Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,106,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 106, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 106);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 106 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(69.8187388595\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{7} + \cdots + 48\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | multiple of \( 2^{111}\cdot 3^{44}\cdot 5^{13}\cdot 7^{7}\cdot 11\cdot 13^{3}\cdot 17 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(4.91848e13\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.93573e15 | 0.931964 | 0.465982 | − | 0.884794i | \(-0.345701\pi\) | ||||
0.465982 | + | 0.884794i | \(0.345701\pi\) | |||||||
\(3\) | 1.55541e25 | 1.38988 | 0.694942 | − | 0.719066i | \(-0.255430\pi\) | ||||
0.694942 | + | 0.719066i | \(0.255430\pi\) | |||||||
\(4\) | −5.33194e30 | −0.131443 | ||||||||
\(5\) | 1.46253e36 | 0.294564 | 0.147282 | − | 0.989095i | \(-0.452947\pi\) | ||||
0.147282 | + | 0.989095i | \(0.452947\pi\) | |||||||
\(6\) | 9.23248e40 | 1.29532 | ||||||||
\(7\) | 8.76445e43 | 0.375905 | 0.187952 | − | 0.982178i | \(-0.439815\pi\) | ||||
0.187952 | + | 0.982178i | \(0.439815\pi\) | |||||||
\(8\) | −2.72431e47 | −1.05446 | ||||||||
\(9\) | 1.16692e50 | 0.931775 | ||||||||
\(10\) | 8.68120e51 | 0.274524 | ||||||||
\(11\) | −7.28669e54 | −1.54673 | −0.773365 | − | 0.633961i | \(-0.781428\pi\) | ||||
−0.773365 | + | 0.633961i | \(0.781428\pi\) | |||||||
\(12\) | −8.29334e55 | −0.182690 | ||||||||
\(13\) | −4.19396e58 | −1.38229 | −0.691144 | − | 0.722717i | \(-0.742893\pi\) | ||||
−0.691144 | + | 0.722717i | \(0.742893\pi\) | |||||||
\(14\) | 5.20234e59 | 0.350330 | ||||||||
\(15\) | 2.27483e61 | 0.409410 | ||||||||
\(16\) | −1.40079e63 | −0.851280 | ||||||||
\(17\) | 8.65740e63 | 0.218182 | 0.109091 | − | 0.994032i | \(-0.465206\pi\) | ||||
0.109091 | + | 0.994032i | \(0.465206\pi\) | |||||||
\(18\) | 6.92655e65 | 0.868381 | ||||||||
\(19\) | −9.21112e66 | −0.675692 | −0.337846 | − | 0.941201i | \(-0.609698\pi\) | ||||
−0.337846 | + | 0.941201i | \(0.609698\pi\) | |||||||
\(20\) | −7.79814e66 | −0.0387183 | ||||||||
\(21\) | 1.36323e69 | 0.522463 | ||||||||
\(22\) | −4.32518e70 | −1.44150 | ||||||||
\(23\) | −1.62076e69 | −0.00523609 | −0.00261804 | − | 0.999997i | \(-0.500833\pi\) | ||||
−0.00261804 | + | 0.999997i | \(0.500833\pi\) | |||||||
\(24\) | −4.23741e72 | −1.46558 | ||||||||
\(25\) | −2.25129e73 | −0.913232 | ||||||||
\(26\) | −2.48942e74 | −1.28824 | ||||||||
\(27\) | −1.32898e74 | −0.0948246 | ||||||||
\(28\) | −4.67316e74 | −0.0494099 | ||||||||
\(29\) | 9.56136e76 | 1.60186 | 0.800931 | − | 0.598757i | \(-0.204338\pi\) | ||||
0.800931 | + | 0.598757i | \(0.204338\pi\) | |||||||
\(30\) | 1.35028e77 | 0.381556 | ||||||||
\(31\) | −1.52589e78 | −0.770967 | −0.385483 | − | 0.922715i | \(-0.625965\pi\) | ||||
−0.385483 | + | 0.922715i | \(0.625965\pi\) | |||||||
\(32\) | 2.73642e78 | 0.261101 | ||||||||
\(33\) | −1.13338e80 | −2.14977 | ||||||||
\(34\) | 5.13880e79 | 0.203338 | ||||||||
\(35\) | 1.28183e80 | 0.110728 | ||||||||
\(36\) | −6.22198e80 | −0.122475 | ||||||||
\(37\) | −2.78360e82 | −1.30022 | −0.650109 | − | 0.759841i | \(-0.725277\pi\) | ||||
−0.650109 | + | 0.759841i | \(0.725277\pi\) | |||||||
\(38\) | −5.46747e82 | −0.629721 | ||||||||
\(39\) | −6.52332e83 | −1.92122 | ||||||||
\(40\) | −3.98439e83 | −0.310608 | ||||||||
\(41\) | 5.59619e84 | 1.19327 | 0.596636 | − | 0.802512i | \(-0.296503\pi\) | ||||
0.596636 | + | 0.802512i | \(0.296503\pi\) | |||||||
\(42\) | 8.09176e84 | 0.486917 | ||||||||
\(43\) | 2.87167e84 | 0.0502389 | 0.0251195 | − | 0.999684i | \(-0.492003\pi\) | ||||
0.0251195 | + | 0.999684i | \(0.492003\pi\) | |||||||
\(44\) | 3.88522e85 | 0.203306 | ||||||||
\(45\) | 1.70667e86 | 0.274468 | ||||||||
\(46\) | −9.62038e84 | −0.00487985 | ||||||||
\(47\) | 8.04149e87 | 1.31886 | 0.659431 | − | 0.751765i | \(-0.270797\pi\) | ||||
0.659431 | + | 0.751765i | \(0.270797\pi\) | |||||||
\(48\) | −2.17879e88 | −1.18318 | ||||||||
\(49\) | −4.66803e88 | −0.858696 | ||||||||
\(50\) | −1.33630e89 | −0.851099 | ||||||||
\(51\) | 1.34658e89 | 0.303248 | ||||||||
\(52\) | 2.23620e89 | 0.181691 | ||||||||
\(53\) | 5.94866e90 | 1.77802 | 0.889008 | − | 0.457892i | \(-0.151395\pi\) | ||||
0.889008 | + | 0.457892i | \(0.151395\pi\) | |||||||
\(54\) | −7.88847e89 | −0.0883732 | ||||||||
\(55\) | −1.06570e91 | −0.455612 | ||||||||
\(56\) | −2.38771e91 | −0.396378 | ||||||||
\(57\) | −1.43271e92 | −0.939133 | ||||||||
\(58\) | 5.67537e92 | 1.49288 | ||||||||
\(59\) | −1.24710e93 | −1.33712 | −0.668559 | − | 0.743659i | \(-0.733089\pi\) | ||||
−0.668559 | + | 0.743659i | \(0.733089\pi\) | |||||||
\(60\) | −1.21293e92 | −0.0538139 | ||||||||
\(61\) | 3.83239e93 | 0.713927 | 0.356963 | − | 0.934118i | \(-0.383812\pi\) | ||||
0.356963 | + | 0.934118i | \(0.383812\pi\) | |||||||
\(62\) | −9.05730e93 | −0.718513 | ||||||||
\(63\) | 1.02275e94 | 0.350259 | ||||||||
\(64\) | 7.30653e94 | 1.09462 | ||||||||
\(65\) | −6.13380e94 | −0.407173 | ||||||||
\(66\) | −6.72742e95 | −2.00351 | ||||||||
\(67\) | −7.25169e95 | −0.980646 | −0.490323 | − | 0.871541i | \(-0.663121\pi\) | ||||
−0.490323 | + | 0.871541i | \(0.663121\pi\) | |||||||
\(68\) | −4.61608e94 | −0.0286784 | ||||||||
\(69\) | −2.52094e94 | −0.00727755 | ||||||||
\(70\) | 7.60859e95 | 0.103195 | ||||||||
\(71\) | −3.02377e96 | −0.194754 | −0.0973768 | − | 0.995248i | \(-0.531045\pi\) | ||||
−0.0973768 | + | 0.995248i | \(0.531045\pi\) | |||||||
\(72\) | −3.17906e97 | −0.982523 | ||||||||
\(73\) | −1.13078e98 | −1.69405 | −0.847026 | − | 0.531551i | \(-0.821609\pi\) | ||||
−0.847026 | + | 0.531551i | \(0.821609\pi\) | |||||||
\(74\) | −1.65227e98 | −1.21176 | ||||||||
\(75\) | −3.50167e98 | −1.26929 | ||||||||
\(76\) | 4.91132e97 | 0.0888146 | ||||||||
\(77\) | −6.38639e98 | −0.581423 | ||||||||
\(78\) | −3.87206e99 | −1.79051 | ||||||||
\(79\) | 1.66730e99 | 0.394994 | 0.197497 | − | 0.980303i | \(-0.436719\pi\) | ||||
0.197497 | + | 0.980303i | \(0.436719\pi\) | |||||||
\(80\) | −2.04869e99 | −0.250757 | ||||||||
\(81\) | −1.66813e100 | −1.06357 | ||||||||
\(82\) | 3.32175e100 | 1.11209 | ||||||||
\(83\) | −3.34613e100 | −0.592847 | −0.296423 | − | 0.955057i | \(-0.595794\pi\) | ||||
−0.296423 | + | 0.955057i | \(0.595794\pi\) | |||||||
\(84\) | −7.26866e99 | −0.0686739 | ||||||||
\(85\) | 1.26617e100 | 0.0642687 | ||||||||
\(86\) | 1.70454e100 | 0.0468209 | ||||||||
\(87\) | 1.48718e102 | 2.22640 | ||||||||
\(88\) | 1.98512e102 | 1.63097 | ||||||||
\(89\) | 3.73253e101 | 0.169445 | 0.0847224 | − | 0.996405i | \(-0.473000\pi\) | ||||
0.0847224 | + | 0.996405i | \(0.473000\pi\) | |||||||
\(90\) | 1.01303e102 | 0.255794 | ||||||||
\(91\) | −3.67578e102 | −0.519608 | ||||||||
\(92\) | 8.64179e99 | 0.000688245 0 | ||||||||
\(93\) | −2.37339e103 | −1.07155 | ||||||||
\(94\) | 4.77321e103 | 1.22913 | ||||||||
\(95\) | −1.34716e103 | −0.199035 | ||||||||
\(96\) | 4.25625e103 | 0.362900 | ||||||||
\(97\) | −2.81285e104 | −1.39197 | −0.695986 | − | 0.718055i | \(-0.745033\pi\) | ||||
−0.695986 | + | 0.718055i | \(0.745033\pi\) | |||||||
\(98\) | −2.77082e104 | −0.800274 | ||||||||
\(99\) | −8.50302e104 | −1.44120 | ||||||||
\(100\) | 1.20038e104 | 0.120038 | ||||||||
\(101\) | 2.44200e104 | 0.144835 | 0.0724175 | − | 0.997374i | \(-0.476929\pi\) | ||||
0.0724175 | + | 0.997374i | \(0.476929\pi\) | |||||||
\(102\) | 7.99293e104 | 0.282616 | ||||||||
\(103\) | −5.07710e105 | −1.07563 | −0.537814 | − | 0.843064i | \(-0.680750\pi\) | ||||
−0.537814 | + | 0.843064i | \(0.680750\pi\) | |||||||
\(104\) | 1.14256e106 | 1.45757 | ||||||||
\(105\) | 1.99377e105 | 0.153899 | ||||||||
