Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, 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("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.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: | \(64.0879326623\) |
Analytic rank: | \(0\) |
Dimension: | \(86\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.06398 | −1.19164 | −0.595819 | − | 0.803119i | \(-0.703172\pi\) | ||||
−0.595819 | + | 0.803119i | \(0.703172\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.63652 | −0.731874 | −0.365937 | − | 0.930640i | \(-0.619251\pi\) | ||||
−0.365937 | + | 0.930640i | \(0.619251\pi\) | |||||||
\(6\) | 2.06398 | 0.842615 | ||||||||
\(7\) | 0.580095 | 0.219255 | 0.109628 | − | 0.993973i | \(-0.465034\pi\) | ||||
0.109628 | + | 0.993973i | \(0.465034\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.26000 | 0.419999 | ||||||||
\(10\) | 1.63652 | 0.517513 | ||||||||
\(11\) | −3.54895 | −1.07005 | −0.535024 | − | 0.844837i | \(-0.679697\pi\) | ||||
−0.535024 | + | 0.844837i | \(0.679697\pi\) | |||||||
\(12\) | −2.06398 | −0.595819 | ||||||||
\(13\) | 0.886296 | 0.245814 | 0.122907 | − | 0.992418i | \(-0.460778\pi\) | ||||
0.122907 | + | 0.992418i | \(0.460778\pi\) | |||||||
\(14\) | −0.580095 | −0.155037 | ||||||||
\(15\) | 3.37774 | 0.872128 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 7.07655 | 1.71632 | 0.858158 | − | 0.513386i | \(-0.171609\pi\) | ||||
0.858158 | + | 0.513386i | \(0.171609\pi\) | |||||||
\(18\) | −1.26000 | −0.296984 | ||||||||
\(19\) | −7.35734 | −1.68789 | −0.843944 | − | 0.536431i | \(-0.819772\pi\) | ||||
−0.843944 | + | 0.536431i | \(0.819772\pi\) | |||||||
\(20\) | −1.63652 | −0.365937 | ||||||||
\(21\) | −1.19730 | −0.261273 | ||||||||
\(22\) | 3.54895 | 0.756638 | ||||||||
\(23\) | 0.578326 | 0.120589 | 0.0602946 | − | 0.998181i | \(-0.480796\pi\) | ||||
0.0602946 | + | 0.998181i | \(0.480796\pi\) | |||||||
\(24\) | 2.06398 | 0.421307 | ||||||||
\(25\) | −2.32181 | −0.464361 | ||||||||
\(26\) | −0.886296 | −0.173817 | ||||||||
\(27\) | 3.59132 | 0.691151 | ||||||||
\(28\) | 0.580095 | 0.109628 | ||||||||
\(29\) | −4.60362 | −0.854871 | −0.427435 | − | 0.904046i | \(-0.640583\pi\) | ||||
−0.427435 | + | 0.904046i | \(0.640583\pi\) | |||||||
\(30\) | −3.37774 | −0.616687 | ||||||||
\(31\) | −1.99169 | −0.357717 | −0.178859 | − | 0.983875i | \(-0.557240\pi\) | ||||
−0.178859 | + | 0.983875i | \(0.557240\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 7.32494 | 1.27511 | ||||||||
\(34\) | −7.07655 | −1.21362 | ||||||||
\(35\) | −0.949336 | −0.160467 | ||||||||
\(36\) | 1.26000 | 0.209999 | ||||||||
\(37\) | 10.0064 | 1.64504 | 0.822519 | − | 0.568737i | \(-0.192568\pi\) | ||||
0.822519 | + | 0.568737i | \(0.192568\pi\) | |||||||
\(38\) | 7.35734 | 1.19352 | ||||||||
\(39\) | −1.82929 | −0.292921 | ||||||||
\(40\) | 1.63652 | 0.258756 | ||||||||
\(41\) | −3.58380 | −0.559695 | −0.279847 | − | 0.960044i | \(-0.590284\pi\) | ||||
−0.279847 | + | 0.960044i | \(0.590284\pi\) | |||||||
\(42\) | 1.19730 | 0.184748 | ||||||||
\(43\) | 10.8843 | 1.65984 | 0.829921 | − | 0.557881i | \(-0.188385\pi\) | ||||
0.829921 | + | 0.557881i | \(0.188385\pi\) | |||||||
\(44\) | −3.54895 | −0.535024 | ||||||||
\(45\) | −2.06201 | −0.307386 | ||||||||
\(46\) | −0.578326 | −0.0852695 | ||||||||
\(47\) | −5.51320 | −0.804182 | −0.402091 | − | 0.915600i | \(-0.631717\pi\) | ||||
−0.402091 | + | 0.915600i | \(0.631717\pi\) | |||||||
\(48\) | −2.06398 | −0.297909 | ||||||||
\(49\) | −6.66349 | −0.951927 | ||||||||
\(50\) | 2.32181 | 0.328353 | ||||||||
\(51\) | −14.6058 | −2.04523 | ||||||||
\(52\) | 0.886296 | 0.122907 | ||||||||
\(53\) | −3.11553 | −0.427951 | −0.213975 | − | 0.976839i | \(-0.568641\pi\) | ||||
−0.213975 | + | 0.976839i | \(0.568641\pi\) | |||||||
\(54\) | −3.59132 | −0.488717 | ||||||||
\(55\) | 5.80792 | 0.783139 | ||||||||
\(56\) | −0.580095 | −0.0775185 | ||||||||
\(57\) | 15.1854 | 2.01135 | ||||||||
\(58\) | 4.60362 | 0.604485 | ||||||||
\(59\) | 0.556133 | 0.0724024 | 0.0362012 | − | 0.999345i | \(-0.488474\pi\) | ||||
0.0362012 | + | 0.999345i | \(0.488474\pi\) | |||||||
\(60\) | 3.37774 | 0.436064 | ||||||||
\(61\) | −14.0553 | −1.79959 | −0.899796 | − | 0.436312i | \(-0.856285\pi\) | ||||
−0.899796 | + | 0.436312i | \(0.856285\pi\) | |||||||
\(62\) | 1.99169 | 0.252944 | ||||||||
\(63\) | 0.730918 | 0.0920870 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.45044 | −0.179905 | ||||||||
\(66\) | −7.32494 | −0.901638 | ||||||||
\(67\) | 2.93561 | 0.358642 | 0.179321 | − | 0.983791i | \(-0.442610\pi\) | ||||
0.179321 | + | 0.983791i | \(0.442610\pi\) | |||||||
\(68\) | 7.07655 | 0.858158 | ||||||||
\(69\) | −1.19365 | −0.143699 | ||||||||
\(70\) | 0.949336 | 0.113467 | ||||||||
\(71\) | 4.80098 | 0.569772 | 0.284886 | − | 0.958561i | \(-0.408044\pi\) | ||||
0.284886 | + | 0.958561i | \(0.408044\pi\) | |||||||
\(72\) | −1.26000 | −0.148492 | ||||||||
\(73\) | −15.2142 | −1.78068 | −0.890342 | − | 0.455292i | \(-0.849535\pi\) | ||||
−0.890342 | + | 0.455292i | \(0.849535\pi\) | |||||||
\(74\) | −10.0064 | −1.16322 | ||||||||
\(75\) | 4.79215 | 0.553350 | ||||||||
\(76\) | −7.35734 | −0.843944 | ||||||||
\(77\) | −2.05873 | −0.234614 | ||||||||
\(78\) | 1.82929 | 0.207127 | ||||||||
\(79\) | −13.2416 | −1.48980 | −0.744900 | − | 0.667176i | \(-0.767503\pi\) | ||||
−0.744900 | + | 0.667176i | \(0.767503\pi\) | |||||||
\(80\) | −1.63652 | −0.182968 | ||||||||
\(81\) | −11.1924 | −1.24360 | ||||||||
\(82\) | 3.58380 | 0.395764 | ||||||||
\(83\) | 10.6332 | 1.16714 | 0.583571 | − | 0.812062i | \(-0.301655\pi\) | ||||
0.583571 | + | 0.812062i | \(0.301655\pi\) | |||||||
\(84\) | −1.19730 | −0.130636 | ||||||||
\(85\) | −11.5809 | −1.25613 | ||||||||
\(86\) | −10.8843 | −1.17369 | ||||||||
\(87\) | 9.50176 | 1.01870 | ||||||||
\(88\) | 3.54895 | 0.378319 | ||||||||
\(89\) | 4.67275 | 0.495311 | 0.247656 | − | 0.968848i | \(-0.420340\pi\) | ||||
0.247656 | + | 0.968848i | \(0.420340\pi\) | |||||||
\(90\) | 2.06201 | 0.217355 | ||||||||
\(91\) | 0.514136 | 0.0538961 | ||||||||
\(92\) | 0.578326 | 0.0602946 | ||||||||
\(93\) | 4.11079 | 0.426269 | ||||||||
\(94\) | 5.51320 | 0.568643 | ||||||||
\(95\) | 12.0404 | 1.23532 | ||||||||
\(96\) | 2.06398 | 0.210654 | ||||||||
\(97\) | −12.5355 | −1.27279 | −0.636394 | − | 0.771364i | \(-0.719575\pi\) | ||||
−0.636394 | + | 0.771364i | \(0.719575\pi\) | |||||||
\(98\) | 6.66349 | 0.673114 | ||||||||
\(99\) | −4.47166 | −0.449419 | ||||||||
\(100\) | −2.32181 | −0.232181 | ||||||||
\(101\) | 13.9965 | 1.39270 | 0.696350 | − | 0.717703i | \(-0.254806\pi\) | ||||
0.696350 | + | 0.717703i | \(0.254806\pi\) | |||||||
\(102\) | 14.6058 | 1.44619 | ||||||||
\(103\) | 12.6899 | 1.25037 | 0.625187 | − | 0.780475i | \(-0.285023\pi\) | ||||
0.625187 | + | 0.780475i | \(0.285023\pi\) | |||||||
\(104\) | −0.886296 | −0.0869084 | ||||||||
\(105\) | 1.95941 | 0.191219 | ||||||||
\(106\) | 3.11553 | 0.302607 | ||||||||
\(107\) | 18.0426 | 1.74425 | 0.872123 | − | 0.489287i | \(-0.162743\pi\) | ||||
0.872123 | + | 0.489287i | \(0.162743\pi\) | |||||||
\(108\) | 3.59132 | 0.345575 | ||||||||
\(109\) | 3.38255 | 0.323989 | 0.161995 | − | 0.986792i | \(-0.448207\pi\) | ||||
