||||
\(57\) | 2.44659 | 0.324058 | ||||||||
\(58\) | −3.08825 | −0.405507 | ||||||||
\(59\) | −2.26955 | −0.295470 | −0.147735 | − | 0.989027i | \(-0.547198\pi\) | ||||
−0.147735 | + | 0.989027i | \(0.547198\pi\) | |||||||
\(60\) | 2.24956 | 0.290417 | ||||||||
\(61\) | 7.81763 | 1.00094 | 0.500472 | − | 0.865753i | \(-0.333160\pi\) | ||||
0.500472 | + | 0.865753i | \(0.333160\pi\) | |||||||
\(62\) | 25.5805 | 3.24872 | ||||||||
\(63\) | 13.1456 | 1.65619 | ||||||||
\(64\) | 5.16737 | 0.645921 | ||||||||
\(65\) | 0.258183 | 0.0320237 | ||||||||
\(66\) | −7.82409 | −0.963078 | ||||||||
\(67\) | 6.71712 | 0.820627 | 0.410313 | − | 0.911945i | \(-0.365419\pi\) | ||||
0.410313 | + | 0.911945i | \(0.365419\pi\) | |||||||
\(68\) | −27.1731 | −3.29522 | ||||||||
\(69\) | −3.85138 | −0.463652 | ||||||||
\(70\) | −12.2898 | −1.46891 | ||||||||
\(71\) | −4.41165 | −0.523566 | −0.261783 | − | 0.965127i | \(-0.584311\pi\) | ||||
−0.261783 | + | 0.965127i | \(0.584311\pi\) | |||||||
\(72\) | 19.5541 | 2.30447 | ||||||||
\(73\) | −12.6241 | −1.47754 | −0.738772 | − | 0.673955i | \(-0.764594\pi\) | ||||
−0.738772 | + | 0.673955i | \(0.764594\pi\) | |||||||
\(74\) | −25.3915 | −2.95170 | ||||||||
\(75\) | −0.476573 | −0.0550299 | ||||||||
\(76\) | −24.2325 | −2.77966 | ||||||||
\(77\) | 30.0235 | 3.42149 | ||||||||
\(78\) | −0.318971 | −0.0361164 | ||||||||
\(79\) | −4.41978 | −0.497264 | −0.248632 | − | 0.968598i | \(-0.579981\pi\) | ||||
−0.248632 | + | 0.968598i | \(0.579981\pi\) | |||||||
\(80\) | −8.84045 | −0.988393 | ||||||||
\(81\) | 7.00749 | 0.778610 | ||||||||
\(82\) | −7.50801 | −0.829121 | ||||||||
\(83\) | 11.4842 | 1.26055 | 0.630277 | − | 0.776371i | \(-0.282941\pi\) | ||||
0.630277 | + | 0.776371i | \(0.282941\pi\) | |||||||
\(84\) | 10.6647 | 1.16361 | ||||||||
\(85\) | 5.75668 | 0.624399 | ||||||||
\(86\) | 25.0668 | 2.70302 | ||||||||
\(87\) | −0.567739 | −0.0608680 | ||||||||
\(88\) | 44.6598 | 4.76075 | ||||||||
\(89\) | −10.2915 | −1.09089 | −0.545446 | − | 0.838146i | \(-0.683640\pi\) | ||||
−0.545446 | + | 0.838146i | \(0.683640\pi\) | |||||||
\(90\) | −7.18827 | −0.757710 | ||||||||
\(91\) | 1.22399 | 0.128309 | ||||||||
\(92\) | 38.1465 | 3.97705 | ||||||||
\(93\) | 4.70267 | 0.487644 | ||||||||
\(94\) | −4.65101 | −0.479715 | ||||||||
\(95\) | 5.13370 | 0.526707 | ||||||||
\(96\) | 4.20039 | 0.428700 | ||||||||
\(97\) | 13.4837 | 1.36906 | 0.684529 | − | 0.728985i | \(-0.260008\pi\) | ||||
0.684529 | + | 0.728985i | \(0.260008\pi\) | |||||||
\(98\) | −40.1168 | −4.05241 | ||||||||
\(99\) | 17.5607 | 1.76491 | ||||||||
\(100\) | 4.72028 | 0.472028 | ||||||||
\(101\) | −0.341340 | −0.0339646 | −0.0169823 | − | 0.999856i | \(-0.505406\pi\) | ||||
−0.0169823 | + | 0.999856i | \(0.505406\pi\) | |||||||
\(102\) | −7.11205 | −0.704198 | ||||||||
\(103\) | −5.83074 | −0.574520 | −0.287260 | − | 0.957853i | \(-0.592744\pi\) | ||||
−0.287260 | + | 0.957853i | \(0.592744\pi\) | |||||||
\(104\) | 1.82068 | 0.178533 | ||||||||
\(105\) | −2.25933 | −0.220488 | ||||||||
\(106\) | −15.6202 | −1.51717 | ||||||||
\(107\) | 15.1834 | 1.46784 | 0.733918 | − | 0.679238i | \(-0.237690\pi\) | ||||
0.733918 | + | 0.679238i | \(0.237690\pi\) | |||||||
\(108\) | 12.9864 | 1.24962 | ||||||||
\(109\) | 8.46282 | 0.810591 | 0.405295 | − | 0.914186i | \(-0.367169\pi\) | ||||
0.405295 | + | 0.914186i | \(0.367169\pi\) | |||||||
\(110\) | −16.4174 | −1.56534 | ||||||||
\(111\) | −4.66793 | −0.443060 | ||||||||
\(112\) | −41.9107 | −3.96019 | ||||||||
\(113\) | 17.8557 | 1.67972 | 0.839859 | − | 0.542804i | \(-0.182637\pi\) | ||||
0.839859 | + | 0.542804i | \(0.182637\pi\) | |||||||
\(114\) | −6.34240 | −0.594021 | ||||||||
\(115\) | −8.08141 | −0.753595 | ||||||||
\(116\) | 5.62324 | 0.522105 | ||||||||
\(117\) | 0.715910 | 0.0661859 | ||||||||
\(118\) | 5.88347 | 0.541617 | ||||||||
\(119\) | 27.2912 | 2.50178 | ||||||||
\(120\) | −3.36075 | −0.306793 | ||||||||
\(121\) | 29.1070 | 2.64609 | ||||||||
\(122\) | −20.2660 | −1.83480 | ||||||||
\(123\) | −1.38026 | −0.124454 | ||||||||
\(124\) | −46.5782 | −4.18284 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −34.0781 | −3.03592 | ||||||||
\(127\) | −5.11518 | −0.453899 | −0.226949 | − | 0.973907i | \(-0.572875\pi\) | ||||
−0.226949 | + | 0.973907i | \(0.572875\pi\) | |||||||
\(128\) | 4.23184 | 0.374045 | ||||||||
\(129\) | 4.60823 | 0.405732 | ||||||||
\(130\) | −0.669301 | −0.0587016 | ||||||||
\(131\) | −4.28861 | −0.374697 | −0.187349 | − | 0.982293i | \(-0.559989\pi\) | ||||
−0.187349 | + | 0.982293i | \(0.559989\pi\) | |||||||
\(132\) | 14.2465 | 1.24000 | ||||||||
\(133\) | 24.3378 | 2.11035 | ||||||||
\(134\) | −17.4131 | −1.50426 | ||||||||
\(135\) | −2.75120 | −0.236786 | ||||||||
\(136\) | 40.5955 | 3.48104 | ||||||||
\(137\) | 0.992308 | 0.0847786 | 0.0423893 | − | 0.999101i | \(-0.486503\pi\) | ||||
0.0423893 | + | 0.999101i | \(0.486503\pi\) | |||||||
\(138\) | 9.98413 | 0.849906 | ||||||||
\(139\) | −5.08248 | −0.431090 | −0.215545 | − | 0.976494i | \(-0.569153\pi\) | ||||
−0.215545 | + | 0.976494i | \(0.569153\pi\) | |||||||
\(140\) | 22.3778 | 1.89127 | ||||||||
\(141\) | −0.855034 | −0.0720069 | ||||||||
\(142\) | 11.4365 | 0.959733 | ||||||||
\(143\) | 1.63508 | 0.136732 | ||||||||
\(144\) | −24.5135 | −2.04279 | ||||||||
\(145\) | −1.19129 | −0.0989316 | ||||||||
\(146\) | 32.7262 | 2.70844 | ||||||||
\(147\) | −7.37501 | −0.608281 | ||||||||
\(148\) | 46.2340 | 3.80041 | ||||||||
\(149\) | 0.292431 | 0.0239569 | 0.0119784 | − | 0.999928i | \(-0.496187\pi\) | ||||
0.0119784 | + | 0.999928i | \(0.496187\pi\) | |||||||
\(150\) | 1.23544 | 0.100874 | ||||||||
\(151\) | −7.43589 | −0.605124 | −0.302562 | − | 0.953130i | \(-0.597842\pi\) | ||||
−0.302562 | + | 0.953130i | \(0.597842\pi\) | |||||||
\(152\) | 36.2024 | 2.93640 | ||||||||
\(153\) | 15.9626 | 1.29050 | ||||||||
\(154\) | −77.8313 | −6.27183 | ||||||||
\(155\) | 9.86768 | 0.792591 | ||||||||
\(156\) | 0.580798 | 0.0465011 | ||||||||
\(157\) | −12.4726 | −0.995425 | −0.497712 | − | 0.867342i | \(-0.665827\pi\) | ||||
−0.497712 | + | 0.867342i | \(0.665827\pi\) | |||||||
\(158\) | 11.4576 | 0.911518 | ||||||||
\(159\) | −2.87159 | −0.227732 | ||||||||
\(160\) | 8.81373 | 0.696787 | ||||||||
\(161\) | −38.3123 | −3.01943 | ||||||||
\(162\) | −18.1659 | −1.42724 | ||||||||
\(163\) | −21.4251 | −1.67814 | −0.839071 | − | 0.544023i | \(-0.816901\pi\) | ||||
−0.839071 | + | 0.544023i | \(0.816901\pi\) | |||||||
\(164\) | 13.6709 | 1.06752 | ||||||||
\(165\) | −3.01814 | −0.234962 | ||||||||
\(166\) | −29.7710 | −2.31068 | ||||||||
\(167\) | −19.3497 | −1.49732 | −0.748662 | − | 0.662952i | \(-0.769303\pi\) | ||||
