Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,22,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(8.38432032861\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{649}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{2} - x - 162 \)
|
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2\cdot 3^{2}\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-12.2377\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1937.96 | 1.33822 | 0.669112 | − | 0.743162i | \(-0.266675\pi\) | ||||
0.669112 | + | 0.743162i | \(0.266675\pi\) | |||||||
\(3\) | 59049.0 | 0.577350 | ||||||||
\(4\) | 1.65852e6 | 0.790843 | ||||||||
\(5\) | 2.22745e7 | 1.02005 | 0.510026 | − | 0.860159i | \(-0.329636\pi\) | ||||
0.510026 | + | 0.860159i | \(0.329636\pi\) | |||||||
\(6\) | 1.14434e8 | 0.772624 | ||||||||
\(7\) | 4.78205e7 | 0.0639860 | 0.0319930 | − | 0.999488i | \(-0.489815\pi\) | ||||
0.0319930 | + | 0.999488i | \(0.489815\pi\) | |||||||
\(8\) | −8.50053e8 | −0.279899 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 4.31669e10 | 1.36506 | ||||||||
\(11\) | 1.60111e11 | 1.86122 | 0.930609 | − | 0.366016i | \(-0.119278\pi\) | ||||
0.930609 | + | 0.366016i | \(0.119278\pi\) | |||||||
\(12\) | 9.79338e10 | 0.456593 | ||||||||
\(13\) | −7.86968e11 | −1.58326 | −0.791630 | − | 0.611001i | \(-0.790767\pi\) | ||||
−0.791630 | + | 0.611001i | \(0.790767\pi\) | |||||||
\(14\) | 9.26741e10 | 0.0856276 | ||||||||
\(15\) | 1.31529e12 | 0.588927 | ||||||||
\(16\) | −5.12553e12 | −1.16541 | ||||||||
\(17\) | −2.97477e12 | −0.357881 | −0.178941 | − | 0.983860i | \(-0.557267\pi\) | ||||
−0.178941 | + | 0.983860i | \(0.557267\pi\) | |||||||
\(18\) | 6.75723e12 | 0.446075 | ||||||||
\(19\) | −2.99456e13 | −1.12052 | −0.560260 | − | 0.828317i | \(-0.689299\pi\) | ||||
−0.560260 | + | 0.828317i | \(0.689299\pi\) | |||||||
\(20\) | 3.69426e13 | 0.806701 | ||||||||
\(21\) | 2.82376e12 | 0.0369423 | ||||||||
\(22\) | 3.10287e14 | 2.49073 | ||||||||
\(23\) | −1.91401e14 | −0.963390 | −0.481695 | − | 0.876339i | \(-0.659979\pi\) | ||||
−0.481695 | + | 0.876339i | \(0.659979\pi\) | |||||||
\(24\) | −5.01948e13 | −0.161600 | ||||||||
\(25\) | 1.93148e13 | 0.0405061 | ||||||||
\(26\) | −1.52511e15 | −2.11876 | ||||||||
\(27\) | 2.05891e14 | 0.192450 | ||||||||
\(28\) | 7.93112e13 | 0.0506029 | ||||||||
\(29\) | 9.68170e14 | 0.427339 | 0.213670 | − | 0.976906i | \(-0.431458\pi\) | ||||
0.213670 | + | 0.976906i | \(0.431458\pi\) | |||||||
\(30\) | 2.54896e15 | 0.788117 | ||||||||
\(31\) | 2.80459e15 | 0.614570 | 0.307285 | − | 0.951618i | \(-0.400580\pi\) | ||||
0.307285 | + | 0.951618i | \(0.400580\pi\) | |||||||
\(32\) | −8.15035e15 | −1.27968 | ||||||||
\(33\) | 9.45437e15 | 1.07457 | ||||||||
\(34\) | −5.76496e15 | −0.478925 | ||||||||
\(35\) | 1.06518e15 | 0.0652691 | ||||||||
\(36\) | 5.78290e15 | 0.263614 | ||||||||
\(37\) | 3.05038e16 | 1.04288 | 0.521441 | − | 0.853287i | \(-0.325395\pi\) | ||||
0.521441 | + | 0.853287i | \(0.325395\pi\) | |||||||
\(38\) | −5.80331e16 | −1.49951 | ||||||||
\(39\) | −4.64697e16 | −0.914095 | ||||||||
\(40\) | −1.89345e16 | −0.285511 | ||||||||
\(41\) | −2.22806e16 | −0.259237 | −0.129618 | − | 0.991564i | \(-0.541375\pi\) | ||||
−0.129618 | + | 0.991564i | \(0.541375\pi\) | |||||||
\(42\) | 5.47231e15 | 0.0494371 | ||||||||
\(43\) | 1.63711e17 | 1.15521 | 0.577604 | − | 0.816317i | \(-0.303988\pi\) | ||||
0.577604 | + | 0.816317i | \(0.303988\pi\) | |||||||
\(44\) | 2.65546e17 | 1.47193 | ||||||||
\(45\) | 7.76663e16 | 0.340017 | ||||||||
\(46\) | −3.70927e17 | −1.28923 | ||||||||
\(47\) | 4.08678e17 | 1.13332 | 0.566662 | − | 0.823951i | \(-0.308235\pi\) | ||||
0.566662 | + | 0.823951i | \(0.308235\pi\) | |||||||
\(48\) | −3.02657e17 | −0.672850 | ||||||||
\(49\) | −5.56259e17 | −0.995906 | ||||||||
\(50\) | 3.74313e16 | 0.0542063 | ||||||||
\(51\) | −1.75657e17 | −0.206623 | ||||||||
\(52\) | −1.30520e18 | −1.25211 | ||||||||
\(53\) | 4.34009e17 | 0.340881 | 0.170440 | − | 0.985368i | \(-0.445481\pi\) | ||||
0.170440 | + | 0.985368i | \(0.445481\pi\) | |||||||
\(54\) | 3.99008e17 | 0.257541 | ||||||||
\(55\) | 3.56638e18 | 1.89854 | ||||||||
\(56\) | −4.06500e16 | −0.0179096 | ||||||||
\(57\) | −1.76826e18 | −0.646932 | ||||||||
\(58\) | 1.87627e18 | 0.571875 | ||||||||
\(59\) | −5.14341e18 | −1.31010 | −0.655051 | − | 0.755584i | \(-0.727353\pi\) | ||||
−0.655051 | + | 0.755584i | \(0.727353\pi\) | |||||||
\(60\) | 2.18142e18 | 0.465749 | ||||||||
\(61\) | 1.98980e18 | 0.357147 | 0.178573 | − | 0.983927i | \(-0.442852\pi\) | ||||
0.178573 | + | 0.983927i | \(0.442852\pi\) | |||||||
\(62\) | 5.43517e18 | 0.822432 | ||||||||
\(63\) | 1.66740e17 | 0.0213287 | ||||||||
\(64\) | −5.04601e18 | −0.547089 | ||||||||
\(65\) | −1.75293e19 | −1.61501 | ||||||||
\(66\) | 1.83222e19 | 1.43802 | ||||||||
\(67\) | −1.36361e19 | −0.913913 | −0.456956 | − | 0.889489i | \(-0.651060\pi\) | ||||
−0.456956 | + | 0.889489i | \(0.651060\pi\) | |||||||
\(68\) | −4.93370e18 | −0.283028 | ||||||||
\(69\) | −1.13020e19 | −0.556213 | ||||||||
\(70\) | 2.06427e18 | 0.0873446 | ||||||||
\(71\) | 7.35641e18 | 0.268196 | 0.134098 | − | 0.990968i | \(-0.457186\pi\) | ||||
0.134098 | + | 0.990968i | \(0.457186\pi\) | |||||||
\(72\) | −2.96395e18 | −0.0932996 | ||||||||
\(73\) | 6.81650e19 | 1.85640 | 0.928200 | − | 0.372081i | \(-0.121356\pi\) | ||||
0.928200 | + | 0.372081i | \(0.121356\pi\) | |||||||
\(74\) | 5.91149e19 | 1.39561 | ||||||||
\(75\) | 1.14052e18 | 0.0233862 | ||||||||
\(76\) | −4.96652e19 | −0.886155 | ||||||||
\(77\) | 7.65658e18 | 0.119092 | ||||||||
\(78\) | −9.00562e19 | −1.22326 | ||||||||
\(79\) | −2.12282e19 | −0.252249 | −0.126124 | − | 0.992014i | \(-0.540254\pi\) | ||||
−0.126124 | + | 0.992014i | \(0.540254\pi\) | |||||||
\(80\) | −1.14168e20 | −1.18878 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | −4.31789e19 | −0.346917 | ||||||||
\(83\) | 1.10803e20 | 0.783849 | 0.391924 | − | 0.919997i | \(-0.371809\pi\) | ||||
0.391924 | + | 0.919997i | \(0.371809\pi\) | |||||||
\(84\) | 4.68325e18 | 0.0292156 | ||||||||
\(85\) | −6.62613e19 | −0.365058 | ||||||||
\(86\) | 3.17266e20 | 1.54593 | ||||||||
\(87\) | 5.71695e19 | 0.246724 | ||||||||
\(88\) | −1.36102e20 | −0.520952 | ||||||||
\(89\) | −7.67205e18 | −0.0260805 | −0.0130403 | − | 0.999915i | \(-0.504151\pi\) | ||||
−0.0130403 | + | 0.999915i | \(0.504151\pi\) | |||||||
\(90\) | 1.50514e20 | 0.455019 | ||||||||
\(91\) | −3.76333e19 | −0.101306 | ||||||||
\(92\) | −3.17442e20 | −0.761890 | ||||||||
\(93\) | 1.65608e20 | 0.354822 | ||||||||
\(94\) | 7.92000e20 | 1.51664 | ||||||||
\(95\) | −6.67021e20 | −1.14299 | ||||||||
\(96\) | −4.81270e20 | −0.738824 | ||||||||
\(97\) | 4.63755e20 | 0.638535 | 0.319268 | − | 0.947665i | \(-0.396563\pi\) | ||||
0.319268 | + | 0.947665i | \(0.396563\pi\) | |||||||
\(98\) | −1.07801e21 | −1.33274 | ||||||||
\(99\) | 5.58271e20 | 0.620406 | ||||||||
\(100\) | 3.20340e19 | 0.0320340 | ||||||||
\(101\) | 1.75642e20 | 0.158217 | 0.0791086 | − | 0.996866i | \(-0.474793\pi\) | ||||
0.0791086 | + | 0.996866i | \(0.474793\pi\) | |||||||
\(102\) | −3.40415e20 | −0.276508 | ||||||||
\(103\) | −1.29018e21 | −0.945933 | −0.472967 | − | 0.881080i | \(-0.656817\pi\) | ||||
−0.472967 | + | 0.881080i | \(0.656817\pi\) | |||||||
\(104\) | 6.68965e20 | 0.443152 | ||||||||
\(105\) | 6.28976e19 | 0.0376831 | ||||||||
\(106\) | 8.41091e20 | 0.456175 | ||||||||
\(107\) | 5.76913e19 | 0.0283518 | 0.0141759 | − | 0.999900i | \(-0.495488\pi\) | ||||
0.0141759 | + | 0.999900i | \(0.495488\pi\) | |||||||
\(108\) | 3.41474e20 | 0.152198 | ||||||||
