Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8035,2,Mod(1,8035)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8035, 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("8035.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8035 = 5 \cdot 1607 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8035.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.1597980241\) |
Analytic rank: | \(0\) |
Dimension: | \(153\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 8035.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52944 | −1.78858 | −0.894291 | − | 0.447487i | \(-0.852319\pi\) | ||||
−0.894291 | + | 0.447487i | \(0.852319\pi\) | |||||||
\(3\) | −2.42468 | −1.39989 | −0.699944 | − | 0.714198i | \(-0.746792\pi\) | ||||
−0.699944 | + | 0.714198i | \(0.746792\pi\) | |||||||
\(4\) | 4.39805 | 2.19902 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 6.13306 | 2.50381 | ||||||||
\(7\) | 0.256968 | 0.0971247 | 0.0485624 | − | 0.998820i | \(-0.484536\pi\) | ||||
0.0485624 | + | 0.998820i | \(0.484536\pi\) | |||||||
\(8\) | −6.06570 | −2.14455 | ||||||||
\(9\) | 2.87905 | 0.959684 | ||||||||
\(10\) | −2.52944 | −0.799878 | ||||||||
\(11\) | 0.560693 | 0.169055 | 0.0845277 | − | 0.996421i | \(-0.473062\pi\) | ||||
0.0845277 | + | 0.996421i | \(0.473062\pi\) | |||||||
\(12\) | −10.6638 | −3.07838 | ||||||||
\(13\) | −5.31322 | −1.47362 | −0.736811 | − | 0.676099i | \(-0.763669\pi\) | ||||
−0.736811 | + | 0.676099i | \(0.763669\pi\) | |||||||
\(14\) | −0.649984 | −0.173715 | ||||||||
\(15\) | −2.42468 | −0.626049 | ||||||||
\(16\) | 6.54671 | 1.63668 | ||||||||
\(17\) | −6.32354 | −1.53368 | −0.766842 | − | 0.641836i | \(-0.778173\pi\) | ||||
−0.766842 | + | 0.641836i | \(0.778173\pi\) | |||||||
\(18\) | −7.28238 | −1.71647 | ||||||||
\(19\) | 0.712431 | 0.163443 | 0.0817215 | − | 0.996655i | \(-0.473958\pi\) | ||||
0.0817215 | + | 0.996655i | \(0.473958\pi\) | |||||||
\(20\) | 4.39805 | 0.983433 | ||||||||
\(21\) | −0.623064 | −0.135964 | ||||||||
\(22\) | −1.41824 | −0.302369 | ||||||||
\(23\) | 6.12771 | 1.27772 | 0.638858 | − | 0.769324i | \(-0.279407\pi\) | ||||
0.638858 | + | 0.769324i | \(0.279407\pi\) | |||||||
\(24\) | 14.7074 | 3.00213 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 13.4394 | 2.63569 | ||||||||
\(27\) | 0.293257 | 0.0564374 | ||||||||
\(28\) | 1.13016 | 0.213579 | ||||||||
\(29\) | −5.89093 | −1.09392 | −0.546959 | − | 0.837159i | \(-0.684215\pi\) | ||||
−0.546959 | + | 0.837159i | \(0.684215\pi\) | |||||||
\(30\) | 6.13306 | 1.11974 | ||||||||
\(31\) | 6.98787 | 1.25506 | 0.627529 | − | 0.778593i | \(-0.284066\pi\) | ||||
0.627529 | + | 0.778593i | \(0.284066\pi\) | |||||||
\(32\) | −4.42808 | −0.782781 | ||||||||
\(33\) | −1.35950 | −0.236658 | ||||||||
\(34\) | 15.9950 | 2.74312 | ||||||||
\(35\) | 0.256968 | 0.0434355 | ||||||||
\(36\) | 12.6622 | 2.11037 | ||||||||
\(37\) | −11.9083 | −1.95771 | −0.978854 | − | 0.204561i | \(-0.934423\pi\) | ||||
−0.978854 | + | 0.204561i | \(0.934423\pi\) | |||||||
\(38\) | −1.80205 | −0.292331 | ||||||||
\(39\) | 12.8828 | 2.06290 | ||||||||
\(40\) | −6.06570 | −0.959071 | ||||||||
\(41\) | 0.740184 | 0.115597 | 0.0577987 | − | 0.998328i | \(-0.481592\pi\) | ||||
0.0577987 | + | 0.998328i | \(0.481592\pi\) | |||||||
\(42\) | 1.57600 | 0.243182 | ||||||||
\(43\) | −6.63627 | −1.01202 | −0.506011 | − | 0.862527i | \(-0.668880\pi\) | ||||
−0.506011 | + | 0.862527i | \(0.668880\pi\) | |||||||
\(44\) | 2.46595 | 0.371756 | ||||||||
\(45\) | 2.87905 | 0.429184 | ||||||||
\(46\) | −15.4997 | −2.28530 | ||||||||
\(47\) | −10.2422 | −1.49398 | −0.746991 | − | 0.664834i | \(-0.768502\pi\) | ||||
−0.746991 | + | 0.664834i | \(0.768502\pi\) | |||||||
\(48\) | −15.8736 | −2.29116 | ||||||||
\(49\) | −6.93397 | −0.990567 | ||||||||
\(50\) | −2.52944 | −0.357716 | ||||||||
\(51\) | 15.3325 | 2.14698 | ||||||||
\(52\) | −23.3678 | −3.24053 | ||||||||
\(53\) | −2.83729 | −0.389731 | −0.194866 | − | 0.980830i | \(-0.562427\pi\) | ||||
−0.194866 | + | 0.980830i | \(0.562427\pi\) | |||||||
\(54\) | −0.741775 | −0.100943 | ||||||||
\(55\) | 0.560693 | 0.0756038 | ||||||||
\(56\) | −1.55869 | −0.208289 | ||||||||
\(57\) | −1.72742 | −0.228802 | ||||||||
\(58\) | 14.9007 | 1.95656 | ||||||||
\(59\) | 2.23817 | 0.291385 | 0.145692 | − | 0.989330i | \(-0.453459\pi\) | ||||
0.145692 | + | 0.989330i | \(0.453459\pi\) | |||||||
\(60\) | −10.6638 | −1.37669 | ||||||||
\(61\) | −8.91289 | −1.14118 | −0.570589 | − | 0.821236i | \(-0.693285\pi\) | ||||
−0.570589 | + | 0.821236i | \(0.693285\pi\) | |||||||
\(62\) | −17.6754 | −2.24477 | ||||||||
\(63\) | 0.739824 | 0.0932091 | ||||||||
\(64\) | −1.89288 | −0.236609 | ||||||||
\(65\) | −5.31322 | −0.659023 | ||||||||
\(66\) | 3.43877 | 0.423283 | ||||||||
\(67\) | −0.700692 | −0.0856031 | −0.0428016 | − | 0.999084i | \(-0.513628\pi\) | ||||
−0.0428016 | + | 0.999084i | \(0.513628\pi\) | |||||||
\(68\) | −27.8112 | −3.37261 | ||||||||
\(69\) | −14.8577 | −1.78866 | ||||||||
\(70\) | −0.649984 | −0.0776879 | ||||||||
\(71\) | −12.3380 | −1.46425 | −0.732125 | − | 0.681171i | \(-0.761471\pi\) | ||||
−0.732125 | + | 0.681171i | \(0.761471\pi\) | |||||||
\(72\) | −17.4635 | −2.05809 | ||||||||
\(73\) | 10.8490 | 1.26978 | 0.634890 | − | 0.772603i | \(-0.281046\pi\) | ||||
0.634890 | + | 0.772603i | \(0.281046\pi\) | |||||||
\(74\) | 30.1212 | 3.50152 | ||||||||
\(75\) | −2.42468 | −0.279977 | ||||||||
\(76\) | 3.13331 | 0.359415 | ||||||||
\(77\) | 0.144080 | 0.0164195 | ||||||||
\(78\) | −32.5863 | −3.68967 | ||||||||
\(79\) | 3.82196 | 0.430005 | 0.215002 | − | 0.976614i | \(-0.431024\pi\) | ||||
0.215002 | + | 0.976614i | \(0.431024\pi\) | |||||||
\(80\) | 6.54671 | 0.731944 | ||||||||
\(81\) | −9.34821 | −1.03869 | ||||||||
\(82\) | −1.87225 | −0.206755 | ||||||||
\(83\) | 4.20223 | 0.461255 | 0.230627 | − | 0.973042i | \(-0.425922\pi\) | ||||
0.230627 | + | 0.973042i | \(0.425922\pi\) | |||||||
\(84\) | −2.74026 | −0.298987 | ||||||||
\(85\) | −6.32354 | −0.685884 | ||||||||
\(86\) | 16.7860 | 1.81008 | ||||||||
\(87\) | 14.2836 | 1.53136 | ||||||||
\(88\) | −3.40100 | −0.362547 | ||||||||
\(89\) | 2.98034 | 0.315915 | 0.157958 | − | 0.987446i | \(-0.449509\pi\) | ||||
0.157958 | + | 0.987446i | \(0.449509\pi\) | |||||||
\(90\) | −7.28238 | −0.767630 | ||||||||
\(91\) | −1.36533 | −0.143125 | ||||||||
\(92\) | 26.9500 | 2.80973 | ||||||||
\(93\) | −16.9433 | −1.75694 | ||||||||
\(94\) | 25.9070 | 2.67211 | ||||||||
\(95\) | 0.712431 | 0.0730939 | ||||||||
\(96\) | 10.7367 | 1.09581 | ||||||||
\(97\) | 7.51559 | 0.763093 | 0.381546 | − | 0.924350i | \(-0.375392\pi\) | ||||
0.381546 | + | 0.924350i | \(0.375392\pi\) | |||||||
\(98\) | 17.5390 | 1.77171 | ||||||||
\(99\) | 1.61427 | 0.162240 | ||||||||
\(100\) | 4.39805 | 0.439805 | ||||||||
\(101\) | 8.33417 | 0.829281 | 0.414640 | − | 0.909985i | \(-0.363907\pi\) | ||||
0.414640 | + | 0.909985i | \(0.363907\pi\) | |||||||
\(102\) | −38.7827 | −3.84006 | ||||||||
\(103\) | −7.14407 | −0.703926 | −0.351963 | − | 0.936014i | \(-0.614486\pi\) | ||||
−0.351963 | + | 0.936014i | \(0.614486\pi\) | |||||||
\(104\) | 32.2284 | 3.16025 | ||||||||
\(105\) | −0.623064 | −0.0608048 | ||||||||
