Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,30,Mod(20,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 30, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.20");
S:= CuspForms(chi, 30);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 30 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.c (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: | \(111.883889004\) |
Analytic rank: | \(0\) |
Dimension: | \(76\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 20.19 | ||
Character | \(\chi\) | \(=\) | 21.20 |
Dual form | 21.30.c.a.20.20 |
$q$-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 \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1646.15i | − | 0.0710451i | −0.999369 | − | 0.0355225i | \(-0.988690\pi\) | ||
0.999369 | − | 0.0355225i | \(-0.0113096\pi\) | |||||||
\(3\) | 2.25912e6 | − | 7.97037e6i | 0.272698 | − | 0.962100i | ||||
\(4\) | 5.34161e8 | 0.994953 | ||||||||
\(5\) | 1.37077e10 | 1.00438 | 0.502190 | − | 0.864757i | \(-0.332528\pi\) | ||||
0.502190 | + | 0.864757i | \(0.332528\pi\) | |||||||
\(6\) | −1.31204e10 | − | 3.71885e9i | −0.0683525 | − | 0.0193738i | ||||
\(7\) | −1.61859e12 | + | 7.74652e11i | −0.902016 | + | 0.431703i | ||||
\(8\) | − | 1.76308e12i | − | 0.141732i | ||||||
\(9\) | −5.84231e13 | − | 3.60121e13i | −0.851272 | − | 0.524725i | ||||
\(10\) | − | 2.25649e13i | − | 0.0713563i | ||||||
\(11\) | 1.65225e15i | 1.31184i | 0.754829 | + | 0.655922i | \(0.227720\pi\) | ||||
−0.754829 | + | 0.655922i | \(0.772280\pi\) | |||||||
\(12\) | 1.20674e15 | − | 4.25746e15i | 0.271321 | − | 0.957244i | ||||
\(13\) | − | 7.11308e15i | − | 0.501048i | −0.968110 | − | 0.250524i | \(-0.919397\pi\) | ||
0.968110 | − | 0.250524i | \(-0.0806029\pi\) | |||||||
\(14\) | 1.27519e15 | + | 2.66443e15i | 0.0306704 | + | 0.0640838i | ||||
\(15\) | 3.09673e16 | − | 1.09255e17i | 0.273892 | − | 0.966315i | ||||
\(16\) | 2.83873e17 | 0.984883 | ||||||||
\(17\) | −1.14786e18 | −1.65341 | −0.826706 | − | 0.562634i | \(-0.809788\pi\) | ||||
−0.826706 | + | 0.562634i | \(0.809788\pi\) | |||||||
\(18\) | −5.92812e16 | + | 9.61731e16i | −0.0372791 | + | 0.0604787i | ||||
\(19\) | − | 4.19951e18i | − | 1.20579i | −0.797821 | − | 0.602895i | \(-0.794014\pi\) | ||
0.797821 | − | 0.602895i | \(-0.205986\pi\) | |||||||
\(20\) | 7.32210e18 | 0.999311 | ||||||||
\(21\) | 2.51768e18 | + | 1.46508e19i | 0.169364 | + | 0.985554i | ||||
\(22\) | 2.71985e18 | 0.0932001 | ||||||||
\(23\) | 6.01642e19i | 1.08214i | 0.840977 | + | 0.541071i | \(0.181981\pi\) | ||||
−0.840977 | + | 0.541071i | \(0.818019\pi\) | |||||||
\(24\) | −1.40524e19 | − | 3.98301e18i | −0.136360 | − | 0.0386499i | ||||
\(25\) | 1.63560e18 | 0.00878107 | ||||||||
\(26\) | −1.17092e19 | −0.0355970 | ||||||||
\(27\) | −4.19014e20 | + | 3.84298e20i | −0.736977 | + | 0.675917i | ||||
\(28\) | −8.64586e20 | + | 4.13789e20i | −0.897463 | + | 0.429524i | ||||
\(29\) | 2.75913e21i | 1.72188i | 0.508710 | + | 0.860938i | \(0.330123\pi\) | ||||
−0.508710 | + | 0.860938i | \(0.669877\pi\) | |||||||
\(30\) | −1.79850e20 | − | 5.09768e19i | −0.0686519 | − | 0.0194587i | ||||
\(31\) | 2.77443e21i | 0.658309i | 0.944276 | + | 0.329154i | \(0.106764\pi\) | ||||
−0.944276 | + | 0.329154i | \(0.893236\pi\) | |||||||
\(32\) | − | 1.41384e21i | − | 0.211703i | ||||||
\(33\) | 1.31691e22 | + | 3.73264e21i | 1.26212 | + | 0.357737i | ||||
\(34\) | 1.88956e21i | 0.117467i | ||||||||
\(35\) | −2.21870e22 | + | 1.06187e22i | −0.905967 | + | 0.433594i | ||||
\(36\) | −3.12074e22 | − | 1.92362e22i | −0.846975 | − | 0.522076i | ||||
\(37\) | −2.45582e22 | −0.447994 | −0.223997 | − | 0.974590i | \(-0.571911\pi\) | ||||
−0.223997 | + | 0.974590i | \(0.571911\pi\) | |||||||
\(38\) | −6.91302e21 | −0.0856654 | ||||||||
\(39\) | −5.66939e22 | − | 1.60693e22i | −0.482058 | − | 0.136635i | ||||
\(40\) | − | 2.41677e22i | − | 0.142353i | ||||||
\(41\) | 2.01845e23 | 0.831099 | 0.415549 | − | 0.909571i | \(-0.363589\pi\) | ||||
0.415549 | + | 0.909571i | \(0.363589\pi\) | |||||||
\(42\) | 2.41173e22 | − | 4.14448e21i | 0.0700187 | − | 0.0120325i | ||||
\(43\) | −7.28553e23 | −1.50373 | −0.751863 | − | 0.659320i | \(-0.770844\pi\) | ||||
−0.751863 | + | 0.659320i | \(0.770844\pi\) | |||||||
\(44\) | 8.82569e23i | 1.30522i | ||||||||
\(45\) | −8.00845e23 | − | 4.93641e23i | −0.855001 | − | 0.527024i | ||||
\(46\) | 9.90392e22 | 0.0768809 | ||||||||
\(47\) | −2.16367e24 | −1.22962 | −0.614812 | − | 0.788674i | \(-0.710768\pi\) | ||||
−0.614812 | + | 0.788674i | \(0.710768\pi\) | |||||||
\(48\) | 6.41304e23 | − | 2.26257e24i | 0.268575 | − | 0.947556i | ||||
\(49\) | 2.01973e24 | − | 2.50768e24i | 0.627265 | − | 0.778806i | ||||
\(50\) | − | 2.69244e21i | − | 0.000623852i | ||||||
\(51\) | −2.59317e24 | + | 9.14890e24i | −0.450882 | + | 1.59075i | ||||
\(52\) | − | 3.79953e24i | − | 0.498519i | ||||||
\(53\) | − | 1.10372e25i | − | 1.09865i | −0.835609 | − | 0.549325i | \(-0.814885\pi\) | ||
0.835609 | − | 0.549325i | \(-0.185115\pi\) | |||||||
\(54\) | 6.32612e23 | + | 6.89760e23i | 0.0480206 | + | 0.0523586i | ||||
\(55\) | 2.26485e25i | 1.31759i | ||||||||
\(56\) | 1.36577e24 | + | 2.85369e24i | 0.0611860 | + | 0.127844i | ||||
\(57\) | −3.34716e25 | − | 9.48721e24i | −1.16009 | − | 0.328816i | ||||
\(58\) | 4.54195e24 | 0.122331 | ||||||||
\(59\) | 2.77774e25 | 0.583898 | 0.291949 | − | 0.956434i | \(-0.405696\pi\) | ||||
0.291949 | + | 0.956434i | \(0.405696\pi\) | |||||||
\(60\) | 1.65415e25 | − | 5.83598e25i | 0.272510 | − | 0.961437i | ||||
\(61\) | 9.03685e25i | 1.17148i | 0.810500 | + | 0.585739i | \(0.199196\pi\) | ||||
−0.810500 | + | 0.585739i | \(0.800804\pi\) | |||||||
\(62\) | 4.56713e24 | 0.0467696 | ||||||||
\(63\) | 1.22460e26 | + | 1.30310e25i | 0.994386 | + | 0.105813i | ||||
\(64\) | 1.50076e26 | 0.969843 | ||||||||
\(65\) | − | 9.75038e25i | − | 0.503243i | ||||||
\(66\) | 6.14448e24 | − | 2.16782e25i | 0.0254154 | − | 0.0896678i | ||||
\(67\) | −2.34833e25 | −0.0781043 | −0.0390521 | − | 0.999237i | \(-0.512434\pi\) | ||||
−0.0390521 | + | 0.999237i | \(0.512434\pi\) | |||||||
\(68\) | −6.13144e26 | −1.64507 | ||||||||
\(69\) | 4.79530e26 | + | 1.35918e26i | 1.04113 | + | 0.295098i | ||||
\(70\) | 1.74799e25 | + | 3.65232e25i | 0.0308048 | + | 0.0643645i | ||||
\(71\) | 4.44198e26i | 0.637280i | 0.947876 | + | 0.318640i | \(0.103226\pi\) | ||||
−0.947876 | + | 0.318640i | \(0.896774\pi\) | |||||||
\(72\) | −6.34921e25 | + | 1.03004e26i | −0.0743701 | + | 0.120652i | ||||
\(73\) | − | 7.29866e25i | − | 0.0699942i | −0.999387 | − | 0.0349971i | \(-0.988858\pi\) | ||
0.999387 | − | 0.0349971i | \(-0.0111422\pi\) | |||||||
\(74\) | 4.04265e25i | 0.0318278i | ||||||||
\(75\) | 3.69503e24 | − | 1.30364e25i | 0.00239458 | − | 0.00844827i | ||||
\(76\) | − | 2.24322e27i | − | 1.19970i | ||||||
\(77\) | −1.27992e27 | − | 2.67431e27i | −0.566327 | − | 1.18330i | ||||
\(78\) | −2.64525e25 | + | 9.33266e25i | −0.00970722 | + | 0.0342479i | ||||
\(79\) | −4.11080e27 | −1.25410 | −0.627052 | − | 0.778978i | \(-0.715739\pi\) | ||||
−0.627052 | + | 0.778978i | \(0.715739\pi\) | |||||||
\(80\) | 3.89124e27 | 0.989198 | ||||||||
\(81\) | 2.11639e27 | + | 4.20787e27i | 0.449328 | + | 0.893367i | ||||
\(82\) | − | 3.32267e26i | − | 0.0590455i | ||||||
\(83\) | −7.11680e27 | −1.06085 | −0.530423 | − | 0.847733i | \(-0.677967\pi\) | ||||
−0.530423 | + | 0.847733i | \(0.677967\pi\) | |||||||
\(84\) | 1.34485e27 | + | 7.82586e27i | 0.168509 | + | 0.980579i | ||||
\(85\) | −1.57345e28 | −1.66066 | ||||||||
\(86\) | 1.19931e27i | 0.106832i | ||||||||
\(87\) | 2.19913e28 | + | 6.23322e27i | 1.65662 | + | 0.469552i | ||||
\(88\) | 2.91305e27 | 0.185930 | ||||||||
\(89\) | −1.23620e28 | −0.669784 | −0.334892 | − | 0.942256i | \(-0.608700\pi\) | ||||
−0.334892 | + | 0.942256i | \(0.608700\pi\) | |||||||
\(90\) | −8.12607e26 | + | 1.31831e27i | −0.0374424 | + | 0.0607436i | ||||
\(91\) | 5.51017e27 | + | 1.15131e28i | 0.216304 | + | 0.451953i | ||||
\(92\) | 3.21374e28i | 1.07668i | ||||||||
\(93\) | 2.21132e28 | + | 6.26778e27i | 0.633359 | + | 0.179519i | ||||
\(94\) | 3.56173e27i | 0.0873588i | ||||||||
\(95\) | − | 5.75655e28i | − | 1.21107i | ||||||
\(96\) | −1.12688e28 | − | 3.19404e27i | −0.203679 | − | 0.0577308i | ||||
\(97\) | − | 2.43776e28i | − | 0.379142i | −0.981867 | − | 0.189571i | \(-0.939290\pi\) | ||
0.981867 | − | 0.189571i | \(-0.0607097\pi\) | |||||||
\(98\) | −4.12802e27 | − | 3.32478e27i | −0.0553304 | − | 0.0445641i | ||||
\(99\) | 5.95010e28 | − | 9.65297e28i | 0.688357 | − | 1.11674i | ||||
\(100\) | 8.73675e26 | 0.00873675 | ||||||||
\(101\) | 1.37010e29 | 1.18602 | 0.593010 | − | 0.805195i | \(-0.297940\pi\) | ||||
0.593010 | + | 0.805195i | \(0.297940\pi\) | |||||||
\(102\) | 1.50604e28 | + | 4.26874e27i | 0.113015 | + | 0.0320329i | ||||
\(103\) | 1.06328e29i | 0.692643i | 0.938116 | + | 0.346321i | \(0.112569\pi\) | ||||
−0.938116 | + | 0.346321i | \(0.887431\pi\) | |||||||
\(104\) | −1.25409e28 | −0.0710143 | ||||||||
\(105\) | 3.45115e28 | + | 2.00828e29i | 0.170106 | + | 0.989871i | ||||
\(106\) | −1.81689e28 | −0.0780537 | ||||||||
\(107\) | − | 3.85749e28i | − | 0.144624i | −0.997382 | − | 0.0723119i | \(-0.976962\pi\) | ||
0.997382 | − | 0.0723119i | \(-0.0230377\pi\) | |||||||
\(108\) | −2.23821e29 | + | 2.05277e29i | −0.733258 | + | 0.672506i | ||||
\(109\) | −5.36212e29 | −1.53692 | −0.768461 | − | 0.639896i | \(-0.778977\pi\) | ||||
