Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,70,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 70, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 70);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 70 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(30.1514953292\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots - 94\!\cdots\!36 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{43}\cdot 3^{17}\cdot 5^{5}\cdot 7^{2}\cdot 17\cdot 23 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-8.63045e7\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.12545e10 | 0.874816 | 0.437408 | − | 0.899263i | \(-0.355896\pi\) | ||||
0.437408 | + | 0.899263i | \(0.355896\pi\) | |||||||
\(3\) | 3.67245e16 | 1.27137 | 0.635687 | − | 0.771947i | \(-0.280717\pi\) | ||||
0.635687 | + | 0.771947i | \(0.280717\pi\) | |||||||
\(4\) | −1.38540e20 | −0.234696 | ||||||||
\(5\) | −2.01597e24 | −1.54889 | −0.774444 | − | 0.632643i | \(-0.781970\pi\) | ||||
−0.774444 | + | 0.632643i | \(0.781970\pi\) | |||||||
\(6\) | 7.80563e26 | 1.11222 | ||||||||
\(7\) | 2.05778e29 | 1.43720 | 0.718600 | − | 0.695423i | \(-0.244783\pi\) | ||||
0.718600 | + | 0.695423i | \(0.244783\pi\) | |||||||
\(8\) | −1.54911e31 | −1.08013 | ||||||||
\(9\) | 5.14307e32 | 0.616390 | ||||||||
\(10\) | −4.28486e34 | −1.35499 | ||||||||
\(11\) | −1.09142e36 | −1.28808 | −0.644040 | − | 0.764991i | \(-0.722743\pi\) | ||||
−0.644040 | + | 0.764991i | \(0.722743\pi\) | |||||||
\(12\) | −5.08782e36 | −0.298386 | ||||||||
\(13\) | −2.46650e37 | −0.0914186 | −0.0457093 | − | 0.998955i | \(-0.514555\pi\) | ||||
−0.0457093 | + | 0.998955i | \(0.514555\pi\) | |||||||
\(14\) | 4.37373e39 | 1.25729 | ||||||||
\(15\) | −7.40358e40 | −1.96921 | ||||||||
\(16\) | −2.47476e41 | −0.710222 | ||||||||
\(17\) | −2.55025e42 | −0.903846 | −0.451923 | − | 0.892057i | \(-0.649262\pi\) | ||||
−0.451923 | + | 0.892057i | \(0.649262\pi\) | |||||||
\(18\) | 1.09314e43 | 0.539228 | ||||||||
\(19\) | −1.09623e44 | −0.837344 | −0.418672 | − | 0.908138i | \(-0.637504\pi\) | ||||
−0.418672 | + | 0.908138i | \(0.637504\pi\) | |||||||
\(20\) | 2.79293e44 | 0.363518 | ||||||||
\(21\) | 7.55712e45 | 1.82722 | ||||||||
\(22\) | −2.31976e46 | −1.12683 | ||||||||
\(23\) | −8.34028e45 | −0.0874118 | −0.0437059 | − | 0.999044i | \(-0.513916\pi\) | ||||
−0.0437059 | + | 0.999044i | \(0.513916\pi\) | |||||||
\(24\) | −5.68903e47 | −1.37325 | ||||||||
\(25\) | 2.37009e48 | 1.39905 | ||||||||
\(26\) | −5.24243e47 | −0.0799745 | ||||||||
\(27\) | −1.17547e49 | −0.487711 | ||||||||
\(28\) | −2.85086e49 | −0.337305 | ||||||||
\(29\) | −4.43119e49 | −0.156239 | −0.0781195 | − | 0.996944i | \(-0.524892\pi\) | ||||
−0.0781195 | + | 0.996944i | \(0.524892\pi\) | |||||||
\(30\) | −1.57360e51 | −1.72270 | ||||||||
\(31\) | −2.07006e51 | −0.731147 | −0.365573 | − | 0.930783i | \(-0.619127\pi\) | ||||
−0.365573 | + | 0.930783i | \(0.619127\pi\) | |||||||
\(32\) | 3.88433e51 | 0.458819 | ||||||||
\(33\) | −4.00818e52 | −1.63763 | ||||||||
\(34\) | −5.42044e52 | −0.790700 | ||||||||
\(35\) | −4.14844e53 | −2.22606 | ||||||||
\(36\) | −7.12521e52 | −0.144664 | ||||||||
\(37\) | 2.01350e54 | 1.58852 | 0.794261 | − | 0.607577i | \(-0.207858\pi\) | ||||
0.794261 | + | 0.607577i | \(0.207858\pi\) | |||||||
\(38\) | −2.32999e54 | −0.732522 | ||||||||
\(39\) | −9.05809e53 | −0.116227 | ||||||||
\(40\) | 3.12296e55 | 1.67300 | ||||||||
\(41\) | −1.70767e55 | −0.390266 | −0.195133 | − | 0.980777i | \(-0.562514\pi\) | ||||
−0.195133 | + | 0.980777i | \(0.562514\pi\) | |||||||
\(42\) | 1.60623e56 | 1.59848 | ||||||||
\(43\) | −1.46418e55 | −0.0647044 | −0.0323522 | − | 0.999477i | \(-0.510300\pi\) | ||||
−0.0323522 | + | 0.999477i | \(0.510300\pi\) | |||||||
\(44\) | 1.51205e56 | 0.302308 | ||||||||
\(45\) | −1.03683e57 | −0.954719 | ||||||||
\(46\) | −1.77269e56 | −0.0764693 | ||||||||
\(47\) | −7.82219e57 | −1.60676 | −0.803382 | − | 0.595464i | \(-0.796968\pi\) | ||||
−0.803382 | + | 0.595464i | \(0.796968\pi\) | |||||||
\(48\) | −9.08845e57 | −0.902957 | ||||||||
\(49\) | 2.18442e58 | 1.06555 | ||||||||
\(50\) | 5.03751e58 | 1.22391 | ||||||||
\(51\) | −9.36567e58 | −1.14913 | ||||||||
\(52\) | 3.41709e57 | 0.0214556 | ||||||||
\(53\) | 4.83946e59 | 1.57500 | 0.787498 | − | 0.616317i | \(-0.211376\pi\) | ||||
0.787498 | + | 0.616317i | \(0.211376\pi\) | |||||||
\(54\) | −2.49841e59 | −0.426658 | ||||||||
\(55\) | 2.20027e60 | 1.99509 | ||||||||
\(56\) | −3.18773e60 | −1.55237 | ||||||||
\(57\) | −4.02587e60 | −1.06458 | ||||||||
\(58\) | −9.41829e59 | −0.136680 | ||||||||
\(59\) | −1.34248e61 | −1.08023 | −0.540113 | − | 0.841592i | \(-0.681619\pi\) | ||||
−0.540113 | + | 0.841592i | \(0.681619\pi\) | |||||||
\(60\) | 1.02569e61 | 0.462167 | ||||||||
\(61\) | 3.06698e61 | 0.781326 | 0.390663 | − | 0.920534i | \(-0.372246\pi\) | ||||
0.390663 | + | 0.920534i | \(0.372246\pi\) | |||||||
\(62\) | −4.39982e61 | −0.639619 | ||||||||
\(63\) | 1.05833e62 | 0.885876 | ||||||||
\(64\) | 2.28644e62 | 1.11160 | ||||||||
\(65\) | 4.97239e61 | 0.141597 | ||||||||
\(66\) | −8.51920e62 | −1.43263 | ||||||||
\(67\) | 5.79237e62 | 0.579796 | 0.289898 | − | 0.957057i | \(-0.406379\pi\) | ||||
0.289898 | + | 0.957057i | \(0.406379\pi\) | |||||||
\(68\) | 3.53312e62 | 0.212129 | ||||||||
\(69\) | −3.06293e62 | −0.111133 | ||||||||
\(70\) | −8.81732e63 | −1.94740 | ||||||||
\(71\) | 5.96461e63 | 0.807549 | 0.403775 | − | 0.914859i | \(-0.367698\pi\) | ||||
0.403775 | + | 0.914859i | \(0.367698\pi\) | |||||||
\(72\) | −7.96717e63 | −0.665783 | ||||||||
\(73\) | −2.58846e63 | −0.134401 | −0.0672004 | − | 0.997739i | \(-0.521407\pi\) | ||||
−0.0672004 | + | 0.997739i | \(0.521407\pi\) | |||||||
\(74\) | 4.27961e64 | 1.38966 | ||||||||
\(75\) | 8.70404e64 | 1.77872 | ||||||||
\(76\) | 1.51872e64 | 0.196521 | ||||||||
\(77\) | −2.24590e65 | −1.85123 | ||||||||
\(78\) | −1.92526e64 | −0.101677 | ||||||||
\(79\) | −1.36419e65 | −0.464237 | −0.232118 | − | 0.972688i | \(-0.574566\pi\) | ||||
−0.232118 | + | 0.972688i | \(0.574566\pi\) | |||||||
\(80\) | 4.98906e65 | 1.10005 | ||||||||
\(81\) | −8.60817e65 | −1.23645 | ||||||||
\(82\) | −3.62958e65 | −0.341411 | ||||||||
\(83\) | 4.54701e65 | 0.281534 | 0.140767 | − | 0.990043i | \(-0.455043\pi\) | ||||
0.140767 | + | 0.990043i | \(0.455043\pi\) | |||||||
\(84\) | −1.04696e66 | −0.428841 | ||||||||
\(85\) | 5.14124e66 | 1.39996 | ||||||||
\(86\) | −3.11206e65 | −0.0566045 | ||||||||
\(87\) | −1.62733e66 | −0.198638 | ||||||||
\(88\) | 1.69072e67 | 1.39130 | ||||||||
\(89\) | −6.95403e66 | −0.387509 | −0.193754 | − | 0.981050i | \(-0.562066\pi\) | ||||
−0.193754 | + | 0.981050i | \(0.562066\pi\) | |||||||
\(90\) | −2.20373e67 | −0.835204 | ||||||||
\(91\) | −5.07552e66 | −0.131387 | ||||||||
\(92\) | 1.15546e66 | 0.0205152 | ||||||||
\(93\) | −7.60220e67 | −0.929560 | ||||||||
\(94\) | −1.66257e68 | −1.40562 | ||||||||
\(95\) | 2.20998e68 | 1.29695 | ||||||||
\(96\) | 1.42650e68 | 0.583330 | ||||||||
\(97\) | 3.36085e68 | 0.961224 | 0.480612 | − | 0.876933i | \(-0.340414\pi\) | ||||
0.480612 | + | 0.876933i | \(0.340414\pi\) | |||||||
\(98\) | 4.64289e68 | 0.932156 | ||||||||
\(99\) | −5.61323e68 | −0.793960 | ||||||||
\(100\) | −3.28352e68 | −0.328352 | ||||||||
\(101\) | −4.26999e68 | −0.302928 | −0.151464 | − | 0.988463i | \(-0.548399\pi\) | ||||
−0.151464 | + | 0.988463i | \(0.548399\pi\) | |||||||
\(102\) | −1.99063e69 | −1.00527 | ||||||||
\(103\) | 4.89975e69 | 1.76721 | 0.883607 | − | 0.468229i | \(-0.155108\pi\) | ||||
0.883607 | + | 0.468229i | \(0.155108\pi\) | |||||||
\(104\) | 3.82087e68 | 0.0987442 | ||||||||
