Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.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: | \(48.0459868962\) |
Analytic rank: | \(1\) |
Dimension: | \(107\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.94021 | −1.37193 | −0.685967 | − | 0.727633i | \(-0.740620\pi\) | ||||
−0.685967 | + | 0.727633i | \(0.740620\pi\) | |||||||
\(3\) | −0.488619 | −0.282104 | −0.141052 | − | 0.990002i | \(-0.545049\pi\) | ||||
−0.141052 | + | 0.990002i | \(0.545049\pi\) | |||||||
\(4\) | 1.76440 | 0.882201 | ||||||||
\(5\) | −3.27450 | −1.46440 | −0.732201 | − | 0.681089i | \(-0.761507\pi\) | ||||
−0.732201 | + | 0.681089i | \(0.761507\pi\) | |||||||
\(6\) | 0.948022 | 0.387029 | ||||||||
\(7\) | −5.11134 | −1.93191 | −0.965953 | − | 0.258717i | \(-0.916700\pi\) | ||||
−0.965953 | + | 0.258717i | \(0.916700\pi\) | |||||||
\(8\) | 0.457109 | 0.161612 | ||||||||
\(9\) | −2.76125 | −0.920417 | ||||||||
\(10\) | 6.35321 | 2.00906 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −0.862121 | −0.248873 | ||||||||
\(13\) | −1.65002 | −0.457632 | −0.228816 | − | 0.973470i | \(-0.573485\pi\) | ||||
−0.228816 | + | 0.973470i | \(0.573485\pi\) | |||||||
\(14\) | 9.91706 | 2.65045 | ||||||||
\(15\) | 1.59999 | 0.413114 | ||||||||
\(16\) | −4.41569 | −1.10392 | ||||||||
\(17\) | −0.361675 | −0.0877191 | −0.0438596 | − | 0.999038i | \(-0.513965\pi\) | ||||
−0.0438596 | + | 0.999038i | \(0.513965\pi\) | |||||||
\(18\) | 5.35740 | 1.26275 | ||||||||
\(19\) | −6.51406 | −1.49443 | −0.747214 | − | 0.664584i | \(-0.768609\pi\) | ||||
−0.747214 | + | 0.664584i | \(0.768609\pi\) | |||||||
\(20\) | −5.77754 | −1.29190 | ||||||||
\(21\) | 2.49750 | 0.544999 | ||||||||
\(22\) | 1.94021 | 0.413653 | ||||||||
\(23\) | −3.28334 | −0.684623 | −0.342312 | − | 0.939586i | \(-0.611210\pi\) | ||||
−0.342312 | + | 0.939586i | \(0.611210\pi\) | |||||||
\(24\) | −0.223352 | −0.0455916 | ||||||||
\(25\) | 5.72237 | 1.14447 | ||||||||
\(26\) | 3.20137 | 0.627841 | ||||||||
\(27\) | 2.81506 | 0.541758 | ||||||||
\(28\) | −9.01846 | −1.70433 | ||||||||
\(29\) | −3.07969 | −0.571884 | −0.285942 | − | 0.958247i | \(-0.592306\pi\) | ||||
−0.285942 | + | 0.958247i | \(0.592306\pi\) | |||||||
\(30\) | −3.10430 | −0.566765 | ||||||||
\(31\) | −0.108979 | −0.0195732 | −0.00978661 | − | 0.999952i | \(-0.503115\pi\) | ||||
−0.00978661 | + | 0.999952i | \(0.503115\pi\) | |||||||
\(32\) | 7.65313 | 1.35290 | ||||||||
\(33\) | 0.488619 | 0.0850577 | ||||||||
\(34\) | 0.701725 | 0.120345 | ||||||||
\(35\) | 16.7371 | 2.82909 | ||||||||
\(36\) | −4.87196 | −0.811993 | ||||||||
\(37\) | 6.91812 | 1.13733 | 0.568666 | − | 0.822568i | \(-0.307460\pi\) | ||||
0.568666 | + | 0.822568i | \(0.307460\pi\) | |||||||
\(38\) | 12.6386 | 2.05026 | ||||||||
\(39\) | 0.806230 | 0.129100 | ||||||||
\(40\) | −1.49680 | −0.236666 | ||||||||
\(41\) | 2.36210 | 0.368898 | 0.184449 | − | 0.982842i | \(-0.440950\pi\) | ||||
0.184449 | + | 0.982842i | \(0.440950\pi\) | |||||||
\(42\) | −4.84567 | −0.747703 | ||||||||
\(43\) | 10.3157 | 1.57313 | 0.786565 | − | 0.617508i | \(-0.211858\pi\) | ||||
0.786565 | + | 0.617508i | \(0.211858\pi\) | |||||||
\(44\) | −1.76440 | −0.265994 | ||||||||
\(45\) | 9.04172 | 1.34786 | ||||||||
\(46\) | 6.37035 | 0.939258 | ||||||||
\(47\) | −9.06923 | −1.32288 | −0.661442 | − | 0.749997i | \(-0.730055\pi\) | ||||
−0.661442 | + | 0.749997i | \(0.730055\pi\) | |||||||
\(48\) | 2.15759 | 0.311421 | ||||||||
\(49\) | 19.1258 | 2.73226 | ||||||||
\(50\) | −11.1026 | −1.57014 | ||||||||
\(51\) | 0.176722 | 0.0247460 | ||||||||
\(52\) | −2.91129 | −0.403723 | ||||||||
\(53\) | −7.86751 | −1.08069 | −0.540343 | − | 0.841445i | \(-0.681705\pi\) | ||||
−0.540343 | + | 0.841445i | \(0.681705\pi\) | |||||||
\(54\) | −5.46180 | −0.743256 | ||||||||
\(55\) | 3.27450 | 0.441534 | ||||||||
\(56\) | −2.33644 | −0.312220 | ||||||||
\(57\) | 3.18290 | 0.421585 | ||||||||
\(58\) | 5.97523 | 0.784586 | ||||||||
\(59\) | 2.89724 | 0.377189 | 0.188594 | − | 0.982055i | \(-0.439607\pi\) | ||||
0.188594 | + | 0.982055i | \(0.439607\pi\) | |||||||
\(60\) | 2.82302 | 0.364450 | ||||||||
\(61\) | −4.56108 | −0.583987 | −0.291993 | − | 0.956420i | \(-0.594319\pi\) | ||||
−0.291993 | + | 0.956420i | \(0.594319\pi\) | |||||||
\(62\) | 0.211442 | 0.0268532 | ||||||||
\(63\) | 14.1137 | 1.77816 | ||||||||
\(64\) | −6.01728 | −0.752160 | ||||||||
\(65\) | 5.40298 | 0.670157 | ||||||||
\(66\) | −0.948022 | −0.116693 | ||||||||
\(67\) | −6.48900 | −0.792758 | −0.396379 | − | 0.918087i | \(-0.629733\pi\) | ||||
−0.396379 | + | 0.918087i | \(0.629733\pi\) | |||||||
\(68\) | −0.638141 | −0.0773859 | ||||||||
\(69\) | 1.60430 | 0.193135 | ||||||||
\(70\) | −32.4734 | −3.88132 | ||||||||
\(71\) | −7.54573 | −0.895514 | −0.447757 | − | 0.894155i | \(-0.647777\pi\) | ||||
−0.447757 | + | 0.894155i | \(0.647777\pi\) | |||||||
\(72\) | −1.26219 | −0.148751 | ||||||||
\(73\) | 9.77411 | 1.14397 | 0.571986 | − | 0.820263i | \(-0.306173\pi\) | ||||
0.571986 | + | 0.820263i | \(0.306173\pi\) | |||||||
\(74\) | −13.4226 | −1.56034 | ||||||||
\(75\) | −2.79606 | −0.322861 | ||||||||
\(76\) | −11.4934 | −1.31839 | ||||||||
\(77\) | 5.11134 | 0.582492 | ||||||||
\(78\) | −1.56425 | −0.177117 | ||||||||
\(79\) | −9.18891 | −1.03383 | −0.516916 | − | 0.856036i | \(-0.672920\pi\) | ||||
−0.516916 | + | 0.856036i | \(0.672920\pi\) | |||||||
\(80\) | 14.4592 | 1.61659 | ||||||||
\(81\) | 6.90826 | 0.767585 | ||||||||
\(82\) | −4.58297 | −0.506104 | ||||||||
\(83\) | −5.65099 | −0.620277 | −0.310138 | − | 0.950691i | \(-0.600375\pi\) | ||||
−0.310138 | + | 0.950691i | \(0.600375\pi\) | |||||||
\(84\) | 4.40660 | 0.480799 | ||||||||
\(85\) | 1.18431 | 0.128456 | ||||||||
\(86\) | −20.0146 | −2.15823 | ||||||||
\(87\) | 1.50480 | 0.161331 | ||||||||
\(88\) | −0.457109 | −0.0487280 | ||||||||
\(89\) | 7.82643 | 0.829600 | 0.414800 | − | 0.909913i | \(-0.363852\pi\) | ||||
0.414800 | + | 0.909913i | \(0.363852\pi\) | |||||||
\(90\) | −17.5428 | −1.84917 | ||||||||
\(91\) | 8.43380 | 0.884102 | ||||||||
\(92\) | −5.79313 | −0.603975 | ||||||||
\(93\) | 0.0532493 | 0.00552169 | ||||||||
\(94\) | 17.5962 | 1.81491 | ||||||||
\(95\) | 21.3303 | 2.18844 | ||||||||
\(96\) | −3.73947 | −0.381658 | ||||||||
\(97\) | 1.34946 | 0.137017 | 0.0685085 | − | 0.997651i | \(-0.478176\pi\) | ||||
0.0685085 | + | 0.997651i | \(0.478176\pi\) | |||||||
\(98\) | −37.1081 | −3.74848 | ||||||||
\(99\) | 2.76125 | 0.277516 | ||||||||
\(100\) | 10.0966 | 1.00966 | ||||||||
\(101\) | 16.2351 | 1.61546 | 0.807728 | − | 0.589555i | \(-0.200697\pi\) | ||||
0.807728 | + | 0.589555i | \(0.200697\pi\) | |||||||
\(102\) | −0.342876 | −0.0339498 | ||||||||
\(103\) | 6.17465 | 0.608406 | 0.304203 | − | 0.952607i | \(-0.401610\pi\) | ||||
0.304203 | + | 0.952607i | \(0.401610\pi\) | |||||||
\(104\) | −0.754237 | −0.0739590 | ||||||||
\(105\) | −8.17807 | −0.798098 | ||||||||
\(106\) | 15.2646 | 1.48263 | ||||||||
\(107\) | 19.8620 | 1.92013 | 0.960065 | − | 0.279776i | \(-0.0902603\pi\) | ||||
0.960065 | + | 0.279776i | \(0.0902603\pi\) | |||||||
\(108\) | 4.96689 | 0.477940 | ||||||||
\(109\) | −7.68956 | −0.736526 | −0.368263 | − | 0.929722i | \(-0.620047\pi\) | ||||
