Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4009,2,Mod(1,4009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4009, 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("4009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4009 = 19 \cdot 211 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4009.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0120261703\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.21501 | −1.56625 | −0.783124 | − | 0.621866i | \(-0.786375\pi\) | ||||
−0.783124 | + | 0.621866i | \(0.786375\pi\) | |||||||
\(3\) | 1.93892 | 1.11944 | 0.559719 | − | 0.828682i | \(-0.310909\pi\) | ||||
0.559719 | + | 0.828682i | \(0.310909\pi\) | |||||||
\(4\) | 2.90626 | 1.45313 | ||||||||
\(5\) | 3.78369 | 1.69212 | 0.846059 | − | 0.533090i | \(-0.178969\pi\) | ||||
0.846059 | + | 0.533090i | \(0.178969\pi\) | |||||||
\(6\) | −4.29473 | −1.75332 | ||||||||
\(7\) | 0.133386 | 0.0504150 | 0.0252075 | − | 0.999682i | \(-0.491975\pi\) | ||||
0.0252075 | + | 0.999682i | \(0.491975\pi\) | |||||||
\(8\) | −2.00737 | −0.709713 | ||||||||
\(9\) | 0.759427 | 0.253142 | ||||||||
\(10\) | −8.38090 | −2.65027 | ||||||||
\(11\) | −1.09409 | −0.329880 | −0.164940 | − | 0.986304i | \(-0.552743\pi\) | ||||
−0.164940 | + | 0.986304i | \(0.552743\pi\) | |||||||
\(12\) | 5.63502 | 1.62669 | ||||||||
\(13\) | 3.29925 | 0.915046 | 0.457523 | − | 0.889198i | \(-0.348737\pi\) | ||||
0.457523 | + | 0.889198i | \(0.348737\pi\) | |||||||
\(14\) | −0.295450 | −0.0789624 | ||||||||
\(15\) | 7.33629 | 1.89422 | ||||||||
\(16\) | −1.36617 | −0.341543 | ||||||||
\(17\) | 1.86199 | 0.451598 | 0.225799 | − | 0.974174i | \(-0.427501\pi\) | ||||
0.225799 | + | 0.974174i | \(0.427501\pi\) | |||||||
\(18\) | −1.68214 | −0.396483 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 10.9964 | 2.45887 | ||||||||
\(21\) | 0.258625 | 0.0564365 | ||||||||
\(22\) | 2.42341 | 0.516673 | ||||||||
\(23\) | 7.74684 | 1.61533 | 0.807664 | − | 0.589642i | \(-0.200731\pi\) | ||||
0.807664 | + | 0.589642i | \(0.200731\pi\) | |||||||
\(24\) | −3.89214 | −0.794480 | ||||||||
\(25\) | 9.31631 | 1.86326 | ||||||||
\(26\) | −7.30786 | −1.43319 | ||||||||
\(27\) | −4.34430 | −0.836061 | ||||||||
\(28\) | 0.387653 | 0.0732596 | ||||||||
\(29\) | −3.39199 | −0.629877 | −0.314939 | − | 0.949112i | \(-0.601984\pi\) | ||||
−0.314939 | + | 0.949112i | \(0.601984\pi\) | |||||||
\(30\) | −16.2499 | −2.96682 | ||||||||
\(31\) | 2.03974 | 0.366347 | 0.183174 | − | 0.983081i | \(-0.441363\pi\) | ||||
0.183174 | + | 0.983081i | \(0.441363\pi\) | |||||||
\(32\) | 7.04083 | 1.24465 | ||||||||
\(33\) | −2.12135 | −0.369280 | ||||||||
\(34\) | −4.12432 | −0.707314 | ||||||||
\(35\) | 0.504690 | 0.0853082 | ||||||||
\(36\) | 2.20709 | 0.367848 | ||||||||
\(37\) | 8.03020 | 1.32016 | 0.660078 | − | 0.751197i | \(-0.270523\pi\) | ||||
0.660078 | + | 0.751197i | \(0.270523\pi\) | |||||||
\(38\) | −2.21501 | −0.359322 | ||||||||
\(39\) | 6.39699 | 1.02434 | ||||||||
\(40\) | −7.59528 | −1.20092 | ||||||||
\(41\) | 5.20858 | 0.813444 | 0.406722 | − | 0.913552i | \(-0.366672\pi\) | ||||
0.406722 | + | 0.913552i | \(0.366672\pi\) | |||||||
\(42\) | −0.572856 | −0.0883936 | ||||||||
\(43\) | −3.74804 | −0.571571 | −0.285785 | − | 0.958294i | \(-0.592254\pi\) | ||||
−0.285785 | + | 0.958294i | \(0.592254\pi\) | |||||||
\(44\) | −3.17970 | −0.479358 | ||||||||
\(45\) | 2.87343 | 0.428346 | ||||||||
\(46\) | −17.1593 | −2.53000 | ||||||||
\(47\) | −4.19531 | −0.611948 | −0.305974 | − | 0.952040i | \(-0.598982\pi\) | ||||
−0.305974 | + | 0.952040i | \(0.598982\pi\) | |||||||
\(48\) | −2.64891 | −0.382337 | ||||||||
\(49\) | −6.98221 | −0.997458 | ||||||||
\(50\) | −20.6357 | −2.91833 | ||||||||
\(51\) | 3.61025 | 0.505536 | ||||||||
\(52\) | 9.58847 | 1.32968 | ||||||||
\(53\) | −9.76739 | −1.34165 | −0.670827 | − | 0.741614i | \(-0.734061\pi\) | ||||
−0.670827 | + | 0.741614i | \(0.734061\pi\) | |||||||
\(54\) | 9.62266 | 1.30948 | ||||||||
\(55\) | −4.13969 | −0.558195 | ||||||||
\(56\) | −0.267755 | −0.0357802 | ||||||||
\(57\) | 1.93892 | 0.256817 | ||||||||
\(58\) | 7.51329 | 0.986543 | ||||||||
\(59\) | −0.931634 | −0.121288 | −0.0606442 | − | 0.998159i | \(-0.519315\pi\) | ||||
−0.0606442 | + | 0.998159i | \(0.519315\pi\) | |||||||
\(60\) | 21.3212 | 2.75255 | ||||||||
\(61\) | 7.87186 | 1.00789 | 0.503944 | − | 0.863736i | \(-0.331882\pi\) | ||||
0.503944 | + | 0.863736i | \(0.331882\pi\) | |||||||
\(62\) | −4.51803 | −0.573790 | ||||||||
\(63\) | 0.101297 | 0.0127622 | ||||||||
\(64\) | −12.8631 | −1.60789 | ||||||||
\(65\) | 12.4833 | 1.54837 | ||||||||
\(66\) | 4.69881 | 0.578384 | ||||||||
\(67\) | 3.01933 | 0.368869 | 0.184435 | − | 0.982845i | \(-0.440955\pi\) | ||||
0.184435 | + | 0.982845i | \(0.440955\pi\) | |||||||
\(68\) | 5.41142 | 0.656231 | ||||||||
\(69\) | 15.0205 | 1.80826 | ||||||||
\(70\) | −1.11789 | −0.133614 | ||||||||
\(71\) | −1.26895 | −0.150597 | −0.0752986 | − | 0.997161i | \(-0.523991\pi\) | ||||
−0.0752986 | + | 0.997161i | \(0.523991\pi\) | |||||||
\(72\) | −1.52445 | −0.179658 | ||||||||
\(73\) | −0.126954 | −0.0148588 | −0.00742942 | − | 0.999972i | \(-0.502365\pi\) | ||||
−0.00742942 | + | 0.999972i | \(0.502365\pi\) | |||||||
\(74\) | −17.7869 | −2.06769 | ||||||||
\(75\) | 18.0636 | 2.08581 | ||||||||
\(76\) | 2.90626 | 0.333371 | ||||||||
\(77\) | −0.145936 | −0.0166309 | ||||||||
\(78\) | −14.1694 | −1.60437 | ||||||||
\(79\) | −0.541512 | −0.0609248 | −0.0304624 | − | 0.999536i | \(-0.509698\pi\) | ||||
−0.0304624 | + | 0.999536i | \(0.509698\pi\) | |||||||
\(80\) | −5.16918 | −0.577932 | ||||||||
\(81\) | −10.7016 | −1.18906 | ||||||||
\(82\) | −11.5370 | −1.27405 | ||||||||
\(83\) | 2.31165 | 0.253736 | 0.126868 | − | 0.991920i | \(-0.459508\pi\) | ||||
0.126868 | + | 0.991920i | \(0.459508\pi\) | |||||||
\(84\) | 0.751631 | 0.0820096 | ||||||||
\(85\) | 7.04518 | 0.764157 | ||||||||
\(86\) | 8.30194 | 0.895221 | ||||||||
\(87\) | −6.57682 | −0.705109 | ||||||||
\(88\) | 2.19624 | 0.234120 | ||||||||
\(89\) | −3.44189 | −0.364839 | −0.182420 | − | 0.983221i | \(-0.558393\pi\) | ||||
−0.182420 | + | 0.983221i | \(0.558393\pi\) | |||||||
\(90\) | −6.36468 | −0.670896 | ||||||||
\(91\) | 0.440072 | 0.0461321 | ||||||||
\(92\) | 22.5143 | 2.34728 | ||||||||
\(93\) | 3.95489 | 0.410103 | ||||||||
\(94\) | 9.29264 | 0.958462 | ||||||||
\(95\) | 3.78369 | 0.388198 | ||||||||
\(96\) | 13.6516 | 1.39331 | ||||||||
\(97\) | −17.7453 | −1.80176 | −0.900879 | − | 0.434070i | \(-0.857077\pi\) | ||||
−0.900879 | + | 0.434070i | \(0.857077\pi\) | |||||||
\(98\) | 15.4656 | 1.56227 | ||||||||
\(99\) | −0.830879 | −0.0835065 | ||||||||
\(100\) | 27.0756 | 2.70756 | ||||||||
\(101\) | −7.49718 | −0.745997 | −0.372999 | − | 0.927832i | \(-0.621670\pi\) | ||||
−0.372999 | + | 0.927832i | \(0.621670\pi\) | |||||||
\(102\) | −7.99674 | −0.791795 | ||||||||
\(103\) | 16.5721 | 1.63289 | 0.816447 | − | 0.577420i | \(-0.195940\pi\) | ||||
0.816447 | + | 0.577420i | \(0.195940\pi\) | |||||||
\(104\) | −6.62282 | −0.649420 | ||||||||
\(105\) | 0.978556 | 0.0954972 | ||||||||
\(106\) | 21.6348 | 2.10136 | ||||||||
\(107\) | 19.0770 | 1.84424 | 0.922121 | − | 0.386901i | \(-0.126454\pi\) | ||||
