Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1669 x^{15} + 2385 x^{14} + 1108684 x^{13} - 848131 x^{12} - 377920980 x^{11} + \cdots + 24\!\cdots\!16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Root | \(15.1891\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 15.1891 | 1.34254 | 0.671272 | − | 0.741211i | \(-0.265748\pi\) | ||||
0.671272 | + | 0.741211i | \(0.265748\pi\) | |||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 102.710 | 0.802423 | ||||||||
\(5\) | −418.807 | −1.49837 | −0.749184 | − | 0.662362i | \(-0.769554\pi\) | ||||
−0.749184 | + | 0.662362i | \(0.769554\pi\) | |||||||
\(6\) | −410.107 | −0.775118 | ||||||||
\(7\) | −814.653 | −0.897696 | −0.448848 | − | 0.893608i | \(-0.648166\pi\) | ||||
−0.448848 | + | 0.893608i | \(0.648166\pi\) | |||||||
\(8\) | −384.131 | −0.265256 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | −6361.32 | −2.01162 | ||||||||
\(11\) | −2422.96 | −0.548874 | −0.274437 | − | 0.961605i | \(-0.588491\pi\) | ||||
−0.274437 | + | 0.961605i | \(0.588491\pi\) | |||||||
\(12\) | −2773.17 | −0.463279 | ||||||||
\(13\) | 10673.2 | 1.34738 | 0.673692 | − | 0.739012i | \(-0.264707\pi\) | ||||
0.673692 | + | 0.739012i | \(0.264707\pi\) | |||||||
\(14\) | −12373.9 | −1.20520 | ||||||||
\(15\) | 11307.8 | 0.865083 | ||||||||
\(16\) | −18981.5 | −1.15854 | ||||||||
\(17\) | −26705.4 | −1.31834 | −0.659171 | − | 0.751993i | \(-0.729093\pi\) | ||||
−0.659171 | + | 0.751993i | \(0.729093\pi\) | |||||||
\(18\) | 11072.9 | 0.447515 | ||||||||
\(19\) | 33854.6 | 1.13235 | 0.566174 | − | 0.824286i | \(-0.308423\pi\) | ||||
0.566174 | + | 0.824286i | \(0.308423\pi\) | |||||||
\(20\) | −43015.7 | −1.20233 | ||||||||
\(21\) | 21995.6 | 0.518285 | ||||||||
\(22\) | −36802.7 | −0.736887 | ||||||||
\(23\) | 15069.2 | 0.258252 | 0.129126 | − | 0.991628i | \(-0.458783\pi\) | ||||
0.129126 | + | 0.991628i | \(0.458783\pi\) | |||||||
\(24\) | 10371.5 | 0.153145 | ||||||||
\(25\) | 97274.0 | 1.24511 | ||||||||
\(26\) | 162116. | 1.80892 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | −83673.1 | −0.720332 | ||||||||
\(29\) | 32501.7 | 0.247464 | 0.123732 | − | 0.992316i | \(-0.460514\pi\) | ||||
0.123732 | + | 0.992316i | \(0.460514\pi\) | |||||||
\(30\) | 171756. | 1.16141 | ||||||||
\(31\) | 26459.3 | 0.159519 | 0.0797594 | − | 0.996814i | \(-0.474585\pi\) | ||||
0.0797594 | + | 0.996814i | \(0.474585\pi\) | |||||||
\(32\) | −239144. | −1.29014 | ||||||||
\(33\) | 65420.0 | 0.316892 | ||||||||
\(34\) | −405632. | −1.76993 | ||||||||
\(35\) | 341182. | 1.34508 | ||||||||
\(36\) | 74875.7 | 0.267474 | ||||||||
\(37\) | 497796. | 1.61564 | 0.807822 | − | 0.589427i | \(-0.200646\pi\) | ||||
0.807822 | + | 0.589427i | \(0.200646\pi\) | |||||||
\(38\) | 514222. | 1.52023 | ||||||||
\(39\) | −288176. | −0.777913 | ||||||||
\(40\) | 160877. | 0.397451 | ||||||||
\(41\) | 366715. | 0.830970 | 0.415485 | − | 0.909600i | \(-0.363612\pi\) | ||||
0.415485 | + | 0.909600i | \(0.363612\pi\) | |||||||
\(42\) | 334095. | 0.695820 | ||||||||
\(43\) | 493861. | 0.947251 | 0.473626 | − | 0.880726i | \(-0.342945\pi\) | ||||
0.473626 | + | 0.880726i | \(0.342945\pi\) | |||||||
\(44\) | −248863. | −0.440429 | ||||||||
\(45\) | −305310. | −0.499456 | ||||||||
\(46\) | 228889. | 0.346715 | ||||||||
\(47\) | −825019. | −1.15910 | −0.579550 | − | 0.814936i | \(-0.696772\pi\) | ||||
−0.579550 | + | 0.814936i | \(0.696772\pi\) | |||||||
\(48\) | 512501. | 0.668884 | ||||||||
\(49\) | −159884. | −0.194142 | ||||||||
\(50\) | 1.47751e6 | 1.67161 | ||||||||
\(51\) | 721046. | 0.761145 | ||||||||
\(52\) | 1.09624e6 | 1.08117 | ||||||||
\(53\) | −1.78313e6 | −1.64520 | −0.822598 | − | 0.568624i | \(-0.807476\pi\) | ||||
−0.822598 | + | 0.568624i | \(0.807476\pi\) | |||||||
\(54\) | −298968. | −0.258373 | ||||||||
\(55\) | 1.01475e6 | 0.822415 | ||||||||
\(56\) | 312933. | 0.238119 | ||||||||
\(57\) | −914074. | −0.653761 | ||||||||
\(58\) | 493673. | 0.332232 | ||||||||
\(59\) | −205379. | −0.130189 | ||||||||
\(60\) | 1.16142e6 | 0.694163 | ||||||||
\(61\) | 628605. | 0.354587 | 0.177294 | − | 0.984158i | \(-0.443266\pi\) | ||||
0.177294 | + | 0.984158i | \(0.443266\pi\) | |||||||
\(62\) | 401894. | 0.214161 | ||||||||
\(63\) | −593882. | −0.299232 | ||||||||
\(64\) | −1.20276e6 | −0.573522 | ||||||||
\(65\) | −4.46999e6 | −2.01888 | ||||||||
\(66\) | 993674. | 0.425442 | ||||||||
\(67\) | 1.85849e6 | 0.754915 | 0.377458 | − | 0.926027i | \(-0.376798\pi\) | ||||
0.377458 | + | 0.926027i | \(0.376798\pi\) | |||||||
\(68\) | −2.74292e6 | −1.05787 | ||||||||
\(69\) | −406870. | −0.149102 | ||||||||
\(70\) | 5.18226e6 | 1.80583 | ||||||||
\(71\) | 3.64832e6 | 1.20973 | 0.604865 | − | 0.796328i | \(-0.293227\pi\) | ||||
0.604865 | + | 0.796328i | \(0.293227\pi\) | |||||||
\(72\) | −280032. | −0.0884185 | ||||||||
\(73\) | 5.50965e6 | 1.65765 | 0.828827 | − | 0.559505i | \(-0.189009\pi\) | ||||
0.828827 | + | 0.559505i | \(0.189009\pi\) | |||||||
\(74\) | 7.56110e6 | 2.16907 | ||||||||
\(75\) | −2.62640e6 | −0.718863 | ||||||||
\(76\) | 3.47721e6 | 0.908622 | ||||||||
\(77\) | 1.97387e6 | 0.492722 | ||||||||
\(78\) | −4.37714e6 | −1.04438 | ||||||||
\(79\) | −6.04365e6 | −1.37913 | −0.689564 | − | 0.724224i | \(-0.742198\pi\) | ||||
−0.689564 | + | 0.724224i | \(0.742198\pi\) | |||||||
\(80\) | 7.94959e6 | 1.73592 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 5.57009e6 | 1.11561 | ||||||||
\(83\) | −4.72119e6 | −0.906313 | −0.453156 | − | 0.891431i | \(-0.649702\pi\) | ||||
−0.453156 | + | 0.891431i | \(0.649702\pi\) | |||||||
\(84\) | 2.25917e6 | 0.415884 | ||||||||
\(85\) | 1.11844e7 | 1.97536 | ||||||||
\(86\) | 7.50133e6 | 1.27173 | ||||||||
\(87\) | −877545. | −0.142874 | ||||||||
\(88\) | 930735. | 0.145592 | ||||||||
\(89\) | −875348. | −0.131618 | −0.0658091 | − | 0.997832i | \(-0.520963\pi\) | ||||
−0.0658091 | + | 0.997832i | \(0.520963\pi\) | |||||||
\(90\) | −4.63740e6 | −0.670541 | ||||||||
\(91\) | −8.69493e6 | −1.20954 | ||||||||
\(92\) | 1.54776e6 | 0.207228 | ||||||||
\(93\) | −714401. | −0.0920983 | ||||||||
\(94\) | −1.25313e7 | −1.55614 | ||||||||
\(95\) | −1.41785e7 | −1.69667 | ||||||||
\(96\) | 6.45690e6 | 0.744860 | ||||||||
\(97\) | −1.26140e7 | −1.40331 | −0.701653 | − | 0.712519i | \(-0.747554\pi\) | ||||
−0.701653 | + | 0.712519i | \(0.747554\pi\) | |||||||
\(98\) | −2.42850e6 | −0.260644 | ||||||||
\(99\) | −1.76634e6 | −0.182958 | ||||||||
\(100\) | 9.99103e6 | 0.999103 | ||||||||
\(101\) | 1.43083e6 | 0.138185 | 0.0690926 | − | 0.997610i | \(-0.477990\pi\) | ||||
0.0690926 | + | 0.997610i | \(0.477990\pi\) | |||||||
\(102\) | 1.09521e7 | 1.02187 | ||||||||
\(103\) | 5.60899e6 | 0.505772 | 0.252886 | − | 0.967496i | \(-0.418620\pi\) | ||||
0.252886 | + | 0.967496i | \(0.418620\pi\) | |||||||
\(104\) | −4.09990e6 | −0.357401 | ||||||||
\(105\) | −9.21191e6 | −0.776582 | ||||||||
\(106\) | −2.70842e7 | −2.20875 | ||||||||
\(107\) | 2.17512e7 | 1.71648 | 0.858241 | − | 0.513247i | \(-0.171558\pi\) | ||||
0.858241 | + | 0.513247i | \(0.171558\pi\) | |||||||
\(108\) | −2.02164e6 | −0.154426 | ||||||||
\(109\) | −9.32545e6 | −0.689727 | −0.344863 | − | 0.938653i | \(-0.612075\pi\) | ||||
−0.344863 | + | 0.938653i | \(0.612075\pi\) | |||||||
\(110\) | 1.54132e7 | 1.10413 | ||||||||
\(111\) | −1.34405e7 | −0.932792 | ||||||||
\(112\) | 1.54634e7 | 1.04002 | ||||||||
