Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
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: | \( x^{8} - 2 x^{7} - 13701836 x^{6} + 201589162 x^{5} + 55078074399586 x^{4} + \cdots + 23\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{10}\cdot 5^{14}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2210.46\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2127.46 | 1.46909 | 0.734543 | − | 0.678562i | \(-0.237396\pi\) | ||||
0.734543 | + | 0.678562i | \(0.237396\pi\) | |||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | 2.42895e6 | 1.15822 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.25625e8 | 0.848178 | ||||||||
\(7\) | −1.04187e9 | −1.39407 | −0.697035 | − | 0.717037i | \(-0.745498\pi\) | ||||
−0.697035 | + | 0.717037i | \(0.745498\pi\) | |||||||
\(8\) | 7.05898e8 | 0.232432 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.38707e10 | 0.277487 | 0.138743 | − | 0.990328i | \(-0.455694\pi\) | ||||
0.138743 | + | 0.990328i | \(0.455694\pi\) | |||||||
\(12\) | 1.43427e11 | 0.668696 | ||||||||
\(13\) | 3.64962e11 | 0.734247 | 0.367123 | − | 0.930172i | \(-0.380343\pi\) | ||||
0.367123 | + | 0.930172i | \(0.380343\pi\) | |||||||
\(14\) | −2.21654e12 | −2.04801 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.59211e12 | −0.816752 | ||||||||
\(17\) | −8.45697e12 | −1.01742 | −0.508711 | − | 0.860937i | \(-0.669878\pi\) | ||||
−0.508711 | + | 0.860937i | \(0.669878\pi\) | |||||||
\(18\) | 7.41801e12 | 0.489696 | ||||||||
\(19\) | 5.34859e11 | 0.0200137 | 0.0100068 | − | 0.999950i | \(-0.496815\pi\) | ||||
0.0100068 | + | 0.999950i | \(0.496815\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.15215e13 | −0.804867 | ||||||||
\(22\) | 5.07841e13 | 0.407652 | ||||||||
\(23\) | 3.10320e14 | 1.56195 | 0.780975 | − | 0.624562i | \(-0.214723\pi\) | ||||
0.780975 | + | 0.624562i | \(0.214723\pi\) | |||||||
\(24\) | 4.16825e13 | 0.134195 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 7.76443e14 | 1.07867 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | −2.53066e15 | −1.61463 | ||||||||
\(29\) | 1.78803e15 | 0.789217 | 0.394608 | − | 0.918849i | \(-0.370880\pi\) | ||||
0.394608 | + | 0.918849i | \(0.370880\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.32789e15 | 1.38663 | 0.693316 | − | 0.720634i | \(-0.256149\pi\) | ||||
0.693316 | + | 0.720634i | \(0.256149\pi\) | |||||||
\(32\) | −9.12247e15 | −1.43231 | ||||||||
\(33\) | 1.40954e15 | 0.160207 | ||||||||
\(34\) | −1.79919e16 | −1.49468 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 8.46924e15 | 0.386072 | ||||||||
\(37\) | −2.11910e16 | −0.724491 | −0.362245 | − | 0.932083i | \(-0.617990\pi\) | ||||
−0.362245 | + | 0.932083i | \(0.617990\pi\) | |||||||
\(38\) | 1.13789e15 | 0.0294018 | ||||||||
\(39\) | 2.15506e16 | 0.423918 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.38647e16 | −0.277668 | −0.138834 | − | 0.990316i | \(-0.544335\pi\) | ||||
−0.138834 | + | 0.990316i | \(0.544335\pi\) | |||||||
\(42\) | −1.30885e17 | −1.18242 | ||||||||
\(43\) | 1.06785e17 | 0.753514 | 0.376757 | − | 0.926312i | \(-0.377039\pi\) | ||||
0.376757 | + | 0.926312i | \(0.377039\pi\) | |||||||
\(44\) | 5.79809e16 | 0.321389 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.60194e17 | 2.29464 | ||||||||
\(47\) | 6.65515e16 | 0.184557 | 0.0922785 | − | 0.995733i | \(-0.470585\pi\) | ||||
0.0922785 | + | 0.995733i | \(0.470585\pi\) | |||||||
\(48\) | −2.12111e17 | −0.471552 | ||||||||
\(49\) | 5.26950e17 | 0.943431 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −4.99375e17 | −0.587409 | ||||||||
\(52\) | 8.86475e17 | 0.850416 | ||||||||
\(53\) | −1.12980e18 | −0.887370 | −0.443685 | − | 0.896183i | \(-0.646329\pi\) | ||||
−0.443685 | + | 0.896183i | \(0.646329\pi\) | |||||||
\(54\) | 4.38026e17 | 0.282726 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.35454e17 | −0.324027 | ||||||||
\(57\) | 3.15829e16 | 0.0115549 | ||||||||
\(58\) | 3.80397e18 | 1.15943 | ||||||||
\(59\) | 3.51140e18 | 0.894405 | 0.447202 | − | 0.894433i | \(-0.352420\pi\) | ||||
0.447202 | + | 0.894433i | \(0.352420\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.16179e18 | 1.46495 | 0.732474 | − | 0.680795i | \(-0.238365\pi\) | ||||
0.732474 | + | 0.680795i | \(0.238365\pi\) | |||||||
\(62\) | 1.34624e19 | 2.03708 | ||||||||
\(63\) | −3.63278e18 | −0.464690 | ||||||||
\(64\) | −1.18745e19 | −1.28744 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.99875e18 | 0.235358 | ||||||||
\(67\) | 1.34455e19 | 0.901137 | 0.450569 | − | 0.892742i | \(-0.351221\pi\) | ||||
0.450569 | + | 0.892742i | \(0.351221\pi\) | |||||||
\(68\) | −2.05416e19 | −1.17839 | ||||||||
\(69\) | 1.83241e19 | 0.901792 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.06302e19 | 1.48128 | 0.740639 | − | 0.671903i | \(-0.234523\pi\) | ||||
0.740639 | + | 0.671903i | \(0.234523\pi\) | |||||||
\(72\) | 2.46131e18 | 0.0774775 | ||||||||
\(73\) | −1.09593e19 | −0.298464 | −0.149232 | − | 0.988802i | \(-0.547680\pi\) | ||||
−0.149232 | + | 0.988802i | \(0.547680\pi\) | |||||||
\(74\) | −4.50830e19 | −1.06434 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.29915e18 | 0.0231801 | ||||||||
\(77\) | −2.48702e19 | −0.386836 | ||||||||
\(78\) | 4.58482e19 | 0.622772 | ||||||||
\(79\) | 3.58892e19 | 0.426461 | 0.213231 | − | 0.977002i | \(-0.431601\pi\) | ||||
0.213231 | + | 0.977002i | \(0.431601\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | −5.07714e19 | −0.407919 | ||||||||
\(83\) | 1.25727e20 | 0.889422 | 0.444711 | − | 0.895674i | \(-0.353306\pi\) | ||||
0.444711 | + | 0.895674i | \(0.353306\pi\) | |||||||
\(84\) | −1.49433e20 | −0.932209 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.27181e20 | 1.10698 | ||||||||
\(87\) | 1.05581e20 | 0.455654 | ||||||||
\(88\) | 1.68503e19 | 0.0644969 | ||||||||
\(89\) | 4.16172e20 | 1.41474 | 0.707372 | − | 0.706841i | \(-0.249880\pi\) | ||||
0.707372 | + | 0.706841i | \(0.249880\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.80243e20 | −1.02359 | ||||||||
\(92\) | 7.53752e20 | 1.80907 | ||||||||
\(93\) | 3.73656e20 | 0.800573 | ||||||||
\(94\) | 1.41586e20 | 0.271130 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −5.38673e20 | −0.826946 | ||||||||
\(97\) | 4.65598e20 | 0.641073 | 0.320537 | − | 0.947236i | \(-0.396137\pi\) | ||||
0.320537 | + | 0.947236i | \(0.396137\pi\) | |||||||
\(98\) | 1.12107e21 | 1.38598 | ||||||||
\(99\) | 8.32320e19 | 0.0924955 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.68773e20 | −0.872665 | −0.436332 | − | 0.899786i | \(-0.643723\pi\) | ||||
−0.436332 | + | 0.899786i | \(0.643723\pi\) | |||||||
\(102\) | −1.06240e21 | −0.862954 | ||||||||
\(103\) | 1.91438e21 | 1.40358 | 0.701790 | − | 0.712383i | \(-0.252384\pi\) | ||||
0.701790 | + | 0.712383i | \(0.252384\pi\) | |||||||
\(104\) | 2.57626e20 | 0.170663 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.40361e21 | −1.30362 | ||||||||
\(107\) | 6.22284e20 | 0.305815 | 0.152907 | − | 0.988241i | \(-0.451136\pi\) | ||||
0.152907 | + | 0.988241i | \(0.451136\pi\) | |||||||
\(108\) | 5.00100e20 | 0.222899 | ||||||||
\(109\) | −3.42222e21 | −1.38462 | −0.692308 | − | 0.721602i | \(-0.743406\pi\) | ||||
−0.692308 | + | 0.721602i | \(0.743406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.25131e21 | −0.418285 | ||||||||
\(112\) | 3.74252e21 | 1.13861 | ||||||||
\(113\) | −6.40614e21 | −1.77530 | −0.887651 | − | 0.460516i | \(-0.847664\pi\) | ||||
−0.887651 | + | 0.460516i | \(0.847664\pi\) | |||||||
\(114\) | 6.71915e19 | 0.0169751 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.34305e21 | 0.914083 | ||||||||
\(117\) | 1.27254e21 | 0.244749 | ||||||||
\(118\) | 7.47038e21 | 1.31396 | ||||||||
\(119\) | 8.81107e21 | 1.41836 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.83044e21 | −0.923001 | ||||||||
\(122\) | 1.73639e22 | 2.15214 | ||||||||
\(123\) | −1.40919e21 | −0.160312 | ||||||||
\(124\) | 1.53702e22 | 1.60602 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −7.72861e21 | −0.682670 | ||||||||
\(127\) | 3.91229e21 | 0.318047 | 0.159024 | − | 0.987275i | \(-0.449165\pi\) | ||||
0.159024 | + | 0.987275i | \(0.449165\pi\) | |||||||
\(128\) | −6.13143e21 | −0.459047 | ||||||||
\(129\) | 6.30555e21 | 0.435042 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.38194e21 | −0.550737 | −0.275368 | − | 0.961339i | \(-0.588800\pi\) | ||||
−0.275368 | + | 0.961339i | \(0.588800\pi\) | |||||||
\(132\) | 3.42371e21 | 0.185554 | ||||||||
\(133\) | −5.57254e20 | −0.0279004 | ||||||||
\(134\) | 2.86048e22 | 1.32385 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.96975e21 | −0.236482 | ||||||||
\(137\) | 3.91869e22 | 1.43739 | 0.718696 | − | 0.695325i | \(-0.244739\pi\) | ||||
0.718696 | + | 0.695325i | \(0.244739\pi\) | |||||||
\(138\) | 3.89838e22 | 1.32481 | ||||||||
\(139\) | 5.75024e22 | 1.81147 | 0.905733 | − | 0.423848i | \(-0.139321\pi\) | ||||
0.905733 | + | 0.423848i | \(0.139321\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.92980e21 | 0.106554 | ||||||||
\(142\) | 8.64394e22 | 2.17613 | ||||||||
\(143\) | 8.71189e21 | 0.203744 | ||||||||
\(144\) | −1.25249e22 | −0.272251 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.33155e22 | −0.438470 | ||||||||
\(147\) | 3.11159e22 | 0.544690 | ||||||||
\(148\) | −5.14719e22 | −0.839116 | ||||||||
\(149\) | 8.30694e22 | 1.26178 | 0.630892 | − | 0.775871i | \(-0.282689\pi\) | ||||
0.630892 | + | 0.775871i | \(0.282689\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.13097e22 | −1.07370 | −0.536852 | − | 0.843676i | \(-0.680387\pi\) | ||||
−0.536852 | + | 0.843676i | \(0.680387\pi\) | |||||||
\(152\) | 3.77556e20 | 0.00465182 | ||||||||
\(153\) | −2.94876e22 | −0.339141 | ||||||||
\(154\) | −5.29105e22 | −0.568295 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 5.23455e22 | 0.490988 | ||||||||
\(157\) | −1.22856e23 | −1.07758 | −0.538791 | − | 0.842439i | \(-0.681119\pi\) | ||||
−0.538791 | + | 0.842439i | \(0.681119\pi\) | |||||||
\(158\) | 7.63530e22 | 0.626508 | ||||||||
\(159\) | −6.67136e22 | −0.512323 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.23313e23 | −2.17747 | ||||||||
\(162\) | 2.58650e22 | 0.163232 | ||||||||
\(163\) | 2.64435e23 | 1.56440 | 0.782202 | − | 0.623025i | \(-0.214096\pi\) | ||||
0.782202 | + | 0.623025i | \(0.214096\pi\) | |||||||
\(164\) | −5.79663e22 | −0.321600 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.67479e23 | 1.30664 | ||||||||
\(167\) | −2.39814e23 | −1.09989 | −0.549947 | − | 0.835200i | \(-0.685352\pi\) | ||||
−0.549947 | + | 0.835200i | \(0.685352\pi\) | |||||||
\(168\) | −4.34278e22 | −0.187077 | ||||||||
\(169\) | −1.13867e23 | −0.460882 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.86494e21 | 0.00667122 | ||||||||
\(172\) | 2.59376e23 | 0.872732 | ||||||||
\(173\) | −3.35267e23 | −1.06147 | −0.530734 | − | 0.847538i | \(-0.678084\pi\) | ||||
−0.530734 | + | 0.847538i | \(0.678084\pi\) | |||||||
\(174\) | 2.24621e23 | 0.669396 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −8.57463e22 | −0.226638 | ||||||||
\(177\) | 2.07345e23 | 0.516385 | ||||||||
\(178\) | 8.85392e23 | 2.07838 | ||||||||
\(179\) | 2.45865e22 | 0.0544177 | 0.0272088 | − | 0.999630i | \(-0.491338\pi\) | ||||
0.0272088 | + | 0.999630i | \(0.491338\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.11848e23 | 0.614212 | 0.307106 | − | 0.951675i | \(-0.400639\pi\) | ||||
0.307106 | + | 0.951675i | \(0.400639\pi\) | |||||||
\(182\) | −8.08954e23 | −1.50374 | ||||||||
\(183\) | 4.81946e23 | 0.845788 | ||||||||
\(184\) | 2.19054e23 | 0.363048 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 7.94939e23 | 1.17611 | ||||||||
\(187\) | −2.01874e23 | −0.282321 | ||||||||
\(188\) | 1.61651e23 | 0.213757 | ||||||||
\(189\) | −2.14512e23 | −0.268289 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.19817e23 | −0.358139 | −0.179070 | − | 0.983836i | \(-0.557309\pi\) | ||||
−0.179070 | + | 0.983836i | \(0.557309\pi\) | |||||||
\(192\) | −7.01179e23 | −0.743303 | ||||||||
\(193\) | −1.38926e24 | −1.39454 | −0.697269 | − | 0.716810i | \(-0.745602\pi\) | ||||
−0.697269 | + | 0.716810i | \(0.745602\pi\) | |||||||
\(194\) | 9.90543e23 | 0.941792 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.27994e24 | 1.09270 | ||||||||
\(197\) | −1.35954e24 | −1.10026 | −0.550132 | − | 0.835078i | \(-0.685423\pi\) | ||||
−0.550132 | + | 0.835078i | \(0.685423\pi\) | |||||||
\(198\) | 1.77073e23 | 0.135884 | ||||||||
\(199\) | −8.32615e23 | −0.606020 | −0.303010 | − | 0.952987i | \(-0.597992\pi\) | ||||
−0.303010 | + | 0.952987i | \(0.597992\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.93942e23 | 0.520272 | ||||||||
\(202\) | −2.06103e24 | −1.28202 | ||||||||
\(203\) | −1.86290e24 | −1.10022 | ||||||||
\(204\) | −1.21296e24 | −0.680346 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 4.07278e24 | 2.06198 | ||||||||
\(207\) | 1.08202e24 | 0.520650 | ||||||||
\(208\) | −1.31098e24 | −0.599698 | ||||||||
\(209\) | 1.27675e22 | 0.00555352 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.90320e24 | 1.92981 | 0.964904 | − | 0.262603i | \(-0.0845809\pi\) | ||||
0.964904 | + | 0.262603i | \(0.0845809\pi\) | |||||||
\(212\) | −2.74423e24 | −1.02777 | ||||||||
\(213\) | 2.39917e24 | 0.855216 | ||||||||
\(214\) | 1.32389e24 | 0.449269 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.45338e23 | 0.0447317 | ||||||||
\(217\) | −6.59285e24 | −1.93306 | ||||||||
\(218\) | −7.28065e24 | −2.03412 | ||||||||
\(219\) | −6.47135e23 | −0.172318 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.08647e24 | −0.747039 | ||||||||
\(222\) | −2.66211e24 | −0.614497 | ||||||||
\(223\) | 7.50133e24 | 1.65172 | 0.825862 | − | 0.563872i | \(-0.190689\pi\) | ||||
0.825862 | + | 0.563872i | \(0.190689\pi\) | |||||||
\(224\) | 9.50444e24 | 1.99674 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.36288e25 | −2.60807 | ||||||||
\(227\) | 3.57793e23 | 0.0653673 | 0.0326836 | − | 0.999466i | \(-0.489595\pi\) | ||||
0.0326836 | + | 0.999466i | \(0.489595\pi\) | |||||||
\(228\) | 7.67134e22 | 0.0133831 | ||||||||
\(229\) | −4.08201e24 | −0.680145 | −0.340072 | − | 0.940399i | \(-0.610452\pi\) | ||||
−0.340072 | + | 0.940399i | \(0.610452\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.46856e24 | −0.223340 | ||||||||
\(232\) | 1.26217e24 | 0.183440 | ||||||||
\(233\) | 6.11617e24 | 0.849655 | 0.424827 | − | 0.905274i | \(-0.360335\pi\) | ||||
0.424827 | + | 0.905274i | \(0.360335\pi\) | |||||||
\(234\) | 2.70729e24 | 0.359557 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.52903e24 | 1.03591 | ||||||||
\(237\) | 2.11922e24 | 0.246217 | ||||||||
\(238\) | 1.87452e25 | 2.08369 | ||||||||
\(239\) | 1.68371e25 | 1.79098 | 0.895488 | − | 0.445085i | \(-0.146827\pi\) | ||||
0.895488 | + | 0.445085i | \(0.146827\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.91923e24 | 0.771799 | 0.385899 | − | 0.922541i | \(-0.373891\pi\) | ||||
0.385899 | + | 0.922541i | \(0.373891\pi\) | |||||||
\(242\) | −1.45315e25 | −1.35597 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | 1.98246e25 | 1.69673 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.99800e24 | −0.235512 | ||||||||
\(247\) | 1.95203e23 | 0.0146950 | ||||||||
\(248\) | 4.46684e24 | 0.322298 | ||||||||
\(249\) | 7.42404e24 | 0.513508 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.00598e25 | −0.639758 | −0.319879 | − | 0.947458i | \(-0.603642\pi\) | ||||
−0.319879 | + | 0.947458i | \(0.603642\pi\) | |||||||
\(252\) | −8.82386e24 | −0.538211 | ||||||||
\(253\) | 7.40755e24 | 0.433420 | ||||||||
\(254\) | 8.32326e24 | 0.467239 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.18583e25 | 0.613059 | ||||||||
\(257\) | 2.24368e25 | 1.11343 | 0.556716 | − | 0.830703i | \(-0.312061\pi\) | ||||
0.556716 | + | 0.830703i | \(0.312061\pi\) | |||||||
\(258\) | 1.34148e25 | 0.639114 | ||||||||
\(259\) | 2.20783e25 | 1.00999 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.23448e24 | 0.263072 | ||||||||
\(262\) | −1.99597e25 | −0.809080 | ||||||||
\(263\) | 1.25135e25 | 0.487353 | 0.243676 | − | 0.969857i | \(-0.421647\pi\) | ||||
0.243676 | + | 0.969857i | \(0.421647\pi\) | |||||||
\(264\) | 9.94992e23 | 0.0372373 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.18554e24 | −0.0409882 | ||||||||
\(267\) | 2.45746e25 | 0.816803 | ||||||||
\(268\) | 3.26585e25 | 1.04371 | ||||||||
\(269\) | −8.81802e24 | −0.271002 | −0.135501 | − | 0.990777i | \(-0.543264\pi\) | ||||
−0.135501 | + | 0.990777i | \(0.543264\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.96008e25 | −1.41030 | −0.705150 | − | 0.709058i | \(-0.749120\pi\) | ||||
−0.705150 | + | 0.709058i | \(0.749120\pi\) | |||||||
\(272\) | 3.03784e25 | 0.830981 | ||||||||
\(273\) | −2.24530e25 | −0.590971 | ||||||||
\(274\) | 8.33688e25 | 2.11165 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 4.45083e25 | 1.04447 | ||||||||
\(277\) | 3.36814e25 | 0.760943 | 0.380471 | − | 0.924793i | \(-0.375762\pi\) | ||||
0.380471 | + | 0.924793i | \(0.375762\pi\) | |||||||
\(278\) | 1.22334e26 | 2.66120 | ||||||||
\(279\) | 2.20640e25 | 0.462211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8.37255e25 | 1.62720 | 0.813601 | − | 0.581423i | \(-0.197504\pi\) | ||||
0.813601 | + | 0.581423i | \(0.197504\pi\) | |||||||
\(282\) | 8.36051e24 | 0.156537 | ||||||||
\(283\) | −7.42339e25 | −1.33920 | −0.669599 | − | 0.742723i | \(-0.733534\pi\) | ||||
−0.669599 | + | 0.742723i | \(0.733534\pi\) | |||||||
\(284\) | 9.86889e25 | 1.71564 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.85342e25 | 0.299317 | ||||||||
\(287\) | 2.48640e25 | 0.387089 | ||||||||
\(288\) | −3.18081e25 | −0.477437 | ||||||||
\(289\) | 2.42835e24 | 0.0351466 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.74931e25 | 0.370124 | ||||||||
\(292\) | −2.66196e25 | −0.345686 | ||||||||
\(293\) | 8.24760e25 | 1.03328 | 0.516639 | − | 0.856203i | \(-0.327183\pi\) | ||||
0.516639 | + | 0.856203i | \(0.327183\pi\) | |||||||
\(294\) | 6.61979e25 | 0.800197 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.49587e25 | −0.168395 | ||||||||
\(297\) | 4.91477e24 | 0.0534023 | ||||||||
\(298\) | 1.76727e26 | 1.85367 | ||||||||
\(299\) | 1.13255e26 | 1.14686 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.11256e26 | −1.05045 | ||||||||
\(302\) | −1.72984e26 | −1.57736 | ||||||||
\(303\) | −5.72051e25 | −0.503833 | ||||||||
\(304\) | −1.92127e24 | −0.0163462 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −6.27339e25 | −0.498227 | ||||||||
\(307\) | −1.43666e26 | −1.10256 | −0.551279 | − | 0.834321i | \(-0.685860\pi\) | ||||
−0.551279 | + | 0.834321i | \(0.685860\pi\) | |||||||
\(308\) | −6.04086e25 | −0.448039 | ||||||||
\(309\) | 1.13042e26 | 0.810358 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.34915e25 | 0.0903811 | 0.0451906 | − | 0.998978i | \(-0.485610\pi\) | ||||
0.0451906 | + | 0.998978i | \(0.485610\pi\) | |||||||
\(312\) | 1.52125e25 | 0.0985322 | ||||||||
\(313\) | 3.83034e25 | 0.239896 | 0.119948 | − | 0.992780i | \(-0.461727\pi\) | ||||
0.119948 | + | 0.992780i | \(0.461727\pi\) | |||||||
\(314\) | −2.61372e26 | −1.58306 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.71733e25 | 0.493934 | ||||||||
\(317\) | −2.08246e26 | −1.14144 | −0.570721 | − | 0.821144i | \(-0.693336\pi\) | ||||
−0.570721 | + | 0.821144i | \(0.693336\pi\) | |||||||
\(318\) | −1.41931e26 | −0.752648 | ||||||||
\(319\) | 4.26816e25 | 0.218997 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.67452e25 | 0.176562 | ||||||||
\(322\) | −6.87837e26 | −3.19889 | ||||||||
\(323\) | −4.52328e24 | −0.0203623 | ||||||||
\(324\) | 2.95304e25 | 0.128691 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 5.62576e26 | 2.29825 | ||||||||
\(327\) | −2.02079e26 | −0.799409 | ||||||||
\(328\) | −1.68461e25 | −0.0645391 | ||||||||
\(329\) | −6.93381e25 | −0.257285 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.16316e26 | −1.44954 | −0.724768 | − | 0.688992i | \(-0.758053\pi\) | ||||
−0.724768 | + | 0.688992i | \(0.758053\pi\) | |||||||
\(332\) | 3.05385e26 | 1.03014 | ||||||||
\(333\) | −7.38883e25 | −0.241497 | ||||||||
\(334\) | −5.10195e26 | −1.61584 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.20992e26 | 0.657377 | ||||||||
\(337\) | −1.00308e26 | −0.289216 | −0.144608 | − | 0.989489i | \(-0.546192\pi\) | ||||
−0.144608 | + | 0.989489i | \(0.546192\pi\) | |||||||
\(338\) | −2.42249e26 | −0.677075 | ||||||||
\(339\) | −3.78276e26 | −1.02497 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.51051e26 | 0.384772 | ||||||||
\(342\) | 3.96759e24 | 0.00980060 | ||||||||
\(343\) | 3.29192e25 | 0.0788607 | ||||||||
\(344\) | 7.53793e25 | 0.175141 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.13269e26 | −1.55939 | ||||||||
\(347\) | 2.62880e26 | 0.557568 | 0.278784 | − | 0.960354i | \(-0.410069\pi\) | ||||
0.278784 | + | 0.960354i | \(0.410069\pi\) | |||||||
\(348\) | 2.56453e26 | 0.527746 | ||||||||
\(349\) | 8.84994e25 | 0.176715 | 0.0883575 | − | 0.996089i | \(-0.471838\pi\) | ||||
0.0883575 | + | 0.996089i | \(0.471838\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.51424e25 | 0.141306 | ||||||||
\(352\) | −2.17760e26 | −0.397447 | ||||||||
\(353\) | −4.85017e26 | −0.859255 | −0.429628 | − | 0.903006i | \(-0.641355\pi\) | ||||
−0.429628 | + | 0.903006i | \(0.641355\pi\) | |||||||
\(354\) | 4.41118e26 | 0.758614 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.01086e27 | 1.63858 | ||||||||
\(357\) | 5.20285e26 | 0.818889 | ||||||||
\(358\) | 5.23069e25 | 0.0799443 | ||||||||
\(359\) | 1.60735e26 | 0.238571 | 0.119285 | − | 0.992860i | \(-0.461940\pi\) | ||||
0.119285 | + | 0.992860i | \(0.461940\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.13923e26 | −0.999599 | ||||||||
\(362\) | 6.63446e26 | 0.902330 | ||||||||
\(363\) | −4.03331e26 | −0.532895 | ||||||||
\(364\) | −9.23593e26 | −1.18554 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.02532e27 | 1.24254 | ||||||||
\(367\) | −8.97540e25 | −0.105696 | −0.0528482 | − | 0.998603i | \(-0.516830\pi\) | ||||
−0.0528482 | + | 0.998603i | \(0.516830\pi\) | |||||||
\(368\) | −1.11470e27 | −1.27573 | ||||||||
\(369\) | −8.32112e25 | −0.0925560 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.17711e27 | 1.23706 | ||||||||
\(372\) | 9.07593e26 | 0.927236 | ||||||||
\(373\) | 1.71990e27 | 1.70828 | 0.854142 | − | 0.520040i | \(-0.174083\pi\) | ||||
0.854142 | + | 0.520040i | \(0.174083\pi\) | |||||||
\(374\) | −4.29479e26 | −0.414754 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.69786e25 | 0.0428970 | ||||||||
\(377\) | 6.52563e26 | 0.579480 | ||||||||
\(378\) | −4.56367e26 | −0.394140 | ||||||||
\(379\) | −6.22737e26 | −0.523110 | −0.261555 | − | 0.965189i | \(-0.584235\pi\) | ||||
−0.261555 | + | 0.965189i | \(0.584235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.31017e26 | 0.183625 | ||||||||
\(382\) | −6.80400e26 | −0.526137 | ||||||||
\(383\) | −3.54226e26 | −0.266498 | −0.133249 | − | 0.991083i | \(-0.542541\pi\) | ||||
−0.133249 | + | 0.991083i | \(0.542541\pi\) | |||||||
\(384\) | −3.62055e26 | −0.265031 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.95559e27 | −2.04870 | ||||||||
\(387\) | 3.72336e26 | 0.251171 | ||||||||
\(388\) | 1.13092e27 | 0.742501 | ||||||||
\(389\) | 1.41987e27 | 0.907356 | 0.453678 | − | 0.891166i | \(-0.350112\pi\) | ||||
0.453678 | + | 0.891166i | \(0.350112\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.62436e27 | −1.58916 | ||||||||
\(392\) | 3.71973e26 | 0.219284 | ||||||||
\(393\) | −5.53994e26 | −0.317968 | ||||||||
\(394\) | −2.89238e27 | −1.61638 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.02167e26 | 0.107130 | ||||||||
\(397\) | 3.01335e27 | 1.55507 | 0.777534 | − | 0.628841i | \(-0.216471\pi\) | ||||
0.777534 | + | 0.628841i | \(0.216471\pi\) | |||||||
\(398\) | −1.77136e27 | −0.890295 | ||||||||
\(399\) | −3.29053e25 | −0.0161083 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −2.47480e27 | −1.14954 | −0.574769 | − | 0.818316i | \(-0.694908\pi\) | ||||
−0.574769 | + | 0.818316i | \(0.694908\pi\) | |||||||
\(402\) | 1.68908e27 | 0.764324 | ||||||||
\(403\) | 2.30944e27 | 1.01813 | ||||||||
\(404\) | −2.35310e27 | −1.01073 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.96325e27 | −1.61632 | ||||||||
\(407\) | −5.05843e26 | −0.201036 | ||||||||
\(408\) | −3.52508e26 | −0.136533 | ||||||||
\(409\) | −2.52746e27 | −0.954090 | −0.477045 | − | 0.878879i | \(-0.658292\pi\) | ||||
−0.477045 | + | 0.878879i | \(0.658292\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.31395e27 | 0.829878 | ||||||||
\(412\) | 4.64994e27 | 1.62565 | ||||||||
\(413\) | −3.65843e27 | −1.24686 | ||||||||
\(414\) | 2.30195e27 | 0.764880 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.32935e27 | −1.05167 | ||||||||
\(417\) | 3.39546e27 | 1.04585 | ||||||||
\(418\) | 2.71623e25 | 0.00815860 | ||||||||
\(419\) | 5.89009e27 | 1.72534 | 0.862670 | − | 0.505768i | \(-0.168791\pi\) | ||||
0.862670 | + | 0.505768i | \(0.168791\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.40338e27 | −1.78421 | −0.892107 | − | 0.451823i | \(-0.850774\pi\) | ||||
−0.892107 | + | 0.451823i | \(0.850774\pi\) | |||||||
\(422\) | 1.04314e28 | 2.83506 | ||||||||
\(423\) | 2.32051e26 | 0.0615190 | ||||||||
\(424\) | −7.97523e26 | −0.206254 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.10416e27 | 1.25639 | ||||||||
\(427\) | −8.50354e27 | −2.04224 | ||||||||
\(428\) | 1.51150e27 | 0.354200 | ||||||||
\(429\) | 5.14429e26 | 0.117631 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.23137e27 | −0.485914 | −0.242957 | − | 0.970037i | \(-0.578117\pi\) | ||||
−0.242957 | + | 0.970037i | \(0.578117\pi\) | |||||||
\(432\) | −7.39584e26 | −0.157184 | ||||||||
\(433\) | −5.24943e27 | −1.08890 | −0.544451 | − | 0.838793i | \(-0.683262\pi\) | ||||
−0.544451 | + | 0.838793i | \(0.683262\pi\) | |||||||
\(434\) | −1.40261e28 | −2.83984 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.31241e27 | −1.60369 | ||||||||
\(437\) | 1.65977e26 | 0.0312603 | ||||||||
\(438\) | −1.37676e27 | −0.253150 | ||||||||
\(439\) | −4.22260e26 | −0.0758058 | −0.0379029 | − | 0.999281i | \(-0.512068\pi\) | ||||
−0.0379029 | + | 0.999281i | \(0.512068\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.83736e27 | 0.314477 | ||||||||
\(442\) | −6.56635e27 | −1.09746 | ||||||||
\(443\) | −6.71148e27 | −1.09542 | −0.547708 | − | 0.836670i | \(-0.684499\pi\) | ||||
−0.547708 | + | 0.836670i | \(0.684499\pi\) | |||||||
\(444\) | −3.03936e27 | −0.484464 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1.59588e28 | 2.42653 | ||||||||
\(447\) | 4.90516e27 | 0.728491 | ||||||||
\(448\) | 1.23717e28 | 1.79478 | ||||||||
\(449\) | 1.36311e28 | 1.93171 | 0.965857 | − | 0.259074i | \(-0.0834173\pi\) | ||||
0.965857 | + | 0.259074i | \(0.0834173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.69668e26 | −0.0770492 | ||||||||
\(452\) | −1.55602e28 | −2.05618 | ||||||||
\(453\) | −4.80126e27 | −0.619903 | ||||||||
\(454\) | 7.61192e26 | 0.0960302 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.22943e25 | 0.00268573 | ||||||||
\(457\) | 6.75530e26 | 0.0795288 | 0.0397644 | − | 0.999209i | \(-0.487339\pi\) | ||||
0.0397644 | + | 0.999209i | \(0.487339\pi\) | |||||||
\(458\) | −8.68433e27 | −0.999191 | ||||||||
\(459\) | −1.74121e27 | −0.195803 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.77372e28 | 1.90557 | 0.952784 | − | 0.303648i | \(-0.0982046\pi\) | ||||
0.952784 | + | 0.303648i | \(0.0982046\pi\) | |||||||
\(462\) | −3.12431e27 | −0.328105 | ||||||||
\(463\) | −1.71011e28 | −1.75559 | −0.877795 | − | 0.479036i | \(-0.840986\pi\) | ||||
−0.877795 | + | 0.479036i | \(0.840986\pi\) | |||||||
\(464\) | −6.42281e27 | −0.644594 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.30119e28 | 1.24822 | ||||||||
\(467\) | 4.22031e27 | 0.395838 | 0.197919 | − | 0.980218i | \(-0.436582\pi\) | ||||
0.197919 | + | 0.980218i | \(0.436582\pi\) | |||||||
\(468\) | 3.09095e27 | 0.283472 | ||||||||
\(469\) | −1.40085e28 | −1.25625 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.25453e27 | −0.622143 | ||||||||
\(472\) | 2.47869e27 | 0.207889 | ||||||||
\(473\) | 2.54903e27 | 0.209090 | ||||||||
\(474\) | 4.50857e27 | 0.361715 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 2.14017e28 | 1.64276 | ||||||||
\(477\) | −3.93937e27 | −0.295790 | ||||||||
\(478\) | 3.58204e28 | 2.63110 | ||||||||
\(479\) | −1.35397e28 | −0.972940 | −0.486470 | − | 0.873697i | \(-0.661716\pi\) | ||||
−0.486470 | + | 0.873697i | \(0.661716\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.73389e27 | −0.531955 | ||||||||
\(482\) | 1.68479e28 | 1.13384 | ||||||||
\(483\) | −1.90913e28 | −1.25716 | ||||||||
\(484\) | −1.65908e28 | −1.06903 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.52730e27 | 0.0942420 | ||||||||
\(487\) | −3.09803e28 | −1.87082 | −0.935409 | − | 0.353566i | \(-0.884969\pi\) | ||||
−0.935409 | + | 0.353566i | \(0.884969\pi\) | |||||||
\(488\) | 5.76139e27 | 0.340502 | ||||||||
\(489\) | 1.56146e28 | 0.903209 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.91039e27 | −0.549206 | −0.274603 | − | 0.961558i | \(-0.588546\pi\) | ||||
−0.274603 | + | 0.961558i | \(0.588546\pi\) | |||||||
\(492\) | −3.42285e27 | −0.185676 | ||||||||
\(493\) | −1.51213e28 | −0.802966 | ||||||||
\(494\) | 4.15288e26 | 0.0215882 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.27305e28 | −1.13253 | ||||||||
\(497\) | −4.23315e28 | −2.06501 | ||||||||
\(498\) | 1.57944e28 | 0.754388 | ||||||||
\(499\) | 1.73803e28 | 0.812833 | 0.406416 | − | 0.913688i | \(-0.366778\pi\) | ||||
0.406416 | + | 0.913688i | \(0.366778\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.41607e28 | −0.635024 | ||||||||
\(502\) | −2.14019e28 | −0.939860 | ||||||||
\(503\) | 2.38152e28 | 1.02421 | 0.512106 | − | 0.858922i | \(-0.328865\pi\) | ||||
0.512106 | + | 0.858922i | \(0.328865\pi\) | |||||||
\(504\) | −2.56437e27 | −0.108009 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1.57593e28 | 0.636732 | ||||||||
\(507\) | −6.72376e27 | −0.266090 | ||||||||
\(508\) | 9.50277e27 | 0.368367 | ||||||||
\(509\) | 1.77287e28 | 0.673195 | 0.336598 | − | 0.941649i | \(-0.390724\pi\) | ||||
0.336598 | + | 0.941649i | \(0.390724\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.14182e28 | 0.416080 | ||||||||
\(512\) | 3.80866e28 | 1.35968 | ||||||||
\(513\) | 1.10123e26 | 0.00385163 | ||||||||
\(514\) | 4.77336e28 | 1.63573 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.53159e28 | 0.503872 | ||||||||
\(517\) | 1.58863e27 | 0.0512121 | ||||||||
\(518\) | 4.69707e28 | 1.48376 | ||||||||
\(519\) | −1.97972e28 | −0.612839 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.06630e28 | −0.317017 | −0.158509 | − | 0.987358i | \(-0.550669\pi\) | ||||
−0.158509 | + | 0.987358i | \(0.550669\pi\) | |||||||
\(522\) | 1.32636e28 | 0.386476 | ||||||||
\(523\) | −4.82119e27 | −0.137685 | −0.0688424 | − | 0.997628i | \(-0.521931\pi\) | ||||
−0.0688424 | + | 0.997628i | \(0.521931\pi\) | |||||||
\(524\) | −2.27883e28 | −0.637872 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.66220e28 | 0.715963 | ||||||||
\(527\) | −5.35148e28 | −1.41079 | ||||||||
\(528\) | −5.06323e27 | −0.130849 | ||||||||
\(529\) | 5.68267e28 | 1.43969 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.22435e28 | 0.298135 | ||||||||
\(532\) | −1.35354e27 | −0.0323147 | ||||||||
\(533\) | −8.70971e27 | −0.203877 | ||||||||
\(534\) | 5.22815e28 | 1.19995 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 9.49113e27 | 0.209454 | ||||||||
\(537\) | 1.45181e27 | 0.0314181 | ||||||||
\(538\) | −1.87600e28 | −0.398125 | ||||||||
\(539\) | 1.25787e28 | 0.261790 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.70287e28 | −1.14162 | −0.570810 | − | 0.821082i | \(-0.693371\pi\) | ||||
−0.570810 | + | 0.821082i | \(0.693371\pi\) | |||||||
\(542\) | −1.05524e29 | −2.07185 | ||||||||
\(543\) | 1.84143e28 | 0.354615 | ||||||||
\(544\) | 7.71484e28 | 1.45727 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −4.77679e28 | −0.868187 | ||||||||
\(547\) | 7.81143e28 | 1.39272 | 0.696360 | − | 0.717693i | \(-0.254802\pi\) | ||||
0.696360 | + | 0.717693i | \(0.254802\pi\) | |||||||
\(548\) | 9.51832e28 | 1.66481 | ||||||||
\(549\) | 2.84584e28 | 0.488316 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.56345e26 | 0.0157951 | ||||||||
\(552\) | 1.29349e28 | 0.209606 | ||||||||
\(553\) | −3.73919e28 | −0.594517 | ||||||||
\(554\) | 7.16559e28 | 1.11789 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.39671e29 | 2.09807 | ||||||||
\(557\) | 8.52376e28 | 1.25647 | 0.628234 | − | 0.778024i | \(-0.283778\pi\) | ||||
0.628234 | + | 0.778024i | \(0.283778\pi\) | |||||||
\(558\) | 4.69404e28 | 0.679028 | ||||||||
\(559\) | 3.89724e28 | 0.553265 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.19204e28 | −0.162998 | ||||||||
\(562\) | 1.78123e29 | 2.39050 | ||||||||
\(563\) | −7.73536e28 | −1.01893 | −0.509463 | − | 0.860493i | \(-0.670156\pi\) | ||||
−0.509463 | + | 0.860493i | \(0.670156\pi\) | |||||||
\(564\) | 9.54531e27 | 0.123413 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.57930e29 | −1.96740 | ||||||||
\(567\) | −1.26667e28 | −0.154897 | ||||||||
\(568\) | 2.86808e28 | 0.344297 | ||||||||
\(569\) | 1.06186e29 | 1.25137 | 0.625687 | − | 0.780074i | \(-0.284819\pi\) | ||||
0.625687 | + | 0.780074i | \(0.284819\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.33038e28 | 0.719036 | 0.359518 | − | 0.933138i | \(-0.382941\pi\) | ||||
0.359518 | + | 0.933138i | \(0.382941\pi\) | |||||||
\(572\) | 2.11608e28 | 0.235979 | ||||||||
\(573\) | −1.88849e28 | −0.206772 | ||||||||
\(574\) | 5.28972e28 | 0.568667 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −4.14039e28 | −0.429146 | ||||||||
\(577\) | 1.30204e29 | 1.32519 | 0.662596 | − | 0.748977i | \(-0.269455\pi\) | ||||
0.662596 | + | 0.748977i | \(0.269455\pi\) | |||||||
\(578\) | 5.16623e27 | 0.0516335 | ||||||||
\(579\) | −8.20341e28 | −0.805137 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.30991e29 | −1.23992 | ||||||||
\(582\) | 5.84905e28 | 0.543744 | ||||||||
\(583\) | −2.69691e28 | −0.246233 | ||||||||
\(584\) | −7.73613e27 | −0.0693727 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.75465e29 | 1.51798 | ||||||||
\(587\) | −2.01309e29 | −1.71066 | −0.855328 | − | 0.518086i | \(-0.826645\pi\) | ||||
−0.855328 | + | 0.518086i | \(0.826645\pi\) | |||||||
\(588\) | 7.55790e28 | 0.630869 | ||||||||
\(589\) | 3.38453e27 | 0.0277516 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.02796e28 | −0.635238 | ||||||||
\(592\) | 7.61204e28 | 0.591729 | ||||||||
\(593\) | −5.38839e28 | −0.411514 | −0.205757 | − | 0.978603i | \(-0.565966\pi\) | ||||
−0.205757 | + | 0.978603i | \(0.565966\pi\) | |||||||
\(594\) | 1.04560e28 | 0.0784526 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.01772e29 | 1.46142 | ||||||||
\(597\) | −4.91651e28 | −0.349886 | ||||||||
\(598\) | 2.40946e29 | 1.68483 | ||||||||
\(599\) | −1.93023e29 | −1.32626 | −0.663128 | − | 0.748506i | \(-0.730772\pi\) | ||||
−0.663128 | + | 0.748506i | \(0.730772\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.42672e28 | −0.161005 | −0.0805023 | − | 0.996754i | \(-0.525652\pi\) | ||||
−0.0805023 | + | 0.996754i | \(0.525652\pi\) | |||||||
\(602\) | −2.36694e29 | −1.54320 | ||||||||
\(603\) | 4.68815e28 | 0.300379 | ||||||||
\(604\) | −1.97498e29 | −1.24358 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.21702e29 | −0.740175 | ||||||||
\(607\) | −3.24649e29 | −1.94058 | −0.970292 | − | 0.241936i | \(-0.922218\pi\) | ||||
−0.970292 | + | 0.241936i | \(0.922218\pi\) | |||||||
\(608\) | −4.87923e27 | −0.0286658 | ||||||||
\(609\) | −1.10002e29 | −0.635214 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.42888e28 | 0.135510 | ||||||||
\(612\) | −7.16241e28 | −0.392798 | ||||||||
\(613\) | −1.28641e29 | −0.693495 | −0.346747 | − | 0.937959i | \(-0.612714\pi\) | ||||
−0.346747 | + | 0.937959i | \(0.612714\pi\) | |||||||
\(614\) | −3.05644e29 | −1.61975 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.75558e28 | −0.0899132 | ||||||||
\(617\) | −1.63967e28 | −0.0825584 | −0.0412792 | − | 0.999148i | \(-0.513143\pi\) | ||||
−0.0412792 | + | 0.999148i | \(0.513143\pi\) | |||||||
\(618\) | 2.40493e29 | 1.19049 | ||||||||
\(619\) | 2.86407e29 | 1.39390 | 0.696949 | − | 0.717120i | \(-0.254540\pi\) | ||||
0.696949 | + | 0.717120i | \(0.254540\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.38921e28 | 0.300597 | ||||||||
\(622\) | 2.87028e28 | 0.132778 | ||||||||
\(623\) | −4.33598e29 | −1.97225 | ||||||||
\(624\) | −7.74123e28 | −0.346236 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 8.14892e28 | 0.352427 | ||||||||
\(627\) | 7.53906e26 | 0.00320633 | ||||||||
\(628\) | −2.98412e29 | −1.24807 | ||||||||
\(629\) | 1.79211e29 | 0.737112 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.17949e29 | 1.26488 | 0.632439 | − | 0.774610i | \(-0.282054\pi\) | ||||
0.632439 | + | 0.774610i | \(0.282054\pi\) | |||||||
\(632\) | 2.53341e28 | 0.0991234 | ||||||||
\(633\) | 2.89529e29 | 1.11418 | ||||||||
\(634\) | −4.43035e29 | −1.67688 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.62044e29 | −0.593381 | ||||||||
\(637\) | 1.92316e29 | 0.692712 | ||||||||
\(638\) | 9.08036e28 | 0.321726 | ||||||||
\(639\) | 1.41669e29 | 0.493759 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.00981e29 | −0.340589 | −0.170294 | − | 0.985393i | \(-0.554472\pi\) | ||||
−0.170294 | + | 0.985393i | \(0.554472\pi\) | |||||||
\(642\) | 7.81742e28 | 0.259385 | ||||||||
\(643\) | −4.70649e29 | −1.53632 | −0.768161 | − | 0.640257i | \(-0.778828\pi\) | ||||
−0.768161 | + | 0.640257i | \(0.778828\pi\) | |||||||
\(644\) | −7.85313e29 | −2.52198 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.62313e27 | −0.0299140 | ||||||||
\(647\) | −4.78801e29 | −1.46440 | −0.732201 | − | 0.681089i | \(-0.761507\pi\) | ||||
−0.732201 | + | 0.681089i | \(0.761507\pi\) | |||||||
\(648\) | 8.58207e27 | 0.0258258 | ||||||||
\(649\) | 8.38196e28 | 0.248185 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.89301e29 | −1.11605 | ||||||||
\(652\) | 6.42300e29 | 1.81192 | ||||||||
\(653\) | −1.11323e29 | −0.309027 | −0.154514 | − | 0.987991i | \(-0.549381\pi\) | ||||
−0.154514 | + | 0.987991i | \(0.549381\pi\) | |||||||
\(654\) | −4.29915e29 | −1.17440 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.57248e28 | 0.226786 | ||||||||
\(657\) | −3.82126e28 | −0.0994880 | ||||||||
\(658\) | −1.47514e29 | −0.377975 | ||||||||
\(659\) | −3.13403e29 | −0.790327 | −0.395163 | − | 0.918611i | \(-0.629312\pi\) | ||||
−0.395163 | + | 0.918611i | \(0.629312\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.94234e29 | 0.474471 | 0.237235 | − | 0.971452i | \(-0.423759\pi\) | ||||
0.237235 | + | 0.971452i | \(0.423759\pi\) | |||||||
\(662\) | −8.85698e29 | −2.12950 | ||||||||
\(663\) | −1.82253e29 | −0.431303 | ||||||||
\(664\) | 8.87503e28 | 0.206731 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.57195e29 | −0.354780 | ||||||||
\(667\) | 5.54861e29 | 1.23272 | ||||||||
\(668\) | −5.82496e29 | −1.27391 | ||||||||
\(669\) | 4.42946e29 | 0.953623 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.94828e29 | 0.406504 | ||||||||
\(672\) | 5.61228e29 | 1.15282 | ||||||||
\(673\) | 2.68841e28 | 0.0543673 | 0.0271836 | − | 0.999630i | \(-0.491346\pi\) | ||||
0.0271836 | + | 0.999630i | \(0.491346\pi\) | |||||||
\(674\) | −2.13402e29 | −0.424884 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.76579e29 | −0.533800 | ||||||||
\(677\) | 8.12214e29 | 1.54344 | 0.771720 | − | 0.635963i | \(-0.219397\pi\) | ||||
0.771720 | + | 0.635963i | \(0.219397\pi\) | |||||||
\(678\) | −8.04769e29 | −1.50577 | ||||||||
\(679\) | −4.85093e29 | −0.893701 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.11273e28 | 0.0377398 | ||||||||
\(682\) | 3.21356e29 | 0.565263 | ||||||||
\(683\) | −2.74550e29 | −0.475559 | −0.237779 | − | 0.971319i | \(-0.576420\pi\) | ||||
−0.237779 | + | 0.971319i | \(0.576420\pi\) | |||||||
\(684\) | 4.52985e27 | 0.00772671 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.00343e28 | 0.115853 | ||||||||
\(687\) | −2.41038e29 | −0.392682 | ||||||||
\(688\) | −3.83584e29 | −0.615434 | ||||||||
\(689\) | −4.12334e29 | −0.651549 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.16099e29 | 1.09762 | 0.548812 | − | 0.835946i | \(-0.315080\pi\) | ||||
0.548812 | + | 0.835946i | \(0.315080\pi\) | |||||||
\(692\) | −8.14349e29 | −1.22941 | ||||||||
\(693\) | −8.67170e28 | −0.128945 | ||||||||
\(694\) | 5.59268e29 | 0.819116 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.45297e28 | 0.105909 | ||||||||
\(697\) | 2.01823e29 | 0.282506 | ||||||||
\(698\) | 1.88279e29 | 0.259610 | ||||||||
\(699\) | 3.61154e29 | 0.490548 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.03091e29 | −0.135888 | −0.0679438 | − | 0.997689i | \(-0.521644\pi\) | ||||
−0.0679438 | + | 0.997689i | \(0.521644\pi\) | |||||||
\(702\) | 1.59863e29 | 0.207591 | ||||||||
\(703\) | −1.13342e28 | −0.0144997 | ||||||||
\(704\) | −2.83453e29 | −0.357247 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.03186e30 | −1.26232 | ||||||||
\(707\) | 1.00934e30 | 1.21656 | ||||||||
\(708\) | 5.03631e29 | 0.598085 | ||||||||
\(709\) | −5.75181e28 | −0.0673006 | −0.0336503 | − | 0.999434i | \(-0.510713\pi\) | ||||
−0.0336503 | + | 0.999434i | \(0.510713\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.25138e29 | 0.142154 | ||||||||
\(712\) | 2.93775e29 | 0.328833 | ||||||||
\(713\) | 1.96367e30 | 2.16585 | ||||||||
\(714\) | 1.10689e30 | 1.20302 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.97195e28 | 0.0630274 | ||||||||
\(717\) | 9.94215e29 | 1.03402 | ||||||||
\(718\) | 3.41957e29 | 0.350481 | ||||||||
\(719\) | −1.09295e30 | −1.10395 | −0.551974 | − | 0.833861i | \(-0.686125\pi\) | ||||
−0.551974 | + | 0.833861i | \(0.686125\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.99454e30 | −1.95669 | ||||||||
\(722\) | −1.51885e30 | −1.46850 | ||||||||
\(723\) | 4.67623e29 | 0.445598 | ||||||||
\(724\) | 7.57465e29 | 0.711389 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −8.58072e29 | −0.782869 | ||||||||
\(727\) | −1.41110e29 | −0.126896 | −0.0634478 | − | 0.997985i | \(-0.520210\pi\) | ||||
−0.0634478 | + | 0.997985i | \(0.520210\pi\) | |||||||
\(728\) | −2.68413e29 | −0.237916 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −9.03077e29 | −0.766642 | ||||||||
\(732\) | 1.17062e30 | 0.979605 | ||||||||
\(733\) | 1.08687e30 | 0.896575 | 0.448287 | − | 0.893890i | \(-0.352034\pi\) | ||||
0.448287 | + | 0.893890i | \(0.352034\pi\) | |||||||
\(734\) | −1.90949e29 | −0.155277 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.83088e30 | −2.23720 | ||||||||
\(737\) | 3.20953e29 | 0.250054 | ||||||||
\(738\) | −1.77029e29 | −0.135973 | ||||||||
\(739\) | 1.32212e30 | 1.00116 | 0.500582 | − | 0.865689i | \(-0.333119\pi\) | ||||
0.500582 | + | 0.865689i | \(0.333119\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.15265e28 | 0.00848414 | ||||||||
\(742\) | 2.50425e30 | 1.81734 | ||||||||
\(743\) | 1.32336e30 | 0.946884 | 0.473442 | − | 0.880825i | \(-0.343011\pi\) | ||||
0.473442 | + | 0.880825i | \(0.343011\pi\) | |||||||
\(744\) | 2.63763e29 | 0.186079 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.65902e30 | 2.50962 | ||||||||
\(747\) | 4.38382e29 | 0.296474 | ||||||||
\(748\) | −4.90342e29 | −0.326988 | ||||||||
\(749\) | −6.48339e29 | −0.426327 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.81366e29 | −0.115968 | −0.0579839 | − | 0.998318i | \(-0.518467\pi\) | ||||
−0.0579839 | + | 0.998318i | \(0.518467\pi\) | |||||||
\(752\) | −2.39061e29 | −0.150737 | ||||||||
\(753\) | −5.94022e29 | −0.369364 | ||||||||
\(754\) | 1.38831e30 | 0.851306 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −5.21040e29 | −0.310736 | ||||||||
\(757\) | −1.12853e30 | −0.663753 | −0.331877 | − | 0.943323i | \(-0.607682\pi\) | ||||
−0.331877 | + | 0.943323i | \(0.607682\pi\) | |||||||
\(758\) | −1.32485e30 | −0.768494 | ||||||||
\(759\) | 4.37408e29 | 0.250235 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.77844e30 | 1.54619 | 0.773093 | − | 0.634293i | \(-0.218709\pi\) | ||||
0.773093 | + | 0.634293i | \(0.218709\pi\) | |||||||
\(762\) | 4.91480e29 | 0.269761 | ||||||||
\(763\) | 3.56551e30 | 1.93025 | ||||||||
\(764\) | −7.76822e29 | −0.414802 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.53604e29 | −0.391509 | ||||||||
\(767\) | 1.28153e30 | 0.656714 | ||||||||
\(768\) | 7.00220e29 | 0.353950 | ||||||||
\(769\) | −2.88419e29 | −0.143813 | −0.0719064 | − | 0.997411i | \(-0.522908\pi\) | ||||
−0.0719064 | + | 0.997411i | \(0.522908\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.32487e30 | 0.642840 | ||||||||
\(772\) | −3.37444e30 | −1.61518 | ||||||||
\(773\) | −3.73885e30 | −1.76544 | −0.882720 | − | 0.469899i | \(-0.844290\pi\) | ||||
−0.882720 | + | 0.469899i | \(0.844290\pi\) | |||||||
\(774\) | 7.92132e29 | 0.368993 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.28664e29 | 0.149006 | ||||||||
\(777\) | 1.30370e30 | 0.583118 | ||||||||
\(778\) | 3.02072e30 | 1.33298 | ||||||||
\(779\) | −1.27643e28 | −0.00555715 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 9.69872e29 | 0.411035 | ||||||||
\(782\) | −5.58324e30 | −2.33462 | ||||||||
\(783\) | 3.68140e29 | 0.151885 | ||||||||
\(784\) | −1.89286e30 | −0.770550 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.17860e30 | −0.467123 | ||||||||
\(787\) | 7.64436e29 | 0.298955 | 0.149478 | − | 0.988765i | \(-0.452241\pi\) | ||||
0.149478 | + | 0.988765i | \(0.452241\pi\) | |||||||
\(788\) | −3.30226e30 | −1.27434 | ||||||||
\(789\) | 7.38909e29 | 0.281373 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.67437e30 | 2.47490 | ||||||||
\(792\) | 5.87533e28 | 0.0214990 | ||||||||
\(793\) | 2.97874e30 | 1.07563 | ||||||||
\(794\) | 6.41079e30 | 2.28453 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.02238e30 | −0.701901 | ||||||||
\(797\) | −4.75836e30 | −1.62984 | −0.814920 | − | 0.579573i | \(-0.803219\pi\) | ||||
−0.814920 | + | 0.579573i | \(0.803219\pi\) | |||||||
\(798\) | −7.00049e28 | −0.0236645 | ||||||||
\(799\) | −5.62824e29 | −0.187772 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.45110e30 | 0.471582 | ||||||||
\(802\) | −5.26504e30 | −1.68877 | ||||||||
\(803\) | −2.61606e29 | −0.0828198 | ||||||||
\(804\) | 1.92845e30 | 0.602587 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 4.91325e30 | 1.49572 | ||||||||
\(807\) | −5.20695e29 | −0.156463 | ||||||||
\(808\) | −6.83854e29 | −0.202836 | ||||||||
\(809\) | 5.90538e27 | 0.00172897 | 0.000864487 | − | 1.00000i | \(-0.499725\pi\) | ||||
0.000864487 | 1.00000i | \(0.499725\pi\) | ||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.54875e29 | 0.186827 | 0.0934134 | − | 0.995627i | \(-0.470222\pi\) | ||||
0.0934134 | + | 0.995627i | \(0.470222\pi\) | |||||||
\(812\) | −4.52490e30 | −1.27430 | ||||||||
\(813\) | −2.92888e30 | −0.814237 | ||||||||
\(814\) | −1.07616e30 | −0.295340 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.79381e30 | 0.479767 | ||||||||
\(817\) | 5.71149e28 | 0.0150806 | ||||||||
\(818\) | −5.37708e30 | −1.40164 | ||||||||
\(819\) | −1.32583e30 | −0.341197 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 4.27671e30 | 1.07277 | 0.536385 | − | 0.843973i | \(-0.319789\pi\) | ||||
0.536385 | + | 0.843973i | \(0.319789\pi\) | |||||||
\(822\) | 4.92284e30 | 1.21916 | ||||||||
\(823\) | −1.27831e30 | −0.312564 | −0.156282 | − | 0.987712i | \(-0.549951\pi\) | ||||
−0.156282 | + | 0.987712i | \(0.549951\pi\) | |||||||
\(824\) | 1.35136e30 | 0.326238 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.78317e30 | −1.83175 | ||||||||
\(827\) | −1.57854e30 | −0.366815 | −0.183408 | − | 0.983037i | \(-0.558713\pi\) | ||||
−0.183408 | + | 0.983037i | \(0.558713\pi\) | |||||||
\(828\) | 2.62817e30 | 0.603025 | ||||||||
\(829\) | 1.72347e30 | 0.390463 | 0.195232 | − | 0.980757i | \(-0.437454\pi\) | ||||
0.195232 | + | 0.980757i | \(0.437454\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.98885e30 | 0.439331 | ||||||||
\(832\) | −4.33375e30 | −0.945298 | ||||||||
\(833\) | −4.45640e30 | −0.959867 | ||||||||
\(834\) | 7.22372e30 | 1.53645 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.10116e28 | 0.00643218 | ||||||||
\(837\) | 1.30286e30 | 0.266858 | ||||||||
\(838\) | 1.25310e31 | 2.53467 | ||||||||
\(839\) | 9.09359e29 | 0.181650 | 0.0908249 | − | 0.995867i | \(-0.471050\pi\) | ||||
0.0908249 | + | 0.995867i | \(0.471050\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.93578e30 | −0.377137 | ||||||||
\(842\) | −1.36230e31 | −2.62117 | ||||||||
\(843\) | 4.94391e30 | 0.939466 | ||||||||
\(844\) | 1.19097e31 | 2.23513 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.93680e29 | 0.0903767 | ||||||||
\(847\) | 7.11644e30 | 1.28673 | ||||||||
\(848\) | 4.05837e30 | 0.724762 | ||||||||
\(849\) | −4.38344e30 | −0.773187 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −6.57597e30 | −1.13162 | ||||||||
\(852\) | 5.82748e30 | 0.990525 | ||||||||
\(853\) | 3.54786e30 | 0.595664 | 0.297832 | − | 0.954618i | \(-0.403736\pi\) | ||||
0.297832 | + | 0.954618i | \(0.403736\pi\) | |||||||
\(854\) | −1.80910e31 | −3.00023 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.39268e29 | 0.0710813 | ||||||||
\(857\) | −3.53257e29 | −0.0564667 | −0.0282334 | − | 0.999601i | \(-0.508988\pi\) | ||||
−0.0282334 | + | 0.999601i | \(0.508988\pi\) | |||||||
\(858\) | 1.09443e30 | 0.172811 | ||||||||
\(859\) | −6.94778e30 | −1.08372 | −0.541861 | − | 0.840468i | \(-0.682280\pi\) | ||||
−0.541861 | + | 0.840468i | \(0.682280\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 1.46819e30 | 0.223486 | ||||||||
\(862\) | −4.74716e30 | −0.713850 | ||||||||
\(863\) | −4.91327e29 | −0.0729890 | −0.0364945 | − | 0.999334i | \(-0.511619\pi\) | ||||
−0.0364945 | + | 0.999334i | \(0.511619\pi\) | |||||||
\(864\) | −1.87824e30 | −0.275649 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1.11680e31 | −1.59969 | ||||||||
\(867\) | 1.43392e29 | 0.0202919 | ||||||||
\(868\) | −1.60137e31 | −2.23890 | ||||||||
\(869\) | 8.56701e29 | 0.118337 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.90709e30 | 0.661657 | ||||||||
\(872\) | −2.41574e30 | −0.321830 | ||||||||
\(873\) | 1.62344e30 | 0.213691 | ||||||||
\(874\) | 3.53111e29 | 0.0459241 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.57186e30 | −0.199582 | ||||||||
\(877\) | −1.31164e30 | −0.164558 | −0.0822790 | − | 0.996609i | \(-0.526220\pi\) | ||||
−0.0822790 | + | 0.996609i | \(0.526220\pi\) | |||||||
\(878\) | −8.98344e29 | −0.111365 | ||||||||
\(879\) | 4.87012e30 | 0.596564 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.32982e31 | 1.59055 | 0.795273 | − | 0.606252i | \(-0.207328\pi\) | ||||
0.795273 | + | 0.606252i | \(0.207328\pi\) | |||||||
\(882\) | 3.90892e30 | 0.461994 | ||||||||
\(883\) | −4.84651e30 | −0.566034 | −0.283017 | − | 0.959115i | \(-0.591335\pi\) | ||||
−0.283017 | + | 0.959115i | \(0.591335\pi\) | |||||||
\(884\) | −7.49689e30 | −0.865232 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.42784e31 | −1.60926 | ||||||||
\(887\) | −3.16217e30 | −0.352198 | −0.176099 | − | 0.984372i | \(-0.556348\pi\) | ||||
−0.176099 | + | 0.984372i | \(0.556348\pi\) | |||||||
\(888\) | −8.83294e29 | −0.0972230 | ||||||||
\(889\) | −4.07610e30 | −0.443380 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.90212e29 | 0.0308318 | ||||||||
\(892\) | 1.82204e31 | 1.91305 | ||||||||
\(893\) | 3.55957e28 | 0.00369366 | ||||||||
\(894\) | 1.04356e31 | 1.07022 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6.38816e30 | 0.639943 | ||||||||
\(897\) | 6.68758e30 | 0.662138 | ||||||||
\(898\) | 2.89996e31 | 2.83786 | ||||||||
\(899\) | 1.13145e31 | 1.09435 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.55468e30 | 0.902830 | ||||||||
\(902\) | −1.21195e30 | −0.113192 | ||||||||
\(903\) | −6.56957e30 | −0.606479 | ||||||||
\(904\) | −4.52208e30 | −0.412638 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.02145e31 | −0.910692 | ||||||||
\(907\) | 1.04066e31 | 0.917137 | 0.458569 | − | 0.888659i | \(-0.348362\pi\) | ||||
0.458569 | + | 0.888659i | \(0.348362\pi\) | |||||||
\(908\) | 8.69063e29 | 0.0757094 | ||||||||
\(909\) | −3.37790e30 | −0.290888 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.24395e31 | 1.04679 | 0.523394 | − | 0.852091i | \(-0.324666\pi\) | ||||
0.523394 | + | 0.852091i | \(0.324666\pi\) | |||||||
\(912\) | −1.13449e29 | −0.00943748 | ||||||||
\(913\) | 3.00119e30 | 0.246803 | ||||||||
\(914\) | 1.43717e30 | 0.116835 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.91501e30 | −0.787754 | ||||||||
\(917\) | 9.77477e30 | 0.767766 | ||||||||
\(918\) | −3.70437e30 | −0.287651 | ||||||||
\(919\) | 1.38734e31 | 1.06505 | 0.532526 | − | 0.846413i | \(-0.321243\pi\) | ||||
0.532526 | + | 0.846413i | \(0.321243\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.48334e30 | −0.636562 | ||||||||
\(922\) | 3.77352e31 | 2.79945 | ||||||||
\(923\) | 1.48285e31 | 1.08762 | ||||||||
\(924\) | −3.56707e30 | −0.258676 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.63820e31 | −2.57911 | ||||||||
\(927\) | 6.67503e30 | 0.467860 | ||||||||
\(928\) | −1.63113e31 | −1.13040 | ||||||||
\(929\) | −5.06678e30 | −0.347190 | −0.173595 | − | 0.984817i | \(-0.555538\pi\) | ||||
−0.173595 | + | 0.984817i | \(0.555538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.81844e29 | 0.0188815 | ||||||||
\(932\) | 1.48559e31 | 0.984083 | ||||||||
\(933\) | 7.96662e29 | 0.0521816 | ||||||||
\(934\) | 8.97856e30 | 0.581520 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 8.98285e29 | 0.0568876 | ||||||||
\(937\) | −2.26921e30 | −0.142105 | −0.0710523 | − | 0.997473i | \(-0.522636\pi\) | ||||
−0.0710523 | + | 0.997473i | \(0.522636\pi\) | |||||||
\(938\) | −2.98025e31 | −1.84554 | ||||||||
\(939\) | 2.26178e30 | 0.138504 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 9.10781e30 | 0.545410 | 0.272705 | − | 0.962098i | \(-0.412082\pi\) | ||||
0.272705 | + | 0.962098i | \(0.412082\pi\) | |||||||
\(942\) | −1.54338e31 | −0.913981 | ||||||||
\(943\) | −7.40570e30 | −0.433704 | ||||||||
\(944\) | −1.26133e31 | −0.730507 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.42298e30 | 0.307172 | ||||||||
\(947\) | 2.33280e31 | 1.30678 | 0.653389 | − | 0.757022i | \(-0.273347\pi\) | ||||
0.653389 | + | 0.757022i | \(0.273347\pi\) | |||||||
\(948\) | 5.14749e30 | 0.285173 | ||||||||
\(949\) | −3.99972e30 | −0.219146 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −1.22967e31 | −0.659012 | ||||||||
\(952\) | 6.21971e30 | 0.329672 | ||||||||
\(953\) | 1.16285e31 | 0.609606 | 0.304803 | − | 0.952415i | \(-0.401409\pi\) | ||||
0.304803 | + | 0.952415i | \(0.401409\pi\) | |||||||
\(954\) | −8.38087e30 | −0.434541 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.08966e31 | 2.07434 | ||||||||
\(957\) | 2.52030e30 | 0.126438 | ||||||||
\(958\) | −2.88052e31 | −1.42933 | ||||||||
\(959\) | −4.08277e31 | −2.00382 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.92167e31 | 0.922749 | ||||||||
\(962\) | −1.64536e31 | −0.781488 | ||||||||
\(963\) | 2.16977e30 | 0.101938 | ||||||||
\(964\) | 1.92354e31 | 0.893909 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.06161e31 | −1.84688 | ||||||||
\(967\) | 9.97749e30 | 0.448790 | 0.224395 | − | 0.974498i | \(-0.427959\pi\) | ||||
0.224395 | + | 0.974498i | \(0.427959\pi\) | |||||||
\(968\) | −4.82159e30 | −0.214535 | ||||||||
\(969\) | −2.67095e29 | −0.0117562 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.69422e30 | 0.159119 | 0.0795593 | − | 0.996830i | \(-0.474649\pi\) | ||||
0.0795593 | + | 0.996830i | \(0.474649\pi\) | |||||||
\(972\) | 1.74374e30 | 0.0742996 | ||||||||
\(973\) | −5.99101e31 | −2.52531 | ||||||||
\(974\) | −6.59095e31 | −2.74840 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.93181e31 | −1.19650 | ||||||||
\(977\) | −2.05704e31 | −0.830518 | −0.415259 | − | 0.909703i | \(-0.636309\pi\) | ||||
−0.415259 | + | 0.909703i | \(0.636309\pi\) | |||||||
\(978\) | 3.32195e31 | 1.32689 | ||||||||
\(979\) | 9.93433e30 | 0.392573 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.19325e31 | −0.461539 | ||||||||
\(982\) | −2.10840e31 | −0.806831 | ||||||||
\(983\) | −7.27829e30 | −0.275561 | −0.137780 | − | 0.990463i | \(-0.543997\pi\) | ||||
−0.137780 | + | 0.990463i | \(0.543997\pi\) | |||||||
\(984\) | −9.94743e29 | −0.0372617 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −3.21701e31 | −1.17963 | ||||||||
\(987\) | −4.09435e30 | −0.148544 | ||||||||
\(988\) | 4.74139e29 | 0.0170199 | ||||||||
\(989\) | 3.31375e31 | 1.17695 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.68737e31 | −0.586728 | −0.293364 | − | 0.956001i | \(-0.594775\pi\) | ||||
−0.293364 | + | 0.956001i | \(0.594775\pi\) | |||||||
\(992\) | −5.77260e31 | −1.98609 | ||||||||
\(993\) | −2.45831e31 | −0.836891 | ||||||||
\(994\) | −9.00587e31 | −3.03367 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 1.80327e31 | 0.594753 | ||||||||
\(997\) | −1.86625e31 | −0.609075 | −0.304538 | − | 0.952500i | \(-0.598502\pi\) | ||||
−0.304538 | + | 0.952500i | \(0.598502\pi\) | |||||||
\(998\) | 3.69760e31 | 1.19412 | ||||||||
\(999\) | −4.36303e30 | −0.139428 |
(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 | 75.22.a.k.1.7 | ✓ | 8 | |
5.2 | odd | 4 | 75.22.b.j.49.14 | 16 | |||
5.3 | odd | 4 | 75.22.b.j.49.3 | 16 | |||
5.4 | even | 2 | 75.22.a.l.1.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.22.a.k.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial | |
75.22.a.l.1.2 | yes | 8 | 5.4 | even | 2 | ||
75.22.b.j.49.3 | 16 | 5.3 | odd | 4 | |||
75.22.b.j.49.14 | 16 | 5.2 | odd | 4 |