0.922121 | + | 0.386901i | \(0.126454\pi\) | |||||||
\(108\) | −12.6257 | −1.21491 | ||||||||
\(109\) | 3.55901 | 0.340892 | 0.170446 | − | 0.985367i | \(-0.445479\pi\) | ||||
0.170446 | + | 0.985367i | \(0.445479\pi\) | |||||||
\(110\) | 9.16944 | 0.874272 | ||||||||
\(111\) | 15.5699 | 1.47783 | ||||||||
\(112\) | −0.182228 | −0.0172189 | ||||||||
\(113\) | 12.9011 | 1.21363 | 0.606816 | − | 0.794842i | \(-0.292447\pi\) | ||||
0.606816 | + | 0.794842i | \(0.292447\pi\) | |||||||
\(114\) | −4.29473 | −0.402239 | ||||||||
\(115\) | 29.3117 | 2.73333 | ||||||||
\(116\) | −9.85801 | −0.915293 | ||||||||
\(117\) | 2.50553 | 0.231637 | ||||||||
\(118\) | 2.06358 | 0.189968 | ||||||||
\(119\) | 0.248362 | 0.0227673 | ||||||||
\(120\) | −14.7267 | −1.34435 | ||||||||
\(121\) | −9.80297 | −0.891179 | ||||||||
\(122\) | −17.4362 | −1.57860 | ||||||||
\(123\) | 10.0990 | 0.910600 | ||||||||
\(124\) | 5.92800 | 0.532350 | ||||||||
\(125\) | 16.3316 | 1.46074 | ||||||||
\(126\) | −0.224373 | −0.0199887 | ||||||||
\(127\) | 12.6975 | 1.12672 | 0.563362 | − | 0.826210i | \(-0.309508\pi\) | ||||
0.563362 | + | 0.826210i | \(0.309508\pi\) | |||||||
\(128\) | 14.4103 | 1.27370 | ||||||||
\(129\) | −7.26717 | −0.639838 | ||||||||
\(130\) | −27.6507 | −2.42512 | ||||||||
\(131\) | 12.7292 | 1.11216 | 0.556080 | − | 0.831129i | \(-0.312305\pi\) | ||||
0.556080 | + | 0.831129i | \(0.312305\pi\) | |||||||
\(132\) | −6.16520 | −0.536612 | ||||||||
\(133\) | 0.133386 | 0.0115660 | ||||||||
\(134\) | −6.68783 | −0.577741 | ||||||||
\(135\) | −16.4375 | −1.41471 | ||||||||
\(136\) | −3.73770 | −0.320505 | ||||||||
\(137\) | 1.95373 | 0.166919 | 0.0834594 | − | 0.996511i | \(-0.473403\pi\) | ||||
0.0834594 | + | 0.996511i | \(0.473403\pi\) | |||||||
\(138\) | −33.2706 | −2.83218 | ||||||||
\(139\) | −5.31613 | −0.450908 | −0.225454 | − | 0.974254i | \(-0.572387\pi\) | ||||
−0.225454 | + | 0.974254i | \(0.572387\pi\) | |||||||
\(140\) | 1.46676 | 0.123964 | ||||||||
\(141\) | −8.13438 | −0.685039 | ||||||||
\(142\) | 2.81074 | 0.235872 | ||||||||
\(143\) | −3.60966 | −0.301855 | ||||||||
\(144\) | −1.03751 | −0.0864590 | ||||||||
\(145\) | −12.8342 | −1.06583 | ||||||||
\(146\) | 0.281204 | 0.0232726 | ||||||||
\(147\) | −13.5380 | −1.11659 | ||||||||
\(148\) | 23.3378 | 1.91836 | ||||||||
\(149\) | −11.3748 | −0.931863 | −0.465932 | − | 0.884821i | \(-0.654281\pi\) | ||||
−0.465932 | + | 0.884821i | \(0.654281\pi\) | |||||||
\(150\) | −40.0110 | −3.26689 | ||||||||
\(151\) | −8.26595 | −0.672673 | −0.336337 | − | 0.941742i | \(-0.609188\pi\) | ||||
−0.336337 | + | 0.941742i | \(0.609188\pi\) | |||||||
\(152\) | −2.00737 | −0.162819 | ||||||||
\(153\) | 1.41404 | 0.114319 | ||||||||
\(154\) | 0.323249 | 0.0260481 | ||||||||
\(155\) | 7.71773 | 0.619903 | ||||||||
\(156\) | 18.5913 | 1.48850 | ||||||||
\(157\) | 8.44089 | 0.673656 | 0.336828 | − | 0.941566i | \(-0.390646\pi\) | ||||
0.336828 | + | 0.941566i | \(0.390646\pi\) | |||||||
\(158\) | 1.19945 | 0.0954234 | ||||||||
\(159\) | −18.9382 | −1.50190 | ||||||||
\(160\) | 26.6403 | 2.10610 | ||||||||
\(161\) | 1.03332 | 0.0814369 | ||||||||
\(162\) | 23.7040 | 1.86236 | ||||||||
\(163\) | 4.73495 | 0.370870 | 0.185435 | − | 0.982657i | \(-0.440631\pi\) | ||||
0.185435 | + | 0.982657i | \(0.440631\pi\) | |||||||
\(164\) | 15.1375 | 1.18204 | ||||||||
\(165\) | −8.02654 | −0.624865 | ||||||||
\(166\) | −5.12032 | −0.397414 | ||||||||
\(167\) | −14.0935 | −1.09059 | −0.545294 | − | 0.838245i | \(-0.683582\pi\) | ||||
−0.545294 | + | 0.838245i | \(0.683582\pi\) | |||||||
\(168\) | −0.519156 | −0.0400538 | ||||||||
\(169\) | −2.11498 | −0.162691 | ||||||||
\(170\) | −15.6051 | −1.19686 | ||||||||
\(171\) | 0.759427 | 0.0580748 | ||||||||
\(172\) | −10.8928 | −0.830567 | ||||||||
\(173\) | 20.9623 | 1.59374 | 0.796868 | − | 0.604153i | \(-0.206489\pi\) | ||||
0.796868 | + | 0.604153i | \(0.206489\pi\) | |||||||
\(174\) | 14.5677 | 1.10437 | ||||||||
\(175\) | 1.24266 | 0.0939364 | ||||||||
\(176\) | 1.49471 | 0.112668 | ||||||||
\(177\) | −1.80637 | −0.135775 | ||||||||
\(178\) | 7.62380 | 0.571428 | ||||||||
\(179\) | −7.19946 | −0.538113 | −0.269056 | − | 0.963124i | \(-0.586712\pi\) | ||||
−0.269056 | + | 0.963124i | \(0.586712\pi\) | |||||||
\(180\) | 8.35095 | 0.622443 | ||||||||
\(181\) | −18.1059 | −1.34580 | −0.672901 | − | 0.739733i | \(-0.734952\pi\) | ||||
−0.672901 | + | 0.739733i | \(0.734952\pi\) | |||||||
\(182\) | −0.974763 | −0.0722543 | ||||||||
\(183\) | 15.2629 | 1.12827 | ||||||||
\(184\) | −15.5508 | −1.14642 | ||||||||
\(185\) | 30.3838 | 2.23386 | ||||||||
\(186\) | −8.76012 | −0.642323 | ||||||||
\(187\) | −2.03718 | −0.148973 | ||||||||
\(188\) | −12.1927 | −0.889241 | ||||||||
\(189\) | −0.579468 | −0.0421501 | ||||||||
\(190\) | −8.38090 | −0.608015 | ||||||||
\(191\) | −9.94658 | −0.719709 | −0.359855 | − | 0.933008i | \(-0.617174\pi\) | ||||
−0.359855 | + | 0.933008i | \(0.617174\pi\) | |||||||
\(192\) | −24.9407 | −1.79994 | ||||||||
\(193\) | 7.40629 | 0.533116 | 0.266558 | − | 0.963819i | \(-0.414114\pi\) | ||||
0.266558 | + | 0.963819i | \(0.414114\pi\) | |||||||
\(194\) | 39.3059 | 2.82200 | ||||||||
\(195\) | 24.2042 | 1.73330 | ||||||||
\(196\) | −20.2921 | −1.44944 | ||||||||
\(197\) | −9.21642 | −0.656642 | −0.328321 | − | 0.944566i | \(-0.606483\pi\) | ||||
−0.328321 | + | 0.944566i | \(0.606483\pi\) | |||||||
\(198\) | 1.84040 | 0.130792 | ||||||||
\(199\) | 3.37710 | 0.239396 | 0.119698 | − | 0.992810i | \(-0.461807\pi\) | ||||
0.119698 | + | 0.992810i | \(0.461807\pi\) | |||||||
\(200\) | −18.7013 | −1.32238 | ||||||||
\(201\) | 5.85424 | 0.412926 | ||||||||
\(202\) | 16.6063 | 1.16842 | ||||||||
\(203\) | −0.452443 | −0.0317553 | ||||||||
\(204\) | 10.4923 | 0.734610 | ||||||||
\(205\) | 19.7077 | 1.37644 | ||||||||
\(206\) | −36.7073 | −2.55752 | ||||||||
\(207\) | 5.88316 | 0.408908 | ||||||||
\(208\) | −4.50734 | −0.312528 | ||||||||
\(209\) | −1.09409 | −0.0756796 | ||||||||
\(210\) | −2.16751 | −0.149572 | ||||||||
\(211\) | −1.00000 | −0.0688428 | ||||||||
\(212\) | −28.3866 | −1.94960 | ||||||||
\(213\) | −2.46041 | −0.168584 | ||||||||
\(214\) | −42.2557 | −2.88854 | ||||||||
\(215\) | −14.1814 | −0.967165 | ||||||||
\(216\) | 8.72063 | 0.593364 | ||||||||
\(217\) | 0.272071 | 0.0184694 | ||||||||
\(218\) | −7.88324 | −0.533921 | ||||||||
\(219\) | −0.246154 | −0.0166336 | ||||||||
\(220\) | −12.0310 | −0.811130 | ||||||||
\(221\) | 6.14315 | 0.413233 | ||||||||
\(222\) | −34.4875 | −2.31465 | ||||||||
\(223\) | −7.59468 | −0.508577 | −0.254289 | − | 0.967128i | \(-0.581841\pi\) | ||||
−0.254289 | + | 0.967128i | \(0.581841\pi\) | |||||||
\(224\) | 0.939146 | 0.0627493 | ||||||||
\(225\) | 7.07505 | 0.471670 | ||||||||
\(226\) | −28.5760 | −1.90085 | ||||||||
\(227\) | 26.1549 | 1.73596 | 0.867982 | − | 0.496596i | \(-0.165417\pi\) | ||||
0.867982 | + | 0.496596i | \(0.165417\pi\) | |||||||
\(228\) | 5.63502 | 0.373188 | ||||||||
\(229\) | −25.7038 | −1.69855 | −0.849277 | − | 0.527948i | \(-0.822961\pi\) | ||||
−0.849277 | + | 0.527948i | \(0.822961\pi\) | |||||||
\(230\) | −64.9256 | −4.28106 | ||||||||
\(231\) | −0.282958 | −0.0186173 | ||||||||