−0.748662 | + | 0.662952i | \(0.769303\pi\) | |||||||
\(168\) | −15.9326 | −1.22923 | ||||||||
\(169\) | −12.9333 | −0.994872 | ||||||||
\(170\) | −14.9233 | −1.14457 | ||||||||
\(171\) | 14.2351 | 1.08859 | ||||||||
\(172\) | −45.6428 | −3.48023 | ||||||||
\(173\) | 1.33845 | 0.101761 | 0.0508804 | − | 0.998705i | \(-0.483797\pi\) | ||||
0.0508804 | + | 0.998705i | \(0.483797\pi\) | |||||||
\(174\) | 1.47178 | 0.111575 | ||||||||
\(175\) | −4.74079 | −0.358370 | ||||||||
\(176\) | −55.9867 | −4.22016 | ||||||||
\(177\) | 1.08161 | 0.0812986 | ||||||||
\(178\) | 26.6790 | 1.99968 | ||||||||
\(179\) | 15.7794 | 1.17941 | 0.589706 | − | 0.807618i | \(-0.299244\pi\) | ||||
0.589706 | + | 0.807618i | \(0.299244\pi\) | |||||||
\(180\) | 13.0887 | 0.975578 | ||||||||
\(181\) | 22.1852 | 1.64901 | 0.824505 | − | 0.565855i | \(-0.191454\pi\) | ||||
0.824505 | + | 0.565855i | \(0.191454\pi\) | |||||||
\(182\) | −3.17302 | −0.235200 | ||||||||
\(183\) | −3.72567 | −0.275410 | ||||||||
\(184\) | −56.9893 | −4.20131 | ||||||||
\(185\) | −9.79477 | −0.720126 | ||||||||
\(186\) | −12.1910 | −0.893885 | ||||||||
\(187\) | 36.4571 | 2.66601 | ||||||||
\(188\) | 8.46879 | 0.617650 | ||||||||
\(189\) | −13.0429 | −0.948728 | ||||||||
\(190\) | −13.3083 | −0.965489 | ||||||||
\(191\) | 5.44896 | 0.394273 | 0.197137 | − | 0.980376i | \(-0.436836\pi\) | ||||
0.197137 | + | 0.980376i | \(0.436836\pi\) | |||||||
\(192\) | −2.46263 | −0.177725 | ||||||||
\(193\) | −24.6678 | −1.77563 | −0.887815 | − | 0.460200i | \(-0.847778\pi\) | ||||
−0.887815 | + | 0.460200i | \(0.847778\pi\) | |||||||
\(194\) | −34.9544 | −2.50958 | ||||||||
\(195\) | −0.123043 | −0.00881131 | ||||||||
\(196\) | 73.0467 | 5.21762 | ||||||||
\(197\) | 2.88676 | 0.205673 | 0.102837 | − | 0.994698i | \(-0.467208\pi\) | ||||
0.102837 | + | 0.994698i | \(0.467208\pi\) | |||||||
\(198\) | −45.5234 | −3.23521 | ||||||||
\(199\) | −23.6574 | −1.67703 | −0.838515 | − | 0.544879i | \(-0.816576\pi\) | ||||
−0.838515 | + | 0.544879i | \(0.816576\pi\) | |||||||
\(200\) | −7.05191 | −0.498645 | ||||||||
\(201\) | −3.20120 | −0.225795 | ||||||||
\(202\) | 0.884873 | 0.0622595 | ||||||||
\(203\) | −5.64768 | −0.396389 | ||||||||
\(204\) | 12.9500 | 0.906680 | ||||||||
\(205\) | −2.89622 | −0.202281 | ||||||||
\(206\) | 15.1153 | 1.05313 | ||||||||
\(207\) | −22.4088 | −1.55752 | ||||||||
\(208\) | −2.28246 | −0.158260 | ||||||||
\(209\) | 32.5118 | 2.24889 | ||||||||
\(210\) | 5.85698 | 0.404170 | ||||||||
\(211\) | −1.51484 | −0.104286 | −0.0521430 | − | 0.998640i | \(-0.516605\pi\) | ||||
−0.0521430 | + | 0.998640i | \(0.516605\pi\) | |||||||
\(212\) | 28.4420 | 1.95340 | ||||||||
\(213\) | 2.10247 | 0.144059 | ||||||||
\(214\) | −39.3607 | −2.69064 | ||||||||
\(215\) | 9.66952 | 0.659456 | ||||||||
\(216\) | −19.4012 | −1.32008 | ||||||||
\(217\) | 46.7806 | 3.17567 | ||||||||
\(218\) | −21.9386 | −1.48587 | ||||||||
\(219\) | 6.01633 | 0.406546 | ||||||||
\(220\) | 29.8936 | 2.01542 | ||||||||
\(221\) | 1.48628 | 0.0999778 | ||||||||
\(222\) | 12.1009 | 0.812159 | ||||||||
\(223\) | 0.946409 | 0.0633762 | 0.0316881 | − | 0.999498i | \(-0.489912\pi\) | ||||
0.0316881 | + | 0.999498i | \(0.489912\pi\) | |||||||
\(224\) | 41.7840 | 2.79181 | ||||||||
\(225\) | −2.77288 | −0.184859 | ||||||||
\(226\) | −46.2881 | −3.07904 | ||||||||
\(227\) | 2.87218 | 0.190633 | 0.0953166 | − | 0.995447i | \(-0.469614\pi\) | ||||
0.0953166 | + | 0.995447i | \(0.469614\pi\) | |||||||
\(228\) | 11.5486 | 0.764822 | ||||||||
\(229\) | −13.7717 | −0.910060 | −0.455030 | − | 0.890476i | \(-0.650371\pi\) | ||||
−0.455030 | + | 0.890476i | \(0.650371\pi\) | |||||||
\(230\) | 20.9498 | 1.38139 | ||||||||
\(231\) | −14.3084 | −0.941423 | ||||||||
\(232\) | −8.40090 | −0.551546 | ||||||||
\(233\) | −9.47782 | −0.620912 | −0.310456 | − | 0.950588i | \(-0.600482\pi\) | ||||
−0.310456 | + | 0.950588i | \(0.600482\pi\) | |||||||
\(234\) | −1.85589 | −0.121323 | ||||||||
\(235\) | −1.79413 | −0.117036 | ||||||||
\(236\) | −10.7129 | −0.697351 | ||||||||
\(237\) | 2.10635 | 0.136822 | ||||||||
\(238\) | −70.7483 | −4.58593 | ||||||||
\(239\) | −17.8262 | −1.15308 | −0.576541 | − | 0.817068i | \(-0.695598\pi\) | ||||
−0.576541 | + | 0.817068i | \(0.695598\pi\) | |||||||
\(240\) | 4.21312 | 0.271956 | ||||||||
\(241\) | −27.0386 | −1.74171 | −0.870855 | − | 0.491540i | \(-0.836434\pi\) | ||||
−0.870855 | + | 0.491540i | \(0.836434\pi\) | |||||||
\(242\) | −75.4556 | −4.85047 | ||||||||
\(243\) | −11.5932 | −0.743703 | ||||||||
\(244\) | 36.9014 | 2.36237 | ||||||||
\(245\) | −15.4751 | −0.988667 | ||||||||
\(246\) | 3.57812 | 0.228132 | ||||||||
\(247\) | 1.32544 | 0.0843354 | ||||||||
\(248\) | 69.5859 | 4.41871 | ||||||||
\(249\) | −5.47306 | −0.346841 | ||||||||
\(250\) | 2.59235 | 0.163955 | ||||||||
\(251\) | −17.1993 | −1.08561 | −0.542805 | − | 0.839859i | \(-0.682638\pi\) | ||||
−0.542805 | + | 0.839859i | \(0.682638\pi\) | |||||||
\(252\) | 62.0510 | 3.90885 | ||||||||
\(253\) | −51.1797 | −3.21764 | ||||||||
\(254\) | 13.2603 | 0.832027 | ||||||||
\(255\) | −2.74348 | −0.171803 | ||||||||
\(256\) | −21.3051 | −1.33157 | ||||||||
\(257\) | 31.0798 | 1.93870 | 0.969352 | − | 0.245678i | \(-0.0790105\pi\) | ||||
0.969352 | + | 0.245678i | \(0.0790105\pi\) | |||||||
\(258\) | −11.9462 | −0.743735 | ||||||||
\(259\) | −46.4350 | −2.88533 | ||||||||
\(260\) | 1.21870 | 0.0755803 | ||||||||
\(261\) | −3.30331 | −0.204470 | ||||||||
\(262\) | 11.1176 | 0.686846 | ||||||||
\(263\) | 21.8505 | 1.34736 | 0.673680 | − | 0.739023i | \(-0.264712\pi\) | ||||
0.673680 | + | 0.739023i | \(0.264712\pi\) | |||||||
\(264\) | −21.2837 | −1.30992 | ||||||||
\(265\) | −6.02549 | −0.370143 | ||||||||
\(266\) | −63.0921 | −3.86842 | ||||||||
\(267\) | 4.90463 | 0.300159 | ||||||||
\(268\) | 31.7067 | 1.93679 | ||||||||
\(269\) | −2.15027 | −0.131104 | −0.0655521 | − | 0.997849i | \(-0.520881\pi\) | ||||
−0.0655521 | + | 0.997849i | \(0.520881\pi\) | |||||||
\(270\) | 7.13207 | 0.434044 | ||||||||
\(271\) | 15.6683 | 0.951780 | 0.475890 | − | 0.879505i | \(-0.342126\pi\) | ||||
0.475890 | + | 0.879505i | \(0.342126\pi\) | |||||||
\(272\) | −50.8916 | −3.08576 | ||||||||
\(273\) | −0.583322 | −0.0353042 | ||||||||
\(274\) | −2.57241 | −0.155405 | ||||||||
\(275\) | −6.33301 | −0.381895 | ||||||||
\(276\) | −18.1796 | −1.09428 | ||||||||
\(277\) | 27.8285 | 1.67205 | 0.836025 | − | 0.548691i | \(-0.184874\pi\) | ||||
0.836025 | + | 0.548691i | \(0.184874\pi\) | |||||||
\(278\) | 13.1756 | 0.790218 | ||||||||
\(279\) | 27.3619 | 1.63811 | ||||||||
\(280\) | −33.4316 | −1.99792 | ||||||||
\(281\) | 15.5529 | 0.927808 | 0.463904 | − | 0.885885i | \(-0.346448\pi\) | ||||
