Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4010,2,Mod(1,4010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4010, 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("4010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4010 = 2 \cdot 5 \cdot 401 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4010.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.0200112105\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 4 x^{19} - 35 x^{18} + 154 x^{17} + 460 x^{16} - 2392 x^{15} - 2591 x^{14} + 19157 x^{13} + 2776 x^{12} - 83577 x^{11} + 34362 x^{10} + 190617 x^{9} - 150697 x^{8} + \cdots + 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.78165\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4010.1 |
$q$-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 | ||||||||
\(3\) | −2.78165 | −1.60599 | −0.802994 | − | 0.595987i | \(-0.796761\pi\) | ||||
−0.802994 | + | 0.595987i | \(0.796761\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 2.78165 | 1.13560 | ||||||||
\(7\) | −3.35211 | −1.26698 | −0.633489 | − | 0.773751i | \(-0.718378\pi\) | ||||
−0.633489 | + | 0.773751i | \(0.718378\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 4.73759 | 1.57920 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 3.90452 | 1.17726 | 0.588628 | − | 0.808404i | \(-0.299668\pi\) | ||||
0.588628 | + | 0.808404i | \(0.299668\pi\) | |||||||
\(12\) | −2.78165 | −0.802994 | ||||||||
\(13\) | −4.76252 | −1.32089 | −0.660443 | − | 0.750876i | \(-0.729632\pi\) | ||||
−0.660443 | + | 0.750876i | \(0.729632\pi\) | |||||||
\(14\) | 3.35211 | 0.895889 | ||||||||
\(15\) | −2.78165 | −0.718220 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −4.89438 | −1.18706 | −0.593531 | − | 0.804811i | \(-0.702267\pi\) | ||||
−0.593531 | + | 0.804811i | \(0.702267\pi\) | |||||||
\(18\) | −4.73759 | −1.11666 | ||||||||
\(19\) | −2.47209 | −0.567136 | −0.283568 | − | 0.958952i | \(-0.591518\pi\) | ||||
−0.283568 | + | 0.958952i | \(0.591518\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 9.32441 | 2.03475 | ||||||||
\(22\) | −3.90452 | −0.832446 | ||||||||
\(23\) | 6.29342 | 1.31227 | 0.656135 | − | 0.754644i | \(-0.272190\pi\) | ||||
0.656135 | + | 0.754644i | \(0.272190\pi\) | |||||||
\(24\) | 2.78165 | 0.567802 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.76252 | 0.934008 | ||||||||
\(27\) | −4.83338 | −0.930184 | ||||||||
\(28\) | −3.35211 | −0.633489 | ||||||||
\(29\) | −2.05132 | −0.380921 | −0.190460 | − | 0.981695i | \(-0.560998\pi\) | ||||
−0.190460 | + | 0.981695i | \(0.560998\pi\) | |||||||
\(30\) | 2.78165 | 0.507858 | ||||||||
\(31\) | −5.06600 | −0.909881 | −0.454941 | − | 0.890522i | \(-0.650340\pi\) | ||||
−0.454941 | + | 0.890522i | \(0.650340\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −10.8610 | −1.89066 | ||||||||
\(34\) | 4.89438 | 0.839380 | ||||||||
\(35\) | −3.35211 | −0.566610 | ||||||||
\(36\) | 4.73759 | 0.789599 | ||||||||
\(37\) | 1.59485 | 0.262191 | 0.131095 | − | 0.991370i | \(-0.458151\pi\) | ||||
0.131095 | + | 0.991370i | \(0.458151\pi\) | |||||||
\(38\) | 2.47209 | 0.401026 | ||||||||
\(39\) | 13.2477 | 2.12133 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −4.70017 | −0.734044 | −0.367022 | − | 0.930212i | \(-0.619623\pi\) | ||||
−0.367022 | + | 0.930212i | \(0.619623\pi\) | |||||||
\(42\) | −9.32441 | −1.43879 | ||||||||
\(43\) | −4.61250 | −0.703400 | −0.351700 | − | 0.936113i | \(-0.614396\pi\) | ||||
−0.351700 | + | 0.936113i | \(0.614396\pi\) | |||||||
\(44\) | 3.90452 | 0.588628 | ||||||||
\(45\) | 4.73759 | 0.706238 | ||||||||
\(46\) | −6.29342 | −0.927915 | ||||||||
\(47\) | −1.83379 | −0.267486 | −0.133743 | − | 0.991016i | \(-0.542700\pi\) | ||||
−0.133743 | + | 0.991016i | \(0.542700\pi\) | |||||||
\(48\) | −2.78165 | −0.401497 | ||||||||
\(49\) | 4.23664 | 0.605235 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 13.6145 | 1.90641 | ||||||||
\(52\) | −4.76252 | −0.660443 | ||||||||
\(53\) | 9.36637 | 1.28657 | 0.643285 | − | 0.765627i | \(-0.277571\pi\) | ||||
0.643285 | + | 0.765627i | \(0.277571\pi\) | |||||||
\(54\) | 4.83338 | 0.657739 | ||||||||
\(55\) | 3.90452 | 0.526485 | ||||||||
\(56\) | 3.35211 | 0.447945 | ||||||||
\(57\) | 6.87649 | 0.910814 | ||||||||
\(58\) | 2.05132 | 0.269352 | ||||||||
\(59\) | 14.0106 | 1.82402 | 0.912011 | − | 0.410166i | \(-0.134529\pi\) | ||||
0.912011 | + | 0.410166i | \(0.134529\pi\) | |||||||
\(60\) | −2.78165 | −0.359110 | ||||||||
\(61\) | −14.8313 | −1.89895 | −0.949477 | − | 0.313837i | \(-0.898385\pi\) | ||||
−0.949477 | + | 0.313837i | \(0.898385\pi\) | |||||||
\(62\) | 5.06600 | 0.643383 | ||||||||
\(63\) | −15.8809 | −2.00081 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −4.76252 | −0.590718 | ||||||||
\(66\) | 10.8610 | 1.33690 | ||||||||
\(67\) | −8.21745 | −1.00392 | −0.501961 | − | 0.864890i | \(-0.667388\pi\) | ||||
−0.501961 | + | 0.864890i | \(0.667388\pi\) | |||||||
\(68\) | −4.89438 | −0.593531 | ||||||||
\(69\) | −17.5061 | −2.10749 | ||||||||
\(70\) | 3.35211 | 0.400654 | ||||||||
\(71\) | −1.00646 | −0.119444 | −0.0597221 | − | 0.998215i | \(-0.519021\pi\) | ||||
−0.0597221 | + | 0.998215i | \(0.519021\pi\) | |||||||
\(72\) | −4.73759 | −0.558331 | ||||||||
\(73\) | −4.30786 | −0.504197 | −0.252099 | − | 0.967702i | \(-0.581121\pi\) | ||||
−0.252099 | + | 0.967702i | \(0.581121\pi\) | |||||||
\(74\) | −1.59485 | −0.185397 | ||||||||
\(75\) | −2.78165 | −0.321198 | ||||||||
\(76\) | −2.47209 | −0.283568 | ||||||||
\(77\) | −13.0884 | −1.49156 | ||||||||
\(78\) | −13.2477 | −1.50001 | ||||||||
\(79\) | 4.93774 | 0.555539 | 0.277769 | − | 0.960648i | \(-0.410405\pi\) | ||||
0.277769 | + | 0.960648i | \(0.410405\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −0.768000 | −0.0853334 | ||||||||
\(82\) | 4.70017 | 0.519047 | ||||||||
\(83\) | 3.19268 | 0.350442 | 0.175221 | − | 0.984529i | \(-0.443936\pi\) | ||||
0.175221 | + | 0.984529i | \(0.443936\pi\) | |||||||
\(84\) | 9.32441 | 1.01738 | ||||||||
\(85\) | −4.89438 | −0.530870 | ||||||||
\(86\) | 4.61250 | 0.497379 | ||||||||
\(87\) | 5.70606 | 0.611754 | ||||||||
\(88\) | −3.90452 | −0.416223 | ||||||||
\(89\) | 12.5863 | 1.33415 | 0.667074 | − | 0.744991i | \(-0.267546\pi\) | ||||
0.667074 | + | 0.744991i | \(0.267546\pi\) | |||||||
\(90\) | −4.73759 | −0.499386 | ||||||||
\(91\) | 15.9645 | 1.67353 | ||||||||
\(92\) | 6.29342 | 0.656135 | ||||||||
\(93\) | 14.0919 | 1.46126 | ||||||||
\(94\) | 1.83379 | 0.189141 | ||||||||
\(95\) | −2.47209 | −0.253631 | ||||||||
\(96\) | 2.78165 | 0.283901 | ||||||||
\(97\) | −0.763398 | −0.0775113 | −0.0387557 | − | 0.999249i | \(-0.512339\pi\) | ||||
−0.0387557 | + | 0.999249i | \(0.512339\pi\) | |||||||
\(98\) | −4.23664 | −0.427966 | ||||||||
\(99\) | 18.4980 | 1.85912 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −14.6484 | −1.45757 | −0.728784 | − | 0.684744i | \(-0.759914\pi\) | ||||
−0.728784 | + | 0.684744i | \(0.759914\pi\) | |||||||
\(102\) | −13.6145 | −1.34803 | ||||||||
\(103\) | −12.3855 | −1.22038 | −0.610192 | − | 0.792254i | \(-0.708908\pi\) | ||||
−0.610192 | + | 0.792254i | \(0.708908\pi\) | |||||||
\(104\) | 4.76252 | 0.467004 | ||||||||