0.161995 | + | 0.986792i | \(0.448207\pi\) | |||||||
\(110\) | −5.80792 | −0.553763 | ||||||||
\(111\) | −20.6529 | −1.96029 | ||||||||
\(112\) | 0.580095 | 0.0548138 | ||||||||
\(113\) | −8.56600 | −0.805822 | −0.402911 | − | 0.915239i | \(-0.632002\pi\) | ||||
−0.402911 | + | 0.915239i | \(0.632002\pi\) | |||||||
\(114\) | −15.1854 | −1.42224 | ||||||||
\(115\) | −0.946441 | −0.0882561 | ||||||||
\(116\) | −4.60362 | −0.427435 | ||||||||
\(117\) | 1.11673 | 0.103242 | ||||||||
\(118\) | −0.556133 | −0.0511962 | ||||||||
\(119\) | 4.10507 | 0.376311 | ||||||||
\(120\) | −3.37774 | −0.308344 | ||||||||
\(121\) | 1.59501 | 0.145001 | ||||||||
\(122\) | 14.0553 | 1.27250 | ||||||||
\(123\) | 7.39687 | 0.666953 | ||||||||
\(124\) | −1.99169 | −0.178859 | ||||||||
\(125\) | 11.9823 | 1.07173 | ||||||||
\(126\) | −0.730918 | −0.0651153 | ||||||||
\(127\) | −15.2144 | −1.35006 | −0.675030 | − | 0.737790i | \(-0.735869\pi\) | ||||
−0.675030 | + | 0.737790i | \(0.735869\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −22.4650 | −1.97793 | ||||||||
\(130\) | 1.45044 | 0.127212 | ||||||||
\(131\) | −21.8752 | −1.91125 | −0.955623 | − | 0.294593i | \(-0.904816\pi\) | ||||
−0.955623 | + | 0.294593i | \(0.904816\pi\) | |||||||
\(132\) | 7.32494 | 0.637554 | ||||||||
\(133\) | −4.26795 | −0.370079 | ||||||||
\(134\) | −2.93561 | −0.253598 | ||||||||
\(135\) | −5.87727 | −0.505835 | ||||||||
\(136\) | −7.07655 | −0.606809 | ||||||||
\(137\) | −14.8111 | −1.26540 | −0.632699 | − | 0.774398i | \(-0.718053\pi\) | ||||
−0.632699 | + | 0.774398i | \(0.718053\pi\) | |||||||
\(138\) | 1.19365 | 0.101610 | ||||||||
\(139\) | 19.4273 | 1.64780 | 0.823901 | − | 0.566734i | \(-0.191793\pi\) | ||||
0.823901 | + | 0.566734i | \(0.191793\pi\) | |||||||
\(140\) | −0.949336 | −0.0802336 | ||||||||
\(141\) | 11.3791 | 0.958293 | ||||||||
\(142\) | −4.80098 | −0.402890 | ||||||||
\(143\) | −3.14542 | −0.263033 | ||||||||
\(144\) | 1.26000 | 0.105000 | ||||||||
\(145\) | 7.53391 | 0.625657 | ||||||||
\(146\) | 15.2142 | 1.25913 | ||||||||
\(147\) | 13.7533 | 1.13435 | ||||||||
\(148\) | 10.0064 | 0.822519 | ||||||||
\(149\) | −23.2174 | −1.90205 | −0.951023 | − | 0.309119i | \(-0.899966\pi\) | ||||
−0.951023 | + | 0.309119i | \(0.899966\pi\) | |||||||
\(150\) | −4.79215 | −0.391277 | ||||||||
\(151\) | 0.268548 | 0.0218542 | 0.0109271 | − | 0.999940i | \(-0.496522\pi\) | ||||
0.0109271 | + | 0.999940i | \(0.496522\pi\) | |||||||
\(152\) | 7.35734 | 0.596759 | ||||||||
\(153\) | 8.91643 | 0.720851 | ||||||||
\(154\) | 2.05873 | 0.165897 | ||||||||
\(155\) | 3.25943 | 0.261804 | ||||||||
\(156\) | −1.82929 | −0.146461 | ||||||||
\(157\) | −7.54517 | −0.602170 | −0.301085 | − | 0.953597i | \(-0.597349\pi\) | ||||
−0.301085 | + | 0.953597i | \(0.597349\pi\) | |||||||
\(158\) | 13.2416 | 1.05345 | ||||||||
\(159\) | 6.43037 | 0.509962 | ||||||||
\(160\) | 1.63652 | 0.129378 | ||||||||
\(161\) | 0.335484 | 0.0264398 | ||||||||
\(162\) | 11.1924 | 0.879358 | ||||||||
\(163\) | −19.8990 | −1.55861 | −0.779303 | − | 0.626647i | \(-0.784427\pi\) | ||||
−0.779303 | + | 0.626647i | \(0.784427\pi\) | |||||||
\(164\) | −3.58380 | −0.279847 | ||||||||
\(165\) | −11.9874 | −0.933218 | ||||||||
\(166\) | −10.6332 | −0.825295 | ||||||||
\(167\) | 20.0497 | 1.55149 | 0.775747 | − | 0.631044i | \(-0.217373\pi\) | ||||
0.775747 | + | 0.631044i | \(0.217373\pi\) | |||||||
\(168\) | 1.19730 | 0.0923739 | ||||||||
\(169\) | −12.2145 | −0.939575 | ||||||||
\(170\) | 11.5809 | 0.888215 | ||||||||
\(171\) | −9.27022 | −0.708912 | ||||||||
\(172\) | 10.8843 | 0.829921 | ||||||||
\(173\) | −5.82014 | −0.442497 | −0.221248 | − | 0.975217i | \(-0.571013\pi\) | ||||
−0.221248 | + | 0.975217i | \(0.571013\pi\) | |||||||
\(174\) | −9.50176 | −0.720327 | ||||||||
\(175\) | −1.34687 | −0.101814 | ||||||||
\(176\) | −3.54895 | −0.267512 | ||||||||
\(177\) | −1.14785 | −0.0862774 | ||||||||
\(178\) | −4.67275 | −0.350238 | ||||||||
\(179\) | −1.45393 | −0.108672 | −0.0543360 | − | 0.998523i | \(-0.517304\pi\) | ||||
−0.0543360 | + | 0.998523i | \(0.517304\pi\) | |||||||
\(180\) | −2.06201 | −0.153693 | ||||||||
\(181\) | −8.41969 | −0.625831 | −0.312915 | − | 0.949781i | \(-0.601306\pi\) | ||||
−0.312915 | + | 0.949781i | \(0.601306\pi\) | |||||||
\(182\) | −0.514136 | −0.0381103 | ||||||||
\(183\) | 29.0097 | 2.14446 | ||||||||
\(184\) | −0.578326 | −0.0426347 | ||||||||
\(185\) | −16.3756 | −1.20396 | ||||||||
\(186\) | −4.11079 | −0.301418 | ||||||||
\(187\) | −25.1143 | −1.83654 | ||||||||
\(188\) | −5.51320 | −0.402091 | ||||||||
\(189\) | 2.08331 | 0.151538 | ||||||||
\(190\) | −12.0404 | −0.873504 | ||||||||
\(191\) | −10.4040 | −0.752807 | −0.376403 | − | 0.926456i | \(-0.622839\pi\) | ||||
−0.376403 | + | 0.926456i | \(0.622839\pi\) | |||||||
\(192\) | −2.06398 | −0.148955 | ||||||||
\(193\) | 14.4951 | 1.04338 | 0.521688 | − | 0.853136i | \(-0.325302\pi\) | ||||
0.521688 | + | 0.853136i | \(0.325302\pi\) | |||||||
\(194\) | 12.5355 | 0.899997 | ||||||||
\(195\) | 2.99367 | 0.214381 | ||||||||
\(196\) | −6.66349 | −0.475964 | ||||||||
\(197\) | −2.10073 | −0.149671 | −0.0748355 | − | 0.997196i | \(-0.523843\pi\) | ||||
−0.0748355 | + | 0.997196i | \(0.523843\pi\) | |||||||
\(198\) | 4.47166 | 0.317787 | ||||||||
\(199\) | −8.51886 | −0.603886 | −0.301943 | − | 0.953326i | \(-0.597635\pi\) | ||||
−0.301943 | + | 0.953326i | \(0.597635\pi\) | |||||||
\(200\) | 2.32181 | 0.164176 | ||||||||
\(201\) | −6.05903 | −0.427371 | ||||||||
\(202\) | −13.9965 | −0.984787 | ||||||||
\(203\) | −2.67054 | −0.187435 | ||||||||
\(204\) | −14.6058 | −1.02261 | ||||||||
\(205\) | 5.86495 | 0.409626 | ||||||||
\(206\) | −12.6899 | −0.884147 | ||||||||
\(207\) | 0.728689 | 0.0506474 | ||||||||
\(208\) | 0.886296 | 0.0614536 | ||||||||
\(209\) | 26.1108 | 1.80612 | ||||||||
\(210\) | −1.95941 | −0.135212 | ||||||||
\(211\) | −6.01330 | −0.413972 | −0.206986 | − | 0.978344i | \(-0.566366\pi\) | ||||
−0.206986 | + | 0.978344i | \(0.566366\pi\) | |||||||
\(212\) | −3.11553 | −0.213975 | ||||||||
\(213\) | −9.90911 | −0.678961 | ||||||||
\(214\) | −18.0426 | −1.23337 | ||||||||
\(215\) | −17.8124 | −1.21479 | ||||||||
\(216\) | −3.59132 | −0.244359 | ||||||||
\(217\) | −1.15537 | −0.0784314 | ||||||||
\(218\) | −3.38255 | −0.229095 | ||||||||
\(219\) | 31.4017 | 2.12193 | ||||||||
\(220\) | 5.80792 | 0.391570 | ||||||||
\(221\) | 6.27192 | 0.421895 | ||||||||
\(222\) | 20.6529 | 1.38613 | ||||||||
\(223\) | 0.468926 | 0.0314016 | 0.0157008 | − | 0.999877i | \(-0.495002\pi\) | ||||
0.0157008 | + | 0.999877i | \(0.495002\pi\) | |||||||
\(224\) | −0.580095 | −0.0387592 | ||||||||
\(225\) | −2.92547 | −0.195031 | ||||||||
\(226\) | 8.56600 | 0.569802 | ||||||||
\(227\) | 26.4649 | 1.75654 | 0.878270 | − | 0.478166i | \(-0.158698\pi\) | ||||
0.878270 | + | 0.478166i | \(0.158698\pi\) | |||||||
\(228\) | 15.1854 | 1.00568 | ||||||||
\(229\) | 13.3509 | 0.882251 | 0.441126 | − | 0.897445i | \(-0.354579\pi\) | ||||
0.441126 | + | 0.897445i | \(0.354579\pi\) | |||||||
\(230\) | 0.946441 | 0.0624065 | ||||||||
\(231\) | 4.24916 | 0.279574 | ||||||||
\(232\) | 4.60362 | 0.302243 | ||||||||
