Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5,20,Mod(4,5)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 20, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5.4");
S:= CuspForms(chi, 20);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5 \) |
Weight: | \( k \) | \(=\) | \( 20 \) |
Character orbit: | \([\chi]\) | \(=\) | 5.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: | \(11.4408348278\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 726881x^{6} + 160513523376x^{4} + 10607307647230976x^{2} + 32429098232548950016 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{20}\cdot 3^{8}\cdot 5^{13} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.7 | ||
Root | \(490.322i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5.4 |
Dual form | 5.20.b.a.4.2 |
$q$-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 \(\left(\mathbb{Z}/5\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 980.644i | 1.35434i | 0.735829 | + | 0.677168i | \(0.236793\pi\) | ||||
−0.735829 | + | 0.677168i | \(0.763207\pi\) | |||||||
\(3\) | 42067.9i | 1.23396i | 0.786981 | + | 0.616978i | \(0.211643\pi\) | ||||
−0.786981 | + | 0.616978i | \(0.788357\pi\) | |||||||
\(4\) | −437374. | −0.834225 | ||||||||
\(5\) | −2.12371e6 | + | 3.81619e6i | −0.486274 | + | 0.873806i | ||||
\(6\) | −4.12537e7 | −1.67119 | ||||||||
\(7\) | 4.16374e7i | 0.389989i | 0.980804 | + | 0.194995i | \(0.0624689\pi\) | ||||
−0.980804 | + | 0.194995i | \(0.937531\pi\) | |||||||
\(8\) | 8.52313e7i | 0.224514i | ||||||||
\(9\) | −6.07450e8 | −0.522645 | ||||||||
\(10\) | −3.74233e9 | − | 2.08261e9i | −1.18343 | − | 0.658578i | ||||
\(11\) | 1.14407e10 | 1.46293 | 0.731463 | − | 0.681881i | \(-0.238838\pi\) | ||||
0.731463 | + | 0.681881i | \(0.238838\pi\) | |||||||
\(12\) | − | 1.83994e10i | − | 1.02940i | ||||||
\(13\) | − | 4.17570e10i | − | 1.09211i | −0.837749 | − | 0.546056i | \(-0.816129\pi\) | ||
0.837749 | − | 0.546056i | \(-0.183871\pi\) | |||||||
\(14\) | −4.08315e10 | −0.528176 | ||||||||
\(15\) | −1.60539e11 | − | 8.93403e10i | −1.07824 | − | 0.600040i | ||||
\(16\) | −3.12892e11 | −1.13829 | ||||||||
\(17\) | 7.42315e9i | 0.0151818i | 0.999971 | + | 0.00759090i | \(0.00241628\pi\) | ||||
−0.999971 | + | 0.00759090i | \(0.997584\pi\) | |||||||
\(18\) | − | 5.95692e11i | − | 0.707837i | ||||||
\(19\) | 2.13723e12 | 1.51947 | 0.759733 | − | 0.650235i | \(-0.225329\pi\) | ||||
0.759733 | + | 0.650235i | \(0.225329\pi\) | |||||||
\(20\) | 9.28858e11 | − | 1.66910e12i | 0.405662 | − | 0.728952i | ||||
\(21\) | −1.75160e12 | −0.481229 | ||||||||
\(22\) | 1.12193e13i | 1.98129i | ||||||||
\(23\) | 9.51745e12i | 1.10181i | 0.834568 | + | 0.550904i | \(0.185717\pi\) | ||||
−0.834568 | + | 0.550904i | \(0.814283\pi\) | |||||||
\(24\) | −3.58551e12 | −0.277041 | ||||||||
\(25\) | −1.00532e13 | − | 1.62090e13i | −0.527076 | − | 0.849818i | ||||
\(26\) | 4.09487e13 | 1.47909 | ||||||||
\(27\) | 2.33398e13i | 0.589035i | ||||||||
\(28\) | − | 1.82111e13i | − | 0.325339i | ||||||
\(29\) | −5.19464e13 | −0.664928 | −0.332464 | − | 0.943116i | \(-0.607880\pi\) | ||||
−0.332464 | + | 0.943116i | \(0.607880\pi\) | |||||||
\(30\) | 8.76110e13 | − | 1.57432e14i | 0.812656 | − | 1.46030i | ||||
\(31\) | −2.16926e14 | −1.47358 | −0.736792 | − | 0.676119i | \(-0.763660\pi\) | ||||
−0.736792 | + | 0.676119i | \(0.763660\pi\) | |||||||
\(32\) | − | 2.62150e14i | − | 1.31712i | ||||||
\(33\) | 4.81287e14i | 1.80518i | ||||||||
\(34\) | −7.27947e12 | −0.0205613 | ||||||||
\(35\) | −1.58896e14 | − | 8.84260e13i | −0.340775 | − | 0.189642i | ||||
\(36\) | 2.65683e14 | 0.436004 | ||||||||
\(37\) | − | 7.79624e14i | − | 0.986209i | −0.869970 | − | 0.493105i | \(-0.835862\pi\) | ||
0.869970 | − | 0.493105i | \(-0.164138\pi\) | |||||||
\(38\) | 2.09586e15i | 2.05787i | ||||||||
\(39\) | 1.75663e15 | 1.34762 | ||||||||
\(40\) | −3.25259e14 | − | 1.81007e14i | −0.196182 | − | 0.109175i | ||||
\(41\) | 1.01438e15 | 0.483897 | 0.241948 | − | 0.970289i | \(-0.422214\pi\) | ||||
0.241948 | + | 0.970289i | \(0.422214\pi\) | |||||||
\(42\) | − | 1.71770e15i | − | 0.651746i | ||||||
\(43\) | 3.59622e15i | 1.09118i | 0.838052 | + | 0.545590i | \(0.183694\pi\) | ||||
−0.838052 | + | 0.545590i | \(0.816306\pi\) | |||||||
\(44\) | −5.00387e15 | −1.22041 | ||||||||
\(45\) | 1.29005e15 | − | 2.31815e15i | 0.254149 | − | 0.456691i | ||||
\(46\) | −9.33323e15 | −1.49222 | ||||||||
\(47\) | 5.35264e14i | 0.0697652i | 0.999391 | + | 0.0348826i | \(0.0111057\pi\) | ||||
−0.999391 | + | 0.0348826i | \(0.988894\pi\) | |||||||
\(48\) | − | 1.31627e16i | − | 1.40460i | ||||||
\(49\) | 9.66522e15 | 0.847908 | ||||||||
\(50\) | 1.58953e16 | − | 9.85858e15i | 1.15094 | − | 0.713837i | ||||
\(51\) | −3.12277e14 | −0.0187337 | ||||||||
\(52\) | 1.82634e16i | 0.911068i | ||||||||
\(53\) | − | 1.44320e16i | − | 0.600767i | −0.953819 | − | 0.300383i | \(-0.902885\pi\) | ||
0.953819 | − | 0.300383i | \(-0.0971146\pi\) | |||||||
\(54\) | −2.28880e16 | −0.797751 | ||||||||
\(55\) | −2.42968e16 | + | 4.36599e16i | −0.711383 | + | 1.27831i | ||||
\(56\) | −3.54881e15 | −0.0875582 | ||||||||
\(57\) | 8.99087e16i | 1.87495i | ||||||||
\(58\) | − | 5.09409e16i | − | 0.900536i | ||||||
\(59\) | 1.09094e17 | 1.63949 | 0.819745 | − | 0.572729i | \(-0.194115\pi\) | ||||
0.819745 | + | 0.572729i | \(0.194115\pi\) | |||||||
\(60\) | 7.02158e16 | + | 3.90751e16i | 0.899493 | + | 0.500569i | ||||
\(61\) | −1.12610e17 | −1.23294 | −0.616472 | − | 0.787377i | \(-0.711439\pi\) | ||||
−0.616472 | + | 0.787377i | \(0.711439\pi\) | |||||||
\(62\) | − | 2.12727e17i | − | 1.99573i | ||||||
\(63\) | − | 2.52927e16i | − | 0.203826i | ||||||
\(64\) | 9.30300e16 | 0.645525 | ||||||||
\(65\) | 1.59353e17 | + | 8.86799e16i | 0.954295 | + | 0.531066i | ||||
\(66\) | −4.71971e17 | −2.44483 | ||||||||
\(67\) | − | 5.23746e16i | − | 0.235185i | −0.993062 | − | 0.117593i | \(-0.962482\pi\) | ||
0.993062 | − | 0.117593i | \(-0.0375177\pi\) | |||||||
\(68\) | − | 3.24670e15i | − | 0.0126650i | ||||||
\(69\) | −4.00380e17 | −1.35958 | ||||||||
\(70\) | 8.67144e16 | − | 1.55821e17i | 0.256838 | − | 0.461524i | ||||
\(71\) | 2.62839e17 | 0.680354 | 0.340177 | − | 0.940361i | \(-0.389513\pi\) | ||||
0.340177 | + | 0.940361i | \(0.389513\pi\) | |||||||
\(72\) | − | 5.17738e16i | − | 0.117341i | ||||||
\(73\) | 4.11875e17i | 0.818838i | 0.912346 | + | 0.409419i | \(0.134269\pi\) | ||||
−0.912346 | + | 0.409419i | \(0.865731\pi\) | |||||||
\(74\) | 7.64534e17 | 1.33566 | ||||||||
\(75\) | 6.81879e17 | − | 4.22916e17i | 1.04864 | − | 0.650387i | ||||
\(76\) | −9.34768e17 | −1.26758 | ||||||||
\(77\) | 4.76361e17i | 0.570525i | ||||||||
\(78\) | 1.72263e18i | 1.82513i | ||||||||
\(79\) | 6.87674e17 | 0.645543 | 0.322771 | − | 0.946477i | \(-0.395386\pi\) | ||||
0.322771 | + | 0.946477i | \(0.395386\pi\) | |||||||
\(80\) | 6.64492e17 | − | 1.19406e18i | 0.553522 | − | 0.994648i | ||||
\(81\) | −1.68787e18 | −1.24949 | ||||||||
\(82\) | 9.94743e17i | 0.655359i | ||||||||
\(83\) | − | 1.74169e18i | − | 1.02266i | −0.859386 | − | 0.511328i | \(-0.829154\pi\) | ||
0.859386 | − | 0.511328i | \(-0.170846\pi\) | |||||||
\(84\) | 7.66105e17 | 0.401453 | ||||||||
\(85\) | −2.83282e16 | − | 1.57646e16i | −0.0132660 | − | 0.00738251i | ||||
\(86\) | −3.52662e18 | −1.47782 | ||||||||
\(87\) | − | 2.18528e18i | − | 0.820491i | ||||||
\(88\) | 9.75106e17i | 0.328448i | ||||||||
\(89\) | −4.41598e17 | −0.133605 | −0.0668023 | − | 0.997766i | \(-0.521280\pi\) | ||||
−0.0668023 | + | 0.997766i | \(0.521280\pi\) | |||||||
\(90\) | 2.27328e18 | + | 1.26508e18i | 0.618512 | + | 0.344203i | ||||
\(91\) | 1.73865e18 | 0.425912 | ||||||||
\(92\) | − | 4.16269e18i | − | 0.919157i | ||||||
\(93\) | − | 9.12562e18i | − | 1.81834i | ||||||
\(94\) | −5.24904e17 | −0.0944854 | ||||||||
\(95\) | −4.53886e18 | + | 8.15607e18i | −0.738877 | + | 1.32772i | ||||
\(96\) | 1.10281e19 | 1.62526 | ||||||||
\(97\) | 8.34283e18i | 1.11425i | 0.830429 | + | 0.557124i | \(0.188095\pi\) | ||||
−0.830429 | + | 0.557124i | \(0.811905\pi\) | |||||||
\(98\) | 9.47814e18i | 1.14835i | ||||||||
\(99\) | −6.94966e18 | −0.764591 | ||||||||
\(100\) | 4.39700e18 | + | 7.08940e18i | 0.439700 | + | 0.708940i | ||||
\(101\) | −1.28630e19 | −1.17028 | −0.585141 | − | 0.810932i | \(-0.698961\pi\) | ||||
−0.585141 | + | 0.810932i | \(0.698961\pi\) | |||||||
\(102\) | − | 3.06232e17i | − | 0.0253717i | ||||||
\(103\) | − | 1.19999e19i | − | 0.906200i | −0.891460 | − | 0.453100i | \(-0.850318\pi\) | ||
0.891460 | − | 0.453100i | \(-0.149682\pi\) | |||||||
\(104\) | 3.55900e18 | 0.245195 | ||||||||
\(105\) | 3.71990e18 | − | 6.68445e18i | 0.234009 | − | 0.420501i | ||||
