Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8031,2,Mod(1,8031)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8031, 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("8031.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8031 = 3 \cdot 2677 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8031.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: | \(64.1278578633\) |
Analytic rank: | \(0\) |
Dimension: | \(132\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 8031.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.57206 | −1.81872 | −0.909360 | − | 0.416011i | \(-0.863428\pi\) | ||||
−0.909360 | + | 0.416011i | \(0.863428\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 4.61548 | 2.30774 | ||||||||
\(5\) | 3.83645 | 1.71571 | 0.857855 | − | 0.513891i | \(-0.171796\pi\) | ||||
0.857855 | + | 0.513891i | \(0.171796\pi\) | |||||||
\(6\) | −2.57206 | −1.05004 | ||||||||
\(7\) | −2.68797 | −1.01596 | −0.507979 | − | 0.861369i | \(-0.669607\pi\) | ||||
−0.507979 | + | 0.861369i | \(0.669607\pi\) | |||||||
\(8\) | −6.72717 | −2.37841 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −9.86756 | −3.12040 | ||||||||
\(11\) | −2.81629 | −0.849143 | −0.424571 | − | 0.905395i | \(-0.639575\pi\) | ||||
−0.424571 | + | 0.905395i | \(0.639575\pi\) | |||||||
\(12\) | 4.61548 | 1.33237 | ||||||||
\(13\) | 4.42524 | 1.22734 | 0.613670 | − | 0.789562i | \(-0.289692\pi\) | ||||
0.613670 | + | 0.789562i | \(0.289692\pi\) | |||||||
\(14\) | 6.91362 | 1.84774 | ||||||||
\(15\) | 3.83645 | 0.990566 | ||||||||
\(16\) | 8.07170 | 2.01793 | ||||||||
\(17\) | 5.87877 | 1.42581 | 0.712905 | − | 0.701260i | \(-0.247379\pi\) | ||||
0.712905 | + | 0.701260i | \(0.247379\pi\) | |||||||
\(18\) | −2.57206 | −0.606240 | ||||||||
\(19\) | −5.15734 | −1.18317 | −0.591587 | − | 0.806241i | \(-0.701498\pi\) | ||||
−0.591587 | + | 0.806241i | \(0.701498\pi\) | |||||||
\(20\) | 17.7070 | 3.95942 | ||||||||
\(21\) | −2.68797 | −0.586564 | ||||||||
\(22\) | 7.24365 | 1.54435 | ||||||||
\(23\) | −6.88942 | −1.43654 | −0.718272 | − | 0.695762i | \(-0.755067\pi\) | ||||
−0.718272 | + | 0.695762i | \(0.755067\pi\) | |||||||
\(24\) | −6.72717 | −1.37318 | ||||||||
\(25\) | 9.71832 | 1.94366 | ||||||||
\(26\) | −11.3820 | −2.23219 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −12.4063 | −2.34457 | ||||||||
\(29\) | −3.16316 | −0.587384 | −0.293692 | − | 0.955900i | \(-0.594884\pi\) | ||||
−0.293692 | + | 0.955900i | \(0.594884\pi\) | |||||||
\(30\) | −9.86756 | −1.80156 | ||||||||
\(31\) | −3.23509 | −0.581038 | −0.290519 | − | 0.956869i | \(-0.593828\pi\) | ||||
−0.290519 | + | 0.956869i | \(0.593828\pi\) | |||||||
\(32\) | −7.30655 | −1.29163 | ||||||||
\(33\) | −2.81629 | −0.490253 | ||||||||
\(34\) | −15.1205 | −2.59315 | ||||||||
\(35\) | −10.3123 | −1.74309 | ||||||||
\(36\) | 4.61548 | 0.769247 | ||||||||
\(37\) | 5.45431 | 0.896683 | 0.448341 | − | 0.893862i | \(-0.352015\pi\) | ||||
0.448341 | + | 0.893862i | \(0.352015\pi\) | |||||||
\(38\) | 13.2650 | 2.15186 | ||||||||
\(39\) | 4.42524 | 0.708606 | ||||||||
\(40\) | −25.8084 | −4.08067 | ||||||||
\(41\) | 7.13649 | 1.11453 | 0.557266 | − | 0.830334i | \(-0.311850\pi\) | ||||
0.557266 | + | 0.830334i | \(0.311850\pi\) | |||||||
\(42\) | 6.91362 | 1.06679 | ||||||||
\(43\) | 11.2124 | 1.70988 | 0.854938 | − | 0.518731i | \(-0.173595\pi\) | ||||
0.854938 | + | 0.518731i | \(0.173595\pi\) | |||||||
\(44\) | −12.9985 | −1.95960 | ||||||||
\(45\) | 3.83645 | 0.571904 | ||||||||
\(46\) | 17.7200 | 2.61267 | ||||||||
\(47\) | 2.04252 | 0.297933 | 0.148966 | − | 0.988842i | \(-0.452405\pi\) | ||||
0.148966 | + | 0.988842i | \(0.452405\pi\) | |||||||
\(48\) | 8.07170 | 1.16505 | ||||||||
\(49\) | 0.225198 | 0.0321711 | ||||||||
\(50\) | −24.9961 | −3.53498 | ||||||||
\(51\) | 5.87877 | 0.823192 | ||||||||
\(52\) | 20.4246 | 2.83238 | ||||||||
\(53\) | 10.0537 | 1.38098 | 0.690489 | − | 0.723342i | \(-0.257395\pi\) | ||||
0.690489 | + | 0.723342i | \(0.257395\pi\) | |||||||
\(54\) | −2.57206 | −0.350013 | ||||||||
\(55\) | −10.8045 | −1.45688 | ||||||||
\(56\) | 18.0824 | 2.41637 | ||||||||
\(57\) | −5.15734 | −0.683106 | ||||||||
\(58\) | 8.13583 | 1.06829 | ||||||||
\(59\) | −11.4678 | −1.49298 | −0.746490 | − | 0.665397i | \(-0.768262\pi\) | ||||
−0.746490 | + | 0.665397i | \(0.768262\pi\) | |||||||
\(60\) | 17.7070 | 2.28597 | ||||||||
\(61\) | 4.97599 | 0.637111 | 0.318555 | − | 0.947904i | \(-0.396802\pi\) | ||||
0.318555 | + | 0.947904i | \(0.396802\pi\) | |||||||
\(62\) | 8.32083 | 1.05675 | ||||||||
\(63\) | −2.68797 | −0.338653 | ||||||||
\(64\) | 2.64946 | 0.331182 | ||||||||
\(65\) | 16.9772 | 2.10576 | ||||||||
\(66\) | 7.24365 | 0.891632 | ||||||||
\(67\) | −7.78664 | −0.951290 | −0.475645 | − | 0.879637i | \(-0.657785\pi\) | ||||
−0.475645 | + | 0.879637i | \(0.657785\pi\) | |||||||
\(68\) | 27.1333 | 3.29040 | ||||||||
\(69\) | −6.88942 | −0.829389 | ||||||||
\(70\) | 26.5237 | 3.17019 | ||||||||
\(71\) | 14.4119 | 1.71038 | 0.855188 | − | 0.518317i | \(-0.173441\pi\) | ||||
0.855188 | + | 0.518317i | \(0.173441\pi\) | |||||||
\(72\) | −6.72717 | −0.792804 | ||||||||
\(73\) | −14.8241 | −1.73503 | −0.867513 | − | 0.497415i | \(-0.834283\pi\) | ||||
−0.867513 | + | 0.497415i | \(0.834283\pi\) | |||||||
\(74\) | −14.0288 | −1.63081 | ||||||||
\(75\) | 9.71832 | 1.12217 | ||||||||
\(76\) | −23.8036 | −2.73046 | ||||||||
\(77\) | 7.57010 | 0.862693 | ||||||||
\(78\) | −11.3820 | −1.28875 | ||||||||
\(79\) | 11.1854 | 1.25846 | 0.629228 | − | 0.777221i | \(-0.283371\pi\) | ||||
0.629228 | + | 0.777221i | \(0.283371\pi\) | |||||||
\(80\) | 30.9666 | 3.46218 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −18.3555 | −2.02702 | ||||||||
\(83\) | −0.358839 | −0.0393877 | −0.0196939 | − | 0.999806i | \(-0.506269\pi\) | ||||
−0.0196939 | + | 0.999806i | \(0.506269\pi\) | |||||||
\(84\) | −12.4063 | −1.35364 | ||||||||
\(85\) | 22.5536 | 2.44628 | ||||||||
\(86\) | −28.8390 | −3.10978 | ||||||||
\(87\) | −3.16316 | −0.339126 | ||||||||
\(88\) | 18.9456 | 2.01961 | ||||||||
\(89\) | −2.28043 | −0.241725 | −0.120862 | − | 0.992669i | \(-0.538566\pi\) | ||||
−0.120862 | + | 0.992669i | \(0.538566\pi\) | |||||||
\(90\) | −9.86756 | −1.04013 | ||||||||
\(91\) | −11.8949 | −1.24693 | ||||||||
\(92\) | −31.7980 | −3.31517 | ||||||||
\(93\) | −3.23509 | −0.335463 | ||||||||
\(94\) | −5.25349 | −0.541856 | ||||||||
\(95\) | −19.7858 | −2.02999 | ||||||||
\(96\) | −7.30655 | −0.745721 | ||||||||
\(97\) | −14.0986 | −1.43149 | −0.715747 | − | 0.698359i | \(-0.753914\pi\) | ||||
−0.715747 | + | 0.698359i | \(0.753914\pi\) | |||||||
\(98\) | −0.579221 | −0.0585102 | ||||||||
\(99\) | −2.81629 | −0.283048 | ||||||||
\(100\) | 44.8547 | 4.48547 | ||||||||
\(101\) | 5.20985 | 0.518400 | 0.259200 | − | 0.965824i | \(-0.416541\pi\) | ||||
0.259200 | + | 0.965824i | \(0.416541\pi\) | |||||||
\(102\) | −15.1205 | −1.49716 | ||||||||
\(103\) | 15.3371 | 1.51121 | 0.755606 | − | 0.655027i | \(-0.227343\pi\) | ||||
0.755606 | + | 0.655027i | \(0.227343\pi\) | |||||||
\(104\) | −29.7693 | −2.91912 | ||||||||
\(105\) | −10.3123 | −1.00637 | ||||||||