\(233\) | −12.7064 | −0.832425 | −0.416212 | − | 0.909267i | \(-0.636643\pi\) | ||||
−0.416212 | + | 0.909267i | \(0.636643\pi\) | |||||||
\(234\) | −1.11673 | −0.0730029 | ||||||||
\(235\) | 9.02245 | 0.588560 | ||||||||
\(236\) | 0.556133 | 0.0362012 | ||||||||
\(237\) | 27.3304 | 1.77530 | ||||||||
\(238\) | −4.10507 | −0.266092 | ||||||||
\(239\) | 23.0565 | 1.49140 | 0.745701 | − | 0.666281i | \(-0.232115\pi\) | ||||
0.745701 | + | 0.666281i | \(0.232115\pi\) | |||||||
\(240\) | 3.37774 | 0.218032 | ||||||||
\(241\) | −23.1288 | −1.48986 | −0.744929 | − | 0.667144i | \(-0.767517\pi\) | ||||
−0.744929 | + | 0.667144i | \(0.767517\pi\) | |||||||
\(242\) | −1.59501 | −0.102531 | ||||||||
\(243\) | 12.3269 | 0.790769 | ||||||||
\(244\) | −14.0553 | −0.899796 | ||||||||
\(245\) | 10.9049 | 0.696690 | ||||||||
\(246\) | −7.39687 | −0.471607 | ||||||||
\(247\) | −6.52078 | −0.414907 | ||||||||
\(248\) | 1.99169 | 0.126472 | ||||||||
\(249\) | −21.9466 | −1.39081 | ||||||||
\(250\) | −11.9823 | −0.757826 | ||||||||
\(251\) | 6.45395 | 0.407370 | 0.203685 | − | 0.979037i | \(-0.434708\pi\) | ||||
0.203685 | + | 0.979037i | \(0.434708\pi\) | |||||||
\(252\) | 0.730918 | 0.0460435 | ||||||||
\(253\) | −2.05245 | −0.129036 | ||||||||
\(254\) | 15.2144 | 0.954636 | ||||||||
\(255\) | 23.9027 | 1.49685 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −14.8905 | −0.928844 | −0.464422 | − | 0.885614i | \(-0.653738\pi\) | ||||
−0.464422 | + | 0.885614i | \(0.653738\pi\) | |||||||
\(258\) | 22.4650 | 1.39861 | ||||||||
\(259\) | 5.80465 | 0.360683 | ||||||||
\(260\) | −1.45044 | −0.0899525 | ||||||||
\(261\) | −5.80055 | −0.359045 | ||||||||
\(262\) | 21.8752 | 1.35145 | ||||||||
\(263\) | −13.7096 | −0.845368 | −0.422684 | − | 0.906277i | \(-0.638912\pi\) | ||||
−0.422684 | + | 0.906277i | \(0.638912\pi\) | |||||||
\(264\) | −7.32494 | −0.450819 | ||||||||
\(265\) | 5.09862 | 0.313206 | ||||||||
\(266\) | 4.26795 | 0.261685 | ||||||||
\(267\) | −9.64445 | −0.590231 | ||||||||
\(268\) | 2.93561 | 0.179321 | ||||||||
\(269\) | −11.7222 | −0.714717 | −0.357358 | − | 0.933967i | \(-0.616322\pi\) | ||||
−0.357358 | + | 0.933967i | \(0.616322\pi\) | |||||||
\(270\) | 5.87727 | 0.357679 | ||||||||
\(271\) | 15.4815 | 0.940434 | 0.470217 | − | 0.882551i | \(-0.344176\pi\) | ||||
0.470217 | + | 0.882551i | \(0.344176\pi\) | |||||||
\(272\) | 7.07655 | 0.429079 | ||||||||
\(273\) | −1.06116 | −0.0642246 | ||||||||
\(274\) | 14.8111 | 0.894771 | ||||||||
\(275\) | 8.23996 | 0.496888 | ||||||||
\(276\) | −1.19365 | −0.0718493 | ||||||||
\(277\) | −30.0761 | −1.80710 | −0.903548 | − | 0.428488i | \(-0.859047\pi\) | ||||
−0.903548 | + | 0.428488i | \(0.859047\pi\) | |||||||
\(278\) | −19.4273 | −1.16517 | ||||||||
\(279\) | −2.50952 | −0.150241 | ||||||||
\(280\) | 0.949336 | 0.0567337 | ||||||||
\(281\) | 1.98841 | 0.118619 | 0.0593094 | − | 0.998240i | \(-0.481110\pi\) | ||||
0.0593094 | + | 0.998240i | \(0.481110\pi\) | |||||||
\(282\) | −11.3791 | −0.677616 | ||||||||
\(283\) | 29.9209 | 1.77861 | 0.889307 | − | 0.457311i | \(-0.151187\pi\) | ||||
0.889307 | + | 0.457311i | \(0.151187\pi\) | |||||||
\(284\) | 4.80098 | 0.284886 | ||||||||
\(285\) | −24.8511 | −1.47205 | ||||||||
\(286\) | 3.14542 | 0.185992 | ||||||||
\(287\) | −2.07894 | −0.122716 | ||||||||
\(288\) | −1.26000 | −0.0742460 | ||||||||
\(289\) | 33.0776 | 1.94574 | ||||||||
\(290\) | −7.53391 | −0.442407 | ||||||||
\(291\) | 25.8730 | 1.51670 | ||||||||
\(292\) | −15.2142 | −0.890342 | ||||||||
\(293\) | 11.1357 | 0.650556 | 0.325278 | − | 0.945619i | \(-0.394542\pi\) | ||||
0.325278 | + | 0.945619i | \(0.394542\pi\) | |||||||
\(294\) | −13.7533 | −0.802108 | ||||||||
\(295\) | −0.910123 | −0.0529894 | ||||||||
\(296\) | −10.0064 | −0.581609 | ||||||||
\(297\) | −12.7454 | −0.739564 | ||||||||
\(298\) | 23.2174 | 1.34495 | ||||||||
\(299\) | 0.512568 | 0.0296426 | ||||||||
\(300\) | 4.79215 | 0.276675 | ||||||||
\(301\) | 6.31394 | 0.363929 | ||||||||
\(302\) | −0.268548 | −0.0154532 | ||||||||
\(303\) | −28.8884 | −1.65959 | ||||||||
\(304\) | −7.35734 | −0.421972 | ||||||||
\(305\) | 23.0017 | 1.31707 | ||||||||
\(306\) | −8.91643 | −0.509718 | ||||||||
\(307\) | −18.5541 | −1.05894 | −0.529470 | − | 0.848329i | \(-0.677609\pi\) | ||||
−0.529470 | + | 0.848329i | \(0.677609\pi\) | |||||||
\(308\) | −2.05873 | −0.117307 | ||||||||
\(309\) | −26.1917 | −1.48999 | ||||||||
\(310\) | −3.25943 | −0.185123 | ||||||||
\(311\) | −6.98601 | −0.396140 | −0.198070 | − | 0.980188i | \(-0.563467\pi\) | ||||
−0.198070 | + | 0.980188i | \(0.563467\pi\) | |||||||
\(312\) | 1.82929 | 0.103563 | ||||||||
\(313\) | 5.17135 | 0.292302 | 0.146151 | − | 0.989262i | \(-0.453311\pi\) | ||||
0.146151 | + | 0.989262i | \(0.453311\pi\) | |||||||
\(314\) | 7.54517 | 0.425799 | ||||||||
\(315\) | −1.19616 | −0.0673960 | ||||||||
\(316\) | −13.2416 | −0.744900 | ||||||||
\(317\) | 8.51799 | 0.478418 | 0.239209 | − | 0.970968i | \(-0.423112\pi\) | ||||
0.239209 | + | 0.970968i | \(0.423112\pi\) | |||||||
\(318\) | −6.43037 | −0.360597 | ||||||||
\(319\) | 16.3380 | 0.914752 | ||||||||
\(320\) | −1.63652 | −0.0914842 | ||||||||
\(321\) | −37.2395 | −2.07851 | ||||||||
\(322\) | −0.335484 | −0.0186958 | ||||||||
\(323\) | −52.0646 | −2.89695 | ||||||||
\(324\) | −11.1924 | −0.621800 | ||||||||
\(325\) | −2.05781 | −0.114147 | ||||||||
\(326\) | 19.8990 | 1.10210 | ||||||||
\(327\) | −6.98150 | −0.386078 | ||||||||
\(328\) | 3.58380 | 0.197882 | ||||||||
\(329\) | −3.19818 | −0.176321 | ||||||||
\(330\) | 11.9874 | 0.659885 | ||||||||
\(331\) | 9.30553 | 0.511478 | 0.255739 | − | 0.966746i | \(-0.417681\pi\) | ||||
0.255739 | + | 0.966746i | \(0.417681\pi\) | |||||||
\(332\) | 10.6332 | 0.583571 | ||||||||
\(333\) | 12.6080 | 0.690914 | ||||||||
\(334\) | −20.0497 | −1.09707 | ||||||||
\(335\) | −4.80418 | −0.262480 | ||||||||
\(336\) | −1.19730 | −0.0653182 | ||||||||
\(337\) | −5.91973 | −0.322468 | −0.161234 | − | 0.986916i | \(-0.551547\pi\) | ||||
−0.161234 | + | 0.986916i | \(0.551547\pi\) | |||||||
\(338\) | 12.2145 | 0.664380 | ||||||||
\(339\) | 17.6800 | 0.960247 | ||||||||
\(340\) | −11.5809 | −0.628063 | ||||||||
\(341\) | 7.06838 | 0.382774 | ||||||||
\(342\) | 9.27022 | 0.501276 | ||||||||
\(343\) | −7.92612 | −0.427970 | ||||||||
\(344\) | −10.8843 | −0.586843 | ||||||||
\(345\) | 1.95343 | 0.105169 | ||||||||
\(346\) | 5.82014 | 0.312892 | ||||||||
\(347\) | 34.1656 | 1.83411 | 0.917054 | − | 0.398764i | \(-0.130561\pi\) | ||||
0.917054 | + | 0.398764i | \(0.130561\pi\) | |||||||
\(348\) | 9.50176 | 0.509348 | ||||||||
\(349\) | 14.9410 | 0.799775 | 0.399887 | − | 0.916564i | \(-0.369049\pi\) | ||||
0.399887 | + | 0.916564i | \(0.369049\pi\) | |||||||
\(350\) | 1.34687 | 0.0719931 | ||||||||
\(351\) | 3.18298 | 0.169895 | ||||||||
\(352\) | 3.54895 | 0.189159 | ||||||||
\(353\) | 10.8111 | 0.575417 | 0.287708 | − | 0.957718i | \(-0.407107\pi\) | ||||
0.287708 | + | 0.957718i | \(0.407107\pi\) | |||||||
\(354\) | 1.14785 | 0.0610073 | ||||||||
\(355\) | −7.85690 | −0.417001 | ||||||||
\(356\) | 4.67275 | 0.247656 | ||||||||
\(357\) | −8.47277 | −0.448426 | ||||||||
