Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + 164 x^{7} + 2332 x^{6} - 440 x^{5} - 1344 x^{4} + 244 x^{3} + 295 x^{2} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-0.136067\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 | ||||||||
\(3\) | −1.13607 | −0.655908 | −0.327954 | − | 0.944694i | \(-0.606359\pi\) | ||||
−0.327954 | + | 0.944694i | \(0.606359\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.13607 | −0.463797 | ||||||||
\(7\) | −1.31630 | −0.497513 | −0.248756 | − | 0.968566i | \(-0.580022\pi\) | ||||
−0.248756 | + | 0.968566i | \(0.580022\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.70935 | −0.569784 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.369645 | −0.111452 | −0.0557261 | − | 0.998446i | \(-0.517747\pi\) | ||||
−0.0557261 | + | 0.998446i | \(0.517747\pi\) | |||||||
\(12\) | −1.13607 | −0.327954 | ||||||||
\(13\) | −5.82020 | −1.61423 | −0.807117 | − | 0.590392i | \(-0.798973\pi\) | ||||
−0.807117 | + | 0.590392i | \(0.798973\pi\) | |||||||
\(14\) | −1.31630 | −0.351795 | ||||||||
\(15\) | −1.13607 | −0.293331 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.05036 | 1.46743 | 0.733714 | − | 0.679459i | \(-0.237785\pi\) | ||||
0.733714 | + | 0.679459i | \(0.237785\pi\) | |||||||
\(18\) | −1.70935 | −0.402898 | ||||||||
\(19\) | 0.866620 | 0.198816 | 0.0994082 | − | 0.995047i | \(-0.468305\pi\) | ||||
0.0994082 | + | 0.995047i | \(0.468305\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 1.49540 | 0.326323 | ||||||||
\(22\) | −0.369645 | −0.0788086 | ||||||||
\(23\) | −1.64764 | −0.343557 | −0.171778 | − | 0.985136i | \(-0.554951\pi\) | ||||
−0.171778 | + | 0.985136i | \(0.554951\pi\) | |||||||
\(24\) | −1.13607 | −0.231899 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −5.82020 | −1.14144 | ||||||||
\(27\) | 5.35014 | 1.02963 | ||||||||
\(28\) | −1.31630 | −0.248756 | ||||||||
\(29\) | 7.34705 | 1.36431 | 0.682156 | − | 0.731206i | \(-0.261042\pi\) | ||||
0.682156 | + | 0.731206i | \(0.261042\pi\) | |||||||
\(30\) | −1.13607 | −0.207416 | ||||||||
\(31\) | −1.21756 | −0.218680 | −0.109340 | − | 0.994004i | \(-0.534874\pi\) | ||||
−0.109340 | + | 0.994004i | \(0.534874\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0.419942 | 0.0731025 | ||||||||
\(34\) | 6.05036 | 1.03763 | ||||||||
\(35\) | −1.31630 | −0.222495 | ||||||||
\(36\) | −1.70935 | −0.284892 | ||||||||
\(37\) | −2.26909 | −0.373036 | −0.186518 | − | 0.982452i | \(-0.559720\pi\) | ||||
−0.186518 | + | 0.982452i | \(0.559720\pi\) | |||||||
\(38\) | 0.866620 | 0.140584 | ||||||||
\(39\) | 6.61214 | 1.05879 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 0.302941 | 0.0473115 | 0.0236558 | − | 0.999720i | \(-0.492469\pi\) | ||||
0.0236558 | + | 0.999720i | \(0.492469\pi\) | |||||||
\(42\) | 1.49540 | 0.230745 | ||||||||
\(43\) | 9.60599 | 1.46490 | 0.732450 | − | 0.680821i | \(-0.238377\pi\) | ||||
0.732450 | + | 0.680821i | \(0.238377\pi\) | |||||||
\(44\) | −0.369645 | −0.0557261 | ||||||||
\(45\) | −1.70935 | −0.254815 | ||||||||
\(46\) | −1.64764 | −0.242931 | ||||||||
\(47\) | −0.473050 | −0.0690014 | −0.0345007 | − | 0.999405i | \(-0.510984\pi\) | ||||
−0.0345007 | + | 0.999405i | \(0.510984\pi\) | |||||||
\(48\) | −1.13607 | −0.163977 | ||||||||
\(49\) | −5.26737 | −0.752481 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −6.87361 | −0.962498 | ||||||||
\(52\) | −5.82020 | −0.807117 | ||||||||
\(53\) | −5.12183 | −0.703537 | −0.351769 | − | 0.936087i | \(-0.614420\pi\) | ||||
−0.351769 | + | 0.936087i | \(0.614420\pi\) | |||||||
\(54\) | 5.35014 | 0.728062 | ||||||||
\(55\) | −0.369645 | −0.0498430 | ||||||||
\(56\) | −1.31630 | −0.175897 | ||||||||
\(57\) | −0.984538 | −0.130405 | ||||||||
\(58\) | 7.34705 | 0.964715 | ||||||||
\(59\) | 13.2821 | 1.72918 | 0.864592 | − | 0.502475i | \(-0.167577\pi\) | ||||
0.864592 | + | 0.502475i | \(0.167577\pi\) | |||||||
\(60\) | −1.13607 | −0.146666 | ||||||||
\(61\) | −14.7830 | −1.89277 | −0.946384 | − | 0.323043i | \(-0.895294\pi\) | ||||
−0.946384 | + | 0.323043i | \(0.895294\pi\) | |||||||
\(62\) | −1.21756 | −0.154630 | ||||||||
\(63\) | 2.25001 | 0.283475 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −5.82020 | −0.721907 | ||||||||
\(66\) | 0.419942 | 0.0516912 | ||||||||
\(67\) | −15.8988 | −1.94235 | −0.971174 | − | 0.238373i | \(-0.923386\pi\) | ||||
−0.971174 | + | 0.238373i | \(0.923386\pi\) | |||||||
\(68\) | 6.05036 | 0.733714 | ||||||||
\(69\) | 1.87183 | 0.225342 | ||||||||
\(70\) | −1.31630 | −0.157327 | ||||||||
\(71\) | −16.2197 | −1.92493 | −0.962463 | − | 0.271411i | \(-0.912510\pi\) | ||||
−0.962463 | + | 0.271411i | \(0.912510\pi\) | |||||||
\(72\) | −1.70935 | −0.201449 | ||||||||
\(73\) | 14.9111 | 1.74521 | 0.872604 | − | 0.488429i | \(-0.162430\pi\) | ||||
0.872604 | + | 0.488429i | \(0.162430\pi\) | |||||||
\(74\) | −2.26909 | −0.263776 | ||||||||
\(75\) | −1.13607 | −0.131182 | ||||||||
\(76\) | 0.866620 | 0.0994082 | ||||||||
\(77\) | 0.486562 | 0.0554489 | ||||||||
\(78\) | 6.61214 | 0.748677 | ||||||||
\(79\) | −10.1102 | −1.13749 | −0.568745 | − | 0.822514i | \(-0.692571\pi\) | ||||
−0.568745 | + | 0.822514i | \(0.692571\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −0.950058 | −0.105562 | ||||||||
\(82\) | 0.302941 | 0.0334543 | ||||||||
\(83\) | −14.7761 | −1.62189 | −0.810946 | − | 0.585122i | \(-0.801047\pi\) | ||||
−0.810946 | + | 0.585122i | \(0.801047\pi\) | |||||||
\(84\) | 1.49540 | 0.163161 | ||||||||
\(85\) | 6.05036 | 0.656253 | ||||||||
\(86\) | 9.60599 | 1.03584 | ||||||||
\(87\) | −8.34674 | −0.894864 | ||||||||
\(88\) | −0.369645 | −0.0394043 | ||||||||
\(89\) | −11.0303 | −1.16921 | −0.584606 | − | 0.811317i | \(-0.698751\pi\) | ||||
−0.584606 | + | 0.811317i | \(0.698751\pi\) | |||||||
\(90\) | −1.70935 | −0.180182 | ||||||||
\(91\) | 7.66110 | 0.803102 | ||||||||
\(92\) | −1.64764 | −0.171778 | ||||||||
\(93\) | 1.38323 | 0.143434 | ||||||||
\(94\) | −0.473050 | −0.0487914 | ||||||||
\(95\) | 0.866620 | 0.0889134 | ||||||||
\(96\) | −1.13607 | −0.115949 | ||||||||
\(97\) | −13.0791 | −1.32798 | −0.663990 | − | 0.747742i | \(-0.731138\pi\) | ||||
−0.663990 | + | 0.747742i | \(0.731138\pi\) | |||||||
\(98\) | −5.26737 | −0.532084 | ||||||||
\(99\) | 0.631854 | 0.0635037 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −14.2016 | −1.41311 | −0.706557 | − | 0.707656i | \(-0.749753\pi\) | ||||
−0.706557 | + | 0.707656i | \(0.749753\pi\) | |||||||
\(102\) | −6.87361 | −0.680589 | ||||||||
\(103\) | 0.292816 | 0.0288520 | 0.0144260 | − | 0.999896i | \(-0.495408\pi\) | ||||
0.0144260 | + | 0.999896i | \(0.495408\pi\) | |||||||
\(104\) | −5.82020 | −0.570718 | ||||||||
\(105\) | 1.49540 | 0.145936 | ||||||||
\(106\) | −5.12183 | −0.497476 | ||||||||
\(107\) | 3.50855 | 0.339184 | 0.169592 | − | 0.985514i | \(-0.445755\pi\) | ||||
0.169592 | + | 0.985514i | \(0.445755\pi\) | |||||||
\(108\) | 5.35014 | 0.514817 | ||||||||
\(109\) | −17.1180 | −1.63961 | −0.819804 | − | 0.572645i | \(-0.805918\pi\) | ||||
−0.819804 | + | 0.572645i | \(0.805918\pi\) | |||||||
\(110\) | −0.369645 | −0.0352443 | ||||||||
\(111\) | 2.57783 | 0.244677 | ||||||||