\(106\) | −25.8586 | −2.51161 | ||||||||
\(107\) | 9.09892 | 0.879626 | 0.439813 | − | 0.898089i | \(-0.355045\pi\) | ||||
0.439813 | + | 0.898089i | \(0.355045\pi\) | |||||||
\(108\) | 4.61548 | 0.444125 | ||||||||
\(109\) | 18.0356 | 1.72750 | 0.863750 | − | 0.503920i | \(-0.168109\pi\) | ||||
0.863750 | + | 0.503920i | \(0.168109\pi\) | |||||||
\(110\) | 27.7899 | 2.64966 | ||||||||
\(111\) | 5.45431 | 0.517700 | ||||||||
\(112\) | −21.6965 | −2.05013 | ||||||||
\(113\) | −15.4150 | −1.45012 | −0.725058 | − | 0.688687i | \(-0.758187\pi\) | ||||
−0.725058 | + | 0.688687i | \(0.758187\pi\) | |||||||
\(114\) | 13.2650 | 1.24238 | ||||||||
\(115\) | −26.4309 | −2.46469 | ||||||||
\(116\) | −14.5995 | −1.35553 | ||||||||
\(117\) | 4.42524 | 0.409114 | ||||||||
\(118\) | 29.4958 | 2.71531 | ||||||||
\(119\) | −15.8020 | −1.44856 | ||||||||
\(120\) | −25.8084 | −2.35598 | ||||||||
\(121\) | −3.06853 | −0.278957 | ||||||||
\(122\) | −12.7985 | −1.15873 | ||||||||
\(123\) | 7.13649 | 0.643475 | ||||||||
\(124\) | −14.9315 | −1.34089 | ||||||||
\(125\) | 18.1016 | 1.61905 | ||||||||
\(126\) | 6.91362 | 0.615914 | ||||||||
\(127\) | 19.4907 | 1.72952 | 0.864762 | − | 0.502182i | \(-0.167469\pi\) | ||||
0.864762 | + | 0.502182i | \(0.167469\pi\) | |||||||
\(128\) | 7.79854 | 0.689300 | ||||||||
\(129\) | 11.2124 | 0.987197 | ||||||||
\(130\) | −43.6663 | −3.82979 | ||||||||
\(131\) | −0.671792 | −0.0586947 | −0.0293474 | − | 0.999569i | \(-0.509343\pi\) | ||||
−0.0293474 | + | 0.999569i | \(0.509343\pi\) | |||||||
\(132\) | −12.9985 | −1.13138 | ||||||||
\(133\) | 13.8628 | 1.20206 | ||||||||
\(134\) | 20.0277 | 1.73013 | ||||||||
\(135\) | 3.83645 | 0.330189 | ||||||||
\(136\) | −39.5475 | −3.39117 | ||||||||
\(137\) | −17.7915 | −1.52003 | −0.760015 | − | 0.649905i | \(-0.774808\pi\) | ||||
−0.760015 | + | 0.649905i | \(0.774808\pi\) | |||||||
\(138\) | 17.7200 | 1.50843 | ||||||||
\(139\) | −12.2753 | −1.04118 | −0.520588 | − | 0.853808i | \(-0.674287\pi\) | ||||
−0.520588 | + | 0.853808i | \(0.674287\pi\) | |||||||
\(140\) | −47.5961 | −4.02260 | ||||||||
\(141\) | 2.04252 | 0.172012 | ||||||||
\(142\) | −37.0682 | −3.11070 | ||||||||
\(143\) | −12.4627 | −1.04219 | ||||||||
\(144\) | 8.07170 | 0.672642 | ||||||||
\(145\) | −12.1353 | −1.00778 | ||||||||
\(146\) | 38.1283 | 3.15552 | ||||||||
\(147\) | 0.225198 | 0.0185740 | ||||||||
\(148\) | 25.1743 | 2.06931 | ||||||||
\(149\) | −18.2342 | −1.49380 | −0.746900 | − | 0.664936i | \(-0.768459\pi\) | ||||
−0.746900 | + | 0.664936i | \(0.768459\pi\) | |||||||
\(150\) | −24.9961 | −2.04092 | ||||||||
\(151\) | 9.27800 | 0.755033 | 0.377516 | − | 0.926003i | \(-0.376778\pi\) | ||||
0.377516 | + | 0.926003i | \(0.376778\pi\) | |||||||
\(152\) | 34.6943 | 2.81408 | ||||||||
\(153\) | 5.87877 | 0.475270 | ||||||||
\(154\) | −19.4707 | −1.56900 | ||||||||
\(155\) | −12.4112 | −0.996894 | ||||||||
\(156\) | 20.4246 | 1.63528 | ||||||||
\(157\) | 17.3396 | 1.38385 | 0.691926 | − | 0.721968i | \(-0.256762\pi\) | ||||
0.691926 | + | 0.721968i | \(0.256762\pi\) | |||||||
\(158\) | −28.7695 | −2.28878 | ||||||||
\(159\) | 10.0537 | 0.797309 | ||||||||
\(160\) | −28.0312 | −2.21606 | ||||||||
\(161\) | 18.5186 | 1.45947 | ||||||||
\(162\) | −2.57206 | −0.202080 | ||||||||
\(163\) | −0.588856 | −0.0461228 | −0.0230614 | − | 0.999734i | \(-0.507341\pi\) | ||||
−0.0230614 | + | 0.999734i | \(0.507341\pi\) | |||||||
\(164\) | 32.9383 | 2.57205 | ||||||||
\(165\) | −10.8045 | −0.841132 | ||||||||
\(166\) | 0.922955 | 0.0716352 | ||||||||
\(167\) | −12.5907 | −0.974301 | −0.487150 | − | 0.873318i | \(-0.661964\pi\) | ||||
−0.487150 | + | 0.873318i | \(0.661964\pi\) | |||||||
\(168\) | 18.0824 | 1.39509 | ||||||||
\(169\) | 6.58275 | 0.506366 | ||||||||
\(170\) | −58.0091 | −4.44909 | ||||||||
\(171\) | −5.15734 | −0.394391 | ||||||||
\(172\) | 51.7506 | 3.94595 | ||||||||
\(173\) | −0.933654 | −0.0709844 | −0.0354922 | − | 0.999370i | \(-0.511300\pi\) | ||||
−0.0354922 | + | 0.999370i | \(0.511300\pi\) | |||||||
\(174\) | 8.13583 | 0.616775 | ||||||||
\(175\) | −26.1226 | −1.97468 | ||||||||
\(176\) | −22.7322 | −1.71351 | ||||||||
\(177\) | −11.4678 | −0.861972 | ||||||||
\(178\) | 5.86539 | 0.439629 | ||||||||
\(179\) | 3.33908 | 0.249574 | 0.124787 | − | 0.992184i | \(-0.460175\pi\) | ||||
0.124787 | + | 0.992184i | \(0.460175\pi\) | |||||||
\(180\) | 17.7070 | 1.31981 | ||||||||
\(181\) | 20.6096 | 1.53190 | 0.765949 | − | 0.642901i | \(-0.222269\pi\) | ||||
0.765949 | + | 0.642901i | \(0.222269\pi\) | |||||||
\(182\) | 30.5944 | 2.26781 | ||||||||
\(183\) | 4.97599 | 0.367836 | ||||||||
\(184\) | 46.3463 | 3.41670 | ||||||||
\(185\) | 20.9252 | 1.53845 | ||||||||
\(186\) | 8.32083 | 0.610113 | ||||||||
\(187\) | −16.5563 | −1.21072 | ||||||||
\(188\) | 9.42723 | 0.687551 | ||||||||
\(189\) | −2.68797 | −0.195521 | ||||||||
\(190\) | 50.8903 | 3.69197 | ||||||||
\(191\) | −4.86708 | −0.352169 | −0.176085 | − | 0.984375i | \(-0.556343\pi\) | ||||
−0.176085 | + | 0.984375i | \(0.556343\pi\) | |||||||
\(192\) | 2.64946 | 0.191208 | ||||||||
\(193\) | 18.1019 | 1.30300 | 0.651502 | − | 0.758647i | \(-0.274139\pi\) | ||||
0.651502 | + | 0.758647i | \(0.274139\pi\) | |||||||
\(194\) | 36.2624 | 2.60349 | ||||||||
\(195\) | 16.9772 | 1.21576 | ||||||||
\(196\) | 1.03940 | 0.0742425 | ||||||||
\(197\) | 8.14430 | 0.580257 | 0.290129 | − | 0.956988i | \(-0.406302\pi\) | ||||
0.290129 | + | 0.956988i | \(0.406302\pi\) | |||||||
\(198\) | 7.24365 | 0.514784 | ||||||||
\(199\) | 23.2617 | 1.64898 | 0.824489 | − | 0.565878i | \(-0.191463\pi\) | ||||
0.824489 | + | 0.565878i | \(0.191463\pi\) | |||||||
\(200\) | −65.3768 | −4.62284 | ||||||||
\(201\) | −7.78664 | −0.549228 | ||||||||
\(202\) | −13.4000 | −0.942824 | ||||||||
\(203\) | 8.50248 | 0.596757 | ||||||||
\(204\) | 27.1333 | 1.89971 | ||||||||
\(205\) | 27.3787 | 1.91221 | ||||||||
\(206\) | −39.4480 | −2.74847 | ||||||||
\(207\) | −6.88942 | −0.478848 | ||||||||
\(208\) | 35.7192 | 2.47668 | ||||||||
\(209\) | 14.5245 | 1.00468 | ||||||||
\(210\) | 26.5237 | 1.83031 | ||||||||
\(211\) | 22.2384 | 1.53095 | 0.765477 | − | 0.643463i | \(-0.222503\pi\) | ||||
0.765477 | + | 0.643463i | \(0.222503\pi\) | |||||||
\(212\) | 46.4026 | 3.18694 | ||||||||
\(213\) | 14.4119 | 0.987486 | ||||||||
\(214\) | −23.4030 | −1.59979 | ||||||||
\(215\) | 43.0158 | 2.93365 | ||||||||
\(216\) | −6.72717 | −0.457726 | ||||||||
\(217\) | 8.69582 | 0.590311 | ||||||||
\(218\) | −46.3887 | −3.14184 | ||||||||
\(219\) | −14.8241 | −1.00172 | ||||||||
\(220\) | −49.8681 | −3.36211 | ||||||||
\(221\) | 26.0150 | 1.74996 | ||||||||
\(222\) | −14.0288 | −0.941551 | ||||||||
\(223\) | 3.42042 | 0.229048 | 0.114524 | − | 0.993420i | \(-0.463466\pi\) | ||||
0.114524 | + | 0.993420i | \(0.463466\pi\) | |||||||
\(224\) | 19.6398 | 1.31224 | ||||||||
\(225\) | 9.71832 | 0.647888 | ||||||||
\(226\) | 39.6482 | 2.63736 | ||||||||
\(227\) | 20.6053 | 1.36762 | 0.683810 | − | 0.729661i | \(-0.260322\pi\) | ||||
0.683810 | + | 0.729661i | \(0.260322\pi\) | |||||||
\(228\) | −23.8036 | −1.57643 | ||||||||
\(229\) | 18.4194 | 1.21719 | 0.608596 | − | 0.793480i | \(-0.291733\pi\) | ||||
