Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3630,2,Mod(1,3630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3630, 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("3630.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3630.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: | \(28.9856959337\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.52625.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 24x^{2} + 19x + 121 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 330) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-4.17549\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3630.1 |
$q$-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 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.19863 | 1.20897 | 0.604484 | − | 0.796618i | \(-0.293379\pi\) | ||||
0.604484 | + | 0.796618i | \(0.293379\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 6.75608 | 1.87380 | 0.936900 | − | 0.349598i | \(-0.113682\pi\) | ||||
0.936900 | + | 0.349598i | \(0.113682\pi\) | |||||||
\(14\) | 3.19863 | 0.854869 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.557453 | −0.135202 | −0.0676012 | − | 0.997712i | \(-0.521535\pi\) | ||||
−0.0676012 | + | 0.997712i | \(0.521535\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −6.41156 | −1.47091 | −0.735456 | − | 0.677573i | \(-0.763032\pi\) | ||||
−0.735456 | + | 0.677573i | \(0.763032\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 3.19863 | 0.697998 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.59489 | 0.541073 | 0.270536 | − | 0.962710i | \(-0.412799\pi\) | ||||
0.270536 | + | 0.962710i | \(0.412799\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 6.75608 | 1.32498 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.19863 | 0.604484 | ||||||||
\(29\) | 4.89154 | 0.908337 | 0.454168 | − | 0.890916i | \(-0.349936\pi\) | ||||
0.454168 | + | 0.890916i | \(0.349936\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 2.41941 | 0.434538 | 0.217269 | − | 0.976112i | \(-0.430285\pi\) | ||||
0.217269 | + | 0.976112i | \(0.430285\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.557453 | −0.0956025 | ||||||||
\(35\) | −3.19863 | −0.540667 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −5.73294 | −0.942490 | −0.471245 | − | 0.882002i | \(-0.656195\pi\) | ||||
−0.471245 | + | 0.882002i | \(0.656195\pi\) | |||||||
\(38\) | −6.41156 | −1.04009 | ||||||||
\(39\) | 6.75608 | 1.08184 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | −1.31979 | −0.206116 | −0.103058 | − | 0.994675i | \(-0.532863\pi\) | ||||
−0.103058 | + | 0.994675i | \(0.532863\pi\) | |||||||
\(42\) | 3.19863 | 0.493559 | ||||||||
\(43\) | 1.32139 | 0.201509 | 0.100755 | − | 0.994911i | \(-0.467874\pi\) | ||||
0.100755 | + | 0.994911i | \(0.467874\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 2.59489 | 0.382596 | ||||||||
\(47\) | −5.99215 | −0.874045 | −0.437022 | − | 0.899451i | \(-0.643967\pi\) | ||||
−0.437022 | + | 0.899451i | \(0.643967\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 3.23122 | 0.461602 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −0.557453 | −0.0780591 | ||||||||
\(52\) | 6.75608 | 0.936900 | ||||||||
\(53\) | −2.43470 | −0.334431 | −0.167216 | − | 0.985920i | \(-0.553478\pi\) | ||||
−0.167216 | + | 0.985920i | \(0.553478\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 3.19863 | 0.427435 | ||||||||
\(57\) | −6.41156 | −0.849231 | ||||||||
\(58\) | 4.89154 | 0.642291 | ||||||||
\(59\) | 10.3262 | 1.34436 | 0.672181 | − | 0.740387i | \(-0.265358\pi\) | ||||
0.672181 | + | 0.740387i | \(0.265358\pi\) | |||||||
\(60\) | −1.00000 | −0.129099 | ||||||||
\(61\) | −3.92512 | −0.502560 | −0.251280 | − | 0.967914i | \(-0.580851\pi\) | ||||
−0.251280 | + | 0.967914i | \(0.580851\pi\) | |||||||
\(62\) | 2.41941 | 0.307265 | ||||||||
\(63\) | 3.19863 | 0.402989 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.75608 | −0.837989 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 15.1676 | 1.85302 | 0.926511 | − | 0.376268i | \(-0.122793\pi\) | ||||
0.926511 | + | 0.376268i | \(0.122793\pi\) | |||||||
\(68\) | −0.557453 | −0.0676012 | ||||||||
\(69\) | 2.59489 | 0.312389 | ||||||||
\(70\) | −3.19863 | −0.382309 | ||||||||
\(71\) | −6.35097 | −0.753722 | −0.376861 | − | 0.926270i | \(-0.622997\pi\) | ||||
−0.376861 | + | 0.926270i | \(0.622997\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 6.94427 | 0.812766 | 0.406383 | − | 0.913703i | \(-0.366790\pi\) | ||||
0.406383 | + | 0.913703i | \(0.366790\pi\) | |||||||
\(74\) | −5.73294 | −0.666441 | ||||||||
\(75\) | 1.00000 | 0.115470 | ||||||||
\(76\) | −6.41156 | −0.735456 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 6.75608 | 0.764975 | ||||||||
\(79\) | −11.6724 | −1.31324 | −0.656622 | − | 0.754220i | \(-0.728015\pi\) | ||||
−0.656622 | + | 0.754220i | \(0.728015\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.31979 | −0.145746 | ||||||||
\(83\) | 8.00000 | 0.878114 | 0.439057 | − | 0.898459i | \(-0.355313\pi\) | ||||
0.439057 | + | 0.898459i | \(0.355313\pi\) | |||||||
\(84\) | 3.19863 | 0.348999 | ||||||||
\(85\) | 0.557453 | 0.0604643 | ||||||||
\(86\) | 1.32139 | 0.142489 | ||||||||
\(87\) | 4.89154 | 0.524428 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −13.0775 | −1.38621 | −0.693104 | − | 0.720837i | \(-0.743757\pi\) | ||||
−0.693104 | + | 0.720837i | \(0.743757\pi\) | |||||||
\(90\) | −1.00000 | −0.105409 | ||||||||
\(91\) | 21.6102 | 2.26536 | ||||||||
\(92\) | 2.59489 | 0.270536 | ||||||||
\(93\) | 2.41941 | 0.250881 | ||||||||
\(94\) | −5.99215 | −0.618043 | ||||||||
\(95\) | 6.41156 | 0.657812 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 7.63332 | 0.775046 | 0.387523 | − | 0.921860i | \(-0.373331\pi\) | ||||
0.387523 | + | 0.921860i | \(0.373331\pi\) | |||||||
\(98\) | 3.23122 | 0.326402 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −15.9739 | −1.58946 | −0.794729 | − | 0.606964i | \(-0.792387\pi\) | ||||
−0.794729 | + | 0.606964i | \(0.792387\pi\) | |||||||
\(102\) | −0.557453 | −0.0551961 | ||||||||
\(103\) | 18.2904 | 1.80221 | 0.901103 | − | 0.433605i | \(-0.142759\pi\) | ||||
0.901103 | + | 0.433605i | \(0.142759\pi\) | |||||||
\(104\) | 6.75608 | 0.662488 | ||||||||
\(105\) | −3.19863 | −0.312154 | ||||||||
\(106\) | −2.43470 | −0.236478 | ||||||||
\(107\) | −17.1149 | −1.65456 | −0.827280 | − | 0.561789i | \(-0.810113\pi\) | ||||
−0.827280 | + | 0.561789i | \(0.810113\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −8.94427 | −0.856706 | −0.428353 | − | 0.903612i | \(-0.640906\pi\) | ||||
−0.428353 | + | 0.903612i | \(0.640906\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.73294 | −0.544147 | ||||||||
\(112\) | 3.19863 | 0.302242 | ||||||||
\(113\) | 4.81666 | 0.453113 | 0.226557 | − | 0.973998i | \(-0.427253\pi\) | ||||
0.226557 | + | 0.973998i | \(0.427253\pi\) | |||||||
\(114\) | −6.41156 | −0.600497 | ||||||||
\(115\) | −2.59489 | −0.241975 | ||||||||
\(116\) | 4.89154 | 0.454168 | ||||||||