\(112\) | −1.31630 | −0.124378 | ||||||||
\(113\) | 5.65902 | 0.532356 | 0.266178 | − | 0.963924i | \(-0.414239\pi\) | ||||
0.266178 | + | 0.963924i | \(0.414239\pi\) | |||||||
\(114\) | −0.984538 | −0.0922105 | ||||||||
\(115\) | −1.64764 | −0.153643 | ||||||||
\(116\) | 7.34705 | 0.682156 | ||||||||
\(117\) | 9.94877 | 0.919764 | ||||||||
\(118\) | 13.2821 | 1.22272 | ||||||||
\(119\) | −7.96406 | −0.730064 | ||||||||
\(120\) | −1.13607 | −0.103708 | ||||||||
\(121\) | −10.8634 | −0.987578 | ||||||||
\(122\) | −14.7830 | −1.33839 | ||||||||
\(123\) | −0.344162 | −0.0310320 | ||||||||
\(124\) | −1.21756 | −0.109340 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 2.25001 | 0.200447 | ||||||||
\(127\) | −12.4503 | −1.10479 | −0.552393 | − | 0.833584i | \(-0.686285\pi\) | ||||
−0.552393 | + | 0.833584i | \(0.686285\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −10.9130 | −0.960840 | ||||||||
\(130\) | −5.82020 | −0.510465 | ||||||||
\(131\) | 17.1914 | 1.50202 | 0.751010 | − | 0.660291i | \(-0.229567\pi\) | ||||
0.751010 | + | 0.660291i | \(0.229567\pi\) | |||||||
\(132\) | 0.419942 | 0.0365512 | ||||||||
\(133\) | −1.14073 | −0.0989137 | ||||||||
\(134\) | −15.8988 | −1.37345 | ||||||||
\(135\) | 5.35014 | 0.460467 | ||||||||
\(136\) | 6.05036 | 0.518814 | ||||||||
\(137\) | 5.83901 | 0.498860 | 0.249430 | − | 0.968393i | \(-0.419757\pi\) | ||||
0.249430 | + | 0.968393i | \(0.419757\pi\) | |||||||
\(138\) | 1.87183 | 0.159341 | ||||||||
\(139\) | −9.86489 | −0.836729 | −0.418364 | − | 0.908279i | \(-0.637396\pi\) | ||||
−0.418364 | + | 0.908279i | \(0.637396\pi\) | |||||||
\(140\) | −1.31630 | −0.111247 | ||||||||
\(141\) | 0.537416 | 0.0452586 | ||||||||
\(142\) | −16.2197 | −1.36113 | ||||||||
\(143\) | 2.15141 | 0.179910 | ||||||||
\(144\) | −1.70935 | −0.142446 | ||||||||
\(145\) | 7.34705 | 0.610139 | ||||||||
\(146\) | 14.9111 | 1.23405 | ||||||||
\(147\) | 5.98408 | 0.493559 | ||||||||
\(148\) | −2.26909 | −0.186518 | ||||||||
\(149\) | 5.03587 | 0.412555 | 0.206277 | − | 0.978494i | \(-0.433865\pi\) | ||||
0.206277 | + | 0.978494i | \(0.433865\pi\) | |||||||
\(150\) | −1.13607 | −0.0927595 | ||||||||
\(151\) | −3.59542 | −0.292591 | −0.146296 | − | 0.989241i | \(-0.546735\pi\) | ||||
−0.146296 | + | 0.989241i | \(0.546735\pi\) | |||||||
\(152\) | 0.866620 | 0.0702922 | ||||||||
\(153\) | −10.3422 | −0.836117 | ||||||||
\(154\) | 0.486562 | 0.0392083 | ||||||||
\(155\) | −1.21756 | −0.0977967 | ||||||||
\(156\) | 6.61214 | 0.529395 | ||||||||
\(157\) | −21.1133 | −1.68502 | −0.842512 | − | 0.538678i | \(-0.818924\pi\) | ||||
−0.842512 | + | 0.538678i | \(0.818924\pi\) | |||||||
\(158\) | −10.1102 | −0.804327 | ||||||||
\(159\) | 5.81874 | 0.461456 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.16878 | 0.170924 | ||||||||
\(162\) | −0.950058 | −0.0746436 | ||||||||
\(163\) | 6.35927 | 0.498096 | 0.249048 | − | 0.968491i | \(-0.419882\pi\) | ||||
0.249048 | + | 0.968491i | \(0.419882\pi\) | |||||||
\(164\) | 0.302941 | 0.0236558 | ||||||||
\(165\) | 0.419942 | 0.0326924 | ||||||||
\(166\) | −14.7761 | −1.14685 | ||||||||
\(167\) | 1.10367 | 0.0854044 | 0.0427022 | − | 0.999088i | \(-0.486403\pi\) | ||||
0.0427022 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(168\) | 1.49540 | 0.115373 | ||||||||
\(169\) | 20.8747 | 1.60575 | ||||||||
\(170\) | 6.05036 | 0.464041 | ||||||||
\(171\) | −1.48136 | −0.113282 | ||||||||
\(172\) | 9.60599 | 0.732450 | ||||||||
\(173\) | 4.02327 | 0.305884 | 0.152942 | − | 0.988235i | \(-0.451125\pi\) | ||||
0.152942 | + | 0.988235i | \(0.451125\pi\) | |||||||
\(174\) | −8.34674 | −0.632764 | ||||||||
\(175\) | −1.31630 | −0.0995026 | ||||||||
\(176\) | −0.369645 | −0.0278631 | ||||||||
\(177\) | −15.0894 | −1.13419 | ||||||||
\(178\) | −11.0303 | −0.826758 | ||||||||
\(179\) | −3.90503 | −0.291875 | −0.145938 | − | 0.989294i | \(-0.546620\pi\) | ||||
−0.145938 | + | 0.989294i | \(0.546620\pi\) | |||||||
\(180\) | −1.70935 | −0.127408 | ||||||||
\(181\) | −19.2250 | −1.42898 | −0.714490 | − | 0.699646i | \(-0.753341\pi\) | ||||
−0.714490 | + | 0.699646i | \(0.753341\pi\) | |||||||
\(182\) | 7.66110 | 0.567879 | ||||||||
\(183\) | 16.7945 | 1.24148 | ||||||||
\(184\) | −1.64764 | −0.121466 | ||||||||
\(185\) | −2.26909 | −0.166827 | ||||||||
\(186\) | 1.38323 | 0.101423 | ||||||||
\(187\) | −2.23649 | −0.163548 | ||||||||
\(188\) | −0.473050 | −0.0345007 | ||||||||
\(189\) | −7.04236 | −0.512257 | ||||||||
\(190\) | 0.866620 | 0.0628712 | ||||||||
\(191\) | 16.5153 | 1.19500 | 0.597501 | − | 0.801868i | \(-0.296160\pi\) | ||||
0.597501 | + | 0.801868i | \(0.296160\pi\) | |||||||
\(192\) | −1.13607 | −0.0819886 | ||||||||
\(193\) | 10.4471 | 0.751998 | 0.375999 | − | 0.926620i | \(-0.377300\pi\) | ||||
0.375999 | + | 0.926620i | \(0.377300\pi\) | |||||||
\(194\) | −13.0791 | −0.939024 | ||||||||
\(195\) | 6.61214 | 0.473505 | ||||||||
\(196\) | −5.26737 | −0.376240 | ||||||||
\(197\) | 5.66850 | 0.403864 | 0.201932 | − | 0.979400i | \(-0.435278\pi\) | ||||
0.201932 | + | 0.979400i | \(0.435278\pi\) | |||||||
\(198\) | 0.631854 | 0.0449039 | ||||||||
\(199\) | 4.57095 | 0.324026 | 0.162013 | − | 0.986789i | \(-0.448201\pi\) | ||||
0.162013 | + | 0.986789i | \(0.448201\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 18.0621 | 1.27400 | ||||||||
\(202\) | −14.2016 | −0.999222 | ||||||||
\(203\) | −9.67089 | −0.678763 | ||||||||
\(204\) | −6.87361 | −0.481249 | ||||||||
\(205\) | 0.302941 | 0.0211584 | ||||||||
\(206\) | 0.292816 | 0.0204015 | ||||||||
\(207\) | 2.81640 | 0.195753 | ||||||||
\(208\) | −5.82020 | −0.403558 | ||||||||
\(209\) | −0.320342 | −0.0221585 | ||||||||
\(210\) | 1.49540 | 0.103192 | ||||||||
\(211\) | −21.2038 | −1.45973 | −0.729865 | − | 0.683591i | \(-0.760417\pi\) | ||||
−0.729865 | + | 0.683591i | \(0.760417\pi\) | |||||||
\(212\) | −5.12183 | −0.351769 | ||||||||
\(213\) | 18.4267 | 1.26258 | ||||||||
\(214\) | 3.50855 | 0.239839 | ||||||||
\(215\) | 9.60599 | 0.655123 | ||||||||
\(216\) | 5.35014 | 0.364031 | ||||||||
\(217\) | 1.60267 | 0.108796 | ||||||||
\(218\) | −17.1180 | −1.15938 | ||||||||
\(219\) | −16.9400 | −1.14470 | ||||||||
\(220\) | −0.369645 | −0.0249215 | ||||||||
\(221\) | −35.2143 | −2.36877 | ||||||||
\(222\) | 2.57783 | 0.173013 | ||||||||
\(223\) | −14.8044 | −0.991374 | −0.495687 | − | 0.868501i | \(-0.665084\pi\) | ||||
−0.495687 | + | 0.868501i | \(0.665084\pi\) | |||||||
\(224\) | −1.31630 | −0.0879487 | ||||||||
\(225\) | −1.70935 | −0.113957 | ||||||||
\(226\) | 5.65902 | 0.376433 | ||||||||
\(227\) | 17.0876 | 1.13414 | 0.567071 | − | 0.823669i | \(-0.308076\pi\) | ||||
0.567071 | + | 0.823669i | \(0.308076\pi\) | |||||||
\(228\) | −0.984538 | −0.0652027 | ||||||||
\(229\) | 17.3259 | 1.14493 | 0.572465 | − | 0.819929i | \(-0.305987\pi\) | ||||
0.572465 | + | 0.819929i | \(0.305987\pi\) | |||||||
\(230\) | −1.64764 | −0.108642 | ||||||||
\(231\) | −0.552767 | −0.0363694 | ||||||||
\(232\) | 7.34705 | 0.482357 | ||||||||
\(233\) | −0.738526 | −0.0483825 | −0.0241912 | − | 0.999707i | \(-0.507701\pi\) | ||||
−0.0241912 | + | 0.999707i | \(0.507701\pi\) | |||||||
\(234\) | 9.94877 | 0.650372 | ||||||||