0.608596 | + | 0.793480i | \(0.291733\pi\) | |||||||
\(230\) | 67.9818 | 4.48259 | ||||||||
\(231\) | 7.57010 | 0.498076 | ||||||||
\(232\) | 21.2791 | 1.39704 | ||||||||
\(233\) | 4.44717 | 0.291344 | 0.145672 | − | 0.989333i | \(-0.453466\pi\) | ||||
0.145672 | + | 0.989333i | \(0.453466\pi\) | |||||||
\(234\) | −11.3820 | −0.744063 | ||||||||
\(235\) | 7.83603 | 0.511166 | ||||||||
\(236\) | −52.9294 | −3.44541 | ||||||||
\(237\) | 11.1854 | 0.726570 | ||||||||
\(238\) | 40.6436 | 2.63453 | ||||||||
\(239\) | 9.55835 | 0.618278 | 0.309139 | − | 0.951017i | \(-0.399959\pi\) | ||||
0.309139 | + | 0.951017i | \(0.399959\pi\) | |||||||
\(240\) | 30.9666 | 1.99889 | ||||||||
\(241\) | −9.35677 | −0.602723 | −0.301361 | − | 0.953510i | \(-0.597441\pi\) | ||||
−0.301361 | + | 0.953510i | \(0.597441\pi\) | |||||||
\(242\) | 7.89242 | 0.507344 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 22.9666 | 1.47029 | ||||||||
\(245\) | 0.863958 | 0.0551963 | ||||||||
\(246\) | −18.3555 | −1.17030 | ||||||||
\(247\) | −22.8225 | −1.45216 | ||||||||
\(248\) | 21.7630 | 1.38195 | ||||||||
\(249\) | −0.358839 | −0.0227405 | ||||||||
\(250\) | −46.5583 | −2.94461 | ||||||||
\(251\) | 2.01942 | 0.127465 | 0.0637324 | − | 0.997967i | \(-0.479700\pi\) | ||||
0.0637324 | + | 0.997967i | \(0.479700\pi\) | |||||||
\(252\) | −12.4063 | −0.781523 | ||||||||
\(253\) | 19.4026 | 1.21983 | ||||||||
\(254\) | −50.1313 | −3.14552 | ||||||||
\(255\) | 22.5536 | 1.41236 | ||||||||
\(256\) | −25.3572 | −1.58483 | ||||||||
\(257\) | −22.1534 | −1.38189 | −0.690946 | − | 0.722906i | \(-0.742806\pi\) | ||||
−0.690946 | + | 0.722906i | \(0.742806\pi\) | |||||||
\(258\) | −28.8390 | −1.79543 | ||||||||
\(259\) | −14.6610 | −0.910992 | ||||||||
\(260\) | 78.3579 | 4.85955 | ||||||||
\(261\) | −3.16316 | −0.195795 | ||||||||
\(262\) | 1.72789 | 0.106749 | ||||||||
\(263\) | 12.0481 | 0.742917 | 0.371458 | − | 0.928450i | \(-0.378858\pi\) | ||||
0.371458 | + | 0.928450i | \(0.378858\pi\) | |||||||
\(264\) | 18.9456 | 1.16602 | ||||||||
\(265\) | 38.5704 | 2.36936 | ||||||||
\(266\) | −35.6559 | −2.18620 | ||||||||
\(267\) | −2.28043 | −0.139560 | ||||||||
\(268\) | −35.9391 | −2.19533 | ||||||||
\(269\) | 1.91786 | 0.116934 | 0.0584670 | − | 0.998289i | \(-0.481379\pi\) | ||||
0.0584670 | + | 0.998289i | \(0.481379\pi\) | |||||||
\(270\) | −9.86756 | −0.600521 | ||||||||
\(271\) | −19.8197 | −1.20396 | −0.601980 | − | 0.798511i | \(-0.705621\pi\) | ||||
−0.601980 | + | 0.798511i | \(0.705621\pi\) | |||||||
\(272\) | 47.4517 | 2.87718 | ||||||||
\(273\) | −11.8949 | −0.719914 | ||||||||
\(274\) | 45.7608 | 2.76451 | ||||||||
\(275\) | −27.3696 | −1.65045 | ||||||||
\(276\) | −31.7980 | −1.91401 | ||||||||
\(277\) | 12.5533 | 0.754253 | 0.377126 | − | 0.926162i | \(-0.376912\pi\) | ||||
0.377126 | + | 0.926162i | \(0.376912\pi\) | |||||||
\(278\) | 31.5728 | 1.89361 | ||||||||
\(279\) | −3.23509 | −0.193679 | ||||||||
\(280\) | 69.3723 | 4.14579 | ||||||||
\(281\) | 6.34273 | 0.378375 | 0.189188 | − | 0.981941i | \(-0.439415\pi\) | ||||
0.189188 | + | 0.981941i | \(0.439415\pi\) | |||||||
\(282\) | −5.25349 | −0.312841 | ||||||||
\(283\) | 2.05838 | 0.122358 | 0.0611789 | − | 0.998127i | \(-0.480514\pi\) | ||||
0.0611789 | + | 0.998127i | \(0.480514\pi\) | |||||||
\(284\) | 66.5178 | 3.94711 | ||||||||
\(285\) | −19.7858 | −1.17201 | ||||||||
\(286\) | 32.0549 | 1.89545 | ||||||||
\(287\) | −19.1827 | −1.13232 | ||||||||
\(288\) | −7.30655 | −0.430542 | ||||||||
\(289\) | 17.5599 | 1.03294 | ||||||||
\(290\) | 31.2127 | 1.83287 | ||||||||
\(291\) | −14.0986 | −0.826474 | ||||||||
\(292\) | −68.4202 | −4.00399 | ||||||||
\(293\) | −25.9128 | −1.51384 | −0.756922 | − | 0.653506i | \(-0.773298\pi\) | ||||
−0.756922 | + | 0.653506i | \(0.773298\pi\) | |||||||
\(294\) | −0.579221 | −0.0337809 | ||||||||
\(295\) | −43.9956 | −2.56152 | ||||||||
\(296\) | −36.6920 | −2.13268 | ||||||||
\(297\) | −2.81629 | −0.163418 | ||||||||
\(298\) | 46.8993 | 2.71680 | ||||||||
\(299\) | −30.4874 | −1.76313 | ||||||||
\(300\) | 44.8547 | 2.58969 | ||||||||
\(301\) | −30.1386 | −1.73716 | ||||||||
\(302\) | −23.8636 | −1.37319 | ||||||||
\(303\) | 5.20985 | 0.299298 | ||||||||
\(304\) | −41.6285 | −2.38756 | ||||||||
\(305\) | 19.0901 | 1.09310 | ||||||||
\(306\) | −15.1205 | −0.864383 | ||||||||
\(307\) | 19.5895 | 1.11803 | 0.559017 | − | 0.829156i | \(-0.311179\pi\) | ||||
0.559017 | + | 0.829156i | \(0.311179\pi\) | |||||||
\(308\) | 34.9397 | 1.99087 | ||||||||
\(309\) | 15.3371 | 0.872498 | ||||||||
\(310\) | 31.9224 | 1.81307 | ||||||||
\(311\) | −29.2485 | −1.65853 | −0.829265 | − | 0.558855i | \(-0.811241\pi\) | ||||
−0.829265 | + | 0.558855i | \(0.811241\pi\) | |||||||
\(312\) | −29.7693 | −1.68536 | ||||||||
\(313\) | −5.66840 | −0.320397 | −0.160199 | − | 0.987085i | \(-0.551213\pi\) | ||||
−0.160199 | + | 0.987085i | \(0.551213\pi\) | |||||||
\(314\) | −44.5985 | −2.51684 | ||||||||
\(315\) | −10.3123 | −0.581030 | ||||||||
\(316\) | 51.6260 | 2.90419 | ||||||||
\(317\) | 13.2127 | 0.742098 | 0.371049 | − | 0.928613i | \(-0.378998\pi\) | ||||
0.371049 | + | 0.928613i | \(0.378998\pi\) | |||||||
\(318\) | −25.8586 | −1.45008 | ||||||||
\(319\) | 8.90836 | 0.498773 | ||||||||
\(320\) | 10.1645 | 0.568213 | ||||||||
\(321\) | 9.09892 | 0.507852 | ||||||||
\(322\) | −47.6309 | −2.65436 | ||||||||
\(323\) | −30.3188 | −1.68698 | ||||||||
\(324\) | 4.61548 | 0.256416 | ||||||||
\(325\) | 43.0059 | 2.38554 | ||||||||
\(326\) | 1.51457 | 0.0838844 | ||||||||
\(327\) | 18.0356 | 0.997373 | ||||||||
\(328\) | −48.0083 | −2.65082 | ||||||||
\(329\) | −5.49025 | −0.302687 | ||||||||
\(330\) | 27.7899 | 1.52978 | ||||||||
\(331\) | 8.88215 | 0.488207 | 0.244104 | − | 0.969749i | \(-0.421506\pi\) | ||||
0.244104 | + | 0.969749i | \(0.421506\pi\) | |||||||
\(332\) | −1.65622 | −0.0908966 | ||||||||
\(333\) | 5.45431 | 0.298894 | ||||||||
\(334\) | 32.3841 | 1.77198 | ||||||||
\(335\) | −29.8730 | −1.63214 | ||||||||
\(336\) | −21.6965 | −1.18364 | ||||||||
\(337\) | 17.3095 | 0.942908 | 0.471454 | − | 0.881891i | \(-0.343729\pi\) | ||||
0.471454 | + | 0.881891i | \(0.343729\pi\) | |||||||
\(338\) | −16.9312 | −0.920937 | ||||||||
\(339\) | −15.4150 | −0.837225 | ||||||||
\(340\) | 104.096 | 5.64538 | ||||||||
\(341\) | 9.11093 | 0.493384 | ||||||||
\(342\) | 13.2650 | 0.717287 | ||||||||
\(343\) | 18.2105 | 0.983274 | ||||||||
\(344\) | −75.4277 | −4.06679 | ||||||||
\(345\) | −26.4309 | −1.42299 | ||||||||
\(346\) | 2.40141 | 0.129101 | ||||||||
\(347\) | 16.0953 | 0.864043 | 0.432021 | − | 0.901863i | \(-0.357801\pi\) | ||||
0.432021 | + | 0.901863i | \(0.357801\pi\) | |||||||
\(348\) | −14.5995 | −0.782615 | ||||||||
\(349\) | 16.6352 | 0.890462 | 0.445231 | − | 0.895416i | \(-0.353121\pi\) | ||||
0.445231 | + | 0.895416i | \(0.353121\pi\) | |||||||
\(350\) | 67.1888 | 3.59139 | ||||||||
\(351\) | 4.42524 | 0.236202 | ||||||||
\(352\) | 20.5773 | 1.09678 | ||||||||
\(353\) | −17.4445 | −0.928479 | −0.464239 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464239 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(354\) | 29.4958 | 1.56769 | ||||||||
