Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1805,2,Mod(1,1805)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1805, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1805.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1805 = 5 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1805.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: | \(14.4129975648\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.7168.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 6x^{2} + 7 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(2.10100\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1805.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.10100 | 1.48563 | 0.742817 | − | 0.669495i | \(-0.233489\pi\) | ||||
0.742817 | + | 0.669495i | \(0.233489\pi\) | |||||||
\(3\) | −2.97127 | −1.71546 | −0.857731 | − | 0.514099i | \(-0.828126\pi\) | ||||
−0.857731 | + | 0.514099i | \(0.828126\pi\) | |||||||
\(4\) | 2.41421 | 1.20711 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −6.24264 | −2.54855 | ||||||||
\(7\) | 4.82843 | 1.82497 | 0.912487 | − | 0.409106i | \(-0.134159\pi\) | ||||
0.912487 | + | 0.409106i | \(0.134159\pi\) | |||||||
\(8\) | 0.870264 | 0.307685 | ||||||||
\(9\) | 5.82843 | 1.94281 | ||||||||
\(10\) | 2.10100 | 0.664395 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −7.17327 | −2.07075 | ||||||||
\(13\) | 1.23074 | 0.341346 | 0.170673 | − | 0.985328i | \(-0.445406\pi\) | ||||
0.170673 | + | 0.985328i | \(0.445406\pi\) | |||||||
\(14\) | 10.1445 | 2.71124 | ||||||||
\(15\) | −2.97127 | −0.767178 | ||||||||
\(16\) | −3.00000 | −0.750000 | ||||||||
\(17\) | −3.65685 | −0.886917 | −0.443459 | − | 0.896295i | \(-0.646249\pi\) | ||||
−0.443459 | + | 0.896295i | \(0.646249\pi\) | |||||||
\(18\) | 12.2455 | 2.88630 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 2.41421 | 0.539835 | ||||||||
\(21\) | −14.3465 | −3.13067 | ||||||||
\(22\) | 4.20201 | 0.895871 | ||||||||
\(23\) | 4.82843 | 1.00680 | 0.503398 | − | 0.864054i | \(-0.332083\pi\) | ||||
0.503398 | + | 0.864054i | \(0.332083\pi\) | |||||||
\(24\) | −2.58579 | −0.527821 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.58579 | 0.507114 | ||||||||
\(27\) | −8.40401 | −1.61735 | ||||||||
\(28\) | 11.6569 | 2.20294 | ||||||||
\(29\) | 2.46148 | 0.457085 | 0.228543 | − | 0.973534i | \(-0.426604\pi\) | ||||
0.228543 | + | 0.973534i | \(0.426604\pi\) | |||||||
\(30\) | −6.24264 | −1.13975 | ||||||||
\(31\) | −5.94253 | −1.06731 | −0.533655 | − | 0.845702i | \(-0.679182\pi\) | ||||
−0.533655 | + | 0.845702i | \(0.679182\pi\) | |||||||
\(32\) | −8.04354 | −1.42191 | ||||||||
\(33\) | −5.94253 | −1.03446 | ||||||||
\(34\) | −7.68306 | −1.31763 | ||||||||
\(35\) | 4.82843 | 0.816153 | ||||||||
\(36\) | 14.0711 | 2.34518 | ||||||||
\(37\) | 7.17327 | 1.17928 | 0.589639 | − | 0.807667i | \(-0.299270\pi\) | ||||
0.589639 | + | 0.807667i | \(0.299270\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.65685 | −0.585565 | ||||||||
\(40\) | 0.870264 | 0.137601 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | −30.1421 | −4.65103 | ||||||||
\(43\) | 0.828427 | 0.126334 | 0.0631670 | − | 0.998003i | \(-0.479880\pi\) | ||||
0.0631670 | + | 0.998003i | \(0.479880\pi\) | |||||||
\(44\) | 4.82843 | 0.727913 | ||||||||
\(45\) | 5.82843 | 0.868851 | ||||||||
\(46\) | 10.1445 | 1.49573 | ||||||||
\(47\) | −6.48528 | −0.945976 | −0.472988 | − | 0.881069i | \(-0.656825\pi\) | ||||
−0.472988 | + | 0.881069i | \(0.656825\pi\) | |||||||
\(48\) | 8.91380 | 1.28660 | ||||||||
\(49\) | 16.3137 | 2.33053 | ||||||||
\(50\) | 2.10100 | 0.297127 | ||||||||
\(51\) | 10.8655 | 1.52147 | ||||||||
\(52\) | 2.97127 | 0.412041 | ||||||||
\(53\) | 4.71179 | 0.647215 | 0.323607 | − | 0.946191i | \(-0.395104\pi\) | ||||
0.323607 | + | 0.946191i | \(0.395104\pi\) | |||||||
\(54\) | −17.6569 | −2.40279 | ||||||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 4.20201 | 0.561517 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.17157 | 0.679061 | ||||||||
\(59\) | 11.8851 | 1.54730 | 0.773652 | − | 0.633611i | \(-0.218428\pi\) | ||||
0.773652 | + | 0.633611i | \(0.218428\pi\) | |||||||
\(60\) | −7.17327 | −0.926066 | ||||||||
\(61\) | 2.82843 | 0.362143 | 0.181071 | − | 0.983470i | \(-0.442043\pi\) | ||||
0.181071 | + | 0.983470i | \(0.442043\pi\) | |||||||
\(62\) | −12.4853 | −1.58563 | ||||||||
\(63\) | 28.1421 | 3.54558 | ||||||||
\(64\) | −10.8995 | −1.36244 | ||||||||
\(65\) | 1.23074 | 0.152654 | ||||||||
\(66\) | −12.4853 | −1.53683 | ||||||||
\(67\) | 5.43275 | 0.663715 | 0.331858 | − | 0.943329i | \(-0.392325\pi\) | ||||
0.331858 | + | 0.943329i | \(0.392325\pi\) | |||||||
\(68\) | −8.82843 | −1.07060 | ||||||||
\(69\) | −14.3465 | −1.72712 | ||||||||
\(70\) | 10.1445 | 1.21250 | ||||||||
\(71\) | 10.8655 | 1.28950 | 0.644748 | − | 0.764395i | \(-0.276962\pi\) | ||||
0.644748 | + | 0.764395i | \(0.276962\pi\) | |||||||
\(72\) | 5.07227 | 0.597773 | ||||||||
\(73\) | −0.343146 | −0.0401622 | −0.0200811 | − | 0.999798i | \(-0.506392\pi\) | ||||
−0.0200811 | + | 0.999798i | \(0.506392\pi\) | |||||||
\(74\) | 15.0711 | 1.75198 | ||||||||
\(75\) | −2.97127 | −0.343092 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.65685 | 1.10050 | ||||||||
\(78\) | −7.68306 | −0.869935 | ||||||||
\(79\) | −11.8851 | −1.33717 | −0.668587 | − | 0.743634i | \(-0.733101\pi\) | ||||
−0.668587 | + | 0.743634i | \(0.733101\pi\) | |||||||
\(80\) | −3.00000 | −0.335410 | ||||||||
\(81\) | 7.48528 | 0.831698 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.17157 | 0.348125 | 0.174063 | − | 0.984735i | \(-0.444310\pi\) | ||||
0.174063 | + | 0.984735i | \(0.444310\pi\) | |||||||
\(84\) | −34.6356 | −3.77906 | ||||||||
\(85\) | −3.65685 | −0.396642 | ||||||||
\(86\) | 1.74053 | 0.187686 | ||||||||
\(87\) | −7.31371 | −0.784112 | ||||||||
\(88\) | 1.74053 | 0.185541 | ||||||||
\(89\) | 9.42359 | 0.998898 | 0.499449 | − | 0.866343i | \(-0.333536\pi\) | ||||
0.499449 | + | 0.866343i | \(0.333536\pi\) | |||||||
\(90\) | 12.2455 | 1.29079 | ||||||||
\(91\) | 5.94253 | 0.622947 | ||||||||
\(92\) | 11.6569 | 1.21531 | ||||||||
\(93\) | 17.6569 | 1.83093 | ||||||||
\(94\) | −13.6256 | −1.40537 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 23.8995 | 2.43923 | ||||||||
\(97\) | 1.23074 | 0.124963 | 0.0624813 | − | 0.998046i | \(-0.480099\pi\) | ||||
0.0624813 | + | 0.998046i | \(0.480099\pi\) | |||||||
\(98\) | 34.2752 | 3.46231 | ||||||||
\(99\) | 11.6569 | 1.17156 | ||||||||
\(100\) | 2.41421 | 0.241421 | ||||||||
\(101\) | −16.4853 | −1.64035 | −0.820173 | − | 0.572115i | \(-0.806123\pi\) | ||||
−0.820173 | + | 0.572115i | \(0.806123\pi\) | |||||||
\(102\) | 22.8284 | 2.26035 | ||||||||
\(103\) | 8.91380 | 0.878303 | 0.439151 | − | 0.898413i | \(-0.355279\pi\) | ||||
0.439151 | + | 0.898413i | \(0.355279\pi\) | |||||||
\(104\) | 1.07107 | 0.105027 | ||||||||
\(105\) | −14.3465 | −1.40008 | ||||||||
\(106\) | 9.89949 | 0.961524 | ||||||||
\(107\) | 6.45232 | 0.623770 | 0.311885 | − | 0.950120i | \(-0.399040\pi\) | ||||