0.463904 | + | 0.885885i | \(0.346448\pi\) | |||||||
\(282\) | 2.21655 | 0.131993 | ||||||||
\(283\) | −4.21635 | −0.250636 | −0.125318 | − | 0.992117i | \(-0.539995\pi\) | ||||
−0.125318 | + | 0.992117i | \(0.539995\pi\) | |||||||
\(284\) | −20.8242 | −1.23569 | ||||||||
\(285\) | −2.44659 | −0.144923 | ||||||||
\(286\) | −4.23869 | −0.250639 | ||||||||
\(287\) | −13.7304 | −0.810477 | ||||||||
\(288\) | 24.4394 | 1.44011 | ||||||||
\(289\) | 16.1393 | 0.949372 | ||||||||
\(290\) | 3.08825 | 0.181348 | ||||||||
\(291\) | −6.42595 | −0.376696 | ||||||||
\(292\) | −59.5894 | −3.48721 | ||||||||
\(293\) | −23.0035 | −1.34388 | −0.671941 | − | 0.740605i | \(-0.734539\pi\) | ||||
−0.671941 | + | 0.740605i | \(0.734539\pi\) | |||||||
\(294\) | 19.1186 | 1.11502 | ||||||||
\(295\) | 2.26955 | 0.132138 | ||||||||
\(296\) | −69.0718 | −4.01472 | ||||||||
\(297\) | −17.4234 | −1.01101 | ||||||||
\(298\) | −0.758084 | −0.0439146 | ||||||||
\(299\) | −2.08648 | −0.120664 | ||||||||
\(300\) | −2.24956 | −0.129878 | ||||||||
\(301\) | 45.8411 | 2.64224 | ||||||||
\(302\) | 19.2764 | 1.10923 | ||||||||
\(303\) | 0.162674 | 0.00934536 | ||||||||
\(304\) | −45.3842 | −2.60297 | ||||||||
\(305\) | −7.81763 | −0.447636 | ||||||||
\(306\) | −41.3805 | −2.36557 | ||||||||
\(307\) | 19.0514 | 1.08732 | 0.543660 | − | 0.839305i | \(-0.317038\pi\) | ||||
0.543660 | + | 0.839305i | \(0.317038\pi\) | |||||||
\(308\) | 141.719 | 8.07519 | ||||||||
\(309\) | 2.77877 | 0.158079 | ||||||||
\(310\) | −25.5805 | −1.45287 | ||||||||
\(311\) | −14.6502 | −0.830738 | −0.415369 | − | 0.909653i | \(-0.636348\pi\) | ||||
−0.415369 | + | 0.909653i | \(0.636348\pi\) | |||||||
\(312\) | −0.867689 | −0.0491232 | ||||||||
\(313\) | 5.86356 | 0.331428 | 0.165714 | − | 0.986174i | \(-0.447007\pi\) | ||||
0.165714 | + | 0.986174i | \(0.447007\pi\) | |||||||
\(314\) | 32.3334 | 1.82468 | ||||||||
\(315\) | −13.1456 | −0.740672 | ||||||||
\(316\) | −20.8626 | −1.17361 | ||||||||
\(317\) | −1.22051 | −0.0685505 | −0.0342752 | − | 0.999412i | \(-0.510912\pi\) | ||||
−0.0342752 | + | 0.999412i | \(0.510912\pi\) | |||||||
\(318\) | 7.44416 | 0.417448 | ||||||||
\(319\) | −7.54448 | −0.422410 | ||||||||
\(320\) | −5.16737 | −0.288865 | ||||||||
\(321\) | −7.23601 | −0.403875 | ||||||||
\(322\) | 99.3188 | 5.53482 | ||||||||
\(323\) | 29.5531 | 1.64438 | ||||||||
\(324\) | 33.0773 | 1.83763 | ||||||||
\(325\) | −0.258183 | −0.0143214 | ||||||||
\(326\) | 55.5413 | 3.07615 | ||||||||
\(327\) | −4.03315 | −0.223034 | ||||||||
\(328\) | −20.4239 | −1.12772 | ||||||||
\(329\) | −8.50559 | −0.468928 | ||||||||
\(330\) | 7.82409 | 0.430702 | ||||||||
\(331\) | 28.5721 | 1.57046 | 0.785231 | − | 0.619203i | \(-0.212544\pi\) | ||||
0.785231 | + | 0.619203i | \(0.212544\pi\) | |||||||
\(332\) | 54.2085 | 2.97508 | ||||||||
\(333\) | −27.1597 | −1.48834 | ||||||||
\(334\) | 50.1612 | 2.74470 | ||||||||
\(335\) | −6.71712 | −0.366996 | ||||||||
\(336\) | 19.9735 | 1.08965 | ||||||||
\(337\) | −6.24100 | −0.339969 | −0.169984 | − | 0.985447i | \(-0.554372\pi\) | ||||
−0.169984 | + | 0.985447i | \(0.554372\pi\) | |||||||
\(338\) | 33.5277 | 1.82367 | ||||||||
\(339\) | −8.50953 | −0.462174 | ||||||||
\(340\) | 27.1731 | 1.47367 | ||||||||
\(341\) | 62.4921 | 3.38414 | ||||||||
\(342\) | −36.9024 | −1.99545 | ||||||||
\(343\) | −40.1786 | −2.16944 | ||||||||
\(344\) | 68.1885 | 3.67648 | ||||||||
\(345\) | 3.85138 | 0.207352 | ||||||||
\(346\) | −3.46974 | −0.186534 | ||||||||
\(347\) | 26.4712 | 1.42105 | 0.710523 | − | 0.703674i | \(-0.248458\pi\) | ||||
0.710523 | + | 0.703674i | \(0.248458\pi\) | |||||||
\(348\) | −2.67989 | −0.143657 | ||||||||
\(349\) | −24.5298 | −1.31305 | −0.656525 | − | 0.754304i | \(-0.727974\pi\) | ||||
−0.656525 | + | 0.754304i | \(0.727974\pi\) | |||||||
\(350\) | 12.2898 | 0.656916 | ||||||||
\(351\) | −0.710313 | −0.0379137 | ||||||||
\(352\) | 55.8175 | 2.97508 | ||||||||
\(353\) | 0.137490 | 0.00731786 | 0.00365893 | − | 0.999993i | \(-0.498835\pi\) | ||||
0.00365893 | + | 0.999993i | \(0.498835\pi\) | |||||||
\(354\) | −2.80390 | −0.149026 | ||||||||
\(355\) | 4.41165 | 0.234146 | ||||||||
\(356\) | −48.5785 | −2.57465 | ||||||||
\(357\) | −13.0063 | −0.688364 | ||||||||
\(358\) | −40.9058 | −2.16194 | ||||||||
\(359\) | 30.9444 | 1.63318 | 0.816591 | − | 0.577217i | \(-0.195861\pi\) | ||||
0.816591 | + | 0.577217i | \(0.195861\pi\) | |||||||
\(360\) | −19.5541 | −1.03059 | ||||||||
\(361\) | 7.35489 | 0.387100 | ||||||||
\(362\) | −57.5117 | −3.02275 | ||||||||
\(363\) | −13.8716 | −0.728072 | ||||||||
\(364\) | 5.77758 | 0.302827 | ||||||||
\(365\) | 12.6241 | 0.660778 | ||||||||
\(366\) | 9.65824 | 0.504845 | ||||||||
\(367\) | 13.4789 | 0.703594 | 0.351797 | − | 0.936076i | \(-0.385571\pi\) | ||||
0.351797 | + | 0.936076i | \(0.385571\pi\) | |||||||
\(368\) | 71.4433 | 3.72424 | ||||||||
\(369\) | −8.03086 | −0.418070 | ||||||||
\(370\) | 25.3915 | 1.32004 | ||||||||
\(371\) | −28.5656 | −1.48305 | ||||||||
\(372\) | 22.1979 | 1.15091 | ||||||||
\(373\) | −9.25520 | −0.479216 | −0.239608 | − | 0.970870i | \(-0.577019\pi\) | ||||
−0.239608 | + | 0.970870i | \(0.577019\pi\) | |||||||
\(374\) | −94.5096 | −4.88697 | ||||||||
\(375\) | 0.476573 | 0.0246101 | ||||||||
\(376\) | −12.6520 | −0.652479 | ||||||||
\(377\) | −0.307572 | −0.0158408 | ||||||||
\(378\) | 33.8116 | 1.73908 | ||||||||
\(379\) | 26.4010 | 1.35613 | 0.678064 | − | 0.735003i | \(-0.262819\pi\) | ||||
0.678064 | + | 0.735003i | \(0.262819\pi\) | |||||||
\(380\) | 24.2325 | 1.24310 | ||||||||
\(381\) | 2.43776 | 0.124890 | ||||||||
\(382\) | −14.1256 | −0.722729 | ||||||||
\(383\) | −23.3400 | −1.19262 | −0.596310 | − | 0.802754i | \(-0.703367\pi\) | ||||
−0.596310 | + | 0.802754i | \(0.703367\pi\) | |||||||
\(384\) | −2.01678 | −0.102918 | ||||||||
\(385\) | −30.0235 | −1.53014 | ||||||||
\(386\) | 63.9477 | 3.25485 | ||||||||
\(387\) | 26.8124 | 1.36295 | ||||||||
\(388\) | 63.6466 | 3.23117 | ||||||||
\(389\) | −19.9581 | −1.01192 | −0.505958 | − | 0.862558i | \(-0.668861\pi\) | ||||
−0.505958 | + | 0.862558i | \(0.668861\pi\) | |||||||
\(390\) | 0.318971 | 0.0161517 | ||||||||
\(391\) | −46.5221 | −2.35272 | ||||||||
\(392\) | −109.129 | −5.51184 | ||||||||
\(393\) | 2.04384 | 0.103098 | ||||||||
\(394\) | −7.48349 | −0.377013 | ||||||||
\(395\) | 4.41978 | 0.222383 | ||||||||
\(396\) | 82.8912 | 4.16544 | ||||||||
\(397\) | 1.69642 | 0.0851408 | 0.0425704 | − | 0.999093i | \(-0.486445\pi\) | ||||
0.0425704 | + | 0.999093i | \(0.486445\pi\) | |||||||
\(398\) | 61.3283 | 3.07411 | ||||||||
\(399\) | −11.5987 | −0.580663 | ||||||||
\(400\) | 8.84045 | 0.442023 | ||||||||
