Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [83,16,Mod(1,83)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(83, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 16, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("83.1");
S:= CuspForms(chi, 16);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 83 \) |
Weight: | \( k \) | \(=\) | \( 16 \) |
Character orbit: | \([\chi]\) | \(=\) | 83.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: | \(118.435609233\) |
Analytic rank: | \(1\) |
Dimension: | \(48\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 83.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −157.812 | −0.871797 | −0.435899 | − | 0.899996i | \(-0.643569\pi\) | ||||
−0.435899 | + | 0.899996i | \(0.643569\pi\) | |||||||
\(3\) | 2699.23 | 0.712574 | 0.356287 | − | 0.934377i | \(-0.384042\pi\) | ||||
0.356287 | + | 0.934377i | \(0.384042\pi\) | |||||||
\(4\) | −7863.32 | −0.239969 | ||||||||
\(5\) | 170610. | 0.976631 | 0.488315 | − | 0.872667i | \(-0.337612\pi\) | ||||
0.488315 | + | 0.872667i | \(0.337612\pi\) | |||||||
\(6\) | −425971. | −0.621220 | ||||||||
\(7\) | −2.85216e6 | −1.30899 | −0.654497 | − | 0.756064i | \(-0.727120\pi\) | ||||
−0.654497 | + | 0.756064i | \(0.727120\pi\) | |||||||
\(8\) | 6.41212e6 | 1.08100 | ||||||||
\(9\) | −7.06308e6 | −0.492238 | ||||||||
\(10\) | −2.69244e7 | −0.851424 | ||||||||
\(11\) | 8.82287e7 | 1.36510 | 0.682551 | − | 0.730838i | \(-0.260871\pi\) | ||||
0.682551 | + | 0.730838i | \(0.260871\pi\) | |||||||
\(12\) | −2.12249e7 | −0.170996 | ||||||||
\(13\) | −4.00613e8 | −1.77072 | −0.885360 | − | 0.464907i | \(-0.846088\pi\) | ||||
−0.885360 | + | 0.464907i | \(0.846088\pi\) | |||||||
\(14\) | 4.50105e8 | 1.14118 | ||||||||
\(15\) | 4.60516e8 | 0.695922 | ||||||||
\(16\) | −7.54245e8 | −0.702445 | ||||||||
\(17\) | 2.05636e9 | 1.21543 | 0.607717 | − | 0.794153i | \(-0.292085\pi\) | ||||
0.607717 | + | 0.794153i | \(0.292085\pi\) | |||||||
\(18\) | 1.11464e9 | 0.429132 | ||||||||
\(19\) | 2.89148e9 | 0.742109 | 0.371054 | − | 0.928611i | \(-0.378996\pi\) | ||||
0.371054 | + | 0.928611i | \(0.378996\pi\) | |||||||
\(20\) | −1.34156e9 | −0.234362 | ||||||||
\(21\) | −7.69862e9 | −0.932756 | ||||||||
\(22\) | −1.39236e10 | −1.19009 | ||||||||
\(23\) | 3.59355e9 | 0.220072 | 0.110036 | − | 0.993928i | \(-0.464903\pi\) | ||||
0.110036 | + | 0.993928i | \(0.464903\pi\) | |||||||
\(24\) | 1.73078e10 | 0.770294 | ||||||||
\(25\) | −1.40969e9 | −0.0461928 | ||||||||
\(26\) | 6.32216e10 | 1.54371 | ||||||||
\(27\) | −5.77958e10 | −1.06333 | ||||||||
\(28\) | 2.24274e10 | 0.314119 | ||||||||
\(29\) | 9.32477e10 | 1.00381 | 0.501907 | − | 0.864922i | \(-0.332632\pi\) | ||||
0.501907 | + | 0.864922i | \(0.332632\pi\) | |||||||
\(30\) | −7.26751e10 | −0.606703 | ||||||||
\(31\) | −8.06682e9 | −0.0526611 | −0.0263305 | − | 0.999653i | \(-0.508382\pi\) | ||||
−0.0263305 | + | 0.999653i | \(0.508382\pi\) | |||||||
\(32\) | −9.10832e10 | −0.468612 | ||||||||
\(33\) | 2.38149e11 | 0.972736 | ||||||||
\(34\) | −3.24518e11 | −1.05961 | ||||||||
\(35\) | −4.86607e11 | −1.27840 | ||||||||
\(36\) | 5.55392e10 | 0.118122 | ||||||||
\(37\) | −2.61215e11 | −0.452361 | −0.226180 | − | 0.974085i | \(-0.572624\pi\) | ||||
−0.226180 | + | 0.974085i | \(0.572624\pi\) | |||||||
\(38\) | −4.56310e11 | −0.646969 | ||||||||
\(39\) | −1.08135e12 | −1.26177 | ||||||||
\(40\) | 1.09397e12 | 1.05574 | ||||||||
\(41\) | 8.52234e11 | 0.683408 | 0.341704 | − | 0.939808i | \(-0.388996\pi\) | ||||
0.341704 | + | 0.939808i | \(0.388996\pi\) | |||||||
\(42\) | 1.21494e12 | 0.813174 | ||||||||
\(43\) | −2.66552e11 | −0.149544 | −0.0747720 | − | 0.997201i | \(-0.523823\pi\) | ||||
−0.0747720 | + | 0.997201i | \(0.523823\pi\) | |||||||
\(44\) | −6.93771e11 | −0.327583 | ||||||||
\(45\) | −1.20503e12 | −0.480735 | ||||||||
\(46\) | −5.67106e11 | −0.191858 | ||||||||
\(47\) | −4.32032e12 | −1.24389 | −0.621944 | − | 0.783061i | \(-0.713657\pi\) | ||||
−0.621944 | + | 0.783061i | \(0.713657\pi\) | |||||||
\(48\) | −2.03588e12 | −0.500544 | ||||||||
\(49\) | 3.38723e12 | 0.713467 | ||||||||
\(50\) | 2.22467e11 | 0.0402708 | ||||||||
\(51\) | 5.55058e12 | 0.866088 | ||||||||
\(52\) | 3.15015e12 | 0.424919 | ||||||||
\(53\) | −7.23066e12 | −0.845491 | −0.422746 | − | 0.906248i | \(-0.638934\pi\) | ||||
−0.422746 | + | 0.906248i | \(0.638934\pi\) | |||||||
\(54\) | 9.12088e12 | 0.927009 | ||||||||
\(55\) | 1.50527e13 | 1.33320 | ||||||||
\(56\) | −1.82884e13 | −1.41503 | ||||||||
\(57\) | 7.80475e12 | 0.528808 | ||||||||
\(58\) | −1.47156e13 | −0.875122 | ||||||||
\(59\) | 3.00946e13 | 1.57434 | 0.787171 | − | 0.616735i | \(-0.211545\pi\) | ||||
0.787171 | + | 0.616735i | \(0.211545\pi\) | |||||||
\(60\) | −3.62119e12 | −0.167000 | ||||||||
\(61\) | −7.17690e12 | −0.292391 | −0.146195 | − | 0.989256i | \(-0.546703\pi\) | ||||
−0.146195 | + | 0.989256i | \(0.546703\pi\) | |||||||
\(62\) | 1.27304e12 | 0.0459098 | ||||||||
\(63\) | 2.01450e13 | 0.644337 | ||||||||
\(64\) | 3.90891e13 | 1.11098 | ||||||||
\(65\) | −6.83487e13 | −1.72934 | ||||||||
\(66\) | −3.75829e13 | −0.848029 | ||||||||
\(67\) | 6.42677e13 | 1.29548 | 0.647742 | − | 0.761860i | \(-0.275713\pi\) | ||||
0.647742 | + | 0.761860i | \(0.275713\pi\) | |||||||
\(68\) | −1.61698e13 | −0.291667 | ||||||||
\(69\) | 9.69981e12 | 0.156818 | ||||||||
\(70\) | 7.67925e13 | 1.11451 | ||||||||
\(71\) | 1.81087e13 | 0.236292 | 0.118146 | − | 0.992996i | \(-0.462305\pi\) | ||||
0.118146 | + | 0.992996i | \(0.462305\pi\) | |||||||
\(72\) | −4.52893e13 | −0.532110 | ||||||||
\(73\) | −5.09547e13 | −0.539838 | −0.269919 | − | 0.962883i | \(-0.586997\pi\) | ||||
−0.269919 | + | 0.962883i | \(0.586997\pi\) | |||||||
\(74\) | 4.12229e13 | 0.394367 | ||||||||
\(75\) | −3.80508e12 | −0.0329158 | ||||||||
\(76\) | −2.27366e13 | −0.178084 | ||||||||
\(77\) | −2.51642e14 | −1.78691 | ||||||||
\(78\) | 1.70649e14 | 1.10001 | ||||||||
\(79\) | −1.19406e14 | −0.699556 | −0.349778 | − | 0.936833i | \(-0.613743\pi\) | ||||
−0.349778 | + | 0.936833i | \(0.613743\pi\) | |||||||
\(80\) | −1.28682e14 | −0.686029 | ||||||||
\(81\) | −5.46567e13 | −0.265464 | ||||||||
\(82\) | −1.34493e14 | −0.595793 | ||||||||
\(83\) | 2.71361e13 | 0.109764 | ||||||||
\(84\) | 6.05367e13 | 0.223833 | ||||||||
\(85\) | 3.50836e14 | 1.18703 | ||||||||
\(86\) | 4.20652e13 | 0.130372 | ||||||||
\(87\) | 2.51697e14 | 0.715292 | ||||||||
\(88\) | 5.65733e14 | 1.47568 | ||||||||
\(89\) | 3.84406e14 | 0.921224 | 0.460612 | − | 0.887602i | \(-0.347630\pi\) | ||||
0.460612 | + | 0.887602i | \(0.347630\pi\) | |||||||
\(90\) | 1.90169e14 | 0.419103 | ||||||||
\(91\) | 1.14261e15 | 2.31786 | ||||||||
\(92\) | −2.82572e13 | −0.0528106 | ||||||||
\(93\) | −2.17742e13 | −0.0375249 | ||||||||
\(94\) | 6.81798e14 | 1.08442 | ||||||||
\(95\) | 4.93316e14 | 0.724766 | ||||||||
\(96\) | −2.45854e14 | −0.333921 | ||||||||
\(97\) | 9.79195e14 | 1.23050 | 0.615250 | − | 0.788332i | \(-0.289055\pi\) | ||||
0.615250 | + | 0.788332i | \(0.289055\pi\) | |||||||
\(98\) | −5.34546e14 | −0.621998 | ||||||||
\(99\) | −6.23166e14 | −0.671954 | ||||||||
\(100\) | 1.10849e13 | 0.0110849 | ||||||||
\(101\) | 1.66476e15 | 1.54505 | 0.772525 | − | 0.634984i | \(-0.218993\pi\) | ||||
0.772525 | + | 0.634984i | \(0.218993\pi\) | |||||||
\(102\) | −8.75949e14 | −0.755053 | ||||||||
\(103\) | −1.03840e15 | −0.831925 | −0.415962 | − | 0.909382i | \(-0.636555\pi\) | ||||
−0.415962 | + | 0.909382i | \(0.636555\pi\) | |||||||
\(104\) | −2.56878e15 | −1.91415 | ||||||||
\(105\) | −1.31346e15 | −0.910958 | ||||||||