\(232\) | 6.80899 | 0.447032 | ||||||||
\(233\) | 10.0026 | 0.655293 | 0.327647 | − | 0.944800i | \(-0.393744\pi\) | ||||
0.327647 | + | 0.944800i | \(0.393744\pi\) | |||||||
\(234\) | −5.54978 | −0.362800 | ||||||||
\(235\) | −15.8737 | −1.03549 | ||||||||
\(236\) | −2.70757 | −0.176248 | ||||||||
\(237\) | −1.04995 | −0.0682016 | ||||||||
\(238\) | −0.550125 | −0.0356593 | ||||||||
\(239\) | −15.1150 | −0.977711 | −0.488855 | − | 0.872365i | \(-0.662585\pi\) | ||||
−0.488855 | + | 0.872365i | \(0.662585\pi\) | |||||||
\(240\) | −10.0226 | −0.646959 | ||||||||
\(241\) | 18.9626 | 1.22149 | 0.610745 | − | 0.791827i | \(-0.290870\pi\) | ||||
0.610745 | + | 0.791827i | \(0.290870\pi\) | |||||||
\(242\) | 21.7137 | 1.39581 | ||||||||
\(243\) | −7.71659 | −0.495019 | ||||||||
\(244\) | 22.8777 | 1.46459 | ||||||||
\(245\) | −26.4185 | −1.68782 | ||||||||
\(246\) | −22.3695 | −1.42622 | ||||||||
\(247\) | 3.29925 | 0.209926 | ||||||||
\(248\) | −4.09451 | −0.260002 | ||||||||
\(249\) | 4.48211 | 0.284042 | ||||||||
\(250\) | −36.1746 | −2.28788 | ||||||||
\(251\) | 3.41922 | 0.215819 | 0.107910 | − | 0.994161i | \(-0.465584\pi\) | ||||
0.107910 | + | 0.994161i | \(0.465584\pi\) | |||||||
\(252\) | 0.294394 | 0.0185451 | ||||||||
\(253\) | −8.47573 | −0.532864 | ||||||||
\(254\) | −28.1251 | −1.76473 | ||||||||
\(255\) | 13.6601 | 0.855427 | ||||||||
\(256\) | −6.19266 | −0.387041 | ||||||||
\(257\) | −23.9928 | −1.49663 | −0.748314 | − | 0.663345i | \(-0.769136\pi\) | ||||
−0.748314 | + | 0.663345i | \(0.769136\pi\) | |||||||
\(258\) | 16.0968 | 1.00214 | ||||||||
\(259\) | 1.07111 | 0.0665557 | ||||||||
\(260\) | 36.2798 | 2.24998 | ||||||||
\(261\) | −2.57597 | −0.159448 | ||||||||
\(262\) | −28.1954 | −1.74192 | ||||||||
\(263\) | 25.7428 | 1.58737 | 0.793684 | − | 0.608330i | \(-0.208160\pi\) | ||||
0.793684 | + | 0.608330i | \(0.208160\pi\) | |||||||
\(264\) | 4.25835 | 0.262083 | ||||||||
\(265\) | −36.9568 | −2.27024 | ||||||||
\(266\) | −0.295450 | −0.0181152 | ||||||||
\(267\) | −6.67355 | −0.408415 | ||||||||
\(268\) | 8.77495 | 0.536015 | ||||||||
\(269\) | −1.47273 | −0.0897942 | −0.0448971 | − | 0.998992i | \(-0.514296\pi\) | ||||
−0.0448971 | + | 0.998992i | \(0.514296\pi\) | |||||||
\(270\) | 36.4092 | 2.21579 | ||||||||
\(271\) | −1.69114 | −0.102729 | −0.0513646 | − | 0.998680i | \(-0.516357\pi\) | ||||
−0.0513646 | + | 0.998680i | \(0.516357\pi\) | |||||||
\(272\) | −2.54380 | −0.154240 | ||||||||
\(273\) | 0.853266 | 0.0516420 | ||||||||
\(274\) | −4.32754 | −0.261436 | ||||||||
\(275\) | −10.1929 | −0.614652 | ||||||||
\(276\) | 43.6536 | 2.62764 | ||||||||
\(277\) | −17.0367 | −1.02364 | −0.511819 | − | 0.859093i | \(-0.671028\pi\) | ||||
−0.511819 | + | 0.859093i | \(0.671028\pi\) | |||||||
\(278\) | 11.7753 | 0.706233 | ||||||||
\(279\) | 1.54903 | 0.0927379 | ||||||||
\(280\) | −1.01310 | −0.0605444 | ||||||||
\(281\) | −5.36336 | −0.319951 | −0.159976 | − | 0.987121i | \(-0.551142\pi\) | ||||
−0.159976 | + | 0.987121i | \(0.551142\pi\) | |||||||
\(282\) | 18.0177 | 1.07294 | ||||||||
\(283\) | −13.8625 | −0.824043 | −0.412021 | − | 0.911174i | \(-0.635177\pi\) | ||||
−0.412021 | + | 0.911174i | \(0.635177\pi\) | |||||||
\(284\) | −3.68791 | −0.218837 | ||||||||
\(285\) | 7.33629 | 0.434564 | ||||||||
\(286\) | 7.99543 | 0.472780 | ||||||||
\(287\) | 0.694750 | 0.0410098 | ||||||||
\(288\) | 5.34699 | 0.315075 | ||||||||
\(289\) | −13.5330 | −0.796059 | ||||||||
\(290\) | 28.4280 | 1.66935 | ||||||||
\(291\) | −34.4067 | −2.01696 | ||||||||
\(292\) | −0.368961 | −0.0215918 | ||||||||
\(293\) | −16.2038 | −0.946639 | −0.473319 | − | 0.880891i | \(-0.656944\pi\) | ||||
−0.473319 | + | 0.880891i | \(0.656944\pi\) | |||||||
\(294\) | 29.9867 | 1.74886 | ||||||||
\(295\) | −3.52501 | −0.205234 | ||||||||
\(296\) | −16.1196 | −0.936933 | ||||||||
\(297\) | 4.75305 | 0.275800 | ||||||||
\(298\) | 25.1954 | 1.45953 | ||||||||
\(299\) | 25.5587 | 1.47810 | ||||||||
\(300\) | 52.4976 | 3.03095 | ||||||||
\(301\) | −0.499935 | −0.0288158 | ||||||||
\(302\) | 18.3091 | 1.05357 | ||||||||
\(303\) | −14.5365 | −0.835098 | ||||||||
\(304\) | −1.36617 | −0.0783554 | ||||||||
\(305\) | 29.7847 | 1.70546 | ||||||||
\(306\) | −3.13211 | −0.179051 | ||||||||
\(307\) | −10.7359 | −0.612729 | −0.306365 | − | 0.951914i | \(-0.599113\pi\) | ||||
−0.306365 | + | 0.951914i | \(0.599113\pi\) | |||||||
\(308\) | −0.424127 | −0.0241669 | ||||||||
\(309\) | 32.1320 | 1.82793 | ||||||||
\(310\) | −17.0948 | −0.970921 | ||||||||
\(311\) | −3.11213 | −0.176473 | −0.0882365 | − | 0.996100i | \(-0.528123\pi\) | ||||
−0.0882365 | + | 0.996100i | \(0.528123\pi\) | |||||||
\(312\) | −12.8411 | −0.726986 | ||||||||
\(313\) | 24.4746 | 1.38339 | 0.691693 | − | 0.722191i | \(-0.256865\pi\) | ||||
0.691693 | + | 0.722191i | \(0.256865\pi\) | |||||||
\(314\) | −18.6966 | −1.05511 | ||||||||
\(315\) | 0.383275 | 0.0215951 | ||||||||
\(316\) | −1.57377 | −0.0885317 | ||||||||
\(317\) | 9.11430 | 0.511910 | 0.255955 | − | 0.966689i | \(-0.417610\pi\) | ||||
0.255955 | + | 0.966689i | \(0.417610\pi\) | |||||||
\(318\) | 41.9483 | 2.35234 | ||||||||
\(319\) | 3.71114 | 0.207784 | ||||||||
\(320\) | −48.6702 | −2.72074 | ||||||||
\(321\) | 36.9888 | 2.06452 | ||||||||
\(322\) | −2.28881 | −0.127550 | ||||||||
\(323\) | 1.86199 | 0.103604 | ||||||||
\(324\) | −31.1015 | −1.72786 | ||||||||
\(325\) | 30.7368 | 1.70497 | ||||||||
\(326\) | −10.4880 | −0.580874 | ||||||||
\(327\) | 6.90066 | 0.381607 | ||||||||
\(328\) | −10.4556 | −0.577312 | ||||||||
\(329\) | −0.559594 | −0.0308514 | ||||||||
\(330\) | 17.7789 | 0.978693 | ||||||||
\(331\) | −5.22913 | −0.287419 | −0.143709 | − | 0.989620i | \(-0.545903\pi\) | ||||
−0.143709 | + | 0.989620i | \(0.545903\pi\) | |||||||
\(332\) | 6.71825 | 0.368712 | ||||||||
\(333\) | 6.09834 | 0.334187 | ||||||||
\(334\) | 31.2172 | 1.70813 | ||||||||
\(335\) | 11.4242 | 0.624170 | ||||||||
\(336\) | −0.353326 | −0.0192755 | ||||||||
\(337\) | 13.1489 | 0.716268 | 0.358134 | − | 0.933670i | \(-0.383413\pi\) | ||||
0.358134 | + | 0.933670i | \(0.383413\pi\) | |||||||
\(338\) | 4.68469 | 0.254814 | ||||||||
\(339\) | 25.0142 | 1.35859 | ||||||||
\(340\) | 20.4751 | 1.11042 | ||||||||
\(341\) | −2.23165 | −0.120851 | ||||||||
\(342\) | −1.68214 | −0.0909595 | ||||||||
\(343\) | −1.86503 | −0.100702 | ||||||||
\(344\) | 7.52371 | 0.405651 | ||||||||
\(345\) | 56.8331 | 3.05979 | ||||||||
\(346\) | −46.4317 | −2.49618 | ||||||||
\(347\) | 20.3548 | 1.09270 | 0.546351 | − | 0.837556i | \(-0.316016\pi\) | ||||
0.546351 | + | 0.837556i | \(0.316016\pi\) | |||||||
\(348\) | −19.1139 | −1.02461 | ||||||||
\(349\) | 3.24662 | 0.173788 | 0.0868938 | − | 0.996218i | \(-0.472306\pi\) | ||||
0.0868938 | + | 0.996218i | \(0.472306\pi\) | |||||||
\(350\) | −2.75251 | −0.147128 | ||||||||
\(351\) | −14.3329 | −0.765035 | ||||||||
\(352\) | −7.70328 | −0.410586 | ||||||||
\(353\) | 17.0312 | 0.906478 | 0.453239 | − | 0.891389i | \(-0.350268\pi\) | ||||
0.453239 | + | 0.891389i | \(0.350268\pi\) | |||||||
\(354\) | 4.00112 | 0.212657 | ||||||||
\(355\) | −4.80133 | −0.254828 | ||||||||
\(356\) | −10.0030 | −0.530159 | ||||||||
