Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,24,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 24, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 24);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 24 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(83.8010093363\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{144169}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 36042 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(190.348\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5096.35 | −1.75960 | −0.879801 | − | 0.475342i | \(-0.842324\pi\) | ||||
−0.879801 | + | 0.475342i | \(0.842324\pi\) | |||||||
\(3\) | 48964.9 | 0.159584 | 0.0797921 | − | 0.996812i | \(-0.474574\pi\) | ||||
0.0797921 | + | 0.996812i | \(0.474574\pi\) | |||||||
\(4\) | 1.75842e7 | 2.09620 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.49542e8 | −0.280805 | ||||||||
\(7\) | 5.17135e9 | 0.988500 | 0.494250 | − | 0.869320i | \(-0.335443\pi\) | ||||
0.494250 | + | 0.869320i | \(0.335443\pi\) | |||||||
\(8\) | −4.68639e10 | −1.92887 | ||||||||
\(9\) | −9.17456e10 | −0.974533 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.04602e11 | 0.638931 | 0.319466 | − | 0.947598i | \(-0.396497\pi\) | ||||
0.319466 | + | 0.947598i | \(0.396497\pi\) | |||||||
\(12\) | 8.61007e11 | 0.334520 | ||||||||
\(13\) | −7.96710e12 | −1.23297 | −0.616484 | − | 0.787367i | \(-0.711444\pi\) | ||||
−0.616484 | + | 0.787367i | \(0.711444\pi\) | |||||||
\(14\) | −2.63550e13 | −1.73937 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 9.13280e13 | 1.29785 | ||||||||
\(17\) | −1.98385e13 | −0.140393 | −0.0701967 | − | 0.997533i | \(-0.522363\pi\) | ||||
−0.0701967 | + | 0.997533i | \(0.522363\pi\) | |||||||
\(18\) | 4.67568e14 | 1.71479 | ||||||||
\(19\) | 6.27346e14 | 1.23550 | 0.617748 | − | 0.786377i | \(-0.288045\pi\) | ||||
0.617748 | + | 0.786377i | \(0.288045\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.53215e14 | 0.157749 | ||||||||
\(22\) | −3.08127e15 | −1.12426 | ||||||||
\(23\) | 4.55685e15 | 0.997229 | 0.498614 | − | 0.866824i | \(-0.333842\pi\) | ||||
0.498614 | + | 0.866824i | \(0.333842\pi\) | |||||||
\(24\) | −2.29468e15 | −0.307818 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.06032e16 | 2.16953 | ||||||||
\(27\) | −9.10202e15 | −0.315104 | ||||||||
\(28\) | 9.09340e16 | 2.07209 | ||||||||
\(29\) | 4.14107e16 | 0.630283 | 0.315142 | − | 0.949045i | \(-0.397948\pi\) | ||||
0.315142 | + | 0.949045i | \(0.397948\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.35683e15 | 0.00959104 | 0.00479552 | − | 0.999989i | \(-0.498474\pi\) | ||||
0.00479552 | + | 0.999989i | \(0.498474\pi\) | |||||||
\(32\) | −7.23169e16 | −0.354826 | ||||||||
\(33\) | 2.96043e16 | 0.101963 | ||||||||
\(34\) | 1.01104e17 | 0.247037 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.61327e18 | −2.04281 | ||||||||
\(37\) | −3.41258e17 | −0.315328 | −0.157664 | − | 0.987493i | \(-0.550396\pi\) | ||||
−0.157664 | + | 0.987493i | \(0.550396\pi\) | |||||||
\(38\) | −3.19718e18 | −2.17398 | ||||||||
\(39\) | −3.90108e17 | −0.196762 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.69518e18 | −1.04863 | −0.524313 | − | 0.851525i | \(-0.675678\pi\) | ||||
−0.524313 | + | 0.851525i | \(0.675678\pi\) | |||||||
\(42\) | −1.29047e18 | −0.277576 | ||||||||
\(43\) | 1.96955e18 | 0.323207 | 0.161603 | − | 0.986856i | \(-0.448333\pi\) | ||||
0.161603 | + | 0.986856i | \(0.448333\pi\) | |||||||
\(44\) | 1.06314e19 | 1.33933 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.32233e19 | −1.75473 | ||||||||
\(47\) | −2.44381e19 | −1.44192 | −0.720962 | − | 0.692975i | \(-0.756300\pi\) | ||||
−0.720962 | + | 0.692975i | \(0.756300\pi\) | |||||||
\(48\) | 4.47186e18 | 0.207116 | ||||||||
\(49\) | −6.25860e17 | −0.0228677 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −9.71391e17 | −0.0224046 | ||||||||
\(52\) | −1.40095e20 | −2.58455 | ||||||||
\(53\) | 6.39437e19 | 0.947600 | 0.473800 | − | 0.880632i | \(-0.342882\pi\) | ||||
0.473800 | + | 0.880632i | \(0.342882\pi\) | |||||||
\(54\) | 4.63871e19 | 0.554458 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.42350e20 | −1.90669 | ||||||||
\(57\) | 3.07179e19 | 0.197166 | ||||||||
\(58\) | −2.11044e20 | −1.10905 | ||||||||
\(59\) | 2.81892e20 | 1.21698 | 0.608491 | − | 0.793561i | \(-0.291775\pi\) | ||||
0.608491 | + | 0.793561i | \(0.291775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.67790e20 | −1.37644 | −0.688221 | − | 0.725501i | \(-0.741608\pi\) | ||||
−0.688221 | + | 0.725501i | \(0.741608\pi\) | |||||||
\(62\) | −6.91488e18 | −0.0168764 | ||||||||
\(63\) | −4.74449e20 | −0.963326 | ||||||||
\(64\) | −3.97563e20 | −0.673498 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.50874e20 | −0.179415 | ||||||||
\(67\) | −2.77406e20 | −0.277495 | −0.138747 | − | 0.990328i | \(-0.544308\pi\) | ||||
−0.138747 | + | 0.990328i | \(0.544308\pi\) | |||||||
\(68\) | −3.48844e20 | −0.294293 | ||||||||
\(69\) | 2.23126e20 | 0.159142 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.29069e21 | 1.17624 | 0.588119 | − | 0.808775i | \(-0.299869\pi\) | ||||
0.588119 | + | 0.808775i | \(0.299869\pi\) | |||||||
\(72\) | 4.29956e21 | 1.87975 | ||||||||
\(73\) | 4.56908e21 | 1.70457 | 0.852286 | − | 0.523075i | \(-0.175215\pi\) | ||||
0.852286 | + | 0.523075i | \(0.175215\pi\) | |||||||
\(74\) | 1.73917e21 | 0.554852 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.10314e22 | 2.58984 | ||||||||
\(77\) | 3.12661e21 | 0.631583 | ||||||||
\(78\) | 1.98813e21 | 0.346223 | ||||||||
\(79\) | −3.99005e21 | −0.600160 | −0.300080 | − | 0.953914i | \(-0.597013\pi\) | ||||
−0.300080 | + | 0.953914i | \(0.597013\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.19155e21 | 0.924247 | ||||||||
\(82\) | 1.88319e22 | 1.84517 | ||||||||
\(83\) | −1.45920e22 | −1.24370 | −0.621850 | − | 0.783136i | \(-0.713619\pi\) | ||||
−0.621850 | + | 0.783136i | \(0.713619\pi\) | |||||||
\(84\) | 4.45257e21 | 0.330673 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.00375e22 | −0.568715 | ||||||||
\(87\) | 2.02767e21 | 0.100583 | ||||||||
\(88\) | −2.83340e22 | −1.23242 | ||||||||
\(89\) | 1.80991e21 | 0.0691310 | 0.0345655 | − | 0.999402i | \(-0.488995\pi\) | ||||
0.0345655 | + | 0.999402i | \(0.488995\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.12007e22 | −1.21879 | ||||||||
\(92\) | 8.01285e22 | 2.09039 | ||||||||
\(93\) | 6.64369e19 | 0.00153058 | ||||||||
\(94\) | 1.24545e23 | 2.53721 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.54099e21 | −0.0566246 | ||||||||
\(97\) | −8.25561e22 | −1.17186 | −0.585928 | − | 0.810363i | \(-0.699270\pi\) | ||||
−0.585928 | + | 0.810363i | \(0.699270\pi\) | |||||||
\(98\) | 3.18960e21 | 0.0402380 | ||||||||
\(99\) | −5.54696e22 | −0.622659 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.84234e22 | 0.431877 | 0.215938 | − | 0.976407i | \(-0.430719\pi\) | ||||
0.215938 | + | 0.976407i | \(0.430719\pi\) | |||||||
\(102\) | 4.95055e21 | 0.0394231 | ||||||||
\(103\) | 3.23687e22 | 0.230408 | 0.115204 | − | 0.993342i | \(-0.463248\pi\) | ||||
0.115204 | + | 0.993342i | \(0.463248\pi\) | |||||||
\(104\) | 3.73370e23 | 2.37824 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.25880e23 | −1.66740 | ||||||||
\(107\) | 5.92757e22 | 0.272247 | 0.136124 | − | 0.990692i | \(-0.456536\pi\) | ||||
