Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.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: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.9 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.26 |
$q$-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 \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 41.1797i | − | 1.28687i | −0.765503 | − | 0.643433i | \(-0.777510\pi\) | ||
0.765503 | − | 0.643433i | \(-0.222490\pi\) | |||||||
\(3\) | − | 18.8325i | − | 0.0775000i | −0.999249 | − | 0.0387500i | \(-0.987662\pi\) | ||
0.999249 | − | 0.0387500i | \(-0.0123376\pi\) | |||||||
\(4\) | −671.767 | −0.656022 | ||||||||
\(5\) | 4211.22i | 1.34759i | 0.738918 | + | 0.673796i | \(0.235337\pi\) | ||||
−0.738918 | + | 0.673796i | \(0.764663\pi\) | |||||||
\(6\) | −775.516 | −0.0997320 | ||||||||
\(7\) | − | 20378.0i | − | 1.21247i | −0.795285 | − | 0.606236i | \(-0.792679\pi\) | ||
0.795285 | − | 0.606236i | \(-0.207321\pi\) | |||||||
\(8\) | − | 14504.9i | − | 0.442653i | ||||||
\(9\) | 58694.3 | 0.993994 | ||||||||
\(10\) | 173417. | 1.73417 | ||||||||
\(11\) | −306949. | −1.90591 | −0.952956 | − | 0.303110i | \(-0.901975\pi\) | ||||
−0.952956 | + | 0.303110i | \(0.901975\pi\) | |||||||
\(12\) | 12651.0i | 0.0508417i | ||||||||
\(13\) | 198968. | 0.535878 | 0.267939 | − | 0.963436i | \(-0.413657\pi\) | ||||
0.267939 | + | 0.963436i | \(0.413657\pi\) | |||||||
\(14\) | −839160. | −1.56029 | ||||||||
\(15\) | 79307.8 | 0.104438 | ||||||||
\(16\) | −1.28519e6 | −1.22566 | ||||||||
\(17\) | −2.08922e6 | −1.47143 | −0.735713 | − | 0.677293i | \(-0.763153\pi\) | ||||
−0.735713 | + | 0.677293i | \(0.763153\pi\) | |||||||
\(18\) | − | 2.41701e6i | − | 1.27914i | ||||||
\(19\) | 2.97711e6i | 1.20234i | 0.799121 | + | 0.601170i | \(0.205298\pi\) | ||||
−0.799121 | + | 0.601170i | \(0.794702\pi\) | |||||||
\(20\) | − | 2.82896e6i | − | 0.884050i | ||||||
\(21\) | −383769. | −0.0939665 | ||||||||
\(22\) | 1.26401e7i | 2.45265i | ||||||||
\(23\) | 1.17271e6 | 0.182201 | 0.0911003 | − | 0.995842i | \(-0.470962\pi\) | ||||
0.0911003 | + | 0.995842i | \(0.470962\pi\) | |||||||
\(24\) | −273163. | −0.0343056 | ||||||||
\(25\) | −7.96877e6 | −0.816002 | ||||||||
\(26\) | − | 8.19343e6i | − | 0.689603i | ||||||
\(27\) | − | 2.21740e6i | − | 0.154534i | ||||||
\(28\) | 1.36893e7i | 0.795408i | ||||||||
\(29\) | − | 2.43453e7i | − | 1.18693i | −0.804860 | − | 0.593464i | \(-0.797760\pi\) | ||
0.804860 | − | 0.593464i | \(-0.202240\pi\) | |||||||
\(30\) | − | 3.26587e6i | − | 0.134398i | ||||||
\(31\) | −3.70189e7 | −1.29305 | −0.646525 | − | 0.762893i | \(-0.723778\pi\) | ||||
−0.646525 | + | 0.762893i | \(0.723778\pi\) | |||||||
\(32\) | 3.80709e7i | 1.13460i | ||||||||
\(33\) | 5.78061e6i | 0.147708i | ||||||||
\(34\) | 8.60332e7i | 1.89353i | ||||||||
\(35\) | 8.58163e7 | 1.63392 | ||||||||
\(36\) | −3.94289e7 | −0.652082 | ||||||||
\(37\) | 7.72003e7i | 1.11330i | 0.830749 | + | 0.556648i | \(0.187913\pi\) | ||||
−0.830749 | + | 0.556648i | \(0.812087\pi\) | |||||||
\(38\) | 1.22597e8 | 1.54725 | ||||||||
\(39\) | − | 3.74706e6i | − | 0.0415305i | ||||||
\(40\) | 6.10832e7 | 0.596516 | ||||||||
\(41\) | −6.69942e7 | −0.578253 | −0.289127 | − | 0.957291i | \(-0.593365\pi\) | ||||
−0.289127 | + | 0.957291i | \(0.593365\pi\) | |||||||
\(42\) | 1.58035e7i | 0.120922i | ||||||||
\(43\) | 2.69450e7 | + | 1.44518e8i | 0.183289 | + | 0.983059i | ||||
\(44\) | 2.06198e8 | 1.25032 | ||||||||
\(45\) | 2.47175e8i | 1.33950i | ||||||||
\(46\) | − | 4.82916e7i | − | 0.234468i | ||||||
\(47\) | −4.29292e8 | −1.87182 | −0.935909 | − | 0.352242i | \(-0.885420\pi\) | ||||
−0.935909 | + | 0.352242i | \(0.885420\pi\) | |||||||
\(48\) | 2.42034e7i | 0.0949884i | ||||||||
\(49\) | −1.32788e8 | −0.470086 | ||||||||
\(50\) | 3.28152e8i | 1.05009i | ||||||||
\(51\) | 3.93451e7i | 0.114036i | ||||||||
\(52\) | −1.33660e8 | −0.351548 | ||||||||
\(53\) | 2.00012e8 | 0.478275 | 0.239137 | − | 0.970986i | \(-0.423135\pi\) | ||||
0.239137 | + | 0.970986i | \(0.423135\pi\) | |||||||
\(54\) | −9.13119e7 | −0.198865 | ||||||||
\(55\) | − | 1.29263e9i | − | 2.56839i | ||||||
\(56\) | −2.95580e8 | −0.536704 | ||||||||
\(57\) | 5.60664e7 | 0.0931813 | ||||||||
\(58\) | −1.00253e9 | −1.52742 | ||||||||
\(59\) | 3.24891e8 | 0.454441 | 0.227221 | − | 0.973843i | \(-0.427036\pi\) | ||||
0.227221 | + | 0.973843i | \(0.427036\pi\) | |||||||
\(60\) | −5.32764e7 | −0.0685138 | ||||||||
\(61\) | 8.68845e8i | 1.02871i | 0.857577 | + | 0.514355i | \(0.171969\pi\) | ||||
−0.857577 | + | 0.514355i | \(0.828031\pi\) | |||||||
\(62\) | 1.52443e9i | 1.66398i | ||||||||
\(63\) | − | 1.19607e9i | − | 1.20519i | ||||||
\(64\) | 2.51710e8 | 0.234423 | ||||||||
\(65\) | 8.37897e8i | 0.722144i | ||||||||
\(66\) | 2.38044e8 | 0.190080 | ||||||||
\(67\) | −1.36258e9 | −1.00923 | −0.504614 | − | 0.863345i | \(-0.668365\pi\) | ||||
−0.504614 | + | 0.863345i | \(0.668365\pi\) | |||||||
\(68\) | 1.40347e9 | 0.965288 | ||||||||
\(69\) | − | 2.20850e7i | − | 0.0141205i | ||||||
\(70\) | − | 3.53389e9i | − | 2.10263i | ||||||
\(71\) | − | 2.65191e9i | − | 1.46983i | −0.678159 | − | 0.734916i | \(-0.737222\pi\) | ||
0.678159 | − | 0.734916i | \(-0.262778\pi\) | |||||||
\(72\) | − | 8.51353e8i | − | 0.439995i | ||||||
\(73\) | 1.07991e7i | 0.00520922i | 0.999997 | + | 0.00260461i | \(0.000829074\pi\) | ||||
−0.999997 | + | 0.00260461i | \(0.999171\pi\) | |||||||
\(74\) | 3.17909e9 | 1.43266 | ||||||||
\(75\) | 1.50072e8i | 0.0632402i | ||||||||
\(76\) | − | 1.99992e9i | − | 0.788761i | ||||||
\(77\) | 6.25501e9i | 2.31086i | ||||||||
\(78\) | −1.54303e8 | −0.0534442 | ||||||||
\(79\) | 8.01396e8 | 0.260442 | 0.130221 | − | 0.991485i | \(-0.458431\pi\) | ||||
0.130221 | + | 0.991485i | \(0.458431\pi\) | |||||||
\(80\) | − | 5.41224e9i | − | 1.65168i | ||||||
\(81\) | 3.42408e9 | 0.982017 | ||||||||
\(82\) | 2.75880e9i | 0.744134i | ||||||||
\(83\) | −5.22410e9 | −1.32624 | −0.663118 | − | 0.748515i | \(-0.730767\pi\) | ||||
−0.663118 | + | 0.748515i | \(0.730767\pi\) | |||||||
\(84\) | 2.57803e8 | 0.0616441 | ||||||||
\(85\) | − | 8.79815e9i | − | 1.98288i | ||||||
\(86\) | 5.95121e9 | − | 1.10959e9i | 1.26506 | − | 0.235868i | ||||
\(87\) | −4.58482e8 | −0.0919869 | ||||||||
\(88\) | 4.45225e9i | 0.843658i | ||||||||
\(89\) | − | 6.11548e9i | − | 1.09517i | −0.836751 | − | 0.547584i | \(-0.815548\pi\) | ||
0.836751 | − | 0.547584i | \(-0.184452\pi\) | |||||||
\(90\) | 1.01786e10 | 1.72375 | ||||||||
\(91\) | − | 4.05456e9i | − | 0.649737i | ||||||
\(92\) | −7.87784e8 | −0.119528 | ||||||||
\(93\) | 6.97159e8i | 0.100211i | ||||||||
\(94\) | 1.76781e10i | 2.40878i | ||||||||
\(95\) | −1.25373e10 | −1.62026 | ||||||||
\(96\) | 7.16971e8 | 0.0879316 | ||||||||
\(97\) | 3.80330e8 | 0.0442897 | 0.0221448 | − | 0.999755i | \(-0.492951\pi\) | ||||
0.0221448 | + | 0.999755i | \(0.492951\pi\) | |||||||
\(98\) | 5.46816e9i | 0.604938i | ||||||||
\(99\) | −1.80162e10 | −1.89446 | ||||||||
\(100\) | 5.35316e9 | 0.535316 | ||||||||
\(101\) | −1.00808e9 | −0.0959149 | −0.0479575 | − | 0.998849i | \(-0.515271\pi\) | ||||
−0.0479575 | + | 0.998849i | \(0.515271\pi\) | |||||||
\(102\) | 1.62022e9 | 0.146748 | ||||||||
\(103\) | −7.72985e9 | −0.666784 | −0.333392 | − | 0.942788i | \(-0.608193\pi\) | ||||
−0.333392 | + | 0.942788i | \(0.608193\pi\) | |||||||
\(104\) | − | 2.88600e9i | − | 0.237208i | ||||||
\(105\) | − | 1.61614e9i | − | 0.126628i | ||||||
\(106\) | − | 8.23644e9i | − | 0.615475i | ||||||
\(107\) | 1.71519e10 | 1.22291 | 0.611453 | − | 0.791281i | \(-0.290585\pi\) | ||||
0.611453 | + | 0.791281i | \(0.290585\pi\) | |||||||
\(108\) | 1.48958e9i | 0.101378i | ||||||||
\(109\) | −1.06240e10 | −0.690490 | −0.345245 | − | 0.938513i | \(-0.612204\pi\) | ||||
−0.345245 | + | 0.938513i | \(0.612204\pi\) | |||||||
\(110\) | −5.32301e10 | −3.30517 | ||||||||
\(111\) | 1.45387e9 | 0.0862804 | ||||||||