\(358\) | 1.45393 | 0.0768428 | ||||||||
\(359\) | −1.35529 | −0.0715293 | −0.0357647 | − | 0.999360i | \(-0.511387\pi\) | ||||
−0.0357647 | + | 0.999360i | \(0.511387\pi\) | |||||||
\(360\) | 2.06201 | 0.108677 | ||||||||
\(361\) | 35.1304 | 1.84897 | ||||||||
\(362\) | 8.41969 | 0.442529 | ||||||||
\(363\) | −3.29207 | −0.172789 | ||||||||
\(364\) | 0.514136 | 0.0269480 | ||||||||
\(365\) | 24.8983 | 1.30324 | ||||||||
\(366\) | −29.0097 | −1.51636 | ||||||||
\(367\) | −33.3341 | −1.74002 | −0.870012 | − | 0.493030i | \(-0.835889\pi\) | ||||
−0.870012 | + | 0.493030i | \(0.835889\pi\) | |||||||
\(368\) | 0.578326 | 0.0301473 | ||||||||
\(369\) | −4.51557 | −0.235071 | ||||||||
\(370\) | 16.3756 | 0.851328 | ||||||||
\(371\) | −1.80730 | −0.0938304 | ||||||||
\(372\) | 4.11079 | 0.213135 | ||||||||
\(373\) | 19.3902 | 1.00399 | 0.501993 | − | 0.864872i | \(-0.332600\pi\) | ||||
0.501993 | + | 0.864872i | \(0.332600\pi\) | |||||||
\(374\) | 25.1143 | 1.29863 | ||||||||
\(375\) | −24.7311 | −1.27711 | ||||||||
\(376\) | 5.51320 | 0.284321 | ||||||||
\(377\) | −4.08017 | −0.210139 | ||||||||
\(378\) | −2.08331 | −0.107154 | ||||||||
\(379\) | −15.0260 | −0.771836 | −0.385918 | − | 0.922533i | \(-0.626115\pi\) | ||||
−0.385918 | + | 0.922533i | \(0.626115\pi\) | |||||||
\(380\) | 12.0404 | 0.617661 | ||||||||
\(381\) | 31.4022 | 1.60878 | ||||||||
\(382\) | 10.4040 | 0.532315 | ||||||||
\(383\) | 19.0690 | 0.974380 | 0.487190 | − | 0.873296i | \(-0.338022\pi\) | ||||
0.487190 | + | 0.873296i | \(0.338022\pi\) | |||||||
\(384\) | 2.06398 | 0.105327 | ||||||||
\(385\) | 3.36914 | 0.171707 | ||||||||
\(386\) | −14.4951 | −0.737779 | ||||||||
\(387\) | 13.7142 | 0.697132 | ||||||||
\(388\) | −12.5355 | −0.636394 | ||||||||
\(389\) | 29.7584 | 1.50881 | 0.754405 | − | 0.656409i | \(-0.227925\pi\) | ||||
0.754405 | + | 0.656409i | \(0.227925\pi\) | |||||||
\(390\) | −2.99367 | −0.151591 | ||||||||
\(391\) | 4.09255 | 0.206969 | ||||||||
\(392\) | 6.66349 | 0.336557 | ||||||||
\(393\) | 45.1499 | 2.27751 | ||||||||
\(394\) | 2.10073 | 0.105833 | ||||||||
\(395\) | 21.6702 | 1.09035 | ||||||||
\(396\) | −4.47166 | −0.224709 | ||||||||
\(397\) | −9.46210 | −0.474889 | −0.237445 | − | 0.971401i | \(-0.576310\pi\) | ||||
−0.237445 | + | 0.971401i | \(0.576310\pi\) | |||||||
\(398\) | 8.51886 | 0.427012 | ||||||||
\(399\) | 8.80896 | 0.440999 | ||||||||
\(400\) | −2.32181 | −0.116090 | ||||||||
\(401\) | 19.0247 | 0.950047 | 0.475023 | − | 0.879973i | \(-0.342440\pi\) | ||||
0.475023 | + | 0.879973i | \(0.342440\pi\) | |||||||
\(402\) | 6.05903 | 0.302197 | ||||||||
\(403\) | −1.76522 | −0.0879320 | ||||||||
\(404\) | 13.9965 | 0.696350 | ||||||||
\(405\) | 18.3166 | 0.910158 | ||||||||
\(406\) | 2.67054 | 0.132537 | ||||||||
\(407\) | −35.5121 | −1.76027 | ||||||||
\(408\) | 14.6058 | 0.723096 | ||||||||
\(409\) | −22.5419 | −1.11462 | −0.557312 | − | 0.830303i | \(-0.688167\pi\) | ||||
−0.557312 | + | 0.830303i | \(0.688167\pi\) | |||||||
\(410\) | −5.86495 | −0.289649 | ||||||||
\(411\) | 30.5697 | 1.50789 | ||||||||
\(412\) | 12.6899 | 0.625187 | ||||||||
\(413\) | 0.322610 | 0.0158746 | ||||||||
\(414\) | −0.728689 | −0.0358131 | ||||||||
\(415\) | −17.4014 | −0.854201 | ||||||||
\(416\) | −0.886296 | −0.0434542 | ||||||||
\(417\) | −40.0975 | −1.96358 | ||||||||
\(418\) | −26.1108 | −1.27712 | ||||||||
\(419\) | 1.55625 | 0.0760278 | 0.0380139 | − | 0.999277i | \(-0.487897\pi\) | ||||
0.0380139 | + | 0.999277i | \(0.487897\pi\) | |||||||
\(420\) | 1.95941 | 0.0956093 | ||||||||
\(421\) | 20.2645 | 0.987629 | 0.493815 | − | 0.869567i | \(-0.335602\pi\) | ||||
0.493815 | + | 0.869567i | \(0.335602\pi\) | |||||||
\(422\) | 6.01330 | 0.292723 | ||||||||
\(423\) | −6.94661 | −0.337756 | ||||||||
\(424\) | 3.11553 | 0.151303 | ||||||||
\(425\) | −16.4304 | −0.796990 | ||||||||
\(426\) | 9.90911 | 0.480098 | ||||||||
\(427\) | −8.15338 | −0.394570 | ||||||||
\(428\) | 18.0426 | 0.872123 | ||||||||
\(429\) | 6.49206 | 0.313440 | ||||||||
\(430\) | 17.8124 | 0.858990 | ||||||||
\(431\) | −37.4088 | −1.80192 | −0.900960 | − | 0.433901i | \(-0.857137\pi\) | ||||
−0.900960 | + | 0.433901i | \(0.857137\pi\) | |||||||
\(432\) | 3.59132 | 0.172788 | ||||||||
\(433\) | 18.2561 | 0.877333 | 0.438666 | − | 0.898650i | \(-0.355451\pi\) | ||||
0.438666 | + | 0.898650i | \(0.355451\pi\) | |||||||
\(434\) | 1.15537 | 0.0554594 | ||||||||
\(435\) | −15.5498 | −0.745557 | ||||||||
\(436\) | 3.38255 | 0.161995 | ||||||||
\(437\) | −4.25494 | −0.203541 | ||||||||
\(438\) | −31.4017 | −1.50043 | ||||||||
\(439\) | −20.4118 | −0.974203 | −0.487102 | − | 0.873345i | \(-0.661946\pi\) | ||||
−0.487102 | + | 0.873345i | \(0.661946\pi\) | |||||||
\(440\) | −5.80792 | −0.276882 | ||||||||
\(441\) | −8.39598 | −0.399808 | ||||||||
\(442\) | −6.27192 | −0.298325 | ||||||||
\(443\) | 8.87416 | 0.421624 | 0.210812 | − | 0.977527i | \(-0.432389\pi\) | ||||
0.210812 | + | 0.977527i | \(0.432389\pi\) | |||||||
\(444\) | −20.6529 | −0.980144 | ||||||||
\(445\) | −7.64705 | −0.362505 | ||||||||
\(446\) | −0.468926 | −0.0222043 | ||||||||
\(447\) | 47.9202 | 2.26655 | ||||||||
\(448\) | 0.580095 | 0.0274069 | ||||||||
\(449\) | 17.7701 | 0.838621 | 0.419311 | − | 0.907843i | \(-0.362272\pi\) | ||||
0.419311 | + | 0.907843i | \(0.362272\pi\) | |||||||
\(450\) | 2.92547 | 0.137908 | ||||||||
\(451\) | 12.7187 | 0.598900 | ||||||||
\(452\) | −8.56600 | −0.402911 | ||||||||
\(453\) | −0.554278 | −0.0260422 | ||||||||
\(454\) | −26.4649 | −1.24206 | ||||||||
\(455\) | −0.841393 | −0.0394451 | ||||||||
\(456\) | −15.1854 | −0.711120 | ||||||||
\(457\) | 1.28600 | 0.0601566 | 0.0300783 | − | 0.999548i | \(-0.490424\pi\) | ||||
0.0300783 | + | 0.999548i | \(0.490424\pi\) | |||||||
\(458\) | −13.3509 | −0.623846 | ||||||||
\(459\) | 25.4142 | 1.18623 | ||||||||
\(460\) | −0.946441 | −0.0441281 | ||||||||
\(461\) | −30.5617 | −1.42340 | −0.711700 | − | 0.702484i | \(-0.752074\pi\) | ||||
−0.711700 | + | 0.702484i | \(0.752074\pi\) | |||||||
\(462\) | −4.24916 | −0.197689 | ||||||||
\(463\) | −16.0653 | −0.746616 | −0.373308 | − | 0.927708i | \(-0.621776\pi\) | ||||
−0.373308 | + | 0.927708i | \(0.621776\pi\) | |||||||
\(464\) | −4.60362 | −0.213718 | ||||||||
\(465\) | −6.72739 | −0.311975 | ||||||||
\(466\) | 12.7064 | 0.588613 | ||||||||
\(467\) | −34.1135 | −1.57858 | −0.789291 | − | 0.614019i | \(-0.789552\pi\) | ||||
−0.789291 | + | 0.614019i | \(0.789552\pi\) | |||||||
\(468\) | 1.11673 | 0.0516209 | ||||||||
\(469\) | 1.70293 | 0.0786341 | ||||||||
\(470\) | −9.02245 | −0.416175 | ||||||||
\(471\) | 15.5731 | 0.717568 | ||||||||
\(472\) | −0.556133 | −0.0255981 | ||||||||
\(473\) | −38.6278 | −1.77611 | ||||||||
\(474\) | −27.3304 | −1.25533 | ||||||||
\(475\) | 17.0823 | 0.783790 | ||||||||
\(476\) | 4.10507 | 0.188156 | ||||||||
\(477\) | −3.92555 | −0.179739 | ||||||||
\(478\) | −23.0565 | −1.05458 | ||||||||
\(479\) | 34.8139 | 1.59069 | 0.795343 | − | 0.606159i | \(-0.207291\pi\) | ||||
0.795343 | + | 0.606159i | \(0.207291\pi\) | |||||||
\(480\) | −3.37774 | −0.154172 | ||||||||
\(481\) | 8.86861 | 0.404374 | ||||||||
\(482\) | 23.1288 | 1.05349 | ||||||||
\(483\) | −0.692431 | −0.0315067 | ||||||||