\(106\) | 1.14109e15 | 0.737097 | ||||||||
\(107\) | −3.08276e15 | −1.85593 | −0.927965 | − | 0.372668i | \(-0.878443\pi\) | ||||
−0.927965 | + | 0.372668i | \(0.878443\pi\) | |||||||
\(108\) | 4.54467e14 | 0.255167 | ||||||||
\(109\) | −1.33594e15 | −0.699984 | −0.349992 | − | 0.936753i | \(-0.613816\pi\) | ||||
−0.349992 | + | 0.936753i | \(0.613816\pi\) | |||||||
\(110\) | −2.37550e15 | −1.16228 | ||||||||
\(111\) | −7.05079e14 | −0.322341 | ||||||||
\(112\) | 2.15122e15 | 0.919497 | ||||||||
\(113\) | −2.62503e15 | −1.04965 | −0.524827 | − | 0.851209i | \(-0.675870\pi\) | ||||
−0.524827 | + | 0.851209i | \(0.675870\pi\) | |||||||
\(114\) | −1.23169e15 | −0.461013 | ||||||||
\(115\) | 6.13096e14 | 0.214929 | ||||||||
\(116\) | −7.33236e14 | −0.240885 | ||||||||
\(117\) | 2.82956e15 | 0.871615 | ||||||||
\(118\) | −4.74930e15 | −1.37251 | ||||||||
\(119\) | −5.86505e15 | −1.59100 | ||||||||
\(120\) | 2.95288e15 | 0.752293 | ||||||||
\(121\) | 3.60706e15 | 0.863501 | ||||||||
\(122\) | 1.13260e15 | 0.254905 | ||||||||
\(123\) | 2.30037e15 | 0.486979 | ||||||||
\(124\) | 6.34320e13 | 0.0126370 | ||||||||
\(125\) | −5.44712e15 | −1.02174 | ||||||||
\(126\) | −3.17912e15 | −0.561731 | ||||||||
\(127\) | 5.61481e14 | 0.0934990 | 0.0467495 | − | 0.998907i | \(-0.485114\pi\) | ||||
0.0467495 | + | 0.998907i | \(0.485114\pi\) | |||||||
\(128\) | −3.18413e15 | −0.499937 | ||||||||
\(129\) | −7.19485e14 | −0.106561 | ||||||||
\(130\) | 1.07863e16 | 1.50763 | ||||||||
\(131\) | −1.50562e16 | −1.98692 | −0.993460 | − | 0.114184i | \(-0.963575\pi\) | ||||
−0.993460 | + | 0.114184i | \(0.963575\pi\) | |||||||
\(132\) | −1.87265e15 | −0.233427 | ||||||||
\(133\) | −8.24694e15 | −0.971417 | ||||||||
\(134\) | −1.01422e16 | −1.12940 | ||||||||
\(135\) | −9.86056e15 | −1.03848 | ||||||||
\(136\) | 1.31856e16 | 1.31389 | ||||||||
\(137\) | −1.69710e16 | −1.60068 | −0.800340 | − | 0.599547i | \(-0.795347\pi\) | ||||
−0.800340 | + | 0.599547i | \(0.795347\pi\) | |||||||
\(138\) | −1.53075e15 | −0.136713 | ||||||||
\(139\) | −1.11003e16 | −0.939122 | −0.469561 | − | 0.882900i | \(-0.655588\pi\) | ||||
−0.469561 | + | 0.882900i | \(0.655588\pi\) | |||||||
\(140\) | 3.82635e15 | 0.306778 | ||||||||
\(141\) | −1.16615e16 | −0.886363 | ||||||||
\(142\) | −2.85777e15 | −0.205999 | ||||||||
\(143\) | −3.53456e16 | −2.41721 | ||||||||
\(144\) | 5.32729e15 | 0.345770 | ||||||||
\(145\) | 1.59090e16 | 0.980355 | ||||||||
\(146\) | 8.04128e15 | 0.470629 | ||||||||
\(147\) | 9.14290e15 | 0.508398 | ||||||||
\(148\) | 2.05402e15 | 0.108553 | ||||||||
\(149\) | 1.68858e16 | 0.848445 | 0.424222 | − | 0.905558i | \(-0.360547\pi\) | ||||
0.424222 | + | 0.905558i | \(0.360547\pi\) | |||||||
\(150\) | 6.00488e14 | 0.0286959 | ||||||||
\(151\) | −2.60907e16 | −1.18620 | −0.593102 | − | 0.805127i | \(-0.702097\pi\) | ||||
−0.593102 | + | 0.805127i | \(0.702097\pi\) | |||||||
\(152\) | 1.85405e16 | 0.802221 | ||||||||
\(153\) | −1.45242e16 | −0.598283 | ||||||||
\(154\) | 3.97122e16 | 1.55782 | ||||||||
\(155\) | −1.37628e15 | −0.0514304 | ||||||||
\(156\) | 8.50297e15 | 0.302786 | ||||||||
\(157\) | −4.08753e16 | −1.38744 | −0.693720 | − | 0.720245i | \(-0.744029\pi\) | ||||
−0.693720 | + | 0.720245i | \(0.744029\pi\) | |||||||
\(158\) | 1.88437e16 | 0.609871 | ||||||||
\(159\) | −1.95172e16 | −0.602475 | ||||||||
\(160\) | −1.55397e16 | −0.457661 | ||||||||
\(161\) | −1.02494e16 | −0.288073 | ||||||||
\(162\) | 8.62549e15 | 0.231431 | ||||||||
\(163\) | −5.04820e16 | −1.29339 | −0.646695 | − | 0.762748i | \(-0.723850\pi\) | ||||
−0.646695 | + | 0.762748i | \(0.723850\pi\) | |||||||
\(164\) | −6.70139e15 | −0.163997 | ||||||||
\(165\) | 4.06307e16 | 0.950004 | ||||||||
\(166\) | −4.28240e15 | −0.0956922 | ||||||||
\(167\) | −3.69593e15 | −0.0789496 | −0.0394748 | − | 0.999221i | \(-0.512568\pi\) | ||||
−0.0394748 | + | 0.999221i | \(0.512568\pi\) | |||||||
\(168\) | −4.93644e16 | −1.00831 | ||||||||
\(169\) | 1.09305e17 | 2.13545 | ||||||||
\(170\) | −5.53662e16 | −1.03485 | ||||||||
\(171\) | −2.04227e16 | −0.365294 | ||||||||
\(172\) | 2.09599e15 | 0.0358860 | ||||||||
\(173\) | −3.91294e16 | −0.641441 | −0.320721 | − | 0.947174i | \(-0.603925\pi\) | ||||
−0.320721 | + | 0.947174i | \(0.603925\pi\) | |||||||
\(174\) | −3.97208e16 | −0.623589 | ||||||||
\(175\) | 4.02066e15 | 0.0604661 | ||||||||
\(176\) | −6.65460e16 | −0.958909 | ||||||||
\(177\) | 8.12323e16 | 1.12184 | ||||||||
\(178\) | −6.06640e16 | −0.803121 | ||||||||
\(179\) | 9.80903e16 | 1.24517 | 0.622585 | − | 0.782552i | \(-0.286083\pi\) | ||||
0.622585 | + | 0.782552i | \(0.286083\pi\) | |||||||
\(180\) | 9.47556e15 | 0.115362 | ||||||||
\(181\) | −3.43233e16 | −0.400866 | −0.200433 | − | 0.979707i | \(-0.564235\pi\) | ||||
−0.200433 | + | 0.979707i | \(0.564235\pi\) | |||||||
\(182\) | −1.80318e17 | −2.02071 | ||||||||
\(183\) | −1.93721e16 | −0.208350 | ||||||||
\(184\) | 2.30422e16 | 0.237898 | ||||||||
\(185\) | −4.45660e16 | −0.441789 | ||||||||
\(186\) | 3.43623e15 | 0.0327141 | ||||||||
\(187\) | 1.81430e17 | 1.65919 | ||||||||
\(188\) | 3.39720e16 | 0.298495 | ||||||||
\(189\) | 1.64843e17 | 1.39189 | ||||||||
\(190\) | −7.78512e16 | −0.631849 | ||||||||
\(191\) | 5.02868e16 | 0.392377 | 0.196189 | − | 0.980566i | \(-0.437144\pi\) | ||||
0.196189 | + | 0.980566i | \(0.437144\pi\) | |||||||
\(192\) | 1.05510e17 | 0.791656 | ||||||||
\(193\) | −1.50024e17 | −1.08263 | −0.541315 | − | 0.840820i | \(-0.682073\pi\) | ||||
−0.541315 | + | 0.840820i | \(0.682073\pi\) | |||||||
\(194\) | −1.54529e17 | −1.07275 | ||||||||
\(195\) | −1.84489e17 | −1.23228 | ||||||||
\(196\) | −2.66349e16 | −0.171210 | ||||||||
\(197\) | −1.44904e17 | −0.896567 | −0.448283 | − | 0.893892i | \(-0.647964\pi\) | ||||
−0.448283 | + | 0.893892i | \(0.647964\pi\) | |||||||
\(198\) | 9.83432e16 | 0.585808 | ||||||||
\(199\) | −2.39762e17 | −1.37525 | −0.687625 | − | 0.726066i | \(-0.741347\pi\) | ||||
−0.687625 | + | 0.726066i | \(0.741347\pi\) | |||||||
\(200\) | −9.03911e15 | −0.0499345 | ||||||||
\(201\) | 1.73473e17 | 0.923129 | ||||||||
\(202\) | −2.62720e17 | −1.34697 | ||||||||
\(203\) | −2.65957e17 | −1.31399 | ||||||||
\(204\) | −4.36460e16 | −0.207835 | ||||||||
\(205\) | 1.45400e17 | 0.667437 | ||||||||
\(206\) | 1.63872e17 | 0.725270 | ||||||||
\(207\) | −2.53815e16 | −0.108328 | ||||||||
\(208\) | 3.02160e17 | 1.24383 | ||||||||
\(209\) | 2.55111e17 | 1.01305 | ||||||||
\(210\) | 2.07281e17 | 0.794171 | ||||||||
\(211\) | 1.99916e17 | 0.739143 | 0.369572 | − | 0.929202i | \(-0.379504\pi\) | ||||
0.369572 | + | 0.929202i | \(0.379504\pi\) | |||||||
\(212\) | 5.68570e16 | 0.202892 | ||||||||
\(213\) | 4.88794e16 | 0.168376 | ||||||||
\(214\) | 4.86497e17 | 1.61799 | ||||||||
\(215\) | −4.54766e16 | −0.146049 | ||||||||
\(216\) | −3.70594e17 | −1.14946 | ||||||||
\(217\) | 2.30078e16 | 0.0689331 | ||||||||
\(218\) | 2.10827e17 | 0.610244 | ||||||||
\(219\) | −1.37538e17 | −0.384674 | ||||||||
\(220\) | −1.18364e17 | −0.319927 | ||||||||
\(221\) | −8.23803e17 | −2.15219 | ||||||||
\(222\) | 1.11270e17 | 0.281016 | ||||||||
\(223\) | 1.46102e17 | 0.356754 | 0.178377 | − | 0.983962i | \(-0.442915\pi\) | ||||
0.178377 | + | 0.983962i | \(0.442915\pi\) | |||||||
\(224\) | 2.59784e17 | 0.613411 | ||||||||
\(225\) | 9.95676e15 | 0.0227378 | ||||||||
\(226\) | 4.14262e17 | 0.915085 | ||||||||
\(227\) | −2.43257e17 | −0.519841 | −0.259921 | − | 0.965630i | \(-0.583696\pi\) | ||||
−0.259921 | + | 0.965630i | \(0.583696\pi\) | |||||||
\(228\) | −6.13713e16 | −0.126898 | ||||||||
\(229\) | 1.31385e17 | 0.262893 | 0.131446 | − | 0.991323i | \(-0.458038\pi\) | ||||