\(357\) | 0.481556 | 0.0254866 | ||||||||
\(358\) | 15.9469 | 0.842817 | ||||||||
\(359\) | 17.4891 | 0.923040 | 0.461520 | − | 0.887130i | \(-0.347304\pi\) | ||||
0.461520 | + | 0.887130i | \(0.347304\pi\) | |||||||
\(360\) | −5.76805 | −0.304003 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 40.1047 | 2.10786 | ||||||||
\(363\) | −19.0072 | −0.997620 | ||||||||
\(364\) | 1.27896 | 0.0670359 | ||||||||
\(365\) | −0.480355 | −0.0251429 | ||||||||
\(366\) | −33.8075 | −1.76715 | ||||||||
\(367\) | −6.71410 | −0.350473 | −0.175237 | − | 0.984526i | \(-0.556069\pi\) | ||||
−0.175237 | + | 0.984526i | \(0.556069\pi\) | |||||||
\(368\) | −10.5835 | −0.551705 | ||||||||
\(369\) | 3.95554 | 0.205917 | ||||||||
\(370\) | −67.3003 | −3.49878 | ||||||||
\(371\) | −1.30283 | −0.0676395 | ||||||||
\(372\) | 11.4939 | 0.595933 | ||||||||
\(373\) | −10.1350 | −0.524773 | −0.262386 | − | 0.964963i | \(-0.584510\pi\) | ||||
−0.262386 | + | 0.964963i | \(0.584510\pi\) | |||||||
\(374\) | 4.51236 | 0.233329 | ||||||||
\(375\) | 31.6657 | 1.63521 | ||||||||
\(376\) | 8.42154 | 0.434308 | ||||||||
\(377\) | −11.1910 | −0.576367 | ||||||||
\(378\) | 1.28353 | 0.0660174 | ||||||||
\(379\) | −3.79265 | −0.194815 | −0.0974077 | − | 0.995245i | \(-0.531055\pi\) | ||||
−0.0974077 | + | 0.995245i | \(0.531055\pi\) | |||||||
\(380\) | 10.9964 | 0.564103 | ||||||||
\(381\) | 24.6195 | 1.26130 | ||||||||
\(382\) | 22.0318 | 1.12724 | ||||||||
\(383\) | 9.68916 | 0.495093 | 0.247547 | − | 0.968876i | \(-0.420376\pi\) | ||||
0.247547 | + | 0.968876i | \(0.420376\pi\) | |||||||
\(384\) | 27.9405 | 1.42583 | ||||||||
\(385\) | −0.552175 | −0.0281414 | ||||||||
\(386\) | −16.4050 | −0.834992 | ||||||||
\(387\) | −2.84636 | −0.144689 | ||||||||
\(388\) | −51.5723 | −2.61819 | ||||||||
\(389\) | −18.9737 | −0.962004 | −0.481002 | − | 0.876719i | \(-0.659727\pi\) | ||||
−0.481002 | + | 0.876719i | \(0.659727\pi\) | |||||||
\(390\) | −53.6125 | −2.71478 | ||||||||
\(391\) | 14.4245 | 0.729480 | ||||||||
\(392\) | 14.0159 | 0.707910 | ||||||||
\(393\) | 24.6810 | 1.24499 | ||||||||
\(394\) | 20.4144 | 1.02846 | ||||||||
\(395\) | −2.04891 | −0.103092 | ||||||||
\(396\) | −2.41475 | −0.121346 | ||||||||
\(397\) | −29.5411 | −1.48263 | −0.741314 | − | 0.671159i | \(-0.765797\pi\) | ||||
−0.741314 | + | 0.671159i | \(0.765797\pi\) | |||||||
\(398\) | −7.48030 | −0.374954 | ||||||||
\(399\) | 0.258625 | 0.0129474 | ||||||||
\(400\) | −12.7277 | −0.636385 | ||||||||
\(401\) | 6.85782 | 0.342463 | 0.171232 | − | 0.985231i | \(-0.445225\pi\) | ||||
0.171232 | + | 0.985231i | \(0.445225\pi\) | |||||||
\(402\) | −12.9672 | −0.646745 | ||||||||
\(403\) | 6.72959 | 0.335225 | ||||||||
\(404\) | −21.7888 | −1.08403 | ||||||||
\(405\) | −40.4913 | −2.01203 | ||||||||
\(406\) | 1.00217 | 0.0497366 | ||||||||
\(407\) | −8.78574 | −0.435493 | ||||||||
\(408\) | −7.24712 | −0.358786 | ||||||||
\(409\) | −5.98969 | −0.296171 | −0.148086 | − | 0.988975i | \(-0.547311\pi\) | ||||
−0.148086 | + | 0.988975i | \(0.547311\pi\) | |||||||
\(410\) | −43.6526 | −2.15585 | ||||||||
\(411\) | 3.78814 | 0.186855 | ||||||||
\(412\) | 48.1627 | 2.37281 | ||||||||
\(413\) | −0.124267 | −0.00611476 | ||||||||
\(414\) | −13.0312 | −0.640451 | ||||||||
\(415\) | 8.74656 | 0.429352 | ||||||||
\(416\) | 23.2294 | 1.13892 | ||||||||
\(417\) | −10.3076 | −0.504764 | ||||||||
\(418\) | 2.42341 | 0.118533 | ||||||||
\(419\) | 1.61323 | 0.0788116 | 0.0394058 | − | 0.999223i | \(-0.487454\pi\) | ||||
0.0394058 | + | 0.999223i | \(0.487454\pi\) | |||||||
\(420\) | 2.84394 | 0.138770 | ||||||||
\(421\) | −19.9700 | −0.973279 | −0.486639 | − | 0.873603i | \(-0.661777\pi\) | ||||
−0.486639 | + | 0.873603i | \(0.661777\pi\) | |||||||
\(422\) | 2.21501 | 0.107825 | ||||||||
\(423\) | −3.18603 | −0.154910 | ||||||||
\(424\) | 19.6068 | 0.952190 | ||||||||
\(425\) | 17.3468 | 0.841446 | ||||||||
\(426\) | 5.44982 | 0.264045 | ||||||||
\(427\) | 1.04999 | 0.0508127 | ||||||||
\(428\) | 55.4427 | 2.67992 | ||||||||
\(429\) | −6.99886 | −0.337908 | ||||||||
\(430\) | 31.4120 | 1.51482 | ||||||||
\(431\) | 37.7877 | 1.82017 | 0.910084 | − | 0.414425i | \(-0.136017\pi\) | ||||
0.910084 | + | 0.414425i | \(0.136017\pi\) | |||||||
\(432\) | 5.93507 | 0.285551 | ||||||||
\(433\) | −15.6294 | −0.751101 | −0.375550 | − | 0.926802i | \(-0.622546\pi\) | ||||
−0.375550 | + | 0.926802i | \(0.622546\pi\) | |||||||
\(434\) | −0.602640 | −0.0289277 | ||||||||
\(435\) | −24.8846 | −1.19313 | ||||||||
\(436\) | 10.3434 | 0.495360 | ||||||||
\(437\) | 7.74684 | 0.370582 | ||||||||
\(438\) | 0.545233 | 0.0260523 | ||||||||
\(439\) | 2.83564 | 0.135338 | 0.0676688 | − | 0.997708i | \(-0.478444\pi\) | ||||
0.0676688 | + | 0.997708i | \(0.478444\pi\) | |||||||
\(440\) | 8.30990 | 0.396159 | ||||||||
\(441\) | −5.30247 | −0.252499 | ||||||||
\(442\) | −13.6071 | −0.647225 | ||||||||
\(443\) | −17.0073 | −0.808041 | −0.404020 | − | 0.914750i | \(-0.632388\pi\) | ||||
−0.404020 | + | 0.914750i | \(0.632388\pi\) | |||||||
\(444\) | 45.2503 | 2.14748 | ||||||||
\(445\) | −13.0230 | −0.617351 | ||||||||
\(446\) | 16.8223 | 0.796557 | ||||||||
\(447\) | −22.0550 | −1.04316 | ||||||||
\(448\) | −1.71576 | −0.0810620 | ||||||||
\(449\) | 19.8904 | 0.938685 | 0.469343 | − | 0.883016i | \(-0.344491\pi\) | ||||
0.469343 | + | 0.883016i | \(0.344491\pi\) | |||||||
\(450\) | −15.6713 | −0.738752 | ||||||||
\(451\) | −5.69864 | −0.268339 | ||||||||
\(452\) | 37.4939 | 1.76356 | ||||||||
\(453\) | −16.0270 | −0.753016 | ||||||||
\(454\) | −57.9334 | −2.71895 | ||||||||
\(455\) | 1.66510 | 0.0780609 | ||||||||
\(456\) | −3.89214 | −0.182266 | ||||||||
\(457\) | 10.0041 | 0.467974 | 0.233987 | − | 0.972240i | \(-0.424823\pi\) | ||||
0.233987 | + | 0.972240i | \(0.424823\pi\) | |||||||
\(458\) | 56.9341 | 2.66035 | ||||||||
\(459\) | −8.08903 | −0.377564 | ||||||||
\(460\) | 85.1873 | 3.97188 | ||||||||
\(461\) | 23.4614 | 1.09270 | 0.546352 | − | 0.837555i | \(-0.316016\pi\) | ||||
0.546352 | + | 0.837555i | \(0.316016\pi\) | |||||||
\(462\) | 0.626754 | 0.0291592 | ||||||||
\(463\) | 39.2805 | 1.82552 | 0.912760 | − | 0.408497i | \(-0.133947\pi\) | ||||
0.912760 | + | 0.408497i | \(0.133947\pi\) | |||||||
\(464\) | 4.63405 | 0.215130 | ||||||||
\(465\) | 14.9641 | 0.693943 | ||||||||
\(466\) | −22.1559 | −1.02635 | ||||||||
\(467\) | 11.9742 | 0.554102 | 0.277051 | − | 0.960855i | \(-0.410643\pi\) | ||||
0.277051 | + | 0.960855i | \(0.410643\pi\) | |||||||
\(468\) | 7.28173 | 0.336598 | ||||||||
\(469\) | 0.402735 | 0.0185966 | ||||||||
\(470\) | 35.1605 | 1.62183 | ||||||||
\(471\) | 16.3662 | 0.754117 | ||||||||
\(472\) | 1.87014 | 0.0860800 | ||||||||
\(473\) | 4.10068 | 0.188550 | ||||||||
\(474\) | 2.32565 | 0.106821 | ||||||||
\(475\) | 9.31631 | 0.427462 | ||||||||
\(476\) | 0.721806 | 0.0330839 | ||||||||
\(477\) | −7.41761 | −0.339629 | ||||||||
\(478\) | 33.4799 | 1.53134 | ||||||||
\(479\) | −20.4965 | −0.936511 | −0.468256 | − | 0.883593i | \(-0.655117\pi\) | ||||
−0.468256 | + | 0.883593i | \(0.655117\pi\) | |||||||
\(480\) | 51.6536 | 2.35765 | ||||||||
\(481\) | 26.4936 | 1.20800 | ||||||||
\(482\) | −42.0024 | −1.91316 | ||||||||
\(483\) | 2.00353 | 0.0911636 | ||||||||
