Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [83,13,Mod(82,83)]
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([1]))
N = Newforms(chi, 13, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("83.82");
S:= CuspForms(chi, 13);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 83 \) |
Weight: | \( k \) | \(=\) | \( 13 \) |
Character orbit: | \([\chi]\) | \(=\) | 83.b (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(75.8614868339\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 82.11 | ||
Character | \(\chi\) | \(=\) | 83.82 |
Dual form | 83.13.b.c.82.70 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/83\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 102.696i | − | 1.60462i | −0.596909 | − | 0.802309i | \(-0.703605\pi\) | ||
0.596909 | − | 0.802309i | \(-0.296395\pi\) | |||||||
\(3\) | −81.5431 | −0.111856 | −0.0559281 | − | 0.998435i | \(-0.517812\pi\) | ||||
−0.0559281 | + | 0.998435i | \(0.517812\pi\) | |||||||
\(4\) | −6450.37 | −1.57480 | ||||||||
\(5\) | 18424.7i | 1.17918i | 0.807703 | + | 0.589589i | \(0.200710\pi\) | ||||
−0.807703 | + | 0.589589i | \(0.799290\pi\) | |||||||
\(6\) | 8374.11i | 0.179486i | ||||||||
\(7\) | 214939. | 1.82695 | 0.913474 | − | 0.406897i | \(-0.133389\pi\) | ||||
0.913474 | + | 0.406897i | \(0.133389\pi\) | |||||||
\(8\) | 241783.i | 0.922330i | ||||||||
\(9\) | −524792. | −0.987488 | ||||||||
\(10\) | 1.89213e6 | 1.89213 | ||||||||
\(11\) | −2.57610e6 | −1.45414 | −0.727070 | − | 0.686563i | \(-0.759119\pi\) | ||||
−0.727070 | + | 0.686563i | \(0.759119\pi\) | |||||||
\(12\) | 525983. | 0.176151 | ||||||||
\(13\) | − | 4.43368e6i | − | 0.918552i | −0.888294 | − | 0.459276i | \(-0.848109\pi\) | ||
0.888294 | − | 0.459276i | \(-0.151891\pi\) | |||||||
\(14\) | − | 2.20732e7i | − | 2.93155i | ||||||
\(15\) | − | 1.50240e6i | − | 0.131898i | ||||||
\(16\) | −1.59065e6 | −0.0948101 | ||||||||
\(17\) | −6.28598e6 | −0.260423 | −0.130212 | − | 0.991486i | \(-0.541566\pi\) | ||||
−0.130212 | + | 0.991486i | \(0.541566\pi\) | |||||||
\(18\) | 5.38938e7i | 1.58454i | ||||||||
\(19\) | − | 1.47181e7i | − | 0.312846i | −0.987690 | − | 0.156423i | \(-0.950004\pi\) | ||
0.987690 | − | 0.156423i | \(-0.0499963\pi\) | |||||||
\(20\) | − | 1.18846e8i | − | 1.85697i | ||||||
\(21\) | −1.75268e7 | −0.204355 | ||||||||
\(22\) | 2.64554e8i | 2.33334i | ||||||||
\(23\) | −9.92752e7 | −0.670616 | −0.335308 | − | 0.942109i | \(-0.608840\pi\) | ||||
−0.335308 | + | 0.942109i | \(0.608840\pi\) | |||||||
\(24\) | − | 1.97158e7i | − | 0.103168i | ||||||
\(25\) | −9.53277e7 | −0.390462 | ||||||||
\(26\) | −4.55319e8 | −1.47393 | ||||||||
\(27\) | 8.61285e7 | 0.222313 | ||||||||
\(28\) | −1.38643e9 | −2.87707 | ||||||||
\(29\) | 1.12330e9 | 1.88846 | 0.944231 | − | 0.329285i | \(-0.106808\pi\) | ||||
0.944231 | + | 0.329285i | \(0.106808\pi\) | |||||||
\(30\) | −1.54290e8 | −0.211646 | ||||||||
\(31\) | −9.73251e8 | −1.09662 | −0.548308 | − | 0.836276i | \(-0.684728\pi\) | ||||
−0.548308 | + | 0.836276i | \(0.684728\pi\) | |||||||
\(32\) | 1.15370e9i | 1.07446i | ||||||||
\(33\) | 2.10063e8 | 0.162655 | ||||||||
\(34\) | 6.45543e8i | 0.417880i | ||||||||
\(35\) | 3.96017e9i | 2.15430i | ||||||||
\(36\) | 3.38510e9 | 1.55509 | ||||||||
\(37\) | 3.95456e9 | 1.54130 | 0.770651 | − | 0.637258i | \(-0.219931\pi\) | ||||
0.770651 | + | 0.637258i | \(0.219931\pi\) | |||||||
\(38\) | −1.51148e9 | −0.501998 | ||||||||
\(39\) | 3.61536e8i | 0.102746i | ||||||||
\(40\) | −4.45478e9 | −1.08759 | ||||||||
\(41\) | 3.30591e9 | 0.695966 | 0.347983 | − | 0.937501i | \(-0.386867\pi\) | ||||
0.347983 | + | 0.937501i | \(0.386867\pi\) | |||||||
\(42\) | 1.79992e9i | 0.327912i | ||||||||
\(43\) | − | 6.34747e9i | − | 1.00413i | −0.864830 | − | 0.502065i | \(-0.832574\pi\) | ||
0.864830 | − | 0.502065i | \(-0.167426\pi\) | |||||||
\(44\) | 1.66168e10 | 2.28998 | ||||||||
\(45\) | − | 9.66911e9i | − | 1.16443i | ||||||
\(46\) | 1.01951e10i | 1.07608i | ||||||||
\(47\) | 1.24063e10i | 1.15094i | 0.817822 | + | 0.575471i | \(0.195181\pi\) | ||||
−0.817822 | + | 0.575471i | \(0.804819\pi\) | |||||||
\(48\) | 1.29706e8 | 0.0106051 | ||||||||
\(49\) | 3.23573e10 | 2.33774 | ||||||||
\(50\) | 9.78973e9i | 0.626543i | ||||||||
\(51\) | 5.12579e8 | 0.0291299 | ||||||||
\(52\) | 2.85989e10i | 1.44653i | ||||||||
\(53\) | 3.84521e10i | 1.73486i | 0.497560 | + | 0.867430i | \(0.334230\pi\) | ||||
−0.497560 | + | 0.867430i | \(0.665770\pi\) | |||||||
\(54\) | − | 8.84501e9i | − | 0.356727i | ||||||
\(55\) | − | 4.74638e10i | − | 1.71469i | ||||||
\(56\) | 5.19686e10i | 1.68505i | ||||||||
\(57\) | 1.20016e9i | 0.0349937i | ||||||||
\(58\) | − | 1.15358e11i | − | 3.03026i | ||||||
\(59\) | −1.08532e10 | −0.257303 | −0.128652 | − | 0.991690i | \(-0.541065\pi\) | ||||
−0.128652 | + | 0.991690i | \(0.541065\pi\) | |||||||
\(60\) | 9.69107e9i | 0.207713i | ||||||||
\(61\) | −5.41860e10 | −1.05174 | −0.525870 | − | 0.850565i | \(-0.676260\pi\) | ||||
−0.525870 | + | 0.850565i | \(0.676260\pi\) | |||||||
\(62\) | 9.99485e10i | 1.75965i | ||||||||
\(63\) | −1.12798e11 | −1.80409 | ||||||||
\(64\) | 1.11964e11 | 1.62929 | ||||||||
\(65\) | 8.16890e10 | 1.08314 | ||||||||
\(66\) | − | 2.15725e10i | − | 0.260998i | ||||||
\(67\) | 1.57078e11i | 1.73647i | 0.496157 | + | 0.868233i | \(0.334744\pi\) | ||||
−0.496157 | + | 0.868233i | \(0.665256\pi\) | |||||||
\(68\) | 4.05469e10 | 0.410114 | ||||||||
\(69\) | 8.09521e9 | 0.0750125 | ||||||||
\(70\) | 4.06692e11 | 3.45683 | ||||||||
\(71\) | 1.65315e11i | 1.29051i | 0.763967 | + | 0.645256i | \(0.223249\pi\) | ||||
−0.763967 | + | 0.645256i | \(0.776751\pi\) | |||||||
\(72\) | − | 1.26886e11i | − | 0.910790i | ||||||
\(73\) | 2.06517e11i | 1.36464i | 0.731052 | + | 0.682321i | \(0.239029\pi\) | ||||
−0.731052 | + | 0.682321i | \(0.760971\pi\) | |||||||
\(74\) | − | 4.06115e11i | − | 2.47320i | ||||||
\(75\) | 7.77332e9 | 0.0436756 | ||||||||
\(76\) | 9.49373e10i | 0.492669i | ||||||||
\(77\) | −5.53703e11 | −2.65664 | ||||||||
\(78\) | 3.71281e10 | 0.164868 | ||||||||
\(79\) | 1.81447e11i | 0.746428i | 0.927745 | + | 0.373214i | \(0.121744\pi\) | ||||
−0.927745 | + | 0.373214i | \(0.878256\pi\) | |||||||
\(80\) | − | 2.93072e10i | − | 0.111798i | ||||||
\(81\) | 2.71873e11 | 0.962621 | ||||||||
\(82\) | − | 3.39502e11i | − | 1.11676i | ||||||
\(83\) | 2.84580e11 | + | 1.60948e11i | 0.870434 | + | 0.492285i | ||||
\(84\) | 1.13054e11 | 0.321818 | ||||||||
\(85\) | − | 1.15817e11i | − | 0.307086i | ||||||
\(86\) | −6.51857e11 | −1.61125 | ||||||||
\(87\) | −9.15974e10 | −0.211236 | ||||||||
\(88\) | − | 6.22858e11i | − | 1.34120i | ||||||
\(89\) | − | 3.14521e11i | − | 0.632863i | −0.948615 | − | 0.316432i | \(-0.897515\pi\) | ||
0.948615 | − | 0.316432i | \(-0.102485\pi\) | |||||||
\(90\) | −9.92975e11 | −1.86846 | ||||||||
\(91\) | − | 9.52969e11i | − | 1.67815i | ||||||
\(92\) | 6.40362e11 | 1.05608 | ||||||||
\(93\) | 7.93619e10 | 0.122663 | ||||||||
\(94\) | 1.27407e12 | 1.84682 | ||||||||
\(95\) | 2.71176e11 | 0.368901 | ||||||||
\(96\) | − | 9.40761e10i | − | 0.120185i | ||||||
\(97\) | − | 1.21462e12i | − | 1.45818i | −0.684418 | − | 0.729089i | \(-0.739944\pi\) | ||
0.684418 | − | 0.729089i | \(-0.260056\pi\) | |||||||
\(98\) | − | 3.32295e12i | − | 3.75118i | ||||||
\(99\) | 1.35192e12 | 1.43595 | ||||||||
\(100\) | 6.14899e11 | 0.614899 | ||||||||
\(101\) | 1.51863e12i | 1.43062i | 0.698809 | + | 0.715308i | \(0.253714\pi\) | ||||
−0.698809 | + | 0.715308i | \(0.746286\pi\) | |||||||
\(102\) | − | 5.26395e10i | − | 0.0467424i | ||||||
\(103\) | − | 4.09363e11i | − | 0.342835i | −0.985198 | − | 0.171417i | \(-0.945165\pi\) | ||
0.985198 | − | 0.171417i | \(-0.0548347\pi\) | |||||||
\(104\) | 1.07199e12 | 0.847209 | ||||||||
\(105\) | − | 3.22925e11i | − | 0.240971i | ||||||
\(106\) | 3.94885e12 | 2.78379 | ||||||||