0.131446 | + | 0.991323i | \(0.458038\pi\) | |||||||
\(230\) | −9.67541e16 | −0.187375 | ||||||||
\(231\) | −6.79239e17 | −1.27331 | ||||||||
\(232\) | 5.97915e17 | 1.08512 | ||||||||
\(233\) | 2.09033e16 | 0.0367321 | 0.0183661 | − | 0.999831i | \(-0.494154\pi\) | ||||
0.0183661 | + | 0.999831i | \(0.494154\pi\) | |||||||
\(234\) | −4.46539e17 | −0.759872 | ||||||||
\(235\) | −7.37090e17 | −1.21482 | ||||||||
\(236\) | −2.36644e17 | −0.377794 | ||||||||
\(237\) | −3.22304e17 | −0.498486 | ||||||||
\(238\) | 9.25576e17 | 1.38703 | ||||||||
\(239\) | 1.23675e17 | 0.179596 | 0.0897981 | − | 0.995960i | \(-0.471378\pi\) | ||||
0.0897981 | + | 0.995960i | \(0.471378\pi\) | |||||||
\(240\) | −3.47342e17 | −0.488847 | ||||||||
\(241\) | 7.36896e17 | 1.00526 | 0.502630 | − | 0.864502i | \(-0.332366\pi\) | ||||
0.502630 | + | 0.864502i | \(0.332366\pi\) | |||||||
\(242\) | −5.69237e17 | −0.752798 | ||||||||
\(243\) | 6.81776e17 | 0.874167 | ||||||||
\(244\) | 5.64343e16 | 0.0701648 | ||||||||
\(245\) | 5.77896e17 | 0.696793 | ||||||||
\(246\) | −3.63027e17 | −0.424547 | ||||||||
\(247\) | −1.15836e18 | −1.31407 | ||||||||
\(248\) | −5.17254e16 | −0.0569267 | ||||||||
\(249\) | 7.32464e16 | 0.0782152 | ||||||||
\(250\) | 8.59622e17 | 0.890754 | ||||||||
\(251\) | −1.58985e18 | −1.59884 | −0.799419 | − | 0.600774i | \(-0.794859\pi\) | ||||
−0.799419 | + | 0.600774i | \(0.794859\pi\) | |||||||
\(252\) | −1.58406e17 | −0.154621 | ||||||||
\(253\) | 3.17054e17 | 0.300420 | ||||||||
\(254\) | −8.86085e16 | −0.0815122 | ||||||||
\(255\) | 9.46986e17 | 0.845848 | ||||||||
\(256\) | −7.78379e17 | −0.675136 | ||||||||
\(257\) | 1.06518e18 | 0.897271 | 0.448636 | − | 0.893715i | \(-0.351910\pi\) | ||||
0.448636 | + | 0.893715i | \(0.351910\pi\) | |||||||
\(258\) | 1.13544e17 | 0.0928998 | ||||||||
\(259\) | 7.45025e17 | 0.592138 | ||||||||
\(260\) | 5.37448e17 | 0.414988 | ||||||||
\(261\) | −6.58615e17 | −0.494115 | ||||||||
\(262\) | 2.37605e18 | 1.73219 | ||||||||
\(263\) | 7.86754e17 | 0.557405 | 0.278702 | − | 0.960378i | \(-0.410096\pi\) | ||||
0.278702 | + | 0.960378i | \(0.410096\pi\) | |||||||
\(264\) | 1.52704e18 | 1.05153 | ||||||||
\(265\) | −1.23363e18 | −0.825733 | ||||||||
\(266\) | 1.30147e18 | 0.846878 | ||||||||
\(267\) | 1.03760e18 | 0.656441 | ||||||||
\(268\) | −5.05358e17 | −0.310877 | ||||||||
\(269\) | 6.58179e16 | 0.0393733 | 0.0196867 | − | 0.999806i | \(-0.493733\pi\) | ||||
0.0196867 | + | 0.999806i | \(0.493733\pi\) | |||||||
\(270\) | 1.55612e18 | 0.905345 | ||||||||
\(271\) | −1.90397e18 | −1.07743 | −0.538717 | − | 0.842486i | \(-0.681091\pi\) | ||||
−0.538717 | + | 0.842486i | \(0.681091\pi\) | |||||||
\(272\) | −1.55100e18 | −0.853776 | ||||||||
\(273\) | 3.08416e18 | 1.65165 | ||||||||
\(274\) | 2.67824e18 | 1.39547 | ||||||||
\(275\) | −1.24375e17 | −0.0630578 | ||||||||
\(276\) | −7.62727e16 | −0.0376314 | ||||||||
\(277\) | −9.72903e17 | −0.467166 | −0.233583 | − | 0.972337i | \(-0.575045\pi\) | ||||
−0.233583 | + | 0.972337i | \(0.575045\pi\) | |||||||
\(278\) | 1.75176e18 | 0.818724 | ||||||||
\(279\) | 5.69766e16 | 0.0259218 | ||||||||
\(280\) | −3.12018e18 | −1.38196 | ||||||||
\(281\) | 3.13534e18 | 1.35203 | 0.676017 | − | 0.736886i | \(-0.263704\pi\) | ||||
0.676017 | + | 0.736886i | \(0.263704\pi\) | |||||||
\(282\) | 1.84033e18 | 0.772729 | ||||||||
\(283\) | −2.49493e18 | −1.02014 | −0.510070 | − | 0.860133i | \(-0.670381\pi\) | ||||
−0.510070 | + | 0.860133i | \(0.670381\pi\) | |||||||
\(284\) | −1.42394e17 | −0.0567028 | ||||||||
\(285\) | 1.33157e18 | 0.516450 | ||||||||
\(286\) | 5.57796e18 | 2.10732 | ||||||||
\(287\) | −2.43070e18 | −0.894577 | ||||||||
\(288\) | 6.43328e17 | 0.230669 | ||||||||
\(289\) | 1.36618e18 | 0.477281 | ||||||||
\(290\) | −2.51064e18 | −0.854671 | ||||||||
\(291\) | 2.64307e18 | 0.876822 | ||||||||
\(292\) | 4.00673e17 | 0.129545 | ||||||||
\(293\) | −4.45469e18 | −1.40382 | −0.701908 | − | 0.712267i | \(-0.747668\pi\) | ||||
−0.701908 | + | 0.712267i | \(0.747668\pi\) | |||||||
\(294\) | −1.44286e18 | −0.443220 | ||||||||
\(295\) | 5.13446e18 | 1.53755 | ||||||||
\(296\) | −1.67494e18 | −0.489003 | ||||||||
\(297\) | −5.09925e18 | −1.45155 | ||||||||
\(298\) | −2.66478e18 | −0.739672 | ||||||||
\(299\) | −1.43962e18 | −0.389686 | ||||||||
\(300\) | 2.99206e16 | 0.00789879 | ||||||||
\(301\) | 7.60248e17 | 0.195752 | ||||||||
\(302\) | 4.11744e18 | 1.03413 | ||||||||
\(303\) | 4.49358e18 | 1.10096 | ||||||||
\(304\) | −2.18088e18 | −0.521291 | ||||||||
\(305\) | −1.22445e18 | −0.285558 | ||||||||
\(306\) | 2.29210e18 | 0.521581 | ||||||||
\(307\) | −2.74229e18 | −0.608942 | −0.304471 | − | 0.952522i | \(-0.598480\pi\) | ||||
−0.304471 | + | 0.952522i | \(0.598480\pi\) | |||||||
\(308\) | 1.97874e18 | 0.428804 | ||||||||
\(309\) | −2.80287e18 | −0.592808 | ||||||||
\(310\) | 2.17194e17 | 0.0448369 | ||||||||
\(311\) | −6.45332e18 | −1.30041 | −0.650205 | − | 0.759759i | \(-0.725317\pi\) | ||||
−0.650205 | + | 0.759759i | \(0.725317\pi\) | |||||||
\(312\) | −6.93371e18 | −1.36398 | ||||||||
\(313\) | −9.52968e18 | −1.83019 | −0.915094 | − | 0.403239i | \(-0.867884\pi\) | ||||
−0.915094 | + | 0.403239i | \(0.867884\pi\) | |||||||
\(314\) | 6.45062e18 | 1.20957 | ||||||||
\(315\) | 3.43694e18 | 0.629279 | ||||||||
\(316\) | 9.38927e17 | 0.167872 | ||||||||
\(317\) | −3.89195e18 | −0.679553 | −0.339776 | − | 0.940506i | \(-0.610351\pi\) | ||||
−0.339776 | + | 0.940506i | \(0.610351\pi\) | |||||||
\(318\) | 3.08005e18 | 0.525236 | ||||||||
\(319\) | 8.22712e18 | 1.37031 | ||||||||
\(320\) | 6.66901e18 | 1.08502 | ||||||||
\(321\) | −8.32107e18 | −1.32249 | ||||||||
\(322\) | 1.61747e18 | 0.251141 | ||||||||
\(323\) | 5.94591e18 | 0.901985 | ||||||||
\(324\) | 4.29783e17 | 0.0637033 | ||||||||
\(325\) | 5.64741e17 | 0.0817945 | ||||||||
\(326\) | 7.96668e18 | 1.12757 | ||||||||
\(327\) | −3.60600e18 | −0.498790 | ||||||||
\(328\) | 5.46462e18 | 0.738765 | ||||||||
\(329\) | 1.23222e19 | 1.62824 | ||||||||
\(330\) | −6.41203e18 | −0.828211 | ||||||||
\(331\) | 5.71521e18 | 0.721643 | 0.360821 | − | 0.932635i | \(-0.382496\pi\) | ||||
0.360821 | + | 0.932635i | \(0.382496\pi\) | |||||||
\(332\) | −2.13379e17 | −0.0263401 | ||||||||
\(333\) | 1.84498e18 | 0.222669 | ||||||||
\(334\) | 5.83263e17 | 0.0688281 | ||||||||
\(335\) | 1.09647e19 | 1.26521 | ||||||||
\(336\) | 5.80664e18 | 0.655210 | ||||||||
\(337\) | −6.86429e17 | −0.0757481 | −0.0378740 | − | 0.999283i | \(-0.512059\pi\) | ||||
−0.0378740 | + | 0.999283i | \(0.512059\pi\) | |||||||
\(338\) | −1.72496e19 | −1.86168 | ||||||||
\(339\) | −7.08555e18 | −0.747956 | ||||||||
\(340\) | −2.75873e18 | −0.284851 | ||||||||
\(341\) | −7.11725e17 | −0.0718877 | ||||||||
\(342\) | 3.22295e18 | 0.318462 | ||||||||
\(343\) | 3.87988e18 | 0.375070 | ||||||||
\(344\) | −1.70916e18 | −0.161657 | ||||||||
\(345\) | 1.65489e18 | 0.153153 | ||||||||
\(346\) | 6.17509e18 | 0.559207 | ||||||||
\(347\) | −2.02412e19 | −1.79376 | −0.896882 | − | 0.442271i | \(-0.854173\pi\) | ||||
−0.896882 | + | 0.442271i | \(0.854173\pi\) | |||||||
\(348\) | −1.97917e18 | −0.171648 | ||||||||
\(349\) | −8.07340e18 | −0.685276 | −0.342638 | − | 0.939467i | \(-0.611320\pi\) | ||||
−0.342638 | + | 0.939467i | \(0.611320\pi\) | |||||||
\(350\) | −6.34509e17 | −0.0527142 | ||||||||
\(351\) | 2.31537e19 | 1.88286 | ||||||||
\(352\) | −8.03616e18 | −0.639703 | ||||||||
\(353\) | −2.36921e19 | −1.84627 | −0.923133 | − | 0.384482i | \(-0.874380\pi\) | ||||
−0.923133 | + | 0.384482i | \(0.874380\pi\) | |||||||
\(354\) | −1.28194e19 | −0.978013 | ||||||||
\(355\) | 3.08953e18 | 0.230770 | ||||||||
\(356\) | −3.02271e18 | −0.221066 | ||||||||
\(357\) | −1.58311e19 | −1.13370 | ||||||||
\(358\) | −1.54798e19 | −1.08554 | ||||||||
\(359\) | −4.23117e18 | −0.290571 | −0.145285 | − | 0.989390i | \(-0.546410\pi\) | ||||
−0.145285 | + | 0.989390i | \(0.546410\pi\) | |||||||
\(360\) | −7.72682e18 | −0.519675 | ||||||||
\(361\) | −6.82049e18 | −0.449274 | ||||||||
\(362\) | 5.41663e18 | 0.349474 | ||||||||
\(363\) | 9.73627e18 | 0.615308 | ||||||||
\(364\) | −8.98471e18 | −0.556216 | ||||||||
\(365\) | −8.69340e18 | −0.527222 | ||||||||
\(366\) | 3.05715e18 | 0.181639 | ||||||||
\(367\) | 1.32911e19 | 0.773687 | 0.386843 | − | 0.922145i | \(-0.373565\pi\) | ||||
0.386843 | + | 0.922145i | \(0.373565\pi\) | |||||||
\(368\) | −2.71041e18 | −0.154588 | ||||||||
\(369\) | −6.01939e18 | −0.336399 | ||||||||
\(370\) | 7.03305e18 | 0.385151 | ||||||||
\(371\) | 2.06230e19 | 1.10674 | ||||||||
\(372\) | 1.71217e17 | 0.00900484 | ||||||||
\(373\) | −1.65517e19 | −0.853150 | −0.426575 | − | 0.904452i | \(-0.640280\pi\) | ||||
−0.426575 | + | 0.904452i | \(0.640280\pi\) | |||||||
\(374\) | −2.86318e19 | −1.44648 | ||||||||
\(375\) | −1.47030e19 | −0.728068 | ||||||||
\(376\) | −2.77024e19 | −1.34465 | ||||||||
\(377\) | −3.73562e19 | −1.77747 | ||||||||
\(378\) | −2.60142e19 | −1.21345 | ||||||||
\(379\) | 7.90359e17 | 0.0361435 | 0.0180718 | − | 0.999837i | \(-0.494247\pi\) | ||||
0.0180718 | + | 0.999837i | \(0.494247\pi\) | |||||||
\(380\) | −3.87910e18 | −0.173922 | ||||||||
\(381\) | 1.51557e18 | 0.0666250 | ||||||||
\(382\) | −7.93587e18 | −0.342073 | ||||||||
\(383\) | 3.32591e19 | 1.40579 | 0.702893 | − | 0.711296i | \(-0.251891\pi\) | ||||
0.702893 | + | 0.711296i | \(0.251891\pi\) | |||||||
\(384\) | −8.59468e18 | −0.356242 | ||||||||
\(385\) | −4.29327e19 | −1.74515 | ||||||||
\(386\) | 2.36756e19 | 0.943834 | ||||||||
\(387\) | 1.88268e18 | 0.0736112 | ||||||||
\(388\) | −7.69973e18 | −0.295282 | ||||||||
\(389\) | 3.15545e19 | 1.18697 | 0.593484 | − | 0.804846i | \(-0.297752\pi\) | ||||
0.593484 | + | 0.804846i | \(0.297752\pi\) | |||||||
\(390\) | 2.91146e19 | 1.07430 | ||||||||
\(391\) | 7.38962e18 | 0.267483 | ||||||||
\(392\) | 2.17193e19 | 0.771259 | ||||||||
\(393\) | −4.06401e19 | −1.41583 | ||||||||
\(394\) | 2.28676e19 | 0.781624 | ||||||||
\(395\) | −2.03719e19 | −0.683208 | ||||||||
\(396\) | 4.90015e18 | 0.161249 | ||||||||
\(397\) | 1.26209e19 | 0.407533 | 0.203766 | − | 0.979020i | \(-0.434682\pi\) | ||||
0.203766 | + | 0.979020i | \(0.434682\pi\) | |||||||
\(398\) | 3.78373e19 | 1.19894 | ||||||||
\(399\) | −2.22604e19 | −0.692206 | ||||||||
\(400\) | 1.06325e18 | 0.0324479 | ||||||||
\(401\) | 4.44097e19 | 1.33013 | 0.665066 | − | 0.746785i | \(-0.268403\pi\) | ||||
0.665066 | + | 0.746785i | \(0.268403\pi\) | |||||||
\(402\) | −2.73762e19 | −0.804781 | ||||||||
\(403\) | 3.23167e18 | 0.0932480 | ||||||||
\(404\) | −1.30906e19 | −0.370765 | ||||||||
\(405\) | −9.32500e18 | −0.259260 | ||||||||
\(406\) | 4.19712e19 | 1.14553 | ||||||||
\(407\) | −2.30467e19 | −0.617518 | ||||||||
\(408\) | 3.55909e19 | 0.936242 | ||||||||
\(409\) | 1.85362e19 | 0.478736 | 0.239368 | − | 0.970929i | \(-0.423060\pi\) | ||||
0.239368 | + | 0.970929i | \(0.423060\pi\) | |||||||
\(410\) | −2.29459e19 | −0.581870 | ||||||||
\(411\) | −4.58087e19 | −1.14060 | ||||||||
\(412\) | 8.16524e18 | 0.199637 | ||||||||
\(413\) | −8.58346e19 | −2.06080 | ||||||||
\(414\) | 4.00551e18 | 0.0944398 | ||||||||
\(415\) | 4.62969e18 | 0.107199 | ||||||||
\(416\) | 3.64891e19 | 0.829781 | ||||||||
\(417\) | −2.99621e19 | −0.669194 | ||||||||
\(418\) | −4.02597e19 | −0.883177 | ||||||||
\(419\) | −9.81436e18 | −0.211474 | −0.105737 | − | 0.994394i | \(-0.533720\pi\) | ||||
−0.105737 | + | 0.994394i | \(0.533720\pi\) | |||||||
\(420\) | 1.03282e19 | 0.218602 | ||||||||
\(421\) | 1.42601e19 | 0.296487 | 0.148244 | − | 0.988951i | \(-0.452638\pi\) | ||||
0.148244 | + | 0.988951i | \(0.452638\pi\) | |||||||
\(422\) | −3.15491e19 | −0.644383 | ||||||||
\(423\) | 3.05147e19 | 0.612289 | ||||||||
\(424\) | −4.63639e19 | −0.913978 | ||||||||
\(425\) | −2.89883e18 | −0.0561443 | ||||||||
\(426\) | −7.71377e18 | −0.146789 | ||||||||
\(427\) | 2.04696e19 | 0.382738 | ||||||||
\(428\) | 2.42407e19 | 0.445366 | ||||||||
\(429\) | −9.54057e19 | −1.72244 | ||||||||
\(430\) | 7.17676e18 | 0.127325 | ||||||||
\(431\) | 5.45748e19 | 0.951508 | 0.475754 | − | 0.879578i | \(-0.342175\pi\) | ||||
0.475754 | + | 0.879578i | \(0.342175\pi\) | |||||||
\(432\) | 4.35922e19 | 0.746931 | ||||||||
\(433\) | 1.11979e20 | 1.88572 | 0.942861 | − | 0.333188i | \(-0.108124\pi\) | ||||
0.942861 | + | 0.333188i | \(0.108124\pi\) | |||||||
\(434\) | −3.63091e18 | −0.0600956 | ||||||||
\(435\) | 4.29421e19 | 0.698576 | ||||||||
\(436\) | 1.05049e19 | 0.167975 | ||||||||
\(437\) | 1.03907e19 | 0.163317 | ||||||||
\(438\) | 2.17052e19 | 0.335358 | ||||||||
\(439\) | −7.46694e19 | −1.13412 | −0.567060 | − | 0.823676i | \(-0.691919\pi\) | ||||
−0.567060 | + | 0.823676i | \(0.691919\pi\) | |||||||
\(440\) | 9.65199e19 | 1.44119 | ||||||||
\(441\) | −2.39242e19 | −0.351195 | ||||||||
\(442\) | 1.30006e20 | 1.87628 | ||||||||
\(443\) | −4.03892e19 | −0.573109 | −0.286555 | − | 0.958064i | \(-0.592510\pi\) | ||||
−0.286555 | + | 0.958064i | \(0.592510\pi\) | |||||||
\(444\) | 5.54426e18 | 0.0773519 | ||||||||
\(445\) | 6.55837e19 | 0.899696 | ||||||||
\(446\) | −2.30566e19 | −0.311017 | ||||||||
\(447\) | 4.55785e19 | 0.604580 | ||||||||
\(448\) | −1.11488e20 | −1.45427 | ||||||||
\(449\) | 1.33981e20 | 1.71868 | 0.859342 | − | 0.511401i | \(-0.170873\pi\) | ||||
0.859342 | + | 0.511401i | \(0.170873\pi\) | |||||||
\(450\) | −1.57130e18 | −0.0198228 | ||||||||
\(451\) | 7.51915e19 | 0.932921 | ||||||||
\(452\) | 2.06414e19 | 0.251885 | ||||||||
\(453\) | −7.04249e19 | −0.845258 | ||||||||
\(454\) | 3.83889e19 | 0.453196 | ||||||||
\(455\) | 1.94941e20 | 2.26369 | ||||||||
\(456\) | 5.00450e19 | 0.571642 | ||||||||
\(457\) | 1.29635e20 | 1.45664 | 0.728320 | − | 0.685237i | \(-0.240301\pi\) | ||||
0.728320 | + | 0.685237i | \(0.240301\pi\) | |||||||
\(458\) | −2.07341e19 | −0.229189 | ||||||||
\(459\) | −1.18849e20 | −1.29241 | ||||||||
\(460\) | −4.82097e18 | −0.0515764 | ||||||||
\(461\) | −4.44166e19 | −0.467507 | −0.233753 | − | 0.972296i | \(-0.575101\pi\) | ||||
−0.233753 | + | 0.972296i | \(0.575101\pi\) | |||||||
\(462\) | 1.07192e20 | 1.11006 | ||||||||
\(463\) | −1.02547e20 | −1.04488 | −0.522438 | − | 0.852677i | \(-0.674978\pi\) | ||||
−0.522438 | + | 0.852677i | \(0.674978\pi\) | |||||||
\(464\) | −7.03316e19 | −0.705124 | ||||||||
\(465\) | −3.71490e18 | −0.0366480 | ||||||||
\(466\) | −3.29880e18 | −0.0320230 | ||||||||
\(467\) | 1.33602e20 | 1.27625 | 0.638124 | − | 0.769933i | \(-0.279711\pi\) | ||||
0.638124 | + | 0.769933i | \(0.279711\pi\) | |||||||
\(468\) | −2.22497e19 | −0.209161 | ||||||||
\(469\) | −1.83302e20 | −1.69578 | ||||||||
\(470\) | 1.16322e20 | 1.05908 | ||||||||
\(471\) | −1.10332e20 | −0.988653 | ||||||||
\(472\) | 1.92970e20 | 1.70187 | ||||||||
\(473\) | −2.35176e19 | −0.204143 | ||||||||
\(474\) | 5.08635e19 | 0.434579 | ||||||||
\(475\) | −4.07609e18 | −0.0342801 | ||||||||
\(476\) | 4.61188e19 | 0.381791 | ||||||||
\(477\) | 5.10707e19 | 0.416183 | ||||||||
\(478\) | −1.95174e19 | −0.156571 | ||||||||
\(479\) | −2.06274e20 | −1.62903 | −0.814515 | − | 0.580143i | \(-0.802997\pi\) | ||||
−0.814515 | + | 0.580143i | \(0.802997\pi\) | |||||||
\(480\) | −4.19453e19 | −0.326117 | ||||||||
\(481\) | 1.04646e20 | 0.801004 | ||||||||
\(482\) | −1.16291e20 | −0.876383 | ||||||||
\(483\) | −2.76654e19 | −0.205273 | ||||||||
\(484\) | −2.83634e19 | −0.207214 | ||||||||
\(485\) | 1.67061e20 | 1.20174 | ||||||||
\(486\) | −1.07593e20 | −0.762097 | ||||||||
\(487\) | −3.42834e19 | −0.239120 | −0.119560 | − | 0.992827i | \(-0.538148\pi\) | ||||
−0.119560 | + | 0.992827i | \(0.538148\pi\) | |||||||
\(488\) | −4.60191e19 | −0.316075 | ||||||||
\(489\) | −1.36263e20 | −0.921637 | ||||||||
\(490\) | −9.11990e19 | −0.607463 | ||||||||
\(491\) | −1.54863e20 | −1.01587 | −0.507935 | − | 0.861396i | \(-0.669591\pi\) | ||||
−0.507935 | + | 0.861396i | \(0.669591\pi\) | |||||||
\(492\) | −1.80886e19 | −0.116860 | ||||||||
\(493\) | 1.91750e20 | 1.22007 | ||||||||
\(494\) | 1.82804e20 | 1.14560 | ||||||||
\(495\) | −1.06319e20 | −0.656251 | ||||||||
\(496\) | 6.08436e18 | 0.0369915 | ||||||||
\(497\) | −5.16487e19 | −0.309305 | ||||||||
\(498\) | −1.15592e19 | −0.0681878 | ||||||||
\(499\) | 1.65842e20 | 0.963699 | 0.481850 | − | 0.876254i | \(-0.339965\pi\) | ||||
0.481850 | + | 0.876254i | \(0.339965\pi\) | |||||||
\(500\) | 4.28325e19 | 0.245187 | ||||||||
\(501\) | −9.97616e18 | −0.0562575 | ||||||||
\(502\) | 2.50898e20 | 1.39386 | ||||||||
\(503\) | 2.78182e20 | 1.52254 | 0.761272 | − | 0.648433i | \(-0.224575\pi\) | ||||
0.761272 | + | 0.648433i | \(0.224575\pi\) | |||||||
\(504\) | 1.29172e20 | 0.696529 | ||||||||
\(505\) | 2.84026e20 | 1.50894 | ||||||||
\(506\) | −5.00350e19 | −0.261906 | ||||||||
\(507\) | 2.95038e20 | 1.52166 | ||||||||
\(508\) | −4.41510e18 | −0.0224369 | ||||||||
\(509\) | −1.42767e20 | −0.714900 | −0.357450 | − | 0.933932i | \(-0.616354\pi\) | ||||
−0.357450 | + | 0.933932i | \(0.616354\pi\) | |||||||
\(510\) | −1.49446e20 | −0.737408 | ||||||||
\(511\) | 1.45331e20 | 0.706644 | ||||||||
\(512\) | 2.27175e20 | 1.08852 | ||||||||
\(513\) | −1.67115e20 | −0.789107 | ||||||||
\(514\) | −1.68098e20 | −0.782239 | ||||||||
\(515\) | −1.77161e20 | −0.812483 | ||||||||
\(516\) | 5.65754e18 | 0.0255714 | ||||||||
\(517\) | −3.81176e20 | −1.69803 | ||||||||
\(518\) | −1.17574e20 | −0.516224 | ||||||||
\(519\) | −1.05619e20 | −0.457075 | ||||||||
\(520\) | −4.38260e20 | −1.86942 | ||||||||
\(521\) | −1.19078e20 | −0.500666 | −0.250333 | − | 0.968160i | \(-0.580540\pi\) | ||||
−0.250333 | + | 0.968160i | \(0.580540\pi\) | |||||||
\(522\) | 1.03937e20 | 0.430768 | ||||||||
\(523\) | 1.27835e20 | 0.522261 | 0.261130 | − | 0.965304i | \(-0.415905\pi\) | ||||
0.261130 | + | 0.965304i | \(0.415905\pi\) | |||||||
\(524\) | 1.18392e20 | 0.476800 | ||||||||
\(525\) | 1.08527e19 | 0.0430866 | ||||||||
\(526\) | −1.24159e20 | −0.485944 | ||||||||
\(527\) | −1.65883e19 | −0.0640061 | ||||||||
\(528\) | −1.79623e20 | −0.683294 | ||||||||
\(529\) | −2.53722e20 | −0.951568 | ||||||||
\(530\) | 1.94681e20 | 0.719871 | ||||||||
\(531\) | −2.12561e20 | −0.774951 | ||||||||
\(532\) | 6.48483e19 | 0.233110 | ||||||||
\(533\) | −3.41416e20 | −1.21012 | ||||||||
\(534\) | −1.63746e20 | −0.572283 | ||||||||
\(535\) | −5.25951e20 | −1.81256 | ||||||||
\(536\) | 4.12092e20 | 1.40042 | ||||||||
\(537\) | 2.64768e20 | 0.887276 | ||||||||
\(538\) | −1.03869e19 | −0.0343255 | ||||||||
\(539\) | 2.98851e20 | 0.973954 | ||||||||
\(540\) | 7.75368e19 | 0.249204 | ||||||||
\(541\) | −2.48542e20 | −0.787809 | −0.393905 | − | 0.919151i | \(-0.628876\pi\) | ||||
−0.393905 | + | 0.919151i | \(0.628876\pi\) | |||||||
\(542\) | 3.00470e20 | 0.939305 | ||||||||
\(543\) | −9.26464e19 | −0.285647 | ||||||||
\(544\) | −1.87300e20 | −0.569568 | ||||||||
\(545\) | −2.27925e20 | −0.683625 | ||||||||
\(546\) | −4.86719e20 | −1.43990 | ||||||||
\(547\) | 2.56672e20 | 0.748986 | 0.374493 | − | 0.927230i | \(-0.377817\pi\) | ||||
0.374493 | + | 0.927230i | \(0.377817\pi\) | |||||||
\(548\) | 1.33449e20 | 0.384114 | ||||||||
\(549\) | 5.06910e19 | 0.143926 | ||||||||
\(550\) | 1.96279e19 | 0.0549737 | ||||||||
\(551\) | 2.69623e20 | 0.744939 | ||||||||
\(552\) | 6.21963e19 | 0.169520 | ||||||||
\(553\) | 3.40564e20 | 0.915716 | ||||||||
\(554\) | 1.53536e20 | 0.407274 | ||||||||
\(555\) | −1.20294e20 | −0.314808 | ||||||||
\(556\) | 8.72849e19 | 0.225361 | ||||||||
\(557\) | 4.27032e19 | 0.108779 | 0.0543896 | − | 0.998520i | \(-0.482679\pi\) | ||||
0.0543896 | + | 0.998520i | \(0.482679\pi\) | |||||||
\(558\) | −8.99159e18 | −0.0225985 | ||||||||
\(559\) | 1.06784e20 | 0.264800 | ||||||||
\(560\) | 3.67021e20 | 0.898009 | ||||||||
\(561\) | 4.89720e20 | 1.18230 | ||||||||
\(562\) | −4.94795e20 | −1.17870 | ||||||||
\(563\) | 7.88211e20 | 1.85280 | 0.926402 | − | 0.376536i | \(-0.122885\pi\) | ||||
0.926402 | + | 0.376536i | \(0.122885\pi\) | |||||||
\(564\) | 9.16982e19 | 0.212700 | ||||||||
\(565\) | −4.47857e20 | −1.02512 | ||||||||
\(566\) | 3.93730e20 | 0.889356 | ||||||||
\(567\) | 1.55889e20 | 0.347491 | ||||||||
\(568\) | 1.16115e20 | 0.255432 | ||||||||
\(569\) | −4.76216e20 | −1.03386 | −0.516931 | − | 0.856027i | \(-0.672925\pi\) | ||||
−0.516931 | + | 0.856027i | \(0.672925\pi\) | |||||||
\(570\) | −2.10138e20 | −0.450240 | ||||||||
\(571\) | −6.11755e20 | −1.29362 | −0.646810 | − | 0.762651i | \(-0.723897\pi\) | ||||
−0.646810 | + | 0.762651i | \(0.723897\pi\) | |||||||
\(572\) | 2.77933e20 | 0.580057 | ||||||||
\(573\) | 1.35735e20 | 0.279598 | ||||||||
\(574\) | 3.83595e20 | 0.779890 | ||||||||
\(575\) | −5.06580e18 | −0.0101657 | ||||||||
\(576\) | −2.76089e20 | −0.546866 | ||||||||
\(577\) | 6.41621e20 | 1.25447 | 0.627234 | − | 0.778831i | \(-0.284187\pi\) | ||||
0.627234 | + | 0.778831i | \(0.284187\pi\) | |||||||
\(578\) | −2.15600e20 | −0.416093 | ||||||||
\(579\) | −4.04948e20 | −0.771454 | ||||||||
\(580\) | −1.25098e20 | −0.235255 | ||||||||
\(581\) | −7.73962e19 | −0.143681 | ||||||||
\(582\) | −4.17109e20 | −0.764411 | ||||||||
\(583\) | −6.37952e20 | −1.15418 | ||||||||
\(584\) | −3.26728e20 | −0.583565 | ||||||||
\(585\) | 4.82752e20 | 0.851246 | ||||||||
\(586\) | 7.03004e20 | 1.22384 | ||||||||
\(587\) | −2.11915e19 | −0.0364229 | −0.0182115 | − | 0.999834i | \(-0.505797\pi\) | ||||
−0.0182115 | + | 0.999834i | \(0.505797\pi\) | |||||||
\(588\) | −7.18935e19 | −0.122000 | ||||||||
\(589\) | −2.33250e19 | −0.0390802 | ||||||||
\(590\) | −8.10280e20 | −1.34043 | ||||||||
\(591\) | −3.91128e20 | −0.638870 | ||||||||
\(592\) | 1.97020e20 | 0.317759 | ||||||||
\(593\) | 2.18834e20 | 0.348502 | 0.174251 | − | 0.984701i | \(-0.444250\pi\) | ||||
0.174251 | + | 0.984701i | \(0.444250\pi\) | |||||||
\(594\) | 8.04724e20 | 1.26546 | ||||||||
\(595\) | −1.00064e21 | −1.55382 | ||||||||
\(596\) | −1.32778e20 | −0.203601 | ||||||||
\(597\) | −6.47171e20 | −0.979968 | ||||||||
\(598\) | 2.27190e20 | 0.339727 | ||||||||
\(599\) | −8.31650e20 | −1.22812 | −0.614058 | − | 0.789261i | \(-0.710464\pi\) | ||||
−0.614058 | + | 0.789261i | \(0.710464\pi\) | |||||||
\(600\) | −2.43986e19 | −0.0355821 | ||||||||
\(601\) | 4.23472e20 | 0.609910 | 0.304955 | − | 0.952367i | \(-0.401359\pi\) | ||||
0.304955 | + | 0.952367i | \(0.401359\pi\) | |||||||
\(602\) | −1.19976e20 | −0.170656 | ||||||||
\(603\) | −4.53928e20 | −0.637686 | ||||||||
\(604\) | 2.05160e20 | 0.284653 | ||||||||
\(605\) | 6.15401e20 | 0.843321 | ||||||||
\(606\) | −7.09141e20 | −0.959816 | ||||||||
\(607\) | 9.89054e20 | 1.32222 | 0.661111 | − | 0.750288i | \(-0.270085\pi\) | ||||
0.661111 | + | 0.750288i | \(0.270085\pi\) | |||||||
\(608\) | −2.63365e20 | −0.347761 | ||||||||
\(609\) | −7.17878e20 | −0.936313 | ||||||||
\(610\) | 1.93234e20 | 0.248948 | ||||||||
\(611\) | 1.73077e21 | 2.20258 | ||||||||
\(612\) | 1.14208e20 | 0.143570 | ||||||||
\(613\) | −1.28885e21 | −1.60048 | −0.800238 | − | 0.599683i | \(-0.795294\pi\) | ||||
−0.800238 | + | 0.599683i | \(0.795294\pi\) | |||||||
\(614\) | 4.32767e20 | 0.530874 | ||||||||
\(615\) | 3.92468e20 | 0.475598 | ||||||||
\(616\) | −1.61356e21 | −1.93165 | ||||||||
\(617\) | 6.20383e20 | 0.733705 | 0.366852 | − | 0.930279i | \(-0.380435\pi\) | ||||
0.366852 | + | 0.930279i | \(0.380435\pi\) | |||||||
\(618\) | 4.42327e20 | 0.516809 | ||||||||
\(619\) | −2.97699e20 | −0.343635 | −0.171818 | − | 0.985129i | \(-0.554964\pi\) | ||||
−0.171818 | + | 0.985129i | \(0.554964\pi\) | |||||||
\(620\) | 1.08222e19 | 0.0123417 | ||||||||
\(621\) | −2.07692e20 | −0.234009 | ||||||||
\(622\) | 1.01841e21 | 1.13369 | ||||||||
\(623\) | −1.09639e21 | −1.20588 | ||||||||
\(624\) | 8.15599e20 | 0.886324 | ||||||||
\(625\) | −8.86315e20 | −0.951673 | ||||||||
\(626\) | 1.50390e21 | 1.59555 | ||||||||
\(627\) | 6.88603e20 | 0.721876 | ||||||||
\(628\) | 3.21416e20 | 0.332943 | ||||||||
\(629\) | −5.37151e20 | −0.549815 | ||||||||
\(630\) | −5.42391e20 | −0.548604 | ||||||||
\(631\) | 1.23950e19 | 0.0123888 | 0.00619438 | − | 0.999981i | \(-0.498028\pi\) | ||||
0.00619438 | + | 0.999981i | \(0.498028\pi\) | |||||||
\(632\) | −7.65645e20 | −0.756222 | ||||||||
\(633\) | 5.39618e20 | 0.526694 | ||||||||
\(634\) | 6.14198e20 | 0.592432 | ||||||||
\(635\) | 9.57945e19 | 0.0913140 | ||||||||
\(636\) | 1.53470e20 | 0.144576 | ||||||||
\(637\) | −1.35697e21 | −1.26335 | ||||||||
\(638\) | −1.29834e21 | −1.19463 | ||||||||
\(639\) | −1.27903e20 | −0.116312 | ||||||||
\(640\) | −5.43245e20 | −0.488254 | ||||||||
\(641\) | −1.60029e21 | −1.42155 | −0.710777 | − | 0.703418i | \(-0.751656\pi\) | ||||
−0.710777 | + | 0.703418i | \(0.751656\pi\) | |||||||
\(642\) | 1.31317e21 | 1.15294 | ||||||||
\(643\) | −9.07785e20 | −0.787773 | −0.393886 | − | 0.919159i | \(-0.628870\pi\) | ||||
−0.393886 | + | 0.919159i | \(0.628870\pi\) | |||||||
\(644\) | 8.05940e19 | 0.0691287 | ||||||||
\(645\) | −1.22752e20 | −0.104071 | ||||||||
\(646\) | −9.38337e20 | −0.786348 | ||||||||
\(647\) | 1.52292e21 | 1.26152 | 0.630762 | − | 0.775976i | \(-0.282742\pi\) | ||||
0.630762 | + | 0.775976i | \(0.282742\pi\) | |||||||
\(648\) | −3.50465e20 | −0.286967 | ||||||||
\(649\) | 2.65521e21 | 2.14914 | ||||||||
\(650\) | −8.91230e19 | −0.0713082 | ||||||||
\(651\) | 6.21034e19 | 0.0491199 | ||||||||
\(652\) | 3.96956e20 | 0.310374 | ||||||||
\(653\) | −2.74506e20 | −0.212179 | −0.106089 | − | 0.994357i | \(-0.533833\pi\) | ||||
−0.106089 | + | 0.994357i | \(0.533833\pi\) | |||||||
\(654\) | 5.69071e20 | 0.434844 | ||||||||
\(655\) | −2.56874e21 | −1.94049 | ||||||||
\(656\) | −6.42793e20 | −0.480056 | ||||||||
\(657\) | 3.59897e20 | 0.265728 | ||||||||
\(658\) | −1.94459e21 | −1.41950 | ||||||||
\(659\) | −8.40586e19 | −0.0606654 | −0.0303327 | − | 0.999540i | \(-0.509657\pi\) | ||||
−0.0303327 | + | 0.999540i | \(0.509657\pi\) | |||||||
\(660\) | −3.19493e20 | −0.227972 | ||||||||
\(661\) | 1.33139e21 | 0.939281 | 0.469641 | − | 0.882858i | \(-0.344384\pi\) | ||||
0.469641 | + | 0.882858i | \(0.344384\pi\) | |||||||
\(662\) | −9.01930e20 | −0.629126 | ||||||||
\(663\) | −2.22363e21 | −1.53360 | ||||||||
\(664\) | 1.74000e20 | 0.118655 | ||||||||
\(665\) | −1.40701e21 | −0.948715 | ||||||||
\(666\) | −2.91160e20 | −0.194122 | ||||||||
\(667\) | 3.35090e20 | 0.220911 | ||||||||
\(668\) | 2.90623e19 | 0.0189455 | ||||||||
\(669\) | 3.94362e20 | 0.254214 | ||||||||
\(670\) | −1.73037e21 | −1.10301 | ||||||||
\(671\) | −6.33209e20 | −0.399143 | ||||||||
\(672\) | 7.01215e20 | 0.437101 | ||||||||
\(673\) | 2.05646e21 | 1.26767 | 0.633837 | − | 0.773466i | \(-0.281479\pi\) | ||||
0.633837 | + | 0.773466i | \(0.281479\pi\) | |||||||
\(674\) | 1.08327e20 | 0.0660370 | ||||||||
\(675\) | 8.14743e19 | 0.0491182 | ||||||||
\(676\) | −8.59498e20 | −0.512442 | ||||||||
\(677\) | 9.82072e20 | 0.579067 | 0.289533 | − | 0.957168i | \(-0.406500\pi\) | ||||
0.289533 | + | 0.957168i | \(0.406500\pi\) | |||||||
\(678\) | 1.11819e21 | 0.652066 | ||||||||
\(679\) | −2.79282e21 | −1.61072 | ||||||||
\(680\) | 2.24960e21 | 1.28318 | ||||||||
\(681\) | −6.56605e20 | −0.370426 | ||||||||
\(682\) | 1.12319e20 | 0.0626715 | ||||||||
\(683\) | 1.17147e20 | 0.0646509 | 0.0323255 | − | 0.999477i | \(-0.489709\pi\) | ||||
0.0323255 | + | 0.999477i | \(0.489709\pi\) | |||||||
\(684\) | 1.60590e20 | 0.0876594 | ||||||||
\(685\) | −2.89544e21 | −1.56327 | ||||||||
\(686\) | −6.12293e20 | −0.326985 | ||||||||
\(687\) | 3.54637e20 | 0.187331 | ||||||||
\(688\) | 2.01046e20 | 0.105046 | ||||||||
\(689\) | 2.89670e21 | 1.49713 | ||||||||
\(690\) | −2.61161e20 | −0.133518 | ||||||||
\(691\) | 7.80177e20 | 0.394555 | 0.197278 | − | 0.980348i | \(-0.436790\pi\) | ||||
0.197278 | + | 0.980348i | \(0.436790\pi\) | |||||||
\(692\) | 3.07687e20 | 0.153926 | ||||||||
\(693\) | 1.77737e21 | 0.879585 | ||||||||
\(694\) | 3.19431e21 | 1.56380 | ||||||||
\(695\) | −1.89382e21 | −0.917176 | ||||||||
\(696\) | 1.61391e21 | 0.773232 | ||||||||
\(697\) | 1.75250e21 | 0.830637 | ||||||||
\(698\) | 1.27408e21 | 0.597422 | ||||||||
\(699\) | 5.64229e19 | 0.0261744 | ||||||||
\(700\) | −3.16157e19 | −0.0145100 | ||||||||
\(701\) | −1.50122e21 | −0.681648 | −0.340824 | − | 0.940127i | \(-0.610706\pi\) | ||||
−0.340824 | + | 0.940127i | \(0.610706\pi\) | |||||||
\(702\) | −3.65394e21 | −1.64147 | ||||||||
\(703\) | −7.55297e20 | −0.335701 | ||||||||
\(704\) | 3.44878e21 | 1.51660 | ||||||||
\(705\) | −1.98958e21 | −0.865649 | ||||||||
\(706\) | 3.73891e21 | 1.60957 | ||||||||
\(707\) | −4.74817e21 | −2.02246 | ||||||||
\(708\) | −6.38755e20 | −0.269206 | ||||||||
\(709\) | −3.48294e21 | −1.45244 | −0.726221 | − | 0.687461i | \(-0.758725\pi\) | ||||
−0.726221 | + | 0.687461i | \(0.758725\pi\) | |||||||
\(710\) | −4.87565e20 | −0.201185 | ||||||||
\(711\) | 8.43373e20 | 0.344348 | ||||||||
\(712\) | 2.46486e21 | 0.995845 | ||||||||
\(713\) | −2.89885e19 | −0.0115892 | ||||||||
\(714\) | 2.49834e21 | 0.988360 | ||||||||
\(715\) | −6.03032e21 | −2.36072 | ||||||||
\(716\) | −7.71316e20 | −0.298803 | ||||||||
\(717\) | 3.33826e20 | 0.127976 | ||||||||
\(718\) | 6.67730e20 | 0.253319 | ||||||||
\(719\) | 3.72828e21 | 1.39972 | 0.699861 | − | 0.714279i | \(-0.253245\pi\) | ||||
0.699861 | + | 0.714279i | \(0.253245\pi\) | |||||||
\(720\) | 9.08890e20 | 0.337690 | ||||||||
\(721\) | 2.96167e21 | 1.08898 | ||||||||
\(722\) | 1.07636e21 | 0.391676 | ||||||||
\(723\) | 1.98905e21 | 0.716323 | ||||||||
\(724\) | 2.69895e20 | 0.0961957 | ||||||||
\(725\) | −1.31451e20 | −0.0463689 | ||||||||
\(726\) | −1.53650e21 | −0.536424 | ||||||||
\(727\) | 3.85885e21 | 1.33337 | 0.666684 | − | 0.745341i | \(-0.267713\pi\) | ||||
0.666684 | + | 0.745341i | \(0.267713\pi\) | |||||||
\(728\) | 7.32655e21 | 2.50561 | ||||||||
\(729\) | 2.62453e21 | 0.888373 | ||||||||
\(730\) | 1.37192e21 | 0.459631 | ||||||||
\(731\) | −5.48127e20 | −0.181761 | ||||||||
\(732\) | 1.52329e20 | 0.0499977 | ||||||||
\(733\) | −9.48275e20 | −0.308074 | −0.154037 | − | 0.988065i | \(-0.549227\pi\) | ||||
−0.154037 | + | 0.988065i | \(0.549227\pi\) | |||||||
\(734\) | −2.09750e21 | −0.674498 | ||||||||
\(735\) | 1.55987e21 | 0.496517 | ||||||||
\(736\) | −3.27312e20 | −0.103128 | ||||||||
\(737\) | 5.67026e21 | 1.76847 | ||||||||
\(738\) | 9.49933e20 | 0.293272 | ||||||||
\(739\) | −2.01265e21 | −0.615086 | −0.307543 | − | 0.951534i | \(-0.599507\pi\) | ||||
−0.307543 | + | 0.951534i | \(0.599507\pi\) | |||||||
