Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4027,2,Mod(1,4027)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4027, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4027.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4027 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4027.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1557568940\) |
Analytic rank: | \(1\) |
Dimension: | \(159\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 4027.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.48250 | −1.75539 | −0.877695 | − | 0.479219i | \(-0.840920\pi\) | ||||
−0.877695 | + | 0.479219i | \(0.840920\pi\) | |||||||
\(3\) | −1.21941 | −0.704025 | −0.352012 | − | 0.935995i | \(-0.614503\pi\) | ||||
−0.352012 | + | 0.935995i | \(0.614503\pi\) | |||||||
\(4\) | 4.16279 | 2.08140 | ||||||||
\(5\) | 0.264971 | 0.118499 | 0.0592494 | − | 0.998243i | \(-0.481129\pi\) | ||||
0.0592494 | + | 0.998243i | \(0.481129\pi\) | |||||||
\(6\) | 3.02717 | 1.23584 | ||||||||
\(7\) | −2.37151 | −0.896345 | −0.448173 | − | 0.893947i | \(-0.647925\pi\) | ||||
−0.448173 | + | 0.893947i | \(0.647925\pi\) | |||||||
\(8\) | −5.36913 | −1.89828 | ||||||||
\(9\) | −1.51305 | −0.504349 | ||||||||
\(10\) | −0.657790 | −0.208012 | ||||||||
\(11\) | 6.00450 | 1.81042 | 0.905212 | − | 0.424960i | \(-0.139712\pi\) | ||||
0.905212 | + | 0.424960i | \(0.139712\pi\) | |||||||
\(12\) | −5.07614 | −1.46536 | ||||||||
\(13\) | −1.83620 | −0.509271 | −0.254635 | − | 0.967037i | \(-0.581955\pi\) | ||||
−0.254635 | + | 0.967037i | \(0.581955\pi\) | |||||||
\(14\) | 5.88726 | 1.57344 | ||||||||
\(15\) | −0.323108 | −0.0834260 | ||||||||
\(16\) | 5.00327 | 1.25082 | ||||||||
\(17\) | 5.24105 | 1.27114 | 0.635571 | − | 0.772043i | \(-0.280765\pi\) | ||||
0.635571 | + | 0.772043i | \(0.280765\pi\) | |||||||
\(18\) | 3.75614 | 0.885330 | ||||||||
\(19\) | 3.52827 | 0.809441 | 0.404720 | − | 0.914440i | \(-0.367369\pi\) | ||||
0.404720 | + | 0.914440i | \(0.367369\pi\) | |||||||
\(20\) | 1.10302 | 0.246643 | ||||||||
\(21\) | 2.89183 | 0.631049 | ||||||||
\(22\) | −14.9062 | −3.17800 | ||||||||
\(23\) | −8.26025 | −1.72238 | −0.861191 | − | 0.508282i | \(-0.830281\pi\) | ||||
−0.861191 | + | 0.508282i | \(0.830281\pi\) | |||||||
\(24\) | 6.54716 | 1.33643 | ||||||||
\(25\) | −4.92979 | −0.985958 | ||||||||
\(26\) | 4.55837 | 0.893969 | ||||||||
\(27\) | 5.50324 | 1.05910 | ||||||||
\(28\) | −9.87210 | −1.86565 | ||||||||
\(29\) | −7.17908 | −1.33312 | −0.666561 | − | 0.745451i | \(-0.732234\pi\) | ||||
−0.666561 | + | 0.745451i | \(0.732234\pi\) | |||||||
\(30\) | 0.802114 | 0.146445 | ||||||||
\(31\) | 0.326356 | 0.0586154 | 0.0293077 | − | 0.999570i | \(-0.490670\pi\) | ||||
0.0293077 | + | 0.999570i | \(0.490670\pi\) | |||||||
\(32\) | −1.68234 | −0.297399 | ||||||||
\(33\) | −7.32193 | −1.27458 | ||||||||
\(34\) | −13.0109 | −2.23135 | ||||||||
\(35\) | −0.628381 | −0.106216 | ||||||||
\(36\) | −6.29850 | −1.04975 | ||||||||
\(37\) | −1.62800 | −0.267641 | −0.133821 | − | 0.991006i | \(-0.542725\pi\) | ||||
−0.133821 | + | 0.991006i | \(0.542725\pi\) | |||||||
\(38\) | −8.75892 | −1.42089 | ||||||||
\(39\) | 2.23908 | 0.358539 | ||||||||
\(40\) | −1.42267 | −0.224943 | ||||||||
\(41\) | 8.47028 | 1.32284 | 0.661418 | − | 0.750018i | \(-0.269955\pi\) | ||||
0.661418 | + | 0.750018i | \(0.269955\pi\) | |||||||
\(42\) | −7.17896 | −1.10774 | ||||||||
\(43\) | 6.35210 | 0.968686 | 0.484343 | − | 0.874878i | \(-0.339059\pi\) | ||||
0.484343 | + | 0.874878i | \(0.339059\pi\) | |||||||
\(44\) | 24.9955 | 3.76821 | ||||||||
\(45\) | −0.400914 | −0.0597647 | ||||||||
\(46\) | 20.5061 | 3.02345 | ||||||||
\(47\) | −9.71840 | −1.41757 | −0.708787 | − | 0.705423i | \(-0.750757\pi\) | ||||
−0.708787 | + | 0.705423i | \(0.750757\pi\) | |||||||
\(48\) | −6.10102 | −0.880607 | ||||||||
\(49\) | −1.37596 | −0.196565 | ||||||||
\(50\) | 12.2382 | 1.73074 | ||||||||
\(51\) | −6.39097 | −0.894915 | ||||||||
\(52\) | −7.64373 | −1.05999 | ||||||||
\(53\) | 9.38787 | 1.28952 | 0.644762 | − | 0.764384i | \(-0.276957\pi\) | ||||
0.644762 | + | 0.764384i | \(0.276957\pi\) | |||||||
\(54\) | −13.6618 | −1.85913 | ||||||||
\(55\) | 1.59102 | 0.214533 | ||||||||
\(56\) | 12.7329 | 1.70151 | ||||||||
\(57\) | −4.30240 | −0.569866 | ||||||||
\(58\) | 17.8221 | 2.34015 | ||||||||
\(59\) | 8.80566 | 1.14640 | 0.573200 | − | 0.819416i | \(-0.305702\pi\) | ||||
0.573200 | + | 0.819416i | \(0.305702\pi\) | |||||||
\(60\) | −1.34503 | −0.173643 | ||||||||
\(61\) | −0.781021 | −0.0999995 | −0.0499997 | − | 0.998749i | \(-0.515922\pi\) | ||||
−0.0499997 | + | 0.998749i | \(0.515922\pi\) | |||||||
\(62\) | −0.810179 | −0.102893 | ||||||||
\(63\) | 3.58820 | 0.452071 | ||||||||
\(64\) | −5.83013 | −0.728766 | ||||||||
\(65\) | −0.486541 | −0.0603479 | ||||||||
\(66\) | 18.1767 | 2.23739 | ||||||||
\(67\) | −14.4187 | −1.76153 | −0.880764 | − | 0.473556i | \(-0.842970\pi\) | ||||
−0.880764 | + | 0.473556i | \(0.842970\pi\) | |||||||
\(68\) | 21.8174 | 2.64575 | ||||||||
\(69\) | 10.0726 | 1.21260 | ||||||||
\(70\) | 1.55995 | 0.186450 | ||||||||
\(71\) | −13.6638 | −1.62159 | −0.810795 | − | 0.585331i | \(-0.800965\pi\) | ||||
−0.810795 | + | 0.585331i | \(0.800965\pi\) | |||||||
\(72\) | 8.12375 | 0.957393 | ||||||||
\(73\) | 7.48284 | 0.875800 | 0.437900 | − | 0.899024i | \(-0.355722\pi\) | ||||
0.437900 | + | 0.899024i | \(0.355722\pi\) | |||||||
\(74\) | 4.04150 | 0.469815 | ||||||||
\(75\) | 6.01142 | 0.694139 | ||||||||
\(76\) | 14.6875 | 1.68477 | ||||||||
\(77\) | −14.2397 | −1.62277 | ||||||||
\(78\) | −5.55850 | −0.629377 | ||||||||
\(79\) | 10.0509 | 1.13081 | 0.565407 | − | 0.824812i | \(-0.308719\pi\) | ||||
0.565407 | + | 0.824812i | \(0.308719\pi\) | |||||||
\(80\) | 1.32572 | 0.148220 | ||||||||
\(81\) | −2.17155 | −0.241283 | ||||||||
\(82\) | −21.0274 | −2.32209 | ||||||||
\(83\) | −4.93575 | −0.541769 | −0.270885 | − | 0.962612i | \(-0.587316\pi\) | ||||
−0.270885 | + | 0.962612i | \(0.587316\pi\) | |||||||
\(84\) | 12.0381 | 1.31346 | ||||||||
\(85\) | 1.38873 | 0.150629 | ||||||||
\(86\) | −15.7691 | −1.70042 | ||||||||
\(87\) | 8.75422 | 0.938551 | ||||||||
\(88\) | −32.2390 | −3.43668 | ||||||||
\(89\) | 12.6440 | 1.34026 | 0.670132 | − | 0.742242i | \(-0.266237\pi\) | ||||
0.670132 | + | 0.742242i | \(0.266237\pi\) | |||||||
\(90\) | 0.995268 | 0.104910 | ||||||||
\(91\) | 4.35456 | 0.456482 | ||||||||
\(92\) | −34.3857 | −3.58496 | ||||||||
\(93\) | −0.397961 | −0.0412667 | ||||||||
\(94\) | 24.1259 | 2.48840 | ||||||||
\(95\) | 0.934890 | 0.0959177 | ||||||||
\(96\) | 2.05146 | 0.209376 | ||||||||
\(97\) | −8.09283 | −0.821703 | −0.410851 | − | 0.911702i | \(-0.634768\pi\) | ||||
−0.410851 | + | 0.911702i | \(0.634768\pi\) | |||||||
\(98\) | 3.41581 | 0.345049 | ||||||||
\(99\) | −9.08509 | −0.913086 | ||||||||
\(100\) | −20.5217 | −2.05217 | ||||||||
\(101\) | −4.36608 | −0.434441 | −0.217221 | − | 0.976123i | \(-0.569699\pi\) | ||||
−0.217221 | + | 0.976123i | \(0.569699\pi\) | |||||||
\(102\) | 15.8656 | 1.57093 | ||||||||
\(103\) | 16.8145 | 1.65678 | 0.828392 | − | 0.560149i | \(-0.189256\pi\) | ||||
0.828392 | + | 0.560149i | \(0.189256\pi\) | |||||||
\(104\) | 9.85881 | 0.966736 | ||||||||