−0.768461 | + | 0.639896i | \(0.778977\pi\) | |||||||
\(110\) | 3.72828e28 | 0.0936084 | ||||||||
\(111\) | −5.54800e28 | + | 1.95738e29i | −0.122167 | + | 0.431015i | ||||
\(112\) | −4.59473e29 | + | 2.19903e29i | −0.888380 | + | 0.425177i | ||||
\(113\) | 2.88250e29i | 0.489927i | 0.969532 | + | 0.244964i | \(0.0787761\pi\) | ||||
−0.969532 | + | 0.244964i | \(0.921224\pi\) | |||||||
\(114\) | −1.56174e28 | + | 5.50993e28i | −0.0233608 | + | 0.0824187i | ||||
\(115\) | 8.24710e29i | 1.08688i | ||||||||
\(116\) | 1.47382e30i | 1.71319i | ||||||||
\(117\) | −2.56157e29 | + | 4.15568e29i | −0.262912 | + | 0.426528i | ||||
\(118\) | − | 4.57257e28i | − | 0.0414831i | ||||||
\(119\) | 1.85792e30 | − | 8.89196e29i | 1.49140 | − | 0.713783i | ||||
\(120\) | −1.92625e29 | − | 5.45977e28i | −0.136957 | − | 0.0388192i | ||||
\(121\) | −1.14363e30 | −0.720935 | ||||||||
\(122\) | 1.48760e29 | 0.0832278 | ||||||||
\(123\) | 4.55993e29 | − | 1.60878e30i | 0.226639 | − | 0.799600i | ||||
\(124\) | 1.48199e30i | 0.654986i | ||||||||
\(125\) | −2.53083e30 | −0.995561 | ||||||||
\(126\) | 2.14510e28 | − | 2.01587e29i | 0.00751751 | − | 0.0706462i | ||||
\(127\) | −1.21450e30 | −0.379528 | −0.189764 | − | 0.981830i | \(-0.560772\pi\) | ||||
−0.189764 | + | 0.981830i | \(0.560772\pi\) | |||||||
\(128\) | − | 1.00610e30i | − | 0.280605i | ||||||
\(129\) | −1.64589e30 | + | 5.80684e30i | −0.410063 | + | 1.44673i | ||||
\(130\) | −1.60506e29 | −0.0357529 | ||||||||
\(131\) | 6.54668e30 | 1.30493 | 0.652465 | − | 0.757819i | \(-0.273735\pi\) | ||||
0.652465 | + | 0.757819i | \(0.273735\pi\) | |||||||
\(132\) | 7.03439e30 | + | 1.99383e30i | 1.25575 | + | 0.355931i | ||||
\(133\) | 3.25316e30 | + | 6.79727e30i | 0.520543 | + | 1.08764i | ||||
\(134\) | 3.86570e28i | 0.00554892i | ||||||||
\(135\) | −5.74371e30 | + | 5.26783e30i | −0.740206 | + | 0.678878i | ||||
\(136\) | 2.02377e30i | 0.234341i | ||||||||
\(137\) | − | 5.00608e30i | − | 0.521254i | −0.965440 | − | 0.260627i | \(-0.916071\pi\) | ||
0.965440 | − | 0.260627i | \(-0.0839293\pi\) | |||||||
\(138\) | 2.23742e29 | − | 7.89378e29i | 0.0209652 | − | 0.0739671i | ||||
\(139\) | 2.24857e31i | 1.89755i | 0.315958 | + | 0.948773i | \(0.397674\pi\) | ||||
−0.315958 | + | 0.948773i | \(0.602326\pi\) | |||||||
\(140\) | −1.18514e31 | + | 5.67208e30i | −0.901395 | + | 0.431406i | ||||
\(141\) | −4.88800e30 | + | 1.72453e31i | −0.335316 | + | 1.18302i | ||||
\(142\) | 7.31216e29 | 0.0452756 | ||||||||
\(143\) | 1.17526e31 | 0.657297 | ||||||||
\(144\) | −1.65848e31 | − | 1.02229e31i | −0.838403 | − | 0.516793i | ||||
\(145\) | 3.78213e31i | 1.72942i | ||||||||
\(146\) | −1.20147e29 | −0.00497274 | ||||||||
\(147\) | −1.54243e31 | − | 2.17632e31i | −0.578235 | − | 0.815870i | ||||
\(148\) | −1.31180e31 | −0.445732 | ||||||||
\(149\) | 8.53378e30i | 0.262991i | 0.991317 | + | 0.131495i | \(0.0419779\pi\) | ||||
−0.991317 | + | 0.131495i | \(0.958022\pi\) | |||||||
\(150\) | −2.14598e28 | − | 6.08256e27i | −0.000600208 | − | 0.000170123i | ||||
\(151\) | −1.60350e31 | −0.407289 | −0.203644 | − | 0.979045i | \(-0.565279\pi\) | ||||
−0.203644 | + | 0.979045i | \(0.565279\pi\) | |||||||
\(152\) | −7.40407e30 | −0.170898 | ||||||||
\(153\) | 6.70618e31 | + | 4.13370e31i | 1.40750 | + | 0.867586i | ||||
\(154\) | −4.40231e30 | + | 2.10694e30i | −0.0840679 | + | 0.0402348i | ||||
\(155\) | 3.80310e31i | 0.661193i | ||||||||
\(156\) | −3.02837e31 | − | 8.58361e30i | −0.479625 | − | 0.135945i | ||||
\(157\) | − | 1.56917e31i | − | 0.226530i | −0.993565 | − | 0.113265i | \(-0.963869\pi\) | ||
0.993565 | − | 0.113265i | \(-0.0361309\pi\) | |||||||
\(158\) | 6.76698e30i | 0.0890979i | ||||||||
\(159\) | −8.79707e31 | − | 2.49344e31i | −1.05701 | − | 0.299600i | ||||
\(160\) | − | 1.93805e31i | − | 0.212630i | ||||||
\(161\) | −4.66063e31 | − | 9.73809e31i | −0.467164 | − | 0.976109i | ||||
\(162\) | 6.92678e30 | − | 3.48390e30i | 0.0634693 | − | 0.0319225i | ||||
\(163\) | 7.51416e31 | 0.629739 | 0.314869 | − | 0.949135i | \(-0.398039\pi\) | ||||
0.314869 | + | 0.949135i | \(0.398039\pi\) | |||||||
\(164\) | 1.07818e32 | 0.826904 | ||||||||
\(165\) | 1.80517e32 | + | 5.11658e31i | 1.26765 | + | 0.359304i | ||||
\(166\) | 1.17153e31i | 0.0753679i | ||||||||
\(167\) | −1.08713e32 | −0.641051 | −0.320526 | − | 0.947240i | \(-0.603860\pi\) | ||||
−0.320526 | + | 0.947240i | \(0.603860\pi\) | |||||||
\(168\) | 2.58304e31 | − | 4.43887e30i | 0.139684 | − | 0.0240042i | ||||
\(169\) | 1.50942e32 | 0.748951 | ||||||||
\(170\) | 2.59014e31i | 0.117981i | ||||||||
\(171\) | −1.51233e32 | + | 2.45349e32i | −0.632708 | + | 1.02645i | ||||
\(172\) | −3.89165e32 | −1.49614 | ||||||||
\(173\) | 4.41231e32 | 1.55954 | 0.779771 | − | 0.626065i | \(-0.215335\pi\) | ||||
0.779771 | + | 0.626065i | \(0.215335\pi\) | |||||||
\(174\) | 1.02608e31 | − | 3.62010e31i | 0.0333593 | − | 0.117694i | ||||
\(175\) | −2.64736e30 | + | 1.26702e30i | −0.00792067 | + | 0.00379082i | ||||
\(176\) | 4.69030e32i | 1.29201i | ||||||||
\(177\) | 6.27524e31 | − | 2.21396e32i | 0.159228 | − | 0.561768i | ||||
\(178\) | 2.03498e31i | 0.0475849i | ||||||||
\(179\) | − | 9.16633e32i | − | 1.97618i | −0.153878 | − | 0.988090i | \(-0.549176\pi\) | ||
0.153878 | − | 0.988090i | \(-0.450824\pi\) | |||||||
\(180\) | −4.27780e32 | − | 2.63684e32i | −0.850686 | − | 0.524363i | ||||
\(181\) | − | 6.74836e32i | − | 1.23839i | −0.785235 | − | 0.619197i | \(-0.787458\pi\) | ||
0.785235 | − | 0.619197i | \(-0.212542\pi\) | |||||||
\(182\) | 1.89523e31 | − | 9.07055e30i | 0.0321091 | − | 0.0153673i | ||||
\(183\) | 7.20270e32 | + | 2.04153e32i | 1.12708 | + | 0.319459i | ||||
\(184\) | 1.06074e32 | 0.153374 | ||||||||
\(185\) | −3.36636e32 | −0.449956 | ||||||||
\(186\) | 1.03177e31 | − | 3.64017e31i | 0.0127540 | − | 0.0449970i | ||||
\(187\) | − | 1.89656e33i | − | 2.16902i | ||||||
\(188\) | −1.15575e33 | −1.22342 | ||||||||
\(189\) | 3.80513e32 | − | 9.46610e32i | 0.372970 | − | 0.927844i | ||||
\(190\) | −9.47614e31 | −0.0860407 | ||||||||
\(191\) | 1.63445e33i | 1.37527i | 0.726059 | + | 0.687633i | \(0.241350\pi\) | ||||
−0.726059 | + | 0.687633i | \(0.758650\pi\) | |||||||
\(192\) | 3.39040e32 | − | 1.19616e33i | 0.264474 | − | 0.933086i | ||||
\(193\) | 2.33949e32 | 0.169255 | 0.0846273 | − | 0.996413i | \(-0.473030\pi\) | ||||
0.0846273 | + | 0.996413i | \(0.473030\pi\) | |||||||
\(194\) | −4.01292e31 | −0.0269362 | ||||||||
\(195\) | −7.77141e32 | − | 2.20273e32i | −0.484170 | − | 0.137233i | ||||
\(196\) | 1.07886e33 | − | 1.33951e33i | 0.624099 | − | 0.774875i | ||||
\(197\) | 2.64605e32i | 0.142180i | 0.997470 | + | 0.0710899i | \(0.0226477\pi\) | ||||
−0.997470 | + | 0.0710899i | \(0.977352\pi\) | |||||||
\(198\) | −1.58902e32 | − | 9.79475e31i | −0.0793386 | − | 0.0489044i | ||||
\(199\) | 2.12781e33i | 0.987558i | 0.869587 | + | 0.493779i | \(0.164385\pi\) | ||||
−0.869587 | + | 0.493779i | \(0.835615\pi\) | |||||||
\(200\) | − | 2.88369e30i | − | 0.00124456i | ||||||
\(201\) | −5.30517e31 | + | 1.87171e32i | −0.0212989 | + | 0.0751441i | ||||
\(202\) | − | 2.25539e32i | − | 0.0842609i | ||||||
\(203\) | −2.13737e33 | − | 4.46590e33i | −0.743339 | − | 1.55316i | ||||
\(204\) | −1.38517e33 | + | 4.88699e33i | −0.448606 | + | 1.58272i | ||||
\(205\) | 2.76683e33 | 0.834740 | ||||||||
\(206\) | 1.75032e32 | 0.0492089 | ||||||||
\(207\) | 2.16664e33 | − | 3.51498e33i | 0.567827 | − | 0.921197i | ||||
\(208\) | − | 2.01921e33i | − | 0.493474i | ||||||
\(209\) | 6.93865e33 | 1.58181 | ||||||||
\(210\) | 3.30592e32 | − | 5.68111e31i | 0.0703255 | − | 0.0120852i | ||||
\(211\) | 1.53466e33 | 0.304731 | 0.152366 | − | 0.988324i | \(-0.451311\pi\) | ||||
0.152366 | + | 0.988324i | \(0.451311\pi\) | |||||||
\(212\) | − | 5.89565e33i | − | 1.09311i | ||||||
\(213\) | 3.54042e33 | + | 1.00350e33i | 0.613127 | + | 0.173785i | ||||
\(214\) | −6.35000e31 | −0.0102748 | ||||||||
\(215\) | −9.98676e33 | −1.51031 | ||||||||
\(216\) | 6.77547e32 | + | 7.38755e32i | 0.0957988 | + | 0.104453i | ||||
\(217\) | −2.14922e33 | − | 4.49066e33i | −0.284194 | − | 0.593805i | ||||
\(218\) | 8.82684e32i | 0.109191i | ||||||||
\(219\) | −5.81730e32 | − | 1.64886e32i | −0.0673414 | − | 0.0190873i | ||||
\(220\) | 1.20980e34i | 1.31094i | ||||||||
\(221\) | 8.16485e33i | 0.828439i | ||||||||
\(222\) | 3.22214e32 | + | 9.13283e31i | 0.0306215 | + | 0.00867936i | ||||
\(223\) | 4.39028e33i | 0.390905i | 0.980713 | + | 0.195453i | \(0.0626176\pi\) | ||||
−0.980713 | + | 0.195453i | \(0.937382\pi\) | |||||||
\(224\) | 1.09524e33 | + | 2.28843e33i | 0.0913927 | + | 0.190959i | ||||
\(225\) | −9.55570e31 | − | 5.89014e31i | −0.00747508 | − | 0.00460765i | ||||
\(226\) | 4.74502e32 | 0.0348069 | ||||||||
\(227\) | 7.33316e33 | 0.504564 | 0.252282 | − | 0.967654i | \(-0.418819\pi\) | ||||
0.252282 | + | 0.967654i | \(0.418819\pi\) | |||||||
\(228\) | −1.78793e34 | − | 5.06770e33i | −1.15423 | − | 0.327156i | ||||
\(229\) | − | 8.31384e33i | − | 0.503717i | −0.967764 | − | 0.251859i | \(-0.918958\pi\) | ||
0.967764 | − | 0.251859i | \(-0.0810418\pi\) | |||||||
\(230\) | 1.35760e33 | 0.0772177 | ||||||||
\(231\) | −2.42067e34 | + | 4.15984e33i | −1.29289 | + | 0.222179i | ||||
\(232\) | 4.86457e33 | 0.244044 | ||||||||
\(233\) | 3.48244e34i | 1.64143i | 0.571337 | + | 0.820716i | \(0.306425\pi\) | ||||
−0.571337 | + | 0.820716i | \(0.693575\pi\) | |||||||