\(106\) | 7.17673 | 0.697066 | ||||||||
\(107\) | 11.4466 | 1.10658 | 0.553291 | − | 0.832988i | \(-0.313372\pi\) | ||||
0.553291 | + | 0.832988i | \(0.313372\pi\) | |||||||
\(108\) | 1.28976 | 0.124107 | ||||||||
\(109\) | 4.92878 | 0.472092 | 0.236046 | − | 0.971742i | \(-0.424148\pi\) | ||||
0.236046 | + | 0.971742i | \(0.424148\pi\) | |||||||
\(110\) | −1.41824 | −0.135224 | ||||||||
\(111\) | 28.8737 | 2.74057 | ||||||||
\(112\) | 1.68229 | 0.158962 | ||||||||
\(113\) | 4.70337 | 0.442456 | 0.221228 | − | 0.975222i | \(-0.428993\pi\) | ||||
0.221228 | + | 0.975222i | \(0.428993\pi\) | |||||||
\(114\) | 4.36939 | 0.409230 | ||||||||
\(115\) | 6.12771 | 0.571412 | ||||||||
\(116\) | −25.9086 | −2.40555 | ||||||||
\(117\) | −15.2970 | −1.41421 | ||||||||
\(118\) | −5.66131 | −0.521166 | ||||||||
\(119\) | −1.62495 | −0.148959 | ||||||||
\(120\) | 14.7074 | 1.34259 | ||||||||
\(121\) | −10.6856 | −0.971420 | ||||||||
\(122\) | 22.5446 | 2.04109 | ||||||||
\(123\) | −1.79471 | −0.161823 | ||||||||
\(124\) | 30.7330 | 2.75990 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −1.87134 | −0.166712 | ||||||||
\(127\) | 2.40934 | 0.213794 | 0.106897 | − | 0.994270i | \(-0.465908\pi\) | ||||
0.106897 | + | 0.994270i | \(0.465908\pi\) | |||||||
\(128\) | 13.6441 | 1.20598 | ||||||||
\(129\) | 16.0908 | 1.41672 | ||||||||
\(130\) | 13.4394 | 1.17872 | ||||||||
\(131\) | −2.66779 | −0.233086 | −0.116543 | − | 0.993186i | \(-0.537181\pi\) | ||||
−0.116543 | + | 0.993186i | \(0.537181\pi\) | |||||||
\(132\) | −5.97914 | −0.520417 | ||||||||
\(133\) | 0.183072 | 0.0158744 | ||||||||
\(134\) | 1.77235 | 0.153108 | ||||||||
\(135\) | 0.293257 | 0.0252396 | ||||||||
\(136\) | 38.3567 | 3.28906 | ||||||||
\(137\) | −15.6485 | −1.33694 | −0.668469 | − | 0.743740i | \(-0.733050\pi\) | ||||
−0.668469 | + | 0.743740i | \(0.733050\pi\) | |||||||
\(138\) | 37.5816 | 3.19916 | ||||||||
\(139\) | −9.47689 | −0.803819 | −0.401910 | − | 0.915679i | \(-0.631653\pi\) | ||||
−0.401910 | + | 0.915679i | \(0.631653\pi\) | |||||||
\(140\) | 1.13016 | 0.0955156 | ||||||||
\(141\) | 24.8341 | 2.09141 | ||||||||
\(142\) | 31.2081 | 2.61893 | ||||||||
\(143\) | −2.97908 | −0.249123 | ||||||||
\(144\) | 18.8483 | 1.57069 | ||||||||
\(145\) | −5.89093 | −0.489215 | ||||||||
\(146\) | −27.4418 | −2.27110 | ||||||||
\(147\) | 16.8126 | 1.38668 | ||||||||
\(148\) | −52.3731 | −4.30504 | ||||||||
\(149\) | 5.41227 | 0.443391 | 0.221695 | − | 0.975116i | \(-0.428841\pi\) | ||||
0.221695 | + | 0.975116i | \(0.428841\pi\) | |||||||
\(150\) | 6.13306 | 0.500762 | ||||||||
\(151\) | −6.02995 | −0.490710 | −0.245355 | − | 0.969433i | \(-0.578905\pi\) | ||||
−0.245355 | + | 0.969433i | \(0.578905\pi\) | |||||||
\(152\) | −4.32140 | −0.350511 | ||||||||
\(153\) | −18.2058 | −1.47185 | ||||||||
\(154\) | −0.364441 | −0.0293675 | ||||||||
\(155\) | 6.98787 | 0.561279 | ||||||||
\(156\) | 56.6593 | 4.53637 | ||||||||
\(157\) | −14.8601 | −1.18596 | −0.592982 | − | 0.805216i | \(-0.702049\pi\) | ||||
−0.592982 | + | 0.805216i | \(0.702049\pi\) | |||||||
\(158\) | −9.66741 | −0.769098 | ||||||||
\(159\) | 6.87950 | 0.545580 | ||||||||
\(160\) | −4.42808 | −0.350070 | ||||||||
\(161\) | 1.57463 | 0.124098 | ||||||||
\(162\) | 23.6457 | 1.85778 | ||||||||
\(163\) | 9.87485 | 0.773458 | 0.386729 | − | 0.922193i | \(-0.373605\pi\) | ||||
0.386729 | + | 0.922193i | \(0.373605\pi\) | |||||||
\(164\) | 3.25536 | 0.254201 | ||||||||
\(165\) | −1.35950 | −0.105837 | ||||||||
\(166\) | −10.6293 | −0.824991 | ||||||||
\(167\) | 7.76686 | 0.601018 | 0.300509 | − | 0.953779i | \(-0.402843\pi\) | ||||
0.300509 | + | 0.953779i | \(0.402843\pi\) | |||||||
\(168\) | 3.77932 | 0.291581 | ||||||||
\(169\) | 15.2303 | 1.17156 | ||||||||
\(170\) | 15.9950 | 1.22676 | ||||||||
\(171\) | 2.05113 | 0.156854 | ||||||||
\(172\) | −29.1866 | −2.22546 | ||||||||
\(173\) | 10.9674 | 0.833834 | 0.416917 | − | 0.908945i | \(-0.363111\pi\) | ||||
0.416917 | + | 0.908945i | \(0.363111\pi\) | |||||||
\(174\) | −36.1294 | −2.73897 | ||||||||
\(175\) | 0.256968 | 0.0194249 | ||||||||
\(176\) | 3.67070 | 0.276689 | ||||||||
\(177\) | −5.42684 | −0.407906 | ||||||||
\(178\) | −7.53858 | −0.565040 | ||||||||
\(179\) | 11.0270 | 0.824200 | 0.412100 | − | 0.911139i | \(-0.364796\pi\) | ||||
0.412100 | + | 0.911139i | \(0.364796\pi\) | |||||||
\(180\) | 12.6622 | 0.943785 | ||||||||
\(181\) | 14.5274 | 1.07981 | 0.539907 | − | 0.841725i | \(-0.318459\pi\) | ||||
0.539907 | + | 0.841725i | \(0.318459\pi\) | |||||||
\(182\) | 3.45350 | 0.255991 | ||||||||
\(183\) | 21.6109 | 1.59752 | ||||||||
\(184\) | −37.1689 | −2.74013 | ||||||||
\(185\) | −11.9083 | −0.875514 | ||||||||
\(186\) | 42.8570 | 3.14243 | ||||||||
\(187\) | −3.54557 | −0.259277 | ||||||||
\(188\) | −45.0457 | −3.28530 | ||||||||
\(189\) | 0.0753577 | 0.00548146 | ||||||||
\(190\) | −1.80205 | −0.130734 | ||||||||
\(191\) | −26.8149 | −1.94026 | −0.970130 | − | 0.242587i | \(-0.922004\pi\) | ||||
−0.970130 | + | 0.242587i | \(0.922004\pi\) | |||||||
\(192\) | 4.58961 | 0.331226 | ||||||||
\(193\) | −3.11703 | −0.224369 | −0.112185 | − | 0.993687i | \(-0.535785\pi\) | ||||
−0.112185 | + | 0.993687i | \(0.535785\pi\) | |||||||
\(194\) | −19.0102 | −1.36485 | ||||||||
\(195\) | 12.8828 | 0.922558 | ||||||||
\(196\) | −30.4959 | −2.17828 | ||||||||
\(197\) | −15.1781 | −1.08139 | −0.540697 | − | 0.841217i | \(-0.681840\pi\) | ||||
−0.540697 | + | 0.841217i | \(0.681840\pi\) | |||||||
\(198\) | −4.08318 | −0.290179 | ||||||||
\(199\) | −11.3538 | −0.804850 | −0.402425 | − | 0.915453i | \(-0.631833\pi\) | ||||
−0.402425 | + | 0.915453i | \(0.631833\pi\) | |||||||
\(200\) | −6.06570 | −0.428910 | ||||||||
\(201\) | 1.69895 | 0.119835 | ||||||||
\(202\) | −21.0807 | −1.48324 | ||||||||
\(203\) | −1.51378 | −0.106247 | ||||||||
\(204\) | 67.4332 | 4.72127 | ||||||||
\(205\) | 0.740184 | 0.0516967 | ||||||||
\(206\) | 18.0705 | 1.25903 | ||||||||
\(207\) | 17.6420 | 1.22620 | ||||||||
\(208\) | −34.7841 | −2.41184 | ||||||||
\(209\) | 0.399455 | 0.0276309 | ||||||||
\(210\) | 1.57600 | 0.108754 | ||||||||
\(211\) | 11.1800 | 0.769665 | 0.384832 | − | 0.922986i | \(-0.374259\pi\) | ||||
0.384832 | + | 0.922986i | \(0.374259\pi\) | |||||||
\(212\) | −12.4785 | −0.857028 | ||||||||
\(213\) | 29.9156 | 2.04978 | ||||||||
\(214\) | −28.9534 | −1.97921 | ||||||||
\(215\) | −6.63627 | −0.452590 | ||||||||
\(216\) | −1.77881 | −0.121033 | ||||||||
\(217\) | 1.79566 | 0.121897 | ||||||||
\(218\) | −12.4670 | −0.844375 | ||||||||
\(219\) | −26.3053 | −1.77755 | ||||||||
\(220\) | 2.46595 | 0.166255 | ||||||||
\(221\) | 33.5983 | 2.26007 | ||||||||
\(222\) | −73.0342 | −4.90173 | ||||||||
\(223\) | −27.4596 | −1.83883 | −0.919415 | − | 0.393289i | \(-0.871337\pi\) | ||||
−0.919415 | + | 0.393289i | \(0.871337\pi\) | |||||||
\(224\) | −1.13787 | −0.0760274 | ||||||||
\(225\) | 2.87905 | 0.191937 | ||||||||
\(226\) | −11.8969 | −0.791369 | ||||||||
\(227\) | 10.5942 | 0.703164 | 0.351582 | − | 0.936157i | \(-0.385644\pi\) | ||||
0.351582 | + | 0.936157i | \(0.385644\pi\) | |||||||
\(228\) | −7.59725 | −0.503140 | ||||||||
\(229\) | −10.6220 | −0.701923 | −0.350962 | − | 0.936390i | \(-0.614145\pi\) | ||||
