Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,68,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 68, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 68);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 68 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(255.861316737\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots + 20\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{20}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(6.06038e8\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.34339e10 | 1.10585 | 0.552927 | − | 0.833229i | \(-0.313511\pi\) | ||||
0.552927 | + | 0.833229i | \(0.313511\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.28965e19 | 0.222915 | ||||||||
\(5\) | 3.01383e23 | 1.15777 | 0.578887 | − | 0.815408i | \(-0.303487\pi\) | ||||
0.578887 | + | 0.815408i | \(0.303487\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.20742e26 | −0.0205699 | −0.0102849 | − | 0.999947i | \(-0.503274\pi\) | ||||
−0.0102849 | + | 0.999947i | \(0.503274\pi\) | |||||||
\(8\) | −1.54057e30 | −0.859343 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 4.04876e33 | 1.28033 | ||||||||
\(11\) | −1.62242e34 | −0.210624 | −0.105312 | − | 0.994439i | \(-0.533584\pi\) | ||||
−0.105312 | + | 0.994439i | \(0.533584\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.08856e37 | −1.48817 | −0.744087 | − | 0.668082i | \(-0.767115\pi\) | ||||
−0.744087 | + | 0.668082i | \(0.767115\pi\) | |||||||
\(14\) | −5.65222e36 | −0.0227473 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.55506e40 | −1.17322 | ||||||||
\(17\) | 1.59490e41 | 0.960936 | 0.480468 | − | 0.877012i | \(-0.340467\pi\) | ||||
0.480468 | + | 0.877012i | \(0.340467\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.03902e43 | 1.50792 | 0.753959 | − | 0.656921i | \(-0.228141\pi\) | ||||
0.753959 | + | 0.656921i | \(0.228141\pi\) | |||||||
\(20\) | 9.91443e42 | 0.258085 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.17954e44 | −0.232919 | ||||||||
\(23\) | 3.59214e45 | 0.865905 | 0.432953 | − | 0.901417i | \(-0.357472\pi\) | ||||
0.432953 | + | 0.901417i | \(0.357472\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.30691e46 | 0.340440 | ||||||||
\(26\) | −4.14915e47 | −1.64571 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.38409e46 | −0.00458534 | ||||||||
\(29\) | −1.54617e49 | −1.58097 | −0.790486 | − | 0.612480i | \(-0.790172\pi\) | ||||
−0.790486 | + | 0.612480i | \(0.790172\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.52983e50 | 1.67504 | 0.837521 | − | 0.546405i | \(-0.184004\pi\) | ||||
0.837521 | + | 0.546405i | \(0.184004\pi\) | |||||||
\(32\) | −1.15896e50 | −0.438072 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.14258e51 | 1.06266 | ||||||||
\(35\) | −1.26805e50 | −0.0238153 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.16261e52 | 0.339372 | 0.169686 | − | 0.985498i | \(-0.445725\pi\) | ||||
0.169686 | + | 0.985498i | \(0.445725\pi\) | |||||||
\(38\) | 1.39581e53 | 1.66754 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.64301e53 | −0.994925 | ||||||||
\(41\) | −1.50280e54 | −1.40813 | −0.704064 | − | 0.710137i | \(-0.748633\pi\) | ||||
−0.704064 | + | 0.710137i | \(0.748633\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.43610e54 | 0.272893 | 0.136447 | − | 0.990647i | \(-0.456432\pi\) | ||||
0.136447 | + | 0.990647i | \(0.456432\pi\) | |||||||
\(44\) | −5.33717e53 | −0.0469512 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.82565e55 | 0.957565 | ||||||||
\(47\) | −9.41631e55 | −0.909081 | −0.454540 | − | 0.890726i | \(-0.650196\pi\) | ||||
−0.454540 | + | 0.890726i | \(0.650196\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.18201e56 | −0.999577 | ||||||||
\(50\) | 3.09909e56 | 0.376477 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.01603e57 | −0.331737 | ||||||||
\(53\) | −4.49370e57 | −0.775109 | −0.387554 | − | 0.921847i | \(-0.626680\pi\) | ||||
−0.387554 | + | 0.921847i | \(0.626680\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.88968e57 | −0.243854 | ||||||||
\(56\) | 6.48182e56 | 0.0176766 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.07711e59 | −1.74833 | ||||||||
\(59\) | −2.81815e59 | −1.33789 | −0.668947 | − | 0.743310i | \(-0.733255\pi\) | ||||
−0.668947 | + | 0.743310i | \(0.733255\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.42593e59 | −0.687789 | −0.343894 | − | 0.939008i | \(-0.611746\pi\) | ||||
−0.343894 | + | 0.939008i | \(0.611746\pi\) | |||||||
\(62\) | 2.05516e60 | 1.85235 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.21365e60 | 0.688780 | ||||||||
\(65\) | −9.30840e60 | −1.72297 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.71985e60 | 0.651859 | 0.325930 | − | 0.945394i | \(-0.394323\pi\) | ||||
0.325930 | + | 0.945394i | \(0.394323\pi\) | |||||||
\(68\) | 5.24666e60 | 0.214207 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.70348e60 | −0.0263362 | ||||||||
\(71\) | 3.66936e61 | 0.352725 | 0.176362 | − | 0.984325i | \(-0.443567\pi\) | ||||
0.176362 | + | 0.984325i | \(0.443567\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.52158e61 | −0.0576740 | −0.0288370 | − | 0.999584i | \(-0.509180\pi\) | ||||
−0.0288370 | + | 0.999584i | \(0.509180\pi\) | |||||||
\(74\) | 1.56184e62 | 0.375296 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.41801e62 | 0.336138 | ||||||||
\(77\) | 6.82619e60 | 0.00433250 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.59876e63 | −0.698649 | −0.349325 | − | 0.937002i | \(-0.613589\pi\) | ||||
−0.349325 | + | 0.937002i | \(0.613589\pi\) | |||||||
\(80\) | −7.70050e63 | −1.35833 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.01885e64 | −1.55719 | ||||||||
\(83\) | 2.25569e64 | 1.15921 | 0.579607 | − | 0.814896i | \(-0.303206\pi\) | ||||
0.579607 | + | 0.814896i | \(0.303206\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.80676e64 | 1.11255 | ||||||||
\(86\) | 1.92925e64 | 0.301780 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.49944e64 | 0.180998 | ||||||||
\(89\) | 2.92327e64 | 0.144978 | 0.0724892 | − | 0.997369i | \(-0.476906\pi\) | ||||
0.0724892 | + | 0.997369i | \(0.476906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.29949e64 | 0.0306116 | ||||||||
\(92\) | 1.18169e65 | 0.193023 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.26498e66 | −1.00531 | ||||||||
\(95\) | 3.13143e66 | 1.74583 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.79797e65 | −0.244078 | −0.122039 | − | 0.992525i | \(-0.538943\pi\) | ||||
−0.122039 | + | 0.992525i | \(0.538943\pi\) | |||||||
\(98\) | −5.61808e66 | −1.10539 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.58891e65 | 0.0758891 | ||||||||
\(101\) | −1.50109e67 | −1.07558 | −0.537789 | − | 0.843080i | \(-0.680740\pi\) | ||||
−0.537789 | + | 0.843080i | \(0.680740\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.56772e67 | −0.582398 | −0.291199 | − | 0.956662i | \(-0.594054\pi\) | ||||
−0.291199 | + | 0.956662i | \(0.594054\pi\) | |||||||