0.311885 | + | 0.950120i | \(0.399040\pi\) | |||||||
\(108\) | −20.2891 | −1.95232 | ||||||||
\(109\) | −19.2695 | −1.84568 | −0.922842 | − | 0.385179i | \(-0.874140\pi\) | ||||
−0.922842 | + | 0.385179i | \(0.874140\pi\) | |||||||
\(110\) | 4.20201 | 0.400646 | ||||||||
\(111\) | −21.3137 | −2.02301 | ||||||||
\(112\) | −14.4853 | −1.36873 | ||||||||
\(113\) | −9.63475 | −0.906361 | −0.453181 | − | 0.891419i | \(-0.649711\pi\) | ||||
−0.453181 | + | 0.891419i | \(0.649711\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.82843 | 0.450253 | ||||||||
\(116\) | 5.94253 | 0.551750 | ||||||||
\(117\) | 7.17327 | 0.663169 | ||||||||
\(118\) | 24.9706 | 2.29873 | ||||||||
\(119\) | −17.6569 | −1.61860 | ||||||||
\(120\) | −2.58579 | −0.236049 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 5.94253 | 0.538012 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.3465 | −1.28836 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 59.1267 | 5.26743 | ||||||||
\(127\) | 12.3949 | 1.09987 | 0.549933 | − | 0.835209i | \(-0.314653\pi\) | ||||
0.549933 | + | 0.835209i | \(0.314653\pi\) | |||||||
\(128\) | −6.81280 | −0.602172 | ||||||||
\(129\) | −2.46148 | −0.216721 | ||||||||
\(130\) | 2.58579 | 0.226788 | ||||||||
\(131\) | −7.31371 | −0.639002 | −0.319501 | − | 0.947586i | \(-0.603515\pi\) | ||||
−0.319501 | + | 0.947586i | \(0.603515\pi\) | |||||||
\(132\) | −14.3465 | −1.24871 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 11.4142 | 0.986038 | ||||||||
\(135\) | −8.40401 | −0.723302 | ||||||||
\(136\) | −3.18243 | −0.272891 | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | −30.1421 | −2.56587 | ||||||||
\(139\) | 8.34315 | 0.707656 | 0.353828 | − | 0.935310i | \(-0.384880\pi\) | ||||
0.353828 | + | 0.935310i | \(0.384880\pi\) | |||||||
\(140\) | 11.6569 | 0.985184 | ||||||||
\(141\) | 19.2695 | 1.62278 | ||||||||
\(142\) | 22.8284 | 1.91572 | ||||||||
\(143\) | 2.46148 | 0.205839 | ||||||||
\(144\) | −17.4853 | −1.45711 | ||||||||
\(145\) | 2.46148 | 0.204415 | ||||||||
\(146\) | −0.720950 | −0.0596663 | ||||||||
\(147\) | −48.4724 | −3.99793 | ||||||||
\(148\) | 17.3178 | 1.42352 | ||||||||
\(149\) | −9.17157 | −0.751365 | −0.375682 | − | 0.926749i | \(-0.622592\pi\) | ||||
−0.375682 | + | 0.926749i | \(0.622592\pi\) | |||||||
\(150\) | −6.24264 | −0.509709 | ||||||||
\(151\) | 17.8276 | 1.45079 | 0.725395 | − | 0.688333i | \(-0.241657\pi\) | ||||
0.725395 | + | 0.688333i | \(0.241657\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −21.3137 | −1.72311 | ||||||||
\(154\) | 20.2891 | 1.63494 | ||||||||
\(155\) | −5.94253 | −0.477316 | ||||||||
\(156\) | −8.82843 | −0.706840 | ||||||||
\(157\) | 18.0000 | 1.43656 | 0.718278 | − | 0.695756i | \(-0.244931\pi\) | ||||
0.718278 | + | 0.695756i | \(0.244931\pi\) | |||||||
\(158\) | −24.9706 | −1.98655 | ||||||||
\(159\) | −14.0000 | −1.11027 | ||||||||
\(160\) | −8.04354 | −0.635897 | ||||||||
\(161\) | 23.3137 | 1.83738 | ||||||||
\(162\) | 15.7266 | 1.23560 | ||||||||
\(163\) | 12.8284 | 1.00480 | 0.502400 | − | 0.864635i | \(-0.332451\pi\) | ||||
0.502400 | + | 0.864635i | \(0.332451\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −5.94253 | −0.462626 | ||||||||
\(166\) | 6.66348 | 0.517187 | ||||||||
\(167\) | −22.2408 | −1.72104 | −0.860521 | − | 0.509415i | \(-0.829862\pi\) | ||||
−0.860521 | + | 0.509415i | \(0.829862\pi\) | |||||||
\(168\) | −12.4853 | −0.963260 | ||||||||
\(169\) | −11.4853 | −0.883483 | ||||||||
\(170\) | −7.68306 | −0.589264 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.00000 | 0.152499 | ||||||||
\(173\) | −13.1158 | −0.997176 | −0.498588 | − | 0.866839i | \(-0.666148\pi\) | ||||
−0.498588 | + | 0.866839i | \(0.666148\pi\) | |||||||
\(174\) | −15.3661 | −1.16490 | ||||||||
\(175\) | 4.82843 | 0.364995 | ||||||||
\(176\) | −6.00000 | −0.452267 | ||||||||
\(177\) | −35.3137 | −2.65434 | ||||||||
\(178\) | 19.7990 | 1.48400 | ||||||||
\(179\) | 4.92296 | 0.367959 | 0.183980 | − | 0.982930i | \(-0.441102\pi\) | ||||
0.183980 | + | 0.982930i | \(0.441102\pi\) | |||||||
\(180\) | 14.0711 | 1.04880 | ||||||||
\(181\) | −16.8080 | −1.24933 | −0.624665 | − | 0.780893i | \(-0.714765\pi\) | ||||
−0.624665 | + | 0.780893i | \(0.714765\pi\) | |||||||
\(182\) | 12.4853 | 0.925471 | ||||||||
\(183\) | −8.40401 | −0.621242 | ||||||||
\(184\) | 4.20201 | 0.309776 | ||||||||
\(185\) | 7.17327 | 0.527390 | ||||||||
\(186\) | 37.0971 | 2.72009 | ||||||||
\(187\) | −7.31371 | −0.534831 | ||||||||
\(188\) | −15.6569 | −1.14189 | ||||||||
\(189\) | −40.5782 | −2.95163 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −13.6569 | −0.988175 | −0.494088 | − | 0.869412i | \(-0.664498\pi\) | ||||
−0.494088 | + | 0.869412i | \(0.664498\pi\) | |||||||
\(192\) | 32.3853 | 2.33721 | ||||||||
\(193\) | 8.19285 | 0.589734 | 0.294867 | − | 0.955538i | \(-0.404725\pi\) | ||||
0.294867 | + | 0.955538i | \(0.404725\pi\) | |||||||
\(194\) | 2.58579 | 0.185649 | ||||||||
\(195\) | −3.65685 | −0.261873 | ||||||||
\(196\) | 39.3848 | 2.81320 | ||||||||
\(197\) | −13.3137 | −0.948562 | −0.474281 | − | 0.880373i | \(-0.657292\pi\) | ||||
−0.474281 | + | 0.880373i | \(0.657292\pi\) | |||||||
\(198\) | 24.4911 | 1.74051 | ||||||||
\(199\) | −4.00000 | −0.283552 | −0.141776 | − | 0.989899i | \(-0.545281\pi\) | ||||
−0.141776 | + | 0.989899i | \(0.545281\pi\) | |||||||
\(200\) | 0.870264 | 0.0615370 | ||||||||
\(201\) | −16.1421 | −1.13858 | ||||||||
\(202\) | −34.6356 | −2.43695 | ||||||||
\(203\) | 11.8851 | 0.834168 | ||||||||
\(204\) | 26.2316 | 1.83658 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 18.7279 | 1.30484 | ||||||||
\(207\) | 28.1421 | 1.95601 | ||||||||
\(208\) | −3.69222 | −0.256009 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −30.1421 | −2.08000 | ||||||||
\(211\) | −10.8655 | −0.748011 | −0.374006 | − | 0.927426i | \(-0.622016\pi\) | ||||
−0.374006 | + | 0.927426i | \(0.622016\pi\) | |||||||
\(212\) | 11.3753 | 0.781257 | ||||||||
\(213\) | −32.2843 | −2.21208 | ||||||||
\(214\) | 13.5563 | 0.926693 | ||||||||
\(215\) | 0.828427 | 0.0564983 | ||||||||
\(216\) | −7.31371 | −0.497635 | ||||||||
\(217\) | −28.6931 | −1.94781 | ||||||||
\(218\) | −40.4853 | −2.74201 | ||||||||
\(219\) | 1.01958 | 0.0688967 | ||||||||
\(220\) | 4.82843 | 0.325532 | ||||||||
\(221\) | −4.50063 | −0.302745 | ||||||||
\(222\) | −44.7802 | −3.00545 | ||||||||
\(223\) | −17.3178 | −1.15969 | −0.579843 | − | 0.814728i | \(-0.696886\pi\) | ||||
−0.579843 | + | 0.814728i | \(0.696886\pi\) | |||||||
\(224\) | −38.8376 | −2.59495 | ||||||||
\(225\) | 5.82843 | 0.388562 | ||||||||
\(226\) | −20.2426 | −1.34652 | ||||||||
\(227\) | −22.2408 | −1.47617 | −0.738086 | − | 0.674707i | \(-0.764270\pi\) | ||||
−0.738086 | + | 0.674707i | \(0.764270\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4853 | 0.825051 | 0.412525 | − | 0.910946i | \(-0.364647\pi\) | ||||
0.412525 | + | 0.910946i | \(0.364647\pi\) | |||||||
\(230\) | 10.1445 | 0.668911 | ||||||||
\(231\) | −28.6931 | −1.88787 | ||||||||
\(232\) | 2.14214 | 0.140638 | ||||||||