\(106\) | 3.53096e106 | 1.65705 | ||||||||
\(107\) | −8.73746e105 | −0.250459 | −0.125230 | − | 0.992128i | \(-0.539967\pi\) | ||||
−0.125230 | + | 0.992128i | \(0.539967\pi\) | |||||||
\(108\) | 7.08605e104 | 0.0124640 | ||||||||
\(109\) | 1.52768e107 | 1.65631 | 0.828156 | − | 0.560497i | \(-0.189390\pi\) | ||||
0.828156 | + | 0.560497i | \(0.189390\pi\) | |||||||
\(110\) | −6.32572e106 | −0.424614 | ||||||||
\(111\) | −4.32963e107 | −1.80715 | ||||||||
\(112\) | −1.22771e107 | −0.320000 | ||||||||
\(113\) | 1.04871e108 | 1.71411 | 0.857054 | − | 0.515227i | \(-0.172292\pi\) | ||||
0.857054 | + | 0.515227i | \(0.172292\pi\) | |||||||
\(114\) | −8.50415e107 | −0.875238 | ||||||||
\(115\) | −2.37041e105 | −0.00154237 | ||||||||
\(116\) | −5.09806e107 | −0.210553 | ||||||||
\(117\) | −4.89404e108 | −1.28798 | ||||||||
\(118\) | −7.40243e108 | −1.24615 | ||||||||
\(119\) | 7.58774e107 | 0.0820157 | ||||||||
\(120\) | −6.19735e108 | −0.431708 | ||||||||
\(121\) | 3.09021e109 | 1.39237 | ||||||||
\(122\) | 2.27481e109 | 0.665354 | ||||||||
\(123\) | 8.70435e109 | 1.65851 | ||||||||
\(124\) | 8.13598e108 | 0.101338 | ||||||||
\(125\) | −6.89801e109 | −0.563570 | ||||||||
\(126\) | 6.07074e109 | 0.326428 | ||||||||
\(127\) | −1.89039e110 | −0.671208 | −0.335604 | − | 0.942003i | \(-0.608940\pi\) | ||||
−0.335604 | + | 0.942003i | \(0.608940\pi\) | |||||||
\(128\) | 3.22693e110 | 0.759043 | ||||||||
\(129\) | 4.46661e109 | 0.0698262 | ||||||||
\(130\) | −3.64086e110 | −0.379470 | ||||||||
\(131\) | −1.66200e111 | −1.15848 | −0.579240 | − | 0.815157i | \(-0.696650\pi\) | ||||
−0.579240 | + | 0.815157i | \(0.696650\pi\) | |||||||
\(132\) | 6.04310e110 | 0.282572 | ||||||||
\(133\) | −8.07305e110 | −0.253996 | ||||||||
\(134\) | −4.30441e111 | −0.913927 | ||||||||
\(135\) | −1.94368e110 | −0.0279320 | ||||||||
\(136\) | −2.35854e111 | −0.230065 | ||||||||
\(137\) | 1.41306e112 | 0.938276 | 0.469138 | − | 0.883125i | \(-0.344565\pi\) | ||||
0.469138 | + | 0.883125i | \(0.344565\pi\) | |||||||
\(138\) | −1.49636e110 | −0.00678242 | ||||||||
\(139\) | −2.16214e112 | −0.670821 | −0.335410 | − | 0.942072i | \(-0.608875\pi\) | ||||
−0.335410 | + | 0.942072i | \(0.608875\pi\) | |||||||
\(140\) | −6.83464e110 | −0.0145544 | ||||||||
\(141\) | 1.25078e113 | 1.83306 | ||||||||
\(142\) | −1.79483e112 | −0.181503 | ||||||||
\(143\) | 3.05601e113 | 2.13803 | ||||||||
\(144\) | −1.63461e113 | −0.793202 | ||||||||
\(145\) | 1.39838e113 | 0.471851 | ||||||||
\(146\) | −6.71199e113 | −1.57880 | ||||||||
\(147\) | −7.26069e113 | −1.19349 | ||||||||
\(148\) | 1.48420e113 | 0.170904 | ||||||||
\(149\) | −5.65399e113 | −0.457169 | −0.228584 | − | 0.973524i | \(-0.573410\pi\) | ||||
−0.228584 | + | 0.973524i | \(0.573410\pi\) | |||||||
\(150\) | −2.07850e114 | −1.18293 | ||||||||
\(151\) | 2.64543e114 | 1.06220 | 0.531100 | − | 0.847309i | \(-0.321779\pi\) | ||||
0.531100 | + | 0.847309i | \(0.321779\pi\) | |||||||
\(152\) | 2.50939e114 | 0.712493 | ||||||||
\(153\) | 1.01025e114 | 0.203297 | ||||||||
\(154\) | −3.79079e114 | −0.541865 | ||||||||
\(155\) | −2.23167e114 | −0.227099 | ||||||||
\(156\) | 3.47820e114 | 0.252530 | ||||||||
\(157\) | −1.17083e115 | −0.607801 | −0.303901 | − | 0.952704i | \(-0.598289\pi\) | ||||
−0.303901 | + | 0.952704i | \(0.598289\pi\) | |||||||
\(158\) | 9.89662e114 | 0.368120 | ||||||||
\(159\) | 9.25258e115 | 2.47123 | ||||||||
\(160\) | 4.00210e114 | 0.0769111 | ||||||||
\(161\) | −1.42051e113 | −0.00196827 | ||||||||
\(162\) | −9.90156e115 | −0.991210 | ||||||||
\(163\) | 1.03779e115 | 0.0752071 | 0.0376035 | − | 0.999293i | \(-0.488028\pi\) | ||||
0.0376035 | + | 0.999293i | \(0.488028\pi\) | |||||||
\(164\) | −2.98386e115 | −0.156847 | ||||||||
\(165\) | −1.65760e116 | −0.633247 | ||||||||
\(166\) | −1.98617e116 | −0.552512 | ||||||||
\(167\) | −3.53472e116 | −0.717364 | −0.358682 | − | 0.933460i | \(-0.616774\pi\) | ||||
−0.358682 | + | 0.933460i | \(0.616774\pi\) | |||||||
\(168\) | −3.71386e116 | −0.550919 | ||||||||
\(169\) | 8.38371e116 | 0.910719 | ||||||||
\(170\) | 7.51566e115 | 0.0598961 | ||||||||
\(171\) | −1.07487e117 | −0.629593 | ||||||||
\(172\) | −1.53116e115 | −0.00660353 | ||||||||
\(173\) | 2.29574e117 | 0.730302 | 0.365151 | − | 0.930948i | \(-0.381017\pi\) | ||||
0.365151 | + | 0.930948i | \(0.381017\pi\) | |||||||
\(174\) | 8.82751e117 | 2.07493 | ||||||||
\(175\) | −1.97313e117 | −0.343288 | ||||||||
\(176\) | 1.02071e118 | 1.31670 | ||||||||
\(177\) | −1.93975e118 | −1.85844 | ||||||||
\(178\) | 2.21553e117 | 0.157916 | ||||||||
\(179\) | −6.76216e117 | −0.359171 | −0.179586 | − | 0.983742i | \(-0.557476\pi\) | ||||
−0.179586 | + | 0.983742i | \(0.557476\pi\) | |||||||
\(180\) | −9.09984e116 | −0.0360767 | ||||||||
\(181\) | −1.36028e118 | −0.403184 | −0.201592 | − | 0.979470i | \(-0.564612\pi\) | ||||
−0.201592 | + | 0.979470i | \(0.564612\pi\) | |||||||
\(182\) | −2.18184e118 | −0.484256 | ||||||||
\(183\) | 5.96093e118 | 0.992275 | ||||||||
\(184\) | 4.41545e116 | 0.00552127 | ||||||||
\(185\) | −4.07111e118 | −0.382998 | ||||||||
\(186\) | −1.40878e119 | −0.998650 | ||||||||
\(187\) | −6.30838e118 | −0.337469 | ||||||||
\(188\) | −4.28768e118 | −0.173355 | ||||||||
\(189\) | −1.16478e118 | −0.0356450 | ||||||||
\(190\) | −7.99636e118 | −0.185493 | ||||||||
\(191\) | 6.87230e119 | 1.21018 | 0.605091 | − | 0.796157i | \(-0.293137\pi\) | ||||
0.605091 | + | 0.796157i | \(0.293137\pi\) | |||||||
\(192\) | 1.13646e120 | 1.52139 | ||||||||
\(193\) | 1.79504e120 | 1.82943 | 0.914714 | − | 0.404103i | \(-0.132416\pi\) | ||||
0.914714 | + | 0.404103i | \(0.132416\pi\) | |||||||
\(194\) | −1.66963e120 | −1.29727 | ||||||||
\(195\) | −9.54056e119 | −0.565922 | ||||||||
\(196\) | 2.48897e119 | 0.112869 | ||||||||
\(197\) | 7.42365e119 | 0.257715 | 0.128858 | − | 0.991663i | \(-0.458869\pi\) | ||||
0.128858 | + | 0.991663i | \(0.458869\pi\) | |||||||
\(198\) | −5.04716e120 | −1.34315 | ||||||||
\(199\) | −4.51807e120 | −0.922926 | −0.461463 | − | 0.887160i | \(-0.652675\pi\) | ||||
−0.461463 | + | 0.887160i | \(0.652675\pi\) | |||||||
\(200\) | 6.13321e120 | 0.962970 | ||||||||
\(201\) | −1.12793e121 | −1.36298 | ||||||||
\(202\) | 1.44950e120 | 0.134981 | ||||||||
\(203\) | 8.38001e120 | 0.602147 | ||||||||
\(204\) | −7.17988e119 | −0.0398596 | ||||||||
\(205\) | 8.18461e120 | 0.351496 | ||||||||
\(206\) | −3.01363e121 | −1.00245 | ||||||||
\(207\) | −1.89130e119 | −0.00487886 | ||||||||
\(208\) | 5.87484e121 | 1.17671 | ||||||||
\(209\) | 6.71186e121 | 1.04511 | ||||||||
\(210\) | 1.18345e121 | 0.143429 | ||||||||
\(211\) | −3.56693e120 | −0.0336872 | −0.0168436 | − | 0.999858i | \(-0.505362\pi\) | ||||
−0.0168436 | + | 0.999858i | \(0.505362\pi\) | |||||||
\(212\) | −3.17179e121 | −0.233707 | ||||||||
\(213\) | −4.70320e121 | −0.270685 | ||||||||
\(214\) | −5.18632e121 | −0.233419 | ||||||||
\(215\) | 4.19991e120 | 0.0147986 | ||||||||
\(216\) | 3.62055e121 | 0.0999892 | ||||||||
\(217\) | −1.33736e122 | −0.289810 | ||||||||
\(218\) | 9.06792e122 | 1.54362 | ||||||||
\(219\) | −1.75882e123 | −2.35454 | ||||||||
\(220\) | 5.68226e121 | 0.0598867 | ||||||||
\(221\) | −3.63088e122 | −0.301590 | ||||||||
\(222\) | −2.56995e123 | −1.68420 | ||||||||
\(223\) | 2.69470e123 | 1.39478 | 0.697388 | − | 0.716694i | \(-0.254345\pi\) | ||||
0.697388 | + | 0.716694i | \(0.254345\pi\) | |||||||
\(224\) | 2.39832e122 | 0.0981491 | ||||||||
\(225\) | −2.62709e123 | −0.850927 | ||||||||
\(226\) | 6.22487e123 | 1.59749 | ||||||||
\(227\) | 7.89252e123 | 1.60642 | 0.803208 | − | 0.595698i | \(-0.203125\pi\) | ||||
0.803208 | + | 0.595698i | \(0.203125\pi\) | |||||||
\(228\) | 7.63910e122 | 0.123442 | ||||||||
\(229\) | 7.09479e123 | 0.911123 | 0.455561 | − | 0.890204i | \(-0.349439\pi\) | ||||