\(104\) | 4.75814e67 | 1.27885 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.03681e67 | −0.857158 | ||||||||
\(107\) | 2.27147e67 | 0.235478 | 0.117739 | − | 0.993045i | \(-0.462435\pi\) | ||||
0.117739 | + | 0.993045i | \(0.462435\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.18578e68 | 1.21848 | 0.609240 | − | 0.792986i | \(-0.291474\pi\) | ||||
0.609240 | + | 0.792986i | \(0.291474\pi\) | |||||||
\(110\) | −6.56877e67 | −0.269668 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.07502e67 | 0.0241331 | ||||||||
\(113\) | −2.20699e68 | −0.367851 | −0.183926 | − | 0.982940i | \(-0.558881\pi\) | ||||
−0.183926 | + | 0.982940i | \(0.558881\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.08261e69 | 1.00252 | ||||||||
\(116\) | −5.08635e68 | −0.352422 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.78588e69 | −1.47952 | ||||||||
\(119\) | −6.71042e67 | −0.0197663 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.67026e69 | −0.955638 | ||||||||
\(122\) | −5.94576e69 | −0.760594 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.03259e69 | 0.373392 | ||||||||
\(125\) | −1.34699e70 | −0.763621 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.39984e70 | 0.466288 | 0.233144 | − | 0.972442i | \(-0.425099\pi\) | ||||
0.233144 | + | 0.972442i | \(0.425099\pi\) | |||||||
\(128\) | 4.68413e70 | 1.19976 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.25048e71 | −1.90535 | ||||||||
\(131\) | −7.06278e70 | −0.832506 | −0.416253 | − | 0.909249i | \(-0.636657\pi\) | ||||
−0.416253 | + | 0.909249i | \(0.636657\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.37159e69 | −0.0310177 | ||||||||
\(134\) | 1.30576e71 | 0.720862 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.45705e71 | −0.825774 | ||||||||
\(137\) | −6.38583e71 | −1.67911 | −0.839553 | − | 0.543277i | \(-0.817183\pi\) | ||||
−0.839553 | + | 0.543277i | \(0.817183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.22134e72 | −1.97625 | −0.988126 | − | 0.153649i | \(-0.950898\pi\) | ||||
−0.988126 | + | 0.153649i | \(0.950898\pi\) | |||||||
\(140\) | −4.17142e69 | −0.00530878 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.92939e71 | 0.390062 | ||||||||
\(143\) | 5.01093e71 | 0.313445 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.65989e72 | −1.83041 | ||||||||
\(146\) | −2.04409e71 | −0.0637791 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.82457e71 | 0.0756512 | ||||||||
\(149\) | −1.00850e73 | −1.59197 | −0.795987 | − | 0.605314i | \(-0.793048\pi\) | ||||
−0.795987 | + | 0.605314i | \(0.793048\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.44915e72 | 0.550302 | 0.275151 | − | 0.961401i | \(-0.411272\pi\) | ||||
0.275151 | + | 0.961401i | \(0.411272\pi\) | |||||||
\(152\) | −1.60068e73 | −1.29582 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 9.17025e70 | 0.00479112 | ||||||||
\(155\) | 4.61064e73 | 1.93932 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.30932e73 | −1.17970 | −0.589848 | − | 0.807514i | \(-0.700813\pi\) | ||||
−0.589848 | + | 0.807514i | \(0.700813\pi\) | |||||||
\(158\) | −3.49116e73 | −0.772605 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.49292e73 | −0.507188 | ||||||||
\(161\) | −1.51136e72 | −0.0178116 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.31839e73 | −0.258608 | −0.129304 | − | 0.991605i | \(-0.541274\pi\) | ||||
−0.129304 | + | 0.991605i | \(0.541274\pi\) | |||||||
\(164\) | −4.94368e73 | −0.313893 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.03028e74 | 1.28192 | ||||||||
\(167\) | 2.50202e74 | 0.865544 | 0.432772 | − | 0.901503i | \(-0.357536\pi\) | ||||
0.432772 | + | 0.901503i | \(0.357536\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.23192e74 | 1.21466 | ||||||||
\(170\) | 6.45736e74 | 1.23032 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.72427e73 | 0.0608320 | ||||||||
\(173\) | −3.99627e74 | −0.423751 | −0.211876 | − | 0.977297i | \(-0.567957\pi\) | ||||
−0.211876 | + | 0.977297i | \(0.567957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.70614e72 | −0.00700280 | ||||||||
\(176\) | 4.14536e74 | 0.247109 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.92710e74 | 0.160325 | ||||||||
\(179\) | −9.62216e74 | −0.325609 | −0.162804 | − | 0.986658i | \(-0.552054\pi\) | ||||
−0.162804 | + | 0.986658i | \(0.552054\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.00912e75 | 1.63468 | 0.817338 | − | 0.576159i | \(-0.195449\pi\) | ||||
0.817338 | + | 0.576159i | \(0.195449\pi\) | |||||||
\(182\) | 1.74572e74 | 0.0338520 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.53393e75 | −0.744110 | ||||||||
\(185\) | 3.50391e75 | 0.392916 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.58759e75 | −0.202396 | ||||||||
\(188\) | −3.09763e75 | −0.202648 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.20674e76 | 1.93063 | ||||||||
\(191\) | 1.34239e75 | 0.0516725 | 0.0258362 | − | 0.999666i | \(-0.491775\pi\) | ||||
0.0258362 | + | 0.999666i | \(0.491775\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.13753e76 | −1.93811 | −0.969054 | − | 0.246849i | \(-0.920605\pi\) | ||||
−0.969054 | + | 0.246849i | \(0.920605\pi\) | |||||||
\(194\) | −1.18191e76 | −0.269915 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.37573e76 | −0.222821 | ||||||||
\(197\) | −2.98948e75 | −0.0408297 | −0.0204149 | − | 0.999792i | \(-0.506499\pi\) | ||||
−0.0204149 | + | 0.999792i | \(0.506499\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.66765e76 | −0.649224 | −0.324612 | − | 0.945847i | \(-0.605234\pi\) | ||||
−0.324612 | + | 0.945847i | \(0.605234\pi\) | |||||||
\(200\) | −3.55395e76 | −0.292555 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.01656e77 | −1.18943 | ||||||||
\(203\) | 6.50539e75 | 0.0325204 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.52919e77 | −1.63029 | ||||||||
\(206\) | −2.10606e77 | −0.644048 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.89145e77 | 1.74596 | ||||||||
\(209\) | −1.68572e77 | −0.317603 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.45267e76 | 0.0746701 | 0.0373351 | − | 0.999303i | \(-0.488113\pi\) | ||||
0.0373351 | + | 0.999303i | \(0.488113\pi\) | |||||||
\(212\) | −1.47827e77 | −0.172783 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.05147e77 | 0.260404 | ||||||||
\(215\) | 4.32817e77 | 0.315948 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.43663e76 | −0.0344554 | ||||||||
\(218\) | 2.93636e78 | 1.34746 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.60853e77 | −0.0543588 | ||||||||
\(221\) | −4.92595e78 | −1.43004 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.27402e78 | 1.34689 | 0.673446 | − | 0.739236i | \(-0.264813\pi\) | ||||
0.673446 | + | 0.739236i | \(0.264813\pi\) | |||||||
\(224\) | 4.87625e76 | 0.00901109 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.96485e78 | −0.406790 | ||||||||
\(227\) | −3.35983e78 | −0.397604 | −0.198802 | − | 0.980040i | \(-0.563705\pi\) | ||||