\(355\) | 55.2904 | 2.93451 | ||||||||
\(356\) | −10.5253 | −0.557838 | ||||||||
\(357\) | −15.8020 | −0.836329 | ||||||||
\(358\) | −8.58830 | −0.453906 | ||||||||
\(359\) | −5.19012 | −0.273924 | −0.136962 | − | 0.990576i | \(-0.543734\pi\) | ||||
−0.136962 | + | 0.990576i | \(0.543734\pi\) | |||||||
\(360\) | −25.8084 | −1.36022 | ||||||||
\(361\) | 7.59813 | 0.399902 | ||||||||
\(362\) | −53.0091 | −2.78609 | ||||||||
\(363\) | −3.06853 | −0.161056 | ||||||||
\(364\) | −54.9008 | −2.87758 | ||||||||
\(365\) | −56.8717 | −2.97680 | ||||||||
\(366\) | −12.7985 | −0.668990 | ||||||||
\(367\) | 21.2962 | 1.11165 | 0.555827 | − | 0.831298i | \(-0.312402\pi\) | ||||
0.555827 | + | 0.831298i | \(0.312402\pi\) | |||||||
\(368\) | −55.6094 | −2.89884 | ||||||||
\(369\) | 7.13649 | 0.371511 | ||||||||
\(370\) | −53.8207 | −2.79801 | ||||||||
\(371\) | −27.0240 | −1.40302 | ||||||||
\(372\) | −14.9315 | −0.774161 | ||||||||
\(373\) | −18.0070 | −0.932368 | −0.466184 | − | 0.884688i | \(-0.654371\pi\) | ||||
−0.466184 | + | 0.884688i | \(0.654371\pi\) | |||||||
\(374\) | 42.5838 | 2.20195 | ||||||||
\(375\) | 18.1016 | 0.934762 | ||||||||
\(376\) | −13.7404 | −0.708607 | ||||||||
\(377\) | −13.9977 | −0.720920 | ||||||||
\(378\) | 6.91362 | 0.355598 | ||||||||
\(379\) | −10.9441 | −0.562163 | −0.281081 | − | 0.959684i | \(-0.590693\pi\) | ||||
−0.281081 | + | 0.959684i | \(0.590693\pi\) | |||||||
\(380\) | −91.3212 | −4.68468 | ||||||||
\(381\) | 19.4907 | 0.998541 | ||||||||
\(382\) | 12.5184 | 0.640497 | ||||||||
\(383\) | −4.73611 | −0.242004 | −0.121002 | − | 0.992652i | \(-0.538611\pi\) | ||||
−0.121002 | + | 0.992652i | \(0.538611\pi\) | |||||||
\(384\) | 7.79854 | 0.397967 | ||||||||
\(385\) | 29.0423 | 1.48013 | ||||||||
\(386\) | −46.5592 | −2.36980 | ||||||||
\(387\) | 11.2124 | 0.569959 | ||||||||
\(388\) | −65.0718 | −3.30352 | ||||||||
\(389\) | −2.36277 | −0.119797 | −0.0598986 | − | 0.998204i | \(-0.519078\pi\) | ||||
−0.0598986 | + | 0.998204i | \(0.519078\pi\) | |||||||
\(390\) | −43.6663 | −2.21113 | ||||||||
\(391\) | −40.5013 | −2.04824 | ||||||||
\(392\) | −1.51494 | −0.0765161 | ||||||||
\(393\) | −0.671792 | −0.0338874 | ||||||||
\(394\) | −20.9476 | −1.05533 | ||||||||
\(395\) | 42.9122 | 2.15915 | ||||||||
\(396\) | −12.9985 | −0.653200 | ||||||||
\(397\) | 6.23818 | 0.313085 | 0.156543 | − | 0.987671i | \(-0.449965\pi\) | ||||
0.156543 | + | 0.987671i | \(0.449965\pi\) | |||||||
\(398\) | −59.8304 | −2.99903 | ||||||||
\(399\) | 13.8628 | 0.694007 | ||||||||
\(400\) | 78.4434 | 3.92217 | ||||||||
\(401\) | −18.3745 | −0.917581 | −0.458790 | − | 0.888545i | \(-0.651717\pi\) | ||||
−0.458790 | + | 0.888545i | \(0.651717\pi\) | |||||||
\(402\) | 20.0277 | 0.998891 | ||||||||
\(403\) | −14.3160 | −0.713132 | ||||||||
\(404\) | 24.0460 | 1.19633 | ||||||||
\(405\) | 3.83645 | 0.190635 | ||||||||
\(406\) | −21.8689 | −1.08533 | ||||||||
\(407\) | −15.3609 | −0.761411 | ||||||||
\(408\) | −39.5475 | −1.95789 | ||||||||
\(409\) | 33.0442 | 1.63393 | 0.816966 | − | 0.576685i | \(-0.195654\pi\) | ||||
0.816966 | + | 0.576685i | \(0.195654\pi\) | |||||||
\(410\) | −70.4197 | −3.47778 | ||||||||
\(411\) | −17.7915 | −0.877590 | ||||||||
\(412\) | 70.7882 | 3.48748 | ||||||||
\(413\) | 30.8251 | 1.51680 | ||||||||
\(414\) | 17.7200 | 0.870890 | ||||||||
\(415\) | −1.37667 | −0.0675779 | ||||||||
\(416\) | −32.3332 | −1.58527 | ||||||||
\(417\) | −12.2753 | −0.601124 | ||||||||
\(418\) | −37.3580 | −1.82724 | ||||||||
\(419\) | −0.0276870 | −0.00135260 | −0.000676299 | − | 1.00000i | \(-0.500215\pi\) | ||||
−0.000676299 | 1.00000i | \(0.500215\pi\) | ||||||||
\(420\) | −47.5961 | −2.32245 | ||||||||
\(421\) | 33.3026 | 1.62307 | 0.811534 | − | 0.584306i | \(-0.198633\pi\) | ||||
0.811534 | + | 0.584306i | \(0.198633\pi\) | |||||||
\(422\) | −57.1984 | −2.78438 | ||||||||
\(423\) | 2.04252 | 0.0993109 | ||||||||
\(424\) | −67.6328 | −3.28454 | ||||||||
\(425\) | 57.1317 | 2.77130 | ||||||||
\(426\) | −37.0682 | −1.79596 | ||||||||
\(427\) | −13.3753 | −0.647278 | ||||||||
\(428\) | 41.9959 | 2.02995 | ||||||||
\(429\) | −12.4627 | −0.601707 | ||||||||
\(430\) | −110.639 | −5.33549 | ||||||||
\(431\) | 11.7691 | 0.566898 | 0.283449 | − | 0.958987i | \(-0.408521\pi\) | ||||
0.283449 | + | 0.958987i | \(0.408521\pi\) | |||||||
\(432\) | 8.07170 | 0.388350 | ||||||||
\(433\) | −34.7155 | −1.66832 | −0.834159 | − | 0.551524i | \(-0.814047\pi\) | ||||
−0.834159 | + | 0.551524i | \(0.814047\pi\) | |||||||
\(434\) | −22.3662 | −1.07361 | ||||||||
\(435\) | −12.1353 | −0.581843 | ||||||||
\(436\) | 83.2431 | 3.98662 | ||||||||
\(437\) | 35.5311 | 1.69968 | ||||||||
\(438\) | 38.1283 | 1.82184 | ||||||||
\(439\) | 21.7387 | 1.03753 | 0.518765 | − | 0.854917i | \(-0.326392\pi\) | ||||
0.518765 | + | 0.854917i | \(0.326392\pi\) | |||||||
\(440\) | 72.6839 | 3.46507 | ||||||||
\(441\) | 0.225198 | 0.0107237 | ||||||||
\(442\) | −66.9120 | −3.18268 | ||||||||
\(443\) | 1.23837 | 0.0588367 | 0.0294183 | − | 0.999567i | \(-0.490634\pi\) | ||||
0.0294183 | + | 0.999567i | \(0.490634\pi\) | |||||||
\(444\) | 25.1743 | 1.19472 | ||||||||
\(445\) | −8.74873 | −0.414730 | ||||||||
\(446\) | −8.79752 | −0.416575 | ||||||||
\(447\) | −18.2342 | −0.862446 | ||||||||
\(448\) | −7.12167 | −0.336467 | ||||||||
\(449\) | −27.9237 | −1.31780 | −0.658901 | − | 0.752230i | \(-0.728978\pi\) | ||||
−0.658901 | + | 0.752230i | \(0.728978\pi\) | |||||||
\(450\) | −24.9961 | −1.17833 | ||||||||
\(451\) | −20.0984 | −0.946397 | ||||||||
\(452\) | −71.1474 | −3.34649 | ||||||||
\(453\) | 9.27800 | 0.435918 | ||||||||
\(454\) | −52.9979 | −2.48732 | ||||||||
\(455\) | −45.6342 | −2.13937 | ||||||||
\(456\) | 34.6943 | 1.62471 | ||||||||
\(457\) | 13.0679 | 0.611292 | 0.305646 | − | 0.952145i | \(-0.401128\pi\) | ||||
0.305646 | + | 0.952145i | \(0.401128\pi\) | |||||||
\(458\) | −47.3759 | −2.21373 | ||||||||
\(459\) | 5.87877 | 0.274397 | ||||||||
\(460\) | −121.991 | −5.68788 | ||||||||
\(461\) | 9.95387 | 0.463598 | 0.231799 | − | 0.972764i | \(-0.425539\pi\) | ||||
0.231799 | + | 0.972764i | \(0.425539\pi\) | |||||||
\(462\) | −19.4707 | −0.905861 | ||||||||
\(463\) | −11.0167 | −0.511989 | −0.255994 | − | 0.966678i | \(-0.582403\pi\) | ||||
−0.255994 | + | 0.966678i | \(0.582403\pi\) | |||||||
\(464\) | −25.5321 | −1.18530 | ||||||||
\(465\) | −12.4112 | −0.575557 | ||||||||
\(466\) | −11.4384 | −0.529873 | ||||||||
\(467\) | 6.45694 | 0.298791 | 0.149396 | − | 0.988777i | \(-0.452267\pi\) | ||||
0.149396 | + | 0.988777i | \(0.452267\pi\) | |||||||
\(468\) | 20.4246 | 0.944128 | ||||||||
\(469\) | 20.9303 | 0.966471 | ||||||||
\(470\) | −20.1547 | −0.929668 | ||||||||
\(471\) | 17.3396 | 0.798967 | ||||||||
\(472\) | 77.1458 | 3.55092 | ||||||||
\(473\) | −31.5774 | −1.45193 | ||||||||
\(474\) | −28.7695 | −1.32143 | ||||||||
\(475\) | −50.1207 | −2.29969 | ||||||||
\(476\) | −72.9337 | −3.34291 | ||||||||
\(477\) | 10.0537 | 0.460326 | ||||||||
\(478\) | −24.5846 | −1.12447 | ||||||||
\(479\) | 17.0126 | 0.777325 | 0.388663 | − | 0.921380i | \(-0.372937\pi\) | ||||
0.388663 | + | 0.921380i | \(0.372937\pi\) | |||||||
