Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8512,2,Mod(1,8512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8512, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8512.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8512 = 2^{6} \cdot 7 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8512.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(67.9686622005\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | 6.6.41027408.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} - 6x^{4} + 15x^{3} + 12x^{2} - 17x - 7 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 4256) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-1.72183\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8512.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.72183 | 0.994098 | 0.497049 | − | 0.867723i | \(-0.334417\pi\) | ||||
0.497049 | + | 0.867723i | \(0.334417\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.54252 | −0.689835 | −0.344917 | − | 0.938633i | \(-0.612093\pi\) | ||||
−0.344917 | + | 0.938633i | \(0.612093\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.0353081 | −0.0117694 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.07847 | −1.22971 | −0.614853 | − | 0.788642i | \(-0.710785\pi\) | ||||
−0.614853 | + | 0.788642i | \(0.710785\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.958129 | −0.265737 | −0.132869 | − | 0.991134i | \(-0.542419\pi\) | ||||
−0.132869 | + | 0.991134i | \(0.542419\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.65595 | −0.685763 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.53595 | 0.372524 | 0.186262 | − | 0.982500i | \(-0.440363\pi\) | ||||
0.186262 | + | 0.982500i | \(0.440363\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.72183 | 0.375734 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.92159 | 1.86028 | 0.930140 | − | 0.367206i | \(-0.119686\pi\) | ||||
0.930140 | + | 0.367206i | \(0.119686\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.62064 | −0.524128 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.22628 | −1.00580 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.51945 | 0.467851 | 0.233925 | − | 0.972255i | \(-0.424843\pi\) | ||||
0.233925 | + | 0.972255i | \(0.424843\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.464046 | 0.0833451 | 0.0416725 | − | 0.999131i | \(-0.486731\pi\) | ||||
0.0416725 | + | 0.999131i | \(0.486731\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −7.02243 | −1.22245 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.54252 | −0.260733 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.79133 | 1.11649 | 0.558244 | − | 0.829677i | \(-0.311475\pi\) | ||||
0.558244 | + | 0.829677i | \(0.311475\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.64973 | −0.264169 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.97970 | 0.309176 | 0.154588 | − | 0.987979i | \(-0.450595\pi\) | ||||
0.154588 | + | 0.987979i | \(0.450595\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.20088 | −0.945625 | −0.472812 | − | 0.881163i | \(-0.656761\pi\) | ||||
−0.472812 | + | 0.881163i | \(0.656761\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.0544633 | 0.00811891 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.22764 | 0.324935 | 0.162468 | − | 0.986714i | \(-0.448055\pi\) | ||||
0.162468 | + | 0.986714i | \(0.448055\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.64465 | 0.370325 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.3396 | −1.42025 | −0.710127 | − | 0.704073i | \(-0.751363\pi\) | ||||
−0.710127 | + | 0.704073i | \(0.751363\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.29111 | 0.848293 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.72183 | 0.228062 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.8496 | −1.67287 | −0.836437 | − | 0.548063i | \(-0.815366\pi\) | ||||
−0.836437 | + | 0.548063i | \(0.815366\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.97107 | 0.508443 | 0.254222 | − | 0.967146i | \(-0.418181\pi\) | ||||
0.254222 | + | 0.967146i | \(0.418181\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −0.0353081 | −0.00444840 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.47793 | 0.183315 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.3944 | 1.51422 | 0.757110 | − | 0.653288i | \(-0.226611\pi\) | ||||
0.757110 | + | 0.653288i | \(0.226611\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 15.3614 | 1.84930 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0908 | −1.67227 | −0.836134 | − | 0.548526i | \(-0.815189\pi\) | ||||
−0.836134 | + | 0.548526i | \(0.815189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.47879 | −1.10941 | −0.554704 | − | 0.832048i | \(-0.687169\pi\) | ||||
−0.554704 | + | 0.832048i | \(0.687169\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.51229 | −0.521035 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −4.07847 | −0.464785 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.03911 | 0.229418 | 0.114709 | − | 0.993399i | \(-0.463406\pi\) | ||||
0.114709 | + | 0.993399i | \(0.463406\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.89283 | −0.988092 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.26012 | 0.138316 | 0.0691581 | − | 0.997606i | \(-0.477969\pi\) | ||||
0.0691581 | + | 0.997606i | \(0.477969\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.36924 | −0.256980 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.33807 | 0.465090 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.48079 | 0.262963 | 0.131482 | − | 0.991319i | \(-0.458027\pi\) | ||||
0.131482 | + | 0.991319i | \(0.458027\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.958129 | −0.100439 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.799007 | 0.0828532 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.54252 | −0.158259 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.57593 | 0.261546 | 0.130773 | − | 0.991412i | \(-0.458254\pi\) | ||||
0.130773 | + | 0.991412i | \(0.458254\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.144003 | 0.0144728 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.78530 | −0.277147 | −0.138574 | − | 0.990352i | \(-0.544252\pi\) | ||||
−0.138574 | + | 0.990352i | \(0.544252\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −5.90034 | −0.581377 | −0.290689 | − | 0.956818i | \(-0.593884\pi\) | ||||
−0.290689 | + | 0.956818i | \(0.593884\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.65595 | −0.259194 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.8893 | −1.05271 | −0.526354 | − | 0.850266i | \(-0.676441\pi\) | ||||