\(233\) | 13.3137 | 0.872210 | 0.436105 | − | 0.899896i | \(-0.356358\pi\) | ||||
0.436105 | + | 0.899896i | \(0.356358\pi\) | |||||||
\(234\) | 15.0711 | 0.985227 | ||||||||
\(235\) | −6.48528 | −0.423053 | ||||||||
\(236\) | 28.6931 | 1.86776 | ||||||||
\(237\) | 35.3137 | 2.29387 | ||||||||
\(238\) | −37.0971 | −2.40465 | ||||||||
\(239\) | −1.65685 | −0.107173 | −0.0535865 | − | 0.998563i | \(-0.517065\pi\) | ||||
−0.0535865 | + | 0.998563i | \(0.517065\pi\) | |||||||
\(240\) | 8.91380 | 0.575383 | ||||||||
\(241\) | −6.96211 | −0.448469 | −0.224235 | − | 0.974535i | \(-0.571988\pi\) | ||||
−0.224235 | + | 0.974535i | \(0.571988\pi\) | |||||||
\(242\) | −14.7070 | −0.945403 | ||||||||
\(243\) | 2.97127 | 0.190607 | ||||||||
\(244\) | 6.82843 | 0.437145 | ||||||||
\(245\) | 16.3137 | 1.04224 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −5.17157 | −0.328395 | ||||||||
\(249\) | −9.42359 | −0.597196 | ||||||||
\(250\) | 2.10100 | 0.132879 | ||||||||
\(251\) | −12.9706 | −0.818695 | −0.409347 | − | 0.912379i | \(-0.634244\pi\) | ||||
−0.409347 | + | 0.912379i | \(0.634244\pi\) | |||||||
\(252\) | 67.9411 | 4.27989 | ||||||||
\(253\) | 9.65685 | 0.607121 | ||||||||
\(254\) | 26.0416 | 1.63400 | ||||||||
\(255\) | 10.8655 | 0.680423 | ||||||||
\(256\) | 7.48528 | 0.467830 | ||||||||
\(257\) | −8.19285 | −0.511056 | −0.255528 | − | 0.966802i | \(-0.582249\pi\) | ||||
−0.255528 | + | 0.966802i | \(0.582249\pi\) | |||||||
\(258\) | −5.17157 | −0.321968 | ||||||||
\(259\) | 34.6356 | 2.15215 | ||||||||
\(260\) | 2.97127 | 0.184270 | ||||||||
\(261\) | 14.3465 | 0.888029 | ||||||||
\(262\) | −15.3661 | −0.949322 | ||||||||
\(263\) | 12.1421 | 0.748716 | 0.374358 | − | 0.927284i | \(-0.377863\pi\) | ||||
0.374358 | + | 0.927284i | \(0.377863\pi\) | |||||||
\(264\) | −5.17157 | −0.318288 | ||||||||
\(265\) | 4.71179 | 0.289443 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −28.0000 | −1.71357 | ||||||||
\(268\) | 13.1158 | 0.801175 | ||||||||
\(269\) | 2.46148 | 0.150079 | 0.0750395 | − | 0.997181i | \(-0.476092\pi\) | ||||
0.0750395 | + | 0.997181i | \(0.476092\pi\) | |||||||
\(270\) | −17.6569 | −1.07456 | ||||||||
\(271\) | −2.97056 | −0.180449 | −0.0902244 | − | 0.995921i | \(-0.528758\pi\) | ||||
−0.0902244 | + | 0.995921i | \(0.528758\pi\) | |||||||
\(272\) | 10.9706 | 0.665188 | ||||||||
\(273\) | −17.6569 | −1.06864 | ||||||||
\(274\) | −4.20201 | −0.253852 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | −34.6356 | −2.08482 | ||||||||
\(277\) | 5.31371 | 0.319270 | 0.159635 | − | 0.987176i | \(-0.448968\pi\) | ||||
0.159635 | + | 0.987176i | \(0.448968\pi\) | |||||||
\(278\) | 17.5290 | 1.05132 | ||||||||
\(279\) | −34.6356 | −2.07358 | ||||||||
\(280\) | 4.20201 | 0.251118 | ||||||||
\(281\) | −23.7701 | −1.41801 | −0.709004 | − | 0.705205i | \(-0.750855\pi\) | ||||
−0.709004 | + | 0.705205i | \(0.750855\pi\) | |||||||
\(282\) | 40.4853 | 2.41086 | ||||||||
\(283\) | 29.7990 | 1.77137 | 0.885683 | − | 0.464290i | \(-0.153691\pi\) | ||||
0.885683 | + | 0.464290i | \(0.153691\pi\) | |||||||
\(284\) | 26.2316 | 1.55656 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.17157 | 0.305802 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −46.8812 | −2.76250 | ||||||||
\(289\) | −3.62742 | −0.213377 | ||||||||
\(290\) | 5.17157 | 0.303685 | ||||||||
\(291\) | −3.65685 | −0.214369 | ||||||||
\(292\) | −0.828427 | −0.0484800 | ||||||||
\(293\) | −12.0962 | −0.706669 | −0.353335 | − | 0.935497i | \(-0.614952\pi\) | ||||
−0.353335 | + | 0.935497i | \(0.614952\pi\) | |||||||
\(294\) | −101.841 | −5.93947 | ||||||||
\(295\) | 11.8851 | 0.691975 | ||||||||
\(296\) | 6.24264 | 0.362846 | ||||||||
\(297\) | −16.8080 | −0.975300 | ||||||||
\(298\) | −19.2695 | −1.11625 | ||||||||
\(299\) | 5.94253 | 0.343666 | ||||||||
\(300\) | −7.17327 | −0.414149 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 37.4558 | 2.15534 | ||||||||
\(303\) | 48.9822 | 2.81395 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.82843 | 0.161955 | ||||||||
\(306\) | −44.7802 | −2.55991 | ||||||||
\(307\) | 11.3753 | 0.649221 | 0.324611 | − | 0.945848i | \(-0.394767\pi\) | ||||
0.324611 | + | 0.945848i | \(0.394767\pi\) | |||||||
\(308\) | 23.3137 | 1.32842 | ||||||||
\(309\) | −26.4853 | −1.50670 | ||||||||
\(310\) | −12.4853 | −0.709116 | ||||||||
\(311\) | −31.6569 | −1.79510 | −0.897548 | − | 0.440917i | \(-0.854653\pi\) | ||||
−0.897548 | + | 0.440917i | \(0.854653\pi\) | |||||||
\(312\) | −3.18243 | −0.180170 | ||||||||
\(313\) | −20.6274 | −1.16593 | −0.582965 | − | 0.812497i | \(-0.698108\pi\) | ||||
−0.582965 | + | 0.812497i | \(0.698108\pi\) | |||||||
\(314\) | 37.8181 | 2.13420 | ||||||||
\(315\) | 28.1421 | 1.58563 | ||||||||
\(316\) | −28.6931 | −1.61411 | ||||||||
\(317\) | −15.5773 | −0.874907 | −0.437454 | − | 0.899241i | \(-0.644120\pi\) | ||||
−0.437454 | + | 0.899241i | \(0.644120\pi\) | |||||||
\(318\) | −29.4140 | −1.64946 | ||||||||
\(319\) | 4.92296 | 0.275633 | ||||||||
\(320\) | −10.8995 | −0.609300 | ||||||||
\(321\) | −19.1716 | −1.07005 | ||||||||
\(322\) | 48.9822 | 2.72967 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 18.0711 | 1.00395 | ||||||||
\(325\) | 1.23074 | 0.0682691 | ||||||||
\(326\) | 26.9526 | 1.49276 | ||||||||
\(327\) | 57.2548 | 3.16620 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.3137 | −1.72638 | ||||||||
\(330\) | −12.4853 | −0.687292 | ||||||||
\(331\) | 29.7127 | 1.63316 | 0.816578 | − | 0.577235i | \(-0.195868\pi\) | ||||
0.816578 | + | 0.577235i | \(0.195868\pi\) | |||||||
\(332\) | 7.65685 | 0.420224 | ||||||||
\(333\) | 41.8089 | 2.29111 | ||||||||
\(334\) | −46.7279 | −2.55684 | ||||||||
\(335\) | 5.43275 | 0.296823 | ||||||||
\(336\) | 43.0396 | 2.34800 | ||||||||
\(337\) | 30.9434 | 1.68559 | 0.842797 | − | 0.538231i | \(-0.180907\pi\) | ||||
0.842797 | + | 0.538231i | \(0.180907\pi\) | |||||||
\(338\) | −24.1306 | −1.31253 | ||||||||
\(339\) | 28.6274 | 1.55483 | ||||||||
\(340\) | −8.82843 | −0.478789 | ||||||||
\(341\) | −11.8851 | −0.643612 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 44.9706 | 2.42818 | ||||||||
\(344\) | 0.720950 | 0.0388710 | ||||||||
\(345\) | −14.3465 | −0.772392 | ||||||||
\(346\) | −27.5563 | −1.48144 | ||||||||
\(347\) | 24.8284 | 1.33286 | 0.666430 | − | 0.745568i | \(-0.267822\pi\) | ||||
0.666430 | + | 0.745568i | \(0.267822\pi\) | |||||||
\(348\) | −17.6569 | −0.946507 | ||||||||
\(349\) | −6.68629 | −0.357909 | −0.178954 | − | 0.983857i | \(-0.557271\pi\) | ||||
−0.178954 | + | 0.983857i | \(0.557271\pi\) | |||||||
\(350\) | 10.1445 | 0.542248 | ||||||||
\(351\) | −10.3431 | −0.552076 | ||||||||
\(352\) | −16.0871 | −0.857444 | ||||||||
\(353\) | −3.65685 | −0.194635 | −0.0973174 | − | 0.995253i | \(-0.531026\pi\) | ||||
−0.0973174 | + | 0.995253i | \(0.531026\pi\) | |||||||
\(354\) | −74.1942 | −3.94338 | ||||||||
\(355\) | 10.8655 | 0.576680 | ||||||||
\(356\) | 22.7506 | 1.20578 | ||||||||
\(357\) | 52.4632 | 2.77665 | ||||||||
\(358\) | 10.3431 | 0.546652 | ||||||||