\(480\) | −28.0312 | −1.27944 | ||||||||
\(481\) | 24.1366 | 1.10054 | ||||||||
\(482\) | 24.0662 | 1.09618 | ||||||||
\(483\) | 18.5186 | 0.842625 | ||||||||
\(484\) | −14.1627 | −0.643760 | ||||||||
\(485\) | −54.0885 | −2.45603 | ||||||||
\(486\) | −2.57206 | −0.116671 | ||||||||
\(487\) | −26.4641 | −1.19920 | −0.599601 | − | 0.800299i | \(-0.704674\pi\) | ||||
−0.599601 | + | 0.800299i | \(0.704674\pi\) | |||||||
\(488\) | −33.4743 | −1.51531 | ||||||||
\(489\) | −0.588856 | −0.0266290 | ||||||||
\(490\) | −2.22215 | −0.100387 | ||||||||
\(491\) | 7.13267 | 0.321893 | 0.160946 | − | 0.986963i | \(-0.448545\pi\) | ||||
0.160946 | + | 0.986963i | \(0.448545\pi\) | |||||||
\(492\) | 32.9383 | 1.48497 | ||||||||
\(493\) | −18.5955 | −0.837498 | ||||||||
\(494\) | 58.7007 | 2.64107 | ||||||||
\(495\) | −10.8045 | −0.485628 | ||||||||
\(496\) | −26.1126 | −1.17249 | ||||||||
\(497\) | −38.7388 | −1.73767 | ||||||||
\(498\) | 0.922955 | 0.0413586 | ||||||||
\(499\) | −33.8760 | −1.51650 | −0.758249 | − | 0.651965i | \(-0.773945\pi\) | ||||
−0.758249 | + | 0.651965i | \(0.773945\pi\) | |||||||
\(500\) | 83.5475 | 3.73636 | ||||||||
\(501\) | −12.5907 | −0.562513 | ||||||||
\(502\) | −5.19407 | −0.231823 | ||||||||
\(503\) | 10.4035 | 0.463870 | 0.231935 | − | 0.972731i | \(-0.425494\pi\) | ||||
0.231935 | + | 0.972731i | \(0.425494\pi\) | |||||||
\(504\) | 18.0824 | 0.805456 | ||||||||
\(505\) | 19.9873 | 0.889424 | ||||||||
\(506\) | −49.9046 | −2.21853 | ||||||||
\(507\) | 6.58275 | 0.292350 | ||||||||
\(508\) | 89.9592 | 3.99129 | ||||||||
\(509\) | 43.7967 | 1.94125 | 0.970627 | − | 0.240590i | \(-0.0773408\pi\) | ||||
0.970627 | + | 0.240590i | \(0.0773408\pi\) | |||||||
\(510\) | −58.0091 | −2.56869 | ||||||||
\(511\) | 39.8467 | 1.76271 | ||||||||
\(512\) | 49.6231 | 2.19305 | ||||||||
\(513\) | −5.15734 | −0.227702 | ||||||||
\(514\) | 56.9799 | 2.51327 | ||||||||
\(515\) | 58.8400 | 2.59280 | ||||||||
\(516\) | 51.7506 | 2.27819 | ||||||||
\(517\) | −5.75233 | −0.252987 | ||||||||
\(518\) | 37.7090 | 1.65684 | ||||||||
\(519\) | −0.933654 | −0.0409828 | ||||||||
\(520\) | −114.208 | −5.00837 | ||||||||
\(521\) | 2.19046 | 0.0959657 | 0.0479828 | − | 0.998848i | \(-0.484721\pi\) | ||||
0.0479828 | + | 0.998848i | \(0.484721\pi\) | |||||||
\(522\) | 8.13583 | 0.356095 | ||||||||
\(523\) | −27.5000 | −1.20249 | −0.601246 | − | 0.799064i | \(-0.705329\pi\) | ||||
−0.601246 | + | 0.799064i | \(0.705329\pi\) | |||||||
\(524\) | −3.10064 | −0.135452 | ||||||||
\(525\) | −26.1226 | −1.14008 | ||||||||
\(526\) | −30.9884 | −1.35116 | ||||||||
\(527\) | −19.0183 | −0.828451 | ||||||||
\(528\) | −22.7322 | −0.989293 | ||||||||
\(529\) | 24.4642 | 1.06366 | ||||||||
\(530\) | −99.2053 | −4.30920 | ||||||||
\(531\) | −11.4678 | −0.497660 | ||||||||
\(532\) | 63.9834 | 2.77403 | ||||||||
\(533\) | 31.5807 | 1.36791 | ||||||||
\(534\) | 5.86539 | 0.253820 | ||||||||
\(535\) | 34.9075 | 1.50918 | ||||||||
\(536\) | 52.3821 | 2.26256 | ||||||||
\(537\) | 3.33908 | 0.144092 | ||||||||
\(538\) | −4.93285 | −0.212670 | ||||||||
\(539\) | −0.634221 | −0.0273178 | ||||||||
\(540\) | 17.7070 | 0.761990 | ||||||||
\(541\) | −39.5768 | −1.70154 | −0.850770 | − | 0.525538i | \(-0.823864\pi\) | ||||
−0.850770 | + | 0.525538i | \(0.823864\pi\) | |||||||
\(542\) | 50.9774 | 2.18967 | ||||||||
\(543\) | 20.6096 | 0.884442 | ||||||||
\(544\) | −42.9535 | −1.84162 | ||||||||
\(545\) | 69.1928 | 2.96389 | ||||||||
\(546\) | 30.5944 | 1.30932 | ||||||||
\(547\) | 6.59572 | 0.282013 | 0.141006 | − | 0.990009i | \(-0.454966\pi\) | ||||
0.141006 | + | 0.990009i | \(0.454966\pi\) | |||||||
\(548\) | −82.1163 | −3.50784 | ||||||||
\(549\) | 4.97599 | 0.212370 | ||||||||
\(550\) | 70.3961 | 3.00170 | ||||||||
\(551\) | 16.3135 | 0.694977 | ||||||||
\(552\) | 46.3463 | 1.97263 | ||||||||
\(553\) | −30.0661 | −1.27854 | ||||||||
\(554\) | −32.2877 | −1.37177 | ||||||||
\(555\) | 20.9252 | 0.888223 | ||||||||
\(556\) | −56.6564 | −2.40277 | ||||||||
\(557\) | 29.9669 | 1.26974 | 0.634869 | − | 0.772619i | \(-0.281054\pi\) | ||||
0.634869 | + | 0.772619i | \(0.281054\pi\) | |||||||
\(558\) | 8.32083 | 0.352249 | ||||||||
\(559\) | 49.6176 | 2.09860 | ||||||||
\(560\) | −83.2375 | −3.51743 | ||||||||
\(561\) | −16.5563 | −0.699007 | ||||||||
\(562\) | −16.3139 | −0.688159 | ||||||||
\(563\) | −42.2715 | −1.78153 | −0.890765 | − | 0.454465i | \(-0.849831\pi\) | ||||
−0.890765 | + | 0.454465i | \(0.849831\pi\) | |||||||
\(564\) | 9.42723 | 0.396958 | ||||||||
\(565\) | −59.1386 | −2.48798 | ||||||||
\(566\) | −5.29426 | −0.222534 | ||||||||
\(567\) | −2.68797 | −0.112884 | ||||||||
\(568\) | −96.9512 | −4.06798 | ||||||||
\(569\) | 0.826136 | 0.0346334 | 0.0173167 | − | 0.999850i | \(-0.494488\pi\) | ||||
0.0173167 | + | 0.999850i | \(0.494488\pi\) | |||||||
\(570\) | 50.8903 | 2.13156 | ||||||||
\(571\) | 13.1838 | 0.551726 | 0.275863 | − | 0.961197i | \(-0.411036\pi\) | ||||
0.275863 | + | 0.961197i | \(0.411036\pi\) | |||||||
\(572\) | −57.5216 | −2.40510 | ||||||||
\(573\) | −4.86708 | −0.203325 | ||||||||
\(574\) | 49.3390 | 2.05937 | ||||||||
\(575\) | −66.9536 | −2.79216 | ||||||||
\(576\) | 2.64946 | 0.110394 | ||||||||
\(577\) | 16.1784 | 0.673516 | 0.336758 | − | 0.941591i | \(-0.390670\pi\) | ||||
0.336758 | + | 0.941591i | \(0.390670\pi\) | |||||||
\(578\) | −45.1651 | −1.87862 | ||||||||
\(579\) | 18.1019 | 0.752290 | ||||||||
\(580\) | −56.0102 | −2.32570 | ||||||||
\(581\) | 0.964550 | 0.0400163 | ||||||||
\(582\) | 36.2624 | 1.50312 | ||||||||
\(583\) | −28.3140 | −1.17265 | ||||||||
\(584\) | 99.7240 | 4.12661 | ||||||||
\(585\) | 16.9772 | 0.701921 | ||||||||
\(586\) | 66.6493 | 2.75326 | ||||||||
\(587\) | 32.6181 | 1.34629 | 0.673146 | − | 0.739510i | \(-0.264943\pi\) | ||||
0.673146 | + | 0.739510i | \(0.264943\pi\) | |||||||
\(588\) | 1.03940 | 0.0428639 | ||||||||
\(589\) | 16.6844 | 0.687470 | ||||||||
\(590\) | 113.159 | 4.65869 | ||||||||
\(591\) | 8.14430 | 0.335012 | ||||||||
\(592\) | 44.0255 | 1.80944 | ||||||||
\(593\) | −6.49879 | −0.266873 | −0.133437 | − | 0.991057i | \(-0.542601\pi\) | ||||
−0.133437 | + | 0.991057i | \(0.542601\pi\) | |||||||
\(594\) | 7.24365 | 0.297211 | ||||||||
\(595\) | −60.6234 | −2.48532 | ||||||||
\(596\) | −84.1594 | −3.44730 | ||||||||
\(597\) | 23.2617 | 0.952038 | ||||||||
\(598\) | 78.4152 | 3.20664 | ||||||||
\(599\) | −20.2303 | −0.826587 | −0.413293 | − | 0.910598i | \(-0.635622\pi\) | ||||
−0.413293 | + | 0.910598i | \(0.635622\pi\) | |||||||
\(600\) | −65.3768 | −2.66900 | ||||||||
\(601\) | 45.6710 | 1.86296 | 0.931479 | − | 0.363796i | \(-0.118520\pi\) | ||||
0.931479 | + | 0.363796i | \(0.118520\pi\) | |||||||
\(602\) | 77.5183 | 3.15941 | ||||||||
\(603\) | −7.78664 | −0.317097 | ||||||||
\(604\) | 42.8224 | 1.74242 | ||||||||
\(605\) | −11.7722 | −0.478609 | ||||||||
\(606\) | −13.4000 | −0.544340 | ||||||||
\(607\) | −25.2483 | −1.02480 | −0.512399 | − | 0.858747i | \(-0.671243\pi\) | ||||
−0.512399 | + | 0.858747i | \(0.671243\pi\) | |||||||
\(608\) | 37.6823 | 1.52822 | ||||||||
\(609\) | 8.50248 | 0.344538 | ||||||||
\(610\) | −49.1009 | −1.98804 | ||||||||
