Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8470,2,Mod(1,8470)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8470, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8470.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8470 = 2 \cdot 5 \cdot 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8470.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: | \(67.6332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.745749504.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 18x^{4} - 4x^{3} + 81x^{2} + 36x - 44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.16996\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8470.1 |
$q$-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 | ||||||||
\(3\) | 1.16996 | 0.675478 | 0.337739 | − | 0.941240i | \(-0.390338\pi\) | ||||
0.337739 | + | 0.941240i | \(0.390338\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | −1.16996 | −0.477635 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −1.63119 | −0.543729 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.16996 | 0.337739 | ||||||||
\(13\) | 1.43479 | 0.397939 | 0.198970 | − | 0.980006i | \(-0.436240\pi\) | ||||
0.198970 | + | 0.980006i | \(0.436240\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | −1.16996 | −0.302083 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −7.28628 | −1.76718 | −0.883591 | − | 0.468259i | \(-0.844882\pi\) | ||||
−0.883591 | + | 0.468259i | \(0.844882\pi\) | |||||||
\(18\) | 1.63119 | 0.384475 | ||||||||
\(19\) | −4.33680 | −0.994931 | −0.497466 | − | 0.867484i | \(-0.665736\pi\) | ||||
−0.497466 | + | 0.867484i | \(0.665736\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.16996 | 0.255307 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.02643 | 0.422541 | 0.211270 | − | 0.977428i | \(-0.432240\pi\) | ||||
0.211270 | + | 0.977428i | \(0.432240\pi\) | |||||||
\(24\) | −1.16996 | −0.238818 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −1.43479 | −0.281386 | ||||||||
\(27\) | −5.41832 | −1.04276 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | 9.11632 | 1.69286 | 0.846429 | − | 0.532502i | \(-0.178748\pi\) | ||||
0.846429 | + | 0.532502i | \(0.178748\pi\) | |||||||
\(30\) | 1.16996 | 0.213605 | ||||||||
\(31\) | 3.65509 | 0.656474 | 0.328237 | − | 0.944595i | \(-0.393546\pi\) | ||||
0.328237 | + | 0.944595i | \(0.393546\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 7.28628 | 1.24959 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | −1.63119 | −0.271865 | ||||||||
\(37\) | −3.11632 | −0.512320 | −0.256160 | − | 0.966634i | \(-0.582457\pi\) | ||||
−0.256160 | + | 0.966634i | \(0.582457\pi\) | |||||||
\(38\) | 4.33680 | 0.703523 | ||||||||
\(39\) | 1.67865 | 0.268799 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −2.05574 | −0.321053 | −0.160527 | − | 0.987031i | \(-0.551319\pi\) | ||||
−0.160527 | + | 0.987031i | \(0.551319\pi\) | |||||||
\(42\) | −1.16996 | −0.180529 | ||||||||
\(43\) | −0.705861 | −0.107643 | −0.0538214 | − | 0.998551i | \(-0.517140\pi\) | ||||
−0.0538214 | + | 0.998551i | \(0.517140\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.63119 | 0.243163 | ||||||||
\(46\) | −2.02643 | −0.298781 | ||||||||
\(47\) | 4.00288 | 0.583880 | 0.291940 | − | 0.956437i | \(-0.405699\pi\) | ||||
0.291940 | + | 0.956437i | \(0.405699\pi\) | |||||||
\(48\) | 1.16996 | 0.168870 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −8.52468 | −1.19369 | ||||||||
\(52\) | 1.43479 | 0.198970 | ||||||||
\(53\) | −4.87480 | −0.669606 | −0.334803 | − | 0.942288i | \(-0.608670\pi\) | ||||
−0.334803 | + | 0.942288i | \(0.608670\pi\) | |||||||
\(54\) | 5.41832 | 0.737339 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | −5.07390 | −0.672054 | ||||||||
\(58\) | −9.11632 | −1.19703 | ||||||||
\(59\) | 12.3811 | 1.61189 | 0.805944 | − | 0.591992i | \(-0.201658\pi\) | ||||
0.805944 | + | 0.591992i | \(0.201658\pi\) | |||||||
\(60\) | −1.16996 | −0.151042 | ||||||||
\(61\) | −6.62309 | −0.847999 | −0.424000 | − | 0.905662i | \(-0.639374\pi\) | ||||
−0.424000 | + | 0.905662i | \(0.639374\pi\) | |||||||
\(62\) | −3.65509 | −0.464197 | ||||||||
\(63\) | −1.63119 | −0.205510 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.43479 | −0.177964 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.89373 | −0.231356 | −0.115678 | − | 0.993287i | \(-0.536904\pi\) | ||||
−0.115678 | + | 0.993287i | \(0.536904\pi\) | |||||||
\(68\) | −7.28628 | −0.883591 | ||||||||
\(69\) | 2.37085 | 0.285417 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | 0.421681 | 0.0500443 | 0.0250222 | − | 0.999687i | \(-0.492034\pi\) | ||||
0.0250222 | + | 0.999687i | \(0.492034\pi\) | |||||||
\(72\) | 1.63119 | 0.192237 | ||||||||
\(73\) | −7.37947 | −0.863702 | −0.431851 | − | 0.901945i | \(-0.642139\pi\) | ||||
−0.431851 | + | 0.901945i | \(0.642139\pi\) | |||||||
\(74\) | 3.11632 | 0.362265 | ||||||||
\(75\) | 1.16996 | 0.135096 | ||||||||
\(76\) | −4.33680 | −0.497466 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −1.67865 | −0.190070 | ||||||||
\(79\) | −3.98377 | −0.448209 | −0.224105 | − | 0.974565i | \(-0.571946\pi\) | ||||
−0.224105 | + | 0.974565i | \(0.571946\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −1.44566 | −0.160629 | ||||||||
\(82\) | 2.05574 | 0.227019 | ||||||||
\(83\) | 7.15061 | 0.784882 | 0.392441 | − | 0.919777i | \(-0.371631\pi\) | ||||
0.392441 | + | 0.919777i | \(0.371631\pi\) | |||||||
\(84\) | 1.16996 | 0.127653 | ||||||||
\(85\) | 7.28628 | 0.790308 | ||||||||
\(86\) | 0.705861 | 0.0761149 | ||||||||
\(87\) | 10.6658 | 1.14349 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.34280 | 0.884335 | 0.442168 | − | 0.896932i | \(-0.354210\pi\) | ||||
0.442168 | + | 0.896932i | \(0.354210\pi\) | |||||||
\(90\) | −1.63119 | −0.171942 | ||||||||
\(91\) | 1.43479 | 0.150407 | ||||||||
\(92\) | 2.02643 | 0.211270 | ||||||||
\(93\) | 4.27632 | 0.443434 | ||||||||
\(94\) | −4.00288 | −0.412865 | ||||||||
\(95\) | 4.33680 | 0.444947 | ||||||||
\(96\) | −1.16996 | −0.119409 | ||||||||
\(97\) | 11.3050 | 1.14785 | 0.573926 | − | 0.818907i | \(-0.305420\pi\) | ||||
0.573926 | + | 0.818907i | \(0.305420\pi\) | |||||||
\(98\) | −1.00000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −11.8936 | −1.18345 | −0.591727 | − | 0.806138i | \(-0.701554\pi\) | ||||
−0.591727 | + | 0.806138i | \(0.701554\pi\) | |||||||
\(102\) | 8.52468 | 0.844069 | ||||||||
\(103\) | −2.57520 | −0.253742 | −0.126871 | − | 0.991919i | \(-0.540493\pi\) | ||||
−0.126871 | + | 0.991919i | \(0.540493\pi\) | |||||||
\(104\) | −1.43479 | −0.140693 | ||||||||
\(105\) | −1.16996 | −0.114177 | ||||||||
\(106\) | 4.87480 | 0.473483 | ||||||||
\(107\) | 0.0210293 | 0.00203298 | 0.00101649 | − | 0.999999i | \(-0.499676\pi\) | ||||
0.00101649 | + | 0.999999i | \(0.499676\pi\) | |||||||
\(108\) | −5.41832 | −0.521378 | ||||||||
\(109\) | 3.22024 | 0.308443 | 0.154222 | − | 0.988036i | \(-0.450713\pi\) | ||||