\(109\) | −5.74941e20 | −0.232619 | −0.116309 | − | 0.993213i | \(-0.537106\pi\) | ||||
−0.116309 | + | 0.993213i | \(0.537106\pi\) | |||||||
\(110\) | 6.91148e21 | 2.54067 | ||||||||
\(111\) | 1.80122e21 | 0.602109 | ||||||||
\(112\) | −2.45106e20 | −0.0745700 | ||||||||
\(113\) | −4.56755e21 | −1.26578 | −0.632892 | − | 0.774240i | \(-0.718132\pi\) | ||||
−0.632892 | + | 0.774240i | \(0.718132\pi\) | |||||||
\(114\) | −3.42680e21 | −0.865740 | ||||||||
\(115\) | −4.26336e21 | −0.982708 | ||||||||
\(116\) | 1.60573e21 | 0.337958 | ||||||||
\(117\) | −2.74399e21 | −0.527753 | ||||||||
\(118\) | −9.96770e21 | −1.75321 | ||||||||
\(119\) | −1.42255e20 | −0.0228994 | ||||||||
\(120\) | −1.11806e21 | −0.164840 | ||||||||
\(121\) | 1.82352e22 | 2.46413 | ||||||||
\(122\) | 3.85615e21 | 0.477942 | ||||||||
\(123\) | −1.31565e21 | −0.149671 | ||||||||
\(124\) | 4.65146e21 | 0.486028 | ||||||||
\(125\) | −1.01911e22 | −0.978734 | ||||||||
\(126\) | 3.23134e20 | 0.0285425 | ||||||||
\(127\) | 1.84938e22 | 1.50344 | 0.751722 | − | 0.659480i | \(-0.229224\pi\) | ||||
0.751722 | + | 0.659480i | \(0.229224\pi\) | |||||||
\(128\) | 7.31359e21 | 0.547553 | ||||||||
\(129\) | 9.66700e21 | 0.666960 | ||||||||
\(130\) | −3.39710e22 | −2.16124 | ||||||||
\(131\) | −1.25296e22 | −0.735509 | −0.367754 | − | 0.929923i | \(-0.619873\pi\) | ||||
−0.367754 | + | 0.929923i | \(0.619873\pi\) | |||||||
\(132\) | 1.56802e22 | 0.849820 | ||||||||
\(133\) | −1.43201e21 | −0.0716976 | ||||||||
\(134\) | −2.64261e22 | −1.22302 | ||||||||
\(135\) | 4.58612e21 | 0.196309 | ||||||||
\(136\) | 2.52871e21 | 0.100171 | ||||||||
\(137\) | 3.84075e22 | 1.40880 | 0.704402 | − | 0.709801i | \(-0.251215\pi\) | ||||
0.704402 | + | 0.709801i | \(0.251215\pi\) | |||||||
\(138\) | −2.19028e22 | −0.744338 | ||||||||
\(139\) | −9.58856e21 | −0.302063 | −0.151032 | − | 0.988529i | \(-0.548260\pi\) | ||||
−0.151032 | + | 0.988529i | \(0.548260\pi\) | |||||||
\(140\) | 1.76662e21 | 0.0516176 | ||||||||
\(141\) | 2.41320e22 | 0.654324 | ||||||||
\(142\) | 1.42564e22 | 0.358907 | ||||||||
\(143\) | −1.26002e23 | −2.94679 | ||||||||
\(144\) | −1.78716e22 | −0.388470 | ||||||||
\(145\) | 2.15655e22 | 0.435908 | ||||||||
\(146\) | 1.32101e23 | 2.48428 | ||||||||
\(147\) | −3.28465e22 | −0.574986 | ||||||||
\(148\) | 5.05911e22 | 0.824757 | ||||||||
\(149\) | 3.44428e22 | 0.523170 | 0.261585 | − | 0.965180i | \(-0.415755\pi\) | ||||
0.261585 | + | 0.965180i | \(0.415755\pi\) | |||||||
\(150\) | 2.21028e21 | 0.0312960 | ||||||||
\(151\) | −3.63152e22 | −0.479546 | −0.239773 | − | 0.970829i | \(-0.577073\pi\) | ||||
−0.239773 | + | 0.970829i | \(0.577073\pi\) | |||||||
\(152\) | 2.54553e22 | 0.313632 | ||||||||
\(153\) | −1.03724e22 | −0.119294 | ||||||||
\(154\) | 1.48381e22 | 0.159372 | ||||||||
\(155\) | 6.24707e22 | 0.626893 | ||||||||
\(156\) | −7.70708e22 | −0.722906 | ||||||||
\(157\) | −9.41986e22 | −0.826225 | −0.413112 | − | 0.910680i | \(-0.635558\pi\) | ||||
−0.413112 | + | 0.910680i | \(0.635558\pi\) | |||||||
\(158\) | −4.11393e22 | −0.337565 | ||||||||
\(159\) | 2.56278e22 | 0.196808 | ||||||||
\(160\) | −1.81545e23 | −1.30534 | ||||||||
\(161\) | −9.15290e21 | −0.0616435 | ||||||||
\(162\) | 2.35610e22 | 0.148692 | ||||||||
\(163\) | −1.80771e23 | −1.06945 | −0.534723 | − | 0.845027i | \(-0.679584\pi\) | ||||
−0.534723 | + | 0.845027i | \(0.679584\pi\) | |||||||
\(164\) | −3.69528e22 | −0.205016 | ||||||||
\(165\) | 2.10591e23 | 1.09612 | ||||||||
\(166\) | 2.14732e23 | 1.04897 | ||||||||
\(167\) | 3.71934e22 | 0.170586 | 0.0852929 | − | 0.996356i | \(-0.472817\pi\) | ||||
0.0852929 | + | 0.996356i | \(0.472817\pi\) | |||||||
\(168\) | −2.40034e21 | −0.0103401 | ||||||||
\(169\) | 3.72255e23 | 1.50671 | ||||||||
\(170\) | −1.28412e23 | −0.488529 | ||||||||
\(171\) | −1.04414e23 | −0.373507 | ||||||||
\(172\) | 2.71518e23 | 0.913589 | ||||||||
\(173\) | 2.58398e23 | 0.818096 | 0.409048 | − | 0.912513i | \(-0.365861\pi\) | ||||
0.409048 | + | 0.912513i | \(0.365861\pi\) | |||||||
\(174\) | 1.10792e23 | 0.330172 | ||||||||
\(175\) | 9.23645e20 | 0.00259183 | ||||||||
\(176\) | −8.20652e23 | −2.16908 | ||||||||
\(177\) | −3.03713e23 | −0.756388 | ||||||||
\(178\) | −1.48681e22 | −0.0349016 | ||||||||
\(179\) | −3.35184e23 | −0.741868 | −0.370934 | − | 0.928659i | \(-0.620962\pi\) | ||||
−0.370934 | + | 0.928659i | \(0.620962\pi\) | |||||||
\(180\) | 1.28811e23 | 0.268900 | ||||||||
\(181\) | −1.92267e23 | −0.378687 | −0.189343 | − | 0.981911i | \(-0.560636\pi\) | ||||
−0.189343 | + | 0.981911i | \(0.560636\pi\) | |||||||
\(182\) | −7.29316e22 | −0.135571 | ||||||||
\(183\) | 1.17496e23 | 0.206199 | ||||||||
\(184\) | 1.62701e23 | 0.269652 | ||||||||
\(185\) | 6.79455e23 | 1.06379 | ||||||||
\(186\) | 3.20941e23 | 0.474831 | ||||||||
\(187\) | −4.76292e23 | −0.666095 | ||||||||
\(188\) | 6.77800e23 | 0.896281 | ||||||||
\(189\) | 9.84583e21 | 0.0123141 | ||||||||
\(190\) | −1.29266e24 | −1.52957 | ||||||||
\(191\) | −4.60821e23 | −0.516038 | −0.258019 | − | 0.966140i | \(-0.583070\pi\) | ||||
−0.258019 | + | 0.966140i | \(0.583070\pi\) | |||||||
\(192\) | −2.97962e23 | −0.315862 | ||||||||
\(193\) | 1.29600e24 | 1.30093 | 0.650465 | − | 0.759536i | \(-0.274574\pi\) | ||||
0.650465 | + | 0.759536i | \(0.274574\pi\) | |||||||
\(194\) | 8.98736e23 | 0.854503 | ||||||||
\(195\) | −1.03509e24 | −0.932425 | ||||||||
\(196\) | −9.22566e23 | −0.787605 | ||||||||
\(197\) | 2.05711e24 | 1.66480 | 0.832402 | − | 0.554172i | \(-0.186965\pi\) | ||||
0.832402 | + | 0.554172i | \(0.186965\pi\) | |||||||
\(198\) | 1.08190e24 | 0.830242 | ||||||||
\(199\) | 5.34557e22 | 0.0389078 | 0.0194539 | − | 0.999811i | \(-0.493807\pi\) | ||||
0.0194539 | + | 0.999811i | \(0.493807\pi\) | |||||||
\(200\) | −1.64186e22 | −0.0113376 | ||||||||
\(201\) | −8.05198e23 | −0.527648 | ||||||||
\(202\) | 3.40386e23 | 0.211730 | ||||||||
\(203\) | 4.62984e22 | 0.0273437 | ||||||||
\(204\) | −2.91330e23 | −0.163406 | ||||||||
\(205\) | −4.96289e23 | −0.264435 | ||||||||
\(206\) | −2.50032e24 | −1.26587 | ||||||||
\(207\) | −6.67374e23 | −0.321130 | ||||||||
\(208\) | 4.03363e24 | 1.84515 | ||||||||
\(209\) | −4.79460e24 | −2.08553 | ||||||||
\(210\) | 1.21893e23 | 0.0504284 | ||||||||
\(211\) | −3.16142e24 | −1.24427 | −0.622137 | − | 0.782908i | \(-0.713735\pi\) | ||||
−0.622137 | + | 0.782908i | \(0.713735\pi\) | |||||||
\(212\) | 7.19813e23 | 0.269583 | ||||||||
\(213\) | 4.34388e23 | 0.154843 | ||||||||
\(214\) | 1.11803e23 | 0.0379410 | ||||||||
\(215\) | 3.64659e24 | 1.17837 | ||||||||
\(216\) | −1.75018e23 | −0.0538665 | ||||||||
\(217\) | 1.34117e23 | 0.0393239 | ||||||||
\(218\) | −1.11421e24 | −0.311296 | ||||||||
\(219\) | 4.02508e24 | 1.07179 | ||||||||
\(220\) | 5.91491e24 | 1.50145 | ||||||||
\(221\) | 2.34105e24 | 0.566619 | ||||||||
\(222\) | 3.49068e24 | 0.805756 | ||||||||
\(223\) | −3.10623e24 | −0.683963 | −0.341981 | − | 0.939707i | \(-0.611098\pi\) | ||||
−0.341981 | + | 0.939707i | \(0.611098\pi\) | |||||||
\(224\) | −3.89754e23 | −0.0818817 | ||||||||
\(225\) | 6.73466e22 | 0.0135020 | ||||||||
\(226\) | −8.85171e24 | −1.69390 | ||||||||
\(227\) | −2.04882e24 | −0.374310 | −0.187155 | − | 0.982330i | \(-0.559927\pi\) | ||||
−0.187155 | + | 0.982330i | \(0.559927\pi\) | |||||||
\(228\) | −2.93268e24 | −0.511622 | ||||||||
\(229\) | 4.12622e24 | 0.687512 | 0.343756 | − | 0.939059i | \(-0.388301\pi\) | ||||
0.343756 | + | 0.939059i | \(0.388301\pi\) | |||||||
\(230\) | −8.26219e24 | −1.31508 | ||||||||
\(231\) | 4.52113e23 | 0.0687577 | ||||||||
\(232\) | −8.22995e23 | −0.119612 | ||||||||
\(233\) | 3.43270e24 | 0.476869 | 0.238434 | − | 0.971159i | \(-0.423366\pi\) | ||||
0.238434 | + | 0.971159i | \(0.423366\pi\) | |||||||
\(234\) | −5.31773e24 | −0.706252 | ||||||||
\(235\) | 9.10308e24 | 1.15605 | ||||||||
\(236\) | −8.53044e24 | −1.03609 | ||||||||
\(237\) | −1.25351e24 | −0.145636 | ||||||||
\(238\) | −2.75684e23 | −0.0306445 | ||||||||
\(239\) | 8.29149e24 | 0.881972 | 0.440986 | − | 0.897514i | \(-0.354629\pi\) | ||||
0.440986 | + | 0.897514i | \(0.354629\pi\) | |||||||
\(240\) | −6.74153e24 | −0.686342 | ||||||||
\(241\) | −1.30526e25 | −1.27209 | −0.636045 | − | 0.771652i | \(-0.719431\pi\) | ||||
−0.636045 | + | 0.771652i | \(0.719431\pi\) | |||||||
\(242\) | 3.53389e25 | 3.29756 | ||||||||
\(243\) | 7.17898e23 | 0.0641500 | ||||||||
\(244\) | 3.30012e24 | 0.282447 | ||||||||
\(245\) | −1.23904e25 | −1.01588 | ||||||||
\(246\) | −2.54967e24 | −0.200293 | ||||||||
\(247\) | 2.35662e25 | 1.77407 | ||||||||
\(248\) | −2.38405e24 | −0.172017 | ||||||||
\(249\) | 6.54282e24 | 0.452555 | ||||||||
\(250\) | −1.97498e25 | −1.30976 | ||||||||
\(251\) | −1.77630e25 | −1.12965 | −0.564823 | − | 0.825212i | \(-0.691056\pi\) | ||||
−0.564823 | + | 0.825212i | \(0.691056\pi\) | |||||||
\(252\) | 2.76541e23 | 0.0168676 | ||||||||
\(253\) | −3.06453e25 | −1.79308 | ||||||||
\(254\) | 3.58402e25 | 2.01194 | ||||||||
\(255\) | −3.91267e24 | −0.210766 | ||||||||
\(256\) | 2.47557e25 | 1.27984 | ||||||||
\(257\) | −5.70058e24 | −0.282893 | −0.141446 | − | 0.989946i | \(-0.545175\pi\) | ||||
−0.141446 | + | 0.989946i | \(0.545175\pi\) | |||||||
\(258\) | 1.87342e25 | 0.892542 | ||||||||
\(259\) | 1.45871e24 | 0.0667299 | ||||||||
\(260\) | −2.90727e25 | −1.27722 | ||||||||
\(261\) | 3.37580e24 | 0.142446 | ||||||||
\(262\) | −2.42818e25 | −0.984275 | ||||||||
\(263\) | 9.73572e23 | 0.0379169 | 0.0189584 | − | 0.999820i | \(-0.493965\pi\) | ||||
0.0189584 | + | 0.999820i | \(0.493965\pi\) | |||||||
\(264\) | −8.03672e24 | −0.300772 | ||||||||
\(265\) | 9.66733e24 | 0.347716 | ||||||||
\(266\) | −2.77518e24 | −0.0959474 | ||||||||
\(267\) | −4.53027e23 | −0.0150576 | ||||||||
\(268\) | −2.26157e25 | −0.722761 | ||||||||
\(269\) | −5.78587e25 | −1.77816 | −0.889078 | − | 0.457756i | \(-0.848653\pi\) | ||||
−0.889078 | + | 0.457756i | \(0.848653\pi\) | |||||||
\(270\) | 8.88769e24 | 0.262706 | ||||||||
\(271\) | 4.29033e25 | 1.21987 | 0.609934 | − | 0.792452i | \(-0.291196\pi\) | ||||
0.609934 | + | 0.792452i | \(0.291196\pi\) | |||||||
\(272\) | 1.52473e25 | 0.417079 | ||||||||
\(273\) | −2.22221e24 | −0.0584893 | ||||||||
\(274\) | 7.44321e25 | 1.88530 | ||||||||
\(275\) | 3.09251e24 | 0.0753907 | ||||||||
\(276\) | −1.87446e25 | −0.439877 | ||||||||
\(277\) | 6.39000e25 | 1.44366 | 0.721828 | − | 0.692073i | \(-0.243302\pi\) | ||||
0.721828 | + | 0.692073i | \(0.243302\pi\) | |||||||
\(278\) | −1.85822e25 | −0.404228 | ||||||||
\(279\) | 9.77899e24 | 0.204857 | ||||||||
\(280\) | −9.05457e23 | −0.0182687 | ||||||||
\(281\) | 3.23104e25 | 0.627951 | 0.313976 | − | 0.949431i | \(-0.398339\pi\) | ||||
0.313976 | + | 0.949431i | \(0.398339\pi\) | |||||||
\(282\) | 4.67668e25 | 0.875632 | ||||||||
\(283\) | −1.00627e25 | −0.181534 | −0.0907668 | − | 0.995872i | \(-0.528932\pi\) | ||||
−0.0907668 | + | 0.995872i | \(0.528932\pi\) | |||||||
\(284\) | 1.22007e25 | 0.212101 | ||||||||
\(285\) | −3.93869e25 | −0.659905 | ||||||||
\(286\) | −2.44186e26 | −3.94346 | ||||||||
\(287\) | −1.06547e24 | −0.0165875 | ||||||||
\(288\) | −2.84185e25 | −0.426560 | ||||||||
\(289\) | −6.02427e25 | −0.871921 | ||||||||
\(290\) | 4.17929e25 | 0.583343 | ||||||||
\(291\) | 2.73842e25 | 0.368659 | ||||||||
\(292\) | 1.13053e26 | 1.46812 | ||||||||
\(293\) | 4.93011e25 | 0.617656 | 0.308828 | − | 0.951118i | \(-0.400063\pi\) | ||||
0.308828 | + | 0.951118i | \(0.400063\pi\) | |||||||
\(294\) | −6.36551e25 | −0.769461 | ||||||||
\(295\) | −1.14567e26 | −1.33637 | ||||||||
\(296\) | −2.59298e25 | −0.291902 | ||||||||
\(297\) | 3.29654e25 | 0.358191 | ||||||||
\(298\) | 6.67487e25 | 0.700119 | ||||||||
\(299\) | 1.50627e26 | 1.52530 | ||||||||
\(300\) | 1.89158e24 | 0.0184948 | ||||||||
\(301\) | 7.82877e24 | 0.0739172 | ||||||||
\(302\) | −7.03772e25 | −0.641740 | ||||||||
\(303\) | 1.03715e25 | 0.0913467 | ||||||||
\(304\) | 1.53487e26 | 1.30587 | ||||||||
\(305\) | 4.43218e25 | 0.364308 | ||||||||
\(306\) | −2.01012e25 | −0.159642 | ||||||||
\(307\) | −1.49828e25 | −0.114985 | −0.0574925 | − | 0.998346i | \(-0.518311\pi\) | ||||
−0.0574925 | + | 0.998346i | \(0.518311\pi\) | |||||||
\(308\) | 1.26986e25 | 0.0941830 | ||||||||
\(309\) | −7.61840e25 | −0.546135 | ||||||||
\(310\) | 1.21065e26 | 0.838924 | ||||||||
\(311\) | −1.48794e26 | −0.996786 | −0.498393 | − | 0.866951i | \(-0.666076\pi\) | ||||
−0.498393 | + | 0.866951i | \(0.666076\pi\) | |||||||
\(312\) | 3.95017e25 | 0.255854 | ||||||||
\(313\) | −1.10961e26 | −0.694951 | −0.347476 | − | 0.937689i | \(-0.612961\pi\) | ||||
−0.347476 | + | 0.937689i | \(0.612961\pi\) | |||||||
\(314\) | −1.82553e26 | −1.10567 | ||||||||
\(315\) | 3.71404e24 | 0.0217564 | ||||||||
\(316\) | −3.52074e25 | −0.199489 | ||||||||
\(317\) | 7.14805e25 | 0.391801 | 0.195900 | − | 0.980624i | \(-0.437237\pi\) | ||||
0.195900 | + | 0.980624i | \(0.437237\pi\) | |||||||
\(318\) | 4.96656e25 | 0.263373 | ||||||||
\(319\) | 1.55014e26 | 0.795371 | ||||||||
\(320\) | −1.12397e26 | −0.558060 | ||||||||
\(321\) | 3.40661e24 | 0.0163689 | ||||||||
\(322\) | −1.77379e25 | −0.0824928 | ||||||||
\(323\) | 8.90810e25 | 0.401013 | ||||||||
\(324\) | 2.01637e25 | 0.0878715 | ||||||||
\(325\) | −1.52002e25 | −0.0641317 | ||||||||
\(326\) | −3.50326e26 | −1.43116 | ||||||||
\(327\) | −3.39497e25 | −0.134302 | ||||||||
\(328\) | 1.89397e25 | 0.0725601 | ||||||||
\(329\) | 1.95432e25 | 0.0725168 | ||||||||
\(330\) | 4.08116e26 | 1.46686 | ||||||||
\(331\) | −5.05668e26 | −1.76065 | −0.880323 | − | 0.474375i | \(-0.842674\pi\) | ||||
−0.880323 | + | 0.474375i | \(0.842674\pi\) | |||||||
\(332\) | 1.83769e26 | 0.619901 | ||||||||
\(333\) | 1.06360e26 | 0.347628 | ||||||||
\(334\) | 7.20791e25 | 0.228282 | ||||||||
\(335\) | −3.03737e26 | −0.932238 | ||||||||
\(336\) | −1.44732e25 | −0.0430530 | ||||||||
\(337\) | 3.50546e26 | 1.01072 | 0.505360 | − | 0.862909i | \(-0.331360\pi\) | ||||
0.505360 | + | 0.862909i | \(0.331360\pi\) | |||||||
\(338\) | 7.21413e26 | 2.01632 | ||||||||
\(339\) | −2.69709e26 | −0.730801 | ||||||||
\(340\) | −1.09896e26 | −0.288703 | ||||||||
\(341\) | 4.49044e26 | 1.14385 | ||||||||
\(342\) | −2.02349e26 | −0.499835 | ||||||||
\(343\) | −5.33106e25 | −0.127710 | ||||||||
\(344\) | −1.39163e26 | −0.323341 | ||||||||
\(345\) | −2.51747e26 | −0.567366 | ||||||||
\(346\) | 5.00763e26 | 1.09480 | ||||||||
\(347\) | −3.51664e26 | −0.745879 | −0.372940 | − | 0.927856i | \(-0.621650\pi\) | ||||
−0.372940 | + | 0.927856i | \(0.621650\pi\) | |||||||
\(348\) | 9.48166e25 | 0.195120 | ||||||||
\(349\) | 5.74285e26 | 1.14673 | 0.573364 | − | 0.819300i | \(-0.305638\pi\) | ||||
0.573364 | + | 0.819300i | \(0.305638\pi\) | |||||||
\(350\) | 1.78998e24 | 0.00346844 | ||||||||
\(351\) | −1.62030e26 | −0.304698 | ||||||||
\(352\) | −1.30496e27 | −2.38176 | ||||||||
\(353\) | 1.85373e25 | 0.0328406 | 0.0164203 | − | 0.999865i | \(-0.494773\pi\) | ||||
0.0164203 | + | 0.999865i | \(0.494773\pi\) | |||||||
\(354\) | −5.88583e26 | −1.01222 | ||||||||
\(355\) | 1.63860e26 | 0.273574 | ||||||||
\(356\) | −1.27242e25 | −0.0206256 | ||||||||
\(357\) | −8.40001e24 | −0.0132210 | ||||||||
\(358\) | −6.49572e26 | −0.992785 | ||||||||
\(359\) | −3.41606e26 | −0.507030 | −0.253515 | − | 0.967331i | \(-0.581587\pi\) | ||||
−0.253515 | + | 0.967331i | \(0.581587\pi\) | |||||||
\(360\) | −6.60204e25 | −0.0951704 | ||||||||
\(361\) | 1.82527e26 | 0.255565 | ||||||||
\(362\) | −3.72605e26 | −0.506768 | ||||||||
\(363\) | 1.07677e27 | 1.42267 | ||||||||
\(364\) | −6.24154e25 | −0.0801175 | ||||||||
\(365\) | 1.51834e27 | 1.89362 | ||||||||
\(366\) | 2.27702e26 | 0.275940 | ||||||||
\(367\) | 5.79162e26 | 0.682034 | 0.341017 | − | 0.940057i | \(-0.389229\pi\) | ||||
0.341017 | + | 0.940057i | \(0.389229\pi\) | |||||||
\(368\) | 9.81031e26 | 1.12274 | ||||||||
\(369\) | −7.76878e25 | −0.0864123 | ||||||||
\(370\) | 1.31675e27 | 1.42360 | ||||||||
\(371\) | 2.07546e25 | 0.0218116 | ||||||||
\(372\) | 2.74664e26 | 0.280609 | ||||||||
\(373\) | −1.74513e27 | −1.73335 | −0.866673 | − | 0.498877i | \(-0.833746\pi\) | ||||
−0.866673 | + | 0.498877i | \(0.833746\pi\) | |||||||
\(374\) | −9.23032e26 | −0.891384 | ||||||||
\(375\) | −6.01772e26 | −0.565072 | ||||||||
\(376\) | −3.47398e26 | −0.317216 | ||||||||
\(377\) | −7.61919e26 | −0.676588 | ||||||||
\(378\) | 1.90808e25 | 0.0164790 | ||||||||
\(379\) | 1.08818e27 | 0.914093 | 0.457046 | − | 0.889443i | \(-0.348907\pi\) | ||||
0.457046 | + | 0.889443i | \(0.348907\pi\) | |||||||
\(380\) | −1.10627e27 | −0.903925 | ||||||||
\(381\) | 1.09204e27 | 0.868014 | ||||||||
\(382\) | −8.93050e26 | −0.690575 | ||||||||
\(383\) | −2.35974e27 | −1.77532 | −0.887661 | − | 0.460498i | \(-0.847671\pi\) | ||||
−0.887661 | + | 0.460498i | \(0.847671\pi\) | |||||||
\(384\) | 4.31860e26 | 0.316130 | ||||||||
\(385\) | 1.70546e26 | 0.121480 | ||||||||
\(386\) | 2.51159e27 | 1.74094 | ||||||||
\(387\) | 5.70827e26 | 0.385070 | ||||||||
\(388\) | 7.69145e26 | 0.504981 | ||||||||
\(389\) | −2.72162e27 | −1.73923 | −0.869616 | − | 0.493729i | \(-0.835633\pi\) | ||||
−0.869616 | + | 0.493729i | \(0.835633\pi\) | |||||||
\(390\) | −2.00595e27 | −1.24779 | ||||||||
\(391\) | 5.69373e26 | 0.344779 | ||||||||
\(392\) | 4.72850e26 | 0.278753 | ||||||||
\(393\) | −7.39859e26 | −0.424646 | ||||||||
\(394\) | 3.98660e27 | 2.22788 | ||||||||
\(395\) | −4.72847e26 | −0.257307 | ||||||||
\(396\) | 9.25903e26 | 0.490644 | ||||||||
\(397\) | −2.20086e27 | −1.13577 | −0.567887 | − | 0.823106i | \(-0.692239\pi\) | ||||
−0.567887 | + | 0.823106i | \(0.692239\pi\) | |||||||
\(398\) | 1.03595e26 | 0.0520673 | ||||||||
\(399\) | −8.45589e25 | −0.0413946 | ||||||||
\(400\) | −9.89987e25 | −0.0472063 | ||||||||
\(401\) | 2.61699e27 | 1.21559 | 0.607793 | − | 0.794096i | \(-0.292055\pi\) | ||||
0.607793 | + | 0.794096i | \(0.292055\pi\) | |||||||
\(402\) | −1.56044e27 | −0.706111 | ||||||||
\(403\) | −2.20712e27 | −0.973023 | ||||||||
\(404\) | 2.91305e26 | 0.125125 | ||||||||
\(405\) | 2.70806e26 | 0.113339 | ||||||||
\(406\) | 8.97242e25 | 0.0365920 | ||||||||
\(407\) | 4.88398e27 | 1.94103 | ||||||||
\(408\) | 1.49318e26 | 0.0578335 | ||||||||
\(409\) | −8.92474e26 | −0.336900 | −0.168450 | − | 0.985710i | \(-0.553876\pi\) | ||||
−0.168450 | + | 0.985710i | \(0.553876\pi\) | |||||||
\(410\) | −9.61786e26 | −0.353874 | ||||||||
\(411\) | 2.26793e27 | 0.813373 | ||||||||
\(412\) | −2.13979e27 | −0.748085 | ||||||||
\(413\) | −2.45961e26 | −0.0838282 | ||||||||
\(414\) | −1.29334e27 | −0.429744 | ||||||||
\(415\) | 2.46808e27 | 0.799567 | ||||||||
\(416\) | 6.41407e27 | 2.02607 | ||||||||
\(417\) | −5.66195e26 | −0.174396 | ||||||||
\(418\) | −9.29172e27 | −2.79091 | ||||||||
\(419\) | −2.48238e27 | −0.727144 | −0.363572 | − | 0.931566i | \(-0.618443\pi\) | ||||
−0.363572 | + | 0.931566i | \(0.618443\pi\) | |||||||
\(420\) | 1.04317e26 | 0.0298014 | ||||||||
\(421\) | 4.09797e27 | 1.14184 | 0.570922 | − | 0.821004i | \(-0.306586\pi\) | ||||
0.570922 | + | 0.821004i | \(0.306586\pi\) | |||||||
\(422\) | −6.12669e27 | −1.66512 | ||||||||
\(423\) | 1.42497e27 | 0.377774 | ||||||||
\(424\) | −3.68931e26 | −0.0954121 | ||||||||
\(425\) | −5.74571e25 | −0.0144964 | ||||||||
\(426\) | 8.41825e26 | 0.207215 | ||||||||
\(427\) | 9.51534e25 | 0.0228524 | ||||||||
\(428\) | 9.56820e25 | 0.0224218 | ||||||||
\(429\) | −7.44029e27 | −1.70133 | ||||||||
\(430\) | 7.06692e27 | 1.57693 | ||||||||
\(431\) | −4.89793e27 | −1.06660 | −0.533299 | − | 0.845927i | \(-0.679048\pi\) | ||||
−0.533299 | + | 0.845927i | \(0.679048\pi\) | |||||||
\(432\) | −1.05530e27 | −0.224283 | ||||||||
\(433\) | −2.06118e27 | −0.427557 | −0.213778 | − | 0.976882i | \(-0.568577\pi\) | ||||
−0.213778 | + | 0.976882i | \(0.568577\pi\) | |||||||
\(434\) | 2.59913e26 | 0.0526242 | ||||||||
\(435\) | 1.27342e27 | 0.251672 | ||||||||
\(436\) | −9.53549e26 | −0.183965 | ||||||||
\(437\) | 5.73161e27 | 1.07950 | ||||||||
\(438\) | 7.80042e27 | 1.43430 | ||||||||
\(439\) | 1.00358e28 | 1.80167 | 0.900835 | − | 0.434161i | \(-0.142955\pi\) | ||||
0.900835 | + | 0.434161i | \(0.142955\pi\) | |||||||
\(440\) | −3.03161e27 | −0.531399 | ||||||||
\(441\) | −1.93956e27 | −0.331969 | ||||||||
\(442\) | 4.53684e27 | 0.758263 | ||||||||
\(443\) | 4.23345e27 | 0.690964 | 0.345482 | − | 0.938425i | \(-0.387715\pi\) | ||||
0.345482 | + | 0.938425i | \(0.387715\pi\) | |||||||
\(444\) | 2.98735e27 | 0.476173 | ||||||||
\(445\) | −1.70891e26 | −0.0266035 | ||||||||
\(446\) | −6.01973e27 | −0.915295 | ||||||||
\(447\) | 2.03382e27 | 0.302053 | ||||||||
\(448\) | −2.41303e26 | −0.0350061 | ||||||||
\(449\) | −6.74432e27 | −0.955766 | −0.477883 | − | 0.878424i | \(-0.658596\pi\) | ||||
−0.477883 | + | 0.878424i | \(0.658596\pi\) | |||||||
\(450\) | 1.30515e26 | 0.0180688 | ||||||||
\(451\) | −3.56737e27 | −0.482496 | ||||||||
\(452\) | −7.57537e27 | −1.00104 | ||||||||
\(453\) | −2.14438e27 | −0.276866 | ||||||||
\(454\) | −3.97052e27 | −0.500911 | ||||||||
\(455\) | −8.38261e26 | −0.103338 | ||||||||
\(456\) | 1.50311e27 | 0.181076 | ||||||||
\(457\) | −1.13821e28 | −1.34000 | −0.669998 | − | 0.742362i | \(-0.733705\pi\) | ||||
−0.669998 | + | 0.742362i | \(0.733705\pi\) | |||||||
\(458\) | 7.99644e27 | 0.920045 | ||||||||
\(459\) | −6.12478e26 | −0.0688743 | ||||||||
\(460\) | −7.07085e27 | −0.777167 | ||||||||
\(461\) | 6.24175e27 | 0.670574 | 0.335287 | − | 0.942116i | \(-0.391167\pi\) | ||||
0.335287 | + | 0.942116i | \(0.391167\pi\) | |||||||
\(462\) | 8.76175e26 | 0.0920132 | ||||||||
\(463\) | −2.31855e27 | −0.238021 | −0.119011 | − | 0.992893i | \(-0.537972\pi\) | ||||
−0.119011 | + | 0.992893i | \(0.537972\pi\) | |||||||
\(464\) | −4.96238e27 | −0.498025 | ||||||||
\(465\) | 3.68883e27 | 0.361937 | ||||||||
\(466\) | 6.65242e27 | 0.638157 | ||||||||
\(467\) | −9.47846e26 | −0.0889018 | −0.0444509 | − | 0.999012i | \(-0.514154\pi\) | ||||
−0.0444509 | + | 0.999012i | \(0.514154\pi\) | |||||||
\(468\) | −4.55096e27 | −0.417370 | ||||||||
\(469\) | −6.52086e26 | −0.0584776 | ||||||||
\(470\) | 1.76414e28 | 1.54705 | ||||||||
\(471\) | −5.56234e27 | −0.477021 | ||||||||
\(472\) | 4.37217e27 | 0.366696 | ||||||||
\(473\) | 2.62120e28 | 2.15009 | ||||||||
\(474\) | −2.42924e27 | −0.194893 | ||||||||
\(475\) | −5.78393e26 | −0.0453879 | ||||||||
\(476\) | −2.35932e26 | −0.0181098 | ||||||||
\(477\) | 1.51330e27 | 0.113627 | ||||||||
\(478\) | 1.60685e28 | 1.18028 | ||||||||
\(479\) | −1.76996e28 | −1.27186 | −0.635932 | − | 0.771745i | \(-0.719384\pi\) | ||||
−0.635932 | + | 0.771745i | \(0.719384\pi\) | |||||||
\(480\) | −1.07200e28 | −0.753639 | ||||||||
\(481\) | −2.40055e28 | −1.65115 | ||||||||
\(482\) | −2.52954e28 | −1.70234 | ||||||||
\(483\) | −5.40470e26 | −0.0355899 | ||||||||
\(484\) | 3.02434e28 | 1.94874 | ||||||||
\(485\) | 1.03299e28 | 0.651339 | ||||||||
\(486\) | 1.39125e27 | 0.0858471 | ||||||||
\(487\) | 1.99209e28 | 1.20297 | 0.601484 | − | 0.798885i | \(-0.294576\pi\) | ||||
0.601484 | + | 0.798885i | \(0.294576\pi\) | |||||||
\(488\) | −1.69144e27 | −0.0999649 | ||||||||
\(489\) | −1.06743e28 | −0.617445 | ||||||||
\(490\) | −2.40120e28 | −1.35947 | ||||||||
\(491\) | −5.71237e27 | −0.316563 | −0.158282 | − | 0.987394i | \(-0.550595\pi\) | ||||
−0.158282 | + | 0.987394i | \(0.550595\pi\) | |||||||
\(492\) | −2.18203e27 | −0.118366 | ||||||||
\(493\) | −2.88008e27 | −0.152937 | ||||||||
\(494\) | 4.56702e28 | 2.37411 | ||||||||
\(495\) | 1.24352e28 | 0.632846 | ||||||||
\(496\) | −1.43750e28 | −0.716226 | ||||||||
\(497\) | 3.51787e26 | 0.0171608 | ||||||||
\(498\) | 1.26797e28 | 0.605620 | ||||||||
\(499\) | −1.17032e28 | −0.547332 | −0.273666 | − | 0.961825i | \(-0.588236\pi\) | ||||
−0.273666 | + | 0.961825i | \(0.588236\pi\) | |||||||
\(500\) | −1.69021e28 | −0.774025 | ||||||||
\(501\) | 2.19623e27 | 0.0984878 | ||||||||
\(502\) | −3.44239e28 | −1.51172 | ||||||||
\(503\) | −3.15184e28 | −1.35550 | −0.677750 | − | 0.735292i | \(-0.737045\pi\) | ||||
−0.677750 | + | 0.735292i | \(0.737045\pi\) | |||||||
\(504\) | −1.41738e26 | −0.00596987 | ||||||||
\(505\) | 3.91233e27 | 0.161390 | ||||||||
\(506\) | −5.93893e28 | −2.39954 | ||||||||
\(507\) | 2.19813e28 | 0.869899 | ||||||||
\(508\) | 3.06723e28 | 1.18899 | ||||||||
\(509\) | 4.58029e28 | 1.73923 | 0.869613 | − | 0.493733i | \(-0.164368\pi\) | ||||
0.869613 | + | 0.493733i | \(0.164368\pi\) | |||||||
\(510\) | −7.58257e27 | −0.282052 | ||||||||
\(511\) | 3.25969e27 | 0.118784 | ||||||||
\(512\) | 3.26377e28 | 1.16516 | ||||||||
\(513\) | −6.16552e27 | −0.215644 | ||||||||
\(514\) | −1.10475e28 | −0.378574 | ||||||||
\(515\) | −2.87382e28 | −0.964901 | ||||||||
\(516\) | 1.60329e28 | 0.527461 | ||||||||
\(517\) | 6.54337e28 | 2.10936 | ||||||||
\(518\) | 2.82691e27 | 0.0892996 | ||||||||
\(519\) | 1.52581e28 | 0.472328 | ||||||||
\(520\) | 1.49008e28 | 0.452038 | ||||||||
\(521\) | −5.19044e27 | −0.154315 | −0.0771575 | − | 0.997019i | \(-0.524584\pi\) | ||||
−0.0771575 | + | 0.997019i | \(0.524584\pi\) | |||||||
\(522\) | 6.54215e27 | 0.190625 | ||||||||
\(523\) | −2.08282e27 | −0.0594817 | −0.0297408 | − | 0.999558i | \(-0.509468\pi\) | ||||
−0.0297408 | + | 0.999558i | \(0.509468\pi\) | |||||||
\(524\) | −2.07805e28 | −0.581672 | ||||||||
\(525\) | 5.45403e25 | 0.00149639 | ||||||||
\(526\) | 1.88674e27 | 0.0507413 | ||||||||
\(527\) | −8.34299e27 | −0.219943 | ||||||||
\(528\) | −4.84587e28 | −1.25232 | ||||||||
\(529\) | −2.83724e27 | −0.0718805 | ||||||||
\(530\) | 1.87349e28 | 0.465322 | ||||||||
\(531\) | −1.79340e28 | −0.436701 | ||||||||
\(532\) | −2.37502e27 | −0.0567016 | ||||||||
\(533\) | 1.75342e28 | 0.410439 | ||||||||
\(534\) | −8.77946e26 | −0.0201504 | ||||||||
\(535\) | 1.28504e27 | 0.0289203 | ||||||||
\(536\) | 1.15914e28 | 0.255803 | ||||||||
\(537\) | −1.97923e28 | −0.428318 | ||||||||
\(538\) | −1.12128e29 | −2.37957 | ||||||||
\(539\) | −8.90630e28 | −1.85360 | ||||||||
\(540\) | 7.60616e27 | 0.155250 | ||||||||
\(541\) | −1.25240e28 | −0.250710 | −0.125355 | − | 0.992112i | \(-0.540007\pi\) | ||||
−0.125355 | + | 0.992112i | \(0.540007\pi\) | |||||||
\(542\) | 8.31446e28 | 1.63246 | ||||||||
\(543\) | −1.13532e28 | −0.218635 | ||||||||
\(544\) | 2.42454e28 | 0.457974 | ||||||||
\(545\) | −1.28065e28 | −0.237283 | ||||||||
\(546\) | −4.30654e27 | −0.0782718 | ||||||||
\(547\) | 5.63104e28 | 1.00397 | 0.501987 | − | 0.864875i | \(-0.332603\pi\) | ||||
0.501987 | + | 0.864875i | \(0.332603\pi\) | |||||||
\(548\) | 6.36996e28 | 1.11414 | ||||||||
\(549\) | 6.93801e27 | 0.119049 | ||||||||
\(550\) | 5.99314e27 | 0.100890 | ||||||||
\(551\) | −2.89924e28 | −0.478842 | ||||||||
\(552\) | 9.60733e27 | 0.155683 | ||||||||
\(553\) | −1.01514e27 | −0.0161404 | ||||||||
\(554\) | 1.23835e29 | 1.93193 | ||||||||
\(555\) | 4.01212e28 | 0.614182 | ||||||||
\(556\) | −1.59028e28 | −0.238885 | ||||||||
\(557\) | 4.80914e28 | 0.708904 | 0.354452 | − | 0.935074i | \(-0.384667\pi\) | ||||
0.354452 | + | 0.935074i | \(0.384667\pi\) | |||||||
\(558\) | 1.89513e28 | 0.274144 | ||||||||
\(559\) | −1.28836e29 | −1.82899 | ||||||||
\(560\) | −5.45960e27 | −0.0760652 | ||||||||
\(561\) | −2.81246e28 | −0.384570 | ||||||||
\(562\) | 6.26161e28 | 0.840339 | ||||||||
\(563\) | −1.81812e28 | −0.239488 | −0.119744 | − | 0.992805i | \(-0.538207\pi\) | ||||
−0.119744 | + | 0.992805i | \(0.538207\pi\) | |||||||
\(564\) | 4.00234e28 | 0.517468 | ||||||||
\(565\) | −1.01740e29 | −1.29117 | ||||||||
\(566\) | −1.95011e28 | −0.242933 | ||||||||
\(567\) | 5.81386e26 | 0.00710956 | ||||||||
\(568\) | −6.25333e27 | −0.0750679 | ||||||||
\(569\) | 1.75144e28 | 0.206403 | 0.103201 | − | 0.994660i | \(-0.467091\pi\) | ||||
0.103201 | + | 0.994660i | \(0.467091\pi\) | |||||||
\(570\) | −7.63301e28 | −0.883100 | ||||||||
\(571\) | 1.67794e29 | 1.90589 | 0.952946 | − | 0.303140i | \(-0.0980350\pi\) | ||||
0.952946 | + | 0.303140i | \(0.0980350\pi\) | |||||||
\(572\) | −2.08977e29 | −2.33045 | ||||||||
\(573\) | −2.72110e28 | −0.297935 | ||||||||
\(574\) | −2.06484e27 | −0.0221978 | ||||||||
\(575\) | −3.69688e27 | −0.0390232 | ||||||||
\(576\) | −1.75943e28 | −0.182363 | ||||||||
\(577\) | 7.49346e28 | 0.762669 | 0.381335 | − | 0.924437i | \(-0.375465\pi\) | ||||
0.381335 | + | 0.924437i | \(0.375465\pi\) | |||||||
\(578\) | −1.16748e29 | −1.16683 | ||||||||
\(579\) | 7.65276e28 | 0.751092 | ||||||||
\(580\) | 3.57667e28 | 0.344735 | ||||||||
\(581\) | 5.29867e27 | 0.0501554 | ||||||||
\(582\) | 5.30694e28 | 0.493348 | ||||||||
\(583\) | 6.94895e28 | 0.634453 | ||||||||
\(584\) | −5.79439e28 | −0.519604 | ||||||||
\(585\) | −6.11209e28 | −0.538336 | ||||||||
\(586\) | 9.55433e28 | 0.826562 | ||||||||
\(587\) | 1.69908e29 | 1.44382 | 0.721912 | − | 0.691985i | \(-0.243264\pi\) | ||||
0.721912 | + | 0.691985i | \(0.243264\pi\) | |||||||
\(588\) | −5.44766e28 | −0.454724 | ||||||||
\(589\) | −8.39849e28 | −0.688638 | ||||||||
\(590\) | −2.22025e29 | −1.78837 | ||||||||
\(591\) | 1.21471e29 | 0.961175 | ||||||||
\(592\) | −1.56348e29 | −1.21539 | ||||||||
\(593\) | −1.26592e29 | −0.966787 | −0.483394 | − | 0.875403i | \(-0.660596\pi\) | ||||
−0.483394 | + | 0.875403i | \(0.660596\pi\) | |||||||
\(594\) | 6.38854e28 | 0.479340 | ||||||||
\(595\) | −3.16865e27 | −0.0233586 | ||||||||
\(596\) | 5.71241e28 | 0.413746 | ||||||||
\(597\) | 3.15650e27 | 0.0224634 | ||||||||
\(598\) | 2.91907e29 | 2.04119 | ||||||||
\(599\) | 1.73983e29 | 1.19544 | 0.597718 | − | 0.801706i | \(-0.296074\pi\) | ||||
0.597718 | + | 0.801706i | \(0.296074\pi\) | |||||||
\(600\) | −9.69503e26 | −0.00654578 | ||||||||
\(601\) | −2.58691e29 | −1.71633 | −0.858164 | − | 0.513376i | \(-0.828395\pi\) | ||||
−0.858164 | + | 0.513376i | \(0.828395\pi\) | |||||||
\(602\) | 1.51718e28 | 0.0989178 | ||||||||
\(603\) | −4.75461e28 | −0.304638 | ||||||||
\(604\) | −6.02294e28 | −0.379246 | ||||||||
\(605\) | 4.06179e29 | 2.51354 | ||||||||
\(606\) | 2.00994e28 | 0.122242 | ||||||||
\(607\) | −1.61646e29 | −0.966238 | −0.483119 | − | 0.875555i | \(-0.660496\pi\) | ||||
−0.483119 | + | 0.875555i | \(0.660496\pi\) | |||||||
\(608\) | 2.44067e29 | 1.43391 | ||||||||
\(609\) | 2.73387e27 | 0.0157869 | ||||||||
\(610\) | 8.58936e28 | 0.487526 | ||||||||
\(611\) | −3.21617e29 | −1.79434 | ||||||||
\(612\) | −1.72028e28 | −0.0943427 | ||||||||
\(613\) | 8.86426e28 | 0.477868 | 0.238934 | − | 0.971036i | \(-0.423202\pi\) | ||||
0.238934 | + | 0.971036i | \(0.423202\pi\) | |||||||
\(614\) | −2.90361e28 | −0.153876 | ||||||||
\(615\) | −2.93054e28 | −0.152672 | ||||||||
\(616\) | −6.50850e27 | −0.0333337 | ||||||||
\(617\) | −7.14976e28 | −0.359996 | −0.179998 | − | 0.983667i | \(-0.557609\pi\) | ||||
−0.179998 | + | 0.983667i | \(0.557609\pi\) | |||||||
\(618\) | −1.47641e29 | −0.730851 | ||||||||
\(619\) | −3.79378e28 | −0.184638 | −0.0923188 | − | 0.995730i | \(-0.529428\pi\) | ||||
−0.0923188 | + | 0.995730i | \(0.529428\pi\) | |||||||
\(620\) | 1.03609e29 | 0.495774 | ||||||||
\(621\) | −3.94078e28 | −0.185404 | ||||||||
\(622\) | −2.88356e29 | −1.33392 | ||||||||
\(623\) | −3.66882e26 | −0.00166879 | ||||||||
\(624\) | 2.38182e29 | 1.06530 | ||||||||
\(625\) | −2.36211e29 | −1.03887 | ||||||||
\(626\) | −2.15037e29 | −0.930000 | ||||||||
\(627\) | −2.83116e29 | −1.20408 | ||||||||
\(628\) | −1.56230e29 | −0.653414 | ||||||||
\(629\) | −9.07416e28 | −0.373228 | ||||||||
\(630\) | 7.19765e27 | 0.0291149 | ||||||||
\(631\) | 4.22002e29 | 1.67883 | 0.839415 | − | 0.543491i | \(-0.182898\pi\) | ||||
0.839415 | + | 0.543491i | \(0.182898\pi\) | |||||||
\(632\) | 1.80451e28 | 0.0706041 | ||||||||
\(633\) | −1.86679e29 | −0.718382 | ||||||||
\(634\) | 1.38526e29 | 0.524317 | ||||||||
\(635\) | 4.11940e29 | 1.53359 | ||||||||
\(636\) | 4.25042e28 | 0.155644 | ||||||||
\(637\) | 4.37758e29 | 1.57678 | ||||||||
\(638\) | 3.00411e29 | 1.06438 | ||||||||
\(639\) | 2.56502e28 | 0.0893988 | ||||||||
\(640\) | 1.62906e29 | 0.558533 | ||||||||
\(641\) | −2.45898e29 | −0.829364 | −0.414682 | − | 0.909966i | \(-0.636107\pi\) | ||||
−0.414682 | + | 0.909966i | \(0.636107\pi\) | |||||||
\(642\) | 6.60186e27 | 0.0219053 | ||||||||
\(643\) | 3.81795e29 | 1.24628 | 0.623139 | − | 0.782111i | \(-0.285857\pi\) | ||||
0.623139 | + | 0.782111i | \(0.285857\pi\) | |||||||
\(644\) | −1.51803e28 | −0.0487503 | ||||||||
\(645\) | 2.15327e29 | 0.680334 | ||||||||
\(646\) | 1.72635e29 | 0.536646 | ||||||||
\(647\) | −3.01566e29 | −0.922332 | −0.461166 | − | 0.887314i | \(-0.652569\pi\) | ||||
−0.461166 | + | 0.887314i | \(0.652569\pi\) | |||||||
\(648\) | −1.03347e28 | −0.0310999 | ||||||||
\(649\) | −8.23515e29 | −2.43839 | ||||||||
\(650\) | −2.94572e28 | −0.0858226 | ||||||||
\(651\) | 7.91947e27 | 0.0227037 | ||||||||
\(652\) | −2.99812e29 | −0.845764 | ||||||||
\(653\) | 2.27685e29 | 0.632042 | 0.316021 | − | 0.948752i | \(-0.397653\pi\) | ||||
0.316021 | + | 0.948752i | \(0.397653\pi\) | |||||||
\(654\) | −6.57929e28 | −0.179727 | ||||||||
\(655\) | −2.79090e29 | −0.750257 | ||||||||
\(656\) | 1.14200e29 | 0.302117 | ||||||||
\(657\) | 2.37677e29 | 0.618800 | ||||||||
\(658\) | 3.78738e28 | 0.0970437 | ||||||||
\(659\) | −4.45804e29 | −1.12421 | −0.562104 | − | 0.827066i | \(-0.690008\pi\) | ||||
−0.562104 | + | 0.827066i | \(0.690008\pi\) | |||||||
\(660\) | 3.49269e29 | 0.866860 | ||||||||
\(661\) | 4.54039e29 | 1.10912 | 0.554559 | − | 0.832144i | \(-0.312887\pi\) | ||||
0.554559 | + | 0.832144i | \(0.312887\pi\) | |||||||
\(662\) | −9.79963e29 | −2.35614 | ||||||||
\(663\) | 1.38236e29 | 0.327138 | ||||||||
\(664\) | −9.41886e28 | −0.219398 | ||||||||
\(665\) | −3.18973e28 | −0.0731353 | ||||||||
\(666\) | 2.06121e29 | 0.465204 | ||||||||
\(667\) | −1.85309e29 | −0.411694 | ||||||||
\(668\) | 6.16859e28 | 0.134907 | ||||||||
\(669\) | −1.83420e29 | −0.394886 | ||||||||
\(670\) | −5.88628e29 | −1.24754 | ||||||||
\(671\) | 3.18588e29 | 0.664727 | ||||||||
\(672\) | −2.30146e28 | −0.0472744 | ||||||||
\(673\) | 5.05512e28 | 0.102229 | 0.0511144 | − | 0.998693i | \(-0.483723\pi\) | ||||
0.0511144 | + | 0.998693i | \(0.483723\pi\) | |||||||
\(674\) | 6.79342e29 | 1.35257 | ||||||||
\(675\) | 3.97675e27 | 0.00779541 | ||||||||
\(676\) | 6.17391e29 | 1.19157 | ||||||||
\(677\) | −3.44673e29 | −0.654977 | −0.327489 | − | 0.944855i | \(-0.606202\pi\) | ||||
−0.327489 | + | 0.944855i | \(0.606202\pi\) | |||||||
\(678\) | −5.22685e29 | −0.977975 | ||||||||
\(679\) | 2.21770e28 | 0.0408573 | ||||||||
\(680\) | 5.63256e28 | 0.102179 | ||||||||
\(681\) | −1.20981e29 | −0.216108 | ||||||||
\(682\) | 8.70228e29 | 1.53072 | ||||||||
\(683\) | 3.07293e29 | 0.532273 | 0.266137 | − | 0.963935i | \(-0.414253\pi\) | ||||
0.266137 | + | 0.963935i | \(0.414253\pi\) | |||||||
\(684\) | −1.73172e29 | −0.295385 | ||||||||
\(685\) | 8.55508e29 | 1.43705 | ||||||||
\(686\) | −1.03314e29 | −0.170905 | ||||||||
\(687\) | 2.43649e29 | 0.396935 | ||||||||
\(688\) | −8.39108e29 | −1.34629 | ||||||||
\(689\) | −3.41552e29 | −0.539703 | ||||||||
\(690\) | −4.87874e29 | −0.759263 | ||||||||
\(691\) | 7.85532e28 | 0.120405 | 0.0602025 | − | 0.998186i | \(-0.480825\pi\) | ||||
0.0602025 | + | 0.998186i | \(0.480825\pi\) | |||||||
\(692\) | 4.28557e29 | 0.646986 | ||||||||
\(693\) | 2.66968e28 | 0.0396973 | ||||||||
\(694\) | −6.81509e29 | −0.998153 | ||||||||
\(695\) | −2.13580e29 | −0.308120 | ||||||||
\(696\) | −4.85971e28 | −0.0690578 | ||||||||
\(697\) | 6.62797e28 | 0.0927761 | ||||||||
\(698\) | 1.11294e30 | 1.53458 | ||||||||
\(699\) | 2.02698e29 | 0.275320 | ||||||||
\(700\) | 1.53188e27 | 0.00204973 | ||||||||
\(701\) | 7.75849e29 | 1.02268 | 0.511338 | − | 0.859380i | \(-0.329150\pi\) | ||||
0.511338 | + | 0.859380i | \(0.329150\pi\) | |||||||
\(702\) | −3.14006e29 | −0.407755 | ||||||||
\(703\) | −9.13453e29 | −1.16857 | ||||||||
\(704\) | −8.07920e29 | −1.01825 | ||||||||
\(705\) | 5.37528e29 | 0.667445 | ||||||||
\(706\) | 3.59244e28 | 0.0439481 | ||||||||
\(707\) | 8.39929e27 | 0.0101237 | ||||||||
\(708\) | −5.03714e29 | −0.598184 | ||||||||
\(709\) | 1.53428e30 | 1.79523 | 0.897613 | − | 0.440785i | \(-0.145300\pi\) | ||||
0.897613 | + | 0.440785i | \(0.145300\pi\) | |||||||
\(710\) | 3.17553e29 | 0.366104 | ||||||||
\(711\) | −7.40182e28 | −0.0840829 | ||||||||
\(712\) | 6.52165e27 | 0.00729991 | ||||||||
\(713\) | −5.36801e29 | −0.592070 | ||||||||
\(714\) | −1.62788e28 | −0.0176926 | ||||||||
\(715\) | −2.80663e30 | −3.00588 | ||||||||
\(716\) | −5.55909e29 | −0.586701 | ||||||||
\(717\) | 4.89604e29 | 0.509206 | ||||||||
\(718\) | −6.62017e29 | −0.678520 | ||||||||
\(719\) | 5.56901e29 | 0.562503 | 0.281252 | − | 0.959634i | \(-0.409250\pi\) | ||||
0.281252 | + | 0.959634i | \(0.409250\pi\) | |||||||
\(720\) | −3.98081e29 | −0.396260 | ||||||||
\(721\) | −6.16973e28 | −0.0605265 | ||||||||
\(722\) | 3.53729e29 | 0.342003 | ||||||||
\(723\) | −7.70743e29 | −0.734442 | ||||||||
\(724\) | −3.18879e29 | −0.299482 | ||||||||
\(725\) | 1.87000e28 | 0.0173098 | ||||||||
\(726\) | 2.08673e30 | 1.90384 | ||||||||
\(727\) | −1.43096e29 | −0.128681 | −0.0643407 | − | 0.997928i | \(-0.520494\pi\) | ||||
−0.0643407 | + | 0.997928i | \(0.520494\pi\) | |||||||
\(728\) | 3.19902e28 | 0.0283556 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 2.94247e30 | 2.53409 | ||||||||
\(731\) | −4.87003e29 | −0.413428 | ||||||||
\(732\) | 1.94869e29 | 0.163071 | ||||||||
\(733\) | −6.81141e29 | −0.561882 | −0.280941 | − | 0.959725i | \(-0.590647\pi\) | ||||
−0.280941 | + | 0.959725i | \(0.590647\pi\) | |||||||
\(734\) | 1.12239e30 | 0.912714 | ||||||||
\(735\) | −7.31639e29 | −0.586516 | ||||||||
\(736\) | 1.55999e30 | 1.23283 | ||||||||
\(737\) | −2.18328e30 | −1.70099 | ||||||||
\(738\) | −1.50555e29 | −0.115639 | ||||||||
\(739\) | 2.16993e30 | 1.64315 | 0.821577 | − | 0.570097i | \(-0.193094\pi\) | ||||
0.821577 | + | 0.570097i | \(0.193094\pi\) | |||||||
\(740\) | 1.12689e30 | 0.841295 | ||||||||
\(741\) | 1.39156e30 | 1.02426 | ||||||||
\(742\) | 4.02214e28 | 0.0291888 | ||||||||
\(743\) | −1.40097e29 | −0.100241 | −0.0501206 | − | 0.998743i | \(-0.515961\pi\) | ||||
−0.0501206 | + | 0.998743i | \(0.515961\pi\) | |||||||
\(744\) | −1.40776e29 | −0.0993143 | ||||||||
\(745\) | 7.67196e29 | 0.533661 | ||||||||