\(611\) | 9.03866 | 0.365665 | ||||||||
\(612\) | 27.1333 | 1.09680 | ||||||||
\(613\) | −43.2229 | −1.74576 | −0.872878 | − | 0.487939i | \(-0.837749\pi\) | ||||
−0.872878 | + | 0.487939i | \(0.837749\pi\) | |||||||
\(614\) | −50.3854 | −2.03339 | ||||||||
\(615\) | 27.3787 | 1.10402 | ||||||||
\(616\) | −50.9254 | −2.05184 | ||||||||
\(617\) | −0.423375 | −0.0170444 | −0.00852222 | − | 0.999964i | \(-0.502713\pi\) | ||||
−0.00852222 | + | 0.999964i | \(0.502713\pi\) | |||||||
\(618\) | −39.4480 | −1.58683 | ||||||||
\(619\) | −34.3392 | −1.38021 | −0.690104 | − | 0.723710i | \(-0.742435\pi\) | ||||
−0.690104 | + | 0.723710i | \(0.742435\pi\) | |||||||
\(620\) | −57.2838 | −2.30057 | ||||||||
\(621\) | −6.88942 | −0.276463 | ||||||||
\(622\) | 75.2288 | 3.01640 | ||||||||
\(623\) | 6.12972 | 0.245582 | ||||||||
\(624\) | 35.7192 | 1.42991 | ||||||||
\(625\) | 20.8541 | 0.834166 | ||||||||
\(626\) | 14.5795 | 0.582713 | ||||||||
\(627\) | 14.5245 | 0.580054 | ||||||||
\(628\) | 80.0307 | 3.19357 | ||||||||
\(629\) | 32.0646 | 1.27850 | ||||||||
\(630\) | 26.5237 | 1.05673 | ||||||||
\(631\) | −18.8473 | −0.750298 | −0.375149 | − | 0.926965i | \(-0.622408\pi\) | ||||
−0.375149 | + | 0.926965i | \(0.622408\pi\) | |||||||
\(632\) | −75.2461 | −2.99313 | ||||||||
\(633\) | 22.2384 | 0.883897 | ||||||||
\(634\) | −33.9838 | −1.34967 | ||||||||
\(635\) | 74.7752 | 2.96736 | ||||||||
\(636\) | 46.4026 | 1.83998 | ||||||||
\(637\) | 0.996553 | 0.0394849 | ||||||||
\(638\) | −22.9128 | −0.907127 | ||||||||
\(639\) | 14.4119 | 0.570126 | ||||||||
\(640\) | 29.9187 | 1.18264 | ||||||||
\(641\) | −4.87013 | −0.192358 | −0.0961792 | − | 0.995364i | \(-0.530662\pi\) | ||||
−0.0961792 | + | 0.995364i | \(0.530662\pi\) | |||||||
\(642\) | −23.4030 | −0.923641 | ||||||||
\(643\) | 3.32173 | 0.130996 | 0.0654980 | − | 0.997853i | \(-0.479136\pi\) | ||||
0.0654980 | + | 0.997853i | \(0.479136\pi\) | |||||||
\(644\) | 85.4722 | 3.36808 | ||||||||
\(645\) | 43.0158 | 1.69374 | ||||||||
\(646\) | 77.9817 | 3.06815 | ||||||||
\(647\) | −37.0096 | −1.45500 | −0.727499 | − | 0.686109i | \(-0.759317\pi\) | ||||
−0.727499 | + | 0.686109i | \(0.759317\pi\) | |||||||
\(648\) | −6.72717 | −0.264268 | ||||||||
\(649\) | 32.2966 | 1.26775 | ||||||||
\(650\) | −110.614 | −4.33862 | ||||||||
\(651\) | 8.69582 | 0.340816 | ||||||||
\(652\) | −2.71786 | −0.106439 | ||||||||
\(653\) | 35.9507 | 1.40686 | 0.703429 | − | 0.710766i | \(-0.251651\pi\) | ||||
0.703429 | + | 0.710766i | \(0.251651\pi\) | |||||||
\(654\) | −46.3887 | −1.81394 | ||||||||
\(655\) | −2.57729 | −0.100703 | ||||||||
\(656\) | 57.6036 | 2.24904 | ||||||||
\(657\) | −14.8241 | −0.578342 | ||||||||
\(658\) | 14.1212 | 0.550503 | ||||||||
\(659\) | −31.0617 | −1.20999 | −0.604997 | − | 0.796228i | \(-0.706826\pi\) | ||||
−0.604997 | + | 0.796228i | \(0.706826\pi\) | |||||||
\(660\) | −49.8681 | −1.94111 | ||||||||
\(661\) | 36.3795 | 1.41500 | 0.707500 | − | 0.706714i | \(-0.249823\pi\) | ||||
0.707500 | + | 0.706714i | \(0.249823\pi\) | |||||||
\(662\) | −22.8454 | −0.887912 | ||||||||
\(663\) | 26.0150 | 1.01034 | ||||||||
\(664\) | 2.41397 | 0.0936803 | ||||||||
\(665\) | 53.1838 | 2.06238 | ||||||||
\(666\) | −14.0288 | −0.543605 | ||||||||
\(667\) | 21.7923 | 0.843803 | ||||||||
\(668\) | −58.1123 | −2.24843 | ||||||||
\(669\) | 3.42042 | 0.132241 | ||||||||
\(670\) | 76.8352 | 2.96840 | ||||||||
\(671\) | −14.0138 | −0.540998 | ||||||||
\(672\) | 19.6398 | 0.757622 | ||||||||
\(673\) | −32.9850 | −1.27148 | −0.635739 | − | 0.771904i | \(-0.719305\pi\) | ||||
−0.635739 | + | 0.771904i | \(0.719305\pi\) | |||||||
\(674\) | −44.5210 | −1.71488 | ||||||||
\(675\) | 9.71832 | 0.374058 | ||||||||
\(676\) | 30.3826 | 1.16856 | ||||||||
\(677\) | −48.7074 | −1.87198 | −0.935989 | − | 0.352028i | \(-0.885492\pi\) | ||||
−0.935989 | + | 0.352028i | \(0.885492\pi\) | |||||||
\(678\) | 39.6482 | 1.52268 | ||||||||
\(679\) | 37.8966 | 1.45434 | ||||||||
\(680\) | −151.722 | −5.81826 | ||||||||
\(681\) | 20.6053 | 0.789595 | ||||||||
\(682\) | −23.4338 | −0.897328 | ||||||||
\(683\) | 18.0998 | 0.692570 | 0.346285 | − | 0.938129i | \(-0.387443\pi\) | ||||
0.346285 | + | 0.938129i | \(0.387443\pi\) | |||||||
\(684\) | −23.8036 | −0.910153 | ||||||||
\(685\) | −68.2561 | −2.60793 | ||||||||
\(686\) | −46.8384 | −1.78830 | ||||||||
\(687\) | 18.4194 | 0.702746 | ||||||||
\(688\) | 90.5032 | 3.45040 | ||||||||
\(689\) | 44.4899 | 1.69493 | ||||||||
\(690\) | 67.9818 | 2.58802 | ||||||||
\(691\) | 42.0561 | 1.59989 | 0.799945 | − | 0.600073i | \(-0.204862\pi\) | ||||
0.799945 | + | 0.600073i | \(0.204862\pi\) | |||||||
\(692\) | −4.30926 | −0.163813 | ||||||||
\(693\) | 7.57010 | 0.287564 | ||||||||
\(694\) | −41.3981 | −1.57145 | ||||||||
\(695\) | −47.0935 | −1.78636 | ||||||||
\(696\) | 21.2791 | 0.806582 | ||||||||
\(697\) | 41.9537 | 1.58911 | ||||||||
\(698\) | −42.7867 | −1.61950 | ||||||||
\(699\) | 4.44717 | 0.168208 | ||||||||
\(700\) | −120.568 | −4.55705 | ||||||||
\(701\) | 24.4343 | 0.922869 | 0.461435 | − | 0.887174i | \(-0.347335\pi\) | ||||
0.461435 | + | 0.887174i | \(0.347335\pi\) | |||||||
\(702\) | −11.3820 | −0.429585 | ||||||||
\(703\) | −28.1297 | −1.06093 | ||||||||
\(704\) | −7.46163 | −0.281221 | ||||||||
\(705\) | 7.83603 | 0.295122 | ||||||||
\(706\) | 44.8683 | 1.68864 | ||||||||
\(707\) | −14.0039 | −0.526673 | ||||||||
\(708\) | −52.9294 | −1.98921 | ||||||||
\(709\) | −28.4948 | −1.07014 | −0.535072 | − | 0.844806i | \(-0.679716\pi\) | ||||
−0.535072 | + | 0.844806i | \(0.679716\pi\) | |||||||
\(710\) | −142.210 | −5.33705 | ||||||||
\(711\) | 11.1854 | 0.419485 | ||||||||
\(712\) | 15.3408 | 0.574921 | ||||||||
\(713\) | 22.2879 | 0.834687 | ||||||||
\(714\) | 40.6436 | 1.52105 | ||||||||
\(715\) | −47.8127 | −1.78809 | ||||||||
\(716\) | 15.4114 | 0.575953 | ||||||||
\(717\) | 9.55835 | 0.356963 | ||||||||
\(718\) | 13.3493 | 0.498191 | ||||||||
\(719\) | 41.6482 | 1.55322 | 0.776608 | − | 0.629984i | \(-0.216939\pi\) | ||||
0.776608 | + | 0.629984i | \(0.216939\pi\) | |||||||
\(720\) | 30.9666 | 1.15406 | ||||||||
\(721\) | −41.2258 | −1.53533 | ||||||||
\(722\) | −19.5428 | −0.727309 | ||||||||
\(723\) | −9.35677 | −0.347982 | ||||||||
\(724\) | 95.1232 | 3.53523 | ||||||||
\(725\) | −30.7406 | −1.14168 | ||||||||
\(726\) | 7.89242 | 0.292915 | ||||||||
\(727\) | 4.25729 | 0.157894 | 0.0789470 | − | 0.996879i | \(-0.474844\pi\) | ||||
0.0789470 | + | 0.996879i | \(0.474844\pi\) | |||||||
\(728\) | 80.0192 | 2.96571 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 146.277 | 5.41397 | ||||||||
\(731\) | 65.9151 | 2.43796 | ||||||||
\(732\) | 22.9666 | 0.848870 | ||||||||
\(733\) | −37.7594 | −1.39468 | −0.697338 | − | 0.716743i | \(-0.745632\pi\) | ||||
−0.697338 | + | 0.716743i | \(0.745632\pi\) | |||||||
\(734\) | −54.7752 | −2.02179 | ||||||||
\(735\) | 0.863958 | 0.0318676 | ||||||||
\(736\) | 50.3379 | 1.85548 | ||||||||
\(737\) | 21.9294 | 0.807781 | ||||||||
\(738\) | −18.3555 | −0.675674 | ||||||||
\(739\) | 4.98373 | 0.183330 | 0.0916648 | − | 0.995790i | \(-0.470781\pi\) | ||||
0.0916648 | + | 0.995790i | \(0.470781\pi\) | |||||||