\(740\) | 3.50436e20 | 0.106016 | ||||||||
\(741\) | −3.12668e21 | −0.936370 | ||||||||
\(742\) | −3.25456e21 | −0.964856 | ||||||||
\(743\) | 2.15678e21 | 0.632979 | 0.316490 | − | 0.948596i | \(-0.397496\pi\) | ||||
0.316490 | + | 0.948596i | \(0.397496\pi\) | |||||||
\(744\) | −1.39619e20 | −0.0405645 | ||||||||
\(745\) | 2.88089e21 | 0.828617 | ||||||||
\(746\) | 2.61205e21 | 0.743774 | ||||||||
\(747\) | −1.91664e20 | −0.0540301 | ||||||||
\(748\) | −1.42664e21 | −0.398155 | ||||||||
\(749\) | 8.79251e21 | 2.42940 | ||||||||
\(750\) | 2.32032e21 | 0.634728 | ||||||||
\(751\) | 3.35901e21 | 0.909728 | 0.454864 | − | 0.890561i | \(-0.349688\pi\) | ||||
0.454864 | + | 0.890561i | \(0.349688\pi\) | |||||||
\(752\) | 3.25858e21 | 0.873764 | ||||||||
\(753\) | −4.29138e21 | −1.13929 | ||||||||
\(754\) | 5.89526e21 | 1.54959 | ||||||||
\(755\) | −4.45135e21 | −1.15848 | ||||||||
\(756\) | −1.29621e21 | −0.334012 | ||||||||
\(757\) | 4.34013e20 | 0.110735 | 0.0553674 | − | 0.998466i | \(-0.482367\pi\) | ||||
0.0553674 | + | 0.998466i | \(0.482367\pi\) | |||||||
\(758\) | −1.24728e20 | −0.0315098 | ||||||||
\(759\) | 8.55801e20 | 0.214072 | ||||||||
\(760\) | 3.16320e21 | 0.783474 | ||||||||
\(761\) | −3.68509e21 | −0.903780 | −0.451890 | − | 0.892074i | \(-0.649250\pi\) | ||||
−0.451890 | + | 0.892074i | \(0.649250\pi\) | |||||||
\(762\) | −2.39175e20 | −0.0580835 | ||||||||
\(763\) | 3.81030e21 | 0.916275 | ||||||||
\(764\) | −3.95421e20 | −0.0941585 | ||||||||
\(765\) | −2.47798e21 | −0.584301 | ||||||||
\(766\) | −5.24868e21 | −1.22556 | ||||||||
\(767\) | −1.20563e22 | −2.78772 | ||||||||
\(768\) | −2.10102e21 | −0.481085 | ||||||||
\(769\) | 7.98353e20 | 0.181029 | 0.0905144 | − | 0.995895i | \(-0.471149\pi\) | ||||
0.0905144 | + | 0.995895i | \(0.471149\pi\) | |||||||
\(770\) | 6.77531e21 | 1.52142 | ||||||||
\(771\) | 2.87516e21 | 0.639373 | ||||||||
\(772\) | 1.17968e21 | 0.259798 | ||||||||
\(773\) | −8.75684e21 | −1.90986 | −0.954930 | − | 0.296832i | \(-0.904070\pi\) | ||||
−0.954930 | + | 0.296832i | \(0.904070\pi\) | |||||||
\(774\) | −2.97110e20 | −0.0641741 | ||||||||
\(775\) | 1.13717e19 | 0.00243256 | ||||||||
\(776\) | 6.27872e21 | 1.33017 | ||||||||
\(777\) | 2.01099e21 | 0.421942 | ||||||||
\(778\) | −4.97968e21 | −1.03480 | ||||||||
\(779\) | 2.46421e21 | 0.507163 | ||||||||
\(780\) | 1.45069e21 | 0.295710 | ||||||||
\(781\) | 1.59770e21 | 0.322562 | ||||||||
\(782\) | −1.16617e21 | −0.233191 | ||||||||
\(783\) | −5.38932e21 | −1.06739 | ||||||||
\(784\) | −2.55480e21 | −0.501171 | ||||||||
\(785\) | −6.97375e21 | −1.35502 | ||||||||
\(786\) | 6.41350e21 | 1.23431 | ||||||||
\(787\) | 5.91376e20 | 0.112734 | 0.0563668 | − | 0.998410i | \(-0.482048\pi\) | ||||
0.0563668 | + | 0.998410i | \(0.482048\pi\) | |||||||
\(788\) | 1.13942e21 | 0.215149 | ||||||||
\(789\) | 2.12363e21 | 0.397192 | ||||||||
\(790\) | 3.21493e21 | 0.595619 | ||||||||
\(791\) | 7.48699e21 | 1.37399 | ||||||||
\(792\) | −3.99581e21 | −0.726384 | ||||||||
\(793\) | 2.87516e21 | 0.517742 | ||||||||
\(794\) | −1.99174e21 | −0.355286 | ||||||||
\(795\) | −3.32984e21 | −0.588396 | ||||||||
\(796\) | 1.88532e21 | 0.330018 | ||||||||
\(797\) | −8.87507e21 | −1.53898 | −0.769492 | − | 0.638656i | \(-0.779491\pi\) | ||||
−0.769492 | + | 0.638656i | \(0.779491\pi\) | |||||||
\(798\) | 3.51296e21 | 0.603464 | ||||||||
\(799\) | −8.88411e21 | −1.51187 | ||||||||
\(800\) | 1.28399e20 | 0.0216465 | ||||||||
\(801\) | −2.71509e21 | −0.453461 | ||||||||
\(802\) | −7.00838e21 | −1.15961 | ||||||||
\(803\) | −4.49567e21 | −0.736933 | ||||||||
\(804\) | −1.36408e21 | −0.221523 | ||||||||
\(805\) | −1.74865e21 | −0.281341 | ||||||||
\(806\) | −5.09997e20 | −0.0812933 | ||||||||
\(807\) | 1.77657e20 | 0.0280564 | ||||||||
\(808\) | 1.06747e22 | 1.67020 | ||||||||
\(809\) | −3.90755e21 | −0.605746 | −0.302873 | − | 0.953031i | \(-0.597946\pi\) | ||||
−0.302873 | + | 0.953031i | \(0.597946\pi\) | |||||||
\(810\) | 1.47160e21 | 0.226022 | ||||||||
\(811\) | 5.69280e21 | 0.866303 | 0.433152 | − | 0.901321i | \(-0.357401\pi\) | ||||
0.433152 | + | 0.901321i | \(0.357401\pi\) | |||||||
\(812\) | 2.09130e21 | 0.315317 | ||||||||
\(813\) | −5.13926e21 | −0.767753 | ||||||||
\(814\) | 3.63704e21 | 0.538351 | ||||||||
\(815\) | −8.61276e21 | −1.26316 | ||||||||
\(816\) | −4.18649e21 | −0.608379 | ||||||||
\(817\) | −7.70730e20 | −0.110978 | ||||||||
\(818\) | −2.92524e21 | −0.417360 | ||||||||
\(819\) | −8.07034e21 | −1.14094 | ||||||||
\(820\) | −1.14333e21 | −0.160164 | ||||||||
\(821\) | 1.08209e22 | 1.50207 | 0.751033 | − | 0.660265i | \(-0.229556\pi\) | ||||
0.751033 | + | 0.660265i | \(0.229556\pi\) | |||||||
\(822\) | 7.22917e21 | 0.994374 | ||||||||
\(823\) | −8.12058e21 | −1.10685 | −0.553424 | − | 0.832899i | \(-0.686679\pi\) | ||||
−0.553424 | + | 0.832899i | \(0.686679\pi\) | |||||||
\(824\) | −6.65832e21 | −0.899312 | ||||||||
\(825\) | −3.35717e20 | −0.0449334 | ||||||||
\(826\) | 1.35457e22 | 1.79660 | ||||||||
\(827\) | 1.23977e22 | 1.62948 | 0.814741 | − | 0.579826i | \(-0.196879\pi\) | ||||
0.814741 | + | 0.579826i | \(0.196879\pi\) | |||||||
\(828\) | 1.99583e20 | 0.0259954 | ||||||||
\(829\) | 1.11379e21 | 0.143762 | 0.0718812 | − | 0.997413i | \(-0.477100\pi\) | ||||
0.0718812 | + | 0.997413i | \(0.477100\pi\) | |||||||
\(830\) | −7.30622e20 | −0.0934559 | ||||||||
\(831\) | −2.62609e21 | −0.332891 | ||||||||
\(832\) | −1.56596e22 | −1.96723 | ||||||||
\(833\) | 6.96535e21 | 0.867172 | ||||||||
\(834\) | 4.72839e21 | 0.583402 | ||||||||
\(835\) | −6.30564e20 | −0.0771046 | ||||||||
\(836\) | −2.00602e21 | −0.243102 | ||||||||
\(837\) | 4.66228e20 | 0.0559961 | ||||||||
\(838\) | 1.54882e21 | 0.184362 | ||||||||
\(839\) | 1.27216e22 | 1.50082 | 0.750409 | − | 0.660974i | \(-0.229857\pi\) | ||||
0.750409 | + | 0.660974i | \(0.229857\pi\) | |||||||
\(840\) | −8.42208e21 | −0.984747 | ||||||||
\(841\) | 6.59366e19 | 0.00764111 | ||||||||
\(842\) | −2.25041e21 | −0.258477 | ||||||||
\(843\) | 8.46301e21 | 0.963425 | ||||||||
\(844\) | −1.57200e21 | −0.177372 | ||||||||
\(845\) | 1.86485e22 | 2.08554 | ||||||||
\(846\) | −4.81559e21 | −0.533792 | ||||||||
\(847\) | −1.02879e22 | −1.13032 | ||||||||
\(848\) | 5.45369e21 | 0.593911 | ||||||||
\(849\) | −6.73438e21 | −0.726926 | ||||||||
\(850\) | 4.57471e20 | 0.0489465 | ||||||||
\(851\) | −9.38688e20 | −0.0995519 | ||||||||
\(852\) | −3.84354e20 | −0.0404050 | ||||||||
\(853\) | 1.15472e22 | 1.20326 | 0.601632 | − | 0.798774i | \(-0.294517\pi\) | ||||
0.601632 | + | 0.798774i | \(0.294517\pi\) | |||||||
\(854\) | −3.23036e21 | −0.333670 | ||||||||
\(855\) | −3.48433e21 | −0.356757 | ||||||||
\(856\) | −1.97670e22 | −2.00626 | ||||||||
\(857\) | 1.38975e20 | 0.0139823 | 0.00699117 | − | 0.999976i | \(-0.497775\pi\) | ||||
0.00699117 | + | 0.999976i | \(0.497775\pi\) | |||||||
\(858\) | 1.50562e22 | 1.50162 | ||||||||
\(859\) | −6.98046e21 | −0.690137 | −0.345069 | − | 0.938577i | \(-0.612144\pi\) | ||||
−0.345069 | + | 0.938577i | \(0.612144\pi\) | |||||||
\(860\) | 3.57597e20 | 0.0350474 | ||||||||
\(861\) | −6.56102e21 | −0.637453 | ||||||||
\(862\) | −8.61256e21 | −0.829522 | ||||||||
\(863\) | 9.38588e21 | 0.896177 | 0.448089 | − | 0.893989i | \(-0.352105\pi\) | ||||
0.448089 | + | 0.893989i | \(0.352105\pi\) | |||||||
\(864\) | 5.26423e21 | 0.498290 | ||||||||
\(865\) | −6.67587e21 | −0.626451 | ||||||||
\(866\) | −1.76717e22 | −1.64397 | ||||||||
\(867\) | 3.68763e21 | 0.340098 | ||||||||
\(868\) | −1.80918e20 | −0.0165418 | ||||||||
\(869\) | −1.05350e22 | −0.954965 | ||||||||
\(870\) | −6.77678e21 | −0.609016 | ||||||||