\(234\) | 6.84087e32 | + | 4.21672e32i | 0.0303027 | + | 0.0186786i | ||||
\(235\) | −2.96589e34 | −1.23501 | ||||||||
\(236\) | 1.48376e34 | 0.580951 | ||||||||
\(237\) | −9.28679e33 | + | 3.27646e34i | −0.341991 | + | 1.20657i | ||||
\(238\) | −1.46375e33 | − | 3.05841e33i | −0.0507108 | − | 0.105957i | ||||
\(239\) | − | 2.34983e34i | − | 0.766067i | −0.923734 | − | 0.383033i | \(-0.874879\pi\) | ||
0.923734 | − | 0.383033i | \(-0.125121\pi\) | |||||||
\(240\) | 8.79079e33 | − | 3.10146e34i | 0.269752 | − | 0.951707i | ||||
\(241\) | 6.85561e34i | 1.98061i | 0.138912 | + | 0.990305i | \(0.455639\pi\) | ||||
−0.138912 | + | 0.990305i | \(0.544361\pi\) | |||||||
\(242\) | 1.88258e33i | 0.0512189i | ||||||||
\(243\) | 3.83195e34 | − | 7.36232e33i | 0.982039 | − | 0.188679i | ||||
\(244\) | 4.82713e34i | 1.16557i | ||||||||
\(245\) | 2.76858e34 | − | 3.43745e34i | 0.630013 | − | 0.782218i | ||||
\(246\) | −2.64829e33 | − | 7.50632e32i | −0.0568077 | − | 0.0161016i | ||||
\(247\) | −2.98715e34 | −0.604158 | ||||||||
\(248\) | 4.89154e33 | 0.0933031 | ||||||||
\(249\) | −1.60777e34 | + | 5.67235e34i | −0.289290 | + | 1.02064i | ||||
\(250\) | 4.16612e33i | 0.0707298i | ||||||||
\(251\) | 4.08692e34 | 0.654828 | 0.327414 | − | 0.944881i | \(-0.393823\pi\) | ||||
0.327414 | + | 0.944881i | \(0.393823\pi\) | |||||||
\(252\) | 6.54132e34 | + | 6.96066e33i | 0.989367 | + | 0.105279i | ||||
\(253\) | −9.94063e34 | −1.41960 | ||||||||
\(254\) | 1.99925e33i | 0.0269636i | ||||||||
\(255\) | −3.55462e34 | + | 1.25410e35i | −0.452857 | + | 1.59772i | ||||
\(256\) | 7.89152e34 | 0.949907 | ||||||||
\(257\) | −8.50905e34 | −0.967945 | −0.483972 | − | 0.875083i | \(-0.660806\pi\) | ||||
−0.483972 | + | 0.875083i | \(0.660806\pi\) | |||||||
\(258\) | 9.55891e33 | + | 2.70938e33i | 0.102783 | + | 0.0291329i | ||||
\(259\) | 3.97496e34 | − | 1.90241e34i | 0.404097 | − | 0.193400i | ||||
\(260\) | − | 5.20827e34i | − | 0.500703i | ||||||
\(261\) | 9.93621e34 | − | 1.61197e35i | 0.903511 | − | 1.46578i | ||||
\(262\) | − | 1.07768e34i | − | 0.0927089i | ||||||
\(263\) | 1.53828e35i | 1.25221i | 0.779740 | + | 0.626103i | \(0.215351\pi\) | ||||
−0.779740 | + | 0.626103i | \(0.784649\pi\) | |||||||
\(264\) | 6.58093e33 | − | 2.32181e34i | 0.0507026 | − | 0.178883i | ||||
\(265\) | − | 1.51295e35i | − | 1.10346i | ||||||
\(266\) | 1.11893e34 | − | 5.35519e33i | 0.0772716 | − | 0.0369820i | ||||
\(267\) | −2.79274e34 | + | 9.85300e34i | −0.182649 | + | 0.644399i | ||||
\(268\) | −1.25439e34 | −0.0777100 | ||||||||
\(269\) | 6.38364e34 | 0.374680 | 0.187340 | − | 0.982295i | \(-0.440013\pi\) | ||||
0.187340 | + | 0.982295i | \(0.440013\pi\) | |||||||
\(270\) | 8.67163e33 | + | 9.45500e33i | 0.0482310 | + | 0.0525880i | ||||
\(271\) | − | 1.91619e35i | − | 1.01015i | −0.863076 | − | 0.505074i | \(-0.831465\pi\) | ||
0.863076 | − | 0.505074i | \(-0.168535\pi\) | |||||||
\(272\) | −3.25848e35 | −1.62842 | ||||||||
\(273\) | 1.04212e35 | − | 1.79085e34i | 0.493810 | − | 0.0848594i | ||||
\(274\) | −8.24075e33 | −0.0370325 | ||||||||
\(275\) | 2.70243e33i | 0.0115194i | ||||||||
\(276\) | 2.56147e35 | + | 7.26022e34i | 1.03587 | + | 0.293608i | ||||
\(277\) | −4.75727e35 | −1.82558 | −0.912791 | − | 0.408427i | \(-0.866077\pi\) | ||||
−0.912791 | + | 0.408427i | \(0.866077\pi\) | |||||||
\(278\) | 3.70149e34 | 0.134811 | ||||||||
\(279\) | 9.99130e34 | − | 1.62091e35i | 0.345431 | − | 0.560400i | ||||
\(280\) | 1.87216e34 | + | 3.91175e34i | 0.0614540 | + | 0.128404i | ||||
\(281\) | − | 5.51041e35i | − | 1.71768i | −0.512245 | − | 0.858839i | \(-0.671186\pi\) | ||
0.512245 | − | 0.858839i | \(-0.328814\pi\) | |||||||
\(282\) | 2.83883e34 | + | 8.04637e33i | 0.0840479 | + | 0.0238225i | ||||
\(283\) | − | 1.66431e35i | − | 0.468092i | −0.972226 | − | 0.234046i | \(-0.924803\pi\) | ||
0.972226 | − | 0.234046i | \(-0.0751966\pi\) | |||||||
\(284\) | 2.37273e35i | 0.634064i | ||||||||
\(285\) | −4.58818e35 | − | 1.30047e35i | −1.16517 | − | 0.330257i | ||||
\(286\) | − | 1.93465e34i | − | 0.0466977i | ||||||
\(287\) | −3.26704e35 | + | 1.56360e35i | −0.749664 | + | 0.358788i | ||||
\(288\) | −5.09154e34 | + | 8.26011e34i | −0.111086 | + | 0.180217i | ||||
\(289\) | 8.35624e35 | 1.73377 | ||||||||
\(290\) | 6.22595e34 | 0.122867 | ||||||||
\(291\) | −1.94299e35 | − | 5.50721e34i | −0.364772 | − | 0.103391i | ||||
\(292\) | − | 3.89866e34i | − | 0.0696409i | ||||||
\(293\) | 4.84366e35 | 0.823366 | 0.411683 | − | 0.911327i | \(-0.364941\pi\) | ||||
0.411683 | + | 0.911327i | \(0.364941\pi\) | |||||||
\(294\) | −3.58254e34 | + | 2.53907e34i | −0.0579636 | + | 0.0410808i | ||||
\(295\) | 3.80763e35 | 0.586456 | ||||||||
\(296\) | 4.32981e34i | 0.0634949i | ||||||||
\(297\) | −6.34957e35 | − | 6.92317e35i | −0.886698 | − | 0.966800i | ||||
\(298\) | 1.40479e34 | 0.0186842 | ||||||||
\(299\) | 4.27953e35 | 0.542205 | ||||||||
\(300\) | 1.97374e33 | − | 6.96351e33i | 0.00238249 | − | 0.00840563i | ||||
\(301\) | 1.17923e36 | − | 5.64375e35i | 1.35638 | − | 0.649163i | ||||
\(302\) | 2.63959e34i | 0.0289359i | ||||||||
\(303\) | 3.09522e35 | − | 1.09202e36i | 0.323425 | − | 1.14107i | ||||
\(304\) | − | 1.19213e36i | − | 1.18756i | ||||||
\(305\) | 1.23874e36i | 1.17661i | ||||||||
\(306\) | 6.80468e34 | − | 1.10394e35i | 0.0616378 | − | 0.0999962i | ||||
\(307\) | 4.14891e35i | 0.358449i | 0.983808 | + | 0.179224i | \(0.0573588\pi\) | ||||
−0.983808 | + | 0.179224i | \(0.942641\pi\) | |||||||
\(308\) | −6.83684e35 | − | 1.42851e36i | −0.563469 | − | 1.17733i | ||||
\(309\) | 8.47476e35 | + | 2.40209e35i | 0.666391 | + | 0.188882i | ||||
\(310\) | 6.26047e34 | 0.0469745 | ||||||||
\(311\) | −7.22914e35 | −0.517680 | −0.258840 | − | 0.965920i | \(-0.583340\pi\) | ||||
−0.258840 | + | 0.965920i | \(0.583340\pi\) | |||||||
\(312\) | −2.83315e34 | + | 9.99557e34i | −0.0193654 | + | 0.0683229i | ||||
\(313\) | 6.81116e35i | 0.444455i | 0.974995 | + | 0.222228i | \(0.0713328\pi\) | ||||
−0.974995 | + | 0.222228i | \(0.928667\pi\) | |||||||
\(314\) | −2.58309e34 | −0.0160938 | ||||||||
\(315\) | 1.67864e36 | + | 1.78625e35i | 0.998742 | + | 0.106277i | ||||
\(316\) | −2.19583e36 | −1.24777 | ||||||||
\(317\) | − | 1.68810e36i | − | 0.916300i | −0.888875 | − | 0.458150i | \(-0.848512\pi\) | ||
0.888875 | − | 0.458150i | \(-0.151488\pi\) | |||||||
\(318\) | −4.10458e34 | + | 1.44813e35i | −0.0212851 | + | 0.0750955i | ||||
\(319\) | −4.55878e36 | −2.25883 | ||||||||
\(320\) | 2.05719e36 | 0.974092 | ||||||||
\(321\) | −3.07456e35 | − | 8.71454e34i | −0.139143 | − | 0.0394386i | ||||
\(322\) | −1.60303e35 | + | 7.67209e34i | −0.0693478 | + | 0.0331897i | ||||
\(323\) | 4.82047e36i | 1.99367i | ||||||||
\(324\) | 1.13049e36 | + | 2.24768e36i | 0.447060 | + | 0.888858i | ||||
\(325\) | − | 1.16342e34i | − | 0.00439974i | ||||||
\(326\) | − | 1.23694e35i | − | 0.0447398i | ||||||
\(327\) | −1.21137e36 | + | 4.27380e36i | −0.419115 | + | 1.47867i | ||||
\(328\) | − | 3.55869e35i | − | 0.117793i | ||||||
\(329\) | 3.50209e36 | − | 1.67609e36i | 1.10914 | − | 0.530833i | ||||
\(330\) | 8.42264e34 | − | 2.97158e35i | 0.0255268 | − | 0.0900606i | ||||
\(331\) | 4.91857e34 | 0.0142670 | 0.00713350 | − | 0.999975i | \(-0.497729\pi\) | ||||
0.00713350 | + | 0.999975i | \(0.497729\pi\) | |||||||
\(332\) | −3.80152e36 | −1.05549 | ||||||||
\(333\) | 1.43477e36 | + | 8.84392e35i | 0.381364 | + | 0.235073i | ||||
\(334\) | 1.78958e35i | 0.0455435i | ||||||||
\(335\) | −3.21901e35 | −0.0784464 | ||||||||
\(336\) | 7.14702e35 | + | 4.15896e36i | 0.166804 | + | 0.970655i | ||||
\(337\) | −3.67526e36 | −0.821589 | −0.410794 | − | 0.911728i | \(-0.634749\pi\) | ||||
−0.410794 | + | 0.911728i | \(0.634749\pi\) | |||||||
\(338\) | − | 2.48473e35i | − | 0.0532093i | ||||||
\(339\) | 2.29746e36 | + | 6.51192e35i | 0.471359 | + | 0.133602i | ||||
\(340\) | −8.40478e36 | −1.65227 | ||||||||
\(341\) | −4.58406e36 | −0.863598 | ||||||||
\(342\) | 4.03880e35 | + | 2.48952e35i | 0.0729246 | + | 0.0449508i | ||||
\(343\) | −1.32653e36 | + | 5.62349e36i | −0.229590 | + | 0.973288i | ||||
\(344\) | 1.28450e36i | 0.213125i | ||||||||
\(345\) | 6.57324e36 | + | 1.86312e36i | 1.04569 | + | 0.296390i | ||||
\(346\) | − | 7.26331e35i | − | 0.110798i | ||||||
\(347\) | − | 6.02613e36i | − | 0.881579i | −0.897610 | − | 0.440790i | \(-0.854698\pi\) | ||
0.897610 | − | 0.440790i | \(-0.145302\pi\) | |||||||
\(348\) | 1.17469e37 | + | 3.32954e36i | 1.64826 | + | 0.467182i | ||||
\(349\) | − | 2.04744e36i | − | 0.275576i | −0.990462 | − | 0.137788i | \(-0.956001\pi\) | ||
0.990462 | − | 0.137788i | \(-0.0439993\pi\) | |||||||
\(350\) | 2.08571e33 | + | 4.35795e33i | 0.000269319 | + | 0.000562725i | ||||
\(351\) | 2.73354e36 | + | 2.98048e36i | 0.338667 | + | 0.369261i | ||||
\(352\) | 2.33602e36 | 0.277721 | ||||||||
\(353\) | 1.26440e37 | 1.44262 | 0.721308 | − | 0.692614i | \(-0.243541\pi\) | ||||
0.721308 | + | 0.692614i | \(0.243541\pi\) | |||||||
\(354\) | −3.64450e35 | − | 1.03300e35i | −0.0399109 | − | 0.0113123i | ||||
\(355\) | 6.08892e36i | 0.640072i | ||||||||
\(356\) | −6.60332e36 | −0.666404 | ||||||||
\(357\) | −2.88996e36 | − | 1.68171e37i | −0.280028 | − | 1.62953i | ||||
\(358\) | −1.50891e36 | −0.140398 | ||||||||
\(359\) | − | 4.98569e36i | − | 0.445508i | −0.974875 | − | 0.222754i | \(-0.928495\pi\) | ||
0.974875 | − | 0.222754i | \(-0.0715047\pi\) | |||||||
\(360\) | −8.70328e35 | + | 1.41195e36i | −0.0746959 | + | 0.121181i | ||||