\(106\) | 1.41527e19 | 0.813640 | ||||||||
\(107\) | 1.09925e19i | 0.578031i | 0.957324 | + | 0.289015i | \(0.0933279\pi\) | ||||
−0.957324 | + | 0.289015i | \(0.906672\pi\) | |||||||
\(108\) | − | 1.02082e19i | − | 0.491388i | ||||||
\(109\) | 2.91204e19 | 1.28424 | 0.642119 | − | 0.766605i | \(-0.278055\pi\) | ||||
0.642119 | + | 0.766605i | \(0.278055\pi\) | |||||||
\(110\) | −4.28148e19 | − | 2.38265e19i | −1.73127 | − | 0.963451i | ||||
\(111\) | 3.27972e19 | 1.21694 | ||||||||
\(112\) | − | 1.30280e19i | − | 0.443922i | ||||||
\(113\) | − | 7.96559e18i | − | 0.249444i | −0.992192 | − | 0.124722i | \(-0.960196\pi\) | ||
0.992192 | − | 0.124722i | \(-0.0398039\pi\) | |||||||
\(114\) | −8.81684e19 | −2.53932 | ||||||||
\(115\) | −3.63204e19 | − | 2.02123e19i | −0.962768 | − | 0.535781i | ||||
\(116\) | 2.27200e19 | 0.554700 | ||||||||
\(117\) | 2.53653e19i | 0.570787i | ||||||||
\(118\) | 1.06983e20i | 2.22042i | ||||||||
\(119\) | −3.09081e17 | −0.00592074 | ||||||||
\(120\) | 7.61459e18 | − | 1.36830e19i | 0.134718 | − | 0.242080i | ||||
\(121\) | 6.97306e19 | 1.14015 | ||||||||
\(122\) | − | 1.10430e20i | − | 1.66982i | ||||||
\(123\) | 4.26728e19i | 0.597107i | ||||||||
\(124\) | 9.48778e19 | 1.22930 | ||||||||
\(125\) | 8.32067e19 | − | 3.94155e18i | 0.998880 | − | 0.0473175i | ||||
\(126\) | 2.48031e19 | 0.276049 | ||||||||
\(127\) | 1.17395e20i | 1.21204i | 0.795450 | + | 0.606019i | \(0.207234\pi\) | ||||
−0.795450 | + | 0.606019i | \(0.792766\pi\) | |||||||
\(128\) | − | 4.62126e19i | − | 0.442859i | ||||||
\(129\) | −1.51286e20 | −1.34647 | ||||||||
\(130\) | −8.69634e19 | + | 1.56268e20i | −0.719241 | + | 1.29244i | ||||
\(131\) | −7.72292e19 | −0.593888 | −0.296944 | − | 0.954895i | \(-0.595967\pi\) | ||||
−0.296944 | + | 0.954895i | \(0.595967\pi\) | |||||||
\(132\) | − | 2.10503e20i | − | 1.50593i | ||||||
\(133\) | 8.89886e19i | 0.592575i | ||||||||
\(134\) | 5.13608e19 | 0.318520 | ||||||||
\(135\) | −8.90691e19 | − | 4.95670e19i | −0.514702 | − | 0.286432i | ||||
\(136\) | −6.32685e17 | −0.00340853 | ||||||||
\(137\) | 5.30215e19i | 0.266444i | 0.991086 | + | 0.133222i | \(0.0425324\pi\) | ||||
−0.991086 | + | 0.133222i | \(0.957468\pi\) | |||||||
\(138\) | − | 3.92630e20i | − | 1.84133i | ||||||
\(139\) | 2.98946e19 | 0.130904 | 0.0654519 | − | 0.997856i | \(-0.479151\pi\) | ||||
0.0654519 | + | 0.997856i | \(0.479151\pi\) | |||||||
\(140\) | 6.94972e19 | + | 3.86753e19i | 0.284283 | + | 0.158204i | ||||
\(141\) | −2.25175e19 | −0.0860871 | ||||||||
\(142\) | 2.57751e20i | 0.921428i | ||||||||
\(143\) | − | 4.77729e20i | − | 1.59768i | ||||||
\(144\) | 1.90066e20 | 0.594923 | ||||||||
\(145\) | 1.10319e20 | − | 1.98238e20i | 0.323337 | − | 0.581018i | ||||
\(146\) | −4.03903e20 | −1.10898 | ||||||||
\(147\) | 4.06596e20i | 1.04628i | ||||||||
\(148\) | 3.40988e20i | 0.822721i | ||||||||
\(149\) | 3.32734e20 | 0.753057 | 0.376529 | − | 0.926405i | \(-0.377118\pi\) | ||||
0.376529 | + | 0.926405i | \(0.377118\pi\) | |||||||
\(150\) | 4.14730e20 | + | 6.68681e20i | 0.880843 | + | 1.42021i | ||||
\(151\) | −2.93056e20 | −0.584345 | −0.292172 | − | 0.956366i | \(-0.594378\pi\) | ||||
−0.292172 | + | 0.956366i | \(0.594378\pi\) | |||||||
\(152\) | 1.82159e20i | 0.341142i | ||||||||
\(153\) | − | 4.50919e18i | − | 0.00793469i | ||||||
\(154\) | −4.67141e20 | −0.772683 | ||||||||
\(155\) | 4.60688e20 | − | 8.27830e20i | 0.716565 | − | 1.28763i | ||||
\(156\) | −7.68305e20 | −1.12422 | ||||||||
\(157\) | − | 8.15273e18i | − | 0.0112268i | −0.999984 | − | 0.00561340i | \(-0.998213\pi\) | ||
0.999984 | − | 0.00561340i | \(-0.00178681\pi\) | |||||||
\(158\) | 6.74363e20i | 0.874282i | ||||||||
\(159\) | 6.07125e20 | 0.741319 | ||||||||
\(160\) | 1.00041e21 | + | 5.56731e20i | 1.15091 | + | 0.640480i | ||||
\(161\) | −3.96282e20 | −0.429693 | ||||||||
\(162\) | − | 1.65520e21i | − | 1.69223i | ||||||
\(163\) | 5.95063e20i | 0.573827i | 0.957957 | + | 0.286913i | \(0.0926292\pi\) | ||||
−0.957957 | + | 0.286913i | \(0.907371\pi\) | |||||||
\(164\) | −4.43663e20 | −0.403679 | ||||||||
\(165\) | −1.83668e21 | − | 1.02212e21i | −1.57738 | − | 0.877814i | ||||
\(166\) | 1.70798e21 | 1.38502 | ||||||||
\(167\) | − | 1.29434e21i | − | 0.991382i | −0.868499 | − | 0.495691i | \(-0.834915\pi\) | ||
0.868499 | − | 0.495691i | \(-0.165085\pi\) | |||||||
\(168\) | − | 1.49291e20i | − | 0.108043i | ||||||
\(169\) | −2.81726e20 | −0.192709 | ||||||||
\(170\) | 1.54595e19 | − | 2.77798e19i | 0.00999840 | − | 0.0179666i | ||||
\(171\) | −1.29826e21 | −0.794142 | ||||||||
\(172\) | − | 1.57290e21i | − | 0.910290i | ||||||
\(173\) | 2.62946e21i | 1.44022i | 0.693859 | + | 0.720111i | \(0.255909\pi\) | ||||
−0.693859 | + | 0.720111i | \(0.744091\pi\) | |||||||
\(174\) | 2.14298e21 | 1.11122 | ||||||||
\(175\) | 6.74901e20 | − | 4.18588e20i | 0.331420 | − | 0.205554i | ||||
\(176\) | −3.57970e21 | −1.66524 | ||||||||
\(177\) | 4.58938e21i | 2.02306i | ||||||||
\(178\) | − | 4.33050e20i | − | 0.180946i | ||||||
\(179\) | −8.09069e20 | −0.320539 | −0.160270 | − | 0.987073i | \(-0.551236\pi\) | ||||
−0.160270 | + | 0.987073i | \(0.551236\pi\) | |||||||
\(180\) | −5.64235e20 | + | 1.01390e21i | −0.212017 | + | 0.380983i | ||||
\(181\) | 3.10735e21 | 1.10776 | 0.553878 | − | 0.832598i | \(-0.313147\pi\) | ||||
0.553878 | + | 0.832598i | \(0.313147\pi\) | |||||||
\(182\) | 1.70500e21i | 0.576828i | ||||||||
\(183\) | − | 4.73727e21i | − | 1.52140i | ||||||
\(184\) | −8.11185e20 | −0.247372 | ||||||||
\(185\) | 2.97520e21 | + | 1.65570e21i | 0.861756 | + | 0.479568i | ||||
\(186\) | 8.94898e21 | 2.46264 | ||||||||
\(187\) | 8.49261e19i | 0.0222099i | ||||||||
\(188\) | − | 2.34111e20i | − | 0.0581999i | ||||||
\(189\) | −9.71808e20 | −0.229717 | ||||||||
\(190\) | −7.99820e21 | − | 4.45100e21i | −1.79818 | − | 1.00069i | ||||
\(191\) | 3.37556e21 | 0.721986 | 0.360993 | − | 0.932569i | \(-0.382438\pi\) | ||||
0.360993 | + | 0.932569i | \(0.382438\pi\) | |||||||
\(192\) | 3.91358e21i | 0.796549i | ||||||||
\(193\) | − | 3.16222e21i | − | 0.612629i | −0.951930 | − | 0.306314i | \(-0.900904\pi\) | ||
0.951930 | − | 0.306314i | \(-0.0990959\pi\) | |||||||
\(194\) | −8.18135e21 | −1.50907 | ||||||||
\(195\) | −3.73058e21 | + | 6.70364e21i | −0.655311 | + | 1.17756i | ||||
\(196\) | −4.22732e21 | −0.707347 | ||||||||
\(197\) | 1.08962e21i | 0.173718i | 0.996221 | + | 0.0868588i | \(0.0276829\pi\) | ||||
−0.996221 | + | 0.0868588i | \(0.972317\pi\) | |||||||
\(198\) | − | 6.81514e21i | − | 1.03551i | ||||||
\(199\) | −1.26294e21 | −0.182927 | −0.0914635 | − | 0.995808i | \(-0.529154\pi\) | ||||
−0.0914635 | + | 0.995808i | \(0.529154\pi\) | |||||||
\(200\) | 1.38151e21 | − | 8.56844e20i | 0.190796 | − | 0.118336i | ||||
\(201\) | 2.20329e21 | 0.290208 | ||||||||
\(202\) | − | 1.26141e22i | − | 1.58495i | ||||||
\(203\) | − | 2.16292e21i | − | 0.259315i | ||||||
\(204\) | 1.36582e20 | 0.0156281 | ||||||||
\(205\) | −2.15425e21 | + | 3.87106e21i | −0.235306 | + | 0.422832i | ||||
\(206\) | 1.17676e22 | 1.22730 | ||||||||
\(207\) | − | 5.78138e21i | − | 0.575855i | ||||||
\(208\) | 1.30654e22i | 1.24314i | ||||||||
\(209\) | 2.44514e22 | 2.22287 | ||||||||
\(210\) | 6.55506e21 | + | 3.64790e21i | 0.569500 | + | 0.316927i | ||||
\(211\) | −1.13686e22 | −0.944110 | −0.472055 | − | 0.881569i | \(-0.656488\pi\) | ||||
−0.472055 | + | 0.881569i | \(0.656488\pi\) | |||||||
\(212\) | 6.31219e21i | 0.501175i | ||||||||
\(213\) | 1.10571e22i | 0.839527i | ||||||||
\(214\) | −1.07797e22 | −0.782848 | ||||||||
\(215\) | −1.37239e22 | − | 7.63735e21i | −0.953480 | − | 0.530612i | ||||
\(216\) | −1.98928e21 | −0.132247 | ||||||||
\(217\) | − | 9.03223e21i | − | 0.574682i | ||||||
\(218\) | 2.85568e22i | 1.73929i | ||||||||
\(219\) | −1.73267e22 | −1.01041 | ||||||||
\(220\) | 1.06268e22 | − | 1.90957e22i | 0.593453 | − | 1.06640i | ||||
\(221\) | 3.09968e20 | 0.0165802 | ||||||||
\(222\) | 3.21624e22i | 1.64814i | ||||||||
\(223\) | − | 1.73802e21i | − | 0.0853414i | −0.999089 | − | 0.0426707i | \(-0.986413\pi\) | ||
0.999089 | − | 0.0426707i | \(-0.0135866\pi\) | |||||||
\(224\) | 1.09152e22 | 0.513661 | ||||||||
\(225\) | 6.10680e21 | + | 9.84616e21i | 0.275473 | + | 0.444153i | ||||
\(226\) | 7.81141e21 | 0.337831 | ||||||||
\(227\) | − | 3.40756e22i | − | 1.41318i | −0.707623 | − | 0.706590i | \(-0.750232\pi\) | ||
0.707623 | − | 0.706590i | \(-0.249768\pi\) | |||||||
\(228\) | − | 3.93238e22i | − | 1.56413i | ||||||
\(229\) | 6.46428e21 | 0.246651 | 0.123326 | − | 0.992366i | \(-0.460644\pi\) | ||||
0.123326 | + | 0.992366i | \(0.460644\pi\) | |||||||
\(230\) | 1.98211e22 | − | 3.56174e22i | 0.725627 | − | 1.30391i | ||||
\(231\) | −2.00395e22 | −0.704002 | ||||||||
\(232\) | − | 4.42746e21i | − | 0.149286i | ||||||
\(233\) | 3.38945e21i | 0.109711i | 0.998494 | + | 0.0548553i | \(0.0174698\pi\) | ||||
−0.998494 | + | 0.0548553i | \(0.982530\pi\) | |||||||
\(234\) | −2.48743e22 | −0.773037 | ||||||||
\(235\) | −2.04267e21 | − | 1.13675e21i | −0.0609612 | − | 0.0339250i | ||||
\(236\) | −4.77151e22 | −1.36770 | ||||||||
\(237\) | 2.89290e22i | 0.796571i | ||||||||
\(238\) | − | 3.03098e20i | − | 0.00801867i | ||||||
\(239\) | 2.86059e22 | 0.727238 | 0.363619 | − | 0.931548i | \(-0.381541\pi\) | ||||
0.363619 | + | 0.931548i | \(0.381541\pi\) | |||||||
\(240\) | 5.02314e22 | + | 2.79538e22i | 1.22735 | + | 0.683022i | ||||
\(241\) | −5.82109e22 | −1.36723 | −0.683616 | − | 0.729842i | \(-0.739594\pi\) | ||||
−0.683616 | + | 0.729842i | \(0.739594\pi\) | |||||||
\(242\) | 6.83809e22i | 1.54415i | ||||||||
\(243\) | − | 4.38784e22i | − | 0.952776i | ||||||
\(244\) | 4.92527e22 | 1.02855 | ||||||||
\(245\) | −2.05262e22 | + | 3.68843e22i | −0.412316 | + | 0.740908i | ||||
\(246\) | −4.18468e22 | −0.808683 | ||||||||
\(247\) | − | 8.92441e22i | − | 1.65943i | ||||||
\(248\) | − | 1.84889e22i | − | 0.330841i | ||||||
\(249\) | 7.32694e22 | 1.26191 | ||||||||
\(250\) | 3.86526e21 | + | 8.15962e22i | 0.0640838 | + | 1.35282i | ||||
\(251\) | 6.40096e22 | 1.02175 | 0.510875 | − | 0.859655i | \(-0.329321\pi\) | ||||
0.510875 | + | 0.859655i | \(0.329321\pi\) | |||||||
\(252\) | 1.10624e22i | 0.170037i | ||||||||
\(253\) | 1.08886e23i | 1.61186i | ||||||||
\(254\) | −1.15123e23 | −1.64151 | ||||||||
\(255\) | 6.63186e20 | − | 1.19171e21i | 0.00910969 | − | 0.0163696i | ||||
\(256\) | 9.40926e22 | 1.24531 | ||||||||
\(257\) | 2.55646e22i | 0.326043i | 0.986623 | + | 0.163021i | \(0.0521239\pi\) | ||||
−0.986623 | + | 0.163021i | \(0.947876\pi\) | |||||||
\(258\) | − | 1.48357e23i | − | 1.82357i | ||||||
\(259\) | 3.24616e22 | 0.384611 | ||||||||
\(260\) | −6.96968e22 | − | 3.87863e22i | −0.796097 | − | 0.443028i | ||||
\(261\) | 3.15549e22 | 0.347521 | ||||||||
\(262\) | − | 7.57344e22i | − | 0.804323i | ||||||
\(263\) | 1.34746e22i | 0.138018i | 0.997616 | + | 0.0690092i | \(0.0219838\pi\) | ||||
−0.997616 | + | 0.0690092i | \(0.978016\pi\) | |||||||
\(264\) | −4.10207e22 | −0.405290 | ||||||||
\(265\) | 5.50753e22 | + | 3.06494e22i | 0.524954 | + | 0.292137i | ||||
\(266\) | −8.72661e22 | −0.802546 | ||||||||
\(267\) | − | 1.85771e22i | − | 0.164862i | ||||||
\(268\) | 2.29073e22i | 0.196197i | ||||||||
\(269\) | −9.65349e22 | −0.798064 | −0.399032 | − | 0.916937i | \(-0.630654\pi\) | ||||
−0.399032 | + | 0.916937i | \(0.630654\pi\) | |||||||
\(270\) | 4.86076e22 | − | 8.73450e22i | 0.387925 | − | 0.697080i | ||||
\(271\) | −1.68889e23 | −1.30135 | −0.650674 | − | 0.759358i | \(-0.725513\pi\) | ||||
−0.650674 | + | 0.759358i | \(0.725513\pi\) | |||||||
\(272\) | − | 2.32264e21i | − | 0.0172813i | ||||||
\(273\) | 7.31416e22i | 0.525556i | ||||||||
\(274\) | −5.19952e22 | −0.360855 | ||||||||
\(275\) | −1.15015e23 | − | 1.85442e23i | −0.771072 | − | 1.24322i | ||||
\(276\) | 1.75116e23 | 1.13420 | ||||||||
\(277\) | 1.67203e23i | 1.04637i | 0.852218 | + | 0.523187i | \(0.175257\pi\) | ||||
−0.852218 | + | 0.523187i | \(0.824743\pi\) | |||||||
\(278\) | 2.93159e22i | 0.177288i | ||||||||
\(279\) | 1.31772e23 | 0.770161 | ||||||||
\(280\) | 7.53666e21 | − | 1.35429e22i | 0.0425772 | − | 0.0765089i | ||||
\(281\) | 3.43594e23 | 1.87644 | 0.938222 | − | 0.346035i | \(-0.112472\pi\) | ||||
0.938222 | + | 0.346035i | \(0.112472\pi\) | |||||||
\(282\) | − | 2.20816e22i | − | 0.116591i | ||||||
\(283\) | 2.60310e23i | 1.32898i | 0.747296 | + | 0.664492i | \(0.231352\pi\) | ||||
−0.747296 | + | 0.664492i | \(0.768648\pi\) | |||||||
\(284\) | −1.14959e23 | −0.567569 | ||||||||
\(285\) | −3.43109e23 | − | 1.90940e23i | −1.63835 | − | 0.911741i | ||||
\(286\) | 4.68482e23 | 2.16379 | ||||||||
\(287\) | 4.22361e22i | 0.188715i | ||||||||
\(288\) | 1.59243e23i | 0.688385i | ||||||||
\(289\) | 2.39017e23 | 0.999770 | ||||||||
\(290\) | 1.94400e23 | + | 1.08184e23i | 0.786894 | + | 0.437907i | ||||
\(291\) | −3.50966e23 | −1.37493 | ||||||||
\(292\) | − | 1.80144e23i | − | 0.683096i | ||||||
\(293\) | − | 3.60152e23i | − | 1.32203i | −0.750371 | − | 0.661017i | \(-0.770125\pi\) | ||
0.750371 | − | 0.661017i | \(-0.229875\pi\) | |||||||
\(294\) | −3.98726e23 | −1.41702 | ||||||||
\(295\) | −2.31685e23 | + | 4.16326e23i | −0.797241 | + | 1.43260i | ||||
\(296\) | 6.64484e22 | 0.221418 | ||||||||
\(297\) | 2.67023e23i | 0.861714i | ||||||||
\(298\) | 3.26294e23i | 1.01989i | ||||||||
\(299\) | 3.97420e23 | 1.20330 | ||||||||
\(300\) | −2.98237e23 | + | 1.84973e23i | −0.874800 | + | 0.542570i | ||||
\(301\) | −1.49738e23 | −0.425548 | ||||||||
\(302\) | − | 2.87383e23i | − | 0.791399i | ||||||
\(303\) | − | 5.41121e23i | − | 1.44407i | ||||||
\(304\) | −6.68720e23 | −1.72960 | ||||||||
\(305\) | 2.39151e23 | − | 4.29741e23i | 0.599548 | − | 1.07735i | ||||
\(306\) | 4.42191e21 | 0.0107462 | ||||||||
\(307\) | − | 7.14964e23i | − | 1.68449i | −0.539092 | − | 0.842247i | \(-0.681233\pi\) | ||
0.539092 | − | 0.842247i | \(-0.318767\pi\) | |||||||
\(308\) | − | 2.08348e23i | − | 0.475947i | ||||||
\(309\) | 5.04811e23 | 1.11821 | ||||||||
\(310\) | 8.11807e23 | + | 4.51771e23i | 1.74388 | + | 0.970470i | ||||
\(311\) | 3.19170e22 | 0.0664965 | 0.0332482 | − | 0.999447i | \(-0.489415\pi\) | ||||
0.0332482 | + | 0.999447i | \(0.489415\pi\) | |||||||
\(312\) | 1.49720e23i | 0.302560i | ||||||||
\(313\) | − | 8.15443e23i | − | 1.59854i | −0.600975 | − | 0.799268i | \(-0.705221\pi\) | ||
0.600975 | − | 0.799268i | \(-0.294779\pi\) | |||||||
\(314\) | 7.99492e21 | 0.0152049 | ||||||||
\(315\) | 9.65217e22 | + | 5.37144e22i | 0.178104 | + | 0.0991152i | ||||
\(316\) | −3.00771e23 | −0.538528 | ||||||||
\(317\) | 1.03020e24i | 1.79003i | 0.446039 | + | 0.895014i | \(0.352834\pi\) | ||||
−0.446039 | + | 0.895014i | \(0.647166\pi\) | |||||||
\(318\) | 5.95373e23i | 1.00400i | ||||||||
\(319\) | −5.94304e23 | −0.972740 | ||||||||
\(320\) | −1.97569e23 | + | 3.55020e23i | −0.313902 | + | 0.564064i | ||||
\(321\) | −4.62432e23 | −0.713264 | ||||||||
\(322\) | − | 3.88612e23i | − | 0.581949i | ||||||
\(323\) | 1.58649e22i | 0.0230682i | ||||||||
\(324\) | 7.38232e23 | 1.04235 | ||||||||
\(325\) | −6.76839e23 | + | 4.19790e23i | −0.928097 | + | 0.575626i | ||||
\(326\) | −5.83545e23 | −0.777154 | ||||||||
\(327\) | 1.22504e24i | 1.58469i | ||||||||
\(328\) | 8.64567e22i | 0.108642i | ||||||||
\(329\) | −2.22870e22 | −0.0272076 | ||||||||
\(330\) | 1.00233e24 | − | 1.80113e24i | 1.18885 | − | 2.13630i | ||||
\(331\) | 6.75312e23 | 0.778285 | 0.389143 | − | 0.921178i | \(-0.372771\pi\) | ||||
0.389143 | + | 0.921178i | \(0.372771\pi\) | |||||||
\(332\) | 7.61772e23i | 0.853126i | ||||||||
\(333\) | 4.73583e23i | 0.515437i | ||||||||
\(334\) | 1.26928e24 | 1.34266 | ||||||||
\(335\) | 1.99871e23 | + | 1.11229e23i | 0.205506 | + | 0.114364i | ||||
\(336\) | 5.48061e23 | 0.547780 | ||||||||
\(337\) | − | 1.16149e24i | − | 1.12858i | −0.825578 | − | 0.564288i | \(-0.809151\pi\) | ||
0.825578 | − | 0.564288i | \(-0.190849\pi\) | |||||||
\(338\) | − | 2.76273e23i | − | 0.260993i | ||||||
\(339\) | 3.35096e23 | 0.307803 | ||||||||
\(340\) | 1.23900e22 | + | 6.89505e21i | 0.0110668 | + | 0.00615868i | ||||
\(341\) | −2.48178e24 | −2.15574 | ||||||||
\(342\) | − | 1.27313e24i | − | 1.07553i | ||||||
\(343\) | 8.77056e23i | 0.720664i | ||||||||
\(344\) | −3.06511e23 | −0.244986 | ||||||||
\(345\) | 8.50292e23 | − | 1.52793e24i | 0.661129 | − | 1.18801i | ||||
\(346\) | −2.57857e24 | −1.95054 | ||||||||
\(347\) | 3.58478e23i | 0.263835i | 0.991261 | + | 0.131918i | \(0.0421134\pi\) | ||||
−0.991261 | + | 0.131918i | \(0.957887\pi\) | |||||||
\(348\) | 9.55785e23i | 0.684475i | ||||||||
\(349\) | 6.18204e23 | 0.430814 | 0.215407 | − | 0.976524i | \(-0.430892\pi\) | ||||
0.215407 | + | 0.976524i | \(0.430892\pi\) | |||||||
\(350\) | 4.10486e23 | + | 6.61838e23i | 0.278389 | + | 0.448854i | ||||
\(351\) | 9.74599e23 | 0.643292 | ||||||||
\(352\) | − | 2.99918e24i | − | 1.92684i | ||||||
\(353\) | 5.21273e23i | 0.325991i | 0.986627 | + | 0.162995i | \(0.0521155\pi\) | ||||
−0.986627 | + | 0.162995i | \(0.947884\pi\) | |||||||
\(354\) | −4.50055e24 | −2.73990 | ||||||||
\(355\) | −5.58194e23 | + | 1.00304e24i | −0.330838 | + | 0.594498i | ||||
\(356\) | 1.93144e23 | 0.111456 | ||||||||
\(357\) | − | 1.30024e22i | − | 0.00730592i | ||||||
\(358\) | − | 7.93408e23i | − | 0.434118i | ||||||