\(484\) | 1.59501 | 0.0725007 | ||||||||
\(485\) | 20.5146 | 0.931519 | ||||||||
\(486\) | −12.3269 | −0.559158 | ||||||||
\(487\) | 28.0533 | 1.27122 | 0.635608 | − | 0.772012i | \(-0.280750\pi\) | ||||
0.635608 | + | 0.772012i | \(0.280750\pi\) | |||||||
\(488\) | 14.0553 | 0.636252 | ||||||||
\(489\) | 41.0710 | 1.85729 | ||||||||
\(490\) | −10.9049 | −0.492634 | ||||||||
\(491\) | −10.1644 | −0.458714 | −0.229357 | − | 0.973342i | \(-0.573662\pi\) | ||||
−0.229357 | + | 0.973342i | \(0.573662\pi\) | |||||||
\(492\) | 7.39687 | 0.333477 | ||||||||
\(493\) | −32.5778 | −1.46723 | ||||||||
\(494\) | 6.52078 | 0.293384 | ||||||||
\(495\) | 7.31796 | 0.328918 | ||||||||
\(496\) | −1.99169 | −0.0894293 | ||||||||
\(497\) | 2.78503 | 0.124926 | ||||||||
\(498\) | 21.9466 | 0.983452 | ||||||||
\(499\) | 15.4814 | 0.693041 | 0.346521 | − | 0.938042i | \(-0.387363\pi\) | ||||
0.346521 | + | 0.938042i | \(0.387363\pi\) | |||||||
\(500\) | 11.9823 | 0.535864 | ||||||||
\(501\) | −41.3821 | −1.84882 | ||||||||
\(502\) | −6.45395 | −0.288054 | ||||||||
\(503\) | −15.1627 | −0.676070 | −0.338035 | − | 0.941134i | \(-0.609762\pi\) | ||||
−0.338035 | + | 0.941134i | \(0.609762\pi\) | |||||||
\(504\) | −0.730918 | −0.0325577 | ||||||||
\(505\) | −22.9055 | −1.01928 | ||||||||
\(506\) | 2.05245 | 0.0912424 | ||||||||
\(507\) | 25.2104 | 1.11963 | ||||||||
\(508\) | −15.2144 | −0.675030 | ||||||||
\(509\) | −21.1340 | −0.936750 | −0.468375 | − | 0.883530i | \(-0.655160\pi\) | ||||
−0.468375 | + | 0.883530i | \(0.655160\pi\) | |||||||
\(510\) | −23.9027 | −1.05843 | ||||||||
\(511\) | −8.82567 | −0.390425 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −26.4226 | −1.16659 | ||||||||
\(514\) | 14.8905 | 0.656792 | ||||||||
\(515\) | −20.7673 | −0.915115 | ||||||||
\(516\) | −22.4650 | −0.988965 | ||||||||
\(517\) | 19.5660 | 0.860513 | ||||||||
\(518\) | −5.80465 | −0.255042 | ||||||||
\(519\) | 12.0126 | 0.527295 | ||||||||
\(520\) | 1.45044 | 0.0636060 | ||||||||
\(521\) | 2.20280 | 0.0965064 | 0.0482532 | − | 0.998835i | \(-0.484635\pi\) | ||||
0.0482532 | + | 0.998835i | \(0.484635\pi\) | |||||||
\(522\) | 5.80055 | 0.253883 | ||||||||
\(523\) | 19.6181 | 0.857838 | 0.428919 | − | 0.903343i | \(-0.358895\pi\) | ||||
0.428919 | + | 0.903343i | \(0.358895\pi\) | |||||||
\(524\) | −21.8752 | −0.955623 | ||||||||
\(525\) | 2.77990 | 0.121325 | ||||||||
\(526\) | 13.7096 | 0.597765 | ||||||||
\(527\) | −14.0943 | −0.613956 | ||||||||
\(528\) | 7.32494 | 0.318777 | ||||||||
\(529\) | −22.6655 | −0.985458 | ||||||||
\(530\) | −5.09862 | −0.221470 | ||||||||
\(531\) | 0.700726 | 0.0304089 | ||||||||
\(532\) | −4.26795 | −0.185039 | ||||||||
\(533\) | −3.17630 | −0.137581 | ||||||||
\(534\) | 9.64445 | 0.417356 | ||||||||
\(535\) | −29.5271 | −1.27657 | ||||||||
\(536\) | −2.93561 | −0.126799 | ||||||||
\(537\) | 3.00088 | 0.129498 | ||||||||
\(538\) | 11.7222 | 0.505381 | ||||||||
\(539\) | 23.6484 | 1.01861 | ||||||||
\(540\) | −5.87727 | −0.252917 | ||||||||
\(541\) | 32.4187 | 1.39379 | 0.696894 | − | 0.717174i | \(-0.254565\pi\) | ||||
0.696894 | + | 0.717174i | \(0.254565\pi\) | |||||||
\(542\) | −15.4815 | −0.664987 | ||||||||
\(543\) | 17.3780 | 0.745763 | ||||||||
\(544\) | −7.07655 | −0.303405 | ||||||||
\(545\) | −5.53560 | −0.237119 | ||||||||
\(546\) | 1.06116 | 0.0454136 | ||||||||
\(547\) | 43.6343 | 1.86567 | 0.932835 | − | 0.360304i | \(-0.117327\pi\) | ||||
0.932835 | + | 0.360304i | \(0.117327\pi\) | |||||||
\(548\) | −14.8111 | −0.632699 | ||||||||
\(549\) | −17.7096 | −0.755826 | ||||||||
\(550\) | −8.23996 | −0.351353 | ||||||||
\(551\) | 33.8704 | 1.44293 | ||||||||
\(552\) | 1.19365 | 0.0508051 | ||||||||
\(553\) | −7.68141 | −0.326647 | ||||||||
\(554\) | 30.0761 | 1.27781 | ||||||||
\(555\) | 33.7989 | 1.43468 | ||||||||
\(556\) | 19.4273 | 0.823901 | ||||||||
\(557\) | 19.6954 | 0.834520 | 0.417260 | − | 0.908787i | \(-0.362991\pi\) | ||||
0.417260 | + | 0.908787i | \(0.362991\pi\) | |||||||
\(558\) | 2.50952 | 0.106236 | ||||||||
\(559\) | 9.64672 | 0.408013 | ||||||||
\(560\) | −0.949336 | −0.0401168 | ||||||||
\(561\) | 51.8353 | 2.18849 | ||||||||
\(562\) | −1.98841 | −0.0838762 | ||||||||
\(563\) | 13.5532 | 0.571201 | 0.285600 | − | 0.958349i | \(-0.407807\pi\) | ||||
0.285600 | + | 0.958349i | \(0.407807\pi\) | |||||||
\(564\) | 11.3791 | 0.479147 | ||||||||
\(565\) | 14.0184 | 0.589760 | ||||||||
\(566\) | −29.9209 | −1.25767 | ||||||||
\(567\) | −6.49265 | −0.272666 | ||||||||
\(568\) | −4.80098 | −0.201445 | ||||||||
\(569\) | −1.63078 | −0.0683658 | −0.0341829 | − | 0.999416i | \(-0.510883\pi\) | ||||
−0.0341829 | + | 0.999416i | \(0.510883\pi\) | |||||||
\(570\) | 24.8511 | 1.04090 | ||||||||
\(571\) | −26.3214 | −1.10151 | −0.550757 | − | 0.834665i | \(-0.685661\pi\) | ||||
−0.550757 | + | 0.834665i | \(0.685661\pi\) | |||||||
\(572\) | −3.14542 | −0.131516 | ||||||||
\(573\) | 21.4736 | 0.897073 | ||||||||
\(574\) | 2.07894 | 0.0867734 | ||||||||
\(575\) | −1.34276 | −0.0559970 | ||||||||
\(576\) | 1.26000 | 0.0524999 | ||||||||
\(577\) | 10.4295 | 0.434188 | 0.217094 | − | 0.976151i | \(-0.430342\pi\) | ||||
0.217094 | + | 0.976151i | \(0.430342\pi\) | |||||||
\(578\) | −33.0776 | −1.37584 | ||||||||
\(579\) | −29.9174 | −1.24333 | ||||||||
\(580\) | 7.53391 | 0.312829 | ||||||||
\(581\) | 6.16825 | 0.255902 | ||||||||
\(582\) | −25.8730 | −1.07247 | ||||||||
\(583\) | 11.0568 | 0.457927 | ||||||||
\(584\) | 15.2142 | 0.629567 | ||||||||
\(585\) | −1.82755 | −0.0755599 | ||||||||
\(586\) | −11.1357 | −0.460012 | ||||||||
\(587\) | 35.8322 | 1.47895 | 0.739476 | − | 0.673183i | \(-0.235073\pi\) | ||||
0.739476 | + | 0.673183i | \(0.235073\pi\) | |||||||
\(588\) | 13.7533 | 0.567176 | ||||||||
\(589\) | 14.6535 | 0.603787 | ||||||||
\(590\) | 0.910123 | 0.0374692 | ||||||||
\(591\) | 4.33586 | 0.178353 | ||||||||
\(592\) | 10.0064 | 0.411260 | ||||||||
\(593\) | −5.36185 | −0.220185 | −0.110092 | − | 0.993921i | \(-0.535115\pi\) | ||||
−0.110092 | + | 0.993921i | \(0.535115\pi\) | |||||||
\(594\) | 12.7454 | 0.522951 | ||||||||
\(595\) | −6.71803 | −0.275412 | ||||||||
\(596\) | −23.2174 | −0.951023 | ||||||||
\(597\) | 17.5827 | 0.719613 | ||||||||
\(598\) | −0.512568 | −0.0209605 | ||||||||
\(599\) | 34.6350 | 1.41515 | 0.707573 | − | 0.706640i | \(-0.249790\pi\) | ||||
0.707573 | + | 0.706640i | \(0.249790\pi\) | |||||||
\(600\) | −4.79215 | −0.195639 | ||||||||
\(601\) | −8.43148 | −0.343927 | −0.171964 | − | 0.985103i | \(-0.555011\pi\) | ||||
−0.171964 | + | 0.985103i | \(0.555011\pi\) | |||||||
\(602\) | −6.31394 | −0.257337 | ||||||||
\(603\) | 3.69886 | 0.150629 | ||||||||
\(604\) | 0.268548 | 0.0109271 | ||||||||
\(605\) | −2.61027 | −0.106123 | ||||||||
\(606\) | 28.8884 | 1.17351 | ||||||||
\(607\) | 3.38534 | 0.137407 | 0.0687034 | − | 0.997637i | \(-0.478114\pi\) | ||||
0.0687034 | + | 0.997637i | \(0.478114\pi\) | |||||||
\(608\) | 7.35734 | 0.298379 | ||||||||
\(609\) | 5.51192 | 0.223354 | ||||||||
\(610\) | −23.0017 | −0.931311 | ||||||||
\(611\) | −4.88632 | −0.197679 | ||||||||
\(612\) | 8.91643 | 0.360425 | ||||||||
\(613\) | 34.4560 | 1.39167 | 0.695833 | − | 0.718204i | \(-0.255035\pi\) | ||||