0.136124 | + | 0.990692i | \(0.456536\pi\) | |||||||
\(108\) | −1.60052e23 | −0.660521 | ||||||||
\(109\) | 2.86887e23 | 1.06490 | 0.532448 | − | 0.846463i | \(-0.321272\pi\) | ||||
0.532448 | + | 0.846463i | \(0.321272\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.67096e22 | −0.0503214 | ||||||||
\(112\) | 4.72290e23 | 1.28292 | ||||||||
\(113\) | 4.87844e22 | 0.119641 | 0.0598204 | − | 0.998209i | \(-0.480947\pi\) | ||||
0.0598204 | + | 0.998209i | \(0.480947\pi\) | |||||||
\(114\) | −1.56549e23 | −0.346933 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 7.28174e23 | 1.32120 | ||||||||
\(117\) | 7.30947e23 | 1.20157 | ||||||||
\(118\) | −1.43662e24 | −2.14140 | ||||||||
\(119\) | −1.02592e23 | −0.138779 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.29886e23 | −0.591767 | ||||||||
\(122\) | 2.38402e24 | 2.42199 | ||||||||
\(123\) | −1.80934e23 | −0.167344 | ||||||||
\(124\) | 2.38587e22 | 0.0201047 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.41796e24 | 1.69507 | ||||||||
\(127\) | −1.36871e24 | −0.876131 | −0.438065 | − | 0.898943i | \(-0.644336\pi\) | ||||
−0.438065 | + | 0.898943i | \(0.644336\pi\) | |||||||
\(128\) | 2.63276e24 | 1.53991 | ||||||||
\(129\) | 9.64389e22 | 0.0515787 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.63272e24 | 1.17974 | 0.589869 | − | 0.807499i | \(-0.299180\pi\) | ||||
0.589869 | + | 0.807499i | \(0.299180\pi\) | |||||||
\(132\) | 5.20567e23 | 0.213735 | ||||||||
\(133\) | 3.24423e24 | 1.22129 | ||||||||
\(134\) | 1.41376e24 | 0.488280 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 9.29711e23 | 0.270801 | ||||||||
\(137\) | 1.21837e24 | 0.326207 | 0.163103 | − | 0.986609i | \(-0.447850\pi\) | ||||
0.163103 | + | 0.986609i | \(0.447850\pi\) | |||||||
\(138\) | −1.13713e24 | −0.280027 | ||||||||
\(139\) | −3.72223e24 | −0.843593 | −0.421797 | − | 0.906690i | \(-0.638600\pi\) | ||||
−0.421797 | + | 0.906690i | \(0.638600\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.19661e24 | −0.230108 | ||||||||
\(142\) | −1.16741e25 | −2.06971 | ||||||||
\(143\) | −4.81693e24 | −0.787782 | ||||||||
\(144\) | −8.37895e24 | −1.26480 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2.32856e25 | −2.99937 | ||||||||
\(147\) | −3.06452e22 | −0.00364932 | ||||||||
\(148\) | −6.00074e24 | −0.660990 | ||||||||
\(149\) | 1.53044e25 | 1.56018 | 0.780088 | − | 0.625670i | \(-0.215174\pi\) | ||||
0.780088 | + | 0.625670i | \(0.215174\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.25232e25 | −1.09516 | −0.547582 | − | 0.836752i | \(-0.684452\pi\) | ||||
−0.547582 | + | 0.836752i | \(0.684452\pi\) | |||||||
\(152\) | −2.93999e25 | −2.38311 | ||||||||
\(153\) | 1.82010e24 | 0.136818 | ||||||||
\(154\) | −1.59343e25 | −1.11134 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6.85973e24 | −0.412453 | ||||||||
\(157\) | −1.92166e23 | −0.0107357 | −0.00536785 | − | 0.999986i | \(-0.501709\pi\) | ||||
−0.00536785 | + | 0.999986i | \(0.501709\pi\) | |||||||
\(158\) | 2.03347e25 | 1.05604 | ||||||||
\(159\) | 3.13099e24 | 0.151222 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.35651e25 | 0.985761 | ||||||||
\(162\) | −4.17470e25 | −1.62631 | ||||||||
\(163\) | 2.27639e25 | 0.826206 | 0.413103 | − | 0.910684i | \(-0.364445\pi\) | ||||
0.413103 | + | 0.910684i | \(0.364445\pi\) | |||||||
\(164\) | −6.49767e25 | −2.19813 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.43657e25 | 2.18842 | ||||||||
\(167\) | 1.17984e25 | 0.324029 | 0.162015 | − | 0.986788i | \(-0.448201\pi\) | ||||
0.162015 | + | 0.986788i | \(0.448201\pi\) | |||||||
\(168\) | −1.18666e25 | −0.304278 | ||||||||
\(169\) | 2.17208e25 | 0.520211 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.75563e25 | −1.20403 | ||||||||
\(172\) | 3.46330e25 | 0.677506 | ||||||||
\(173\) | 4.75865e25 | 0.870871 | 0.435435 | − | 0.900220i | \(-0.356594\pi\) | ||||
0.435435 | + | 0.900220i | \(0.356594\pi\) | |||||||
\(174\) | −1.03337e25 | −0.176987 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.52172e25 | 0.829236 | ||||||||
\(177\) | 1.38028e25 | 0.194211 | ||||||||
\(178\) | −9.22395e24 | −0.121643 | ||||||||
\(179\) | 9.84804e25 | 1.21770 | 0.608850 | − | 0.793286i | \(-0.291631\pi\) | ||||
0.608850 | + | 0.793286i | \(0.291631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.76456e25 | 0.518465 | 0.259233 | − | 0.965815i | \(-0.416530\pi\) | ||||
0.259233 | + | 0.965815i | \(0.416530\pi\) | |||||||
\(182\) | 2.09973e26 | 2.14458 | ||||||||
\(183\) | −2.29053e25 | −0.219659 | ||||||||
\(184\) | −2.13552e26 | −1.92353 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.38586e23 | −0.00269321 | ||||||||
\(187\) | −1.19944e25 | −0.0897017 | ||||||||
\(188\) | −4.29724e26 | −3.02256 | ||||||||
\(189\) | −4.70697e25 | −0.311481 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.54117e25 | −0.500765 | −0.250382 | − | 0.968147i | \(-0.580556\pi\) | ||||
−0.250382 | + | 0.968147i | \(0.580556\pi\) | |||||||
\(192\) | −1.94666e25 | −0.107480 | ||||||||
\(193\) | 2.66797e26 | 1.38762 | 0.693812 | − | 0.720156i | \(-0.255930\pi\) | ||||
0.693812 | + | 0.720156i | \(0.255930\pi\) | |||||||
\(194\) | 4.20735e26 | 2.06200 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.10052e25 | −0.0479352 | ||||||||
\(197\) | 1.00070e26 | 0.411095 | 0.205547 | − | 0.978647i | \(-0.434103\pi\) | ||||
0.205547 | + | 0.978647i | \(0.434103\pi\) | |||||||
\(198\) | 2.82693e26 | 1.09563 | ||||||||
\(199\) | 4.46897e26 | 1.63454 | 0.817272 | − | 0.576251i | \(-0.195485\pi\) | ||||
0.817272 | + | 0.576251i | \(0.195485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.35831e25 | −0.0442838 | ||||||||
\(202\) | −2.46783e26 | −0.759931 | ||||||||
\(203\) | 2.14149e26 | 0.623035 | ||||||||
\(204\) | −1.70811e25 | −0.0469645 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1.64962e26 | −0.405426 | ||||||||
\(207\) | −4.18071e26 | −0.971832 | ||||||||
\(208\) | −7.27620e26 | −1.60021 | ||||||||
\(209\) | 3.79295e26 | 0.789396 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.96987e26 | −1.48663 | −0.743315 | − | 0.668941i | \(-0.766748\pi\) | ||||
−0.743315 | + | 0.668941i | \(0.766748\pi\) | |||||||
\(212\) | 1.12440e27 | 1.98636 | ||||||||
\(213\) | 1.12163e26 | 0.187709 | ||||||||
\(214\) | −3.02090e26 | −0.479047 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 4.26556e26 | 0.607796 | ||||||||
\(217\) | 7.01664e24 | 0.00948074 | ||||||||
\(218\) | −1.46208e27 | −1.87379 | ||||||||
\(219\) | 2.23724e26 | 0.272023 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.58056e26 | 0.173101 | ||||||||
\(222\) | 8.51582e25 | 0.0885456 | ||||||||
\(223\) | 5.69004e26 | 0.561836 | 0.280918 | − | 0.959732i | \(-0.409361\pi\) | ||||
0.280918 | + | 0.959732i | \(0.409361\pi\) | |||||||
\(224\) | −3.73976e26 | −0.350745 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.48623e26 | −0.210520 | ||||||||
\(227\) | 1.82165e27 | 1.46611 | 0.733056 | − | 0.680168i | \(-0.238093\pi\) | ||||
0.733056 | + | 0.680168i | \(0.238093\pi\) | |||||||
\(228\) | 5.40150e26 | 0.413298 | ||||||||
\(229\) | 1.11330e27 | 0.810032 | 0.405016 | − | 0.914310i | \(-0.367266\pi\) | ||||
0.405016 | + | 0.914310i | \(0.367266\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.53094e26 | 0.100791 | ||||||||