\(105\) | 0.766252 | 0.0747785 | ||||||||
\(106\) | −23.3054 | −2.26362 | ||||||||
\(107\) | −16.8224 | −1.62629 | −0.813143 | − | 0.582065i | \(-0.802245\pi\) | ||||
−0.813143 | + | 0.582065i | \(0.802245\pi\) | |||||||
\(108\) | 22.9089 | 2.20441 | ||||||||
\(109\) | −4.06081 | −0.388955 | −0.194478 | − | 0.980907i | \(-0.562301\pi\) | ||||
−0.194478 | + | 0.980907i | \(0.562301\pi\) | |||||||
\(110\) | −3.94970 | −0.376589 | ||||||||
\(111\) | 1.98519 | 0.188426 | ||||||||
\(112\) | −11.8653 | −1.12116 | ||||||||
\(113\) | −9.46979 | −0.890843 | −0.445421 | − | 0.895321i | \(-0.646946\pi\) | ||||
−0.445421 | + | 0.895321i | \(0.646946\pi\) | |||||||
\(114\) | 10.6807 | 1.00034 | ||||||||
\(115\) | −2.18873 | −0.204100 | ||||||||
\(116\) | −29.8850 | −2.77476 | ||||||||
\(117\) | 2.77826 | 0.256850 | ||||||||
\(118\) | −21.8600 | −2.01238 | ||||||||
\(119\) | −12.4292 | −1.13938 | ||||||||
\(120\) | 1.73481 | 0.158366 | ||||||||
\(121\) | 25.0540 | 2.27764 | ||||||||
\(122\) | 1.93888 | 0.175538 | ||||||||
\(123\) | −10.3287 | −0.931309 | ||||||||
\(124\) | 1.35856 | 0.122002 | ||||||||
\(125\) | −2.63111 | −0.235333 | ||||||||
\(126\) | −8.90770 | −0.793561 | ||||||||
\(127\) | −0.887955 | −0.0787933 | −0.0393966 | − | 0.999224i | \(-0.512544\pi\) | ||||
−0.0393966 | + | 0.999224i | \(0.512544\pi\) | |||||||
\(128\) | 17.8380 | 1.57667 | ||||||||
\(129\) | −7.74579 | −0.681979 | ||||||||
\(130\) | 1.20784 | 0.105934 | ||||||||
\(131\) | −5.00037 | −0.436884 | −0.218442 | − | 0.975850i | \(-0.570097\pi\) | ||||
−0.218442 | + | 0.975850i | \(0.570097\pi\) | |||||||
\(132\) | −30.4797 | −2.65292 | ||||||||
\(133\) | −8.36732 | −0.725538 | ||||||||
\(134\) | 35.7945 | 3.09217 | ||||||||
\(135\) | 1.45820 | 0.125502 | ||||||||
\(136\) | −28.1399 | −2.41298 | ||||||||
\(137\) | −3.93808 | −0.336453 | −0.168226 | − | 0.985748i | \(-0.553804\pi\) | ||||
−0.168226 | + | 0.985748i | \(0.553804\pi\) | |||||||
\(138\) | −25.0052 | −2.12859 | ||||||||
\(139\) | 20.0298 | 1.69890 | 0.849451 | − | 0.527667i | \(-0.176933\pi\) | ||||
0.849451 | + | 0.527667i | \(0.176933\pi\) | |||||||
\(140\) | −2.61582 | −0.221077 | ||||||||
\(141\) | 11.8507 | 0.998007 | ||||||||
\(142\) | 33.9202 | 2.84652 | ||||||||
\(143\) | −11.0255 | −0.921996 | ||||||||
\(144\) | −7.57019 | −0.630849 | ||||||||
\(145\) | −1.90225 | −0.157973 | ||||||||
\(146\) | −18.5761 | −1.53737 | ||||||||
\(147\) | 1.67785 | 0.138387 | ||||||||
\(148\) | −6.77702 | −0.557068 | ||||||||
\(149\) | 22.2667 | 1.82416 | 0.912081 | − | 0.410011i | \(-0.134475\pi\) | ||||
0.912081 | + | 0.410011i | \(0.134475\pi\) | |||||||
\(150\) | −14.9233 | −1.21849 | ||||||||
\(151\) | −3.33649 | −0.271519 | −0.135760 | − | 0.990742i | \(-0.543348\pi\) | ||||
−0.135760 | + | 0.990742i | \(0.543348\pi\) | |||||||
\(152\) | −18.9438 | −1.53654 | ||||||||
\(153\) | −7.92995 | −0.641099 | ||||||||
\(154\) | 35.3500 | 2.84859 | ||||||||
\(155\) | 0.0864751 | 0.00694584 | ||||||||
\(156\) | 9.32082 | 0.746263 | ||||||||
\(157\) | 22.8269 | 1.82178 | 0.910891 | − | 0.412647i | \(-0.135396\pi\) | ||||
0.910891 | + | 0.412647i | \(0.135396\pi\) | |||||||
\(158\) | −24.9513 | −1.98502 | ||||||||
\(159\) | −11.4476 | −0.907857 | ||||||||
\(160\) | −0.445773 | −0.0352414 | ||||||||
\(161\) | 19.5892 | 1.54385 | ||||||||
\(162\) | 5.39086 | 0.423546 | ||||||||
\(163\) | 6.57738 | 0.515180 | 0.257590 | − | 0.966254i | \(-0.417072\pi\) | ||||
0.257590 | + | 0.966254i | \(0.417072\pi\) | |||||||
\(164\) | 35.2600 | 2.75335 | ||||||||
\(165\) | −1.94010 | −0.151037 | ||||||||
\(166\) | 12.2530 | 0.951017 | ||||||||
\(167\) | −7.56768 | −0.585605 | −0.292802 | − | 0.956173i | \(-0.594588\pi\) | ||||
−0.292802 | + | 0.956173i | \(0.594588\pi\) | |||||||
\(168\) | −15.5266 | −1.19791 | ||||||||
\(169\) | −9.62836 | −0.740643 | ||||||||
\(170\) | −3.44751 | −0.264412 | ||||||||
\(171\) | −5.33844 | −0.408241 | ||||||||
\(172\) | 26.4425 | 2.01622 | ||||||||
\(173\) | 9.00406 | 0.684566 | 0.342283 | − | 0.939597i | \(-0.388800\pi\) | ||||
0.342283 | + | 0.939597i | \(0.388800\pi\) | |||||||
\(174\) | −21.7323 | −1.64752 | ||||||||
\(175\) | 11.6910 | 0.883759 | ||||||||
\(176\) | 30.0421 | 2.26451 | ||||||||
\(177\) | −10.7377 | −0.807094 | ||||||||
\(178\) | −31.3888 | −2.35269 | ||||||||
\(179\) | −5.19012 | −0.387928 | −0.193964 | − | 0.981009i | \(-0.562134\pi\) | ||||
−0.193964 | + | 0.981009i | \(0.562134\pi\) | |||||||
\(180\) | −1.66892 | −0.124394 | ||||||||
\(181\) | 10.5159 | 0.781637 | 0.390819 | − | 0.920468i | \(-0.372192\pi\) | ||||
0.390819 | + | 0.920468i | \(0.372192\pi\) | |||||||
\(182\) | −10.8102 | −0.801305 | ||||||||
\(183\) | 0.952382 | 0.0704021 | ||||||||
\(184\) | 44.3504 | 3.26955 | ||||||||
\(185\) | −0.431373 | −0.0317151 | ||||||||
\(186\) | 0.987938 | 0.0724391 | ||||||||
\(187\) | 31.4699 | 2.30131 | ||||||||
\(188\) | −40.4557 | −2.95054 | ||||||||
\(189\) | −13.0510 | −0.949318 | ||||||||
\(190\) | −2.32086 | −0.168373 | ||||||||
\(191\) | −2.17097 | −0.157086 | −0.0785429 | − | 0.996911i | \(-0.525027\pi\) | ||||
−0.0785429 | + | 0.996911i | \(0.525027\pi\) | |||||||
\(192\) | 7.10930 | 0.513069 | ||||||||
\(193\) | −16.3330 | −1.17567 | −0.587837 | − | 0.808979i | \(-0.700020\pi\) | ||||
−0.587837 | + | 0.808979i | \(0.700020\pi\) | |||||||
\(194\) | 20.0904 | 1.44241 | ||||||||
\(195\) | 0.593291 | 0.0424864 | ||||||||
\(196\) | −5.72782 | −0.409130 | ||||||||
\(197\) | −9.69574 | −0.690793 | −0.345396 | − | 0.938457i | \(-0.612256\pi\) | ||||
−0.345396 | + | 0.938457i | \(0.612256\pi\) | |||||||
\(198\) | 22.5537 | 1.60282 | ||||||||
\(199\) | −13.7039 | −0.971444 | −0.485722 | − | 0.874113i | \(-0.661443\pi\) | ||||
−0.485722 | + | 0.874113i | \(0.661443\pi\) | |||||||
\(200\) | 26.4687 | 1.87162 | ||||||||
\(201\) | 17.5823 | 1.24016 | ||||||||
\(202\) | 10.8388 | 0.762614 | ||||||||
\(203\) | 17.0252 | 1.19494 | ||||||||
\(204\) | −26.6043 | −1.86267 | ||||||||
\(205\) | 2.24438 | 0.156754 | ||||||||
\(206\) | −41.7420 | −2.90830 | ||||||||
\(207\) | 12.4981 | 0.868681 | ||||||||
\(208\) | −9.18702 | −0.637005 | ||||||||
\(209\) | 21.1855 | 1.46543 | ||||||||
\(210\) | −1.90222 | −0.131266 | ||||||||
\(211\) | 9.50573 | 0.654401 | 0.327201 | − | 0.944955i | \(-0.393895\pi\) | ||||
0.327201 | + | 0.944955i | \(0.393895\pi\) | |||||||
\(212\) | 39.0798 | 2.68401 | ||||||||
\(213\) | 16.6617 | 1.14164 | ||||||||
\(214\) | 41.7616 | 2.85477 | ||||||||
\(215\) | 1.68312 | 0.114788 | ||||||||
\(216\) | −29.5476 | −2.01046 | ||||||||
\(217\) | −0.773957 | −0.0525396 | ||||||||
\(218\) | 10.0810 | 0.682768 | ||||||||
\(219\) | −9.12462 | −0.616585 | ||||||||
\(220\) | 6.62309 | 0.446528 | ||||||||
\(221\) | −9.62362 | −0.647355 | ||||||||
\(222\) | −4.92823 | −0.330761 | ||||||||
\(223\) | 15.4460 | 1.03434 | 0.517171 | − | 0.855882i | \(-0.326985\pi\) | ||||
0.517171 | + | 0.855882i | \(0.326985\pi\) | |||||||
\(224\) | 3.98969 | 0.266572 | ||||||||
\(225\) | 7.45900 | 0.497267 | ||||||||
\(226\) | 23.5087 | 1.56378 | ||||||||
\(227\) | 17.9896 | 1.19401 | 0.597005 | − | 0.802238i | \(-0.296357\pi\) | ||||
0.597005 | + | 0.802238i | \(0.296357\pi\) | |||||||
\(228\) | −17.9100 | −1.18612 | ||||||||