\(117\) | 6.75608 | 0.624600 | ||||||||
\(118\) | 10.3262 | 0.950607 | ||||||||
\(119\) | −1.78309 | −0.163455 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −3.92512 | −0.355364 | ||||||||
\(123\) | −1.31979 | −0.119001 | ||||||||
\(124\) | 2.41941 | 0.217269 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 3.19863 | 0.284956 | ||||||||
\(127\) | 16.2155 | 1.43889 | 0.719447 | − | 0.694547i | \(-0.244395\pi\) | ||||
0.719447 | + | 0.694547i | \(0.244395\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.32139 | 0.116342 | ||||||||
\(130\) | −6.75608 | −0.592547 | ||||||||
\(131\) | −17.2888 | −1.51053 | −0.755265 | − | 0.655420i | \(-0.772492\pi\) | ||||
−0.755265 | + | 0.655420i | \(0.772492\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −20.5082 | −1.77828 | ||||||||
\(134\) | 15.1676 | 1.31028 | ||||||||
\(135\) | −1.00000 | −0.0860663 | ||||||||
\(136\) | −0.557453 | −0.0478012 | ||||||||
\(137\) | 7.93157 | 0.677640 | 0.338820 | − | 0.940851i | \(-0.389972\pi\) | ||||
0.338820 | + | 0.940851i | \(0.389972\pi\) | |||||||
\(138\) | 2.59489 | 0.220892 | ||||||||
\(139\) | 8.21778 | 0.697023 | 0.348512 | − | 0.937304i | \(-0.386687\pi\) | ||||
0.348512 | + | 0.937304i | \(0.386687\pi\) | |||||||
\(140\) | −3.19863 | −0.270333 | ||||||||
\(141\) | −5.99215 | −0.504630 | ||||||||
\(142\) | −6.35097 | −0.532962 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −4.89154 | −0.406221 | ||||||||
\(146\) | 6.94427 | 0.574712 | ||||||||
\(147\) | 3.23122 | 0.266506 | ||||||||
\(148\) | −5.73294 | −0.471245 | ||||||||
\(149\) | 6.08532 | 0.498529 | 0.249264 | − | 0.968435i | \(-0.419811\pi\) | ||||
0.249264 | + | 0.968435i | \(0.419811\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −18.2761 | −1.48729 | −0.743644 | − | 0.668576i | \(-0.766904\pi\) | ||||
−0.743644 | + | 0.668576i | \(0.766904\pi\) | |||||||
\(152\) | −6.41156 | −0.520046 | ||||||||
\(153\) | −0.557453 | −0.0450674 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.41941 | −0.194331 | ||||||||
\(156\) | 6.75608 | 0.540919 | ||||||||
\(157\) | 18.4874 | 1.47546 | 0.737729 | − | 0.675097i | \(-0.235898\pi\) | ||||
0.737729 | + | 0.675097i | \(0.235898\pi\) | |||||||
\(158\) | −11.6724 | −0.928603 | ||||||||
\(159\) | −2.43470 | −0.193084 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 8.30010 | 0.654139 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 11.5480 | 0.904510 | 0.452255 | − | 0.891889i | \(-0.350620\pi\) | ||||
0.452255 | + | 0.891889i | \(0.350620\pi\) | |||||||
\(164\) | −1.31979 | −0.103058 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.00000 | 0.620920 | ||||||||
\(167\) | −2.95212 | −0.228442 | −0.114221 | − | 0.993455i | \(-0.536437\pi\) | ||||
−0.114221 | + | 0.993455i | \(0.536437\pi\) | |||||||
\(168\) | 3.19863 | 0.246779 | ||||||||
\(169\) | 32.6446 | 2.51112 | ||||||||
\(170\) | 0.557453 | 0.0427547 | ||||||||
\(171\) | −6.41156 | −0.490304 | ||||||||
\(172\) | 1.32139 | 0.100755 | ||||||||
\(173\) | −1.84140 | −0.139999 | −0.0699994 | − | 0.997547i | \(-0.522300\pi\) | ||||
−0.0699994 | + | 0.997547i | \(0.522300\pi\) | |||||||
\(174\) | 4.89154 | 0.370827 | ||||||||
\(175\) | 3.19863 | 0.241793 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.3262 | 0.776168 | ||||||||
\(178\) | −13.0775 | −0.980198 | ||||||||
\(179\) | −18.5623 | −1.38741 | −0.693706 | − | 0.720258i | \(-0.744023\pi\) | ||||
−0.693706 | + | 0.720258i | \(0.744023\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 9.52786 | 0.708201 | 0.354100 | − | 0.935207i | \(-0.384787\pi\) | ||||
0.354100 | + | 0.935207i | \(0.384787\pi\) | |||||||
\(182\) | 21.6102 | 1.60185 | ||||||||
\(183\) | −3.92512 | −0.290153 | ||||||||
\(184\) | 2.59489 | 0.191298 | ||||||||
\(185\) | 5.73294 | 0.421494 | ||||||||
\(186\) | 2.41941 | 0.177400 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −5.99215 | −0.437022 | ||||||||
\(189\) | 3.19863 | 0.232666 | ||||||||
\(190\) | 6.41156 | 0.465143 | ||||||||
\(191\) | 0.913695 | 0.0661127 | 0.0330563 | − | 0.999453i | \(-0.489476\pi\) | ||||
0.0330563 | + | 0.999453i | \(0.489476\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −23.2952 | −1.67683 | −0.838414 | − | 0.545033i | \(-0.816517\pi\) | ||||
−0.838414 | + | 0.545033i | \(0.816517\pi\) | |||||||
\(194\) | 7.63332 | 0.548041 | ||||||||
\(195\) | −6.75608 | −0.483813 | ||||||||
\(196\) | 3.23122 | 0.230801 | ||||||||
\(197\) | 24.5896 | 1.75194 | 0.875969 | − | 0.482367i | \(-0.160223\pi\) | ||||
0.875969 | + | 0.482367i | \(0.160223\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5112 | 0.745117 | 0.372559 | − | 0.928009i | \(-0.378481\pi\) | ||||
0.372559 | + | 0.928009i | \(0.378481\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 15.1676 | 1.06984 | ||||||||
\(202\) | −15.9739 | −1.12392 | ||||||||
\(203\) | 15.6462 | 1.09815 | ||||||||
\(204\) | −0.557453 | −0.0390295 | ||||||||
\(205\) | 1.31979 | 0.0921780 | ||||||||
\(206\) | 18.2904 | 1.27435 | ||||||||
\(207\) | 2.59489 | 0.180358 | ||||||||
\(208\) | 6.75608 | 0.468450 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −3.19863 | −0.220726 | ||||||||
\(211\) | 7.06863 | 0.486624 | 0.243312 | − | 0.969948i | \(-0.421766\pi\) | ||||
0.243312 | + | 0.969948i | \(0.421766\pi\) | |||||||
\(212\) | −2.43470 | −0.167216 | ||||||||
\(213\) | −6.35097 | −0.435162 | ||||||||
\(214\) | −17.1149 | −1.16995 | ||||||||
\(215\) | −1.32139 | −0.0901177 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 7.73878 | 0.525343 | ||||||||
\(218\) | −8.94427 | −0.605783 | ||||||||
\(219\) | 6.94427 | 0.469250 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.76620 | −0.253342 | ||||||||
\(222\) | −5.73294 | −0.384770 | ||||||||
\(223\) | 0.801373 | 0.0536639 | 0.0268319 | − | 0.999640i | \(-0.491458\pi\) | ||||
0.0268319 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(224\) | 3.19863 | 0.213717 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 4.81666 | 0.320400 | ||||||||
\(227\) | 4.86939 | 0.323193 | 0.161596 | − | 0.986857i | \(-0.448336\pi\) | ||||
0.161596 | + | 0.986857i | \(0.448336\pi\) | |||||||
\(228\) | −6.41156 | −0.424616 | ||||||||
\(229\) | −1.16119 | −0.0767333 | −0.0383667 | − | 0.999264i | \(-0.512215\pi\) | ||||
−0.0383667 | + | 0.999264i | \(0.512215\pi\) | |||||||
\(230\) | −2.59489 | −0.171102 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 4.89154 | 0.321146 | ||||||||
\(233\) | −12.0527 | −0.789601 | −0.394800 | − | 0.918767i | \(-0.629186\pi\) | ||||
−0.394800 | + | 0.918767i | \(0.629186\pi\) | |||||||
\(234\) | 6.75608 | 0.441659 | ||||||||
\(235\) | 5.99215 | 0.390885 | ||||||||
\(236\) | 10.3262 | 0.672181 | ||||||||
\(237\) | −11.6724 | −0.758201 | ||||||||
\(238\) | −1.78309 | −0.115580 | ||||||||
\(239\) | 28.2604 | 1.82801 | 0.914006 | − | 0.405700i | \(-0.132972\pi\) | ||||
0.914006 | + | 0.405700i | \(0.132972\pi\) | |||||||
\(240\) | −1.00000 | −0.0645497 | ||||||||
\(241\) | −24.7857 | −1.59659 | −0.798293 | − | 0.602270i | \(-0.794263\pi\) | ||||