\(740\) | 96.5797 | 3.55034 | ||||||||
\(741\) | −22.8225 | −0.838404 | ||||||||
\(742\) | 69.5073 | 2.55169 | ||||||||
\(743\) | −15.6328 | −0.573511 | −0.286755 | − | 0.958004i | \(-0.592577\pi\) | ||||
−0.286755 | + | 0.958004i | \(0.592577\pi\) | |||||||
\(744\) | 21.7630 | 0.797869 | ||||||||
\(745\) | −69.9544 | −2.56293 | ||||||||
\(746\) | 46.3151 | 1.69572 | ||||||||
\(747\) | −0.358839 | −0.0131292 | ||||||||
\(748\) | −76.4153 | −2.79402 | ||||||||
\(749\) | −24.4577 | −0.893663 | ||||||||
\(750\) | −46.5583 | −1.70007 | ||||||||
\(751\) | −10.1825 | −0.371564 | −0.185782 | − | 0.982591i | \(-0.559482\pi\) | ||||
−0.185782 | + | 0.982591i | \(0.559482\pi\) | |||||||
\(752\) | 16.4866 | 0.601206 | ||||||||
\(753\) | 2.01942 | 0.0735918 | ||||||||
\(754\) | 36.0030 | 1.31115 | ||||||||
\(755\) | 35.5945 | 1.29542 | ||||||||
\(756\) | −12.4063 | −0.451212 | ||||||||
\(757\) | 25.1100 | 0.912637 | 0.456318 | − | 0.889817i | \(-0.349168\pi\) | ||||
0.456318 | + | 0.889817i | \(0.349168\pi\) | |||||||
\(758\) | 28.1490 | 1.02242 | ||||||||
\(759\) | 19.4026 | 0.704270 | ||||||||
\(760\) | 133.103 | 4.82814 | ||||||||
\(761\) | −20.1061 | −0.728845 | −0.364423 | − | 0.931234i | \(-0.618734\pi\) | ||||
−0.364423 | + | 0.931234i | \(0.618734\pi\) | |||||||
\(762\) | −50.1313 | −1.81607 | ||||||||
\(763\) | −48.4793 | −1.75507 | ||||||||
\(764\) | −22.4639 | −0.812715 | ||||||||
\(765\) | 22.5536 | 0.815426 | ||||||||
\(766\) | 12.1815 | 0.440137 | ||||||||
\(767\) | −50.7477 | −1.83239 | ||||||||
\(768\) | −25.3572 | −0.914999 | ||||||||
\(769\) | 34.6635 | 1.25000 | 0.624999 | − | 0.780625i | \(-0.285099\pi\) | ||||
0.624999 | + | 0.780625i | \(0.285099\pi\) | |||||||
\(770\) | −74.6985 | −2.69195 | ||||||||
\(771\) | −22.1534 | −0.797836 | ||||||||
\(772\) | 83.5491 | 3.00700 | ||||||||
\(773\) | 1.83788 | 0.0661041 | 0.0330520 | − | 0.999454i | \(-0.489477\pi\) | ||||
0.0330520 | + | 0.999454i | \(0.489477\pi\) | |||||||
\(774\) | −28.8390 | −1.03659 | ||||||||
\(775\) | −31.4396 | −1.12934 | ||||||||
\(776\) | 94.8436 | 3.40469 | ||||||||
\(777\) | −14.6610 | −0.525961 | ||||||||
\(778\) | 6.07718 | 0.217877 | ||||||||
\(779\) | −36.8053 | −1.31869 | ||||||||
\(780\) | 78.3579 | 2.80566 | ||||||||
\(781\) | −40.5880 | −1.45235 | ||||||||
\(782\) | 104.172 | 3.72517 | ||||||||
\(783\) | −3.16316 | −0.113042 | ||||||||
\(784\) | 1.81773 | 0.0649188 | ||||||||
\(785\) | 66.5225 | 2.37429 | ||||||||
\(786\) | 1.72789 | 0.0616317 | ||||||||
\(787\) | 12.9160 | 0.460406 | 0.230203 | − | 0.973143i | \(-0.426061\pi\) | ||||
0.230203 | + | 0.973143i | \(0.426061\pi\) | |||||||
\(788\) | 37.5899 | 1.33908 | ||||||||
\(789\) | 12.0481 | 0.428923 | ||||||||
\(790\) | −110.373 | −3.92688 | ||||||||
\(791\) | 41.4350 | 1.47326 | ||||||||
\(792\) | 18.9456 | 0.673204 | ||||||||
\(793\) | 22.0200 | 0.781952 | ||||||||
\(794\) | −16.0450 | −0.569414 | ||||||||
\(795\) | 38.5704 | 1.36795 | ||||||||
\(796\) | 107.364 | 3.80541 | ||||||||
\(797\) | −16.1326 | −0.571446 | −0.285723 | − | 0.958312i | \(-0.592234\pi\) | ||||
−0.285723 | + | 0.958312i | \(0.592234\pi\) | |||||||
\(798\) | −35.6559 | −1.26220 | ||||||||
\(799\) | 12.0075 | 0.424796 | ||||||||
\(800\) | −71.0074 | −2.51049 | ||||||||
\(801\) | −2.28043 | −0.0805749 | ||||||||
\(802\) | 47.2604 | 1.66882 | ||||||||
\(803\) | 41.7488 | 1.47328 | ||||||||
\(804\) | −35.9391 | −1.26747 | ||||||||
\(805\) | 71.0456 | 2.50403 | ||||||||
\(806\) | 36.8217 | 1.29699 | ||||||||
\(807\) | 1.91786 | 0.0675119 | ||||||||
\(808\) | −35.0476 | −1.23297 | ||||||||
\(809\) | 16.8840 | 0.593610 | 0.296805 | − | 0.954938i | \(-0.404079\pi\) | ||||
0.296805 | + | 0.954938i | \(0.404079\pi\) | |||||||
\(810\) | −9.86756 | −0.346711 | ||||||||
\(811\) | −1.58705 | −0.0557289 | −0.0278645 | − | 0.999612i | \(-0.508871\pi\) | ||||
−0.0278645 | + | 0.999612i | \(0.508871\pi\) | |||||||
\(812\) | 39.2431 | 1.37716 | ||||||||
\(813\) | −19.8197 | −0.695107 | ||||||||
\(814\) | 39.5091 | 1.38479 | ||||||||
\(815\) | −2.25912 | −0.0791334 | ||||||||
\(816\) | 47.4517 | 1.66114 | ||||||||
\(817\) | −57.8262 | −2.02308 | ||||||||
\(818\) | −84.9917 | −2.97167 | ||||||||
\(819\) | −11.8949 | −0.415642 | ||||||||
\(820\) | 126.366 | 4.41290 | ||||||||
\(821\) | −17.5015 | −0.610807 | −0.305403 | − | 0.952223i | \(-0.598791\pi\) | ||||
−0.305403 | + | 0.952223i | \(0.598791\pi\) | |||||||
\(822\) | 45.7608 | 1.59609 | ||||||||
\(823\) | 8.53337 | 0.297455 | 0.148727 | − | 0.988878i | \(-0.452482\pi\) | ||||
0.148727 | + | 0.988878i | \(0.452482\pi\) | |||||||
\(824\) | −103.175 | −3.59428 | ||||||||
\(825\) | −27.3696 | −0.952887 | ||||||||
\(826\) | −79.2840 | −2.75864 | ||||||||
\(827\) | −36.2648 | −1.26105 | −0.630526 | − | 0.776168i | \(-0.717161\pi\) | ||||
−0.630526 | + | 0.776168i | \(0.717161\pi\) | |||||||
\(828\) | −31.7980 | −1.10506 | ||||||||
\(829\) | 17.6559 | 0.613216 | 0.306608 | − | 0.951836i | \(-0.400806\pi\) | ||||
0.306608 | + | 0.951836i | \(0.400806\pi\) | |||||||
\(830\) | 3.54087 | 0.122905 | ||||||||
\(831\) | 12.5533 | 0.435468 | ||||||||
\(832\) | 11.7245 | 0.406473 | ||||||||
\(833\) | 1.32388 | 0.0458699 | ||||||||
\(834\) | 31.5728 | 1.09328 | ||||||||
\(835\) | −48.3037 | −1.67162 | ||||||||
\(836\) | 67.0378 | 2.31855 | ||||||||
\(837\) | −3.23509 | −0.111821 | ||||||||
\(838\) | 0.0712125 | 0.00246000 | ||||||||
\(839\) | −11.5870 | −0.400027 | −0.200013 | − | 0.979793i | \(-0.564099\pi\) | ||||
−0.200013 | + | 0.979793i | \(0.564099\pi\) | |||||||
\(840\) | 69.3723 | 2.39357 | ||||||||
\(841\) | −18.9944 | −0.654980 | ||||||||
\(842\) | −85.6561 | −2.95190 | ||||||||
\(843\) | 6.34273 | 0.218455 | ||||||||
\(844\) | 102.641 | 3.53304 | ||||||||
\(845\) | 25.2544 | 0.868777 | ||||||||
\(846\) | −5.25349 | −0.180619 | ||||||||
\(847\) | 8.24811 | 0.283408 | ||||||||
\(848\) | 81.1503 | 2.78671 | ||||||||
\(849\) | 2.05838 | 0.0706433 | ||||||||
\(850\) | −146.946 | −5.04021 | ||||||||
\(851\) | −37.5770 | −1.28812 | ||||||||
\(852\) | 66.5178 | 2.27886 | ||||||||
\(853\) | 0.449358 | 0.0153857 | 0.00769286 | − | 0.999970i | \(-0.497551\pi\) | ||||
0.00769286 | + | 0.999970i | \(0.497551\pi\) | |||||||
\(854\) | 34.4021 | 1.17722 | ||||||||
\(855\) | −19.7858 | −0.676662 | ||||||||
\(856\) | −61.2100 | −2.09211 | ||||||||
\(857\) | −56.5401 | −1.93137 | −0.965687 | − | 0.259710i | \(-0.916373\pi\) | ||||
−0.965687 | + | 0.259710i | \(0.916373\pi\) | |||||||
\(858\) | 32.0549 | 1.09434 | ||||||||
\(859\) | 29.4197 | 1.00379 | 0.501893 | − | 0.864929i | \(-0.332637\pi\) | ||||
0.501893 | + | 0.864929i | \(0.332637\pi\) | |||||||
\(860\) | 198.539 | 6.77011 | ||||||||
\(861\) | −19.1827 | −0.653744 | ||||||||
\(862\) | −30.2708 | −1.03103 | ||||||||
\(863\) | 45.7070 | 1.55588 | 0.777942 | − | 0.628336i | \(-0.216264\pi\) | ||||
0.777942 | + | 0.628336i | \(0.216264\pi\) | |||||||
\(864\) | −7.30655 | −0.248574 | ||||||||
\(865\) | −3.58191 | −0.121789 | ||||||||
\(866\) | 89.2902 | 3.03420 | ||||||||
\(867\) | 17.5599 | 0.596366 | ||||||||
\(868\) | 40.1354 | 1.36228 | ||||||||
\(869\) | −31.5013 | −1.06861 | ||||||||
\(870\) | 31.2127 | 1.05821 | ||||||||
