Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [22,14,Mod(1,22)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(22, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("22.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 22 = 2 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 22.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: | \(23.5908043694\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{100039}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 100039 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-316.289\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 22.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −64.0000 | −0.707107 | ||||||||
\(3\) | −1596.16 | −1.26412 | −0.632059 | − | 0.774920i | \(-0.717790\pi\) | ||||
−0.632059 | + | 0.774920i | \(0.717790\pi\) | |||||||
\(4\) | 4096.00 | 0.500000 | ||||||||
\(5\) | −57177.1 | −1.63650 | −0.818252 | − | 0.574860i | \(-0.805057\pi\) | ||||
−0.818252 | + | 0.574860i | \(0.805057\pi\) | |||||||
\(6\) | 102154. | 0.893866 | ||||||||
\(7\) | 550172. | 1.76751 | 0.883754 | − | 0.467951i | \(-0.155008\pi\) | ||||
0.883754 | + | 0.467951i | \(0.155008\pi\) | |||||||
\(8\) | −262144. | −0.353553 | ||||||||
\(9\) | 953396. | 0.597995 | ||||||||
\(10\) | 3.65933e6 | 1.15718 | ||||||||
\(11\) | −1.77156e6 | −0.301511 | ||||||||
\(12\) | −6.53786e6 | −0.632059 | ||||||||
\(13\) | 2.35813e7 | 1.35499 | 0.677496 | − | 0.735526i | \(-0.263065\pi\) | ||||
0.677496 | + | 0.735526i | \(0.263065\pi\) | |||||||
\(14\) | −3.52110e7 | −1.24982 | ||||||||
\(15\) | 9.12637e7 | 2.06873 | ||||||||
\(16\) | 1.67772e7 | 0.250000 | ||||||||
\(17\) | 1.01512e8 | 1.02000 | 0.510001 | − | 0.860174i | \(-0.329645\pi\) | ||||
0.510001 | + | 0.860174i | \(0.329645\pi\) | |||||||
\(18\) | −6.10174e7 | −0.422846 | ||||||||
\(19\) | −1.12633e8 | −0.549244 | −0.274622 | − | 0.961552i | \(-0.588553\pi\) | ||||
−0.274622 | + | 0.961552i | \(0.588553\pi\) | |||||||
\(20\) | −2.34197e8 | −0.818252 | ||||||||
\(21\) | −8.78162e8 | −2.23434 | ||||||||
\(22\) | 1.13380e8 | 0.213201 | ||||||||
\(23\) | −6.98413e8 | −0.983742 | −0.491871 | − | 0.870668i | \(-0.663687\pi\) | ||||
−0.491871 | + | 0.870668i | \(0.663687\pi\) | |||||||
\(24\) | 4.18423e8 | 0.446933 | ||||||||
\(25\) | 2.04852e9 | 1.67815 | ||||||||
\(26\) | −1.50921e9 | −0.958124 | ||||||||
\(27\) | 1.02302e9 | 0.508182 | ||||||||
\(28\) | 2.25351e9 | 0.883754 | ||||||||
\(29\) | −5.69290e9 | −1.77724 | −0.888621 | − | 0.458642i | \(-0.848336\pi\) | ||||
−0.888621 | + | 0.458642i | \(0.848336\pi\) | |||||||
\(30\) | −5.84087e9 | −1.46282 | ||||||||
\(31\) | −2.48239e9 | −0.502364 | −0.251182 | − | 0.967940i | \(-0.580819\pi\) | ||||
−0.251182 | + | 0.967940i | \(0.580819\pi\) | |||||||
\(32\) | −1.07374e9 | −0.176777 | ||||||||
\(33\) | 2.82769e9 | 0.381146 | ||||||||
\(34\) | −6.49679e9 | −0.721250 | ||||||||
\(35\) | −3.14573e10 | −2.89253 | ||||||||
\(36\) | 3.90511e9 | 0.298997 | ||||||||
\(37\) | 1.34083e7 | 0.000859135 0 | 0.000429568 | − | 1.00000i | \(-0.499863\pi\) | ||||
0.000429568 | 1.00000i | \(0.499863\pi\) | ||||||||
\(38\) | 7.20848e9 | 0.388374 | ||||||||
\(39\) | −3.76395e10 | −1.71287 | ||||||||
\(40\) | 1.49886e10 | 0.578592 | ||||||||
\(41\) | 3.85108e10 | 1.26616 | 0.633079 | − | 0.774087i | \(-0.281791\pi\) | ||||
0.633079 | + | 0.774087i | \(0.281791\pi\) | |||||||
\(42\) | 5.62024e10 | 1.57992 | ||||||||
\(43\) | 9.49634e9 | 0.229093 | 0.114546 | − | 0.993418i | \(-0.463459\pi\) | ||||
0.114546 | + | 0.993418i | \(0.463459\pi\) | |||||||
\(44\) | −7.25631e9 | −0.150756 | ||||||||
\(45\) | −5.45124e10 | −0.978620 | ||||||||
\(46\) | 4.46984e10 | 0.695611 | ||||||||
\(47\) | −1.90209e10 | −0.257391 | −0.128696 | − | 0.991684i | \(-0.541079\pi\) | ||||
−0.128696 | + | 0.991684i | \(0.541079\pi\) | |||||||
\(48\) | −2.67791e10 | −0.316030 | ||||||||
\(49\) | 2.05801e11 | 2.12409 | ||||||||
\(50\) | −1.31105e11 | −1.18663 | ||||||||
\(51\) | −1.62030e11 | −1.28940 | ||||||||
\(52\) | 9.65892e10 | 0.677496 | ||||||||
\(53\) | −2.12042e10 | −0.131410 | −0.0657050 | − | 0.997839i | \(-0.520930\pi\) | ||||
−0.0657050 | + | 0.997839i | \(0.520930\pi\) | |||||||
\(54\) | −6.54733e10 | −0.359339 | ||||||||
\(55\) | 1.01293e11 | 0.493425 | ||||||||
\(56\) | −1.44224e11 | −0.624909 | ||||||||
\(57\) | 1.79779e11 | 0.694309 | ||||||||
\(58\) | 3.64346e11 | 1.25670 | ||||||||
\(59\) | 1.43149e11 | 0.441825 | 0.220913 | − | 0.975294i | \(-0.429096\pi\) | ||||
0.220913 | + | 0.975294i | \(0.429096\pi\) | |||||||
\(60\) | 3.73816e11 | 1.03437 | ||||||||
\(61\) | −4.46635e11 | −1.10996 | −0.554982 | − | 0.831863i | \(-0.687275\pi\) | ||||
−0.554982 | + | 0.831863i | \(0.687275\pi\) | |||||||
\(62\) | 1.58873e11 | 0.355225 | ||||||||
\(63\) | 5.24532e11 | 1.05696 | ||||||||
\(64\) | 6.87195e10 | 0.125000 | ||||||||
\(65\) | −1.34831e12 | −2.21745 | ||||||||
\(66\) | −1.80972e11 | −0.269511 | ||||||||
\(67\) | −2.32131e11 | −0.313507 | −0.156753 | − | 0.987638i | \(-0.550103\pi\) | ||||
−0.156753 | + | 0.987638i | \(0.550103\pi\) | |||||||
\(68\) | 4.15794e11 | 0.510001 | ||||||||
\(69\) | 1.11478e12 | 1.24357 | ||||||||
\(70\) | 2.01326e12 | 2.04533 | ||||||||
\(71\) | 1.59319e12 | 1.47601 | 0.738005 | − | 0.674795i | \(-0.235768\pi\) | ||||
0.738005 | + | 0.674795i | \(0.235768\pi\) | |||||||
\(72\) | −2.49927e11 | −0.211423 | ||||||||
\(73\) | −1.31830e12 | −1.01957 | −0.509785 | − | 0.860302i | \(-0.670275\pi\) | ||||
−0.509785 | + | 0.860302i | \(0.670275\pi\) | |||||||
\(74\) | −8.58129e8 | −0.000607501 0 | ||||||||
\(75\) | −3.26976e12 | −2.12137 | ||||||||
\(76\) | −4.61343e11 | −0.274622 | ||||||||
\(77\) | −9.74664e11 | −0.532924 | ||||||||
\(78\) | 2.40893e12 | 1.21118 | ||||||||
\(79\) | −6.52882e11 | −0.302175 | −0.151088 | − | 0.988520i | \(-0.548278\pi\) | ||||
−0.151088 | + | 0.988520i | \(0.548278\pi\) | |||||||
\(80\) | −9.59273e11 | −0.409126 | ||||||||
\(81\) | −3.15292e12 | −1.24040 | ||||||||
\(82\) | −2.46469e12 | −0.895308 | ||||||||
\(83\) | −4.15430e12 | −1.39473 | −0.697365 | − | 0.716716i | \(-0.745644\pi\) | ||||
−0.697365 | + | 0.716716i | \(0.745644\pi\) | |||||||
\(84\) | −3.59695e12 | −1.11717 | ||||||||
\(85\) | −5.80418e12 | −1.66924 | ||||||||
\(86\) | −6.07766e11 | −0.161993 | ||||||||
\(87\) | 9.08677e12 | 2.24664 | ||||||||
\(88\) | 4.64404e11 | 0.106600 | ||||||||
\(89\) | −3.61368e12 | −0.770752 | −0.385376 | − | 0.922760i | \(-0.625928\pi\) | ||||
−0.385376 | + | 0.922760i | \(0.625928\pi\) | |||||||
\(90\) | 3.48880e12 | 0.691989 | ||||||||
\(91\) | 1.29738e13 | 2.39496 | ||||||||
\(92\) | −2.86070e12 | −0.491871 | ||||||||
\(93\) | 3.96228e12 | 0.635048 | ||||||||
\(94\) | 1.21734e12 | 0.182003 | ||||||||
\(95\) | 6.44000e12 | 0.898840 | ||||||||
\(96\) | 1.71386e12 | 0.223467 | ||||||||
\(97\) | −1.33685e13 | −1.62955 | −0.814776 | − | 0.579776i | \(-0.803140\pi\) | ||||
−0.814776 | + | 0.579776i | \(0.803140\pi\) | |||||||
\(98\) | −1.31712e13 | −1.50196 | ||||||||
\(99\) | −1.68900e12 | −0.180302 | ||||||||
\(100\) | 8.39073e12 | 0.839073 | ||||||||
\(101\) | 1.23469e13 | 1.15736 | 0.578679 | − | 0.815555i | \(-0.303568\pi\) | ||||
0.578679 | + | 0.815555i | \(0.303568\pi\) | |||||||
\(102\) | 1.03699e13 | 0.911745 | ||||||||
\(103\) | −1.94307e13 | −1.60342 | −0.801708 | − | 0.597716i | \(-0.796075\pi\) | ||||
−0.801708 | + | 0.597716i | \(0.796075\pi\) | |||||||
\(104\) | −6.18171e12 | −0.479062 | ||||||||
\(105\) | 5.02107e13 | 3.65651 | ||||||||
\(106\) | 1.35707e12 | 0.0929209 | ||||||||
\(107\) | 8.96933e12 | 0.577784 | 0.288892 | − | 0.957362i | \(-0.406713\pi\) | ||||