−0.526354 | + | 0.850266i | \(0.676441\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.42638 | −0.519753 | −0.259876 | − | 0.965642i | \(-0.583682\pi\) | ||||
−0.259876 | + | 0.965642i | \(0.583682\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.6935 | 1.10990 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.91255 | −0.556206 | −0.278103 | − | 0.960551i | \(-0.589706\pi\) | ||||
−0.278103 | + | 0.960551i | \(0.589706\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −13.7617 | −1.28329 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.0338297 | 0.00312756 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.53595 | 0.140801 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.63393 | 0.512175 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.40870 | 0.307352 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7550 | 1.05140 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.86075 | 0.342586 | 0.171293 | − | 0.985220i | \(-0.445206\pi\) | ||||
0.171293 | + | 0.985220i | \(0.445206\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.6768 | −0.940044 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.9493 | −1.30613 | −0.653064 | − | 0.757303i | \(-0.726517\pi\) | ||||
−0.653064 | + | 0.757303i | \(0.726517\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.00000 | 0.0867110 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.06162 | 0.693834 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.40454 | 0.119998 | 0.0599991 | − | 0.998198i | \(-0.480890\pi\) | ||||
0.0599991 | + | 0.998198i | \(0.480890\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −22.0324 | −1.86876 | −0.934382 | − | 0.356274i | \(-0.884047\pi\) | ||||
−0.934382 | + | 0.356274i | \(0.884047\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.83562 | 0.323017 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.90770 | 0.326778 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.88630 | −0.322740 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 1.72183 | 0.142014 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.01028 | −0.492381 | −0.246191 | − | 0.969221i | \(-0.579179\pi\) | ||||
−0.246191 | + | 0.969221i | \(0.579179\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.04677 | −0.410700 | −0.205350 | − | 0.978689i | \(-0.565833\pi\) | ||||
−0.205350 | + | 0.978689i | \(0.565833\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −0.0542316 | −0.00438436 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.715799 | −0.0574943 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.06889 | −0.484350 | −0.242175 | − | 0.970233i | \(-0.577861\pi\) | ||||
−0.242175 | + | 0.970233i | \(0.577861\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −17.8030 | −1.41187 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.92159 | 0.703120 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −7.03167 | −0.550763 | −0.275381 | − | 0.961335i | \(-0.588804\pi\) | ||||
−0.275381 | + | 0.961335i | \(0.588804\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 10.8322 | 0.843287 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.4751 | −0.887967 | −0.443983 | − | 0.896035i | \(-0.646435\pi\) | ||||
−0.443983 | + | 0.896035i | \(0.646435\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.0820 | −0.929384 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.0353081 | −0.00270008 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.9653 | −1.28985 | −0.644925 | − | 0.764246i | \(-0.723112\pi\) | ||||
−0.644925 | + | 0.764246i | \(0.723112\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.62064 | −0.198102 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −22.1248 | −1.66300 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.3181 | 1.51865 | 0.759324 | − | 0.650713i | \(-0.225530\pi\) | ||||
0.759324 | + | 0.650713i | \(0.225530\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.3642 | 1.29067 | 0.645335 | − | 0.763900i | \(-0.276718\pi\) | ||||
0.645335 | + | 0.763900i | \(0.276718\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.83750 | 0.505442 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.4757 | −0.770191 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.26435 | −0.458094 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.22628 | −0.380156 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.0293 | −0.798053 | −0.399027 | − | 0.916939i | \(-0.630652\pi\) | ||||
−0.399027 | + | 0.916939i | \(0.630652\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.46871 | 0.105720 | 0.0528600 | − | 0.998602i | \(-0.483166\pi\) | ||||
0.0528600 | + | 0.998602i | \(0.483166\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.54474 | 0.182233 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0687 | −1.28734 | −0.643670 | − | 0.765303i | \(-0.722589\pi\) | ||||
−0.643670 | + | 0.765303i | \(0.722589\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.92999 | 0.278589 | 0.139295 | − | 0.990251i | \(-0.455516\pi\) | ||||
0.139295 | + | 0.990251i | \(0.455516\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 21.3411 | 1.50528 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.51945 | 0.176831 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.05371 | −0.213281 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.315004 | −0.0218943 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.07847 | −0.282114 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.0342 | −1.58574 | −0.792871 | − | 0.609389i | \(-0.791415\pi\) | ||||
−0.792871 | + | 0.609389i | \(0.791415\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −24.2619 | −1.66240 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.56496 | 0.652325 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0.464046 | 0.0315015 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −16.3208 | −1.10286 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.47164 | −0.0989934 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.77688 | −0.520779 | −0.260389 | − | 0.965504i | \(-0.583851\pi\) | ||||
−0.260389 | + | 0.965504i | \(0.583851\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.0925298 | 0.00616865 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.7785 | −0.781768 | −0.390884 | − | 0.920440i | \(-0.627831\pi\) | ||||
−0.390884 | + | 0.920440i | \(0.627831\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −22.8995 | −1.51324 | −0.756620 | − | 0.653855i | \(-0.773151\pi\) | ||||
