Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2,74,Mod(1,2)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 74, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2.1");
S:= CuspForms(chi, 74);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2 \) |
Weight: | \( k \) | \(=\) | \( 74 \) |
Character orbit: | \([\chi]\) | \(=\) | 2.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: | \(67.4967947474\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2 x^{3} + \cdots + 21\!\cdots\!44 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{45}\cdot 3^{14}\cdot 5^{5}\cdot 7^{2}\cdot 11 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(2.29885e14\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 6.87195e10 | 0.707107 | ||||||||
\(3\) | −3.65112e17 | −1.40443 | −0.702216 | − | 0.711964i | \(-0.747806\pi\) | ||||
−0.702216 | + | 0.711964i | \(0.747806\pi\) | |||||||
\(4\) | 4.72237e21 | 0.500000 | ||||||||
\(5\) | −6.80519e24 | −0.209139 | −0.104570 | − | 0.994518i | \(-0.533346\pi\) | ||||
−0.104570 | + | 0.994518i | \(0.533346\pi\) | |||||||
\(6\) | −2.50903e28 | −0.993083 | ||||||||
\(7\) | 6.19950e30 | 0.883646 | 0.441823 | − | 0.897102i | \(-0.354332\pi\) | ||||
0.441823 | + | 0.897102i | \(0.354332\pi\) | |||||||
\(8\) | 3.24519e32 | 0.353553 | ||||||||
\(9\) | 6.57217e34 | 0.972427 | ||||||||
\(10\) | −4.67649e35 | −0.147884 | ||||||||
\(11\) | 3.23190e37 | 0.315228 | 0.157614 | − | 0.987501i | \(-0.449620\pi\) | ||||
0.157614 | + | 0.987501i | \(0.449620\pi\) | |||||||
\(12\) | −1.72419e39 | −0.702216 | ||||||||
\(13\) | −6.31056e40 | −1.38400 | −0.691999 | − | 0.721899i | \(-0.743270\pi\) | ||||
−0.691999 | + | 0.721899i | \(0.743270\pi\) | |||||||
\(14\) | 4.26026e41 | 0.624832 | ||||||||
\(15\) | 2.48466e42 | 0.293721 | ||||||||
\(16\) | 2.23007e43 | 0.250000 | ||||||||
\(17\) | −4.49909e44 | −0.551746 | −0.275873 | − | 0.961194i | \(-0.588967\pi\) | ||||
−0.275873 | + | 0.961194i | \(0.588967\pi\) | |||||||
\(18\) | 4.51636e45 | 0.687610 | ||||||||
\(19\) | 3.27330e46 | 0.692596 | 0.346298 | − | 0.938125i | \(-0.387439\pi\) | ||||
0.346298 | + | 0.938125i | \(0.387439\pi\) | |||||||
\(20\) | −3.21366e46 | −0.104570 | ||||||||
\(21\) | −2.26351e48 | −1.24102 | ||||||||
\(22\) | 2.22095e48 | 0.222900 | ||||||||
\(23\) | −8.46773e49 | −1.67765 | −0.838824 | − | 0.544403i | \(-0.816756\pi\) | ||||
−0.838824 | + | 0.544403i | \(0.816756\pi\) | |||||||
\(24\) | −1.18486e50 | −0.496541 | ||||||||
\(25\) | −1.01248e51 | −0.956261 | ||||||||
\(26\) | −4.33658e51 | −0.978634 | ||||||||
\(27\) | 6.80388e50 | 0.0387239 | ||||||||
\(28\) | 2.92763e52 | 0.441823 | ||||||||
\(29\) | 7.55802e51 | 0.0316870 | 0.0158435 | − | 0.999874i | \(-0.494957\pi\) | ||||
0.0158435 | + | 0.999874i | \(0.494957\pi\) | |||||||
\(30\) | 1.70744e53 | 0.207692 | ||||||||
\(31\) | 5.30479e54 | 1.94970 | 0.974848 | − | 0.222872i | \(-0.0715432\pi\) | ||||
0.974848 | + | 0.222872i | \(0.0715432\pi\) | |||||||
\(32\) | 1.53250e54 | 0.176777 | ||||||||
\(33\) | −1.18001e55 | −0.442717 | ||||||||
\(34\) | −3.09175e55 | −0.390143 | ||||||||
\(35\) | −4.21888e55 | −0.184805 | ||||||||
\(36\) | 3.10362e56 | 0.486214 | ||||||||
\(37\) | 1.75519e57 | 1.01149 | 0.505743 | − | 0.862684i | \(-0.331218\pi\) | ||||
0.505743 | + | 0.862684i | \(0.331218\pi\) | |||||||
\(38\) | 2.24940e57 | 0.489739 | ||||||||
\(39\) | 2.30406e58 | 1.94373 | ||||||||
\(40\) | −2.20841e57 | −0.0739418 | ||||||||
\(41\) | −4.90971e58 | −0.667491 | −0.333745 | − | 0.942663i | \(-0.608313\pi\) | ||||
−0.333745 | + | 0.942663i | \(0.608313\pi\) | |||||||
\(42\) | −1.55547e59 | −0.877533 | ||||||||
\(43\) | −7.94351e58 | −0.189852 | −0.0949258 | − | 0.995484i | \(-0.530261\pi\) | ||||
−0.0949258 | + | 0.995484i | \(0.530261\pi\) | |||||||
\(44\) | 1.52622e59 | 0.157614 | ||||||||
\(45\) | −4.47249e59 | −0.203373 | ||||||||
\(46\) | −5.81898e60 | −1.18628 | ||||||||
\(47\) | 1.68814e61 | 1.56978 | 0.784888 | − | 0.619638i | \(-0.212720\pi\) | ||||
0.784888 | + | 0.619638i | \(0.212720\pi\) | |||||||
\(48\) | −8.14227e60 | −0.351108 | ||||||||
\(49\) | −1.07880e61 | −0.219171 | ||||||||
\(50\) | −6.95771e61 | −0.676179 | ||||||||
\(51\) | 1.64267e62 | 0.774889 | ||||||||
\(52\) | −2.98008e62 | −0.691999 | ||||||||
\(53\) | 1.52771e63 | 1.76999 | 0.884996 | − | 0.465599i | \(-0.154161\pi\) | ||||
0.884996 | + | 0.465599i | \(0.154161\pi\) | |||||||
\(54\) | 4.67559e61 | 0.0273819 | ||||||||
\(55\) | −2.19937e62 | −0.0659266 | ||||||||
\(56\) | 2.01185e63 | 0.312416 | ||||||||
\(57\) | −1.19512e64 | −0.972703 | ||||||||
\(58\) | 5.19383e62 | 0.0224061 | ||||||||
\(59\) | −5.86986e64 | −1.35684 | −0.678422 | − | 0.734673i | \(-0.737336\pi\) | ||||
−0.678422 | + | 0.734673i | \(0.737336\pi\) | |||||||
\(60\) | 1.17335e64 | 0.146861 | ||||||||
\(61\) | 1.23093e65 | 0.842741 | 0.421371 | − | 0.906889i | \(-0.361549\pi\) | ||||
0.421371 | + | 0.906889i | \(0.361549\pi\) | |||||||
\(62\) | 3.64543e65 | 1.37864 | ||||||||
\(63\) | 4.07442e65 | 0.859281 | ||||||||
\(64\) | 1.05312e65 | 0.125000 | ||||||||
\(65\) | 4.29445e65 | 0.289448 | ||||||||
\(66\) | −8.10895e65 | −0.313048 | ||||||||
\(67\) | 4.29028e64 | 0.00956654 | 0.00478327 | − | 0.999989i | \(-0.498477\pi\) | ||||
0.00478327 | + | 0.999989i | \(0.498477\pi\) | |||||||
\(68\) | −2.12463e66 | −0.275873 | ||||||||
\(69\) | 3.09167e67 | 2.35614 | ||||||||
\(70\) | −2.89919e66 | −0.130677 | ||||||||
\(71\) | 3.23078e67 | 0.867715 | 0.433858 | − | 0.900981i | \(-0.357152\pi\) | ||||
0.433858 | + | 0.900981i | \(0.357152\pi\) | |||||||
\(72\) | 2.13279e67 | 0.343805 | ||||||||
\(73\) | 5.08128e67 | 0.495095 | 0.247547 | − | 0.968876i | \(-0.420375\pi\) | ||||
0.247547 | + | 0.968876i | \(0.420375\pi\) | |||||||
\(74\) | 1.20615e68 | 0.715229 | ||||||||
\(75\) | 3.69669e68 | 1.34300 | ||||||||
\(76\) | 1.54577e68 | 0.346298 | ||||||||
\(77\) | 2.00362e68 | 0.278550 | ||||||||
\(78\) | 1.58334e69 | 1.37442 | ||||||||
\(79\) | 2.74338e69 | 1.49588 | 0.747940 | − | 0.663767i | \(-0.231043\pi\) | ||||
0.747940 | + | 0.663767i | \(0.231043\pi\) | |||||||
\(80\) | −1.51761e68 | −0.0522848 | ||||||||
\(81\) | −4.69023e69 | −1.02681 | ||||||||
\(82\) | −3.37393e69 | −0.471987 | ||||||||
\(83\) | 6.35075e69 | 0.570787 | 0.285394 | − | 0.958410i | \(-0.407876\pi\) | ||||
0.285394 | + | 0.958410i | \(0.407876\pi\) | |||||||
\(84\) | −1.06891e70 | −0.620510 | ||||||||
\(85\) | 3.06171e69 | 0.115392 | ||||||||
\(86\) | −5.45874e69 | −0.134245 | ||||||||
\(87\) | −2.75952e69 | −0.0445022 | ||||||||
\(88\) | 1.04881e70 | 0.111450 | ||||||||
\(89\) | −4.25484e70 | −0.299329 | −0.149664 | − | 0.988737i | \(-0.547819\pi\) | ||||
−0.149664 | + | 0.988737i | \(0.547819\pi\) | |||||||
\(90\) | −3.07347e70 | −0.143806 | ||||||||
\(91\) | −3.91223e71 | −1.22296 | ||||||||
\(92\) | −3.99877e71 | −0.838824 | ||||||||
\(93\) | −1.93685e72 | −2.73821 | ||||||||
\(94\) | 1.16008e72 | 1.11000 | ||||||||
\(95\) | −2.22754e71 | −0.144849 | ||||||||
\(96\) | −5.59533e71 | −0.248271 | ||||||||
\(97\) | 6.06774e72 | 1.84442 | 0.922208 | − | 0.386694i | \(-0.126383\pi\) | ||||
0.922208 | + | 0.386694i | \(0.126383\pi\) | |||||||
\(98\) | −7.41343e71 | −0.154977 | ||||||||
\(99\) | 2.12406e72 | 0.306537 | ||||||||
\(100\) | −4.78130e72 | −0.478130 | ||||||||
\(101\) | 1.11331e73 | 0.774255 | 0.387128 | − | 0.922026i | \(-0.373467\pi\) | ||||
0.387128 | + | 0.922026i | \(0.373467\pi\) | |||||||
\(102\) | 1.12884e73 | 0.547929 | ||||||||
\(103\) | 1.61632e73 | 0.549502 | 0.274751 | − | 0.961515i | \(-0.411405\pi\) | ||||
0.274751 | + | 0.961515i | \(0.411405\pi\) | |||||||
\(104\) | −2.04789e73 | −0.489317 | ||||||||