\(105\) | 9.32441 | 0.909969 | ||||||||
\(106\) | −9.36637 | −0.909742 | ||||||||
\(107\) | −5.02509 | −0.485794 | −0.242897 | − | 0.970052i | \(-0.578098\pi\) | ||||
−0.242897 | + | 0.970052i | \(0.578098\pi\) | |||||||
\(108\) | −4.83338 | −0.465092 | ||||||||
\(109\) | −13.2297 | −1.26717 | −0.633587 | − | 0.773671i | \(-0.718418\pi\) | ||||
−0.633587 | + | 0.773671i | \(0.718418\pi\) | |||||||
\(110\) | −3.90452 | −0.372281 | ||||||||
\(111\) | −4.43631 | −0.421076 | ||||||||
\(112\) | −3.35211 | −0.316745 | ||||||||
\(113\) | −13.7021 | −1.28899 | −0.644495 | − | 0.764609i | \(-0.722932\pi\) | ||||
−0.644495 | + | 0.764609i | \(0.722932\pi\) | |||||||
\(114\) | −6.87649 | −0.644043 | ||||||||
\(115\) | 6.29342 | 0.586865 | ||||||||
\(116\) | −2.05132 | −0.190460 | ||||||||
\(117\) | −22.5629 | −2.08594 | ||||||||
\(118\) | −14.0106 | −1.28978 | ||||||||
\(119\) | 16.4065 | 1.50398 | ||||||||
\(120\) | 2.78165 | 0.253929 | ||||||||
\(121\) | 4.24525 | 0.385931 | ||||||||
\(122\) | 14.8313 | 1.34276 | ||||||||
\(123\) | 13.0742 | 1.17887 | ||||||||
\(124\) | −5.06600 | −0.454941 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 15.8809 | 1.41479 | ||||||||
\(127\) | 16.0966 | 1.42834 | 0.714170 | − | 0.699972i | \(-0.246804\pi\) | ||||
0.714170 | + | 0.699972i | \(0.246804\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 12.8304 | 1.12965 | ||||||||
\(130\) | 4.76252 | 0.417701 | ||||||||
\(131\) | 11.7477 | 1.02640 | 0.513199 | − | 0.858270i | \(-0.328460\pi\) | ||||
0.513199 | + | 0.858270i | \(0.328460\pi\) | |||||||
\(132\) | −10.8610 | −0.945329 | ||||||||
\(133\) | 8.28671 | 0.718549 | ||||||||
\(134\) | 8.21745 | 0.709879 | ||||||||
\(135\) | −4.83338 | −0.415991 | ||||||||
\(136\) | 4.89438 | 0.419690 | ||||||||
\(137\) | 4.15454 | 0.354946 | 0.177473 | − | 0.984126i | \(-0.443208\pi\) | ||||
0.177473 | + | 0.984126i | \(0.443208\pi\) | |||||||
\(138\) | 17.5061 | 1.49022 | ||||||||
\(139\) | −16.2327 | −1.37684 | −0.688421 | − | 0.725311i | \(-0.741696\pi\) | ||||
−0.688421 | + | 0.725311i | \(0.741696\pi\) | |||||||
\(140\) | −3.35211 | −0.283305 | ||||||||
\(141\) | 5.10097 | 0.429579 | ||||||||
\(142\) | 1.00646 | 0.0844598 | ||||||||
\(143\) | −18.5954 | −1.55502 | ||||||||
\(144\) | 4.73759 | 0.394799 | ||||||||
\(145\) | −2.05132 | −0.170353 | ||||||||
\(146\) | 4.30786 | 0.356521 | ||||||||
\(147\) | −11.7849 | −0.971999 | ||||||||
\(148\) | 1.59485 | 0.131095 | ||||||||
\(149\) | −20.1588 | −1.65147 | −0.825737 | − | 0.564056i | \(-0.809240\pi\) | ||||
−0.825737 | + | 0.564056i | \(0.809240\pi\) | |||||||
\(150\) | 2.78165 | 0.227121 | ||||||||
\(151\) | 15.2001 | 1.23696 | 0.618482 | − | 0.785799i | \(-0.287748\pi\) | ||||
0.618482 | + | 0.785799i | \(0.287748\pi\) | |||||||
\(152\) | 2.47209 | 0.200513 | ||||||||
\(153\) | −23.1876 | −1.87461 | ||||||||
\(154\) | 13.0884 | 1.05469 | ||||||||
\(155\) | −5.06600 | −0.406911 | ||||||||
\(156\) | 13.2477 | 1.06066 | ||||||||
\(157\) | 18.0499 | 1.44054 | 0.720268 | − | 0.693696i | \(-0.244019\pi\) | ||||
0.720268 | + | 0.693696i | \(0.244019\pi\) | |||||||
\(158\) | −4.93774 | −0.392825 | ||||||||
\(159\) | −26.0540 | −2.06622 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | −21.0962 | −1.66262 | ||||||||
\(162\) | 0.768000 | 0.0603398 | ||||||||
\(163\) | −15.5264 | −1.21612 | −0.608061 | − | 0.793890i | \(-0.708052\pi\) | ||||
−0.608061 | + | 0.793890i | \(0.708052\pi\) | |||||||
\(164\) | −4.70017 | −0.367022 | ||||||||
\(165\) | −10.8610 | −0.845528 | ||||||||
\(166\) | −3.19268 | −0.247800 | ||||||||
\(167\) | 8.16505 | 0.631830 | 0.315915 | − | 0.948787i | \(-0.397688\pi\) | ||||
0.315915 | + | 0.948787i | \(0.397688\pi\) | |||||||
\(168\) | −9.32441 | −0.719394 | ||||||||
\(169\) | 9.68163 | 0.744741 | ||||||||
\(170\) | 4.89438 | 0.375382 | ||||||||
\(171\) | −11.7117 | −0.895620 | ||||||||
\(172\) | −4.61250 | −0.351700 | ||||||||
\(173\) | 7.06357 | 0.537033 | 0.268517 | − | 0.963275i | \(-0.413467\pi\) | ||||
0.268517 | + | 0.963275i | \(0.413467\pi\) | |||||||
\(174\) | −5.70606 | −0.432576 | ||||||||
\(175\) | −3.35211 | −0.253396 | ||||||||
\(176\) | 3.90452 | 0.294314 | ||||||||
\(177\) | −38.9726 | −2.92936 | ||||||||
\(178\) | −12.5863 | −0.943386 | ||||||||
\(179\) | 6.59782 | 0.493144 | 0.246572 | − | 0.969124i | \(-0.420696\pi\) | ||||
0.246572 | + | 0.969124i | \(0.420696\pi\) | |||||||
\(180\) | 4.73759 | 0.353119 | ||||||||
\(181\) | −13.7708 | −1.02357 | −0.511786 | − | 0.859113i | \(-0.671016\pi\) | ||||
−0.511786 | + | 0.859113i | \(0.671016\pi\) | |||||||
\(182\) | −15.9645 | −1.18337 | ||||||||
\(183\) | 41.2555 | 3.04970 | ||||||||
\(184\) | −6.29342 | −0.463957 | ||||||||
\(185\) | 1.59485 | 0.117255 | ||||||||
\(186\) | −14.0919 | −1.03327 | ||||||||
\(187\) | −19.1102 | −1.39748 | ||||||||
\(188\) | −1.83379 | −0.133743 | ||||||||
\(189\) | 16.2020 | 1.17852 | ||||||||
\(190\) | 2.47209 | 0.179344 | ||||||||
\(191\) | −25.8062 | −1.86727 | −0.933635 | − | 0.358224i | \(-0.883382\pi\) | ||||
−0.933635 | + | 0.358224i | \(0.883382\pi\) | |||||||
\(192\) | −2.78165 | −0.200748 | ||||||||
\(193\) | 6.45048 | 0.464316 | 0.232158 | − | 0.972678i | \(-0.425421\pi\) | ||||
0.232158 | + | 0.972678i | \(0.425421\pi\) | |||||||
\(194\) | 0.763398 | 0.0548088 | ||||||||
\(195\) | 13.2477 | 0.948687 | ||||||||
\(196\) | 4.23664 | 0.302617 | ||||||||
\(197\) | 20.5238 | 1.46226 | 0.731130 | − | 0.682239i | \(-0.238993\pi\) | ||||
0.731130 | + | 0.682239i | \(0.238993\pi\) | |||||||
\(198\) | −18.4980 | −1.31460 | ||||||||
\(199\) | 2.93538 | 0.208084 | 0.104042 | − | 0.994573i | \(-0.466822\pi\) | ||||
0.104042 | + | 0.994573i | \(0.466822\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 22.8581 | 1.61229 | ||||||||
\(202\) | 14.6484 | 1.03066 | ||||||||
\(203\) | 6.87626 | 0.482619 | ||||||||
\(204\) | 13.6145 | 0.953204 | ||||||||
\(205\) | −4.70017 | −0.328274 | ||||||||
\(206\) | 12.3855 | 0.862942 | ||||||||
\(207\) | 29.8157 | 2.07233 | ||||||||
\(208\) | −4.76252 | −0.330222 | ||||||||
\(209\) | −9.65231 | −0.667664 | ||||||||
\(210\) | −9.32441 | −0.643445 | ||||||||
\(211\) | 24.7638 | 1.70481 | 0.852404 | − | 0.522883i | \(-0.175144\pi\) | ||||
0.852404 | + | 0.522883i | \(0.175144\pi\) | |||||||
\(212\) | 9.36637 | 0.643285 | ||||||||
\(213\) | 2.79961 | 0.191826 | ||||||||
\(214\) | 5.02509 | 0.343508 | ||||||||
\(215\) | −4.61250 | −0.314570 | ||||||||
\(216\) | 4.83338 | 0.328870 | ||||||||
\(217\) | 16.9818 | 1.15280 | ||||||||
\(218\) | 13.2297 | 0.896027 | ||||||||
\(219\) | 11.9830 | 0.809735 | ||||||||
\(220\) | 3.90452 | 0.263242 | ||||||||
\(221\) | 23.3096 | 1.56797 | ||||||||
\(222\) | 4.43631 | 0.297745 | ||||||||
\(223\) | −2.06642 | −0.138378 | −0.0691888 | − | 0.997604i | \(-0.522041\pi\) | ||||
−0.0691888 | + | 0.997604i | \(0.522041\pi\) | |||||||
\(224\) | 3.35211 | 0.223972 | ||||||||
\(225\) | 4.73759 | 0.315839 | ||||||||
\(226\) | 13.7021 | 0.911453 | ||||||||
\(227\) | 15.1770 | 1.00733 | 0.503666 | − | 0.863898i | \(-0.331984\pi\) | ||||
0.503666 | + | 0.863898i | \(0.331984\pi\) | |||||||
\(228\) | 6.87649 | 0.455407 | ||||||||
\(229\) | 0.871005 | 0.0575576 | 0.0287788 | − | 0.999586i | \(-0.490838\pi\) | ||||