\(113\) | 1.50397e7 | 0.980537 | 0.490268 | − | 0.871572i | \(-0.336899\pi\) | ||||
0.490268 | + | 0.871572i | \(0.336899\pi\) | |||||||
\(114\) | −1.38840e7 | −0.877703 | ||||||||
\(115\) | −6.31110e6 | −0.386957 | ||||||||
\(116\) | 3.33825e6 | 0.198571 | ||||||||
\(117\) | 7.78074e6 | 0.449128 | ||||||||
\(118\) | −3.11953e6 | −0.174784 | ||||||||
\(119\) | 2.17556e7 | 1.18347 | ||||||||
\(120\) | −4.34367e6 | −0.229468 | ||||||||
\(121\) | −1.36164e7 | −0.698738 | ||||||||
\(122\) | 9.54797e6 | 0.476049 | ||||||||
\(123\) | −9.90131e6 | −0.479761 | ||||||||
\(124\) | 2.71764e6 | 0.128002 | ||||||||
\(125\) | −8.01973e6 | −0.367261 | ||||||||
\(126\) | −9.02056e6 | −0.401732 | ||||||||
\(127\) | 1.78413e7 | 0.772883 | 0.386441 | − | 0.922314i | \(-0.373704\pi\) | ||||
0.386441 | + | 0.922314i | \(0.373704\pi\) | |||||||
\(128\) | 1.23415e7 | 0.520156 | ||||||||
\(129\) | −1.33342e7 | −0.546896 | ||||||||
\(130\) | −6.78954e7 | −2.71043 | ||||||||
\(131\) | 3.78349e6 | 0.147043 | 0.0735214 | − | 0.997294i | \(-0.476576\pi\) | ||||
0.0735214 | + | 0.997294i | \(0.476576\pi\) | |||||||
\(132\) | 6.71930e6 | 0.254282 | ||||||||
\(133\) | −2.75797e7 | −1.01650 | ||||||||
\(134\) | 2.82289e7 | 1.01351 | ||||||||
\(135\) | 8.24337e6 | 0.288361 | ||||||||
\(136\) | 1.02584e7 | 0.349697 | ||||||||
\(137\) | −2.85640e7 | −0.949069 | −0.474534 | − | 0.880237i | \(-0.657384\pi\) | ||||
−0.474534 | + | 0.880237i | \(0.657384\pi\) | |||||||
\(138\) | −6.18000e6 | −0.200176 | ||||||||
\(139\) | 3.44323e7 | 1.08746 | 0.543731 | − | 0.839260i | \(-0.317011\pi\) | ||||
0.543731 | + | 0.839260i | \(0.317011\pi\) | |||||||
\(140\) | 3.50429e7 | 1.07932 | ||||||||
\(141\) | 2.22755e7 | 0.669207 | ||||||||
\(142\) | 5.54148e7 | 1.62412 | ||||||||
\(143\) | −2.58607e7 | −0.739544 | ||||||||
\(144\) | −1.38375e7 | −0.386180 | ||||||||
\(145\) | −1.36119e7 | −0.370793 | ||||||||
\(146\) | 8.36868e7 | 2.22547 | ||||||||
\(147\) | 4.31687e6 | 0.112088 | ||||||||
\(148\) | 5.11287e7 | 1.29643 | ||||||||
\(149\) | 4.80665e6 | 0.119039 | 0.0595196 | − | 0.998227i | \(-0.481043\pi\) | ||||
0.0595196 | + | 0.998227i | \(0.481043\pi\) | |||||||
\(150\) | −3.98927e7 | −0.965105 | ||||||||
\(151\) | −5.09354e6 | −0.120393 | −0.0601964 | − | 0.998187i | \(-0.519173\pi\) | ||||
−0.0601964 | + | 0.998187i | \(0.519173\pi\) | |||||||
\(152\) | −1.30046e7 | −0.300362 | ||||||||
\(153\) | −1.94682e7 | −0.439447 | ||||||||
\(154\) | 2.99815e7 | 0.661500 | ||||||||
\(155\) | −1.10813e7 | −0.239018 | ||||||||
\(156\) | −2.95986e7 | −0.624215 | ||||||||
\(157\) | 2.01246e7 | 0.415028 | 0.207514 | − | 0.978232i | \(-0.433463\pi\) | ||||
0.207514 | + | 0.978232i | \(0.433463\pi\) | |||||||
\(158\) | −9.17980e7 | −1.85154 | ||||||||
\(159\) | 4.81445e7 | 0.949854 | ||||||||
\(160\) | 1.00155e8 | 1.93310 | ||||||||
\(161\) | −1.22762e7 | −0.231832 | ||||||||
\(162\) | 8.07213e6 | 0.149172 | ||||||||
\(163\) | −6.76023e7 | −1.22266 | −0.611328 | − | 0.791377i | \(-0.709365\pi\) | ||||
−0.611328 | + | 0.791377i | \(0.709365\pi\) | |||||||
\(164\) | 3.76654e7 | 0.666790 | ||||||||
\(165\) | −2.73983e7 | −0.474821 | ||||||||
\(166\) | −7.17108e7 | −1.21676 | ||||||||
\(167\) | 1.10791e8 | 1.84076 | 0.920382 | − | 0.391020i | \(-0.127878\pi\) | ||||
0.920382 | + | 0.391020i | \(0.127878\pi\) | |||||||
\(168\) | −8.44920e6 | −0.137478 | ||||||||
\(169\) | 5.11680e7 | 0.815446 | ||||||||
\(170\) | 1.69881e8 | 2.65201 | ||||||||
\(171\) | 2.46800e7 | 0.377449 | ||||||||
\(172\) | 5.07245e7 | 0.760096 | ||||||||
\(173\) | 1.14352e8 | 1.67912 | 0.839559 | − | 0.543269i | \(-0.182814\pi\) | ||||
0.839559 | + | 0.543269i | \(0.182814\pi\) | |||||||
\(174\) | −1.33292e7 | −0.191814 | ||||||||
\(175\) | −7.92445e7 | −1.11773 | ||||||||
\(176\) | 4.59915e7 | 0.635892 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −1.32958e7 | −0.176703 | ||||||||
\(179\) | −1.89246e7 | −0.246627 | −0.123313 | − | 0.992368i | \(-0.539352\pi\) | ||||
−0.123313 | + | 0.992368i | \(0.539352\pi\) | |||||||
\(180\) | −3.13584e7 | −0.400775 | ||||||||
\(181\) | 9.30564e7 | 1.16646 | 0.583232 | − | 0.812306i | \(-0.301788\pi\) | ||||
0.583232 | + | 0.812306i | \(0.301788\pi\) | |||||||
\(182\) | −1.32069e8 | −1.62386 | ||||||||
\(183\) | −1.69723e7 | −0.204721 | ||||||||
\(184\) | −5.78857e6 | −0.0685029 | ||||||||
\(185\) | −2.08480e8 | −2.42083 | ||||||||
\(186\) | −1.08511e7 | −0.123646 | ||||||||
\(187\) | 6.47062e7 | 0.723603 | ||||||||
\(188\) | −8.47378e7 | −0.930089 | ||||||||
\(189\) | 1.60348e7 | 0.172762 | ||||||||
\(190\) | −2.15360e8 | −2.27786 | ||||||||
\(191\) | 1.28269e8 | 1.33200 | 0.666001 | − | 0.745951i | \(-0.268005\pi\) | ||||
0.666001 | + | 0.745951i | \(0.268005\pi\) | |||||||
\(192\) | 3.24746e7 | 0.331123 | ||||||||
\(193\) | −7.49379e7 | −0.750327 | −0.375164 | − | 0.926959i | \(-0.622413\pi\) | ||||
−0.375164 | + | 0.926959i | \(0.622413\pi\) | |||||||
\(194\) | −1.91596e8 | −1.88400 | ||||||||
\(195\) | 1.20690e8 | 1.16560 | ||||||||
\(196\) | −1.64217e7 | −0.155784 | ||||||||
\(197\) | −1.42886e8 | −1.33155 | −0.665775 | − | 0.746152i | \(-0.731899\pi\) | ||||
−0.665775 | + | 0.746152i | \(0.731899\pi\) | |||||||
\(198\) | −2.68292e7 | −0.245629 | ||||||||
\(199\) | −7.59209e7 | −0.682929 | −0.341465 | − | 0.939895i | \(-0.610923\pi\) | ||||
−0.341465 | + | 0.939895i | \(0.610923\pi\) | |||||||
\(200\) | −3.73660e7 | −0.330272 | ||||||||
\(201\) | −5.01792e7 | −0.435851 | ||||||||
\(202\) | 2.17330e7 | 0.185520 | ||||||||
\(203\) | −2.64776e7 | −0.222148 | ||||||||
\(204\) | 7.40587e7 | 0.610760 | ||||||||
\(205\) | −1.53583e8 | −1.24510 | ||||||||
\(206\) | 8.51958e7 | 0.679021 | ||||||||
\(207\) | 1.09855e7 | 0.0860841 | ||||||||
\(208\) | −2.02593e8 | −1.56100 | ||||||||
\(209\) | −8.20284e7 | −0.621516 | ||||||||
\(210\) | −1.39921e8 | −1.04260 | ||||||||
\(211\) | −6.90924e7 | −0.506339 | −0.253170 | − | 0.967422i | \(-0.581473\pi\) | ||||
−0.253170 | + | 0.967422i | \(0.581473\pi\) | |||||||
\(212\) | −1.83146e8 | −1.32014 | ||||||||
\(213\) | −9.85046e7 | −0.698438 | ||||||||
\(214\) | 3.30381e8 | 2.30445 | ||||||||
\(215\) | −2.06832e8 | −1.41933 | ||||||||
\(216\) | 7.56085e6 | 0.0510485 | ||||||||
\(217\) | −2.15551e7 | −0.143199 | ||||||||
\(218\) | −1.41646e8 | −0.925988 | ||||||||
\(219\) | −1.48760e8 | −0.957047 | ||||||||
\(220\) | 1.04225e8 | 0.659925 | ||||||||
\(221\) | −2.85031e8 | −1.77631 | ||||||||
\(222\) | −2.04150e8 | −1.25231 | ||||||||
\(223\) | −2.23657e8 | −1.35057 | −0.675284 | − | 0.737558i | \(-0.735979\pi\) | ||||
−0.675284 | + | 0.737558i | \(0.735979\pi\) | |||||||
\(224\) | 1.94820e8 | 1.15815 | ||||||||
\(225\) | 7.09127e7 | 0.415036 | ||||||||
\(226\) | 2.28440e8 | 1.31641 | ||||||||
\(227\) | −2.62570e7 | −0.148989 | −0.0744945 | − | 0.997221i | \(-0.523734\pi\) | ||||
−0.0744945 | + | 0.997221i | \(0.523734\pi\) | |||||||
\(228\) | −9.38847e7 | −0.524593 | ||||||||
\(229\) | 2.78378e8 | 1.53183 | 0.765916 | − | 0.642940i | \(-0.222286\pi\) | ||||
0.765916 | + | 0.642940i | \(0.222286\pi\) | |||||||
\(230\) | −9.58602e7 | −0.519507 | ||||||||
\(231\) | −5.32946e7 | −0.284473 | ||||||||
\(232\) | −1.24849e7 | −0.0656413 | ||||||||
\(233\) | 4.33659e7 | 0.224596 | 0.112298 | − | 0.993675i | \(-0.464179\pi\) | ||||
0.112298 | + | 0.993675i | \(0.464179\pi\) | |||||||
\(234\) | 1.18183e8 | 0.602974 | ||||||||
\(235\) | 3.45523e8 | 1.73676 | ||||||||
\(236\) | −2.10945e7 | −0.104467 | ||||||||