\(401\) | −19.8208 | −0.989802 | −0.494901 | − | 0.868949i | \(-0.664796\pi\) | ||||
−0.494901 | + | 0.868949i | \(0.664796\pi\) | |||||||
\(402\) | 8.29863 | 0.413898 | ||||||||
\(403\) | 2.54767 | 0.126908 | ||||||||
\(404\) | −1.61122 | −0.0801612 | ||||||||
\(405\) | −7.00749 | −0.348205 | ||||||||
\(406\) | 14.6408 | 0.726608 | ||||||||
\(407\) | −62.0304 | −3.07473 | ||||||||
\(408\) | −19.3468 | −0.957807 | ||||||||
\(409\) | 6.66554 | 0.329590 | 0.164795 | − | 0.986328i | \(-0.447304\pi\) | ||||
0.164795 | + | 0.986328i | \(0.447304\pi\) | |||||||
\(410\) | 7.50801 | 0.370794 | ||||||||
\(411\) | −0.472907 | −0.0233268 | ||||||||
\(412\) | −27.5227 | −1.35595 | ||||||||
\(413\) | 10.7595 | 0.529438 | ||||||||
\(414\) | 58.0913 | 2.85503 | ||||||||
\(415\) | −11.4842 | −0.563737 | ||||||||
\(416\) | 2.27556 | 0.111568 | ||||||||
\(417\) | 2.42217 | 0.118614 | ||||||||
\(418\) | −84.2819 | −4.12236 | ||||||||
\(419\) | 17.0950 | 0.835145 | 0.417573 | − | 0.908644i | \(-0.362881\pi\) | ||||
0.417573 | + | 0.908644i | \(0.362881\pi\) | |||||||
\(420\) | −10.6647 | −0.520383 | ||||||||
\(421\) | 22.8432 | 1.11331 | 0.556654 | − | 0.830745i | \(-0.312085\pi\) | ||||
0.556654 | + | 0.830745i | \(0.312085\pi\) | |||||||
\(422\) | 3.92700 | 0.191163 | ||||||||
\(423\) | −4.97490 | −0.241888 | ||||||||
\(424\) | −42.4912 | −2.06355 | ||||||||
\(425\) | −5.75668 | −0.279240 | ||||||||
\(426\) | −5.45035 | −0.264070 | ||||||||
\(427\) | −37.0617 | −1.79354 | ||||||||
\(428\) | 71.6699 | 3.46429 | ||||||||
\(429\) | −0.779234 | −0.0376218 | ||||||||
\(430\) | −25.0668 | −1.20883 | ||||||||
\(431\) | −9.18431 | −0.442393 | −0.221196 | − | 0.975229i | \(-0.570996\pi\) | ||||
−0.221196 | + | 0.975229i | \(0.570996\pi\) | |||||||
\(432\) | 24.3219 | 1.17019 | ||||||||
\(433\) | −9.92294 | −0.476866 | −0.238433 | − | 0.971159i | \(-0.576634\pi\) | ||||
−0.238433 | + | 0.971159i | \(0.576634\pi\) | |||||||
\(434\) | −121.272 | −5.82122 | ||||||||
\(435\) | 0.567739 | 0.0272210 | ||||||||
\(436\) | 39.9468 | 1.91311 | ||||||||
\(437\) | −41.4875 | −1.98462 | ||||||||
\(438\) | −15.5964 | −0.745226 | ||||||||
\(439\) | −11.0486 | −0.527322 | −0.263661 | − | 0.964615i | \(-0.584930\pi\) | ||||
−0.263661 | + | 0.964615i | \(0.584930\pi\) | |||||||
\(440\) | −44.6598 | −2.12907 | ||||||||
\(441\) | −42.9105 | −2.04336 | ||||||||
\(442\) | −3.85295 | −0.183266 | ||||||||
\(443\) | −9.99508 | −0.474881 | −0.237440 | − | 0.971402i | \(-0.576308\pi\) | ||||
−0.237440 | + | 0.971402i | \(0.576308\pi\) | |||||||
\(444\) | −22.0339 | −1.04568 | ||||||||
\(445\) | 10.2915 | 0.487862 | ||||||||
\(446\) | −2.45342 | −0.116173 | ||||||||
\(447\) | −0.139365 | −0.00659173 | ||||||||
\(448\) | −24.4974 | −1.15739 | ||||||||
\(449\) | −1.24600 | −0.0588026 | −0.0294013 | − | 0.999568i | \(-0.509360\pi\) | ||||
−0.0294013 | + | 0.999568i | \(0.509360\pi\) | |||||||
\(450\) | 7.18827 | 0.338858 | ||||||||
\(451\) | −18.3418 | −0.863681 | ||||||||
\(452\) | 84.2836 | 3.96437 | ||||||||
\(453\) | 3.54375 | 0.166500 | ||||||||
\(454\) | −7.44569 | −0.349444 | ||||||||
\(455\) | −1.22399 | −0.0573816 | ||||||||
\(456\) | −17.2531 | −0.807950 | ||||||||
\(457\) | 10.1025 | 0.472576 | 0.236288 | − | 0.971683i | \(-0.424069\pi\) | ||||
0.236288 | + | 0.971683i | \(0.424069\pi\) | |||||||
\(458\) | 35.7011 | 1.66820 | ||||||||
\(459\) | −15.8378 | −0.739244 | ||||||||
\(460\) | −38.1465 | −1.77859 | ||||||||
\(461\) | −6.74221 | −0.314016 | −0.157008 | − | 0.987597i | \(-0.550185\pi\) | ||||
−0.157008 | + | 0.987597i | \(0.550185\pi\) | |||||||
\(462\) | 37.0923 | 1.72569 | ||||||||
\(463\) | 11.2097 | 0.520957 | 0.260479 | − | 0.965480i | \(-0.416120\pi\) | ||||
0.260479 | + | 0.965480i | \(0.416120\pi\) | |||||||
\(464\) | 10.5316 | 0.488917 | ||||||||
\(465\) | −4.70267 | −0.218081 | ||||||||
\(466\) | 24.5698 | 1.13817 | ||||||||
\(467\) | −14.2759 | −0.660612 | −0.330306 | − | 0.943874i | \(-0.607152\pi\) | ||||
−0.330306 | + | 0.943874i | \(0.607152\pi\) | |||||||
\(468\) | 3.37930 | 0.156208 | ||||||||
\(469\) | −31.8445 | −1.47044 | ||||||||
\(470\) | 4.65101 | 0.214535 | ||||||||
\(471\) | 5.94413 | 0.273891 | ||||||||
\(472\) | 16.0047 | 0.736674 | ||||||||
\(473\) | 61.2372 | 2.81569 | ||||||||
\(474\) | −5.46039 | −0.250804 | ||||||||
\(475\) | −5.13370 | −0.235550 | ||||||||
\(476\) | 128.822 | 5.90454 | ||||||||
\(477\) | −16.7080 | −0.765004 | ||||||||
\(478\) | 46.2118 | 2.11368 | ||||||||
\(479\) | 21.2100 | 0.969109 | 0.484554 | − | 0.874761i | \(-0.338982\pi\) | ||||
0.484554 | + | 0.874761i | \(0.338982\pi\) | |||||||
\(480\) | −4.20039 | −0.191721 | ||||||||
\(481\) | −2.52885 | −0.115305 | ||||||||
\(482\) | 70.0935 | 3.19267 | ||||||||
\(483\) | 18.2586 | 0.830795 | ||||||||
\(484\) | 137.393 | 6.24515 | ||||||||
\(485\) | −13.4837 | −0.612262 | ||||||||
\(486\) | 30.0536 | 1.36326 | ||||||||
\(487\) | 29.8026 | 1.35049 | 0.675243 | − | 0.737595i | \(-0.264039\pi\) | ||||
0.675243 | + | 0.737595i | \(0.264039\pi\) | |||||||
\(488\) | −55.1292 | −2.49558 | ||||||||
\(489\) | 10.2106 | 0.461740 | ||||||||
\(490\) | 40.1168 | 1.81229 | ||||||||
\(491\) | 7.21911 | 0.325794 | 0.162897 | − | 0.986643i | \(-0.447916\pi\) | ||||
0.162897 | + | 0.986643i | \(0.447916\pi\) | |||||||
\(492\) | −6.51521 | −0.293728 | ||||||||
\(493\) | −6.85790 | −0.308864 | ||||||||
\(494\) | −3.43599 | −0.154593 | ||||||||
\(495\) | −17.5607 | −0.789293 | ||||||||
\(496\) | −87.2347 | −3.91696 | ||||||||
\(497\) | 20.9147 | 0.938152 | ||||||||
\(498\) | 14.1881 | 0.635783 | ||||||||
\(499\) | 27.0547 | 1.21114 | 0.605568 | − | 0.795793i | \(-0.292946\pi\) | ||||
0.605568 | + | 0.795793i | \(0.292946\pi\) | |||||||
\(500\) | −4.72028 | −0.211097 | ||||||||
\(501\) | 9.22155 | 0.411988 | ||||||||
\(502\) | 44.5866 | 1.99000 | ||||||||
\(503\) | 25.9863 | 1.15867 | 0.579336 | − | 0.815089i | \(-0.303312\pi\) | ||||
0.579336 | + | 0.815089i | \(0.303312\pi\) | |||||||
\(504\) | −92.7017 | −4.12926 | ||||||||
\(505\) | 0.341340 | 0.0151894 | ||||||||
\(506\) | 132.676 | 5.89815 | ||||||||
\(507\) | 6.16369 | 0.273739 | ||||||||
\(508\) | −24.1451 | −1.07126 | ||||||||
\(509\) | 12.9395 | 0.573535 | 0.286767 | − | 0.958000i | \(-0.407419\pi\) | ||||
0.286767 | + | 0.958000i | \(0.407419\pi\) | |||||||
\(510\) | 7.11205 | 0.314927 | ||||||||
\(511\) | 59.8484 | 2.64754 | ||||||||
\(512\) | 46.7667 | 2.06682 | ||||||||
\(513\) | −14.1238 | −0.623583 | ||||||||
\(514\) | −80.5696 | −3.55377 | ||||||||
\(515\) | 5.83074 | 0.256933 | ||||||||
\(516\) | 21.7521 | 0.957584 | ||||||||
\(517\) | −11.3622 | −0.499711 | ||||||||
\(518\) | 120.376 | 5.28900 | ||||||||
\(519\) | −0.637872 | −0.0279995 | ||||||||