−0.198802 | + | 0.980040i | \(0.563705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.16052e78 | −0.455203 | −0.227601 | − | 0.973754i | \(-0.573088\pi\) | ||||
−0.227601 | + | 0.973754i | \(0.573088\pi\) | |||||||
\(230\) | 1.45437e79 | 1.10864 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.38198e79 | 1.35860 | ||||||||
\(233\) | −2.55175e78 | −0.126013 | −0.0630065 | − | 0.998013i | \(-0.520069\pi\) | ||||
−0.0630065 | + | 0.998013i | \(0.520069\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.83791e79 | −1.05251 | ||||||||
\(236\) | −9.27071e78 | −0.298237 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −9.01473e77 | −0.0218587 | ||||||||
\(239\) | 4.05778e79 | 0.854985 | 0.427492 | − | 0.904019i | \(-0.359397\pi\) | ||||
0.427492 | + | 0.904019i | \(0.359397\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.01993e79 | 0.640689 | 0.320345 | − | 0.947301i | \(-0.396201\pi\) | ||||
0.320345 | + | 0.947301i | \(0.396201\pi\) | |||||||
\(242\) | −7.61739e79 | −1.05680 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.45597e79 | −0.153318 | ||||||||
\(245\) | −1.26039e80 | −1.15728 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.20908e80 | −2.24405 | ||||||||
\(248\) | −2.35680e80 | −1.43944 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.80953e80 | −0.844455 | ||||||||
\(251\) | −1.29030e80 | −0.526771 | −0.263385 | − | 0.964691i | \(-0.584839\pi\) | ||||
−0.263385 | + | 0.964691i | \(0.584839\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.82794e79 | −0.182380 | ||||||||
\(254\) | 1.88054e80 | 0.515647 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.02586e80 | 0.637984 | ||||||||
\(257\) | −5.23305e80 | −0.968268 | −0.484134 | − | 0.874994i | \(-0.660865\pi\) | ||||
−0.484134 | + | 0.874994i | \(0.660865\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.89159e78 | −0.00698084 | ||||||||
\(260\) | −3.06213e80 | −0.384076 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.48809e80 | −0.920631 | ||||||||
\(263\) | −9.85079e80 | −0.841305 | −0.420652 | − | 0.907222i | \(-0.638199\pi\) | ||||
−0.420652 | + | 0.907222i | \(0.638199\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.35433e81 | −0.897400 | ||||||||
\(266\) | −5.87277e79 | −0.0343011 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.19749e80 | 0.145309 | ||||||||
\(269\) | 1.08276e81 | 0.434343 | 0.217171 | − | 0.976134i | \(-0.430317\pi\) | ||||
0.217171 | + | 0.976134i | \(0.430317\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.87334e81 | 1.52530 | 0.762650 | − | 0.646811i | \(-0.223898\pi\) | ||||
0.762650 | + | 0.646811i | \(0.223898\pi\) | |||||||
\(272\) | −4.07506e81 | −1.12739 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.57868e81 | −1.85685 | ||||||||
\(275\) | −3.74277e80 | −0.0717047 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.18997e81 | 1.23086 | 0.615432 | − | 0.788190i | \(-0.288981\pi\) | ||||
0.615432 | + | 0.788190i | \(0.288981\pi\) | |||||||
\(278\) | −1.64074e82 | −2.18545 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.95351e80 | 0.0204655 | ||||||||
\(281\) | −1.82919e81 | −0.170058 | −0.0850289 | − | 0.996378i | \(-0.527098\pi\) | ||||
−0.0850289 | + | 0.996378i | \(0.527098\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.71714e82 | −1.25881 | −0.629403 | − | 0.777079i | \(-0.716701\pi\) | ||||
−0.629403 | + | 0.777079i | \(0.716701\pi\) | |||||||
\(284\) | 1.20709e81 | 0.0786276 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.73165e81 | 0.346625 | ||||||||
\(287\) | 6.32292e80 | 0.0289650 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.11015e81 | −0.0766012 | ||||||||
\(290\) | −6.26007e82 | −2.02417 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −5.00547e80 | −0.0128564 | ||||||||
\(293\) | −4.86284e82 | −1.11385 | −0.556923 | − | 0.830564i | \(-0.688018\pi\) | ||||
−0.556923 | + | 0.830564i | \(0.688018\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.49342e82 | −1.54898 | ||||||||
\(296\) | −1.79108e82 | −0.291637 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.35481e83 | −1.76049 | ||||||||
\(299\) | −1.10945e83 | −1.28862 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.04229e80 | −0.00561338 | ||||||||
\(302\) | 7.32035e82 | 0.608555 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.65475e83 | −1.76913 | ||||||||
\(305\) | −1.33390e83 | −0.796304 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.34655e81 | 0.0256412 | 0.0128206 | − | 0.999918i | \(-0.495919\pi\) | ||||
0.0128206 | + | 0.999918i | \(0.495919\pi\) | |||||||
\(308\) | 2.24557e80 | 0.000965780 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.19390e83 | 2.14461 | ||||||||
\(311\) | 4.84522e82 | 0.150605 | 0.0753027 | − | 0.997161i | \(-0.476008\pi\) | ||||
0.0753027 | + | 0.997161i | \(0.476008\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.01435e82 | −0.0254363 | −0.0127182 | − | 0.999919i | \(-0.504048\pi\) | ||||
−0.0127182 | + | 0.999919i | \(0.504048\pi\) | |||||||
\(314\) | −5.78911e83 | −1.30457 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.54901e82 | −0.155739 | ||||||||
\(317\) | −3.02253e83 | −0.495319 | −0.247660 | − | 0.968847i | \(-0.579661\pi\) | ||||
−0.247660 | + | 0.968847i | \(0.579661\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.50853e83 | 0.332990 | ||||||||
\(320\) | 6.67157e83 | 0.797451 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.03035e82 | −0.0196970 | ||||||||
\(323\) | 1.65713e84 | 1.44901 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.12503e83 | −0.506634 | ||||||||
\(326\) | −4.45790e83 | −0.285983 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.31517e84 | 1.21007 | ||||||||
\(329\) | 3.96184e82 | 0.0186997 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.27713e84 | 0.877303 | 0.438652 | − | 0.898657i | \(-0.355456\pi\) | ||||
0.438652 | + | 0.898657i | \(0.355456\pi\) | |||||||
\(332\) | 7.42042e83 | 0.258406 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 3.36120e84 | 0.957166 | ||||||||
\(335\) | 2.92940e84 | 0.754705 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.83609e84 | −1.65386 | −0.826928 | − | 0.562308i | \(-0.809914\pi\) | ||||
−0.826928 | + | 0.562308i | \(0.809914\pi\) | |||||||
\(338\) | 7.02852e84 | 1.34324 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.58125e84 | 0.248003 | ||||||||
\(341\) | −2.48202e84 | −0.352803 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.51984e83 | 0.0411311 | ||||||||
\(344\) | −2.21242e84 | −0.234509 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.36856e84 | −0.468607 | ||||||||
\(347\) | 1.79418e85 | 1.42177 | 0.710884 | − | 0.703309i | \(-0.248295\pi\) | ||||
0.710884 | + | 0.703309i | \(0.248295\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.77493e83 | −0.0246750 | −0.0123375 | − | 0.999924i | \(-0.503927\pi\) | ||||
−0.0123375 | + | 0.999924i | \(0.503927\pi\) | |||||||
\(350\) | −1.30392e83 | −0.00774409 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.88032e84 | 0.0922684 | ||||||||
\(353\) | −1.83957e85 | −0.820848 | −0.410424 | − | 0.911895i | \(-0.634619\pi\) | ||||
−0.410424 | + | 0.911895i | \(0.634619\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.10588e85 | 0.408375 | ||||||||
\(356\) | 9.61652e83 | 0.0323179 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.29263e85 | −0.360076 | ||||||||
\(359\) | 5.72913e85 | 1.45353 | 0.726766 | − | 0.686885i | \(-0.241022\pi\) | ||||
0.726766 | + | 0.686885i | \(0.241022\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.04782e85 | 1.27382 | ||||||||
\(362\) | 9.41601e85 | 1.80771 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.27486e83 | 0.00682378 | ||||||||
\(365\) | −4.58580e84 | −0.0667735 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.37834e85 | 1.13714 | 0.568568 | − | 0.822636i | \(-0.307497\pi\) | ||||
0.568568 | + | 0.822636i | \(0.307497\pi\) | |||||||
\(368\) | −9.17811e85 | −1.01590 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.70713e85 | 0.434508 | ||||||||
\(371\) | 1.89069e84 | 0.0159439 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8.38977e85 | −0.590886 | −0.295443 | − | 0.955360i | \(-0.595467\pi\) | ||||
−0.295443 | + | 0.955360i | \(0.595467\pi\) | |||||||
\(374\) | −3.47615e85 | −0.223821 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.45065e86 | 0.781212 | ||||||||
\(377\) | 4.77544e86 | 2.35276 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.46586e86 | −1.43020 | −0.715102 | − | 0.699020i | \(-0.753620\pi\) | ||||
−0.715102 | + | 0.699020i | \(0.753620\pi\) | |||||||
\(380\) | 1.03013e86 | 0.389172 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.80335e85 | 0.0571423 | ||||||||
\(383\) | −4.41090e86 | −1.28047 | −0.640234 | − | 0.768180i | \(-0.721163\pi\) | ||||
−0.640234 | + | 0.768180i | \(0.721163\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.05730e84 | 0.00501606 | ||||||||
\(386\) | −9.58850e86 | −2.14327 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −2.89422e85 | −0.0544087 | ||||||||
\(389\) | −2.14221e86 | −0.369446 | −0.184723 | − | 0.982791i | \(-0.559139\pi\) | ||||
−0.184723 | + | 0.982791i | \(0.559139\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5.72910e86 | 0.832080 | ||||||||
\(392\) | 6.44267e86 | 0.858980 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.01604e85 | −0.0451518 | ||||||||
\(395\) | −7.83223e86 | −0.808878 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.53266e87 | −1.33649 | −0.668244 | − | 0.743942i | \(-0.732954\pi\) | ||||
−0.668244 | + | 0.743942i | \(0.732954\pi\) | |||||||
\(398\) | −8.95727e86 | −0.717948 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.89428e86 | −0.399412 | ||||||||
\(401\) | −1.77468e87 | −1.10607 | −0.553035 | − | 0.833158i | \(-0.686530\pi\) | ||||
−0.553035 | + | 0.833158i | \(0.686530\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.72497e87 | −2.49276 | ||||||||
\(404\) | −4.93807e86 | −0.239762 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.73929e85 | 0.0359628 | ||||||||
\(407\) | −1.88624e86 | −0.0714798 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.64558e86 | 0.213699 | 0.106849 | − | 0.994275i | \(-0.465924\pi\) | ||||
0.106849 | + | 0.994275i | \(0.465924\pi\) | |||||||
\(410\) | −6.08447e87 | −1.80287 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −5.15723e86 | −0.129825 | ||||||||
\(413\) | 1.18571e86 | 0.0275203 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.79827e87 | 1.34211 | ||||||||
\(416\) | 3.57953e87 | 0.651928 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.26459e87 | −0.351223 | ||||||||
\(419\) | 7.12912e87 | 1.02063 | 0.510313 | − | 0.859989i | \(-0.329530\pi\) | ||||
0.510313 | + | 0.859989i | \(0.329530\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.54353e87 | 0.188393 | 0.0941965 | − | 0.995554i | \(-0.469972\pi\) | ||||
0.0941965 | + | 0.995554i | \(0.469972\pi\) | |||||||
\(422\) | 7.32508e86 | 0.0825744 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.92286e87 | 0.666084 | ||||||||
\(425\) | 3.67929e87 | 0.327141 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.86218e86 | 0.0141477 | ||||||||
\(428\) | 7.47232e86 | 0.0524915 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5.81444e87 | 0.349393 | ||||||||
\(431\) | −2.09290e88 | −1.16348 | −0.581742 | − | 0.813373i | \(-0.697629\pi\) | ||||
−0.581742 | + | 0.813373i | \(0.697629\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.32958e87 | −0.0632951 | −0.0316476 | − | 0.999499i | \(-0.510075\pi\) | ||||
−0.0316476 | + | 0.999499i | \(0.510075\pi\) | |||||||
\(434\) | −8.64692e86 | −0.0381027 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.19044e87 | 0.271618 | ||||||||
\(437\) | 3.73230e88 | 1.30571 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.72682e88 | 1.11886 | 0.559432 | − | 0.828876i | \(-0.311019\pi\) | ||||
0.559432 | + | 0.828876i | \(0.311019\pi\) | |||||||
\(440\) | 7.53290e87 | 0.209555 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.61748e88 | −1.58142 | ||||||||
\(443\) | −3.13151e88 | −0.693793 | −0.346896 | − | 0.937904i | \(-0.612764\pi\) | ||||
−0.346896 | + | 0.937904i | \(0.612764\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.81023e87 | 0.167852 | ||||||||
\(446\) | 8.42847e88 | 1.48947 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.31377e86 | −0.0141681 | ||||||||
\(449\) | 5.09792e88 | 0.719683 | 0.359841 | − | 0.933014i | \(-0.382831\pi\) | ||||
0.359841 | + | 0.933014i | \(0.382831\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.43817e88 | 0.296585 | ||||||||
\(452\) | −7.26021e87 | −0.0819996 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −4.51357e88 | −0.439693 | ||||||||
\(455\) | 3.91644e87 | 0.0354413 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.22735e88 | 0.330275 | 0.165137 | − | 0.986271i | \(-0.447193\pi\) | ||||
0.165137 | + | 0.986271i | \(0.447193\pi\) | |||||||
\(458\) | −6.93261e88 | −0.503388 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.56140e88 | 0.223477 | ||||||||
\(461\) | 2.47810e89 | 1.44590 | 0.722949 | − | 0.690901i | \(-0.242786\pi\) | ||||
0.722949 | + | 0.690901i | \(0.242786\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −8.10015e88 | −0.408818 | −0.204409 | − | 0.978886i | \(-0.565527\pi\) | ||||
−0.204409 | + | 0.978886i | \(0.565527\pi\) | |||||||
\(464\) | 3.95055e89 | 1.85483 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.42801e88 | −0.139352 | ||||||||
\(467\) | −3.15046e89 | −1.19195 | −0.595977 | − | 0.803002i | \(-0.703235\pi\) | ||||
−0.595977 | + | 0.803002i | \(0.703235\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.08955e87 | −0.0134087 | ||||||||
\(470\) | −3.81243e89 | −1.16392 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.34155e89 | 1.14971 | ||||||||
\(473\) | −2.32996e88 | −0.0574777 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.39692e89 | 0.513356 | ||||||||
\(476\) | −2.20749e87 | −0.00440622 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 5.45119e89 | 0.945489 | ||||||||
\(479\) | 2.89428e89 | 0.468059 | 0.234029 | − | 0.972230i | \(-0.424809\pi\) | ||||
0.234029 | + | 0.972230i | \(0.424809\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.59079e89 | −0.505045 | ||||||||
\(482\) | 5.40035e89 | 0.708510 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.86532e89 | −0.213026 | ||||||||
\(485\) | −2.65156e89 | −0.282587 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.75391e90 | 1.62850 | 0.814250 | − | 0.580514i | \(-0.197148\pi\) | ||||
0.814250 | + | 0.580514i | \(0.197148\pi\) | |||||||
\(488\) | 6.81845e89 | 0.591047 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.69319e90 | −1.27979 | ||||||||
\(491\) | −8.85050e89 | −0.624795 | −0.312398 | − | 0.949951i | \(-0.601132\pi\) | ||||
−0.312398 | + | 0.949951i | \(0.601132\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.46599e90 | −1.51921 | ||||||||
\(494\) | −4.31105e90 | −2.48159 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3.90879e90 | −1.96520 | ||||||||
\(497\) | −1.54386e88 | −0.00725550 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.21399e90 | 1.73111 | 0.865555 | − | 0.500813i | \(-0.166966\pi\) | ||||
0.865555 | + | 0.500813i | \(0.166966\pi\) | |||||||
\(500\) | −4.43111e89 | −0.170223 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.73338e90 | −0.582532 | ||||||||
\(503\) | −2.77704e90 | −0.873081 | −0.436540 | − | 0.899685i | \(-0.643796\pi\) | ||||
−0.436540 | + | 0.899685i | \(0.643796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.52404e90 | −1.24528 | ||||||||
\(506\) | −7.82921e89 | −0.201686 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.60498e89 | 0.103943 | ||||||||
\(509\) | 2.09998e90 | 0.443782 | 0.221891 | − | 0.975071i | \(-0.428777\pi\) | ||||
0.221891 | + | 0.975071i | \(0.428777\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.40195e87 | 0.00118635 | ||||||||
\(512\) | −2.84765e90 | −0.494245 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −7.03004e90 | −1.07076 | ||||||||
\(515\) | −4.72483e90 | −0.674285 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.52772e90 | 0.191474 | ||||||||
\(518\) | −6.57133e88 | −0.00771980 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.43402e91 | 1.48062 | ||||||||
\(521\) | −3.31742e90 | −0.321171 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.46798e91 | 1.25001 | 0.625004 | − | 0.780622i | \(-0.285097\pi\) | ||||
0.625004 | + | 0.780622i | \(0.285097\pi\) | |||||||
\(524\) | −2.32340e90 | −0.185578 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.32335e91 | −0.930361 | ||||||||
\(527\) | 2.43992e91 | 1.60961 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −4.30593e90 | −0.250208 | ||||||||
\(530\) | −1.81939e91 | −0.992395 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.43810e89 | −0.00691431 | ||||||||
\(533\) | 4.64149e91 | 2.09554 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.84581e90 | 0.272630 | ||||||||
\(536\) | −1.49741e91 | −0.560171 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.45458e91 | 0.480320 | ||||||||
\(539\) | 6.78495e90 | 0.210535 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.22060e91 | 1.43091 | 0.715454 | − | 0.698660i | \(-0.246220\pi\) | ||||
0.715454 | + | 0.698660i | \(0.246220\pi\) | |||||||
\(542\) | 6.54681e91 | 1.68676 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.84843e91 | −0.420960 | ||||||||
\(545\) | 6.58757e91 | 1.41072 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.90185e91 | 0.549667 | 0.274834 | − | 0.961492i | \(-0.411377\pi\) | ||||
0.274834 | + | 0.961492i | \(0.411377\pi\) | |||||||
\(548\) | −2.10071e91 | −0.374298 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.02800e90 | −0.0792950 | ||||||||
\(551\) | −1.60650e92 | −2.38398 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.09341e90 | 0.0143711 | ||||||||
\(554\) | 1.10024e92 | 1.36116 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −4.01779e91 | −0.440536 | ||||||||
\(557\) | 5.90102e91 | 0.609226 | 0.304613 | − | 0.952476i | \(-0.401473\pi\) | ||||
0.304613 | + | 0.952476i | \(0.401473\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.43549e91 | −0.406113 | ||||||||
\(560\) | 3.23993e90 | 0.0279406 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.45732e91 | −0.188059 | ||||||||
\(563\) | 8.31074e91 | 0.599251 | 0.299625 | − | 0.954057i | \(-0.403138\pi\) | ||||
0.299625 | + | 0.954057i | \(0.403138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.65149e91 | −0.425888 | ||||||||
\(566\) | −2.30679e92 | −1.39206 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.65290e91 | −0.303112 | ||||||||
\(569\) | −7.52878e90 | −0.0380596 | −0.0190298 | − | 0.999819i | \(-0.506058\pi\) | ||||
−0.0190298 | + | 0.999819i | \(0.506058\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.98233e92 | 0.890979 | 0.445489 | − | 0.895287i | \(-0.353030\pi\) | ||||
0.445489 | + | 0.895287i | \(0.353030\pi\) | |||||||
\(572\) | 1.64842e91 | 0.0698716 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.49416e90 | 0.0320311 | ||||||||
\(575\) | 8.28673e91 | 0.294789 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.56912e91 | −0.0813570 | −0.0406785 | − | 0.999172i | \(-0.512952\pi\) | ||||
−0.0406785 | + | 0.999172i | \(0.512952\pi\) | |||||||
\(578\) | −2.83476e91 | −0.0847098 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −1.53294e92 | −0.408025 | ||||||||
\(581\) | −9.49064e90 | −0.0238449 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.29065e91 | 0.163256 | ||||||||
\(584\) | 2.34411e91 | 0.0495618 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.53271e92 | −1.23175 | ||||||||
\(587\) | 3.55629e92 | 0.633317 | 0.316658 | − | 0.948540i | \(-0.397439\pi\) | ||||
0.316658 | + | 0.948540i | \(0.397439\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.58952e93 | 2.52583 | ||||||||
\(590\) | −1.14100e93 | −1.71294 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.97053e92 | −0.398160 | ||||||||
\(593\) | −1.39162e92 | −0.176274 | −0.0881368 | − | 0.996108i | \(-0.528091\pi\) | ||||
−0.0881368 | + | 0.996108i | \(0.528091\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.02241e91 | −0.0228850 | ||||||||
\(596\) | −3.31761e92 | −0.354875 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.49043e93 | −1.42502 | ||||||||
\(599\) | −7.02635e91 | −0.0635230 | −0.0317615 | − | 0.999495i | \(-0.510112\pi\) | ||||
−0.0317615 | + | 0.999495i | \(0.510112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.73639e92 | 0.140395 | 0.0701977 | − | 0.997533i | \(-0.477637\pi\) | ||||
0.0701977 | + | 0.997533i | \(0.477637\pi\) | |||||||
\(602\) | −8.11717e90 | −0.00620758 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.79258e92 | 0.122671 | ||||||||
\(605\) | −1.70892e93 | −1.10641 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.53328e91 | 0.0494646 | 0.0247323 | − | 0.999694i | \(-0.492127\pi\) | ||||
0.0247323 | + | 0.999694i | \(0.492127\pi\) | |||||||
\(608\) | −1.20419e93 | −0.660577 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.79195e93 | −0.880596 | ||||||||