0.288892 | + | 0.957362i | \(0.406713\pi\) | |||||||
\(108\) | 4.19029e12 | 0.254091 | ||||||||
\(109\) | −3.01725e13 | −1.72322 | −0.861608 | − | 0.507575i | \(-0.830542\pi\) | ||||
−0.861608 | + | 0.507575i | \(0.830542\pi\) | |||||||
\(110\) | −6.48273e12 | −0.348904 | ||||||||
\(111\) | −2.14017e10 | −0.00108605 | ||||||||
\(112\) | 9.23036e12 | 0.441877 | ||||||||
\(113\) | −1.82775e13 | −0.825860 | −0.412930 | − | 0.910763i | \(-0.635495\pi\) | ||||
−0.412930 | + | 0.910763i | \(0.635495\pi\) | |||||||
\(114\) | −1.15059e13 | −0.490951 | ||||||||
\(115\) | 3.99332e13 | 1.60990 | ||||||||
\(116\) | −2.33181e13 | −0.888621 | ||||||||
\(117\) | 2.24824e13 | 0.810278 | ||||||||
\(118\) | −9.16155e12 | −0.312418 | ||||||||
\(119\) | 5.58493e13 | 1.80286 | ||||||||
\(120\) | −2.39242e13 | −0.731408 | ||||||||
\(121\) | 3.13843e12 | 0.0909091 | ||||||||
\(122\) | 2.85846e13 | 0.784862 | ||||||||
\(123\) | −6.14693e13 | −1.60057 | ||||||||
\(124\) | −1.01679e13 | −0.251182 | ||||||||
\(125\) | −4.73320e13 | −1.10979 | ||||||||
\(126\) | −3.35701e13 | −0.747384 | ||||||||
\(127\) | 6.08576e13 | 1.28704 | 0.643518 | − | 0.765431i | \(-0.277474\pi\) | ||||
0.643518 | + | 0.765431i | \(0.277474\pi\) | |||||||
\(128\) | −4.39805e12 | −0.0883883 | ||||||||
\(129\) | −1.51577e13 | −0.289600 | ||||||||
\(130\) | 8.62920e13 | 1.56797 | ||||||||
\(131\) | −4.11962e13 | −0.712187 | −0.356093 | − | 0.934450i | \(-0.615891\pi\) | ||||
−0.356093 | + | 0.934450i | \(0.615891\pi\) | |||||||
\(132\) | 1.15822e13 | 0.190573 | ||||||||
\(133\) | −6.19673e13 | −0.970794 | ||||||||
\(134\) | 1.48564e13 | 0.221683 | ||||||||
\(135\) | −5.84933e13 | −0.831643 | ||||||||
\(136\) | −2.66108e13 | −0.360625 | ||||||||
\(137\) | 8.81865e13 | 1.13951 | 0.569755 | − | 0.821814i | \(-0.307038\pi\) | ||||
0.569755 | + | 0.821814i | \(0.307038\pi\) | |||||||
\(138\) | −7.13457e13 | −0.879334 | ||||||||
\(139\) | −4.18391e13 | −0.492023 | −0.246012 | − | 0.969267i | \(-0.579120\pi\) | ||||
−0.246012 | + | 0.969267i | \(0.579120\pi\) | |||||||
\(140\) | −1.28849e14 | −1.44627 | ||||||||
\(141\) | 3.03603e13 | 0.325373 | ||||||||
\(142\) | −1.01964e14 | −1.04370 | ||||||||
\(143\) | −4.17758e13 | −0.408546 | ||||||||
\(144\) | 1.59953e13 | 0.149499 | ||||||||
\(145\) | 3.25504e14 | 2.90846 | ||||||||
\(146\) | 8.43714e13 | 0.720944 | ||||||||
\(147\) | −3.28490e14 | −2.68510 | ||||||||
\(148\) | 5.49203e10 | 0.000429568 0 | ||||||||
\(149\) | −1.09308e14 | −0.818356 | −0.409178 | − | 0.912455i | \(-0.634185\pi\) | ||||
−0.409178 | + | 0.912455i | \(0.634185\pi\) | |||||||
\(150\) | 2.09264e14 | 1.50004 | ||||||||
\(151\) | −6.17494e12 | −0.0423919 | −0.0211959 | − | 0.999775i | \(-0.506747\pi\) | ||||
−0.0211959 | + | 0.999775i | \(0.506747\pi\) | |||||||
\(152\) | 2.95259e13 | 0.194187 | ||||||||
\(153\) | 9.67815e13 | 0.609955 | ||||||||
\(154\) | 6.23785e13 | 0.376834 | ||||||||
\(155\) | 1.41936e14 | 0.822121 | ||||||||
\(156\) | −1.54172e14 | −0.856435 | ||||||||
\(157\) | 2.50232e13 | 0.133351 | 0.0666753 | − | 0.997775i | \(-0.478761\pi\) | ||||
0.0666753 | + | 0.997775i | \(0.478761\pi\) | |||||||
\(158\) | 4.17845e13 | 0.213670 | ||||||||
\(159\) | 3.38452e13 | 0.166118 | ||||||||
\(160\) | 6.13934e13 | 0.289296 | ||||||||
\(161\) | −3.84247e14 | −1.73877 | ||||||||
\(162\) | 2.01787e14 | 0.877093 | ||||||||
\(163\) | −1.60361e14 | −0.669697 | −0.334849 | − | 0.942272i | \(-0.608685\pi\) | ||||
−0.334849 | + | 0.942272i | \(0.608685\pi\) | |||||||
\(164\) | 1.57740e14 | 0.633079 | ||||||||
\(165\) | −1.61679e14 | −0.623747 | ||||||||
\(166\) | 2.65875e14 | 0.986223 | ||||||||
\(167\) | −7.33398e13 | −0.261627 | −0.130814 | − | 0.991407i | \(-0.541759\pi\) | ||||
−0.130814 | + | 0.991407i | \(0.541759\pi\) | |||||||
\(168\) | 2.30205e14 | 0.789958 | ||||||||
\(169\) | 2.53205e14 | 0.836004 | ||||||||
\(170\) | 3.71468e14 | 1.18033 | ||||||||
\(171\) | −1.07383e14 | −0.328445 | ||||||||
\(172\) | 3.88970e13 | 0.114546 | ||||||||
\(173\) | −4.42176e14 | −1.25399 | −0.626997 | − | 0.779022i | \(-0.715716\pi\) | ||||
−0.626997 | + | 0.779022i | \(0.715716\pi\) | |||||||
\(174\) | −5.81553e14 | −1.58862 | ||||||||
\(175\) | 1.12704e15 | 2.96614 | ||||||||
\(176\) | −2.97219e13 | −0.0753778 | ||||||||
\(177\) | −2.28489e14 | −0.558520 | ||||||||
\(178\) | 2.31275e14 | 0.545004 | ||||||||
\(179\) | −2.35232e14 | −0.534504 | −0.267252 | − | 0.963627i | \(-0.586116\pi\) | ||||
−0.267252 | + | 0.963627i | \(0.586116\pi\) | |||||||
\(180\) | −2.23283e14 | −0.489310 | ||||||||
\(181\) | −1.49801e14 | −0.316667 | −0.158334 | − | 0.987386i | \(-0.550612\pi\) | ||||
−0.158334 | + | 0.987386i | \(0.550612\pi\) | |||||||
\(182\) | −8.30324e14 | −1.69349 | ||||||||
\(183\) | 7.12899e14 | 1.40312 | ||||||||
\(184\) | 1.83085e14 | 0.347805 | ||||||||
\(185\) | −7.66646e11 | −0.00140598 | ||||||||
\(186\) | −2.53586e14 | −0.449046 | ||||||||
\(187\) | −1.79835e14 | −0.307542 | ||||||||
\(188\) | −7.79094e13 | −0.128696 | ||||||||
\(189\) | 5.62837e14 | 0.898217 | ||||||||
\(190\) | −4.12160e14 | −0.635576 | ||||||||
\(191\) | 8.53215e14 | 1.27157 | 0.635787 | − | 0.771865i | \(-0.280676\pi\) | ||||
0.635787 | + | 0.771865i | \(0.280676\pi\) | |||||||
\(192\) | −1.09687e14 | −0.158015 | ||||||||
\(193\) | −7.34539e14 | −1.02304 | −0.511520 | − | 0.859271i | \(-0.670917\pi\) | ||||
−0.511520 | + | 0.859271i | \(0.670917\pi\) | |||||||
\(194\) | 8.55587e14 | 1.15227 | ||||||||
\(195\) | 2.15212e15 | 2.80312 | ||||||||
\(196\) | 8.42959e14 | 1.06204 | ||||||||
\(197\) | −2.60261e14 | −0.317233 | −0.158617 | − | 0.987340i | \(-0.550703\pi\) | ||||
−0.158617 | + | 0.987340i | \(0.550703\pi\) | |||||||
\(198\) | 1.08096e14 | 0.127493 | ||||||||
\(199\) | −7.73756e14 | −0.883200 | −0.441600 | − | 0.897212i | \(-0.645589\pi\) | ||||
−0.441600 | + | 0.897212i | \(0.645589\pi\) | |||||||
\(200\) | −5.37007e14 | −0.593314 | ||||||||
\(201\) | 3.70518e14 | 0.396309 | ||||||||
\(202\) | −7.90200e14 | −0.818376 | ||||||||
\(203\) | −3.13208e15 | −3.14129 | ||||||||
\(204\) | −6.63673e14 | −0.644701 | ||||||||
\(205\) | −2.20194e15 | −2.07207 | ||||||||
\(206\) | 1.24356e15 | 1.13379 | ||||||||
\(207\) | −6.65864e14 | −0.588272 | ||||||||
\(208\) | 3.95629e14 | 0.338748 | ||||||||
\(209\) | 1.99535e14 | 0.165603 | ||||||||
\(210\) | −3.21349e15 | −2.58554 | ||||||||
\(211\) | 1.07625e15 | 0.839608 | 0.419804 | − | 0.907615i | \(-0.362099\pi\) | ||||
0.419804 | + | 0.907615i | \(0.362099\pi\) | |||||||
\(212\) | −8.68523e13 | −0.0657050 | ||||||||
\(213\) | −2.54299e15 | −1.86585 | ||||||||
\(214\) | −5.74037e14 | −0.408555 | ||||||||
\(215\) | −5.42973e14 | −0.374911 | ||||||||
\(216\) | −2.68179e14 | −0.179670 | ||||||||
\(217\) | −1.36574e15 | −0.887933 | ||||||||
\(218\) | 1.93104e15 | 1.21850 | ||||||||
\(219\) | 2.10422e15 | 1.28886 | ||||||||
\(220\) | 4.14895e14 | 0.246712 | ||||||||
\(221\) | 2.39380e15 | 1.38209 | ||||||||
\(222\) | 1.36971e12 | 0.000767952 0 | ||||||||
\(223\) | 1.47017e15 | 0.800545 | 0.400272 | − | 0.916396i | \(-0.368915\pi\) | ||||
0.400272 | + | 0.916396i | \(0.368915\pi\) | |||||||
\(224\) | −5.90743e14 | −0.312454 | ||||||||
\(225\) | 1.95305e15 | 1.00352 | ||||||||
\(226\) | 1.16976e15 | 0.583971 | ||||||||
\(227\) | 3.30482e15 | 1.60317 | 0.801586 | − | 0.597879i | \(-0.203990\pi\) | ||||
0.801586 | + | 0.597879i | \(0.203990\pi\) | |||||||
\(228\) | 7.36376e14 | 0.347155 | ||||||||
\(229\) | 1.73135e15 | 0.793329 | 0.396664 | − | 0.917964i | \(-0.370168\pi\) | ||||
0.396664 | + | 0.917964i | \(0.370168\pi\) | |||||||
\(230\) | −2.55573e15 | −1.13837 | ||||||||
