Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 16x^{6} - 4x^{5} + 75x^{4} + 32x^{3} - 90x^{2} - 28x - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.93433\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −2.48823 | −1.43658 | −0.718289 | − | 0.695745i | \(-0.755074\pi\) | ||||
−0.718289 | + | 0.695745i | \(0.755074\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.25915 | 1.45754 | 0.728768 | − | 0.684761i | \(-0.240093\pi\) | ||||
0.728768 | + | 0.684761i | \(0.240093\pi\) | |||||||
\(6\) | 2.48823 | 1.01581 | ||||||||
\(7\) | −4.58972 | −1.73475 | −0.867376 | − | 0.497654i | \(-0.834195\pi\) | ||||
−0.867376 | + | 0.497654i | \(0.834195\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.19127 | 1.06376 | ||||||||
\(10\) | −3.25915 | −1.03063 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −2.48823 | −0.718289 | ||||||||
\(13\) | 4.82326 | 1.33773 | 0.668865 | − | 0.743384i | \(-0.266780\pi\) | ||||
0.668865 | + | 0.743384i | \(0.266780\pi\) | |||||||
\(14\) | 4.58972 | 1.22665 | ||||||||
\(15\) | −8.10950 | −2.09386 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.77745 | −0.431095 | −0.215548 | − | 0.976493i | \(-0.569154\pi\) | ||||
−0.215548 | + | 0.976493i | \(0.569154\pi\) | |||||||
\(18\) | −3.19127 | −0.752189 | ||||||||
\(19\) | 1.00000 | 0.229416 | ||||||||
\(20\) | 3.25915 | 0.728768 | ||||||||
\(21\) | 11.4203 | 2.49210 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.51169 | 1.35778 | 0.678891 | − | 0.734239i | \(-0.262461\pi\) | ||||
0.678891 | + | 0.734239i | \(0.262461\pi\) | |||||||
\(24\) | 2.48823 | 0.507907 | ||||||||
\(25\) | 5.62205 | 1.12441 | ||||||||
\(26\) | −4.82326 | −0.945919 | ||||||||
\(27\) | −0.475914 | −0.0915896 | ||||||||
\(28\) | −4.58972 | −0.867376 | ||||||||
\(29\) | 0.0103559 | 0.00192304 | 0.000961522 | − | 1.00000i | \(-0.499694\pi\) | ||||
0.000961522 | 1.00000i | \(0.499694\pi\) | ||||||||
\(30\) | 8.10950 | 1.48059 | ||||||||
\(31\) | −3.91892 | −0.703860 | −0.351930 | − | 0.936026i | \(-0.614474\pi\) | ||||
−0.351930 | + | 0.936026i | \(0.614474\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.77745 | 0.304830 | ||||||||
\(35\) | −14.9586 | −2.52846 | ||||||||
\(36\) | 3.19127 | 0.531878 | ||||||||
\(37\) | 0.688142 | 0.113130 | 0.0565650 | − | 0.998399i | \(-0.481985\pi\) | ||||
0.0565650 | + | 0.998399i | \(0.481985\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | −12.0014 | −1.92175 | ||||||||
\(40\) | −3.25915 | −0.515317 | ||||||||
\(41\) | −3.27479 | −0.511436 | −0.255718 | − | 0.966751i | \(-0.582312\pi\) | ||||
−0.255718 | + | 0.966751i | \(0.582312\pi\) | |||||||
\(42\) | −11.4203 | −1.76218 | ||||||||
\(43\) | −1.38020 | −0.210479 | −0.105240 | − | 0.994447i | \(-0.533561\pi\) | ||||
−0.105240 | + | 0.994447i | \(0.533561\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.4008 | 1.55046 | ||||||||
\(46\) | −6.51169 | −0.960096 | ||||||||
\(47\) | −6.30125 | −0.919132 | −0.459566 | − | 0.888144i | \(-0.651995\pi\) | ||||
−0.459566 | + | 0.888144i | \(0.651995\pi\) | |||||||
\(48\) | −2.48823 | −0.359144 | ||||||||
\(49\) | 14.0655 | 2.00936 | ||||||||
\(50\) | −5.62205 | −0.795078 | ||||||||
\(51\) | 4.42270 | 0.619302 | ||||||||
\(52\) | 4.82326 | 0.668865 | ||||||||
\(53\) | 14.4636 | 1.98673 | 0.993365 | − | 0.115003i | \(-0.0366877\pi\) | ||||
0.993365 | + | 0.115003i | \(0.0366877\pi\) | |||||||
\(54\) | 0.475914 | 0.0647636 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 4.58972 | 0.613327 | ||||||||
\(57\) | −2.48823 | −0.329574 | ||||||||
\(58\) | −0.0103559 | −0.00135980 | ||||||||
\(59\) | −9.20149 | −1.19793 | −0.598966 | − | 0.800775i | \(-0.704421\pi\) | ||||
−0.598966 | + | 0.800775i | \(0.704421\pi\) | |||||||
\(60\) | −8.10950 | −1.04693 | ||||||||
\(61\) | −13.4651 | −1.72403 | −0.862017 | − | 0.506879i | \(-0.830799\pi\) | ||||
−0.862017 | + | 0.506879i | \(0.830799\pi\) | |||||||
\(62\) | 3.91892 | 0.497704 | ||||||||
\(63\) | −14.6470 | −1.84535 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 15.7197 | 1.94979 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.08657 | 0.621424 | 0.310712 | − | 0.950504i | \(-0.399433\pi\) | ||||
0.310712 | + | 0.950504i | \(0.399433\pi\) | |||||||
\(68\) | −1.77745 | −0.215548 | ||||||||
\(69\) | −16.2026 | −1.95056 | ||||||||
\(70\) | 14.9586 | 1.78789 | ||||||||
\(71\) | 9.43943 | 1.12025 | 0.560127 | − | 0.828406i | \(-0.310752\pi\) | ||||
0.560127 | + | 0.828406i | \(0.310752\pi\) | |||||||
\(72\) | −3.19127 | −0.376094 | ||||||||
\(73\) | 15.2769 | 1.78803 | 0.894014 | − | 0.448039i | \(-0.147877\pi\) | ||||
0.894014 | + | 0.448039i | \(0.147877\pi\) | |||||||
\(74\) | −0.688142 | −0.0799949 | ||||||||
\(75\) | −13.9889 | −1.61530 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 12.0014 | 1.35889 | ||||||||
\(79\) | −12.9416 | −1.45604 | −0.728019 | − | 0.685557i | \(-0.759559\pi\) | ||||
−0.728019 | + | 0.685557i | \(0.759559\pi\) | |||||||
\(80\) | 3.25915 | 0.364384 | ||||||||
\(81\) | −8.38962 | −0.932180 | ||||||||
\(82\) | 3.27479 | 0.361640 | ||||||||
\(83\) | −2.32216 | −0.254890 | −0.127445 | − | 0.991846i | \(-0.540678\pi\) | ||||
−0.127445 | + | 0.991846i | \(0.540678\pi\) | |||||||
\(84\) | 11.4203 | 1.24605 | ||||||||
\(85\) | −5.79298 | −0.628337 | ||||||||
\(86\) | 1.38020 | 0.148831 | ||||||||
\(87\) | −0.0257678 | −0.00276260 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.04905 | −0.641198 | −0.320599 | − | 0.947215i | \(-0.603884\pi\) | ||||
−0.320599 | + | 0.947215i | \(0.603884\pi\) | |||||||
\(90\) | −10.4008 | −1.09634 | ||||||||
\(91\) | −22.1374 | −2.32063 | ||||||||
\(92\) | 6.51169 | 0.678891 | ||||||||
\(93\) | 9.75117 | 1.01115 | ||||||||
\(94\) | 6.30125 | 0.649924 | ||||||||
\(95\) | 3.25915 | 0.334382 | ||||||||
\(96\) | 2.48823 | 0.253953 | ||||||||
\(97\) | −19.4094 | −1.97073 | −0.985364 | − | 0.170462i | \(-0.945474\pi\) | ||||
−0.985364 | + | 0.170462i | \(0.945474\pi\) | |||||||
\(98\) | −14.0655 | −1.42083 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.62205 | 0.562205 | ||||||||
\(101\) | 7.13850 | 0.710308 | 0.355154 | − | 0.934808i | \(-0.384428\pi\) | ||||
0.355154 | + | 0.934808i | \(0.384428\pi\) | |||||||
\(102\) | −4.42270 | −0.437912 | ||||||||
\(103\) | 8.65120 | 0.852428 | 0.426214 | − | 0.904622i | \(-0.359847\pi\) | ||||
0.426214 | + | 0.904622i | \(0.359847\pi\) | |||||||
\(104\) | −4.82326 | −0.472959 | ||||||||
\(105\) | 37.2203 | 3.63233 | ||||||||
\(106\) | −14.4636 | −1.40483 | ||||||||
\(107\) | 13.3149 | 1.28720 | 0.643599 | − | 0.765363i | \(-0.277440\pi\) | ||||
0.643599 | + | 0.765363i | \(0.277440\pi\) | |||||||
\(108\) | −0.475914 | −0.0457948 | ||||||||
\(109\) | 14.3467 | 1.37416 | 0.687080 | − | 0.726581i | \(-0.258892\pi\) | ||||
0.687080 | + | 0.726581i | \(0.258892\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.71225 | −0.162520 | ||||||||
\(112\) | −4.58972 | −0.433688 | ||||||||
\(113\) | 17.6690 | 1.66216 | 0.831080 | − | 0.556153i | \(-0.187723\pi\) | ||||