−0.350962 | + | 0.936390i | \(0.614145\pi\) | |||||||
\(230\) | −15.4997 | −1.02202 | ||||||||
\(231\) | −0.349348 | −0.0229854 | ||||||||
\(232\) | 35.7326 | 2.34596 | ||||||||
\(233\) | −6.38347 | −0.418195 | −0.209097 | − | 0.977895i | \(-0.567053\pi\) | ||||
−0.209097 | + | 0.977895i | \(0.567053\pi\) | |||||||
\(234\) | 38.6929 | 2.52943 | ||||||||
\(235\) | −10.2422 | −0.668129 | ||||||||
\(236\) | 9.84357 | 0.640762 | ||||||||
\(237\) | −9.26702 | −0.601958 | ||||||||
\(238\) | 4.11020 | 0.266425 | ||||||||
\(239\) | −0.689703 | −0.0446132 | −0.0223066 | − | 0.999751i | \(-0.507101\pi\) | ||||
−0.0223066 | + | 0.999751i | \(0.507101\pi\) | |||||||
\(240\) | −15.8736 | −1.02464 | ||||||||
\(241\) | −16.4419 | −1.05911 | −0.529557 | − | 0.848274i | \(-0.677642\pi\) | ||||
−0.529557 | + | 0.848274i | \(0.677642\pi\) | |||||||
\(242\) | 27.0286 | 1.73746 | ||||||||
\(243\) | 21.7866 | 1.39761 | ||||||||
\(244\) | −39.1993 | −2.50948 | ||||||||
\(245\) | −6.93397 | −0.442995 | ||||||||
\(246\) | 4.53960 | 0.289434 | ||||||||
\(247\) | −3.78530 | −0.240853 | ||||||||
\(248\) | −42.3863 | −2.69153 | ||||||||
\(249\) | −10.1890 | −0.645704 | ||||||||
\(250\) | −2.52944 | −0.159976 | ||||||||
\(251\) | 13.0815 | 0.825695 | 0.412847 | − | 0.910800i | \(-0.364534\pi\) | ||||
0.412847 | + | 0.910800i | \(0.364534\pi\) | |||||||
\(252\) | 3.25378 | 0.204969 | ||||||||
\(253\) | 3.43577 | 0.216005 | ||||||||
\(254\) | −6.09427 | −0.382389 | ||||||||
\(255\) | 15.3325 | 0.960161 | ||||||||
\(256\) | −30.7260 | −1.92038 | ||||||||
\(257\) | −8.24367 | −0.514226 | −0.257113 | − | 0.966381i | \(-0.582771\pi\) | ||||
−0.257113 | + | 0.966381i | \(0.582771\pi\) | |||||||
\(258\) | −40.7007 | −2.53391 | ||||||||
\(259\) | −3.06004 | −0.190142 | ||||||||
\(260\) | −23.3678 | −1.44921 | ||||||||
\(261\) | −16.9603 | −1.04982 | ||||||||
\(262\) | 6.74800 | 0.416893 | ||||||||
\(263\) | 11.3850 | 0.702031 | 0.351015 | − | 0.936370i | \(-0.385836\pi\) | ||||
0.351015 | + | 0.936370i | \(0.385836\pi\) | |||||||
\(264\) | 8.24631 | 0.507526 | ||||||||
\(265\) | −2.83729 | −0.174293 | ||||||||
\(266\) | −0.463069 | −0.0283926 | ||||||||
\(267\) | −7.22636 | −0.442246 | ||||||||
\(268\) | −3.08167 | −0.188243 | ||||||||
\(269\) | 23.3969 | 1.42653 | 0.713267 | − | 0.700893i | \(-0.247215\pi\) | ||||
0.713267 | + | 0.700893i | \(0.247215\pi\) | |||||||
\(270\) | −0.741775 | −0.0451430 | ||||||||
\(271\) | −2.63333 | −0.159964 | −0.0799818 | − | 0.996796i | \(-0.525486\pi\) | ||||
−0.0799818 | + | 0.996796i | \(0.525486\pi\) | |||||||
\(272\) | −41.3984 | −2.51015 | ||||||||
\(273\) | 3.31047 | 0.200359 | ||||||||
\(274\) | 39.5818 | 2.39122 | ||||||||
\(275\) | 0.560693 | 0.0338111 | ||||||||
\(276\) | −65.3449 | −3.93330 | ||||||||
\(277\) | 23.2174 | 1.39500 | 0.697500 | − | 0.716585i | \(-0.254296\pi\) | ||||
0.697500 | + | 0.716585i | \(0.254296\pi\) | |||||||
\(278\) | 23.9712 | 1.43770 | ||||||||
\(279\) | 20.1184 | 1.20446 | ||||||||
\(280\) | −1.55869 | −0.0931496 | ||||||||
\(281\) | 6.70722 | 0.400119 | 0.200060 | − | 0.979784i | \(-0.435886\pi\) | ||||
0.200060 | + | 0.979784i | \(0.435886\pi\) | |||||||
\(282\) | −62.8162 | −3.74065 | ||||||||
\(283\) | −27.8629 | −1.65628 | −0.828139 | − | 0.560523i | \(-0.810600\pi\) | ||||
−0.828139 | + | 0.560523i | \(0.810600\pi\) | |||||||
\(284\) | −54.2630 | −3.21992 | ||||||||
\(285\) | −1.72742 | −0.102323 | ||||||||
\(286\) | 7.53540 | 0.445578 | ||||||||
\(287\) | 0.190204 | 0.0112274 | ||||||||
\(288\) | −12.7487 | −0.751223 | ||||||||
\(289\) | 22.9872 | 1.35219 | ||||||||
\(290\) | 14.9007 | 0.875001 | ||||||||
\(291\) | −18.2229 | −1.06824 | ||||||||
\(292\) | 47.7144 | 2.79227 | ||||||||
\(293\) | 19.2210 | 1.12291 | 0.561453 | − | 0.827509i | \(-0.310243\pi\) | ||||
0.561453 | + | 0.827509i | \(0.310243\pi\) | |||||||
\(294\) | −42.5265 | −2.48019 | ||||||||
\(295\) | 2.23817 | 0.130311 | ||||||||
\(296\) | 72.2320 | 4.19840 | ||||||||
\(297\) | 0.164427 | 0.00954104 | ||||||||
\(298\) | −13.6900 | −0.793040 | ||||||||
\(299\) | −32.5579 | −1.88287 | ||||||||
\(300\) | −10.6638 | −0.615677 | ||||||||
\(301\) | −1.70531 | −0.0982924 | ||||||||
\(302\) | 15.2524 | 0.877675 | ||||||||
\(303\) | −20.2077 | −1.16090 | ||||||||
\(304\) | 4.66408 | 0.267503 | ||||||||
\(305\) | −8.91289 | −0.510351 | ||||||||
\(306\) | 46.0504 | 2.63253 | ||||||||
\(307\) | −5.71845 | −0.326369 | −0.163185 | − | 0.986596i | \(-0.552177\pi\) | ||||
−0.163185 | + | 0.986596i | \(0.552177\pi\) | |||||||
\(308\) | 0.633671 | 0.0361067 | ||||||||
\(309\) | 17.3220 | 0.985417 | ||||||||
\(310\) | −17.6754 | −1.00389 | ||||||||
\(311\) | −19.8674 | −1.12657 | −0.563287 | − | 0.826261i | \(-0.690464\pi\) | ||||
−0.563287 | + | 0.826261i | \(0.690464\pi\) | |||||||
\(312\) | −78.1434 | −4.42400 | ||||||||
\(313\) | −27.7658 | −1.56942 | −0.784709 | − | 0.619865i | \(-0.787187\pi\) | ||||
−0.784709 | + | 0.619865i | \(0.787187\pi\) | |||||||
\(314\) | 37.5876 | 2.12119 | ||||||||
\(315\) | 0.739824 | 0.0416844 | ||||||||
\(316\) | 16.8092 | 0.945590 | ||||||||
\(317\) | 10.5408 | 0.592031 | 0.296015 | − | 0.955183i | \(-0.404342\pi\) | ||||
0.296015 | + | 0.955183i | \(0.404342\pi\) | |||||||
\(318\) | −17.4013 | −0.975814 | ||||||||
\(319\) | −3.30300 | −0.184933 | ||||||||
\(320\) | −1.89288 | −0.105815 | ||||||||
\(321\) | −27.7542 | −1.54909 | ||||||||
\(322\) | −3.98291 | −0.221959 | ||||||||
\(323\) | −4.50509 | −0.250670 | ||||||||
\(324\) | −41.1139 | −2.28410 | ||||||||
\(325\) | −5.31322 | −0.294724 | ||||||||
\(326\) | −24.9778 | −1.38339 | ||||||||
\(327\) | −11.9507 | −0.660875 | ||||||||
\(328\) | −4.48974 | −0.247904 | ||||||||
\(329\) | −2.63192 | −0.145103 | ||||||||
\(330\) | 3.43877 | 0.189298 | ||||||||
\(331\) | 23.1138 | 1.27045 | 0.635224 | − | 0.772328i | \(-0.280908\pi\) | ||||
0.635224 | + | 0.772328i | \(0.280908\pi\) | |||||||
\(332\) | 18.4816 | 1.01431 | ||||||||
\(333\) | −34.2845 | −1.87878 | ||||||||
\(334\) | −19.6458 | −1.07497 | ||||||||
\(335\) | −0.700692 | −0.0382829 | ||||||||
\(336\) | −4.07902 | −0.222529 | ||||||||
\(337\) | −30.9590 | −1.68645 | −0.843223 | − | 0.537564i | \(-0.819345\pi\) | ||||
−0.843223 | + | 0.537564i | \(0.819345\pi\) | |||||||
\(338\) | −38.5240 | −2.09543 | ||||||||
\(339\) | −11.4042 | −0.619389 | ||||||||
\(340\) | −27.8112 | −1.50828 | ||||||||
\(341\) | 3.91805 | 0.212174 | ||||||||
\(342\) | −5.18820 | −0.280545 | ||||||||
\(343\) | −3.58058 | −0.193333 | ||||||||
\(344\) | 40.2536 | 2.17033 | ||||||||
\(345\) | −14.8577 | −0.799913 | ||||||||
\(346\) | −27.7413 | −1.49138 | ||||||||
\(347\) | 19.3837 | 1.04057 | 0.520286 | − | 0.853992i | \(-0.325825\pi\) | ||||
0.520286 | + | 0.853992i | \(0.325825\pi\) | |||||||
\(348\) | 62.8199 | 3.36750 | ||||||||
\(349\) | 0.0165295 | 0.000884806 0 | 0.000442403 | − | 1.00000i | \(-0.499859\pi\) | ||||
0.000442403 | 1.00000i | \(0.499859\pi\) | ||||||||
\(350\) | −0.649984 | −0.0347431 | ||||||||
\(351\) | −1.55814 | −0.0831673 | ||||||||
\(352\) | −2.48279 | −0.132333 | ||||||||
\(353\) | −6.58197 | −0.350323 | −0.175161 | − | 0.984540i | \(-0.556045\pi\) | ||||
−0.175161 | + | 0.984540i | \(0.556045\pi\) | |||||||