0.455561 | + | 0.890204i | \(0.349439\pi\) | |||||||
\(230\) | −1.40701e121 | −0.00143743 | ||||||||
\(231\) | −9.93343e123 | −0.808110 | ||||||||
\(232\) | −2.60481e124 | −1.68911 | ||||||||
\(233\) | 7.64294e123 | 0.395434 | 0.197717 | − | 0.980259i | \(-0.436647\pi\) | ||||
0.197717 | + | 0.980259i | \(0.436647\pi\) | |||||||
\(234\) | −2.90497e124 | −1.20035 | ||||||||
\(235\) | 1.17609e124 | 0.388490 | ||||||||
\(236\) | 6.64945e123 | 0.175754 | ||||||||
\(237\) | 2.59333e124 | 0.548996 | ||||||||
\(238\) | 4.50388e123 | 0.0764357 | ||||||||
\(239\) | −8.75129e124 | −1.19174 | −0.595871 | − | 0.803080i | \(-0.703193\pi\) | ||||
−0.595871 | + | 0.803080i | \(0.703193\pi\) | |||||||
\(240\) | −3.18655e124 | −0.348523 | ||||||||
\(241\) | 6.50591e124 | 0.572023 | 0.286011 | − | 0.958226i | \(-0.407671\pi\) | ||||
0.286011 | + | 0.958226i | \(0.407671\pi\) | |||||||
\(242\) | 1.83426e125 | 1.29764 | ||||||||
\(243\) | −2.42818e125 | −1.38341 | ||||||||
\(244\) | −2.04341e124 | −0.0938404 | ||||||||
\(245\) | −6.82714e124 | −0.252941 | ||||||||
\(246\) | 5.16667e125 | 1.54567 | ||||||||
\(247\) | 3.86311e125 | 0.934000 | ||||||||
\(248\) | 4.15701e125 | 0.812957 | ||||||||
\(249\) | −5.20459e125 | −0.823988 | ||||||||
\(250\) | −4.09447e125 | −0.525227 | ||||||||
\(251\) | −1.04222e125 | −0.108415 | −0.0542077 | − | 0.998530i | \(-0.517263\pi\) | ||||
−0.0542077 | + | 0.998530i | \(0.517263\pi\) | |||||||
\(252\) | −5.45322e124 | −0.0460389 | ||||||||
\(253\) | 1.18100e124 | 0.00809882 | ||||||||
\(254\) | −1.12209e126 | −0.625542 | ||||||||
\(255\) | 1.96942e125 | 0.0893260 | ||||||||
\(256\) | −1.04846e126 | −0.387216 | ||||||||
\(257\) | −3.16211e126 | −0.951675 | −0.475838 | − | 0.879533i | \(-0.657855\pi\) | ||||
−0.475838 | + | 0.879533i | \(0.657855\pi\) | |||||||
\(258\) | 2.65126e125 | 0.0650756 | ||||||||
\(259\) | −2.43967e126 | −0.488758 | ||||||||
\(260\) | 3.27051e125 | 0.0535198 | ||||||||
\(261\) | 1.11574e127 | 1.49257 | ||||||||
\(262\) | −9.86519e126 | −1.07966 | ||||||||
\(263\) | 2.05656e126 | 0.184274 | 0.0921371 | − | 0.995746i | \(-0.470630\pi\) | ||||
0.0921371 | + | 0.995746i | \(0.470630\pi\) | |||||||
\(264\) | 3.08767e127 | 2.26686 | ||||||||
\(265\) | 8.70010e126 | 0.523740 | ||||||||
\(266\) | −4.79194e126 | −0.236715 | ||||||||
\(267\) | 5.80561e126 | 0.235508 | ||||||||
\(268\) | 3.86656e126 | 0.128899 | ||||||||
\(269\) | −3.70566e127 | −1.01595 | −0.507974 | − | 0.861373i | \(-0.669605\pi\) | ||||
−0.507974 | + | 0.861373i | \(0.669605\pi\) | |||||||
\(270\) | −1.15371e126 | −0.0260316 | ||||||||
\(271\) | −8.71045e127 | −1.61865 | −0.809324 | − | 0.587362i | \(-0.800167\pi\) | ||||
−0.809324 | + | 0.587362i | \(0.800167\pi\) | |||||||
\(272\) | −1.21272e127 | −0.185734 | ||||||||
\(273\) | −5.71733e127 | −0.722195 | ||||||||
\(274\) | 8.38754e127 | 0.874440 | ||||||||
\(275\) | 1.64045e128 | 1.41252 | ||||||||
\(276\) | 1.34415e125 | 0.000956580 0 | ||||||||
\(277\) | −6.76019e127 | −0.397897 | −0.198949 | − | 0.980010i | \(-0.563753\pi\) | ||||
−0.198949 | + | 0.980010i | \(0.563753\pi\) | |||||||
\(278\) | −1.28339e128 | −0.625181 | ||||||||
\(279\) | −1.78060e128 | −0.718368 | ||||||||
\(280\) | −3.49210e127 | −0.116759 | ||||||||
\(281\) | −1.03457e128 | −0.286866 | −0.143433 | − | 0.989660i | \(-0.545814\pi\) | ||||
−0.143433 | + | 0.989660i | \(0.545814\pi\) | |||||||
\(282\) | 7.42429e128 | 1.70835 | ||||||||
\(283\) | −1.78925e128 | −0.341887 | −0.170943 | − | 0.985281i | \(-0.554682\pi\) | ||||
−0.170943 | + | 0.985281i | \(0.554682\pi\) | |||||||
\(284\) | 1.61226e127 | 0.0255989 | ||||||||
\(285\) | −2.09538e128 | −0.276635 | ||||||||
\(286\) | 1.81396e129 | 1.99256 | ||||||||
\(287\) | 4.90475e128 | 0.448557 | ||||||||
\(288\) | 3.19320e128 | 0.243288 | ||||||||
\(289\) | −1.49953e129 | −0.952397 | ||||||||
\(290\) | 8.30041e128 | 0.439749 | ||||||||
\(291\) | −4.37513e129 | −1.93468 | ||||||||
\(292\) | 6.02924e128 | 0.222671 | ||||||||
\(293\) | −1.69501e129 | −0.523145 | −0.261572 | − | 0.965184i | \(-0.584241\pi\) | ||||
−0.261572 | + | 0.965184i | \(0.584241\pi\) | |||||||
\(294\) | −4.30975e129 | −1.11229 | ||||||||
\(295\) | −1.82392e129 | −0.393868 | ||||||||
\(296\) | 7.58339e129 | 1.37103 | ||||||||
\(297\) | 9.68388e128 | 0.146668 | ||||||||
\(298\) | −3.35606e129 | −0.426065 | ||||||||
\(299\) | 6.79740e127 | 0.00723778 | ||||||||
\(300\) | 1.86707e129 | 0.166838 | ||||||||
\(301\) | 2.51686e128 | 0.0188850 | ||||||||
\(302\) | 1.57025e130 | 0.989932 | ||||||||
\(303\) | 3.79830e129 | 0.201304 | ||||||||
\(304\) | 1.29028e130 | 0.575203 | ||||||||
\(305\) | 5.60500e129 | 0.210297 | ||||||||
\(306\) | 5.99659e129 | 0.189465 | ||||||||
\(307\) | 4.16550e129 | 0.110893 | 0.0554463 | − | 0.998462i | \(-0.482342\pi\) | ||||
0.0554463 | + | 0.998462i | \(0.482342\pi\) | |||||||
\(308\) | 3.40518e129 | 0.0764237 | ||||||||
\(309\) | −7.89696e130 | −1.49500 | ||||||||
\(310\) | −1.32466e130 | −0.211648 | ||||||||
\(311\) | −7.28115e130 | −0.982381 | −0.491190 | − | 0.871052i | \(-0.663438\pi\) | ||||
−0.491190 | + | 0.871052i | \(0.663438\pi\) | |||||||
\(312\) | 1.77715e131 | 2.02586 | ||||||||
\(313\) | −1.68114e131 | −1.62004 | −0.810019 | − | 0.586403i | \(-0.800543\pi\) | ||||
−0.810019 | + | 0.586403i | \(0.800543\pi\) | |||||||
\(314\) | −6.94972e130 | −0.566449 | ||||||||
\(315\) | 1.49580e130 | 0.103174 | ||||||||
\(316\) | −8.88993e129 | −0.0519190 | ||||||||
\(317\) | 1.20789e131 | 0.597609 | 0.298804 | − | 0.954314i | \(-0.403412\pi\) | ||||
0.298804 | + | 0.954314i | \(0.403412\pi\) | |||||||
\(318\) | 5.49208e131 | 2.30310 | ||||||||
\(319\) | −6.96707e131 | −2.47765 | ||||||||
\(320\) | 1.06860e131 | 0.322435 | ||||||||
\(321\) | −1.35903e131 | −0.348109 | ||||||||
\(322\) | −8.43174e128 | −0.00183436 | ||||||||
\(323\) | −7.97444e130 | −0.147424 | ||||||||
\(324\) | 8.89437e130 | 0.139798 | ||||||||
\(325\) | 9.44182e131 | 1.26235 | ||||||||
\(326\) | 6.16002e130 | 0.0700903 | ||||||||
\(327\) | 2.37617e132 | 2.30208 | ||||||||
\(328\) | −1.52457e132 | −1.25826 | ||||||||
\(329\) | 7.04793e131 | 0.495766 | ||||||||
\(330\) | −9.83907e131 | −0.590164 | ||||||||
\(331\) | −1.75907e132 | −0.900146 | −0.450073 | − | 0.892992i | \(-0.648602\pi\) | ||||
−0.450073 | + | 0.892992i | \(0.648602\pi\) | |||||||
\(332\) | 1.78414e131 | 0.0779253 | ||||||||
\(333\) | −3.24825e132 | −1.21151 | ||||||||
\(334\) | −2.09811e132 | −0.668558 | ||||||||
\(335\) | −1.06058e132 | −0.288863 | ||||||||
\(336\) | −1.90959e132 | −0.444763 | ||||||||
\(337\) | −5.46915e132 | −1.08981 | −0.544904 | − | 0.838498i | \(-0.683434\pi\) | ||||
−0.544904 | + | 0.838498i | \(0.683434\pi\) | |||||||
\(338\) | 4.97634e132 | 0.848757 | ||||||||
\(339\) | 1.63117e133 | 2.38241 | ||||||||
\(340\) | −6.75116e130 | −0.00844764 | ||||||||
\(341\) | 1.11187e133 | 1.19248 | ||||||||
\(342\) | −6.38013e132 | −0.586758 | ||||||||
\(343\) | −8.85579e132 | −0.698692 | ||||||||
\(344\) | −7.82331e131 | −0.0529751 | ||||||||
\(345\) | −3.68696e130 | −0.00214371 | ||||||||
\(346\) | 1.36269e133 | 0.680615 | ||||||||
\(347\) | 1.69890e133 | 0.729238 | 0.364619 | − | 0.931157i | \(-0.381199\pi\) | ||||
0.364619 | + | 0.931157i | \(0.381199\pi\) | |||||||
\(348\) | −7.92957e132 | −0.292644 | ||||||||
\(349\) | −1.33296e133 | −0.423137 | −0.211568 | − | 0.977363i | \(-0.567857\pi\) | ||||
−0.211568 | + | 0.977363i | \(0.567857\pi\) | |||||||
\(350\) | −1.17120e133 | −0.319932 | ||||||||
\(351\) | 5.57369e132 | 0.131075 | ||||||||
\(352\) | −1.99394e133 | −0.403853 | ||||||||
\(353\) | 4.25860e133 | 0.743181 | 0.371591 | − | 0.928397i | \(-0.378812\pi\) | ||||
0.371591 | + | 0.928397i | \(0.378812\pi\) | |||||||