−0.756620 | + | 0.653855i | \(0.773151\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.02243 | −0.462042 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 18.5286 | 1.21385 | 0.606926 | − | 0.794758i | \(-0.292402\pi\) | ||||
0.606926 | + | 0.794758i | \(0.292402\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.43618 | −0.224152 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.51100 | 0.228064 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.249079 | 0.0161116 | 0.00805581 | − | 0.999968i | \(-0.497436\pi\) | ||||
0.00805581 | + | 0.999968i | \(0.497436\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.81520 | 0.439006 | 0.219503 | − | 0.975612i | \(-0.429556\pi\) | ||||
0.219503 | + | 0.975612i | \(0.429556\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.366913 | 0.0235375 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.54252 | −0.0985478 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.958129 | −0.0609643 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.16971 | 0.137500 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −0.414081 | −0.0261366 | −0.0130683 | − | 0.999915i | \(-0.504160\pi\) | ||||
−0.0130683 | + | 0.999915i | \(0.504160\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −36.3864 | −2.28760 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.07942 | −0.255463 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.762240 | 0.0475472 | 0.0237736 | − | 0.999717i | \(-0.492432\pi\) | ||||
0.0237736 | + | 0.999717i | \(0.492432\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.79133 | 0.421992 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.0889571 | −0.00550630 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 28.2110 | 1.73957 | 0.869783 | − | 0.493435i | \(-0.164259\pi\) | ||||
0.869783 | + | 0.493435i | \(0.164259\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.9490 | 0.979741 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.27149 | 0.261411 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −15.6272 | −0.952807 | −0.476403 | − | 0.879227i | \(-0.658060\pi\) | ||||
−0.476403 | + | 0.879227i | \(0.658060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.29871 | 0.321874 | 0.160937 | − | 0.986965i | \(-0.448548\pi\) | ||||
0.160937 | + | 0.986965i | \(0.448548\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.64973 | −0.0998464 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.6882 | 0.644523 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.66726 | 0.340512 | 0.170256 | − | 0.985400i | \(-0.445540\pi\) | ||||
0.170256 | + | 0.985400i | \(0.445540\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.0163846 | −0.000980918 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.4634 | −1.28040 | −0.640200 | − | 0.768209i | \(-0.721148\pi\) | ||||
−0.640200 | + | 0.768209i | \(0.721148\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −8.71153 | −0.517847 | −0.258923 | − | 0.965898i | \(-0.583368\pi\) | ||||
−0.258923 | + | 0.965898i | \(0.583368\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −2.65595 | −0.157325 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.97970 | 0.116858 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.6408 | −0.861226 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.43530 | 0.260002 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.459648 | −0.0268529 | −0.0134265 | − | 0.999910i | \(-0.504274\pi\) | ||||
−0.0134265 | + | 0.999910i | \(0.504274\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 19.8207 | 1.15401 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 21.3152 | 1.23683 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −8.54803 | −0.494345 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.20088 | −0.357413 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −4.79580 | −0.275512 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.12544 | −0.350742 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.9441 | 1.36656 | 0.683282 | − | 0.730154i | \(-0.260552\pi\) | ||||
0.683282 | + | 0.730154i | \(0.260552\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.1594 | −0.577946 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 24.7979 | 1.40616 | 0.703080 | − | 0.711111i | \(-0.251808\pi\) | ||||
0.703080 | + | 0.711111i | \(0.251808\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.74984 | −0.494570 | −0.247285 | − | 0.968943i | \(-0.579538\pi\) | ||||
−0.247285 | + | 0.968943i | \(0.579538\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0544633 | 0.00306866 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.70906 | 0.152156 | 0.0760779 | − | 0.997102i | \(-0.475760\pi\) | ||||
0.0760779 | + | 0.997102i | \(0.475760\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −10.2755 | −0.575319 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.7495 | −1.04649 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.53595 | 0.0854628 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.51091 | 0.139280 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −9.34329 | −0.516685 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.22764 | 0.122814 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.09703 | 0.445053 | 0.222526 | − | 0.974927i | \(-0.428570\pi\) | ||||
0.222526 | + | 0.974927i | \(0.428570\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −0.239789 | −0.0131403 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.1186 | −1.04456 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.33064 | 0.235905 | 0.117952 | − | 0.993019i | \(-0.462367\pi\) | ||||
0.117952 | + | 0.993019i | \(0.462367\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.1804 | −0.552924 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.89260 | −0.102490 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −23.6953 | −1.27571 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.59896 | −0.193202 | −0.0966010 | − | 0.995323i | \(-0.530797\pi\) | ||||
−0.0966010 | + | 0.995323i | \(0.530797\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.5143 | −1.25869 | −0.629346 | − | 0.777125i | \(-0.716677\pi\) | ||||
−0.629346 | + | 0.777125i | \(0.716677\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.00745 | 0.267278 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.69809 | −0.303279 | −0.151639 | − | 0.988436i | \(-0.548455\pi\) | ||||
−0.151639 | + | 0.988436i | \(0.548455\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 21.7353 | 1.15359 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 2.64465 | 0.139970 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.7605 | 1.35959 | 0.679793 | − | 0.733404i | \(-0.262070\pi\) | ||||