−0.368263 | + | 0.929722i | \(0.620047\pi\) | |||||||
\(110\) | −6.35321 | −0.605755 | ||||||||
\(111\) | −3.38033 | −0.320847 | ||||||||
\(112\) | 22.5701 | 2.13267 | ||||||||
\(113\) | 13.9204 | 1.30952 | 0.654762 | − | 0.755835i | \(-0.272769\pi\) | ||||
0.654762 | + | 0.755835i | \(0.272769\pi\) | |||||||
\(114\) | −6.17548 | −0.578386 | ||||||||
\(115\) | 10.7513 | 1.00256 | ||||||||
\(116\) | −5.43381 | −0.504516 | ||||||||
\(117\) | 4.55611 | 0.421212 | ||||||||
\(118\) | −5.62124 | −0.517478 | ||||||||
\(119\) | 1.84865 | 0.169465 | ||||||||
\(120\) | 0.731368 | 0.0667644 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 8.84944 | 0.801191 | ||||||||
\(123\) | −1.15417 | −0.104068 | ||||||||
\(124\) | −0.192283 | −0.0172675 | ||||||||
\(125\) | −2.36539 | −0.211567 | ||||||||
\(126\) | −27.3835 | −2.43952 | ||||||||
\(127\) | −17.7158 | −1.57202 | −0.786010 | − | 0.618213i | \(-0.787857\pi\) | ||||
−0.786010 | + | 0.618213i | \(0.787857\pi\) | |||||||
\(128\) | −3.63150 | −0.320982 | ||||||||
\(129\) | −5.04045 | −0.443787 | ||||||||
\(130\) | −10.4829 | −0.919411 | ||||||||
\(131\) | 20.3593 | 1.77880 | 0.889399 | − | 0.457132i | \(-0.151123\pi\) | ||||
0.889399 | + | 0.457132i | \(0.151123\pi\) | |||||||
\(132\) | 0.862121 | 0.0750380 | ||||||||
\(133\) | 33.2956 | 2.88709 | ||||||||
\(134\) | 12.5900 | 1.08761 | ||||||||
\(135\) | −9.21792 | −0.793352 | ||||||||
\(136\) | −0.165325 | −0.0141765 | ||||||||
\(137\) | −5.39588 | −0.461001 | −0.230501 | − | 0.973072i | \(-0.574036\pi\) | ||||
−0.230501 | + | 0.973072i | \(0.574036\pi\) | |||||||
\(138\) | −3.11268 | −0.264969 | ||||||||
\(139\) | −8.52650 | −0.723208 | −0.361604 | − | 0.932332i | \(-0.617771\pi\) | ||||
−0.361604 | + | 0.932332i | \(0.617771\pi\) | |||||||
\(140\) | 29.5310 | 2.49582 | ||||||||
\(141\) | 4.43140 | 0.373191 | ||||||||
\(142\) | 14.6403 | 1.22859 | ||||||||
\(143\) | 1.65002 | 0.137981 | ||||||||
\(144\) | 12.1928 | 1.01607 | ||||||||
\(145\) | 10.0844 | 0.837468 | ||||||||
\(146\) | −18.9638 | −1.56945 | ||||||||
\(147\) | −9.34525 | −0.770783 | ||||||||
\(148\) | 12.2063 | 1.00336 | ||||||||
\(149\) | −9.43989 | −0.773346 | −0.386673 | − | 0.922217i | \(-0.626376\pi\) | ||||
−0.386673 | + | 0.922217i | \(0.626376\pi\) | |||||||
\(150\) | 5.42493 | 0.442944 | ||||||||
\(151\) | 13.0255 | 1.06000 | 0.529999 | − | 0.847998i | \(-0.322192\pi\) | ||||
0.529999 | + | 0.847998i | \(0.322192\pi\) | |||||||
\(152\) | −2.97763 | −0.241518 | ||||||||
\(153\) | 0.998676 | 0.0807382 | ||||||||
\(154\) | −9.91706 | −0.799140 | ||||||||
\(155\) | 0.356852 | 0.0286631 | ||||||||
\(156\) | 1.42251 | 0.113892 | ||||||||
\(157\) | −10.3279 | −0.824253 | −0.412126 | − | 0.911127i | \(-0.635214\pi\) | ||||
−0.412126 | + | 0.911127i | \(0.635214\pi\) | |||||||
\(158\) | 17.8284 | 1.41835 | ||||||||
\(159\) | 3.84422 | 0.304866 | ||||||||
\(160\) | −25.0602 | −1.98118 | ||||||||
\(161\) | 16.7823 | 1.32263 | ||||||||
\(162\) | −13.4035 | −1.05307 | ||||||||
\(163\) | −23.3460 | −1.82860 | −0.914299 | − | 0.405039i | \(-0.867258\pi\) | ||||
−0.914299 | + | 0.405039i | \(0.867258\pi\) | |||||||
\(164\) | 4.16770 | 0.325443 | ||||||||
\(165\) | −1.59999 | −0.124559 | ||||||||
\(166\) | 10.9641 | 0.850978 | ||||||||
\(167\) | −13.6832 | −1.05884 | −0.529418 | − | 0.848361i | \(-0.677590\pi\) | ||||
−0.529418 | + | 0.848361i | \(0.677590\pi\) | |||||||
\(168\) | 1.14163 | 0.0880787 | ||||||||
\(169\) | −10.2774 | −0.790573 | ||||||||
\(170\) | −2.29780 | −0.176233 | ||||||||
\(171\) | 17.9870 | 1.37550 | ||||||||
\(172\) | 18.2010 | 1.38782 | ||||||||
\(173\) | −9.32965 | −0.709320 | −0.354660 | − | 0.934995i | \(-0.615403\pi\) | ||||
−0.354660 | + | 0.934995i | \(0.615403\pi\) | |||||||
\(174\) | −2.91961 | −0.221335 | ||||||||
\(175\) | −29.2490 | −2.21102 | ||||||||
\(176\) | 4.41569 | 0.332845 | ||||||||
\(177\) | −1.41565 | −0.106407 | ||||||||
\(178\) | −15.1849 | −1.13816 | ||||||||
\(179\) | 13.5365 | 1.01176 | 0.505882 | − | 0.862603i | \(-0.331167\pi\) | ||||
0.505882 | + | 0.862603i | \(0.331167\pi\) | |||||||
\(180\) | 15.9532 | 1.18908 | ||||||||
\(181\) | 1.52476 | 0.113335 | 0.0566674 | − | 0.998393i | \(-0.481953\pi\) | ||||
0.0566674 | + | 0.998393i | \(0.481953\pi\) | |||||||
\(182\) | −16.3633 | −1.21293 | ||||||||
\(183\) | 2.22863 | 0.164745 | ||||||||
\(184\) | −1.50084 | −0.110644 | ||||||||
\(185\) | −22.6534 | −1.66551 | ||||||||
\(186\) | −0.103315 | −0.00757540 | ||||||||
\(187\) | 0.361675 | 0.0264483 | ||||||||
\(188\) | −16.0018 | −1.16705 | ||||||||
\(189\) | −14.3887 | −1.04663 | ||||||||
\(190\) | −41.3852 | −3.00240 | ||||||||
\(191\) | −10.1873 | −0.737128 | −0.368564 | − | 0.929602i | \(-0.620150\pi\) | ||||
−0.368564 | + | 0.929602i | \(0.620150\pi\) | |||||||
\(192\) | 2.94016 | 0.212188 | ||||||||
\(193\) | 14.6455 | 1.05420 | 0.527102 | − | 0.849802i | \(-0.323279\pi\) | ||||
0.527102 | + | 0.849802i | \(0.323279\pi\) | |||||||
\(194\) | −2.61823 | −0.187978 | ||||||||
\(195\) | −2.64000 | −0.189054 | ||||||||
\(196\) | 33.7457 | 2.41040 | ||||||||
\(197\) | −2.51361 | −0.179088 | −0.0895438 | − | 0.995983i | \(-0.528541\pi\) | ||||
−0.0895438 | + | 0.995983i | \(0.528541\pi\) | |||||||
\(198\) | −5.35740 | −0.380734 | ||||||||
\(199\) | −2.59262 | −0.183786 | −0.0918930 | − | 0.995769i | \(-0.529292\pi\) | ||||
−0.0918930 | + | 0.995769i | \(0.529292\pi\) | |||||||
\(200\) | 2.61575 | 0.184961 | ||||||||
\(201\) | 3.17065 | 0.223640 | ||||||||
\(202\) | −31.4995 | −2.21630 | ||||||||
\(203\) | 15.7413 | 1.10483 | ||||||||
\(204\) | 0.311808 | 0.0218309 | ||||||||
\(205\) | −7.73471 | −0.540216 | ||||||||
\(206\) | −11.9801 | −0.834693 | ||||||||
\(207\) | 9.06612 | 0.630139 | ||||||||
\(208\) | 7.28596 | 0.505190 | ||||||||
\(209\) | 6.51406 | 0.450587 | ||||||||
\(210\) | 15.8672 | 1.09494 | ||||||||
\(211\) | 17.3270 | 1.19284 | 0.596418 | − | 0.802674i | \(-0.296590\pi\) | ||||
0.596418 | + | 0.802674i | \(0.296590\pi\) | |||||||
\(212\) | −13.8815 | −0.953382 | ||||||||
\(213\) | 3.68699 | 0.252628 | ||||||||
\(214\) | −38.5364 | −2.63429 | ||||||||
\(215\) | −33.7788 | −2.30369 | ||||||||
\(216\) | 1.28679 | 0.0875549 | ||||||||
\(217\) | 0.557030 | 0.0378136 | ||||||||
\(218\) | 14.9193 | 1.01046 | ||||||||
\(219\) | −4.77582 | −0.322720 | ||||||||
\(220\) | 5.77754 | 0.389522 | ||||||||
\(221\) | 0.596770 | 0.0401431 | ||||||||
\(222\) | 6.55854 | 0.440180 | ||||||||
\(223\) | 21.6868 | 1.45225 | 0.726126 | − | 0.687561i | \(-0.241319\pi\) | ||||
0.726126 | + | 0.687561i | \(0.241319\pi\) | |||||||
\(224\) | −39.1178 | −2.61367 | ||||||||
\(225\) | −15.8009 | −1.05339 | ||||||||
\(226\) | −27.0085 | −1.79658 | ||||||||
\(227\) | 13.0956 | 0.869188 | 0.434594 | − | 0.900626i | \(-0.356892\pi\) | ||||
0.434594 | + | 0.900626i | \(0.356892\pi\) | |||||||
\(228\) | 5.61591 | 0.371923 | ||||||||
\(229\) | 19.7395 | 1.30442 | 0.652212 | − | 0.758036i | \(-0.273841\pi\) | ||||
0.652212 | + | 0.758036i | \(0.273841\pi\) | |||||||
\(230\) | −20.8597 | −1.37545 | ||||||||
\(231\) | −2.49750 | −0.164324 | ||||||||
\(232\) | −1.40775 | −0.0924235 | ||||||||
\(233\) | −14.1692 | −0.928253 | −0.464126 | − | 0.885769i | \(-0.653632\pi\) | ||||
−0.464126 | + | 0.885769i | \(0.653632\pi\) | |||||||
\(234\) | −8.83979 | −0.577875 | ||||||||
\(235\) | 29.6972 | 1.93723 | ||||||||
\(236\) | 5.11190 | 0.332756 | ||||||||
\(237\) | 4.48988 | 0.291649 | ||||||||
\(238\) | −3.58676 | −0.232495 | ||||||||
\(239\) | 12.4553 | 0.805664 | 0.402832 | − | 0.915274i | \(-0.368026\pi\) | ||||
0.402832 | + | 0.915274i | \(0.368026\pi\) | |||||||
\(240\) | −7.06504 | −0.456046 | ||||||||
\(241\) | 13.8102 | 0.889593 | 0.444796 | − | 0.895632i | \(-0.353276\pi\) | ||||
0.444796 | + | 0.895632i | \(0.353276\pi\) | |||||||
\(242\) | −1.94021 | −0.124721 | ||||||||
\(243\) | −11.8207 | −0.758297 | ||||||||
\(244\) | −8.04758 | −0.515194 | ||||||||
\(245\) | −62.6276 | −4.00113 | ||||||||
\(246\) | 2.23933 | 0.142774 | ||||||||
\(247\) | 10.7483 | 0.683898 | ||||||||
\(248\) | −0.0498153 | −0.00316328 | ||||||||
\(249\) | 2.76118 | 0.174983 | ||||||||
\(250\) | 4.58935 | 0.290256 | ||||||||
\(251\) | −19.7467 | −1.24640 | −0.623199 | − | 0.782063i | \(-0.714167\pi\) | ||||
−0.623199 | + | 0.782063i | \(0.714167\pi\) | |||||||
\(252\) | 24.9022 | 1.56869 | ||||||||
\(253\) | 3.28334 | 0.206422 | ||||||||
\(254\) | 34.3723 | 2.15671 | ||||||||
\(255\) | −0.578675 | −0.0362380 | ||||||||
\(256\) | 19.0804 | 1.19253 | ||||||||
\(257\) | 15.5863 | 0.972244 | 0.486122 | − | 0.873891i | \(-0.338411\pi\) | ||||
0.486122 | + | 0.873891i | \(0.338411\pi\) | |||||||
\(258\) | 9.77952 | 0.608846 | ||||||||
\(259\) | −35.3609 | −2.19722 | ||||||||
\(260\) | 9.53303 | 0.591213 | ||||||||
\(261\) | 8.50379 | 0.526372 | ||||||||
\(262\) | −39.5012 | −2.44039 | ||||||||
\(263\) | −2.31352 | −0.142657 | −0.0713287 | − | 0.997453i | \(-0.522724\pi\) | ||||
−0.0713287 | + | 0.997453i | \(0.522724\pi\) | |||||||
\(264\) | 0.223352 | 0.0137464 | ||||||||
\(265\) | 25.7622 | 1.58256 | ||||||||
\(266\) | −64.6003 | −3.96090 | ||||||||
\(267\) | −3.82414 | −0.234034 | ||||||||
\(268\) | −11.4492 | −0.699372 | ||||||||
\(269\) | 1.62022 | 0.0987867 | 0.0493933 | − | 0.998779i | \(-0.484271\pi\) | ||||
0.0493933 | + | 0.998779i | \(0.484271\pi\) | |||||||
\(270\) | 17.8847 | 1.08843 | ||||||||
\(271\) | −3.68946 | −0.224119 | −0.112059 | − | 0.993702i | \(-0.535745\pi\) | ||||
−0.112059 | + | 0.993702i | \(0.535745\pi\) | |||||||
\(272\) | 1.59705 | 0.0968351 | ||||||||
\(273\) | −4.12092 | −0.249409 | ||||||||
\(274\) | 10.4691 | 0.632463 | ||||||||
\(275\) | −5.72237 | −0.345072 | ||||||||
\(276\) | 2.83063 | 0.170384 | ||||||||
\(277\) | −25.2818 | −1.51904 | −0.759519 | − | 0.650485i | \(-0.774566\pi\) | ||||
−0.759519 | + | 0.650485i | \(0.774566\pi\) | |||||||
\(278\) | 16.5432 | 0.992193 | ||||||||
\(279\) | 0.300919 | 0.0180155 | ||||||||
\(280\) | 7.65068 | 0.457216 | ||||||||
\(281\) | 13.8071 | 0.823661 | 0.411830 | − | 0.911261i | \(-0.364890\pi\) | ||||
0.411830 | + | 0.911261i | \(0.364890\pi\) | |||||||
\(282\) | −8.59783 | −0.511994 | ||||||||
\(283\) | −17.0626 | −1.01427 | −0.507134 | − | 0.861867i | \(-0.669295\pi\) | ||||
−0.507134 | + | 0.861867i | \(0.669295\pi\) | |||||||
\(284\) | −13.3137 | −0.790023 | ||||||||
\(285\) | −10.4224 | −0.617370 | ||||||||
\(286\) | −3.20137 | −0.189301 | ||||||||
\(287\) | −12.0735 | −0.712677 | ||||||||
\(288\) | −21.1322 | −1.24523 | ||||||||
\(289\) | −16.8692 | −0.992305 | ||||||||
\(290\) | −19.5659 | −1.14895 | ||||||||
\(291\) | −0.659373 | −0.0386531 | ||||||||
\(292\) | 17.2455 | 1.00921 | ||||||||
\(293\) | 9.73080 | 0.568479 | 0.284240 | − | 0.958753i | \(-0.408259\pi\) | ||||
0.284240 | + | 0.958753i | \(0.408259\pi\) | |||||||
\(294\) | 18.1317 | 1.05746 | ||||||||
\(295\) | −9.48702 | −0.552356 | ||||||||
\(296\) | 3.16234 | 0.183807 | ||||||||
\(297\) | −2.81506 | −0.163346 | ||||||||
\(298\) | 18.3153 | 1.06098 | ||||||||
\(299\) | 5.41756 | 0.313306 | ||||||||
\(300\) | −4.93337 | −0.284828 | ||||||||
\(301\) | −52.7271 | −3.03914 | ||||||||
\(302\) | −25.2721 | −1.45425 | ||||||||
\(303\) | −7.93280 | −0.455727 | ||||||||
\(304\) | 28.7641 | 1.64973 | ||||||||
\(305\) | 14.9353 | 0.855191 | ||||||||
\(306\) | −1.93764 | −0.110767 | ||||||||
\(307\) | −15.7531 | −0.899075 | −0.449537 | − | 0.893262i | \(-0.648411\pi\) | ||||
−0.449537 | + | 0.893262i | \(0.648411\pi\) | |||||||
\(308\) | 9.01846 | 0.513875 | ||||||||
\(309\) | −3.01705 | −0.171634 | ||||||||
\(310\) | −0.692367 | −0.0393238 | ||||||||
\(311\) | 31.5579 | 1.78948 | 0.894742 | − | 0.446583i | \(-0.147359\pi\) | ||||
0.894742 | + | 0.446583i | \(0.147359\pi\) | |||||||
\(312\) | 0.368535 | 0.0208642 | ||||||||
\(313\) | 3.90631 | 0.220798 | 0.110399 | − | 0.993887i | \(-0.464787\pi\) | ||||
0.110399 | + | 0.993887i | \(0.464787\pi\) | |||||||
\(314\) | 20.0382 | 1.13082 | ||||||||
\(315\) | −46.2154 | −2.60394 | ||||||||
\(316\) | −16.2129 | −0.912048 | ||||||||
\(317\) | 8.87227 | 0.498316 | 0.249158 | − | 0.968463i | \(-0.419846\pi\) | ||||
0.249158 | + | 0.968463i | \(0.419846\pi\) | |||||||
\(318\) | −7.45858 | −0.418256 | ||||||||
\(319\) | 3.07969 | 0.172429 | ||||||||
\(320\) | 19.7036 | 1.10146 | ||||||||
\(321\) | −9.70495 | −0.541677 | ||||||||
\(322\) | −32.5611 | −1.81456 | ||||||||
\(323\) | 2.35597 | 0.131090 | ||||||||
\(324\) | 12.1889 | 0.677164 | ||||||||
\(325\) | −9.44200 | −0.523748 | ||||||||
\(326\) | 45.2960 | 2.50872 | ||||||||
\(327\) | 3.75727 | 0.207777 | ||||||||
\(328\) | 1.07974 | 0.0596186 | ||||||||
\(329\) | 46.3560 | 2.55569 | ||||||||
\(330\) | 3.10430 | 0.170886 | ||||||||
\(331\) | −12.7756 | −0.702209 | −0.351104 | − | 0.936336i | \(-0.614194\pi\) | ||||
−0.351104 | + | 0.936336i | \(0.614194\pi\) | |||||||
\(332\) | −9.97062 | −0.547209 | ||||||||
\(333\) | −19.1027 | −1.04682 | ||||||||
\(334\) | 26.5482 | 1.45265 | ||||||||
\(335\) | 21.2483 | 1.16092 | ||||||||
\(336\) | −11.0282 | −0.601637 | ||||||||
\(337\) | −9.02825 | −0.491800 | −0.245900 | − | 0.969295i | \(-0.579083\pi\) | ||||
−0.245900 | + | 0.969295i | \(0.579083\pi\) | |||||||
\(338\) | 19.9404 | 1.08461 | ||||||||
\(339\) | −6.80179 | −0.369423 | ||||||||
\(340\) | 2.08959 | 0.113324 | ||||||||
\(341\) | 0.108979 | 0.00590155 | ||||||||
\(342\) | −34.8984 | −1.88709 | ||||||||
\(343\) | −61.9793 | −3.34657 | ||||||||
\(344\) | 4.71540 | 0.254237 | ||||||||
\(345\) | −5.25329 | −0.282828 | ||||||||
\(346\) | 18.1015 | 0.973140 | ||||||||
\(347\) | 0.317896 | 0.0170655 | 0.00853276 | − | 0.999964i | \(-0.497284\pi\) | ||||
0.00853276 | + | 0.999964i | \(0.497284\pi\) | |||||||
\(348\) | 2.65506 | 0.142326 | ||||||||
\(349\) | 1.72771 | 0.0924819 | 0.0462410 | − | 0.998930i | \(-0.485276\pi\) | ||||
0.0462410 | + | 0.998930i | \(0.485276\pi\) | |||||||
\(350\) | 56.7491 | 3.03337 | ||||||||
\(351\) | −4.64489 | −0.247926 | ||||||||
\(352\) | −7.65313 | −0.407913 | ||||||||
\(353\) | −30.3094 | −1.61321 | −0.806604 | − | 0.591092i | \(-0.798697\pi\) | ||||
−0.806604 | + | 0.591092i | \(0.798697\pi\) | |||||||
\(354\) | 2.74665 | 0.145983 | ||||||||
\(355\) | 24.7085 | 1.31139 | ||||||||
\(356\) | 13.8090 | 0.731874 | ||||||||
\(357\) | −0.903285 | −0.0478069 | ||||||||
\(358\) | −26.2636 | −1.38807 | ||||||||
\(359\) | 23.7197 | 1.25188 | 0.625939 | − | 0.779872i | \(-0.284716\pi\) | ||||
0.625939 | + | 0.779872i | \(0.284716\pi\) | |||||||
\(360\) | 4.13305 | 0.217831 | ||||||||
\(361\) | 23.4330 | 1.23331 | ||||||||
\(362\) | −2.95836 | −0.155488 | ||||||||
\(363\) | −0.488619 | −0.0256459 | ||||||||
\(364\) | 14.8806 | 0.779956 | ||||||||
\(365\) | −32.0053 | −1.67524 | ||||||||
\(366\) | −4.32401 | −0.226020 | ||||||||
\(367\) | 8.06560 | 0.421021 | 0.210511 | − | 0.977592i | \(-0.432487\pi\) | ||||
0.210511 | + | 0.977592i | \(0.432487\pi\) | |||||||
\(368\) | 14.4982 | 0.755771 | ||||||||
\(369\) | −6.52236 | −0.339540 | ||||||||
\(370\) | 43.9523 | 2.28497 | ||||||||
\(371\) | 40.2136 | 2.08778 | ||||||||
\(372\) | 0.0939531 | 0.00487124 | ||||||||
\(373\) | 19.4001 | 1.00450 | 0.502248 | − | 0.864723i | \(-0.332506\pi\) | ||||
0.502248 | + | 0.864723i | \(0.332506\pi\) | |||||||
\(374\) | −0.701725 | −0.0362853 | ||||||||
\(375\) | 1.15578 | 0.0596841 | ||||||||
\(376\) | −4.14563 | −0.213794 | ||||||||
\(377\) | 5.08153 | 0.261712 | ||||||||
\(378\) | 27.9171 | 1.43590 | ||||||||
\(379\) | −32.1355 | −1.65069 | −0.825344 | − | 0.564630i | \(-0.809019\pi\) | ||||
−0.825344 | + | 0.564630i | \(0.809019\pi\) | |||||||
\(380\) | 37.6352 | 1.93065 | ||||||||
\(381\) | 8.65627 | 0.443474 | ||||||||
\(382\) | 19.7655 | 1.01129 | ||||||||
\(383\) | −0.920470 | −0.0470338 | −0.0235169 | − | 0.999723i | \(-0.507486\pi\) | ||||
−0.0235169 | + | 0.999723i | \(0.507486\pi\) | |||||||
\(384\) | 1.77442 | 0.0905505 | ||||||||
\(385\) | −16.7371 | −0.853002 | ||||||||
\(386\) | −28.4152 | −1.44630 | ||||||||
\(387\) | −28.4842 | −1.44794 | ||||||||
\(388\) | 2.38099 | 0.120877 | ||||||||
\(389\) | 27.2608 | 1.38218 | 0.691090 | − | 0.722769i | \(-0.257131\pi\) | ||||
0.691090 | + | 0.722769i | \(0.257131\pi\) | |||||||
\(390\) | 5.12215 | 0.259370 | ||||||||
\(391\) | 1.18750 | 0.0600546 | ||||||||
\(392\) | 8.74259 | 0.441567 | ||||||||
\(393\) | −9.94793 | −0.501807 | ||||||||
\(394\) | 4.87693 | 0.245696 | ||||||||
\(395\) | 30.0891 | 1.51395 | ||||||||
\(396\) | 4.87196 | 0.244825 | ||||||||
\(397\) | −9.11001 | −0.457218 | −0.228609 | − | 0.973518i | \(-0.573418\pi\) | ||||
−0.228609 | + | 0.973518i | \(0.573418\pi\) | |||||||
\(398\) | 5.03022 | 0.252142 | ||||||||
\(399\) | −16.2689 | −0.814462 | ||||||||
\(400\) | −25.2682 | −1.26341 | ||||||||
\(401\) | 9.00268 | 0.449572 | 0.224786 | − | 0.974408i | \(-0.427832\pi\) | ||||
0.224786 | + | 0.974408i | \(0.427832\pi\) | |||||||
\(402\) | −6.15172 | −0.306820 | ||||||||
\(403\) | 0.179817 | 0.00895733 | ||||||||
\(404\) | 28.6453 | 1.42516 | ||||||||
\(405\) | −22.6211 | −1.12405 | ||||||||
\(406\) | −30.5415 | −1.51575 | ||||||||
\(407\) | −6.91812 | −0.342919 | ||||||||
\(408\) | 0.0807810 | 0.00399926 | ||||||||
\(409\) | −15.1035 | −0.746818 | −0.373409 | − | 0.927667i | \(-0.621811\pi\) | ||||
−0.373409 | + | 0.927667i | \(0.621811\pi\) | |||||||
\(410\) | 15.0069 | 0.741140 | ||||||||
\(411\) | 2.63653 | 0.130051 | ||||||||
\(412\) | 10.8946 | 0.536736 | ||||||||
\(413\) | −14.8088 | −0.728693 | ||||||||
\(414\) | −17.5901 | −0.864509 | ||||||||
\(415\) | 18.5042 | 0.908334 | ||||||||
\(416\) | −12.6278 | −0.619128 | ||||||||
\(417\) | 4.16621 | 0.204020 | ||||||||
\(418\) | −12.6386 | −0.618175 | ||||||||
\(419\) | −5.76354 | −0.281568 | −0.140784 | − | 0.990040i | \(-0.544962\pi\) | ||||
−0.140784 | + | 0.990040i | \(0.544962\pi\) | |||||||
\(420\) | −14.4294 | −0.704083 | ||||||||
\(421\) | 8.39019 | 0.408913 | 0.204457 | − | 0.978876i | \(-0.434457\pi\) | ||||
0.204457 | + | 0.978876i | \(0.434457\pi\) | |||||||
\(422\) | −33.6179 | −1.63649 | ||||||||
\(423\) | 25.0424 | 1.21760 | ||||||||
\(424\) | −3.59631 | −0.174652 | ||||||||
\(425\) | −2.06964 | −0.100392 | ||||||||
\(426\) | −7.15352 | −0.346589 | ||||||||
\(427\) | 23.3133 | 1.12821 | ||||||||
\(428\) | 35.0445 | 1.69394 | ||||||||
\(429\) | −0.806230 | −0.0389251 | ||||||||
\(430\) | 65.5378 | 3.16051 | ||||||||
\(431\) | −32.9025 | −1.58486 | −0.792430 | − | 0.609963i | \(-0.791184\pi\) | ||||
−0.792430 | + | 0.609963i | \(0.791184\pi\) | |||||||
\(432\) | −12.4304 | −0.598059 | ||||||||
\(433\) | −38.2281 | −1.83712 | −0.918562 | − | 0.395276i | \(-0.870649\pi\) | ||||
−0.918562 | + | 0.395276i | \(0.870649\pi\) | |||||||
\(434\) | −1.08075 | −0.0518778 | ||||||||
\(435\) | −4.92746 | −0.236253 | ||||||||
\(436\) | −13.5675 | −0.649764 | ||||||||
\(437\) | 21.3879 | 1.02312 | ||||||||
\(438\) | 9.26608 | 0.442750 | ||||||||
\(439\) | −8.85289 | −0.422525 | −0.211263 | − | 0.977429i | \(-0.567758\pi\) | ||||
−0.211263 | + | 0.977429i | \(0.567758\pi\) | |||||||
\(440\) | 1.49680 | 0.0713573 | ||||||||
\(441\) | −52.8112 | −2.51482 | ||||||||
\(442\) | −1.15786 | −0.0550736 | ||||||||
\(443\) | 7.31931 | 0.347751 | 0.173876 | − | 0.984768i | \(-0.444371\pi\) | ||||
0.173876 | + | 0.984768i | \(0.444371\pi\) | |||||||
\(444\) | −5.96426 | −0.283051 | ||||||||
\(445\) | −25.6277 | −1.21487 | ||||||||
\(446\) | −42.0768 | −1.99239 | ||||||||
\(447\) | 4.61251 | 0.218164 | ||||||||
\(448\) | 30.7564 | 1.45310 | ||||||||
\(449\) | 18.9455 | 0.894093 | 0.447046 | − | 0.894511i | \(-0.352476\pi\) | ||||
0.447046 | + | 0.894511i | \(0.352476\pi\) | |||||||
\(450\) | 30.6570 | 1.44518 | ||||||||
\(451\) | −2.36210 | −0.111227 | ||||||||
\(452\) | 24.5612 | 1.15526 | ||||||||
\(453\) | −6.36450 | −0.299030 | ||||||||
\(454\) | −25.4082 | −1.19247 | ||||||||
\(455\) | −27.6165 | −1.29468 | ||||||||
\(456\) | 1.45493 | 0.0681333 | ||||||||
\(457\) | 35.2067 | 1.64690 | 0.823450 | − | 0.567389i | \(-0.192046\pi\) | ||||
0.823450 | + | 0.567389i | \(0.192046\pi\) | |||||||
\(458\) | −38.2988 | −1.78958 | ||||||||
\(459\) | −1.01814 | −0.0475226 | ||||||||
\(460\) | 18.9696 | 0.884463 | ||||||||
\(461\) | −23.0972 | −1.07574 | −0.537871 | − | 0.843027i | \(-0.680771\pi\) | ||||
−0.537871 | + | 0.843027i | \(0.680771\pi\) | |||||||
\(462\) | 4.84567 | 0.225441 | ||||||||
\(463\) | −4.85058 | −0.225426 | −0.112713 | − | 0.993628i | \(-0.535954\pi\) | ||||
−0.112713 | + | 0.993628i | \(0.535954\pi\) | |||||||
\(464\) | 13.5989 | 0.631315 | ||||||||
\(465\) | −0.174365 | −0.00808598 | ||||||||
\(466\) | 27.4911 | 1.27350 | ||||||||
\(467\) | 15.4737 | 0.716038 | 0.358019 | − | 0.933714i | \(-0.383452\pi\) | ||||
0.358019 | + | 0.933714i | \(0.383452\pi\) | |||||||
\(468\) | 8.03881 | 0.371594 | ||||||||
\(469\) | 33.1675 | 1.53153 | ||||||||
\(470\) | −57.6187 | −2.65775 | ||||||||
\(471\) | 5.04639 | 0.232525 | ||||||||
\(472\) | 1.32435 | 0.0609583 | ||||||||
\(473\) | −10.3157 | −0.474316 | ||||||||
\(474\) | −8.71129 | −0.400123 | ||||||||
\(475\) | −37.2758 | −1.71033 | ||||||||
\(476\) | 3.26176 | 0.149502 | ||||||||
\(477\) | 21.7242 | 0.994682 | ||||||||
\(478\) | −24.1658 | −1.10532 | ||||||||
\(479\) | 9.88432 | 0.451626 | 0.225813 | − | 0.974171i | \(-0.427496\pi\) | ||||
0.225813 | + | 0.974171i | \(0.427496\pi\) | |||||||
\(480\) | 12.2449 | 0.558901 | ||||||||
\(481\) | −11.4150 | −0.520480 | ||||||||
\(482\) | −26.7946 | −1.22046 | ||||||||
\(483\) | −8.20014 | −0.373119 | ||||||||
\(484\) | 1.76440 | 0.0802001 | ||||||||
\(485\) | −4.41881 | −0.200648 | ||||||||
\(486\) | 22.9346 | 1.04033 | ||||||||
\(487\) | 1.77137 | 0.0802684 | 0.0401342 | − | 0.999194i | \(-0.487221\pi\) | ||||
0.0401342 | + | 0.999194i | \(0.487221\pi\) | |||||||
\(488\) | −2.08491 | −0.0943795 | ||||||||
\(489\) | 11.4073 | 0.515856 | ||||||||
\(490\) | 121.510 | 5.48928 | ||||||||
\(491\) | 34.8247 | 1.57162 | 0.785808 | − | 0.618471i | \(-0.212248\pi\) | ||||
0.785808 | + | 0.618471i | \(0.212248\pi\) | |||||||
\(492\) | −2.03642 | −0.0918088 | ||||||||
\(493\) | 1.11385 | 0.0501651 | ||||||||
\(494\) | −20.8539 | −0.938262 | ||||||||
\(495\) | −9.04172 | −0.406395 | ||||||||
\(496\) | 0.481218 | 0.0216073 | ||||||||
\(497\) | 38.5688 | 1.73005 | ||||||||
\(498\) | −5.35726 | −0.240065 | ||||||||
\(499\) | −40.9804 | −1.83453 | −0.917267 | − | 0.398273i | \(-0.869610\pi\) | ||||
−0.917267 | + | 0.398273i | \(0.869610\pi\) | |||||||
\(500\) | −4.17351 | −0.186645 | ||||||||
\(501\) | 6.68586 | 0.298702 | ||||||||
\(502\) | 38.3126 | 1.70997 | ||||||||
\(503\) | 16.2627 | 0.725117 | 0.362559 | − | 0.931961i | \(-0.381903\pi\) | ||||
0.362559 | + | 0.931961i | \(0.381903\pi\) | |||||||
\(504\) | 6.45150 | 0.287373 | ||||||||
\(505\) | −53.1620 | −2.36568 | ||||||||
\(506\) | −6.37035 | −0.283197 | ||||||||
\(507\) | 5.02176 | 0.223024 | ||||||||
\(508\) | −31.2577 | −1.38684 | ||||||||
\(509\) | −8.85673 | −0.392568 | −0.196284 | − | 0.980547i | \(-0.562887\pi\) | ||||
−0.196284 | + | 0.980547i | \(0.562887\pi\) | |||||||
\(510\) | 1.12275 | 0.0497162 | ||||||||
\(511\) | −49.9588 | −2.21005 | ||||||||
\(512\) | −29.7570 | −1.31508 | ||||||||
\(513\) | −18.3375 | −0.809619 | ||||||||
\(514\) | −30.2406 | −1.33385 | ||||||||
\(515\) | −20.2189 | −0.890951 | ||||||||
\(516\) | −8.89338 | −0.391509 | ||||||||
\(517\) | 9.06923 | 0.398864 | ||||||||
\(518\) | 68.6075 | 3.01444 | ||||||||
\(519\) | 4.55865 | 0.200102 | ||||||||
\(520\) | 2.46975 | 0.108306 | ||||||||
\(521\) | 22.0038 | 0.964004 | 0.482002 | − | 0.876170i | \(-0.339910\pi\) | ||||
0.482002 | + | 0.876170i | \(0.339910\pi\) | |||||||
\(522\) | −16.4991 | −0.722147 | ||||||||
\(523\) | −16.6957 | −0.730053 | −0.365026 | − | 0.930997i | \(-0.618940\pi\) | ||||
−0.365026 | + | 0.930997i | \(0.618940\pi\) | |||||||
\(524\) | 35.9219 | 1.56926 | ||||||||
\(525\) | 14.2916 | 0.623737 | ||||||||
\(526\) | 4.48870 | 0.195717 | ||||||||
\(527\) | 0.0394150 | 0.00171695 | ||||||||
\(528\) | −2.15759 | −0.0938971 | ||||||||
\(529\) | −12.2197 | −0.531291 | ||||||||
\(530\) | −49.9840 | −2.17116 | ||||||||
\(531\) | −8.00001 | −0.347171 | ||||||||
\(532\) | 58.7468 | 2.54700 | ||||||||
\(533\) | −3.89751 | −0.168820 | ||||||||
\(534\) | 7.41963 | 0.321079 | ||||||||
\(535\) | −65.0381 | −2.81184 | ||||||||
\(536\) | −2.96618 | −0.128119 | ||||||||
\(537\) | −6.61419 | −0.285423 | ||||||||
\(538\) | −3.14357 | −0.135529 | ||||||||
\(539\) | −19.1258 | −0.823808 | ||||||||
\(540\) | −16.2641 | −0.699896 | ||||||||
\(541\) | 12.8557 | 0.552710 | 0.276355 | − | 0.961056i | \(-0.410874\pi\) | ||||
0.276355 | + | 0.961056i | \(0.410874\pi\) | |||||||
\(542\) | 7.15832 | 0.307476 | ||||||||
\(543\) | −0.745029 | −0.0319723 | ||||||||
\(544\) | −2.76795 | −0.118675 | ||||||||
\(545\) | 25.1795 | 1.07857 | ||||||||
\(546\) | 7.99543 | 0.342173 | ||||||||
\(547\) | −1.00000 | −0.0427569 | ||||||||
\(548\) | −9.52050 | −0.406696 | ||||||||
\(549\) | 12.5943 | 0.537511 | ||||||||
\(550\) | 11.1026 | 0.473415 | ||||||||
\(551\) | 20.0613 | 0.854639 | ||||||||
\(552\) | 0.733341 | 0.0312131 | ||||||||
\(553\) | 46.9677 | 1.99727 | ||||||||
\(554\) | 49.0520 | 2.08402 | ||||||||
\(555\) | 11.0689 | 0.469848 | ||||||||
\(556\) | −15.0442 | −0.638015 | ||||||||
\(557\) | −20.6132 | −0.873410 | −0.436705 | − | 0.899605i | \(-0.643855\pi\) | ||||
−0.436705 | + | 0.899605i | \(0.643855\pi\) | |||||||
\(558\) | −0.583844 | −0.0247161 | ||||||||
\(559\) | −17.0211 | −0.719914 | ||||||||
\(560\) | −73.9059 | −3.12309 | ||||||||
\(561\) | −0.176722 | −0.00746119 | ||||||||
\(562\) | −26.7886 | −1.13001 | ||||||||
\(563\) | 17.7405 | 0.747671 | 0.373836 | − | 0.927495i | \(-0.378042\pi\) | ||||
0.373836 | + | 0.927495i | \(0.378042\pi\) | |||||||
\(564\) | 7.81877 | 0.329230 | ||||||||
\(565\) | −45.5825 | −1.91767 | ||||||||
\(566\) | 33.1050 | 1.39151 | ||||||||
\(567\) | −35.3105 | −1.48290 | ||||||||
\(568\) | −3.44922 | −0.144726 | ||||||||
\(569\) | 11.2057 | 0.469769 | 0.234884 | − | 0.972023i | \(-0.424529\pi\) | ||||
0.234884 | + | 0.972023i | \(0.424529\pi\) | |||||||
\(570\) | 20.2216 | 0.846990 | ||||||||
\(571\) | 18.9788 | 0.794240 | 0.397120 | − | 0.917767i | \(-0.370010\pi\) | ||||
0.397120 | + | 0.917767i | \(0.370010\pi\) | |||||||
\(572\) | 2.91129 | 0.121727 | ||||||||
\(573\) | 4.97772 | 0.207947 | ||||||||
\(574\) | 23.4251 | 0.977746 | ||||||||
\(575\) | −18.7885 | −0.783533 | ||||||||
\(576\) | 16.6152 | 0.692301 | ||||||||
\(577\) | −39.7154 | −1.65337 | −0.826687 | − | 0.562662i | \(-0.809777\pi\) | ||||
−0.826687 | + | 0.562662i | \(0.809777\pi\) | |||||||
\(578\) | 32.7297 | 1.36138 | ||||||||
\(579\) | −7.15605 | −0.297395 | ||||||||
\(580\) | 17.7930 | 0.738815 | ||||||||
\(581\) | 28.8841 | 1.19832 | ||||||||
\(582\) | 1.27932 | 0.0530295 | ||||||||
\(583\) | 7.86751 | 0.325839 | ||||||||
\(584\) | 4.46783 | 0.184880 | ||||||||
\(585\) | −14.9190 | −0.616824 | ||||||||
\(586\) | −18.8798 | −0.779915 | ||||||||
\(587\) | −24.4578 | −1.00948 | −0.504740 | − | 0.863271i | \(-0.668412\pi\) | ||||
−0.504740 | + | 0.863271i | \(0.668412\pi\) | |||||||
\(588\) | −16.4888 | −0.679986 | ||||||||
\(589\) | 0.709896 | 0.0292508 | ||||||||
\(590\) | 18.4068 | 0.757795 | ||||||||
\(591\) | 1.22820 | 0.0505214 | ||||||||
\(592\) | −30.5483 | −1.25553 | ||||||||
\(593\) | −2.76514 | −0.113551 | −0.0567753 | − | 0.998387i | \(-0.518082\pi\) | ||||
−0.0567753 | + | 0.998387i | \(0.518082\pi\) | |||||||
\(594\) | 5.46180 | 0.224100 | ||||||||
\(595\) | −6.05340 | −0.248165 | ||||||||
\(596\) | −16.6558 | −0.682247 | ||||||||
\(597\) | 1.26680 | 0.0518468 | ||||||||
\(598\) | −10.5112 | −0.429834 | ||||||||
\(599\) | 15.8915 | 0.649310 | 0.324655 | − | 0.945832i | \(-0.394752\pi\) | ||||
0.324655 | + | 0.945832i | \(0.394752\pi\) | |||||||
\(600\) | −1.27810 | −0.0521784 | ||||||||
\(601\) | 11.9971 | 0.489373 | 0.244686 | − | 0.969602i | \(-0.421315\pi\) | ||||
0.244686 | + | 0.969602i | \(0.421315\pi\) | |||||||
\(602\) | 102.301 | 4.16950 | ||||||||
\(603\) | 17.9178 | 0.729668 | ||||||||
\(604\) | 22.9822 | 0.935131 | ||||||||
\(605\) | −3.27450 | −0.133127 | ||||||||
\(606\) | 15.3913 | 0.625228 | ||||||||
\(607\) | −22.2404 | −0.902710 | −0.451355 | − | 0.892345i | \(-0.649059\pi\) | ||||
−0.451355 | + | 0.892345i | \(0.649059\pi\) | |||||||
\(608\) | −49.8530 | −2.02180 | ||||||||
\(609\) | −7.69152 | −0.311676 | ||||||||
\(610\) | −28.9775 | −1.17327 | ||||||||
\(611\) | 14.9644 | 0.605394 | ||||||||
\(612\) | 1.76207 | 0.0712273 | ||||||||
\(613\) | 5.48896 | 0.221697 | 0.110848 | − | 0.993837i | \(-0.464643\pi\) | ||||