\(231\) | 1.55572e15 | 0.673679 | ||||||||
\(232\) | 1.49236e15 | 0.628350 | ||||||||
\(233\) | 4.23290e14 | 0.173310 | 0.0866551 | − | 0.996238i | \(-0.472382\pi\) | ||||
0.0866551 | + | 0.996238i | \(0.472382\pi\) | |||||||
\(234\) | −1.43887e15 | −0.572953 | ||||||||
\(235\) | 1.08756e15 | 0.421222 | ||||||||
\(236\) | 5.86339e14 | 0.220913 | ||||||||
\(237\) | 1.04210e15 | 0.381985 | ||||||||
\(238\) | −3.57435e15 | −1.27482 | ||||||||
\(239\) | −3.81996e14 | −0.132578 | −0.0662892 | − | 0.997800i | \(-0.521116\pi\) | ||||
−0.0662892 | + | 0.997800i | \(0.521116\pi\) | |||||||
\(240\) | 1.53115e15 | 0.517184 | ||||||||
\(241\) | 2.50661e15 | 0.824093 | 0.412047 | − | 0.911163i | \(-0.364814\pi\) | ||||
0.412047 | + | 0.911163i | \(0.364814\pi\) | |||||||
\(242\) | −2.00859e14 | −0.0642824 | ||||||||
\(243\) | 3.40154e15 | 1.05983 | ||||||||
\(244\) | −1.82942e15 | −0.554982 | ||||||||
\(245\) | −1.17671e16 | −3.47608 | ||||||||
\(246\) | 3.93404e15 | 1.13178 | ||||||||
\(247\) | −2.65603e15 | −0.744222 | ||||||||
\(248\) | 6.50743e14 | 0.177613 | ||||||||
\(249\) | 6.63092e15 | 1.76310 | ||||||||
\(250\) | 3.02925e15 | 0.784739 | ||||||||
\(251\) | −6.17245e15 | −1.55804 | −0.779020 | − | 0.626999i | \(-0.784283\pi\) | ||||
−0.779020 | + | 0.626999i | \(0.784283\pi\) | |||||||
\(252\) | 2.14848e15 | 0.528480 | ||||||||
\(253\) | 1.23728e15 | 0.296609 | ||||||||
\(254\) | −3.89489e15 | −0.910072 | ||||||||
\(255\) | 9.26439e15 | 2.11011 | ||||||||
\(256\) | 2.81475e14 | 0.0625000 | ||||||||
\(257\) | −7.04282e15 | −1.52469 | −0.762344 | − | 0.647172i | \(-0.775952\pi\) | ||||
−0.762344 | + | 0.647172i | \(0.775952\pi\) | |||||||
\(258\) | 9.70090e14 | 0.204778 | ||||||||
\(259\) | 7.37686e12 | 0.00151853 | ||||||||
\(260\) | −5.52269e15 | −1.10873 | ||||||||
\(261\) | −5.42759e15 | −1.06278 | ||||||||
\(262\) | 2.63656e15 | 0.503592 | ||||||||
\(263\) | 2.19808e15 | 0.409572 | 0.204786 | − | 0.978807i | \(-0.434350\pi\) | ||||
0.204786 | + | 0.978807i | \(0.434350\pi\) | |||||||
\(264\) | −7.41262e14 | −0.134755 | ||||||||
\(265\) | 1.21239e15 | 0.215053 | ||||||||
\(266\) | 3.96591e15 | 0.686455 | ||||||||
\(267\) | 5.76800e15 | 0.974321 | ||||||||
\(268\) | −9.50808e14 | −0.156753 | ||||||||
\(269\) | −5.10332e15 | −0.821227 | −0.410614 | − | 0.911809i | \(-0.634685\pi\) | ||||
−0.410614 | + | 0.911809i | \(0.634685\pi\) | |||||||
\(270\) | 3.74357e15 | 0.588060 | ||||||||
\(271\) | −5.82993e15 | −0.894053 | −0.447026 | − | 0.894521i | \(-0.647517\pi\) | ||||
−0.447026 | + | 0.894521i | \(0.647517\pi\) | |||||||
\(272\) | 1.70309e15 | 0.255000 | ||||||||
\(273\) | −2.07082e16 | −3.02751 | ||||||||
\(274\) | −5.64393e15 | −0.805756 | ||||||||
\(275\) | −3.62907e15 | −0.505980 | ||||||||
\(276\) | 4.56613e15 | 0.621783 | ||||||||
\(277\) | −2.72263e15 | −0.362135 | −0.181067 | − | 0.983471i | \(-0.557955\pi\) | ||||
−0.181067 | + | 0.983471i | \(0.557955\pi\) | |||||||
\(278\) | 2.67770e15 | 0.347913 | ||||||||
\(279\) | −2.36670e15 | −0.300411 | ||||||||
\(280\) | 8.24633e15 | 1.02267 | ||||||||
\(281\) | 6.94126e15 | 0.841100 | 0.420550 | − | 0.907269i | \(-0.361837\pi\) | ||||
0.420550 | + | 0.907269i | \(0.361837\pi\) | |||||||
\(282\) | −1.94306e15 | −0.230074 | ||||||||
\(283\) | −2.19270e15 | −0.253728 | −0.126864 | − | 0.991920i | \(-0.540491\pi\) | ||||
−0.126864 | + | 0.991920i | \(0.540491\pi\) | |||||||
\(284\) | 6.52572e15 | 0.738005 | ||||||||
\(285\) | −1.02793e16 | −1.13624 | ||||||||
\(286\) | 2.67365e15 | 0.288885 | ||||||||
\(287\) | 2.11876e16 | 2.23794 | ||||||||
\(288\) | −1.02370e15 | −0.105711 | ||||||||
\(289\) | 4.00172e14 | 0.0404027 | ||||||||
\(290\) | −2.08322e16 | −2.05659 | ||||||||
\(291\) | 2.13383e16 | 2.05995 | ||||||||
\(292\) | −5.39977e15 | −0.509785 | ||||||||
\(293\) | −1.73532e16 | −1.60229 | −0.801145 | − | 0.598470i | \(-0.795775\pi\) | ||||
−0.801145 | + | 0.598470i | \(0.795775\pi\) | |||||||
\(294\) | 2.10234e16 | 1.89865 | ||||||||
\(295\) | −8.18485e15 | −0.723049 | ||||||||
\(296\) | −3.51490e12 | −0.000303750 0 | ||||||||
\(297\) | −1.81234e15 | −0.153223 | ||||||||
\(298\) | 6.99573e15 | 0.578665 | ||||||||
\(299\) | −1.64695e16 | −1.33296 | ||||||||
\(300\) | −1.33929e16 | −1.06069 | ||||||||
\(301\) | 5.22462e15 | 0.404923 | ||||||||
\(302\) | 3.95196e14 | 0.0299756 | ||||||||
\(303\) | −1.97076e16 | −1.46304 | ||||||||
\(304\) | −1.88966e15 | −0.137311 | ||||||||
\(305\) | 2.55373e16 | 1.81646 | ||||||||
\(306\) | −6.19401e15 | −0.431303 | ||||||||
\(307\) | −9.28494e15 | −0.632965 | −0.316482 | − | 0.948598i | \(-0.602502\pi\) | ||||
−0.316482 | + | 0.948598i | \(0.602502\pi\) | |||||||
\(308\) | −3.99222e15 | −0.266462 | ||||||||
\(309\) | 3.10144e16 | 2.02691 | ||||||||
\(310\) | −9.08389e15 | −0.581327 | ||||||||
\(311\) | 8.22137e15 | 0.515231 | 0.257615 | − | 0.966248i | \(-0.417063\pi\) | ||||
0.257615 | + | 0.966248i | \(0.417063\pi\) | |||||||
\(312\) | 9.86698e15 | 0.605591 | ||||||||
\(313\) | 1.31274e16 | 0.789113 | 0.394557 | − | 0.918872i | \(-0.370898\pi\) | ||||
0.394557 | + | 0.918872i | \(0.370898\pi\) | |||||||
\(314\) | −1.60148e15 | −0.0942931 | ||||||||
\(315\) | −2.99912e16 | −1.72972 | ||||||||
\(316\) | −2.67421e15 | −0.151088 | ||||||||
\(317\) | 3.62350e15 | 0.200559 | 0.100280 | − | 0.994959i | \(-0.468026\pi\) | ||||
0.100280 | + | 0.994959i | \(0.468026\pi\) | |||||||
\(318\) | −2.16609e15 | −0.117463 | ||||||||
\(319\) | 1.00853e16 | 0.535859 | ||||||||
\(320\) | −3.92918e15 | −0.204563 | ||||||||
\(321\) | −1.43165e16 | −0.730387 | ||||||||
\(322\) | 2.45918e16 | 1.22950 | ||||||||
\(323\) | −1.14336e16 | −0.560230 | ||||||||
\(324\) | −1.29144e16 | −0.620199 | ||||||||
\(325\) | 4.83068e16 | 2.27387 | ||||||||
\(326\) | 1.02631e16 | 0.473548 | ||||||||
\(327\) | 4.81601e16 | 2.17835 | ||||||||
\(328\) | −1.00954e16 | −0.447654 | ||||||||
\(329\) | −1.04648e16 | −0.454942 | ||||||||
\(330\) | 1.03475e16 | 0.441056 | ||||||||
\(331\) | 1.32109e16 | 0.552140 | 0.276070 | − | 0.961138i | \(-0.410968\pi\) | ||||
0.276070 | + | 0.961138i | \(0.410968\pi\) | |||||||
\(332\) | −1.70160e16 | −0.697365 | ||||||||
\(333\) | 1.27834e13 | 0.000513758 0 | ||||||||
\(334\) | 4.69375e15 | 0.184998 | ||||||||
\(335\) | 1.32726e16 | 0.513055 | ||||||||
\(336\) | −1.47331e16 | −0.558585 | ||||||||
\(337\) | −1.36437e16 | −0.507387 | −0.253693 | − | 0.967285i | \(-0.581645\pi\) | ||||
−0.253693 | + | 0.967285i | \(0.581645\pi\) | |||||||
\(338\) | −1.62051e16 | −0.591144 | ||||||||
\(339\) | 2.91737e16 | 1.04398 | ||||||||
\(340\) | −2.37739e16 | −0.834618 | ||||||||
\(341\) | 4.39770e15 | 0.151468 | ||||||||
\(342\) | 6.87254e15 | 0.232246 | ||||||||
\(343\) | 5.99202e16 | 1.98683 | ||||||||
\(344\) | −2.48941e15 | −0.0809965 | ||||||||
\(345\) | −6.37397e16 | −2.03510 | ||||||||
\(346\) | 2.82993e16 | 0.886708 | ||||||||
\(347\) | −1.84147e16 | −0.566268 | −0.283134 | − | 0.959080i | \(-0.591374\pi\) | ||||
−0.283134 | + | 0.959080i | \(0.591374\pi\) | |||||||
\(348\) | 3.72194e16 | 1.12332 | ||||||||
\(349\) | 3.04103e16 | 0.900855 | 0.450428 | − | 0.892813i | \(-0.351271\pi\) | ||||
0.450428 | + | 0.892813i | \(0.351271\pi\) | |||||||
\(350\) | −7.21304e16 | −2.09738 | ||||||||
\(351\) | 2.41242e16 | 0.688583 | ||||||||
\(352\) | 1.90220e15 | 0.0533002 | ||||||||
\(353\) | −4.38109e16 | −1.20516 | −0.602582 | − | 0.798057i | \(-0.705861\pi\) | ||||
−0.602582 | + | 0.798057i | \(0.705861\pi\) | |||||||
\(354\) | 1.46233e16 | 0.394933 | ||||||||
\(355\) | −9.10942e16 | −2.41550 | ||||||||
\(356\) | −1.48016e16 | −0.385376 | ||||||||
