Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [91,8,Mod(1,91)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(91, 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("91.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 91 = 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 91.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: | \(28.4270373191\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3 x^{9} - 816 x^{8} + 2298 x^{7} + 213848 x^{6} - 507132 x^{5} - 19919976 x^{4} + 24331248 x^{3} + 727257184 x^{2} - 56397312 x - 7335224320 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(8.95987\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 91.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.95987 | −0.791948 | −0.395974 | − | 0.918262i | \(-0.629593\pi\) | ||||
−0.395974 | + | 0.918262i | \(0.629593\pi\) | |||||||
\(3\) | −21.0756 | −0.450668 | −0.225334 | − | 0.974282i | \(-0.572347\pi\) | ||||
−0.225334 | + | 0.974282i | \(0.572347\pi\) | |||||||
\(4\) | −47.7208 | −0.372819 | ||||||||
\(5\) | −55.0053 | −0.196793 | −0.0983964 | − | 0.995147i | \(-0.531371\pi\) | ||||
−0.0983964 | + | 0.995147i | \(0.531371\pi\) | |||||||
\(6\) | 188.835 | 0.356905 | ||||||||
\(7\) | −343.000 | −0.377964 | ||||||||
\(8\) | 1574.43 | 1.08720 | ||||||||
\(9\) | −1742.82 | −0.796899 | ||||||||
\(10\) | 492.840 | 0.155850 | ||||||||
\(11\) | −6313.17 | −1.43012 | −0.715061 | − | 0.699062i | \(-0.753601\pi\) | ||||
−0.715061 | + | 0.699062i | \(0.753601\pi\) | |||||||
\(12\) | 1005.75 | 0.168017 | ||||||||
\(13\) | −2197.00 | −0.277350 | ||||||||
\(14\) | 3073.23 | 0.299328 | ||||||||
\(15\) | 1159.27 | 0.0886882 | ||||||||
\(16\) | −7998.46 | −0.488188 | ||||||||
\(17\) | −32863.9 | −1.62236 | −0.811181 | − | 0.584795i | \(-0.801175\pi\) | ||||
−0.811181 | + | 0.584795i | \(0.801175\pi\) | |||||||
\(18\) | 15615.4 | 0.631102 | ||||||||
\(19\) | −39983.1 | −1.33733 | −0.668665 | − | 0.743564i | \(-0.733134\pi\) | ||||
−0.668665 | + | 0.743564i | \(0.733134\pi\) | |||||||
\(20\) | 2624.89 | 0.0733680 | ||||||||
\(21\) | 7228.94 | 0.170336 | ||||||||
\(22\) | 56565.1 | 1.13258 | ||||||||
\(23\) | 90391.6 | 1.54910 | 0.774552 | − | 0.632510i | \(-0.217975\pi\) | ||||
0.774552 | + | 0.632510i | \(0.217975\pi\) | |||||||
\(24\) | −33182.2 | −0.489966 | ||||||||
\(25\) | −75099.4 | −0.961273 | ||||||||
\(26\) | 19684.8 | 0.219647 | ||||||||
\(27\) | 82823.4 | 0.809804 | ||||||||
\(28\) | 16368.2 | 0.140912 | ||||||||
\(29\) | −221283. | −1.68483 | −0.842414 | − | 0.538831i | \(-0.818866\pi\) | ||||
−0.842414 | + | 0.538831i | \(0.818866\pi\) | |||||||
\(30\) | −10386.9 | −0.0702364 | ||||||||
\(31\) | 71297.6 | 0.429842 | 0.214921 | − | 0.976631i | \(-0.431051\pi\) | ||||
0.214921 | + | 0.976631i | \(0.431051\pi\) | |||||||
\(32\) | −129862. | −0.700582 | ||||||||
\(33\) | 133054. | 0.644510 | ||||||||
\(34\) | 294456. | 1.28483 | ||||||||
\(35\) | 18866.8 | 0.0743807 | ||||||||
\(36\) | 83168.6 | 0.297099 | ||||||||
\(37\) | 39592.1 | 0.128500 | 0.0642500 | − | 0.997934i | \(-0.479535\pi\) | ||||
0.0642500 | + | 0.997934i | \(0.479535\pi\) | |||||||
\(38\) | 358243. | 1.05910 | ||||||||
\(39\) | 46303.2 | 0.124993 | ||||||||
\(40\) | −86602.2 | −0.213953 | ||||||||
\(41\) | 379303. | 0.859493 | 0.429747 | − | 0.902949i | \(-0.358603\pi\) | ||||
0.429747 | + | 0.902949i | \(0.358603\pi\) | |||||||
\(42\) | −64770.4 | −0.134898 | ||||||||
\(43\) | 302309. | 0.579844 | 0.289922 | − | 0.957050i | \(-0.406371\pi\) | ||||
0.289922 | + | 0.957050i | \(0.406371\pi\) | |||||||
\(44\) | 301269. | 0.533176 | ||||||||
\(45\) | 95864.1 | 0.156824 | ||||||||
\(46\) | −809897. | −1.22681 | ||||||||
\(47\) | 489575. | 0.687823 | 0.343911 | − | 0.939002i | \(-0.388248\pi\) | ||||
0.343911 | + | 0.939002i | \(0.388248\pi\) | |||||||
\(48\) | 168573. | 0.220010 | ||||||||
\(49\) | 117649. | 0.142857 | ||||||||
\(50\) | 672881. | 0.761278 | ||||||||
\(51\) | 692628. | 0.731146 | ||||||||
\(52\) | 104843. | 0.103401 | ||||||||
\(53\) | 1.15378e6 | 1.06453 | 0.532267 | − | 0.846577i | \(-0.321340\pi\) | ||||
0.532267 | + | 0.846577i | \(0.321340\pi\) | |||||||
\(54\) | −742087. | −0.641323 | ||||||||
\(55\) | 347258. | 0.281438 | ||||||||
\(56\) | −540031. | −0.410923 | ||||||||
\(57\) | 842669. | 0.602692 | ||||||||
\(58\) | 1.98267e6 | 1.33430 | ||||||||
\(59\) | −2.19644e6 | −1.39232 | −0.696158 | − | 0.717889i | \(-0.745109\pi\) | ||||
−0.696158 | + | 0.717889i | \(0.745109\pi\) | |||||||
\(60\) | −55321.3 | −0.0330646 | ||||||||
\(61\) | 2.03500e6 | 1.14792 | 0.573959 | − | 0.818884i | \(-0.305407\pi\) | ||||
0.573959 | + | 0.818884i | \(0.305407\pi\) | |||||||
\(62\) | −638817. | −0.340413 | ||||||||
\(63\) | 597786. | 0.301199 | ||||||||
\(64\) | 2.18735e6 | 1.04301 | ||||||||
\(65\) | 120847. | 0.0545805 | ||||||||
\(66\) | −1.19215e6 | −0.510418 | ||||||||
\(67\) | 2.15818e6 | 0.876650 | 0.438325 | − | 0.898817i | \(-0.355572\pi\) | ||||
0.438325 | + | 0.898817i | \(0.355572\pi\) | |||||||
\(68\) | 1.56829e6 | 0.604847 | ||||||||
\(69\) | −1.90506e6 | −0.698131 | ||||||||
\(70\) | −169044. | −0.0589056 | ||||||||
\(71\) | −4.49029e6 | −1.48892 | −0.744458 | − | 0.667670i | \(-0.767292\pi\) | ||||
−0.744458 | + | 0.667670i | \(0.767292\pi\) | |||||||
\(72\) | −2.74395e6 | −0.866389 | ||||||||
\(73\) | −789659. | −0.237580 | −0.118790 | − | 0.992919i | \(-0.537902\pi\) | ||||
−0.118790 | + | 0.992919i | \(0.537902\pi\) | |||||||
\(74\) | −354740. | −0.101765 | ||||||||
\(75\) | 1.58277e6 | 0.433214 | ||||||||
\(76\) | 1.90802e6 | 0.498582 | ||||||||
\(77\) | 2.16542e6 | 0.540535 | ||||||||
\(78\) | −414870. | −0.0989877 | ||||||||
\(79\) | −6.59926e6 | −1.50592 | −0.752958 | − | 0.658069i | \(-0.771373\pi\) | ||||
−0.752958 | + | 0.658069i | \(0.771373\pi\) | |||||||
\(80\) | 439958. | 0.0960718 | ||||||||
\(81\) | 2.06598e6 | 0.431946 | ||||||||
\(82\) | −3.39850e6 | −0.680674 | ||||||||
\(83\) | 659464. | 0.126595 | 0.0632977 | − | 0.997995i | \(-0.479838\pi\) | ||||
0.0632977 | + | 0.997995i | \(0.479838\pi\) | |||||||
\(84\) | −344971. | −0.0635046 | ||||||||
\(85\) | 1.80769e6 | 0.319269 | ||||||||
\(86\) | −2.70865e6 | −0.459206 | ||||||||
\(87\) | 4.66368e6 | 0.759297 | ||||||||
\(88\) | −9.93967e6 | −1.55483 | ||||||||
\(89\) | −7.89272e6 | −1.18676 | −0.593378 | − | 0.804924i | \(-0.702206\pi\) | ||||
−0.593378 | + | 0.804924i | \(0.702206\pi\) | |||||||
\(90\) | −858930. | −0.124196 | ||||||||
\(91\) | 753571. | 0.104828 | ||||||||
\(92\) | −4.31356e6 | −0.577535 | ||||||||
\(93\) | −1.50264e6 | −0.193716 | ||||||||
\(94\) | −4.38653e6 | −0.544720 | ||||||||
\(95\) | 2.19928e6 | 0.263177 | ||||||||
\(96\) | 2.73694e6 | 0.315730 | ||||||||
\(97\) | 3.32359e6 | 0.369749 | 0.184874 | − | 0.982762i | \(-0.440812\pi\) | ||||
0.184874 | + | 0.982762i | \(0.440812\pi\) | |||||||
\(98\) | −1.05412e6 | −0.113135 | ||||||||
\(99\) | 1.10027e7 | 1.13966 | ||||||||
\(100\) | 3.58380e6 | 0.358380 | ||||||||
\(101\) | 5.68139e6 | 0.548693 | 0.274347 | − | 0.961631i | \(-0.411538\pi\) | ||||
0.274347 | + | 0.961631i | \(0.411538\pi\) | |||||||
\(102\) | −6.20585e6 | −0.579030 | ||||||||
\(103\) | −9.71526e6 | −0.876041 | −0.438020 | − | 0.898965i | \(-0.644320\pi\) | ||||
−0.438020 | + | 0.898965i | \(0.644320\pi\) | |||||||
\(104\) | −3.45903e6 | −0.301535 | ||||||||
\(105\) | −397630. | −0.0335210 | ||||||||
\(106\) | −1.03378e7 | −0.843055 | ||||||||
\(107\) | 2.32695e6 | 0.183630 | 0.0918150 | − | 0.995776i | \(-0.470733\pi\) | ||||