\(520\) | −1.82068 | −0.0798423 | ||||||||
\(521\) | 6.60962 | 0.289573 | 0.144786 | − | 0.989463i | \(-0.453750\pi\) | ||||
0.144786 | + | 0.989463i | \(0.453750\pi\) | |||||||
\(522\) | 8.56335 | 0.374807 | ||||||||
\(523\) | −14.3861 | −0.629062 | −0.314531 | − | 0.949247i | \(-0.601847\pi\) | ||||
−0.314531 | + | 0.949247i | \(0.601847\pi\) | |||||||
\(524\) | −20.2434 | −0.884338 | ||||||||
\(525\) | 2.25933 | 0.0986054 | ||||||||
\(526\) | −56.6442 | −2.46980 | ||||||||
\(527\) | 56.8050 | 2.47447 | ||||||||
\(528\) | 26.6818 | 1.16117 | ||||||||
\(529\) | 42.3092 | 1.83953 | ||||||||
\(530\) | 15.6202 | 0.678497 | ||||||||
\(531\) | 6.29319 | 0.273101 | ||||||||
\(532\) | 114.881 | 4.98073 | ||||||||
\(533\) | −0.747755 | −0.0323889 | ||||||||
\(534\) | −12.7145 | −0.550211 | ||||||||
\(535\) | −15.1834 | −0.656436 | ||||||||
\(536\) | −47.3685 | −2.04601 | ||||||||
\(537\) | −7.52006 | −0.324515 | ||||||||
\(538\) | 5.57425 | 0.240323 | ||||||||
\(539\) | −98.0039 | −4.22133 | ||||||||
\(540\) | −12.9864 | −0.558847 | ||||||||
\(541\) | −6.07273 | −0.261087 | −0.130544 | − | 0.991443i | \(-0.541672\pi\) | ||||
−0.130544 | + | 0.991443i | \(0.541672\pi\) | |||||||
\(542\) | −40.6176 | −1.74468 | ||||||||
\(543\) | −10.5729 | −0.453724 | ||||||||
\(544\) | 50.7378 | 2.17537 | ||||||||
\(545\) | −8.46282 | −0.362507 | ||||||||
\(546\) | 1.51217 | 0.0647151 | ||||||||
\(547\) | −12.6019 | −0.538818 | −0.269409 | − | 0.963026i | \(-0.586828\pi\) | ||||
−0.269409 | + | 0.963026i | \(0.586828\pi\) | |||||||
\(548\) | 4.68397 | 0.200089 | ||||||||
\(549\) | −21.6773 | −0.925166 | ||||||||
\(550\) | 16.4174 | 0.700039 | ||||||||
\(551\) | −6.11575 | −0.260540 | ||||||||
\(552\) | 27.1596 | 1.15599 | ||||||||
\(553\) | 20.9532 | 0.891022 | ||||||||
\(554\) | −72.1411 | −3.06498 | ||||||||
\(555\) | 4.66793 | 0.198142 | ||||||||
\(556\) | −23.9907 | −1.01743 | ||||||||
\(557\) | 11.4955 | 0.487081 | 0.243541 | − | 0.969891i | \(-0.421691\pi\) | ||||
0.243541 | + | 0.969891i | \(0.421691\pi\) | |||||||
\(558\) | −70.9315 | −3.00277 | ||||||||
\(559\) | 2.49651 | 0.105591 | ||||||||
\(560\) | 41.9107 | 1.77105 | ||||||||
\(561\) | −17.3745 | −0.733551 | ||||||||
\(562\) | −40.3186 | −1.70074 | ||||||||
\(563\) | 24.4086 | 1.02870 | 0.514351 | − | 0.857580i | \(-0.328033\pi\) | ||||
0.514351 | + | 0.857580i | \(0.328033\pi\) | |||||||
\(564\) | −4.03600 | −0.169946 | ||||||||
\(565\) | −17.8557 | −0.751193 | ||||||||
\(566\) | 10.9302 | 0.459432 | ||||||||
\(567\) | −33.2210 | −1.39515 | ||||||||
\(568\) | 31.1105 | 1.30537 | ||||||||
\(569\) | 30.5123 | 1.27914 | 0.639572 | − | 0.768731i | \(-0.279112\pi\) | ||||
0.639572 | + | 0.768731i | \(0.279112\pi\) | |||||||
\(570\) | 6.34240 | 0.265654 | ||||||||
\(571\) | 1.60704 | 0.0672524 | 0.0336262 | − | 0.999434i | \(-0.489294\pi\) | ||||
0.0336262 | + | 0.999434i | \(0.489294\pi\) | |||||||
\(572\) | 7.71802 | 0.322706 | ||||||||
\(573\) | −2.59683 | −0.108484 | ||||||||
\(574\) | 35.5939 | 1.48566 | ||||||||
\(575\) | 8.08141 | 0.337018 | ||||||||
\(576\) | −14.3285 | −0.597020 | ||||||||
\(577\) | 23.8958 | 0.994795 | 0.497397 | − | 0.867523i | \(-0.334289\pi\) | ||||
0.497397 | + | 0.867523i | \(0.334289\pi\) | |||||||
\(578\) | −41.8388 | −1.74026 | ||||||||
\(579\) | 11.7560 | 0.488564 | ||||||||
\(580\) | −5.62324 | −0.233492 | ||||||||
\(581\) | −54.4441 | −2.25872 | ||||||||
\(582\) | 16.6583 | 0.690509 | ||||||||
\(583\) | −38.1595 | −1.58041 | ||||||||
\(584\) | 89.0243 | 3.68385 | ||||||||
\(585\) | −0.715910 | −0.0295993 | ||||||||
\(586\) | 59.6332 | 2.46343 | ||||||||
\(587\) | 44.2954 | 1.82827 | 0.914133 | − | 0.405415i | \(-0.132873\pi\) | ||||
0.914133 | + | 0.405415i | \(0.132873\pi\) | |||||||
\(588\) | −34.8121 | −1.43563 | ||||||||
\(589\) | 50.6577 | 2.08731 | ||||||||
\(590\) | −5.88347 | −0.242219 | ||||||||
\(591\) | −1.37575 | −0.0565909 | ||||||||
\(592\) | 86.5902 | 3.55884 | ||||||||
\(593\) | 6.99096 | 0.287084 | 0.143542 | − | 0.989644i | \(-0.454151\pi\) | ||||
0.143542 | + | 0.989644i | \(0.454151\pi\) | |||||||
\(594\) | 45.1675 | 1.85324 | ||||||||
\(595\) | −27.2912 | −1.11883 | ||||||||
\(596\) | 1.38036 | 0.0565416 | ||||||||
\(597\) | 11.2745 | 0.461434 | ||||||||
\(598\) | 5.40890 | 0.221186 | ||||||||
\(599\) | 0.223153 | 0.00911779 | 0.00455890 | − | 0.999990i | \(-0.498549\pi\) | ||||
0.00455890 | + | 0.999990i | \(0.498549\pi\) | |||||||
\(600\) | 3.36075 | 0.137202 | ||||||||
\(601\) | −29.6741 | −1.21043 | −0.605217 | − | 0.796061i | \(-0.706914\pi\) | ||||
−0.605217 | + | 0.796061i | \(0.706914\pi\) | |||||||
\(602\) | −118.836 | −4.84340 | ||||||||
\(603\) | −18.6258 | −0.758499 | ||||||||
\(604\) | −35.0994 | −1.42818 | ||||||||
\(605\) | −29.1070 | −1.18337 | ||||||||
\(606\) | −0.421707 | −0.0171307 | ||||||||
\(607\) | −44.9240 | −1.82341 | −0.911704 | − | 0.410848i | \(-0.865233\pi\) | ||||
−0.911704 | + | 0.410848i | \(0.865233\pi\) | |||||||
\(608\) | 45.2471 | 1.83501 | ||||||||
\(609\) | 2.69153 | 0.109066 | ||||||||
\(610\) | 20.2660 | 0.820547 | ||||||||
\(611\) | −0.463214 | −0.0187396 | ||||||||
\(612\) | 75.3477 | 3.04575 | ||||||||
\(613\) | 15.2195 | 0.614712 | 0.307356 | − | 0.951595i | \(-0.400556\pi\) | ||||
0.307356 | + | 0.951595i | \(0.400556\pi\) | |||||||
\(614\) | −49.3879 | −1.99313 | ||||||||
\(615\) | 1.38026 | 0.0556575 | ||||||||
\(616\) | −211.723 | −8.53055 | ||||||||
\(617\) | −14.8585 | −0.598181 | −0.299090 | − | 0.954225i | \(-0.596683\pi\) | ||||
−0.299090 | + | 0.954225i | \(0.596683\pi\) | |||||||
\(618\) | −7.20356 | −0.289769 | ||||||||
\(619\) | −6.82364 | −0.274265 | −0.137133 | − | 0.990553i | \(-0.543789\pi\) | ||||
−0.137133 | + | 0.990553i | \(0.543789\pi\) | |||||||
\(620\) | 46.5782 | 1.87062 | ||||||||
\(621\) | 22.2336 | 0.892202 | ||||||||
\(622\) | 37.9785 | 1.52280 | ||||||||
\(623\) | 48.7896 | 1.95471 | ||||||||
\(624\) | 1.08776 | 0.0435452 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −15.2004 | −0.607530 | ||||||||
\(627\) | −15.4943 | −0.618781 | ||||||||
\(628\) | −58.8743 | −2.34934 | ||||||||
\(629\) | −56.3853 | −2.24823 | ||||||||
\(630\) | 34.0781 | 1.35770 | ||||||||
\(631\) | −9.75479 | −0.388332 | −0.194166 | − | 0.980969i | \(-0.562200\pi\) | ||||
−0.194166 | + | 0.980969i | \(0.562200\pi\) | |||||||
\(632\) | 31.1678 | 1.23979 | ||||||||
\(633\) | 0.721933 | 0.0286943 | ||||||||
\(634\) | 3.16398 | 0.125658 | ||||||||
\(635\) | 5.11518 | 0.202990 | ||||||||
\(636\) | −13.5547 | −0.537478 | ||||||||
\(637\) | −3.99541 | −0.158304 | ||||||||
\(638\) | 19.5579 | 0.774306 | ||||||||
\(639\) | 12.2330 | 0.483929 | ||||||||
\(640\) | −4.23184 | −0.167278 | ||||||||
