Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6002,2,Mod(1,6002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6002 = 2 \cdot 3001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6002.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: | \(47.9262112932\) |
Analytic rank: | \(0\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.17 | ||
Character | \(\chi\) | \(=\) | 6002.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.43088 | −0.826117 | −0.413059 | − | 0.910704i | \(-0.635540\pi\) | ||||
−0.413059 | + | 0.910704i | \(0.635540\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.76140 | 0.787721 | 0.393860 | − | 0.919170i | \(-0.371139\pi\) | ||||
0.393860 | + | 0.919170i | \(0.371139\pi\) | |||||||
\(6\) | 1.43088 | 0.584153 | ||||||||
\(7\) | −2.51027 | −0.948792 | −0.474396 | − | 0.880312i | \(-0.657333\pi\) | ||||
−0.474396 | + | 0.880312i | \(0.657333\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.952590 | −0.317530 | ||||||||
\(10\) | −1.76140 | −0.557003 | ||||||||
\(11\) | 0.426115 | 0.128478 | 0.0642392 | − | 0.997935i | \(-0.479538\pi\) | ||||
0.0642392 | + | 0.997935i | \(0.479538\pi\) | |||||||
\(12\) | −1.43088 | −0.413059 | ||||||||
\(13\) | 2.36812 | 0.656799 | 0.328400 | − | 0.944539i | \(-0.393491\pi\) | ||||
0.328400 | + | 0.944539i | \(0.393491\pi\) | |||||||
\(14\) | 2.51027 | 0.670897 | ||||||||
\(15\) | −2.52034 | −0.650750 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.17786 | 0.285674 | 0.142837 | − | 0.989746i | \(-0.454378\pi\) | ||||
0.142837 | + | 0.989746i | \(0.454378\pi\) | |||||||
\(18\) | 0.952590 | 0.224528 | ||||||||
\(19\) | 4.16191 | 0.954808 | 0.477404 | − | 0.878684i | \(-0.341578\pi\) | ||||
0.477404 | + | 0.878684i | \(0.341578\pi\) | |||||||
\(20\) | 1.76140 | 0.393860 | ||||||||
\(21\) | 3.59188 | 0.783813 | ||||||||
\(22\) | −0.426115 | −0.0908480 | ||||||||
\(23\) | 0.564874 | 0.117784 | 0.0588921 | − | 0.998264i | \(-0.481243\pi\) | ||||
0.0588921 | + | 0.998264i | \(0.481243\pi\) | |||||||
\(24\) | 1.43088 | 0.292077 | ||||||||
\(25\) | −1.89748 | −0.379496 | ||||||||
\(26\) | −2.36812 | −0.464427 | ||||||||
\(27\) | 5.65567 | 1.08843 | ||||||||
\(28\) | −2.51027 | −0.474396 | ||||||||
\(29\) | 5.56470 | 1.03334 | 0.516669 | − | 0.856185i | \(-0.327172\pi\) | ||||
0.516669 | + | 0.856185i | \(0.327172\pi\) | |||||||
\(30\) | 2.52034 | 0.460150 | ||||||||
\(31\) | 4.96269 | 0.891326 | 0.445663 | − | 0.895201i | \(-0.352968\pi\) | ||||
0.445663 | + | 0.895201i | \(0.352968\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.609718 | −0.106138 | ||||||||
\(34\) | −1.17786 | −0.202002 | ||||||||
\(35\) | −4.42158 | −0.747383 | ||||||||
\(36\) | −0.952590 | −0.158765 | ||||||||
\(37\) | −7.80266 | −1.28275 | −0.641375 | − | 0.767228i | \(-0.721636\pi\) | ||||
−0.641375 | + | 0.767228i | \(0.721636\pi\) | |||||||
\(38\) | −4.16191 | −0.675151 | ||||||||
\(39\) | −3.38849 | −0.542593 | ||||||||
\(40\) | −1.76140 | −0.278501 | ||||||||
\(41\) | 2.79972 | 0.437242 | 0.218621 | − | 0.975810i | \(-0.429844\pi\) | ||||
0.218621 | + | 0.975810i | \(0.429844\pi\) | |||||||
\(42\) | −3.59188 | −0.554240 | ||||||||
\(43\) | 4.58262 | 0.698843 | 0.349422 | − | 0.936966i | \(-0.386378\pi\) | ||||
0.349422 | + | 0.936966i | \(0.386378\pi\) | |||||||
\(44\) | 0.426115 | 0.0642392 | ||||||||
\(45\) | −1.67789 | −0.250125 | ||||||||
\(46\) | −0.564874 | −0.0832861 | ||||||||
\(47\) | 2.12678 | 0.310223 | 0.155112 | − | 0.987897i | \(-0.450426\pi\) | ||||
0.155112 | + | 0.987897i | \(0.450426\pi\) | |||||||
\(48\) | −1.43088 | −0.206529 | ||||||||
\(49\) | −0.698559 | −0.0997941 | ||||||||
\(50\) | 1.89748 | 0.268344 | ||||||||
\(51\) | −1.68538 | −0.236000 | ||||||||
\(52\) | 2.36812 | 0.328400 | ||||||||
\(53\) | −2.64144 | −0.362829 | −0.181415 | − | 0.983407i | \(-0.558068\pi\) | ||||
−0.181415 | + | 0.983407i | \(0.558068\pi\) | |||||||
\(54\) | −5.65567 | −0.769639 | ||||||||
\(55\) | 0.750558 | 0.101205 | ||||||||
\(56\) | 2.51027 | 0.335449 | ||||||||
\(57\) | −5.95518 | −0.788783 | ||||||||
\(58\) | −5.56470 | −0.730681 | ||||||||
\(59\) | −10.8114 | −1.40752 | −0.703762 | − | 0.710435i | \(-0.748498\pi\) | ||||
−0.703762 | + | 0.710435i | \(0.748498\pi\) | |||||||
\(60\) | −2.52034 | −0.325375 | ||||||||
\(61\) | −10.5327 | −1.34857 | −0.674287 | − | 0.738469i | \(-0.735549\pi\) | ||||
−0.674287 | + | 0.738469i | \(0.735549\pi\) | |||||||
\(62\) | −4.96269 | −0.630263 | ||||||||
\(63\) | 2.39126 | 0.301270 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.17121 | 0.517374 | ||||||||
\(66\) | 0.609718 | 0.0750511 | ||||||||
\(67\) | 1.61399 | 0.197180 | 0.0985902 | − | 0.995128i | \(-0.468567\pi\) | ||||
0.0985902 | + | 0.995128i | \(0.468567\pi\) | |||||||
\(68\) | 1.17786 | 0.142837 | ||||||||
\(69\) | −0.808265 | −0.0973036 | ||||||||
\(70\) | 4.42158 | 0.528480 | ||||||||
\(71\) | −7.61236 | −0.903420 | −0.451710 | − | 0.892165i | \(-0.649186\pi\) | ||||
−0.451710 | + | 0.892165i | \(0.649186\pi\) | |||||||
\(72\) | 0.952590 | 0.112264 | ||||||||
\(73\) | 7.66690 | 0.897343 | 0.448671 | − | 0.893697i | \(-0.351897\pi\) | ||||
0.448671 | + | 0.893697i | \(0.351897\pi\) | |||||||
\(74\) | 7.80266 | 0.907041 | ||||||||
\(75\) | 2.71506 | 0.313508 | ||||||||
\(76\) | 4.16191 | 0.477404 | ||||||||
\(77\) | −1.06966 | −0.121899 | ||||||||
\(78\) | 3.38849 | 0.383671 | ||||||||
\(79\) | −6.21483 | −0.699223 | −0.349612 | − | 0.936895i | \(-0.613686\pi\) | ||||
−0.349612 | + | 0.936895i | \(0.613686\pi\) | |||||||
\(80\) | 1.76140 | 0.196930 | ||||||||
\(81\) | −5.23480 | −0.581645 | ||||||||
\(82\) | −2.79972 | −0.309177 | ||||||||
\(83\) | 3.39551 | 0.372705 | 0.186353 | − | 0.982483i | \(-0.440333\pi\) | ||||
0.186353 | + | 0.982483i | \(0.440333\pi\) | |||||||
\(84\) | 3.59188 | 0.391907 | ||||||||
\(85\) | 2.07469 | 0.225031 | ||||||||
\(86\) | −4.58262 | −0.494157 | ||||||||
\(87\) | −7.96240 | −0.853659 | ||||||||
\(88\) | −0.426115 | −0.0454240 | ||||||||
\(89\) | −7.55320 | −0.800637 | −0.400319 | − | 0.916376i | \(-0.631101\pi\) | ||||
−0.400319 | + | 0.916376i | \(0.631101\pi\) | |||||||
\(90\) | 1.67789 | 0.176865 | ||||||||
\(91\) | −5.94462 | −0.623166 | ||||||||
\(92\) | 0.564874 | 0.0588921 | ||||||||
\(93\) | −7.10100 | −0.736340 | ||||||||
\(94\) | −2.12678 | −0.219361 | ||||||||
\(95\) | 7.33078 | 0.752122 | ||||||||
\(96\) | 1.43088 | 0.146038 | ||||||||
\(97\) | −0.830275 | −0.0843017 | −0.0421508 | − | 0.999111i | \(-0.513421\pi\) | ||||
−0.0421508 | + | 0.999111i | \(0.513421\pi\) | |||||||
\(98\) | 0.698559 | 0.0705651 | ||||||||
\(99\) | −0.405913 | −0.0407958 | ||||||||
\(100\) | −1.89748 | −0.189748 | ||||||||
\(101\) | 9.46598 | 0.941901 | 0.470950 | − | 0.882160i | \(-0.343911\pi\) | ||||
0.470950 | + | 0.882160i | \(0.343911\pi\) | |||||||
\(102\) | 1.68538 | 0.166877 | ||||||||
\(103\) | 11.4877 | 1.13191 | 0.565957 | − | 0.824435i | \(-0.308507\pi\) | ||||
0.565957 | + | 0.824435i | \(0.308507\pi\) | |||||||
\(104\) | −2.36812 | −0.232214 | ||||||||
\(105\) | 6.32674 | 0.617426 | ||||||||
\(106\) | 2.64144 | 0.256559 | ||||||||
\(107\) | 12.8788 | 1.24504 | 0.622518 | − | 0.782606i | \(-0.286110\pi\) | ||||
0.622518 | + | 0.782606i | \(0.286110\pi\) | |||||||