\(237\) | 1.63179e8 | 0.796240 | ||||||||
\(238\) | 3.30449e8 | 1.58886 | ||||||||
\(239\) | −3.28872e8 | −1.55824 | −0.779120 | − | 0.626875i | \(-0.784334\pi\) | ||||
−0.779120 | + | 0.626875i | \(0.784334\pi\) | |||||||
\(240\) | −2.14639e8 | −1.00223 | ||||||||
\(241\) | 3.31564e7 | 0.152583 | 0.0762917 | − | 0.997086i | \(-0.475692\pi\) | ||||
0.0762917 | + | 0.997086i | \(0.475692\pi\) | |||||||
\(242\) | −2.06822e8 | −0.938086 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 6.45641e7 | 0.284529 | ||||||||
\(245\) | 6.69604e7 | 0.290896 | ||||||||
\(246\) | −1.50392e8 | −0.644100 | ||||||||
\(247\) | 3.61336e8 | 1.52571 | ||||||||
\(248\) | −1.01638e7 | −0.0423133 | ||||||||
\(249\) | 1.27472e8 | 0.523260 | ||||||||
\(250\) | −1.21813e8 | −0.493063 | ||||||||
\(251\) | 2.94819e8 | 1.17679 | 0.588394 | − | 0.808574i | \(-0.299760\pi\) | ||||
0.588394 | + | 0.808574i | \(0.299760\pi\) | |||||||
\(252\) | −6.09977e7 | −0.240111 | ||||||||
\(253\) | −3.65122e7 | −0.141748 | ||||||||
\(254\) | 2.70994e8 | 1.03763 | ||||||||
\(255\) | −3.01979e8 | −1.14047 | ||||||||
\(256\) | 3.41411e8 | 1.27186 | ||||||||
\(257\) | −2.56922e8 | −0.944139 | −0.472069 | − | 0.881561i | \(-0.656493\pi\) | ||||
−0.472069 | + | 0.881561i | \(0.656493\pi\) | |||||||
\(258\) | −2.02536e8 | −0.734231 | ||||||||
\(259\) | −4.05531e8 | −1.45036 | ||||||||
\(260\) | −4.59114e8 | −1.61999 | ||||||||
\(261\) | 2.36937e7 | 0.0824881 | ||||||||
\(262\) | 5.74680e7 | 0.197411 | ||||||||
\(263\) | 3.01656e8 | 1.02251 | 0.511255 | − | 0.859429i | \(-0.329181\pi\) | ||||
0.511255 | + | 0.859429i | \(0.329181\pi\) | |||||||
\(264\) | −2.51299e7 | −0.0840575 | ||||||||
\(265\) | 7.46787e8 | 2.46511 | ||||||||
\(266\) | −4.18913e8 | −1.36470 | ||||||||
\(267\) | 2.36344e7 | 0.0759898 | ||||||||
\(268\) | 1.90886e8 | 0.605762 | ||||||||
\(269\) | −2.61569e8 | −0.819318 | −0.409659 | − | 0.912239i | \(-0.634352\pi\) | ||||
−0.409659 | + | 0.912239i | \(0.634352\pi\) | |||||||
\(270\) | 1.25210e8 | 0.387137 | ||||||||
\(271\) | −1.44509e8 | −0.441064 | −0.220532 | − | 0.975380i | \(-0.570779\pi\) | ||||
−0.220532 | + | 0.975380i | \(0.570779\pi\) | |||||||
\(272\) | 5.06909e8 | 1.52735 | ||||||||
\(273\) | 2.34763e8 | 0.698330 | ||||||||
\(274\) | −4.33863e8 | −1.27417 | ||||||||
\(275\) | −2.35691e8 | −0.683406 | ||||||||
\(276\) | −4.17897e7 | −0.119643 | ||||||||
\(277\) | −4.66473e7 | −0.131870 | −0.0659352 | − | 0.997824i | \(-0.521003\pi\) | ||||
−0.0659352 | + | 0.997824i | \(0.521003\pi\) | |||||||
\(278\) | 5.22997e8 | 1.45996 | ||||||||
\(279\) | 1.92888e7 | 0.0531730 | ||||||||
\(280\) | −1.31059e8 | −0.356790 | ||||||||
\(281\) | 6.78292e8 | 1.82366 | 0.911832 | − | 0.410564i | \(-0.134668\pi\) | ||||
0.911832 | + | 0.410564i | \(0.134668\pi\) | |||||||
\(282\) | 3.38346e8 | 0.898440 | ||||||||
\(283\) | 2.33845e8 | 0.613305 | 0.306652 | − | 0.951822i | \(-0.400791\pi\) | ||||
0.306652 | + | 0.951822i | \(0.400791\pi\) | |||||||
\(284\) | 3.74719e8 | 0.970715 | ||||||||
\(285\) | 3.82820e8 | 0.979575 | ||||||||
\(286\) | −3.92802e8 | −0.992870 | ||||||||
\(287\) | −2.98746e8 | −0.745959 | ||||||||
\(288\) | −1.74336e8 | −0.430045 | ||||||||
\(289\) | 3.02840e8 | 0.738024 | ||||||||
\(290\) | −2.06753e8 | −0.497805 | ||||||||
\(291\) | 3.40579e8 | 0.810199 | ||||||||
\(292\) | 5.65897e8 | 1.33014 | ||||||||
\(293\) | 3.28205e8 | 0.762270 | 0.381135 | − | 0.924519i | \(-0.375533\pi\) | ||||
0.381135 | + | 0.924519i | \(0.375533\pi\) | |||||||
\(294\) | 6.55695e7 | 0.150483 | ||||||||
\(295\) | 8.60141e7 | 0.195071 | ||||||||
\(296\) | −1.91219e8 | −0.428559 | ||||||||
\(297\) | 4.76912e7 | 0.105631 | ||||||||
\(298\) | 7.30089e7 | 0.159815 | ||||||||
\(299\) | 1.60837e8 | 0.347965 | ||||||||
\(300\) | −2.69758e8 | −0.576832 | ||||||||
\(301\) | −4.02325e8 | −0.850344 | ||||||||
\(302\) | −7.73665e7 | −0.161632 | ||||||||
\(303\) | −3.86323e7 | −0.0797813 | ||||||||
\(304\) | −6.42612e8 | −1.31187 | ||||||||
\(305\) | −2.63264e8 | −0.531302 | ||||||||
\(306\) | −2.95706e8 | −0.589977 | ||||||||
\(307\) | 1.82586e8 | 0.360150 | 0.180075 | − | 0.983653i | \(-0.442366\pi\) | ||||
0.180075 | + | 0.983653i | \(0.442366\pi\) | |||||||
\(308\) | 2.02737e8 | 0.395371 | ||||||||
\(309\) | −1.51443e8 | −0.292007 | ||||||||
\(310\) | −1.68316e8 | −0.320892 | ||||||||
\(311\) | −5.84419e8 | −1.10170 | −0.550850 | − | 0.834605i | \(-0.685696\pi\) | ||||
−0.550850 | + | 0.834605i | \(0.685696\pi\) | |||||||
\(312\) | 1.10697e8 | 0.206346 | ||||||||
\(313\) | 9.32347e8 | 1.71859 | 0.859295 | − | 0.511480i | \(-0.170903\pi\) | ||||
0.859295 | + | 0.511480i | \(0.170903\pi\) | |||||||
\(314\) | 3.05675e8 | 0.557194 | ||||||||
\(315\) | 2.48722e8 | 0.448360 | ||||||||
\(316\) | −6.20745e8 | −1.10664 | ||||||||
\(317\) | 8.93740e8 | 1.57581 | 0.787905 | − | 0.615797i | \(-0.211166\pi\) | ||||
0.787905 | + | 0.615797i | \(0.211166\pi\) | |||||||
\(318\) | 7.31274e8 | 1.27522 | ||||||||
\(319\) | −7.87503e7 | −0.135827 | ||||||||
\(320\) | 5.03725e8 | 0.859348 | ||||||||
\(321\) | −5.87281e8 | −0.991011 | ||||||||
\(322\) | −1.86465e8 | −0.311245 | ||||||||
\(323\) | −9.04100e8 | −1.49282 | ||||||||
\(324\) | 5.45844e7 | 0.0891581 | ||||||||
\(325\) | 1.03822e9 | 1.67764 | ||||||||
\(326\) | −1.02682e9 | −1.64147 | ||||||||
\(327\) | 2.51787e8 | 0.398214 | ||||||||
\(328\) | −1.40867e8 | −0.220419 | ||||||||
\(329\) | 6.72104e8 | 1.04052 | ||||||||
\(330\) | −4.16157e8 | −0.637468 | ||||||||
\(331\) | 9.07658e8 | 1.37570 | 0.687851 | − | 0.725852i | \(-0.258554\pi\) | ||||
0.687851 | + | 0.725852i | \(0.258554\pi\) | |||||||
\(332\) | −4.84914e8 | −0.727246 | ||||||||
\(333\) | 3.62893e8 | 0.538548 | ||||||||
\(334\) | 1.68283e9 | 2.47131 | ||||||||
\(335\) | −7.78348e8 | −1.13114 | ||||||||
\(336\) | −4.17510e8 | −0.600454 | ||||||||
\(337\) | 7.89412e8 | 1.12357 | 0.561784 | − | 0.827284i | \(-0.310115\pi\) | ||||
0.561784 | + | 0.827284i | \(0.310115\pi\) | |||||||
\(338\) | 7.77198e8 | 1.09477 | ||||||||
\(339\) | −4.06071e8 | −0.566113 | ||||||||
\(340\) | 1.14875e9 | 1.58507 | ||||||||
\(341\) | −6.41099e7 | −0.0875557 | ||||||||
\(342\) | 3.74868e8 | 0.506742 | ||||||||
\(343\) | 8.01151e8 | 1.07198 | ||||||||
\(344\) | −1.89707e8 | −0.251264 | ||||||||
\(345\) | 1.70400e8 | 0.223410 | ||||||||
\(346\) | 1.73690e9 | 2.25429 | ||||||||
\(347\) | −5.28902e8 | −0.679551 | −0.339775 | − | 0.940507i | \(-0.610351\pi\) | ||||
−0.339775 | + | 0.940507i | \(0.610351\pi\) | |||||||
\(348\) | −9.01328e7 | −0.114645 | ||||||||
\(349\) | 2.00046e8 | 0.251908 | 0.125954 | − | 0.992036i | \(-0.459801\pi\) | ||||
0.125954 | + | 0.992036i | \(0.459801\pi\) | |||||||
\(350\) | −1.20366e9 | −1.50060 | ||||||||
\(351\) | −2.10080e8 | −0.259304 | ||||||||
\(352\) | 5.79438e8 | 0.708121 | ||||||||
\(353\) | 2.52531e8 | 0.305565 | 0.152782 | − | 0.988260i | \(-0.451177\pi\) | ||||
0.152782 | + | 0.988260i | \(0.451177\pi\) | |||||||
\(354\) | 8.42274e7 | 0.100912 | ||||||||
\(355\) | −1.52794e9 | −1.81262 | ||||||||
\(356\) | −8.99072e7 | −0.105613 | ||||||||
\(357\) | −5.87402e8 | −0.683277 | ||||||||
\(358\) | −2.87448e8 | −0.331107 | ||||||||
\(359\) | −6.83126e8 | −0.779238 | −0.389619 | − | 0.920976i | \(-0.627393\pi\) | ||||
−0.389619 | + | 0.920976i | \(0.627393\pi\) | |||||||
\(360\) | 1.17279e8 | 0.132484 | ||||||||
\(361\) | 2.52261e8 | 0.282212 | ||||||||
\(362\) | 1.41345e9 | 1.56603 | ||||||||