0.831080 | + | 0.556153i | \(0.187723\pi\) | |||||||
\(114\) | 2.48823 | 0.233044 | ||||||||
\(115\) | 21.2226 | 1.97902 | ||||||||
\(116\) | 0.0103559 | 0.000961522 0 | ||||||||
\(117\) | 15.3923 | 1.42302 | ||||||||
\(118\) | 9.20149 | 0.847065 | ||||||||
\(119\) | 8.15800 | 0.747843 | ||||||||
\(120\) | 8.10950 | 0.740293 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 13.4651 | 1.21908 | ||||||||
\(123\) | 8.14842 | 0.734718 | ||||||||
\(124\) | −3.91892 | −0.351930 | ||||||||
\(125\) | 2.02737 | 0.181333 | ||||||||
\(126\) | 14.6470 | 1.30486 | ||||||||
\(127\) | 10.6201 | 0.942381 | 0.471191 | − | 0.882031i | \(-0.343824\pi\) | ||||
0.471191 | + | 0.882031i | \(0.343824\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 3.43426 | 0.302369 | ||||||||
\(130\) | −15.7197 | −1.37871 | ||||||||
\(131\) | −16.9361 | −1.47971 | −0.739856 | − | 0.672765i | \(-0.765106\pi\) | ||||
−0.739856 | + | 0.672765i | \(0.765106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.58972 | −0.397979 | ||||||||
\(134\) | −5.08657 | −0.439413 | ||||||||
\(135\) | −1.55107 | −0.133495 | ||||||||
\(136\) | 1.77745 | 0.152415 | ||||||||
\(137\) | −8.12858 | −0.694472 | −0.347236 | − | 0.937778i | \(-0.612880\pi\) | ||||
−0.347236 | + | 0.937778i | \(0.612880\pi\) | |||||||
\(138\) | 16.2026 | 1.37925 | ||||||||
\(139\) | 0.909211 | 0.0771183 | 0.0385591 | − | 0.999256i | \(-0.487723\pi\) | ||||
0.0385591 | + | 0.999256i | \(0.487723\pi\) | |||||||
\(140\) | −14.9586 | −1.26423 | ||||||||
\(141\) | 15.6789 | 1.32040 | ||||||||
\(142\) | −9.43943 | −0.792140 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 3.19127 | 0.265939 | ||||||||
\(145\) | 0.0337514 | 0.00280290 | ||||||||
\(146\) | −15.2769 | −1.26433 | ||||||||
\(147\) | −34.9982 | −2.88660 | ||||||||
\(148\) | 0.688142 | 0.0565650 | ||||||||
\(149\) | −13.2547 | −1.08587 | −0.542933 | − | 0.839776i | \(-0.682686\pi\) | ||||
−0.542933 | + | 0.839776i | \(0.682686\pi\) | |||||||
\(150\) | 13.9889 | 1.14219 | ||||||||
\(151\) | −2.29362 | −0.186652 | −0.0933261 | − | 0.995636i | \(-0.529750\pi\) | ||||
−0.0933261 | + | 0.995636i | \(0.529750\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | −5.67232 | −0.458580 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.7724 | −1.02590 | ||||||||
\(156\) | −12.0014 | −0.960877 | ||||||||
\(157\) | −11.2813 | −0.900345 | −0.450172 | − | 0.892942i | \(-0.648637\pi\) | ||||
−0.450172 | + | 0.892942i | \(0.648637\pi\) | |||||||
\(158\) | 12.9416 | 1.02957 | ||||||||
\(159\) | −35.9887 | −2.85409 | ||||||||
\(160\) | −3.25915 | −0.257658 | ||||||||
\(161\) | −29.8868 | −2.35541 | ||||||||
\(162\) | 8.38962 | 0.659151 | ||||||||
\(163\) | −6.52158 | −0.510810 | −0.255405 | − | 0.966834i | \(-0.582209\pi\) | ||||
−0.255405 | + | 0.966834i | \(0.582209\pi\) | |||||||
\(164\) | −3.27479 | −0.255718 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.32216 | 0.180235 | ||||||||
\(167\) | −20.7099 | −1.60258 | −0.801289 | − | 0.598278i | \(-0.795852\pi\) | ||||
−0.801289 | + | 0.598278i | \(0.795852\pi\) | |||||||
\(168\) | −11.4203 | −0.881092 | ||||||||
\(169\) | 10.2638 | 0.789524 | ||||||||
\(170\) | 5.79298 | 0.444301 | ||||||||
\(171\) | 3.19127 | 0.244042 | ||||||||
\(172\) | −1.38020 | −0.105240 | ||||||||
\(173\) | 2.02529 | 0.153980 | 0.0769899 | − | 0.997032i | \(-0.475469\pi\) | ||||
0.0769899 | + | 0.997032i | \(0.475469\pi\) | |||||||
\(174\) | 0.0257678 | 0.00195345 | ||||||||
\(175\) | −25.8037 | −1.95057 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 22.8954 | 1.72092 | ||||||||
\(178\) | 6.04905 | 0.453395 | ||||||||
\(179\) | 20.7205 | 1.54873 | 0.774363 | − | 0.632742i | \(-0.218071\pi\) | ||||
0.774363 | + | 0.632742i | \(0.218071\pi\) | |||||||
\(180\) | 10.4008 | 0.775231 | ||||||||
\(181\) | −7.63695 | −0.567650 | −0.283825 | − | 0.958876i | \(-0.591604\pi\) | ||||
−0.283825 | + | 0.958876i | \(0.591604\pi\) | |||||||
\(182\) | 22.1374 | 1.64093 | ||||||||
\(183\) | 33.5043 | 2.47671 | ||||||||
\(184\) | −6.51169 | −0.480048 | ||||||||
\(185\) | 2.24276 | 0.164891 | ||||||||
\(186\) | −9.75117 | −0.714990 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.30125 | −0.459566 | ||||||||
\(189\) | 2.18431 | 0.158885 | ||||||||
\(190\) | −3.25915 | −0.236444 | ||||||||
\(191\) | 20.6340 | 1.49302 | 0.746512 | − | 0.665372i | \(-0.231727\pi\) | ||||
0.746512 | + | 0.665372i | \(0.231727\pi\) | |||||||
\(192\) | −2.48823 | −0.179572 | ||||||||
\(193\) | −8.64747 | −0.622458 | −0.311229 | − | 0.950335i | \(-0.600741\pi\) | ||||
−0.311229 | + | 0.950335i | \(0.600741\pi\) | |||||||
\(194\) | 19.4094 | 1.39352 | ||||||||
\(195\) | −39.1142 | −2.80103 | ||||||||
\(196\) | 14.0655 | 1.00468 | ||||||||
\(197\) | 10.6030 | 0.755430 | 0.377715 | − | 0.925922i | \(-0.376710\pi\) | ||||
0.377715 | + | 0.925922i | \(0.376710\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.19833 | 0.155836 | 0.0779179 | − | 0.996960i | \(-0.475173\pi\) | ||||
0.0779179 | + | 0.996960i | \(0.475173\pi\) | |||||||
\(200\) | −5.62205 | −0.397539 | ||||||||
\(201\) | −12.6565 | −0.892724 | ||||||||
\(202\) | −7.13850 | −0.502263 | ||||||||
\(203\) | −0.0475307 | −0.00333600 | ||||||||
\(204\) | 4.42270 | 0.309651 | ||||||||
\(205\) | −10.6730 | −0.745437 | ||||||||
\(206\) | −8.65120 | −0.602758 | ||||||||
\(207\) | 20.7805 | 1.44435 | ||||||||
\(208\) | 4.82326 | 0.334433 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −37.2203 | −2.56845 | ||||||||
\(211\) | 13.9756 | 0.962118 | 0.481059 | − | 0.876688i | \(-0.340252\pi\) | ||||
0.481059 | + | 0.876688i | \(0.340252\pi\) | |||||||
\(212\) | 14.4636 | 0.993365 | ||||||||
\(213\) | −23.4874 | −1.60933 | ||||||||
\(214\) | −13.3149 | −0.910187 | ||||||||
\(215\) | −4.49829 | −0.306781 | ||||||||
\(216\) | 0.475914 | 0.0323818 | ||||||||
\(217\) | 17.9868 | 1.22102 | ||||||||
\(218\) | −14.3467 | −0.971678 | ||||||||
\(219\) | −38.0124 | −2.56864 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.57310 | −0.576689 | ||||||||
\(222\) | 1.71225 | 0.114919 | ||||||||
\(223\) | 8.82515 | 0.590976 | 0.295488 | − | 0.955346i | \(-0.404518\pi\) | ||||
0.295488 | + | 0.955346i | \(0.404518\pi\) | |||||||
\(224\) | 4.58972 | 0.306664 | ||||||||
\(225\) | 17.9415 | 1.19610 | ||||||||
\(226\) | −17.6690 | −1.17532 | ||||||||
\(227\) | 4.53586 | 0.301055 | 0.150528 | − | 0.988606i | \(-0.451903\pi\) | ||||
0.150528 | + | 0.988606i | \(0.451903\pi\) | |||||||
\(228\) | −2.48823 | −0.164787 | ||||||||
\(229\) | −6.29059 | −0.415694 | −0.207847 | − | 0.978161i | \(-0.566646\pi\) | ||||
−0.207847 | + | 0.978161i | \(0.566646\pi\) | |||||||
\(230\) | −21.2226 | −1.39938 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.0103559 | −0.000679898 0 | ||||||||
\(233\) | 16.6897 | 1.09338 | 0.546689 | − | 0.837336i | \(-0.315888\pi\) | ||||
0.546689 | + | 0.837336i | \(0.315888\pi\) | |||||||
\(234\) | −15.3923 | −1.00623 | ||||||||
\(235\) | −20.5367 | −1.33967 | ||||||||
\(236\) | −9.20149 | −0.598966 | ||||||||
\(237\) | 32.2015 | 2.09171 | ||||||||