\(641\) | 48.0353 | 1.89728 | 0.948640 | − | 0.316356i | \(-0.102459\pi\) | ||||
0.948640 | + | 0.316356i | \(0.102459\pi\) | |||||||
\(642\) | 18.7583 | 0.740329 | ||||||||
\(643\) | −20.8122 | −0.820753 | −0.410377 | − | 0.911916i | \(-0.634603\pi\) | ||||
−0.410377 | + | 0.911916i | \(0.634603\pi\) | |||||||
\(644\) | −180.844 | −7.12627 | ||||||||
\(645\) | −4.60823 | −0.181449 | ||||||||
\(646\) | −76.6119 | −3.01425 | ||||||||
\(647\) | −3.39284 | −0.133386 | −0.0666932 | − | 0.997774i | \(-0.521245\pi\) | ||||
−0.0666932 | + | 0.997774i | \(0.521245\pi\) | |||||||
\(648\) | −49.4161 | −1.94125 | ||||||||
\(649\) | 14.3731 | 0.564193 | ||||||||
\(650\) | 0.669301 | 0.0262521 | ||||||||
\(651\) | −22.2944 | −0.873785 | ||||||||
\(652\) | −101.132 | −3.96064 | ||||||||
\(653\) | 1.38477 | 0.0541904 | 0.0270952 | − | 0.999633i | \(-0.491374\pi\) | ||||
0.0270952 | + | 0.999633i | \(0.491374\pi\) | |||||||
\(654\) | 10.4553 | 0.408836 | ||||||||
\(655\) | 4.28861 | 0.167570 | ||||||||
\(656\) | 25.6039 | 0.999664 | ||||||||
\(657\) | 35.0052 | 1.36568 | ||||||||
\(658\) | 22.0495 | 0.859578 | ||||||||
\(659\) | 5.73217 | 0.223293 | 0.111647 | − | 0.993748i | \(-0.464387\pi\) | ||||
0.111647 | + | 0.993748i | \(0.464387\pi\) | |||||||
\(660\) | −14.2465 | −0.554543 | ||||||||
\(661\) | 23.3052 | 0.906466 | 0.453233 | − | 0.891392i | \(-0.350271\pi\) | ||||
0.453233 | + | 0.891392i | \(0.350271\pi\) | |||||||
\(662\) | −74.0688 | −2.87876 | ||||||||
\(663\) | −0.708320 | −0.0275089 | ||||||||
\(664\) | −80.9854 | −3.14284 | ||||||||
\(665\) | −24.3378 | −0.943779 | ||||||||
\(666\) | 70.4075 | 2.72823 | ||||||||
\(667\) | 9.62734 | 0.372772 | ||||||||
\(668\) | −91.3359 | −3.53389 | ||||||||
\(669\) | −0.451033 | −0.0174380 | ||||||||
\(670\) | 17.4131 | 0.672728 | ||||||||
\(671\) | −49.5091 | −1.91128 | ||||||||
\(672\) | −19.9132 | −0.768167 | ||||||||
\(673\) | −12.0448 | −0.464292 | −0.232146 | − | 0.972681i | \(-0.574575\pi\) | ||||
−0.232146 | + | 0.972681i | \(0.574575\pi\) | |||||||
\(674\) | 16.1789 | 0.623186 | ||||||||
\(675\) | 2.75120 | 0.105894 | ||||||||
\(676\) | −61.0489 | −2.34804 | ||||||||
\(677\) | −7.63676 | −0.293504 | −0.146752 | − | 0.989173i | \(-0.546882\pi\) | ||||
−0.146752 | + | 0.989173i | \(0.546882\pi\) | |||||||
\(678\) | 22.0597 | 0.847197 | ||||||||
\(679\) | −63.9232 | −2.45315 | ||||||||
\(680\) | −40.5955 | −1.55677 | ||||||||
\(681\) | −1.36880 | −0.0524527 | ||||||||
\(682\) | −162.001 | −6.20335 | ||||||||
\(683\) | −0.450082 | −0.0172219 | −0.00861095 | − | 0.999963i | \(-0.502741\pi\) | ||||
−0.00861095 | + | 0.999963i | \(0.502741\pi\) | |||||||
\(684\) | 67.1937 | 2.56922 | ||||||||
\(685\) | −0.992308 | −0.0379141 | ||||||||
\(686\) | 104.157 | 3.97673 | ||||||||
\(687\) | 6.56323 | 0.250403 | ||||||||
\(688\) | −85.4829 | −3.25901 | ||||||||
\(689\) | −1.55568 | −0.0592667 | ||||||||
\(690\) | −9.98413 | −0.380089 | ||||||||
\(691\) | 27.9171 | 1.06202 | 0.531009 | − | 0.847366i | \(-0.321813\pi\) | ||||
0.531009 | + | 0.847366i | \(0.321813\pi\) | |||||||
\(692\) | 6.31788 | 0.240170 | ||||||||
\(693\) | −83.2514 | −3.16246 | ||||||||
\(694\) | −68.6225 | −2.60487 | ||||||||
\(695\) | 5.08248 | 0.192789 | ||||||||
\(696\) | 4.00364 | 0.151758 | ||||||||
\(697\) | −16.6726 | −0.631519 | ||||||||
\(698\) | 63.5898 | 2.40691 | ||||||||
\(699\) | 4.51687 | 0.170844 | ||||||||
\(700\) | −22.3778 | −0.845803 | ||||||||
\(701\) | 2.21888 | 0.0838059 | 0.0419030 | − | 0.999122i | \(-0.486658\pi\) | ||||
0.0419030 | + | 0.999122i | \(0.486658\pi\) | |||||||
\(702\) | 1.84138 | 0.0694984 | ||||||||
\(703\) | −50.2834 | −1.89648 | ||||||||
\(704\) | −32.7250 | −1.23337 | ||||||||
\(705\) | 0.855034 | 0.0322025 | ||||||||
\(706\) | −0.356422 | −0.0134141 | ||||||||
\(707\) | 1.61822 | 0.0608595 | ||||||||
\(708\) | 5.10548 | 0.191876 | ||||||||
\(709\) | 45.3720 | 1.70398 | 0.851990 | − | 0.523558i | \(-0.175396\pi\) | ||||
0.851990 | + | 0.523558i | \(0.175396\pi\) | |||||||
\(710\) | −11.4365 | −0.429206 | ||||||||
\(711\) | 12.2555 | 0.459617 | ||||||||
\(712\) | 72.5744 | 2.71984 | ||||||||
\(713\) | −79.7447 | −2.98646 | ||||||||
\(714\) | 33.7168 | 1.26182 | ||||||||
\(715\) | −1.63508 | −0.0611484 | ||||||||
\(716\) | 74.4833 | 2.78357 | ||||||||
\(717\) | 8.49550 | 0.317270 | ||||||||
\(718\) | −80.2187 | −2.99373 | ||||||||
\(719\) | 1.56136 | 0.0582289 | 0.0291144 | − | 0.999576i | \(-0.490731\pi\) | ||||
0.0291144 | + | 0.999576i | \(0.490731\pi\) | |||||||
\(720\) | 24.5135 | 0.913564 | ||||||||
\(721\) | 27.6423 | 1.02945 | ||||||||
\(722\) | −19.0664 | −0.709580 | ||||||||
\(723\) | 12.8859 | 0.479231 | ||||||||
\(724\) | 104.720 | 3.89189 | ||||||||
\(725\) | 1.19129 | 0.0442436 | ||||||||
\(726\) | 35.9601 | 1.33461 | ||||||||
\(727\) | 8.01315 | 0.297191 | 0.148596 | − | 0.988898i | \(-0.452525\pi\) | ||||
0.148596 | + | 0.988898i | \(0.452525\pi\) | |||||||
\(728\) | −8.63148 | −0.319904 | ||||||||
\(729\) | −15.4975 | −0.573980 | ||||||||
\(730\) | −32.7262 | −1.21125 | ||||||||
\(731\) | 55.6643 | 2.05882 | ||||||||
\(732\) | −17.5862 | −0.650005 | ||||||||
\(733\) | 18.8716 | 0.697037 | 0.348519 | − | 0.937302i | \(-0.386685\pi\) | ||||
0.348519 | + | 0.937302i | \(0.386685\pi\) | |||||||
\(734\) | −34.9421 | −1.28973 | ||||||||
\(735\) | 7.37501 | 0.272031 | ||||||||
\(736\) | −71.2274 | −2.62548 | ||||||||
\(737\) | −42.5396 | −1.56697 | ||||||||
\(738\) | 20.8188 | 0.766350 | ||||||||
\(739\) | −20.9337 | −0.770060 | −0.385030 | − | 0.922904i | \(-0.625809\pi\) | ||||
−0.385030 | + | 0.922904i | \(0.625809\pi\) | |||||||
\(740\) | −46.2340 | −1.69960 | ||||||||
\(741\) | −0.631667 | −0.0232049 | ||||||||
\(742\) | 74.0520 | 2.71853 | ||||||||
\(743\) | −12.2430 | −0.449152 | −0.224576 | − | 0.974457i | \(-0.572100\pi\) | ||||
−0.224576 | + | 0.974457i | \(0.572100\pi\) | |||||||
\(744\) | −33.1628 | −1.21581 | ||||||||
\(745\) | −0.292431 | −0.0107138 | ||||||||
\(746\) | 23.9927 | 0.878436 | ||||||||
\(747\) | −31.8442 | −1.16512 | ||||||||
\(748\) | 172.088 | 6.29215 | ||||||||
\(749\) | −71.9813 | −2.63014 | ||||||||
\(750\) | −1.23544 | −0.0451121 | ||||||||
\(751\) | −29.5282 | −1.07750 | −0.538750 | − | 0.842466i | \(-0.681103\pi\) | ||||
−0.538750 | + | 0.842466i | \(0.681103\pi\) | |||||||
\(752\) | 15.8609 | 0.578388 | ||||||||
\(753\) | 8.19673 | 0.298705 | ||||||||
\(754\) | 0.797335 | 0.0290372 | ||||||||
\(755\) | 7.43589 | 0.270620 | ||||||||
\(756\) | −61.5659 | −2.23913 | ||||||||
\(757\) | −29.7713 | −1.08206 | −0.541029 | − | 0.841004i | \(-0.681965\pi\) | ||||
−0.541029 | + | 0.841004i | \(0.681965\pi\) | |||||||