\(235\) | −0.473050 | −0.0308584 | ||||||||
\(236\) | 13.2821 | 0.864592 | ||||||||
\(237\) | 11.4859 | 0.746090 | ||||||||
\(238\) | −7.96406 | −0.516233 | ||||||||
\(239\) | −7.74912 | −0.501249 | −0.250625 | − | 0.968084i | \(-0.580636\pi\) | ||||
−0.250625 | + | 0.968084i | \(0.580636\pi\) | |||||||
\(240\) | −1.13607 | −0.0733328 | ||||||||
\(241\) | −18.0098 | −1.16012 | −0.580058 | − | 0.814575i | \(-0.696970\pi\) | ||||
−0.580058 | + | 0.814575i | \(0.696970\pi\) | |||||||
\(242\) | −10.8634 | −0.698323 | ||||||||
\(243\) | −14.9711 | −0.960396 | ||||||||
\(244\) | −14.7830 | −0.946384 | ||||||||
\(245\) | −5.26737 | −0.336520 | ||||||||
\(246\) | −0.344162 | −0.0219430 | ||||||||
\(247\) | −5.04390 | −0.320936 | ||||||||
\(248\) | −1.21756 | −0.0773151 | ||||||||
\(249\) | 16.7867 | 1.06381 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 20.4697 | 1.29204 | 0.646019 | − | 0.763321i | \(-0.276433\pi\) | ||||
0.646019 | + | 0.763321i | \(0.276433\pi\) | |||||||
\(252\) | 2.25001 | 0.141737 | ||||||||
\(253\) | 0.609043 | 0.0382902 | ||||||||
\(254\) | −12.4503 | −0.781202 | ||||||||
\(255\) | −6.87361 | −0.430442 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.0700 | 0.628151 | 0.314075 | − | 0.949398i | \(-0.398306\pi\) | ||||
0.314075 | + | 0.949398i | \(0.398306\pi\) | |||||||
\(258\) | −10.9130 | −0.679416 | ||||||||
\(259\) | 2.98679 | 0.185590 | ||||||||
\(260\) | −5.82020 | −0.360954 | ||||||||
\(261\) | −12.5587 | −0.777363 | ||||||||
\(262\) | 17.1914 | 1.06209 | ||||||||
\(263\) | 17.5066 | 1.07950 | 0.539752 | − | 0.841824i | \(-0.318518\pi\) | ||||
0.539752 | + | 0.841824i | \(0.318518\pi\) | |||||||
\(264\) | 0.419942 | 0.0258456 | ||||||||
\(265\) | −5.12183 | −0.314631 | ||||||||
\(266\) | −1.14073 | −0.0699425 | ||||||||
\(267\) | 12.5312 | 0.766896 | ||||||||
\(268\) | −15.8988 | −0.971174 | ||||||||
\(269\) | 2.08606 | 0.127190 | 0.0635948 | − | 0.997976i | \(-0.479743\pi\) | ||||
0.0635948 | + | 0.997976i | \(0.479743\pi\) | |||||||
\(270\) | 5.35014 | 0.325599 | ||||||||
\(271\) | 3.58645 | 0.217861 | 0.108931 | − | 0.994049i | \(-0.465257\pi\) | ||||
0.108931 | + | 0.994049i | \(0.465257\pi\) | |||||||
\(272\) | 6.05036 | 0.366857 | ||||||||
\(273\) | −8.70353 | −0.526761 | ||||||||
\(274\) | 5.83901 | 0.352747 | ||||||||
\(275\) | −0.369645 | −0.0222904 | ||||||||
\(276\) | 1.87183 | 0.112671 | ||||||||
\(277\) | −11.8816 | −0.713898 | −0.356949 | − | 0.934124i | \(-0.616183\pi\) | ||||
−0.356949 | + | 0.934124i | \(0.616183\pi\) | |||||||
\(278\) | −9.86489 | −0.591657 | ||||||||
\(279\) | 2.08124 | 0.124600 | ||||||||
\(280\) | −1.31630 | −0.0786637 | ||||||||
\(281\) | 3.65872 | 0.218261 | 0.109130 | − | 0.994027i | \(-0.465193\pi\) | ||||
0.109130 | + | 0.994027i | \(0.465193\pi\) | |||||||
\(282\) | 0.537416 | 0.0320027 | ||||||||
\(283\) | −10.6073 | −0.630541 | −0.315271 | − | 0.949002i | \(-0.602095\pi\) | ||||
−0.315271 | + | 0.949002i | \(0.602095\pi\) | |||||||
\(284\) | −16.2197 | −0.962463 | ||||||||
\(285\) | −0.984538 | −0.0583190 | ||||||||
\(286\) | 2.15141 | 0.127215 | ||||||||
\(287\) | −0.398761 | −0.0235381 | ||||||||
\(288\) | −1.70935 | −0.100725 | ||||||||
\(289\) | 19.6068 | 1.15334 | ||||||||
\(290\) | 7.34705 | 0.431433 | ||||||||
\(291\) | 14.8587 | 0.871033 | ||||||||
\(292\) | 14.9111 | 0.872604 | ||||||||
\(293\) | −18.5346 | −1.08280 | −0.541401 | − | 0.840765i | \(-0.682106\pi\) | ||||
−0.541401 | + | 0.840765i | \(0.682106\pi\) | |||||||
\(294\) | 5.98408 | 0.348999 | ||||||||
\(295\) | 13.2821 | 0.773314 | ||||||||
\(296\) | −2.26909 | −0.131888 | ||||||||
\(297\) | −1.97765 | −0.114755 | ||||||||
\(298\) | 5.03587 | 0.291720 | ||||||||
\(299\) | 9.58960 | 0.554581 | ||||||||
\(300\) | −1.13607 | −0.0655908 | ||||||||
\(301\) | −12.6443 | −0.728806 | ||||||||
\(302\) | −3.59542 | −0.206893 | ||||||||
\(303\) | 16.1340 | 0.926873 | ||||||||
\(304\) | 0.866620 | 0.0497041 | ||||||||
\(305\) | −14.7830 | −0.846472 | ||||||||
\(306\) | −10.3422 | −0.591224 | ||||||||
\(307\) | 31.5036 | 1.79801 | 0.899003 | − | 0.437941i | \(-0.144292\pi\) | ||||
0.899003 | + | 0.437941i | \(0.144292\pi\) | |||||||
\(308\) | 0.486562 | 0.0277245 | ||||||||
\(309\) | −0.332659 | −0.0189243 | ||||||||
\(310\) | −1.21756 | −0.0691527 | ||||||||
\(311\) | 4.14482 | 0.235031 | 0.117516 | − | 0.993071i | \(-0.462507\pi\) | ||||
0.117516 | + | 0.993071i | \(0.462507\pi\) | |||||||
\(312\) | 6.61214 | 0.374339 | ||||||||
\(313\) | 8.30083 | 0.469191 | 0.234595 | − | 0.972093i | \(-0.424624\pi\) | ||||
0.234595 | + | 0.972093i | \(0.424624\pi\) | |||||||
\(314\) | −21.1133 | −1.19149 | ||||||||
\(315\) | 2.25001 | 0.126774 | ||||||||
\(316\) | −10.1102 | −0.568745 | ||||||||
\(317\) | −32.1457 | −1.80548 | −0.902740 | − | 0.430187i | \(-0.858448\pi\) | ||||
−0.902740 | + | 0.430187i | \(0.858448\pi\) | |||||||
\(318\) | 5.81874 | 0.326299 | ||||||||
\(319\) | −2.71580 | −0.152056 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | −3.98595 | −0.222474 | ||||||||
\(322\) | 2.16878 | 0.120862 | ||||||||
\(323\) | 5.24336 | 0.291748 | ||||||||
\(324\) | −0.950058 | −0.0527810 | ||||||||
\(325\) | −5.82020 | −0.322847 | ||||||||
\(326\) | 6.35927 | 0.352207 | ||||||||
\(327\) | 19.4472 | 1.07543 | ||||||||
\(328\) | 0.302941 | 0.0167271 | ||||||||
\(329\) | 0.622673 | 0.0343291 | ||||||||
\(330\) | 0.419942 | 0.0231170 | ||||||||
\(331\) | 10.3413 | 0.568409 | 0.284204 | − | 0.958764i | \(-0.408271\pi\) | ||||
0.284204 | + | 0.958764i | \(0.408271\pi\) | |||||||
\(332\) | −14.7761 | −0.810946 | ||||||||
\(333\) | 3.87867 | 0.212550 | ||||||||
\(334\) | 1.10367 | 0.0603900 | ||||||||
\(335\) | −15.8988 | −0.868644 | ||||||||
\(336\) | 1.49540 | 0.0815807 | ||||||||
\(337\) | −0.770786 | −0.0419874 | −0.0209937 | − | 0.999780i | \(-0.506683\pi\) | ||||
−0.0209937 | + | 0.999780i | \(0.506683\pi\) | |||||||
\(338\) | 20.8747 | 1.13544 | ||||||||
\(339\) | −6.42903 | −0.349177 | ||||||||
\(340\) | 6.05036 | 0.328127 | ||||||||
\(341\) | 0.450065 | 0.0243724 | ||||||||
\(342\) | −1.48136 | −0.0801027 | ||||||||
\(343\) | 16.1475 | 0.871882 | ||||||||
\(344\) | 9.60599 | 0.517920 | ||||||||
\(345\) | 1.87183 | 0.100776 | ||||||||
\(346\) | 4.02327 | 0.216292 | ||||||||
\(347\) | 36.6959 | 1.96994 | 0.984970 | − | 0.172725i | \(-0.0552572\pi\) | ||||
0.984970 | + | 0.172725i | \(0.0552572\pi\) | |||||||
\(348\) | −8.34674 | −0.447432 | ||||||||
\(349\) | −21.2787 | −1.13902 | −0.569511 | − | 0.821984i | \(-0.692867\pi\) | ||||
−0.569511 | + | 0.821984i | \(0.692867\pi\) | |||||||
\(350\) | −1.31630 | −0.0703590 | ||||||||
\(351\) | −31.1389 | −1.66207 | ||||||||
\(352\) | −0.369645 | −0.0197022 | ||||||||
\(353\) | 19.6791 | 1.04741 | 0.523706 | − | 0.851899i | \(-0.324549\pi\) | ||||
0.523706 | + | 0.851899i | \(0.324549\pi\) | |||||||
\(354\) | −15.0894 | −0.801991 | ||||||||
\(355\) | −16.2197 | −0.860854 | ||||||||
\(356\) | −11.0303 | −0.584606 | ||||||||
\(357\) | 9.04770 | 0.478855 | ||||||||
\(358\) | −3.90503 | −0.206387 | ||||||||
\(359\) | 8.74875 | 0.461741 | 0.230871 | − | 0.972984i | \(-0.425843\pi\) | ||||
0.230871 | + | 0.972984i | \(0.425843\pi\) | |||||||
\(360\) | −1.70935 | −0.0900908 | ||||||||
\(361\) | −18.2490 | −0.960472 | ||||||||
\(362\) | −19.2250 | −1.01044 | ||||||||
\(363\) | 12.3415 | 0.647761 | ||||||||
\(364\) | 7.66110 | 0.401551 | ||||||||
\(365\) | 14.9111 | 0.780480 | ||||||||
\(366\) | 16.7945 | 0.877861 | ||||||||
\(367\) | −21.8025 | −1.13808 | −0.569040 | − | 0.822310i | \(-0.692685\pi\) | ||||
−0.569040 | + | 0.822310i | \(0.692685\pi\) | |||||||
\(368\) | −1.64764 | −0.0858892 | ||||||||
\(369\) | −0.517834 | −0.0269573 | ||||||||
\(370\) | −2.26909 | −0.117964 | ||||||||
\(371\) | 6.74184 | 0.350019 | ||||||||
\(372\) | 1.38323 | 0.0717171 | ||||||||
\(373\) | 17.6367 | 0.913193 | 0.456596 | − | 0.889674i | \(-0.349068\pi\) | ||||
0.456596 | + | 0.889674i | \(0.349068\pi\) | |||||||
\(374\) | −2.23649 | −0.115646 | ||||||||
\(375\) | −1.13607 | −0.0586662 | ||||||||
\(376\) | −0.473050 | −0.0243957 | ||||||||
\(377\) | −42.7613 | −2.20232 | ||||||||
\(378\) | −7.04236 | −0.362220 | ||||||||
\(379\) | 3.12987 | 0.160771 | 0.0803853 | − | 0.996764i | \(-0.474385\pi\) | ||||
0.0803853 | + | 0.996764i | \(0.474385\pi\) | |||||||
\(380\) | 0.866620 | 0.0444567 | ||||||||
\(381\) | 14.1444 | 0.724639 | ||||||||
\(382\) | 16.5153 | 0.844995 | ||||||||
\(383\) | −4.78232 | −0.244365 | −0.122183 | − | 0.992508i | \(-0.538989\pi\) | ||||
−0.122183 | + | 0.992508i | \(0.538989\pi\) | |||||||
\(384\) | −1.13607 | −0.0579747 | ||||||||
\(385\) | 0.486562 | 0.0247975 | ||||||||
\(386\) | 10.4471 | 0.531743 | ||||||||
\(387\) | −16.4200 | −0.834676 | ||||||||
\(388\) | −13.0791 | −0.663990 | ||||||||
\(389\) | 24.0116 | 1.21743 | 0.608717 | − | 0.793387i | \(-0.291684\pi\) | ||||
0.608717 | + | 0.793387i | \(0.291684\pi\) | |||||||
\(390\) | 6.61214 | 0.334819 | ||||||||
\(391\) | −9.96882 | −0.504145 | ||||||||
\(392\) | −5.26737 | −0.266042 | ||||||||
\(393\) | −19.5306 | −0.985188 | ||||||||
\(394\) | 5.66850 | 0.285575 | ||||||||
\(395\) | −10.1102 | −0.508701 | ||||||||
\(396\) | 0.631854 | 0.0317519 | ||||||||
\(397\) | 14.4230 | 0.723870 | 0.361935 | − | 0.932203i | \(-0.382116\pi\) | ||||
0.361935 | + | 0.932203i | \(0.382116\pi\) | |||||||
\(398\) | 4.57095 | 0.229121 | ||||||||
\(399\) | 1.29594 | 0.0648783 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 14.6177 | 0.729971 | 0.364985 | − | 0.931013i | \(-0.381074\pi\) | ||||
0.364985 | + | 0.931013i | \(0.381074\pi\) | |||||||
\(402\) | 18.0621 | 0.900856 | ||||||||
\(403\) | 7.08644 | 0.353001 | ||||||||
\(404\) | −14.2016 | −0.706557 | ||||||||
\(405\) | −0.950058 | −0.0472088 | ||||||||
\(406\) | −9.67089 | −0.479958 | ||||||||
\(407\) | 0.838757 | 0.0415756 | ||||||||
\(408\) | −6.87361 | −0.340294 | ||||||||
\(409\) | −18.7903 | −0.929122 | −0.464561 | − | 0.885541i | \(-0.653788\pi\) | ||||
−0.464561 | + | 0.885541i | \(0.653788\pi\) | |||||||
\(410\) | 0.302941 | 0.0149612 | ||||||||
\(411\) | −6.63350 | −0.327207 | ||||||||
\(412\) | 0.292816 | 0.0144260 | ||||||||
\(413\) | −17.4832 | −0.860291 | ||||||||
\(414\) | 2.81640 | 0.138418 | ||||||||
\(415\) | −14.7761 | −0.725332 | ||||||||
\(416\) | −5.82020 | −0.285359 | ||||||||
\(417\) | 11.2072 | 0.548818 | ||||||||
\(418\) | −0.320342 | −0.0156684 | ||||||||
\(419\) | 7.37928 | 0.360502 | 0.180251 | − | 0.983621i | \(-0.442309\pi\) | ||||
0.180251 | + | 0.983621i | \(0.442309\pi\) | |||||||
\(420\) | 1.49540 | 0.0729680 | ||||||||
\(421\) | 7.33963 | 0.357712 | 0.178856 | − | 0.983875i | \(-0.442760\pi\) | ||||
0.178856 | + | 0.983875i | \(0.442760\pi\) | |||||||
\(422\) | −21.2038 | −1.03219 | ||||||||
\(423\) | 0.808609 | 0.0393159 | ||||||||
\(424\) | −5.12183 | −0.248738 | ||||||||
\(425\) | 6.05036 | 0.293485 | ||||||||
\(426\) | 18.4267 | 0.892776 | ||||||||
\(427\) | 19.4588 | 0.941677 | ||||||||
\(428\) | 3.50855 | 0.169592 | ||||||||
\(429\) | −2.44414 | −0.118004 | ||||||||
\(430\) | 9.60599 | 0.463242 | ||||||||
\(431\) | 16.6986 | 0.804345 | 0.402173 | − | 0.915564i | \(-0.368255\pi\) | ||||
0.402173 | + | 0.915564i | \(0.368255\pi\) | |||||||
\(432\) | 5.35014 | 0.257409 | ||||||||
\(433\) | −29.9018 | −1.43699 | −0.718495 | − | 0.695532i | \(-0.755169\pi\) | ||||
−0.718495 | + | 0.695532i | \(0.755169\pi\) | |||||||
\(434\) | 1.60267 | 0.0769305 | ||||||||
\(435\) | −8.34674 | −0.400195 | ||||||||
\(436\) | −17.1180 | −0.819804 | ||||||||
\(437\) | −1.42788 | −0.0683047 | ||||||||
\(438\) | −16.9400 | −0.809422 | ||||||||
\(439\) | −33.8204 | −1.61416 | −0.807080 | − | 0.590442i | \(-0.798953\pi\) | ||||
−0.807080 | + | 0.590442i | \(0.798953\pi\) | |||||||
\(440\) | −0.369645 | −0.0176221 | ||||||||
\(441\) | 9.00378 | 0.428752 | ||||||||
\(442\) | −35.2143 | −1.67497 | ||||||||
\(443\) | 8.00923 | 0.380530 | 0.190265 | − | 0.981733i | \(-0.439065\pi\) | ||||
0.190265 | + | 0.981733i | \(0.439065\pi\) | |||||||
\(444\) | 2.57783 | 0.122339 | ||||||||
\(445\) | −11.0303 | −0.522887 | ||||||||
\(446\) | −14.8044 | −0.701007 | ||||||||
\(447\) | −5.72109 | −0.270598 | ||||||||
\(448\) | −1.31630 | −0.0621891 | ||||||||
\(449\) | −8.81951 | −0.416219 | −0.208109 | − | 0.978106i | \(-0.566731\pi\) | ||||
−0.208109 | + | 0.978106i | \(0.566731\pi\) | |||||||
\(450\) | −1.70935 | −0.0805796 | ||||||||
\(451\) | −0.111981 | −0.00527297 | ||||||||
\(452\) | 5.65902 | 0.266178 | ||||||||
\(453\) | 4.08464 | 0.191913 | ||||||||
\(454\) | 17.0876 | 0.801960 | ||||||||
\(455\) | 7.66110 | 0.359158 | ||||||||
\(456\) | −0.984538 | −0.0461052 | ||||||||
\(457\) | −2.75550 | −0.128897 | −0.0644484 | − | 0.997921i | \(-0.520529\pi\) | ||||
−0.0644484 | + | 0.997921i | \(0.520529\pi\) | |||||||
\(458\) | 17.3259 | 0.809588 | ||||||||
\(459\) | 32.3703 | 1.51091 | ||||||||
\(460\) | −1.64764 | −0.0768217 | ||||||||
\(461\) | −4.50213 | −0.209685 | −0.104843 | − | 0.994489i | \(-0.533434\pi\) | ||||
−0.104843 | + | 0.994489i | \(0.533434\pi\) | |||||||
\(462\) | −0.552767 | −0.0257171 | ||||||||
\(463\) | −23.3048 | −1.08306 | −0.541532 | − | 0.840680i | \(-0.682155\pi\) | ||||
−0.541532 | + | 0.840680i | \(0.682155\pi\) | |||||||
\(464\) | 7.34705 | 0.341078 | ||||||||
\(465\) | 1.38323 | 0.0641457 | ||||||||
\(466\) | −0.738526 | −0.0342116 | ||||||||
\(467\) | 5.67434 | 0.262577 | 0.131289 | − | 0.991344i | \(-0.458089\pi\) | ||||
0.131289 | + | 0.991344i | \(0.458089\pi\) | |||||||
\(468\) | 9.94877 | 0.459882 | ||||||||
\(469\) | 20.9275 | 0.966343 | ||||||||
\(470\) | −0.473050 | −0.0218202 | ||||||||
\(471\) | 23.9861 | 1.10522 | ||||||||
\(472\) | 13.2821 | 0.611359 | ||||||||
\(473\) | −3.55081 | −0.163266 | ||||||||
\(474\) | 11.4859 | 0.527565 | ||||||||
\(475\) | 0.866620 | 0.0397633 | ||||||||
\(476\) | −7.96406 | −0.365032 | ||||||||
\(477\) | 8.75501 | 0.400864 | ||||||||
\(478\) | −7.74912 | −0.354437 | ||||||||
\(479\) | −29.8542 | −1.36407 | −0.682037 | − | 0.731317i | \(-0.738906\pi\) | ||||
−0.682037 | + | 0.731317i | \(0.738906\pi\) | |||||||
\(480\) | −1.13607 | −0.0518541 | ||||||||
\(481\) | 13.2065 | 0.602166 | ||||||||
\(482\) | −18.0098 | −0.820326 | ||||||||
\(483\) | −2.46388 | −0.112111 | ||||||||
\(484\) | −10.8634 | −0.493789 | ||||||||
\(485\) | −13.0791 | −0.593891 | ||||||||
\(486\) | −14.9711 | −0.679102 | ||||||||
\(487\) | −37.7136 | −1.70897 | −0.854484 | − | 0.519478i | \(-0.826126\pi\) | ||||
−0.854484 | + | 0.519478i | \(0.826126\pi\) | |||||||
\(488\) | −14.7830 | −0.669195 | ||||||||
\(489\) | −7.22455 | −0.326706 | ||||||||
\(490\) | −5.26737 | −0.237955 | ||||||||
\(491\) | −28.3165 | −1.27791 | −0.638954 | − | 0.769245i | \(-0.720632\pi\) | ||||
−0.638954 | + | 0.769245i | \(0.720632\pi\) | |||||||
\(492\) | −0.344162 | −0.0155160 | ||||||||
\(493\) | 44.4523 | 2.00203 | ||||||||
\(494\) | −5.04390 | −0.226936 | ||||||||
\(495\) | 0.631854 | 0.0283997 | ||||||||
\(496\) | −1.21756 | −0.0546700 | ||||||||
\(497\) | 21.3500 | 0.957676 | ||||||||
\(498\) | 16.7867 | 0.752229 | ||||||||
\(499\) | −25.6119 | −1.14655 | −0.573273 | − | 0.819364i | \(-0.694327\pi\) | ||||
−0.573273 | + | 0.819364i | \(0.694327\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −1.25384 | −0.0560175 | ||||||||
\(502\) | 20.4697 | 0.913609 | ||||||||
\(503\) | 8.17948 | 0.364705 | 0.182352 | − | 0.983233i | \(-0.441629\pi\) | ||||
0.182352 | + | 0.983233i | \(0.441629\pi\) | |||||||
\(504\) | 2.25001 | 0.100224 | ||||||||
\(505\) | −14.2016 | −0.631964 | ||||||||
\(506\) | 0.609043 | 0.0270752 | ||||||||
\(507\) | −23.7151 | −1.05322 | ||||||||
\(508\) | −12.4503 | −0.552393 | ||||||||
\(509\) | −1.70424 | −0.0755390 | −0.0377695 | − | 0.999286i | \(-0.512025\pi\) | ||||
−0.0377695 | + | 0.999286i | \(0.512025\pi\) | |||||||
\(510\) | −6.87361 | −0.304369 | ||||||||
\(511\) | −19.6274 | −0.868263 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.63654 | 0.204708 | ||||||||
\(514\) | 10.0700 | 0.444170 | ||||||||
\(515\) | 0.292816 | 0.0129030 | ||||||||
\(516\) | −10.9130 | −0.480420 | ||||||||
\(517\) | 0.174861 | 0.00769036 | ||||||||
\(518\) | 2.98679 | 0.131232 | ||||||||
\(519\) | −4.57070 | −0.200632 | ||||||||
\(520\) | −5.82020 | −0.255233 | ||||||||
\(521\) | −25.1989 | −1.10398 | −0.551991 | − | 0.833850i | \(-0.686132\pi\) | ||||
−0.551991 | + | 0.833850i | \(0.686132\pi\) | |||||||
\(522\) | −12.5587 | −0.549679 | ||||||||
\(523\) | 40.2666 | 1.76074 | 0.880368 | − | 0.474292i | \(-0.157296\pi\) | ||||
0.880368 | + | 0.474292i | \(0.157296\pi\) | |||||||
\(524\) | 17.1914 | 0.751010 | ||||||||
\(525\) | 1.49540 | 0.0652646 | ||||||||
\(526\) | 17.5066 | 0.763324 | ||||||||
\(527\) | −7.36667 | −0.320897 | ||||||||
\(528\) | 0.419942 | 0.0182756 | ||||||||
\(529\) | −20.2853 | −0.881969 | ||||||||
\(530\) | −5.12183 | −0.222478 | ||||||||
\(531\) | −22.7038 | −0.985261 | ||||||||
\(532\) | −1.14073 | −0.0494568 | ||||||||
\(533\) | −1.76318 | −0.0763718 | ||||||||
\(534\) | 12.5312 | 0.542277 | ||||||||
\(535\) | 3.50855 | 0.151688 | ||||||||
\(536\) | −15.8988 | −0.686724 | ||||||||
\(537\) | 4.43637 | 0.191443 | ||||||||
\(538\) | 2.08606 | 0.0899366 | ||||||||
\(539\) | 1.94706 | 0.0838657 | ||||||||
\(540\) | 5.35014 | 0.230233 | ||||||||
\(541\) | 16.6343 | 0.715163 | 0.357581 | − | 0.933882i | \(-0.383602\pi\) | ||||
0.357581 | + | 0.933882i | \(0.383602\pi\) | |||||||
\(542\) | 3.58645 | 0.154051 | ||||||||
\(543\) | 21.8408 | 0.937280 | ||||||||
\(544\) | 6.05036 | 0.259407 | ||||||||
\(545\) | −17.1180 | −0.733255 | ||||||||
\(546\) | −8.70353 | −0.372477 | ||||||||
\(547\) | 12.2347 | 0.523118 | 0.261559 | − | 0.965187i | \(-0.415763\pi\) | ||||
0.261559 | + | 0.965187i | \(0.415763\pi\) | |||||||
\(548\) | 5.83901 | 0.249430 | ||||||||
\(549\) | 25.2693 | 1.07847 | ||||||||
\(550\) | −0.369645 | −0.0157617 | ||||||||
\(551\) | 6.36710 | 0.271248 | ||||||||
\(552\) | 1.87183 | 0.0796704 | ||||||||
\(553\) | 13.3081 | 0.565916 | ||||||||
\(554\) | −11.8816 | −0.504802 | ||||||||
\(555\) | 2.57783 | 0.109423 | ||||||||
\(556\) | −9.86489 | −0.418364 | ||||||||
\(557\) | −29.6081 | −1.25454 | −0.627268 | − | 0.778804i | \(-0.715827\pi\) | ||||
−0.627268 | + | 0.778804i | \(0.715827\pi\) | |||||||
\(558\) | 2.08124 | 0.0881058 | ||||||||
\(559\) | −55.9088 | −2.36469 | ||||||||
\(560\) | −1.31630 | −0.0556236 | ||||||||
\(561\) | 2.54080 | 0.107273 | ||||||||
\(562\) | 3.65872 | 0.154334 | ||||||||
\(563\) | −6.36777 | −0.268370 | −0.134185 | − | 0.990956i | \(-0.542842\pi\) | ||||
−0.134185 | + | 0.990956i | \(0.542842\pi\) | |||||||
\(564\) | 0.537416 | 0.0226293 | ||||||||
\(565\) | 5.65902 | 0.238077 | ||||||||
\(566\) | −10.6073 | −0.445860 | ||||||||
\(567\) | 1.25056 | 0.0525185 | ||||||||
\(568\) | −16.2197 | −0.680564 | ||||||||
\(569\) | 5.58077 | 0.233958 | 0.116979 | − | 0.993134i | \(-0.462679\pi\) | ||||
0.116979 | + | 0.993134i | \(0.462679\pi\) | |||||||
\(570\) | −0.984538 | −0.0412378 | ||||||||
\(571\) | −22.0264 | −0.921778 | −0.460889 | − | 0.887458i | \(-0.652469\pi\) | ||||
−0.460889 | + | 0.887458i | \(0.652469\pi\) | |||||||
\(572\) | 2.15141 | 0.0899549 | ||||||||
\(573\) | −18.7624 | −0.783812 | ||||||||
\(574\) | −0.398761 | −0.0166439 | ||||||||
\(575\) | −1.64764 | −0.0687114 | ||||||||
\(576\) | −1.70935 | −0.0712230 | ||||||||
\(577\) | −5.35466 | −0.222918 | −0.111459 | − | 0.993769i | \(-0.535552\pi\) | ||||
−0.111459 | + | 0.993769i | \(0.535552\pi\) | |||||||
\(578\) | 19.6068 | 0.815536 | ||||||||
\(579\) | −11.8686 | −0.493242 | ||||||||
\(580\) | 7.34705 | 0.305070 | ||||||||
\(581\) | 19.4498 | 0.806912 | ||||||||
\(582\) | 14.8587 | 0.615914 | ||||||||
\(583\) | 1.89326 | 0.0784108 | ||||||||
\(584\) | 14.9111 | 0.617024 | ||||||||
\(585\) | 9.94877 | 0.411331 | ||||||||
\(586\) | −18.5346 | −0.765657 | ||||||||
\(587\) | −0.510618 | −0.0210755 | −0.0105377 | − | 0.999944i | \(-0.503354\pi\) | ||||
−0.0105377 | + | 0.999944i | \(0.503354\pi\) | |||||||
\(588\) | 5.98408 | 0.246779 | ||||||||
\(589\) | −1.05516 | −0.0434772 | ||||||||
\(590\) | 13.2821 | 0.546816 | ||||||||
\(591\) | −6.43979 | −0.264898 | ||||||||
\(592\) | −2.26909 | −0.0932589 | ||||||||
\(593\) | −1.84834 | −0.0759023 | −0.0379511 | − | 0.999280i | \(-0.512083\pi\) | ||||
−0.0379511 | + | 0.999280i | \(0.512083\pi\) | |||||||
\(594\) | −1.97765 | −0.0811441 | ||||||||
\(595\) | −7.96406 | −0.326495 | ||||||||
\(596\) | 5.03587 | 0.206277 | ||||||||
\(597\) | −5.19291 | −0.212532 | ||||||||
\(598\) | 9.58960 | 0.392148 | ||||||||
\(599\) | 35.1951 | 1.43803 | 0.719016 | − | 0.694993i | \(-0.244593\pi\) | ||||
0.719016 | + | 0.694993i | \(0.244593\pi\) | |||||||
\(600\) | −1.13607 | −0.0463797 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | −12.6443 | −0.515344 | ||||||||
\(603\) | 27.1766 | 1.10672 | ||||||||
\(604\) | −3.59542 | −0.146296 | ||||||||
\(605\) | −10.8634 | −0.441658 | ||||||||
\(606\) | 16.1340 | 0.655398 | ||||||||
\(607\) | 27.3914 | 1.11178 | 0.555891 | − | 0.831255i | \(-0.312377\pi\) | ||||
0.555891 | + | 0.831255i | \(0.312377\pi\) | |||||||
\(608\) | 0.866620 | 0.0351461 | ||||||||
\(609\) | 10.9868 | 0.445207 | ||||||||
\(610\) | −14.7830 | −0.598546 | ||||||||
\(611\) | 2.75325 | 0.111384 | ||||||||
\(612\) | −10.3422 | −0.418058 | ||||||||
\(613\) | 1.27636 | 0.0515518 | 0.0257759 | − | 0.999668i | \(-0.491794\pi\) | ||||
0.0257759 | + | 0.999668i | \(0.491794\pi\) | |||||||
\(614\) | 31.5036 | 1.27138 | ||||||||
\(615\) | −0.344162 | −0.0138779 | ||||||||
\(616\) | 0.486562 | 0.0196042 | ||||||||
\(617\) | 22.5375 | 0.907326 | 0.453663 | − | 0.891173i | \(-0.350117\pi\) | ||||
0.453663 | + | 0.891173i | \(0.350117\pi\) | |||||||
\(618\) | −0.332659 | −0.0133815 | ||||||||
\(619\) | 5.54288 | 0.222787 | 0.111394 | − | 0.993776i | \(-0.464469\pi\) | ||||
0.111394 | + | 0.993776i | \(0.464469\pi\) | |||||||
\(620\) | −1.21756 | −0.0488984 | ||||||||
\(621\) | −8.81511 | −0.353738 | ||||||||
\(622\) | 4.14482 | 0.166192 | ||||||||
\(623\) | 14.5192 | 0.581698 | ||||||||
\(624\) | 6.61214 | 0.264697 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 8.30083 | 0.331768 | ||||||||
\(627\) | 0.363930 | 0.0145340 | ||||||||
\(628\) | −21.1133 | −0.842512 | ||||||||
\(629\) | −13.7288 | −0.547403 | ||||||||
\(630\) | 2.25001 | 0.0896427 | ||||||||
\(631\) | 26.5157 | 1.05557 | 0.527787 | − | 0.849377i | \(-0.323022\pi\) | ||||
0.527787 | + | 0.849377i | \(0.323022\pi\) | |||||||
\(632\) | −10.1102 | −0.402164 | ||||||||
\(633\) | 24.0889 | 0.957450 | ||||||||
\(634\) | −32.1457 | −1.27667 | ||||||||
\(635\) | −12.4503 | −0.494076 | ||||||||
\(636\) | 5.81874 | 0.230728 | ||||||||
\(637\) | 30.6571 | 1.21468 | ||||||||
\(638\) | −2.71580 | −0.107520 | ||||||||
\(639\) | 27.7252 | 1.09679 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 26.0522 | 1.02900 | 0.514501 | − | 0.857490i | \(-0.327977\pi\) | ||||
0.514501 | + | 0.857490i | \(0.327977\pi\) | |||||||
\(642\) | −3.98595 | −0.157313 | ||||||||
\(643\) | 36.0166 | 1.42036 | 0.710178 | − | 0.704022i | \(-0.248615\pi\) | ||||
0.710178 | + | 0.704022i | \(0.248615\pi\) | |||||||
\(644\) | 2.16878 | 0.0854620 | ||||||||
\(645\) | −10.9130 | −0.429701 | ||||||||
\(646\) | 5.24336 | 0.206297 | ||||||||
\(647\) | 31.9782 | 1.25719 | 0.628597 | − | 0.777731i | \(-0.283630\pi\) | ||||
0.628597 | + | 0.777731i | \(0.283630\pi\) | |||||||
\(648\) | −0.950058 | −0.0373218 | ||||||||
\(649\) | −4.90967 | −0.192721 | ||||||||
\(650\) | −5.82020 | −0.228287 | ||||||||
\(651\) | −1.82074 | −0.0713604 | ||||||||
\(652\) | 6.35927 | 0.249048 | ||||||||
\(653\) | 13.6903 | 0.535741 | 0.267871 | − | 0.963455i | \(-0.413680\pi\) | ||||
0.267871 | + | 0.963455i | \(0.413680\pi\) | |||||||
\(654\) | 19.4472 | 0.760446 | ||||||||
\(655\) | 17.1914 | 0.671724 | ||||||||
\(656\) | 0.302941 | 0.0118279 | ||||||||
\(657\) | −25.4882 | −0.994391 | ||||||||
\(658\) | 0.622673 | 0.0242743 | ||||||||
\(659\) | −30.0868 | −1.17202 | −0.586008 | − | 0.810305i | \(-0.699301\pi\) | ||||
−0.586008 | + | 0.810305i | \(0.699301\pi\) | |||||||
\(660\) | 0.419942 | 0.0163462 | ||||||||
\(661\) | −22.8812 | −0.889976 | −0.444988 | − | 0.895536i | \(-0.646792\pi\) | ||||
−0.444988 | + | 0.895536i | \(0.646792\pi\) | |||||||
\(662\) | 10.3413 | 0.401926 | ||||||||
\(663\) | 40.0058 | 1.55370 | ||||||||
\(664\) | −14.7761 | −0.573425 | ||||||||
\(665\) | −1.14073 | −0.0442356 | ||||||||
\(666\) | 3.87867 | 0.150295 | ||||||||
\(667\) | −12.1053 | −0.468719 | ||||||||
\(668\) | 1.10367 | 0.0427022 | ||||||||
\(669\) | 16.8188 | 0.650251 | ||||||||
\(670\) | −15.8988 | −0.614224 | ||||||||
\(671\) | 5.46446 | 0.210953 | ||||||||
\(672\) | 1.49540 | 0.0576863 | ||||||||
\(673\) | −22.5000 | −0.867312 | −0.433656 | − | 0.901079i | \(-0.642777\pi\) | ||||
−0.433656 | + | 0.901079i | \(0.642777\pi\) | |||||||
\(674\) | −0.770786 | −0.0296896 | ||||||||
\(675\) | 5.35014 | 0.205927 | ||||||||
\(676\) | 20.8747 | 0.802874 | ||||||||
\(677\) | −23.6948 | −0.910666 | −0.455333 | − | 0.890321i | \(-0.650480\pi\) | ||||
−0.455333 | + | 0.890321i | \(0.650480\pi\) | |||||||
\(678\) | −6.42903 | −0.246905 | ||||||||
\(679\) | 17.2159 | 0.660687 | ||||||||
\(680\) | 6.05036 | 0.232021 | ||||||||
\(681\) | −19.4126 | −0.743893 | ||||||||
\(682\) | 0.450065 | 0.0172339 | ||||||||
\(683\) | −47.3804 | −1.81296 | −0.906481 | − | 0.422246i | \(-0.861242\pi\) | ||||
−0.906481 | + | 0.422246i | \(0.861242\pi\) | |||||||
\(684\) | −1.48136 | −0.0566412 | ||||||||
\(685\) | 5.83901 | 0.223097 | ||||||||
\(686\) | 16.1475 | 0.616514 | ||||||||
\(687\) | −19.6834 | −0.750970 | ||||||||
\(688\) | 9.60599 | 0.366225 | ||||||||
\(689\) | 29.8101 | 1.13567 | ||||||||
\(690\) | 1.87183 | 0.0712594 | ||||||||
\(691\) | 4.42633 | 0.168385 | 0.0841927 | − | 0.996449i | \(-0.473169\pi\) | ||||
0.0841927 | + | 0.996449i | \(0.473169\pi\) | |||||||
\(692\) | 4.02327 | 0.152942 | ||||||||
\(693\) | −0.831706 | −0.0315939 | ||||||||
\(694\) | 36.6959 | 1.39296 | ||||||||
\(695\) | −9.86489 | −0.374196 | ||||||||
\(696\) | −8.34674 | −0.316382 | ||||||||
\(697\) | 1.83290 | 0.0694262 | ||||||||
\(698\) | −21.2787 | −0.805410 | ||||||||
\(699\) | 0.839015 | 0.0317345 | ||||||||
\(700\) | −1.31630 | −0.0497513 | ||||||||
\(701\) | −8.81618 | −0.332982 | −0.166491 | − | 0.986043i | \(-0.553244\pi\) | ||||
−0.166491 | + | 0.986043i | \(0.553244\pi\) | |||||||
\(702\) | −31.1389 | −1.17526 | ||||||||
\(703\) | −1.96644 | −0.0741656 | ||||||||
\(704\) | −0.369645 | −0.0139315 | ||||||||
\(705\) | 0.537416 | 0.0202403 | ||||||||
\(706\) | 19.6791 | 0.740632 | ||||||||
\(707\) | 18.6935 | 0.703042 | ||||||||
\(708\) | −15.0894 | −0.567093 | ||||||||
\(709\) | −24.7455 | −0.929338 | −0.464669 | − | 0.885484i | \(-0.653827\pi\) | ||||
−0.464669 | + | 0.885484i | \(0.653827\pi\) | |||||||
\(710\) | −16.2197 | −0.608715 | ||||||||
\(711\) | 17.2820 | 0.648124 | ||||||||
\(712\) | −11.0303 | −0.413379 | ||||||||
\(713\) | 2.00610 | 0.0751291 | ||||||||
\(714\) | 9.04770 | 0.338602 | ||||||||
\(715\) | 2.15141 | 0.0804581 | ||||||||
\(716\) | −3.90503 | −0.145938 | ||||||||
\(717\) | 8.80352 | 0.328774 | ||||||||
\(718\) | 8.74875 | 0.326500 | ||||||||
\(719\) | −0.234057 | −0.00872886 | −0.00436443 | − | 0.999990i | \(-0.501389\pi\) | ||||
−0.00436443 | + | 0.999990i | \(0.501389\pi\) | |||||||
\(720\) | −1.70935 | −0.0637038 | ||||||||
\(721\) | −0.385433 | −0.0143543 | ||||||||
\(722\) | −18.2490 | −0.679156 | ||||||||
\(723\) | 20.4604 | 0.760930 | ||||||||
\(724\) | −19.2250 | −0.714490 | ||||||||
\(725\) | 7.34705 | 0.272862 | ||||||||
\(726\) | 12.3415 | 0.458036 | ||||||||
\(727\) | −36.6345 | −1.35870 | −0.679350 | − | 0.733814i | \(-0.737738\pi\) | ||||
−0.679350 | + | 0.733814i | \(0.737738\pi\) | |||||||
\(728\) | 7.66110 | 0.283939 | ||||||||
\(729\) | 19.8583 | 0.735494 | ||||||||
\(730\) | 14.9111 | 0.551883 | ||||||||
\(731\) | 58.1197 | 2.14963 | ||||||||
\(732\) | 16.7945 | 0.620742 | ||||||||
\(733\) | 26.7468 | 0.987917 | 0.493959 | − | 0.869485i | \(-0.335549\pi\) | ||||
0.493959 | + | 0.869485i | \(0.335549\pi\) | |||||||
\(734\) | −21.8025 | −0.804744 | ||||||||
\(735\) | 5.98408 | 0.220726 | ||||||||
\(736\) | −1.64764 | −0.0607329 | ||||||||
\(737\) | 5.87691 | 0.216479 | ||||||||
\(738\) | −0.517834 | −0.0190617 | ||||||||
\(739\) | 8.19880 | 0.301598 | 0.150799 | − | 0.988564i | \(-0.451815\pi\) | ||||
0.150799 | + | 0.988564i | \(0.451815\pi\) | |||||||
\(740\) | −2.26909 | −0.0834133 | ||||||||
\(741\) | 5.73021 | 0.210505 | ||||||||
\(742\) | 6.74184 | 0.247501 | ||||||||
\(743\) | −11.2264 | −0.411855 | −0.205928 | − | 0.978567i | \(-0.566021\pi\) | ||||
−0.205928 | + | 0.978567i | \(0.566021\pi\) | |||||||
\(744\) | 1.38323 | 0.0507116 | ||||||||
\(745\) | 5.03587 | 0.184500 | ||||||||
\(746\) | 17.6367 | 0.645725 | ||||||||
\(747\) | 25.2576 | 0.924128 | ||||||||
\(748\) | −2.23649 | −0.0817740 | ||||||||
\(749\) | −4.61829 | −0.168749 | ||||||||
\(750\) | −1.13607 | −0.0414833 | ||||||||
\(751\) | −33.2136 | −1.21198 | −0.605991 | − | 0.795471i | \(-0.707223\pi\) | ||||
−0.605991 | + | 0.795471i | \(0.707223\pi\) | |||||||
\(752\) | −0.473050 | −0.0172504 | ||||||||
\(753\) | −23.2550 | −0.847459 | ||||||||
\(754\) | −42.7613 | −1.55727 | ||||||||
\(755\) | −3.59542 | −0.130851 | ||||||||
\(756\) | −7.04236 | −0.256128 | ||||||||
\(757\) | −1.70262 | −0.0618827 | −0.0309414 | − | 0.999521i | \(-0.509851\pi\) | ||||
−0.0309414 | + | 0.999521i | \(0.509851\pi\) | |||||||
\(758\) | 3.12987 | 0.113682 | ||||||||
\(759\) | −0.691913 | −0.0251149 | ||||||||
\(760\) | 0.866620 | 0.0314356 | ||||||||
\(761\) | −28.0640 | −1.01732 | −0.508659 | − | 0.860968i | \(-0.669859\pi\) | ||||
−0.508659 | + | 0.860968i | \(0.669859\pi\) | |||||||
\(762\) | 14.1444 | 0.512397 | ||||||||
\(763\) | 22.5324 | 0.815726 | ||||||||
\(764\) | 16.5153 | 0.597501 | ||||||||
\(765\) | −10.3422 | −0.373923 | ||||||||
\(766\) | −4.78232 | −0.172792 | ||||||||
\(767\) | −77.3045 | −2.79130 | ||||||||
\(768\) | −1.13607 | −0.0409943 | ||||||||
\(769\) | 37.2306 | 1.34257 | 0.671285 | − | 0.741199i | \(-0.265743\pi\) | ||||
0.671285 | + | 0.741199i | \(0.265743\pi\) | |||||||
\(770\) | 0.486562 | 0.0175345 | ||||||||
\(771\) | −11.4402 | −0.412009 | ||||||||
\(772\) | 10.4471 | 0.375999 | ||||||||
\(773\) | −28.4453 | −1.02311 | −0.511554 | − | 0.859251i | \(-0.670930\pi\) | ||||
−0.511554 | + | 0.859251i | \(0.670930\pi\) | |||||||
\(774\) | −16.4200 | −0.590205 | ||||||||
\(775\) | −1.21756 | −0.0437360 | ||||||||
\(776\) | −13.0791 | −0.469512 | ||||||||
\(777\) | −3.39319 | −0.121730 | ||||||||
\(778\) | 24.0116 | 0.860856 | ||||||||
\(779\) | 0.262535 | 0.00940630 | ||||||||
\(780\) | 6.61214 | 0.236752 | ||||||||
\(781\) | 5.99554 | 0.214537 | ||||||||
\(782\) | −9.96882 | −0.356484 | ||||||||
\(783\) | 39.3077 | 1.40474 | ||||||||
\(784\) | −5.26737 | −0.188120 | ||||||||
\(785\) | −21.1133 | −0.753565 | ||||||||
\(786\) | −19.5306 | −0.696633 | ||||||||
\(787\) | 30.5131 | 1.08767 | 0.543837 | − | 0.839191i | \(-0.316971\pi\) | ||||
0.543837 | + | 0.839191i | \(0.316971\pi\) | |||||||
\(788\) | 5.66850 | 0.201932 | ||||||||
\(789\) | −19.8887 | −0.708056 | ||||||||
\(790\) | −10.1102 | −0.359706 | ||||||||
\(791\) | −7.44895 | −0.264854 | ||||||||
\(792\) | 0.631854 | 0.0224519 | ||||||||
\(793\) | 86.0400 | 3.05537 | ||||||||
\(794\) | 14.4230 | 0.511853 | ||||||||
\(795\) | 5.81874 | 0.206369 | ||||||||
\(796\) | 4.57095 | 0.162013 | ||||||||
\(797\) | −27.2930 | −0.966766 | −0.483383 | − | 0.875409i | \(-0.660592\pi\) | ||||
−0.483383 | + | 0.875409i | \(0.660592\pi\) | |||||||
\(798\) | 1.29594 | 0.0458759 | ||||||||
\(799\) | −2.86212 | −0.101255 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 18.8547 | 0.666198 | ||||||||
\(802\) | 14.6177 | 0.516167 | ||||||||
\(803\) | −5.51180 | −0.194507 | ||||||||
\(804\) | 18.0621 | 0.637001 | ||||||||
\(805\) | 2.16878 | 0.0764395 | ||||||||
\(806\) | 7.08644 | 0.249609 | ||||||||
\(807\) | −2.36991 | −0.0834247 | ||||||||
\(808\) | −14.2016 | −0.499611 | ||||||||
\(809\) | 30.4224 | 1.06959 | 0.534797 | − | 0.844980i | \(-0.320388\pi\) | ||||
0.534797 | + | 0.844980i | \(0.320388\pi\) | |||||||
\(810\) | −0.950058 | −0.0333816 | ||||||||
\(811\) | −7.08206 | −0.248685 | −0.124342 | − | 0.992239i | \(-0.539682\pi\) | ||||
−0.124342 | + | 0.992239i | \(0.539682\pi\) | |||||||
\(812\) | −9.67089 | −0.339382 | ||||||||
\(813\) | −4.07444 | −0.142897 | ||||||||
\(814\) | 0.838757 | 0.0293984 | ||||||||
\(815\) | 6.35927 | 0.222755 | ||||||||
\(816\) | −6.87361 | −0.240624 | ||||||||
\(817\) | 8.32474 | 0.291246 | ||||||||
\(818\) | −18.7903 | −0.656989 | ||||||||
\(819\) | −13.0955 | −0.457595 | ||||||||
\(820\) | 0.302941 | 0.0105792 | ||||||||
\(821\) | 36.2527 | 1.26523 | 0.632614 | − | 0.774468i | \(-0.281982\pi\) | ||||
0.632614 | + | 0.774468i | \(0.281982\pi\) | |||||||
\(822\) | −6.63350 | −0.231370 | ||||||||
\(823\) | 16.8269 | 0.586548 | 0.293274 | − | 0.956028i | \(-0.405255\pi\) | ||||
0.293274 | + | 0.956028i | \(0.405255\pi\) | |||||||
\(824\) | 0.292816 | 0.0102007 | ||||||||
\(825\) | 0.419942 | 0.0146205 | ||||||||
\(826\) | −17.4832 | −0.608318 | ||||||||
\(827\) | 47.8389 | 1.66352 | 0.831761 | − | 0.555135i | \(-0.187333\pi\) | ||||
0.831761 | + | 0.555135i | \(0.187333\pi\) | |||||||
\(828\) | 2.81640 | 0.0978766 | ||||||||
\(829\) | −19.4286 | −0.674782 | −0.337391 | − | 0.941365i | \(-0.609545\pi\) | ||||
−0.337391 | + | 0.941365i | \(0.609545\pi\) | |||||||
\(830\) | −14.7761 | −0.512887 | ||||||||
\(831\) | 13.4983 | 0.468251 | ||||||||
\(832\) | −5.82020 | −0.201779 | ||||||||
\(833\) | −31.8694 | −1.10421 | ||||||||
\(834\) | 11.2072 | 0.388073 | ||||||||
\(835\) | 1.10367 | 0.0381940 | ||||||||
\(836\) | −0.320342 | −0.0110793 | ||||||||
\(837\) | −6.51411 | −0.225161 | ||||||||
\(838\) | 7.37928 | 0.254913 | ||||||||
\(839\) | 25.6879 | 0.886845 | 0.443422 | − | 0.896313i | \(-0.353764\pi\) | ||||
0.443422 | + | 0.896313i | \(0.353764\pi\) | |||||||
\(840\) | 1.49540 | 0.0515962 | ||||||||
\(841\) | 24.9791 | 0.861348 | ||||||||
\(842\) | 7.33963 | 0.252940 | ||||||||
\(843\) | −4.15655 | −0.143159 | ||||||||
\(844\) | −21.2038 | −0.729865 | ||||||||
\(845\) | 20.8747 | 0.718113 | ||||||||
\(846\) | 0.808609 | 0.0278005 | ||||||||
\(847\) | 14.2994 | 0.491333 | ||||||||
\(848\) | −5.12183 | −0.175884 | ||||||||
\(849\) | 12.0507 | 0.413577 | ||||||||
\(850\) | 6.05036 | 0.207526 | ||||||||
\(851\) | 3.73864 | 0.128159 | ||||||||
\(852\) | 18.4267 | 0.631288 | ||||||||
\(853\) | 5.13181 | 0.175710 | 0.0878549 | − | 0.996133i | \(-0.471999\pi\) | ||||
0.0878549 | + | 0.996133i | \(0.471999\pi\) | |||||||
\(854\) | 19.4588 | 0.665866 | ||||||||
\(855\) | −1.48136 | −0.0506614 | ||||||||
\(856\) | 3.50855 | 0.119920 | ||||||||
\(857\) | −57.5631 | −1.96632 | −0.983159 | − | 0.182754i | \(-0.941499\pi\) | ||||
−0.983159 | + | 0.182754i | \(0.941499\pi\) | |||||||
\(858\) | −2.44414 | −0.0834417 | ||||||||
\(859\) | −11.8463 | −0.404192 | −0.202096 | − | 0.979366i | \(-0.564775\pi\) | ||||
−0.202096 | + | 0.979366i | \(0.564775\pi\) | |||||||
\(860\) | 9.60599 | 0.327561 | ||||||||
\(861\) | 0.453019 | 0.0154388 | ||||||||
\(862\) | 16.6986 | 0.568758 | ||||||||
\(863\) | 29.7253 | 1.01186 | 0.505930 | − | 0.862574i | \(-0.331149\pi\) | ||||
0.505930 | + | 0.862574i | \(0.331149\pi\) | |||||||
\(864\) | 5.35014 | 0.182015 | ||||||||
\(865\) | 4.02327 | 0.136795 | ||||||||
\(866\) | −29.9018 | −1.01610 | ||||||||
\(867\) | −22.2747 | −0.756487 | ||||||||
\(868\) | 1.60267 | 0.0543981 | ||||||||
\(869\) | 3.73720 | 0.126776 | ||||||||
\(870\) | −8.34674 | −0.282981 | ||||||||
\(871\) | 92.5342 | 3.13540 | ||||||||
\(872\) | −17.1180 | −0.579689 | ||||||||
\(873\) | 22.3568 | 0.756662 | ||||||||
\(874\) | −1.42788 | −0.0482987 | ||||||||
\(875\) | −1.31630 | −0.0444989 | ||||||||
\(876\) | −16.9400 | −0.572348 | ||||||||
\(877\) | 18.9424 | 0.639640 | 0.319820 | − | 0.947478i | \(-0.396378\pi\) | ||||
0.319820 | + | 0.947478i | \(0.396378\pi\) | |||||||
\(878\) | −33.8204 | −1.14138 | ||||||||
\(879\) | 21.0565 | 0.710219 | ||||||||
\(880\) | −0.369645 | −0.0124607 | ||||||||
\(881\) | −27.7289 | −0.934212 | −0.467106 | − | 0.884201i | \(-0.654703\pi\) | ||||
−0.467106 | + | 0.884201i | \(0.654703\pi\) | |||||||
\(882\) | 9.00378 | 0.303173 | ||||||||
\(883\) | 18.5282 | 0.623525 | 0.311762 | − | 0.950160i | \(-0.399081\pi\) | ||||
0.311762 | + | 0.950160i | \(0.399081\pi\) | |||||||
\(884\) | −35.2143 | −1.18438 | ||||||||
\(885\) | −15.0894 | −0.507223 | ||||||||
\(886\) | 8.00923 | 0.269076 | ||||||||
\(887\) | −8.28570 | −0.278207 | −0.139103 | − | 0.990278i | \(-0.544422\pi\) | ||||
−0.139103 | + | 0.990278i | \(0.544422\pi\) | |||||||
\(888\) | 2.57783 | 0.0865064 | ||||||||
\(889\) | 16.3883 | 0.549646 | ||||||||
\(890\) | −11.0303 | −0.369737 | ||||||||
\(891\) | 0.351185 | 0.0117651 | ||||||||
\(892\) | −14.8044 | −0.495687 | ||||||||
\(893\) | −0.409955 | −0.0137186 | ||||||||
\(894\) | −5.72109 | −0.191342 | ||||||||
\(895\) | −3.90503 | −0.130531 | ||||||||
\(896\) | −1.31630 | −0.0439744 | ||||||||
\(897\) | −10.8944 | −0.363754 | ||||||||
\(898\) | −8.81951 | −0.294311 | ||||||||
\(899\) | −8.94547 | −0.298348 | ||||||||
\(900\) | −1.70935 | −0.0569784 | ||||||||
\(901\) | −30.9889 | −1.03239 | ||||||||
\(902\) | −0.111981 | −0.00372856 | ||||||||
\(903\) | 14.3648 | 0.478030 | ||||||||
\(904\) | 5.65902 | 0.188216 | ||||||||
\(905\) | −19.2250 | −0.639059 | ||||||||
\(906\) | 4.08464 | 0.135703 | ||||||||
\(907\) | 35.5442 | 1.18023 | 0.590113 | − | 0.807321i | \(-0.299083\pi\) | ||||
0.590113 | + | 0.807321i | \(0.299083\pi\) | |||||||
\(908\) | 17.0876 | 0.567071 | ||||||||
\(909\) | 24.2756 | 0.805170 | ||||||||
\(910\) | 7.66110 | 0.253963 | ||||||||
\(911\) | 16.1787 | 0.536026 | 0.268013 | − | 0.963415i | \(-0.413633\pi\) | ||||
0.268013 | + | 0.963415i | \(0.413633\pi\) | |||||||
\(912\) | −0.984538 | −0.0326013 | ||||||||
\(913\) | 5.46193 | 0.180763 | ||||||||
\(914\) | −2.75550 | −0.0911438 | ||||||||
\(915\) | 16.7945 | 0.555208 | ||||||||
\(916\) | 17.3259 | 0.572465 | ||||||||
\(917\) | −22.6290 | −0.747275 | ||||||||
\(918\) | 32.3703 | 1.06838 | ||||||||
\(919\) | 37.2319 | 1.22817 | 0.614083 | − | 0.789242i | \(-0.289526\pi\) | ||||
0.614083 | + | 0.789242i | \(0.289526\pi\) | |||||||
\(920\) | −1.64764 | −0.0543211 | ||||||||
\(921\) | −35.7902 | −1.17933 | ||||||||
\(922\) | −4.50213 | −0.148270 | ||||||||
\(923\) | 94.4020 | 3.10728 | ||||||||
\(924\) | −0.552767 | −0.0181847 | ||||||||
\(925\) | −2.26909 | −0.0746071 | ||||||||
\(926\) | −23.3048 | −0.765842 | ||||||||
\(927\) | −0.500526 | −0.0164394 | ||||||||
\(928\) | 7.34705 | 0.241179 | ||||||||
\(929\) | −51.7214 | −1.69692 | −0.848462 | − | 0.529256i | \(-0.822471\pi\) | ||||
−0.848462 | + | 0.529256i | \(0.822471\pi\) | |||||||
\(930\) | 1.38323 | 0.0453579 | ||||||||
\(931\) | −4.56481 | −0.149605 | ||||||||
\(932\) | −0.738526 | −0.0241912 | ||||||||
\(933\) | −4.70879 | −0.154159 | ||||||||
\(934\) | 5.67434 | 0.185670 | ||||||||
\(935\) | −2.23649 | −0.0731409 | ||||||||
\(936\) | 9.94877 | 0.325186 | ||||||||
\(937\) | −18.8974 | −0.617350 | −0.308675 | − | 0.951168i | \(-0.599886\pi\) | ||||
−0.308675 | + | 0.951168i | \(0.599886\pi\) | |||||||
\(938\) | 20.9275 | 0.683308 | ||||||||
\(939\) | −9.43030 | −0.307746 | ||||||||
\(940\) | −0.473050 | −0.0154292 | ||||||||
\(941\) | −50.5652 | −1.64838 | −0.824189 | − | 0.566315i | \(-0.808368\pi\) | ||||
−0.824189 | + | 0.566315i | \(0.808368\pi\) | |||||||
\(942\) | 23.9861 | 0.781509 | ||||||||
\(943\) | −0.499139 | −0.0162542 | ||||||||
\(944\) | 13.2821 | 0.432296 | ||||||||
\(945\) | −7.04236 | −0.229088 | ||||||||
\(946\) | −3.55081 | −0.115447 | ||||||||
\(947\) | −26.8304 | −0.871871 | −0.435935 | − | 0.899978i | \(-0.643582\pi\) | ||||
−0.435935 | + | 0.899978i | \(0.643582\pi\) | |||||||
\(948\) | 11.4859 | 0.373045 | ||||||||
\(949\) | −86.7853 | −2.81717 | ||||||||
\(950\) | 0.866620 | 0.0281169 | ||||||||
\(951\) | 36.5196 | 1.18423 | ||||||||
\(952\) | −7.96406 | −0.258117 | ||||||||
\(953\) | 53.1760 | 1.72254 | 0.861270 | − | 0.508147i | \(-0.169669\pi\) | ||||
0.861270 | + | 0.508147i | \(0.169669\pi\) | |||||||
\(954\) | 8.75501 | 0.283454 | ||||||||
\(955\) | 16.5153 | 0.534421 | ||||||||
\(956\) | −7.74912 | −0.250625 | ||||||||
\(957\) | 3.08533 | 0.0997346 | ||||||||
\(958\) | −29.8542 | −0.964547 | ||||||||
\(959\) | −7.68586 | −0.248189 | ||||||||
\(960\) | −1.13607 | −0.0366664 | ||||||||
\(961\) | −29.5175 | −0.952179 | ||||||||
\(962\) | 13.2065 | 0.425796 | ||||||||
\(963\) | −5.99735 | −0.193262 | ||||||||
\(964\) | −18.0098 | −0.580058 | ||||||||
\(965\) | 10.4471 | 0.336304 | ||||||||
\(966\) | −2.46388 | −0.0792741 | ||||||||
\(967\) | −18.6025 | −0.598217 | −0.299109 | − | 0.954219i | \(-0.596689\pi\) | ||||
−0.299109 | + | 0.954219i | \(0.596689\pi\) | |||||||
\(968\) | −10.8634 | −0.349162 | ||||||||
\(969\) | −5.95681 | −0.191360 | ||||||||
\(970\) | −13.0791 | −0.419944 | ||||||||
\(971\) | 0.967502 | 0.0310486 | 0.0155243 | − | 0.999879i | \(-0.495058\pi\) | ||||
0.0155243 | + | 0.999879i | \(0.495058\pi\) | |||||||
\(972\) | −14.9711 | −0.480198 | ||||||||
\(973\) | 12.9851 | 0.416283 | ||||||||
\(974\) | −37.7136 | −1.20842 | ||||||||
\(975\) | 6.61214 | 0.211758 | ||||||||
\(976\) | −14.7830 | −0.473192 | ||||||||
\(977\) | −27.6148 | −0.883475 | −0.441737 | − | 0.897144i | \(-0.645638\pi\) | ||||
−0.441737 | + | 0.897144i | \(0.645638\pi\) | |||||||
\(978\) | −7.22455 | −0.231016 | ||||||||
\(979\) | 4.07731 | 0.130311 | ||||||||
\(980\) | −5.26737 | −0.168260 | ||||||||
\(981\) | 29.2607 | 0.934222 | ||||||||
\(982\) | −28.3165 | −0.903617 | ||||||||
\(983\) | 11.6694 | 0.372197 | 0.186098 | − | 0.982531i | \(-0.440416\pi\) | ||||
0.186098 | + | 0.982531i | \(0.440416\pi\) | |||||||
\(984\) | −0.344162 | −0.0109715 | ||||||||
\(985\) | 5.66850 | 0.180613 | ||||||||
\(986\) | 44.4523 | 1.41565 | ||||||||
\(987\) | −0.707399 | −0.0225167 | ||||||||
\(988\) | −5.04390 | −0.160468 | ||||||||
\(989\) | −15.8272 | −0.503276 | ||||||||
\(990\) | 0.631854 | 0.0200816 | ||||||||
\(991\) | −44.3184 | −1.40782 | −0.703911 | − | 0.710288i | \(-0.748565\pi\) | ||||
−0.703911 | + | 0.710288i | \(0.748565\pi\) | |||||||
\(992\) | −1.21756 | −0.0386576 | ||||||||
\(993\) | −11.7484 | −0.372824 | ||||||||
\(994\) | 21.3500 | 0.677179 | ||||||||
\(995\) | 4.57095 | 0.144909 | ||||||||
\(996\) | 16.7867 | 0.531906 | ||||||||
\(997\) | −4.38308 | −0.138813 | −0.0694067 | − | 0.997588i | \(-0.522111\pi\) | ||||
−0.0694067 | + | 0.997588i | \(0.522111\pi\) | |||||||
\(998\) | −25.6119 | −0.810731 | ||||||||
\(999\) | −12.1399 | −0.384090 |
(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 | 6010.2.a.c.1.7 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.7 | ✓ | 16 | 1.1 | even | 1 | trivial |