\(746\) | −3.38199e30 | −2.31960 | ||||||||
\(747\) | 3.86347e29 | 0.261283 | ||||||||
\(748\) | −7.89939e29 | −0.526777 | ||||||||
\(749\) | 2.75883e27 | 0.00181412 | ||||||||
\(750\) | −1.16621e30 | −0.756193 | ||||||||
\(751\) | 8.06099e29 | 0.515429 | 0.257715 | − | 0.966221i | \(-0.417031\pi\) | ||||
0.257715 | + | 0.966221i | \(0.417031\pi\) | |||||||
\(752\) | −2.09469e30 | −1.32079 | ||||||||
\(753\) | −1.04889e30 | −0.652202 | ||||||||
\(754\) | −1.47656e30 | −0.905427 | ||||||||
\(755\) | −8.08901e29 | −0.489162 | ||||||||
\(756\) | 1.63295e28 | 0.00973853 | ||||||||
\(757\) | −1.54959e30 | −0.911401 | −0.455700 | − | 0.890133i | \(-0.650611\pi\) | ||||
−0.455700 | + | 0.890133i | \(0.650611\pi\) | |||||||
\(758\) | 2.10885e30 | 1.22326 | ||||||||
\(759\) | −1.80958e30 | −1.03523 | ||||||||
\(760\) | 5.67003e29 | 0.319921 | ||||||||
\(761\) | 2.04061e29 | 0.113559 | 0.0567793 | − | 0.998387i | \(-0.481917\pi\) | ||||
0.0567793 | + | 0.998387i | \(0.481917\pi\) | |||||||
\(762\) | 2.11633e30 | 1.16160 | ||||||||
\(763\) | −2.74940e28 | −0.0148843 | ||||||||
\(764\) | −7.64280e29 | −0.408105 | ||||||||
\(765\) | −2.31039e29 | −0.121686 | ||||||||
\(766\) | −4.57307e30 | −2.37578 | ||||||||
\(767\) | 4.04770e30 | 2.07423 | ||||||||
\(768\) | 1.46180e30 | 0.738915 | ||||||||
\(769\) | 1.27880e30 | 0.637641 | 0.318821 | − | 0.947815i | \(-0.396713\pi\) | ||||
0.318821 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(770\) | 3.30511e29 | 0.162567 | ||||||||
\(771\) | −3.36614e29 | −0.163328 | ||||||||
\(772\) | 2.14944e30 | 1.02883 | ||||||||
\(773\) | 3.43774e30 | 1.62326 | 0.811630 | − | 0.584172i | \(-0.198581\pi\) | ||||
0.811630 | + | 0.584172i | \(0.198581\pi\) | |||||||
\(774\) | 1.10624e30 | 0.515309 | ||||||||
\(775\) | 5.41701e28 | 0.0248938 | ||||||||
\(776\) | −3.94216e29 | −0.178725 | ||||||||
\(777\) | 8.61352e28 | 0.0385265 | ||||||||
\(778\) | −5.27439e30 | −2.32748 | ||||||||
\(779\) | 6.67206e29 | 0.290480 | ||||||||
\(780\) | −1.71671e30 | −0.737402 | ||||||||
\(781\) | 1.17784e30 | 0.499172 | ||||||||
\(782\) | 1.10342e30 | 0.461392 | ||||||||
\(783\) | 1.99338e29 | 0.0822414 | ||||||||
\(784\) | 2.85112e30 | 1.16064 | ||||||||
\(785\) | −2.09822e30 | −0.842792 | ||||||||
\(786\) | −1.43381e30 | −0.568271 | ||||||||
\(787\) | 1.06317e30 | 0.415784 | 0.207892 | − | 0.978152i | \(-0.433340\pi\) | ||||
0.207892 | + | 0.978152i | \(0.433340\pi\) | |||||||
\(788\) | 3.41176e30 | 1.31660 | ||||||||
\(789\) | 5.74885e28 | 0.0218913 | ||||||||
\(790\) | −9.16357e29 | −0.344334 | ||||||||
\(791\) | −2.18423e29 | −0.0809925 | ||||||||
\(792\) | −4.74560e29 | −0.173651 | ||||||||
\(793\) | −1.56591e30 | −0.565456 | ||||||||
\(794\) | −4.26517e30 | −1.51992 | ||||||||
\(795\) | 5.70846e29 | 0.200754 | ||||||||
\(796\) | 8.86572e28 | 0.0307699 | ||||||||
\(797\) | −2.59470e30 | −0.888742 | −0.444371 | − | 0.895843i | \(-0.646573\pi\) | ||||
−0.444371 | + | 0.895843i | \(0.646573\pi\) | |||||||
\(798\) | −1.63871e29 | −0.0553953 | ||||||||
\(799\) | −1.21572e30 | −0.405595 | ||||||||
\(800\) | −1.57423e29 | −0.0518349 | ||||||||
\(801\) | −2.67508e28 | −0.00869351 | ||||||||
\(802\) | 5.07160e30 | 1.62672 | ||||||||
\(803\) | 1.09139e31 | 3.45516 | ||||||||
\(804\) | −1.33544e30 | −0.417286 | ||||||||
\(805\) | −2.03876e29 | −0.0628795 | ||||||||
\(806\) | −4.27730e30 | −1.30212 | ||||||||
\(807\) | −3.41650e30 | −1.02662 | ||||||||
\(808\) | −1.49305e29 | −0.0442848 | ||||||||
\(809\) | −4.54632e30 | −1.33107 | −0.665534 | − | 0.746367i | \(-0.731796\pi\) | ||||
−0.665534 | + | 0.746367i | \(0.731796\pi\) | |||||||
\(810\) | 5.24809e29 | 0.151673 | ||||||||
\(811\) | −5.33885e30 | −1.52310 | −0.761550 | − | 0.648106i | \(-0.775561\pi\) | ||||
−0.761550 | + | 0.648106i | \(0.775561\pi\) | |||||||
\(812\) | 7.67867e28 | 0.0216246 | ||||||||
\(813\) | 2.53339e30 | 0.704291 | ||||||||
\(814\) | 9.46493e30 | 2.59753 | ||||||||
\(815\) | −4.02658e30 | −1.09089 | ||||||||
\(816\) | 9.00335e29 | 0.240801 | ||||||||
\(817\) | −4.90243e30 | −1.29443 | ||||||||
\(818\) | −1.72957e30 | −0.450847 | ||||||||
\(819\) | −1.31219e29 | −0.0337688 | ||||||||
\(820\) | −8.23105e29 | −0.209127 | ||||||||
\(821\) | −6.77652e30 | −1.69982 | −0.849911 | − | 0.526926i | \(-0.823344\pi\) | ||||
−0.849911 | + | 0.526926i | \(0.823344\pi\) | |||||||
\(822\) | 4.39514e30 | 1.08848 | ||||||||
\(823\) | 2.32096e30 | 0.567506 | 0.283753 | − | 0.958897i | \(-0.408420\pi\) | ||||
0.283753 | + | 0.958897i | \(0.408420\pi\) | |||||||
\(824\) | 1.09672e30 | 0.264766 | ||||||||
\(825\) | 1.82610e29 | 0.0435268 | ||||||||
\(826\) | −4.76661e29 | −0.112181 | ||||||||
\(827\) | 3.93890e30 | 0.915307 | 0.457654 | − | 0.889131i | \(-0.348690\pi\) | ||||
0.457654 | + | 0.889131i | \(0.348690\pi\) | |||||||
\(828\) | −1.10685e30 | −0.253963 | ||||||||
\(829\) | 3.15777e30 | 0.715415 | 0.357708 | − | 0.933834i | \(-0.383558\pi\) | ||||
0.357708 | + | 0.933834i | \(0.383558\pi\) | |||||||
\(830\) | 4.78303e30 | 1.07000 | ||||||||
\(831\) | 3.77323e30 | 0.833495 | ||||||||
\(832\) | 3.97105e30 | 0.866184 | ||||||||
\(833\) | 1.65474e30 | 0.356416 | ||||||||
\(834\) | −1.09726e30 | −0.233381 | ||||||||
\(835\) | 8.28463e29 | 0.174006 | ||||||||
\(836\) | −7.95194e30 | −1.64933 | ||||||||
\(837\) | 5.77440e29 | 0.118274 | ||||||||
\(838\) | −4.81074e30 | −0.973082 | ||||||||
\(839\) | −1.71221e28 | −0.00342024 | −0.00171012 | − | 0.999999i | \(-0.500544\pi\) | ||||
−0.00171012 | + | 0.999999i | \(0.500544\pi\) | |||||||
\(840\) | −5.34663e28 | −0.0105475 | ||||||||
\(841\) | −4.19549e30 | −0.817381 | ||||||||
\(842\) | 7.94168e30 | 1.52804 | ||||||||
\(843\) | 1.90790e30 | 0.362548 | ||||||||
\(844\) | −5.24327e30 | −0.984026 | ||||||||
\(845\) | 8.29177e30 | 1.53692 | ||||||||
\(846\) | 2.76153e30 | 0.505547 | ||||||||
\(847\) | 8.72016e29 | 0.157670 | ||||||||
\(848\) | −2.22453e30 | −0.397266 | ||||||||
\(849\) | −5.94193e29 | −0.104809 | ||||||||
\(850\) | −1.11349e29 | −0.0193994 | ||||||||
\(851\) | −5.83845e30 | −1.00470 | ||||||||
\(852\) | 7.20441e29 | 0.122457 | ||||||||
\(853\) | 2.27930e30 | 0.382680 | 0.191340 | − | 0.981524i | \(-0.438717\pi\) | ||||
0.191340 | + | 0.981524i | \(0.438717\pi\) | |||||||
\(854\) | 1.84403e29 | 0.0305816 | ||||||||
\(855\) | −2.32576e30 | −0.380996 | ||||||||
\(856\) | −4.90406e28 | −0.00793563 | ||||||||
\(857\) | −1.06629e31 | −1.70441 | −0.852207 | − | 0.523204i | \(-0.824737\pi\) | ||||
−0.852207 | + | 0.523204i | \(0.824737\pi\) | |||||||
\(858\) | −1.44190e31 | −2.27676 | ||||||||
\(859\) | −8.93547e29 | −0.139376 | −0.0696882 | − | 0.997569i | \(-0.522200\pi\) | ||||
−0.0696882 | + | 0.997569i | \(0.522200\pi\) | |||||||
\(860\) | 6.04793e30 | 0.931908 | ||||||||
\(861\) | −6.29150e28 | −0.00957682 | ||||||||
\(862\) | −9.49196e30 | −1.42735 | ||||||||
\(863\) | 2.82417e30 | 0.419543 | 0.209772 | − | 0.977750i | \(-0.432728\pi\) | ||||
0.209772 | + | 0.977750i | \(0.432728\pi\) | |||||||
\(864\) | −1.67809e30 | −0.246275 | ||||||||
\(865\) | 5.75567e30 | 0.834501 | ||||||||
\(866\) | −3.99448e30 | −0.572167 | ||||||||
\(867\) | −3.55727e30 | −0.503404 | ||||||||
\(868\) | 2.22435e29 | 0.0310990 | ||||||||
\(869\) | −3.39886e30 | −0.469490 | ||||||||
\(870\) | 2.46783e30 | 0.336793 | ||||||||
\(871\) | 1.07312e31 | 1.44696 | ||||||||
\(872\) | 4.88730e29 | 0.0651097 | ||||||||
\(873\) | 1.61701e30 | 0.212845 | ||||||||
\(874\) | 1.11076e31 | 1.44461 | ||||||||
\(875\) | −4.87342e29 | −0.0626253 | ||||||||
\(876\) | 6.67566e30 | 0.847620 | ||||||||
\(877\) | 9.06575e30 | 1.13739 | 0.568693 | − | 0.822550i | \(-0.307449\pi\) | ||||