\(354\) | 13.7268 | 0.729573 | ||||||||
\(355\) | −12.3380 | −0.654832 | ||||||||
\(356\) | 13.1077 | 0.694705 | ||||||||
\(357\) | 3.93997 | 0.208525 | ||||||||
\(358\) | −27.8922 | −1.47415 | ||||||||
\(359\) | 12.0294 | 0.634889 | 0.317444 | − | 0.948277i | \(-0.397175\pi\) | ||||
0.317444 | + | 0.948277i | \(0.397175\pi\) | |||||||
\(360\) | −17.4635 | −0.920406 | ||||||||
\(361\) | −18.4924 | −0.973286 | ||||||||
\(362\) | −36.7462 | −1.93133 | ||||||||
\(363\) | 25.9092 | 1.35988 | ||||||||
\(364\) | −6.00476 | −0.314735 | ||||||||
\(365\) | 10.8490 | 0.567863 | ||||||||
\(366\) | −54.6633 | −2.85730 | ||||||||
\(367\) | 25.3888 | 1.32528 | 0.662641 | − | 0.748937i | \(-0.269435\pi\) | ||||
0.662641 | + | 0.748937i | \(0.269435\pi\) | |||||||
\(368\) | 40.1164 | 2.09121 | ||||||||
\(369\) | 2.13103 | 0.110937 | ||||||||
\(370\) | 30.1212 | 1.56593 | ||||||||
\(371\) | −0.729092 | −0.0378525 | ||||||||
\(372\) | −74.5174 | −3.86355 | ||||||||
\(373\) | −24.3993 | −1.26335 | −0.631673 | − | 0.775235i | \(-0.717632\pi\) | ||||
−0.631673 | + | 0.775235i | \(0.717632\pi\) | |||||||
\(374\) | 8.96828 | 0.463739 | ||||||||
\(375\) | −2.42468 | −0.125210 | ||||||||
\(376\) | 62.1262 | 3.20392 | ||||||||
\(377\) | 31.2998 | 1.61202 | ||||||||
\(378\) | −0.190612 | −0.00980404 | ||||||||
\(379\) | 4.08624 | 0.209896 | 0.104948 | − | 0.994478i | \(-0.466532\pi\) | ||||
0.104948 | + | 0.994478i | \(0.466532\pi\) | |||||||
\(380\) | 3.13331 | 0.160735 | ||||||||
\(381\) | −5.84187 | −0.299288 | ||||||||
\(382\) | 67.8266 | 3.47031 | ||||||||
\(383\) | −0.228835 | −0.0116929 | −0.00584645 | − | 0.999983i | \(-0.501861\pi\) | ||||
−0.00584645 | + | 0.999983i | \(0.501861\pi\) | |||||||
\(384\) | −33.0824 | −1.68823 | ||||||||
\(385\) | 0.144080 | 0.00734300 | ||||||||
\(386\) | 7.88434 | 0.401302 | ||||||||
\(387\) | −19.1062 | −0.971222 | ||||||||
\(388\) | 33.0539 | 1.67806 | ||||||||
\(389\) | 21.2474 | 1.07729 | 0.538644 | − | 0.842534i | \(-0.318937\pi\) | ||||
0.538644 | + | 0.842534i | \(0.318937\pi\) | |||||||
\(390\) | −32.5863 | −1.65007 | ||||||||
\(391\) | −38.7489 | −1.95961 | ||||||||
\(392\) | 42.0594 | 2.12432 | ||||||||
\(393\) | 6.46853 | 0.326294 | ||||||||
\(394\) | 38.3920 | 1.93416 | ||||||||
\(395\) | 3.82196 | 0.192304 | ||||||||
\(396\) | 7.09961 | 0.356769 | ||||||||
\(397\) | 30.2025 | 1.51582 | 0.757910 | − | 0.652359i | \(-0.226220\pi\) | ||||
0.757910 | + | 0.652359i | \(0.226220\pi\) | |||||||
\(398\) | 28.7187 | 1.43954 | ||||||||
\(399\) | −0.443890 | −0.0222223 | ||||||||
\(400\) | 6.54671 | 0.327335 | ||||||||
\(401\) | −5.88318 | −0.293792 | −0.146896 | − | 0.989152i | \(-0.546928\pi\) | ||||
−0.146896 | + | 0.989152i | \(0.546928\pi\) | |||||||
\(402\) | −4.29738 | −0.214334 | ||||||||
\(403\) | −37.1280 | −1.84948 | ||||||||
\(404\) | 36.6540 | 1.82361 | ||||||||
\(405\) | −9.34821 | −0.464516 | ||||||||
\(406\) | 3.82901 | 0.190031 | ||||||||
\(407\) | −6.67689 | −0.330961 | ||||||||
\(408\) | −93.0026 | −4.60431 | ||||||||
\(409\) | 12.4334 | 0.614792 | 0.307396 | − | 0.951582i | \(-0.400542\pi\) | ||||
0.307396 | + | 0.951582i | \(0.400542\pi\) | |||||||
\(410\) | −1.87225 | −0.0924638 | ||||||||
\(411\) | 37.9424 | 1.87156 | ||||||||
\(412\) | −31.4199 | −1.54795 | ||||||||
\(413\) | 0.575138 | 0.0283007 | ||||||||
\(414\) | −44.6243 | −2.19317 | ||||||||
\(415\) | 4.20223 | 0.206279 | ||||||||
\(416\) | 23.5273 | 1.15352 | ||||||||
\(417\) | 22.9784 | 1.12526 | ||||||||
\(418\) | −1.01040 | −0.0494201 | ||||||||
\(419\) | 0.268305 | 0.0131076 | 0.00655378 | − | 0.999979i | \(-0.497914\pi\) | ||||
0.00655378 | + | 0.999979i | \(0.497914\pi\) | |||||||
\(420\) | −2.74026 | −0.133711 | ||||||||
\(421\) | 9.42360 | 0.459278 | 0.229639 | − | 0.973276i | \(-0.426245\pi\) | ||||
0.229639 | + | 0.973276i | \(0.426245\pi\) | |||||||
\(422\) | −28.2792 | −1.37661 | ||||||||
\(423\) | −29.4879 | −1.43375 | ||||||||
\(424\) | 17.2101 | 0.835798 | ||||||||
\(425\) | −6.32354 | −0.306737 | ||||||||
\(426\) | −75.6696 | −3.66621 | ||||||||
\(427\) | −2.29033 | −0.110837 | ||||||||
\(428\) | 50.3426 | 2.43340 | ||||||||
\(429\) | 7.22331 | 0.348745 | ||||||||
\(430\) | 16.7860 | 0.809494 | ||||||||
\(431\) | −7.08354 | −0.341202 | −0.170601 | − | 0.985340i | \(-0.554571\pi\) | ||||
−0.170601 | + | 0.985340i | \(0.554571\pi\) | |||||||
\(432\) | 1.91987 | 0.0923697 | ||||||||
\(433\) | −9.61195 | −0.461921 | −0.230961 | − | 0.972963i | \(-0.574187\pi\) | ||||
−0.230961 | + | 0.972963i | \(0.574187\pi\) | |||||||
\(434\) | −4.54200 | −0.218023 | ||||||||
\(435\) | 14.2836 | 0.684846 | ||||||||
\(436\) | 21.6770 | 1.03814 | ||||||||
\(437\) | 4.36558 | 0.208834 | ||||||||
\(438\) | 66.5376 | 3.17929 | ||||||||
\(439\) | 0.649770 | 0.0310118 | 0.0155059 | − | 0.999880i | \(-0.495064\pi\) | ||||
0.0155059 | + | 0.999880i | \(0.495064\pi\) | |||||||
\(440\) | −3.40100 | −0.162136 | ||||||||
\(441\) | −19.9633 | −0.950631 | ||||||||
\(442\) | −84.9848 | −4.04232 | ||||||||
\(443\) | 7.71222 | 0.366418 | 0.183209 | − | 0.983074i | \(-0.441351\pi\) | ||||
0.183209 | + | 0.983074i | \(0.441351\pi\) | |||||||
\(444\) | 126.988 | 6.02658 | ||||||||
\(445\) | 2.98034 | 0.141282 | ||||||||
\(446\) | 69.4572 | 3.28890 | ||||||||
\(447\) | −13.1230 | −0.620697 | ||||||||
\(448\) | −0.486408 | −0.0229806 | ||||||||
\(449\) | −32.4820 | −1.53292 | −0.766460 | − | 0.642292i | \(-0.777983\pi\) | ||||
−0.766460 | + | 0.642292i | \(0.777983\pi\) | |||||||
\(450\) | −7.28238 | −0.343295 | ||||||||
\(451\) | 0.415016 | 0.0195424 | ||||||||
\(452\) | 20.6856 | 0.972971 | ||||||||
\(453\) | 14.6207 | 0.686939 | ||||||||
\(454\) | −26.7974 | −1.25767 | ||||||||
\(455\) | −1.36533 | −0.0640075 | ||||||||
\(456\) | 10.4780 | 0.490677 | ||||||||
\(457\) | 11.1553 | 0.521825 | 0.260912 | − | 0.965362i | \(-0.415977\pi\) | ||||
0.260912 | + | 0.965362i | \(0.415977\pi\) | |||||||
\(458\) | 26.8677 | 1.25545 | ||||||||
\(459\) | −1.85442 | −0.0865571 | ||||||||
\(460\) | 26.9500 | 1.25655 | ||||||||
\(461\) | 29.8157 | 1.38866 | 0.694328 | − | 0.719659i | \(-0.255702\pi\) | ||||
0.694328 | + | 0.719659i | \(0.255702\pi\) | |||||||
\(462\) | 0.883652 | 0.0411112 | ||||||||
\(463\) | −7.56499 | −0.351575 | −0.175787 | − | 0.984428i | \(-0.556247\pi\) | ||||
−0.175787 | + | 0.984428i | \(0.556247\pi\) | |||||||
\(464\) | −38.5662 | −1.79039 | ||||||||
\(465\) | −16.9433 | −0.785727 | ||||||||
\(466\) | 16.1466 | 0.747976 | ||||||||
\(467\) | −24.9538 | −1.15473 | −0.577363 | − | 0.816488i | \(-0.695918\pi\) | ||||
−0.577363 | + | 0.816488i | \(0.695918\pi\) | |||||||
\(468\) | −67.2770 | −3.10988 | ||||||||
\(469\) | −0.180055 | −0.00831418 | ||||||||
\(470\) | 25.9070 | 1.19500 | ||||||||
\(471\) | 36.0309 | 1.66022 | ||||||||
\(472\) | −13.5761 | −0.624889 | ||||||||
\(473\) | −3.72091 | −0.171088 | ||||||||
\(474\) | 23.4403 | 1.07665 | ||||||||
\(475\) | 0.712431 | 0.0326886 | ||||||||
\(476\) | −7.14659 | −0.327563 | ||||||||
\(477\) | −8.16870 | −0.374019 | ||||||||
\(478\) | 1.74456 | 0.0797943 | ||||||||
\(479\) | 37.2881 | 1.70374 | 0.851869 | − | 0.523756i | \(-0.175469\pi\) | ||||
0.851869 | + | 0.523756i | \(0.175469\pi\) | |||||||