\(363\) | 3.67643e8 | 0.403416 | ||||||||
\(364\) | −8.93057e8 | −0.970565 | ||||||||
\(365\) | −2.30748e9 | −2.48378 | ||||||||
\(366\) | −2.57795e8 | −0.274847 | ||||||||
\(367\) | 5.09383e8 | 0.537914 | 0.268957 | − | 0.963152i | \(-0.413321\pi\) | ||||
0.268957 | + | 0.963152i | \(0.413321\pi\) | |||||||
\(368\) | −2.86037e8 | −0.299196 | ||||||||
\(369\) | 2.67335e8 | 0.276990 | ||||||||
\(370\) | −3.16664e9 | −3.25007 | ||||||||
\(371\) | 1.45263e9 | 1.47689 | ||||||||
\(372\) | −7.33762e7 | −0.0739018 | ||||||||
\(373\) | 7.78305e8 | 0.776549 | 0.388274 | − | 0.921544i | \(-0.373071\pi\) | ||||
0.388274 | + | 0.921544i | \(0.373071\pi\) | |||||||
\(374\) | 9.82832e8 | 0.971468 | ||||||||
\(375\) | 2.16533e8 | 0.212038 | ||||||||
\(376\) | 3.16915e8 | 0.307458 | ||||||||
\(377\) | 3.46896e8 | 0.333430 | ||||||||
\(378\) | 2.43555e8 | 0.231940 | ||||||||
\(379\) | 1.51777e9 | 1.43209 | 0.716043 | − | 0.698056i | \(-0.245951\pi\) | ||||
0.716043 | + | 0.698056i | \(0.245951\pi\) | |||||||
\(380\) | −1.45628e9 | −1.36145 | ||||||||
\(381\) | −4.81715e8 | −0.446224 | ||||||||
\(382\) | 1.94830e9 | 1.78827 | ||||||||
\(383\) | 1.35344e9 | 1.23096 | 0.615481 | − | 0.788152i | \(-0.288962\pi\) | ||||
0.615481 | + | 0.788152i | \(0.288962\pi\) | |||||||
\(384\) | −3.33221e8 | −0.300312 | ||||||||
\(385\) | −8.26671e8 | −0.738279 | ||||||||
\(386\) | −1.13824e9 | −1.00735 | ||||||||
\(387\) | 3.60025e8 | 0.315750 | ||||||||
\(388\) | −1.29559e9 | −1.12605 | ||||||||
\(389\) | −2.16650e7 | −0.0186610 | −0.00933052 | − | 0.999956i | \(-0.502970\pi\) | ||||
−0.00933052 | + | 0.999956i | \(0.502970\pi\) | |||||||
\(390\) | 1.83318e9 | 1.56487 | ||||||||
\(391\) | −4.02430e8 | −0.340465 | ||||||||
\(392\) | 6.14164e7 | 0.0514971 | ||||||||
\(393\) | −1.02154e8 | −0.0848951 | ||||||||
\(394\) | −2.17031e9 | −1.78766 | ||||||||
\(395\) | 2.53112e9 | 2.06644 | ||||||||
\(396\) | −1.81421e8 | −0.146810 | ||||||||
\(397\) | 9.27708e8 | 0.744123 | 0.372061 | − | 0.928208i | \(-0.378651\pi\) | ||||
0.372061 | + | 0.928208i | \(0.378651\pi\) | |||||||
\(398\) | −1.15317e9 | −0.916862 | ||||||||
\(399\) | 7.44653e8 | 0.586879 | ||||||||
\(400\) | −1.84641e9 | −1.44251 | ||||||||
\(401\) | −2.89379e8 | −0.224110 | −0.112055 | − | 0.993702i | \(-0.535743\pi\) | ||||
−0.112055 | + | 0.993702i | \(0.535743\pi\) | |||||||
\(402\) | −7.62179e8 | −0.585148 | ||||||||
\(403\) | 2.82404e8 | 0.214933 | ||||||||
\(404\) | 1.46960e8 | 0.110883 | ||||||||
\(405\) | −2.22571e8 | −0.166485 | ||||||||
\(406\) | −4.02172e8 | −0.298243 | ||||||||
\(407\) | −1.20614e9 | −0.886784 | ||||||||
\(408\) | −2.76976e8 | −0.201898 | ||||||||
\(409\) | 1.85339e9 | 1.33947 | 0.669737 | − | 0.742598i | \(-0.266407\pi\) | ||||
0.669737 | + | 0.742598i | \(0.266407\pi\) | |||||||
\(410\) | −2.33279e9 | −1.67160 | ||||||||
\(411\) | 7.71229e8 | 0.547945 | ||||||||
\(412\) | 5.76100e8 | 0.405843 | ||||||||
\(413\) | 1.67313e8 | 0.116870 | ||||||||
\(414\) | 1.66860e8 | 0.115572 | ||||||||
\(415\) | 1.97727e9 | 1.35799 | ||||||||
\(416\) | −2.55243e9 | −1.73831 | ||||||||
\(417\) | −9.29671e8 | −0.627846 | ||||||||
\(418\) | −1.24594e9 | −0.834412 | ||||||||
\(419\) | 2.29514e9 | 1.52427 | 0.762133 | − | 0.647420i | \(-0.224152\pi\) | ||||
0.762133 | + | 0.647420i | \(0.224152\pi\) | |||||||
\(420\) | −9.46157e8 | −0.623147 | ||||||||
\(421\) | 1.32746e9 | 0.867028 | 0.433514 | − | 0.901147i | \(-0.357273\pi\) | ||||
0.433514 | + | 0.901147i | \(0.357273\pi\) | |||||||
\(422\) | −1.04945e9 | −0.679782 | ||||||||
\(423\) | −6.01439e8 | −0.386367 | ||||||||
\(424\) | 6.84956e8 | 0.436397 | ||||||||
\(425\) | −2.59774e9 | −1.64148 | ||||||||
\(426\) | −1.49620e9 | −0.937683 | ||||||||
\(427\) | −5.12094e8 | −0.318312 | ||||||||
\(428\) | 2.23406e9 | 1.37734 | ||||||||
\(429\) | 6.98239e8 | 0.426976 | ||||||||
\(430\) | −3.14161e9 | −1.90551 | ||||||||
\(431\) | 4.95028e8 | 0.297823 | 0.148912 | − | 0.988850i | \(-0.452423\pi\) | ||||
0.148912 | + | 0.988850i | \(0.452423\pi\) | |||||||
\(432\) | 3.73613e8 | 0.222961 | ||||||||
\(433\) | −1.81935e9 | −1.07698 | −0.538491 | − | 0.842631i | \(-0.681005\pi\) | ||||
−0.538491 | + | 0.842631i | \(0.681005\pi\) | |||||||
\(434\) | −3.27404e8 | −0.192252 | ||||||||
\(435\) | 3.67522e8 | 0.214077 | ||||||||
\(436\) | −9.57818e8 | −0.553453 | ||||||||
\(437\) | 5.10163e8 | 0.292431 | ||||||||
\(438\) | −2.25954e9 | −1.28488 | ||||||||
\(439\) | −3.28149e9 | −1.85117 | −0.925583 | − | 0.378546i | \(-0.876424\pi\) | ||||
−0.925583 | + | 0.378546i | \(0.876424\pi\) | |||||||
\(440\) | −3.89798e8 | −0.218150 | ||||||||
\(441\) | −1.16555e8 | −0.0647139 | ||||||||
\(442\) | −4.32938e9 | −2.38478 | ||||||||
\(443\) | −2.09880e9 | −1.14699 | −0.573493 | − | 0.819210i | \(-0.694412\pi\) | ||||
−0.573493 | + | 0.819210i | \(0.694412\pi\) | |||||||
\(444\) | −1.38048e9 | −0.748494 | ||||||||
\(445\) | 3.66602e8 | 0.197212 | ||||||||
\(446\) | −3.39716e9 | −1.81320 | ||||||||
\(447\) | −1.29779e8 | −0.0687274 | ||||||||
\(448\) | 9.79835e8 | 0.514849 | ||||||||
\(449\) | 8.92700e7 | 0.0465418 | 0.0232709 | − | 0.999729i | \(-0.492592\pi\) | ||||
0.0232709 | + | 0.999729i | \(0.492592\pi\) | |||||||
\(450\) | 1.07710e9 | 0.557203 | ||||||||
\(451\) | −8.88537e8 | −0.456098 | ||||||||
\(452\) | 1.54473e9 | 0.786805 | ||||||||
\(453\) | 1.37526e8 | 0.0695088 | ||||||||
\(454\) | −3.98821e8 | −0.200024 | ||||||||
\(455\) | 3.64149e9 | 1.81234 | ||||||||
\(456\) | 3.51124e8 | 0.173414 | ||||||||
\(457\) | −1.68348e9 | −0.825092 | −0.412546 | − | 0.910937i | \(-0.635360\pi\) | ||||
−0.412546 | + | 0.910937i | \(0.635360\pi\) | |||||||
\(458\) | 4.22833e9 | 2.05655 | ||||||||
\(459\) | 5.25642e8 | 0.253715 | ||||||||
\(460\) | −6.48214e8 | −0.310503 | ||||||||
\(461\) | −1.92435e9 | −0.914811 | −0.457406 | − | 0.889258i | \(-0.651221\pi\) | ||||
−0.457406 | + | 0.889258i | \(0.651221\pi\) | |||||||
\(462\) | −8.09499e8 | −0.381917 | ||||||||
\(463\) | −1.42542e9 | −0.667437 | −0.333718 | − | 0.942673i | \(-0.608303\pi\) | ||||
−0.333718 | + | 0.942673i | \(0.608303\pi\) | |||||||
\(464\) | −6.16931e8 | −0.286697 | ||||||||
\(465\) | 2.99196e8 | 0.137997 | ||||||||
\(466\) | 6.58691e8 | 0.301530 | ||||||||
\(467\) | 1.67879e9 | 0.762759 | 0.381380 | − | 0.924418i | \(-0.375449\pi\) | ||||
0.381380 | + | 0.924418i | \(0.375449\pi\) | |||||||
\(468\) | 7.99161e8 | 0.360391 | ||||||||
\(469\) | −1.51402e9 | −0.677685 | ||||||||
\(470\) | 5.24820e9 | 2.33168 | ||||||||
\(471\) | −5.43363e8 | −0.239617 | ||||||||
\(472\) | 7.88925e7 | 0.0345333 | ||||||||
\(473\) | −1.19661e9 | −0.519921 | ||||||||
\(474\) | 2.47854e9 | 1.06899 | ||||||||
\(475\) | 3.29317e9 | 1.40989 | ||||||||
\(476\) | 2.23452e9 | 0.949644 | ||||||||
\(477\) | −1.29990e9 | −0.548398 | ||||||||
\(478\) | −4.99528e9 | −2.09200 | ||||||||
\(479\) | 2.45408e9 | 1.02027 | 0.510135 | − | 0.860094i | \(-0.329595\pi\) | ||||
0.510135 | + | 0.860094i | \(0.329595\pi\) | |||||||
\(480\) | −2.70419e9 | −1.11607 | ||||||||
\(481\) | 5.31306e9 | 2.17689 | ||||||||
\(482\) | 5.03617e8 | 0.204850 | ||||||||
\(483\) | 3.31458e8 | 0.133848 | ||||||||
\(484\) | −1.39854e9 | −0.560683 | ||||||||
\(485\) | 5.28283e9 | 2.10267 | ||||||||
\(486\) | −2.17948e8 | −0.0861242 | ||||||||
\(487\) | 1.22859e9 | 0.482008 | 0.241004 | − | 0.970524i | \(-0.422523\pi\) | ||||
0.241004 | + | 0.970524i | \(0.422523\pi\) | |||||||
\(488\) | −2.41467e8 | −0.0940563 | ||||||||
\(489\) | 1.82526e9 | 0.705901 | ||||||||
\(490\) | 1.01707e9 | 0.390540 | ||||||||
\(491\) | −4.00300e9 | −1.52616 | −0.763081 | − | 0.646303i | \(-0.776314\pi\) | ||||
−0.763081 | + | 0.646303i | \(0.776314\pi\) | |||||||
\(492\) | −1.01697e9 | −0.384971 | ||||||||
\(493\) | −8.67970e8 | −0.326242 | ||||||||
\(494\) | 5.48838e9 | 2.04833 | ||||||||
\(495\) | 7.39755e8 | 0.274138 | ||||||||
\(496\) | −5.02237e8 | −0.184809 | ||||||||
\(497\) | −2.97211e9 | −1.08597 | ||||||||
\(498\) | 1.93619e9 | 0.702499 | ||||||||
\(499\) | −6.37493e8 | −0.229680 | −0.114840 | − | 0.993384i | \(-0.536636\pi\) | ||||
−0.114840 | + | 0.993384i | \(0.536636\pi\) | |||||||
\(500\) | −8.23707e8 | −0.294698 | ||||||||
\(501\) | −2.99137e9 | −1.06277 | ||||||||
\(502\) | 4.47806e9 | 1.57989 | ||||||||
\(503\) | 3.52591e9 | 1.23533 | 0.617666 | − | 0.786440i | \(-0.288078\pi\) | ||||
0.617666 | + | 0.786440i | \(0.288078\pi\) | |||||||
\(504\) | 2.28128e8 | 0.0793730 | ||||||||
\(505\) | −5.99239e8 | −0.207052 | ||||||||
\(506\) | −5.54590e8 | −0.190303 | ||||||||
\(507\) | −1.38154e9 | −0.470798 | ||||||||
\(508\) | 1.83248e9 | 0.620179 | ||||||||
\(509\) | −1.03941e9 | −0.349360 | −0.174680 | − | 0.984625i | \(-0.555889\pi\) | ||||
−0.174680 | + | 0.984625i | \(0.555889\pi\) | |||||||
\(510\) | −4.58680e9 | −1.53114 | ||||||||
\(511\) | −4.48845e9 | −1.48807 | ||||||||
\(512\) | 3.60603e9 | 1.18736 | ||||||||
\(513\) | −6.66360e8 | −0.217920 | ||||||||
\(514\) | −3.90243e9 | −1.26755 | ||||||||
\(515\) | −2.34908e9 | −0.757832 | ||||||||
\(516\) | −1.36956e9 | −0.438842 | ||||||||
\(517\) | 1.99899e9 | 0.636200 | ||||||||
\(518\) | −6.15967e9 | −1.94717 | ||||||||
\(519\) | −3.08749e9 | −0.969439 | ||||||||
\(520\) | 1.71706e9 | 0.535519 | ||||||||
\(521\) | −1.04135e9 | −0.322600 | −0.161300 | − | 0.986905i | \(-0.551569\pi\) | ||||
−0.161300 | + | 0.986905i | \(0.551569\pi\) | |||||||
\(522\) | 3.59887e8 | 0.110744 | ||||||||
\(523\) | 4.18130e9 | 1.27807 | 0.639036 | − | 0.769177i | \(-0.279334\pi\) | ||||
0.639036 | + | 0.769177i | \(0.279334\pi\) | |||||||
\(524\) | 3.88603e8 | 0.117990 | ||||||||
\(525\) | 2.13960e9 | 0.645320 | ||||||||
\(526\) | 4.58190e9 | 1.37276 | ||||||||
\(527\) | −7.06606e8 | −0.210300 | ||||||||
\(528\) | −1.24177e9 | −0.367133 | ||||||||
\(529\) | −3.17774e9 | −0.933306 | ||||||||
\(530\) | 1.13431e10 | 3.30952 | ||||||||
\(531\) | −1.49721e8 | −0.0433963 | ||||||||
\(532\) | −2.83272e9 | −0.815667 | ||||||||
\(533\) | 3.91401e9 | 1.11964 | ||||||||
\(534\) | 3.58986e8 | 0.102020 | ||||||||
\(535\) | −9.10953e9 | −2.57192 | ||||||||
\(536\) | −7.13904e8 | −0.200246 | ||||||||
\(537\) | 5.10964e8 | 0.142390 | ||||||||
\(538\) | −3.97300e9 | −1.09997 | ||||||||
\(539\) | 3.87393e8 | 0.106559 | ||||||||
\(540\) | 8.46678e8 | 0.231388 | ||||||||
\(541\) | −5.65879e9 | −1.53650 | −0.768251 | − | 0.640149i | \(-0.778873\pi\) | ||||
−0.768251 | + | 0.640149i | \(0.778873\pi\) | |||||||
\(542\) | −2.19497e9 | −0.592148 | ||||||||
\(543\) | −2.51252e9 | −0.673458 | ||||||||
\(544\) | 6.38645e9 | 1.70084 | ||||||||
\(545\) | 3.90556e9 | 1.03346 | ||||||||
\(546\) | 3.56585e9 | 0.937538 | ||||||||
\(547\) | 5.02175e8 | 0.131190 | 0.0655948 | − | 0.997846i | \(-0.479106\pi\) | ||||
0.0655948 | + | 0.997846i | \(0.479106\pi\) | |||||||
\(548\) | −2.93382e9 | −0.761555 | ||||||||
\(549\) | 4.58253e8 | 0.118196 | ||||||||
\(550\) | −3.57995e9 | −0.917503 | ||||||||
\(551\) | 1.10033e9 | 0.280216 | ||||||||
\(552\) | 1.56291e8 | 0.0395501 | ||||||||
\(553\) | 4.92348e9 | 1.23804 | ||||||||
\(554\) | −7.08533e8 | −0.177042 | ||||||||
\(555\) | 5.62897e9 | 1.39767 | ||||||||
\(556\) | 3.53654e9 | 0.872604 | ||||||||
\(557\) | −2.86842e9 | −0.703314 | −0.351657 | − | 0.936129i | \(-0.614382\pi\) | ||||
−0.351657 | + | 0.936129i | \(0.614382\pi\) | |||||||
\(558\) | 2.92981e8 | 0.0713870 | ||||||||
\(559\) | 5.27106e9 | 1.27631 | ||||||||
\(560\) | −6.47615e9 | −1.55833 | ||||||||
\(561\) | −1.74707e9 | −0.417772 | ||||||||
\(562\) | 1.03027e10 | 2.44835 | ||||||||
\(563\) | 3.72076e9 | 0.878723 | 0.439361 | − | 0.898310i | \(-0.355205\pi\) | ||||
0.439361 | + | 0.898310i | \(0.355205\pi\) | |||||||
\(564\) | 2.28792e9 | 0.536987 | ||||||||
\(565\) | −6.29871e9 | −1.46920 | ||||||||
\(566\) | 3.55191e9 | 0.823388 | ||||||||
\(567\) | −4.32940e8 | −0.0997440 | ||||||||
\(568\) | −1.40143e9 | −0.320888 | ||||||||
\(569\) | −5.12299e9 | −1.16582 | −0.582909 | − | 0.812538i | \(-0.698085\pi\) | ||||
−0.582909 | + | 0.812538i | \(0.698085\pi\) | |||||||
\(570\) | 5.81471e9 | 1.31512 | ||||||||
\(571\) | −3.51571e9 | −0.790289 | −0.395145 | − | 0.918619i | \(-0.629306\pi\) | ||||
−0.395145 | + | 0.918619i | \(0.629306\pi\) | |||||||
\(572\) | −2.65616e9 | −0.593427 | ||||||||
\(573\) | −3.46326e9 | −0.769031 | ||||||||
\(574\) | −4.53769e9 | −1.00148 | ||||||||
\(575\) | 1.46585e9 | 0.321552 | ||||||||
\(576\) | −8.76815e8 | −0.191174 | ||||||||
\(577\) | −9.70425e8 | −0.210304 | −0.105152 | − | 0.994456i | \(-0.533533\pi\) | ||||
−0.105152 | + | 0.994456i | \(0.533533\pi\) | |||||||
\(578\) | 4.59988e9 | 0.990829 | ||||||||
\(579\) | 2.02332e9 | 0.433202 | ||||||||
\(580\) | −1.39808e9 | −0.297533 | ||||||||
\(581\) | 3.84613e9 | 0.813593 | ||||||||
\(582\) | 5.17310e9 | 1.08773 | ||||||||
\(583\) | 4.32046e9 | 0.903004 | ||||||||
\(584\) | −2.11643e9 | −0.439702 | ||||||||
\(585\) | −3.25863e9 | −0.672959 | ||||||||
\(586\) | 4.98516e9 | 1.02338 | ||||||||
\(587\) | 5.54244e9 | 1.13101 | 0.565506 | − | 0.824744i | \(-0.308681\pi\) | ||||
0.565506 | + | 0.824744i | \(0.308681\pi\) | |||||||
\(588\) | 4.43386e8 | 0.0899418 | ||||||||
\(589\) | 8.95768e8 | 0.180631 | ||||||||
\(590\) | 1.30648e9 | 0.261891 | ||||||||
\(591\) | 3.85792e9 | 0.768771 | ||||||||
\(592\) | −9.44893e9 | −1.87179 | ||||||||
\(593\) | −5.71802e8 | −0.112604 | −0.0563021 | − | 0.998414i | \(-0.517931\pi\) | ||||
−0.0563021 | + | 0.998414i | \(0.517931\pi\) | |||||||
\(594\) | 7.24388e8 | 0.141814 | ||||||||
\(595\) | −9.11140e9 | −1.77327 | ||||||||
\(596\) | 4.93691e8 | 0.0955199 | ||||||||
\(597\) | 2.04986e9 | 0.394289 | ||||||||
\(598\) | 2.44297e9 | 0.467158 | ||||||||
\(599\) | 1.65083e9 | 0.313840 | 0.156920 | − | 0.987611i | \(-0.449843\pi\) | ||||
0.156920 | + | 0.987611i | \(0.449843\pi\) | |||||||
\(600\) | 1.00888e9 | 0.190682 | ||||||||
\(601\) | 4.29026e9 | 0.806163 | 0.403081 | − | 0.915164i | \(-0.367939\pi\) | ||||
0.403081 | + | 0.915164i | \(0.367939\pi\) | |||||||
\(602\) | −6.11098e9 | −1.14162 | ||||||||
\(603\) | 1.35484e9 | 0.251638 | ||||||||
\(604\) | −5.23158e8 | −0.0966059 | ||||||||
\(605\) | 5.70265e9 | 1.04697 | ||||||||
\(606\) | −5.86791e8 | −0.107110 | ||||||||
\(607\) | 8.68657e8 | 0.157648 | 0.0788239 | − | 0.996889i | \(-0.474884\pi\) | ||||
0.0788239 | + | 0.996889i | \(0.474884\pi\) | |||||||
\(608\) | −8.09613e9 | −1.46088 | ||||||||
\(609\) | 7.14894e8 | 0.128257 | ||||||||
\(610\) | −3.99875e9 | −0.713296 | ||||||||
\(611\) | −8.80556e9 | −1.56175 | ||||||||
\(612\) | −1.99959e9 | −0.352623 | ||||||||
\(613\) | 2.12755e9 | 0.373050 | 0.186525 | − | 0.982450i | \(-0.440277\pi\) | ||||
0.186525 | + | 0.982450i | \(0.440277\pi\) | |||||||
\(614\) | 2.77333e9 | 0.483517 | ||||||||
\(615\) | 4.14673e9 | 0.718858 | ||||||||
\(616\) | −7.58226e8 | −0.130697 | ||||||||
\(617\) | −8.95889e9 | −1.53552 | −0.767761 | − | 0.640736i | \(-0.778629\pi\) | ||||
−0.767761 | + | 0.640736i | \(0.778629\pi\) | |||||||
\(618\) | −2.30029e9 | −0.392033 | ||||||||
\(619\) | −5.17081e9 | −0.876277 | −0.438138 | − | 0.898908i | \(-0.644362\pi\) | ||||
−0.438138 | + | 0.898908i | \(0.644362\pi\) | |||||||
\(620\) | −1.13816e9 | −0.191794 | ||||||||
\(621\) | −2.96608e8 | −0.0497007 | ||||||||
\(622\) | −8.87683e9 | −1.47908 | ||||||||
\(623\) | 7.13105e8 | 0.118153 | ||||||||
\(624\) | 5.47001e9 | 0.901244 | ||||||||
\(625\) | −4.24082e9 | −0.694815 | ||||||||
\(626\) | 1.41616e10 | 2.30728 | ||||||||
\(627\) | 2.21477e9 | 0.358832 | ||||||||
\(628\) | 2.06700e9 | 0.333028 | ||||||||
\(629\) | −1.32938e10 | −2.12997 | ||||||||
\(630\) | 3.77787e9 | 0.601943 | ||||||||
\(631\) | −2.71332e9 | −0.429931 | −0.214965 | − | 0.976622i | \(-0.568964\pi\) | ||||
−0.214965 | + | 0.976622i | \(0.568964\pi\) | |||||||
\(632\) | 2.32156e9 | 0.365822 | ||||||||
\(633\) | 1.86549e9 | 0.292335 | ||||||||
\(634\) | 1.35751e10 | 2.11559 | ||||||||
\(635\) | −7.47206e9 | −1.15806 | ||||||||
\(636\) | 4.94493e9 | 0.762185 | ||||||||
\(637\) | −1.70647e9 | −0.261583 | ||||||||
\(638\) | −1.19615e9 | −0.182353 | ||||||||
\(639\) | 2.65962e9 | 0.403243 | ||||||||
\(640\) | −5.16871e9 | −0.779386 | ||||||||
\(641\) | 3.35162e9 | 0.502634 | 0.251317 | − | 0.967905i | \(-0.419136\pi\) | ||||
0.251317 | + | 0.967905i | \(0.419136\pi\) | |||||||
\(642\) | −8.92030e9 | −1.33048 | ||||||||
\(643\) | 7.57020e9 | 1.12297 | 0.561486 | − | 0.827486i | \(-0.310230\pi\) | ||||
0.561486 | + | 0.827486i | \(0.310230\pi\) | |||||||
\(644\) | −1.26089e9 | −0.186027 | ||||||||
\(645\) | 5.58447e9 | 0.819451 | ||||||||
\(646\) | −1.37325e10 | −2.00418 | ||||||||
\(647\) | −3.82356e9 | −0.555013 | −0.277507 | − | 0.960724i | \(-0.589508\pi\) | ||||
−0.277507 | + | 0.960724i | \(0.589508\pi\) | |||||||
\(648\) | −2.04143e8 | −0.0294728 | ||||||||
\(649\) | 4.97626e8 | 0.0714573 | ||||||||
\(650\) | 1.57697e10 | 2.25230 | ||||||||
\(651\) | 5.81988e8 | 0.0826763 | ||||||||
\(652\) | −6.94344e9 | −0.981088 | ||||||||
\(653\) | −9.84140e9 | −1.38312 | −0.691561 | − | 0.722318i | \(-0.743077\pi\) | ||||
−0.691561 | + | 0.722318i | \(0.743077\pi\) | |||||||
\(654\) | 3.82443e9 | 0.534619 | ||||||||
\(655\) | −1.58455e9 | −0.220324 | ||||||||
\(656\) | −6.96081e9 | −0.962712 | ||||||||
\(657\) | 4.01653e9 | 0.552551 | ||||||||
\(658\) | 1.02087e10 | 1.39694 | ||||||||
\(659\) | 1.04889e10 | 1.42768 | 0.713842 | − | 0.700307i | \(-0.246954\pi\) | ||||
0.713842 | + | 0.700307i | \(0.246954\pi\) | |||||||
\(660\) | −2.81409e9 | −0.381008 | ||||||||
\(661\) | −5.13152e8 | −0.0691100 | −0.0345550 | − | 0.999403i | \(-0.511001\pi\) | ||||
−0.0345550 | + | 0.999403i | \(0.511001\pi\) | |||||||
\(662\) | 1.37866e10 | 1.84694 | ||||||||
\(663\) | 7.69584e9 | 1.02555 | ||||||||
\(664\) | 1.81356e9 | 0.240404 | ||||||||
\(665\) | 1.15506e10 | 1.52310 | ||||||||
\(666\) | 5.51204e9 | 0.723024 | ||||||||
\(667\) | 4.89776e8 | 0.0639082 | ||||||||
\(668\) | 1.13794e10 | 1.47707 | ||||||||
\(669\) | 6.03875e9 | 0.779750 | ||||||||
\(670\) | −1.18224e10 | −1.51861 | ||||||||
\(671\) | −1.52309e9 | −0.194624 | ||||||||
\(672\) | −5.26013e9 | −0.668658 | ||||||||
\(673\) | 4.59671e8 | 0.0581292 | 0.0290646 | − | 0.999578i | \(-0.490747\pi\) | ||||
0.0290646 | + | 0.999578i | \(0.490747\pi\) | |||||||
\(674\) | 1.19905e10 | 1.50844 | ||||||||
\(675\) | −1.91464e9 | −0.239621 | ||||||||
\(676\) | 5.25547e9 | 0.654333 | ||||||||
\(677\) | −1.30244e10 | −1.61324 | −0.806619 | − | 0.591072i | \(-0.798705\pi\) | ||||
−0.806619 | + | 0.591072i | \(0.798705\pi\) | |||||||
\(678\) | −6.16787e9 | −0.760031 | ||||||||
\(679\) | 1.02760e10 | 1.25974 | ||||||||
\(680\) | −4.29628e9 | −0.523975 | ||||||||
\(681\) | 7.08939e8 | 0.0860189 | ||||||||
\(682\) | −9.73774e8 | −0.117547 | ||||||||
\(683\) | −1.27703e9 | −0.153366 | −0.0766830 | − | 0.997056i | \(-0.524433\pi\) | ||||
−0.0766830 | + | 0.997056i | \(0.524433\pi\) | |||||||
\(684\) | 2.53489e9 | 0.302874 | ||||||||
\(685\) | 1.19628e10 | 1.42205 | ||||||||
\(686\) | 1.21688e10 | 1.43917 | ||||||||
\(687\) | −7.51622e9 | −0.884404 | ||||||||
\(688\) | −9.37423e9 | −1.09743 | ||||||||
\(689\) | −1.90316e10 | −2.21671 | ||||||||
\(690\) | 2.58823e9 | 0.299937 | ||||||||
\(691\) | 1.46413e10 | 1.68813 | 0.844063 | − | 0.536243i | \(-0.180157\pi\) | ||||
0.844063 | + | 0.536243i | \(0.180157\pi\) | |||||||
\(692\) | 1.17451e10 | 1.34736 | ||||||||
\(693\) | 1.43895e9 | 0.164241 | ||||||||
\(694\) | −8.03356e9 | −0.912326 | ||||||||
\(695\) | −1.44205e10 | −1.62942 | ||||||||
\(696\) | 3.37092e8 | 0.0378980 | ||||||||
\(697\) | −9.79328e9 | −1.09550 | ||||||||
\(698\) | 3.03853e9 | 0.338197 | ||||||||
\(699\) | −1.17088e9 | −0.129671 | ||||||||
\(700\) | −8.13922e9 | −0.896891 | ||||||||
\(701\) | −1.79391e10 | −1.96692 | −0.983460 | − | 0.181127i | \(-0.942026\pi\) | ||||
−0.983460 | + | 0.181127i | \(0.942026\pi\) | |||||||
\(702\) | −3.19094e9 | −0.348127 | ||||||||
\(703\) | 1.68527e10 | 1.82947 | ||||||||
\(704\) | 2.91425e9 | 0.314791 | ||||||||
\(705\) | −9.32913e9 | −1.00272 | ||||||||
\(706\) | 3.83573e9 | 0.410234 | ||||||||
\(707\) | −1.16563e9 | −0.124048 | ||||||||
\(708\) | 5.69552e8 | 0.0603138 | ||||||||
\(709\) | −1.11761e10 | −1.17769 | −0.588843 | − | 0.808248i | \(-0.700416\pi\) | ||||
−0.588843 | + | 0.808248i | \(0.700416\pi\) | |||||||
\(710\) | −2.32081e10 | −2.43352 | ||||||||
\(711\) | −4.40582e9 | −0.459710 | ||||||||
\(712\) | 3.36248e8 | 0.0349125 | ||||||||
\(713\) | 3.98721e8 | 0.0411961 | ||||||||
\(714\) | −8.92213e9 | −0.917329 | ||||||||
\(715\) | 1.08306e10 | 1.10811 | ||||||||
\(716\) | −1.94375e9 | −0.197899 | ||||||||
\(717\) | 8.87954e9 | 0.899650 | ||||||||
\(718\) | −1.03761e10 | −1.04616 | ||||||||
\(719\) | 9.74647e9 | 0.977904 | 0.488952 | − | 0.872311i | \(-0.337379\pi\) | ||||
0.488952 | + | 0.872311i | \(0.337379\pi\) | |||||||
\(720\) | 5.79525e9 | 0.578640 | ||||||||
\(721\) | −4.56938e9 | −0.454029 | ||||||||
\(722\) | 3.83163e9 | 0.378881 | ||||||||
\(723\) | −8.95222e8 | −0.0880940 | ||||||||
\(724\) | 9.55784e9 | 0.935997 | ||||||||
\(725\) | 3.16157e9 | 0.308120 | ||||||||
\(726\) | 5.58419e9 | 0.541604 | ||||||||
\(727\) | 1.00742e10 | 0.972389 | 0.486195 | − | 0.873851i | \(-0.338385\pi\) | ||||
0.486195 | + | 0.873851i | \(0.338385\pi\) | |||||||
\(728\) | 3.33999e9 | 0.320838 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | −3.50486e10 | −3.33458 | ||||||||
\(731\) | −1.31888e10 | −1.24880 | ||||||||
\(732\) | −1.74323e9 | −0.164273 | ||||||||
\(733\) | 1.97006e10 | 1.84763 | 0.923814 | − | 0.382841i | \(-0.125054\pi\) | ||||
0.923814 | + | 0.382841i | \(0.125054\pi\) | |||||||
\(734\) | 7.73709e9 | 0.722173 | ||||||||
\(735\) | −1.80793e9 | −0.167949 | ||||||||
\(736\) | −3.60373e9 | −0.333180 | ||||||||
\(737\) | −4.50305e9 | −0.414353 | ||||||||
\(738\) | 4.06060e9 | 0.371871 | ||||||||
\(739\) | −9.78856e9 | −0.892202 | −0.446101 | − | 0.894983i | \(-0.647188\pi\) | ||||
−0.446101 | + | 0.894983i | \(0.647188\pi\) | |||||||
\(740\) | −2.14131e10 | −1.94253 | ||||||||
\(741\) | −9.75606e9 | −0.880868 | ||||||||
\(742\) | 2.20642e10 | 1.98278 | ||||||||
\(743\) | 7.25852e9 | 0.649213 | 0.324607 | − | 0.945849i | \(-0.394768\pi\) | ||||
0.324607 | + | 0.945849i | \(0.394768\pi\) | |||||||
\(744\) | 2.74423e8 | 0.0244296 | ||||||||