\(232\) | −1.94067e27 | −1.21574 | ||||||||
\(233\) | 1.63214e27 | 0.973118 | 0.486559 | − | 0.873648i | \(-0.338252\pi\) | ||||
0.486559 | + | 0.873648i | \(0.338252\pi\) | |||||||
\(234\) | −3.72516e27 | −2.11428 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.95683e27 | 2.55104 | ||||||||
\(237\) | −1.95372e26 | −0.0957761 | ||||||||
\(238\) | 5.22845e26 | 0.244196 | ||||||||
\(239\) | 2.58550e27 | 1.15072 | 0.575358 | − | 0.817902i | \(-0.304863\pi\) | ||||
0.575358 | + | 0.817902i | \(0.304863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.86784e27 | 0.755340 | 0.377670 | − | 0.925940i | \(-0.376725\pi\) | ||||
0.377670 | + | 0.925940i | \(0.376725\pi\) | |||||||
\(242\) | 2.70049e27 | 1.04127 | ||||||||
\(243\) | 1.25799e27 | 0.462600 | ||||||||
\(244\) | −8.22571e27 | −2.88530 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.22102e26 | 0.294459 | ||||||||
\(247\) | −4.99813e27 | −1.52333 | ||||||||
\(248\) | −6.35863e25 | −0.0184999 | ||||||||
\(249\) | −7.14493e26 | −0.198475 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.11170e27 | −1.04177 | −0.520887 | − | 0.853626i | \(-0.674399\pi\) | ||||
−0.520887 | + | 0.853626i | \(0.674399\pi\) | |||||||
\(252\) | −8.34280e27 | −2.01932 | ||||||||
\(253\) | 2.75508e27 | 0.637160 | ||||||||
\(254\) | 6.97543e27 | 1.54164 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.00825e28 | −2.03614 | ||||||||
\(257\) | 5.10426e27 | 0.985603 | 0.492802 | − | 0.870142i | \(-0.335973\pi\) | ||||
0.492802 | + | 0.870142i | \(0.335973\pi\) | |||||||
\(258\) | −4.91487e26 | −0.0907580 | ||||||||
\(259\) | −1.76476e27 | −0.311702 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.79925e27 | −0.614232 | ||||||||
\(262\) | −1.34173e28 | −2.07587 | ||||||||
\(263\) | −9.95433e27 | −1.47408 | −0.737040 | − | 0.675849i | \(-0.763777\pi\) | ||||
−0.737040 | + | 0.675849i | \(0.763777\pi\) | |||||||
\(264\) | −1.38737e27 | −0.196674 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.65337e28 | −2.14898 | ||||||||
\(267\) | 8.86222e25 | 0.0110322 | ||||||||
\(268\) | −4.87795e27 | −0.581684 | ||||||||
\(269\) | 6.42524e26 | 0.0734071 | 0.0367036 | − | 0.999326i | \(-0.488314\pi\) | ||||
0.0367036 | + | 0.999326i | \(0.488314\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.19246e28 | 1.25111 | 0.625557 | − | 0.780178i | \(-0.284872\pi\) | ||||
0.625557 | + | 0.780178i | \(0.284872\pi\) | |||||||
\(272\) | −1.81181e27 | −0.182210 | ||||||||
\(273\) | −2.01739e27 | −0.194500 | ||||||||
\(274\) | −6.20925e27 | −0.573994 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.92348e27 | 0.333593 | ||||||||
\(277\) | 5.29510e27 | 0.431874 | 0.215937 | − | 0.976407i | \(-0.430719\pi\) | ||||
0.215937 | + | 0.976407i | \(0.430719\pi\) | |||||||
\(278\) | 1.89698e28 | 1.48439 | ||||||||
\(279\) | −1.24483e26 | −0.00934678 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.67433e27 | 0.669111 | 0.334556 | − | 0.942376i | \(-0.391414\pi\) | ||||
0.334556 | + | 0.942376i | \(0.391414\pi\) | |||||||
\(282\) | 6.09834e27 | 0.404899 | ||||||||
\(283\) | 2.62436e28 | 1.67294 | 0.836468 | − | 0.548016i | \(-0.184617\pi\) | ||||
0.836468 | + | 0.548016i | \(0.184617\pi\) | |||||||
\(284\) | 4.02799e28 | 2.46563 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.45488e28 | 1.38618 | ||||||||
\(287\) | −1.91091e28 | −1.03657 | ||||||||
\(288\) | 6.63476e27 | 0.345789 | ||||||||
\(289\) | −1.95740e28 | −0.980290 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.04235e27 | −0.187010 | ||||||||
\(292\) | 8.03435e28 | 3.57312 | ||||||||
\(293\) | −3.20151e28 | −1.36892 | −0.684458 | − | 0.729052i | \(-0.739961\pi\) | ||||
−0.684458 | + | 0.729052i | \(0.739961\pi\) | |||||||
\(294\) | 1.56178e26 | 0.00642136 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.59927e28 | 0.608228 | ||||||||
\(297\) | −5.50310e27 | −0.201330 | ||||||||
\(298\) | −7.79965e28 | −2.74529 | ||||||||
\(299\) | −3.63049e28 | −1.22955 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.01853e28 | 0.319490 | ||||||||
\(302\) | 6.38225e28 | 1.92705 | ||||||||
\(303\) | 2.37105e27 | 0.0689207 | ||||||||
\(304\) | 5.72943e28 | 1.60349 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −9.27586e27 | −0.240745 | ||||||||
\(307\) | 1.15407e28 | 0.288496 | 0.144248 | − | 0.989542i | \(-0.453924\pi\) | ||||
0.144248 | + | 0.989542i | \(0.453924\pi\) | |||||||
\(308\) | 5.49789e28 | 1.32392 | ||||||||
\(309\) | 1.58493e27 | 0.0367695 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.62817e28 | 0.781525 | 0.390763 | − | 0.920491i | \(-0.372211\pi\) | ||||
0.390763 | + | 0.920491i | \(0.372211\pi\) | |||||||
\(312\) | 1.82820e28 | 0.379530 | ||||||||
\(313\) | −2.56117e28 | −0.512481 | −0.256241 | − | 0.966613i | \(-0.582484\pi\) | ||||
−0.256241 | + | 0.966613i | \(0.582484\pi\) | |||||||
\(314\) | 9.79346e26 | 0.0188906 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.01618e28 | −1.25805 | ||||||||
\(317\) | 2.91424e27 | 0.0503899 | 0.0251950 | − | 0.999683i | \(-0.491979\pi\) | ||||
0.0251950 | + | 0.999683i | \(0.491979\pi\) | |||||||
\(318\) | −1.59566e28 | −0.266091 | ||||||||
\(319\) | 2.50370e28 | 0.402708 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.90243e27 | 0.0434464 | ||||||||
\(322\) | −1.20096e29 | −1.73455 | ||||||||
\(323\) | −1.24456e28 | −0.173455 | ||||||||
\(324\) | 1.44042e29 | 1.93741 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.16013e29 | −1.45379 | ||||||||
\(327\) | 1.40474e28 | 0.169940 | ||||||||
\(328\) | 1.73170e29 | 2.02267 | ||||||||
\(329\) | −1.26378e29 | −1.42534 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.00537e28 | 0.421328 | 0.210664 | − | 0.977558i | \(-0.432437\pi\) | ||||
0.210664 | + | 0.977558i | \(0.432437\pi\) | |||||||
\(332\) | −2.56588e29 | −2.60704 | ||||||||
\(333\) | 3.13089e28 | 0.307298 | ||||||||
\(334\) | −6.01289e28 | −0.570163 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.31256e28 | 0.204735 | ||||||||
\(337\) | −1.31131e29 | −1.12192 | −0.560959 | − | 0.827843i | \(-0.689568\pi\) | ||||
−0.560959 | + | 0.827843i | \(0.689568\pi\) | |||||||
\(338\) | −1.10697e29 | −0.915364 | ||||||||
\(339\) | 2.38872e27 | 0.0190928 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8.20342e26 | 0.00612801 | ||||||||
\(342\) | 2.93327e29 | 2.11861 | ||||||||
\(343\) | −1.44770e29 | −1.01110 | ||||||||
\(344\) | −9.23010e28 | −0.623425 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.42518e29 | −1.53239 | ||||||||
\(347\) | −1.14051e29 | −0.697126 | −0.348563 | − | 0.937285i | \(-0.613330\pi\) | ||||
−0.348563 | + | 0.937285i | \(0.613330\pi\) | |||||||
\(348\) | 3.56549e28 | 0.210843 | ||||||||
\(349\) | 7.28518e28 | 0.416820 | 0.208410 | − | 0.978042i | \(-0.433171\pi\) | ||||
0.208410 | + | 0.978042i | \(0.433171\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.25167e28 | 0.388514 | ||||||||
\(352\) | −4.37230e28 | −0.226709 | ||||||||
\(353\) | 3.68425e29 | 1.84902 | 0.924508 | − | 0.381164i | \(-0.124477\pi\) | ||||
0.924508 | + | 0.381164i | \(0.124477\pi\) | |||||||
\(354\) | −7.03438e28 | −0.341734 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.18259e28 | 0.144912 | ||||||||
\(357\) | −5.02340e27 | −0.0221469 | ||||||||
\(358\) | −5.01891e29 | −2.14267 | ||||||||
\(359\) | −2.45802e29 | −1.01625 | −0.508123 | − | 0.861284i | \(-0.669661\pi\) | ||||