0.0918150 | + | 0.995776i | \(0.470733\pi\) | |||||||
\(108\) | −3.95240e6 | −0.301910 | ||||||||
\(109\) | −1.71300e7 | −1.26696 | −0.633482 | − | 0.773757i | \(-0.718375\pi\) | ||||
−0.633482 | + | 0.773757i | \(0.718375\pi\) | |||||||
\(110\) | −3.11138e6 | −0.222884 | ||||||||
\(111\) | −834430. | −0.0579108 | ||||||||
\(112\) | 2.74347e6 | 0.184518 | ||||||||
\(113\) | −1.35164e7 | −0.881222 | −0.440611 | − | 0.897698i | \(-0.645238\pi\) | ||||
−0.440611 | + | 0.897698i | \(0.645238\pi\) | |||||||
\(114\) | −7.55020e6 | −0.477300 | ||||||||
\(115\) | −4.97202e6 | −0.304853 | ||||||||
\(116\) | 1.05598e7 | 0.628135 | ||||||||
\(117\) | 3.82897e6 | 0.221020 | ||||||||
\(118\) | 1.96798e7 | 1.10264 | ||||||||
\(119\) | 1.12723e7 | 0.613195 | ||||||||
\(120\) | 1.82520e6 | 0.0964218 | ||||||||
\(121\) | 2.03689e7 | 1.04525 | ||||||||
\(122\) | −1.82334e7 | −0.909091 | ||||||||
\(123\) | −7.99405e6 | −0.387346 | ||||||||
\(124\) | −3.40238e6 | −0.160253 | ||||||||
\(125\) | 8.42815e6 | 0.385964 | ||||||||
\(126\) | −5.35609e6 | −0.238534 | ||||||||
\(127\) | −3.70618e6 | −0.160551 | −0.0802755 | − | 0.996773i | \(-0.525580\pi\) | ||||
−0.0802755 | + | 0.996773i | \(0.525580\pi\) | |||||||
\(128\) | −2.97600e6 | −0.125429 | ||||||||
\(129\) | −6.37135e6 | −0.261317 | ||||||||
\(130\) | −1.08277e6 | −0.0432249 | ||||||||
\(131\) | 4.35220e7 | 1.69145 | 0.845726 | − | 0.533617i | \(-0.179168\pi\) | ||||
0.845726 | + | 0.533617i | \(0.179168\pi\) | |||||||
\(132\) | −6.34945e6 | −0.240285 | ||||||||
\(133\) | 1.37142e7 | 0.505463 | ||||||||
\(134\) | −1.93370e7 | −0.694261 | ||||||||
\(135\) | −4.55572e6 | −0.159364 | ||||||||
\(136\) | −5.17421e7 | −1.76383 | ||||||||
\(137\) | 5.59159e7 | 1.85786 | 0.928930 | − | 0.370255i | \(-0.120730\pi\) | ||||
0.928930 | + | 0.370255i | \(0.120730\pi\) | |||||||
\(138\) | 1.70691e7 | 0.552884 | ||||||||
\(139\) | 1.61731e7 | 0.510788 | 0.255394 | − | 0.966837i | \(-0.417795\pi\) | ||||
0.255394 | + | 0.966837i | \(0.417795\pi\) | |||||||
\(140\) | −900339. | −0.0277305 | ||||||||
\(141\) | −1.03181e7 | −0.309980 | ||||||||
\(142\) | 4.02324e7 | 1.17914 | ||||||||
\(143\) | 1.38700e7 | 0.396644 | ||||||||
\(144\) | 1.39399e7 | 0.389036 | ||||||||
\(145\) | 1.21717e7 | 0.331562 | ||||||||
\(146\) | 7.07524e6 | 0.188151 | ||||||||
\(147\) | −2.47953e6 | −0.0643811 | ||||||||
\(148\) | −1.88937e6 | −0.0479072 | ||||||||
\(149\) | 5.07725e7 | 1.25741 | 0.628705 | − | 0.777644i | \(-0.283585\pi\) | ||||
0.628705 | + | 0.777644i | \(0.283585\pi\) | |||||||
\(150\) | −1.41814e7 | −0.343083 | ||||||||
\(151\) | −7.64411e7 | −1.80679 | −0.903395 | − | 0.428809i | \(-0.858933\pi\) | ||||
−0.903395 | + | 0.428809i | \(0.858933\pi\) | |||||||
\(152\) | −6.29508e7 | −1.45395 | ||||||||
\(153\) | 5.72758e7 | 1.29286 | ||||||||
\(154\) | −1.94018e7 | −0.428076 | ||||||||
\(155\) | −3.92175e6 | −0.0845899 | ||||||||
\(156\) | −2.20962e6 | −0.0465996 | ||||||||
\(157\) | −6.98540e7 | −1.44060 | −0.720298 | − | 0.693664i | \(-0.755995\pi\) | ||||
−0.720298 | + | 0.693664i | \(0.755995\pi\) | |||||||
\(158\) | 5.91285e7 | 1.19261 | ||||||||
\(159\) | −2.43168e7 | −0.479751 | ||||||||
\(160\) | 7.14312e6 | 0.137869 | ||||||||
\(161\) | −3.10043e7 | −0.585507 | ||||||||
\(162\) | −1.85109e7 | −0.342079 | ||||||||
\(163\) | 1.50400e7 | 0.272014 | 0.136007 | − | 0.990708i | \(-0.456573\pi\) | ||||
0.136007 | + | 0.990708i | \(0.456573\pi\) | |||||||
\(164\) | −1.81006e7 | −0.320435 | ||||||||
\(165\) | −7.31868e6 | −0.126835 | ||||||||
\(166\) | −5.90871e6 | −0.100257 | ||||||||
\(167\) | 8.73370e7 | 1.45108 | 0.725538 | − | 0.688182i | \(-0.241591\pi\) | ||||
0.725538 | + | 0.688182i | \(0.241591\pi\) | |||||||
\(168\) | 1.13815e7 | 0.185190 | ||||||||
\(169\) | 4.82681e6 | 0.0769231 | ||||||||
\(170\) | −1.61966e7 | −0.252845 | ||||||||
\(171\) | 6.96832e7 | 1.06572 | ||||||||
\(172\) | −1.44264e7 | −0.216177 | ||||||||
\(173\) | 3.18347e7 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(174\) | −4.17860e7 | −0.601324 | ||||||||
\(175\) | 2.57591e7 | 0.363327 | ||||||||
\(176\) | 5.04957e7 | 0.698168 | ||||||||
\(177\) | 4.62914e7 | 0.627472 | ||||||||
\(178\) | 7.07177e7 | 0.939849 | ||||||||
\(179\) | −1.09583e7 | −0.142809 | −0.0714045 | − | 0.997447i | \(-0.522748\pi\) | ||||
−0.0714045 | + | 0.997447i | \(0.522748\pi\) | |||||||
\(180\) | −4.57471e6 | −0.0584669 | ||||||||
\(181\) | −1.01099e8 | −1.26727 | −0.633637 | − | 0.773631i | \(-0.718439\pi\) | ||||
−0.633637 | + | 0.773631i | \(0.718439\pi\) | |||||||
\(182\) | −6.75190e6 | −0.0830187 | ||||||||
\(183\) | −4.28890e7 | −0.517329 | ||||||||
\(184\) | 1.42316e8 | 1.68419 | ||||||||
\(185\) | −2.17778e6 | −0.0252879 | ||||||||
\(186\) | 1.34635e7 | 0.153413 | ||||||||
\(187\) | 2.07475e8 | 2.32018 | ||||||||
\(188\) | −2.33629e7 | −0.256433 | ||||||||
\(189\) | −2.84084e7 | −0.306077 | ||||||||
\(190\) | −1.97053e7 | −0.208422 | ||||||||
\(191\) | 5.05592e6 | 0.0525029 | 0.0262514 | − | 0.999655i | \(-0.491643\pi\) | ||||
0.0262514 | + | 0.999655i | \(0.491643\pi\) | |||||||
\(192\) | −4.60999e7 | −0.470052 | ||||||||
\(193\) | 7.76809e7 | 0.777792 | 0.388896 | − | 0.921282i | \(-0.372856\pi\) | ||||
0.388896 | + | 0.921282i | \(0.372856\pi\) | |||||||
\(194\) | −2.97790e7 | −0.292822 | ||||||||
\(195\) | −2.54692e6 | −0.0245977 | ||||||||
\(196\) | −5.61430e6 | −0.0532598 | ||||||||
\(197\) | −1.26008e8 | −1.17427 | −0.587134 | − | 0.809490i | \(-0.699744\pi\) | ||||
−0.587134 | + | 0.809490i | \(0.699744\pi\) | |||||||
\(198\) | −9.85827e7 | −0.902553 | ||||||||
\(199\) | −1.55002e8 | −1.39428 | −0.697141 | − | 0.716934i | \(-0.745545\pi\) | ||||
−0.697141 | + | 0.716934i | \(0.745545\pi\) | |||||||
\(200\) | −1.18239e8 | −1.04510 | ||||||||
\(201\) | −4.54851e7 | −0.395078 | ||||||||
\(202\) | −5.09045e7 | −0.434536 | ||||||||
\(203\) | 7.59001e7 | 0.636805 | ||||||||
\(204\) | −3.30528e7 | −0.272585 | ||||||||
\(205\) | −2.08637e7 | −0.169142 | ||||||||
\(206\) | 8.70475e7 | 0.693778 | ||||||||
\(207\) | −1.57536e8 | −1.23448 | ||||||||
\(208\) | 1.75726e7 | 0.135399 | ||||||||
\(209\) | 2.52420e8 | 1.91255 | ||||||||
\(210\) | 3.56271e6 | 0.0265469 | ||||||||
\(211\) | 1.07390e8 | 0.787003 | 0.393502 | − | 0.919324i | \(-0.371264\pi\) | ||||
0.393502 | + | 0.919324i | \(0.371264\pi\) | |||||||
\(212\) | −5.50595e7 | −0.396878 | ||||||||
\(213\) | 9.46357e7 | 0.671006 | ||||||||
\(214\) | −2.08491e7 | −0.145425 | ||||||||
\(215\) | −1.66286e7 | −0.114109 | ||||||||
\(216\) | 1.30400e8 | 0.880420 | ||||||||
\(217\) | −2.44551e7 | −0.162465 | ||||||||
\(218\) | 1.53482e8 | 1.00337 | ||||||||
\(219\) | 1.66426e7 | 0.107070 | ||||||||
\(220\) | −1.65714e7 | −0.104925 | ||||||||
\(221\) | 7.22020e7 | 0.449962 | ||||||||
\(222\) | 7.47638e6 | 0.0458623 | ||||||||
\(223\) | −5.43261e7 | −0.328051 | −0.164026 | − | 0.986456i | \(-0.552448\pi\) | ||||
−0.164026 | + | 0.986456i | \(0.552448\pi\) | |||||||
\(224\) | 4.45428e7 | 0.264795 | ||||||||
\(225\) | 1.30885e8 | 0.766037 | ||||||||
\(226\) | 1.21105e8 | 0.697882 | ||||||||
\(227\) | −2.42395e8 | −1.37541 | −0.687707 | − | 0.725989i | \(-0.741383\pi\) | ||||
−0.687707 | + | 0.725989i | \(0.741383\pi\) | |||||||
\(228\) | −4.02128e7 | −0.224695 | ||||||||
\(229\) | −1.02369e8 | −0.563304 | −0.281652 | − | 0.959517i | \(-0.590882\pi\) | ||||
−0.281652 | + | 0.959517i | \(0.590882\pi\) | |||||||
\(230\) | 4.45486e7 | 0.241427 | ||||||||