\(745\) | −2.01306e9 | −0.178365 | ||||||||
\(746\) | 1.18218e10 | 1.04255 | ||||||||
\(747\) | −3.44175e9 | −0.302104 | ||||||||
\(748\) | 6.64598e9 | 0.580636 | ||||||||
\(749\) | −1.77196e10 | −1.54088 | ||||||||
\(750\) | 3.28894e9 | 0.284670 | ||||||||
\(751\) | 1.17654e10 | 1.01360 | 0.506799 | − | 0.862064i | \(-0.330829\pi\) | ||||
0.506799 | + | 0.862064i | \(0.330829\pi\) | |||||||
\(752\) | 1.56601e10 | 1.34287 | ||||||||
\(753\) | −7.96013e9 | −0.679419 | ||||||||
\(754\) | 5.26905e9 | 0.447644 | ||||||||
\(755\) | 2.13321e9 | 0.180393 | ||||||||
\(756\) | 1.64694e9 | 0.138628 | ||||||||
\(757\) | −1.11582e10 | −0.934886 | −0.467443 | − | 0.884023i | \(-0.654825\pi\) | ||||
−0.467443 | + | 0.884023i | \(0.654825\pi\) | |||||||
\(758\) | 2.30537e10 | 1.92264 | ||||||||
\(759\) | 9.85830e8 | 0.0818382 | ||||||||
\(760\) | 5.44641e9 | 0.450052 | ||||||||
\(761\) | −5.87504e9 | −0.483242 | −0.241621 | − | 0.970371i | \(-0.577679\pi\) | ||||
−0.241621 | + | 0.970371i | \(0.577679\pi\) | |||||||
\(762\) | −7.31684e9 | −0.599075 | ||||||||
\(763\) | 7.59700e9 | 0.619165 | ||||||||
\(764\) | 1.31745e10 | 1.06883 | ||||||||
\(765\) | 8.15343e9 | 0.658454 | ||||||||
\(766\) | 2.05577e10 | 1.65262 | ||||||||
\(767\) | −2.19204e9 | −0.175415 | ||||||||
\(768\) | −9.21810e9 | −0.734306 | ||||||||
\(769\) | 1.13603e10 | 0.900841 | 0.450420 | − | 0.892817i | \(-0.351274\pi\) | ||||
0.450420 | + | 0.892817i | \(0.351274\pi\) | |||||||
\(770\) | −1.25564e10 | −0.991171 | ||||||||
\(771\) | 6.93690e9 | 0.545099 | ||||||||
\(772\) | −7.69688e9 | −0.602080 | ||||||||
\(773\) | −1.76385e10 | −1.37352 | −0.686759 | − | 0.726885i | \(-0.740967\pi\) | ||||
−0.686759 | + | 0.726885i | \(0.740967\pi\) | |||||||
\(774\) | 5.46847e9 | 0.423909 | ||||||||
\(775\) | 2.57380e9 | 0.198618 | ||||||||
\(776\) | 4.84544e9 | 0.372235 | ||||||||
\(777\) | 1.09493e10 | 0.837364 | ||||||||
\(778\) | −3.29074e8 | −0.0250533 | ||||||||
\(779\) | 1.24150e10 | 0.940947 | ||||||||
\(780\) | 1.23961e10 | 0.935304 | ||||||||
\(781\) | −8.83974e9 | −0.663989 | ||||||||
\(782\) | −6.11257e9 | −0.457089 | ||||||||
\(783\) | −6.39730e8 | −0.0476245 | ||||||||
\(784\) | 3.03484e9 | 0.224921 | ||||||||
\(785\) | −8.42830e9 | −0.621865 | ||||||||
\(786\) | −1.55164e9 | −0.113975 | ||||||||
\(787\) | −2.46188e10 | −1.80034 | −0.900172 | − | 0.435534i | \(-0.856560\pi\) | ||||
−0.900172 | + | 0.435534i | \(0.856560\pi\) | |||||||
\(788\) | −1.46758e10 | −1.06847 | ||||||||
\(789\) | −8.14472e9 | −0.590346 | ||||||||
\(790\) | 3.84456e10 | 2.77429 | ||||||||
\(791\) | −1.22521e10 | −0.880224 | ||||||||
\(792\) | 6.78506e8 | 0.0485306 | ||||||||
\(793\) | 6.70920e9 | 0.477766 | ||||||||
\(794\) | 1.40911e10 | 0.999017 | ||||||||
\(795\) | −2.01632e10 | −1.42323 | ||||||||
\(796\) | −7.79785e9 | −0.547998 | ||||||||
\(797\) | −1.36580e10 | −0.955612 | −0.477806 | − | 0.878465i | \(-0.658568\pi\) | ||||
−0.477806 | + | 0.878465i | \(0.658568\pi\) | |||||||
\(798\) | 1.13106e10 | 0.787911 | ||||||||
\(799\) | 2.20325e10 | 1.52809 | ||||||||
\(800\) | −2.32625e10 | −1.60636 | ||||||||
\(801\) | −6.38129e8 | −0.0438727 | ||||||||
\(802\) | −4.39542e9 | −0.300878 | ||||||||
\(803\) | −1.33497e10 | −0.909843 | ||||||||
\(804\) | −5.15392e9 | −0.349737 | ||||||||
\(805\) | 5.14136e9 | 0.347370 | ||||||||
\(806\) | 4.28948e9 | 0.288557 | ||||||||
\(807\) | 7.06235e9 | 0.473034 | ||||||||
\(808\) | −5.49624e8 | −0.0366544 | ||||||||
\(809\) | −4.59136e9 | −0.304875 | −0.152438 | − | 0.988313i | \(-0.548712\pi\) | ||||
−0.152438 | + | 0.988313i | \(0.548712\pi\) | |||||||
\(810\) | −3.38066e9 | −0.223514 | ||||||||
\(811\) | −2.86469e10 | −1.88584 | −0.942919 | − | 0.333022i | \(-0.891931\pi\) | ||||
−0.942919 | + | 0.333022i | \(0.891931\pi\) | |||||||
\(812\) | −2.71952e9 | −0.178257 | ||||||||
\(813\) | 3.90174e9 | 0.254649 | ||||||||
\(814\) | −1.83203e10 | −1.19055 | ||||||||
\(815\) | 2.83123e10 | 1.83199 | ||||||||
\(816\) | −1.36865e10 | −0.881817 | ||||||||
\(817\) | 1.67195e10 | 1.07262 | ||||||||
\(818\) | 2.81513e10 | 1.79830 | ||||||||
\(819\) | −6.33860e9 | −0.403181 | ||||||||
\(820\) | −1.57745e10 | −0.999096 | ||||||||
\(821\) | −1.33387e10 | −0.841225 | −0.420613 | − | 0.907240i | \(-0.638185\pi\) | ||||
−0.420613 | + | 0.907240i | \(0.638185\pi\) | |||||||
\(822\) | 1.17143e10 | 0.735640 | ||||||||
\(823\) | 1.33719e10 | 0.836171 | 0.418085 | − | 0.908408i | \(-0.362701\pi\) | ||||
0.418085 | + | 0.908408i | \(0.362701\pi\) | |||||||
\(824\) | −2.15459e9 | −0.134159 | ||||||||
\(825\) | 6.36366e9 | 0.394565 | ||||||||
\(826\) | 2.54133e9 | 0.156903 | ||||||||
\(827\) | −1.27792e10 | −0.785658 | −0.392829 | − | 0.919612i | \(-0.628503\pi\) | ||||
−0.392829 | + | 0.919612i | \(0.628503\pi\) | |||||||
\(828\) | 1.12832e9 | 0.0690759 | ||||||||
\(829\) | 3.01708e10 | 1.83927 | 0.919635 | − | 0.392775i | \(-0.128485\pi\) | ||||
0.919635 | + | 0.392775i | \(0.128485\pi\) | |||||||
\(830\) | 3.00330e10 | 1.82316 | ||||||||
\(831\) | 1.25948e9 | 0.0761354 | ||||||||
\(832\) | −1.28373e10 | −0.772755 | ||||||||
\(833\) | 4.26976e9 | 0.255945 | ||||||||
\(834\) | −1.41209e10 | −0.842911 | ||||||||
\(835\) | −4.64002e10 | −2.75814 | ||||||||
\(836\) | −8.42515e9 | −0.498719 | ||||||||
\(837\) | −5.20798e8 | −0.0306994 | ||||||||
\(838\) | 3.48613e10 | 2.04639 | ||||||||
\(839\) | 1.99280e10 | 1.16492 | 0.582460 | − | 0.812859i | \(-0.302090\pi\) | ||||
0.582460 | + | 0.812859i | \(0.302090\pi\) | |||||||
\(840\) | 3.53858e9 | 0.205993 | ||||||||
\(841\) | −1.61935e10 | −0.938761 | ||||||||
\(842\) | 2.01629e10 | 1.16402 | ||||||||
\(843\) | −1.83139e10 | −1.05289 | ||||||||
\(844\) | −7.09649e9 | −0.406298 | ||||||||
\(845\) | −2.14295e10 | −1.22184 | ||||||||
\(846\) | −9.13534e9 | −0.518714 | ||||||||
\(847\) | 1.10927e10 | 0.627254 | ||||||||
\(848\) | 3.38465e10 | 1.90603 | ||||||||
\(849\) | −6.31383e9 | −0.354092 | ||||||||
\(850\) | −3.94575e10 | −2.20375 | ||||||||
\(851\) | 7.50142e9 | 0.417244 | ||||||||
\(852\) | −1.01174e10 | −0.560443 | ||||||||
\(853\) | −2.14201e10 | −1.18168 | −0.590840 | − | 0.806789i | \(-0.701204\pi\) | ||||
−0.590840 | + | 0.806789i | \(0.701204\pi\) | |||||||
\(854\) | −7.77828e9 | −0.427347 | ||||||||
\(855\) | −1.03361e10 | −0.565558 | ||||||||
\(856\) | −8.35529e9 | −0.455306 | ||||||||
\(857\) | 3.13832e10 | 1.70320 | 0.851599 | − | 0.524195i | \(-0.175634\pi\) | ||||
0.851599 | + | 0.524195i | \(0.175634\pi\) | |||||||
\(858\) | 1.06056e10 | 0.573234 | ||||||||
\(859\) | −1.10229e10 | −0.593362 | −0.296681 | − | 0.954977i | \(-0.595880\pi\) | ||||
−0.296681 | + | 0.954977i | \(0.595880\pi\) | |||||||
\(860\) | −2.12438e10 | −1.13890 | ||||||||
\(861\) | 8.06613e9 | 0.430679 | ||||||||
\(862\) | 7.51905e9 | 0.399841 | ||||||||
\(863\) | 2.63685e10 | 1.39652 | 0.698260 | − | 0.715844i | \(-0.253958\pi\) | ||||
0.698260 | + | 0.715844i | \(0.253958\pi\) | |||||||
\(864\) | 4.70708e9 | 0.248287 | ||||||||
\(865\) | −4.78912e10 | −2.51594 | ||||||||
\(866\) | −2.76344e10 | −1.44590 | ||||||||
\(867\) | −8.17667e9 | −0.426098 | ||||||||
\(868\) | −2.21393e9 | −0.114907 | ||||||||
\(869\) | 1.46436e10 | 0.756967 | ||||||||
\(870\) | 5.58234e9 | 0.287408 | ||||||||
\(871\) | 1.98360e10 | 1.01716 | ||||||||
\(872\) | 3.58220e9 | 0.182954 | ||||||||
\(873\) | −9.19562e9 | −0.467769 | ||||||||
\(874\) | 7.74894e9 | 0.392602 | ||||||||
\(875\) | 6.53329e9 | 0.329689 | ||||||||