\(105\) | 1.54036e73 | 0.259546 | ||||||||
\(106\) | 1.04983e74 | 1.25157 | ||||||||
\(107\) | 8.46135e73 | 0.716031 | 0.358015 | − | 0.933716i | \(-0.383454\pi\) | ||||
0.358015 | + | 0.933716i | \(0.383454\pi\) | |||||||
\(108\) | 3.21304e72 | 0.0193620 | ||||||||
\(109\) | −1.73263e74 | −0.745828 | −0.372914 | − | 0.927866i | \(-0.621641\pi\) | ||||
−0.372914 | + | 0.927866i | \(0.621641\pi\) | |||||||
\(110\) | −1.51140e73 | −0.0466171 | ||||||||
\(111\) | −6.40840e74 | −1.42056 | ||||||||
\(112\) | 1.38253e74 | 0.220911 | ||||||||
\(113\) | 5.79341e74 | 0.669223 | 0.334611 | − | 0.942356i | \(-0.391395\pi\) | ||||
0.334611 | + | 0.942356i | \(0.391395\pi\) | |||||||
\(114\) | −8.21282e74 | −0.687805 | ||||||||
\(115\) | 5.76245e74 | 0.350862 | ||||||||
\(116\) | 3.56917e73 | 0.0158435 | ||||||||
\(117\) | −4.14741e75 | −1.34584 | ||||||||
\(118\) | −4.03374e75 | −0.959433 | ||||||||
\(119\) | −2.78921e75 | −0.487547 | ||||||||
\(120\) | 8.06318e74 | 0.103846 | ||||||||
\(121\) | −9.46701e75 | −0.900631 | ||||||||
\(122\) | 8.45888e75 | 0.595908 | ||||||||
\(123\) | 1.79260e76 | 0.937445 | ||||||||
\(124\) | 2.50512e76 | 0.974848 | ||||||||
\(125\) | 1.40954e76 | 0.409131 | ||||||||
\(126\) | 2.79992e76 | 0.607603 | ||||||||
\(127\) | 4.55552e76 | 0.740802 | 0.370401 | − | 0.928872i | \(-0.379220\pi\) | ||||
0.370401 | + | 0.928872i | \(0.379220\pi\) | |||||||
\(128\) | 7.23701e75 | 0.0883883 | ||||||||
\(129\) | 2.90027e76 | 0.266633 | ||||||||
\(130\) | 2.95113e76 | 0.204671 | ||||||||
\(131\) | −2.83392e77 | −1.48589 | −0.742943 | − | 0.669355i | \(-0.766571\pi\) | ||||
−0.742943 | + | 0.669355i | \(0.766571\pi\) | |||||||
\(132\) | −5.57243e76 | −0.221358 | ||||||||
\(133\) | 2.02928e77 | 0.612009 | ||||||||
\(134\) | 2.94826e75 | 0.00676457 | ||||||||
\(135\) | −4.63017e75 | −0.00809868 | ||||||||
\(136\) | −1.46004e77 | −0.195072 | ||||||||
\(137\) | −5.93749e77 | −0.607158 | −0.303579 | − | 0.952806i | \(-0.598182\pi\) | ||||
−0.303579 | + | 0.952806i | \(0.598182\pi\) | |||||||
\(138\) | 2.12458e78 | 1.66604 | ||||||||
\(139\) | −2.47728e78 | −1.49257 | −0.746284 | − | 0.665627i | \(-0.768164\pi\) | ||||
−0.746284 | + | 0.665627i | \(0.768164\pi\) | |||||||
\(140\) | −1.99231e77 | −0.0924024 | ||||||||
\(141\) | −6.16362e78 | −2.20464 | ||||||||
\(142\) | 2.22017e78 | 0.613567 | ||||||||
\(143\) | −2.03951e78 | −0.436275 | ||||||||
\(144\) | 1.46564e78 | 0.243107 | ||||||||
\(145\) | −5.14337e76 | −0.00662699 | ||||||||
\(146\) | 3.49183e78 | 0.350085 | ||||||||
\(147\) | 3.93881e78 | 0.307810 | ||||||||
\(148\) | 8.28863e78 | 0.505743 | ||||||||
\(149\) | 1.12793e79 | 0.538248 | 0.269124 | − | 0.963106i | \(-0.413266\pi\) | ||||
0.269124 | + | 0.963106i | \(0.413266\pi\) | |||||||
\(150\) | 2.54035e79 | 0.949646 | ||||||||
\(151\) | 2.13431e78 | 0.0626036 | 0.0313018 | − | 0.999510i | \(-0.490035\pi\) | ||||
0.0313018 | + | 0.999510i | \(0.490035\pi\) | |||||||
\(152\) | 1.06225e79 | 0.244870 | ||||||||
\(153\) | −2.95688e79 | −0.536532 | ||||||||
\(154\) | 1.37688e79 | 0.196965 | ||||||||
\(155\) | −3.61001e79 | −0.407757 | ||||||||
\(156\) | 1.08806e80 | 0.971865 | ||||||||
\(157\) | 8.40883e79 | 0.594837 | 0.297419 | − | 0.954747i | \(-0.403874\pi\) | ||||
0.297419 | + | 0.954747i | \(0.403874\pi\) | |||||||
\(158\) | 1.88523e80 | 1.05775 | ||||||||
\(159\) | −5.57785e80 | −2.48583 | ||||||||
\(160\) | −1.04289e79 | −0.0369709 | ||||||||
\(161\) | −5.24957e80 | −1.48245 | ||||||||
\(162\) | −3.22310e80 | −0.726066 | ||||||||
\(163\) | 1.13703e80 | 0.204608 | 0.102304 | − | 0.994753i | \(-0.467378\pi\) | ||||
0.102304 | + | 0.994753i | \(0.467378\pi\) | |||||||
\(164\) | −2.31855e80 | −0.333745 | ||||||||
\(165\) | 8.03017e79 | 0.0925893 | ||||||||
\(166\) | 4.36420e80 | 0.403608 | ||||||||
\(167\) | 6.33317e80 | 0.470403 | 0.235202 | − | 0.971947i | \(-0.424425\pi\) | ||||
0.235202 | + | 0.971947i | \(0.424425\pi\) | |||||||
\(168\) | −7.34552e80 | −0.438767 | ||||||||
\(169\) | 1.90327e81 | 0.915450 | ||||||||
\(170\) | 2.10399e80 | 0.0815941 | ||||||||
\(171\) | 2.15127e81 | 0.673499 | ||||||||
\(172\) | −3.75122e80 | −0.0949258 | ||||||||
\(173\) | −2.16055e81 | −0.442468 | −0.221234 | − | 0.975221i | \(-0.571009\pi\) | ||||
−0.221234 | + | 0.975221i | \(0.571009\pi\) | |||||||
\(174\) | −1.89633e80 | −0.0314678 | ||||||||
\(175\) | −6.27687e81 | −0.844996 | ||||||||
\(176\) | 7.20738e80 | 0.0788071 | ||||||||
\(177\) | 2.14316e82 | 1.90559 | ||||||||
\(178\) | −2.92391e81 | −0.211657 | ||||||||
\(179\) | 1.27274e82 | 0.750936 | 0.375468 | − | 0.926835i | \(-0.377482\pi\) | ||||
0.375468 | + | 0.926835i | \(0.377482\pi\) | |||||||
\(180\) | −2.11207e81 | −0.101686 | ||||||||
\(181\) | 4.19463e82 | 1.64978 | 0.824888 | − | 0.565296i | \(-0.191238\pi\) | ||||
0.824888 | + | 0.565296i | \(0.191238\pi\) | |||||||
\(182\) | −2.68846e82 | −0.864766 | ||||||||
\(183\) | −4.49427e82 | −1.18357 | ||||||||
\(184\) | −2.74793e82 | −0.593138 | ||||||||
\(185\) | −1.19444e82 | −0.211541 | ||||||||
\(186\) | −1.33099e83 | −1.93621 | ||||||||
\(187\) | −1.45406e82 | −0.173926 | ||||||||
\(188\) | 7.97203e82 | 0.784888 | ||||||||
\(189\) | 4.21806e81 | 0.0342182 | ||||||||
\(190\) | −1.53076e82 | −0.102424 | ||||||||
\(191\) | −2.37720e83 | −1.31325 | −0.656627 | − | 0.754216i | \(-0.728017\pi\) | ||||
−0.656627 | + | 0.754216i | \(0.728017\pi\) | |||||||
\(192\) | −3.84508e82 | −0.175554 | ||||||||
\(193\) | 4.02354e83 | 1.51973 | 0.759865 | − | 0.650081i | \(-0.225265\pi\) | ||||
0.759865 | + | 0.650081i | \(0.225265\pi\) | |||||||
\(194\) | 4.16972e83 | 1.30420 | ||||||||
\(195\) | −1.56796e83 | −0.406510 | ||||||||
\(196\) | −5.09447e82 | −0.109585 | ||||||||
\(197\) | 6.77095e83 | 1.20957 | 0.604787 | − | 0.796387i | \(-0.293258\pi\) | ||||
0.604787 | + | 0.796387i | \(0.293258\pi\) | |||||||
\(198\) | 1.45964e83 | 0.216754 | ||||||||
\(199\) | −2.88518e83 | −0.356480 | −0.178240 | − | 0.983987i | \(-0.557040\pi\) | ||||
−0.178240 | + | 0.983987i | \(0.557040\pi\) | |||||||
\(200\) | −3.28569e83 | −0.338089 | ||||||||
\(201\) | −1.56643e82 | −0.0134356 | ||||||||
\(202\) | 7.65058e83 | 0.547481 | ||||||||
\(203\) | 4.68559e82 | 0.0280001 | ||||||||
\(204\) | 7.75730e83 | 0.387444 | ||||||||
\(205\) | 3.34115e83 | 0.139598 | ||||||||
\(206\) | 1.11073e84 | 0.388556 | ||||||||
\(207\) | −5.56513e84 | −1.63139 | ||||||||
\(208\) | −1.40730e84 | −0.345999 | ||||||||
\(209\) | 1.05790e84 | 0.218326 | ||||||||
\(210\) | 1.05853e84 | 0.183526 | ||||||||
\(211\) | −1.26798e85 | −1.84842 | −0.924212 | − | 0.381879i | \(-0.875277\pi\) | ||||
−0.924212 | + | 0.381879i | \(0.875277\pi\) | |||||||
\(212\) | 7.21440e84 | 0.884996 | ||||||||
\(213\) | −1.17960e85 | −1.21865 | ||||||||
\(214\) | 5.81459e84 | 0.506310 | ||||||||
\(215\) | 5.40571e83 | 0.0397054 | ||||||||
\(216\) | 2.20799e83 | 0.0136910 | ||||||||
\(217\) | 3.28871e85 | 1.72284 | ||||||||
\(218\) | −1.19065e85 | −0.527380 | ||||||||
\(219\) | −1.85524e85 | −0.695327 | ||||||||
\(220\) | −1.03862e84 | −0.0329633 | ||||||||
\(221\) | 2.83918e85 | 0.763615 | ||||||||
\(222\) | −4.40382e85 | −1.00449 | ||||||||
\(223\) | 6.38051e85 | 1.23517 | 0.617587 | − | 0.786503i | \(-0.288110\pi\) | ||||
0.617587 | + | 0.786503i | \(0.288110\pi\) | |||||||
\(224\) | 9.50070e84 | 0.156208 | ||||||||
\(225\) | −6.65419e85 | −0.929894 | ||||||||
\(226\) | 3.98120e85 | 0.473212 | ||||||||
\(227\) | 1.70860e86 | 1.72860 | 0.864302 | − | 0.502973i | \(-0.167761\pi\) | ||||
0.864302 | + | 0.502973i | \(0.167761\pi\) | |||||||
\(228\) | −5.64381e85 | −0.486351 | ||||||||
\(229\) | 1.58156e86 | 1.16169 | 0.580846 | − | 0.814014i | \(-0.302722\pi\) | ||||
0.580846 | + | 0.814014i | \(0.302722\pi\) | |||||||