\(480\) | 10.7367 | 0.490059 | ||||||||
\(481\) | 63.2712 | 2.88492 | ||||||||
\(482\) | 41.5886 | 1.89431 | ||||||||
\(483\) | −3.81796 | −0.173723 | ||||||||
\(484\) | −46.9959 | −2.13618 | ||||||||
\(485\) | 7.51559 | 0.341265 | ||||||||
\(486\) | −55.1078 | −2.49974 | ||||||||
\(487\) | −2.90652 | −0.131707 | −0.0658536 | − | 0.997829i | \(-0.520977\pi\) | ||||
−0.0658536 | + | 0.997829i | \(0.520977\pi\) | |||||||
\(488\) | 54.0629 | 2.44731 | ||||||||
\(489\) | −23.9433 | −1.08275 | ||||||||
\(490\) | 17.5390 | 0.792332 | ||||||||
\(491\) | 1.75165 | 0.0790508 | 0.0395254 | − | 0.999219i | \(-0.487415\pi\) | ||||
0.0395254 | + | 0.999219i | \(0.487415\pi\) | |||||||
\(492\) | −7.89320 | −0.355853 | ||||||||
\(493\) | 37.2515 | 1.67773 | ||||||||
\(494\) | 9.57468 | 0.430785 | ||||||||
\(495\) | 1.61427 | 0.0725558 | ||||||||
\(496\) | 45.7475 | 2.05412 | ||||||||
\(497\) | −3.17047 | −0.142215 | ||||||||
\(498\) | 25.7725 | 1.15489 | ||||||||
\(499\) | −11.0372 | −0.494094 | −0.247047 | − | 0.969004i | \(-0.579460\pi\) | ||||
−0.247047 | + | 0.969004i | \(0.579460\pi\) | |||||||
\(500\) | 4.39805 | 0.196687 | ||||||||
\(501\) | −18.8321 | −0.841357 | ||||||||
\(502\) | −33.0887 | −1.47682 | ||||||||
\(503\) | −17.5668 | −0.783265 | −0.391633 | − | 0.920122i | \(-0.628090\pi\) | ||||
−0.391633 | + | 0.920122i | \(0.628090\pi\) | |||||||
\(504\) | −4.48755 | −0.199891 | ||||||||
\(505\) | 8.33417 | 0.370866 | ||||||||
\(506\) | −8.69055 | −0.386342 | ||||||||
\(507\) | −36.9285 | −1.64005 | ||||||||
\(508\) | 10.5964 | 0.470139 | ||||||||
\(509\) | −35.7059 | −1.58264 | −0.791318 | − | 0.611405i | \(-0.790605\pi\) | ||||
−0.791318 | + | 0.611405i | \(0.790605\pi\) | |||||||
\(510\) | −38.7827 | −1.71733 | ||||||||
\(511\) | 2.78784 | 0.123327 | ||||||||
\(512\) | 50.4314 | 2.22877 | ||||||||
\(513\) | 0.208926 | 0.00922429 | ||||||||
\(514\) | 20.8518 | 0.919734 | ||||||||
\(515\) | −7.14407 | −0.314805 | ||||||||
\(516\) | 70.7681 | 3.11539 | ||||||||
\(517\) | −5.74274 | −0.252566 | ||||||||
\(518\) | 7.74018 | 0.340084 | ||||||||
\(519\) | −26.5923 | −1.16727 | ||||||||
\(520\) | 32.2284 | 1.41331 | ||||||||
\(521\) | −31.5676 | −1.38300 | −0.691500 | − | 0.722376i | \(-0.743050\pi\) | ||||
−0.691500 | + | 0.722376i | \(0.743050\pi\) | |||||||
\(522\) | 42.9000 | 1.87768 | ||||||||
\(523\) | 14.1432 | 0.618437 | 0.309219 | − | 0.950991i | \(-0.399933\pi\) | ||||
0.309219 | + | 0.950991i | \(0.399933\pi\) | |||||||
\(524\) | −11.7331 | −0.512561 | ||||||||
\(525\) | −0.623064 | −0.0271927 | ||||||||
\(526\) | −28.7977 | −1.25564 | ||||||||
\(527\) | −44.1881 | −1.92486 | ||||||||
\(528\) | −8.90025 | −0.387333 | ||||||||
\(529\) | 14.5489 | 0.632560 | ||||||||
\(530\) | 7.17673 | 0.311737 | ||||||||
\(531\) | 6.44381 | 0.279638 | ||||||||
\(532\) | 0.805159 | 0.0349081 | ||||||||
\(533\) | −3.93276 | −0.170347 | ||||||||
\(534\) | 18.2786 | 0.790992 | ||||||||
\(535\) | 11.4466 | 0.494879 | ||||||||
\(536\) | 4.25019 | 0.183580 | ||||||||
\(537\) | −26.7370 | −1.15379 | ||||||||
\(538\) | −59.1809 | −2.55147 | ||||||||
\(539\) | −3.88783 | −0.167461 | ||||||||
\(540\) | 1.28976 | 0.0555023 | ||||||||
\(541\) | −1.17196 | −0.0503864 | −0.0251932 | − | 0.999683i | \(-0.508020\pi\) | ||||
−0.0251932 | + | 0.999683i | \(0.508020\pi\) | |||||||
\(542\) | 6.66085 | 0.286108 | ||||||||
\(543\) | −35.2243 | −1.51162 | ||||||||
\(544\) | 28.0011 | 1.20054 | ||||||||
\(545\) | 4.92878 | 0.211126 | ||||||||
\(546\) | −8.37363 | −0.358358 | ||||||||
\(547\) | −22.0249 | −0.941715 | −0.470857 | − | 0.882209i | \(-0.656055\pi\) | ||||
−0.470857 | + | 0.882209i | \(0.656055\pi\) | |||||||
\(548\) | −68.8226 | −2.93996 | ||||||||
\(549\) | −25.6607 | −1.09517 | ||||||||
\(550\) | −1.41824 | −0.0604738 | ||||||||
\(551\) | −4.19688 | −0.178793 | ||||||||
\(552\) | 90.1225 | 3.83587 | ||||||||
\(553\) | 0.982122 | 0.0417641 | ||||||||
\(554\) | −58.7269 | −2.49507 | ||||||||
\(555\) | 28.8737 | 1.22562 | ||||||||
\(556\) | −41.6798 | −1.76762 | ||||||||
\(557\) | −19.3907 | −0.821610 | −0.410805 | − | 0.911723i | \(-0.634752\pi\) | ||||
−0.410805 | + | 0.911723i | \(0.634752\pi\) | |||||||
\(558\) | −50.8883 | −2.15427 | ||||||||
\(559\) | 35.2599 | 1.49134 | ||||||||
\(560\) | 1.68229 | 0.0710899 | ||||||||
\(561\) | 8.59685 | 0.362959 | ||||||||
\(562\) | −16.9655 | −0.715646 | ||||||||
\(563\) | −0.659476 | −0.0277936 | −0.0138968 | − | 0.999903i | \(-0.504424\pi\) | ||||
−0.0138968 | + | 0.999903i | \(0.504424\pi\) | |||||||
\(564\) | 109.221 | 4.59905 | ||||||||
\(565\) | 4.70337 | 0.197872 | ||||||||
\(566\) | 70.4774 | 2.96239 | ||||||||
\(567\) | −2.40219 | −0.100883 | ||||||||
\(568\) | 74.8385 | 3.14016 | ||||||||
\(569\) | 16.4349 | 0.688986 | 0.344493 | − | 0.938789i | \(-0.388051\pi\) | ||||
0.344493 | + | 0.938789i | \(0.388051\pi\) | |||||||
\(570\) | 4.36939 | 0.183013 | ||||||||
\(571\) | −25.7096 | −1.07591 | −0.537957 | − | 0.842973i | \(-0.680804\pi\) | ||||
−0.537957 | + | 0.842973i | \(0.680804\pi\) | |||||||
\(572\) | −13.1021 | −0.547828 | ||||||||
\(573\) | 65.0175 | 2.71614 | ||||||||
\(574\) | −0.481108 | −0.0200811 | ||||||||
\(575\) | 6.12771 | 0.255543 | ||||||||
\(576\) | −5.44969 | −0.227070 | ||||||||
\(577\) | −1.71956 | −0.0715861 | −0.0357930 | − | 0.999359i | \(-0.511396\pi\) | ||||
−0.0357930 | + | 0.999359i | \(0.511396\pi\) | |||||||
\(578\) | −58.1446 | −2.41850 | ||||||||
\(579\) | 7.55780 | 0.314091 | ||||||||
\(580\) | −25.9086 | −1.07580 | ||||||||
\(581\) | 1.07984 | 0.0447992 | ||||||||
\(582\) | 46.0936 | 1.91064 | ||||||||
\(583\) | −1.59085 | −0.0658862 | ||||||||
\(584\) | −65.8068 | −2.72310 | ||||||||
\(585\) | −15.2970 | −0.632454 | ||||||||
\(586\) | −48.6184 | −2.00841 | ||||||||
\(587\) | 31.9336 | 1.31804 | 0.659020 | − | 0.752125i | \(-0.270971\pi\) | ||||
0.659020 | + | 0.752125i | \(0.270971\pi\) | |||||||
\(588\) | 73.9427 | 3.04934 | ||||||||
\(589\) | 4.97838 | 0.205130 | ||||||||
\(590\) | −5.66131 | −0.233072 | ||||||||
\(591\) | 36.8020 | 1.51383 | ||||||||
\(592\) | −77.9600 | −3.20414 | ||||||||
\(593\) | 33.1485 | 1.36125 | 0.680624 | − | 0.732633i | \(-0.261709\pi\) | ||||
0.680624 | + | 0.732633i | \(0.261709\pi\) | |||||||
\(594\) | −0.415908 | −0.0170649 | ||||||||
\(595\) | −1.62495 | −0.0666163 | ||||||||
\(596\) | 23.8034 | 0.975026 | ||||||||
\(597\) | 27.5293 | 1.12670 | ||||||||
\(598\) | 82.3530 | 3.36767 | ||||||||
\(599\) | 41.2813 | 1.68671 | 0.843355 | − | 0.537358i | \(-0.180577\pi\) | ||||
0.843355 | + | 0.537358i | \(0.180577\pi\) | |||||||
\(600\) | 14.7074 | 0.600425 | ||||||||
\(601\) | −42.9948 | −1.75380 | −0.876898 | − | 0.480677i | \(-0.840391\pi\) | ||||
−0.876898 | + | 0.480677i | \(0.840391\pi\) | |||||||
\(602\) | 4.31347 | 0.175804 | ||||||||
\(603\) | −2.01733 | −0.0821520 | ||||||||
\(604\) | −26.5200 | −1.07908 | ||||||||
\(605\) | −10.6856 | −0.434432 | ||||||||
\(606\) | 51.1140 | 2.07636 | ||||||||
\(607\) | 13.2110 | 0.536216 | 0.268108 | − | 0.963389i | \(-0.413602\pi\) | ||||
0.268108 | + | 0.963389i | \(0.413602\pi\) | |||||||
\(608\) | −3.15470 | −0.127940 | ||||||||
\(609\) | 3.67043 | 0.148733 | ||||||||
\(610\) | 22.5446 | 0.912804 | ||||||||