0.154222 | + | 0.988036i | \(0.450713\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.64598 | −0.346061 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | 16.8832 | 1.58824 | 0.794118 | − | 0.607764i | \(-0.207933\pi\) | ||||
0.794118 | + | 0.607764i | \(0.207933\pi\) | |||||||
\(114\) | 5.07390 | 0.475214 | ||||||||
\(115\) | −2.02643 | −0.188966 | ||||||||
\(116\) | 9.11632 | 0.846429 | ||||||||
\(117\) | −2.34041 | −0.216371 | ||||||||
\(118\) | −12.3811 | −1.13978 | ||||||||
\(119\) | −7.28628 | −0.667932 | ||||||||
\(120\) | 1.16996 | 0.106802 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.62309 | 0.599626 | ||||||||
\(123\) | −2.40514 | −0.216865 | ||||||||
\(124\) | 3.65509 | 0.328237 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 1.63119 | 0.145318 | ||||||||
\(127\) | 3.83782 | 0.340551 | 0.170276 | − | 0.985396i | \(-0.445534\pi\) | ||||
0.170276 | + | 0.985396i | \(0.445534\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −0.825831 | −0.0727103 | ||||||||
\(130\) | 1.43479 | 0.125839 | ||||||||
\(131\) | 19.4691 | 1.70102 | 0.850511 | − | 0.525958i | \(-0.176293\pi\) | ||||
0.850511 | + | 0.525958i | \(0.176293\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.33680 | −0.376049 | ||||||||
\(134\) | 1.89373 | 0.163594 | ||||||||
\(135\) | 5.41832 | 0.466334 | ||||||||
\(136\) | 7.28628 | 0.624793 | ||||||||
\(137\) | 16.1146 | 1.37677 | 0.688383 | − | 0.725347i | \(-0.258321\pi\) | ||||
0.688383 | + | 0.725347i | \(0.258321\pi\) | |||||||
\(138\) | −2.37085 | −0.201820 | ||||||||
\(139\) | 16.9156 | 1.43476 | 0.717382 | − | 0.696680i | \(-0.245340\pi\) | ||||
0.717382 | + | 0.696680i | \(0.245340\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 4.68321 | 0.394398 | ||||||||
\(142\) | −0.421681 | −0.0353867 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −1.63119 | −0.135932 | ||||||||
\(145\) | −9.11632 | −0.757069 | ||||||||
\(146\) | 7.37947 | 0.610729 | ||||||||
\(147\) | 1.16996 | 0.0964969 | ||||||||
\(148\) | −3.11632 | −0.256160 | ||||||||
\(149\) | 5.12256 | 0.419656 | 0.209828 | − | 0.977738i | \(-0.432710\pi\) | ||||
0.209828 | + | 0.977738i | \(0.432710\pi\) | |||||||
\(150\) | −1.16996 | −0.0955270 | ||||||||
\(151\) | −22.4051 | −1.82330 | −0.911652 | − | 0.410964i | \(-0.865192\pi\) | ||||
−0.911652 | + | 0.410964i | \(0.865192\pi\) | |||||||
\(152\) | 4.33680 | 0.351761 | ||||||||
\(153\) | 11.8853 | 0.960869 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.65509 | −0.293584 | ||||||||
\(156\) | 1.67865 | 0.134400 | ||||||||
\(157\) | 14.9308 | 1.19161 | 0.595804 | − | 0.803130i | \(-0.296834\pi\) | ||||
0.595804 | + | 0.803130i | \(0.296834\pi\) | |||||||
\(158\) | 3.98377 | 0.316932 | ||||||||
\(159\) | −5.70334 | −0.452304 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 2.02643 | 0.159705 | ||||||||
\(162\) | 1.44566 | 0.113582 | ||||||||
\(163\) | 3.69439 | 0.289367 | 0.144684 | − | 0.989478i | \(-0.453784\pi\) | ||||
0.144684 | + | 0.989478i | \(0.453784\pi\) | |||||||
\(164\) | −2.05574 | −0.160527 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.15061 | −0.554995 | ||||||||
\(167\) | 9.33915 | 0.722685 | 0.361343 | − | 0.932433i | \(-0.382318\pi\) | ||||
0.361343 | + | 0.932433i | \(0.382318\pi\) | |||||||
\(168\) | −1.16996 | −0.0902646 | ||||||||
\(169\) | −10.9414 | −0.841644 | ||||||||
\(170\) | −7.28628 | −0.558832 | ||||||||
\(171\) | 7.07414 | 0.540973 | ||||||||
\(172\) | −0.705861 | −0.0538214 | ||||||||
\(173\) | −1.89895 | −0.144375 | −0.0721874 | − | 0.997391i | \(-0.522998\pi\) | ||||
−0.0721874 | + | 0.997391i | \(0.522998\pi\) | |||||||
\(174\) | −10.6658 | −0.808568 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.4855 | 1.08880 | ||||||||
\(178\) | −8.34280 | −0.625319 | ||||||||
\(179\) | 6.00288 | 0.448676 | 0.224338 | − | 0.974511i | \(-0.427978\pi\) | ||||
0.224338 | + | 0.974511i | \(0.427978\pi\) | |||||||
\(180\) | 1.63119 | 0.121582 | ||||||||
\(181\) | −6.73019 | −0.500251 | −0.250126 | − | 0.968213i | \(-0.580472\pi\) | ||||
−0.250126 | + | 0.968213i | \(0.580472\pi\) | |||||||
\(182\) | −1.43479 | −0.106354 | ||||||||
\(183\) | −7.74876 | −0.572805 | ||||||||
\(184\) | −2.02643 | −0.149391 | ||||||||
\(185\) | 3.11632 | 0.229116 | ||||||||
\(186\) | −4.27632 | −0.313555 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 4.00288 | 0.291940 | ||||||||
\(189\) | −5.41832 | −0.394124 | ||||||||
\(190\) | −4.33680 | −0.314625 | ||||||||
\(191\) | 15.9464 | 1.15384 | 0.576919 | − | 0.816801i | \(-0.304255\pi\) | ||||
0.576919 | + | 0.816801i | \(0.304255\pi\) | |||||||
\(192\) | 1.16996 | 0.0844348 | ||||||||
\(193\) | −11.7470 | −0.845569 | −0.422784 | − | 0.906230i | \(-0.638947\pi\) | ||||
−0.422784 | + | 0.906230i | \(0.638947\pi\) | |||||||
\(194\) | −11.3050 | −0.811655 | ||||||||
\(195\) | −1.67865 | −0.120211 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 2.70088 | 0.192430 | 0.0962148 | − | 0.995361i | \(-0.469326\pi\) | ||||
0.0962148 | + | 0.995361i | \(0.469326\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5804 | 1.03358 | 0.516789 | − | 0.856113i | \(-0.327127\pi\) | ||||
0.516789 | + | 0.856113i | \(0.327127\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | −2.21560 | −0.156276 | ||||||||
\(202\) | 11.8936 | 0.836828 | ||||||||
\(203\) | 9.11632 | 0.639840 | ||||||||
\(204\) | −8.52468 | −0.596847 | ||||||||
\(205\) | 2.05574 | 0.143579 | ||||||||
\(206\) | 2.57520 | 0.179423 | ||||||||
\(207\) | −3.30550 | −0.229748 | ||||||||
\(208\) | 1.43479 | 0.0994849 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 1.16996 | 0.0807351 | ||||||||
\(211\) | −18.2347 | −1.25533 | −0.627666 | − | 0.778483i | \(-0.715990\pi\) | ||||
−0.627666 | + | 0.778483i | \(0.715990\pi\) | |||||||
\(212\) | −4.87480 | −0.334803 | ||||||||
\(213\) | 0.493351 | 0.0338038 | ||||||||
\(214\) | −0.0210293 | −0.00143754 | ||||||||
\(215\) | 0.705861 | 0.0481393 | ||||||||
\(216\) | 5.41832 | 0.368670 | ||||||||
\(217\) | 3.65509 | 0.248124 | ||||||||
\(218\) | −3.22024 | −0.218102 | ||||||||
\(219\) | −8.63370 | −0.583412 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.4543 | −0.703232 | ||||||||
\(222\) | 3.64598 | 0.244702 | ||||||||
\(223\) | 1.41856 | 0.0949938 | 0.0474969 | − | 0.998871i | \(-0.484876\pi\) | ||||
0.0474969 | + | 0.998871i | \(0.484876\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | −1.63119 | −0.108746 | ||||||||
\(226\) | −16.8832 | −1.12305 | ||||||||
\(227\) | −8.18601 | −0.543325 | −0.271662 | − | 0.962393i | \(-0.587573\pi\) | ||||
−0.271662 | + | 0.962393i | \(0.587573\pi\) | |||||||
\(228\) | −5.07390 | −0.336027 | ||||||||
\(229\) | −1.88578 | −0.124616 | −0.0623080 | − | 0.998057i | \(-0.519846\pi\) | ||||
−0.0623080 | + | 0.998057i | \(0.519846\pi\) | |||||||
\(230\) | 2.02643 | 0.133619 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.11632 | −0.598516 | ||||||||
\(233\) | −22.9570 | −1.50396 | −0.751982 | − | 0.659184i | \(-0.770902\pi\) | ||||
−0.751982 | + | 0.659184i | \(0.770902\pi\) | |||||||
\(234\) | 2.34041 | 0.152998 | ||||||||
\(235\) | −4.00288 | −0.261119 | ||||||||