\(354\) | −1.15138e134 | −1.73200 | ||||||||
\(355\) | −4.42236e132 | −0.0573675 | ||||||||
\(356\) | −1.99016e132 | −0.0222722 | ||||||||
\(357\) | 1.18020e133 | 0.113992 | ||||||||
\(358\) | −4.01383e133 | −0.334735 | ||||||||
\(359\) | 1.29130e134 | 0.930187 | 0.465093 | − | 0.885262i | \(-0.346021\pi\) | ||||
0.465093 | + | 0.885262i | \(0.346021\pi\) | |||||||
\(360\) | −4.64948e133 | −0.289416 | ||||||||
\(361\) | −1.00990e134 | −0.543441 | ||||||||
\(362\) | −8.07426e133 | −0.375753 | ||||||||
\(363\) | 4.80653e134 | 1.93524 | ||||||||
\(364\) | 1.95990e133 | 0.0682986 | ||||||||
\(365\) | −1.65380e134 | −0.499008 | ||||||||
\(366\) | 3.53825e134 | 0.924765 | ||||||||
\(367\) | −4.52119e134 | −1.02396 | −0.511982 | − | 0.858996i | \(-0.671088\pi\) | ||||
−0.511982 | + | 0.858996i | \(0.671088\pi\) | |||||||
\(368\) | 2.27034e132 | 0.00445738 | ||||||||
\(369\) | 6.53033e134 | 1.11186 | ||||||||
\(370\) | −2.41650e134 | −0.356941 | ||||||||
\(371\) | 5.21367e134 | 0.668364 | ||||||||
\(372\) | 1.26548e134 | 0.140848 | ||||||||
\(373\) | 2.53939e134 | 0.245480 | 0.122740 | − | 0.992439i | \(-0.460832\pi\) | ||||
0.122740 | + | 0.992439i | \(0.460832\pi\) | |||||||
\(374\) | −3.74448e134 | −0.314509 | ||||||||
\(375\) | −1.07292e135 | −0.783297 | ||||||||
\(376\) | −2.19075e135 | −1.39069 | ||||||||
\(377\) | −4.01000e135 | −2.21423 | ||||||||
\(378\) | −6.91381e133 | −0.0332199 | ||||||||
\(379\) | 4.23774e135 | 1.77246 | 0.886228 | − | 0.463250i | \(-0.153317\pi\) | ||||
0.886228 | + | 0.463250i | \(0.153317\pi\) | |||||||
\(380\) | 7.18296e133 | 0.0261616 | ||||||||
\(381\) | −2.94033e135 | −0.932901 | ||||||||
\(382\) | 4.07921e135 | 1.12785 | ||||||||
\(383\) | 1.40505e135 | 0.338653 | 0.169327 | − | 0.985560i | \(-0.445841\pi\) | ||||
0.169327 | + | 0.985560i | \(0.445841\pi\) | |||||||
\(384\) | 5.01919e135 | 1.05498 | ||||||||
\(385\) | −9.34030e134 | −0.171266 | ||||||||
\(386\) | 1.06549e136 | 1.70496 | ||||||||
\(387\) | 3.35102e134 | 0.0468114 | ||||||||
\(388\) | 1.49980e135 | 0.182964 | ||||||||
\(389\) | −1.50971e136 | −1.60894 | −0.804468 | − | 0.593996i | \(-0.797549\pi\) | ||||
−0.804468 | + | 0.593996i | \(0.797549\pi\) | |||||||
\(390\) | −5.66302e135 | −0.527420 | ||||||||
\(391\) | −1.40316e133 | −0.00114242 | ||||||||
\(392\) | 1.27171e136 | 0.905464 | ||||||||
\(393\) | −2.58509e136 | −1.61015 | ||||||||
\(394\) | 4.40648e135 | 0.240182 | ||||||||
\(395\) | 2.43848e135 | 0.116351 | ||||||||
\(396\) | 4.53376e135 | 0.189436 | ||||||||
\(397\) | 3.01792e136 | 1.10460 | 0.552301 | − | 0.833645i | \(-0.313750\pi\) | ||||
0.552301 | + | 0.833645i | \(0.313750\pi\) | |||||||
\(398\) | −2.68181e136 | −0.860134 | ||||||||
\(399\) | −1.25569e136 | −0.353024 | ||||||||
\(400\) | 3.15357e136 | 0.777416 | ||||||||
\(401\) | −7.19899e136 | −1.55665 | −0.778326 | − | 0.627860i | \(-0.783931\pi\) | ||||
−0.778326 | + | 0.627860i | \(0.783931\pi\) | |||||||
\(402\) | −6.69511e136 | −1.27025 | ||||||||
\(403\) | 6.39954e136 | 1.06570 | ||||||||
\(404\) | −1.30206e135 | −0.0190375 | ||||||||
\(405\) | −2.43969e136 | −0.313290 | ||||||||
\(406\) | 4.97415e136 | 0.561180 | ||||||||
\(407\) | 2.02832e137 | 2.01109 | ||||||||
\(408\) | −3.66849e136 | −0.319764 | ||||||||
\(409\) | −1.05041e137 | −0.805163 | −0.402581 | − | 0.915384i | \(-0.631887\pi\) | ||||
−0.402581 | + | 0.915384i | \(0.631887\pi\) | |||||||
\(410\) | 4.85816e136 | 0.327581 | ||||||||
\(411\) | 2.19788e137 | 1.30409 | ||||||||
\(412\) | 2.70708e136 | 0.141383 | ||||||||
\(413\) | −1.09301e137 | −0.502629 | ||||||||
\(414\) | −1.12263e135 | −0.00454692 | ||||||||
\(415\) | −4.89382e136 | −0.174632 | ||||||||
\(416\) | −1.14764e137 | −0.360917 | ||||||||
\(417\) | −3.36301e137 | −0.932363 | ||||||||
\(418\) | 3.98398e137 | 0.974008 | ||||||||
\(419\) | −5.13603e137 | −1.10762 | −0.553811 | − | 0.832643i | \(-0.686827\pi\) | ||||
−0.553811 | + | 0.832643i | \(0.686827\pi\) | |||||||
\(420\) | −1.06307e136 | −0.0202289 | ||||||||
\(421\) | −3.41684e137 | −0.573871 | −0.286935 | − | 0.957950i | \(-0.592636\pi\) | ||||
−0.286935 | + | 0.957950i | \(0.592636\pi\) | |||||||
\(422\) | −2.11723e136 | −0.0313953 | ||||||||
\(423\) | 9.38382e137 | 1.22888 | ||||||||
\(424\) | −1.62060e138 | −1.87485 | ||||||||
\(425\) | −1.94903e137 | −0.199251 | ||||||||
\(426\) | −2.79169e137 | −0.252269 | ||||||||
\(427\) | 3.35888e137 | 0.268368 | ||||||||
\(428\) | 4.65877e136 | 0.0329210 | ||||||||
\(429\) | 4.75334e138 | 2.97161 | ||||||||
\(430\) | 2.49295e136 | 0.0137918 | ||||||||
\(431\) | 2.04799e138 | 1.00293 | 0.501466 | − | 0.865177i | \(-0.332794\pi\) | ||||
0.501466 | + | 0.865177i | \(0.332794\pi\) | |||||||
\(432\) | 1.86162e137 | 0.0807223 | ||||||||
\(433\) | −3.08552e138 | −1.18499 | −0.592494 | − | 0.805575i | \(-0.701857\pi\) | ||||
−0.592494 | + | 0.805575i | \(0.701857\pi\) | |||||||
\(434\) | −7.93822e137 | −0.270092 | ||||||||
\(435\) | 2.17505e138 | 0.655818 | ||||||||
\(436\) | −8.14552e137 | −0.217710 | ||||||||
\(437\) | 1.49290e136 | 0.00353798 | ||||||||
\(438\) | −1.04399e139 | −2.19434 | ||||||||
\(439\) | 2.64684e138 | 0.493561 | 0.246780 | − | 0.969071i | \(-0.420627\pi\) | ||||
0.246780 | + | 0.969071i | \(0.420627\pi\) | |||||||
\(440\) | 2.90330e138 | 0.480426 | ||||||||
\(441\) | −5.44724e138 | −0.800111 | ||||||||
\(442\) | −2.15519e138 | −0.281072 | ||||||||
\(443\) | 1.00847e138 | 0.116806 | 0.0584032 | − | 0.998293i | \(-0.481399\pi\) | ||||
0.0584032 | + | 0.998293i | \(0.481399\pi\) | |||||||
\(444\) | 2.30854e138 | 0.237537 | ||||||||
\(445\) | 5.45895e137 | 0.0499124 | ||||||||
\(446\) | 1.59950e139 | 1.29988 | ||||||||
\(447\) | −8.79426e138 | −0.635411 | ||||||||
\(448\) | 6.40377e138 | 0.411472 | ||||||||
\(449\) | −4.95920e137 | −0.0283452 | −0.0141726 | − | 0.999900i | \(-0.504511\pi\) | ||||
−0.0141726 | + | 0.999900i | \(0.504511\pi\) | |||||||
\(450\) | −1.55937e139 | −0.793033 | ||||||||
\(451\) | −4.07777e139 | −1.84567 | ||||||||
\(452\) | −5.59167e138 | −0.225307 | ||||||||
\(453\) | 4.11472e139 | 1.47633 | ||||||||
\(454\) | 4.68479e139 | 1.49712 | ||||||||
\(455\) | −5.37594e138 | −0.153058 | ||||||||
\(456\) | 3.90313e139 | 0.990282 | ||||||||
\(457\) | −1.67962e139 | −0.379848 | −0.189924 | − | 0.981799i | \(-0.560824\pi\) | ||||
−0.189924 | + | 0.981799i | \(0.560824\pi\) | |||||||
\(458\) | 4.21128e139 | 0.849134 | ||||||||
\(459\) | −1.15055e138 | −0.0206890 | ||||||||
\(460\) | 1.26389e136 | 0.000202732 0 | ||||||||
\(461\) | 2.43974e139 | 0.349176 | 0.174588 | − | 0.984642i | \(-0.444141\pi\) | ||||
0.174588 | + | 0.984642i | \(0.444141\pi\) | |||||||
\(462\) | −5.89622e139 | −0.753130 | ||||||||
\(463\) | −8.04930e139 | −0.917817 | −0.458909 | − | 0.888484i | \(-0.651759\pi\) | ||||
−0.458909 | + | 0.888484i | \(0.651759\pi\) | |||||||
\(464\) | −1.33934e140 | −1.36363 | ||||||||
\(465\) | −3.47116e139 | −0.315642 | ||||||||
\(466\) | 4.53664e139 | 0.368531 | ||||||||
\(467\) | −6.71585e139 | −0.487489 | −0.243744 | − | 0.969840i | \(-0.578376\pi\) | ||||
−0.243744 | + | 0.969840i | \(0.578376\pi\) | |||||||
\(468\) | 2.60947e139 | 0.169295 | ||||||||
\(469\) | −6.35571e139 | −0.368629 | ||||||||
\(470\) | 6.98098e139 | 0.362059 | ||||||||
\(471\) | −1.82112e140 | −0.844773 | ||||||||
\(472\) | 3.39748e140 | 1.40994 | ||||||||
\(473\) | −2.09250e139 | −0.0777060 | ||||||||
\(474\) | 1.53933e140 | 0.511644 | ||||||||
\(475\) | 2.07369e140 | 0.617063 | ||||||||
\(476\) | −4.04574e138 | −0.0107803 | ||||||||
\(477\) | 6.94163e140 | 1.65671 | ||||||||
\(478\) | −5.19453e140 | −1.11066 | ||||||||
\(479\) | −7.93981e140 | −1.52123 | −0.760616 | − | 0.649202i | \(-0.775103\pi\) | ||||
−0.760616 | + | 0.649202i | \(0.775103\pi\) | |||||||
\(480\) | 6.22490e139 | 0.106897 | ||||||||