\(229\) | 7.42490 | 0.490651 | 0.245326 | − | 0.969441i | \(-0.421105\pi\) | ||||
0.245326 | + | 0.969441i | \(0.421105\pi\) | |||||||
\(230\) | 5.43351 | 0.358275 | ||||||||
\(231\) | 17.3640 | 1.14247 | ||||||||
\(232\) | 38.5454 | 2.53063 | ||||||||
\(233\) | −5.49326 | −0.359876 | −0.179938 | − | 0.983678i | \(-0.557590\pi\) | ||||
−0.179938 | + | 0.983678i | \(0.557590\pi\) | |||||||
\(234\) | −6.89702 | −0.450873 | ||||||||
\(235\) | −2.57510 | −0.167981 | ||||||||
\(236\) | 36.6562 | 2.38611 | ||||||||
\(237\) | −12.2561 | −0.796122 | ||||||||
\(238\) | 30.8554 | 2.00006 | ||||||||
\(239\) | −6.33907 | −0.410040 | −0.205020 | − | 0.978758i | \(-0.565726\pi\) | ||||
−0.205020 | + | 0.978758i | \(0.565726\pi\) | |||||||
\(240\) | −1.61660 | −0.104351 | ||||||||
\(241\) | −15.3575 | −0.989261 | −0.494631 | − | 0.869103i | \(-0.664697\pi\) | ||||
−0.494631 | + | 0.869103i | \(0.664697\pi\) | |||||||
\(242\) | −62.1965 | −3.99814 | ||||||||
\(243\) | −13.8617 | −0.889230 | ||||||||
\(244\) | −3.25123 | −0.208139 | ||||||||
\(245\) | −0.364589 | −0.0232927 | ||||||||
\(246\) | 25.6410 | 1.63481 | ||||||||
\(247\) | −6.47862 | −0.412225 | ||||||||
\(248\) | −1.75225 | −0.111268 | ||||||||
\(249\) | 6.01869 | 0.381419 | ||||||||
\(250\) | 6.53172 | 0.413102 | ||||||||
\(251\) | −7.76111 | −0.489877 | −0.244938 | − | 0.969539i | \(-0.578768\pi\) | ||||
−0.244938 | + | 0.969539i | \(0.578768\pi\) | |||||||
\(252\) | 14.9369 | 0.940939 | ||||||||
\(253\) | −49.5987 | −3.11824 | ||||||||
\(254\) | 2.20435 | 0.138313 | ||||||||
\(255\) | −1.69342 | −0.106046 | ||||||||
\(256\) | −32.6225 | −2.03890 | ||||||||
\(257\) | −25.4349 | −1.58659 | −0.793293 | − | 0.608841i | \(-0.791635\pi\) | ||||
−0.793293 | + | 0.608841i | \(0.791635\pi\) | |||||||
\(258\) | 19.2289 | 1.19714 | ||||||||
\(259\) | 3.86081 | 0.239899 | ||||||||
\(260\) | −2.02537 | −0.125608 | ||||||||
\(261\) | 10.8623 | 0.672359 | ||||||||
\(262\) | 12.4134 | 0.766902 | ||||||||
\(263\) | −16.6127 | −1.02438 | −0.512191 | − | 0.858871i | \(-0.671166\pi\) | ||||
−0.512191 | + | 0.858871i | \(0.671166\pi\) | |||||||
\(264\) | 39.3124 | 2.41951 | ||||||||
\(265\) | 2.48752 | 0.152807 | ||||||||
\(266\) | 20.7718 | 1.27360 | ||||||||
\(267\) | −15.4182 | −0.943580 | ||||||||
\(268\) | −60.0222 | −3.66644 | ||||||||
\(269\) | 13.9887 | 0.852907 | 0.426454 | − | 0.904509i | \(-0.359763\pi\) | ||||
0.426454 | + | 0.904509i | \(0.359763\pi\) | |||||||
\(270\) | −3.61998 | −0.220305 | ||||||||
\(271\) | −10.1675 | −0.617630 | −0.308815 | − | 0.951122i | \(-0.599932\pi\) | ||||
−0.308815 | + | 0.951122i | \(0.599932\pi\) | |||||||
\(272\) | 26.2224 | 1.58997 | ||||||||
\(273\) | −5.30999 | −0.321375 | ||||||||
\(274\) | 9.77627 | 0.590606 | ||||||||
\(275\) | −29.6009 | −1.78500 | ||||||||
\(276\) | 41.9302 | 2.52390 | ||||||||
\(277\) | −4.91106 | −0.295077 | −0.147539 | − | 0.989056i | \(-0.547135\pi\) | ||||
−0.147539 | + | 0.989056i | \(0.547135\pi\) | |||||||
\(278\) | −49.7238 | −2.98224 | ||||||||
\(279\) | −0.493793 | −0.0295626 | ||||||||
\(280\) | 3.37386 | 0.201627 | ||||||||
\(281\) | −15.9906 | −0.953922 | −0.476961 | − | 0.878924i | \(-0.658262\pi\) | ||||
−0.476961 | + | 0.878924i | \(0.658262\pi\) | |||||||
\(282\) | −29.4193 | −1.75189 | ||||||||
\(283\) | 28.5193 | 1.69530 | 0.847648 | − | 0.530558i | \(-0.178018\pi\) | ||||
0.847648 | + | 0.530558i | \(0.178018\pi\) | |||||||
\(284\) | −56.8794 | −3.37517 | ||||||||
\(285\) | −1.14001 | −0.0675284 | ||||||||
\(286\) | 27.3707 | 1.61846 | ||||||||
\(287\) | −20.0873 | −1.18572 | ||||||||
\(288\) | 2.54547 | 0.149993 | ||||||||
\(289\) | 10.4686 | 0.615800 | ||||||||
\(290\) | 4.72233 | 0.277305 | ||||||||
\(291\) | 9.86845 | 0.578499 | ||||||||
\(292\) | 31.1495 | 1.82289 | ||||||||
\(293\) | −25.7391 | −1.50370 | −0.751848 | − | 0.659337i | \(-0.770837\pi\) | ||||
−0.751848 | + | 0.659337i | \(0.770837\pi\) | |||||||
\(294\) | −4.16526 | −0.242923 | ||||||||
\(295\) | 2.33325 | 0.135847 | ||||||||
\(296\) | 8.74094 | 0.508057 | ||||||||
\(297\) | 33.0442 | 1.91742 | ||||||||
\(298\) | −55.2771 | −3.20212 | ||||||||
\(299\) | 15.1675 | 0.877158 | ||||||||
\(300\) | 25.0243 | 1.44478 | ||||||||
\(301\) | −15.0640 | −0.868277 | ||||||||
\(302\) | 8.28282 | 0.476623 | ||||||||
\(303\) | 5.32403 | 0.305858 | ||||||||
\(304\) | 17.6529 | 1.01246 | ||||||||
\(305\) | −0.206948 | −0.0118498 | ||||||||
\(306\) | 19.6861 | 1.12538 | ||||||||
\(307\) | −0.541119 | −0.0308833 | −0.0154416 | − | 0.999881i | \(-0.504915\pi\) | ||||
−0.0154416 | + | 0.999881i | \(0.504915\pi\) | |||||||
\(308\) | −59.2770 | −3.37762 | ||||||||
\(309\) | −20.5037 | −1.16642 | ||||||||
\(310\) | −0.214674 | −0.0121927 | ||||||||
\(311\) | −3.22763 | −0.183022 | −0.0915111 | − | 0.995804i | \(-0.529170\pi\) | ||||
−0.0915111 | + | 0.995804i | \(0.529170\pi\) | |||||||
\(312\) | −12.0219 | −0.680606 | ||||||||
\(313\) | −14.7400 | −0.833152 | −0.416576 | − | 0.909101i | \(-0.636770\pi\) | ||||
−0.416576 | + | 0.909101i | \(0.636770\pi\) | |||||||
\(314\) | −56.6676 | −3.19794 | ||||||||
\(315\) | 0.950770 | 0.0535698 | ||||||||
\(316\) | 41.8398 | 2.35368 | ||||||||
\(317\) | −10.2062 | −0.573239 | −0.286620 | − | 0.958044i | \(-0.592532\pi\) | ||||
−0.286620 | + | 0.958044i | \(0.592532\pi\) | |||||||
\(318\) | 28.4187 | 1.59364 | ||||||||
\(319\) | −43.1068 | −2.41352 | ||||||||
\(320\) | −1.54482 | −0.0863578 | ||||||||
\(321\) | 20.5134 | 1.14495 | ||||||||
\(322\) | −48.6302 | −2.71006 | ||||||||
\(323\) | 18.4918 | 1.02891 | ||||||||
\(324\) | −9.03971 | −0.502206 | ||||||||
\(325\) | 9.05209 | 0.502120 | ||||||||
\(326\) | −16.3283 | −0.904342 | ||||||||
\(327\) | 4.95178 | 0.273834 | ||||||||
\(328\) | −45.4781 | −2.51111 | ||||||||
\(329\) | 23.0472 | 1.27064 | ||||||||
\(330\) | 4.81629 | 0.265128 | ||||||||
\(331\) | 2.67916 | 0.147260 | 0.0736299 | − | 0.997286i | \(-0.476542\pi\) | ||||
0.0736299 | + | 0.997286i | \(0.476542\pi\) | |||||||
\(332\) | −20.5465 | −1.12764 | ||||||||
\(333\) | 2.46324 | 0.134985 | ||||||||
\(334\) | 18.7868 | 1.02797 | ||||||||
\(335\) | −3.82055 | −0.208739 | ||||||||
\(336\) | 14.4686 | 0.789328 | ||||||||
\(337\) | −9.91763 | −0.540248 | −0.270124 | − | 0.962826i | \(-0.587065\pi\) | ||||
−0.270124 | + | 0.962826i | \(0.587065\pi\) | |||||||
\(338\) | 23.9024 | 1.30012 | ||||||||
\(339\) | 11.5475 | 0.627176 | ||||||||
\(340\) | 5.78099 | 0.313518 | ||||||||
\(341\) | 1.95961 | 0.106119 | ||||||||
\(342\) | 13.2527 | 0.716622 | ||||||||
\(343\) | 19.8636 | 1.07254 | ||||||||
\(344\) | −34.1053 | −1.83883 | ||||||||
\(345\) | 2.66895 | 0.143691 | ||||||||
\(346\) | −22.3526 | −1.20168 | ||||||||
\(347\) | 21.8183 | 1.17127 | 0.585634 | − | 0.810575i | \(-0.300845\pi\) | ||||
0.585634 | + | 0.810575i | \(0.300845\pi\) | |||||||
\(348\) | 36.4420 | 1.95350 | ||||||||
\(349\) | 6.11082 | 0.327105 | 0.163552 | − | 0.986535i | \(-0.447705\pi\) | ||||
0.163552 | + | 0.986535i | \(0.447705\pi\) | |||||||
\(350\) | −29.0230 | −1.55134 | ||||||||
\(351\) | −10.1051 | −0.539368 | ||||||||
\(352\) | −10.1016 | −0.538419 | ||||||||
\(353\) | −12.6946 | −0.675666 | −0.337833 | − | 0.941206i | \(-0.609694\pi\) | ||||