\(107\) | − | 8.14800e11i | − | 0.542936i | −0.962447 | − | 0.271468i | \(-0.912491\pi\) | ||
0.962447 | − | 0.271468i | \(-0.0875091\pi\) | |||||||
\(108\) | −5.55561e11 | −0.350098 | ||||||||
\(109\) | 1.69615e11 | 0.101136 | 0.0505679 | − | 0.998721i | \(-0.483897\pi\) | ||||
0.0505679 | + | 0.998721i | \(0.483897\pi\) | |||||||
\(110\) | −4.87432e12 | −2.75142 | ||||||||
\(111\) | −3.22467e11 | −0.172404 | ||||||||
\(112\) | −3.41892e11 | −0.173213 | ||||||||
\(113\) | 2.14626e12 | 1.03089 | 0.515445 | − | 0.856923i | \(-0.327627\pi\) | ||||
0.515445 | + | 0.856923i | \(0.327627\pi\) | |||||||
\(114\) | 1.23251e11 | 0.0561516 | ||||||||
\(115\) | − | 1.82911e12i | − | 0.790776i | ||||||
\(116\) | −7.24571e12 | −2.97394 | ||||||||
\(117\) | 2.32676e12i | 0.907060i | ||||||||
\(118\) | 1.11457e12i | 0.412873i | ||||||||
\(119\) | −1.35110e12 | −0.475780 | ||||||||
\(120\) | 3.63256e11 | 0.121654 | ||||||||
\(121\) | 3.49785e12 | 1.11452 | ||||||||
\(122\) | 5.56466e12i | 1.68764i | ||||||||
\(123\) | −2.69574e11 | −0.0778480 | ||||||||
\(124\) | 6.27783e12 | 1.72695 | ||||||||
\(125\) | 2.74183e12i | 0.718754i | ||||||||
\(126\) | 1.15839e13i | 2.89487i | ||||||||
\(127\) | 5.61719e12 | 1.33874 | 0.669370 | − | 0.742929i | \(-0.266564\pi\) | ||||
0.669370 | + | 0.742929i | \(0.266564\pi\) | |||||||
\(128\) | − | 6.77268e12i | − | 1.53993i | ||||||
\(129\) | 5.17593e11i | 0.112318i | ||||||||
\(130\) | − | 8.38910e12i | − | 1.73802i | ||||||
\(131\) | −2.88968e12 | −0.571772 | −0.285886 | − | 0.958264i | \(-0.592288\pi\) | ||||
−0.285886 | + | 0.958264i | \(0.592288\pi\) | |||||||
\(132\) | −1.35498e12 | −0.256148 | ||||||||
\(133\) | − | 3.16349e12i | − | 0.571553i | ||||||
\(134\) | 1.61312e13 | 2.78636 | ||||||||
\(135\) | 1.58689e12i | 0.262146i | ||||||||
\(136\) | − | 1.51985e12i | − | 0.240196i | ||||||
\(137\) | − | 7.34209e12i | − | 1.11044i | −0.831702 | − | 0.555222i | \(-0.812633\pi\) | ||
0.831702 | − | 0.555222i | \(-0.187367\pi\) | |||||||
\(138\) | − | 8.31341e11i | − | 0.120366i | ||||||
\(139\) | 9.72175e12i | 1.34789i | 0.738780 | + | 0.673947i | \(0.235402\pi\) | ||||
−0.738780 | + | 0.673947i | \(0.764598\pi\) | |||||||
\(140\) | − | 2.55446e13i | − | 3.39258i | ||||||
\(141\) | − | 1.01165e12i | − | 0.128740i | ||||||
\(142\) | 1.69771e13 | 2.07078 | ||||||||
\(143\) | 1.14216e13i | 1.33570i | ||||||||
\(144\) | 8.34759e11 | 0.0936238 | ||||||||
\(145\) | 2.06964e13i | 2.22683i | ||||||||
\(146\) | 2.12084e13 | 2.18973 | ||||||||
\(147\) | −2.63852e12 | −0.261491 | ||||||||
\(148\) | −2.55084e13 | −2.42724 | ||||||||
\(149\) | 1.04941e13i | 0.959016i | 0.877538 | + | 0.479508i | \(0.159185\pi\) | ||||
−0.877538 | + | 0.479508i | \(0.840815\pi\) | |||||||
\(150\) | − | 7.98285e11i | − | 0.0700826i | ||||||
\(151\) | −5.02885e12 | −0.424236 | −0.212118 | − | 0.977244i | \(-0.568036\pi\) | ||||
−0.212118 | + | 0.977244i | \(0.568036\pi\) | |||||||
\(152\) | 3.55859e12 | 0.288547 | ||||||||
\(153\) | 3.29883e12 | 0.257165 | ||||||||
\(154\) | 5.68628e13i | 4.26289i | ||||||||
\(155\) | − | 1.79318e13i | − | 1.29311i | ||||||
\(156\) | − | 2.33204e12i | − | 0.161804i | ||||||
\(157\) | − | 1.60128e13i | − | 1.06922i | −0.845098 | − | 0.534611i | \(-0.820458\pi\) | ||
0.845098 | − | 0.534611i | \(-0.179542\pi\) | |||||||
\(158\) | 1.86338e13 | 1.19773 | ||||||||
\(159\) | − | 3.13550e12i | − | 0.194055i | ||||||
\(160\) | −2.12565e13 | −1.26699 | ||||||||
\(161\) | −2.13381e13 | −1.22518 | ||||||||
\(162\) | − | 2.79201e13i | − | 1.54464i | ||||||
\(163\) | − | 1.20510e13i | − | 0.642535i | −0.946989 | − | 0.321267i | \(-0.895891\pi\) | ||
0.946989 | − | 0.321267i | \(-0.104109\pi\) | |||||||
\(164\) | −2.13243e13 | −1.09600 | ||||||||
\(165\) | 3.87034e12i | 0.191799i | ||||||||
\(166\) | 1.65286e13 | − | 2.92251e13i | 0.789929 | − | 1.39671i | ||||
\(167\) | −7.21540e12 | −0.332630 | −0.166315 | − | 0.986073i | \(-0.553187\pi\) | ||||
−0.166315 | + | 0.986073i | \(0.553187\pi\) | |||||||
\(168\) | − | 4.23768e12i | − | 0.188483i | ||||||
\(169\) | 3.64059e12 | 0.156262 | ||||||||
\(170\) | −1.18939e13 | −0.492755 | ||||||||
\(171\) | 7.72394e12i | 0.308932i | ||||||||
\(172\) | 4.09435e13i | 1.58130i | ||||||||
\(173\) | 5.99192e12 | 0.223506 | 0.111753 | − | 0.993736i | \(-0.464353\pi\) | ||||
0.111753 | + | 0.993736i | \(0.464353\pi\) | |||||||
\(174\) | 9.40665e12i | 0.338953i | ||||||||
\(175\) | −2.04896e13 | −0.713355 | ||||||||
\(176\) | 4.09767e12 | 0.137867 | ||||||||
\(177\) | 8.85002e11 | 0.0287809 | ||||||||
\(178\) | −3.22999e13 | −1.01550 | ||||||||
\(179\) | 1.99120e13i | 0.605336i | 0.953096 | + | 0.302668i | \(0.0978774\pi\) | ||||
−0.953096 | + | 0.302668i | \(0.902123\pi\) | |||||||
\(180\) | 6.23694e13i | 1.83373i | ||||||||
\(181\) | − | 3.03193e13i | − | 0.862279i | −0.902285 | − | 0.431140i | \(-0.858112\pi\) | ||
0.902285 | − | 0.431140i | \(-0.141888\pi\) | |||||||
\(182\) | −9.78656e13 | −2.69279 | ||||||||
\(183\) | 4.41850e12 | 0.117643 | ||||||||
\(184\) | − | 2.40031e13i | − | 0.618529i | ||||||
\(185\) | 7.28614e13i | 1.81747i | ||||||||
\(186\) | − | 8.15012e12i | − | 0.196828i | ||||||
\(187\) | 1.61933e13 | 0.378692 | ||||||||
\(188\) | − | 8.00250e13i | − | 1.81250i | ||||||
\(189\) | 1.85123e13 | 0.406154 | ||||||||
\(190\) | − | 2.78486e13i | − | 0.591945i | ||||||
\(191\) | 3.21566e13 | 0.662324 | 0.331162 | − | 0.943574i | \(-0.392559\pi\) | ||||
0.331162 | + | 0.943574i | \(0.392559\pi\) | |||||||
\(192\) | −9.12991e12 | −0.182247 | ||||||||
\(193\) | −9.98454e13 | −1.93190 | −0.965949 | − | 0.258734i | \(-0.916695\pi\) | ||||
−0.965949 | + | 0.258734i | \(0.916695\pi\) | |||||||
\(194\) | −1.24736e14 | −2.33982 | ||||||||
\(195\) | −6.66118e12 | −0.121156 | ||||||||
\(196\) | −2.08717e14 | −3.68147 | ||||||||
\(197\) | 3.28214e13 | 0.561512 | 0.280756 | − | 0.959779i | \(-0.409415\pi\) | ||||
0.280756 | + | 0.959779i | \(0.409415\pi\) | |||||||
\(198\) | − | 1.38836e14i | − | 2.30415i | ||||||
\(199\) | −3.57560e12 | −0.0575745 | −0.0287873 | − | 0.999586i | \(-0.509165\pi\) | ||||
−0.0287873 | + | 0.999586i | \(0.509165\pi\) | |||||||
\(200\) | − | 2.30487e13i | − | 0.360135i | ||||||
\(201\) | − | 1.28086e13i | − | 0.194234i | ||||||
\(202\) | 1.55956e14 | 2.29559 | ||||||||
\(203\) | 2.41441e14 | 3.45012 | ||||||||
\(204\) | −3.30632e12 | −0.0458738 | ||||||||
\(205\) | 6.09103e13i | 0.820668i | ||||||||
\(206\) | −4.20397e13 | −0.550119 | ||||||||
\(207\) | 5.20988e13 | 0.662225 | ||||||||
\(208\) | 7.05242e12i | 0.0870880i | ||||||||
\(209\) | 3.79153e13i | 0.454922i | ||||||||
\(210\) | −3.31629e13 | −0.386667 | ||||||||
\(211\) | 5.10791e13i | 0.578827i | 0.957204 | + | 0.289413i | \(0.0934602\pi\) | ||||
−0.957204 | + | 0.289413i | \(0.906540\pi\) | |||||||
\(212\) | − | 2.48030e14i | − | 2.73205i | ||||||
\(213\) | − | 1.34803e13i | − | 0.144352i | ||||||
\(214\) | −8.36764e13 | −0.871205 | ||||||||
\(215\) | 1.16950e14 | 1.18405 | ||||||||
\(216\) | 2.08244e13i | 0.205046i | ||||||||
\(217\) | −2.09189e14 | −2.00346 | ||||||||
\(218\) | − | 1.74187e13i | − | 0.162284i | ||||||
\(219\) | − | 1.68400e13i | − | 0.152644i | ||||||
\(220\) | 3.06159e14i | 2.70029i | ||||||||
\(221\) | 2.78700e13i | 0.239212i | ||||||||
\(222\) | 3.31159e13i | 0.276642i | ||||||||
\(223\) | 1.09046e14i | 0.886709i | 0.896346 | + | 0.443354i | \(0.146212\pi\) | ||||
−0.896346 | + | 0.443354i | \(0.853788\pi\) | |||||||
\(224\) | 2.47974e14i | 1.96299i | ||||||||
\(225\) | 5.00272e13 | 0.385577 | ||||||||
\(226\) | − | 2.20411e14i | − | 1.65418i | ||||||
\(227\) | 7.92511e13 | 0.579229 | 0.289614 | − | 0.957143i | \(-0.406473\pi\) | ||||
0.289614 | + | 0.957143i | \(0.406473\pi\) | |||||||
\(228\) | − | 7.74148e12i | − | 0.0551080i | ||||||
\(229\) | 1.49134e14 | 1.03410 | 0.517051 | − | 0.855954i | \(-0.327030\pi\) | ||||
0.517051 | + | 0.855954i | \(0.327030\pi\) | |||||||
\(230\) | −1.87842e14 | −1.26889 | ||||||||
\(231\) | 4.51507e13 | 0.297161 | ||||||||
\(232\) | 2.71595e14i | 1.74178i | ||||||||
\(233\) | 7.16947e13i | 0.448076i | 0.974580 | + | 0.224038i | \(0.0719239\pi\) | ||||
−0.974580 | + | 0.224038i | \(0.928076\pi\) | |||||||
\(234\) | 2.38948e14 | 1.45548 | ||||||||
\(235\) | −2.28581e14 | −1.35717 | ||||||||
\(236\) | 7.00070e13 | 0.405200 | ||||||||
\(237\) | − | 1.47958e13i | − | 0.0834925i | ||||||
\(238\) | 1.38752e14i | 0.763445i | ||||||||
\(239\) | 2.17256e14i | 1.16569i | 0.812582 | + | 0.582847i | \(0.198061\pi\) | ||||
−0.812582 | + | 0.582847i | \(0.801939\pi\) | |||||||
\(240\) | 2.38980e12i | 0.0125053i | ||||||||
\(241\) | −1.99050e14 | −1.01592 | −0.507961 | − | 0.861380i | \(-0.669601\pi\) | ||||
−0.507961 | + | 0.861380i | \(0.669601\pi\) | |||||||
\(242\) | − | 3.59214e14i | − | 1.78839i | ||||||
\(243\) | −6.79416e13 | −0.329988 | ||||||||
\(244\) | 3.49520e14 | 1.65628 | ||||||||
\(245\) | 5.96173e14i | 2.75661i | ||||||||
\(246\) | 2.76841e13i | 0.124916i | ||||||||
\(247\) | −6.52554e13 | −0.287365 | ||||||||
\(248\) | − | 2.35316e14i | − | 1.01144i | ||||||
\(249\) | −2.32055e13 | − | 1.31242e13i | −0.0973634 | − | 0.0550650i | ||||
\(250\) | 2.81574e14 | 1.15333 | ||||||||
\(251\) | − | 1.42409e14i | − | 0.569502i | −0.958601 | − | 0.284751i | \(-0.908089\pi\) | ||
0.958601 | − | 0.284751i | \(-0.0919109\pi\) | |||||||
\(252\) | 7.27589e14 | 2.84108 | ||||||||
\(253\) | 2.55743e14 | 0.975169 | ||||||||
\(254\) | − | 5.76860e14i | − | 2.14817i | ||||||
\(255\) | 9.44409e12i | 0.0343494i | ||||||||
\(256\) | −2.36919e14 | −0.841704 | ||||||||
\(257\) | 1.30773e14i | 0.453858i | 0.973911 | + | 0.226929i | \(0.0728685\pi\) | ||||
−0.973911 | + | 0.226929i | \(0.927132\pi\) | |||||||
\(258\) | 5.31544e13 | 0.180228 | ||||||||
\(259\) | 8.49987e14 | 2.81588 | ||||||||
\(260\) | −5.26924e14 | −1.70572 | ||||||||
\(261\) | −5.89499e14 | −1.86483 | ||||||||
\(262\) | 2.96758e14i | 0.917475i | ||||||||
\(263\) | 1.51194e13i | 0.0456878i | 0.999739 | + | 0.0228439i | \(0.00727207\pi\) | ||||
−0.999739 | + | 0.0228439i | \(0.992728\pi\) | |||||||
\(264\) | 5.07898e13i | 0.150021i | ||||||||
\(265\) | −7.08466e14 | −2.04571 | ||||||||
\(266\) | −3.24876e14 | −0.917125 | ||||||||
\(267\) | 2.56470e13i | 0.0707896i | ||||||||
\(268\) | − | 1.01321e15i | − | 2.73458i | ||||||
\(269\) | − | 7.32663e14i | − | 1.93371i | −0.255331 | − | 0.966854i | \(-0.582184\pi\) | ||
0.255331 | − | 0.966854i | \(-0.417816\pi\) | |||||||
\(270\) | 1.62966e14 | 0.420645 | ||||||||
\(271\) | 7.84010e14i | 1.97927i | 0.143595 | + | 0.989637i | \(0.454134\pi\) | ||||
−0.143595 | + | 0.989637i | \(0.545866\pi\) | |||||||
\(272\) | 9.99879e12 | 0.0246907 | ||||||||
\(273\) | 7.77080e13i | 0.187711i | ||||||||
\(274\) | −7.54000e14 | −1.78184 | ||||||||
\(275\) | 2.45574e14 | 0.567787 | ||||||||
\(276\) | −5.22171e13 | −0.118129 | ||||||||
\(277\) | −2.68014e14 | −0.593305 | −0.296653 | − | 0.954985i | \(-0.595870\pi\) | ||||
−0.296653 | + | 0.954985i | \(0.595870\pi\) | |||||||
\(278\) | 9.98380e14 | 2.16285 | ||||||||
\(279\) | 5.10754e14 | 1.08290 | ||||||||
\(280\) | −9.57504e14 | −1.98698 | ||||||||
\(281\) | 4.90304e14i | 0.995928i | 0.867198 | + | 0.497964i | \(0.165919\pi\) | ||||
−0.867198 | + | 0.497964i | \(0.834081\pi\) | |||||||
\(282\) | −1.03891e14 | −0.206578 | ||||||||
\(283\) | − | 3.93873e14i | − | 0.766721i | −0.923599 | − | 0.383360i | \(-0.874767\pi\) | ||
0.923599 | − | 0.383360i | \(-0.125233\pi\) | |||||||
\(284\) | − | 1.06634e15i | − | 2.03229i | ||||||
\(285\) | −2.21126e13 | −0.0412639 | ||||||||
\(286\) | 1.17295e15 | 2.14329 | ||||||||
\(287\) | 7.10568e14 | 1.27149 | ||||||||
\(288\) | − | 6.05451e14i | − | 1.06102i | ||||||
\(289\) | −5.43109e14 | −0.932180 | ||||||||
\(290\) | 2.12543e15 | 3.57322 | ||||||||
\(291\) | 9.90441e13i | 0.163106i | ||||||||
\(292\) | − | 1.33211e15i | − | 2.14904i | ||||||
\(293\) | −1.83625e14 | −0.290219 | −0.145109 | − | 0.989416i | \(-0.546353\pi\) | ||||
−0.145109 | + | 0.989416i | \(0.546353\pi\) | |||||||
\(294\) | 2.70964e14i | 0.419592i | ||||||||
\(295\) | − | 1.99966e14i | − | 0.303406i | ||||||
\(296\) | 9.56146e14i | 1.42159i | ||||||||
\(297\) | −2.21876e14 | −0.323274 | ||||||||
\(298\) | 1.07769e15 | 1.53885 | ||||||||
\(299\) | 4.40154e14i | 0.615996i | ||||||||
\(300\) | −5.01408e13 | −0.0687802 | ||||||||
\(301\) | − | 1.36432e15i | − | 1.83449i | ||||||
\(302\) | 5.16440e14i | 0.680736i | ||||||||
\(303\) | − | 1.23834e14i | − | 0.160023i | ||||||
\(304\) | 2.34113e13i | 0.0296609i | ||||||||
\(305\) | − | 9.98359e14i | − | 1.24019i | ||||||
\(306\) | − | 3.38775e14i | − | 0.412651i | ||||||
\(307\) | − | 1.51936e14i | − | 0.181481i | −0.995875 | − | 0.0907406i | \(-0.971077\pi\) | ||
0.995875 | − | 0.0907406i | \(-0.0289234\pi\) | |||||||
\(308\) | 3.57159e15 | 4.18367 | ||||||||
\(309\) | 3.33807e13i | 0.0383482i | ||||||||
\(310\) | −1.84152e15 | −2.07494 | ||||||||
\(311\) | − | 3.30490e14i | − | 0.365255i | −0.983182 | − | 0.182627i | \(-0.941540\pi\) | ||
0.983182 | − | 0.182627i | \(-0.0584602\pi\) | |||||||
\(312\) | −8.74134e13 | −0.0947655 | ||||||||
\(313\) | −3.22547e14 | −0.343026 | −0.171513 | − | 0.985182i | \(-0.554866\pi\) | ||||
−0.171513 | + | 0.985182i | \(0.554866\pi\) | |||||||
\(314\) | −1.64444e15 | −1.71569 | ||||||||
\(315\) | − | 2.07827e15i | − | 2.12734i | ||||||
\(316\) | − | 1.17040e15i | − | 1.17547i | ||||||
\(317\) | 3.09162e14 | 0.304670 | 0.152335 | − | 0.988329i | \(-0.451321\pi\) | ||||
0.152335 | + | 0.988329i | \(0.451321\pi\) | |||||||
\(318\) | −3.22002e14 | −0.311384 | ||||||||
\(319\) | −2.89373e15 | −2.74609 | ||||||||
\(320\) | 2.06290e15i | 1.92123i | ||||||||
\(321\) | 6.64414e13i | 0.0607307i | ||||||||
\(322\) | 2.19132e15i | 1.96595i | ||||||||
\(323\) | 9.25178e13i | 0.0814724i | ||||||||
\(324\) | −1.75368e15 | −1.51593 | ||||||||
\(325\) | 4.22652e14i | 0.358660i | ||||||||
\(326\) | −1.23758e15 | −1.03102 | ||||||||
\(327\) | −1.38309e13 | −0.0113127 | ||||||||
\(328\) | 7.99314e14i | 0.641910i | ||||||||
\(329\) | 2.66659e15i | 2.10271i | ||||||||
\(330\) | 3.97467e14 | 0.307764 | ||||||||
\(331\) | 1.85040e15i | 1.40701i | 0.710690 | + | 0.703505i | \(0.248383\pi\) | ||||
−0.710690 | + | 0.703505i | \(0.751617\pi\) | |||||||
\(332\) | −1.83565e15 | − | 1.03817e15i | −1.37076 | − | 0.775249i | ||||
\(333\) | −2.07532e15 | −1.52202 | ||||||||
\(334\) | 7.40989e14i | 0.533744i | ||||||||
\(335\) | −2.89411e15 | −2.04760 | ||||||||
\(336\) | 2.78789e13 | 0.0193749 | ||||||||
\(337\) | − | 8.56215e14i | − | 0.584525i | −0.956338 | − | 0.292263i | \(-0.905592\pi\) | ||
0.956338 | − | 0.292263i | \(-0.0944081\pi\) | |||||||
\(338\) | − | 3.73873e14i | − | 0.250740i | ||||||
\(339\) | −1.75013e14 | −0.115311 | ||||||||
\(340\) | 7.47064e14i | 0.483598i | ||||||||
\(341\) | 2.50719e15 | 1.59463 | ||||||||
\(342\) | 7.93214e14 | 0.495717 | ||||||||
\(343\) | 3.97982e15 | 2.44398 | ||||||||
\(344\) | 1.53471e15 | 0.926140 | ||||||||
\(345\) | 1.49151e14i | 0.0884531i | ||||||||
\(346\) | − | 6.15343e14i | − | 0.358642i | ||||||
\(347\) | − | 3.98226e14i | − | 0.228114i | −0.993474 | − | 0.114057i | \(-0.963615\pi\) | ||
0.993474 | − | 0.114057i | \(-0.0363847\pi\) | |||||||
\(348\) | 5.90837e14 | 0.332654 | ||||||||
\(349\) | −8.29039e14 | −0.458799 | −0.229399 | − | 0.973332i | \(-0.573676\pi\) | ||||
−0.229399 | + | 0.973332i | \(0.573676\pi\) | |||||||
\(350\) | 2.10419e15i | 1.14466i | ||||||||
\(351\) | − | 3.81866e14i | − | 0.204206i | ||||||
\(352\) | − | 2.97204e15i | − | 1.56242i | ||||||
\(353\) | 2.39223e15 | 1.23639 | 0.618193 | − | 0.786026i | \(-0.287865\pi\) | ||||
0.618193 | + | 0.786026i | \(0.287865\pi\) | |||||||
\(354\) | − | 9.08858e13i | − | 0.0461824i | ||||||
\(355\) | −3.04587e15 | −1.52174 | ||||||||
\(356\) | 2.02878e15i | 0.996631i | ||||||||
\(357\) | 1.10173e14 | 0.0532189 | ||||||||
\(358\) | 2.04487e15 | 0.971333 | ||||||||
\(359\) | 2.33002e15 | 1.08841 | 0.544205 | − | 0.838952i | \(-0.316831\pi\) | ||||
0.544205 | + | 0.838952i | \(0.316831\pi\) | |||||||
\(360\) | 2.33783e15 | 1.07398 | ||||||||
\(361\) | 1.99669e15 | 0.902127 | ||||||||
\(362\) | −3.11366e15 | −1.38363 | ||||||||
\(363\) | −2.85226e14 | −0.124666 | ||||||||
\(364\) | 6.14700e15i | 2.64274i | ||||||||
\(365\) | −3.80501e15 | −1.60916 | ||||||||
\(366\) | − | 4.53760e14i | − | 0.188773i | ||||||
\(367\) | − | 1.84378e15i | − | 0.754591i | −0.926093 | − | 0.377296i | \(-0.876854\pi\) | ||
0.926093 | − | 0.377296i | \(-0.123146\pi\) | |||||||
\(368\) | 1.57912e14 | 0.0635811 | ||||||||
\(369\) | −1.73491e15 | −0.687258 | ||||||||
\(370\) | 7.48254e15 | 2.91634 | ||||||||
\(371\) | 8.26483e15i | 3.16950i | ||||||||
\(372\) | −5.11914e14 | −0.193170 | ||||||||
\(373\) | 1.69100e15 | 0.627901 | 0.313951 | − | 0.949439i | \(-0.398347\pi\) | ||||
0.313951 | + | 0.949439i | \(0.398347\pi\) | |||||||
\(374\) | − | 1.66298e15i | − | 0.607656i | ||||||
\(375\) | − | 2.23577e14i | − | 0.0803970i | ||||||
\(376\) | −2.99963e15 | −1.06155 | ||||||||
\(377\) | − | 4.98035e15i | − | 1.73465i | ||||||
\(378\) | − | 1.90114e15i | − | 0.651722i | ||||||
\(379\) | 2.01260e15i | 0.679081i | 0.940591 | + | 0.339541i | \(0.110272\pi\) | ||||
−0.940591 | + | 0.339541i | \(0.889728\pi\) | |||||||
\(380\) | −1.74919e15 | −0.580945 | ||||||||
\(381\) | −4.58043e14 | −0.149746 | ||||||||
\(382\) | − | 3.30234e15i | − | 1.06278i | ||||||
\(383\) | −3.40783e15 | −1.07965 | −0.539827 | − | 0.841776i | \(-0.681510\pi\) | ||||
−0.539827 | + | 0.841776i | \(0.681510\pi\) | |||||||
\(384\) | 5.52266e14i | 0.172251i | ||||||||
\(385\) | − | 1.02018e16i | − | 3.13265i | ||||||
\(386\) | 1.02537e16i | 3.09996i | ||||||||
\(387\) | 3.33110e15i | 0.991567i | ||||||||
\(388\) | 7.83476e15i | 2.29634i | ||||||||
\(389\) | 1.05007e15i | 0.303053i | 0.988453 | + | 0.151527i | \(0.0484189\pi\) | ||||
−0.988453 | + | 0.151527i | \(0.951581\pi\) | |||||||
\(390\) | 6.84073e14i | 0.194408i | ||||||||
\(391\) | 6.24042e14 | 0.174644 | ||||||||
\(392\) | 7.82347e15i | 2.15617i | ||||||||
\(393\) | 2.35634e14 | 0.0639562 | ||||||||
\(394\) | − | 3.37061e15i | − | 0.901012i | ||||||
\(395\) | −3.34310e15 | −0.880172 | ||||||||
\(396\) | −8.72035e15 | −2.26133 | ||||||||
\(397\) | −9.40540e14 | −0.240234 | −0.120117 | − | 0.992760i | \(-0.538327\pi\) | ||||
−0.120117 | + | 0.992760i | \(0.538327\pi\) | |||||||
\(398\) | 3.67198e14i | 0.0923851i | ||||||||
\(399\) | 2.57961e14i | 0.0639317i | ||||||||
\(400\) | 1.51633e14 | 0.0370198 | ||||||||
\(401\) | 1.03495e15 | 0.248917 | 0.124458 | − | 0.992225i | \(-0.460281\pi\) | ||||
0.124458 | + | 0.992225i | \(0.460281\pi\) | |||||||
\(402\) | −1.31539e15 | −0.311672 | ||||||||
\(403\) | 4.31508e15i | 1.00730i | ||||||||
\(404\) | − | 9.79572e15i | − | 2.25293i | ||||||
\(405\) | 5.00916e15i | 1.13510i | ||||||||
\(406\) | − | 2.47949e16i | − | 5.53612i | ||||||
\(407\) | −1.01873e16 | −2.24127 | ||||||||
\(408\) | 1.23933e14i | 0.0268674i | ||||||||
\(409\) | 2.26576e15 | 0.484031 | 0.242016 | − | 0.970272i | \(-0.422191\pi\) | ||||
0.242016 | + | 0.970272i | \(0.422191\pi\) | |||||||
\(410\) | 6.25521e15 | 1.31686 | ||||||||
\(411\) | 5.98697e14i | 0.124210i | ||||||||
\(412\) | 2.64054e15i | 0.539896i | ||||||||
\(413\) | −2.33277e15 | −0.470079 | ||||||||
\(414\) | − | 5.35031e15i | − | 1.06262i | ||||||
\(415\) | −2.96541e15 | + | 5.24329e15i | −0.580491 | + | 1.02640i | ||||
\(416\) | 5.11512e15 | 0.986952 | ||||||||
\(417\) | − | 7.92742e14i | − | 0.150770i | ||||||
\(418\) | 3.89373e15 | 0.729976 | ||||||||
\(419\) | 2.70313e15 | 0.499555 | 0.249777 | − | 0.968303i | \(-0.419643\pi\) | ||||
0.249777 | + | 0.968303i | \(0.419643\pi\) | |||||||
\(420\) | 2.08299e15i | 0.379481i | ||||||||
\(421\) | − | 6.43430e15i | − | 1.15560i | −0.816177 | − | 0.577802i | \(-0.803911\pi\) | ||
0.816177 | − | 0.577802i | \(-0.196089\pi\) | |||||||
\(422\) | 5.24560e15 | 0.928796 | ||||||||
\(423\) | − | 6.51070e15i | − | 1.13654i | ||||||
\(424\) | −9.29707e15 | −1.60011 | ||||||||
\(425\) | 5.99229e14 | 0.101685 | ||||||||
\(426\) | −1.38437e15 | −0.231629 | ||||||||
\(427\) | −1.16467e16 | −1.92147 | ||||||||
\(428\) | 5.25577e15i | 0.855014i | ||||||||
\(429\) | − | 9.31352e14i | − | 0.149407i | ||||||
\(430\) | − | 1.20102e16i | − | 1.89995i | ||||||
\(431\) | −6.83958e15 | −1.06700 | −0.533502 | − | 0.845799i | \(-0.679124\pi\) | ||||
−0.533502 | + | 0.845799i | \(0.679124\pi\) | |||||||
\(432\) | −1.37000e14 | −0.0210775 | ||||||||
\(433\) | − | 9.06436e15i | − | 1.37534i | −0.726024 | − | 0.687670i | \(-0.758634\pi\) | ||
0.726024 | − | 0.687670i | \(-0.241366\pi\) | |||||||
\(434\) | 2.14828e16i | 3.21479i | ||||||||
\(435\) | − | 1.68765e15i | − | 0.249085i | ||||||
\(436\) | −1.09408e15 | −0.159268 | ||||||||
\(437\) | 1.46114e15i | 0.209799i | ||||||||
\(438\) | −1.72940e15 | −0.244935 | ||||||||
\(439\) | − | 4.13303e15i | − | 0.577406i | −0.957419 | − | 0.288703i | \(-0.906776\pi\) | ||
0.957419 | − | 0.288703i | \(-0.0932240\pi\) | |||||||
\(440\) | 1.14759e16 | 1.58151 | ||||||||
\(441\) | −1.69809e16 | −2.30849 | ||||||||
\(442\) | 2.86213e15 | 0.383844 | ||||||||
\(443\) | −3.22185e15 | −0.426268 | −0.213134 | − | 0.977023i | \(-0.568367\pi\) | ||||
−0.213134 | + | 0.977023i | \(0.568367\pi\) | |||||||
\(444\) | 2.08003e15 | 0.271501 | ||||||||
\(445\) | 5.79495e15 | 0.746259 | ||||||||
\(446\) | 1.11985e16 | 1.42283 | ||||||||
\(447\) | − | 8.55718e14i | − | 0.107272i | ||||||
\(448\) | 2.40654e16 | 2.97664 | ||||||||
\(449\) | 6.09869e15i | 0.744318i | 0.928169 | + | 0.372159i | \(0.121382\pi\) | ||||
−0.928169 | + | 0.372159i | \(0.878618\pi\) | |||||||
\(450\) | − | 5.13757e15i | − | 0.618704i | ||||||
\(451\) | −8.51635e15 | −1.01203 | ||||||||
\(452\) | −1.38442e16 | −1.62344 | ||||||||
\(453\) | 4.10068e14 | 0.0474533 | ||||||||
\(454\) | − | 8.13873e15i | − | 0.929441i | ||||||
\(455\) | 1.75581e16 | 1.97884 | ||||||||
\(456\) | −2.90179e14 | −0.0322758 | ||||||||
\(457\) | − | 9.68950e15i | − | 1.06366i | −0.846850 | − | 0.531832i | \(-0.821504\pi\) | ||
0.846850 | − | 0.531832i | \(-0.178496\pi\) | |||||||
\(458\) | − | 1.53154e16i | − | 1.65934i | ||||||
\(459\) | −5.41402e14 | −0.0578954 | ||||||||
\(460\) | 1.17985e16i | 1.24531i | ||||||||
\(461\) | − | 7.26262e15i | − | 0.756637i | −0.925675 | − | 0.378319i | \(-0.876502\pi\) | ||
0.925675 | − | 0.378319i | \(-0.123498\pi\) | |||||||
\(462\) | − | 4.63677e15i | − | 0.476830i | ||||||
\(463\) | 8.03002e15 | 0.815137 | 0.407568 | − | 0.913175i | \(-0.366377\pi\) | ||||
0.407568 | + | 0.913175i | \(0.366377\pi\) | |||||||
\(464\) | −1.78678e15 | −0.179045 | ||||||||
\(465\) | 1.46222e15i | 0.144642i | ||||||||
\(466\) | 7.36272e15 | 0.718990 | ||||||||
\(467\) | − | 1.15742e15i | − | 0.111581i | −0.998442 | − | 0.0557906i | \(-0.982232\pi\) | ||
0.998442 | − | 0.0557906i | \(-0.0177679\pi\) | |||||||
\(468\) | − | 1.50084e16i | − | 1.42844i | ||||||
\(469\) | 3.37621e16i | 3.17243i | ||||||||
\(470\) | 2.34743e16i | 2.17773i | ||||||||
\(471\) | 1.30573e15i | 0.119599i | ||||||||
\(472\) | − | 2.62412e15i | − | 0.237318i | ||||||
\(473\) | 1.63517e16i | 1.46015i | ||||||||
\(474\) | −1.51946e15 | −0.133974 | ||||||||
\(475\) | 1.40304e15i | 0.122155i | ||||||||
\(476\) | 8.71510e15 | 0.749257 | ||||||||
\(477\) | − | 2.01793e16i | − | 1.71315i | ||||||
\(478\) | 2.23112e16 | 1.87049 | ||||||||
\(479\) | 1.55276e16 | 1.28555 | 0.642777 | − | 0.766053i | \(-0.277782\pi\) | ||||
0.642777 | + | 0.766053i | \(0.277782\pi\) | |||||||
\(480\) | 1.73332e15 | 0.141720 | ||||||||
\(481\) | − | 1.75332e16i | − | 1.41577i | ||||||
\(482\) | 2.04416e16i | 1.63017i | ||||||||
\(483\) | 1.73997e15 | 0.137044 | ||||||||
\(484\) | −2.25625e16 | −1.75515 | ||||||||
\(485\) | 2.23790e16 | 1.71945 | ||||||||
\(486\) | 6.97729e15i | 0.529504i | ||||||||
\(487\) | − | 5.25307e15i | − | 0.393767i | −0.980427 | − | 0.196883i | \(-0.936918\pi\) | ||
0.980427 | − | 0.196883i | \(-0.0630820\pi\) | |||||||
\(488\) | − | 1.31013e16i | − | 0.970051i | ||||||
\(489\) | 9.82674e14i | 0.0718715i | ||||||||
\(490\) | 6.12243e16 | 4.42331 | ||||||||
\(491\) | − | 4.61810e15i | − | 0.329591i | −0.986328 | − | 0.164795i | \(-0.947304\pi\) | ||
0.986328 | − | 0.164795i | \(-0.0526963\pi\) | |||||||
\(492\) | 1.73885e15 | 0.122595 | ||||||||
\(493\) | −7.06105e15 | −0.491799 | ||||||||
\(494\) | 6.70143e15i | 0.461112i | ||||||||
\(495\) | 2.49086e16i | 1.69324i | ||||||||
\(496\) | 1.54810e15 | 0.103970 | ||||||||
\(497\) | 3.55326e16i | 2.35770i | ||||||||
\(498\) | −1.34779e15 | + | 2.38311e15i | −0.0883583 | + | 0.156231i | ||||
\(499\) | −1.90552e16 | −1.23427 | −0.617134 | − | 0.786858i | \(-0.711706\pi\) | ||||
−0.617134 | + | 0.786858i | \(0.711706\pi\) | |||||||
\(500\) | − | 1.76858e16i | − | 1.13189i | ||||||
\(501\) | 5.88366e14 | 0.0372067 | ||||||||
\(502\) | −1.46248e16 | −0.913833 | ||||||||
\(503\) | − | 1.16281e16i | − | 0.717963i | −0.933345 | − | 0.358982i | \(-0.883124\pi\) | ||
0.933345 | − | 0.358982i | \(-0.116876\pi\) | |||||||
\(504\) | − | 2.72727e16i | − | 1.66397i | ||||||
\(505\) | −2.79802e16 | −1.68695 | ||||||||
\(506\) | − | 2.62636e16i | − | 1.56477i | ||||||
\(507\) | −2.96865e14 | −0.0174788 | ||||||||
\(508\) | −3.62329e16 | −2.10825 | ||||||||
\(509\) | −4.52400e15 | −0.260145 | −0.130072 | − | 0.991504i | \(-0.541521\pi\) | ||||
−0.130072 | + | 0.991504i | \(0.541521\pi\) | |||||||
\(510\) | 9.69866e14 | 0.0551177 | ||||||||
\(511\) | 4.43885e16i | 2.49313i | ||||||||
\(512\) | − | 3.41042e15i | − | 0.189316i | ||||||
\(513\) | − | 1.26765e15i | − | 0.0695496i | ||||||
\(514\) | 1.34298e16 | 0.728268 | ||||||||
\(515\) | 7.54237e15 | 0.404264 | ||||||||
\(516\) | − | 3.33866e15i | − | 0.176878i | ||||||
\(517\) | − | 3.19597e16i | − | 1.67363i | ||||||
\(518\) | − | 8.72899e16i | − | 4.51841i | ||||||
\(519\) | −4.88600e14 | −0.0250005 | ||||||||
\(520\) | 1.97510e16i | 0.999010i | ||||||||
\(521\) | 1.72950e16 | 0.864759 | 0.432379 | − | 0.901692i | \(-0.357674\pi\) | ||||
0.432379 | + | 0.901692i | \(0.357674\pi\) | |||||||
\(522\) | 6.05389e16i | 2.99234i | ||||||||
\(523\) | 2.75403e16 | 1.34573 | 0.672865 | − | 0.739765i | \(-0.265063\pi\) | ||||
0.672865 | + | 0.739765i | \(0.265063\pi\) | |||||||
\(524\) | 1.86395e16 | 0.900425 | ||||||||
\(525\) | 1.67079e15 | 0.0797931 | ||||||||
\(526\) | 1.55270e15 | 0.0733115 | ||||||||
\(527\) | 6.11784e15 | 0.285584 | ||||||||
\(528\) | −3.34137e14 | −0.0154213 | ||||||||
\(529\) | −1.20591e16 | −0.550275 | ||||||||
\(530\) | 7.27563e16i | 3.28258i | ||||||||
\(531\) | 5.69566e15 | 0.254084 | ||||||||
\(532\) | 2.04057e16i | 0.900081i | ||||||||
\(533\) | − | 1.46573e16i | − | 0.639281i | ||||||
\(534\) | 2.63384e15 | 0.113590 | ||||||||
\(535\) | 1.50124e16 | 0.640219 | ||||||||
\(536\) | −3.79788e16 | −1.60159 | ||||||||
\(537\) | − | 1.62369e15i | − | 0.0677106i | ||||||
\(538\) | −7.52413e16 | −3.10286 | ||||||||
\(539\) | −8.33557e16 | −3.39940 | ||||||||
\(540\) | − | 1.02360e16i | − | 0.412828i | ||||||
\(541\) | 3.79875e16i | 1.51515i | 0.652746 | + | 0.757577i | \(0.273617\pi\) | ||||
−0.652746 | + | 0.757577i | \(0.726383\pi\) | |||||||
\(542\) | 8.05143e16 | 3.17598 | ||||||||
\(543\) | 2.47233e15i | 0.0964512i | ||||||||
\(544\) | − | 7.25212e15i | − | 0.279816i | ||||||
\(545\) | 3.12510e15i | 0.119257i | ||||||||
\(546\) | 7.98027e15 | 0.301205 | ||||||||
\(547\) | −1.06702e16 | −0.398334 | −0.199167 | − | 0.979966i | \(-0.563824\pi\) | ||||
−0.199167 | + | 0.979966i | \(0.563824\pi\) | |||||||
\(548\) | 4.73592e16i | 1.74872i | ||||||||
\(549\) | 2.84364e16 | 1.03858 | ||||||||
\(550\) | − | 2.52193e16i | − | 0.911081i | ||||||
\(551\) | − | 1.65329e16i | − | 0.590797i | ||||||
\(552\) | 1.95729e15i | 0.0691863i | ||||||||
\(553\) | 3.90000e16i | 1.36369i | ||||||||
\(554\) | 2.75238e16i | 0.952028i | ||||||||
\(555\) | − | 5.94134e15i | − | 0.203295i | ||||||
\(556\) | − | 6.27089e16i | − | 2.12266i | ||||||
\(557\) | −3.66460e16 | −1.22714 | −0.613572 | − | 0.789639i | \(-0.710268\pi\) | ||||
−0.613572 | + | 0.789639i | \(0.710268\pi\) | |||||||
\(558\) | − | 5.24522e16i | − | 1.73763i | ||||||
\(559\) | −2.81426e16 | −0.922346 | ||||||||
\(560\) | − | 6.29924e15i | − | 0.204249i | ||||||
\(561\) | −1.32045e15 | −0.0423590 | ||||||||
\(562\) | 5.03521e16 | 1.59808 | ||||||||
\(563\) | −2.52291e16 | −0.792229 | −0.396114 | − | 0.918201i | \(-0.629642\pi\) | ||||
−0.396114 | + | 0.918201i | \(0.629642\pi\) | |||||||
\(564\) | 6.52549e15i | 0.202739i | ||||||||
\(565\) | 3.95442e16i | 1.21560i | ||||||||
\(566\) | −4.04490e16 | −1.23029 | ||||||||
\(567\) | 5.84359e16 | 1.75866 | ||||||||
\(568\) | −3.99704e16 | −1.19028 | ||||||||
\(569\) | − | 3.56960e16i | − | 1.05183i | −0.850537 | − | 0.525915i | \(-0.823723\pi\) | ||
0.850537 | − | 0.525915i | \(-0.176277\pi\) | |||||||
\(570\) | 2.27086e15i | 0.0662127i | ||||||||
\(571\) | 5.20726e14i | 0.0150242i | 0.999972 | + | 0.00751212i | \(0.00239120\pi\) | ||||
−0.999972 | + | 0.00751212i | \(0.997609\pi\) | |||||||
\(572\) | − | 7.36735e16i | − | 2.10346i | ||||||
\(573\) | −2.62215e15 | −0.0740850 | ||||||||
\(574\) | − | 7.29721e16i | − | 2.04026i | ||||||
\(575\) | 9.46367e15 | 0.261850 | ||||||||
\(576\) | −5.87579e16 | −1.60891 | ||||||||
\(577\) | 7.04619e16i | 1.90941i | 0.297550 | + | 0.954706i | \(0.403830\pi\) | ||||
−0.297550 | + | 0.954706i | \(0.596170\pi\) | |||||||
\(578\) | 5.57748e16i | 1.49579i | ||||||||
\(579\) | 8.14170e15 | 0.216095 | ||||||||
\(580\) | − | 1.33500e17i | − | 3.50681i | ||||||
\(581\) | 6.11673e16 | + | 3.45939e16i | 1.59024 | + | 0.899379i | ||||
\(582\) | 1.01714e16 | 0.261723 | ||||||||
\(583\) | − | 9.90563e16i | − | 2.52273i | ||||||
\(584\) | −4.99324e16 | −1.25865 | ||||||||
\(585\) | −4.28697e16 | −1.06959 | ||||||||
\(586\) | 1.88574e16i | 0.465690i | ||||||||
\(587\) | 4.25316e16i | 1.03964i | 0.854276 | + | 0.519820i | \(0.174001\pi\) | ||||
−0.854276 | + | 0.519820i | \(0.825999\pi\) | |||||||
\(588\) | 1.70194e16 | 0.411795 | ||||||||
\(589\) | 1.43244e16i | 0.343072i | ||||||||
\(590\) | −2.05356e16 | −0.486851 | ||||||||
\(591\) | −2.67636e15 | −0.0628086 | ||||||||
\(592\) | −6.29031e15 | −0.146131 | ||||||||
\(593\) | 3.18595e16 | 0.732675 | 0.366338 | − | 0.930482i | \(-0.380612\pi\) | ||||
0.366338 | + | 0.930482i | \(0.380612\pi\) | |||||||
\(594\) | 2.27856e16i | 0.518731i | ||||||||
\(595\) | − | 2.48936e16i | − | 0.561030i | ||||||
\(596\) | − | 6.76906e16i | − | 1.51026i | ||||||
\(597\) | 2.91565e14 | 0.00644006 | ||||||||
\(598\) | 4.52018e16 | 0.988437 | ||||||||
\(599\) | 6.64467e16i | 1.43851i | 0.694747 | + | 0.719254i | \(0.255516\pi\) | ||||
−0.694747 | + | 0.719254i | \(0.744484\pi\) | |||||||
\(600\) | 1.87946e15i | 0.0402833i | ||||||||
\(601\) | 2.19119e16i | 0.464979i | 0.972599 | + | 0.232490i | \(0.0746872\pi\) | ||||
−0.972599 | + | 0.232490i | \(0.925313\pi\) | |||||||
\(602\) | −1.40109e17 | −2.94366 | ||||||||
\(603\) | − | 8.24331e16i | − | 1.71474i | ||||||
\(604\) | 3.24380e16 | 0.668085 | ||||||||
\(605\) | 6.44468e16i | 1.31422i | ||||||||
\(606\) | −1.27172e16 | −0.256776 | ||||||||
\(607\) | 9.29933e16 | 1.85917 | 0.929586 | − | 0.368605i | \(-0.120164\pi\) | ||||
0.929586 | + | 0.368605i | \(0.120164\pi\) | |||||||
\(608\) | 1.69802e16 | 0.336142 | ||||||||
\(609\) | −1.96878e16 | −0.385917 | ||||||||
\(610\) | −1.02527e17 | −1.99003 | ||||||||
\(611\) | 5.50054e16 | 1.05720 | ||||||||
\(612\) | −2.12787e16 | −0.404983 | ||||||||
\(613\) | 7.15582e16i | 1.34864i | 0.738438 | + | 0.674321i | \(0.235564\pi\) | ||||
−0.738438 | + | 0.674321i | \(0.764436\pi\) | |||||||
\(614\) | −1.56032e16 | −0.291208 | ||||||||
\(615\) | − | 4.96681e15i | − | 0.0917967i | ||||||
\(616\) | − | 1.33876e17i | − | 2.45030i | ||||||
\(617\) | 2.30947e16 | 0.418602 | 0.209301 | − | 0.977851i | \(-0.432881\pi\) | ||||
0.209301 | + | 0.977851i | \(0.432881\pi\) | |||||||
\(618\) | 3.42805e15 | 0.0615342 | ||||||||
\(619\) | −5.23539e16 | −0.930691 | −0.465345 | − | 0.885129i | \(-0.654070\pi\) | ||||
−0.465345 | + | 0.885129i | \(0.654070\pi\) | |||||||
\(620\) | 1.15667e17i | 2.03638i | ||||||||
\(621\) | −8.55042e15 | −0.149086 | ||||||||
\(622\) | −3.39398e16 | −0.586094 | ||||||||
\(623\) | − | 6.76028e16i | − | 1.15621i | ||||||
\(624\) | − | 5.75077e14i | − | 0.00974133i | ||||||
\(625\) | −7.37906e16 | −1.23800 | ||||||||
\(626\) | 3.31241e16i | 0.550425i | ||||||||
\(627\) | − | 3.09173e15i | − | 0.0508858i | ||||||
\(628\) | 1.03288e17i | 1.68381i | ||||||||
\(629\) | −2.48583e16 | −0.401391 | ||||||||
\(630\) | −2.13429e17 | −3.41357 | ||||||||
\(631\) | 5.54192e16i | 0.877979i | 0.898492 | + | 0.438990i | \(0.144663\pi\) | ||||
−0.898492 | + | 0.438990i | \(0.855337\pi\) | |||||||
\(632\) | −4.38709e16 | −0.688453 | ||||||||
\(633\) | − | 4.16515e15i | − | 0.0647453i | ||||||
\(634\) | − | 3.17495e16i | − | 0.488880i | ||||||
\(635\) | 1.03495e17i | 1.57861i | ||||||||
\(636\) | 2.02251e16i | 0.305597i | ||||||||
\(637\) | − | 1.43462e17i | − | 2.14734i | ||||||
\(638\) | 2.97173e17i | 4.40642i | ||||||||
\(639\) | − | 8.67559e16i | − | 1.27436i | ||||||
\(640\) | 1.24784e17 | 1.81585 | ||||||||
\(641\) | 7.13287e16i | 1.02829i | 0.857703 | + | 0.514146i | \(0.171891\pi\) | ||||
−0.857703 | + | 0.514146i | \(0.828109\pi\) | |||||||
\(642\) | 6.82323e15 | 0.0974496 | ||||||||
\(643\) | 7.81020e16i | 1.10509i | 0.833484 | + | 0.552544i | \(0.186343\pi\) | ||||
−0.833484 | + | 0.552544i | \(0.813657\pi\) | |||||||
\(644\) | 1.37638e17 | 1.92941 | ||||||||
\(645\) | −9.53647e15 | −0.132443 | ||||||||
\(646\) | 9.50117e15 | 0.130732 | ||||||||
\(647\) | 6.30278e15i | 0.0859224i | 0.999077 | + | 0.0429612i | \(0.0136792\pi\) | ||||
−0.999077 | + | 0.0429612i | \(0.986321\pi\) | |||||||
\(648\) | 6.57343e16i | 0.887855i | ||||||||
\(649\) | 2.79589e16 | 0.374155 | ||||||||
\(650\) | 4.34045e16 | 0.575512 | ||||||||
\(651\) | 1.70579e16 | 0.224099 | ||||||||
\(652\) | 7.77333e16i | 1.01186i | ||||||||
\(653\) | − | 9.55730e16i | − | 1.23270i | −0.787474 | − | 0.616348i | \(-0.788611\pi\) | ||
0.787474 | − | 0.616348i | \(-0.211389\pi\) | |||||||
\(654\) | 1.42037e15i | 0.0181525i | ||||||||
\(655\) | − | 5.32415e16i | − | 0.674221i | ||||||
\(656\) | −5.25854e15 | −0.0659845 | ||||||||
\(657\) | − | 1.08378e17i | − | 1.34757i | ||||||
\(658\) | 2.73846e17 | 3.37405 | ||||||||
\(659\) | −3.13363e16 | −0.382592 | −0.191296 | − | 0.981532i | \(-0.561269\pi\) | ||||
−0.191296 | + | 0.981532i | \(0.561269\pi\) | |||||||
\(660\) | − | 2.49651e16i | − | 0.302044i | ||||||
\(661\) | 9.47187e15i | 0.113560i | 0.998387 | + | 0.0567802i | \(0.0180834\pi\) | ||||
−0.998387 | + | 0.0567802i | \(0.981917\pi\) | |||||||
\(662\) | 1.90028e17 | 2.25771 | ||||||||
\(663\) | − | 2.27261e15i | − | 0.0267574i | ||||||
\(664\) | −3.89145e16 | + | 6.88067e16i | −0.454049 | + | 0.802828i | ||||
\(665\) | 5.82863e16 | 0.673964 | ||||||||
\(666\) | 2.13126e17i | 2.44225i | ||||||||
\(667\) | −1.11516e17 | −1.26643 | ||||||||
\(668\) | 4.65420e16 | 0.523825 | ||||||||
\(669\) | − | 8.89196e15i | − | 0.0991838i | ||||||
\(670\) | 2.97212e17i | 3.28562i | ||||||||
\(671\) | 1.39588e17 | 1.52938 | ||||||||
\(672\) | − | 2.02206e16i | − | 0.219573i | ||||||
\(673\) | −1.51920e17 | −1.63503 | −0.817515 | − | 0.575908i | \(-0.804649\pi\) | ||||
−0.817515 | + | 0.575908i | \(0.804649\pi\) | |||||||
\(674\) | −8.79294e16 | −0.937939 | ||||||||
\(675\) | −8.21043e15 | −0.0868047 | ||||||||
\(676\) | −2.34832e16 | −0.246080 | ||||||||
\(677\) | − | 4.73122e16i | − | 0.491407i | −0.969345 | − | 0.245703i | \(-0.920981\pi\) | ||
0.969345 | − | 0.245703i | \(-0.0790189\pi\) | |||||||
\(678\) | 1.79730e16i | 0.185031i | ||||||||
\(679\) | − | 2.61069e17i | − | 2.66402i | ||||||
\(680\) | 2.80027e16 | 0.283234 | ||||||||
\(681\) | −6.46238e15 | −0.0647903 | ||||||||
\(682\) | − | 2.57477e17i | − | 2.55878i | ||||||
\(683\) | − | 5.54012e16i | − | 0.545751i | −0.962049 | − | 0.272876i | \(-0.912025\pi\) | ||
0.962049 | − | 0.272876i | \(-0.0879748\pi\) | |||||||
\(684\) | − | 4.98223e16i | − | 0.486505i | ||||||
\(685\) | 1.35276e17 | 1.30941 | ||||||||
\(686\) | − | 4.08709e17i | − | 3.92166i | ||||||
\(687\) | −1.21608e16 | −0.115671 | ||||||||
\(688\) | 1.00966e16i | 0.0952016i | ||||||||
\(689\) | 1.70484e17 | 1.59356 | ||||||||
\(690\) | 1.53172e16 | 0.141933 | ||||||||
\(691\) | 1.00223e17 | 0.920656 | 0.460328 | − | 0.887749i | \(-0.347732\pi\) | ||||
0.460328 | + | 0.887749i | \(0.347732\pi\) | |||||||
\(692\) | −3.86501e16 | −0.351977 | ||||||||
\(693\) | 2.90579e17 | 2.62340 | ||||||||
\(694\) | −4.08960e16 | −0.366036 | ||||||||
\(695\) | −1.79120e17 | −1.58941 | ||||||||
\(696\) | − | 2.21467e16i | − | 0.194829i | ||||||
\(697\) | −2.07809e16 | −0.181246 | ||||||||
\(698\) | 8.51386e16i | 0.736197i | ||||||||
\(699\) | − | 5.84621e15i | − | 0.0501200i | ||||||
\(700\) | 1.32166e17 | 1.12339 | ||||||||
\(701\) | 1.50777e17 | 1.27066 | 0.635328 | − | 0.772242i | \(-0.280865\pi\) | ||||
0.635328 | + | 0.772242i | \(0.280865\pi\) | |||||||
\(702\) | −3.92159e16 | −0.327672 | ||||||||
\(703\) | − | 5.82036e16i | − | 0.482190i | ||||||
\(704\) | −2.88431e17 | −2.36922 | ||||||||
\(705\) | 1.86392e16 | 0.151807 | ||||||||
\(706\) | − | 2.45671e17i | − | 1.98393i | ||||||
\(707\) | 3.26412e17i | 2.61366i | ||||||||
\(708\) | −5.70859e15 | −0.0453241 | ||||||||
\(709\) | 1.30643e17i | 1.02851i | 0.857636 | + | 0.514257i | \(0.171932\pi\) | ||||
−0.857636 | + | 0.514257i | \(0.828068\pi\) | |||||||
\(710\) | 3.12797e17i | 2.44182i | ||||||||
\(711\) | − | 9.52220e16i | − | 0.737089i | ||||||
\(712\) | 7.60460e16 | 0.583709 | ||||||||
\(713\) | 9.66197e16 | 0.735408 | ||||||||
\(714\) | − | 1.13143e16i | − | 0.0853960i | ||||||
\(715\) | −2.10439e17 | −1.57503 | ||||||||
\(716\) | − | 1.28440e17i | − | 0.953282i | ||||||
\(717\) | − | 1.77158e16i | − | 0.130390i | ||||||
\(718\) | − | 2.39282e17i | − | 1.74648i | ||||||
\(719\) | 1.18102e17i | 0.854838i | 0.904054 | + | 0.427419i | \(0.140577\pi\) | ||||
−0.904054 | + | 0.427419i | \(0.859423\pi\) | |||||||
\(720\) | 1.53802e16i | 0.110399i | ||||||||
\(721\) | − | 8.79879e16i | − | 0.626342i | ||||||
\(722\) | − | 2.05051e17i | − | 1.44757i | ||||||
\(723\) | 1.62312e16 | 0.113637 | ||||||||
\(724\) | 1.95571e17i | 1.35792i | ||||||||
\(725\) | −1.07082e17 | −0.737373 | ||||||||
\(726\) | 2.92914e16i | 0.200042i | ||||||||
\(727\) | −5.12825e16 | −0.347346 | −0.173673 | − | 0.984803i | \(-0.555564\pi\) | ||||
−0.173673 | + | 0.984803i | \(0.555564\pi\) | |||||||
\(728\) | 2.30412e17 | 1.54781 | ||||||||
\(729\) | −1.38944e17 | −0.925710 | ||||||||
\(730\) | 3.90757e17i | 2.58208i | ||||||||
\(731\) | 3.99001e16i | 0.261499i | ||||||||
\(732\) | −2.85009e16 | −0.185265 | ||||||||
\(733\) | −2.20545e17 | −1.42192 | −0.710958 | − | 0.703235i | \(-0.751738\pi\) | ||||
−0.710958 | + | 0.703235i | \(0.751738\pi\) | |||||||
\(734\) | −1.89348e17 | −1.21083 | ||||||||
\(735\) | − | 4.86138e16i | − | 0.308344i | ||||||
\(736\) | − | 1.14533e17i | − | 0.720552i | ||||||
\(737\) | − | 4.04648e17i | − | 2.52506i | ||||||
\(738\) | 1.78168e17i | 1.10279i | ||||||||
\(739\) | −1.92698e15 | −0.0118307 | −0.00591534 | − | 0.999983i | \(-0.501883\pi\) | ||||
−0.00591534 | + | 0.999983i | \(0.501883\pi\) | |||||||
\(740\) | − | 4.69983e17i | − | 2.86215i | ||||||
\(741\) | 5.32112e15 | 0.0321436 | ||||||||
\(742\) | 8.48761e17 | 5.08583 | ||||||||
\(743\) | − | 5.93516e16i | − | 0.352776i | −0.984321 | − | 0.176388i | \(-0.943559\pi\) | ||
0.984321 | − | 0.176388i | \(-0.0564414\pi\) | |||||||
\(744\) | 1.91884e16i | 0.113136i | ||||||||
\(745\) | −1.93350e17 | −1.13085 | ||||||||
\(746\) | − | 1.73658e17i | − | 1.00754i | ||||||
\(747\) | −1.49345e17 | − | 8.44640e16i | −0.859544 | − | 0.486125i | ||||
\(748\) | −1.04453e17 | −0.596363 | ||||||||
\(749\) | − | 1.75132e17i | − | 0.991916i | ||||||
\(750\) | −2.29604e16 | −0.129006 | ||||||||
\(751\) | 1.41646e17 | 0.789522 | 0.394761 | − | 0.918784i | \(-0.370827\pi\) | ||||
0.394761 | + | 0.918784i | \(0.370827\pi\) | |||||||
\(752\) | − | 1.97340e16i | − | 0.109121i | ||||||
\(753\) | 1.16125e16i | 0.0637023i | ||||||||
\(754\) | −5.11460e17 | −2.78345 | ||||||||
\(755\) | − | 9.26549e16i | − | 0.500250i | ||||||
\(756\) | −1.19411e17 | −0.639610 | ||||||||
\(757\) | 1.17817e17 | 0.626086 | 0.313043 | − | 0.949739i | \(-0.398652\pi\) | ||||
0.313043 | + | 0.949739i | \(0.398652\pi\) | |||||||
\(758\) | 2.06685e17 | 1.08967 | ||||||||
\(759\) | −2.08540e16 | −0.109079 | ||||||||
\(760\) | 6.55659e16i | 0.340249i | ||||||||
\(761\) | 1.12418e17i | 0.578800i | 0.957208 | + | 0.289400i | \(0.0934558\pi\) | ||||
−0.957208 | + | 0.289400i | \(0.906544\pi\) | |||||||
\(762\) | 4.70389e16i | 0.240286i | ||||||||
\(763\) | 3.64568e16 | 0.184770 | ||||||||
\(764\) | −2.07422e17 | −1.04303 | ||||||||
\(765\) | 6.07799e16i | 0.303243i | ||||||||
\(766\) | 3.49968e17i | 1.73243i | ||||||||
\(767\) | 4.81195e16i | 0.236346i | ||||||||
\(768\) | 1.93191e16 | 0.0941498 | ||||||||
\(769\) | 3.08796e16i | 0.149318i | 0.997209 | + | 0.0746592i | \(0.0237869\pi\) | ||||
−0.997209 | + | 0.0746592i | \(0.976213\pi\) | |||||||
\(770\) | −1.04768e18 | −5.02671 | ||||||||
\(771\) | − | 1.06636e16i | − | 0.0507668i | ||||||
\(772\) | 6.44040e17 | 3.04235 | ||||||||
\(773\) | −1.25105e17 | −0.586405 | −0.293203 | − | 0.956050i | \(-0.594721\pi\) | ||||
−0.293203 | + | 0.956050i | \(0.594721\pi\) | |||||||
\(774\) | 3.42089e17 | 1.59109 | ||||||||
\(775\) | 9.27778e16 | 0.428187 | ||||||||
\(776\) | 2.93675e17 | 1.34492 | ||||||||
\(777\) | −6.93106e16 | −0.314973 | ||||||||
\(778\) | 1.07837e17 | 0.486284 | ||||||||
\(779\) | − | 4.86567e16i | − | 0.217730i | ||||||
\(780\) | 4.29671e16 | 0.190795 | ||||||||
\(781\) | − | 4.25867e17i | − | 1.87658i | ||||||
\(782\) | − | 6.40863e16i | − | 0.280237i | ||||||
\(783\) | 9.67482e16 | 0.419829 | ||||||||
\(784\) | −5.14692e16 | −0.221641 | ||||||||
\(785\) | 2.95030e17 | 1.26080 | ||||||||
\(786\) | − | 2.41985e16i | − | 0.102625i | ||||||
\(787\) | −3.31873e17 | −1.39677 | −0.698383 | − | 0.715725i | \(-0.746097\pi\) | ||||
−0.698383 | + | 0.715725i | \(0.746097\pi\) | |||||||
\(788\) | −2.11710e17 | −0.884268 | ||||||||
\(789\) | − | 1.23288e15i | − | 0.00511046i | ||||||
\(790\) | 3.43322e17i | 1.41234i | ||||||||
\(791\) | 4.61315e17 | 1.88338 | ||||||||
\(792\) | 3.26871e17i | 1.32442i | ||||||||
\(793\) | 2.40243e17i | 0.966078i | ||||||||
\(794\) | 9.65892e16i | 0.385483i | ||||||||
\(795\) | 5.77705e16 | 0.228825 | ||||||||
\(796\) | 2.30639e16 | 0.0906682 | ||||||||
\(797\) | − | 8.04085e16i | − | 0.313727i | −0.987620 | − | 0.156863i | \(-0.949862\pi\) | ||
0.987620 | − | 0.156863i | \(-0.0501383\pi\) | |||||||
\(798\) | 2.64914e16 | 0.102586 | ||||||||
\(799\) | − | 7.79856e16i | − | 0.299732i | ||||||
\(800\) | − | 1.09979e17i | − | 0.419538i | ||||||
\(801\) | 1.65058e17i | 0.624945i | ||||||||
\(802\) | − | 1.06285e17i | − | 0.399416i | ||||||
\(803\) | − | 5.32008e17i | − | 1.98438i | ||||||
\(804\) | 8.26203e16i | 0.305880i | ||||||||
\(805\) | − | 3.93147e17i | − | 1.44471i | ||||||
\(806\) | 4.43140e17 | 1.61633 | ||||||||
\(807\) | 5.97437e16i | 0.216297i | ||||||||
\(808\) | −3.67179e17 | −1.31950 | ||||||||
\(809\) | 7.72796e16i | 0.275660i | 0.990456 | + | 0.137830i | \(0.0440128\pi\) | ||||
−0.990456 | + | 0.137830i | \(0.955987\pi\) | |||||||
\(810\) | 5.14419e17 | 1.82141 | ||||||||
\(811\) | −1.03923e17 | −0.365248 | −0.182624 | − | 0.983183i | \(-0.558459\pi\) | ||||
−0.182624 | + | 0.983183i | \(0.558459\pi\) | |||||||
\(812\) | −1.55738e18 | −5.43324 | ||||||||
\(813\) | − | 6.39306e16i | − | 0.221394i | ||||||
\(814\) | 1.04619e18i | 3.59638i | ||||||||
\(815\) | 2.22035e17 | 0.757663 | ||||||||
\(816\) | −8.15333e14 | −0.00276181 | ||||||||
\(817\) | −9.34228e16 | −0.314138 | ||||||||
\(818\) | − | 2.32683e17i | − | 0.776685i | ||||||
\(819\) | 5.00110e17i | 1.65715i | ||||||||
\(820\) | − | 3.92894e17i | − | 1.29239i | ||||||
\(821\) | 4.67469e17i | 1.52649i | 0.646110 | + | 0.763244i | \(0.276395\pi\) | ||||
−0.646110 | + | 0.763244i | \(0.723605\pi\) | |||||||
\(822\) | 6.14835e16 | 0.199309 | ||||||||
\(823\) | 1.31783e17i | 0.424092i | 0.977260 | + | 0.212046i | \(0.0680127\pi\) | ||||
−0.977260 | + | 0.212046i | \(0.931987\pi\) | |||||||
\(824\) | 9.89771e16 | 0.316207 | ||||||||
\(825\) | −2.00248e16 | −0.0635105 | ||||||||
\(826\) | 2.39565e17i | 0.754298i | ||||||||
\(827\) | 3.87435e17i | 1.21106i | 0.795822 | + | 0.605530i | \(0.207039\pi\) | ||||
−0.795822 | + | 0.605530i | \(0.792961\pi\) | |||||||
\(828\) | −3.36057e17 | −1.04287 | ||||||||
\(829\) | − | 1.94458e17i | − | 0.599099i | −0.954081 | − | 0.299549i | \(-0.903164\pi\) | ||
0.954081 | − | 0.299549i | \(-0.0968363\pi\) | |||||||
\(830\) | 5.38463e17 | + | 3.04534e17i | 1.64698 | + | 0.931467i | ||||
\(831\) | 2.18547e16 | 0.0663648 | ||||||||
\(832\) | − | 4.96413e17i | − | 1.49659i | ||||||
\(833\) | −2.03398e17 | −0.608802 | ||||||||
\(834\) | −8.14110e16 | −0.241928 | ||||||||
\(835\) | − | 1.32941e17i | − | 0.392230i | ||||||
\(836\) | − | 2.44568e17i | − | 0.716410i | ||||||
\(837\) | −8.38247e16 | −0.243792 | ||||||||
\(838\) | − | 2.77600e17i | − | 0.801595i | ||||||
\(839\) | 6.41957e16 | 0.184049 | 0.0920247 | − | 0.995757i | \(-0.470666\pi\) | ||||
0.0920247 | + | 0.995757i | \(0.470666\pi\) | |||||||
\(840\) | 7.80779e16 | 0.222255 | ||||||||
\(841\) | 9.07990e17 | 2.56629 | ||||||||
\(842\) | −6.60774e17 | −1.85430 | ||||||||
\(843\) | − | 3.99809e16i | − | 0.111401i | ||||||
\(844\) | − | 3.29479e17i | − | 0.911535i | ||||||
\(845\) | 6.70767e16i | 0.184260i | ||||||||
\(846\) | −6.68620e17 | −1.82372 | ||||||||
\(847\) | 7.51824e17 | 2.03618 | ||||||||
\(848\) | − | 6.11637e16i | − | 0.164482i | ||||||
\(849\) | 3.21176e16i | 0.0857624i | ||||||||
\(850\) | − | 6.15381e16i | − | 0.163166i | ||||||
\(851\) | −3.92589e17 | −1.03362 | ||||||||
\(852\) | 8.69529e16i | 0.227325i | ||||||||
\(853\) | 3.91663e17 | 1.01676 | 0.508380 | − | 0.861133i | \(-0.330245\pi\) | ||||
0.508380 | + | 0.861133i | \(0.330245\pi\) | |||||||
\(854\) | 1.19606e18i | 3.08323i | ||||||||
\(855\) | −1.42311e17 | −0.364286 | ||||||||
\(856\) | 1.97005e17 | 0.500766 | ||||||||
\(857\) | −4.25240e17 | −1.07337 | −0.536685 | − | 0.843783i | \(-0.680323\pi\) | ||||
−0.536685 | + | 0.843783i | \(0.680323\pi\) | |||||||
\(858\) | −9.56457e16 | −0.239741 | ||||||||
\(859\) | 2.19889e17 | 0.547325 | 0.273663 | − | 0.961826i | \(-0.411765\pi\) | ||||
0.273663 | + | 0.961826i | \(0.411765\pi\) | |||||||
\(860\) | −7.54371e17 | −1.86464 | ||||||||
\(861\) | −5.79419e16 | −0.142224 | ||||||||
\(862\) | 7.02394e17i | 1.71213i | ||||||||
\(863\) | 8.05630e16 | 0.195016 | 0.0975082 | − | 0.995235i | \(-0.468913\pi\) | ||||
0.0975082 | + | 0.995235i | \(0.468913\pi\) | |||||||
\(864\) | 9.93662e16i | 0.238867i | ||||||||
\(865\) | 1.10399e17i | 0.263554i | ||||||||
\(866\) | −9.30870e17 | −2.20689 | ||||||||
\(867\) | 4.42868e16 | 0.104270 | ||||||||
\(868\) | 1.34935e18 | 3.15505 | ||||||||
\(869\) | − | 4.67426e17i | − | 1.08541i | ||||||
\(870\) | −1.73314e17 | −0.399686 | ||||||||
\(871\) | 6.96432e17 | 1.59503 | ||||||||
\(872\) | 4.10101e16i | 0.0932807i | ||||||||
\(873\) | 6.37424e17i | 1.43993i | ||||||||
\(874\) | 1.50053e17 | 0.336648 | ||||||||
\(875\) | 5.89325e17i | 1.31313i | ||||||||
\(876\) | 1.08625e17i | 0.240383i | ||||||||
\(877\) | − | 1.48669e17i | − | 0.326754i | −0.986564 | − | 0.163377i | \(-0.947761\pi\) | ||
0.986564 | − | 0.163377i | \(-0.0522388\pi\) | |||||||
\(878\) | −4.24444e17 | −0.926516 | ||||||||
\(879\) | 1.49733e16 | 0.0324627 | ||||||||
\(880\) | 7.54982e16i | 0.162570i | ||||||||
\(881\) | −7.44384e17 | −1.59199 | −0.795997 | − | 0.605301i | \(-0.793053\pi\) | ||||
−0.795997 | + | 0.605301i | \(0.793053\pi\) | |||||||
\(882\) | 1.74386e18i | 3.70425i | ||||||||
\(883\) | 2.88314e16i | 0.0608278i | 0.999537 | + | 0.0304139i | \(0.00968253\pi\) | ||||
−0.999537 | + | 0.0304139i | \(0.990317\pi\) | |||||||
\(884\) | − | 1.79772e17i | − | 0.376711i | ||||||
\(885\) | 1.63059e16i | 0.0339378i | ||||||||
\(886\) | 3.30870e17i | 0.683998i | ||||||||
\(887\) | − | 1.49033e17i | − | 0.306013i | −0.988225 | − | 0.153006i | \(-0.951105\pi\) | ||
0.988225 | − | 0.153006i | \(-0.0488955\pi\) | |||||||
\(888\) | − | 7.79671e16i | − | 0.159013i | ||||||
\(889\) | 1.20735e18 | 2.44581 | ||||||||
\(890\) | − | 5.95115e17i | − | 1.19746i | ||||||
\(891\) | −7.00371e17 | −1.39979 | ||||||||
\(892\) | − | 7.03388e17i | − | 1.39639i | ||||||
\(893\) | 1.82597e17 | 0.360068 | ||||||||
\(894\) | −8.78784e16 | −0.172130 | ||||||||
\(895\) | −3.66872e17 | −0.713800 | ||||||||
\(896\) | − | 1.45571e18i | − | 2.81337i | ||||||
\(897\) | − | 3.58915e16i | − | 0.0689029i | ||||||
\(898\) | 6.26308e17 | 1.19435 | ||||||||
\(899\) | −1.09325e18 | −2.07092 | ||||||||
\(900\) | −3.22694e17 | −0.607206 | ||||||||
\(901\) | − | 2.41709e17i | − | 0.451798i | ||||||
\(902\) | 8.74591e17i | 1.62392i | ||||||||
\(903\) | 1.11251e17i | 0.205199i | ||||||||
\(904\) | 5.18930e17i | 0.950821i | ||||||||
\(905\) | 5.58623e17 | 1.01678 | ||||||||
\(906\) | − | 4.21122e16i | − | 0.0761445i | ||||||
\(907\) | 8.92521e15 | 0.0160315 | 0.00801576 | − | 0.999968i | \(-0.497448\pi\) | ||||
0.00801576 | + | 0.999968i | \(0.497448\pi\) | |||||||
\(908\) | −5.11199e17 | −0.912168 | ||||||||
\(909\) | − | 7.96964e17i | − | 1.41272i | ||||||
\(910\) | − | 1.80314e18i | − | 3.17528i | ||||||
\(911\) | −1.45200e17 | −0.254013 | −0.127006 | − | 0.991902i | \(-0.540537\pi\) | ||||
−0.127006 | + | 0.991902i | \(0.540537\pi\) | |||||||
\(912\) | − | 1.90903e15i | − | 0.00331776i | ||||||
\(913\) | −7.33106e17 | − | 4.14617e17i | −1.26573 | − | 0.715851i | ||||
\(914\) | −9.95068e17 | −1.70677 | ||||||||
\(915\) | 8.14093e16i | 0.138723i | ||||||||
\(916\) | −9.61970e17 | −1.62850 | ||||||||
\(917\) | −6.21105e17 | −1.04460 | ||||||||
\(918\) | 5.55996e16i | 0.0929000i | ||||||||
\(919\) | 6.56309e17i | 1.08947i | 0.838608 | + | 0.544735i | \(0.183370\pi\) | ||||
−0.838608 | + | 0.544735i | \(0.816630\pi\) | |||||||
\(920\) | 4.42249e17 | 0.729356 | ||||||||
\(921\) | 1.23894e16i | 0.0202998i | ||||||||
\(922\) | −7.45838e17 | −1.21411 | ||||||||
\(923\) | 7.32953e17 | 1.18540 | ||||||||
\(924\) | −2.91239e17 | −0.467969 | ||||||||
\(925\) | −3.76979e17 | −0.601820 | ||||||||
\(926\) | − | 8.24647e17i | − | 1.30798i | ||||||
\(927\) | 2.14830e17i | 0.338545i | ||||||||
\(928\) | 1.29595e18i | 2.02908i | ||||||||
\(929\) | 5.41171e17 | 0.841860 | 0.420930 | − | 0.907093i | \(-0.361704\pi\) | ||||
0.420930 | + | 0.907093i | \(0.361704\pi\) | |||||||
\(930\) | 1.50163e17 | 0.232095 | ||||||||
\(931\) | − | 4.76239e17i | − | 0.731353i | ||||||
\(932\) | − | 4.62457e17i | − | 0.705629i | ||||||
\(933\) | 2.69492e16i | 0.0408560i | ||||||||
\(934\) | −1.18862e17 | −0.179045 | ||||||||
\(935\) | 2.98356e17i | 0.446546i | ||||||||
\(936\) | −5.62571e17 | −0.836609 | ||||||||
\(937\) | − | 4.20352e17i | − | 0.621120i | −0.950554 | − | 0.310560i | \(-0.899483\pi\) | ||
0.950554 | − | 0.310560i | \(-0.100517\pi\) | |||||||
\(938\) | 3.46722e18 | 5.09054 | ||||||||
\(939\) | 2.63015e16 | 0.0383695 | ||||||||
\(940\) | 1.47443e18 | 2.13726 | ||||||||
\(941\) | −5.20024e17 | −0.749006 | −0.374503 | − | 0.927226i | \(-0.622187\pi\) | ||||
−0.374503 | + | 0.927226i | \(0.622187\pi\) | |||||||
\(942\) | 1.34093e17 | 0.191911 | ||||||||
\(943\) | −3.28195e17 | −0.466725 | ||||||||
\(944\) | 1.72636e16 | 0.0243949 | ||||||||
\(945\) | 3.41084e17i | 0.478928i | ||||||||
\(946\) | 1.67925e18 | 2.34298 | ||||||||
\(947\) | − | 8.76164e17i | − | 1.21475i | −0.794417 | − | 0.607373i | \(-0.792223\pi\) | ||
0.794417 | − | 0.607373i | \(-0.207777\pi\) | |||||||
\(948\) | 9.54382e16i | 0.131484i | ||||||||
\(949\) | 9.15630e17 | 1.25350 | ||||||||
\(950\) | 1.44086e17 | 0.196011 | ||||||||
\(951\) | −2.52100e16 | −0.0340793 | ||||||||
\(952\) | − | 3.26674e17i | − | 0.438826i | ||||||
\(953\) | −4.66013e17 | −0.622072 | −0.311036 | − | 0.950398i | \(-0.600676\pi\) | ||||
−0.311036 | + | 0.950398i | \(0.600676\pi\) | |||||||
\(954\) | −2.07233e18 | −2.74896 | ||||||||
\(955\) | 5.92475e17i | 0.780998i | ||||||||
\(956\) | − | 1.40138e18i | − | 1.83573i | ||||||
\(957\) | 2.35964e17 | 0.307167 | ||||||||
\(958\) | − | 1.59461e18i | − | 2.06282i | ||||||
\(959\) | − | 1.57810e18i | − | 2.02872i | ||||||
\(960\) | − | 1.68216e17i | − | 0.214901i | ||||||
\(961\) | 1.59555e17 | 0.202568 | ||||||||
\(962\) | −1.80058e18 | −2.27176 | ||||||||
\(963\) | 4.27601e17i | 0.536143i | ||||||||
\(964\) | 1.28395e18 | 1.59987 | ||||||||
\(965\) | − | 1.83962e18i | − | 2.27805i | ||||||
\(966\) | − | 1.78687e17i | − | 0.219903i | ||||||
\(967\) | − | 1.04397e18i | − | 1.27682i | −0.769697 | − | 0.638409i | \(-0.779593\pi\) | ||
0.769697 | − | 0.638409i | \(-0.220407\pi\) | |||||||
\(968\) | 8.45723e17i | 1.02796i | ||||||||
\(969\) | − | 7.54419e15i | − | 0.00911318i | ||||||
\(970\) | − | 2.29822e18i | − | 2.75907i | ||||||
\(971\) | 1.35130e18i | 1.61227i | 0.591733 | + | 0.806134i | \(0.298444\pi\) | ||||
−0.591733 | + | 0.806134i | \(0.701556\pi\) | |||||||
\(972\) | 4.38248e17 | 0.519664 | ||||||||
\(973\) | 2.08958e18i | 2.46253i | ||||||||
\(974\) | −5.39466e17 | −0.631845 | ||||||||
\(975\) | − | 3.44644e16i | − | 0.0401183i | ||||||
\(976\) | 8.61909e16 | 0.0997155 | ||||||||
\(977\) | 6.44626e17 | 0.741209 | 0.370604 | − | 0.928791i | \(-0.379151\pi\) | ||||
0.370604 | + | 0.928791i | \(0.379151\pi\) | |||||||
\(978\) | 1.00916e17 | 0.115326 | ||||||||
\(979\) | 8.10237e17i | 0.920272i | ||||||||
\(980\) | − | 3.84554e18i | − | 4.34111i | ||||||
\(981\) | −8.90125e16 | −0.0998704 | ||||||||
\(982\) | −4.74259e17 | −0.528867 | ||||||||
\(983\) | −5.46795e17 | −0.606043 | −0.303022 | − | 0.952984i | \(-0.597995\pi\) | ||||
−0.303022 | + | 0.952984i | \(0.597995\pi\) | |||||||
\(984\) | − | 6.51785e16i | − | 0.0718016i | ||||||
\(985\) | 6.04723e17i | 0.662123i | ||||||||
\(986\) | 7.25138e17i | 0.789150i | ||||||||
\(987\) | − | 2.17442e17i | − | 0.235201i | ||||||
\(988\) | 4.20921e17 | 0.452542 | ||||||||
\(989\) | 6.30146e17i | 0.673385i | ||||||||
\(990\) | 2.55800e18 | 2.71700 | ||||||||
\(991\) | 1.26745e17 | 0.133810 | 0.0669049 | − | 0.997759i | \(-0.478688\pi\) | ||||
0.0669049 | + | 0.997759i | \(0.478688\pi\) | |||||||
\(992\) | − | 1.12284e18i | − | 1.17828i | ||||||
\(993\) | − | 1.50887e17i | − | 0.157383i | ||||||
\(994\) | 3.64903e18 | 3.78320 | ||||||||
\(995\) | − | 6.58792e16i | − | 0.0678906i | ||||||
\(996\) | 1.49684e17 | + | 8.46558e16i | 0.153328 | + | 0.0867163i | ||||
\(997\) | 1.49108e17 | 0.151820 | 0.0759102 | − | 0.997115i | \(-0.475814\pi\) | ||||
0.0759102 | + | 0.997115i | \(0.475814\pi\) | |||||||
\(998\) | 1.95688e18i | 1.98053i | ||||||||
\(999\) | 3.40600e17 | 0.342651 |
(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 | 83.13.b.c.82.11 | ✓ | 80 | |
83.82 | odd | 2 | inner | 83.13.b.c.82.70 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
83.13.b.c.82.11 | ✓ | 80 | 1.1 | even | 1 | trivial | |
83.13.b.c.82.70 | yes | 80 | 83.82 | odd | 2 | inner |