−0.798293 | + | 0.602270i | \(0.794263\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −3.92512 | −0.251280 | ||||||||
\(245\) | −3.23122 | −0.206435 | ||||||||
\(246\) | −1.31979 | −0.0841466 | ||||||||
\(247\) | −43.3170 | −2.75619 | ||||||||
\(248\) | 2.41941 | 0.153632 | ||||||||
\(249\) | 8.00000 | 0.506979 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −17.8615 | −1.12741 | −0.563705 | − | 0.825976i | \(-0.690625\pi\) | ||||
−0.563705 | + | 0.825976i | \(0.690625\pi\) | |||||||
\(252\) | 3.19863 | 0.201495 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 16.2155 | 1.01745 | ||||||||
\(255\) | 0.557453 | 0.0349091 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.32237 | 0.269622 | 0.134811 | − | 0.990871i | \(-0.456957\pi\) | ||||
0.134811 | + | 0.990871i | \(0.456957\pi\) | |||||||
\(258\) | 1.32139 | 0.0822659 | ||||||||
\(259\) | −18.3375 | −1.13944 | ||||||||
\(260\) | −6.75608 | −0.418994 | ||||||||
\(261\) | 4.89154 | 0.302779 | ||||||||
\(262\) | −17.2888 | −1.06811 | ||||||||
\(263\) | −23.0282 | −1.41998 | −0.709989 | − | 0.704212i | \(-0.751300\pi\) | ||||
−0.709989 | + | 0.704212i | \(0.751300\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.43470 | 0.149562 | ||||||||
\(266\) | −20.5082 | −1.25744 | ||||||||
\(267\) | −13.0775 | −0.800328 | ||||||||
\(268\) | 15.1676 | 0.926511 | ||||||||
\(269\) | −11.8567 | −0.722915 | −0.361457 | − | 0.932389i | \(-0.617721\pi\) | ||||
−0.361457 | + | 0.932389i | \(0.617721\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −11.4268 | −0.694131 | −0.347066 | − | 0.937841i | \(-0.612822\pi\) | ||||
−0.347066 | + | 0.937841i | \(0.612822\pi\) | |||||||
\(272\) | −0.557453 | −0.0338006 | ||||||||
\(273\) | 21.6102 | 1.30791 | ||||||||
\(274\) | 7.93157 | 0.479164 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.59489 | 0.156194 | ||||||||
\(277\) | −15.0384 | −0.903572 | −0.451786 | − | 0.892126i | \(-0.649213\pi\) | ||||
−0.451786 | + | 0.892126i | \(0.649213\pi\) | |||||||
\(278\) | 8.21778 | 0.492870 | ||||||||
\(279\) | 2.41941 | 0.144846 | ||||||||
\(280\) | −3.19863 | −0.191155 | ||||||||
\(281\) | 13.2666 | 0.791422 | 0.395711 | − | 0.918375i | \(-0.370498\pi\) | ||||
0.395711 | + | 0.918375i | \(0.370498\pi\) | |||||||
\(282\) | −5.99215 | −0.356827 | ||||||||
\(283\) | 15.1214 | 0.898871 | 0.449436 | − | 0.893313i | \(-0.351625\pi\) | ||||
0.449436 | + | 0.893313i | \(0.351625\pi\) | |||||||
\(284\) | −6.35097 | −0.376861 | ||||||||
\(285\) | 6.41156 | 0.379788 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.22151 | −0.249188 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.6892 | −0.981720 | ||||||||
\(290\) | −4.89154 | −0.287241 | ||||||||
\(291\) | 7.63332 | 0.447473 | ||||||||
\(292\) | 6.94427 | 0.406383 | ||||||||
\(293\) | −13.9163 | −0.812998 | −0.406499 | − | 0.913651i | \(-0.633250\pi\) | ||||
−0.406499 | + | 0.913651i | \(0.633250\pi\) | |||||||
\(294\) | 3.23122 | 0.188448 | ||||||||
\(295\) | −10.3262 | −0.601217 | ||||||||
\(296\) | −5.73294 | −0.333220 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.08532 | 0.352513 | ||||||||
\(299\) | 17.5313 | 1.01386 | ||||||||
\(300\) | 1.00000 | 0.0577350 | ||||||||
\(301\) | 4.22662 | 0.243618 | ||||||||
\(302\) | −18.2761 | −1.05167 | ||||||||
\(303\) | −15.9739 | −0.917674 | ||||||||
\(304\) | −6.41156 | −0.367728 | ||||||||
\(305\) | 3.92512 | 0.224752 | ||||||||
\(306\) | −0.557453 | −0.0318675 | ||||||||
\(307\) | 24.0813 | 1.37439 | 0.687197 | − | 0.726471i | \(-0.258841\pi\) | ||||
0.687197 | + | 0.726471i | \(0.258841\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 18.2904 | 1.04050 | ||||||||
\(310\) | −2.41941 | −0.137413 | ||||||||
\(311\) | −30.3816 | −1.72278 | −0.861390 | − | 0.507944i | \(-0.830406\pi\) | ||||
−0.861390 | + | 0.507944i | \(0.830406\pi\) | |||||||
\(312\) | 6.75608 | 0.382488 | ||||||||
\(313\) | 16.2012 | 0.915747 | 0.457873 | − | 0.889017i | \(-0.348611\pi\) | ||||
0.457873 | + | 0.889017i | \(0.348611\pi\) | |||||||
\(314\) | 18.4874 | 1.04331 | ||||||||
\(315\) | −3.19863 | −0.180222 | ||||||||
\(316\) | −11.6724 | −0.656622 | ||||||||
\(317\) | −33.0640 | −1.85706 | −0.928531 | − | 0.371256i | \(-0.878927\pi\) | ||||
−0.928531 | + | 0.371256i | \(0.878927\pi\) | |||||||
\(318\) | −2.43470 | −0.136531 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | −17.1149 | −0.955261 | ||||||||
\(322\) | 8.30010 | 0.462546 | ||||||||
\(323\) | 3.57414 | 0.198871 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 6.75608 | 0.374760 | ||||||||
\(326\) | 11.5480 | 0.639585 | ||||||||
\(327\) | −8.94427 | −0.494619 | ||||||||
\(328\) | −1.31979 | −0.0728731 | ||||||||
\(329\) | −19.1666 | −1.05669 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.733928 | −0.0403403 | −0.0201702 | − | 0.999797i | \(-0.506421\pi\) | ||||
−0.0201702 | + | 0.999797i | \(0.506421\pi\) | |||||||
\(332\) | 8.00000 | 0.439057 | ||||||||
\(333\) | −5.73294 | −0.314163 | ||||||||
\(334\) | −2.95212 | −0.161533 | ||||||||
\(335\) | −15.1676 | −0.828696 | ||||||||
\(336\) | 3.19863 | 0.174499 | ||||||||
\(337\) | −16.3816 | −0.892360 | −0.446180 | − | 0.894943i | \(-0.647216\pi\) | ||||
−0.446180 | + | 0.894943i | \(0.647216\pi\) | |||||||
\(338\) | 32.6446 | 1.77563 | ||||||||
\(339\) | 4.81666 | 0.261605 | ||||||||
\(340\) | 0.557453 | 0.0302322 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −6.41156 | −0.346697 | ||||||||
\(343\) | −12.0549 | −0.650905 | ||||||||
\(344\) | 1.32139 | 0.0712443 | ||||||||
\(345\) | −2.59489 | −0.139704 | ||||||||
\(346\) | −1.84140 | −0.0989942 | ||||||||
\(347\) | −16.2012 | −0.869727 | −0.434863 | − | 0.900496i | \(-0.643203\pi\) | ||||
−0.434863 | + | 0.900496i | \(0.643203\pi\) | |||||||
\(348\) | 4.89154 | 0.262214 | ||||||||
\(349\) | 4.19604 | 0.224609 | 0.112305 | − | 0.993674i | \(-0.464177\pi\) | ||||
0.112305 | + | 0.993674i | \(0.464177\pi\) | |||||||
\(350\) | 3.19863 | 0.170974 | ||||||||
\(351\) | 6.75608 | 0.360613 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.32139 | 0.176780 | 0.0883898 | − | 0.996086i | \(-0.471828\pi\) | ||||
0.0883898 | + | 0.996086i | \(0.471828\pi\) | |||||||
\(354\) | 10.3262 | 0.548833 | ||||||||
\(355\) | 6.35097 | 0.337075 | ||||||||
\(356\) | −13.0775 | −0.693104 | ||||||||
\(357\) | −1.78309 | −0.0943709 | ||||||||
\(358\) | −18.5623 | −0.981048 | ||||||||
\(359\) | −22.1803 | −1.17063 | −0.585317 | − | 0.810805i | \(-0.699030\pi\) | ||||
−0.585317 | + | 0.810805i | \(0.699030\pi\) | |||||||
\(360\) | −1.00000 | −0.0527046 | ||||||||
\(361\) | 22.1080 | 1.16358 | ||||||||
\(362\) | 9.52786 | 0.500773 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 21.6102 | 1.13268 | ||||||||
\(365\) | −6.94427 | −0.363480 | ||||||||
\(366\) | −3.92512 | −0.205169 | ||||||||
\(367\) | −17.0497 | −0.889989 | −0.444994 | − | 0.895533i | \(-0.646794\pi\) | ||||
−0.444994 | + | 0.895533i | \(0.646794\pi\) | |||||||
\(368\) | 2.59489 | 0.135268 | ||||||||