\(238\) | −8.15800 | −0.528805 | ||||||||
\(239\) | 7.23299 | 0.467863 | 0.233932 | − | 0.972253i | \(-0.424841\pi\) | ||||
0.233932 | + | 0.972253i | \(0.424841\pi\) | |||||||
\(240\) | −8.10950 | −0.523466 | ||||||||
\(241\) | −13.5156 | −0.870618 | −0.435309 | − | 0.900281i | \(-0.643361\pi\) | ||||
−0.435309 | + | 0.900281i | \(0.643361\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3030 | 1.43074 | ||||||||
\(244\) | −13.4651 | −0.862017 | ||||||||
\(245\) | 45.8417 | 2.92872 | ||||||||
\(246\) | −8.14842 | −0.519524 | ||||||||
\(247\) | 4.82326 | 0.306897 | ||||||||
\(248\) | 3.91892 | 0.248852 | ||||||||
\(249\) | 5.77806 | 0.366170 | ||||||||
\(250\) | −2.02737 | −0.128222 | ||||||||
\(251\) | 3.08810 | 0.194919 | 0.0974595 | − | 0.995239i | \(-0.468928\pi\) | ||||
0.0974595 | + | 0.995239i | \(0.468928\pi\) | |||||||
\(252\) | −14.6470 | −0.922676 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −10.6201 | −0.666364 | ||||||||
\(255\) | 14.4142 | 0.902654 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 17.3396 | 1.08161 | 0.540806 | − | 0.841147i | \(-0.318119\pi\) | ||||
0.540806 | + | 0.841147i | \(0.318119\pi\) | |||||||
\(258\) | −3.43426 | −0.213808 | ||||||||
\(259\) | −3.15838 | −0.196252 | ||||||||
\(260\) | 15.7197 | 0.974895 | ||||||||
\(261\) | 0.0330484 | 0.00204565 | ||||||||
\(262\) | 16.9361 | 1.04631 | ||||||||
\(263\) | 16.8383 | 1.03830 | 0.519148 | − | 0.854684i | \(-0.326249\pi\) | ||||
0.519148 | + | 0.854684i | \(0.326249\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 47.1391 | 2.89573 | ||||||||
\(266\) | 4.58972 | 0.281414 | ||||||||
\(267\) | 15.0514 | 0.921130 | ||||||||
\(268\) | 5.08657 | 0.310712 | ||||||||
\(269\) | −4.84616 | −0.295475 | −0.147738 | − | 0.989027i | \(-0.547199\pi\) | ||||
−0.147738 | + | 0.989027i | \(0.547199\pi\) | |||||||
\(270\) | 1.55107 | 0.0943953 | ||||||||
\(271\) | −5.89504 | −0.358098 | −0.179049 | − | 0.983840i | \(-0.557302\pi\) | ||||
−0.179049 | + | 0.983840i | \(0.557302\pi\) | |||||||
\(272\) | −1.77745 | −0.107774 | ||||||||
\(273\) | 55.0828 | 3.33377 | ||||||||
\(274\) | 8.12858 | 0.491066 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −16.2026 | −0.975279 | ||||||||
\(277\) | −30.7017 | −1.84468 | −0.922342 | − | 0.386375i | \(-0.873727\pi\) | ||||
−0.922342 | + | 0.386375i | \(0.873727\pi\) | |||||||
\(278\) | −0.909211 | −0.0545309 | ||||||||
\(279\) | −12.5063 | −0.748734 | ||||||||
\(280\) | 14.9586 | 0.893946 | ||||||||
\(281\) | 14.4108 | 0.859678 | 0.429839 | − | 0.902905i | \(-0.358570\pi\) | ||||
0.429839 | + | 0.902905i | \(0.358570\pi\) | |||||||
\(282\) | −15.6789 | −0.933667 | ||||||||
\(283\) | −15.1624 | −0.901313 | −0.450657 | − | 0.892697i | \(-0.648810\pi\) | ||||
−0.450657 | + | 0.892697i | \(0.648810\pi\) | |||||||
\(284\) | 9.43943 | 0.560127 | ||||||||
\(285\) | −8.10950 | −0.480365 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 15.0304 | 0.887215 | ||||||||
\(288\) | −3.19127 | −0.188047 | ||||||||
\(289\) | −13.8407 | −0.814157 | ||||||||
\(290\) | −0.0337514 | −0.00198195 | ||||||||
\(291\) | 48.2950 | 2.83110 | ||||||||
\(292\) | 15.2769 | 0.894014 | ||||||||
\(293\) | 30.5088 | 1.78234 | 0.891172 | − | 0.453665i | \(-0.149884\pi\) | ||||
0.891172 | + | 0.453665i | \(0.149884\pi\) | |||||||
\(294\) | 34.9982 | 2.04114 | ||||||||
\(295\) | −29.9890 | −1.74603 | ||||||||
\(296\) | −0.688142 | −0.0399975 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 13.2547 | 0.767823 | ||||||||
\(299\) | 31.4076 | 1.81635 | ||||||||
\(300\) | −13.9889 | −0.807652 | ||||||||
\(301\) | 6.33475 | 0.365129 | ||||||||
\(302\) | 2.29362 | 0.131983 | ||||||||
\(303\) | −17.7622 | −1.02041 | ||||||||
\(304\) | 1.00000 | 0.0573539 | ||||||||
\(305\) | −43.8849 | −2.51284 | ||||||||
\(306\) | 5.67232 | 0.324265 | ||||||||
\(307\) | 10.4099 | 0.594123 | 0.297062 | − | 0.954858i | \(-0.403993\pi\) | ||||
0.297062 | + | 0.954858i | \(0.403993\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.5261 | −1.22458 | ||||||||
\(310\) | 12.7724 | 0.725421 | ||||||||
\(311\) | 28.6601 | 1.62516 | 0.812582 | − | 0.582847i | \(-0.198061\pi\) | ||||
0.812582 | + | 0.582847i | \(0.198061\pi\) | |||||||
\(312\) | 12.0014 | 0.679443 | ||||||||
\(313\) | 32.8105 | 1.85456 | 0.927279 | − | 0.374370i | \(-0.122141\pi\) | ||||
0.927279 | + | 0.374370i | \(0.122141\pi\) | |||||||
\(314\) | 11.2813 | 0.636640 | ||||||||
\(315\) | −47.7368 | −2.68967 | ||||||||
\(316\) | −12.9416 | −0.728019 | ||||||||
\(317\) | −11.3871 | −0.639564 | −0.319782 | − | 0.947491i | \(-0.603610\pi\) | ||||
−0.319782 | + | 0.947491i | \(0.603610\pi\) | |||||||
\(318\) | 35.9887 | 2.01815 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 3.25915 | 0.182192 | ||||||||
\(321\) | −33.1304 | −1.84916 | ||||||||
\(322\) | 29.8868 | 1.66553 | ||||||||
\(323\) | −1.77745 | −0.0989000 | ||||||||
\(324\) | −8.38962 | −0.466090 | ||||||||
\(325\) | 27.1166 | 1.50416 | ||||||||
\(326\) | 6.52158 | 0.361197 | ||||||||
\(327\) | −35.6977 | −1.97409 | ||||||||
\(328\) | 3.27479 | 0.180820 | ||||||||
\(329\) | 28.9210 | 1.59446 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.1649 | 0.723609 | 0.361805 | − | 0.932254i | \(-0.382161\pi\) | ||||
0.361805 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(332\) | −2.32216 | −0.127445 | ||||||||
\(333\) | 2.19605 | 0.120343 | ||||||||
\(334\) | 20.7099 | 1.13319 | ||||||||
\(335\) | 16.5779 | 0.905747 | ||||||||
\(336\) | 11.4203 | 0.623026 | ||||||||
\(337\) | 17.3554 | 0.945407 | 0.472704 | − | 0.881221i | \(-0.343278\pi\) | ||||
0.472704 | + | 0.881221i | \(0.343278\pi\) | |||||||
\(338\) | −10.2638 | −0.558278 | ||||||||
\(339\) | −43.9644 | −2.38782 | ||||||||
\(340\) | −5.79298 | −0.314168 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | −3.19127 | −0.172564 | ||||||||
\(343\) | −32.4288 | −1.75099 | ||||||||
\(344\) | 1.38020 | 0.0744156 | ||||||||
\(345\) | −52.8065 | −2.84301 | ||||||||
\(346\) | −2.02529 | −0.108880 | ||||||||
\(347\) | −5.01412 | −0.269172 | −0.134586 | − | 0.990902i | \(-0.542970\pi\) | ||||
−0.134586 | + | 0.990902i | \(0.542970\pi\) | |||||||
\(348\) | −0.0257678 | −0.00138130 | ||||||||
\(349\) | 36.1563 | 1.93540 | 0.967701 | − | 0.252100i | \(-0.0811213\pi\) | ||||
0.967701 | + | 0.252100i | \(0.0811213\pi\) | |||||||
\(350\) | 25.8037 | 1.37926 | ||||||||
\(351\) | −2.29545 | −0.122522 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 16.1472 | 0.859429 | 0.429714 | − | 0.902965i | \(-0.358614\pi\) | ||||
0.429714 | + | 0.902965i | \(0.358614\pi\) | |||||||
\(354\) | −22.8954 | −1.21688 | ||||||||
\(355\) | 30.7645 | 1.63281 | ||||||||
\(356\) | −6.04905 | −0.320599 | ||||||||
\(357\) | −20.2990 | −1.07433 | ||||||||
\(358\) | −20.7205 | −1.09511 | ||||||||
\(359\) | −8.01403 | −0.422964 | −0.211482 | − | 0.977382i | \(-0.567829\pi\) | ||||
−0.211482 | + | 0.977382i | \(0.567829\pi\) | |||||||
\(360\) | −10.4008 | −0.548171 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 7.63695 | 0.401389 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −22.1374 | −1.16032 | ||||||||