\(361\) | −5.50607e36 | −0.453929 | ||||||||
\(362\) | −1.11088e36 | −0.0879819 | ||||||||
\(363\) | −2.58359e36 | + | 9.11512e36i | −0.196597 | + | 0.693611i | ||||
\(364\) | 2.94332e36 | + | 6.14987e36i | 0.215212 | + | 0.449672i | ||||
\(365\) | − | 1.00048e36i | − | 0.0703008i | ||||||
\(366\) | 3.36067e35 | − | 1.18567e36i | 0.0226960 | − | 0.0800734i | ||||
\(367\) | − | 1.86060e37i | − | 1.20780i | −0.797059 | − | 0.603901i | \(-0.793612\pi\) | ||
0.797059 | − | 0.603901i | \(-0.206388\pi\) | |||||||
\(368\) | 1.70790e37i | 1.06578i | ||||||||
\(369\) | −1.17924e37 | − | 7.26886e36i | −0.707491 | − | 0.436098i | ||||
\(370\) | 5.54153e35i | 0.0319672i | ||||||||
\(371\) | 8.55001e36 | + | 1.78647e37i | 0.474291 | + | 0.991000i | ||||
\(372\) | 1.18120e37 | + | 3.34800e36i | 0.630162 | + | 0.178613i | ||||
\(373\) | −2.32369e37 | −1.19234 | −0.596169 | − | 0.802859i | \(-0.703311\pi\) | ||||
−0.596169 | + | 0.802859i | \(0.703311\pi\) | |||||||
\(374\) | −3.12202e36 | −0.154098 | ||||||||
\(375\) | −5.71746e36 | + | 2.01717e37i | −0.271487 | + | 0.957829i | ||||
\(376\) | 3.81472e36i | 0.174277i | ||||||||
\(377\) | 1.96260e37 | 0.862743 | ||||||||
\(378\) | −1.55826e36 | − | 6.26381e35i | −0.0659187 | − | 0.0264977i | ||||
\(379\) | −8.33717e36 | −0.339430 | −0.169715 | − | 0.985493i | \(-0.554285\pi\) | ||||
−0.169715 | + | 0.985493i | \(0.554285\pi\) | |||||||
\(380\) | − | 3.07493e37i | − | 1.20496i | ||||||
\(381\) | −2.74370e36 | + | 9.68001e36i | −0.103496 | + | 0.365144i | ||||
\(382\) | 2.69054e36 | 0.0977059 | ||||||||
\(383\) | −1.59429e37 | −0.557424 | −0.278712 | − | 0.960375i | \(-0.589907\pi\) | ||||
−0.278712 | + | 0.960375i | \(0.589907\pi\) | |||||||
\(384\) | −8.01897e36 | − | 2.27290e36i | −0.269970 | − | 0.0765204i | ||||
\(385\) | −1.75447e37 | − | 3.66586e37i | −0.568808 | − | 1.18849i | ||||
\(386\) | − | 3.85115e35i | − | 0.0120247i | ||||||
\(387\) | 4.25643e37 | + | 2.62367e37i | 1.28008 | + | 0.789042i | ||||
\(388\) | − | 1.30216e37i | − | 0.377228i | ||||||
\(389\) | − | 4.83465e36i | − | 0.134926i | −0.997722 | − | 0.0674630i | \(-0.978510\pi\) | ||
0.997722 | − | 0.0674630i | \(-0.0214905\pi\) | |||||||
\(390\) | −3.62602e35 | + | 1.27929e36i | −0.00974975 | + | 0.0343979i | ||||
\(391\) | − | 6.90603e37i | − | 1.78923i | ||||||
\(392\) | −4.42124e36 | − | 3.56095e36i | −0.110381 | − | 0.0889032i | ||||
\(393\) | 1.47897e37 | − | 5.21794e37i | 0.355852 | − | 1.25547i | ||||
\(394\) | 4.35579e35 | 0.0101012 | ||||||||
\(395\) | −5.63494e37 | −1.25960 | ||||||||
\(396\) | 3.17831e37 | − | 5.15624e37i | 0.684883 | − | 1.11110i | ||||
\(397\) | − | 8.92922e37i | − | 1.85503i | −0.373786 | − | 0.927515i | \(-0.621940\pi\) | ||
0.373786 | − | 0.927515i | \(-0.378060\pi\) | |||||||
\(398\) | 3.50269e36 | 0.0701612 | ||||||||
\(399\) | 6.15260e37 | − | 1.05730e37i | 1.18837 | − | 0.204217i | ||||
\(400\) | 4.64304e35 | 0.00864833 | ||||||||
\(401\) | 2.41874e37i | 0.434505i | 0.976115 | + | 0.217253i | \(0.0697095\pi\) | ||||
−0.976115 | + | 0.217253i | \(0.930290\pi\) | |||||||
\(402\) | 3.08111e35 | + | 8.73309e34i | 0.00533862 | + | 0.00151318i | ||||
\(403\) | 1.97348e37 | 0.329844 | ||||||||
\(404\) | 7.31853e37 | 1.18003 | ||||||||
\(405\) | 2.90108e37 | + | 5.76801e37i | 0.451296 | + | 0.897281i | ||||
\(406\) | −7.35153e36 | + | 3.51843e36i | −0.110344 | + | 0.0528106i | ||||
\(407\) | − | 4.05764e37i | − | 0.587698i | ||||||
\(408\) | 1.61302e37 | + | 4.57195e36i | 0.225459 | + | 0.0639042i | ||||
\(409\) | 6.27784e37i | 0.846881i | 0.905924 | + | 0.423441i | \(0.139178\pi\) | ||||
−0.905924 | + | 0.423441i | \(0.860822\pi\) | |||||||
\(410\) | − | 4.55461e36i | − | 0.0593042i | ||||||
\(411\) | −3.99003e37 | − | 1.13093e37i | −0.501498 | − | 0.142145i | ||||
\(412\) | 5.67965e37i | 0.689147i | ||||||||
\(413\) | −4.49600e37 | + | 2.15178e37i | −0.526685 | + | 0.252070i | ||||
\(414\) | −5.78618e36 | − | 3.56660e36i | −0.0654465 | − | 0.0403413i | ||||
\(415\) | −9.75547e37 | −1.06549 | ||||||||
\(416\) | −1.00568e37 | −0.106073 | ||||||||
\(417\) | 1.79220e38 | + | 5.07980e37i | 1.82563 | + | 0.517457i | ||||
\(418\) | − | 1.14220e37i | − | 0.112380i | ||||||
\(419\) | −1.17454e38 | −1.11626 | −0.558130 | − | 0.829754i | \(-0.688481\pi\) | ||||
−0.558130 | + | 0.829754i | \(0.688481\pi\) | |||||||
\(420\) | 1.84347e37 | + | 1.07274e38i | 0.169247 | + | 0.984875i | ||||
\(421\) | −1.73657e38 | −1.54029 | −0.770145 | − | 0.637869i | \(-0.779816\pi\) | ||||
−0.770145 | + | 0.637869i | \(0.779816\pi\) | |||||||
\(422\) | − | 2.52628e36i | − | 0.0216496i | ||||||
\(423\) | 1.26408e38 | + | 7.79183e37i | 1.04674 | + | 0.645214i | ||||
\(424\) | −1.94595e37 | −0.155714 | ||||||||
\(425\) | −1.87745e36 | −0.0145187 | ||||||||
\(426\) | 1.65191e36 | − | 5.82806e36i | 0.0123466 | − | 0.0435597i | ||||
\(427\) | −7.00041e37 | − | 1.46269e38i | −0.505731 | − | 1.05669i | ||||
\(428\) | − | 2.06052e37i | − | 0.143894i | ||||||
\(429\) | 2.65506e37 | − | 9.36726e37i | 0.179243 | − | 0.632385i | ||||
\(430\) | 1.64397e37i | 0.107300i | ||||||||
\(431\) | − | 3.99375e37i | − | 0.252034i | −0.992028 | − | 0.126017i | \(-0.959781\pi\) | ||
0.992028 | − | 0.126017i | \(-0.0402195\pi\) | |||||||
\(432\) | −1.18947e38 | + | 1.09092e38i | −0.725837 | + | 0.665700i | ||||
\(433\) | 2.69975e37i | 0.159312i | 0.996822 | + | 0.0796562i | \(0.0253822\pi\) | ||||
−0.996822 | + | 0.0796562i | \(0.974618\pi\) | |||||||
\(434\) | −7.39229e36 | + | 3.53794e36i | −0.0421869 | + | 0.0201906i | ||||
\(435\) | 3.01450e38 | + | 8.54429e37i | 1.66387 | + | 0.471609i | ||||
\(436\) | −2.86423e38 | −1.52917 | ||||||||
\(437\) | 2.52660e38 | 1.30484 | ||||||||
\(438\) | −2.71426e35 | + | 9.57615e35i | −0.00135606 | + | 0.00478427i | ||||
\(439\) | − | 2.22268e38i | − | 1.07434i | −0.843475 | − | 0.537169i | \(-0.819494\pi\) | ||
0.843475 | − | 0.537169i | \(-0.180506\pi\) | |||||||
\(440\) | 3.99311e37 | 0.186744 | ||||||||
\(441\) | −2.08306e38 | + | 7.37718e37i | −0.942632 | + | 0.333834i | ||||
\(442\) | 1.34406e37 | 0.0588565 | ||||||||
\(443\) | 1.84884e38i | 0.783509i | 0.920070 | + | 0.391755i | \(0.128132\pi\) | ||||
−0.920070 | + | 0.391755i | \(0.871868\pi\) | |||||||
\(444\) | −2.96353e37 | + | 1.04556e38i | −0.121550 | + | 0.428839i | ||||
\(445\) | −1.69455e38 | −0.672719 | ||||||||
\(446\) | 7.22705e36 | 0.0277719 | ||||||||
\(447\) | 6.80174e37 | + | 1.92788e37i | 0.253023 | + | 0.0717170i | ||||
\(448\) | −2.42911e38 | + | 1.16257e38i | −0.874813 | + | 0.418684i | ||||
\(449\) | − | 2.08938e38i | − | 0.728525i | −0.931296 | − | 0.364263i | \(-0.881321\pi\) | ||
0.931296 | − | 0.364263i | \(-0.118679\pi\) | |||||||
\(450\) | −9.69605e34 | + | 1.57301e35i | −0.000327351 | + | 0.000531068i | ||||
\(451\) | 3.33499e38i | 1.09027i | ||||||||
\(452\) | 1.53972e38i | 0.487455i | ||||||||
\(453\) | −3.62249e37 | + | 1.27805e38i | −0.111067 | + | 0.391852i | ||||
\(454\) | − | 1.20715e37i | − | 0.0358468i | ||||||
\(455\) | 7.55315e37 | + | 1.57818e38i | 0.217252 | + | 0.453933i | ||||
\(456\) | −1.67267e37 | + | 5.90131e37i | −0.0466036 | + | 0.164421i | ||||
\(457\) | −1.08516e38 | −0.292892 | −0.146446 | − | 0.989219i | \(-0.546783\pi\) | ||||
−0.146446 | + | 0.989219i | \(0.546783\pi\) | |||||||
\(458\) | −1.36858e37 | −0.0357867 | ||||||||
\(459\) | 4.80971e38 | − | 4.41122e38i | 1.21853 | − | 1.11757i | ||||
\(460\) | 4.40528e38i | 1.08140i | ||||||||
\(461\) | −2.64900e36 | −0.00630114 | −0.00315057 | − | 0.999995i | \(-0.501003\pi\) | ||||
−0.00315057 | + | 0.999995i | \(0.501003\pi\) | |||||||
\(462\) | 6.84772e36 | + | 3.98479e37i | 0.0157847 | + | 0.0918537i | ||||
\(463\) | 2.91043e38 | 0.650179 | 0.325089 | − | 0.945683i | \(-0.394606\pi\) | ||||
0.325089 | + | 0.945683i | \(0.394606\pi\) | |||||||
\(464\) | 7.83245e38i | 1.69585i | ||||||||
\(465\) | 3.03121e38 | + | 8.59166e37i | 0.636133 | + | 0.180306i | ||||
\(466\) | 5.73261e37 | 0.116616 | ||||||||
\(467\) | 1.17358e38 | 0.231430 | 0.115715 | − | 0.993282i | \(-0.463084\pi\) | ||||
0.115715 | + | 0.993282i | \(0.463084\pi\) | |||||||
\(468\) | −1.36829e38 | + | 2.21981e38i | −0.261585 | + | 0.424375i | ||||
\(469\) | 3.80098e37 | − | 1.81914e37i | 0.0704513 | − | 0.0337179i | ||||
\(470\) | 4.88229e37i | 0.0877415i | ||||||||
\(471\) | −1.25069e38 | − | 3.54495e37i | −0.217944 | − | 0.0617742i | ||||
\(472\) | − | 4.89736e37i | − | 0.0827568i | ||||||
\(473\) | − | 1.20375e39i | − | 1.97265i | ||||||
\(474\) | 5.39353e37 | + | 1.52874e37i | 0.0857211 | + | 0.0242968i | ||||
\(475\) | − | 6.86873e36i | − | 0.0105881i | ||||||
\(476\) | 9.92427e38 | − | 4.74974e38i | 1.48388 | − | 0.710181i | ||||
\(477\) | −3.97473e38 | + | 6.44829e38i | −0.576489 | + | 0.935251i | ||||
\(478\) | −3.86817e37 | −0.0544253 | ||||||||
\(479\) | −1.15260e39 | −1.57331 | −0.786654 | − | 0.617394i | \(-0.788188\pi\) | ||||
−0.786654 | + | 0.617394i | \(0.788188\pi\) | |||||||
\(480\) | −1.54470e38 | − | 4.37829e37i | −0.204571 | − | 0.0579838i | ||||
\(481\) | 1.74685e38i | 0.224466i | ||||||||
\(482\) | 1.12853e38 | 0.140713 | ||||||||
\(483\) | −8.81451e38 | + | 1.51474e38i | −1.06651 | + | 0.183276i | ||||
\(484\) | −6.10880e38 | −0.717296 | ||||||||
\(485\) | − | 3.34161e38i | − | 0.380803i | ||||||
\(486\) | −1.21195e37 | − | 6.30796e37i | −0.0134047 | − | 0.0697690i | ||||
\(487\) | 1.01199e39 | 1.08644 | 0.543219 | − | 0.839591i | \(-0.317205\pi\) | ||||