−0.508123 | + | 0.861284i | \(0.669661\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.35734e29 | 0.526448 | ||||||||
\(362\) | −2.42819e29 | −0.912292 | ||||||||
\(363\) | −2.59458e28 | −0.0944367 | ||||||||
\(364\) | −7.24481e29 | −2.55482 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 1.16733e29 | 0.386512 | ||||||||
\(367\) | 4.73025e29 | 1.51783 | 0.758917 | − | 0.651187i | \(-0.225729\pi\) | ||||
0.758917 | + | 0.651187i | \(0.225729\pi\) | |||||||
\(368\) | 4.16168e29 | 1.29425 | ||||||||
\(369\) | 3.39016e29 | 1.02192 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.30675e29 | 0.936703 | ||||||||
\(372\) | 1.16824e27 | 0.00320840 | ||||||||
\(373\) | 2.90241e29 | 0.772872 | 0.386436 | − | 0.922316i | \(-0.373706\pi\) | ||||
0.386436 | + | 0.922316i | \(0.373706\pi\) | |||||||
\(374\) | 6.11278e28 | 0.157839 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.14526e30 | 2.78129 | ||||||||
\(377\) | −3.29924e29 | −0.777120 | ||||||||
\(378\) | 2.39884e29 | 0.548082 | ||||||||
\(379\) | 2.72591e29 | 0.604172 | 0.302086 | − | 0.953281i | \(-0.402317\pi\) | ||||
0.302086 | + | 0.953281i | \(0.402317\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.70187e28 | −0.139817 | ||||||||
\(382\) | 4.35288e29 | 0.881147 | ||||||||
\(383\) | 9.91721e29 | 1.94806 | 0.974032 | − | 0.226408i | \(-0.0726984\pi\) | ||||
0.974032 | + | 0.226408i | \(0.0726984\pi\) | |||||||
\(384\) | 1.28913e29 | 0.245746 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.35969e30 | −2.44166 | ||||||||
\(387\) | −1.80698e29 | −0.314976 | ||||||||
\(388\) | −1.45168e30 | −2.45644 | ||||||||
\(389\) | 8.39840e29 | 1.37967 | 0.689836 | − | 0.723966i | \(-0.257683\pi\) | ||||
0.689836 | + | 0.723966i | \(0.257683\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −9.04012e28 | −0.140004 | ||||||||
\(392\) | 2.93303e28 | 0.0441089 | ||||||||
\(393\) | 1.28911e29 | 0.188268 | ||||||||
\(394\) | −5.09992e29 | −0.723363 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.75388e29 | −1.30522 | ||||||||
\(397\) | −9.94808e27 | −0.0129315 | −0.00646574 | − | 0.999979i | \(-0.502058\pi\) | ||||
−0.00646574 | + | 0.999979i | \(0.502058\pi\) | |||||||
\(398\) | −2.27754e30 | −2.87615 | ||||||||
\(399\) | 1.58853e29 | 0.194898 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.81480e29 | −0.557723 | −0.278861 | − | 0.960331i | \(-0.589957\pi\) | ||||
−0.278861 | + | 0.960331i | \(0.589957\pi\) | |||||||
\(402\) | 6.92244e28 | 0.0779219 | ||||||||
\(403\) | −1.08100e28 | −0.0118254 | ||||||||
\(404\) | 8.51487e29 | 0.905299 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.09138e30 | −1.09629 | ||||||||
\(407\) | −2.06325e29 | −0.201473 | ||||||||
\(408\) | 4.55232e28 | 0.0432156 | ||||||||
\(409\) | −8.22531e29 | −0.759162 | −0.379581 | − | 0.925159i | \(-0.623932\pi\) | ||||
−0.379581 | + | 0.925159i | \(0.623932\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.96573e28 | 0.0520575 | ||||||||
\(412\) | 5.69178e29 | 0.482981 | ||||||||
\(413\) | 1.45776e30 | 1.20299 | ||||||||
\(414\) | 2.13064e30 | 1.71004 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.76156e29 | 0.437489 | ||||||||
\(417\) | −1.82259e29 | −0.134624 | ||||||||
\(418\) | −1.93302e30 | −1.38902 | ||||||||
\(419\) | 2.72055e30 | 1.90194 | 0.950969 | − | 0.309287i | \(-0.100090\pi\) | ||||
0.950969 | + | 0.309287i | \(0.100090\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.73534e30 | 1.14852 | 0.574261 | − | 0.818672i | \(-0.305289\pi\) | ||||
0.574261 | + | 0.818672i | \(0.305289\pi\) | |||||||
\(422\) | 4.06173e30 | 2.61588 | ||||||||
\(423\) | 2.24209e30 | 1.40520 | ||||||||
\(424\) | −2.99665e30 | −1.82780 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.71623e29 | −0.330293 | ||||||||
\(427\) | −2.41911e30 | −1.36061 | ||||||||
\(428\) | 1.04232e30 | 0.570684 | ||||||||
\(429\) | −2.35860e29 | −0.125718 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2.30954e30 | 1.16691 | 0.583455 | − | 0.812146i | \(-0.301701\pi\) | ||||
0.583455 | + | 0.812146i | \(0.301701\pi\) | |||||||
\(432\) | −8.31270e29 | −0.408958 | ||||||||
\(433\) | 4.49441e29 | 0.215309 | 0.107655 | − | 0.994188i | \(-0.465666\pi\) | ||||
0.107655 | + | 0.994188i | \(0.465666\pi\) | |||||||
\(434\) | −3.57593e28 | −0.0166823 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.04468e30 | 2.23223 | ||||||||
\(437\) | 2.85872e30 | 1.23207 | ||||||||
\(438\) | −1.14018e30 | −0.478652 | ||||||||
\(439\) | −1.98640e30 | −0.812315 | −0.406157 | − | 0.913803i | \(-0.633132\pi\) | ||||
−0.406157 | + | 0.913803i | \(0.633132\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.74199e28 | 0.0222853 | ||||||||
\(442\) | −8.05507e29 | −0.304588 | ||||||||
\(443\) | 2.09074e30 | 0.770294 | 0.385147 | − | 0.922855i | \(-0.374151\pi\) | ||||
0.385147 | + | 0.922855i | \(0.374151\pi\) | |||||||
\(444\) | −2.93825e29 | −0.105484 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.89984e30 | −0.988607 | ||||||||
\(447\) | 7.49376e29 | 0.248979 | ||||||||
\(448\) | −2.05594e30 | −0.665753 | ||||||||
\(449\) | 2.38796e30 | 0.753694 | 0.376847 | − | 0.926276i | \(-0.377008\pi\) | ||||
0.376847 | + | 0.926276i | \(0.377008\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.23411e30 | −0.670000 | ||||||||
\(452\) | 8.57834e29 | 0.250791 | ||||||||
\(453\) | −6.13195e29 | −0.174771 | ||||||||
\(454\) | −9.28376e30 | −2.57977 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.43956e30 | −0.380307 | ||||||||
\(457\) | −1.54921e30 | −0.399093 | −0.199547 | − | 0.979888i | \(-0.563947\pi\) | ||||
−0.199547 | + | 0.979888i | \(0.563947\pi\) | |||||||
\(458\) | −5.67374e30 | −1.42533 | ||||||||
\(459\) | 1.80571e29 | 0.0442386 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.06665e30 | 0.947711 | 0.473855 | − | 0.880603i | \(-0.342862\pi\) | ||||
0.473855 | + | 0.880603i | \(0.342862\pi\) | |||||||
\(462\) | −7.80221e29 | −0.177352 | ||||||||
\(463\) | 6.37975e29 | 0.141456 | 0.0707282 | − | 0.997496i | \(-0.477468\pi\) | ||||
0.0707282 | + | 0.997496i | \(0.477468\pi\) | |||||||
\(464\) | 3.78196e30 | 0.818013 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −8.31798e30 | −1.71230 | ||||||||
\(467\) | −1.15365e30 | −0.231701 | −0.115851 | − | 0.993267i | \(-0.536959\pi\) | ||||
−0.115851 | + | 0.993267i | \(0.536959\pi\) | |||||||
\(468\) | 1.28531e31 | 2.51873 | ||||||||
\(469\) | −1.43456e30 | −0.274304 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −9.40938e27 | −0.00171325 | ||||||||
\(472\) | −1.32105e31 | −2.34740 | ||||||||
\(473\) | 1.19080e30 | 0.206507 | ||||||||
\(474\) | 9.95686e29 | 0.168528 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1.80400e30 | −0.290908 | ||||||||
\(477\) | −5.86655e30 | −0.923468 | ||||||||
\(478\) | −1.31766e31 | −2.02480 | ||||||||
\(479\) | −2.12936e30 | −0.319441 | −0.159721 | − | 0.987162i | \(-0.551059\pi\) | ||||
−0.159721 | + | 0.987162i | \(0.551059\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.71884e30 | 0.388790 | ||||||||
\(482\) | −9.51914e30 | −1.32910 | ||||||||
\(483\) | 1.15386e30 | 0.157312 | ||||||||
\(484\) | −9.31762e30 | −1.24046 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −6.41116e30 | −0.813991 | ||||||||
\(487\) | −4.84200e30 | −0.600401 | −0.300201 | − | 0.953876i | \(-0.597054\pi\) | ||||