\(365\) | 49.7898 | 2.60612 | ||||||||
\(366\) | −33.5043 | −1.75130 | ||||||||
\(367\) | 22.3199 | 1.16509 | 0.582544 | − | 0.812799i | \(-0.302058\pi\) | ||||
0.582544 | + | 0.812799i | \(0.302058\pi\) | |||||||
\(368\) | 6.51169 | 0.339445 | ||||||||
\(369\) | −10.4507 | −0.544043 | ||||||||
\(370\) | −2.24276 | −0.116595 | ||||||||
\(371\) | −66.3839 | −3.44648 | ||||||||
\(372\) | 9.75117 | 0.505574 | ||||||||
\(373\) | 11.0167 | 0.570423 | 0.285211 | − | 0.958465i | \(-0.407936\pi\) | ||||
0.285211 | + | 0.958465i | \(0.407936\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.04454 | −0.260499 | ||||||||
\(376\) | 6.30125 | 0.324962 | ||||||||
\(377\) | 0.0499492 | 0.00257251 | ||||||||
\(378\) | −2.18431 | −0.112349 | ||||||||
\(379\) | 19.2812 | 0.990410 | 0.495205 | − | 0.868776i | \(-0.335093\pi\) | ||||
0.495205 | + | 0.868776i | \(0.335093\pi\) | |||||||
\(380\) | 3.25915 | 0.167191 | ||||||||
\(381\) | −26.4252 | −1.35380 | ||||||||
\(382\) | −20.6340 | −1.05573 | ||||||||
\(383\) | 15.5005 | 0.792039 | 0.396019 | − | 0.918242i | \(-0.370391\pi\) | ||||
0.396019 | + | 0.918242i | \(0.370391\pi\) | |||||||
\(384\) | 2.48823 | 0.126977 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.64747 | 0.440145 | ||||||||
\(387\) | −4.40460 | −0.223898 | ||||||||
\(388\) | −19.4094 | −0.985364 | ||||||||
\(389\) | 2.57878 | 0.130749 | 0.0653746 | − | 0.997861i | \(-0.479176\pi\) | ||||
0.0653746 | + | 0.997861i | \(0.479176\pi\) | |||||||
\(390\) | 39.1142 | 1.98062 | ||||||||
\(391\) | −11.5742 | −0.585333 | ||||||||
\(392\) | −14.0655 | −0.710417 | ||||||||
\(393\) | 42.1408 | 2.12572 | ||||||||
\(394\) | −10.6030 | −0.534170 | ||||||||
\(395\) | −42.1784 | −2.12223 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.30951 | 0.216288 | 0.108144 | − | 0.994135i | \(-0.465509\pi\) | ||||
0.108144 | + | 0.994135i | \(0.465509\pi\) | |||||||
\(398\) | −2.19833 | −0.110193 | ||||||||
\(399\) | 11.4203 | 0.571728 | ||||||||
\(400\) | 5.62205 | 0.281103 | ||||||||
\(401\) | −12.0460 | −0.601551 | −0.300775 | − | 0.953695i | \(-0.597245\pi\) | ||||
−0.300775 | + | 0.953695i | \(0.597245\pi\) | |||||||
\(402\) | 12.6565 | 0.631251 | ||||||||
\(403\) | −18.9020 | −0.941575 | ||||||||
\(404\) | 7.13850 | 0.355154 | ||||||||
\(405\) | −27.3430 | −1.35869 | ||||||||
\(406\) | 0.0475307 | 0.00235891 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −4.42270 | −0.218956 | ||||||||
\(409\) | 35.2394 | 1.74248 | 0.871239 | − | 0.490859i | \(-0.163317\pi\) | ||||
0.871239 | + | 0.490859i | \(0.163317\pi\) | |||||||
\(410\) | 10.6730 | 0.527104 | ||||||||
\(411\) | 20.2257 | 0.997663 | ||||||||
\(412\) | 8.65120 | 0.426214 | ||||||||
\(413\) | 42.2322 | 2.07811 | ||||||||
\(414\) | −20.7805 | −1.02131 | ||||||||
\(415\) | −7.56827 | −0.371512 | ||||||||
\(416\) | −4.82326 | −0.236480 | ||||||||
\(417\) | −2.26232 | −0.110786 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −8.29185 | −0.405083 | −0.202542 | − | 0.979274i | \(-0.564920\pi\) | ||||
−0.202542 | + | 0.979274i | \(0.564920\pi\) | |||||||
\(420\) | 37.2203 | 1.81617 | ||||||||
\(421\) | −25.2575 | −1.23098 | −0.615488 | − | 0.788146i | \(-0.711041\pi\) | ||||
−0.615488 | + | 0.788146i | \(0.711041\pi\) | |||||||
\(422\) | −13.9756 | −0.680320 | ||||||||
\(423\) | −20.1090 | −0.977731 | ||||||||
\(424\) | −14.4636 | −0.702415 | ||||||||
\(425\) | −9.99292 | −0.484728 | ||||||||
\(426\) | 23.4874 | 1.13797 | ||||||||
\(427\) | 61.8012 | 2.99077 | ||||||||
\(428\) | 13.3149 | 0.643599 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.49829 | 0.216927 | ||||||||
\(431\) | 5.62638 | 0.271013 | 0.135507 | − | 0.990776i | \(-0.456734\pi\) | ||||
0.135507 | + | 0.990776i | \(0.456734\pi\) | |||||||
\(432\) | −0.475914 | −0.0228974 | ||||||||
\(433\) | 24.2774 | 1.16670 | 0.583349 | − | 0.812222i | \(-0.301742\pi\) | ||||
0.583349 | + | 0.812222i | \(0.301742\pi\) | |||||||
\(434\) | −17.9868 | −0.863392 | ||||||||
\(435\) | −0.0839812 | −0.00402659 | ||||||||
\(436\) | 14.3467 | 0.687080 | ||||||||
\(437\) | 6.51169 | 0.311496 | ||||||||
\(438\) | 38.0124 | 1.81630 | ||||||||
\(439\) | 23.6907 | 1.13070 | 0.565348 | − | 0.824853i | \(-0.308742\pi\) | ||||
0.565348 | + | 0.824853i | \(0.308742\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 44.8869 | 2.13747 | ||||||||
\(442\) | 8.57310 | 0.407781 | ||||||||
\(443\) | −26.9144 | −1.27874 | −0.639371 | − | 0.768899i | \(-0.720805\pi\) | ||||
−0.639371 | + | 0.768899i | \(0.720805\pi\) | |||||||
\(444\) | −1.71225 | −0.0812600 | ||||||||
\(445\) | −19.7147 | −0.934569 | ||||||||
\(446\) | −8.82515 | −0.417883 | ||||||||
\(447\) | 32.9806 | 1.55993 | ||||||||
\(448\) | −4.58972 | −0.216844 | ||||||||
\(449\) | 15.5953 | 0.735987 | 0.367993 | − | 0.929828i | \(-0.380045\pi\) | ||||
0.367993 | + | 0.929828i | \(0.380045\pi\) | |||||||
\(450\) | −17.9415 | −0.845769 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 17.6690 | 0.831080 | ||||||||
\(453\) | 5.70705 | 0.268140 | ||||||||
\(454\) | −4.53586 | −0.212878 | ||||||||
\(455\) | −72.1491 | −3.38240 | ||||||||
\(456\) | 2.48823 | 0.116522 | ||||||||
\(457\) | 24.0214 | 1.12367 | 0.561837 | − | 0.827248i | \(-0.310095\pi\) | ||||
0.561837 | + | 0.827248i | \(0.310095\pi\) | |||||||
\(458\) | 6.29059 | 0.293940 | ||||||||
\(459\) | 0.845913 | 0.0394838 | ||||||||
\(460\) | 21.2226 | 0.989508 | ||||||||
\(461\) | 19.8822 | 0.926005 | 0.463003 | − | 0.886357i | \(-0.346772\pi\) | ||||
0.463003 | + | 0.886357i | \(0.346772\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.7710 | 1.75537 | 0.877684 | − | 0.479240i | \(-0.159087\pi\) | ||||
0.877684 | + | 0.479240i | \(0.159087\pi\) | |||||||
\(464\) | 0.0103559 | 0.000480761 0 | ||||||||
\(465\) | 31.7805 | 1.47379 | ||||||||
\(466\) | −16.6897 | −0.773135 | ||||||||
\(467\) | −42.9098 | −1.98563 | −0.992815 | − | 0.119656i | \(-0.961821\pi\) | ||||
−0.992815 | + | 0.119656i | \(0.961821\pi\) | |||||||
\(468\) | 15.3923 | 0.711509 | ||||||||
\(469\) | −23.3459 | −1.07802 | ||||||||
\(470\) | 20.5367 | 0.947288 | ||||||||
\(471\) | 28.0704 | 1.29342 | ||||||||
\(472\) | 9.20149 | 0.423533 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −32.2015 | −1.47906 | ||||||||
\(475\) | 5.62205 | 0.257958 | ||||||||
\(476\) | 8.15800 | 0.373921 | ||||||||
\(477\) | 46.1572 | 2.11340 | ||||||||
\(478\) | −7.23299 | −0.330829 | ||||||||
\(479\) | −26.1271 | −1.19378 | −0.596888 | − | 0.802324i | \(-0.703596\pi\) | ||||
−0.596888 | + | 0.802324i | \(0.703596\pi\) | |||||||
\(480\) | 8.10950 | 0.370146 | ||||||||
\(481\) | 3.31909 | 0.151337 | ||||||||
\(482\) | 13.5156 | 0.615620 | ||||||||
\(483\) | 74.3652 | 3.38373 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −63.2582 | −2.87241 | ||||||||
\(486\) | −22.3030 | −1.01168 | ||||||||
\(487\) | 13.0467 | 0.591204 | 0.295602 | − | 0.955311i | \(-0.404480\pi\) | ||||
0.295602 | + | 0.955311i | \(0.404480\pi\) | |||||||