\(236\) | 12.3811 | 0.805944 | ||||||||
\(237\) | −4.66086 | −0.302755 | ||||||||
\(238\) | 7.28628 | 0.472299 | ||||||||
\(239\) | −0.315230 | −0.0203905 | −0.0101953 | − | 0.999948i | \(-0.503245\pi\) | ||||
−0.0101953 | + | 0.999948i | \(0.503245\pi\) | |||||||
\(240\) | −1.16996 | −0.0755208 | ||||||||
\(241\) | 5.61640 | 0.361784 | 0.180892 | − | 0.983503i | \(-0.442102\pi\) | ||||
0.180892 | + | 0.983503i | \(0.442102\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.5636 | 0.934254 | ||||||||
\(244\) | −6.62309 | −0.424000 | ||||||||
\(245\) | −1.00000 | −0.0638877 | ||||||||
\(246\) | 2.40514 | 0.153346 | ||||||||
\(247\) | −6.22241 | −0.395922 | ||||||||
\(248\) | −3.65509 | −0.232099 | ||||||||
\(249\) | 8.36595 | 0.530170 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 14.3205 | 0.903903 | 0.451951 | − | 0.892043i | \(-0.350728\pi\) | ||||
0.451951 | + | 0.892043i | \(0.350728\pi\) | |||||||
\(252\) | −1.63119 | −0.102755 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −3.83782 | −0.240806 | ||||||||
\(255\) | 8.52468 | 0.533836 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 28.8932 | 1.80231 | 0.901153 | − | 0.433501i | \(-0.142722\pi\) | ||||
0.901153 | + | 0.433501i | \(0.142722\pi\) | |||||||
\(258\) | 0.825831 | 0.0514140 | ||||||||
\(259\) | −3.11632 | −0.193639 | ||||||||
\(260\) | −1.43479 | −0.0889820 | ||||||||
\(261\) | −14.8704 | −0.920456 | ||||||||
\(262\) | −19.4691 | −1.20280 | ||||||||
\(263\) | −21.9055 | −1.35075 | −0.675377 | − | 0.737473i | \(-0.736019\pi\) | ||||
−0.675377 | + | 0.737473i | \(0.736019\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 4.87480 | 0.299457 | ||||||||
\(266\) | 4.33680 | 0.265907 | ||||||||
\(267\) | 9.76076 | 0.597349 | ||||||||
\(268\) | −1.89373 | −0.115678 | ||||||||
\(269\) | −2.97854 | −0.181605 | −0.0908025 | − | 0.995869i | \(-0.528943\pi\) | ||||
−0.0908025 | + | 0.995869i | \(0.528943\pi\) | |||||||
\(270\) | −5.41832 | −0.329748 | ||||||||
\(271\) | −0.202215 | −0.0122837 | −0.00614183 | − | 0.999981i | \(-0.501955\pi\) | ||||
−0.00614183 | + | 0.999981i | \(0.501955\pi\) | |||||||
\(272\) | −7.28628 | −0.441796 | ||||||||
\(273\) | 1.67865 | 0.101597 | ||||||||
\(274\) | −16.1146 | −0.973521 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.37085 | 0.142709 | ||||||||
\(277\) | 4.93157 | 0.296309 | 0.148155 | − | 0.988964i | \(-0.452667\pi\) | ||||
0.148155 | + | 0.988964i | \(0.452667\pi\) | |||||||
\(278\) | −16.9156 | −1.01453 | ||||||||
\(279\) | −5.96214 | −0.356944 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 17.8483 | 1.06474 | 0.532370 | − | 0.846512i | \(-0.321302\pi\) | ||||
0.532370 | + | 0.846512i | \(0.321302\pi\) | |||||||
\(282\) | −4.68321 | −0.278881 | ||||||||
\(283\) | 29.2721 | 1.74005 | 0.870023 | − | 0.493010i | \(-0.164104\pi\) | ||||
0.870023 | + | 0.493010i | \(0.164104\pi\) | |||||||
\(284\) | 0.421681 | 0.0250222 | ||||||||
\(285\) | 5.07390 | 0.300552 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2.05574 | −0.121347 | ||||||||
\(288\) | 1.63119 | 0.0961187 | ||||||||
\(289\) | 36.0899 | 2.12293 | ||||||||
\(290\) | 9.11632 | 0.535329 | ||||||||
\(291\) | 13.2265 | 0.775350 | ||||||||
\(292\) | −7.37947 | −0.431851 | ||||||||
\(293\) | 29.9025 | 1.74692 | 0.873460 | − | 0.486895i | \(-0.161871\pi\) | ||||
0.873460 | + | 0.486895i | \(0.161871\pi\) | |||||||
\(294\) | −1.16996 | −0.0682336 | ||||||||
\(295\) | −12.3811 | −0.720858 | ||||||||
\(296\) | 3.11632 | 0.181132 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −5.12256 | −0.296742 | ||||||||
\(299\) | 2.90751 | 0.168146 | ||||||||
\(300\) | 1.16996 | 0.0675478 | ||||||||
\(301\) | −0.705861 | −0.0406851 | ||||||||
\(302\) | 22.4051 | 1.28927 | ||||||||
\(303\) | −13.9150 | −0.799397 | ||||||||
\(304\) | −4.33680 | −0.248733 | ||||||||
\(305\) | 6.62309 | 0.379237 | ||||||||
\(306\) | −11.8853 | −0.679437 | ||||||||
\(307\) | −13.6023 | −0.776324 | −0.388162 | − | 0.921591i | \(-0.626890\pi\) | ||||
−0.388162 | + | 0.921591i | \(0.626890\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.01289 | −0.171397 | ||||||||
\(310\) | 3.65509 | 0.207595 | ||||||||
\(311\) | 29.5607 | 1.67623 | 0.838117 | − | 0.545490i | \(-0.183656\pi\) | ||||
0.838117 | + | 0.545490i | \(0.183656\pi\) | |||||||
\(312\) | −1.67865 | −0.0950349 | ||||||||
\(313\) | 9.23518 | 0.522003 | 0.261002 | − | 0.965338i | \(-0.415947\pi\) | ||||
0.261002 | + | 0.965338i | \(0.415947\pi\) | |||||||
\(314\) | −14.9308 | −0.842593 | ||||||||
\(315\) | 1.63119 | 0.0919070 | ||||||||
\(316\) | −3.98377 | −0.224105 | ||||||||
\(317\) | −5.25554 | −0.295180 | −0.147590 | − | 0.989049i | \(-0.547152\pi\) | ||||
−0.147590 | + | 0.989049i | \(0.547152\pi\) | |||||||
\(318\) | 5.70334 | 0.319827 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0.0246035 | 0.00137324 | ||||||||
\(322\) | −2.02643 | −0.112929 | ||||||||
\(323\) | 31.5992 | 1.75823 | ||||||||
\(324\) | −1.44566 | −0.0803146 | ||||||||
\(325\) | 1.43479 | 0.0795879 | ||||||||
\(326\) | −3.69439 | −0.204614 | ||||||||
\(327\) | 3.76756 | 0.208347 | ||||||||
\(328\) | 2.05574 | 0.113510 | ||||||||
\(329\) | 4.00288 | 0.220686 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.4150 | −1.28700 | −0.643501 | − | 0.765445i | \(-0.722519\pi\) | ||||
−0.643501 | + | 0.765445i | \(0.722519\pi\) | |||||||
\(332\) | 7.15061 | 0.392441 | ||||||||
\(333\) | 5.08330 | 0.278563 | ||||||||
\(334\) | −9.33915 | −0.511016 | ||||||||
\(335\) | 1.89373 | 0.103466 | ||||||||
\(336\) | 1.16996 | 0.0638267 | ||||||||
\(337\) | −2.73973 | −0.149242 | −0.0746212 | − | 0.997212i | \(-0.523775\pi\) | ||||
−0.0746212 | + | 0.997212i | \(0.523775\pi\) | |||||||
\(338\) | 10.9414 | 0.595132 | ||||||||
\(339\) | 19.7527 | 1.07282 | ||||||||
\(340\) | 7.28628 | 0.395154 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −7.07414 | −0.382526 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0.705861 | 0.0380575 | ||||||||
\(345\) | −2.37085 | −0.127642 | ||||||||
\(346\) | 1.89895 | 0.102088 | ||||||||
\(347\) | −5.82295 | −0.312592 | −0.156296 | − | 0.987710i | \(-0.549955\pi\) | ||||
−0.156296 | + | 0.987710i | \(0.549955\pi\) | |||||||
\(348\) | 10.6658 | 0.571744 | ||||||||
\(349\) | −8.42897 | −0.451193 | −0.225596 | − | 0.974221i | \(-0.572433\pi\) | ||||
−0.225596 | + | 0.974221i | \(0.572433\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | −7.77415 | −0.414953 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.9658 | −1.27557 | −0.637786 | − | 0.770214i | \(-0.720149\pi\) | ||||
−0.637786 | + | 0.770214i | \(0.720149\pi\) | |||||||
\(354\) | −14.4855 | −0.769894 | ||||||||
\(355\) | −0.421681 | −0.0223805 | ||||||||
\(356\) | 8.34280 | 0.442168 | ||||||||
\(357\) | −8.52468 | −0.451174 | ||||||||
\(358\) | −6.00288 | −0.317262 | ||||||||
\(359\) | 16.0490 | 0.847032 | 0.423516 | − | 0.905889i | \(-0.360796\pi\) | ||||
0.423516 | + | 0.905889i | \(0.360796\pi\) | |||||||
\(360\) | −1.63119 | −0.0859711 | ||||||||
\(361\) | −0.192129 | −0.0101120 | ||||||||