−0.300201 | + | 0.953876i | \(0.597054\pi\) | |||||||
\(488\) | 2.19225e31 | 2.65498 | ||||||||
\(489\) | 1.11463e30 | 0.131849 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.44338e29 | −0.0388640 | −0.0194320 | − | 0.999811i | \(-0.506186\pi\) | ||||
−0.0194320 | + | 0.999811i | \(0.506186\pi\) | |||||||
\(492\) | −3.18157e30 | −0.350787 | ||||||||
\(493\) | −8.21528e29 | −0.0884877 | ||||||||
\(494\) | 2.54722e31 | 2.68045 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.23917e29 | 0.0124477 | ||||||||
\(497\) | 1.18460e31 | 1.16271 | ||||||||
\(498\) | 3.64131e30 | 0.349237 | ||||||||
\(499\) | −1.27549e31 | −1.19542 | −0.597711 | − | 0.801711i | \(-0.703923\pi\) | ||||
−0.597711 | + | 0.801711i | \(0.703923\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.77708e29 | 0.0517100 | ||||||||
\(502\) | 2.09546e31 | 1.83311 | ||||||||
\(503\) | −1.67840e31 | −1.43504 | −0.717520 | − | 0.696538i | \(-0.754723\pi\) | ||||
−0.717520 | + | 0.696538i | \(0.754723\pi\) | |||||||
\(504\) | 2.22345e31 | 1.85813 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.40409e31 | −1.12115 | ||||||||
\(507\) | 1.06356e30 | 0.0830175 | ||||||||
\(508\) | −2.40677e31 | −1.83654 | ||||||||
\(509\) | −2.11935e31 | −1.58106 | −0.790529 | − | 0.612425i | \(-0.790194\pi\) | ||||
−0.790529 | + | 0.612425i | \(0.790194\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.36283e31 | 1.68497 | ||||||||
\(512\) | 2.92986e31 | 2.04288 | ||||||||
\(513\) | −5.71012e30 | −0.389310 | ||||||||
\(514\) | −2.60131e31 | −1.73427 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.69580e30 | 0.108119 | ||||||||
\(517\) | −1.47753e31 | −0.921290 | ||||||||
\(518\) | 8.99386e30 | 0.548471 | ||||||||
\(519\) | 2.33007e30 | 0.138977 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.22820e30 | −0.0700869 | −0.0350434 | − | 0.999386i | \(-0.511157\pi\) | ||||
−0.0350434 | + | 0.999386i | \(0.511157\pi\) | |||||||
\(522\) | 1.93623e31 | 1.08080 | ||||||||
\(523\) | −7.24558e30 | −0.395643 | −0.197821 | − | 0.980238i | \(-0.563387\pi\) | ||||
−0.197821 | + | 0.980238i | \(0.563387\pi\) | |||||||
\(524\) | 4.62943e31 | 2.47296 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.07308e31 | 2.59379 | ||||||||
\(527\) | −2.69175e28 | −0.00134652 | ||||||||
\(528\) | 2.70370e30 | 0.132333 | ||||||||
\(529\) | −1.15570e29 | −0.00553483 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.58623e31 | −1.18599 | ||||||||
\(532\) | 5.70471e31 | 2.56006 | ||||||||
\(533\) | 2.94399e31 | 1.29292 | ||||||||
\(534\) | −4.51650e29 | −0.0194123 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.30003e31 | 0.535252 | ||||||||
\(537\) | 4.82208e30 | 0.194326 | ||||||||
\(538\) | −3.27453e30 | −0.129167 | ||||||||
\(539\) | −3.78397e29 | −0.0146109 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.30820e30 | 0.344427 | 0.172214 | − | 0.985060i | \(-0.444908\pi\) | ||||
0.172214 | + | 0.985060i | \(0.444908\pi\) | |||||||
\(542\) | −6.07719e31 | −2.20146 | ||||||||
\(543\) | 2.33296e30 | 0.0827389 | ||||||||
\(544\) | 1.43466e30 | 0.0498152 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.02813e31 | 0.342242 | ||||||||
\(547\) | 2.67466e31 | 0.871796 | 0.435898 | − | 0.899996i | \(-0.356431\pi\) | ||||
0.435898 | + | 0.899996i | \(0.356431\pi\) | |||||||
\(548\) | 2.14241e31 | 0.683794 | ||||||||
\(549\) | 4.29177e31 | 1.34139 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.59789e31 | 0.778712 | ||||||||
\(552\) | −1.04565e31 | −0.306965 | ||||||||
\(553\) | −2.06340e31 | −0.593258 | ||||||||
\(554\) | −2.69857e31 | −0.759926 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.54524e31 | −1.76834 | ||||||||
\(557\) | −2.40510e31 | −0.636501 | −0.318250 | − | 0.948007i | \(-0.603095\pi\) | ||||
−0.318250 | + | 0.948007i | \(0.603095\pi\) | |||||||
\(558\) | 6.34410e29 | 0.0164466 | ||||||||
\(559\) | −1.56916e31 | −0.398504 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.87305e29 | −0.0143150 | ||||||||
\(562\) | −4.93038e31 | −1.17737 | ||||||||
\(563\) | −2.15437e31 | −0.504049 | −0.252025 | − | 0.967721i | \(-0.581096\pi\) | ||||
−0.252025 | + | 0.967721i | \(0.581096\pi\) | |||||||
\(564\) | −2.10414e31 | −0.482353 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.33747e32 | −2.94370 | ||||||||
\(567\) | 4.23614e31 | 0.913618 | ||||||||
\(568\) | −1.07351e32 | −2.26881 | ||||||||
\(569\) | 1.70978e31 | 0.354120 | 0.177060 | − | 0.984200i | \(-0.443341\pi\) | ||||
0.177060 | + | 0.984200i | \(0.443341\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.69138e31 | −1.72891 | −0.864457 | − | 0.502707i | \(-0.832337\pi\) | ||||
−0.864457 | + | 0.502707i | \(0.832337\pi\) | |||||||
\(572\) | −8.47018e31 | −1.65135 | ||||||||
\(573\) | −4.18217e30 | −0.0799142 | ||||||||
\(574\) | 9.73865e31 | 1.82395 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.64747e31 | 0.656346 | ||||||||
\(577\) | −1.59167e31 | −0.280757 | −0.140378 | − | 0.990098i | \(-0.544832\pi\) | ||||
−0.140378 | + | 0.990098i | \(0.544832\pi\) | |||||||
\(578\) | 9.97560e31 | 1.72492 | ||||||||
\(579\) | 1.30637e31 | 0.221443 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −7.54602e31 | −1.22940 | ||||||||
\(582\) | 2.06012e31 | 0.329063 | ||||||||
\(583\) | 3.86605e31 | 0.605451 | ||||||||
\(584\) | −2.14125e32 | −3.28790 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.63160e32 | 2.40875 | ||||||||
\(587\) | −5.71080e31 | −0.826721 | −0.413361 | − | 0.910567i | \(-0.635645\pi\) | ||||
−0.413361 | + | 0.910567i | \(0.635645\pi\) | |||||||
\(588\) | −5.38870e29 | −0.00764971 | ||||||||
\(589\) | 8.51202e29 | 0.0118497 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.89991e30 | 0.0656043 | ||||||||
\(592\) | −3.11664e31 | −0.409248 | ||||||||
\(593\) | −2.68653e31 | −0.345989 | −0.172995 | − | 0.984923i | \(-0.555344\pi\) | ||||
−0.172995 | + | 0.984923i | \(0.555344\pi\) | |||||||
\(594\) | 2.80457e31 | 0.354261 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.69115e32 | 3.27044 | ||||||||
\(597\) | 2.18822e31 | 0.260848 | ||||||||
\(598\) | 1.85023e32 | 2.16352 | ||||||||
\(599\) | 1.35452e30 | 0.0155373 | 0.00776867 | − | 0.999970i | \(-0.497527\pi\) | ||||
0.00776867 | + | 0.999970i | \(0.497527\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.37959e31 | −0.814659 | −0.407329 | − | 0.913281i | \(-0.633540\pi\) | ||||
−0.407329 | + | 0.913281i | \(0.633540\pi\) | |||||||
\(602\) | −5.19077e31 | −0.562175 | ||||||||
\(603\) | 2.54507e31 | 0.270428 | ||||||||
\(604\) | −2.20210e32 | −2.29568 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −1.20837e31 | −0.121273 | ||||||||
\(607\) | 3.23323e31 | 0.318395 | 0.159198 | − | 0.987247i | \(-0.449109\pi\) | ||||
0.159198 | + | 0.987247i | \(0.449109\pi\) | |||||||
\(608\) | −4.53677e31 | −0.438385 | ||||||||
\(609\) | 1.04858e31 | 0.0994266 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.94701e32 | 1.77785 | ||||||||
\(612\) | 3.20049e31 | 0.286798 | ||||||||
\(613\) | −4.35574e31 | −0.383059 | −0.191530 | − | 0.981487i | \(-0.561345\pi\) | ||||
−0.191530 | + | 0.981487i | \(0.561345\pi\) | |||||||
\(614\) | −5.88154e31 | −0.507639 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.46525e32 | −1.21824 | ||||||||
\(617\) | 2.29127e32 | 1.86981 | 0.934904 | − | 0.354902i | \(-0.115486\pi\) | ||||
0.934904 | + | 0.354902i | \(0.115486\pi\) | |||||||