\(871\) | −34.4578 | −1.16756 | ||||||||
\(872\) | −121.329 | −4.10871 | ||||||||
\(873\) | −14.0986 | −0.477165 | ||||||||
\(874\) | −91.3880 | −3.09125 | ||||||||
\(875\) | −48.6566 | −1.64489 | ||||||||
\(876\) | −68.4202 | −2.31170 | ||||||||
\(877\) | 21.2195 | 0.716531 | 0.358266 | − | 0.933620i | \(-0.383368\pi\) | ||||
0.358266 | + | 0.933620i | \(0.383368\pi\) | |||||||
\(878\) | −55.9131 | −1.88698 | ||||||||
\(879\) | −25.9128 | −0.874018 | ||||||||
\(880\) | −87.2110 | −2.93988 | ||||||||
\(881\) | 35.1817 | 1.18530 | 0.592651 | − | 0.805460i | \(-0.298082\pi\) | ||||
0.592651 | + | 0.805460i | \(0.298082\pi\) | |||||||
\(882\) | −0.579221 | −0.0195034 | ||||||||
\(883\) | −32.8862 | −1.10671 | −0.553355 | − | 0.832946i | \(-0.686653\pi\) | ||||
−0.553355 | + | 0.832946i | \(0.686653\pi\) | |||||||
\(884\) | 120.072 | 4.03844 | ||||||||
\(885\) | −43.9956 | −1.47890 | ||||||||
\(886\) | −3.18516 | −0.107007 | ||||||||
\(887\) | 13.8102 | 0.463702 | 0.231851 | − | 0.972751i | \(-0.425522\pi\) | ||||
0.231851 | + | 0.972751i | \(0.425522\pi\) | |||||||
\(888\) | −36.6920 | −1.23130 | ||||||||
\(889\) | −52.3906 | −1.75712 | ||||||||
\(890\) | 22.5022 | 0.754277 | ||||||||
\(891\) | −2.81629 | −0.0943492 | ||||||||
\(892\) | 15.7869 | 0.528584 | ||||||||
\(893\) | −10.5340 | −0.352506 | ||||||||
\(894\) | 46.8993 | 1.56855 | ||||||||
\(895\) | 12.8102 | 0.428197 | ||||||||
\(896\) | −20.9623 | −0.700300 | ||||||||
\(897\) | −30.4874 | −1.01794 | ||||||||
\(898\) | 71.8214 | 2.39671 | ||||||||
\(899\) | 10.2331 | 0.341293 | ||||||||
\(900\) | 44.8547 | 1.49516 | ||||||||
\(901\) | 59.1032 | 1.96901 | ||||||||
\(902\) | 51.6942 | 1.72123 | ||||||||
\(903\) | −30.1386 | −1.00295 | ||||||||
\(904\) | 103.699 | 3.44898 | ||||||||
\(905\) | 79.0676 | 2.62830 | ||||||||
\(906\) | −23.8636 | −0.792813 | ||||||||
\(907\) | −18.6535 | −0.619379 | −0.309690 | − | 0.950838i | \(-0.600225\pi\) | ||||
−0.309690 | + | 0.950838i | \(0.600225\pi\) | |||||||
\(908\) | 95.1032 | 3.15611 | ||||||||
\(909\) | 5.20985 | 0.172800 | ||||||||
\(910\) | 117.374 | 3.89091 | ||||||||
\(911\) | 14.6054 | 0.483899 | 0.241949 | − | 0.970289i | \(-0.422213\pi\) | ||||
0.241949 | + | 0.970289i | \(0.422213\pi\) | |||||||
\(912\) | −41.6285 | −1.37846 | ||||||||
\(913\) | 1.01059 | 0.0334458 | ||||||||
\(914\) | −33.6115 | −1.11177 | ||||||||
\(915\) | 19.0901 | 0.631100 | ||||||||
\(916\) | 85.0146 | 2.80896 | ||||||||
\(917\) | 1.80576 | 0.0596314 | ||||||||
\(918\) | −15.1205 | −0.499052 | ||||||||
\(919\) | −31.4267 | −1.03667 | −0.518335 | − | 0.855177i | \(-0.673448\pi\) | ||||
−0.518335 | + | 0.855177i | \(0.673448\pi\) | |||||||
\(920\) | 177.805 | 5.86206 | ||||||||
\(921\) | 19.5895 | 0.645497 | ||||||||
\(922\) | −25.6019 | −0.843155 | ||||||||
\(923\) | 63.7761 | 2.09922 | ||||||||
\(924\) | 34.9397 | 1.14943 | ||||||||
\(925\) | 53.0067 | 1.74285 | ||||||||
\(926\) | 28.3356 | 0.931164 | ||||||||
\(927\) | 15.3371 | 0.503737 | ||||||||
\(928\) | 23.1118 | 0.758681 | ||||||||
\(929\) | 43.4149 | 1.42440 | 0.712198 | − | 0.701979i | \(-0.247700\pi\) | ||||
0.712198 | + | 0.701979i | \(0.247700\pi\) | |||||||
\(930\) | 31.9224 | 1.04678 | ||||||||
\(931\) | −1.16142 | −0.0380640 | ||||||||
\(932\) | 20.5258 | 0.672346 | ||||||||
\(933\) | −29.2485 | −0.957553 | ||||||||
\(934\) | −16.6076 | −0.543418 | ||||||||
\(935\) | −63.5174 | −2.07724 | ||||||||
\(936\) | −29.7693 | −0.973041 | ||||||||
\(937\) | 35.8374 | 1.17076 | 0.585378 | − | 0.810760i | \(-0.300946\pi\) | ||||
0.585378 | + | 0.810760i | \(0.300946\pi\) | |||||||
\(938\) | −53.8339 | −1.75774 | ||||||||
\(939\) | −5.66840 | −0.184981 | ||||||||
\(940\) | 36.1671 | 1.17964 | ||||||||
\(941\) | 46.1799 | 1.50542 | 0.752710 | − | 0.658352i | \(-0.228746\pi\) | ||||
0.752710 | + | 0.658352i | \(0.228746\pi\) | |||||||
\(942\) | −44.5985 | −1.45310 | ||||||||
\(943\) | −49.1663 | −1.60107 | ||||||||
\(944\) | −92.5646 | −3.01272 | ||||||||
\(945\) | −10.3123 | −0.335458 | ||||||||
\(946\) | 81.2188 | 2.64065 | ||||||||
\(947\) | 17.1774 | 0.558190 | 0.279095 | − | 0.960263i | \(-0.409966\pi\) | ||||
0.279095 | + | 0.960263i | \(0.409966\pi\) | |||||||
\(948\) | 51.6260 | 1.67673 | ||||||||
\(949\) | −65.6000 | −2.12947 | ||||||||
\(950\) | 128.913 | 4.18250 | ||||||||
\(951\) | 13.2127 | 0.428451 | ||||||||
\(952\) | 106.302 | 3.44528 | ||||||||
\(953\) | −55.1301 | −1.78584 | −0.892920 | − | 0.450215i | \(-0.851347\pi\) | ||||
−0.892920 | + | 0.450215i | \(0.851347\pi\) | |||||||
\(954\) | −25.8586 | −0.837204 | ||||||||
\(955\) | −18.6723 | −0.604221 | ||||||||
\(956\) | 44.1164 | 1.42683 | ||||||||
\(957\) | 8.90836 | 0.287967 | ||||||||
\(958\) | −43.7574 | −1.41374 | ||||||||
\(959\) | 47.8231 | 1.54429 | ||||||||
\(960\) | 10.1645 | 0.328058 | ||||||||
\(961\) | −20.5342 | −0.662394 | ||||||||
\(962\) | −62.0808 | −2.00156 | ||||||||
\(963\) | 9.09892 | 0.293209 | ||||||||
\(964\) | −43.1860 | −1.39093 | ||||||||
\(965\) | 69.4471 | 2.23558 | ||||||||
\(966\) | −47.6309 | −1.53250 | ||||||||
\(967\) | 40.8535 | 1.31376 | 0.656881 | − | 0.753995i | \(-0.271876\pi\) | ||||
0.656881 | + | 0.753995i | \(0.271876\pi\) | |||||||
\(968\) | 20.6425 | 0.663475 | ||||||||
\(969\) | −30.3188 | −0.973980 | ||||||||
\(970\) | 139.119 | 4.46683 | ||||||||
\(971\) | −11.2321 | −0.360456 | −0.180228 | − | 0.983625i | \(-0.557684\pi\) | ||||
−0.180228 | + | 0.983625i | \(0.557684\pi\) | |||||||
\(972\) | 4.61548 | 0.148042 | ||||||||
\(973\) | 32.9957 | 1.05779 | ||||||||
\(974\) | 68.0672 | 2.18101 | ||||||||
\(975\) | 43.0059 | 1.37729 | ||||||||
\(976\) | 40.1647 | 1.28564 | ||||||||
\(977\) | −39.5761 | −1.26615 | −0.633076 | − | 0.774090i | \(-0.718208\pi\) | ||||
−0.633076 | + | 0.774090i | \(0.718208\pi\) | |||||||
\(978\) | 1.51457 | 0.0484307 | ||||||||
\(979\) | 6.42234 | 0.205259 | ||||||||
\(980\) | 3.98758 | 0.127379 | ||||||||
\(981\) | 18.0356 | 0.575834 | ||||||||
\(982\) | −18.3456 | −0.585433 | ||||||||
\(983\) | −51.6348 | −1.64690 | −0.823448 | − | 0.567392i | \(-0.807953\pi\) | ||||
−0.823448 | + | 0.567392i | \(0.807953\pi\) | |||||||
\(984\) | −48.0083 | −1.53045 | ||||||||
\(985\) | 31.2452 | 0.995554 | ||||||||
\(986\) | 47.8286 | 1.52317 | ||||||||
\(987\) | −5.49025 | −0.174757 | ||||||||
\(988\) | −105.337 | −3.35120 | ||||||||
\(989\) | −77.2470 | −2.45631 | ||||||||
\(990\) | 27.7899 | 0.883221 | ||||||||
\(991\) | 26.3986 | 0.838580 | 0.419290 | − | 0.907852i | \(-0.362279\pi\) | ||||
0.419290 | + | 0.907852i | \(0.362279\pi\) | |||||||
\(992\) | 23.6373 | 0.750485 | ||||||||
\(993\) | 8.88215 | 0.281867 | ||||||||
\(994\) | 99.6383 | 3.16034 | ||||||||
\(995\) | 89.2422 | 2.82917 | ||||||||
\(996\) | −1.65622 | −0.0524792 | ||||||||
\(997\) | −23.9106 | −0.757258 | −0.378629 | − | 0.925549i | \(-0.623604\pi\) | ||||
−0.378629 | + | 0.925549i | \(0.623604\pi\) | |||||||
\(998\) | 87.1310 | 2.75808 | ||||||||
\(999\) | 5.45431 | 0.172567 |
(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 | 8031.2.a.d.1.9 | ✓ | 132 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8031.2.a.d.1.9 | ✓ | 132 | 1.1 | even | 1 | trivial |