0.110848 | + | 0.993837i | \(0.464643\pi\) | |||||||
\(614\) | 30.5642 | 1.23347 | ||||||||
\(615\) | 3.77933 | 0.152397 | ||||||||
\(616\) | 2.33644 | 0.0941379 | ||||||||
\(617\) | −35.2720 | −1.42000 | −0.709998 | − | 0.704203i | \(-0.751304\pi\) | ||||
−0.709998 | + | 0.704203i | \(0.751304\pi\) | |||||||
\(618\) | 5.85370 | 0.235471 | ||||||||
\(619\) | −13.1948 | −0.530344 | −0.265172 | − | 0.964201i | \(-0.585429\pi\) | ||||
−0.265172 | + | 0.964201i | \(0.585429\pi\) | |||||||
\(620\) | 0.629631 | 0.0252866 | ||||||||
\(621\) | −9.24279 | −0.370900 | ||||||||
\(622\) | −61.2289 | −2.45505 | ||||||||
\(623\) | −40.0036 | −1.60271 | ||||||||
\(624\) | −3.56006 | −0.142516 | ||||||||
\(625\) | −20.8663 | −0.834654 | ||||||||
\(626\) | −7.57906 | −0.302920 | ||||||||
\(627\) | −3.18290 | −0.127113 | ||||||||
\(628\) | −18.2225 | −0.727156 | ||||||||
\(629\) | −2.50211 | −0.0997658 | ||||||||
\(630\) | 89.6673 | 3.57243 | ||||||||
\(631\) | −9.09116 | −0.361913 | −0.180957 | − | 0.983491i | \(-0.557919\pi\) | ||||
−0.180957 | + | 0.983491i | \(0.557919\pi\) | |||||||
\(632\) | −4.20033 | −0.167080 | ||||||||
\(633\) | −8.46629 | −0.336505 | ||||||||
\(634\) | −17.2140 | −0.683656 | ||||||||
\(635\) | 58.0104 | 2.30207 | ||||||||
\(636\) | 6.78275 | 0.268953 | ||||||||
\(637\) | −31.5579 | −1.25037 | ||||||||
\(638\) | −5.97523 | −0.236562 | ||||||||
\(639\) | 20.8357 | 0.824246 | ||||||||
\(640\) | 11.8914 | 0.470047 | ||||||||
\(641\) | 6.75915 | 0.266970 | 0.133485 | − | 0.991051i | \(-0.457383\pi\) | ||||
0.133485 | + | 0.991051i | \(0.457383\pi\) | |||||||
\(642\) | 18.8296 | 0.743145 | ||||||||
\(643\) | 19.9750 | 0.787739 | 0.393869 | − | 0.919166i | \(-0.371136\pi\) | ||||
0.393869 | + | 0.919166i | \(0.371136\pi\) | |||||||
\(644\) | 29.6107 | 1.16682 | ||||||||
\(645\) | 16.5050 | 0.649882 | ||||||||
\(646\) | −4.57108 | −0.179847 | ||||||||
\(647\) | 20.2495 | 0.796091 | 0.398046 | − | 0.917366i | \(-0.369689\pi\) | ||||
0.398046 | + | 0.917366i | \(0.369689\pi\) | |||||||
\(648\) | 3.15783 | 0.124051 | ||||||||
\(649\) | −2.89724 | −0.113727 | ||||||||
\(650\) | 18.3194 | 0.718547 | ||||||||
\(651\) | −0.272175 | −0.0106674 | ||||||||
\(652\) | −41.1917 | −1.61319 | ||||||||
\(653\) | 27.4286 | 1.07337 | 0.536683 | − | 0.843784i | \(-0.319677\pi\) | ||||
0.536683 | + | 0.843784i | \(0.319677\pi\) | |||||||
\(654\) | −7.28987 | −0.285057 | ||||||||
\(655\) | −66.6665 | −2.60488 | ||||||||
\(656\) | −10.4303 | −0.407235 | ||||||||
\(657\) | −26.9888 | −1.05293 | ||||||||
\(658\) | −89.9401 | −3.50623 | ||||||||
\(659\) | 34.9071 | 1.35979 | 0.679894 | − | 0.733311i | \(-0.262026\pi\) | ||||
0.679894 | + | 0.733311i | \(0.262026\pi\) | |||||||
\(660\) | −2.82302 | −0.109886 | ||||||||
\(661\) | 26.4739 | 1.02972 | 0.514858 | − | 0.857275i | \(-0.327845\pi\) | ||||
0.514858 | + | 0.857275i | \(0.327845\pi\) | |||||||
\(662\) | 24.7872 | 0.963383 | ||||||||
\(663\) | −0.291593 | −0.0113245 | ||||||||
\(664\) | −2.58312 | −0.100244 | ||||||||
\(665\) | −109.027 | −4.22787 | ||||||||
\(666\) | 37.0631 | 1.43617 | ||||||||
\(667\) | 10.1117 | 0.391525 | ||||||||
\(668\) | −24.1426 | −0.934106 | ||||||||
\(669\) | −10.5966 | −0.409687 | ||||||||
\(670\) | −41.2260 | −1.59270 | ||||||||
\(671\) | 4.56108 | 0.176079 | ||||||||
\(672\) | 19.1137 | 0.737327 | ||||||||
\(673\) | 20.0735 | 0.773775 | 0.386888 | − | 0.922127i | \(-0.373550\pi\) | ||||
0.386888 | + | 0.922127i | \(0.373550\pi\) | |||||||
\(674\) | 17.5167 | 0.674717 | ||||||||
\(675\) | 16.1088 | 0.620028 | ||||||||
\(676\) | −18.1336 | −0.697444 | ||||||||
\(677\) | −10.1734 | −0.390995 | −0.195497 | − | 0.980704i | \(-0.562632\pi\) | ||||
−0.195497 | + | 0.980704i | \(0.562632\pi\) | |||||||
\(678\) | 13.1969 | 0.506823 | ||||||||
\(679\) | −6.89756 | −0.264704 | ||||||||
\(680\) | 0.541357 | 0.0207601 | ||||||||
\(681\) | −6.39878 | −0.245202 | ||||||||
\(682\) | −0.211442 | −0.00809653 | ||||||||
\(683\) | 20.2889 | 0.776334 | 0.388167 | − | 0.921589i | \(-0.373108\pi\) | ||||
0.388167 | + | 0.921589i | \(0.373108\pi\) | |||||||
\(684\) | 31.7362 | 1.21346 | ||||||||
\(685\) | 17.6688 | 0.675091 | ||||||||
\(686\) | 120.253 | 4.59127 | ||||||||
\(687\) | −9.64511 | −0.367984 | ||||||||
\(688\) | −45.5509 | −1.73661 | ||||||||
\(689\) | 12.9815 | 0.494556 | ||||||||
\(690\) | 10.1925 | 0.388021 | ||||||||
\(691\) | 43.0784 | 1.63878 | 0.819389 | − | 0.573237i | \(-0.194313\pi\) | ||||
0.819389 | + | 0.573237i | \(0.194313\pi\) | |||||||
\(692\) | −16.4613 | −0.625763 | ||||||||
\(693\) | −14.1137 | −0.536135 | ||||||||
\(694\) | −0.616783 | −0.0234128 | ||||||||
\(695\) | 27.9200 | 1.05907 | ||||||||
\(696\) | 0.687855 | 0.0260731 | ||||||||
\(697\) | −0.854314 | −0.0323595 | ||||||||
\(698\) | −3.35211 | −0.126879 | ||||||||
\(699\) | 6.92333 | 0.261864 | ||||||||
\(700\) | −51.6070 | −1.95056 | ||||||||
\(701\) | 30.4733 | 1.15096 | 0.575480 | − | 0.817816i | \(-0.304815\pi\) | ||||
0.575480 | + | 0.817816i | \(0.304815\pi\) | |||||||
\(702\) | 9.01205 | 0.340138 | ||||||||
\(703\) | −45.0651 | −1.69966 | ||||||||
\(704\) | 6.01728 | 0.226785 | ||||||||
\(705\) | −14.5106 | −0.546502 | ||||||||
\(706\) | 58.8066 | 2.21321 | ||||||||
\(707\) | −82.9833 | −3.12091 | ||||||||
\(708\) | −2.49777 | −0.0938720 | ||||||||
\(709\) | 32.2468 | 1.21105 | 0.605526 | − | 0.795825i | \(-0.292963\pi\) | ||||
0.605526 | + | 0.795825i | \(0.292963\pi\) | |||||||
\(710\) | −47.9396 | −1.79914 | ||||||||
\(711\) | 25.3729 | 0.951557 | ||||||||
\(712\) | 3.57753 | 0.134074 | ||||||||
\(713\) | 0.357815 | 0.0134003 | ||||||||
\(714\) | 1.75256 | 0.0655879 | ||||||||
\(715\) | −5.40298 | −0.202060 | ||||||||
\(716\) | 23.8838 | 0.892580 | ||||||||
\(717\) | −6.08588 | −0.227282 | ||||||||
\(718\) | −46.0211 | −1.71749 | ||||||||
\(719\) | −33.2211 | −1.23894 | −0.619469 | − | 0.785021i | \(-0.712652\pi\) | ||||
−0.619469 | + | 0.785021i | \(0.712652\pi\) | |||||||
\(720\) | −39.9254 | −1.48793 | ||||||||
\(721\) | −31.5607 | −1.17538 | ||||||||
\(722\) | −45.4648 | −1.69203 | ||||||||
\(723\) | −6.74793 | −0.250958 | ||||||||
\(724\) | 2.69030 | 0.0999841 | ||||||||
\(725\) | −17.6231 | −0.654506 | ||||||||
\(726\) | 0.948022 | 0.0351844 | ||||||||
\(727\) | −21.2412 | −0.787793 | −0.393897 | − | 0.919155i | \(-0.628873\pi\) | ||||
−0.393897 | + | 0.919155i | \(0.628873\pi\) | |||||||
\(728\) | 3.85516 | 0.142882 | ||||||||
\(729\) | −14.9490 | −0.553666 | ||||||||
\(730\) | 62.0970 | 2.29831 | ||||||||
\(731\) | −3.73093 | −0.137994 | ||||||||
\(732\) | 3.93220 | 0.145338 | ||||||||
\(733\) | −45.5654 | −1.68300 | −0.841498 | − | 0.540261i | \(-0.818326\pi\) | ||||
−0.841498 | + | 0.540261i | \(0.818326\pi\) | |||||||
\(734\) | −15.6489 | −0.577613 | ||||||||
\(735\) | 30.6011 | 1.12874 | ||||||||
\(736\) | −25.1278 | −0.926224 | ||||||||
\(737\) | 6.48900 | 0.239025 | ||||||||
\(738\) | 12.6547 | 0.465827 | ||||||||
\(739\) | −10.4760 | −0.385367 | −0.192684 | − | 0.981261i | \(-0.561719\pi\) | ||||
−0.192684 | + | 0.981261i | \(0.561719\pi\) | |||||||
\(740\) | −39.9697 | −1.46932 | ||||||||
\(741\) | −5.25183 | −0.192931 | ||||||||
\(742\) | −78.0226 | −2.86430 | ||||||||