\(359\) | −25.3137 | −1.33601 | −0.668003 | − | 0.744158i | \(-0.732851\pi\) | ||||
−0.668003 | + | 0.744158i | \(0.732851\pi\) | |||||||
\(360\) | 5.07227 | 0.267332 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −35.3137 | −1.85605 | ||||||||
\(363\) | 20.7989 | 1.09166 | ||||||||
\(364\) | 14.3465 | 0.751963 | ||||||||
\(365\) | −0.343146 | −0.0179611 | ||||||||
\(366\) | −17.6569 | −0.922939 | ||||||||
\(367\) | 8.82843 | 0.460840 | 0.230420 | − | 0.973091i | \(-0.425990\pi\) | ||||
0.230420 | + | 0.973091i | \(0.425990\pi\) | |||||||
\(368\) | −14.4853 | −0.755097 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 15.0711 | 0.783508 | ||||||||
\(371\) | 22.7506 | 1.18115 | ||||||||
\(372\) | 42.6274 | 2.21013 | ||||||||
\(373\) | −23.9813 | −1.24170 | −0.620852 | − | 0.783928i | \(-0.713213\pi\) | ||||
−0.620852 | + | 0.783928i | \(0.713213\pi\) | |||||||
\(374\) | −15.3661 | −0.794563 | ||||||||
\(375\) | −2.97127 | −0.153436 | ||||||||
\(376\) | −5.64391 | −0.291062 | ||||||||
\(377\) | 3.02944 | 0.156024 | ||||||||
\(378\) | −85.2548 | −4.38504 | ||||||||
\(379\) | −4.92296 | −0.252875 | −0.126438 | − | 0.991975i | \(-0.540354\pi\) | ||||
−0.126438 | + | 0.991975i | \(0.540354\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −36.8284 | −1.88678 | ||||||||
\(382\) | −28.6931 | −1.46807 | ||||||||
\(383\) | 12.8172 | 0.654927 | 0.327464 | − | 0.944864i | \(-0.393806\pi\) | ||||
0.327464 | + | 0.944864i | \(0.393806\pi\) | |||||||
\(384\) | 20.2426 | 1.03300 | ||||||||
\(385\) | 9.65685 | 0.492159 | ||||||||
\(386\) | 17.2132 | 0.876129 | ||||||||
\(387\) | 4.82843 | 0.245443 | ||||||||
\(388\) | 2.97127 | 0.150843 | ||||||||
\(389\) | 24.6274 | 1.24866 | 0.624330 | − | 0.781161i | \(-0.285372\pi\) | ||||
0.624330 | + | 0.781161i | \(0.285372\pi\) | |||||||
\(390\) | −7.68306 | −0.389047 | ||||||||
\(391\) | −17.6569 | −0.892946 | ||||||||
\(392\) | 14.1972 | 0.717069 | ||||||||
\(393\) | 21.7310 | 1.09618 | ||||||||
\(394\) | −27.9721 | −1.40922 | ||||||||
\(395\) | −11.8851 | −0.598003 | ||||||||
\(396\) | 28.1421 | 1.41420 | ||||||||
\(397\) | −14.0000 | −0.702640 | −0.351320 | − | 0.936255i | \(-0.614267\pi\) | ||||
−0.351320 | + | 0.936255i | \(0.614267\pi\) | |||||||
\(398\) | −8.40401 | −0.421255 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.00000 | −0.150000 | ||||||||
\(401\) | −16.8080 | −0.839353 | −0.419676 | − | 0.907674i | \(-0.637856\pi\) | ||||
−0.419676 | + | 0.907674i | \(0.637856\pi\) | |||||||
\(402\) | −33.9147 | −1.69151 | ||||||||
\(403\) | −7.31371 | −0.364322 | ||||||||
\(404\) | −39.7990 | −1.98007 | ||||||||
\(405\) | 7.48528 | 0.371947 | ||||||||
\(406\) | 24.9706 | 1.23927 | ||||||||
\(407\) | 14.3465 | 0.711132 | ||||||||
\(408\) | 9.45584 | 0.468134 | ||||||||
\(409\) | −38.1167 | −1.88475 | −0.942374 | − | 0.334560i | \(-0.891412\pi\) | ||||
−0.942374 | + | 0.334560i | \(0.891412\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.94253 | 0.293124 | ||||||||
\(412\) | 21.5198 | 1.06021 | ||||||||
\(413\) | 57.3862 | 2.82379 | ||||||||
\(414\) | 59.1267 | 2.90592 | ||||||||
\(415\) | 3.17157 | 0.155686 | ||||||||
\(416\) | −9.89949 | −0.485363 | ||||||||
\(417\) | −24.7897 | −1.21396 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.97056 | 0.438241 | 0.219120 | − | 0.975698i | \(-0.429681\pi\) | ||||
0.219120 | + | 0.975698i | \(0.429681\pi\) | |||||||
\(420\) | −34.6356 | −1.69005 | ||||||||
\(421\) | −16.8080 | −0.819173 | −0.409586 | − | 0.912271i | \(-0.634327\pi\) | ||||
−0.409586 | + | 0.912271i | \(0.634327\pi\) | |||||||
\(422\) | −22.8284 | −1.11127 | ||||||||
\(423\) | −37.7990 | −1.83785 | ||||||||
\(424\) | 4.10051 | 0.199138 | ||||||||
\(425\) | −3.65685 | −0.177383 | ||||||||
\(426\) | −67.8294 | −3.28634 | ||||||||
\(427\) | 13.6569 | 0.660901 | ||||||||
\(428\) | 15.5773 | 0.752956 | ||||||||
\(429\) | −7.31371 | −0.353109 | ||||||||
\(430\) | 1.74053 | 0.0839357 | ||||||||
\(431\) | −5.94253 | −0.286242 | −0.143121 | − | 0.989705i | \(-0.545714\pi\) | ||||
−0.143121 | + | 0.989705i | \(0.545714\pi\) | |||||||
\(432\) | 25.2120 | 1.21301 | ||||||||
\(433\) | −33.4049 | −1.60534 | −0.802668 | − | 0.596426i | \(-0.796587\pi\) | ||||
−0.802668 | + | 0.596426i | \(0.796587\pi\) | |||||||
\(434\) | −60.2843 | −2.89374 | ||||||||
\(435\) | −7.31371 | −0.350665 | ||||||||
\(436\) | −46.5207 | −2.22794 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 2.14214 | 0.102355 | ||||||||
\(439\) | 28.6931 | 1.36945 | 0.684723 | − | 0.728803i | \(-0.259923\pi\) | ||||
0.684723 | + | 0.728803i | \(0.259923\pi\) | |||||||
\(440\) | 1.74053 | 0.0829764 | ||||||||
\(441\) | 95.0833 | 4.52777 | ||||||||
\(442\) | −9.45584 | −0.449769 | ||||||||
\(443\) | −8.14214 | −0.386845 | −0.193422 | − | 0.981116i | \(-0.561959\pi\) | ||||
−0.193422 | + | 0.981116i | \(0.561959\pi\) | |||||||
\(444\) | −51.4558 | −2.44199 | ||||||||
\(445\) | 9.42359 | 0.446721 | ||||||||
\(446\) | −36.3848 | −1.72287 | ||||||||
\(447\) | 27.2512 | 1.28894 | ||||||||
\(448\) | −52.6274 | −2.48641 | ||||||||
\(449\) | −2.46148 | −0.116164 | −0.0580822 | − | 0.998312i | \(-0.518499\pi\) | ||||
−0.0580822 | + | 0.998312i | \(0.518499\pi\) | |||||||
\(450\) | 12.2455 | 0.577260 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −23.2603 | −1.09407 | ||||||||
\(453\) | −52.9706 | −2.48877 | ||||||||
\(454\) | −46.7279 | −2.19305 | ||||||||
\(455\) | 5.94253 | 0.278590 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.3137 | −0.809901 | −0.404951 | − | 0.914339i | \(-0.632711\pi\) | ||||
−0.404951 | + | 0.914339i | \(0.632711\pi\) | |||||||
\(458\) | 26.2316 | 1.22572 | ||||||||
\(459\) | 30.7322 | 1.43446 | ||||||||
\(460\) | 11.6569 | 0.543504 | ||||||||
\(461\) | −33.3137 | −1.55157 | −0.775787 | − | 0.630995i | \(-0.782647\pi\) | ||||
−0.775787 | + | 0.630995i | \(0.782647\pi\) | |||||||
\(462\) | −60.2843 | −2.80468 | ||||||||
\(463\) | −27.1716 | −1.26277 | −0.631385 | − | 0.775469i | \(-0.717513\pi\) | ||||
−0.631385 | + | 0.775469i | \(0.717513\pi\) | |||||||
\(464\) | −7.38443 | −0.342814 | ||||||||
\(465\) | 17.6569 | 0.818817 | ||||||||
\(466\) | 27.9721 | 1.29578 | ||||||||
\(467\) | 21.5147 | 0.995582 | 0.497791 | − | 0.867297i | \(-0.334145\pi\) | ||||
0.497791 | + | 0.867297i | \(0.334145\pi\) | |||||||
\(468\) | 17.3178 | 0.800516 | ||||||||
\(469\) | 26.2316 | 1.21126 | ||||||||
\(470\) | −13.6256 | −0.628502 | ||||||||
\(471\) | −53.4828 | −2.46436 | ||||||||
\(472\) | 10.3431 | 0.476082 | ||||||||
\(473\) | 1.65685 | 0.0761822 | ||||||||
\(474\) | 74.1942 | 3.40785 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −42.6274 | −1.95382 | ||||||||
\(477\) | 27.4624 | 1.25741 | ||||||||
\(478\) | −3.48106 | −0.159220 | ||||||||
\(479\) | 10.0000 | 0.456912 | 0.228456 | − | 0.973554i | \(-0.426632\pi\) | ||||
0.228456 | + | 0.973554i | \(0.426632\pi\) | |||||||
\(480\) | 23.8995 | 1.09086 | ||||||||
\(481\) | 8.82843 | 0.402542 | ||||||||
\(482\) | −14.6274 | −0.666261 | ||||||||
\(483\) | −69.2713 | −3.15195 | ||||||||
\(484\) | −16.8995 | −0.768159 | ||||||||