\(231\) | −4.56375e7 | −0.243602 | ||||||||
\(232\) | −3.48396e8 | −1.83175 | ||||||||
\(233\) | 2.28645e8 | 1.18418 | 0.592088 | − | 0.805873i | \(-0.298304\pi\) | ||||
0.592088 | + | 0.805873i | \(0.298304\pi\) | |||||||
\(234\) | −3.43071e7 | −0.175036 | ||||||||
\(235\) | −2.69292e7 | −0.135359 | ||||||||
\(236\) | 1.04816e8 | 0.519081 | ||||||||
\(237\) | 1.39084e8 | 0.678667 | ||||||||
\(238\) | −1.00998e8 | −0.485619 | ||||||||
\(239\) | −4.10470e7 | −0.194486 | −0.0972431 | − | 0.995261i | \(-0.531002\pi\) | ||||
−0.0972431 | + | 0.995261i | \(0.531002\pi\) | |||||||
\(240\) | −9.27239e6 | −0.0432965 | ||||||||
\(241\) | −1.33632e8 | −0.614967 | −0.307483 | − | 0.951553i | \(-0.599487\pi\) | ||||
−0.307483 | + | 0.951553i | \(0.599487\pi\) | |||||||
\(242\) | −1.82503e8 | −0.827782 | ||||||||
\(243\) | −2.24677e8 | −1.00447 | ||||||||
\(244\) | −9.71120e7 | −0.427965 | ||||||||
\(245\) | −6.47131e6 | −0.0281133 | ||||||||
\(246\) | 7.16256e7 | 0.306758 | ||||||||
\(247\) | 8.78429e7 | 0.370909 | ||||||||
\(248\) | 1.12253e8 | 0.467325 | ||||||||
\(249\) | −1.38986e7 | −0.0570524 | ||||||||
\(250\) | −7.55151e7 | −0.305664 | ||||||||
\(251\) | −3.88436e8 | −1.55046 | −0.775232 | − | 0.631676i | \(-0.782367\pi\) | ||||
−0.775232 | + | 0.631676i | \(0.782367\pi\) | |||||||
\(252\) | −2.85268e7 | −0.112293 | ||||||||
\(253\) | −5.70658e8 | −2.21541 | ||||||||
\(254\) | 3.32068e7 | 0.127148 | ||||||||
\(255\) | −3.80982e7 | −0.143884 | ||||||||
\(256\) | −2.53317e8 | −0.943678 | ||||||||
\(257\) | −3.88086e8 | −1.42614 | −0.713070 | − | 0.701093i | \(-0.752696\pi\) | ||||
−0.713070 | + | 0.701093i | \(0.752696\pi\) | |||||||
\(258\) | 5.70865e7 | 0.206949 | ||||||||
\(259\) | −1.35801e7 | −0.0485684 | ||||||||
\(260\) | −5.76689e6 | −0.0203486 | ||||||||
\(261\) | 3.85656e8 | 1.34264 | ||||||||
\(262\) | −3.89952e8 | −1.33954 | ||||||||
\(263\) | −9.75048e7 | −0.330507 | −0.165254 | − | 0.986251i | \(-0.552844\pi\) | ||||
−0.165254 | + | 0.986251i | \(0.552844\pi\) | |||||||
\(264\) | 2.09485e8 | 0.700711 | ||||||||
\(265\) | −6.34643e7 | −0.209493 | ||||||||
\(266\) | −1.22877e8 | −0.400301 | ||||||||
\(267\) | 1.66344e8 | 0.534833 | ||||||||
\(268\) | −1.02990e8 | −0.326832 | ||||||||
\(269\) | 4.03040e8 | 1.26245 | 0.631227 | − | 0.775598i | \(-0.282552\pi\) | ||||
0.631227 | + | 0.775598i | \(0.282552\pi\) | |||||||
\(270\) | 4.08187e7 | 0.126208 | ||||||||
\(271\) | 5.09554e7 | 0.155524 | 0.0777621 | − | 0.996972i | \(-0.475223\pi\) | ||||
0.0777621 | + | 0.996972i | \(0.475223\pi\) | |||||||
\(272\) | 2.62861e8 | 0.792017 | ||||||||
\(273\) | −1.58820e7 | −0.0472428 | ||||||||
\(274\) | −5.00999e8 | −1.47133 | ||||||||
\(275\) | 4.74115e8 | 1.37474 | ||||||||
\(276\) | 9.09110e7 | 0.260276 | ||||||||
\(277\) | −8.41430e7 | −0.237869 | −0.118935 | − | 0.992902i | \(-0.537948\pi\) | ||||
−0.118935 | + | 0.992902i | \(0.537948\pi\) | |||||||
\(278\) | −1.44909e8 | −0.404518 | ||||||||
\(279\) | −1.24259e8 | −0.342541 | ||||||||
\(280\) | 2.97046e7 | 0.0808667 | ||||||||
\(281\) | 6.00251e8 | 1.61384 | 0.806921 | − | 0.590659i | \(-0.201132\pi\) | ||||
0.806921 | + | 0.590659i | \(0.201132\pi\) | |||||||
\(282\) | 9.24488e7 | 0.245488 | ||||||||
\(283\) | −5.69977e8 | −1.49488 | −0.747438 | − | 0.664332i | \(-0.768716\pi\) | ||||
−0.747438 | + | 0.664332i | \(0.768716\pi\) | |||||||
\(284\) | 2.14280e8 | 0.555095 | ||||||||
\(285\) | −4.63512e7 | −0.118605 | ||||||||
\(286\) | −1.24274e8 | −0.314122 | ||||||||
\(287\) | −1.30101e8 | −0.324858 | ||||||||
\(288\) | 2.26327e8 | 0.558293 | ||||||||
\(289\) | 6.69698e8 | 1.63206 | ||||||||
\(290\) | −1.09057e8 | −0.262580 | ||||||||
\(291\) | −7.00469e7 | −0.166634 | ||||||||
\(292\) | 3.76832e7 | 0.0885742 | ||||||||
\(293\) | 3.51911e8 | 0.817327 | 0.408663 | − | 0.912685i | \(-0.365995\pi\) | ||||
0.408663 | + | 0.912685i | \(0.365995\pi\) | |||||||
\(294\) | 2.22162e7 | 0.0509865 | ||||||||
\(295\) | 1.20816e8 | 0.273998 | ||||||||
\(296\) | 6.23352e7 | 0.139705 | ||||||||
\(297\) | −5.22878e8 | −1.15812 | ||||||||
\(298\) | −4.54915e8 | −0.995803 | ||||||||
\(299\) | −1.98590e8 | −0.429644 | ||||||||
\(300\) | −7.55310e7 | −0.161510 | ||||||||
\(301\) | −1.03692e8 | −0.219160 | ||||||||
\(302\) | 6.84902e8 | 1.43088 | ||||||||
\(303\) | −1.19739e8 | −0.247278 | ||||||||
\(304\) | 3.19803e8 | 0.652868 | ||||||||
\(305\) | −1.11936e8 | −0.225902 | ||||||||
\(306\) | −5.13183e8 | −1.02388 | ||||||||
\(307\) | 6.45364e8 | 1.27298 | 0.636488 | − | 0.771286i | \(-0.280386\pi\) | ||||
0.636488 | + | 0.771286i | \(0.280386\pi\) | |||||||
\(308\) | −1.03335e8 | −0.201522 | ||||||||
\(309\) | 2.04755e8 | 0.394803 | ||||||||
\(310\) | 3.51383e7 | 0.0669908 | ||||||||
\(311\) | 3.79660e8 | 0.715703 | 0.357852 | − | 0.933778i | \(-0.383509\pi\) | ||||
0.357852 | + | 0.933778i | \(0.383509\pi\) | |||||||
\(312\) | 7.29013e7 | 0.135892 | ||||||||
\(313\) | −6.75218e8 | −1.24463 | −0.622313 | − | 0.782769i | \(-0.713807\pi\) | ||||
−0.622313 | + | 0.782769i | \(0.713807\pi\) | |||||||
\(314\) | 6.25882e8 | 1.14088 | ||||||||
\(315\) | −3.28814e7 | −0.0592739 | ||||||||
\(316\) | 3.14922e8 | 0.561433 | ||||||||
\(317\) | 7.42853e8 | 1.30977 | 0.654886 | − | 0.755728i | \(-0.272717\pi\) | ||||
0.654886 | + | 0.755728i | \(0.272717\pi\) | |||||||
\(318\) | 2.17875e8 | 0.379938 | ||||||||
\(319\) | 1.39700e9 | 2.40951 | ||||||||
\(320\) | −1.20316e8 | −0.205257 | ||||||||
\(321\) | −4.90419e7 | −0.0827561 | ||||||||
\(322\) | 2.77795e8 | 0.463691 | ||||||||
\(323\) | 1.31400e9 | 2.16964 | ||||||||
\(324\) | −9.85904e7 | −0.161038 | ||||||||
\(325\) | 1.64993e8 | 0.266609 | ||||||||
\(326\) | −1.34756e8 | −0.215421 | ||||||||
\(327\) | 3.61025e8 | 0.570980 | ||||||||
\(328\) | 5.97188e8 | 0.934442 | ||||||||
\(329\) | −1.67924e8 | −0.259973 | ||||||||
\(330\) | 6.55744e7 | 0.100447 | ||||||||
\(331\) | −4.52244e8 | −0.685449 | −0.342724 | − | 0.939436i | \(-0.611350\pi\) | ||||
−0.342724 | + | 0.939436i | \(0.611350\pi\) | |||||||
\(332\) | −3.14701e7 | −0.0471971 | ||||||||
\(333\) | −6.90019e7 | −0.102401 | ||||||||
\(334\) | −7.82528e8 | −1.14918 | ||||||||
\(335\) | −1.18711e8 | −0.172518 | ||||||||
\(336\) | −5.78205e7 | −0.0831561 | ||||||||
\(337\) | −6.95318e7 | −0.0989643 | −0.0494822 | − | 0.998775i | \(-0.515757\pi\) | ||||
−0.0494822 | + | 0.998775i | \(0.515757\pi\) | |||||||
\(338\) | −4.32476e7 | −0.0609191 | ||||||||
\(339\) | 2.84866e8 | 0.397138 | ||||||||
\(340\) | −8.62643e7 | −0.119030 | ||||||||
\(341\) | −4.50114e8 | −0.614727 | ||||||||
\(342\) | −6.24352e8 | −0.843992 | ||||||||
\(343\) | −4.03536e7 | −0.0539949 | ||||||||
\(344\) | 4.75966e8 | 0.630407 | ||||||||
\(345\) | 1.04788e8 | 0.137387 | ||||||||
\(346\) | −2.85234e8 | −0.370199 | ||||||||
\(347\) | −1.02087e9 | −1.31165 | −0.655827 | − | 0.754911i | \(-0.727680\pi\) | ||||
−0.655827 | + | 0.754911i | \(0.727680\pi\) | |||||||
\(348\) | −2.22555e8 | −0.283080 | ||||||||
\(349\) | 5.69930e8 | 0.717682 | 0.358841 | − | 0.933399i | \(-0.383172\pi\) | ||||
0.358841 | + | 0.933399i | \(0.383172\pi\) | |||||||
\(350\) | −2.30798e8 | −0.287736 | ||||||||
\(351\) | −1.81963e8 | −0.224599 | ||||||||
\(352\) | 8.19844e8 | 1.00192 | ||||||||
\(353\) | −5.92530e7 | −0.0716966 | −0.0358483 | − | 0.999357i | \(-0.511413\pi\) | ||||
−0.0358483 | + | 0.999357i | \(0.511413\pi\) | |||||||
\(354\) | −4.14765e8 | −0.496925 | ||||||||
\(355\) | 2.46989e8 | 0.293008 | ||||||||
\(356\) | 3.76647e8 | 0.442445 | ||||||||