0.543219 | + | 0.839591i | \(0.317205\pi\) | |||||||
\(488\) | 1.59327e38 | 0.166035 | ||||||||
\(489\) | 1.69754e38 | − | 5.98906e38i | 0.171728 | − | 0.605871i | ||||
\(490\) | −5.65855e37 | − | 4.55750e37i | −0.0555728 | − | 0.0447593i | ||||
\(491\) | 1.37756e39i | 1.31350i | 0.754109 | + | 0.656749i | \(0.228069\pi\) | ||||
−0.754109 | + | 0.656749i | \(0.771931\pi\) | |||||||
\(492\) | 2.43574e38 | − | 8.59348e38i | 0.225495 | − | 0.795564i | ||||
\(493\) | − | 3.16711e39i | − | 2.84697i | ||||||
\(494\) | 4.91729e37i | 0.0429225i | ||||||||
\(495\) | 8.15620e38 | − | 1.32320e39i | 0.691373 | − | 1.12163i | ||||
\(496\) | 7.87587e38i | 0.648357i | ||||||||
\(497\) | −3.44099e38 | − | 7.18972e38i | −0.275116 | − | 0.574837i | ||||
\(498\) | 9.33753e37 | + | 2.64663e37i | 0.0725115 | + | 0.0205527i | ||||
\(499\) | −3.04074e38 | −0.229362 | −0.114681 | − | 0.993402i | \(-0.536585\pi\) | ||||
−0.114681 | + | 0.993402i | \(0.536585\pi\) | |||||||
\(500\) | −1.35187e39 | −0.990536 | ||||||||
\(501\) | −2.45596e38 | + | 8.66483e38i | −0.174813 | + | 0.616755i | ||||
\(502\) | − | 6.72768e37i | − | 0.0465223i | ||||||
\(503\) | −1.49463e39 | −1.00415 | −0.502073 | − | 0.864825i | \(-0.667429\pi\) | ||||
−0.502073 | + | 0.864825i | \(0.667429\pi\) | |||||||
\(504\) | 2.29747e37 | − | 2.15906e38i | 0.0149971 | − | 0.140936i | ||||
\(505\) | 1.87809e39 | 1.19122 | ||||||||
\(506\) | 1.63638e38i | 0.100856i | ||||||||
\(507\) | 3.40997e38 | − | 1.20306e39i | 0.204237 | − | 0.720566i | ||||
\(508\) | −6.48739e38 | −0.377612 | ||||||||
\(509\) | −4.02828e37 | −0.0227883 | −0.0113941 | − | 0.999935i | \(-0.503627\pi\) | ||||
−0.0113941 | + | 0.999935i | \(0.503627\pi\) | |||||||
\(510\) | 2.06444e38 | + | 5.85144e37i | 0.113510 | + | 0.0321733i | ||||
\(511\) | 5.65393e37 | + | 1.18135e38i | 0.0302167 | + | 0.0631359i | ||||
\(512\) | − | 6.70051e38i | − | 0.348092i | ||||||
\(513\) | 1.61386e39 | + | 1.75966e39i | 0.815014 | + | 0.888640i | ||||
\(514\) | 1.40072e38i | 0.0687677i | ||||||||
\(515\) | 1.45751e39i | 0.695677i | ||||||||
\(516\) | −8.79171e38 | + | 3.10179e39i | −0.407993 | + | 1.43943i | ||||
\(517\) | − | 3.57493e39i | − | 1.61308i | ||||||
\(518\) | −3.13165e37 | − | 6.54337e37i | −0.0137401 | − | 0.0287091i | ||||
\(519\) | 9.96794e38 | − | 3.51677e39i | 0.425284 | − | 1.50043i | ||||
\(520\) | −1.71907e38 | −0.0713254 | ||||||||
\(521\) | 3.08072e38 | 0.124310 | 0.0621550 | − | 0.998067i | \(-0.480203\pi\) | ||||
0.0621550 | + | 0.998067i | \(0.480203\pi\) | |||||||
\(522\) | −2.65355e38 | − | 1.63565e38i | −0.104137 | − | 0.0641900i | ||||
\(523\) | 4.34830e38i | 0.165976i | 0.996551 | + | 0.0829880i | \(0.0264463\pi\) | ||||
−0.996551 | + | 0.0829880i | \(0.973554\pi\) | |||||||
\(524\) | 3.49698e39 | 1.29834 | ||||||||
\(525\) | 4.11792e36 | + | 2.39628e37i | 0.00148720 | + | 0.00865422i | ||||
\(526\) | 2.53223e38 | 0.0889632 | ||||||||
\(527\) | − | 3.18467e39i | − | 1.08846i | ||||||
\(528\) | 3.73834e39 | + | 1.05960e39i | 1.24305 | + | 0.352329i | ||||
\(529\) | −5.28669e38 | −0.171032 | ||||||||
\(530\) | −2.49053e38 | −0.0783957 | ||||||||
\(531\) | −1.62284e39 | − | 1.00032e39i | −0.497056 | − | 0.306386i | ||||
\(532\) | 1.73771e39 | + | 3.63084e39i | 0.517916 | + | 1.08215i | ||||
\(533\) | − | 1.43574e39i | − | 0.416420i | ||||||
\(534\) | 1.62195e38 | + | 4.59726e37i | 0.0457814 | + | 0.0129763i | ||||
\(535\) | − | 5.28772e38i | − | 0.145257i | ||||||
\(536\) | 4.14029e37i | 0.0110698i | ||||||||
\(537\) | −7.30590e39 | − | 2.07079e39i | −1.90128 | − | 0.538900i | ||||
\(538\) | − | 1.05084e38i | − | 0.0266192i | ||||||
\(539\) | 4.14332e39 | + | 3.33711e39i | 1.02167 | + | 0.822874i | ||||
\(540\) | −3.06807e39 | + | 2.81387e39i | −0.736470 | + | 0.675452i | ||||
\(541\) | 2.94250e39 | 0.687632 | 0.343816 | − | 0.939037i | \(-0.388280\pi\) | ||||
0.343816 | + | 0.939037i | \(0.388280\pi\) | |||||||
\(542\) | −3.15434e38 | −0.0717660 | ||||||||
\(543\) | −5.37869e39 | − | 1.52454e39i | −1.19146 | − | 0.337707i | ||||
\(544\) | 1.62290e39i | 0.350032i | ||||||||
\(545\) | −7.35021e39 | −1.54366 | ||||||||
\(546\) | −2.94800e37 | − | 1.71549e38i | −0.00602885 | − | 0.0350828i | ||||
\(547\) | 4.86226e38 | 0.0968326 | 0.0484163 | − | 0.998827i | \(-0.484583\pi\) | ||||
0.0484163 | + | 0.998827i | \(0.484583\pi\) | |||||||
\(548\) | − | 2.67405e39i | − | 0.518623i | ||||||
\(549\) | 3.25435e39 | − | 5.27961e39i | 0.614704 | − | 0.997247i | ||||
\(550\) | 4.44860e36 | 0.000818397 | ||||||||
\(551\) | 1.15870e40 | 2.07622 | ||||||||
\(552\) | 2.39634e38 | − | 8.45450e38i | 0.0418247 | − | 0.147561i | ||||
\(553\) | 6.65368e39 | − | 3.18444e39i | 1.13122 | − | 0.541400i | ||||
\(554\) | 7.83118e38i | 0.129699i | ||||||||
\(555\) | −7.60502e38 | + | 2.68311e39i | −0.122702 | + | 0.432903i | ||||
\(556\) | 1.20110e40i | 1.88797i | ||||||||
\(557\) | 9.72938e39i | 1.49000i | 0.667067 | + | 0.744998i | \(0.267550\pi\) | ||||
−0.667067 | + | 0.744998i | \(0.732450\pi\) | |||||||
\(558\) | −2.66826e38 | − | 1.64472e38i | −0.0398136 | − | 0.0245412i | ||||
\(559\) | 5.18226e39i | 0.753439i | ||||||||
\(560\) | −6.29831e39 | + | 3.01436e39i | −0.892272 | + | 0.427040i | ||||
\(561\) | −1.51163e40 | − | 4.28456e39i | −2.08681 | − | 0.591487i | ||||
\(562\) | −9.07095e38 | −0.122033 | ||||||||
\(563\) | −8.04726e39 | −1.05506 | −0.527529 | − | 0.849537i | \(-0.676881\pi\) | ||||
−0.527529 | + | 0.849537i | \(0.676881\pi\) | |||||||
\(564\) | −2.61098e39 | + | 9.21175e39i | −0.333623 | + | 1.17705i | ||||
\(565\) | 3.95123e39i | 0.492074i | ||||||||
\(566\) | −2.73970e38 | −0.0332556 | ||||||||
\(567\) | −6.68520e39 | − | 5.17134e39i | −0.790970 | − | 0.611855i | ||||
\(568\) | 7.83155e38 | 0.0903227 | ||||||||
\(569\) | − | 4.92946e39i | − | 0.554206i | −0.960840 | − | 0.277103i | \(-0.910626\pi\) | ||
0.960840 | − | 0.277103i | \(-0.0893744\pi\) | |||||||
\(570\) | −2.14077e38 | + | 7.55283e38i | −0.0234631 | + | 0.0827798i | ||||
\(571\) | −3.01134e39 | −0.321763 | −0.160881 | − | 0.986974i | \(-0.551434\pi\) | ||||
−0.160881 | + | 0.986974i | \(0.551434\pi\) | |||||||
\(572\) | 6.27778e39 | 0.653979 | ||||||||
\(573\) | 1.30271e40 | + | 3.69241e39i | 1.32314 | + | 0.375032i | ||||
\(574\) | 2.57392e38 | + | 5.37803e38i | 0.0254901 | + | 0.0532600i | ||||
\(575\) | 9.84047e37i | 0.00950237i | ||||||||
\(576\) | −8.76790e39 | − | 5.40454e39i | −0.825600 | − | 0.508901i | ||||
\(577\) | 1.29813e40i | 1.19198i | 0.802990 | + | 0.595992i | \(0.203241\pi\) | ||||
−0.802990 | + | 0.595992i | \(0.796759\pi\) | |||||||
\(578\) | − | 1.37556e39i | − | 0.123176i | ||||||
\(579\) | 5.28520e38 | − | 1.86466e39i | 0.0461554 | − | 0.162840i | ||||
\(580\) | 2.02027e40i | 1.72069i | ||||||||
\(581\) | 1.15192e40 | − | 5.51305e39i | 0.956900 | − | 0.457971i | ||||
\(582\) | −9.06568e37 | + | 3.19845e38i | −0.00734543 | + | 0.0259153i | ||||
\(583\) | 1.82363e40 | 1.44126 | ||||||||
\(584\) | −1.28681e38 | −0.00992039 | ||||||||
\(585\) | −3.51131e39 | + | 5.69647e39i | −0.264064 | + | 0.428397i | ||||
\(586\) | − | 7.97338e38i | − | 0.0584961i | ||||||
\(587\) | 3.87385e38 | 0.0277262 | 0.0138631 | − | 0.999904i | \(-0.495587\pi\) | ||||
0.0138631 | + | 0.999904i | \(0.495587\pi\) | |||||||
\(588\) | −8.23907e39 | − | 1.16250e40i | −0.575317 | − | 0.811752i | ||||
\(589\) | 1.16513e40 | 0.793782 | ||||||||
\(590\) | − | 6.26792e38i | − | 0.0416648i | ||||||
\(591\) | 2.10900e39 | + | 5.97775e38i | 0.136791 | + | 0.0387721i | ||||
\(592\) | −6.97142e39 | −0.441221 | ||||||||
\(593\) | −1.25692e40 | −0.776274 | −0.388137 | − | 0.921602i | \(-0.626881\pi\) | ||||
−0.388137 | + | 0.921602i | \(0.626881\pi\) | |||||||
\(594\) | −1.13966e39 | + | 1.04523e39i | −0.0686864 | + | 0.0629956i | ||||
\(595\) | 2.54677e40 | − | 1.21888e40i | 1.49794 | − | 0.716910i | ||||
\(596\) | 4.55841e39i | 0.261663i | ||||||||
\(597\) | 1.69594e40 | + | 4.80698e39i | 0.950130 | + | 0.269305i | ||||
\(598\) | − | 7.04474e38i | − | 0.0385210i | ||||||
\(599\) | − | 2.11358e40i | − | 1.12805i | −0.825756 | − | 0.564027i | \(-0.809251\pi\) | ||
0.825756 | − | 0.564027i | \(-0.190749\pi\) | |||||||
\(600\) | −2.29841e37 | − | 6.51462e36i | −0.00119739 | − | 0.000339387i | ||||
\(601\) | − | 2.64978e40i | − | 1.34750i | −0.738957 | − | 0.673752i | \(-0.764682\pi\) | ||
0.738957 | − | 0.673752i | \(-0.235318\pi\) | |||||||
\(602\) | −9.29046e38 | − | 1.94118e39i | −0.0461199 | − | 0.0963644i | ||||
\(603\) | 1.37197e39 | + | 8.45683e38i | 0.0664880 | + | 0.0409832i | ||||
\(604\) | −8.56525e39 | −0.405233 | ||||||||
\(605\) | −1.56764e40 | −0.724093 | ||||||||
\(606\) | −1.79763e39 | − | 5.09519e38i | −0.0810674 | − | 0.0229777i | ||||
\(607\) | − | 5.48665e39i | − | 0.241586i | −0.992678 | − | 0.120793i | \(-0.961456\pi\) | ||
0.992678 | − | 0.120793i | \(-0.0385437\pi\) | |||||||
\(608\) | −5.93745e39 | −0.255269 | ||||||||
\(609\) | −4.04234e40 | + | 6.94662e39i | −1.69700 | + | 0.291624i | ||||
\(610\) | 2.03915e39 | 0.0835924 | ||||||||
\(611\) | 1.53904e40i | 0.616101i | ||||||||
\(612\) | 3.58218e40 | + | 2.20806e40i | 1.40040 | + | 0.863207i | ||||
\(613\) | −7.35368e38 | −0.0280755 | −0.0140378 | − | 0.999901i | \(-0.504469\pi\) | ||||
−0.0140378 | + | 0.999901i | \(0.504469\pi\) | |||||||
\(614\) | 6.82972e38 | 0.0254660 | ||||||||
\(615\) | 6.25060e39 | − | 2.20526e40i | 0.227632 | − | 0.803103i | ||||
\(616\) | −4.71502e39 | + | 2.25660e39i | −0.167712 | + | 0.0802665i | ||||