\(105\) | −1.52350e70 | −2.83016 | ||||||||
\(106\) | 1.02861e70 | 1.37783 | ||||||||
\(107\) | −2.44106e69 | −0.236504 | −0.118252 | − | 0.992984i | \(-0.537729\pi\) | ||||
−0.118252 | + | 0.992984i | \(0.537729\pi\) | |||||||
\(108\) | 1.62850e69 | 0.114464 | ||||||||
\(109\) | −1.65662e70 | −0.847245 | −0.423623 | − | 0.905839i | \(-0.639242\pi\) | ||||
−0.423623 | + | 0.905839i | \(0.639242\pi\) | |||||||
\(110\) | 4.67657e70 | 1.74534 | ||||||||
\(111\) | 7.39450e70 | 2.01960 | ||||||||
\(112\) | −5.09252e70 | −1.02073 | ||||||||
\(113\) | −4.32535e70 | −0.637992 | −0.318996 | − | 0.947756i | \(-0.603346\pi\) | ||||
−0.318996 | + | 0.947756i | \(0.603346\pi\) | |||||||
\(114\) | −8.55679e70 | −0.931309 | ||||||||
\(115\) | 1.68138e70 | 0.135391 | ||||||||
\(116\) | 6.13897e69 | 0.0366687 | ||||||||
\(117\) | −1.26854e70 | −0.0563496 | ||||||||
\(118\) | −2.85339e71 | −0.945000 | ||||||||
\(119\) | −5.24786e71 | −1.29901 | ||||||||
\(120\) | 1.14689e72 | 2.12701 | ||||||||
\(121\) | 4.73239e71 | 0.659152 | ||||||||
\(122\) | 6.51873e71 | 0.683517 | ||||||||
\(123\) | −6.27134e71 | −0.496174 | ||||||||
\(124\) | 2.86786e71 | 0.171597 | ||||||||
\(125\) | −1.36284e72 | −0.618089 | ||||||||
\(126\) | 2.24944e72 | 0.774979 | ||||||||
\(127\) | −5.32946e72 | −1.39783 | −0.698916 | − | 0.715204i | \(-0.746334\pi\) | ||||
−0.698916 | + | 0.715204i | \(0.746334\pi\) | |||||||
\(128\) | 2.56682e72 | 0.513631 | ||||||||
\(129\) | −5.37715e71 | −0.0822635 | ||||||||
\(130\) | 1.05686e72 | 0.123872 | ||||||||
\(131\) | −9.29599e72 | −0.836442 | −0.418221 | − | 0.908345i | \(-0.637346\pi\) | ||||
−0.418221 | + | 0.908345i | \(0.637346\pi\) | |||||||
\(132\) | 5.55294e72 | 0.384346 | ||||||||
\(133\) | −2.25581e73 | −1.20343 | ||||||||
\(134\) | 1.23114e73 | 0.507215 | ||||||||
\(135\) | 2.36972e73 | 0.755410 | ||||||||
\(136\) | 3.95061e73 | 0.976274 | ||||||||
\(137\) | 7.89544e73 | 1.51536 | 0.757681 | − | 0.652625i | \(-0.226332\pi\) | ||||
0.757681 | + | 0.652625i | \(0.226332\pi\) | |||||||
\(138\) | −6.51012e72 | −0.0972210 | ||||||||
\(139\) | −1.62132e74 | −1.88737 | −0.943686 | − | 0.330842i | \(-0.892667\pi\) | ||||
−0.943686 | + | 0.330842i | \(0.892667\pi\) | |||||||
\(140\) | 5.74725e73 | 0.522448 | ||||||||
\(141\) | −2.87266e74 | −2.04280 | ||||||||
\(142\) | 1.26775e74 | 0.706457 | ||||||||
\(143\) | 2.69198e73 | 0.117755 | ||||||||
\(144\) | −1.27279e74 | −0.437774 | ||||||||
\(145\) | 8.93316e73 | 0.241997 | ||||||||
\(146\) | −5.50164e73 | −0.117576 | ||||||||
\(147\) | 8.02219e74 | 1.35471 | ||||||||
\(148\) | −2.78951e74 | −0.372820 | ||||||||
\(149\) | −4.94682e74 | −0.524083 | −0.262041 | − | 0.965057i | \(-0.584396\pi\) | ||||
−0.262041 | + | 0.965057i | \(0.584396\pi\) | |||||||
\(150\) | 1.85000e75 | 1.55605 | ||||||||
\(151\) | −1.17268e75 | −0.784287 | −0.392144 | − | 0.919904i | \(-0.628266\pi\) | ||||
−0.392144 | + | 0.919904i | \(0.628266\pi\) | |||||||
\(152\) | 1.69818e75 | 0.904442 | ||||||||
\(153\) | −1.31161e75 | −0.557122 | ||||||||
\(154\) | −4.77356e75 | −1.61949 | ||||||||
\(155\) | 4.17319e75 | 1.13246 | ||||||||
\(156\) | 1.25491e74 | 0.0272781 | ||||||||
\(157\) | −8.35431e75 | −1.45671 | −0.728354 | − | 0.685201i | \(-0.759715\pi\) | ||||
−0.728354 | + | 0.685201i | \(0.759715\pi\) | |||||||
\(158\) | −2.89952e75 | −0.406122 | ||||||||
\(159\) | 1.77727e76 | 2.00241 | ||||||||
\(160\) | −7.83070e75 | −0.710659 | ||||||||
\(161\) | −1.71625e75 | −0.125628 | ||||||||
\(162\) | −1.82963e76 | −1.08167 | ||||||||
\(163\) | 2.80579e76 | 1.34148 | 0.670738 | − | 0.741695i | \(-0.265978\pi\) | ||||
0.670738 | + | 0.741695i | \(0.265978\pi\) | |||||||
\(164\) | 2.36581e75 | 0.0915940 | ||||||||
\(165\) | 8.08039e76 | 2.53651 | ||||||||
\(166\) | 9.66446e75 | 0.246291 | ||||||||
\(167\) | −6.66449e76 | −1.38054 | −0.690269 | − | 0.723553i | \(-0.742508\pi\) | ||||
−0.690269 | + | 0.723553i | \(0.742508\pi\) | |||||||
\(168\) | −1.17068e77 | −1.97364 | ||||||||
\(169\) | −7.21849e76 | −0.991643 | ||||||||
\(170\) | 1.09275e77 | 1.22471 | ||||||||
\(171\) | −5.63800e76 | −0.516130 | ||||||||
\(172\) | 2.02848e75 | 0.0151859 | ||||||||
\(173\) | −4.02628e76 | −0.246782 | −0.123391 | − | 0.992358i | \(-0.539377\pi\) | ||||
−0.123391 | + | 0.992358i | \(0.539377\pi\) | |||||||
\(174\) | −3.45882e76 | −0.173772 | ||||||||
\(175\) | 4.87713e77 | 2.01072 | ||||||||
\(176\) | 2.70100e77 | 0.914823 | ||||||||
\(177\) | −4.93021e77 | −1.37337 | ||||||||
\(178\) | −1.47805e77 | −0.338999 | ||||||||
\(179\) | 1.65322e77 | 0.312537 | 0.156268 | − | 0.987715i | \(-0.450054\pi\) | ||||
0.156268 | + | 0.987715i | \(0.450054\pi\) | |||||||
\(180\) | 1.43643e77 | 0.224069 | ||||||||
\(181\) | −7.58549e76 | −0.0977401 | −0.0488700 | − | 0.998805i | \(-0.515562\pi\) | ||||
−0.0488700 | + | 0.998805i | \(0.515562\pi\) | |||||||
\(182\) | −1.07878e77 | −0.114939 | ||||||||
\(183\) | 1.12634e78 | 0.993357 | ||||||||
\(184\) | 1.29200e77 | 0.0944164 | ||||||||
\(185\) | −4.05917e78 | −2.46044 | ||||||||
\(186\) | −1.61581e78 | −0.813195 | ||||||||
\(187\) | 2.78338e78 | 1.16423 | ||||||||
\(188\) | 1.08369e78 | 0.377101 | ||||||||
\(189\) | −2.41887e78 | −0.700939 | ||||||||
\(190\) | 4.69721e78 | 1.13459 | ||||||||
\(191\) | −2.53179e78 | −0.510243 | −0.255121 | − | 0.966909i | \(-0.582115\pi\) | ||||
−0.255121 | + | 0.966909i | \(0.582115\pi\) | |||||||
\(192\) | 8.39683e78 | 1.41326 | ||||||||
\(193\) | −6.20489e78 | −0.872985 | −0.436492 | − | 0.899708i | \(-0.643779\pi\) | ||||
−0.436492 | + | 0.899708i | \(0.643779\pi\) | |||||||
\(194\) | 7.14334e78 | 0.840895 | ||||||||
\(195\) | 1.82609e78 | 0.180023 | ||||||||
\(196\) | −3.02630e78 | −0.250079 | ||||||||
\(197\) | 7.90415e78 | 0.547987 | 0.273994 | − | 0.961732i | \(-0.411655\pi\) | ||||
0.273994 | + | 0.961732i | \(0.411655\pi\) | |||||||
\(198\) | −1.19307e79 | −0.694570 | ||||||||
\(199\) | −1.63250e79 | −0.798769 | −0.399385 | − | 0.916783i | \(-0.630776\pi\) | ||||
−0.399385 | + | 0.916783i | \(0.630776\pi\) | |||||||
\(200\) | −3.67152e79 | −1.51116 | ||||||||
\(201\) | 2.12722e79 | 0.737138 | ||||||||
\(202\) | −9.07567e78 | −0.265006 | ||||||||
\(203\) | −9.11843e78 | −0.224547 | ||||||||
\(204\) | 1.29752e79 | 0.269695 | ||||||||
\(205\) | 3.44262e79 | 0.604479 | ||||||||
\(206\) | 1.04142e80 | 1.54599 | ||||||||
\(207\) | −4.28946e78 | −0.0538798 | ||||||||
\(208\) | 6.10399e78 | 0.0649275 | ||||||||
\(209\) | 1.19645e80 | 1.07857 | ||||||||
\(210\) | −3.23812e80 | −2.47587 | ||||||||
\(211\) | 1.14615e79 | 0.0743866 | 0.0371933 | − | 0.999308i | \(-0.488158\pi\) | ||||
0.0371933 | + | 0.999308i | \(0.488158\pi\) | |||||||
\(212\) | −6.70460e79 | −0.369645 | ||||||||
\(213\) | 2.19048e80 | 1.02670 | ||||||||
\(214\) | −5.18837e79 | −0.206898 | ||||||||
\(215\) | 2.95176e79 | 0.100220 | ||||||||
\(216\) | 1.82093e80 | 0.526793 | ||||||||
\(217\) | −4.25974e80 | −1.05080 | ||||||||
\(218\) | −3.52107e80 | −0.741184 | ||||||||
\(219\) | −9.50599e79 | −0.170874 | ||||||||
\(220\) | −3.04826e80 | −0.468240 | ||||||||
\(221\) | 6.29018e79 | 0.0826284 | ||||||||
\(222\) | 1.57167e81 | 1.76678 | ||||||||
\(223\) | 7.96925e79 | 0.0767184 | 0.0383592 | − | 0.999264i | \(-0.487787\pi\) | ||||
0.0383592 | + | 0.999264i | \(0.487787\pi\) | |||||||
\(224\) | 7.99310e80 | 0.659415 | ||||||||
\(225\) | 1.21895e81 | 0.862363 | ||||||||
\(226\) | −9.19334e80 | −0.558126 | ||||||||
\(227\) | −2.05085e81 | −1.06916 | −0.534578 | − | 0.845119i | \(-0.679529\pi\) | ||||
−0.534578 | + | 0.845119i | \(0.679529\pi\) | |||||||
\(228\) | 5.57744e80 | 0.249852 | ||||||||