\(357\) | −2.37571e8 | −0.276347 | ||||||||
\(358\) | 9.81845e7 | 0.113097 | ||||||||
\(359\) | −2.50331e8 | −0.285551 | −0.142775 | − | 0.989755i | \(-0.545603\pi\) | ||||
−0.142775 | + | 0.989755i | \(0.545603\pi\) | |||||||
\(360\) | 1.50932e8 | 0.170499 | ||||||||
\(361\) | 7.04776e8 | 0.788453 | ||||||||
\(362\) | 9.05831e8 | 1.00361 | ||||||||
\(363\) | −4.29288e8 | −0.471060 | ||||||||
\(364\) | −3.59610e7 | −0.0390820 | ||||||||
\(365\) | 4.34354e7 | 0.0467540 | ||||||||
\(366\) | 3.84280e8 | 0.409698 | ||||||||
\(367\) | −1.29540e8 | −0.136796 | −0.0683981 | − | 0.997658i | \(-0.521789\pi\) | ||||
−0.0683981 | + | 0.997658i | \(0.521789\pi\) | |||||||
\(368\) | −7.22994e8 | −0.756254 | ||||||||
\(369\) | −6.61055e8 | −0.684929 | ||||||||
\(370\) | 1.95126e7 | 0.0200267 | ||||||||
\(371\) | −3.95748e8 | −0.402356 | ||||||||
\(372\) | 7.17073e7 | 0.0722210 | ||||||||
\(373\) | −9.94161e8 | −0.991918 | −0.495959 | − | 0.868346i | \(-0.665183\pi\) | ||||
−0.495959 | + | 0.868346i | \(0.665183\pi\) | |||||||
\(374\) | −1.85895e9 | −1.83746 | ||||||||
\(375\) | −1.77629e8 | −0.173942 | ||||||||
\(376\) | 7.70804e8 | 0.747802 | ||||||||
\(377\) | 4.86159e8 | 0.467287 | ||||||||
\(378\) | 2.54536e8 | 0.242397 | ||||||||
\(379\) | 8.11711e8 | 0.765886 | 0.382943 | − | 0.923772i | \(-0.374911\pi\) | ||||
0.382943 | + | 0.923772i | \(0.374911\pi\) | |||||||
\(380\) | −1.04951e8 | −0.0981173 | ||||||||
\(381\) | 7.81100e7 | 0.0723551 | ||||||||
\(382\) | −4.53003e7 | −0.0415795 | ||||||||
\(383\) | −1.05588e9 | −0.960331 | −0.480165 | − | 0.877178i | \(-0.659423\pi\) | ||||
−0.480165 | + | 0.877178i | \(0.659423\pi\) | |||||||
\(384\) | 6.27211e7 | 0.0565268 | ||||||||
\(385\) | −1.19109e8 | −0.106373 | ||||||||
\(386\) | −6.96010e8 | −0.615971 | ||||||||
\(387\) | −5.26869e8 | −0.462077 | ||||||||
\(388\) | −1.58605e8 | −0.137849 | ||||||||
\(389\) | 2.90409e8 | 0.250142 | 0.125071 | − | 0.992148i | \(-0.460084\pi\) | ||||
0.125071 | + | 0.992148i | \(0.460084\pi\) | |||||||
\(390\) | 2.28201e7 | 0.0194801 | ||||||||
\(391\) | −2.97062e9 | −2.51321 | ||||||||
\(392\) | 1.85231e8 | 0.155314 | ||||||||
\(393\) | −9.17255e8 | −0.762283 | ||||||||
\(394\) | 1.12902e9 | 0.929958 | ||||||||
\(395\) | 3.62994e8 | 0.296353 | ||||||||
\(396\) | −5.25058e8 | −0.424887 | ||||||||
\(397\) | 5.09106e8 | 0.408358 | 0.204179 | − | 0.978934i | \(-0.434548\pi\) | ||||
0.204179 | + | 0.978934i | \(0.434548\pi\) | |||||||
\(398\) | 1.38879e9 | 1.10420 | ||||||||
\(399\) | −2.89036e8 | −0.227796 | ||||||||
\(400\) | 6.00680e8 | 0.469281 | ||||||||
\(401\) | 1.36139e9 | 1.05433 | 0.527166 | − | 0.849762i | \(-0.323254\pi\) | ||||
0.527166 | + | 0.849762i | \(0.323254\pi\) | |||||||
\(402\) | 4.07540e8 | 0.312881 | ||||||||
\(403\) | −1.56641e8 | −0.119217 | ||||||||
\(404\) | −2.71120e8 | −0.204563 | ||||||||
\(405\) | −1.13640e8 | −0.0850039 | ||||||||
\(406\) | −6.80055e8 | −0.504316 | ||||||||
\(407\) | −2.49952e8 | −0.183771 | ||||||||
\(408\) | 1.09050e9 | 0.794903 | ||||||||
\(409\) | −2.07113e9 | −1.49684 | −0.748419 | − | 0.663226i | \(-0.769187\pi\) | ||||
−0.748419 | + | 0.663226i | \(0.769187\pi\) | |||||||
\(410\) | 1.86936e8 | 0.133952 | ||||||||
\(411\) | −1.17846e9 | −0.837278 | ||||||||
\(412\) | 4.63620e8 | 0.326604 | ||||||||
\(413\) | 7.53380e8 | 0.526246 | ||||||||
\(414\) | 1.41150e9 | 0.977643 | ||||||||
\(415\) | −3.62740e7 | −0.0249131 | ||||||||
\(416\) | 2.85308e8 | 0.194306 | ||||||||
\(417\) | −3.40858e8 | −0.230196 | ||||||||
\(418\) | −2.26165e9 | −1.51464 | ||||||||
\(419\) | −2.56819e9 | −1.70561 | −0.852803 | − | 0.522233i | \(-0.825099\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(420\) | 1.89752e7 | 0.0124972 | ||||||||
\(421\) | −5.09167e8 | −0.332562 | −0.166281 | − | 0.986078i | \(-0.553176\pi\) | ||||
−0.166281 | + | 0.986078i | \(0.553176\pi\) | |||||||
\(422\) | −9.62203e8 | −0.623266 | ||||||||
\(423\) | −8.53240e8 | −0.548125 | ||||||||
\(424\) | 1.81656e9 | 1.15736 | ||||||||
\(425\) | 2.46806e9 | 1.55953 | ||||||||
\(426\) | −8.47923e8 | −0.531402 | ||||||||
\(427\) | −6.98006e8 | −0.433872 | ||||||||
\(428\) | −1.11044e8 | −0.0684607 | ||||||||
\(429\) | −2.92320e8 | −0.178755 | ||||||||
\(430\) | 1.48990e8 | 0.0903685 | ||||||||
\(431\) | 2.94447e9 | 1.77148 | 0.885742 | − | 0.464178i | \(-0.153650\pi\) | ||||
0.885742 | + | 0.464178i | \(0.153650\pi\) | |||||||
\(432\) | −6.62460e8 | −0.395336 | ||||||||
\(433\) | 8.41535e8 | 0.498155 | 0.249078 | − | 0.968484i | \(-0.419873\pi\) | ||||
0.249078 | + | 0.968484i | \(0.419873\pi\) | |||||||
\(434\) | 2.19114e8 | 0.128664 | ||||||||
\(435\) | −2.56527e8 | −0.149424 | ||||||||
\(436\) | 8.17457e8 | 0.472348 | ||||||||
\(437\) | −3.61414e9 | −2.07167 | ||||||||
\(438\) | −1.49115e8 | −0.0847935 | ||||||||
\(439\) | −3.11478e9 | −1.75712 | −0.878560 | − | 0.477632i | \(-0.841495\pi\) | ||||
−0.878560 | + | 0.477632i | \(0.841495\pi\) | |||||||
\(440\) | 5.46734e8 | 0.305979 | ||||||||
\(441\) | −2.05041e8 | −0.113843 | ||||||||
\(442\) | −6.46920e8 | −0.356347 | ||||||||
\(443\) | 1.41246e9 | 0.771906 | 0.385953 | − | 0.922518i | \(-0.373873\pi\) | ||||
0.385953 | + | 0.922518i | \(0.373873\pi\) | |||||||
\(444\) | 3.98196e7 | 0.0215902 | ||||||||
\(445\) | 4.34141e8 | 0.233545 | ||||||||
\(446\) | 4.86755e8 | 0.259799 | ||||||||
\(447\) | −1.07006e9 | −0.566674 | ||||||||
\(448\) | −7.50262e8 | −0.394221 | ||||||||
\(449\) | 9.76669e8 | 0.509196 | 0.254598 | − | 0.967047i | \(-0.418057\pi\) | ||||
0.254598 | + | 0.967047i | \(0.418057\pi\) | |||||||
\(450\) | −1.17271e9 | −0.606661 | ||||||||
\(451\) | −2.39460e9 | −1.22918 | ||||||||
\(452\) | 6.45012e8 | 0.328536 | ||||||||
\(453\) | 1.61105e9 | 0.814262 | ||||||||
\(454\) | 2.17183e9 | 1.08926 | ||||||||
\(455\) | −4.14504e7 | −0.0206295 | ||||||||
\(456\) | 1.32673e9 | 0.655247 | ||||||||
\(457\) | −1.13924e8 | −0.0558352 | −0.0279176 | − | 0.999610i | \(-0.508888\pi\) | ||||
−0.0279176 | + | 0.999610i | \(0.508888\pi\) | |||||||
\(458\) | 9.17209e8 | 0.446107 | ||||||||
\(459\) | −2.72190e9 | −1.31380 | ||||||||
\(460\) | 2.37269e8 | 0.113655 | ||||||||
\(461\) | 3.73061e9 | 1.77348 | 0.886741 | − | 0.462266i | \(-0.152963\pi\) | ||||
0.886741 | + | 0.462266i | \(0.152963\pi\) | |||||||
\(462\) | 4.08906e8 | 0.192920 | ||||||||
\(463\) | 2.18894e9 | 1.02495 | 0.512473 | − | 0.858703i | \(-0.328730\pi\) | ||||
0.512473 | + | 0.858703i | \(0.328730\pi\) | |||||||
\(464\) | 1.76993e9 | 0.822512 | ||||||||
\(465\) | 8.26533e7 | 0.0381219 | ||||||||
\(466\) | −2.04863e9 | −0.937805 | ||||||||
\(467\) | −2.01447e9 | −0.915273 | −0.457637 | − | 0.889139i | \(-0.651304\pi\) | ||||
−0.457637 | + | 0.889139i | \(0.651304\pi\) | |||||||
\(468\) | −1.82721e8 | −0.0824004 | ||||||||
\(469\) | −7.40256e8 | −0.331343 | ||||||||
\(470\) | 2.41282e8 | 0.107197 | ||||||||
\(471\) | 1.47222e9 | 0.649230 | ||||||||
\(472\) | −3.45816e9 | −1.51373 | ||||||||
\(473\) | −1.90853e9 | −0.829248 | ||||||||
\(474\) | −1.24617e9 | −0.537469 | ||||||||
\(475\) | 3.00271e9 | 1.28554 | ||||||||
\(476\) | −5.37924e8 | −0.228611 | ||||||||
\(477\) | −2.01084e9 | −0.848325 | ||||||||
\(478\) | 3.67776e8 | 0.154023 | ||||||||
\(479\) | 1.94687e9 | 0.809398 | 0.404699 | − | 0.914450i | \(-0.367376\pi\) | ||||
0.404699 | + | 0.914450i | \(0.367376\pi\) | |||||||
\(480\) | −1.50546e8 | −0.0621333 | ||||||||
\(481\) | −8.69839e7 | −0.0356395 | ||||||||
\(482\) | 1.19733e9 | 0.487022 | ||||||||
\(483\) | 6.53436e8 | 0.263869 | ||||||||
\(484\) | −9.72022e8 | −0.389688 | ||||||||
\(485\) | −1.82815e8 | −0.0727639 | ||||||||
\(486\) | 2.01307e9 | 0.795486 | ||||||||
\(487\) | −1.02425e9 | −0.401843 | −0.200922 | − | 0.979607i | \(-0.564394\pi\) | ||||
−0.200922 | + | 0.979607i | \(0.564394\pi\) | |||||||
\(488\) | 3.20398e9 | 1.24802 | ||||||||
\(489\) | −3.16978e8 | −0.122588 | ||||||||
\(490\) | 5.79821e7 | 0.0222642 | ||||||||
\(491\) | −2.79896e9 | −1.06711 | −0.533557 | − | 0.845764i | \(-0.679145\pi\) | ||||
−0.533557 | + | 0.845764i | \(0.679145\pi\) | |||||||
\(492\) | 3.81482e8 | 0.144410 | ||||||||
\(493\) | 7.27223e9 | 2.73340 | ||||||||
\(494\) | −7.87060e8 | −0.293740 | ||||||||
\(495\) | −6.05206e8 | −0.224277 | ||||||||
\(496\) | −5.70272e8 | −0.209844 | ||||||||
\(497\) | 1.54017e9 | 0.562757 | ||||||||
\(498\) | 1.24530e8 | 0.0451826 | ||||||||
\(499\) | 1.60143e9 | 0.576972 | 0.288486 | − | 0.957484i | \(-0.406848\pi\) | ||||
0.288486 | + | 0.957484i | \(0.406848\pi\) | |||||||
\(500\) | −4.02198e8 | −0.143895 | ||||||||
\(501\) | −1.84068e9 | −0.653953 | ||||||||
\(502\) | 3.48034e9 | 1.22789 | ||||||||
\(503\) | −2.26818e9 | −0.794675 | −0.397337 | − | 0.917673i | \(-0.630066\pi\) | ||||
−0.397337 | + | 0.917673i | \(0.630066\pi\) | |||||||
\(504\) | 9.41176e8 | 0.327464 | ||||||||
\(505\) | −3.12506e8 | −0.107979 | ||||||||
\(506\) | 5.11302e9 | 1.75449 | ||||||||
\(507\) | −1.01728e8 | −0.0346667 | ||||||||
\(508\) | 1.76862e8 | 0.0598564 | ||||||||
\(509\) | −5.34607e9 | −1.79689 | −0.898447 | − | 0.439083i | \(-0.855303\pi\) | ||||
−0.898447 | + | 0.439083i | \(0.855303\pi\) | |||||||
\(510\) | 3.41355e8 | 0.113949 | ||||||||
\(511\) | 2.70853e8 | 0.0897968 | ||||||||
\(512\) | 2.65061e9 | 0.872773 | ||||||||
\(513\) | −3.31154e9 | −1.08298 | ||||||||
\(514\) | 3.47720e9 | 1.12943 | ||||||||
\(515\) | 5.34391e8 | 0.172399 | ||||||||
\(516\) | 3.04046e8 | 0.0974239 | ||||||||
\(517\) | −3.09077e9 | −0.983670 | ||||||||
\(518\) | 1.21676e8 | 0.0384636 | ||||||||
\(519\) | −6.70936e8 | −0.210667 | ||||||||
\(520\) | 1.90265e8 | 0.0593400 | ||||||||
\(521\) | 1.81151e9 | 0.561190 | 0.280595 | − | 0.959826i | \(-0.409468\pi\) | ||||
0.280595 | + | 0.959826i | \(0.409468\pi\) | |||||||
\(522\) | −3.45543e9 | −1.06330 | ||||||||
\(523\) | −1.49653e9 | −0.457435 | −0.228717 | − | 0.973493i | \(-0.573453\pi\) | ||||
−0.228717 | + | 0.973493i | \(0.573453\pi\) | |||||||
\(524\) | −2.07691e9 | −0.630605 | ||||||||
\(525\) | −5.42890e8 | −0.163740 | ||||||||
\(526\) | 8.73630e8 | 0.261745 | ||||||||
\(527\) | −2.34312e9 | −0.697360 | ||||||||
\(528\) | −1.06423e9 | −0.314642 | ||||||||
\(529\) | 4.76582e9 | 1.39973 | ||||||||
\(530\) | 5.68631e8 | 0.165907 | ||||||||
\(531\) | 3.82800e9 | 1.10953 | ||||||||
\(532\) | −6.54453e8 | −0.188446 | ||||||||
\(533\) | −8.33328e8 | −0.238381 | ||||||||
\(534\) | −1.49042e9 | −0.423560 | ||||||||
\(535\) | −1.27994e8 | −0.0361371 | ||||||||
\(536\) | 3.39792e9 | 0.953095 | ||||||||
\(537\) | 2.30952e8 | 0.0643594 | ||||||||
\(538\) | −3.61119e9 | −0.999798 | ||||||||
\(539\) | −7.42738e8 | −0.204303 | ||||||||
\(540\) | 2.17403e8 | 0.0594137 | ||||||||
\(541\) | 2.25044e9 | 0.611052 | 0.305526 | − | 0.952184i | \(-0.401168\pi\) | ||||
0.305526 | + | 0.952184i | \(0.401168\pi\) | |||||||
\(542\) | −4.56554e8 | −0.123167 | ||||||||
\(543\) | 2.13072e9 | 0.571119 | ||||||||
\(544\) | 4.26779e9 | 1.13660 | ||||||||
\(545\) | 9.42239e8 | 0.249329 | ||||||||
\(546\) | 1.42301e8 | 0.0374138 | ||||||||
\(547\) | 4.26901e9 | 1.11525 | 0.557624 | − | 0.830094i | \(-0.311713\pi\) | ||||
0.557624 | + | 0.830094i | \(0.311713\pi\) | |||||||
\(548\) | −2.66835e9 | −0.692645 | ||||||||
\(549\) | −3.54664e9 | −0.914774 | ||||||||
\(550\) | −4.24801e9 | −1.08872 | ||||||||
\(551\) | 8.84759e9 | 2.25317 | ||||||||
\(552\) | −2.99940e9 | −0.759009 | ||||||||
\(553\) | 2.26355e9 | 0.569182 | ||||||||
\(554\) | 7.53910e8 | 0.188380 | ||||||||
\(555\) | 4.58980e7 | 0.0113964 | ||||||||
\(556\) | −7.71793e8 | −0.190432 | ||||||||
\(557\) | 2.19978e9 | 0.539369 | 0.269685 | − | 0.962949i | \(-0.413081\pi\) | ||||
0.269685 | + | 0.962949i | \(0.413081\pi\) | |||||||
\(558\) | 1.11334e9 | 0.271274 | ||||||||
\(559\) | −6.64172e8 | −0.160820 | ||||||||
\(560\) | −1.50905e8 | −0.0363117 | ||||||||
\(561\) | −4.37268e9 | −1.04563 | ||||||||
\(562\) | −5.37817e9 | −1.27808 | ||||||||
\(563\) | 4.69544e9 | 1.10891 | 0.554456 | − | 0.832213i | \(-0.312927\pi\) | ||||
0.554456 | + | 0.832213i | \(0.312927\pi\) | |||||||
\(564\) | 4.92388e8 | 0.115566 | ||||||||
\(565\) | 7.43471e8 | 0.173418 | ||||||||
\(566\) | 5.10692e9 | 1.18386 | ||||||||
\(567\) | −7.08633e8 | −0.163260 | ||||||||
\(568\) | −7.06966e9 | −1.61875 | ||||||||
\(569\) | 6.31379e9 | 1.43680 | 0.718402 | − | 0.695629i | \(-0.244874\pi\) | ||||
0.718402 | + | 0.695629i | \(0.244874\pi\) | |||||||
\(570\) | 4.15301e8 | 0.0939293 | ||||||||
\(571\) | 6.12408e9 | 1.37662 | 0.688311 | − | 0.725416i | \(-0.258352\pi\) | ||||
0.688311 | + | 0.725416i | \(0.258352\pi\) | |||||||
\(572\) | −6.61889e8 | −0.147876 | ||||||||
\(573\) | −1.06557e8 | −0.0236613 | ||||||||
\(574\) | 1.16569e9 | 0.257271 | ||||||||
\(575\) | −6.78836e9 | −1.48911 | ||||||||
\(576\) | −3.81216e9 | −0.831175 | ||||||||
\(577\) | −3.41672e9 | −0.740446 | −0.370223 | − | 0.928943i | \(-0.620719\pi\) | ||||
−0.370223 | + | 0.928943i | \(0.620719\pi\) | |||||||
\(578\) | −6.00040e9 | −1.29251 | ||||||||
\(579\) | −1.63717e9 | −0.350526 | ||||||||
\(580\) | −5.80845e8 | −0.123612 | ||||||||
\(581\) | −2.26196e8 | −0.0478486 | ||||||||
\(582\) | 6.27611e8 | 0.131965 | ||||||||
\(583\) | −7.28404e9 | −1.52241 | ||||||||
\(584\) | −1.24327e9 | −0.258297 | ||||||||
\(585\) | −2.10614e8 | −0.0434951 | ||||||||
\(586\) | −3.15307e9 | −0.647280 | ||||||||
\(587\) | 4.56212e9 | 0.930964 | 0.465482 | − | 0.885057i | \(-0.345881\pi\) | ||||
0.465482 | + | 0.885057i | \(0.345881\pi\) | |||||||
\(588\) | 1.18325e8 | 0.0240025 | ||||||||
\(589\) | −2.85070e9 | −0.574841 | ||||||||
\(590\) | −1.08249e9 | −0.216992 | ||||||||
\(591\) | 2.65570e9 | 0.529204 | ||||||||
\(592\) | −3.16676e8 | −0.0627321 | ||||||||
\(593\) | 7.49087e9 | 1.47517 | 0.737583 | − | 0.675256i | \(-0.235967\pi\) | ||||
0.737583 | + | 0.675256i | \(0.235967\pi\) | |||||||
\(594\) | 4.68492e9 | 0.917169 | ||||||||
\(595\) | −6.20037e8 | −0.120672 | ||||||||
\(596\) | −2.42291e9 | −0.468786 | ||||||||
\(597\) | 3.26676e9 | 0.628358 | ||||||||
\(598\) | 1.77934e9 | 0.340256 | ||||||||
\(599\) | 1.23635e9 | 0.235043 | 0.117521 | − | 0.993070i | \(-0.462505\pi\) | ||||
0.117521 | + | 0.993070i | \(0.462505\pi\) | |||||||
\(600\) | 2.49197e9 | 0.470991 | ||||||||
\(601\) | −5.00324e9 | −0.940135 | −0.470068 | − | 0.882630i | \(-0.655770\pi\) | ||||
−0.470068 | + | 0.882630i | \(0.655770\pi\) | |||||||
\(602\) | 9.29066e8 | 0.173564 | ||||||||
\(603\) | −3.76132e9 | −0.698601 | ||||||||
\(604\) | 3.64783e9 | 0.673605 | ||||||||
\(605\) | −1.12040e9 | −0.205697 | ||||||||
\(606\) | 1.07284e9 | 0.195832 | ||||||||
\(607\) | −2.75374e9 | −0.499761 | −0.249881 | − | 0.968277i | \(-0.580391\pi\) | ||||
−0.249881 | + | 0.968277i | \(0.580391\pi\) | |||||||
\(608\) | 5.19230e9 | 0.936909 | ||||||||
\(609\) | −1.59964e9 | −0.286987 | ||||||||
\(610\) | 1.00293e9 | 0.178903 | ||||||||
\(611\) | −1.07560e9 | −0.190768 | ||||||||
\(612\) | −2.73325e9 | −0.482002 | ||||||||
\(613\) | 5.52898e9 | 0.969468 | 0.484734 | − | 0.874662i | \(-0.338916\pi\) | ||||
0.484734 | + | 0.874662i | \(0.338916\pi\) | |||||||
\(614\) | −5.78238e9 | −1.00813 | ||||||||
\(615\) | 4.39715e8 | 0.0762269 | ||||||||
\(616\) | 3.40931e9 | 0.587670 | ||||||||
\(617\) | −7.43691e8 | −0.127466 | −0.0637330 | − | 0.997967i | \(-0.520301\pi\) | ||||
−0.0637330 | + | 0.997967i | \(0.520301\pi\) | |||||||
\(618\) | −1.83458e9 | −0.312664 | ||||||||
\(619\) | −2.46617e9 | −0.417932 | −0.208966 | − | 0.977923i | \(-0.567010\pi\) | ||||
−0.208966 | + | 0.977923i | \(0.567010\pi\) | |||||||
\(620\) | 1.87149e8 | 0.0315367 | ||||||||
\(621\) | 7.48654e9 | 1.25447 | ||||||||
\(622\) | −3.40170e9 | −0.566800 | ||||||||
\(623\) | 2.70720e9 | 0.448552 | ||||||||
\(624\) | −3.70354e8 | −0.0610199 | ||||||||
\(625\) | 5.40355e9 | 0.885318 | ||||||||
\(626\) | 6.04986e9 | 0.985678 | ||||||||
\(627\) | −5.31991e9 | −0.861922 | ||||||||
\(628\) | 3.33349e9 | 0.537081 | ||||||||
\(629\) | −1.30115e9 | −0.208473 | ||||||||
\(630\) | 2.94613e8 | 0.0469418 | ||||||||
\(631\) | 3.59113e9 | 0.569020 | 0.284510 | − | 0.958673i | \(-0.408169\pi\) | ||||
0.284510 | + | 0.958673i | \(0.408169\pi\) | |||||||
\(632\) | −1.03901e10 | −1.63723 | ||||||||
\(633\) | −2.26332e9 | −0.354677 | ||||||||
\(634\) | −6.65586e9 | −1.03727 | ||||||||
\(635\) | 2.03859e8 | 0.0315953 | ||||||||
\(636\) | 1.16041e9 | 0.178860 | ||||||||
\(637\) | −2.58475e8 | −0.0396214 | ||||||||
\(638\) | −1.25169e10 | −1.90820 | ||||||||
\(639\) | 7.82575e9 | 1.18651 | ||||||||
\(640\) | 1.63696e8 | 0.0246835 | ||||||||
\(641\) | −1.01250e10 | −1.51841 | −0.759207 | − | 0.650849i | \(-0.774413\pi\) | ||||
−0.759207 | + | 0.650849i | \(0.774413\pi\) | |||||||
\(642\) | 4.39409e8 | 0.0655385 | ||||||||
\(643\) | −3.41022e9 | −0.505876 | −0.252938 | − | 0.967483i | \(-0.581397\pi\) | ||||
−0.252938 | + | 0.967483i | \(0.581397\pi\) | |||||||
\(644\) | 1.47955e9 | 0.218288 | ||||||||
\(645\) | 3.50458e8 | 0.0514253 | ||||||||
\(646\) | −1.17733e10 | −1.71824 | ||||||||
\(647\) | 7.62526e9 | 1.10685 | 0.553426 | − | 0.832898i | \(-0.313320\pi\) | ||||
0.553426 | + | 0.832898i | \(0.313320\pi\) | |||||||
\(648\) | 3.25276e9 | 0.469612 | ||||||||
\(649\) | 1.38665e10 | 1.99118 | ||||||||
\(650\) | −1.47832e9 | −0.211140 | ||||||||
\(651\) | 5.15407e8 | 0.0732178 | ||||||||
\(652\) | −7.17721e8 | −0.101412 | ||||||||
\(653\) | −8.05772e8 | −0.113244 | −0.0566221 | − | 0.998396i | \(-0.518033\pi\) | ||||
−0.0566221 | + | 0.998396i | \(0.518033\pi\) | |||||||
\(654\) | −3.23474e9 | −0.452186 | ||||||||
\(655\) | −2.39394e9 | −0.332866 | ||||||||
\(656\) | −3.03384e9 | −0.419594 | ||||||||
\(657\) | 1.37623e9 | 0.189327 | ||||||||
\(658\) | 1.50458e9 | 0.205885 | ||||||||
\(659\) | −1.78678e8 | −0.0243205 | −0.0121602 | − | 0.999926i | \(-0.503871\pi\) | ||||
−0.0121602 | + | 0.999926i | \(0.503871\pi\) | |||||||
\(660\) | 3.49253e8 | 0.0472864 | ||||||||
\(661\) | 7.73824e9 | 1.04217 | 0.521083 | − | 0.853506i | \(-0.325528\pi\) | ||||
0.521083 | + | 0.853506i | \(0.325528\pi\) | |||||||
\(662\) | 4.05205e9 | 0.542839 | ||||||||
\(663\) | −1.52170e9 | −0.202784 | ||||||||
\(664\) | 1.03828e9 | 0.137635 | ||||||||
\(665\) | −7.54353e8 | −0.0994716 | ||||||||
\(666\) | 6.18247e8 | 0.0810966 | ||||||||
\(667\) | −2.00021e10 | −2.60997 | ||||||||
\(668\) | −4.16779e9 | −0.540989 | ||||||||
\(669\) | 1.14496e9 | 0.147842 | ||||||||
\(670\) | 1.06364e9 | 0.136626 | ||||||||
\(671\) | −1.28473e10 | −1.64166 | ||||||||
\(672\) | −9.38769e8 | −0.119335 | ||||||||
\(673\) | 2.14358e9 | 0.271073 | 0.135537 | − | 0.990772i | \(-0.456724\pi\) | ||||
0.135537 | + | 0.990772i | \(0.456724\pi\) | |||||||
\(674\) | 6.22995e8 | 0.0783746 | ||||||||
\(675\) | −6.21999e9 | −0.778443 | ||||||||
\(676\) | −2.30339e8 | −0.0286784 | ||||||||
\(677\) | −5.36251e8 | −0.0664214 | −0.0332107 | − | 0.999448i | \(-0.510573\pi\) | ||||
−0.0332107 | + | 0.999448i | \(0.510573\pi\) | |||||||
\(678\) | −2.55236e9 | −0.314513 | ||||||||
\(679\) | −1.13999e9 | −0.139752 | ||||||||
\(680\) | 2.84609e9 | 0.347110 | ||||||||
\(681\) | 5.10863e9 | 0.619854 | ||||||||
\(682\) | 4.03296e9 | 0.486832 | ||||||||
\(683\) | 1.21466e10 | 1.45875 | 0.729377 | − | 0.684112i | \(-0.239810\pi\) | ||||
0.729377 | + | 0.684112i | \(0.239810\pi\) | |||||||
\(684\) | −3.32534e9 | −0.397319 | ||||||||
\(685\) | −3.07567e9 | −0.365614 | ||||||||
\(686\) | 3.61563e8 | 0.0427612 | ||||||||
\(687\) | 2.15748e9 | 0.253863 | ||||||||
\(688\) | −2.41801e9 | −0.283073 | ||||||||
\(689\) | −2.53487e9 | −0.295248 | ||||||||
\(690\) | −9.38890e8 | −0.108804 | ||||||||
\(691\) | −1.22397e10 | −1.41123 | −0.705615 | − | 0.708595i | \(-0.749329\pi\) | ||||
−0.705615 | + | 0.708595i | \(0.749329\pi\) | |||||||
\(692\) | −1.51918e9 | −0.174276 | ||||||||
\(693\) | −3.77393e9 | −0.430752 | ||||||||
\(694\) | 9.14690e9 | 1.03876 | ||||||||
\(695\) | −8.89605e8 | −0.100520 | ||||||||
\(696\) | 7.34267e9 | 0.825508 | ||||||||
\(697\) | −1.24654e10 | −1.39441 | ||||||||
\(698\) | −5.10649e9 | −0.568367 | ||||||||
\(699\) | −4.81884e9 | −0.533670 | ||||||||
\(700\) | −1.22924e9 | −0.135455 | ||||||||
\(701\) | 1.38399e10 | 1.51746 | 0.758732 | − | 0.651403i | \(-0.225819\pi\) | ||||
0.758732 | + | 0.651403i | \(0.225819\pi\) | |||||||
\(702\) | 1.63036e9 | 0.177871 | ||||||||
\(703\) | −1.58302e9 | −0.171847 | ||||||||
\(704\) | −1.38091e10 | −1.49163 | ||||||||
\(705\) | 5.67550e8 | 0.0610017 | ||||||||
\(706\) | 5.30899e8 | 0.0567800 | ||||||||
\(707\) | −1.94872e9 | −0.207387 | ||||||||
\(708\) | −2.20906e9 | −0.233933 | ||||||||
\(709\) | 9.16180e9 | 0.965426 | 0.482713 | − | 0.875779i | \(-0.339651\pi\) | ||||
0.482713 | + | 0.875779i | \(0.339651\pi\) | |||||||
\(710\) | −2.21299e9 | −0.232047 | ||||||||
\(711\) | 1.15013e10 | 1.20006 | ||||||||
\(712\) | −1.24266e10 | −1.29024 | ||||||||
\(713\) | 6.44471e9 | 0.665871 | ||||||||
\(714\) | 2.12861e9 | 0.218853 | ||||||||
\(715\) | −7.62925e8 | −0.0780568 | ||||||||
\(716\) | 5.22937e8 | 0.0532419 | ||||||||
\(717\) | 8.65092e8 | 0.0876486 | ||||||||
\(718\) | 2.24293e9 | 0.226141 | ||||||||
\(719\) | 1.05119e10 | 1.05470 | 0.527352 | − | 0.849647i | \(-0.323185\pi\) | ||||
0.527352 | + | 0.849647i | \(0.323185\pi\) | |||||||
\(720\) | −7.66766e8 | −0.0765595 | ||||||||
\(721\) | 3.33234e9 | 0.331112 | ||||||||
\(722\) | −6.31470e9 | −0.624414 | ||||||||
\(723\) | 2.81639e9 | 0.277146 | ||||||||
\(724\) | 4.82451e9 | 0.472463 | ||||||||
\(725\) | 1.66182e10 | 1.61958 | ||||||||
\(726\) | 3.84637e9 | 0.373055 | ||||||||
\(727\) | 4.67722e9 | 0.451458 | 0.225729 | − | 0.974190i | \(-0.427524\pi\) | ||||
0.225729 | + | 0.974190i | \(0.427524\pi\) | |||||||
\(728\) | 1.18645e9 | 0.113970 | ||||||||
\(729\) | 2.16898e8 | 0.0207352 | ||||||||
\(730\) | −3.89176e8 | −0.0370267 | ||||||||
\(731\) | −9.93505e9 | −0.940717 | ||||||||
\(732\) | 2.04670e9 | 0.192870 | ||||||||
\(733\) | 4.12754e9 | 0.387103 | 0.193552 | − | 0.981090i | \(-0.437999\pi\) | ||||
0.193552 | + | 0.981090i | \(0.437999\pi\) | |||||||
\(734\) | 1.16066e9 | 0.108335 | ||||||||
\(735\) | 1.36387e8 | 0.0126697 | ||||||||
\(736\) | −1.17385e10 | −1.08527 | ||||||||
\(737\) | −1.36250e10 | −1.25372 | ||||||||
\(738\) | 5.92297e9 | 0.542428 | ||||||||
\(739\) | 1.29359e9 | 0.117907 | 0.0589535 | − | 0.998261i | \(-0.481224\pi\) | ||||
0.0589535 | + | 0.998261i | \(0.481224\pi\) | |||||||
\(740\) | 1.03925e8 | 0.00942779 | ||||||||
\(741\) | −1.85134e9 | −0.167157 | ||||||||
\(742\) | 3.54585e9 | 0.318645 | ||||||||
\(743\) | −9.59715e9 | −0.858383 | −0.429192 | − | 0.903213i | \(-0.641202\pi\) | ||||
−0.429192 | + | 0.903213i | \(0.641202\pi\) | |||||||
\(744\) | −2.36581e9 | −0.210608 | ||||||||
\(745\) | −2.79276e9 | −0.247449 | ||||||||
\(746\) | 8.90755e9 | 0.785547 | ||||||||
\(747\) | −1.14933e9 | −0.100884 | ||||||||
\(748\) | −9.90089e9 | −0.865005 | ||||||||
\(749\) | −7.98143e8 | −0.0694056 | ||||||||
\(750\) | 1.59153e9 | 0.137753 | ||||||||
\(751\) | −1.95130e10 | −1.68106 | −0.840532 | − | 0.541762i | \(-0.817757\pi\) | ||||
−0.840532 | + | 0.541762i | \(0.817757\pi\) | |||||||
\(752\) | −3.91585e9 | −0.335787 | ||||||||
\(753\) | 8.18655e9 | 0.698744 | ||||||||
\(754\) | −4.35592e9 | −0.370067 | ||||||||
\(755\) | 4.20466e9 | 0.355563 | ||||||||
\(756\) | 1.35567e9 | 0.114111 | ||||||||
\(757\) | 1.68500e10 | 1.41177 | 0.705886 | − | 0.708325i | \(-0.250549\pi\) | ||||
0.705886 | + | 0.708325i | \(0.250549\pi\) | |||||||
\(758\) | −7.27282e9 | −0.606542 | ||||||||
\(759\) | 1.20270e10 | 0.998413 | ||||||||
\(760\) | 3.46262e9 | 0.286126 | ||||||||
\(761\) | 1.27730e10 | 1.05062 | 0.525310 | − | 0.850911i | \(-0.323949\pi\) | ||||
0.525310 | + | 0.850911i | \(0.323949\pi\) | |||||||
\(762\) | −6.99855e8 | −0.0573015 | ||||||||
\(763\) | 5.87559e9 | 0.478867 | ||||||||
\(764\) | −2.41272e8 | −0.0195741 | ||||||||
\(765\) | −3.15047e9 | −0.254425 | ||||||||
\(766\) | 9.46059e9 | 0.760532 | ||||||||
\(767\) | 4.82558e9 | 0.386159 | ||||||||
\(768\) | 5.33881e9 | 0.425285 | ||||||||
\(769\) | 1.00489e9 | 0.0796851 | 0.0398426 | − | 0.999206i | \(-0.487314\pi\) | ||||
0.0398426 | + | 0.999206i | \(0.487314\pi\) | |||||||
\(770\) | 1.06720e9 | 0.0842422 | ||||||||
\(771\) | 8.17917e9 | 0.642715 | ||||||||
\(772\) | −3.70699e9 | −0.289976 | ||||||||
\(773\) | −1.07528e10 | −0.837323 | −0.418661 | − | 0.908142i | \(-0.637501\pi\) | ||||
−0.418661 | + | 0.908142i | \(0.637501\pi\) | |||||||
\(774\) | 4.72068e9 | 0.365941 | ||||||||
\(775\) | −5.35441e9 | −0.413196 | ||||||||
\(776\) | 5.23278e9 | 0.401991 | ||||||||
\(777\) | 2.86209e8 | 0.0218882 | ||||||||
\(778\) | −2.60203e9 | −0.198100 | ||||||||
\(779\) | −1.51657e10 | −1.14943 | ||||||||
\(780\) | 1.21541e8 | 0.00917047 | ||||||||
\(781\) | 2.83479e10 | 2.12933 | ||||||||
\(782\) | 2.66164e10 | 1.99033 | ||||||||
\(783\) | −1.83274e10 | −1.36438 | ||||||||
\(784\) | −9.41011e8 | −0.0697411 | ||||||||
\(785\) | 3.84234e9 | 0.283499 | ||||||||
\(786\) | 8.21848e9 | 0.603688 | ||||||||
\(787\) | 2.22554e10 | 1.62751 | 0.813755 | − | 0.581208i | \(-0.197420\pi\) | ||||
0.813755 | + | 0.581208i | \(0.197420\pi\) | |||||||
\(788\) | 6.01321e9 | 0.437789 | ||||||||
\(789\) | 2.05498e9 | 0.148949 | ||||||||
\(790\) | −3.25238e9 | −0.234696 | ||||||||
\(791\) | 4.63611e9 | 0.333071 | ||||||||
\(792\) | 1.73230e10 | 1.23904 | ||||||||
\(793\) | −4.47090e9 | −0.318375 | ||||||||
\(794\) | −4.56152e9 | −0.323398 | ||||||||
\(795\) | 1.33755e9 | 0.0944115 | ||||||||
\(796\) | 7.39680e9 | 0.519814 | ||||||||
\(797\) | −2.35507e10 | −1.64778 | −0.823892 | − | 0.566746i | \(-0.808202\pi\) | ||||
−0.823892 | + | 0.566746i | \(0.808202\pi\) | |||||||
\(798\) | 2.58972e9 | 0.180403 | ||||||||
\(799\) | −1.60893e10 | −1.11590 | ||||||||
\(800\) | 9.75260e9 | 0.673450 | ||||||||
\(801\) | 1.37556e10 | 0.945725 | ||||||||
\(802\) | −1.21979e10 | −0.834976 | ||||||||
\(803\) | 4.98525e9 | 0.339768 | ||||||||
\(804\) | 2.17058e9 | 0.147292 | ||||||||
\(805\) | 1.70540e9 | 0.115223 | ||||||||
\(806\) | 1.40348e9 | 0.0944135 | ||||||||
\(807\) | −8.49434e9 | −0.568947 | ||||||||
\(808\) | 8.94498e9 | 0.596540 | ||||||||
\(809\) | 1.02800e9 | 0.0682611 | 0.0341306 | − | 0.999417i | \(-0.489134\pi\) | ||||
0.0341306 | + | 0.999417i | \(0.489134\pi\) | |||||||
\(810\) | 1.01820e9 | 0.0673186 | ||||||||
\(811\) | −1.89814e9 | −0.124956 | −0.0624778 | − | 0.998046i | \(-0.519900\pi\) | ||||
−0.0624778 | + | 0.998046i | \(0.519900\pi\) | |||||||
\(812\) | −3.62201e9 | −0.237413 | ||||||||
\(813\) | −1.07392e9 | −0.0700897 | ||||||||
\(814\) | 2.23953e9 | 0.145537 | ||||||||
\(815\) | −8.27280e8 | −0.0535304 | ||||||||
\(816\) | −5.53996e9 | −0.356937 | ||||||||
\(817\) | −1.20872e10 | −0.775443 | ||||||||
\(818\) | 1.85570e10 | 1.18542 | ||||||||
\(819\) | −1.31334e9 | −0.0835377 | ||||||||
\(820\) | 9.95630e8 | 0.0630593 | ||||||||
\(821\) | −2.48565e9 | −0.156762 | −0.0783808 | − | 0.996923i | \(-0.524975\pi\) | ||||
−0.0783808 | + | 0.996923i | \(0.524975\pi\) | |||||||
\(822\) | 1.05589e10 | 0.663080 | ||||||||
\(823\) | 5.91392e9 | 0.369808 | 0.184904 | − | 0.982757i | \(-0.440803\pi\) | ||||
0.184904 | + | 0.982757i | \(0.440803\pi\) | |||||||
\(824\) | −1.52960e10 | −0.952432 | ||||||||
\(825\) | −9.99228e9 | −0.619549 | ||||||||
\(826\) | −6.75018e9 | −0.416759 | ||||||||
\(827\) | −8.94815e9 | −0.550128 | −0.275064 | − | 0.961426i | \(-0.588699\pi\) | ||||
−0.275064 | + | 0.961426i | \(0.588699\pi\) | |||||||
\(828\) | 7.51775e9 | 0.460237 | ||||||||
\(829\) | 2.96249e10 | 1.80599 | 0.902996 | − | 0.429648i | \(-0.141362\pi\) | ||||
0.902996 | + | 0.429648i | \(0.141362\pi\) | |||||||
\(830\) | 3.25010e8 | 0.0197298 | ||||||||
\(831\) | 1.77337e9 | 0.107200 | ||||||||
\(832\) | −4.80562e9 | −0.289279 | ||||||||
\(833\) | −3.86641e9 | −0.231766 | ||||||||
\(834\) | 3.05404e9 | 0.182303 | ||||||||
\(835\) | −4.80399e9 | −0.285562 | ||||||||
\(836\) | −1.20457e10 | −0.713033 | ||||||||
\(837\) | 5.90511e9 | 0.348088 | ||||||||
\(838\) | 2.30107e10 | 1.35075 | ||||||||
\(839\) | −3.03954e10 | −1.77681 | −0.888404 | − | 0.459063i | \(-0.848185\pi\) | ||||
−0.888404 | + | 0.459063i | \(0.848185\pi\) | |||||||
\(840\) | −6.26043e8 | −0.0364440 | ||||||||
\(841\) | 3.17164e10 | 1.83864 | ||||||||
\(842\) | 4.56207e9 | 0.263372 | ||||||||
\(843\) | −1.26507e10 | −0.727306 | ||||||||
\(844\) | −5.12475e9 | −0.293410 | ||||||||
\(845\) | −2.65500e8 | −0.0151379 | ||||||||
\(846\) | 7.64491e9 | 0.434086 | ||||||||
\(847\) | −6.98654e9 | −0.395067 | ||||||||
\(848\) | −9.22851e9 | −0.519692 | ||||||||
\(849\) | 1.20126e10 | 0.673692 | ||||||||
\(850\) | −2.21135e10 | −1.23507 | ||||||||
\(851\) | 3.57880e9 | 0.199060 | ||||||||
\(852\) | −4.51609e9 | −0.250164 | ||||||||
\(853\) | 3.02337e10 | 1.66790 | 0.833950 | − | 0.551840i | \(-0.186074\pi\) | ||||
0.833950 | + | 0.551840i | \(0.186074\pi\) | |||||||
\(854\) | 6.25404e9 | 0.343604 | ||||||||
\(855\) | −3.83294e9 | −0.209725 | ||||||||
\(856\) | 3.66363e9 | 0.199643 | ||||||||
\(857\) | 6.83987e9 | 0.371206 | 0.185603 | − | 0.982625i | \(-0.440576\pi\) | ||||
0.185603 | + | 0.982625i | \(0.440576\pi\) | |||||||
\(858\) | 2.61915e9 | 0.141564 | ||||||||
\(859\) | 2.91105e9 | 0.156702 | 0.0783509 | − | 0.996926i | \(-0.475035\pi\) | ||||
0.0783509 | + | 0.996926i | \(0.475035\pi\) | |||||||
\(860\) | 7.93529e8 | 0.0425420 | ||||||||
\(861\) | 2.74196e9 | 0.146403 | ||||||||
\(862\) | −2.63821e10 | −1.40292 | ||||||||
\(863\) | −2.34751e10 | −1.24328 | −0.621641 | − | 0.783303i | \(-0.713534\pi\) | ||||
−0.621641 | + | 0.783303i | \(0.713534\pi\) | |||||||
\(864\) | −1.07557e10 | −0.567334 | ||||||||
\(865\) | −1.75108e9 | −0.0919916 | ||||||||
\(866\) | −7.54004e9 | −0.394513 | ||||||||
\(867\) | −1.41143e10 | −0.735517 | ||||||||
\(868\) | 1.16702e9 | 0.0605700 | ||||||||
\(869\) | 4.16623e10 | 2.15364 | ||||||||
\(870\) | 2.29845e9 | 0.118336 | ||||||||
\(871\) | −4.74153e9 | −0.243139 | ||||||||