\(617\) | 1.29963e40i | 0.451530i | 0.974182 | + | 0.225765i | \(0.0724881\pi\) | ||||
−0.974182 | + | 0.225765i | \(0.927512\pi\) | |||||||
\(618\) | 3.95419e38 | − | 1.39507e39i | 0.0134191 | − | 0.0473438i | ||||
\(619\) | − | 1.74106e40i | − | 0.577164i | −0.957455 | − | 0.288582i | \(-0.906816\pi\) | ||
0.957455 | − | 0.288582i | \(-0.0931838\pi\) | |||||||
\(620\) | 2.03147e40i | 0.657855i | ||||||||
\(621\) | −2.31210e40 | − | 2.52096e40i | −0.731439 | − | 0.797514i | ||||
\(622\) | 1.19002e39i | 0.0367786i | ||||||||
\(623\) | 2.00090e40 | − | 9.57628e39i | 0.604156 | − | 0.289148i | ||||
\(624\) | −1.60939e40 | − | 4.56165e39i | −0.474771 | − | 0.134569i | ||||
\(625\) | −3.49964e40 | −1.00870 | ||||||||
\(626\) | 1.12122e39 | 0.0315764 | ||||||||
\(627\) | 1.56753e40 | − | 5.53036e40i | 0.431355 | − | 1.52186i | ||||
\(628\) | − | 8.38191e39i | − | 0.225387i | ||||||
\(629\) | 2.81895e40 | 0.740718 | ||||||||
\(630\) | 2.94043e38 | − | 2.76328e39i | 0.00755045 | − | 0.0709557i | ||||
\(631\) | 5.93501e40 | 1.48935 | 0.744673 | − | 0.667429i | \(-0.232605\pi\) | ||||
0.744673 | + | 0.667429i | \(0.232605\pi\) | |||||||
\(632\) | 7.24766e39i | 0.177746i | ||||||||
\(633\) | 3.46699e39 | − | 1.22318e40i | 0.0830995 | − | 0.293182i | ||||
\(634\) | −2.77886e39 | −0.0650987 | ||||||||
\(635\) | −1.66480e40 | −0.381190 | ||||||||
\(636\) | −4.69905e40 | − | 1.33190e40i | −1.05168 | − | 0.298087i | ||||
\(637\) | −1.78374e40 | − | 1.43665e40i | −0.390219 | − | 0.314290i | ||||
\(638\) | 7.50444e39i | 0.160479i | ||||||||
\(639\) | 1.59965e40 | − | 2.59514e40i | 0.334397 | − | 0.542499i | ||||
\(640\) | − | 1.37913e40i | − | 0.281835i | ||||||
\(641\) | − | 1.93964e39i | − | 0.0387507i | −0.999812 | − | 0.0193753i | \(-0.993832\pi\) | ||
0.999812 | − | 0.0193753i | \(-0.00616774\pi\) | |||||||
\(642\) | −1.43454e38 | + | 5.06118e38i | −0.00280192 | + | 0.00988540i | ||||
\(643\) | − | 3.24762e40i | − | 0.620164i | −0.950710 | − | 0.310082i | \(-0.899643\pi\) | ||
0.950710 | − | 0.310082i | \(-0.100357\pi\) | |||||||
\(644\) | −2.48953e40 | − | 5.20171e40i | −0.464806 | − | 0.971182i | ||||
\(645\) | −2.25613e40 | + | 7.95982e40i | −0.411859 | + | 1.45307i | ||||
\(646\) | 7.93521e39 | 0.141640 | ||||||||
\(647\) | −1.25775e40 | −0.219525 | −0.109762 | − | 0.993958i | \(-0.535009\pi\) | ||||
−0.109762 | + | 0.993958i | \(0.535009\pi\) | |||||||
\(648\) | 7.41881e39 | − | 3.73136e39i | 0.126618 | − | 0.0636839i | ||||
\(649\) | 4.58952e40i | 0.765983i | ||||||||
\(650\) | −1.91516e37 | −0.000312580 | ||||||||
\(651\) | −4.06475e40 | + | 6.98513e39i | −0.648798 | + | 0.111494i | ||||
\(652\) | 4.01377e40 | 0.626560 | ||||||||
\(653\) | 2.19281e40i | 0.334780i | 0.985891 | + | 0.167390i | \(0.0535339\pi\) | ||||
−0.985891 | + | 0.167390i | \(0.946466\pi\) | |||||||
\(654\) | 7.03532e39 | + | 1.99409e39i | 0.105052 | + | 0.0297761i | ||||
\(655\) | 8.97397e40 | 1.31065 | ||||||||
\(656\) | 5.72985e40 | 0.818535 | ||||||||
\(657\) | −2.62840e39 | + | 4.26411e39i | −0.0367277 | + | 0.0595841i | ||||
\(658\) | −2.75910e39 | − | 5.76496e39i | −0.0377131 | − | 0.0787990i | ||||
\(659\) | − | 9.04042e40i | − | 1.20879i | −0.796686 | − | 0.604394i | \(-0.793415\pi\) | ||
0.796686 | − | 0.604394i | \(-0.206585\pi\) | |||||||
\(660\) | 9.64251e40 | + | 2.73308e40i | 1.26126 | + | 0.357491i | ||||
\(661\) | − | 9.58277e39i | − | 0.122622i | −0.998119 | − | 0.0613112i | \(-0.980472\pi\) | ||
0.998119 | − | 0.0613112i | \(-0.0195282\pi\) | |||||||
\(662\) | − | 8.09670e37i | − | 0.00101360i | ||||||
\(663\) | 6.50769e40 | + | 1.84454e40i | 0.797041 | + | 0.225913i | ||||
\(664\) | 1.25475e40i | 0.150355i | ||||||||
\(665\) | 4.45932e40 | + | 9.31747e40i | 0.522824 | + | 1.09241i | ||||
\(666\) | 1.45584e39 | − | 2.36184e39i | 0.0167008 | − | 0.0270941i | ||||
\(667\) | −1.66001e41 | −1.86331 | ||||||||
\(668\) | −5.80703e40 | −0.637816 | ||||||||
\(669\) | 3.49921e40 | + | 9.91817e39i | 0.376090 | + | 0.106599i | ||||
\(670\) | 5.29898e38i | 0.00557323i | ||||||||
\(671\) | −1.49311e41 | −1.53680 | ||||||||
\(672\) | 2.07139e40 | − | 3.55960e39i | 0.208644 | − | 0.0358548i | ||||
\(673\) | −7.68644e40 | −0.757717 | −0.378858 | − | 0.925455i | \(-0.623683\pi\) | ||||
−0.378858 | + | 0.925455i | \(0.623683\pi\) | |||||||
\(674\) | 6.05003e39i | 0.0583699i | ||||||||
\(675\) | −6.85341e38 | + | 6.28559e38i | −0.00647145 | + | 0.00593528i | ||||
\(676\) | 8.06274e40 | 0.745171 | ||||||||
\(677\) | 9.98234e40 | 0.903018 | 0.451509 | − | 0.892266i | \(-0.350886\pi\) | ||||
0.451509 | + | 0.892266i | \(0.350886\pi\) | |||||||
\(678\) | 1.07196e39 | − | 3.78196e39i | 0.00949177 | − | 0.0334878i | ||||
\(679\) | 1.88842e40 | + | 3.94573e40i | 0.163677 | + | 0.341992i | ||||
\(680\) | 2.77412e40i | 0.235367i | ||||||||
\(681\) | 1.65665e40 | − | 5.84480e40i | 0.137594 | − | 0.485441i | ||||
\(682\) | 7.54604e39i | 0.0613544i | ||||||||
\(683\) | − | 2.16857e41i | − | 1.72613i | −0.505092 | − | 0.863065i | \(-0.668541\pi\) | ||
0.505092 | − | 0.863065i | \(-0.331459\pi\) | |||||||
\(684\) | −8.07828e40 | + | 1.31056e41i | −0.629514 | + | 1.02127i | ||||
\(685\) | − | 6.86216e40i | − | 0.523538i | ||||||
\(686\) | 9.25710e39 | + | 2.18367e39i | 0.0691473 | + | 0.0163112i | ||||
\(687\) | −6.62643e40 | − | 1.87820e40i | −0.484626 | − | 0.137363i | ||||
\(688\) | −2.06817e41 | −1.48099 | ||||||||
\(689\) | −7.85087e40 | −0.550477 | ||||||||
\(690\) | 3.06697e39 | − | 1.08205e40i | 0.0210571 | − | 0.0742911i | ||||
\(691\) | 2.37839e41i | 1.59901i | 0.600657 | + | 0.799507i | \(0.294906\pi\) | ||||
−0.600657 | + | 0.799507i | \(0.705094\pi\) | |||||||
\(692\) | 2.35688e41 | 1.55167 | ||||||||
\(693\) | −2.15305e40 | + | 2.02334e41i | −0.138810 | + | 1.30448i | ||||
\(694\) | −9.91991e39 | −0.0626319 | ||||||||
\(695\) | 3.08227e41i | 1.90586i | ||||||||
\(696\) | 1.09897e40 | − | 3.87724e40i | 0.0665503 | − | 0.234795i | ||||
\(697\) | −2.31691e41 | −1.37415 | ||||||||
\(698\) | −3.37038e39 | −0.0195783 | ||||||||
\(699\) | 2.77563e41 | + | 7.86726e40i | 1.57922 | + | 0.447615i | ||||
\(700\) | −1.41412e39 | + | 6.76795e38i | −0.00788069 | + | 0.00377168i | ||||
\(701\) | − | 1.20046e41i | − | 0.655293i | −0.944800 | − | 0.327647i | \(-0.893744\pi\) | ||
0.944800 | − | 0.327647i | \(-0.106256\pi\) | |||||||
\(702\) | 4.90632e39 | − | 4.49982e39i | 0.0262342 | − | 0.0240606i | ||||
\(703\) | 1.03133e41i | 0.540186i | ||||||||
\(704\) | 2.47963e41i | 1.27228i | ||||||||
\(705\) | −6.70031e40 | + | 2.36392e41i | −0.336785 | + | 1.18820i | ||||
\(706\) | − | 2.08139e40i | − | 0.102491i | ||||||
\(707\) | −2.21762e41 | + | 1.06135e41i | −1.06981 | + | 0.512008i | ||||
\(708\) | 3.35199e40 | − | 1.18261e41i | 0.158424 | − | 0.558932i | ||||
\(709\) | −2.47898e41 | −1.14790 | −0.573948 | − | 0.818892i | \(-0.694589\pi\) | ||||
−0.573948 | + | 0.818892i | \(0.694589\pi\) | |||||||
\(710\) | 1.00233e40 | 0.0454740 | ||||||||
\(711\) | 2.40166e41 | + | 1.48038e41i | 1.06758 | + | 0.658059i | ||||
\(712\) | 2.17952e40i | 0.0949296i | ||||||||
\(713\) | −1.66921e41 | −0.712384 | ||||||||
\(714\) | −2.76834e40 | + | 4.75730e39i | −0.115770 | + | 0.0198946i | ||||
\(715\) | 1.61101e41 | 0.660176 | ||||||||
\(716\) | − | 4.89630e41i | − | 1.96621i | ||||||
\(717\) | −1.87290e41 | − | 5.30855e40i | −0.737033 | − | 0.208905i | ||||
\(718\) | −8.20719e39 | −0.0316512 | ||||||||
\(719\) | 1.70882e41 | 0.645843 | 0.322921 | − | 0.946426i | \(-0.395335\pi\) | ||||
0.322921 | + | 0.946426i | \(0.395335\pi\) | |||||||
\(720\) | −2.27338e41 | − | 1.40132e41i | −0.842076 | − | 0.519057i | ||||
\(721\) | −8.23675e40 | − | 1.72102e41i | −0.299016 | − | 0.624775i | ||||
\(722\) | 9.06382e39i | 0.0322494i | ||||||||
\(723\) | 5.46417e41 | + | 1.54877e41i | 1.90554 | + | 0.540108i | ||||
\(724\) | − | 3.60471e41i | − | 1.23214i | ||||||
\(725\) | 4.51285e39i | 0.0151199i | ||||||||
\(726\) | 1.50048e40 | + | 4.25297e39i | 0.0492777 | + | 0.0139673i | ||||
\(727\) | 1.00781e41i | 0.324437i | 0.986755 | + | 0.162219i | \(0.0518650\pi\) | ||||
−0.986755 | + | 0.162219i | \(0.948135\pi\) | |||||||
\(728\) | 2.02986e40 | − | 9.71485e39i | 0.0640560 | − | 0.0306571i | ||||
\(729\) | 2.78880e40 | − | 3.22053e41i | 0.0862716 | − | 0.996272i | ||||
\(730\) | −1.64693e39 | −0.00499453 | ||||||||
\(731\) | 8.36280e41 | 2.48628 | ||||||||
\(732\) | 3.84740e41 | + | 1.09051e41i | 1.12139 | + | 0.317847i | ||||
\(733\) | − | 2.15111e39i | − | 0.00614689i | −0.999995 | − | 0.00307345i | \(-0.999022\pi\) | ||
0.999995 | − | 0.00307345i | \(-0.000978310\pi\) | |||||||
\(734\) | −3.06283e40 | −0.0858084 | ||||||||
\(735\) | −2.11431e41 | − | 2.98322e41i | −0.580769 | − | 0.819444i | ||||
\(736\) | 8.50627e40 | 0.229092 | ||||||||
\(737\) | − | 3.88003e40i | − | 0.102461i | ||||||
\(738\) | −1.19656e40 | + | 1.94121e40i | −0.0309826 | + | 0.0502638i | ||||
\(739\) | −3.98177e41 | −1.01095 | −0.505477 | − | 0.862840i | \(-0.668684\pi\) | ||||
−0.505477 | + | 0.862840i | \(0.668684\pi\) | |||||||
\(740\) | −1.79818e41 | −0.447685 | ||||||||
\(741\) | −6.74833e40 | + | 2.38087e41i | −0.164753 | + | 0.581261i | ||||
\(742\) | 2.94079e40 | − | 1.40746e40i | 0.0704057 | − | 0.0336960i | ||||
\(743\) | 2.27165e40i | 0.0533338i | 0.999644 | + | 0.0266669i | \(0.00848935\pi\) | ||||
−0.999644 | + | 0.0266669i | \(0.991511\pi\) | |||||||
\(744\) | 1.10506e40 | − | 3.89874e40i | 0.0254435 | − | 0.0897669i | ||||
\(745\) | 1.16978e41i | 0.264143i | ||||||||
\(746\) | 3.82513e40i | 0.0847098i | ||||||||
\(747\) | 4.15786e41 | + | 2.56291e41i | 0.903069 | + | 0.556652i | ||||
\(748\) | − | 1.01307e42i | − | 2.15807i | ||||||
\(749\) | 2.98821e40 | + | 6.24368e40i | 0.0624346 | + | 0.130453i | ||||
\(750\) | 3.32055e40 | + | 9.41178e39i | 0.0680491 | + | 0.0192878i | ||||
\(751\) | −4.42565e41 | −0.889606 | −0.444803 | − | 0.895628i | \(-0.646726\pi\) | ||||
−0.444803 | + | 0.895628i | \(0.646726\pi\) | |||||||
\(752\) | −6.14209e41 | −1.21104 | ||||||||
\(753\) | 9.23286e40 | − | 3.25743e41i | 0.178570 | − | 0.630010i | ||||
\(754\) | − | 3.23072e40i | − | 0.0612936i | ||||||
\(755\) | −2.19802e41 | −0.409073 | ||||||||
\(756\) | 2.03255e41 | − | 5.05642e41i | 0.371087 | − | 0.923160i | ||||
\(757\) | −6.37836e41 | −1.14240 | −0.571201 | − | 0.820810i | \(-0.693522\pi\) | ||||
−0.571201 | + | 0.820810i | \(0.693522\pi\) | |||||||
\(758\) | 1.37242e40i | 0.0241148i | ||||||||
\(759\) | −2.24571e41 | + | 7.92305e41i | −0.387122 | + | 1.36580i | ||||
\(760\) | −1.01492e41 | −0.171647 | ||||||||
\(761\) | −6.94568e41 | −1.15249 | −0.576245 | − | 0.817277i | \(-0.695483\pi\) | ||||
−0.576245 | + | 0.817277i | \(0.695483\pi\) | |||||||
\(762\) | 1.59347e40 | + | 4.51654e39i | 0.0259417 | + | 0.00735291i | ||||
\(763\) | 8.67905e41 | − | 4.15378e41i | 1.38633 | − | 0.663494i | ||||
\(764\) | 8.73057e41i | 1.36832i | ||||||||
\(765\) | 9.19261e41 | + | 5.66633e41i | 1.41367 | + | 0.871387i | ||||
\(766\) | 2.62444e40i | 0.0396022i | ||||||||
\(767\) | − | 1.97583e41i | − | 0.292561i | ||||||
\(768\) | 1.78279e41 | − | 6.28983e41i | 0.259038 | − | 0.913905i | ||||
\(769\) | − | 9.66671e41i | − | 1.37831i | −0.724614 | − | 0.689155i | \(-0.757982\pi\) | ||
0.724614 | − | 0.689155i | \(-0.242018\pi\) | |||||||
\(770\) | −6.03454e40 | + | 2.88812e40i | −0.0844362 | + | 0.0404110i | ||||
\(771\) | −1.92230e41 | + | 6.78202e41i | −0.263956 | + | 0.931259i | ||||
\(772\) | 1.24967e41 | 0.168400 | ||||||||
\(773\) | 5.03598e41 | 0.666011 | 0.333005 | − | 0.942925i | \(-0.391937\pi\) | ||||
0.333005 | + | 0.942925i | \(0.391937\pi\) | |||||||
\(774\) | 4.31895e40 | − | 7.00672e40i | 0.0560576 | − | 0.0909434i | ||||
\(775\) | 4.53787e39i | 0.00578066i | ||||||||
\(776\) | −4.29797e40 | −0.0537364 | ||||||||
\(777\) | −6.18297e40 | − | 3.59796e41i | −0.0758740 | − | 0.441522i | ||||
\(778\) | −7.95855e39 | −0.00958583 | ||||||||
\(779\) | − | 8.47651e41i | − | 1.00213i | ||||||
\(780\) | −4.15118e41 | − | 1.17661e41i | −0.481726 | − | 0.136541i | ||||
\(781\) | −7.33927e41 | −0.836012 | ||||||||
\(782\) | −1.13684e41 | −0.127116 | ||||||||
\(783\) | −1.06033e42 | − | 1.15612e42i | −1.16385 | − | 1.26898i | ||||
\(784\) | 5.73348e41 | − | 7.11864e41i | 0.617783 | − | 0.767033i | ||||
\(785\) | − | 2.15097e41i | − | 0.227522i | ||||||
\(786\) | −8.58951e40 | − | 2.43461e40i | −0.0891952 | − | 0.0252815i | ||||
\(787\) | 1.30227e42i | 1.32760i | 0.747910 | + | 0.663800i | \(0.231057\pi\) | ||||
−0.747910 | + | 0.663800i | \(0.768943\pi\) | |||||||
\(788\) | 1.41342e41i | 0.141462i | ||||||||
\(789\) | 1.22606e42 | + | 3.47515e41i | 1.20475 | + | 0.341474i | ||||
\(790\) | 9.27596e40i | 0.0894882i | ||||||||
\(791\) | −2.23293e41 | − | 4.66557e41i | −0.211503 | − | 0.441922i | ||||
\(792\) | −1.70189e41 | − | 1.04905e41i | −0.158277 | − | 0.0975620i | ||||
\(793\) | 6.42798e41 | 0.586967 | ||||||||
\(794\) | −1.46988e41 | −0.131791 | ||||||||
\(795\) | −1.20587e42 | − | 3.41793e41i | −1.06164 | − | 0.300912i | ||||
\(796\) | 1.13659e42i | 0.982574i | ||||||||
\(797\) | 8.91144e41 | 0.756489 | 0.378244 | − | 0.925706i | \(-0.376528\pi\) | ||||
0.378244 | + | 0.925706i | \(0.376528\pi\) | |||||||
\(798\) | −1.74048e40 | − | 1.01281e41i | −0.0145086 | − | 0.0844279i | ||||
\(799\) | 2.48360e42 | 2.03308 | ||||||||
\(800\) | − | 2.31249e39i | − | 0.00185898i | ||||||
\(801\) | 7.22229e41 | + | 4.45182e41i | 0.570169 | + | 0.351452i | ||||
\(802\) | 3.98160e40 | 0.0308695 | ||||||||
\(803\) | 1.20592e41 | 0.0918215 | ||||||||
\(804\) | −2.83381e40 | + | 9.99793e40i | −0.0211913 | + | 0.0747648i | ||||
\(805\) | −6.38864e41 | − | 1.33486e42i | −0.469211 | − | 0.980386i | ||||
\(806\) | − | 3.24864e40i | − | 0.0234338i | ||||||
\(807\) | 1.44214e41 | − | 5.08800e41i | 0.102174 | − | 0.360480i | ||||
\(808\) | − | 2.41559e41i | − | 0.168096i | ||||||
\(809\) | 3.84262e41i | 0.262648i | 0.991339 | + | 0.131324i | \(0.0419228\pi\) | ||||
−0.991339 | + | 0.131324i | \(0.958077\pi\) | |||||||
\(810\) | 9.49501e40 | − | 4.77561e40i | 0.0637474 | − | 0.0320624i | ||||
\(811\) | 2.60021e42i | 1.71477i | 0.514677 | + | 0.857384i | \(0.327912\pi\) | ||||
−0.514677 | + | 0.857384i | \(0.672088\pi\) | |||||||
\(812\) | −1.14170e42 | − | 2.38551e42i | −0.739587 | − | 1.54532i | ||||
\(813\) | −1.52728e42 | − | 4.32892e41i | −0.971863 | − | 0.275465i | ||||
\(814\) | −6.67947e40 | −0.0417531 | ||||||||
\(815\) | 1.03002e42 | 0.632497 | ||||||||
\(816\) | −7.36130e41 | + | 2.59713e42i | −0.444066 | + | 1.56670i | ||||
\(817\) | 3.05957e42i | 1.81318i | ||||||||
\(818\) | 1.03343e41 | 0.0601667 | ||||||||
\(819\) | 9.26906e40 | − | 8.71066e41i | 0.0530175 | − | 0.498235i | ||||
\(820\) | 1.47793e42 | 0.830526 | ||||||||
\(821\) | 1.56827e42i | 0.865852i | 0.901429 | + | 0.432926i | \(0.142519\pi\) | ||||
−0.901429 | + | 0.432926i | \(0.857481\pi\) | |||||||
\(822\) | −1.86169e40 | + | 6.56818e40i | −0.0100987 | + | 0.0356290i | ||||
\(823\) | −1.49843e42 | −0.798616 | −0.399308 | − | 0.916817i | \(-0.630750\pi\) | ||||
−0.399308 | + | 0.916817i | \(0.630750\pi\) | |||||||
\(824\) | 1.87465e41 | 0.0981693 | ||||||||
\(825\) | 2.15393e40 | + | 6.10511e39i | 0.0110828 | + | 0.00314131i | ||||
\(826\) | 3.54215e40 | + | 7.40109e40i | 0.0179084 | + | 0.0374184i | ||||
\(827\) | 2.87755e42i | 1.42953i | 0.699365 | + | 0.714765i | \(0.253466\pi\) | ||||
−0.699365 | + | 0.714765i | \(0.746534\pi\) | |||||||
\(828\) | 1.15733e42 | − | 1.87756e42i | 0.564961 | − | 0.916548i | ||||
\(829\) | 2.26722e42i | 1.08756i | 0.839227 | + | 0.543781i | \(0.183008\pi\) | ||||
−0.839227 | + | 0.543781i | \(0.816992\pi\) | |||||||
\(830\) | 1.60590e41i | 0.0756981i | ||||||||
\(831\) | −1.07473e42 | + | 3.79172e42i | −0.497832 | + | 1.75639i | ||||
\(832\) | − | 1.06750e42i | − | 0.485938i | ||||||
\(833\) | −2.31838e42 | + | 2.87848e42i | −1.03713 | + | 1.28769i | ||||
\(834\) | 8.36211e40 | − | 2.95022e41i | 0.0367628 | − | 0.129702i | ||||
\(835\) | −1.49020e42 | −0.643860 | ||||||||
\(836\) | 3.70636e42 | 1.57382 | ||||||||
\(837\) | −1.06621e42 | − | 1.16253e42i | −0.444962 | − | 0.485159i | ||||
\(838\) | 1.93347e41i | 0.0793048i | ||||||||
\(839\) | 1.16752e42 | 0.470669 | 0.235335 | − | 0.971914i | \(-0.424381\pi\) | ||||
0.235335 | + | 0.971914i | \(0.424381\pi\) | |||||||
\(840\) | 3.54075e41 | − | 6.08465e40i | 0.140296 | − | 0.0241094i | ||||
\(841\) | −5.04514e42 | −1.96486 | ||||||||
\(842\) | 2.85866e41i | 0.109430i | ||||||||
\(843\) | −4.39200e42 | − | 1.24487e42i | −1.65258 | − | 0.468407i | ||||
\(844\) | 8.19756e41 | 0.303193 | ||||||||
\(845\) | 2.06906e42 | 0.752232 | ||||||||
\(846\) | 1.28265e41 | − | 2.08087e41i | 0.0458393 | − | 0.0743661i | ||||
\(847\) | 1.85106e42 | − | 8.85912e41i | 0.650295 | − | 0.311230i | ||||
\(848\) | − | 3.13317e42i | − | 1.08204i | ||||||
\(849\) | −1.32652e42 | − | 3.75988e41i | −0.450351 | − | 0.127648i | ||||
\(850\) | 3.09056e39i | 0.00103149i | ||||||||
\(851\) | − | 1.47752e42i | − | 0.484793i | ||||||
\(852\) | 1.89115e42 | + | 5.36029e41i | 0.610032 | + | 0.172908i | ||||
\(853\) | − | 5.10638e42i | − | 1.61939i | −0.586848 | − | 0.809697i | \(-0.699631\pi\) | ||
0.586848 | − | 0.809697i | \(-0.300369\pi\) | |||||||
\(854\) | −2.40781e41 | + | 1.15237e41i | −0.0750728 | + | 0.0359297i | ||||
\(855\) | −2.07305e42 | + | 3.36316e42i | −0.635480 | + | 1.03095i | ||||
\(856\) | −6.80105e40 | −0.0204978 | ||||||||
\(857\) | 5.00930e41 | 0.148442 | 0.0742208 | − | 0.997242i | \(-0.476353\pi\) | ||||
0.0742208 | + | 0.997242i | \(0.476353\pi\) | |||||||
\(858\) | −1.54199e41 | − | 4.37062e40i | −0.0449279 | − | 0.0127344i | ||||
\(859\) | 5.99895e42i | 1.71860i | 0.511474 | + | 0.859299i | \(0.329100\pi\) | ||||
−0.511474 | + | 0.859299i | \(0.670900\pi\) | |||||||
\(860\) | −5.33454e42 | −1.50269 | ||||||||
\(861\) | 5.08182e41 | + | 2.95719e42i | 0.140758 | + | 0.819092i | ||||
\(862\) | −6.57430e40 | −0.0179058 | ||||||||
\(863\) | 3.24682e41i | 0.0869563i | 0.999054 | + | 0.0434782i | \(0.0138439\pi\) | ||||
−0.999054 | + | 0.0434782i | \(0.986156\pi\) | |||||||
\(864\) | 5.43337e41 | + | 5.92420e41i | 0.143094 | + | 0.156020i | ||||
\(865\) | 6.04824e42 | 1.56637 | ||||||||
\(866\) | 4.44419e40 | 0.0113184 | ||||||||
\(867\) | 1.88778e42 | − | 6.66023e42i | 0.472796 | − | 1.66806i | ||||
\(868\) | −1.14803e42 | − | 2.39873e42i | −0.282759 | − | 0.590808i | ||||
\(869\) | − | 6.79207e42i | − | 1.64519i | ||||||
\(870\) | 1.40652e41 | − | 4.96231e41i | 0.0335055 | − | 0.118210i | ||||
\(871\) | 1.67039e41i | 0.0391340i | ||||||||
\(872\) | 9.45383e41i | 0.217831i | ||||||||
\(873\) | −8.77889e41 | + | 1.42422e42i | −0.198945 | + | 0.322753i | ||||
\(874\) | − | 4.15916e41i | − | 0.0927022i | ||||||
\(875\) | 4.09637e42 | − | 1.96051e42i | 0.898012 | − | 0.429787i | ||||