−0.337833 | + | 0.941206i | \(0.609694\pi\) | |||||||
\(354\) | 26.6563 | 1.41676 | ||||||||
\(355\) | −3.62050 | −0.192156 | ||||||||
\(356\) | 52.6345 | 2.78962 | ||||||||
\(357\) | 15.1562 | 0.802153 | ||||||||
\(358\) | 12.8845 | 0.680965 | ||||||||
\(359\) | −2.43139 | −0.128324 | −0.0641619 | − | 0.997940i | \(-0.520437\pi\) | ||||
−0.0641619 | + | 0.997940i | \(0.520437\pi\) | |||||||
\(360\) | 2.15256 | 0.113450 | ||||||||
\(361\) | −6.55131 | −0.344806 | ||||||||
\(362\) | −26.1056 | −1.37208 | ||||||||
\(363\) | −30.5510 | −1.60351 | ||||||||
\(364\) | 18.1272 | 0.950121 | ||||||||
\(365\) | 1.98274 | 0.103781 | ||||||||
\(366\) | −2.36429 | −0.123583 | ||||||||
\(367\) | −14.3644 | −0.749813 | −0.374907 | − | 0.927063i | \(-0.622325\pi\) | ||||
−0.374907 | + | 0.927063i | \(0.622325\pi\) | |||||||
\(368\) | −41.3283 | −2.15439 | ||||||||
\(369\) | −12.8159 | −0.667171 | ||||||||
\(370\) | 1.07088 | 0.0556725 | ||||||||
\(371\) | −22.2634 | −1.15586 | ||||||||
\(372\) | −1.65663 | −0.0858923 | ||||||||
\(373\) | −21.3886 | −1.10746 | −0.553730 | − | 0.832697i | \(-0.686796\pi\) | ||||
−0.553730 | + | 0.832697i | \(0.686796\pi\) | |||||||
\(374\) | −78.1239 | −4.03969 | ||||||||
\(375\) | 3.20839 | 0.165681 | ||||||||
\(376\) | 52.1794 | 2.69095 | ||||||||
\(377\) | 13.1822 | 0.678920 | ||||||||
\(378\) | 32.3990 | 1.66643 | ||||||||
\(379\) | 18.4420 | 0.947300 | 0.473650 | − | 0.880713i | \(-0.342936\pi\) | ||||
0.473650 | + | 0.880713i | \(0.342936\pi\) | |||||||
\(380\) | 3.89176 | 0.199643 | ||||||||
\(381\) | 1.08278 | 0.0554724 | ||||||||
\(382\) | 5.38942 | 0.275747 | ||||||||
\(383\) | −11.7768 | −0.601764 | −0.300882 | − | 0.953661i | \(-0.597281\pi\) | ||||
−0.300882 | + | 0.953661i | \(0.597281\pi\) | |||||||
\(384\) | −21.7517 | −1.11001 | ||||||||
\(385\) | −3.77311 | −0.192296 | ||||||||
\(386\) | 40.5466 | 2.06377 | ||||||||
\(387\) | −9.61103 | −0.488556 | ||||||||
\(388\) | −33.6888 | −1.71029 | ||||||||
\(389\) | −28.4961 | −1.44481 | −0.722404 | − | 0.691472i | \(-0.756963\pi\) | ||||
−0.722404 | + | 0.691472i | \(0.756963\pi\) | |||||||
\(390\) | −1.47284 | −0.0745803 | ||||||||
\(391\) | −43.2924 | −2.18939 | ||||||||
\(392\) | 7.38769 | 0.373135 | ||||||||
\(393\) | 6.09748 | 0.307577 | ||||||||
\(394\) | 24.0696 | 1.21261 | ||||||||
\(395\) | 2.66320 | 0.134000 | ||||||||
\(396\) | −37.8194 | −1.90049 | ||||||||
\(397\) | −4.74194 | −0.237991 | −0.118996 | − | 0.992895i | \(-0.537967\pi\) | ||||
−0.118996 | + | 0.992895i | \(0.537967\pi\) | |||||||
\(398\) | 34.0199 | 1.70526 | ||||||||
\(399\) | 10.2032 | 0.510797 | ||||||||
\(400\) | −24.6651 | −1.23325 | ||||||||
\(401\) | −30.1137 | −1.50380 | −0.751902 | − | 0.659274i | \(-0.770864\pi\) | ||||
−0.751902 | + | 0.659274i | \(0.770864\pi\) | |||||||
\(402\) | −43.6480 | −2.17696 | ||||||||
\(403\) | −0.599256 | −0.0298511 | ||||||||
\(404\) | −18.1751 | −0.904245 | ||||||||
\(405\) | −0.575398 | −0.0285917 | ||||||||
\(406\) | −42.2651 | −2.09758 | ||||||||
\(407\) | −9.77531 | −0.484544 | ||||||||
\(408\) | 34.3140 | 1.69880 | ||||||||
\(409\) | 9.02321 | 0.446169 | 0.223084 | − | 0.974799i | \(-0.428387\pi\) | ||||
0.223084 | + | 0.974799i | \(0.428387\pi\) | |||||||
\(410\) | −5.57167 | −0.275165 | ||||||||
\(411\) | 4.80212 | 0.236871 | ||||||||
\(412\) | 69.9954 | 3.44843 | ||||||||
\(413\) | −20.8827 | −1.02757 | ||||||||
\(414\) | −31.0266 | −1.52488 | ||||||||
\(415\) | −1.30783 | −0.0641990 | ||||||||
\(416\) | 3.08912 | 0.151457 | ||||||||
\(417\) | −24.4244 | −1.19607 | ||||||||
\(418\) | −52.5929 | −2.57241 | ||||||||
\(419\) | −19.1627 | −0.936158 | −0.468079 | − | 0.883687i | \(-0.655054\pi\) | ||||
−0.468079 | + | 0.883687i | \(0.655054\pi\) | |||||||
\(420\) | 3.18975 | 0.155644 | ||||||||
\(421\) | 4.88450 | 0.238056 | 0.119028 | − | 0.992891i | \(-0.462022\pi\) | ||||
0.119028 | + | 0.992891i | \(0.462022\pi\) | |||||||
\(422\) | −23.5979 | −1.14873 | ||||||||
\(423\) | 14.7044 | 0.714952 | ||||||||
\(424\) | −50.4047 | −2.44787 | ||||||||
\(425\) | −25.8373 | −1.25329 | ||||||||
\(426\) | −41.3626 | −2.00402 | ||||||||
\(427\) | 1.85220 | 0.0896341 | ||||||||
\(428\) | −70.0283 | −3.38495 | ||||||||
\(429\) | 13.4445 | 0.649108 | ||||||||
\(430\) | −4.17835 | −0.201498 | ||||||||
\(431\) | 20.1375 | 0.969989 | 0.484995 | − | 0.874517i | \(-0.338822\pi\) | ||||
0.484995 | + | 0.874517i | \(0.338822\pi\) | |||||||
\(432\) | 27.5342 | 1.32474 | ||||||||
\(433\) | −15.2084 | −0.730870 | −0.365435 | − | 0.930837i | \(-0.619080\pi\) | ||||
−0.365435 | + | 0.930837i | \(0.619080\pi\) | |||||||
\(434\) | 1.92135 | 0.0922275 | ||||||||
\(435\) | 2.31962 | 0.111217 | ||||||||
\(436\) | −16.9043 | −0.809570 | ||||||||
\(437\) | −29.1444 | −1.39417 | ||||||||
\(438\) | 22.6518 | 1.08235 | ||||||||
\(439\) | 9.02803 | 0.430884 | 0.215442 | − | 0.976517i | \(-0.430881\pi\) | ||||
0.215442 | + | 0.976517i | \(0.430881\pi\) | |||||||
\(440\) | −8.54239 | −0.407243 | ||||||||
\(441\) | 2.08189 | 0.0991374 | ||||||||
\(442\) | 23.8906 | 1.13636 | ||||||||
\(443\) | 31.2572 | 1.48507 | 0.742537 | − | 0.669805i | \(-0.233622\pi\) | ||||
0.742537 | + | 0.669805i | \(0.233622\pi\) | |||||||
\(444\) | 8.26395 | 0.392190 | ||||||||
\(445\) | 3.35030 | 0.158820 | ||||||||
\(446\) | −38.3447 | −1.81567 | ||||||||
\(447\) | −27.1522 | −1.28425 | ||||||||
\(448\) | 13.8262 | 0.653226 | ||||||||
\(449\) | −25.7636 | −1.21586 | −0.607930 | − | 0.793991i | \(-0.708000\pi\) | ||||
−0.607930 | + | 0.793991i | \(0.708000\pi\) | |||||||
\(450\) | −18.5170 | −0.872898 | ||||||||
\(451\) | 50.8598 | 2.39489 | ||||||||
\(452\) | −39.4208 | −1.85420 | ||||||||
\(453\) | 4.06853 | 0.191156 | ||||||||
\(454\) | −44.6591 | −2.09595 | ||||||||
\(455\) | 1.15383 | 0.0540926 | ||||||||
\(456\) | 23.1001 | 1.08176 | ||||||||
\(457\) | −19.6752 | −0.920367 | −0.460184 | − | 0.887824i | \(-0.652216\pi\) | ||||
−0.460184 | + | 0.887824i | \(0.652216\pi\) | |||||||
\(458\) | −18.4323 | −0.861285 | ||||||||
\(459\) | 28.8428 | 1.34626 | ||||||||
\(460\) | −9.11123 | −0.424813 | ||||||||
\(461\) | 16.1792 | 0.753541 | 0.376771 | − | 0.926307i | \(-0.377034\pi\) | ||||
0.376771 | + | 0.926307i | \(0.377034\pi\) | |||||||
\(462\) | −43.1061 | −2.00548 | ||||||||
\(463\) | −26.5226 | −1.23261 | −0.616304 | − | 0.787508i | \(-0.711371\pi\) | ||||
−0.616304 | + | 0.787508i | \(0.711371\pi\) | |||||||
\(464\) | −35.9189 | −1.66749 | ||||||||
\(465\) | −0.105448 | −0.00489005 | ||||||||
\(466\) | 13.6370 | 0.631722 | ||||||||
\(467\) | −21.3131 | −0.986251 | −0.493125 | − | 0.869958i | \(-0.664146\pi\) | ||||
−0.493125 | + | 0.869958i | \(0.664146\pi\) | |||||||
\(468\) | 11.5653 | 0.534607 | ||||||||
\(469\) | 34.1941 | 1.57894 | ||||||||
\(470\) | 6.39267 | 0.294872 | ||||||||
\(471\) | −27.8352 | −1.28258 | ||||||||
\(472\) | −47.2788 | −2.17618 | ||||||||
\(473\) | 38.1412 | 1.75373 | ||||||||
\(474\) | 30.4258 | 1.39751 | ||||||||
\(475\) | −17.3936 | −0.798075 | ||||||||
\(476\) | −51.7401 | −2.37151 | ||||||||
\(477\) | −14.2043 | −0.650370 | ||||||||
\(478\) | 15.7367 | 0.719781 | ||||||||
\(479\) | −20.0615 | −0.916632 | −0.458316 | − | 0.888789i | \(-0.651547\pi\) | ||||