\(108\) | 5.65567 | 0.544217 | ||||||||
\(109\) | −5.89737 | −0.564866 | −0.282433 | − | 0.959287i | \(-0.591141\pi\) | ||||
−0.282433 | + | 0.959287i | \(0.591141\pi\) | |||||||
\(110\) | −0.750558 | −0.0715629 | ||||||||
\(111\) | 11.1646 | 1.05970 | ||||||||
\(112\) | −2.51027 | −0.237198 | ||||||||
\(113\) | −3.52585 | −0.331684 | −0.165842 | − | 0.986152i | \(-0.553034\pi\) | ||||
−0.165842 | + | 0.986152i | \(0.553034\pi\) | |||||||
\(114\) | 5.95518 | 0.557754 | ||||||||
\(115\) | 0.994967 | 0.0927811 | ||||||||
\(116\) | 5.56470 | 0.516669 | ||||||||
\(117\) | −2.25585 | −0.208553 | ||||||||
\(118\) | 10.8114 | 0.995270 | ||||||||
\(119\) | −2.95675 | −0.271045 | ||||||||
\(120\) | 2.52034 | 0.230075 | ||||||||
\(121\) | −10.8184 | −0.983493 | ||||||||
\(122\) | 10.5327 | 0.953586 | ||||||||
\(123\) | −4.00605 | −0.361213 | ||||||||
\(124\) | 4.96269 | 0.445663 | ||||||||
\(125\) | −12.1492 | −1.08666 | ||||||||
\(126\) | −2.39126 | −0.213030 | ||||||||
\(127\) | 15.5817 | 1.38265 | 0.691327 | − | 0.722542i | \(-0.257027\pi\) | ||||
0.691327 | + | 0.722542i | \(0.257027\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −6.55717 | −0.577327 | ||||||||
\(130\) | −4.17121 | −0.365839 | ||||||||
\(131\) | 5.16970 | 0.451678 | 0.225839 | − | 0.974165i | \(-0.427488\pi\) | ||||
0.225839 | + | 0.974165i | \(0.427488\pi\) | |||||||
\(132\) | −0.609718 | −0.0530691 | ||||||||
\(133\) | −10.4475 | −0.905914 | ||||||||
\(134\) | −1.61399 | −0.139428 | ||||||||
\(135\) | 9.96189 | 0.857383 | ||||||||
\(136\) | −1.17786 | −0.101001 | ||||||||
\(137\) | 12.1938 | 1.04179 | 0.520893 | − | 0.853622i | \(-0.325599\pi\) | ||||
0.520893 | + | 0.853622i | \(0.325599\pi\) | |||||||
\(138\) | 0.808265 | 0.0688041 | ||||||||
\(139\) | 0.705047 | 0.0598013 | 0.0299007 | − | 0.999553i | \(-0.490481\pi\) | ||||
0.0299007 | + | 0.999553i | \(0.490481\pi\) | |||||||
\(140\) | −4.42158 | −0.373692 | ||||||||
\(141\) | −3.04316 | −0.256281 | ||||||||
\(142\) | 7.61236 | 0.638815 | ||||||||
\(143\) | 1.00909 | 0.0843845 | ||||||||
\(144\) | −0.952590 | −0.0793825 | ||||||||
\(145\) | 9.80165 | 0.813982 | ||||||||
\(146\) | −7.66690 | −0.634517 | ||||||||
\(147\) | 0.999552 | 0.0824416 | ||||||||
\(148\) | −7.80266 | −0.641375 | ||||||||
\(149\) | 5.63205 | 0.461395 | 0.230698 | − | 0.973025i | \(-0.425899\pi\) | ||||
0.230698 | + | 0.973025i | \(0.425899\pi\) | |||||||
\(150\) | −2.71506 | −0.221684 | ||||||||
\(151\) | 0.488897 | 0.0397859 | 0.0198929 | − | 0.999802i | \(-0.493667\pi\) | ||||
0.0198929 | + | 0.999802i | \(0.493667\pi\) | |||||||
\(152\) | −4.16191 | −0.337575 | ||||||||
\(153\) | −1.12202 | −0.0907101 | ||||||||
\(154\) | 1.06966 | 0.0861958 | ||||||||
\(155\) | 8.74127 | 0.702116 | ||||||||
\(156\) | −3.38849 | −0.271297 | ||||||||
\(157\) | 22.3445 | 1.78329 | 0.891643 | − | 0.452739i | \(-0.149553\pi\) | ||||
0.891643 | + | 0.452739i | \(0.149553\pi\) | |||||||
\(158\) | 6.21483 | 0.494426 | ||||||||
\(159\) | 3.77957 | 0.299740 | ||||||||
\(160\) | −1.76140 | −0.139251 | ||||||||
\(161\) | −1.41798 | −0.111753 | ||||||||
\(162\) | 5.23480 | 0.411285 | ||||||||
\(163\) | −8.34256 | −0.653440 | −0.326720 | − | 0.945121i | \(-0.605943\pi\) | ||||
−0.326720 | + | 0.945121i | \(0.605943\pi\) | |||||||
\(164\) | 2.79972 | 0.218621 | ||||||||
\(165\) | −1.07396 | −0.0836074 | ||||||||
\(166\) | −3.39551 | −0.263543 | ||||||||
\(167\) | 6.70379 | 0.518755 | 0.259377 | − | 0.965776i | \(-0.416483\pi\) | ||||
0.259377 | + | 0.965776i | \(0.416483\pi\) | |||||||
\(168\) | −3.59188 | −0.277120 | ||||||||
\(169\) | −7.39199 | −0.568615 | ||||||||
\(170\) | −2.07469 | −0.159121 | ||||||||
\(171\) | −3.96459 | −0.303180 | ||||||||
\(172\) | 4.58262 | 0.349422 | ||||||||
\(173\) | −15.7600 | −1.19821 | −0.599107 | − | 0.800669i | \(-0.704478\pi\) | ||||
−0.599107 | + | 0.800669i | \(0.704478\pi\) | |||||||
\(174\) | 7.96240 | 0.603628 | ||||||||
\(175\) | 4.76318 | 0.360062 | ||||||||
\(176\) | 0.426115 | 0.0321196 | ||||||||
\(177\) | 15.4698 | 1.16278 | ||||||||
\(178\) | 7.55320 | 0.566136 | ||||||||
\(179\) | 14.4410 | 1.07937 | 0.539686 | − | 0.841866i | \(-0.318543\pi\) | ||||
0.539686 | + | 0.841866i | \(0.318543\pi\) | |||||||
\(180\) | −1.67789 | −0.125063 | ||||||||
\(181\) | 19.5217 | 1.45103 | 0.725517 | − | 0.688204i | \(-0.241601\pi\) | ||||
0.725517 | + | 0.688204i | \(0.241601\pi\) | |||||||
\(182\) | 5.94462 | 0.440645 | ||||||||
\(183\) | 15.0710 | 1.11408 | ||||||||
\(184\) | −0.564874 | −0.0416430 | ||||||||
\(185\) | −13.7436 | −1.01045 | ||||||||
\(186\) | 7.10100 | 0.520671 | ||||||||
\(187\) | 0.501905 | 0.0367029 | ||||||||
\(188\) | 2.12678 | 0.155112 | ||||||||
\(189\) | −14.1972 | −1.03270 | ||||||||
\(190\) | −7.33078 | −0.531831 | ||||||||
\(191\) | −7.70373 | −0.557422 | −0.278711 | − | 0.960375i | \(-0.589907\pi\) | ||||
−0.278711 | + | 0.960375i | \(0.589907\pi\) | |||||||
\(192\) | −1.43088 | −0.103265 | ||||||||
\(193\) | −12.8259 | −0.923227 | −0.461613 | − | 0.887081i | \(-0.652729\pi\) | ||||
−0.461613 | + | 0.887081i | \(0.652729\pi\) | |||||||
\(194\) | 0.830275 | 0.0596103 | ||||||||
\(195\) | −5.96848 | −0.427412 | ||||||||
\(196\) | −0.698559 | −0.0498970 | ||||||||
\(197\) | 9.87114 | 0.703290 | 0.351645 | − | 0.936133i | \(-0.385622\pi\) | ||||
0.351645 | + | 0.936133i | \(0.385622\pi\) | |||||||
\(198\) | 0.405913 | 0.0288470 | ||||||||
\(199\) | −6.75899 | −0.479132 | −0.239566 | − | 0.970880i | \(-0.577005\pi\) | ||||
−0.239566 | + | 0.970880i | \(0.577005\pi\) | |||||||
\(200\) | 1.89748 | 0.134172 | ||||||||
\(201\) | −2.30942 | −0.162894 | ||||||||
\(202\) | −9.46598 | −0.666024 | ||||||||
\(203\) | −13.9689 | −0.980423 | ||||||||
\(204\) | −1.68538 | −0.118000 | ||||||||
\(205\) | 4.93141 | 0.344425 | ||||||||
\(206\) | −11.4877 | −0.800384 | ||||||||
\(207\) | −0.538093 | −0.0374000 | ||||||||
\(208\) | 2.36812 | 0.164200 | ||||||||
\(209\) | 1.77345 | 0.122672 | ||||||||
\(210\) | −6.32674 | −0.436586 | ||||||||
\(211\) | 10.7534 | 0.740298 | 0.370149 | − | 0.928972i | \(-0.379307\pi\) | ||||
0.370149 | + | 0.928972i | \(0.379307\pi\) | |||||||
\(212\) | −2.64144 | −0.181415 | ||||||||
\(213\) | 10.8923 | 0.746331 | ||||||||
\(214\) | −12.8788 | −0.880373 | ||||||||
\(215\) | 8.07182 | 0.550493 | ||||||||
\(216\) | −5.65567 | −0.384820 | ||||||||
\(217\) | −12.4577 | −0.845683 | ||||||||
\(218\) | 5.89737 | 0.399420 | ||||||||
\(219\) | −10.9704 | −0.741310 | ||||||||
\(220\) | 0.750558 | 0.0506026 | ||||||||
\(221\) | 2.78933 | 0.187630 | ||||||||
\(222\) | −11.1646 | −0.749322 | ||||||||
\(223\) | −1.45424 | −0.0973832 | −0.0486916 | − | 0.998814i | \(-0.515505\pi\) | ||||
−0.0486916 | + | 0.998814i | \(0.515505\pi\) | |||||||
\(224\) | 2.51027 | 0.167724 | ||||||||
\(225\) | 1.80752 | 0.120501 | ||||||||
\(226\) | 3.52585 | 0.234536 | ||||||||
\(227\) | −6.34583 | −0.421188 | −0.210594 | − | 0.977574i | \(-0.567540\pi\) | ||||
−0.210594 | + | 0.977574i | \(0.567540\pi\) | |||||||
\(228\) | −5.95518 | −0.394392 | ||||||||
\(229\) | 20.2609 | 1.33888 | 0.669438 | − | 0.742868i | \(-0.266535\pi\) | ||||
0.669438 | + | 0.742868i | \(0.266535\pi\) | |||||||
\(230\) | −0.994967 | −0.0656062 | ||||||||