\(230\) | 3.95992e85 | 0.248097 | ||||||||
\(231\) | −7.31545e85 | −0.391205 | ||||||||
\(232\) | 2.45272e84 | 0.0112030 | ||||||||
\(233\) | −2.31351e86 | −0.903192 | −0.451596 | − | 0.892223i | \(-0.649145\pi\) | ||||
−0.451596 | + | 0.892223i | \(0.649145\pi\) | |||||||
\(234\) | −2.85008e86 | −0.951651 | ||||||||
\(235\) | −1.14881e86 | −0.328301 | ||||||||
\(236\) | −2.77197e86 | −0.678422 | ||||||||
\(237\) | −1.00164e87 | −2.10086 | ||||||||
\(238\) | −1.91673e86 | −0.344748 | ||||||||
\(239\) | 7.57770e86 | 1.16954 | 0.584769 | − | 0.811200i | \(-0.301185\pi\) | ||||
0.584769 | + | 0.811200i | \(0.301185\pi\) | |||||||
\(240\) | 5.54097e85 | 0.0734304 | ||||||||
\(241\) | 8.09092e86 | 0.921246 | 0.460623 | − | 0.887596i | \(-0.347626\pi\) | ||||
0.460623 | + | 0.887596i | \(0.347626\pi\) | |||||||
\(242\) | −6.50568e86 | −0.636842 | ||||||||
\(243\) | 1.66648e87 | 1.40336 | ||||||||
\(244\) | 5.81290e86 | 0.421371 | ||||||||
\(245\) | 7.34141e85 | 0.0458371 | ||||||||
\(246\) | 1.23186e87 | 0.662874 | ||||||||
\(247\) | −2.06564e87 | −0.958551 | ||||||||
\(248\) | 1.72150e87 | 0.689321 | ||||||||
\(249\) | −2.31873e87 | −0.801632 | ||||||||
\(250\) | 9.68628e86 | 0.289299 | ||||||||
\(251\) | 2.18094e87 | 0.563059 | 0.281529 | − | 0.959553i | \(-0.409158\pi\) | ||||
0.281529 | + | 0.959553i | \(0.409158\pi\) | |||||||
\(252\) | 1.92409e87 | 0.429641 | ||||||||
\(253\) | −2.73669e87 | −0.528842 | ||||||||
\(254\) | 3.13053e87 | 0.523826 | ||||||||
\(255\) | −1.11787e87 | −0.162059 | ||||||||
\(256\) | 4.97323e86 | 0.0625000 | ||||||||
\(257\) | −7.57378e87 | −0.825569 | −0.412785 | − | 0.910829i | \(-0.635444\pi\) | ||||
−0.412785 | + | 0.910829i | \(0.635444\pi\) | |||||||
\(258\) | 1.99305e87 | 0.188538 | ||||||||
\(259\) | 1.08813e88 | 0.893796 | ||||||||
\(260\) | 2.02800e87 | 0.144724 | ||||||||
\(261\) | 4.96726e86 | 0.0308133 | ||||||||
\(262\) | −1.94746e88 | −1.05068 | ||||||||
\(263\) | −4.19276e88 | −1.96841 | −0.984205 | − | 0.177033i | \(-0.943350\pi\) | ||||
−0.984205 | + | 0.177033i | \(0.943350\pi\) | |||||||
\(264\) | −3.82934e87 | −0.156524 | ||||||||
\(265\) | −1.03963e88 | −0.370174 | ||||||||
\(266\) | 1.39451e88 | 0.432756 | ||||||||
\(267\) | 1.55349e88 | 0.420386 | ||||||||
\(268\) | 2.02603e86 | 0.00478327 | ||||||||
\(269\) | 6.40106e88 | 1.31915 | 0.659574 | − | 0.751640i | \(-0.270737\pi\) | ||||
0.659574 | + | 0.751640i | \(0.270737\pi\) | |||||||
\(270\) | −3.18183e86 | −0.00572663 | ||||||||
\(271\) | −9.97779e88 | −1.56912 | −0.784558 | − | 0.620055i | \(-0.787110\pi\) | ||||
−0.784558 | + | 0.620055i | \(0.787110\pi\) | |||||||
\(272\) | −1.00333e88 | −0.137936 | ||||||||
\(273\) | 1.42840e89 | 1.71757 | ||||||||
\(274\) | −4.08021e88 | −0.429326 | ||||||||
\(275\) | −3.27224e88 | −0.301441 | ||||||||
\(276\) | 1.46000e89 | 1.17807 | ||||||||
\(277\) | 9.16008e88 | 0.647720 | 0.323860 | − | 0.946105i | \(-0.395019\pi\) | ||||
0.323860 | + | 0.946105i | \(0.395019\pi\) | |||||||
\(278\) | −1.70237e89 | −1.05541 | ||||||||
\(279\) | 3.48640e89 | 1.89594 | ||||||||
\(280\) | −1.36910e88 | −0.0653384 | ||||||||
\(281\) | −1.14673e88 | −0.0480486 | −0.0240243 | − | 0.999711i | \(-0.507648\pi\) | ||||
−0.0240243 | + | 0.999711i | \(0.507648\pi\) | |||||||
\(282\) | −4.23561e89 | −1.55892 | ||||||||
\(283\) | 1.46679e89 | 0.474420 | 0.237210 | − | 0.971458i | \(-0.423767\pi\) | ||||
0.237210 | + | 0.971458i | \(0.423767\pi\) | |||||||
\(284\) | 1.52569e89 | 0.433858 | ||||||||
\(285\) | 8.13304e88 | 0.203430 | ||||||||
\(286\) | −1.40154e89 | −0.308493 | ||||||||
\(287\) | −3.04378e89 | −0.589825 | ||||||||
\(288\) | 1.00718e89 | 0.171902 | ||||||||
\(289\) | −4.62505e89 | −0.695577 | ||||||||
\(290\) | −3.53450e87 | −0.00468599 | ||||||||
\(291\) | −2.21541e90 | −2.59036 | ||||||||
\(292\) | 2.39956e89 | 0.247547 | ||||||||
\(293\) | −2.04263e89 | −0.186004 | −0.0930020 | − | 0.995666i | \(-0.529646\pi\) | ||||
−0.0930020 | + | 0.995666i | \(0.529646\pi\) | |||||||
\(294\) | 2.70673e89 | 0.217655 | ||||||||
\(295\) | 3.99455e89 | 0.283769 | ||||||||
\(296\) | 5.69590e89 | 0.357615 | ||||||||
\(297\) | 2.19895e88 | 0.0122069 | ||||||||
\(298\) | 7.75106e89 | 0.380599 | ||||||||
\(299\) | 5.34361e90 | 2.32186 | ||||||||
\(300\) | 1.74571e90 | 0.671501 | ||||||||
\(301\) | −4.92458e89 | −0.167761 | ||||||||
\(302\) | 1.46669e89 | 0.0442674 | ||||||||
\(303\) | −4.06481e90 | −1.08739 | ||||||||
\(304\) | 7.29971e89 | 0.173149 | ||||||||
\(305\) | −8.37671e89 | −0.176250 | ||||||||
\(306\) | −2.03195e90 | −0.379386 | ||||||||
\(307\) | 2.07621e90 | 0.344129 | 0.172064 | − | 0.985086i | \(-0.444956\pi\) | ||||
0.172064 | + | 0.985086i | \(0.444956\pi\) | |||||||
\(308\) | 9.46182e89 | 0.139275 | ||||||||
\(309\) | −5.90139e90 | −0.771738 | ||||||||
\(310\) | −2.48078e90 | −0.288328 | ||||||||
\(311\) | 1.27144e91 | 1.31384 | 0.656918 | − | 0.753962i | \(-0.271860\pi\) | ||||
0.656918 | + | 0.753962i | \(0.271860\pi\) | |||||||
\(312\) | 7.47711e90 | 0.687212 | ||||||||
\(313\) | −1.63787e91 | −1.33940 | −0.669699 | − | 0.742632i | \(-0.733577\pi\) | ||||
−0.669699 | + | 0.742632i | \(0.733577\pi\) | |||||||
\(314\) | 5.77850e90 | 0.420613 | ||||||||
\(315\) | −2.77272e90 | −0.179709 | ||||||||
\(316\) | 1.29552e91 | 0.747940 | ||||||||
\(317\) | 7.29724e90 | 0.375401 | 0.187701 | − | 0.982226i | \(-0.439897\pi\) | ||||
0.187701 | + | 0.982226i | \(0.439897\pi\) | |||||||
\(318\) | −3.83307e91 | −1.75775 | ||||||||
\(319\) | 2.44268e89 | 0.00998864 | ||||||||
\(320\) | −7.16670e89 | −0.0261424 | ||||||||
\(321\) | −3.08934e91 | −1.00562 | ||||||||
\(322\) | −3.60747e91 | −1.04825 | ||||||||
\(323\) | −1.47269e91 | −0.382137 | ||||||||
\(324\) | −2.21490e91 | −0.513406 | ||||||||
\(325\) | 6.38932e91 | 1.32346 | ||||||||
\(326\) | 7.81360e90 | 0.144680 | ||||||||
\(327\) | 6.32604e91 | 1.04746 | ||||||||
\(328\) | −1.59329e91 | −0.235994 | ||||||||
\(329\) | 1.04656e92 | 1.38713 | ||||||||
\(330\) | 5.51829e90 | 0.0654705 | ||||||||
\(331\) | −3.52411e91 | −0.374393 | −0.187196 | − | 0.982323i | \(-0.559940\pi\) | ||||
−0.187196 | + | 0.982323i | \(0.559940\pi\) | |||||||
\(332\) | 2.99906e91 | 0.285394 | ||||||||
\(333\) | 1.15354e92 | 0.983597 | ||||||||
\(334\) | 4.35212e91 | 0.332625 | ||||||||
\(335\) | −2.91962e89 | −0.00200074 | ||||||||
\(336\) | −5.04780e91 | −0.310255 | ||||||||
\(337\) | −1.52250e92 | −0.839589 | −0.419794 | − | 0.907619i | \(-0.637898\pi\) | ||||
−0.419794 | + | 0.907619i | \(0.637898\pi\) | |||||||
\(338\) | 1.30791e92 | 0.647321 | ||||||||
\(339\) | −2.11524e92 | −0.939878 | ||||||||
\(340\) | 1.44585e91 | 0.0576958 | ||||||||
\(341\) | 1.71446e92 | 0.614599 | ||||||||
\(342\) | 1.47834e92 | 0.476236 | ||||||||
\(343\) | −3.72030e92 | −1.07731 | ||||||||
\(344\) | −2.57782e91 | −0.0671226 | ||||||||
\(345\) | −2.10394e92 | −0.492761 | ||||||||
\(346\) | −1.48472e92 | −0.312872 | ||||||||
\(347\) | −2.38741e92 | −0.452794 | −0.226397 | − | 0.974035i | \(-0.572695\pi\) | ||||
−0.226397 | + | 0.974035i | \(0.572695\pi\) | |||||||
\(348\) | −1.30315e91 | −0.0222511 | ||||||||
\(349\) | −2.35163e92 | −0.361610 | −0.180805 | − | 0.983519i | \(-0.557870\pi\) | ||||
−0.180805 | + | 0.983519i | \(0.557870\pi\) | |||||||
\(350\) | −4.31343e92 | −0.597502 | ||||||||
\(351\) | −4.29363e91 | −0.0535938 | ||||||||
\(352\) | 4.95288e91 | 0.0557250 | ||||||||
\(353\) | −1.91135e92 | −0.193893 | −0.0969466 | − | 0.995290i | \(-0.530908\pi\) | ||||
−0.0969466 | + | 0.995290i | \(0.530908\pi\) | |||||||
\(354\) | 1.47277e93 | 1.34746 | ||||||||
\(355\) | −2.19861e92 | −0.181473 | ||||||||
\(356\) | −2.00929e92 | −0.149664 | ||||||||