\(758\) | −68.4406 | −2.48588 | ||||||||
\(759\) | 24.3909 | 0.885332 | ||||||||
\(760\) | −36.2024 | −1.31320 | ||||||||
\(761\) | 21.9275 | 0.794871 | 0.397435 | − | 0.917630i | \(-0.369900\pi\) | ||||
0.397435 | + | 0.917630i | \(0.369900\pi\) | |||||||
\(762\) | −6.31952 | −0.228932 | ||||||||
\(763\) | −40.1204 | −1.45246 | ||||||||
\(764\) | 25.7206 | 0.930539 | ||||||||
\(765\) | −15.9626 | −0.577128 | ||||||||
\(766\) | 60.5055 | 2.18615 | ||||||||
\(767\) | 0.585960 | 0.0211578 | ||||||||
\(768\) | 10.1535 | 0.366382 | ||||||||
\(769\) | 15.9077 | 0.573647 | 0.286823 | − | 0.957983i | \(-0.407401\pi\) | ||||
0.286823 | + | 0.957983i | \(0.407401\pi\) | |||||||
\(770\) | 77.8313 | 2.80485 | ||||||||
\(771\) | −14.8118 | −0.533434 | ||||||||
\(772\) | −116.439 | −4.19073 | ||||||||
\(773\) | −27.7464 | −0.997969 | −0.498984 | − | 0.866611i | \(-0.666293\pi\) | ||||
−0.498984 | + | 0.866611i | \(0.666293\pi\) | |||||||
\(774\) | −69.5071 | −2.49838 | ||||||||
\(775\) | −9.86768 | −0.354457 | ||||||||
\(776\) | −95.0855 | −3.41337 | ||||||||
\(777\) | 22.1297 | 0.793897 | ||||||||
\(778\) | 51.7384 | 1.85491 | ||||||||
\(779\) | −14.8683 | −0.532713 | ||||||||
\(780\) | −0.580798 | −0.0207959 | ||||||||
\(781\) | 27.9390 | 0.999737 | ||||||||
\(782\) | 120.601 | 4.31270 | ||||||||
\(783\) | 3.27749 | 0.117128 | ||||||||
\(784\) | 136.807 | 4.88595 | ||||||||
\(785\) | 12.4726 | 0.445168 | ||||||||
\(786\) | −5.29834 | −0.188985 | ||||||||
\(787\) | 6.87006 | 0.244891 | 0.122446 | − | 0.992475i | \(-0.460926\pi\) | ||||
0.122446 | + | 0.992475i | \(0.460926\pi\) | |||||||
\(788\) | 13.6263 | 0.485417 | ||||||||
\(789\) | −10.4134 | −0.370726 | ||||||||
\(790\) | −11.4576 | −0.407643 | ||||||||
\(791\) | −84.6499 | −3.00980 | ||||||||
\(792\) | −123.836 | −4.40033 | ||||||||
\(793\) | −2.01838 | −0.0716748 | ||||||||
\(794\) | −4.39771 | −0.156069 | ||||||||
\(795\) | 2.87159 | 0.101845 | ||||||||
\(796\) | −111.670 | −3.95802 | ||||||||
\(797\) | −11.4810 | −0.406677 | −0.203338 | − | 0.979109i | \(-0.565179\pi\) | ||||
−0.203338 | + | 0.979109i | \(0.565179\pi\) | |||||||
\(798\) | 30.0680 | 1.06440 | ||||||||
\(799\) | −10.3282 | −0.365386 | ||||||||
\(800\) | −8.81373 | −0.311613 | ||||||||
\(801\) | 28.5369 | 1.00830 | ||||||||
\(802\) | 51.3824 | 1.81437 | ||||||||
\(803\) | 79.9488 | 2.82133 | ||||||||
\(804\) | −15.1105 | −0.532908 | ||||||||
\(805\) | 38.3123 | 1.35033 | ||||||||
\(806\) | −6.60445 | −0.232632 | ||||||||
\(807\) | 1.02476 | 0.0360733 | ||||||||
\(808\) | 2.40710 | 0.0846815 | ||||||||
\(809\) | −50.9641 | −1.79180 | −0.895901 | − | 0.444253i | \(-0.853469\pi\) | ||||
−0.895901 | + | 0.444253i | \(0.853469\pi\) | |||||||
\(810\) | 18.1659 | 0.638283 | ||||||||
\(811\) | 4.26572 | 0.149790 | 0.0748948 | − | 0.997191i | \(-0.476138\pi\) | ||||
0.0748948 | + | 0.997191i | \(0.476138\pi\) | |||||||
\(812\) | −26.6586 | −0.935533 | ||||||||
\(813\) | −7.46708 | −0.261882 | ||||||||
\(814\) | 160.805 | 5.63620 | ||||||||
\(815\) | 21.4251 | 0.750488 | ||||||||
\(816\) | 24.2536 | 0.849046 | ||||||||
\(817\) | 49.6404 | 1.73670 | ||||||||
\(818\) | −17.2794 | −0.604160 | ||||||||
\(819\) | −3.39398 | −0.118595 | ||||||||
\(820\) | −13.6709 | −0.477410 | ||||||||
\(821\) | −8.04193 | −0.280665 | −0.140333 | − | 0.990104i | \(-0.544817\pi\) | ||||
−0.140333 | + | 0.990104i | \(0.544817\pi\) | |||||||
\(822\) | 1.22594 | 0.0427596 | ||||||||
\(823\) | 34.6286 | 1.20708 | 0.603539 | − | 0.797334i | \(-0.293757\pi\) | ||||
0.603539 | + | 0.797334i | \(0.293757\pi\) | |||||||
\(824\) | 41.1178 | 1.43241 | ||||||||
\(825\) | 3.01814 | 0.105078 | ||||||||
\(826\) | −27.8923 | −0.970497 | ||||||||
\(827\) | 31.1771 | 1.08413 | 0.542066 | − | 0.840336i | \(-0.317642\pi\) | ||||
0.542066 | + | 0.840336i | \(0.317642\pi\) | |||||||
\(828\) | −105.776 | −3.67595 | ||||||||
\(829\) | 24.3141 | 0.844463 | 0.422231 | − | 0.906488i | \(-0.361247\pi\) | ||||
0.422231 | + | 0.906488i | \(0.361247\pi\) | |||||||
\(830\) | 29.7710 | 1.03337 | ||||||||
\(831\) | −13.2623 | −0.460064 | ||||||||
\(832\) | −1.33413 | −0.0462526 | ||||||||
\(833\) | −89.0850 | −3.08661 | ||||||||
\(834\) | −6.27912 | −0.217428 | ||||||||
\(835\) | 19.3497 | 0.669624 | ||||||||
\(836\) | 153.465 | 5.30769 | ||||||||
\(837\) | −27.1479 | −0.938370 | ||||||||
\(838\) | −44.3162 | −1.53088 | ||||||||
\(839\) | 24.0474 | 0.830210 | 0.415105 | − | 0.909774i | \(-0.363745\pi\) | ||||
0.415105 | + | 0.909774i | \(0.363745\pi\) | |||||||
\(840\) | 15.9326 | 0.549727 | ||||||||
\(841\) | −27.5808 | −0.951063 | ||||||||
\(842\) | −59.2174 | −2.04077 | ||||||||
\(843\) | −7.41210 | −0.255286 | ||||||||
\(844\) | −7.15047 | −0.246129 | ||||||||
\(845\) | 12.9333 | 0.444920 | ||||||||
\(846\) | 12.8967 | 0.443397 | ||||||||
\(847\) | −137.990 | −4.74140 | ||||||||
\(848\) | 53.2681 | 1.82923 | ||||||||
\(849\) | 2.00940 | 0.0689624 | ||||||||
\(850\) | 14.9233 | 0.511866 | ||||||||
\(851\) | 79.1556 | 2.71342 | ||||||||
\(852\) | 9.92426 | 0.339999 | ||||||||
\(853\) | −23.6269 | −0.808970 | −0.404485 | − | 0.914545i | \(-0.632549\pi\) | ||||
−0.404485 | + | 0.914545i | \(0.632549\pi\) | |||||||
\(854\) | 96.0769 | 3.28768 | ||||||||
\(855\) | −14.2351 | −0.486831 | ||||||||
\(856\) | −107.072 | −3.65964 | ||||||||
\(857\) | 6.14053 | 0.209757 | 0.104878 | − | 0.994485i | \(-0.466555\pi\) | ||||
0.104878 | + | 0.994485i | \(0.466555\pi\) | |||||||
\(858\) | 2.02005 | 0.0689633 | ||||||||
\(859\) | −55.2066 | −1.88362 | −0.941812 | − | 0.336141i | \(-0.890878\pi\) | ||||
−0.941812 | + | 0.336141i | \(0.890878\pi\) | |||||||
\(860\) | 45.6428 | 1.55641 | ||||||||
\(861\) | 6.54352 | 0.223003 | ||||||||
\(862\) | 23.8089 | 0.810936 | ||||||||
\(863\) | 7.93344 | 0.270057 | 0.135029 | − | 0.990842i | \(-0.456887\pi\) | ||||
0.135029 | + | 0.990842i | \(0.456887\pi\) | |||||||
\(864\) | −24.2483 | −0.824945 | ||||||||
\(865\) | −1.33845 | −0.0455088 | ||||||||
\(866\) | 25.7237 | 0.874128 | ||||||||
\(867\) | −7.69157 | −0.261220 | ||||||||
\(868\) | 220.817 | 7.49502 | ||||||||
\(869\) | 27.9905 | 0.949513 | ||||||||
\(870\) | −1.47178 | −0.0498980 | ||||||||
\(871\) | −1.73425 | −0.0587627 | ||||||||
\(872\) | −59.6790 | −2.02099 | ||||||||
\(873\) | −37.3885 | −1.26541 | ||||||||
\(874\) | 107.550 | 3.63794 | ||||||||
\(875\) | 4.74079 | 0.160268 | ||||||||
\(876\) | 28.3987 | 0.959504 | ||||||||
\(877\) | −12.6137 | −0.425933 | −0.212966 | − | 0.977060i | \(-0.568313\pi\) | ||||
−0.212966 | + | 0.977060i | \(0.568313\pi\) | |||||||
\(878\) | 28.6419 | 0.966616 | ||||||||
\(879\) | 10.9629 | 0.369769 | ||||||||
\(880\) | 55.9867 | 1.88731 | ||||||||