\(231\) | 1.53056 | 0.100703 | ||||||||
\(232\) | −5.56470 | −0.365340 | ||||||||
\(233\) | 11.9803 | 0.784855 | 0.392427 | − | 0.919783i | \(-0.371635\pi\) | ||||
0.392427 | + | 0.919783i | \(0.371635\pi\) | |||||||
\(234\) | 2.25585 | 0.147470 | ||||||||
\(235\) | 3.74611 | 0.244369 | ||||||||
\(236\) | −10.8114 | −0.703762 | ||||||||
\(237\) | 8.89267 | 0.577641 | ||||||||
\(238\) | 2.95675 | 0.191658 | ||||||||
\(239\) | −17.2958 | −1.11877 | −0.559385 | − | 0.828908i | \(-0.688963\pi\) | ||||
−0.559385 | + | 0.828908i | \(0.688963\pi\) | |||||||
\(240\) | −2.52034 | −0.162687 | ||||||||
\(241\) | −1.24242 | −0.0800312 | −0.0400156 | − | 0.999199i | \(-0.512741\pi\) | ||||
−0.0400156 | + | 0.999199i | \(0.512741\pi\) | |||||||
\(242\) | 10.8184 | 0.695435 | ||||||||
\(243\) | −9.47666 | −0.607928 | ||||||||
\(244\) | −10.5327 | −0.674287 | ||||||||
\(245\) | −1.23044 | −0.0786099 | ||||||||
\(246\) | 4.00605 | 0.255417 | ||||||||
\(247\) | 9.85591 | 0.627117 | ||||||||
\(248\) | −4.96269 | −0.315131 | ||||||||
\(249\) | −4.85855 | −0.307898 | ||||||||
\(250\) | 12.1492 | 0.768383 | ||||||||
\(251\) | 8.89754 | 0.561608 | 0.280804 | − | 0.959765i | \(-0.409399\pi\) | ||||
0.280804 | + | 0.959765i | \(0.409399\pi\) | |||||||
\(252\) | 2.39126 | 0.150635 | ||||||||
\(253\) | 0.240701 | 0.0151327 | ||||||||
\(254\) | −15.5817 | −0.977683 | ||||||||
\(255\) | −2.96862 | −0.185902 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.39597 | 0.523726 | 0.261863 | − | 0.965105i | \(-0.415663\pi\) | ||||
0.261863 | + | 0.965105i | \(0.415663\pi\) | |||||||
\(258\) | 6.55717 | 0.408232 | ||||||||
\(259\) | 19.5868 | 1.21706 | ||||||||
\(260\) | 4.17121 | 0.258687 | ||||||||
\(261\) | −5.30088 | −0.328116 | ||||||||
\(262\) | −5.16970 | −0.319385 | ||||||||
\(263\) | 22.8986 | 1.41199 | 0.705994 | − | 0.708218i | \(-0.250501\pi\) | ||||
0.705994 | + | 0.708218i | \(0.250501\pi\) | |||||||
\(264\) | 0.609718 | 0.0375256 | ||||||||
\(265\) | −4.65262 | −0.285808 | ||||||||
\(266\) | 10.4475 | 0.640578 | ||||||||
\(267\) | 10.8077 | 0.661420 | ||||||||
\(268\) | 1.61399 | 0.0985902 | ||||||||
\(269\) | 12.7598 | 0.777979 | 0.388990 | − | 0.921242i | \(-0.372824\pi\) | ||||
0.388990 | + | 0.921242i | \(0.372824\pi\) | |||||||
\(270\) | −9.96189 | −0.606261 | ||||||||
\(271\) | −13.8926 | −0.843915 | −0.421957 | − | 0.906616i | \(-0.638657\pi\) | ||||
−0.421957 | + | 0.906616i | \(0.638657\pi\) | |||||||
\(272\) | 1.17786 | 0.0714185 | ||||||||
\(273\) | 8.50602 | 0.514808 | ||||||||
\(274\) | −12.1938 | −0.736654 | ||||||||
\(275\) | −0.808544 | −0.0487570 | ||||||||
\(276\) | −0.808265 | −0.0486518 | ||||||||
\(277\) | −26.2001 | −1.57421 | −0.787106 | − | 0.616818i | \(-0.788421\pi\) | ||||
−0.787106 | + | 0.616818i | \(0.788421\pi\) | |||||||
\(278\) | −0.705047 | −0.0422859 | ||||||||
\(279\) | −4.72741 | −0.283023 | ||||||||
\(280\) | 4.42158 | 0.264240 | ||||||||
\(281\) | −19.0989 | −1.13934 | −0.569671 | − | 0.821873i | \(-0.692929\pi\) | ||||
−0.569671 | + | 0.821873i | \(0.692929\pi\) | |||||||
\(282\) | 3.04316 | 0.181218 | ||||||||
\(283\) | 24.0563 | 1.43000 | 0.714998 | − | 0.699127i | \(-0.246428\pi\) | ||||
0.714998 | + | 0.699127i | \(0.246428\pi\) | |||||||
\(284\) | −7.61236 | −0.451710 | ||||||||
\(285\) | −10.4894 | −0.621341 | ||||||||
\(286\) | −1.00909 | −0.0596689 | ||||||||
\(287\) | −7.02804 | −0.414852 | ||||||||
\(288\) | 0.952590 | 0.0561319 | ||||||||
\(289\) | −15.6126 | −0.918390 | ||||||||
\(290\) | −9.80165 | −0.575572 | ||||||||
\(291\) | 1.18802 | 0.0696431 | ||||||||
\(292\) | 7.66690 | 0.448671 | ||||||||
\(293\) | 20.1575 | 1.17761 | 0.588805 | − | 0.808275i | \(-0.299598\pi\) | ||||
0.588805 | + | 0.808275i | \(0.299598\pi\) | |||||||
\(294\) | −0.999552 | −0.0582950 | ||||||||
\(295\) | −19.0432 | −1.10874 | ||||||||
\(296\) | 7.80266 | 0.453520 | ||||||||
\(297\) | 2.40997 | 0.139840 | ||||||||
\(298\) | −5.63205 | −0.326256 | ||||||||
\(299\) | 1.33769 | 0.0773606 | ||||||||
\(300\) | 2.71506 | 0.156754 | ||||||||
\(301\) | −11.5036 | −0.663057 | ||||||||
\(302\) | −0.488897 | −0.0281329 | ||||||||
\(303\) | −13.5447 | −0.778121 | ||||||||
\(304\) | 4.16191 | 0.238702 | ||||||||
\(305\) | −18.5523 | −1.06230 | ||||||||
\(306\) | 1.12202 | 0.0641417 | ||||||||
\(307\) | 34.0889 | 1.94556 | 0.972778 | − | 0.231737i | \(-0.0744409\pi\) | ||||
0.972778 | + | 0.231737i | \(0.0744409\pi\) | |||||||
\(308\) | −1.06966 | −0.0609497 | ||||||||
\(309\) | −16.4375 | −0.935094 | ||||||||
\(310\) | −8.74127 | −0.496471 | ||||||||
\(311\) | 26.9597 | 1.52875 | 0.764373 | − | 0.644774i | \(-0.223049\pi\) | ||||
0.764373 | + | 0.644774i | \(0.223049\pi\) | |||||||
\(312\) | 3.38849 | 0.191836 | ||||||||
\(313\) | −28.4742 | −1.60946 | −0.804729 | − | 0.593642i | \(-0.797690\pi\) | ||||
−0.804729 | + | 0.593642i | \(0.797690\pi\) | |||||||
\(314\) | −22.3445 | −1.26097 | ||||||||
\(315\) | 4.21195 | 0.237317 | ||||||||
\(316\) | −6.21483 | −0.349612 | ||||||||
\(317\) | −9.74107 | −0.547113 | −0.273556 | − | 0.961856i | \(-0.588200\pi\) | ||||
−0.273556 | + | 0.961856i | \(0.588200\pi\) | |||||||
\(318\) | −3.77957 | −0.211948 | ||||||||
\(319\) | 2.37120 | 0.132762 | ||||||||
\(320\) | 1.76140 | 0.0984651 | ||||||||
\(321\) | −18.4279 | −1.02855 | ||||||||
\(322\) | 1.41798 | 0.0790211 | ||||||||
\(323\) | 4.90216 | 0.272764 | ||||||||
\(324\) | −5.23480 | −0.290822 | ||||||||
\(325\) | −4.49346 | −0.249252 | ||||||||
\(326\) | 8.34256 | 0.462052 | ||||||||
\(327\) | 8.43841 | 0.466645 | ||||||||
\(328\) | −2.79972 | −0.154589 | ||||||||
\(329\) | −5.33879 | −0.294337 | ||||||||
\(330\) | 1.07396 | 0.0591193 | ||||||||
\(331\) | 14.9670 | 0.822663 | 0.411331 | − | 0.911486i | \(-0.365064\pi\) | ||||
0.411331 | + | 0.911486i | \(0.365064\pi\) | |||||||
\(332\) | 3.39551 | 0.186353 | ||||||||
\(333\) | 7.43274 | 0.407312 | ||||||||
\(334\) | −6.70379 | −0.366815 | ||||||||
\(335\) | 2.84288 | 0.155323 | ||||||||
\(336\) | 3.59188 | 0.195953 | ||||||||
\(337\) | 2.60810 | 0.142072 | 0.0710362 | − | 0.997474i | \(-0.477369\pi\) | ||||
0.0710362 | + | 0.997474i | \(0.477369\pi\) | |||||||
\(338\) | 7.39199 | 0.402071 | ||||||||
\(339\) | 5.04506 | 0.274010 | ||||||||
\(340\) | 2.07469 | 0.112516 | ||||||||
\(341\) | 2.11468 | 0.114516 | ||||||||
\(342\) | 3.96459 | 0.214381 | ||||||||
\(343\) | 19.3254 | 1.04348 | ||||||||
\(344\) | −4.58262 | −0.247078 | ||||||||
\(345\) | −1.42368 | −0.0766481 | ||||||||
\(346\) | 15.7600 | 0.847265 | ||||||||
\(347\) | 22.3793 | 1.20139 | 0.600693 | − | 0.799480i | \(-0.294891\pi\) | ||||
0.600693 | + | 0.799480i | \(0.294891\pi\) | |||||||
\(348\) | −7.96240 | −0.426829 | ||||||||
\(349\) | −21.6245 | −1.15753 | −0.578765 | − | 0.815494i | \(-0.696465\pi\) | ||||
−0.578765 | + | 0.815494i | \(0.696465\pi\) | |||||||
\(350\) | −4.76318 | −0.254603 | ||||||||
\(351\) | 13.3933 | 0.714883 | ||||||||
\(352\) | −0.426115 | −0.0227120 | ||||||||
\(353\) | −19.7148 | −1.04931 | −0.524657 | − | 0.851314i | \(-0.675806\pi\) | ||||
−0.524657 | + | 0.851314i | \(0.675806\pi\) | |||||||
\(354\) | −15.4698 | −0.822210 | ||||||||
\(355\) | −13.4084 | −0.711643 | ||||||||
\(356\) | −7.55320 | −0.400319 | ||||||||