\(871\) | −2.57465e22 | −2.29394 | ||||||||
\(872\) | −8.56620e21 | −0.756684 | ||||||||
\(873\) | −6.91613e21 | −0.605698 | ||||||||
\(874\) | −1.63977e21 | −0.142380 | ||||||||
\(875\) | 1.55360e22 | 1.33746 | ||||||||
\(876\) | 1.08151e21 | 0.0923101 | ||||||||
\(877\) | 5.39503e20 | 0.0456559 | 0.0228279 | − | 0.999739i | \(-0.492733\pi\) | ||||
0.0228279 | + | 0.999739i | \(0.492733\pi\) | |||||||
\(878\) | 1.17837e22 | 0.988723 | ||||||||
\(879\) | −1.20242e22 | −1.00032 | ||||||||
\(880\) | −1.13534e22 | −0.936499 | ||||||||
\(881\) | 8.51459e21 | 0.696377 | 0.348188 | − | 0.937425i | \(-0.386797\pi\) | ||||
0.348188 | + | 0.937425i | \(0.386797\pi\) | |||||||
\(882\) | 3.77554e21 | 0.306171 | ||||||||
\(883\) | 1.42198e22 | 1.14337 | 0.571687 | − | 0.820472i | \(-0.306289\pi\) | ||||
0.571687 | + | 0.820472i | \(0.306289\pi\) | |||||||
\(884\) | 6.47783e21 | 0.516461 | ||||||||
\(885\) | 1.38591e22 | 1.09562 | ||||||||
\(886\) | 6.37391e21 | 0.499635 | ||||||||
\(887\) | 1.23600e22 | 0.960704 | 0.480352 | − | 0.877076i | \(-0.340509\pi\) | ||||
0.480352 | + | 0.877076i | \(0.340509\pi\) | |||||||
\(888\) | −4.52105e21 | −0.348451 | ||||||||
\(889\) | −1.60143e21 | −0.122390 | ||||||||
\(890\) | −1.03499e22 | −0.784352 | ||||||||
\(891\) | −4.82229e21 | −0.362385 | ||||||||
\(892\) | −1.14884e21 | −0.0856100 | ||||||||
\(893\) | −1.24921e22 | −0.923101 | ||||||||
\(894\) | −7.19284e21 | −0.527071 | ||||||||
\(895\) | 1.67352e22 | 1.21607 | ||||||||
\(896\) | 9.08162e21 | 0.654415 | ||||||||
\(897\) | −3.88587e21 | −0.277680 | ||||||||
\(898\) | −2.11439e22 | −1.49834 | ||||||||
\(899\) | −7.52212e20 | −0.0528619 | ||||||||
\(900\) | −7.82932e19 | −0.00545639 | ||||||||
\(901\) | −1.48688e22 | −1.02764 | ||||||||
\(902\) | −1.18661e22 | −0.813318 | ||||||||
\(903\) | 2.05208e21 | 0.139488 | ||||||||
\(904\) | −1.68320e22 | −1.13468 | ||||||||
\(905\) | −5.85591e21 | −0.391498 | ||||||||
\(906\) | 1.11139e22 | 0.736894 | ||||||||
\(907\) | −1.69475e22 | −1.11442 | −0.557212 | − | 0.830370i | \(-0.688129\pi\) | ||||
−0.557212 | + | 0.830370i | \(0.688129\pi\) | |||||||
\(908\) | 1.91280e21 | 0.124746 | ||||||||
\(909\) | −1.17584e22 | −0.760532 | ||||||||
\(910\) | −3.07641e22 | −1.97348 | ||||||||
\(911\) | −1.10351e22 | −0.702083 | −0.351041 | − | 0.936360i | \(-0.614172\pi\) | ||||
−0.351041 | + | 0.936360i | \(0.614172\pi\) | |||||||
\(912\) | −5.88670e21 | −0.371458 | ||||||||
\(913\) | 2.39418e21 | 0.149839 | ||||||||
\(914\) | −2.04581e22 | −1.26990 | ||||||||
\(915\) | −3.30508e21 | −0.203481 | ||||||||
\(916\) | −1.03312e21 | −0.0630863 | ||||||||
\(917\) | 4.29426e22 | 2.60087 | ||||||||
\(918\) | 1.87558e22 | 1.12672 | ||||||||
\(919\) | −2.66487e22 | −1.58785 | −0.793924 | − | 0.608016i | \(-0.791965\pi\) | ||||
−0.793924 | + | 0.608016i | \(0.791965\pi\) | |||||||
\(920\) | 3.93125e21 | 0.232339 | ||||||||
\(921\) | −7.40207e21 | −0.433916 | ||||||||
\(922\) | 7.00948e21 | 0.407571 | ||||||||
\(923\) | −7.25456e21 | −0.418407 | ||||||||
\(924\) | 5.34107e21 | 0.305555 | ||||||||
\(925\) | 3.68233e20 | 0.0208958 | ||||||||
\(926\) | 1.61831e22 | 0.910921 | ||||||||
\(927\) | 7.33427e21 | 0.409505 | ||||||||
\(928\) | −8.49330e21 | −0.470399 | ||||||||
\(929\) | −1.40482e21 | −0.0771798 | −0.0385899 | − | 0.999255i | \(-0.512287\pi\) | ||||
−0.0385899 | + | 0.999255i | \(0.512287\pi\) | |||||||
\(930\) | 5.86257e20 | 0.0319496 | ||||||||
\(931\) | 9.79409e21 | 0.529470 | ||||||||
\(932\) | −1.64370e20 | −0.00881459 | ||||||||
\(933\) | −1.74190e22 | −0.926639 | ||||||||
\(934\) | −2.10840e22 | −1.11263 | ||||||||
\(935\) | 3.09538e22 | 1.62042 | ||||||||
\(936\) | 1.81435e22 | 0.942218 | ||||||||
\(937\) | 2.14268e21 | 0.110385 | 0.0551925 | − | 0.998476i | \(-0.482423\pi\) | ||||
0.0551925 | + | 0.998476i | \(0.482423\pi\) | |||||||
\(938\) | 2.89272e22 | 1.47838 | ||||||||
\(939\) | −2.57228e22 | −1.30415 | ||||||||
\(940\) | 5.79598e21 | 0.291520 | ||||||||
\(941\) | 2.72168e22 | 1.35804 | 0.679022 | − | 0.734117i | \(-0.262404\pi\) | ||||
0.679022 | + | 0.734117i | \(0.262404\pi\) | |||||||
\(942\) | 1.74117e22 | 0.861905 | ||||||||
\(943\) | 3.06254e21 | 0.150399 | ||||||||
\(944\) | −2.26987e22 | −1.10589 | ||||||||
\(945\) | 2.81239e22 | 1.35937 | ||||||||
\(946\) | 3.71136e21 | 0.177971 | ||||||||
\(947\) | −1.55881e22 | −0.741597 | −0.370799 | − | 0.928713i | \(-0.620916\pi\) | ||||
−0.370799 | + | 0.928713i | \(0.620916\pi\) | |||||||
\(948\) | 2.53438e21 | 0.119621 | ||||||||
\(949\) | 2.04131e22 | 0.955901 | ||||||||
\(950\) | 6.43257e20 | 0.0298853 | ||||||||
\(951\) | −1.05053e22 | −0.484232 | ||||||||
\(952\) | −3.76074e22 | −1.71987 | ||||||||
\(953\) | −2.02888e22 | −0.920576 | −0.460288 | − | 0.887770i | \(-0.652254\pi\) | ||||
−0.460288 | + | 0.887770i | \(0.652254\pi\) | |||||||
\(954\) | −8.05958e21 | −0.362827 | ||||||||
\(955\) | 8.57944e21 | 0.383207 | ||||||||
\(956\) | −9.72494e20 | −0.0430976 | ||||||||
\(957\) | 2.22069e22 | 0.976445 | ||||||||
\(958\) | 3.25526e22 | 1.42018 | ||||||||
\(959\) | 4.84040e22 | 2.09528 | ||||||||
\(960\) | 1.80012e22 | 0.773155 | ||||||||
\(961\) | −2.34002e22 | −0.997227 | ||||||||
\(962\) | −1.65144e22 | −0.698313 | ||||||||
\(963\) | 2.17738e22 | 0.913559 | ||||||||
\(964\) | −5.79445e21 | −0.241232 | ||||||||
\(965\) | −2.55956e22 | −1.05733 | ||||||||
\(966\) | 4.36593e21 | 0.178957 | ||||||||
\(967\) | 1.17451e22 | 0.477705 | 0.238853 | − | 0.971056i | \(-0.423229\pi\) | ||||
0.238853 | + | 0.971056i | \(0.423229\pi\) | |||||||
\(968\) | 2.31289e22 | 0.933446 | ||||||||
\(969\) | 1.60494e22 | 0.642731 | ||||||||
\(970\) | −2.63642e22 | −1.04768 | ||||||||
\(971\) | −2.20415e22 | −0.869153 | −0.434576 | − | 0.900635i | \(-0.643102\pi\) | ||||
−0.434576 | + | 0.900635i | \(0.643102\pi\) | |||||||
\(972\) | −5.36102e21 | −0.209774 | ||||||||
\(973\) | 3.16597e22 | 1.22931 | ||||||||
\(974\) | 5.41034e21 | 0.208464 | ||||||||
\(975\) | 1.52436e21 | 0.0582847 | ||||||||
\(976\) | 5.41314e21 | 0.205388 | ||||||||
\(977\) | 2.46112e22 | 0.926667 | 0.463334 | − | 0.886184i | \(-0.346653\pi\) | ||||
0.463334 | + | 0.886184i | \(0.346653\pi\) | |||||||
\(978\) | 2.15039e22 | 0.803481 | ||||||||
\(979\) | 3.39157e22 | 1.25756 | ||||||||
\(980\) | −4.54418e21 | −0.167209 | ||||||||
\(981\) | 9.43584e21 | 0.344558 | ||||||||
\(982\) | 2.44393e22 | 0.885632 | ||||||||
\(983\) | −4.92044e22 | −1.76951 | −0.884754 | − | 0.466059i | \(-0.845673\pi\) | ||||
−0.884754 | + | 0.466059i | \(0.845673\pi\) | |||||||
\(984\) | 1.47503e22 | 0.526425 | ||||||||
\(985\) | −2.47221e22 | −0.875614 | ||||||||
\(986\) | −3.02606e22 | −1.06365 | ||||||||
\(987\) | 3.32605e22 | 1.16024 | ||||||||
\(988\) | 9.10858e21 | 0.315336 | ||||||||
\(989\) | −9.57868e20 | −0.0329104 | ||||||||
\(990\) | 1.67784e22 | 0.572118 | ||||||||
\(991\) | −1.29143e22 | −0.437037 | −0.218518 | − | 0.975833i | \(-0.570122\pi\) | ||||
−0.218518 | + | 0.975833i | \(0.570122\pi\) | |||||||
\(992\) | 7.34752e20 | 0.0246776 | ||||||||
\(993\) | 1.54267e22 | 0.514224 | ||||||||
\(994\) | 8.15080e21 | 0.269651 | ||||||||
\(995\) | −4.09058e22 | −1.34311 | ||||||||
\(996\) | −5.75960e20 | −0.0187693 | ||||||||
\(997\) | 4.74704e22 | 1.53535 | 0.767677 | − | 0.640836i | \(-0.221412\pi\) | ||||
0.767677 | + | 0.640836i | \(0.221412\pi\) | |||||||
\(998\) | −2.61720e22 | −0.840150 | ||||||||
\(999\) | 1.50971e22 | 0.481009 |
(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 | 83.16.a.a.1.18 | ✓ | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
83.16.a.a.1.18 | ✓ | 48 | 1.1 | even | 1 | trivial |