−0.458316 | + | 0.888789i | \(0.651547\pi\) | |||||||
\(480\) | 0.543578 | 0.0248108 | ||||||||
\(481\) | 2.98933 | 0.136302 | ||||||||
\(482\) | 38.1249 | 1.73654 | ||||||||
\(483\) | −23.8872 | −1.08691 | ||||||||
\(484\) | 104.295 | 4.74067 | ||||||||
\(485\) | −2.14437 | −0.0973707 | ||||||||
\(486\) | 34.4117 | 1.56095 | ||||||||
\(487\) | −21.9050 | −0.992611 | −0.496305 | − | 0.868148i | \(-0.665310\pi\) | ||||
−0.496305 | + | 0.868148i | \(0.665310\pi\) | |||||||
\(488\) | 4.19341 | 0.189827 | ||||||||
\(489\) | −8.02050 | −0.362699 | ||||||||
\(490\) | 0.905091 | 0.0408878 | ||||||||
\(491\) | −23.9843 | −1.08240 | −0.541198 | − | 0.840895i | \(-0.682029\pi\) | ||||
−0.541198 | + | 0.840895i | \(0.682029\pi\) | |||||||
\(492\) | −42.9963 | −1.93842 | ||||||||
\(493\) | −37.6259 | −1.69459 | ||||||||
\(494\) | 16.0832 | 0.723615 | ||||||||
\(495\) | −2.40729 | −0.108199 | ||||||||
\(496\) | 1.63285 | 0.0733171 | ||||||||
\(497\) | 32.4037 | 1.45350 | ||||||||
\(498\) | −14.9414 | −0.669540 | ||||||||
\(499\) | 8.86921 | 0.397040 | 0.198520 | − | 0.980097i | \(-0.436386\pi\) | ||||
0.198520 | + | 0.980097i | \(0.436386\pi\) | |||||||
\(500\) | −10.9528 | −0.489823 | ||||||||
\(501\) | 9.22809 | 0.412280 | ||||||||
\(502\) | 19.2669 | 0.859925 | ||||||||
\(503\) | −19.4076 | −0.865343 | −0.432671 | − | 0.901552i | \(-0.642429\pi\) | ||||
−0.432671 | + | 0.901552i | \(0.642429\pi\) | |||||||
\(504\) | −19.2655 | −0.858155 | ||||||||
\(505\) | −1.15689 | −0.0514807 | ||||||||
\(506\) | 123.129 | 5.47373 | ||||||||
\(507\) | 11.7409 | 0.521431 | ||||||||
\(508\) | −3.69638 | −0.164000 | ||||||||
\(509\) | 16.8751 | 0.747976 | 0.373988 | − | 0.927434i | \(-0.377990\pi\) | ||||
0.373988 | + | 0.927434i | \(0.377990\pi\) | |||||||
\(510\) | 4.20392 | 0.186153 | ||||||||
\(511\) | −17.7456 | −0.785019 | ||||||||
\(512\) | 45.3092 | 2.00240 | ||||||||
\(513\) | 19.4169 | 0.857278 | ||||||||
\(514\) | 63.1421 | 2.78508 | ||||||||
\(515\) | 4.45536 | 0.196327 | ||||||||
\(516\) | −32.2442 | −1.41947 | ||||||||
\(517\) | −58.3541 | −2.56641 | ||||||||
\(518\) | −9.58445 | −0.421116 | ||||||||
\(519\) | −10.9796 | −0.481952 | ||||||||
\(520\) | 2.61230 | 0.114557 | ||||||||
\(521\) | −33.8774 | −1.48420 | −0.742098 | − | 0.670291i | \(-0.766169\pi\) | ||||
−0.742098 | + | 0.670291i | \(0.766169\pi\) | |||||||
\(522\) | −26.9656 | −1.18025 | ||||||||
\(523\) | 19.0930 | 0.834878 | 0.417439 | − | 0.908705i | \(-0.362928\pi\) | ||||
0.417439 | + | 0.908705i | \(0.362928\pi\) | |||||||
\(524\) | −20.8155 | −0.909329 | ||||||||
\(525\) | −14.2561 | −0.622188 | ||||||||
\(526\) | 41.2410 | 1.79819 | ||||||||
\(527\) | 1.71045 | 0.0745084 | ||||||||
\(528\) | −36.6336 | −1.59427 | ||||||||
\(529\) | 45.2317 | 1.96660 | ||||||||
\(530\) | −6.17525 | −0.268236 | ||||||||
\(531\) | −13.3234 | −0.578185 | ||||||||
\(532\) | −34.8314 | −1.51013 | ||||||||
\(533\) | −15.5531 | −0.673681 | ||||||||
\(534\) | 38.2757 | 1.65635 | ||||||||
\(535\) | −4.45746 | −0.192713 | ||||||||
\(536\) | 77.4161 | 3.34386 | ||||||||
\(537\) | 6.32887 | 0.273111 | ||||||||
\(538\) | −34.7270 | −1.49719 | ||||||||
\(539\) | −8.26193 | −0.355866 | ||||||||
\(540\) | 6.07019 | 0.261219 | ||||||||
\(541\) | −36.2281 | −1.55757 | −0.778783 | − | 0.627294i | \(-0.784163\pi\) | ||||
−0.778783 | + | 0.627294i | \(0.784163\pi\) | |||||||
\(542\) | 25.2407 | 1.08418 | ||||||||
\(543\) | −12.8231 | −0.550292 | ||||||||
\(544\) | −8.81725 | −0.378036 | ||||||||
\(545\) | −1.07600 | −0.0460907 | ||||||||
\(546\) | 13.1820 | 0.564139 | ||||||||
\(547\) | −15.9910 | −0.683727 | −0.341864 | − | 0.939750i | \(-0.611058\pi\) | ||||
−0.341864 | + | 0.939750i | \(0.611058\pi\) | |||||||
\(548\) | −16.3934 | −0.700292 | ||||||||
\(549\) | 1.18172 | 0.0504346 | ||||||||
\(550\) | 73.4842 | 3.13338 | ||||||||
\(551\) | −25.3297 | −1.07908 | ||||||||
\(552\) | −54.0812 | −2.30185 | ||||||||
\(553\) | −23.8358 | −1.01360 | ||||||||
\(554\) | 12.1917 | 0.517976 | ||||||||
\(555\) | 0.526019 | 0.0223282 | ||||||||
\(556\) | 83.3798 | 3.53609 | ||||||||
\(557\) | −1.22214 | −0.0517836 | −0.0258918 | − | 0.999665i | \(-0.508243\pi\) | ||||
−0.0258918 | + | 0.999665i | \(0.508243\pi\) | |||||||
\(558\) | 1.22584 | 0.0518939 | ||||||||
\(559\) | −11.6637 | −0.493324 | ||||||||
\(560\) | −3.14396 | −0.132857 | ||||||||
\(561\) | −38.3746 | −1.62018 | ||||||||
\(562\) | 39.6968 | 1.67451 | ||||||||
\(563\) | 33.9167 | 1.42942 | 0.714709 | − | 0.699421i | \(-0.246559\pi\) | ||||
0.714709 | + | 0.699421i | \(0.246559\pi\) | |||||||
\(564\) | 49.3320 | 2.07725 | ||||||||
\(565\) | −2.50922 | −0.105564 | ||||||||
\(566\) | −70.7991 | −2.97591 | ||||||||
\(567\) | 5.14984 | 0.216273 | ||||||||
\(568\) | 73.3625 | 3.07822 | ||||||||
\(569\) | −12.5611 | −0.526588 | −0.263294 | − | 0.964716i | \(-0.584809\pi\) | ||||
−0.263294 | + | 0.964716i | \(0.584809\pi\) | |||||||
\(570\) | 2.83008 | 0.118539 | ||||||||
\(571\) | 44.8390 | 1.87645 | 0.938227 | − | 0.346019i | \(-0.112467\pi\) | ||||
0.938227 | + | 0.346019i | \(0.112467\pi\) | |||||||
\(572\) | −45.8968 | −1.91904 | ||||||||
\(573\) | 2.64729 | 0.110592 | ||||||||
\(574\) | 49.8667 | 2.08140 | ||||||||
\(575\) | 40.7213 | 1.69820 | ||||||||
\(576\) | 8.82126 | 0.367552 | ||||||||
\(577\) | −24.1099 | −1.00371 | −0.501853 | − | 0.864953i | \(-0.667348\pi\) | ||||
−0.501853 | + | 0.864953i | \(0.667348\pi\) | |||||||
\(578\) | −25.9883 | −1.08097 | ||||||||
\(579\) | 19.9166 | 0.827704 | ||||||||
\(580\) | −7.91868 | −0.328805 | ||||||||
\(581\) | 11.7052 | 0.485612 | ||||||||
\(582\) | −24.4984 | −1.01549 | ||||||||
\(583\) | 56.3695 | 2.33458 | ||||||||
\(584\) | −40.1763 | −1.66251 | ||||||||
\(585\) | 0.736159 | 0.0304364 | ||||||||
\(586\) | 63.8973 | 2.63957 | ||||||||
\(587\) | −2.66685 | −0.110073 | −0.0550363 | − | 0.998484i | \(-0.517527\pi\) | ||||
−0.0550363 | + | 0.998484i | \(0.517527\pi\) | |||||||
\(588\) | 6.98455 | 0.288038 | ||||||||
\(589\) | 1.15147 | 0.0474457 | ||||||||
\(590\) | −5.79228 | −0.238464 | ||||||||
\(591\) | 11.8230 | 0.486335 | ||||||||
\(592\) | −8.14532 | −0.334770 | ||||||||
\(593\) | −7.19207 | −0.295343 | −0.147672 | − | 0.989036i | \(-0.547178\pi\) | ||||
−0.147672 | + | 0.989036i | \(0.547178\pi\) | |||||||
\(594\) | −82.0321 | −3.36582 | ||||||||
\(595\) | −3.29338 | −0.135015 | ||||||||
\(596\) | 92.6918 | 3.79680 | ||||||||
\(597\) | 16.7106 | 0.683921 | ||||||||
\(598\) | −37.6532 | −1.53976 | ||||||||
\(599\) | −43.1837 | −1.76444 | −0.882218 | − | 0.470841i | \(-0.843951\pi\) | ||||
−0.882218 | + | 0.470841i | \(0.843951\pi\) | |||||||
\(600\) | −32.2761 | −1.31767 | ||||||||
\(601\) | −23.9680 | −0.977676 | −0.488838 | − | 0.872375i | \(-0.662579\pi\) | ||||
−0.488838 | + | 0.872375i | \(0.662579\pi\) | |||||||
\(602\) | 37.3965 | 1.52417 | ||||||||
\(603\) | 21.8162 | 0.888425 | ||||||||
\(604\) | −13.8891 | −0.565140 | ||||||||
\(605\) | 6.63859 | 0.269897 | ||||||||
\(606\) | −13.2169 | −0.536900 | ||||||||
\(607\) | 13.9887 | 0.567782 | 0.283891 | − | 0.958856i | \(-0.408375\pi\) | ||||
0.283891 | + | 0.958856i | \(0.408375\pi\) | |||||||
\(608\) | −5.93576 | −0.240727 | ||||||||
\(609\) | −20.7607 | −0.841266 | ||||||||
\(610\) | 0.513748 | 0.0208011 | ||||||||
\(611\) | 17.8449 | 0.721929 | ||||||||
\(612\) | −33.0108 | −1.33438 | ||||||||
\(613\) | −42.4272 | −1.71362 | −0.856810 | − | 0.515632i | \(-0.827557\pi\) | ||||
−0.856810 | + | 0.515632i | \(0.827557\pi\) | |||||||
\(614\) | 1.34333 | 0.0542122 | ||||||||
\(615\) | −2.73681 | −0.110359 | ||||||||
\(616\) | 76.4549 | 3.08046 | ||||||||
\(617\) | −43.5957 | −1.75510 | −0.877548 | − | 0.479489i | \(-0.840822\pi\) | ||||
−0.877548 | + | 0.479489i | \(0.840822\pi\) | |||||||
\(618\) | 50.9005 | 2.04752 | ||||||||
\(619\) | 38.5008 | 1.54748 | 0.773739 | − | 0.633504i | \(-0.218384\pi\) | ||||
0.773739 | + | 0.633504i | \(0.218384\pi\) | |||||||
\(620\) | 0.359978 | 0.0144571 | ||||||||
\(621\) | −45.4581 | −1.82417 | ||||||||
\(622\) | 8.01259 | 0.321276 | ||||||||
\(623\) | −29.9854 | −1.20134 | ||||||||
\(624\) | 11.2027 | 0.448467 | ||||||||
\(625\) | 23.9518 | 0.958071 | ||||||||
\(626\) | 36.5919 | 1.46251 | ||||||||
\(627\) | −25.8337 | −1.03170 | ||||||||
\(628\) | 95.0236 | 3.79185 | ||||||||
\(629\) | −8.53242 | −0.340210 | ||||||||
\(630\) | −2.36028 | −0.0940360 | ||||||||
\(631\) | −10.2390 | −0.407609 | −0.203804 | − | 0.979012i | \(-0.565331\pi\) | ||||
−0.203804 | + | 0.979012i | \(0.565331\pi\) | |||||||
\(632\) | −53.9646 | −2.14660 | ||||||||
\(633\) | −11.5913 | −0.460715 | ||||||||
\(634\) | 25.3369 | 1.00626 | ||||||||
\(635\) | −0.235283 | −0.00933690 | ||||||||
\(636\) | −47.6542 | −1.88961 | ||||||||
\(637\) | 2.52653 | 0.100105 | ||||||||
\(638\) | 107.012 | 4.23667 | ||||||||
\(639\) | 20.6739 | 0.817847 | ||||||||
\(640\) | 4.72655 | 0.186833 | ||||||||
\(641\) | −21.8330 | −0.862353 | −0.431177 | − | 0.902268i | \(-0.641901\pi\) | ||||
−0.431177 | + | 0.902268i | \(0.641901\pi\) | |||||||
\(642\) | −50.9244 | −2.00983 | ||||||||
\(643\) | 20.0091 | 0.789083 | 0.394542 | − | 0.918878i | \(-0.370903\pi\) | ||||
0.394542 | + | 0.918878i | \(0.370903\pi\) | |||||||
\(644\) | 81.5460 | 3.21336 | ||||||||
\(645\) | −2.05241 | −0.0808137 | ||||||||
\(646\) | −45.9060 | −1.80615 | ||||||||
\(647\) | −15.7883 | −0.620701 | −0.310350 | − | 0.950622i | \(-0.600446\pi\) | ||||
−0.310350 | + | 0.950622i | \(0.600446\pi\) | |||||||
\(648\) | 11.6593 | 0.458022 | ||||||||
\(649\) | 52.8736 | 2.07547 | ||||||||
\(650\) | −22.4718 | −0.881416 | ||||||||
\(651\) | 0.943768 | 0.0369892 | ||||||||
\(652\) | 27.3803 | 1.07229 | ||||||||
\(653\) | 34.3250 | 1.34324 | 0.671620 | − | 0.740896i | \(-0.265599\pi\) | ||||
0.671620 | + | 0.740896i | \(0.265599\pi\) | |||||||
\(654\) | −12.2928 | −0.480686 | ||||||||
\(655\) | −1.32495 | −0.0517702 | ||||||||
\(656\) | 42.3791 | 1.65463 | ||||||||
\(657\) | −11.3219 | −0.441709 | ||||||||
\(658\) | −57.2147 | −2.23046 | ||||||||
\(659\) | −38.4005 | −1.49587 | −0.747935 | − | 0.663772i | \(-0.768954\pi\) | ||||
−0.747935 | + | 0.663772i | \(0.768954\pi\) | |||||||
\(660\) | −8.07624 | −0.314367 | ||||||||
\(661\) | −21.8838 | −0.851180 | −0.425590 | − | 0.904916i | \(-0.639933\pi\) | ||||
−0.425590 | + | 0.904916i | \(0.639933\pi\) | |||||||
\(662\) | −6.65100 | −0.258499 | ||||||||
\(663\) | 11.7351 | 0.455754 | ||||||||
\(664\) | 26.5007 | 1.02843 | ||||||||
\(665\) | −2.21710 | −0.0859754 | ||||||||
\(666\) | −6.11498 | −0.236951 | ||||||||
\(667\) | 59.3010 | 2.29614 | ||||||||
\(668\) | −31.5027 | −1.21888 | ||||||||
\(669\) | −18.8350 | −0.728202 | ||||||||
\(670\) | 9.48450 | 0.366418 | ||||||||
\(671\) | −4.68964 | −0.181042 | ||||||||
\(672\) | −4.86505 | −0.187674 | ||||||||
\(673\) | 17.9544 | 0.692090 | 0.346045 | − | 0.938218i | \(-0.387524\pi\) | ||||
0.346045 | + | 0.938218i | \(0.387524\pi\) | |||||||
\(674\) | 24.6205 | 0.948346 | ||||||||
\(675\) | −27.1298 | −1.04423 | ||||||||
\(676\) | −40.0809 | −1.54157 | ||||||||
\(677\) | −49.5603 | −1.90476 | −0.952379 | − | 0.304917i | \(-0.901371\pi\) | ||||
−0.952379 | + | 0.304917i | \(0.901371\pi\) | |||||||
\(678\) | −28.6667 | −1.10094 | ||||||||
\(679\) | 19.1922 | 0.736529 | ||||||||
\(680\) | −7.45626 | −0.285935 | ||||||||
\(681\) | −21.9366 | −0.840612 | ||||||||
\(682\) | −4.86472 | −0.186280 | ||||||||
\(683\) | 6.60277 | 0.252648 | 0.126324 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126324 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(684\) | −22.2228 | −0.849711 | ||||||||
\(685\) | −1.04348 | −0.0398692 | ||||||||
\(686\) | −49.3114 | −1.88272 | ||||||||
\(687\) | −9.05397 | −0.345431 | ||||||||
\(688\) | 31.7813 | 1.21165 | ||||||||
\(689\) | −17.2380 | −0.656717 | ||||||||
\(690\) | −6.62566 | −0.252235 | ||||||||
\(691\) | −26.4393 | −1.00580 | −0.502898 | − | 0.864346i | \(-0.667733\pi\) | ||||
−0.502898 | + | 0.864346i | \(0.667733\pi\) | |||||||
\(692\) | 37.4821 | 1.42485 | ||||||||
\(693\) | 21.5453 | 0.818440 | ||||||||
\(694\) | −54.1639 | −2.05603 | ||||||||
\(695\) | 5.30731 | 0.201318 | ||||||||
\(696\) | −47.0026 | −1.78163 | ||||||||
\(697\) | 44.3931 | 1.68151 | ||||||||
\(698\) | −15.1701 | −0.574197 | ||||||||
\(699\) | 6.69852 | 0.253361 | ||||||||
\(700\) | 48.6674 | 1.83945 | ||||||||
\(701\) | −28.4769 | −1.07556 | −0.537779 | − | 0.843086i | \(-0.680737\pi\) | ||||
−0.537779 | + | 0.843086i | \(0.680737\pi\) | |||||||
\(702\) | 25.0858 | 0.946802 | ||||||||
\(703\) | −5.74402 | −0.216640 | ||||||||
\(704\) | −35.0070 | −1.31938 | ||||||||
\(705\) | 3.14009 | 0.118263 | ||||||||
\(706\) | 31.5143 | 1.18606 | ||||||||
\(707\) | 10.3542 | 0.389409 | ||||||||
\(708\) | −44.6988 | −1.67988 | ||||||||
\(709\) | −4.21519 | −0.158305 | −0.0791524 | − | 0.996863i | \(-0.525221\pi\) | ||||
−0.0791524 | + | 0.996863i | \(0.525221\pi\) | |||||||
\(710\) | 8.98789 | 0.337309 | ||||||||
\(711\) | −15.2075 | −0.570325 | ||||||||
\(712\) | −67.8875 | −2.54419 | ||||||||
\(713\) | −2.69579 | −0.100958 | ||||||||
\(714\) | −37.6253 | −1.40809 | ||||||||
\(715\) | −2.92143 | −0.109255 | ||||||||
\(716\) | −21.6054 | −0.807432 | ||||||||
\(717\) | 7.72990 | 0.288678 | ||||||||
\(718\) | 6.03591 | 0.225258 | ||||||||
\(719\) | −12.1077 | −0.451542 | −0.225771 | − | 0.974180i | \(-0.572490\pi\) | ||||
−0.225771 | + | 0.974180i | \(0.572490\pi\) | |||||||
\(720\) | −2.00588 | −0.0747548 | ||||||||
\(721\) | −39.8758 | −1.48505 | ||||||||
\(722\) | 16.2636 | 0.605269 | ||||||||
\(723\) | 18.7270 | 0.696465 | ||||||||
\(724\) | 43.7753 | 1.62690 | ||||||||
\(725\) | 35.3914 | 1.31440 | ||||||||
\(726\) | 75.8428 | 2.81479 | ||||||||
\(727\) | −13.0624 | −0.484459 | −0.242230 | − | 0.970219i | \(-0.577879\pi\) | ||||
−0.242230 | + | 0.970219i | \(0.577879\pi\) | |||||||
\(728\) | −23.3802 | −0.866529 | ||||||||
\(729\) | 23.4177 | 0.867323 | ||||||||
\(730\) | −4.92214 | −0.182176 | ||||||||
\(731\) | 33.2917 | 1.23134 | ||||||||
\(732\) | 3.96457 | 0.146535 | ||||||||
\(733\) | −25.7839 | −0.952352 | −0.476176 | − | 0.879350i | \(-0.657977\pi\) | ||||
−0.476176 | + | 0.879350i | \(0.657977\pi\) | |||||||
\(734\) | 35.6595 | 1.31622 | ||||||||
\(735\) | 0.444582 | 0.0163987 | ||||||||
\(736\) | 13.8966 | 0.512235 | ||||||||
\(737\) | −86.5772 | −3.18911 | ||||||||
\(738\) | 31.8155 | 1.17115 | ||||||||
\(739\) | −46.9760 | −1.72804 | −0.864019 | − | 0.503458i | \(-0.832061\pi\) | ||||
−0.864019 | + | 0.503458i | \(0.832061\pi\) | |||||||
\(740\) | −1.79572 | −0.0660118 | ||||||||
\(741\) | 7.90007 | 0.290216 | ||||||||
\(742\) | 55.2688 | 2.02898 | ||||||||
\(743\) | −18.0135 | −0.660852 | −0.330426 | − | 0.943832i | \(-0.607192\pi\) | ||||
−0.330426 | + | 0.943832i | \(0.607192\pi\) | |||||||
\(744\) | 2.13671 | 0.0783355 | ||||||||
\(745\) | 5.90004 | 0.216161 | ||||||||
\(746\) | 53.0971 | 1.94402 | ||||||||
\(747\) | 7.46803 | 0.273241 | ||||||||
\(748\) | 131.003 | 4.78993 | ||||||||
\(749\) | 39.8945 | 1.45771 | ||||||||
\(750\) | −7.96482 | −0.290834 | ||||||||
\(751\) | 23.5472 | 0.859248 | 0.429624 | − | 0.903008i | \(-0.358646\pi\) | ||||
0.429624 | + | 0.903008i | \(0.358646\pi\) | |||||||
\(752\) | −48.6238 | −1.77313 | ||||||||
\(753\) | 9.46395 | 0.344885 | ||||||||
\(754\) | −32.7249 | −1.19177 | ||||||||
\(755\) | −0.884073 | −0.0321747 | ||||||||
\(756\) | −54.3285 | −1.97591 | ||||||||
\(757\) | 20.8393 | 0.757416 | 0.378708 | − | 0.925516i | \(-0.376368\pi\) | ||||
0.378708 | + | 0.925516i | \(0.376368\pi\) | |||||||
\(758\) | −45.7821 | −1.66288 | ||||||||
\(759\) | 60.4809 | 2.19532 | ||||||||
\(760\) | −5.01955 | −0.182078 | ||||||||
\(761\) | −0.0647869 | −0.00234852 | −0.00117426 | − | 0.999999i | \(-0.500374\pi\) | ||||
−0.00117426 | + | 0.999999i | \(0.500374\pi\) | |||||||
\(762\) | −2.68800 | −0.0973758 | ||||||||
\(763\) | 9.63024 | 0.348638 | ||||||||
\(764\) | −9.03730 | −0.326958 | ||||||||
\(765\) | −2.10121 | −0.0759694 | ||||||||
\(766\) | 29.2358 | 1.05633 | ||||||||
\(767\) | −16.1690 | −0.583828 | ||||||||
\(768\) | 39.7801 | 1.43544 | ||||||||
\(769\) | −23.7707 | −0.857192 | −0.428596 | − | 0.903496i | \(-0.640992\pi\) | ||||
−0.428596 | + | 0.903496i | \(0.640992\pi\) | |||||||
\(770\) | 9.36674 | 0.337554 | ||||||||
\(771\) | 31.0155 | 1.11700 | ||||||||
\(772\) | −67.9909 | −2.44705 | ||||||||
\(773\) | 28.8855 | 1.03894 | 0.519469 | − | 0.854489i | \(-0.326130\pi\) | ||||
0.519469 | + | 0.854489i | \(0.326130\pi\) | |||||||
\(774\) | 23.8594 | 0.857607 | ||||||||
\(775\) | −1.60887 | −0.0577923 | ||||||||
\(776\) | 43.4515 | 1.55982 | ||||||||
\(777\) | −4.70790 | −0.168895 | ||||||||
\(778\) | 70.7414 | 2.53620 | ||||||||
\(779\) | 29.8854 | 1.07076 | ||||||||
\(780\) | 2.46975 | 0.0884312 | ||||||||
\(781\) | −82.0440 | −2.93576 | ||||||||
\(782\) | 107.473 | 3.84323 | ||||||||
\(783\) | −39.5082 | −1.41191 | ||||||||
\(784\) | −6.88428 | −0.245867 | ||||||||
\(785\) | 6.04846 | 0.215879 | ||||||||
\(786\) | −15.1370 | −0.539918 | ||||||||
\(787\) | −2.84239 | −0.101320 | −0.0506602 | − | 0.998716i | \(-0.516133\pi\) | ||||
−0.0506602 | + | 0.998716i | \(0.516133\pi\) | |||||||
\(788\) | −40.3614 | −1.43781 | ||||||||
\(789\) | 20.2576 | 0.721191 | ||||||||
\(790\) | −6.61139 | −0.235223 | ||||||||
\(791\) | 22.4577 | 0.798503 | ||||||||
\(792\) | 48.7791 | 1.73329 | ||||||||
\(793\) | 1.43411 | 0.0509268 | ||||||||
\(794\) | 11.7719 | 0.417768 | ||||||||
\(795\) | −3.03329 | −0.107580 | ||||||||
\(796\) | −57.0466 | −2.02196 | ||||||||
\(797\) | 8.63802 | 0.305974 | 0.152987 | − | 0.988228i | \(-0.451111\pi\) | ||||
0.152987 | + | 0.988228i | \(0.451111\pi\) | |||||||
\(798\) | −25.3293 | −0.896649 | ||||||||
\(799\) | −50.9346 | −1.80194 | ||||||||
\(800\) | 8.29360 | 0.293223 | ||||||||
\(801\) | −19.1310 | −0.675961 | ||||||||
\(802\) | 74.7571 | 2.63977 | ||||||||
\(803\) | 44.9307 | 1.58557 | ||||||||
\(804\) | 73.1915 | 2.58126 | ||||||||
\(805\) | 5.19058 | 0.182944 | ||||||||
\(806\) | 1.48765 | 0.0524003 | ||||||||
\(807\) | −17.0579 | −0.600468 | ||||||||
\(808\) | 23.4421 | 0.824689 | ||||||||
\(809\) | 45.1019 | 1.58570 | 0.792850 | − | 0.609417i | \(-0.208597\pi\) | ||||
0.792850 | + | 0.609417i | \(0.208597\pi\) | |||||||
\(810\) | 1.42842 | 0.0501897 | ||||||||
\(811\) | 6.00101 | 0.210724 | 0.105362 | − | 0.994434i | \(-0.466400\pi\) | ||||
0.105362 | + | 0.994434i | \(0.466400\pi\) | |||||||
\(812\) | 70.8726 | 2.48714 | ||||||||
\(813\) | 12.3983 | 0.434827 | ||||||||
\(814\) | 24.2672 | 0.850565 | ||||||||
\(815\) | 1.74281 | 0.0610481 | ||||||||
\(816\) | −31.9758 | −1.11938 | ||||||||
\(817\) | 22.4119 | 0.784094 | ||||||||
\(818\) | −22.4001 | −0.783201 | ||||||||
\(819\) | −6.58866 | −0.230226 | ||||||||
\(820\) | 9.34289 | 0.326268 | ||||||||
\(821\) | −22.3234 | −0.779093 | −0.389547 | − | 0.921007i | \(-0.627368\pi\) | ||||
−0.389547 | + | 0.921007i | \(0.627368\pi\) | |||||||
\(822\) | −11.9212 | −0.415801 | ||||||||
\(823\) | −47.5203 | −1.65645 | −0.828226 | − | 0.560394i | \(-0.810650\pi\) | ||||
−0.828226 | + | 0.560394i | \(0.810650\pi\) | |||||||
\(824\) | −90.2794 | −3.14503 | ||||||||
\(825\) | 36.0956 | 1.25669 | ||||||||
\(826\) | 51.8412 | 1.80379 | ||||||||
\(827\) | 7.41373 | 0.257801 | 0.128900 | − | 0.991658i | \(-0.458855\pi\) | ||||
0.128900 | + | 0.991658i | \(0.458855\pi\) | |||||||
\(828\) | 52.0272 | 1.80807 | ||||||||
\(829\) | 44.7893 | 1.55560 | 0.777798 | − | 0.628514i | \(-0.216337\pi\) | ||||
0.777798 | + | 0.628514i | \(0.216337\pi\) | |||||||
\(830\) | 3.24669 | 0.112694 | ||||||||
\(831\) | 5.98858 | 0.207742 | ||||||||
\(832\) | 10.7053 | 0.371139 | ||||||||
\(833\) | −7.21145 | −0.249862 | ||||||||
\(834\) | 60.6336 | 2.09957 | ||||||||
\(835\) | −2.00522 | −0.0693934 | ||||||||
\(836\) | 88.1909 | 3.05015 | ||||||||
\(837\) | 1.79602 | 0.0620795 | ||||||||
\(838\) | 47.5713 | 1.64332 | ||||||||
\(839\) | 18.3082 | 0.632071 | 0.316035 | − | 0.948747i | \(-0.397648\pi\) | ||||
0.316035 | + | 0.948747i | \(0.397648\pi\) | |||||||
\(840\) | −4.11411 | −0.141950 | ||||||||
\(841\) | 22.5392 | 0.777214 | ||||||||
\(842\) | −12.1258 | −0.417881 | ||||||||
\(843\) | 19.4991 | 0.671585 | ||||||||
\(844\) | 39.5704 | 1.36207 | ||||||||
\(845\) | −2.55124 | −0.0877653 | ||||||||
\(846\) | −36.5036 | −1.25502 | ||||||||
\(847\) | −59.4157 | −2.04155 | ||||||||
\(848\) | 46.9701 | 1.61296 | ||||||||
\(849\) | −34.7766 | −1.19353 | ||||||||
\(850\) | 64.1410 | 2.20002 | ||||||||
\(851\) | 13.4477 | 0.460980 | ||||||||
\(852\) | 69.3591 | 2.37620 | ||||||||
\(853\) | 39.4987 | 1.35241 | 0.676205 | − | 0.736713i | \(-0.263623\pi\) | ||||
0.676205 | + | 0.736713i | \(0.263623\pi\) | |||||||
\(854\) | −4.59807 | −0.157343 | ||||||||
\(855\) | −1.41453 | −0.0483760 | ||||||||
\(856\) | 90.3218 | 3.08714 | ||||||||
\(857\) | 5.44390 | 0.185960 | 0.0929801 | − | 0.995668i | \(-0.470361\pi\) | ||||
0.0929801 | + | 0.995668i | \(0.470361\pi\) | |||||||
\(858\) | −33.3760 | −1.13944 | ||||||||
\(859\) | 13.3333 | 0.454926 | 0.227463 | − | 0.973787i | \(-0.426957\pi\) | ||||
0.227463 | + | 0.973787i | \(0.426957\pi\) | |||||||
\(860\) | 7.00650 | 0.238920 | ||||||||
\(861\) | 24.4946 | 0.834774 | ||||||||
\(862\) | −49.9913 | −1.70271 | ||||||||
\(863\) | 25.8321 | 0.879334 | 0.439667 | − | 0.898161i | \(-0.355096\pi\) | ||||
0.439667 | + | 0.898161i | \(0.355096\pi\) | |||||||
\(864\) | −9.25834 | −0.314975 | ||||||||
\(865\) | 2.38582 | 0.0811202 | ||||||||
\(866\) | 37.7549 | 1.28296 | ||||||||
\(867\) | −12.7655 | −0.433538 | ||||||||
\(868\) | −3.22182 | −0.109356 | ||||||||
\(869\) | 60.3506 | 2.04726 | ||||||||
\(870\) | −5.75844 | −0.195229 | ||||||||
\(871\) | 26.4757 | 0.897094 | ||||||||
\(872\) | 21.8030 | 0.738344 | ||||||||
\(873\) | 12.2448 | 0.414425 | ||||||||
\(874\) | 72.3509 | 2.44731 | ||||||||
\(875\) | 6.23969 | 0.210940 | ||||||||
\(876\) | −37.9839 | −1.28336 | ||||||||
\(877\) | −39.9734 | −1.34981 | −0.674903 | − | 0.737907i | \(-0.735814\pi\) | ||||
−0.674903 | + | 0.737907i | \(0.735814\pi\) | |||||||
\(878\) | −22.4121 | −0.756371 | ||||||||
\(879\) | 31.3865 | 1.05864 | ||||||||
\(880\) | 7.96030 | 0.268342 | ||||||||
\(881\) | 1.08796 | 0.0366542 | 0.0183271 | − | 0.999832i | \(-0.494166\pi\) | ||||
0.0183271 | + | 0.999832i | \(0.494166\pi\) | |||||||
\(882\) | −5.16828 | −0.174025 | ||||||||
\(883\) | 3.54749 | 0.119383 | 0.0596913 | − | 0.998217i | \(-0.480988\pi\) | ||||
0.0596913 | + | 0.998217i | \(0.480988\pi\) | |||||||
\(884\) | −40.0612 | −1.34740 | ||||||||
\(885\) | −2.84518 | −0.0956396 | ||||||||
\(886\) | −77.5959 | −2.60689 | ||||||||
\(887\) | 33.1529 | 1.11317 | 0.556583 | − | 0.830792i | \(-0.312112\pi\) | ||||
0.556583 | + | 0.830792i | \(0.312112\pi\) | |||||||
\(888\) | −10.6588 | −0.357685 | ||||||||
\(889\) | 2.10579 | 0.0706260 | ||||||||
\(890\) | −8.31712 | −0.278791 | ||||||||
\(891\) | −13.0391 | −0.436825 | ||||||||
\(892\) | 64.2986 | 2.15288 | ||||||||
\(893\) | −34.2891 | −1.14744 | ||||||||
\(894\) | 67.4053 | 2.25437 | ||||||||
\(895\) | −1.37523 | −0.0459690 | ||||||||
\(896\) | −42.3029 | −1.41324 | ||||||||
\(897\) | −18.4953 | −0.617541 | ||||||||
\(898\) | 63.9581 | 2.13431 | ||||||||
\(899\) | −2.34294 | −0.0781414 | ||||||||
\(900\) | 31.0503 | 1.03501 | ||||||||
\(901\) | 49.2023 | 1.63917 | ||||||||
\(902\) | −126.259 | −4.20397 | ||||||||
\(903\) | 18.3692 | 0.611289 | ||||||||
\(904\) | 50.8446 | 1.69107 | ||||||||
\(905\) | 2.78640 | 0.0926230 | ||||||||
\(906\) | −10.1001 | −0.335554 | ||||||||
\(907\) | −33.3094 | −1.10602 | −0.553009 | − | 0.833175i | \(-0.686521\pi\) | ||||
−0.553009 | + | 0.833175i | \(0.686521\pi\) | |||||||
\(908\) | 74.8869 | 2.48521 | ||||||||
\(909\) | 6.60609 | 0.219110 | ||||||||
\(910\) | −2.86439 | −0.0949536 | ||||||||
\(911\) | −13.4263 | −0.444832 | −0.222416 | − | 0.974952i | \(-0.571394\pi\) | ||||
−0.222416 | + | 0.974952i | \(0.571394\pi\) | |||||||
\(912\) | −21.5261 | −0.712799 | ||||||||
\(913\) | −29.6367 | −0.980832 | ||||||||
\(914\) | 48.8437 | 1.61560 | ||||||||
\(915\) | 0.252354 | 0.00834256 | ||||||||
\(916\) | 30.9083 | 1.02124 | ||||||||
\(917\) | 11.8584 | 0.391599 | ||||||||
\(918\) | −71.6021 | −2.36322 | ||||||||
\(919\) | −26.9017 | −0.887405 | −0.443703 | − | 0.896174i | \(-0.646335\pi\) | ||||
−0.443703 | + | 0.896174i | \(0.646335\pi\) | |||||||
\(920\) | 11.7516 | 0.387438 | ||||||||
\(921\) | 0.659844 | 0.0217426 | ||||||||
\(922\) | −40.1649 | −1.32276 | ||||||||
\(923\) | 25.0894 | 0.825828 | ||||||||
\(924\) | 72.2828 | 2.37793 | ||||||||
\(925\) | 8.02569 | 0.263883 | ||||||||
\(926\) | 65.8422 | 2.16371 | ||||||||
\(927\) | −25.4412 | −0.835598 | ||||||||
\(928\) | 12.0777 | 0.396469 | ||||||||
\(929\) | −30.6354 | −1.00512 | −0.502558 | − | 0.864543i | \(-0.667608\pi\) | ||||
−0.502558 | + | 0.864543i | \(0.667608\pi\) | |||||||
\(930\) | 0.261775 | 0.00858394 | ||||||||
\(931\) | −4.85475 | −0.159108 | ||||||||
\(932\) | −22.8673 | −0.749044 | ||||||||
\(933\) | 3.93580 | 0.128852 | ||||||||
\(934\) | 52.9096 | 1.73126 | ||||||||
\(935\) | 8.33861 | 0.272702 | ||||||||
\(936\) | −14.9168 | −0.487572 | ||||||||
\(937\) | 31.5800 | 1.03167 | 0.515837 | − | 0.856686i | \(-0.327481\pi\) | ||||
0.515837 | + | 0.856686i | \(0.327481\pi\) | |||||||
\(938\) | −84.8868 | −2.77165 | ||||||||
\(939\) | 17.9740 | 0.586559 | ||||||||
\(940\) | −10.7196 | −0.349635 | ||||||||
\(941\) | −9.97044 | −0.325027 | −0.162513 | − | 0.986706i | \(-0.551960\pi\) | ||||
−0.162513 | + | 0.986706i | \(0.551960\pi\) | |||||||
\(942\) | 69.1009 | 2.25143 | ||||||||
\(943\) | −69.9666 | −2.27843 | ||||||||
\(944\) | 44.0571 | 1.43394 | ||||||||
\(945\) | −3.45813 | −0.112493 | ||||||||
\(946\) | −94.6854 | −3.07849 | ||||||||
\(947\) | 45.3892 | 1.47495 | 0.737476 | − | 0.675373i | \(-0.236017\pi\) | ||||
0.737476 | + | 0.675373i | \(0.236017\pi\) | |||||||
\(948\) | −51.0198 | −1.65705 | ||||||||
\(949\) | −13.7400 | −0.446019 | ||||||||
\(950\) | 43.1797 | 1.40093 | ||||||||
\(951\) | 12.4455 | 0.403575 | ||||||||
\(952\) | 66.7339 | 2.16286 | ||||||||
\(953\) | −41.2142 | −1.33506 | −0.667529 | − | 0.744584i | \(-0.732648\pi\) | ||||
−0.667529 | + | 0.744584i | \(0.732648\pi\) | |||||||
\(954\) | 35.2621 | 1.14165 | ||||||||
\(955\) | −0.575244 | −0.0186145 | ||||||||
\(956\) | −26.3882 | −0.853456 | ||||||||
\(957\) | 52.5647 | 1.69918 | ||||||||
\(958\) | 49.8026 | 1.60905 | ||||||||
\(959\) | 9.33917 | 0.301578 | ||||||||
\(960\) | 1.88376 | 0.0607981 | ||||||||
\(961\) | −30.8935 | −0.996564 | ||||||||
\(962\) | −7.42101 | −0.239263 | ||||||||
\(963\) | 25.4531 | 0.820215 | ||||||||
\(964\) | −63.9300 | −2.05905 | ||||||||
\(965\) | −4.32777 | −0.139316 | ||||||||
\(966\) | 59.3000 | 1.90795 | ||||||||
\(967\) | −13.0625 | −0.420060 | −0.210030 | − | 0.977695i | \(-0.567356\pi\) | ||||
−0.210030 | + | 0.977695i | \(0.567356\pi\) | |||||||
\(968\) | −134.518 | −4.32358 | ||||||||
\(969\) | −22.5491 | −0.724381 | ||||||||
\(970\) | 5.32339 | 0.170924 | ||||||||
\(971\) | −12.3999 | −0.397933 | −0.198966 | − | 0.980006i | \(-0.563758\pi\) | ||||
−0.198966 | + | 0.980006i | \(0.563758\pi\) | |||||||
\(972\) | −57.7035 | −1.85084 | ||||||||
\(973\) | −47.5007 | −1.52280 | ||||||||
\(974\) | 54.3791 | 1.74242 | ||||||||
\(975\) | −11.0382 | −0.353505 | ||||||||
\(976\) | −3.90766 | −0.125081 | ||||||||
\(977\) | 45.0656 | 1.44178 | 0.720889 | − | 0.693051i | \(-0.243734\pi\) | ||||
0.720889 | + | 0.693051i | \(0.243734\pi\) | |||||||
\(978\) | 19.9109 | 0.636679 | ||||||||
\(979\) | 75.9211 | 2.42645 | ||||||||
\(980\) | −1.51771 | −0.0484814 | ||||||||
\(981\) | 6.14420 | 0.196169 | ||||||||
\(982\) | 59.5409 | 1.90003 | ||||||||
\(983\) | 48.2994 | 1.54051 | 0.770256 | − | 0.637735i | \(-0.220129\pi\) | ||||
0.770256 | + | 0.637735i | \(0.220129\pi\) | |||||||
\(984\) | 55.4563 | 1.76788 | ||||||||
\(985\) | −2.56909 | −0.0818580 | ||||||||
\(986\) | 93.4063 | 2.97466 | ||||||||
\(987\) | −28.1040 | −0.894559 | ||||||||
\(988\) | −26.9692 | −0.858003 | ||||||||
\(989\) | −52.4699 | −1.66845 | ||||||||
\(990\) | 5.97608 | 0.189932 | ||||||||
\(991\) | −12.0213 | −0.381868 | −0.190934 | − | 0.981603i | \(-0.561152\pi\) | ||||
−0.190934 | + | 0.981603i | \(0.561152\pi\) | |||||||
\(992\) | −0.549044 | −0.0174322 | ||||||||
\(993\) | −3.26698 | −0.103675 | ||||||||
\(994\) | −80.4421 | −2.55147 | ||||||||
\(995\) | −3.63114 | −0.115115 | ||||||||
\(996\) | 25.0546 | 0.793885 | ||||||||
\(997\) | −14.1684 | −0.448717 | −0.224359 | − | 0.974507i | \(-0.572029\pi\) | ||||
−0.224359 | + | 0.974507i | \(0.572029\pi\) | |||||||
\(998\) | −22.0178 | −0.696961 | ||||||||
\(999\) | −8.95926 | −0.283459 |
(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 | 4027.2.a.b.1.16 | ✓ | 159 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4027.2.a.b.1.16 | ✓ | 159 | 1.1 | even | 1 | trivial |