\(229\) | 1.65307e81 | 0.636747 | 0.318374 | − | 0.947965i | \(-0.396863\pi\) | ||||
0.318374 | + | 0.947965i | \(0.396863\pi\) | |||||||
\(230\) | 3.57370e80 | 0.118442 | ||||||||
\(231\) | −8.24797e81 | −2.35360 | ||||||||
\(232\) | 6.86439e80 | 0.168759 | ||||||||
\(233\) | −5.09024e81 | −1.07884 | −0.539422 | − | 0.842035i | \(-0.681357\pi\) | ||||
−0.539422 | + | 0.842035i | \(0.681357\pi\) | |||||||
\(234\) | −2.69622e80 | −0.0492955 | ||||||||
\(235\) | 1.57693e82 | 2.48870 | ||||||||
\(236\) | 1.85988e81 | 0.253525 | ||||||||
\(237\) | −5.00991e81 | −0.590218 | ||||||||
\(238\) | −1.11541e82 | −1.13639 | ||||||||
\(239\) | 2.60321e81 | 0.229500 | 0.114750 | − | 0.993394i | \(-0.463393\pi\) | ||||
0.114750 | + | 0.993394i | \(0.463393\pi\) | |||||||
\(240\) | 1.83221e82 | 1.39858 | ||||||||
\(241\) | 1.75774e82 | 1.16243 | 0.581214 | − | 0.813751i | \(-0.302578\pi\) | ||||
0.581214 | + | 0.813751i | \(0.302578\pi\) | |||||||
\(242\) | 1.00585e82 | 0.576637 | ||||||||
\(243\) | −2.18051e82 | −1.08428 | ||||||||
\(244\) | −4.24900e81 | −0.183374 | ||||||||
\(245\) | −4.40374e82 | −1.65041 | ||||||||
\(246\) | −1.33295e82 | −0.434061 | ||||||||
\(247\) | 2.70385e81 | 0.0765488 | ||||||||
\(248\) | 3.20675e82 | 0.789735 | ||||||||
\(249\) | 1.66987e82 | 0.357935 | ||||||||
\(250\) | −2.89666e82 | −0.540714 | ||||||||
\(251\) | 1.40922e82 | 0.229212 | 0.114606 | − | 0.993411i | \(-0.463440\pi\) | ||||
0.114606 | + | 0.993411i | \(0.463440\pi\) | |||||||
\(252\) | −1.46621e82 | −0.207912 | ||||||||
\(253\) | 9.10272e81 | 0.112594 | ||||||||
\(254\) | −1.13275e83 | −1.22285 | ||||||||
\(255\) | 1.88810e83 | 1.77987 | ||||||||
\(256\) | −8.04109e82 | −0.662272 | ||||||||
\(257\) | −1.05298e81 | −0.00758099 | −0.00379050 | − | 0.999993i | \(-0.501207\pi\) | ||||
−0.00379050 | + | 0.999993i | \(0.501207\pi\) | |||||||
\(258\) | −1.14289e82 | −0.0719654 | ||||||||
\(259\) | 4.14336e83 | 2.28302 | ||||||||
\(260\) | −6.88876e81 | −0.0332323 | ||||||||
\(261\) | −2.27899e82 | −0.0963041 | ||||||||
\(262\) | −1.97582e83 | −0.731733 | ||||||||
\(263\) | −3.38100e83 | −1.09792 | −0.548962 | − | 0.835847i | \(-0.684977\pi\) | ||||
−0.548962 | + | 0.835847i | \(0.684977\pi\) | |||||||
\(264\) | 6.20910e83 | 1.76886 | ||||||||
\(265\) | −9.75623e83 | −2.43949 | ||||||||
\(266\) | −4.79462e83 | −1.05278 | ||||||||
\(267\) | −2.55384e83 | −0.492668 | ||||||||
\(268\) | −8.02476e82 | −0.136076 | ||||||||
\(269\) | 1.30658e84 | 1.94841 | 0.974206 | − | 0.225661i | \(-0.0724541\pi\) | ||||
0.974206 | + | 0.225661i | \(0.0724541\pi\) | |||||||
\(270\) | 5.03674e83 | 0.660845 | ||||||||
\(271\) | −1.19681e83 | −0.138225 | −0.0691124 | − | 0.997609i | \(-0.522017\pi\) | ||||
−0.0691124 | + | 0.997609i | \(0.522017\pi\) | |||||||
\(272\) | 6.31125e83 | 0.641931 | ||||||||
\(273\) | −1.86396e83 | −0.167042 | ||||||||
\(274\) | 1.67814e84 | 1.32566 | ||||||||
\(275\) | −2.58675e84 | −1.80209 | ||||||||
\(276\) | 4.24339e82 | 0.0260825 | ||||||||
\(277\) | 2.91614e84 | 1.58218 | 0.791090 | − | 0.611700i | \(-0.209514\pi\) | ||||
0.791090 | + | 0.611700i | \(0.209514\pi\) | |||||||
\(278\) | −3.44604e84 | −1.65110 | ||||||||
\(279\) | −1.06465e84 | −0.450672 | ||||||||
\(280\) | 6.42638e84 | 2.40444 | ||||||||
\(281\) | −2.47628e84 | −0.819279 | −0.409639 | − | 0.912248i | \(-0.634345\pi\) | ||||
−0.409639 | + | 0.912248i | \(0.634345\pi\) | |||||||
\(282\) | −6.10571e84 | −1.78707 | ||||||||
\(283\) | −3.68218e84 | −0.953833 | −0.476917 | − | 0.878949i | \(-0.658246\pi\) | ||||
−0.476917 | + | 0.878949i | \(0.658246\pi\) | |||||||
\(284\) | −8.26338e83 | −0.189529 | ||||||||
\(285\) | 8.11604e84 | 1.64891 | ||||||||
\(286\) | 5.72167e83 | 0.103014 | ||||||||
\(287\) | −3.51402e84 | −0.560891 | ||||||||
\(288\) | 1.99774e84 | 0.282811 | ||||||||
\(289\) | −1.45738e84 | −0.183062 | ||||||||
\(290\) | 1.89870e84 | 0.211703 | ||||||||
\(291\) | 1.23426e85 | 1.22207 | ||||||||
\(292\) | 3.58605e83 | 0.0315434 | ||||||||
\(293\) | −2.21476e85 | −1.73139 | −0.865694 | − | 0.500573i | \(-0.833123\pi\) | ||||
−0.865694 | + | 0.500573i | \(0.833123\pi\) | |||||||
\(294\) | 1.70508e85 | 1.18512 | ||||||||
\(295\) | 2.70642e85 | 1.67315 | ||||||||
\(296\) | −3.11913e85 | −1.71581 | ||||||||
\(297\) | 1.28293e85 | 0.628212 | ||||||||
\(298\) | −1.05142e85 | −0.458476 | ||||||||
\(299\) | 2.05713e83 | 0.00799107 | ||||||||
\(300\) | −1.20586e85 | −0.417458 | ||||||||
\(301\) | −3.01297e84 | −0.0929932 | ||||||||
\(302\) | −2.49248e85 | −0.686107 | ||||||||
\(303\) | −1.56813e85 | −0.385135 | ||||||||
\(304\) | 2.71291e85 | 0.594699 | ||||||||
\(305\) | −6.18296e85 | −1.21019 | ||||||||
\(306\) | −2.78777e85 | −0.487380 | ||||||||
\(307\) | 3.33336e85 | 0.520725 | 0.260363 | − | 0.965511i | \(-0.416158\pi\) | ||||
0.260363 | + | 0.965511i | \(0.416158\pi\) | |||||||
\(308\) | 3.11147e85 | 0.434477 | ||||||||
\(309\) | 1.79941e86 | 2.24679 | ||||||||
\(310\) | 8.86992e85 | 0.990698 | ||||||||
\(311\) | 5.41154e85 | 0.540863 | 0.270432 | − | 0.962739i | \(-0.412834\pi\) | ||||
0.270432 | + | 0.962739i | \(0.412834\pi\) | |||||||
\(312\) | 1.40320e85 | 0.125541 | ||||||||
\(313\) | −1.40450e86 | −1.12523 | −0.562615 | − | 0.826719i | \(-0.690205\pi\) | ||||
−0.562615 | + | 0.826719i | \(0.690205\pi\) | |||||||
\(314\) | −1.77567e86 | −1.27435 | ||||||||
\(315\) | −2.13357e86 | −1.37212 | ||||||||
\(316\) | 1.88995e85 | 0.108955 | ||||||||
\(317\) | −1.70168e85 | −0.0879699 | −0.0439849 | − | 0.999032i | \(-0.514005\pi\) | ||||
−0.0439849 | + | 0.999032i | \(0.514005\pi\) | |||||||
\(318\) | 3.77751e86 | 1.75174 | ||||||||
\(319\) | 4.83627e85 | 0.201248 | ||||||||
\(320\) | −4.60940e86 | −1.72175 | ||||||||
\(321\) | −8.96469e85 | −0.300685 | ||||||||
\(322\) | −3.64781e85 | −0.109902 | ||||||||
\(323\) | 2.79567e86 | 0.756830 | ||||||||
\(324\) | 1.19258e86 | 0.290191 | ||||||||
\(325\) | −5.84581e85 | −0.127900 | ||||||||
\(326\) | 5.96358e86 | 1.17354 | ||||||||
\(327\) | −6.08387e86 | −1.07716 | ||||||||
\(328\) | 2.64537e86 | 0.421539 | ||||||||
\(329\) | −1.60964e87 | −2.30924 | ||||||||
\(330\) | 1.71745e87 | 2.21898 | ||||||||
\(331\) | 1.21390e87 | 1.41292 | 0.706462 | − | 0.707751i | \(-0.250290\pi\) | ||||
0.706462 | + | 0.707751i | \(0.250290\pi\) | |||||||
\(332\) | −6.29943e85 | −0.0660750 | ||||||||
\(333\) | 1.03556e87 | 0.979149 | ||||||||
\(334\) | −1.41651e87 | −1.20772 | ||||||||
\(335\) | −1.16773e87 | −0.898040 | ||||||||
\(336\) | −1.87021e87 | −1.29773 | ||||||||
\(337\) | 2.61386e87 | 1.63701 | 0.818505 | − | 0.574499i | \(-0.194803\pi\) | ||||
0.818505 | + | 0.574499i | \(0.194803\pi\) | |||||||
\(338\) | −1.53426e87 | −0.867505 | ||||||||
\(339\) | −1.58847e87 | −0.811126 | ||||||||
\(340\) | −7.12267e86 | −0.328564 | ||||||||
\(341\) | 2.25930e87 | 0.941776 | ||||||||
\(342\) | −1.19833e87 | −0.451519 | ||||||||
\(343\) | 2.76506e86 | 0.0942013 | ||||||||
\(344\) | 2.26818e86 | 0.0698893 | ||||||||
\(345\) | 6.17479e86 | 0.172133 | ||||||||
\(346\) | −8.55768e86 | −0.215889 | ||||||||
\(347\) | 2.58424e87 | 0.590155 | 0.295078 | − | 0.955473i | \(-0.404655\pi\) | ||||
0.295078 | + | 0.955473i | \(0.404655\pi\) | |||||||
\(348\) | 2.25451e86 | 0.0466196 | ||||||||
\(349\) | 1.39983e87 | 0.262180 | 0.131090 | − | 0.991370i | \(-0.458152\pi\) | ||||
0.131090 | + | 0.991370i | \(0.458152\pi\) | |||||||
\(350\) | 1.03661e88 | 1.75901 | ||||||||
\(351\) | 2.89930e86 | 0.0445859 | ||||||||
\(352\) | −4.23942e87 | −0.590996 | ||||||||
\(353\) | 7.18553e87 | 0.908304 | 0.454152 | − | 0.890924i | \(-0.349942\pi\) | ||||
0.454152 | + | 0.890924i | \(0.349942\pi\) | |||||||
\(354\) | −1.04789e88 | −1.20145 | ||||||||