\(876\) | −1.52792e10 | −0.767957 | ||||||||
\(877\) | −9.58767e9 | −0.479970 | −0.239985 | − | 0.970777i | \(-0.577143\pi\) | ||||
−0.239985 | + | 0.970777i | \(0.577143\pi\) | |||||||
\(878\) | −4.98430e10 | −2.48527 | ||||||||
\(879\) | −8.86154e9 | −0.440097 | ||||||||
\(880\) | −1.92616e10 | −0.952801 | ||||||||
\(881\) | −2.62769e10 | −1.29467 | −0.647334 | − | 0.762206i | \(-0.724116\pi\) | ||||
−0.647334 | + | 0.762206i | \(0.724116\pi\) | |||||||
\(882\) | −1.77038e9 | −0.0868812 | ||||||||
\(883\) | −9.16067e9 | −0.447780 | −0.223890 | − | 0.974614i | \(-0.571876\pi\) | ||||
−0.223890 | + | 0.974614i | \(0.571876\pi\) | |||||||
\(884\) | −2.92756e10 | −1.42535 | ||||||||
\(885\) | −2.32238e9 | −0.112624 | ||||||||
\(886\) | −3.18790e10 | −1.53988 | ||||||||
\(887\) | −2.61104e10 | −1.25626 | −0.628132 | − | 0.778107i | \(-0.716180\pi\) | ||||
−0.628132 | + | 0.778107i | \(0.716180\pi\) | |||||||
\(888\) | 5.16291e9 | 0.247428 | ||||||||
\(889\) | −1.45345e10 | −0.693814 | ||||||||
\(890\) | 5.56837e9 | 0.264766 | ||||||||
\(891\) | −1.28766e9 | −0.0609860 | ||||||||
\(892\) | −2.29719e10 | −1.08373 | ||||||||
\(893\) | −2.79307e10 | −1.31251 | ||||||||
\(894\) | −1.97124e9 | −0.0922695 | ||||||||
\(895\) | 7.92574e9 | 0.369538 | ||||||||
\(896\) | −1.00541e10 | −0.466942 | ||||||||
\(897\) | −4.34259e9 | −0.200898 | ||||||||
\(898\) | 1.35593e9 | 0.0624844 | ||||||||
\(899\) | 8.59971e8 | 0.0394752 | ||||||||
\(900\) | 7.28346e9 | 0.333034 | ||||||||
\(901\) | 4.76192e10 | 2.16893 | ||||||||
\(902\) | −1.34961e10 | −0.612331 | ||||||||
\(903\) | 1.08628e10 | 0.490946 | ||||||||
\(904\) | −5.77721e9 | −0.260093 | ||||||||
\(905\) | −3.89726e10 | −1.74779 | ||||||||
\(906\) | 2.08890e9 | 0.0933185 | ||||||||
\(907\) | 7.07125e9 | 0.314681 | 0.157340 | − | 0.987544i | \(-0.449708\pi\) | ||||
0.157340 | + | 0.987544i | \(0.449708\pi\) | |||||||
\(908\) | −2.69686e9 | −0.119552 | ||||||||
\(909\) | 1.04307e9 | 0.0460618 | ||||||||
\(910\) | 5.53112e10 | 2.43314 | ||||||||
\(911\) | 2.11411e10 | 0.926432 | 0.463216 | − | 0.886245i | \(-0.346695\pi\) | ||||
0.463216 | + | 0.886245i | \(0.346695\pi\) | |||||||
\(912\) | 1.73505e10 | 0.757409 | ||||||||
\(913\) | 1.14393e10 | 0.497451 | ||||||||
\(914\) | −2.55707e10 | −1.10772 | ||||||||
\(915\) | 7.10812e9 | 0.306748 | ||||||||
\(916\) | 2.85923e10 | 1.22918 | ||||||||
\(917\) | −3.08223e9 | −0.132000 | ||||||||
\(918\) | 7.98406e9 | 0.340623 | ||||||||
\(919\) | 3.00700e9 | 0.127799 | 0.0638997 | − | 0.997956i | \(-0.479646\pi\) | ||||
0.0638997 | + | 0.997956i | \(0.479646\pi\) | |||||||
\(920\) | 2.42429e9 | 0.102642 | ||||||||
\(921\) | −4.92983e9 | −0.207933 | ||||||||
\(922\) | −2.92293e10 | −1.22817 | ||||||||
\(923\) | 3.89391e10 | 1.62997 | ||||||||
\(924\) | −5.47390e9 | −0.228268 | ||||||||
\(925\) | 4.84226e10 | 2.01165 | ||||||||
\(926\) | −2.16509e10 | −0.896063 | ||||||||
\(927\) | 4.08895e9 | 0.168591 | ||||||||
\(928\) | −7.77259e9 | −0.319262 | ||||||||
\(929\) | −2.87222e9 | −0.117534 | −0.0587668 | − | 0.998272i | \(-0.518717\pi\) | ||||
−0.0587668 | + | 0.998272i | \(0.518717\pi\) | |||||||
\(930\) | 4.54453e9 | 0.185267 | ||||||||
\(931\) | −5.41280e9 | −0.219836 | ||||||||
\(932\) | 4.45412e9 | 0.180221 | ||||||||
\(933\) | 1.57793e10 | 0.636066 | ||||||||
\(934\) | 2.54994e10 | 1.02404 | ||||||||
\(935\) | −2.70994e10 | −1.08422 | ||||||||
\(936\) | −2.98882e9 | −0.119134 | ||||||||
\(937\) | −2.25687e10 | −0.896227 | −0.448114 | − | 0.893977i | \(-0.647904\pi\) | ||||
−0.448114 | + | 0.893977i | \(0.647904\pi\) | |||||||
\(938\) | −2.29967e10 | −0.909821 | ||||||||
\(939\) | −2.51734e10 | −0.992228 | ||||||||
\(940\) | 3.54887e10 | 1.39362 | ||||||||
\(941\) | 1.01256e10 | 0.396149 | 0.198075 | − | 0.980187i | \(-0.436531\pi\) | ||||
0.198075 | + | 0.980187i | \(0.436531\pi\) | |||||||
\(942\) | −8.25323e9 | −0.321696 | ||||||||
\(943\) | 5.52612e9 | 0.214600 | ||||||||
\(944\) | 3.89841e9 | 0.150829 | ||||||||
\(945\) | −6.71548e9 | −0.258861 | ||||||||
\(946\) | −1.81754e10 | −0.698017 | ||||||||
\(947\) | −6.73699e9 | −0.257775 | −0.128888 | − | 0.991659i | \(-0.541141\pi\) | ||||
−0.128888 | + | 0.991659i | \(0.541141\pi\) | |||||||
\(948\) | 1.67601e10 | 0.638922 | ||||||||
\(949\) | 5.88054e10 | 2.23350 | ||||||||
\(950\) | 5.00204e10 | 1.89284 | ||||||||
\(951\) | −2.41310e10 | −0.909794 | ||||||||
\(952\) | −8.35701e9 | −0.313922 | ||||||||
\(953\) | 2.23147e10 | 0.835153 | 0.417577 | − | 0.908642i | \(-0.362880\pi\) | ||||
0.417577 | + | 0.908642i | \(0.362880\pi\) | |||||||
\(954\) | −1.97444e10 | −0.736249 | ||||||||
\(955\) | −5.37199e10 | −1.99583 | ||||||||
\(956\) | −3.37785e10 | −1.25037 | ||||||||
\(957\) | 2.12626e9 | 0.0784196 | ||||||||
\(958\) | 3.72754e10 | 1.36976 | ||||||||
\(959\) | 2.32698e10 | 0.851975 | ||||||||
\(960\) | −1.36006e10 | −0.496145 | ||||||||
\(961\) | −2.68125e10 | −0.974554 | ||||||||
\(962\) | 8.07009e10 | 2.92257 | ||||||||
\(963\) | 1.58566e10 | 0.572160 | ||||||||
\(964\) | 3.40549e9 | 0.122436 | ||||||||
\(965\) | 3.13845e10 | 1.12427 | ||||||||
\(966\) | 5.03456e9 | 0.179697 | ||||||||
\(967\) | −2.22573e9 | −0.0791554 | −0.0395777 | − | 0.999216i | \(-0.512601\pi\) | ||||
−0.0395777 | + | 0.999216i | \(0.512601\pi\) | |||||||
\(968\) | 5.23049e9 | 0.185344 | ||||||||
\(969\) | 2.44107e10 | 0.861881 | ||||||||
\(970\) | 8.02417e10 | 2.82292 | ||||||||
\(971\) | −3.19447e9 | −0.111978 | −0.0559888 | − | 0.998431i | \(-0.517831\pi\) | ||||
−0.0559888 | + | 0.998431i | \(0.517831\pi\) | |||||||
\(972\) | −1.47378e9 | −0.0514755 | ||||||||
\(973\) | −2.80503e10 | −0.976210 | ||||||||
\(974\) | 1.86612e10 | 0.647116 | ||||||||
\(975\) | −2.80320e10 | −0.968585 | ||||||||
\(976\) | −1.19319e10 | −0.410804 | ||||||||
\(977\) | −1.60496e10 | −0.550598 | −0.275299 | − | 0.961359i | \(-0.588777\pi\) | ||||
−0.275299 | + | 0.961359i | \(0.588777\pi\) | |||||||
\(978\) | 2.77242e10 | 0.947703 | ||||||||
\(979\) | 2.12094e9 | 0.0722417 | ||||||||
\(980\) | 6.87752e9 | 0.233421 | ||||||||
\(981\) | −6.79825e9 | −0.229909 | ||||||||
\(982\) | −6.08022e10 | −2.04894 | ||||||||
\(983\) | 3.86768e10 | 1.29871 | 0.649357 | − | 0.760484i | \(-0.275038\pi\) | ||||
0.649357 | + | 0.760484i | \(0.275038\pi\) | |||||||
\(984\) | 3.80340e9 | 0.127259 | ||||||||
\(985\) | 5.98416e10 | 1.99515 | ||||||||
\(986\) | −1.31837e10 | −0.437995 | ||||||||
\(987\) | −1.81468e10 | −0.600745 | ||||||||
\(988\) | 3.71128e10 | 1.22426 | ||||||||
\(989\) | 7.44211e9 | 0.244630 | ||||||||
\(990\) | 1.12362e10 | 0.368043 | ||||||||
\(991\) | 1.63094e10 | 0.532328 | 0.266164 | − | 0.963928i | \(-0.414244\pi\) | ||||
0.266164 | + | 0.963928i | \(0.414244\pi\) | |||||||
\(992\) | −6.32759e9 | −0.205801 | ||||||||
\(993\) | −2.45068e10 | −0.794262 | ||||||||
\(994\) | −4.51438e10 | −1.45796 | ||||||||
\(995\) | 3.17962e10 | 1.02328 | ||||||||
\(996\) | 1.30927e10 | 0.419876 | ||||||||
\(997\) | 2.35819e10 | 0.753608 | 0.376804 | − | 0.926293i | \(-0.377023\pi\) | ||||
0.376804 | + | 0.926293i | \(0.377023\pi\) | |||||||
\(998\) | −9.68298e9 | −0.308356 | ||||||||
\(999\) | −9.79812e9 | −0.310931 |
(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 | 177.8.a.c.1.14 | ✓ | 17 | |
3.2 | odd | 2 | 531.8.a.c.1.4 | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.c.1.14 | ✓ | 17 | 1.1 | even | 1 | trivial | |
531.8.a.c.1.4 | 17 | 3.2 | odd | 2 |