\(484\) | −28.4900 | −1.29500 | ||||||||
\(485\) | −67.1426 | −3.04879 | ||||||||
\(486\) | 17.0923 | 0.775323 | ||||||||
\(487\) | −42.8780 | −1.94299 | −0.971494 | − | 0.237065i | \(-0.923815\pi\) | ||||
−0.971494 | + | 0.237065i | \(0.923815\pi\) | |||||||
\(488\) | −15.8017 | −0.715312 | ||||||||
\(489\) | 9.18071 | 0.415166 | ||||||||
\(490\) | 58.5172 | 2.64354 | ||||||||
\(491\) | 25.9281 | 1.17012 | 0.585060 | − | 0.810990i | \(-0.301071\pi\) | ||||
0.585060 | + | 0.810990i | \(0.301071\pi\) | |||||||
\(492\) | 29.3504 | 1.32322 | ||||||||
\(493\) | −6.31585 | −0.284451 | ||||||||
\(494\) | −7.30786 | −0.328796 | ||||||||
\(495\) | −3.14379 | −0.141303 | ||||||||
\(496\) | −2.78663 | −0.125123 | ||||||||
\(497\) | −0.169260 | −0.00759236 | ||||||||
\(498\) | −9.92790 | −0.444880 | ||||||||
\(499\) | −15.3463 | −0.686995 | −0.343498 | − | 0.939154i | \(-0.611612\pi\) | ||||
−0.343498 | + | 0.939154i | \(0.611612\pi\) | |||||||
\(500\) | 47.4638 | 2.12265 | ||||||||
\(501\) | −27.3262 | −1.22085 | ||||||||
\(502\) | −7.57359 | −0.338026 | ||||||||
\(503\) | −3.16345 | −0.141051 | −0.0705256 | − | 0.997510i | \(-0.522468\pi\) | ||||
−0.0705256 | + | 0.997510i | \(0.522468\pi\) | |||||||
\(504\) | −0.203340 | −0.00905749 | ||||||||
\(505\) | −28.3670 | −1.26232 | ||||||||
\(506\) | 18.7738 | 0.834597 | ||||||||
\(507\) | −4.10078 | −0.182122 | ||||||||
\(508\) | 36.9023 | 1.63728 | ||||||||
\(509\) | 31.2968 | 1.38721 | 0.693603 | − | 0.720357i | \(-0.256022\pi\) | ||||
0.693603 | + | 0.720357i | \(0.256022\pi\) | |||||||
\(510\) | −30.2572 | −1.33981 | ||||||||
\(511\) | −0.0169338 | −0.000749109 0 | ||||||||
\(512\) | −15.1038 | −0.667502 | ||||||||
\(513\) | −4.34430 | −0.191806 | ||||||||
\(514\) | 53.1442 | 2.34409 | ||||||||
\(515\) | 62.7036 | 2.76305 | ||||||||
\(516\) | −21.1203 | −0.929768 | ||||||||
\(517\) | 4.59003 | 0.201869 | ||||||||
\(518\) | −2.37252 | −0.104243 | ||||||||
\(519\) | 40.6444 | 1.78409 | ||||||||
\(520\) | −25.0587 | −1.09890 | ||||||||
\(521\) | −13.4515 | −0.589323 | −0.294661 | − | 0.955602i | \(-0.595207\pi\) | ||||
−0.294661 | + | 0.955602i | \(0.595207\pi\) | |||||||
\(522\) | 5.70579 | 0.249736 | ||||||||
\(523\) | −16.8159 | −0.735307 | −0.367653 | − | 0.929963i | \(-0.619839\pi\) | ||||
−0.367653 | + | 0.929963i | \(0.619839\pi\) | |||||||
\(524\) | 36.9945 | 1.61611 | ||||||||
\(525\) | 2.40943 | 0.105156 | ||||||||
\(526\) | −57.0205 | −2.48621 | ||||||||
\(527\) | 3.79796 | 0.165442 | ||||||||
\(528\) | 2.89814 | 0.126125 | ||||||||
\(529\) | 37.0136 | 1.60929 | ||||||||
\(530\) | 81.8595 | 3.55575 | ||||||||
\(531\) | −0.707507 | −0.0307032 | ||||||||
\(532\) | 0.387653 | 0.0168069 | ||||||||
\(533\) | 17.1844 | 0.744339 | ||||||||
\(534\) | 14.7820 | 0.639679 | ||||||||
\(535\) | 72.1814 | 3.12068 | ||||||||
\(536\) | −6.06091 | −0.261792 | ||||||||
\(537\) | −13.9592 | −0.602384 | ||||||||
\(538\) | 3.26212 | 0.140640 | ||||||||
\(539\) | 7.63915 | 0.329041 | ||||||||
\(540\) | −47.7716 | −2.05576 | ||||||||
\(541\) | −30.1432 | −1.29596 | −0.647979 | − | 0.761658i | \(-0.724386\pi\) | ||||
−0.647979 | + | 0.761658i | \(0.724386\pi\) | |||||||
\(542\) | 3.74588 | 0.160899 | ||||||||
\(543\) | −35.1060 | −1.50654 | ||||||||
\(544\) | 13.1099 | 0.562084 | ||||||||
\(545\) | 13.4662 | 0.576829 | ||||||||
\(546\) | −1.88999 | −0.0808842 | ||||||||
\(547\) | 17.4722 | 0.747058 | 0.373529 | − | 0.927619i | \(-0.378148\pi\) | ||||
0.373529 | + | 0.927619i | \(0.378148\pi\) | |||||||
\(548\) | 5.67806 | 0.242555 | ||||||||
\(549\) | 5.97810 | 0.255139 | ||||||||
\(550\) | 22.5773 | 0.962698 | ||||||||
\(551\) | −3.39199 | −0.144504 | ||||||||
\(552\) | −30.1518 | −1.28335 | ||||||||
\(553\) | −0.0722299 | −0.00307153 | ||||||||
\(554\) | 37.7365 | 1.60327 | ||||||||
\(555\) | 58.9118 | 2.50067 | ||||||||
\(556\) | −15.4500 | −0.655228 | ||||||||
\(557\) | −2.69500 | −0.114191 | −0.0570954 | − | 0.998369i | \(-0.518184\pi\) | ||||
−0.0570954 | + | 0.998369i | \(0.518184\pi\) | |||||||
\(558\) | −3.43111 | −0.145251 | ||||||||
\(559\) | −12.3657 | −0.523014 | ||||||||
\(560\) | −0.689494 | −0.0291364 | ||||||||
\(561\) | −3.94993 | −0.166766 | ||||||||
\(562\) | 11.8799 | 0.501123 | ||||||||
\(563\) | −21.0355 | −0.886540 | −0.443270 | − | 0.896388i | \(-0.646182\pi\) | ||||
−0.443270 | + | 0.896388i | \(0.646182\pi\) | |||||||
\(564\) | −23.6406 | −0.995450 | ||||||||
\(565\) | 48.8137 | 2.05361 | ||||||||
\(566\) | 30.7056 | 1.29065 | ||||||||
\(567\) | −1.42743 | −0.0599466 | ||||||||
\(568\) | 2.54726 | 0.106881 | ||||||||
\(569\) | −23.9589 | −1.00441 | −0.502204 | − | 0.864749i | \(-0.667477\pi\) | ||||
−0.502204 | + | 0.864749i | \(0.667477\pi\) | |||||||
\(570\) | −16.2499 | −0.680635 | ||||||||
\(571\) | −7.47725 | −0.312913 | −0.156457 | − | 0.987685i | \(-0.550007\pi\) | ||||
−0.156457 | + | 0.987685i | \(0.550007\pi\) | |||||||
\(572\) | −10.4906 | −0.438635 | ||||||||
\(573\) | −19.2857 | −0.805670 | ||||||||
\(574\) | −1.53888 | −0.0642315 | ||||||||
\(575\) | 72.1720 | 3.00978 | ||||||||
\(576\) | −9.76862 | −0.407026 | ||||||||
\(577\) | −16.9353 | −0.705025 | −0.352512 | − | 0.935807i | \(-0.614673\pi\) | ||||
−0.352512 | + | 0.935807i | \(0.614673\pi\) | |||||||
\(578\) | 29.9757 | 1.24683 | ||||||||
\(579\) | 14.3602 | 0.596791 | ||||||||
\(580\) | −37.2997 | −1.54878 | ||||||||
\(581\) | 0.308341 | 0.0127921 | ||||||||
\(582\) | 76.2112 | 3.15905 | ||||||||
\(583\) | 10.6864 | 0.442585 | ||||||||
\(584\) | 0.254844 | 0.0105455 | ||||||||
\(585\) | 9.48017 | 0.391957 | ||||||||
\(586\) | 35.8916 | 1.48267 | ||||||||
\(587\) | −14.3523 | −0.592383 | −0.296192 | − | 0.955129i | \(-0.595717\pi\) | ||||
−0.296192 | + | 0.955129i | \(0.595717\pi\) | |||||||
\(588\) | −39.3449 | −1.62255 | ||||||||
\(589\) | 2.03974 | 0.0840458 | ||||||||
\(590\) | 7.80793 | 0.321447 | ||||||||
\(591\) | −17.8699 | −0.735071 | ||||||||
\(592\) | −10.9706 | −0.450891 | ||||||||
\(593\) | −26.6774 | −1.09551 | −0.547755 | − | 0.836639i | \(-0.684517\pi\) | ||||
−0.547755 | + | 0.836639i | \(0.684517\pi\) | |||||||
\(594\) | −10.5280 | −0.431971 | ||||||||
\(595\) | 0.939726 | 0.0385250 | ||||||||
\(596\) | −33.0582 | −1.35412 | ||||||||
\(597\) | 6.54794 | 0.267989 | ||||||||
\(598\) | −56.6128 | −2.31507 | ||||||||
\(599\) | 48.7765 | 1.99295 | 0.996477 | − | 0.0838624i | \(-0.0267256\pi\) | ||||
0.996477 | + | 0.0838624i | \(0.0267256\pi\) | |||||||
\(600\) | −36.2604 | −1.48032 | ||||||||
\(601\) | −40.4504 | −1.65001 | −0.825003 | − | 0.565129i | \(-0.808826\pi\) | ||||
−0.825003 | + | 0.565129i | \(0.808826\pi\) | |||||||
\(602\) | 1.10736 | 0.0451326 | ||||||||
\(603\) | 2.29296 | 0.0933764 | ||||||||
\(604\) | −24.0230 | −0.977482 | ||||||||
\(605\) | −37.0914 | −1.50798 | ||||||||
\(606\) | 32.1984 | 1.30797 | ||||||||
\(607\) | 39.5777 | 1.60641 | 0.803204 | − | 0.595704i | \(-0.203127\pi\) | ||||
0.803204 | + | 0.595704i | \(0.203127\pi\) | |||||||
\(608\) | 7.04083 | 0.285543 | ||||||||
\(609\) | −0.877253 | −0.0355481 | ||||||||
\(610\) | −65.9733 | −2.67118 | ||||||||
\(611\) | −13.8413 | −0.559961 | ||||||||
\(612\) | 4.10957 | 0.166120 | ||||||||