\(369\) | −1.31979 | −0.0687054 | ||||||||
\(370\) | 5.73294 | 0.298041 | ||||||||
\(371\) | −7.78768 | −0.404316 | ||||||||
\(372\) | 2.41941 | 0.125440 | ||||||||
\(373\) | −0.231215 | −0.0119719 | −0.00598594 | − | 0.999982i | \(-0.501905\pi\) | ||||
−0.00598594 | + | 0.999982i | \(0.501905\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.00000 | −0.0516398 | ||||||||
\(376\) | −5.99215 | −0.309021 | ||||||||
\(377\) | 33.0477 | 1.70204 | ||||||||
\(378\) | 3.19863 | 0.164520 | ||||||||
\(379\) | −11.9723 | −0.614974 | −0.307487 | − | 0.951552i | \(-0.599488\pi\) | ||||
−0.307487 | + | 0.951552i | \(0.599488\pi\) | |||||||
\(380\) | 6.41156 | 0.328906 | ||||||||
\(381\) | 16.2155 | 0.830746 | ||||||||
\(382\) | 0.913695 | 0.0467487 | ||||||||
\(383\) | 3.07102 | 0.156922 | 0.0784608 | − | 0.996917i | \(-0.474999\pi\) | ||||
0.0784608 | + | 0.996917i | \(0.474999\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −23.2952 | −1.18570 | ||||||||
\(387\) | 1.32139 | 0.0671698 | ||||||||
\(388\) | 7.63332 | 0.387523 | ||||||||
\(389\) | 19.7569 | 1.00172 | 0.500858 | − | 0.865529i | \(-0.333018\pi\) | ||||
0.500858 | + | 0.865529i | \(0.333018\pi\) | |||||||
\(390\) | −6.75608 | −0.342107 | ||||||||
\(391\) | −1.44653 | −0.0731543 | ||||||||
\(392\) | 3.23122 | 0.163201 | ||||||||
\(393\) | −17.2888 | −0.872104 | ||||||||
\(394\) | 24.5896 | 1.23881 | ||||||||
\(395\) | 11.6724 | 0.587300 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −11.4546 | −0.574889 | −0.287444 | − | 0.957797i | \(-0.592806\pi\) | ||||
−0.287444 | + | 0.957797i | \(0.592806\pi\) | |||||||
\(398\) | 10.5112 | 0.526878 | ||||||||
\(399\) | −20.5082 | −1.02669 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 22.3001 | 1.11361 | 0.556807 | − | 0.830642i | \(-0.312026\pi\) | ||||
0.556807 | + | 0.830642i | \(0.312026\pi\) | |||||||
\(402\) | 15.1676 | 0.756493 | ||||||||
\(403\) | 16.3457 | 0.814238 | ||||||||
\(404\) | −15.9739 | −0.794729 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 15.6462 | 0.776509 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −0.557453 | −0.0275981 | ||||||||
\(409\) | 36.2811 | 1.79399 | 0.896993 | − | 0.442044i | \(-0.145746\pi\) | ||||
0.896993 | + | 0.442044i | \(0.145746\pi\) | |||||||
\(410\) | 1.31979 | 0.0651797 | ||||||||
\(411\) | 7.93157 | 0.391235 | ||||||||
\(412\) | 18.2904 | 0.901103 | ||||||||
\(413\) | 33.0298 | 1.62529 | ||||||||
\(414\) | 2.59489 | 0.127532 | ||||||||
\(415\) | −8.00000 | −0.392705 | ||||||||
\(416\) | 6.75608 | 0.331244 | ||||||||
\(417\) | 8.21778 | 0.402426 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 9.06157 | 0.442687 | 0.221343 | − | 0.975196i | \(-0.428956\pi\) | ||||
0.221343 | + | 0.975196i | \(0.428956\pi\) | |||||||
\(420\) | −3.19863 | −0.156077 | ||||||||
\(421\) | −2.42586 | −0.118229 | −0.0591145 | − | 0.998251i | \(-0.518828\pi\) | ||||
−0.0591145 | + | 0.998251i | \(0.518828\pi\) | |||||||
\(422\) | 7.06863 | 0.344095 | ||||||||
\(423\) | −5.99215 | −0.291348 | ||||||||
\(424\) | −2.43470 | −0.118239 | ||||||||
\(425\) | −0.557453 | −0.0270405 | ||||||||
\(426\) | −6.35097 | −0.307706 | ||||||||
\(427\) | −12.5550 | −0.607579 | ||||||||
\(428\) | −17.1149 | −0.827280 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.32139 | −0.0637229 | ||||||||
\(431\) | −2.65847 | −0.128054 | −0.0640271 | − | 0.997948i | \(-0.520394\pi\) | ||||
−0.0640271 | + | 0.997948i | \(0.520394\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −19.1918 | −0.922297 | −0.461149 | − | 0.887323i | \(-0.652563\pi\) | ||||
−0.461149 | + | 0.887323i | \(0.652563\pi\) | |||||||
\(434\) | 7.73878 | 0.371473 | ||||||||
\(435\) | −4.89154 | −0.234532 | ||||||||
\(436\) | −8.94427 | −0.428353 | ||||||||
\(437\) | −16.6373 | −0.795870 | ||||||||
\(438\) | 6.94427 | 0.331810 | ||||||||
\(439\) | −12.6955 | −0.605923 | −0.302962 | − | 0.953003i | \(-0.597975\pi\) | ||||
−0.302962 | + | 0.953003i | \(0.597975\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.23122 | 0.153867 | ||||||||
\(442\) | −3.76620 | −0.179140 | ||||||||
\(443\) | 16.9189 | 0.803839 | 0.401920 | − | 0.915675i | \(-0.368343\pi\) | ||||
0.401920 | + | 0.915675i | \(0.368343\pi\) | |||||||
\(444\) | −5.73294 | −0.272073 | ||||||||
\(445\) | 13.0775 | 0.619931 | ||||||||
\(446\) | 0.801373 | 0.0379461 | ||||||||
\(447\) | 6.08532 | 0.287826 | ||||||||
\(448\) | 3.19863 | 0.151121 | ||||||||
\(449\) | −19.2809 | −0.909924 | −0.454962 | − | 0.890511i | \(-0.650347\pi\) | ||||
−0.454962 | + | 0.890511i | \(0.650347\pi\) | |||||||
\(450\) | 1.00000 | 0.0471405 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 4.81666 | 0.226557 | ||||||||
\(453\) | −18.2761 | −0.858686 | ||||||||
\(454\) | 4.86939 | 0.228532 | ||||||||
\(455\) | −21.6102 | −1.01310 | ||||||||
\(456\) | −6.41156 | −0.300249 | ||||||||
\(457\) | −39.5219 | −1.84875 | −0.924377 | − | 0.381479i | \(-0.875415\pi\) | ||||
−0.924377 | + | 0.381479i | \(0.875415\pi\) | |||||||
\(458\) | −1.16119 | −0.0542587 | ||||||||
\(459\) | −0.557453 | −0.0260197 | ||||||||
\(460\) | −2.59489 | −0.120988 | ||||||||
\(461\) | −13.8398 | −0.644584 | −0.322292 | − | 0.946640i | \(-0.604453\pi\) | ||||
−0.322292 | + | 0.946640i | \(0.604453\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5919 | 0.585195 | 0.292598 | − | 0.956236i | \(-0.405480\pi\) | ||||
0.292598 | + | 0.956236i | \(0.405480\pi\) | |||||||
\(464\) | 4.89154 | 0.227084 | ||||||||
\(465\) | −2.41941 | −0.112197 | ||||||||
\(466\) | −12.0527 | −0.558332 | ||||||||
\(467\) | −11.7368 | −0.543115 | −0.271557 | − | 0.962422i | \(-0.587539\pi\) | ||||
−0.271557 | + | 0.962422i | \(0.587539\pi\) | |||||||
\(468\) | 6.75608 | 0.312300 | ||||||||
\(469\) | 48.5156 | 2.24024 | ||||||||
\(470\) | 5.99215 | 0.276397 | ||||||||
\(471\) | 18.4874 | 0.851856 | ||||||||
\(472\) | 10.3262 | 0.475304 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −11.6724 | −0.536129 | ||||||||
\(475\) | −6.41156 | −0.294182 | ||||||||
\(476\) | −1.78309 | −0.0817276 | ||||||||
\(477\) | −2.43470 | −0.111477 | ||||||||
\(478\) | 28.2604 | 1.29260 | ||||||||
\(479\) | −21.4007 | −0.977823 | −0.488912 | − | 0.872333i | \(-0.662606\pi\) | ||||
−0.488912 | + | 0.872333i | \(0.662606\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | −38.7322 | −1.76604 | ||||||||
\(482\) | −24.7857 | −1.12896 | ||||||||
\(483\) | 8.30010 | 0.377668 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.63332 | −0.346611 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −15.8502 | −0.718243 | −0.359121 | − | 0.933291i | \(-0.616924\pi\) | ||||
−0.359121 | + | 0.933291i | \(0.616924\pi\) | |||||||
\(488\) | −3.92512 | −0.177682 | ||||||||
\(489\) | 11.5480 | 0.522219 | ||||||||
\(490\) | −3.23122 | −0.145971 | ||||||||
\(491\) | −27.6698 | −1.24872 | −0.624360 | − | 0.781137i | \(-0.714640\pi\) | ||||
−0.624360 | + | 0.781137i | \(0.714640\pi\) | |||||||
\(492\) | −1.31979 | −0.0595007 | ||||||||
\(493\) | −2.72681 | −0.122809 | ||||||||