\(611\) | 54.4191 | 2.20156 | ||||||||
\(612\) | −80.0700 | −3.23664 | ||||||||
\(613\) | −4.08552 | −0.165012 | −0.0825062 | − | 0.996591i | \(-0.526292\pi\) | ||||
−0.0825062 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(614\) | 14.4645 | 0.583738 | ||||||||
\(615\) | −1.79471 | −0.0723696 | ||||||||
\(616\) | −0.873947 | −0.0352123 | ||||||||
\(617\) | −8.56336 | −0.344748 | −0.172374 | − | 0.985032i | \(-0.555144\pi\) | ||||
−0.172374 | + | 0.985032i | \(0.555144\pi\) | |||||||
\(618\) | −43.8150 | −1.76250 | ||||||||
\(619\) | 13.6141 | 0.547196 | 0.273598 | − | 0.961844i | \(-0.411786\pi\) | ||||
0.273598 | + | 0.961844i | \(0.411786\pi\) | |||||||
\(620\) | 30.7330 | 1.23426 | ||||||||
\(621\) | 1.79700 | 0.0721110 | ||||||||
\(622\) | 50.2532 | 2.01497 | ||||||||
\(623\) | 0.765851 | 0.0306832 | ||||||||
\(624\) | 84.3401 | 3.37631 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 70.2319 | 2.80703 | ||||||||
\(627\) | −0.968550 | −0.0386802 | ||||||||
\(628\) | −65.3553 | −2.60796 | ||||||||
\(629\) | 75.3024 | 3.00250 | ||||||||
\(630\) | −1.87134 | −0.0745559 | ||||||||
\(631\) | −31.6516 | −1.26003 | −0.630014 | − | 0.776583i | \(-0.716951\pi\) | ||||
−0.630014 | + | 0.776583i | \(0.716951\pi\) | |||||||
\(632\) | −23.1829 | −0.922166 | ||||||||
\(633\) | −27.1079 | −1.07744 | ||||||||
\(634\) | −26.6623 | −1.05890 | ||||||||
\(635\) | 2.40934 | 0.0956118 | ||||||||
\(636\) | 30.2564 | 1.19974 | ||||||||
\(637\) | 36.8417 | 1.45972 | ||||||||
\(638\) | 8.35474 | 0.330767 | ||||||||
\(639\) | −35.5217 | −1.40522 | ||||||||
\(640\) | 13.6441 | 0.539329 | ||||||||
\(641\) | −23.7758 | −0.939086 | −0.469543 | − | 0.882910i | \(-0.655581\pi\) | ||||
−0.469543 | + | 0.882910i | \(0.655581\pi\) | |||||||
\(642\) | 70.2026 | 2.77067 | ||||||||
\(643\) | −16.1474 | −0.636791 | −0.318395 | − | 0.947958i | \(-0.603144\pi\) | ||||
−0.318395 | + | 0.947958i | \(0.603144\pi\) | |||||||
\(644\) | 6.92527 | 0.272894 | ||||||||
\(645\) | 16.0908 | 0.633575 | ||||||||
\(646\) | 11.3953 | 0.448343 | ||||||||
\(647\) | −36.0772 | −1.41834 | −0.709170 | − | 0.705037i | \(-0.750930\pi\) | ||||
−0.709170 | + | 0.705037i | \(0.750930\pi\) | |||||||
\(648\) | 56.7035 | 2.22752 | ||||||||
\(649\) | 1.25493 | 0.0492602 | ||||||||
\(650\) | 13.4394 | 0.527138 | ||||||||
\(651\) | −4.35389 | −0.170642 | ||||||||
\(652\) | 43.4300 | 1.70085 | ||||||||
\(653\) | −26.9875 | −1.05610 | −0.528050 | − | 0.849213i | \(-0.677077\pi\) | ||||
−0.528050 | + | 0.849213i | \(0.677077\pi\) | |||||||
\(654\) | 30.2285 | 1.18203 | ||||||||
\(655\) | −2.66779 | −0.104239 | ||||||||
\(656\) | 4.84577 | 0.189196 | ||||||||
\(657\) | 31.2348 | 1.21859 | ||||||||
\(658\) | 6.65728 | 0.259528 | ||||||||
\(659\) | 12.1382 | 0.472836 | 0.236418 | − | 0.971651i | \(-0.424027\pi\) | ||||
0.236418 | + | 0.971651i | \(0.424027\pi\) | |||||||
\(660\) | −5.97914 | −0.232738 | ||||||||
\(661\) | −26.4559 | −1.02901 | −0.514507 | − | 0.857486i | \(-0.672025\pi\) | ||||
−0.514507 | + | 0.857486i | \(0.672025\pi\) | |||||||
\(662\) | −58.4648 | −2.27230 | ||||||||
\(663\) | −81.4651 | −3.16384 | ||||||||
\(664\) | −25.4895 | −0.989183 | ||||||||
\(665\) | 0.183072 | 0.00709923 | ||||||||
\(666\) | 86.7206 | 3.36035 | ||||||||
\(667\) | −36.0979 | −1.39772 | ||||||||
\(668\) | 34.1590 | 1.32165 | ||||||||
\(669\) | 66.5806 | 2.57415 | ||||||||
\(670\) | 1.77235 | 0.0684720 | ||||||||
\(671\) | −4.99740 | −0.192922 | ||||||||
\(672\) | 2.75898 | 0.106430 | ||||||||
\(673\) | 38.0008 | 1.46482 | 0.732412 | − | 0.680861i | \(-0.238394\pi\) | ||||
0.732412 | + | 0.680861i | \(0.238394\pi\) | |||||||
\(674\) | 78.3089 | 3.01635 | ||||||||
\(675\) | 0.293257 | 0.0112875 | ||||||||
\(676\) | 66.9834 | 2.57628 | ||||||||
\(677\) | −16.8012 | −0.645722 | −0.322861 | − | 0.946446i | \(-0.604645\pi\) | ||||
−0.322861 | + | 0.946446i | \(0.604645\pi\) | |||||||
\(678\) | 28.8461 | 1.10783 | ||||||||
\(679\) | 1.93127 | 0.0741152 | ||||||||
\(680\) | 38.3567 | 1.47091 | ||||||||
\(681\) | −25.6876 | −0.984350 | ||||||||
\(682\) | −9.91045 | −0.379491 | ||||||||
\(683\) | −23.6603 | −0.905335 | −0.452668 | − | 0.891679i | \(-0.649528\pi\) | ||||
−0.452668 | + | 0.891679i | \(0.649528\pi\) | |||||||
\(684\) | 9.02095 | 0.344925 | ||||||||
\(685\) | −15.6485 | −0.597897 | ||||||||
\(686\) | 9.05685 | 0.345792 | ||||||||
\(687\) | 25.7550 | 0.982613 | ||||||||
\(688\) | −43.4457 | −1.65635 | ||||||||
\(689\) | 15.0751 | 0.574316 | ||||||||
\(690\) | 37.5816 | 1.43071 | ||||||||
\(691\) | −44.5630 | −1.69526 | −0.847629 | − | 0.530590i | \(-0.821970\pi\) | ||||
−0.847629 | + | 0.530590i | \(0.821970\pi\) | |||||||
\(692\) | 48.2350 | 1.83362 | ||||||||
\(693\) | 0.414814 | 0.0157575 | ||||||||
\(694\) | −49.0298 | −1.86115 | ||||||||
\(695\) | −9.47689 | −0.359479 | ||||||||
\(696\) | −86.6400 | −3.28408 | ||||||||
\(697\) | −4.68059 | −0.177290 | ||||||||
\(698\) | −0.0418104 | −0.00158255 | ||||||||
\(699\) | 15.4778 | 0.585426 | ||||||||
\(700\) | 1.13016 | 0.0427159 | ||||||||
\(701\) | 42.1789 | 1.59307 | 0.796537 | − | 0.604590i | \(-0.206663\pi\) | ||||
0.796537 | + | 0.604590i | \(0.206663\pi\) | |||||||
\(702\) | 3.94121 | 0.148751 | ||||||||
\(703\) | −8.48383 | −0.319974 | ||||||||
\(704\) | −1.06132 | −0.0400001 | ||||||||
\(705\) | 24.8341 | 0.935305 | ||||||||
\(706\) | 16.6487 | 0.626581 | ||||||||
\(707\) | 2.14161 | 0.0805436 | ||||||||
\(708\) | −23.8675 | −0.896995 | ||||||||
\(709\) | −36.1417 | −1.35733 | −0.678665 | − | 0.734448i | \(-0.737441\pi\) | ||||
−0.678665 | + | 0.734448i | \(0.737441\pi\) | |||||||
\(710\) | 31.2081 | 1.17122 | ||||||||
\(711\) | 11.0036 | 0.412669 | ||||||||
\(712\) | −18.0778 | −0.677496 | ||||||||
\(713\) | 42.8196 | 1.60361 | ||||||||
\(714\) | −9.96590 | −0.372964 | ||||||||
\(715\) | −2.97908 | −0.111411 | ||||||||
\(716\) | 48.4974 | 1.81243 | ||||||||
\(717\) | 1.67231 | 0.0624534 | ||||||||
\(718\) | −30.4277 | −1.13555 | ||||||||
\(719\) | −20.6227 | −0.769099 | −0.384549 | − | 0.923104i | \(-0.625643\pi\) | ||||
−0.384549 | + | 0.923104i | \(0.625643\pi\) | |||||||
\(720\) | 18.8483 | 0.702436 | ||||||||
\(721\) | −1.83580 | −0.0683686 | ||||||||
\(722\) | 46.7754 | 1.74080 | ||||||||
\(723\) | 39.8662 | 1.48264 | ||||||||
\(724\) | 63.8922 | 2.37454 | ||||||||
\(725\) | −5.89093 | −0.218784 | ||||||||
\(726\) | −65.5356 | −2.43225 | ||||||||
\(727\) | −27.4176 | −1.01686 | −0.508431 | − | 0.861103i | \(-0.669774\pi\) | ||||
−0.508431 | + | 0.861103i | \(0.669774\pi\) | |||||||
\(728\) | 8.28166 | 0.306939 | ||||||||
\(729\) | −24.7808 | −0.917809 | ||||||||
\(730\) | −27.4418 | −1.01567 | ||||||||
\(731\) | 41.9647 | 1.55212 | ||||||||
\(732\) | 95.0456 | 3.51299 | ||||||||
\(733\) | 19.8461 | 0.733034 | 0.366517 | − | 0.930411i | \(-0.380550\pi\) | ||||
0.366517 | + | 0.930411i | \(0.380550\pi\) | |||||||
\(734\) | −64.2192 | −2.37038 | ||||||||
\(735\) | 16.8126 | 0.620143 | ||||||||
\(736\) | −27.1340 | −1.00017 | ||||||||
\(737\) | −0.392873 | −0.0144717 | ||||||||
\(738\) | −5.39030 | −0.198420 | ||||||||
\(739\) | 22.3901 | 0.823632 | 0.411816 | − | 0.911267i | \(-0.364895\pi\) | ||||
0.411816 | + | 0.911267i | \(0.364895\pi\) | |||||||
