Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3549,2,Mod(1,3549)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3549, 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("3549.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3549 = 3 \cdot 7 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3549.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: | \(28.3389076774\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.121819537.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 25x^{4} + 55x^{3} + 224x^{2} - 252x - 728 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-3.06987\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3549.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.24698 | −0.881748 | −0.440874 | − | 0.897569i | \(-0.645331\pi\) | ||||
−0.440874 | + | 0.897569i | \(0.645331\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −0.445042 | −0.222521 | ||||||||
\(5\) | −4.06987 | −1.82010 | −0.910050 | − | 0.414498i | \(-0.863957\pi\) | ||||
−0.910050 | + | 0.414498i | \(0.863957\pi\) | |||||||
\(6\) | 1.24698 | 0.509077 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 3.04892 | 1.07796 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 5.07504 | 1.60487 | ||||||||
\(11\) | 0.456669 | 0.137691 | 0.0688454 | − | 0.997627i | \(-0.478068\pi\) | ||||
0.0688454 | + | 0.997627i | \(0.478068\pi\) | |||||||
\(12\) | 0.445042 | 0.128473 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | −1.24698 | −0.333269 | ||||||||
\(15\) | 4.06987 | 1.05084 | ||||||||
\(16\) | −2.91185 | −0.727963 | ||||||||
\(17\) | −5.72977 | −1.38967 | −0.694837 | − | 0.719167i | \(-0.744524\pi\) | ||||
−0.694837 | + | 0.719167i | \(0.744524\pi\) | |||||||
\(18\) | −1.24698 | −0.293916 | ||||||||
\(19\) | −0.188738 | −0.0432995 | −0.0216498 | − | 0.999766i | \(-0.506892\pi\) | ||||
−0.0216498 | + | 0.999766i | \(0.506892\pi\) | |||||||
\(20\) | 1.81126 | 0.405010 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | −0.569457 | −0.121409 | ||||||||
\(23\) | −5.05824 | −1.05472 | −0.527358 | − | 0.849643i | \(-0.676817\pi\) | ||||
−0.527358 | + | 0.849643i | \(0.676817\pi\) | |||||||
\(24\) | −3.04892 | −0.622358 | ||||||||
\(25\) | 11.5638 | 2.31277 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.445042 | −0.0841050 | ||||||||
\(29\) | −6.16401 | −1.14463 | −0.572314 | − | 0.820035i | \(-0.693954\pi\) | ||||
−0.572314 | + | 0.820035i | \(0.693954\pi\) | |||||||
\(30\) | −5.07504 | −0.926572 | ||||||||
\(31\) | −1.19391 | −0.214433 | −0.107217 | − | 0.994236i | \(-0.534194\pi\) | ||||
−0.107217 | + | 0.994236i | \(0.534194\pi\) | |||||||
\(32\) | −2.46681 | −0.436075 | ||||||||
\(33\) | −0.456669 | −0.0794958 | ||||||||
\(34\) | 7.14491 | 1.22534 | ||||||||
\(35\) | −4.06987 | −0.687933 | ||||||||
\(36\) | −0.445042 | −0.0741736 | ||||||||
\(37\) | 10.7880 | 1.77354 | 0.886769 | − | 0.462212i | \(-0.152944\pi\) | ||||
0.886769 | + | 0.462212i | \(0.152944\pi\) | |||||||
\(38\) | 0.235353 | 0.0381793 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −12.4087 | −1.96199 | ||||||||
\(41\) | 2.45519 | 0.383436 | 0.191718 | − | 0.981450i | \(-0.438594\pi\) | ||||
0.191718 | + | 0.981450i | \(0.438594\pi\) | |||||||
\(42\) | 1.24698 | 0.192413 | ||||||||
\(43\) | 4.28991 | 0.654205 | 0.327102 | − | 0.944989i | \(-0.393928\pi\) | ||||
0.327102 | + | 0.944989i | \(0.393928\pi\) | |||||||
\(44\) | −0.203237 | −0.0306391 | ||||||||
\(45\) | −4.06987 | −0.606700 | ||||||||
\(46\) | 6.30752 | 0.929994 | ||||||||
\(47\) | 7.89748 | 1.15197 | 0.575983 | − | 0.817462i | \(-0.304620\pi\) | ||||
0.575983 | + | 0.817462i | \(0.304620\pi\) | |||||||
\(48\) | 2.91185 | 0.420290 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −14.4199 | −2.03928 | ||||||||
\(51\) | 5.72977 | 0.802329 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.67810 | 0.779947 | 0.389973 | − | 0.920826i | \(-0.372484\pi\) | ||||
0.389973 | + | 0.920826i | \(0.372484\pi\) | |||||||
\(54\) | 1.24698 | 0.169692 | ||||||||
\(55\) | −1.85858 | −0.250611 | ||||||||
\(56\) | 3.04892 | 0.407429 | ||||||||
\(57\) | 0.188738 | 0.0249990 | ||||||||
\(58\) | 7.68639 | 1.00927 | ||||||||
\(59\) | 13.4353 | 1.74912 | 0.874561 | − | 0.484915i | \(-0.161150\pi\) | ||||
0.874561 | + | 0.484915i | \(0.161150\pi\) | |||||||
\(60\) | −1.81126 | −0.233833 | ||||||||
\(61\) | −0.497739 | −0.0637289 | −0.0318644 | − | 0.999492i | \(-0.510144\pi\) | ||||
−0.0318644 | + | 0.999492i | \(0.510144\pi\) | |||||||
\(62\) | 1.48878 | 0.189076 | ||||||||
\(63\) | 1.00000 | 0.125988 | ||||||||
\(64\) | 8.89977 | 1.11247 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.569457 | 0.0700953 | ||||||||
\(67\) | −12.6957 | −1.55103 | −0.775514 | − | 0.631330i | \(-0.782509\pi\) | ||||
−0.775514 | + | 0.631330i | \(0.782509\pi\) | |||||||
\(68\) | 2.54999 | 0.309232 | ||||||||
\(69\) | 5.05824 | 0.608941 | ||||||||
\(70\) | 5.07504 | 0.606584 | ||||||||
\(71\) | 13.4669 | 1.59823 | 0.799115 | − | 0.601178i | \(-0.205302\pi\) | ||||
0.799115 | + | 0.601178i | \(0.205302\pi\) | |||||||
\(72\) | 3.04892 | 0.359318 | ||||||||
\(73\) | −7.94961 | −0.930431 | −0.465216 | − | 0.885197i | \(-0.654023\pi\) | ||||
−0.465216 | + | 0.885197i | \(0.654023\pi\) | |||||||
\(74\) | −13.4524 | −1.56381 | ||||||||
\(75\) | −11.5638 | −1.33528 | ||||||||
\(76\) | 0.0839964 | 0.00963505 | ||||||||
\(77\) | 0.456669 | 0.0520422 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.07089 | 0.458011 | 0.229006 | − | 0.973425i | \(-0.426453\pi\) | ||||
0.229006 | + | 0.973425i | \(0.426453\pi\) | |||||||
\(80\) | 11.8509 | 1.32497 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.06157 | −0.338093 | ||||||||
\(83\) | 11.0702 | 1.21512 | 0.607558 | − | 0.794275i | \(-0.292149\pi\) | ||||
0.607558 | + | 0.794275i | \(0.292149\pi\) | |||||||
\(84\) | 0.445042 | 0.0485580 | ||||||||
\(85\) | 23.3194 | 2.52935 | ||||||||
\(86\) | −5.34943 | −0.576843 | ||||||||
\(87\) | 6.16401 | 0.660851 | ||||||||
\(88\) | 1.39235 | 0.148425 | ||||||||
\(89\) | −15.7948 | −1.67425 | −0.837124 | − | 0.547013i | \(-0.815765\pi\) | ||||
−0.837124 | + | 0.547013i | \(0.815765\pi\) | |||||||
\(90\) | 5.07504 | 0.534956 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.25113 | 0.234696 | ||||||||
\(93\) | 1.19391 | 0.123803 | ||||||||
\(94\) | −9.84799 | −1.01574 | ||||||||
\(95\) | 0.768140 | 0.0788095 | ||||||||
\(96\) | 2.46681 | 0.251768 | ||||||||
\(97\) | 9.85870 | 1.00100 | 0.500500 | − | 0.865737i | \(-0.333150\pi\) | ||||
0.500500 | + | 0.865737i | \(0.333150\pi\) | |||||||
\(98\) | −1.24698 | −0.125964 | ||||||||
\(99\) | 0.456669 | 0.0458969 | ||||||||
\(100\) | −5.14639 | −0.514639 | ||||||||
\(101\) | −2.65786 | −0.264467 | −0.132233 | − | 0.991219i | \(-0.542215\pi\) | ||||
−0.132233 | + | 0.991219i | \(0.542215\pi\) | |||||||
\(102\) | −7.14491 | −0.707452 | ||||||||
\(103\) | −4.48234 | −0.441658 | −0.220829 | − | 0.975313i | \(-0.570876\pi\) | ||||
−0.220829 | + | 0.975313i | \(0.570876\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.06987 | 0.397178 | ||||||||
\(106\) | −7.08047 | −0.687716 | ||||||||