\(494\) | −43.3170 | −1.94892 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.41941 | 0.108635 | ||||||||
\(497\) | −20.3144 | −0.911225 | ||||||||
\(498\) | 8.00000 | 0.358489 | ||||||||
\(499\) | −7.06176 | −0.316128 | −0.158064 | − | 0.987429i | \(-0.550525\pi\) | ||||
−0.158064 | + | 0.987429i | \(0.550525\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −2.95212 | −0.131891 | ||||||||
\(502\) | −17.8615 | −0.797199 | ||||||||
\(503\) | −1.15333 | −0.0514247 | −0.0257123 | − | 0.999669i | \(-0.508185\pi\) | ||||
−0.0257123 | + | 0.999669i | \(0.508185\pi\) | |||||||
\(504\) | 3.19863 | 0.142478 | ||||||||
\(505\) | 15.9739 | 0.710827 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 32.6446 | 1.44980 | ||||||||
\(508\) | 16.2155 | 0.719447 | ||||||||
\(509\) | −8.47539 | −0.375665 | −0.187833 | − | 0.982201i | \(-0.560146\pi\) | ||||
−0.187833 | + | 0.982201i | \(0.560146\pi\) | |||||||
\(510\) | 0.557453 | 0.0246845 | ||||||||
\(511\) | 22.2121 | 0.982607 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −6.41156 | −0.283077 | ||||||||
\(514\) | 4.32237 | 0.190652 | ||||||||
\(515\) | −18.2904 | −0.805971 | ||||||||
\(516\) | 1.32139 | 0.0581708 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −18.3375 | −0.805705 | ||||||||
\(519\) | −1.84140 | −0.0808284 | ||||||||
\(520\) | −6.75608 | −0.296274 | ||||||||
\(521\) | 31.0618 | 1.36084 | 0.680420 | − | 0.732822i | \(-0.261797\pi\) | ||||
0.680420 | + | 0.732822i | \(0.261797\pi\) | |||||||
\(522\) | 4.89154 | 0.214097 | ||||||||
\(523\) | −19.8326 | −0.867217 | −0.433609 | − | 0.901101i | \(-0.642760\pi\) | ||||
−0.433609 | + | 0.901101i | \(0.642760\pi\) | |||||||
\(524\) | −17.2888 | −0.755265 | ||||||||
\(525\) | 3.19863 | 0.139600 | ||||||||
\(526\) | −23.0282 | −1.00408 | ||||||||
\(527\) | −1.34871 | −0.0587506 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.2665 | −0.707240 | ||||||||
\(530\) | 2.43470 | 0.105756 | ||||||||
\(531\) | 10.3262 | 0.448121 | ||||||||
\(532\) | −20.5082 | −0.889142 | ||||||||
\(533\) | −8.91660 | −0.386221 | ||||||||
\(534\) | −13.0775 | −0.565917 | ||||||||
\(535\) | 17.1149 | 0.739942 | ||||||||
\(536\) | 15.1676 | 0.655142 | ||||||||
\(537\) | −18.5623 | −0.801023 | ||||||||
\(538\) | −11.8567 | −0.511178 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.00000 | −0.0430331 | ||||||||
\(541\) | −25.2333 | −1.08486 | −0.542431 | − | 0.840100i | \(-0.682496\pi\) | ||||
−0.542431 | + | 0.840100i | \(0.682496\pi\) | |||||||
\(542\) | −11.4268 | −0.490825 | ||||||||
\(543\) | 9.52786 | 0.408880 | ||||||||
\(544\) | −0.557453 | −0.0239006 | ||||||||
\(545\) | 8.94427 | 0.383131 | ||||||||
\(546\) | 21.6102 | 0.924830 | ||||||||
\(547\) | −13.4900 | −0.576791 | −0.288396 | − | 0.957511i | \(-0.593122\pi\) | ||||
−0.288396 | + | 0.957511i | \(0.593122\pi\) | |||||||
\(548\) | 7.93157 | 0.338820 | ||||||||
\(549\) | −3.92512 | −0.167520 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −31.3624 | −1.33608 | ||||||||
\(552\) | 2.59489 | 0.110446 | ||||||||
\(553\) | −37.3355 | −1.58767 | ||||||||
\(554\) | −15.0384 | −0.638922 | ||||||||
\(555\) | 5.73294 | 0.243350 | ||||||||
\(556\) | 8.21778 | 0.348512 | ||||||||
\(557\) | −38.4550 | −1.62939 | −0.814696 | − | 0.579888i | \(-0.803096\pi\) | ||||
−0.814696 | + | 0.579888i | \(0.803096\pi\) | |||||||
\(558\) | 2.41941 | 0.102422 | ||||||||
\(559\) | 8.92739 | 0.377588 | ||||||||
\(560\) | −3.19863 | −0.135167 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 13.2666 | 0.559620 | ||||||||
\(563\) | 27.8423 | 1.17341 | 0.586706 | − | 0.809800i | \(-0.300425\pi\) | ||||
0.586706 | + | 0.809800i | \(0.300425\pi\) | |||||||
\(564\) | −5.99215 | −0.252315 | ||||||||
\(565\) | −4.81666 | −0.202638 | ||||||||
\(566\) | 15.1214 | 0.635598 | ||||||||
\(567\) | 3.19863 | 0.134330 | ||||||||
\(568\) | −6.35097 | −0.266481 | ||||||||
\(569\) | 8.26209 | 0.346365 | 0.173182 | − | 0.984890i | \(-0.444595\pi\) | ||||
0.173182 | + | 0.984890i | \(0.444595\pi\) | |||||||
\(570\) | 6.41156 | 0.268551 | ||||||||
\(571\) | 6.71079 | 0.280838 | 0.140419 | − | 0.990092i | \(-0.455155\pi\) | ||||
0.140419 | + | 0.990092i | \(0.455155\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.913695 | 0.0381702 | ||||||||
\(574\) | −4.22151 | −0.176202 | ||||||||
\(575\) | 2.59489 | 0.108215 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −39.8137 | −1.65746 | −0.828732 | − | 0.559645i | \(-0.810937\pi\) | ||||
−0.828732 | + | 0.559645i | \(0.810937\pi\) | |||||||
\(578\) | −16.6892 | −0.694181 | ||||||||
\(579\) | −23.2952 | −0.968117 | ||||||||
\(580\) | −4.89154 | −0.203110 | ||||||||
\(581\) | 25.5890 | 1.06161 | ||||||||
\(582\) | 7.63332 | 0.316411 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.94427 | 0.287356 | ||||||||
\(585\) | −6.75608 | −0.279330 | ||||||||
\(586\) | −13.9163 | −0.574876 | ||||||||
\(587\) | −10.0592 | −0.415187 | −0.207593 | − | 0.978215i | \(-0.566563\pi\) | ||||
−0.207593 | + | 0.978215i | \(0.566563\pi\) | |||||||
\(588\) | 3.23122 | 0.133253 | ||||||||
\(589\) | −15.5122 | −0.639167 | ||||||||
\(590\) | −10.3262 | −0.425124 | ||||||||
\(591\) | 24.5896 | 1.01148 | ||||||||
\(592\) | −5.73294 | −0.235622 | ||||||||
\(593\) | 23.6430 | 0.970900 | 0.485450 | − | 0.874264i | \(-0.338656\pi\) | ||||
0.485450 | + | 0.874264i | \(0.338656\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.78309 | 0.0730994 | ||||||||
\(596\) | 6.08532 | 0.249264 | ||||||||
\(597\) | 10.5112 | 0.430194 | ||||||||
\(598\) | 17.5313 | 0.716909 | ||||||||
\(599\) | 31.4007 | 1.28300 | 0.641499 | − | 0.767124i | \(-0.278313\pi\) | ||||
0.641499 | + | 0.767124i | \(0.278313\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −17.1469 | −0.699436 | −0.349718 | − | 0.936855i | \(-0.613723\pi\) | ||||
−0.349718 | + | 0.936855i | \(0.613723\pi\) | |||||||
\(602\) | 4.22662 | 0.172264 | ||||||||
\(603\) | 15.1676 | 0.617674 | ||||||||
\(604\) | −18.2761 | −0.743644 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −15.9739 | −0.648894 | ||||||||
\(607\) | 1.40153 | 0.0568865 | 0.0284433 | − | 0.999595i | \(-0.490945\pi\) | ||||
0.0284433 | + | 0.999595i | \(0.490945\pi\) | |||||||
\(608\) | −6.41156 | −0.260023 | ||||||||
\(609\) | 15.6462 | 0.634017 | ||||||||
\(610\) | 3.92512 | 0.158923 | ||||||||
\(611\) | −40.4834 | −1.63778 | ||||||||
\(612\) | −0.557453 | −0.0225337 | ||||||||
\(613\) | −12.0383 | −0.486223 | −0.243111 | − | 0.969998i | \(-0.578168\pi\) | ||||
−0.243111 | + | 0.969998i | \(0.578168\pi\) | |||||||
\(614\) | 24.0813 | 0.971843 | ||||||||
\(615\) | 1.31979 | 0.0532190 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.25177 | −0.211428 | −0.105714 | − | 0.994397i | \(-0.533713\pi\) | ||||
−0.105714 | + | 0.994397i | \(0.533713\pi\) | |||||||
\(618\) | 18.2904 | 0.735748 | ||||||||
\(619\) | 42.0324 | 1.68942 | 0.844712 | − | 0.535221i | \(-0.179772\pi\) | ||||
0.844712 | + | 0.535221i | \(0.179772\pi\) | |||||||
\(620\) | −2.41941 | −0.0971657 | ||||||||