\(876\) | −3.10738e41 | − | 8.80755e40i | −0.0670015 | − | 0.0189909i | ||||
\(877\) | 4.47941e42 | 0.950007 | 0.475003 | − | 0.879984i | \(-0.342447\pi\) | ||||
0.475003 | + | 0.879984i | \(0.342447\pi\) | |||||||
\(878\) | −3.65886e41 | −0.0763264 | ||||||||
\(879\) | 1.09424e42 | − | 3.86057e42i | 0.224530 | − | 0.792160i | ||||
\(880\) | 6.42931e42i | 1.29767i | ||||||||
\(881\) | −5.93686e42 | −1.17871 | −0.589354 | − | 0.807875i | \(-0.700618\pi\) | ||||
−0.589354 | + | 0.807875i | \(0.700618\pi\) | |||||||
\(882\) | 1.21439e41 | + | 3.42902e41i | 0.0237173 | + | 0.0669694i | ||||
\(883\) | 8.97460e42 | 1.72419 | 0.862094 | − | 0.506748i | \(-0.169153\pi\) | ||||
0.862094 | + | 0.506748i | \(0.169153\pi\) | |||||||
\(884\) | 4.36135e42i | 0.824257i | ||||||||
\(885\) | 8.60190e41 | − | 3.03482e42i | 0.159925 | − | 0.564229i | ||||
\(886\) | 3.04346e41 | 0.0556645 | ||||||||
\(887\) | 2.15017e42 | 0.386884 | 0.193442 | − | 0.981112i | \(-0.438035\pi\) | ||||
0.193442 | + | 0.981112i | \(0.438035\pi\) | |||||||
\(888\) | 3.45101e41 | + | 9.78156e40i | 0.0610884 | + | 0.0173149i | ||||
\(889\) | 1.96577e42 | − | 9.40815e41i | 0.342340 | − | 0.163843i | ||||
\(890\) | 2.78948e41i | 0.0477934i | ||||||||
\(891\) | −6.95247e42 | + | 3.49681e42i | −1.17196 | + | 0.589448i | ||||
\(892\) | 2.34511e42i | 0.388932i | ||||||||
\(893\) | 9.08636e42i | 1.48267i | ||||||||
\(894\) | 3.17359e40 | − | 1.11967e41i | 0.00509514 | − | 0.0179761i | ||||
\(895\) | − | 1.25649e43i | − | 1.98484i | ||||||
\(896\) | 7.79376e41 | + | 1.62846e42i | 0.121138 | + | 0.253110i | ||||
\(897\) | 9.66797e41 | − | 3.41094e42i | 0.147858 | − | 0.521655i | ||||
\(898\) | −3.43942e41 | −0.0517582 | ||||||||
\(899\) | −7.65503e42 | −1.13353 | ||||||||
\(900\) | −5.10428e40 | − | 3.14628e40i | −0.00743735 | − | 0.00458439i | ||||
\(901\) | 1.26692e43i | 1.81652i | ||||||||
\(902\) | 5.48989e41 | 0.0774585 | ||||||||
\(903\) | −1.83426e42 | − | 1.06739e43i | −0.254677 | − | 1.48200i | ||||
\(904\) | 5.08207e41 | 0.0694382 | ||||||||
\(905\) | − | 9.25043e42i | − | 1.24382i | ||||||
\(906\) | 2.10385e41 | + | 5.96316e40i | 0.0278392 | + | 0.00789074i | ||||
\(907\) | 6.97609e42 | 0.908461 | 0.454231 | − | 0.890884i | \(-0.349914\pi\) | ||||
0.454231 | + | 0.890884i | \(0.349914\pi\) | |||||||
\(908\) | 3.91709e42 | 0.502018 | ||||||||
\(909\) | −8.00454e42 | − | 4.93401e42i | −1.00963 | − | 0.622334i | ||||
\(910\) | 2.59792e41 | − | 1.24336e41i | 0.0322497 | − | 0.0154347i | ||||
\(911\) | − | 9.01807e42i | − | 1.10179i | −0.834576 | − | 0.550893i | \(-0.814287\pi\) | ||
0.834576 | − | 0.550893i | \(-0.185713\pi\) | |||||||
\(912\) | −9.50171e42 | − | 2.69316e42i | −1.14255 | − | 0.323845i | ||||
\(913\) | − | 1.17587e43i | − | 1.39167i | ||||||
\(914\) | 1.78633e41i | 0.0208085i | ||||||||
\(915\) | 9.87322e42 | + | 2.79847e42i | 1.13202 | + | 0.320859i | ||||
\(916\) | − | 4.44093e42i | − | 0.501175i | ||||||
\(917\) | −1.05964e43 | + | 5.07140e42i | −1.17707 | + | 0.563343i | ||||
\(918\) | −7.26152e41 | − | 7.91750e41i | −0.0793979 | − | 0.0865704i | ||||
\(919\) | 1.24267e43 | 1.33746 | 0.668729 | − | 0.743506i | \(-0.266838\pi\) | ||||
0.668729 | + | 0.743506i | \(0.266838\pi\) | |||||||
\(920\) | 1.45403e42 | 0.154046 | ||||||||
\(921\) | 3.30683e42 | + | 9.37289e41i | 0.344864 | + | 0.0977482i | ||||
\(922\) | 4.36066e39i | 0.000447665i | ||||||||
\(923\) | 3.15962e42 | 0.319308 | ||||||||
\(924\) | −1.29303e43 | + | 2.22203e42i | −1.28637 | + | 0.221058i | ||||
\(925\) | −4.01675e40 | −0.00393387 | ||||||||
\(926\) | − | 4.79100e41i | − | 0.0461920i | ||||||
\(927\) | 3.82910e42 | − | 6.21203e42i | 0.363447 | − | 0.589627i | ||||
\(928\) | 3.90098e42 | 0.364526 | ||||||||
\(929\) | −2.01687e42 | −0.185546 | −0.0927728 | − | 0.995687i | \(-0.529573\pi\) | ||||
−0.0927728 | + | 0.995687i | \(0.529573\pi\) | |||||||
\(930\) | 1.41432e41 | − | 4.98982e41i | 0.0128098 | − | 0.0451941i | ||||
\(931\) | −1.05310e43 | − | 8.48189e42i | −0.939076 | − | 0.756349i | ||||
\(932\) | 1.86018e43i | 1.63315i | ||||||||
\(933\) | −1.63315e42 | + | 5.76189e42i | −0.141170 | + | 0.498059i | ||||
\(934\) | − | 1.93189e41i | − | 0.0164419i | ||||||
\(935\) | − | 2.59974e43i | − | 2.17852i | ||||||
\(936\) | 7.32680e41 | + | 4.51624e41i | 0.0604525 | + | 0.0372630i | ||||
\(937\) | − | 8.46691e42i | − | 0.687861i | −0.938995 | − | 0.343931i | \(-0.888241\pi\) | ||
0.938995 | − | 0.343931i | \(-0.111759\pi\) | |||||||
\(938\) | −2.99458e40 | − | 6.25697e40i | −0.00239549 | − | 0.00500522i | ||||
\(939\) | 5.42874e42 | + | 1.53872e42i | 0.427610 | + | 0.121202i | ||||
\(940\) | −1.58426e43 | −1.22878 | ||||||||
\(941\) | 8.42086e42 | 0.643142 | 0.321571 | − | 0.946886i | \(-0.395789\pi\) | ||||
0.321571 | + | 0.946886i | \(0.395789\pi\) | |||||||
\(942\) | −5.83552e40 | + | 2.05882e41i | −0.00438875 | + | 0.0154839i | ||||
\(943\) | 1.21439e43i | 0.899367i | ||||||||
\(944\) | 7.88525e42 | 0.575071 | ||||||||
\(945\) | 5.21595e42 | − | 1.29758e43i | 0.374604 | − | 0.931908i | ||||
\(946\) | −1.98156e42 | −0.140147 | ||||||||
\(947\) | 2.00844e43i | 1.39889i | 0.714686 | + | 0.699446i | \(0.246570\pi\) | ||||
−0.714686 | + | 0.699446i | \(0.753430\pi\) | |||||||
\(948\) | −4.96064e42 | + | 1.75016e43i | −0.340265 | + | 1.20048i | ||||
\(949\) | −5.19160e41 | −0.0350704 | ||||||||
\(950\) | −1.13070e40 | −0.000752235 | ||||||||
\(951\) | −1.34547e43 | − | 3.81362e42i | −0.881572 | − | 0.249873i | ||||
\(952\) | −1.56772e42 | − | 3.27565e42i | −0.101166 | − | 0.211379i | ||||
\(953\) | 1.10066e43i | 0.699532i | 0.936837 | + | 0.349766i | \(0.113739\pi\) | ||||
−0.936837 | + | 0.349766i | \(0.886261\pi\) | |||||||
\(954\) | 1.06148e42 | + | 6.54300e41i | 0.0664450 | + | 0.0409567i | ||||
\(955\) | 2.24044e43i | 1.38129i | ||||||||
\(956\) | − | 1.25519e43i | − | 0.762200i | ||||||
\(957\) | −1.02988e43 | + | 3.63352e43i | −0.615979 | + | 2.17322i | ||||
\(958\) | 1.89735e42i | 0.111776i | ||||||||
\(959\) | 3.87797e42 | + | 8.10277e42i | 0.225027 | + | 0.470179i | ||||
\(960\) | 4.64744e42 | − | 1.63966e43i | 0.265633 | − | 0.937173i | ||||
\(961\) | 1.00644e43 | 0.566630 | ||||||||
\(962\) | 2.87557e41 | 0.0159472 | ||||||||
\(963\) | −1.38916e42 | + | 2.25367e42i | −0.0758877 | + | 0.123114i | ||||
\(964\) | 3.66200e43i | 1.97061i | ||||||||
\(965\) | 3.20690e42 | 0.169996 | ||||||||
\(966\) | 2.49349e41 | + | 1.45100e42i | 0.0130208 | + | 0.0757702i | ||||
\(967\) | −2.47113e43 | −1.27119 | −0.635596 | − | 0.772022i | \(-0.719246\pi\) | ||||
−0.635596 | + | 0.772022i | \(0.719246\pi\) | |||||||
\(968\) | 2.01630e42i | 0.102179i | ||||||||
\(969\) | 3.84209e43 | + | 1.08900e43i | 1.91811 | + | 0.543669i | ||||
\(970\) | −5.50078e41 | −0.0270542 | ||||||||
\(971\) | 1.78850e43 | 0.866585 | 0.433293 | − | 0.901253i | \(-0.357352\pi\) | ||||
0.433293 | + | 0.901253i | \(0.357352\pi\) | |||||||
\(972\) | 2.04688e43 | − | 3.93266e42i | 0.977082 | − | 0.187727i | ||||
\(973\) | −1.74186e43 | − | 3.63951e43i | −0.819177 | − | 1.71162i | ||||
\(974\) | − | 1.66588e42i | − | 0.0771861i | ||||||
\(975\) | −9.27287e40 | − | 2.62830e40i | −0.00423299 | − | 0.00119980i | ||||
\(976\) | 2.56532e43i | 1.15377i | ||||||||
\(977\) | 9.02248e42i | 0.399811i | 0.979815 | + | 0.199905i | \(0.0640635\pi\) | ||||
−0.979815 | + | 0.199905i | \(0.935936\pi\) | |||||||
\(978\) | −9.85889e41 | − | 2.79440e41i | −0.0430442 | − | 0.0122005i | ||||
\(979\) | − | 2.04252e43i | − | 0.878653i | ||||||
\(980\) | 1.47887e43 | − | 1.83615e43i | 0.626833 | − | 0.778270i | ||||
\(981\) | 3.13272e43 | + | 1.93101e43i | 1.30834 | + | 0.806462i | ||||
\(982\) | 2.26767e42 | 0.0933176 | ||||||||
\(983\) | −4.43159e43 | −1.79694 | −0.898470 | − | 0.439035i | \(-0.855321\pi\) | ||||
−0.898470 | + | 0.439035i | \(0.855321\pi\) | |||||||
\(984\) | −2.83641e42 | − | 8.03951e41i | −0.113329 | − | 0.0321219i | ||||
\(985\) | 3.62712e42i | 0.142803i | ||||||||
\(986\) | −5.21354e42 | −0.202263 | ||||||||
\(987\) | −5.44743e42 | − | 3.16994e43i | −0.208254 | − | 1.21186i | ||||
\(988\) | −1.59562e43 | −0.601109 | ||||||||
\(989\) | − | 4.38328e43i | − | 1.62724i | ||||||
\(990\) | −2.17818e42 | − | 1.34263e42i | −0.0796862 | − | 0.0491186i | ||||
\(991\) | 1.15255e42 | 0.0415521 | 0.0207761 | − | 0.999784i | \(-0.493386\pi\) | ||||
0.0207761 | + | 0.999784i | \(0.493386\pi\) | |||||||
\(992\) | 3.92261e42 | 0.139366 | ||||||||
\(993\) | 1.11116e41 | − | 3.92028e41i | 0.00389058 | − | 0.0137263i | ||||
\(994\) | −1.18354e42 | + | 5.66438e41i | −0.0408393 | + | 0.0195456i | ||||
\(995\) | 2.91673e43i | 0.991885i | ||||||||
\(996\) | −8.58809e42 | + | 3.02995e43i | −0.287830 | + | 1.01549i | ||||
\(997\) | 2.62939e43i | 0.868510i | 0.900790 | + | 0.434255i | \(0.142988\pi\) | ||||
−0.900790 | + | 0.434255i | \(0.857012\pi\) | |||||||
\(998\) | 5.00552e41i | 0.0162951i | ||||||||
\(999\) | 1.02902e43 | − | 9.43768e42i | 0.330161 | − | 0.302807i |
(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 | 21.30.c.a.20.19 | ✓ | 76 | |
3.2 | odd | 2 | inner | 21.30.c.a.20.58 | yes | 76 | |
7.6 | odd | 2 | inner | 21.30.c.a.20.57 | yes | 76 | |
21.20 | even | 2 | inner | 21.30.c.a.20.20 | yes | 76 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.30.c.a.20.19 | ✓ | 76 | 1.1 | even | 1 | trivial | |
21.30.c.a.20.20 | yes | 76 | 21.20 | even | 2 | inner | |
21.30.c.a.20.57 | yes | 76 | 7.6 | odd | 2 | inner | |
21.30.c.a.20.58 | yes | 76 | 3.2 | odd | 2 | inner |