\(481\) | 1.16743e141 | 1.79728 | ||||||||
\(482\) | 3.86173e140 | 0.533105 | ||||||||
\(483\) | −2.20947e138 | −0.00273566 | ||||||||
\(484\) | −1.64768e140 | −0.183017 | ||||||||
\(485\) | −4.11389e140 | −0.410026 | ||||||||
\(486\) | −1.44130e141 | −1.28929 | ||||||||
\(487\) | −6.81986e140 | −0.547652 | −0.273826 | − | 0.961779i | \(-0.588289\pi\) | ||||
−0.273826 | + | 0.961779i | \(0.588289\pi\) | |||||||
\(488\) | −1.04406e141 | −0.752810 | ||||||||
\(489\) | 1.61418e140 | 0.104529 | ||||||||
\(490\) | −4.05241e140 | −0.235732 | ||||||||
\(491\) | 7.17413e140 | 0.374965 | 0.187483 | − | 0.982268i | \(-0.439967\pi\) | ||||
0.187483 | + | 0.982268i | \(0.439967\pi\) | |||||||
\(492\) | −4.64111e140 | −0.217999 | ||||||||
\(493\) | 8.27766e140 | 0.349498 | ||||||||
\(494\) | 2.29304e141 | 0.870455 | ||||||||
\(495\) | −1.24359e141 | −0.424528 | ||||||||
\(496\) | 2.13745e141 | 0.656309 | ||||||||
\(497\) | −2.65017e140 | −0.0732088 | ||||||||
\(498\) | −3.08930e141 | −0.767927 | ||||||||
\(499\) | 5.28030e141 | 1.18135 | 0.590677 | − | 0.806908i | \(-0.298861\pi\) | ||||
0.590677 | + | 0.806908i | \(0.298861\pi\) | |||||||
\(500\) | 3.67798e140 | 0.0740771 | ||||||||
\(501\) | −5.49792e141 | −0.997052 | ||||||||
\(502\) | −6.18636e140 | −0.101039 | ||||||||
\(503\) | 6.45019e141 | 0.948971 | 0.474486 | − | 0.880263i | \(-0.342634\pi\) | ||||
0.474486 | + | 0.880263i | \(0.342634\pi\) | |||||||
\(504\) | −2.78627e141 | −0.369335 | ||||||||
\(505\) | 3.57150e140 | 0.0426632 | ||||||||
\(506\) | 7.01008e139 | 0.00754781 | ||||||||
\(507\) | 1.30401e142 | 1.26579 | ||||||||
\(508\) | 1.00795e141 | 0.0882253 | ||||||||
\(509\) | 5.45984e141 | 0.431019 | 0.215509 | − | 0.976502i | \(-0.430859\pi\) | ||||
0.215509 | + | 0.976502i | \(0.430859\pi\) | |||||||
\(510\) | 1.16899e141 | 0.0832486 | ||||||||
\(511\) | −9.91064e141 | −0.636802 | ||||||||
\(512\) | −1.93134e142 | −1.11991 | ||||||||
\(513\) | 1.22414e141 | 0.0640722 | ||||||||
\(514\) | −1.87695e142 | −0.886927 | ||||||||
\(515\) | −7.42543e141 | −0.316841 | ||||||||
\(516\) | −2.38157e140 | −0.00917814 | ||||||||
\(517\) | −5.85959e142 | −2.03992 | ||||||||
\(518\) | −1.44812e142 | −0.455505 | ||||||||
\(519\) | 3.57081e142 | 1.01503 | ||||||||
\(520\) | 1.67104e142 | 0.429349 | ||||||||
\(521\) | 4.91559e142 | 1.14181 | 0.570906 | − | 0.821015i | \(-0.306592\pi\) | ||||
0.570906 | + | 0.821015i | \(0.306592\pi\) | |||||||
\(522\) | 6.62273e142 | 1.39103 | ||||||||
\(523\) | 2.21300e142 | 0.420381 | 0.210190 | − | 0.977660i | \(-0.432592\pi\) | ||||
0.210190 | + | 0.977660i | \(0.432592\pi\) | |||||||
\(524\) | 8.86169e141 | 0.152273 | ||||||||
\(525\) | −3.06902e142 | −0.477130 | ||||||||
\(526\) | 1.22072e142 | 0.171737 | ||||||||
\(527\) | −1.32103e142 | −0.168211 | ||||||||
\(528\) | 1.58762e143 | 1.83006 | ||||||||
\(529\) | −9.58100e142 | −0.999973 | ||||||||
\(530\) | 5.16414e142 | 0.488107 | ||||||||
\(531\) | −1.45527e143 | −1.24589 | ||||||||
\(532\) | 4.30450e141 | 0.0333858 | ||||||||
\(533\) | −2.34702e143 | −1.64945 | ||||||||
\(534\) | 3.44605e142 | 0.219485 | ||||||||
\(535\) | −1.27788e142 | −0.0737764 | ||||||||
\(536\) | 1.97558e143 | 1.03406 | ||||||||
\(537\) | −1.05179e143 | −0.499206 | ||||||||
\(538\) | −2.19958e143 | −0.946827 | ||||||||
\(539\) | 3.40145e143 | 1.32817 | ||||||||
\(540\) | 1.03636e141 | 0.00367145 | ||||||||
\(541\) | 6.21110e142 | 0.199670 | 0.0998348 | − | 0.995004i | \(-0.468169\pi\) | ||||
0.0998348 | + | 0.995004i | \(0.468169\pi\) | |||||||
\(542\) | −5.17028e143 | −1.50852 | ||||||||
\(543\) | −2.11579e143 | −0.560379 | ||||||||
\(544\) | 2.36903e142 | 0.0569676 | ||||||||
\(545\) | 2.23429e143 | 0.487891 | ||||||||
\(546\) | −3.39365e143 | −0.673060 | ||||||||
\(547\) | 9.88009e143 | 1.78003 | 0.890013 | − | 0.455936i | \(-0.150695\pi\) | ||||
0.890013 | + | 0.455936i | \(0.150695\pi\) | |||||||
\(548\) | −7.53435e142 | −0.123329 | ||||||||
\(549\) | 4.47212e143 | 0.665219 | ||||||||
\(550\) | 9.73724e143 | 1.31642 | ||||||||
\(551\) | −8.80709e143 | −1.08236 | ||||||||
\(552\) | 6.86782e141 | 0.00767392 | ||||||||
\(553\) | 1.46129e143 | 0.148480 | ||||||||
\(554\) | −4.01267e143 | −0.370826 | ||||||||
\(555\) | −6.33223e143 | −0.532323 | ||||||||
\(556\) | 1.15284e143 | 0.0881744 | ||||||||
\(557\) | 2.14551e144 | 1.49325 | 0.746626 | − | 0.665244i | \(-0.231672\pi\) | ||||
0.746626 | + | 0.665244i | \(0.231672\pi\) | |||||||
\(558\) | −1.05692e144 | −0.669493 | ||||||||
\(559\) | −1.20437e143 | −0.0694446 | ||||||||
\(560\) | −1.79557e143 | −0.0942607 | ||||||||
\(561\) | −9.81210e143 | −0.469042 | ||||||||
\(562\) | −6.14094e143 | −0.267349 | ||||||||
\(563\) | −9.74563e143 | −0.386473 | −0.193237 | − | 0.981152i | \(-0.561898\pi\) | ||||
−0.193237 | + | 0.981152i | \(0.561898\pi\) | |||||||
\(564\) | −6.66909e143 | −0.240943 | ||||||||
\(565\) | 1.53378e144 | 0.504915 | ||||||||
\(566\) | −1.06205e144 | −0.318626 | ||||||||
\(567\) | −1.46202e144 | −0.399801 | ||||||||
\(568\) | 8.23768e143 | 0.205361 | ||||||||
\(569\) | −3.93707e144 | −0.894909 | −0.447454 | − | 0.894307i | \(-0.647669\pi\) | ||||
−0.447454 | + | 0.894307i | \(0.647669\pi\) | |||||||
\(570\) | −1.24376e144 | −0.257814 | ||||||||
\(571\) | −1.88688e144 | −0.356738 | −0.178369 | − | 0.983964i | \(-0.557082\pi\) | ||||
−0.178369 | + | 0.983964i | \(0.557082\pi\) | |||||||
\(572\) | −1.62945e144 | −0.281027 | ||||||||
\(573\) | 1.06892e145 | 1.68201 | ||||||||
\(574\) | 2.91133e144 | 0.418039 | ||||||||
\(575\) | 3.64880e142 | 0.00478176 | ||||||||
\(576\) | 8.52617e144 | 1.01994 | ||||||||
\(577\) | 1.05199e145 | 1.14889 | 0.574446 | − | 0.818542i | \(-0.305217\pi\) | ||||
0.574446 | + | 0.818542i | \(0.305217\pi\) | |||||||
\(578\) | −8.90079e144 | −0.887600 | ||||||||
\(579\) | 2.79202e145 | 2.54269 | ||||||||
\(580\) | −7.45609e143 | −0.0620213 | ||||||||
\(581\) | −2.93270e144 | −0.222854 | ||||||||
\(582\) | −2.59696e145 | −1.80305 | ||||||||
\(583\) | −4.33460e145 | −2.75011 | ||||||||
\(584\) | 3.08058e145 | 1.78632 | ||||||||
\(585\) | −7.15769e144 | −0.379393 | ||||||||
\(586\) | −1.00611e145 | −0.487552 | ||||||||
\(587\) | −3.35704e145 | −1.48750 | −0.743748 | − | 0.668460i | \(-0.766954\pi\) | ||||
−0.743748 | + | 0.668460i | \(0.766954\pi\) | |||||||
\(588\) | 3.87136e144 | 0.156875 | ||||||||
\(589\) | 1.40552e145 | 0.520936 | ||||||||
\(590\) | −1.08263e145 | −0.367071 | ||||||||
\(591\) | 1.15468e145 | 0.358194 | ||||||||
\(592\) | 3.89923e145 | 1.10685 | ||||||||
\(593\) | 9.74195e143 | 0.0253090 | 0.0126545 | − | 0.999920i | \(-0.495972\pi\) | ||||
0.0126545 | + | 0.999920i | \(0.495972\pi\) | |||||||
\(594\) | 5.74809e144 | 0.136689 | ||||||||
\(595\) | 1.10973e144 | 0.0241589 | ||||||||
\(596\) | 3.01468e144 | 0.0600914 | ||||||||
\(597\) | −7.02744e145 | −1.28276 | ||||||||
\(598\) | 4.03475e143 | 0.00674535 | ||||||||
\(599\) | 7.73768e145 | 1.18496 | 0.592478 | − | 0.805586i | \(-0.298150\pi\) | ||||
0.592478 | + | 0.805586i | \(0.298150\pi\) | |||||||
\(600\) | 9.53963e145 | 1.33842 | ||||||||
\(601\) | −7.70795e145 | −0.990899 | −0.495449 | − | 0.868637i | \(-0.664997\pi\) | ||||
−0.495449 | + | 0.868637i | \(0.664997\pi\) | |||||||
\(602\) | 1.49394e144 | 0.0176002 | ||||||||
\(603\) | −8.46218e145 | −0.913741 | ||||||||
\(604\) | −1.41053e145 | −0.139618 | ||||||||
\(605\) | 4.51953e145 | 0.410144 | ||||||||
\(606\) | 2.25457e145 | 0.187608 | ||||||||
\(607\) | 2.37938e146 | 1.81576 | 0.907880 | − | 0.419231i | \(-0.137700\pi\) | ||||
0.907880 | + | 0.419231i | \(0.137700\pi\) | |||||||
\(608\) | −2.52055e145 | −0.176424 | ||||||||
\(609\) | 1.30343e146 | 0.836914 | ||||||||
\(610\) | 3.32698e145 | 0.195990 | ||||||||
\(611\) | −3.37257e146 | −1.82305 | ||||||||