\(488\) | 13.4651 | 0.609538 | ||||||||
\(489\) | 16.2272 | 0.733818 | ||||||||
\(490\) | −45.8417 | −2.07092 | ||||||||
\(491\) | 16.0017 | 0.722145 | 0.361072 | − | 0.932538i | \(-0.382411\pi\) | ||||
0.361072 | + | 0.932538i | \(0.382411\pi\) | |||||||
\(492\) | 8.14842 | 0.367359 | ||||||||
\(493\) | −0.0184071 | −0.000829015 0 | ||||||||
\(494\) | −4.82326 | −0.217009 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.91892 | −0.175965 | ||||||||
\(497\) | −43.3244 | −1.94336 | ||||||||
\(498\) | −5.77806 | −0.258921 | ||||||||
\(499\) | −29.3850 | −1.31545 | −0.657727 | − | 0.753256i | \(-0.728482\pi\) | ||||
−0.657727 | + | 0.753256i | \(0.728482\pi\) | |||||||
\(500\) | 2.02737 | 0.0906665 | ||||||||
\(501\) | 51.5308 | 2.30223 | ||||||||
\(502\) | −3.08810 | −0.137829 | ||||||||
\(503\) | 8.80839 | 0.392747 | 0.196373 | − | 0.980529i | \(-0.437084\pi\) | ||||
0.196373 | + | 0.980529i | \(0.437084\pi\) | |||||||
\(504\) | 14.6470 | 0.652430 | ||||||||
\(505\) | 23.2655 | 1.03530 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −25.5387 | −1.13421 | ||||||||
\(508\) | 10.6201 | 0.471191 | ||||||||
\(509\) | −15.7974 | −0.700209 | −0.350104 | − | 0.936711i | \(-0.613854\pi\) | ||||
−0.350104 | + | 0.936711i | \(0.613854\pi\) | |||||||
\(510\) | −14.4142 | −0.638273 | ||||||||
\(511\) | −70.1168 | −3.10178 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −0.475914 | −0.0210121 | ||||||||
\(514\) | −17.3396 | −0.764815 | ||||||||
\(515\) | 28.1955 | 1.24244 | ||||||||
\(516\) | 3.43426 | 0.151185 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 3.15838 | 0.138771 | ||||||||
\(519\) | −5.03938 | −0.221204 | ||||||||
\(520\) | −15.7197 | −0.689355 | ||||||||
\(521\) | 27.2791 | 1.19512 | 0.597560 | − | 0.801824i | \(-0.296137\pi\) | ||||
0.597560 | + | 0.801824i | \(0.296137\pi\) | |||||||
\(522\) | −0.0330484 | −0.00144649 | ||||||||
\(523\) | 24.3662 | 1.06546 | 0.532730 | − | 0.846285i | \(-0.321166\pi\) | ||||
0.532730 | + | 0.846285i | \(0.321166\pi\) | |||||||
\(524\) | −16.9361 | −0.739856 | ||||||||
\(525\) | 64.2053 | 2.80215 | ||||||||
\(526\) | −16.8383 | −0.734186 | ||||||||
\(527\) | 6.96570 | 0.303430 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.4021 | 0.843571 | ||||||||
\(530\) | −47.1391 | −2.04759 | ||||||||
\(531\) | −29.3644 | −1.27431 | ||||||||
\(532\) | −4.58972 | −0.198990 | ||||||||
\(533\) | −15.7952 | −0.684164 | ||||||||
\(534\) | −15.0514 | −0.651337 | ||||||||
\(535\) | 43.3952 | 1.87614 | ||||||||
\(536\) | −5.08657 | −0.219706 | ||||||||
\(537\) | −51.5574 | −2.22486 | ||||||||
\(538\) | 4.84616 | 0.208933 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −1.55107 | −0.0667476 | ||||||||
\(541\) | −15.4651 | −0.664897 | −0.332449 | − | 0.943121i | \(-0.607875\pi\) | ||||
−0.332449 | + | 0.943121i | \(0.607875\pi\) | |||||||
\(542\) | 5.89504 | 0.253214 | ||||||||
\(543\) | 19.0025 | 0.815474 | ||||||||
\(544\) | 1.77745 | 0.0762076 | ||||||||
\(545\) | 46.7579 | 2.00289 | ||||||||
\(546\) | −55.0828 | −2.35733 | ||||||||
\(547\) | 1.33234 | 0.0569667 | 0.0284834 | − | 0.999594i | \(-0.490932\pi\) | ||||
0.0284834 | + | 0.999594i | \(0.490932\pi\) | |||||||
\(548\) | −8.12858 | −0.347236 | ||||||||
\(549\) | −42.9708 | −1.83395 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.0103559 | 0.000441176 0 | ||||||||
\(552\) | 16.2026 | 0.689627 | ||||||||
\(553\) | 59.3981 | 2.52586 | ||||||||
\(554\) | 30.7017 | 1.30439 | ||||||||
\(555\) | −5.58049 | −0.236879 | ||||||||
\(556\) | 0.909211 | 0.0385591 | ||||||||
\(557\) | −26.6638 | −1.12978 | −0.564892 | − | 0.825165i | \(-0.691082\pi\) | ||||
−0.564892 | + | 0.825165i | \(0.691082\pi\) | |||||||
\(558\) | 12.5063 | 0.529435 | ||||||||
\(559\) | −6.65708 | −0.281564 | ||||||||
\(560\) | −14.9586 | −0.632116 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −14.4108 | −0.607884 | ||||||||
\(563\) | 25.1226 | 1.05879 | 0.529396 | − | 0.848375i | \(-0.322418\pi\) | ||||
0.529396 | + | 0.848375i | \(0.322418\pi\) | |||||||
\(564\) | 15.6789 | 0.660202 | ||||||||
\(565\) | 57.5859 | 2.42266 | ||||||||
\(566\) | 15.1624 | 0.637325 | ||||||||
\(567\) | 38.5060 | 1.61710 | ||||||||
\(568\) | −9.43943 | −0.396070 | ||||||||
\(569\) | 16.6061 | 0.696162 | 0.348081 | − | 0.937464i | \(-0.386833\pi\) | ||||
0.348081 | + | 0.937464i | \(0.386833\pi\) | |||||||
\(570\) | 8.10950 | 0.339670 | ||||||||
\(571\) | 27.1795 | 1.13743 | 0.568713 | − | 0.822536i | \(-0.307442\pi\) | ||||
0.568713 | + | 0.822536i | \(0.307442\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −51.3421 | −2.14485 | ||||||||
\(574\) | −15.0304 | −0.627356 | ||||||||
\(575\) | 36.6091 | 1.52670 | ||||||||
\(576\) | 3.19127 | 0.132969 | ||||||||
\(577\) | −20.5578 | −0.855831 | −0.427915 | − | 0.903819i | \(-0.640752\pi\) | ||||
−0.427915 | + | 0.903819i | \(0.640752\pi\) | |||||||
\(578\) | 13.8407 | 0.575696 | ||||||||
\(579\) | 21.5168 | 0.894210 | ||||||||
\(580\) | 0.0337514 | 0.00140145 | ||||||||
\(581\) | 10.6581 | 0.442171 | ||||||||
\(582\) | −48.2950 | −2.00189 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −15.2769 | −0.632163 | ||||||||
\(585\) | 50.1658 | 2.07410 | ||||||||
\(586\) | −30.5088 | −1.26031 | ||||||||
\(587\) | −13.6615 | −0.563872 | −0.281936 | − | 0.959433i | \(-0.590977\pi\) | ||||
−0.281936 | + | 0.959433i | \(0.590977\pi\) | |||||||
\(588\) | −34.9982 | −1.44330 | ||||||||
\(589\) | −3.91892 | −0.161476 | ||||||||
\(590\) | 29.9890 | 1.23463 | ||||||||
\(591\) | −26.3826 | −1.08523 | ||||||||
\(592\) | 0.688142 | 0.0282825 | ||||||||
\(593\) | −8.26443 | −0.339380 | −0.169690 | − | 0.985498i | \(-0.554277\pi\) | ||||
−0.169690 | + | 0.985498i | \(0.554277\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 26.5881 | 1.09001 | ||||||||
\(596\) | −13.2547 | −0.542933 | ||||||||
\(597\) | −5.46995 | −0.223870 | ||||||||
\(598\) | −31.4076 | −1.28435 | ||||||||
\(599\) | −11.3663 | −0.464413 | −0.232207 | − | 0.972666i | \(-0.574595\pi\) | ||||
−0.232207 | + | 0.972666i | \(0.574595\pi\) | |||||||
\(600\) | 13.9889 | 0.571096 | ||||||||
\(601\) | 17.2129 | 0.702130 | 0.351065 | − | 0.936351i | \(-0.385820\pi\) | ||||
0.351065 | + | 0.936351i | \(0.385820\pi\) | |||||||
\(602\) | −6.33475 | −0.258185 | ||||||||
\(603\) | 16.2326 | 0.661043 | ||||||||
\(604\) | −2.29362 | −0.0933261 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 17.7622 | 0.721540 | ||||||||
\(607\) | 2.71425 | 0.110168 | 0.0550841 | − | 0.998482i | \(-0.482457\pi\) | ||||
0.0550841 | + | 0.998482i | \(0.482457\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 0.118267 | 0.00479242 | ||||||||
\(610\) | 43.8849 | 1.77685 | ||||||||
\(611\) | −30.3925 | −1.22955 | ||||||||
\(612\) | −5.67232 | −0.229290 | ||||||||
\(613\) | 0.970155 | 0.0391842 | 0.0195921 | − | 0.999808i | \(-0.493763\pi\) | ||||
0.0195921 | + | 0.999808i | \(0.493763\pi\) | |||||||
\(614\) | −10.4099 | −0.420109 | ||||||||
\(615\) | 26.5569 | 1.07088 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.377035 | 0.0151789 | 0.00758944 | − | 0.999971i | \(-0.497584\pi\) | ||||
0.00758944 | + | 0.999971i | \(0.497584\pi\) | |||||||
\(618\) | 21.5261 | 0.865908 | ||||||||
\(619\) | −11.6033 | −0.466377 | −0.233188 | − | 0.972432i | \(-0.574916\pi\) | ||||
−0.233188 | + | 0.972432i | \(0.574916\pi\) | |||||||
\(620\) | −12.7724 | −0.512950 | ||||||||
\(621\) | −3.09900 | −0.124359 | ||||||||
\(622\) | −28.6601 | −1.14916 | ||||||||
\(623\) | 27.7634 | 1.11232 | ||||||||
\(624\) | −12.0014 | −0.480439 | ||||||||
\(625\) | −21.5028 | −0.860111 | ||||||||
\(626\) | −32.8105 | −1.31137 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −11.2813 | −0.450172 | ||||||||
\(629\) | −1.22314 | −0.0487698 | ||||||||
\(630\) | 47.7368 | 1.90188 | ||||||||
\(631\) | 13.9531 | 0.555464 | 0.277732 | − | 0.960659i | \(-0.410417\pi\) | ||||
0.277732 | + | 0.960659i | \(0.410417\pi\) | |||||||
\(632\) | 12.9416 | 0.514787 | ||||||||
\(633\) | −34.7744 | −1.38216 | ||||||||
\(634\) | 11.3871 | 0.452240 | ||||||||
\(635\) | 34.6125 | 1.37355 | ||||||||
\(636\) | −35.9887 | −1.42705 | ||||||||
\(637\) | 67.8417 | 2.68799 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.1238 | 1.19168 | ||||||||
\(640\) | −3.25915 | −0.128829 | ||||||||
\(641\) | 3.80584 | 0.150322 | 0.0751608 | − | 0.997171i | \(-0.476053\pi\) | ||||
0.0751608 | + | 0.997171i | \(0.476053\pi\) | |||||||
\(642\) | 33.1304 | 1.30755 | ||||||||
\(643\) | 8.46396 | 0.333786 | 0.166893 | − | 0.985975i | \(-0.446627\pi\) | ||||
0.166893 | + | 0.985975i | \(0.446627\pi\) | |||||||
\(644\) | −29.8868 | −1.17771 | ||||||||
\(645\) | 11.1928 | 0.440714 | ||||||||
\(646\) | 1.77745 | 0.0699329 | ||||||||
\(647\) | −10.1179 | −0.397775 | −0.198888 | − | 0.980022i | \(-0.563733\pi\) | ||||
−0.198888 | + | 0.980022i | \(0.563733\pi\) | |||||||
\(648\) | 8.38962 | 0.329575 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −27.1166 | −1.06360 | ||||||||
\(651\) | −44.7551 | −1.75409 | ||||||||
\(652\) | −6.52158 | −0.255405 | ||||||||
\(653\) | 7.24197 | 0.283400 | 0.141700 | − | 0.989910i | \(-0.454743\pi\) | ||||
0.141700 | + | 0.989910i | \(0.454743\pi\) | |||||||
\(654\) | 35.6977 | 1.39589 | ||||||||
\(655\) | −55.1972 | −2.15673 | ||||||||
\(656\) | −3.27479 | −0.127859 | ||||||||
\(657\) | 48.7527 | 1.90202 | ||||||||
\(658\) | −28.9210 | −1.12746 | ||||||||
\(659\) | 11.1870 | 0.435783 | 0.217891 | − | 0.975973i | \(-0.430082\pi\) | ||||
0.217891 | + | 0.975973i | \(0.430082\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.73868 | 0.262104 | 0.131052 | − | 0.991375i | \(-0.458164\pi\) | ||||
0.131052 | + | 0.991375i | \(0.458164\pi\) | |||||||
\(662\) | −13.1649 | −0.511669 | ||||||||
\(663\) | 21.3318 | 0.828459 | ||||||||
\(664\) | 2.32216 | 0.0901173 | ||||||||
\(665\) | −14.9586 | −0.580069 | ||||||||
\(666\) | −2.19605 | −0.0850950 | ||||||||
\(667\) | 0.0674344 | 0.00261107 | ||||||||
\(668\) | −20.7099 | −0.801289 | ||||||||
\(669\) | −21.9590 | −0.848983 | ||||||||
\(670\) | −16.5779 | −0.640460 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −11.4203 | −0.440546 | ||||||||
\(673\) | −3.80683 | −0.146743 | −0.0733713 | − | 0.997305i | \(-0.523376\pi\) | ||||
−0.0733713 | + | 0.997305i | \(0.523376\pi\) | |||||||
\(674\) | −17.3554 | −0.668504 | ||||||||
\(675\) | −2.67561 | −0.102984 | ||||||||
\(676\) | 10.2638 | 0.394762 | ||||||||
\(677\) | −14.9987 | −0.576446 | −0.288223 | − | 0.957563i | \(-0.593064\pi\) | ||||
−0.288223 | + | 0.957563i | \(0.593064\pi\) | |||||||
\(678\) | 43.9644 | 1.68844 | ||||||||
\(679\) | 89.0838 | 3.41872 | ||||||||
\(680\) | 5.79298 | 0.222151 | ||||||||
\(681\) | −11.2862 | −0.432489 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −12.7603 | −0.488260 | −0.244130 | − | 0.969742i | \(-0.578502\pi\) | ||||
−0.244130 | + | 0.969742i | \(0.578502\pi\) | |||||||
\(684\) | 3.19127 | 0.122021 | ||||||||
\(685\) | −26.4923 | −1.01222 | ||||||||
\(686\) | 32.4288 | 1.23814 | ||||||||
\(687\) | 15.6524 | 0.597177 | ||||||||
\(688\) | −1.38020 | −0.0526198 | ||||||||
\(689\) | 69.7617 | 2.65771 | ||||||||
\(690\) | 52.8065 | 2.01031 | ||||||||
\(691\) | 29.5740 | 1.12505 | 0.562525 | − | 0.826780i | \(-0.309830\pi\) | ||||
0.562525 | + | 0.826780i | \(0.309830\pi\) | |||||||
\(692\) | 2.02529 | 0.0769899 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.01412 | 0.190333 | ||||||||
\(695\) | 2.96326 | 0.112403 | ||||||||
\(696\) | 0.0257678 | 0.000976727 0 | ||||||||
\(697\) | 5.82078 | 0.220478 | ||||||||
\(698\) | −36.1563 | −1.36854 | ||||||||
\(699\) | −41.5277 | −1.57072 | ||||||||
\(700\) | −25.8037 | −0.975286 | ||||||||
\(701\) | 35.4860 | 1.34029 | 0.670143 | − | 0.742232i | \(-0.266233\pi\) | ||||
0.670143 | + | 0.742232i | \(0.266233\pi\) | |||||||
\(702\) | 2.29545 | 0.0866363 | ||||||||
\(703\) | 0.688142 | 0.0259538 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 51.1000 | 1.92454 | ||||||||
\(706\) | −16.1472 | −0.607708 | ||||||||
\(707\) | −32.7637 | −1.23221 | ||||||||
\(708\) | 22.8954 | 0.860461 | ||||||||
\(709\) | 7.58291 | 0.284782 | 0.142391 | − | 0.989810i | \(-0.454521\pi\) | ||||
0.142391 | + | 0.989810i | \(0.454521\pi\) | |||||||
\(710\) | −30.7645 | −1.15457 | ||||||||
\(711\) | −41.2999 | −1.54887 | ||||||||
\(712\) | 6.04905 | 0.226698 | ||||||||
\(713\) | −25.5188 | −0.955687 | ||||||||
\(714\) | 20.2990 | 0.759669 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 20.7205 | 0.774363 | ||||||||
\(717\) | −17.9973 | −0.672122 | ||||||||
\(718\) | 8.01403 | 0.299081 | ||||||||
\(719\) | 10.5644 | 0.393985 | 0.196993 | − | 0.980405i | \(-0.436883\pi\) | ||||
0.196993 | + | 0.980405i | \(0.436883\pi\) | |||||||
\(720\) | 10.4008 | 0.387615 | ||||||||
\(721\) | −39.7066 | −1.47875 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 33.6299 | 1.25071 | ||||||||
\(724\) | −7.63695 | −0.283825 | ||||||||
\(725\) | 0.0582214 | 0.00216229 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −13.9031 | −0.515638 | −0.257819 | − | 0.966193i | \(-0.583004\pi\) | ||||
−0.257819 | + | 0.966193i | \(0.583004\pi\) | |||||||
\(728\) | 22.1374 | 0.820467 | ||||||||
\(729\) | −30.3260 | −1.12319 | ||||||||
\(730\) | −49.7898 | −1.84280 | ||||||||
\(731\) | 2.45324 | 0.0907365 | ||||||||
\(732\) | 33.5043 | 1.23835 | ||||||||
\(733\) | −24.9256 | −0.920649 | −0.460325 | − | 0.887751i | \(-0.652267\pi\) | ||||
−0.460325 | + | 0.887751i | \(0.652267\pi\) | |||||||
\(734\) | −22.3199 | −0.823841 | ||||||||
\(735\) | −114.064 | −4.20733 | ||||||||
\(736\) | −6.51169 | −0.240024 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 10.4507 | 0.384697 | ||||||||
\(739\) | 9.43289 | 0.346995 | 0.173497 | − | 0.984834i | \(-0.444493\pi\) | ||||
0.173497 | + | 0.984834i | \(0.444493\pi\) | |||||||
\(740\) | 2.24276 | 0.0824455 | ||||||||
\(741\) | −12.0014 | −0.440881 | ||||||||
\(742\) | 66.3839 | 2.43703 | ||||||||
\(743\) | −50.6746 | −1.85907 | −0.929535 | − | 0.368735i | \(-0.879791\pi\) | ||||
−0.929535 | + | 0.368735i | \(0.879791\pi\) | |||||||
\(744\) | −9.75117 | −0.357495 | ||||||||
\(745\) | −43.1990 | −1.58269 | ||||||||
\(746\) | −11.0167 | −0.403350 | ||||||||
\(747\) | −7.41063 | −0.271141 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −61.1116 | −2.23297 | ||||||||
\(750\) | 5.04454 | 0.184201 | ||||||||
\(751\) | 53.0962 | 1.93751 | 0.968754 | − | 0.248025i | \(-0.0797815\pi\) | ||||
0.968754 | + | 0.248025i | \(0.0797815\pi\) | |||||||
\(752\) | −6.30125 | −0.229783 | ||||||||
\(753\) | −7.68388 | −0.280016 | ||||||||
\(754\) | −0.0499492 | −0.00181904 | ||||||||
\(755\) | −7.47525 | −0.272052 | ||||||||
\(756\) | 2.18431 | 0.0794426 | ||||||||
\(757\) | −30.2934 | −1.10103 | −0.550517 | − | 0.834824i | \(-0.685569\pi\) | ||||
−0.550517 | + | 0.834824i | \(0.685569\pi\) | |||||||
\(758\) | −19.2812 | −0.700326 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.25915 | −0.118222 | ||||||||
\(761\) | 4.83983 | 0.175444 | 0.0877219 | − | 0.996145i | \(-0.472041\pi\) | ||||
0.0877219 | + | 0.996145i | \(0.472041\pi\) | |||||||
\(762\) | 26.4252 | 0.957284 | ||||||||
\(763\) | −65.8471 | −2.38383 | ||||||||
\(764\) | 20.6340 | 0.746512 | ||||||||
\(765\) | −18.4869 | −0.668397 | ||||||||
\(766\) | −15.5005 | −0.560056 | ||||||||
\(767\) | −44.3811 | −1.60251 | ||||||||
\(768\) | −2.48823 | −0.0897861 | ||||||||
\(769\) | 30.9675 | 1.11672 | 0.558358 | − | 0.829600i | \(-0.311432\pi\) | ||||
0.558358 | + | 0.829600i | \(0.311432\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −43.1447 | −1.55382 | ||||||||
\(772\) | −8.64747 | −0.311229 | ||||||||
\(773\) | −30.9296 | −1.11246 | −0.556229 | − | 0.831029i | \(-0.687752\pi\) | ||||
−0.556229 | + | 0.831029i | \(0.687752\pi\) | |||||||
\(774\) | 4.40460 | 0.158320 | ||||||||
\(775\) | −22.0324 | −0.791427 | ||||||||
\(776\) | 19.4094 | 0.696758 | ||||||||
\(777\) | 7.85877 | 0.281932 | ||||||||
\(778\) | −2.57878 | −0.0924536 | ||||||||
\(779\) | −3.27479 | −0.117332 | ||||||||
\(780\) | −39.1142 | −1.40051 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 11.5742 | 0.413893 | ||||||||
\(783\) | −0.00492852 | −0.000176131 0 | ||||||||
\(784\) | 14.0655 | 0.502340 | ||||||||
\(785\) | −36.7674 | −1.31228 | ||||||||
\(786\) | −42.1408 | −1.50311 | ||||||||
\(787\) | 7.58212 | 0.270274 | 0.135137 | − | 0.990827i | \(-0.456853\pi\) | ||||
0.135137 | + | 0.990827i | \(0.456853\pi\) | |||||||
\(788\) | 10.6030 | 0.377715 | ||||||||
\(789\) | −41.8975 | −1.49159 | ||||||||
\(790\) | 42.1784 | 1.50064 | ||||||||
\(791\) | −81.0957 | −2.88343 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −64.9458 | −2.30629 | ||||||||
\(794\) | −4.30951 | −0.152939 | ||||||||
\(795\) | −117.293 | −4.15994 | ||||||||
\(796\) | 2.19833 | 0.0779179 | ||||||||
\(797\) | −1.66912 | −0.0591232 | −0.0295616 | − | 0.999563i | \(-0.509411\pi\) | ||||
−0.0295616 | + | 0.999563i | \(0.509411\pi\) | |||||||
\(798\) | −11.4203 | −0.404273 | ||||||||
\(799\) | 11.2002 | 0.396233 | ||||||||
\(800\) | −5.62205 | −0.198770 | ||||||||
\(801\) | −19.3041 | −0.682078 | ||||||||
\(802\) | 12.0460 | 0.425361 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −12.6565 | −0.446362 | ||||||||
\(805\) | −97.4057 | −3.43310 | ||||||||
\(806\) | 18.9020 | 0.665794 | ||||||||
\(807\) | 12.0583 | 0.424473 | ||||||||
\(808\) | −7.13850 | −0.251132 | ||||||||
\(809\) | −27.4251 | −0.964215 | −0.482107 | − | 0.876112i | \(-0.660129\pi\) | ||||
−0.482107 | + | 0.876112i | \(0.660129\pi\) | |||||||
\(810\) | 27.3430 | 0.960736 | ||||||||
\(811\) | 52.1412 | 1.83093 | 0.915463 | − | 0.402401i | \(-0.131824\pi\) | ||||
0.915463 | + | 0.402401i | \(0.131824\pi\) | |||||||
\(812\) | −0.0475307 | −0.00166800 | ||||||||
\(813\) | 14.6682 | 0.514436 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −21.2548 | −0.744523 | ||||||||
\(816\) | 4.42270 | 0.154825 | ||||||||
\(817\) | −1.38020 | −0.0482872 | ||||||||
\(818\) | −35.2394 | −1.23212 | ||||||||
\(819\) | −70.6463 | −2.46858 | ||||||||
\(820\) | −10.6730 | −0.372718 | ||||||||
\(821\) | 19.2406 | 0.671502 | 0.335751 | − | 0.941951i | \(-0.391010\pi\) | ||||
0.335751 | + | 0.941951i | \(0.391010\pi\) | |||||||
\(822\) | −20.2257 | −0.705454 | ||||||||
\(823\) | 23.7426 | 0.827614 | 0.413807 | − | 0.910365i | \(-0.364199\pi\) | ||||
0.413807 | + | 0.910365i | \(0.364199\pi\) | |||||||
\(824\) | −8.65120 | −0.301379 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −42.2322 | −1.46945 | ||||||||
\(827\) | 19.7786 | 0.687769 | 0.343885 | − | 0.939012i | \(-0.388257\pi\) | ||||
0.343885 | + | 0.939012i | \(0.388257\pi\) | |||||||
\(828\) | 20.7805 | 0.722174 | ||||||||
\(829\) | 9.35784 | 0.325011 | 0.162506 | − | 0.986708i | \(-0.448042\pi\) | ||||
0.162506 | + | 0.986708i | \(0.448042\pi\) | |||||||
\(830\) | 7.56827 | 0.262698 | ||||||||
\(831\) | 76.3926 | 2.65003 | ||||||||
\(832\) | 4.82326 | 0.167216 | ||||||||
\(833\) | −25.0008 | −0.866226 | ||||||||
\(834\) | 2.26232 | 0.0783378 | ||||||||
\(835\) | −67.4965 | −2.33581 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.86507 | 0.0644662 | ||||||||
\(838\) | 8.29185 | 0.286437 | ||||||||
\(839\) | −7.65538 | −0.264293 | −0.132147 | − | 0.991230i | \(-0.542187\pi\) | ||||
−0.132147 | + | 0.991230i | \(0.542187\pi\) | |||||||
\(840\) | −37.2203 | −1.28422 | ||||||||
\(841\) | −28.9999 | −0.999996 | ||||||||
\(842\) | 25.2575 | 0.870431 | ||||||||
\(843\) | −35.8574 | −1.23499 | ||||||||
\(844\) | 13.9756 | 0.481059 | ||||||||
\(845\) | 33.4513 | 1.15076 | ||||||||
\(846\) | 20.1090 | 0.691360 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 14.4636 | 0.496683 | ||||||||
\(849\) | 37.7276 | 1.29481 | ||||||||
\(850\) | 9.99292 | 0.342754 | ||||||||
\(851\) | 4.48097 | 0.153606 | ||||||||
\(852\) | −23.4874 | −0.804667 | ||||||||
\(853\) | −27.9084 | −0.955565 | −0.477783 | − | 0.878478i | \(-0.658559\pi\) | ||||
−0.477783 | + | 0.878478i | \(0.658559\pi\) | |||||||
\(854\) | −61.8012 | −2.11479 | ||||||||
\(855\) | 10.4008 | 0.355700 | ||||||||
\(856\) | −13.3149 | −0.455093 | ||||||||
\(857\) | −38.8157 | −1.32592 | −0.662960 | − | 0.748655i | \(-0.730700\pi\) | ||||
−0.662960 | + | 0.748655i | \(0.730700\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −12.5352 | −0.427697 | −0.213848 | − | 0.976867i | \(-0.568600\pi\) | ||||
−0.213848 | + | 0.976867i | \(0.568600\pi\) | |||||||
\(860\) | −4.49829 | −0.153390 | ||||||||
\(861\) | −37.3990 | −1.27455 | ||||||||
\(862\) | −5.62638 | −0.191635 | ||||||||
\(863\) | −12.4527 | −0.423896 | −0.211948 | − | 0.977281i | \(-0.567981\pi\) | ||||
−0.211948 | + | 0.977281i | \(0.567981\pi\) | |||||||
\(864\) | 0.475914 | 0.0161909 | ||||||||
\(865\) | 6.60072 | 0.224431 | ||||||||
\(866\) | −24.2774 | −0.824980 | ||||||||
\(867\) | 34.4387 | 1.16960 | ||||||||
\(868\) | 17.9868 | 0.610511 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0.0839812 | 0.00284723 | ||||||||
\(871\) | 24.5338 | 0.831298 | ||||||||
\(872\) | −14.3467 | −0.485839 | ||||||||
\(873\) | −61.9406 | −2.09637 | ||||||||
\(874\) | −6.51169 | −0.220261 | ||||||||