\(355\) | −1.20245e88 | −1.25080 | ||||||||
\(356\) | 9.63412e86 | 0.0909467 | ||||||||
\(357\) | −1.92725e88 | −1.65152 | ||||||||
\(358\) | 3.51384e87 | 0.273412 | ||||||||
\(359\) | −2.70510e87 | −0.191172 | −0.0955860 | − | 0.995421i | \(-0.530472\pi\) | ||||
−0.0955860 | + | 0.995421i | \(0.530472\pi\) | |||||||
\(360\) | 1.60616e88 | 1.03122 | ||||||||
\(361\) | −5.12224e87 | −0.298856 | ||||||||
\(362\) | −1.61226e87 | −0.0855046 | ||||||||
\(363\) | 1.73795e88 | 0.838028 | ||||||||
\(364\) | 7.03163e86 | 0.0308360 | ||||||||
\(365\) | 5.21826e87 | 0.208172 | ||||||||
\(366\) | 2.39398e88 | 0.869005 | ||||||||
\(367\) | −6.88002e86 | −0.0227306 | −0.0113653 | − | 0.999935i | \(-0.503618\pi\) | ||||
−0.0113653 | + | 0.999935i | \(0.503618\pi\) | |||||||
\(368\) | 2.06402e87 | 0.0620818 | ||||||||
\(369\) | −8.78267e87 | −0.240556 | ||||||||
\(370\) | −8.62759e88 | −2.15243 | ||||||||
\(371\) | 9.95856e88 | 2.26359 | ||||||||
\(372\) | 1.05321e88 | 0.218164 | ||||||||
\(373\) | −8.56864e88 | −1.61792 | −0.808960 | − | 0.587864i | \(-0.799969\pi\) | ||||
−0.808960 | + | 0.587864i | \(0.799969\pi\) | |||||||
\(374\) | 5.91596e88 | 1.01849 | ||||||||
\(375\) | −5.00498e88 | −0.785821 | ||||||||
\(376\) | 1.21174e89 | 1.73552 | ||||||||
\(377\) | 1.09295e87 | 0.0142831 | ||||||||
\(378\) | −5.14120e88 | −0.613193 | ||||||||
\(379\) | −8.36126e88 | −0.910373 | −0.455186 | − | 0.890396i | \(-0.650427\pi\) | ||||
−0.455186 | + | 0.890396i | \(0.650427\pi\) | |||||||
\(380\) | −3.06171e88 | −0.304389 | ||||||||
\(381\) | −1.95722e89 | −1.77717 | ||||||||
\(382\) | −5.38121e88 | −0.446369 | ||||||||
\(383\) | 2.17691e88 | 0.164999 | 0.0824997 | − | 0.996591i | \(-0.473710\pi\) | ||||
0.0824997 | + | 0.996591i | \(0.473710\pi\) | |||||||
\(384\) | 9.42652e88 | 0.653016 | ||||||||
\(385\) | 4.52768e89 | 2.86735 | ||||||||
\(386\) | −1.31882e89 | −0.763702 | ||||||||
\(387\) | −7.53040e87 | −0.0398832 | ||||||||
\(388\) | −4.65613e88 | −0.225596 | ||||||||
\(389\) | 3.57077e89 | 1.58307 | 0.791537 | − | 0.611122i | \(-0.209281\pi\) | ||||
0.791537 | + | 0.611122i | \(0.209281\pi\) | |||||||
\(390\) | 3.88127e88 | 0.157487 | ||||||||
\(391\) | 2.12698e88 | 0.0790069 | ||||||||
\(392\) | −3.38390e89 | −1.15093 | ||||||||
\(393\) | −3.41391e89 | −1.06343 | ||||||||
\(394\) | 1.67999e89 | 0.479388 | ||||||||
\(395\) | 2.75017e89 | 0.719050 | ||||||||
\(396\) | 7.77658e88 | 0.186339 | ||||||||
\(397\) | −1.10958e89 | −0.243717 | −0.121859 | − | 0.992547i | \(-0.538885\pi\) | ||||
−0.121859 | + | 0.992547i | \(0.538885\pi\) | |||||||
\(398\) | −3.46980e89 | −0.698777 | ||||||||
\(399\) | −8.28436e89 | −1.53001 | ||||||||
\(400\) | −5.86540e89 | −0.993638 | ||||||||
\(401\) | 4.75128e89 | 0.738465 | 0.369233 | − | 0.929337i | \(-0.379621\pi\) | ||||
0.369233 | + | 0.929337i | \(0.379621\pi\) | |||||||
\(402\) | 4.52131e89 | 0.644860 | ||||||||
\(403\) | 5.10580e88 | 0.0668404 | ||||||||
\(404\) | 5.91565e88 | 0.0710960 | ||||||||
\(405\) | 1.73539e90 | 1.91513 | ||||||||
\(406\) | −1.93808e89 | −0.196437 | ||||||||
\(407\) | −2.19757e90 | −2.04614 | ||||||||
\(408\) | 1.45084e90 | 1.24121 | ||||||||
\(409\) | 2.42528e89 | 0.190681 | 0.0953406 | − | 0.995445i | \(-0.469606\pi\) | ||||
0.0953406 | + | 0.995445i | \(0.469606\pi\) | |||||||
\(410\) | 7.31713e89 | 0.528808 | ||||||||
\(411\) | 2.89956e90 | 1.92659 | ||||||||
\(412\) | −6.78811e89 | −0.414758 | ||||||||
\(413\) | −2.76254e90 | −1.55250 | ||||||||
\(414\) | −9.11706e88 | −0.0471349 | ||||||||
\(415\) | −9.16665e89 | −0.436065 | ||||||||
\(416\) | −9.58067e88 | −0.0419446 | ||||||||
\(417\) | −5.95422e90 | −2.39955 | ||||||||
\(418\) | 2.54299e90 | 0.943547 | ||||||||
\(419\) | 1.70435e90 | 0.582338 | 0.291169 | − | 0.956672i | \(-0.405956\pi\) | ||||
0.291169 | + | 0.956672i | \(0.405956\pi\) | |||||||
\(420\) | 2.11065e90 | 0.664227 | ||||||||
\(421\) | 4.90128e90 | 1.42094 | 0.710472 | − | 0.703725i | \(-0.248481\pi\) | ||||
0.710472 | + | 0.703725i | \(0.248481\pi\) | |||||||
\(422\) | 2.43608e89 | 0.0650747 | ||||||||
\(423\) | −4.02300e90 | −0.990393 | ||||||||
\(424\) | −7.49685e90 | −1.70120 | ||||||||
\(425\) | −6.04431e90 | −1.26453 | ||||||||
\(426\) | 4.65576e90 | 0.898171 | ||||||||
\(427\) | 6.31119e90 | 1.12292 | ||||||||
\(428\) | 3.38185e89 | 0.0555066 | ||||||||
\(429\) | 9.88616e89 | 0.149710 | ||||||||
\(430\) | 6.27383e89 | 0.0876740 | ||||||||
\(431\) | 3.44401e90 | 0.444221 | 0.222111 | − | 0.975021i | \(-0.428705\pi\) | ||||
0.222111 | + | 0.975021i | \(0.428705\pi\) | |||||||
\(432\) | 2.90901e90 | 0.346383 | ||||||||
\(433\) | 1.42290e91 | 1.56438 | 0.782189 | − | 0.623041i | \(-0.214103\pi\) | ||||
0.782189 | + | 0.623041i | \(0.214103\pi\) | |||||||
\(434\) | −9.05388e90 | −0.919261 | ||||||||
\(435\) | 3.28066e90 | 0.307668 | ||||||||
\(436\) | 2.29509e90 | 0.198845 | ||||||||
\(437\) | 9.14289e89 | 0.0731937 | ||||||||
\(438\) | −2.02045e90 | −0.149483 | ||||||||
\(439\) | −2.33620e91 | −1.59766 | −0.798828 | − | 0.601559i | \(-0.794546\pi\) | ||||
−0.798828 | + | 0.601559i | \(0.794546\pi\) | |||||||
\(440\) | −3.40845e91 | −2.15496 | ||||||||
\(441\) | 1.12346e91 | 0.656791 | ||||||||
\(442\) | 1.33695e90 | 0.0722847 | ||||||||
\(443\) | 3.82184e90 | 0.191136 | 0.0955682 | − | 0.995423i | \(-0.469533\pi\) | ||||
0.0955682 | + | 0.995423i | \(0.469533\pi\) | |||||||
\(444\) | −1.02444e91 | −0.473993 | ||||||||
\(445\) | 1.40191e91 | 0.600207 | ||||||||
\(446\) | 1.69383e90 | 0.0671145 | ||||||||
\(447\) | −1.81670e91 | −0.666305 | ||||||||
\(448\) | 4.70499e91 | 1.59760 | ||||||||
\(449\) | 1.14776e91 | 0.360871 | 0.180436 | − | 0.983587i | \(-0.442249\pi\) | ||||
0.180436 | + | 0.983587i | \(0.442249\pi\) | |||||||
\(450\) | 2.59083e91 | 0.754409 | ||||||||
\(451\) | 1.86378e91 | 0.502695 | ||||||||
\(452\) | 5.99235e90 | 0.149734 | ||||||||
\(453\) | −4.30662e91 | −0.997122 | ||||||||
\(454\) | −4.35898e91 | −0.935315 | ||||||||
\(455\) | 1.02321e91 | 0.203504 | ||||||||
\(456\) | 6.23650e91 | 1.14988 | ||||||||
\(457\) | −7.31030e91 | −1.24976 | −0.624880 | − | 0.780721i | \(-0.714852\pi\) | ||||
−0.624880 | + | 0.780721i | \(0.714852\pi\) | |||||||
\(458\) | 3.51352e91 | 0.557037 | ||||||||
\(459\) | 2.99775e91 | 0.440816 | ||||||||
\(460\) | −2.32939e90 | −0.0317758 | ||||||||
\(461\) | 7.71415e91 | 0.976351 | 0.488176 | − | 0.872745i | \(-0.337663\pi\) | ||||
0.488176 | + | 0.872745i | \(0.337663\pi\) | |||||||
\(462\) | −1.75307e92 | −2.05897 | ||||||||
\(463\) | −1.44206e92 | −1.57195 | −0.785974 | − | 0.618260i | \(-0.787838\pi\) | ||||
−0.785974 | + | 0.618260i | \(0.787838\pi\) | |||||||
\(464\) | 1.09661e91 | 0.110964 | ||||||||
\(465\) | 1.53258e92 | 1.43978 | ||||||||
\(466\) | −1.08191e92 | −0.943791 | ||||||||
\(467\) | −4.34642e91 | −0.352127 | −0.176063 | − | 0.984379i | \(-0.556336\pi\) | ||||
−0.176063 | + | 0.984379i | \(0.556336\pi\) | |||||||
\(468\) | 1.75743e90 | 0.0132250 | ||||||||
\(469\) | 1.19194e92 | 0.833284 | ||||||||
\(470\) | 3.35170e92 | 2.17715 | ||||||||
\(471\) | −3.06808e92 | −1.85202 | ||||||||
\(472\) | 2.07965e92 | 1.16679 | ||||||||
\(473\) | 1.59803e91 | 0.0833445 | ||||||||
\(474\) | −1.06483e92 | −0.516332 | ||||||||
\(475\) | −2.59817e92 | −1.17149 | ||||||||
\(476\) | 7.27039e91 | 0.304872 | ||||||||
\(477\) | 2.48897e92 | 0.970812 | ||||||||
\(478\) | 5.53301e91 | 0.200770 | ||||||||
\(479\) | 2.77463e92 | 0.936764 | 0.468382 | − | 0.883526i | \(-0.344837\pi\) | ||||
0.468382 | + | 0.883526i | \(0.344837\pi\) | |||||||
\(480\) | −2.87579e92 | −0.903513 | ||||||||
\(481\) | −4.96630e91 | −0.145220 | ||||||||
\(482\) | 3.73599e92 | 1.01691 | ||||||||
\(483\) | −6.30285e91 | −0.159721 | ||||||||
\(484\) | −6.55627e91 | −0.154700 | ||||||||
\(485\) | −6.77540e92 | −1.48883 | ||||||||
\(486\) | −4.63458e92 | −0.948548 | ||||||||
\(487\) | 3.06757e91 | 0.0584851 | 0.0292426 | − | 0.999572i | \(-0.490690\pi\) | ||||
0.0292426 | + | 0.999572i | \(0.490690\pi\) | |||||||
\(488\) | −4.75109e92 | −0.843935 | ||||||||
\(489\) | 1.03041e93 | 1.70552 | ||||||||
\(490\) | −9.35995e92 | −1.44381 | ||||||||
\(491\) | 6.50375e91 | 0.0935088 | 0.0467544 | − | 0.998906i | \(-0.485112\pi\) | ||||
0.0467544 | + | 0.998906i | \(0.485112\pi\) | |||||||
\(492\) | 8.68833e91 | 0.116450 | ||||||||
\(493\) | 1.13006e92 | 0.141216 | ||||||||
\(494\) | 5.74692e91 | 0.0669662 | ||||||||
\(495\) | 1.13161e93 | 1.22976 | ||||||||
\(496\) | 5.12290e92 | 0.519276 | ||||||||
\(497\) | 1.22739e93 | 1.16061 | ||||||||
\(498\) | 3.54923e92 | 0.313128 | ||||||||
\(499\) | 1.05364e93 | 0.867412 | 0.433706 | − | 0.901054i | \(-0.357206\pi\) | ||||
0.433706 | + | 0.901054i | \(0.357206\pi\) | |||||||
\(500\) | 1.88809e92 | 0.145063 | ||||||||
\(501\) | −2.44750e93 | −1.75518 | ||||||||
\(502\) | 2.99524e92 | 0.200518 | ||||||||
\(503\) | −2.42087e93 | −1.51313 | −0.756564 | − | 0.653919i | \(-0.773124\pi\) | ||||
−0.756564 | + | 0.653919i | \(0.773124\pi\) | |||||||
\(504\) | −1.63947e93 | −0.956864 | ||||||||
\(505\) | 8.60819e92 | 0.469201 | ||||||||
\(506\) | 1.93474e92 | 0.0984987 | ||||||||
\(507\) | −2.65096e93 | −1.26075 | ||||||||
\(508\) | 7.38344e92 | 0.328066 | ||||||||
\(509\) | 1.96613e93 | 0.816298 | 0.408149 | − | 0.912915i | \(-0.366174\pi\) | ||||
0.408149 | + | 0.912915i | \(0.366174\pi\) | |||||||
\(510\) | 4.01306e93 | 1.55706 | ||||||||
\(511\) | −5.32648e92 | −0.193161 | ||||||||
\(512\) | −3.22428e93 | −1.09300 | ||||||||
\(513\) | 1.28859e93 | 0.408382 | ||||||||
\(514\) | −2.23805e91 | −0.00663198 | ||||||||
\(515\) | −9.87776e93 | −2.73722 | ||||||||
\(516\) | 7.44951e91 | 0.0193069 | ||||||||
\(517\) | 8.53727e93 | 2.06964 | ||||||||
\(518\) | 8.80651e93 | 1.99723 | ||||||||
\(519\) | −1.47863e93 | −0.313752 | ||||||||
\(520\) | −7.70277e92 | −0.152944 | ||||||||
\(521\) | 1.44982e92 | 0.0269409 | 0.0134704 | − | 0.999909i | \(-0.495712\pi\) | ||||
0.0134704 | + | 0.999909i | \(0.495712\pi\) | |||||||
\(522\) | −4.84389e92 | −0.0842484 | ||||||||
\(523\) | −1.14702e94 | −1.86750 | −0.933751 | − | 0.357923i | \(-0.883485\pi\) | ||||
−0.933751 | + | 0.357923i | \(0.883485\pi\) | |||||||
\(524\) | 1.28787e93 | 0.196310 | ||||||||
\(525\) | 1.79110e94 | 2.55638 | ||||||||
\(526\) | −7.18617e93 | −0.960482 | ||||||||
\(527\) | 5.27917e93 | 0.660844 | ||||||||
\(528\) | 9.91929e93 | 1.16308 | ||||||||
\(529\) | −9.03420e93 | −0.992359 | ||||||||
\(530\) | −2.07364e94 | −2.13411 | ||||||||
\(531\) | −6.90449e93 | −0.665841 | ||||||||
\(532\) | 3.12520e93 | 0.282440 | ||||||||
\(533\) | 4.21196e92 | 0.0356776 | ||||||||
\(534\) | −5.42806e93 | −0.430994 | ||||||||
\(535\) | 4.92112e93 | 0.366318 | ||||||||
\(536\) | −8.97300e93 | −0.626257 | ||||||||
\(537\) | 6.07137e93 | 0.397351 | ||||||||
\(538\) | 2.77707e94 | 1.70450 | ||||||||
\(539\) | −2.38412e94 | −1.37251 | ||||||||
\(540\) | −3.28302e93 | −0.177292 | ||||||||
\(541\) | 1.83776e94 | 0.931072 | 0.465536 | − | 0.885029i | \(-0.345862\pi\) | ||||
0.465536 | + | 0.885029i | \(0.345862\pi\) | |||||||
\(542\) | −2.54377e93 | −0.120921 | ||||||||
\(543\) | −2.78574e93 | −0.124264 | ||||||||
\(544\) | −9.90599e93 | −0.414702 | ||||||||
\(545\) | 3.33971e94 | 1.31229 | ||||||||
\(546\) | −3.96176e93 | −0.146131 | ||||||||
\(547\) | 5.34702e94 | 1.85161 | 0.925805 | − | 0.378002i | \(-0.123389\pi\) | ||||
0.925805 | + | 0.378002i | \(0.123389\pi\) | |||||||
\(548\) | −1.09383e94 | −0.355650 | ||||||||
\(549\) | 1.57737e94 | 0.481602 | ||||||||
\(550\) | −5.49803e94 | −1.57650 | ||||||||
\(551\) | 4.85761e93 | 0.130826 | ||||||||
\(552\) | 4.74481e93 | 0.120038 | ||||||||
\(553\) | −2.80720e94 | −0.667201 | ||||||||
\(554\) | 6.19811e94 | 1.38412 | ||||||||
\(555\) | −1.49071e95 | −3.12814 | ||||||||
\(556\) | 2.24618e94 | 0.442959 | ||||||||
\(557\) | −9.92032e94 | −1.83874 | −0.919372 | − | 0.393389i | \(-0.871302\pi\) | ||||
−0.919372 | + | 0.393389i | \(0.871302\pi\) | |||||||
\(558\) | −2.26286e94 | −0.394255 | ||||||||
\(559\) | 3.61140e92 | 0.00591519 | ||||||||
\(560\) | 1.02664e95 | 1.58100 | ||||||||
\(561\) | 1.02219e95 | 1.48017 | ||||||||
\(562\) | −5.26322e94 | −0.716718 | ||||||||
\(563\) | 1.16398e95 | 1.49076 | 0.745379 | − | 0.666641i | \(-0.232268\pi\) | ||||
0.745379 | + | 0.666641i | \(0.232268\pi\) | |||||||
\(564\) | 3.97979e94 | 0.479436 | ||||||||
\(565\) | 8.71980e94 | 0.988178 | ||||||||
\(566\) | −7.82630e94 | −0.834429 | ||||||||
\(567\) | −1.77138e95 | −1.77703 | ||||||||
\(568\) | −9.23982e94 | −0.872260 | ||||||||
\(569\) | 1.17606e95 | 1.04485 | 0.522426 | − | 0.852685i | \(-0.325027\pi\) | ||||
0.522426 | + | 0.852685i | \(0.325027\pi\) | |||||||
\(570\) | 1.72503e95 | 1.44249 | ||||||||
\(571\) | −1.80537e94 | −0.142108 | −0.0710542 | − | 0.997472i | \(-0.522636\pi\) | ||||
−0.0710542 | + | 0.997472i | \(0.522636\pi\) | |||||||
\(572\) | −3.72947e93 | −0.0276365 | ||||||||
\(573\) | −9.29789e94 | −0.648709 | ||||||||
\(574\) | −7.46888e94 | −0.490677 | ||||||||
\(575\) | −1.97672e94 | −0.122294 | ||||||||
\(576\) | 1.17593e95 | 0.685182 | ||||||||
\(577\) | 1.06348e95 | 0.583667 | 0.291834 | − | 0.956469i | \(-0.405735\pi\) | ||||
0.291834 | + | 0.956469i | \(0.405735\pi\) | |||||||
\(578\) | −3.09760e94 | −0.160145 | ||||||||
\(579\) | −2.27872e95 | −1.10989 | ||||||||
\(580\) | −1.23760e94 | −0.0567957 | ||||||||
\(581\) | 9.35676e94 | 0.404621 | ||||||||
\(582\) | 2.62336e95 | 1.06909 | ||||||||
\(583\) | −5.28187e95 | −2.02872 | ||||||||
\(584\) | 4.00980e94 | 0.145171 | ||||||||
\(585\) | 2.55734e94 | 0.0872791 | ||||||||
\(586\) | −4.70738e95 | −1.51465 | ||||||||
\(587\) | 7.48046e94 | 0.226941 | 0.113471 | − | 0.993541i | \(-0.463803\pi\) | ||||
0.113471 | + | 0.993541i | \(0.463803\pi\) | |||||||
\(588\) | −1.11140e95 | −0.317944 | ||||||||
\(589\) | 2.26927e95 | 0.612221 | ||||||||
\(590\) | 5.75236e95 | 1.46370 | ||||||||
\(591\) | 2.90276e95 | 0.696696 | ||||||||
\(592\) | −4.98294e95 | −1.12820 | ||||||||
\(593\) | 3.74120e95 | 0.799142 | 0.399571 | − | 0.916702i | \(-0.369159\pi\) | ||||
0.399571 | + | 0.916702i | \(0.369159\pi\) | |||||||
\(594\) | 2.72681e95 | 0.549570 | ||||||||
\(595\) | 1.05796e96 | 2.01202 | ||||||||
\(596\) | 6.85333e94 | 0.123000 | ||||||||
\(597\) | −5.99527e95 | −1.01553 | ||||||||
\(598\) | 4.37233e93 | 0.00699072 | ||||||||
\(599\) | −9.07159e95 | −1.36917 | −0.684586 | − | 0.728932i | \(-0.740017\pi\) | ||||
−0.684586 | + | 0.728932i | \(0.740017\pi\) | |||||||
\(600\) | −1.34835e96 | −1.92125 | ||||||||
\(601\) | 1.14169e96 | 1.53596 | 0.767979 | − | 0.640475i | \(-0.221262\pi\) | ||||
0.767979 | + | 0.640475i | \(0.221262\pi\) | |||||||
\(602\) | −6.40394e94 | −0.0813520 | ||||||||
\(603\) | 2.97905e95 | 0.357381 | ||||||||
\(604\) | 1.62463e95 | 0.184069 | ||||||||
\(605\) | −9.54039e95 | −1.02095 | ||||||||
\(606\) | −3.33300e95 | −0.336922 | ||||||||
\(607\) | 4.17459e95 | 0.398661 | 0.199330 | − | 0.979932i | \(-0.436123\pi\) | ||||
0.199330 | + | 0.979932i | \(0.436123\pi\) | |||||||
\(608\) | −4.25813e95 | −0.384189 | ||||||||
\(609\) | −3.34870e95 | −0.285483 | ||||||||
\(610\) | −1.31416e96 | −1.05869 | ||||||||
\(611\) | 1.92934e95 | 0.146888 | ||||||||
\(612\) | 1.81711e95 | 0.130754 | ||||||||
\(613\) | 6.32712e95 | 0.430348 | 0.215174 | − | 0.976576i | \(-0.430968\pi\) | ||||
0.215174 | + | 0.976576i | \(0.430968\pi\) | |||||||
\(614\) | 7.08491e95 | 0.455539 | ||||||||
\(615\) | 1.26429e96 | 0.768518 | ||||||||
\(616\) | 3.47914e96 | 1.99957 | ||||||||
\(617\) | −2.85759e96 | −1.55297 | −0.776483 | − | 0.630138i | \(-0.782998\pi\) | ||||
−0.776483 | + | 0.630138i | \(0.782998\pi\) | |||||||
\(618\) | 3.82456e96 | 1.96553 | ||||||||
\(619\) | −2.33642e96 | −1.13560 | −0.567798 | − | 0.823168i | \(-0.692205\pi\) | ||||
−0.567798 | + | 0.823168i | \(0.692205\pi\) | |||||||
\(620\) | −5.78154e95 | −0.265785 | ||||||||
\(621\) | 9.80377e94 | 0.0426317 | ||||||||
\(622\) | 1.15020e96 | 0.473156 | ||||||||
\(623\) | −1.43099e96 | −0.556927 | ||||||||
\(624\) | 2.24166e95 | 0.0825471 | ||||||||
\(625\) | −1.26763e96 | −0.441703 | ||||||||
\(626\) | −2.98520e96 | −0.984370 | ||||||||
\(627\) | 4.39390e96 | 1.37126 | ||||||||
\(628\) | 1.15741e96 | 0.341884 | ||||||||
\(629\) | −5.13493e96 | −1.43578 | ||||||||
\(630\) | −4.53481e96 | −1.20036 | ||||||||
\(631\) | −1.91201e96 | −0.479157 | −0.239578 | − | 0.970877i | \(-0.577009\pi\) | ||||
−0.239578 | + | 0.970877i | \(0.577009\pi\) | |||||||
\(632\) | 2.11327e96 | 0.501437 | ||||||||
\(633\) | 4.20917e95 | 0.0945732 | ||||||||
\(634\) | −3.61685e95 | −0.0769575 | ||||||||
\(635\) | 1.07441e97 | 2.16508 | ||||||||
\(636\) | −2.46223e96 | −0.469957 | ||||||||
\(637\) | −5.38787e95 | −0.0974107 | ||||||||
\(638\) | 1.02793e96 | 0.176055 | ||||||||
\(639\) | 3.06764e96 | 0.497765 | ||||||||
\(640\) | −5.17464e96 | −0.795556 | ||||||||
\(641\) | −6.94117e96 | −1.01119 | −0.505593 | − | 0.862772i | \(-0.668726\pi\) | ||||
−0.505593 | + | 0.862772i | \(0.668726\pi\) | |||||||
\(642\) | −1.90540e96 | −0.263044 | ||||||||
\(643\) | −1.73392e96 | −0.226856 | −0.113428 | − | 0.993546i | \(-0.536183\pi\) | ||||
−0.113428 | + | 0.993546i | \(0.536183\pi\) | |||||||
\(644\) | 2.37769e95 | 0.0294845 | ||||||||
\(645\) | 1.08402e96 | 0.127417 | ||||||||
\(646\) | 5.94206e96 | 0.662087 | ||||||||
\(647\) | 1.35608e97 | 1.43248 | 0.716241 | − | 0.697853i | \(-0.245861\pi\) | ||||
0.716241 | + | 0.697853i | \(0.245861\pi\) | |||||||
\(648\) | 1.33350e97 | 1.33553 | ||||||||
\(649\) | 1.46521e97 | 1.39142 | ||||||||
\(650\) | −1.24250e96 | −0.111889 | ||||||||
\(651\) | −1.56437e97 | −1.33596 | ||||||||
\(652\) | −3.88714e96 | −0.314839 | ||||||||
\(653\) | −2.52462e97 | −1.93950 | −0.969752 | − | 0.244090i | \(-0.921511\pi\) | ||||
−0.969752 | + | 0.244090i | \(0.921511\pi\) | |||||||
\(654\) | −1.29310e97 | −0.942322 | ||||||||
\(655\) | 1.87405e97 | 1.29555 | ||||||||
\(656\) | 4.22608e96 | 0.277176 | ||||||||
\(657\) | −1.33126e96 | −0.0828434 | ||||||||
\(658\) | −3.42121e97 | −2.02016 | ||||||||
\(659\) | −1.64922e95 | −0.00924128 | −0.00462064 | − | 0.999989i | \(-0.501471\pi\) | ||||
−0.00462064 | + | 0.999989i | \(0.501471\pi\) | |||||||
\(660\) | −1.11946e97 | −0.595308 | ||||||||
\(661\) | −1.36393e97 | −0.688403 | −0.344202 | − | 0.938896i | \(-0.611850\pi\) | ||||
−0.344202 | + | 0.938896i | \(0.611850\pi\) | |||||||
\(662\) | 2.58010e97 | 1.23605 | ||||||||
\(663\) | 2.31004e96 | 0.105052 | ||||||||
\(664\) | −7.04380e96 | −0.304094 | ||||||||
\(665\) | 4.54766e97 | 1.86398 | ||||||||
\(666\) | 2.20103e97 | 0.856576 | ||||||||
\(667\) | 3.69573e95 | 0.0136571 | ||||||||
\(668\) | 9.23299e96 | 0.324007 | ||||||||
\(669\) | 2.92667e96 | 0.0975377 | ||||||||
\(670\) | −2.48195e97 | −0.785620 | ||||||||
\(671\) | −3.34736e97 | −1.00641 | ||||||||
\(672\) | 2.93543e97 | 0.838362 | ||||||||
\(673\) | 2.24509e97 | 0.609135 | 0.304567 | − | 0.952491i | \(-0.401488\pi\) | ||||
0.304567 | + | 0.952491i | \(0.401488\pi\) | |||||||
\(674\) | 5.55565e97 | 1.43208 | ||||||||
\(675\) | −2.78597e97 | −0.682334 | ||||||||
\(676\) | 1.00005e97 | 0.232735 | ||||||||
\(677\) | −6.81276e97 | −1.50666 | −0.753328 | − | 0.657645i | \(-0.771553\pi\) | ||||
−0.753328 | + | 0.657645i | \(0.771553\pi\) | |||||||
\(678\) | −3.37621e97 | −0.709587 | ||||||||
\(679\) | 6.91591e97 | 1.38147 | ||||||||
\(680\) | −7.96433e97 | −1.51214 | ||||||||
\(681\) | −7.53164e97 | −1.35930 | ||||||||
\(682\) | 4.80204e97 | 0.823881 | ||||||||
\(683\) | 1.00743e98 | 1.64324 | 0.821618 | − | 0.570039i | \(-0.193072\pi\) | ||||
0.821618 | + | 0.570039i | \(0.193072\pi\) | |||||||
\(684\) | 7.81089e96 | 0.121134 | ||||||||
\(685\) | −1.59170e98 | −2.34713 | ||||||||
\(686\) | 5.87700e96 | 0.0824089 | ||||||||
\(687\) | 6.07082e97 | 0.809544 | ||||||||
\(688\) | 3.62350e96 | 0.0459545 | ||||||||
\(689\) | −1.19365e97 | −0.143984 | ||||||||
\(690\) | 1.31242e97 | 0.150584 | ||||||||
\(691\) | −2.94162e97 | −0.321066 | −0.160533 | − | 0.987030i | \(-0.551321\pi\) | ||||
−0.160533 | + | 0.987030i | \(0.551321\pi\) | |||||||
\(692\) | 5.57802e96 | 0.0579188 | ||||||||
\(693\) | −1.15508e98 | −1.14108 | ||||||||
\(694\) | 5.49269e97 | 0.516277 | ||||||||
\(695\) | 3.26854e98 | 2.92333 | ||||||||
\(696\) | 2.52091e97 | 0.214555 | ||||||||
\(697\) | 4.35498e97 | 0.352741 | ||||||||
\(698\) | 2.97528e97 | 0.229359 | ||||||||
\(699\) | −1.86937e98 | −1.37161 | ||||||||
\(700\) | −6.75678e97 | −0.471908 | ||||||||
\(701\) | 1.33034e97 | 0.0884485 | 0.0442243 | − | 0.999022i | \(-0.485918\pi\) | ||||
0.0442243 | + | 0.999022i | \(0.485918\pi\) | |||||||
\(702\) | 6.16233e96 | 0.0390045 | ||||||||
\(703\) | −2.20727e98 | −1.33014 | ||||||||
\(704\) | −2.49546e98 | −1.43184 | ||||||||
\(705\) | 5.79121e98 | 3.16406 | ||||||||
\(706\) | 1.52725e98 | 0.794599 | ||||||||
\(707\) | −8.78671e97 | −0.435368 | ||||||||
\(708\) | 6.83032e97 | 0.322325 | ||||||||
\(709\) | −1.39958e98 | −0.629075 | −0.314537 | − | 0.949245i | \(-0.601849\pi\) | ||||
−0.314537 | + | 0.949245i | \(0.601849\pi\) | |||||||
\(710\) | −2.55575e98 | −1.09422 | ||||||||
\(711\) | −7.01611e97 | −0.286151 | ||||||||
\(712\) | 1.07725e98 | 0.418561 | ||||||||
\(713\) | 1.72649e97 | 0.0639109 | ||||||||
\(714\) | −4.09629e98 | −1.44478 | ||||||||
\(715\) | −5.42696e97 | −0.182389 | ||||||||
\(716\) | −2.29037e97 | −0.0733511 | ||||||||
\(717\) | 9.56019e97 | 0.291780 | ||||||||
\(718\) | −5.74956e97 | −0.167240 | ||||||||
\(719\) | −6.02544e98 | −1.67048 | −0.835241 | − | 0.549884i | \(-0.814672\pi\) | ||||
−0.835241 | + | 0.549884i | \(0.814672\pi\) | |||||||
\(720\) | 2.56591e98 | 0.678062 | ||||||||
\(721\) | 1.00826e99 | 2.53984 | ||||||||
\(722\) | −1.08871e98 | −0.261444 | ||||||||
\(723\) | 6.45521e98 | 1.47788 | ||||||||
\(724\) | 1.05089e97 | 0.0229392 | ||||||||
\(725\) | −1.05023e98 | −0.218587 | ||||||||
\(726\) | 3.69393e98 | 0.733121 | ||||||||
\(727\) | −9.25498e97 | −0.175161 | −0.0875807 | − | 0.996157i | \(-0.527914\pi\) | ||||
−0.0875807 | + | 0.996157i | \(0.527914\pi\) | |||||||
\(728\) | 7.86252e97 | 0.141915 | ||||||||
\(729\) | −8.25308e97 | −0.142075 | ||||||||
\(730\) | 1.10912e98 | 0.182112 | ||||||||
\(731\) | 3.73403e97 | 0.0584828 | ||||||||
\(732\) | −1.56043e98 | −0.233137 | ||||||||
\(733\) | −4.12420e98 | −0.587831 | −0.293916 | − | 0.955831i | \(-0.594959\pi\) | ||||
−0.293916 | + | 0.955831i | \(0.594959\pi\) | |||||||
\(734\) | −1.46232e97 | −0.0198851 | ||||||||
\(735\) | −1.61725e99 | −2.09829 | ||||||||
\(736\) | −3.23964e97 | −0.0401062 | ||||||||
\(737\) | −6.32189e98 | −0.746825 | ||||||||
\(738\) | −1.86672e98 | −0.210443 | ||||||||
\(739\) | −6.23242e98 | −0.670539 | −0.335269 | − | 0.942122i | \(-0.608827\pi\) | ||||
−0.335269 | + | 0.942122i | \(0.608827\pi\) | |||||||
\(740\) | 5.62358e98 | 0.577456 | ||||||||
\(741\) | 9.92978e97 | 0.0973221 | ||||||||
\(742\) | 2.11665e99 | 1.98022 | ||||||||
\(743\) | −9.37642e97 | −0.0837381 | −0.0418690 | − | 0.999123i | \(-0.513331\pi\) | ||||
−0.0418690 | + | 0.999123i | \(0.513331\pi\) | |||||||
\(744\) | 1.17766e99 | 1.00405 | ||||||||
\(745\) | 9.97267e98 | 0.811745 | ||||||||
\(746\) | −1.82122e99 | −1.41538 | ||||||||
\(747\) | 2.33856e98 | 0.173535 | ||||||||
\(748\) | −3.85610e98 | −0.273240 | ||||||||
\(749\) | −5.02318e98 | −0.339904 | ||||||||
\(750\) | −1.06379e99 | −0.687450 | ||||||||
\(751\) | −8.97025e98 | −0.553639 | −0.276819 | − | 0.960922i | \(-0.589280\pi\) | ||||
−0.276819 | + | 0.960922i | \(0.589280\pi\) | |||||||
\(752\) | 1.93580e99 | 1.14116 | ||||||||
\(753\) | 5.17531e98 | 0.291413 | ||||||||
\(754\) | 2.32302e97 | 0.0124951 | ||||||||
\(755\) | 2.36409e99 | 1.21477 | ||||||||
\(756\) | 3.35110e98 | 0.164508 | ||||||||
\(757\) | 2.27469e99 | 1.06688 | 0.533439 | − | 0.845839i | \(-0.320899\pi\) | ||||
0.533439 | + | 0.845839i | \(0.320899\pi\) | |||||||
\(758\) | −1.77715e99 | −0.796409 | ||||||||
\(759\) | 3.34293e98 | 0.143148 | ||||||||
\(760\) | −3.42349e99 | −1.40088 | ||||||||
\(761\) | 3.10760e99 | 1.21522 | 0.607608 | − | 0.794237i | \(-0.292129\pi\) | ||||
0.607608 | + | 0.794237i | \(0.292129\pi\) | |||||||
\(762\) | −4.15998e99 | −1.55469 | ||||||||
\(763\) | −3.40897e99 | −1.21766 | ||||||||
\(764\) | 3.50755e98 | 0.119752 | ||||||||
\(765\) | 2.64417e99 | 0.862919 | ||||||||
\(766\) | 4.62692e98 | 0.144344 | ||||||||
\(767\) | 3.31123e98 | 0.0987529 | ||||||||
\(768\) | −2.95305e99 | −0.841994 | ||||||||
\(769\) | −6.21896e99 | −1.69535 | −0.847674 | − | 0.530517i | \(-0.821998\pi\) | ||||
−0.847674 | + | 0.530517i | \(0.821998\pi\) | |||||||
\(770\) | 9.62337e99 | 2.50840 | ||||||||
\(771\) | −3.86701e97 | −0.00963827 | ||||||||
\(772\) | 8.59626e98 | 0.204886 | ||||||||
\(773\) | −5.78018e99 | −1.31749 | −0.658747 | − | 0.752364i | \(-0.728913\pi\) | ||||
−0.658747 | + | 0.752364i | \(0.728913\pi\) | |||||||
\(774\) | −1.60055e98 | −0.0348904 | ||||||||
\(775\) | −4.90623e99 | −1.02291 | ||||||||
\(776\) | −5.20632e99 | −1.03825 | ||||||||
\(777\) | 1.52163e100 | 2.90258 | ||||||||
\(778\) | 7.58952e99 | 1.38490 | ||||||||
\(779\) | 1.87200e99 | 0.326787 | ||||||||
\(780\) | −2.52987e98 | −0.0422507 | ||||||||
\(781\) | −6.50988e99 | −1.04019 | ||||||||
\(782\) | 4.52079e98 | 0.0691165 | ||||||||
\(783\) | 5.20874e98 | 0.0761995 | ||||||||
\(784\) | −5.40592e99 | −0.756773 | ||||||||
\(785\) | 1.68421e100 | 2.25628 | ||||||||
\(786\) | −7.25611e99 | −0.930306 | ||||||||
\(787\) | 8.49135e99 | 1.04195 | 0.520977 | − | 0.853571i | \(-0.325568\pi\) | ||||
0.520977 | + | 0.853571i | \(0.325568\pi\) | |||||||
\(788\) | −1.09504e99 | −0.128610 | ||||||||
\(789\) | −1.24166e100 | −1.39587 | ||||||||
\(790\) | 5.84535e99 | 0.629037 | ||||||||
\(791\) | −8.90064e99 | −0.916923 | ||||||||
\(792\) | 8.69550e99 | 0.857582 | ||||||||
\(793\) | −7.56470e98 | −0.0714278 | ||||||||
\(794\) | −2.35836e99 | −0.213208 | ||||||||
\(795\) | −3.58293e100 | −3.10151 | ||||||||
\(796\) | 2.26166e99 | 0.187468 | ||||||||
\(797\) | 6.54680e98 | 0.0519657 | 0.0259829 | − | 0.999662i | \(-0.491728\pi\) | ||||
0.0259829 | + | 0.999662i | \(0.491728\pi\) | |||||||
\(798\) | −1.76080e100 | −1.33848 | ||||||||
\(799\) | 1.99485e100 | 1.45227 | ||||||||
\(800\) | 9.20619e99 | 0.641912 | ||||||||
\(801\) | −3.57650e99 | −0.238856 | ||||||||
\(802\) | 1.00986e100 | 0.646021 | ||||||||
\(803\) | 2.82508e99 | 0.173119 | ||||||||
\(804\) | −2.94705e99 | −0.173003 | ||||||||
\(805\) | 3.45991e99 | 0.194584 | ||||||||
\(806\) | 1.08521e99 | 0.0584731 | ||||||||
\(807\) | 4.79834e100 | 2.47716 | ||||||||
\(808\) | 6.61467e99 | 0.327202 | ||||||||
\(809\) | −1.91402e100 | −0.907239 | −0.453620 | − | 0.891195i | \(-0.649868\pi\) | ||||
−0.453620 | + | 0.891195i | \(0.649868\pi\) | |||||||
\(810\) | 3.68848e100 | 1.67539 | ||||||||
\(811\) | −1.81091e100 | −0.788275 | −0.394138 | − | 0.919051i | \(-0.628957\pi\) | ||||
−0.394138 | + | 0.919051i | \(0.628957\pi\) | |||||||
\(812\) | 1.26327e99 | 0.0527002 | ||||||||
\(813\) | −4.39524e99 | −0.175735 | ||||||||
\(814\) | −4.67084e100 | −1.79000 | ||||||||
\(815\) | −5.65640e100 | −2.07779 | ||||||||
\(816\) | 2.31778e100 | 0.816134 | ||||||||
\(817\) | 1.60509e99 | 0.0541798 | ||||||||
\(818\) | 5.15482e99 | 0.166811 | ||||||||
\(819\) | −2.61037e99 | −0.0809856 | ||||||||
\(820\) | −4.76941e99 | −0.141869 | ||||||||
\(821\) | 4.37394e100 | 1.24748 | 0.623740 | − | 0.781632i | \(-0.285612\pi\) | ||||
0.623740 | + | 0.781632i | \(0.285612\pi\) | |||||||
\(822\) | 6.16289e100 | 1.68541 | ||||||||
\(823\) | 4.69012e100 | 1.22996 | 0.614978 | − | 0.788544i | \(-0.289165\pi\) | ||||
0.614978 | + | 0.788544i | \(0.289165\pi\) | |||||||
\(824\) | −7.59023e100 | −1.90883 | ||||||||
\(825\) | −9.49974e100 | −2.29113 | ||||||||
\(826\) | −5.87166e100 | −1.35815 | ||||||||
\(827\) | 4.85405e100 | 1.07687 | 0.538436 | − | 0.842666i | \(-0.319015\pi\) | ||||
0.538436 | + | 0.842666i | \(0.319015\pi\) | |||||||
\(828\) | 5.94263e98 | 0.0126454 | ||||||||
\(829\) | 1.00919e100 | 0.205988 | 0.102994 | − | 0.994682i | \(-0.467158\pi\) | ||||
0.102994 | + | 0.994682i | \(0.467158\pi\) | |||||||
\(830\) | −1.94833e100 | −0.381477 | ||||||||
\(831\) | 1.07094e101 | 2.01154 | ||||||||
\(832\) | −5.63949e99 | −0.101621 | ||||||||
\(833\) | −5.57082e100 | −0.963089 | ||||||||
\(834\) | −1.26554e101 | −2.09917 | ||||||||
\(835\) | 1.34354e101 | 2.13830 | ||||||||
\(836\) | −1.65756e100 | −0.253135 | ||||||||
\(837\) | 2.43330e100 | 0.356589 | ||||||||
\(838\) | 3.62252e100 | 0.509439 | ||||||||
\(839\) | −9.55850e100 | −1.29004 | −0.645019 | − | 0.764167i | \(-0.723150\pi\) | ||||
−0.645019 | + | 0.764167i | \(0.723150\pi\) | |||||||
\(840\) | 2.36006e101 | 3.05694 | ||||||||
\(841\) | −7.84746e100 | −0.975589 | ||||||||
\(842\) | 1.04174e101 | 1.24307 | ||||||||
\(843\) | −9.09402e100 | −1.04161 | ||||||||
\(844\) | −1.58787e99 | −0.0174583 | ||||||||
\(845\) | 1.45523e101 | 1.53594 | ||||||||
\(846\) | −8.55071e100 | −0.866413 | ||||||||
\(847\) | 9.73824e100 | 0.947334 | ||||||||
\(848\) | −1.19765e101 | −1.11860 | ||||||||
\(849\) | −1.35226e101 | −1.21268 | ||||||||
\(850\) | −1.28469e101 | −1.10623 | ||||||||
\(851\) | −1.67932e100 | −0.138856 | ||||||||
\(852\) | −3.03469e100 | −0.240962 | ||||||||
\(853\) | −1.93739e101 | −1.47732 | −0.738662 | − | 0.674076i | \(-0.764542\pi\) | ||||
−0.738662 | + | 0.674076i | \(0.764542\pi\) | |||||||
\(854\) | 1.34141e101 | 0.982351 | ||||||||
\(855\) | 1.13661e101 | 0.799428 | ||||||||
\(856\) | 3.78147e100 | 0.255456 | ||||||||
\(857\) | −1.15045e101 | −0.746500 | −0.373250 | − | 0.927731i | \(-0.621757\pi\) | ||||
−0.373250 | + | 0.927731i | \(0.621757\pi\) | |||||||
\(858\) | 2.10126e100 | 0.130969 | ||||||||
\(859\) | 1.59766e101 | 0.956578 | 0.478289 | − | 0.878203i | \(-0.341257\pi\) | ||||
0.478289 | + | 0.878203i | \(0.341257\pi\) | |||||||
\(860\) | −4.08937e99 | −0.0235212 | ||||||||
\(861\) | −1.29051e101 | −0.713102 | ||||||||
\(862\) | 7.32010e100 | 0.388612 | ||||||||
\(863\) | −1.27110e101 | −0.648345 | −0.324172 | − | 0.945998i | \(-0.605086\pi\) | ||||
−0.324172 | + | 0.945998i | \(0.605086\pi\) | |||||||
\(864\) | −4.56592e100 | −0.223771 | ||||||||
\(865\) | 8.11688e100 | 0.382238 | ||||||||
\(866\) | 3.02431e101 | 1.36854 | ||||||||
\(867\) | −5.35217e100 | −0.232740 | ||||||||
\(868\) | 5.90144e100 | 0.246620 | ||||||||
\(869\) | 1.48890e101 | 0.597974 | ||||||||
\(870\) | 6.97290e100 | 0.269153 | ||||||||
\(871\) | −1.42869e100 | −0.0530042 | ||||||||
\(872\) | 2.56628e101 | 0.915137 | ||||||||
\(873\) | 1.72851e101 | 0.592489 | ||||||||
\(874\) | 1.94328e100 | 0.0640311 | ||||||||
\(875\) | −2.80444e101 | −0.888317 | ||||||||
\(876\) | 1.31696e100 | 0.0401034 | ||||||||
\(877\) | 9.97885e100 | 0.292142 | 0.146071 | − | 0.989274i | \(-0.453337\pi\) | ||||
0.146071 | + | 0.989274i | \(0.453337\pi\) | |||||||
\(878\) | −4.96548e101 | −1.39766 | ||||||||
\(879\) | −8.13362e101 | −2.20124 | ||||||||
\(880\) | −5.44514e101 | −1.41696 | ||||||||
\(881\) | 7.47754e100 | 0.187107 | 0.0935535 | − | 0.995614i | \(-0.470177\pi\) | ||||
0.0935535 | + | 0.995614i | \(0.470177\pi\) | |||||||
\(882\) | 2.38787e101 | 0.574572 | ||||||||
\(883\) | 1.70719e101 | 0.395036 | 0.197518 | − | 0.980299i | \(-0.436712\pi\) | ||||
0.197518 | + | 0.980299i | \(0.436712\pi\) | |||||||
\(884\) | −8.71442e99 | −0.0193926 | ||||||||
\(885\) | 9.93919e101 | 2.12720 | ||||||||
\(886\) | 8.12314e100 | 0.167209 | ||||||||
\(887\) | 5.22741e101 | 1.03496 | 0.517478 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517478 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(888\) | −1.14549e102 | −2.18144 | ||||||||
\(889\) | −1.09669e102 | −2.00896 | ||||||||
\(890\) | 2.97971e101 | 0.525071 | ||||||||
\(891\) | 9.39510e101 | 1.59265 | ||||||||
\(892\) | −1.10406e100 | −0.0180055 | ||||||||
\(893\) | 8.57494e101 | 1.34541 | ||||||||
\(894\) | −3.86131e101 | −0.582895 | ||||||||
\(895\) | −3.33285e101 | −0.484084 | ||||||||
\(896\) | 5.28195e101 | 0.738190 | ||||||||
\(897\) | 7.55470e99 | 0.0101596 | ||||||||
\(898\) | 2.43951e101 | 0.315696 | ||||||||
\(899\) | 9.17283e100 | 0.114234 | ||||||||
\(900\) | −1.68874e101 | −0.202393 | ||||||||
\(901\) | −1.23418e102 | −1.42355 | ||||||||
\(902\) | 3.96138e101 | 0.439765 | ||||||||
\(903\) | −1.10650e101 | −0.118229 | ||||||||
\(904\) | 6.70044e101 | 0.689116 | ||||||||
\(905\) | 1.52922e101 | 0.151388 | ||||||||
\(906\) | −9.15352e101 | −0.872298 | ||||||||
\(907\) | 1.78006e102 | 1.63299 | 0.816497 | − | 0.577350i | \(-0.195913\pi\) | ||||
0.816497 | + | 0.577350i | \(0.195913\pi\) | |||||||
\(908\) | 2.84125e101 | 0.250927 | ||||||||
\(909\) | −2.19608e101 | −0.186722 | ||||||||
\(910\) | 2.17479e101 | 0.178028 | ||||||||
\(911\) | −5.06510e101 | −0.399213 | −0.199606 | − | 0.979876i | \(-0.563966\pi\) | ||||
−0.199606 | + | 0.979876i | \(0.563966\pi\) | |||||||
\(912\) | 9.96306e101 | 0.756085 | ||||||||
\(913\) | −4.96268e101 | −0.362639 | ||||||||
\(914\) | −1.55377e102 | −1.09331 | ||||||||
\(915\) | −2.27066e102 | −1.53860 | ||||||||
\(916\) | −2.29017e101 | −0.149442 | ||||||||
\(917\) | −1.91291e102 | −1.20213 | ||||||||
\(918\) | 6.37158e101 | 0.385633 | ||||||||
\(919\) | −1.40587e102 | −0.819523 | −0.409762 | − | 0.912193i | \(-0.634388\pi\) | ||||
−0.409762 | + | 0.912193i | \(0.634388\pi\) | |||||||
\(920\) | −2.60464e101 | −0.146240 | ||||||||
\(921\) | 1.22416e102 | 0.662037 | ||||||||
\(922\) | 1.63961e102 | 0.854128 | ||||||||
\(923\) | −1.47117e101 | −0.0738250 | ||||||||
\(924\) | 1.14267e102 | 0.552382 | ||||||||
\(925\) | 4.77218e102 | 2.22243 | ||||||||
\(926\) | −3.06502e102 | −1.37517 | ||||||||
\(927\) | 2.51997e102 | 1.08929 | ||||||||
\(928\) | −1.72122e101 | −0.0716854 | ||||||||
\(929\) | 6.77380e101 | 0.271826 | 0.135913 | − | 0.990721i | \(-0.456603\pi\) | ||||
0.135913 | + | 0.990721i | \(0.456603\pi\) | |||||||
\(930\) | 3.25744e102 | 1.25955 | ||||||||
\(931\) | −2.39464e102 | −0.892227 | ||||||||
\(932\) | 7.05202e101 | 0.253201 | ||||||||
\(933\) | 1.98736e102 | 0.687639 | ||||||||
\(934\) | −9.23811e101 | −0.308046 | ||||||||
\(935\) | −5.61123e102 | −1.80326 | ||||||||
\(936\) | 1.96510e101 | 0.0608650 | ||||||||
\(937\) | 1.41794e102 | 0.423295 | 0.211647 | − | 0.977346i | \(-0.432117\pi\) | ||||
0.211647 | + | 0.977346i | \(0.432117\pi\) | |||||||
\(938\) | 2.53342e102 | 0.728970 | ||||||||
\(939\) | −5.15795e102 | −1.43059 | ||||||||
\(940\) | −2.18469e102 | −0.584087 | ||||||||
\(941\) | 2.70724e102 | 0.697726 | 0.348863 | − | 0.937174i | \(-0.386568\pi\) | ||||
0.348863 | + | 0.937174i | \(0.386568\pi\) | |||||||
\(942\) | −6.52107e102 | −1.62018 | ||||||||
\(943\) | 1.42424e101 | 0.0341139 | ||||||||
\(944\) | 3.32233e102 | 0.767200 | ||||||||
\(945\) | 4.87638e102 | 1.08568 | ||||||||
\(946\) | 3.39655e101 | 0.0729111 | ||||||||
\(947\) | −8.25080e102 | −1.70774 | −0.853870 | − | 0.520487i | \(-0.825750\pi\) | ||||
−0.853870 | + | 0.520487i | \(0.825750\pi\) | |||||||
\(948\) | 6.94074e101 | 0.138522 | ||||||||
\(949\) | 6.38442e100 | 0.0122867 | ||||||||
\(950\) | −5.52229e102 | −1.02484 | ||||||||
\(951\) | −6.24935e101 | −0.111843 | ||||||||
\(952\) | 8.12950e102 | 1.40310 | ||||||||
\(953\) | −5.79812e102 | −0.965122 | −0.482561 | − | 0.875862i | \(-0.660293\pi\) | ||||
−0.482561 | + | 0.875862i | \(0.660293\pi\) | |||||||
\(954\) | 5.29019e102 | 0.849282 | ||||||||
\(955\) | 5.10403e102 | 0.790309 | ||||||||
\(956\) | −3.60650e101 | −0.0538627 | ||||||||
\(957\) | 1.77610e102 | 0.255862 | ||||||||
\(958\) | 5.89735e102 | 0.819496 | ||||||||
\(959\) | 1.62471e103 | 2.17788 | ||||||||
\(960\) | −1.69278e103 | −2.18899 | ||||||||
\(961\) | −3.73084e102 | −0.465424 | ||||||||
\(962\) | −1.05556e102 | −0.127041 | ||||||||
\(963\) | −1.25546e102 | −0.145779 | ||||||||
\(964\) | −2.43517e102 | −0.272817 | ||||||||
\(965\) | 1.25089e103 | 1.35216 | ||||||||
\(966\) | −1.33964e102 | −0.139726 | ||||||||
\(967\) | 4.01425e102 | 0.404009 | 0.202004 | − | 0.979385i | \(-0.435254\pi\) | ||||
0.202004 | + | 0.979385i | \(0.435254\pi\) | |||||||
\(968\) | −7.33099e102 | −0.711972 | ||||||||
\(969\) | 1.02670e103 | 0.962213 | ||||||||
\(970\) | −1.44008e103 | −1.30245 | ||||||||
\(971\) | 5.69960e102 | 0.497486 | 0.248743 | − | 0.968570i | \(-0.419983\pi\) | ||||
0.248743 | + | 0.968570i | \(0.419983\pi\) | |||||||
\(972\) | 3.02089e102 | 0.254477 | ||||||||
\(973\) | −3.33632e103 | −2.71253 | ||||||||
\(974\) | 6.51998e101 | 0.0511638 | ||||||||
\(975\) | −2.14685e102 | −0.162608 | ||||||||
\(976\) | −7.59005e102 | −0.554915 | ||||||||
\(977\) | 8.26703e102 | 0.583428 | 0.291714 | − | 0.956506i | \(-0.405774\pi\) | ||||
0.291714 | + | 0.956506i | \(0.405774\pi\) | |||||||
\(978\) | 2.19010e103 | 1.49201 | ||||||||
\(979\) | 7.58975e102 | 0.499142 | ||||||||
\(980\) | 6.10095e102 | 0.387345 | ||||||||
\(981\) | −8.52012e102 | −0.522234 | ||||||||
\(982\) | 1.38234e102 | 0.0818030 | ||||||||
\(983\) | −6.43048e102 | −0.367407 | −0.183703 | − | 0.982982i | \(-0.558809\pi\) | ||||
−0.183703 | + | 0.982982i | \(0.558809\pi\) | |||||||
\(984\) | 9.71498e102 | 0.535934 | ||||||||
\(985\) | −1.59346e103 | −0.848770 | ||||||||
\(986\) | 2.40190e102 | 0.123538 | ||||||||
\(987\) | −5.91132e103 | −2.93591 | ||||||||
\(988\) | −3.74592e101 | −0.0179657 | ||||||||
\(989\) | 1.22117e101 | 0.00565593 | ||||||||
\(990\) | 2.40519e103 | 1.07581 | ||||||||
\(991\) | 3.91036e103 | 1.68918 | 0.844590 | − | 0.535413i | \(-0.179844\pi\) | ||||
0.844590 | + | 0.535413i | \(0.179844\pi\) | |||||||
\(992\) | −8.04079e102 | −0.335464 | ||||||||
\(993\) | 4.45801e103 | 1.79635 | ||||||||
\(994\) | 2.60876e103 | 1.01532 | ||||||||
\(995\) | 3.29107e103 | 1.23720 | ||||||||
\(996\) | −2.31344e102 | −0.0840060 | ||||||||
\(997\) | −5.45024e103 | −1.91176 | −0.955878 | − | 0.293763i | \(-0.905092\pi\) | ||||
−0.955878 | + | 0.293763i | \(0.905092\pi\) | |||||||
\(998\) | 2.23947e103 | 0.758826 | ||||||||
\(999\) | −2.36682e103 | −0.774740 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1.70.a.a.1.4 | ✓ | 5 | |
3.2 | odd | 2 | 9.70.a.b.1.2 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.70.a.a.1.4 | ✓ | 5 | 1.1 | even | 1 | trivial | |
9.70.a.b.1.2 | 5 | 3.2 | odd | 2 |