\(612\) | −5.38661e144 | −0.0267218 | ||||||||
\(613\) | −4.21329e146 | −1.91843 | −0.959217 | − | 0.282672i | \(-0.908779\pi\) | ||||
−0.959217 | + | 0.282672i | \(0.908779\pi\) | |||||||
\(614\) | 2.47253e145 | 0.103348 | ||||||||
\(615\) | 1.27304e146 | 0.488538 | ||||||||
\(616\) | 1.73985e146 | 0.613090 | ||||||||
\(617\) | −2.51057e146 | −0.812457 | −0.406228 | − | 0.913772i | \(-0.633156\pi\) | ||||
−0.406228 | + | 0.913772i | \(0.633156\pi\) | |||||||
\(618\) | −4.68742e146 | −1.39328 | ||||||||
\(619\) | 4.37224e146 | 1.19384 | 0.596919 | − | 0.802302i | \(-0.296392\pi\) | ||||
0.596919 | + | 0.802302i | \(0.296392\pi\) | |||||||
\(620\) | 1.18991e145 | 0.0298505 | ||||||||
\(621\) | 2.15396e143 | 0.000496510 0 | ||||||||
\(622\) | −4.32190e146 | −0.915544 | ||||||||
\(623\) | 3.27136e145 | 0.0636950 | ||||||||
\(624\) | 9.13777e146 | 1.63550 | ||||||||
\(625\) | 4.54100e146 | 0.747224 | ||||||||
\(626\) | −9.97877e146 | −1.50982 | ||||||||
\(627\) | 1.04397e147 | 1.45258 | ||||||||
\(628\) | 6.24279e145 | 0.0798909 | ||||||||
\(629\) | −2.40988e146 | −0.283685 | ||||||||
\(630\) | 8.87865e145 | 0.0961542 | ||||||||
\(631\) | 1.17893e147 | 1.17475 | 0.587375 | − | 0.809315i | \(-0.300161\pi\) | ||||
0.587375 | + | 0.809315i | \(0.300161\pi\) | |||||||
\(632\) | −4.54223e146 | −0.416507 | ||||||||
\(633\) | −5.54803e145 | −0.0468213 | ||||||||
\(634\) | 7.16972e146 | 0.556950 | ||||||||
\(635\) | −2.76476e146 | −0.197714 | ||||||||
\(636\) | −4.93342e146 | −0.324825 | ||||||||
\(637\) | 1.95775e147 | 1.18696 | ||||||||
\(638\) | −4.13547e147 | −2.30908 | ||||||||
\(639\) | −3.52851e146 | −0.181467 | ||||||||
\(640\) | 4.71949e146 | 0.223587 | ||||||||
\(641\) | −1.42300e147 | −0.621096 | −0.310548 | − | 0.950558i | \(-0.600513\pi\) | ||||
−0.310548 | + | 0.950558i | \(0.600513\pi\) | |||||||
\(642\) | −8.06684e146 | −0.324425 | ||||||||
\(643\) | −3.56269e147 | −1.32039 | −0.660195 | − | 0.751095i | \(-0.729526\pi\) | ||||
−0.660195 | + | 0.751095i | \(0.729526\pi\) | |||||||
\(644\) | 7.57406e143 | 0.000258714 0 | ||||||||
\(645\) | 6.53257e145 | 0.0205683 | ||||||||
\(646\) | −4.73341e146 | −0.137394 | ||||||||
\(647\) | −2.08851e147 | −0.558934 | −0.279467 | − | 0.960155i | \(-0.590158\pi\) | ||||
−0.279467 | + | 0.960155i | \(0.590158\pi\) | |||||||
\(648\) | 4.54450e147 | 1.12150 | ||||||||
\(649\) | 9.08722e147 | 2.06816 | ||||||||
\(650\) | 5.60441e147 | 1.17646 | ||||||||
\(651\) | −2.08014e147 | −0.402802 | ||||||||
\(652\) | −5.53342e145 | −0.00988541 | ||||||||
\(653\) | −7.12364e147 | −1.17425 | −0.587124 | − | 0.809497i | \(-0.699740\pi\) | ||||
−0.587124 | + | 0.809497i | \(0.699740\pi\) | |||||||
\(654\) | 1.41043e148 | 2.14546 | ||||||||
\(655\) | −2.43073e147 | −0.341247 | ||||||||
\(656\) | −7.83906e147 | −1.01581 | ||||||||
\(657\) | −1.31953e148 | −1.57848 | ||||||||
\(658\) | 4.18346e147 | 0.462036 | ||||||||
\(659\) | 2.60531e147 | 0.265690 | 0.132845 | − | 0.991137i | \(-0.457589\pi\) | ||||
0.132845 | + | 0.991137i | \(0.457589\pi\) | |||||||
\(660\) | 8.83824e146 | 0.0832356 | ||||||||
\(661\) | 1.69983e148 | 1.47852 | 0.739262 | − | 0.673418i | \(-0.235175\pi\) | ||||
0.739262 | + | 0.673418i | \(0.235175\pi\) | |||||||
\(662\) | −1.04413e148 | −0.838903 | ||||||||
\(663\) | −5.64750e147 | −0.419175 | ||||||||
\(664\) | 9.11587e147 | 0.625136 | ||||||||
\(665\) | −1.18071e147 | −0.0748181 | ||||||||
\(666\) | −1.92807e148 | −1.12909 | ||||||||
\(667\) | −1.54967e146 | −0.00838749 | ||||||||
\(668\) | 1.88469e147 | 0.0942922 | ||||||||
\(669\) | 4.19135e148 | 1.93858 | ||||||||
\(670\) | −6.29533e147 | −0.269210 | ||||||||
\(671\) | −2.79255e148 | −1.10425 | ||||||||
\(672\) | 3.73037e147 | 0.136416 | ||||||||
\(673\) | −5.70050e148 | −1.92807 | −0.964033 | − | 0.265783i | \(-0.914369\pi\) | ||||
−0.964033 | + | 0.265783i | \(0.914369\pi\) | |||||||
\(674\) | −3.24634e148 | −1.01566 | ||||||||
\(675\) | 2.99192e147 | 0.0865969 | ||||||||
\(676\) | −4.47015e147 | −0.119707 | ||||||||
\(677\) | −1.15809e148 | −0.286971 | −0.143486 | − | 0.989652i | \(-0.545831\pi\) | ||||
−0.143486 | + | 0.989652i | \(0.545831\pi\) | |||||||
\(678\) | 9.68221e148 | 2.22032 | ||||||||
\(679\) | −2.46531e148 | −0.523249 | ||||||||
\(680\) | −3.44944e147 | −0.0677690 | ||||||||
\(681\) | 1.22761e149 | 2.23273 | ||||||||
\(682\) | 6.59977e148 | 1.11135 | ||||||||
\(683\) | −4.36434e148 | −0.680506 | −0.340253 | − | 0.940334i | \(-0.610513\pi\) | ||||
−0.340253 | + | 0.940334i | \(0.610513\pi\) | |||||||
\(684\) | 5.73114e147 | 0.0827553 | ||||||||
\(685\) | 2.06665e148 | 0.276383 | ||||||||
\(686\) | −5.25656e148 | −0.651156 | ||||||||
\(687\) | 1.10353e149 | 1.26635 | ||||||||
\(688\) | −4.02259e147 | −0.0427674 | ||||||||
\(689\) | −2.49484e149 | −2.45773 | ||||||||
\(690\) | −2.18848e146 | −0.00199786 | ||||||||
\(691\) | 9.93176e148 | 0.840289 | 0.420144 | − | 0.907457i | \(-0.361979\pi\) | ||||
0.420144 | + | 0.907457i | \(0.361979\pi\) | |||||||
\(692\) | −1.22408e148 | −0.0959927 | ||||||||
\(693\) | −7.45243e148 | −0.541755 | ||||||||
\(694\) | 1.00842e149 | 0.679624 | ||||||||
\(695\) | −3.16220e148 | −0.197600 | ||||||||
\(696\) | −4.05154e149 | −2.34766 | ||||||||
\(697\) | 4.84484e148 | 0.260351 | ||||||||
\(698\) | −7.91206e148 | −0.394348 | ||||||||
\(699\) | 1.18879e149 | 0.549608 | ||||||||
\(700\) | 1.05206e148 | 0.0451226 | ||||||||
\(701\) | 8.46981e148 | 0.337037 | 0.168519 | − | 0.985698i | \(-0.446102\pi\) | ||||
0.168519 | + | 0.985698i | \(0.446102\pi\) | |||||||
\(702\) | 3.30839e148 | 0.122157 | ||||||||
\(703\) | 2.56401e149 | 0.878547 | ||||||||
\(704\) | −5.32404e149 | −1.69308 | ||||||||
\(705\) | 1.82931e149 | 0.539955 | ||||||||
\(706\) | 2.52779e149 | 0.692619 | ||||||||
\(707\) | 2.14028e148 | 0.0544441 | ||||||||
\(708\) | 1.03426e149 | 0.244278 | ||||||||
\(709\) | 5.21147e149 | 1.14296 | 0.571482 | − | 0.820615i | \(-0.306369\pi\) | ||||
0.571482 | + | 0.820615i | \(0.306369\pi\) | |||||||
\(710\) | −2.62500e148 | −0.0534645 | ||||||||
\(711\) | 1.94561e149 | 0.368046 | ||||||||
\(712\) | −1.01686e149 | −0.178673 | ||||||||
\(713\) | 2.47311e147 | 0.00403685 | ||||||||
\(714\) | 7.00536e148 | 0.106237 | ||||||||
\(715\) | 4.46951e149 | 0.629786 | ||||||||
\(716\) | 3.60554e148 | 0.0472104 | ||||||||
\(717\) | −1.36118e150 | −1.65638 | ||||||||
\(718\) | 7.66483e149 | 0.866901 | ||||||||
\(719\) | −1.22999e150 | −1.29311 | −0.646553 | − | 0.762869i | \(-0.723790\pi\) | ||||
−0.646553 | + | 0.762869i | \(0.723790\pi\) | |||||||
\(720\) | −2.39067e149 | −0.233649 | ||||||||
\(721\) | −4.44980e149 | −0.404333 | ||||||||
\(722\) | −5.99452e149 | −0.506467 | ||||||||
\(723\) | 1.01193e150 | 0.795045 | ||||||||
\(724\) | 7.25294e148 | 0.0529955 | ||||||||
\(725\) | −2.15254e150 | −1.46287 | ||||||||
\(726\) | 2.85303e150 | 1.80357 | ||||||||
\(727\) | 6.70077e149 | 0.394065 | 0.197033 | − | 0.980397i | \(-0.436870\pi\) | ||||
0.197033 | + | 0.980397i | \(0.436870\pi\) | |||||||
\(728\) | 1.00139e150 | 0.547908 | ||||||||
\(729\) | −1.68770e150 | −0.859213 | ||||||||
\(730\) | −9.81650e149 | −0.465057 | ||||||||
\(731\) | 2.48612e148 | 0.0109612 | ||||||||
\(732\) | −3.17834e149 | −0.130427 | ||||||||
\(733\) | 3.97348e149 | 0.151779 | 0.0758897 | − | 0.997116i | \(-0.475820\pi\) | ||||
0.0758897 | + | 0.997116i | \(0.475820\pi\) | |||||||
\(734\) | −2.68366e150 | −0.954297 | ||||||||
\(735\) | −1.06190e150 | −0.351559 | ||||||||
\(736\) | −4.43508e147 | −0.00136715 | ||||||||
\(737\) | 5.28408e150 | 1.51679 | ||||||||
\(738\) | 3.87623e150 | 1.03622 | ||||||||
\(739\) | −6.00249e150 | −1.49451 | −0.747254 | − | 0.664538i | \(-0.768628\pi\) | ||||
−0.747254 | + | 0.664538i | \(0.768628\pi\) | |||||||
\(740\) | 2.17069e149 | 0.0503423 | ||||||||
\(741\) | 6.00871e150 | 1.29815 | ||||||||
\(742\) | 3.09469e150 | 0.622892 | ||||||||
\(743\) | −2.11116e148 | −0.00395922 | −0.00197961 | − | 0.999998i | \(-0.500630\pi\) | ||||
−0.00197961 | + | 0.999998i | \(0.500630\pi\) | |||||||
\(744\) | 6.46584e150 | 1.12991 | ||||||||
\(745\) | −8.26915e149 | −0.134666 | ||||||||
\(746\) | 1.50731e150 | 0.228779 | ||||||||
\(747\) | −3.90468e150 | −0.552400 | ||||||||
\(748\) | 3.36359e149 | 0.0443578 | ||||||||
\(749\) | −7.65791e149 | −0.0941488 | ||||||||
\(750\) | −6.36857e150 | −0.730004 | ||||||||
\(751\) | −1.19849e151 | −1.28097 | −0.640483 | − | 0.767972i | \(-0.721266\pi\) | ||||
−0.640483 | + | 0.767972i | \(0.721266\pi\) | |||||||
\(752\) | −1.12644e151 | −1.12272 | ||||||||
\(753\) | −1.62108e150 | −0.150685 | ||||||||
\(754\) | −2.38023e151 | −2.06359 | ||||||||
\(755\) | 3.86902e150 | 0.312886 | ||||||||
\(756\) | 6.21053e148 | 0.00468527 | ||||||||
\(757\) | 1.35251e151 | 0.951933 | 0.475966 | − | 0.879464i | \(-0.342098\pi\) | ||||
0.475966 | + | 0.879464i | \(0.342098\pi\) | |||||||
\(758\) | 2.51540e151 | 1.65187 | ||||||||
\(759\) | 1.83693e149 | 0.0112564 | ||||||||
\(760\) | 3.67007e150 | 0.209875 | ||||||||
\(761\) | 1.16327e151 | 0.620848 | 0.310424 | − | 0.950598i | \(-0.399529\pi\) | ||||
0.310424 | + | 0.950598i | \(0.399529\pi\) | |||||||
\(762\) | −1.74530e151 | −0.869430 | ||||||||
\(763\) | 1.33893e151 | 0.622615 | ||||||||
\(764\) | −3.66427e150 | −0.159069 | ||||||||
\(765\) | 1.47753e150 | 0.0598840 | ||||||||
\(766\) | 8.33997e150 | 0.315613 | ||||||||
\(767\) | 5.23028e151 | 1.84828 | ||||||||
\(768\) | −1.63078e151 | −0.538185 | ||||||||
\(769\) | 9.66156e149 | 0.0297793 | 0.0148896 | − | 0.999889i | \(-0.495260\pi\) | ||||
0.0148896 | + | 0.999889i | \(0.495260\pi\) | |||||||
\(770\) | −5.54415e150 | −0.159614 | ||||||||
\(771\) | −4.91838e151 | −1.32272 | ||||||||
\(772\) | −9.57105e150 | −0.240465 | ||||||||
\(773\) | 4.94920e150 | 0.116175 | 0.0580873 | − | 0.998312i | \(-0.481500\pi\) | ||||
0.0580873 | + | 0.998312i | \(0.481500\pi\) | |||||||
\(774\) | 1.98907e150 | 0.0436265 | ||||||||
\(775\) | 3.43523e151 | 0.704071 | ||||||||
\(776\) | 7.66307e151 | 1.46779 | ||||||||
\(777\) | −3.79469e151 | −0.679317 | ||||||||
\(778\) | −8.96121e151 | −1.49947 | ||||||||
\(779\) | −5.15472e151 | −0.806285 | ||||||||
\(780\) | 5.08697e150 | 0.0743863 | ||||||||
\(781\) | 2.20333e151 | 0.301231 | ||||||||
\(782\) | −8.32875e148 | −0.00106470 | ||||||||
\(783\) | −1.27069e151 | −0.151896 | ||||||||
\(784\) | 6.53891e151 | 0.730991 | ||||||||
\(785\) | −1.71237e151 | −0.179037 | ||||||||
\(786\) | −1.53444e152 | −1.50060 | ||||||||
\(787\) | −3.96812e151 | −0.363004 | −0.181502 | − | 0.983391i | \(-0.558096\pi\) | ||||
−0.181502 | + | 0.983391i | \(0.558096\pi\) | |||||||
\(788\) | −3.95825e150 | −0.0338748 | ||||||||
\(789\) | 3.19879e151 | 0.256120 | ||||||||
\(790\) | 1.44741e151 | 0.108435 | ||||||||
\(791\) | 9.19139e151 | 0.644341 | ||||||||
\(792\) | 2.31648e152 | 1.51970 | ||||||||
\(793\) | −1.60729e152 | −0.986852 | ||||||||
\(794\) | 1.79135e152 | 1.02945 | ||||||||
\(795\) | 1.35322e152 | 0.727938 | ||||||||
\(796\) | 2.40901e151 | 0.121312 | ||||||||
\(797\) | −2.62714e152 | −1.23857 | −0.619287 | − | 0.785165i | \(-0.712578\pi\) | ||||
−0.619287 | + | 0.785165i | \(0.712578\pi\) | |||||||
\(798\) | −7.45342e151 | −0.329006 | ||||||||
\(799\) | 6.96185e151 | 0.287752 | ||||||||
\(800\) | −6.16047e151 | −0.238446 | ||||||||
\(801\) | 4.35558e151 | 0.157884 | ||||||||
\(802\) | −4.27312e152 | −1.45074 | ||||||||
\(803\) | 8.23963e152 | 2.62024 | ||||||||
\(804\) | 6.01407e151 | 0.179154 | ||||||||
\(805\) | −2.07754e149 | −0.000579782 0 | ||||||||
\(806\) | 3.79859e152 | 0.993192 | ||||||||
\(807\) | −5.76382e152 | −1.41205 | ||||||||
\(808\) | −6.65275e151 | −0.152723 | ||||||||
\(809\) | 1.80159e152 | 0.387578 | 0.193789 | − | 0.981043i | \(-0.437922\pi\) | ||||
0.193789 | + | 0.981043i | \(0.437922\pi\) | |||||||
\(810\) | −1.44814e152 | −0.291975 | ||||||||
\(811\) | −7.80264e152 | −1.47451 | −0.737253 | − | 0.675617i | \(-0.763877\pi\) | ||||
−0.737253 | + | 0.675617i | \(0.763877\pi\) | |||||||
\(812\) | −4.46817e151 | −0.0791477 | ||||||||
\(813\) | −1.35483e153 | −2.24973 | ||||||||
\(814\) | 1.20396e153 | 1.87426 | ||||||||
\(815\) | 1.51780e151 | 0.0221533 | ||||||||
\(816\) | −1.88627e152 | −0.258149 | ||||||||
\(817\) | −2.64513e151 | −0.0339460 | ||||||||
\(818\) | −6.23493e152 | −0.750383 | ||||||||
\(819\) | −4.28935e152 | −0.484158 | ||||||||
\(820\) | −4.36399e151 | −0.0462015 | ||||||||
\(821\) | 3.35866e152 | 0.333542 | 0.166771 | − | 0.985996i | \(-0.446666\pi\) | ||||
0.166771 | + | 0.985996i | \(0.446666\pi\) | |||||||
\(822\) | 1.30460e153 | 1.21537 | ||||||||
\(823\) | −8.67106e152 | −0.757846 | −0.378923 | − | 0.925428i | \(-0.623705\pi\) | ||||
−0.378923 | + | 0.925428i | \(0.623705\pi\) | |||||||
\(824\) | 1.38316e153 | 1.13421 | ||||||||
\(825\) | 2.55156e153 | 1.96324 | ||||||||
\(826\) | −6.48783e152 | −0.468432 | ||||||||
\(827\) | 2.50977e153 | 1.70057 | 0.850284 | − | 0.526324i | \(-0.176430\pi\) | ||||
0.850284 | + | 0.526324i | \(0.176430\pi\) | |||||||
\(828\) | 1.00843e150 | 0.000641289 0 | ||||||||
\(829\) | 8.67655e152 | 0.517886 | 0.258943 | − | 0.965893i | \(-0.416626\pi\) | ||||
0.258943 | + | 0.965893i | \(0.416626\pi\) | |||||||
\(830\) | −2.90484e152 | −0.162750 | ||||||||
\(831\) | −1.05149e153 | −0.553031 | ||||||||
\(832\) | −3.06433e153 | −1.51308 | ||||||||
\(833\) | −4.04130e152 | −0.187352 | ||||||||
\(834\) | −1.99619e153 | −0.868929 | ||||||||
\(835\) | −5.16964e152 | −0.211310 | ||||||||
\(836\) | −3.57873e152 | −0.137372 | ||||||||
\(837\) | 2.02788e152 | 0.0731066 | ||||||||
\(838\) | −3.04861e153 | −1.03226 | ||||||||
\(839\) | 1.69754e152 | 0.0539904 | 0.0269952 | − | 0.999636i | \(-0.491406\pi\) | ||||
0.0269952 | + | 0.999636i | \(0.491406\pi\) | |||||||
\(840\) | −5.43163e152 | −0.162281 | ||||||||
\(841\) | 5.57918e153 | 1.56596 | ||||||||
\(842\) | −2.02814e153 | −0.534827 | ||||||||
\(843\) | −1.60918e153 | −0.398710 | ||||||||
\(844\) | 1.90187e151 | 0.00442794 | ||||||||
\(845\) | 1.22614e153 | 0.268265 | ||||||||
\(846\) | 5.56998e153 | 1.14527 | ||||||||
\(847\) | 2.70840e153 | 0.523400 | ||||||||
\(848\) | −8.33279e153 | −1.51359 | ||||||||
\(849\) | −2.78301e153 | −0.475183 | ||||||||
\(850\) | −1.15689e153 | −0.185695 | ||||||||
\(851\) | 4.51155e151 | 0.00680806 | ||||||||
\(852\) | 2.50772e152 | 0.0355795 | ||||||||
\(853\) | 5.71396e153 | 0.762278 | 0.381139 | − | 0.924518i | \(-0.375532\pi\) | ||||
0.381139 | + | 0.924518i | \(0.375532\pi\) | |||||||
\(854\) | 1.99374e153 | 0.250110 | ||||||||
\(855\) | −1.57203e153 | −0.185456 | ||||||||
\(856\) | 2.38035e153 | 0.264100 | ||||||||
\(857\) | −1.55632e154 | −1.62407 | −0.812035 | − | 0.583609i | \(-0.801640\pi\) | ||||
−0.812035 | + | 0.583609i | \(0.801640\pi\) | |||||||
\(858\) | 2.82145e154 | 2.76943 | ||||||||
\(859\) | −9.58283e153 | −0.884815 | −0.442408 | − | 0.896814i | \(-0.645876\pi\) | ||||
−0.442408 | + | 0.896814i | \(0.645876\pi\) | |||||||
\(860\) | −2.23937e151 | −0.00194517 | ||||||||
\(861\) | 7.62889e153 | 0.623441 | ||||||||
\(862\) | 1.21563e154 | 0.934697 | ||||||||
\(863\) | 5.02429e153 | 0.363503 | 0.181751 | − | 0.983345i | \(-0.441823\pi\) | ||||
0.181751 | + | 0.983345i | \(0.441823\pi\) | |||||||
\(864\) | −3.63665e152 | −0.0247588 | ||||||||
\(865\) | 3.35760e153 | 0.215121 | ||||||||
\(866\) | −1.83148e154 | −1.10437 | ||||||||
\(867\) | −2.33238e154 | −1.32372 | ||||||||
\(868\) | 7.13074e152 | 0.0380933 | ||||||||
\(869\) | −1.21491e154 | −0.610949 | ||||||||
\(870\) | 1.29105e154 | 0.611199 | ||||||||