\(740\) | −52.3731 | −1.92527 | ||||||||
\(741\) | 9.17813 | 0.337167 | ||||||||
\(742\) | 1.84419 | 0.0677023 | ||||||||
\(743\) | 39.2243 | 1.43900 | 0.719499 | − | 0.694493i | \(-0.244371\pi\) | ||||
0.719499 | + | 0.694493i | \(0.244371\pi\) | |||||||
\(744\) | 102.773 | 3.76784 | ||||||||
\(745\) | 5.41227 | 0.198290 | ||||||||
\(746\) | 61.7164 | 2.25960 | ||||||||
\(747\) | 12.0984 | 0.442659 | ||||||||
\(748\) | −15.5936 | −0.570157 | ||||||||
\(749\) | 2.94140 | 0.107476 | ||||||||
\(750\) | 6.13306 | 0.223948 | ||||||||
\(751\) | −27.7488 | −1.01257 | −0.506285 | − | 0.862366i | \(-0.668982\pi\) | ||||
−0.506285 | + | 0.862366i | \(0.668982\pi\) | |||||||
\(752\) | −67.0529 | −2.44517 | ||||||||
\(753\) | −31.7183 | −1.15588 | ||||||||
\(754\) | −79.1708 | −2.88323 | ||||||||
\(755\) | −6.02995 | −0.219452 | ||||||||
\(756\) | 0.331426 | 0.0120539 | ||||||||
\(757\) | 13.3443 | 0.485008 | 0.242504 | − | 0.970150i | \(-0.422031\pi\) | ||||
0.242504 | + | 0.970150i | \(0.422031\pi\) | |||||||
\(758\) | −10.3359 | −0.375416 | ||||||||
\(759\) | −8.33062 | −0.302382 | ||||||||
\(760\) | −4.32140 | −0.156753 | ||||||||
\(761\) | 3.62843 | 0.131530 | 0.0657652 | − | 0.997835i | \(-0.479051\pi\) | ||||
0.0657652 | + | 0.997835i | \(0.479051\pi\) | |||||||
\(762\) | 14.7766 | 0.535301 | ||||||||
\(763\) | 1.26654 | 0.0458518 | ||||||||
\(764\) | −117.933 | −4.26667 | ||||||||
\(765\) | −18.2058 | −0.658232 | ||||||||
\(766\) | 0.578823 | 0.0209137 | ||||||||
\(767\) | −11.8919 | −0.429391 | ||||||||
\(768\) | 74.5007 | 2.68831 | ||||||||
\(769\) | 7.27894 | 0.262485 | 0.131243 | − | 0.991350i | \(-0.458103\pi\) | ||||
0.131243 | + | 0.991350i | \(0.458103\pi\) | |||||||
\(770\) | −0.364441 | −0.0131336 | ||||||||
\(771\) | 19.9882 | 0.719858 | ||||||||
\(772\) | −13.7089 | −0.493393 | ||||||||
\(773\) | 37.3601 | 1.34375 | 0.671875 | − | 0.740665i | \(-0.265489\pi\) | ||||
0.671875 | + | 0.740665i | \(0.265489\pi\) | |||||||
\(774\) | 48.3279 | 1.73711 | ||||||||
\(775\) | 6.98787 | 0.251012 | ||||||||
\(776\) | −45.5873 | −1.63649 | ||||||||
\(777\) | 7.41961 | 0.266177 | ||||||||
\(778\) | −53.7440 | −1.92682 | ||||||||
\(779\) | 0.527331 | 0.0188936 | ||||||||
\(780\) | 56.6593 | 2.02873 | ||||||||
\(781\) | −6.91782 | −0.247539 | ||||||||
\(782\) | 98.0127 | 3.50493 | ||||||||
\(783\) | −1.72756 | −0.0617379 | ||||||||
\(784\) | −45.3947 | −1.62124 | ||||||||
\(785\) | −14.8601 | −0.530379 | ||||||||
\(786\) | −16.3617 | −0.583603 | ||||||||
\(787\) | −5.81874 | −0.207416 | −0.103708 | − | 0.994608i | \(-0.533071\pi\) | ||||
−0.103708 | + | 0.994608i | \(0.533071\pi\) | |||||||
\(788\) | −66.7539 | −2.37801 | ||||||||
\(789\) | −27.6050 | −0.982764 | ||||||||
\(790\) | −9.66741 | −0.343951 | ||||||||
\(791\) | 1.20862 | 0.0429734 | ||||||||
\(792\) | −9.79165 | −0.347931 | ||||||||
\(793\) | 47.3561 | 1.68167 | ||||||||
\(794\) | −76.3953 | −2.71117 | ||||||||
\(795\) | 6.87950 | 0.243991 | ||||||||
\(796\) | −49.9346 | −1.76988 | ||||||||
\(797\) | 32.3175 | 1.14475 | 0.572373 | − | 0.819993i | \(-0.306023\pi\) | ||||
0.572373 | + | 0.819993i | \(0.306023\pi\) | |||||||
\(798\) | 1.12279 | 0.0397464 | ||||||||
\(799\) | 64.7671 | 2.29130 | ||||||||
\(800\) | −4.42808 | −0.156556 | ||||||||
\(801\) | 8.58055 | 0.303179 | ||||||||
\(802\) | 14.8811 | 0.525471 | ||||||||
\(803\) | 6.08296 | 0.214663 | ||||||||
\(804\) | 7.47206 | 0.263519 | ||||||||
\(805\) | 1.57463 | 0.0554983 | ||||||||
\(806\) | 93.9130 | 3.30794 | ||||||||
\(807\) | −56.7299 | −1.99699 | ||||||||
\(808\) | −50.5526 | −1.77843 | ||||||||
\(809\) | −37.6548 | −1.32387 | −0.661937 | − | 0.749560i | \(-0.730265\pi\) | ||||
−0.661937 | + | 0.749560i | \(0.730265\pi\) | |||||||
\(810\) | 23.6457 | 0.830825 | ||||||||
\(811\) | −3.12197 | −0.109627 | −0.0548137 | − | 0.998497i | \(-0.517456\pi\) | ||||
−0.0548137 | + | 0.998497i | \(0.517456\pi\) | |||||||
\(812\) | −6.65767 | −0.233639 | ||||||||
\(813\) | 6.38498 | 0.223931 | ||||||||
\(814\) | 16.8888 | 0.591950 | ||||||||
\(815\) | 9.87485 | 0.345901 | ||||||||
\(816\) | 100.378 | 3.51392 | ||||||||
\(817\) | −4.72789 | −0.165408 | ||||||||
\(818\) | −31.4495 | −1.09961 | ||||||||
\(819\) | −3.93085 | −0.137355 | ||||||||
\(820\) | 3.25536 | 0.113682 | ||||||||
\(821\) | 47.2997 | 1.65077 | 0.825386 | − | 0.564569i | \(-0.190958\pi\) | ||||
0.825386 | + | 0.564569i | \(0.190958\pi\) | |||||||
\(822\) | −95.9730 | −3.34744 | ||||||||
\(823\) | 16.2203 | 0.565405 | 0.282702 | − | 0.959208i | \(-0.408769\pi\) | ||||
0.282702 | + | 0.959208i | \(0.408769\pi\) | |||||||
\(824\) | 43.3338 | 1.50960 | ||||||||
\(825\) | −1.35950 | −0.0473317 | ||||||||
\(826\) | −1.45477 | −0.0506181 | ||||||||
\(827\) | 41.1812 | 1.43201 | 0.716006 | − | 0.698094i | \(-0.245968\pi\) | ||||
0.716006 | + | 0.698094i | \(0.245968\pi\) | |||||||
\(828\) | 77.5904 | 2.69645 | ||||||||
\(829\) | 12.1916 | 0.423431 | 0.211716 | − | 0.977331i | \(-0.432095\pi\) | ||||
0.211716 | + | 0.977331i | \(0.432095\pi\) | |||||||
\(830\) | −10.6293 | −0.368947 | ||||||||
\(831\) | −56.2947 | −1.95284 | ||||||||
\(832\) | 10.0573 | 0.348673 | ||||||||
\(833\) | 43.8472 | 1.51922 | ||||||||
\(834\) | −58.1224 | −2.01261 | ||||||||
\(835\) | 7.76686 | 0.268783 | ||||||||
\(836\) | 1.75682 | 0.0607610 | ||||||||
\(837\) | 2.04924 | 0.0708321 | ||||||||
\(838\) | −0.678660 | −0.0234439 | ||||||||
\(839\) | −19.6117 | −0.677072 | −0.338536 | − | 0.940953i | \(-0.609932\pi\) | ||||
−0.338536 | + | 0.940953i | \(0.609932\pi\) | |||||||
\(840\) | 3.77932 | 0.130399 | ||||||||
\(841\) | 5.70307 | 0.196658 | ||||||||
\(842\) | −23.8364 | −0.821456 | ||||||||
\(843\) | −16.2628 | −0.560122 | ||||||||
\(844\) | 49.1703 | 1.69251 | ||||||||
\(845\) | 15.2303 | 0.523937 | ||||||||
\(846\) | 74.5877 | 2.56438 | ||||||||
\(847\) | −2.74586 | −0.0943489 | ||||||||
\(848\) | −18.5749 | −0.637864 | ||||||||
\(849\) | 67.5585 | 2.31860 | ||||||||
\(850\) | 15.9950 | 0.548624 | ||||||||
\(851\) | −72.9705 | −2.50140 | ||||||||
\(852\) | 131.570 | 4.50752 | ||||||||
\(853\) | −4.16124 | −0.142478 | −0.0712391 | − | 0.997459i | \(-0.522695\pi\) | ||||
−0.0712391 | + | 0.997459i | \(0.522695\pi\) | |||||||
\(854\) | 5.79323 | 0.198240 | ||||||||
\(855\) | 2.05113 | 0.0701471 | ||||||||
\(856\) | −69.4315 | −2.37312 | ||||||||
\(857\) | 1.45006 | 0.0495330 | 0.0247665 | − | 0.999693i | \(-0.492116\pi\) | ||||
0.0247665 | + | 0.999693i | \(0.492116\pi\) | |||||||
\(858\) | −18.2709 | −0.623758 | ||||||||
\(859\) | 7.62894 | 0.260296 | 0.130148 | − | 0.991495i | \(-0.458455\pi\) | ||||
0.130148 | + | 0.991495i | \(0.458455\pi\) | |||||||
\(860\) | −29.1866 | −0.995256 | ||||||||
\(861\) | −0.461182 | −0.0157170 | ||||||||
\(862\) | 17.9174 | 0.610268 | ||||||||
\(863\) | 30.8038 | 1.04857 | 0.524286 | − | 0.851542i | \(-0.324332\pi\) | ||||
0.524286 | + | 0.851542i | \(0.324332\pi\) | |||||||
\(864\) | −1.29857 | −0.0441781 | ||||||||
\(865\) | 10.9674 | 0.372902 | ||||||||
\(866\) | 24.3128 | 0.826183 | ||||||||
\(867\) | −55.7364 | −1.89291 | ||||||||
\(868\) | 7.89738 | 0.268055 | ||||||||
\(869\) | 2.14295 | 0.0726946 | ||||||||
\(870\) | −36.1294 | −1.22490 | ||||||||