\(618\) | −8.07736e30 | −0.0646997 | ||||||||
\(619\) | 2.32366e32 | 1.82697 | 0.913484 | − | 0.406875i | \(-0.133382\pi\) | ||||
0.913484 | + | 0.406875i | \(0.133382\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.14765e31 | −0.314231 | ||||||||
\(622\) | −1.84904e32 | −1.37517 | ||||||||
\(623\) | 9.35970e30 | 0.0683360 | ||||||||
\(624\) | −3.56278e31 | −0.255368 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.30526e32 | 0.901763 | ||||||||
\(627\) | 1.85721e31 | 0.125975 | ||||||||
\(628\) | −3.37908e30 | −0.0225042 | ||||||||
\(629\) | 6.77005e30 | 0.0442700 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.22944e32 | −1.40559 | −0.702793 | − | 0.711394i | \(-0.748064\pi\) | ||||
−0.702793 | + | 0.711394i | \(0.748064\pi\) | |||||||
\(632\) | 1.86989e32 | 1.15763 | ||||||||
\(633\) | −3.90244e31 | −0.237243 | ||||||||
\(634\) | −1.48520e31 | −0.0886662 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 5.50560e31 | 0.316992 | ||||||||
\(637\) | 4.98629e30 | 0.0281951 | ||||||||
\(638\) | −1.27597e32 | −0.708605 | ||||||||
\(639\) | −2.10161e32 | −1.14628 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.75021e32 | −1.44710 | −0.723550 | − | 0.690272i | \(-0.757491\pi\) | ||||
−0.723550 | + | 0.690272i | \(0.757491\pi\) | |||||||
\(642\) | −1.47918e31 | −0.0764483 | ||||||||
\(643\) | −1.47614e32 | −0.749377 | −0.374689 | − | 0.927151i | \(-0.622250\pi\) | ||||
−0.374689 | + | 0.927151i | \(0.622250\pi\) | |||||||
\(644\) | 4.14373e32 | 2.06635 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.34273e31 | 0.305212 | ||||||||
\(647\) | −1.82358e32 | −0.862036 | −0.431018 | − | 0.902343i | \(-0.641846\pi\) | ||||
−0.431018 | + | 0.902343i | \(0.641846\pi\) | |||||||
\(648\) | −3.83888e32 | −1.78276 | ||||||||
\(649\) | 1.70432e32 | 0.777567 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.43569e29 | 0.00151298 | ||||||||
\(652\) | 4.00284e32 | 1.73189 | ||||||||
\(653\) | 4.35899e31 | 0.185304 | 0.0926519 | − | 0.995699i | \(-0.470466\pi\) | ||||
0.0926519 | + | 0.995699i | \(0.470466\pi\) | |||||||
\(654\) | −7.15905e31 | −0.299028 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −3.37473e32 | −1.36096 | ||||||||
\(657\) | −4.19193e32 | −1.66116 | ||||||||
\(658\) | 6.44067e32 | 2.50803 | ||||||||
\(659\) | −3.58880e31 | −0.137331 | −0.0686653 | − | 0.997640i | \(-0.521874\pi\) | ||||
−0.0686653 | + | 0.997640i | \(0.521874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.78803e32 | 1.03034 | 0.515171 | − | 0.857088i | \(-0.327729\pi\) | ||||
0.515171 | + | 0.857088i | \(0.327729\pi\) | |||||||
\(662\) | −2.04128e32 | −0.741370 | ||||||||
\(663\) | 7.73917e30 | 0.0276241 | ||||||||
\(664\) | 6.83836e32 | 2.39894 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.59561e32 | −0.540721 | ||||||||
\(667\) | 1.88703e32 | 0.628537 | ||||||||
\(668\) | 2.07466e32 | 0.679230 | ||||||||
\(669\) | 2.78612e31 | 0.0896601 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.82827e32 | −0.879452 | ||||||||
\(672\) | −1.83117e31 | −0.0559734 | ||||||||
\(673\) | −1.90131e31 | −0.0571320 | −0.0285660 | − | 0.999592i | \(-0.509094\pi\) | ||||
−0.0285660 | + | 0.999592i | \(0.509094\pi\) | |||||||
\(674\) | 6.68289e32 | 1.97413 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.81943e32 | 1.09047 | ||||||||
\(677\) | 3.87840e32 | 1.08864 | 0.544318 | − | 0.838879i | \(-0.316788\pi\) | ||||
0.544318 | + | 0.838879i | \(0.316788\pi\) | |||||||
\(678\) | −1.21738e31 | −0.0335957 | ||||||||
\(679\) | −4.26927e32 | −1.15838 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.91968e31 | 0.233969 | ||||||||
\(682\) | −4.18075e30 | −0.0107829 | ||||||||
\(683\) | −6.51681e32 | −1.65271 | −0.826356 | − | 0.563148i | \(-0.809590\pi\) | ||||
−0.826356 | + | 0.563148i | \(0.809590\pi\) | |||||||
\(684\) | −1.01208e33 | −2.52389 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 7.37799e32 | 1.77914 | ||||||||
\(687\) | 5.45123e31 | 0.129268 | ||||||||
\(688\) | 1.79876e32 | 0.419474 | ||||||||
\(689\) | −5.09446e32 | −1.16836 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.18205e31 | −0.137131 | −0.0685654 | − | 0.997647i | \(-0.521842\pi\) | ||||
−0.0685654 | + | 0.997647i | \(0.521842\pi\) | |||||||
\(692\) | 8.36770e32 | 1.82552 | ||||||||
\(693\) | −2.86853e32 | −0.615499 | ||||||||
\(694\) | 5.81246e32 | 1.22666 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.50245e31 | −0.194012 | ||||||||
\(697\) | 7.33069e31 | 0.147220 | ||||||||
\(698\) | −3.71278e32 | −0.733436 | ||||||||
\(699\) | 7.99177e31 | 0.155294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.26483e32 | 0.989982 | 0.494991 | − | 0.868898i | \(-0.335171\pi\) | ||||
0.494991 | + | 0.868898i | \(0.335171\pi\) | |||||||
\(702\) | −3.69571e32 | −0.683629 | ||||||||
\(703\) | −2.14087e32 | −0.389586 | ||||||||
\(704\) | −2.40367e32 | −0.430319 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.87763e33 | −3.25353 | ||||||||
\(707\) | 2.50415e32 | 0.426910 | ||||||||
\(708\) | 2.42711e32 | 0.407105 | ||||||||
\(709\) | −7.09958e32 | −1.17166 | −0.585829 | − | 0.810435i | \(-0.699231\pi\) | ||||
−0.585829 | + | 0.810435i | \(0.699231\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.66070e32 | 0.584876 | ||||||||
\(712\) | −8.48196e31 | −0.133345 | ||||||||
\(713\) | 6.18287e30 | 0.00956446 | ||||||||
\(714\) | 2.56010e31 | 0.0389698 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.73170e33 | 2.55254 | ||||||||
\(717\) | 1.26598e32 | 0.183636 | ||||||||
\(718\) | 1.25269e33 | 1.78819 | ||||||||
\(719\) | 4.58875e32 | 0.644633 | 0.322316 | − | 0.946632i | \(-0.395539\pi\) | ||||
0.322316 | + | 0.946632i | \(0.395539\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.67390e32 | 0.227758 | ||||||||
\(722\) | −6.91748e32 | −0.926339 | ||||||||
\(723\) | 9.14583e31 | 0.120540 | ||||||||
\(724\) | 8.37810e32 | 1.08681 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.32229e32 | 0.166171 | ||||||||
\(727\) | −1.25284e33 | −1.54970 | −0.774851 | − | 0.632144i | \(-0.782175\pi\) | ||||
−0.774851 | + | 0.632144i | \(0.782175\pi\) | |||||||
\(728\) | 1.93083e33 | 2.35089 | ||||||||
\(729\) | −7.09581e32 | −0.850424 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.90730e31 | −0.0453761 | ||||||||
\(732\) | −4.02771e32 | −0.460448 | ||||||||
\(733\) | 1.67809e30 | 0.00188852 | 0.000944258 | − | 1.00000i | \(-0.499699\pi\) | ||||
0.000944258 | 1.00000i | \(0.499699\pi\) | ||||||||
\(734\) | −2.41070e33 | −2.67078 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.29537e32 | −0.353842 | ||||||||
\(737\) | −1.67720e32 | −0.177300 | ||||||||
\(738\) | −1.72775e33 | −1.79817 | ||||||||
\(739\) | 2.96573e32 | 0.303893 | 0.151946 | − | 0.988389i | \(-0.451446\pi\) | ||||
0.151946 | + | 0.988389i | \(0.451446\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.44733e32 | −0.243099 | ||||||||
\(742\) | −1.68524e33 | −1.64822 | ||||||||
\(743\) | 4.48312e32 | 0.431727 | 0.215863 | − | 0.976424i | \(-0.430743\pi\) | ||||
0.215863 | + | 0.976424i | \(0.430743\pi\) | |||||||
\(744\) | −3.11349e30 | −0.00295229 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.47917e33 | −1.35995 | ||||||||
\(747\) | 1.33875e33 | 1.21203 | ||||||||
\(748\) | −2.10912e32 | −0.188033 | ||||||||
\(749\) | 3.06536e32 | 0.269116 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.50465e32 | −0.298391 | −0.149195 | − | 0.988808i | \(-0.547668\pi\) | ||||
−0.149195 | + | 0.988808i | \(0.547668\pi\) | |||||||
\(752\) | −2.23188e33 | −1.87140 | ||||||||
\(753\) | −2.01329e32 | −0.166251 | ||||||||
\(754\) | 1.68141e33 | 1.36742 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.27683e32 | −0.652925 | ||||||||
\(757\) | −4.37490e32 | −0.339911 | −0.169956 | − | 0.985452i | \(-0.554362\pi\) | ||||
−0.169956 | + | 0.985452i | \(0.554362\pi\) | |||||||
\(758\) | −1.38922e33 | −1.06310 | ||||||||
\(759\) | 1.34902e32 | 0.101681 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.53089e31 | −0.0111949 | −0.00559744 | − | 0.999984i | \(-0.501782\pi\) | ||||
−0.00559744 | + | 0.999984i | \(0.501782\pi\) | |||||||
\(762\) | 3.41551e32 | 0.246022 | ||||||||
\(763\) | 1.48360e33 | 1.05265 | ||||||||
\(764\) | −1.50190e33 | −1.04970 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.05416e33 | −3.42782 | ||||||||
\(767\) | −2.24586e33 | −1.50050 | ||||||||
\(768\) | −4.93686e32 | −0.324935 | ||||||||
\(769\) | 2.67481e33 | 1.73436 | 0.867180 | − | 0.497995i | \(-0.165930\pi\) | ||||
0.867180 | + | 0.497995i | \(0.165930\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.49929e32 | 0.157287 | ||||||||
\(772\) | 4.69141e33 | 2.90873 | ||||||||
\(773\) | −8.38808e31 | −0.0512387 | −0.0256194 | − | 0.999672i | \(-0.508156\pi\) | ||||
−0.0256194 | + | 0.999672i | \(0.508156\pi\) | |||||||
\(774\) | 9.20900e32 | 0.554232 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 3.86890e33 | 2.26036 | ||||||||
\(777\) | −8.64114e31 | −0.0497427 | ||||||||
\(778\) | −4.28012e33 | −2.42767 | ||||||||
\(779\) | −2.31816e33 | −1.29557 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.38496e33 | 0.751534 | ||||||||
\(782\) | 4.60716e32 | 0.246352 | ||||||||
\(783\) | −3.76921e32 | −0.198605 | ||||||||
\(784\) | −5.71586e31 | −0.0296788 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −6.56975e32 | −0.331276 | ||||||||
\(787\) | 3.07440e33 | 1.52775 | 0.763874 | − | 0.645366i | \(-0.223295\pi\) | ||||
0.763874 | + | 0.645366i | \(0.223295\pi\) | |||||||
\(788\) | 1.75965e33 | 0.861737 | ||||||||
\(789\) | −4.87412e32 | −0.235240 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.52281e32 | 0.118265 | ||||||||
\(792\) | 2.59952e33 | 1.20103 | ||||||||
\(793\) | 3.72693e33 | 1.69711 | ||||||||
\(794\) | 5.06989e31 | 0.0227543 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.85832e33 | 3.42633 | ||||||||
\(797\) | −2.31415e33 | −0.994535 | −0.497268 | − | 0.867597i | \(-0.665663\pi\) | ||||
−0.497268 | + | 0.867597i | \(0.665663\pi\) | |||||||
\(798\) | −8.09572e32 | −0.342943 | ||||||||
\(799\) | 4.84816e32 | 0.202437 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1.66052e32 | −0.0673704 | ||||||||
\(802\) | 2.45379e33 | 0.981370 | ||||||||
\(803\) | 2.76247e33 | 1.08910 | ||||||||
\(804\) | −2.38848e32 | −0.0928276 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.50915e31 | 0.0208081 | ||||||||
\(807\) | 3.14611e31 | 0.0117146 | ||||||||
\(808\) | −2.26931e33 | −0.833035 | ||||||||
\(809\) | 3.80662e33 | 1.37763 | 0.688814 | − | 0.724938i | \(-0.258132\pi\) | ||||
0.688814 | + | 0.724938i | \(0.258132\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.24454e33 | 1.49311 | 0.746554 | − | 0.665325i | \(-0.231707\pi\) | ||||
0.746554 | + | 0.665325i | \(0.231707\pi\) | |||||||
\(812\) | 3.76564e33 | 1.30601 | ||||||||
\(813\) | 5.83886e32 | 0.199658 | ||||||||
\(814\) | 1.05151e33 | 0.354512 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −8.87152e31 | −0.0290778 | ||||||||
\(817\) | 1.23559e33 | 0.399321 | ||||||||
\(818\) | 4.19191e33 | 1.33582 | ||||||||
\(819\) | 3.77998e33 | 1.18775 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.99736e33 | −0.915784 | −0.457892 | − | 0.889008i | \(-0.651395\pi\) | ||||
−0.457892 | + | 0.889008i | \(0.651395\pi\) | |||||||
\(822\) | −3.04035e32 | −0.0916004 | ||||||||
\(823\) | 5.19319e32 | 0.154289 | 0.0771447 | − | 0.997020i | \(-0.475420\pi\) | ||||
0.0771447 | + | 0.997020i | \(0.475420\pi\) | |||||||
\(824\) | −1.51692e33 | −0.444428 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.42926e33 | −2.11678 | ||||||||
\(827\) | −4.81781e32 | −0.135374 | −0.0676872 | − | 0.997707i | \(-0.521562\pi\) | ||||
−0.0676872 | + | 0.997707i | \(0.521562\pi\) | |||||||
\(828\) | −7.35144e33 | −2.03715 | ||||||||
\(829\) | −2.15627e33 | −0.589287 | −0.294644 | − | 0.955607i | \(-0.595201\pi\) | ||||
−0.294644 | + | 0.955607i | \(0.595201\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.59274e32 | 0.0689202 | ||||||||
\(832\) | 3.16743e33 | 0.830401 | ||||||||
\(833\) | 1.24161e31 | 0.00321048 | ||||||||
\(834\) | 9.28853e32 | 0.236885 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 6.66960e33 | 1.65473 | ||||||||
\(837\) | −1.23499e31 | −0.00302218 | ||||||||
\(838\) | −1.38649e34 | −3.34665 | ||||||||
\(839\) | −2.38371e32 | −0.0567532 | −0.0283766 | − | 0.999597i | \(-0.509034\pi\) | ||||
−0.0283766 | + | 0.999597i | \(0.509034\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.60187e33 | −0.602743 | ||||||||
\(842\) | −8.84388e33 | −2.02094 | ||||||||
\(843\) | 4.73702e32 | 0.106780 | ||||||||
\(844\) | −1.40144e34 | −3.11627 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.14265e34 | −2.47260 | ||||||||
\(847\) | −2.74023e33 | −0.584962 | ||||||||
\(848\) | 5.83985e33 | 1.22984 | ||||||||
\(849\) | 1.28501e33 | 0.266974 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.55506e33 | −0.314454 | ||||||||
\(852\) | 1.97230e33 | 0.393475 | ||||||||
\(853\) | 1.94872e32 | 0.0383563 | 0.0191781 | − | 0.999816i | \(-0.493895\pi\) | ||||
0.0191781 | + | 0.999816i | \(0.493895\pi\) | |||||||
\(854\) | 1.23286e34 | 2.39414 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.77789e33 | −0.525130 | ||||||||
\(857\) | 1.87495e33 | 0.349711 | 0.174855 | − | 0.984594i | \(-0.444054\pi\) | ||||
0.174855 | + | 0.984594i | \(0.444054\pi\) | |||||||
\(858\) | 1.20203e33 | 0.221213 | ||||||||
\(859\) | 6.46779e33 | 1.17445 | 0.587225 | − | 0.809424i | \(-0.300220\pi\) | ||||
0.587225 | + | 0.809424i | \(0.300220\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −9.35673e32 | −0.165420 | ||||||||
\(862\) | −1.17702e34 | −2.05330 | ||||||||
\(863\) | 1.04050e34 | 1.79110 | 0.895550 | − | 0.444961i | \(-0.146782\pi\) | ||||
0.895550 | + | 0.444961i | \(0.146782\pi\) | |||||||
\(864\) | 6.58230e32 | 0.111807 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.29051e33 | −0.378858 | ||||||||
\(867\) | −9.58438e32 | −0.156439 | ||||||||
\(868\) | 1.23382e32 | 0.0198735 | ||||||||
\(869\) | −2.41239e33 | −0.383461 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.21012e33 | 0.342142 | ||||||||
\(872\) | −1.34447e34 | −2.05405 | ||||||||
\(873\) | 7.57417e33 | 1.14201 | ||||||||
\(874\) | −1.45691e34 | −2.16795 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 3.93401e33 | 0.570214 | ||||||||
\(877\) | −8.52438e33 | −1.21946 | −0.609730 | − | 0.792609i | \(-0.708722\pi\) | ||||
−0.609730 | + | 0.792609i | \(0.708722\pi\) | |||||||
\(878\) | 1.01234e34 | 1.42935 | ||||||||
\(879\) | −1.56761e33 | −0.218457 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.20706e34 | 1.63872 | 0.819362 | − | 0.573276i | \(-0.194328\pi\) | ||||
0.819362 | + | 0.573276i | \(0.194328\pi\) | |||||||
\(882\) | −2.92632e32 | −0.0392133 | ||||||||
\(883\) | −4.60310e33 | −0.608839 | −0.304420 | − | 0.952538i | \(-0.598462\pi\) | ||||
−0.304420 | + | 0.952538i | \(0.598462\pi\) | |||||||
\(884\) | 2.77928e33 | 0.362853 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.06551e34 | −1.35541 | ||||||||
\(887\) | 7.25037e33 | 0.910413 | 0.455207 | − | 0.890386i | \(-0.349565\pi\) | ||||
0.455207 | + | 0.890386i | \(0.349565\pi\) | |||||||
\(888\) | 7.83079e32 | 0.0970636 | ||||||||
\(889\) | −7.07809e33 | −0.866055 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.95263e33 | 0.590530 | ||||||||
\(892\) | 1.00055e34 | 1.17772 | ||||||||
\(893\) | −1.53312e34 | −1.78149 | ||||||||
\(894\) | −3.81909e33 | −0.438105 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.36149e34 | 1.52220 | ||||||||
\(897\) | −1.77766e33 | −0.196217 | ||||||||
\(898\) | −1.21699e34 | −1.32620 | ||||||||
\(899\) | 5.61873e31 | 0.00604507 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.26855e33 | −0.133037 | ||||||||
\(902\) | 1.13858e34 | 1.17893 | ||||||||
\(903\) | 4.98720e32 | 0.0509856 | ||||||||
\(904\) | −2.28623e33 | −0.230772 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 3.12506e33 | 0.307528 | ||||||||
\(907\) | 3.03876e33 | 0.295266 | 0.147633 | − | 0.989042i | \(-0.452835\pi\) | ||||
0.147633 | + | 0.989042i | \(0.452835\pi\) | |||||||
\(908\) | 3.20322e34 | 3.07326 | ||||||||
\(909\) | −4.44264e33 | −0.420878 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.60065e34 | −1.47855 | −0.739273 | − | 0.673406i | \(-0.764831\pi\) | ||||
−0.739273 | + | 0.673406i | \(0.764831\pi\) | |||||||
\(912\) | 2.80541e33 | 0.255891 | ||||||||
\(913\) | −8.82233e33 | −0.794638 | ||||||||
\(914\) | 7.89533e33 | 0.702245 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.95764e34 | 1.69799 | ||||||||
\(917\) | 1.36147e34 | 1.16617 | ||||||||
\(918\) | −9.20251e32 | −0.0778423 | ||||||||
\(919\) | −1.54454e34 | −1.29024 | −0.645120 | − | 0.764081i | \(-0.723193\pi\) | ||||
−0.645120 | + | 0.764081i | \(0.723193\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5.65088e32 | 0.0460395 | ||||||||
\(922\) | −2.07251e34 | −1.66759 | ||||||||
\(923\) | −1.82501e34 | −1.45026 | ||||||||
\(924\) | 2.69204e33 | 0.211277 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.25135e33 | −0.248907 | ||||||||
\(927\) | −2.96969e33 | −0.224540 | ||||||||
\(928\) | −2.99469e33 | −0.223641 | ||||||||
\(929\) | 1.19786e34 | 0.883535 | 0.441768 | − | 0.897129i | \(-0.354352\pi\) | ||||
0.441768 | + | 0.897129i | \(0.354352\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.92631e32 | −0.0282529 | ||||||||
\(932\) | 2.86999e34 | 2.03985 | ||||||||
\(933\) | 1.77653e33 | 0.124719 | ||||||||
\(934\) | 5.87939e33 | 0.407702 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.42550e34 | −2.31767 | ||||||||
\(937\) | 2.83646e33 | 0.189570 | 0.0947852 | − | 0.995498i | \(-0.469784\pi\) | ||||
0.0947852 | + | 0.995498i | \(0.469784\pi\) | |||||||
\(938\) | 7.31103e33 | 0.482665 | ||||||||
\(939\) | −1.25407e33 | −0.0817839 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.88589e34 | 1.83653 | 0.918267 | − | 0.395961i | \(-0.129588\pi\) | ||||
0.918267 | + | 0.395961i | \(0.129588\pi\) | |||||||
\(942\) | 4.79535e31 | 0.00301464 | ||||||||
\(943\) | −1.68384e34 | −1.04572 | ||||||||
\(944\) | 2.57446e34 | 1.57946 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.06872e33 | −0.363370 | ||||||||
\(947\) | −2.29990e34 | −1.36045 | −0.680226 | − | 0.733002i | \(-0.738118\pi\) | ||||
−0.680226 | + | 0.733002i | \(0.738118\pi\) | |||||||
\(948\) | −3.43546e33 | −0.200766 | ||||||||
\(949\) | −3.64023e34 | −2.10168 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.42695e32 | 0.00804144 | ||||||||
\(952\) | 4.80786e33 | 0.267687 | ||||||||
\(953\) | 2.39769e34 | 1.31894 | 0.659470 | − | 0.751731i | \(-0.270781\pi\) | ||||
0.659470 | + | 0.751731i | \(0.270781\pi\) | |||||||
\(954\) | 2.98980e34 | 1.62494 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.54638e34 | 2.41213 | ||||||||
\(957\) | 1.22593e33 | 0.0642658 | ||||||||
\(958\) | 1.08520e34 | 0.562090 | ||||||||
\(959\) | 6.30062e33 | 0.322455 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.00115e34 | −0.999908 | ||||||||
\(962\) | −1.38561e34 | −0.684115 | ||||||||
\(963\) | −5.43829e33 | −0.265314 | ||||||||
\(964\) | 3.28444e34 | 1.58334 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5.88048e33 | −0.276806 | ||||||||
\(967\) | 6.66196e33 | 0.309883 | 0.154942 | − | 0.987924i | \(-0.450481\pi\) | ||||
0.154942 | + | 0.987924i | \(0.450481\pi\) | |||||||
\(968\) | 2.48325e34 | 1.14144 | ||||||||
\(969\) | −6.09398e32 | −0.0276808 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.35172e34 | −1.48678 | −0.743390 | − | 0.668858i | \(-0.766783\pi\) | ||||
−0.743390 | + | 0.668858i | \(0.766783\pi\) | |||||||
\(972\) | 2.21207e34 | 0.969701 | ||||||||
\(973\) | −1.92490e34 | −0.833892 | ||||||||
\(974\) | 2.46765e34 | 1.05647 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.27224e34 | −1.78642 | ||||||||
\(977\) | −1.17263e34 | −0.484590 | −0.242295 | − | 0.970203i | \(-0.577900\pi\) | ||||
−0.242295 | + | 0.970203i | \(0.577900\pi\) | |||||||
\(978\) | −5.68054e33 | −0.232003 | ||||||||
\(979\) | 1.09428e33 | 0.0441699 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.63207e34 | −1.03778 | ||||||||
\(982\) | 1.75487e33 | 0.0683851 | ||||||||
\(983\) | −1.51439e34 | −0.583274 | −0.291637 | − | 0.956529i | \(-0.594200\pi\) | ||||
−0.291637 | + | 0.956529i | \(0.594200\pi\) | |||||||
\(984\) | 8.47927e33 | 0.322786 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.18679e33 | 0.155703 | ||||||||
\(987\) | −6.18808e33 | −0.227462 | ||||||||
\(988\) | −8.78881e34 | −3.19319 | ||||||||
\(989\) | 8.97497e33 | 0.322311 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.60260e34 | 0.913187 | 0.456593 | − | 0.889675i | \(-0.349069\pi\) | ||||
0.456593 | + | 0.889675i | \(0.349069\pi\) | |||||||
\(992\) | −9.81216e31 | −0.00340315 | ||||||||
\(993\) | 1.96122e33 | 0.0672374 | ||||||||
\(994\) | −6.03711e34 | −2.04591 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.25638e34 | −0.416043 | ||||||||
\(997\) | 1.96863e34 | 0.644422 | 0.322211 | − | 0.946668i | \(-0.395574\pi\) | ||||
0.322211 | + | 0.946668i | \(0.395574\pi\) | |||||||
\(998\) | 6.50036e34 | 2.10347 | ||||||||
\(999\) | 3.10613e33 | 0.0993613 |
(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 | 25.24.a.a.1.1 | 2 | ||
5.2 | odd | 4 | 25.24.b.a.24.1 | 4 | |||
5.3 | odd | 4 | 25.24.b.a.24.4 | 4 | |||
5.4 | even | 2 | 1.24.a.a.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 9.24.a.b.1.1 | 2 | |||
20.19 | odd | 2 | 16.24.a.b.1.2 | 2 | |||
35.34 | odd | 2 | 49.24.a.b.1.2 | 2 | |||
40.19 | odd | 2 | 64.24.a.g.1.1 | 2 | |||
40.29 | even | 2 | 64.24.a.d.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.24.a.a.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
9.24.a.b.1.1 | 2 | 15.14 | odd | 2 | |||
16.24.a.b.1.2 | 2 | 20.19 | odd | 2 | |||
25.24.a.a.1.1 | 2 | 1.1 | even | 1 | trivial | ||
25.24.b.a.24.1 | 4 | 5.2 | odd | 4 | |||
25.24.b.a.24.4 | 4 | 5.3 | odd | 4 | |||
49.24.a.b.1.2 | 2 | 35.34 | odd | 2 | |||
64.24.a.d.1.2 | 2 | 40.29 | even | 2 | |||
64.24.a.g.1.1 | 2 | 40.19 | odd | 2 |