\(613\) | −34.8981 | −1.40952 | −0.704761 | − | 0.709445i | \(-0.748946\pi\) | ||||
−0.704761 | + | 0.709445i | \(0.748946\pi\) | |||||||
\(614\) | 23.7801 | 0.959685 | ||||||||
\(615\) | 38.2117 | 1.54084 | ||||||||
\(616\) | 0.292947 | 0.0118032 | ||||||||
\(617\) | −5.60470 | −0.225637 | −0.112818 | − | 0.993616i | \(-0.535988\pi\) | ||||
−0.112818 | + | 0.993616i | \(0.535988\pi\) | |||||||
\(618\) | −71.1726 | −2.86298 | ||||||||
\(619\) | 3.95757 | 0.159068 | 0.0795342 | − | 0.996832i | \(-0.474657\pi\) | ||||
0.0795342 | + | 0.996832i | \(0.474657\pi\) | |||||||
\(620\) | 22.4297 | 0.900799 | ||||||||
\(621\) | −33.6546 | −1.35051 | ||||||||
\(622\) | 6.89340 | 0.276400 | ||||||||
\(623\) | −0.459098 | −0.0183934 | ||||||||
\(624\) | −8.73939 | −0.349856 | ||||||||
\(625\) | 15.2121 | 0.608482 | ||||||||
\(626\) | −54.2115 | −2.16673 | ||||||||
\(627\) | −2.12135 | −0.0847187 | ||||||||
\(628\) | 24.5314 | 0.978910 | ||||||||
\(629\) | 14.9521 | 0.596180 | ||||||||
\(630\) | −0.848957 | −0.0338233 | ||||||||
\(631\) | 22.0798 | 0.878982 | 0.439491 | − | 0.898247i | \(-0.355159\pi\) | ||||
0.439491 | + | 0.898247i | \(0.355159\pi\) | |||||||
\(632\) | 1.08702 | 0.0432392 | ||||||||
\(633\) | −1.93892 | −0.0770653 | ||||||||
\(634\) | −20.1883 | −0.801778 | ||||||||
\(635\) | 48.0435 | 1.90655 | ||||||||
\(636\) | −55.0394 | −2.18245 | ||||||||
\(637\) | −23.0360 | −0.912720 | ||||||||
\(638\) | −8.22020 | −0.325441 | ||||||||
\(639\) | −0.963678 | −0.0381225 | ||||||||
\(640\) | 54.5241 | 2.15526 | ||||||||
\(641\) | 19.9360 | 0.787423 | 0.393711 | − | 0.919234i | \(-0.371191\pi\) | ||||
0.393711 | + | 0.919234i | \(0.371191\pi\) | |||||||
\(642\) | −81.9306 | −3.23354 | ||||||||
\(643\) | −11.3083 | −0.445956 | −0.222978 | − | 0.974823i | \(-0.571578\pi\) | ||||
−0.222978 | + | 0.974823i | \(0.571578\pi\) | |||||||
\(644\) | 3.00309 | 0.118338 | ||||||||
\(645\) | −27.4967 | −1.08268 | ||||||||
\(646\) | −4.12432 | −0.162269 | ||||||||
\(647\) | −45.7563 | −1.79887 | −0.899433 | − | 0.437058i | \(-0.856021\pi\) | ||||
−0.899433 | + | 0.437058i | \(0.856021\pi\) | |||||||
\(648\) | 21.4820 | 0.843893 | ||||||||
\(649\) | 1.01929 | 0.0400106 | ||||||||
\(650\) | −68.0822 | −2.67040 | ||||||||
\(651\) | 0.527526 | 0.0206754 | ||||||||
\(652\) | 13.7610 | 0.538922 | ||||||||
\(653\) | 12.2945 | 0.481119 | 0.240560 | − | 0.970634i | \(-0.422669\pi\) | ||||
0.240560 | + | 0.970634i | \(0.422669\pi\) | |||||||
\(654\) | −15.2850 | −0.597691 | ||||||||
\(655\) | 48.1635 | 1.88190 | ||||||||
\(656\) | −7.11583 | −0.277826 | ||||||||
\(657\) | −0.0964122 | −0.00376140 | ||||||||
\(658\) | 1.23950 | 0.0483209 | ||||||||
\(659\) | 30.1860 | 1.17588 | 0.587940 | − | 0.808905i | \(-0.299939\pi\) | ||||
0.587940 | + | 0.808905i | \(0.299939\pi\) | |||||||
\(660\) | −23.3272 | −0.908010 | ||||||||
\(661\) | 47.8970 | 1.86298 | 0.931489 | − | 0.363770i | \(-0.118511\pi\) | ||||
0.931489 | + | 0.363770i | \(0.118511\pi\) | |||||||
\(662\) | 11.5826 | 0.450169 | ||||||||
\(663\) | 11.9111 | 0.462589 | ||||||||
\(664\) | −4.64034 | −0.180080 | ||||||||
\(665\) | 0.504690 | 0.0195710 | ||||||||
\(666\) | −13.5079 | −0.523420 | ||||||||
\(667\) | −26.2772 | −1.01746 | ||||||||
\(668\) | −40.9594 | −1.58477 | ||||||||
\(669\) | −14.7255 | −0.569321 | ||||||||
\(670\) | −25.3047 | −0.977605 | ||||||||
\(671\) | −8.61250 | −0.332482 | ||||||||
\(672\) | 1.82093 | 0.0702440 | ||||||||
\(673\) | 13.8506 | 0.533900 | 0.266950 | − | 0.963710i | \(-0.413984\pi\) | ||||
0.266950 | + | 0.963710i | \(0.413984\pi\) | |||||||
\(674\) | −29.1250 | −1.12185 | ||||||||
\(675\) | −40.4729 | −1.55780 | ||||||||
\(676\) | −6.14667 | −0.236411 | ||||||||
\(677\) | 35.7238 | 1.37298 | 0.686488 | − | 0.727141i | \(-0.259151\pi\) | ||||
0.686488 | + | 0.727141i | \(0.259151\pi\) | |||||||
\(678\) | −55.4067 | −2.12788 | ||||||||
\(679\) | −2.36696 | −0.0908357 | ||||||||
\(680\) | −14.1423 | −0.542333 | ||||||||
\(681\) | 50.7124 | 1.94330 | ||||||||
\(682\) | 4.94312 | 0.189282 | ||||||||
\(683\) | 17.5216 | 0.670446 | 0.335223 | − | 0.942139i | \(-0.391188\pi\) | ||||
0.335223 | + | 0.942139i | \(0.391188\pi\) | |||||||
\(684\) | 2.20709 | 0.0843902 | ||||||||
\(685\) | 7.39233 | 0.282446 | ||||||||
\(686\) | 4.13105 | 0.157724 | ||||||||
\(687\) | −49.8377 | −1.90143 | ||||||||
\(688\) | 5.12047 | 0.195216 | ||||||||
\(689\) | −32.2250 | −1.22768 | ||||||||
\(690\) | −125.886 | −4.79239 | ||||||||
\(691\) | 28.7634 | 1.09421 | 0.547105 | − | 0.837064i | \(-0.315730\pi\) | ||||
0.547105 | + | 0.837064i | \(0.315730\pi\) | |||||||
\(692\) | 60.9220 | 2.31591 | ||||||||
\(693\) | −0.110827 | −0.00420998 | ||||||||
\(694\) | −45.0860 | −1.71144 | ||||||||
\(695\) | −20.1146 | −0.762989 | ||||||||
\(696\) | 13.2021 | 0.500425 | ||||||||
\(697\) | 9.69831 | 0.367350 | ||||||||
\(698\) | −7.19129 | −0.272194 | ||||||||
\(699\) | 19.3943 | 0.733560 | ||||||||
\(700\) | 3.61150 | 0.136502 | ||||||||
\(701\) | 11.8718 | 0.448393 | 0.224196 | − | 0.974544i | \(-0.428024\pi\) | ||||
0.224196 | + | 0.974544i | \(0.428024\pi\) | |||||||
\(702\) | 31.7475 | 1.19823 | ||||||||
\(703\) | 8.03020 | 0.302865 | ||||||||
\(704\) | 14.0734 | 0.530412 | ||||||||
\(705\) | −30.7780 | −1.15917 | ||||||||
\(706\) | −37.7242 | −1.41977 | ||||||||
\(707\) | −1.00002 | −0.0376095 | ||||||||
\(708\) | −5.24977 | −0.197299 | ||||||||
\(709\) | 49.2027 | 1.84785 | 0.923923 | − | 0.382579i | \(-0.124964\pi\) | ||||
0.923923 | + | 0.382579i | \(0.124964\pi\) | |||||||
\(710\) | 10.6350 | 0.399124 | ||||||||
\(711\) | −0.411238 | −0.0154226 | ||||||||
\(712\) | 6.90915 | 0.258931 | ||||||||
\(713\) | 15.8015 | 0.591771 | ||||||||
\(714\) | −1.06665 | −0.0399184 | ||||||||
\(715\) | −13.6578 | −0.510775 | ||||||||
\(716\) | −20.9235 | −0.781947 | ||||||||
\(717\) | −29.3069 | −1.09449 | ||||||||
\(718\) | −38.7385 | −1.44571 | ||||||||
\(719\) | −3.00601 | −0.112105 | −0.0560525 | − | 0.998428i | \(-0.517851\pi\) | ||||
−0.0560525 | + | 0.998428i | \(0.517851\pi\) | |||||||
\(720\) | −3.92561 | −0.146299 | ||||||||
\(721\) | 2.21048 | 0.0823225 | ||||||||
\(722\) | −2.21501 | −0.0824341 | ||||||||
\(723\) | 36.7671 | 1.36738 | ||||||||
\(724\) | −52.6205 | −1.95562 | ||||||||
\(725\) | −31.6009 | −1.17363 | ||||||||
\(726\) | 42.1011 | 1.56252 | ||||||||
\(727\) | −43.0194 | −1.59550 | −0.797751 | − | 0.602987i | \(-0.793977\pi\) | ||||
−0.797751 | + | 0.602987i | \(0.793977\pi\) | |||||||
\(728\) | −0.883389 | −0.0327406 | ||||||||
\(729\) | 17.1428 | 0.634918 | ||||||||
\(730\) | 1.06399 | 0.0393800 | ||||||||
\(731\) | −6.97880 | −0.258120 | ||||||||
\(732\) | 44.3580 | 1.63952 | ||||||||
\(733\) | −47.7648 | −1.76423 | −0.882116 | − | 0.471032i | \(-0.843882\pi\) | ||||
−0.882116 | + | 0.471032i | \(0.843882\pi\) | |||||||
\(734\) | 14.8718 | 0.548928 | ||||||||
\(735\) | −51.2235 | −1.88941 | ||||||||
\(736\) | 54.5442 | 2.01053 | ||||||||
\(737\) | −3.30341 | −0.121683 | ||||||||
\(738\) | −8.76154 | −0.322517 | ||||||||
\(739\) | −9.86435 | −0.362866 | −0.181433 | − | 0.983403i | \(-0.558074\pi\) | ||||
−0.181433 | + | 0.983403i | \(0.558074\pi\) | |||||||
\(740\) | 88.3031 | 3.24609 | ||||||||
\(741\) | 6.39699 | 0.234999 | ||||||||