0.0287788 | + | 0.999586i | \(0.490838\pi\) | |||||||
\(230\) | −6.29342 | −0.414976 | ||||||||
\(231\) | 36.4073 | 2.39542 | ||||||||
\(232\) | 2.05132 | 0.134676 | ||||||||
\(233\) | 1.34295 | 0.0879798 | 0.0439899 | − | 0.999032i | \(-0.485993\pi\) | ||||
0.0439899 | + | 0.999032i | \(0.485993\pi\) | |||||||
\(234\) | 22.5629 | 1.47498 | ||||||||
\(235\) | −1.83379 | −0.119623 | ||||||||
\(236\) | 14.0106 | 0.912011 | ||||||||
\(237\) | −13.7351 | −0.892188 | ||||||||
\(238\) | −16.4065 | −1.06348 | ||||||||
\(239\) | 26.2745 | 1.69956 | 0.849779 | − | 0.527139i | \(-0.176735\pi\) | ||||
0.849779 | + | 0.527139i | \(0.176735\pi\) | |||||||
\(240\) | −2.78165 | −0.179555 | ||||||||
\(241\) | −5.07033 | −0.326609 | −0.163304 | − | 0.986576i | \(-0.552215\pi\) | ||||
−0.163304 | + | 0.986576i | \(0.552215\pi\) | |||||||
\(242\) | −4.24525 | −0.272895 | ||||||||
\(243\) | 16.6364 | 1.06723 | ||||||||
\(244\) | −14.8313 | −0.949477 | ||||||||
\(245\) | 4.23664 | 0.270669 | ||||||||
\(246\) | −13.0742 | −0.833584 | ||||||||
\(247\) | 11.7734 | 0.749122 | ||||||||
\(248\) | 5.06600 | 0.321692 | ||||||||
\(249\) | −8.88091 | −0.562805 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | 13.9205 | 0.878653 | 0.439327 | − | 0.898327i | \(-0.355217\pi\) | ||||
0.439327 | + | 0.898327i | \(0.355217\pi\) | |||||||
\(252\) | −15.8809 | −1.00040 | ||||||||
\(253\) | 24.5728 | 1.54488 | ||||||||
\(254\) | −16.0966 | −1.00999 | ||||||||
\(255\) | 13.6145 | 0.852572 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.2699 | 1.20202 | 0.601011 | − | 0.799241i | \(-0.294765\pi\) | ||||
0.601011 | + | 0.799241i | \(0.294765\pi\) | |||||||
\(258\) | −12.8304 | −0.798785 | ||||||||
\(259\) | −5.34610 | −0.332190 | ||||||||
\(260\) | −4.76252 | −0.295359 | ||||||||
\(261\) | −9.71833 | −0.601549 | ||||||||
\(262\) | −11.7477 | −0.725772 | ||||||||
\(263\) | 21.1485 | 1.30407 | 0.652036 | − | 0.758188i | \(-0.273915\pi\) | ||||
0.652036 | + | 0.758188i | \(0.273915\pi\) | |||||||
\(264\) | 10.8610 | 0.668449 | ||||||||
\(265\) | 9.36637 | 0.575371 | ||||||||
\(266\) | −8.28671 | −0.508091 | ||||||||
\(267\) | −35.0108 | −2.14263 | ||||||||
\(268\) | −8.21745 | −0.501961 | ||||||||
\(269\) | 21.3660 | 1.30271 | 0.651355 | − | 0.758773i | \(-0.274201\pi\) | ||||
0.651355 | + | 0.758773i | \(0.274201\pi\) | |||||||
\(270\) | 4.83338 | 0.294150 | ||||||||
\(271\) | 1.49664 | 0.0909145 | 0.0454572 | − | 0.998966i | \(-0.485526\pi\) | ||||
0.0454572 | + | 0.998966i | \(0.485526\pi\) | |||||||
\(272\) | −4.89438 | −0.296766 | ||||||||
\(273\) | −44.4077 | −2.68768 | ||||||||
\(274\) | −4.15454 | −0.250985 | ||||||||
\(275\) | 3.90452 | 0.235451 | ||||||||
\(276\) | −17.5061 | −1.05374 | ||||||||
\(277\) | 19.6599 | 1.18125 | 0.590625 | − | 0.806946i | \(-0.298881\pi\) | ||||
0.590625 | + | 0.806946i | \(0.298881\pi\) | |||||||
\(278\) | 16.2327 | 0.973574 | ||||||||
\(279\) | −24.0007 | −1.43688 | ||||||||
\(280\) | 3.35211 | 0.200327 | ||||||||
\(281\) | −21.3948 | −1.27631 | −0.638153 | − | 0.769909i | \(-0.720301\pi\) | ||||
−0.638153 | + | 0.769909i | \(0.720301\pi\) | |||||||
\(282\) | −5.10097 | −0.303758 | ||||||||
\(283\) | −14.3052 | −0.850354 | −0.425177 | − | 0.905110i | \(-0.639788\pi\) | ||||
−0.425177 | + | 0.905110i | \(0.639788\pi\) | |||||||
\(284\) | −1.00646 | −0.0597221 | ||||||||
\(285\) | 6.87649 | 0.407328 | ||||||||
\(286\) | 18.5954 | 1.09957 | ||||||||
\(287\) | 15.7555 | 0.930017 | ||||||||
\(288\) | −4.73759 | −0.279165 | ||||||||
\(289\) | 6.95500 | 0.409117 | ||||||||
\(290\) | 2.05132 | 0.120458 | ||||||||
\(291\) | 2.12351 | 0.124482 | ||||||||
\(292\) | −4.30786 | −0.252099 | ||||||||
\(293\) | −26.8485 | −1.56851 | −0.784254 | − | 0.620440i | \(-0.786954\pi\) | ||||
−0.784254 | + | 0.620440i | \(0.786954\pi\) | |||||||
\(294\) | 11.7849 | 0.687307 | ||||||||
\(295\) | 14.0106 | 0.815727 | ||||||||
\(296\) | −1.59485 | −0.0926985 | ||||||||
\(297\) | −18.8720 | −1.09506 | ||||||||
\(298\) | 20.1588 | 1.16777 | ||||||||
\(299\) | −29.9726 | −1.73336 | ||||||||
\(300\) | −2.78165 | −0.160599 | ||||||||
\(301\) | 15.4616 | 0.891193 | ||||||||
\(302\) | −15.2001 | −0.874666 | ||||||||
\(303\) | 40.7467 | 2.34084 | ||||||||
\(304\) | −2.47209 | −0.141784 | ||||||||
\(305\) | −14.8313 | −0.849238 | ||||||||
\(306\) | 23.1876 | 1.32555 | ||||||||
\(307\) | 10.3721 | 0.591970 | 0.295985 | − | 0.955193i | \(-0.404352\pi\) | ||||
0.295985 | + | 0.955193i | \(0.404352\pi\) | |||||||
\(308\) | −13.0884 | −0.745779 | ||||||||
\(309\) | 34.4523 | 1.95992 | ||||||||
\(310\) | 5.06600 | 0.287730 | ||||||||
\(311\) | 9.19579 | 0.521445 | 0.260723 | − | 0.965414i | \(-0.416039\pi\) | ||||
0.260723 | + | 0.965414i | \(0.416039\pi\) | |||||||
\(312\) | −13.2477 | −0.750003 | ||||||||
\(313\) | −1.64229 | −0.0928279 | −0.0464139 | − | 0.998922i | \(-0.514779\pi\) | ||||
−0.0464139 | + | 0.998922i | \(0.514779\pi\) | |||||||
\(314\) | −18.0499 | −1.01861 | ||||||||
\(315\) | −15.8809 | −0.894789 | ||||||||
\(316\) | 4.93774 | 0.277769 | ||||||||
\(317\) | 11.8898 | 0.667798 | 0.333899 | − | 0.942609i | \(-0.391635\pi\) | ||||
0.333899 | + | 0.942609i | \(0.391635\pi\) | |||||||
\(318\) | 26.0540 | 1.46103 | ||||||||
\(319\) | −8.00942 | −0.448441 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 13.9781 | 0.780179 | ||||||||
\(322\) | 21.0962 | 1.17565 | ||||||||
\(323\) | 12.0994 | 0.673226 | ||||||||
\(324\) | −0.768000 | −0.0426667 | ||||||||
\(325\) | −4.76252 | −0.264177 | ||||||||
\(326\) | 15.5264 | 0.859928 | ||||||||
\(327\) | 36.8004 | 2.03507 | ||||||||
\(328\) | 4.70017 | 0.259524 | ||||||||
\(329\) | 6.14707 | 0.338899 | ||||||||
\(330\) | 10.8610 | 0.597879 | ||||||||
\(331\) | 27.8492 | 1.53073 | 0.765364 | − | 0.643598i | \(-0.222559\pi\) | ||||
0.765364 | + | 0.643598i | \(0.222559\pi\) | |||||||
\(332\) | 3.19268 | 0.175221 | ||||||||
\(333\) | 7.55573 | 0.414051 | ||||||||
\(334\) | −8.16505 | −0.446772 | ||||||||
\(335\) | −8.21745 | −0.448967 | ||||||||
\(336\) | 9.32441 | 0.508688 | ||||||||
\(337\) | 2.30475 | 0.125548 | 0.0627739 | − | 0.998028i | \(-0.480005\pi\) | ||||
0.0627739 | + | 0.998028i | \(0.480005\pi\) | |||||||
\(338\) | −9.68163 | −0.526611 | ||||||||
\(339\) | 38.1146 | 2.07010 | ||||||||
\(340\) | −4.89438 | −0.265435 | ||||||||
\(341\) | −19.7803 | −1.07116 | ||||||||
\(342\) | 11.7117 | 0.633299 | ||||||||
\(343\) | 9.26308 | 0.500159 | ||||||||
\(344\) | 4.61250 | 0.248690 | ||||||||
\(345\) | −17.5061 | −0.942498 | ||||||||
\(346\) | −7.06357 | −0.379740 | ||||||||
\(347\) | −12.0815 | −0.648568 | −0.324284 | − | 0.945960i | \(-0.605123\pi\) | ||||
−0.324284 | + | 0.945960i | \(0.605123\pi\) | |||||||
\(348\) | 5.70606 | 0.305877 | ||||||||
\(349\) | −16.6586 | −0.891716 | −0.445858 | − | 0.895104i | \(-0.647101\pi\) | ||||
−0.445858 | + | 0.895104i | \(0.647101\pi\) | |||||||
\(350\) | 3.35211 | 0.179178 | ||||||||
\(351\) | 23.0191 | 1.22867 | ||||||||
\(352\) | −3.90452 | −0.208111 | ||||||||
\(353\) | 1.81409 | 0.0965543 | 0.0482772 | − | 0.998834i | \(-0.484627\pi\) | ||||
0.0482772 | + | 0.998834i | \(0.484627\pi\) | |||||||
\(354\) | 38.9726 | 2.07137 | ||||||||
\(355\) | −1.00646 | −0.0534171 | ||||||||
\(356\) | 12.5863 | 0.667074 | ||||||||
\(357\) | −45.6372 | −2.41538 | ||||||||
\(358\) | −6.59782 | −0.348706 | ||||||||
\(359\) | 6.16066 | 0.325147 | 0.162574 | − | 0.986696i | \(-0.448020\pi\) | ||||
0.162574 | + | 0.986696i | \(0.448020\pi\) | |||||||
\(360\) | −4.73759 | −0.249693 | ||||||||
\(361\) | −12.8888 | −0.678357 | ||||||||
\(362\) | 13.7708 | 0.723775 | ||||||||
\(363\) | −11.8088 | −0.619801 | ||||||||
\(364\) | 15.9645 | 0.836767 | ||||||||
\(365\) | −4.30786 | −0.225484 | ||||||||
\(366\) | −41.2555 | −2.15646 | ||||||||
\(367\) | 26.0479 | 1.35969 | 0.679844 | − | 0.733357i | \(-0.262047\pi\) | ||||
0.679844 | + | 0.733357i | \(0.262047\pi\) | |||||||
\(368\) | 6.29342 | 0.328067 | ||||||||
\(369\) | −22.2675 | −1.15920 | ||||||||
\(370\) | −1.59485 | −0.0829121 | ||||||||
\(371\) | −31.3971 | −1.63006 | ||||||||
\(372\) | 14.0919 | 0.730629 | ||||||||
\(373\) | 6.44018 | 0.333460 | 0.166730 | − | 0.986003i | \(-0.446679\pi\) | ||||
0.166730 | + | 0.986003i | \(0.446679\pi\) | |||||||
\(374\) | 19.1102 | 0.988165 | ||||||||
\(375\) | −2.78165 | −0.143644 | ||||||||
\(376\) | 1.83379 | 0.0945705 | ||||||||
\(377\) | 9.76947 | 0.503153 | ||||||||
\(378\) | −16.2020 | −0.833341 | ||||||||
\(379\) | −7.87991 | −0.404764 | −0.202382 | − | 0.979307i | \(-0.564868\pi\) | ||||
−0.202382 | + | 0.979307i | \(0.564868\pi\) | |||||||
\(380\) | −2.47209 | −0.126815 | ||||||||
\(381\) | −44.7751 | −2.29390 | ||||||||
\(382\) | 25.8062 | 1.32036 | ||||||||
\(383\) | −20.5899 | −1.05209 | −0.526047 | − | 0.850455i | \(-0.676326\pi\) | ||||
−0.526047 | + | 0.850455i | \(0.676326\pi\) | |||||||
\(384\) | 2.78165 | 0.141951 | ||||||||
\(385\) | −13.0884 | −0.667045 | ||||||||
\(386\) | −6.45048 | −0.328321 | ||||||||
\(387\) | −21.8522 | −1.11081 | ||||||||
\(388\) | −0.763398 | −0.0387557 | ||||||||
\(389\) | 34.7031 | 1.75952 | 0.879758 | − | 0.475423i | \(-0.157705\pi\) | ||||
0.879758 | + | 0.475423i | \(0.157705\pi\) | |||||||
\(390\) | −13.2477 | −0.670823 | ||||||||
\(391\) | −30.8024 | −1.55775 | ||||||||
\(392\) | −4.23664 | −0.213983 | ||||||||
\(393\) | −32.6779 | −1.64838 | ||||||||
\(394\) | −20.5238 | −1.03397 | ||||||||
\(395\) | 4.93774 | 0.248444 | ||||||||
\(396\) | 18.4980 | 0.929560 | ||||||||
\(397\) | 0.294316 | 0.0147713 | 0.00738566 | − | 0.999973i | \(-0.497649\pi\) | ||||
0.00738566 | + | 0.999973i | \(0.497649\pi\) | |||||||
\(398\) | −2.93538 | −0.147137 | ||||||||
\(399\) | −23.0508 | −1.15398 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −1.00000 | −0.0499376 | ||||||||
\(402\) | −22.8581 | −1.14006 | ||||||||
\(403\) | 24.1270 | 1.20185 | ||||||||
\(404\) | −14.6484 | −0.728784 | ||||||||
\(405\) | −0.768000 | −0.0381623 | ||||||||
\(406\) | −6.87626 | −0.341263 | ||||||||
\(407\) | 6.22710 | 0.308666 | ||||||||
\(408\) | −13.6145 | −0.674017 | ||||||||
\(409\) | 8.24295 | 0.407588 | 0.203794 | − | 0.979014i | \(-0.434673\pi\) | ||||
0.203794 | + | 0.979014i | \(0.434673\pi\) | |||||||
\(410\) | 4.70017 | 0.232125 | ||||||||
\(411\) | −11.5565 | −0.570039 | ||||||||
\(412\) | −12.3855 | −0.610192 | ||||||||
\(413\) | −46.9650 | −2.31100 | ||||||||
\(414\) | −29.8157 | −1.46536 | ||||||||
\(415\) | 3.19268 | 0.156722 | ||||||||
\(416\) | 4.76252 | 0.233502 | ||||||||
\(417\) | 45.1538 | 2.21119 | ||||||||
\(418\) | 9.65231 | 0.472110 | ||||||||
\(419\) | 27.0969 | 1.32377 | 0.661885 | − | 0.749605i | \(-0.269757\pi\) | ||||
0.661885 | + | 0.749605i | \(0.269757\pi\) | |||||||
\(420\) | 9.32441 | 0.454984 | ||||||||
\(421\) | 30.6725 | 1.49488 | 0.747442 | − | 0.664327i | \(-0.231282\pi\) | ||||
0.747442 | + | 0.664327i | \(0.231282\pi\) | |||||||
\(422\) | −24.7638 | −1.20548 | ||||||||
\(423\) | −8.68775 | −0.422413 | ||||||||
\(424\) | −9.36637 | −0.454871 | ||||||||
\(425\) | −4.89438 | −0.237413 | ||||||||
\(426\) | −2.79961 | −0.135641 | ||||||||
\(427\) | 49.7162 | 2.40593 | ||||||||
\(428\) | −5.02509 | −0.242897 | ||||||||
\(429\) | 51.7258 | 2.49735 | ||||||||
\(430\) | 4.61250 | 0.222435 | ||||||||
\(431\) | −27.4086 | −1.32022 | −0.660112 | − | 0.751167i | \(-0.729491\pi\) | ||||
−0.660112 | + | 0.751167i | \(0.729491\pi\) | |||||||
\(432\) | −4.83338 | −0.232546 | ||||||||
\(433\) | 19.8145 | 0.952223 | 0.476112 | − | 0.879385i | \(-0.342046\pi\) | ||||
0.476112 | + | 0.879385i | \(0.342046\pi\) | |||||||
\(434\) | −16.9818 | −0.815153 | ||||||||
\(435\) | 5.70606 | 0.273585 | ||||||||
\(436\) | −13.2297 | −0.633587 | ||||||||
\(437\) | −15.5579 | −0.744235 | ||||||||
\(438\) | −11.9830 | −0.572569 | ||||||||
\(439\) | 13.3948 | 0.639298 | 0.319649 | − | 0.947536i | \(-0.396435\pi\) | ||||
0.319649 | + | 0.947536i | \(0.396435\pi\) | |||||||
\(440\) | −3.90452 | −0.186140 | ||||||||
\(441\) | 20.0715 | 0.955785 | ||||||||
\(442\) | −23.3096 | −1.10873 | ||||||||
\(443\) | 20.8818 | 0.992124 | 0.496062 | − | 0.868287i | \(-0.334779\pi\) | ||||
0.496062 | + | 0.868287i | \(0.334779\pi\) | |||||||
\(444\) | −4.43631 | −0.210538 | ||||||||
\(445\) | 12.5863 | 0.596650 | ||||||||
\(446\) | 2.06642 | 0.0978478 | ||||||||
\(447\) | 56.0748 | 2.65225 | ||||||||
\(448\) | −3.35211 | −0.158372 | ||||||||
\(449\) | 35.9911 | 1.69852 | 0.849262 | − | 0.527972i | \(-0.177048\pi\) | ||||
0.849262 | + | 0.527972i | \(0.177048\pi\) | |||||||
\(450\) | −4.73759 | −0.223332 | ||||||||
\(451\) | −18.3519 | −0.864157 | ||||||||
\(452\) | −13.7021 | −0.644495 | ||||||||
\(453\) | −42.2813 | −1.98655 | ||||||||
\(454\) | −15.1770 | −0.712291 | ||||||||
\(455\) | 15.9645 | 0.748427 | ||||||||
\(456\) | −6.87649 | −0.322021 | ||||||||
\(457\) | 34.2136 | 1.60045 | 0.800223 | − | 0.599703i | \(-0.204715\pi\) | ||||
0.800223 | + | 0.599703i | \(0.204715\pi\) | |||||||
\(458\) | −0.871005 | −0.0406994 | ||||||||
\(459\) | 23.6564 | 1.10419 | ||||||||
\(460\) | 6.29342 | 0.293432 | ||||||||
\(461\) | −15.9895 | −0.744707 | −0.372354 | − | 0.928091i | \(-0.621449\pi\) | ||||
−0.372354 | + | 0.928091i | \(0.621449\pi\) | |||||||
\(462\) | −36.4073 | −1.69382 | ||||||||
\(463\) | −17.7535 | −0.825074 | −0.412537 | − | 0.910941i | \(-0.635357\pi\) | ||||
−0.412537 | + | 0.910941i | \(0.635357\pi\) | |||||||
\(464\) | −2.05132 | −0.0952302 | ||||||||
\(465\) | 14.0919 | 0.653494 | ||||||||
\(466\) | −1.34295 | −0.0622111 | ||||||||
\(467\) | 20.1913 | 0.934343 | 0.467172 | − | 0.884167i | \(-0.345273\pi\) | ||||
0.467172 | + | 0.884167i | \(0.345273\pi\) | |||||||
\(468\) | −22.5629 | −1.04297 | ||||||||
\(469\) | 27.5458 | 1.27195 | ||||||||
\(470\) | 1.83379 | 0.0845865 | ||||||||
\(471\) | −50.2084 | −2.31348 | ||||||||
\(472\) | −14.0106 | −0.644889 | ||||||||
\(473\) | −18.0096 | −0.828082 | ||||||||
\(474\) | 13.7351 | 0.630872 | ||||||||
\(475\) | −2.47209 | −0.113427 | ||||||||
\(476\) | 16.4065 | 0.751991 | ||||||||
\(477\) | 44.3740 | 2.03175 | ||||||||
\(478\) | −26.2745 | −1.20177 | ||||||||
\(479\) | 14.8374 | 0.677939 | 0.338969 | − | 0.940797i | \(-0.389922\pi\) | ||||
0.338969 | + | 0.940797i | \(0.389922\pi\) | |||||||
\(480\) | 2.78165 | 0.126964 | ||||||||
\(481\) | −7.59549 | −0.346325 | ||||||||
\(482\) | 5.07033 | 0.230947 | ||||||||
\(483\) | 58.6824 | 2.67014 | ||||||||
\(484\) | 4.24525 | 0.192966 | ||||||||
\(485\) | −0.763398 | −0.0346641 | ||||||||
\(486\) | −16.6364 | −0.754644 | ||||||||
\(487\) | 13.9455 | 0.631933 | 0.315967 | − | 0.948770i | \(-0.397671\pi\) | ||||
0.315967 | + | 0.948770i | \(0.397671\pi\) | |||||||
\(488\) | 14.8313 | 0.671381 | ||||||||
\(489\) | 43.1891 | 1.95308 | ||||||||
\(490\) | −4.23664 | −0.191392 | ||||||||
\(491\) | 25.8866 | 1.16825 | 0.584124 | − | 0.811664i | \(-0.301438\pi\) | ||||
0.584124 | + | 0.811664i | \(0.301438\pi\) | |||||||
\(492\) | 13.0742 | 0.589433 | ||||||||
\(493\) | 10.0400 | 0.452177 | ||||||||
\(494\) | −11.7734 | −0.529710 | ||||||||
\(495\) | 18.4980 | 0.831423 | ||||||||
\(496\) | −5.06600 | −0.227470 | ||||||||
\(497\) | 3.37375 | 0.151333 | ||||||||
\(498\) | 8.88091 | 0.397963 | ||||||||
\(499\) | 0.374418 | 0.0167612 | 0.00838062 | − | 0.999965i | \(-0.497332\pi\) | ||||
0.00838062 | + | 0.999965i | \(0.497332\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −22.7123 | −1.01471 | ||||||||
\(502\) | −13.9205 | −0.621302 | ||||||||
\(503\) | −19.3432 | −0.862471 | −0.431235 | − | 0.902239i | \(-0.641922\pi\) | ||||
−0.431235 | + | 0.902239i | \(0.641922\pi\) | |||||||
\(504\) | 15.8809 | 0.707393 | ||||||||
\(505\) | −14.6484 | −0.651844 | ||||||||
\(506\) | −24.5728 | −1.09239 | ||||||||
\(507\) | −26.9309 | −1.19605 | ||||||||
\(508\) | 16.0966 | 0.714170 | ||||||||
\(509\) | −2.61635 | −0.115968 | −0.0579838 | − | 0.998318i | \(-0.518467\pi\) | ||||
−0.0579838 | + | 0.998318i | \(0.518467\pi\) | |||||||
\(510\) | −13.6145 | −0.602859 | ||||||||
\(511\) | 14.4404 | 0.638807 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 11.9485 | 0.527541 | ||||||||
\(514\) | −19.2699 | −0.849958 | ||||||||
\(515\) | −12.3855 | −0.545772 | ||||||||
\(516\) | 12.8304 | 0.564826 | ||||||||
\(517\) | −7.16007 | −0.314899 | ||||||||
\(518\) | 5.34610 | 0.234894 | ||||||||
\(519\) | −19.6484 | −0.862469 | ||||||||
\(520\) | 4.76252 | 0.208850 | ||||||||
\(521\) | −44.6210 | −1.95488 | −0.977440 | − | 0.211213i | \(-0.932259\pi\) | ||||
−0.977440 | + | 0.211213i | \(0.932259\pi\) | |||||||
\(522\) | 9.71833 | 0.425360 | ||||||||
\(523\) | 28.1019 | 1.22881 | 0.614404 | − | 0.788992i | \(-0.289396\pi\) | ||||
0.614404 | + | 0.788992i | \(0.289396\pi\) | |||||||
\(524\) | 11.7477 | 0.513199 | ||||||||
\(525\) | 9.32441 | 0.406950 | ||||||||
\(526\) | −21.1485 | −0.922118 | ||||||||
\(527\) | 24.7950 | 1.08009 | ||||||||
\(528\) | −10.8610 | −0.472665 | ||||||||
\(529\) | 16.6072 | 0.722051 | ||||||||
\(530\) | −9.36637 | −0.406849 | ||||||||
\(531\) | 66.3764 | 2.88049 | ||||||||
\(532\) | 8.28671 | 0.359275 | ||||||||
\(533\) | 22.3847 | 0.969588 | ||||||||
\(534\) | 35.0108 | 1.51507 | ||||||||
\(535\) | −5.02509 | −0.217254 | ||||||||
\(536\) | 8.21745 | 0.354940 | ||||||||
\(537\) | −18.3528 | −0.791984 | ||||||||
\(538\) | −21.3660 | −0.921155 | ||||||||
\(539\) | 16.5420 | 0.712516 | ||||||||
\(540\) | −4.83338 | −0.207995 | ||||||||
\(541\) | 30.2716 | 1.30148 | 0.650739 | − | 0.759302i | \(-0.274459\pi\) | ||||
0.650739 | + | 0.759302i | \(0.274459\pi\) | |||||||
\(542\) | −1.49664 | −0.0642862 | ||||||||
\(543\) | 38.3055 | 1.64385 | ||||||||
\(544\) | 4.89438 | 0.209845 | ||||||||
\(545\) | −13.2297 | −0.566697 | ||||||||
\(546\) | 44.4077 | 1.90047 | ||||||||
\(547\) | 4.71926 | 0.201781 | 0.100890 | − | 0.994898i | \(-0.467831\pi\) | ||||
0.100890 | + | 0.994898i | \(0.467831\pi\) | |||||||
\(548\) | 4.15454 | 0.177473 | ||||||||
\(549\) | −70.2647 | −2.99882 | ||||||||
\(550\) | −3.90452 | −0.166489 | ||||||||
\(551\) | 5.07105 | 0.216034 | ||||||||
\(552\) | 17.5061 | 0.745110 | ||||||||
\(553\) | −16.5518 | −0.703856 | ||||||||
\(554\) | −19.6599 | −0.835270 | ||||||||
\(555\) | −4.43631 | −0.188311 | ||||||||
\(556\) | −16.2327 | −0.688421 | ||||||||
\(557\) | −33.3579 | −1.41342 | −0.706709 | − | 0.707504i | \(-0.749821\pi\) | ||||
−0.706709 | + | 0.707504i | \(0.749821\pi\) | |||||||
\(558\) | 24.0007 | 1.01603 | ||||||||
\(559\) | 21.9672 | 0.929112 | ||||||||
\(560\) | −3.35211 | −0.141653 | ||||||||
\(561\) | 53.1579 | 2.24433 | ||||||||
\(562\) | 21.3948 | 0.902485 | ||||||||
\(563\) | 33.1694 | 1.39792 | 0.698962 | − | 0.715158i | \(-0.253645\pi\) | ||||
0.698962 | + | 0.715158i | \(0.253645\pi\) | |||||||
\(564\) | 5.10097 | 0.214790 | ||||||||
\(565\) | −13.7021 | −0.576454 | ||||||||
\(566\) | 14.3052 | 0.601291 | ||||||||
\(567\) | 2.57442 | 0.108116 | ||||||||
\(568\) | 1.00646 | 0.0422299 | ||||||||
\(569\) | −10.4438 | −0.437826 | −0.218913 | − | 0.975744i | \(-0.570251\pi\) | ||||
−0.218913 | + | 0.975744i | \(0.570251\pi\) | |||||||
\(570\) | −6.87649 | −0.288025 | ||||||||
\(571\) | 20.4106 | 0.854158 | 0.427079 | − | 0.904214i | \(-0.359543\pi\) | ||||
0.427079 | + | 0.904214i | \(0.359543\pi\) | |||||||
\(572\) | −18.5954 | −0.777511 | ||||||||
\(573\) | 71.7839 | 2.99881 | ||||||||
\(574\) | −15.7555 | −0.657622 | ||||||||
\(575\) | 6.29342 | 0.262454 | ||||||||
\(576\) | 4.73759 | 0.197400 | ||||||||
\(577\) | 8.73757 | 0.363750 | 0.181875 | − | 0.983322i | \(-0.441783\pi\) | ||||
0.181875 | + | 0.983322i | \(0.441783\pi\) | |||||||
\(578\) | −6.95500 | −0.289290 | ||||||||
\(579\) | −17.9430 | −0.745686 | ||||||||
\(580\) | −2.05132 | −0.0851765 | ||||||||
\(581\) | −10.7022 | −0.444002 | ||||||||
\(582\) | −2.12351 | −0.0880223 | ||||||||
\(583\) | 36.5711 | 1.51462 | ||||||||
\(584\) | 4.30786 | 0.178261 | ||||||||
\(585\) | −22.5629 | −0.932861 | ||||||||
\(586\) | 26.8485 | 1.10910 | ||||||||
\(587\) | −32.8822 | −1.35719 | −0.678597 | − | 0.734511i | \(-0.737412\pi\) | ||||
−0.678597 | + | 0.734511i | \(0.737412\pi\) | |||||||
\(588\) | −11.7849 | −0.486000 | ||||||||
\(589\) | 12.5236 | 0.516026 | ||||||||
\(590\) | −14.0106 | −0.576806 | ||||||||
\(591\) | −57.0901 | −2.34837 | ||||||||
\(592\) | 1.59485 | 0.0655477 | ||||||||
\(593\) | −31.9516 | −1.31210 | −0.656048 | − | 0.754719i | \(-0.727773\pi\) | ||||
−0.656048 | + | 0.754719i | \(0.727773\pi\) | |||||||
\(594\) | 18.8720 | 0.774327 | ||||||||
\(595\) | 16.4065 | 0.672602 | ||||||||
\(596\) | −20.1588 | −0.825737 | ||||||||
\(597\) | −8.16521 | −0.334180 | ||||||||
\(598\) | 29.9726 | 1.22567 | ||||||||
\(599\) | −27.2584 | −1.11375 | −0.556874 | − | 0.830597i | \(-0.688000\pi\) | ||||
−0.556874 | + | 0.830597i | \(0.688000\pi\) | |||||||
\(600\) | 2.78165 | 0.113560 | ||||||||
\(601\) | 17.4698 | 0.712610 | 0.356305 | − | 0.934370i | \(-0.384036\pi\) | ||||
0.356305 | + | 0.934370i | \(0.384036\pi\) | |||||||
\(602\) | −15.4616 | −0.630169 | ||||||||
\(603\) | −38.9309 | −1.58539 | ||||||||
\(604\) | 15.2001 | 0.618482 | ||||||||
\(605\) | 4.24525 | 0.172594 | ||||||||
\(606\) | −40.7467 | −1.65522 | ||||||||
\(607\) | 10.0867 | 0.409405 | 0.204703 | − | 0.978824i | \(-0.434377\pi\) | ||||
0.204703 | + | 0.978824i | \(0.434377\pi\) | |||||||
\(608\) | 2.47209 | 0.100256 | ||||||||
\(609\) | −19.1274 | −0.775080 | ||||||||
\(610\) | 14.8313 | 0.600502 | ||||||||
\(611\) | 8.73347 | 0.353318 | ||||||||
\(612\) | −23.1876 | −0.937303 | ||||||||
\(613\) | −33.2200 | −1.34174 | −0.670871 | − | 0.741574i | \(-0.734080\pi\) | ||||
−0.670871 | + | 0.741574i | \(0.734080\pi\) | |||||||
\(614\) | −10.3721 | −0.418586 | ||||||||
\(615\) | 13.0742 | 0.527205 | ||||||||
\(616\) | 13.0884 | 0.527345 | ||||||||
\(617\) | −16.6887 | −0.671863 | −0.335932 | − | 0.941886i | \(-0.609051\pi\) | ||||
−0.335932 | + | 0.941886i | \(0.609051\pi\) | |||||||
\(618\) | −34.4523 | −1.38587 | ||||||||
\(619\) | 27.9923 | 1.12511 | 0.562553 | − | 0.826761i | \(-0.309819\pi\) | ||||
0.562553 | + | 0.826761i | \(0.309819\pi\) | |||||||
\(620\) | −5.06600 | −0.203456 | ||||||||
\(621\) | −30.4185 | −1.22065 | ||||||||
\(622\) | −9.19579 | −0.368718 | ||||||||
\(623\) | −42.1908 | −1.69034 | ||||||||
\(624\) | 13.2477 | 0.530332 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.64229 | 0.0656392 | ||||||||
\(627\) | 26.8494 | 1.07226 | ||||||||
\(628\) | 18.0499 | 0.720268 | ||||||||
\(629\) | −7.80579 | −0.311237 | ||||||||
\(630\) | 15.8809 | 0.632711 | ||||||||
\(631\) | 6.41953 | 0.255558 | 0.127779 | − | 0.991803i | \(-0.459215\pi\) | ||||
0.127779 | + | 0.991803i | \(0.459215\pi\) | |||||||
\(632\) | −4.93774 | −0.196413 | ||||||||
\(633\) | −68.8842 | −2.73790 | ||||||||
\(634\) | −11.8898 | −0.472205 | ||||||||
\(635\) | 16.0966 | 0.638773 | ||||||||
\(636\) | −26.0540 | −1.03311 | ||||||||
\(637\) | −20.1771 | −0.799446 | ||||||||
\(638\) | 8.00942 | 0.317096 | ||||||||
\(639\) | −4.76817 | −0.188626 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 14.5422 | 0.574380 | 0.287190 | − | 0.957874i | \(-0.407279\pi\) | ||||
0.287190 | + | 0.957874i | \(0.407279\pi\) | |||||||
\(642\) | −13.9781 | −0.551670 | ||||||||
\(643\) | −15.9655 | −0.629619 | −0.314809 | − | 0.949155i | \(-0.601941\pi\) | ||||
−0.314809 | + | 0.949155i | \(0.601941\pi\) | |||||||
\(644\) | −21.0962 | −0.831309 | ||||||||
\(645\) | 12.8304 | 0.505196 | ||||||||
\(646\) | −12.0994 | −0.476043 | ||||||||
\(647\) | −0.286663 | −0.0112699 | −0.00563494 | − | 0.999984i | \(-0.501794\pi\) | ||||
−0.00563494 | + | 0.999984i | \(0.501794\pi\) | |||||||
\(648\) | 0.768000 | 0.0301699 | ||||||||
\(649\) | 54.7045 | 2.14734 | ||||||||
\(650\) | 4.76252 | 0.186802 | ||||||||
\(651\) | −47.2375 | −1.85138 | ||||||||
\(652\) | −15.5264 | −0.608061 | ||||||||
\(653\) | −32.0906 | −1.25580 | −0.627902 | − | 0.778293i | \(-0.716086\pi\) | ||||
−0.627902 | + | 0.778293i | \(0.716086\pi\) | |||||||
\(654\) | −36.8004 | −1.43901 | ||||||||
\(655\) | 11.7477 | 0.459019 | ||||||||
\(656\) | −4.70017 | −0.183511 | ||||||||
\(657\) | −20.4089 | −0.796227 | ||||||||
\(658\) | −6.14707 | −0.239638 | ||||||||
\(659\) | −13.7101 | −0.534071 | −0.267035 | − | 0.963687i | \(-0.586044\pi\) | ||||
−0.267035 | + | 0.963687i | \(0.586044\pi\) | |||||||
\(660\) | −10.8610 | −0.422764 | ||||||||
\(661\) | −9.37600 | −0.364684 | −0.182342 | − | 0.983235i | \(-0.558368\pi\) | ||||
−0.182342 | + | 0.983235i | \(0.558368\pi\) | |||||||
\(662\) | −27.8492 | −1.08239 | ||||||||
\(663\) | −64.8393 | −2.51815 | ||||||||
\(664\) | −3.19268 | −0.123900 | ||||||||
\(665\) | 8.28671 | 0.321345 | ||||||||
\(666\) | −7.55573 | −0.292778 | ||||||||
\(667\) | −12.9098 | −0.499871 | ||||||||
\(668\) | 8.16505 | 0.315915 | ||||||||
\(669\) | 5.74806 | 0.222233 | ||||||||
\(670\) | 8.21745 | 0.317468 | ||||||||
\(671\) | −57.9091 | −2.23555 | ||||||||
\(672\) | −9.32441 | −0.359697 | ||||||||
\(673\) | 14.4602 | 0.557401 | 0.278701 | − | 0.960378i | \(-0.410096\pi\) | ||||
0.278701 | + | 0.960378i | \(0.410096\pi\) | |||||||
\(674\) | −2.30475 | −0.0887757 | ||||||||
\(675\) | −4.83338 | −0.186037 | ||||||||
\(676\) | 9.68163 | 0.372370 | ||||||||
\(677\) | 18.0780 | 0.694795 | 0.347398 | − | 0.937718i | \(-0.387065\pi\) | ||||
0.347398 | + | 0.937718i | \(0.387065\pi\) | |||||||
\(678\) | −38.1146 | −1.46378 | ||||||||
\(679\) | 2.55899 | 0.0982052 | ||||||||
\(680\) | 4.89438 | 0.187691 | ||||||||
\(681\) | −42.2171 | −1.61776 | ||||||||
\(682\) | 19.7803 | 0.757427 | ||||||||
\(683\) | 23.8751 | 0.913556 | 0.456778 | − | 0.889581i | \(-0.349003\pi\) | ||||
0.456778 | + | 0.889581i | \(0.349003\pi\) | |||||||
\(684\) | −11.7117 | −0.447810 | ||||||||
\(685\) | 4.15454 | 0.158737 | ||||||||
\(686\) | −9.26308 | −0.353666 | ||||||||
\(687\) | −2.42283 | −0.0924368 | ||||||||
\(688\) | −4.61250 | −0.175850 | ||||||||
\(689\) | −44.6076 | −1.69941 | ||||||||
\(690\) | 17.5061 | 0.666447 | ||||||||
\(691\) | −45.1913 | −1.71916 | −0.859580 | − | 0.511002i | \(-0.829275\pi\) | ||||
−0.859580 | + | 0.511002i | \(0.829275\pi\) | |||||||
\(692\) | 7.06357 | 0.268517 | ||||||||
\(693\) | −62.0073 | −2.35546 | ||||||||
\(694\) | 12.0815 | 0.458607 | ||||||||
\(695\) | −16.2327 | −0.615742 | ||||||||
\(696\) | −5.70606 | −0.216288 | ||||||||
\(697\) | 23.0044 | 0.871356 | ||||||||
\(698\) | 16.6586 | 0.630538 | ||||||||
\(699\) | −3.73563 | −0.141295 | ||||||||
\(700\) | −3.35211 | −0.126698 | ||||||||
\(701\) | 44.8665 | 1.69458 | 0.847292 | − | 0.531128i | \(-0.178232\pi\) | ||||
0.847292 | + | 0.531128i | \(0.178232\pi\) | |||||||
\(702\) | −23.0191 | −0.868799 | ||||||||
\(703\) | −3.94260 | −0.148698 | ||||||||
\(704\) | 3.90452 | 0.147157 | ||||||||
\(705\) | 5.10097 | 0.192114 | ||||||||
\(706\) | −1.81409 | −0.0682742 | ||||||||
\(707\) | 49.1030 | 1.84671 | ||||||||
\(708\) | −38.9726 | −1.46468 | ||||||||
\(709\) | 31.6879 | 1.19006 | 0.595031 | − | 0.803703i | \(-0.297140\pi\) | ||||
0.595031 | + | 0.803703i | \(0.297140\pi\) | |||||||
\(710\) | 1.00646 | 0.0377716 | ||||||||
\(711\) | 23.3930 | 0.877305 | ||||||||
\(712\) | −12.5863 | −0.471693 | ||||||||
\(713\) | −31.8825 | −1.19401 | ||||||||
\(714\) | 45.6372 | 1.70793 | ||||||||
\(715\) | −18.5954 | −0.695427 | ||||||||
\(716\) | 6.59782 | 0.246572 | ||||||||
\(717\) | −73.0866 | −2.72947 | ||||||||
\(718\) | −6.16066 | −0.229914 | ||||||||
\(719\) | 3.34223 | 0.124644 | 0.0623220 | − | 0.998056i | \(-0.480149\pi\) | ||||
0.0623220 | + | 0.998056i | \(0.480149\pi\) | |||||||
\(720\) | 4.73759 | 0.176560 | ||||||||
\(721\) | 41.5177 | 1.54620 | ||||||||
\(722\) | 12.8888 | 0.479671 | ||||||||
\(723\) | 14.1039 | 0.524529 | ||||||||
\(724\) | −13.7708 | −0.511786 | ||||||||
\(725\) | −2.05132 | −0.0761842 | ||||||||
\(726\) | 11.8088 | 0.438266 | ||||||||
\(727\) | −31.9893 | −1.18642 | −0.593208 | − | 0.805049i | \(-0.702139\pi\) | ||||
−0.593208 | + | 0.805049i | \(0.702139\pi\) | |||||||
\(728\) | −15.9645 | −0.591684 | ||||||||
\(729\) | −43.9728 | −1.62862 | ||||||||
\(730\) | 4.30786 | 0.159441 | ||||||||
\(731\) | 22.5754 | 0.834980 | ||||||||
\(732\) | 41.2555 | 1.52485 | ||||||||
\(733\) | 7.68058 | 0.283689 | 0.141844 | − | 0.989889i | \(-0.454697\pi\) | ||||
0.141844 | + | 0.989889i | \(0.454697\pi\) | |||||||
\(734\) | −26.0479 | −0.961445 | ||||||||
\(735\) | −11.7849 | −0.434691 | ||||||||
\(736\) | −6.29342 | −0.231979 | ||||||||
\(737\) | −32.0852 | −1.18187 | ||||||||
\(738\) | 22.2675 | 0.819678 | ||||||||
\(739\) | 4.71296 | 0.173369 | 0.0866846 | − | 0.996236i | \(-0.472373\pi\) | ||||
0.0866846 | + | 0.996236i | \(0.472373\pi\) | |||||||
\(740\) | 1.59485 | 0.0586277 | ||||||||
\(741\) | −32.7495 | −1.20308 | ||||||||
\(742\) | 31.3971 | 1.15262 | ||||||||
\(743\) | 32.3832 | 1.18802 | 0.594012 | − | 0.804456i | \(-0.297543\pi\) | ||||
0.594012 | + | 0.804456i | \(0.297543\pi\) | |||||||
\(744\) | −14.0919 | −0.516633 | ||||||||
\(745\) | −20.1588 | −0.738561 | ||||||||
\(746\) | −6.44018 | −0.235792 | ||||||||
\(747\) | 15.1256 | 0.553417 | ||||||||
\(748\) | −19.1102 | −0.698738 | ||||||||
\(749\) | 16.8447 | 0.615491 | ||||||||
\(750\) | 2.78165 | 0.101572 | ||||||||
\(751\) | −15.4349 | −0.563229 | −0.281614 | − | 0.959528i | \(-0.590870\pi\) | ||||
−0.281614 | + | 0.959528i | \(0.590870\pi\) | |||||||
\(752\) | −1.83379 | −0.0668715 | ||||||||
\(753\) | −38.7220 | −1.41111 | ||||||||
\(754\) | −9.76947 | −0.355783 | ||||||||
\(755\) | 15.2001 | 0.553187 | ||||||||
\(756\) | 16.2020 | 0.589261 | ||||||||
\(757\) | −45.5686 | −1.65622 | −0.828109 | − | 0.560567i | \(-0.810583\pi\) | ||||
−0.828109 | + | 0.560567i | \(0.810583\pi\) | |||||||
\(758\) | 7.87991 | 0.286211 | ||||||||
\(759\) | −68.3529 | −2.48105 | ||||||||
\(760\) | 2.47209 | 0.0896721 | ||||||||
\(761\) | 34.3933 | 1.24676 | 0.623379 | − | 0.781920i | \(-0.285759\pi\) | ||||
0.623379 | + | 0.781920i | \(0.285759\pi\) | |||||||
\(762\) | 44.7751 | 1.62203 | ||||||||
\(763\) | 44.3474 | 1.60548 | ||||||||
\(764\) | −25.8062 | −0.933635 | ||||||||
\(765\) | −23.1876 | −0.838349 | ||||||||
\(766\) | 20.5899 | 0.743943 | ||||||||
\(767\) | −66.7257 | −2.40933 | ||||||||
\(768\) | −2.78165 | −0.100374 | ||||||||
\(769\) | 18.9543 | 0.683511 | 0.341756 | − | 0.939789i | \(-0.388978\pi\) | ||||
0.341756 | + | 0.939789i | \(0.388978\pi\) | |||||||
\(770\) | 13.0884 | 0.471672 | ||||||||
\(771\) | −53.6021 | −1.93043 | ||||||||
\(772\) | 6.45048 | 0.232158 | ||||||||
\(773\) | −18.7400 | −0.674031 | −0.337016 | − | 0.941499i | \(-0.609417\pi\) | ||||
−0.337016 | + | 0.941499i | \(0.609417\pi\) | |||||||
\(774\) | 21.8522 | 0.785460 | ||||||||
\(775\) | −5.06600 | −0.181976 | ||||||||
\(776\) | 0.763398 | 0.0274044 | ||||||||
\(777\) | 14.8710 | 0.533494 | ||||||||
\(778\) | −34.7031 | −1.24417 | ||||||||
\(779\) | 11.6192 | 0.416303 | ||||||||
\(780\) | 13.2477 | 0.474343 | ||||||||
\(781\) | −3.92972 | −0.140616 | ||||||||
\(782\) | 30.8024 | 1.10149 | ||||||||
\(783\) | 9.91481 | 0.354326 | ||||||||
\(784\) | 4.23664 | 0.151309 | ||||||||
\(785\) | 18.0499 | 0.644227 | ||||||||
\(786\) | 32.6779 | 1.16558 | ||||||||
\(787\) | −31.1940 | −1.11195 | −0.555973 | − | 0.831200i | \(-0.687654\pi\) | ||||
−0.555973 | + | 0.831200i | \(0.687654\pi\) | |||||||
\(788\) | 20.5238 | 0.731130 | ||||||||
\(789\) | −58.8278 | −2.09432 | ||||||||
\(790\) | −4.93774 | −0.175677 | ||||||||
\(791\) | 45.9311 | 1.63312 | ||||||||
\(792\) | −18.4980 | −0.657298 | ||||||||
\(793\) | 70.6344 | 2.50830 | ||||||||
\(794\) | −0.294316 | −0.0104449 | ||||||||
\(795\) | −26.0540 | −0.924040 | ||||||||
\(796\) | 2.93538 | 0.104042 | ||||||||
\(797\) | −22.3821 | −0.792816 | −0.396408 | − | 0.918075i | \(-0.629743\pi\) | ||||
−0.396408 | + | 0.918075i | \(0.629743\pi\) | |||||||
\(798\) | 23.0508 | 0.815988 | ||||||||
\(799\) | 8.97528 | 0.317522 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 59.6289 | 2.10688 | ||||||||
\(802\) | 1.00000 | 0.0353112 | ||||||||
\(803\) | −16.8201 | −0.593569 | ||||||||
\(804\) | 22.8581 | 0.806143 | ||||||||
\(805\) | −21.0962 | −0.743545 | ||||||||
\(806\) | −24.1270 | −0.849836 | ||||||||
\(807\) | −59.4329 | −2.09214 | ||||||||
\(808\) | 14.6484 | 0.515328 | ||||||||
\(809\) | −38.8534 | −1.36601 | −0.683007 | − | 0.730412i | \(-0.739328\pi\) | ||||
−0.683007 | + | 0.730412i | \(0.739328\pi\) | |||||||
\(810\) | 0.768000 | 0.0269848 | ||||||||
\(811\) | 1.91575 | 0.0672712 | 0.0336356 | − | 0.999434i | \(-0.489291\pi\) | ||||
0.0336356 | + | 0.999434i | \(0.489291\pi\) | |||||||
\(812\) | 6.87626 | 0.241309 | ||||||||
\(813\) | −4.16314 | −0.146008 | ||||||||
\(814\) | −6.22710 | −0.218260 | ||||||||
\(815\) | −15.5264 | −0.543866 | ||||||||
\(816\) | 13.6145 | 0.476602 | ||||||||
\(817\) | 11.4025 | 0.398924 | ||||||||
\(818\) | −8.24295 | −0.288208 | ||||||||
\(819\) | 75.6333 | 2.64284 | ||||||||
\(820\) | −4.70017 | −0.164137 | ||||||||
\(821\) | −48.9423 | −1.70810 | −0.854049 | − | 0.520192i | \(-0.825860\pi\) | ||||
−0.854049 | + | 0.520192i | \(0.825860\pi\) | |||||||
\(822\) | 11.5565 | 0.403079 | ||||||||
\(823\) | −51.3985 | −1.79164 | −0.895820 | − | 0.444418i | \(-0.853411\pi\) | ||||
−0.895820 | + | 0.444418i | \(0.853411\pi\) | |||||||
\(824\) | 12.3855 | 0.431471 | ||||||||
\(825\) | −10.8610 | −0.378132 | ||||||||
\(826\) | 46.9650 | 1.63412 | ||||||||
\(827\) | 17.0730 | 0.593688 | 0.296844 | − | 0.954926i | \(-0.404066\pi\) | ||||
0.296844 | + | 0.954926i | \(0.404066\pi\) | |||||||
\(828\) | 29.8157 | 1.03617 | ||||||||
\(829\) | −7.12097 | −0.247322 | −0.123661 | − | 0.992325i | \(-0.539463\pi\) | ||||
−0.123661 | + | 0.992325i | \(0.539463\pi\) | |||||||
\(830\) | −3.19268 | −0.110819 | ||||||||
\(831\) | −54.6871 | −1.89707 | ||||||||
\(832\) | −4.76252 | −0.165111 | ||||||||
\(833\) | −20.7358 | −0.718451 | ||||||||
\(834\) | −45.1538 | −1.56355 | ||||||||
\(835\) | 8.16505 | 0.282563 | ||||||||
\(836\) | −9.65231 | −0.333832 | ||||||||
\(837\) | 24.4859 | 0.846357 | ||||||||
\(838\) | −27.0969 | −0.936047 | ||||||||
\(839\) | 7.18510 | 0.248057 | 0.124029 | − | 0.992279i | \(-0.460419\pi\) | ||||
0.124029 | + | 0.992279i | \(0.460419\pi\) | |||||||
\(840\) | −9.32441 | −0.321723 | ||||||||
\(841\) | −24.7921 | −0.854899 | ||||||||
\(842\) | −30.6725 | −1.05704 | ||||||||
\(843\) | 59.5129 | 2.04973 | ||||||||
\(844\) | 24.7638 | 0.852404 | ||||||||
\(845\) | 9.68163 | 0.333058 | ||||||||
\(846\) | 8.68775 | 0.298691 | ||||||||
\(847\) | −14.2305 | −0.488967 | ||||||||
\(848\) | 9.36637 | 0.321642 | ||||||||
\(849\) | 39.7920 | 1.36566 | ||||||||
\(850\) | 4.89438 | 0.167876 | ||||||||
\(851\) | 10.0370 | 0.344065 | ||||||||
\(852\) | 2.79961 | 0.0959130 | ||||||||
\(853\) | 16.4768 | 0.564156 | 0.282078 | − | 0.959391i | \(-0.408976\pi\) | ||||
0.282078 | + | 0.959391i | \(0.408976\pi\) | |||||||
\(854\) | −49.7162 | −1.70125 | ||||||||
\(855\) | −11.7117 | −0.400533 | ||||||||
\(856\) | 5.02509 | 0.171754 | ||||||||
\(857\) | −11.1040 | −0.379306 | −0.189653 | − | 0.981851i | \(-0.560736\pi\) | ||||
−0.189653 | + | 0.981851i | \(0.560736\pi\) | |||||||
\(858\) | −51.7258 | −1.76589 | ||||||||
\(859\) | −9.03637 | −0.308317 | −0.154158 | − | 0.988046i | \(-0.549267\pi\) | ||||
−0.154158 | + | 0.988046i | \(0.549267\pi\) | |||||||
\(860\) | −4.61250 | −0.157285 | ||||||||
\(861\) | −43.8263 | −1.49360 | ||||||||
\(862\) | 27.4086 | 0.933539 | ||||||||
\(863\) | −21.3777 | −0.727704 | −0.363852 | − | 0.931457i | \(-0.618539\pi\) | ||||
−0.363852 | + | 0.931457i | \(0.618539\pi\) | |||||||
\(864\) | 4.83338 | 0.164435 | ||||||||
\(865\) | 7.06357 | 0.240169 | ||||||||
\(866\) | −19.8145 | −0.673324 | ||||||||
\(867\) | −19.3464 | −0.657038 | ||||||||
\(868\) | 16.9818 | 0.576400 | ||||||||
\(869\) | 19.2795 | 0.654011 | ||||||||
\(870\) | −5.70606 | −0.193454 | ||||||||
\(871\) | 39.1358 | 1.32607 | ||||||||
\(872\) | 13.2297 | 0.448014 | ||||||||
\(873\) | −3.61667 | −0.122406 | ||||||||
\(874\) | 15.5579 | 0.526254 | ||||||||
\(875\) | −3.35211 | −0.113322 | ||||||||
\(876\) | 11.9830 | 0.404867 | ||||||||
\(877\) | −7.38760 | −0.249462 | −0.124731 | − | 0.992191i | \(-0.539807\pi\) | ||||
−0.124731 | + | 0.992191i | \(0.539807\pi\) | |||||||
\(878\) | −13.3948 | −0.452052 | ||||||||
\(879\) | 74.6833 | 2.51900 | ||||||||
\(880\) | 3.90452 | 0.131621 | ||||||||
\(881\) | −11.6556 | −0.392688 | −0.196344 | − | 0.980535i | \(-0.562907\pi\) | ||||
−0.196344 | + | 0.980535i | \(0.562907\pi\) | |||||||
\(882\) | −20.0715 | −0.675842 | ||||||||
\(883\) | −26.0091 | −0.875275 | −0.437638 | − | 0.899151i | \(-0.644185\pi\) | ||||
−0.437638 | + | 0.899151i | \(0.644185\pi\) | |||||||
\(884\) | 23.3096 | 0.783987 | ||||||||
\(885\) | −38.9726 | −1.31005 | ||||||||
\(886\) | −20.8818 | −0.701537 | ||||||||
\(887\) | −51.8479 | −1.74088 | −0.870441 | − | 0.492273i | \(-0.836166\pi\) | ||||
−0.870441 | + | 0.492273i | \(0.836166\pi\) | |||||||
\(888\) | 4.43631 | 0.148873 | ||||||||
\(889\) | −53.9575 | −1.80968 | ||||||||
\(890\) | −12.5863 | −0.421895 | ||||||||
\(891\) | −2.99867 | −0.100459 | ||||||||
\(892\) | −2.06642 | −0.0691888 | ||||||||
\(893\) | 4.53329 | 0.151701 | ||||||||
\(894\) | −56.0748 | −1.87542 | ||||||||
\(895\) | 6.59782 | 0.220541 | ||||||||
\(896\) | 3.35211 | 0.111986 | ||||||||
\(897\) | 83.3733 | 2.78375 | ||||||||
\(898\) | −35.9911 | −1.20104 | ||||||||
\(899\) | 10.3920 | 0.346593 | ||||||||
\(900\) | 4.73759 | 0.157920 | ||||||||
\(901\) | −45.8426 | −1.52724 | ||||||||
\(902\) | 18.3519 | 0.611051 | ||||||||
\(903\) | −43.0089 | −1.43125 | ||||||||
\(904\) | 13.7021 | 0.455727 | ||||||||
\(905\) | −13.7708 | −0.457756 | ||||||||
\(906\) | 42.2813 | 1.40470 | ||||||||
\(907\) | 15.8793 | 0.527263 | 0.263631 | − | 0.964624i | \(-0.415080\pi\) | ||||
0.263631 | + | 0.964624i | \(0.415080\pi\) | |||||||
\(908\) | 15.1770 | 0.503666 | ||||||||
\(909\) | −69.3980 | −2.30179 | ||||||||
\(910\) | −15.9645 | −0.529218 | ||||||||
\(911\) | 31.1585 | 1.03233 | 0.516163 | − | 0.856490i | \(-0.327360\pi\) | ||||
0.516163 | + | 0.856490i | \(0.327360\pi\) | |||||||
\(912\) | 6.87649 | 0.227703 | ||||||||
\(913\) | 12.4659 | 0.412560 | ||||||||
\(914\) | −34.2136 | −1.13169 | ||||||||
\(915\) | 41.2555 | 1.36387 | ||||||||
\(916\) | 0.871005 | 0.0287788 | ||||||||
\(917\) | −39.3794 | −1.30042 | ||||||||
\(918\) | −23.6564 | −0.780778 | ||||||||
\(919\) | −37.4097 | −1.23403 | −0.617017 | − | 0.786950i | \(-0.711659\pi\) | ||||
−0.617017 | + | 0.786950i | \(0.711659\pi\) | |||||||
\(920\) | −6.29342 | −0.207488 | ||||||||
\(921\) | −28.8517 | −0.950696 | ||||||||
\(922\) | 15.9895 | 0.526587 | ||||||||
\(923\) | 4.79327 | 0.157772 | ||||||||
\(924\) | 36.4073 | 1.19771 | ||||||||
\(925\) | 1.59485 | 0.0524382 | ||||||||
\(926\) | 17.7535 | 0.583415 | ||||||||
\(927\) | −58.6776 | −1.92723 | ||||||||
\(928\) | 2.05132 | 0.0673379 | ||||||||
\(929\) | −16.1968 | −0.531399 | −0.265699 | − | 0.964056i | \(-0.585603\pi\) | ||||
−0.265699 | + | 0.964056i | \(0.585603\pi\) | |||||||
\(930\) | −14.0919 | −0.462090 | ||||||||
\(931\) | −10.4734 | −0.343250 | ||||||||
\(932\) | 1.34295 | 0.0439899 | ||||||||
\(933\) | −25.5795 | −0.837435 | ||||||||
\(934\) | −20.1913 | −0.660680 | ||||||||
\(935\) | −19.1102 | −0.624970 | ||||||||
\(936\) | 22.5629 | 0.737491 | ||||||||
\(937\) | −25.0407 | −0.818043 | −0.409022 | − | 0.912525i | \(-0.634130\pi\) | ||||
−0.409022 | + | 0.912525i | \(0.634130\pi\) | |||||||
\(938\) | −27.5458 | −0.899402 | ||||||||
\(939\) | 4.56829 | 0.149080 | ||||||||
\(940\) | −1.83379 | −0.0598117 | ||||||||
\(941\) | 55.6029 | 1.81260 | 0.906301 | − | 0.422633i | \(-0.138894\pi\) | ||||
0.906301 | + | 0.422633i | \(0.138894\pi\) | |||||||
\(942\) | 50.2084 | 1.63588 | ||||||||
\(943\) | −29.5802 | −0.963263 | ||||||||
\(944\) | 14.0106 | 0.456005 | ||||||||
\(945\) | 16.2020 | 0.527051 | ||||||||
\(946\) | 18.0096 | 0.585543 | ||||||||
\(947\) | 6.24011 | 0.202776 | 0.101388 | − | 0.994847i | \(-0.467672\pi\) | ||||
0.101388 | + | 0.994847i | \(0.467672\pi\) | |||||||
\(948\) | −13.7351 | −0.446094 | ||||||||
\(949\) | 20.5163 | 0.665987 | ||||||||
\(950\) | 2.47209 | 0.0802052 | ||||||||
\(951\) | −33.0733 | −1.07248 | ||||||||
\(952\) | −16.4065 | −0.531738 | ||||||||
\(953\) | 37.0942 | 1.20160 | 0.600799 | − | 0.799400i | \(-0.294849\pi\) | ||||
0.600799 | + | 0.799400i | \(0.294849\pi\) | |||||||
\(954\) | −44.3740 | −1.43666 | ||||||||
\(955\) | −25.8062 | −0.835069 | ||||||||
\(956\) | 26.2745 | 0.849779 | ||||||||
\(957\) | 22.2794 | 0.720191 | ||||||||
\(958\) | −14.8374 | −0.479375 | ||||||||
\(959\) | −13.9265 | −0.449709 | ||||||||
\(960\) | −2.78165 | −0.0897775 | ||||||||
\(961\) | −5.33561 | −0.172116 | ||||||||
\(962\) | 7.59549 | 0.244888 | ||||||||
\(963\) | −23.8068 | −0.767165 | ||||||||
\(964\) | −5.07033 | −0.163304 | ||||||||
\(965\) | 6.45048 | 0.207648 | ||||||||
\(966\) | −58.6824 | −1.88808 | ||||||||
\(967\) | 27.4648 | 0.883210 | 0.441605 | − | 0.897210i | \(-0.354409\pi\) | ||||
0.441605 | + | 0.897210i | \(0.354409\pi\) | |||||||
\(968\) | −4.24525 | −0.136447 | ||||||||
\(969\) | −33.6562 | −1.08119 | ||||||||
\(970\) | 0.763398 | 0.0245112 | ||||||||
\(971\) | 6.78986 | 0.217897 | 0.108948 | − | 0.994047i | \(-0.465252\pi\) | ||||
0.108948 | + | 0.994047i | \(0.465252\pi\) | |||||||
\(972\) | 16.6364 | 0.533614 | ||||||||
\(973\) | 54.4139 | 1.74443 | ||||||||
\(974\) | −13.9455 | −0.446844 | ||||||||
\(975\) | 13.2477 | 0.424266 | ||||||||
\(976\) | −14.8313 | −0.474738 | ||||||||
\(977\) | 26.4271 | 0.845477 | 0.422738 | − | 0.906252i | \(-0.361069\pi\) | ||||
0.422738 | + | 0.906252i | \(0.361069\pi\) | |||||||
\(978\) | −43.1891 | −1.38103 | ||||||||
\(979\) | 49.1435 | 1.57063 | ||||||||
\(980\) | 4.23664 | 0.135335 | ||||||||
\(981\) | −62.6768 | −2.00112 | ||||||||
\(982\) | −25.8866 | −0.826076 | ||||||||
\(983\) | −42.2133 | −1.34639 | −0.673197 | − | 0.739463i | \(-0.735080\pi\) | ||||
−0.673197 | + | 0.739463i | \(0.735080\pi\) | |||||||
\(984\) | −13.0742 | −0.416792 | ||||||||
\(985\) | 20.5238 | 0.653942 | ||||||||
\(986\) | −10.0400 | −0.319737 | ||||||||
\(987\) | −17.0990 | −0.544267 | ||||||||
\(988\) | 11.7734 | 0.374561 | ||||||||
\(989\) | −29.0284 | −0.923051 | ||||||||
\(990\) | −18.4980 | −0.587905 | ||||||||
\(991\) | −42.5555 | −1.35182 | −0.675911 | − | 0.736984i | \(-0.736249\pi\) | ||||
−0.675911 | + | 0.736984i | \(0.736249\pi\) | |||||||
\(992\) | 5.06600 | 0.160846 | ||||||||
\(993\) | −77.4667 | −2.45833 | ||||||||
\(994\) | −3.37375 | −0.107009 | ||||||||
\(995\) | 2.93538 | 0.0930578 | ||||||||
\(996\) | −8.88091 | −0.281403 | ||||||||
\(997\) | 23.1029 | 0.731677 | 0.365839 | − | 0.930678i | \(-0.380782\pi\) | ||||
0.365839 | + | 0.930678i | \(0.380782\pi\) | |||||||
\(998\) | −0.374418 | −0.0118520 | ||||||||
\(999\) | −7.70849 | −0.243886 |
(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 | 4010.2.a.m.1.3 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4010.2.a.m.1.3 | ✓ | 20 | 1.1 | even | 1 | trivial |