0.695833 | + | 0.718204i | \(0.255035\pi\) | |||||||
\(614\) | 18.5541 | 0.748783 | ||||||||
\(615\) | −12.1051 | −0.488125 | ||||||||
\(616\) | 2.05873 | 0.0829484 | ||||||||
\(617\) | 4.46033 | 0.179566 | 0.0897830 | − | 0.995961i | \(-0.471383\pi\) | ||||
0.0897830 | + | 0.995961i | \(0.471383\pi\) | |||||||
\(618\) | 26.1917 | 1.05358 | ||||||||
\(619\) | 21.4026 | 0.860245 | 0.430123 | − | 0.902771i | \(-0.358470\pi\) | ||||
0.430123 | + | 0.902771i | \(0.358470\pi\) | |||||||
\(620\) | 3.25943 | 0.130902 | ||||||||
\(621\) | 2.07696 | 0.0833454 | ||||||||
\(622\) | 6.98601 | 0.280114 | ||||||||
\(623\) | 2.71064 | 0.108600 | ||||||||
\(624\) | −1.82929 | −0.0732303 | ||||||||
\(625\) | −8.00019 | −0.320008 | ||||||||
\(626\) | −5.17135 | −0.206689 | ||||||||
\(627\) | −53.8920 | −2.15224 | ||||||||
\(628\) | −7.54517 | −0.301085 | ||||||||
\(629\) | 70.8106 | 2.82340 | ||||||||
\(630\) | 1.19616 | 0.0476562 | ||||||||
\(631\) | −32.5941 | −1.29755 | −0.648775 | − | 0.760981i | \(-0.724718\pi\) | ||||
−0.648775 | + | 0.760981i | \(0.724718\pi\) | |||||||
\(632\) | 13.2416 | 0.526724 | ||||||||
\(633\) | 12.4113 | 0.493305 | ||||||||
\(634\) | −8.51799 | −0.338293 | ||||||||
\(635\) | 24.8987 | 0.988073 | ||||||||
\(636\) | 6.43037 | 0.254981 | ||||||||
\(637\) | −5.90582 | −0.233997 | ||||||||
\(638\) | −16.3380 | −0.646828 | ||||||||
\(639\) | 6.04922 | 0.239304 | ||||||||
\(640\) | 1.63652 | 0.0646891 | ||||||||
\(641\) | 42.5099 | 1.67904 | 0.839520 | − | 0.543328i | \(-0.182836\pi\) | ||||
0.839520 | + | 0.543328i | \(0.182836\pi\) | |||||||
\(642\) | 37.2395 | 1.46973 | ||||||||
\(643\) | 12.2811 | 0.484319 | 0.242159 | − | 0.970236i | \(-0.422144\pi\) | ||||
0.242159 | + | 0.970236i | \(0.422144\pi\) | |||||||
\(644\) | 0.335484 | 0.0132199 | ||||||||
\(645\) | 36.7643 | 1.44759 | ||||||||
\(646\) | 52.0646 | 2.04845 | ||||||||
\(647\) | 27.6649 | 1.08762 | 0.543809 | − | 0.839209i | \(-0.316982\pi\) | ||||
0.543809 | + | 0.839209i | \(0.316982\pi\) | |||||||
\(648\) | 11.1924 | 0.439679 | ||||||||
\(649\) | −1.97369 | −0.0774740 | ||||||||
\(650\) | 2.05781 | 0.0807138 | ||||||||
\(651\) | 2.38465 | 0.0934618 | ||||||||
\(652\) | −19.8990 | −0.779303 | ||||||||
\(653\) | 37.7337 | 1.47663 | 0.738317 | − | 0.674454i | \(-0.235621\pi\) | ||||
0.738317 | + | 0.674454i | \(0.235621\pi\) | |||||||
\(654\) | 6.98150 | 0.272998 | ||||||||
\(655\) | 35.7992 | 1.39879 | ||||||||
\(656\) | −3.58380 | −0.139924 | ||||||||
\(657\) | −19.1698 | −0.747886 | ||||||||
\(658\) | 3.19818 | 0.124678 | ||||||||
\(659\) | 33.0208 | 1.28631 | 0.643154 | − | 0.765737i | \(-0.277626\pi\) | ||||
0.643154 | + | 0.765737i | \(0.277626\pi\) | |||||||
\(660\) | −11.9874 | −0.466609 | ||||||||
\(661\) | 6.76166 | 0.262998 | 0.131499 | − | 0.991316i | \(-0.458021\pi\) | ||||
0.131499 | + | 0.991316i | \(0.458021\pi\) | |||||||
\(662\) | −9.30553 | −0.361670 | ||||||||
\(663\) | −12.9451 | −0.502745 | ||||||||
\(664\) | −10.6332 | −0.412647 | ||||||||
\(665\) | 6.98459 | 0.270851 | ||||||||
\(666\) | −12.6080 | −0.488550 | ||||||||
\(667\) | −2.66239 | −0.103088 | ||||||||
\(668\) | 20.0497 | 0.775747 | ||||||||
\(669\) | −0.967852 | −0.0374193 | ||||||||
\(670\) | 4.80418 | 0.185602 | ||||||||
\(671\) | 49.8813 | 1.92565 | ||||||||
\(672\) | 1.19730 | 0.0461869 | ||||||||
\(673\) | 8.86041 | 0.341544 | 0.170772 | − | 0.985311i | \(-0.445374\pi\) | ||||
0.170772 | + | 0.985311i | \(0.445374\pi\) | |||||||
\(674\) | 5.91973 | 0.228019 | ||||||||
\(675\) | −8.33836 | −0.320944 | ||||||||
\(676\) | −12.2145 | −0.469788 | ||||||||
\(677\) | 3.50774 | 0.134813 | 0.0674066 | − | 0.997726i | \(-0.478528\pi\) | ||||
0.0674066 | + | 0.997726i | \(0.478528\pi\) | |||||||
\(678\) | −17.6800 | −0.678997 | ||||||||
\(679\) | −7.27178 | −0.279065 | ||||||||
\(680\) | 11.5809 | 0.444108 | ||||||||
\(681\) | −54.6230 | −2.09316 | ||||||||
\(682\) | −7.06838 | −0.270662 | ||||||||
\(683\) | 6.99027 | 0.267475 | 0.133738 | − | 0.991017i | \(-0.457302\pi\) | ||||
0.133738 | + | 0.991017i | \(0.457302\pi\) | |||||||
\(684\) | −9.27022 | −0.354456 | ||||||||
\(685\) | 24.2386 | 0.926111 | ||||||||
\(686\) | 7.92612 | 0.302621 | ||||||||
\(687\) | −27.5559 | −1.05132 | ||||||||
\(688\) | 10.8843 | 0.414961 | ||||||||
\(689\) | −2.76128 | −0.105196 | ||||||||
\(690\) | −1.95343 | −0.0743659 | ||||||||
\(691\) | −28.8446 | −1.09730 | −0.548651 | − | 0.836052i | \(-0.684858\pi\) | ||||
−0.548651 | + | 0.836052i | \(0.684858\pi\) | |||||||
\(692\) | −5.82014 | −0.221248 | ||||||||
\(693\) | −2.59399 | −0.0985374 | ||||||||
\(694\) | −34.1656 | −1.29691 | ||||||||
\(695\) | −31.7931 | −1.20598 | ||||||||
\(696\) | −9.50176 | −0.360163 | ||||||||
\(697\) | −25.3609 | −0.960613 | ||||||||
\(698\) | −14.9410 | −0.565526 | ||||||||
\(699\) | 26.2257 | 0.991948 | ||||||||
\(700\) | −1.34687 | −0.0509068 | ||||||||
\(701\) | 0.128202 | 0.00484214 | 0.00242107 | − | 0.999997i | \(-0.499229\pi\) | ||||
0.00242107 | + | 0.999997i | \(0.499229\pi\) | |||||||
\(702\) | −3.18298 | −0.120134 | ||||||||
\(703\) | −73.6203 | −2.77664 | ||||||||
\(704\) | −3.54895 | −0.133756 | ||||||||
\(705\) | −18.6221 | −0.701350 | ||||||||
\(706\) | −10.8111 | −0.406881 | ||||||||
\(707\) | 8.11928 | 0.305357 | ||||||||
\(708\) | −1.14785 | −0.0431387 | ||||||||
\(709\) | 48.8473 | 1.83450 | 0.917249 | − | 0.398314i | \(-0.130404\pi\) | ||||
0.917249 | + | 0.398314i | \(0.130404\pi\) | |||||||
\(710\) | 7.85690 | 0.294864 | ||||||||
\(711\) | −16.6844 | −0.625715 | ||||||||
\(712\) | −4.67275 | −0.175119 | ||||||||
\(713\) | −1.15184 | −0.0431369 | ||||||||
\(714\) | 8.47277 | 0.317085 | ||||||||
\(715\) | 5.14753 | 0.192507 | ||||||||
\(716\) | −1.45393 | −0.0543360 | ||||||||
\(717\) | −47.5881 | −1.77721 | ||||||||
\(718\) | 1.35529 | 0.0505789 | ||||||||
\(719\) | 16.1131 | 0.600918 | 0.300459 | − | 0.953795i | \(-0.402860\pi\) | ||||
0.300459 | + | 0.953795i | \(0.402860\pi\) | |||||||
\(720\) | −2.06201 | −0.0768465 | ||||||||
\(721\) | 7.36135 | 0.274151 | ||||||||
\(722\) | −35.1304 | −1.30742 | ||||||||
\(723\) | 47.7373 | 1.77537 | ||||||||
\(724\) | −8.41969 | −0.312915 | ||||||||
\(725\) | 10.6887 | 0.396969 | ||||||||
\(726\) | 3.29207 | 0.122180 | ||||||||
\(727\) | 38.3930 | 1.42392 | 0.711959 | − | 0.702221i | \(-0.247808\pi\) | ||||
0.711959 | + | 0.702221i | \(0.247808\pi\) | |||||||
\(728\) | −0.514136 | −0.0190551 | ||||||||
\(729\) | 8.13484 | 0.301290 | ||||||||
\(730\) | −24.8983 | −0.921527 | ||||||||
\(731\) | 77.0234 | 2.84881 | ||||||||
\(732\) | 29.0097 | 1.07223 | ||||||||
\(733\) | −7.76343 | −0.286749 | −0.143374 | − | 0.989669i | \(-0.545795\pi\) | ||||
−0.143374 | + | 0.989669i | \(0.545795\pi\) | |||||||
\(734\) | 33.3341 | 1.23038 | ||||||||
\(735\) | −22.5075 | −0.830202 | ||||||||
\(736\) | −0.578326 | −0.0213174 | ||||||||
\(737\) | −10.4183 | −0.383764 | ||||||||
\(738\) | 4.51557 | 0.166220 | ||||||||
\(739\) | −18.2426 | −0.671065 | −0.335533 | − | 0.942029i | \(-0.608916\pi\) | ||||
−0.335533 | + | 0.942029i | \(0.608916\pi\) | |||||||
\(740\) | −16.3756 | −0.601980 | ||||||||
\(741\) | 13.4587 | 0.494419 | ||||||||