\(875\) | −9.30504 | −0.314568 | ||||||||
\(876\) | −38.0124 | −1.28432 | ||||||||
\(877\) | 11.4582 | 0.386917 | 0.193458 | − | 0.981108i | \(-0.438030\pi\) | ||||
0.193458 | + | 0.981108i | \(0.438030\pi\) | |||||||
\(878\) | −23.6907 | −0.799523 | ||||||||
\(879\) | −75.9128 | −2.56048 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.3649 | 0.888257 | 0.444129 | − | 0.895963i | \(-0.353513\pi\) | ||||
0.444129 | + | 0.895963i | \(0.353513\pi\) | |||||||
\(882\) | −44.8869 | −1.51142 | ||||||||
\(883\) | 52.5648 | 1.76895 | 0.884474 | − | 0.466590i | \(-0.154517\pi\) | ||||
0.884474 | + | 0.466590i | \(0.154517\pi\) | |||||||
\(884\) | −8.57310 | −0.288345 | ||||||||
\(885\) | 74.6194 | 2.50830 | ||||||||
\(886\) | 26.9144 | 0.904207 | ||||||||
\(887\) | −29.5635 | −0.992644 | −0.496322 | − | 0.868138i | \(-0.665317\pi\) | ||||
−0.496322 | + | 0.868138i | \(0.665317\pi\) | |||||||
\(888\) | 1.71225 | 0.0574595 | ||||||||
\(889\) | −48.7433 | −1.63480 | ||||||||
\(890\) | 19.7147 | 0.660840 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.82515 | 0.295488 | ||||||||
\(893\) | −6.30125 | −0.210863 | ||||||||
\(894\) | −32.9806 | −1.10304 | ||||||||
\(895\) | 67.5313 | 2.25732 | ||||||||
\(896\) | 4.58972 | 0.153332 | ||||||||
\(897\) | −78.1491 | −2.60932 | ||||||||
\(898\) | −15.5953 | −0.520421 | ||||||||
\(899\) | −0.0405840 | −0.00135355 | ||||||||
\(900\) | 17.9415 | 0.598049 | ||||||||
\(901\) | −25.7084 | −0.856470 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.7623 | −0.524536 | ||||||||
\(904\) | −17.6690 | −0.587662 | ||||||||
\(905\) | −24.8900 | −0.827371 | ||||||||
\(906\) | −5.70705 | −0.189604 | ||||||||
\(907\) | 49.2004 | 1.63367 | 0.816836 | − | 0.576870i | \(-0.195726\pi\) | ||||
0.816836 | + | 0.576870i | \(0.195726\pi\) | |||||||
\(908\) | 4.53586 | 0.150528 | ||||||||
\(909\) | 22.7809 | 0.755594 | ||||||||
\(910\) | 72.1491 | 2.39172 | ||||||||
\(911\) | −11.8309 | −0.391976 | −0.195988 | − | 0.980606i | \(-0.562791\pi\) | ||||
−0.195988 | + | 0.980606i | \(0.562791\pi\) | |||||||
\(912\) | −2.48823 | −0.0823934 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −24.0214 | −0.794557 | ||||||||
\(915\) | 109.196 | 3.60989 | ||||||||
\(916\) | −6.29059 | −0.207847 | ||||||||
\(917\) | 77.7319 | 2.56693 | ||||||||
\(918\) | −0.845913 | −0.0279193 | ||||||||
\(919\) | −8.32413 | −0.274588 | −0.137294 | − | 0.990530i | \(-0.543840\pi\) | ||||
−0.137294 | + | 0.990530i | \(0.543840\pi\) | |||||||
\(920\) | −21.2226 | −0.699688 | ||||||||
\(921\) | −25.9021 | −0.853504 | ||||||||
\(922\) | −19.8822 | −0.654784 | ||||||||
\(923\) | 45.5288 | 1.49860 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.86877 | 0.127204 | ||||||||
\(926\) | −37.7710 | −1.24123 | ||||||||
\(927\) | 27.6083 | 0.906775 | ||||||||
\(928\) | −0.0103559 | −0.000339949 0 | ||||||||
\(929\) | −56.0858 | −1.84011 | −0.920057 | − | 0.391784i | \(-0.871858\pi\) | ||||
−0.920057 | + | 0.391784i | \(0.871858\pi\) | |||||||
\(930\) | −31.7805 | −1.04212 | ||||||||
\(931\) | 14.0655 | 0.460979 | ||||||||
\(932\) | 16.6897 | 0.546689 | ||||||||
\(933\) | −71.3127 | −2.33467 | ||||||||
\(934\) | 42.9098 | 1.40405 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −15.3923 | −0.503113 | ||||||||
\(937\) | −25.2464 | −0.824764 | −0.412382 | − | 0.911011i | \(-0.635303\pi\) | ||||
−0.412382 | + | 0.911011i | \(0.635303\pi\) | |||||||
\(938\) | 23.3459 | 0.762272 | ||||||||
\(939\) | −81.6399 | −2.66422 | ||||||||
\(940\) | −20.5367 | −0.669834 | ||||||||
\(941\) | 2.72172 | 0.0887257 | 0.0443628 | − | 0.999015i | \(-0.485874\pi\) | ||||
0.0443628 | + | 0.999015i | \(0.485874\pi\) | |||||||
\(942\) | −28.0704 | −0.914583 | ||||||||
\(943\) | −21.3244 | −0.694419 | ||||||||
\(944\) | −9.20149 | −0.299483 | ||||||||
\(945\) | 7.11899 | 0.231581 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.7838 | −0.935347 | −0.467674 | − | 0.883901i | \(-0.654908\pi\) | ||||
−0.467674 | + | 0.883901i | \(0.654908\pi\) | |||||||
\(948\) | 32.2015 | 1.04586 | ||||||||
\(949\) | 73.6845 | 2.39190 | ||||||||
\(950\) | −5.62205 | −0.182404 | ||||||||
\(951\) | 28.3337 | 0.918784 | ||||||||
\(952\) | −8.15800 | −0.264402 | ||||||||
\(953\) | 19.3594 | 0.627113 | 0.313556 | − | 0.949570i | \(-0.398480\pi\) | ||||
0.313556 | + | 0.949570i | \(0.398480\pi\) | |||||||
\(954\) | −46.1572 | −1.49440 | ||||||||
\(955\) | 67.2493 | 2.17614 | ||||||||
\(956\) | 7.23299 | 0.233932 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 26.1271 | 0.844127 | ||||||||
\(959\) | 37.3079 | 1.20474 | ||||||||
\(960\) | −8.10950 | −0.261733 | ||||||||
\(961\) | −15.6420 | −0.504582 | ||||||||
\(962\) | −3.31909 | −0.107012 | ||||||||
\(963\) | 42.4913 | 1.36926 | ||||||||
\(964\) | −13.5156 | −0.435309 | ||||||||
\(965\) | −28.1834 | −0.907255 | ||||||||
\(966\) | −74.3652 | −2.39266 | ||||||||
\(967\) | 16.2018 | 0.521016 | 0.260508 | − | 0.965472i | \(-0.416110\pi\) | ||||
0.260508 | + | 0.965472i | \(0.416110\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.42270 | 0.142078 | ||||||||
\(970\) | 63.2582 | 2.03110 | ||||||||
\(971\) | −38.0152 | −1.21996 | −0.609982 | − | 0.792415i | \(-0.708824\pi\) | ||||
−0.609982 | + | 0.792415i | \(0.708824\pi\) | |||||||
\(972\) | 22.3030 | 0.715369 | ||||||||
\(973\) | −4.17303 | −0.133781 | ||||||||
\(974\) | −13.0467 | −0.418044 | ||||||||
\(975\) | −67.4722 | −2.16084 | ||||||||
\(976\) | −13.4651 | −0.431009 | ||||||||
\(977\) | 11.0980 | 0.355055 | 0.177528 | − | 0.984116i | \(-0.443190\pi\) | ||||
0.177528 | + | 0.984116i | \(0.443190\pi\) | |||||||
\(978\) | −16.2272 | −0.518888 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 45.8417 | 1.46436 | ||||||||
\(981\) | 45.7840 | 1.46177 | ||||||||
\(982\) | −16.0017 | −0.510633 | ||||||||
\(983\) | −29.1596 | −0.930045 | −0.465023 | − | 0.885299i | \(-0.653954\pi\) | ||||
−0.465023 | + | 0.885299i | \(0.653954\pi\) | |||||||
\(984\) | −8.14842 | −0.259762 | ||||||||
\(985\) | 34.5566 | 1.10107 | ||||||||
\(986\) | 0.0184071 | 0.000586202 0 | ||||||||
\(987\) | −71.9619 | −2.29057 | ||||||||
\(988\) | 4.82326 | 0.153448 | ||||||||
\(989\) | −8.98746 | −0.285785 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.72841 | 0.245501 | 0.122751 | − | 0.992438i | \(-0.460828\pi\) | ||||
0.122751 | + | 0.992438i | \(0.460828\pi\) | |||||||
\(992\) | 3.91892 | 0.124426 | ||||||||
\(993\) | −32.7573 | −1.03952 | ||||||||
\(994\) | 43.3244 | 1.37417 | ||||||||
\(995\) | 7.16470 | 0.227136 | ||||||||
\(996\) | 5.77806 | 0.183085 | ||||||||
\(997\) | 43.8825 | 1.38977 | 0.694886 | − | 0.719120i | \(-0.255455\pi\) | ||||
0.694886 | + | 0.719120i | \(0.255455\pi\) | |||||||
\(998\) | 29.3850 | 0.930166 | ||||||||
\(999\) | −0.327496 | −0.0103615 |
(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 | 4598.2.a.by.1.1 | ✓ | 8 | |
11.10 | odd | 2 | 4598.2.a.cb.1.1 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.by.1.1 | ✓ | 8 | 1.1 | even | 1 | trivial | |
4598.2.a.cb.1.1 | yes | 8 | 11.10 | odd | 2 |