\(742\) | 2.88578 | 0.105940 | ||||||||
\(743\) | 32.8173 | 1.20395 | 0.601975 | − | 0.798515i | \(-0.294381\pi\) | ||||
0.601975 | + | 0.798515i | \(0.294381\pi\) | |||||||
\(744\) | −7.93894 | −0.291056 | ||||||||
\(745\) | −43.0389 | −1.57682 | ||||||||
\(746\) | 22.4492 | 0.821924 | ||||||||
\(747\) | 1.75553 | 0.0642313 | ||||||||
\(748\) | −5.92057 | −0.216477 | ||||||||
\(749\) | 2.54460 | 0.0929776 | ||||||||
\(750\) | −70.1397 | −2.56114 | ||||||||
\(751\) | −40.2147 | −1.46745 | −0.733727 | − | 0.679444i | \(-0.762221\pi\) | ||||
−0.733727 | + | 0.679444i | \(0.762221\pi\) | |||||||
\(752\) | 5.73152 | 0.209007 | ||||||||
\(753\) | 6.62960 | 0.241596 | ||||||||
\(754\) | 24.7882 | 0.902733 | ||||||||
\(755\) | −31.2758 | −1.13824 | ||||||||
\(756\) | −1.68408 | −0.0612495 | ||||||||
\(757\) | −48.1991 | −1.75183 | −0.875914 | − | 0.482467i | \(-0.839741\pi\) | ||||
−0.875914 | + | 0.482467i | \(0.839741\pi\) | |||||||
\(758\) | 8.40076 | 0.305129 | ||||||||
\(759\) | −16.4338 | −0.596509 | ||||||||
\(760\) | −7.59528 | −0.275510 | ||||||||
\(761\) | −5.42956 | −0.196822 | −0.0984108 | − | 0.995146i | \(-0.531376\pi\) | ||||
−0.0984108 | + | 0.995146i | \(0.531376\pi\) | |||||||
\(762\) | −54.5325 | −1.97550 | ||||||||
\(763\) | 0.474721 | 0.0171861 | ||||||||
\(764\) | −28.9073 | −1.04583 | ||||||||
\(765\) | 5.35030 | 0.193440 | ||||||||
\(766\) | −21.4616 | −0.775438 | ||||||||
\(767\) | −3.07369 | −0.110984 | ||||||||
\(768\) | −12.0071 | −0.433269 | ||||||||
\(769\) | 28.3638 | 1.02282 | 0.511412 | − | 0.859336i | \(-0.329123\pi\) | ||||
0.511412 | + | 0.859336i | \(0.329123\pi\) | |||||||
\(770\) | 1.22307 | 0.0440765 | ||||||||
\(771\) | −46.5202 | −1.67538 | ||||||||
\(772\) | 21.5246 | 0.774687 | ||||||||
\(773\) | 15.9944 | 0.575279 | 0.287639 | − | 0.957739i | \(-0.407130\pi\) | ||||
0.287639 | + | 0.957739i | \(0.407130\pi\) | |||||||
\(774\) | 6.30471 | 0.226618 | ||||||||
\(775\) | 19.0028 | 0.682601 | ||||||||
\(776\) | 35.6214 | 1.27873 | ||||||||
\(777\) | 2.07681 | 0.0745050 | ||||||||
\(778\) | 42.0269 | 1.50674 | ||||||||
\(779\) | 5.20858 | 0.186617 | ||||||||
\(780\) | 70.3437 | 2.51871 | ||||||||
\(781\) | 1.38835 | 0.0496790 | ||||||||
\(782\) | −31.9504 | −1.14255 | ||||||||
\(783\) | 14.7358 | 0.526616 | ||||||||
\(784\) | 9.53891 | 0.340675 | ||||||||
\(785\) | 31.9377 | 1.13991 | ||||||||
\(786\) | −54.6687 | −1.94997 | ||||||||
\(787\) | −30.5297 | −1.08827 | −0.544133 | − | 0.838999i | \(-0.683141\pi\) | ||||
−0.544133 | + | 0.838999i | \(0.683141\pi\) | |||||||
\(788\) | −26.7853 | −0.954187 | ||||||||
\(789\) | 49.9133 | 1.77696 | ||||||||
\(790\) | 4.53836 | 0.161468 | ||||||||
\(791\) | 1.72082 | 0.0611853 | ||||||||
\(792\) | 1.66788 | 0.0592657 | ||||||||
\(793\) | 25.9712 | 0.922264 | ||||||||
\(794\) | 65.4339 | 2.32216 | ||||||||
\(795\) | −71.6564 | −2.54139 | ||||||||
\(796\) | 9.81473 | 0.347874 | ||||||||
\(797\) | −26.6068 | −0.942463 | −0.471231 | − | 0.882010i | \(-0.656190\pi\) | ||||
−0.471231 | + | 0.882010i | \(0.656190\pi\) | |||||||
\(798\) | −0.572856 | −0.0202789 | ||||||||
\(799\) | −7.81161 | −0.276355 | ||||||||
\(800\) | 65.5945 | 2.31912 | ||||||||
\(801\) | −2.61386 | −0.0923562 | ||||||||
\(802\) | −15.1901 | −0.536382 | ||||||||
\(803\) | 0.138899 | 0.00490163 | ||||||||
\(804\) | 17.0140 | 0.600036 | ||||||||
\(805\) | 3.90976 | 0.137801 | ||||||||
\(806\) | −14.9061 | −0.525045 | ||||||||
\(807\) | −2.85552 | −0.100519 | ||||||||
\(808\) | 15.0496 | 0.529444 | ||||||||
\(809\) | 13.8396 | 0.486575 | 0.243287 | − | 0.969954i | \(-0.421774\pi\) | ||||
0.243287 | + | 0.969954i | \(0.421774\pi\) | |||||||
\(810\) | 89.6887 | 3.15134 | ||||||||
\(811\) | −19.0621 | −0.669362 | −0.334681 | − | 0.942331i | \(-0.608629\pi\) | ||||
−0.334681 | + | 0.942331i | \(0.608629\pi\) | |||||||
\(812\) | −1.31492 | −0.0461446 | ||||||||
\(813\) | −3.27899 | −0.114999 | ||||||||
\(814\) | 19.4605 | 0.682089 | ||||||||
\(815\) | 17.9156 | 0.627556 | ||||||||
\(816\) | −4.93223 | −0.172663 | ||||||||
\(817\) | −3.74804 | −0.131127 | ||||||||
\(818\) | 13.2672 | 0.463877 | ||||||||
\(819\) | 0.334202 | 0.0116780 | ||||||||
\(820\) | 57.2756 | 2.00015 | ||||||||
\(821\) | −18.7960 | −0.655985 | −0.327993 | − | 0.944680i | \(-0.606372\pi\) | ||||
−0.327993 | + | 0.944680i | \(0.606372\pi\) | |||||||
\(822\) | −8.39077 | −0.292662 | ||||||||
\(823\) | −36.8738 | −1.28534 | −0.642670 | − | 0.766143i | \(-0.722173\pi\) | ||||
−0.642670 | + | 0.766143i | \(0.722173\pi\) | |||||||
\(824\) | −33.2663 | −1.15889 | ||||||||
\(825\) | −19.7632 | −0.688065 | ||||||||
\(826\) | 0.275251 | 0.00957722 | ||||||||
\(827\) | −7.32533 | −0.254727 | −0.127363 | − | 0.991856i | \(-0.540651\pi\) | ||||
−0.127363 | + | 0.991856i | \(0.540651\pi\) | |||||||
\(828\) | 17.0980 | 0.594196 | ||||||||
\(829\) | −5.97441 | −0.207500 | −0.103750 | − | 0.994603i | \(-0.533084\pi\) | ||||
−0.103750 | + | 0.994603i | \(0.533084\pi\) | |||||||
\(830\) | −19.3737 | −0.672471 | ||||||||
\(831\) | −33.0329 | −1.14590 | ||||||||
\(832\) | −42.4387 | −1.47130 | ||||||||
\(833\) | −13.0008 | −0.450450 | ||||||||
\(834\) | 22.8313 | 0.790585 | ||||||||
\(835\) | −53.3255 | −1.84540 | ||||||||
\(836\) | −3.17970 | −0.109972 | ||||||||
\(837\) | −8.86123 | −0.306289 | ||||||||
\(838\) | −3.57332 | −0.123438 | ||||||||
\(839\) | −0.781041 | −0.0269645 | −0.0134823 | − | 0.999909i | \(-0.504292\pi\) | ||||
−0.0134823 | + | 0.999909i | \(0.504292\pi\) | |||||||
\(840\) | −1.96433 | −0.0677757 | ||||||||
\(841\) | −17.4944 | −0.603255 | ||||||||
\(842\) | 44.2337 | 1.52440 | ||||||||
\(843\) | −10.3992 | −0.358166 | ||||||||
\(844\) | −2.90626 | −0.100038 | ||||||||
\(845\) | −8.00242 | −0.275292 | ||||||||
\(846\) | 7.05708 | 0.242627 | ||||||||
\(847\) | −1.30758 | −0.0449288 | ||||||||
\(848\) | 13.3439 | 0.458233 | ||||||||
\(849\) | −26.8784 | −0.922465 | ||||||||
\(850\) | −38.4234 | −1.31791 | ||||||||
\(851\) | 62.2087 | 2.13249 | ||||||||
\(852\) | −7.15058 | −0.244975 | ||||||||
\(853\) | −9.63724 | −0.329973 | −0.164986 | − | 0.986296i | \(-0.552758\pi\) | ||||
−0.164986 | + | 0.986296i | \(0.552758\pi\) | |||||||
\(854\) | −2.32574 | −0.0795853 | ||||||||
\(855\) | 2.87343 | 0.0982694 | ||||||||
\(856\) | −38.2946 | −1.30888 | ||||||||
\(857\) | −57.7223 | −1.97176 | −0.985878 | − | 0.167462i | \(-0.946443\pi\) | ||||
−0.985878 | + | 0.167462i | \(0.946443\pi\) | |||||||
\(858\) | 15.5025 | 0.529248 | ||||||||
\(859\) | −41.7538 | −1.42462 | −0.712310 | − | 0.701865i | \(-0.752351\pi\) | ||||
−0.712310 | + | 0.701865i | \(0.752351\pi\) | |||||||
\(860\) | −41.2149 | −1.40542 | ||||||||
\(861\) | 1.34707 | 0.0459079 | ||||||||
\(862\) | −83.6999 | −2.85083 | ||||||||
\(863\) | 25.5299 | 0.869048 | 0.434524 | − | 0.900660i | \(-0.356917\pi\) | ||||
0.434524 | + | 0.900660i | \(0.356917\pi\) | |||||||
\(864\) | −30.5875 | −1.04061 | ||||||||
\(865\) | 79.3149 | 2.69679 | ||||||||
\(866\) | 34.6192 | 1.17641 | ||||||||
\(867\) | −26.2395 | −0.891139 | ||||||||
\(868\) | 0.790710 | 0.0268385 | ||||||||
\(869\) | 0.592461 | 0.0200979 | ||||||||
\(870\) | 55.1197 | 1.86873 | ||||||||
\(871\) | 9.96150 | 0.337532 | ||||||||