\(485\) | 1.23074 | 0.0558850 | ||||||||
\(486\) | 6.24264 | 0.283172 | ||||||||
\(487\) | 15.8759 | 0.719406 | 0.359703 | − | 0.933067i | \(-0.382878\pi\) | ||||
0.359703 | + | 0.933067i | \(0.382878\pi\) | |||||||
\(488\) | 2.46148 | 0.111426 | ||||||||
\(489\) | −38.1167 | −1.72370 | ||||||||
\(490\) | 34.2752 | 1.54839 | ||||||||
\(491\) | −24.2843 | −1.09593 | −0.547967 | − | 0.836500i | \(-0.684598\pi\) | ||||
−0.547967 | + | 0.836500i | \(0.684598\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −9.00127 | −0.405397 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 11.6569 | 0.523937 | ||||||||
\(496\) | 17.8276 | 0.800483 | ||||||||
\(497\) | 52.4632 | 2.35330 | ||||||||
\(498\) | −19.7990 | −0.887214 | ||||||||
\(499\) | 34.9706 | 1.56550 | 0.782749 | − | 0.622338i | \(-0.213817\pi\) | ||||
0.782749 | + | 0.622338i | \(0.213817\pi\) | |||||||
\(500\) | 2.41421 | 0.107967 | ||||||||
\(501\) | 66.0833 | 2.95238 | ||||||||
\(502\) | −27.2512 | −1.21628 | ||||||||
\(503\) | −14.4853 | −0.645867 | −0.322933 | − | 0.946422i | \(-0.604669\pi\) | ||||
−0.322933 | + | 0.946422i | \(0.604669\pi\) | |||||||
\(504\) | 24.4911 | 1.09092 | ||||||||
\(505\) | −16.4853 | −0.733585 | ||||||||
\(506\) | 20.2891 | 0.901960 | ||||||||
\(507\) | 34.1258 | 1.51558 | ||||||||
\(508\) | 29.9238 | 1.32766 | ||||||||
\(509\) | 4.50063 | 0.199487 | 0.0997435 | − | 0.995013i | \(-0.468198\pi\) | ||||
0.0997435 | + | 0.995013i | \(0.468198\pi\) | |||||||
\(510\) | 22.8284 | 1.01086 | ||||||||
\(511\) | −1.65685 | −0.0732949 | ||||||||
\(512\) | 29.3522 | 1.29720 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −17.2132 | −0.759242 | ||||||||
\(515\) | 8.91380 | 0.392789 | ||||||||
\(516\) | −5.94253 | −0.261605 | ||||||||
\(517\) | −12.9706 | −0.570445 | ||||||||
\(518\) | 72.7696 | 3.19731 | ||||||||
\(519\) | 38.9706 | 1.71062 | ||||||||
\(520\) | 1.07107 | 0.0469694 | ||||||||
\(521\) | −4.92296 | −0.215679 | −0.107839 | − | 0.994168i | \(-0.534393\pi\) | ||||
−0.107839 | + | 0.994168i | \(0.534393\pi\) | |||||||
\(522\) | 30.1421 | 1.31929 | ||||||||
\(523\) | 7.89422 | 0.345190 | 0.172595 | − | 0.984993i | \(-0.444785\pi\) | ||||
0.172595 | + | 0.984993i | \(0.444785\pi\) | |||||||
\(524\) | −17.6569 | −0.771343 | ||||||||
\(525\) | −14.3465 | −0.626135 | ||||||||
\(526\) | 25.5107 | 1.11232 | ||||||||
\(527\) | 21.7310 | 0.946616 | ||||||||
\(528\) | 17.8276 | 0.775847 | ||||||||
\(529\) | 0.313708 | 0.0136395 | ||||||||
\(530\) | 9.89949 | 0.430007 | ||||||||
\(531\) | 69.2713 | 3.00612 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −58.8281 | −2.54574 | ||||||||
\(535\) | 6.45232 | 0.278958 | ||||||||
\(536\) | 4.72792 | 0.204215 | ||||||||
\(537\) | −14.6274 | −0.631220 | ||||||||
\(538\) | 5.17157 | 0.222962 | ||||||||
\(539\) | 32.6274 | 1.40536 | ||||||||
\(540\) | −20.2891 | −0.873103 | ||||||||
\(541\) | −6.14214 | −0.264071 | −0.132036 | − | 0.991245i | \(-0.542151\pi\) | ||||
−0.132036 | + | 0.991245i | \(0.542151\pi\) | |||||||
\(542\) | −6.24116 | −0.268081 | ||||||||
\(543\) | 49.9411 | 2.14318 | ||||||||
\(544\) | 29.4140 | 1.26112 | ||||||||
\(545\) | −19.2695 | −0.825415 | ||||||||
\(546\) | −37.0971 | −1.58761 | ||||||||
\(547\) | 13.8368 | 0.591617 | 0.295809 | − | 0.955247i | \(-0.404411\pi\) | ||||
0.295809 | + | 0.955247i | \(0.404411\pi\) | |||||||
\(548\) | −4.82843 | −0.206260 | ||||||||
\(549\) | 16.4853 | 0.703575 | ||||||||
\(550\) | 4.20201 | 0.179174 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −12.4853 | −0.531409 | ||||||||
\(553\) | −57.3862 | −2.44031 | ||||||||
\(554\) | 11.1641 | 0.474318 | ||||||||
\(555\) | −21.3137 | −0.904717 | ||||||||
\(556\) | 20.1421 | 0.854217 | ||||||||
\(557\) | 16.6274 | 0.704526 | 0.352263 | − | 0.935901i | \(-0.385412\pi\) | ||||
0.352263 | + | 0.935901i | \(0.385412\pi\) | |||||||
\(558\) | −72.7696 | −3.08058 | ||||||||
\(559\) | 1.01958 | 0.0431235 | ||||||||
\(560\) | −14.4853 | −0.612115 | ||||||||
\(561\) | 21.7310 | 0.917483 | ||||||||
\(562\) | −49.9411 | −2.10664 | ||||||||
\(563\) | 9.93338 | 0.418642 | 0.209321 | − | 0.977847i | \(-0.432875\pi\) | ||||
0.209321 | + | 0.977847i | \(0.432875\pi\) | |||||||
\(564\) | 46.5207 | 1.95887 | ||||||||
\(565\) | −9.63475 | −0.405337 | ||||||||
\(566\) | 62.6078 | 2.63160 | ||||||||
\(567\) | 36.1421 | 1.51783 | ||||||||
\(568\) | 9.45584 | 0.396758 | ||||||||
\(569\) | 9.42359 | 0.395057 | 0.197529 | − | 0.980297i | \(-0.436708\pi\) | ||||
0.197529 | + | 0.980297i | \(0.436708\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.31371 | −0.389767 | −0.194883 | − | 0.980826i | \(-0.562433\pi\) | ||||
−0.194883 | + | 0.980826i | \(0.562433\pi\) | |||||||
\(572\) | 5.94253 | 0.248470 | ||||||||
\(573\) | 40.5782 | 1.69518 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.82843 | 0.201359 | ||||||||
\(576\) | −63.5269 | −2.64695 | ||||||||
\(577\) | 10.0000 | 0.416305 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(578\) | −7.62121 | −0.317001 | ||||||||
\(579\) | −24.3431 | −1.01167 | ||||||||
\(580\) | 5.94253 | 0.246750 | ||||||||
\(581\) | 15.3137 | 0.635320 | ||||||||
\(582\) | −7.68306 | −0.318473 | ||||||||
\(583\) | 9.42359 | 0.390285 | ||||||||
\(584\) | −0.298627 | −0.0123573 | ||||||||
\(585\) | 7.17327 | 0.296578 | ||||||||
\(586\) | −25.4142 | −1.04985 | ||||||||
\(587\) | 1.51472 | 0.0625191 | 0.0312596 | − | 0.999511i | \(-0.490048\pi\) | ||||
0.0312596 | + | 0.999511i | \(0.490048\pi\) | |||||||
\(588\) | −117.023 | −4.82593 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 24.9706 | 1.02802 | ||||||||
\(591\) | 39.5586 | 1.62722 | ||||||||
\(592\) | −21.5198 | −0.884459 | ||||||||
\(593\) | 13.3137 | 0.546728 | 0.273364 | − | 0.961911i | \(-0.411864\pi\) | ||||
0.273364 | + | 0.961911i | \(0.411864\pi\) | |||||||
\(594\) | −35.3137 | −1.44894 | ||||||||
\(595\) | −17.6569 | −0.723860 | ||||||||
\(596\) | −22.1421 | −0.906977 | ||||||||
\(597\) | 11.8851 | 0.486423 | ||||||||
\(598\) | 12.4853 | 0.510561 | ||||||||
\(599\) | −9.84591 | −0.402293 | −0.201147 | − | 0.979561i | \(-0.564467\pi\) | ||||
−0.201147 | + | 0.979561i | \(0.564467\pi\) | |||||||
\(600\) | −2.58579 | −0.105564 | ||||||||
\(601\) | −4.92296 | −0.200812 | −0.100406 | − | 0.994947i | \(-0.532014\pi\) | ||||
−0.100406 | + | 0.994947i | \(0.532014\pi\) | |||||||
\(602\) | 8.40401 | 0.342522 | ||||||||
\(603\) | 31.6644 | 1.28947 | ||||||||
\(604\) | 43.0396 | 1.75126 | ||||||||
\(605\) | −7.00000 | −0.284590 | ||||||||
\(606\) | 102.912 | 4.18050 | ||||||||
\(607\) | −21.8184 | −0.885583 | −0.442792 | − | 0.896625i | \(-0.646012\pi\) | ||||
−0.442792 | + | 0.896625i | \(0.646012\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −35.3137 | −1.43098 | ||||||||
\(610\) | 5.94253 | 0.240606 | ||||||||
\(611\) | −7.98169 | −0.322905 | ||||||||
\(612\) | −51.4558 | −2.07998 | ||||||||
\(613\) | 42.2843 | 1.70785 | 0.853923 | − | 0.520400i | \(-0.174217\pi\) | ||||
0.853923 | + | 0.520400i | \(0.174217\pi\) | |||||||
\(614\) | 23.8995 | 0.964505 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.40401 | 0.338607 | ||||||||