0.568693 | + | 0.822550i | \(0.307449\pi\) | |||||||
\(878\) | 1.94490e31 | 2.41104 | ||||||||
\(879\) | 2.91118e30 | 0.356604 | ||||||||
\(880\) | −1.82796e31 | −2.21258 | ||||||||
\(881\) | 1.51630e31 | 1.81359 | 0.906794 | − | 0.421574i | \(-0.138522\pi\) | ||||
0.906794 | + | 0.421574i | \(0.138522\pi\) | |||||||
\(882\) | −3.75877e30 | −0.444248 | ||||||||
\(883\) | −1.16543e31 | −1.36113 | −0.680565 | − | 0.732688i | \(-0.738265\pi\) | ||||
−0.680565 | + | 0.732688i | \(0.738265\pi\) | |||||||
\(884\) | 3.88267e30 | 0.448107 | ||||||||
\(885\) | −6.76505e30 | −0.771555 | ||||||||
\(886\) | 8.20424e30 | 0.924664 | ||||||||
\(887\) | −7.76908e30 | −0.865309 | −0.432655 | − | 0.901560i | \(-0.642423\pi\) | ||||
−0.432655 | + | 0.901560i | \(0.642423\pi\) | |||||||
\(888\) | −1.53113e30 | −0.168529 | ||||||||
\(889\) | 8.84384e29 | 0.0961994 | ||||||||
\(890\) | −3.31179e29 | −0.0356014 | ||||||||
\(891\) | 1.94657e30 | 0.206802 | ||||||||
\(892\) | −5.15174e30 | −0.540907 | ||||||||
\(893\) | −1.22381e31 | −1.26991 | ||||||||
\(894\) | 3.94144e30 | 0.404214 | ||||||||
\(895\) | −7.46605e30 | −0.756744 | ||||||||
\(896\) | 3.49740e29 | 0.0350357 | ||||||||
\(897\) | 8.89435e30 | 0.880630 | ||||||||
\(898\) | −1.30702e31 | −1.27903 | ||||||||
\(899\) | 2.71532e30 | 0.262630 | ||||||||
\(900\) | 1.11696e29 | 0.0106780 | ||||||||
\(901\) | −1.29108e30 | −0.121995 | ||||||||
\(902\) | −6.91340e30 | −0.645688 | ||||||||
\(903\) | 4.62281e29 | 0.0426761 | ||||||||
\(904\) | 3.88266e30 | 0.354292 | ||||||||
\(905\) | −4.28265e30 | −0.386280 | ||||||||
\(906\) | −4.15570e30 | −0.370509 | ||||||||
\(907\) | 5.71533e30 | 0.503692 | 0.251846 | − | 0.967767i | \(-0.418962\pi\) | ||||
0.251846 | + | 0.967767i | \(0.418962\pi\) | |||||||
\(908\) | −3.39800e30 | −0.296021 | ||||||||
\(909\) | 6.12425e29 | 0.0527390 | ||||||||
\(910\) | −1.62451e30 | −0.138289 | ||||||||
\(911\) | 2.22259e30 | 0.187032 | 0.0935160 | − | 0.995618i | \(-0.470189\pi\) | ||||
0.0935160 | + | 0.995618i | \(0.470189\pi\) | |||||||
\(912\) | 9.06324e30 | 0.753942 | ||||||||
\(913\) | 1.77408e31 | 1.45891 | ||||||||
\(914\) | −2.20581e31 | −1.79322 | ||||||||
\(915\) | 2.61716e30 | 0.210333 | ||||||||
\(916\) | 6.84342e30 | 0.543714 | ||||||||
\(917\) | −5.99171e29 | −0.0470623 | ||||||||
\(918\) | −1.18695e30 | −0.0921693 | ||||||||
\(919\) | −9.94638e30 | −0.763576 | −0.381788 | − | 0.924250i | \(-0.624692\pi\) | ||||
−0.381788 | + | 0.924250i | \(0.624692\pi\) | |||||||
\(920\) | 3.62408e30 | 0.275059 | ||||||||
\(921\) | −8.84722e29 | −0.0663866 | ||||||||
\(922\) | 1.20962e31 | 0.897378 | ||||||||
\(923\) | −5.78926e30 | −0.424624 | ||||||||
\(924\) | 7.49838e29 | 0.0543766 | ||||||||
\(925\) | 5.89175e29 | 0.0422431 | ||||||||
\(926\) | −4.49324e30 | −0.318526 | ||||||||
\(927\) | −4.49859e30 | −0.315311 | ||||||||
\(928\) | −7.89093e30 | −0.546858 | ||||||||
\(929\) | 6.57341e30 | 0.450429 | 0.225214 | − | 0.974309i | \(-0.427692\pi\) | ||||
0.225214 | + | 0.974309i | \(0.427692\pi\) | |||||||
\(930\) | 7.14879e30 | 0.484353 | ||||||||
\(931\) | 1.66575e31 | 1.11593 | ||||||||
\(932\) | 5.69320e30 | 0.377128 | ||||||||
\(933\) | −8.78615e30 | −0.575495 | ||||||||
\(934\) | −1.83688e30 | −0.118970 | ||||||||
\(935\) | −1.06091e31 | −0.679452 | ||||||||
\(936\) | 2.33254e30 | 0.147717 | ||||||||
\(937\) | −9.88672e30 | −0.619137 | −0.309568 | − | 0.950877i | \(-0.600185\pi\) | ||||
−0.309568 | + | 0.950877i | \(0.600185\pi\) | |||||||
\(938\) | −1.26371e30 | −0.0782561 | ||||||||
\(939\) | −6.55213e30 | −0.401230 | ||||||||
\(940\) | 1.50976e31 | 0.914253 | ||||||||
\(941\) | 1.35253e31 | 0.809947 | 0.404973 | − | 0.914328i | \(-0.367281\pi\) | ||||
0.404973 | + | 0.914328i | \(0.367281\pi\) | |||||||
\(942\) | −1.07796e31 | −0.638361 | ||||||||
\(943\) | 4.26454e30 | 0.249746 | ||||||||
\(944\) | 2.63627e31 | 1.52681 | ||||||||
\(945\) | 2.19311e29 | 0.0125610 | ||||||||
\(946\) | 5.07976e31 | 2.87731 | ||||||||
\(947\) | −2.26830e31 | −1.27065 | −0.635325 | − | 0.772245i | \(-0.719134\pi\) | ||||
−0.635325 | + | 0.772245i | \(0.719134\pi\) | |||||||
\(948\) | −2.07896e30 | −0.115175 | ||||||||
\(949\) | −5.36437e31 | −2.93916 | ||||||||
\(950\) | −1.12090e30 | −0.0607392 | ||||||||
\(951\) | 4.22085e30 | 0.226206 | ||||||||
\(952\) | 1.20924e29 | 0.00640952 | ||||||||
\(953\) | 3.45875e31 | 1.81319 | 0.906595 | − | 0.422002i | \(-0.138673\pi\) | ||||
0.906595 | + | 0.422002i | \(0.138673\pi\) | |||||||
\(954\) | 2.93270e30 | 0.152058 | ||||||||
\(955\) | −1.02645e31 | −0.526386 | ||||||||
\(956\) | 1.37516e31 | 0.697501 | ||||||||
\(957\) | 9.15344e30 | 0.459207 | ||||||||
\(958\) | −3.43011e31 | −1.70204 | ||||||||
\(959\) | 1.83667e30 | 0.0901438 | ||||||||
\(960\) | −6.63694e30 | −0.322196 | ||||||||
\(961\) | −1.29598e31 | −0.622304 | ||||||||
\(962\) | −4.65216e31 | −2.20961 | ||||||||
\(963\) | 2.01157e29 | 0.00945059 | ||||||||
\(964\) | −2.16480e31 | −1.00602 | ||||||||
\(965\) | 2.88678e31 | 1.32702 | ||||||||
\(966\) | −1.04741e30 | −0.0476272 | ||||||||
\(967\) | −1.92820e31 | −0.867311 | −0.433655 | − | 0.901079i | \(-0.642776\pi\) | ||||
−0.433655 | + | 0.901079i | \(0.642776\pi\) | |||||||
\(968\) | −1.55009e31 | −0.689707 | ||||||||
\(969\) | 5.26015e30 | 0.231525 | ||||||||
\(970\) | 2.00189e31 | 0.871638 | ||||||||
\(971\) | −2.95793e31 | −1.27405 | −0.637024 | − | 0.770844i | \(-0.719835\pi\) | ||||
−0.637024 | + | 0.770844i | \(0.719835\pi\) | |||||||
\(972\) | 1.19065e30 | 0.0507326 | ||||||||
\(973\) | −4.58530e29 | −0.0193278 | ||||||||
\(974\) | 3.86058e31 | 1.60984 | ||||||||
\(975\) | −8.97554e29 | −0.0370265 | ||||||||
\(976\) | −1.01988e31 | −0.416222 | ||||||||
\(977\) | 4.86581e31 | 1.96455 | 0.982274 | − | 0.187453i | \(-0.0600233\pi\) | ||||
0.982274 | + | 0.187453i | \(0.0600233\pi\) | |||||||
\(978\) | −2.06864e31 | −0.826280 | ||||||||
\(979\) | −1.22838e30 | −0.0485415 | ||||||||
\(980\) | −2.05497e31 | −0.803398 | ||||||||
\(981\) | −2.00469e30 | −0.0775396 | ||||||||
\(982\) | −1.10703e31 | −0.423633 | ||||||||
\(983\) | 4.31738e31 | 1.63459 | 0.817294 | − | 0.576220i | \(-0.195473\pi\) | ||||
0.817294 | + | 0.576220i | \(0.195473\pi\) | |||||||
\(984\) | 1.11837e30 | 0.0418926 | ||||||||
\(985\) | 4.58211e31 | 1.69819 | ||||||||
\(986\) | −5.58146e30 | −0.204664 | ||||||||
\(987\) | 1.15401e30 | 0.0418676 | ||||||||
\(988\) | 3.90850e31 | 1.40301 | ||||||||
\(989\) | −3.13345e31 | −1.11292 | ||||||||
\(990\) | 2.40989e31 | 0.846890 | ||||||||
\(991\) | 3.44591e31 | 1.19820 | 0.599101 | − | 0.800673i | \(-0.295525\pi\) | ||||
0.599101 | + | 0.800673i | \(0.295525\pi\) | |||||||
\(992\) | −2.28584e31 | −0.786453 | ||||||||
\(993\) | −2.98592e31 | −1.01651 | ||||||||
\(994\) | 6.81748e29 | 0.0229650 | ||||||||
\(995\) | 1.19070e30 | 0.0396880 | ||||||||
\(996\) | 1.08514e31 | 0.357900 | ||||||||
\(997\) | 3.62353e31 | 1.18259 | 0.591293 | − | 0.806457i | \(-0.298618\pi\) | ||||
0.591293 | + | 0.806457i | \(0.298618\pi\) | |||||||
\(998\) | −2.26804e31 | −0.732452 | ||||||||
\(999\) | 6.28046e30 | 0.200703 |
(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 | 3.22.a.c.1.2 | ✓ | 2 | |
3.2 | odd | 2 | 9.22.a.e.1.1 | 2 | |||
4.3 | odd | 2 | 48.22.a.g.1.2 | 2 | |||
5.2 | odd | 4 | 75.22.b.d.49.4 | 4 | |||
5.3 | odd | 4 | 75.22.b.d.49.1 | 4 | |||
5.4 | even | 2 | 75.22.a.d.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.22.a.c.1.2 | ✓ | 2 | 1.1 | even | 1 | trivial | |
9.22.a.e.1.1 | 2 | 3.2 | odd | 2 | |||
48.22.a.g.1.2 | 2 | 4.3 | odd | 2 | |||
75.22.a.d.1.1 | 2 | 5.4 | even | 2 | |||
75.22.b.d.49.1 | 4 | 5.3 | odd | 4 | |||
75.22.b.d.49.4 | 4 | 5.2 | odd | 4 |