\(743\) | −38.7806 | −1.42272 | −0.711360 | − | 0.702828i | \(-0.751921\pi\) | ||||
−0.711360 | + | 0.702828i | \(0.751921\pi\) | |||||||
\(744\) | 0.0243407 | 0.000892374 0 | ||||||||
\(745\) | 30.9110 | 1.13249 | ||||||||
\(746\) | −37.6401 | −1.37810 | ||||||||
\(747\) | 15.6038 | 0.570913 | ||||||||
\(748\) | 0.638141 | 0.0233327 | ||||||||
\(749\) | −101.521 | −3.70951 | ||||||||
\(750\) | −2.24245 | −0.0818826 | ||||||||
\(751\) | 20.5384 | 0.749456 | 0.374728 | − | 0.927135i | \(-0.377736\pi\) | ||||
0.374728 | + | 0.927135i | \(0.377736\pi\) | |||||||
\(752\) | 40.0469 | 1.46036 | ||||||||
\(753\) | 9.64860 | 0.351614 | ||||||||
\(754\) | −9.85922 | −0.359052 | ||||||||
\(755\) | −42.6520 | −1.55226 | ||||||||
\(756\) | −25.3875 | −0.923335 | ||||||||
\(757\) | −49.1282 | −1.78560 | −0.892798 | − | 0.450457i | \(-0.851261\pi\) | ||||
−0.892798 | + | 0.450457i | \(0.851261\pi\) | |||||||
\(758\) | 62.3494 | 2.26463 | ||||||||
\(759\) | −1.60430 | −0.0582325 | ||||||||
\(760\) | 9.75027 | 0.353680 | ||||||||
\(761\) | −15.0139 | −0.544254 | −0.272127 | − | 0.962261i | \(-0.587727\pi\) | ||||
−0.272127 | + | 0.962261i | \(0.587727\pi\) | |||||||
\(762\) | −16.7950 | −0.608417 | ||||||||
\(763\) | 39.3040 | 1.42290 | ||||||||
\(764\) | −17.9745 | −0.650295 | ||||||||
\(765\) | −3.27017 | −0.118233 | ||||||||
\(766\) | 1.78590 | 0.0645272 | ||||||||
\(767\) | −4.78049 | −0.172614 | ||||||||
\(768\) | −9.32306 | −0.336417 | ||||||||
\(769\) | −2.01229 | −0.0725649 | −0.0362825 | − | 0.999342i | \(-0.511552\pi\) | ||||
−0.0362825 | + | 0.999342i | \(0.511552\pi\) | |||||||
\(770\) | 32.4734 | 1.17026 | ||||||||
\(771\) | −7.61575 | −0.274274 | ||||||||
\(772\) | 25.8405 | 0.930019 | ||||||||
\(773\) | 25.0292 | 0.900237 | 0.450119 | − | 0.892969i | \(-0.351382\pi\) | ||||
0.450119 | + | 0.892969i | \(0.351382\pi\) | |||||||
\(774\) | 55.2653 | 1.98647 | ||||||||
\(775\) | −0.623618 | −0.0224010 | ||||||||
\(776\) | 0.616851 | 0.0221437 | ||||||||
\(777\) | 17.2780 | 0.619846 | ||||||||
\(778\) | −52.8917 | −1.89626 | ||||||||
\(779\) | −15.3869 | −0.551292 | ||||||||
\(780\) | −4.65802 | −0.166784 | ||||||||
\(781\) | 7.54573 | 0.270008 | ||||||||
\(782\) | −2.30400 | −0.0823909 | ||||||||
\(783\) | −8.66950 | −0.309823 | ||||||||
\(784\) | −84.4537 | −3.01621 | ||||||||
\(785\) | 33.8186 | 1.20704 | ||||||||
\(786\) | 19.3010 | 0.688446 | ||||||||
\(787\) | −26.9062 | −0.959104 | −0.479552 | − | 0.877514i | \(-0.659201\pi\) | ||||
−0.479552 | + | 0.877514i | \(0.659201\pi\) | |||||||
\(788\) | −4.43503 | −0.157991 | ||||||||
\(789\) | 1.13043 | 0.0402443 | ||||||||
\(790\) | −58.3791 | −2.07703 | ||||||||
\(791\) | −71.1521 | −2.52988 | ||||||||
\(792\) | 1.26219 | 0.0448501 | ||||||||
\(793\) | 7.52586 | 0.267251 | ||||||||
\(794\) | 17.6753 | 0.627273 | ||||||||
\(795\) | −12.5879 | −0.446447 | ||||||||
\(796\) | −4.57442 | −0.162136 | ||||||||
\(797\) | −33.8435 | −1.19880 | −0.599399 | − | 0.800450i | \(-0.704594\pi\) | ||||
−0.599399 | + | 0.800450i | \(0.704594\pi\) | |||||||
\(798\) | 31.5650 | 1.11739 | ||||||||
\(799\) | 3.28012 | 0.116042 | ||||||||
\(800\) | 43.7940 | 1.54835 | ||||||||
\(801\) | −21.6107 | −0.763578 | ||||||||
\(802\) | −17.4671 | −0.616783 | ||||||||
\(803\) | −9.77411 | −0.344921 | ||||||||
\(804\) | 5.59430 | 0.197296 | ||||||||
\(805\) | −54.9536 | −1.93686 | ||||||||
\(806\) | −0.348883 | −0.0122889 | ||||||||
\(807\) | −0.791672 | −0.0278682 | ||||||||
\(808\) | 7.42122 | 0.261078 | ||||||||
\(809\) | 55.3092 | 1.94457 | 0.972283 | − | 0.233806i | \(-0.0751181\pi\) | ||||
0.972283 | + | 0.233806i | \(0.0751181\pi\) | |||||||
\(810\) | 43.8896 | 1.54213 | ||||||||
\(811\) | −36.4249 | −1.27905 | −0.639526 | − | 0.768770i | \(-0.720869\pi\) | ||||
−0.639526 | + | 0.768770i | \(0.720869\pi\) | |||||||
\(812\) | 27.7741 | 0.974678 | ||||||||
\(813\) | 1.80274 | 0.0632249 | ||||||||
\(814\) | 13.4226 | 0.470461 | ||||||||
\(815\) | 76.4465 | 2.67780 | ||||||||
\(816\) | −0.780347 | −0.0273176 | ||||||||
\(817\) | −67.1971 | −2.35093 | ||||||||
\(818\) | 29.3038 | 1.02458 | ||||||||
\(819\) | −23.2878 | −0.813743 | ||||||||
\(820\) | −13.6471 | −0.476579 | ||||||||
\(821\) | −4.81530 | −0.168055 | −0.0840276 | − | 0.996463i | \(-0.526778\pi\) | ||||
−0.0840276 | + | 0.996463i | \(0.526778\pi\) | |||||||
\(822\) | −5.11542 | −0.178421 | ||||||||
\(823\) | −41.8330 | −1.45821 | −0.729103 | − | 0.684404i | \(-0.760062\pi\) | ||||
−0.729103 | + | 0.684404i | \(0.760062\pi\) | |||||||
\(824\) | 2.82249 | 0.0983260 | ||||||||
\(825\) | 2.79606 | 0.0973463 | ||||||||
\(826\) | 28.7321 | 0.999718 | ||||||||
\(827\) | 37.8199 | 1.31513 | 0.657564 | − | 0.753399i | \(-0.271587\pi\) | ||||
0.657564 | + | 0.753399i | \(0.271587\pi\) | |||||||
\(828\) | 15.9963 | 0.555909 | ||||||||
\(829\) | −24.9835 | −0.867713 | −0.433857 | − | 0.900982i | \(-0.642848\pi\) | ||||
−0.433857 | + | 0.900982i | \(0.642848\pi\) | |||||||
\(830\) | −35.9019 | −1.24617 | ||||||||
\(831\) | 12.3532 | 0.428528 | ||||||||
\(832\) | 9.92861 | 0.344212 | ||||||||
\(833\) | −6.91734 | −0.239672 | ||||||||
\(834\) | −8.08331 | −0.279902 | ||||||||
\(835\) | 44.8056 | 1.55056 | ||||||||
\(836\) | 11.4934 | 0.397508 | ||||||||
\(837\) | −0.306783 | −0.0106040 | ||||||||
\(838\) | 11.1825 | 0.386292 | ||||||||
\(839\) | −26.0845 | −0.900537 | −0.450269 | − | 0.892893i | \(-0.648672\pi\) | ||||
−0.450269 | + | 0.892893i | \(0.648672\pi\) | |||||||
\(840\) | −3.73827 | −0.128983 | ||||||||
\(841\) | −19.5155 | −0.672949 | ||||||||
\(842\) | −16.2787 | −0.561001 | ||||||||
\(843\) | −6.74640 | −0.232358 | ||||||||
\(844\) | 30.5717 | 1.05232 | ||||||||
\(845\) | 33.6535 | 1.15772 | ||||||||
\(846\) | −48.5875 | −1.67047 | ||||||||
\(847\) | −5.11134 | −0.175628 | ||||||||
\(848\) | 34.7405 | 1.19299 | ||||||||
\(849\) | 8.33713 | 0.286129 | ||||||||
\(850\) | 4.01553 | 0.137731 | ||||||||
\(851\) | −22.7145 | −0.778644 | ||||||||
\(852\) | 6.50533 | 0.222869 | ||||||||
\(853\) | 46.4101 | 1.58905 | 0.794526 | − | 0.607230i | \(-0.207719\pi\) | ||||
0.794526 | + | 0.607230i | \(0.207719\pi\) | |||||||
\(854\) | −45.2325 | −1.54783 | ||||||||
\(855\) | −58.8983 | −2.01428 | ||||||||
\(856\) | 9.07909 | 0.310317 | ||||||||
\(857\) | 12.5345 | 0.428171 | 0.214086 | − | 0.976815i | \(-0.431323\pi\) | ||||
0.214086 | + | 0.976815i | \(0.431323\pi\) | |||||||
\(858\) | 1.56425 | 0.0534027 | ||||||||
\(859\) | 10.1386 | 0.345926 | 0.172963 | − | 0.984928i | \(-0.444666\pi\) | ||||
0.172963 | + | 0.984928i | \(0.444666\pi\) | |||||||
\(860\) | −59.5994 | −2.03232 | ||||||||
\(861\) | 5.89935 | 0.201049 | ||||||||
\(862\) | 63.8377 | 2.17432 | ||||||||
\(863\) | −24.6810 | −0.840151 | −0.420075 | − | 0.907489i | \(-0.637996\pi\) | ||||
−0.420075 | + | 0.907489i | \(0.637996\pi\) | |||||||
\(864\) | 21.5440 | 0.732942 | ||||||||
\(865\) | 30.5500 | 1.03873 | ||||||||
\(866\) | 74.1704 | 2.52041 | ||||||||
\(867\) | 8.24261 | 0.279934 | ||||||||
\(868\) | 0.982824 | 0.0333592 | ||||||||
\(869\) | 9.18891 | 0.311712 | ||||||||
\(870\) | 9.56028 | 0.324124 | ||||||||
\(871\) | 10.7070 | 0.362791 | ||||||||