\(871\) | 3.72293 | 0.126147 | ||||||||
\(872\) | −29.8965 | −1.01242 | ||||||||
\(873\) | 21.6378 | 0.732328 | ||||||||
\(874\) | −11.0424 | −0.373516 | ||||||||
\(875\) | 0.256968 | 0.00868710 | ||||||||
\(876\) | −115.692 | −3.90887 | ||||||||
\(877\) | 42.4825 | 1.43453 | 0.717267 | − | 0.696799i | \(-0.245393\pi\) | ||||
0.717267 | + | 0.696799i | \(0.245393\pi\) | |||||||
\(878\) | −1.64355 | −0.0554672 | ||||||||
\(879\) | −46.6048 | −1.57194 | ||||||||
\(880\) | 3.67070 | 0.123739 | ||||||||
\(881\) | −25.3391 | −0.853695 | −0.426848 | − | 0.904324i | \(-0.640376\pi\) | ||||
−0.426848 | + | 0.904324i | \(0.640376\pi\) | |||||||
\(882\) | 50.4958 | 1.70028 | ||||||||
\(883\) | 50.6192 | 1.70347 | 0.851737 | − | 0.523970i | \(-0.175550\pi\) | ||||
0.851737 | + | 0.523970i | \(0.175550\pi\) | |||||||
\(884\) | 147.767 | 4.96994 | ||||||||
\(885\) | −5.42684 | −0.182421 | ||||||||
\(886\) | −19.5076 | −0.655369 | ||||||||
\(887\) | 42.1374 | 1.41484 | 0.707418 | − | 0.706795i | \(-0.249860\pi\) | ||||
0.707418 | + | 0.706795i | \(0.249860\pi\) | |||||||
\(888\) | −175.139 | −5.87729 | ||||||||
\(889\) | 0.619123 | 0.0207647 | ||||||||
\(890\) | −7.53858 | −0.252694 | ||||||||
\(891\) | −5.24148 | −0.175596 | ||||||||
\(892\) | −120.768 | −4.04363 | ||||||||
\(893\) | −7.29688 | −0.244181 | ||||||||
\(894\) | 33.1938 | 1.11017 | ||||||||
\(895\) | 11.0270 | 0.368593 | ||||||||
\(896\) | 3.50609 | 0.117130 | ||||||||
\(897\) | 78.9423 | 2.63581 | ||||||||
\(898\) | 82.1611 | 2.74175 | ||||||||
\(899\) | −41.1650 | −1.37293 | ||||||||
\(900\) | 12.6622 | 0.422073 | ||||||||
\(901\) | 17.9417 | 0.597725 | ||||||||
\(902\) | −1.04976 | −0.0349531 | ||||||||
\(903\) | 4.13482 | 0.137598 | ||||||||
\(904\) | −28.5293 | −0.948869 | ||||||||
\(905\) | 14.5274 | 0.482907 | ||||||||
\(906\) | −36.9820 | −1.22865 | ||||||||
\(907\) | −19.6576 | −0.652721 | −0.326360 | − | 0.945245i | \(-0.605822\pi\) | ||||
−0.326360 | + | 0.945245i | \(0.605822\pi\) | |||||||
\(908\) | 46.5939 | 1.54627 | ||||||||
\(909\) | 23.9945 | 0.795848 | ||||||||
\(910\) | 3.45350 | 0.114483 | ||||||||
\(911\) | 31.9613 | 1.05893 | 0.529463 | − | 0.848333i | \(-0.322393\pi\) | ||||
0.529463 | + | 0.848333i | \(0.322393\pi\) | |||||||
\(912\) | −11.3089 | −0.374475 | ||||||||
\(913\) | 2.35616 | 0.0779775 | ||||||||
\(914\) | −28.2167 | −0.933326 | ||||||||
\(915\) | 21.6109 | 0.714433 | ||||||||
\(916\) | −46.7161 | −1.54354 | ||||||||
\(917\) | −0.685536 | −0.0226384 | ||||||||
\(918\) | 4.69064 | 0.154814 | ||||||||
\(919\) | 27.0232 | 0.891413 | 0.445707 | − | 0.895179i | \(-0.352952\pi\) | ||||
0.445707 | + | 0.895179i | \(0.352952\pi\) | |||||||
\(920\) | −37.1689 | −1.22542 | ||||||||
\(921\) | 13.8654 | 0.456880 | ||||||||
\(922\) | −75.4169 | −2.48372 | ||||||||
\(923\) | 65.5544 | 2.15775 | ||||||||
\(924\) | −1.53645 | −0.0505454 | ||||||||
\(925\) | −11.9083 | −0.391542 | ||||||||
\(926\) | 19.1352 | 0.628820 | ||||||||
\(927\) | −20.5681 | −0.675547 | ||||||||
\(928\) | 26.0855 | 0.856299 | ||||||||
\(929\) | 53.0777 | 1.74142 | 0.870711 | − | 0.491795i | \(-0.163659\pi\) | ||||
0.870711 | + | 0.491795i | \(0.163659\pi\) | |||||||
\(930\) | 42.8570 | 1.40534 | ||||||||
\(931\) | −4.93998 | −0.161901 | ||||||||
\(932\) | −28.0748 | −0.919620 | ||||||||
\(933\) | 48.1719 | 1.57708 | ||||||||
\(934\) | 63.1191 | 2.06532 | ||||||||
\(935\) | −3.54557 | −0.115952 | ||||||||
\(936\) | 92.7872 | 3.03285 | ||||||||
\(937\) | 39.8321 | 1.30126 | 0.650629 | − | 0.759396i | \(-0.274505\pi\) | ||||
0.650629 | + | 0.759396i | \(0.274505\pi\) | |||||||
\(938\) | 0.455438 | 0.0148706 | ||||||||
\(939\) | 67.3231 | 2.19701 | ||||||||
\(940\) | −45.0457 | −1.46923 | ||||||||
\(941\) | 19.4679 | 0.634634 | 0.317317 | − | 0.948319i | \(-0.397218\pi\) | ||||
0.317317 | + | 0.948319i | \(0.397218\pi\) | |||||||
\(942\) | −91.1378 | −2.96943 | ||||||||
\(943\) | 4.53564 | 0.147701 | ||||||||
\(944\) | 14.6526 | 0.476903 | ||||||||
\(945\) | 0.0753577 | 0.00245138 | ||||||||
\(946\) | 9.41181 | 0.306004 | ||||||||
\(947\) | −22.2190 | −0.722020 | −0.361010 | − | 0.932562i | \(-0.617568\pi\) | ||||
−0.361010 | + | 0.932562i | \(0.617568\pi\) | |||||||
\(948\) | −40.7568 | −1.32372 | ||||||||
\(949\) | −57.6431 | −1.87117 | ||||||||
\(950\) | −1.80205 | −0.0584662 | ||||||||
\(951\) | −25.5580 | −0.828776 | ||||||||
\(952\) | 9.85644 | 0.319449 | ||||||||
\(953\) | 34.6986 | 1.12400 | 0.561999 | − | 0.827138i | \(-0.310032\pi\) | ||||
0.561999 | + | 0.827138i | \(0.310032\pi\) | |||||||
\(954\) | 20.6622 | 0.668963 | ||||||||
\(955\) | −26.8149 | −0.867710 | ||||||||
\(956\) | −3.03334 | −0.0981054 | ||||||||
\(957\) | 8.00872 | 0.258885 | ||||||||
\(958\) | −94.3179 | −3.04727 | ||||||||
\(959\) | −4.02115 | −0.129850 | ||||||||
\(960\) | 4.58961 | 0.148129 | ||||||||
\(961\) | 17.8303 | 0.575170 | ||||||||
\(962\) | −160.040 | −5.15991 | ||||||||
\(963\) | 32.9553 | 1.06197 | ||||||||
\(964\) | −72.3121 | −2.32901 | ||||||||
\(965\) | −3.11703 | −0.100341 | ||||||||
\(966\) | 9.65728 | 0.310718 | ||||||||
\(967\) | −12.0819 | −0.388527 | −0.194264 | − | 0.980949i | \(-0.562232\pi\) | ||||
−0.194264 | + | 0.980949i | \(0.562232\pi\) | |||||||
\(968\) | 64.8158 | 2.08326 | ||||||||
\(969\) | 10.9234 | 0.350910 | ||||||||
\(970\) | −19.0102 | −0.610381 | ||||||||
\(971\) | −35.3199 | −1.13347 | −0.566736 | − | 0.823900i | \(-0.691794\pi\) | ||||
−0.566736 | + | 0.823900i | \(0.691794\pi\) | |||||||
\(972\) | 95.8185 | 3.07338 | ||||||||
\(973\) | −2.43526 | −0.0780707 | ||||||||
\(974\) | 7.35186 | 0.235569 | ||||||||
\(975\) | 12.8828 | 0.412581 | ||||||||
\(976\) | −58.3501 | −1.86774 | ||||||||
\(977\) | 47.9789 | 1.53498 | 0.767490 | − | 0.641061i | \(-0.221506\pi\) | ||||
0.767490 | + | 0.641061i | \(0.221506\pi\) | |||||||
\(978\) | 60.5631 | 1.93659 | ||||||||
\(979\) | 1.67106 | 0.0534072 | ||||||||
\(980\) | −30.4959 | −0.974156 | ||||||||
\(981\) | 14.1902 | 0.453059 | ||||||||
\(982\) | −4.43068 | −0.141389 | ||||||||
\(983\) | 52.8181 | 1.68463 | 0.842317 | − | 0.538982i | \(-0.181191\pi\) | ||||
0.842317 | + | 0.538982i | \(0.181191\pi\) | |||||||
\(984\) | 10.8862 | 0.347038 | ||||||||
\(985\) | −15.1781 | −0.483614 | ||||||||
\(986\) | −94.2254 | −3.00075 | ||||||||
\(987\) | 6.38156 | 0.203127 | ||||||||
\(988\) | −16.6479 | −0.529641 | ||||||||
\(989\) | −40.6652 | −1.29308 | ||||||||
\(990\) | −4.08318 | −0.129772 | ||||||||
\(991\) | 17.2468 | 0.547862 | 0.273931 | − | 0.961749i | \(-0.411676\pi\) | ||||
0.273931 | + | 0.961749i | \(0.411676\pi\) | |||||||
\(992\) | −30.9428 | −0.982436 | ||||||||
\(993\) | −56.0434 | −1.77849 | ||||||||
\(994\) | 8.01949 | 0.254363 | ||||||||
\(995\) | −11.3538 | −0.359940 | ||||||||
\(996\) | −44.8119 | −1.41992 | ||||||||
\(997\) | −0.846695 | −0.0268151 | −0.0134076 | − | 0.999910i | \(-0.504268\pi\) | ||||
−0.0134076 | + | 0.999910i | \(0.504268\pi\) | |||||||
\(998\) | 27.9179 | 0.883727 | ||||||||
\(999\) | −3.49219 | −0.110488 |
(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 | 8035.2.a.e.1.11 | ✓ | 153 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8035.2.a.e.1.11 | ✓ | 153 | 1.1 | even | 1 | trivial |