\(617\) | −26.2843 | −1.05816 | −0.529082 | − | 0.848570i | \(-0.677464\pi\) | ||||
−0.529082 | + | 0.848570i | \(0.677464\pi\) | |||||||
\(618\) | −55.6457 | −2.23840 | ||||||||
\(619\) | 14.9706 | 0.601718 | 0.300859 | − | 0.953669i | \(-0.402727\pi\) | ||||
0.300859 | + | 0.953669i | \(0.402727\pi\) | |||||||
\(620\) | −14.3465 | −0.576171 | ||||||||
\(621\) | −40.5782 | −1.62835 | ||||||||
\(622\) | −66.5111 | −2.66685 | ||||||||
\(623\) | 45.5011 | 1.82296 | ||||||||
\(624\) | 10.9706 | 0.439174 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −43.3383 | −1.73215 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 43.4558 | 1.73408 | ||||||||
\(629\) | −26.2316 | −1.04592 | ||||||||
\(630\) | 59.1267 | 2.35566 | ||||||||
\(631\) | −38.2843 | −1.52407 | −0.762036 | − | 0.647534i | \(-0.775800\pi\) | ||||
−0.762036 | + | 0.647534i | \(0.775800\pi\) | |||||||
\(632\) | −10.3431 | −0.411428 | ||||||||
\(633\) | 32.2843 | 1.28318 | ||||||||
\(634\) | −32.7279 | −1.29979 | ||||||||
\(635\) | 12.3949 | 0.491875 | ||||||||
\(636\) | −33.7990 | −1.34022 | ||||||||
\(637\) | 20.0779 | 0.795516 | ||||||||
\(638\) | 10.3431 | 0.409489 | ||||||||
\(639\) | 63.3287 | 2.50525 | ||||||||
\(640\) | −6.81280 | −0.269299 | ||||||||
\(641\) | 35.6552 | 1.40830 | 0.704148 | − | 0.710053i | \(-0.251329\pi\) | ||||
0.704148 | + | 0.710053i | \(0.251329\pi\) | |||||||
\(642\) | −40.2795 | −1.58971 | ||||||||
\(643\) | 26.4853 | 1.04448 | 0.522239 | − | 0.852799i | \(-0.325097\pi\) | ||||
0.522239 | + | 0.852799i | \(0.325097\pi\) | |||||||
\(644\) | 56.2843 | 2.21791 | ||||||||
\(645\) | −2.46148 | −0.0969206 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.8284 | −1.29062 | −0.645309 | − | 0.763921i | \(-0.723272\pi\) | ||||
−0.645309 | + | 0.763921i | \(0.723272\pi\) | |||||||
\(648\) | 6.51417 | 0.255901 | ||||||||
\(649\) | 23.7701 | 0.933059 | ||||||||
\(650\) | 2.58579 | 0.101423 | ||||||||
\(651\) | 85.2548 | 3.34140 | ||||||||
\(652\) | 30.9706 | 1.21290 | ||||||||
\(653\) | 16.3431 | 0.639557 | 0.319778 | − | 0.947492i | \(-0.396392\pi\) | ||||
0.319778 | + | 0.947492i | \(0.396392\pi\) | |||||||
\(654\) | 120.293 | 4.70381 | ||||||||
\(655\) | −7.31371 | −0.285770 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.00000 | −0.0780274 | ||||||||
\(658\) | −65.7902 | −2.56477 | ||||||||
\(659\) | −33.6160 | −1.30950 | −0.654748 | − | 0.755848i | \(-0.727225\pi\) | ||||
−0.654748 | + | 0.755848i | \(0.727225\pi\) | |||||||
\(660\) | −14.3465 | −0.558439 | ||||||||
\(661\) | 28.6931 | 1.11603 | 0.558016 | − | 0.829830i | \(-0.311563\pi\) | ||||
0.558016 | + | 0.829830i | \(0.311563\pi\) | |||||||
\(662\) | 62.4264 | 2.42627 | ||||||||
\(663\) | 13.3726 | 0.519348 | ||||||||
\(664\) | 2.76011 | 0.107113 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 87.8406 | 3.40375 | ||||||||
\(667\) | 11.8851 | 0.460192 | ||||||||
\(668\) | −53.6940 | −2.07748 | ||||||||
\(669\) | 51.4558 | 1.98940 | ||||||||
\(670\) | 11.4142 | 0.440970 | ||||||||
\(671\) | 5.65685 | 0.218380 | ||||||||
\(672\) | 115.397 | 4.45153 | ||||||||
\(673\) | 7.59560 | 0.292789 | 0.146394 | − | 0.989226i | \(-0.453233\pi\) | ||||
0.146394 | + | 0.989226i | \(0.453233\pi\) | |||||||
\(674\) | 65.0122 | 2.50418 | ||||||||
\(675\) | −8.40401 | −0.323471 | ||||||||
\(676\) | −27.7279 | −1.06646 | ||||||||
\(677\) | 21.5198 | 0.827074 | 0.413537 | − | 0.910487i | \(-0.364293\pi\) | ||||
0.413537 | + | 0.910487i | \(0.364293\pi\) | |||||||
\(678\) | 60.1463 | 2.30990 | ||||||||
\(679\) | 5.94253 | 0.228054 | ||||||||
\(680\) | −3.18243 | −0.122041 | ||||||||
\(681\) | 66.0833 | 2.53232 | ||||||||
\(682\) | −24.9706 | −0.956172 | ||||||||
\(683\) | −13.8368 | −0.529449 | −0.264724 | − | 0.964324i | \(-0.585281\pi\) | ||||
−0.264724 | + | 0.964324i | \(0.585281\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.00000 | −0.0764161 | ||||||||
\(686\) | 94.4833 | 3.60739 | ||||||||
\(687\) | −37.0971 | −1.41534 | ||||||||
\(688\) | −2.48528 | −0.0947505 | ||||||||
\(689\) | 5.79899 | 0.220924 | ||||||||
\(690\) | −30.1421 | −1.14749 | ||||||||
\(691\) | −28.6274 | −1.08904 | −0.544519 | − | 0.838748i | \(-0.683288\pi\) | ||||
−0.544519 | + | 0.838748i | \(0.683288\pi\) | |||||||
\(692\) | −31.6644 | −1.20370 | ||||||||
\(693\) | 56.2843 | 2.13806 | ||||||||
\(694\) | 52.1646 | 1.98014 | ||||||||
\(695\) | 8.34315 | 0.316474 | ||||||||
\(696\) | −6.36486 | −0.241259 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −14.0479 | −0.531722 | ||||||||
\(699\) | −39.5586 | −1.49624 | ||||||||
\(700\) | 11.6569 | 0.440588 | ||||||||
\(701\) | −7.51472 | −0.283827 | −0.141914 | − | 0.989879i | \(-0.545325\pi\) | ||||
−0.141914 | + | 0.989879i | \(0.545325\pi\) | |||||||
\(702\) | −21.7310 | −0.820183 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −21.7990 | −0.821580 | ||||||||
\(705\) | 19.2695 | 0.725731 | ||||||||
\(706\) | −7.68306 | −0.289156 | ||||||||
\(707\) | −79.5980 | −2.99359 | ||||||||
\(708\) | −85.2548 | −3.20407 | ||||||||
\(709\) | 17.3137 | 0.650230 | 0.325115 | − | 0.945674i | \(-0.394597\pi\) | ||||
0.325115 | + | 0.945674i | \(0.394597\pi\) | |||||||
\(710\) | 22.8284 | 0.856736 | ||||||||
\(711\) | −69.2713 | −2.59787 | ||||||||
\(712\) | 8.20101 | 0.307346 | ||||||||
\(713\) | −28.6931 | −1.07456 | ||||||||
\(714\) | 110.225 | 4.12508 | ||||||||
\(715\) | 2.46148 | 0.0920541 | ||||||||
\(716\) | 11.8851 | 0.444166 | ||||||||
\(717\) | 4.92296 | 0.183851 | ||||||||
\(718\) | −53.1842 | −1.98482 | ||||||||
\(719\) | −35.9411 | −1.34038 | −0.670189 | − | 0.742191i | \(-0.733787\pi\) | ||||
−0.670189 | + | 0.742191i | \(0.733787\pi\) | |||||||
\(720\) | −17.4853 | −0.651638 | ||||||||
\(721\) | 43.0396 | 1.60288 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 20.6863 | 0.769331 | ||||||||
\(724\) | −40.5782 | −1.50808 | ||||||||
\(725\) | 2.46148 | 0.0914170 | ||||||||
\(726\) | 43.6985 | 1.62180 | ||||||||
\(727\) | −10.4853 | −0.388878 | −0.194439 | − | 0.980915i | \(-0.562289\pi\) | ||||
−0.194439 | + | 0.980915i | \(0.562289\pi\) | |||||||
\(728\) | 5.17157 | 0.191671 | ||||||||
\(729\) | −31.2843 | −1.15868 | ||||||||
\(730\) | −0.720950 | −0.0266836 | ||||||||
\(731\) | −3.02944 | −0.112048 | ||||||||
\(732\) | −20.2891 | −0.749906 | ||||||||
\(733\) | −24.3431 | −0.899135 | −0.449567 | − | 0.893246i | \(-0.648422\pi\) | ||||
−0.449567 | + | 0.893246i | \(0.648422\pi\) | |||||||
\(734\) | 18.5486 | 0.684640 | ||||||||
\(735\) | −48.4724 | −1.78793 | ||||||||
\(736\) | −38.8376 | −1.43157 | ||||||||
\(737\) | 10.8655 | 0.400235 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.6274 | 1.71522 | 0.857609 | − | 0.514303i | \(-0.171949\pi\) | ||||
0.857609 | + | 0.514303i | \(0.171949\pi\) | |||||||
\(740\) | 17.3178 | 0.636615 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 47.7990 | 1.75476 | ||||||||
\(743\) | 5.43275 | 0.199308 | 0.0996540 | − | 0.995022i | \(-0.468226\pi\) | ||||
0.0996540 | + | 0.995022i | \(0.468226\pi\) | |||||||