\(112\) | 2.61897e10i | 1.48607i | ||||||||
\(113\) | − | 1.02518e10i | − | 0.556426i | −0.960519 | − | 0.278213i | \(-0.910258\pi\) | ||
0.960519 | − | 0.278213i | \(-0.0897420\pi\) | |||||||
\(114\) | − | 2.30880e9i | − | 0.119912i | ||||||
\(115\) | 4.93852e9i | 0.245532i | ||||||||
\(116\) | 1.63543e10i | 0.778651i | ||||||||
\(117\) | 1.16783e10 | 0.532659 | ||||||||
\(118\) | − | 1.33789e10i | − | 0.584804i | ||||||
\(119\) | 4.25740e10i | 1.78406i | ||||||||
\(120\) | − | 1.15035e9i | − | 0.0462299i | ||||||
\(121\) | 6.82802e10 | 2.63250 | ||||||||
\(122\) | 3.57788e10 | 1.32381 | ||||||||
\(123\) | 1.26167e9i | 0.0448146i | ||||||||
\(124\) | 2.48681e10 | 0.848269 | ||||||||
\(125\) | 7.56694e9i | 0.247953i | ||||||||
\(126\) | −4.92539e10 | −1.55092 | ||||||||
\(127\) | −4.52404e10 | −1.36933 | −0.684664 | − | 0.728858i | \(-0.740051\pi\) | ||||
−0.684664 | + | 0.728858i | \(0.740051\pi\) | |||||||
\(128\) | 2.86193e10i | 0.832931i | ||||||||
\(129\) | 2.72163e9 | − | 5.07441e8i | 0.0761871 | − | 0.0142049i | ||||
\(130\) | 3.45044e10 | 0.929303 | ||||||||
\(131\) | − | 2.50465e10i | − | 0.649218i | −0.945848 | − | 0.324609i | \(-0.894767\pi\) | ||
0.945848 | − | 0.324609i | \(-0.105233\pi\) | |||||||
\(132\) | − | 3.88322e9i | − | 0.0968998i | ||||||
\(133\) | 6.06676e10 | 1.45780 | ||||||||
\(134\) | 5.61108e10i | 1.29874i | ||||||||
\(135\) | 9.33797e9 | 0.208249 | ||||||||
\(136\) | 3.03038e10i | 0.651332i | ||||||||
\(137\) | − | 9.00858e10i | − | 1.86661i | −0.359086 | − | 0.933304i | \(-0.616912\pi\) | ||
0.359086 | − | 0.933304i | \(-0.383088\pi\) | |||||||
\(138\) | −9.09452e8 | −0.0181712 | ||||||||
\(139\) | 5.76790e10 | 1.11159 | 0.555794 | − | 0.831320i | \(-0.312414\pi\) | ||||
0.555794 | + | 0.831320i | \(0.312414\pi\) | |||||||
\(140\) | −5.76485e10 | −1.07188 | ||||||||
\(141\) | 8.08464e9i | 0.145066i | ||||||||
\(142\) | −1.09205e11 | −1.89147 | ||||||||
\(143\) | −6.10729e10 | −1.02134 | ||||||||
\(144\) | −7.54336e10 | −1.21830 | ||||||||
\(145\) | 1.02523e11 | 1.59949 | ||||||||
\(146\) | 4.44703e8 | 0.00670356 | ||||||||
\(147\) | 2.50072e9i | 0.0364317i | ||||||||
\(148\) | − | 5.18606e10i | − | 0.730347i | ||||||
\(149\) | − | 2.29987e10i | − | 0.313164i | −0.987665 | − | 0.156582i | \(-0.949952\pi\) | ||
0.987665 | − | 0.156582i | \(-0.0500476\pi\) | |||||||
\(150\) | 6.17991e9 | 0.0813816 | ||||||||
\(151\) | − | 9.49837e10i | − | 1.20994i | −0.796248 | − | 0.604971i | \(-0.793185\pi\) | ||
0.796248 | − | 0.604971i | \(-0.206815\pi\) | |||||||
\(152\) | 4.31826e10 | 0.532219 | ||||||||
\(153\) | −1.22625e11 | −1.46259 | ||||||||
\(154\) | 2.57579e11 | 2.97377 | ||||||||
\(155\) | − | 1.55895e11i | − | 1.74250i | ||||||
\(156\) | 2.51715e9i | 0.0272449i | ||||||||
\(157\) | 1.21491e11i | 1.27364i | 0.771012 | + | 0.636820i | \(0.219751\pi\) | ||||
−0.771012 | + | 0.636820i | \(0.780249\pi\) | |||||||
\(158\) | − | 3.30012e10i | − | 0.335154i | ||||||
\(159\) | − | 3.76673e9i | − | 0.0370663i | ||||||
\(160\) | −1.60325e11 | −1.52898 | ||||||||
\(161\) | − | 2.38974e10i | − | 0.220913i | ||||||
\(162\) | − | 1.41003e11i | − | 1.26372i | ||||||
\(163\) | − | 1.84974e11i | − | 1.60758i | −0.594912 | − | 0.803791i | \(-0.702813\pi\) | ||
0.594912 | − | 0.803791i | \(-0.297187\pi\) | |||||||
\(164\) | 4.50045e10 | 0.379347 | ||||||||
\(165\) | −2.43435e10 | −0.199050 | ||||||||
\(166\) | 2.15127e11i | 1.70669i | ||||||||
\(167\) | 8.11760e10 | 0.624950 | 0.312475 | − | 0.949926i | \(-0.398842\pi\) | ||||
0.312475 | + | 0.949926i | \(0.398842\pi\) | |||||||
\(168\) | 5.56651e9i | 0.0415946i | ||||||||
\(169\) | −9.82703e10 | −0.712835 | ||||||||
\(170\) | −3.62305e11 | −2.55170 | ||||||||
\(171\) | 1.74740e11i | 1.19512i | ||||||||
\(172\) | −1.81007e10 | − | 9.70824e10i | −0.120241 | − | 0.644908i | ||||
\(173\) | 1.35005e10 | 0.0871203 | 0.0435602 | − | 0.999051i | \(-0.486130\pi\) | ||||
0.0435602 | + | 0.999051i | \(0.486130\pi\) | |||||||
\(174\) | 1.88802e10i | 0.118375i | ||||||||
\(175\) | 1.62388e11i | 0.989380i | ||||||||
\(176\) | 3.94489e11 | 2.33599 | ||||||||
\(177\) | − | 6.11851e9i | − | 0.0352192i | ||||||
\(178\) | −2.51834e11 | −1.40933 | ||||||||
\(179\) | − | 2.77340e11i | − | 1.50920i | −0.656185 | − | 0.754600i | \(-0.727831\pi\) | ||
0.656185 | − | 0.754600i | \(-0.272169\pi\) | |||||||
\(180\) | − | 1.66044e11i | − | 0.878740i | ||||||
\(181\) | 1.47844e11 | 0.761044 | 0.380522 | − | 0.924772i | \(-0.375744\pi\) | ||||
0.380522 | + | 0.924772i | \(0.375744\pi\) | |||||||
\(182\) | −1.66966e11 | −0.836123 | ||||||||
\(183\) | 1.63625e10 | 0.0797251 | ||||||||
\(184\) | − | 1.70099e10i | − | 0.0806517i | ||||||
\(185\) | −3.25108e11 | −1.50027 | ||||||||
\(186\) | 2.87088e10 | 0.128958 | ||||||||
\(187\) | 6.41283e11 | 2.80441 | ||||||||
\(188\) | 2.88384e11 | 1.22795 | ||||||||
\(189\) | −4.51862e10 | −0.187369 | ||||||||
\(190\) | 5.16281e11i | 2.08506i | ||||||||
\(191\) | − | 2.41346e10i | − | 0.0949452i | −0.998873 | − | 0.0474726i | \(-0.984883\pi\) | ||
0.998873 | − | 0.0474726i | \(-0.0151167\pi\) | |||||||
\(192\) | − | 4.74032e9i | − | 0.0181678i | ||||||
\(193\) | 3.27870e11 | 1.22438 | 0.612188 | − | 0.790712i | \(-0.290290\pi\) | ||||
0.612188 | + | 0.790712i | \(0.290290\pi\) | |||||||
\(194\) | − | 1.56619e10i | − | 0.0569948i | ||||||
\(195\) | 1.57797e10 | 0.0559662 | ||||||||
\(196\) | 8.92024e10 | 0.308387 | ||||||||
\(197\) | 2.22343e11 | 0.749362 | 0.374681 | − | 0.927154i | \(-0.377752\pi\) | ||||
0.374681 | + | 0.927154i | \(0.377752\pi\) | |||||||
\(198\) | 7.41900e11i | 2.43792i | ||||||||
\(199\) | 8.68831e10i | 0.278401i | 0.990264 | + | 0.139200i | \(0.0444532\pi\) | ||||
−0.990264 | + | 0.139200i | \(0.955547\pi\) | |||||||
\(200\) | 1.15586e11i | 0.361206i | ||||||||
\(201\) | 2.56609e10i | 0.0782152i | ||||||||
\(202\) | 4.15122e10i | 0.123430i | ||||||||
\(203\) | −4.96108e11 | −1.43912 | ||||||||
\(204\) | − | 2.64308e10i | − | 0.0748098i | ||||||
\(205\) | − | 2.82128e11i | − | 0.779249i | ||||||
\(206\) | 3.18313e11i | 0.858060i | ||||||||
\(207\) | 6.88312e10 | 0.181106 | ||||||||
\(208\) | −2.55712e11 | −0.656803 | ||||||||
\(209\) | − | 9.13821e11i | − | 2.29155i | ||||||
\(210\) | −6.65519e10 | −0.162954 | ||||||||
\(211\) | 6.37697e10i | 0.152476i | 0.997090 | + | 0.0762381i | \(0.0242909\pi\) | ||||
−0.997090 | + | 0.0762381i | \(0.975709\pi\) | |||||||
\(212\) | −1.34362e11 | −0.313759 | ||||||||
\(213\) | −4.99421e10 | −0.113912 | ||||||||
\(214\) | − | 7.06309e11i | − | 1.57372i | ||||||
\(215\) | −6.08598e11 | + | 1.13471e11i | −1.32476 | + | 0.246998i | ||||
\(216\) | −3.21631e10 | −0.0684052 | ||||||||
\(217\) | 7.54372e11i | 1.56779i | ||||||||
\(218\) | 4.37495e11i | 0.888568i | ||||||||
\(219\) | 2.03374e8 | 0.000403714 | ||||||||
\(220\) | 8.68346e11i | 1.68492i | ||||||||
\(221\) | −4.15686e11 | −0.788505 | ||||||||
\(222\) | − | 5.98701e10i | − | 0.111031i | ||||||
\(223\) | 2.01118e11i | 0.364692i | 0.983234 | + | 0.182346i | \(0.0583691\pi\) | ||||
−0.983234 | + | 0.182346i | \(0.941631\pi\) | |||||||
\(224\) | 7.75810e11 | 1.37567 | ||||||||
\(225\) | −4.67722e11 | −0.811101 | ||||||||
\(226\) | −4.22165e11 | −0.716045 | ||||||||
\(227\) | 7.86063e11i | 1.30415i | 0.758154 | + | 0.652076i | \(0.226102\pi\) | ||||
−0.758154 | + | 0.652076i | \(0.773898\pi\) | |||||||
\(228\) | −3.76636e10 | −0.0611290 | ||||||||
\(229\) | −6.66086e11 | −1.05768 | −0.528839 | − | 0.848722i | \(-0.677372\pi\) | ||||
−0.528839 | + | 0.848722i | \(0.677372\pi\) | |||||||
\(230\) | 2.03367e11 | 0.315966 | ||||||||
\(231\) | 1.17797e11 | 0.179092 | ||||||||
\(232\) | −3.53125e11 | −0.525398 | ||||||||
\(233\) | 6.74973e11i | 0.982895i | 0.870907 | + | 0.491447i | \(0.163532\pi\) | ||||
−0.870907 | + | 0.491447i | \(0.836468\pi\) | |||||||
\(234\) | − | 4.80908e11i | − | 0.685461i | ||||||
\(235\) | − | 1.80784e12i | − | 2.52245i | ||||||