\(362\) | 6.73019 | 0.353731 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.43479 | 0.0752035 | ||||||||
\(365\) | 7.37947 | 0.386259 | ||||||||
\(366\) | 7.74876 | 0.405034 | ||||||||
\(367\) | −2.17504 | −0.113536 | −0.0567680 | − | 0.998387i | \(-0.518080\pi\) | ||||
−0.0567680 | + | 0.998387i | \(0.518080\pi\) | |||||||
\(368\) | 2.02643 | 0.105635 | ||||||||
\(369\) | 3.35331 | 0.174566 | ||||||||
\(370\) | −3.11632 | −0.162010 | ||||||||
\(371\) | −4.87480 | −0.253087 | ||||||||
\(372\) | 4.27632 | 0.221717 | ||||||||
\(373\) | 16.5044 | 0.854566 | 0.427283 | − | 0.904118i | \(-0.359471\pi\) | ||||
0.427283 | + | 0.904118i | \(0.359471\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.16996 | −0.0604166 | ||||||||
\(376\) | −4.00288 | −0.206433 | ||||||||
\(377\) | 13.0800 | 0.673655 | ||||||||
\(378\) | 5.41832 | 0.278688 | ||||||||
\(379\) | 22.3263 | 1.14683 | 0.573413 | − | 0.819267i | \(-0.305619\pi\) | ||||
0.573413 | + | 0.819267i | \(0.305619\pi\) | |||||||
\(380\) | 4.33680 | 0.222473 | ||||||||
\(381\) | 4.49010 | 0.230035 | ||||||||
\(382\) | −15.9464 | −0.815887 | ||||||||
\(383\) | −21.4500 | −1.09604 | −0.548021 | − | 0.836465i | \(-0.684619\pi\) | ||||
−0.548021 | + | 0.836465i | \(0.684619\pi\) | |||||||
\(384\) | −1.16996 | −0.0597044 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.7470 | 0.597907 | ||||||||
\(387\) | 1.15139 | 0.0585285 | ||||||||
\(388\) | 11.3050 | 0.573926 | ||||||||
\(389\) | −37.9771 | −1.92552 | −0.962759 | − | 0.270362i | \(-0.912857\pi\) | ||||
−0.962759 | + | 0.270362i | \(0.912857\pi\) | |||||||
\(390\) | 1.67865 | 0.0850018 | ||||||||
\(391\) | −14.7652 | −0.746707 | ||||||||
\(392\) | −1.00000 | −0.0505076 | ||||||||
\(393\) | 22.7781 | 1.14900 | ||||||||
\(394\) | −2.70088 | −0.136068 | ||||||||
\(395\) | 3.98377 | 0.200445 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −24.9220 | −1.25080 | −0.625399 | − | 0.780305i | \(-0.715064\pi\) | ||||
−0.625399 | + | 0.780305i | \(0.715064\pi\) | |||||||
\(398\) | −14.5804 | −0.730850 | ||||||||
\(399\) | −5.07390 | −0.254013 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −23.7936 | −1.18819 | −0.594097 | − | 0.804393i | \(-0.702491\pi\) | ||||
−0.594097 | + | 0.804393i | \(0.702491\pi\) | |||||||
\(402\) | 2.21560 | 0.110504 | ||||||||
\(403\) | 5.24430 | 0.261237 | ||||||||
\(404\) | −11.8936 | −0.591727 | ||||||||
\(405\) | 1.44566 | 0.0718355 | ||||||||
\(406\) | −9.11632 | −0.452435 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 8.52468 | 0.422034 | ||||||||
\(409\) | 17.4118 | 0.860958 | 0.430479 | − | 0.902601i | \(-0.358345\pi\) | ||||
0.430479 | + | 0.902601i | \(0.358345\pi\) | |||||||
\(410\) | −2.05574 | −0.101526 | ||||||||
\(411\) | 18.8535 | 0.929976 | ||||||||
\(412\) | −2.57520 | −0.126871 | ||||||||
\(413\) | 12.3811 | 0.609236 | ||||||||
\(414\) | 3.30550 | 0.162456 | ||||||||
\(415\) | −7.15061 | −0.351010 | ||||||||
\(416\) | −1.43479 | −0.0703464 | ||||||||
\(417\) | 19.7906 | 0.969151 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.77394 | 0.330929 | 0.165464 | − | 0.986216i | \(-0.447088\pi\) | ||||
0.165464 | + | 0.986216i | \(0.447088\pi\) | |||||||
\(420\) | −1.16996 | −0.0570883 | ||||||||
\(421\) | 16.3820 | 0.798409 | 0.399205 | − | 0.916862i | \(-0.369286\pi\) | ||||
0.399205 | + | 0.916862i | \(0.369286\pi\) | |||||||
\(422\) | 18.2347 | 0.887653 | ||||||||
\(423\) | −6.52944 | −0.317472 | ||||||||
\(424\) | 4.87480 | 0.236741 | ||||||||
\(425\) | −7.28628 | −0.353437 | ||||||||
\(426\) | −0.493351 | −0.0239029 | ||||||||
\(427\) | −6.62309 | −0.320514 | ||||||||
\(428\) | 0.0210293 | 0.00101649 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −0.705861 | −0.0340396 | ||||||||
\(431\) | 35.7762 | 1.72328 | 0.861638 | − | 0.507523i | \(-0.169439\pi\) | ||||
0.861638 | + | 0.507523i | \(0.169439\pi\) | |||||||
\(432\) | −5.41832 | −0.260689 | ||||||||
\(433\) | 12.5667 | 0.603919 | 0.301959 | − | 0.953321i | \(-0.402359\pi\) | ||||
0.301959 | + | 0.953321i | \(0.402359\pi\) | |||||||
\(434\) | −3.65509 | −0.175450 | ||||||||
\(435\) | −10.6658 | −0.511384 | ||||||||
\(436\) | 3.22024 | 0.154222 | ||||||||
\(437\) | −8.78825 | −0.420399 | ||||||||
\(438\) | 8.63370 | 0.412534 | ||||||||
\(439\) | 34.6171 | 1.65218 | 0.826092 | − | 0.563535i | \(-0.190559\pi\) | ||||
0.826092 | + | 0.563535i | \(0.190559\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.63119 | −0.0776756 | ||||||||
\(442\) | 10.4543 | 0.497260 | ||||||||
\(443\) | 18.9816 | 0.901841 | 0.450921 | − | 0.892564i | \(-0.351096\pi\) | ||||
0.450921 | + | 0.892564i | \(0.351096\pi\) | |||||||
\(444\) | −3.64598 | −0.173030 | ||||||||
\(445\) | −8.34280 | −0.395487 | ||||||||
\(446\) | −1.41856 | −0.0671708 | ||||||||
\(447\) | 5.99320 | 0.283469 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | 13.7748 | 0.650072 | 0.325036 | − | 0.945702i | \(-0.394624\pi\) | ||||
0.325036 | + | 0.945702i | \(0.394624\pi\) | |||||||
\(450\) | 1.63119 | 0.0768949 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 16.8832 | 0.794118 | ||||||||
\(453\) | −26.2132 | −1.23160 | ||||||||
\(454\) | 8.18601 | 0.384188 | ||||||||
\(455\) | −1.43479 | −0.0672640 | ||||||||
\(456\) | 5.07390 | 0.237607 | ||||||||
\(457\) | −36.0763 | −1.68758 | −0.843789 | − | 0.536676i | \(-0.819680\pi\) | ||||
−0.843789 | + | 0.536676i | \(0.819680\pi\) | |||||||
\(458\) | 1.88578 | 0.0881168 | ||||||||
\(459\) | 39.4794 | 1.84274 | ||||||||
\(460\) | −2.02643 | −0.0944830 | ||||||||
\(461\) | 23.2972 | 1.08506 | 0.542529 | − | 0.840037i | \(-0.317467\pi\) | ||||
0.542529 | + | 0.840037i | \(0.317467\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −31.8729 | −1.48126 | −0.740629 | − | 0.671914i | \(-0.765472\pi\) | ||||
−0.740629 | + | 0.671914i | \(0.765472\pi\) | |||||||
\(464\) | 9.11632 | 0.423214 | ||||||||
\(465\) | −4.27632 | −0.198310 | ||||||||
\(466\) | 22.9570 | 1.06346 | ||||||||
\(467\) | −11.5661 | −0.535216 | −0.267608 | − | 0.963528i | \(-0.586233\pi\) | ||||
−0.267608 | + | 0.963528i | \(0.586233\pi\) | |||||||
\(468\) | −2.34041 | −0.108186 | ||||||||
\(469\) | −1.89373 | −0.0874444 | ||||||||
\(470\) | 4.00288 | 0.184639 | ||||||||
\(471\) | 17.4685 | 0.804905 | ||||||||
\(472\) | −12.3811 | −0.569889 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 4.66086 | 0.214080 | ||||||||
\(475\) | −4.33680 | −0.198986 | ||||||||
\(476\) | −7.28628 | −0.333966 | ||||||||
\(477\) | 7.95172 | 0.364084 | ||||||||
\(478\) | 0.315230 | 0.0144183 | ||||||||
\(479\) | 13.2561 | 0.605689 | 0.302844 | − | 0.953040i | \(-0.402064\pi\) | ||||
0.302844 | + | 0.953040i | \(0.402064\pi\) | |||||||
\(480\) | 1.16996 | 0.0534012 | ||||||||
\(481\) | −4.47127 | −0.203872 | ||||||||
\(482\) | −5.61640 | −0.255820 | ||||||||
\(483\) | 2.37085 | 0.107878 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −11.3050 | −0.513335 | ||||||||
\(486\) | −14.5636 | −0.660617 | ||||||||
\(487\) | 5.42232 | 0.245709 | 0.122854 | − | 0.992425i | \(-0.460795\pi\) | ||||
