Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [10,26,Mod(1,10)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(10, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 26, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("10.1");
S:= CuspForms(chi, 26);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 10 = 2 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 26 \) |
Character orbit: | \([\chi]\) | \(=\) | 10.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: | \(39.5996779952\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{2} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 6900880 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{3}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2626.45\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 10.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4096.00 | −0.707107 | ||||||||
\(3\) | 1.19926e6 | 1.30286 | 0.651430 | − | 0.758709i | \(-0.274169\pi\) | ||||
0.651430 | + | 0.758709i | \(0.274169\pi\) | |||||||
\(4\) | 1.67772e7 | 0.500000 | ||||||||
\(5\) | 2.44141e8 | 0.447214 | ||||||||
\(6\) | −4.91217e9 | −0.921261 | ||||||||
\(7\) | −1.32210e10 | −0.361027 | −0.180513 | − | 0.983573i | \(-0.557776\pi\) | ||||
−0.180513 | + | 0.983573i | \(0.557776\pi\) | |||||||
\(8\) | −6.87195e10 | −0.353553 | ||||||||
\(9\) | 5.90937e11 | 0.697445 | ||||||||
\(10\) | −1.00000e12 | −0.316228 | ||||||||
\(11\) | 1.51986e13 | 1.46015 | 0.730073 | − | 0.683370i | \(-0.239486\pi\) | ||||
0.730073 | + | 0.683370i | \(0.239486\pi\) | |||||||
\(12\) | 2.01203e13 | 0.651430 | ||||||||
\(13\) | 3.15848e12 | 0.0375999 | 0.0187999 | − | 0.999823i | \(-0.494015\pi\) | ||||
0.0187999 | + | 0.999823i | \(0.494015\pi\) | |||||||
\(14\) | 5.41533e13 | 0.255284 | ||||||||
\(15\) | 2.92788e14 | 0.582657 | ||||||||
\(16\) | 2.81475e14 | 0.250000 | ||||||||
\(17\) | 1.62591e15 | 0.676840 | 0.338420 | − | 0.940995i | \(-0.390108\pi\) | ||||
0.338420 | + | 0.940995i | \(0.390108\pi\) | |||||||
\(18\) | −2.42048e15 | −0.493168 | ||||||||
\(19\) | 5.64080e15 | 0.584683 | 0.292342 | − | 0.956314i | \(-0.405566\pi\) | ||||
0.292342 | + | 0.956314i | \(0.405566\pi\) | |||||||
\(20\) | 4.09600e15 | 0.223607 | ||||||||
\(21\) | −1.58554e16 | −0.470367 | ||||||||
\(22\) | −6.22536e16 | −1.03248 | ||||||||
\(23\) | −1.52235e17 | −1.44849 | −0.724247 | − | 0.689540i | \(-0.757813\pi\) | ||||
−0.724247 | + | 0.689540i | \(0.757813\pi\) | |||||||
\(24\) | −8.24125e16 | −0.460631 | ||||||||
\(25\) | 5.96046e16 | 0.200000 | ||||||||
\(26\) | −1.29371e16 | −0.0265871 | ||||||||
\(27\) | −3.07432e17 | −0.394187 | ||||||||
\(28\) | −2.21812e17 | −0.180513 | ||||||||
\(29\) | 1.86158e17 | 0.0977025 | 0.0488512 | − | 0.998806i | \(-0.484444\pi\) | ||||
0.0488512 | + | 0.998806i | \(0.484444\pi\) | |||||||
\(30\) | −1.19926e18 | −0.412001 | ||||||||
\(31\) | 6.41559e18 | 1.46290 | 0.731451 | − | 0.681894i | \(-0.238843\pi\) | ||||
0.731451 | + | 0.681894i | \(0.238843\pi\) | |||||||
\(32\) | −1.15292e18 | −0.176777 | ||||||||
\(33\) | 1.82271e19 | 1.90236 | ||||||||
\(34\) | −6.65974e18 | −0.478598 | ||||||||
\(35\) | −3.22779e18 | −0.161456 | ||||||||
\(36\) | 9.91428e18 | 0.348722 | ||||||||
\(37\) | 3.10993e19 | 0.776657 | 0.388328 | − | 0.921521i | \(-0.373053\pi\) | ||||
0.388328 | + | 0.921521i | \(0.373053\pi\) | |||||||
\(38\) | −2.31047e19 | −0.413434 | ||||||||
\(39\) | 3.78784e18 | 0.0489874 | ||||||||
\(40\) | −1.67772e19 | −0.158114 | ||||||||
\(41\) | −2.12615e19 | −0.147162 | −0.0735810 | − | 0.997289i | \(-0.523443\pi\) | ||||
−0.0735810 | + | 0.997289i | \(0.523443\pi\) | |||||||
\(42\) | 6.49439e19 | 0.332600 | ||||||||
\(43\) | 4.45949e20 | 1.70188 | 0.850942 | − | 0.525260i | \(-0.176032\pi\) | ||||
0.850942 | + | 0.525260i | \(0.176032\pi\) | |||||||
\(44\) | 2.54991e20 | 0.730073 | ||||||||
\(45\) | 1.44272e20 | 0.311907 | ||||||||
\(46\) | 6.23555e20 | 1.02424 | ||||||||
\(47\) | 5.28278e19 | 0.0663192 | 0.0331596 | − | 0.999450i | \(-0.489443\pi\) | ||||
0.0331596 | + | 0.999450i | \(0.489443\pi\) | |||||||
\(48\) | 3.37562e20 | 0.325715 | ||||||||
\(49\) | −1.16627e21 | −0.869660 | ||||||||
\(50\) | −2.44141e20 | −0.141421 | ||||||||
\(51\) | 1.94989e21 | 0.881827 | ||||||||
\(52\) | 5.29905e19 | 0.0187999 | ||||||||
\(53\) | 2.38642e21 | 0.667266 | 0.333633 | − | 0.942703i | \(-0.391725\pi\) | ||||
0.333633 | + | 0.942703i | \(0.391725\pi\) | |||||||
\(54\) | 1.25924e21 | 0.278732 | ||||||||
\(55\) | 3.71060e21 | 0.652997 | ||||||||
\(56\) | 9.08541e20 | 0.127642 | ||||||||
\(57\) | 6.76479e21 | 0.761761 | ||||||||
\(58\) | −7.62501e20 | −0.0690861 | ||||||||
\(59\) | 1.91973e22 | 1.40472 | 0.702361 | − | 0.711821i | \(-0.252129\pi\) | ||||
0.702361 | + | 0.711821i | \(0.252129\pi\) | |||||||
\(60\) | 4.91217e21 | 0.291328 | ||||||||
\(61\) | 1.98905e21 | 0.0959450 | 0.0479725 | − | 0.998849i | \(-0.484724\pi\) | ||||
0.0479725 | + | 0.998849i | \(0.484724\pi\) | |||||||
\(62\) | −2.62783e22 | −1.03443 | ||||||||
\(63\) | −7.81279e21 | −0.251796 | ||||||||
\(64\) | 4.72237e21 | 0.125000 | ||||||||
\(65\) | 7.71113e20 | 0.0168152 | ||||||||
\(66\) | −7.46583e22 | −1.34518 | ||||||||
\(67\) | −1.03138e23 | −1.53987 | −0.769933 | − | 0.638125i | \(-0.779710\pi\) | ||||
−0.769933 | + | 0.638125i | \(0.779710\pi\) | |||||||
\(68\) | 2.72783e22 | 0.338420 | ||||||||
\(69\) | −1.82570e23 | −1.88719 | ||||||||
\(70\) | 1.32210e22 | 0.114167 | ||||||||
\(71\) | −1.01960e23 | −0.737393 | −0.368697 | − | 0.929550i | \(-0.620196\pi\) | ||||
−0.368697 | + | 0.929550i | \(0.620196\pi\) | |||||||
\(72\) | −4.06089e22 | −0.246584 | ||||||||
\(73\) | 3.26795e23 | 1.67009 | 0.835044 | − | 0.550183i | \(-0.185442\pi\) | ||||
0.835044 | + | 0.550183i | \(0.185442\pi\) | |||||||
\(74\) | −1.27383e23 | −0.549179 | ||||||||
\(75\) | 7.14815e22 | 0.260572 | ||||||||
\(76\) | 9.46369e22 | 0.292342 | ||||||||
\(77\) | −2.00941e23 | −0.527151 | ||||||||
\(78\) | −1.55150e22 | −0.0346393 | ||||||||
\(79\) | 2.14410e23 | 0.408231 | 0.204115 | − | 0.978947i | \(-0.434568\pi\) | ||||
0.204115 | + | 0.978947i | \(0.434568\pi\) | |||||||
\(80\) | 6.87195e22 | 0.111803 | ||||||||
\(81\) | −8.69386e23 | −1.21102 | ||||||||
\(82\) | 8.70871e22 | 0.104059 | ||||||||
\(83\) | 1.80482e24 | 1.85335 | 0.926674 | − | 0.375865i | \(-0.122654\pi\) | ||||
0.926674 | + | 0.375865i | \(0.122654\pi\) | |||||||
\(84\) | −2.66010e23 | −0.235184 | ||||||||
\(85\) | 3.96951e23 | 0.302692 | ||||||||
\(86\) | −1.82661e24 | −1.20341 | ||||||||
\(87\) | 2.23251e23 | 0.127293 | ||||||||
\(88\) | −1.04444e24 | −0.516239 | ||||||||
\(89\) | 3.14740e24 | 1.35076 | 0.675378 | − | 0.737472i | \(-0.263981\pi\) | ||||
0.675378 | + | 0.737472i | \(0.263981\pi\) | |||||||
\(90\) | −5.90937e23 | −0.220551 | ||||||||
\(91\) | −4.17583e22 | −0.0135745 | ||||||||
\(92\) | −2.55408e24 | −0.724247 | ||||||||
\(93\) | 7.69396e24 | 1.90596 | ||||||||
\(94\) | −2.16383e23 | −0.0468948 | ||||||||
\(95\) | 1.37715e24 | 0.261478 | ||||||||
\(96\) | −1.38265e24 | −0.230315 | ||||||||
\(97\) | 4.10993e24 | 0.601433 | 0.300717 | − | 0.953714i | \(-0.402774\pi\) | ||||
0.300717 | + | 0.953714i | \(0.402774\pi\) | |||||||
\(98\) | 4.77706e24 | 0.614942 | ||||||||
\(99\) | 8.98144e24 | 1.01837 | ||||||||
\(100\) | 1.00000e24 | 0.100000 | ||||||||
\(101\) | 7.38400e24 | 0.652040 | 0.326020 | − | 0.945363i | \(-0.394292\pi\) | ||||
0.326020 | + | 0.945363i | \(0.394292\pi\) | |||||||
\(102\) | −7.98676e24 | −0.623546 | ||||||||
\(103\) | −1.77047e25 | −1.22355 | −0.611777 | − | 0.791030i | \(-0.709545\pi\) | ||||
−0.611777 | + | 0.791030i | \(0.709545\pi\) | |||||||
\(104\) | −2.17049e23 | −0.0132936 | ||||||||
\(105\) | −3.87096e24 | −0.210355 | ||||||||
\(106\) | −9.77478e24 | −0.471828 | ||||||||
\(107\) | −3.05016e25 | −1.30926 | −0.654630 | − | 0.755949i | \(-0.727176\pi\) | ||||
−0.654630 | + | 0.755949i | \(0.727176\pi\) | |||||||
\(108\) | −5.15786e24 | −0.197094 | ||||||||
\(109\) | −7.07393e23 | −0.0240896 | −0.0120448 | − | 0.999927i | \(-0.503834\pi\) | ||||
−0.0120448 | + | 0.999927i | \(0.503834\pi\) | |||||||
\(110\) | −1.51986e25 | −0.461738 | ||||||||
\(111\) | 3.72962e25 | 1.01188 | ||||||||
\(112\) | −3.72138e24 | −0.0902567 | ||||||||
\(113\) | −4.42998e24 | −0.0961437 | −0.0480719 | − | 0.998844i | \(-0.515308\pi\) | ||||
−0.0480719 | + | 0.998844i | \(0.515308\pi\) | |||||||
\(114\) | −2.77086e25 | −0.538646 | ||||||||
\(115\) | −3.71668e25 | −0.647786 | ||||||||
\(116\) | 3.12320e24 | 0.0488512 | ||||||||
\(117\) | 1.86646e24 | 0.0262238 | ||||||||
\(118\) | −7.86322e25 | −0.993289 | ||||||||
\(119\) | −2.14962e25 | −0.244357 | ||||||||
\(120\) | −2.01203e25 | −0.206000 | ||||||||
\(121\) | 1.22651e26 | 1.13202 | ||||||||
\(122\) | −8.14714e24 | −0.0678433 | ||||||||
\(123\) | −2.54981e25 | −0.191732 | ||||||||
\(124\) | 1.07636e26 | 0.731451 | ||||||||
\(125\) | 1.45519e25 | 0.0894427 | ||||||||
\(126\) | 3.20012e25 | 0.178047 | ||||||||
\(127\) | −3.71403e26 | −1.87197 | −0.935985 | − | 0.352040i | \(-0.885488\pi\) | ||||
−0.935985 | + | 0.352040i | \(0.885488\pi\) | |||||||
\(128\) | −1.93428e25 | −0.0883883 | ||||||||
\(129\) | 5.34810e26 | 2.21732 | ||||||||
\(130\) | −3.15848e24 | −0.0118901 | ||||||||
\(131\) | 1.04713e26 | 0.358187 | 0.179093 | − | 0.983832i | \(-0.442684\pi\) | ||||
0.179093 | + | 0.983832i | \(0.442684\pi\) | |||||||
\(132\) | 3.05800e26 | 0.951182 | ||||||||
\(133\) | −7.45771e25 | −0.211086 | ||||||||
\(134\) | 4.22452e26 | 1.08885 | ||||||||
\(135\) | −7.50567e25 | −0.176286 | ||||||||
\(136\) | −1.11732e26 | −0.239299 | ||||||||
\(137\) | 5.94307e25 | 0.116146 | 0.0580729 | − | 0.998312i | \(-0.481504\pi\) | ||||
0.0580729 | + | 0.998312i | \(0.481504\pi\) | |||||||
\(138\) | 7.47805e26 | 1.33444 | ||||||||
\(139\) | −4.16988e26 | −0.679890 | −0.339945 | − | 0.940445i | \(-0.610408\pi\) | ||||
−0.339945 | + | 0.940445i | \(0.610408\pi\) | |||||||
\(140\) | −5.41533e25 | −0.0807280 | ||||||||
\(141\) | 6.33543e25 | 0.0864047 | ||||||||
\(142\) | 4.17627e26 | 0.521416 | ||||||||
\(143\) | 4.80046e25 | 0.0549012 | ||||||||
\(144\) | 1.66334e26 | 0.174361 | ||||||||
\(145\) | 4.54486e25 | 0.0436939 | ||||||||
\(146\) | −1.33855e27 | −1.18093 | ||||||||
\(147\) | −1.39867e27 | −1.13305 | ||||||||
\(148\) | 5.21760e26 | 0.388328 | ||||||||
\(149\) | −2.31720e27 | −1.58539 | −0.792693 | − | 0.609621i | \(-0.791322\pi\) | ||||
−0.792693 | + | 0.609621i | \(0.791322\pi\) | |||||||
\(150\) | −2.92788e26 | −0.184252 | ||||||||
\(151\) | −1.72926e27 | −1.00149 | −0.500747 | − | 0.865593i | \(-0.666941\pi\) | ||||
−0.500747 | + | 0.865593i | \(0.666941\pi\) | |||||||
\(152\) | −3.87633e26 | −0.206717 | ||||||||
\(153\) | 9.60812e26 | 0.472058 | ||||||||
\(154\) | 8.23056e26 | 0.372752 | ||||||||
\(155\) | 1.56631e27 | 0.654230 | ||||||||
\(156\) | 6.35494e25 | 0.0244937 | ||||||||
\(157\) | −1.99124e27 | −0.708561 | −0.354280 | − | 0.935139i | \(-0.615274\pi\) | ||||
−0.354280 | + | 0.935139i | \(0.615274\pi\) | |||||||
\(158\) | −8.78222e26 | −0.288663 | ||||||||
\(159\) | 2.86194e27 | 0.869354 | ||||||||
\(160\) | −2.81475e26 | −0.0790569 | ||||||||
\(161\) | 2.01270e27 | 0.522945 | ||||||||
\(162\) | 3.56100e27 | 0.856317 | ||||||||
\(163\) | 5.29799e26 | 0.117968 | 0.0589842 | − | 0.998259i | \(-0.481214\pi\) | ||||
0.0589842 | + | 0.998259i | \(0.481214\pi\) | |||||||
\(164\) | −3.56709e26 | −0.0735810 | ||||||||
\(165\) | 4.44998e27 | 0.850763 | ||||||||
\(166\) | −7.39253e27 | −1.31052 | ||||||||
\(167\) | −8.51848e27 | −1.40090 | −0.700449 | − | 0.713703i | \(-0.747017\pi\) | ||||
−0.700449 | + | 0.713703i | \(0.747017\pi\) | |||||||
\(168\) | 1.08958e27 | 0.166300 | ||||||||
\(169\) | −7.04643e27 | −0.998586 | ||||||||
\(170\) | −1.62591e27 | −0.214035 | ||||||||
\(171\) | 3.33336e27 | 0.407784 | ||||||||
\(172\) | 7.48179e27 | 0.850942 | ||||||||
\(173\) | −1.49682e28 | −1.58341 | −0.791705 | − | 0.610904i | \(-0.790806\pi\) | ||||
−0.791705 | + | 0.610904i | \(0.790806\pi\) | |||||||
\(174\) | −9.14437e26 | −0.0900095 | ||||||||
\(175\) | −7.88034e26 | −0.0722053 | ||||||||
\(176\) | 4.27804e27 | 0.365036 | ||||||||
\(177\) | 2.30226e28 | 1.83016 | ||||||||
\(178\) | −1.28917e28 | −0.955128 | ||||||||
\(179\) | 1.97459e28 | 1.36400 | 0.681999 | − | 0.731353i | \(-0.261111\pi\) | ||||
0.681999 | + | 0.731353i | \(0.261111\pi\) | |||||||
\(180\) | 2.42048e27 | 0.155953 | ||||||||
\(181\) | 2.28995e28 | 1.37672 | 0.688358 | − | 0.725371i | \(-0.258332\pi\) | ||||
0.688358 | + | 0.725371i | \(0.258332\pi\) | |||||||
\(182\) | 1.71042e26 | 0.00959866 | ||||||||
\(183\) | 2.38539e27 | 0.125003 | ||||||||
\(184\) | 1.04615e28 | 0.512120 | ||||||||
\(185\) | 7.59261e27 | 0.347332 | ||||||||
\(186\) | −3.15145e28 | −1.34772 | ||||||||
\(187\) | 2.47117e28 | 0.988284 | ||||||||
\(188\) | 8.86304e26 | 0.0331596 | ||||||||
\(189\) | 4.06457e27 | 0.142312 | ||||||||
\(190\) | −5.64080e27 | −0.184893 | ||||||||
\(191\) | 6.00777e28 | 1.84415 | 0.922074 | − | 0.387013i | \(-0.126493\pi\) | ||||
0.922074 | + | 0.387013i | \(0.126493\pi\) | |||||||
\(192\) | 5.66335e27 | 0.162858 | ||||||||
\(193\) | −6.00445e28 | −1.61810 | −0.809052 | − | 0.587736i | \(-0.800019\pi\) | ||||
−0.809052 | + | 0.587736i | \(0.800019\pi\) | |||||||
\(194\) | −1.68343e28 | −0.425277 | ||||||||
\(195\) | 9.24766e26 | 0.0219078 | ||||||||
\(196\) | −1.95668e28 | −0.434830 | ||||||||
\(197\) | −3.69371e27 | −0.0770255 | −0.0385128 | − | 0.999258i | \(-0.512262\pi\) | ||||
−0.0385128 | + | 0.999258i | \(0.512262\pi\) | |||||||
\(198\) | −3.67880e28 | −0.720097 | ||||||||
\(199\) | −1.22806e28 | −0.225713 | −0.112856 | − | 0.993611i | \(-0.536000\pi\) | ||||
−0.112856 | + | 0.993611i | \(0.536000\pi\) | |||||||
\(200\) | −4.09600e27 | −0.0707107 | ||||||||
\(201\) | −1.23689e29 | −2.00623 | ||||||||
\(202\) | −3.02448e28 | −0.461062 | ||||||||
\(203\) | −2.46119e27 | −0.0352732 | ||||||||
\(204\) | 3.27138e28 | 0.440914 | ||||||||
\(205\) | −5.19080e27 | −0.0658129 | ||||||||
\(206\) | 7.25184e28 | 0.865183 | ||||||||
\(207\) | −8.99613e28 | −1.01024 | ||||||||
\(208\) | 8.89033e26 | 0.00939996 | ||||||||
\(209\) | 8.57325e28 | 0.853723 | ||||||||
\(210\) | 1.58554e28 | 0.148743 | ||||||||
\(211\) | −2.20546e29 | −1.94970 | −0.974850 | − | 0.222861i | \(-0.928460\pi\) | ||||
−0.974850 | + | 0.222861i | \(0.928460\pi\) | |||||||
\(212\) | 4.00375e28 | 0.333633 | ||||||||
\(213\) | −1.22276e29 | −0.960720 | ||||||||
\(214\) | 1.24935e29 | 0.925787 | ||||||||
\(215\) | 1.08874e29 | 0.761106 | ||||||||
\(216\) | 2.11266e28 | 0.139366 | ||||||||
\(217\) | −8.48206e28 | −0.528147 | ||||||||
\(218\) | 2.89748e27 | 0.0170339 | ||||||||
\(219\) | 3.91912e29 | 2.17589 | ||||||||
\(220\) | 6.22536e28 | 0.326498 | ||||||||
\(221\) | 5.13541e27 | 0.0254491 | ||||||||
\(222\) | −1.52765e29 | −0.715504 | ||||||||
\(223\) | −2.23533e27 | −0.00989761 | −0.00494880 | − | 0.999988i | \(-0.501575\pi\) | ||||
−0.00494880 | + | 0.999988i | \(0.501575\pi\) | |||||||
\(224\) | 1.52428e28 | 0.0638211 | ||||||||
\(225\) | 3.52226e28 | 0.139489 | ||||||||
\(226\) | 1.81452e28 | 0.0679839 | ||||||||
\(227\) | −2.34973e29 | −0.833094 | −0.416547 | − | 0.909114i | \(-0.636760\pi\) | ||||
−0.416547 | + | 0.909114i | \(0.636760\pi\) | |||||||
\(228\) | 1.13494e29 | 0.380880 | ||||||||
\(229\) | 3.37494e29 | 1.07232 | 0.536158 | − | 0.844118i | \(-0.319875\pi\) | ||||
0.536158 | + | 0.844118i | \(0.319875\pi\) | |||||||
\(230\) | 1.52235e29 | 0.458054 | ||||||||
\(231\) | −2.40981e29 | −0.686804 | ||||||||
\(232\) | −1.27926e28 | −0.0345430 | ||||||||
\(233\) | 2.45486e29 | 0.628172 | 0.314086 | − | 0.949395i | \(-0.398302\pi\) | ||||
0.314086 | + | 0.949395i | \(0.398302\pi\) | |||||||
\(234\) | −7.64503e27 | −0.0185430 | ||||||||
\(235\) | 1.28974e28 | 0.0296589 | ||||||||
\(236\) | 3.22078e29 | 0.702361 | ||||||||
\(237\) | 2.57133e29 | 0.531868 | ||||||||
\(238\) | 8.80485e28 | 0.172787 | ||||||||
\(239\) | 2.75069e29 | 0.512234 | 0.256117 | − | 0.966646i | \(-0.417557\pi\) | ||||
0.256117 | + | 0.966646i | \(0.417557\pi\) | |||||||
\(240\) | 8.24125e28 | 0.145664 | ||||||||
\(241\) | −3.54884e29 | −0.595489 | −0.297744 | − | 0.954646i | \(-0.596234\pi\) | ||||
−0.297744 | + | 0.954646i | \(0.596234\pi\) | |||||||
\(242\) | −5.02380e29 | −0.800462 | ||||||||
\(243\) | −7.82136e29 | −1.18360 | ||||||||
\(244\) | 3.33707e28 | 0.0479725 | ||||||||
\(245\) | −2.84735e29 | −0.388924 | ||||||||
\(246\) | 1.04440e29 | 0.135575 | ||||||||
\(247\) | 1.78164e28 | 0.0219840 | ||||||||
\(248\) | −4.40876e29 | −0.517214 | ||||||||
\(249\) | 2.16445e30 | 2.41465 | ||||||||
\(250\) | −5.96046e28 | −0.0632456 | ||||||||
\(251\) | −1.45056e30 | −1.46425 | −0.732124 | − | 0.681171i | \(-0.761471\pi\) | ||||
−0.732124 | + | 0.681171i | \(0.761471\pi\) | |||||||
\(252\) | −1.31077e29 | −0.125898 | ||||||||
\(253\) | −2.31377e30 | −2.11501 | ||||||||
\(254\) | 1.52127e30 | 1.32368 | ||||||||
\(255\) | 4.76048e29 | 0.394365 | ||||||||
\(256\) | 7.92282e28 | 0.0625000 | ||||||||
\(257\) | 2.49157e28 | 0.0187201 | 0.00936006 | − | 0.999956i | \(-0.497021\pi\) | ||||
0.00936006 | + | 0.999956i | \(0.497021\pi\) | |||||||
\(258\) | −2.19058e30 | −1.56788 | ||||||||
\(259\) | −4.11164e29 | −0.280394 | ||||||||
\(260\) | 1.29371e28 | 0.00840758 | ||||||||
\(261\) | 1.10007e29 | 0.0681421 | ||||||||
\(262\) | −4.28905e29 | −0.253276 | ||||||||
\(263\) | −1.49953e30 | −0.844325 | −0.422162 | − | 0.906520i | \(-0.638729\pi\) | ||||
−0.422162 | + | 0.906520i | \(0.638729\pi\) | |||||||
\(264\) | −1.25256e30 | −0.672588 | ||||||||
\(265\) | 5.82622e29 | 0.298410 | ||||||||
\(266\) | 3.05468e29 | 0.149261 | ||||||||
\(267\) | 3.77455e30 | 1.75985 | ||||||||
\(268\) | −1.73036e30 | −0.769933 | ||||||||
\(269\) | 1.77042e30 | 0.751920 | 0.375960 | − | 0.926636i | \(-0.377313\pi\) | ||||
0.375960 | + | 0.926636i | \(0.377313\pi\) | |||||||
\(270\) | 3.07432e29 | 0.124653 | ||||||||
\(271\) | 2.89777e30 | 1.12188 | 0.560941 | − | 0.827855i | \(-0.310439\pi\) | ||||
0.560941 | + | 0.827855i | \(0.310439\pi\) | |||||||
\(272\) | 4.57654e29 | 0.169210 | ||||||||
\(273\) | −5.00791e28 | −0.0176857 | ||||||||
\(274\) | −2.43428e29 | −0.0821275 | ||||||||
\(275\) | 9.05909e29 | 0.292029 | ||||||||
\(276\) | −3.06301e30 | −0.943593 | ||||||||
\(277\) | −1.66393e30 | −0.489935 | −0.244968 | − | 0.969531i | \(-0.578777\pi\) | ||||
−0.244968 | + | 0.969531i | \(0.578777\pi\) | |||||||
\(278\) | 1.70798e30 | 0.480755 | ||||||||
\(279\) | 3.79121e30 | 1.02029 | ||||||||
\(280\) | 2.21812e29 | 0.0570833 | ||||||||
\(281\) | −2.85222e30 | −0.702027 | −0.351013 | − | 0.936370i | \(-0.614163\pi\) | ||||
−0.351013 | + | 0.936370i | \(0.614163\pi\) | |||||||
\(282\) | −2.59499e29 | −0.0610973 | ||||||||
\(283\) | −1.34367e30 | −0.302665 | −0.151333 | − | 0.988483i | \(-0.548356\pi\) | ||||
−0.151333 | + | 0.988483i | \(0.548356\pi\) | |||||||
\(284\) | −1.71060e30 | −0.368697 | ||||||||
\(285\) | 1.65156e30 | 0.340670 | ||||||||
\(286\) | −1.96627e29 | −0.0388210 | ||||||||
\(287\) | 2.81099e29 | 0.0531294 | ||||||||
\(288\) | −6.81304e29 | −0.123292 | ||||||||
\(289\) | −3.12704e30 | −0.541888 | ||||||||
\(290\) | −1.86158e29 | −0.0308962 | ||||||||
\(291\) | 4.92887e30 | 0.783583 | ||||||||
\(292\) | 5.48271e30 | 0.835044 | ||||||||
\(293\) | 1.77083e30 | 0.258423 | 0.129212 | − | 0.991617i | \(-0.458755\pi\) | ||||
0.129212 | + | 0.991617i | \(0.458755\pi\) | |||||||
\(294\) | 5.72893e30 | 0.801184 | ||||||||
\(295\) | 4.68685e30 | 0.628211 | ||||||||
\(296\) | −2.13713e30 | −0.274590 | ||||||||
\(297\) | −4.67255e30 | −0.575571 | ||||||||
\(298\) | 9.49125e30 | 1.12104 | ||||||||
\(299\) | −4.80831e29 | −0.0544632 | ||||||||
\(300\) | 1.19926e30 | 0.130286 | ||||||||
\(301\) | −5.89590e30 | −0.614425 | ||||||||
\(302\) | 7.08305e30 | 0.708164 | ||||||||
\(303\) | 8.85533e30 | 0.849517 | ||||||||
\(304\) | 1.58774e30 | 0.146171 | ||||||||
\(305\) | 4.85607e29 | 0.0429079 | ||||||||
\(306\) | −3.93549e30 | −0.333796 | ||||||||
\(307\) | −1.28750e31 | −1.04838 | −0.524189 | − | 0.851602i | \(-0.675631\pi\) | ||||
−0.524189 | + | 0.851602i | \(0.675631\pi\) | |||||||
\(308\) | −3.37124e30 | −0.263576 | ||||||||
\(309\) | −2.12325e31 | −1.59412 | ||||||||
\(310\) | −6.41559e30 | −0.462610 | ||||||||
\(311\) | −4.08326e29 | −0.0282815 | −0.0141407 | − | 0.999900i | \(-0.504501\pi\) | ||||
−0.0141407 | + | 0.999900i | \(0.504501\pi\) | |||||||
\(312\) | −2.60298e29 | −0.0173196 | ||||||||
\(313\) | −9.20841e30 | −0.588682 | −0.294341 | − | 0.955701i | \(-0.595100\pi\) | ||||
−0.294341 | + | 0.955701i | \(0.595100\pi\) | |||||||
\(314\) | 8.15610e30 | 0.501028 | ||||||||
\(315\) | −1.90742e30 | −0.112607 | ||||||||
\(316\) | 3.59720e30 | 0.204115 | ||||||||
\(317\) | −1.73757e31 | −0.947764 | −0.473882 | − | 0.880588i | \(-0.657148\pi\) | ||||
−0.473882 | + | 0.880588i | \(0.657148\pi\) | |||||||
\(318\) | −1.17225e31 | −0.614726 | ||||||||
\(319\) | 2.82934e30 | 0.142660 | ||||||||
\(320\) | 1.15292e30 | 0.0559017 | ||||||||
\(321\) | −3.65794e31 | −1.70578 | ||||||||
\(322\) | −8.24403e30 | −0.369778 | ||||||||
\(323\) | 9.17145e30 | 0.395737 | ||||||||
\(324\) | −1.45859e31 | −0.605508 | ||||||||
\(325\) | 1.88260e29 | 0.00751997 | ||||||||
\(326\) | −2.17006e30 | −0.0834163 | ||||||||
\(327\) | −8.48349e29 | −0.0313854 | ||||||||
\(328\) | 1.46108e30 | 0.0520296 | ||||||||
\(329\) | −6.98437e29 | −0.0239430 | ||||||||
\(330\) | −1.82271e31 | −0.601581 | ||||||||
\(331\) | 5.61759e31 | 1.78525 | 0.892627 | − | 0.450797i | \(-0.148860\pi\) | ||||
0.892627 | + | 0.450797i | \(0.148860\pi\) | |||||||
\(332\) | 3.02798e31 | 0.926674 | ||||||||
\(333\) | 1.83777e31 | 0.541675 | ||||||||
\(334\) | 3.48917e31 | 0.990584 | ||||||||
\(335\) | −2.51801e31 | −0.688649 | ||||||||
\(336\) | −4.46291e30 | −0.117592 | ||||||||
\(337\) | 4.19121e31 | 1.06406 | 0.532029 | − | 0.846726i | \(-0.321430\pi\) | ||||
0.532029 | + | 0.846726i | \(0.321430\pi\) | |||||||
\(338\) | 2.88622e31 | 0.706107 | ||||||||
\(339\) | −5.31270e30 | −0.125262 | ||||||||
\(340\) | 6.65974e30 | 0.151346 | ||||||||
\(341\) | 9.75082e31 | 2.13605 | ||||||||
\(342\) | −1.36534e31 | −0.288347 | ||||||||
\(343\) | 3.31496e31 | 0.674997 | ||||||||
\(344\) | −3.06454e31 | −0.601707 | ||||||||
\(345\) | −4.45726e31 | −0.843975 | ||||||||
\(346\) | 6.13098e31 | 1.11964 | ||||||||
\(347\) | −1.70880e31 | −0.301004 | −0.150502 | − | 0.988610i | \(-0.548089\pi\) | ||||
−0.150502 | + | 0.988610i | \(0.548089\pi\) | |||||||
\(348\) | 3.74554e30 | 0.0636463 | ||||||||
\(349\) | −8.15918e31 | −1.33761 | −0.668803 | − | 0.743439i | \(-0.733193\pi\) | ||||
−0.668803 | + | 0.743439i | \(0.733193\pi\) | |||||||
\(350\) | 3.22779e30 | 0.0510569 | ||||||||
\(351\) | −9.71019e29 | −0.0148214 | ||||||||
\(352\) | −1.75228e31 | −0.258120 | ||||||||
\(353\) | 5.64031e31 | 0.801899 | 0.400949 | − | 0.916100i | \(-0.368680\pi\) | ||||
0.400949 | + | 0.916100i | \(0.368680\pi\) | |||||||
\(354\) | −9.43005e31 | −1.29412 | ||||||||
\(355\) | −2.48925e31 | −0.329772 | ||||||||
\(356\) | 5.28046e31 | 0.675378 | ||||||||
\(357\) | −2.57796e31 | −0.318363 | ||||||||
\(358\) | −8.08791e31 | −0.964492 | ||||||||
\(359\) | 4.12655e31 | 0.475233 | 0.237616 | − | 0.971359i | \(-0.423634\pi\) | ||||
0.237616 | + | 0.971359i | \(0.423634\pi\) | |||||||
\(360\) | −9.91428e30 | −0.110276 | ||||||||
\(361\) | −6.12579e31 | −0.658145 | ||||||||
\(362\) | −9.37965e31 | −0.973485 | ||||||||
\(363\) | 1.47091e32 | 1.47487 | ||||||||
\(364\) | −7.00588e29 | −0.00678727 | ||||||||
\(365\) | 7.97839e31 | 0.746886 | ||||||||
\(366\) | −9.77054e30 | −0.0883904 | ||||||||
\(367\) | 1.10522e32 | 0.966323 | 0.483161 | − | 0.875531i | \(-0.339488\pi\) | ||||
0.483161 | + | 0.875531i | \(0.339488\pi\) | |||||||
\(368\) | −4.28504e31 | −0.362124 | ||||||||
\(369\) | −1.25642e31 | −0.102637 | ||||||||
\(370\) | −3.10993e31 | −0.245601 | ||||||||
\(371\) | −3.15509e31 | −0.240901 | ||||||||
\(372\) | 1.29083e32 | 0.952979 | ||||||||
\(373\) | −1.60774e31 | −0.114777 | −0.0573885 | − | 0.998352i | \(-0.518277\pi\) | ||||
−0.0573885 | + | 0.998352i | \(0.518277\pi\) | |||||||
\(374\) | −1.01219e32 | −0.698822 | ||||||||
\(375\) | 1.74515e31 | 0.116531 | ||||||||
\(376\) | −3.63030e30 | −0.0234474 | ||||||||
\(377\) | 5.87975e29 | 0.00367360 | ||||||||
\(378\) | −1.66485e31 | −0.100630 | ||||||||
\(379\) | −2.27403e32 | −1.32986 | −0.664930 | − | 0.746906i | \(-0.731539\pi\) | ||||
−0.664930 | + | 0.746906i | \(0.731539\pi\) | |||||||
\(380\) | 2.31047e31 | 0.130739 | ||||||||
\(381\) | −4.45409e32 | −2.43892 | ||||||||
\(382\) | −2.46078e32 | −1.30401 | ||||||||
\(383\) | 3.38623e32 | 1.73673 | 0.868363 | − | 0.495929i | \(-0.165172\pi\) | ||||
0.868363 | + | 0.495929i | \(0.165172\pi\) | |||||||
\(384\) | −2.31971e31 | −0.115158 | ||||||||
\(385\) | −4.90579e31 | −0.235749 | ||||||||
\(386\) | 2.45942e32 | 1.14417 | ||||||||
\(387\) | 2.63528e32 | 1.18697 | ||||||||
\(388\) | 6.89531e31 | 0.300717 | ||||||||
\(389\) | −3.10148e32 | −1.30978 | −0.654890 | − | 0.755724i | \(-0.727285\pi\) | ||||
−0.654890 | + | 0.755724i | \(0.727285\pi\) | |||||||
\(390\) | −3.78784e30 | −0.0154912 | ||||||||
\(391\) | −2.47521e32 | −0.980398 | ||||||||
\(392\) | 8.01457e31 | 0.307471 | ||||||||
\(393\) | 1.25578e32 | 0.466667 | ||||||||
\(394\) | 1.51294e31 | 0.0544653 | ||||||||
\(395\) | 5.23461e31 | 0.182566 | ||||||||
\(396\) | 1.50683e32 | 0.509185 | ||||||||
\(397\) | −3.84570e32 | −1.25920 | −0.629599 | − | 0.776920i | \(-0.716781\pi\) | ||||
−0.629599 | + | 0.776920i | \(0.716781\pi\) | |||||||
\(398\) | 5.03013e31 | 0.159603 | ||||||||
\(399\) | −8.94374e31 | −0.275016 | ||||||||
\(400\) | 1.67772e31 | 0.0500000 | ||||||||
\(401\) | 3.65396e32 | 1.05550 | 0.527751 | − | 0.849399i | \(-0.323035\pi\) | ||||
0.527751 | + | 0.849399i | \(0.323035\pi\) | |||||||
\(402\) | 5.06630e32 | 1.41862 | ||||||||
\(403\) | 2.02635e31 | 0.0550049 | ||||||||
\(404\) | 1.23883e32 | 0.326020 | ||||||||
\(405\) | −2.12252e32 | −0.541583 | ||||||||
\(406\) | 1.00810e31 | 0.0249419 | ||||||||
\(407\) | 4.72667e32 | 1.13403 | ||||||||
\(408\) | −1.33996e32 | −0.311773 | ||||||||
\(409\) | −1.30167e31 | −0.0293737 | −0.0146868 | − | 0.999892i | \(-0.504675\pi\) | ||||
−0.0146868 | + | 0.999892i | \(0.504675\pi\) | |||||||
\(410\) | 2.12615e31 | 0.0465367 | ||||||||
\(411\) | 7.12729e31 | 0.151322 | ||||||||
\(412\) | −2.97036e32 | −0.611777 | ||||||||
\(413\) | −2.53808e32 | −0.507142 | ||||||||
\(414\) | 3.68482e32 | 0.714351 | ||||||||
\(415\) | 4.40629e32 | 0.828843 | ||||||||
\(416\) | −3.64148e30 | −0.00664678 | ||||||||
\(417\) | −5.00077e32 | −0.885802 | ||||||||
\(418\) | −3.51160e32 | −0.603673 | ||||||||
\(419\) | 8.70006e32 | 1.45160 | 0.725800 | − | 0.687905i | \(-0.241470\pi\) | ||||
0.725800 | + | 0.687905i | \(0.241470\pi\) | |||||||
\(420\) | −6.49439e31 | −0.105177 | ||||||||
\(421\) | −5.04763e32 | −0.793527 | −0.396763 | − | 0.917921i | \(-0.629867\pi\) | ||||
−0.396763 | + | 0.917921i | \(0.629867\pi\) | |||||||
\(422\) | 9.03355e32 | 1.37865 | ||||||||
\(423\) | 3.12179e31 | 0.0462540 | ||||||||
\(424\) | −1.63994e32 | −0.235914 | ||||||||
\(425\) | 9.69120e31 | 0.135368 | ||||||||
\(426\) | 5.00843e32 | 0.679332 | ||||||||
\(427\) | −2.62972e31 | −0.0346387 | ||||||||
\(428\) | −5.11733e32 | −0.654630 | ||||||||
\(429\) | 5.75700e31 | 0.0715286 | ||||||||
\(430\) | −4.45949e32 | −0.538183 | ||||||||
\(431\) | 8.61019e32 | 1.00936 | 0.504681 | − | 0.863306i | \(-0.331610\pi\) | ||||
0.504681 | + | 0.863306i | \(0.331610\pi\) | |||||||
\(432\) | −8.65345e31 | −0.0985468 | ||||||||
\(433\) | −1.24809e33 | −1.38085 | −0.690427 | − | 0.723402i | \(-0.742577\pi\) | ||||
−0.690427 | + | 0.723402i | \(0.742577\pi\) | |||||||
\(434\) | 3.47425e32 | 0.373456 | ||||||||
\(435\) | 5.45047e31 | 0.0569270 | ||||||||
\(436\) | −1.18681e31 | −0.0120448 | ||||||||
\(437\) | −8.58728e32 | −0.846910 | ||||||||
\(438\) | −1.60527e33 | −1.53859 | ||||||||
\(439\) | 3.66479e32 | 0.341384 | 0.170692 | − | 0.985324i | \(-0.445400\pi\) | ||||
0.170692 | + | 0.985324i | \(0.445400\pi\) | |||||||
\(440\) | −2.54991e32 | −0.230869 | ||||||||
\(441\) | −6.89194e32 | −0.606540 | ||||||||
\(442\) | −2.10346e31 | −0.0179952 | ||||||||
\(443\) | 1.58140e33 | 1.31521 | 0.657606 | − | 0.753362i | \(-0.271569\pi\) | ||||
0.657606 | + | 0.753362i | \(0.271569\pi\) | |||||||
\(444\) | 6.25726e32 | 0.505938 | ||||||||
\(445\) | 7.68408e32 | 0.604076 | ||||||||
\(446\) | 9.15590e30 | 0.00699866 | ||||||||
\(447\) | −2.77892e33 | −2.06554 | ||||||||
\(448\) | −6.24345e31 | −0.0451283 | ||||||||
\(449\) | 2.03169e33 | 1.42817 | 0.714083 | − | 0.700061i | \(-0.246844\pi\) | ||||
0.714083 | + | 0.700061i | \(0.246844\pi\) | |||||||
\(450\) | −1.44272e32 | −0.0986336 | ||||||||
\(451\) | −3.23146e32 | −0.214878 | ||||||||
\(452\) | −7.43227e31 | −0.0480719 | ||||||||
\(453\) | −2.07383e33 | −1.30481 | ||||||||
\(454\) | 9.62448e32 | 0.589086 | ||||||||
\(455\) | −1.01949e31 | −0.00607072 | ||||||||
\(456\) | −4.64873e32 | −0.269323 | ||||||||
\(457\) | −1.28100e33 | −0.722097 | −0.361048 | − | 0.932547i | \(-0.617581\pi\) | ||||
−0.361048 | + | 0.932547i | \(0.617581\pi\) | |||||||
\(458\) | −1.38238e33 | −0.758241 | ||||||||
\(459\) | −4.99858e32 | −0.266801 | ||||||||
\(460\) | −6.23555e32 | −0.323893 | ||||||||
\(461\) | −1.55893e33 | −0.788071 | −0.394036 | − | 0.919095i | \(-0.628921\pi\) | ||||
−0.394036 | + | 0.919095i | \(0.628921\pi\) | |||||||
\(462\) | 9.87058e32 | 0.485644 | ||||||||
\(463\) | 5.69235e32 | 0.272602 | 0.136301 | − | 0.990667i | \(-0.456479\pi\) | ||||
0.136301 | + | 0.990667i | \(0.456479\pi\) | |||||||
\(464\) | 5.23987e31 | 0.0244256 | ||||||||
\(465\) | 1.87841e33 | 0.852370 | ||||||||
\(466\) | −1.00551e33 | −0.444185 | ||||||||
\(467\) | 2.08645e33 | 0.897321 | 0.448661 | − | 0.893702i | \(-0.351901\pi\) | ||||
0.448661 | + | 0.893702i | \(0.351901\pi\) | |||||||
\(468\) | 3.13140e31 | 0.0131119 | ||||||||
\(469\) | 1.36359e33 | 0.555932 | ||||||||
\(470\) | −5.28278e31 | −0.0209720 | ||||||||
\(471\) | −2.38801e33 | −0.923156 | ||||||||
\(472\) | −1.31923e33 | −0.496644 | ||||||||
\(473\) | 6.77782e33 | 2.48500 | ||||||||
\(474\) | −1.05322e33 | −0.376087 | ||||||||
\(475\) | 3.36218e32 | 0.116937 | ||||||||
\(476\) | −3.60647e32 | −0.122179 | ||||||||
\(477\) | 1.41022e33 | 0.465381 | ||||||||
\(478\) | −1.12668e33 | −0.362204 | ||||||||
\(479\) | 4.90036e33 | 1.53474 | 0.767368 | − | 0.641207i | \(-0.221566\pi\) | ||||
0.767368 | + | 0.641207i | \(0.221566\pi\) | |||||||
\(480\) | −3.37562e32 | −0.103000 | ||||||||
\(481\) | 9.82265e31 | 0.0292022 | ||||||||
\(482\) | 1.45361e33 | 0.421074 | ||||||||
\(483\) | 2.41375e33 | 0.681324 | ||||||||
\(484\) | 2.05775e33 | 0.566012 | ||||||||
\(485\) | 1.00340e33 | 0.268969 | ||||||||
\(486\) | 3.20363e33 | 0.836929 | ||||||||
\(487\) | −1.04707e33 | −0.266603 | −0.133302 | − | 0.991076i | \(-0.542558\pi\) | ||||
−0.133302 | + | 0.991076i | \(0.542558\pi\) | |||||||
\(488\) | −1.36686e32 | −0.0339217 | ||||||||
\(489\) | 6.35367e32 | 0.153696 | ||||||||
\(490\) | 1.16627e33 | 0.275011 | ||||||||
\(491\) | −2.78591e33 | −0.640397 | −0.320198 | − | 0.947351i | \(-0.603750\pi\) | ||||
−0.320198 | + | 0.947351i | \(0.603750\pi\) | |||||||
\(492\) | −4.27787e32 | −0.0958658 | ||||||||
\(493\) | 3.02676e32 | 0.0661289 | ||||||||
\(494\) | −7.29758e31 | −0.0155450 | ||||||||
\(495\) | 2.19273e33 | 0.455429 | ||||||||
\(496\) | 1.80583e33 | 0.365726 | ||||||||
\(497\) | 1.34801e33 | 0.266219 | ||||||||
\(498\) | −8.86557e33 | −1.70742 | ||||||||
\(499\) | −2.70519e33 | −0.508090 | −0.254045 | − | 0.967192i | \(-0.581761\pi\) | ||||
−0.254045 | + | 0.967192i | \(0.581761\pi\) | |||||||
\(500\) | 2.44141e32 | 0.0447214 | ||||||||
\(501\) | −1.02159e34 | −1.82517 | ||||||||
\(502\) | 5.94150e33 | 1.03538 | ||||||||
\(503\) | −6.75761e33 | −1.14867 | −0.574333 | − | 0.818622i | \(-0.694738\pi\) | ||||
−0.574333 | + | 0.818622i | \(0.694738\pi\) | |||||||
\(504\) | 5.36891e32 | 0.0890234 | ||||||||
\(505\) | 1.80273e33 | 0.291601 | ||||||||
\(506\) | 9.47718e33 | 1.49554 | ||||||||
\(507\) | −8.45051e33 | −1.30102 | ||||||||
\(508\) | −6.23111e33 | −0.935985 | ||||||||
\(509\) | −5.92051e33 | −0.867734 | −0.433867 | − | 0.900977i | \(-0.642851\pi\) | ||||
−0.433867 | + | 0.900977i | \(0.642851\pi\) | |||||||
\(510\) | −1.94989e33 | −0.278858 | ||||||||
\(511\) | −4.32056e33 | −0.602946 | ||||||||
\(512\) | −3.24519e32 | −0.0441942 | ||||||||
\(513\) | −1.73416e33 | −0.230475 | ||||||||
\(514\) | −1.02055e32 | −0.0132371 | ||||||||
\(515\) | −4.32244e33 | −0.547190 | ||||||||
\(516\) | 8.97261e33 | 1.10866 | ||||||||
\(517\) | 8.02911e32 | 0.0968357 | ||||||||
\(518\) | 1.68413e33 | 0.198268 | ||||||||
\(519\) | −1.79508e34 | −2.06296 | ||||||||
\(520\) | −5.29905e31 | −0.00594506 | ||||||||
\(521\) | 1.90773e33 | 0.208951 | 0.104476 | − | 0.994527i | \(-0.466684\pi\) | ||||
0.104476 | + | 0.994527i | \(0.466684\pi\) | |||||||
\(522\) | −4.50590e32 | −0.0481837 | ||||||||
\(523\) | 7.03264e33 | 0.734255 | 0.367128 | − | 0.930171i | \(-0.380341\pi\) | ||||
0.367128 | + | 0.930171i | \(0.380341\pi\) | |||||||
\(524\) | 1.75679e33 | 0.179093 | ||||||||
\(525\) | −9.45058e32 | −0.0940734 | ||||||||
\(526\) | 6.14209e33 | 0.597028 | ||||||||
\(527\) | 1.04312e34 | 0.990150 | ||||||||
\(528\) | 5.13048e33 | 0.475591 | ||||||||
\(529\) | 1.21298e34 | 1.09814 | ||||||||
\(530\) | −2.38642e33 | −0.211008 | ||||||||
\(531\) | 1.13444e34 | 0.979716 | ||||||||
\(532\) | −1.25120e33 | −0.105543 | ||||||||
\(533\) | −6.71540e31 | −0.00553327 | ||||||||
\(534\) | −1.54606e34 | −1.24440 | ||||||||
\(535\) | −7.44669e33 | −0.585519 | ||||||||
\(536\) | 7.08757e33 | 0.544425 | ||||||||
\(537\) | 2.36805e34 | 1.77710 | ||||||||
\(538\) | −7.25162e33 | −0.531688 | ||||||||
\(539\) | −1.77258e34 | −1.26983 | ||||||||
\(540\) | −1.25924e33 | −0.0881429 | ||||||||
\(541\) | −1.92351e34 | −1.31561 | −0.657806 | − | 0.753188i | \(-0.728515\pi\) | ||||
−0.657806 | + | 0.753188i | \(0.728515\pi\) | |||||||
\(542\) | −1.18693e34 | −0.793291 | ||||||||
\(543\) | 2.74625e34 | 1.79367 | ||||||||
\(544\) | −1.87455e33 | −0.119649 | ||||||||
\(545\) | −1.72703e32 | −0.0107732 | ||||||||
\(546\) | 2.05124e32 | 0.0125057 | ||||||||
\(547\) | −2.85894e33 | −0.170358 | −0.0851791 | − | 0.996366i | \(-0.527146\pi\) | ||||
−0.0851791 | + | 0.996366i | \(0.527146\pi\) | |||||||
\(548\) | 9.97082e32 | 0.0580729 | ||||||||
\(549\) | 1.17540e33 | 0.0669163 | ||||||||
\(550\) | −3.71060e33 | −0.206496 | ||||||||
\(551\) | 1.05008e33 | 0.0571250 | ||||||||
\(552\) | 1.25461e34 | 0.667221 | ||||||||
\(553\) | −2.83471e33 | −0.147382 | ||||||||
\(554\) | 6.81547e33 | 0.346437 | ||||||||
\(555\) | 9.10551e33 | 0.452524 | ||||||||
\(556\) | −6.99590e33 | −0.339945 | ||||||||
\(557\) | −3.74961e34 | −1.78154 | −0.890770 | − | 0.454454i | \(-0.849834\pi\) | ||||
−0.890770 | + | 0.454454i | \(0.849834\pi\) | |||||||
\(558\) | −1.55288e34 | −0.721457 | ||||||||
\(559\) | 1.40852e33 | 0.0639906 | ||||||||
\(560\) | −9.08541e32 | −0.0403640 | ||||||||
\(561\) | 2.96357e34 | 1.28760 | ||||||||
\(562\) | 1.16827e34 | 0.496408 | ||||||||
\(563\) | 3.46228e34 | 1.43882 | 0.719410 | − | 0.694585i | \(-0.244412\pi\) | ||||
0.719410 | + | 0.694585i | \(0.244412\pi\) | |||||||
\(564\) | 1.06291e33 | 0.0432023 | ||||||||
\(565\) | −1.08154e33 | −0.0429968 | ||||||||
\(566\) | 5.50368e33 | 0.214017 | ||||||||
\(567\) | 1.14942e34 | 0.437209 | ||||||||
\(568\) | 7.00661e33 | 0.260708 | ||||||||
\(569\) | 3.03324e34 | 1.10409 | 0.552043 | − | 0.833816i | \(-0.313848\pi\) | ||||
0.552043 | + | 0.833816i | \(0.313848\pi\) | |||||||
\(570\) | −6.76479e33 | −0.240890 | ||||||||
\(571\) | −2.05373e34 | −0.715472 | −0.357736 | − | 0.933823i | \(-0.616451\pi\) | ||||
−0.357736 | + | 0.933823i | \(0.616451\pi\) | |||||||
\(572\) | 8.05383e32 | 0.0274506 | ||||||||
\(573\) | 7.20488e34 | 2.40267 | ||||||||
\(574\) | −1.15138e33 | −0.0375682 | ||||||||
\(575\) | −9.07392e33 | −0.289699 | ||||||||
\(576\) | 2.79062e33 | 0.0871806 | ||||||||
\(577\) | −1.73765e34 | −0.531209 | −0.265604 | − | 0.964082i | \(-0.585571\pi\) | ||||
−0.265604 | + | 0.964082i | \(0.585571\pi\) | |||||||
\(578\) | 1.28083e34 | 0.383173 | ||||||||
\(579\) | −7.20090e34 | −2.10816 | ||||||||
\(580\) | 7.62501e32 | 0.0218469 | ||||||||
\(581\) | −2.38615e34 | −0.669108 | ||||||||
\(582\) | −2.01887e34 | −0.554077 | ||||||||
\(583\) | 3.62703e34 | 0.974305 | ||||||||
\(584\) | −2.24572e34 | −0.590465 | ||||||||
\(585\) | 4.55679e32 | 0.0117276 | ||||||||
\(586\) | −7.25332e33 | −0.182733 | ||||||||
\(587\) | −4.89727e34 | −1.20775 | −0.603876 | − | 0.797078i | \(-0.706378\pi\) | ||||
−0.603876 | + | 0.797078i | \(0.706378\pi\) | |||||||
\(588\) | −2.34657e34 | −0.566523 | ||||||||
\(589\) | 3.61891e34 | 0.855335 | ||||||||
\(590\) | −1.91973e34 | −0.444212 | ||||||||
\(591\) | −4.42972e33 | −0.100353 | ||||||||
\(592\) | 8.75368e33 | 0.194164 | ||||||||
\(593\) | 1.10421e34 | 0.239810 | 0.119905 | − | 0.992785i | \(-0.461741\pi\) | ||||
0.119905 | + | 0.992785i | \(0.461741\pi\) | |||||||
\(594\) | 1.91388e34 | 0.406990 | ||||||||
\(595\) | −5.24810e33 | −0.109280 | ||||||||
\(596\) | −3.88761e34 | −0.792693 | ||||||||
\(597\) | −1.47276e34 | −0.294072 | ||||||||
\(598\) | 1.96949e33 | 0.0385113 | ||||||||
\(599\) | −1.03520e35 | −1.98240 | −0.991198 | − | 0.132391i | \(-0.957735\pi\) | ||||
−0.991198 | + | 0.132391i | \(0.957735\pi\) | |||||||
\(600\) | −4.91217e33 | −0.0921261 | ||||||||
\(601\) | 9.90327e34 | 1.81906 | 0.909532 | − | 0.415635i | \(-0.136441\pi\) | ||||
0.909532 | + | 0.415635i | \(0.136441\pi\) | |||||||
\(602\) | 2.41496e34 | 0.434464 | ||||||||
\(603\) | −6.09479e34 | −1.07397 | ||||||||
\(604\) | −2.90122e34 | −0.500747 | ||||||||
\(605\) | 2.99442e34 | 0.506256 | ||||||||
\(606\) | −3.62714e34 | −0.600699 | ||||||||
\(607\) | −6.59371e34 | −1.06972 | −0.534862 | − | 0.844940i | \(-0.679636\pi\) | ||||
−0.534862 | + | 0.844940i | \(0.679636\pi\) | |||||||
\(608\) | −6.50340e33 | −0.103358 | ||||||||
\(609\) | −2.95161e33 | −0.0459560 | ||||||||
\(610\) | −1.98905e33 | −0.0303405 | ||||||||
\(611\) | 1.66856e32 | 0.00249359 | ||||||||
\(612\) | 1.61198e34 | 0.236029 | ||||||||
\(613\) | −7.31630e34 | −1.04963 | −0.524814 | − | 0.851217i | \(-0.675865\pi\) | ||||
−0.524814 | + | 0.851217i | \(0.675865\pi\) | |||||||
\(614\) | 5.27360e34 | 0.741315 | ||||||||
\(615\) | −6.22512e33 | −0.0857450 | ||||||||
\(616\) | 1.38086e34 | 0.186376 | ||||||||
\(617\) | 9.91183e34 | 1.31096 | 0.655480 | − | 0.755213i | \(-0.272466\pi\) | ||||
0.655480 | + | 0.755213i | \(0.272466\pi\) | |||||||
\(618\) | 8.69685e34 | 1.12721 | ||||||||
\(619\) | 4.22193e34 | 0.536263 | 0.268131 | − | 0.963382i | \(-0.413594\pi\) | ||||
0.268131 | + | 0.963382i | \(0.413594\pi\) | |||||||
\(620\) | 2.62783e34 | 0.327115 | ||||||||
\(621\) | 4.68020e34 | 0.570978 | ||||||||
\(622\) | 1.67250e33 | 0.0199980 | ||||||||
\(623\) | −4.16118e34 | −0.487659 | ||||||||
\(624\) | 1.06618e33 | 0.0122468 | ||||||||
\(625\) | 3.55271e33 | 0.0400000 | ||||||||
\(626\) | 3.77177e34 | 0.416261 | ||||||||
\(627\) | 1.02816e35 | 1.11228 | ||||||||
\(628\) | −3.34074e34 | −0.354280 | ||||||||
\(629\) | 5.05648e34 | 0.525672 | ||||||||
\(630\) | 7.81279e33 | 0.0796249 | ||||||||
\(631\) | 8.43792e34 | 0.843080 | 0.421540 | − | 0.906810i | \(-0.361490\pi\) | ||||
0.421540 | + | 0.906810i | \(0.361490\pi\) | |||||||
\(632\) | −1.47341e34 | −0.144331 | ||||||||
\(633\) | −2.64492e35 | −2.54019 | ||||||||
\(634\) | 7.11707e34 | 0.670171 | ||||||||
\(635\) | −9.06746e34 | −0.837170 | ||||||||
\(636\) | 4.80154e34 | 0.434677 | ||||||||
\(637\) | −3.68365e33 | −0.0326991 | ||||||||
\(638\) | −1.15890e34 | −0.100876 | ||||||||
\(639\) | −6.02517e34 | −0.514291 | ||||||||
\(640\) | −4.72237e33 | −0.0395285 | ||||||||
\(641\) | −1.28702e35 | −1.05647 | −0.528236 | − | 0.849097i | \(-0.677147\pi\) | ||||
−0.528236 | + | 0.849097i | \(0.677147\pi\) | |||||||
\(642\) | 1.49829e35 | 1.20617 | ||||||||
\(643\) | 8.92172e34 | 0.704387 | 0.352194 | − | 0.935927i | \(-0.385436\pi\) | ||||
0.352194 | + | 0.935927i | \(0.385436\pi\) | |||||||
\(644\) | 3.37675e34 | 0.261473 | ||||||||
\(645\) | 1.30569e35 | 0.991614 | ||||||||
\(646\) | −3.75663e34 | −0.279828 | ||||||||
\(647\) | 1.63366e33 | 0.0119360 | 0.00596800 | − | 0.999982i | \(-0.498100\pi\) | ||||
0.00596800 | + | 0.999982i | \(0.498100\pi\) | |||||||
\(648\) | 5.97437e34 | 0.428159 | ||||||||
\(649\) | 2.91773e35 | 2.05110 | ||||||||
\(650\) | −7.71113e32 | −0.00531742 | ||||||||
\(651\) | −1.01722e35 | −0.688101 | ||||||||
\(652\) | 8.88855e33 | 0.0589842 | ||||||||
\(653\) | −1.93507e35 | −1.25974 | −0.629871 | − | 0.776700i | \(-0.716892\pi\) | ||||
−0.629871 | + | 0.776700i | \(0.716892\pi\) | |||||||
\(654\) | 3.47484e33 | 0.0221928 | ||||||||
\(655\) | 2.55647e34 | 0.160186 | ||||||||
\(656\) | −5.98458e33 | −0.0367905 | ||||||||
\(657\) | 1.93115e35 | 1.16479 | ||||||||
\(658\) | 2.86080e33 | 0.0169303 | ||||||||
\(659\) | 1.10886e35 | 0.643889 | 0.321944 | − | 0.946759i | \(-0.395664\pi\) | ||||
0.321944 | + | 0.946759i | \(0.395664\pi\) | |||||||
\(660\) | 7.46583e34 | 0.425382 | ||||||||
\(661\) | −1.40626e35 | −0.786224 | −0.393112 | − | 0.919490i | \(-0.628602\pi\) | ||||
−0.393112 | + | 0.919490i | \(0.628602\pi\) | |||||||
\(662\) | −2.30096e35 | −1.26236 | ||||||||
\(663\) | 6.15870e33 | 0.0331566 | ||||||||
\(664\) | −1.24026e35 | −0.655258 | ||||||||
\(665\) | −1.82073e34 | −0.0944006 | ||||||||
\(666\) | −7.52752e34 | −0.383022 | ||||||||
\(667\) | −2.83397e34 | −0.141521 | ||||||||
\(668\) | −1.42916e35 | −0.700449 | ||||||||
\(669\) | −2.68074e33 | −0.0128952 | ||||||||
\(670\) | 1.03138e35 | 0.486948 | ||||||||
\(671\) | 3.02308e34 | 0.140094 | ||||||||
\(672\) | 1.82801e34 | 0.0831500 | ||||||||
\(673\) | −1.02658e35 | −0.458358 | −0.229179 | − | 0.973384i | \(-0.573604\pi\) | ||||
−0.229179 | + | 0.973384i | \(0.573604\pi\) | |||||||
\(674\) | −1.71672e35 | −0.752403 | ||||||||
\(675\) | −1.83244e34 | −0.0788374 | ||||||||
\(676\) | −1.18220e35 | −0.499293 | ||||||||
\(677\) | −3.50696e35 | −1.45403 | −0.727014 | − | 0.686622i | \(-0.759093\pi\) | ||||
−0.727014 | + | 0.686622i | \(0.759093\pi\) | |||||||
\(678\) | 2.17608e34 | 0.0885735 | ||||||||
\(679\) | −5.43374e34 | −0.217133 | ||||||||
\(680\) | −2.72783e34 | −0.107018 | ||||||||
\(681\) | −2.81793e35 | −1.08540 | ||||||||
\(682\) | −3.99394e35 | −1.51042 | ||||||||
\(683\) | 1.09953e35 | 0.408270 | 0.204135 | − | 0.978943i | \(-0.434562\pi\) | ||||
0.204135 | + | 0.978943i | \(0.434562\pi\) | |||||||
\(684\) | 5.59245e34 | 0.203892 | ||||||||
\(685\) | 1.45094e34 | 0.0519420 | ||||||||
\(686\) | −1.35781e35 | −0.477295 | ||||||||
\(687\) | 4.04743e35 | 1.39708 | ||||||||
\(688\) | 1.25524e35 | 0.425471 | ||||||||
\(689\) | 7.53746e33 | 0.0250891 | ||||||||
\(690\) | 1.82570e35 | 0.596780 | ||||||||
\(691\) | 4.88341e35 | 1.56764 | 0.783822 | − | 0.620985i | \(-0.213267\pi\) | ||||
0.783822 | + | 0.620985i | \(0.213267\pi\) | |||||||
\(692\) | −2.51125e35 | −0.791705 | ||||||||
\(693\) | −1.18744e35 | −0.367659 | ||||||||
\(694\) | 6.99924e34 | 0.212842 | ||||||||
\(695\) | −1.01804e35 | −0.304056 | ||||||||
\(696\) | −1.53417e34 | −0.0450048 | ||||||||
\(697\) | −3.45694e34 | −0.0996051 | ||||||||
\(698\) | 3.34200e35 | 0.945831 | ||||||||
\(699\) | 2.94402e35 | 0.818420 | ||||||||
\(700\) | −1.32210e34 | −0.0361027 | ||||||||
\(701\) | −1.82400e35 | −0.489270 | −0.244635 | − | 0.969615i | \(-0.578668\pi\) | ||||
−0.244635 | + | 0.969615i | \(0.578668\pi\) | |||||||
\(702\) | 3.97729e33 | 0.0104803 | ||||||||
\(703\) | 1.75425e35 | 0.454098 | ||||||||
\(704\) | 7.17735e34 | 0.182518 | ||||||||
\(705\) | 1.54674e34 | 0.0386413 | ||||||||
\(706\) | −2.31027e35 | −0.567028 | ||||||||
\(707\) | −9.76239e34 | −0.235404 | ||||||||
\(708\) | 3.86255e35 | 0.915079 | ||||||||
\(709\) | 7.70973e35 | 1.79457 | 0.897287 | − | 0.441447i | \(-0.145535\pi\) | ||||
0.897287 | + | 0.441447i | \(0.145535\pi\) | |||||||
\(710\) | 1.01960e35 | 0.233184 | ||||||||
\(711\) | 1.26703e35 | 0.284718 | ||||||||
\(712\) | −2.16288e35 | −0.477564 | ||||||||
\(713\) | −9.76678e35 | −2.11901 | ||||||||
\(714\) | 1.05593e35 | 0.225117 | ||||||||
\(715\) | 1.17199e34 | 0.0245526 | ||||||||
\(716\) | 3.31281e35 | 0.681999 | ||||||||
\(717\) | 3.29880e35 | 0.667370 | ||||||||
\(718\) | −1.69023e35 | −0.336040 | ||||||||
\(719\) | 3.81081e35 | 0.744570 | 0.372285 | − | 0.928118i | \(-0.378574\pi\) | ||||
0.372285 | + | 0.928118i | \(0.378574\pi\) | |||||||
\(720\) | 4.06089e34 | 0.0779767 | ||||||||
\(721\) | 2.34074e35 | 0.441736 | ||||||||
\(722\) | 2.50912e35 | 0.465379 | ||||||||
\(723\) | −4.25598e35 | −0.775838 | ||||||||
\(724\) | 3.84190e35 | 0.688358 | ||||||||
\(725\) | 1.10959e34 | 0.0195405 | ||||||||
\(726\) | −6.02485e35 | −1.04289 | ||||||||
\(727\) | 2.79252e35 | 0.475133 | 0.237567 | − | 0.971371i | \(-0.423650\pi\) | ||||
0.237567 | + | 0.971371i | \(0.423650\pi\) | |||||||
\(728\) | 2.86961e33 | 0.00479933 | ||||||||
\(729\) | −2.01364e35 | −0.331046 | ||||||||
\(730\) | −3.26795e35 | −0.528128 | ||||||||
\(731\) | 7.25075e35 | 1.15190 | ||||||||
\(732\) | 4.00201e34 | 0.0625015 | ||||||||
\(733\) | 9.44086e35 | 1.44948 | 0.724739 | − | 0.689023i | \(-0.241960\pi\) | ||||
0.724739 | + | 0.689023i | \(0.241960\pi\) | |||||||
\(734\) | −4.52697e35 | −0.683293 | ||||||||
\(735\) | −3.41471e35 | −0.506713 | ||||||||
\(736\) | 1.75515e35 | 0.256060 | ||||||||
\(737\) | −1.56755e36 | −2.24843 | ||||||||
\(738\) | 5.14630e34 | 0.0725756 | ||||||||
\(739\) | −9.13826e35 | −1.26709 | −0.633546 | − | 0.773705i | \(-0.718401\pi\) | ||||
−0.633546 | + | 0.773705i | \(0.718401\pi\) | |||||||
\(740\) | 1.27383e35 | 0.173666 | ||||||||
\(741\) | 2.13664e34 | 0.0286421 | ||||||||
\(742\) | 1.29233e35 | 0.170342 | ||||||||
\(743\) | 3.11791e35 | 0.404114 | 0.202057 | − | 0.979374i | \(-0.435237\pi\) | ||||
0.202057 | + | 0.979374i | \(0.435237\pi\) | |||||||
\(744\) | −5.28725e35 | −0.673858 | ||||||||
\(745\) | −5.65722e35 | −0.709006 | ||||||||
\(746\) | 6.58530e34 | 0.0811597 | ||||||||
\(747\) | 1.06653e36 | 1.29261 | ||||||||
\(748\) | 4.14593e35 | 0.494142 | ||||||||
\(749\) | 4.03263e35 | 0.472678 | ||||||||
\(750\) | −7.14815e34 | −0.0824001 | ||||||||
\(751\) | 6.99901e35 | 0.793482 | 0.396741 | − | 0.917930i | \(-0.370141\pi\) | ||||
0.396741 | + | 0.917930i | \(0.370141\pi\) | |||||||
\(752\) | 1.48697e34 | 0.0165798 | ||||||||
\(753\) | −1.73960e36 | −1.90771 | ||||||||
\(754\) | −2.40834e33 | −0.00259763 | ||||||||
\(755\) | −4.22183e35 | −0.447882 | ||||||||
\(756\) | 6.81921e34 | 0.0711560 | ||||||||
\(757\) | 5.56975e35 | 0.571660 | 0.285830 | − | 0.958280i | \(-0.407731\pi\) | ||||
0.285830 | + | 0.958280i | \(0.407731\pi\) | |||||||
\(758\) | 9.31442e35 | 0.940353 | ||||||||
\(759\) | −2.77481e36 | −2.75556 | ||||||||
\(760\) | −9.46369e34 | −0.0924466 | ||||||||
\(761\) | 1.53099e36 | 1.47117 | 0.735586 | − | 0.677431i | \(-0.236907\pi\) | ||||
0.735586 | + | 0.677431i | \(0.236907\pi\) | |||||||
\(762\) | 1.82440e36 | 1.72457 | ||||||||
\(763\) | 9.35246e33 | 0.00869699 | ||||||||
\(764\) | 1.00794e36 | 0.922074 | ||||||||
\(765\) | 2.34573e35 | 0.211111 | ||||||||
\(766\) | −1.38700e36 | −1.22805 | ||||||||
\(767\) | 6.06344e34 | 0.0528174 | ||||||||
\(768\) | 9.50152e34 | 0.0814288 | ||||||||
\(769\) | −1.03936e36 | −0.876371 | −0.438185 | − | 0.898885i | \(-0.644379\pi\) | ||||
−0.438185 | + | 0.898885i | \(0.644379\pi\) | |||||||
\(770\) | 2.00941e35 | 0.166700 | ||||||||
\(771\) | 2.98804e34 | 0.0243897 | ||||||||
\(772\) | −1.00738e36 | −0.809052 | ||||||||
\(773\) | −6.50514e34 | −0.0514059 | −0.0257030 | − | 0.999670i | \(-0.508182\pi\) | ||||
−0.0257030 | + | 0.999670i | \(0.508182\pi\) | |||||||
\(774\) | −1.07941e36 | −0.839315 | ||||||||
\(775\) | 3.82399e35 | 0.292580 | ||||||||
\(776\) | −2.82432e35 | −0.212639 | ||||||||
\(777\) | −4.93093e35 | −0.365314 | ||||||||
\(778\) | 1.27036e36 | 0.926154 | ||||||||
\(779\) | −1.19932e35 | −0.0860432 | ||||||||
\(780\) | 1.55150e34 | 0.0109539 | ||||||||
\(781\) | −1.54965e36 | −1.07670 | ||||||||
\(782\) | 1.01385e36 | 0.693246 | ||||||||
\(783\) | −5.72308e34 | −0.0385131 | ||||||||
\(784\) | −3.28277e35 | −0.217415 | ||||||||
\(785\) | −4.86142e35 | −0.316878 | ||||||||
\(786\) | −5.14368e35 | −0.329984 | ||||||||
\(787\) | −2.59764e36 | −1.64019 | −0.820097 | − | 0.572224i | \(-0.806081\pi\) | ||||
−0.820097 | + | 0.572224i | \(0.806081\pi\) | |||||||
\(788\) | −6.19701e34 | −0.0385128 | ||||||||
\(789\) | −1.79833e36 | −1.10004 | ||||||||
\(790\) | −2.14410e35 | −0.129094 | ||||||||
\(791\) | 5.85688e34 | 0.0347104 | ||||||||
\(792\) | −6.17200e35 | −0.360048 | ||||||||
\(793\) | 6.28237e33 | 0.00360752 | ||||||||
\(794\) | 1.57520e36 | 0.890388 | ||||||||
\(795\) | 6.98716e35 | 0.388787 | ||||||||
\(796\) | −2.06034e35 | −0.112856 | ||||||||
\(797\) | 2.04990e36 | 1.10536 | 0.552680 | − | 0.833394i | \(-0.313605\pi\) | ||||
0.552680 | + | 0.833394i | \(0.313605\pi\) | |||||||
\(798\) | 3.66335e35 | 0.194466 | ||||||||
\(799\) | 8.58934e34 | 0.0448875 | ||||||||
\(800\) | −6.87195e34 | −0.0353553 | ||||||||
\(801\) | 1.85991e36 | 0.942077 | ||||||||
\(802\) | −1.49666e36 | −0.746352 | ||||||||
\(803\) | 4.96684e36 | 2.43857 | ||||||||
\(804\) | −2.07516e36 | −1.00311 | ||||||||
\(805\) | 4.91382e35 | 0.233868 | ||||||||
\(806\) | −8.29993e34 | −0.0388944 | ||||||||
\(807\) | 2.12319e36 | 0.979647 | ||||||||
\(808\) | −5.07424e35 | −0.230531 | ||||||||
\(809\) | 3.73106e35 | 0.166907 | 0.0834537 | − | 0.996512i | \(-0.473405\pi\) | ||||
0.0834537 | + | 0.996512i | \(0.473405\pi\) | |||||||
\(810\) | 8.69386e35 | 0.382957 | ||||||||
\(811\) | 2.01608e36 | 0.874474 | 0.437237 | − | 0.899346i | \(-0.355957\pi\) | ||||
0.437237 | + | 0.899346i | \(0.355957\pi\) | |||||||
\(812\) | −4.12919e34 | −0.0176366 | ||||||||
\(813\) | 3.47518e36 | 1.46166 | ||||||||
\(814\) | −1.93604e36 | −0.801882 | ||||||||
\(815\) | 1.29345e35 | 0.0527571 | ||||||||
\(816\) | 5.48846e35 | 0.220457 | ||||||||
\(817\) | 2.51551e36 | 0.995063 | ||||||||
\(818\) | 5.33163e34 | 0.0207703 | ||||||||
\(819\) | −2.46765e34 | −0.00946750 | ||||||||
\(820\) | −8.70871e34 | −0.0329064 | ||||||||
\(821\) | −5.48657e35 | −0.204179 | −0.102090 | − | 0.994775i | \(-0.532553\pi\) | ||||
−0.102090 | + | 0.994775i | \(0.532553\pi\) | |||||||
\(822\) | −2.91934e35 | −0.107001 | ||||||||
\(823\) | 1.67463e36 | 0.604535 | 0.302267 | − | 0.953223i | \(-0.402256\pi\) | ||||
0.302267 | + | 0.953223i | \(0.402256\pi\) | |||||||
\(824\) | 1.21666e36 | 0.432592 | ||||||||
\(825\) | 1.08642e36 | 0.380473 | ||||||||
\(826\) | 1.03960e36 | 0.358604 | ||||||||
\(827\) | −2.91183e35 | −0.0989345 | −0.0494673 | − | 0.998776i | \(-0.515752\pi\) | ||||
−0.0494673 | + | 0.998776i | \(0.515752\pi\) | |||||||
\(828\) | −1.50930e36 | −0.505122 | ||||||||
\(829\) | −5.85863e35 | −0.193136 | −0.0965682 | − | 0.995326i | \(-0.530787\pi\) | ||||
−0.0965682 | + | 0.995326i | \(0.530787\pi\) | |||||||
\(830\) | −1.80482e36 | −0.586080 | ||||||||
\(831\) | −1.99549e36 | −0.638317 | ||||||||
\(832\) | 1.49155e34 | 0.00469998 | ||||||||
\(833\) | −1.89626e36 | −0.588620 | ||||||||
\(834\) | 2.04832e36 | 0.626356 | ||||||||
\(835\) | −2.07971e36 | −0.626500 | ||||||||
\(836\) | 1.43835e36 | 0.426861 | ||||||||
\(837\) | −1.97236e36 | −0.576657 | ||||||||
\(838\) | −3.56355e36 | −1.02644 | ||||||||
\(839\) | 3.47157e36 | 0.985147 | 0.492574 | − | 0.870271i | \(-0.336056\pi\) | ||||
0.492574 | + | 0.870271i | \(0.336056\pi\) | |||||||
\(840\) | 2.66010e35 | 0.0743716 | ||||||||
\(841\) | −3.59571e36 | −0.990454 | ||||||||
\(842\) | 2.06751e36 | 0.561108 | ||||||||
\(843\) | −3.42055e36 | −0.914643 | ||||||||
\(844\) | −3.70014e36 | −0.974850 | ||||||||
\(845\) | −1.72032e36 | −0.446581 | ||||||||
\(846\) | −1.27869e35 | −0.0327065 | ||||||||
\(847\) | −1.62158e36 | −0.408691 | ||||||||
\(848\) | 6.71718e35 | 0.166816 | ||||||||
\(849\) | −1.61141e36 | −0.394331 | ||||||||
\(850\) | −3.96951e35 | −0.0957196 | ||||||||
\(851\) | −4.73441e36 | −1.12498 | ||||||||
\(852\) | −2.05145e36 | −0.480360 | ||||||||
\(853\) | 3.68459e35 | 0.0850210 | 0.0425105 | − | 0.999096i | \(-0.486464\pi\) | ||||
0.0425105 | + | 0.999096i | \(0.486464\pi\) | |||||||
\(854\) | 1.07713e35 | 0.0244933 | ||||||||
\(855\) | 8.13808e35 | 0.182367 | ||||||||
\(856\) | 2.09606e36 | 0.462893 | ||||||||
\(857\) | 2.02730e36 | 0.441222 | 0.220611 | − | 0.975362i | \(-0.429195\pi\) | ||||
0.220611 | + | 0.975362i | \(0.429195\pi\) | |||||||
\(858\) | −2.35807e35 | −0.0505784 | ||||||||
\(859\) | 7.42092e36 | 1.56871 | 0.784356 | − | 0.620311i | \(-0.212994\pi\) | ||||
0.784356 | + | 0.620311i | \(0.212994\pi\) | |||||||
\(860\) | 1.82661e36 | 0.380553 | ||||||||
\(861\) | 3.37111e35 | 0.0692202 | ||||||||
\(862\) | −3.52673e36 | −0.713726 | ||||||||
\(863\) | −9.61540e36 | −1.91793 | −0.958965 | − | 0.283526i | \(-0.908496\pi\) | ||||
−0.958965 | + | 0.283526i | \(0.908496\pi\) | |||||||
\(864\) | 3.54445e35 | 0.0696831 | ||||||||
\(865\) | −3.65435e36 | −0.708123 | ||||||||
\(866\) | 5.11218e36 | 0.976411 | ||||||||
\(867\) | −3.75013e36 | −0.706005 | ||||||||
\(868\) | −1.42305e36 | −0.264073 | ||||||||
\(869\) | 3.25873e36 | 0.596076 | ||||||||
\(870\) | −2.23251e35 | −0.0402535 | ||||||||
\(871\) | −3.25759e35 | −0.0578987 | ||||||||
\(872\) | 4.86117e34 | 0.00851696 | ||||||||
\(873\) | 2.42871e36 | 0.419466 | ||||||||
\(874\) | 3.51735e36 | 0.598856 | ||||||||
\(875\) | −1.92391e35 | −0.0322912 | ||||||||
\(876\) | 6.57519e36 | 1.08795 | ||||||||
\(877\) | −4.33793e36 | −0.707600 | −0.353800 | − | 0.935321i | \(-0.615111\pi\) | ||||
−0.353800 | + | 0.935321i | \(0.615111\pi\) | |||||||
\(878\) | −1.50110e36 | −0.241395 | ||||||||
\(879\) | 2.12369e36 | 0.336690 | ||||||||
\(880\) | 1.04444e36 | 0.163249 | ||||||||
\(881\) | 3.45165e36 | 0.531898 | 0.265949 | − | 0.963987i | \(-0.414315\pi\) | ||||
0.265949 | + | 0.963987i | \(0.414315\pi\) | |||||||
\(882\) | 2.82294e36 | 0.428888 | ||||||||
\(883\) | −1.53217e36 | −0.229509 | −0.114754 | − | 0.993394i | \(-0.536608\pi\) | ||||
−0.114754 | + | 0.993394i | \(0.536608\pi\) | |||||||
\(884\) | 8.61579e34 | 0.0127245 | ||||||||
\(885\) | 5.62075e36 | 0.818471 | ||||||||
\(886\) | −6.47742e36 | −0.929995 | ||||||||
\(887\) | −1.76030e35 | −0.0249196 | −0.0124598 | − | 0.999922i | \(-0.503966\pi\) | ||||
−0.0124598 | + | 0.999922i | \(0.503966\pi\) | |||||||
\(888\) | −2.56297e36 | −0.357752 | ||||||||
\(889\) | 4.91032e36 | 0.675831 | ||||||||
\(890\) | −3.14740e36 | −0.427146 | ||||||||
\(891\) | −1.32135e37 | −1.76826 | ||||||||
\(892\) | −3.75026e34 | −0.00494880 | ||||||||
\(893\) | 2.97991e35 | 0.0387757 | ||||||||
\(894\) | 1.13825e37 | 1.46055 | ||||||||
\(895\) | 4.82077e36 | 0.609998 | ||||||||
\(896\) | 2.55732e35 | 0.0319105 | ||||||||
\(897\) | −5.76642e35 | −0.0709579 | ||||||||
\(898\) | −8.32181e36 | −1.00987 | ||||||||
\(899\) | 1.19431e36 | 0.142929 | ||||||||
\(900\) | 5.90937e35 | 0.0697445 | ||||||||
\(901\) | 3.88011e36 | 0.451632 | ||||||||
\(902\) | 1.32361e36 | 0.151942 | ||||||||
\(903\) | −7.07072e36 | −0.800510 | ||||||||
\(904\) | 3.04426e35 | 0.0339919 | ||||||||
\(905\) | 5.59071e36 | 0.615686 | ||||||||
\(906\) | 8.49443e36 | 0.922638 | ||||||||
\(907\) | 4.42056e36 | 0.473572 | 0.236786 | − | 0.971562i | \(-0.423906\pi\) | ||||
0.236786 | + | 0.971562i | \(0.423906\pi\) | |||||||
\(908\) | −3.94219e36 | −0.416547 | ||||||||
\(909\) | 4.36348e36 | 0.454762 | ||||||||
\(910\) | 4.17583e34 | 0.00429265 | ||||||||
\(911\) | −4.66761e36 | −0.473277 | −0.236638 | − | 0.971598i | \(-0.576046\pi\) | ||||
−0.236638 | + | 0.971598i | \(0.576046\pi\) | |||||||
\(912\) | 1.90412e36 | 0.190440 | ||||||||
\(913\) | 2.74308e37 | 2.70616 | ||||||||
\(914\) | 5.24696e36 | 0.510600 | ||||||||
\(915\) | 5.82370e35 | 0.0559030 | ||||||||
\(916\) | 5.66221e36 | 0.536158 | ||||||||
\(917\) | −1.38441e36 | −0.129315 | ||||||||
\(918\) | 2.04742e36 | 0.188657 | ||||||||
\(919\) | −1.51994e36 | −0.138160 | −0.0690801 | − | 0.997611i | \(-0.522006\pi\) | ||||
−0.0690801 | + | 0.997611i | \(0.522006\pi\) | |||||||
\(920\) | 2.55408e36 | 0.229027 | ||||||||
\(921\) | −1.54405e37 | −1.36589 | ||||||||
\(922\) | 6.38538e36 | 0.557251 | ||||||||
\(923\) | −3.22038e35 | −0.0277259 | ||||||||
\(924\) | −4.04299e36 | −0.343402 | ||||||||
\(925\) | 1.85366e36 | 0.155331 | ||||||||
\(926\) | −2.33159e36 | −0.192759 | ||||||||
\(927\) | −1.04624e37 | −0.853361 | ||||||||
\(928\) | −2.14625e35 | −0.0172715 | ||||||||
\(929\) | −1.16057e37 | −0.921460 | −0.460730 | − | 0.887540i | \(-0.652412\pi\) | ||||
−0.460730 | + | 0.887540i | \(0.652412\pi\) | |||||||
\(930\) | −7.69396e36 | −0.602717 | ||||||||
\(931\) | −6.57872e36 | −0.508476 | ||||||||
\(932\) | 4.11858e36 | 0.314086 | ||||||||
\(933\) | −4.89689e35 | −0.0368468 | ||||||||
\(934\) | −8.54612e36 | −0.634502 | ||||||||
\(935\) | 6.03312e36 | 0.441974 | ||||||||
\(936\) | −1.28262e35 | −0.00927152 | ||||||||
\(937\) | 1.23945e36 | 0.0884062 | 0.0442031 | − | 0.999023i | \(-0.485925\pi\) | ||||
0.0442031 | + | 0.999023i | \(0.485925\pi\) | |||||||
\(938\) | −5.58525e36 | −0.393104 | ||||||||
\(939\) | −1.10433e37 | −0.766970 | ||||||||
\(940\) | 2.16383e35 | 0.0148294 | ||||||||
\(941\) | 1.07673e37 | 0.728176 | 0.364088 | − | 0.931365i | \(-0.381381\pi\) | ||||
0.364088 | + | 0.931365i | \(0.381381\pi\) | |||||||
\(942\) | 9.78129e36 | 0.652770 | ||||||||
\(943\) | 3.23675e36 | 0.213163 | ||||||||
\(944\) | 5.40357e36 | 0.351181 | ||||||||
\(945\) | 9.92326e35 | 0.0636439 | ||||||||
\(946\) | −2.77620e37 | −1.75716 | ||||||||
\(947\) | −2.09189e37 | −1.30667 | −0.653333 | − | 0.757071i | \(-0.726630\pi\) | ||||
−0.653333 | + | 0.757071i | \(0.726630\pi\) | |||||||
\(948\) | 4.31398e36 | 0.265934 | ||||||||
\(949\) | 1.03217e36 | 0.0627951 | ||||||||
\(950\) | −1.37715e36 | −0.0826867 | ||||||||
\(951\) | −2.08379e37 | −1.23480 | ||||||||
\(952\) | 1.47721e36 | 0.0863933 | ||||||||
\(953\) | 7.62955e36 | 0.440390 | 0.220195 | − | 0.975456i | \(-0.429331\pi\) | ||||
0.220195 | + | 0.975456i | \(0.429331\pi\) | |||||||
\(954\) | −5.77628e36 | −0.329074 | ||||||||
\(955\) | 1.46674e37 | 0.824728 | ||||||||
\(956\) | 4.61490e36 | 0.256117 | ||||||||
\(957\) | 3.39312e36 | 0.185866 | ||||||||
\(958\) | −2.00719e37 | −1.08522 | ||||||||
\(959\) | −7.85734e35 | −0.0419317 | ||||||||
\(960\) | 1.38265e36 | 0.0728321 | ||||||||
\(961\) | 2.19270e37 | 1.14008 | ||||||||
\(962\) | −4.02336e35 | −0.0206491 | ||||||||
\(963\) | −1.80245e37 | −0.913137 | ||||||||
\(964\) | −5.95397e36 | −0.297744 | ||||||||
\(965\) | −1.46593e37 | −0.723639 | ||||||||
\(966\) | −9.88674e36 | −0.481769 | ||||||||
\(967\) | 2.91319e37 | 1.40132 | 0.700661 | − | 0.713495i | \(-0.252889\pi\) | ||||
0.700661 | + | 0.713495i | \(0.252889\pi\) | |||||||
\(968\) | −8.42854e36 | −0.400231 | ||||||||
\(969\) | 1.09990e37 | 0.515590 | ||||||||
\(970\) | −4.10993e36 | −0.190190 | ||||||||
\(971\) | 2.71465e37 | 1.24015 | 0.620073 | − | 0.784544i | \(-0.287103\pi\) | ||||
0.620073 | + | 0.784544i | \(0.287103\pi\) | |||||||
\(972\) | −1.31221e37 | −0.591798 | ||||||||
\(973\) | 5.51300e36 | 0.245458 | ||||||||
\(974\) | 4.28882e36 | 0.188517 | ||||||||
\(975\) | 2.25773e35 | 0.00979747 | ||||||||
\(976\) | 5.59867e35 | 0.0239862 | ||||||||
\(977\) | 1.23101e37 | 0.520689 | 0.260344 | − | 0.965516i | \(-0.416164\pi\) | ||||
0.260344 | + | 0.965516i | \(0.416164\pi\) | |||||||
\(978\) | −2.60246e36 | −0.108680 | ||||||||
\(979\) | 4.78362e37 | 1.97230 | ||||||||
\(980\) | −4.77706e36 | −0.194462 | ||||||||
\(981\) | −4.18025e35 | −0.0168012 | ||||||||
\(982\) | 1.14111e37 | 0.452829 | ||||||||
\(983\) | −3.87996e37 | −1.52023 | −0.760114 | − | 0.649790i | \(-0.774857\pi\) | ||||
−0.760114 | + | 0.649790i | \(0.774857\pi\) | |||||||
\(984\) | 1.75222e36 | 0.0677874 | ||||||||
\(985\) | −9.01784e35 | −0.0344469 | ||||||||
\(986\) | −1.23976e36 | −0.0467602 | ||||||||
\(987\) | −8.37608e35 | −0.0311944 | ||||||||
\(988\) | 2.98909e35 | 0.0109920 | ||||||||
\(989\) | −6.78891e37 | −2.46517 | ||||||||
\(990\) | −8.98144e36 | −0.322037 | ||||||||
\(991\) | 2.23853e35 | 0.00792577 | 0.00396288 | − | 0.999992i | \(-0.498739\pi\) | ||||
0.00396288 | + | 0.999992i | \(0.498739\pi\) | |||||||
\(992\) | −7.39667e36 | −0.258607 | ||||||||
\(993\) | 6.73695e37 | 2.32594 | ||||||||
\(994\) | −5.52145e36 | −0.188245 | ||||||||
\(995\) | −2.99819e36 | −0.100942 | ||||||||
\(996\) | 3.63134e37 | 1.20733 | ||||||||
\(997\) | −2.76187e37 | −0.906806 | −0.453403 | − | 0.891306i | \(-0.649790\pi\) | ||||
−0.453403 | + | 0.891306i | \(0.649790\pi\) | |||||||
\(998\) | 1.10805e37 | 0.359274 | ||||||||
\(999\) | −9.56094e36 | −0.306148 |
(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 | 10.26.a.b.1.2 | ✓ | 2 | |
5.2 | odd | 4 | 50.26.b.f.49.1 | 4 | |||
5.3 | odd | 4 | 50.26.b.f.49.4 | 4 | |||
5.4 | even | 2 | 50.26.a.f.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
10.26.a.b.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
50.26.a.f.1.1 | 2 | 5.4 | even | 2 | |||
50.26.b.f.49.1 | 4 | 5.2 | odd | 4 | |||
50.26.b.f.49.4 | 4 | 5.3 | odd | 4 |