Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.08608 | −1.47508 | −0.737540 | − | 0.675304i | \(-0.764012\pi\) | ||||
−0.737540 | + | 0.675304i | \(0.764012\pi\) | |||||||
\(3\) | 1.06648 | 0.615731 | 0.307865 | − | 0.951430i | \(-0.400385\pi\) | ||||
0.307865 | + | 0.951430i | \(0.400385\pi\) | |||||||
\(4\) | 2.35172 | 1.17586 | ||||||||
\(5\) | −3.22907 | −1.44409 | −0.722043 | − | 0.691848i | \(-0.756797\pi\) | ||||
−0.722043 | + | 0.691848i | \(0.756797\pi\) | |||||||
\(6\) | −2.22475 | −0.908251 | ||||||||
\(7\) | 0.560788 | 0.211958 | 0.105979 | − | 0.994368i | \(-0.466202\pi\) | ||||
0.105979 | + | 0.994368i | \(0.466202\pi\) | |||||||
\(8\) | −0.733710 | −0.259406 | ||||||||
\(9\) | −1.86263 | −0.620876 | ||||||||
\(10\) | 6.73610 | 2.13014 | ||||||||
\(11\) | −4.80950 | −1.45012 | −0.725059 | − | 0.688687i | \(-0.758188\pi\) | ||||
−0.725059 | + | 0.688687i | \(0.758188\pi\) | |||||||
\(12\) | 2.50805 | 0.724012 | ||||||||
\(13\) | −3.57901 | −0.992639 | −0.496319 | − | 0.868140i | \(-0.665315\pi\) | ||||
−0.496319 | + | 0.868140i | \(0.665315\pi\) | |||||||
\(14\) | −1.16985 | −0.312655 | ||||||||
\(15\) | −3.44373 | −0.889168 | ||||||||
\(16\) | −3.17286 | −0.793215 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 3.88558 | 0.915841 | ||||||||
\(19\) | −2.21771 | −0.508779 | −0.254389 | − | 0.967102i | \(-0.581874\pi\) | ||||
−0.254389 | + | 0.967102i | \(0.581874\pi\) | |||||||
\(20\) | −7.59387 | −1.69804 | ||||||||
\(21\) | 0.598068 | 0.130509 | ||||||||
\(22\) | 10.0330 | 2.13904 | ||||||||
\(23\) | 0.337685 | 0.0704122 | 0.0352061 | − | 0.999380i | \(-0.488791\pi\) | ||||
0.0352061 | + | 0.999380i | \(0.488791\pi\) | |||||||
\(24\) | −0.782484 | −0.159724 | ||||||||
\(25\) | 5.42692 | 1.08538 | ||||||||
\(26\) | 7.46609 | 1.46422 | ||||||||
\(27\) | −5.18588 | −0.998023 | ||||||||
\(28\) | 1.31882 | 0.249233 | ||||||||
\(29\) | 6.91401 | 1.28390 | 0.641949 | − | 0.766747i | \(-0.278126\pi\) | ||||
0.641949 | + | 0.766747i | \(0.278126\pi\) | |||||||
\(30\) | 7.18389 | 1.31159 | ||||||||
\(31\) | −2.48752 | −0.446772 | −0.223386 | − | 0.974730i | \(-0.571711\pi\) | ||||
−0.223386 | + | 0.974730i | \(0.571711\pi\) | |||||||
\(32\) | 8.08625 | 1.42946 | ||||||||
\(33\) | −5.12922 | −0.892882 | ||||||||
\(34\) | 2.08608 | 0.357759 | ||||||||
\(35\) | −1.81083 | −0.306086 | ||||||||
\(36\) | −4.38037 | −0.730062 | ||||||||
\(37\) | −5.39565 | −0.887040 | −0.443520 | − | 0.896264i | \(-0.646271\pi\) | ||||
−0.443520 | + | 0.896264i | \(0.646271\pi\) | |||||||
\(38\) | 4.62632 | 0.750489 | ||||||||
\(39\) | −3.81693 | −0.611198 | ||||||||
\(40\) | 2.36920 | 0.374604 | ||||||||
\(41\) | 3.91482 | 0.611391 | 0.305696 | − | 0.952129i | \(-0.401111\pi\) | ||||
0.305696 | + | 0.952129i | \(0.401111\pi\) | |||||||
\(42\) | −1.24762 | −0.192511 | ||||||||
\(43\) | −9.72258 | −1.48268 | −0.741340 | − | 0.671130i | \(-0.765809\pi\) | ||||
−0.741340 | + | 0.671130i | \(0.765809\pi\) | |||||||
\(44\) | −11.3106 | −1.70513 | ||||||||
\(45\) | 6.01456 | 0.896598 | ||||||||
\(46\) | −0.704437 | −0.103864 | ||||||||
\(47\) | −4.67653 | −0.682142 | −0.341071 | − | 0.940038i | \(-0.610790\pi\) | ||||
−0.341071 | + | 0.940038i | \(0.610790\pi\) | |||||||
\(48\) | −3.38378 | −0.488407 | ||||||||
\(49\) | −6.68552 | −0.955074 | ||||||||
\(50\) | −11.3210 | −1.60103 | ||||||||
\(51\) | −1.06648 | −0.149337 | ||||||||
\(52\) | −8.41682 | −1.16720 | ||||||||
\(53\) | −10.9237 | −1.50049 | −0.750245 | − | 0.661159i | \(-0.770065\pi\) | ||||
−0.750245 | + | 0.661159i | \(0.770065\pi\) | |||||||
\(54\) | 10.8181 | 1.47216 | ||||||||
\(55\) | 15.5302 | 2.09410 | ||||||||
\(56\) | −0.411456 | −0.0549831 | ||||||||
\(57\) | −2.36514 | −0.313271 | ||||||||
\(58\) | −14.4231 | −1.89385 | ||||||||
\(59\) | −3.30514 | −0.430293 | −0.215146 | − | 0.976582i | \(-0.569023\pi\) | ||||
−0.215146 | + | 0.976582i | \(0.569023\pi\) | |||||||
\(60\) | −8.09868 | −1.04554 | ||||||||
\(61\) | −13.8268 | −1.77033 | −0.885167 | − | 0.465273i | \(-0.845956\pi\) | ||||
−0.885167 | + | 0.465273i | \(0.845956\pi\) | |||||||
\(62\) | 5.18916 | 0.659024 | ||||||||
\(63\) | −1.04454 | −0.131600 | ||||||||
\(64\) | −10.5228 | −1.31535 | ||||||||
\(65\) | 11.5569 | 1.43346 | ||||||||
\(66\) | 10.6999 | 1.31707 | ||||||||
\(67\) | −13.2574 | −1.61965 | −0.809827 | − | 0.586668i | \(-0.800439\pi\) | ||||
−0.809827 | + | 0.586668i | \(0.800439\pi\) | |||||||
\(68\) | −2.35172 | −0.285188 | ||||||||
\(69\) | 0.360133 | 0.0433549 | ||||||||
\(70\) | 3.77752 | 0.451501 | ||||||||
\(71\) | −3.80132 | −0.451133 | −0.225567 | − | 0.974228i | \(-0.572423\pi\) | ||||
−0.225567 | + | 0.974228i | \(0.572423\pi\) | |||||||
\(72\) | 1.36663 | 0.161059 | ||||||||
\(73\) | −0.206208 | −0.0241348 | −0.0120674 | − | 0.999927i | \(-0.503841\pi\) | ||||
−0.0120674 | + | 0.999927i | \(0.503841\pi\) | |||||||
\(74\) | 11.2558 | 1.30845 | ||||||||
\(75\) | 5.78768 | 0.668304 | ||||||||
\(76\) | −5.21544 | −0.598252 | ||||||||
\(77\) | −2.69711 | −0.307364 | ||||||||
\(78\) | 7.96241 | 0.901565 | ||||||||
\(79\) | −1.11553 | −0.125507 | −0.0627534 | − | 0.998029i | \(-0.519988\pi\) | ||||
−0.0627534 | + | 0.998029i | \(0.519988\pi\) | |||||||
\(80\) | 10.2454 | 1.14547 | ||||||||
\(81\) | 0.0572646 | 0.00636273 | ||||||||
\(82\) | −8.16661 | −0.901851 | ||||||||
\(83\) | 5.89905 | 0.647505 | 0.323752 | − | 0.946142i | \(-0.395056\pi\) | ||||
0.323752 | + | 0.946142i | \(0.395056\pi\) | |||||||
\(84\) | 1.40649 | 0.153460 | ||||||||
\(85\) | 3.22907 | 0.350242 | ||||||||
\(86\) | 20.2820 | 2.18707 | ||||||||
\(87\) | 7.37363 | 0.790536 | ||||||||
\(88\) | 3.52878 | 0.376169 | ||||||||
\(89\) | 3.33870 | 0.353902 | 0.176951 | − | 0.984220i | \(-0.443377\pi\) | ||||
0.176951 | + | 0.984220i | \(0.443377\pi\) | |||||||
\(90\) | −12.5468 | −1.32255 | ||||||||
\(91\) | −2.00707 | −0.210398 | ||||||||
\(92\) | 0.794139 | 0.0827948 | ||||||||
\(93\) | −2.65288 | −0.275091 | ||||||||
\(94\) | 9.75560 | 1.00621 | ||||||||
\(95\) | 7.16116 | 0.734720 | ||||||||
\(96\) | 8.62380 | 0.880163 | ||||||||
\(97\) | −9.71130 | −0.986033 | −0.493017 | − | 0.870020i | \(-0.664106\pi\) | ||||
−0.493017 | + | 0.870020i | \(0.664106\pi\) | |||||||
\(98\) | 13.9465 | 1.40881 | ||||||||
\(99\) | 8.95831 | 0.900344 | ||||||||
\(100\) | 12.7626 | 1.27626 | ||||||||
\(101\) | −13.1438 | −1.30786 | −0.653930 | − | 0.756555i | \(-0.726881\pi\) | ||||
−0.653930 | + | 0.756555i | \(0.726881\pi\) | |||||||
\(102\) | 2.22475 | 0.220283 | ||||||||
\(103\) | 2.20797 | 0.217558 | 0.108779 | − | 0.994066i | \(-0.465306\pi\) | ||||
0.108779 | + | 0.994066i | \(0.465306\pi\) | |||||||
\(104\) | 2.62595 | 0.257496 | ||||||||
\(105\) | −1.93120 | −0.188466 | ||||||||
\(106\) | 22.7878 | 2.21334 | ||||||||
\(107\) | −2.83512 | −0.274081 | −0.137040 | − | 0.990565i | \(-0.543759\pi\) | ||||
−0.137040 | + | 0.990565i | \(0.543759\pi\) | |||||||
\(108\) | −12.1957 | −1.17353 | ||||||||
\(109\) | 1.61581 | 0.154767 | 0.0773834 | − | 0.997001i | \(-0.475343\pi\) | ||||
0.0773834 | + | 0.997001i | \(0.475343\pi\) | |||||||
\(110\) | −32.3973 | −3.08896 | ||||||||
\(111\) | −5.75434 | −0.546178 | ||||||||
\(112\) | −1.77930 | −0.168128 | ||||||||
\(113\) | 9.76321 | 0.918445 | 0.459223 | − | 0.888321i | \(-0.348128\pi\) | ||||
0.459223 | + | 0.888321i | \(0.348128\pi\) | |||||||
\(114\) | 4.93387 | 0.462099 | ||||||||
\(115\) | −1.09041 | −0.101681 | ||||||||
\(116\) | 16.2598 | 1.50968 | ||||||||
\(117\) | 6.66636 | 0.616305 | ||||||||
\(118\) | 6.89478 | 0.634716 | ||||||||
\(119\) | −0.560788 | −0.0514074 | ||||||||
\(120\) | 2.52670 | 0.230655 | ||||||||
\(121\) | 12.1313 | 1.10284 | ||||||||
\(122\) | 28.8437 | 2.61138 | ||||||||
\(123\) | 4.17506 | 0.376452 | ||||||||
\(124\) | −5.84994 | −0.525341 | ||||||||
\(125\) | −1.37856 | −0.123302 | ||||||||
\(126\) | 2.17899 | 0.194120 | ||||||||
\(127\) | 13.9965 | 1.24199 | 0.620996 | − | 0.783813i | \(-0.286728\pi\) | ||||
0.620996 | + | 0.783813i | \(0.286728\pi\) | |||||||
\(128\) | 5.77891 | 0.510789 | ||||||||
\(129\) | −10.3689 | −0.912931 | ||||||||
\(130\) | −24.1086 | −2.11446 | ||||||||
\(131\) | 10.5151 | 0.918706 | 0.459353 | − | 0.888254i | \(-0.348081\pi\) | ||||
0.459353 | + | 0.888254i | \(0.348081\pi\) | |||||||
\(132\) | −12.0625 | −1.04990 | ||||||||
\(133\) | −1.24367 | −0.107840 | ||||||||
\(134\) | 27.6561 | 2.38912 | ||||||||
\(135\) | 16.7456 | 1.44123 | ||||||||
\(136\) | 0.733710 | 0.0629151 | ||||||||
\(137\) | −4.66687 | −0.398717 | −0.199359 | − | 0.979927i | \(-0.563886\pi\) | ||||
−0.199359 | + | 0.979927i | \(0.563886\pi\) | |||||||
\(138\) | −0.751265 | −0.0639519 | ||||||||
\(139\) | −0.175209 | −0.0148610 | −0.00743052 | − | 0.999972i | \(-0.502365\pi\) | ||||
−0.00743052 | + | 0.999972i | \(0.502365\pi\) | |||||||
\(140\) | −4.25855 | −0.359913 | ||||||||
\(141\) | −4.98741 | −0.420016 | ||||||||
\(142\) | 7.92984 | 0.665457 | ||||||||
\(143\) | 17.2132 | 1.43944 | ||||||||
\(144\) | 5.90986 | 0.492488 | ||||||||
\(145\) | −22.3258 | −1.85406 | ||||||||
\(146\) | 0.430165 | 0.0356007 | ||||||||
\(147\) | −7.12995 | −0.588068 | ||||||||
\(148\) | −12.6891 | −1.04303 | ||||||||
\(149\) | 5.84453 | 0.478803 | 0.239401 | − | 0.970921i | \(-0.423049\pi\) | ||||
0.239401 | + | 0.970921i | \(0.423049\pi\) | |||||||
\(150\) | −12.0736 | −0.985802 | ||||||||
\(151\) | −8.68232 | −0.706557 | −0.353279 | − | 0.935518i | \(-0.614933\pi\) | ||||
−0.353279 | + | 0.935518i | \(0.614933\pi\) | |||||||
\(152\) | 1.62716 | 0.131980 | ||||||||
\(153\) | 1.86263 | 0.150585 | ||||||||
\(154\) | 5.62638 | 0.453387 | ||||||||
\(155\) | 8.03239 | 0.645177 | ||||||||
\(156\) | −8.97634 | −0.718682 | ||||||||
\(157\) | −11.3570 | −0.906386 | −0.453193 | − | 0.891412i | \(-0.649715\pi\) | ||||
−0.453193 | + | 0.891412i | \(0.649715\pi\) | |||||||
\(158\) | 2.32708 | 0.185133 | ||||||||
\(159\) | −11.6499 | −0.923898 | ||||||||
\(160\) | −26.1111 | −2.06426 | ||||||||
\(161\) | 0.189370 | 0.0149244 | ||||||||
\(162\) | −0.119458 | −0.00938553 | ||||||||
\(163\) | 0.00171347 | 0.000134209 0 | 6.71046e−5 | − | 1.00000i | \(-0.499979\pi\) | ||||
6.71046e−5 | 1.00000i | \(0.499979\pi\) | ||||||||
\(164\) | 9.20654 | 0.718910 | ||||||||
\(165\) | 16.5626 | 1.28940 | ||||||||
\(166\) | −12.3059 | −0.955121 | ||||||||
\(167\) | 17.3447 | 1.34217 | 0.671086 | − | 0.741380i | \(-0.265828\pi\) | ||||
0.671086 | + | 0.741380i | \(0.265828\pi\) | |||||||
\(168\) | −0.438808 | −0.0338548 | ||||||||
\(169\) | −0.190694 | −0.0146688 | ||||||||
\(170\) | −6.73610 | −0.516635 | ||||||||
\(171\) | 4.13078 | 0.315888 | ||||||||
\(172\) | −22.8648 | −1.74342 | ||||||||
\(173\) | −12.2300 | −0.929832 | −0.464916 | − | 0.885355i | \(-0.653915\pi\) | ||||
−0.464916 | + | 0.885355i | \(0.653915\pi\) | |||||||
\(174\) | −15.3820 | −1.16610 | ||||||||
\(175\) | 3.04335 | 0.230056 | ||||||||
\(176\) | 15.2599 | 1.15026 | ||||||||
\(177\) | −3.52486 | −0.264945 | ||||||||
\(178\) | −6.96479 | −0.522033 | ||||||||
\(179\) | −17.7791 | −1.32887 | −0.664436 | − | 0.747345i | \(-0.731328\pi\) | ||||
−0.664436 | + | 0.747345i | \(0.731328\pi\) | |||||||
\(180\) | 14.1446 | 1.05427 | ||||||||
\(181\) | −15.6198 | −1.16101 | −0.580507 | − | 0.814256i | \(-0.697145\pi\) | ||||
−0.580507 | + | 0.814256i | \(0.697145\pi\) | |||||||
\(182\) | 4.18689 | 0.310353 | ||||||||
\(183\) | −14.7459 | −1.09005 | ||||||||
\(184\) | −0.247763 | −0.0182653 | ||||||||
\(185\) | 17.4230 | 1.28096 | ||||||||
\(186\) | 5.53412 | 0.405781 | ||||||||
\(187\) | 4.80950 | 0.351705 | ||||||||
\(188\) | −10.9979 | −0.802103 | ||||||||
\(189\) | −2.90818 | −0.211539 | ||||||||
\(190\) | −14.9387 | −1.08377 | ||||||||
\(191\) | −20.2427 | −1.46471 | −0.732357 | − | 0.680921i | \(-0.761580\pi\) | ||||
−0.732357 | + | 0.680921i | \(0.761580\pi\) | |||||||
\(192\) | −11.2223 | −0.809903 | ||||||||
\(193\) | 2.91165 | 0.209585 | 0.104792 | − | 0.994494i | \(-0.466582\pi\) | ||||
0.104792 | + | 0.994494i | \(0.466582\pi\) | |||||||
\(194\) | 20.2585 | 1.45448 | ||||||||
\(195\) | 12.3251 | 0.882622 | ||||||||
\(196\) | −15.7224 | −1.12303 | ||||||||
\(197\) | −5.08391 | −0.362213 | −0.181107 | − | 0.983463i | \(-0.557968\pi\) | ||||
−0.181107 | + | 0.983463i | \(0.557968\pi\) | |||||||
\(198\) | −18.6877 | −1.32808 | ||||||||
\(199\) | 4.47982 | 0.317566 | 0.158783 | − | 0.987314i | \(-0.449243\pi\) | ||||
0.158783 | + | 0.987314i | \(0.449243\pi\) | |||||||
\(200\) | −3.98178 | −0.281555 | ||||||||
\(201\) | −14.1388 | −0.997271 | ||||||||
\(202\) | 27.4190 | 1.92920 | ||||||||
\(203\) | 3.87729 | 0.272133 | ||||||||
\(204\) | −2.50805 | −0.175599 | ||||||||
\(205\) | −12.6412 | −0.882902 | ||||||||
\(206\) | −4.60600 | −0.320915 | ||||||||
\(207\) | −0.628981 | −0.0437172 | ||||||||
\(208\) | 11.3557 | 0.787376 | ||||||||
\(209\) | 10.6661 | 0.737789 | ||||||||
\(210\) | 4.02864 | 0.278003 | ||||||||
\(211\) | −5.43985 | −0.374495 | −0.187247 | − | 0.982313i | \(-0.559957\pi\) | ||||
−0.187247 | + | 0.982313i | \(0.559957\pi\) | |||||||
\(212\) | −25.6895 | −1.76437 | ||||||||
\(213\) | −4.05401 | −0.277777 | ||||||||
\(214\) | 5.91427 | 0.404291 | ||||||||
\(215\) | 31.3949 | 2.14112 | ||||||||
\(216\) | 3.80493 | 0.258893 | ||||||||
\(217\) | −1.39497 | −0.0946969 | ||||||||
\(218\) | −3.37071 | −0.228293 | ||||||||
\(219\) | −0.219916 | −0.0148605 | ||||||||
\(220\) | 36.5227 | 2.46236 | ||||||||
\(221\) | 3.57901 | 0.240750 | ||||||||
\(222\) | 12.0040 | 0.805655 | ||||||||
\(223\) | 19.6450 | 1.31553 | 0.657763 | − | 0.753225i | \(-0.271503\pi\) | ||||
0.657763 | + | 0.753225i | \(0.271503\pi\) | |||||||
\(224\) | 4.53467 | 0.302986 | ||||||||
\(225\) | −10.1083 | −0.673889 | ||||||||
\(226\) | −20.3668 | −1.35478 | ||||||||
\(227\) | 8.02162 | 0.532414 | 0.266207 | − | 0.963916i | \(-0.414230\pi\) | ||||
0.266207 | + | 0.963916i | \(0.414230\pi\) | |||||||
\(228\) | −5.56214 | −0.368362 | ||||||||
\(229\) | −24.0625 | −1.59010 | −0.795048 | − | 0.606546i | \(-0.792555\pi\) | ||||
−0.795048 | + | 0.606546i | \(0.792555\pi\) | |||||||
\(230\) | 2.27468 | 0.149988 | ||||||||
\(231\) | −2.87641 | −0.189254 | ||||||||
\(232\) | −5.07287 | −0.333050 | ||||||||
\(233\) | 9.24278 | 0.605515 | 0.302757 | − | 0.953068i | \(-0.402093\pi\) | ||||
0.302757 | + | 0.953068i | \(0.402093\pi\) | |||||||
\(234\) | −13.9065 | −0.909099 | ||||||||
\(235\) | 15.1009 | 0.985072 | ||||||||
\(236\) | −7.77276 | −0.505964 | ||||||||
\(237\) | −1.18969 | −0.0772784 | ||||||||
\(238\) | 1.16985 | 0.0758300 | ||||||||
\(239\) | 6.94259 | 0.449079 | 0.224539 | − | 0.974465i | \(-0.427912\pi\) | ||||
0.224539 | + | 0.974465i | \(0.427912\pi\) | |||||||
\(240\) | 10.9265 | 0.705301 | ||||||||
\(241\) | −1.53946 | −0.0991656 | −0.0495828 | − | 0.998770i | \(-0.515789\pi\) | ||||
−0.0495828 | + | 0.998770i | \(0.515789\pi\) | |||||||
\(242\) | −25.3068 | −1.62678 | ||||||||
\(243\) | 15.6187 | 1.00194 | ||||||||
\(244\) | −32.5166 | −2.08166 | ||||||||
\(245\) | 21.5880 | 1.37921 | ||||||||
\(246\) | −8.70949 | −0.555297 | ||||||||
\(247\) | 7.93722 | 0.505033 | ||||||||
\(248\) | 1.82512 | 0.115895 | ||||||||
\(249\) | 6.29120 | 0.398689 | ||||||||
\(250\) | 2.87578 | 0.181880 | ||||||||
\(251\) | 6.40614 | 0.404352 | 0.202176 | − | 0.979349i | \(-0.435199\pi\) | ||||
0.202176 | + | 0.979349i | \(0.435199\pi\) | |||||||
\(252\) | −2.45646 | −0.154743 | ||||||||
\(253\) | −1.62409 | −0.102106 | ||||||||
\(254\) | −29.1979 | −1.83204 | ||||||||
\(255\) | 3.44373 | 0.215655 | ||||||||
\(256\) | 8.99038 | 0.561899 | ||||||||
\(257\) | 23.7207 | 1.47966 | 0.739829 | − | 0.672795i | \(-0.234906\pi\) | ||||
0.739829 | + | 0.672795i | \(0.234906\pi\) | |||||||
\(258\) | 21.6303 | 1.34665 | ||||||||
\(259\) | −3.02582 | −0.188015 | ||||||||
\(260\) | 27.1785 | 1.68554 | ||||||||
\(261\) | −12.8782 | −0.797142 | ||||||||
\(262\) | −21.9352 | −1.35516 | ||||||||
\(263\) | −12.3571 | −0.761971 | −0.380985 | − | 0.924581i | \(-0.624415\pi\) | ||||
−0.380985 | + | 0.924581i | \(0.624415\pi\) | |||||||
\(264\) | 3.76336 | 0.231619 | ||||||||
\(265\) | 35.2736 | 2.16684 | ||||||||
\(266\) | 2.59439 | 0.159072 | ||||||||
\(267\) | 3.56065 | 0.217908 | ||||||||
\(268\) | −31.1778 | −1.90449 | ||||||||
\(269\) | 9.64544 | 0.588093 | 0.294046 | − | 0.955791i | \(-0.404998\pi\) | ||||
0.294046 | + | 0.955791i | \(0.404998\pi\) | |||||||
\(270\) | −34.9326 | −2.12593 | ||||||||
\(271\) | 9.23952 | 0.561261 | 0.280630 | − | 0.959816i | \(-0.409457\pi\) | ||||
0.280630 | + | 0.959816i | \(0.409457\pi\) | |||||||
\(272\) | 3.17286 | 0.192383 | ||||||||
\(273\) | −2.14049 | −0.129548 | ||||||||
\(274\) | 9.73545 | 0.588140 | ||||||||
\(275\) | −26.1008 | −1.57394 | ||||||||
\(276\) | 0.846931 | 0.0509793 | ||||||||
\(277\) | 30.1084 | 1.80904 | 0.904519 | − | 0.426433i | \(-0.140230\pi\) | ||||
0.904519 | + | 0.426433i | \(0.140230\pi\) | |||||||
\(278\) | 0.365500 | 0.0219212 | ||||||||
\(279\) | 4.63332 | 0.277390 | ||||||||
\(280\) | 1.32862 | 0.0794003 | ||||||||
\(281\) | −0.490449 | −0.0292577 | −0.0146289 | − | 0.999893i | \(-0.504657\pi\) | ||||
−0.0146289 | + | 0.999893i | \(0.504657\pi\) | |||||||
\(282\) | 10.4041 | 0.619557 | ||||||||
\(283\) | −15.2346 | −0.905600 | −0.452800 | − | 0.891612i | \(-0.649575\pi\) | ||||
−0.452800 | + | 0.891612i | \(0.649575\pi\) | |||||||
\(284\) | −8.93962 | −0.530469 | ||||||||
\(285\) | 7.63721 | 0.452390 | ||||||||
\(286\) | −35.9081 | −2.12329 | ||||||||
\(287\) | 2.19538 | 0.129589 | ||||||||
\(288\) | −15.0617 | −0.887518 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 46.5734 | 2.73489 | ||||||||
\(291\) | −10.3569 | −0.607131 | ||||||||
\(292\) | −0.484942 | −0.0283791 | ||||||||
\(293\) | 16.4987 | 0.963862 | 0.481931 | − | 0.876209i | \(-0.339936\pi\) | ||||
0.481931 | + | 0.876209i | \(0.339936\pi\) | |||||||
\(294\) | 14.8736 | 0.867447 | ||||||||
\(295\) | 10.6726 | 0.621380 | ||||||||
\(296\) | 3.95884 | 0.230103 | ||||||||
\(297\) | 24.9415 | 1.44725 | ||||||||
\(298\) | −12.1921 | −0.706272 | ||||||||
\(299\) | −1.20858 | −0.0698938 | ||||||||
\(300\) | 13.6110 | 0.785831 | ||||||||
\(301\) | −5.45231 | −0.314266 | ||||||||
\(302\) | 18.1120 | 1.04223 | ||||||||
\(303\) | −14.0176 | −0.805289 | ||||||||
\(304\) | 7.03650 | 0.403571 | ||||||||
\(305\) | 44.6476 | 2.55651 | ||||||||
\(306\) | −3.88558 | −0.222124 | ||||||||
\(307\) | −3.46829 | −0.197946 | −0.0989729 | − | 0.995090i | \(-0.531556\pi\) | ||||
−0.0989729 | + | 0.995090i | \(0.531556\pi\) | |||||||
\(308\) | −6.34284 | −0.361417 | ||||||||
\(309\) | 2.35475 | 0.133957 | ||||||||
\(310\) | −16.7562 | −0.951687 | ||||||||
\(311\) | −22.9136 | −1.29931 | −0.649656 | − | 0.760229i | \(-0.725087\pi\) | ||||
−0.649656 | + | 0.760229i | \(0.725087\pi\) | |||||||
\(312\) | 2.80052 | 0.158548 | ||||||||
\(313\) | −23.0308 | −1.30178 | −0.650888 | − | 0.759174i | \(-0.725603\pi\) | ||||
−0.650888 | + | 0.759174i | \(0.725603\pi\) | |||||||
\(314\) | 23.6915 | 1.33699 | ||||||||
\(315\) | 3.37290 | 0.190041 | ||||||||
\(316\) | −2.62341 | −0.147578 | ||||||||
\(317\) | 6.24887 | 0.350972 | 0.175486 | − | 0.984482i | \(-0.443850\pi\) | ||||
0.175486 | + | 0.984482i | \(0.443850\pi\) | |||||||
\(318\) | 24.3026 | 1.36282 | ||||||||
\(319\) | −33.2529 | −1.86181 | ||||||||
\(320\) | 33.9790 | 1.89948 | ||||||||
\(321\) | −3.02358 | −0.168760 | ||||||||
\(322\) | −0.395040 | −0.0220147 | ||||||||
\(323\) | 2.21771 | 0.123397 | ||||||||
\(324\) | 0.134670 | 0.00748167 | ||||||||
\(325\) | −19.4230 | −1.07739 | ||||||||
\(326\) | −0.00357443 | −0.000197969 0 | ||||||||
\(327\) | 1.72323 | 0.0952947 | ||||||||
\(328\) | −2.87234 | −0.158598 | ||||||||
\(329\) | −2.62254 | −0.144586 | ||||||||
\(330\) | −34.5509 | −1.90197 | ||||||||
\(331\) | 17.8893 | 0.983282 | 0.491641 | − | 0.870798i | \(-0.336397\pi\) | ||||
0.491641 | + | 0.870798i | \(0.336397\pi\) | |||||||
\(332\) | 13.8729 | 0.761374 | ||||||||
\(333\) | 10.0501 | 0.550742 | ||||||||
\(334\) | −36.1823 | −1.97981 | ||||||||
\(335\) | 42.8093 | 2.33892 | ||||||||
\(336\) | −1.89758 | −0.103522 | ||||||||
\(337\) | 10.3762 | 0.565227 | 0.282613 | − | 0.959234i | \(-0.408799\pi\) | ||||
0.282613 | + | 0.959234i | \(0.408799\pi\) | |||||||
\(338\) | 0.397803 | 0.0216376 | ||||||||
\(339\) | 10.4122 | 0.565515 | ||||||||
\(340\) | 7.59387 | 0.411835 | ||||||||
\(341\) | 11.9637 | 0.647872 | ||||||||
\(342\) | −8.61712 | −0.465960 | ||||||||
\(343\) | −7.67468 | −0.414394 | ||||||||
\(344\) | 7.13355 | 0.384615 | ||||||||
\(345\) | −1.16290 | −0.0626082 | ||||||||
\(346\) | 25.5128 | 1.37158 | ||||||||
\(347\) | −7.66934 | −0.411712 | −0.205856 | − | 0.978582i | \(-0.565998\pi\) | ||||
−0.205856 | + | 0.978582i | \(0.565998\pi\) | |||||||
\(348\) | 17.3407 | 0.929558 | ||||||||
\(349\) | 18.7418 | 1.00322 | 0.501612 | − | 0.865093i | \(-0.332740\pi\) | ||||
0.501612 | + | 0.865093i | \(0.332740\pi\) | |||||||
\(350\) | −6.34867 | −0.339351 | ||||||||
\(351\) | 18.5603 | 0.990676 | ||||||||
\(352\) | −38.8908 | −2.07289 | ||||||||
\(353\) | 1.00000 | 0.0532246 | ||||||||
\(354\) | 7.35312 | 0.390814 | ||||||||
\(355\) | 12.2747 | 0.651475 | ||||||||
\(356\) | 7.85169 | 0.416138 | ||||||||
\(357\) | −0.598068 | −0.0316531 | ||||||||
\(358\) | 37.0886 | 1.96019 | ||||||||
\(359\) | 21.1863 | 1.11817 | 0.559085 | − | 0.829110i | \(-0.311153\pi\) | ||||
0.559085 | + | 0.829110i | \(0.311153\pi\) | |||||||
\(360\) | −4.41294 | −0.232583 | ||||||||
\(361\) | −14.0817 | −0.741144 | ||||||||
\(362\) | 32.5842 | 1.71259 | ||||||||
\(363\) | 12.9377 | 0.679054 | ||||||||
\(364\) | −4.72005 | −0.247398 | ||||||||
\(365\) | 0.665860 | 0.0348527 | ||||||||
\(366\) | 30.7611 | 1.60791 | ||||||||
\(367\) | −9.38132 | −0.489701 | −0.244850 | − | 0.969561i | \(-0.578739\pi\) | ||||
−0.244850 | + | 0.969561i | \(0.578739\pi\) | |||||||
\(368\) | −1.07143 | −0.0558520 | ||||||||
\(369\) | −7.29184 | −0.379598 | ||||||||
\(370\) | −36.3457 | −1.88952 | ||||||||
\(371\) | −6.12590 | −0.318041 | ||||||||
\(372\) | −6.23883 | −0.323468 | ||||||||
\(373\) | 2.71449 | 0.140551 | 0.0702756 | − | 0.997528i | \(-0.477612\pi\) | ||||
0.0702756 | + | 0.997528i | \(0.477612\pi\) | |||||||
\(374\) | −10.0330 | −0.518793 | ||||||||
\(375\) | −1.47020 | −0.0759207 | ||||||||
\(376\) | 3.43122 | 0.176951 | ||||||||
\(377\) | −24.7453 | −1.27445 | ||||||||
\(378\) | 6.06669 | 0.312037 | ||||||||
\(379\) | −1.60046 | −0.0822100 | −0.0411050 | − | 0.999155i | \(-0.513088\pi\) | ||||
−0.0411050 | + | 0.999155i | \(0.513088\pi\) | |||||||
\(380\) | 16.8410 | 0.863927 | ||||||||
\(381\) | 14.9270 | 0.764733 | ||||||||
\(382\) | 42.2279 | 2.16057 | ||||||||
\(383\) | −34.5022 | −1.76298 | −0.881490 | − | 0.472202i | \(-0.843459\pi\) | ||||
−0.881490 | + | 0.472202i | \(0.843459\pi\) | |||||||
\(384\) | 6.16308 | 0.314508 | ||||||||
\(385\) | 8.70917 | 0.443860 | ||||||||
\(386\) | −6.07392 | −0.309154 | ||||||||
\(387\) | 18.1095 | 0.920560 | ||||||||
\(388\) | −22.8382 | −1.15944 | ||||||||
\(389\) | −7.02093 | −0.355975 | −0.177988 | − | 0.984033i | \(-0.556959\pi\) | ||||
−0.177988 | + | 0.984033i | \(0.556959\pi\) | |||||||
\(390\) | −25.7112 | −1.30194 | ||||||||
\(391\) | −0.337685 | −0.0170775 | ||||||||
\(392\) | 4.90523 | 0.247751 | ||||||||
\(393\) | 11.2141 | 0.565675 | ||||||||
\(394\) | 10.6054 | 0.534294 | ||||||||
\(395\) | 3.60213 | 0.181243 | ||||||||
\(396\) | 21.0674 | 1.05868 | ||||||||
\(397\) | −27.7653 | −1.39350 | −0.696751 | − | 0.717313i | \(-0.745372\pi\) | ||||
−0.696751 | + | 0.717313i | \(0.745372\pi\) | |||||||
\(398\) | −9.34524 | −0.468435 | ||||||||
\(399\) | −1.32634 | −0.0664002 | ||||||||
\(400\) | −17.2189 | −0.860943 | ||||||||
\(401\) | 8.77925 | 0.438415 | 0.219207 | − | 0.975678i | \(-0.429653\pi\) | ||||
0.219207 | + | 0.975678i | \(0.429653\pi\) | |||||||
\(402\) | 29.4945 | 1.47105 | ||||||||
\(403\) | 8.90286 | 0.443483 | ||||||||
\(404\) | −30.9106 | −1.53786 | ||||||||
\(405\) | −0.184912 | −0.00918833 | ||||||||
\(406\) | −8.08833 | −0.401417 | ||||||||
\(407\) | 25.9504 | 1.28631 | ||||||||
\(408\) | 0.782484 | 0.0387387 | ||||||||
\(409\) | 2.23229 | 0.110380 | 0.0551899 | − | 0.998476i | \(-0.482424\pi\) | ||||
0.0551899 | + | 0.998476i | \(0.482424\pi\) | |||||||
\(410\) | 26.3706 | 1.30235 | ||||||||
\(411\) | −4.97711 | −0.245502 | ||||||||
\(412\) | 5.19252 | 0.255817 | ||||||||
\(413\) | −1.85349 | −0.0912041 | ||||||||
\(414\) | 1.31210 | 0.0644864 | ||||||||
\(415\) | −19.0485 | −0.935053 | ||||||||
\(416\) | −28.9408 | −1.41894 | ||||||||
\(417\) | −0.186856 | −0.00915040 | ||||||||
\(418\) | −22.2503 | −1.08830 | ||||||||
\(419\) | −15.9671 | −0.780043 | −0.390022 | − | 0.920806i | \(-0.627532\pi\) | ||||
−0.390022 | + | 0.920806i | \(0.627532\pi\) | |||||||
\(420\) | −4.54165 | −0.221610 | ||||||||
\(421\) | −14.2219 | −0.693135 | −0.346568 | − | 0.938025i | \(-0.612653\pi\) | ||||
−0.346568 | + | 0.938025i | \(0.612653\pi\) | |||||||
\(422\) | 11.3479 | 0.552409 | ||||||||
\(423\) | 8.71064 | 0.423526 | ||||||||
\(424\) | 8.01485 | 0.389236 | ||||||||
\(425\) | −5.42692 | −0.263244 | ||||||||
\(426\) | 8.45699 | 0.409742 | ||||||||
\(427\) | −7.75388 | −0.375237 | ||||||||
\(428\) | −6.66739 | −0.322281 | ||||||||
\(429\) | 18.3575 | 0.886309 | ||||||||
\(430\) | −65.4922 | −3.15832 | ||||||||
\(431\) | −5.90289 | −0.284332 | −0.142166 | − | 0.989843i | \(-0.545407\pi\) | ||||
−0.142166 | + | 0.989843i | \(0.545407\pi\) | |||||||
\(432\) | 16.4541 | 0.791647 | ||||||||
\(433\) | 19.6620 | 0.944894 | 0.472447 | − | 0.881359i | \(-0.343371\pi\) | ||||
0.472447 | + | 0.881359i | \(0.343371\pi\) | |||||||
\(434\) | 2.91002 | 0.139685 | ||||||||
\(435\) | −23.8100 | −1.14160 | ||||||||
\(436\) | 3.79994 | 0.181984 | ||||||||
\(437\) | −0.748889 | −0.0358242 | ||||||||
\(438\) | 0.458761 | 0.0219204 | ||||||||
\(439\) | 26.8979 | 1.28376 | 0.641882 | − | 0.766803i | \(-0.278154\pi\) | ||||
0.641882 | + | 0.766803i | \(0.278154\pi\) | |||||||
\(440\) | −11.3947 | −0.543220 | ||||||||
\(441\) | 12.4526 | 0.592982 | ||||||||
\(442\) | −7.46609 | −0.355126 | ||||||||
\(443\) | −18.2912 | −0.869041 | −0.434521 | − | 0.900662i | \(-0.643082\pi\) | ||||
−0.434521 | + | 0.900662i | \(0.643082\pi\) | |||||||
\(444\) | −13.5326 | −0.642228 | ||||||||
\(445\) | −10.7809 | −0.511065 | ||||||||
\(446\) | −40.9809 | −1.94050 | ||||||||
\(447\) | 6.23305 | 0.294813 | ||||||||
\(448\) | −5.90107 | −0.278800 | ||||||||
\(449\) | −37.7023 | −1.77928 | −0.889642 | − | 0.456659i | \(-0.849046\pi\) | ||||
−0.889642 | + | 0.456659i | \(0.849046\pi\) | |||||||
\(450\) | 21.0868 | 0.994039 | ||||||||
\(451\) | −18.8283 | −0.886590 | ||||||||
\(452\) | 22.9603 | 1.07996 | ||||||||
\(453\) | −9.25949 | −0.435049 | ||||||||
\(454\) | −16.7337 | −0.785353 | ||||||||
\(455\) | 6.48097 | 0.303832 | ||||||||
\(456\) | 1.73533 | 0.0812641 | ||||||||
\(457\) | 27.8993 | 1.30507 | 0.652537 | − | 0.757756i | \(-0.273705\pi\) | ||||
0.652537 | + | 0.757756i | \(0.273705\pi\) | |||||||
\(458\) | 50.1963 | 2.34552 | ||||||||
\(459\) | 5.18588 | 0.242056 | ||||||||
\(460\) | −2.56433 | −0.119563 | ||||||||
\(461\) | −23.1024 | −1.07598 | −0.537992 | − | 0.842950i | \(-0.680817\pi\) | ||||
−0.537992 | + | 0.842950i | \(0.680817\pi\) | |||||||
\(462\) | 6.00040 | 0.279164 | ||||||||
\(463\) | 20.6800 | 0.961081 | 0.480541 | − | 0.876972i | \(-0.340440\pi\) | ||||
0.480541 | + | 0.876972i | \(0.340440\pi\) | |||||||
\(464\) | −21.9372 | −1.01841 | ||||||||
\(465\) | 8.56635 | 0.397255 | ||||||||
\(466\) | −19.2812 | −0.893182 | ||||||||
\(467\) | −9.36778 | −0.433489 | −0.216745 | − | 0.976228i | \(-0.569544\pi\) | ||||
−0.216745 | + | 0.976228i | \(0.569544\pi\) | |||||||
\(468\) | 15.6774 | 0.724688 | ||||||||
\(469\) | −7.43462 | −0.343299 | ||||||||
\(470\) | −31.5016 | −1.45306 | ||||||||
\(471\) | −12.1120 | −0.558090 | ||||||||
\(472\) | 2.42502 | 0.111620 | ||||||||
\(473\) | 46.7607 | 2.15006 | ||||||||
\(474\) | 2.48178 | 0.113992 | ||||||||
\(475\) | −12.0354 | −0.552220 | ||||||||
\(476\) | −1.31882 | −0.0604478 | ||||||||
\(477\) | 20.3469 | 0.931619 | ||||||||
\(478\) | −14.4828 | −0.662427 | ||||||||
\(479\) | 27.1593 | 1.24094 | 0.620469 | − | 0.784231i | \(-0.286942\pi\) | ||||
0.620469 | + | 0.784231i | \(0.286942\pi\) | |||||||
\(480\) | −27.8469 | −1.27103 | ||||||||
\(481\) | 19.3111 | 0.880510 | ||||||||
\(482\) | 3.21144 | 0.146277 | ||||||||
\(483\) | 0.201958 | 0.00918942 | ||||||||
\(484\) | 28.5293 | 1.29679 | ||||||||
\(485\) | 31.3585 | 1.42392 | ||||||||
\(486\) | −32.5818 | −1.47794 | ||||||||
\(487\) | −5.08454 | −0.230402 | −0.115201 | − | 0.993342i | \(-0.536751\pi\) | ||||
−0.115201 | + | 0.993342i | \(0.536751\pi\) | |||||||
\(488\) | 10.1448 | 0.459234 | ||||||||
\(489\) | 0.00182737 | 8.26367e−5 0 | ||||||||
\(490\) | −45.0343 | −2.03444 | ||||||||
\(491\) | 25.0489 | 1.13044 | 0.565221 | − | 0.824939i | \(-0.308791\pi\) | ||||
0.565221 | + | 0.824939i | \(0.308791\pi\) | |||||||
\(492\) | 9.81856 | 0.442655 | ||||||||
\(493\) | −6.91401 | −0.311391 | ||||||||
\(494\) | −16.5577 | −0.744964 | ||||||||
\(495\) | −28.9270 | −1.30017 | ||||||||
\(496\) | 7.89255 | 0.354386 | ||||||||
\(497\) | −2.13173 | −0.0956213 | ||||||||
\(498\) | −13.1239 | −0.588097 | ||||||||
\(499\) | 25.1580 | 1.12623 | 0.563114 | − | 0.826379i | \(-0.309603\pi\) | ||||
0.563114 | + | 0.826379i | \(0.309603\pi\) | |||||||
\(500\) | −3.24198 | −0.144986 | ||||||||
\(501\) | 18.4977 | 0.826416 | ||||||||
\(502\) | −13.3637 | −0.596451 | ||||||||
\(503\) | −13.4428 | −0.599384 | −0.299692 | − | 0.954036i | \(-0.596884\pi\) | ||||
−0.299692 | + | 0.954036i | \(0.596884\pi\) | |||||||
\(504\) | 0.766389 | 0.0341377 | ||||||||
\(505\) | 42.4424 | 1.88866 | ||||||||
\(506\) | 3.38799 | 0.150614 | ||||||||
\(507\) | −0.203371 | −0.00903202 | ||||||||
\(508\) | 32.9159 | 1.46041 | ||||||||
\(509\) | −1.48980 | −0.0660342 | −0.0330171 | − | 0.999455i | \(-0.510512\pi\) | ||||
−0.0330171 | + | 0.999455i | \(0.510512\pi\) | |||||||
\(510\) | −7.18389 | −0.318108 | ||||||||
\(511\) | −0.115639 | −0.00511556 | ||||||||
\(512\) | −30.3125 | −1.33963 | ||||||||
\(513\) | 11.5008 | 0.507773 | ||||||||
\(514\) | −49.4833 | −2.18261 | ||||||||
\(515\) | −7.12970 | −0.314172 | ||||||||
\(516\) | −24.3847 | −1.07348 | ||||||||
\(517\) | 22.4918 | 0.989187 | ||||||||
\(518\) | 6.31209 | 0.277337 | ||||||||
\(519\) | −13.0430 | −0.572526 | ||||||||
\(520\) | −8.47940 | −0.371846 | ||||||||
\(521\) | −4.19345 | −0.183718 | −0.0918591 | − | 0.995772i | \(-0.529281\pi\) | ||||
−0.0918591 | + | 0.995772i | \(0.529281\pi\) | |||||||
\(522\) | 26.8650 | 1.17585 | ||||||||
\(523\) | −28.6471 | −1.25265 | −0.626325 | − | 0.779562i | \(-0.715442\pi\) | ||||
−0.626325 | + | 0.779562i | \(0.715442\pi\) | |||||||
\(524\) | 24.7285 | 1.08027 | ||||||||
\(525\) | 3.24567 | 0.141652 | ||||||||
\(526\) | 25.7778 | 1.12397 | ||||||||
\(527\) | 2.48752 | 0.108358 | ||||||||
\(528\) | 16.2743 | 0.708248 | ||||||||
\(529\) | −22.8860 | −0.995042 | ||||||||
\(530\) | −73.5834 | −3.19626 | ||||||||
\(531\) | 6.15625 | 0.267159 | ||||||||
\(532\) | −2.92476 | −0.126804 | ||||||||
\(533\) | −14.0112 | −0.606891 | ||||||||
\(534\) | −7.42779 | −0.321432 | ||||||||
\(535\) | 9.15480 | 0.395796 | ||||||||
\(536\) | 9.72712 | 0.420147 | ||||||||
\(537\) | −18.9610 | −0.818227 | ||||||||
\(538\) | −20.1211 | −0.867484 | ||||||||
\(539\) | 32.1540 | 1.38497 | ||||||||
\(540\) | 39.3809 | 1.69468 | ||||||||
\(541\) | 5.18487 | 0.222915 | 0.111457 | − | 0.993769i | \(-0.464448\pi\) | ||||
0.111457 | + | 0.993769i | \(0.464448\pi\) | |||||||
\(542\) | −19.2743 | −0.827904 | ||||||||
\(543\) | −16.6582 | −0.714871 | ||||||||
\(544\) | −8.08625 | −0.346695 | ||||||||
\(545\) | −5.21758 | −0.223497 | ||||||||
\(546\) | 4.46523 | 0.191094 | ||||||||
\(547\) | −19.4823 | −0.833004 | −0.416502 | − | 0.909135i | \(-0.636744\pi\) | ||||
−0.416502 | + | 0.909135i | \(0.636744\pi\) | |||||||
\(548\) | −10.9752 | −0.468835 | ||||||||
\(549\) | 25.7541 | 1.09916 | ||||||||
\(550\) | 54.4482 | 2.32168 | ||||||||
\(551\) | −15.3333 | −0.653220 | ||||||||
\(552\) | −0.264233 | −0.0112465 | ||||||||
\(553\) | −0.625576 | −0.0266022 | ||||||||
\(554\) | −62.8085 | −2.66848 | ||||||||
\(555\) | 18.5812 | 0.788728 | ||||||||
\(556\) | −0.412042 | −0.0174745 | ||||||||
\(557\) | −28.4787 | −1.20668 | −0.603340 | − | 0.797484i | \(-0.706164\pi\) | ||||
−0.603340 | + | 0.797484i | \(0.706164\pi\) | |||||||
\(558\) | −9.66547 | −0.409172 | ||||||||
\(559\) | 34.7972 | 1.47176 | ||||||||
\(560\) | 5.74550 | 0.242792 | ||||||||
\(561\) | 5.12922 | 0.216556 | ||||||||
\(562\) | 1.02311 | 0.0431575 | ||||||||
\(563\) | −14.7093 | −0.619924 | −0.309962 | − | 0.950749i | \(-0.600316\pi\) | ||||
−0.309962 | + | 0.950749i | \(0.600316\pi\) | |||||||
\(564\) | −11.7290 | −0.493879 | ||||||||
\(565\) | −31.5261 | −1.32631 | ||||||||
\(566\) | 31.7805 | 1.33583 | ||||||||
\(567\) | 0.0321133 | 0.00134863 | ||||||||
\(568\) | 2.78906 | 0.117026 | ||||||||
\(569\) | 7.97714 | 0.334419 | 0.167210 | − | 0.985921i | \(-0.446524\pi\) | ||||
0.167210 | + | 0.985921i | \(0.446524\pi\) | |||||||
\(570\) | −15.9318 | −0.667310 | ||||||||
\(571\) | 8.20806 | 0.343496 | 0.171748 | − | 0.985141i | \(-0.445058\pi\) | ||||
0.171748 | + | 0.985141i | \(0.445058\pi\) | |||||||
\(572\) | 40.4807 | 1.69258 | ||||||||
\(573\) | −21.5884 | −0.901869 | ||||||||
\(574\) | −4.57974 | −0.191155 | ||||||||
\(575\) | 1.83259 | 0.0764242 | ||||||||
\(576\) | 19.6001 | 0.816671 | ||||||||
\(577\) | 5.63411 | 0.234551 | 0.117275 | − | 0.993099i | \(-0.462584\pi\) | ||||
0.117275 | + | 0.993099i | \(0.462584\pi\) | |||||||
\(578\) | −2.08608 | −0.0867694 | ||||||||
\(579\) | 3.10520 | 0.129048 | ||||||||
\(580\) | −52.5041 | −2.18011 | ||||||||
\(581\) | 3.30812 | 0.137244 | ||||||||
\(582\) | 21.6052 | 0.895566 | ||||||||
\(583\) | 52.5377 | 2.17589 | ||||||||
\(584\) | 0.151297 | 0.00626070 | ||||||||
\(585\) | −21.5262 | −0.889998 | ||||||||
\(586\) | −34.4175 | −1.42177 | ||||||||
\(587\) | −5.23935 | −0.216251 | −0.108126 | − | 0.994137i | \(-0.534485\pi\) | ||||
−0.108126 | + | 0.994137i | \(0.534485\pi\) | |||||||
\(588\) | −16.7676 | −0.691485 | ||||||||
\(589\) | 5.51661 | 0.227308 | ||||||||
\(590\) | −22.2638 | −0.916585 | ||||||||
\(591\) | −5.42187 | −0.223026 | ||||||||
\(592\) | 17.1197 | 0.703614 | ||||||||
\(593\) | −1.19935 | −0.0492513 | −0.0246257 | − | 0.999697i | \(-0.507839\pi\) | ||||
−0.0246257 | + | 0.999697i | \(0.507839\pi\) | |||||||
\(594\) | −52.0298 | −2.13481 | ||||||||
\(595\) | 1.81083 | 0.0742367 | ||||||||
\(596\) | 13.7447 | 0.563004 | ||||||||
\(597\) | 4.77762 | 0.195535 | ||||||||
\(598\) | 2.52119 | 0.103099 | ||||||||
\(599\) | −21.0202 | −0.858862 | −0.429431 | − | 0.903100i | \(-0.641286\pi\) | ||||
−0.429431 | + | 0.903100i | \(0.641286\pi\) | |||||||
\(600\) | −4.24648 | −0.173362 | ||||||||
\(601\) | 16.9386 | 0.690939 | 0.345470 | − | 0.938430i | \(-0.387720\pi\) | ||||
0.345470 | + | 0.938430i | \(0.387720\pi\) | |||||||
\(602\) | 11.3739 | 0.463567 | ||||||||
\(603\) | 24.6937 | 1.00560 | ||||||||
\(604\) | −20.4184 | −0.830812 | ||||||||
\(605\) | −39.1728 | −1.59260 | ||||||||
\(606\) | 29.2418 | 1.18787 | ||||||||
\(607\) | −19.7260 | −0.800655 | −0.400328 | − | 0.916372i | \(-0.631104\pi\) | ||||
−0.400328 | + | 0.916372i | \(0.631104\pi\) | |||||||
\(608\) | −17.9330 | −0.727279 | ||||||||
\(609\) | 4.13504 | 0.167560 | ||||||||
\(610\) | −93.1383 | −3.77106 | ||||||||
\(611\) | 16.7373 | 0.677121 | ||||||||
\(612\) | 4.38037 | 0.177066 | ||||||||
\(613\) | 21.4113 | 0.864795 | 0.432398 | − | 0.901683i | \(-0.357668\pi\) | ||||
0.432398 | + | 0.901683i | \(0.357668\pi\) | |||||||
\(614\) | 7.23512 | 0.291986 | ||||||||
\(615\) | −13.4816 | −0.543630 | ||||||||
\(616\) | 1.97890 | 0.0797320 | ||||||||
\(617\) | 25.4589 | 1.02494 | 0.512469 | − | 0.858706i | \(-0.328731\pi\) | ||||
0.512469 | + | 0.858706i | \(0.328731\pi\) | |||||||
\(618\) | −4.91219 | −0.197597 | ||||||||
\(619\) | 35.3510 | 1.42088 | 0.710439 | − | 0.703759i | \(-0.248496\pi\) | ||||
0.710439 | + | 0.703759i | \(0.248496\pi\) | |||||||
\(620\) | 18.8899 | 0.758637 | ||||||||
\(621\) | −1.75119 | −0.0702729 | ||||||||
\(622\) | 47.7995 | 1.91659 | ||||||||
\(623\) | 1.87231 | 0.0750123 | ||||||||
\(624\) | 12.1106 | 0.484811 | ||||||||
\(625\) | −22.6831 | −0.907326 | ||||||||
\(626\) | 48.0439 | 1.92022 | ||||||||
\(627\) | 11.3751 | 0.454279 | ||||||||
\(628\) | −26.7084 | −1.06578 | ||||||||
\(629\) | 5.39565 | 0.215139 | ||||||||
\(630\) | −7.03612 | −0.280326 | ||||||||
\(631\) | 4.31592 | 0.171814 | 0.0859070 | − | 0.996303i | \(-0.472621\pi\) | ||||
0.0859070 | + | 0.996303i | \(0.472621\pi\) | |||||||
\(632\) | 0.818474 | 0.0325572 | ||||||||
\(633\) | −5.80147 | −0.230588 | ||||||||
\(634\) | −13.0356 | −0.517711 | ||||||||
\(635\) | −45.1959 | −1.79354 | ||||||||
\(636\) | −27.3973 | −1.08637 | ||||||||
\(637\) | 23.9275 | 0.948043 | ||||||||
\(638\) | 69.3681 | 2.74631 | ||||||||
\(639\) | 7.08044 | 0.280098 | ||||||||
\(640\) | −18.6605 | −0.737623 | ||||||||
\(641\) | 17.9220 | 0.707877 | 0.353938 | − | 0.935269i | \(-0.384842\pi\) | ||||
0.353938 | + | 0.935269i | \(0.384842\pi\) | |||||||
\(642\) | 6.30743 | 0.248934 | ||||||||
\(643\) | −25.8639 | −1.01997 | −0.509986 | − | 0.860183i | \(-0.670350\pi\) | ||||
−0.509986 | + | 0.860183i | \(0.670350\pi\) | |||||||
\(644\) | 0.445344 | 0.0175490 | ||||||||
\(645\) | 33.4820 | 1.31835 | ||||||||
\(646\) | −4.62632 | −0.182020 | ||||||||
\(647\) | 22.6735 | 0.891387 | 0.445694 | − | 0.895186i | \(-0.352957\pi\) | ||||
0.445694 | + | 0.895186i | \(0.352957\pi\) | |||||||
\(648\) | −0.0420156 | −0.00165053 | ||||||||
\(649\) | 15.8961 | 0.623976 | ||||||||
\(650\) | 40.5179 | 1.58924 | ||||||||
\(651\) | −1.48771 | −0.0583078 | ||||||||
\(652\) | 0.00402959 | 0.000157811 0 | ||||||||
\(653\) | 26.1553 | 1.02354 | 0.511768 | − | 0.859124i | \(-0.328991\pi\) | ||||
0.511768 | + | 0.859124i | \(0.328991\pi\) | |||||||
\(654\) | −3.59478 | −0.140567 | ||||||||
\(655\) | −33.9539 | −1.32669 | ||||||||
\(656\) | −12.4212 | −0.484965 | ||||||||
\(657\) | 0.384088 | 0.0149847 | ||||||||
\(658\) | 5.47083 | 0.213275 | ||||||||
\(659\) | 2.80826 | 0.109394 | 0.0546971 | − | 0.998503i | \(-0.482581\pi\) | ||||
0.0546971 | + | 0.998503i | \(0.482581\pi\) | |||||||
\(660\) | 38.9506 | 1.51615 | ||||||||
\(661\) | 40.7092 | 1.58340 | 0.791702 | − | 0.610908i | \(-0.209195\pi\) | ||||
0.791702 | + | 0.610908i | \(0.209195\pi\) | |||||||
\(662\) | −37.3184 | −1.45042 | ||||||||
\(663\) | 3.81693 | 0.148237 | ||||||||
\(664\) | −4.32819 | −0.167966 | ||||||||
\(665\) | 4.01590 | 0.155730 | ||||||||
\(666\) | −20.9653 | −0.812388 | ||||||||
\(667\) | 2.33476 | 0.0904021 | ||||||||
\(668\) | 40.7898 | 1.57820 | ||||||||
\(669\) | 20.9509 | 0.810009 | ||||||||
\(670\) | −89.3035 | −3.45009 | ||||||||
\(671\) | 66.4997 | 2.56719 | ||||||||
\(672\) | 4.83612 | 0.186558 | ||||||||
\(673\) | −10.1874 | −0.392695 | −0.196348 | − | 0.980534i | \(-0.562908\pi\) | ||||
−0.196348 | + | 0.980534i | \(0.562908\pi\) | |||||||
\(674\) | −21.6455 | −0.833754 | ||||||||
\(675\) | −28.1433 | −1.08324 | ||||||||
\(676\) | −0.448459 | −0.0172484 | ||||||||
\(677\) | 16.2983 | 0.626394 | 0.313197 | − | 0.949688i | \(-0.398600\pi\) | ||||
0.313197 | + | 0.949688i | \(0.398600\pi\) | |||||||
\(678\) | −21.7207 | −0.834179 | ||||||||
\(679\) | −5.44598 | −0.208998 | ||||||||
\(680\) | −2.36920 | −0.0908548 | ||||||||
\(681\) | 8.55487 | 0.327824 | ||||||||
\(682\) | −24.9573 | −0.955663 | ||||||||
\(683\) | 29.7744 | 1.13929 | 0.569643 | − | 0.821893i | \(-0.307082\pi\) | ||||
0.569643 | + | 0.821893i | \(0.307082\pi\) | |||||||
\(684\) | 9.71442 | 0.371440 | ||||||||
\(685\) | 15.0697 | 0.575782 | ||||||||
\(686\) | 16.0100 | 0.611263 | ||||||||
\(687\) | −25.6621 | −0.979071 | ||||||||
\(688\) | 30.8484 | 1.17608 | ||||||||
\(689\) | 39.0962 | 1.48944 | ||||||||
\(690\) | 2.42589 | 0.0923521 | ||||||||
\(691\) | −36.4041 | −1.38488 | −0.692439 | − | 0.721476i | \(-0.743464\pi\) | ||||
−0.692439 | + | 0.721476i | \(0.743464\pi\) | |||||||
\(692\) | −28.7616 | −1.09335 | ||||||||
\(693\) | 5.02371 | 0.190835 | ||||||||
\(694\) | 15.9988 | 0.607307 | ||||||||
\(695\) | 0.565763 | 0.0214606 | ||||||||
\(696\) | −5.41010 | −0.205069 | ||||||||
\(697\) | −3.91482 | −0.148284 | ||||||||
\(698\) | −39.0968 | −1.47984 | ||||||||
\(699\) | 9.85721 | 0.372834 | ||||||||
\(700\) | 7.15711 | 0.270513 | ||||||||
\(701\) | 16.7515 | 0.632696 | 0.316348 | − | 0.948643i | \(-0.397543\pi\) | ||||
0.316348 | + | 0.948643i | \(0.397543\pi\) | |||||||
\(702\) | −38.7182 | −1.46133 | ||||||||
\(703\) | 11.9660 | 0.451307 | ||||||||
\(704\) | 50.6095 | 1.90742 | ||||||||
\(705\) | 16.1047 | 0.606539 | ||||||||
\(706\) | −2.08608 | −0.0785105 | ||||||||
\(707\) | −7.37090 | −0.277211 | ||||||||
\(708\) | −8.28947 | −0.311537 | ||||||||
\(709\) | 38.0588 | 1.42933 | 0.714664 | − | 0.699467i | \(-0.246579\pi\) | ||||
0.714664 | + | 0.699467i | \(0.246579\pi\) | |||||||
\(710\) | −25.6060 | −0.960977 | ||||||||
\(711\) | 2.07782 | 0.0779242 | ||||||||
\(712\) | −2.44964 | −0.0918041 | ||||||||
\(713\) | −0.839998 | −0.0314582 | ||||||||
\(714\) | 1.24762 | 0.0466908 | ||||||||
\(715\) | −55.5828 | −2.07868 | ||||||||
\(716\) | −41.8114 | −1.56257 | ||||||||
\(717\) | 7.40411 | 0.276512 | ||||||||
\(718\) | −44.1962 | −1.64939 | ||||||||
\(719\) | 13.0052 | 0.485011 | 0.242505 | − | 0.970150i | \(-0.422031\pi\) | ||||
0.242505 | + | 0.970150i | \(0.422031\pi\) | |||||||
\(720\) | −19.0834 | −0.711195 | ||||||||
\(721\) | 1.23820 | 0.0461131 | ||||||||
\(722\) | 29.3756 | 1.09325 | ||||||||
\(723\) | −1.64180 | −0.0610593 | ||||||||
\(724\) | −36.7334 | −1.36519 | ||||||||
\(725\) | 37.5218 | 1.39352 | ||||||||
\(726\) | −26.9891 | −1.00166 | ||||||||
\(727\) | −6.67830 | −0.247684 | −0.123842 | − | 0.992302i | \(-0.539522\pi\) | ||||
−0.123842 | + | 0.992302i | \(0.539522\pi\) | |||||||
\(728\) | 1.47260 | 0.0545783 | ||||||||
\(729\) | 16.4852 | 0.610563 | ||||||||
\(730\) | −1.38904 | −0.0514105 | ||||||||
\(731\) | 9.72258 | 0.359603 | ||||||||
\(732\) | −34.6782 | −1.28174 | ||||||||
\(733\) | −33.0732 | −1.22159 | −0.610794 | − | 0.791790i | \(-0.709150\pi\) | ||||
−0.610794 | + | 0.791790i | \(0.709150\pi\) | |||||||
\(734\) | 19.5702 | 0.722348 | ||||||||
\(735\) | 23.0231 | 0.849221 | ||||||||
\(736\) | 2.73060 | 0.100651 | ||||||||
\(737\) | 63.7617 | 2.34869 | ||||||||
\(738\) | 15.2113 | 0.559937 | ||||||||
\(739\) | −0.193535 | −0.00711931 | −0.00355966 | − | 0.999994i | \(-0.501133\pi\) | ||||
−0.00355966 | + | 0.999994i | \(0.501133\pi\) | |||||||
\(740\) | 40.9739 | 1.50623 | ||||||||
\(741\) | 8.46486 | 0.310964 | ||||||||
\(742\) | 12.7791 | 0.469136 | ||||||||
\(743\) | 18.5264 | 0.679667 | 0.339833 | − | 0.940486i | \(-0.389629\pi\) | ||||
0.339833 | + | 0.940486i | \(0.389629\pi\) | |||||||
\(744\) | 1.94645 | 0.0713601 | ||||||||
\(745\) | −18.8724 | −0.691432 | ||||||||
\(746\) | −5.66264 | −0.207324 | ||||||||
\(747\) | −10.9877 | −0.402020 | ||||||||
\(748\) | 11.3106 | 0.413556 | ||||||||
\(749\) | −1.58990 | −0.0580937 | ||||||||
\(750\) | 3.06695 | 0.111989 | ||||||||
\(751\) | −21.4966 | −0.784423 | −0.392211 | − | 0.919875i | \(-0.628290\pi\) | ||||
−0.392211 | + | 0.919875i | \(0.628290\pi\) | |||||||
\(752\) | 14.8380 | 0.541085 | ||||||||
\(753\) | 6.83200 | 0.248972 | ||||||||
\(754\) | 51.6206 | 1.87991 | ||||||||
\(755\) | 28.0359 | 1.02033 | ||||||||
\(756\) | −6.83922 | −0.248740 | ||||||||
\(757\) | −33.2874 | −1.20985 | −0.604926 | − | 0.796282i | \(-0.706797\pi\) | ||||
−0.604926 | + | 0.796282i | \(0.706797\pi\) | |||||||
\(758\) | 3.33868 | 0.121266 | ||||||||
\(759\) | −1.73206 | −0.0628698 | ||||||||
\(760\) | −5.25422 | −0.190590 | ||||||||
\(761\) | −14.6687 | −0.531739 | −0.265869 | − | 0.964009i | \(-0.585659\pi\) | ||||
−0.265869 | + | 0.964009i | \(0.585659\pi\) | |||||||
\(762\) | −31.1389 | −1.12804 | ||||||||
\(763\) | 0.906129 | 0.0328041 | ||||||||
\(764\) | −47.6052 | −1.72230 | ||||||||
\(765\) | −6.01456 | −0.217457 | ||||||||
\(766\) | 71.9743 | 2.60054 | ||||||||
\(767\) | 11.8291 | 0.427125 | ||||||||
\(768\) | 9.58803 | 0.345978 | ||||||||
\(769\) | 3.73594 | 0.134722 | 0.0673608 | − | 0.997729i | \(-0.478542\pi\) | ||||
0.0673608 | + | 0.997729i | \(0.478542\pi\) | |||||||
\(770\) | −18.1680 | −0.654729 | ||||||||
\(771\) | 25.2976 | 0.911071 | ||||||||
\(772\) | 6.84737 | 0.246442 | ||||||||
\(773\) | 35.4005 | 1.27327 | 0.636634 | − | 0.771166i | \(-0.280326\pi\) | ||||
0.636634 | + | 0.771166i | \(0.280326\pi\) | |||||||
\(774\) | −37.7779 | −1.35790 | ||||||||
\(775\) | −13.4996 | −0.484919 | ||||||||
\(776\) | 7.12528 | 0.255783 | ||||||||
\(777\) | −3.22697 | −0.115767 | ||||||||
\(778\) | 14.6462 | 0.525092 | ||||||||
\(779\) | −8.68194 | −0.311063 | ||||||||
\(780\) | 28.9853 | 1.03784 | ||||||||
\(781\) | 18.2824 | 0.654197 | ||||||||
\(782\) | 0.704437 | 0.0251906 | ||||||||
\(783\) | −35.8552 | −1.28136 | ||||||||
\(784\) | 21.2122 | 0.757579 | ||||||||
\(785\) | 36.6725 | 1.30890 | ||||||||
\(786\) | −23.3934 | −0.834416 | ||||||||
\(787\) | 12.6983 | 0.452644 | 0.226322 | − | 0.974053i | \(-0.427330\pi\) | ||||
0.226322 | + | 0.974053i | \(0.427330\pi\) | |||||||
\(788\) | −11.9559 | −0.425912 | ||||||||
\(789\) | −13.1785 | −0.469169 | ||||||||
\(790\) | −7.51431 | −0.267347 | ||||||||
\(791\) | 5.47509 | 0.194672 | ||||||||
\(792\) | −6.57280 | −0.233554 | ||||||||
\(793\) | 49.4861 | 1.75730 | ||||||||
\(794\) | 57.9206 | 2.05552 | ||||||||
\(795\) | 37.6184 | 1.33419 | ||||||||
\(796\) | 10.5353 | 0.373412 | ||||||||
\(797\) | 9.88699 | 0.350215 | 0.175108 | − | 0.984549i | \(-0.443973\pi\) | ||||
0.175108 | + | 0.984549i | \(0.443973\pi\) | |||||||
\(798\) | 2.76685 | 0.0979456 | ||||||||
\(799\) | 4.67653 | 0.165444 | ||||||||
\(800\) | 43.8834 | 1.55151 | ||||||||
\(801\) | −6.21876 | −0.219729 | ||||||||
\(802\) | −18.3142 | −0.646696 | ||||||||
\(803\) | 0.991756 | 0.0349983 | ||||||||
\(804\) | −33.2504 | −1.17265 | ||||||||
\(805\) | −0.611489 | −0.0215521 | ||||||||
\(806\) | −18.5720 | −0.654172 | ||||||||
\(807\) | 10.2866 | 0.362107 | ||||||||
\(808\) | 9.64375 | 0.339266 | ||||||||
\(809\) | 2.09291 | 0.0735826 | 0.0367913 | − | 0.999323i | \(-0.488286\pi\) | ||||
0.0367913 | + | 0.999323i | \(0.488286\pi\) | |||||||
\(810\) | 0.385740 | 0.0135535 | ||||||||
\(811\) | 29.4504 | 1.03414 | 0.517072 | − | 0.855942i | \(-0.327022\pi\) | ||||
0.517072 | + | 0.855942i | \(0.327022\pi\) | |||||||
\(812\) | 9.11830 | 0.319990 | ||||||||
\(813\) | 9.85373 | 0.345585 | ||||||||
\(814\) | −54.1345 | −1.89741 | ||||||||
\(815\) | −0.00553291 | −0.000193810 0 | ||||||||
\(816\) | 3.38378 | 0.118456 | ||||||||
\(817\) | 21.5619 | 0.754355 | ||||||||
\(818\) | −4.65674 | −0.162819 | ||||||||
\(819\) | 3.73842 | 0.130631 | ||||||||
\(820\) | −29.7286 | −1.03817 | ||||||||
\(821\) | −48.2691 | −1.68460 | −0.842302 | − | 0.539005i | \(-0.818800\pi\) | ||||
−0.842302 | + | 0.539005i | \(0.818800\pi\) | |||||||
\(822\) | 10.3826 | 0.362136 | ||||||||
\(823\) | −45.9851 | −1.60294 | −0.801469 | − | 0.598036i | \(-0.795948\pi\) | ||||
−0.801469 | + | 0.598036i | \(0.795948\pi\) | |||||||
\(824\) | −1.62001 | −0.0564357 | ||||||||
\(825\) | −27.8359 | −0.969120 | ||||||||
\(826\) | 3.86651 | 0.134533 | ||||||||
\(827\) | −48.6520 | −1.69180 | −0.845899 | − | 0.533344i | \(-0.820935\pi\) | ||||
−0.845899 | + | 0.533344i | \(0.820935\pi\) | |||||||
\(828\) | −1.47919 | −0.0514053 | ||||||||
\(829\) | −29.9283 | −1.03945 | −0.519727 | − | 0.854332i | \(-0.673966\pi\) | ||||
−0.519727 | + | 0.854332i | \(0.673966\pi\) | |||||||
\(830\) | 39.7366 | 1.37928 | ||||||||
\(831\) | 32.1099 | 1.11388 | ||||||||
\(832\) | 37.6613 | 1.30567 | ||||||||
\(833\) | 6.68552 | 0.231639 | ||||||||
\(834\) | 0.389797 | 0.0134976 | ||||||||
\(835\) | −56.0072 | −1.93821 | ||||||||
\(836\) | 25.0836 | 0.867536 | ||||||||
\(837\) | 12.9000 | 0.445888 | ||||||||
\(838\) | 33.3086 | 1.15063 | ||||||||
\(839\) | −19.2990 | −0.666276 | −0.333138 | − | 0.942878i | \(-0.608108\pi\) | ||||
−0.333138 | + | 0.942878i | \(0.608108\pi\) | |||||||
\(840\) | 1.41694 | 0.0488892 | ||||||||
\(841\) | 18.8035 | 0.648396 | ||||||||
\(842\) | 29.6681 | 1.02243 | ||||||||
\(843\) | −0.523052 | −0.0180149 | ||||||||
\(844\) | −12.7930 | −0.440353 | ||||||||
\(845\) | 0.615766 | 0.0211830 | ||||||||
\(846\) | −18.1711 | −0.624734 | ||||||||
\(847\) | 6.80308 | 0.233757 | ||||||||
\(848\) | 34.6595 | 1.19021 | ||||||||
\(849\) | −16.2473 | −0.557606 | ||||||||
\(850\) | 11.3210 | 0.388306 | ||||||||
\(851\) | −1.82203 | −0.0624584 | ||||||||
\(852\) | −9.53390 | −0.326626 | ||||||||
\(853\) | 41.7617 | 1.42989 | 0.714946 | − | 0.699179i | \(-0.246451\pi\) | ||||
0.714946 | + | 0.699179i | \(0.246451\pi\) | |||||||
\(854\) | 16.1752 | 0.553504 | ||||||||
\(855\) | −13.3386 | −0.456170 | ||||||||
\(856\) | 2.08015 | 0.0710981 | ||||||||
\(857\) | −23.6322 | −0.807262 | −0.403631 | − | 0.914922i | \(-0.632252\pi\) | ||||
−0.403631 | + | 0.914922i | \(0.632252\pi\) | |||||||
\(858\) | −38.2952 | −1.30738 | ||||||||
\(859\) | 8.49085 | 0.289704 | 0.144852 | − | 0.989453i | \(-0.453729\pi\) | ||||
0.144852 | + | 0.989453i | \(0.453729\pi\) | |||||||
\(860\) | 73.8320 | 2.51765 | ||||||||
\(861\) | 2.34132 | 0.0797921 | ||||||||
\(862\) | 12.3139 | 0.419413 | ||||||||
\(863\) | −54.0966 | −1.84147 | −0.920735 | − | 0.390189i | \(-0.872410\pi\) | ||||
−0.920735 | + | 0.390189i | \(0.872410\pi\) | |||||||
\(864\) | −41.9343 | −1.42663 | ||||||||
\(865\) | 39.4917 | 1.34276 | ||||||||
\(866\) | −41.0164 | −1.39379 | ||||||||
\(867\) | 1.06648 | 0.0362194 | ||||||||
\(868\) | −3.28058 | −0.111350 | ||||||||
\(869\) | 5.36514 | 0.182000 | ||||||||
\(870\) | 49.6695 | 1.68395 | ||||||||
\(871\) | 47.4485 | 1.60773 | ||||||||
\(872\) | −1.18554 | −0.0401474 | ||||||||
\(873\) | 18.0885 | 0.612204 | ||||||||
\(874\) | 1.56224 | 0.0528435 | ||||||||
\(875\) | −0.773079 | −0.0261348 | ||||||||
\(876\) | −0.517180 | −0.0174739 | ||||||||
\(877\) | 6.93772 | 0.234270 | 0.117135 | − | 0.993116i | \(-0.462629\pi\) | ||||
0.117135 | + | 0.993116i | \(0.462629\pi\) | |||||||
\(878\) | −56.1110 | −1.89365 | ||||||||
\(879\) | 17.5954 | 0.593479 | ||||||||
\(880\) | −49.2752 | −1.66107 | ||||||||
\(881\) | 0.275969 | 0.00929765 | 0.00464882 | − | 0.999989i | \(-0.498520\pi\) | ||||
0.00464882 | + | 0.999989i | \(0.498520\pi\) | |||||||
\(882\) | −25.9771 | −0.874696 | ||||||||
\(883\) | −21.0756 | −0.709250 | −0.354625 | − | 0.935009i | \(-0.615391\pi\) | ||||
−0.354625 | + | 0.935009i | \(0.615391\pi\) | |||||||
\(884\) | 8.41682 | 0.283088 | ||||||||
\(885\) | 11.3820 | 0.382603 | ||||||||
\(886\) | 38.1569 | 1.28191 | ||||||||
\(887\) | −14.7381 | −0.494858 | −0.247429 | − | 0.968906i | \(-0.579586\pi\) | ||||
−0.247429 | + | 0.968906i | \(0.579586\pi\) | |||||||
\(888\) | 4.22201 | 0.141682 | ||||||||
\(889\) | 7.84910 | 0.263250 | ||||||||
\(890\) | 22.4898 | 0.753861 | ||||||||
\(891\) | −0.275414 | −0.00922671 | ||||||||
\(892\) | 46.1994 | 1.54687 | ||||||||
\(893\) | 10.3712 | 0.347059 | ||||||||
\(894\) | −13.0026 | −0.434873 | ||||||||
\(895\) | 57.4100 | 1.91900 | ||||||||
\(896\) | 3.24075 | 0.108266 | ||||||||
\(897\) | −1.28892 | −0.0430358 | ||||||||
\(898\) | 78.6500 | 2.62458 | ||||||||
\(899\) | −17.1987 | −0.573610 | ||||||||
\(900\) | −23.7719 | −0.792398 | ||||||||
\(901\) | 10.9237 | 0.363922 | ||||||||
\(902\) | 39.2773 | 1.30779 | ||||||||
\(903\) | −5.81476 | −0.193503 | ||||||||
\(904\) | −7.16336 | −0.238250 | ||||||||
\(905\) | 50.4376 | 1.67660 | ||||||||
\(906\) | 19.3160 | 0.641732 | ||||||||
\(907\) | −7.92771 | −0.263235 | −0.131618 | − | 0.991301i | \(-0.542017\pi\) | ||||
−0.131618 | + | 0.991301i | \(0.542017\pi\) | |||||||
\(908\) | 18.8646 | 0.626044 | ||||||||
\(909\) | 24.4821 | 0.812019 | ||||||||
\(910\) | −13.5198 | −0.448177 | ||||||||
\(911\) | 53.7889 | 1.78211 | 0.891053 | − | 0.453899i | \(-0.149967\pi\) | ||||
0.891053 | + | 0.453899i | \(0.149967\pi\) | |||||||
\(912\) | 7.50426 | 0.248491 | ||||||||
\(913\) | −28.3715 | −0.938959 | ||||||||
\(914\) | −58.2001 | −1.92509 | ||||||||
\(915\) | 47.6156 | 1.57412 | ||||||||
\(916\) | −56.5883 | −1.86973 | ||||||||
\(917\) | 5.89673 | 0.194727 | ||||||||
\(918\) | −10.8181 | −0.357052 | ||||||||
\(919\) | −27.1516 | −0.895650 | −0.447825 | − | 0.894121i | \(-0.647801\pi\) | ||||
−0.447825 | + | 0.894121i | \(0.647801\pi\) | |||||||
\(920\) | 0.800044 | 0.0263767 | ||||||||
\(921\) | −3.69885 | −0.121881 | ||||||||
\(922\) | 48.1933 | 1.58716 | ||||||||
\(923\) | 13.6049 | 0.447812 | ||||||||
\(924\) | −6.76449 | −0.222535 | ||||||||
\(925\) | −29.2818 | −0.962779 | ||||||||
\(926\) | −43.1401 | −1.41767 | ||||||||
\(927\) | −4.11263 | −0.135076 | ||||||||
\(928\) | 55.9084 | 1.83528 | ||||||||
\(929\) | −38.0531 | −1.24848 | −0.624241 | − | 0.781232i | \(-0.714592\pi\) | ||||
−0.624241 | + | 0.781232i | \(0.714592\pi\) | |||||||
\(930\) | −17.8701 | −0.585983 | ||||||||
\(931\) | 14.8266 | 0.485921 | ||||||||
\(932\) | 21.7364 | 0.712000 | ||||||||
\(933\) | −24.4368 | −0.800026 | ||||||||
\(934\) | 19.5419 | 0.639431 | ||||||||
\(935\) | −15.5302 | −0.507893 | ||||||||
\(936\) | −4.89117 | −0.159873 | ||||||||
\(937\) | 9.41013 | 0.307415 | 0.153708 | − | 0.988116i | \(-0.450879\pi\) | ||||
0.153708 | + | 0.988116i | \(0.450879\pi\) | |||||||
\(938\) | 15.5092 | 0.506393 | ||||||||
\(939\) | −24.5618 | −0.801543 | ||||||||
\(940\) | 35.5130 | 1.15831 | ||||||||
\(941\) | −10.9388 | −0.356593 | −0.178297 | − | 0.983977i | \(-0.557059\pi\) | ||||
−0.178297 | + | 0.983977i | \(0.557059\pi\) | |||||||
\(942\) | 25.2665 | 0.823226 | ||||||||
\(943\) | 1.32197 | 0.0430494 | ||||||||
\(944\) | 10.4868 | 0.341315 | ||||||||
\(945\) | 9.39073 | 0.305480 | ||||||||
\(946\) | −97.5465 | −3.17151 | ||||||||
\(947\) | −35.7233 | −1.16085 | −0.580426 | − | 0.814313i | \(-0.697114\pi\) | ||||
−0.580426 | + | 0.814313i | \(0.697114\pi\) | |||||||
\(948\) | −2.79780 | −0.0908685 | ||||||||
\(949\) | 0.738019 | 0.0239571 | ||||||||
\(950\) | 25.1067 | 0.814568 | ||||||||
\(951\) | 6.66428 | 0.216104 | ||||||||
\(952\) | 0.411456 | 0.0133354 | ||||||||
\(953\) | 3.81958 | 0.123728 | 0.0618642 | − | 0.998085i | \(-0.480295\pi\) | ||||
0.0618642 | + | 0.998085i | \(0.480295\pi\) | |||||||
\(954\) | −42.4451 | −1.37421 | ||||||||
\(955\) | 65.3653 | 2.11517 | ||||||||
\(956\) | 16.3270 | 0.528053 | ||||||||
\(957\) | −35.4634 | −1.14637 | ||||||||
\(958\) | −56.6563 | −1.83048 | ||||||||
\(959\) | −2.61712 | −0.0845114 | ||||||||
\(960\) | 36.2378 | 1.16957 | ||||||||
\(961\) | −24.8122 | −0.800395 | ||||||||
\(962\) | −40.2844 | −1.29882 | ||||||||
\(963\) | 5.28077 | 0.170170 | ||||||||
\(964\) | −3.62038 | −0.116605 | ||||||||
\(965\) | −9.40192 | −0.302659 | ||||||||
\(966\) | −0.421301 | −0.0135551 | ||||||||
\(967\) | 24.5428 | 0.789243 | 0.394621 | − | 0.918844i | \(-0.370876\pi\) | ||||
0.394621 | + | 0.918844i | \(0.370876\pi\) | |||||||
\(968\) | −8.90084 | −0.286084 | ||||||||
\(969\) | 2.36514 | 0.0759793 | ||||||||
\(970\) | −65.4163 | −2.10039 | ||||||||
\(971\) | 17.6867 | 0.567592 | 0.283796 | − | 0.958885i | \(-0.408406\pi\) | ||||
0.283796 | + | 0.958885i | \(0.408406\pi\) | |||||||
\(972\) | 36.7308 | 1.17814 | ||||||||
\(973\) | −0.0982553 | −0.00314992 | ||||||||
\(974\) | 10.6067 | 0.339862 | ||||||||
\(975\) | −20.7142 | −0.663384 | ||||||||
\(976\) | 43.8703 | 1.40426 | ||||||||
\(977\) | −55.2401 | −1.76729 | −0.883643 | − | 0.468161i | \(-0.844917\pi\) | ||||
−0.883643 | + | 0.468161i | \(0.844917\pi\) | |||||||
\(978\) | −0.00381204 | −0.000121896 0 | ||||||||
\(979\) | −16.0575 | −0.513199 | ||||||||
\(980\) | 50.7689 | 1.62175 | ||||||||
\(981\) | −3.00966 | −0.0960910 | ||||||||
\(982\) | −52.2540 | −1.66749 | ||||||||
\(983\) | −43.2983 | −1.38100 | −0.690501 | − | 0.723332i | \(-0.742610\pi\) | ||||
−0.690501 | + | 0.723332i | \(0.742610\pi\) | |||||||
\(984\) | −3.06328 | −0.0976538 | ||||||||
\(985\) | 16.4163 | 0.523067 | ||||||||
\(986\) | 14.4231 | 0.459327 | ||||||||
\(987\) | −2.79688 | −0.0890257 | ||||||||
\(988\) | 18.6661 | 0.593848 | ||||||||
\(989\) | −3.28317 | −0.104399 | ||||||||
\(990\) | 60.3440 | 1.91786 | ||||||||
\(991\) | −51.4564 | −1.63457 | −0.817284 | − | 0.576235i | \(-0.804521\pi\) | ||||
−0.817284 | + | 0.576235i | \(0.804521\pi\) | |||||||
\(992\) | −20.1147 | −0.638643 | ||||||||
\(993\) | 19.0785 | 0.605437 | ||||||||
\(994\) | 4.44696 | 0.141049 | ||||||||
\(995\) | −14.4657 | −0.458592 | ||||||||
\(996\) | 14.7951 | 0.468801 | ||||||||
\(997\) | 0.871346 | 0.0275958 | 0.0137979 | − | 0.999905i | \(-0.495608\pi\) | ||||
0.0137979 | + | 0.999905i | \(0.495608\pi\) | |||||||
\(998\) | −52.4816 | −1.66128 | ||||||||
\(999\) | 27.9812 | 0.885286 |
(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 | 6001.2.a.c.1.18 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.c.1.18 | ✓ | 121 | 1.1 | even | 1 | trivial |