\(357\) | 1.01837e93 | 0.684727 | ||||||||
\(358\) | 8.74618e92 | 0.530992 | ||||||||
\(359\) | 8.27181e92 | 0.453579 | 0.226790 | − | 0.973944i | \(-0.427177\pi\) | ||||
0.226790 | + | 0.973944i | \(0.427177\pi\) | |||||||
\(360\) | −1.45140e92 | −0.0719030 | ||||||||
\(361\) | −1.16219e93 | −0.520311 | ||||||||
\(362\) | 2.88252e93 | 1.16657 | ||||||||
\(363\) | 3.45652e93 | 1.26487 | ||||||||
\(364\) | −1.84750e93 | −0.611482 | ||||||||
\(365\) | −3.45790e92 | −0.103544 | ||||||||
\(366\) | −3.08844e93 | −0.836912 | ||||||||
\(367\) | −1.02598e93 | −0.251668 | −0.125834 | − | 0.992051i | \(-0.540161\pi\) | ||||
−0.125834 | + | 0.992051i | \(0.540161\pi\) | |||||||
\(368\) | −1.88837e93 | −0.419412 | ||||||||
\(369\) | −3.22675e93 | −0.649086 | ||||||||
\(370\) | −8.20811e92 | −0.149582 | ||||||||
\(371\) | 9.47102e93 | 1.56404 | ||||||||
\(372\) | −9.14649e93 | −1.36911 | ||||||||
\(373\) | 5.02008e93 | 0.681300 | 0.340650 | − | 0.940190i | \(-0.389353\pi\) | ||||
0.340650 | + | 0.940190i | \(0.389353\pi\) | |||||||
\(374\) | −9.99224e92 | −0.122984 | ||||||||
\(375\) | −5.14640e93 | −0.574596 | ||||||||
\(376\) | 5.47834e93 | 0.555000 | ||||||||
\(377\) | −4.76953e92 | −0.0438547 | ||||||||
\(378\) | 2.89863e92 | 0.0241959 | ||||||||
\(379\) | 2.34857e93 | 0.178022 | 0.0890108 | − | 0.996031i | \(-0.471629\pi\) | ||||
0.0890108 | + | 0.996031i | \(0.471629\pi\) | |||||||
\(380\) | −1.05193e93 | −0.0724244 | ||||||||
\(381\) | −1.66328e94 | −1.04041 | ||||||||
\(382\) | −1.63360e94 | −0.928610 | ||||||||
\(383\) | −4.28352e93 | −0.221333 | −0.110666 | − | 0.993858i | \(-0.535298\pi\) | ||||
−0.110666 | + | 0.993858i | \(0.535298\pi\) | |||||||
\(384\) | −2.64232e93 | −0.124135 | ||||||||
\(385\) | −1.36350e93 | −0.0582557 | ||||||||
\(386\) | 2.76495e94 | 1.07461 | ||||||||
\(387\) | −5.22061e93 | −0.184617 | ||||||||
\(388\) | 2.86541e94 | 0.922208 | ||||||||
\(389\) | −3.13280e94 | −0.917850 | −0.458925 | − | 0.888475i | \(-0.651765\pi\) | ||||
−0.458925 | + | 0.888475i | \(0.651765\pi\) | |||||||
\(390\) | −1.07749e94 | −0.287446 | ||||||||
\(391\) | 3.80970e94 | 0.925635 | ||||||||
\(392\) | −3.50089e93 | −0.0774885 | ||||||||
\(393\) | 1.03470e95 | 2.08682 | ||||||||
\(394\) | 4.65296e94 | 0.855298 | ||||||||
\(395\) | −1.86692e94 | −0.312847 | ||||||||
\(396\) | 1.00306e94 | 0.153268 | ||||||||
\(397\) | 1.09838e95 | 1.53074 | 0.765369 | − | 0.643592i | \(-0.222557\pi\) | ||||
0.765369 | + | 0.643592i | \(0.222557\pi\) | |||||||
\(398\) | −1.98268e94 | −0.252069 | ||||||||
\(399\) | −7.40916e94 | −0.859525 | ||||||||
\(400\) | −2.25791e94 | −0.239065 | ||||||||
\(401\) | −1.82977e95 | −1.76859 | −0.884296 | − | 0.466927i | \(-0.845361\pi\) | ||||
−0.884296 | + | 0.466927i | \(0.845361\pi\) | |||||||
\(402\) | −1.07644e93 | −0.00950037 | ||||||||
\(403\) | −3.34762e95 | −2.69837 | ||||||||
\(404\) | 5.25744e94 | 0.387128 | ||||||||
\(405\) | 3.19179e94 | 0.214747 | ||||||||
\(406\) | 3.21991e93 | 0.0197990 | ||||||||
\(407\) | 5.67259e94 | 0.318849 | ||||||||
\(408\) | 5.33077e94 | 0.273965 | ||||||||
\(409\) | 3.39276e94 | 0.159460 | 0.0797301 | − | 0.996816i | \(-0.474594\pi\) | ||||
0.0797301 | + | 0.996816i | \(0.474594\pi\) | |||||||
\(410\) | 2.29602e94 | 0.0987110 | ||||||||
\(411\) | 2.16785e95 | 0.852712 | ||||||||
\(412\) | 7.63286e94 | 0.274751 | ||||||||
\(413\) | −3.63902e95 | −1.19897 | ||||||||
\(414\) | −3.82433e95 | −1.15357 | ||||||||
\(415\) | −4.32180e94 | −0.119374 | ||||||||
\(416\) | −9.67090e94 | −0.244659 | ||||||||
\(417\) | 9.04484e95 | 2.09621 | ||||||||
\(418\) | 7.26983e94 | 0.154380 | ||||||||
\(419\) | 2.28986e95 | 0.445654 | 0.222827 | − | 0.974858i | \(-0.428472\pi\) | ||||
0.222827 | + | 0.974858i | \(0.428472\pi\) | |||||||
\(420\) | 7.27416e94 | 0.129773 | ||||||||
\(421\) | −3.12668e95 | −0.511431 | −0.255716 | − | 0.966752i | \(-0.582311\pi\) | ||||
−0.255716 | + | 0.966752i | \(0.582311\pi\) | |||||||
\(422\) | −8.71347e95 | −1.30703 | ||||||||
\(423\) | 1.10948e96 | 1.52649 | ||||||||
\(424\) | 4.95770e95 | 0.625786 | ||||||||
\(425\) | 4.55524e95 | 0.527613 | ||||||||
\(426\) | −8.10612e95 | −0.861713 | ||||||||
\(427\) | 7.63114e95 | 0.744684 | ||||||||
\(428\) | 3.99576e95 | 0.358015 | ||||||||
\(429\) | 7.44650e95 | 0.612719 | ||||||||
\(430\) | 3.71478e94 | 0.0280759 | ||||||||
\(431\) | −2.02504e96 | −1.40609 | −0.703045 | − | 0.711145i | \(-0.748177\pi\) | ||||
−0.703045 | + | 0.711145i | \(0.748177\pi\) | |||||||
\(432\) | 1.51732e94 | 0.00968098 | ||||||||
\(433\) | −2.48577e96 | −1.45765 | −0.728824 | − | 0.684701i | \(-0.759933\pi\) | ||||
−0.728824 | + | 0.684701i | \(0.759933\pi\) | |||||||
\(434\) | 2.25998e96 | 1.21823 | ||||||||
\(435\) | 1.87791e94 | 0.00930715 | ||||||||
\(436\) | −8.18211e95 | −0.372914 | ||||||||
\(437\) | −2.77174e96 | −1.16193 | ||||||||
\(438\) | −1.27491e96 | −0.491670 | ||||||||
\(439\) | 8.00456e95 | 0.284042 | 0.142021 | − | 0.989864i | \(-0.454640\pi\) | ||||
0.142021 | + | 0.989864i | \(0.454640\pi\) | |||||||
\(440\) | −7.13737e94 | −0.0233086 | ||||||||
\(441\) | −7.09003e95 | −0.213128 | ||||||||
\(442\) | 1.95107e96 | 0.539957 | ||||||||
\(443\) | 2.79973e96 | 0.713479 | 0.356739 | − | 0.934204i | \(-0.383888\pi\) | ||||
0.356739 | + | 0.934204i | \(0.383888\pi\) | |||||||
\(444\) | −3.02628e96 | −0.710282 | ||||||||
\(445\) | 2.89550e95 | 0.0626013 | ||||||||
\(446\) | 4.38466e96 | 0.873400 | ||||||||
\(447\) | −4.11820e96 | −0.755932 | ||||||||
\(448\) | 6.52883e95 | 0.110456 | ||||||||
\(449\) | −1.66076e96 | −0.259009 | −0.129504 | − | 0.991579i | \(-0.541339\pi\) | ||||
−0.129504 | + | 0.991579i | \(0.541339\pi\) | |||||||
\(450\) | −4.57273e96 | −0.657534 | ||||||||
\(451\) | −1.58677e96 | −0.210412 | ||||||||
\(452\) | 2.73586e96 | 0.334611 | ||||||||
\(453\) | −7.79263e95 | −0.0879224 | ||||||||
\(454\) | 1.17414e97 | 1.22231 | ||||||||
\(455\) | 2.66235e96 | 0.255769 | ||||||||
\(456\) | −3.87839e96 | −0.343902 | ||||||||
\(457\) | 8.70589e96 | 0.712643 | 0.356321 | − | 0.934363i | \(-0.384031\pi\) | ||||
0.356321 | + | 0.934363i | \(0.384031\pi\) | |||||||
\(458\) | 1.08684e97 | 0.821440 | ||||||||
\(459\) | −3.06113e95 | −0.0213657 | ||||||||
\(460\) | 2.72124e96 | 0.175431 | ||||||||
\(461\) | 2.15290e97 | 1.28216 | 0.641078 | − | 0.767476i | \(-0.278487\pi\) | ||||
0.641078 | + | 0.767476i | \(0.278487\pi\) | |||||||
\(462\) | −5.02714e96 | −0.276623 | ||||||||
\(463\) | −1.55171e97 | −0.789048 | −0.394524 | − | 0.918886i | \(-0.629090\pi\) | ||||
−0.394524 | + | 0.918886i | \(0.629090\pi\) | |||||||
\(464\) | 1.68549e95 | 0.00792175 | ||||||||
\(465\) | 1.31806e97 | 0.572667 | ||||||||
\(466\) | −1.58983e97 | −0.638653 | ||||||||
\(467\) | −1.90434e97 | −0.707420 | −0.353710 | − | 0.935355i | \(-0.615080\pi\) | ||||
−0.353710 | + | 0.935355i | \(0.615080\pi\) | |||||||
\(468\) | −1.95856e97 | −0.672919 | ||||||||
\(469\) | 2.65976e95 | 0.00845343 | ||||||||
\(470\) | −7.89459e96 | −0.232144 | ||||||||
\(471\) | −3.07016e97 | −0.835408 | ||||||||
\(472\) | −1.90488e97 | −0.479717 | ||||||||
\(473\) | −2.56727e96 | −0.0598466 | ||||||||
\(474\) | −6.88322e97 | −1.48553 | ||||||||
\(475\) | −3.31416e97 | −0.662302 | ||||||||
\(476\) | −1.31717e97 | −0.243774 | ||||||||
\(477\) | 1.00404e98 | 1.72119 | ||||||||
\(478\) | 5.20736e97 | 0.826988 | ||||||||
\(479\) | 6.66159e97 | 0.980238 | 0.490119 | − | 0.871655i | \(-0.336953\pi\) | ||||
0.490119 | + | 0.871655i | \(0.336953\pi\) | |||||||
\(480\) | 3.80773e96 | 0.0519231 | ||||||||
\(481\) | −1.10762e98 | −1.39990 | ||||||||
\(482\) | 5.56003e97 | 0.651419 | ||||||||
\(483\) | 1.91668e98 | 2.08199 | ||||||||
\(484\) | −4.47067e97 | −0.450316 | ||||||||
\(485\) | −4.12921e97 | −0.385739 | ||||||||
\(486\) | 1.14519e98 | 0.992328 | ||||||||
\(487\) | −1.71633e97 | −0.137973 | −0.0689863 | − | 0.997618i | \(-0.521976\pi\) | ||||
−0.0689863 | + | 0.997618i | \(0.521976\pi\) | |||||||
\(488\) | 3.99459e97 | 0.297954 | ||||||||
\(489\) | −4.15143e97 | −0.287359 | ||||||||
\(490\) | 5.04498e96 | 0.0324117 | ||||||||
\(491\) | −2.05703e98 | −1.22678 | −0.613388 | − | 0.789781i | \(-0.710194\pi\) | ||||
−0.613388 | + | 0.789781i | \(0.710194\pi\) | |||||||
\(492\) | 8.46529e97 | 0.468722 | ||||||||
\(493\) | −3.40042e96 | −0.0174832 | ||||||||
\(494\) | −1.41949e98 | −0.677798 | ||||||||
\(495\) | −1.44546e97 | −0.0641088 | ||||||||
\(496\) | 1.18301e98 | 0.487424 | ||||||||
\(497\) | 2.00292e98 | 0.766753 | ||||||||
\(498\) | −1.59342e98 | −0.566839 | ||||||||
\(499\) | 2.56755e98 | 0.848886 | 0.424443 | − | 0.905455i | \(-0.360470\pi\) | ||||
0.424443 | + | 0.905455i | \(0.360470\pi\) | |||||||
\(500\) | 6.65636e97 | 0.204565 | ||||||||
\(501\) | −2.31232e98 | −0.660649 | ||||||||
\(502\) | 1.49873e98 | 0.398143 | ||||||||
\(503\) | −3.81022e98 | −0.941279 | −0.470640 | − | 0.882326i | \(-0.655977\pi\) | ||||
−0.470640 | + | 0.882326i | \(0.655977\pi\) | |||||||
\(504\) | 1.32222e98 | 0.303802 | ||||||||
\(505\) | −7.57626e97 | −0.161927 | ||||||||
\(506\) | −1.88064e98 | −0.373948 | ||||||||
\(507\) | −6.94905e98 | −1.28569 | ||||||||
\(508\) | 2.15128e98 | 0.370401 | ||||||||
\(509\) | −4.83731e98 | −0.775184 | −0.387592 | − | 0.921831i | \(-0.626693\pi\) | ||||
−0.387592 | + | 0.921831i | \(0.626693\pi\) | |||||||
\(510\) | −7.68194e97 | −0.114593 | ||||||||
\(511\) | 3.15014e98 | 0.437488 | ||||||||
\(512\) | 3.41758e97 | 0.0441942 | ||||||||
\(513\) | 2.22712e97 | 0.0268200 | ||||||||
\(514\) | −5.20466e98 | −0.583766 | ||||||||
\(515\) | −1.09994e98 | −0.114922 | ||||||||
\(516\) | 1.36962e98 | 0.133317 | ||||||||
\(517\) | 5.45592e98 | 0.494838 | ||||||||
\(518\) | 7.47755e98 | 0.632009 | ||||||||
\(519\) | 7.88844e98 | 0.621416 | ||||||||
\(520\) | 1.39363e98 | 0.102335 | ||||||||
\(521\) | 2.04685e99 | 1.40123 | 0.700613 | − | 0.713541i | \(-0.252910\pi\) | ||||
0.700613 | + | 0.713541i | \(0.252910\pi\) | |||||||
\(522\) | 3.41347e97 | 0.0217883 | ||||||||
\(523\) | 7.07713e98 | 0.421256 | 0.210628 | − | 0.977566i | \(-0.432449\pi\) | ||||
0.210628 | + | 0.977566i | \(0.432449\pi\) | |||||||
\(524\) | −1.33828e99 | −0.742943 | ||||||||
\(525\) | 2.29176e99 | 1.18674 | ||||||||
\(526\) | −2.88125e99 | −1.39188 | ||||||||
\(527\) | −2.38667e99 | −1.07574 | ||||||||
\(528\) | −2.63150e98 | −0.110679 | ||||||||
\(529\) | 4.62263e99 | 1.81450 | ||||||||
\(530\) | −7.14431e98 | −0.261753 | ||||||||
\(531\) | −3.85777e99 | −1.31943 | ||||||||
\(532\) | 9.58302e98 | 0.306004 | ||||||||
\(533\) | 3.09830e99 | 0.923806 | ||||||||
\(534\) | 1.06755e99 | 0.297258 | ||||||||
\(535\) | −5.75811e98 | −0.149750 | ||||||||
\(536\) | 1.39227e97 | 0.00338228 | ||||||||
\(537\) | −4.64692e99 | −1.05464 | ||||||||
\(538\) | 4.39877e99 | 0.932779 | ||||||||
\(539\) | −3.48656e98 | −0.0690888 | ||||||||
\(540\) | −2.18654e97 | −0.00404934 | ||||||||
\(541\) | −6.09127e99 | −1.05440 | −0.527202 | − | 0.849740i | \(-0.676759\pi\) | ||||
−0.527202 | + | 0.849740i | \(0.676759\pi\) | |||||||
\(542\) | −6.85668e99 | −1.10953 | ||||||||
\(543\) | −1.53151e100 | −2.31700 | ||||||||
\(544\) | −6.89483e98 | −0.0975358 | ||||||||
\(545\) | 1.17909e99 | 0.155982 | ||||||||
\(546\) | 9.81591e99 | 1.21450 | ||||||||
\(547\) | 1.07778e99 | 0.124736 | 0.0623681 | − | 0.998053i | \(-0.480135\pi\) | ||||
0.0623681 | + | 0.998053i | \(0.480135\pi\) | |||||||
\(548\) | −2.80390e99 | −0.303579 | ||||||||
\(549\) | 8.08988e99 | 0.819504 | ||||||||
\(550\) | −2.24867e99 | −0.213151 | ||||||||
\(551\) | 2.47397e98 | 0.0219463 | ||||||||
\(552\) | 1.00330e100 | 0.833022 | ||||||||
\(553\) | 1.70076e100 | 1.32183 | ||||||||
\(554\) | 6.29476e99 | 0.458007 | ||||||||
\(555\) | 4.36104e99 | 0.297095 | ||||||||
\(556\) | −1.16986e100 | −0.746284 | ||||||||
\(557\) | −4.55868e99 | −0.272348 | −0.136174 | − | 0.990685i | \(-0.543481\pi\) | ||||
−0.136174 | + | 0.990685i | \(0.543481\pi\) | |||||||
\(558\) | 2.39584e100 | 1.34063 | ||||||||
\(559\) | 5.01280e99 | 0.262754 | ||||||||
\(560\) | −9.40841e98 | −0.0462012 | ||||||||
\(561\) | 5.30896e99 | 0.244267 | ||||||||
\(562\) | −7.88028e98 | −0.0339755 | ||||||||
\(563\) | 4.14423e99 | 0.167451 | 0.0837255 | − | 0.996489i | \(-0.473318\pi\) | ||||
0.0837255 | + | 0.996489i | \(0.473318\pi\) | |||||||
\(564\) | −2.91069e100 | −1.10232 | ||||||||
\(565\) | −3.94252e99 | −0.139961 | ||||||||
\(566\) | 1.00797e100 | 0.335466 | ||||||||
\(567\) | −2.90771e100 | −0.907338 | ||||||||
\(568\) | 1.04845e100 | 0.306784 | ||||||||
\(569\) | −5.61680e100 | −1.54131 | −0.770657 | − | 0.637250i | \(-0.780072\pi\) | ||||
−0.770657 | + | 0.637250i | \(0.780072\pi\) | |||||||
\(570\) | 5.58898e99 | 0.143847 | ||||||||
\(571\) | −6.13398e100 | −1.48090 | −0.740448 | − | 0.672113i | \(-0.765387\pi\) | ||||
−0.740448 | + | 0.672113i | \(0.765387\pi\) | |||||||
\(572\) | −9.63132e99 | −0.218138 | ||||||||
\(573\) | 8.67946e100 | 1.84437 | ||||||||
\(574\) | −2.09167e100 | −0.417069 | ||||||||
\(575\) | 8.57341e100 | 1.60427 | ||||||||
\(576\) | 6.92130e99 | 0.121553 | ||||||||
\(577\) | 7.13815e100 | 1.17671 | 0.588354 | − | 0.808603i | \(-0.299776\pi\) | ||||
0.588354 | + | 0.808603i | \(0.299776\pi\) | |||||||
\(578\) | −3.17831e100 | −0.491847 | ||||||||
\(579\) | −1.46904e101 | −2.13436 | ||||||||
\(580\) | −2.42889e98 | −0.00331349 | ||||||||
\(581\) | 3.93714e100 | 0.504374 | ||||||||
\(582\) | −1.52242e101 | −1.83166 | ||||||||
\(583\) | 4.93740e100 | 0.557951 | ||||||||
\(584\) | 1.64897e100 | 0.175042 | ||||||||
\(585\) | 2.82239e100 | 0.281467 | ||||||||
\(586\) | −1.40369e100 | −0.131525 | ||||||||
\(587\) | −5.83655e100 | −0.513885 | −0.256942 | − | 0.966427i | \(-0.582715\pi\) | ||||
−0.256942 | + | 0.966427i | \(0.582715\pi\) | |||||||
\(588\) | 1.86005e100 | 0.153905 | ||||||||
\(589\) | 1.73642e101 | 1.35035 | ||||||||
\(590\) | 2.74504e100 | 0.200655 | ||||||||
\(591\) | −2.47216e101 | −1.69876 | ||||||||
\(592\) | 3.91419e100 | 0.252872 | ||||||||
\(593\) | 2.33205e101 | 1.41658 | 0.708290 | − | 0.705922i | \(-0.249467\pi\) | ||||
0.708290 | + | 0.705922i | \(0.249467\pi\) | |||||||
\(594\) | 1.51111e99 | 0.00863157 | ||||||||
\(595\) | 1.89811e100 | 0.101965 | ||||||||
\(596\) | 5.32649e100 | 0.269124 | ||||||||
\(597\) | 1.05341e101 | 0.500652 | ||||||||
\(598\) | 3.67210e101 | 1.64180 | ||||||||
\(599\) | −2.51022e101 | −1.05593 | −0.527963 | − | 0.849268i | \(-0.677044\pi\) | ||||
−0.527963 | + | 0.849268i | \(0.677044\pi\) | |||||||
\(600\) | 1.19964e101 | 0.474823 | ||||||||
\(601\) | 9.46626e100 | 0.352582 | 0.176291 | − | 0.984338i | \(-0.443590\pi\) | ||||
0.176291 | + | 0.984338i | \(0.443590\pi\) | |||||||
\(602\) | −3.38415e100 | −0.118625 | ||||||||
\(603\) | 2.81964e99 | 0.00930277 | ||||||||
\(604\) | 1.00790e100 | 0.0313018 | ||||||||
\(605\) | 6.44248e100 | 0.188357 | ||||||||
\(606\) | −2.79332e101 | −0.768900 | ||||||||
\(607\) | −6.32704e101 | −1.63988 | −0.819942 | − | 0.572446i | \(-0.805995\pi\) | ||||
−0.819942 | + | 0.572446i | \(0.805995\pi\) | |||||||
\(608\) | 5.01632e100 | 0.122435 | ||||||||
\(609\) | −1.71077e100 | −0.0393242 | ||||||||
\(610\) | −5.75643e100 | −0.124628 | ||||||||
\(611\) | −1.06531e102 | −2.17257 | ||||||||
\(612\) | −1.39635e101 | −0.268266 | ||||||||
\(613\) | 6.70863e101 | 1.21430 | 0.607150 | − | 0.794587i | \(-0.292313\pi\) | ||||
0.607150 | + | 0.794587i | \(0.292313\pi\) | |||||||
\(614\) | 1.42676e101 | 0.243336 | ||||||||
\(615\) | −1.21990e101 | −0.196056 | ||||||||
\(616\) | 6.50211e100 | 0.0984823 | ||||||||
\(617\) | −5.79164e101 | −0.826785 | −0.413393 | − | 0.910553i | \(-0.635656\pi\) | ||||
−0.413393 | + | 0.910553i | \(0.635656\pi\) | |||||||
\(618\) | −4.05540e101 | −0.545701 | ||||||||
\(619\) | 1.13125e102 | 1.43499 | 0.717495 | − | 0.696564i | \(-0.245289\pi\) | ||||
0.717495 | + | 0.696564i | \(0.245289\pi\) | |||||||
\(620\) | −1.70478e101 | −0.203879 | ||||||||
\(621\) | −5.76134e100 | −0.0649651 | ||||||||
\(622\) | 8.73726e101 | 0.929022 | ||||||||
\(623\) | −2.63779e101 | −0.264500 | ||||||||
\(624\) | 5.13823e101 | 0.485932 | ||||||||
\(625\) | 9.76084e101 | 0.870696 | ||||||||
\(626\) | −1.12553e102 | −0.947098 | ||||||||
\(627\) | −3.86252e101 | −0.306624 | ||||||||
\(628\) | 3.97096e101 | 0.297419 | ||||||||
\(629\) | −7.89673e101 | −0.558083 | ||||||||
\(630\) | −1.90540e101 | −0.127074 | ||||||||
\(631\) | 2.61303e101 | 0.164465 | 0.0822325 | − | 0.996613i | \(-0.473795\pi\) | ||||
0.0822325 | + | 0.996613i | \(0.473795\pi\) | |||||||
\(632\) | 8.90277e101 | 0.528873 | ||||||||
\(633\) | 4.62954e102 | 2.59599 | ||||||||
\(634\) | 5.01463e101 | 0.265449 | ||||||||
\(635\) | −3.10012e101 | −0.154931 | ||||||||
\(636\) | −2.63406e102 | −1.24292 | ||||||||
\(637\) | 6.80780e101 | 0.303332 | ||||||||
\(638\) | 1.67860e100 | 0.00706303 | ||||||||
\(639\) | 2.12332e102 | 0.843790 | ||||||||
\(640\) | −4.92492e100 | −0.0184855 | ||||||||
\(641\) | −3.98775e102 | −1.41387 | −0.706936 | − | 0.707278i | \(-0.749923\pi\) | ||||
−0.706936 | + | 0.707278i | \(0.749923\pi\) | |||||||
\(642\) | −2.12298e102 | −0.711078 | ||||||||
\(643\) | 4.29748e102 | 1.35992 | 0.679960 | − | 0.733250i | \(-0.261997\pi\) | ||||
0.679960 | + | 0.733250i | \(0.261997\pi\) | |||||||
\(644\) | −2.47904e102 | −0.741223 | ||||||||
\(645\) | −1.97369e101 | −0.0557635 | ||||||||
\(646\) | −1.01202e102 | −0.270211 | ||||||||
\(647\) | −5.32563e102 | −1.34389 | −0.671946 | − | 0.740600i | \(-0.734542\pi\) | ||||
−0.671946 | + | 0.740600i | \(0.734542\pi\) | |||||||
\(648\) | −1.52207e102 | −0.363033 | ||||||||
\(649\) | −1.89708e102 | −0.427715 | ||||||||
\(650\) | 4.39071e102 | 0.935830 | ||||||||
\(651\) | −1.20075e103 | −2.41961 | ||||||||
\(652\) | 5.36946e101 | 0.102304 | ||||||||
\(653\) | 4.80226e102 | 0.865197 | 0.432598 | − | 0.901587i | \(-0.357597\pi\) | ||||
0.432598 | + | 0.901587i | \(0.357597\pi\) | |||||||
\(654\) | 4.34722e102 | 0.740669 | ||||||||
\(655\) | 1.92854e102 | 0.310757 | ||||||||
\(656\) | −1.09490e102 | −0.166873 | ||||||||
\(657\) | 3.33950e102 | 0.481444 | ||||||||
\(658\) | 7.19194e102 | 0.980846 | ||||||||
\(659\) | −4.43880e102 | −0.572727 | −0.286363 | − | 0.958121i | \(-0.592446\pi\) | ||||
−0.286363 | + | 0.958121i | \(0.592446\pi\) | |||||||
\(660\) | 3.79214e101 | 0.0462947 | ||||||||
\(661\) | 1.19501e103 | 1.38044 | 0.690222 | − | 0.723597i | \(-0.257513\pi\) | ||||
0.690222 | + | 0.723597i | \(0.257513\pi\) | |||||||
\(662\) | −2.42175e102 | −0.264736 | ||||||||
\(663\) | −1.03662e103 | −1.07244 | ||||||||
\(664\) | 2.06094e102 | 0.201804 | ||||||||
\(665\) | −1.38097e102 | −0.127995 | ||||||||
\(666\) | 7.92705e102 | 0.695508 | ||||||||
\(667\) | −6.39992e101 | −0.0531596 | ||||||||
\(668\) | 2.99076e102 | 0.235202 | ||||||||
\(669\) | −2.32960e103 | −1.73472 | ||||||||
\(670\) | −2.00634e100 | −0.00141474 | ||||||||
\(671\) | 3.97824e102 | 0.265656 | ||||||||
\(672\) | −3.46882e102 | −0.219383 | ||||||||
\(673\) | 2.75588e103 | 1.65086 | 0.825430 | − | 0.564504i | \(-0.190932\pi\) | ||||
0.825430 | + | 0.564504i | \(0.190932\pi\) | |||||||
\(674\) | −1.04626e103 | −0.593679 | ||||||||
\(675\) | −6.88880e101 | −0.0370302 | ||||||||
\(676\) | 8.98792e102 | 0.457725 | ||||||||
\(677\) | 3.22081e103 | 1.55410 | 0.777050 | − | 0.629439i | \(-0.216715\pi\) | ||||
0.777050 | + | 0.629439i | \(0.216715\pi\) | |||||||
\(678\) | −1.45358e103 | −0.664594 | ||||||||
\(679\) | 3.76170e103 | 1.62981 | ||||||||
\(680\) | 9.93583e101 | 0.0407971 | ||||||||
\(681\) | −6.23829e103 | −2.42771 | ||||||||
\(682\) | 1.17817e103 | 0.434587 | ||||||||
\(683\) | 2.97295e103 | 1.03952 | 0.519760 | − | 0.854312i | \(-0.326021\pi\) | ||||
0.519760 | + | 0.854312i | \(0.326021\pi\) | |||||||
\(684\) | 1.01591e103 | 0.336749 | ||||||||
\(685\) | 4.04057e102 | 0.126981 | ||||||||
\(686\) | −2.55657e103 | −0.761776 | ||||||||
\(687\) | −5.77447e103 | −1.63152 | ||||||||
\(688\) | −1.77146e102 | −0.0474629 | ||||||||
\(689\) | −9.64069e103 | −2.44966 | ||||||||
\(690\) | −1.44582e103 | −0.348435 | ||||||||
\(691\) | 2.23381e103 | 0.510619 | 0.255310 | − | 0.966859i | \(-0.417823\pi\) | ||||
0.255310 | + | 0.966859i | \(0.417823\pi\) | |||||||
\(692\) | −1.02029e103 | −0.221234 | ||||||||
\(693\) | 1.31681e103 | 0.270870 | ||||||||
\(694\) | −1.64061e103 | −0.320174 | ||||||||
\(695\) | 1.68583e103 | 0.312154 | ||||||||
\(696\) | −8.95517e101 | −0.0157339 | ||||||||
\(697\) | 2.20892e103 | 0.368285 | ||||||||
\(698\) | −1.61603e103 | −0.255697 | ||||||||
\(699\) | 8.44690e103 | 1.26847 | ||||||||
\(700\) | −2.96417e103 | −0.422498 | ||||||||
\(701\) | 6.41226e102 | 0.0867568 | 0.0433784 | − | 0.999059i | \(-0.486188\pi\) | ||||
0.0433784 | + | 0.999059i | \(0.486188\pi\) | |||||||
\(702\) | −2.95056e102 | −0.0378965 | ||||||||
\(703\) | 5.74525e103 | 0.700551 | ||||||||
\(704\) | 3.40359e102 | 0.0394035 | ||||||||
\(705\) | 4.19446e103 | 0.461077 | ||||||||
\(706\) | −1.31347e103 | −0.137103 | ||||||||
\(707\) | 6.90193e103 | 0.684167 | ||||||||
\(708\) | 1.01208e104 | 0.952797 | ||||||||
\(709\) | 1.09588e104 | 0.979889 | 0.489944 | − | 0.871754i | \(-0.337017\pi\) | ||||
0.489944 | + | 0.871754i | \(0.337017\pi\) | |||||||
\(710\) | −1.51087e103 | −0.128321 | ||||||||
\(711\) | 1.80299e104 | 1.45463 | ||||||||
\(712\) | −1.38078e103 | −0.105829 | ||||||||
\(713\) | −4.49196e104 | −3.27090 | ||||||||
\(714\) | 6.99821e103 | 0.484175 | ||||||||
\(715\) | 1.38793e103 | 0.0912422 | ||||||||
\(716\) | 6.01033e103 | 0.375468 | ||||||||
\(717\) | −2.76671e104 | −1.64254 | ||||||||
\(718\) | 5.68434e103 | 0.320729 | ||||||||
\(719\) | 9.49446e102 | 0.0509173 | 0.0254587 | − | 0.999676i | \(-0.491895\pi\) | ||||
0.0254587 | + | 0.999676i | \(0.491895\pi\) | |||||||
\(720\) | −9.97398e102 | −0.0508431 | ||||||||
\(721\) | 1.00204e104 | 0.485565 | ||||||||
\(722\) | −7.98649e103 | −0.367916 | ||||||||
\(723\) | −2.95409e104 | −1.29383 | ||||||||
\(724\) | 1.98086e104 | 0.824888 | ||||||||
\(725\) | −7.65235e102 | −0.0303010 | ||||||||
\(726\) | 2.37530e104 | 0.894401 | ||||||||
\(727\) | 2.91800e103 | 0.104491 | 0.0522455 | − | 0.998634i | \(-0.483362\pi\) | ||||
0.0522455 | + | 0.998634i | \(0.483362\pi\) | |||||||
\(728\) | −1.26959e104 | −0.432383 | ||||||||
\(729\) | −2.91461e104 | −0.944115 | ||||||||
\(730\) | −2.37625e103 | −0.0732164 | ||||||||
\(731\) | 3.57386e103 | 0.104750 | ||||||||
\(732\) | −2.12236e104 | −0.591786 | ||||||||
\(733\) | −6.57120e103 | −0.174321 | −0.0871604 | − | 0.996194i | \(-0.527779\pi\) | ||||
−0.0871604 | + | 0.996194i | \(0.527779\pi\) | |||||||
\(734\) | −7.05048e103 | −0.177956 | ||||||||
\(735\) | −2.68044e103 | −0.0643751 | ||||||||
\(736\) | −1.29768e104 | −0.296569 | ||||||||
\(737\) | 1.38658e102 | 0.00301565 | ||||||||
\(738\) | −2.21740e104 | −0.458973 | ||||||||
\(739\) | 4.98322e104 | 0.981721 | 0.490861 | − | 0.871238i | \(-0.336682\pi\) | ||||
0.490861 | + | 0.871238i | \(0.336682\pi\) | |||||||
\(740\) | −5.64057e103 | −0.105771 | ||||||||
\(741\) | 7.54189e104 | 1.34622 | ||||||||
\(742\) | 6.50844e104 | 1.10595 | ||||||||