\(611\) | 2.90828e93 | 1.35287 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.00190e93 | 0.417732 | 0.208866 | − | 0.977944i | \(-0.433023\pi\) | ||||
0.208866 | + | 0.977944i | \(0.433023\pi\) | |||||||
\(614\) | 7.18251e91 | 0.0283554 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.05162e91 | −0.00372311 | ||||||||
\(617\) | −5.41310e93 | −1.81507 | −0.907534 | − | 0.419978i | \(-0.862038\pi\) | ||||
−0.907534 | + | 0.419978i | \(0.862038\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.39465e93 | 0.419595 | 0.209797 | − | 0.977745i | \(-0.432720\pi\) | ||||
0.209797 | + | 0.977745i | \(0.432720\pi\) | |||||||
\(620\) | 1.51674e93 | 0.432303 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.50903e92 | 0.166548 | ||||||||
\(623\) | −1.22994e91 | −0.00298219 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.62281e93 | −1.22454 | ||||||||
\(626\) | −1.36268e92 | −0.0281289 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.41761e93 | −0.262972 | ||||||||
\(629\) | 1.85425e93 | 0.326115 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.08460e94 | −1.71508 | −0.857541 | − | 0.514416i | \(-0.828009\pi\) | ||||
−0.857541 | + | 0.514416i | \(0.828009\pi\) | |||||||
\(632\) | 4.00358e93 | 0.600380 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.06044e93 | −0.547751 | ||||||||
\(635\) | 4.21888e93 | 0.539856 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.29164e94 | 1.48755 | ||||||||
\(638\) | 3.36994e93 | 0.368239 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.41172e94 | 1.38905 | ||||||||
\(641\) | 1.43305e94 | 1.33819 | 0.669095 | − | 0.743177i | \(-0.266682\pi\) | ||||
0.669095 | + | 0.743177i | \(0.266682\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.53129e94 | 1.28822 | 0.644109 | − | 0.764934i | \(-0.277228\pi\) | ||||
0.644109 | + | 0.764934i | \(0.277228\pi\) | |||||||
\(644\) | −4.97185e91 | −0.00397047 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.22618e94 | 1.60240 | ||||||||
\(647\) | 1.58467e94 | 1.08304 | 0.541521 | − | 0.840687i | \(-0.317849\pi\) | ||||
0.541521 | + | 0.840687i | \(0.317849\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.57221e93 | 0.281792 | ||||||||
\(650\) | −9.57172e93 | −0.560264 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.09163e93 | −0.0576477 | ||||||||
\(653\) | −1.67109e94 | −0.838317 | −0.419159 | − | 0.907913i | \(-0.637675\pi\) | ||||
−0.419159 | + | 0.907913i | \(0.637675\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.12860e94 | −0.963854 | ||||||||
\(656\) | 3.83974e94 | 1.65205 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.32230e92 | 0.0206791 | ||||||||
\(659\) | −2.14450e94 | −0.791888 | −0.395944 | − | 0.918275i | \(-0.629583\pi\) | ||||
−0.395944 | + | 0.918275i | \(0.629583\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.49680e94 | 1.50022 | 0.750109 | − | 0.661314i | \(-0.230001\pi\) | ||||
0.750109 | + | 0.661314i | \(0.230001\pi\) | |||||||
\(662\) | 3.05908e94 | 0.970170 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.47505e94 | −0.996162 | ||||||||
\(665\) | −1.31752e93 | −0.0359115 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.55405e94 | −1.36897 | ||||||||
\(668\) | 8.23076e93 | 0.192943 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 3.93533e94 | 0.834595 | ||||||||
\(671\) | 7.18070e93 | 0.144865 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −4.87646e94 | −0.890431 | −0.445216 | − | 0.895423i | \(-0.646873\pi\) | ||||
−0.445216 | + | 0.895423i | \(0.646873\pi\) | |||||||
\(674\) | −1.05269e95 | −1.82892 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.72112e94 | 0.270767 | ||||||||
\(677\) | 8.08569e93 | 0.121059 | 0.0605294 | − | 0.998166i | \(-0.480721\pi\) | ||||
0.0605294 | + | 0.998166i | \(0.480721\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.70168e92 | 0.00502066 | ||||||||
\(680\) | −7.40514e94 | −0.956060 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.33432e94 | −0.390149 | ||||||||
\(683\) | −5.83902e93 | −0.0650499 | −0.0325249 | − | 0.999471i | \(-0.510355\pi\) | ||||
−0.0325249 | + | 0.999471i | \(0.510355\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.92458e95 | −1.94403 | ||||||||
\(686\) | 4.72853e93 | 0.0454850 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.66932e94 | −0.320165 | ||||||||
\(689\) | 1.38791e95 | 1.15350 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.45504e94 | 0.713098 | 0.356549 | − | 0.934277i | \(-0.383953\pi\) | ||||
0.356549 | + | 0.934277i | \(0.383953\pi\) | |||||||
\(692\) | −1.31463e94 | −0.0944605 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.41029e95 | 1.57227 | ||||||||
\(695\) | −3.68092e95 | −2.28805 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.39682e95 | −1.35312 | ||||||||
\(698\) | −5.07122e93 | −0.0272870 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.19298e92 | −0.00156103 | ||||||||
\(701\) | −2.89282e95 | −1.34824 | −0.674122 | − | 0.738620i | \(-0.735478\pi\) | ||||
−0.674122 | + | 0.738620i | \(0.735478\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.20797e95 | 0.511746 | ||||||||
\(704\) | −3.59146e94 | −0.145073 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.47126e95 | −0.907739 | ||||||||
\(707\) | 6.31573e93 | 0.0221245 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.32934e95 | 0.423632 | 0.211816 | − | 0.977310i | \(-0.432062\pi\) | ||||
0.211816 | + | 0.977310i | \(0.432062\pi\) | |||||||
\(710\) | 1.48564e95 | 0.451604 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.50350e94 | −0.124586 | ||||||||
\(713\) | 5.49535e95 | 1.45043 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.51021e95 | 0.362898 | ||||||||
\(716\) | −3.16535e94 | −0.0725831 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 7.69647e95 | 1.60740 | ||||||||
\(719\) | −4.51429e95 | −0.899853 | −0.449927 | − | 0.893065i | \(-0.648550\pi\) | ||||
−0.449927 | + | 0.893065i | \(0.648550\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.59604e93 | 0.0119799 | ||||||||
\(722\) | 8.12460e95 | 1.40866 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.30575e95 | 0.364394 | ||||||||
\(725\) | −3.56687e95 | −0.538226 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.14098e95 | −1.12014 | −0.560072 | − | 0.828444i | \(-0.689227\pi\) | ||||
−0.560072 | + | 0.828444i | \(0.689227\pi\) | |||||||
\(728\) | −2.00195e94 | −0.0263059 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.16053e94 | −0.0738418 | ||||||||
\(731\) | 2.29044e95 | 0.262233 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 4.16267e95 | 0.434899 | 0.217450 | − | 0.976072i | \(-0.430226\pi\) | ||||
0.217450 | + | 0.976072i | \(0.430226\pi\) | |||||||
\(734\) | 1.25988e96 | 1.25751 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.16316e95 | −0.379329 | ||||||||
\(737\) | −1.57696e95 | −0.137297 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.08509e95 | −0.563322 | −0.281661 | − | 0.959514i | \(-0.590885\pi\) | ||||
−0.281661 | + | 0.959514i | \(0.590885\pi\) | |||||||