\(744\) | 15.3661 | 0.563349 | ||||||||
\(745\) | −9.17157 | −0.336020 | ||||||||
\(746\) | −50.3848 | −1.84472 | ||||||||
\(747\) | 18.4853 | 0.676341 | ||||||||
\(748\) | −17.6569 | −0.645599 | ||||||||
\(749\) | 31.1546 | 1.13836 | ||||||||
\(750\) | −6.24264 | −0.227949 | ||||||||
\(751\) | −22.7506 | −0.830180 | −0.415090 | − | 0.909780i | \(-0.636250\pi\) | ||||
−0.415090 | + | 0.909780i | \(0.636250\pi\) | |||||||
\(752\) | 19.4558 | 0.709482 | ||||||||
\(753\) | 38.5390 | 1.40444 | ||||||||
\(754\) | 6.36486 | 0.231794 | ||||||||
\(755\) | 17.8276 | 0.648813 | ||||||||
\(756\) | −97.9643 | −3.56293 | ||||||||
\(757\) | −29.3137 | −1.06542 | −0.532712 | − | 0.846296i | \(-0.678827\pi\) | ||||
−0.532712 | + | 0.846296i | \(0.678827\pi\) | |||||||
\(758\) | −10.3431 | −0.375680 | ||||||||
\(759\) | −28.6931 | −1.04149 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −14.8284 | −0.537530 | −0.268765 | − | 0.963206i | \(-0.586616\pi\) | ||||
−0.268765 | + | 0.963206i | \(0.586616\pi\) | |||||||
\(762\) | −77.3766 | −2.80306 | ||||||||
\(763\) | −93.0414 | −3.36832 | ||||||||
\(764\) | −32.9706 | −1.19283 | ||||||||
\(765\) | −21.3137 | −0.770599 | ||||||||
\(766\) | 26.9289 | 0.972982 | ||||||||
\(767\) | 14.6274 | 0.528165 | ||||||||
\(768\) | −22.2408 | −0.802545 | ||||||||
\(769\) | −14.1421 | −0.509978 | −0.254989 | − | 0.966944i | \(-0.582072\pi\) | ||||
−0.254989 | + | 0.966944i | \(0.582072\pi\) | |||||||
\(770\) | 20.2891 | 0.731168 | ||||||||
\(771\) | 24.3431 | 0.876697 | ||||||||
\(772\) | 19.7793 | 0.711872 | ||||||||
\(773\) | −22.5394 | −0.810686 | −0.405343 | − | 0.914165i | \(-0.632848\pi\) | ||||
−0.405343 | + | 0.914165i | \(0.632848\pi\) | |||||||
\(774\) | 10.1445 | 0.364638 | ||||||||
\(775\) | −5.94253 | −0.213462 | ||||||||
\(776\) | 1.07107 | 0.0384491 | ||||||||
\(777\) | −102.912 | −3.69194 | ||||||||
\(778\) | 51.7423 | 1.85505 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −8.82843 | −0.316108 | ||||||||
\(781\) | 21.7310 | 0.777596 | ||||||||
\(782\) | −37.0971 | −1.32659 | ||||||||
\(783\) | −20.6863 | −0.739268 | ||||||||
\(784\) | −48.9411 | −1.74790 | ||||||||
\(785\) | 18.0000 | 0.642448 | ||||||||
\(786\) | 45.6569 | 1.62853 | ||||||||
\(787\) | 23.6827 | 0.844196 | 0.422098 | − | 0.906550i | \(-0.361294\pi\) | ||||
0.422098 | + | 0.906550i | \(0.361294\pi\) | |||||||
\(788\) | −32.1421 | −1.14502 | ||||||||
\(789\) | −36.0775 | −1.28439 | ||||||||
\(790\) | −24.9706 | −0.888413 | ||||||||
\(791\) | −46.5207 | −1.65409 | ||||||||
\(792\) | 10.1445 | 0.360471 | ||||||||
\(793\) | 3.48106 | 0.123616 | ||||||||
\(794\) | −29.4140 | −1.04387 | ||||||||
\(795\) | −14.0000 | −0.496529 | ||||||||
\(796\) | −9.65685 | −0.342278 | ||||||||
\(797\) | −7.17327 | −0.254090 | −0.127045 | − | 0.991897i | \(-0.540549\pi\) | ||||
−0.127045 | + | 0.991897i | \(0.540549\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7157 | 0.839002 | ||||||||
\(800\) | −8.04354 | −0.284382 | ||||||||
\(801\) | 54.9247 | 1.94067 | ||||||||
\(802\) | −35.3137 | −1.24697 | ||||||||
\(803\) | −0.686292 | −0.0242187 | ||||||||
\(804\) | −38.9706 | −1.37439 | ||||||||
\(805\) | 23.3137 | 0.821700 | ||||||||
\(806\) | −15.3661 | −0.541249 | ||||||||
\(807\) | −7.31371 | −0.257455 | ||||||||
\(808\) | −14.3465 | −0.504710 | ||||||||
\(809\) | 9.31371 | 0.327453 | 0.163726 | − | 0.986506i | \(-0.447649\pi\) | ||||
0.163726 | + | 0.986506i | \(0.447649\pi\) | |||||||
\(810\) | 15.7266 | 0.552576 | ||||||||
\(811\) | −44.4815 | −1.56196 | −0.780979 | − | 0.624557i | \(-0.785279\pi\) | ||||
−0.780979 | + | 0.624557i | \(0.785279\pi\) | |||||||
\(812\) | 28.6931 | 1.00693 | ||||||||
\(813\) | 8.82633 | 0.309553 | ||||||||
\(814\) | 30.1421 | 1.05648 | ||||||||
\(815\) | 12.8284 | 0.449360 | ||||||||
\(816\) | −32.5965 | −1.14110 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −80.0833 | −2.80005 | ||||||||
\(819\) | 34.6356 | 1.21027 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 25.3137 | 0.883455 | 0.441727 | − | 0.897149i | \(-0.354366\pi\) | ||||
0.441727 | + | 0.897149i | \(0.354366\pi\) | |||||||
\(822\) | 12.4853 | 0.435474 | ||||||||
\(823\) | −54.0833 | −1.88522 | −0.942612 | − | 0.333890i | \(-0.891639\pi\) | ||||
−0.942612 | + | 0.333890i | \(0.891639\pi\) | |||||||
\(824\) | 7.75736 | 0.270240 | ||||||||
\(825\) | −5.94253 | −0.206892 | ||||||||
\(826\) | 120.569 | 4.19512 | ||||||||
\(827\) | −1.95169 | −0.0678669 | −0.0339334 | − | 0.999424i | \(-0.510803\pi\) | ||||
−0.0339334 | + | 0.999424i | \(0.510803\pi\) | |||||||
\(828\) | 67.9411 | 2.36112 | ||||||||
\(829\) | 12.3074 | 0.427453 | 0.213727 | − | 0.976893i | \(-0.431440\pi\) | ||||
0.213727 | + | 0.976893i | \(0.431440\pi\) | |||||||
\(830\) | 6.66348 | 0.231293 | ||||||||
\(831\) | −15.7884 | −0.547695 | ||||||||
\(832\) | −13.4144 | −0.465062 | ||||||||
\(833\) | −59.6569 | −2.06699 | ||||||||
\(834\) | −52.0833 | −1.80350 | ||||||||
\(835\) | −22.2408 | −0.769674 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 49.9411 | 1.72622 | ||||||||
\(838\) | 18.8472 | 0.651065 | ||||||||
\(839\) | 18.8472 | 0.650677 | 0.325338 | − | 0.945598i | \(-0.394522\pi\) | ||||
0.325338 | + | 0.945598i | \(0.394522\pi\) | |||||||
\(840\) | −12.4853 | −0.430783 | ||||||||
\(841\) | −22.9411 | −0.791073 | ||||||||
\(842\) | −35.3137 | −1.21699 | ||||||||
\(843\) | 70.6274 | 2.43254 | ||||||||
\(844\) | −26.2316 | −0.902929 | ||||||||
\(845\) | −11.4853 | −0.395106 | ||||||||
\(846\) | −79.4158 | −2.73037 | ||||||||
\(847\) | −33.7990 | −1.16135 | ||||||||
\(848\) | −14.1354 | −0.485411 | ||||||||
\(849\) | −88.5408 | −3.03871 | ||||||||
\(850\) | −7.68306 | −0.263527 | ||||||||
\(851\) | 34.6356 | 1.18729 | ||||||||
\(852\) | −77.9411 | −2.67022 | ||||||||
\(853\) | 47.6569 | 1.63174 | 0.815870 | − | 0.578236i | \(-0.196259\pi\) | ||||
0.815870 | + | 0.578236i | \(0.196259\pi\) | |||||||
\(854\) | 28.6931 | 0.981857 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 5.61522 | 0.191924 | ||||||||
\(857\) | −36.8859 | −1.26000 | −0.630000 | − | 0.776595i | \(-0.716945\pi\) | ||||
−0.630000 | + | 0.776595i | \(0.716945\pi\) | |||||||
\(858\) | −15.3661 | −0.524591 | ||||||||
\(859\) | 12.2843 | 0.419134 | 0.209567 | − | 0.977794i | \(-0.432795\pi\) | ||||
0.209567 | + | 0.977794i | \(0.432795\pi\) | |||||||
\(860\) | 2.00000 | 0.0681994 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −12.4853 | −0.425250 | ||||||||
\(863\) | 24.2799 | 0.826498 | 0.413249 | − | 0.910618i | \(-0.364394\pi\) | ||||
0.413249 | + | 0.910618i | \(0.364394\pi\) | |||||||
\(864\) | 67.5980 | 2.29973 | ||||||||
\(865\) | −13.1158 | −0.445951 | ||||||||
\(866\) | −70.1838 | −2.38494 | ||||||||
\(867\) | 10.7780 | 0.366041 | ||||||||
\(868\) | −69.2713 | −2.35122 | ||||||||
\(869\) | −23.7701 | −0.806347 | ||||||||
\(870\) | −15.3661 | −0.520960 | ||||||||
\(871\) | 6.68629 | 0.226556 | ||||||||
\(872\) | −16.7696 | −0.567889 | ||||||||
\(873\) | 7.17327 | 0.242779 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.82843 | 0.163231 | ||||||||
\(876\) | 2.46148 | 0.0831656 | ||||||||
\(877\) | −23.9813 | −0.809791 | −0.404895 | − | 0.914363i | \(-0.632692\pi\) | ||||
−0.404895 | + | 0.914363i | \(0.632692\pi\) | |||||||
\(878\) | 60.2843 | 2.03450 | ||||||||
\(879\) | 35.9411 | 1.21226 | ||||||||
\(880\) | −6.00000 | −0.202260 | ||||||||
\(881\) | −12.4853 | −0.420640 | −0.210320 | − | 0.977633i | \(-0.567451\pi\) | ||||
−0.210320 | + | 0.977633i | \(0.567451\pi\) | |||||||
\(882\) | 199.770 | 6.72661 | ||||||||
\(883\) | 32.1421 | 1.08167 | 0.540834 | − | 0.841129i | \(-0.318109\pi\) | ||||
0.540834 | + | 0.841129i | \(0.318109\pi\) | |||||||
\(884\) | −10.8655 | −0.365446 | ||||||||
\(885\) | −35.3137 | −1.18706 | ||||||||
\(886\) | −17.1067 | −0.574709 | ||||||||
\(887\) | 31.6644 | 1.06319 | 0.531593 | − | 0.847000i | \(-0.321594\pi\) | ||||
0.531593 | + | 0.847000i | \(0.321594\pi\) | |||||||
\(888\) | −18.5486 | −0.622449 | ||||||||
\(889\) | 59.8477 | 2.00723 | ||||||||
\(890\) | 19.7990 | 0.663664 | ||||||||
\(891\) | 14.9706 | 0.501533 | ||||||||
\(892\) | −41.8089 | −1.39987 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 57.2548 | 1.91489 | ||||||||
\(895\) | 4.92296 | 0.164556 | ||||||||
\(896\) | −32.8951 | −1.09895 | ||||||||
\(897\) | −17.6569 | −0.589545 | ||||||||
\(898\) | −5.17157 | −0.172578 | ||||||||
\(899\) | −14.6274 | −0.487852 | ||||||||
\(900\) | 14.0711 | 0.469036 | ||||||||
\(901\) | −17.2303 | −0.574026 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.8851 | −0.395510 | ||||||||
\(904\) | −8.38478 | −0.278874 | ||||||||
\(905\) | −16.8080 | −0.558718 | ||||||||
\(906\) | −111.291 | −3.69741 | ||||||||
\(907\) | 33.1063 | 1.09928 | 0.549638 | − | 0.835403i | \(-0.314766\pi\) | ||||
0.549638 | + | 0.835403i | \(0.314766\pi\) | |||||||
\(908\) | −53.6940 | −1.78190 | ||||||||
\(909\) | −96.0833 | −3.18688 | ||||||||
\(910\) | 12.4853 | 0.413883 | ||||||||
\(911\) | −56.3666 | −1.86751 | −0.933754 | − | 0.357914i | \(-0.883488\pi\) | ||||
−0.933754 | + | 0.357914i | \(0.883488\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.34315 | 0.209927 | ||||||||
\(914\) | −36.3762 | −1.20322 | ||||||||
\(915\) | −8.40401 | −0.277828 | ||||||||
\(916\) | 30.1421 | 0.995924 | ||||||||
\(917\) | −35.3137 | −1.16616 | ||||||||
\(918\) | 64.5685 | 2.13108 | ||||||||
\(919\) | −56.2843 | −1.85665 | −0.928323 | − | 0.371774i | \(-0.878750\pi\) | ||||
−0.928323 | + | 0.371774i | \(0.878750\pi\) | |||||||
\(920\) | 4.20201 | 0.138536 | ||||||||
\(921\) | −33.7990 | −1.11371 | ||||||||
\(922\) | −69.9922 | −2.30507 | ||||||||
\(923\) | 13.3726 | 0.440164 | ||||||||
\(924\) | −69.2713 | −2.27886 | ||||||||
\(925\) | 7.17327 | 0.235856 | ||||||||
\(926\) | −57.0876 | −1.87601 | ||||||||
\(927\) | 51.9534 | 1.70637 | ||||||||
\(928\) | −19.7990 | −0.649934 | ||||||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 37.0971 | 1.21646 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 32.1421 | 1.05285 | ||||||||
\(933\) | 94.0610 | 3.07942 | ||||||||
\(934\) | 45.2025 | 1.47907 | ||||||||
\(935\) | −7.31371 | −0.239184 | ||||||||
\(936\) | 6.24264 | 0.204047 | ||||||||
\(937\) | −22.9706 | −0.750416 | −0.375208 | − | 0.926941i | \(-0.622429\pi\) | ||||
−0.375208 | + | 0.926941i | \(0.622429\pi\) | |||||||
\(938\) | 55.1127 | 1.79949 | ||||||||
\(939\) | 61.2896 | 2.00011 | ||||||||
\(940\) | −15.6569 | −0.510670 | ||||||||
\(941\) | 28.6931 | 0.935368 | 0.467684 | − | 0.883896i | \(-0.345089\pi\) | ||||
0.467684 | + | 0.883896i | \(0.345089\pi\) | |||||||
\(942\) | −112.368 | −3.66113 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | −35.6552 | −1.16048 | ||||||||
\(945\) | −40.5782 | −1.32001 | ||||||||
\(946\) | 3.48106 | 0.113179 | ||||||||
\(947\) | 24.1421 | 0.784514 | 0.392257 | − | 0.919856i | \(-0.371694\pi\) | ||||
0.392257 | + | 0.919856i | \(0.371694\pi\) | |||||||
\(948\) | 85.2548 | 2.76895 | ||||||||
\(949\) | −0.422323 | −0.0137092 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 46.2843 | 1.50087 | ||||||||
\(952\) | −15.3661 | −0.498019 | ||||||||
\(953\) | 27.4624 | 0.889593 | 0.444796 | − | 0.895632i | \(-0.353276\pi\) | ||||
0.444796 | + | 0.895632i | \(0.353276\pi\) | |||||||
\(954\) | 57.6985 | 1.86806 | ||||||||
\(955\) | −13.6569 | −0.441925 | ||||||||
\(956\) | −4.00000 | −0.129369 | ||||||||
\(957\) | −14.6274 | −0.472837 | ||||||||
\(958\) | 21.0100 | 0.678803 | ||||||||
\(959\) | −9.65685 | −0.311836 | ||||||||
\(960\) | 32.3853 | 1.04523 | ||||||||
\(961\) | 4.31371 | 0.139152 | ||||||||
\(962\) | 18.5486 | 0.598029 | ||||||||
\(963\) | 37.6069 | 1.21187 | ||||||||
\(964\) | −16.8080 | −0.541350 | ||||||||
\(965\) | 8.19285 | 0.263737 | ||||||||
\(966\) | −145.539 | −4.68264 | ||||||||
\(967\) | 38.4853 | 1.23760 | 0.618802 | − | 0.785547i | \(-0.287618\pi\) | ||||
0.618802 | + | 0.785547i | \(0.287618\pi\) | |||||||
\(968\) | −6.09185 | −0.195799 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.58579 | 0.0830246 | ||||||||
\(971\) | −46.5207 | −1.49292 | −0.746460 | − | 0.665430i | \(-0.768248\pi\) | ||||
−0.746460 | + | 0.665430i | \(0.768248\pi\) | |||||||
\(972\) | 7.17327 | 0.230083 | ||||||||
\(973\) | 40.2843 | 1.29145 | ||||||||
\(974\) | 33.3553 | 1.06877 | ||||||||
\(975\) | −3.65685 | −0.117113 | ||||||||
\(976\) | −8.48528 | −0.271607 | ||||||||
\(977\) | −21.0975 | −0.674969 | −0.337484 | − | 0.941331i | \(-0.609576\pi\) | ||||
−0.337484 | + | 0.941331i | \(0.609576\pi\) | |||||||
\(978\) | −80.0833 | −2.56078 | ||||||||
\(979\) | 18.8472 | 0.602358 | ||||||||
\(980\) | 39.3848 | 1.25810 | ||||||||
\(981\) | −112.311 | −3.58581 | ||||||||
\(982\) | −51.0213 | −1.62816 | ||||||||
\(983\) | −56.4541 | −1.80061 | −0.900303 | − | 0.435265i | \(-0.856655\pi\) | ||||
−0.900303 | + | 0.435265i | \(0.856655\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.3137 | −0.424210 | ||||||||
\(986\) | −18.9117 | −0.602271 | ||||||||
\(987\) | 93.0414 | 2.96154 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4.00000 | 0.127193 | ||||||||
\(990\) | 24.4911 | 0.778378 | ||||||||
\(991\) | −12.9046 | −0.409930 | −0.204965 | − | 0.978769i | \(-0.565708\pi\) | ||||
−0.204965 | + | 0.978769i | \(0.565708\pi\) | |||||||
\(992\) | 47.7990 | 1.51762 | ||||||||
\(993\) | −88.2843 | −2.80162 | ||||||||
\(994\) | 110.225 | 3.49614 | ||||||||
\(995\) | −4.00000 | −0.126809 | ||||||||
\(996\) | −22.7506 | −0.720879 | ||||||||
\(997\) | 3.65685 | 0.115814 | 0.0579069 | − | 0.998322i | \(-0.481557\pi\) | ||||
0.0579069 | + | 0.998322i | \(0.481557\pi\) | |||||||
\(998\) | 73.4733 | 2.32576 | ||||||||
\(999\) | −60.2843 | −1.90731 |
(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 | 1805.2.a.m.1.4 | yes | 4 | |
5.4 | even | 2 | 9025.2.a.bn.1.1 | 4 | |||
19.18 | odd | 2 | inner | 1805.2.a.m.1.1 | ✓ | 4 | |
95.94 | odd | 2 | 9025.2.a.bn.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1805.2.a.m.1.1 | ✓ | 4 | 19.18 | odd | 2 | inner | |
1805.2.a.m.1.4 | yes | 4 | 1.1 | even | 1 | trivial | |
9025.2.a.bn.1.1 | 4 | 5.4 | even | 2 | |||
9025.2.a.bn.1.4 | 4 | 95.94 | odd | 2 |