\(743\) | −2.21775e104 | −0.358775 | −0.179387 | − | 0.983779i | \(-0.557412\pi\) | ||||
−0.179387 | + | 0.983779i | \(0.557412\pi\) | |||||||
\(744\) | −6.28542e104 | −0.968105 | ||||||||
\(745\) | −7.67576e103 | −0.112569 | ||||||||
\(746\) | 3.44978e104 | 0.481752 | ||||||||
\(747\) | 4.17382e104 | 0.555049 | ||||||||
\(748\) | −6.86661e103 | −0.0869629 | ||||||||
\(749\) | 5.24561e104 | 0.632717 | ||||||||
\(750\) | −3.53658e104 | −0.406301 | ||||||||
\(751\) | 7.02988e104 | 0.769290 | 0.384645 | − | 0.923065i | \(-0.374324\pi\) | ||||
0.384645 | + | 0.923065i | \(0.374324\pi\) | |||||||
\(752\) | 3.76469e104 | 0.392444 | ||||||||
\(753\) | −7.96289e104 | −0.790778 | ||||||||
\(754\) | −3.27760e103 | −0.0310100 | ||||||||
\(755\) | −1.45244e103 | −0.0130928 | ||||||||
\(756\) | 1.99192e103 | 0.0171091 | ||||||||
\(757\) | 2.99786e104 | 0.245365 | 0.122682 | − | 0.992446i | \(-0.460850\pi\) | ||||
0.122682 | + | 0.992446i | \(0.460850\pi\) | |||||||
\(758\) | 1.61393e104 | 0.125880 | ||||||||
\(759\) | 9.99198e104 | 0.742723 | ||||||||
\(760\) | −7.22880e103 | −0.0512118 | ||||||||
\(761\) | −2.11804e105 | −1.43019 | −0.715095 | − | 0.699027i | \(-0.753617\pi\) | ||||
−0.715095 | + | 0.699027i | \(0.753617\pi\) | |||||||
\(762\) | −1.14299e105 | −0.735678 | ||||||||
\(763\) | −1.07414e105 | −0.659047 | ||||||||
\(764\) | −1.12260e105 | −0.656627 | ||||||||
\(765\) | 2.01221e104 | 0.112210 | ||||||||
\(766\) | −2.94361e104 | −0.156506 | ||||||||
\(767\) | 3.70421e105 | 1.87787 | ||||||||
\(768\) | −1.81579e104 | −0.0877770 | ||||||||
\(769\) | −2.30856e105 | −1.06422 | −0.532108 | − | 0.846677i | \(-0.678600\pi\) | ||||
−0.532108 | + | 0.846677i | \(0.678600\pi\) | |||||||
\(770\) | −9.36990e103 | −0.0411930 | ||||||||
\(771\) | 2.76528e105 | 1.15946 | ||||||||
\(772\) | 1.90006e105 | 0.759865 | ||||||||
\(773\) | −3.96296e104 | −0.151171 | −0.0755855 | − | 0.997139i | \(-0.524083\pi\) | ||||
−0.0755855 | + | 0.997139i | \(0.524083\pi\) | |||||||
\(774\) | −3.58758e104 | −0.130544 | ||||||||
\(775\) | −5.37100e105 | −1.86442 | ||||||||
\(776\) | 1.96909e105 | 0.652099 | ||||||||
\(777\) | −3.97288e105 | −1.25527 | ||||||||
\(778\) | −2.15284e105 | −0.649018 | ||||||||
\(779\) | −1.60710e105 | −0.462301 | ||||||||
\(780\) | −7.40447e104 | −0.203255 | ||||||||
\(781\) | 1.04416e105 | 0.273529 | ||||||||
\(782\) | 2.61801e105 | 0.654523 | ||||||||
\(783\) | 5.14238e102 | 0.00122704 | ||||||||
\(784\) | −2.40580e104 | −0.0547927 | ||||||||
\(785\) | −5.72237e104 | −0.124404 | ||||||||
\(786\) | 7.11040e105 | 1.47561 | ||||||||
\(787\) | −3.96236e105 | −0.785012 | −0.392506 | − | 0.919749i | \(-0.628392\pi\) | ||||
−0.392506 | + | 0.919749i | \(0.628392\pi\) | |||||||
\(788\) | 3.19749e105 | 0.604787 | ||||||||
\(789\) | 1.53083e106 | 2.76450 | ||||||||
\(790\) | −1.28294e105 | −0.221216 | ||||||||
\(791\) | 3.59162e105 | 0.591356 | ||||||||
\(792\) | 6.89297e104 | 0.108377 | ||||||||
\(793\) | −7.76785e105 | −1.16635 | ||||||||
\(794\) | 7.54804e105 | 1.08239 | ||||||||
\(795\) | 3.79583e105 | 0.519884 | ||||||||
\(796\) | −1.36249e105 | −0.178240 | ||||||||
\(797\) | 8.51051e105 | 1.06347 | 0.531737 | − | 0.846909i | \(-0.321539\pi\) | ||||
0.531737 | + | 0.846909i | \(0.321539\pi\) | |||||||
\(798\) | −5.09154e105 | −0.607776 | ||||||||
\(799\) | −7.59511e105 | −0.866117 | ||||||||
\(800\) | −1.55162e105 | −0.169045 | ||||||||
\(801\) | −2.79635e105 | −0.291075 | ||||||||
\(802\) | −1.25741e106 | −1.25058 | ||||||||
\(803\) | 1.64222e105 | 0.156068 | ||||||||
\(804\) | −7.39727e103 | −0.00671778 | ||||||||
\(805\) | 3.57243e105 | 0.310037 | ||||||||
\(806\) | −2.30047e106 | −1.90804 | ||||||||
\(807\) | −2.33710e106 | −1.85265 | ||||||||
\(808\) | 3.61288e105 | 0.273741 | ||||||||
\(809\) | −2.64445e105 | −0.191520 | −0.0957602 | − | 0.995404i | \(-0.530528\pi\) | ||||
−0.0957602 | + | 0.995404i | \(0.530528\pi\) | |||||||
\(810\) | 2.19338e105 | 0.151849 | ||||||||
\(811\) | −5.57507e105 | −0.368969 | −0.184484 | − | 0.982835i | \(-0.559061\pi\) | ||||
−0.184484 | + | 0.982835i | \(0.559061\pi\) | |||||||
\(812\) | 2.21271e104 | 0.0140000 | ||||||||
\(813\) | 3.64301e106 | 2.20372 | ||||||||
\(814\) | 3.89817e105 | 0.225461 | ||||||||
\(815\) | −7.73769e104 | −0.0427916 | ||||||||
\(816\) | 3.66328e105 | 0.193722 | ||||||||
\(817\) | −2.60015e105 | −0.131490 | ||||||||
\(818\) | 2.33149e105 | 0.112755 | ||||||||
\(819\) | −2.57118e106 | −1.18924 | ||||||||
\(820\) | 1.57781e105 | 0.0697992 | ||||||||
\(821\) | 2.59339e106 | 1.09735 | 0.548673 | − | 0.836037i | \(-0.315133\pi\) | ||||
0.548673 | + | 0.836037i | \(0.315133\pi\) | |||||||
\(822\) | 1.48973e106 | 0.602959 | ||||||||
\(823\) | −3.77001e105 | −0.145965 | −0.0729824 | − | 0.997333i | \(-0.523252\pi\) | ||||
−0.0729824 | + | 0.997333i | \(0.523252\pi\) | |||||||
\(824\) | 5.24526e105 | 0.194278 | ||||||||
\(825\) | 1.19473e106 | 0.423353 | ||||||||
\(826\) | −2.50072e106 | −0.847799 | ||||||||
\(827\) | 1.56745e106 | 0.508442 | 0.254221 | − | 0.967146i | \(-0.418181\pi\) | ||||
0.254221 | + | 0.967146i | \(0.418181\pi\) | |||||||
\(828\) | −2.62806e106 | −0.815695 | ||||||||
\(829\) | 2.25285e106 | 0.669100 | 0.334550 | − | 0.942378i | \(-0.391416\pi\) | ||||
0.334550 | + | 0.942378i | \(0.391416\pi\) | |||||||
\(830\) | −2.96992e105 | −0.0844101 | ||||||||
\(831\) | −3.34446e106 | −0.909679 | ||||||||
\(832\) | −6.64579e105 | −0.173000 | ||||||||
\(833\) | 4.85360e105 | 0.120926 | ||||||||
\(834\) | 6.21557e106 | 1.48224 | ||||||||
\(835\) | −4.30984e105 | −0.0983797 | ||||||||
\(836\) | 4.99579e105 | 0.109163 | ||||||||
\(837\) | 3.60932e105 | 0.0754998 | ||||||||
\(838\) | 1.57358e106 | 0.315125 | ||||||||
\(839\) | 8.27024e106 | 1.58565 | 0.792823 | − | 0.609452i | \(-0.208610\pi\) | ||||
0.792823 | + | 0.609452i | \(0.208610\pi\) | |||||||
\(840\) | 4.99876e105 | 0.0917632 | ||||||||
\(841\) | −5.68352e106 | −0.998996 | ||||||||
\(842\) | −2.14864e106 | −0.361636 | ||||||||
\(843\) | 4.18686e105 | 0.0674810 | ||||||||
\(844\) | −5.98785e106 | −0.924212 | ||||||||
\(845\) | −1.29521e106 | −0.191456 | ||||||||
\(846\) | 7.62427e106 | 1.07939 | ||||||||
\(847\) | −5.86907e106 | −0.795839 | ||||||||
\(848\) | 3.40690e106 | 0.442498 | ||||||||
\(849\) | −5.35543e106 | −0.666291 | ||||||||
\(850\) | 3.13034e106 | 0.373079 | ||||||||
\(851\) | −1.48624e107 | −1.69692 | ||||||||
\(852\) | −5.57048e106 | −0.609323 | ||||||||
\(853\) | 4.93407e106 | 0.517089 | 0.258544 | − | 0.965999i | \(-0.416757\pi\) | ||||
0.258544 | + | 0.965999i | \(0.416757\pi\) | |||||||
\(854\) | 5.24408e106 | 0.526571 | ||||||||
\(855\) | −1.46398e106 | −0.140855 | ||||||||
\(856\) | 2.74586e106 | 0.253155 | ||||||||
\(857\) | −1.34172e107 | −1.18539 | −0.592695 | − | 0.805427i | \(-0.701936\pi\) | ||||
−0.592695 | + | 0.805427i | \(0.701936\pi\) | |||||||
\(858\) | 5.11720e106 | 0.433258 | ||||||||
\(859\) | −9.86198e106 | −0.800228 | −0.400114 | − | 0.916465i | \(-0.631030\pi\) | ||||
−0.400114 | + | 0.916465i | \(0.631030\pi\) | |||||||
\(860\) | 2.55278e105 | 0.0198527 | ||||||||
\(861\) | 1.11132e107 | 0.828369 | ||||||||
\(862\) | −1.39160e107 | −0.994256 | ||||||||
\(863\) | 1.07941e107 | 0.739252 | 0.369626 | − | 0.929181i | \(-0.379486\pi\) | ||||
0.369626 | + | 0.929181i | \(0.379486\pi\) | |||||||
\(864\) | 1.04269e105 | 0.00684549 | ||||||||
\(865\) | 1.47030e106 | 0.0925374 | ||||||||
\(866\) | −1.70821e107 | −1.03071 | ||||||||
\(867\) | 1.68866e107 | 0.976890 | ||||||||
\(868\) | 1.55305e107 | 0.861420 | ||||||||
\(869\) | 8.86633e106 | 0.471544 | ||||||||
\(870\) | 1.29049e105 | 0.00658115 | ||||||||
\(871\) | −2.70740e105 | −0.0132401 | ||||||||
\(872\) | −5.62270e106 | −0.263690 | ||||||||