\(742\) | 1.80730 | 0.0663481 | ||||||||
\(743\) | 36.0693 | 1.32326 | 0.661628 | − | 0.749832i | \(-0.269866\pi\) | ||||
0.661628 | + | 0.749832i | \(0.269866\pi\) | |||||||
\(744\) | −4.11079 | −0.150709 | ||||||||
\(745\) | 37.9958 | 1.39206 | ||||||||
\(746\) | −19.3902 | −0.709925 | ||||||||
\(747\) | 13.3978 | 0.490199 | ||||||||
\(748\) | −25.1143 | −0.918269 | ||||||||
\(749\) | 10.4664 | 0.382435 | ||||||||
\(750\) | 24.7311 | 0.903053 | ||||||||
\(751\) | −11.9477 | −0.435977 | −0.217989 | − | 0.975951i | \(-0.569950\pi\) | ||||
−0.217989 | + | 0.975951i | \(0.569950\pi\) | |||||||
\(752\) | −5.51320 | −0.201046 | ||||||||
\(753\) | −13.3208 | −0.485437 | ||||||||
\(754\) | 4.08017 | 0.148591 | ||||||||
\(755\) | −0.439485 | −0.0159945 | ||||||||
\(756\) | 2.08331 | 0.0757692 | ||||||||
\(757\) | −11.0711 | −0.402386 | −0.201193 | − | 0.979552i | \(-0.564482\pi\) | ||||
−0.201193 | + | 0.979552i | \(0.564482\pi\) | |||||||
\(758\) | 15.0260 | 0.545770 | ||||||||
\(759\) | 4.23620 | 0.153764 | ||||||||
\(760\) | −12.0404 | −0.436752 | ||||||||
\(761\) | 41.1837 | 1.49291 | 0.746453 | − | 0.665438i | \(-0.231755\pi\) | ||||
0.746453 | + | 0.665438i | \(0.231755\pi\) | |||||||
\(762\) | −31.4022 | −1.13758 | ||||||||
\(763\) | 1.96220 | 0.0710364 | ||||||||
\(764\) | −10.4040 | −0.376403 | ||||||||
\(765\) | −14.5919 | −0.527571 | ||||||||
\(766\) | −19.0690 | −0.688990 | ||||||||
\(767\) | 0.492899 | 0.0177975 | ||||||||
\(768\) | −2.06398 | −0.0744773 | ||||||||
\(769\) | 3.50895 | 0.126536 | 0.0632680 | − | 0.997997i | \(-0.479848\pi\) | ||||
0.0632680 | + | 0.997997i | \(0.479848\pi\) | |||||||
\(770\) | −3.36914 | −0.121416 | ||||||||
\(771\) | 30.7336 | 1.10685 | ||||||||
\(772\) | 14.4951 | 0.521688 | ||||||||
\(773\) | 16.6590 | 0.599181 | 0.299590 | − | 0.954068i | \(-0.403150\pi\) | ||||
0.299590 | + | 0.954068i | \(0.403150\pi\) | |||||||
\(774\) | −13.7142 | −0.492947 | ||||||||
\(775\) | 4.62431 | 0.166110 | ||||||||
\(776\) | 12.5355 | 0.449998 | ||||||||
\(777\) | −11.9807 | −0.429804 | ||||||||
\(778\) | −29.7584 | −1.06689 | ||||||||
\(779\) | 26.3672 | 0.944703 | ||||||||
\(780\) | 2.99367 | 0.107191 | ||||||||
\(781\) | −17.0384 | −0.609683 | ||||||||
\(782\) | −4.09255 | −0.146349 | ||||||||
\(783\) | −16.5331 | −0.590845 | ||||||||
\(784\) | −6.66349 | −0.237982 | ||||||||
\(785\) | 12.3478 | 0.440712 | ||||||||
\(786\) | −45.1499 | −1.61044 | ||||||||
\(787\) | 20.9581 | 0.747077 | 0.373539 | − | 0.927615i | \(-0.378144\pi\) | ||||
0.373539 | + | 0.927615i | \(0.378144\pi\) | |||||||
\(788\) | −2.10073 | −0.0748355 | ||||||||
\(789\) | 28.2962 | 1.00737 | ||||||||
\(790\) | −21.6702 | −0.770991 | ||||||||
\(791\) | −4.96909 | −0.176681 | ||||||||
\(792\) | 4.47166 | 0.158894 | ||||||||
\(793\) | −12.4571 | −0.442365 | ||||||||
\(794\) | 9.46210 | 0.335797 | ||||||||
\(795\) | −10.5234 | −0.373228 | ||||||||
\(796\) | −8.51886 | −0.301943 | ||||||||
\(797\) | 39.2309 | 1.38963 | 0.694815 | − | 0.719188i | \(-0.255486\pi\) | ||||
0.694815 | + | 0.719188i | \(0.255486\pi\) | |||||||
\(798\) | −8.80896 | −0.311834 | ||||||||
\(799\) | −39.0144 | −1.38023 | ||||||||
\(800\) | 2.32181 | 0.0820882 | ||||||||
\(801\) | 5.88766 | 0.208030 | ||||||||
\(802\) | −19.0247 | −0.671784 | ||||||||
\(803\) | 53.9943 | 1.90542 | ||||||||
\(804\) | −6.05903 | −0.213685 | ||||||||
\(805\) | −0.549026 | −0.0193506 | ||||||||
\(806\) | 1.76522 | 0.0621773 | ||||||||
\(807\) | 24.1944 | 0.851683 | ||||||||
\(808\) | −13.9965 | −0.492394 | ||||||||
\(809\) | −17.6706 | −0.621264 | −0.310632 | − | 0.950530i | \(-0.600541\pi\) | ||||
−0.310632 | + | 0.950530i | \(0.600541\pi\) | |||||||
\(810\) | −18.3166 | −0.643579 | ||||||||
\(811\) | −21.9218 | −0.769779 | −0.384889 | − | 0.922963i | \(-0.625760\pi\) | ||||
−0.384889 | + | 0.922963i | \(0.625760\pi\) | |||||||
\(812\) | −2.67054 | −0.0937175 | ||||||||
\(813\) | −31.9534 | −1.12066 | ||||||||
\(814\) | 35.5121 | 1.24470 | ||||||||
\(815\) | 32.5650 | 1.14070 | ||||||||
\(816\) | −14.6058 | −0.511306 | ||||||||
\(817\) | −80.0796 | −2.80163 | ||||||||
\(818\) | 22.5419 | 0.788158 | ||||||||
\(819\) | 0.647809 | 0.0226363 | ||||||||
\(820\) | 5.86495 | 0.204813 | ||||||||
\(821\) | −15.7495 | −0.549663 | −0.274831 | − | 0.961492i | \(-0.588622\pi\) | ||||
−0.274831 | + | 0.961492i | \(0.588622\pi\) | |||||||
\(822\) | −30.5697 | −1.06624 | ||||||||
\(823\) | 14.8321 | 0.517015 | 0.258508 | − | 0.966009i | \(-0.416769\pi\) | ||||
0.258508 | + | 0.966009i | \(0.416769\pi\) | |||||||
\(824\) | −12.6899 | −0.442074 | ||||||||
\(825\) | −17.0071 | −0.592111 | ||||||||
\(826\) | −0.322610 | −0.0112250 | ||||||||
\(827\) | 25.7520 | 0.895486 | 0.447743 | − | 0.894162i | \(-0.352228\pi\) | ||||
0.447743 | + | 0.894162i | \(0.352228\pi\) | |||||||
\(828\) | 0.728689 | 0.0253237 | ||||||||
\(829\) | −3.06235 | −0.106360 | −0.0531799 | − | 0.998585i | \(-0.516936\pi\) | ||||
−0.0531799 | + | 0.998585i | \(0.516936\pi\) | |||||||
\(830\) | 17.4014 | 0.604011 | ||||||||
\(831\) | 62.0763 | 2.15340 | ||||||||
\(832\) | 0.886296 | 0.0307268 | ||||||||
\(833\) | −47.1545 | −1.63381 | ||||||||
\(834\) | 40.0975 | 1.38846 | ||||||||
\(835\) | −32.8117 | −1.13550 | ||||||||
\(836\) | 26.1108 | 0.903061 | ||||||||
\(837\) | −7.15279 | −0.247237 | ||||||||
\(838\) | −1.55625 | −0.0537597 | ||||||||
\(839\) | −24.5276 | −0.846786 | −0.423393 | − | 0.905946i | \(-0.639161\pi\) | ||||
−0.423393 | + | 0.905946i | \(0.639161\pi\) | |||||||
\(840\) | −1.95941 | −0.0676060 | ||||||||
\(841\) | −7.80668 | −0.269196 | ||||||||
\(842\) | −20.2645 | −0.698359 | ||||||||
\(843\) | −4.10404 | −0.141351 | ||||||||
\(844\) | −6.01330 | −0.206986 | ||||||||
\(845\) | 19.9892 | 0.687650 | ||||||||
\(846\) | 6.94661 | 0.238829 | ||||||||
\(847\) | 0.925260 | 0.0317923 | ||||||||
\(848\) | −3.11553 | −0.106988 | ||||||||
\(849\) | −61.7560 | −2.11946 | ||||||||
\(850\) | 16.4304 | 0.563557 | ||||||||
\(851\) | 5.78695 | 0.198374 | ||||||||
\(852\) | −9.90911 | −0.339481 | ||||||||
\(853\) | 16.1547 | 0.553128 | 0.276564 | − | 0.960996i | \(-0.410804\pi\) | ||||
0.276564 | + | 0.960996i | \(0.410804\pi\) | |||||||
\(854\) | 8.15338 | 0.279003 | ||||||||
\(855\) | 15.1709 | 0.518834 | ||||||||
\(856\) | −18.0426 | −0.616684 | ||||||||
\(857\) | −39.3885 | −1.34549 | −0.672743 | − | 0.739876i | \(-0.734884\pi\) | ||||
−0.672743 | + | 0.739876i | \(0.734884\pi\) | |||||||
\(858\) | −6.49206 | −0.221635 | ||||||||
\(859\) | 32.6720 | 1.11475 | 0.557377 | − | 0.830260i | \(-0.311808\pi\) | ||||
0.557377 | + | 0.830260i | \(0.311808\pi\) | |||||||
\(860\) | −17.8124 | −0.607397 | ||||||||
\(861\) | 4.29089 | 0.146233 | ||||||||
\(862\) | 37.4088 | 1.27415 | ||||||||
\(863\) | 0.727083 | 0.0247502 | 0.0123751 | − | 0.999923i | \(-0.496061\pi\) | ||||
0.0123751 | + | 0.999923i | \(0.496061\pi\) | |||||||
\(864\) | −3.59132 | −0.122179 | ||||||||
\(865\) | 9.52476 | 0.323852 | ||||||||
\(866\) | −18.2561 | −0.620368 | ||||||||
\(867\) | −68.2713 | −2.31861 | ||||||||
\(868\) | −1.15537 | −0.0392157 | ||||||||
\(869\) | 46.9938 | 1.59416 | ||||||||
\(870\) | 15.5498 | 0.527188 | ||||||||
\(871\) | 2.60182 | 0.0881592 | ||||||||