0.679793 | + | 0.733404i | \(0.262070\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 9.70066 | 0.509152 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 14.6212 | 0.765308 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 36.9046 | 1.92640 | 0.963202 | − | 0.268778i | \(-0.0866198\pi\) | ||||
0.963202 | + | 0.268778i | \(0.0866198\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0698992 | −0.00363881 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −10.3396 | −0.536806 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.3997 | −0.849142 | −0.424571 | − | 0.905395i | \(-0.639575\pi\) | ||||
−0.424571 | + | 0.905395i | \(0.639575\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 20.2400 | 1.04519 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.41396 | −0.124325 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.5177 | 0.951188 | 0.475594 | − | 0.879665i | \(-0.342233\pi\) | ||||
0.475594 | + | 0.879665i | \(0.342233\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.64755 | 0.340564 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.3346 | 1.65222 | 0.826110 | − | 0.563509i | \(-0.190549\pi\) | ||||
0.826110 | + | 0.563509i | \(0.190549\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.29111 | 0.320625 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.218941 | 0.0111294 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.3717 | −1.28640 | −0.643198 | − | 0.765700i | \(-0.722393\pi\) | ||||
−0.643198 | + | 0.765700i | \(0.722393\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 13.7031 | 0.692998 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −25.7401 | −1.29842 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.14537 | −0.158261 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.2599 | 1.11719 | 0.558596 | − | 0.829440i | \(-0.311340\pi\) | ||||
0.558596 | + | 0.829440i | \(0.311340\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.72183 | 0.0861992 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −17.3432 | −0.866076 | −0.433038 | − | 0.901376i | \(-0.642558\pi\) | ||||
−0.433038 | + | 0.901376i | \(0.642558\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.444616 | −0.0221479 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 13.7173 | 0.681620 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −27.6982 | −1.37295 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 35.8282 | 1.77159 | 0.885795 | − | 0.464077i | \(-0.153614\pi\) | ||||
0.885795 | + | 0.464077i | \(0.153614\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.41838 | 0.119290 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.8496 | −0.632287 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.94376 | −0.0954153 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −37.9360 | −1.85773 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2.89443 | −0.141402 | −0.0707011 | − | 0.997498i | \(-0.522524\pi\) | ||||
−0.0707011 | + | 0.997498i | \(0.522524\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.2319 | −1.08352 | −0.541759 | − | 0.840534i | \(-0.682242\pi\) | ||||
−0.541759 | + | 0.840534i | \(0.682242\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.0786538 | −0.00382428 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.02518 | −0.195250 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.97107 | 0.192173 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.72839 | 0.324850 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.5425 | −0.604152 | −0.302076 | − | 0.953284i | \(-0.597680\pi\) | ||||
−0.302076 | + | 0.953284i | \(0.597680\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.76196 | −0.469130 | −0.234565 | − | 0.972100i | \(-0.575367\pi\) | ||||
−0.234565 | + | 0.972100i | \(0.575367\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.69154 | −0.320835 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 8.92159 | 0.426777 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 36.0623 | 1.72116 | 0.860579 | − | 0.509317i | \(-0.170102\pi\) | ||||
0.860579 | + | 0.509317i | \(0.170102\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −0.0353081 | −0.00168134 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.4276 | 1.63570 | 0.817852 | − | 0.575428i | \(-0.195165\pi\) | ||||
0.817852 | + | 0.575428i | \(0.195165\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.82666 | −0.181401 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −10.3487 | −0.489475 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.0491 | 0.663017 | 0.331509 | − | 0.943452i | \(-0.392442\pi\) | ||||
0.331509 | + | 0.943452i | \(0.392442\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.07413 | −0.380196 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.68967 | −0.408276 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.47793 | 0.0692864 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.7557 | −0.830578 | −0.415289 | − | 0.909689i | \(-0.636320\pi\) | ||||
−0.415289 | + | 0.909689i | \(0.636320\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −8.02732 | −0.374683 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 39.9013 | 1.85839 | 0.929194 | − | 0.369592i | \(-0.120503\pi\) | ||||
0.929194 | + | 0.369592i | \(0.120503\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.76594 | 0.267966 | 0.133983 | − | 0.990984i | \(-0.457223\pi\) | ||||
0.133983 | + | 0.990984i | \(0.457223\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.23248 | −0.0571550 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.2761 | −1.07709 | −0.538545 | − | 0.842597i | \(-0.681026\pi\) | ||||
−0.538545 | + | 0.842597i | \(0.681026\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.3944 | 0.572321 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −10.4496 | −0.481491 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.2901 | 1.16284 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.62064 | −0.120243 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0.365072 | 0.0167155 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.08460 | 0.140939 | 0.0704695 | − | 0.997514i | \(-0.477550\pi\) | ||||
0.0704695 | + | 0.997514i | \(0.477550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.50697 | −0.296692 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.3614 | 0.698970 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.97341 | −0.180423 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.4573 | 0.519181 | 0.259590 | − | 0.965719i | \(-0.416412\pi\) | ||||