\(872\) | −7.14427 | −0.241935 | ||||||||
\(873\) | −13.4762 | −0.456101 | ||||||||
\(874\) | −17.1593 | −0.580423 | ||||||||
\(875\) | 2.17840 | 0.0736433 | ||||||||
\(876\) | −0.715388 | −0.0241707 | ||||||||
\(877\) | 47.3418 | 1.59862 | 0.799309 | − | 0.600921i | \(-0.205199\pi\) | ||||
0.799309 | + | 0.600921i | \(0.205199\pi\) | |||||||
\(878\) | −6.28096 | −0.211972 | ||||||||
\(879\) | −31.4180 | −1.05970 | ||||||||
\(880\) | 5.65553 | 0.190648 | ||||||||
\(881\) | 31.9711 | 1.07714 | 0.538568 | − | 0.842582i | \(-0.318966\pi\) | ||||
0.538568 | + | 0.842582i | \(0.318966\pi\) | |||||||
\(882\) | 11.7450 | 0.395475 | ||||||||
\(883\) | 15.2184 | 0.512140 | 0.256070 | − | 0.966658i | \(-0.417572\pi\) | ||||
0.256070 | + | 0.966658i | \(0.417572\pi\) | |||||||
\(884\) | 17.8536 | 0.600481 | ||||||||
\(885\) | −6.83473 | −0.229747 | ||||||||
\(886\) | 37.6713 | 1.26559 | ||||||||
\(887\) | −27.2918 | −0.916369 | −0.458184 | − | 0.888857i | \(-0.651500\pi\) | ||||
−0.458184 | + | 0.888857i | \(0.651500\pi\) | |||||||
\(888\) | −31.2547 | −1.04884 | ||||||||
\(889\) | 1.69367 | 0.0568038 | ||||||||
\(890\) | 28.8461 | 0.966924 | ||||||||
\(891\) | 11.7084 | 0.392247 | ||||||||
\(892\) | −22.0721 | −0.739029 | ||||||||
\(893\) | −4.19531 | −0.140391 | ||||||||
\(894\) | 48.8519 | 1.63385 | ||||||||
\(895\) | −27.2405 | −0.910550 | ||||||||
\(896\) | 1.92213 | 0.0642138 | ||||||||
\(897\) | 49.5565 | 1.65464 | ||||||||
\(898\) | −44.0574 | −1.47021 | ||||||||
\(899\) | −6.91877 | −0.230754 | ||||||||
\(900\) | 20.5619 | 0.685398 | ||||||||
\(901\) | −18.1868 | −0.605889 | ||||||||
\(902\) | 12.6225 | 0.420285 | ||||||||
\(903\) | −0.969336 | −0.0322575 | ||||||||
\(904\) | −25.8973 | −0.861331 | ||||||||
\(905\) | −68.5071 | −2.27725 | ||||||||
\(906\) | 35.5000 | 1.17941 | ||||||||
\(907\) | −22.4136 | −0.744231 | −0.372115 | − | 0.928187i | \(-0.621367\pi\) | ||||
−0.372115 | + | 0.928187i | \(0.621367\pi\) | |||||||
\(908\) | 76.0130 | 2.52258 | ||||||||
\(909\) | −5.69356 | −0.188843 | ||||||||
\(910\) | −3.68820 | −0.122263 | ||||||||
\(911\) | 17.5758 | 0.582311 | 0.291156 | − | 0.956676i | \(-0.405960\pi\) | ||||
0.291156 | + | 0.956676i | \(0.405960\pi\) | |||||||
\(912\) | −2.64891 | −0.0877141 | ||||||||
\(913\) | −2.52914 | −0.0837025 | ||||||||
\(914\) | −22.1592 | −0.732962 | ||||||||
\(915\) | 57.7502 | 1.90916 | ||||||||
\(916\) | −74.7018 | −2.46822 | ||||||||
\(917\) | 1.69790 | 0.0560696 | ||||||||
\(918\) | 17.9173 | 0.591358 | ||||||||
\(919\) | 2.54400 | 0.0839190 | 0.0419595 | − | 0.999119i | \(-0.486640\pi\) | ||||
0.0419595 | + | 0.999119i | \(0.486640\pi\) | |||||||
\(920\) | −58.8394 | −1.93988 | ||||||||
\(921\) | −20.8161 | −0.685913 | ||||||||
\(922\) | −51.9671 | −1.71145 | ||||||||
\(923\) | −4.18659 | −0.137803 | ||||||||
\(924\) | −0.822350 | −0.0270533 | ||||||||
\(925\) | 74.8118 | 2.45980 | ||||||||
\(926\) | −87.0066 | −2.85921 | ||||||||
\(927\) | 12.5853 | 0.413355 | ||||||||
\(928\) | −23.8824 | −0.783980 | ||||||||
\(929\) | 4.75504 | 0.156008 | 0.0780040 | − | 0.996953i | \(-0.475145\pi\) | ||||
0.0780040 | + | 0.996953i | \(0.475145\pi\) | |||||||
\(930\) | −33.1456 | −1.08689 | ||||||||
\(931\) | −6.98221 | −0.228833 | ||||||||
\(932\) | 29.0702 | 0.952226 | ||||||||
\(933\) | −6.03419 | −0.197551 | ||||||||
\(934\) | −26.5230 | −0.867860 | ||||||||
\(935\) | −7.70805 | −0.252080 | ||||||||
\(936\) | −5.02954 | −0.164396 | ||||||||
\(937\) | −50.9314 | −1.66386 | −0.831929 | − | 0.554882i | \(-0.812763\pi\) | ||||
−0.831929 | + | 0.554882i | \(0.812763\pi\) | |||||||
\(938\) | −0.892061 | −0.0291268 | ||||||||
\(939\) | 47.4544 | 1.54862 | ||||||||
\(940\) | −46.1332 | −1.50470 | ||||||||
\(941\) | −45.9920 | −1.49930 | −0.749648 | − | 0.661837i | \(-0.769777\pi\) | ||||
−0.749648 | + | 0.661837i | \(0.769777\pi\) | |||||||
\(942\) | −36.2514 | −1.18113 | ||||||||
\(943\) | 40.3501 | 1.31398 | ||||||||
\(944\) | 1.27277 | 0.0414252 | ||||||||
\(945\) | −2.19253 | −0.0713229 | ||||||||
\(946\) | −9.08305 | −0.295315 | ||||||||
\(947\) | −21.9572 | −0.713514 | −0.356757 | − | 0.934197i | \(-0.616118\pi\) | ||||
−0.356757 | + | 0.934197i | \(0.616118\pi\) | |||||||
\(948\) | −3.05143 | −0.0991058 | ||||||||
\(949\) | −0.418852 | −0.0135965 | ||||||||
\(950\) | −20.6357 | −0.669510 | ||||||||
\(951\) | 17.6719 | 0.573052 | ||||||||
\(952\) | −0.498556 | −0.0161583 | ||||||||
\(953\) | −7.15874 | −0.231894 | −0.115947 | − | 0.993255i | \(-0.536990\pi\) | ||||
−0.115947 | + | 0.993255i | \(0.536990\pi\) | |||||||
\(954\) | 16.4301 | 0.531943 | ||||||||
\(955\) | −37.6348 | −1.21783 | ||||||||
\(956\) | −43.9282 | −1.42074 | ||||||||
\(957\) | 7.19561 | 0.232601 | ||||||||
\(958\) | 45.4000 | 1.46681 | ||||||||
\(959\) | 0.260600 | 0.00841522 | ||||||||
\(960\) | −94.3677 | −3.04571 | ||||||||
\(961\) | −26.8395 | −0.865790 | ||||||||
\(962\) | −58.6835 | −1.89203 | ||||||||
\(963\) | 14.4876 | 0.466856 | ||||||||
\(964\) | 55.1104 | 1.77499 | ||||||||
\(965\) | 28.0231 | 0.902095 | ||||||||
\(966\) | −4.43782 | −0.142785 | ||||||||
\(967\) | −15.7504 | −0.506499 | −0.253249 | − | 0.967401i | \(-0.581499\pi\) | ||||
−0.253249 | + | 0.967401i | \(0.581499\pi\) | |||||||
\(968\) | 19.6782 | 0.632482 | ||||||||
\(969\) | 3.61025 | 0.115978 | ||||||||
\(970\) | 148.721 | 4.77515 | ||||||||
\(971\) | 27.6116 | 0.886100 | 0.443050 | − | 0.896497i | \(-0.353896\pi\) | ||||
0.443050 | + | 0.896497i | \(0.353896\pi\) | |||||||
\(972\) | −22.4264 | −0.719328 | ||||||||
\(973\) | −0.709095 | −0.0227325 | ||||||||
\(974\) | 94.9751 | 3.04320 | ||||||||
\(975\) | 59.5963 | 1.90861 | ||||||||
\(976\) | −10.7543 | −0.344237 | ||||||||
\(977\) | −6.07091 | −0.194226 | −0.0971129 | − | 0.995273i | \(-0.530961\pi\) | ||||
−0.0971129 | + | 0.995273i | \(0.530961\pi\) | |||||||
\(978\) | −20.3353 | −0.650253 | ||||||||
\(979\) | 3.76572 | 0.120353 | ||||||||
\(980\) | −76.7791 | −2.45262 | ||||||||
\(981\) | 2.70281 | 0.0862941 | ||||||||
\(982\) | −57.4310 | −1.83270 | ||||||||
\(983\) | 45.2595 | 1.44355 | 0.721777 | − | 0.692125i | \(-0.243326\pi\) | ||||
0.721777 | + | 0.692125i | \(0.243326\pi\) | |||||||
\(984\) | −20.2725 | −0.646265 | ||||||||
\(985\) | −34.8721 | −1.11112 | ||||||||
\(986\) | 13.9897 | 0.445521 | ||||||||
\(987\) | −1.08501 | −0.0345362 | ||||||||
\(988\) | 9.58847 | 0.305050 | ||||||||
\(989\) | −29.0355 | −0.923275 | ||||||||
\(990\) | 6.96352 | 0.221315 | ||||||||
\(991\) | 35.1589 | 1.11686 | 0.558429 | − | 0.829552i | \(-0.311404\pi\) | ||||
0.558429 | + | 0.829552i | \(0.311404\pi\) | |||||||
\(992\) | 14.3614 | 0.455976 | ||||||||
\(993\) | −10.1389 | −0.321748 | ||||||||
\(994\) | 0.374913 | 0.0118915 | ||||||||
\(995\) | 12.7779 | 0.405086 | ||||||||
\(996\) | 13.0262 | 0.412750 | ||||||||
\(997\) | −14.8559 | −0.470490 | −0.235245 | − | 0.971936i | \(-0.575589\pi\) | ||||
−0.235245 | + | 0.971936i | \(0.575589\pi\) | |||||||
\(998\) | 33.9922 | 1.07600 | ||||||||
\(999\) | −34.8856 | −1.10373 |
(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 | 4009.2.a.e.1.10 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4009.2.a.e.1.10 | ✓ | 82 | 1.1 | even | 1 | trivial |