\(873\) | 3.98782e107 | 1.79356 | ||||||||
\(874\) | −1.90473e107 | −0.821610 | ||||||||
\(875\) | 8.73844e106 | 0.361526 | ||||||||
\(876\) | −8.76110e106 | −0.347663 | ||||||||
\(877\) | −1.29026e107 | −0.491124 | −0.245562 | − | 0.969381i | \(-0.578972\pi\) | ||||
−0.245562 | + | 0.969381i | \(0.578972\pi\) | |||||||
\(878\) | 5.50069e106 | 0.200848 | ||||||||
\(879\) | 7.45790e106 | 0.261230 | ||||||||
\(880\) | −4.90476e105 | −0.0164816 | ||||||||
\(881\) | 2.43115e107 | 0.783775 | 0.391887 | − | 0.920013i | \(-0.371822\pi\) | ||||
0.391887 | + | 0.920013i | \(0.371822\pi\) | |||||||
\(882\) | −4.87223e106 | −0.150704 | ||||||||
\(883\) | 1.86783e107 | 0.554333 | 0.277166 | − | 0.960822i | \(-0.410605\pi\) | ||||
0.277166 | + | 0.960822i | \(0.410605\pi\) | |||||||
\(884\) | 1.34076e107 | 0.381807 | ||||||||
\(885\) | −1.45846e107 | −0.398534 | ||||||||
\(886\) | 1.92396e107 | 0.504506 | ||||||||
\(887\) | −7.39573e107 | −1.86110 | −0.930549 | − | 0.366169i | \(-0.880669\pi\) | ||||
−0.930549 | + | 0.366169i | \(0.880669\pi\) | |||||||
\(888\) | −2.07964e107 | −0.502245 | ||||||||
\(889\) | 2.82419e107 | 0.654607 | ||||||||
\(890\) | 1.98977e106 | 0.0442658 | ||||||||
\(891\) | −1.51584e107 | −0.323680 | ||||||||
\(892\) | 3.01311e107 | 0.617587 | ||||||||
\(893\) | 5.52581e107 | 1.08722 | ||||||||
\(894\) | −2.83001e107 | −0.534525 | ||||||||
\(895\) | −8.66122e106 | −0.157050 | ||||||||
\(896\) | 4.48658e106 | 0.0781040 | ||||||||
\(897\) | −1.95102e108 | −3.26089 | ||||||||
\(898\) | −1.14126e107 | −0.183147 | ||||||||
\(899\) | 4.00937e106 | 0.0617800 | ||||||||
\(900\) | −3.14235e107 | −0.464947 | ||||||||
\(901\) | −6.87329e107 | −0.976585 | ||||||||
\(902\) | −1.09042e107 | −0.148784 | ||||||||
\(903\) | 1.79802e107 | 0.235609 | ||||||||
\(904\) | 1.88007e107 | 0.236606 | ||||||||
\(905\) | −2.85452e107 | −0.345033 | ||||||||
\(906\) | −5.35505e106 | −0.0621705 | ||||||||
\(907\) | 1.15651e108 | 1.28969 | 0.644843 | − | 0.764315i | \(-0.276923\pi\) | ||||
0.644843 | + | 0.764315i | \(0.276923\pi\) | |||||||
\(908\) | 8.06862e107 | 0.864302 | ||||||||
\(909\) | 7.31683e107 | 0.752907 | ||||||||
\(910\) | 1.82955e107 | 0.180856 | ||||||||
\(911\) | 9.43725e107 | 0.896241 | 0.448121 | − | 0.893973i | \(-0.352094\pi\) | ||||
0.448121 | + | 0.893973i | \(0.352094\pi\) | |||||||
\(912\) | −2.66521e107 | −0.243176 | ||||||||
\(913\) | 2.05250e107 | 0.179928 | ||||||||
\(914\) | 5.98264e107 | 0.503915 | ||||||||
\(915\) | 3.05844e107 | 0.247531 | ||||||||
\(916\) | 7.46871e107 | 0.580846 | ||||||||
\(917\) | −1.75689e108 | −1.31300 | ||||||||
\(918\) | −2.10359e106 | −0.0151079 | ||||||||
\(919\) | 2.59097e108 | 1.78833 | 0.894163 | − | 0.447742i | \(-0.147772\pi\) | ||||
0.894163 | + | 0.447742i | \(0.147772\pi\) | |||||||
\(920\) | 1.87002e107 | 0.124048 | ||||||||
\(921\) | −7.58050e107 | −0.483305 | ||||||||
\(922\) | 1.47946e108 | 0.906622 | ||||||||
\(923\) | −2.03880e108 | −1.20092 | ||||||||
\(924\) | −3.45462e107 | −0.195602 | ||||||||
\(925\) | −1.77709e108 | −0.967245 | ||||||||
\(926\) | −1.06632e108 | −0.557941 | ||||||||
\(927\) | 1.06227e108 | 0.534351 | ||||||||
\(928\) | 1.15826e106 | 0.00560152 | ||||||||
\(929\) | 5.78288e107 | 0.268888 | 0.134444 | − | 0.990921i | \(-0.457075\pi\) | ||||
0.134444 | + | 0.990921i | \(0.457075\pi\) | |||||||
\(930\) | 9.05764e107 | 0.404937 | ||||||||
\(931\) | −3.53123e107 | −0.151797 | ||||||||
\(932\) | −1.09252e108 | −0.451596 | ||||||||
\(933\) | −4.64217e108 | −1.84519 | ||||||||
\(934\) | −1.30865e108 | −0.500222 | ||||||||
\(935\) | 9.89517e106 | 0.0363747 | ||||||||
\(936\) | −1.34591e108 | −0.475825 | ||||||||
\(937\) | 4.62342e108 | 1.57206 | 0.786028 | − | 0.618191i | \(-0.212134\pi\) | ||||
0.786028 | + | 0.618191i | \(0.212134\pi\) | |||||||
\(938\) | 1.82777e106 | 0.00597748 | ||||||||
\(939\) | 5.98005e108 | 1.88109 | ||||||||
\(940\) | −5.42512e107 | −0.164151 | ||||||||
\(941\) | −3.22102e107 | −0.0937503 | −0.0468751 | − | 0.998901i | \(-0.514926\pi\) | ||||
−0.0468751 | + | 0.998901i | \(0.514926\pi\) | |||||||
\(942\) | −2.10980e108 | −0.590723 | ||||||||
\(943\) | 4.15741e108 | 1.11981 | ||||||||
\(944\) | −1.30902e108 | −0.339211 | ||||||||
\(945\) | −2.87047e106 | −0.00715636 | ||||||||
\(946\) | −1.76421e107 | −0.0423179 | ||||||||
\(947\) | −3.71646e108 | −0.857739 | −0.428869 | − | 0.903367i | \(-0.641088\pi\) | ||||
−0.428869 | + | 0.903367i | \(0.641088\pi\) | |||||||
\(948\) | −4.73011e108 | −1.05043 | ||||||||
\(949\) | −3.20657e108 | −0.685210 | ||||||||
\(950\) | −2.27747e108 | −0.468318 | ||||||||
\(951\) | −2.66431e108 | −0.527225 | ||||||||
\(952\) | −9.05150e107 | −0.172374 | ||||||||
\(953\) | −6.51962e108 | −1.19490 | −0.597450 | − | 0.801906i | \(-0.703819\pi\) | ||||
−0.597450 | + | 0.801906i | \(0.703819\pi\) | |||||||
\(954\) | 6.89968e108 | 1.21706 | ||||||||
\(955\) | 1.61773e108 | 0.274653 | ||||||||
\(956\) | 3.57847e108 | 0.584769 | ||||||||
\(957\) | −8.91851e106 | −0.0140284 | ||||||||
\(958\) | 4.57781e108 | 0.693133 | ||||||||
\(959\) | −3.68094e108 | −0.536513 | ||||||||
\(960\) | 2.61665e107 | 0.0367152 | ||||||||
\(961\) | 2.07379e109 | 2.80131 | ||||||||
\(962\) | −7.61151e108 | −0.989875 | ||||||||
\(963\) | 5.56094e108 | 0.696288 | ||||||||
\(964\) | 3.82083e108 | 0.460623 | ||||||||
\(965\) | −2.73809e108 | −0.317835 | ||||||||
\(966\) | 1.31713e109 | 1.47219 | ||||||||
\(967\) | −4.57894e108 | −0.492832 | −0.246416 | − | 0.969164i | \(-0.579253\pi\) | ||||
−0.246416 | + | 0.969164i | \(0.579253\pi\) | |||||||
\(968\) | −3.07222e108 | −0.318421 | ||||||||
\(969\) | 5.37696e108 | 0.536685 | ||||||||
\(970\) | −2.83757e108 | −0.272759 | ||||||||
\(971\) | 5.02125e108 | 0.464847 | 0.232424 | − | 0.972615i | \(-0.425334\pi\) | ||||
0.232424 | + | 0.972615i | \(0.425334\pi\) | |||||||
\(972\) | 7.86971e108 | 0.701682 | ||||||||
\(973\) | −1.53579e109 | −1.31890 | ||||||||
\(974\) | −1.17945e108 | −0.0975614 | ||||||||
\(975\) | −2.33282e109 | −1.85871 | ||||||||
\(976\) | 2.74506e108 | 0.210685 | ||||||||
\(977\) | 1.87265e109 | 1.38454 | 0.692270 | − | 0.721639i | \(-0.256611\pi\) | ||||
0.692270 | + | 0.721639i | \(0.256611\pi\) | |||||||
\(978\) | −2.85284e108 | −0.203193 | ||||||||
\(979\) | −1.37512e108 | −0.0943569 | ||||||||
\(980\) | 3.46688e107 | 0.0229186 | ||||||||
\(981\) | −1.13871e109 | −0.725263 | ||||||||
\(982\) | −1.41358e109 | −0.867462 | ||||||||
\(983\) | 3.33453e108 | 0.197165 | 0.0985827 | − | 0.995129i | \(-0.468569\pi\) | ||||
0.0985827 | + | 0.995129i | \(0.468569\pi\) | |||||||
\(984\) | 5.81731e108 | 0.331437 | ||||||||
\(985\) | −4.60776e108 | −0.252969 | ||||||||
\(986\) | −2.33675e107 | −0.0123625 | ||||||||
\(987\) | −3.82113e109 | −1.94812 | ||||||||
\(988\) | −9.75469e108 | −0.479275 | ||||||||
\(989\) | 6.72635e108 | 0.318504 | ||||||||
\(990\) | −9.93315e107 | −0.0453318 | ||||||||
\(991\) | 1.14253e109 | 0.502552 | 0.251276 | − | 0.967916i | \(-0.419150\pi\) | ||||
0.251276 | + | 0.967916i | \(0.419150\pi\) | |||||||
\(992\) | 8.12957e108 | 0.344661 | ||||||||
\(993\) | 1.28669e109 | 0.525809 | ||||||||
\(994\) | 1.37640e109 | 0.542176 | ||||||||
\(995\) | 1.96342e108 | 0.0745539 | ||||||||
\(996\) | −1.09499e109 | −0.400816 | ||||||||
\(997\) | −2.91782e109 | −1.02964 | −0.514819 | − | 0.857299i | \(-0.672141\pi\) | ||||
−0.514819 | + | 0.857299i | \(0.672141\pi\) | |||||||
\(998\) | 1.76441e109 | 0.600253 | ||||||||
\(999\) | 1.19421e108 | 0.0391687 |
(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 | 2.74.a.b.1.1 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2.74.a.b.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial |