Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,90,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, 90, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 90);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 90 \) |
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: | \(50.1624291928\) |
Analytic rank: | \(1\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{83}\cdot 3^{29}\cdot 5^{9}\cdot 7^{5}\cdot 11^{2}\cdot 13^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(9.08809e11\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.81096e13 | −1.93373 | −0.966867 | − | 0.255279i | \(-0.917833\pi\) | ||||
−0.966867 | + | 0.255279i | \(0.917833\pi\) | |||||||
\(3\) | −1.58991e21 | −0.932131 | −0.466066 | − | 0.884750i | \(-0.654329\pi\) | ||||
−0.466066 | + | 0.884750i | \(0.654329\pi\) | |||||||
\(4\) | 1.69556e27 | 2.73933 | ||||||||
\(5\) | 1.07790e31 | 0.848032 | 0.424016 | − | 0.905655i | \(-0.360620\pi\) | ||||
0.424016 | + | 0.905655i | \(0.360620\pi\) | |||||||
\(6\) | 7.64900e34 | 1.80249 | ||||||||
\(7\) | 5.70296e37 | 1.41006 | 0.705030 | − | 0.709177i | \(-0.250933\pi\) | ||||
0.705030 | + | 0.709177i | \(0.250933\pi\) | |||||||
\(8\) | −5.17945e40 | −3.36340 | ||||||||
\(9\) | −3.81503e41 | −0.131131 | ||||||||
\(10\) | −5.18572e44 | −1.63987 | ||||||||
\(11\) | 1.25806e46 | 0.572435 | 0.286217 | − | 0.958165i | \(-0.407602\pi\) | ||||
0.286217 | + | 0.958165i | \(0.407602\pi\) | |||||||
\(12\) | −2.69579e48 | −2.55341 | ||||||||
\(13\) | −3.04674e49 | −0.819136 | −0.409568 | − | 0.912280i | \(-0.634320\pi\) | ||||
−0.409568 | + | 0.912280i | \(0.634320\pi\) | |||||||
\(14\) | −2.74367e51 | −2.72668 | ||||||||
\(15\) | −1.71376e52 | −0.790477 | ||||||||
\(16\) | 1.44231e54 | 3.76460 | ||||||||
\(17\) | −1.44307e54 | −0.253695 | −0.126847 | − | 0.991922i | \(-0.540486\pi\) | ||||
−0.126847 | + | 0.991922i | \(0.540486\pi\) | |||||||
\(18\) | 1.83540e55 | 0.253573 | ||||||||
\(19\) | −2.63820e56 | −0.328680 | −0.164340 | − | 0.986404i | \(-0.552549\pi\) | ||||
−0.164340 | + | 0.986404i | \(0.552549\pi\) | |||||||
\(20\) | 1.82764e58 | 2.32304 | ||||||||
\(21\) | −9.06721e58 | −1.31436 | ||||||||
\(22\) | −6.05246e59 | −1.10694 | ||||||||
\(23\) | 1.82853e60 | 0.462609 | 0.231304 | − | 0.972881i | \(-0.425701\pi\) | ||||
0.231304 | + | 0.972881i | \(0.425701\pi\) | |||||||
\(24\) | 8.23486e61 | 3.13513 | ||||||||
\(25\) | −4.53723e61 | −0.280841 | ||||||||
\(26\) | 1.46577e63 | 1.58399 | ||||||||
\(27\) | 5.23212e63 | 1.05436 | ||||||||
\(28\) | 9.66973e64 | 3.86262 | ||||||||
\(29\) | −1.87067e65 | −1.56778 | −0.783890 | − | 0.620899i | \(-0.786768\pi\) | ||||
−0.783890 | + | 0.620899i | \(0.786768\pi\) | |||||||
\(30\) | 8.24484e65 | 1.52857 | ||||||||
\(31\) | 9.55617e65 | 0.411802 | 0.205901 | − | 0.978573i | \(-0.433988\pi\) | ||||
0.205901 | + | 0.978573i | \(0.433988\pi\) | |||||||
\(32\) | −3.73296e67 | −3.91633 | ||||||||
\(33\) | −2.00020e67 | −0.533584 | ||||||||
\(34\) | 6.94257e67 | 0.490579 | ||||||||
\(35\) | 6.14721e68 | 1.19578 | ||||||||
\(36\) | −6.46863e68 | −0.359212 | ||||||||
\(37\) | 6.40520e69 | 1.05089 | 0.525443 | − | 0.850829i | \(-0.323899\pi\) | ||||
0.525443 | + | 0.850829i | \(0.323899\pi\) | |||||||
\(38\) | 1.26923e70 | 0.635580 | ||||||||
\(39\) | 4.84404e70 | 0.763542 | ||||||||
\(40\) | −5.58291e71 | −2.85227 | ||||||||
\(41\) | −1.04557e72 | −1.78021 | −0.890106 | − | 0.455754i | \(-0.849370\pi\) | ||||
−0.890106 | + | 0.455754i | \(0.849370\pi\) | |||||||
\(42\) | 4.36220e72 | 2.54163 | ||||||||
\(43\) | −3.49195e72 | −0.714039 | −0.357019 | − | 0.934097i | \(-0.616207\pi\) | ||||
−0.357019 | + | 0.934097i | \(0.616207\pi\) | |||||||
\(44\) | 2.13312e73 | 1.56809 | ||||||||
\(45\) | −4.11221e72 | −0.111204 | ||||||||
\(46\) | −8.79700e73 | −0.894563 | ||||||||
\(47\) | 6.29528e72 | 0.0245845 | 0.0122922 | − | 0.999924i | \(-0.496087\pi\) | ||||
0.0122922 | + | 0.999924i | \(0.496087\pi\) | |||||||
\(48\) | −2.29314e75 | −3.50910 | ||||||||
\(49\) | 1.61660e75 | 0.988271 | ||||||||
\(50\) | 2.18284e75 | 0.543072 | ||||||||
\(51\) | 2.29436e75 | 0.236477 | ||||||||
\(52\) | −5.16593e76 | −2.24388 | ||||||||
\(53\) | 6.67038e75 | 0.124129 | 0.0620647 | − | 0.998072i | \(-0.480231\pi\) | ||||
0.0620647 | + | 0.998072i | \(0.480231\pi\) | |||||||
\(54\) | −2.51715e77 | −2.03886 | ||||||||
\(55\) | 1.35606e77 | 0.485443 | ||||||||
\(56\) | −2.95382e78 | −4.74260 | ||||||||
\(57\) | 4.19451e77 | 0.306373 | ||||||||
\(58\) | 8.99970e78 | 3.03167 | ||||||||
\(59\) | −1.69313e78 | −0.266549 | −0.133274 | − | 0.991079i | \(-0.542549\pi\) | ||||
−0.133274 | + | 0.991079i | \(0.542549\pi\) | |||||||
\(60\) | −2.90579e79 | −2.16538 | ||||||||
\(61\) | 1.46459e79 | 0.523044 | 0.261522 | − | 0.965197i | \(-0.415776\pi\) | ||||
0.261522 | + | 0.965197i | \(0.415776\pi\) | |||||||
\(62\) | −4.59743e79 | −0.796316 | ||||||||
\(63\) | −2.17570e79 | −0.184903 | ||||||||
\(64\) | 9.03167e80 | 3.80855 | ||||||||
\(65\) | −3.28407e80 | −0.694653 | ||||||||
\(66\) | 9.62288e80 | 1.03181 | ||||||||
\(67\) | 2.58895e81 | 1.42166 | 0.710828 | − | 0.703366i | \(-0.248321\pi\) | ||||
0.710828 | + | 0.703366i | \(0.248321\pi\) | |||||||
\(68\) | −2.44682e81 | −0.694954 | ||||||||
\(69\) | −2.90720e81 | −0.431212 | ||||||||
\(70\) | −2.95740e82 | −2.31232 | ||||||||
\(71\) | 2.08753e82 | 0.868234 | 0.434117 | − | 0.900856i | \(-0.357060\pi\) | ||||
0.434117 | + | 0.900856i | \(0.357060\pi\) | |||||||
\(72\) | 1.97597e82 | 0.441047 | ||||||||
\(73\) | 2.80058e82 | 0.338361 | 0.169181 | − | 0.985585i | \(-0.445888\pi\) | ||||
0.169181 | + | 0.985585i | \(0.445888\pi\) | |||||||
\(74\) | −3.08152e83 | −2.03214 | ||||||||
\(75\) | 7.21380e82 | 0.261781 | ||||||||
\(76\) | −4.47324e83 | −0.900362 | ||||||||
\(77\) | 7.17466e83 | 0.807168 | ||||||||
\(78\) | −2.33045e84 | −1.47649 | ||||||||
\(79\) | 1.45733e84 | 0.523783 | 0.261892 | − | 0.965097i | \(-0.415654\pi\) | ||||
0.261892 | + | 0.965097i | \(0.415654\pi\) | |||||||
\(80\) | 1.55466e85 | 3.19250 | ||||||||
\(81\) | −7.20869e84 | −0.851673 | ||||||||
\(82\) | 5.03020e85 | 3.44246 | ||||||||
\(83\) | −3.27919e85 | −1.30855 | −0.654276 | − | 0.756256i | \(-0.727027\pi\) | ||||
−0.654276 | + | 0.756256i | \(0.727027\pi\) | |||||||
\(84\) | −1.53740e86 | −3.60047 | ||||||||
\(85\) | −1.55549e85 | −0.215141 | ||||||||
\(86\) | 1.67996e86 | 1.38076 | ||||||||
\(87\) | 2.97419e86 | 1.46138 | ||||||||
\(88\) | −6.51604e86 | −1.92533 | ||||||||
\(89\) | −3.07472e86 | −0.549478 | −0.274739 | − | 0.961519i | \(-0.588591\pi\) | ||||
−0.274739 | + | 0.961519i | \(0.588591\pi\) | |||||||
\(90\) | 1.97837e86 | 0.215038 | ||||||||
\(91\) | −1.73754e87 | −1.15503 | ||||||||
\(92\) | 3.10039e87 | 1.26724 | ||||||||
\(93\) | −1.51935e87 | −0.383854 | ||||||||
\(94\) | −3.02863e86 | −0.0475398 | ||||||||
\(95\) | −2.84371e87 | −0.278731 | ||||||||
\(96\) | 5.93508e88 | 3.65053 | ||||||||
\(97\) | 1.70392e88 | 0.660856 | 0.330428 | − | 0.943831i | \(-0.392807\pi\) | ||||
0.330428 | + | 0.943831i | \(0.392807\pi\) | |||||||
\(98\) | −7.77738e88 | −1.91105 | ||||||||
\(99\) | −4.79953e87 | −0.0750641 | ||||||||
\(100\) | −7.69317e88 | −0.769317 | ||||||||
\(101\) | −1.94636e89 | −1.25003 | −0.625016 | − | 0.780612i | \(-0.714908\pi\) | ||||
−0.625016 | + | 0.780612i | \(0.714908\pi\) | |||||||
\(102\) | −1.10381e89 | −0.457284 | ||||||||
\(103\) | −2.49750e89 | −0.670270 | −0.335135 | − | 0.942170i | \(-0.608782\pi\) | ||||
−0.335135 | + | 0.942170i | \(0.608782\pi\) | |||||||
\(104\) | 1.57804e90 | 2.75508 | ||||||||
\(105\) | −9.77352e89 | −1.11462 | ||||||||
\(106\) | −3.20909e89 | −0.240033 | ||||||||
\(107\) | −1.15673e90 | −0.569708 | −0.284854 | − | 0.958571i | \(-0.591945\pi\) | ||||
−0.284854 | + | 0.958571i | \(0.591945\pi\) | |||||||
\(108\) | 8.87139e90 | 2.88825 | ||||||||
\(109\) | −7.89198e90 | −1.70493 | −0.852466 | − | 0.522783i | \(-0.824894\pi\) | ||||
−0.852466 | + | 0.522783i | \(0.824894\pi\) | |||||||
\(110\) | −6.52394e90 | −0.938718 | ||||||||
\(111\) | −1.01837e91 | −0.979564 | ||||||||
\(112\) | 8.22543e91 | 5.30831 | ||||||||
\(113\) | −2.57271e91 | −1.11789 | −0.558946 | − | 0.829204i | \(-0.688794\pi\) | ||||
−0.558946 | + | 0.829204i | \(0.688794\pi\) | |||||||
\(114\) | −2.01796e91 | −0.592444 | ||||||||
\(115\) | 1.97097e91 | 0.392307 | ||||||||
\(116\) | −3.17183e92 | −4.29467 | ||||||||
\(117\) | 1.16234e91 | 0.107414 | ||||||||
\(118\) | 8.14559e91 | 0.515434 | ||||||||
\(119\) | −8.22980e91 | −0.357725 | ||||||||
\(120\) | 8.87634e92 | 2.65869 | ||||||||
\(121\) | −3.24731e92 | −0.672318 | ||||||||
\(122\) | −7.04609e92 | −1.01143 | ||||||||
\(123\) | 1.66236e93 | 1.65939 | ||||||||
\(124\) | 1.62031e93 | 1.12806 | ||||||||
\(125\) | −2.23051e93 | −1.08619 | ||||||||
\(126\) | 1.04672e93 | 0.357554 | ||||||||
\(127\) | 2.77892e93 | 0.667744 | 0.333872 | − | 0.942618i | \(-0.391645\pi\) | ||||
0.333872 | + | 0.942618i | \(0.391645\pi\) | |||||||
\(128\) | −2.03451e94 | −3.44839 | ||||||||
\(129\) | 5.55189e93 | 0.665578 | ||||||||
\(130\) | 1.57995e94 | 1.34328 | ||||||||
\(131\) | 2.61791e94 | 1.58264 | 0.791318 | − | 0.611404i | \(-0.209395\pi\) | ||||
0.791318 | + | 0.611404i | \(0.209395\pi\) | |||||||
\(132\) | −3.39147e94 | −1.46166 | ||||||||
\(133\) | −1.50456e94 | −0.463458 | ||||||||
\(134\) | −1.24553e95 | −2.74910 | ||||||||
\(135\) | 5.63969e94 | 0.894134 | ||||||||
\(136\) | 7.47433e94 | 0.853278 | ||||||||
\(137\) | 1.28376e95 | 1.05784 | 0.528920 | − | 0.848672i | \(-0.322597\pi\) | ||||
0.528920 | + | 0.848672i | \(0.322597\pi\) | |||||||
\(138\) | 1.39864e95 | 0.833850 | ||||||||
\(139\) | −3.19520e95 | −1.38146 | −0.690732 | − | 0.723111i | \(-0.742712\pi\) | ||||
−0.690732 | + | 0.723111i | \(0.742712\pi\) | |||||||
\(140\) | 1.04230e96 | 3.27563 | ||||||||
\(141\) | −1.00089e94 | −0.0229159 | ||||||||
\(142\) | −1.00430e96 | −1.67893 | ||||||||
\(143\) | −3.83297e95 | −0.468902 | ||||||||
\(144\) | −5.50245e95 | −0.493657 | ||||||||
\(145\) | −2.01639e96 | −1.32953 | ||||||||
\(146\) | −1.34735e96 | −0.654301 | ||||||||
\(147\) | −2.57024e96 | −0.921198 | ||||||||
\(148\) | 1.08604e97 | 2.87873 | ||||||||
\(149\) | 5.65429e96 | 1.11068 | 0.555340 | − | 0.831624i | \(-0.312588\pi\) | ||||
0.555340 | + | 0.831624i | \(0.312588\pi\) | |||||||
\(150\) | −3.47053e96 | −0.506215 | ||||||||
\(151\) | −1.22003e97 | −1.32402 | −0.662011 | − | 0.749495i | \(-0.730297\pi\) | ||||
−0.662011 | + | 0.749495i | \(0.730297\pi\) | |||||||
\(152\) | 1.36644e97 | 1.10548 | ||||||||
\(153\) | 5.50538e95 | 0.0332674 | ||||||||
\(154\) | −3.45170e97 | −1.56085 | ||||||||
\(155\) | 1.03006e97 | 0.349221 | ||||||||
\(156\) | 8.21338e97 | 2.09159 | ||||||||
\(157\) | 5.80043e97 | 1.11154 | 0.555771 | − | 0.831335i | \(-0.312423\pi\) | ||||
0.555771 | + | 0.831335i | \(0.312423\pi\) | |||||||
\(158\) | −7.01114e97 | −1.01286 | ||||||||
\(159\) | −1.06053e97 | −0.115705 | ||||||||
\(160\) | −4.02375e98 | −3.32118 | ||||||||
\(161\) | 1.04281e98 | 0.652307 | ||||||||
\(162\) | 3.46807e98 | 1.64691 | ||||||||
\(163\) | 4.97994e98 | 1.79835 | 0.899177 | − | 0.437584i | \(-0.144166\pi\) | ||||
0.899177 | + | 0.437584i | \(0.144166\pi\) | |||||||
\(164\) | −1.77283e99 | −4.87659 | ||||||||
\(165\) | −2.15601e98 | −0.452497 | ||||||||
\(166\) | 1.57760e99 | 2.53039 | ||||||||
\(167\) | −1.16618e99 | −1.43180 | −0.715900 | − | 0.698202i | \(-0.753984\pi\) | ||||
−0.715900 | + | 0.698202i | \(0.753984\pi\) | |||||||
\(168\) | 4.69631e99 | 4.42073 | ||||||||
\(169\) | −4.55173e98 | −0.329017 | ||||||||
\(170\) | 7.48338e98 | 0.416027 | ||||||||
\(171\) | 1.00648e98 | 0.0431002 | ||||||||
\(172\) | −5.92082e99 | −1.95599 | ||||||||
\(173\) | 1.56484e99 | 0.399410 | 0.199705 | − | 0.979856i | \(-0.436002\pi\) | ||||
0.199705 | + | 0.979856i | \(0.436002\pi\) | |||||||
\(174\) | −1.43087e100 | −2.82592 | ||||||||
\(175\) | −2.58757e99 | −0.396003 | ||||||||
\(176\) | 1.81451e100 | 2.15499 | ||||||||
\(177\) | 2.69193e99 | 0.248458 | ||||||||
\(178\) | 1.47924e100 | 1.06254 | ||||||||
\(179\) | −3.09061e100 | −1.73015 | −0.865077 | − | 0.501639i | \(-0.832730\pi\) | ||||
−0.865077 | + | 0.501639i | \(0.832730\pi\) | |||||||
\(180\) | −6.97252e99 | −0.304623 | ||||||||
\(181\) | −9.98755e99 | −0.341006 | −0.170503 | − | 0.985357i | \(-0.554539\pi\) | ||||
−0.170503 | + | 0.985357i | \(0.554539\pi\) | |||||||
\(182\) | 8.35925e100 | 2.23352 | ||||||||
\(183\) | −2.32857e100 | −0.487546 | ||||||||
\(184\) | −9.47078e100 | −1.55594 | ||||||||
\(185\) | 6.90415e100 | 0.891186 | ||||||||
\(186\) | 7.30951e100 | 0.742271 | ||||||||
\(187\) | −1.81547e100 | −0.145224 | ||||||||
\(188\) | 1.06740e100 | 0.0673449 | ||||||||
\(189\) | 2.98386e101 | 1.48672 | ||||||||
\(190\) | 1.36810e101 | 0.538992 | ||||||||
\(191\) | −8.28952e100 | −0.258550 | −0.129275 | − | 0.991609i | \(-0.541265\pi\) | ||||
−0.129275 | + | 0.991609i | \(0.541265\pi\) | |||||||
\(192\) | −1.43596e102 | −3.55007 | ||||||||
\(193\) | −2.59064e101 | −0.508284 | −0.254142 | − | 0.967167i | \(-0.581793\pi\) | ||||
−0.254142 | + | 0.967167i | \(0.581793\pi\) | |||||||
\(194\) | −8.19749e101 | −1.27792 | ||||||||
\(195\) | 5.22138e101 | 0.647508 | ||||||||
\(196\) | 2.74104e102 | 2.70720 | ||||||||
\(197\) | −1.12650e102 | −0.887121 | −0.443560 | − | 0.896244i | \(-0.646285\pi\) | ||||
−0.443560 | + | 0.896244i | \(0.646285\pi\) | |||||||
\(198\) | 2.30903e101 | 0.145154 | ||||||||
\(199\) | 2.12882e102 | 1.06949 | 0.534745 | − | 0.845013i | \(-0.320408\pi\) | ||||
0.534745 | + | 0.845013i | \(0.320408\pi\) | |||||||
\(200\) | 2.35004e102 | 0.944582 | ||||||||
\(201\) | −4.11620e102 | −1.32517 | ||||||||
\(202\) | 9.36385e102 | 2.41723 | ||||||||
\(203\) | −1.06683e103 | −2.21067 | ||||||||
\(204\) | 3.89023e102 | 0.647788 | ||||||||
\(205\) | −1.12702e103 | −1.50968 | ||||||||
\(206\) | 1.20154e103 | 1.29612 | ||||||||
\(207\) | −6.97591e101 | −0.0606625 | ||||||||
\(208\) | −4.39433e103 | −3.08372 | ||||||||
\(209\) | −3.31901e102 | −0.188148 | ||||||||
\(210\) | 4.70200e103 | 2.15538 | ||||||||
\(211\) | 2.09663e103 | 0.777950 | 0.388975 | − | 0.921248i | \(-0.372829\pi\) | ||||
0.388975 | + | 0.921248i | \(0.372829\pi\) | |||||||
\(212\) | 1.13101e103 | 0.340031 | ||||||||
\(213\) | −3.31899e103 | −0.809308 | ||||||||
\(214\) | 5.56496e103 | 1.10166 | ||||||||
\(215\) | −3.76396e103 | −0.605528 | ||||||||
\(216\) | −2.70995e104 | −3.54625 | ||||||||
\(217\) | 5.44985e103 | 0.580666 | ||||||||
\(218\) | 3.79680e104 | 3.29688 | ||||||||
\(219\) | −4.45267e103 | −0.315397 | ||||||||
\(220\) | 2.29928e104 | 1.32979 | ||||||||
\(221\) | 4.39667e103 | 0.207811 | ||||||||
\(222\) | 4.89934e104 | 1.89422 | ||||||||
\(223\) | −3.38231e104 | −1.07065 | −0.535325 | − | 0.844646i | \(-0.679811\pi\) | ||||
−0.535325 | + | 0.844646i | \(0.679811\pi\) | |||||||
\(224\) | −2.12889e105 | −5.52226 | ||||||||
\(225\) | 1.73097e103 | 0.0368271 | ||||||||
\(226\) | 1.23772e105 | 2.16171 | ||||||||
\(227\) | −3.05939e104 | −0.439020 | −0.219510 | − | 0.975610i | \(-0.570446\pi\) | ||||
−0.219510 | + | 0.975610i | \(0.570446\pi\) | |||||||
\(228\) | 7.11205e104 | 0.839256 | ||||||||
\(229\) | −1.51461e105 | −1.47103 | −0.735514 | − | 0.677509i | \(-0.763059\pi\) | ||||
−0.735514 | + | 0.677509i | \(0.763059\pi\) | |||||||
\(230\) | −9.48226e104 | −0.758618 | ||||||||
\(231\) | −1.14071e105 | −0.752386 | ||||||||
\(232\) | 9.68901e105 | 5.27308 | ||||||||
\(233\) | −8.75172e104 | −0.393328 | −0.196664 | − | 0.980471i | \(-0.563011\pi\) | ||||
−0.196664 | + | 0.980471i | \(0.563011\pi\) | |||||||
\(234\) | −5.59197e104 | −0.207711 | ||||||||
\(235\) | 6.78567e103 | 0.0208484 | ||||||||
\(236\) | −2.87081e105 | −0.730165 | ||||||||
\(237\) | −2.31702e105 | −0.488235 | ||||||||
\(238\) | 3.95932e105 | 0.691746 | ||||||||
\(239\) | −2.25016e105 | −0.326217 | −0.163109 | − | 0.986608i | \(-0.552152\pi\) | ||||
−0.163109 | + | 0.986608i | \(0.552152\pi\) | |||||||
\(240\) | −2.47177e106 | −2.97583 | ||||||||
\(241\) | 7.69108e105 | 0.769536 | 0.384768 | − | 0.923013i | \(-0.374281\pi\) | ||||
0.384768 | + | 0.923013i | \(0.374281\pi\) | |||||||
\(242\) | 1.56227e106 | 1.30009 | ||||||||
\(243\) | −3.76074e105 | −0.260492 | ||||||||
\(244\) | 2.48331e106 | 1.43279 | ||||||||
\(245\) | 1.74253e106 | 0.838086 | ||||||||
\(246\) | −7.99757e106 | −3.20882 | ||||||||
\(247\) | 8.03791e105 | 0.269233 | ||||||||
\(248\) | −4.94957e106 | −1.38506 | ||||||||
\(249\) | 5.21362e106 | 1.21974 | ||||||||
\(250\) | 1.07309e107 | 2.10041 | ||||||||
\(251\) | 2.20478e105 | 0.0361314 | 0.0180657 | − | 0.999837i | \(-0.494249\pi\) | ||||
0.0180657 | + | 0.999837i | \(0.494249\pi\) | |||||||
\(252\) | −3.68903e106 | −0.506511 | ||||||||
\(253\) | 2.30040e106 | 0.264813 | ||||||||
\(254\) | −1.33693e107 | −1.29124 | ||||||||
\(255\) | 2.47309e106 | 0.200540 | ||||||||
\(256\) | 4.19761e107 | 2.85972 | ||||||||
\(257\) | −9.37238e106 | −0.536816 | −0.268408 | − | 0.963305i | \(-0.586498\pi\) | ||||
−0.268408 | + | 0.963305i | \(0.586498\pi\) | |||||||
\(258\) | −2.67099e107 | −1.28705 | ||||||||
\(259\) | 3.65286e107 | 1.48181 | ||||||||
\(260\) | −5.56835e107 | −1.90288 | ||||||||
\(261\) | 7.13665e106 | 0.205585 | ||||||||
\(262\) | −1.25946e108 | −3.06040 | ||||||||
\(263\) | −6.07350e107 | −1.24569 | −0.622843 | − | 0.782347i | \(-0.714022\pi\) | ||||
−0.622843 | + | 0.782347i | \(0.714022\pi\) | |||||||
\(264\) | 1.03599e108 | 1.79466 | ||||||||
\(265\) | 7.18999e106 | 0.105266 | ||||||||
\(266\) | 7.23837e107 | 0.896206 | ||||||||
\(267\) | 4.88853e107 | 0.512186 | ||||||||
\(268\) | 4.38972e108 | 3.89438 | ||||||||
\(269\) | −3.10570e107 | −0.233444 | −0.116722 | − | 0.993165i | \(-0.537239\pi\) | ||||
−0.116722 | + | 0.993165i | \(0.537239\pi\) | |||||||
\(270\) | −2.71323e108 | −1.72902 | ||||||||
\(271\) | −3.28545e107 | −0.177607 | −0.0888037 | − | 0.996049i | \(-0.528304\pi\) | ||||
−0.0888037 | + | 0.996049i | \(0.528304\pi\) | |||||||
\(272\) | −2.08136e108 | −0.955059 | ||||||||
\(273\) | 2.76254e108 | 1.07664 | ||||||||
\(274\) | −6.17614e108 | −2.04558 | ||||||||
\(275\) | −5.70810e107 | −0.160763 | ||||||||
\(276\) | −4.92935e108 | −1.18123 | ||||||||
\(277\) | 8.23734e108 | 1.68050 | 0.840248 | − | 0.542203i | \(-0.182410\pi\) | ||||
0.840248 | + | 0.542203i | \(0.182410\pi\) | |||||||
\(278\) | 1.53720e109 | 2.67139 | ||||||||
\(279\) | −3.64571e107 | −0.0540001 | ||||||||
\(280\) | −3.18391e109 | −4.02188 | ||||||||
\(281\) | 7.73806e108 | 0.834067 | 0.417034 | − | 0.908891i | \(-0.363070\pi\) | ||||
0.417034 | + | 0.908891i | \(0.363070\pi\) | |||||||
\(282\) | 4.81526e107 | 0.0443133 | ||||||||
\(283\) | −1.50030e109 | −1.17946 | −0.589728 | − | 0.807602i | \(-0.700765\pi\) | ||||
−0.589728 | + | 0.807602i | \(0.700765\pi\) | |||||||
\(284\) | 3.53954e109 | 2.37838 | ||||||||
\(285\) | 4.52125e108 | 0.259814 | ||||||||
\(286\) | 1.84403e109 | 0.906732 | ||||||||
\(287\) | −5.96285e109 | −2.51021 | ||||||||
\(288\) | 1.42414e109 | 0.513554 | ||||||||
\(289\) | −3.02735e109 | −0.935639 | ||||||||
\(290\) | 9.70076e109 | 2.57096 | ||||||||
\(291\) | −2.70908e109 | −0.616005 | ||||||||
\(292\) | 4.74856e109 | 0.926883 | ||||||||
\(293\) | −2.42775e108 | −0.0407001 | −0.0203500 | − | 0.999793i | \(-0.506478\pi\) | ||||
−0.0203500 | + | 0.999793i | \(0.506478\pi\) | |||||||
\(294\) | 1.23653e110 | 1.78135 | ||||||||
\(295\) | −1.82502e109 | −0.226042 | ||||||||
\(296\) | −3.31754e110 | −3.53456 | ||||||||
\(297\) | 6.58231e109 | 0.603554 | ||||||||
\(298\) | −2.72025e110 | −2.14776 | ||||||||
\(299\) | −5.57106e109 | −0.378939 | ||||||||
\(300\) | 1.22315e110 | 0.717104 | ||||||||
\(301\) | −1.99145e110 | −1.00684 | ||||||||
\(302\) | 5.86949e110 | 2.56031 | ||||||||
\(303\) | 3.09454e110 | 1.16519 | ||||||||
\(304\) | −3.80510e110 | −1.23735 | ||||||||
\(305\) | 1.57868e110 | 0.443559 | ||||||||
\(306\) | −2.64861e109 | −0.0643302 | ||||||||
\(307\) | −2.66215e107 | −0.000559209 0 | −0.000279604 | − | 1.00000i | \(-0.500089\pi\) | ||||
−0.000279604 | 1.00000i | \(0.500089\pi\) | ||||||||
\(308\) | 1.21651e111 | 2.21110 | ||||||||
\(309\) | 3.97081e110 | 0.624780 | ||||||||
\(310\) | −4.95556e110 | −0.675302 | ||||||||
\(311\) | −5.79663e110 | −0.684444 | −0.342222 | − | 0.939619i | \(-0.611179\pi\) | ||||
−0.342222 | + | 0.939619i | \(0.611179\pi\) | |||||||
\(312\) | −2.50894e111 | −2.56810 | ||||||||
\(313\) | 1.83417e111 | 1.62823 | 0.814117 | − | 0.580701i | \(-0.197221\pi\) | ||||
0.814117 | + | 0.580701i | \(0.197221\pi\) | |||||||
\(314\) | −2.79057e111 | −2.14943 | ||||||||
\(315\) | −2.34518e110 | −0.156804 | ||||||||
\(316\) | 2.47099e111 | 1.43481 | ||||||||
\(317\) | −1.33808e111 | −0.675062 | −0.337531 | − | 0.941314i | \(-0.609592\pi\) | ||||
−0.337531 | + | 0.941314i | \(0.609592\pi\) | |||||||
\(318\) | 5.10217e110 | 0.223742 | ||||||||
\(319\) | −2.35341e111 | −0.897452 | ||||||||
\(320\) | 9.73522e111 | 3.22977 | ||||||||
\(321\) | 1.83909e111 | 0.531043 | ||||||||
\(322\) | −5.01689e111 | −1.26139 | ||||||||
\(323\) | 3.80712e110 | 0.0833844 | ||||||||
\(324\) | −1.22228e112 | −2.33301 | ||||||||
\(325\) | 1.38238e111 | 0.230047 | ||||||||
\(326\) | −2.39583e112 | −3.47754 | ||||||||
\(327\) | 1.25475e112 | 1.58922 | ||||||||
\(328\) | 5.41548e112 | 5.98757 | ||||||||
\(329\) | 3.59018e110 | 0.0346656 | ||||||||
\(330\) | 1.03725e112 | 0.875009 | ||||||||
\(331\) | −1.40461e112 | −1.03564 | −0.517821 | − | 0.855489i | \(-0.673257\pi\) | ||||
−0.517821 | + | 0.855489i | \(0.673257\pi\) | |||||||
\(332\) | −5.56007e112 | −3.58456 | ||||||||
\(333\) | −2.44360e111 | −0.137804 | ||||||||
\(334\) | 5.61044e112 | 2.76872 | ||||||||
\(335\) | 2.79062e112 | 1.20561 | ||||||||
\(336\) | −1.30777e113 | −4.94804 | ||||||||
\(337\) | −1.78572e112 | −0.591949 | −0.295974 | − | 0.955196i | \(-0.595644\pi\) | ||||
−0.295974 | + | 0.955196i | \(0.595644\pi\) | |||||||
\(338\) | 2.18982e112 | 0.636232 | ||||||||
\(339\) | 4.09038e112 | 1.04202 | ||||||||
\(340\) | −2.63743e112 | −0.589344 | ||||||||
\(341\) | 1.20222e112 | 0.235730 | ||||||||
\(342\) | −4.84215e111 | −0.0833444 | ||||||||
\(343\) | −1.09418e111 | −0.0165386 | ||||||||
\(344\) | 1.80864e113 | 2.40160 | ||||||||
\(345\) | −3.13367e112 | −0.365682 | ||||||||
\(346\) | −7.52838e112 | −0.772352 | ||||||||
\(347\) | −1.99873e112 | −0.180340 | −0.0901700 | − | 0.995926i | \(-0.528741\pi\) | ||||
−0.0901700 | + | 0.995926i | \(0.528741\pi\) | |||||||
\(348\) | 5.04293e113 | 4.00320 | ||||||||
\(349\) | −2.76100e113 | −1.92901 | −0.964504 | − | 0.264067i | \(-0.914936\pi\) | ||||
−0.964504 | + | 0.264067i | \(0.914936\pi\) | |||||||
\(350\) | 1.24487e113 | 0.765765 | ||||||||
\(351\) | −1.59409e113 | −0.863666 | ||||||||
\(352\) | −4.69628e113 | −2.24184 | ||||||||
\(353\) | −1.57593e113 | −0.663075 | −0.331537 | − | 0.943442i | \(-0.607567\pi\) | ||||
−0.331537 | + | 0.943442i | \(0.607567\pi\) | |||||||
\(354\) | −1.29508e113 | −0.480453 | ||||||||
\(355\) | 2.25015e113 | 0.736291 | ||||||||
\(356\) | −5.21338e113 | −1.50520 | ||||||||
\(357\) | 1.30847e113 | 0.333447 | ||||||||
\(358\) | 1.48688e114 | 3.34566 | ||||||||
\(359\) | −4.80149e113 | −0.954274 | −0.477137 | − | 0.878829i | \(-0.658325\pi\) | ||||
−0.477137 | + | 0.878829i | \(0.658325\pi\) | |||||||
\(360\) | 2.12990e113 | 0.374022 | ||||||||
\(361\) | −5.74673e113 | −0.891970 | ||||||||
\(362\) | 4.80497e113 | 0.659416 | ||||||||
\(363\) | 5.16294e113 | 0.626689 | ||||||||
\(364\) | −2.94611e114 | −3.16401 | ||||||||
\(365\) | 3.01874e113 | 0.286941 | ||||||||
\(366\) | 1.12027e114 | 0.942785 | ||||||||
\(367\) | 1.15953e114 | 0.864255 | 0.432128 | − | 0.901812i | \(-0.357763\pi\) | ||||
0.432128 | + | 0.901812i | \(0.357763\pi\) | |||||||
\(368\) | 2.63731e114 | 1.74154 | ||||||||
\(369\) | 3.98888e113 | 0.233442 | ||||||||
\(370\) | −3.32156e114 | −1.72332 | ||||||||
\(371\) | 3.80409e113 | 0.175030 | ||||||||
\(372\) | −2.57615e114 | −1.05150 | ||||||||
\(373\) | 2.55903e114 | 0.926900 | 0.463450 | − | 0.886123i | \(-0.346611\pi\) | ||||
0.463450 | + | 0.886123i | \(0.346611\pi\) | |||||||
\(374\) | 8.73416e113 | 0.280824 | ||||||||
\(375\) | 3.54631e114 | 1.01248 | ||||||||
\(376\) | −3.26061e113 | −0.0826874 | ||||||||
\(377\) | 5.69943e114 | 1.28423 | ||||||||
\(378\) | −1.43552e115 | −2.87491 | ||||||||
\(379\) | −9.87836e114 | −1.75890 | −0.879448 | − | 0.475995i | \(-0.842088\pi\) | ||||
−0.879448 | + | 0.475995i | \(0.842088\pi\) | |||||||
\(380\) | −4.82170e114 | −0.763536 | ||||||||
\(381\) | −4.41823e114 | −0.622425 | ||||||||
\(382\) | 3.98805e114 | 0.499967 | ||||||||
\(383\) | −9.67896e114 | −1.08015 | −0.540074 | − | 0.841617i | \(-0.681604\pi\) | ||||
−0.540074 | + | 0.841617i | \(0.681604\pi\) | |||||||
\(384\) | 3.23469e115 | 3.21435 | ||||||||
\(385\) | 7.73355e114 | 0.684504 | ||||||||
\(386\) | 1.24635e115 | 0.982887 | ||||||||
\(387\) | 1.33219e114 | 0.0936328 | ||||||||
\(388\) | 2.88910e115 | 1.81030 | ||||||||
\(389\) | 1.42694e115 | 0.797352 | 0.398676 | − | 0.917092i | \(-0.369470\pi\) | ||||
0.398676 | + | 0.917092i | \(0.369470\pi\) | |||||||
\(390\) | −2.51199e115 | −1.25211 | ||||||||
\(391\) | −2.63871e114 | −0.117362 | ||||||||
\(392\) | −8.37307e115 | −3.32395 | ||||||||
\(393\) | −4.16224e115 | −1.47523 | ||||||||
\(394\) | 5.41953e115 | 1.71546 | ||||||||
\(395\) | 1.57085e115 | 0.444185 | ||||||||
\(396\) | −8.13791e114 | −0.205625 | ||||||||
\(397\) | 5.95174e115 | 1.34421 | 0.672104 | − | 0.740456i | \(-0.265391\pi\) | ||||
0.672104 | + | 0.740456i | \(0.265391\pi\) | |||||||
\(398\) | −1.02417e116 | −2.06811 | ||||||||
\(399\) | 2.39211e115 | 0.432004 | ||||||||
\(400\) | −6.54409e115 | −1.05725 | ||||||||
\(401\) | 4.18136e115 | 0.604495 | 0.302248 | − | 0.953229i | \(-0.402263\pi\) | ||||
0.302248 | + | 0.953229i | \(0.402263\pi\) | |||||||
\(402\) | 1.98028e116 | 2.56253 | ||||||||
\(403\) | −2.91151e115 | −0.337322 | ||||||||
\(404\) | −3.30017e116 | −3.42425 | ||||||||
\(405\) | −7.77023e115 | −0.722246 | ||||||||
\(406\) | 5.13249e116 | 4.27484 | ||||||||
\(407\) | 8.05811e115 | 0.601564 | ||||||||
\(408\) | −1.18835e116 | −0.795367 | ||||||||
\(409\) | −2.79410e116 | −1.67709 | −0.838543 | − | 0.544836i | \(-0.816592\pi\) | ||||
−0.838543 | + | 0.544836i | \(0.816592\pi\) | |||||||
\(410\) | 5.42204e116 | 2.91932 | ||||||||
\(411\) | −2.04107e116 | −0.986045 | ||||||||
\(412\) | −4.23468e116 | −1.83609 | ||||||||
\(413\) | −9.65587e115 | −0.375850 | ||||||||
\(414\) | 3.35608e115 | 0.117305 | ||||||||
\(415\) | −3.53463e116 | −1.10969 | ||||||||
\(416\) | 1.13733e117 | 3.20801 | ||||||||
\(417\) | 5.08009e116 | 1.28771 | ||||||||
\(418\) | 1.59676e116 | 0.363828 | ||||||||
\(419\) | −7.53082e115 | −0.154283 | −0.0771415 | − | 0.997020i | \(-0.524579\pi\) | ||||
−0.0771415 | + | 0.997020i | \(0.524579\pi\) | |||||||
\(420\) | −1.65716e117 | −3.05331 | ||||||||
\(421\) | −1.74478e116 | −0.289193 | −0.144596 | − | 0.989491i | \(-0.546188\pi\) | ||||
−0.144596 | + | 0.989491i | \(0.546188\pi\) | |||||||
\(422\) | −1.00868e117 | −1.50435 | ||||||||
\(423\) | −2.40167e114 | −0.00322379 | ||||||||
\(424\) | −3.45489e116 | −0.417497 | ||||||||
\(425\) | 6.54757e115 | 0.0712480 | ||||||||
\(426\) | 1.59675e117 | 1.56499 | ||||||||
\(427\) | 8.35251e116 | 0.737524 | ||||||||
\(428\) | −1.96130e117 | −1.56062 | ||||||||
\(429\) | 6.09408e116 | 0.437078 | ||||||||
\(430\) | 1.81083e117 | 1.17093 | ||||||||
\(431\) | 6.52772e116 | 0.380648 | 0.190324 | − | 0.981721i | \(-0.439046\pi\) | ||||
0.190324 | + | 0.981721i | \(0.439046\pi\) | |||||||
\(432\) | 7.54632e117 | 3.96925 | ||||||||
\(433\) | −1.58060e117 | −0.750083 | −0.375042 | − | 0.927008i | \(-0.622372\pi\) | ||||
−0.375042 | + | 0.927008i | \(0.622372\pi\) | |||||||
\(434\) | −2.62190e117 | −1.12285 | ||||||||
\(435\) | 3.20588e117 | 1.23930 | ||||||||
\(436\) | −1.33813e118 | −4.67037 | ||||||||
\(437\) | −4.82404e116 | −0.152050 | ||||||||
\(438\) | 2.14216e117 | 0.609894 | ||||||||
\(439\) | 6.33463e117 | 1.62948 | 0.814742 | − | 0.579823i | \(-0.196878\pi\) | ||||
0.814742 | + | 0.579823i | \(0.196878\pi\) | |||||||
\(440\) | −7.02363e117 | −1.63274 | ||||||||
\(441\) | −6.16737e116 | −0.129593 | ||||||||
\(442\) | −2.11522e117 | −0.401850 | ||||||||
\(443\) | 4.84950e117 | 0.833165 | 0.416583 | − | 0.909098i | \(-0.363228\pi\) | ||||
0.416583 | + | 0.909098i | \(0.363228\pi\) | |||||||
\(444\) | −1.72671e118 | −2.68335 | ||||||||
\(445\) | −3.31424e117 | −0.465975 | ||||||||
\(446\) | 1.62722e118 | 2.07035 | ||||||||
\(447\) | −8.98981e117 | −1.03530 | ||||||||
\(448\) | 5.15073e118 | 5.37028 | ||||||||
\(449\) | −2.82363e117 | −0.266591 | −0.133296 | − | 0.991076i | \(-0.542556\pi\) | ||||
−0.133296 | + | 0.991076i | \(0.542556\pi\) | |||||||
\(450\) | −8.32762e116 | −0.0712138 | ||||||||
\(451\) | −1.31539e118 | −1.01906 | ||||||||
\(452\) | −4.36219e118 | −3.06228 | ||||||||
\(453\) | 1.93973e118 | 1.23416 | ||||||||
\(454\) | 1.47186e118 | 0.848948 | ||||||||
\(455\) | −1.87289e118 | −0.979503 | ||||||||
\(456\) | −2.17252e118 | −1.03045 | ||||||||
\(457\) | −1.85598e118 | −0.798552 | −0.399276 | − | 0.916831i | \(-0.630738\pi\) | ||||
−0.399276 | + | 0.916831i | \(0.630738\pi\) | |||||||
\(458\) | 7.28671e118 | 2.84458 | ||||||||
\(459\) | −7.55034e117 | −0.267487 | ||||||||
\(460\) | 3.34191e118 | 1.07466 | ||||||||
\(461\) | 1.46775e118 | 0.428510 | 0.214255 | − | 0.976778i | \(-0.431268\pi\) | ||||
0.214255 | + | 0.976778i | \(0.431268\pi\) | |||||||
\(462\) | 5.48789e118 | 1.45492 | ||||||||
\(463\) | 2.77498e118 | 0.668198 | 0.334099 | − | 0.942538i | \(-0.391568\pi\) | ||||
0.334099 | + | 0.942538i | \(0.391568\pi\) | |||||||
\(464\) | −2.69808e119 | −5.90206 | ||||||||
\(465\) | −1.63770e118 | −0.325520 | ||||||||
\(466\) | 4.21042e118 | 0.760592 | ||||||||
\(467\) | −6.20631e118 | −1.01914 | −0.509568 | − | 0.860430i | \(-0.670195\pi\) | ||||
−0.509568 | + | 0.860430i | \(0.670195\pi\) | |||||||
\(468\) | 1.97082e118 | 0.294243 | ||||||||
\(469\) | 1.47647e119 | 2.00462 | ||||||||
\(470\) | −3.26456e117 | −0.0403153 | ||||||||
\(471\) | −9.22218e118 | −1.03610 | ||||||||
\(472\) | 8.76949e118 | 0.896510 | ||||||||
\(473\) | −4.39307e118 | −0.408741 | ||||||||
\(474\) | 1.11471e119 | 0.944116 | ||||||||
\(475\) | 1.19701e118 | 0.0923068 | ||||||||
\(476\) | −1.39541e119 | −0.979927 | ||||||||
\(477\) | −2.54477e117 | −0.0162772 | ||||||||
\(478\) | 1.08254e119 | 0.630817 | ||||||||
\(479\) | 2.47010e119 | 1.31155 | 0.655774 | − | 0.754958i | \(-0.272343\pi\) | ||||
0.655774 | + | 0.754958i | \(0.272343\pi\) | |||||||
\(480\) | 6.39741e119 | 3.09577 | ||||||||
\(481\) | −1.95150e119 | −0.860819 | ||||||||
\(482\) | −3.70015e119 | −1.48808 | ||||||||
\(483\) | −1.65797e119 | −0.608035 | ||||||||
\(484\) | −5.50602e119 | −1.84170 | ||||||||
\(485\) | 1.83665e119 | 0.560427 | ||||||||
\(486\) | 1.80928e119 | 0.503722 | ||||||||
\(487\) | −3.27475e119 | −0.832031 | −0.416015 | − | 0.909358i | \(-0.636574\pi\) | ||||
−0.416015 | + | 0.909358i | \(0.636574\pi\) | |||||||
\(488\) | −7.58577e119 | −1.75921 | ||||||||
\(489\) | −7.91766e119 | −1.67630 | ||||||||
\(490\) | −8.38322e119 | −1.62064 | ||||||||
\(491\) | 7.69474e119 | 1.35852 | 0.679262 | − | 0.733896i | \(-0.262300\pi\) | ||||
0.679262 | + | 0.733896i | \(0.262300\pi\) | |||||||
\(492\) | 2.81864e120 | 4.54562 | ||||||||
\(493\) | 2.69951e119 | 0.397738 | ||||||||
\(494\) | −3.86701e119 | −0.520626 | ||||||||
\(495\) | −5.17340e118 | −0.0636568 | ||||||||
\(496\) | 1.37829e120 | 1.55027 | ||||||||
\(497\) | 1.19051e120 | 1.22426 | ||||||||
\(498\) | −2.50825e120 | −2.35866 | ||||||||
\(499\) | 6.79740e119 | 0.584613 | 0.292306 | − | 0.956325i | \(-0.405577\pi\) | ||||
0.292306 | + | 0.956325i | \(0.405577\pi\) | |||||||
\(500\) | −3.78196e120 | −2.97545 | ||||||||
\(501\) | 1.85412e120 | 1.33463 | ||||||||
\(502\) | −1.06071e119 | −0.0698686 | ||||||||
\(503\) | 9.48767e119 | 0.571985 | 0.285992 | − | 0.958232i | \(-0.407677\pi\) | ||||
0.285992 | + | 0.958232i | \(0.407677\pi\) | |||||||
\(504\) | 1.12689e120 | 0.621904 | ||||||||
\(505\) | −2.09797e120 | −1.06007 | ||||||||
\(506\) | −1.10671e120 | −0.512079 | ||||||||
\(507\) | 7.23685e119 | 0.306687 | ||||||||
\(508\) | 4.71183e120 | 1.82917 | ||||||||
\(509\) | −1.57324e120 | −0.559569 | −0.279784 | − | 0.960063i | \(-0.590263\pi\) | ||||
−0.279784 | + | 0.960063i | \(0.590263\pi\) | |||||||
\(510\) | −1.18979e120 | −0.387791 | ||||||||
\(511\) | 1.59716e120 | 0.477110 | ||||||||
\(512\) | −7.60153e120 | −2.08155 | ||||||||
\(513\) | −1.38034e120 | −0.346548 | ||||||||
\(514\) | 4.50901e120 | 1.03806 | ||||||||
\(515\) | −2.69206e120 | −0.568411 | ||||||||
\(516\) | 9.41358e120 | 1.82324 | ||||||||
\(517\) | 7.91983e118 | 0.0140730 | ||||||||
\(518\) | −1.75738e121 | −2.86544 | ||||||||
\(519\) | −2.48796e120 | −0.372302 | ||||||||
\(520\) | 1.70097e121 | 2.33640 | ||||||||
\(521\) | −1.40305e121 | −1.76927 | −0.884637 | − | 0.466280i | \(-0.845594\pi\) | ||||
−0.884637 | + | 0.466280i | \(0.845594\pi\) | |||||||
\(522\) | −3.43341e120 | −0.397547 | ||||||||
\(523\) | −7.70708e120 | −0.819530 | −0.409765 | − | 0.912191i | \(-0.634389\pi\) | ||||
−0.409765 | + | 0.912191i | \(0.634389\pi\) | |||||||
\(524\) | 4.43882e121 | 4.33536 | ||||||||
\(525\) | 4.11400e120 | 0.369127 | ||||||||
\(526\) | 2.92194e121 | 2.40882 | ||||||||
\(527\) | −1.37903e120 | −0.104472 | ||||||||
\(528\) | −2.88490e121 | −2.00873 | ||||||||
\(529\) | −1.22799e121 | −0.785993 | ||||||||
\(530\) | −3.45908e120 | −0.203556 | ||||||||
\(531\) | 6.45936e119 | 0.0349529 | ||||||||
\(532\) | −2.55107e121 | −1.26957 | ||||||||
\(533\) | 3.18558e121 | 1.45823 | ||||||||
\(534\) | −2.35185e121 | −0.990431 | ||||||||
\(535\) | −1.24683e121 | −0.483131 | ||||||||
\(536\) | −1.34093e122 | −4.78160 | ||||||||
\(537\) | 4.91380e121 | 1.61273 | ||||||||
\(538\) | 1.49414e121 | 0.451419 | ||||||||
\(539\) | 2.03377e121 | 0.565721 | ||||||||
\(540\) | 9.56245e121 | 2.44933 | ||||||||
\(541\) | 1.41172e121 | 0.333019 | 0.166510 | − | 0.986040i | \(-0.446750\pi\) | ||||
0.166510 | + | 0.986040i | \(0.446750\pi\) | |||||||
\(542\) | 1.58061e121 | 0.343445 | ||||||||
\(543\) | 1.58793e121 | 0.317863 | ||||||||
\(544\) | 5.38694e121 | 0.993553 | ||||||||
\(545\) | −8.50675e121 | −1.44584 | ||||||||
\(546\) | −1.32905e122 | −2.08194 | ||||||||
\(547\) | −2.47148e121 | −0.356879 | −0.178440 | − | 0.983951i | \(-0.557105\pi\) | ||||
−0.178440 | + | 0.983951i | \(0.557105\pi\) | |||||||
\(548\) | 2.17670e122 | 2.89777 | ||||||||
\(549\) | −5.58746e120 | −0.0685875 | ||||||||
\(550\) | 2.74614e121 | 0.310874 | ||||||||
\(551\) | 4.93520e121 | 0.515298 | ||||||||
\(552\) | 1.50577e122 | 1.45034 | ||||||||
\(553\) | 8.31108e121 | 0.738566 | ||||||||
\(554\) | −3.96295e122 | −3.24963 | ||||||||
\(555\) | −1.09770e122 | −0.830702 | ||||||||
\(556\) | −5.41767e122 | −3.78429 | ||||||||
\(557\) | 9.31061e121 | 0.600374 | 0.300187 | − | 0.953880i | \(-0.402951\pi\) | ||||
0.300187 | + | 0.953880i | \(0.402951\pi\) | |||||||
\(558\) | 1.75394e121 | 0.104422 | ||||||||
\(559\) | 1.06391e122 | 0.584894 | ||||||||
\(560\) | 8.86617e122 | 4.50162 | ||||||||
\(561\) | 2.88644e121 | 0.135368 | ||||||||
\(562\) | −3.72275e122 | −1.61286 | ||||||||
\(563\) | 3.11201e121 | 0.124571 | 0.0622855 | − | 0.998058i | \(-0.480161\pi\) | ||||
0.0622855 | + | 0.998058i | \(0.480161\pi\) | |||||||
\(564\) | −1.69708e121 | −0.0627743 | ||||||||
\(565\) | −2.77312e122 | −0.948009 | ||||||||
\(566\) | 7.21788e122 | 2.28075 | ||||||||
\(567\) | −4.11109e122 | −1.20091 | ||||||||
\(568\) | −1.08123e123 | −2.92022 | ||||||||
\(569\) | 2.71930e122 | 0.679142 | 0.339571 | − | 0.940580i | \(-0.389718\pi\) | ||||
0.339571 | + | 0.940580i | \(0.389718\pi\) | |||||||
\(570\) | −2.17516e122 | −0.502411 | ||||||||
\(571\) | 2.89172e122 | 0.617801 | 0.308901 | − | 0.951094i | \(-0.400039\pi\) | ||||
0.308901 | + | 0.951094i | \(0.400039\pi\) | |||||||
\(572\) | −6.49904e122 | −1.28448 | ||||||||
\(573\) | 1.31796e122 | 0.241003 | ||||||||
\(574\) | 2.86870e123 | 4.85407 | ||||||||
\(575\) | −8.29648e121 | −0.129920 | ||||||||
\(576\) | −3.44561e122 | −0.499420 | ||||||||
\(577\) | 3.49596e122 | 0.469075 | 0.234538 | − | 0.972107i | \(-0.424642\pi\) | ||||
0.234538 | + | 0.972107i | \(0.424642\pi\) | |||||||
\(578\) | 1.45644e123 | 1.80928 | ||||||||
\(579\) | 4.11889e122 | 0.473788 | ||||||||
\(580\) | −3.41891e123 | −3.64202 | ||||||||
\(581\) | −1.87011e123 | −1.84514 | ||||||||
\(582\) | 1.30333e123 | 1.19119 | ||||||||
\(583\) | 8.39173e121 | 0.0710560 | ||||||||
\(584\) | −1.45054e123 | −1.13804 | ||||||||
\(585\) | 1.25288e122 | 0.0910908 | ||||||||
\(586\) | 1.16798e122 | 0.0787031 | ||||||||
\(587\) | −5.88136e121 | −0.0367352 | −0.0183676 | − | 0.999831i | \(-0.505847\pi\) | ||||
−0.0183676 | + | 0.999831i | \(0.505847\pi\) | |||||||
\(588\) | −4.35801e123 | −2.52347 | ||||||||
\(589\) | −2.52111e122 | −0.135351 | ||||||||
\(590\) | 8.78012e122 | 0.437105 | ||||||||
\(591\) | 1.79103e123 | 0.826913 | ||||||||
\(592\) | 9.23827e123 | 3.95617 | ||||||||
\(593\) | −3.21670e123 | −1.27784 | −0.638920 | − | 0.769273i | \(-0.720618\pi\) | ||||
−0.638920 | + | 0.769273i | \(0.720618\pi\) | |||||||
\(594\) | −3.16672e123 | −1.16711 | ||||||||
\(595\) | −8.87088e122 | −0.303363 | ||||||||
\(596\) | 9.58720e123 | 3.04252 | ||||||||
\(597\) | −3.38463e123 | −0.996905 | ||||||||
\(598\) | 2.68021e123 | 0.732768 | ||||||||
\(599\) | −3.33166e122 | −0.0845603 | −0.0422802 | − | 0.999106i | \(-0.513462\pi\) | ||||
−0.0422802 | + | 0.999106i | \(0.513462\pi\) | |||||||
\(600\) | −3.73635e123 | −0.880474 | ||||||||
\(601\) | 3.45390e123 | 0.755781 | 0.377890 | − | 0.925850i | \(-0.376650\pi\) | ||||
0.377890 | + | 0.925850i | \(0.376650\pi\) | |||||||
\(602\) | 9.58077e123 | 1.94696 | ||||||||
\(603\) | −9.87691e122 | −0.186424 | ||||||||
\(604\) | −2.06863e124 | −3.62693 | ||||||||
\(605\) | −3.50027e123 | −0.570148 | ||||||||
\(606\) | −1.48877e124 | −2.25318 | ||||||||
\(607\) | 8.57587e122 | 0.120609 | 0.0603047 | − | 0.998180i | \(-0.480793\pi\) | ||||
0.0603047 | + | 0.998180i | \(0.480793\pi\) | |||||||
\(608\) | 9.84831e123 | 1.28722 | ||||||||
\(609\) | 1.69617e124 | 2.06063 | ||||||||
\(610\) | −7.59496e123 | −0.857725 | ||||||||
\(611\) | −1.91801e122 | −0.0201380 | ||||||||
\(612\) | 9.33471e122 | 0.0911303 | ||||||||
\(613\) | 7.99900e123 | 0.726180 | 0.363090 | − | 0.931754i | \(-0.381722\pi\) | ||||
0.363090 | + | 0.931754i | \(0.381722\pi\) | |||||||
\(614\) | 1.28075e121 | 0.00108136 | ||||||||
\(615\) | 1.79186e124 | 1.40722 | ||||||||
\(616\) | −3.71607e124 | −2.71483 | ||||||||
\(617\) | 2.42228e124 | 1.64640 | 0.823199 | − | 0.567752i | \(-0.192187\pi\) | ||||
0.823199 | + | 0.567752i | \(0.192187\pi\) | |||||||
\(618\) | −1.91034e124 | −1.20816 | ||||||||
\(619\) | −3.19334e124 | −1.87936 | −0.939682 | − | 0.342050i | \(-0.888879\pi\) | ||||
−0.939682 | + | 0.342050i | \(0.888879\pi\) | |||||||
\(620\) | 1.74653e124 | 0.956633 | ||||||||
\(621\) | 9.56710e123 | 0.487758 | ||||||||
\(622\) | 2.78873e124 | 1.32353 | ||||||||
\(623\) | −1.75350e124 | −0.774798 | ||||||||
\(624\) | 6.98660e124 | 2.87443 | ||||||||
\(625\) | −1.67123e124 | −0.640287 | ||||||||
\(626\) | −8.82412e124 | −3.14857 | ||||||||
\(627\) | 5.27693e123 | 0.175378 | ||||||||
\(628\) | 9.83500e124 | 3.04488 | ||||||||
\(629\) | −9.24318e123 | −0.266605 | ||||||||
\(630\) | 1.12826e124 | 0.303217 | ||||||||
\(631\) | −1.27838e124 | −0.320151 | −0.160076 | − | 0.987105i | \(-0.551174\pi\) | ||||
−0.160076 | + | 0.987105i | \(0.551174\pi\) | |||||||
\(632\) | −7.54815e124 | −1.76169 | ||||||||
\(633\) | −3.33345e124 | −0.725151 | ||||||||
\(634\) | 6.43743e124 | 1.30539 | ||||||||
\(635\) | 2.99539e124 | 0.566269 | ||||||||
\(636\) | −1.79820e124 | −0.316954 | ||||||||
\(637\) | −4.92534e124 | −0.809528 | ||||||||
\(638\) | 1.13221e125 | 1.73543 | ||||||||
\(639\) | −7.96400e123 | −0.113853 | ||||||||
\(640\) | −2.19299e125 | −2.92435 | ||||||||
\(641\) | −1.15177e125 | −1.43279 | −0.716393 | − | 0.697697i | \(-0.754208\pi\) | ||||
−0.716393 | + | 0.697697i | \(0.754208\pi\) | |||||||
\(642\) | −8.84780e124 | −1.02690 | ||||||||
\(643\) | 1.29646e123 | 0.0140401 | 0.00702004 | − | 0.999975i | \(-0.497765\pi\) | ||||
0.00702004 | + | 0.999975i | \(0.497765\pi\) | |||||||
\(644\) | 1.76814e125 | 1.78688 | ||||||||
\(645\) | 5.98437e124 | 0.564431 | ||||||||
\(646\) | −1.83159e124 | −0.161243 | ||||||||
\(647\) | 4.09400e124 | 0.336440 | 0.168220 | − | 0.985750i | \(-0.446198\pi\) | ||||
0.168220 | + | 0.985750i | \(0.446198\pi\) | |||||||
\(648\) | 3.73370e125 | 2.86452 | ||||||||
\(649\) | −2.13006e124 | −0.152582 | ||||||||
\(650\) | −6.65055e124 | −0.444850 | ||||||||
\(651\) | −8.66478e124 | −0.541257 | ||||||||
\(652\) | 8.44380e125 | 4.92629 | ||||||||
\(653\) | 2.61194e125 | 1.42340 | 0.711698 | − | 0.702485i | \(-0.247926\pi\) | ||||
0.711698 | + | 0.702485i | \(0.247926\pi\) | |||||||
\(654\) | −6.03657e125 | −3.07313 | ||||||||
\(655\) | 2.82183e125 | 1.34213 | ||||||||
\(656\) | −1.50803e126 | −6.70178 | ||||||||
\(657\) | −1.06843e124 | −0.0443698 | ||||||||
\(658\) | −1.72722e124 | −0.0670340 | ||||||||
\(659\) | −4.17300e124 | −0.151373 | −0.0756864 | − | 0.997132i | \(-0.524115\pi\) | ||||
−0.0756864 | + | 0.997132i | \(0.524115\pi\) | |||||||
\(660\) | −3.65565e125 | −1.23954 | ||||||||
\(661\) | −1.80404e125 | −0.571850 | −0.285925 | − | 0.958252i | \(-0.592301\pi\) | ||||
−0.285925 | + | 0.958252i | \(0.592301\pi\) | |||||||
\(662\) | 6.75752e125 | 2.00266 | ||||||||
\(663\) | −6.99031e124 | −0.193707 | ||||||||
\(664\) | 1.69844e126 | 4.40119 | ||||||||
\(665\) | −1.62176e125 | −0.393028 | ||||||||
\(666\) | 1.17561e125 | 0.266477 | ||||||||
\(667\) | −3.42057e125 | −0.725269 | ||||||||
\(668\) | −1.97733e126 | −3.92217 | ||||||||
\(669\) | 5.37758e125 | 0.997986 | ||||||||
\(670\) | −1.34256e126 | −2.33133 | ||||||||
\(671\) | 1.84254e125 | 0.299409 | ||||||||
\(672\) | 3.38475e126 | 5.14748 | ||||||||
\(673\) | −4.58978e125 | −0.653313 | −0.326656 | − | 0.945143i | \(-0.605922\pi\) | ||||
−0.326656 | + | 0.945143i | \(0.605922\pi\) | |||||||
\(674\) | 8.59105e125 | 1.14467 | ||||||||
\(675\) | −2.37393e125 | −0.296109 | ||||||||
\(676\) | −7.71775e125 | −0.901286 | ||||||||
\(677\) | −4.89209e125 | −0.534932 | −0.267466 | − | 0.963567i | \(-0.586186\pi\) | ||||
−0.267466 | + | 0.963567i | \(0.586186\pi\) | |||||||
\(678\) | −1.96786e126 | −2.01499 | ||||||||
\(679\) | 9.71739e125 | 0.931847 | ||||||||
\(680\) | 8.05656e125 | 0.723607 | ||||||||
\(681\) | 4.86416e125 | 0.409224 | ||||||||
\(682\) | −5.78384e125 | −0.455839 | ||||||||
\(683\) | 2.01226e124 | 0.0148581 | 0.00742905 | − | 0.999972i | \(-0.497635\pi\) | ||||
0.00742905 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(684\) | 1.70656e125 | 0.118066 | ||||||||
\(685\) | 1.38377e126 | 0.897082 | ||||||||
\(686\) | 5.26404e124 | 0.0319813 | ||||||||
\(687\) | 2.40809e126 | 1.37119 | ||||||||
\(688\) | −5.03646e126 | −2.68807 | ||||||||
\(689\) | −2.03229e125 | −0.101679 | ||||||||
\(690\) | 1.50760e126 | 0.707132 | ||||||||
\(691\) | −2.29357e126 | −1.00865 | −0.504324 | − | 0.863515i | \(-0.668258\pi\) | ||||
−0.504324 | + | 0.863515i | \(0.668258\pi\) | |||||||
\(692\) | 2.65329e126 | 1.09411 | ||||||||
\(693\) | −2.73715e125 | −0.105845 | ||||||||
\(694\) | 9.61580e125 | 0.348730 | ||||||||
\(695\) | −3.44410e126 | −1.17153 | ||||||||
\(696\) | −1.54047e127 | −4.91520 | ||||||||
\(697\) | 1.50884e126 | 0.451631 | ||||||||
\(698\) | 1.32830e127 | 3.73019 | ||||||||
\(699\) | 1.39145e126 | 0.366634 | ||||||||
\(700\) | −4.38738e126 | −1.08478 | ||||||||
\(701\) | 2.57316e126 | 0.597057 | 0.298528 | − | 0.954401i | \(-0.403504\pi\) | ||||
0.298528 | + | 0.954401i | \(0.403504\pi\) | |||||||
\(702\) | 7.66910e126 | 1.67010 | ||||||||
\(703\) | −1.68982e126 | −0.345405 | ||||||||
\(704\) | 1.13624e127 | 2.18015 | ||||||||
\(705\) | −1.07886e125 | −0.0194335 | ||||||||
\(706\) | 7.58173e126 | 1.28221 | ||||||||
\(707\) | −1.11000e127 | −1.76262 | ||||||||
\(708\) | 4.56434e126 | 0.680609 | ||||||||
\(709\) | −6.78467e126 | −0.950104 | −0.475052 | − | 0.879958i | \(-0.657571\pi\) | ||||
−0.475052 | + | 0.879958i | \(0.657571\pi\) | |||||||
\(710\) | −1.08254e127 | −1.42379 | ||||||||
\(711\) | −5.55975e125 | −0.0686844 | ||||||||
\(712\) | 1.59253e127 | 1.84812 | ||||||||
\(713\) | 1.74738e126 | 0.190503 | ||||||||
\(714\) | −6.29497e126 | −0.644798 | ||||||||
\(715\) | −4.13155e126 | −0.397644 | ||||||||
\(716\) | −5.24033e127 | −4.73946 | ||||||||
\(717\) | 3.57755e126 | 0.304077 | ||||||||
\(718\) | 2.30998e127 | 1.84531 | ||||||||
\(719\) | 1.13360e127 | 0.851182 | 0.425591 | − | 0.904916i | \(-0.360066\pi\) | ||||
0.425591 | + | 0.904916i | \(0.360066\pi\) | |||||||
\(720\) | −5.93108e126 | −0.418637 | ||||||||
\(721\) | −1.42432e127 | −0.945121 | ||||||||
\(722\) | 2.76473e127 | 1.72483 | ||||||||
\(723\) | −1.22281e127 | −0.717309 | ||||||||
\(724\) | −1.69345e127 | −0.934129 | ||||||||
\(725\) | 8.48765e126 | 0.440297 | ||||||||
\(726\) | −2.48387e127 | −1.21185 | ||||||||
\(727\) | 3.79015e127 | 1.73930 | 0.869651 | − | 0.493666i | \(-0.164344\pi\) | ||||
0.869651 | + | 0.493666i | \(0.164344\pi\) | |||||||
\(728\) | 8.99951e127 | 3.88483 | ||||||||
\(729\) | 2.69516e127 | 1.09449 | ||||||||
\(730\) | −1.45230e127 | −0.554868 | ||||||||
\(731\) | 5.03914e126 | 0.181148 | ||||||||
\(732\) | −3.94824e127 | −1.33555 | ||||||||
\(733\) | −1.80508e127 | −0.574606 | −0.287303 | − | 0.957840i | \(-0.592759\pi\) | ||||
−0.287303 | + | 0.957840i | \(0.592759\pi\) | |||||||
\(734\) | −5.57845e127 | −1.67124 | ||||||||
\(735\) | −2.77046e127 | −0.781206 | ||||||||
\(736\) | −6.82584e127 | −1.81173 | ||||||||
\(737\) | 3.25704e127 | 0.813805 | ||||||||
\(738\) | −1.91904e127 | −0.451414 | ||||||||
\(739\) | 4.14460e127 | 0.917921 | 0.458960 | − | 0.888457i | \(-0.348222\pi\) | ||||
0.458960 | + | 0.888457i | \(0.348222\pi\) | |||||||
\(740\) | 1.17064e128 | 2.44125 | ||||||||
\(741\) | −1.27796e127 | −0.250961 | ||||||||
\(742\) | −1.83013e127 | −0.338461 | ||||||||
\(743\) | −3.30910e126 | −0.0576379 | −0.0288189 | − | 0.999585i | \(-0.509175\pi\) | ||||
−0.0288189 | + | 0.999585i | \(0.509175\pi\) | |||||||
\(744\) | 7.86937e127 | 1.29105 | ||||||||
\(745\) | 6.09474e127 | 0.941892 | ||||||||
\(746\) | −1.23114e128 | −1.79238 | ||||||||
\(747\) | 1.25102e127 | 0.171592 | ||||||||
\(748\) | −3.07825e127 | −0.397816 | ||||||||
\(749\) | −6.59677e127 | −0.803323 | ||||||||
\(750\) | −1.70611e128 | −1.95786 | ||||||||
\(751\) | 6.11801e127 | 0.661657 | 0.330829 | − | 0.943691i | \(-0.392672\pi\) | ||||
0.330829 | + | 0.943691i | \(0.392672\pi\) | |||||||
\(752\) | 9.07973e126 | 0.0925506 | ||||||||
\(753\) | −3.50541e126 | −0.0336793 | ||||||||
\(754\) | −2.74197e128 | −2.48335 | ||||||||
\(755\) | −1.31506e128 | −1.12281 | ||||||||
\(756\) | 5.05932e128 | 4.07260 | ||||||||
\(757\) | −1.17540e128 | −0.892110 | −0.446055 | − | 0.895005i | \(-0.647171\pi\) | ||||
−0.446055 | + | 0.895005i | \(0.647171\pi\) | |||||||
\(758\) | 4.75244e128 | 3.40124 | ||||||||
\(759\) | −3.65743e127 | −0.246841 | ||||||||
\(760\) | 1.47289e128 | 0.937485 | ||||||||
\(761\) | −3.45209e127 | −0.207236 | −0.103618 | − | 0.994617i | \(-0.533042\pi\) | ||||
−0.103618 | + | 0.994617i | \(0.533042\pi\) | |||||||
\(762\) | 2.12559e128 | 1.20361 | ||||||||
\(763\) | −4.50077e128 | −2.40406 | ||||||||
\(764\) | −1.40554e128 | −0.708254 | ||||||||
\(765\) | 5.93423e126 | 0.0282118 | ||||||||
\(766\) | 4.65651e128 | 2.08872 | ||||||||
\(767\) | 5.15853e127 | 0.218339 | ||||||||
\(768\) | −6.67383e128 | −2.66564 | ||||||||
\(769\) | 4.31920e128 | 1.62810 | 0.814050 | − | 0.580794i | \(-0.197258\pi\) | ||||
0.814050 | + | 0.580794i | \(0.197258\pi\) | |||||||
\(770\) | −3.72058e128 | −1.32365 | ||||||||
\(771\) | 1.49013e128 | 0.500383 | ||||||||
\(772\) | −4.39259e128 | −1.39236 | ||||||||
\(773\) | 5.58575e128 | 1.67145 | 0.835727 | − | 0.549145i | \(-0.185047\pi\) | ||||
0.835727 | + | 0.549145i | \(0.185047\pi\) | |||||||
\(774\) | −6.40911e127 | −0.181061 | ||||||||
\(775\) | −4.33586e127 | −0.115651 | ||||||||
\(776\) | −8.82536e128 | −2.22272 | ||||||||
\(777\) | −5.80773e128 | −1.38125 | ||||||||
\(778\) | −6.86497e128 | −1.54187 | ||||||||
\(779\) | 2.75843e128 | 0.585120 | ||||||||
\(780\) | 8.85318e128 | 1.77374 | ||||||||
\(781\) | 2.62624e128 | 0.497007 | ||||||||
\(782\) | 1.26947e128 | 0.226946 | ||||||||
\(783\) | −9.78755e128 | −1.65301 | ||||||||
\(784\) | 2.33163e129 | 3.72044 | ||||||||
\(785\) | 6.25228e128 | 0.942624 | ||||||||
\(786\) | 2.00244e129 | 2.85269 | ||||||||
\(787\) | −2.16044e128 | −0.290849 | −0.145424 | − | 0.989369i | \(-0.546455\pi\) | ||||
−0.145424 | + | 0.989369i | \(0.546455\pi\) | |||||||
\(788\) | −1.91005e129 | −2.43012 | ||||||||
\(789\) | 9.65633e128 | 1.16114 | ||||||||
\(790\) | −7.55729e128 | −0.858936 | ||||||||
\(791\) | −1.46721e129 | −1.57630 | ||||||||
\(792\) | 2.48589e128 | 0.252471 | ||||||||
\(793\) | −4.46222e128 | −0.428444 | ||||||||
\(794\) | −2.86336e129 | −2.59934 | ||||||||
\(795\) | −1.14314e128 | −0.0981215 | ||||||||
\(796\) | 3.60955e129 | 2.92969 | ||||||||
\(797\) | 5.79107e128 | 0.444492 | 0.222246 | − | 0.974991i | \(-0.428661\pi\) | ||||
0.222246 | + | 0.974991i | \(0.428661\pi\) | |||||||
\(798\) | −1.15084e129 | −0.835381 | ||||||||
\(799\) | −9.08456e126 | −0.00623695 | ||||||||
\(800\) | 1.69373e129 | 1.09987 | ||||||||
\(801\) | 1.17302e128 | 0.0720538 | ||||||||
\(802\) | −2.01164e129 | −1.16893 | ||||||||
\(803\) | 3.52329e128 | 0.193690 | ||||||||
\(804\) | −6.97927e129 | −3.63008 | ||||||||
\(805\) | 1.12404e129 | 0.553177 | ||||||||
\(806\) | 1.40072e129 | 0.652291 | ||||||||
\(807\) | 4.93779e128 | 0.217601 | ||||||||
\(808\) | 1.00810e130 | 4.20436 | ||||||||
\(809\) | −1.68676e129 | −0.665799 | −0.332899 | − | 0.942962i | \(-0.608027\pi\) | ||||
−0.332899 | + | 0.942962i | \(0.608027\pi\) | |||||||
\(810\) | 3.73823e129 | 1.39663 | ||||||||
\(811\) | 1.55157e129 | 0.548712 | 0.274356 | − | 0.961628i | \(-0.411535\pi\) | ||||
0.274356 | + | 0.961628i | \(0.411535\pi\) | |||||||
\(812\) | −1.80888e130 | −6.05574 | ||||||||
\(813\) | 5.22357e128 | 0.165553 | ||||||||
\(814\) | −3.87672e129 | −1.16327 | ||||||||
\(815\) | 5.36786e129 | 1.52506 | ||||||||
\(816\) | 3.30917e129 | 0.890241 | ||||||||
\(817\) | 9.21247e128 | 0.234690 | ||||||||
\(818\) | 1.34423e130 | 3.24304 | ||||||||
\(819\) | 6.62878e128 | 0.151461 | ||||||||
\(820\) | −1.91093e130 | −4.13550 | ||||||||
\(821\) | 3.14500e129 | 0.644689 | 0.322345 | − | 0.946622i | \(-0.395529\pi\) | ||||
0.322345 | + | 0.946622i | \(0.395529\pi\) | |||||||
\(822\) | 9.81951e129 | 1.90675 | ||||||||
\(823\) | −9.23589e129 | −1.69897 | −0.849486 | − | 0.527612i | \(-0.823088\pi\) | ||||
−0.849486 | + | 0.527612i | \(0.823088\pi\) | |||||||
\(824\) | 1.29357e130 | 2.25439 | ||||||||
\(825\) | 9.07538e128 | 0.149852 | ||||||||
\(826\) | 4.64540e129 | 0.726794 | ||||||||
\(827\) | −3.35499e129 | −0.497389 | −0.248694 | − | 0.968582i | \(-0.580001\pi\) | ||||
−0.248694 | + | 0.968582i | \(0.580001\pi\) | |||||||
\(828\) | −1.18281e129 | −0.166175 | ||||||||
\(829\) | 4.80463e129 | 0.639711 | 0.319855 | − | 0.947466i | \(-0.396366\pi\) | ||||
0.319855 | + | 0.947466i | \(0.396366\pi\) | |||||||
\(830\) | 1.70050e130 | 2.14586 | ||||||||
\(831\) | −1.30966e130 | −1.56644 | ||||||||
\(832\) | −2.75171e130 | −3.11972 | ||||||||
\(833\) | −2.33287e129 | −0.250719 | ||||||||
\(834\) | −2.44401e130 | −2.49008 | ||||||||
\(835\) | −1.25702e130 | −1.21421 | ||||||||
\(836\) | −5.62759e129 | −0.515399 | ||||||||
\(837\) | 4.99990e129 | 0.434189 | ||||||||
\(838\) | 3.62305e129 | 0.298342 | ||||||||
\(839\) | −1.24765e130 | −0.974282 | −0.487141 | − | 0.873323i | \(-0.661960\pi\) | ||||
−0.487141 | + | 0.873323i | \(0.661960\pi\) | |||||||
\(840\) | 5.06214e130 | 3.74892 | ||||||||
\(841\) | 2.07568e130 | 1.45794 | ||||||||
\(842\) | 8.39407e129 | 0.559222 | ||||||||
\(843\) | −1.23028e130 | −0.777460 | ||||||||
\(844\) | 3.55496e130 | 2.13106 | ||||||||
\(845\) | −4.90630e129 | −0.279017 | ||||||||
\(846\) | 1.15543e128 | 0.00623396 | ||||||||
\(847\) | −1.85193e130 | −0.948010 | ||||||||
\(848\) | 9.62074e129 | 0.467297 | ||||||||
\(849\) | 2.38534e130 | 1.09941 | ||||||||
\(850\) | −3.15001e129 | −0.137775 | ||||||||
\(851\) | 1.17121e130 | 0.486150 | ||||||||
\(852\) | −5.62756e130 | −2.21696 | ||||||||
\(853\) | −3.16115e130 | −1.18199 | −0.590993 | − | 0.806676i | \(-0.701264\pi\) | ||||
−0.590993 | + | 0.806676i | \(0.701264\pi\) | |||||||
\(854\) | −4.01836e130 | −1.42618 | ||||||||
\(855\) | 1.08489e129 | 0.0365504 | ||||||||
\(856\) | 5.99120e130 | 1.91616 | ||||||||
\(857\) | 4.85246e130 | 1.47338 | 0.736692 | − | 0.676229i | \(-0.236387\pi\) | ||||
0.736692 | + | 0.676229i | \(0.236387\pi\) | |||||||
\(858\) | −2.93184e130 | −0.845193 | ||||||||
\(859\) | 1.53494e129 | 0.0420141 | 0.0210070 | − | 0.999779i | \(-0.493313\pi\) | ||||
0.0210070 | + | 0.999779i | \(0.493313\pi\) | |||||||
\(860\) | −6.38204e130 | −1.65874 | ||||||||
\(861\) | 9.48040e130 | 2.33984 | ||||||||
\(862\) | −3.14046e130 | −0.736072 | ||||||||
\(863\) | −2.23394e130 | −0.497269 | −0.248634 | − | 0.968597i | \(-0.579982\pi\) | ||||
−0.248634 | + | 0.968597i | \(0.579982\pi\) | |||||||
\(864\) | −1.95313e131 | −4.12923 | ||||||||
\(865\) | 1.68674e130 | 0.338712 | ||||||||
\(866\) | 7.60418e130 | 1.45046 | ||||||||
\(867\) | 4.81321e130 | 0.872138 | ||||||||
\(868\) | 9.24056e130 | 1.59064 | ||||||||
\(869\) | 1.83340e130 | 0.299832 | ||||||||
\(870\) | −1.54233e131 | −2.39647 | ||||||||
\(871\) | −7.88784e130 | −1.16453 | ||||||||
\(872\) | 4.08761e131 | 5.73437 | ||||||||
\(873\) | −6.50051e129 | −0.0866589 | ||||||||
\(874\) | 2.32083e130 | 0.294025 | ||||||||
\(875\) | −1.27205e131 | −1.53160 | ||||||||
\(876\) | −7.54979e130 | −0.863977 | ||||||||
\(877\) | −9.11800e129 | −0.0991785 | −0.0495892 | − | 0.998770i | \(-0.515791\pi\) | ||||
−0.0495892 | + | 0.998770i | \(0.515791\pi\) | |||||||
\(878\) | −3.04757e131 | −3.15099 | ||||||||
\(879\) | 3.85991e129 | 0.0379378 | ||||||||
\(880\) | 1.95585e131 | 1.82750 | ||||||||
\(881\) | 1.41911e131 | 1.26063 | 0.630314 | − | 0.776340i | \(-0.282926\pi\) | ||||
0.630314 | + | 0.776340i | \(0.282926\pi\) | |||||||
\(882\) | 2.96709e130 | 0.250599 | ||||||||
\(883\) | −6.40533e130 | −0.514388 | −0.257194 | − | 0.966360i | \(-0.582798\pi\) | ||||
−0.257194 | + | 0.966360i | \(0.582798\pi\) | |||||||
\(884\) | 7.45483e130 | 0.569262 | ||||||||
\(885\) | 2.90163e130 | 0.210701 | ||||||||
\(886\) | −2.33307e131 | −1.61112 | ||||||||
\(887\) | −1.13778e131 | −0.747235 | −0.373617 | − | 0.927583i | \(-0.621883\pi\) | ||||
−0.373617 | + | 0.927583i | \(0.621883\pi\) | |||||||
\(888\) | 5.27459e131 | 3.29467 | ||||||||
\(889\) | 1.58481e131 | 0.941560 | ||||||||
\(890\) | 1.59447e131 | 0.901072 | ||||||||
\(891\) | −9.06895e130 | −0.487527 | ||||||||
\(892\) | −5.73492e131 | −2.93286 | ||||||||
\(893\) | −1.66082e129 | −0.00808041 | ||||||||
\(894\) | 4.32496e131 | 2.00199 | ||||||||
\(895\) | −3.33136e131 | −1.46723 | ||||||||
\(896\) | −1.16027e132 | −4.86244 | ||||||||
\(897\) | 8.85749e130 | 0.353221 | ||||||||
\(898\) | 1.35844e131 | 0.515517 | ||||||||
\(899\) | −1.78764e131 | −0.645615 | ||||||||
\(900\) | 2.93497e130 | 0.100882 | ||||||||
\(901\) | −9.62586e129 | −0.0314910 | ||||||||
\(902\) | 6.32828e131 | 1.97058 | ||||||||
\(903\) | 3.16622e131 | 0.938505 | ||||||||
\(904\) | 1.33252e132 | 3.75992 | ||||||||
\(905\) | −1.07656e131 | −0.289184 | ||||||||
\(906\) | −9.33198e131 | −2.38654 | ||||||||
\(907\) | −2.07157e131 | −0.504401 | −0.252201 | − | 0.967675i | \(-0.581154\pi\) | ||||
−0.252201 | + | 0.967675i | \(0.581154\pi\) | |||||||
\(908\) | −5.18739e131 | −1.20262 | ||||||||
\(909\) | 7.42541e130 | 0.163918 | ||||||||
\(910\) | 9.01042e131 | 1.89410 | ||||||||
\(911\) | 7.32060e131 | 1.46548 | 0.732738 | − | 0.680511i | \(-0.238242\pi\) | ||||
0.732738 | + | 0.680511i | \(0.238242\pi\) | |||||||
\(912\) | 6.04977e131 | 1.15337 | ||||||||
\(913\) | −4.12541e131 | −0.749061 | ||||||||
\(914\) | 8.92906e131 | 1.54419 | ||||||||
\(915\) | −2.50996e131 | −0.413455 | ||||||||
\(916\) | −2.56811e132 | −4.02963 | ||||||||
\(917\) | 1.49298e132 | 2.23161 | ||||||||
\(918\) | 3.63244e131 | 0.517248 | ||||||||
\(919\) | −9.54003e131 | −1.29422 | −0.647112 | − | 0.762395i | \(-0.724023\pi\) | ||||
−0.647112 | + | 0.762395i | \(0.724023\pi\) | |||||||
\(920\) | −1.02085e132 | −1.31949 | ||||||||
\(921\) | 4.23258e128 | 0.000521256 0 | ||||||||
\(922\) | −7.06128e131 | −0.828624 | ||||||||
\(923\) | −6.36016e131 | −0.711201 | ||||||||
\(924\) | −1.93414e132 | −2.06103 | ||||||||
\(925\) | −2.90619e131 | −0.295132 | ||||||||
\(926\) | −1.33503e132 | −1.29212 | ||||||||
\(927\) | 9.52806e130 | 0.0878934 | ||||||||
\(928\) | 6.98312e132 | 6.13995 | ||||||||
\(929\) | −6.90699e130 | −0.0578882 | −0.0289441 | − | 0.999581i | \(-0.509214\pi\) | ||||
−0.0289441 | + | 0.999581i | \(0.509214\pi\) | |||||||
\(930\) | 7.87891e131 | 0.629470 | ||||||||
\(931\) | −4.26491e131 | −0.324825 | ||||||||
\(932\) | −1.48391e132 | −1.07746 | ||||||||
\(933\) | 9.21612e131 | 0.637992 | ||||||||
\(934\) | 2.98583e132 | 1.97074 | ||||||||
\(935\) | −1.95689e131 | −0.123154 | ||||||||
\(936\) | −6.02027e131 | −0.361278 | ||||||||
\(937\) | 9.96476e131 | 0.570237 | 0.285118 | − | 0.958492i | \(-0.407967\pi\) | ||||
0.285118 | + | 0.958492i | \(0.407967\pi\) | |||||||
\(938\) | −7.10322e132 | −3.87640 | ||||||||
\(939\) | −2.91617e132 | −1.51773 | ||||||||
\(940\) | 1.15055e131 | 0.0571107 | ||||||||
\(941\) | 3.96538e132 | 1.87736 | 0.938678 | − | 0.344795i | \(-0.112052\pi\) | ||||
0.938678 | + | 0.344795i | \(0.112052\pi\) | |||||||
\(942\) | 4.43675e132 | 2.00355 | ||||||||
\(943\) | −1.91186e132 | −0.823542 | ||||||||
\(944\) | −2.44202e132 | −1.00345 | ||||||||
\(945\) | 3.21629e132 | 1.26078 | ||||||||
\(946\) | 2.11349e132 | 0.790396 | ||||||||
\(947\) | 7.97066e131 | 0.284394 | 0.142197 | − | 0.989838i | \(-0.454583\pi\) | ||||
0.142197 | + | 0.989838i | \(0.454583\pi\) | |||||||
\(948\) | −3.92865e132 | −1.33744 | ||||||||
\(949\) | −8.53263e131 | −0.277164 | ||||||||
\(950\) | −5.75879e131 | −0.178497 | ||||||||
\(951\) | 2.12742e132 | 0.629246 | ||||||||
\(952\) | 4.26258e132 | 1.20317 | ||||||||
\(953\) | −1.94714e132 | −0.524521 | −0.262260 | − | 0.964997i | \(-0.584468\pi\) | ||||
−0.262260 | + | 0.964997i | \(0.584468\pi\) | |||||||
\(954\) | 1.22428e131 | 0.0314759 | ||||||||
\(955\) | −8.93526e131 | −0.219259 | ||||||||
\(956\) | −3.81529e132 | −0.893616 | ||||||||
\(957\) | 3.74171e132 | 0.836543 | ||||||||
\(958\) | −1.18835e133 | −2.53618 | ||||||||
\(959\) | 7.32126e132 | 1.49162 | ||||||||
\(960\) | −1.54781e133 | −3.01057 | ||||||||
\(961\) | −4.47186e132 | −0.830419 | ||||||||
\(962\) | 9.38857e132 | 1.66459 | ||||||||
\(963\) | 4.41295e131 | 0.0747066 | ||||||||
\(964\) | 1.30407e133 | 2.10801 | ||||||||
\(965\) | −2.79244e132 | −0.431041 | ||||||||
\(966\) | 7.97642e132 | 1.17578 | ||||||||
\(967\) | −1.33124e133 | −1.87403 | −0.937017 | − | 0.349283i | \(-0.886425\pi\) | ||||
−0.937017 | + | 0.349283i | \(0.886425\pi\) | |||||||
\(968\) | 1.68193e133 | 2.26128 | ||||||||
\(969\) | −6.05299e131 | −0.0777252 | ||||||||
\(970\) | −8.83605e132 | −1.08372 | ||||||||
\(971\) | 2.41972e132 | 0.283471 | 0.141735 | − | 0.989905i | \(-0.454732\pi\) | ||||
0.141735 | + | 0.989905i | \(0.454732\pi\) | |||||||
\(972\) | −6.37657e132 | −0.713572 | ||||||||
\(973\) | −1.82221e133 | −1.94795 | ||||||||
\(974\) | 1.57547e133 | 1.60893 | ||||||||
\(975\) | −2.19785e132 | −0.214434 | ||||||||
\(976\) | 2.11239e133 | 1.96905 | ||||||||
\(977\) | −3.12470e132 | −0.278292 | −0.139146 | − | 0.990272i | \(-0.544436\pi\) | ||||
−0.139146 | + | 0.990272i | \(0.544436\pi\) | |||||||
\(978\) | 3.80915e133 | 3.24152 | ||||||||
\(979\) | −3.86818e132 | −0.314540 | ||||||||
\(980\) | 2.95456e133 | 2.29579 | ||||||||
\(981\) | 3.01082e132 | 0.223570 | ||||||||
\(982\) | −3.70191e133 | −2.62703 | ||||||||
\(983\) | 6.48939e132 | 0.440121 | 0.220061 | − | 0.975486i | \(-0.429374\pi\) | ||||
0.220061 | + | 0.975486i | \(0.429374\pi\) | |||||||
\(984\) | −8.61013e133 | −5.58120 | ||||||||
\(985\) | −1.21425e133 | −0.752307 | ||||||||
\(986\) | −1.29872e133 | −0.769120 | ||||||||
\(987\) | −5.70806e131 | −0.0323129 | ||||||||
\(988\) | 1.36288e133 | 0.737519 | ||||||||
\(989\) | −6.38514e132 | −0.330321 | ||||||||
\(990\) | 2.48890e132 | 0.123095 | ||||||||
\(991\) | 3.49977e133 | 1.65486 | 0.827432 | − | 0.561566i | \(-0.189801\pi\) | ||||
0.827432 | + | 0.561566i | \(0.189801\pi\) | |||||||
\(992\) | −3.56728e133 | −1.61275 | ||||||||
\(993\) | 2.23320e133 | 0.965355 | ||||||||
\(994\) | −5.72751e133 | −2.36740 | ||||||||
\(995\) | 2.29465e133 | 0.906962 | ||||||||
\(996\) | 8.84002e133 | 3.34128 | ||||||||
\(997\) | 2.65956e133 | 0.961336 | 0.480668 | − | 0.876903i | \(-0.340394\pi\) | ||||
0.480668 | + | 0.876903i | \(0.340394\pi\) | |||||||
\(998\) | −3.27020e133 | −1.13049 | ||||||||
\(999\) | 3.35128e133 | 1.10802 |
(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 | 1.90.a.a.1.1 | ✓ | 7 | |
3.2 | odd | 2 | 9.90.a.b.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.90.a.a.1.1 | ✓ | 7 | 1.1 | even | 1 | trivial | |
9.90.a.b.1.7 | 7 | 3.2 | odd | 2 |