\(872\) | −3.38255 | −0.114547 | ||||||||
\(873\) | −15.7947 | −0.534569 | ||||||||
\(874\) | 4.25494 | 0.143925 | ||||||||
\(875\) | 6.95086 | 0.234982 | ||||||||
\(876\) | 31.4017 | 1.06096 | ||||||||
\(877\) | −14.3756 | −0.485430 | −0.242715 | − | 0.970098i | \(-0.578038\pi\) | ||||
−0.242715 | + | 0.970098i | \(0.578038\pi\) | |||||||
\(878\) | 20.4118 | 0.688866 | ||||||||
\(879\) | −22.9839 | −0.775226 | ||||||||
\(880\) | 5.80792 | 0.195785 | ||||||||
\(881\) | 0.375440 | 0.0126489 | 0.00632446 | − | 0.999980i | \(-0.497987\pi\) | ||||
0.00632446 | + | 0.999980i | \(0.497987\pi\) | |||||||
\(882\) | 8.39598 | 0.282707 | ||||||||
\(883\) | −43.2463 | −1.45536 | −0.727678 | − | 0.685919i | \(-0.759400\pi\) | ||||
−0.727678 | + | 0.685919i | \(0.759400\pi\) | |||||||
\(884\) | 6.27192 | 0.210947 | ||||||||
\(885\) | 1.87847 | 0.0631441 | ||||||||
\(886\) | −8.87416 | −0.298133 | ||||||||
\(887\) | −21.4600 | −0.720556 | −0.360278 | − | 0.932845i | \(-0.617318\pi\) | ||||
−0.360278 | + | 0.932845i | \(0.617318\pi\) | |||||||
\(888\) | 20.6529 | 0.693067 | ||||||||
\(889\) | −8.82580 | −0.296008 | ||||||||
\(890\) | 7.64705 | 0.256330 | ||||||||
\(891\) | 39.7212 | 1.33071 | ||||||||
\(892\) | 0.468926 | 0.0157008 | ||||||||
\(893\) | 40.5624 | 1.35737 | ||||||||
\(894\) | −47.9202 | −1.60269 | ||||||||
\(895\) | 2.37939 | 0.0795342 | ||||||||
\(896\) | −0.580095 | −0.0193796 | ||||||||
\(897\) | −1.05793 | −0.0353232 | ||||||||
\(898\) | −17.7701 | −0.592995 | ||||||||
\(899\) | 9.16897 | 0.305802 | ||||||||
\(900\) | −2.92547 | −0.0975156 | ||||||||
\(901\) | −22.0472 | −0.734498 | ||||||||
\(902\) | −12.7187 | −0.423486 | ||||||||
\(903\) | −13.0318 | −0.433672 | ||||||||
\(904\) | 8.56600 | 0.284901 | ||||||||
\(905\) | 13.7790 | 0.458029 | ||||||||
\(906\) | 0.554278 | 0.0184146 | ||||||||
\(907\) | 24.4614 | 0.812229 | 0.406114 | − | 0.913822i | \(-0.366883\pi\) | ||||
0.406114 | + | 0.913822i | \(0.366883\pi\) | |||||||
\(908\) | 26.4649 | 0.878270 | ||||||||
\(909\) | 17.6355 | 0.584932 | ||||||||
\(910\) | 0.841393 | 0.0278919 | ||||||||
\(911\) | −26.6311 | −0.882329 | −0.441164 | − | 0.897426i | \(-0.645434\pi\) | ||||
−0.441164 | + | 0.897426i | \(0.645434\pi\) | |||||||
\(912\) | 15.1854 | 0.502838 | ||||||||
\(913\) | −37.7366 | −1.24890 | ||||||||
\(914\) | −1.28600 | −0.0425372 | ||||||||
\(915\) | −47.4749 | −1.56947 | ||||||||
\(916\) | 13.3509 | 0.441126 | ||||||||
\(917\) | −12.6897 | −0.419051 | ||||||||
\(918\) | −25.4142 | −0.838793 | ||||||||
\(919\) | 20.3921 | 0.672672 | 0.336336 | − | 0.941742i | \(-0.390812\pi\) | ||||
0.336336 | + | 0.941742i | \(0.390812\pi\) | |||||||
\(920\) | 0.946441 | 0.0312032 | ||||||||
\(921\) | 38.2953 | 1.26187 | ||||||||
\(922\) | 30.5617 | 1.00650 | ||||||||
\(923\) | 4.25509 | 0.140058 | ||||||||
\(924\) | 4.24916 | 0.139787 | ||||||||
\(925\) | −23.2329 | −0.763892 | ||||||||
\(926\) | 16.0653 | 0.527937 | ||||||||
\(927\) | 15.9892 | 0.525155 | ||||||||
\(928\) | 4.60362 | 0.151121 | ||||||||
\(929\) | 23.8756 | 0.783334 | 0.391667 | − | 0.920107i | \(-0.371898\pi\) | ||||
0.391667 | + | 0.920107i | \(0.371898\pi\) | |||||||
\(930\) | 6.72739 | 0.220600 | ||||||||
\(931\) | 49.0255 | 1.60675 | ||||||||
\(932\) | −12.7064 | −0.416212 | ||||||||
\(933\) | 14.4190 | 0.472055 | ||||||||
\(934\) | 34.1135 | 1.11623 | ||||||||
\(935\) | 41.1000 | 1.34411 | ||||||||
\(936\) | −1.11673 | −0.0365015 | ||||||||
\(937\) | 23.6248 | 0.771789 | 0.385894 | − | 0.922543i | \(-0.373893\pi\) | ||||
0.385894 | + | 0.922543i | \(0.373893\pi\) | |||||||
\(938\) | −1.70293 | −0.0556027 | ||||||||
\(939\) | −10.6735 | −0.348318 | ||||||||
\(940\) | 9.02245 | 0.294280 | ||||||||
\(941\) | 1.21747 | 0.0396885 | 0.0198442 | − | 0.999803i | \(-0.493683\pi\) | ||||
0.0198442 | + | 0.999803i | \(0.493683\pi\) | |||||||
\(942\) | −15.5731 | −0.507397 | ||||||||
\(943\) | −2.07260 | −0.0674932 | ||||||||
\(944\) | 0.556133 | 0.0181006 | ||||||||
\(945\) | −3.40938 | −0.110907 | ||||||||
\(946\) | 38.6278 | 1.25590 | ||||||||
\(947\) | 18.7484 | 0.609242 | 0.304621 | − | 0.952474i | \(-0.401470\pi\) | ||||
0.304621 | + | 0.952474i | \(0.401470\pi\) | |||||||
\(948\) | 27.3304 | 0.887651 | ||||||||
\(949\) | −13.4843 | −0.437718 | ||||||||
\(950\) | −17.0823 | −0.554223 | ||||||||
\(951\) | −17.5809 | −0.570101 | ||||||||
\(952\) | −4.10507 | −0.133046 | ||||||||
\(953\) | 28.7090 | 0.929976 | 0.464988 | − | 0.885317i | \(-0.346059\pi\) | ||||
0.464988 | + | 0.885317i | \(0.346059\pi\) | |||||||
\(954\) | 3.92555 | 0.127095 | ||||||||
\(955\) | 17.0263 | 0.550960 | ||||||||
\(956\) | 23.0565 | 0.745701 | ||||||||
\(957\) | −33.7212 | −1.09005 | ||||||||
\(958\) | −34.8139 | −1.12479 | ||||||||
\(959\) | −8.59184 | −0.277445 | ||||||||
\(960\) | 3.37774 | 0.109016 | ||||||||
\(961\) | −27.0332 | −0.872038 | ||||||||
\(962\) | −8.86861 | −0.285935 | ||||||||
\(963\) | 22.7336 | 0.732581 | ||||||||
\(964\) | −23.1288 | −0.744929 | ||||||||
\(965\) | −23.7214 | −0.763620 | ||||||||
\(966\) | 0.692431 | 0.0222786 | ||||||||
\(967\) | −1.21791 | −0.0391653 | −0.0195826 | − | 0.999808i | \(-0.506234\pi\) | ||||
−0.0195826 | + | 0.999808i | \(0.506234\pi\) | |||||||
\(968\) | −1.59501 | −0.0512657 | ||||||||
\(969\) | 107.460 | 3.45211 | ||||||||
\(970\) | −20.5146 | −0.658684 | ||||||||
\(971\) | −23.6957 | −0.760430 | −0.380215 | − | 0.924898i | \(-0.624150\pi\) | ||||
−0.380215 | + | 0.924898i | \(0.624150\pi\) | |||||||
\(972\) | 12.3269 | 0.395384 | ||||||||
\(973\) | 11.2697 | 0.361289 | ||||||||
\(974\) | −28.0533 | −0.898885 | ||||||||
\(975\) | 4.24726 | 0.136021 | ||||||||
\(976\) | −14.0553 | −0.449898 | ||||||||
\(977\) | −19.4644 | −0.622722 | −0.311361 | − | 0.950292i | \(-0.600785\pi\) | ||||
−0.311361 | + | 0.950292i | \(0.600785\pi\) | |||||||
\(978\) | −41.0710 | −1.31330 | ||||||||
\(979\) | −16.5834 | −0.530006 | ||||||||
\(980\) | 10.9049 | 0.348345 | ||||||||
\(981\) | 4.26200 | 0.136075 | ||||||||
\(982\) | 10.1644 | 0.324360 | ||||||||
\(983\) | 29.2353 | 0.932460 | 0.466230 | − | 0.884663i | \(-0.345612\pi\) | ||||
0.466230 | + | 0.884663i | \(0.345612\pi\) | |||||||
\(984\) | −7.39687 | −0.235804 | ||||||||
\(985\) | 3.43789 | 0.109540 | ||||||||
\(986\) | 32.5778 | 1.03749 | ||||||||
\(987\) | 6.60096 | 0.210111 | ||||||||
\(988\) | −6.52078 | −0.207454 | ||||||||
\(989\) | 6.29468 | 0.200159 | ||||||||
\(990\) | −7.31796 | −0.232580 | ||||||||
\(991\) | −40.9951 | −1.30225 | −0.651126 | − | 0.758970i | \(-0.725703\pi\) | ||||
−0.651126 | + | 0.758970i | \(0.725703\pi\) | |||||||
\(992\) | 1.99169 | 0.0632361 | ||||||||
\(993\) | −19.2064 | −0.609497 | ||||||||
\(994\) | −2.78503 | −0.0883357 | ||||||||
\(995\) | 13.9413 | 0.441968 | ||||||||
\(996\) | −21.9466 | −0.695405 | ||||||||
\(997\) | −49.2156 | −1.55867 | −0.779337 | − | 0.626605i | \(-0.784444\pi\) | ||||
−0.779337 | + | 0.626605i | \(0.784444\pi\) | |||||||
\(998\) | −15.4814 | −0.490054 | ||||||||
\(999\) | 35.9362 | 1.13697 |
(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 | 8026.2.a.c.1.17 | ✓ | 86 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.c.1.17 | ✓ | 86 | 1.1 | even | 1 | trivial |