\(236\) | −2.18251e11 | −0.298123 | ||||||||
\(237\) | − | 1.50923e10i | − | 0.0201843i | ||||||
\(238\) | 1.75319e12 | 2.29585 | ||||||||
\(239\) | 2.80487e11 | 0.359686 | 0.179843 | − | 0.983695i | \(-0.442441\pi\) | ||||
0.179843 | + | 0.983695i | \(0.442441\pi\) | |||||||
\(240\) | −1.01926e11 | −0.128006 | ||||||||
\(241\) | 8.56037e9i | 0.0105295i | 0.999986 | + | 0.00526474i | \(0.00167583\pi\) | ||||
−0.999986 | + | 0.00526474i | \(0.998324\pi\) | |||||||
\(242\) | − | 2.81176e12i | − | 3.38767i | ||||||
\(243\) | − | 1.95419e11i | − | 0.230641i | ||||||
\(244\) | − | 5.83661e11i | − | 0.674857i | ||||||
\(245\) | − | 5.59199e11i | − | 0.633484i | ||||||
\(246\) | 5.19551e10 | 0.0576704 | ||||||||
\(247\) | 5.92349e11i | 0.644307i | ||||||||
\(248\) | 5.36954e11i | 0.572373i | ||||||||
\(249\) | 9.83828e10i | 0.102783i | ||||||||
\(250\) | 3.11604e11 | 0.319083 | ||||||||
\(251\) | −1.08237e12 | −1.08645 | −0.543224 | − | 0.839588i | \(-0.682797\pi\) | ||||
−0.543224 | + | 0.839588i | \(0.682797\pi\) | |||||||
\(252\) | 8.03482e11i | 0.790630i | ||||||||
\(253\) | −3.59961e11 | −0.347258 | ||||||||
\(254\) | 1.86299e12i | 1.76214i | ||||||||
\(255\) | −1.65691e11 | −0.153673 | ||||||||
\(256\) | 1.43628e12 | 1.30629 | ||||||||
\(257\) | 1.25145e11i | 0.111621i | 0.998441 | + | 0.0558106i | \(0.0177743\pi\) | ||||
−0.998441 | + | 0.0558106i | \(0.982226\pi\) | |||||||
\(258\) | −2.08963e10 | − | 1.12076e11i | −0.0182797 | − | 0.0980425i | ||||
\(259\) | 1.57319e12 | 1.34984 | ||||||||
\(260\) | − | 5.62872e11i | − | 0.473743i | ||||||
\(261\) | − | 1.42893e12i | − | 1.17980i | ||||||
\(262\) | −1.03141e12 | −0.835456 | ||||||||
\(263\) | − | 8.17179e10i | − | 0.0649439i | −0.999473 | − | 0.0324720i | \(-0.989662\pi\) | ||
0.999473 | − | 0.0324720i | \(-0.0103380\pi\) | |||||||
\(264\) | 8.38470e10 | 0.0653835 | ||||||||
\(265\) | 8.42296e11i | 0.644519i | ||||||||
\(266\) | − | 2.49827e12i | − | 1.87599i | ||||||
\(267\) | −1.15170e11 | −0.0848755 | ||||||||
\(268\) | 9.15339e11 | 0.662076 | ||||||||
\(269\) | 1.08953e12 | 0.773534 | 0.386767 | − | 0.922177i | \(-0.373592\pi\) | ||||
0.386767 | + | 0.922177i | \(0.373592\pi\) | |||||||
\(270\) | − | 3.84535e11i | − | 0.267989i | ||||||
\(271\) | 1.20425e12 | 0.823892 | 0.411946 | − | 0.911208i | \(-0.364849\pi\) | ||||
0.411946 | + | 0.911208i | \(0.364849\pi\) | |||||||
\(272\) | 2.68505e12 | 1.80346 | ||||||||
\(273\) | −7.63576e10 | −0.0503546 | ||||||||
\(274\) | −3.70970e12 | −2.40207 | ||||||||
\(275\) | 2.44601e12 | 1.55523 | ||||||||
\(276\) | 1.48359e10i | 0.00926339i | ||||||||
\(277\) | 9.20016e11i | 0.564153i | 0.959392 | + | 0.282076i | \(0.0910231\pi\) | ||||
−0.959392 | + | 0.282076i | \(0.908977\pi\) | |||||||
\(278\) | − | 2.37520e12i | − | 1.43046i | ||||||
\(279\) | −2.17280e12 | −1.28528 | ||||||||
\(280\) | − | 1.24475e12i | − | 0.723258i | ||||||
\(281\) | −1.19875e12 | −0.684224 | −0.342112 | − | 0.939659i | \(-0.611142\pi\) | ||||
−0.342112 | + | 0.939659i | \(0.611142\pi\) | |||||||
\(282\) | 3.32923e11 | 0.186680 | ||||||||
\(283\) | −2.28969e12 | −1.26137 | −0.630687 | − | 0.776037i | \(-0.717227\pi\) | ||||
−0.630687 | + | 0.776037i | \(0.717227\pi\) | |||||||
\(284\) | 1.78147e12i | 0.964242i | ||||||||
\(285\) | 2.36108e11i | 0.125570i | ||||||||
\(286\) | 2.51496e12i | 1.31432i | ||||||||
\(287\) | 1.36521e12i | 0.701116i | ||||||||
\(288\) | 2.23455e12i | 1.12779i | ||||||||
\(289\) | 2.34883e12 | 1.16510 | ||||||||
\(290\) | − | 4.22188e12i | − | 2.05833i | ||||||
\(291\) | − | 7.16257e9i | − | 0.00343245i | ||||||
\(292\) | − | 7.25446e9i | − | 0.00341736i | ||||||
\(293\) | −2.04015e11 | −0.0944767 | −0.0472384 | − | 0.998884i | \(-0.515042\pi\) | ||||
−0.0472384 | + | 0.998884i | \(0.515042\pi\) | |||||||
\(294\) | 1.02979e11 | 0.0468827 | ||||||||
\(295\) | 1.36819e12i | 0.612401i | ||||||||
\(296\) | 1.11978e12 | 0.492804 | ||||||||
\(297\) | 6.80629e11i | 0.294529i | ||||||||
\(298\) | −9.47080e11 | −0.403000 | ||||||||
\(299\) | 2.33331e11 | 0.0976373 | ||||||||
\(300\) | − | 1.00813e11i | − | 0.0414869i | ||||||
\(301\) | 2.94499e12 | − | 5.49085e11i | 1.19193 | − | 0.222232i | ||||
\(302\) | −3.91140e12 | −1.55703 | ||||||||
\(303\) | 1.89846e10i | 0.00743340i | ||||||||
\(304\) | − | 3.82617e12i | − | 1.47366i | ||||||
\(305\) | −3.65890e12 | −1.38628 | ||||||||
\(306\) | 5.04966e12i | 1.88215i | ||||||||
\(307\) | −1.58303e12 | −0.580492 | −0.290246 | − | 0.956952i | \(-0.593737\pi\) | ||||
−0.290246 | + | 0.956952i | \(0.593737\pi\) | |||||||
\(308\) | − | 4.20190e12i | − | 1.51598i | ||||||
\(309\) | 1.45572e11i | 0.0516757i | ||||||||
\(310\) | −6.41970e12 | −2.24237 | ||||||||
\(311\) | −1.19646e12 | −0.411242 | −0.205621 | − | 0.978632i | \(-0.565921\pi\) | ||||
−0.205621 | + | 0.978632i | \(0.565921\pi\) | |||||||
\(312\) | −5.43506e10 | −0.0183836 | ||||||||
\(313\) | 3.25449e12i | 1.08333i | 0.840594 | + | 0.541665i | \(0.182206\pi\) | ||||
−0.840594 | + | 0.541665i | \(0.817794\pi\) | |||||||
\(314\) | 5.00297e12 | 1.63900 | ||||||||
\(315\) | 5.03693e12 | 1.62410 | ||||||||
\(316\) | −5.38351e11 | −0.170856 | ||||||||
\(317\) | −5.13842e11 | −0.160521 | −0.0802607 | − | 0.996774i | \(-0.525575\pi\) | ||||
−0.0802607 | + | 0.996774i | \(0.525575\pi\) | |||||||
\(318\) | −1.55113e11 | −0.0476993 | ||||||||
\(319\) | 7.47275e12i | 2.26218i | ||||||||
\(320\) | 1.06001e12i | 0.315907i | ||||||||
\(321\) | − | 3.23013e11i | − | 0.0947752i | ||||||
\(322\) | −9.84087e11 | −0.284285 | ||||||||
\(323\) | − | 6.21983e12i | − | 1.76915i | ||||||
\(324\) | −2.30018e12 | −0.644225 | ||||||||
\(325\) | −1.58553e12 | −0.437278 | ||||||||
\(326\) | −7.61718e12 | −2.06874 | ||||||||
\(327\) | 2.00077e11i | 0.0535130i | ||||||||
\(328\) | 9.71742e11i | 0.255966i | ||||||||
\(329\) | 8.74812e12i | 2.26953i | ||||||||
\(330\) | 1.00246e12i | 0.256151i | ||||||||
\(331\) | 2.16998e12i | 0.546154i | 0.961992 | + | 0.273077i | \(0.0880413\pi\) | ||||
−0.961992 | + | 0.273077i | \(0.911959\pi\) | |||||||
\(332\) | 3.50937e12 | 0.870040 | ||||||||
\(333\) | 4.53122e12i | 1.10661i | ||||||||
\(334\) | − | 3.34280e12i | − | 0.804226i | ||||||
\(335\) | − | 5.73815e12i | − | 1.36003i | ||||||
\(336\) | 4.93217e11 | 0.115171 | ||||||||
\(337\) | 4.97435e11 | 0.114442 | 0.0572211 | − | 0.998362i | \(-0.481776\pi\) | ||||
0.0572211 | + | 0.998362i | \(0.481776\pi\) | |||||||
\(338\) | 4.04674e12i | 0.917322i | ||||||||
\(339\) | −1.93067e11 | −0.0431230 | ||||||||
\(340\) | 5.91031e12i | 1.30081i | ||||||||
\(341\) | 1.13629e13 | 2.46444 | ||||||||
\(342\) | 7.19572e12 | 1.53796 | ||||||||
\(343\) | − | 3.05033e12i | − | 0.642505i | ||||||
\(344\) | 2.09621e12 | − | 3.90833e11i | 0.435154 | − | 0.0811333i | ||||
\(345\) | 9.30047e10 | 0.0190287 | ||||||||
\(346\) | − | 5.55947e11i | − | 0.112112i | ||||||
\(347\) | 5.03418e12i | 1.00065i | 0.865838 | + | 0.500324i | \(0.166786\pi\) | ||||
−0.865838 | + | 0.500324i | \(0.833214\pi\) | |||||||
\(348\) | 3.07993e11 | 0.0603455 | ||||||||
\(349\) | − | 7.27438e12i | − | 1.40498i | −0.711695 | − | 0.702488i | \(-0.752072\pi\) | ||
0.711695 | − | 0.702488i | \(-0.247928\pi\) | |||||||
\(350\) | 6.68708e12 | 1.27320 | ||||||||
\(351\) | − | 4.41191e11i | − | 0.0828116i | ||||||
\(352\) | − | 1.16858e13i | − | 2.16245i | ||||||
\(353\) | 7.54518e11 | 0.137656 | 0.0688282 | − | 0.997629i | \(-0.478074\pi\) | ||||
0.0688282 | + | 0.997629i | \(0.478074\pi\) | |||||||
\(354\) | −2.51958e11 | −0.0453223 | ||||||||
\(355\) | 1.11678e13 | 1.98073 | ||||||||
\(356\) | 4.10818e12i | 0.718454i | ||||||||
\(357\) | 8.01775e11 | 0.138265 | ||||||||
\(358\) | −1.14208e13 | −1.94214 | ||||||||
\(359\) | −6.02737e12 | −1.01078 | −0.505389 | − | 0.862892i | \(-0.668651\pi\) | ||||
−0.505389 | + | 0.862892i | \(0.668651\pi\) | |||||||
\(360\) | 3.58524e12 | 0.592933 | ||||||||
\(361\) | −2.73212e12 | −0.445620 | ||||||||
\(362\) | − | 6.08815e12i | − | 0.979361i | ||||||
\(363\) | − | 1.28589e12i | − | 0.204019i | ||||||
\(364\) | 2.72372e12i | 0.426242i | ||||||||
\(365\) | −4.54774e10 | −0.00701990 | ||||||||
\(366\) | − | 6.73804e11i | − | 0.102595i | ||||||
\(367\) | −9.28837e12 | −1.39511 | −0.697556 | − | 0.716530i | \(-0.745729\pi\) | ||||
−0.697556 | + | 0.716530i | \(0.745729\pi\) | |||||||
\(368\) | −1.50715e12 | −0.223315 | ||||||||
\(369\) | −3.93218e12 | −0.574780 | ||||||||
\(370\) | 1.33878e13i | 1.93064i | ||||||||
\(371\) | − | 4.07585e12i | − | 0.579894i | ||||||
\(372\) | − | 4.68328e11i | − | 0.0657408i | ||||||
\(373\) | 3.36263e12i | 0.465731i | 0.972509 | + | 0.232866i | \(0.0748102\pi\) | ||||
−0.972509 | + | 0.232866i | \(0.925190\pi\) | |||||||
\(374\) | − | 2.64078e13i | − | 3.60890i | ||||||
\(375\) | 1.42504e11 | 0.0192164 | ||||||||
\(376\) | 6.22682e12i | 0.828566i | ||||||||
\(377\) | − | 4.84392e12i | − | 0.636049i | ||||||
\(378\) | 1.86075e12i | 0.241118i | ||||||||
\(379\) | 5.76499e11 | 0.0737229 | 0.0368615 | − | 0.999320i | \(-0.488264\pi\) | ||||
0.0368615 | + | 0.999320i | \(0.488264\pi\) | |||||||
\(380\) | 8.42213e12 | 1.06293 | ||||||||
\(381\) | 8.51989e11i | 0.106123i | ||||||||
\(382\) | −9.93854e11 | −0.122182 | ||||||||
\(383\) | − | 4.64396e12i | − | 0.563501i | −0.959488 | − | 0.281751i | \(-0.909085\pi\) | ||
0.959488 | − | 0.281751i | \(-0.0909151\pi\) | |||||||
\(384\) | 5.38973e11 | 0.0645522 | ||||||||
\(385\) | −2.63412e13 | −3.11410 | ||||||||
\(386\) | − | 1.35016e13i | − | 1.57561i | ||||||
\(387\) | 1.58152e12 | + | 8.48239e12i | 0.182188 | + | 0.977155i | ||||
\(388\) | −2.55493e11 | −0.0290550 | ||||||||
\(389\) | − | 6.56720e12i | − | 0.737279i | −0.929572 | − | 0.368640i | \(-0.879824\pi\) | ||
0.929572 | − | 0.368640i | \(-0.120176\pi\) | |||||||
\(390\) | − | 6.49803e11i | − | 0.0720209i | ||||||
\(391\) | −2.45003e12 | −0.268095 | ||||||||
\(392\) | 1.92607e12i | 0.208085i | ||||||||
\(393\) | −4.71688e11 | −0.0503143 | ||||||||
\(394\) | − | 9.15600e12i | − | 0.964328i | ||||||
\(395\) | 3.37486e12i | 0.350970i | ||||||||
\(396\) | 1.21027e13 | 1.24281 | ||||||||
\(397\) | 3.69878e11 | 0.0375064 | 0.0187532 | − | 0.999824i | \(-0.494030\pi\) | ||||
0.0187532 | + | 0.999824i | \(0.494030\pi\) | |||||||
\(398\) | 3.57782e12 | 0.358264 | ||||||||
\(399\) | − | 1.14252e12i | − | 0.112980i | ||||||
\(400\) | 1.02414e13 | 1.00014 | ||||||||
\(401\) | 1.28581e13 | 1.24009 | 0.620047 | − | 0.784564i | \(-0.287113\pi\) | ||||
0.620047 | + | 0.784564i | \(0.287113\pi\) | |||||||
\(402\) | 1.05671e12 | 0.100652 | ||||||||
\(403\) | −7.36557e12 | −0.692917 | ||||||||
\(404\) | 6.77191e11 | 0.0629223 | ||||||||
\(405\) | 1.44196e13i | 1.32336i | ||||||||
\(406\) | 2.04296e13i | 1.85195i | ||||||||
\(407\) | − | 2.36966e13i | − | 2.12184i | ||||||
\(408\) | 5.70696e11 | 0.0504782 | ||||||||
\(409\) | 1.08776e13i | 0.950424i | 0.879871 | + | 0.475212i | \(0.157629\pi\) | ||||
−0.879871 | + | 0.475212i | \(0.842371\pi\) | |||||||
\(410\) | −1.16179e13 | −1.00279 | ||||||||
\(411\) | −1.69654e12 | −0.144662 | ||||||||
\(412\) | 5.19265e12 | 0.437425 | ||||||||
\(413\) | − | 6.62063e12i | − | 0.550997i | ||||||
\(414\) | − | 2.83445e12i | − | 0.233059i | ||||||
\(415\) | − | 2.19998e13i | − | 1.78722i | ||||||
\(416\) | 7.57489e12i | 0.608008i | ||||||||
\(417\) | − | 1.08624e12i | − | 0.0861481i | ||||||
\(418\) | −3.76309e13 | −2.94892 | ||||||||
\(419\) | 1.20480e13i | 0.932919i | 0.884543 | + | 0.466459i | \(0.154471\pi\) | ||||
−0.884543 | + | 0.466459i | \(0.845529\pi\) | |||||||
\(420\) | 1.08567e12i | 0.0830710i | ||||||||
\(421\) | − | 2.17260e12i | − | 0.164274i | −0.996621 | − | 0.0821372i | \(-0.973825\pi\) | ||
0.996621 | − | 0.0821372i | \(-0.0261746\pi\) | |||||||
\(422\) | 2.62602e12 | 0.196216 | ||||||||
\(423\) | −2.51970e13 | −1.86058 | ||||||||
\(424\) | − | 2.90115e12i | − | 0.211710i | ||||||
\(425\) | 1.66485e13 | 1.20069 | ||||||||
\(426\) | 2.05660e12i | 0.146589i | ||||||||
\(427\) | 1.77053e13 | 1.24728 | ||||||||
\(428\) | −1.15221e13 | −0.802253 | ||||||||
\(429\) | 1.15016e12i | 0.0791535i | ||||||||
\(430\) | 4.67271e12 | + | 2.50619e13i | 0.317853 | + | 1.70479i | ||||
\(431\) | 2.01490e13 | 1.35477 | 0.677386 | − | 0.735628i | \(-0.263113\pi\) | ||||
0.677386 | + | 0.735628i | \(0.263113\pi\) | |||||||
\(432\) | 2.84979e12i | 0.189406i | ||||||||
\(433\) | − | 2.69988e13i | − | 1.77380i | −0.461961 | − | 0.886900i | \(-0.652854\pi\) | ||
0.461961 | − | 0.886900i | \(-0.347146\pi\) | |||||||
\(434\) | 3.10648e13 | 2.01753 | ||||||||
\(435\) | − | 1.93077e12i | − | 0.123961i | ||||||
\(436\) | 7.13688e12 | 0.452977 | ||||||||
\(437\) | 3.49127e12i | 0.219067i | ||||||||
\(438\) | − | 8.37486e9i | − | 0.000519526i | ||||||
\(439\) | −2.46701e12 | −0.151303 | −0.0756516 | − | 0.997134i | \(-0.524104\pi\) | ||||
−0.0756516 | + | 0.997134i | \(0.524104\pi\) | |||||||
\(440\) | −1.87494e13 | −1.13691 | ||||||||
\(441\) | −7.79389e12 | −0.467263 | ||||||||
\(442\) | 1.71178e13i | 1.01470i | ||||||||
\(443\) | −2.40592e13 | −1.41014 | −0.705070 | − | 0.709138i | \(-0.749084\pi\) | ||||
−0.705070 | + | 0.709138i | \(0.749084\pi\) | |||||||
\(444\) | −9.76665e11 | −0.0566018 | ||||||||
\(445\) | 2.57537e13 | 1.47584 | ||||||||
\(446\) | 8.28197e12 | 0.469309 | ||||||||
\(447\) | −4.33123e11 | −0.0242702 | ||||||||
\(448\) | − | 5.12934e12i | − | 0.284231i | ||||||
\(449\) | 2.08597e13i | 1.14308i | 0.820575 | + | 0.571539i | \(0.193654\pi\) | ||||
−0.820575 | + | 0.571539i | \(0.806346\pi\) | |||||||
\(450\) | 1.92606e13i | 1.04378i | ||||||||
\(451\) | 2.05638e13 | 1.10210 | ||||||||
\(452\) | 6.88680e12i | 0.365027i | ||||||||
\(453\) | −1.78878e12 | −0.0937704 | ||||||||
\(454\) | 3.23698e13 | 1.67827 | ||||||||
\(455\) | 1.70747e13 | 0.875579 | ||||||||
\(456\) | − | 8.13236e11i | − | 0.0412470i | ||||||
\(457\) | 5.28568e12i | 0.265167i | 0.991172 | + | 0.132583i | \(0.0423273\pi\) | ||||
−0.991172 | + | 0.132583i | \(0.957673\pi\) | |||||||
\(458\) | 2.74292e13i | 1.36109i | ||||||||
\(459\) | 4.63263e12i | 0.227386i | ||||||||
\(460\) | − | 3.31754e12i | − | 0.161074i | ||||||
\(461\) | −2.05871e13 | −0.988760 | −0.494380 | − | 0.869246i | \(-0.664605\pi\) | ||||
−0.494380 | + | 0.869246i | \(0.664605\pi\) | |||||||
\(462\) | − | 4.85086e12i | − | 0.230467i | ||||||
\(463\) | − | 5.27910e12i | − | 0.248116i | −0.992275 | − | 0.124058i | \(-0.960409\pi\) | ||
0.992275 | − | 0.124058i | \(-0.0395909\pi\) | |||||||
\(464\) | 3.12884e13i | 1.45477i | ||||||||
\(465\) | −2.93589e12 | −0.135044 | ||||||||
\(466\) | 2.77952e13 | 1.26485 | ||||||||
\(467\) | 2.92808e13i | 1.31825i | 0.752032 | + | 0.659127i | \(0.229074\pi\) | ||||
−0.752032 | + | 0.659127i | \(0.770926\pi\) | |||||||
\(468\) | −7.84508e12 | −0.349436 | ||||||||
\(469\) | 2.77668e13i | 1.22366i | ||||||||
\(470\) | −7.44465e13 | −3.24605 | ||||||||
\(471\) | 2.28798e12 | 0.0987071 | ||||||||
\(472\) | − | 4.71250e12i | − | 0.201160i | ||||||
\(473\) | −8.27073e12 | − | 4.43596e13i | −0.349332 | − | 1.87362i | ||||
\(474\) | −6.21495e11 | −0.0259744 | ||||||||
\(475\) | − | 2.37239e13i | − | 0.981112i | ||||||
\(476\) | − | 2.85998e13i | − | 1.17038i | ||||||
\(477\) | 1.17396e13 | 0.475402 | ||||||||
\(478\) | − | 1.15504e13i | − | 0.462868i | ||||||
\(479\) | −2.31846e13 | −0.919435 | −0.459718 | − | 0.888065i | \(-0.652049\pi\) | ||||
−0.459718 | + | 0.888065i | \(0.652049\pi\) | |||||||
\(480\) | 3.01932e12i | 0.118496i | ||||||||
\(481\) | 1.53604e13i | 0.596591i | ||||||||
\(482\) | 3.52513e11 | 0.0135500 | ||||||||
\(483\) | −4.50047e11 | −0.0171207 | ||||||||
\(484\) | −4.58684e13 | −1.72698 | ||||||||
\(485\) | 1.60166e12i | 0.0596844i | ||||||||
\(486\) | −8.04731e12 | −0.296804 | ||||||||
\(487\) | −6.90238e12 | −0.251973 | −0.125986 | − | 0.992032i | \(-0.540210\pi\) | ||||
−0.125986 | + | 0.992032i | \(0.540210\pi\) | |||||||
\(488\) | 1.26025e13 | 0.455362 | ||||||||
\(489\) | −3.48352e12 | −0.124588 | ||||||||
\(490\) | −2.30276e13 | −0.815209 | ||||||||
\(491\) | − | 4.35665e13i | − | 1.52667i | −0.646002 | − | 0.763336i | \(-0.723560\pi\) | ||
0.646002 | − | 0.763336i | \(-0.276440\pi\) | |||||||
\(492\) | − | 8.47547e11i | − | 0.0293994i | ||||||
\(493\) | 5.08625e13i | 1.74648i | ||||||||
\(494\) | 2.43927e13 | 0.829136 | ||||||||
\(495\) | − | 7.58701e13i | − | 2.55296i | ||||||
\(496\) | 4.75765e13 | 1.58484 | ||||||||
\(497\) | −5.40407e13 | −1.78213 | ||||||||
\(498\) | 4.05137e12 | 0.132268 | ||||||||
\(499\) | − | 1.71296e13i | − | 0.553660i | −0.960919 | − | 0.276830i | \(-0.910716\pi\) | ||
0.960919 | − | 0.276830i | \(-0.0892839\pi\) | |||||||
\(500\) | − | 5.08322e12i | − | 0.162663i | ||||||
\(501\) | − | 1.52875e12i | − | 0.0484336i | ||||||
\(502\) | 4.45718e13i | 1.39811i | ||||||||
\(503\) | 8.11768e11i | 0.0252111i | 0.999921 | + | 0.0126056i | \(0.00401258\pi\) | ||||
−0.999921 | + | 0.0126056i | \(0.995987\pi\) | |||||||
\(504\) | −1.73489e13 | −0.533481 | ||||||||
\(505\) | − | 4.24523e12i | − | 0.129254i | ||||||
\(506\) | 1.48231e13i | 0.446874i | ||||||||
\(507\) | 1.85068e12i | 0.0552447i | ||||||||
\(508\) | 3.03910e13 | 0.898310 | ||||||||
\(509\) | −5.59364e13 | −1.63721 | −0.818607 | − | 0.574355i | \(-0.805253\pi\) | ||||
−0.818607 | + | 0.574355i | \(0.805253\pi\) | |||||||
\(510\) | 6.82311e12i | 0.197757i | ||||||||
\(511\) | 2.20064e11 | 0.00631603 | ||||||||
\(512\) | − | 2.98396e13i | − | 0.848092i | ||||||
\(513\) | 6.60145e12 | 0.185803 | ||||||||
\(514\) | 5.15342e12 | 0.143641 | ||||||||
\(515\) | − | 3.25521e13i | − | 0.898552i | ||||||
\(516\) | −1.82830e12 | + | 3.40882e11i | −0.0499804 | + | 0.00931870i | ||||
\(517\) | 1.31771e14 | 3.56752 | ||||||||
\(518\) | − | 6.47834e13i | − | 1.73706i | ||||||
\(519\) | − | 2.54248e11i | − | 0.00675182i | ||||||
\(520\) | 1.21536e13 | 0.319660 | ||||||||
\(521\) | 1.30236e12i | 0.0339267i | 0.999856 | + | 0.0169633i | \(0.00539985\pi\) | ||||
−0.999856 | + | 0.0169633i | \(0.994600\pi\) | |||||||
\(522\) | −5.88429e13 | −1.51824 | ||||||||
\(523\) | 1.21766e13i | 0.311185i | 0.987821 | + | 0.155592i | \(0.0497287\pi\) | ||||
−0.987821 | + | 0.155592i | \(0.950271\pi\) | |||||||
\(524\) | 1.68254e13i | 0.425901i | ||||||||
\(525\) | 3.05817e12 | 0.0766769 | ||||||||
\(526\) | −3.36512e12 | −0.0835741 | ||||||||
\(527\) | 7.73405e13 | 1.90263 | ||||||||
\(528\) | − | 7.42921e12i | − | 0.181039i | ||||||
\(529\) | −4.00513e13 | −0.966803 | ||||||||
\(530\) | 3.46855e13 | 0.829409 | ||||||||
\(531\) | 1.90693e13 | 0.451712 | ||||||||
\(532\) | −4.07545e13 | −0.956350 | ||||||||
\(533\) | −1.33297e13 | −0.309873 | ||||||||
\(534\) | 4.74266e12i | 0.109223i | ||||||||
\(535\) | 7.22304e13i | 1.64798i | ||||||||
\(536\) | 1.97641e13i | 0.446738i | ||||||||
\(537\) | −5.22299e12 | −0.116963 | ||||||||
\(538\) | − | 4.48667e13i | − | 0.995434i | ||||||
\(539\) | 4.07591e13 | 0.895943 | ||||||||
\(540\) | −6.27294e12 | −0.136616 | ||||||||
\(541\) | −1.10489e13 | −0.238414 | −0.119207 | − | 0.992869i | \(-0.538035\pi\) | ||||
−0.119207 | + | 0.992869i | \(0.538035\pi\) | |||||||
\(542\) | − | 4.95906e13i | − | 1.06024i | ||||||
\(543\) | − | 2.78426e12i | − | 0.0589809i | ||||||
\(544\) | − | 7.95384e13i | − | 1.66948i | ||||||
\(545\) | − | 4.47402e13i | − | 0.930499i | ||||||
\(546\) | 3.14438e12i | 0.0647995i | ||||||||
\(547\) | 8.07039e13 | 1.64800 | 0.824002 | − | 0.566588i | \(-0.191737\pi\) | ||||
0.824002 | + | 0.566588i | \(0.191737\pi\) | |||||||
\(548\) | 6.05166e13i | 1.22454i | ||||||||
\(549\) | 5.09963e13i | 1.02253i | ||||||||
\(550\) | − | 1.00726e14i | − | 2.00137i | ||||||
\(551\) | 7.24786e13 | 1.42709 | ||||||||
\(552\) | −3.20339e11 | −0.00625050 | ||||||||
\(553\) | − | 1.63308e13i | − | 0.315779i | ||||||
\(554\) | 3.78860e13 | 0.725988 | ||||||||
\(555\) | 6.12259e12i | 0.116271i | ||||||||
\(556\) | −3.87468e13 | −0.729226 | ||||||||
\(557\) | 3.13382e12 | 0.0584518 | 0.0292259 | − | 0.999573i | \(-0.490696\pi\) | ||||
0.0292259 | + | 0.999573i | \(0.490696\pi\) | |||||||
\(558\) | 8.94753e13i | 1.65399i | ||||||||
\(559\) | 5.36118e12 | + | 2.87544e13i | 0.0982203 | + | 0.526800i | ||||
\(560\) | −1.10291e14 | −2.00262 | ||||||||
\(561\) | − | 1.20769e13i | − | 0.217342i | ||||||
\(562\) | 4.93643e13i | 0.880504i | ||||||||
\(563\) | −5.11185e13 | −0.903725 | −0.451863 | − | 0.892088i | \(-0.649240\pi\) | ||||
−0.451863 | + | 0.892088i | \(0.649240\pi\) | |||||||
\(564\) | − | 5.43099e12i | − | 0.0951664i | ||||||
\(565\) | 4.31725e13 | 0.749834 | ||||||||
\(566\) | 9.42885e13i | 1.62322i | ||||||||
\(567\) | − | 6.97760e13i | − | 1.19067i | ||||||
\(568\) | −3.84656e13 | −0.650625 | ||||||||
\(569\) | −2.55807e13 | −0.428895 | −0.214447 | − | 0.976736i | \(-0.568795\pi\) | ||||
−0.214447 | + | 0.976736i | \(0.568795\pi\) | |||||||
\(570\) | 9.72286e12 | 0.161592 | ||||||||
\(571\) | − | 2.03558e13i | − | 0.335357i | −0.985842 | − | 0.167678i | \(-0.946373\pi\) | ||
0.985842 | − | 0.167678i | \(-0.0536270\pi\) | |||||||
\(572\) | 4.10268e13 | 0.670019 | ||||||||
\(573\) | −4.54514e11 | −0.00735825 | ||||||||
\(574\) | 5.62189e13 | 0.902241 | ||||||||
\(575\) | −9.34502e12 | −0.148676 | ||||||||
\(576\) | 1.47739e13 | 0.233015 | ||||||||
\(577\) | − | 3.08235e13i | − | 0.481951i | −0.970531 | − | 0.240976i | \(-0.922533\pi\) | ||
0.970531 | − | 0.240976i | \(-0.0774674\pi\) | |||||||
\(578\) | − | 9.67240e13i | − | 1.49932i | ||||||
\(579\) | − | 6.17460e12i | − | 0.0948891i | ||||||
\(580\) | −6.88718e13 | −1.04930 | ||||||||
\(581\) | 1.06457e14i | 1.60802i | ||||||||
\(582\) | −2.94952e11 | −0.00441710 | ||||||||
\(583\) | −6.13935e13 | −0.911549 | ||||||||
\(584\) | 1.56639e11 | 0.00230588 | ||||||||
\(585\) | 4.91798e13i | 0.717807i | ||||||||
\(586\) | 8.40129e12i | 0.121579i | ||||||||
\(587\) | − | 1.42551e13i | − | 0.204541i | −0.994757 | − | 0.102270i | \(-0.967389\pi\) | ||
0.994757 | − | 0.102270i | \(-0.0326107\pi\) | |||||||
\(588\) | − | 1.67990e12i | − | 0.0239000i | ||||||
\(589\) | − | 1.10209e14i | − | 1.55468i | ||||||
\(590\) | 5.63416e13 | 0.788077 | ||||||||
\(591\) | − | 4.18727e12i | − | 0.0580755i | ||||||
\(592\) | − | 9.92175e13i | − | 1.36452i | ||||||
\(593\) | 8.86135e13i | 1.20844i | 0.796816 | + | 0.604222i | \(0.206516\pi\) | ||||
−0.796816 | + | 0.604222i | \(0.793484\pi\) | |||||||
\(594\) | 2.80281e13 | 0.379019 | ||||||||
\(595\) | −1.79289e14 | −2.40419 | ||||||||
\(596\) | 1.54498e13i | 0.205443i | ||||||||
\(597\) | 1.63623e12 | 0.0215760 | ||||||||
\(598\) | − | 9.60848e12i | − | 0.125646i | ||||||
\(599\) | 1.17392e14 | 1.52232 | 0.761159 | − | 0.648566i | \(-0.224631\pi\) | ||||
0.761159 | + | 0.648566i | \(0.224631\pi\) | |||||||
\(600\) | 2.17677e12 | 0.0279935 | ||||||||
\(601\) | 8.60541e13i | 1.09749i | 0.835991 | + | 0.548743i | \(0.184894\pi\) | ||||
−0.835991 | + | 0.548743i | \(0.815106\pi\) | |||||||
\(602\) | −2.26111e13 | − | 1.21274e14i | −0.285983 | − | 1.53385i | ||||
\(603\) | −7.99760e13 | −1.00317 | ||||||||
\(604\) | 6.38069e13i | 0.793748i | ||||||||
\(605\) | 2.87543e14i | 3.54753i | ||||||||
\(606\) | 7.81779e11 | 0.00956579 | ||||||||
\(607\) | 2.31920e12i | 0.0281446i | 0.999901 | + | 0.0140723i | \(0.00447950\pi\) | ||||
−0.999901 | + | 0.0140723i | \(0.995521\pi\) | |||||||
\(608\) | −1.13341e14 | −1.36418 | ||||||||
\(609\) | 9.34295e12i | 0.111532i | ||||||||
\(610\) | 1.50672e14i | 1.78396i | ||||||||
\(611\) | −8.54153e13 | −1.00307 | ||||||||
\(612\) | 8.23755e13 | 0.959491 | ||||||||
\(613\) | −4.60706e13 | −0.532257 | −0.266129 | − | 0.963938i | \(-0.585745\pi\) | ||||
−0.266129 | + | 0.963938i | \(0.585745\pi\) | |||||||
\(614\) | 6.51885e13i | 0.747014i | ||||||||
\(615\) | −5.31317e12 | −0.0603918 | ||||||||
\(616\) | 9.07280e13 | 1.02291 | ||||||||
\(617\) | −1.11511e14 | −1.24707 | −0.623535 | − | 0.781796i | \(-0.714304\pi\) | ||||
−0.623535 | + | 0.781796i | \(0.714304\pi\) | |||||||
\(618\) | 5.99462e12 | 0.0664997 | ||||||||
\(619\) | 1.41742e14 | 1.55972 | 0.779859 | − | 0.625955i | \(-0.215291\pi\) | ||||
0.779859 | + | 0.625955i | \(0.215291\pi\) | |||||||
\(620\) | 1.04725e14i | 1.14312i | ||||||||
\(621\) | − | 2.60036e12i | − | 0.0281563i | ||||||
\(622\) | 4.92700e13i | 0.529213i | ||||||||
\(623\) | −1.24621e14 | −1.32786 | ||||||||
\(624\) | 4.81570e12i | 0.0509022i | ||||||||
\(625\) | −1.09686e14 | −1.15014 | ||||||||
\(626\) | 1.34019e14 | 1.39410 | ||||||||
\(627\) | −1.72095e13 | −0.177595 | ||||||||
\(628\) | − | 8.16138e13i | − | 0.835536i | ||||||
\(629\) | − | 1.61288e14i | − | 1.63813i | ||||||
\(630\) | − | 2.07419e14i | − | 2.09000i | ||||||
\(631\) | 1.17813e14i | 1.17774i | 0.808230 | + | 0.588868i | \(0.200426\pi\) | ||||
−0.808230 | + | 0.588868i | \(0.799574\pi\) | |||||||
\(632\) | − | 1.16241e13i | − | 0.115286i | ||||||
\(633\) | 1.20094e12 | 0.0118169 | ||||||||
\(634\) | 2.11598e13i | 0.206569i | ||||||||
\(635\) | − | 1.90517e14i | − | 1.84530i | ||||||
\(636\) | 2.53036e12i | 0.0243163i | ||||||||
\(637\) | −2.64205e13 | −0.251909 | ||||||||
\(638\) | 3.07726e14 | 2.91112 | ||||||||
\(639\) | − | 1.55652e14i | − | 1.46100i | ||||||
\(640\) | −1.20522e14 | −1.12245 | ||||||||
\(641\) | 1.89395e14i | 1.75017i | 0.483973 | + | 0.875083i | \(0.339193\pi\) | ||||
−0.483973 | + | 0.875083i | \(0.660807\pi\) | |||||||
\(642\) | −1.33016e13 | −0.121963 | ||||||||
\(643\) | 4.33309e13 | 0.394224 | 0.197112 | − | 0.980381i | \(-0.436844\pi\) | ||||
0.197112 | + | 0.980381i | \(0.436844\pi\) | |||||||
\(644\) | 1.60535e13i | 0.144924i | ||||||||
\(645\) | 2.13695e12 | + | 1.14614e13i | 0.0191424 | + | 0.102669i | ||||
\(646\) | −2.56131e14 | −2.27666 | ||||||||
\(647\) | 5.57765e13i | 0.491960i | 0.969275 | + | 0.245980i | \(0.0791098\pi\) | ||||
−0.969275 | + | 0.245980i | \(0.920890\pi\) | |||||||
\(648\) | − | 4.96658e13i | − | 0.434693i | ||||||
\(649\) | −9.97249e13 | −0.866124 | ||||||||
\(650\) | 6.52916e13i | 0.562717i | ||||||||
\(651\) | 1.42067e13 | 0.121503 | ||||||||
\(652\) | 1.24259e14i | 1.05461i | ||||||||
\(653\) | − | 8.97054e13i | − | 0.755531i | −0.925901 | − | 0.377766i | \(-0.876692\pi\) | ||
0.925901 | − | 0.377766i | \(-0.123308\pi\) | |||||||
\(654\) | 8.23912e12 | 0.0688640 | ||||||||
\(655\) | 1.05476e14 | 0.874880 | ||||||||
\(656\) | 8.61006e13 | 0.708740 | ||||||||
\(657\) | 6.33845e11i | 0.00517793i | ||||||||
\(658\) | 3.60245e14 | 2.92057 | ||||||||
\(659\) | −1.01949e14 | −0.820264 | −0.410132 | − | 0.912026i | \(-0.634517\pi\) | ||||
−0.410132 | + | 0.912026i | \(0.634517\pi\) | |||||||
\(660\) | 1.63531e13 | 0.130581 | ||||||||
\(661\) | 1.91888e14 | 1.52069 | 0.760346 | − | 0.649518i | \(-0.225029\pi\) | ||||
0.760346 | + | 0.649518i | \(0.225029\pi\) | |||||||
\(662\) | 8.93589e13 | 0.702826 | ||||||||
\(663\) | 7.82841e12i | 0.0611091i | ||||||||
\(664\) | 7.57748e13i | 0.587063i | ||||||||
\(665\) | 2.55485e14i | 1.96452i | ||||||||
\(666\) | 1.86594e14 | 1.42406 | ||||||||
\(667\) | − | 2.85498e13i | − | 0.216259i | ||||||
\(668\) | −5.45313e13 | −0.409981 | ||||||||
\(669\) | 3.78755e12 | 0.0282636 | ||||||||
\(670\) | −2.36295e14 | −1.75017 | ||||||||
\(671\) | − | 2.66691e14i | − | 1.96063i | ||||||
\(672\) | − | 1.46104e13i | − | 0.106615i | ||||||
\(673\) | − | 2.47373e14i | − | 1.79174i | −0.444311 | − | 0.895872i | \(-0.646552\pi\) | ||
0.444311 | − | 0.895872i | \(-0.353448\pi\) | |||||||
\(674\) | − | 2.04842e13i | − | 0.147272i | ||||||
\(675\) | 1.76700e13i | 0.126101i | ||||||||
\(676\) | 6.60147e13 | 0.467635 | ||||||||
\(677\) | 1.53590e14i | 1.07999i | 0.841667 | + | 0.539996i | \(0.181574\pi\) | ||||
−0.841667 | + | 0.539996i | \(0.818426\pi\) | |||||||
\(678\) | 7.95042e12i | 0.0554935i | ||||||||
\(679\) | − | 7.75037e12i | − | 0.0536999i | ||||||
\(680\) | −1.27616e14 | −0.877729 | ||||||||
\(681\) | 1.48035e13 | 0.101072 | ||||||||
\(682\) | − | 4.67921e14i | − | 3.17140i | ||||||
\(683\) | 5.59491e13 | 0.376434 | 0.188217 | − | 0.982127i | \(-0.439729\pi\) | ||||
0.188217 | + | 0.982127i | \(0.439729\pi\) | |||||||
\(684\) | − | 1.17384e14i | − | 0.784024i | ||||||
\(685\) | 3.79371e14 | 2.51543 | ||||||||
\(686\) | −1.25612e14 | −0.826817 | ||||||||
\(687\) | 1.25441e13i | 0.0819699i | ||||||||
\(688\) | −3.46295e13 | − | 1.85734e14i | −0.224649 | − | 1.20489i | ||||
\(689\) | 3.97960e13 | 0.256297 | ||||||||
\(690\) | − | 3.82990e12i | − | 0.0244874i | ||||||
\(691\) | − | 5.03376e13i | − | 0.319523i | −0.987156 | − | 0.159762i | \(-0.948927\pi\) | ||
0.987156 | − | 0.159762i | \(-0.0510726\pi\) | |||||||
\(692\) | −9.06919e12 | −0.0571529 | ||||||||
\(693\) | 3.67133e14i | 2.29698i | ||||||||
\(694\) | 2.07306e14 | 1.28770 | ||||||||
\(695\) | 2.42899e14i | 1.49797i | ||||||||
\(696\) | 6.65022e12i | 0.0407183i | ||||||||
\(697\) | 1.39965e14 | 0.850858 | ||||||||
\(698\) | −2.99557e14 | −1.80802 | ||||||||
\(699\) | 1.27114e13 | 0.0761743 | ||||||||
\(700\) | − | 1.09087e14i | − | 0.649055i | ||||||
\(701\) | −1.59980e14 | −0.945095 | −0.472548 | − | 0.881305i | \(-0.656666\pi\) | ||||
−0.472548 | + | 0.881305i | \(0.656666\pi\) | |||||||
\(702\) | −1.81681e13 | −0.106567 | ||||||||
\(703\) | −2.29834e14 | −1.33856 | ||||||||
\(704\) | −7.72621e13 | −0.446790 | ||||||||
\(705\) | −3.40462e13 | −0.195489 | ||||||||
\(706\) | − | 3.10708e13i | − | 0.177145i | ||||||
\(707\) | 2.05426e13i | 0.116294i | ||||||||
\(708\) | 4.11021e12i | 0.0231046i | ||||||||
\(709\) | −3.37818e14 | −1.88561 | −0.942803 | − | 0.333350i | \(-0.891821\pi\) | ||||
−0.942803 | + | 0.333350i | \(0.891821\pi\) | |||||||
\(710\) | − | 4.59886e14i | − | 2.54893i | ||||||
\(711\) | 4.70374e13 | 0.258878 | ||||||||
\(712\) | −8.87042e13 | −0.484780 | ||||||||
\(713\) | −4.34123e13 | −0.235594 | ||||||||
\(714\) | − | 3.30169e13i | − | 0.177928i | ||||||
\(715\) | − | 2.57192e14i | − | 1.37634i | ||||||
\(716\) | 1.86307e14i | 0.990068i | ||||||||
\(717\) | − | 5.28228e12i | − | 0.0278757i | ||||||
\(718\) | 2.48205e14i | 1.30074i | ||||||||
\(719\) | −1.71498e14 | −0.892512 | −0.446256 | − | 0.894905i | \(-0.647243\pi\) | ||||
−0.446256 | + | 0.894905i | \(0.647243\pi\) | |||||||
\(720\) | − | 3.17668e14i | − | 1.64176i | ||||||
\(721\) | 1.57519e14i | 0.808456i | ||||||||
\(722\) | 1.12508e14i | 0.573453i | ||||||||
\(723\) | 1.61213e11 | 0.000816035 | ||||||||
\(724\) | −9.93164e13 | −0.499262 | ||||||||
\(725\) | 1.94002e14i | 0.968537i | ||||||||
\(726\) | −5.29524e13 | −0.262544 | ||||||||
\(727\) | 3.28609e13i | 0.161811i | 0.996722 | + | 0.0809053i | \(0.0257811\pi\) | ||||
−0.996722 | + | 0.0809053i | \(0.974219\pi\) | |||||||
\(728\) | −5.88109e13 | −0.287608 | ||||||||
\(729\) | 1.98508e14 | 0.964143 | ||||||||
\(730\) | 1.87274e12i | 0.00903366i | ||||||||
\(731\) | −5.62939e13 | − | 3.01929e14i | −0.269696 | − | 1.44650i | ||||
\(732\) | −1.09918e13 | −0.0523014 | ||||||||
\(733\) | − | 3.08912e14i | − | 1.45987i | −0.683515 | − | 0.729937i | \(-0.739549\pi\) | ||
0.683515 | − | 0.729937i | \(-0.260451\pi\) | |||||||
\(734\) | 3.82492e14i | 1.79532i | ||||||||
\(735\) | −1.05311e13 | −0.0490950 | ||||||||
\(736\) | 4.46460e13i | 0.206725i | ||||||||
\(737\) | 4.18244e14 | 1.92350 | ||||||||
\(738\) | 1.61926e14i | 0.739665i | ||||||||
\(739\) | − | 2.73153e14i | − | 1.23932i | −0.784869 | − | 0.619661i | \(-0.787270\pi\) | ||
0.784869 | − | 0.619661i | \(-0.212730\pi\) | |||||||
\(740\) | 2.18397e14 | 0.984209 | ||||||||
\(741\) | 1.11554e13 | 0.0499338 | ||||||||
\(742\) | −1.67842e14 | −0.746246 | ||||||||
\(743\) | 2.07176e14i | 0.914946i | 0.889224 | + | 0.457473i | \(0.151245\pi\) | ||||
−0.889224 | + | 0.457473i | \(0.848755\pi\) | |||||||
\(744\) | 1.01122e13 | 0.0443589 | ||||||||
\(745\) | 9.68527e13 | 0.422017 | ||||||||
\(746\) | 1.38472e14 | 0.599333 | ||||||||
\(747\) | −3.06625e14 | −1.31827 | ||||||||
\(748\) | −4.30792e14 | −1.83975 | ||||||||
\(749\) | − | 3.49521e14i | − | 1.48274i | ||||||
\(750\) | − | 5.86828e12i | − | 0.0247289i | ||||||
\(751\) | 2.30080e13i | 0.0963115i | 0.998840 | + | 0.0481558i | \(0.0153344\pi\) | ||||
−0.998840 | + | 0.0481558i | \(0.984666\pi\) | |||||||
\(752\) | 5.51724e14 | 2.29421 | ||||||||
\(753\) | 2.03838e13i | 0.0841997i | ||||||||
\(754\) | −1.99471e14 | −0.818509 | ||||||||
\(755\) | 3.99998e14 | 1.63051 | ||||||||
\(756\) | 3.03546e13 | 0.122918 | ||||||||
\(757\) | − | 1.51453e14i | − | 0.609256i | −0.952471 | − | 0.304628i | \(-0.901468\pi\) | ||
0.952471 | − | 0.304628i | \(-0.0985321\pi\) | |||||||
\(758\) | − | 2.37401e13i | − | 0.0948715i | ||||||
\(759\) | 6.77896e12i | 0.0269125i | ||||||||
\(760\) | 1.81851e14i | 0.717214i | ||||||||
\(761\) | 1.71220e14i | 0.670858i | 0.942065 | + | 0.335429i | \(0.108881\pi\) | ||||
−0.942065 | + | 0.335429i | \(0.891119\pi\) | |||||||
\(762\) | 3.50847e13 | 0.136566 | ||||||||
\(763\) | 2.16497e14i | 0.837200i | ||||||||
\(764\) | 1.62128e13i | 0.0622861i | ||||||||
\(765\) | − | 5.16402e14i | − | 1.97097i | ||||||
\(766\) | −1.91237e14 | −0.725150 | ||||||||
\(767\) | 6.46428e13 | 0.243525 | ||||||||
\(768\) | − | 2.70488e13i | − | 0.101238i | ||||||
\(769\) | 1.83718e14 | 0.683155 | 0.341577 | − | 0.939854i | \(-0.389039\pi\) | ||||
0.341577 | + | 0.939854i | \(0.389039\pi\) | |||||||
\(770\) | 1.08472e15i | 4.00743i | ||||||||
\(771\) | 2.35679e12 | 0.00865064 | ||||||||
\(772\) | −2.20252e14 | −0.803218 | ||||||||
\(773\) | 3.49327e14i | 1.26571i | 0.774270 | + | 0.632855i | \(0.218117\pi\) | ||||
−0.774270 | + | 0.632855i | \(0.781883\pi\) | |||||||
\(774\) | 3.49302e14 | − | 6.51264e13i | 1.25747 | − | 0.234451i | ||||
\(775\) | 2.94995e14 | 1.05513 | ||||||||
\(776\) | − | 5.51664e12i | − | 0.0196050i | ||||||
\(777\) | − | 2.96271e13i | − | 0.104612i | ||||||
\(778\) | −2.70435e14 | −0.948779 | ||||||||
\(779\) | − | 1.99449e14i | − | 0.695257i | ||||||
\(780\) | −1.06003e13 | −0.0367150 | ||||||||
\(781\) | 8.14002e14i | 2.80137i | ||||||||
\(782\) | 1.00892e14i | 0.345002i | ||||||||
\(783\) | −5.39832e13 | −0.183421 | ||||||||
\(784\) | 1.70658e14 | 0.576165 | ||||||||
\(785\) | −5.11627e14 | −1.71635 | ||||||||
\(786\) | 1.94240e13i | 0.0647478i | ||||||||
\(787\) | −3.93245e14 | −1.30253 | −0.651267 | − | 0.758848i | \(-0.725762\pi\) | ||||
−0.651267 | + | 0.758848i | \(0.725762\pi\) | |||||||
\(788\) | −1.49362e14 | −0.491598 | ||||||||
\(789\) | −1.53895e12 | −0.00503315 | ||||||||
\(790\) | 1.38976e14 | 0.451651 | ||||||||
\(791\) | −2.08911e14 | −0.674650 | ||||||||
\(792\) | 2.61322e14i | 0.838591i | ||||||||
\(793\) | 1.72872e14i | 0.551263i | ||||||||
\(794\) | − | 1.52315e13i | − | 0.0482657i | ||||||
\(795\) | 1.58625e13 | 0.0499502 | ||||||||
\(796\) | − | 5.83652e13i | − | 0.182637i | ||||||
\(797\) | −2.18666e13 | −0.0679969 | −0.0339984 | − | 0.999422i | \(-0.510824\pi\) | ||||
−0.0339984 | + | 0.999422i | \(0.510824\pi\) | |||||||
\(798\) | −4.70487e13 | −0.145390 | ||||||||
\(799\) | 8.96884e14 | 2.75424 | ||||||||
\(800\) | − | 3.03379e14i | − | 0.925838i | ||||||
\(801\) | − | 3.58944e14i | − | 1.08859i | ||||||
\(802\) | − | 5.29493e14i | − | 1.59584i | ||||||
\(803\) | − | 3.31477e12i | − | 0.00992831i | ||||||
\(804\) | − | 1.72381e13i | − | 0.0513109i | ||||||
\(805\) | 1.00637e14 | 0.297700 | ||||||||
\(806\) | 3.03312e14i | 0.891691i | ||||||||
\(807\) | − | 2.05186e13i | − | 0.0599489i | ||||||
\(808\) | 1.46220e13i | 0.0424570i | ||||||||
\(809\) | −5.48438e14 | −1.58265 | −0.791326 | − | 0.611395i | \(-0.790609\pi\) | ||||
−0.791326 | + | 0.611395i | \(0.790609\pi\) | |||||||
\(810\) | 5.93794e14 | 1.70298 | ||||||||
\(811\) | 2.07834e14i | 0.592395i | 0.955127 | + | 0.296198i | \(0.0957187\pi\) | ||||
−0.955127 | + | 0.296198i | \(0.904281\pi\) | |||||||
\(812\) | 3.33269e14 | 0.944092 | ||||||||
\(813\) | − | 2.26790e13i | − | 0.0638516i | ||||||
\(814\) | −9.75817e14 | −2.73053 | ||||||||
\(815\) | 7.78967e14 | 2.16636 | ||||||||
\(816\) | − | 5.05662e13i | − | 0.139768i | ||||||
\(817\) | −4.30246e14 | + | 8.02182e13i | −1.18197 | + | 0.220375i | ||||
\(818\) | 4.47937e14 | 1.22307 | ||||||||
\(819\) | − | 2.37980e14i | − | 0.645834i | ||||||
\(820\) | 1.89524e14i | 0.511205i | ||||||||
\(821\) | 2.05536e14 | 0.551027 | 0.275513 | − | 0.961297i | \(-0.411152\pi\) | ||||
0.275513 | + | 0.961297i | \(0.411152\pi\) | |||||||
\(822\) | 6.98630e13i | 0.186161i | ||||||||
\(823\) | 3.65767e14 | 0.968734 | 0.484367 | − | 0.874865i | \(-0.339050\pi\) | ||||
0.484367 | + | 0.874865i | \(0.339050\pi\) | |||||||
\(824\) | 1.12120e14i | 0.295154i | ||||||||
\(825\) | − | 4.60644e13i | − | 0.120530i | ||||||
\(826\) | −2.72635e14 | −0.709058 | ||||||||
\(827\) | 1.09701e14 | 0.283584 | 0.141792 | − | 0.989896i | \(-0.454714\pi\) | ||||
0.141792 | + | 0.989896i | \(0.454714\pi\) | |||||||
\(828\) | −4.62385e13 | −0.118810 | ||||||||
\(829\) | 3.06525e14i | 0.782876i | 0.920205 | + | 0.391438i | \(0.128022\pi\) | ||||
−0.920205 | + | 0.391438i | \(0.871978\pi\) | |||||||
\(830\) | −9.05947e14 | −2.29992 | ||||||||
\(831\) | 1.73262e13 | 0.0437218 | ||||||||
\(832\) | 5.00821e13 | 0.125622 | ||||||||
\(833\) | 2.77422e14 | 0.691698 | ||||||||
\(834\) | −4.47310e13 | −0.110861 | ||||||||
\(835\) | 3.41850e14i | 0.842177i | ||||||||
\(836\) | 6.13875e14i | 1.50331i | ||||||||
\(837\) | 8.20858e13i | 0.199821i | ||||||||
\(838\) | 4.96132e14 | 1.20054 | ||||||||
\(839\) | − | 6.66576e14i | − | 1.60339i | −0.597731 | − | 0.801697i | \(-0.703931\pi\) | ||
0.597731 | − | 0.801697i | \(-0.296069\pi\) | |||||||
\(840\) | −2.34418e13 | −0.0560525 | ||||||||
\(841\) | −1.71985e14 | −0.408800 | ||||||||
\(842\) | −8.94672e13 | −0.211399 | ||||||||
\(843\) | 2.25755e13i | 0.0530273i | ||||||||
\(844\) | − | 4.28384e13i | − | 0.100028i | ||||||
\(845\) | − | 4.13838e14i | − | 0.960610i | ||||||
\(846\) | 1.03761e15i | 2.39431i | ||||||||
\(847\) | − | 1.39141e15i | − | 3.19183i | ||||||
\(848\) | −2.57055e14 | −0.586201 | ||||||||
\(849\) | 4.31205e13i | 0.0977564i | ||||||||
\(850\) | − | 6.85580e14i | − | 1.54512i | ||||||
\(851\) | 9.05332e13i | 0.202843i | ||||||||
\(852\) | 3.35494e13 | 0.0747287 | ||||||||
\(853\) | −3.35384e14 | −0.742673 | −0.371337 | − | 0.928498i | \(-0.621100\pi\) | ||||
−0.371337 | + | 0.928498i | \(0.621100\pi\) | |||||||
\(854\) | − | 7.29100e14i | − | 1.60508i | ||||||
\(855\) | −7.35867e14 | −1.61053 | ||||||||
\(856\) | − | 2.48786e14i | − | 0.541323i | ||||||
\(857\) | −1.16896e14 | −0.252868 | −0.126434 | − | 0.991975i | \(-0.540353\pi\) | ||||
−0.126434 | + | 0.991975i | \(0.540353\pi\) | |||||||
\(858\) | 4.73630e13 | 0.101860 | ||||||||
\(859\) | − | 2.09378e14i | − | 0.447678i | −0.974626 | − | 0.223839i | \(-0.928141\pi\) | ||
0.974626 | − | 0.223839i | \(-0.0718589\pi\) | |||||||
\(860\) | 4.08835e14 | − | 7.62262e13i | 0.869073 | − | 0.162036i | ||||
\(861\) | 2.57103e13 | 0.0543364 | ||||||||
\(862\) | − | 8.29728e14i | − | 1.74341i | ||||||
\(863\) | 2.08207e12i | 0.00434952i | 0.999998 | + | 0.00217476i | \(0.000692249\pi\) | ||||
−0.999998 | + | 0.00217476i | \(0.999308\pi\) | |||||||
\(864\) | 8.44185e13 | 0.175335 | ||||||||
\(865\) | 5.68536e13i | 0.117403i | ||||||||
\(866\) | −1.11180e15 | −2.28264 | ||||||||
\(867\) | − | 4.42343e13i | − | 0.0902950i | ||||||
\(868\) | − | 5.06762e14i | − | 1.02850i | ||||||
\(869\) | −2.45988e14 | −0.496380 | ||||||||
\(870\) | −7.95085e13 | −0.159521 | ||||||||
\(871\) | −2.71110e14 | −0.540823 | ||||||||
\(872\) | 1.54100e14i | 0.305648i | ||||||||
\(873\) | 2.23232e13 | 0.0440236 | ||||||||
\(874\) | 1.43770e14 | 0.281910 | ||||||||
\(875\) | 1.54199e14 | 0.300636 | ||||||||
\(876\) | −1.36620e11 | −0.000264846 | ||||||||
\(877\) | −5.29764e14 | −1.02114 | −0.510569 | − | 0.859837i | \(-0.670565\pi\) | ||||
−0.510569 | + | 0.859837i | \(0.670565\pi\) | |||||||
\(878\) | 1.01591e14i | 0.194707i | ||||||||
\(879\) | 3.84212e12i | 0.00732194i | ||||||||
\(880\) | 1.66128e15i | 3.14797i | ||||||||
\(881\) | −2.91535e14 | −0.549301 | −0.274651 | − | 0.961544i | \(-0.588562\pi\) | ||||
−0.274651 | + | 0.961544i | \(0.588562\pi\) | |||||||
\(882\) | 3.20950e14i | 0.601304i | ||||||||
\(883\) | 7.92798e14 | 1.47693 | 0.738464 | − | 0.674293i | \(-0.235552\pi\) | ||||
0.738464 | + | 0.674293i | \(0.235552\pi\) | |||||||
\(884\) | 2.79244e14 | 0.517277 | ||||||||
\(885\) | 2.57664e13 | 0.0474610 | ||||||||
\(886\) | 9.90749e14i | 1.81466i | ||||||||
\(887\) | − | 8.53074e14i | − | 1.55370i | −0.629683 | − | 0.776852i | \(-0.716815\pi\) | ||
0.629683 | − | 0.776852i | \(-0.283185\pi\) | |||||||
\(888\) | − | 2.10883e13i | − | 0.0381923i | ||||||
\(889\) | 9.21909e14i | 1.66027i | ||||||||
\(890\) | − | 1.06053e15i | − | 1.89921i | ||||||
\(891\) | −1.05102e15 | −1.87164 | ||||||||
\(892\) | − | 1.35104e14i | − | 0.239246i | ||||||
\(893\) | − | 1.27805e15i | − | 2.25056i | ||||||
\(894\) | 1.78359e13i | 0.0312325i | ||||||||
\(895\) | 1.16794e15 | 2.03378 | ||||||||
\(896\) | 5.83204e14 | 1.00991 | ||||||||
\(897\) | − | 4.39420e12i | − | 0.00756688i | ||||||
\(898\) | 8.58996e14 | 1.47099 | ||||||||
\(899\) | 9.01236e14i | 1.53476i | ||||||||
\(900\) | 3.14200e14 | 0.532100 | ||||||||
\(901\) | −4.17869e14 | −0.703746 | ||||||||
\(902\) | − | 8.46811e14i | − | 1.41825i | ||||||
\(903\) | −1.03406e13 | − | 5.54615e13i | −0.0172230 | − | 0.0923746i | ||||
\(904\) | −1.48701e14 | −0.246304 | ||||||||
\(905\) | 6.22602e14i | 1.02558i | ||||||||
\(906\) | 7.36614e13i | 0.120670i | ||||||||
\(907\) | 7.23935e14 | 1.17940 | 0.589702 | − | 0.807621i | \(-0.299245\pi\) | ||||
0.589702 | + | 0.807621i | \(0.299245\pi\) | |||||||
\(908\) | − | 5.28051e14i | − | 0.855552i | ||||||
\(909\) | −5.91683e13 | −0.0953388 | ||||||||
\(910\) | − | 7.03130e14i | − | 1.12675i | ||||||
\(911\) | − | 5.12940e13i | − | 0.0817476i | −0.999164 | − | 0.0408738i | \(-0.986986\pi\) | ||
0.999164 | − | 0.0408738i | \(-0.0130142\pi\) | |||||||
\(912\) | −7.20563e13 | −0.114208 | ||||||||
\(913\) | 1.60353e15 | 2.52769 | ||||||||
\(914\) | 2.17662e14 | 0.341234 | ||||||||
\(915\) | 6.89062e13i | 0.107437i | ||||||||
\(916\) | 4.47455e14 | 0.693859 | ||||||||
\(917\) | −5.10397e14 | −0.787158 | ||||||||
\(918\) | 1.90770e14 | 0.292615 | ||||||||
\(919\) | −3.73452e14 | −0.569715 | −0.284858 | − | 0.958570i | \(-0.591946\pi\) | ||||
−0.284858 | + | 0.958570i | \(0.591946\pi\) | |||||||
\(920\) | 7.16326e13 | 0.108685 | ||||||||
\(921\) | 2.98123e13i | 0.0449881i | ||||||||
\(922\) | 8.47771e14i | 1.27240i | ||||||||
\(923\) | − | 5.27645e14i | − | 0.787650i | ||||||
\(924\) | −7.91323e13 | −0.117488 | ||||||||
\(925\) | − | 6.15192e14i | − | 0.908452i | ||||||
\(926\) | −2.17392e14 | −0.319292 | ||||||||
\(927\) | −4.53698e14 | −0.662779 | ||||||||
\(928\) | 9.26847e14 | 1.34669 | ||||||||
\(929\) | − | 1.34751e15i | − | 1.94739i | −0.227863 | − | 0.973693i | \(-0.573174\pi\) | ||
0.227863 | − | 0.973693i | \(-0.426826\pi\) | |||||||
\(930\) | 1.20899e14i | 0.173783i | ||||||||
\(931\) | − | 3.95324e14i | − | 0.565203i | ||||||
\(932\) | − | 4.53424e14i | − | 0.644801i | ||||||
\(933\) | 2.25324e13i | 0.0318713i | ||||||||
\(934\) | 1.20578e15 | 1.69641 | ||||||||
\(935\) | 2.70058e15i | 3.77920i | ||||||||
\(936\) | − | 1.69392e14i | − | 0.235783i | ||||||
\(937\) | 5.65207e13i | 0.0782545i | 0.999234 | + | 0.0391272i | \(0.0124578\pi\) | ||||
−0.999234 | + | 0.0391272i | \(0.987542\pi\) | |||||||
\(938\) | 1.14343e15 | 1.57469 | ||||||||
\(939\) | 6.12901e13 | 0.0839580 | ||||||||
\(940\) | 1.21445e15i | 1.65478i | ||||||||
\(941\) | −7.49414e14 | −1.01572 | −0.507860 | − | 0.861440i | \(-0.669563\pi\) | ||||
−0.507860 | + | 0.861440i | \(0.669563\pi\) | |||||||
\(942\) | − | 9.42184e13i | − | 0.127023i | ||||||
\(943\) | −7.85645e13 | −0.105358 | ||||||||
\(944\) | −4.17548e14 | −0.556989 | ||||||||
\(945\) | − | 1.90289e14i | − | 0.252496i | ||||||
\(946\) | −1.82672e15 | + | 3.40586e14i | −2.41110 | + | 0.449543i | ||||
\(947\) | −9.26325e14 | −1.21622 | −0.608112 | − | 0.793851i | \(-0.708073\pi\) | ||||
−0.608112 | + | 0.793851i | \(0.708073\pi\) | |||||||
\(948\) | 1.01385e13i | 0.0132413i | ||||||||
\(949\) | 2.14867e12i | 0.00279151i | ||||||||
\(950\) | −9.76944e14 | −1.26256 | ||||||||
\(951\) | 9.67692e12i | 0.0124404i | ||||||||
\(952\) | 6.17531e14 | 0.789721 | ||||||||
\(953\) | 3.90713e14i | 0.497043i | 0.968626 | + | 0.248521i | \(0.0799446\pi\) | ||||
−0.968626 | + | 0.248521i | \(0.920055\pi\) | |||||||
\(954\) | − | 4.83433e14i | − | 0.611778i | ||||||
\(955\) | 1.01636e14 | 0.127947 | ||||||||
\(956\) | −1.88422e14 | −0.235962 | ||||||||
\(957\) | 1.40731e14 | 0.175319 | ||||||||
\(958\) | 9.54733e14i | 1.18319i | ||||||||
\(959\) | −1.83577e15 | −2.26321 | ||||||||
\(960\) | 1.99626e13 | 0.0244827 | ||||||||
\(961\) | 5.50772e14 | 0.671978 | ||||||||
\(962\) | 6.32535e14 | 0.767732 | ||||||||
\(963\) | 1.00672e15 | 1.21556 | ||||||||
\(964\) | − | 5.75057e12i | − | 0.00690758i | ||||||
\(965\) | 1.38073e15i | 1.64996i | ||||||||
\(966\) | 1.85328e13i | 0.0220321i | ||||||||
\(967\) | −1.60988e14 | −0.190397 | −0.0951985 | − | 0.995458i | \(-0.530349\pi\) | ||||
−0.0951985 | + | 0.995458i | \(0.530349\pi\) | |||||||
\(968\) | − | 9.90395e14i | − | 1.16528i | ||||||
\(969\) | −1.17135e14 | −0.137109 | ||||||||
\(970\) | 6.59557e13 | 0.0768057 | ||||||||
\(971\) | −5.69117e14 | −0.659334 | −0.329667 | − | 0.944097i | \(-0.606936\pi\) | ||||
−0.329667 | + | 0.944097i | \(0.606936\pi\) | |||||||
\(972\) | 1.31276e14i | 0.151305i | ||||||||
\(973\) | − | 1.17538e15i | − | 1.34777i | ||||||
\(974\) | 2.84238e14i | 0.324255i | ||||||||
\(975\) | 2.98595e13i | 0.0338890i | ||||||||
\(976\) | − | 1.11664e15i | − | 1.26085i | ||||||
\(977\) | 1.19917e15 | 1.34713 | 0.673565 | − | 0.739128i | \(-0.264762\pi\) | ||||
0.673565 | + | 0.739128i | \(0.264762\pi\) | |||||||
\(978\) | 1.43450e14i | 0.160327i | ||||||||
\(979\) | 1.87714e15i | 2.08729i | ||||||||
\(980\) | 3.75651e14i | 0.415580i | ||||||||
\(981\) | −6.23572e14 | −0.686343 | ||||||||
\(982\) | −1.79406e15 | −1.96462 | ||||||||
\(983\) | 5.25418e14i | 0.572450i | 0.958162 | + | 0.286225i | \(0.0924005\pi\) | ||||
−0.958162 | + | 0.286225i | \(0.907599\pi\) | |||||||
\(984\) | 1.83003e13 | 0.0198373 | ||||||||
\(985\) | 9.36334e14i | 1.00983i | ||||||||
\(986\) | 2.09450e15 | 2.24748 | ||||||||
\(987\) | 1.64749e14 | 0.175888 | ||||||||
\(988\) | − | 3.97920e14i | − | 0.422680i | ||||||
\(989\) | 3.15985e13 | + | 1.69477e14i | 0.0333953 | + | 0.179114i | ||||
\(990\) | −3.12431e15 | −3.28532 | ||||||||
\(991\) | − | 1.60507e15i | − | 1.67929i | −0.543134 | − | 0.839646i | \(-0.682763\pi\) | ||
0.543134 | − | 0.839646i | \(-0.317237\pi\) | |||||||
\(992\) | − | 1.40935e15i | − | 1.46710i | ||||||
\(993\) | 4.08660e13 | 0.0423269 | ||||||||
\(994\) | 2.22538e15i | 2.29336i | ||||||||
\(995\) | −3.65884e14 | −0.375170 | ||||||||
\(996\) | − | 6.60903e13i | − | 0.0674281i | ||||||
\(997\) | − | 7.58882e13i | − | 0.0770368i | −0.999258 | − | 0.0385184i | \(-0.987736\pi\) | ||
0.999258 | − | 0.0385184i | \(-0.0122638\pi\) | |||||||
\(998\) | −7.05390e14 | −0.712486 | ||||||||
\(999\) | 1.71184e14 | 0.172043 |
(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 | 43.11.b.b.42.9 | ✓ | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.26 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.9 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.11.b.b.42.26 | yes | 34 | 43.42 | odd | 2 | inner |