0.259590 | + | 0.965719i | \(0.416412\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.1073 | −0.547512 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.4849 | 0.473175 | 0.236588 | − | 0.971610i | \(-0.423971\pi\) | ||||
0.236588 | + | 0.971610i | \(0.423971\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3.86977 | 0.174286 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.222127 | −0.00998387 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −14.0908 | −0.632058 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −40.9058 | −1.83119 | −0.915597 | − | 0.402098i | \(-0.868281\pi\) | ||||
−0.915597 | + | 0.402098i | \(0.868281\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −19.7581 | −0.882726 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −37.6788 | −1.68002 | −0.840008 | − | 0.542573i | \(-0.817450\pi\) | ||||
−0.840008 | + | 0.542573i | \(0.817450\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 4.29637 | 0.191186 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.8031 | −0.923898 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −32.6186 | −1.44579 | −0.722897 | − | 0.690956i | \(-0.757190\pi\) | ||||
−0.722897 | + | 0.690956i | \(0.757190\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.47879 | −0.419317 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −5.22628 | −0.230746 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 9.10137 | 0.401054 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.08538 | −0.399575 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −29.2114 | −1.28224 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.58355 | 0.419863 | 0.209931 | − | 0.977716i | \(-0.432676\pi\) | ||||
0.209931 | + | 0.977716i | \(0.432676\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.43831 | 0.325254 | 0.162627 | − | 0.986688i | \(-0.448003\pi\) | ||||
0.162627 | + | 0.986688i | \(0.448003\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.51229 | −0.196933 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.712753 | 0.0310480 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 56.5947 | 2.46064 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0.453694 | 0.0196887 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.89680 | −0.0821597 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.7969 | 0.726194 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34.9843 | 1.50968 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.07847 | −0.175672 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −15.8767 | −0.682591 | −0.341295 | − | 0.939956i | \(-0.610866\pi\) | ||||
−0.341295 | + | 0.939956i | \(0.610866\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 29.8982 | 1.28305 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.37028 | 0.358543 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 29.3980 | 1.25697 | 0.628484 | − | 0.777822i | \(-0.283676\pi\) | ||||
0.628484 | + | 0.777822i | \(0.283676\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.140211 | −0.00598405 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.51945 | 0.107332 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.03911 | 0.0867119 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −18.0374 | −0.765646 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.5091 | −0.572401 | −0.286200 | − | 0.958170i | \(-0.592392\pi\) | ||||
−0.286200 | + | 0.958170i | \(0.592392\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.94124 | 0.251288 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.7861 | −0.455391 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 22.4945 | 0.948031 | 0.474016 | − | 0.880516i | \(-0.342804\pi\) | ||||
0.474016 | + | 0.880516i | \(0.342804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.12022 | 0.383690 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.89283 | −0.373464 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.9924 | −0.880046 | −0.440023 | − | 0.897986i | \(-0.645030\pi\) | ||||
−0.440023 | + | 0.897986i | \(0.645030\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 44.9996 | 1.88318 | 0.941588 | − | 0.336766i | \(-0.109333\pi\) | ||||
0.941588 | + | 0.336766i | \(0.109333\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −18.9906 | −0.793343 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.3803 | −0.975025 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.2515 | 0.676560 | 0.338280 | − | 0.941045i | \(-0.390155\pi\) | ||||
0.338280 | + | 0.941045i | \(0.390155\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.52887 | 0.105096 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.26012 | 0.0522786 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 42.1698 | 1.74649 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0521829 | −0.00215750 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −44.6567 | −1.84318 | −0.921590 | − | 0.388165i | \(-0.873109\pi\) | ||||
−0.921590 | + | 0.388165i | \(0.873109\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.464046 | 0.0191207 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −31.1112 | −1.27974 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −40.1075 | −1.64702 | −0.823509 | − | 0.567303i | \(-0.807987\pi\) | ||||
−0.823509 | + | 0.567303i | \(0.807987\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.36924 | −0.0971292 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.76676 | 0.276945 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.7938 | −1.05391 | −0.526954 | − | 0.849894i | \(-0.676666\pi\) | ||||
−0.526954 | + | 0.849894i | \(0.676666\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.1526 | −1.31153 | −0.655765 | − | 0.754965i | \(-0.727654\pi\) | ||||
−0.655765 | + | 0.754965i | \(0.727654\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.437623 | −0.0178214 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −8.69043 | −0.353316 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.6642 | −0.919911 | −0.459956 | − | 0.887942i | \(-0.652135\pi\) | ||||
−0.459956 | + | 0.887942i | \(0.652135\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.33807 | 0.175787 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.13437 | −0.0863474 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 43.8074 | 1.76936 | 0.884682 | − | 0.466196i | \(-0.154376\pi\) | ||||
0.884682 | + | 0.466196i | \(0.154376\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.25797 | −0.212022 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −46.2073 | −1.86024 | −0.930118 | − | 0.367261i | \(-0.880295\pi\) | ||||
−0.930118 | + | 0.367261i | \(0.880295\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.9085 | 0.759996 | 0.379998 | − | 0.924987i | \(-0.375925\pi\) | ||||
0.379998 | + | 0.924987i | \(0.375925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −46.6267 | −1.87106 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.48079 | 0.0993907 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.02903 | −0.201161 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.02243 | −0.280449 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 10.4312 | 0.415918 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.9351 | −0.793604 | −0.396802 | − | 0.917904i | \(-0.629880\pi\) | ||||
−0.396802 | + | 0.917904i | \(0.629880\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −39.6610 | −1.57638 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.95527 | −0.236328 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.958129 | −0.0379625 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.497518 | 0.0196815 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −35.8503 | −1.41600 | −0.708000 | − | 0.706212i | \(-0.750403\pi\) | ||||
−0.708000 | + | 0.706212i | \(0.750403\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 26.6068 | 1.04927 | 0.524635 | − | 0.851327i | \(-0.324202\pi\) | ||||
0.524635 | + | 0.851327i | \(0.324202\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 16.4692 | 0.648475 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −19.5860 | −0.770005 | −0.385003 | − | 0.922915i | \(-0.625799\pi\) | ||||
−0.385003 | + | 0.922915i | \(0.625799\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 52.4067 | 2.05714 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.799007 | 0.0313156 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.2709 | 0.910659 | 0.455330 | − | 0.890323i | \(-0.349521\pi\) | ||||
0.455330 | + | 0.890323i | \(0.349521\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.0596 | 0.901012 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.334678 | 0.0130570 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.3819 | 0.716058 | 0.358029 | − | 0.933710i | \(-0.383449\pi\) | ||||
0.358029 | + | 0.933710i | \(0.383449\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −3.28306 | −0.127696 | −0.0638482 | − | 0.997960i | \(-0.520337\pi\) | ||||
−0.0638482 | + | 0.997960i | \(0.520337\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.53392 | −0.0984091 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.54252 | −0.0598162 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22.4775 | 0.870333 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −13.3905 | −0.517705 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −16.1959 | −0.625235 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −32.2466 | −1.24302 | −0.621508 | − | 0.783408i | \(-0.713480\pi\) | ||||
−0.621508 | + | 0.783408i | \(0.713480\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 13.6962 | 0.527167 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −17.5452 | −0.674316 | −0.337158 | − | 0.941448i | \(-0.609466\pi\) | ||||
−0.337158 | + | 0.941448i | \(0.609466\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.57593 | 0.0988550 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −20.2806 | −0.777154 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −9.60539 | −0.367540 | −0.183770 | − | 0.982969i | \(-0.558830\pi\) | ||||
−0.183770 | + | 0.982969i | \(0.558830\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2.16653 | −0.0827790 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −39.4289 | −1.50431 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 9.90668 | 0.377414 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.8826 | −0.832451 | −0.416226 | − | 0.909261i | \(-0.636647\pi\) | ||||
−0.416226 | + | 0.909261i | \(0.636647\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.144003 | 0.00547022 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 33.9853 | 1.28914 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.04072 | 0.115176 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.9031 | 1.20669 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.18985 | −0.347096 | −0.173548 | − | 0.984825i | \(-0.555523\pi\) | ||||
−0.173548 | + | 0.984825i | \(0.555523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.79133 | 0.256140 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −5.91651 | −0.222829 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.78530 | −0.104752 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.5389 | 1.07180 | 0.535901 | − | 0.844281i | \(-0.319972\pi\) | ||||
0.535901 | + | 0.844281i | \(0.319972\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.0719971 | −0.00270010 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4.14002 | 0.155045 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.02770 | −0.225423 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0.428872 | 0.0160165 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.7733 | −0.886593 | −0.443296 | − | 0.896375i | \(-0.646191\pi\) | ||||
−0.443296 | + | 0.896375i | \(0.646191\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.90034 | −0.219740 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11.7346 | 0.436415 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.60259 | −0.245214 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.39111 | −0.125769 | −0.0628846 | − | 0.998021i | \(-0.520030\pi\) | ||||
−0.0628846 | + | 0.998021i | \(0.520030\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.3102 | 1.01149 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.52426 | −0.352268 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.62579 | 0.244729 | 0.122364 | − | 0.992485i | \(-0.460952\pi\) | ||||
0.122364 | + | 0.992485i | \(0.460952\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.65595 | −0.0979662 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −50.5503 | −1.86204 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10.1808 | −0.374505 | −0.187253 | − | 0.982312i | \(-0.559958\pi\) | ||||
−0.187253 | + | 0.982312i | \(0.559958\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.64973 | −0.0606045 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.22858 | 0.228504 | 0.114252 | − | 0.993452i | \(-0.463553\pi\) | ||||
0.114252 | + | 0.993452i | \(0.463553\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.27096 | 0.339662 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.0444924 | −0.00162789 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.8893 | −0.397886 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 27.8628 | 1.01673 | 0.508364 | − | 0.861143i | \(-0.330251\pi\) | ||||
0.508364 | + | 0.861143i | \(0.330251\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.712977 | −0.0259823 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 7.78472 | 0.283315 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.18222 | 0.333734 | 0.166867 | − | 0.985979i | \(-0.446635\pi\) | ||||
0.166867 | + | 0.985979i | \(0.446635\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −62.6512 | −2.27409 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28.3945 | 1.02930 | 0.514650 | − | 0.857400i | \(-0.327922\pi\) | ||||
0.514650 | + | 0.857400i | \(0.327922\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.42638 | −0.196448 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0.0836531 | 0.00302449 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 12.3116 | 0.444545 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.85252 | 0.0668035 | 0.0334018 | − | 0.999442i | \(-0.489366\pi\) | ||||
0.0334018 | + | 0.999442i | \(0.489366\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.31245 | 0.0472666 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.0734 | 0.470217 | 0.235109 | − | 0.971969i | \(-0.424455\pi\) | ||||
0.235109 | + | 0.971969i | \(0.424455\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.21610 | −0.0436835 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 11.6935 | 0.419502 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1.97970 | 0.0709300 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 57.4688 | 2.05640 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −13.1674 | −0.470563 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.36136 | 0.334121 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.5749 | 0.555187 | 0.277593 | − | 0.960699i | \(-0.410463\pi\) | ||||
0.277593 | + | 0.960699i | \(0.410463\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 48.5745 | 1.72930 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.91255 | −0.210226 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.80480 | −0.135112 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 27.4615 | 0.973958 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.3360 | 0.578649 | 0.289325 | − | 0.957231i | \(-0.406569\pi\) | ||||
0.289325 | + | 0.957231i | \(0.406569\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.42156 | 0.121046 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −0.0875919 | −0.00309491 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.6590 | 1.36425 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.7617 | −0.485036 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −26.9073 | −0.947183 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.41795 | −0.155327 | −0.0776635 | − | 0.996980i | \(-0.524746\pi\) | ||||
−0.0776635 | + | 0.996980i | \(0.524746\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −22.3329 | −0.784215 | −0.392107 | − | 0.919919i | \(-0.628254\pi\) | ||||
−0.392107 | + | 0.919919i | \(0.628254\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.12348 | 0.319974 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.8465 | 0.379935 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.20088 | −0.216941 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.0338297 | 0.00118210 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.1268 | −0.597729 | −0.298864 | − | 0.954296i | \(-0.596608\pi\) | ||||
−0.298864 | + | 0.954296i | \(0.596608\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 23.4609 | 0.817795 | 0.408898 | − | 0.912580i | \(-0.365913\pi\) | ||||
0.408898 | + | 0.912580i | \(0.365913\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 18.4033 | 0.640719 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.0744 | 0.628507 | 0.314253 | − | 0.949339i | \(-0.398246\pi\) | ||||
0.314253 | + | 0.949339i | \(0.398246\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.59196 | −0.124754 | −0.0623770 | − | 0.998053i | \(-0.519868\pi\) | ||||
−0.0623770 | + | 0.998053i | \(0.519868\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.75804 | 0.338503 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.53595 | 0.0532177 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.7005 | 0.612550 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.42523 | −0.0838283 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 31.8764 | 1.10050 | 0.550248 | − | 0.835001i | \(-0.314533\pi\) | ||||
0.550248 | + | 0.835001i | \(0.314533\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.6524 | −0.781116 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.9563 | −1.27284 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18.6367 | 0.641121 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.63393 | 0.193584 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.9998 | −0.514790 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 60.5894 | 2.07698 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.0420 | 1.78189 | 0.890943 | − | 0.454116i | \(-0.150045\pi\) | ||||
0.890943 | + | 0.454116i | \(0.150045\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0544633 | 0.00186261 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 47.3779 | 1.61840 | 0.809199 | − | 0.587534i | \(-0.199901\pi\) | ||||
0.809199 | + | 0.587534i | \(0.199901\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.87430 | −0.0639502 | −0.0319751 | − | 0.999489i | \(-0.510180\pi\) | ||||
−0.0319751 | + | 0.999489i | \(0.510180\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.40870 | 0.116168 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.6321 | −0.430000 | −0.215000 | − | 0.976614i | \(-0.568975\pi\) | ||||
−0.215000 | + | 0.976614i | \(0.568975\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 26.1693 | 0.889784 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −25.2090 | −0.856143 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8.31646 | −0.282117 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −11.8755 | −0.402384 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.0909510 | −0.00307822 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.7550 | 0.397390 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.6355 | 0.696811 | 0.348406 | − | 0.937344i | \(-0.386723\pi\) | ||||
0.348406 | + | 0.937344i | \(0.386723\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.791435 | −0.0266944 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.70171 | −0.0573321 | −0.0286660 | − | 0.999589i | \(-0.509126\pi\) | ||||
−0.0286660 | + | 0.999589i | \(0.509126\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 32.9265 | 1.10806 | 0.554032 | − | 0.832495i | \(-0.313089\pi\) | ||||
0.554032 | + | 0.832495i | \(0.313089\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 34.1279 | 1.14720 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29.7341 | −0.998372 | −0.499186 | − | 0.866495i | \(-0.666368\pi\) | ||||
−0.499186 | + | 0.866495i | \(0.666368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.86075 | 0.129485 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.2691 | 1.21506 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.22764 | 0.0745453 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.3410 | −1.04762 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14.7182 | −0.491428 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 1.16914 | 0.0389931 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.8812 | −0.529078 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −10.6768 | −0.355303 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −26.7846 | −0.890349 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.1920 | 0.570851 | 0.285425 | − | 0.958401i | \(-0.407865\pi\) | ||||
0.285425 | + | 0.958401i | \(0.407865\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0.0983434 | 0.00326185 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32.7334 | −1.08450 | −0.542252 | − | 0.840216i | \(-0.682428\pi\) | ||||
−0.542252 | + | 0.840216i | \(0.682428\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.13937 | −0.170088 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.5470 | −0.348672 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −14.9493 | −0.493670 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.93326 | 0.129746 | 0.0648732 | − | 0.997894i | \(-0.479336\pi\) | ||||
0.0648732 | + | 0.997894i | \(0.479336\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 41.2277 | 1.35850 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.5008 | 0.444384 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −17.7976 | −0.585182 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0.208330 | 0.00684244 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −52.8729 | −1.73470 | −0.867352 | − | 0.497694i | \(-0.834180\pi\) | ||||
−0.867352 | + | 0.497694i | \(0.834180\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.00000 | 0.0327737 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 42.6977 | 1.39786 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 9.66286 | 0.316009 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.33464 | −0.272281 | −0.136140 | − | 0.990690i | \(-0.543470\pi\) | ||||
−0.136140 | + | 0.990690i | \(0.543470\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15.0657 | −0.491651 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −59.1436 | −1.92803 | −0.964013 | − | 0.265854i | \(-0.914346\pi\) | ||||
−0.964013 | + | 0.265854i | \(0.914346\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.6620 | 0.575155 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.06162 | 0.262245 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 51.7202 | 1.68068 | 0.840340 | − | 0.542060i | \(-0.182355\pi\) | ||||
0.840340 | + | 0.542060i | \(0.182355\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.08190 | 0.294811 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.66453 | 0.151258 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −26.6904 | −0.864588 | −0.432294 | − | 0.901733i | \(-0.642296\pi\) | ||||
−0.432294 | + | 0.901733i | \(0.642296\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 17.0129 | 0.550525 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.6927 | −0.571923 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.40454 | 0.0453551 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.7847 | −0.993054 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0.384480 | 0.0123897 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −2.26551 | −0.0729294 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 18.3963 | 0.591584 | 0.295792 | − | 0.955252i | \(-0.404417\pi\) | ||||
0.295792 | + | 0.955252i | \(0.404417\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.64465 | 0.0849584 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.87813 | 0.0923637 | 0.0461818 | − | 0.998933i | \(-0.485295\pi\) | ||||
0.0461818 | + | 0.998933i | \(0.485295\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −22.0324 | −0.706326 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.32336 | 0.138458 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 36.4521 | 1.16621 | 0.583103 | − | 0.812398i | \(-0.301838\pi\) | ||||
0.583103 | + | 0.812398i | \(0.301838\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −10.1178 | −0.323367 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0.191595 | 0.00611716 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 41.9792 | 1.33893 | 0.669465 | − | 0.742844i | \(-0.266524\pi\) | ||||
0.669465 | + | 0.742844i | \(0.266524\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.8712 | 0.888052 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 3.83562 | 0.122089 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −55.3217 | −1.75913 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.34878 | −0.169910 | −0.0849548 | − | 0.996385i | \(-0.527075\pi\) | ||||
−0.0849548 | + | 0.996385i | \(0.527075\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 13.9417 | 0.442426 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6.06207 | −0.192181 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.13068 | 0.289171 | 0.144586 | − | 0.989492i | \(-0.453815\pi\) | ||||
0.144586 | + | 0.989492i | \(0.453815\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −35.4934 | −1.12296 |
(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 | 8512.2.a.ca.1.6 | 6 | ||
4.3 | odd | 2 | 8512.2.a.cf.1.1 | 6 | |||
8.3 | odd | 2 | 4256.2.a.i.1.6 | ✓ | 6 | ||
8.5 | even | 2 | 4256.2.a.n.1.1 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4256.2.a.i.1.6 | ✓ | 6 | 8.3 | odd | 2 | ||
4256.2.a.n.1.1 | yes | 6 | 8.5 | even | 2 | ||
8512.2.a.ca.1.6 | 6 | 1.1 | even | 1 | trivial | ||
8512.2.a.cf.1.1 | 6 | 4.3 | odd | 2 |