\(881\) | −12.4845 | −0.420615 | −0.210307 | − | 0.977635i | \(-0.567446\pi\) | ||||
−0.210307 | + | 0.977635i | \(0.567446\pi\) | |||||||
\(882\) | 111.239 | 3.74561 | ||||||||
\(883\) | −49.0722 | −1.65141 | −0.825705 | − | 0.564102i | \(-0.809222\pi\) | ||||
−0.825705 | + | 0.564102i | \(0.809222\pi\) | |||||||
\(884\) | 7.01564 | 0.235961 | ||||||||
\(885\) | −1.08161 | −0.0363578 | ||||||||
\(886\) | 25.9107 | 0.870489 | ||||||||
\(887\) | 39.7658 | 1.33520 | 0.667602 | − | 0.744519i | \(-0.267321\pi\) | ||||
0.667602 | + | 0.744519i | \(0.267321\pi\) | |||||||
\(888\) | 32.9178 | 1.10465 | ||||||||
\(889\) | 24.2500 | 0.813319 | ||||||||
\(890\) | −26.6790 | −0.894283 | ||||||||
\(891\) | −44.3785 | −1.48674 | ||||||||
\(892\) | 4.46731 | 0.149577 | ||||||||
\(893\) | −9.21053 | −0.308219 | ||||||||
\(894\) | 0.361283 | 0.0120831 | ||||||||
\(895\) | −15.7794 | −0.527449 | ||||||||
\(896\) | −20.0623 | −0.670233 | ||||||||
\(897\) | 0.994363 | 0.0332008 | ||||||||
\(898\) | 3.23008 | 0.107789 | ||||||||
\(899\) | −11.7553 | −0.392062 | ||||||||
\(900\) | −13.0887 | −0.436292 | ||||||||
\(901\) | −34.6868 | −1.15558 | ||||||||
\(902\) | 47.5483 | 1.58319 | ||||||||
\(903\) | −21.8467 | −0.727011 | ||||||||
\(904\) | −125.916 | −4.18792 | ||||||||
\(905\) | −22.1852 | −0.737459 | ||||||||
\(906\) | −9.18663 | −0.305205 | ||||||||
\(907\) | −11.1211 | −0.369270 | −0.184635 | − | 0.982807i | \(-0.559110\pi\) | ||||
−0.184635 | + | 0.982807i | \(0.559110\pi\) | |||||||
\(908\) | 13.5575 | 0.449921 | ||||||||
\(909\) | 0.946495 | 0.0313933 | ||||||||
\(910\) | 3.17302 | 0.105184 | ||||||||
\(911\) | −18.4124 | −0.610031 | −0.305015 | − | 0.952347i | \(-0.598662\pi\) | ||||
−0.305015 | + | 0.952347i | \(0.598662\pi\) | |||||||
\(912\) | 21.6289 | 0.716205 | ||||||||
\(913\) | −72.7295 | −2.40699 | ||||||||
\(914\) | −26.1893 | −0.866263 | ||||||||
\(915\) | 3.72567 | 0.123167 | ||||||||
\(916\) | −65.0063 | −2.14787 | ||||||||
\(917\) | 20.3314 | 0.671402 | ||||||||
\(918\) | 41.0570 | 1.35508 | ||||||||
\(919\) | 11.8351 | 0.390405 | 0.195203 | − | 0.980763i | \(-0.437464\pi\) | ||||
0.195203 | + | 0.980763i | \(0.437464\pi\) | |||||||
\(920\) | 56.9893 | 1.87888 | ||||||||
\(921\) | −9.07938 | −0.299176 | ||||||||
\(922\) | 17.4782 | 0.575613 | ||||||||
\(923\) | 1.13901 | 0.0374911 | ||||||||
\(924\) | −67.5395 | −2.22189 | ||||||||
\(925\) | 9.79477 | 0.322050 | ||||||||
\(926\) | −29.0594 | −0.954950 | ||||||||
\(927\) | 16.1679 | 0.531024 | ||||||||
\(928\) | −10.4998 | −0.344671 | ||||||||
\(929\) | 47.1164 | 1.54584 | 0.772919 | − | 0.634505i | \(-0.218796\pi\) | ||||
0.772919 | + | 0.634505i | \(0.218796\pi\) | |||||||
\(930\) | 12.1910 | 0.399758 | ||||||||
\(931\) | −79.4444 | −2.60369 | ||||||||
\(932\) | −44.7379 | −1.46544 | ||||||||
\(933\) | 6.98191 | 0.228577 | ||||||||
\(934\) | 37.0082 | 1.21095 | ||||||||
\(935\) | −36.4571 | −1.19227 | ||||||||
\(936\) | −5.04853 | −0.165016 | ||||||||
\(937\) | −12.3302 | −0.402809 | −0.201404 | − | 0.979508i | \(-0.564551\pi\) | ||||
−0.201404 | + | 0.979508i | \(0.564551\pi\) | |||||||
\(938\) | 82.5519 | 2.69542 | ||||||||
\(939\) | −2.79441 | −0.0911923 | ||||||||
\(940\) | −8.46879 | −0.276221 | ||||||||
\(941\) | −0.432330 | −0.0140935 | −0.00704677 | − | 0.999975i | \(-0.502243\pi\) | ||||
−0.00704677 | + | 0.999975i | \(0.502243\pi\) | |||||||
\(942\) | −15.4093 | −0.502061 | ||||||||
\(943\) | 23.4055 | 0.762189 | ||||||||
\(944\) | −20.0639 | −0.653023 | ||||||||
\(945\) | 13.0429 | 0.424284 | ||||||||
\(946\) | −158.748 | −5.16135 | ||||||||
\(947\) | 13.0107 | 0.422790 | 0.211395 | − | 0.977401i | \(-0.432199\pi\) | ||||
0.211395 | + | 0.977401i | \(0.432199\pi\) | |||||||
\(948\) | 9.94254 | 0.322919 | ||||||||
\(949\) | 3.25934 | 0.105803 | ||||||||
\(950\) | 13.3083 | 0.431780 | ||||||||
\(951\) | 0.581661 | 0.0188616 | ||||||||
\(952\) | −192.455 | −6.23750 | ||||||||
\(953\) | −29.6517 | −0.960513 | −0.480257 | − | 0.877128i | \(-0.659456\pi\) | ||||
−0.480257 | + | 0.877128i | \(0.659456\pi\) | |||||||
\(954\) | 43.3128 | 1.40231 | ||||||||
\(955\) | −5.44896 | −0.176324 | ||||||||
\(956\) | −84.1447 | −2.72143 | ||||||||
\(957\) | 3.59550 | 0.116226 | ||||||||
\(958\) | −54.9837 | −1.77644 | ||||||||
\(959\) | −4.70432 | −0.151910 | ||||||||
\(960\) | 2.46263 | 0.0794810 | ||||||||
\(961\) | 66.3710 | 2.14100 | ||||||||
\(962\) | 6.55565 | 0.211363 | ||||||||
\(963\) | −42.1017 | −1.35671 | ||||||||
\(964\) | −127.630 | −4.11068 | ||||||||
\(965\) | 24.6678 | 0.794086 | ||||||||
\(966\) | −47.3327 | −1.52290 | ||||||||
\(967\) | 47.1633 | 1.51667 | 0.758335 | − | 0.651865i | \(-0.226013\pi\) | ||||
0.758335 | + | 0.651865i | \(0.226013\pi\) | |||||||
\(968\) | −205.260 | −6.59731 | ||||||||
\(969\) | −14.0842 | −0.452450 | ||||||||
\(970\) | 34.9544 | 1.12232 | ||||||||
\(971\) | −48.1479 | −1.54514 | −0.772570 | − | 0.634929i | \(-0.781029\pi\) | ||||
−0.772570 | + | 0.634929i | \(0.781029\pi\) | |||||||
\(972\) | −54.7230 | −1.75524 | ||||||||
\(973\) | 24.0950 | 0.772449 | ||||||||
\(974\) | −77.2589 | −2.47553 | ||||||||
\(975\) | 0.123043 | 0.00394054 | ||||||||
\(976\) | 69.1114 | 2.21220 | ||||||||
\(977\) | 14.7257 | 0.471116 | 0.235558 | − | 0.971860i | \(-0.424308\pi\) | ||||
0.235558 | + | 0.971860i | \(0.424308\pi\) | |||||||
\(978\) | −26.4695 | −0.846401 | ||||||||
\(979\) | 65.1759 | 2.08303 | ||||||||
\(980\) | −73.0467 | −2.33339 | ||||||||
\(981\) | −23.4664 | −0.749223 | ||||||||
\(982\) | −18.7145 | −0.597203 | ||||||||
\(983\) | −0.987474 | −0.0314955 | −0.0157478 | − | 0.999876i | \(-0.505013\pi\) | ||||
−0.0157478 | + | 0.999876i | \(0.505013\pi\) | |||||||
\(984\) | 9.73347 | 0.310292 | ||||||||
\(985\) | −2.88676 | −0.0919798 | ||||||||
\(986\) | 17.7781 | 0.566169 | ||||||||
\(987\) | 4.05354 | 0.129026 | ||||||||
\(988\) | 6.25642 | 0.199043 | ||||||||
\(989\) | −78.1433 | −2.48481 | ||||||||
\(990\) | 45.5234 | 1.44683 | ||||||||
\(991\) | −0.0597053 | −0.00189660 | −0.000948301 | − | 1.00000i | \(-0.500302\pi\) | ||||
−0.000948301 | 1.00000i | \(0.500302\pi\) | ||||||||
\(992\) | 86.9711 | 2.76133 | ||||||||
\(993\) | −13.6167 | −0.432112 | ||||||||
\(994\) | −54.2182 | −1.71970 | ||||||||
\(995\) | 23.6574 | 0.749990 | ||||||||
\(996\) | −25.8343 | −0.818592 | ||||||||
\(997\) | −46.2885 | −1.46597 | −0.732986 | − | 0.680243i | \(-0.761874\pi\) | ||||
−0.732986 | + | 0.680243i | \(0.761874\pi\) | |||||||
\(998\) | −70.1354 | −2.22010 | ||||||||
\(999\) | 26.9474 | 0.852577 |
(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 | 8045.2.a.b.1.3 | ✓ | 126 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8045.2.a.b.1.3 | ✓ | 126 | 1.1 | even | 1 | trivial |