\(621\) | 2.59489 | 0.104130 | ||||||||
\(622\) | −30.3816 | −1.21819 | ||||||||
\(623\) | −41.8299 | −1.67588 | ||||||||
\(624\) | 6.75608 | 0.270460 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 16.2012 | 0.647531 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.4874 | 0.737729 | ||||||||
\(629\) | 3.19585 | 0.127427 | ||||||||
\(630\) | −3.19863 | −0.127436 | ||||||||
\(631\) | −16.9950 | −0.676561 | −0.338281 | − | 0.941045i | \(-0.609845\pi\) | ||||
−0.338281 | + | 0.941045i | \(0.609845\pi\) | |||||||
\(632\) | −11.6724 | −0.464302 | ||||||||
\(633\) | 7.06863 | 0.280953 | ||||||||
\(634\) | −33.0640 | −1.31314 | ||||||||
\(635\) | −16.2155 | −0.643493 | ||||||||
\(636\) | −2.43470 | −0.0965419 | ||||||||
\(637\) | 21.8304 | 0.864950 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −6.35097 | −0.251241 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −49.9080 | −1.97125 | −0.985624 | − | 0.168954i | \(-0.945961\pi\) | ||||
−0.985624 | + | 0.168954i | \(0.945961\pi\) | |||||||
\(642\) | −17.1149 | −0.675471 | ||||||||
\(643\) | −26.7579 | −1.05523 | −0.527614 | − | 0.849484i | \(-0.676913\pi\) | ||||
−0.527614 | + | 0.849484i | \(0.676913\pi\) | |||||||
\(644\) | 8.30010 | 0.327070 | ||||||||
\(645\) | −1.32139 | −0.0520295 | ||||||||
\(646\) | 3.57414 | 0.140623 | ||||||||
\(647\) | −7.85550 | −0.308832 | −0.154416 | − | 0.988006i | \(-0.549350\pi\) | ||||
−0.154416 | + | 0.988006i | \(0.549350\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 6.75608 | 0.264995 | ||||||||
\(651\) | 7.73878 | 0.303307 | ||||||||
\(652\) | 11.5480 | 0.452255 | ||||||||
\(653\) | 0.290394 | 0.0113640 | 0.00568200 | − | 0.999984i | \(-0.498191\pi\) | ||||
0.00568200 | + | 0.999984i | \(0.498191\pi\) | |||||||
\(654\) | −8.94427 | −0.349749 | ||||||||
\(655\) | 17.2888 | 0.675529 | ||||||||
\(656\) | −1.31979 | −0.0515291 | ||||||||
\(657\) | 6.94427 | 0.270922 | ||||||||
\(658\) | −19.1666 | −0.747194 | ||||||||
\(659\) | 17.7202 | 0.690282 | 0.345141 | − | 0.938551i | \(-0.387831\pi\) | ||||
0.345141 | + | 0.938551i | \(0.387831\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.9494 | 0.892630 | 0.446315 | − | 0.894876i | \(-0.352736\pi\) | ||||
0.446315 | + | 0.894876i | \(0.352736\pi\) | |||||||
\(662\) | −0.733928 | −0.0285249 | ||||||||
\(663\) | −3.76620 | −0.146267 | ||||||||
\(664\) | 8.00000 | 0.310460 | ||||||||
\(665\) | 20.5082 | 0.795273 | ||||||||
\(666\) | −5.73294 | −0.222147 | ||||||||
\(667\) | 12.6930 | 0.491476 | ||||||||
\(668\) | −2.95212 | −0.114221 | ||||||||
\(669\) | 0.801373 | 0.0309829 | ||||||||
\(670\) | −15.1676 | −0.585977 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 3.19863 | 0.123390 | ||||||||
\(673\) | 35.3081 | 1.36103 | 0.680515 | − | 0.732735i | \(-0.261756\pi\) | ||||
0.680515 | + | 0.732735i | \(0.261756\pi\) | |||||||
\(674\) | −16.3816 | −0.630994 | ||||||||
\(675\) | 1.00000 | 0.0384900 | ||||||||
\(676\) | 32.6446 | 1.25556 | ||||||||
\(677\) | 42.2238 | 1.62279 | 0.811397 | − | 0.584496i | \(-0.198708\pi\) | ||||
0.811397 | + | 0.584496i | \(0.198708\pi\) | |||||||
\(678\) | 4.81666 | 0.184983 | ||||||||
\(679\) | 24.4162 | 0.937006 | ||||||||
\(680\) | 0.557453 | 0.0213774 | ||||||||
\(681\) | 4.86939 | 0.186595 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 34.7325 | 1.32900 | 0.664502 | − | 0.747287i | \(-0.268644\pi\) | ||||
0.664502 | + | 0.747287i | \(0.268644\pi\) | |||||||
\(684\) | −6.41156 | −0.245152 | ||||||||
\(685\) | −7.93157 | −0.303050 | ||||||||
\(686\) | −12.0549 | −0.460260 | ||||||||
\(687\) | −1.16119 | −0.0443020 | ||||||||
\(688\) | 1.32139 | 0.0503773 | ||||||||
\(689\) | −16.4490 | −0.626657 | ||||||||
\(690\) | −2.59489 | −0.0987859 | ||||||||
\(691\) | 16.7185 | 0.636002 | 0.318001 | − | 0.948090i | \(-0.396988\pi\) | ||||
0.318001 | + | 0.948090i | \(0.396988\pi\) | |||||||
\(692\) | −1.84140 | −0.0699994 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −16.2012 | −0.614990 | ||||||||
\(695\) | −8.21778 | −0.311718 | ||||||||
\(696\) | 4.89154 | 0.185413 | ||||||||
\(697\) | 0.735720 | 0.0278674 | ||||||||
\(698\) | 4.19604 | 0.158823 | ||||||||
\(699\) | −12.0527 | −0.455876 | ||||||||
\(700\) | 3.19863 | 0.120897 | ||||||||
\(701\) | 0.639577 | 0.0241565 | 0.0120782 | − | 0.999927i | \(-0.496155\pi\) | ||||
0.0120782 | + | 0.999927i | \(0.496155\pi\) | |||||||
\(702\) | 6.75608 | 0.254992 | ||||||||
\(703\) | 36.7571 | 1.38632 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 5.99215 | 0.225677 | ||||||||
\(706\) | 3.32139 | 0.125002 | ||||||||
\(707\) | −51.0944 | −1.92160 | ||||||||
\(708\) | 10.3262 | 0.388084 | ||||||||
\(709\) | 12.6396 | 0.474689 | 0.237345 | − | 0.971426i | \(-0.423723\pi\) | ||||
0.237345 | + | 0.971426i | \(0.423723\pi\) | |||||||
\(710\) | 6.35097 | 0.238348 | ||||||||
\(711\) | −11.6724 | −0.437748 | ||||||||
\(712\) | −13.0775 | −0.490099 | ||||||||
\(713\) | 6.27811 | 0.235117 | ||||||||
\(714\) | −1.78309 | −0.0667303 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.5623 | −0.693706 | ||||||||
\(717\) | 28.2604 | 1.05540 | ||||||||
\(718\) | −22.1803 | −0.827763 | ||||||||
\(719\) | 41.0960 | 1.53262 | 0.766311 | − | 0.642469i | \(-0.222090\pi\) | ||||
0.766311 | + | 0.642469i | \(0.222090\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | 58.5042 | 2.17881 | ||||||||
\(722\) | 22.1080 | 0.822776 | ||||||||
\(723\) | −24.7857 | −0.921789 | ||||||||
\(724\) | 9.52786 | 0.354100 | ||||||||
\(725\) | 4.89154 | 0.181667 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −15.8668 | −0.588467 | −0.294234 | − | 0.955734i | \(-0.595064\pi\) | ||||
−0.294234 | + | 0.955734i | \(0.595064\pi\) | |||||||
\(728\) | 21.6102 | 0.800927 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −6.94427 | −0.257019 | ||||||||
\(731\) | −0.736611 | −0.0272445 | ||||||||
\(732\) | −3.92512 | −0.145077 | ||||||||
\(733\) | −20.7873 | −0.767795 | −0.383898 | − | 0.923376i | \(-0.625418\pi\) | ||||
−0.383898 | + | 0.923376i | \(0.625418\pi\) | |||||||
\(734\) | −17.0497 | −0.629317 | ||||||||
\(735\) | −3.23122 | −0.119185 | ||||||||
\(736\) | 2.59489 | 0.0956491 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −1.31979 | −0.0485821 | ||||||||
\(739\) | 34.6150 | 1.27333 | 0.636667 | − | 0.771139i | \(-0.280312\pi\) | ||||
0.636667 | + | 0.771139i | \(0.280312\pi\) | |||||||
\(740\) | 5.73294 | 0.210747 | ||||||||
\(741\) | −43.3170 | −1.59129 | ||||||||
\(742\) | −7.78768 | −0.285895 | ||||||||
\(743\) | 41.2454 | 1.51315 | 0.756573 | − | 0.653910i | \(-0.226872\pi\) | ||||
0.756573 | + | 0.653910i | \(0.226872\pi\) | |||||||
\(744\) | 2.41941 | 0.0886998 | ||||||||
\(745\) | −6.08532 | −0.222949 | ||||||||
\(746\) | −0.231215 | −0.00846540 | ||||||||
\(747\) | 8.00000 | 0.292705 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −54.7442 | −2.00031 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | 3.35796 | 0.122534 | 0.0612668 | − | 0.998121i | \(-0.480486\pi\) | ||||
0.0612668 | + | 0.998121i | \(0.480486\pi\) | |||||||
\(752\) | −5.99215 | −0.218511 | ||||||||
\(753\) | −17.8615 | −0.650911 | ||||||||
\(754\) | 33.0477 | 1.20352 | ||||||||
\(755\) | 18.2761 | 0.665135 | ||||||||
\(756\) | 3.19863 | 0.116333 | ||||||||
\(757\) | 14.7247 | 0.535177 | 0.267589 | − | 0.963533i | \(-0.413773\pi\) | ||||
0.267589 | + | 0.963533i | \(0.413773\pi\) | |||||||
\(758\) | −11.9723 | −0.434852 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.41156 | 0.232572 | ||||||||
\(761\) | 0.229814 | 0.00833074 | 0.00416537 | − | 0.999991i | \(-0.498674\pi\) | ||||
0.00416537 | + | 0.999991i | \(0.498674\pi\) | |||||||
\(762\) | 16.2155 | 0.587426 | ||||||||
\(763\) | −28.6094 | −1.03573 | ||||||||
\(764\) | 0.913695 | 0.0330563 | ||||||||
\(765\) | 0.557453 | 0.0201548 | ||||||||
\(766\) | 3.07102 | 0.110960 | ||||||||
\(767\) | 69.7649 | 2.51906 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −26.3568 | −0.950451 | −0.475226 | − | 0.879864i | \(-0.657634\pi\) | ||||
−0.475226 | + | 0.879864i | \(0.657634\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.32237 | 0.155666 | ||||||||
\(772\) | −23.2952 | −0.838414 | ||||||||
\(773\) | −54.7575 | −1.96949 | −0.984744 | − | 0.174007i | \(-0.944329\pi\) | ||||
−0.984744 | + | 0.174007i | \(0.944329\pi\) | |||||||
\(774\) | 1.32139 | 0.0474962 | ||||||||
\(775\) | 2.41941 | 0.0869077 | ||||||||
\(776\) | 7.63332 | 0.274020 | ||||||||
\(777\) | −18.3375 | −0.657856 | ||||||||
\(778\) | 19.7569 | 0.708321 | ||||||||
\(779\) | 8.46190 | 0.303179 | ||||||||
\(780\) | −6.75608 | −0.241906 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −1.44653 | −0.0517279 | ||||||||
\(783\) | 4.89154 | 0.174809 | ||||||||
\(784\) | 3.23122 | 0.115401 | ||||||||
\(785\) | −18.4874 | −0.659844 | ||||||||
\(786\) | −17.2888 | −0.616671 | ||||||||
\(787\) | 7.45825 | 0.265858 | 0.132929 | − | 0.991126i | \(-0.457562\pi\) | ||||
0.132929 | + | 0.991126i | \(0.457562\pi\) | |||||||
\(788\) | 24.5896 | 0.875969 | ||||||||
\(789\) | −23.0282 | −0.819825 | ||||||||
\(790\) | 11.6724 | 0.415284 | ||||||||
\(791\) | 15.4067 | 0.547799 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −26.5184 | −0.941697 | ||||||||
\(794\) | −11.4546 | −0.406508 | ||||||||
\(795\) | 2.43470 | 0.0863497 | ||||||||
\(796\) | 10.5112 | 0.372559 | ||||||||
\(797\) | 35.0946 | 1.24311 | 0.621557 | − | 0.783369i | \(-0.286500\pi\) | ||||
0.621557 | + | 0.783369i | \(0.286500\pi\) | |||||||
\(798\) | −20.5082 | −0.725982 | ||||||||
\(799\) | 3.34034 | 0.118173 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −13.0775 | −0.462070 | ||||||||
\(802\) | 22.3001 | 0.787444 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 15.1676 | 0.534921 | ||||||||
\(805\) | −8.30010 | −0.292540 | ||||||||
\(806\) | 16.3457 | 0.575753 | ||||||||
\(807\) | −11.8567 | −0.417375 | ||||||||
\(808\) | −15.9739 | −0.561958 | ||||||||
\(809\) | −22.7625 | −0.800288 | −0.400144 | − | 0.916452i | \(-0.631040\pi\) | ||||
−0.400144 | + | 0.916452i | \(0.631040\pi\) | |||||||
\(810\) | −1.00000 | −0.0351364 | ||||||||
\(811\) | 21.7665 | 0.764326 | 0.382163 | − | 0.924095i | \(-0.375179\pi\) | ||||
0.382163 | + | 0.924095i | \(0.375179\pi\) | |||||||
\(812\) | 15.6462 | 0.549075 | ||||||||
\(813\) | −11.4268 | −0.400757 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.5480 | −0.404509 | ||||||||
\(816\) | −0.557453 | −0.0195148 | ||||||||
\(817\) | −8.47214 | −0.296403 | ||||||||
\(818\) | 36.2811 | 1.26854 | ||||||||
\(819\) | 21.6102 | 0.755121 | ||||||||
\(820\) | 1.31979 | 0.0460890 | ||||||||
\(821\) | 35.5251 | 1.23983 | 0.619917 | − | 0.784668i | \(-0.287166\pi\) | ||||
0.619917 | + | 0.784668i | \(0.287166\pi\) | |||||||
\(822\) | 7.93157 | 0.276645 | ||||||||
\(823\) | 39.6319 | 1.38148 | 0.690741 | − | 0.723102i | \(-0.257284\pi\) | ||||
0.690741 | + | 0.723102i | \(0.257284\pi\) | |||||||
\(824\) | 18.2904 | 0.637176 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 33.0298 | 1.14925 | ||||||||
\(827\) | 17.6236 | 0.612833 | 0.306417 | − | 0.951898i | \(-0.400870\pi\) | ||||
0.306417 | + | 0.951898i | \(0.400870\pi\) | |||||||
\(828\) | 2.59489 | 0.0901788 | ||||||||
\(829\) | 7.04973 | 0.244847 | 0.122424 | − | 0.992478i | \(-0.460933\pi\) | ||||
0.122424 | + | 0.992478i | \(0.460933\pi\) | |||||||
\(830\) | −8.00000 | −0.277684 | ||||||||
\(831\) | −15.0384 | −0.521677 | ||||||||
\(832\) | 6.75608 | 0.234225 | ||||||||
\(833\) | −1.80125 | −0.0624097 | ||||||||
\(834\) | 8.21778 | 0.284558 | ||||||||
\(835\) | 2.95212 | 0.102162 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.41941 | 0.0836269 | ||||||||
\(838\) | 9.06157 | 0.313027 | ||||||||
\(839\) | −22.5599 | −0.778855 | −0.389427 | − | 0.921057i | \(-0.627327\pi\) | ||||
−0.389427 | + | 0.921057i | \(0.627327\pi\) | |||||||
\(840\) | −3.19863 | −0.110363 | ||||||||
\(841\) | −5.07281 | −0.174924 | ||||||||
\(842\) | −2.42586 | −0.0836005 | ||||||||
\(843\) | 13.2666 | 0.456928 | ||||||||
\(844\) | 7.06863 | 0.243312 | ||||||||
\(845\) | −32.6446 | −1.12301 | ||||||||
\(846\) | −5.99215 | −0.206014 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.43470 | −0.0836078 | ||||||||
\(849\) | 15.1214 | 0.518964 | ||||||||
\(850\) | −0.557453 | −0.0191205 | ||||||||
\(851\) | −14.8764 | −0.509956 | ||||||||
\(852\) | −6.35097 | −0.217581 | ||||||||
\(853\) | −18.3884 | −0.629607 | −0.314804 | − | 0.949157i | \(-0.601939\pi\) | ||||
−0.314804 | + | 0.949157i | \(0.601939\pi\) | |||||||
\(854\) | −12.5550 | −0.429623 | ||||||||
\(855\) | 6.41156 | 0.219271 | ||||||||
\(856\) | −17.1149 | −0.584975 | ||||||||
\(857\) | −21.9179 | −0.748700 | −0.374350 | − | 0.927287i | \(-0.622134\pi\) | ||||
−0.374350 | + | 0.927287i | \(0.622134\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −32.0841 | −1.09470 | −0.547348 | − | 0.836905i | \(-0.684363\pi\) | ||||
−0.547348 | + | 0.836905i | \(0.684363\pi\) | |||||||
\(860\) | −1.32139 | −0.0450589 | ||||||||
\(861\) | −4.22151 | −0.143869 | ||||||||
\(862\) | −2.65847 | −0.0905480 | ||||||||
\(863\) | 0.406288 | 0.0138302 | 0.00691511 | − | 0.999976i | \(-0.497799\pi\) | ||||
0.00691511 | + | 0.999976i | \(0.497799\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 1.84140 | 0.0626094 | ||||||||
\(866\) | −19.1918 | −0.652163 | ||||||||
\(867\) | −16.6892 | −0.566796 | ||||||||
\(868\) | 7.73878 | 0.262671 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −4.89154 | −0.165839 | ||||||||
\(871\) | 102.474 | 3.47219 | ||||||||
\(872\) | −8.94427 | −0.302891 | ||||||||
\(873\) | 7.63332 | 0.258349 | ||||||||
\(874\) | −16.6373 | −0.562765 | ||||||||
\(875\) | −3.19863 | −0.108133 | ||||||||
\(876\) | 6.94427 | 0.234625 | ||||||||
\(877\) | 6.38542 | 0.215620 | 0.107810 | − | 0.994172i | \(-0.465616\pi\) | ||||
0.107810 | + | 0.994172i | \(0.465616\pi\) | |||||||
\(878\) | −12.6955 | −0.428452 | ||||||||
\(879\) | −13.9163 | −0.469384 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −39.6551 | −1.33601 | −0.668006 | − | 0.744155i | \(-0.732852\pi\) | ||||
−0.668006 | + | 0.744155i | \(0.732852\pi\) | |||||||
\(882\) | 3.23122 | 0.108801 | ||||||||
\(883\) | −4.90523 | −0.165074 | −0.0825371 | − | 0.996588i | \(-0.526302\pi\) | ||||
−0.0825371 | + | 0.996588i | \(0.526302\pi\) | |||||||
\(884\) | −3.76620 | −0.126671 | ||||||||
\(885\) | −10.3262 | −0.347113 | ||||||||
\(886\) | 16.9189 | 0.568400 | ||||||||
\(887\) | 7.61724 | 0.255762 | 0.127881 | − | 0.991790i | \(-0.459182\pi\) | ||||
0.127881 | + | 0.991790i | \(0.459182\pi\) | |||||||
\(888\) | −5.73294 | −0.192385 | ||||||||
\(889\) | 51.8674 | 1.73958 | ||||||||
\(890\) | 13.0775 | 0.438358 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0.801373 | 0.0268319 | ||||||||
\(893\) | 38.4190 | 1.28564 | ||||||||
\(894\) | 6.08532 | 0.203523 | ||||||||
\(895\) | 18.5623 | 0.620469 | ||||||||
\(896\) | 3.19863 | 0.106859 | ||||||||
\(897\) | 17.5313 | 0.585354 | ||||||||
\(898\) | −19.2809 | −0.643413 | ||||||||
\(899\) | 11.8346 | 0.394707 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 1.35723 | 0.0452159 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.22662 | 0.140653 | ||||||||
\(904\) | 4.81666 | 0.160200 | ||||||||
\(905\) | −9.52786 | −0.316717 | ||||||||
\(906\) | −18.2761 | −0.607183 | ||||||||
\(907\) | −51.7186 | −1.71729 | −0.858645 | − | 0.512571i | \(-0.828693\pi\) | ||||
−0.858645 | + | 0.512571i | \(0.828693\pi\) | |||||||
\(908\) | 4.86939 | 0.161596 | ||||||||
\(909\) | −15.9739 | −0.529820 | ||||||||
\(910\) | −21.6102 | −0.716371 | ||||||||
\(911\) | −32.2012 | −1.06687 | −0.533437 | − | 0.845840i | \(-0.679100\pi\) | ||||
−0.533437 | + | 0.845840i | \(0.679100\pi\) | |||||||
\(912\) | −6.41156 | −0.212308 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −39.5219 | −1.30727 | ||||||||
\(915\) | 3.92512 | 0.129760 | ||||||||
\(916\) | −1.16119 | −0.0383667 | ||||||||
\(917\) | −55.3004 | −1.82618 | ||||||||
\(918\) | −0.557453 | −0.0183987 | ||||||||
\(919\) | 31.5512 | 1.04078 | 0.520389 | − | 0.853929i | \(-0.325787\pi\) | ||||
0.520389 | + | 0.853929i | \(0.325787\pi\) | |||||||
\(920\) | −2.59489 | −0.0855511 | ||||||||
\(921\) | 24.0813 | 0.793507 | ||||||||
\(922\) | −13.8398 | −0.455790 | ||||||||
\(923\) | −42.9077 | −1.41232 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5.73294 | −0.188498 | ||||||||
\(926\) | 12.5919 | 0.413795 | ||||||||
\(927\) | 18.2904 | 0.600735 | ||||||||
\(928\) | 4.89154 | 0.160573 | ||||||||
\(929\) | 26.7857 | 0.878809 | 0.439405 | − | 0.898289i | \(-0.355189\pi\) | ||||
0.439405 | + | 0.898289i | \(0.355189\pi\) | |||||||
\(930\) | −2.41941 | −0.0793355 | ||||||||
\(931\) | −20.7171 | −0.678976 | ||||||||
\(932\) | −12.0527 | −0.394800 | ||||||||
\(933\) | −30.3816 | −0.994647 | ||||||||
\(934\) | −11.7368 | −0.384040 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 6.75608 | 0.220829 | ||||||||
\(937\) | −21.3572 | −0.697710 | −0.348855 | − | 0.937177i | \(-0.613429\pi\) | ||||
−0.348855 | + | 0.937177i | \(0.613429\pi\) | |||||||
\(938\) | 48.5156 | 1.58409 | ||||||||
\(939\) | 16.2012 | 0.528707 | ||||||||
\(940\) | 5.99215 | 0.195442 | ||||||||
\(941\) | −41.5778 | −1.35540 | −0.677699 | − | 0.735340i | \(-0.737023\pi\) | ||||
−0.677699 | + | 0.735340i | \(0.737023\pi\) | |||||||
\(942\) | 18.4874 | 0.602353 | ||||||||
\(943\) | −3.42471 | −0.111524 | ||||||||
\(944\) | 10.3262 | 0.336090 | ||||||||
\(945\) | −3.19863 | −0.104051 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.59847 | 0.279413 | 0.139706 | − | 0.990193i | \(-0.455384\pi\) | ||||
0.139706 | + | 0.990193i | \(0.455384\pi\) | |||||||
\(948\) | −11.6724 | −0.379101 | ||||||||
\(949\) | 46.9161 | 1.52296 | ||||||||
\(950\) | −6.41156 | −0.208018 | ||||||||
\(951\) | −33.0640 | −1.07217 | ||||||||
\(952\) | −1.78309 | −0.0577901 | ||||||||
\(953\) | 5.86067 | 0.189846 | 0.0949229 | − | 0.995485i | \(-0.469740\pi\) | ||||
0.0949229 | + | 0.995485i | \(0.469740\pi\) | |||||||
\(954\) | −2.43470 | −0.0788262 | ||||||||
\(955\) | −0.913695 | −0.0295665 | ||||||||
\(956\) | 28.2604 | 0.914006 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −21.4007 | −0.691425 | ||||||||
\(959\) | 25.3701 | 0.819244 | ||||||||
\(960\) | −1.00000 | −0.0322749 | ||||||||
\(961\) | −25.1465 | −0.811176 | ||||||||
\(962\) | −38.7322 | −1.24878 | ||||||||
\(963\) | −17.1149 | −0.551520 | ||||||||
\(964\) | −24.7857 | −0.798293 | ||||||||
\(965\) | 23.2952 | 0.749901 | ||||||||
\(966\) | 8.30010 | 0.267051 | ||||||||
\(967\) | 24.7496 | 0.795894 | 0.397947 | − | 0.917408i | \(-0.369723\pi\) | ||||
0.397947 | + | 0.917408i | \(0.369723\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.57414 | 0.114818 | ||||||||
\(970\) | −7.63332 | −0.245091 | ||||||||
\(971\) | 43.1418 | 1.38449 | 0.692243 | − | 0.721664i | \(-0.256622\pi\) | ||||
0.692243 | + | 0.721664i | \(0.256622\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 26.2856 | 0.842678 | ||||||||
\(974\) | −15.8502 | −0.507874 | ||||||||
\(975\) | 6.75608 | 0.216368 | ||||||||
\(976\) | −3.92512 | −0.125640 | ||||||||
\(977\) | −42.5522 | −1.36137 | −0.680683 | − | 0.732579i | \(-0.738317\pi\) | ||||
−0.680683 | + | 0.732579i | \(0.738317\pi\) | |||||||
\(978\) | 11.5480 | 0.369264 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −3.23122 | −0.103217 | ||||||||
\(981\) | −8.94427 | −0.285569 | ||||||||
\(982\) | −27.6698 | −0.882978 | ||||||||
\(983\) | 18.3473 | 0.585188 | 0.292594 | − | 0.956237i | \(-0.405482\pi\) | ||||
0.292594 | + | 0.956237i | \(0.405482\pi\) | |||||||
\(984\) | −1.31979 | −0.0420733 | ||||||||
\(985\) | −24.5896 | −0.783491 | ||||||||
\(986\) | −2.72681 | −0.0868392 | ||||||||
\(987\) | −19.1666 | −0.610081 | ||||||||
\(988\) | −43.3170 | −1.37810 | ||||||||
\(989\) | 3.42886 | 0.109031 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.48883 | 0.0472941 | 0.0236471 | − | 0.999720i | \(-0.492472\pi\) | ||||
0.0236471 | + | 0.999720i | \(0.492472\pi\) | |||||||
\(992\) | 2.41941 | 0.0768162 | ||||||||
\(993\) | −0.733928 | −0.0232905 | ||||||||
\(994\) | −20.3144 | −0.644334 | ||||||||
\(995\) | −10.5112 | −0.333227 | ||||||||
\(996\) | 8.00000 | 0.253490 | ||||||||
\(997\) | 55.9405 | 1.77165 | 0.885826 | − | 0.464017i | \(-0.153592\pi\) | ||||
0.885826 | + | 0.464017i | \(0.153592\pi\) | |||||||
\(998\) | −7.06176 | −0.223536 | ||||||||
\(999\) | −5.73294 | −0.181382 |
(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 | 3630.2.a.bs.1.3 | 4 | ||
11.7 | odd | 10 | 330.2.m.f.181.2 | yes | 8 | ||
11.8 | odd | 10 | 330.2.m.f.31.2 | ✓ | 8 | ||
11.10 | odd | 2 | 3630.2.a.bq.1.2 | 4 | |||
33.8 | even | 10 | 990.2.n.i.361.2 | 8 | |||
33.29 | even | 10 | 990.2.n.i.181.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
330.2.m.f.31.2 | ✓ | 8 | 11.8 | odd | 10 | ||
330.2.m.f.181.2 | yes | 8 | 11.7 | odd | 10 | ||
990.2.n.i.181.2 | 8 | 33.29 | even | 10 | |||
990.2.n.i.361.2 | 8 | 33.8 | even | 10 | |||
3630.2.a.bq.1.2 | 4 | 11.10 | odd | 2 | |||
3630.2.a.bs.1.3 | 4 | 1.1 | even | 1 | trivial |