\(872\) | −3.51497 | −0.119032 | ||||||||
\(873\) | −3.72620 | −0.126113 | ||||||||
\(874\) | −41.4969 | −1.40365 | ||||||||
\(875\) | 12.0903 | 0.408728 | ||||||||
\(876\) | −8.42646 | −0.284704 | ||||||||
\(877\) | 33.0435 | 1.11580 | 0.557900 | − | 0.829908i | \(-0.311607\pi\) | ||||
0.557900 | + | 0.829908i | \(0.311607\pi\) | |||||||
\(878\) | 17.1764 | 0.579676 | ||||||||
\(879\) | −4.75465 | −0.160371 | ||||||||
\(880\) | −14.4592 | −0.487419 | ||||||||
\(881\) | −2.12325 | −0.0715341 | −0.0357671 | − | 0.999360i | \(-0.511387\pi\) | ||||
−0.0357671 | + | 0.999360i | \(0.511387\pi\) | |||||||
\(882\) | 102.465 | 3.45017 | ||||||||
\(883\) | 32.2644 | 1.08578 | 0.542891 | − | 0.839803i | \(-0.317330\pi\) | ||||
0.542891 | + | 0.839803i | \(0.317330\pi\) | |||||||
\(884\) | 1.05294 | 0.0354143 | ||||||||
\(885\) | 4.63554 | 0.155822 | ||||||||
\(886\) | −14.2010 | −0.477091 | ||||||||
\(887\) | 0.265292 | 0.00890763 | 0.00445381 | − | 0.999990i | \(-0.498582\pi\) | ||||
0.00445381 | + | 0.999990i | \(0.498582\pi\) | |||||||
\(888\) | −1.54518 | −0.0518528 | ||||||||
\(889\) | 90.5514 | 3.03700 | ||||||||
\(890\) | 49.7230 | 1.66672 | ||||||||
\(891\) | −6.90826 | −0.231435 | ||||||||
\(892\) | 38.2642 | 1.28118 | ||||||||
\(893\) | 59.0775 | 1.97695 | ||||||||
\(894\) | −8.94923 | −0.299307 | ||||||||
\(895\) | −44.3253 | −1.48163 | ||||||||
\(896\) | 18.5618 | 0.620108 | ||||||||
\(897\) | −2.64712 | −0.0883849 | ||||||||
\(898\) | −36.7582 | −1.22664 | ||||||||
\(899\) | 0.335622 | 0.0111936 | ||||||||
\(900\) | −27.8791 | −0.929304 | ||||||||
\(901\) | 2.84548 | 0.0947968 | ||||||||
\(902\) | 4.58297 | 0.152596 | ||||||||
\(903\) | 25.7635 | 0.857355 | ||||||||
\(904\) | 6.36315 | 0.211635 | ||||||||
\(905\) | −4.99285 | −0.165968 | ||||||||
\(906\) | 12.3484 | 0.410250 | ||||||||
\(907\) | 11.4845 | 0.381338 | 0.190669 | − | 0.981654i | \(-0.438934\pi\) | ||||
0.190669 | + | 0.981654i | \(0.438934\pi\) | |||||||
\(908\) | 23.1060 | 0.766798 | ||||||||
\(909\) | −44.8293 | −1.48689 | ||||||||
\(910\) | 53.5817 | 1.77622 | ||||||||
\(911\) | −33.6860 | −1.11607 | −0.558034 | − | 0.829818i | \(-0.688444\pi\) | ||||
−0.558034 | + | 0.829818i | \(0.688444\pi\) | |||||||
\(912\) | −14.0547 | −0.465397 | ||||||||
\(913\) | 5.65099 | 0.187020 | ||||||||
\(914\) | −68.3083 | −2.25944 | ||||||||
\(915\) | −7.29766 | −0.241253 | ||||||||
\(916\) | 34.8285 | 1.15076 | ||||||||
\(917\) | −104.063 | −3.43647 | ||||||||
\(918\) | 1.97540 | 0.0651978 | ||||||||
\(919\) | 28.5969 | 0.943325 | 0.471662 | − | 0.881779i | \(-0.343654\pi\) | ||||
0.471662 | + | 0.881779i | \(0.343654\pi\) | |||||||
\(920\) | 4.91451 | 0.162027 | ||||||||
\(921\) | 7.69725 | 0.253633 | ||||||||
\(922\) | 44.8133 | 1.47585 | ||||||||
\(923\) | 12.4506 | 0.409816 | ||||||||
\(924\) | −4.40660 | −0.144966 | ||||||||
\(925\) | 39.5880 | 1.30165 | ||||||||
\(926\) | 9.41113 | 0.309269 | ||||||||
\(927\) | −17.0498 | −0.559987 | ||||||||
\(928\) | −23.5693 | −0.773699 | ||||||||
\(929\) | −23.1997 | −0.761157 | −0.380579 | − | 0.924749i | \(-0.624275\pi\) | ||||
−0.380579 | + | 0.924749i | \(0.624275\pi\) | |||||||
\(930\) | 0.338304 | 0.0110934 | ||||||||
\(931\) | −124.587 | −4.08317 | ||||||||
\(932\) | −25.0001 | −0.818905 | ||||||||
\(933\) | −15.4198 | −0.504822 | ||||||||
\(934\) | −30.0222 | −0.982357 | ||||||||
\(935\) | −1.18431 | −0.0387310 | ||||||||
\(936\) | 2.08264 | 0.0680731 | ||||||||
\(937\) | 54.4489 | 1.77877 | 0.889384 | − | 0.457160i | \(-0.151133\pi\) | ||||
0.889384 | + | 0.457160i | \(0.151133\pi\) | |||||||
\(938\) | −64.3518 | −2.10116 | ||||||||
\(939\) | −1.90870 | −0.0622881 | ||||||||
\(940\) | 52.3978 | 1.70903 | ||||||||
\(941\) | 52.6826 | 1.71740 | 0.858701 | − | 0.512476i | \(-0.171272\pi\) | ||||
0.858701 | + | 0.512476i | \(0.171272\pi\) | |||||||
\(942\) | −9.79104 | −0.319009 | ||||||||
\(943\) | −7.75558 | −0.252557 | ||||||||
\(944\) | −12.7933 | −0.416387 | ||||||||
\(945\) | 47.1159 | 1.53268 | ||||||||
\(946\) | 20.0146 | 0.650730 | ||||||||
\(947\) | −35.7126 | −1.16050 | −0.580251 | − | 0.814437i | \(-0.697046\pi\) | ||||
−0.580251 | + | 0.814437i | \(0.697046\pi\) | |||||||
\(948\) | 7.92195 | 0.257293 | ||||||||
\(949\) | −16.1274 | −0.523519 | ||||||||
\(950\) | 72.3228 | 2.34646 | ||||||||
\(951\) | −4.33516 | −0.140577 | ||||||||
\(952\) | 0.845033 | 0.0273877 | ||||||||
\(953\) | 12.8011 | 0.414667 | 0.207334 | − | 0.978270i | \(-0.433521\pi\) | ||||
0.207334 | + | 0.978270i | \(0.433521\pi\) | |||||||
\(954\) | −42.1494 | −1.36464 | ||||||||
\(955\) | 33.3584 | 1.07945 | ||||||||
\(956\) | 21.9761 | 0.710758 | ||||||||
\(957\) | −1.50480 | −0.0486431 | ||||||||
\(958\) | −19.1776 | −0.619601 | ||||||||
\(959\) | 27.5802 | 0.890611 | ||||||||
\(960\) | −9.62756 | −0.310728 | ||||||||
\(961\) | −30.9881 | −0.999617 | ||||||||
\(962\) | 22.1475 | 0.714063 | ||||||||
\(963\) | −54.8439 | −1.76732 | ||||||||
\(964\) | 24.3667 | 0.784799 | ||||||||
\(965\) | −47.9566 | −1.54378 | ||||||||
\(966\) | 15.9100 | 0.511895 | ||||||||
\(967\) | −5.76620 | −0.185429 | −0.0927143 | − | 0.995693i | \(-0.529554\pi\) | ||||
−0.0927143 | + | 0.995693i | \(0.529554\pi\) | |||||||
\(968\) | 0.457109 | 0.0146920 | ||||||||
\(969\) | −1.15117 | −0.0369811 | ||||||||
\(970\) | 8.57341 | 0.275276 | ||||||||
\(971\) | −36.5647 | −1.17342 | −0.586709 | − | 0.809798i | \(-0.699577\pi\) | ||||
−0.586709 | + | 0.809798i | \(0.699577\pi\) | |||||||
\(972\) | −20.8564 | −0.668971 | ||||||||
\(973\) | 43.5819 | 1.39717 | ||||||||
\(974\) | −3.43682 | −0.110123 | ||||||||
\(975\) | 4.61354 | 0.147752 | ||||||||
\(976\) | 20.1403 | 0.644676 | ||||||||
\(977\) | 21.1331 | 0.676108 | 0.338054 | − | 0.941127i | \(-0.390231\pi\) | ||||
0.338054 | + | 0.941127i | \(0.390231\pi\) | |||||||
\(978\) | −22.1325 | −0.707720 | ||||||||
\(979\) | −7.82643 | −0.250134 | ||||||||
\(980\) | −110.500 | −3.52980 | ||||||||
\(981\) | 21.2328 | 0.677911 | ||||||||
\(982\) | −67.5671 | −2.15615 | ||||||||
\(983\) | −3.79218 | −0.120952 | −0.0604758 | − | 0.998170i | \(-0.519262\pi\) | ||||
−0.0604758 | + | 0.998170i | \(0.519262\pi\) | |||||||
\(984\) | −0.527581 | −0.0168187 | ||||||||
\(985\) | 8.23084 | 0.262256 | ||||||||
\(986\) | −2.16109 | −0.0688232 | ||||||||
\(987\) | −22.6504 | −0.720971 | ||||||||
\(988\) | 18.9643 | 0.603335 | ||||||||
\(989\) | −33.8699 | −1.07700 | ||||||||
\(990\) | 17.5428 | 0.557547 | ||||||||
\(991\) | 53.1928 | 1.68972 | 0.844862 | − | 0.534985i | \(-0.179683\pi\) | ||||
0.844862 | + | 0.534985i | \(0.179683\pi\) | |||||||
\(992\) | −0.834031 | −0.0264805 | ||||||||
\(993\) | 6.24239 | 0.198096 | ||||||||
\(994\) | −74.8315 | −2.37351 | ||||||||
\(995\) | 8.48954 | 0.269136 | ||||||||
\(996\) | 4.87184 | 0.154370 | ||||||||
\(997\) | 0.472238 | 0.0149559 | 0.00747796 | − | 0.999972i | \(-0.497620\pi\) | ||||
0.00747796 | + | 0.999972i | \(0.497620\pi\) | |||||||
\(998\) | 79.5104 | 2.51686 | ||||||||
\(999\) | 19.4749 | 0.616159 |
(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 | 6017.2.a.d.1.20 | ✓ | 107 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.d.1.20 | ✓ | 107 | 1.1 | even | 1 | trivial |