0.122854 | + | 0.992425i | \(0.460795\pi\) | |||||||
\(488\) | 6.62309 | 0.299813 | ||||||||
\(489\) | 4.32230 | 0.195461 | ||||||||
\(490\) | 1.00000 | 0.0451754 | ||||||||
\(491\) | 36.0238 | 1.62573 | 0.812866 | − | 0.582450i | \(-0.197906\pi\) | ||||
0.812866 | + | 0.582450i | \(0.197906\pi\) | |||||||
\(492\) | −2.40514 | −0.108432 | ||||||||
\(493\) | −66.4241 | −2.99159 | ||||||||
\(494\) | 6.22241 | 0.279959 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.65509 | 0.164119 | ||||||||
\(497\) | 0.421681 | 0.0189150 | ||||||||
\(498\) | −8.36595 | −0.374887 | ||||||||
\(499\) | −3.26974 | −0.146374 | −0.0731869 | − | 0.997318i | \(-0.523317\pi\) | ||||
−0.0731869 | + | 0.997318i | \(0.523317\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 10.9265 | 0.488158 | ||||||||
\(502\) | −14.3205 | −0.639156 | ||||||||
\(503\) | 41.9101 | 1.86868 | 0.934339 | − | 0.356384i | \(-0.115991\pi\) | ||||
0.934339 | + | 0.356384i | \(0.115991\pi\) | |||||||
\(504\) | 1.63119 | 0.0726589 | ||||||||
\(505\) | 11.8936 | 0.529257 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.8010 | −0.568512 | ||||||||
\(508\) | 3.83782 | 0.170276 | ||||||||
\(509\) | 19.3235 | 0.856500 | 0.428250 | − | 0.903660i | \(-0.359130\pi\) | ||||
0.428250 | + | 0.903660i | \(0.359130\pi\) | |||||||
\(510\) | −8.52468 | −0.377479 | ||||||||
\(511\) | −7.37947 | −0.326449 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 23.4982 | 1.03747 | ||||||||
\(514\) | −28.8932 | −1.27442 | ||||||||
\(515\) | 2.57520 | 0.113477 | ||||||||
\(516\) | −0.825831 | −0.0363552 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.11632 | 0.136923 | ||||||||
\(519\) | −2.22170 | −0.0975220 | ||||||||
\(520\) | 1.43479 | 0.0629197 | ||||||||
\(521\) | −22.0283 | −0.965078 | −0.482539 | − | 0.875874i | \(-0.660285\pi\) | ||||
−0.482539 | + | 0.875874i | \(0.660285\pi\) | |||||||
\(522\) | 14.8704 | 0.650861 | ||||||||
\(523\) | 20.3706 | 0.890745 | 0.445373 | − | 0.895345i | \(-0.353071\pi\) | ||||
0.445373 | + | 0.895345i | \(0.353071\pi\) | |||||||
\(524\) | 19.4691 | 0.850511 | ||||||||
\(525\) | 1.16996 | 0.0510613 | ||||||||
\(526\) | 21.9055 | 0.955127 | ||||||||
\(527\) | −26.6320 | −1.16011 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −18.8936 | −0.821459 | ||||||||
\(530\) | −4.87480 | −0.211748 | ||||||||
\(531\) | −20.1960 | −0.876431 | ||||||||
\(532\) | −4.33680 | −0.188024 | ||||||||
\(533\) | −2.94956 | −0.127760 | ||||||||
\(534\) | −9.76076 | −0.422390 | ||||||||
\(535\) | −0.0210293 | −0.000909178 0 | ||||||||
\(536\) | 1.89373 | 0.0817968 | ||||||||
\(537\) | 7.02314 | 0.303071 | ||||||||
\(538\) | 2.97854 | 0.128414 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 5.41832 | 0.233167 | ||||||||
\(541\) | −29.5866 | −1.27203 | −0.636013 | − | 0.771678i | \(-0.719418\pi\) | ||||
−0.636013 | + | 0.771678i | \(0.719418\pi\) | |||||||
\(542\) | 0.202215 | 0.00868587 | ||||||||
\(543\) | −7.87407 | −0.337909 | ||||||||
\(544\) | 7.28628 | 0.312397 | ||||||||
\(545\) | −3.22024 | −0.137940 | ||||||||
\(546\) | −1.67865 | −0.0718397 | ||||||||
\(547\) | 31.5318 | 1.34820 | 0.674102 | − | 0.738638i | \(-0.264531\pi\) | ||||
0.674102 | + | 0.738638i | \(0.264531\pi\) | |||||||
\(548\) | 16.1146 | 0.688383 | ||||||||
\(549\) | 10.8035 | 0.461082 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −39.5357 | −1.68428 | ||||||||
\(552\) | −2.37085 | −0.100910 | ||||||||
\(553\) | −3.98377 | −0.169407 | ||||||||
\(554\) | −4.93157 | −0.209522 | ||||||||
\(555\) | 3.64598 | 0.154763 | ||||||||
\(556\) | 16.9156 | 0.717382 | ||||||||
\(557\) | 2.97938 | 0.126240 | 0.0631202 | − | 0.998006i | \(-0.479895\pi\) | ||||
0.0631202 | + | 0.998006i | \(0.479895\pi\) | |||||||
\(558\) | 5.96214 | 0.252398 | ||||||||
\(559\) | −1.01276 | −0.0428353 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −17.8483 | −0.752885 | ||||||||
\(563\) | −15.7256 | −0.662754 | −0.331377 | − | 0.943498i | \(-0.607513\pi\) | ||||
−0.331377 | + | 0.943498i | \(0.607513\pi\) | |||||||
\(564\) | 4.68321 | 0.197199 | ||||||||
\(565\) | −16.8832 | −0.710281 | ||||||||
\(566\) | −29.2721 | −1.23040 | ||||||||
\(567\) | −1.44566 | −0.0607121 | ||||||||
\(568\) | −0.421681 | −0.0176933 | ||||||||
\(569\) | −37.0851 | −1.55469 | −0.777345 | − | 0.629074i | \(-0.783434\pi\) | ||||
−0.777345 | + | 0.629074i | \(0.783434\pi\) | |||||||
\(570\) | −5.07390 | −0.212522 | ||||||||
\(571\) | 14.5281 | 0.607982 | 0.303991 | − | 0.952675i | \(-0.401681\pi\) | ||||
0.303991 | + | 0.952675i | \(0.401681\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 18.6566 | 0.779392 | ||||||||
\(574\) | 2.05574 | 0.0858051 | ||||||||
\(575\) | 2.02643 | 0.0845082 | ||||||||
\(576\) | −1.63119 | −0.0679662 | ||||||||
\(577\) | 2.22693 | 0.0927082 | 0.0463541 | − | 0.998925i | \(-0.485240\pi\) | ||||
0.0463541 | + | 0.998925i | \(0.485240\pi\) | |||||||
\(578\) | −36.0899 | −1.50114 | ||||||||
\(579\) | −13.7436 | −0.571163 | ||||||||
\(580\) | −9.11632 | −0.378535 | ||||||||
\(581\) | 7.15061 | 0.296657 | ||||||||
\(582\) | −13.2265 | −0.548255 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 7.37947 | 0.305365 | ||||||||
\(585\) | 2.34041 | 0.0967642 | ||||||||
\(586\) | −29.9025 | −1.23526 | ||||||||
\(587\) | −8.50637 | −0.351095 | −0.175548 | − | 0.984471i | \(-0.556170\pi\) | ||||
−0.175548 | + | 0.984471i | \(0.556170\pi\) | |||||||
\(588\) | 1.16996 | 0.0482484 | ||||||||
\(589\) | −15.8514 | −0.653147 | ||||||||
\(590\) | 12.3811 | 0.509724 | ||||||||
\(591\) | 3.15993 | 0.129982 | ||||||||
\(592\) | −3.11632 | −0.128080 | ||||||||
\(593\) | −24.9289 | −1.02371 | −0.511853 | − | 0.859073i | \(-0.671041\pi\) | ||||
−0.511853 | + | 0.859073i | \(0.671041\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.28628 | 0.298708 | ||||||||
\(596\) | 5.12256 | 0.209828 | ||||||||
\(597\) | 17.0585 | 0.698160 | ||||||||
\(598\) | −2.90751 | −0.118897 | ||||||||
\(599\) | 35.1526 | 1.43630 | 0.718149 | − | 0.695889i | \(-0.244990\pi\) | ||||
0.718149 | + | 0.695889i | \(0.244990\pi\) | |||||||
\(600\) | −1.16996 | −0.0477635 | ||||||||
\(601\) | −34.7898 | −1.41910 | −0.709552 | − | 0.704653i | \(-0.751103\pi\) | ||||
−0.709552 | + | 0.704653i | \(0.751103\pi\) | |||||||
\(602\) | 0.705861 | 0.0287687 | ||||||||
\(603\) | 3.08903 | 0.125795 | ||||||||
\(604\) | −22.4051 | −0.911652 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 13.9150 | 0.565259 | ||||||||
\(607\) | −14.7721 | −0.599581 | −0.299791 | − | 0.954005i | \(-0.596917\pi\) | ||||
−0.299791 | + | 0.954005i | \(0.596917\pi\) | |||||||
\(608\) | 4.33680 | 0.175881 | ||||||||
\(609\) | 10.6658 | 0.432198 | ||||||||
\(610\) | −6.62309 | −0.268161 | ||||||||
\(611\) | 5.74329 | 0.232349 | ||||||||
\(612\) | 11.8853 | 0.480435 | ||||||||
\(613\) | −10.3889 | −0.419602 | −0.209801 | − | 0.977744i | \(-0.567282\pi\) | ||||
−0.209801 | + | 0.977744i | \(0.567282\pi\) | |||||||
\(614\) | 13.6023 | 0.548944 | ||||||||
\(615\) | 2.40514 | 0.0969848 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 35.7962 | 1.44110 | 0.720551 | − | 0.693402i | \(-0.243889\pi\) | ||||