\(871\) | 3.04133e154 | 1.35553 | ||||||||
\(872\) | −4.16188e154 | −1.74652 | ||||||||
\(873\) | −3.28239e154 | −1.29701 | ||||||||
\(874\) | 8.86146e151 | 0.00329727 | ||||||||
\(875\) | −6.04572e153 | −0.211849 | ||||||||
\(876\) | 9.37792e153 | 0.309486 | ||||||||
\(877\) | 2.68630e154 | 0.834981 | 0.417490 | − | 0.908681i | \(-0.362910\pi\) | ||||
0.417490 | + | 0.908681i | \(0.362910\pi\) | |||||||
\(878\) | 1.57109e154 | 0.459981 | ||||||||
\(879\) | −2.63643e154 | −0.727110 | ||||||||
\(880\) | 1.49282e154 | 0.387853 | ||||||||
\(881\) | −5.37696e151 | −0.00131614 | −0.000658069 | − | 1.00000i | \(-0.500209\pi\) | ||||
−0.000658069 | 1.00000i | \(0.500209\pi\) | ||||||||
\(882\) | −3.23333e154 | −0.745675 | ||||||||
\(883\) | 2.65925e154 | 0.577861 | 0.288930 | − | 0.957350i | \(-0.406700\pi\) | ||||
0.288930 | + | 0.957350i | \(0.406700\pi\) | |||||||
\(884\) | 1.93596e153 | 0.0396418 | ||||||||
\(885\) | −2.83694e154 | −0.547430 | ||||||||
\(886\) | 5.98600e153 | 0.108859 | ||||||||
\(887\) | 4.10224e154 | 0.703122 | 0.351561 | − | 0.936165i | \(-0.385651\pi\) | ||||
0.351561 | + | 0.936165i | \(0.385651\pi\) | |||||||
\(888\) | 1.17953e155 | 1.90558 | ||||||||
\(889\) | −1.65683e154 | −0.252310 | ||||||||
\(890\) | 3.24028e153 | 0.0465166 | ||||||||
\(891\) | 1.21551e155 | 1.64506 | ||||||||
\(892\) | −1.43680e154 | −0.183333 | ||||||||
\(893\) | −7.40712e154 | −0.891144 | ||||||||
\(894\) | −5.22004e154 | −0.592180 | ||||||||
\(895\) | −9.88988e153 | −0.105799 | ||||||||
\(896\) | 2.82823e154 | 0.285328 | ||||||||
\(897\) | 1.05727e153 | 0.0100597 | ||||||||
\(898\) | −2.94365e153 | −0.0264167 | ||||||||
\(899\) | −1.45896e155 | −1.23498 | ||||||||
\(900\) | 1.40075e154 | 0.111848 | ||||||||
\(901\) | 5.14999e154 | 0.387931 | ||||||||
\(902\) | −2.42045e155 | −1.72010 | ||||||||
\(903\) | 3.91474e153 | 0.0262480 | ||||||||
\(904\) | −2.85701e155 | −1.80746 | ||||||||
\(905\) | −1.98946e154 | −0.118764 | ||||||||
\(906\) | 2.44238e155 | 1.37589 | ||||||||
\(907\) | −4.27645e154 | −0.227353 | −0.113677 | − | 0.993518i | \(-0.536263\pi\) | ||||
−0.113677 | + | 0.993518i | \(0.536263\pi\) | |||||||
\(908\) | −4.20825e154 | −0.211151 | ||||||||
\(909\) | 2.84963e154 | 0.134954 | ||||||||
\(910\) | −3.19101e154 | −0.142645 | ||||||||
\(911\) | 4.52642e155 | 1.91003 | 0.955015 | − | 0.296556i | \(-0.0958383\pi\) | ||||
0.955015 | + | 0.296556i | \(0.0958383\pi\) | |||||||
\(912\) | 2.00691e155 | 0.799465 | ||||||||
\(913\) | 2.43822e155 | 0.916974 | ||||||||
\(914\) | −9.96974e154 | −0.354004 | ||||||||
\(915\) | 8.71806e154 | 0.292289 | ||||||||
\(916\) | −3.78290e154 | −0.119760 | ||||||||
\(917\) | −1.45665e155 | −0.435478 | ||||||||
\(918\) | −6.82937e153 | −0.0192814 | ||||||||
\(919\) | −5.60391e155 | −1.49426 | −0.747132 | − | 0.664676i | \(-0.768569\pi\) | ||||
−0.747132 | + | 0.664676i | \(0.768569\pi\) | |||||||
\(920\) | 6.45773e152 | 0.00162637 | ||||||||
\(921\) | 6.47905e154 | 0.154128 | ||||||||
\(922\) | 1.44816e155 | 0.325419 | ||||||||
\(923\) | 1.26816e155 | 0.269206 | ||||||||
\(924\) | 5.29645e154 | 0.106220 | ||||||||
\(925\) | 6.26669e155 | 1.18740 | ||||||||
\(926\) | −4.77785e155 | −0.855373 | ||||||||
\(927\) | −5.92460e155 | −1.00224 | ||||||||
\(928\) | 2.61639e155 | 0.418248 | ||||||||
\(929\) | 8.70215e155 | 1.31462 | 0.657312 | − | 0.753619i | \(-0.271693\pi\) | ||||
0.657312 | + | 0.753619i | \(0.271693\pi\) | |||||||
\(930\) | −2.06038e155 | −0.294167 | ||||||||
\(931\) | 4.29978e155 | 0.580214 | ||||||||
\(932\) | −4.07517e154 | −0.0519769 | ||||||||
\(933\) | −1.13252e156 | −1.36539 | ||||||||
\(934\) | −3.98634e155 | −0.454322 | ||||||||
\(935\) | −9.22621e154 | −0.0994063 | ||||||||
\(936\) | 1.33329e156 | 1.35813 | ||||||||
\(937\) | −8.48069e155 | −0.816775 | −0.408388 | − | 0.912809i | \(-0.633909\pi\) | ||||
−0.408388 | + | 0.912809i | \(0.633909\pi\) | |||||||
\(938\) | −3.77258e155 | −0.343549 | ||||||||
\(939\) | −2.61485e156 | −2.25166 | ||||||||
\(940\) | −6.27087e154 | −0.0510641 | ||||||||
\(941\) | 1.20312e156 | 0.926517 | 0.463258 | − | 0.886223i | \(-0.346680\pi\) | ||||
0.463258 | + | 0.886223i | \(0.346680\pi\) | |||||||
\(942\) | −1.08096e156 | −0.787298 | ||||||||
\(943\) | −9.07007e153 | −0.00624808 | ||||||||
\(944\) | 1.74692e156 | 1.13826 | ||||||||
\(945\) | −1.70353e154 | −0.0104998 | ||||||||
\(946\) | −1.24205e155 | −0.0724193 | ||||||||
\(947\) | −9.05317e155 | −0.499375 | −0.249687 | − | 0.968326i | \(-0.580328\pi\) | ||||
−0.249687 | + | 0.968326i | \(0.580328\pi\) | |||||||
\(948\) | −1.38275e155 | −0.0721614 | ||||||||
\(949\) | 4.74244e156 | 2.34167 | ||||||||
\(950\) | 1.23089e156 | 0.575081 | ||||||||
\(951\) | 1.87876e156 | 0.830606 | ||||||||
\(952\) | −2.06713e155 | −0.0864826 | ||||||||
\(953\) | −3.42515e155 | −0.135613 | −0.0678067 | − | 0.997698i | \(-0.521600\pi\) | ||||
−0.0678067 | + | 0.997698i | \(0.521600\pi\) | |||||||
\(954\) | 4.12036e156 | 1.54400 | ||||||||
\(955\) | 1.00510e156 | 0.356476 | ||||||||
\(956\) | 4.66614e155 | 0.156646 | ||||||||
\(957\) | −1.08366e157 | −3.44364 | ||||||||
\(958\) | −4.71285e156 | −1.41773 | ||||||||
\(959\) | 1.23847e156 | 0.352702 | ||||||||
\(960\) | 1.66211e156 | 0.448147 | ||||||||
\(961\) | −1.58887e156 | −0.405610 | ||||||||
\(962\) | 6.92956e156 | 1.67500 | ||||||||
\(963\) | −1.01960e156 | −0.233372 | ||||||||
\(964\) | −3.46891e155 | −0.0751881 | ||||||||
\(965\) | 2.62530e156 | 0.538884 | ||||||||
\(966\) | −1.31148e154 | −0.00254954 | ||||||||
\(967\) | −9.59776e156 | −1.76718 | −0.883588 | − | 0.468265i | \(-0.844879\pi\) | ||||
−0.883588 | + | 0.468265i | \(0.844879\pi\) | |||||||
\(968\) | −8.41868e156 | −1.46821 | ||||||||
\(969\) | −1.24035e156 | −0.204902 | ||||||||
\(970\) | −2.44189e156 | −0.382129 | ||||||||
\(971\) | 8.31538e156 | 1.23274 | 0.616372 | − | 0.787455i | \(-0.288602\pi\) | ||||
0.616372 | + | 0.787455i | \(0.288602\pi\) | |||||||
\(972\) | 1.29469e156 | 0.181839 | ||||||||
\(973\) | −1.89500e156 | −0.252165 | ||||||||
\(974\) | −4.04808e156 | −0.510392 | ||||||||
\(975\) | 1.46859e157 | 1.75452 | ||||||||
\(976\) | −5.36836e156 | −0.607752 | ||||||||
\(977\) | 2.36789e156 | 0.254037 | 0.127018 | − | 0.991900i | \(-0.459459\pi\) | ||||
0.127018 | + | 0.991900i | \(0.459459\pi\) | |||||||
\(978\) | 9.58134e155 | 0.0974174 | ||||||||
\(979\) | −2.71978e156 | −0.262085 | ||||||||
\(980\) | 3.64019e155 | 0.0332472 | ||||||||
\(981\) | 1.78269e157 | 1.54331 | ||||||||
\(982\) | 4.25837e156 | 0.349454 | ||||||||
\(983\) | 1.74866e157 | 1.36033 | 0.680167 | − | 0.733057i | \(-0.261907\pi\) | ||||
0.680167 | + | 0.733057i | \(0.261907\pi\) | |||||||
\(984\) | −2.37133e157 | −1.74884 | ||||||||
\(985\) | 1.08573e156 | 0.0759138 | ||||||||
\(986\) | 4.91339e156 | 0.325719 | ||||||||
\(987\) | 1.09624e157 | 0.689057 | ||||||||
\(988\) | −2.05979e156 | −0.122767 | ||||||||
\(989\) | −4.65428e153 | −0.000263055 0 | ||||||||
\(990\) | −7.38164e156 | −0.395645 | ||||||||
\(991\) | −1.15467e157 | −0.586938 | −0.293469 | − | 0.955969i | \(-0.594810\pi\) | ||||
−0.293469 | + | 0.955969i | \(0.594810\pi\) | |||||||
\(992\) | −4.17549e156 | −0.201300 | ||||||||
\(993\) | −2.73607e157 | −1.25110 | ||||||||
\(994\) | −1.57307e156 | −0.0682280 | ||||||||
\(995\) | −6.60783e156 | −0.271861 | ||||||||
\(996\) | 2.77506e156 | 0.108307 | ||||||||
\(997\) | −2.03200e157 | −0.752364 | −0.376182 | − | 0.926546i | \(-0.622763\pi\) | ||||
−0.376182 | + | 0.926546i | \(0.622763\pi\) | |||||||
\(998\) | 3.13425e157 | 1.10098 | ||||||||
\(999\) | 3.69935e156 | 0.123293 |
(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 | 1.106.a.a.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.106.a.a.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial |