Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,90,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, 90, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 90);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 90 \) |
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: | \(451.461862736\) |
Analytic rank: | \(0\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - 3 x^{6} + \cdots + 56\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | multiple of \( 2^{83}\cdot 3^{43}\cdot 5^{9}\cdot 7^{5}\cdot 11^{2}\cdot 13^{2} \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-4.68207e11\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.79872e13 | −0.722984 | −0.361492 | − | 0.932375i | \(-0.617732\pi\) | ||||
−0.361492 | + | 0.932375i | \(0.617732\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.95431e26 | −0.477294 | ||||||||
\(5\) | 4.75717e30 | 0.374268 | 0.187134 | − | 0.982334i | \(-0.440080\pi\) | ||||
0.187134 | + | 0.982334i | \(0.440080\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.90338e37 | 0.965114 | 0.482557 | − | 0.875865i | \(-0.339708\pi\) | ||||
0.482557 | + | 0.875865i | \(0.339708\pi\) | |||||||
\(8\) | 1.64475e40 | 1.06806 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −8.55680e43 | −0.270590 | ||||||||
\(11\) | 2.01197e45 | 0.0915476 | 0.0457738 | − | 0.998952i | \(-0.485425\pi\) | ||||
0.0457738 | + | 0.998952i | \(0.485425\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.05046e49 | −0.282424 | −0.141212 | − | 0.989979i | \(-0.545100\pi\) | ||||
−0.141212 | + | 0.989979i | \(0.545100\pi\) | |||||||
\(14\) | −7.02109e50 | −0.697761 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.12982e53 | −0.294895 | ||||||||
\(17\) | −1.05148e55 | −1.84852 | −0.924260 | − | 0.381763i | \(-0.875317\pi\) | ||||
−0.924260 | + | 0.381763i | \(0.875317\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.08050e57 | 1.34613 | 0.673067 | − | 0.739581i | \(-0.264976\pi\) | ||||
0.673067 | + | 0.739581i | \(0.264976\pi\) | |||||||
\(20\) | −1.40541e57 | −0.178636 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.61897e58 | −0.0661874 | ||||||||
\(23\) | 5.03802e60 | 1.27459 | 0.637295 | − | 0.770620i | \(-0.280053\pi\) | ||||
0.637295 | + | 0.770620i | \(0.280053\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.38928e62 | −0.859923 | ||||||||
\(26\) | 1.88949e62 | 0.204188 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.15318e64 | −0.460643 | ||||||||
\(29\) | −1.12164e65 | −0.940032 | −0.470016 | − | 0.882658i | \(-0.655752\pi\) | ||||
−0.470016 | + | 0.882658i | \(0.655752\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.18722e66 | −1.37346 | −0.686731 | − | 0.726912i | \(-0.740955\pi\) | ||||
−0.686731 | + | 0.726912i | \(0.740955\pi\) | |||||||
\(32\) | −8.14829e66 | −0.854855 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.89132e68 | 1.33645 | ||||||||
\(35\) | 1.85690e68 | 0.361211 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.99627e69 | −1.14786 | −0.573931 | − | 0.818904i | \(-0.694582\pi\) | ||||
−0.573931 | + | 0.818904i | \(0.694582\pi\) | |||||||
\(38\) | −1.94351e70 | −0.973233 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 7.82435e70 | 0.399741 | ||||||||
\(41\) | 7.38883e70 | 0.125804 | 0.0629020 | − | 0.998020i | \(-0.479964\pi\) | ||||
0.0629020 | + | 0.998020i | \(0.479964\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.97212e72 | 1.01671 | 0.508353 | − | 0.861149i | \(-0.330255\pi\) | ||||
0.508353 | + | 0.861149i | \(0.330255\pi\) | |||||||
\(44\) | −5.94398e71 | −0.0436952 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −9.06197e73 | −0.921508 | ||||||||
\(47\) | −5.91267e73 | −0.230903 | −0.115451 | − | 0.993313i | \(-0.536831\pi\) | ||||
−0.115451 | + | 0.993313i | \(0.536831\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.12142e74 | −0.0685558 | ||||||||
\(50\) | 2.49893e75 | 0.621711 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.10339e75 | 0.134799 | ||||||||
\(53\) | −2.39386e76 | −0.445475 | −0.222738 | − | 0.974878i | \(-0.571499\pi\) | ||||
−0.222738 | + | 0.974878i | \(0.571499\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.57127e75 | 0.0342634 | ||||||||
\(56\) | 6.42009e77 | 1.03080 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.01752e78 | 0.679628 | ||||||||
\(59\) | 1.72292e78 | 0.271239 | 0.135619 | − | 0.990761i | \(-0.456698\pi\) | ||||
0.135619 | + | 0.990761i | \(0.456698\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.90453e79 | 0.680158 | 0.340079 | − | 0.940397i | \(-0.389546\pi\) | ||||
0.340079 | + | 0.940397i | \(0.389546\pi\) | |||||||
\(62\) | 5.73291e79 | 0.992990 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.16497e80 | 0.912942 | ||||||||
\(65\) | −4.99723e79 | −0.105702 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.04228e80 | 0.386709 | 0.193355 | − | 0.981129i | \(-0.438063\pi\) | ||||
0.193355 | + | 0.981129i | \(0.438063\pi\) | |||||||
\(68\) | 3.10640e81 | 0.882289 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.34005e81 | −0.261150 | ||||||||
\(71\) | 1.27373e82 | 0.529762 | 0.264881 | − | 0.964281i | \(-0.414667\pi\) | ||||
0.264881 | + | 0.964281i | \(0.414667\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.75786e82 | −0.454018 | −0.227009 | − | 0.973893i | \(-0.572895\pi\) | ||||
−0.227009 | + | 0.973893i | \(0.572895\pi\) | |||||||
\(74\) | 1.25843e83 | 0.829886 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.19212e83 | −0.642503 | ||||||||
\(77\) | 7.85349e82 | 0.0883538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.21546e83 | 0.115568 | 0.0577840 | − | 0.998329i | \(-0.481597\pi\) | ||||
0.0577840 | + | 0.998329i | \(0.481597\pi\) | |||||||
\(80\) | −5.37472e83 | −0.110370 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.32904e84 | −0.0909542 | ||||||||
\(83\) | 2.22227e85 | 0.886793 | 0.443396 | − | 0.896326i | \(-0.353773\pi\) | ||||
0.443396 | + | 0.896326i | \(0.353773\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.00207e85 | −0.691843 | ||||||||
\(86\) | −8.94344e85 | −0.735062 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.30919e85 | 0.0977783 | ||||||||
\(89\) | 5.54352e86 | 0.990672 | 0.495336 | − | 0.868701i | \(-0.335045\pi\) | ||||
0.495336 | + | 0.868701i | \(0.335045\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.10036e86 | −0.272571 | ||||||||
\(92\) | −1.48839e87 | −0.608355 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.06352e87 | 0.166939 | ||||||||
\(95\) | 5.14011e87 | 0.503816 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.88818e88 | 1.89585 | 0.947927 | − | 0.318488i | \(-0.103175\pi\) | ||||
0.947927 | + | 0.318488i | \(0.103175\pi\) | |||||||
\(98\) | 2.01713e87 | 0.0495647 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 4.10437e88 | 0.410437 | ||||||||
\(101\) | −6.30836e88 | −0.405150 | −0.202575 | − | 0.979267i | \(-0.564931\pi\) | ||||
−0.202575 | + | 0.979267i | \(0.564931\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.95925e89 | −1.06257 | −0.531284 | − | 0.847194i | \(-0.678290\pi\) | ||||
−0.531284 | + | 0.847194i | \(0.678290\pi\) | |||||||
\(104\) | −1.72775e89 | −0.301646 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.30589e89 | 0.322071 | ||||||||
\(107\) | −5.08196e88 | −0.0250296 | −0.0125148 | − | 0.999922i | \(-0.503984\pi\) | ||||
−0.0125148 | + | 0.999922i | \(0.503984\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.00179e90 | −0.648487 | −0.324244 | − | 0.945974i | \(-0.605110\pi\) | ||||
−0.324244 | + | 0.945974i | \(0.605110\pi\) | |||||||
\(110\) | −1.72160e89 | −0.0247719 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.41010e90 | −0.284608 | ||||||||
\(113\) | 1.01787e91 | 0.442284 | 0.221142 | − | 0.975242i | \(-0.429022\pi\) | ||||
0.221142 | + | 0.975242i | \(0.429022\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.39667e91 | 0.477039 | ||||||||
\(116\) | 3.31367e91 | 0.448672 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.09906e91 | −0.196101 | ||||||||
\(119\) | −4.10433e92 | −1.78403 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.78954e92 | −0.991619 | ||||||||
\(122\) | −3.42571e92 | −0.491743 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.41603e92 | 0.655546 | ||||||||
\(125\) | −1.42947e93 | −0.696110 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.42465e93 | −0.822908 | −0.411454 | − | 0.911431i | \(-0.634979\pi\) | ||||
−0.411454 | + | 0.911431i | \(0.634979\pi\) | |||||||
\(128\) | 1.14937e93 | 0.194813 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.98861e92 | 0.0764211 | ||||||||
\(131\) | 2.21360e94 | 1.33821 | 0.669107 | − | 0.743166i | \(-0.266677\pi\) | ||||
0.669107 | + | 0.743166i | \(0.266677\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.21760e94 | 1.29917 | ||||||||
\(134\) | −1.26671e94 | −0.279585 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.72942e95 | −1.97433 | ||||||||
\(137\) | −1.50357e93 | −0.0123896 | −0.00619482 | − | 0.999981i | \(-0.501972\pi\) | ||||
−0.00619482 | + | 0.999981i | \(0.501972\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.85854e95 | 0.803550 | 0.401775 | − | 0.915738i | \(-0.368393\pi\) | ||||
0.401775 | + | 0.915738i | \(0.368393\pi\) | |||||||
\(140\) | −5.48587e94 | −0.172404 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −2.29108e95 | −0.383009 | ||||||||
\(143\) | −2.11350e94 | −0.0258552 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.33583e95 | −0.351824 | ||||||||
\(146\) | 6.75933e95 | 0.328248 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.06691e96 | 0.547868 | ||||||||
\(149\) | 6.69346e96 | 1.31481 | 0.657403 | − | 0.753539i | \(-0.271655\pi\) | ||||
0.657403 | + | 0.753539i | \(0.271655\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.94714e96 | −0.970980 | −0.485490 | − | 0.874242i | \(-0.661359\pi\) | ||||
−0.485490 | + | 0.874242i | \(0.661359\pi\) | |||||||
\(152\) | 1.77715e97 | 1.43775 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.41262e96 | −0.0638784 | ||||||||
\(155\) | −1.51621e97 | −0.514043 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −7.99466e97 | −1.53202 | −0.766012 | − | 0.642826i | \(-0.777762\pi\) | ||||
−0.766012 | + | 0.642826i | \(0.777762\pi\) | |||||||
\(158\) | −5.78371e96 | −0.0835538 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.87628e97 | −0.319945 | ||||||||
\(161\) | 1.96653e98 | 1.23012 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.25331e97 | 0.298044 | 0.149022 | − | 0.988834i | \(-0.452388\pi\) | ||||
0.149022 | + | 0.988834i | \(0.452388\pi\) | |||||||
\(164\) | −2.18289e97 | −0.0600455 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.99724e98 | −0.641137 | ||||||||
\(167\) | 2.58266e98 | 0.317091 | 0.158546 | − | 0.987352i | \(-0.449320\pi\) | ||||
0.158546 | + | 0.987352i | \(0.449320\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.27309e99 | −0.920237 | ||||||||
\(170\) | 8.99732e98 | 0.500191 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.46892e99 | −0.485268 | ||||||||
\(173\) | 2.87467e99 | 0.733730 | 0.366865 | − | 0.930274i | \(-0.380431\pi\) | ||||
0.366865 | + | 0.930274i | \(0.380431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.42290e99 | −0.829924 | ||||||||
\(176\) | −2.27315e98 | −0.0269970 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.97123e99 | −0.716240 | ||||||||
\(179\) | 7.10087e99 | 0.397513 | 0.198757 | − | 0.980049i | \(-0.436310\pi\) | ||||
0.198757 | + | 0.980049i | \(0.436310\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.14165e100 | 1.07266 | 0.536329 | − | 0.844009i | \(-0.319811\pi\) | ||||
0.536329 | + | 0.844009i | \(0.319811\pi\) | |||||||
\(182\) | 7.37540e99 | 0.197065 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.28628e100 | 1.36134 | ||||||||
\(185\) | −3.32824e100 | −0.429608 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.11555e100 | −0.169228 | ||||||||
\(188\) | 1.74679e100 | 0.110209 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −9.24561e100 | −0.364250 | ||||||||
\(191\) | −1.75148e101 | −0.546285 | −0.273142 | − | 0.961974i | \(-0.588063\pi\) | ||||
−0.273142 | + | 0.961974i | \(0.588063\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.08614e101 | 0.605502 | 0.302751 | − | 0.953070i | \(-0.402095\pi\) | ||||
0.302751 | + | 0.953070i | \(0.402095\pi\) | |||||||
\(194\) | −8.79246e101 | −1.37067 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.31303e100 | 0.0327213 | ||||||||
\(197\) | 6.10297e101 | 0.480612 | 0.240306 | − | 0.970697i | \(-0.422752\pi\) | ||||
0.240306 | + | 0.970697i | \(0.422752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.92591e100 | 0.0498665 | 0.0249332 | − | 0.999689i | \(-0.492063\pi\) | ||||
0.0249332 | + | 0.999689i | \(0.492063\pi\) | |||||||
\(200\) | −2.28502e102 | −0.918450 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.13470e102 | 0.292917 | ||||||||
\(203\) | −4.37819e102 | −0.907238 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.51499e101 | 0.0470844 | ||||||||
\(206\) | 7.12158e102 | 0.768219 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.18683e102 | 0.0832856 | ||||||||
\(209\) | 2.17393e102 | 0.123235 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.33167e102 | −0.309145 | −0.154573 | − | 0.987981i | \(-0.549400\pi\) | ||||
−0.154573 | + | 0.987981i | \(0.549400\pi\) | |||||||
\(212\) | 7.07222e102 | 0.212623 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 9.14103e101 | 0.0180960 | ||||||||
\(215\) | 2.36532e103 | 0.380521 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.24409e104 | −1.32555 | ||||||||
\(218\) | 5.39938e103 | 0.468846 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.82765e102 | −0.0163537 | ||||||||
\(221\) | 1.10454e104 | 0.522067 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.60785e104 | −1.77513 | −0.887564 | − | 0.460684i | \(-0.847604\pi\) | ||||
−0.887564 | + | 0.460684i | \(0.847604\pi\) | |||||||
\(224\) | −3.18059e104 | −0.825032 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.83086e104 | −0.319764 | ||||||||
\(227\) | 4.37425e104 | 0.627701 | 0.313851 | − | 0.949472i | \(-0.398381\pi\) | ||||
0.313851 | + | 0.949472i | \(0.398381\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.98125e104 | 0.678038 | 0.339019 | − | 0.940779i | \(-0.389905\pi\) | ||||
0.339019 | + | 0.940779i | \(0.389905\pi\) | |||||||
\(230\) | −4.31093e104 | −0.344891 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.84482e105 | −1.00401 | ||||||||
\(233\) | −2.70074e105 | −1.21379 | −0.606897 | − | 0.794781i | \(-0.707586\pi\) | ||||
−0.606897 | + | 0.794781i | \(0.707586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.81276e104 | −0.0864196 | ||||||||
\(236\) | −5.09005e104 | −0.129461 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 7.38254e105 | 1.28983 | ||||||||
\(239\) | −8.33363e105 | −1.20817 | −0.604084 | − | 0.796920i | \(-0.706461\pi\) | ||||
−0.604084 | + | 0.796920i | \(0.706461\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.56610e106 | −1.56697 | −0.783487 | − | 0.621408i | \(-0.786561\pi\) | ||||
−0.783487 | + | 0.621408i | \(0.786561\pi\) | |||||||
\(242\) | 8.61504e105 | 0.716924 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −5.62657e105 | −0.324636 | ||||||||
\(245\) | −5.33480e104 | −0.0256583 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.13502e106 | −0.380181 | ||||||||
\(248\) | −5.24218e106 | −1.46694 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.57121e106 | 0.503276 | ||||||||
\(251\) | 1.03640e106 | 0.169843 | 0.0849217 | − | 0.996388i | \(-0.472936\pi\) | ||||
0.0849217 | + | 0.996388i | \(0.472936\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.01363e106 | 0.116686 | ||||||||
\(254\) | 6.15999e106 | 0.594949 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.54679e107 | −1.05379 | ||||||||
\(257\) | −2.59608e107 | −1.48694 | −0.743471 | − | 0.668768i | \(-0.766822\pi\) | ||||
−0.743471 | + | 0.668768i | \(0.766822\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.73091e107 | −1.10782 | ||||||||
\(260\) | 1.47634e106 | 0.0504512 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.98164e107 | −0.967508 | ||||||||
\(263\) | 9.18230e107 | 1.88331 | 0.941653 | − | 0.336586i | \(-0.109272\pi\) | ||||
0.941653 | + | 0.336586i | \(0.109272\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.13880e107 | −0.166727 | ||||||||
\(266\) | −7.58627e107 | −0.939281 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2.08051e107 | −0.184574 | ||||||||
\(269\) | 4.34307e107 | 0.326453 | 0.163227 | − | 0.986589i | \(-0.447810\pi\) | ||||
0.163227 | + | 0.986589i | \(0.447810\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.01852e107 | −0.109119 | −0.0545595 | − | 0.998511i | \(-0.517375\pi\) | ||||
−0.0545595 | + | 0.998511i | \(0.517375\pi\) | |||||||
\(272\) | 1.18798e108 | 0.545120 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.70450e106 | 0.00895751 | ||||||||
\(275\) | −2.79519e107 | −0.0787239 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.30470e108 | 1.28622 | 0.643109 | − | 0.765774i | \(-0.277644\pi\) | ||||
0.643109 | + | 0.765774i | \(0.277644\pi\) | |||||||
\(278\) | −3.34299e108 | −0.580954 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.05414e108 | 0.385795 | ||||||||
\(281\) | −2.21025e108 | −0.238238 | −0.119119 | − | 0.992880i | \(-0.538007\pi\) | ||||
−0.119119 | + | 0.992880i | \(0.538007\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.73795e108 | −0.451087 | −0.225544 | − | 0.974233i | \(-0.572416\pi\) | ||||
−0.225544 | + | 0.974233i | \(0.572416\pi\) | |||||||
\(284\) | −3.76299e108 | −0.252853 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.80159e107 | 0.0186929 | ||||||||
\(287\) | 2.88414e108 | 0.121415 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.82052e109 | 2.41703 | ||||||||
\(290\) | 9.59766e108 | 0.254363 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.11019e109 | 0.216700 | ||||||||
\(293\) | 8.06470e109 | 1.35201 | 0.676004 | − | 0.736898i | \(-0.263710\pi\) | ||||
0.676004 | + | 0.736898i | \(0.263710\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.19624e108 | 0.101516 | ||||||||
\(296\) | −1.15071e110 | −1.22599 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.20397e110 | −0.950584 | ||||||||
\(299\) | −5.29225e109 | −0.359975 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.94081e110 | 0.981236 | ||||||||
\(302\) | 1.60934e110 | 0.702002 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.22076e110 | −0.396969 | ||||||||
\(305\) | 9.06015e109 | 0.254562 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.28891e110 | −1.11099 | −0.555493 | − | 0.831521i | \(-0.687471\pi\) | ||||
−0.555493 | + | 0.831521i | \(0.687471\pi\) | |||||||
\(308\) | −2.32016e109 | −0.0421708 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.72724e110 | 0.371645 | ||||||||
\(311\) | 1.09333e111 | 1.29097 | 0.645484 | − | 0.763773i | \(-0.276656\pi\) | ||||
0.645484 | + | 0.763773i | \(0.276656\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4.11236e110 | 0.365063 | 0.182531 | − | 0.983200i | \(-0.441571\pi\) | ||||
0.182531 | + | 0.983200i | \(0.441571\pi\) | |||||||
\(314\) | 1.43802e111 | 1.10763 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.49947e109 | −0.0551600 | ||||||||
\(317\) | −1.98612e111 | −1.00200 | −0.501000 | − | 0.865447i | \(-0.667034\pi\) | ||||
−0.501000 | + | 0.865447i | \(0.667034\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.25671e110 | −0.0860577 | ||||||||
\(320\) | 1.02991e111 | 0.341685 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.53724e111 | −0.889360 | ||||||||
\(323\) | −1.13612e112 | −2.48836 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.45939e111 | 0.242863 | ||||||||
\(326\) | −1.48454e111 | −0.215481 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.21528e111 | 0.134366 | ||||||||
\(329\) | −2.30794e111 | −0.222847 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.49334e110 | 0.0478765 | 0.0239383 | − | 0.999713i | \(-0.492379\pi\) | ||||
0.0239383 | + | 0.999713i | \(0.492379\pi\) | |||||||
\(332\) | −6.56528e111 | −0.423261 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.64548e111 | −0.229252 | ||||||||
\(335\) | 3.35013e111 | 0.144733 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.31744e112 | −0.436718 | −0.218359 | − | 0.975869i | \(-0.570070\pi\) | ||||
−0.218359 | + | 0.975869i | \(0.570070\pi\) | |||||||
\(338\) | 2.28992e112 | 0.665316 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.47777e112 | 0.330213 | ||||||||
\(341\) | −6.41259e111 | −0.125737 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.82282e112 | −1.03128 | ||||||||
\(344\) | 8.17789e112 | 1.08590 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.17072e112 | −0.530475 | ||||||||
\(347\) | −1.51622e113 | −1.36805 | −0.684023 | − | 0.729461i | \(-0.739771\pi\) | ||||
−0.684023 | + | 0.729461i | \(0.739771\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.52478e113 | 1.06531 | 0.532653 | − | 0.846334i | \(-0.321195\pi\) | ||||
0.532653 | + | 0.846334i | \(0.321195\pi\) | |||||||
\(350\) | 9.75427e112 | 0.600021 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.63941e112 | −0.0782600 | ||||||||
\(353\) | 2.78663e113 | 1.17248 | 0.586239 | − | 0.810138i | \(-0.300608\pi\) | ||||
0.586239 | + | 0.810138i | \(0.300608\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.05934e112 | 0.198273 | ||||||||
\(356\) | −1.63773e113 | −0.472842 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.27725e113 | −0.287396 | ||||||||
\(359\) | 5.91157e113 | 1.17490 | 0.587448 | − | 0.809262i | \(-0.300133\pi\) | ||||
0.587448 | + | 0.809262i | \(0.300133\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.23201e113 | 0.812078 | ||||||||
\(362\) | −5.65094e113 | −0.775514 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.21137e113 | 0.130097 | ||||||||
\(365\) | −1.78768e113 | −0.169925 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.85230e113 | −0.212596 | −0.106298 | − | 0.994334i | \(-0.533900\pi\) | ||||
−0.106298 | + | 0.994334i | \(0.533900\pi\) | |||||||
\(368\) | −5.69203e113 | −0.375871 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.98657e113 | 0.310600 | ||||||||
\(371\) | −9.34417e113 | −0.429934 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.52146e114 | 1.63770 | 0.818852 | − | 0.574005i | \(-0.194611\pi\) | ||||
0.818852 | + | 0.574005i | \(0.194611\pi\) | |||||||
\(374\) | 3.80528e113 | 0.122349 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −9.72487e113 | −0.246618 | ||||||||
\(377\) | 1.17824e114 | 0.265488 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.92623e113 | 0.176742 | 0.0883709 | − | 0.996088i | \(-0.471834\pi\) | ||||
0.0883709 | + | 0.996088i | \(0.471834\pi\) | |||||||
\(380\) | −1.51855e114 | −0.240468 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.15041e114 | 0.394955 | ||||||||
\(383\) | 1.05705e115 | 1.17964 | 0.589821 | − | 0.807534i | \(-0.299198\pi\) | ||||
0.589821 | + | 0.807534i | \(0.299198\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.73604e113 | 0.0330680 | ||||||||
\(386\) | −5.55110e114 | −0.437768 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.44412e115 | −0.904881 | ||||||||
\(389\) | 2.17710e114 | 0.121653 | 0.0608263 | − | 0.998148i | \(-0.480626\pi\) | ||||
0.0608263 | + | 0.998148i | \(0.480626\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.29738e115 | −2.35611 | ||||||||
\(392\) | −1.84446e114 | −0.0732217 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.09775e115 | −0.347475 | ||||||||
\(395\) | 1.52965e114 | 0.0432535 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.00607e113 | 0.00904776 | 0.00452388 | − | 0.999990i | \(-0.498560\pi\) | ||||
0.00452388 | + | 0.999990i | \(0.498560\pi\) | |||||||
\(398\) | −1.78539e114 | −0.0360526 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.56963e115 | 0.253587 | ||||||||
\(401\) | −6.23287e114 | −0.0901080 | −0.0450540 | − | 0.998985i | \(-0.514346\pi\) | ||||
−0.0450540 | + | 0.998985i | \(0.514346\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.34806e115 | 0.387899 | ||||||||
\(404\) | 1.86368e115 | 0.193376 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.87514e115 | 0.655918 | ||||||||
\(407\) | −1.40763e115 | −0.105084 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.55225e115 | −0.393281 | −0.196641 | − | 0.980476i | \(-0.563003\pi\) | ||||
−0.196641 | + | 0.980476i | \(0.563003\pi\) | |||||||
\(410\) | −6.32248e114 | −0.0340413 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.16969e116 | 0.507158 | ||||||||
\(413\) | 6.72523e115 | 0.261776 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.05717e116 | 0.331898 | ||||||||
\(416\) | 8.55948e115 | 0.241432 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.91029e115 | −0.0890972 | ||||||||
\(419\) | −3.38221e116 | −0.692909 | −0.346454 | − | 0.938067i | \(-0.612614\pi\) | ||||
−0.346454 | + | 0.938067i | \(0.612614\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.60301e116 | 1.26018 | 0.630090 | − | 0.776522i | \(-0.283018\pi\) | ||||
0.630090 | + | 0.776522i | \(0.283018\pi\) | |||||||
\(422\) | 1.49863e116 | 0.223507 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −3.93731e116 | −0.475794 | ||||||||
\(425\) | 1.46080e117 | 1.58959 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.43410e116 | 0.656430 | ||||||||
\(428\) | 1.50137e115 | 0.0119465 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.25454e116 | −0.275110 | ||||||||
\(431\) | −1.02975e117 | −0.600470 | −0.300235 | − | 0.953865i | \(-0.597065\pi\) | ||||
−0.300235 | + | 0.953865i | \(0.597065\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.72587e117 | 1.29358 | 0.646791 | − | 0.762668i | \(-0.276111\pi\) | ||||
0.646791 | + | 0.762668i | \(0.276111\pi\) | |||||||
\(434\) | 2.23777e117 | 0.958348 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.86823e116 | 0.309519 | ||||||||
\(437\) | 5.44356e117 | 1.71577 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.39464e117 | −1.38769 | −0.693843 | − | 0.720126i | \(-0.744084\pi\) | ||||
−0.693843 | + | 0.720126i | \(0.744084\pi\) | |||||||
\(440\) | 1.57424e116 | 0.0365953 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.98676e117 | −0.377446 | ||||||||
\(443\) | −5.69469e117 | −0.978372 | −0.489186 | − | 0.872179i | \(-0.662706\pi\) | ||||
−0.489186 | + | 0.872179i | \(0.662706\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.63714e117 | 0.370777 | ||||||||
\(446\) | 1.00869e118 | 1.28339 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 8.45071e117 | 0.881093 | ||||||||
\(449\) | 1.50535e118 | 1.42126 | 0.710631 | − | 0.703565i | \(-0.248410\pi\) | ||||
0.710631 | + | 0.703565i | \(0.248410\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.48661e116 | 0.0115170 | ||||||||
\(452\) | −3.00710e117 | −0.211100 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −7.86805e117 | −0.453818 | ||||||||
\(455\) | −1.95061e117 | −0.102015 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.94233e118 | 1.26596 | 0.632980 | − | 0.774168i | \(-0.281831\pi\) | ||||
0.632980 | + | 0.774168i | \(0.281831\pi\) | |||||||
\(458\) | −1.25573e118 | −0.490211 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −7.08050e117 | −0.227688 | ||||||||
\(461\) | −1.09403e117 | −0.0319402 | −0.0159701 | − | 0.999872i | \(-0.505084\pi\) | ||||
−0.0159701 | + | 0.999872i | \(0.505084\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.51518e118 | −0.364847 | −0.182423 | − | 0.983220i | \(-0.558394\pi\) | ||||
−0.182423 | + | 0.983220i | \(0.558394\pi\) | |||||||
\(464\) | 1.26725e118 | 0.277211 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.85788e118 | 0.877553 | ||||||||
\(467\) | 8.24498e118 | 1.35391 | 0.676953 | − | 0.736026i | \(-0.263300\pi\) | ||||
0.676953 | + | 0.736026i | \(0.263300\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.74887e118 | 0.373219 | ||||||||
\(470\) | 5.05936e117 | 0.0624799 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.83378e118 | 0.289699 | ||||||||
\(473\) | 1.00038e118 | 0.0930770 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.50111e119 | −1.15757 | ||||||||
\(476\) | 1.21255e119 | 0.851509 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.49899e119 | 0.873487 | ||||||||
\(479\) | 3.05065e119 | 1.61980 | 0.809900 | − | 0.586567i | \(-0.199521\pi\) | ||||
0.809900 | + | 0.586567i | \(0.199521\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.34932e118 | 0.324184 | ||||||||
\(482\) | 2.81698e119 | 1.13290 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.41498e119 | 0.473294 | ||||||||
\(485\) | 2.32539e119 | 0.709558 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.88865e118 | −0.0479857 | −0.0239929 | − | 0.999712i | \(-0.507638\pi\) | ||||
−0.0239929 | + | 0.999712i | \(0.507638\pi\) | |||||||
\(488\) | 3.13247e119 | 0.726449 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 9.59580e117 | 0.0185505 | ||||||||
\(491\) | 7.35262e119 | 1.29812 | 0.649061 | − | 0.760736i | \(-0.275162\pi\) | ||||
0.649061 | + | 0.760736i | \(0.275162\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.17938e120 | 1.73767 | ||||||||
\(494\) | 2.04159e119 | 0.274865 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.60097e119 | 0.405028 | ||||||||
\(497\) | 4.97186e119 | 0.511281 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.88248e120 | 1.61903 | 0.809515 | − | 0.587099i | \(-0.199730\pi\) | ||||
0.809515 | + | 0.587099i | \(0.199730\pi\) | |||||||
\(500\) | 4.22308e119 | 0.332250 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.86420e119 | −0.122794 | ||||||||
\(503\) | 2.65462e119 | 0.160039 | 0.0800197 | − | 0.996793i | \(-0.474502\pi\) | ||||
0.0800197 | + | 0.996793i | \(0.474502\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.00099e119 | −0.151635 | ||||||||
\(506\) | −1.82324e119 | −0.0843619 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.01175e120 | 0.392769 | ||||||||
\(509\) | 3.57212e120 | 1.27053 | 0.635265 | − | 0.772294i | \(-0.280891\pi\) | ||||
0.635265 | + | 0.772294i | \(0.280891\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.46684e120 | −0.438179 | ||||||||
\(512\) | 2.07082e120 | 0.567059 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.66962e120 | 1.07503 | ||||||||
\(515\) | −1.88348e120 | −0.397685 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.18961e119 | −0.0211386 | ||||||||
\(518\) | 4.91214e120 | 0.800934 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.21919e119 | −0.112896 | ||||||||
\(521\) | −9.79424e119 | −0.123507 | −0.0617535 | − | 0.998091i | \(-0.519669\pi\) | ||||
−0.0617535 | + | 0.998091i | \(0.519669\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.44190e120 | 0.153324 | 0.0766618 | − | 0.997057i | \(-0.475574\pi\) | ||||
0.0766618 | + | 0.997057i | \(0.475574\pi\) | |||||||
\(524\) | −6.53965e120 | −0.638722 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.65164e121 | −1.36160 | ||||||||
\(527\) | 3.35130e121 | 2.53887 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.75813e120 | 0.624582 | ||||||||
\(530\) | 2.04838e120 | 0.120541 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.24601e121 | −0.620088 | ||||||||
\(533\) | −7.76170e119 | −0.0355301 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.41757e119 | −0.00936778 | ||||||||
\(536\) | 1.15828e121 | 0.413029 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.81197e120 | −0.236020 | ||||||||
\(539\) | −2.25627e119 | −0.00627612 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.32756e121 | −0.784960 | −0.392480 | − | 0.919761i | \(-0.628383\pi\) | ||||
−0.392480 | + | 0.919761i | \(0.628383\pi\) | |||||||
\(542\) | 3.63076e120 | 0.0788913 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 8.56777e121 | 1.58022 | ||||||||
\(545\) | −1.42800e121 | −0.242708 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.03429e121 | 1.16014 | 0.580072 | − | 0.814565i | \(-0.303025\pi\) | ||||
0.580072 | + | 0.814565i | \(0.303025\pi\) | |||||||
\(548\) | 4.44201e119 | 0.00591351 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 5.02776e120 | 0.0569161 | ||||||||
\(551\) | −1.21193e122 | −1.26541 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.25512e121 | 0.111536 | ||||||||
\(554\) | −1.13404e122 | −0.929915 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.49070e121 | −0.383530 | ||||||||
\(557\) | −4.95449e121 | −0.319479 | −0.159740 | − | 0.987159i | \(-0.551065\pi\) | ||||
−0.159740 | + | 0.987159i | \(0.551065\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.22303e121 | −0.287142 | ||||||||
\(560\) | −2.09796e121 | −0.106520 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.97562e121 | 0.172242 | ||||||||
\(563\) | 1.54057e122 | 0.616679 | 0.308340 | − | 0.951276i | \(-0.400227\pi\) | ||||
0.308340 | + | 0.951276i | \(0.400227\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.84217e121 | 0.165533 | ||||||||
\(566\) | 1.03210e122 | 0.326129 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.09497e122 | 0.565818 | ||||||||
\(569\) | 5.08576e121 | 0.127017 | 0.0635083 | − | 0.997981i | \(-0.479771\pi\) | ||||
0.0635083 | + | 0.997981i | \(0.479771\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.07440e122 | −1.29777 | −0.648883 | − | 0.760888i | \(-0.724764\pi\) | ||||
−0.648883 | + | 0.760888i | \(0.724764\pi\) | |||||||
\(572\) | 6.24394e120 | 0.0123406 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.18777e121 | −0.0877811 | ||||||||
\(575\) | −6.99922e122 | −1.09605 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.97444e122 | −1.33834 | −0.669168 | − | 0.743111i | \(-0.733349\pi\) | ||||
−0.669168 | + | 0.743111i | \(0.733349\pi\) | |||||||
\(578\) | −1.40669e123 | −1.74747 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.57637e122 | 0.167924 | ||||||||
\(581\) | 8.67438e122 | 0.855856 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.81638e121 | −0.0407822 | ||||||||
\(584\) | −6.18074e122 | −0.484919 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.45061e123 | −0.977479 | ||||||||
\(587\) | −3.03625e123 | −1.89645 | −0.948226 | − | 0.317595i | \(-0.897125\pi\) | ||||
−0.948226 | + | 0.317595i | \(0.897125\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.44378e123 | −1.84886 | ||||||||
\(590\) | −1.47427e122 | −0.0733945 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 7.90449e122 | 0.338499 | ||||||||
\(593\) | −3.31837e123 | −1.31823 | −0.659114 | − | 0.752043i | \(-0.729069\pi\) | ||||
−0.659114 | + | 0.752043i | \(0.729069\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.95250e123 | −0.667707 | ||||||||
\(596\) | −1.97746e123 | −0.627550 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.51927e122 | 0.260256 | ||||||||
\(599\) | 4.88132e123 | 1.23892 | 0.619460 | − | 0.785028i | \(-0.287352\pi\) | ||||
0.619460 | + | 0.785028i | \(0.287352\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.45254e123 | 1.41194 | 0.705970 | − | 0.708241i | \(-0.250511\pi\) | ||||
0.705970 | + | 0.708241i | \(0.250511\pi\) | |||||||
\(602\) | −3.49097e123 | −0.709418 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.64326e123 | 0.463443 | ||||||||
\(605\) | −2.27846e123 | −0.371132 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.71680e123 | −0.522724 | −0.261362 | − | 0.965241i | \(-0.584172\pi\) | ||||
−0.261362 | + | 0.965241i | \(0.584172\pi\) | |||||||
\(608\) | −8.80421e123 | −1.15075 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.62967e123 | −0.184044 | ||||||||
\(611\) | 6.21104e122 | 0.0652125 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.51871e123 | −0.228658 | −0.114329 | − | 0.993443i | \(-0.536472\pi\) | ||||
−0.114329 | + | 0.993443i | \(0.536472\pi\) | |||||||
\(614\) | 9.51327e123 | 0.803225 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.29170e123 | 0.0943672 | ||||||||
\(617\) | −1.46315e124 | −0.994484 | −0.497242 | − | 0.867612i | \(-0.665654\pi\) | ||||
−0.497242 | + | 0.867612i | \(0.665654\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.24631e123 | 0.426465 | 0.213232 | − | 0.977002i | \(-0.431601\pi\) | ||||
0.213232 | + | 0.977002i | \(0.431601\pi\) | |||||||
\(620\) | 4.47936e123 | 0.245350 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.96660e124 | −0.933350 | ||||||||
\(623\) | 2.16385e124 | 0.956111 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.56448e124 | 0.599391 | ||||||||
\(626\) | −7.39697e123 | −0.263935 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.36187e124 | 0.731227 | ||||||||
\(629\) | 7.35644e124 | 2.12185 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.53146e124 | −1.13483 | −0.567416 | − | 0.823431i | \(-0.692057\pi\) | ||||
−0.567416 | + | 0.823431i | \(0.692057\pi\) | |||||||
\(632\) | 5.28863e123 | 0.123434 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.57247e124 | 0.724430 | ||||||||
\(635\) | −1.62916e124 | −0.307988 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.17801e123 | 0.0193618 | ||||||||
\(638\) | 4.05918e123 | 0.0622183 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 5.46777e123 | 0.0729124 | ||||||||
\(641\) | 7.56055e124 | 0.940526 | 0.470263 | − | 0.882526i | \(-0.344159\pi\) | ||||
0.470263 | + | 0.882526i | \(0.344159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.06237e124 | −0.439937 | −0.219969 | − | 0.975507i | \(-0.570596\pi\) | ||||
−0.219969 | + | 0.975507i | \(0.570596\pi\) | |||||||
\(644\) | −5.80974e124 | −0.587132 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.04356e125 | 1.79904 | ||||||||
\(647\) | −7.70585e124 | −0.633257 | −0.316629 | − | 0.948550i | \(-0.602551\pi\) | ||||
−0.316629 | + | 0.948550i | \(0.602551\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.46647e123 | 0.0248313 | ||||||||
\(650\) | −2.62503e124 | −0.175586 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.43828e124 | −0.142255 | ||||||||
\(653\) | 2.83307e125 | 1.54391 | 0.771954 | − | 0.635678i | \(-0.219279\pi\) | ||||
0.771954 | + | 0.635678i | \(0.219279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.05304e125 | 0.500851 | ||||||||
\(656\) | −8.34801e123 | −0.0370990 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.15134e124 | 0.161115 | ||||||||
\(659\) | 3.52918e125 | 1.28018 | 0.640092 | − | 0.768298i | \(-0.278896\pi\) | ||||
0.640092 | + | 0.768298i | \(0.278896\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.91190e125 | −0.606037 | −0.303019 | − | 0.952985i | \(-0.597994\pi\) | ||||
−0.303019 | + | 0.952985i | \(0.597994\pi\) | |||||||
\(662\) | −1.16797e124 | −0.0346139 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.65508e125 | 0.947148 | ||||||||
\(665\) | 2.00638e125 | 0.486239 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.65084e125 | −1.19816 | ||||||||
\(668\) | −7.62998e124 | −0.151346 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.02594e124 | −0.104640 | ||||||||
\(671\) | 3.83185e124 | 0.0622668 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.51200e125 | −0.926924 | −0.463462 | − | 0.886117i | \(-0.653393\pi\) | ||||
−0.463462 | + | 0.886117i | \(0.653393\pi\) | |||||||
\(674\) | 2.36971e125 | 0.315740 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3.76109e125 | 0.439224 | ||||||||
\(677\) | 7.27595e125 | 0.795599 | 0.397799 | − | 0.917472i | \(-0.369774\pi\) | ||||
0.397799 | + | 0.917472i | \(0.369774\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.90804e126 | 1.82971 | ||||||||
\(680\) | −8.22715e125 | −0.738930 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.15344e125 | 0.0909059 | ||||||||
\(683\) | 2.25576e126 | 1.66560 | 0.832802 | − | 0.553571i | \(-0.186735\pi\) | ||||
0.832802 | + | 0.553571i | \(0.186735\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7.15274e123 | −0.00463705 | ||||||||
\(686\) | 1.22723e126 | 0.745597 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.61757e125 | −0.299822 | ||||||||
\(689\) | 2.51467e125 | 0.125813 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.57630e125 | 0.421138 | 0.210569 | − | 0.977579i | \(-0.432468\pi\) | ||||
0.210569 | + | 0.977579i | \(0.432468\pi\) | |||||||
\(692\) | −8.49267e125 | −0.350205 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.72725e126 | 0.989075 | ||||||||
\(695\) | 8.84137e125 | 0.300743 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.76921e125 | −0.232551 | ||||||||
\(698\) | −2.74264e126 | −0.770199 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.60209e126 | 0.396118 | ||||||||
\(701\) | −7.40940e126 | −1.71922 | −0.859610 | − | 0.510951i | \(-0.829293\pi\) | ||||
−0.859610 | + | 0.510951i | \(0.829293\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.55945e126 | −1.54518 | ||||||||
\(704\) | 4.35586e125 | 0.0835777 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.01237e126 | −0.847683 | ||||||||
\(707\) | −2.46239e126 | −0.391015 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.85411e126 | 0.819792 | 0.409896 | − | 0.912132i | \(-0.365565\pi\) | ||||
0.409896 | + | 0.912132i | \(0.365565\pi\) | |||||||
\(710\) | −1.08991e126 | −0.143348 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.11770e126 | 1.05810 | ||||||||
\(713\) | −1.60573e127 | −1.75060 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.00543e125 | −0.00967680 | ||||||||
\(716\) | −2.09782e126 | −0.189731 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.06332e127 | −0.849431 | ||||||||
\(719\) | 8.16889e126 | 0.613377 | 0.306689 | − | 0.951810i | \(-0.400779\pi\) | ||||
0.306689 | + | 0.951810i | \(0.400779\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.54545e127 | −1.02550 | ||||||||
\(722\) | −9.41091e126 | −0.587119 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.28141e126 | −0.511974 | ||||||||
\(725\) | 1.55827e127 | 0.808356 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.60710e127 | −1.65530 | −0.827651 | − | 0.561243i | \(-0.810323\pi\) | ||||
−0.827651 | + | 0.561243i | \(0.810323\pi\) | |||||||
\(728\) | −6.74407e126 | −0.291122 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 3.21553e126 | 0.122853 | ||||||||
\(731\) | −5.22809e127 | −1.87940 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.35200e127 | −0.430377 | −0.215188 | − | 0.976573i | \(-0.569037\pi\) | ||||
−0.215188 | + | 0.976573i | \(0.569037\pi\) | |||||||
\(734\) | 5.13048e126 | 0.153703 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.10512e127 | −1.08959 | ||||||||
\(737\) | 1.41689e126 | 0.0354023 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.74269e127 | 0.607434 | 0.303717 | − | 0.952762i | \(-0.401772\pi\) | ||||
0.303717 | + | 0.952762i | \(0.401772\pi\) | |||||||
\(740\) | 9.83265e126 | 0.205050 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.68075e127 | 0.310835 | ||||||||
\(743\) | 3.00345e126 | 0.0523139 | 0.0261570 | − | 0.999658i | \(-0.491673\pi\) | ||||
0.0261570 | + | 0.999658i | \(0.491673\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.18419e127 | 0.492091 | ||||||||
\(746\) | −8.13283e127 | −1.18403 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 6.24998e126 | 0.0807714 | ||||||||
\(749\) | −1.98369e126 | −0.0241564 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.58766e127 | 0.820599 | 0.410299 | − | 0.911951i | \(-0.365424\pi\) | ||||
0.410299 | + | 0.911951i | \(0.365424\pi\) | |||||||
\(752\) | 6.68022e126 | 0.0680922 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.11933e127 | −0.191943 | ||||||||
\(755\) | −4.25630e127 | −0.363407 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.94772e128 | 1.47829 | 0.739145 | − | 0.673546i | \(-0.235230\pi\) | ||||
0.739145 | + | 0.673546i | \(0.235230\pi\) | |||||||
\(758\) | −1.78545e127 | −0.127782 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.45419e127 | 0.538105 | ||||||||
\(761\) | 9.33020e127 | 0.560111 | 0.280055 | − | 0.959984i | \(-0.409647\pi\) | ||||
0.280055 | + | 0.959984i | \(0.409647\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.17171e128 | −0.625864 | ||||||||
\(764\) | 5.17440e127 | 0.260739 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.90134e128 | −0.852861 | ||||||||
\(767\) | −1.80987e127 | −0.0766043 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.54824e127 | 0.0583602 | 0.0291801 | − | 0.999574i | \(-0.490710\pi\) | ||||
0.0291801 | + | 0.999574i | \(0.490710\pi\) | |||||||
\(770\) | −6.72008e126 | −0.0239077 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −9.11742e127 | −0.289003 | ||||||||
\(773\) | 5.49356e127 | 0.164387 | 0.0821933 | − | 0.996616i | \(-0.473808\pi\) | ||||
0.0821933 | + | 0.996616i | \(0.473808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.42794e128 | 1.18107 | ||||||||
\(776\) | 8.03983e128 | 2.02489 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −3.91599e127 | −0.0879528 | ||||||||
\(779\) | 7.98361e127 | 0.169349 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.56271e127 | 0.0484985 | ||||||||
\(782\) | 9.52849e128 | 1.70343 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 1.26700e127 | 0.0202168 | ||||||||
\(785\) | −3.80319e128 | −0.573388 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3.53123e128 | −0.475391 | −0.237695 | − | 0.971340i | \(-0.576392\pi\) | ||||
−0.237695 | + | 0.971340i | \(0.576392\pi\) | |||||||
\(788\) | −1.80301e128 | −0.229393 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.75141e127 | −0.0312716 | ||||||||
\(791\) | 3.97313e128 | 0.426854 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.00064e128 | −0.192093 | ||||||||
\(794\) | −7.20579e126 | −0.00654138 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.93242e127 | −0.0238010 | ||||||||
\(797\) | 7.97738e127 | 0.0612301 | 0.0306151 | − | 0.999531i | \(-0.490253\pi\) | ||||
0.0306151 | + | 0.999531i | \(0.490253\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.21706e128 | 0.426828 | ||||||||
\(800\) | 1.13203e129 | 0.735110 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.12112e128 | 0.0651466 | ||||||||
\(803\) | −7.56070e127 | −0.0415643 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 9.35511e128 | 0.460397 | ||||||||
\(806\) | −6.02221e128 | −0.280444 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.03757e129 | −0.432724 | ||||||||
\(809\) | −1.78703e129 | −0.705379 | −0.352690 | − | 0.935740i | \(-0.614733\pi\) | ||||
−0.352690 | + | 0.935740i | \(0.614733\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.09543e129 | 0.387396 | 0.193698 | − | 0.981061i | \(-0.437952\pi\) | ||||
0.193698 | + | 0.981061i | \(0.437952\pi\) | |||||||
\(812\) | 1.29345e129 | 0.433020 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.53193e128 | 0.0759740 | ||||||||
\(815\) | 3.92624e128 | 0.111548 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.37236e129 | 1.36862 | ||||||||
\(818\) | 1.17857e129 | 0.284336 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.03844e128 | −0.0224731 | ||||||||
\(821\) | 3.64821e129 | 0.747840 | 0.373920 | − | 0.927461i | \(-0.378013\pi\) | ||||
0.373920 | + | 0.927461i | \(0.378013\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.97364e129 | 0.730964 | 0.365482 | − | 0.930818i | \(-0.380904\pi\) | ||||
0.365482 | + | 0.930818i | \(0.380904\pi\) | |||||||
\(824\) | −6.51198e129 | −1.13489 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.20968e129 | −0.189260 | ||||||||
\(827\) | 5.47831e129 | 0.812178 | 0.406089 | − | 0.913834i | \(-0.366892\pi\) | ||||
0.406089 | + | 0.913834i | \(0.366892\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.19299e130 | −1.58840 | −0.794199 | − | 0.607658i | \(-0.792109\pi\) | ||||
−0.794199 | + | 0.607658i | \(0.792109\pi\) | |||||||
\(830\) | −1.90155e129 | −0.239957 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.27422e129 | −0.257837 | ||||||||
\(833\) | 1.17916e129 | 0.126727 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.22861e129 | 0.118677 | ||||||||
\(836\) | −6.42246e128 | −0.0588196 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.08364e129 | 0.500962 | ||||||||
\(839\) | 9.99439e129 | 0.780457 | 0.390228 | − | 0.920718i | \(-0.372396\pi\) | ||||
0.390228 | + | 0.920718i | \(0.372396\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.65633e129 | −0.116339 | ||||||||
\(842\) | −1.36757e130 | −0.911089 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.46143e129 | 0.147553 | ||||||||
\(845\) | −6.05628e129 | −0.344415 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.86954e130 | −0.957025 | ||||||||
\(848\) | 2.70462e129 | 0.131369 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.62757e130 | −1.14924 | ||||||||
\(851\) | −3.52473e130 | −1.46305 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.76906e130 | 0.661470 | 0.330735 | − | 0.943724i | \(-0.392703\pi\) | ||||
0.330735 | + | 0.943724i | \(0.392703\pi\) | |||||||
\(854\) | −1.33719e130 | −0.474588 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.35856e128 | −0.0267331 | ||||||||
\(857\) | −4.47933e130 | −1.36009 | −0.680044 | − | 0.733171i | \(-0.738039\pi\) | ||||
−0.680044 | + | 0.733171i | \(0.738039\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −4.95328e130 | −1.35580 | −0.677902 | − | 0.735152i | \(-0.737111\pi\) | ||||
−0.677902 | + | 0.735152i | \(0.737111\pi\) | |||||||
\(860\) | −6.98789e129 | −0.181620 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.85222e130 | 0.434130 | ||||||||
\(863\) | −2.69455e129 | −0.0599798 | −0.0299899 | − | 0.999550i | \(-0.509548\pi\) | ||||
−0.0299899 | + | 0.999550i | \(0.509548\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.36753e130 | 0.274612 | ||||||||
\(866\) | −4.90307e130 | −0.935238 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.67544e130 | 0.632676 | ||||||||
\(869\) | 6.46941e128 | 0.0105800 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.39766e129 | −0.109216 | ||||||||
\(872\) | −4.93720e130 | −0.692623 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −9.79144e130 | −1.24047 | ||||||||
\(875\) | −5.57975e130 | −0.671826 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.89651e130 | 0.315060 | 0.157530 | − | 0.987514i | \(-0.449647\pi\) | ||||
0.157530 | + | 0.987514i | \(0.449647\pi\) | |||||||
\(878\) | 9.70344e130 | 1.00327 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.08138e129 | −0.0101041 | ||||||||
\(881\) | 1.34623e131 | 1.19589 | 0.597944 | − | 0.801538i | \(-0.295985\pi\) | ||||
0.597944 | + | 0.801538i | \(0.295985\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.82317e130 | −0.708554 | −0.354277 | − | 0.935140i | \(-0.615273\pi\) | ||||
−0.354277 | + | 0.935140i | \(0.615273\pi\) | |||||||
\(884\) | −3.26316e130 | −0.249180 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.02431e131 | 0.707347 | ||||||||
\(887\) | 8.56098e130 | 0.562241 | 0.281120 | − | 0.959673i | \(-0.409294\pi\) | ||||
0.281120 | + | 0.959673i | \(0.409294\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.33677e131 | −0.794199 | ||||||||
\(890\) | −4.74348e130 | −0.268066 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.65673e131 | 0.847259 | ||||||||
\(893\) | −6.38863e130 | −0.310826 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.37800e130 | 0.148777 | ||||||||
\(896\) | 4.48645e130 | 0.188017 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.70769e131 | −1.02755 | ||||||||
\(899\) | 3.57491e131 | 1.29110 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.51710e131 | 0.823470 | ||||||||
\(902\) | −2.67400e129 | −0.00832664 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.67414e131 | 0.472386 | ||||||||
\(905\) | 1.49453e131 | 0.401462 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5.43134e131 | 1.32246 | 0.661230 | − | 0.750184i | \(-0.270035\pi\) | ||||
0.661230 | + | 0.750184i | \(0.270035\pi\) | |||||||
\(908\) | −1.29229e131 | −0.299598 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 3.50860e130 | 0.0737550 | ||||||||
\(911\) | 6.55369e131 | 1.31195 | 0.655976 | − | 0.754782i | \(-0.272257\pi\) | ||||
0.655976 | + | 0.754782i | \(0.272257\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4.47114e130 | 0.0811837 | ||||||||
\(914\) | −5.29242e131 | −0.915269 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.06248e131 | −0.323624 | ||||||||
\(917\) | 8.64052e131 | 1.29153 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.69672e131 | 0.501506 | 0.250753 | − | 0.968051i | \(-0.419322\pi\) | ||||
0.250753 | + | 0.968051i | \(0.419322\pi\) | |||||||
\(920\) | 3.94192e131 | 0.509506 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.96785e130 | 0.0230922 | ||||||||
\(923\) | −1.33801e131 | −0.149618 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.71978e131 | 0.987073 | ||||||||
\(926\) | 2.72539e131 | 0.263778 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.13946e131 | 0.803592 | ||||||||
\(929\) | −2.08057e131 | −0.174375 | −0.0871873 | − | 0.996192i | \(-0.527788\pi\) | ||||
−0.0871873 | + | 0.996192i | \(0.527788\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.21170e131 | −0.0922853 | ||||||||
\(932\) | 7.97883e131 | 0.579337 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.48304e132 | −0.978852 | ||||||||
\(935\) | −1.00640e131 | −0.0633366 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.38597e132 | −0.793124 | −0.396562 | − | 0.918008i | \(-0.629797\pi\) | ||||
−0.396562 | + | 0.918008i | \(0.629797\pi\) | |||||||
\(938\) | −4.94445e131 | −0.269831 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.30975e130 | 0.0412476 | ||||||||
\(941\) | −1.36215e132 | −0.644890 | −0.322445 | − | 0.946588i | \(-0.604505\pi\) | ||||
−0.322445 | + | 0.946588i | \(0.604505\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.72250e131 | 0.160349 | ||||||||
\(944\) | −1.94659e131 | −0.0799871 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.79939e131 | −0.0672931 | ||||||||
\(947\) | −1.23478e130 | −0.00440572 | −0.00220286 | − | 0.999998i | \(-0.500701\pi\) | ||||
−0.00220286 | + | 0.999998i | \(0.500701\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.94749e131 | 0.128226 | ||||||||
\(950\) | 2.70008e132 | 0.836906 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.75060e132 | −1.90545 | ||||||||
\(953\) | 2.21160e130 | 0.00595762 | 0.00297881 | − | 0.999996i | \(-0.499052\pi\) | ||||
0.00297881 | + | 0.999996i | \(0.499052\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.33206e131 | −0.204457 | ||||||||
\(956\) | 2.46201e132 | 0.576652 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −5.48726e132 | −1.17109 | ||||||||
\(959\) | −5.86901e130 | −0.0119574 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.77330e132 | 0.886396 | ||||||||
\(962\) | −1.32194e132 | −0.234380 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.62675e132 | 0.747908 | ||||||||
\(965\) | 1.46813e132 | 0.226620 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.28780e133 | 1.81288 | 0.906440 | − | 0.422334i | \(-0.138789\pi\) | ||||
0.906440 | + | 0.422334i | \(0.138789\pi\) | |||||||
\(968\) | −7.87760e132 | −1.05911 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −4.18272e132 | −0.512999 | ||||||||
\(971\) | −1.86631e132 | −0.218639 | −0.109320 | − | 0.994007i | \(-0.534867\pi\) | ||||
−0.109320 | + | 0.994007i | \(0.534867\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.25459e132 | 0.775517 | ||||||||
\(974\) | 3.39715e131 | 0.0346929 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.15176e132 | −0.200575 | ||||||||
\(977\) | −1.65586e133 | −1.47474 | −0.737370 | − | 0.675489i | \(-0.763933\pi\) | ||||
−0.737370 | + | 0.675489i | \(0.763933\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.11534e132 | 0.0906937 | ||||||||
\(980\) | 1.57606e131 | 0.0122465 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.32253e133 | −0.938522 | ||||||||
\(983\) | −2.57060e133 | −1.74342 | −0.871711 | − | 0.490021i | \(-0.836989\pi\) | ||||
−0.871711 | + | 0.490021i | \(0.836989\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.90329e132 | 0.179878 | ||||||||
\(986\) | −2.12138e133 | −1.25631 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.35321e132 | 0.181458 | ||||||||
\(989\) | 2.50496e133 | 1.29588 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.75768e133 | −1.30397 | −0.651984 | − | 0.758233i | \(-0.726063\pi\) | ||||
−0.651984 | + | 0.758233i | \(0.726063\pi\) | |||||||
\(992\) | 2.59704e133 | 1.17411 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −8.94297e132 | −0.369648 | ||||||||
\(995\) | 4.72192e131 | 0.0186634 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.36932e133 | 1.21789 | 0.608945 | − | 0.793213i | \(-0.291593\pi\) | ||||
0.608945 | + | 0.793213i | \(0.291593\pi\) | |||||||
\(998\) | −3.38604e133 | −1.17053 | ||||||||
\(999\) | 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 | 9.90.a.b.1.3 | 7 | ||
3.2 | odd | 2 | 1.90.a.a.1.5 | ✓ | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.90.a.a.1.5 | ✓ | 7 | 3.2 | odd | 2 | ||
9.90.a.b.1.3 | 7 | 1.1 | even | 1 | trivial |