\(359\) | 3.25395e24 | 1.73386 | 0.866930 | − | 0.498430i | \(-0.166090\pi\) | ||||
0.866930 | + | 0.498430i | \(0.166090\pi\) | |||||||
\(360\) | 1.97579e23 | + | 1.09953e23i | 0.102534 | + | 0.0570600i | ||||
\(361\) | 2.58931e24 | 1.30878 | ||||||||
\(362\) | 3.04721e24i | 1.50027i | ||||||||
\(363\) | 2.93342e24i | 1.40690i | ||||||||
\(364\) | −7.60442e23 | −0.355307 | ||||||||
\(365\) | −1.57179e24 | − | 8.74704e23i | −0.715506 | − | 0.398180i | ||||
\(366\) | 4.64557e24 | 2.06048 | ||||||||
\(367\) | − | 3.66499e24i | − | 1.58396i | −0.610546 | − | 0.791981i | \(-0.709050\pi\) | ||
0.610546 | − | 0.791981i | \(-0.290950\pi\) | |||||||
\(368\) | − | 2.97793e24i | − | 1.25418i | ||||||
\(369\) | −6.16184e23 | −0.252906 | ||||||||
\(370\) | −1.62365e24 | + | 2.91761e24i | −0.649496 | + | 1.16711i | ||||
\(371\) | 6.00912e23 | 0.234293 | ||||||||
\(372\) | 3.99131e24i | 1.51690i | ||||||||
\(373\) | − | 2.72449e24i | − | 1.00937i | −0.863303 | − | 0.504685i | \(-0.831608\pi\) | ||
0.863303 | − | 0.504685i | \(-0.168392\pi\) | |||||||
\(374\) | −8.32822e22 | −0.0300796 | ||||||||
\(375\) | 1.65813e23 | + | 3.50034e24i | 0.0583877 | + | 1.23257i | ||||
\(376\) | −4.56213e22 | −0.0156633 | ||||||||
\(377\) | 2.16913e24i | 0.726176i | ||||||||
\(378\) | − | 9.52997e23i | − | 0.311114i | ||||||
\(379\) | 1.76456e23 | 0.0561777 | 0.0280889 | − | 0.999605i | \(-0.491058\pi\) | ||||
0.0280889 | + | 0.999605i | \(0.491058\pi\) | |||||||
\(380\) | 1.98518e24 | − | 3.56725e24i | 0.616390 | − | 1.10762i | ||||
\(381\) | −4.93859e24 | −1.49560 | ||||||||
\(382\) | 3.31022e24i | 0.977811i | ||||||||
\(383\) | − | 1.90659e23i | − | 0.0549375i | −0.999623 | − | 0.0274687i | \(-0.991255\pi\) | ||
0.999623 | − | 0.0274687i | \(-0.00874467\pi\) | |||||||
\(384\) | 1.94407e24 | 0.546468 | ||||||||
\(385\) | −1.81789e24 | − | 1.01166e24i | −0.498529 | − | 0.277431i | ||||
\(386\) | 3.10101e24 | 0.829705 | ||||||||
\(387\) | − | 2.18453e24i | − | 0.570300i | ||||||
\(388\) | − | 3.64894e24i | − | 0.929535i | ||||||
\(389\) | −2.68719e24 | −0.668000 | −0.334000 | − | 0.942573i | \(-0.608399\pi\) | ||||
−0.334000 | + | 0.942573i | \(0.608399\pi\) | |||||||
\(390\) | −6.57388e24 | − | 3.65837e24i | −1.59481 | − | 0.887511i | ||||
\(391\) | −7.06495e22 | −0.0167274 | ||||||||
\(392\) | 8.23779e23i | 0.190368i | ||||||||
\(393\) | − | 3.24887e24i | − | 0.732831i | ||||||
\(394\) | −1.06852e24 | −0.235272 | ||||||||
\(395\) | −1.46042e24 | + | 2.62430e24i | −0.313911 | + | 0.564079i | ||||
\(396\) | 3.03960e24 | 0.637841 | ||||||||
\(397\) | − | 3.03148e24i | − | 0.621077i | −0.950561 | − | 0.310538i | \(-0.899491\pi\) | ||
0.950561 | − | 0.310538i | \(-0.100509\pi\) | |||||||
\(398\) | − | 1.23849e24i | − | 0.247745i | ||||||
\(399\) | −3.74357e24 | −0.731211 | ||||||||
\(400\) | 3.14555e24 | + | 5.07166e24i | 0.599967 | + | 0.967343i | ||||
\(401\) | 8.40661e24 | 1.56585 | 0.782923 | − | 0.622118i | \(-0.213728\pi\) | ||||
0.782923 | + | 0.622118i | \(0.213728\pi\) | |||||||
\(402\) | 2.16064e24i | 0.393039i | ||||||||
\(403\) | 9.05816e24i | 1.60932i | ||||||||
\(404\) | 5.62596e24 | 0.976279 | ||||||||
\(405\) | 3.58456e24 | − | 6.44124e24i | 0.607593 | − | 1.09181i | ||||
\(406\) | 2.12105e24 | 0.351199 | ||||||||
\(407\) | − | 8.91945e24i | − | 1.44275i | ||||||
\(408\) | − | 2.66157e22i | − | 0.00420598i | ||||||
\(409\) | −8.70689e24 | −1.34429 | −0.672143 | − | 0.740421i | \(-0.734626\pi\) | ||||
−0.672143 | + | 0.740421i | \(0.734626\pi\) | |||||||
\(410\) | −3.79613e24 | − | 2.11255e24i | −0.572657 | − | 0.318684i | ||||
\(411\) | −2.23050e24 | −0.328780 | ||||||||
\(412\) | 5.24845e24i | 0.755975i | ||||||||
\(413\) | 4.54241e24i | 0.639383i | ||||||||
\(414\) | 5.66947e24 | 0.779901 | ||||||||
\(415\) | 6.64664e24 | + | 3.69886e24i | 0.893604 | + | 0.497291i | ||||
\(416\) | −1.09466e25 | −1.43844 | ||||||||
\(417\) | 1.25760e24i | 0.161529i | ||||||||
\(418\) | 2.39781e25i | 3.01051i | ||||||||
\(419\) | −4.91947e24 | −0.603789 | −0.301895 | − | 0.953341i | \(-0.597619\pi\) | ||||
−0.301895 | + | 0.953341i | \(0.597619\pi\) | |||||||
\(420\) | −1.62699e24 | + | 2.92361e24i | −0.195216 | + | 0.350793i | ||||
\(421\) | 4.45443e24 | 0.522531 | 0.261266 | − | 0.965267i | \(-0.415860\pi\) | ||||
0.261266 | + | 0.965267i | \(0.415860\pi\) | |||||||
\(422\) | − | 1.11485e25i | − | 1.27864i | ||||||
\(423\) | − | 3.25146e23i | − | 0.0364624i | ||||||
\(424\) | 1.23006e24 | 0.134881 | ||||||||
\(425\) | 1.20322e23 | − | 7.46262e22i | 0.0129018 | − | 0.00800196i | ||||
\(426\) | −1.08431e25 | −1.13700 | ||||||||
\(427\) | − | 4.68879e24i | − | 0.480835i | ||||||
\(428\) | − | 4.80784e24i | − | 0.482208i | ||||||
\(429\) | 2.00971e25 | 1.97146 | ||||||||
\(430\) | 7.48952e24 | − | 1.34582e25i | 0.718627 | − | 1.29133i | ||||
\(431\) | −8.48482e24 | −0.796359 | −0.398179 | − | 0.917308i | \(-0.630358\pi\) | ||||
−0.398179 | + | 0.917308i | \(0.630358\pi\) | |||||||
\(432\) | − | 7.30282e24i | − | 0.670494i | ||||||
\(433\) | − | 1.61543e25i | − | 1.45095i | −0.688247 | − | 0.725476i | \(-0.741620\pi\) | ||
0.688247 | − | 0.725476i | \(-0.258380\pi\) | |||||||
\(434\) | 8.85740e24 | 0.778312 | ||||||||
\(435\) | 8.33945e24 | + | 4.64091e24i | 0.716951 | + | 0.398983i | ||||
\(436\) | −1.27365e25 | −1.07134 | ||||||||
\(437\) | 2.03409e25i | 1.67416i | ||||||||
\(438\) | − | 1.69914e25i | − | 1.36843i | ||||||
\(439\) | −2.83535e23 | −0.0223457 | −0.0111729 | − | 0.999938i | \(-0.503557\pi\) | ||||
−0.0111729 | + | 0.999938i | \(0.503557\pi\) | |||||||
\(440\) | −3.72119e24 | − | 2.07085e24i | −0.287000 | − | 0.159716i | ||||
\(441\) | −5.87114e24 | −0.443155 | ||||||||
\(442\) | 3.03969e23i | 0.0224552i | ||||||||
\(443\) | − | 2.95742e23i | − | 0.0213834i | −0.999943 | − | 0.0106917i | \(-0.996597\pi\) | ||
0.999943 | − | 0.0106917i | \(-0.00340334\pi\) | |||||||
\(444\) | −1.43447e25 | −1.01520 | ||||||||
\(445\) | 9.37827e23 | − | 1.68522e24i | 0.0649685 | − | 0.116745i | ||||
\(446\) | 1.70438e24 | 0.115581 | ||||||||
\(447\) | 1.39974e25i | 0.929239i | ||||||||
\(448\) | 3.87353e24i | 0.251748i | ||||||||
\(449\) | −3.12295e25 | −1.98712 | −0.993560 | − | 0.113303i | \(-0.963857\pi\) | ||||
−0.993560 | + | 0.113303i | \(0.963857\pi\) | |||||||
\(450\) | −9.65558e24 | + | 5.98859e24i | −0.601533 | + | 0.373083i | ||||
\(451\) | 1.16052e25 | 0.707905 | ||||||||
\(452\) | 3.48395e24i | 0.208092i | ||||||||
\(453\) | − | 1.23283e25i | − | 0.721055i | ||||||
\(454\) | 3.34160e25 | 1.91392 | ||||||||
\(455\) | −3.69240e24 | + | 6.63504e24i | −0.207110 | + | 0.372165i | ||||
\(456\) | −7.66303e24 | −0.420954 | ||||||||
\(457\) | 2.81853e25i | 1.51641i | 0.652013 | + | 0.758207i | \(0.273925\pi\) | ||||
−0.652013 | + | 0.758207i | \(0.726075\pi\) | |||||||
\(458\) | 6.33916e24i | 0.334048i | ||||||||
\(459\) | −1.73255e23 | −0.00894261 | ||||||||
\(460\) | 1.58856e25 | + | 8.84036e24i | 0.803165 | + | 0.446962i | ||||
\(461\) | 9.39614e24 | 0.465362 | 0.232681 | − | 0.972553i | \(-0.425250\pi\) | ||||
0.232681 | + | 0.972553i | \(0.425250\pi\) | |||||||
\(462\) | − | 1.96517e25i | − | 0.953456i | ||||||
\(463\) | − | 2.13716e25i | − | 1.01582i | −0.861409 | − | 0.507911i | \(-0.830418\pi\) | ||
0.861409 | − | 0.507911i | \(-0.169582\pi\) | |||||||
\(464\) | 1.62536e25 | 0.756883 | ||||||||
\(465\) | 3.48251e25 | + | 1.93802e25i | 1.58887 | + | 0.884210i | ||||
\(466\) | −3.32385e24 | −0.148585 | ||||||||
\(467\) | − | 2.08363e25i | − | 0.912663i | −0.889810 | − | 0.456332i | \(-0.849163\pi\) | ||
0.889810 | − | 0.456332i | \(-0.150837\pi\) | |||||||
\(468\) | − | 1.10941e25i | − | 0.476165i | ||||||
\(469\) | 2.18074e24 | 0.0917196 | ||||||||
\(470\) | 1.11474e24 | − | 2.00313e24i | 0.0459458 | − | 0.0825620i | ||||
\(471\) | 3.42969e23 | 0.0138534 | ||||||||
\(472\) | 9.29826e24i | 0.368089i | ||||||||
\(473\) | 4.11433e25i | 1.59632i | ||||||||
\(474\) | −2.83691e25 | −1.07882 | ||||||||
\(475\) | −2.14859e25 | − | 3.46423e25i | −0.800874 | − | 1.29127i | ||||
\(476\) | 1.35184e23 | 0.00493923 | ||||||||
\(477\) | 8.76672e24i | 0.313988i | ||||||||
\(478\) | 2.80522e25i | 0.984924i | ||||||||
\(479\) | 7.09286e24 | 0.244137 | 0.122069 | − | 0.992522i | \(-0.461047\pi\) | ||||
0.122069 | + | 0.992522i | \(0.461047\pi\) | |||||||
\(480\) | −2.34205e25 | + | 4.20853e25i | −0.790323 | + | 1.42017i | ||||
\(481\) | −3.25548e25 | −1.07705 | ||||||||
\(482\) | − | 5.70842e25i | − | 1.85169i | ||||||
\(483\) | − | 1.66708e25i | − | 0.530222i | ||||||
\(484\) | −3.04984e25 | −0.951144 | ||||||||
\(485\) | −3.18379e25 | − | 1.77178e25i | −0.973638 | − | 0.541830i | ||||
\(486\) | 4.30291e25 | 1.29038 | ||||||||
\(487\) | − | 2.13989e25i | − | 0.629313i | −0.949206 | − | 0.314657i | \(-0.898111\pi\) | ||
0.949206 | − | 0.314657i | \(-0.101889\pi\) | |||||||
\(488\) | − | 9.59789e24i | − | 0.276814i | ||||||
\(489\) | −2.50331e25 | −0.708077 | ||||||||
\(490\) | −3.61704e25 | − | 2.01289e25i | −1.00344 | − | 0.558414i | ||||
\(491\) | 4.33772e25 | 1.18029 | 0.590143 | − | 0.807299i | \(-0.299071\pi\) | ||||
0.590143 | + | 0.807299i | \(0.299071\pi\) | |||||||
\(492\) | − | 1.86640e25i | − | 0.498122i | ||||||
\(493\) | − | 3.85606e23i | − | 0.0100948i | ||||||
\(494\) | 8.75167e25 | 2.24742 | ||||||||
\(495\) | 1.47591e25 | − | 2.65212e25i | 0.371800 | − | 0.668104i | ||||
\(496\) | 6.78743e25 | 1.67737 | ||||||||
\(497\) | 1.09439e25i | 0.265331i | ||||||||
\(498\) | 7.18512e25i | 1.70905i | ||||||||
\(499\) | −7.92853e25 | −1.85028 | −0.925140 | − | 0.379627i | \(-0.876052\pi\) | ||||
−0.925140 | + | 0.379627i | \(0.876052\pi\) | |||||||
\(500\) | −3.63925e25 | + | 1.72393e24i | −0.833291 | + | 0.0394735i | ||||
\(501\) | 5.44501e25 | 1.22332 | ||||||||
\(502\) | 6.27706e25i | 1.38379i | ||||||||
\(503\) | 1.33196e25i | 0.288136i | 0.989568 | + | 0.144068i | \(0.0460183\pi\) | ||||
−0.989568 | + | 0.144068i | \(0.953982\pi\) | |||||||
\(504\) | 2.15573e24 | 0.0457618 | ||||||||
\(505\) | 2.73174e25 | − | 4.90878e25i | 0.569077 | − | 1.02260i | ||||
\(506\) | −1.06779e26 | −2.18301 | ||||||||
\(507\) | − | 1.18516e25i | − | 0.237795i | ||||||
\(508\) | − | 5.13458e25i | − | 1.01111i | ||||||
\(509\) | 6.86620e25 | 1.32708 | 0.663541 | − | 0.748140i | \(-0.269053\pi\) | ||||
0.663541 | + | 0.748140i | \(0.269053\pi\) | |||||||
\(510\) | 1.16864e24 | + | 6.50349e23i | 0.0221699 | + | 0.0123376i | ||||
\(511\) | −1.71494e25 | −0.319338 | ||||||||
\(512\) | 6.80426e25i | 1.24370i | ||||||||
\(513\) | 4.98824e25i | 0.895018i | ||||||||
\(514\) | −2.50698e25 | −0.441571 | ||||||||
\(515\) | 4.57939e25 | + | 2.54844e25i | 0.791843 | + | 0.440661i | ||||
\(516\) | 6.61685e25 | 1.12326 | ||||||||
\(517\) | 6.12380e24i | 0.102061i | ||||||||
\(518\) | 3.18332e25i | 0.520892i | ||||||||
\(519\) | −1.10616e26 | −1.77717 | ||||||||
\(520\) | −7.55830e24 | + | 1.35818e25i | −0.119232 | + | 0.214253i | ||||
\(521\) | 2.67103e25 | 0.413734 | 0.206867 | − | 0.978369i | \(-0.433673\pi\) | ||||
0.206867 | + | 0.978369i | \(0.433673\pi\) | |||||||
\(522\) | 3.09441e25i | 0.470661i | ||||||||
\(523\) | − | 5.66730e25i | − | 0.846467i | −0.906021 | − | 0.423233i | \(-0.860895\pi\) | ||
0.906021 | − | 0.423233i | \(-0.139105\pi\) | |||||||
\(524\) | 3.37781e25 | 0.495436 | ||||||||
\(525\) | 1.76091e25 | + | 2.83917e25i | 0.253644 | + | 0.408957i | ||||
\(526\) | −1.32138e25 | −0.186923 | ||||||||
\(527\) | − | 1.61027e24i | − | 0.0223717i | ||||||
\(528\) | − | 1.50591e26i | − | 2.05483i | ||||||
\(529\) | −1.59664e25 | −0.213983 | ||||||||
\(530\) | −3.00562e25 | + | 5.40093e25i | −0.395652 | + | 0.710964i | ||||
\(531\) | −6.62694e25 | −0.856871 | ||||||||
\(532\) | − | 3.89213e25i | − | 0.494342i | ||||||
\(533\) | − | 4.23573e25i | − | 0.528470i | ||||||
\(534\) | 1.82175e25 | 0.223279 | ||||||||
\(535\) | −4.19495e25 | − | 2.33449e25i | −0.505087 | − | 0.281081i | ||||
\(536\) | 4.46395e24 | 0.0528025 | ||||||||
\(537\) | − | 3.40358e25i | − | 0.395531i | ||||||
\(538\) | − | 9.46664e25i | − | 1.08085i | ||||||
\(539\) | 1.10577e26 | 1.24043 | ||||||||
\(540\) | 3.89565e25 | + | 2.16793e25i | 0.429378 | + | 0.238949i | ||||
\(541\) | −6.52211e24 | −0.0706341 | −0.0353171 | − | 0.999376i | \(-0.511244\pi\) | ||||
−0.0353171 | + | 0.999376i | \(0.511244\pi\) | |||||||
\(542\) | − | 1.65620e26i | − | 1.76246i | ||||||
\(543\) | 1.30720e26i | 1.36692i | ||||||||
\(544\) | 1.94598e24 | 0.0199962 | ||||||||
\(545\) | −6.18434e25 | + | 1.11129e26i | −0.624492 | + | 1.12218i | ||||
\(546\) | −7.17258e25 | −0.711779 | ||||||||
\(547\) | 8.52380e25i | 0.831292i | 0.909526 | + | 0.415646i | \(0.136444\pi\) | ||||
−0.909526 | + | 0.415646i | \(0.863556\pi\) | |||||||
\(548\) | − | 2.31902e25i | − | 0.222275i | ||||||
\(549\) | 6.84049e25 | 0.644392 | ||||||||
\(550\) | 1.81853e26 | − | 1.12789e26i | 1.68374 | − | 1.04429i | ||||
\(551\) | −1.11021e26 | −1.01034 | ||||||||
\(552\) | − | 3.41249e25i | − | 0.305246i | ||||||
\(553\) | 2.86330e25i | 0.251755i | ||||||||
\(554\) | −1.63967e26 | −1.41714 | ||||||||
\(555\) | −6.96518e25 | + | 1.25160e26i | −0.591765 | + | 1.06337i | ||||
\(556\) | −1.30751e25 | −0.109203 | ||||||||
\(557\) | − | 9.71730e25i | − | 0.797850i | −0.916984 | − | 0.398925i | \(-0.869383\pi\) | ||
0.916984 | − | 0.398925i | \(-0.130617\pi\) | |||||||
\(558\) | 1.29221e26i | 1.04306i | ||||||||
\(559\) | 1.50167e26 | 1.19169 | ||||||||
\(560\) | 4.97174e25 | + | 2.76677e25i | 0.387902 | + | 0.215868i | ||||
\(561\) | −3.57266e24 | −0.0274060 | ||||||||
\(562\) | 3.36943e26i | 2.54133i | ||||||||
\(563\) | − | 6.87630e25i | − | 0.509947i | −0.966948 | − | 0.254973i | \(-0.917933\pi\) | ||
0.966948 | − | 0.254973i | \(-0.0820667\pi\) | |||||||
\(564\) | 9.84856e24 | 0.0718160 | ||||||||
\(565\) | 3.03982e25 | + | 1.69166e25i | 0.217966 | + | 0.121298i | ||||
\(566\) | −2.55271e26 | −1.79989 | ||||||||
\(567\) | − | 7.02786e25i | − | 0.487286i | ||||||
\(568\) | 2.24021e25i | 0.152749i | ||||||||
\(569\) | 9.27451e25 | 0.621905 | 0.310953 | − | 0.950425i | \(-0.399352\pi\) | ||||
0.310953 | + | 0.950425i | \(0.399352\pi\) | |||||||
\(570\) | 1.87244e26 | − | 3.36468e26i | 1.23480 | − | 2.21887i | ||||
\(571\) | 6.52681e25 | 0.423310 | 0.211655 | − | 0.977344i | \(-0.432115\pi\) | ||||
0.211655 | + | 0.977344i | \(0.432115\pi\) | |||||||
\(572\) | 2.08947e26i | 1.33282i | ||||||||
\(573\) | 1.42003e26i | 0.890898i | ||||||||
\(574\) | −4.14185e25 | −0.255583 | ||||||||
\(575\) | 1.54268e26 | − | 9.56805e25i | 0.936337 | − | 0.580736i | ||||
\(576\) | −5.65111e25 | −0.337381 | ||||||||
\(577\) | − | 1.80949e26i | − | 1.06264i | −0.847172 | − | 0.531319i | \(-0.821697\pi\) | ||
0.847172 | − | 0.531319i | \(-0.178303\pi\) | |||||||
\(578\) | 2.34391e26i | 1.35402i | ||||||||
\(579\) | 1.33028e26 | 0.755957 | ||||||||
\(580\) | −4.82508e25 | + | 8.67040e25i | −0.269736 | + | 0.484700i | ||||
\(581\) | 7.25196e25 | 0.398825 | ||||||||
\(582\) | − | 3.44173e26i | − | 1.86212i | ||||||
\(583\) | − | 1.65112e26i | − | 0.878877i | ||||||
\(584\) | −3.51046e25 | −0.183841 | ||||||||
\(585\) | −9.67988e25 | − | 5.38686e25i | −0.498757 | − | 0.277559i | ||||
\(586\) | 3.53180e26 | 1.79048 | ||||||||
\(587\) | 1.28037e26i | 0.638663i | 0.947643 | + | 0.319332i | \(0.103458\pi\) | ||||
−0.947643 | + | 0.319332i | \(0.896542\pi\) | |||||||
\(588\) | − | 1.77835e26i | − | 0.872834i | ||||||
\(589\) | −4.63619e26 | −2.23906 | ||||||||
\(590\) | −4.08267e26 | − | 2.27201e26i | −1.94022 | − | 1.07973i | ||||
\(591\) | −4.58379e25 | −0.214360 | ||||||||
\(592\) | 2.43938e26i | 1.12260i | ||||||||
\(593\) | − | 2.74621e25i | − | 0.124370i | −0.998065 | − | 0.0621849i | \(-0.980193\pi\) | ||
0.998065 | − | 0.0621849i | \(-0.0198068\pi\) | |||||||
\(594\) | −2.61855e26 | −1.16705 | ||||||||
\(595\) | 6.56399e23 | − | 1.17951e24i | 0.00287910 | − | 0.00517358i | ||||
\(596\) | −1.45529e26 | −0.628219 | ||||||||
\(597\) | − | 5.31292e25i | − | 0.225724i | ||||||
\(598\) | 3.89728e26i | 1.62967i | ||||||||
\(599\) | 2.61932e26 | 1.07804 | 0.539019 | − | 0.842294i | \(-0.318795\pi\) | ||||
0.539019 | + | 0.842294i | \(0.318795\pi\) | |||||||
\(600\) | 3.60457e25 | + | 5.81175e25i | 0.146021 | + | 0.235434i | ||||
\(601\) | −2.34392e26 | −0.934621 | −0.467310 | − | 0.884093i | \(-0.654777\pi\) | ||||
−0.467310 | + | 0.884093i | \(0.654777\pi\) | |||||||
\(602\) | − | 1.46839e26i | − | 0.576335i | ||||||
\(603\) | 3.18149e25i | 0.122918i | ||||||||
\(604\) | 1.28175e26 | 0.487475 | ||||||||
\(605\) | −1.48088e26 | + | 2.66106e26i | −0.554426 | + | 0.996272i | ||||
\(606\) | 5.30647e26 | 1.95576 | ||||||||
\(607\) | 8.78652e24i | 0.0318804i | 0.999873 | + | 0.0159402i | \(0.00507414\pi\) | ||||
−0.999873 | + | 0.0159402i | \(0.994926\pi\) | |||||||
\(608\) | − | 5.60273e26i | − | 2.00132i | ||||||
\(609\) | 9.09894e25 | 0.319983 | ||||||||
\(610\) | 4.21423e26 | + | 2.34522e26i | 1.45910 | + | 0.811990i | ||||
\(611\) | 2.23510e25 | 0.0761914 | ||||||||
\(612\) | 1.97221e24i | 0.00661932i | ||||||||
\(613\) | − | 2.55308e26i | − | 0.843703i | −0.906665 | − | 0.421852i | \(-0.861380\pi\) | ||
0.906665 | − | 0.421852i | \(-0.138620\pi\) | |||||||
\(614\) | 7.01125e26 | 2.28137 | ||||||||
\(615\) | −1.62847e26 | − | 9.06247e25i | −0.521756 | − | 0.290358i | ||||
\(616\) | −4.06009e25 | −0.128091 | ||||||||
\(617\) | − | 4.69474e26i | − | 1.45849i | −0.684254 | − | 0.729244i | \(-0.739872\pi\) | ||
0.684254 | − | 0.729244i | \(-0.260128\pi\) | |||||||
\(618\) | 4.95040e26i | 1.51443i | ||||||||
\(619\) | −1.55379e26 | −0.468093 | −0.234046 | − | 0.972225i | \(-0.575197\pi\) | ||||
−0.234046 | + | 0.972225i | \(0.575197\pi\) | |||||||
\(620\) | −2.01493e26 | + | 3.62072e26i | −0.597777 | + | 1.07417i | ||||
\(621\) | −2.22135e26 | −0.649004 | ||||||||
\(622\) | 3.12992e25i | 0.0900585i | ||||||||
\(623\) | − | 1.83870e25i | − | 0.0521044i | ||||||
\(624\) | −5.49635e26 | −1.53398 | ||||||||
\(625\) | −1.61666e26 | + | 3.25904e26i | −0.444383 | + | 0.895837i | ||||
\(626\) | 7.99659e26 | 2.16495 | ||||||||
\(627\) | 1.02862e27i | 2.74292i | ||||||||
\(628\) | 3.56579e24i | 0.00936569i | ||||||||
\(629\) | 5.78727e24 | 0.0149724 | ||||||||
\(630\) | −5.26747e25 | + | 9.46534e25i | −0.134235 | + | 0.241213i | ||||
\(631\) | 4.79202e26 | 1.20293 | 0.601464 | − | 0.798900i | \(-0.294584\pi\) | ||||
0.601464 | + | 0.798900i | \(0.294584\pi\) | |||||||
\(632\) | 5.86113e25i | 0.144934i | ||||||||
\(633\) | − | 4.78252e26i | − | 1.16499i | ||||||
\(634\) | −1.01026e27 | −2.42430 | ||||||||
\(635\) | −4.48004e26 | − | 2.49314e26i | −1.05909 | − | 0.589382i | ||||
\(636\) | −2.65541e26 | −0.618427 | ||||||||
\(637\) | − | 4.03590e26i | − | 0.926011i | ||||||
\(638\) | − | 5.82800e26i | − | 1.31742i | ||||||
\(639\) | −1.59661e26 | −0.355584 | ||||||||
\(640\) | 1.76356e26 | + | 9.81423e25i | 0.386973 | + | 0.215351i | ||||
\(641\) | 1.42467e26 | 0.308010 | 0.154005 | − | 0.988070i | \(-0.450783\pi\) | ||||
0.154005 | + | 0.988070i | \(0.450783\pi\) | |||||||
\(642\) | − | 4.53481e26i | − | 0.965999i | ||||||
\(643\) | 3.85589e26i | 0.809320i | 0.914467 | + | 0.404660i | \(0.132610\pi\) | ||||
−0.914467 | + | 0.404660i | \(0.867390\pi\) | |||||||
\(644\) | 1.73324e26 | 0.358461 | ||||||||
\(645\) | 3.21288e26 | − | 5.77336e26i | 0.654752 | − | 1.17655i | ||||
\(646\) | −1.55579e25 | −0.0312422 | ||||||||
\(647\) | 6.19721e26i | 1.22633i | 0.789957 | + | 0.613163i | \(0.210103\pi\) | ||||
−0.789957 | + | 0.613163i | \(0.789897\pi\) | |||||||
\(648\) | − | 1.43860e26i | − | 0.280528i | ||||||
\(649\) | 1.24812e27 | 2.39845 | ||||||||
\(650\) | −4.11664e26 | − | 6.63738e26i | −0.779590 | − | 1.25696i | ||||
\(651\) | 3.79967e26 | 0.709131 | ||||||||
\(652\) | − | 2.60265e26i | − | 0.478701i | ||||||
\(653\) | 3.56634e26i | 0.646469i | 0.946319 | + | 0.323235i | \(0.104770\pi\) | ||||
−0.946319 | + | 0.323235i | \(0.895230\pi\) | |||||||
\(654\) | −1.20132e27 | −2.14621 | ||||||||
\(655\) | 1.64013e26 | − | 2.94722e26i | 0.288792 | − | 0.518943i | ||||
\(656\) | −3.17390e26 | −0.550817 | ||||||||
\(657\) | − | 2.50193e26i | − | 0.427962i | ||||||
\(658\) | − | 2.18556e25i | − | 0.0368483i | ||||||
\(659\) | 6.41633e26 | 1.06629 | 0.533145 | − | 0.846024i | \(-0.321010\pi\) | ||||
0.533145 | + | 0.846024i | \(0.321010\pi\) | |||||||
\(660\) | 8.03318e26 | + | 4.47047e26i | 1.31589 | + | 0.732295i | ||||
\(661\) | −7.50359e26 | −1.21159 | −0.605794 | − | 0.795621i | \(-0.707144\pi\) | ||||
−0.605794 | + | 0.795621i | \(0.707144\pi\) | |||||||
\(662\) | 6.62241e26i | 1.05406i | ||||||||
\(663\) | 1.30397e25i | 0.0204593i | ||||||||
\(664\) | 1.48447e26 | 0.229601 | ||||||||
\(665\) | −3.39598e26 | − | 1.88986e26i | −0.517796 | − | 0.288154i | ||||
\(666\) | −4.64416e26 | −0.698075 | ||||||||
\(667\) | − | 4.94397e26i | − | 0.732623i | ||||||
\(668\) | 5.66110e26i | 0.827036i | ||||||||
\(669\) | 7.31151e25 | 0.105307 | ||||||||
\(670\) | −1.09076e26 | + | 1.96003e26i | −0.154888 | + | 0.278325i | ||||
\(671\) | −1.28834e27 | −1.80370 | ||||||||
\(672\) | 4.59181e26i | 0.633835i | ||||||||
\(673\) | 8.83509e26i | 1.20245i | 0.799079 | + | 0.601226i | \(0.205321\pi\) | ||||
−0.799079 | + | 0.601226i | \(0.794679\pi\) | |||||||
\(674\) | 1.13901e27 | 1.52847 | ||||||||
\(675\) | 3.78314e26 | − | 2.34639e26i | 0.500573 | − | 0.310466i | ||||
\(676\) | 1.23220e26 | 0.160763 | ||||||||
\(677\) | 1.08791e27i | 1.39959i | 0.714346 | + | 0.699793i | \(0.246725\pi\) | ||||
−0.714346 | + | 0.699793i | \(0.753275\pi\) | |||||||
\(678\) | 3.28610e26i | 0.416868i | ||||||||
\(679\) | −3.47374e26 | −0.434545 | ||||||||
\(680\) | 1.34364e24 | − | 2.41445e24i | 0.00165748 | − | 0.00297840i | ||||
\(681\) | 1.43349e27 | 1.74380 | ||||||||
\(682\) | − | 2.43375e27i | − | 2.91960i | ||||||
\(683\) | 1.43692e27i | 1.69995i | 0.526825 | + | 0.849974i | \(0.323382\pi\) | ||||
−0.526825 | + | 0.849974i | \(0.676618\pi\) | |||||||
\(684\) | 5.67825e26 | 0.662493 | ||||||||
\(685\) | −2.02340e26 | − | 1.12602e26i | −0.232821 | − | 0.129565i | ||||
\(686\) | −8.60079e26 | −0.976021 | ||||||||
\(687\) | 2.71939e26i | 0.304356i | ||||||||
\(688\) | − | 1.12523e27i | − | 1.24208i | ||||||
\(689\) | −6.02637e26 | −0.656105 | ||||||||
\(690\) | 1.49835e27 | + | 8.33833e26i | 1.60897 | + | 0.895391i | ||||
\(691\) | −2.88640e26 | −0.305714 | −0.152857 | − | 0.988248i | \(-0.548847\pi\) | ||||
−0.152857 | + | 0.988248i | \(0.548847\pi\) | |||||||
\(692\) | − | 1.15006e27i | − | 1.20147i | ||||||
\(693\) | − | 2.89366e26i | − | 0.298182i | ||||||
\(694\) | −3.51539e26 | −0.357321 | ||||||||
\(695\) | −6.34875e25 | + | 1.14084e26i | −0.0636551 | + | 0.114385i | ||||
\(696\) | 1.86254e26 | 0.184212 | ||||||||
\(697\) | 7.52987e24i | 0.00734643i | ||||||||
\(698\) | 6.06238e26i | 0.583467i | ||||||||
\(699\) | −1.42587e26 | −0.135378 | ||||||||
\(700\) | −2.95184e26 | + | 1.83080e26i | −0.276479 | + | 0.171478i | ||||
\(701\) | −7.83699e26 | −0.724149 | −0.362075 | − | 0.932149i | \(-0.617931\pi\) | ||||
−0.362075 | + | 0.932149i | \(0.617931\pi\) | |||||||
\(702\) | 9.55734e26i | 0.871233i | ||||||||
\(703\) | − | 1.66623e27i | − | 1.49851i | ||||||
\(704\) | 1.06433e27 | 0.944356 | ||||||||
\(705\) | 4.78206e25 | − | 8.59310e25i | 0.0418619 | − | 0.0752234i | ||||
\(706\) | −5.11183e26 | −0.441501 | ||||||||
\(707\) | − | 5.35584e26i | − | 0.456397i | ||||||
\(708\) | − | 2.00728e27i | − | 1.68768i | ||||||
\(709\) | −1.61337e27 | −1.33843 | −0.669215 | − | 0.743068i | \(-0.733370\pi\) | ||||
−0.669215 | + | 0.743068i | \(0.733370\pi\) | |||||||
\(710\) | −9.83628e26 | − | 5.47390e26i | −0.805150 | − | 0.448066i | ||||
\(711\) | −4.17727e26 | −0.337390 | ||||||||
\(712\) | − | 3.76379e25i | − | 0.0299962i | ||||||
\(713\) | − | 2.06458e27i | − | 1.62361i | ||||||
\(714\) | 1.27507e25 | 0.00989468 | ||||||||
\(715\) | 1.82311e27 | + | 1.01456e27i | 1.39606 | + | 0.776910i | ||||
\(716\) | 3.53866e26 | 0.267402 | ||||||||
\(717\) | 1.20339e27i | 0.897378i | ||||||||
\(718\) | 3.19097e27i | 2.34823i | ||||||||
\(719\) | 8.92361e26 | 0.648061 | 0.324031 | − | 0.946047i | \(-0.394962\pi\) | ||||
0.324031 | + | 0.946047i | \(0.394962\pi\) | |||||||
\(720\) | −4.03646e26 | + | 7.25329e26i | −0.289296 | + | 0.519848i | ||||
\(721\) | 4.99645e26 | 0.353408 | ||||||||
\(722\) | 2.53919e27i | 1.77253i | ||||||||
\(723\) | − | 2.44881e27i | − | 1.68710i | ||||||
\(724\) | −1.35908e27 | −0.924119 | ||||||||
\(725\) | 5.22226e26 | + | 8.42000e26i | 0.350467 | + | 0.565068i | ||||
\(726\) | −2.87664e27 | −1.90541 | ||||||||
\(727\) | − | 1.51778e27i | − | 0.992274i | −0.868244 | − | 0.496137i | \(-0.834751\pi\) | ||
0.868244 | − | 0.496137i | \(-0.165249\pi\) | |||||||
\(728\) | 1.48188e26i | 0.0956234i | ||||||||
\(729\) | −1.15875e26 | −0.0738040 | ||||||||
\(730\) | 8.57773e26 | − | 1.54137e27i | 0.539269 | − | 0.969036i | ||||
\(731\) | −2.66953e25 | −0.0165661 | ||||||||
\(732\) | 2.07196e27i | 1.26919i | ||||||||
\(733\) | 1.49384e27i | 0.903267i | 0.892204 | + | 0.451633i | \(0.149158\pi\) | ||||
−0.892204 | + | 0.451633i | \(0.850842\pi\) | |||||||
\(734\) | 3.59405e27 | 2.14522 | ||||||||
\(735\) | −1.55165e27 | − | 8.63493e26i | −0.914247 | − | 0.508779i | ||||
\(736\) | 2.49500e27 | 1.45121 | ||||||||
\(737\) | − | 5.99202e26i | − | 0.344058i | ||||||
\(738\) | − | 6.04257e26i | − | 0.342520i | ||||||
\(739\) | −4.93504e26 | −0.276165 | −0.138083 | − | 0.990421i | \(-0.544094\pi\) | ||||
−0.138083 | + | 0.990421i | \(0.544094\pi\) | |||||||
\(740\) | −1.30128e27 | − | 7.24160e26i | −0.718899 | − | 0.400068i | ||||
\(741\) | 3.75432e27 | 2.04766 | ||||||||
\(742\) | 5.89280e26i | 0.317311i | ||||||||
\(743\) | − | 1.02399e26i | − | 0.0544378i | −0.999629 | − | 0.0272189i | \(-0.991335\pi\) | ||
0.999629 | − | 0.0272189i | \(-0.00866512\pi\) | |||||||
\(744\) | 7.77788e26 | 0.408243 | ||||||||
\(745\) | −7.06632e26 | + | 1.26978e27i | −0.366192 | + | 0.658026i | ||||
\(746\) | 2.67175e27 | 1.36703 | ||||||||
\(747\) | 1.05799e27i | 0.534486i | ||||||||
\(748\) | − | 3.71445e25i | − | 0.0185280i | ||||||
\(749\) | −4.57700e26 | −0.225426 | ||||||||
\(750\) | −3.43258e27 | + | 1.62603e26i | −1.66932 | + | 0.0790765i | ||||
\(751\) | 5.99732e26 | 0.287990 | 0.143995 | − | 0.989578i | \(-0.454005\pi\) | ||||
0.143995 | + | 0.989578i | \(0.454005\pi\) | |||||||
\(752\) | − | 1.67480e26i | − | 0.0794132i | ||||||
\(753\) | 2.69275e27i | 1.26079i | ||||||||
\(754\) | −2.12714e27 | −0.983486 | ||||||||
\(755\) | 6.22366e26 | − | 1.11836e27i | 0.284152 | − | 0.510604i | ||||
\(756\) | 4.25044e26 | 0.191636 | ||||||||
\(757\) | − | 1.93512e27i | − | 0.861583i | −0.902451 | − | 0.430792i | \(-0.858234\pi\) | ||
0.902451 | − | 0.430792i | \(-0.141766\pi\) | |||||||
\(758\) | 1.73041e26i | 0.0760835i | ||||||||
\(759\) | −4.58062e27 | −1.98897 | ||||||||
\(760\) | −6.95152e26 | − | 3.86853e26i | −0.298092 | − | 0.165889i | ||||
\(761\) | −2.57157e27 | −1.08904 | −0.544520 | − | 0.838748i | \(-0.683288\pi\) | ||||
−0.544520 | + | 0.838748i | \(0.683288\pi\) | |||||||
\(762\) | − | 4.84299e27i | − | 2.02554i | ||||||
\(763\) | 1.21250e27i | 0.500839i | ||||||||
\(764\) | −1.47638e27 | −0.602299 | ||||||||
\(765\) | 1.72079e25 | + | 9.57623e24i | 0.00693339 | + | 0.00385843i | ||||
\(766\) | 1.86968e26 | 0.0744038 | ||||||||
\(767\) | − | 4.55546e27i | − | 1.79051i | ||||||
\(768\) | 3.95828e27i | 1.53665i | ||||||||
\(769\) | 1.16936e27 | 0.448380 | 0.224190 | − | 0.974545i | \(-0.428026\pi\) | ||||
0.224190 | + | 0.974545i | \(0.428026\pi\) | |||||||
\(770\) | 9.92074e26 | − | 1.78270e27i | 0.375735 | − | 0.675175i | ||||
\(771\) | −1.07545e27 | −0.402322 | ||||||||
\(772\) | 1.38307e27i | 0.511071i | ||||||||
\(773\) | − | 4.80957e26i | − | 0.175550i | −0.996140 | − | 0.0877750i | \(-0.972024\pi\) | ||
0.996140 | − | 0.0877750i | \(-0.0279757\pi\) | |||||||
\(774\) | 2.14224e27 | 0.772377 | ||||||||
\(775\) | 2.18079e27 | + | 3.51615e27i | 0.776690 | + | 1.25228i | ||||
\(776\) | −7.11071e26 | −0.250165 | ||||||||
\(777\) | 1.36559e27i | 0.474592i | ||||||||
\(778\) | − | 2.63517e27i | − | 0.904697i | ||||||
\(779\) | 2.16795e27 | 0.735265 | ||||||||
\(780\) | 1.63166e27 | − | 2.93200e27i | 0.546677 | − | 0.982348i | ||||
\(781\) | 3.00706e27 | 0.995308 | ||||||||
\(782\) | − | 6.92820e25i | − | 0.0226546i | ||||||
\(783\) | − | 1.21242e27i | − | 0.391666i | ||||||
\(784\) | −3.02417e27 | −0.965169 | ||||||||
\(785\) | 3.11124e25 | + | 1.73141e25i | 0.00981006 | + | 0.00545930i | ||||
\(786\) | 3.18599e27 | 0.992499 | ||||||||
\(787\) | − | 3.62998e26i | − | 0.111723i | −0.998439 | − | 0.0558616i | \(-0.982209\pi\) | ||
0.998439 | − | 0.0558616i | \(-0.0177906\pi\) | |||||||
\(788\) | − | 4.76570e26i | − | 0.144920i | ||||||
\(789\) | −5.66850e26 | −0.170308 | ||||||||
\(790\) | −2.57350e27 | − | 1.43215e27i | −0.763953 | − | 0.425140i | ||||
\(791\) | 3.31667e26 | 0.0972804 | ||||||||
\(792\) | − | 5.92328e26i | − | 0.171662i | ||||||
\(793\) | 4.70225e27i | 1.34651i | ||||||||
\(794\) | 2.97280e27 | 0.841146 | ||||||||
\(795\) | −1.28936e27 | + | 2.31691e27i | −0.360484 | + | 0.647770i | ||||
\(796\) | 5.52377e26 | 0.152602 | ||||||||
\(797\) | 5.25128e27i | 1.43355i | 0.697307 | + | 0.716773i | \(0.254381\pi\) | ||||
−0.697307 | + | 0.716773i | \(0.745619\pi\) | |||||||
\(798\) | − | 3.67111e27i | − | 0.990306i | ||||||
\(799\) | −3.97335e24 | −0.00105916 | ||||||||
\(800\) | −4.24918e27 | + | 2.63543e27i | −1.11931 | + | 0.694220i | ||||
\(801\) | 2.68249e26 | 0.0698278 | ||||||||
\(802\) | 8.24389e27i | 2.12068i | ||||||||
\(803\) | 4.71214e27i | 1.19790i | ||||||||
\(804\) | −9.63663e26 | −0.242099 | ||||||||
\(805\) | 8.41590e26 | − | 1.51229e27i | 0.208949 | − | 0.375469i | ||||
\(806\) | −8.88283e27 | −2.17956 | ||||||||
\(807\) | − | 4.06103e27i | − | 0.984775i | ||||||
\(808\) | − | 1.09633e27i | − | 0.262745i | ||||||
\(809\) | −2.41547e27 | −0.572126 | −0.286063 | − | 0.958211i | \(-0.592347\pi\) | ||||
−0.286063 | + | 0.958211i | \(0.592347\pi\) | |||||||
\(810\) | 6.31657e27 | + | 3.51517e27i | 1.47868 | + | 0.822885i | ||||
\(811\) | −9.47666e26 | −0.219259 | −0.109629 | − | 0.993973i | \(-0.534966\pi\) | ||||
−0.109629 | + | 0.993973i | \(0.534966\pi\) | |||||||
\(812\) | 9.46004e26i | 0.216327i | ||||||||
\(813\) | − | 7.10481e27i | − | 1.60580i | ||||||
\(814\) | 8.74681e27 | 1.95397 | ||||||||
\(815\) | −2.27088e27 | − | 1.26374e27i | −0.501414 | − | 0.279037i | ||||
\(816\) | 9.77087e25 | 0.0213244 | ||||||||
\(817\) | 7.68594e27i | 1.65801i | ||||||||
\(818\) | − | 8.53836e27i | − | 1.82062i | ||||||
\(819\) | −1.05615e27 | −0.222601 | ||||||||
\(820\) | 9.42212e26 | − | 1.69310e27i | 0.196299 | − | 0.352737i | ||||
\(821\) | 5.43634e27 | 1.11956 | 0.559780 | − | 0.828642i | \(-0.310886\pi\) | ||||
0.559780 | + | 0.828642i | \(0.310886\pi\) | |||||||
\(822\) | − | 2.18733e27i | − | 0.445279i | ||||||
\(823\) | − | 6.66652e27i | − | 1.34153i | −0.741670 | − | 0.670765i | \(-0.765966\pi\) | ||
0.741670 | − | 0.670765i | \(-0.234034\pi\) | |||||||
\(824\) | 1.02277e27 | 0.203455 | ||||||||
\(825\) | 7.80118e27 | − | 4.83846e27i | 1.53408 | − | 0.951469i | ||||
\(826\) | −4.45449e27 | −0.865939 | ||||||||
\(827\) | − | 4.87544e27i | − | 0.936939i | −0.883480 | − | 0.468469i | \(-0.844806\pi\) | ||
0.883480 | − | 0.468469i | \(-0.155194\pi\) | |||||||
\(828\) | 2.52863e27i | 0.480393i | ||||||||
\(829\) | 2.36253e27 | 0.443720 | 0.221860 | − | 0.975079i | \(-0.428787\pi\) | ||||
0.221860 | + | 0.975079i | \(0.428787\pi\) | |||||||
\(830\) | −3.62726e27 | + | 6.51798e27i | −0.673499 | + | 1.21024i | ||||
\(831\) | −7.03390e27 | −1.29118 | ||||||||
\(832\) | − | 3.88465e27i | − | 0.704986i | ||||||
\(833\) | 7.17464e25i | 0.0128728i | ||||||||
\(834\) | −1.23326e27 | −0.218765 | ||||||||
\(835\) | 4.93944e27 | + | 2.74880e27i | 0.866276 | + | 0.482083i | ||||
\(836\) | −1.06944e28 | −1.85437 | ||||||||
\(837\) | − | 5.06300e27i | − | 0.867992i | ||||||
\(838\) | − | 4.82425e27i | − | 0.817734i | ||||||
\(839\) | −5.58105e27 | −0.935356 | −0.467678 | − | 0.883899i | \(-0.654909\pi\) | ||||
−0.467678 | + | 0.883899i | \(0.654909\pi\) | |||||||
\(840\) | 5.69724e26 | + | 3.17052e26i | 0.0944085 | + | 0.0525384i | ||||
\(841\) | −3.40483e27 | −0.557871 | ||||||||
\(842\) | 4.36821e27i | 0.707683i | ||||||||
\(843\) | 1.44543e28i | 2.31545i | ||||||||
\(844\) | 4.97232e27 | 0.787600 | ||||||||
\(845\) | 5.98305e26 | − | 1.07512e27i | 0.0937095 | − | 0.168391i | ||||
\(846\) | 3.18853e26 | 0.0493823 | ||||||||
\(847\) | 2.90340e27i | 0.444647i | ||||||||
\(848\) | 4.51565e27i | 0.683849i | ||||||||
\(849\) | −1.09507e28 | −1.63991 | ||||||||
\(850\) | 7.31817e25 | + | 1.17993e26i | 0.0108373 | + | 0.0174733i | ||||
\(851\) | 7.42004e27 | 1.08661 | ||||||||
\(852\) | − | 4.83609e27i | − | 0.700354i | ||||||
\(853\) | − | 3.15672e27i | − | 0.452085i | −0.974117 | − | 0.226042i | \(-0.927421\pi\) | ||
0.974117 | − | 0.226042i | \(-0.0725788\pi\) | |||||||
\(854\) | 4.59803e27 | 0.651211 | ||||||||
\(855\) | 2.75713e27 | − | 4.95440e27i | 0.386170 | − | 0.693926i | ||||
\(856\) | −9.36906e26 | −0.129776 | ||||||||
\(857\) | − | 8.00001e27i | − | 1.09590i | −0.836510 | − | 0.547952i | \(-0.815408\pi\) | ||
0.836510 | − | 0.547952i | \(-0.184592\pi\) | |||||||
\(858\) | 1.97081e28i | 2.67002i | ||||||||
\(859\) | 2.39064e27 | 0.320316 | 0.160158 | − | 0.987091i | \(-0.448800\pi\) | ||||
0.160158 | + | 0.987091i | \(0.448800\pi\) | |||||||
\(860\) | 6.00248e27 | + | 3.34038e27i | 0.795417 | + | 0.442650i | ||||
\(861\) | −1.77678e27 | −0.232865 | ||||||||
\(862\) | − | 8.32059e27i | − | 1.07854i | ||||||
\(863\) | − | 4.56844e27i | − | 0.585687i | −0.956160 | − | 0.292843i | \(-0.905399\pi\) | ||
0.956160 | − | 0.292843i | \(-0.0946015\pi\) | |||||||
\(864\) | 6.11851e27 | 0.775828 | ||||||||
\(865\) | −1.00345e28 | − | 5.58423e27i | −1.25847 | − | 0.700342i | ||||
\(866\) | 1.58416e28 | 1.96508 | ||||||||
\(867\) | 1.00550e28i | 1.23367i | ||||||||
\(868\) | 3.95047e27i | 0.479414i | ||||||||
\(869\) | 7.86747e27 | 0.944381 | ||||||||
\(870\) | −4.55108e27 | + | 8.17803e27i | −0.540358 | + | 0.970992i | ||||
\(871\) | −2.18700e27 | −0.256849 | ||||||||
\(872\) | 2.48197e27i | 0.288330i | ||||||||
\(873\) | − | 5.06786e27i | − | 0.582357i | ||||||
\(874\) | −1.99472e28 | −2.26738 | ||||||||
\(875\) | 1.64116e26 | + | 3.46451e27i | 0.0184533 | + | 0.389552i | ||||
\(876\) | 7.57827e27 | 0.842909 | ||||||||
\(877\) | 1.23776e28i | 1.36189i | 0.732335 | + | 0.680945i | \(0.238431\pi\) | ||||
−0.732335 | + | 0.680945i | \(0.761569\pi\) | |||||||
\(878\) | − | 2.78047e26i | − | 0.0302636i | ||||||
\(879\) | 1.51508e28 | 1.63133 | ||||||||
\(880\) | 7.60226e27 | − | 1.36608e28i | 0.809762 | − | 1.45510i | ||||
\(881\) | −6.55182e26 | −0.0690384 | −0.0345192 | − | 0.999404i | \(-0.510990\pi\) | ||||
−0.0345192 | + | 0.999404i | \(0.510990\pi\) | |||||||
\(882\) | − | 5.75750e27i | − | 0.600181i | ||||||
\(883\) | 8.50704e27i | 0.877308i | 0.898656 | + | 0.438654i | \(0.144545\pi\) | ||||
−0.898656 | + | 0.438654i | \(0.855455\pi\) | |||||||
\(884\) | −1.35572e26 | −0.0138317 | ||||||||
\(885\) | −1.75140e28 | − | 9.74653e27i | −1.76776 | − | 0.983759i | ||||
\(886\) | 2.90017e26 | 0.0289603 | ||||||||
\(887\) | − | 1.88564e28i | − | 1.86288i | −0.363894 | − | 0.931440i | \(-0.618553\pi\) | ||
0.363894 | − | 0.931440i | \(-0.381447\pi\) | |||||||
\(888\) | 2.79535e27i | 0.273220i | ||||||||
\(889\) | −4.88804e27 | −0.472681 | ||||||||
\(890\) | 1.65260e27 | + | 9.19674e26i | 0.158111 | + | 0.0879891i | ||||
\(891\) | −1.93104e28 | −1.82791 | ||||||||
\(892\) | 7.60167e26i | 0.0711939i | ||||||||
\(893\) | 1.14398e27i | 0.106006i | ||||||||
\(894\) | −1.37265e28 | −1.25850 | ||||||||
\(895\) | 1.71823e27 | − | 3.08756e27i | 0.155870 | − | 0.280089i | ||||
\(896\) | 1.92417e27 | 0.172710 | ||||||||
\(897\) | 1.67186e28i | 1.48482i | ||||||||
\(898\) | − | 3.06250e28i | − | 2.69123i | ||||||
\(899\) | 1.12685e28 | 0.979827 | ||||||||
\(900\) | −2.67096e27 | − | 4.30646e27i | −0.229807 | − | 0.370524i | ||||
\(901\) | 1.07131e26 | 0.00912072 | ||||||||
\(902\) | 1.13806e28i | 0.958741i | ||||||||
\(903\) | − | 6.29915e27i | − | 0.525108i | ||||||
\(904\) | 6.78918e26 | 0.0560038 | ||||||||
\(905\) | −6.59913e27 | + | 1.18583e28i | −0.538673 | + | 0.967965i | ||||
\(906\) | 1.20896e28 | 0.976551 | ||||||||
\(907\) | 1.92154e28i | 1.53596i | 0.640474 | + | 0.767980i | \(0.278738\pi\) | ||||
−0.640474 | + | 0.767980i | \(0.721262\pi\) | |||||||
\(908\) | 1.49038e28i | 1.17891i | ||||||||
\(909\) | 7.81365e27 | 0.611642 | ||||||||
\(910\) | −6.50661e27 | − | 3.62093e27i | −0.504036 | − | 0.280496i | ||||
\(911\) | 1.12959e28 | 0.865959 | 0.432979 | − | 0.901404i | \(-0.357462\pi\) | ||||
0.432979 | + | 0.901404i | \(0.357462\pi\) | |||||||
\(912\) | − | 2.81317e28i | − | 2.13425i | ||||||
\(913\) | − | 1.99262e28i | − | 1.49607i | ||||||
\(914\) | −2.76397e28 | −2.05374 | ||||||||
\(915\) | 1.80783e28 | + | 1.00606e28i | 1.32941 | + | 0.739815i | ||||
\(916\) | −2.82731e27 | −0.205763 | ||||||||
\(917\) | − | 3.21563e27i | − | 0.231610i | ||||||
\(918\) | − | 1.69901e26i | − | 0.0121113i | ||||||
\(919\) | −1.54023e28 | −1.08664 | −0.543321 | − | 0.839525i | \(-0.682833\pi\) | ||||
−0.543321 | + | 0.839525i | \(0.682833\pi\) | |||||||
\(920\) | 1.72272e27 | − | 3.09564e27i | 0.120291 | − | 0.216155i | ||||
\(921\) | 3.00770e28 | 2.07859 | ||||||||
\(922\) | 9.21426e27i | 0.630256i | ||||||||
\(923\) | − | 1.09754e28i | − | 0.743023i | ||||||
\(924\) | 8.76478e27 | 0.587297 | ||||||||
\(925\) | −1.26369e28 | + | 7.83770e27i | −0.838099 | + | 0.519807i | ||||
\(926\) | 2.09579e28 | 1.37576 | ||||||||
\(927\) | 7.28934e27i | 0.473621i | ||||||||
\(928\) | 1.36177e28i | 0.875788i | ||||||||
\(929\) | −1.68314e28 | −1.07145 | −0.535724 | − | 0.844393i | \(-0.679961\pi\) | ||||
−0.535724 | + | 0.844393i | \(0.679961\pi\) | |||||||
\(930\) | −1.90051e28 | + | 3.41510e28i | −1.19752 | + | 2.15187i | ||||
\(931\) | 2.06568e28 | 1.28837 | ||||||||
\(932\) | − | 1.48246e27i | − | 0.0915234i | ||||||
\(933\) | 1.34268e27i | 0.0820536i | ||||||||
\(934\) | 2.04330e28 | 1.23605 | ||||||||
\(935\) | −3.24094e26 | − | 1.80359e26i | −0.0194071 | − | 0.0108001i | ||||
\(936\) | −2.16192e27 | −0.128150 | ||||||||
\(937\) | − | 2.26174e28i | − | 1.32714i | −0.748115 | − | 0.663569i | \(-0.769041\pi\) | ||
0.748115 | − | 0.663569i | \(-0.230959\pi\) | |||||||
\(938\) | 2.13853e27i | 0.124219i | ||||||||
\(939\) | 3.43040e28 | 1.97252 | ||||||||
\(940\) | 8.93412e26 | + | 4.97184e26i | 0.0508554 | + | 0.0283011i | ||||
\(941\) | −1.47239e28 | −0.829701 | −0.414850 | − | 0.909890i | \(-0.636166\pi\) | ||||
−0.414850 | + | 0.909890i | \(0.636166\pi\) | |||||||
\(942\) | 3.36330e26i | 0.0187621i | ||||||||
\(943\) | 9.65429e27i | 0.533162i | ||||||||
\(944\) | −3.41348e28 | −1.86622 | ||||||||
\(945\) | 2.06384e27 | − | 3.70861e27i | 0.111705 | − | 0.200728i | ||||
\(946\) | −4.03470e28 | −2.16195 | ||||||||
\(947\) | 3.07941e28i | 1.63359i | 0.576927 | + | 0.816796i | \(0.304252\pi\) | ||||
−0.576927 | + | 0.816796i | \(0.695748\pi\) | |||||||
\(948\) | − | 1.26528e28i | − | 0.664520i | ||||||
\(949\) | 1.71987e28 | 0.894263 | ||||||||
\(950\) | 3.39718e28 | − | 2.10700e28i | 1.74881 | − | 1.08465i | ||||
\(951\) | −4.33385e28 | −2.20881 | ||||||||
\(952\) | − | 2.63434e25i | − | 0.00132929i | ||||||
\(953\) | 9.87591e27i | 0.493395i | 0.969093 | + | 0.246697i | \(0.0793454\pi\) | ||||
−0.969093 | + | 0.246697i | \(0.920655\pi\) | |||||||
\(954\) | −8.59703e27 | −0.425245 | ||||||||
\(955\) | −7.16872e27 | + | 1.28818e28i | −0.351083 | + | 0.630876i | ||||
\(956\) | −1.25115e28 | −0.606680 | ||||||||
\(957\) | − | 2.50011e28i | − | 1.20032i | ||||||
\(958\) | 6.95557e27i | 0.330644i | ||||||||
\(959\) | −2.20768e27 | −0.103910 | ||||||||
\(960\) | −1.49350e28 | − | 8.31133e27i | −0.696030 | − | 0.387341i | ||||
\(961\) | 2.53861e28 | 1.17145 | ||||||||
\(962\) | − | 3.19246e28i | − | 1.45869i | ||||||
\(963\) | − | 6.67740e27i | − | 0.302105i | ||||||
\(964\) | 2.54600e28 | 1.14058 | ||||||||
\(965\) | 1.20676e28 | + | 6.71565e27i | 0.535319 | + | 0.297905i | ||||
\(966\) | 1.63481e28 | 0.718099 | ||||||||
\(967\) | − | 1.51028e28i | − | 0.656910i | −0.944520 | − | 0.328455i | \(-0.893472\pi\) | ||
0.944520 | − | 0.328455i | \(-0.106528\pi\) | |||||||
\(968\) | 5.94323e27i | 0.255980i | ||||||||
\(969\) | −6.67406e26 | −0.0284652 | ||||||||
\(970\) | 1.73748e28 | − | 3.12216e28i | 0.733820 | − | 1.31863i | ||||
\(971\) | −3.73488e28 | −1.56205 | −0.781023 | − | 0.624502i | \(-0.785302\pi\) | ||||
−0.781023 | + | 0.624502i | \(0.785302\pi\) | |||||||
\(972\) | 1.91913e28i | 0.794830i | ||||||||
\(973\) | 1.24473e27i | 0.0510510i | ||||||||
\(974\) | 2.09847e28 | 0.852302 | ||||||||
\(975\) | −1.76597e28 | − | 2.84732e28i | −0.710296 | − | 1.14523i | ||||
\(976\) | 3.52347e28 | 1.40345 | ||||||||
\(977\) | − | 2.10264e28i | − | 0.829403i | −0.909958 | − | 0.414701i | \(-0.863886\pi\) | ||
0.909958 | − | 0.414701i | \(-0.136114\pi\) | |||||||
\(978\) | − | 2.45485e28i | − | 0.958973i | ||||||
\(979\) | −5.05219e27 | −0.195454 | ||||||||
\(980\) | 8.97762e27 | − | 1.61323e28i | 0.343964 | − | 0.618084i | ||||
\(981\) | −1.76892e28 | −0.671201 | ||||||||
\(982\) | 4.25376e28i | 1.59850i | ||||||||
\(983\) | 4.82839e28i | 1.79698i | 0.438990 | + | 0.898492i | \(0.355336\pi\) | ||||
−0.438990 | + | 0.898492i | \(0.644664\pi\) | |||||||
\(984\) | −3.63705e27 | −0.134059 | ||||||||
\(985\) | −4.15818e27 | − | 2.31403e27i | −0.151796 | − | 0.0844744i | ||||
\(986\) | 3.78142e26 | 0.0136718 | ||||||||
\(987\) | − | 9.37569e26i | − | 0.0335730i | ||||||
\(988\) | 3.90331e28i | 1.38434i | ||||||||
\(989\) | −3.42269e28 | −1.20227 | ||||||||
\(990\) | 2.60079e28 | + | 1.44734e28i | 0.904838 | + | 0.503543i | ||||
\(991\) | −3.64175e28 | −1.25490 | −0.627452 | − | 0.778655i | \(-0.715902\pi\) | ||||
−0.627452 | + | 0.778655i | \(0.715902\pi\) | |||||||
\(992\) | 5.68670e28i | 1.94088i | ||||||||
\(993\) | 2.84090e28i | 0.960369i | ||||||||
\(994\) | −1.07321e28 | −0.359347 | ||||||||
\(995\) | 2.68212e27 | − | 4.81961e27i | 0.0889526 | − | 0.159843i | ||||
\(996\) | −3.20462e28 | −1.05272 | ||||||||
\(997\) | − | 2.05615e28i | − | 0.669037i | −0.942389 | − | 0.334519i | \(-0.891426\pi\) | ||
0.942389 | − | 0.334519i | \(-0.108574\pi\) | |||||||
\(998\) | − | 7.77506e28i | − | 2.50590i | ||||||
\(999\) | 1.81963e28 | 0.580911 |
(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 | 5.20.b.a.4.7 | yes | 8 | |
3.2 | odd | 2 | 45.20.b.b.19.2 | 8 | |||
4.3 | odd | 2 | 80.20.c.a.49.1 | 8 | |||
5.2 | odd | 4 | 25.20.a.f.1.2 | 8 | |||
5.3 | odd | 4 | 25.20.a.f.1.7 | 8 | |||
5.4 | even | 2 | inner | 5.20.b.a.4.2 | ✓ | 8 | |
15.14 | odd | 2 | 45.20.b.b.19.7 | 8 | |||
20.19 | odd | 2 | 80.20.c.a.49.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.20.b.a.4.2 | ✓ | 8 | 5.4 | even | 2 | inner | |
5.20.b.a.4.7 | yes | 8 | 1.1 | even | 1 | trivial | |
25.20.a.f.1.2 | 8 | 5.2 | odd | 4 | |||
25.20.a.f.1.7 | 8 | 5.3 | odd | 4 | |||
45.20.b.b.19.2 | 8 | 3.2 | odd | 2 | |||
45.20.b.b.19.7 | 8 | 15.14 | odd | 2 | |||
80.20.c.a.49.1 | 8 | 4.3 | odd | 2 | |||
80.20.c.a.49.8 | 8 | 20.19 | odd | 2 |