\(107\) | −14.4760 | −1.39945 | −0.699726 | − | 0.714411i | \(-0.746695\pi\) | ||||
−0.699726 | + | 0.714411i | \(0.746695\pi\) | |||||||
\(108\) | 0.445042 | 0.0428242 | ||||||||
\(109\) | 13.9209 | 1.33338 | 0.666692 | − | 0.745334i | \(-0.267710\pi\) | ||||
0.666692 | + | 0.745334i | \(0.267710\pi\) | |||||||
\(110\) | 2.31761 | 0.220976 | ||||||||
\(111\) | −10.7880 | −1.02395 | ||||||||
\(112\) | −2.91185 | −0.275144 | ||||||||
\(113\) | 19.8159 | 1.86412 | 0.932061 | − | 0.362300i | \(-0.118009\pi\) | ||||
0.932061 | + | 0.362300i | \(0.118009\pi\) | |||||||
\(114\) | −0.235353 | −0.0220428 | ||||||||
\(115\) | 20.5864 | 1.91969 | ||||||||
\(116\) | 2.74324 | 0.254704 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −16.7535 | −1.54228 | ||||||||
\(119\) | −5.72977 | −0.525247 | ||||||||
\(120\) | 12.4087 | 1.13275 | ||||||||
\(121\) | −10.7915 | −0.981041 | ||||||||
\(122\) | 0.620670 | 0.0561928 | ||||||||
\(123\) | −2.45519 | −0.221377 | ||||||||
\(124\) | 0.531341 | 0.0477158 | ||||||||
\(125\) | −26.7139 | −2.38936 | ||||||||
\(126\) | −1.24698 | −0.111090 | ||||||||
\(127\) | 9.40331 | 0.834409 | 0.417205 | − | 0.908813i | \(-0.363010\pi\) | ||||
0.417205 | + | 0.908813i | \(0.363010\pi\) | |||||||
\(128\) | −6.16421 | −0.544844 | ||||||||
\(129\) | −4.28991 | −0.377705 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.94710 | −0.869082 | −0.434541 | − | 0.900652i | \(-0.643089\pi\) | ||||
−0.434541 | + | 0.900652i | \(0.643089\pi\) | |||||||
\(132\) | 0.203237 | 0.0176895 | ||||||||
\(133\) | −0.188738 | −0.0163657 | ||||||||
\(134\) | 15.8313 | 1.36762 | ||||||||
\(135\) | 4.06987 | 0.350278 | ||||||||
\(136\) | −17.4696 | −1.49801 | ||||||||
\(137\) | −1.17436 | −0.100332 | −0.0501662 | − | 0.998741i | \(-0.515975\pi\) | ||||
−0.0501662 | + | 0.998741i | \(0.515975\pi\) | |||||||
\(138\) | −6.30752 | −0.536932 | ||||||||
\(139\) | 1.64097 | 0.139185 | 0.0695925 | − | 0.997576i | \(-0.477830\pi\) | ||||
0.0695925 | + | 0.997576i | \(0.477830\pi\) | |||||||
\(140\) | 1.81126 | 0.153080 | ||||||||
\(141\) | −7.89748 | −0.665088 | ||||||||
\(142\) | −16.7930 | −1.40924 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −2.91185 | −0.242654 | ||||||||
\(145\) | 25.0867 | 2.08334 | ||||||||
\(146\) | 9.91300 | 0.820405 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | −4.80112 | −0.394649 | ||||||||
\(149\) | −24.0833 | −1.97298 | −0.986489 | − | 0.163829i | \(-0.947616\pi\) | ||||
−0.986489 | + | 0.163829i | \(0.947616\pi\) | |||||||
\(150\) | 14.4199 | 1.17738 | ||||||||
\(151\) | 2.86662 | 0.233283 | 0.116641 | − | 0.993174i | \(-0.462787\pi\) | ||||
0.116641 | + | 0.993174i | \(0.462787\pi\) | |||||||
\(152\) | −0.575447 | −0.0466749 | ||||||||
\(153\) | −5.72977 | −0.463225 | ||||||||
\(154\) | −0.569457 | −0.0458881 | ||||||||
\(155\) | 4.85907 | 0.390290 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.16734 | −0.0931637 | −0.0465819 | − | 0.998914i | \(-0.514833\pi\) | ||||
−0.0465819 | + | 0.998914i | \(0.514833\pi\) | |||||||
\(158\) | −5.07632 | −0.403850 | ||||||||
\(159\) | −5.67810 | −0.450303 | ||||||||
\(160\) | 10.0396 | 0.793700 | ||||||||
\(161\) | −5.05824 | −0.398645 | ||||||||
\(162\) | −1.24698 | −0.0979720 | ||||||||
\(163\) | 11.3245 | 0.887003 | 0.443501 | − | 0.896274i | \(-0.353736\pi\) | ||||
0.443501 | + | 0.896274i | \(0.353736\pi\) | |||||||
\(164\) | −1.09266 | −0.0853224 | ||||||||
\(165\) | 1.85858 | 0.144690 | ||||||||
\(166\) | −13.8044 | −1.07143 | ||||||||
\(167\) | −18.2168 | −1.40966 | −0.704830 | − | 0.709376i | \(-0.748977\pi\) | ||||
−0.704830 | + | 0.709376i | \(0.748977\pi\) | |||||||
\(168\) | −3.04892 | −0.235229 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | −29.0788 | −2.23025 | ||||||||
\(171\) | −0.188738 | −0.0144332 | ||||||||
\(172\) | −1.90919 | −0.145574 | ||||||||
\(173\) | −20.0690 | −1.52581 | −0.762907 | − | 0.646508i | \(-0.776229\pi\) | ||||
−0.762907 | + | 0.646508i | \(0.776229\pi\) | |||||||
\(174\) | −7.68639 | −0.582704 | ||||||||
\(175\) | 11.5638 | 0.874143 | ||||||||
\(176\) | −1.32975 | −0.100234 | ||||||||
\(177\) | −13.4353 | −1.00986 | ||||||||
\(178\) | 19.6958 | 1.47627 | ||||||||
\(179\) | −9.37645 | −0.700829 | −0.350415 | − | 0.936595i | \(-0.613959\pi\) | ||||
−0.350415 | + | 0.936595i | \(0.613959\pi\) | |||||||
\(180\) | 1.81126 | 0.135003 | ||||||||
\(181\) | 2.71444 | 0.201763 | 0.100881 | − | 0.994898i | \(-0.467834\pi\) | ||||
0.100881 | + | 0.994898i | \(0.467834\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0.497739 | 0.0367939 | ||||||||
\(184\) | −15.4222 | −1.13694 | ||||||||
\(185\) | −43.9058 | −3.22802 | ||||||||
\(186\) | −1.48878 | −0.109163 | ||||||||
\(187\) | −2.61661 | −0.191345 | ||||||||
\(188\) | −3.51471 | −0.256336 | ||||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | −0.957855 | −0.0694901 | ||||||||
\(191\) | −3.19539 | −0.231210 | −0.115605 | − | 0.993295i | \(-0.536881\pi\) | ||||
−0.115605 | + | 0.993295i | \(0.536881\pi\) | |||||||
\(192\) | −8.89977 | −0.642286 | ||||||||
\(193\) | 5.98812 | 0.431034 | 0.215517 | − | 0.976500i | \(-0.430856\pi\) | ||||
0.215517 | + | 0.976500i | \(0.430856\pi\) | |||||||
\(194\) | −12.2936 | −0.882629 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.445042 | −0.0317887 | ||||||||
\(197\) | −3.38614 | −0.241253 | −0.120626 | − | 0.992698i | \(-0.538490\pi\) | ||||
−0.120626 | + | 0.992698i | \(0.538490\pi\) | |||||||
\(198\) | −0.569457 | −0.0404695 | ||||||||
\(199\) | −15.8519 | −1.12371 | −0.561855 | − | 0.827235i | \(-0.689912\pi\) | ||||
−0.561855 | + | 0.827235i | \(0.689912\pi\) | |||||||
\(200\) | 35.2572 | 2.49306 | ||||||||
\(201\) | 12.6957 | 0.895487 | ||||||||
\(202\) | 3.31430 | 0.233193 | ||||||||
\(203\) | −6.16401 | −0.432629 | ||||||||
\(204\) | −2.54999 | −0.178535 | ||||||||
\(205\) | −9.99228 | −0.697891 | ||||||||
\(206\) | 5.58939 | 0.389431 | ||||||||
\(207\) | −5.05824 | −0.351572 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0861909 | −0.00596195 | ||||||||
\(210\) | −5.07504 | −0.350211 | ||||||||
\(211\) | −15.1520 | −1.04311 | −0.521554 | − | 0.853218i | \(-0.674647\pi\) | ||||
−0.521554 | + | 0.853218i | \(0.674647\pi\) | |||||||
\(212\) | −2.52699 | −0.173555 | ||||||||
\(213\) | −13.4669 | −0.922739 | ||||||||
\(214\) | 18.0513 | 1.23396 | ||||||||
\(215\) | −17.4594 | −1.19072 | ||||||||
\(216\) | −3.04892 | −0.207453 | ||||||||
\(217\) | −1.19391 | −0.0810481 | ||||||||
\(218\) | −17.3591 | −1.17571 | ||||||||
\(219\) | 7.94961 | 0.537185 | ||||||||
\(220\) | 0.827147 | 0.0557662 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 13.4524 | 0.902868 | ||||||||
\(223\) | 3.29902 | 0.220918 | 0.110459 | − | 0.993881i | \(-0.464768\pi\) | ||||
0.110459 | + | 0.993881i | \(0.464768\pi\) | |||||||
\(224\) | −2.46681 | −0.164821 | ||||||||
\(225\) | 11.5638 | 0.770922 | ||||||||
\(226\) | −24.7100 | −1.64369 | ||||||||
\(227\) | 4.46977 | 0.296669 | 0.148335 | − | 0.988937i | \(-0.452609\pi\) | ||||
0.148335 | + | 0.988937i | \(0.452609\pi\) | |||||||
\(228\) | −0.0839964 | −0.00556280 | ||||||||
\(229\) | −1.06941 | −0.0706684 | −0.0353342 | − | 0.999376i | \(-0.511250\pi\) | ||||
−0.0353342 | + | 0.999376i | \(0.511250\pi\) | |||||||
\(230\) | −25.6708 | −1.69268 | ||||||||
\(231\) | −0.456669 | −0.0300466 | ||||||||
\(232\) | −18.7936 | −1.23386 | ||||||||
\(233\) | 0.549905 | 0.0360255 | 0.0180127 | − | 0.999838i | \(-0.494266\pi\) | ||||
0.0180127 | + | 0.999838i | \(0.494266\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −32.1417 | −2.09669 | ||||||||
\(236\) | −5.97925 | −0.389216 | ||||||||
\(237\) | −4.07089 | −0.264433 | ||||||||
\(238\) | 7.14491 | 0.463136 | ||||||||
\(239\) | 26.8711 | 1.73815 | 0.869074 | − | 0.494682i | \(-0.164716\pi\) | ||||
0.869074 | + | 0.494682i | \(0.164716\pi\) | |||||||
\(240\) | −11.8509 | −0.764970 | ||||||||
\(241\) | −5.20011 | −0.334969 | −0.167484 | − | 0.985875i | \(-0.553564\pi\) | ||||
−0.167484 | + | 0.985875i | \(0.553564\pi\) | |||||||
\(242\) | 13.4567 | 0.865031 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0.221514 | 0.0141810 | ||||||||
\(245\) | −4.06987 | −0.260014 | ||||||||
\(246\) | 3.06157 | 0.195198 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −3.64014 | −0.231149 | ||||||||
\(249\) | −11.0702 | −0.701548 | ||||||||
\(250\) | 33.3117 | 2.10682 | ||||||||
\(251\) | 4.29627 | 0.271178 | 0.135589 | − | 0.990765i | \(-0.456707\pi\) | ||||
0.135589 | + | 0.990765i | \(0.456707\pi\) | |||||||
\(252\) | −0.445042 | −0.0280350 | ||||||||
\(253\) | −2.30994 | −0.145225 | ||||||||
\(254\) | −11.7257 | −0.735738 | ||||||||
\(255\) | −23.3194 | −1.46032 | ||||||||
\(256\) | −10.1129 | −0.632056 | ||||||||
\(257\) | −6.70512 | −0.418254 | −0.209127 | − | 0.977888i | \(-0.567062\pi\) | ||||
−0.209127 | + | 0.977888i | \(0.567062\pi\) | |||||||
\(258\) | 5.34943 | 0.333041 | ||||||||
\(259\) | 10.7880 | 0.670335 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.16401 | −0.381543 | ||||||||
\(262\) | 12.4038 | 0.766311 | ||||||||
\(263\) | −2.52812 | −0.155891 | −0.0779453 | − | 0.996958i | \(-0.524836\pi\) | ||||
−0.0779453 | + | 0.996958i | \(0.524836\pi\) | |||||||
\(264\) | −1.39235 | −0.0856929 | ||||||||
\(265\) | −23.1091 | −1.41958 | ||||||||
\(266\) | 0.235353 | 0.0144304 | ||||||||
\(267\) | 15.7948 | 0.966628 | ||||||||
\(268\) | 5.65013 | 0.345136 | ||||||||
\(269\) | 9.69741 | 0.591261 | 0.295631 | − | 0.955302i | \(-0.404470\pi\) | ||||
0.295631 | + | 0.955302i | \(0.404470\pi\) | |||||||
\(270\) | −5.07504 | −0.308857 | ||||||||
\(271\) | 13.1875 | 0.801081 | 0.400541 | − | 0.916279i | \(-0.368822\pi\) | ||||
0.400541 | + | 0.916279i | \(0.368822\pi\) | |||||||
\(272\) | 16.6843 | 1.01163 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.46440 | 0.0884679 | ||||||||
\(275\) | 5.28084 | 0.318447 | ||||||||
\(276\) | −2.25113 | −0.135502 | ||||||||
\(277\) | 6.42805 | 0.386224 | 0.193112 | − | 0.981177i | \(-0.438142\pi\) | ||||
0.193112 | + | 0.981177i | \(0.438142\pi\) | |||||||
\(278\) | −2.04625 | −0.122726 | ||||||||
\(279\) | −1.19391 | −0.0714777 | ||||||||
\(280\) | −12.4087 | −0.741561 | ||||||||
\(281\) | 20.0959 | 1.19882 | 0.599411 | − | 0.800442i | \(-0.295402\pi\) | ||||
0.599411 | + | 0.800442i | \(0.295402\pi\) | |||||||
\(282\) | 9.84799 | 0.586439 | ||||||||
\(283\) | 21.0787 | 1.25300 | 0.626500 | − | 0.779421i | \(-0.284487\pi\) | ||||
0.626500 | + | 0.779421i | \(0.284487\pi\) | |||||||
\(284\) | −5.99335 | −0.355640 | ||||||||
\(285\) | −0.768140 | −0.0455007 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.45519 | 0.144925 | ||||||||
\(288\) | −2.46681 | −0.145358 | ||||||||
\(289\) | 15.8303 | 0.931194 | ||||||||
\(290\) | −31.2826 | −1.83698 | ||||||||
\(291\) | −9.85870 | −0.577927 | ||||||||
\(292\) | 3.53791 | 0.207040 | ||||||||
\(293\) | −28.0069 | −1.63618 | −0.818091 | − | 0.575089i | \(-0.804968\pi\) | ||||
−0.818091 | + | 0.575089i | \(0.804968\pi\) | |||||||
\(294\) | 1.24698 | 0.0727253 | ||||||||
\(295\) | −54.6798 | −3.18358 | ||||||||
\(296\) | 32.8918 | 1.91180 | ||||||||
\(297\) | −0.456669 | −0.0264986 | ||||||||
\(298\) | 30.0313 | 1.73967 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 5.14639 | 0.297127 | ||||||||
\(301\) | 4.28991 | 0.247266 | ||||||||
\(302\) | −3.57462 | −0.205696 | ||||||||
\(303\) | 2.65786 | 0.152690 | ||||||||
\(304\) | 0.549578 | 0.0315205 | ||||||||
\(305\) | 2.02573 | 0.115993 | ||||||||
\(306\) | 7.14491 | 0.408447 | ||||||||
\(307\) | −24.2095 | −1.38171 | −0.690855 | − | 0.722994i | \(-0.742766\pi\) | ||||
−0.690855 | + | 0.722994i | \(0.742766\pi\) | |||||||
\(308\) | −0.203237 | −0.0115805 | ||||||||
\(309\) | 4.48234 | 0.254991 | ||||||||
\(310\) | −6.05916 | −0.344137 | ||||||||
\(311\) | −8.75175 | −0.496266 | −0.248133 | − | 0.968726i | \(-0.579817\pi\) | ||||
−0.248133 | + | 0.968726i | \(0.579817\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.44801 | 0.194893 | 0.0974465 | − | 0.995241i | \(-0.468933\pi\) | ||||
0.0974465 | + | 0.995241i | \(0.468933\pi\) | |||||||
\(314\) | 1.45565 | 0.0821469 | ||||||||
\(315\) | −4.06987 | −0.229311 | ||||||||
\(316\) | −1.81172 | −0.101917 | ||||||||
\(317\) | −15.2632 | −0.857269 | −0.428635 | − | 0.903478i | \(-0.641005\pi\) | ||||
−0.428635 | + | 0.903478i | \(0.641005\pi\) | |||||||
\(318\) | 7.08047 | 0.397053 | ||||||||
\(319\) | −2.81491 | −0.157605 | ||||||||
\(320\) | −36.2209 | −2.02481 | ||||||||
\(321\) | 14.4760 | 0.807974 | ||||||||
\(322\) | 6.30752 | 0.351505 | ||||||||
\(323\) | 1.08143 | 0.0601722 | ||||||||
\(324\) | −0.445042 | −0.0247245 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −14.1214 | −0.782113 | ||||||||
\(327\) | −13.9209 | −0.769829 | ||||||||
\(328\) | 7.48566 | 0.413326 | ||||||||
\(329\) | 7.89748 | 0.435402 | ||||||||
\(330\) | −2.31761 | −0.127580 | ||||||||
\(331\) | 34.2089 | 1.88029 | 0.940145 | − | 0.340776i | \(-0.110690\pi\) | ||||
0.940145 | + | 0.340776i | \(0.110690\pi\) | |||||||
\(332\) | −4.92672 | −0.270389 | ||||||||
\(333\) | 10.7880 | 0.591180 | ||||||||
\(334\) | 22.7160 | 1.24296 | ||||||||
\(335\) | 51.6699 | 2.82303 | ||||||||
\(336\) | 2.91185 | 0.158855 | ||||||||
\(337\) | 30.2804 | 1.64948 | 0.824739 | − | 0.565513i | \(-0.191322\pi\) | ||||
0.824739 | + | 0.565513i | \(0.191322\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −19.8159 | −1.07625 | ||||||||
\(340\) | −10.3781 | −0.562833 | ||||||||
\(341\) | −0.545223 | −0.0295255 | ||||||||
\(342\) | 0.235353 | 0.0127264 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 13.0796 | 0.705203 | ||||||||
\(345\) | −20.5864 | −1.10833 | ||||||||
\(346\) | 25.0256 | 1.34538 | ||||||||
\(347\) | 18.6458 | 1.00096 | 0.500479 | − | 0.865749i | \(-0.333157\pi\) | ||||
0.500479 | + | 0.865749i | \(0.333157\pi\) | |||||||
\(348\) | −2.74324 | −0.147053 | ||||||||
\(349\) | −21.5364 | −1.15282 | −0.576410 | − | 0.817161i | \(-0.695547\pi\) | ||||
−0.576410 | + | 0.817161i | \(0.695547\pi\) | |||||||
\(350\) | −14.4199 | −0.770774 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.12652 | −0.0600435 | ||||||||
\(353\) | 13.8056 | 0.734799 | 0.367400 | − | 0.930063i | \(-0.380248\pi\) | ||||
0.367400 | + | 0.930063i | \(0.380248\pi\) | |||||||
\(354\) | 16.7535 | 0.890438 | ||||||||
\(355\) | −54.8086 | −2.90894 | ||||||||
\(356\) | 7.02936 | 0.372555 | ||||||||
\(357\) | 5.72977 | 0.303252 | ||||||||
\(358\) | 11.6922 | 0.617954 | ||||||||
\(359\) | 16.2256 | 0.856356 | 0.428178 | − | 0.903694i | \(-0.359156\pi\) | ||||
0.428178 | + | 0.903694i | \(0.359156\pi\) | |||||||
\(360\) | −12.4087 | −0.653995 | ||||||||
\(361\) | −18.9644 | −0.998125 | ||||||||
\(362\) | −3.38486 | −0.177904 | ||||||||
\(363\) | 10.7915 | 0.566404 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.3538 | 1.69348 | ||||||||
\(366\) | −0.620670 | −0.0324429 | ||||||||
\(367\) | 17.5526 | 0.916237 | 0.458118 | − | 0.888891i | \(-0.348524\pi\) | ||||
0.458118 | + | 0.888891i | \(0.348524\pi\) | |||||||
\(368\) | 14.7289 | 0.767795 | ||||||||
\(369\) | 2.45519 | 0.127812 | ||||||||
\(370\) | 54.7496 | 2.84630 | ||||||||
\(371\) | 5.67810 | 0.294792 | ||||||||
\(372\) | −0.531341 | −0.0275488 | ||||||||
\(373\) | −5.20801 | −0.269661 | −0.134830 | − | 0.990869i | \(-0.543049\pi\) | ||||
−0.134830 | + | 0.990869i | \(0.543049\pi\) | |||||||
\(374\) | 3.26286 | 0.168718 | ||||||||
\(375\) | 26.7139 | 1.37950 | ||||||||
\(376\) | 24.0788 | 1.24177 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 1.24698 | 0.0641377 | ||||||||
\(379\) | 8.81996 | 0.453051 | 0.226525 | − | 0.974005i | \(-0.427263\pi\) | ||||
0.226525 | + | 0.974005i | \(0.427263\pi\) | |||||||
\(380\) | −0.341854 | −0.0175368 | ||||||||
\(381\) | −9.40331 | −0.481746 | ||||||||
\(382\) | 3.98459 | 0.203869 | ||||||||
\(383\) | −4.36919 | −0.223255 | −0.111628 | − | 0.993750i | \(-0.535606\pi\) | ||||
−0.111628 | + | 0.993750i | \(0.535606\pi\) | |||||||
\(384\) | 6.16421 | 0.314566 | ||||||||
\(385\) | −1.85858 | −0.0947221 | ||||||||
\(386\) | −7.46706 | −0.380064 | ||||||||
\(387\) | 4.28991 | 0.218068 | ||||||||
\(388\) | −4.38754 | −0.222743 | ||||||||
\(389\) | −27.6044 | −1.39960 | −0.699798 | − | 0.714341i | \(-0.746727\pi\) | ||||
−0.699798 | + | 0.714341i | \(0.746727\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.9826 | 1.46571 | ||||||||
\(392\) | 3.04892 | 0.153994 | ||||||||
\(393\) | 9.94710 | 0.501765 | ||||||||
\(394\) | 4.22245 | 0.212724 | ||||||||
\(395\) | −16.5680 | −0.833626 | ||||||||
\(396\) | −0.203237 | −0.0102130 | ||||||||
\(397\) | −25.8215 | −1.29595 | −0.647973 | − | 0.761664i | \(-0.724383\pi\) | ||||
−0.647973 | + | 0.761664i | \(0.724383\pi\) | |||||||
\(398\) | 19.7670 | 0.990830 | ||||||||
\(399\) | 0.188738 | 0.00944873 | ||||||||
\(400\) | −33.6722 | −1.68361 | ||||||||
\(401\) | 24.5840 | 1.22767 | 0.613834 | − | 0.789435i | \(-0.289626\pi\) | ||||
0.613834 | + | 0.789435i | \(0.289626\pi\) | |||||||
\(402\) | −15.8313 | −0.789594 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.18286 | 0.0588494 | ||||||||
\(405\) | −4.06987 | −0.202233 | ||||||||
\(406\) | 7.68639 | 0.381469 | ||||||||
\(407\) | 4.92655 | 0.244200 | ||||||||
\(408\) | 17.4696 | 0.864874 | ||||||||
\(409\) | −34.7781 | −1.71966 | −0.859832 | − | 0.510577i | \(-0.829432\pi\) | ||||
−0.859832 | + | 0.510577i | \(0.829432\pi\) | |||||||
\(410\) | 12.4602 | 0.615364 | ||||||||
\(411\) | 1.17436 | 0.0579269 | ||||||||
\(412\) | 1.99483 | 0.0982782 | ||||||||
\(413\) | 13.4353 | 0.661106 | ||||||||
\(414\) | 6.30752 | 0.309998 | ||||||||
\(415\) | −45.0544 | −2.21163 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.64097 | −0.0803585 | ||||||||
\(418\) | 0.107478 | 0.00525693 | ||||||||
\(419\) | −23.8666 | −1.16596 | −0.582981 | − | 0.812486i | \(-0.698114\pi\) | ||||
−0.582981 | + | 0.812486i | \(0.698114\pi\) | |||||||
\(420\) | −1.81126 | −0.0883805 | ||||||||
\(421\) | −23.7194 | −1.15601 | −0.578005 | − | 0.816033i | \(-0.696169\pi\) | ||||
−0.578005 | + | 0.816033i | \(0.696169\pi\) | |||||||
\(422\) | 18.8943 | 0.919758 | ||||||||
\(423\) | 7.89748 | 0.383988 | ||||||||
\(424\) | 17.3121 | 0.840748 | ||||||||
\(425\) | −66.2581 | −3.21399 | ||||||||
\(426\) | 16.7930 | 0.813623 | ||||||||
\(427\) | −0.497739 | −0.0240873 | ||||||||
\(428\) | 6.44245 | 0.311407 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 21.7715 | 1.04991 | ||||||||
\(431\) | −31.8528 | −1.53430 | −0.767148 | − | 0.641470i | \(-0.778325\pi\) | ||||
−0.767148 | + | 0.641470i | \(0.778325\pi\) | |||||||
\(432\) | 2.91185 | 0.140097 | ||||||||
\(433\) | −38.8011 | −1.86466 | −0.932331 | − | 0.361605i | \(-0.882229\pi\) | ||||
−0.932331 | + | 0.361605i | \(0.882229\pi\) | |||||||
\(434\) | 1.48878 | 0.0714640 | ||||||||
\(435\) | −25.0867 | −1.20282 | ||||||||
\(436\) | −6.19540 | −0.296706 | ||||||||
\(437\) | 0.954684 | 0.0456687 | ||||||||
\(438\) | −9.91300 | −0.473661 | ||||||||
\(439\) | 34.1627 | 1.63049 | 0.815247 | − | 0.579113i | \(-0.196601\pi\) | ||||
0.815247 | + | 0.579113i | \(0.196601\pi\) | |||||||
\(440\) | −5.66666 | −0.270147 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −8.98444 | −0.426864 | −0.213432 | − | 0.976958i | \(-0.568464\pi\) | ||||
−0.213432 | + | 0.976958i | \(0.568464\pi\) | |||||||
\(444\) | 4.80112 | 0.227851 | ||||||||
\(445\) | 64.2829 | 3.04730 | ||||||||
\(446\) | −4.11381 | −0.194794 | ||||||||
\(447\) | 24.0833 | 1.13910 | ||||||||
\(448\) | 8.89977 | 0.420475 | ||||||||
\(449\) | −21.1704 | −0.999092 | −0.499546 | − | 0.866287i | \(-0.666500\pi\) | ||||
−0.499546 | + | 0.866287i | \(0.666500\pi\) | |||||||
\(450\) | −14.4199 | −0.679759 | ||||||||
\(451\) | 1.12121 | 0.0527955 | ||||||||
\(452\) | −8.81890 | −0.414806 | ||||||||
\(453\) | −2.86662 | −0.134686 | ||||||||
\(454\) | −5.57371 | −0.261587 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.575447 | 0.0269478 | ||||||||
\(457\) | −15.6357 | −0.731409 | −0.365704 | − | 0.930731i | \(-0.619172\pi\) | ||||
−0.365704 | + | 0.930731i | \(0.619172\pi\) | |||||||
\(458\) | 1.33353 | 0.0623117 | ||||||||
\(459\) | 5.72977 | 0.267443 | ||||||||
\(460\) | −9.16180 | −0.427171 | ||||||||
\(461\) | −7.86852 | −0.366474 | −0.183237 | − | 0.983069i | \(-0.558658\pi\) | ||||
−0.183237 | + | 0.983069i | \(0.558658\pi\) | |||||||
\(462\) | 0.569457 | 0.0264935 | ||||||||
\(463\) | −4.47009 | −0.207743 | −0.103871 | − | 0.994591i | \(-0.533123\pi\) | ||||
−0.103871 | + | 0.994591i | \(0.533123\pi\) | |||||||
\(464\) | 17.9487 | 0.833247 | ||||||||
\(465\) | −4.85907 | −0.225334 | ||||||||
\(466\) | −0.685720 | −0.0317654 | ||||||||
\(467\) | −23.3252 | −1.07936 | −0.539680 | − | 0.841870i | \(-0.681455\pi\) | ||||
−0.539680 | + | 0.841870i | \(0.681455\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.6957 | −0.586234 | ||||||||
\(470\) | 40.0800 | 1.84875 | ||||||||
\(471\) | 1.16734 | 0.0537881 | ||||||||
\(472\) | 40.9630 | 1.88548 | ||||||||
\(473\) | 1.95907 | 0.0900780 | ||||||||
\(474\) | 5.07632 | 0.233163 | ||||||||
\(475\) | −2.18254 | −0.100142 | ||||||||
\(476\) | 2.54999 | 0.116879 | ||||||||
\(477\) | 5.67810 | 0.259982 | ||||||||
\(478\) | −33.5077 | −1.53261 | ||||||||
\(479\) | 19.0742 | 0.871522 | 0.435761 | − | 0.900062i | \(-0.356479\pi\) | ||||
0.435761 | + | 0.900062i | \(0.356479\pi\) | |||||||
\(480\) | −10.0396 | −0.458243 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6.48444 | 0.295358 | ||||||||
\(483\) | 5.05824 | 0.230158 | ||||||||
\(484\) | 4.80265 | 0.218302 | ||||||||
\(485\) | −40.1236 | −1.82192 | ||||||||
\(486\) | 1.24698 | 0.0565641 | ||||||||
\(487\) | −32.1344 | −1.45615 | −0.728075 | − | 0.685497i | \(-0.759585\pi\) | ||||
−0.728075 | + | 0.685497i | \(0.759585\pi\) | |||||||
\(488\) | −1.51756 | −0.0686969 | ||||||||
\(489\) | −11.3245 | −0.512111 | ||||||||
\(490\) | 5.07504 | 0.229267 | ||||||||
\(491\) | −13.4490 | −0.606944 | −0.303472 | − | 0.952840i | \(-0.598146\pi\) | ||||
−0.303472 | + | 0.952840i | \(0.598146\pi\) | |||||||
\(492\) | 1.09266 | 0.0492609 | ||||||||
\(493\) | 35.3184 | 1.59066 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −1.85858 | −0.0835370 | ||||||||
\(496\) | 3.47650 | 0.156099 | ||||||||
\(497\) | 13.4669 | 0.604075 | ||||||||
\(498\) | 13.8044 | 0.618588 | ||||||||
\(499\) | −18.4105 | −0.824165 | −0.412083 | − | 0.911146i | \(-0.635199\pi\) | ||||
−0.412083 | + | 0.911146i | \(0.635199\pi\) | |||||||
\(500\) | 11.8888 | 0.531684 | ||||||||
\(501\) | 18.2168 | 0.813868 | ||||||||
\(502\) | −5.35736 | −0.239111 | ||||||||
\(503\) | 28.0595 | 1.25111 | 0.625555 | − | 0.780180i | \(-0.284872\pi\) | ||||
0.625555 | + | 0.780180i | \(0.284872\pi\) | |||||||
\(504\) | 3.04892 | 0.135810 | ||||||||
\(505\) | 10.8171 | 0.481356 | ||||||||
\(506\) | 2.88045 | 0.128052 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.18487 | −0.185673 | ||||||||
\(509\) | −32.0230 | −1.41940 | −0.709698 | − | 0.704506i | \(-0.751169\pi\) | ||||
−0.709698 | + | 0.704506i | \(0.751169\pi\) | |||||||
\(510\) | 29.0788 | 1.28763 | ||||||||
\(511\) | −7.94961 | −0.351670 | ||||||||
\(512\) | 24.9390 | 1.10216 | ||||||||
\(513\) | 0.188738 | 0.00833300 | ||||||||
\(514\) | 8.36115 | 0.368795 | ||||||||
\(515\) | 18.2425 | 0.803862 | ||||||||
\(516\) | 1.90919 | 0.0840473 | ||||||||
\(517\) | 3.60653 | 0.158615 | ||||||||
\(518\) | −13.4524 | −0.591066 | ||||||||
\(519\) | 20.0690 | 0.880930 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −3.26582 | −0.143078 | −0.0715392 | − | 0.997438i | \(-0.522791\pi\) | ||||
−0.0715392 | + | 0.997438i | \(0.522791\pi\) | |||||||
\(522\) | 7.68639 | 0.336424 | ||||||||
\(523\) | −39.8760 | −1.74366 | −0.871828 | − | 0.489813i | \(-0.837065\pi\) | ||||
−0.871828 | + | 0.489813i | \(0.837065\pi\) | |||||||
\(524\) | 4.42688 | 0.193389 | ||||||||
\(525\) | −11.5638 | −0.504687 | ||||||||
\(526\) | 3.15252 | 0.137456 | ||||||||
\(527\) | 6.84085 | 0.297992 | ||||||||
\(528\) | 1.32975 | 0.0578701 | ||||||||
\(529\) | 2.58581 | 0.112426 | ||||||||
\(530\) | 28.8166 | 1.25171 | ||||||||
\(531\) | 13.4353 | 0.583041 | ||||||||
\(532\) | 0.0839964 | 0.00364171 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −19.6958 | −0.852322 | ||||||||
\(535\) | 58.9156 | 2.54714 | ||||||||
\(536\) | −38.7082 | −1.67194 | ||||||||
\(537\) | 9.37645 | 0.404624 | ||||||||
\(538\) | −12.0925 | −0.521343 | ||||||||
\(539\) | 0.456669 | 0.0196701 | ||||||||
\(540\) | −1.81126 | −0.0779443 | ||||||||
\(541\) | 15.7774 | 0.678324 | 0.339162 | − | 0.940728i | \(-0.389857\pi\) | ||||
0.339162 | + | 0.940728i | \(0.389857\pi\) | |||||||
\(542\) | −16.4445 | −0.706352 | ||||||||
\(543\) | −2.71444 | −0.116488 | ||||||||
\(544\) | 14.1343 | 0.606002 | ||||||||
\(545\) | −56.6563 | −2.42689 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.17231 | −0.0928814 | −0.0464407 | − | 0.998921i | \(-0.514788\pi\) | ||||
−0.0464407 | + | 0.998921i | \(0.514788\pi\) | |||||||
\(548\) | 0.522640 | 0.0223261 | ||||||||
\(549\) | −0.497739 | −0.0212430 | ||||||||
\(550\) | −6.58510 | −0.280790 | ||||||||
\(551\) | 1.16338 | 0.0495618 | ||||||||
\(552\) | 15.4222 | 0.656411 | ||||||||
\(553\) | 4.07089 | 0.173112 | ||||||||
\(554\) | −8.01565 | −0.340552 | ||||||||
\(555\) | 43.9058 | 1.86370 | ||||||||
\(556\) | −0.730299 | −0.0309716 | ||||||||
\(557\) | −15.2813 | −0.647490 | −0.323745 | − | 0.946144i | \(-0.604942\pi\) | ||||
−0.323745 | + | 0.946144i | \(0.604942\pi\) | |||||||
\(558\) | 1.48878 | 0.0630253 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 11.8509 | 0.500790 | ||||||||
\(561\) | 2.61661 | 0.110473 | ||||||||
\(562\) | −25.0592 | −1.05706 | ||||||||
\(563\) | 29.2981 | 1.23477 | 0.617384 | − | 0.786662i | \(-0.288193\pi\) | ||||
0.617384 | + | 0.786662i | \(0.288193\pi\) | |||||||
\(564\) | 3.51471 | 0.147996 | ||||||||
\(565\) | −80.6481 | −3.39289 | ||||||||
\(566\) | −26.2848 | −1.10483 | ||||||||
\(567\) | 1.00000 | 0.0419961 | ||||||||
\(568\) | 41.0596 | 1.72282 | ||||||||
\(569\) | 17.8243 | 0.747233 | 0.373616 | − | 0.927583i | \(-0.378118\pi\) | ||||
0.373616 | + | 0.927583i | \(0.378118\pi\) | |||||||
\(570\) | 0.957855 | 0.0401201 | ||||||||
\(571\) | −3.46247 | −0.144900 | −0.0724499 | − | 0.997372i | \(-0.523082\pi\) | ||||
−0.0724499 | + | 0.997372i | \(0.523082\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 3.19539 | 0.133489 | ||||||||
\(574\) | −3.06157 | −0.127787 | ||||||||
\(575\) | −58.4926 | −2.43931 | ||||||||
\(576\) | 8.89977 | 0.370824 | ||||||||
\(577\) | −15.2026 | −0.632892 | −0.316446 | − | 0.948610i | \(-0.602490\pi\) | ||||
−0.316446 | + | 0.948610i | \(0.602490\pi\) | |||||||
\(578\) | −19.7401 | −0.821079 | ||||||||
\(579\) | −5.98812 | −0.248858 | ||||||||
\(580\) | −11.1646 | −0.463586 | ||||||||
\(581\) | 11.0702 | 0.459271 | ||||||||
\(582\) | 12.2936 | 0.509586 | ||||||||
\(583\) | 2.59301 | 0.107392 | ||||||||
\(584\) | −24.2377 | −1.00296 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 34.9241 | 1.44270 | ||||||||
\(587\) | −26.0354 | −1.07459 | −0.537297 | − | 0.843393i | \(-0.680555\pi\) | ||||
−0.537297 | + | 0.843393i | \(0.680555\pi\) | |||||||
\(588\) | 0.445042 | 0.0183532 | ||||||||
\(589\) | 0.225337 | 0.00928485 | ||||||||
\(590\) | 68.1845 | 2.80711 | ||||||||
\(591\) | 3.38614 | 0.139287 | ||||||||
\(592\) | −31.4131 | −1.29107 | ||||||||
\(593\) | 18.5431 | 0.761473 | 0.380737 | − | 0.924684i | \(-0.375670\pi\) | ||||
0.380737 | + | 0.924684i | \(0.375670\pi\) | |||||||
\(594\) | 0.569457 | 0.0233651 | ||||||||
\(595\) | 23.3194 | 0.956003 | ||||||||
\(596\) | 10.7181 | 0.439029 | ||||||||
\(597\) | 15.8519 | 0.648775 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −17.9744 | −0.734416 | −0.367208 | − | 0.930139i | \(-0.619686\pi\) | ||||
−0.367208 | + | 0.930139i | \(0.619686\pi\) | |||||||
\(600\) | −35.2572 | −1.43937 | ||||||||
\(601\) | −2.38652 | −0.0973480 | −0.0486740 | − | 0.998815i | \(-0.515500\pi\) | ||||
−0.0486740 | + | 0.998815i | \(0.515500\pi\) | |||||||
\(602\) | −5.34943 | −0.218026 | ||||||||
\(603\) | −12.6957 | −0.517010 | ||||||||
\(604\) | −1.27577 | −0.0519103 | ||||||||
\(605\) | 43.9198 | 1.78559 | ||||||||
\(606\) | −3.31430 | −0.134634 | ||||||||
\(607\) | 36.9416 | 1.49941 | 0.749706 | − | 0.661771i | \(-0.230195\pi\) | ||||
0.749706 | + | 0.661771i | \(0.230195\pi\) | |||||||
\(608\) | 0.465582 | 0.0188818 | ||||||||
\(609\) | 6.16401 | 0.249778 | ||||||||
\(610\) | −2.52604 | −0.102277 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.54999 | 0.103077 | ||||||||
\(613\) | 10.2820 | 0.415286 | 0.207643 | − | 0.978205i | \(-0.433421\pi\) | ||||
0.207643 | + | 0.978205i | \(0.433421\pi\) | |||||||
\(614\) | 30.1888 | 1.21832 | ||||||||
\(615\) | 9.99228 | 0.402928 | ||||||||
\(616\) | 1.39235 | 0.0560992 | ||||||||
\(617\) | −21.9165 | −0.882325 | −0.441162 | − | 0.897427i | \(-0.645434\pi\) | ||||
−0.441162 | + | 0.897427i | \(0.645434\pi\) | |||||||
\(618\) | −5.58939 | −0.224838 | ||||||||
\(619\) | −32.5945 | −1.31008 | −0.655041 | − | 0.755593i | \(-0.727349\pi\) | ||||
−0.655041 | + | 0.755593i | \(0.727349\pi\) | |||||||
\(620\) | −2.16249 | −0.0868476 | ||||||||
\(621\) | 5.05824 | 0.202980 | ||||||||
\(622\) | 10.9133 | 0.437582 | ||||||||
\(623\) | −15.7948 | −0.632807 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 50.9030 | 2.03612 | ||||||||
\(626\) | −4.29960 | −0.171847 | ||||||||
\(627\) | 0.0861909 | 0.00344213 | ||||||||
\(628\) | 0.519514 | 0.0207309 | ||||||||
\(629\) | −61.8129 | −2.46464 | ||||||||
\(630\) | 5.07504 | 0.202195 | ||||||||
\(631\) | 16.1040 | 0.641091 | 0.320546 | − | 0.947233i | \(-0.396134\pi\) | ||||
0.320546 | + | 0.947233i | \(0.396134\pi\) | |||||||
\(632\) | 12.4118 | 0.493716 | ||||||||
\(633\) | 15.1520 | 0.602239 | ||||||||
\(634\) | 19.0330 | 0.755895 | ||||||||
\(635\) | −38.2702 | −1.51871 | ||||||||
\(636\) | 2.52699 | 0.100202 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.51014 | 0.138968 | ||||||||
\(639\) | 13.4669 | 0.532744 | ||||||||
\(640\) | 25.0875 | 0.991671 | ||||||||
\(641\) | −28.6147 | −1.13021 | −0.565106 | − | 0.825019i | \(-0.691165\pi\) | ||||
−0.565106 | + | 0.825019i | \(0.691165\pi\) | |||||||
\(642\) | −18.0513 | −0.712429 | ||||||||
\(643\) | −13.3312 | −0.525731 | −0.262865 | − | 0.964832i | \(-0.584668\pi\) | ||||
−0.262865 | + | 0.964832i | \(0.584668\pi\) | |||||||
\(644\) | 2.25113 | 0.0887069 | ||||||||
\(645\) | 17.4594 | 0.687461 | ||||||||
\(646\) | −1.34852 | −0.0530567 | ||||||||
\(647\) | 2.90219 | 0.114097 | 0.0570484 | − | 0.998371i | \(-0.481831\pi\) | ||||
0.0570484 | + | 0.998371i | \(0.481831\pi\) | |||||||
\(648\) | 3.04892 | 0.119773 | ||||||||
\(649\) | 6.13546 | 0.240838 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.19391 | 0.0467931 | ||||||||
\(652\) | −5.03987 | −0.197377 | ||||||||
\(653\) | 45.4716 | 1.77944 | 0.889721 | − | 0.456504i | \(-0.150899\pi\) | ||||
0.889721 | + | 0.456504i | \(0.150899\pi\) | |||||||
\(654\) | 17.3591 | 0.678795 | ||||||||
\(655\) | 40.4834 | 1.58182 | ||||||||
\(656\) | −7.14914 | −0.279127 | ||||||||
\(657\) | −7.94961 | −0.310144 | ||||||||
\(658\) | −9.84799 | −0.383915 | ||||||||
\(659\) | −21.4211 | −0.834447 | −0.417224 | − | 0.908804i | \(-0.636997\pi\) | ||||
−0.417224 | + | 0.908804i | \(0.636997\pi\) | |||||||
\(660\) | −0.827147 | −0.0321966 | ||||||||
\(661\) | −8.32956 | −0.323982 | −0.161991 | − | 0.986792i | \(-0.551792\pi\) | ||||
−0.161991 | + | 0.986792i | \(0.551792\pi\) | |||||||
\(662\) | −42.6578 | −1.65794 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 33.7522 | 1.30984 | ||||||||
\(665\) | 0.768140 | 0.0297872 | ||||||||
\(666\) | −13.4524 | −0.521271 | ||||||||
\(667\) | 31.1790 | 1.20726 | ||||||||
\(668\) | 8.10725 | 0.313679 | ||||||||
\(669\) | −3.29902 | −0.127547 | ||||||||
\(670\) | −64.4313 | −2.48920 | ||||||||
\(671\) | −0.227302 | −0.00877488 | ||||||||
\(672\) | 2.46681 | 0.0951593 | ||||||||
\(673\) | −10.8310 | −0.417505 | −0.208752 | − | 0.977969i | \(-0.566940\pi\) | ||||
−0.208752 | + | 0.977969i | \(0.566940\pi\) | |||||||
\(674\) | −37.7591 | −1.45442 | ||||||||
\(675\) | −11.5638 | −0.445092 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.9707 | 0.805969 | 0.402984 | − | 0.915207i | \(-0.367973\pi\) | ||||
0.402984 | + | 0.915207i | \(0.367973\pi\) | |||||||
\(678\) | 24.7100 | 0.948983 | ||||||||
\(679\) | 9.85870 | 0.378342 | ||||||||
\(680\) | 71.0990 | 2.72652 | ||||||||
\(681\) | −4.46977 | −0.171282 | ||||||||
\(682\) | 0.679881 | 0.0260340 | ||||||||
\(683\) | −16.5639 | −0.633801 | −0.316901 | − | 0.948459i | \(-0.602642\pi\) | ||||
−0.316901 | + | 0.948459i | \(0.602642\pi\) | |||||||
\(684\) | 0.0839964 | 0.00321168 | ||||||||
\(685\) | 4.77949 | 0.182615 | ||||||||
\(686\) | −1.24698 | −0.0476099 | ||||||||
\(687\) | 1.06941 | 0.0408004 | ||||||||
\(688\) | −12.4916 | −0.476237 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 25.6708 | 0.977270 | ||||||||
\(691\) | −42.9786 | −1.63498 | −0.817491 | − | 0.575942i | \(-0.804635\pi\) | ||||
−0.817491 | + | 0.575942i | \(0.804635\pi\) | |||||||
\(692\) | 8.93153 | 0.339526 | ||||||||
\(693\) | 0.456669 | 0.0173474 | ||||||||
\(694\) | −23.2509 | −0.882593 | ||||||||
\(695\) | −6.67852 | −0.253331 | ||||||||
\(696\) | 18.7936 | 0.712368 | ||||||||
\(697\) | −14.0677 | −0.532850 | ||||||||
\(698\) | 26.8555 | 1.01650 | ||||||||
\(699\) | −0.549905 | −0.0207993 | ||||||||
\(700\) | −5.14639 | −0.194515 | ||||||||
\(701\) | −8.79731 | −0.332270 | −0.166135 | − | 0.986103i | \(-0.553129\pi\) | ||||
−0.166135 | + | 0.986103i | \(0.553129\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.03611 | −0.0767934 | ||||||||
\(704\) | 4.06425 | 0.153177 | ||||||||
\(705\) | 32.1417 | 1.21053 | ||||||||
\(706\) | −17.2153 | −0.647908 | ||||||||
\(707\) | −2.65786 | −0.0999591 | ||||||||
\(708\) | 5.97925 | 0.224714 | ||||||||
\(709\) | 9.83203 | 0.369249 | 0.184625 | − | 0.982809i | \(-0.440893\pi\) | ||||
0.184625 | + | 0.982809i | \(0.440893\pi\) | |||||||
\(710\) | 68.3453 | 2.56495 | ||||||||
\(711\) | 4.07089 | 0.152670 | ||||||||
\(712\) | −48.1571 | −1.80477 | ||||||||
\(713\) | 6.03910 | 0.226166 | ||||||||
\(714\) | −7.14491 | −0.267392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 4.17291 | 0.155949 | ||||||||
\(717\) | −26.8711 | −1.00352 | ||||||||
\(718\) | −20.2330 | −0.755090 | ||||||||
\(719\) | −10.7411 | −0.400575 | −0.200288 | − | 0.979737i | \(-0.564188\pi\) | ||||
−0.200288 | + | 0.979737i | \(0.564188\pi\) | |||||||
\(720\) | 11.8509 | 0.441656 | ||||||||
\(721\) | −4.48234 | −0.166931 | ||||||||
\(722\) | 23.6482 | 0.880095 | ||||||||
\(723\) | 5.20011 | 0.193394 | ||||||||
\(724\) | −1.20804 | −0.0448965 | ||||||||
\(725\) | −71.2795 | −2.64726 | ||||||||
\(726\) | −13.4567 | −0.499426 | ||||||||
\(727\) | −18.8015 | −0.697308 | −0.348654 | − | 0.937251i | \(-0.613361\pi\) | ||||
−0.348654 | + | 0.937251i | \(0.613361\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −40.3446 | −1.49322 | ||||||||
\(731\) | −24.5802 | −0.909131 | ||||||||
\(732\) | −0.221514 | −0.00818741 | ||||||||
\(733\) | 32.0870 | 1.18516 | 0.592580 | − | 0.805512i | \(-0.298109\pi\) | ||||
0.592580 | + | 0.805512i | \(0.298109\pi\) | |||||||
\(734\) | −21.8877 | −0.807890 | ||||||||
\(735\) | 4.06987 | 0.150119 | ||||||||
\(736\) | 12.4777 | 0.459935 | ||||||||
\(737\) | −5.79774 | −0.213562 | ||||||||
\(738\) | −3.06157 | −0.112698 | ||||||||
\(739\) | −12.8616 | −0.473122 | −0.236561 | − | 0.971617i | \(-0.576020\pi\) | ||||
−0.236561 | + | 0.971617i | \(0.576020\pi\) | |||||||
\(740\) | 19.5399 | 0.718302 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.08047 | −0.259932 | ||||||||
\(743\) | 30.5328 | 1.12014 | 0.560070 | − | 0.828445i | \(-0.310774\pi\) | ||||
0.560070 | + | 0.828445i | \(0.310774\pi\) | |||||||
\(744\) | 3.64014 | 0.133454 | ||||||||
\(745\) | 98.0157 | 3.59102 | ||||||||
\(746\) | 6.49429 | 0.237773 | ||||||||
\(747\) | 11.0702 | 0.405039 | ||||||||
\(748\) | 1.16450 | 0.0425783 | ||||||||
\(749\) | −14.4760 | −0.528943 | ||||||||
\(750\) | −33.3117 | −1.21637 | ||||||||
\(751\) | 7.15312 | 0.261021 | 0.130511 | − | 0.991447i | \(-0.458338\pi\) | ||||
0.130511 | + | 0.991447i | \(0.458338\pi\) | |||||||
\(752\) | −22.9963 | −0.838589 | ||||||||
\(753\) | −4.29627 | −0.156565 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −11.6668 | −0.424598 | ||||||||
\(756\) | 0.445042 | 0.0161860 | ||||||||
\(757\) | −42.7488 | −1.55373 | −0.776866 | − | 0.629666i | \(-0.783192\pi\) | ||||
−0.776866 | + | 0.629666i | \(0.783192\pi\) | |||||||
\(758\) | −10.9983 | −0.399476 | ||||||||
\(759\) | 2.30994 | 0.0838455 | ||||||||
\(760\) | 2.34199 | 0.0849531 | ||||||||
\(761\) | −8.40665 | −0.304741 | −0.152370 | − | 0.988323i | \(-0.548691\pi\) | ||||
−0.152370 | + | 0.988323i | \(0.548691\pi\) | |||||||
\(762\) | 11.7257 | 0.424779 | ||||||||
\(763\) | 13.9209 | 0.503971 | ||||||||
\(764\) | 1.42208 | 0.0514491 | ||||||||
\(765\) | 23.3194 | 0.843116 | ||||||||
\(766\) | 5.44829 | 0.196855 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 10.1129 | 0.364918 | ||||||||
\(769\) | −39.4149 | −1.42134 | −0.710669 | − | 0.703526i | \(-0.751608\pi\) | ||||
−0.710669 | + | 0.703526i | \(0.751608\pi\) | |||||||
\(770\) | 2.31761 | 0.0835210 | ||||||||
\(771\) | 6.70512 | 0.241479 | ||||||||
\(772\) | −2.66496 | −0.0959142 | ||||||||
\(773\) | 36.9933 | 1.33056 | 0.665279 | − | 0.746595i | \(-0.268313\pi\) | ||||
0.665279 | + | 0.746595i | \(0.268313\pi\) | |||||||
\(774\) | −5.34943 | −0.192281 | ||||||||
\(775\) | −13.8062 | −0.495933 | ||||||||
\(776\) | 30.0584 | 1.07903 | ||||||||
\(777\) | −10.7880 | −0.387018 | ||||||||
\(778\) | 34.4221 | 1.23409 | ||||||||
\(779\) | −0.463387 | −0.0166026 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.14993 | 0.220062 | ||||||||
\(782\) | −36.1407 | −1.29239 | ||||||||
\(783\) | 6.16401 | 0.220284 | ||||||||
\(784\) | −2.91185 | −0.103995 | ||||||||
\(785\) | 4.75091 | 0.169567 | ||||||||
\(786\) | −12.4038 | −0.442430 | ||||||||
\(787\) | −18.1555 | −0.647175 | −0.323588 | − | 0.946198i | \(-0.604889\pi\) | ||||
−0.323588 | + | 0.946198i | \(0.604889\pi\) | |||||||
\(788\) | 1.50697 | 0.0536837 | ||||||||
\(789\) | 2.52812 | 0.0900035 | ||||||||
\(790\) | 20.6600 | 0.735048 | ||||||||
\(791\) | 19.8159 | 0.704572 | ||||||||
\(792\) | 1.39235 | 0.0494748 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 32.1989 | 1.14270 | ||||||||
\(795\) | 23.1091 | 0.819596 | ||||||||
\(796\) | 7.05476 | 0.250049 | ||||||||
\(797\) | 45.3521 | 1.60645 | 0.803227 | − | 0.595673i | \(-0.203114\pi\) | ||||
0.803227 | + | 0.595673i | \(0.203114\pi\) | |||||||
\(798\) | −0.235353 | −0.00833140 | ||||||||
\(799\) | −45.2508 | −1.60086 | ||||||||
\(800\) | −28.5258 | −1.00854 | ||||||||
\(801\) | −15.7948 | −0.558083 | ||||||||
\(802\) | −30.6558 | −1.08249 | ||||||||
\(803\) | −3.63034 | −0.128112 | ||||||||
\(804\) | −5.65013 | −0.199265 | ||||||||
\(805\) | 20.5864 | 0.725574 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.69741 | −0.341365 | ||||||||
\(808\) | −8.10359 | −0.285083 | ||||||||
\(809\) | 34.5412 | 1.21440 | 0.607202 | − | 0.794547i | \(-0.292292\pi\) | ||||
0.607202 | + | 0.794547i | \(0.292292\pi\) | |||||||
\(810\) | 5.07504 | 0.178319 | ||||||||
\(811\) | −27.2550 | −0.957054 | −0.478527 | − | 0.878073i | \(-0.658829\pi\) | ||||
−0.478527 | + | 0.878073i | \(0.658829\pi\) | |||||||
\(812\) | 2.74324 | 0.0962689 | ||||||||
\(813\) | −13.1875 | −0.462505 | ||||||||
\(814\) | −6.14331 | −0.215323 | ||||||||
\(815\) | −46.0892 | −1.61443 | ||||||||
\(816\) | −16.6843 | −0.584066 | ||||||||
\(817\) | −0.809669 | −0.0283267 | ||||||||
\(818\) | 43.3675 | 1.51631 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.44698 | 0.155295 | ||||||||
\(821\) | 43.7047 | 1.52530 | 0.762652 | − | 0.646809i | \(-0.223897\pi\) | ||||
0.762652 | + | 0.646809i | \(0.223897\pi\) | |||||||
\(822\) | −1.46440 | −0.0510770 | ||||||||
\(823\) | 11.0857 | 0.386422 | 0.193211 | − | 0.981157i | \(-0.438110\pi\) | ||||
0.193211 | + | 0.981157i | \(0.438110\pi\) | |||||||
\(824\) | −13.6663 | −0.476087 | ||||||||
\(825\) | −5.28084 | −0.183855 | ||||||||
\(826\) | −16.7535 | −0.582929 | ||||||||
\(827\) | 0.590813 | 0.0205446 | 0.0102723 | − | 0.999947i | \(-0.496730\pi\) | ||||
0.0102723 | + | 0.999947i | \(0.496730\pi\) | |||||||
\(828\) | 2.25113 | 0.0782321 | ||||||||
\(829\) | −15.3785 | −0.534118 | −0.267059 | − | 0.963680i | \(-0.586052\pi\) | ||||
−0.267059 | + | 0.963680i | \(0.586052\pi\) | |||||||
\(830\) | 56.1819 | 1.95010 | ||||||||
\(831\) | −6.42805 | −0.222987 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.72977 | −0.198525 | ||||||||
\(834\) | 2.04625 | 0.0708559 | ||||||||
\(835\) | 74.1401 | 2.56572 | ||||||||
\(836\) | 0.0383585 | 0.00132666 | ||||||||
\(837\) | 1.19391 | 0.0412677 | ||||||||
\(838\) | 29.7612 | 1.02808 | ||||||||
\(839\) | −6.54912 | −0.226101 | −0.113050 | − | 0.993589i | \(-0.536062\pi\) | ||||
−0.113050 | + | 0.993589i | \(0.536062\pi\) | |||||||
\(840\) | 12.4087 | 0.428141 | ||||||||
\(841\) | 8.99500 | 0.310172 | ||||||||
\(842\) | 29.5775 | 1.01931 | ||||||||
\(843\) | −20.0959 | −0.692140 | ||||||||
\(844\) | 6.74328 | 0.232113 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −9.84799 | −0.338581 | ||||||||
\(847\) | −10.7915 | −0.370799 | ||||||||
\(848\) | −16.5338 | −0.567773 | ||||||||
\(849\) | −21.0787 | −0.723420 | ||||||||
\(850\) | 82.6225 | 2.83393 | ||||||||
\(851\) | −54.5684 | −1.87058 | ||||||||
\(852\) | 5.99335 | 0.205329 | ||||||||
\(853\) | 30.0196 | 1.02785 | 0.513925 | − | 0.857835i | \(-0.328191\pi\) | ||||
0.513925 | + | 0.857835i | \(0.328191\pi\) | |||||||
\(854\) | 0.620670 | 0.0212389 | ||||||||
\(855\) | 0.768140 | 0.0262698 | ||||||||
\(856\) | −44.1363 | −1.50855 | ||||||||
\(857\) | 44.5939 | 1.52330 | 0.761650 | − | 0.647989i | \(-0.224390\pi\) | ||||
0.761650 | + | 0.647989i | \(0.224390\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.5987 | −1.55581 | −0.777904 | − | 0.628383i | \(-0.783717\pi\) | ||||
−0.777904 | + | 0.628383i | \(0.783717\pi\) | |||||||
\(860\) | 7.77014 | 0.264960 | ||||||||
\(861\) | −2.45519 | −0.0836725 | ||||||||
\(862\) | 39.7198 | 1.35286 | ||||||||
\(863\) | 15.5188 | 0.528265 | 0.264132 | − | 0.964486i | \(-0.414914\pi\) | ||||
0.264132 | + | 0.964486i | \(0.414914\pi\) | |||||||
\(864\) | 2.46681 | 0.0839227 | ||||||||
\(865\) | 81.6780 | 2.77714 | ||||||||
\(866\) | 48.3842 | 1.64416 | ||||||||
\(867\) | −15.8303 | −0.537625 | ||||||||
\(868\) | 0.531341 | 0.0180349 | ||||||||
\(869\) | 1.85905 | 0.0630639 | ||||||||
\(870\) | 31.2826 | 1.06058 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 42.4438 | 1.43733 | ||||||||
\(873\) | 9.85870 | 0.333667 | ||||||||
\(874\) | −1.19047 | −0.0402683 | ||||||||
\(875\) | −26.7139 | −0.903095 | ||||||||
\(876\) | −3.53791 | −0.119535 | ||||||||
\(877\) | −22.6489 | −0.764799 | −0.382400 | − | 0.923997i | \(-0.624902\pi\) | ||||
−0.382400 | + | 0.923997i | \(0.624902\pi\) | |||||||
\(878\) | −42.6001 | −1.43768 | ||||||||
\(879\) | 28.0069 | 0.944650 | ||||||||
\(880\) | 5.41192 | 0.182436 | ||||||||
\(881\) | −4.99915 | −0.168426 | −0.0842129 | − | 0.996448i | \(-0.526838\pi\) | ||||
−0.0842129 | + | 0.996448i | \(0.526838\pi\) | |||||||
\(882\) | −1.24698 | −0.0419880 | ||||||||
\(883\) | −29.1039 | −0.979424 | −0.489712 | − | 0.871884i | \(-0.662898\pi\) | ||||
−0.489712 | + | 0.871884i | \(0.662898\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 54.6798 | 1.83804 | ||||||||
\(886\) | 11.2034 | 0.376386 | ||||||||
\(887\) | −5.81964 | −0.195404 | −0.0977022 | − | 0.995216i | \(-0.531149\pi\) | ||||
−0.0977022 | + | 0.995216i | \(0.531149\pi\) | |||||||
\(888\) | −32.8918 | −1.10378 | ||||||||
\(889\) | 9.40331 | 0.315377 | ||||||||
\(890\) | −80.1594 | −2.68695 | ||||||||
\(891\) | 0.456669 | 0.0152990 | ||||||||
\(892\) | −1.46820 | −0.0491590 | ||||||||
\(893\) | −1.49056 | −0.0498795 | ||||||||
\(894\) | −30.0313 | −1.00440 | ||||||||
\(895\) | 38.1609 | 1.27558 | ||||||||
\(896\) | −6.16421 | −0.205932 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.3990 | 0.880947 | ||||||||
\(899\) | 7.35929 | 0.245446 | ||||||||
\(900\) | −5.14639 | −0.171546 | ||||||||
\(901\) | −32.5342 | −1.08387 | ||||||||
\(902\) | −1.39812 | −0.0465524 | ||||||||
\(903\) | −4.28991 | −0.142759 | ||||||||
\(904\) | 60.4170 | 2.00944 | ||||||||
\(905\) | −11.0474 | −0.367229 | ||||||||
\(906\) | 3.57462 | 0.118759 | ||||||||
\(907\) | −46.7976 | −1.55389 | −0.776945 | − | 0.629569i | \(-0.783232\pi\) | ||||
−0.776945 | + | 0.629569i | \(0.783232\pi\) | |||||||
\(908\) | −1.98924 | −0.0660151 | ||||||||
\(909\) | −2.65786 | −0.0881556 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.8194 | 0.789171 | 0.394586 | − | 0.918859i | \(-0.370888\pi\) | ||||
0.394586 | + | 0.918859i | \(0.370888\pi\) | |||||||
\(912\) | −0.549578 | −0.0181984 | ||||||||
\(913\) | 5.05543 | 0.167310 | ||||||||
\(914\) | 19.4974 | 0.644918 | ||||||||
\(915\) | −2.02573 | −0.0669686 | ||||||||
\(916\) | 0.475931 | 0.0157252 | ||||||||
\(917\) | −9.94710 | −0.328482 | ||||||||
\(918\) | −7.14491 | −0.235817 | ||||||||
\(919\) | −46.1841 | −1.52347 | −0.761736 | − | 0.647887i | \(-0.775653\pi\) | ||||
−0.761736 | + | 0.647887i | \(0.775653\pi\) | |||||||
\(920\) | 62.7662 | 2.06934 | ||||||||
\(921\) | 24.2095 | 0.797730 | ||||||||
\(922\) | 9.81189 | 0.323137 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0.203237 | 0.00668600 | ||||||||
\(925\) | 124.751 | 4.10178 | ||||||||
\(926\) | 5.57411 | 0.183177 | ||||||||
\(927\) | −4.48234 | −0.147219 | ||||||||
\(928\) | 15.2054 | 0.499143 | ||||||||
\(929\) | 46.4387 | 1.52360 | 0.761802 | − | 0.647810i | \(-0.224315\pi\) | ||||
0.761802 | + | 0.647810i | \(0.224315\pi\) | |||||||
\(930\) | 6.05916 | 0.198688 | ||||||||
\(931\) | −0.188738 | −0.00618565 | ||||||||
\(932\) | −0.244731 | −0.00801642 | ||||||||
\(933\) | 8.75175 | 0.286520 | ||||||||
\(934\) | 29.0860 | 0.951723 | ||||||||
\(935\) | 10.6493 | 0.348268 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.8068 | 0.647059 | 0.323529 | − | 0.946218i | \(-0.395131\pi\) | ||||
0.323529 | + | 0.946218i | \(0.395131\pi\) | |||||||
\(938\) | 15.8313 | 0.516910 | ||||||||
\(939\) | −3.44801 | −0.112522 | ||||||||
\(940\) | 14.3044 | 0.466558 | ||||||||
\(941\) | −24.2373 | −0.790112 | −0.395056 | − | 0.918657i | \(-0.629275\pi\) | ||||
−0.395056 | + | 0.918657i | \(0.629275\pi\) | |||||||
\(942\) | −1.45565 | −0.0474275 | ||||||||
\(943\) | −12.4189 | −0.404416 | ||||||||
\(944\) | −39.1215 | −1.27330 | ||||||||
\(945\) | 4.06987 | 0.132393 | ||||||||
\(946\) | −2.44292 | −0.0794260 | ||||||||
\(947\) | 27.9615 | 0.908625 | 0.454313 | − | 0.890842i | \(-0.349885\pi\) | ||||
0.454313 | + | 0.890842i | \(0.349885\pi\) | |||||||
\(948\) | 1.81172 | 0.0588419 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 2.72158 | 0.0882997 | ||||||||
\(951\) | 15.2632 | 0.494945 | ||||||||
\(952\) | −17.4696 | −0.566193 | ||||||||
\(953\) | 1.81197 | 0.0586956 | 0.0293478 | − | 0.999569i | \(-0.490657\pi\) | ||||
0.0293478 | + | 0.999569i | \(0.490657\pi\) | |||||||
\(954\) | −7.08047 | −0.229239 | ||||||||
\(955\) | 13.0048 | 0.420826 | ||||||||
\(956\) | −11.9588 | −0.386774 | ||||||||
\(957\) | 2.81491 | 0.0909931 | ||||||||
\(958\) | −23.7851 | −0.768462 | ||||||||
\(959\) | −1.17436 | −0.0379221 | ||||||||
\(960\) | 36.2209 | 1.16902 | ||||||||
\(961\) | −29.5746 | −0.954018 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.4760 | −0.466484 | ||||||||
\(964\) | 2.31427 | 0.0745376 | ||||||||
\(965\) | −24.3709 | −0.784526 | ||||||||
\(966\) | −6.30752 | −0.202941 | ||||||||
\(967\) | −19.2910 | −0.620357 | −0.310179 | − | 0.950678i | \(-0.600389\pi\) | ||||
−0.310179 | + | 0.950678i | \(0.600389\pi\) | |||||||
\(968\) | −32.9023 | −1.05752 | ||||||||
\(969\) | −1.08143 | −0.0347405 | ||||||||
\(970\) | 50.0333 | 1.60647 | ||||||||
\(971\) | −2.63417 | −0.0845344 | −0.0422672 | − | 0.999106i | \(-0.513458\pi\) | ||||
−0.0422672 | + | 0.999106i | \(0.513458\pi\) | |||||||
\(972\) | 0.445042 | 0.0142747 | ||||||||
\(973\) | 1.64097 | 0.0526070 | ||||||||
\(974\) | 40.0710 | 1.28396 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.44934 | 0.0463923 | ||||||||
\(977\) | 58.1325 | 1.85982 | 0.929912 | − | 0.367783i | \(-0.119883\pi\) | ||||
0.929912 | + | 0.367783i | \(0.119883\pi\) | |||||||
\(978\) | 14.1214 | 0.451553 | ||||||||
\(979\) | −7.21301 | −0.230529 | ||||||||
\(980\) | 1.81126 | 0.0578586 | ||||||||
\(981\) | 13.9209 | 0.444461 | ||||||||
\(982\) | 16.7706 | 0.535172 | ||||||||
\(983\) | 45.0158 | 1.43578 | 0.717891 | − | 0.696156i | \(-0.245108\pi\) | ||||
0.717891 | + | 0.696156i | \(0.245108\pi\) | |||||||
\(984\) | −7.48566 | −0.238634 | ||||||||
\(985\) | 13.7811 | 0.439104 | ||||||||
\(986\) | −44.0413 | −1.40256 | ||||||||
\(987\) | −7.89748 | −0.251379 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −21.6994 | −0.690000 | ||||||||
\(990\) | 2.31761 | 0.0736586 | ||||||||
\(991\) | −5.10840 | −0.162274 | −0.0811368 | − | 0.996703i | \(-0.525855\pi\) | ||||
−0.0811368 | + | 0.996703i | \(0.525855\pi\) | |||||||
\(992\) | 2.94516 | 0.0935089 | ||||||||
\(993\) | −34.2089 | −1.08559 | ||||||||
\(994\) | −16.7930 | −0.532641 | ||||||||
\(995\) | 64.5151 | 2.04527 | ||||||||
\(996\) | 4.92672 | 0.156109 | ||||||||
\(997\) | −7.52662 | −0.238371 | −0.119185 | − | 0.992872i | \(-0.538028\pi\) | ||||
−0.119185 | + | 0.992872i | \(0.538028\pi\) | |||||||
\(998\) | 22.9575 | 0.726706 | ||||||||
\(999\) | −10.7880 | −0.341318 |
(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 | 3549.2.a.z.1.1 | yes | 6 | |
13.12 | even | 2 | 3549.2.a.y.1.6 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3549.2.a.y.1.6 | ✓ | 6 | 13.12 | even | 2 | ||
3549.2.a.z.1.1 | yes | 6 | 1.1 | even | 1 | trivial |