\(872\) | −2.69700e10 | −1.37744 | ||||||||
\(873\) | −5.79242e9 | −0.294652 | ||||||||
\(874\) | 3.23822e10 | 1.64065 | ||||||||
\(875\) | −2.89086e9 | −0.145881 | ||||||||
\(876\) | −7.94197e8 | −0.0399175 | ||||||||
\(877\) | −2.17287e10 | −1.08777 | −0.543883 | − | 0.839161i | \(-0.683046\pi\) | ||||
−0.543883 | + | 0.839161i | \(0.683046\pi\) | |||||||
\(878\) | 2.79080e10 | 1.39155 | ||||||||
\(879\) | −7.41674e9 | −0.368343 | ||||||||
\(880\) | −2.77753e9 | −0.137394 | ||||||||
\(881\) | −2.61248e10 | −1.28717 | −0.643586 | − | 0.765374i | \(-0.722554\pi\) | ||||
−0.643586 | + | 0.765374i | \(0.722554\pi\) | |||||||
\(882\) | 1.83714e9 | 0.0901574 | ||||||||
\(883\) | −4.27316e9 | −0.208875 | −0.104437 | − | 0.994531i | \(-0.533304\pi\) | ||||
−0.104437 | + | 0.994531i | \(0.533304\pi\) | |||||||
\(884\) | −3.44554e9 | −0.167754 | ||||||||
\(885\) | −2.54627e9 | −0.123482 | ||||||||
\(886\) | −1.26555e10 | −0.611309 | ||||||||
\(887\) | −2.94661e10 | −1.41772 | −0.708859 | − | 0.705350i | \(-0.750790\pi\) | ||||
−0.708859 | + | 0.705350i | \(0.750790\pi\) | |||||||
\(888\) | −1.31376e9 | −0.0629606 | ||||||||
\(889\) | 1.27122e9 | 0.0606826 | ||||||||
\(890\) | −3.88985e9 | −0.184956 | ||||||||
\(891\) | −1.30429e10 | −0.617736 | ||||||||
\(892\) | 2.59249e9 | 0.122304 | ||||||||
\(893\) | −1.95747e10 | −0.919847 | ||||||||
\(894\) | 9.58763e9 | 0.448776 | ||||||||
\(895\) | 6.02762e8 | 0.0281038 | ||||||||
\(896\) | 1.02077e9 | 0.0474077 | ||||||||
\(897\) | 4.18542e9 | 0.193627 | ||||||||
\(898\) | −8.75082e9 | −0.403257 | ||||||||
\(899\) | −1.57770e10 | −0.724210 | ||||||||
\(900\) | −6.24592e9 | −0.285593 | ||||||||
\(901\) | −3.79179e10 | −1.72706 | ||||||||
\(902\) | 2.14553e10 | 0.973447 | ||||||||
\(903\) | 2.18537e9 | 0.0987685 | ||||||||
\(904\) | −2.12806e10 | −0.958065 | ||||||||
\(905\) | 5.56096e9 | 0.249390 | ||||||||
\(906\) | −1.44348e10 | −0.644853 | ||||||||
\(907\) | −5.35206e9 | −0.238175 | −0.119087 | − | 0.992884i | \(-0.537997\pi\) | ||||
−0.119087 | + | 0.992884i | \(0.537997\pi\) | |||||||
\(908\) | 1.15673e10 | 0.512780 | ||||||||
\(909\) | −9.90162e9 | −0.437253 | ||||||||
\(910\) | 3.71390e8 | 0.0163375 | ||||||||
\(911\) | −9.37687e9 | −0.410907 | −0.205454 | − | 0.978667i | \(-0.565867\pi\) | ||||
−0.205454 | + | 0.978667i | \(0.565867\pi\) | |||||||
\(912\) | −6.74006e9 | −0.294227 | ||||||||
\(913\) | −4.16331e9 | −0.181047 | ||||||||
\(914\) | 1.02074e9 | 0.0442186 | ||||||||
\(915\) | 2.35912e9 | 0.101807 | ||||||||
\(916\) | 4.88511e9 | 0.210010 | ||||||||
\(917\) | −1.49281e10 | −0.639309 | ||||||||
\(918\) | 2.43879e10 | 1.04046 | ||||||||
\(919\) | −8.37753e9 | −0.356051 | −0.178025 | − | 0.984026i | \(-0.556971\pi\) | ||||
−0.178025 | + | 0.984026i | \(0.556971\pi\) | |||||||
\(920\) | −7.82811e9 | −0.331436 | ||||||||
\(921\) | −1.36015e10 | −0.573690 | ||||||||
\(922\) | −3.34258e10 | −1.40451 | ||||||||
\(923\) | 9.86516e9 | 0.412951 | ||||||||
\(924\) | 2.17786e9 | 0.0908193 | ||||||||
\(925\) | −2.97335e9 | −0.123523 | ||||||||
\(926\) | −1.96126e10 | −0.811704 | ||||||||
\(927\) | 1.69319e10 | 0.698116 | ||||||||
\(928\) | 2.87364e10 | 1.18036 | ||||||||
\(929\) | −7.25975e9 | −0.297075 | −0.148538 | − | 0.988907i | \(-0.547457\pi\) | ||||
−0.148538 | + | 0.988907i | \(0.547457\pi\) | |||||||
\(930\) | −7.40563e8 | −0.0301906 | ||||||||
\(931\) | −4.70397e9 | −0.191047 | ||||||||
\(932\) | −1.09111e10 | −0.441483 | ||||||||
\(933\) | −8.00157e9 | −0.322544 | ||||||||
\(934\) | 1.80493e10 | 0.724849 | ||||||||
\(935\) | −1.14122e10 | −0.456594 | ||||||||
\(936\) | 6.02846e9 | 0.240293 | ||||||||
\(937\) | −7.83263e9 | −0.311042 | −0.155521 | − | 0.987833i | \(-0.549706\pi\) | ||||
−0.155521 | + | 0.987833i | \(0.549706\pi\) | |||||||
\(938\) | 6.63260e9 | 0.262406 | ||||||||
\(939\) | 1.42306e10 | 0.560912 | ||||||||
\(940\) | 1.28508e9 | 0.0504642 | ||||||||
\(941\) | 5.59550e9 | 0.218915 | 0.109457 | − | 0.993991i | \(-0.465089\pi\) | ||||
0.109457 | + | 0.993991i | \(0.465089\pi\) | |||||||
\(942\) | −1.31909e10 | −0.514157 | ||||||||
\(943\) | 3.42858e10 | 1.33145 | ||||||||
\(944\) | 1.75682e10 | 0.679711 | ||||||||
\(945\) | 1.56261e9 | 0.0602338 | ||||||||
\(946\) | 1.71001e10 | 0.656721 | ||||||||
\(947\) | 2.79447e10 | 1.06924 | 0.534620 | − | 0.845093i | \(-0.320455\pi\) | ||||
0.534620 | + | 0.845093i | \(0.320455\pi\) | |||||||
\(948\) | −6.63718e9 | −0.253020 | ||||||||
\(949\) | 1.73488e9 | 0.0658928 | ||||||||
\(950\) | −2.69039e10 | −1.01808 | ||||||||
\(951\) | −1.56561e10 | −0.590271 | ||||||||
\(952\) | 1.77475e10 | 0.666667 | ||||||||
\(953\) | −1.05088e10 | −0.393304 | −0.196652 | − | 0.980473i | \(-0.563007\pi\) | ||||
−0.196652 | + | 0.980473i | \(0.563007\pi\) | |||||||
\(954\) | 1.80168e10 | 0.671829 | ||||||||
\(955\) | −2.78102e8 | −0.0103322 | ||||||||
\(956\) | 1.95880e9 | 0.0725081 | ||||||||
\(957\) | −2.94426e10 | −1.08589 | ||||||||
\(958\) | −1.74437e10 | −0.641001 | ||||||||
\(959\) | −1.91791e10 | −0.702205 | ||||||||
\(960\) | 2.53574e9 | 0.0925028 | ||||||||
\(961\) | −2.24293e10 | −0.815236 | ||||||||
\(962\) | 7.79364e8 | 0.0282246 | ||||||||
\(963\) | −4.05545e9 | −0.146334 | ||||||||
\(964\) | 6.37704e9 | 0.229271 | ||||||||
\(965\) | −4.27286e9 | −0.153064 | ||||||||
\(966\) | −5.85470e9 | −0.208970 | ||||||||
\(967\) | −1.23602e10 | −0.439575 | −0.219788 | − | 0.975548i | \(-0.570536\pi\) | ||||
−0.219788 | + | 0.975548i | \(0.570536\pi\) | |||||||
\(968\) | 3.20696e10 | 1.13639 | ||||||||
\(969\) | −2.76934e10 | −0.977784 | ||||||||
\(970\) | 1.63800e9 | 0.0576252 | ||||||||
\(971\) | 1.64550e10 | 0.576806 | 0.288403 | − | 0.957509i | \(-0.406876\pi\) | ||||
0.288403 | + | 0.957509i | \(0.406876\pi\) | |||||||
\(972\) | 1.07218e10 | 0.374485 | ||||||||
\(973\) | −5.54737e9 | −0.193060 | ||||||||
\(974\) | 9.17718e9 | 0.318239 | ||||||||
\(975\) | −3.47734e9 | −0.120152 | ||||||||
\(976\) | −1.62769e10 | −0.560399 | ||||||||
\(977\) | 1.77865e10 | 0.610182 | 0.305091 | − | 0.952323i | \(-0.401313\pi\) | ||||
0.305091 | + | 0.952323i | \(0.401313\pi\) | |||||||
\(978\) | 2.84008e9 | 0.0970833 | ||||||||
\(979\) | 4.98281e10 | 1.69721 | ||||||||
\(980\) | 3.08816e8 | 0.0104811 | ||||||||
\(981\) | 2.98544e10 | 1.00964 | ||||||||
\(982\) | 2.50783e10 | 0.845099 | ||||||||
\(983\) | 8.74911e9 | 0.293783 | 0.146892 | − | 0.989153i | \(-0.453073\pi\) | ||||
0.146892 | + | 0.989153i | \(0.453073\pi\) | |||||||
\(984\) | −1.25861e10 | −0.421123 | ||||||||
\(985\) | 6.93111e9 | 0.231087 | ||||||||
\(986\) | −6.51582e10 | −2.16471 | ||||||||
\(987\) | 3.53911e9 | 0.117161 | ||||||||
\(988\) | −4.19193e9 | −0.138282 | ||||||||
\(989\) | 2.73262e10 | 0.898239 | ||||||||
\(990\) | 5.42257e9 | 0.177616 | ||||||||
\(991\) | −3.28407e10 | −1.07190 | −0.535951 | − | 0.844249i | \(-0.680047\pi\) | ||||
−0.535951 | + | 0.844249i | \(0.680047\pi\) | |||||||
\(992\) | −9.25889e9 | −0.301140 | ||||||||
\(993\) | 9.53133e9 | 0.308909 | ||||||||
\(994\) | −1.37997e10 | −0.445674 | ||||||||
\(995\) | 8.52590e9 | 0.274385 | ||||||||
\(996\) | 6.63254e8 | 0.0212702 | ||||||||
\(997\) | 2.19468e10 | 0.701356 | 0.350678 | − | 0.936496i | \(-0.385951\pi\) | ||||
0.350678 | + | 0.936496i | \(0.385951\pi\) | |||||||
\(998\) | −1.43486e10 | −0.456932 | ||||||||
\(999\) | 3.27916e9 | 0.104060 |
(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 | 91.8.a.d.1.4 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
91.8.a.d.1.4 | ✓ | 10 | 1.1 | even | 1 | trivial |