0.720551 | + | 0.693402i | \(0.243889\pi\) | |||||||
\(618\) | 3.01289 | 0.121196 | ||||||||
\(619\) | 31.2901 | 1.25765 | 0.628827 | − | 0.777545i | \(-0.283535\pi\) | ||||
0.628827 | + | 0.777545i | \(0.283535\pi\) | |||||||
\(620\) | −3.65509 | −0.146792 | ||||||||
\(621\) | −10.9799 | −0.440607 | ||||||||
\(622\) | −29.5607 | −1.18528 | ||||||||
\(623\) | 8.34280 | 0.334247 | ||||||||
\(624\) | 1.67865 | 0.0671998 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −9.23518 | −0.369112 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 14.9308 | 0.595804 | ||||||||
\(629\) | 22.7064 | 0.905362 | ||||||||
\(630\) | −1.63119 | −0.0649881 | ||||||||
\(631\) | 47.2969 | 1.88286 | 0.941429 | − | 0.337211i | \(-0.109484\pi\) | ||||
0.941429 | + | 0.337211i | \(0.109484\pi\) | |||||||
\(632\) | 3.98377 | 0.158466 | ||||||||
\(633\) | −21.3340 | −0.847949 | ||||||||
\(634\) | 5.25554 | 0.208724 | ||||||||
\(635\) | −3.83782 | −0.152299 | ||||||||
\(636\) | −5.70334 | −0.226152 | ||||||||
\(637\) | 1.43479 | 0.0568485 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −0.687841 | −0.0272106 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | 3.57172 | 0.141074 | 0.0705371 | − | 0.997509i | \(-0.477529\pi\) | ||||
0.0705371 | + | 0.997509i | \(0.477529\pi\) | |||||||
\(642\) | −0.0246035 | −0.000971025 0 | ||||||||
\(643\) | −8.20306 | −0.323497 | −0.161749 | − | 0.986832i | \(-0.551713\pi\) | ||||
−0.161749 | + | 0.986832i | \(0.551713\pi\) | |||||||
\(644\) | 2.02643 | 0.0798527 | ||||||||
\(645\) | 0.825831 | 0.0325171 | ||||||||
\(646\) | −31.5992 | −1.24325 | ||||||||
\(647\) | −33.2763 | −1.30823 | −0.654113 | − | 0.756397i | \(-0.726958\pi\) | ||||
−0.654113 | + | 0.756397i | \(0.726958\pi\) | |||||||
\(648\) | 1.44566 | 0.0567910 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −1.43479 | −0.0562771 | ||||||||
\(651\) | 4.27632 | 0.167602 | ||||||||
\(652\) | 3.69439 | 0.144684 | ||||||||
\(653\) | −20.5390 | −0.803754 | −0.401877 | − | 0.915694i | \(-0.631642\pi\) | ||||
−0.401877 | + | 0.915694i | \(0.631642\pi\) | |||||||
\(654\) | −3.76756 | −0.147323 | ||||||||
\(655\) | −19.4691 | −0.760720 | ||||||||
\(656\) | −2.05574 | −0.0802634 | ||||||||
\(657\) | 12.0373 | 0.469620 | ||||||||
\(658\) | −4.00288 | −0.156048 | ||||||||
\(659\) | −4.70889 | −0.183432 | −0.0917161 | − | 0.995785i | \(-0.529235\pi\) | ||||
−0.0917161 | + | 0.995785i | \(0.529235\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.57967 | −0.333710 | −0.166855 | − | 0.985981i | \(-0.553361\pi\) | ||||
−0.166855 | + | 0.985981i | \(0.553361\pi\) | |||||||
\(662\) | 23.4150 | 0.910048 | ||||||||
\(663\) | −12.2311 | −0.475018 | ||||||||
\(664\) | −7.15061 | −0.277498 | ||||||||
\(665\) | 4.33680 | 0.168174 | ||||||||
\(666\) | −5.08330 | −0.196974 | ||||||||
\(667\) | 18.4736 | 0.715302 | ||||||||
\(668\) | 9.33915 | 0.361343 | ||||||||
\(669\) | 1.65966 | 0.0641663 | ||||||||
\(670\) | −1.89373 | −0.0731613 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.16996 | −0.0451323 | ||||||||
\(673\) | 37.8109 | 1.45750 | 0.728751 | − | 0.684779i | \(-0.240101\pi\) | ||||
0.728751 | + | 0.684779i | \(0.240101\pi\) | |||||||
\(674\) | 2.73973 | 0.105530 | ||||||||
\(675\) | −5.41832 | −0.208551 | ||||||||
\(676\) | −10.9414 | −0.420822 | ||||||||
\(677\) | −19.9974 | −0.768562 | −0.384281 | − | 0.923216i | \(-0.625551\pi\) | ||||
−0.384281 | + | 0.923216i | \(0.625551\pi\) | |||||||
\(678\) | −19.7527 | −0.758597 | ||||||||
\(679\) | 11.3050 | 0.433848 | ||||||||
\(680\) | −7.28628 | −0.279416 | ||||||||
\(681\) | −9.57732 | −0.367004 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.1577 | −0.886106 | −0.443053 | − | 0.896495i | \(-0.646105\pi\) | ||||
−0.443053 | + | 0.896495i | \(0.646105\pi\) | |||||||
\(684\) | 7.07414 | 0.270487 | ||||||||
\(685\) | −16.1146 | −0.615709 | ||||||||
\(686\) | −1.00000 | −0.0381802 | ||||||||
\(687\) | −2.20629 | −0.0841754 | ||||||||
\(688\) | −0.705861 | −0.0269107 | ||||||||
\(689\) | −6.99433 | −0.266463 | ||||||||
\(690\) | 2.37085 | 0.0902568 | ||||||||
\(691\) | 4.71821 | 0.179489 | 0.0897446 | − | 0.995965i | \(-0.471395\pi\) | ||||
0.0897446 | + | 0.995965i | \(0.471395\pi\) | |||||||
\(692\) | −1.89895 | −0.0721874 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.82295 | 0.221036 | ||||||||
\(695\) | −16.9156 | −0.641646 | ||||||||
\(696\) | −10.6658 | −0.404284 | ||||||||
\(697\) | 14.9787 | 0.567360 | ||||||||
\(698\) | 8.42897 | 0.319041 | ||||||||
\(699\) | −26.8588 | −1.01589 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −8.58415 | −0.324219 | −0.162109 | − | 0.986773i | \(-0.551830\pi\) | ||||
−0.162109 | + | 0.986773i | \(0.551830\pi\) | |||||||
\(702\) | 7.77415 | 0.293416 | ||||||||
\(703\) | 13.5149 | 0.509723 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.68321 | −0.176380 | ||||||||
\(706\) | 23.9658 | 0.901965 | ||||||||
\(707\) | −11.8936 | −0.447303 | ||||||||
\(708\) | 14.4855 | 0.544398 | ||||||||
\(709\) | −28.0704 | −1.05421 | −0.527103 | − | 0.849802i | \(-0.676722\pi\) | ||||
−0.527103 | + | 0.849802i | \(0.676722\pi\) | |||||||
\(710\) | 0.421681 | 0.0158254 | ||||||||
\(711\) | 6.49828 | 0.243704 | ||||||||
\(712\) | −8.34280 | −0.312660 | ||||||||
\(713\) | 7.40681 | 0.277387 | ||||||||
\(714\) | 8.52468 | 0.319028 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.00288 | 0.224338 | ||||||||
\(717\) | −0.368807 | −0.0137734 | ||||||||
\(718\) | −16.0490 | −0.598942 | ||||||||
\(719\) | 30.4817 | 1.13678 | 0.568388 | − | 0.822761i | \(-0.307567\pi\) | ||||
0.568388 | + | 0.822761i | \(0.307567\pi\) | |||||||
\(720\) | 1.63119 | 0.0607908 | ||||||||
\(721\) | −2.57520 | −0.0959054 | ||||||||
\(722\) | 0.192129 | 0.00715029 | ||||||||
\(723\) | 6.57098 | 0.244377 | ||||||||
\(724\) | −6.73019 | −0.250126 | ||||||||
\(725\) | 9.11632 | 0.338572 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.25367 | 0.0464961 | 0.0232480 | − | 0.999730i | \(-0.492599\pi\) | ||||
0.0232480 | + | 0.999730i | \(0.492599\pi\) | |||||||
\(728\) | −1.43479 | −0.0531769 | ||||||||
\(729\) | 21.3758 | 0.791697 | ||||||||
\(730\) | −7.37947 | −0.273126 | ||||||||
\(731\) | 5.14310 | 0.190224 | ||||||||
\(732\) | −7.74876 | −0.286402 | ||||||||
\(733\) | 7.95330 | 0.293762 | 0.146881 | − | 0.989154i | \(-0.453077\pi\) | ||||
0.146881 | + | 0.989154i | \(0.453077\pi\) | |||||||
\(734\) | 2.17504 | 0.0802820 | ||||||||
\(735\) | −1.16996 | −0.0431547 | ||||||||
\(736\) | −2.02643 | −0.0746954 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −3.35331 | −0.123437 | ||||||||
\(739\) | 11.8074 | 0.434342 | 0.217171 | − | 0.976134i | \(-0.430317\pi\) | ||||
0.217171 | + | 0.976134i | \(0.430317\pi\) | |||||||
\(740\) | 3.11632 | 0.114558 | ||||||||
\(741\) | −7.27998 | −0.267437 | ||||||||
\(742\) | 4.87480 | 0.178960 | ||||||||
\(743\) | −41.2546 | −1.51348 | −0.756742 | − | 0.653714i | \(-0.773210\pi\) | ||||
−0.756742 | + | 0.653714i | \(0.773210\pi\) | |||||||
\(744\) | −4.27632 | −0.156778 | ||||||||
\(745\) | −5.12256 | −0.187676 | ||||||||
\(746\) | −16.5044 | −0.604270 | ||||||||
\(747\) | −11.6640 | −0.426763 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.0210293 | 0.000768396 0 | ||||||||
\(750\) | 1.16996 | 0.0427210 | ||||||||
\(751\) | −18.2805 | −0.667066 | −0.333533 | − | 0.942738i | \(-0.608241\pi\) | ||||
−0.333533 | + | 0.942738i | \(0.608241\pi\) | |||||||
\(752\) | 4.00288 | 0.145970 | ||||||||
\(753\) | 16.7545 | 0.610567 | ||||||||
\(754\) | −13.0800 | −0.476346 | ||||||||
\(755\) | 22.4051 | 0.815406 | ||||||||
\(756\) | −5.41832 | −0.197062 | ||||||||
\(757\) | 46.8864 | 1.70411 | 0.852057 | − | 0.523449i | \(-0.175355\pi\) | ||||
0.852057 | + | 0.523449i | \(0.175355\pi\) | |||||||
\(758\) | −22.3263 | −0.810928 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.33680 | −0.157312 | ||||||||
\(761\) | 50.8809 | 1.84443 | 0.922216 | − | 0.386675i | \(-0.126376\pi\) | ||||
0.922216 | + | 0.386675i | \(0.126376\pi\) | |||||||
\(762\) | −4.49010 | −0.162659 | ||||||||
\(763\) | 3.22024 | 0.116581 | ||||||||
\(764\) | 15.9464 | 0.576919 | ||||||||
\(765\) | −11.8853 | −0.429714 | ||||||||
\(766\) | 21.4500 | 0.775019 | ||||||||
\(767\) | 17.7644 | 0.641434 | ||||||||
\(768\) | 1.16996 | 0.0422174 | ||||||||
\(769\) | 26.5666 | 0.958017 | 0.479008 | − | 0.877810i | \(-0.340996\pi\) | ||||
0.479008 | + | 0.877810i | \(0.340996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.8039 | 1.21742 | ||||||||
\(772\) | −11.7470 | −0.422784 | ||||||||
\(773\) | −30.5526 | −1.09890 | −0.549450 | − | 0.835527i | \(-0.685163\pi\) | ||||
−0.549450 | + | 0.835527i | \(0.685163\pi\) | |||||||
\(774\) | −1.15139 | −0.0413859 | ||||||||
\(775\) | 3.65509 | 0.131295 | ||||||||
\(776\) | −11.3050 | −0.405827 | ||||||||
\(777\) | −3.64598 | −0.130799 | ||||||||
\(778\) | 37.9771 | 1.36155 | ||||||||
\(779\) | 8.91536 | 0.319426 | ||||||||
\(780\) | −1.67865 | −0.0601054 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 14.7652 | 0.528001 | ||||||||
\(783\) | −49.3951 | −1.76524 | ||||||||
\(784\) | 1.00000 | 0.0357143 | ||||||||
\(785\) | −14.9308 | −0.532903 | ||||||||
\(786\) | −22.7781 | −0.812468 | ||||||||
\(787\) | 27.0074 | 0.962710 | 0.481355 | − | 0.876526i | \(-0.340145\pi\) | ||||
0.481355 | + | 0.876526i | \(0.340145\pi\) | |||||||
\(788\) | 2.70088 | 0.0962148 | ||||||||
\(789\) | −25.6287 | −0.912405 | ||||||||
\(790\) | −3.98377 | −0.141736 | ||||||||
\(791\) | 16.8832 | 0.600297 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.50274 | −0.337452 | ||||||||
\(794\) | 24.9220 | 0.884447 | ||||||||
\(795\) | 5.70334 | 0.202277 | ||||||||
\(796\) | 14.5804 | 0.516789 | ||||||||
\(797\) | −37.5786 | −1.33110 | −0.665551 | − | 0.746352i | \(-0.731803\pi\) | ||||
−0.665551 | + | 0.746352i | \(0.731803\pi\) | |||||||
\(798\) | 5.07390 | 0.179614 | ||||||||
\(799\) | −29.1661 | −1.03182 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | −13.6087 | −0.480839 | ||||||||
\(802\) | 23.7936 | 0.840180 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −2.21560 | −0.0781380 | ||||||||
\(805\) | −2.02643 | −0.0714224 | ||||||||
\(806\) | −5.24430 | −0.184722 | ||||||||
\(807\) | −3.48478 | −0.122670 | ||||||||
\(808\) | 11.8936 | 0.418414 | ||||||||
\(809\) | 37.3166 | 1.31198 | 0.655991 | − | 0.754769i | \(-0.272251\pi\) | ||||
0.655991 | + | 0.754769i | \(0.272251\pi\) | |||||||
\(810\) | −1.44566 | −0.0507954 | ||||||||
\(811\) | −43.9822 | −1.54443 | −0.772213 | − | 0.635364i | \(-0.780850\pi\) | ||||
−0.772213 | + | 0.635364i | \(0.780850\pi\) | |||||||
\(812\) | 9.11632 | 0.319920 | ||||||||
\(813\) | −0.236584 | −0.00829735 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.69439 | −0.129409 | ||||||||
\(816\) | −8.52468 | −0.298423 | ||||||||
\(817\) | 3.06118 | 0.107097 | ||||||||
\(818\) | −17.4118 | −0.608789 | ||||||||
\(819\) | −2.34041 | −0.0817807 | ||||||||
\(820\) | 2.05574 | 0.0717897 | ||||||||
\(821\) | −30.6054 | −1.06814 | −0.534068 | − | 0.845442i | \(-0.679337\pi\) | ||||
−0.534068 | + | 0.845442i | \(0.679337\pi\) | |||||||
\(822\) | −18.8535 | −0.657592 | ||||||||
\(823\) | −20.5472 | −0.716230 | −0.358115 | − | 0.933677i | \(-0.616580\pi\) | ||||
−0.358115 | + | 0.933677i | \(0.616580\pi\) | |||||||
\(824\) | 2.57520 | 0.0897113 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −12.3811 | −0.430795 | ||||||||
\(827\) | 45.3404 | 1.57664 | 0.788319 | − | 0.615266i | \(-0.210952\pi\) | ||||
0.788319 | + | 0.615266i | \(0.210952\pi\) | |||||||
\(828\) | −3.30550 | −0.114874 | ||||||||
\(829\) | 41.2595 | 1.43300 | 0.716500 | − | 0.697587i | \(-0.245743\pi\) | ||||
0.716500 | + | 0.697587i | \(0.245743\pi\) | |||||||
\(830\) | 7.15061 | 0.248201 | ||||||||
\(831\) | 5.76975 | 0.200150 | ||||||||
\(832\) | 1.43479 | 0.0497424 | ||||||||
\(833\) | −7.28628 | −0.252455 | ||||||||
\(834\) | −19.7906 | −0.685293 | ||||||||
\(835\) | −9.33915 | −0.323195 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.8045 | −0.684542 | ||||||||
\(838\) | −6.77394 | −0.234002 | ||||||||
\(839\) | −27.6981 | −0.956243 | −0.478122 | − | 0.878294i | \(-0.658682\pi\) | ||||
−0.478122 | + | 0.878294i | \(0.658682\pi\) | |||||||
\(840\) | 1.16996 | 0.0403675 | ||||||||
\(841\) | 54.1073 | 1.86577 | ||||||||
\(842\) | −16.3820 | −0.564560 | ||||||||
\(843\) | 20.8818 | 0.719209 | ||||||||
\(844\) | −18.2347 | −0.627666 | ||||||||
\(845\) | 10.9414 | 0.376395 | ||||||||
\(846\) | 6.52944 | 0.224487 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −4.87480 | −0.167401 | ||||||||
\(849\) | 34.2473 | 1.17536 | ||||||||
\(850\) | 7.28628 | 0.249917 | ||||||||
\(851\) | −6.31502 | −0.216476 | ||||||||
\(852\) | 0.493351 | 0.0169019 | ||||||||
\(853\) | 41.7746 | 1.43033 | 0.715167 | − | 0.698954i | \(-0.246351\pi\) | ||||
0.715167 | + | 0.698954i | \(0.246351\pi\) | |||||||
\(854\) | 6.62309 | 0.226637 | ||||||||
\(855\) | −7.07414 | −0.241931 | ||||||||
\(856\) | −0.0210293 | −0.000718768 0 | ||||||||
\(857\) | −45.5421 | −1.55569 | −0.777845 | − | 0.628457i | \(-0.783687\pi\) | ||||
−0.777845 | + | 0.628457i | \(0.783687\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.44024 | −0.253858 | −0.126929 | − | 0.991912i | \(-0.540512\pi\) | ||||
−0.126929 | + | 0.991912i | \(0.540512\pi\) | |||||||
\(860\) | 0.705861 | 0.0240697 | ||||||||
\(861\) | −2.40514 | −0.0819671 | ||||||||
\(862\) | −35.7762 | −1.21854 | ||||||||
\(863\) | 9.39601 | 0.319844 | 0.159922 | − | 0.987130i | \(-0.448876\pi\) | ||||
0.159922 | + | 0.987130i | \(0.448876\pi\) | |||||||
\(864\) | 5.41832 | 0.184335 | ||||||||
\(865\) | 1.89895 | 0.0645664 | ||||||||
\(866\) | −12.5667 | −0.427035 | ||||||||
\(867\) | 42.2238 | 1.43400 | ||||||||
\(868\) | 3.65509 | 0.124062 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 10.6658 | 0.361603 | ||||||||
\(871\) | −2.71711 | −0.0920658 | ||||||||
\(872\) | −3.22024 | −0.109051 | ||||||||
\(873\) | −18.4406 | −0.624121 | ||||||||
\(874\) | 8.78825 | 0.297267 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | −8.63370 | −0.291706 | ||||||||
\(877\) | −9.96978 | −0.336655 | −0.168328 | − | 0.985731i | \(-0.553837\pi\) | ||||
−0.168328 | + | 0.985731i | \(0.553837\pi\) | |||||||
\(878\) | −34.6171 | −1.16827 | ||||||||
\(879\) | 34.9848 | 1.18001 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3.94025 | −0.132750 | −0.0663752 | − | 0.997795i | \(-0.521143\pi\) | ||||
−0.0663752 | + | 0.997795i | \(0.521143\pi\) | |||||||
\(882\) | 1.63119 | 0.0549250 | ||||||||
\(883\) | −41.4577 | −1.39516 | −0.697582 | − | 0.716505i | \(-0.745741\pi\) | ||||
−0.697582 | + | 0.716505i | \(0.745741\pi\) | |||||||
\(884\) | −10.4543 | −0.351616 | ||||||||
\(885\) | −14.4855 | −0.486924 | ||||||||
\(886\) | −18.9816 | −0.637698 | ||||||||
\(887\) | 31.2649 | 1.04977 | 0.524886 | − | 0.851172i | \(-0.324108\pi\) | ||||
0.524886 | + | 0.851172i | \(0.324108\pi\) | |||||||
\(888\) | 3.64598 | 0.122351 | ||||||||
\(889\) | 3.83782 | 0.128716 | ||||||||
\(890\) | 8.34280 | 0.279651 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.41856 | 0.0474969 | ||||||||
\(893\) | −17.3597 | −0.580920 | ||||||||
\(894\) | −5.99320 | −0.200443 | ||||||||
\(895\) | −6.00288 | −0.200654 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 3.40168 | 0.113579 | ||||||||
\(898\) | −13.7748 | −0.459670 | ||||||||
\(899\) | 33.3210 | 1.11132 | ||||||||
\(900\) | −1.63119 | −0.0543729 | ||||||||
\(901\) | 35.5192 | 1.18332 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −0.825831 | −0.0274819 | ||||||||
\(904\) | −16.8832 | −0.561526 | ||||||||
\(905\) | 6.73019 | 0.223719 | ||||||||
\(906\) | 26.2132 | 0.870874 | ||||||||
\(907\) | 11.8441 | 0.393277 | 0.196638 | − | 0.980476i | \(-0.436997\pi\) | ||||
0.196638 | + | 0.980476i | \(0.436997\pi\) | |||||||
\(908\) | −8.18601 | −0.271662 | ||||||||
\(909\) | 19.4006 | 0.643479 | ||||||||
\(910\) | 1.43479 | 0.0475629 | ||||||||
\(911\) | 52.8126 | 1.74976 | 0.874879 | − | 0.484341i | \(-0.160941\pi\) | ||||
0.874879 | + | 0.484341i | \(0.160941\pi\) | |||||||
\(912\) | −5.07390 | −0.168014 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 36.0763 | 1.19330 | ||||||||
\(915\) | 7.74876 | 0.256166 | ||||||||
\(916\) | −1.88578 | −0.0623080 | ||||||||
\(917\) | 19.4691 | 0.642926 | ||||||||
\(918\) | −39.4794 | −1.30301 | ||||||||
\(919\) | 26.4724 | 0.873243 | 0.436621 | − | 0.899645i | \(-0.356175\pi\) | ||||
0.436621 | + | 0.899645i | \(0.356175\pi\) | |||||||
\(920\) | 2.02643 | 0.0668096 | ||||||||
\(921\) | −15.9142 | −0.524390 | ||||||||
\(922\) | −23.2972 | −0.767252 | ||||||||
\(923\) | 0.605024 | 0.0199146 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.11632 | −0.102464 | ||||||||
\(926\) | 31.8729 | 1.04741 | ||||||||
\(927\) | 4.20063 | 0.137967 | ||||||||
\(928\) | −9.11632 | −0.299258 | ||||||||
\(929\) | 39.7722 | 1.30488 | 0.652442 | − | 0.757838i | \(-0.273744\pi\) | ||||
0.652442 | + | 0.757838i | \(0.273744\pi\) | |||||||
\(930\) | 4.27632 | 0.140226 | ||||||||
\(931\) | −4.33680 | −0.142133 | ||||||||
\(932\) | −22.9570 | −0.751982 | ||||||||
\(933\) | 34.5849 | 1.13226 | ||||||||
\(934\) | 11.5661 | 0.378455 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.34041 | 0.0764988 | ||||||||
\(937\) | 27.1898 | 0.888251 | 0.444126 | − | 0.895965i | \(-0.353514\pi\) | ||||
0.444126 | + | 0.895965i | \(0.353514\pi\) | |||||||
\(938\) | 1.89373 | 0.0618325 | ||||||||
\(939\) | 10.8048 | 0.352602 | ||||||||
\(940\) | −4.00288 | −0.130559 | ||||||||
\(941\) | 39.2513 | 1.27956 | 0.639778 | − | 0.768560i | \(-0.279026\pi\) | ||||
0.639778 | + | 0.768560i | \(0.279026\pi\) | |||||||
\(942\) | −17.4685 | −0.569153 | ||||||||
\(943\) | −4.16583 | −0.135658 | ||||||||
\(944\) | 12.3811 | 0.402972 | ||||||||
\(945\) | 5.41832 | 0.176258 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −42.7008 | −1.38759 | −0.693795 | − | 0.720173i | \(-0.744062\pi\) | ||||
−0.693795 | + | 0.720173i | \(0.744062\pi\) | |||||||
\(948\) | −4.66086 | −0.151378 | ||||||||
\(949\) | −10.5880 | −0.343701 | ||||||||
\(950\) | 4.33680 | 0.140705 | ||||||||
\(951\) | −6.14878 | −0.199388 | ||||||||
\(952\) | 7.28628 | 0.236150 | ||||||||
\(953\) | −22.7464 | −0.736828 | −0.368414 | − | 0.929662i | \(-0.620099\pi\) | ||||
−0.368414 | + | 0.929662i | \(0.620099\pi\) | |||||||
\(954\) | −7.95172 | −0.257446 | ||||||||
\(955\) | −15.9464 | −0.516012 | ||||||||
\(956\) | −0.315230 | −0.0101953 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −13.2561 | −0.428287 | ||||||||
\(959\) | 16.1146 | 0.520369 | ||||||||
\(960\) | −1.16996 | −0.0377604 | ||||||||
\(961\) | −17.6403 | −0.569042 | ||||||||
\(962\) | 4.47127 | 0.144159 | ||||||||
\(963\) | −0.0343028 | −0.00110539 | ||||||||
\(964\) | 5.61640 | 0.180892 | ||||||||
\(965\) | 11.7470 | 0.378150 | ||||||||
\(966\) | −2.37085 | −0.0762809 | ||||||||
\(967\) | −5.16517 | −0.166101 | −0.0830504 | − | 0.996545i | \(-0.526466\pi\) | ||||
−0.0830504 | + | 0.996545i | \(0.526466\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 36.9698 | 1.18764 | ||||||||
\(970\) | 11.3050 | 0.362983 | ||||||||
\(971\) | 28.1375 | 0.902977 | 0.451488 | − | 0.892277i | \(-0.350893\pi\) | ||||
0.451488 | + | 0.892277i | \(0.350893\pi\) | |||||||
\(972\) | 14.5636 | 0.467127 | ||||||||
\(973\) | 16.9156 | 0.542289 | ||||||||
\(974\) | −5.42232 | −0.173742 | ||||||||
\(975\) | 1.67865 | 0.0537599 | ||||||||
\(976\) | −6.62309 | −0.212000 | ||||||||
\(977\) | 24.0697 | 0.770058 | 0.385029 | − | 0.922905i | \(-0.374191\pi\) | ||||
0.385029 | + | 0.922905i | \(0.374191\pi\) | |||||||
\(978\) | −4.32230 | −0.138212 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −1.00000 | −0.0319438 | ||||||||
\(981\) | −5.25282 | −0.167710 | ||||||||
\(982\) | −36.0238 | −1.14957 | ||||||||
\(983\) | 20.4577 | 0.652500 | 0.326250 | − | 0.945284i | \(-0.394215\pi\) | ||||
0.326250 | + | 0.945284i | \(0.394215\pi\) | |||||||
\(984\) | 2.40514 | 0.0766732 | ||||||||
\(985\) | −2.70088 | −0.0860572 | ||||||||
\(986\) | 66.4241 | 2.11537 | ||||||||
\(987\) | 4.68321 | 0.149068 | ||||||||
\(988\) | −6.22241 | −0.197961 | ||||||||
\(989\) | −1.43038 | −0.0454835 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.8003 | −0.914870 | −0.457435 | − | 0.889243i | \(-0.651232\pi\) | ||||
−0.457435 | + | 0.889243i | \(0.651232\pi\) | |||||||
\(992\) | −3.65509 | −0.116049 | ||||||||
\(993\) | −27.3946 | −0.869342 | ||||||||
\(994\) | −0.421681 | −0.0133749 | ||||||||
\(995\) | −14.5804 | −0.462230 | ||||||||
\(996\) | 8.36595 | 0.265085 | ||||||||
\(997\) | −18.0825 | −0.572680 | −0.286340 | − | 0.958128i | \(-0.592439\pi\) | ||||
−0.286340 | + | 0.958128i | \(0.592439\pi\) | |||||||
\(998\) | 3.26974 | 0.103502 | ||||||||
\(999\) | 16.8852 | 0.534224 |
(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 | 8470.2.a.cx.1.4 | ✓ | 6 | |
11.10 | odd | 2 | 8470.2.a.dd.1.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8470.2.a.cx.1.4 | ✓ | 6 | 1.1 | even | 1 | trivial | |
8470.2.a.dd.1.4 | yes | 6 | 11.10 | odd | 2 |