\(357\) | −8.91442e16 | −2.27903 | ||||||||
\(358\) | 1.50548e16 | 0.377952 | ||||||||
\(359\) | −1.99730e16 | −0.492412 | −0.246206 | − | 0.969218i | \(-0.579184\pi\) | ||||
−0.246206 | + | 0.969218i | \(0.579184\pi\) | |||||||
\(360\) | 1.42901e16 | 0.345995 | ||||||||
\(361\) | −2.93669e16 | −0.698331 | ||||||||
\(362\) | 9.58724e15 | 0.223917 | ||||||||
\(363\) | −5.00943e15 | −0.114920 | ||||||||
\(364\) | 5.31407e16 | 1.19748 | ||||||||
\(365\) | 7.53768e16 | 1.66853 | ||||||||
\(366\) | −4.56256e16 | −0.992159 | ||||||||
\(367\) | 2.51327e16 | 0.536920 | 0.268460 | − | 0.963291i | \(-0.413485\pi\) | ||||
0.268460 | + | 0.963291i | \(0.413485\pi\) | |||||||
\(368\) | −1.17174e16 | −0.245935 | ||||||||
\(369\) | 3.67161e16 | 0.757155 | ||||||||
\(370\) | 4.90654e13 | 0.000994177 0 | ||||||||
\(371\) | −1.16660e16 | −0.232268 | ||||||||
\(372\) | 1.62295e16 | 0.317524 | ||||||||
\(373\) | 4.48712e16 | 0.862701 | 0.431351 | − | 0.902184i | \(-0.358037\pi\) | ||||
0.431351 | + | 0.902184i | \(0.358037\pi\) | |||||||
\(374\) | 1.15095e16 | 0.217465 | ||||||||
\(375\) | 7.55494e16 | 1.40290 | ||||||||
\(376\) | 4.98620e15 | 0.0910016 | ||||||||
\(377\) | −1.34246e17 | −2.40815 | ||||||||
\(378\) | −3.60216e16 | −0.635135 | ||||||||
\(379\) | 8.14810e16 | 1.41222 | 0.706108 | − | 0.708104i | \(-0.250449\pi\) | ||||
0.706108 | + | 0.708104i | \(0.250449\pi\) | |||||||
\(380\) | 2.63782e16 | 0.449420 | ||||||||
\(381\) | −9.71384e16 | −1.62697 | ||||||||
\(382\) | −5.46057e16 | −0.899138 | ||||||||
\(383\) | −7.68561e16 | −1.24419 | −0.622095 | − | 0.782942i | \(-0.713718\pi\) | ||||
−0.622095 | + | 0.782942i | \(0.713718\pi\) | |||||||
\(384\) | 7.01998e15 | 0.111733 | ||||||||
\(385\) | 5.57285e16 | 0.872132 | ||||||||
\(386\) | 4.70105e16 | 0.723398 | ||||||||
\(387\) | 9.05378e15 | 0.136996 | ||||||||
\(388\) | −5.47576e16 | −0.814776 | ||||||||
\(389\) | −1.01853e16 | −0.149040 | −0.0745200 | − | 0.997220i | \(-0.523742\pi\) | ||||
−0.0745200 | + | 0.997220i | \(0.523742\pi\) | |||||||
\(390\) | −1.37736e17 | −1.98210 | ||||||||
\(391\) | −7.08975e16 | −1.00342 | ||||||||
\(392\) | −5.39494e16 | −0.750978 | ||||||||
\(393\) | 6.57556e16 | 0.900288 | ||||||||
\(394\) | 1.66567e16 | 0.224318 | ||||||||
\(395\) | 3.73299e16 | 0.494511 | ||||||||
\(396\) | −6.91814e15 | −0.0901511 | ||||||||
\(397\) | −5.19589e16 | −0.666072 | −0.333036 | − | 0.942914i | \(-0.608073\pi\) | ||||
−0.333036 | + | 0.942914i | \(0.608073\pi\) | |||||||
\(398\) | 4.95204e16 | 0.624517 | ||||||||
\(399\) | 9.89096e16 | 1.22720 | ||||||||
\(400\) | 3.43684e16 | 0.419536 | ||||||||
\(401\) | −4.16402e16 | −0.500120 | −0.250060 | − | 0.968230i | \(-0.580450\pi\) | ||||
−0.250060 | + | 0.968230i | \(0.580450\pi\) | |||||||
\(402\) | −2.37131e16 | −0.280233 | ||||||||
\(403\) | −5.85380e16 | −0.680699 | ||||||||
\(404\) | 5.05728e16 | 0.578679 | ||||||||
\(405\) | 1.80275e17 | 2.02991 | ||||||||
\(406\) | 2.00453e17 | 2.22123 | ||||||||
\(407\) | −2.37536e13 | −0.000259039 0 | ||||||||
\(408\) | 4.24751e16 | 0.455872 | ||||||||
\(409\) | −1.52221e17 | −1.60795 | −0.803977 | − | 0.594660i | \(-0.797287\pi\) | ||||
−0.803977 | + | 0.594660i | \(0.797287\pi\) | |||||||
\(410\) | 1.40924e17 | 1.46518 | ||||||||
\(411\) | −1.40760e17 | −1.44048 | ||||||||
\(412\) | −7.95881e16 | −0.801708 | ||||||||
\(413\) | 7.87567e16 | 0.780930 | ||||||||
\(414\) | 4.26153e16 | 0.415971 | ||||||||
\(415\) | 2.37531e17 | 2.28248 | ||||||||
\(416\) | −2.53203e16 | −0.239531 | ||||||||
\(417\) | 6.67817e16 | 0.621976 | ||||||||
\(418\) | −1.27703e16 | −0.117099 | ||||||||
\(419\) | −1.80246e17 | −1.62732 | −0.813661 | − | 0.581339i | \(-0.802529\pi\) | ||||
−0.813661 | + | 0.581339i | \(0.802529\pi\) | |||||||
\(420\) | 2.05663e17 | 1.82825 | ||||||||
\(421\) | −1.53615e17 | −1.34462 | −0.672310 | − | 0.740269i | \(-0.734698\pi\) | ||||
−0.672310 | + | 0.740269i | \(0.734698\pi\) | |||||||
\(422\) | −6.88799e16 | −0.593693 | ||||||||
\(423\) | −1.81344e16 | −0.153919 | ||||||||
\(424\) | 5.55855e15 | 0.0464604 | ||||||||
\(425\) | 2.07950e17 | 1.71171 | ||||||||
\(426\) | 1.62751e17 | 1.31936 | ||||||||
\(427\) | −2.45726e17 | −1.96187 | ||||||||
\(428\) | 3.67384e16 | 0.288892 | ||||||||
\(429\) | 6.66808e16 | 0.516450 | ||||||||
\(430\) | 3.47503e16 | 0.265102 | ||||||||
\(431\) | 1.39142e17 | 1.04558 | 0.522788 | − | 0.852463i | \(-0.324892\pi\) | ||||
0.522788 | + | 0.852463i | \(0.324892\pi\) | |||||||
\(432\) | 1.71634e16 | 0.127046 | ||||||||
\(433\) | 2.08757e17 | 1.52220 | 0.761098 | − | 0.648637i | \(-0.224661\pi\) | ||||
0.761098 | + | 0.648637i | \(0.224661\pi\) | |||||||
\(434\) | 8.74074e16 | 0.627863 | ||||||||
\(435\) | −5.19555e17 | −3.67664 | ||||||||
\(436\) | −1.23587e17 | −0.861608 | ||||||||
\(437\) | 7.86640e16 | 0.540315 | ||||||||
\(438\) | −1.34670e17 | −0.911359 | ||||||||
\(439\) | −2.48828e17 | −1.65913 | −0.829565 | − | 0.558410i | \(-0.811411\pi\) | ||||
−0.829565 | + | 0.558410i | \(0.811411\pi\) | |||||||
\(440\) | −2.65533e16 | −0.174452 | ||||||||
\(441\) | 1.96210e17 | 1.27019 | ||||||||
\(442\) | −1.53203e17 | −0.977288 | ||||||||
\(443\) | 2.88116e17 | 1.81110 | 0.905550 | − | 0.424238i | \(-0.139458\pi\) | ||||
0.905550 | + | 0.424238i | \(0.139458\pi\) | |||||||
\(444\) | −8.76614e13 | −0.000543024 0 | ||||||||
\(445\) | 2.06620e17 | 1.26134 | ||||||||
\(446\) | −9.40908e16 | −0.566071 | ||||||||
\(447\) | 1.74473e17 | 1.03450 | ||||||||
\(448\) | 3.78076e16 | 0.220939 | ||||||||
\(449\) | 2.89374e17 | 1.66670 | 0.833352 | − | 0.552742i | \(-0.186418\pi\) | ||||
0.833352 | + | 0.552742i | \(0.186418\pi\) | |||||||
\(450\) | −1.24995e17 | −0.709597 | ||||||||
\(451\) | −6.82243e16 | −0.381761 | ||||||||
\(452\) | −7.48645e16 | −0.412930 | ||||||||
\(453\) | 9.85618e15 | 0.0535883 | ||||||||
\(454\) | −2.11509e17 | −1.13361 | ||||||||
\(455\) | −7.41805e17 | −3.91936 | ||||||||
\(456\) | −4.71281e16 | −0.245475 | ||||||||
\(457\) | −1.46985e17 | −0.754778 | −0.377389 | − | 0.926055i | \(-0.623178\pi\) | ||||
−0.377389 | + | 0.926055i | \(0.623178\pi\) | |||||||
\(458\) | −1.10806e17 | −0.560968 | ||||||||
\(459\) | 1.03849e17 | 0.518347 | ||||||||
\(460\) | 1.63566e17 | 0.804949 | ||||||||
\(461\) | −1.25707e17 | −0.609962 | −0.304981 | − | 0.952359i | \(-0.598650\pi\) | ||||
−0.304981 | + | 0.952359i | \(0.598650\pi\) | |||||||
\(462\) | −9.95659e16 | −0.476363 | ||||||||
\(463\) | 8.57739e15 | 0.0404649 | 0.0202325 | − | 0.999795i | \(-0.493559\pi\) | ||||
0.0202325 | + | 0.999795i | \(0.493559\pi\) | |||||||
\(464\) | −9.55110e16 | −0.444311 | ||||||||
\(465\) | −2.26552e17 | −1.03926 | ||||||||
\(466\) | −2.70905e16 | −0.122549 | ||||||||
\(467\) | 2.14149e17 | 0.955337 | 0.477669 | − | 0.878540i | \(-0.341482\pi\) | ||||
0.477669 | + | 0.878540i | \(0.341482\pi\) | |||||||
\(468\) | 9.20878e16 | 0.405139 | ||||||||
\(469\) | −1.27712e17 | −0.554126 | ||||||||
\(470\) | −6.96037e16 | −0.297849 | ||||||||
\(471\) | −3.99410e16 | −0.168571 | ||||||||
\(472\) | −3.75257e16 | −0.156209 | ||||||||
\(473\) | −1.68233e16 | −0.0690741 | ||||||||
\(474\) | −6.66946e16 | −0.270104 | ||||||||
\(475\) | −2.30730e17 | −0.921712 | ||||||||
\(476\) | 2.28759e17 | 0.901431 | ||||||||
\(477\) | −2.02160e16 | −0.0785824 | ||||||||
\(478\) | 2.44478e16 | 0.0937471 | ||||||||
\(479\) | −1.75601e17 | −0.664272 | −0.332136 | − | 0.943232i | \(-0.607769\pi\) | ||||
−0.332136 | + | 0.943232i | \(0.607769\pi\) | |||||||
\(480\) | −9.79936e16 | −0.365704 | ||||||||
\(481\) | 3.16185e14 | 0.00116412 | ||||||||
\(482\) | −1.60423e17 | −0.582722 | ||||||||
\(483\) | 6.13319e17 | 2.19801 | ||||||||
\(484\) | 1.28550e16 | 0.0454545 | ||||||||
\(485\) | 7.64375e17 | 2.66677 | ||||||||
\(486\) | −2.17698e17 | −0.749410 | ||||||||
\(487\) | 1.40825e17 | 0.478345 | 0.239172 | − | 0.970977i | \(-0.423124\pi\) | ||||
0.239172 | + | 0.970977i | \(0.423124\pi\) | |||||||
\(488\) | 1.17083e17 | 0.392431 | ||||||||
\(489\) | 2.55961e17 | 0.846577 | ||||||||
\(490\) | 7.53093e17 | 2.45796 | ||||||||
\(491\) | −1.30979e17 | −0.421864 | −0.210932 | − | 0.977501i | \(-0.567650\pi\) | ||||
−0.210932 | + | 0.977501i | \(0.567650\pi\) | |||||||
\(492\) | −2.51778e17 | −0.800286 | ||||||||
\(493\) | −5.77900e17 | −1.81279 | ||||||||
\(494\) | 1.69986e17 | 0.526244 | ||||||||
\(495\) | 9.65721e16 | 0.295065 | ||||||||
\(496\) | −4.16476e16 | −0.125591 | ||||||||
\(497\) | 8.76531e17 | 2.60886 | ||||||||
\(498\) | −4.24379e17 | −1.24670 | ||||||||
\(499\) | 4.75923e17 | 1.38001 | 0.690007 | − | 0.723803i | \(-0.257607\pi\) | ||||
0.690007 | + | 0.723803i | \(0.257607\pi\) | |||||||
\(500\) | −1.93872e17 | −0.554894 | ||||||||
\(501\) | 1.17062e17 | 0.330728 | ||||||||
\(502\) | 3.95037e17 | 1.10170 | ||||||||
\(503\) | −4.15310e17 | −1.14335 | −0.571676 | − | 0.820479i | \(-0.693707\pi\) | ||||
−0.571676 | + | 0.820479i | \(0.693707\pi\) | |||||||
\(504\) | −1.37503e17 | −0.373692 | ||||||||
\(505\) | −7.05958e17 | −1.89402 | ||||||||
\(506\) | −7.91860e16 | −0.209734 | ||||||||
\(507\) | −4.04155e17 | −1.05681 | ||||||||
\(508\) | 2.49273e17 | 0.643518 | ||||||||
\(509\) | 4.04654e16 | 0.103138 | 0.0515690 | − | 0.998669i | \(-0.483578\pi\) | ||||
0.0515690 | + | 0.998669i | \(0.483578\pi\) | |||||||
\(510\) | −5.92921e17 | −1.49207 | ||||||||
\(511\) | −7.25294e17 | −1.80210 | ||||||||
\(512\) | −1.80144e16 | −0.0441942 | ||||||||
\(513\) | −1.15225e17 | −0.279116 | ||||||||
\(514\) | 4.50740e17 | 1.07812 | ||||||||
\(515\) | 1.11099e18 | 2.62400 | ||||||||
\(516\) | −6.20858e16 | −0.144800 | ||||||||
\(517\) | 3.36966e16 | 0.0776064 | ||||||||
\(518\) | −4.72119e14 | −0.00107376 | ||||||||
\(519\) | 7.05783e17 | 1.58520 | ||||||||
\(520\) | 3.53452e17 | 0.783987 | ||||||||
\(521\) | −8.30318e16 | −0.181886 | −0.0909430 | − | 0.995856i | \(-0.528988\pi\) | ||||
−0.0909430 | + | 0.995856i | \(0.528988\pi\) | |||||||
\(522\) | 3.47366e17 | 0.751500 | ||||||||
\(523\) | 5.86014e17 | 1.25212 | 0.626062 | − | 0.779773i | \(-0.284666\pi\) | ||||
0.626062 | + | 0.779773i | \(0.284666\pi\) | |||||||
\(524\) | −1.68740e17 | −0.356093 | ||||||||
\(525\) | −1.79893e18 | −3.74955 | ||||||||
\(526\) | −1.40677e17 | −0.289611 | ||||||||
\(527\) | −2.51993e17 | −0.512412 | ||||||||
\(528\) | 4.74408e16 | 0.0952865 | ||||||||
\(529\) | −1.62560e16 | −0.0322517 | ||||||||
\(530\) | −7.75932e16 | −0.152065 | ||||||||
\(531\) | 1.36478e17 | 0.264209 | ||||||||
\(532\) | −2.53818e17 | −0.485397 | ||||||||
\(533\) | 9.08137e17 | 1.71563 | ||||||||
\(534\) | −3.69152e17 | −0.688949 | ||||||||
\(535\) | −5.12840e17 | −0.945545 | ||||||||
\(536\) | 6.08517e16 | 0.110841 | ||||||||
\(537\) | 3.75467e17 | 0.675677 | ||||||||
\(538\) | 3.26613e17 | 0.580695 | ||||||||
\(539\) | −3.64588e17 | −0.640436 | ||||||||
\(540\) | −2.39589e17 | −0.415821 | ||||||||
\(541\) | −8.76345e17 | −1.50277 | −0.751385 | − | 0.659864i | \(-0.770614\pi\) | ||||
−0.751385 | + | 0.659864i | \(0.770614\pi\) | |||||||
\(542\) | 3.73116e17 | 0.632191 | ||||||||
\(543\) | 2.39105e17 | 0.400304 | ||||||||
\(544\) | −1.08998e17 | −0.180312 | ||||||||
\(545\) | 1.72518e18 | 2.82005 | ||||||||
\(546\) | 1.32533e18 | 2.14077 | ||||||||
\(547\) | −6.52221e17 | −1.04106 | −0.520532 | − | 0.853842i | \(-0.674266\pi\) | ||||
−0.520532 | + | 0.853842i | \(0.674266\pi\) | |||||||
\(548\) | 3.61212e17 | 0.569755 | ||||||||
\(549\) | −4.25820e17 | −0.663752 | ||||||||
\(550\) | 2.32261e17 | 0.357782 | ||||||||
\(551\) | 6.41206e17 | 0.976140 | ||||||||
\(552\) | −2.92232e17 | −0.439667 | ||||||||
\(553\) | −3.59198e17 | −0.534097 | ||||||||
\(554\) | 1.74248e17 | 0.256068 | ||||||||
\(555\) | 1.22369e15 | 0.00177732 | ||||||||
\(556\) | −1.71373e17 | −0.246012 | ||||||||
\(557\) | 4.61565e16 | 0.0654898 | 0.0327449 | − | 0.999464i | \(-0.489575\pi\) | ||||
0.0327449 | + | 0.999464i | \(0.489575\pi\) | |||||||
\(558\) | 1.51469e17 | 0.212423 | ||||||||
\(559\) | 2.23937e17 | 0.310419 | ||||||||
\(560\) | −5.27765e17 | −0.723134 | ||||||||
\(561\) | 2.87045e17 | 0.388769 | ||||||||
\(562\) | −4.44241e17 | −0.594747 | ||||||||
\(563\) | 1.35065e16 | 0.0178747 | 0.00893733 | − | 0.999960i | \(-0.497155\pi\) | ||||
0.00893733 | + | 0.999960i | \(0.497155\pi\) | |||||||
\(564\) | 1.24356e17 | 0.162687 | ||||||||
\(565\) | 1.04505e18 | 1.35152 | ||||||||
\(566\) | 1.40333e17 | 0.179413 | ||||||||
\(567\) | −1.73465e18 | −2.19241 | ||||||||
\(568\) | −4.17646e17 | −0.521849 | ||||||||
\(569\) | 7.00697e17 | 0.865567 | 0.432783 | − | 0.901498i | \(-0.357531\pi\) | ||||
0.432783 | + | 0.901498i | \(0.357531\pi\) | |||||||
\(570\) | 6.57872e17 | 0.803443 | ||||||||
\(571\) | 6.01608e17 | 0.726405 | 0.363202 | − | 0.931710i | \(-0.381683\pi\) | ||||
0.363202 | + | 0.931710i | \(0.381683\pi\) | |||||||
\(572\) | −1.71114e17 | −0.204273 | ||||||||
\(573\) | −1.36187e18 | −1.60742 | ||||||||
\(574\) | −1.35601e18 | −1.58247 | ||||||||
\(575\) | −1.43071e18 | −1.65086 | ||||||||
\(576\) | 6.55169e16 | 0.0747493 | ||||||||
\(577\) | −1.20723e18 | −1.36191 | −0.680954 | − | 0.732326i | \(-0.738435\pi\) | ||||
−0.680954 | + | 0.732326i | \(0.738435\pi\) | |||||||
\(578\) | −2.56110e16 | −0.0285690 | ||||||||
\(579\) | 1.17244e18 | 1.29324 | ||||||||
\(580\) | 1.33326e18 | 1.45423 | ||||||||
\(581\) | −2.28558e18 | −2.46520 | ||||||||
\(582\) | −1.36565e18 | −1.45660 | ||||||||
\(583\) | 3.75645e16 | 0.0396216 | ||||||||
\(584\) | 3.45585e17 | 0.360472 | ||||||||
\(585\) | −1.28548e18 | −1.32602 | ||||||||
\(586\) | 1.11061e18 | 1.13299 | ||||||||
\(587\) | 6.11321e17 | 0.616768 | 0.308384 | − | 0.951262i | \(-0.400212\pi\) | ||||
0.308384 | + | 0.951262i | \(0.400212\pi\) | |||||||
\(588\) | −1.34550e18 | −1.34255 | ||||||||
\(589\) | 2.79598e17 | 0.275921 | ||||||||
\(590\) | 5.23831e17 | 0.511273 | ||||||||
\(591\) | 4.15417e17 | 0.401020 | ||||||||
\(592\) | 2.24953e14 | 0.000214784 0 | ||||||||
\(593\) | −1.45118e18 | −1.37046 | −0.685231 | − | 0.728325i | \(-0.740299\pi\) | ||||
−0.685231 | + | 0.728325i | \(0.740299\pi\) | |||||||
\(594\) | 1.15990e17 | 0.108345 | ||||||||
\(595\) | −3.19330e18 | −2.95039 | ||||||||
\(596\) | −4.47727e17 | −0.409178 | ||||||||
\(597\) | 1.23504e18 | 1.11647 | ||||||||
\(598\) | 1.05405e18 | 0.942547 | ||||||||
\(599\) | 1.87155e18 | 1.65549 | 0.827744 | − | 0.561106i | \(-0.189624\pi\) | ||||
0.827744 | + | 0.561106i | \(0.189624\pi\) | |||||||
\(600\) | 8.57147e17 | 0.750019 | ||||||||
\(601\) | −8.49533e17 | −0.735353 | −0.367677 | − | 0.929954i | \(-0.619847\pi\) | ||||
−0.367677 | + | 0.929954i | \(0.619847\pi\) | |||||||
\(602\) | −3.34376e17 | −0.286324 | ||||||||
\(603\) | −2.21313e17 | −0.187475 | ||||||||
\(604\) | −2.52926e16 | −0.0211959 | ||||||||
\(605\) | −1.79446e17 | −0.148773 | ||||||||
\(606\) | 1.26128e18 | 1.03452 | ||||||||
\(607\) | 8.39863e17 | 0.681526 | 0.340763 | − | 0.940149i | \(-0.389315\pi\) | ||||
0.340763 | + | 0.940149i | \(0.389315\pi\) | |||||||
\(608\) | 1.20938e17 | 0.0970936 | ||||||||
\(609\) | 4.99929e18 | 3.97096 | ||||||||
\(610\) | −1.63439e18 | −1.28443 | ||||||||
\(611\) | −4.48538e17 | −0.348763 | ||||||||
\(612\) | 3.96417e17 | 0.304978 | ||||||||
\(613\) | −5.83068e17 | −0.443840 | −0.221920 | − | 0.975065i | \(-0.571232\pi\) | ||||
−0.221920 | + | 0.975065i | \(0.571232\pi\) | |||||||
\(614\) | 5.94236e17 | 0.447574 | ||||||||
\(615\) | 3.51464e18 | 2.61934 | ||||||||
\(616\) | 2.55502e17 | 0.188417 | ||||||||
\(617\) | −1.08213e18 | −0.789637 | −0.394818 | − | 0.918759i | \(-0.629192\pi\) | ||||
−0.394818 | + | 0.918759i | \(0.629192\pi\) | |||||||
\(618\) | −1.98492e18 | −1.43324 | ||||||||
\(619\) | 1.81567e18 | 1.29732 | 0.648660 | − | 0.761078i | \(-0.275330\pi\) | ||||
0.648660 | + | 0.761078i | \(0.275330\pi\) | |||||||
\(620\) | 5.81369e17 | 0.411060 | ||||||||
\(621\) | −7.14490e17 | −0.499920 | ||||||||
\(622\) | −5.26168e17 | −0.364323 | ||||||||
\(623\) | −1.98815e18 | −1.36231 | ||||||||
\(624\) | −6.31487e17 | −0.428218 | ||||||||
\(625\) | 2.05677e17 | 0.138027 | ||||||||
\(626\) | −8.40151e17 | −0.557987 | ||||||||
\(627\) | −3.18490e17 | −0.209342 | ||||||||
\(628\) | 1.02495e17 | 0.0666753 | ||||||||
\(629\) | 1.36110e15 | 0.000876319 0 | ||||||||
\(630\) | 1.91944e18 | 1.22310 | ||||||||
\(631\) | −5.64428e17 | −0.355973 | −0.177987 | − | 0.984033i | \(-0.556958\pi\) | ||||
−0.177987 | + | 0.984033i | \(0.556958\pi\) | |||||||
\(632\) | 1.71149e17 | 0.106835 | ||||||||
\(633\) | −1.71786e18 | −1.06136 | ||||||||
\(634\) | −2.31904e17 | −0.141817 | ||||||||
\(635\) | −3.47966e18 | −2.10624 | ||||||||
\(636\) | 1.38630e17 | 0.0830589 | ||||||||
\(637\) | 4.85306e18 | 2.87812 | ||||||||
\(638\) | −6.45461e17 | −0.378909 | ||||||||
\(639\) | 1.51895e18 | 0.882646 | ||||||||
\(640\) | 2.51468e17 | 0.144648 | ||||||||
\(641\) | 4.65459e17 | 0.265036 | 0.132518 | − | 0.991181i | \(-0.457694\pi\) | ||||
0.132518 | + | 0.991181i | \(0.457694\pi\) | |||||||
\(642\) | 9.16253e17 | 0.516461 | ||||||||
\(643\) | 2.52025e18 | 1.40628 | 0.703141 | − | 0.711050i | \(-0.251780\pi\) | ||||
0.703141 | + | 0.711050i | \(0.251780\pi\) | |||||||
\(644\) | −1.57388e18 | −0.869386 | ||||||||
\(645\) | 8.66671e17 | 0.473932 | ||||||||
\(646\) | 7.31750e17 | 0.396142 | ||||||||
\(647\) | 1.73833e18 | 0.931651 | 0.465826 | − | 0.884877i | \(-0.345757\pi\) | ||||
0.465826 | + | 0.884877i | \(0.345757\pi\) | |||||||
\(648\) | 8.26520e17 | 0.438547 | ||||||||
\(649\) | −2.53597e17 | −0.133215 | ||||||||
\(650\) | −3.09164e18 | −1.60787 | ||||||||
\(651\) | 2.17994e18 | 1.12245 | ||||||||
\(652\) | −6.56838e17 | −0.334849 | ||||||||
\(653\) | 2.64589e17 | 0.133548 | 0.0667738 | − | 0.997768i | \(-0.478729\pi\) | ||||
0.0667738 | + | 0.997768i | \(0.478729\pi\) | |||||||
\(654\) | −3.08225e18 | −1.54032 | ||||||||
\(655\) | 2.35548e18 | 1.16550 | ||||||||
\(656\) | 6.46104e17 | 0.316539 | ||||||||
\(657\) | −1.25687e18 | −0.609697 | ||||||||
\(658\) | 6.69744e17 | 0.321692 | ||||||||
\(659\) | 8.71362e17 | 0.414423 | 0.207211 | − | 0.978296i | \(-0.433561\pi\) | ||||
0.207211 | + | 0.978296i | \(0.433561\pi\) | |||||||
\(660\) | −6.62238e17 | −0.311873 | ||||||||
\(661\) | 1.51786e18 | 0.707817 | 0.353908 | − | 0.935280i | \(-0.384852\pi\) | ||||
0.353908 | + | 0.935280i | \(0.384852\pi\) | |||||||
\(662\) | −8.45495e17 | −0.390422 | ||||||||
\(663\) | −3.82088e18 | −1.74713 | ||||||||
\(664\) | 1.08902e18 | 0.493111 | ||||||||
\(665\) | 3.54311e18 | 1.58871 | ||||||||
\(666\) | −8.18138e14 | −0.000363282 0 | ||||||||
\(667\) | 3.97599e18 | 1.74835 | ||||||||
\(668\) | −3.00400e17 | −0.130814 | ||||||||
\(669\) | −2.34662e18 | −1.01198 | ||||||||
\(670\) | −8.49445e17 | −0.362785 | ||||||||
\(671\) | 7.91241e17 | 0.334666 | ||||||||
\(672\) | 9.42919e17 | 0.394979 | ||||||||
\(673\) | −4.01721e18 | −1.66658 | −0.833291 | − | 0.552834i | \(-0.813546\pi\) | ||||
−0.833291 | + | 0.552834i | \(0.813546\pi\) | |||||||
\(674\) | 8.73199e17 | 0.358776 | ||||||||
\(675\) | 2.09567e18 | 0.852804 | ||||||||
\(676\) | 1.03713e18 | 0.418002 | ||||||||
\(677\) | 2.88503e18 | 1.15166 | 0.575830 | − | 0.817569i | \(-0.304679\pi\) | ||||
0.575830 | + | 0.817569i | \(0.304679\pi\) | |||||||
\(678\) | −1.86712e18 | −0.738208 | ||||||||
\(679\) | −7.35501e18 | −2.88025 | ||||||||
\(680\) | 1.52153e18 | 0.590164 | ||||||||
\(681\) | −5.27502e18 | −2.02660 | ||||||||
\(682\) | −2.81453e17 | −0.107104 | ||||||||
\(683\) | −2.23743e18 | −0.843362 | −0.421681 | − | 0.906744i | \(-0.638560\pi\) | ||||
−0.421681 | + | 0.906744i | \(0.638560\pi\) | |||||||
\(684\) | −4.39843e17 | −0.164222 | ||||||||
\(685\) | −5.04225e18 | −1.86481 | ||||||||
\(686\) | −3.83489e18 | −1.40490 | ||||||||
\(687\) | −2.76350e18 | −1.00286 | ||||||||
\(688\) | 1.59322e17 | 0.0572732 | ||||||||
\(689\) | −5.00023e17 | −0.178059 | ||||||||
\(690\) | 4.07934e18 | 1.43903 | ||||||||
\(691\) | 5.27201e17 | 0.184234 | 0.0921168 | − | 0.995748i | \(-0.470637\pi\) | ||||
0.0921168 | + | 0.995748i | \(0.470637\pi\) | |||||||
\(692\) | −1.81115e18 | −0.626997 | ||||||||
\(693\) | −9.29241e17 | −0.318686 | ||||||||
\(694\) | 1.17854e18 | 0.400412 | ||||||||
\(695\) | 2.39224e18 | 0.805198 | ||||||||
\(696\) | −2.38204e18 | −0.794309 | ||||||||
\(697\) | 3.90932e18 | 1.29148 | ||||||||
\(698\) | −1.94626e18 | −0.637001 | ||||||||
\(699\) | −6.75637e17 | −0.219085 | ||||||||
\(700\) | 4.61635e18 | 1.48307 | ||||||||
\(701\) | −2.64738e18 | −0.842653 | −0.421326 | − | 0.906909i | \(-0.638435\pi\) | ||||
−0.421326 | + | 0.906909i | \(0.638435\pi\) | |||||||
\(702\) | −1.54395e18 | −0.486902 | ||||||||
\(703\) | −1.51021e15 | −0.000471875 0 | ||||||||
\(704\) | −1.21741e17 | −0.0376889 | ||||||||
\(705\) | −1.73591e18 | −0.532475 | ||||||||
\(706\) | 2.80390e18 | 0.852180 | ||||||||
\(707\) | 6.79291e18 | 2.04564 | ||||||||
\(708\) | −9.35889e17 | −0.279260 | ||||||||
\(709\) | 7.30026e17 | 0.215843 | 0.107922 | − | 0.994159i | \(-0.465580\pi\) | ||||
0.107922 | + | 0.994159i | \(0.465580\pi\) | |||||||
\(710\) | 5.83003e18 | 1.70801 | ||||||||
\(711\) | −6.22456e17 | −0.180699 | ||||||||
\(712\) | 9.47304e17 | 0.272502 | ||||||||
\(713\) | 1.73373e18 | 0.494197 | ||||||||
\(714\) | 5.70523e18 | 1.61152 | ||||||||
\(715\) | 2.38862e18 | 0.668586 | ||||||||
\(716\) | −9.63509e17 | −0.267252 | ||||||||
\(717\) | 6.09726e17 | 0.167595 | ||||||||
\(718\) | 1.27827e18 | 0.348188 | ||||||||
\(719\) | −7.24722e18 | −1.95629 | −0.978146 | − | 0.207920i | \(-0.933331\pi\) | ||||
−0.978146 | + | 0.207920i | \(0.933331\pi\) | |||||||
\(720\) | −9.14567e17 | −0.244655 | ||||||||
\(721\) | −1.06902e19 | −2.83405 | ||||||||
\(722\) | 1.87948e18 | 0.493795 | ||||||||
\(723\) | −4.00095e18 | −1.04175 | ||||||||
\(724\) | −6.13583e17 | −0.158334 | ||||||||
\(725\) | −1.16620e19 | −2.98247 | ||||||||
\(726\) | 3.20603e17 | 0.0812606 | ||||||||
\(727\) | −4.93763e18 | −1.24035 | −0.620176 | − | 0.784463i | \(-0.712939\pi\) | ||||
−0.620176 | + | 0.784463i | \(0.712939\pi\) | |||||||
\(728\) | −3.40101e18 | −0.846746 | ||||||||
\(729\) | −4.02614e17 | −0.0993481 | ||||||||
\(730\) | −4.82411e18 | −1.17983 | ||||||||
\(731\) | 9.63996e17 | 0.233675 | ||||||||
\(732\) | 2.92004e18 | 0.701562 | ||||||||
\(733\) | −3.23406e17 | −0.0770144 | −0.0385072 | − | 0.999258i | \(-0.512260\pi\) | ||||
−0.0385072 | + | 0.999258i | \(0.512260\pi\) | |||||||
\(734\) | −1.60849e18 | −0.379660 | ||||||||
\(735\) | 1.87821e19 | 4.39417 | ||||||||
\(736\) | 7.49915e17 | 0.173903 | ||||||||
\(737\) | 4.11234e17 | 0.0945258 | ||||||||
\(738\) | −2.34983e18 | −0.535390 | ||||||||
\(739\) | 5.87474e18 | 1.32678 | 0.663392 | − | 0.748272i | \(-0.269116\pi\) | ||||
0.663392 | + | 0.748272i | \(0.269116\pi\) | |||||||
\(740\) | −3.14018e15 | −0.000702989 0 | ||||||||
\(741\) | 4.23944e18 | 0.940784 | ||||||||
\(742\) | 7.46621e17 | 0.164238 | ||||||||
\(743\) | 2.43053e18 | 0.529998 | 0.264999 | − | 0.964249i | \(-0.414628\pi\) | ||||
0.264999 | + | 0.964249i | \(0.414628\pi\) | |||||||
\(744\) | −1.03869e18 | −0.224523 | ||||||||
\(745\) | 6.24993e18 | 1.33924 | ||||||||
\(746\) | −2.87176e18 | −0.610022 | ||||||||
\(747\) | −3.96069e18 | −0.834041 | ||||||||
\(748\) | −7.36605e17 | −0.153771 | ||||||||
\(749\) | 4.93468e18 | 1.02124 | ||||||||
\(750\) | −4.83516e18 | −0.992002 | ||||||||
\(751\) | 4.44249e18 | 0.903581 | 0.451791 | − | 0.892124i | \(-0.350785\pi\) | ||||
0.451791 | + | 0.892124i | \(0.350785\pi\) | |||||||
\(752\) | −3.19117e17 | −0.0643479 | ||||||||
\(753\) | 9.85221e18 | 1.96955 | ||||||||
\(754\) | 8.59176e18 | 1.70282 | ||||||||
\(755\) | 3.53065e17 | 0.0693745 | ||||||||
\(756\) | 2.30538e18 | 0.449108 | ||||||||
\(757\) | −1.55345e18 | −0.300037 | −0.150019 | − | 0.988683i | \(-0.547933\pi\) | ||||
−0.150019 | + | 0.988683i | \(0.547933\pi\) | |||||||
\(758\) | −5.21478e18 | −0.998588 | ||||||||
\(759\) | −1.97490e18 | −0.374949 | ||||||||
\(760\) | −1.68821e18 | −0.317788 | ||||||||
\(761\) | 6.74934e18 | 1.25968 | 0.629841 | − | 0.776724i | \(-0.283120\pi\) | ||||
0.629841 | + | 0.776724i | \(0.283120\pi\) | |||||||
\(762\) | 6.21686e18 | 1.15044 | ||||||||
\(763\) | −1.66001e19 | −3.04580 | ||||||||
\(764\) | 3.49477e18 | 0.635787 | ||||||||
\(765\) | −5.53368e18 | −0.998194 | ||||||||
\(766\) | 4.91879e18 | 0.879775 | ||||||||
\(767\) | 3.37565e18 | 0.598670 | ||||||||
\(768\) | −4.49278e17 | −0.0790074 | ||||||||
\(769\) | 8.13936e18 | 1.41928 | 0.709642 | − | 0.704563i | \(-0.248857\pi\) | ||||
0.709642 | + | 0.704563i | \(0.248857\pi\) | |||||||
\(770\) | −3.56662e18 | −0.616691 | ||||||||
\(771\) | 1.12414e19 | 1.92739 | ||||||||
\(772\) | −3.00867e18 | −0.511520 | ||||||||
\(773\) | 3.06638e17 | 0.0516963 | 0.0258481 | − | 0.999666i | \(-0.491771\pi\) | ||||
0.0258481 | + | 0.999666i | \(0.491771\pi\) | |||||||
\(774\) | −5.79442e17 | −0.0968710 | ||||||||
\(775\) | −5.08521e18 | −0.843040 | ||||||||
\(776\) | 3.50448e18 | 0.576133 | ||||||||
\(777\) | −1.17746e16 | −0.00191960 | ||||||||
\(778\) | 6.51861e17 | 0.105387 | ||||||||
\(779\) | −4.33757e18 | −0.695430 | ||||||||
\(780\) | 8.81508e18 | 1.40156 | ||||||||
\(781\) | −2.82244e18 | −0.445034 | ||||||||
\(782\) | 4.53744e18 | 0.709524 | ||||||||
\(783\) | −5.82395e18 | −0.903163 | ||||||||
\(784\) | 3.45276e18 | 0.531022 | ||||||||
\(785\) | −1.43075e18 | −0.218229 | ||||||||
\(786\) | −4.20836e18 | −0.636600 | ||||||||
\(787\) | −5.81951e18 | −0.873073 | −0.436536 | − | 0.899687i | \(-0.643795\pi\) | ||||
−0.436536 | + | 0.899687i | \(0.643795\pi\) | |||||||
\(788\) | −1.06603e18 | −0.158617 | ||||||||
\(789\) | −3.50847e18 | −0.517747 | ||||||||
\(790\) | −2.38912e18 | −0.349672 | ||||||||
\(791\) | −1.00558e19 | −1.45971 | ||||||||
\(792\) | 4.42761e17 | 0.0637464 | ||||||||
\(793\) | −1.05322e19 | −1.50399 | ||||||||
\(794\) | 3.32537e18 | 0.470984 | ||||||||
\(795\) | −1.93517e18 | −0.271852 | ||||||||
\(796\) | −3.16930e18 | −0.441600 | ||||||||
\(797\) | −6.36403e18 | −0.879535 | −0.439768 | − | 0.898112i | \(-0.644939\pi\) | ||||
−0.439768 | + | 0.898112i | \(0.644939\pi\) | |||||||
\(798\) | −6.33021e18 | −0.867760 | ||||||||
\(799\) | −1.93085e18 | −0.262540 | ||||||||
\(800\) | −2.19958e18 | −0.296657 | ||||||||
\(801\) | −3.44527e18 | −0.460905 | ||||||||
\(802\) | 2.66497e18 | 0.353638 | ||||||||
\(803\) | 2.33545e18 | 0.307412 | ||||||||
\(804\) | 1.51764e18 | 0.198155 | ||||||||
\(805\) | 2.19702e19 | 2.84551 | ||||||||
\(806\) | 3.74643e18 | 0.481327 | ||||||||
\(807\) | 8.14571e18 | 1.03813 | ||||||||
\(808\) | −3.23666e18 | −0.409188 | ||||||||
\(809\) | −4.31747e18 | −0.541457 | −0.270728 | − | 0.962656i | \(-0.587265\pi\) | ||||
−0.270728 | + | 0.962656i | \(0.587265\pi\) | |||||||
\(810\) | −1.15376e19 | −1.43537 | ||||||||
\(811\) | −2.75385e18 | −0.339864 | −0.169932 | − | 0.985456i | \(-0.554355\pi\) | ||||
−0.169932 | + | 0.985456i | \(0.554355\pi\) | |||||||
\(812\) | −1.28290e19 | −1.57065 | ||||||||
\(813\) | 9.30549e18 | 1.13019 | ||||||||
\(814\) | 1.52023e15 | 0.000183168 0 | ||||||||
\(815\) | 9.16896e18 | 1.09596 | ||||||||
\(816\) | −2.71841e18 | −0.322351 | ||||||||
\(817\) | −1.06960e18 | −0.125828 | ||||||||
\(818\) | 9.74216e18 | 1.13700 | ||||||||
\(819\) | 1.23692e19 | 1.43217 | ||||||||
\(820\) | −9.01913e18 | −1.03604 | ||||||||
\(821\) | −1.61263e19 | −1.83782 | −0.918911 | − | 0.394466i | \(-0.870930\pi\) | ||||
−0.918911 | + | 0.394466i | \(0.870930\pi\) | |||||||
\(822\) | 9.00861e18 | 1.01857 | ||||||||
\(823\) | −1.08258e19 | −1.21440 | −0.607199 | − | 0.794550i | \(-0.707707\pi\) | ||||
−0.607199 | + | 0.794550i | \(0.707707\pi\) | |||||||
\(824\) | 5.09364e18 | 0.566893 | ||||||||
\(825\) | 5.79257e18 | 0.639618 | ||||||||
\(826\) | −5.04043e18 | −0.552201 | ||||||||
\(827\) | −8.99840e18 | −0.978091 | −0.489046 | − | 0.872258i | \(-0.662655\pi\) | ||||
−0.489046 | + | 0.872258i | \(0.662655\pi\) | |||||||
\(828\) | −2.72738e18 | −0.294136 | ||||||||
\(829\) | 1.13173e19 | 1.21098 | 0.605492 | − | 0.795852i | \(-0.292977\pi\) | ||||
0.605492 | + | 0.795852i | \(0.292977\pi\) | |||||||
\(830\) | −1.52020e19 | −1.61396 | ||||||||
\(831\) | 4.34574e18 | 0.457781 | ||||||||
\(832\) | 1.62050e18 | 0.169374 | ||||||||
\(833\) | 2.08913e19 | 2.16657 | ||||||||
\(834\) | −4.27403e18 | −0.439803 | ||||||||
\(835\) | 4.19336e18 | 0.428154 | ||||||||
\(836\) | 8.17297e17 | 0.0828017 | ||||||||
\(837\) | −2.53953e18 | −0.255293 | ||||||||
\(838\) | 1.15357e19 | 1.15069 | ||||||||
\(839\) | −5.11110e18 | −0.505896 | −0.252948 | − | 0.967480i | \(-0.581400\pi\) | ||||
−0.252948 | + | 0.967480i | \(0.581400\pi\) | |||||||
\(840\) | −1.31624e19 | −1.29277 | ||||||||
\(841\) | 2.21485e19 | 2.15859 | ||||||||
\(842\) | 9.83136e18 | 0.950791 | ||||||||
\(843\) | −1.10793e19 | −1.06325 | ||||||||
\(844\) | 4.40831e18 | 0.419804 | ||||||||
\(845\) | −1.44775e19 | −1.36812 | ||||||||
\(846\) | 1.16060e18 | 0.108837 | ||||||||
\(847\) | 1.72668e18 | 0.160683 | ||||||||
\(848\) | −3.55747e17 | −0.0328525 | ||||||||
\(849\) | 3.49990e18 | 0.320742 | ||||||||
\(850\) | −1.33088e19 | −1.21036 | ||||||||
\(851\) | −9.36451e15 | −0.000845168 0 | ||||||||
\(852\) | −1.04161e19 | −0.932926 | ||||||||
\(853\) | −4.20223e18 | −0.373518 | −0.186759 | − | 0.982406i | \(-0.559798\pi\) | ||||
−0.186759 | + | 0.982406i | \(0.559798\pi\) | |||||||
\(854\) | 1.57265e19 | 1.38725 | ||||||||
\(855\) | 6.13987e18 | 0.537502 | ||||||||
\(856\) | −2.35125e18 | −0.204277 | ||||||||
\(857\) | −5.24084e18 | −0.451883 | −0.225941 | − | 0.974141i | \(-0.572546\pi\) | ||||
−0.225941 | + | 0.974141i | \(0.572546\pi\) | |||||||
\(858\) | −4.26757e18 | −0.365185 | ||||||||
\(859\) | −6.62592e18 | −0.562718 | −0.281359 | − | 0.959603i | \(-0.590785\pi\) | ||||
−0.281359 | + | 0.959603i | \(0.590785\pi\) | |||||||
\(860\) | −2.22402e18 | −0.187456 | ||||||||
\(861\) | −3.38187e19 | −2.82903 | ||||||||
\(862\) | −8.90508e18 | −0.739334 | ||||||||
\(863\) | 4.51292e18 | 0.371867 | 0.185933 | − | 0.982562i | \(-0.440469\pi\) | ||||
0.185933 | + | 0.982562i | \(0.440469\pi\) | |||||||
\(864\) | −1.09846e18 | −0.0898348 | ||||||||
\(865\) | 2.52823e19 | 2.05217 | ||||||||
\(866\) | −1.33605e19 | −1.07635 | ||||||||
\(867\) | −6.38737e17 | −0.0510738 | ||||||||
\(868\) | −5.59408e18 | −0.443966 | ||||||||
\(869\) | 1.15662e18 | 0.0911093 | ||||||||
\(870\) | 3.32515e19 | 2.59978 | ||||||||
\(871\) | −5.47396e18 | −0.424799 | ||||||||
\(872\) | 7.90955e18 | 0.609249 | ||||||||
\(873\) | −1.27455e19 | −0.974463 | ||||||||
\(874\) | −5.03450e18 | −0.382060 | ||||||||
\(875\) | −2.60408e19 | −1.96156 | ||||||||
\(876\) | 8.61888e18 | 0.644428 | ||||||||
\(877\) | −8.14871e18 | −0.604772 | −0.302386 | − | 0.953186i | \(-0.597783\pi\) | ||||
−0.302386 | + | 0.953186i | \(0.597783\pi\) | |||||||
\(878\) | 1.59250e19 | 1.17318 | ||||||||
\(879\) | 2.76985e19 | 2.02548 | ||||||||
\(880\) | 1.69941e18 | 0.123356 | ||||||||
\(881\) | 3.53169e18 | 0.254472 | 0.127236 | − | 0.991872i | \(-0.459389\pi\) | ||||
0.127236 | + | 0.991872i | \(0.459389\pi\) | |||||||
\(882\) | −1.25574e19 | −0.898161 | ||||||||
\(883\) | −4.22219e18 | −0.299773 | −0.149887 | − | 0.988703i | \(-0.547891\pi\) | ||||
−0.149887 | + | 0.988703i | \(0.547891\pi\) | |||||||
\(884\) | 9.80499e18 | 0.691047 | ||||||||
\(885\) | 1.30643e19 | 0.914020 | ||||||||
\(886\) | −1.84394e19 | −1.28064 | ||||||||
\(887\) | −2.82399e19 | −1.94697 | −0.973487 | − | 0.228741i | \(-0.926539\pi\) | ||||
−0.973487 | + | 0.228741i | \(0.926539\pi\) | |||||||
\(888\) | 5.61033e15 | 0.000383976 0 | ||||||||
\(889\) | 3.34822e19 | 2.27485 | ||||||||
\(890\) | −1.32237e19 | −0.891901 | ||||||||
\(891\) | 5.58560e18 | 0.373994 | ||||||||
\(892\) | 6.02181e18 | 0.400272 | ||||||||
\(893\) | 2.14237e18 | 0.141371 | ||||||||
\(894\) | −1.11663e19 | −0.731501 | ||||||||
\(895\) | 1.34499e19 | 0.874719 | ||||||||
\(896\) | −2.41968e18 | −0.156227 | ||||||||
\(897\) | 2.62879e19 | 1.68502 | ||||||||
\(898\) | −1.85200e19 | −1.17854 | ||||||||
\(899\) | 1.41320e19 | 0.892823 | ||||||||
\(900\) | 7.99969e18 | 0.501761 | ||||||||
\(901\) | −2.15249e18 | −0.134038 | ||||||||
\(902\) | 4.36635e18 | 0.269946 | ||||||||
\(903\) | −8.33933e18 | −0.511871 | ||||||||
\(904\) | 4.79133e18 | 0.291985 | ||||||||
\(905\) | 8.56516e18 | 0.518227 | ||||||||
\(906\) | −6.30795e17 | −0.0378927 | ||||||||
\(907\) | −3.06265e19 | −1.82662 | −0.913312 | − | 0.407259i | \(-0.866484\pi\) | ||||
−0.913312 | + | 0.407259i | \(0.866484\pi\) | |||||||
\(908\) | 1.35366e19 | 0.801586 | ||||||||
\(909\) | 1.17715e19 | 0.692094 | ||||||||
\(910\) | 4.74755e19 | 2.77141 | ||||||||
\(911\) | 1.12833e19 | 0.653985 | 0.326993 | − | 0.945027i | \(-0.393965\pi\) | ||||
0.326993 | + | 0.945027i | \(0.393965\pi\) | |||||||
\(912\) | 3.01620e18 | 0.173577 | ||||||||
\(913\) | 7.35959e18 | 0.420527 | ||||||||
\(914\) | 9.40707e18 | 0.533708 | ||||||||
\(915\) | −4.07615e19 | −2.29622 | ||||||||
\(916\) | 7.09159e18 | 0.396664 | ||||||||
\(917\) | −2.26650e19 | −1.25880 | ||||||||
\(918\) | −6.64634e18 | −0.366526 | ||||||||
\(919\) | 1.90702e19 | 1.04425 | 0.522125 | − | 0.852869i | \(-0.325139\pi\) | ||||
0.522125 | + | 0.852869i | \(0.325139\pi\) | |||||||
\(920\) | −1.04683e19 | −0.569185 | ||||||||
\(921\) | 1.48202e19 | 0.800142 | ||||||||
\(922\) | 8.04523e18 | 0.431308 | ||||||||
\(923\) | 3.75697e19 | 1.99998 | ||||||||
\(924\) | 6.37222e18 | 0.336839 | ||||||||
\(925\) | 2.74671e16 | 0.00144175 | ||||||||
\(926\) | −5.48953e17 | −0.0286130 | ||||||||
\(927\) | −1.85251e19 | −0.958834 | ||||||||
\(928\) | 6.11271e18 | 0.314175 | ||||||||
\(929\) | −6.07406e18 | −0.310011 | −0.155005 | − | 0.987914i | \(-0.549539\pi\) | ||||
−0.155005 | + | 0.987914i | \(0.549539\pi\) | |||||||
\(930\) | 1.44993e19 | 0.734866 | ||||||||
\(931\) | −2.31798e19 | −1.16664 | ||||||||
\(932\) | 1.73379e18 | 0.0866551 | ||||||||
\(933\) | −1.31226e19 | −0.651313 | ||||||||
\(934\) | −1.37055e19 | −0.675525 | ||||||||
\(935\) | 1.02825e19 | 0.503294 | ||||||||
\(936\) | −5.89362e18 | −0.286477 | ||||||||
\(937\) | 2.58159e19 | 1.24618 | 0.623089 | − | 0.782151i | \(-0.285877\pi\) | ||||
0.623089 | + | 0.782151i | \(0.285877\pi\) | |||||||
\(938\) | 8.17357e18 | 0.391826 | ||||||||
\(939\) | −2.09533e19 | −0.997533 | ||||||||
\(940\) | 4.45464e18 | 0.210611 | ||||||||
\(941\) | 1.18315e19 | 0.555532 | 0.277766 | − | 0.960649i | \(-0.410406\pi\) | ||||
0.277766 | + | 0.960649i | \(0.410406\pi\) | |||||||
\(942\) | 2.55622e18 | 0.119198 | ||||||||
\(943\) | −2.68964e19 | −1.24557 | ||||||||
\(944\) | 2.40164e18 | 0.110456 | ||||||||
\(945\) | −3.21814e19 | −1.46994 | ||||||||
\(946\) | 1.07669e18 | 0.0488427 | ||||||||
\(947\) | 1.59848e19 | 0.720166 | 0.360083 | − | 0.932920i | \(-0.382748\pi\) | ||||
0.360083 | + | 0.932920i | \(0.382748\pi\) | |||||||
\(948\) | 4.26846e18 | 0.190993 | ||||||||
\(949\) | −3.10874e19 | −1.38151 | ||||||||
\(950\) | 1.47667e19 | 0.651749 | ||||||||
\(951\) | −5.78368e18 | −0.253531 | ||||||||
\(952\) | −1.46406e19 | −0.637408 | ||||||||
\(953\) | 4.13637e18 | 0.178861 | 0.0894304 | − | 0.995993i | \(-0.471495\pi\) | ||||
0.0894304 | + | 0.995993i | \(0.471495\pi\) | |||||||
\(954\) | 1.29382e18 | 0.0555662 | ||||||||
\(955\) | −4.87843e19 | −2.08094 | ||||||||
\(956\) | −1.56466e18 | −0.0662892 | ||||||||
\(957\) | −1.60978e19 | −0.677389 | ||||||||
\(958\) | 1.12385e19 | 0.469711 | ||||||||
\(959\) | 4.85178e19 | 2.01409 | ||||||||
\(960\) | 6.27159e18 | 0.258592 | ||||||||
\(961\) | −1.82553e19 | −0.747630 | ||||||||
\(962\) | −2.02358e16 | −0.000823159 0 | ||||||||
\(963\) | 8.55132e18 | 0.345511 | ||||||||
\(964\) | 1.02671e19 | 0.412047 | ||||||||
\(965\) | 4.19988e19 | 1.67421 | ||||||||
\(966\) | −3.92524e19 | −1.55423 | ||||||||
\(967\) | −2.38637e19 | −0.938566 | −0.469283 | − | 0.883048i | \(-0.655488\pi\) | ||||
−0.469283 | + | 0.883048i | \(0.655488\pi\) | |||||||
\(968\) | −8.22720e17 | −0.0321412 | ||||||||
\(969\) | 1.82498e19 | 0.708197 | ||||||||
\(970\) | −4.89200e19 | −1.88569 | ||||||||
\(971\) | −2.32623e19 | −0.890692 | −0.445346 | − | 0.895359i | \(-0.646919\pi\) | ||||
−0.445346 | + | 0.895359i | \(0.646919\pi\) | |||||||
\(972\) | 1.39327e19 | 0.529913 | ||||||||
\(973\) | −2.30187e19 | −0.869655 | ||||||||
\(974\) | −9.01279e18 | −0.338241 | ||||||||
\(975\) | −7.71053e19 | −2.87445 | ||||||||
\(976\) | −7.49329e18 | −0.277491 | ||||||||
\(977\) | −3.26857e19 | −1.20238 | −0.601192 | − | 0.799105i | \(-0.705307\pi\) | ||||
−0.601192 | + | 0.799105i | \(0.705307\pi\) | |||||||
\(978\) | −1.63815e19 | −0.598620 | ||||||||
\(979\) | 6.40185e18 | 0.232390 | ||||||||
\(980\) | −4.81980e19 | −1.73804 | ||||||||
\(981\) | −2.87664e19 | −1.03047 | ||||||||
\(982\) | 8.38266e18 | 0.298303 | ||||||||
\(983\) | 5.16168e19 | 1.82471 | 0.912353 | − | 0.409404i | \(-0.134263\pi\) | ||||
0.912353 | + | 0.409404i | \(0.134263\pi\) | |||||||
\(984\) | 1.61138e19 | 0.565888 | ||||||||
\(985\) | 1.48810e19 | 0.519153 | ||||||||
\(986\) | 3.69856e19 | 1.28184 | ||||||||
\(987\) | 1.67034e19 | 0.575100 | ||||||||
\(988\) | −1.08791e19 | −0.372111 | ||||||||
\(989\) | −6.63237e18 | −0.225368 | ||||||||
\(990\) | −6.18062e18 | −0.208643 | ||||||||
\(991\) | 4.73013e19 | 1.58633 | 0.793167 | − | 0.609005i | \(-0.208431\pi\) | ||||
0.793167 | + | 0.609005i | \(0.208431\pi\) | |||||||
\(992\) | 2.66544e18 | 0.0888063 | ||||||||
\(993\) | −2.10866e19 | −0.697970 | ||||||||
\(994\) | −5.60980e19 | −1.84474 | ||||||||
\(995\) | 4.42411e19 | 1.44536 | ||||||||
\(996\) | 2.71602e19 | 0.881552 | ||||||||
\(997\) | 3.86881e19 | 1.24755 | 0.623776 | − | 0.781603i | \(-0.285598\pi\) | ||||
0.623776 | + | 0.781603i | \(0.285598\pi\) | |||||||
\(998\) | −3.04591e19 | −0.975817 | ||||||||
\(999\) | 1.37169e16 | 0.000436598 0 |
(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 | 22.14.a.a.1.1 | ✓ | 2 | |
3.2 | odd | 2 | 198.14.a.e.1.2 | 2 | |||
4.3 | odd | 2 | 176.14.a.b.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
22.14.a.a.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
176.14.a.b.1.2 | 2 | 4.3 | odd | 2 | |||
198.14.a.e.1.2 | 2 | 3.2 | odd | 2 |