\(357\) | 4.23075 | 0.223915 | ||||||||
\(358\) | −14.4410 | −0.763232 | ||||||||
\(359\) | −16.1402 | −0.851845 | −0.425923 | − | 0.904760i | \(-0.640050\pi\) | ||||
−0.425923 | + | 0.904760i | \(0.640050\pi\) | |||||||
\(360\) | 1.67789 | 0.0884326 | ||||||||
\(361\) | −1.67851 | −0.0883424 | ||||||||
\(362\) | −19.5217 | −1.02604 | ||||||||
\(363\) | 15.4798 | 0.812481 | ||||||||
\(364\) | −5.94462 | −0.311583 | ||||||||
\(365\) | 13.5045 | 0.706856 | ||||||||
\(366\) | −15.0710 | −0.787774 | ||||||||
\(367\) | 9.31697 | 0.486342 | 0.243171 | − | 0.969983i | \(-0.421812\pi\) | ||||
0.243171 | + | 0.969983i | \(0.421812\pi\) | |||||||
\(368\) | 0.564874 | 0.0294461 | ||||||||
\(369\) | −2.66698 | −0.138838 | ||||||||
\(370\) | 13.7436 | 0.714495 | ||||||||
\(371\) | 6.63071 | 0.344249 | ||||||||
\(372\) | −7.10100 | −0.368170 | ||||||||
\(373\) | 34.6757 | 1.79544 | 0.897721 | − | 0.440565i | \(-0.145222\pi\) | ||||
0.897721 | + | 0.440565i | \(0.145222\pi\) | |||||||
\(374\) | −0.501905 | −0.0259529 | ||||||||
\(375\) | 17.3840 | 0.897707 | ||||||||
\(376\) | −2.12678 | −0.109680 | ||||||||
\(377\) | 13.1779 | 0.678696 | ||||||||
\(378\) | 14.1972 | 0.730228 | ||||||||
\(379\) | 30.9474 | 1.58966 | 0.794831 | − | 0.606831i | \(-0.207560\pi\) | ||||
0.794831 | + | 0.606831i | \(0.207560\pi\) | |||||||
\(380\) | 7.33078 | 0.376061 | ||||||||
\(381\) | −22.2955 | −1.14223 | ||||||||
\(382\) | 7.70373 | 0.394157 | ||||||||
\(383\) | 1.36435 | 0.0697149 | 0.0348574 | − | 0.999392i | \(-0.488902\pi\) | ||||
0.0348574 | + | 0.999392i | \(0.488902\pi\) | |||||||
\(384\) | 1.43088 | 0.0730192 | ||||||||
\(385\) | −1.88410 | −0.0960226 | ||||||||
\(386\) | 12.8259 | 0.652820 | ||||||||
\(387\) | −4.36536 | −0.221904 | ||||||||
\(388\) | −0.830275 | −0.0421508 | ||||||||
\(389\) | 11.7924 | 0.597900 | 0.298950 | − | 0.954269i | \(-0.403364\pi\) | ||||
0.298950 | + | 0.954269i | \(0.403364\pi\) | |||||||
\(390\) | 5.96848 | 0.302226 | ||||||||
\(391\) | 0.665344 | 0.0336479 | ||||||||
\(392\) | 0.698559 | 0.0352825 | ||||||||
\(393\) | −7.39720 | −0.373139 | ||||||||
\(394\) | −9.87114 | −0.497301 | ||||||||
\(395\) | −10.9468 | −0.550793 | ||||||||
\(396\) | −0.405913 | −0.0203979 | ||||||||
\(397\) | 6.16089 | 0.309206 | 0.154603 | − | 0.987977i | \(-0.450590\pi\) | ||||
0.154603 | + | 0.987977i | \(0.450590\pi\) | |||||||
\(398\) | 6.75899 | 0.338798 | ||||||||
\(399\) | 14.9491 | 0.748391 | ||||||||
\(400\) | −1.89748 | −0.0948739 | ||||||||
\(401\) | −11.9466 | −0.596582 | −0.298291 | − | 0.954475i | \(-0.596417\pi\) | ||||
−0.298291 | + | 0.954475i | \(0.596417\pi\) | |||||||
\(402\) | 2.30942 | 0.115184 | ||||||||
\(403\) | 11.7523 | 0.585422 | ||||||||
\(404\) | 9.46598 | 0.470950 | ||||||||
\(405\) | −9.22057 | −0.458174 | ||||||||
\(406\) | 13.9689 | 0.693264 | ||||||||
\(407\) | −3.32483 | −0.164806 | ||||||||
\(408\) | 1.68538 | 0.0834387 | ||||||||
\(409\) | 33.6358 | 1.66318 | 0.831591 | − | 0.555389i | \(-0.187431\pi\) | ||||
0.831591 | + | 0.555389i | \(0.187431\pi\) | |||||||
\(410\) | −4.93141 | −0.243545 | ||||||||
\(411\) | −17.4478 | −0.860638 | ||||||||
\(412\) | 11.4877 | 0.565957 | ||||||||
\(413\) | 27.1395 | 1.33545 | ||||||||
\(414\) | 0.538093 | 0.0264458 | ||||||||
\(415\) | 5.98084 | 0.293588 | ||||||||
\(416\) | −2.36812 | −0.116107 | ||||||||
\(417\) | −1.00884 | −0.0494029 | ||||||||
\(418\) | −1.77345 | −0.0867424 | ||||||||
\(419\) | 23.4147 | 1.14388 | 0.571942 | − | 0.820294i | \(-0.306190\pi\) | ||||
0.571942 | + | 0.820294i | \(0.306190\pi\) | |||||||
\(420\) | 6.32674 | 0.308713 | ||||||||
\(421\) | −12.8635 | −0.626928 | −0.313464 | − | 0.949600i | \(-0.601489\pi\) | ||||
−0.313464 | + | 0.949600i | \(0.601489\pi\) | |||||||
\(422\) | −10.7534 | −0.523469 | ||||||||
\(423\) | −2.02595 | −0.0985052 | ||||||||
\(424\) | 2.64144 | 0.128279 | ||||||||
\(425\) | −2.23497 | −0.108412 | ||||||||
\(426\) | −10.8923 | −0.527736 | ||||||||
\(427\) | 26.4399 | 1.27952 | ||||||||
\(428\) | 12.8788 | 0.622518 | ||||||||
\(429\) | −1.44389 | −0.0697115 | ||||||||
\(430\) | −8.07182 | −0.389258 | ||||||||
\(431\) | −14.9811 | −0.721614 | −0.360807 | − | 0.932640i | \(-0.617499\pi\) | ||||
−0.360807 | + | 0.932640i | \(0.617499\pi\) | |||||||
\(432\) | 5.65567 | 0.272109 | ||||||||
\(433\) | 40.0900 | 1.92660 | 0.963300 | − | 0.268426i | \(-0.0865036\pi\) | ||||
0.963300 | + | 0.268426i | \(0.0865036\pi\) | |||||||
\(434\) | 12.4577 | 0.597988 | ||||||||
\(435\) | −14.0250 | −0.672445 | ||||||||
\(436\) | −5.89737 | −0.282433 | ||||||||
\(437\) | 2.35095 | 0.112461 | ||||||||
\(438\) | 10.9704 | 0.524186 | ||||||||
\(439\) | 30.2196 | 1.44230 | 0.721151 | − | 0.692778i | \(-0.243613\pi\) | ||||
0.721151 | + | 0.692778i | \(0.243613\pi\) | |||||||
\(440\) | −0.750558 | −0.0357814 | ||||||||
\(441\) | 0.665440 | 0.0316876 | ||||||||
\(442\) | −2.78933 | −0.132675 | ||||||||
\(443\) | −32.0110 | −1.52089 | −0.760444 | − | 0.649403i | \(-0.775019\pi\) | ||||
−0.760444 | + | 0.649403i | \(0.775019\pi\) | |||||||
\(444\) | 11.1646 | 0.529851 | ||||||||
\(445\) | −13.3042 | −0.630679 | ||||||||
\(446\) | 1.45424 | 0.0688603 | ||||||||
\(447\) | −8.05877 | −0.381167 | ||||||||
\(448\) | −2.51027 | −0.118599 | ||||||||
\(449\) | −22.5351 | −1.06349 | −0.531747 | − | 0.846903i | \(-0.678464\pi\) | ||||
−0.531747 | + | 0.846903i | \(0.678464\pi\) | |||||||
\(450\) | −1.80752 | −0.0852073 | ||||||||
\(451\) | 1.19300 | 0.0561762 | ||||||||
\(452\) | −3.52585 | −0.165842 | ||||||||
\(453\) | −0.699552 | −0.0328678 | ||||||||
\(454\) | 6.34583 | 0.297825 | ||||||||
\(455\) | −10.4708 | −0.490881 | ||||||||
\(456\) | 5.95518 | 0.278877 | ||||||||
\(457\) | −15.9868 | −0.747832 | −0.373916 | − | 0.927463i | \(-0.621985\pi\) | ||||
−0.373916 | + | 0.927463i | \(0.621985\pi\) | |||||||
\(458\) | −20.2609 | −0.946729 | ||||||||
\(459\) | 6.66161 | 0.310937 | ||||||||
\(460\) | 0.994967 | 0.0463906 | ||||||||
\(461\) | 38.1422 | 1.77646 | 0.888229 | − | 0.459401i | \(-0.151936\pi\) | ||||
0.888229 | + | 0.459401i | \(0.151936\pi\) | |||||||
\(462\) | −1.53056 | −0.0712079 | ||||||||
\(463\) | 4.50852 | 0.209528 | 0.104764 | − | 0.994497i | \(-0.466591\pi\) | ||||
0.104764 | + | 0.994497i | \(0.466591\pi\) | |||||||
\(464\) | 5.56470 | 0.258335 | ||||||||
\(465\) | −12.5077 | −0.580030 | ||||||||
\(466\) | −11.9803 | −0.554976 | ||||||||
\(467\) | 9.68145 | 0.448004 | 0.224002 | − | 0.974589i | \(-0.428088\pi\) | ||||
0.224002 | + | 0.974589i | \(0.428088\pi\) | |||||||
\(468\) | −2.25585 | −0.104277 | ||||||||
\(469\) | −4.05155 | −0.187083 | ||||||||
\(470\) | −3.74611 | −0.172795 | ||||||||
\(471\) | −31.9723 | −1.47320 | ||||||||
\(472\) | 10.8114 | 0.497635 | ||||||||
\(473\) | 1.95272 | 0.0897863 | ||||||||
\(474\) | −8.89267 | −0.408454 | ||||||||
\(475\) | −7.89713 | −0.362345 | ||||||||
\(476\) | −2.95675 | −0.135523 | ||||||||
\(477\) | 2.51621 | 0.115209 | ||||||||
\(478\) | 17.2958 | 0.791090 | ||||||||
\(479\) | 21.5955 | 0.986724 | 0.493362 | − | 0.869824i | \(-0.335768\pi\) | ||||
0.493362 | + | 0.869824i | \(0.335768\pi\) | |||||||
\(480\) | 2.52034 | 0.115037 | ||||||||
\(481\) | −18.4777 | −0.842509 | ||||||||
\(482\) | 1.24242 | 0.0565906 | ||||||||
\(483\) | 2.02896 | 0.0923209 | ||||||||
\(484\) | −10.8184 | −0.491747 | ||||||||
\(485\) | −1.46244 | −0.0664062 | ||||||||
\(486\) | 9.47666 | 0.429870 | ||||||||
\(487\) | −32.9715 | −1.49408 | −0.747041 | − | 0.664778i | \(-0.768526\pi\) | ||||
−0.747041 | + | 0.664778i | \(0.768526\pi\) | |||||||
\(488\) | 10.5327 | 0.476793 | ||||||||
\(489\) | 11.9372 | 0.539818 | ||||||||
\(490\) | 1.23044 | 0.0555856 | ||||||||
\(491\) | −8.47458 | −0.382452 | −0.191226 | − | 0.981546i | \(-0.561246\pi\) | ||||
−0.191226 | + | 0.981546i | \(0.561246\pi\) | |||||||
\(492\) | −4.00605 | −0.180607 | ||||||||
\(493\) | 6.55446 | 0.295198 | ||||||||
\(494\) | −9.85591 | −0.443439 | ||||||||
\(495\) | −0.714974 | −0.0321357 | ||||||||
\(496\) | 4.96269 | 0.222831 | ||||||||
\(497\) | 19.1090 | 0.857158 | ||||||||
\(498\) | 4.85855 | 0.217717 | ||||||||
\(499\) | −2.95237 | −0.132166 | −0.0660832 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660832 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(500\) | −12.1492 | −0.543329 | ||||||||
\(501\) | −9.59230 | −0.428553 | ||||||||
\(502\) | −8.89754 | −0.397117 | ||||||||
\(503\) | −16.8983 | −0.753459 | −0.376730 | − | 0.926323i | \(-0.622951\pi\) | ||||
−0.376730 | + | 0.926323i | \(0.622951\pi\) | |||||||
\(504\) | −2.39126 | −0.106515 | ||||||||
\(505\) | 16.6734 | 0.741955 | ||||||||
\(506\) | −0.240701 | −0.0107005 | ||||||||
\(507\) | 10.5770 | 0.469743 | ||||||||
\(508\) | 15.5817 | 0.691327 | ||||||||
\(509\) | −27.5333 | −1.22039 | −0.610196 | − | 0.792251i | \(-0.708909\pi\) | ||||
−0.610196 | + | 0.792251i | \(0.708909\pi\) | |||||||
\(510\) | 2.96862 | 0.131453 | ||||||||
\(511\) | −19.2460 | −0.851391 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 23.5384 | 1.03925 | ||||||||
\(514\) | −8.39597 | −0.370330 | ||||||||
\(515\) | 20.2344 | 0.891633 | ||||||||
\(516\) | −6.55717 | −0.288663 | ||||||||
\(517\) | 0.906254 | 0.0398570 | ||||||||
\(518\) | −19.5868 | −0.860593 | ||||||||
\(519\) | 22.5507 | 0.989865 | ||||||||
\(520\) | −4.17121 | −0.182919 | ||||||||
\(521\) | −36.3939 | −1.59445 | −0.797223 | − | 0.603685i | \(-0.793698\pi\) | ||||
−0.797223 | + | 0.603685i | \(0.793698\pi\) | |||||||
\(522\) | 5.30088 | 0.232013 | ||||||||
\(523\) | 30.3188 | 1.32575 | 0.662874 | − | 0.748731i | \(-0.269336\pi\) | ||||
0.662874 | + | 0.748731i | \(0.269336\pi\) | |||||||
\(524\) | 5.16970 | 0.225839 | ||||||||
\(525\) | −6.81552 | −0.297454 | ||||||||
\(526\) | −22.8986 | −0.998426 | ||||||||
\(527\) | 5.84538 | 0.254629 | ||||||||
\(528\) | −0.609718 | −0.0265346 | ||||||||
\(529\) | −22.6809 | −0.986127 | ||||||||
\(530\) | 4.65262 | 0.202097 | ||||||||
\(531\) | 10.2988 | 0.446931 | ||||||||
\(532\) | −10.4475 | −0.452957 | ||||||||
\(533\) | 6.63007 | 0.287180 | ||||||||
\(534\) | −10.8077 | −0.467695 | ||||||||
\(535\) | 22.6846 | 0.980741 | ||||||||
\(536\) | −1.61399 | −0.0697138 | ||||||||
\(537\) | −20.6633 | −0.891689 | ||||||||
\(538\) | −12.7598 | −0.550114 | ||||||||
\(539\) | −0.297666 | −0.0128214 | ||||||||
\(540\) | 9.96189 | 0.428691 | ||||||||
\(541\) | −0.720278 | −0.0309672 | −0.0154836 | − | 0.999880i | \(-0.504929\pi\) | ||||
−0.0154836 | + | 0.999880i | \(0.504929\pi\) | |||||||
\(542\) | 13.8926 | 0.596738 | ||||||||
\(543\) | −27.9331 | −1.19872 | ||||||||
\(544\) | −1.17786 | −0.0505005 | ||||||||
\(545\) | −10.3876 | −0.444957 | ||||||||
\(546\) | −8.50602 | −0.364024 | ||||||||
\(547\) | −14.2282 | −0.608355 | −0.304177 | − | 0.952615i | \(-0.598382\pi\) | ||||
−0.304177 | + | 0.952615i | \(0.598382\pi\) | |||||||
\(548\) | 12.1938 | 0.520893 | ||||||||
\(549\) | 10.0333 | 0.428213 | ||||||||
\(550\) | 0.808544 | 0.0344764 | ||||||||
\(551\) | 23.1598 | 0.986639 | ||||||||
\(552\) | 0.808265 | 0.0344020 | ||||||||
\(553\) | 15.6009 | 0.663418 | ||||||||
\(554\) | 26.2001 | 1.11314 | ||||||||
\(555\) | 19.6654 | 0.834749 | ||||||||
\(556\) | 0.705047 | 0.0299007 | ||||||||
\(557\) | 35.7714 | 1.51568 | 0.757842 | − | 0.652438i | \(-0.226254\pi\) | ||||
0.757842 | + | 0.652438i | \(0.226254\pi\) | |||||||
\(558\) | 4.72741 | 0.200127 | ||||||||
\(559\) | 10.8522 | 0.459000 | ||||||||
\(560\) | −4.42158 | −0.186846 | ||||||||
\(561\) | −0.718165 | −0.0303209 | ||||||||
\(562\) | 19.0989 | 0.805637 | ||||||||
\(563\) | −5.96451 | −0.251374 | −0.125687 | − | 0.992070i | \(-0.540114\pi\) | ||||
−0.125687 | + | 0.992070i | \(0.540114\pi\) | |||||||
\(564\) | −3.04316 | −0.128140 | ||||||||
\(565\) | −6.21043 | −0.261275 | ||||||||
\(566\) | −24.0563 | −1.01116 | ||||||||
\(567\) | 13.1408 | 0.551860 | ||||||||
\(568\) | 7.61236 | 0.319407 | ||||||||
\(569\) | 16.6588 | 0.698372 | 0.349186 | − | 0.937053i | \(-0.386458\pi\) | ||||
0.349186 | + | 0.937053i | \(0.386458\pi\) | |||||||
\(570\) | 10.4894 | 0.439354 | ||||||||
\(571\) | 46.4120 | 1.94228 | 0.971141 | − | 0.238508i | \(-0.0766583\pi\) | ||||
0.971141 | + | 0.238508i | \(0.0766583\pi\) | |||||||
\(572\) | 1.00909 | 0.0421923 | ||||||||
\(573\) | 11.0231 | 0.460496 | ||||||||
\(574\) | 7.02804 | 0.293345 | ||||||||
\(575\) | −1.07184 | −0.0446986 | ||||||||
\(576\) | −0.952590 | −0.0396913 | ||||||||
\(577\) | 31.8256 | 1.32492 | 0.662460 | − | 0.749098i | \(-0.269513\pi\) | ||||
0.662460 | + | 0.749098i | \(0.269513\pi\) | |||||||
\(578\) | 15.6126 | 0.649400 | ||||||||
\(579\) | 18.3523 | 0.762694 | ||||||||
\(580\) | 9.80165 | 0.406991 | ||||||||
\(581\) | −8.52363 | −0.353620 | ||||||||
\(582\) | −1.18802 | −0.0492451 | ||||||||
\(583\) | −1.12556 | −0.0466157 | ||||||||
\(584\) | −7.66690 | −0.317259 | ||||||||
\(585\) | −3.97345 | −0.164282 | ||||||||
\(586\) | −20.1575 | −0.832697 | ||||||||
\(587\) | 32.4731 | 1.34031 | 0.670154 | − | 0.742222i | \(-0.266228\pi\) | ||||
0.670154 | + | 0.742222i | \(0.266228\pi\) | |||||||
\(588\) | 0.999552 | 0.0412208 | ||||||||
\(589\) | 20.6543 | 0.851045 | ||||||||
\(590\) | 19.0432 | 0.783995 | ||||||||
\(591\) | −14.1244 | −0.581000 | ||||||||
\(592\) | −7.80266 | −0.320687 | ||||||||
\(593\) | 32.5180 | 1.33535 | 0.667677 | − | 0.744451i | \(-0.267289\pi\) | ||||
0.667677 | + | 0.744451i | \(0.267289\pi\) | |||||||
\(594\) | −2.40997 | −0.0988821 | ||||||||
\(595\) | −5.20802 | −0.213508 | ||||||||
\(596\) | 5.63205 | 0.230698 | ||||||||
\(597\) | 9.67129 | 0.395820 | ||||||||
\(598\) | −1.33769 | −0.0547022 | ||||||||
\(599\) | −20.8382 | −0.851425 | −0.425712 | − | 0.904859i | \(-0.639976\pi\) | ||||
−0.425712 | + | 0.904859i | \(0.639976\pi\) | |||||||
\(600\) | −2.71506 | −0.110842 | ||||||||
\(601\) | 28.5665 | 1.16525 | 0.582626 | − | 0.812740i | \(-0.302025\pi\) | ||||
0.582626 | + | 0.812740i | \(0.302025\pi\) | |||||||
\(602\) | 11.5036 | 0.468852 | ||||||||
\(603\) | −1.53747 | −0.0626107 | ||||||||
\(604\) | 0.488897 | 0.0198929 | ||||||||
\(605\) | −19.0555 | −0.774718 | ||||||||
\(606\) | 13.5447 | 0.550214 | ||||||||
\(607\) | 34.8420 | 1.41419 | 0.707097 | − | 0.707117i | \(-0.250005\pi\) | ||||
0.707097 | + | 0.707117i | \(0.250005\pi\) | |||||||
\(608\) | −4.16191 | −0.168788 | ||||||||
\(609\) | 19.9878 | 0.809945 | ||||||||
\(610\) | 18.5523 | 0.751159 | ||||||||
\(611\) | 5.03648 | 0.203754 | ||||||||
\(612\) | −1.12202 | −0.0453550 | ||||||||
\(613\) | 25.1927 | 1.01752 | 0.508761 | − | 0.860908i | \(-0.330104\pi\) | ||||
0.508761 | + | 0.860908i | \(0.330104\pi\) | |||||||
\(614\) | −34.0889 | −1.37572 | ||||||||
\(615\) | −7.05625 | −0.284535 | ||||||||
\(616\) | 1.06966 | 0.0430979 | ||||||||
\(617\) | 17.2947 | 0.696257 | 0.348129 | − | 0.937447i | \(-0.386817\pi\) | ||||
0.348129 | + | 0.937447i | \(0.386817\pi\) | |||||||
\(618\) | 16.4375 | 0.661211 | ||||||||
\(619\) | 42.9877 | 1.72782 | 0.863910 | − | 0.503646i | \(-0.168008\pi\) | ||||
0.863910 | + | 0.503646i | \(0.168008\pi\) | |||||||
\(620\) | 8.74127 | 0.351058 | ||||||||
\(621\) | 3.19474 | 0.128200 | ||||||||
\(622\) | −26.9597 | −1.08099 | ||||||||
\(623\) | 18.9605 | 0.759638 | ||||||||
\(624\) | −3.38849 | −0.135648 | ||||||||
\(625\) | −11.9122 | −0.476487 | ||||||||
\(626\) | 28.4742 | 1.13806 | ||||||||
\(627\) | −2.53759 | −0.101342 | ||||||||
\(628\) | 22.3445 | 0.891643 | ||||||||
\(629\) | −9.19047 | −0.366448 | ||||||||
\(630\) | −4.21195 | −0.167808 | ||||||||
\(631\) | 30.1710 | 1.20109 | 0.600544 | − | 0.799592i | \(-0.294951\pi\) | ||||
0.600544 | + | 0.799592i | \(0.294951\pi\) | |||||||
\(632\) | 6.21483 | 0.247213 | ||||||||
\(633\) | −15.3869 | −0.611573 | ||||||||
\(634\) | 9.74107 | 0.386867 | ||||||||
\(635\) | 27.4456 | 1.08914 | ||||||||
\(636\) | 3.77957 | 0.149870 | ||||||||
\(637\) | −1.65427 | −0.0655447 | ||||||||
\(638\) | −2.37120 | −0.0938767 | ||||||||
\(639\) | 7.25145 | 0.286863 | ||||||||
\(640\) | −1.76140 | −0.0696254 | ||||||||
\(641\) | 47.9556 | 1.89413 | 0.947067 | − | 0.321036i | \(-0.104031\pi\) | ||||
0.947067 | + | 0.321036i | \(0.104031\pi\) | |||||||
\(642\) | 18.4279 | 0.727292 | ||||||||
\(643\) | −2.06124 | −0.0812876 | −0.0406438 | − | 0.999174i | \(-0.512941\pi\) | ||||
−0.0406438 | + | 0.999174i | \(0.512941\pi\) | |||||||
\(644\) | −1.41798 | −0.0558764 | ||||||||
\(645\) | −11.5498 | −0.454772 | ||||||||
\(646\) | −4.90216 | −0.192873 | ||||||||
\(647\) | −5.63284 | −0.221450 | −0.110725 | − | 0.993851i | \(-0.535317\pi\) | ||||
−0.110725 | + | 0.993851i | \(0.535317\pi\) | |||||||
\(648\) | 5.23480 | 0.205642 | ||||||||
\(649\) | −4.60690 | −0.180837 | ||||||||
\(650\) | 4.49346 | 0.176248 | ||||||||
\(651\) | 17.8254 | 0.698633 | ||||||||
\(652\) | −8.34256 | −0.326720 | ||||||||
\(653\) | 9.14797 | 0.357988 | 0.178994 | − | 0.983850i | \(-0.442716\pi\) | ||||
0.178994 | + | 0.983850i | \(0.442716\pi\) | |||||||
\(654\) | −8.43841 | −0.329968 | ||||||||
\(655\) | 9.10589 | 0.355797 | ||||||||
\(656\) | 2.79972 | 0.109311 | ||||||||
\(657\) | −7.30341 | −0.284933 | ||||||||
\(658\) | 5.33879 | 0.208128 | ||||||||
\(659\) | −45.7066 | −1.78048 | −0.890238 | − | 0.455495i | \(-0.849462\pi\) | ||||
−0.890238 | + | 0.455495i | \(0.849462\pi\) | |||||||
\(660\) | −1.07396 | −0.0418037 | ||||||||
\(661\) | 13.9077 | 0.540947 | 0.270474 | − | 0.962727i | \(-0.412820\pi\) | ||||
0.270474 | + | 0.962727i | \(0.412820\pi\) | |||||||
\(662\) | −14.9670 | −0.581710 | ||||||||
\(663\) | −3.99118 | −0.155005 | ||||||||
\(664\) | −3.39551 | −0.131771 | ||||||||
\(665\) | −18.4022 | −0.713607 | ||||||||
\(666\) | −7.43274 | −0.288013 | ||||||||
\(667\) | 3.14335 | 0.121711 | ||||||||
\(668\) | 6.70379 | 0.259377 | ||||||||
\(669\) | 2.08084 | 0.0804500 | ||||||||
\(670\) | −2.84288 | −0.109830 | ||||||||
\(671\) | −4.48814 | −0.173263 | ||||||||
\(672\) | −3.59188 | −0.138560 | ||||||||
\(673\) | −37.4249 | −1.44263 | −0.721313 | − | 0.692610i | \(-0.756461\pi\) | ||||
−0.721313 | + | 0.692610i | \(0.756461\pi\) | |||||||
\(674\) | −2.60810 | −0.100460 | ||||||||
\(675\) | −10.7315 | −0.413056 | ||||||||
\(676\) | −7.39199 | −0.284307 | ||||||||
\(677\) | −14.8597 | −0.571106 | −0.285553 | − | 0.958363i | \(-0.592177\pi\) | ||||
−0.285553 | + | 0.958363i | \(0.592177\pi\) | |||||||
\(678\) | −5.04506 | −0.193754 | ||||||||
\(679\) | 2.08421 | 0.0799847 | ||||||||
\(680\) | −2.07469 | −0.0795606 | ||||||||
\(681\) | 9.08011 | 0.347950 | ||||||||
\(682\) | −2.11468 | −0.0809752 | ||||||||
\(683\) | 7.73460 | 0.295956 | 0.147978 | − | 0.988991i | \(-0.452723\pi\) | ||||
0.147978 | + | 0.988991i | \(0.452723\pi\) | |||||||
\(684\) | −3.96459 | −0.151590 | ||||||||
\(685\) | 21.4781 | 0.820637 | ||||||||
\(686\) | −19.3254 | −0.737849 | ||||||||
\(687\) | −28.9908 | −1.10607 | ||||||||
\(688\) | 4.58262 | 0.174711 | ||||||||
\(689\) | −6.25525 | −0.238306 | ||||||||
\(690\) | 1.42368 | 0.0541984 | ||||||||
\(691\) | 2.77263 | 0.105476 | 0.0527379 | − | 0.998608i | \(-0.483205\pi\) | ||||
0.0527379 | + | 0.998608i | \(0.483205\pi\) | |||||||
\(692\) | −15.7600 | −0.599107 | ||||||||
\(693\) | 1.01895 | 0.0387067 | ||||||||
\(694\) | −22.3793 | −0.849508 | ||||||||
\(695\) | 1.24187 | 0.0471068 | ||||||||
\(696\) | 7.96240 | 0.301814 | ||||||||
\(697\) | 3.29768 | 0.124909 | ||||||||
\(698\) | 21.6245 | 0.818498 | ||||||||
\(699\) | −17.1423 | −0.648382 | ||||||||
\(700\) | 4.76318 | 0.180031 | ||||||||
\(701\) | 14.3787 | 0.543075 | 0.271537 | − | 0.962428i | \(-0.412468\pi\) | ||||
0.271537 | + | 0.962428i | \(0.412468\pi\) | |||||||
\(702\) | −13.3933 | −0.505498 | ||||||||
\(703\) | −32.4740 | −1.22478 | ||||||||
\(704\) | 0.426115 | 0.0160598 | ||||||||
\(705\) | −5.36022 | −0.201878 | ||||||||
\(706\) | 19.7148 | 0.741977 | ||||||||
\(707\) | −23.7622 | −0.893668 | ||||||||
\(708\) | 15.4698 | 0.581390 | ||||||||
\(709\) | 13.3959 | 0.503092 | 0.251546 | − | 0.967845i | \(-0.419061\pi\) | ||||
0.251546 | + | 0.967845i | \(0.419061\pi\) | |||||||
\(710\) | 13.4084 | 0.503208 | ||||||||
\(711\) | 5.92019 | 0.222024 | ||||||||
\(712\) | 7.55320 | 0.283068 | ||||||||
\(713\) | 2.80329 | 0.104984 | ||||||||
\(714\) | −4.23075 | −0.158332 | ||||||||
\(715\) | 1.77741 | 0.0664715 | ||||||||
\(716\) | 14.4410 | 0.539686 | ||||||||
\(717\) | 24.7481 | 0.924236 | ||||||||
\(718\) | 16.1402 | 0.602346 | ||||||||
\(719\) | −12.6088 | −0.470230 | −0.235115 | − | 0.971968i | \(-0.575547\pi\) | ||||
−0.235115 | + | 0.971968i | \(0.575547\pi\) | |||||||
\(720\) | −1.67789 | −0.0625313 | ||||||||
\(721\) | −28.8371 | −1.07395 | ||||||||
\(722\) | 1.67851 | 0.0624675 | ||||||||
\(723\) | 1.77775 | 0.0661151 | ||||||||
\(724\) | 19.5217 | 0.725517 | ||||||||
\(725\) | −10.5589 | −0.392148 | ||||||||
\(726\) | −15.4798 | −0.574511 | ||||||||
\(727\) | 33.7211 | 1.25065 | 0.625323 | − | 0.780366i | \(-0.284967\pi\) | ||||
0.625323 | + | 0.780366i | \(0.284967\pi\) | |||||||
\(728\) | 5.94462 | 0.220322 | ||||||||
\(729\) | 29.2643 | 1.08386 | ||||||||
\(730\) | −13.5045 | −0.499822 | ||||||||
\(731\) | 5.39770 | 0.199641 | ||||||||
\(732\) | 15.0710 | 0.557040 | ||||||||
\(733\) | −26.6972 | −0.986084 | −0.493042 | − | 0.870006i | \(-0.664115\pi\) | ||||
−0.493042 | + | 0.870006i | \(0.664115\pi\) | |||||||
\(734\) | −9.31697 | −0.343896 | ||||||||
\(735\) | 1.76061 | 0.0649410 | ||||||||
\(736\) | −0.564874 | −0.0208215 | ||||||||
\(737\) | 0.687746 | 0.0253334 | ||||||||
\(738\) | 2.66698 | 0.0981730 | ||||||||
\(739\) | −12.3855 | −0.455610 | −0.227805 | − | 0.973707i | \(-0.573155\pi\) | ||||
−0.227805 | + | 0.973707i | \(0.573155\pi\) | |||||||
\(740\) | −13.7436 | −0.505224 | ||||||||
\(741\) | −14.1026 | −0.518072 | ||||||||
\(742\) | −6.63071 | −0.243421 | ||||||||
\(743\) | −4.03390 | −0.147990 | −0.0739948 | − | 0.997259i | \(-0.523575\pi\) | ||||
−0.0739948 | + | 0.997259i | \(0.523575\pi\) | |||||||
\(744\) | 7.10100 | 0.260335 | ||||||||
\(745\) | 9.92027 | 0.363451 | ||||||||
\(746\) | −34.6757 | −1.26957 | ||||||||
\(747\) | −3.23453 | −0.118345 | ||||||||
\(748\) | 0.501905 | 0.0183515 | ||||||||
\(749\) | −32.3291 | −1.18128 | ||||||||
\(750\) | −17.3840 | −0.634775 | ||||||||
\(751\) | 18.2252 | 0.665047 | 0.332523 | − | 0.943095i | \(-0.392100\pi\) | ||||
0.332523 | + | 0.943095i | \(0.392100\pi\) | |||||||
\(752\) | 2.12678 | 0.0775558 | ||||||||
\(753\) | −12.7313 | −0.463954 | ||||||||
\(754\) | −13.1779 | −0.479910 | ||||||||
\(755\) | 0.861142 | 0.0313402 | ||||||||
\(756\) | −14.1972 | −0.516349 | ||||||||
\(757\) | −37.7544 | −1.37221 | −0.686103 | − | 0.727504i | \(-0.740680\pi\) | ||||
−0.686103 | + | 0.727504i | \(0.740680\pi\) | |||||||
\(758\) | −30.9474 | −1.12406 | ||||||||
\(759\) | −0.344414 | −0.0125014 | ||||||||
\(760\) | −7.33078 | −0.265915 | ||||||||
\(761\) | 36.0971 | 1.30852 | 0.654259 | − | 0.756271i | \(-0.272981\pi\) | ||||
0.654259 | + | 0.756271i | \(0.272981\pi\) | |||||||
\(762\) | 22.2955 | 0.807681 | ||||||||
\(763\) | 14.8040 | 0.535940 | ||||||||
\(764\) | −7.70373 | −0.278711 | ||||||||
\(765\) | −1.97633 | −0.0714542 | ||||||||
\(766\) | −1.36435 | −0.0492959 | ||||||||
\(767\) | −25.6027 | −0.924461 | ||||||||
\(768\) | −1.43088 | −0.0516323 | ||||||||
\(769\) | 13.2284 | 0.477029 | 0.238515 | − | 0.971139i | \(-0.423340\pi\) | ||||
0.238515 | + | 0.971139i | \(0.423340\pi\) | |||||||
\(770\) | 1.88410 | 0.0678983 | ||||||||
\(771\) | −12.0136 | −0.432659 | ||||||||
\(772\) | −12.8259 | −0.461613 | ||||||||
\(773\) | 41.3528 | 1.48736 | 0.743679 | − | 0.668537i | \(-0.233079\pi\) | ||||
0.743679 | + | 0.668537i | \(0.233079\pi\) | |||||||
\(774\) | 4.36536 | 0.156910 | ||||||||
\(775\) | −9.41660 | −0.338254 | ||||||||
\(776\) | 0.830275 | 0.0298051 | ||||||||
\(777\) | −28.0263 | −1.00544 | ||||||||
\(778\) | −11.7924 | −0.422779 | ||||||||
\(779\) | 11.6522 | 0.417482 | ||||||||
\(780\) | −5.96848 | −0.213706 | ||||||||
\(781\) | −3.24374 | −0.116070 | ||||||||
\(782\) | −0.665344 | −0.0237927 | ||||||||
\(783\) | 31.4721 | 1.12472 | ||||||||
\(784\) | −0.698559 | −0.0249485 | ||||||||
\(785\) | 39.3576 | 1.40473 | ||||||||
\(786\) | 7.39720 | 0.263849 | ||||||||
\(787\) | −8.80428 | −0.313839 | −0.156919 | − | 0.987611i | \(-0.550156\pi\) | ||||
−0.156919 | + | 0.987611i | \(0.550156\pi\) | |||||||
\(788\) | 9.87114 | 0.351645 | ||||||||
\(789\) | −32.7651 | −1.16647 | ||||||||
\(790\) | 10.9468 | 0.389469 | ||||||||
\(791\) | 8.85083 | 0.314699 | ||||||||
\(792\) | 0.405913 | 0.0144235 | ||||||||
\(793\) | −24.9427 | −0.885742 | ||||||||
\(794\) | −6.16089 | −0.218642 | ||||||||
\(795\) | 6.65733 | 0.236111 | ||||||||
\(796\) | −6.75899 | −0.239566 | ||||||||
\(797\) | −39.6977 | −1.40617 | −0.703083 | − | 0.711108i | \(-0.748194\pi\) | ||||
−0.703083 | + | 0.711108i | \(0.748194\pi\) | |||||||
\(798\) | −14.9491 | −0.529192 | ||||||||
\(799\) | 2.50506 | 0.0886226 | ||||||||
\(800\) | 1.89748 | 0.0670860 | ||||||||
\(801\) | 7.19510 | 0.254226 | ||||||||
\(802\) | 11.9466 | 0.421847 | ||||||||
\(803\) | 3.26698 | 0.115289 | ||||||||
\(804\) | −2.30942 | −0.0814471 | ||||||||
\(805\) | −2.49763 | −0.0880300 | ||||||||
\(806\) | −11.7523 | −0.413956 | ||||||||
\(807\) | −18.2577 | −0.642702 | ||||||||
\(808\) | −9.46598 | −0.333012 | ||||||||
\(809\) | 17.8953 | 0.629166 | 0.314583 | − | 0.949230i | \(-0.398135\pi\) | ||||
0.314583 | + | 0.949230i | \(0.398135\pi\) | |||||||
\(810\) | 9.22057 | 0.323978 | ||||||||
\(811\) | −4.73690 | −0.166335 | −0.0831675 | − | 0.996536i | \(-0.526504\pi\) | ||||
−0.0831675 | + | 0.996536i | \(0.526504\pi\) | |||||||
\(812\) | −13.9689 | −0.490212 | ||||||||
\(813\) | 19.8786 | 0.697173 | ||||||||
\(814\) | 3.32483 | 0.116535 | ||||||||
\(815\) | −14.6946 | −0.514728 | ||||||||
\(816\) | −1.68538 | −0.0590000 | ||||||||
\(817\) | 19.0725 | 0.667261 | ||||||||
\(818\) | −33.6358 | −1.17605 | ||||||||
\(819\) | 5.66279 | 0.197874 | ||||||||
\(820\) | 4.93141 | 0.172212 | ||||||||
\(821\) | 28.0651 | 0.979478 | 0.489739 | − | 0.871869i | \(-0.337092\pi\) | ||||
0.489739 | + | 0.871869i | \(0.337092\pi\) | |||||||
\(822\) | 17.4478 | 0.608563 | ||||||||
\(823\) | −13.7752 | −0.480172 | −0.240086 | − | 0.970752i | \(-0.577176\pi\) | ||||
−0.240086 | + | 0.970752i | \(0.577176\pi\) | |||||||
\(824\) | −11.4877 | −0.400192 | ||||||||
\(825\) | 1.15693 | 0.0402790 | ||||||||
\(826\) | −27.1395 | −0.944304 | ||||||||
\(827\) | −21.1312 | −0.734802 | −0.367401 | − | 0.930063i | \(-0.619752\pi\) | ||||
−0.367401 | + | 0.930063i | \(0.619752\pi\) | |||||||
\(828\) | −0.538093 | −0.0187000 | ||||||||
\(829\) | −29.2125 | −1.01459 | −0.507296 | − | 0.861772i | \(-0.669355\pi\) | ||||
−0.507296 | + | 0.861772i | \(0.669355\pi\) | |||||||
\(830\) | −5.98084 | −0.207598 | ||||||||
\(831\) | 37.4891 | 1.30048 | ||||||||
\(832\) | 2.36812 | 0.0820999 | ||||||||
\(833\) | −0.822807 | −0.0285086 | ||||||||
\(834\) | 1.00884 | 0.0349331 | ||||||||
\(835\) | 11.8080 | 0.408634 | ||||||||
\(836\) | 1.77345 | 0.0613361 | ||||||||
\(837\) | 28.0674 | 0.970150 | ||||||||
\(838\) | −23.4147 | −0.808849 | ||||||||
\(839\) | 0.222246 | 0.00767278 | 0.00383639 | − | 0.999993i | \(-0.498779\pi\) | ||||
0.00383639 | + | 0.999993i | \(0.498779\pi\) | |||||||
\(840\) | −6.32674 | −0.218293 | ||||||||
\(841\) | 1.96587 | 0.0677885 | ||||||||
\(842\) | 12.8635 | 0.443305 | ||||||||
\(843\) | 27.3281 | 0.941230 | ||||||||
\(844\) | 10.7534 | 0.370149 | ||||||||
\(845\) | −13.0202 | −0.447910 | ||||||||
\(846\) | 2.02595 | 0.0696537 | ||||||||
\(847\) | 27.1571 | 0.933130 | ||||||||
\(848\) | −2.64144 | −0.0907073 | ||||||||
\(849\) | −34.4215 | −1.18134 | ||||||||
\(850\) | 2.23497 | 0.0766589 | ||||||||
\(851\) | −4.40752 | −0.151088 | ||||||||
\(852\) | 10.8923 | 0.373166 | ||||||||
\(853\) | −29.7487 | −1.01858 | −0.509288 | − | 0.860596i | \(-0.670091\pi\) | ||||
−0.509288 | + | 0.860596i | \(0.670091\pi\) | |||||||
\(854\) | −26.4399 | −0.904754 | ||||||||
\(855\) | −6.98323 | −0.238821 | ||||||||
\(856\) | −12.8788 | −0.440187 | ||||||||
\(857\) | 16.2028 | 0.553476 | 0.276738 | − | 0.960945i | \(-0.410747\pi\) | ||||
0.276738 | + | 0.960945i | \(0.410747\pi\) | |||||||
\(858\) | 1.44389 | 0.0492935 | ||||||||
\(859\) | −14.8527 | −0.506769 | −0.253384 | − | 0.967366i | \(-0.581544\pi\) | ||||
−0.253384 | + | 0.967366i | \(0.581544\pi\) | |||||||
\(860\) | 8.07182 | 0.275247 | ||||||||
\(861\) | 10.0563 | 0.342716 | ||||||||
\(862\) | 14.9811 | 0.510258 | ||||||||
\(863\) | −33.2835 | −1.13298 | −0.566491 | − | 0.824068i | \(-0.691699\pi\) | ||||
−0.566491 | + | 0.824068i | \(0.691699\pi\) | |||||||
\(864\) | −5.65567 | −0.192410 | ||||||||
\(865\) | −27.7597 | −0.943858 | ||||||||
\(866\) | −40.0900 | −1.36231 | ||||||||
\(867\) | 22.3398 | 0.758698 | ||||||||
\(868\) | −12.4577 | −0.422841 | ||||||||
\(869\) | −2.64823 | −0.0898352 | ||||||||
\(870\) | 14.0250 | 0.475490 | ||||||||
\(871\) | 3.82213 | 0.129508 | ||||||||
\(872\) | 5.89737 | 0.199710 | ||||||||
\(873\) | 0.790912 | 0.0267683 | ||||||||
\(874\) | −2.35095 | −0.0795222 | ||||||||
\(875\) | 30.4977 | 1.03101 | ||||||||
\(876\) | −10.9704 | −0.370655 | ||||||||
\(877\) | 23.6628 | 0.799035 | 0.399517 | − | 0.916726i | \(-0.369178\pi\) | ||||
0.399517 | + | 0.916726i | \(0.369178\pi\) | |||||||
\(878\) | −30.2196 | −1.01986 | ||||||||
\(879\) | −28.8428 | −0.972845 | ||||||||
\(880\) | 0.750558 | 0.0253013 | ||||||||
\(881\) | −32.3440 | −1.08970 | −0.544848 | − | 0.838535i | \(-0.683413\pi\) | ||||
−0.544848 | + | 0.838535i | \(0.683413\pi\) | |||||||
\(882\) | −0.665440 | −0.0224065 | ||||||||
\(883\) | −12.2889 | −0.413553 | −0.206777 | − | 0.978388i | \(-0.566297\pi\) | ||||
−0.206777 | + | 0.978388i | \(0.566297\pi\) | |||||||
\(884\) | 2.78933 | 0.0938152 | ||||||||
\(885\) | 27.2485 | 0.915947 | ||||||||
\(886\) | 32.0110 | 1.07543 | ||||||||
\(887\) | 17.6252 | 0.591798 | 0.295899 | − | 0.955219i | \(-0.404381\pi\) | ||||
0.295899 | + | 0.955219i | \(0.404381\pi\) | |||||||
\(888\) | −11.1646 | −0.374661 | ||||||||
\(889\) | −39.1143 | −1.31185 | ||||||||
\(890\) | 13.3042 | 0.445957 | ||||||||
\(891\) | −2.23063 | −0.0747288 | ||||||||
\(892\) | −1.45424 | −0.0486916 | ||||||||
\(893\) | 8.85148 | 0.296203 | ||||||||
\(894\) | 8.05877 | 0.269526 | ||||||||
\(895\) | 25.4364 | 0.850244 | ||||||||
\(896\) | 2.51027 | 0.0838621 | ||||||||
\(897\) | −1.91407 | −0.0639089 | ||||||||
\(898\) | 22.5351 | 0.752004 | ||||||||
\(899\) | 27.6159 | 0.921041 | ||||||||
\(900\) | 1.80752 | 0.0602506 | ||||||||
\(901\) | −3.11125 | −0.103651 | ||||||||
\(902\) | −1.19300 | −0.0397226 | ||||||||
\(903\) | 16.4602 | 0.547763 | ||||||||
\(904\) | 3.52585 | 0.117268 | ||||||||
\(905\) | 34.3854 | 1.14301 | ||||||||
\(906\) | 0.699552 | 0.0232411 | ||||||||
\(907\) | 26.0347 | 0.864468 | 0.432234 | − | 0.901762i | \(-0.357726\pi\) | ||||
0.432234 | + | 0.901762i | \(0.357726\pi\) | |||||||
\(908\) | −6.34583 | −0.210594 | ||||||||
\(909\) | −9.01720 | −0.299082 | ||||||||
\(910\) | 10.4708 | 0.347105 | ||||||||
\(911\) | 2.67283 | 0.0885549 | 0.0442775 | − | 0.999019i | \(-0.485901\pi\) | ||||
0.0442775 | + | 0.999019i | \(0.485901\pi\) | |||||||
\(912\) | −5.95518 | −0.197196 | ||||||||
\(913\) | 1.44688 | 0.0478846 | ||||||||
\(914\) | 15.9868 | 0.528797 | ||||||||
\(915\) | 26.5460 | 0.877584 | ||||||||
\(916\) | 20.2609 | 0.669438 | ||||||||
\(917\) | −12.9773 | −0.428549 | ||||||||
\(918\) | −6.66161 | −0.219866 | ||||||||
\(919\) | 46.0978 | 1.52063 | 0.760313 | − | 0.649557i | \(-0.225046\pi\) | ||||
0.760313 | + | 0.649557i | \(0.225046\pi\) | |||||||
\(920\) | −0.994967 | −0.0328031 | ||||||||
\(921\) | −48.7770 | −1.60726 | ||||||||
\(922\) | −38.1422 | −1.25615 | ||||||||
\(923\) | −18.0270 | −0.593366 | ||||||||
\(924\) | 1.53056 | 0.0503516 | ||||||||
\(925\) | 14.8054 | 0.486798 | ||||||||
\(926\) | −4.50852 | −0.148159 | ||||||||
\(927\) | −10.9430 | −0.359417 | ||||||||
\(928\) | −5.56470 | −0.182670 | ||||||||
\(929\) | −45.1771 | −1.48221 | −0.741106 | − | 0.671388i | \(-0.765699\pi\) | ||||
−0.741106 | + | 0.671388i | \(0.765699\pi\) | |||||||
\(930\) | 12.5077 | 0.410143 | ||||||||
\(931\) | −2.90734 | −0.0952841 | ||||||||
\(932\) | 11.9803 | 0.392427 | ||||||||
\(933\) | −38.5761 | −1.26292 | ||||||||
\(934\) | −9.68145 | −0.316787 | ||||||||
\(935\) | 0.884055 | 0.0289117 | ||||||||
\(936\) | 2.25585 | 0.0737348 | ||||||||
\(937\) | 8.97779 | 0.293291 | 0.146646 | − | 0.989189i | \(-0.453152\pi\) | ||||
0.146646 | + | 0.989189i | \(0.453152\pi\) | |||||||
\(938\) | 4.05155 | 0.132288 | ||||||||
\(939\) | 40.7431 | 1.32960 | ||||||||
\(940\) | 3.74611 | 0.122185 | ||||||||
\(941\) | 39.9776 | 1.30323 | 0.651617 | − | 0.758548i | \(-0.274091\pi\) | ||||
0.651617 | + | 0.758548i | \(0.274091\pi\) | |||||||
\(942\) | 31.9723 | 1.04171 | ||||||||
\(943\) | 1.58149 | 0.0515003 | ||||||||
\(944\) | −10.8114 | −0.351881 | ||||||||
\(945\) | −25.0070 | −0.813478 | ||||||||
\(946\) | −1.95272 | −0.0634885 | ||||||||
\(947\) | −31.6606 | −1.02883 | −0.514415 | − | 0.857541i | \(-0.671991\pi\) | ||||
−0.514415 | + | 0.857541i | \(0.671991\pi\) | |||||||
\(948\) | 8.89267 | 0.288820 | ||||||||
\(949\) | 18.1562 | 0.589374 | ||||||||
\(950\) | 7.89713 | 0.256217 | ||||||||
\(951\) | 13.9383 | 0.451979 | ||||||||
\(952\) | 2.95675 | 0.0958289 | ||||||||
\(953\) | −53.3129 | −1.72698 | −0.863488 | − | 0.504370i | \(-0.831725\pi\) | ||||
−0.863488 | + | 0.504370i | \(0.831725\pi\) | |||||||
\(954\) | −2.51621 | −0.0814652 | ||||||||
\(955\) | −13.5693 | −0.439093 | ||||||||
\(956\) | −17.2958 | −0.559385 | ||||||||
\(957\) | −3.39290 | −0.109677 | ||||||||
\(958\) | −21.5955 | −0.697719 | ||||||||
\(959\) | −30.6097 | −0.988438 | ||||||||
\(960\) | −2.52034 | −0.0813437 | ||||||||
\(961\) | −6.37169 | −0.205538 | ||||||||
\(962\) | 18.4777 | 0.595744 | ||||||||
\(963\) | −12.2682 | −0.395336 | ||||||||
\(964\) | −1.24242 | −0.0400156 | ||||||||
\(965\) | −22.5915 | −0.727245 | ||||||||
\(966\) | −2.02896 | −0.0652807 | ||||||||
\(967\) | −14.4647 | −0.465154 | −0.232577 | − | 0.972578i | \(-0.574716\pi\) | ||||
−0.232577 | + | 0.972578i | \(0.574716\pi\) | |||||||
\(968\) | 10.8184 | 0.347717 | ||||||||
\(969\) | −7.01439 | −0.225335 | ||||||||
\(970\) | 1.46244 | 0.0469563 | ||||||||
\(971\) | 18.5075 | 0.593933 | 0.296967 | − | 0.954888i | \(-0.404025\pi\) | ||||
0.296967 | + | 0.954888i | \(0.404025\pi\) | |||||||
\(972\) | −9.47666 | −0.303964 | ||||||||
\(973\) | −1.76986 | −0.0567390 | ||||||||
\(974\) | 32.9715 | 1.05648 | ||||||||
\(975\) | 6.42959 | 0.205912 | ||||||||
\(976\) | −10.5327 | −0.337143 | ||||||||
\(977\) | 29.6838 | 0.949670 | 0.474835 | − | 0.880075i | \(-0.342508\pi\) | ||||
0.474835 | + | 0.880075i | \(0.342508\pi\) | |||||||
\(978\) | −11.9372 | −0.381709 | ||||||||
\(979\) | −3.21853 | −0.102865 | ||||||||
\(980\) | −1.23044 | −0.0393049 | ||||||||
\(981\) | 5.61778 | 0.179362 | ||||||||
\(982\) | 8.47458 | 0.270435 | ||||||||
\(983\) | −16.8347 | −0.536944 | −0.268472 | − | 0.963287i | \(-0.586519\pi\) | ||||
−0.268472 | + | 0.963287i | \(0.586519\pi\) | |||||||
\(984\) | 4.00605 | 0.127708 | ||||||||
\(985\) | 17.3870 | 0.553996 | ||||||||
\(986\) | −6.55446 | −0.208736 | ||||||||
\(987\) | 7.63916 | 0.243157 | ||||||||
\(988\) | 9.85591 | 0.313558 | ||||||||
\(989\) | 2.58860 | 0.0823128 | ||||||||
\(990\) | 0.714974 | 0.0227234 | ||||||||
\(991\) | −27.3533 | −0.868905 | −0.434452 | − | 0.900695i | \(-0.643058\pi\) | ||||
−0.434452 | + | 0.900695i | \(0.643058\pi\) | |||||||
\(992\) | −4.96269 | −0.157566 | ||||||||
\(993\) | −21.4160 | −0.679616 | ||||||||
\(994\) | −19.1090 | −0.606102 | ||||||||
\(995\) | −11.9053 | −0.377423 | ||||||||
\(996\) | −4.85855 | −0.153949 | ||||||||
\(997\) | 22.0371 | 0.697923 | 0.348961 | − | 0.937137i | \(-0.386534\pi\) | ||||
0.348961 | + | 0.937137i | \(0.386534\pi\) | |||||||
\(998\) | 2.95237 | 0.0934557 | ||||||||
\(999\) | −44.1293 | −1.39619 |
(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 | 6002.2.a.c.1.17 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6002.2.a.c.1.17 | ✓ | 69 | 1.1 | even | 1 | trivial |