\(740\) | 1.15266e95 | 0.0875869 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.53994e94 | 0.0176316 | ||||||||
\(743\) | −2.43728e95 | −0.161726 | −0.0808631 | − | 0.996725i | \(-0.525768\pi\) | ||||
−0.0808631 | + | 0.996725i | \(0.525768\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.03945e96 | −1.84315 | ||||||||
\(746\) | −1.12708e96 | −0.653435 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −8.51226e94 | −0.0451171 | ||||||||
\(749\) | −9.55701e93 | −0.00484375 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.39345e96 | 1.10940 | 0.554698 | − | 0.832052i | \(-0.312834\pi\) | ||||
0.554698 | + | 0.832052i | \(0.312834\pi\) | |||||||
\(752\) | 2.40592e96 | 1.06656 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.41529e96 | 2.60181 | ||||||||
\(755\) | 1.64228e96 | 0.637126 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.70408e96 | 1.31513 | 0.657565 | − | 0.753398i | \(-0.271586\pi\) | ||||
0.657565 | + | 0.753398i | \(0.271586\pi\) | |||||||
\(758\) | −4.65602e96 | −1.58160 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.82418e96 | −1.50027 | ||||||||
\(761\) | 3.66225e96 | 1.08984 | 0.544919 | − | 0.838489i | \(-0.316560\pi\) | ||||
0.544919 | + | 0.838489i | \(0.316560\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.19650e94 | −0.0250640 | ||||||||
\(764\) | 4.41597e94 | 0.0115186 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.92558e96 | −1.41601 | ||||||||
\(767\) | 8.70403e96 | 1.99102 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.83109e96 | 1.22241 | 0.611206 | − | 0.791472i | \(-0.290685\pi\) | ||||
0.611206 | + | 0.791472i | \(0.290685\pi\) | |||||||
\(770\) | 2.76376e94 | 0.00554703 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.34799e96 | −0.432033 | ||||||||
\(773\) | −2.14263e96 | −0.377515 | −0.188757 | − | 0.982024i | \(-0.560446\pi\) | ||||
−0.188757 | + | 0.982024i | \(0.560446\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.52917e96 | 0.570251 | ||||||||
\(776\) | 1.35539e96 | 0.209747 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.87783e96 | −0.408553 | ||||||||
\(779\) | −1.56144e97 | −2.12334 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.95323e95 | −0.0742921 | ||||||||
\(782\) | 7.69643e96 | 0.920159 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.06853e97 | 1.17273 | ||||||||
\(785\) | −1.29876e97 | −1.36582 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −9.20529e96 | −0.888964 | −0.444482 | − | 0.895788i | \(-0.646612\pi\) | ||||
−0.444482 | + | 0.895788i | \(0.646612\pi\) | |||||||
\(788\) | −9.83432e94 | −0.00910156 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.05218e97 | −0.894501 | ||||||||
\(791\) | 9.28573e94 | 0.00756666 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.36698e97 | 1.02355 | ||||||||
\(794\) | −2.05897e97 | −1.47796 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.19342e96 | −0.144722 | ||||||||
\(797\) | 2.70098e97 | 1.70871 | 0.854355 | − | 0.519690i | \(-0.173953\pi\) | ||||
0.854355 | + | 0.519690i | \(0.173953\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.50181e97 | −0.873569 | ||||||||
\(800\) | −2.67363e96 | −0.149137 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.38409e97 | −1.22315 | ||||||||
\(803\) | 2.46864e95 | 0.0121475 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.55499e95 | −0.0206218 | ||||||||
\(806\) | −6.34749e97 | −2.75663 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.31254e97 | 0.924290 | ||||||||
\(809\) | −6.43872e96 | −0.246902 | −0.123451 | − | 0.992351i | \(-0.539396\pi\) | ||||
−0.123451 | + | 0.992351i | \(0.539396\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.69417e97 | −1.30412 | −0.652061 | − | 0.758166i | \(-0.726095\pi\) | ||||
−0.652061 | + | 0.758166i | \(0.726095\pi\) | |||||||
\(812\) | 2.14004e95 | 0.00724929 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2.53396e96 | −0.0790463 | ||||||||
\(815\) | −1.00011e97 | −0.299410 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.49214e97 | 0.411501 | ||||||||
\(818\) | 8.92763e96 | 0.236320 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.48994e97 | −0.363417 | ||||||||
\(821\) | −9.41677e96 | −0.220499 | −0.110249 | − | 0.993904i | \(-0.535165\pi\) | ||||
−0.110249 | + | 0.993904i | \(0.535165\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.85526e97 | −0.400415 | −0.200208 | − | 0.979754i | \(-0.564162\pi\) | ||||
−0.200208 | + | 0.979754i | \(0.564162\pi\) | |||||||
\(824\) | 2.41517e97 | 0.500480 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.59288e96 | 0.0304335 | ||||||||
\(827\) | 8.33671e97 | 1.52954 | 0.764769 | − | 0.644304i | \(-0.222853\pi\) | ||||
0.764769 | + | 0.644304i | \(0.222853\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.04318e97 | 0.853351 | 0.426675 | − | 0.904405i | \(-0.359685\pi\) | ||||
0.426675 | + | 0.904405i | \(0.359685\pi\) | |||||||
\(830\) | 9.13274e97 | 1.48418 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −6.83700e97 | −1.02502 | ||||||||
\(833\) | −6.66989e97 | −0.960530 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7.54066e97 | 1.00210 | ||||||||
\(836\) | −5.54542e96 | −0.0707986 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 9.57721e97 | 1.12866 | ||||||||
\(839\) | −1.80988e97 | −0.204939 | −0.102469 | − | 0.994736i | \(-0.532674\pi\) | ||||
−0.102469 | + | 0.994736i | \(0.532674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.43418e98 | 1.49947 | ||||||||
\(842\) | 2.07357e97 | 0.208335 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.79374e96 | 0.0166451 | ||||||||
\(845\) | 1.57681e98 | 1.40631 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.38572e96 | 0.0196574 | ||||||||
\(848\) | 1.14817e98 | 0.909376 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 4.94273e97 | 0.361770 | ||||||||
\(851\) | 4.17625e97 | 0.293864 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.65760e95 | −0.00433037 | −0.00216519 | − | 0.999998i | \(-0.500689\pi\) | ||||
−0.00216519 | + | 0.999998i | \(0.500689\pi\) | |||||||
\(854\) | 2.50163e96 | 0.0156453 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.49935e97 | −0.202356 | ||||||||
\(857\) | −1.10050e97 | −0.0611976 | −0.0305988 | − | 0.999532i | \(-0.509741\pi\) | ||||
−0.0305988 | + | 0.999532i | \(0.509741\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.29581e98 | 0.666457 | 0.333228 | − | 0.942846i | \(-0.391862\pi\) | ||||
0.333228 | + | 0.942846i | \(0.391862\pi\) | |||||||
\(860\) | 1.42382e97 | 0.0704297 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.81159e98 | −1.28665 | ||||||||
\(863\) | −1.83648e98 | −0.808398 | −0.404199 | − | 0.914671i | \(-0.632450\pi\) | ||||
−0.404199 | + | 0.914671i | \(0.632450\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.20441e98 | −0.490608 | ||||||||
\(866\) | −1.78615e97 | −0.0699952 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2.11742e96 | −0.00768063 | ||||||||
\(869\) | 4.21627e97 | 0.147152 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.00204e98 | −0.970081 | ||||||||
\(872\) | −3.36734e98 | −1.04709 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.01394e98 | 1.44393 | ||||||||
\(875\) | 5.66734e96 | 0.0157076 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8.00025e96 | −0.0205408 | −0.0102704 | − | 0.999947i | \(-0.503269\pi\) | ||||
−0.0102704 | + | 0.999947i | \(0.503269\pi\) | |||||||
\(878\) | 5.00658e98 | 1.23730 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.24934e98 | 0.286096 | ||||||||
\(881\) | 2.46360e98 | 0.543096 | 0.271548 | − | 0.962425i | \(-0.412464\pi\) | ||||
0.271548 | + | 0.962425i | \(0.412464\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.44617e98 | −1.72574 | −0.862872 | − | 0.505423i | \(-0.831336\pi\) | ||||
−0.862872 | + | 0.505423i | \(0.831336\pi\) | |||||||
\(884\) | −1.62046e98 | −0.318778 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −4.20685e98 | −0.767234 | ||||||||
\(887\) | −4.82704e98 | −0.847695 | −0.423848 | − | 0.905734i | \(-0.639321\pi\) | ||||
−0.423848 | + | 0.905734i | \(0.639321\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.88972e96 | −0.00959148 | ||||||||
\(890\) | 1.18356e98 | 0.185620 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.06393e98 | 0.300243 | ||||||||
\(893\) | −9.78372e98 | −1.37082 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.89996e98 | −0.376981 | ||||||||
\(896\) | −1.97081e97 | −0.0246790 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.84851e98 | 0.795864 | ||||||||
\(899\) | −2.36537e99 | −2.64819 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.16701e98 | −0.744830 | ||||||||
\(902\) | 3.27542e98 | 0.327980 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.40002e98 | 0.316110 | ||||||||
\(905\) | 2.11243e99 | 1.89258 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.79940e99 | 1.49722 | 0.748608 | − | 0.663012i | \(-0.230722\pi\) | ||||
0.748608 | + | 0.663012i | \(0.230722\pi\) | |||||||
\(908\) | −1.10526e98 | −0.0886320 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5.26131e97 | 0.0391929 | ||||||||
\(911\) | −1.49982e98 | −0.107690 | −0.0538449 | − | 0.998549i | \(-0.517148\pi\) | ||||
−0.0538449 | + | 0.998549i | \(0.517148\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.65967e98 | −0.244158 | ||||||||
\(914\) | 5.67899e98 | 0.365236 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.69763e98 | −0.101472 | ||||||||
\(917\) | 2.97161e97 | 0.0171245 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.19761e99 | −1.17728 | −0.588641 | − | 0.808394i | \(-0.700337\pi\) | ||||
−0.588641 | + | 0.808394i | \(0.700337\pi\) | |||||||
\(920\) | −1.66783e99 | −0.861511 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.32906e99 | 1.59895 | ||||||||
\(923\) | −1.13330e99 | −0.524916 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.68204e98 | 0.115536 | ||||||||
\(926\) | −1.08817e99 | −0.452093 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.79196e99 | 0.692580 | ||||||||
\(929\) | 4.06848e99 | 1.51672 | 0.758361 | − | 0.651835i | \(-0.226000\pi\) | ||||
0.758361 | + | 0.651835i | \(0.226000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.34519e99 | −1.50728 | ||||||||
\(932\) | −8.39436e97 | −0.0280902 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.23231e99 | −1.31813 | ||||||||
\(935\) | −7.79856e98 | −0.234329 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.26633e99 | 1.19338 | 0.596689 | − | 0.802473i | \(-0.296483\pi\) | ||||
0.596689 | + | 0.802473i | \(0.296483\pi\) | |||||||
\(938\) | −5.49388e97 | −0.0148280 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.33573e98 | −0.234620 | ||||||||
\(941\) | −5.86101e99 | −1.42141 | −0.710706 | − | 0.703489i | \(-0.751624\pi\) | ||||
−0.710706 | + | 0.703489i | \(0.751624\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.39826e99 | −1.21931 | ||||||||
\(944\) | 7.20053e99 | 1.56965 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.13005e98 | −0.0635620 | ||||||||
\(947\) | 4.54626e99 | 0.891107 | 0.445553 | − | 0.895255i | \(-0.353007\pi\) | ||||
0.445553 | + | 0.895255i | \(0.353007\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 4.69951e98 | 0.0858290 | ||||||||
\(950\) | 3.22001e99 | 0.567697 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.03379e98 | 0.0169861 | ||||||||
\(953\) | 5.35590e99 | 0.849611 | 0.424806 | − | 0.905285i | \(-0.360342\pi\) | ||||
0.424806 | + | 0.905285i | \(0.360342\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.04572e98 | 0.0598250 | ||||||||
\(956\) | 1.33486e99 | 0.190589 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.88815e99 | 0.517605 | ||||||||
\(959\) | 2.68679e98 | 0.0345390 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.50624e100 | 1.80577 | ||||||||
\(962\) | −4.82384e99 | −0.558507 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.32241e99 | 0.142819 | ||||||||
\(965\) | −2.15113e100 | −2.24389 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.14687e99 | 0.598228 | 0.299114 | − | 0.954217i | \(-0.403309\pi\) | ||||
0.299114 | + | 0.954217i | \(0.403309\pi\) | |||||||
\(968\) | 8.73543e99 | 0.821221 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −3.56208e99 | −0.312501 | ||||||||
\(971\) | 1.66038e100 | 1.40723 | 0.703613 | − | 0.710583i | \(-0.251569\pi\) | ||||
0.703613 | + | 0.710583i | \(0.251569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.13871e98 | 0.0406512 | ||||||||
\(974\) | 2.35619e100 | 1.80089 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.13085e100 | 0.806930 | ||||||||
\(977\) | 1.88759e99 | 0.130149 | 0.0650743 | − | 0.997880i | \(-0.479272\pi\) | ||||
0.0650743 | + | 0.997880i | \(0.479272\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.74276e98 | −0.0305359 | ||||||||
\(980\) | −4.14622e99 | −0.257976 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.18897e100 | −0.690933 | ||||||||
\(983\) | 9.21278e97 | 0.00517426 | 0.00258713 | − | 0.999997i | \(-0.499176\pi\) | ||||
0.00258713 | + | 0.999997i | \(0.499176\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.00977e98 | −0.0472716 | ||||||||
\(986\) | −3.31279e100 | −1.68003 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.05567e100 | −0.500232 | ||||||||
\(989\) | 5.15868e99 | 0.236299 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.75044e100 | −0.749340 | −0.374670 | − | 0.927158i | \(-0.622244\pi\) | ||||
−0.374670 | + | 0.927158i | \(0.622244\pi\) | |||||||
\(992\) | −1.77302e100 | −0.733789 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.07400e98 | −0.00802353 | ||||||||
\(995\) | −2.00952e100 | −0.751655 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.70311e100 | 1.29503 | 0.647513 | − | 0.762054i | \(-0.275809\pi\) | ||||
0.647513 | + | 0.762054i | \(0.275809\pi\) | |||||||
\(998\) | 5.66104e100 | 1.91436 | ||||||||
\(999\) | 0 | 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 | 9.68.a.a.1.4 | 5 | ||
3.2 | odd | 2 | 1.68.a.a.1.2 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.68.a.a.1.2 | ✓ | 5 | 3.2 | odd | 2 | ||
9.68.a.a.1.4 | 5 | 1.1 | even | 1 | trivial |