Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4,25,Mod(3,4)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 25, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4.3");
S:= CuspForms(chi, 25);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4 = 2^{2} \) |
Weight: | \( k \) | \(=\) | \( 25 \) |
Character orbit: | \([\chi]\) | \(=\) | 4.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: | \(14.5986860903\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 3 x^{9} + 1157886 x^{8} - 1182314620 x^{7} + 1715110302918 x^{6} + \cdots + 10\!\cdots\!86 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{90}\cdot 3^{8}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 3.6 | ||
Root | \(112.122 + 988.545i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4.3 |
Dual form | 4.25.b.b.3.5 |
$q$-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 \(\left(\mathbb{Z}/4\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1068.49 | + | 3954.18i | −0.260861 | + | 0.965376i | ||||
\(3\) | 193889.i | 0.364836i | 0.983221 | + | 0.182418i | \(0.0583924\pi\) | ||||
−0.983221 | + | 0.182418i | \(0.941608\pi\) | |||||||
\(4\) | −1.44939e7 | − | 8.44998e6i | −0.863903 | − | 0.503658i | ||||
\(5\) | 3.74285e8 | 1.53307 | 0.766536 | − | 0.642202i | \(-0.221979\pi\) | ||||
0.766536 | + | 0.642202i | \(0.221979\pi\) | |||||||
\(6\) | −7.66672e8 | − | 2.07168e8i | −0.352204 | − | 0.0951714i | ||||
\(7\) | 2.47654e10i | 1.78924i | 0.446830 | + | 0.894619i | \(0.352553\pi\) | ||||
−0.446830 | + | 0.894619i | \(0.647447\pi\) | |||||||
\(8\) | 4.88993e10 | − | 4.82828e10i | 0.711578 | − | 0.702607i | ||||
\(9\) | 2.44837e11 | 0.866895 | ||||||||
\(10\) | −3.99918e11 | + | 1.47999e12i | −0.399918 | + | 1.47999i | ||||
\(11\) | − | 7.20071e11i | − | 0.229437i | −0.993398 | − | 0.114718i | \(-0.963403\pi\) | ||
0.993398 | − | 0.114718i | \(-0.0365966\pi\) | |||||||
\(12\) | 1.63836e12 | − | 2.81020e12i | 0.183753 | − | 0.315183i | ||||
\(13\) | −1.13495e13 | −0.487144 | −0.243572 | − | 0.969883i | \(-0.578319\pi\) | ||||
−0.243572 | + | 0.969883i | \(0.578319\pi\) | |||||||
\(14\) | −9.79267e13 | − | 2.64614e13i | −1.72729 | − | 0.466742i | ||||
\(15\) | 7.25697e13i | 0.559319i | ||||||||
\(16\) | 1.38671e14 | + | 2.44946e14i | 0.492657 | + | 0.870223i | ||||
\(17\) | −7.24578e14 | −1.24365 | −0.621825 | − | 0.783156i | \(-0.713608\pi\) | ||||
−0.621825 | + | 0.783156i | \(0.713608\pi\) | |||||||
\(18\) | −2.61605e14 | + | 9.68129e14i | −0.226139 | + | 0.836880i | ||||
\(19\) | 1.99560e15i | 0.901634i | 0.892617 | + | 0.450817i | \(0.148867\pi\) | ||||
−0.892617 | + | 0.450817i | \(0.851133\pi\) | |||||||
\(20\) | −5.42484e15 | − | 3.16270e15i | −1.32442 | − | 0.772143i | ||||
\(21\) | −4.80173e15 | −0.652778 | ||||||||
\(22\) | 2.84729e15 | + | 7.69386e14i | 0.221493 | + | 0.0598511i | ||||
\(23\) | − | 4.43802e15i | − | 0.202514i | −0.994860 | − | 0.101257i | \(-0.967714\pi\) | ||
0.994860 | − | 0.101257i | \(-0.0322865\pi\) | |||||||
\(24\) | 9.36149e15 | + | 9.48102e15i | 0.256336 | + | 0.259609i | ||||
\(25\) | 8.04846e16 | 1.35031 | ||||||||
\(26\) | 1.21268e16 | − | 4.48781e16i | 0.127077 | − | 0.470277i | ||||
\(27\) | 1.02231e17i | 0.681110i | ||||||||
\(28\) | 2.09267e17 | − | 3.58946e17i | 0.901164 | − | 1.54573i | ||||
\(29\) | 2.02893e16 | 0.0573445 | 0.0286722 | − | 0.999589i | \(-0.490872\pi\) | ||||
0.0286722 | + | 0.999589i | \(0.490872\pi\) | |||||||
\(30\) | −2.86954e17 | − | 7.75397e16i | −0.539954 | − | 0.145905i | ||||
\(31\) | 4.90083e17i | 0.622199i | 0.950377 | + | 0.311100i | \(0.100697\pi\) | ||||
−0.950377 | + | 0.311100i | \(0.899303\pi\) | |||||||
\(32\) | −1.11673e18 | + | 2.86608e17i | −0.968608 | + | 0.248593i | ||||
\(33\) | 1.39614e17 | 0.0837068 | ||||||||
\(34\) | 7.74202e17 | − | 2.86511e18i | 0.324420 | − | 1.20059i | ||||
\(35\) | 9.26930e18i | 2.74303i | ||||||||
\(36\) | −3.54864e18 | − | 2.06886e18i | −0.748913 | − | 0.436618i | ||||
\(37\) | 1.00235e17 | 0.0152264 | 0.00761319 | − | 0.999971i | \(-0.497577\pi\) | ||||
0.00761319 | + | 0.999971i | \(0.497577\pi\) | |||||||
\(38\) | −7.89096e18 | − | 2.13227e18i | −0.870416 | − | 0.235201i | ||||
\(39\) | − | 2.20054e18i | − | 0.177728i | ||||||
\(40\) | 1.83023e19 | − | 1.80715e19i | 1.09090 | − | 1.07715i | ||||
\(41\) | 9.03467e18 | 0.400411 | 0.200206 | − | 0.979754i | \(-0.435839\pi\) | ||||
0.200206 | + | 0.979754i | \(0.435839\pi\) | |||||||
\(42\) | 5.13058e18 | − | 1.89869e19i | 0.170284 | − | 0.630177i | ||||
\(43\) | 4.53303e19i | 1.13440i | 0.823580 | + | 0.567201i | \(0.191974\pi\) | ||||
−0.823580 | + | 0.567201i | \(0.808026\pi\) | |||||||
\(44\) | −6.08458e18 | + | 1.04366e19i | −0.115558 | + | 0.198211i | ||||
\(45\) | 9.16387e19 | 1.32901 | ||||||||
\(46\) | 1.75487e19 | + | 4.74197e18i | 0.195502 | + | 0.0528280i | ||||
\(47\) | − | 1.32515e20i | − | 1.14048i | −0.821477 | − | 0.570242i | \(-0.806849\pi\) | ||
0.821477 | − | 0.570242i | \(-0.193151\pi\) | |||||||
\(48\) | −4.74923e19 | + | 2.68867e19i | −0.317489 | + | 0.179739i | ||||
\(49\) | −4.21742e20 | −2.20137 | ||||||||
\(50\) | −8.59966e19 | + | 3.18251e20i | −0.352242 | + | 1.30355i | ||||
\(51\) | − | 1.40488e20i | − | 0.453728i | ||||||
\(52\) | 1.64499e20 | + | 9.59032e19i | 0.420845 | + | 0.245354i | ||||
\(53\) | 2.48218e20 | 0.505269 | 0.252635 | − | 0.967562i | \(-0.418703\pi\) | ||||
0.252635 | + | 0.967562i | \(0.418703\pi\) | |||||||
\(54\) | −4.04240e20 | − | 1.09232e20i | −0.657528 | − | 0.177675i | ||||
\(55\) | − | 2.69512e20i | − | 0.351743i | ||||||
\(56\) | 1.19574e21 | + | 1.21101e21i | 1.25713 | + | 1.27318i | ||||
\(57\) | −3.86924e20 | −0.328948 | ||||||||
\(58\) | −2.16789e19 | + | 8.02277e19i | −0.0149589 | + | 0.0553590i | ||||
\(59\) | − | 3.17904e21i | − | 1.78679i | −0.449276 | − | 0.893393i | \(-0.648318\pi\) | ||
0.449276 | − | 0.893393i | \(-0.351682\pi\) | |||||||
\(60\) | 6.13212e20 | − | 1.05182e21i | 0.281706 | − | 0.483198i | ||||
\(61\) | 2.83808e21 | 1.06922 | 0.534610 | − | 0.845099i | \(-0.320458\pi\) | ||||
0.534610 | + | 0.845099i | \(0.320458\pi\) | |||||||
\(62\) | −1.93788e21 | − | 5.23647e20i | −0.600657 | − | 0.162307i | ||||
\(63\) | 6.06347e21i | 1.55108i | ||||||||
\(64\) | 5.99104e19 | − | 4.72199e21i | 0.0126865 | − | 0.999920i | ||||
\(65\) | −4.24795e21 | −0.746826 | ||||||||
\(66\) | −1.49175e20 | + | 5.52058e20i | −0.0218358 | + | 0.0808086i | ||||
\(67\) | 8.09517e21i | 0.989301i | 0.869092 | + | 0.494651i | \(0.164704\pi\) | ||||
−0.869092 | + | 0.494651i | \(0.835296\pi\) | |||||||
\(68\) | 1.05020e22 | + | 6.12267e21i | 1.07439 | + | 0.626374i | ||||
\(69\) | 8.60483e20 | 0.0738845 | ||||||||
\(70\) | −3.66525e22 | − | 9.90412e21i | −2.64806 | − | 0.715549i | ||||
\(71\) | 7.22794e21i | 0.440468i | 0.975447 | + | 0.220234i | \(0.0706821\pi\) | ||||
−0.975447 | + | 0.220234i | \(0.929318\pi\) | |||||||
\(72\) | 1.19723e22 | − | 1.18214e22i | 0.616863 | − | 0.609086i | ||||
\(73\) | 2.43394e21 | 0.106276 | 0.0531380 | − | 0.998587i | \(-0.483078\pi\) | ||||
0.0531380 | + | 0.998587i | \(0.483078\pi\) | |||||||
\(74\) | −1.07099e20 | + | 3.96346e20i | −0.00397197 | + | 0.0146992i | ||||
\(75\) | 1.56051e22i | 0.492640i | ||||||||
\(76\) | 1.68628e22 | − | 2.89240e22i | 0.454115 | − | 0.778924i | ||||
\(77\) | 1.78328e22 | 0.410517 | ||||||||
\(78\) | 8.70135e21 | + | 2.35125e21i | 0.171574 | + | 0.0463622i | ||||
\(79\) | − | 8.02491e22i | − | 1.35805i | −0.734116 | − | 0.679024i | \(-0.762403\pi\) | ||
0.734116 | − | 0.679024i | \(-0.237597\pi\) | |||||||
\(80\) | 5.19024e22 | + | 9.16796e22i | 0.755279 | + | 1.33411i | ||||
\(81\) | 4.93277e22 | 0.618401 | ||||||||
\(82\) | −9.65342e21 | + | 3.57247e22i | −0.104452 | + | 0.386547i | ||||
\(83\) | − | 5.98824e22i | − | 0.560224i | −0.959967 | − | 0.280112i | \(-0.909628\pi\) | ||
0.959967 | − | 0.280112i | \(-0.0903716\pi\) | |||||||
\(84\) | 6.95957e22 | + | 4.05745e22i | 0.563937 | + | 0.328777i | ||||
\(85\) | −2.71199e23 | −1.90660 | ||||||||
\(86\) | −1.79244e23 | − | 4.84348e22i | −1.09512 | − | 0.295921i | ||||
\(87\) | 3.93387e21i | 0.0209213i | ||||||||
\(88\) | −3.47670e22 | − | 3.52109e22i | −0.161204 | − | 0.163262i | ||||
\(89\) | 1.56264e23 | 0.632671 | 0.316336 | − | 0.948647i | \(-0.397547\pi\) | ||||
0.316336 | + | 0.948647i | \(0.397547\pi\) | |||||||
\(90\) | −9.79147e22 | + | 3.62356e23i | −0.346687 | + | 1.28300i | ||||
\(91\) | − | 2.81075e23i | − | 0.871616i | ||||||
\(92\) | −3.75012e22 | + | 6.43242e22i | −0.101998 | + | 0.174953i | ||||
\(93\) | −9.50217e22 | −0.227001 | ||||||||
\(94\) | 5.23987e23 | + | 1.41590e23i | 1.10100 | + | 0.297508i | ||||
\(95\) | 7.46923e23i | 1.38227i | ||||||||
\(96\) | −5.55700e22 | − | 2.16521e23i | −0.0906955 | − | 0.353383i | ||||
\(97\) | 2.43631e23 | 0.351133 | 0.175566 | − | 0.984468i | \(-0.443824\pi\) | ||||
0.175566 | + | 0.984468i | \(0.443824\pi\) | |||||||
\(98\) | 4.50625e23 | − | 1.66764e24i | 0.574252 | − | 2.12515i | ||||
\(99\) | − | 1.76300e23i | − | 0.198898i | ||||||
\(100\) | −1.16653e24 | − | 6.80093e23i | −1.16653 | − | 0.680093i | ||||
\(101\) | 1.26417e24 | 1.12189 | 0.560943 | − | 0.827855i | \(-0.310439\pi\) | ||||
0.560943 | + | 0.827855i | \(0.310439\pi\) | |||||||
\(102\) | 5.55513e23 | + | 1.50109e23i | 0.438019 | + | 0.118360i | ||||
\(103\) | 1.05068e24i | 0.736926i | 0.929642 | + | 0.368463i | \(0.120116\pi\) | ||||
−0.929642 | + | 0.368463i | \(0.879884\pi\) | |||||||
\(104\) | −5.54983e23 | + | 5.47986e23i | −0.346641 | + | 0.342271i | ||||
\(105\) | −1.79721e24 | −1.00076 | ||||||||
\(106\) | −2.65217e23 | + | 9.81499e23i | −0.131805 | + | 0.487775i | ||||
\(107\) | 1.04580e24i | 0.464350i | 0.972674 | + | 0.232175i | \(0.0745842\pi\) | ||||
−0.972674 | + | 0.232175i | \(0.925416\pi\) | |||||||
\(108\) | 8.63850e23 | − | 1.48173e24i | 0.343047 | − | 0.588413i | ||||
\(109\) | 1.69869e24 | 0.603945 | 0.301972 | − | 0.953317i | \(-0.402355\pi\) | ||||
0.301972 | + | 0.953317i | \(0.402355\pi\) | |||||||
\(110\) | 1.06570e24 | + | 2.87970e23i | 0.339564 | + | 0.0917560i | ||||
\(111\) | 1.94344e22i | 0.00555513i | ||||||||
\(112\) | −6.06618e24 | + | 3.43423e24i | −1.55704 | + | 0.881481i | ||||
\(113\) | −4.13350e24 | −0.953622 | −0.476811 | − | 0.879006i | \(-0.658207\pi\) | ||||
−0.476811 | + | 0.879006i | \(0.658207\pi\) | |||||||
\(114\) | 4.13423e23 | − | 1.52997e24i | 0.0858098 | − | 0.317559i | ||||
\(115\) | − | 1.66108e24i | − | 0.310469i | ||||||
\(116\) | −2.94071e23 | − | 1.71444e23i | −0.0495401 | − | 0.0288820i | ||||
\(117\) | −2.77878e24 | −0.422302 | ||||||||
\(118\) | 1.25705e25 | + | 3.39677e24i | 1.72492 | + | 0.466102i | ||||
\(119\) | − | 1.79444e25i | − | 2.22519i | ||||||
\(120\) | 3.50387e24 | + | 3.54860e24i | 0.392982 | + | 0.397999i | ||||
\(121\) | 9.33123e24 | 0.947359 | ||||||||
\(122\) | −3.03245e24 | + | 1.12223e25i | −0.278918 | + | 1.03220i | ||||
\(123\) | 1.75172e24i | 0.146084i | ||||||||
\(124\) | 4.14119e24 | − | 7.10321e24i | 0.313376 | − | 0.537520i | ||||
\(125\) | 7.81503e24 | 0.537045 | ||||||||
\(126\) | −2.39761e25 | − | 6.47873e24i | −1.49738 | − | 0.404616i | ||||
\(127\) | 1.80124e25i | 1.02312i | 0.859248 | + | 0.511560i | \(0.170932\pi\) | ||||
−0.859248 | + | 0.511560i | \(0.829068\pi\) | |||||||
\(128\) | 1.86076e25 | + | 5.28227e24i | 0.961989 | + | 0.273087i | ||||
\(129\) | −8.78903e24 | −0.413870 | ||||||||
\(130\) | 4.53888e24 | − | 1.67972e25i | 0.194818 | − | 0.720968i | ||||
\(131\) | − | 1.16233e25i | − | 0.455065i | −0.973771 | − | 0.227532i | \(-0.926934\pi\) | ||
0.973771 | − | 0.227532i | \(-0.0730658\pi\) | |||||||
\(132\) | −2.02355e24 | − | 1.17973e24i | −0.0723146 | − | 0.0421596i | ||||
\(133\) | −4.94217e25 | −1.61324 | ||||||||
\(134\) | −3.20098e25 | − | 8.64958e24i | −0.955048 | − | 0.258070i | ||||
\(135\) | 3.82635e25i | 1.04419i | ||||||||
\(136\) | −3.54313e25 | + | 3.49847e25i | −0.884954 | + | 0.873797i | ||||
\(137\) | 5.72851e25 | 1.31037 | 0.655186 | − | 0.755467i | \(-0.272590\pi\) | ||||
0.655186 | + | 0.755467i | \(0.272590\pi\) | |||||||
\(138\) | −9.19414e23 | + | 3.40251e24i | −0.0192736 | + | 0.0713263i | ||||
\(139\) | 5.65058e25i | 1.08621i | 0.839663 | + | 0.543107i | \(0.182752\pi\) | ||||
−0.839663 | + | 0.543107i | \(0.817248\pi\) | |||||||
\(140\) | 7.83254e25 | − | 1.34348e26i | 1.38155 | − | 2.36971i | ||||
\(141\) | 2.56931e25 | 0.416090 | ||||||||
\(142\) | −2.85806e25 | − | 7.72296e24i | −0.425217 | − | 0.114901i | ||||
\(143\) | 8.17246e24i | 0.111769i | ||||||||
\(144\) | 3.39517e25 | + | 5.99718e25i | 0.427082 | + | 0.754392i | ||||
\(145\) | 7.59399e24 | 0.0879131 | ||||||||
\(146\) | −2.60063e24 | + | 9.62423e24i | −0.0277233 | + | 0.102596i | ||||
\(147\) | − | 8.17710e25i | − | 0.803140i | ||||||
\(148\) | −1.45279e24 | − | 8.46980e23i | −0.0131541 | − | 0.00766889i | ||||
\(149\) | 5.90844e25 | 0.493443 | 0.246722 | − | 0.969086i | \(-0.420647\pi\) | ||||
0.246722 | + | 0.969086i | \(0.420647\pi\) | |||||||
\(150\) | −6.17052e25 | − | 1.66738e25i | −0.475583 | − | 0.128511i | ||||
\(151\) | − | 2.49594e26i | − | 1.77628i | −0.459575 | − | 0.888139i | \(-0.651998\pi\) | ||
0.459575 | − | 0.888139i | \(-0.348002\pi\) | |||||||
\(152\) | 9.63531e25 | + | 9.75833e25i | 0.633494 | + | 0.641583i | ||||
\(153\) | −1.77403e26 | −1.07811 | ||||||||
\(154\) | −1.90541e25 | + | 7.05142e25i | −0.107088 | + | 0.396304i | ||||
\(155\) | 1.83431e26i | 0.953876i | ||||||||
\(156\) | −1.85945e25 | + | 3.18944e25i | −0.0895139 | + | 0.153539i | ||||
\(157\) | −1.35514e26 | −0.604212 | −0.302106 | − | 0.953274i | \(-0.597690\pi\) | ||||
−0.302106 | + | 0.953274i | \(0.597690\pi\) | |||||||
\(158\) | 3.17319e26 | + | 8.57450e25i | 1.31103 | + | 0.354261i | ||||
\(159\) | 4.81267e25i | 0.184340i | ||||||||
\(160\) | −4.17975e26 | + | 1.07273e26i | −1.48495 | + | 0.381110i | ||||
\(161\) | 1.09909e26 | 0.362346 | ||||||||
\(162\) | −5.27059e25 | + | 1.95051e26i | −0.161317 | + | 0.596990i | ||||
\(163\) | − | 2.30376e26i | − | 0.654917i | −0.944866 | − | 0.327458i | \(-0.893808\pi\) | ||
0.944866 | − | 0.327458i | \(-0.106192\pi\) | |||||||
\(164\) | −1.30948e26 | − | 7.63428e25i | −0.345916 | − | 0.201670i | ||||
\(165\) | 5.22553e25 | 0.128328 | ||||||||
\(166\) | 2.36786e26 | + | 6.39835e25i | 0.540827 | + | 0.146141i | ||||
\(167\) | − | 4.45920e26i | − | 0.947674i | −0.880613 | − | 0.473837i | \(-0.842869\pi\) | ||
0.880613 | − | 0.473837i | \(-0.157131\pi\) | |||||||
\(168\) | −2.34801e26 | + | 2.31841e26i | −0.464503 | + | 0.458647i | ||||
\(169\) | −4.13989e26 | −0.762691 | ||||||||
\(170\) | 2.89772e26 | − | 1.07237e27i | 0.497358 | − | 1.84059i | ||||
\(171\) | 4.88596e26i | 0.781621i | ||||||||
\(172\) | 3.83040e26 | − | 6.57012e26i | 0.571350 | − | 0.980013i | ||||
\(173\) | 1.19303e27 | 1.65997 | 0.829984 | − | 0.557787i | \(-0.188349\pi\) | ||||
0.829984 | + | 0.557787i | \(0.188349\pi\) | |||||||
\(174\) | −1.55552e25 | − | 4.20329e24i | −0.0201970 | − | 0.00545756i | ||||
\(175\) | 1.99323e27i | 2.41602i | ||||||||
\(176\) | 1.76379e26 | − | 9.98528e25i | 0.199661 | − | 0.113034i | ||||
\(177\) | 6.16381e26 | 0.651884 | ||||||||
\(178\) | −1.66966e26 | + | 6.17895e26i | −0.165039 | + | 0.610766i | ||||
\(179\) | − | 1.36574e27i | − | 1.26221i | −0.775697 | − | 0.631105i | \(-0.782602\pi\) | ||
0.775697 | − | 0.631105i | \(-0.217398\pi\) | |||||||
\(180\) | −1.32820e27 | − | 7.74345e26i | −1.14814 | − | 0.669367i | ||||
\(181\) | −1.53542e27 | −1.24190 | −0.620948 | − | 0.783852i | \(-0.713252\pi\) | ||||
−0.620948 | + | 0.783852i | \(0.713252\pi\) | |||||||
\(182\) | 1.11142e27 | + | 3.00325e26i | 0.841438 | + | 0.227371i | ||||
\(183\) | 5.50273e26i | 0.390090i | ||||||||
\(184\) | −2.14280e26 | − | 2.17016e26i | −0.142288 | − | 0.144105i | ||||
\(185\) | 3.75163e25 | 0.0233431 | ||||||||
\(186\) | 1.01529e26 | − | 3.75733e26i | 0.0592156 | − | 0.219141i | ||||
\(187\) | 5.21748e26i | 0.285339i | ||||||||
\(188\) | −1.11975e27 | + | 1.92065e27i | −0.574414 | + | 0.985268i | ||||
\(189\) | −2.53179e27 | −1.21867 | ||||||||
\(190\) | −2.95347e27 | − | 7.98076e26i | −1.33441 | − | 0.360580i | ||||
\(191\) | − | 8.58551e26i | − | 0.364222i | −0.983278 | − | 0.182111i | \(-0.941707\pi\) | ||
0.983278 | − | 0.182111i | \(-0.0582930\pi\) | |||||||
\(192\) | 9.15540e26 | + | 1.16160e25i | 0.364807 | + | 0.00462850i | ||||
\(193\) | 4.66261e27 | 1.74559 | 0.872793 | − | 0.488090i | \(-0.162306\pi\) | ||||
0.872793 | + | 0.488090i | \(0.162306\pi\) | |||||||
\(194\) | −2.60316e26 | + | 9.63360e26i | −0.0915968 | + | 0.338975i | ||||
\(195\) | − | 8.23631e26i | − | 0.272469i | ||||||
\(196\) | 6.11268e27 | + | 3.56371e27i | 1.90177 | + | 1.10874i | ||||
\(197\) | −2.52221e27 | −0.738222 | −0.369111 | − | 0.929385i | \(-0.620338\pi\) | ||||
−0.369111 | + | 0.929385i | \(0.620338\pi\) | |||||||
\(198\) | 6.97121e26 | + | 1.88374e26i | 0.192011 | + | 0.0518846i | ||||
\(199\) | − | 6.79518e27i | − | 1.76183i | −0.473273 | − | 0.880916i | \(-0.656928\pi\) | ||
0.473273 | − | 0.880916i | \(-0.343072\pi\) | |||||||
\(200\) | 3.93564e27 | − | 3.88602e27i | 0.960849 | − | 0.948735i | ||||
\(201\) | −1.56956e27 | −0.360933 | ||||||||
\(202\) | −1.35075e27 | + | 4.99875e27i | −0.292656 | + | 1.08304i | ||||
\(203\) | 5.02472e26i | 0.102603i | ||||||||
\(204\) | −1.18712e27 | + | 2.03621e27i | −0.228524 | + | 0.391977i | ||||
\(205\) | 3.38154e27 | 0.613859 | ||||||||
\(206\) | −4.15458e27 | − | 1.12264e27i | −0.711411 | − | 0.192235i | ||||
\(207\) | − | 1.08659e27i | − | 0.175558i | ||||||
\(208\) | −1.57385e27 | − | 2.78002e27i | −0.239995 | − | 0.423924i | ||||
\(209\) | 1.43697e27 | 0.206868 | ||||||||
\(210\) | 1.92030e27 | − | 7.10651e27i | 0.261058 | − | 0.966106i | ||||
\(211\) | 4.14619e27i | 0.532426i | 0.963914 | + | 0.266213i | \(0.0857725\pi\) | ||||
−0.963914 | + | 0.266213i | \(0.914228\pi\) | |||||||
\(212\) | −3.59764e27 | − | 2.09744e27i | −0.436504 | − | 0.254483i | ||||
\(213\) | −1.40142e27 | −0.160699 | ||||||||
\(214\) | −4.13530e27 | − | 1.11743e27i | −0.448272 | − | 0.121131i | ||||
\(215\) | 1.69664e28i | 1.73912i | ||||||||
\(216\) | 4.93600e27 | + | 4.99902e27i | 0.478553 | + | 0.484663i | ||||
\(217\) | −1.21371e28 | −1.11326 | ||||||||
\(218\) | −1.81503e27 | + | 6.71694e27i | −0.157546 | + | 0.583034i | ||||
\(219\) | 4.71913e26i | 0.0387733i | ||||||||
\(220\) | −2.27737e27 | + | 3.90627e27i | −0.177158 | + | 0.303872i | ||||
\(221\) | 8.22361e27 | 0.605836 | ||||||||
\(222\) | −7.68470e25 | − | 2.07653e25i | −0.00536280 | − | 0.00144912i | ||||
\(223\) | − | 3.05138e27i | − | 0.201761i | −0.994899 | − | 0.100881i | \(-0.967834\pi\) | ||
0.994899 | − | 0.100881i | \(-0.0321660\pi\) | |||||||
\(224\) | −7.09794e27 | − | 2.76562e28i | −0.444791 | − | 1.73307i | ||||
\(225\) | 1.97056e28 | 1.17057 | ||||||||
\(226\) | 4.41659e27 | − | 1.63446e28i | 0.248763 | − | 0.920604i | ||||
\(227\) | 1.18793e28i | 0.634571i | 0.948330 | + | 0.317285i | \(0.102771\pi\) | ||||
−0.948330 | + | 0.317285i | \(0.897229\pi\) | |||||||
\(228\) | 5.60804e27 | + | 3.26950e27i | 0.284180 | + | 0.165677i | ||||
\(229\) | −2.06279e28 | −0.991814 | −0.495907 | − | 0.868376i | \(-0.665164\pi\) | ||||
−0.495907 | + | 0.868376i | \(0.665164\pi\) | |||||||
\(230\) | 6.56823e27 | + | 1.77485e27i | 0.299719 | + | 0.0809891i | ||||
\(231\) | 3.45758e27i | 0.149771i | ||||||||
\(232\) | 9.92133e26 | − | 9.79625e26i | 0.0408051 | − | 0.0402906i | ||||
\(233\) | 5.02642e27 | 0.196331 | 0.0981653 | − | 0.995170i | \(-0.468703\pi\) | ||||
0.0981653 | + | 0.995170i | \(0.468703\pi\) | |||||||
\(234\) | 2.96909e27 | − | 1.09878e28i | 0.110162 | − | 0.407681i | ||||
\(235\) | − | 4.95982e28i | − | 1.74844i | ||||||
\(236\) | −2.68629e28 | + | 4.60767e28i | −0.899929 | + | 1.54361i | ||||
\(237\) | 1.55594e28 | 0.495464 | ||||||||
\(238\) | 7.09556e28 | + | 1.91734e28i | 2.14814 | + | 0.580464i | ||||
\(239\) | − | 2.91320e28i | − | 0.838678i | −0.907830 | − | 0.419339i | \(-0.862262\pi\) | ||
0.907830 | − | 0.419339i | \(-0.137738\pi\) | |||||||
\(240\) | −1.77757e28 | + | 1.00633e28i | −0.486733 | + | 0.275553i | ||||
\(241\) | 5.47767e28 | 1.42689 | 0.713447 | − | 0.700709i | \(-0.247133\pi\) | ||||
0.713447 | + | 0.700709i | \(0.247133\pi\) | |||||||
\(242\) | −9.97029e27 | + | 3.68974e28i | −0.247129 | + | 0.914558i | ||||
\(243\) | 3.84371e28i | 0.906725i | ||||||||
\(244\) | −4.11349e28 | − | 2.39817e28i | −0.923703 | − | 0.538521i | ||||
\(245\) | −1.57852e29 | −3.37486 | ||||||||
\(246\) | −6.92663e27 | − | 1.87169e27i | −0.141026 | − | 0.0381077i | ||||
\(247\) | − | 2.26491e28i | − | 0.439225i | ||||||
\(248\) | 2.36626e28 | + | 2.39647e28i | 0.437162 | + | 0.442743i | ||||
\(249\) | 1.16105e28 | 0.204390 | ||||||||
\(250\) | −8.35026e27 | + | 3.09021e28i | −0.140094 | + | 0.518451i | ||||
\(251\) | 1.94301e28i | 0.310735i | 0.987857 | + | 0.155368i | \(0.0496562\pi\) | ||||
−0.987857 | + | 0.155368i | \(0.950344\pi\) | |||||||
\(252\) | 5.12362e28 | − | 8.78832e28i | 0.781214 | − | 1.33998i | ||||
\(253\) | −3.19569e27 | −0.0464642 | ||||||||
\(254\) | −7.12243e28 | − | 1.92460e28i | −0.987696 | − | 0.266892i | ||||
\(255\) | − | 5.25824e28i | − | 0.695598i | ||||||
\(256\) | −4.07690e28 | + | 6.79337e28i | −0.514577 | + | 0.857444i | ||||
\(257\) | 1.05899e29 | 1.27555 | 0.637773 | − | 0.770224i | \(-0.279856\pi\) | ||||
0.637773 | + | 0.770224i | \(0.279856\pi\) | |||||||
\(258\) | 9.39096e27 | − | 3.47534e28i | 0.107963 | − | 0.399541i | ||||
\(259\) | 2.48235e27i | 0.0272436i | ||||||||
\(260\) | 6.15694e28 | + | 3.58951e28i | 0.645185 | + | 0.376145i | ||||
\(261\) | 4.96757e27 | 0.0497116 | ||||||||
\(262\) | 4.59606e28 | + | 1.24193e28i | 0.439309 | + | 0.118709i | ||||
\(263\) | 1.64096e29i | 1.49840i | 0.662343 | + | 0.749201i | \(0.269562\pi\) | ||||
−0.662343 | + | 0.749201i | \(0.730438\pi\) | |||||||
\(264\) | 6.82701e27 | − | 6.74094e27i | 0.0595639 | − | 0.0588130i | ||||
\(265\) | 9.29042e28 | 0.774613 | ||||||||
\(266\) | 5.28064e28 | − | 1.95422e29i | 0.420830 | − | 1.55738i | ||||
\(267\) | 3.02978e28i | 0.230821i | ||||||||
\(268\) | 6.84040e28 | − | 1.17331e29i | 0.498269 | − | 0.854660i | ||||
\(269\) | −9.71636e27 | −0.0676825 | −0.0338412 | − | 0.999427i | \(-0.510774\pi\) | ||||
−0.0338412 | + | 0.999427i | \(0.510774\pi\) | |||||||
\(270\) | −1.51301e29 | − | 4.08840e28i | −1.00804 | − | 0.272388i | ||||
\(271\) | 4.33237e28i | 0.276118i | 0.990424 | + | 0.138059i | \(0.0440863\pi\) | ||||
−0.990424 | + | 0.138059i | \(0.955914\pi\) | |||||||
\(272\) | −1.00478e29 | − | 1.77483e29i | −0.612693 | − | 1.08225i | ||||
\(273\) | 5.44973e28 | 0.317997 | ||||||||
\(274\) | −6.12083e28 | + | 2.26516e29i | −0.341825 | + | 1.26500i | ||||
\(275\) | − | 5.79546e28i | − | 0.309810i | ||||||
\(276\) | −1.24717e28 | − | 7.27106e27i | −0.0638290 | − | 0.0372125i | ||||
\(277\) | −3.24171e29 | −1.58861 | −0.794305 | − | 0.607520i | \(-0.792165\pi\) | ||||
−0.794305 | + | 0.607520i | \(0.792165\pi\) | |||||||
\(278\) | −2.23434e29 | − | 6.03757e28i | −1.04861 | − | 0.283351i | ||||
\(279\) | 1.19990e29i | 0.539381i | ||||||||
\(280\) | 4.47548e29 | + | 4.53262e29i | 1.92727 | + | 1.95188i | ||||
\(281\) | 3.64011e28 | 0.150189 | 0.0750946 | − | 0.997176i | \(-0.476074\pi\) | ||||
0.0750946 | + | 0.997176i | \(0.476074\pi\) | |||||||
\(282\) | −2.74527e28 | + | 1.01595e29i | −0.108542 | + | 0.401683i | ||||
\(283\) | − | 3.18947e29i | − | 1.20860i | −0.796758 | − | 0.604299i | \(-0.793453\pi\) | ||
0.796758 | − | 0.604299i | \(-0.206547\pi\) | |||||||
\(284\) | 6.10759e28 | − | 1.04761e29i | 0.221845 | − | 0.380522i | ||||
\(285\) | −1.44820e29 | −0.504301 | ||||||||
\(286\) | −3.23154e28 | − | 8.73216e27i | −0.107899 | − | 0.0291561i | ||||
\(287\) | 2.23747e29i | 0.716431i | ||||||||
\(288\) | −2.73416e29 | + | 7.01721e28i | −0.839681 | + | 0.215504i | ||||
\(289\) | 1.85565e29 | 0.546665 | ||||||||
\(290\) | −8.11407e27 | + | 3.00280e28i | −0.0229331 | + | 0.0848693i | ||||
\(291\) | 4.72373e28i | 0.128106i | ||||||||
\(292\) | −3.52772e28 | − | 2.05667e28i | −0.0918122 | − | 0.0535267i | ||||
\(293\) | 3.12973e29 | 0.781799 | 0.390899 | − | 0.920433i | \(-0.372164\pi\) | ||||
0.390899 | + | 0.920433i | \(0.372164\pi\) | |||||||
\(294\) | 3.23337e29 | + | 8.73712e28i | 0.775332 | + | 0.209508i | ||||
\(295\) | − | 1.18987e30i | − | 2.73927i | ||||||
\(296\) | 4.90140e27 | − | 4.83961e27i | 0.0108348 | − | 0.0106982i | ||||
\(297\) | 7.36136e28 | 0.156272 | ||||||||
\(298\) | −6.31308e28 | + | 2.33630e29i | −0.128720 | + | 0.476359i | ||||
\(299\) | 5.03694e28i | 0.0986535i | ||||||||
\(300\) | 1.31862e29 | − | 2.26178e29i | 0.248122 | − | 0.425594i | ||||
\(301\) | −1.12262e30 | −2.02971 | ||||||||
\(302\) | 9.86940e29 | + | 2.66688e29i | 1.71478 | + | 0.463361i | ||||
\(303\) | 2.45108e29i | 0.409304i | ||||||||
\(304\) | −4.88814e29 | + | 2.76731e29i | −0.784623 | + | 0.444196i | ||||
\(305\) | 1.06225e30 | 1.63919 | ||||||||
\(306\) | 1.89553e29 | − | 7.01485e29i | 0.281238 | − | 1.04079i | ||||
\(307\) | 2.32663e29i | 0.331945i | 0.986130 | + | 0.165972i | \(0.0530763\pi\) | ||||
−0.986130 | + | 0.165972i | \(0.946924\pi\) | |||||||
\(308\) | −2.58467e29 | − | 1.50687e29i | −0.354647 | − | 0.206760i | ||||
\(309\) | −2.03715e29 | −0.268857 | ||||||||
\(310\) | −7.25319e29 | − | 1.95993e29i | −0.920849 | − | 0.248829i | ||||
\(311\) | 3.34060e29i | 0.408037i | 0.978967 | + | 0.204019i | \(0.0654003\pi\) | ||||
−0.978967 | + | 0.204019i | \(0.934600\pi\) | |||||||
\(312\) | −1.06248e29 | − | 1.07605e29i | −0.124873 | − | 0.126467i | ||||
\(313\) | 9.52149e29 | 1.07689 | 0.538447 | − | 0.842659i | \(-0.319011\pi\) | ||||
0.538447 | + | 0.842659i | \(0.319011\pi\) | |||||||
\(314\) | 1.44795e29 | − | 5.35848e29i | 0.157615 | − | 0.583292i | ||||
\(315\) | 2.26946e30i | 2.37792i | ||||||||
\(316\) | −6.78103e29 | + | 1.16312e30i | −0.683991 | + | 1.17322i | ||||
\(317\) | −1.44546e30 | −1.40376 | −0.701881 | − | 0.712294i | \(-0.747656\pi\) | ||||
−0.701881 | + | 0.712294i | \(0.747656\pi\) | |||||||
\(318\) | −1.90302e29 | − | 5.14227e28i | −0.177958 | − | 0.0480872i | ||||
\(319\) | − | 1.46098e28i | − | 0.0131569i | ||||||
\(320\) | 2.24236e28 | − | 1.76737e30i | 0.0194493 | − | 1.53295i | ||||
\(321\) | −2.02770e29 | −0.169411 | ||||||||
\(322\) | −1.17436e29 | + | 4.34601e29i | −0.0945219 | + | 0.349800i | ||||
\(323\) | − | 1.44597e30i | − | 1.12132i | ||||||
\(324\) | −7.14950e29 | − | 4.16818e29i | −0.534239 | − | 0.311463i | ||||
\(325\) | −9.13461e29 | −0.657794 | ||||||||
\(326\) | 9.10949e29 | + | 2.46154e29i | 0.632241 | + | 0.170842i | ||||
\(327\) | 3.29358e29i | 0.220341i | ||||||||
\(328\) | 4.41789e29 | − | 4.36219e29i | 0.284924 | − | 0.281332i | ||||
\(329\) | 3.28177e30 | 2.04060 | ||||||||
\(330\) | −5.58341e28 | + | 2.06627e29i | −0.0334759 | + | 0.123885i | ||||
\(331\) | − | 1.57998e30i | − | 0.913514i | −0.889591 | − | 0.456757i | \(-0.849011\pi\) | ||
0.889591 | − | 0.456757i | \(-0.150989\pi\) | |||||||
\(332\) | −5.06005e29 | + | 8.67928e29i | −0.282161 | + | 0.483979i | ||||
\(333\) | 2.45411e28 | 0.0131997 | ||||||||
\(334\) | 1.76325e30 | + | 4.76459e29i | 0.914862 | + | 0.247211i | ||||
\(335\) | 3.02990e30i | 1.51667i | ||||||||
\(336\) | −6.65859e29 | − | 1.17616e30i | −0.321596 | − | 0.568063i | ||||
\(337\) | −1.45755e30 | −0.679303 | −0.339651 | − | 0.940551i | \(-0.610309\pi\) | ||||
−0.339651 | + | 0.940551i | \(0.610309\pi\) | |||||||
\(338\) | 4.42342e29 | − | 1.63699e30i | 0.198956 | − | 0.736284i | ||||
\(339\) | − | 8.01439e29i | − | 0.347916i | ||||||
\(340\) | 3.93072e30 | + | 2.29162e30i | 1.64712 | + | 0.960276i | ||||
\(341\) | 3.52895e29 | 0.142755 | ||||||||
\(342\) | −1.93200e30 | − | 5.22058e29i | −0.754559 | − | 0.203894i | ||||
\(343\) | − | 5.70001e30i | − | 2.14954i | ||||||
\(344\) | 2.18867e30 | + | 2.21662e30i | 0.797038 | + | 0.807215i | ||||
\(345\) | 3.22066e29 | 0.113270 | ||||||||
\(346\) | −1.27474e30 | + | 4.71748e30i | −0.433021 | + | 1.60249i | ||||
\(347\) | − | 1.66816e30i | − | 0.547372i | −0.961819 | − | 0.273686i | \(-0.911757\pi\) | ||
0.961819 | − | 0.273686i | \(-0.0882430\pi\) | |||||||
\(348\) | 3.32411e28 | − | 5.70171e28i | 0.0105372 | − | 0.0180740i | ||||
\(349\) | −1.34472e30 | −0.411839 | −0.205919 | − | 0.978569i | \(-0.566018\pi\) | ||||
−0.205919 | + | 0.978569i | \(0.566018\pi\) | |||||||
\(350\) | −7.88159e30 | − | 2.12974e30i | −2.33237 | − | 0.630245i | ||||
\(351\) | − | 1.16027e30i | − | 0.331799i | ||||||
\(352\) | 2.06378e29 | + | 8.04124e29i | 0.0570363 | + | 0.222234i | ||||
\(353\) | −5.79218e30 | −1.54720 | −0.773599 | − | 0.633676i | \(-0.781545\pi\) | ||||
−0.773599 | + | 0.633676i | \(0.781545\pi\) | |||||||
\(354\) | −6.58595e29 | + | 2.43728e30i | −0.170051 | + | 0.629313i | ||||
\(355\) | 2.70531e30i | 0.675269i | ||||||||
\(356\) | −2.26487e30 | − | 1.32042e30i | −0.546567 | − | 0.318650i | ||||
\(357\) | 3.47922e30 | 0.811828 | ||||||||
\(358\) | 5.40038e30 | + | 1.45927e30i | 1.21851 | + | 0.329261i | ||||
\(359\) | 7.40160e30i | 1.61507i | 0.589818 | + | 0.807536i | \(0.299200\pi\) | ||||
−0.589818 | + | 0.807536i | \(0.700800\pi\) | |||||||
\(360\) | 4.48106e30 | − | 4.42457e30i | 0.945695 | − | 0.933773i | ||||
\(361\) | 9.16348e29 | 0.187057 | ||||||||
\(362\) | 1.64058e30 | − | 6.07135e30i | 0.323962 | − | 1.19890i | ||||
\(363\) | 1.80922e30i | 0.345631i | ||||||||
\(364\) | −2.37508e30 | + | 4.07387e30i | −0.438996 | + | 0.752992i | ||||
\(365\) | 9.10986e29 | 0.162929 | ||||||||
\(366\) | −2.17588e30 | − | 5.87959e29i | −0.376584 | − | 0.101759i | ||||
\(367\) | − | 6.64670e30i | − | 1.11330i | −0.830746 | − | 0.556651i | \(-0.812086\pi\) | ||
0.830746 | − | 0.556651i | \(-0.187914\pi\) | |||||||
\(368\) | 1.08708e30 | − | 6.15424e29i | 0.176233 | − | 0.0997701i | ||||
\(369\) | 2.21202e30 | 0.347114 | ||||||||
\(370\) | −4.00856e28 | + | 1.48346e29i | −0.00608931 | + | 0.0225349i | ||||
\(371\) | 6.14721e30i | 0.904047i | ||||||||
\(372\) | 1.37723e30 | + | 8.02931e29i | 0.196107 | + | 0.114331i | ||||
\(373\) | 5.19114e30 | 0.715742 | 0.357871 | − | 0.933771i | \(-0.383503\pi\) | ||||
0.357871 | + | 0.933771i | \(0.383503\pi\) | |||||||
\(374\) | −2.06309e30 | − | 5.57480e29i | −0.275460 | − | 0.0744338i | ||||
\(375\) | 1.51525e30i | 0.195933i | ||||||||
\(376\) | −6.39817e30 | − | 6.47987e30i | −0.801312 | − | 0.811544i | ||||
\(377\) | −2.30274e29 | −0.0279350 | ||||||||
\(378\) | 2.70518e30 | − | 1.00111e31i | 0.317903 | − | 1.17647i | ||||
\(379\) | − | 8.29858e30i | − | 0.944786i | −0.881388 | − | 0.472393i | \(-0.843390\pi\) | ||
0.881388 | − | 0.472393i | \(-0.156610\pi\) | |||||||
\(380\) | 6.31148e30 | − | 1.08258e31i | 0.696190 | − | 1.19415i | ||||
\(381\) | −3.49240e30 | −0.373271 | ||||||||
\(382\) | 3.39487e30 | + | 9.17350e29i | 0.351611 | + | 0.0950112i | ||||
\(383\) | 1.01279e31i | 1.01656i | 0.861191 | + | 0.508281i | \(0.169719\pi\) | ||||
−0.861191 | + | 0.508281i | \(0.830281\pi\) | |||||||
\(384\) | −1.02417e30 | + | 3.60780e30i | −0.0996320 | + | 0.350968i | ||||
\(385\) | 6.67455e30 | 0.629352 | ||||||||
\(386\) | −4.98193e30 | + | 1.84368e31i | −0.455355 | + | 1.68515i | ||||
\(387\) | 1.10985e31i | 0.983406i | ||||||||
\(388\) | −3.53116e30 | − | 2.05867e30i | −0.303345 | − | 0.176851i | ||||
\(389\) | −8.77832e30 | −0.731166 | −0.365583 | − | 0.930779i | \(-0.619130\pi\) | ||||
−0.365583 | + | 0.930779i | \(0.619130\pi\) | |||||||
\(390\) | 3.25678e30 | + | 8.80038e29i | 0.263035 | + | 0.0710765i | ||||
\(391\) | 3.21569e30i | 0.251857i | ||||||||
\(392\) | −2.06229e31 | + | 2.03629e31i | −1.56645 | + | 1.54670i | ||||
\(393\) | 2.25362e30 | 0.166024 | ||||||||
\(394\) | 2.69495e30 | − | 9.97329e30i | 0.192573 | − | 0.712662i | ||||
\(395\) | − | 3.00360e31i | − | 2.08198i | ||||||
\(396\) | −1.48973e30 | + | 2.55527e30i | −0.100176 | + | 0.171828i | ||||
\(397\) | −1.02352e31 | −0.667743 | −0.333871 | − | 0.942619i | \(-0.608355\pi\) | ||||
−0.333871 | + | 0.942619i | \(0.608355\pi\) | |||||||
\(398\) | 2.68694e31 | + | 7.26056e30i | 1.70083 | + | 0.459593i | ||||
\(399\) | − | 9.58232e30i | − | 0.588567i | ||||||
\(400\) | 1.11609e31 | + | 1.97144e31i | 0.665239 | + | 1.17507i | ||||
\(401\) | −2.49862e31 | −1.44533 | −0.722665 | − | 0.691198i | \(-0.757083\pi\) | ||||
−0.722665 | + | 0.691198i | \(0.757083\pi\) | |||||||
\(402\) | 1.67706e30 | − | 6.20634e30i | 0.0941532 | − | 0.348436i | ||||
\(403\) | − | 5.56221e30i | − | 0.303101i | ||||||
\(404\) | −1.83227e31 | − | 1.06822e31i | −0.969200 | − | 0.565047i | ||||
\(405\) | 1.84626e31 | 0.948053 | ||||||||
\(406\) | −1.98687e30 | − | 5.36885e29i | −0.0990504 | − | 0.0267651i | ||||
\(407\) | − | 7.21760e28i | − | 0.00349349i | ||||||
\(408\) | −6.78313e30 | − | 6.86974e30i | −0.318793 | − | 0.322863i | ||||
\(409\) | −2.13620e31 | −0.974906 | −0.487453 | − | 0.873149i | \(-0.662074\pi\) | ||||
−0.487453 | + | 0.873149i | \(0.662074\pi\) | |||||||
\(410\) | −3.61313e30 | + | 1.33712e31i | −0.160132 | + | 0.592605i | ||||
\(411\) | 1.11069e31i | 0.478071i | ||||||||
\(412\) | 8.87823e30 | − | 1.52284e31i | 0.371159 | − | 0.636633i | ||||
\(413\) | 7.87302e31 | 3.19698 | ||||||||
\(414\) | 4.29658e30 | + | 1.16101e30i | 0.169480 | + | 0.0457963i | ||||
\(415\) | − | 2.24131e31i | − | 0.858863i | ||||||
\(416\) | 1.26743e31 | − | 3.25286e30i | 0.471851 | − | 0.121100i | ||||
\(417\) | −1.09559e31 | −0.396290 | ||||||||
\(418\) | −1.53539e30 | + | 5.68205e30i | −0.0539638 | + | 0.199705i | ||||
\(419\) | 1.58008e31i | 0.539648i | 0.962910 | + | 0.269824i | \(0.0869656\pi\) | ||||
−0.962910 | + | 0.269824i | \(0.913034\pi\) | |||||||
\(420\) | 2.60486e31 | + | 1.51864e31i | 0.864556 | + | 0.504038i | ||||
\(421\) | 1.16728e30 | 0.0376523 | 0.0188261 | − | 0.999823i | \(-0.494007\pi\) | ||||
0.0188261 | + | 0.999823i | \(0.494007\pi\) | |||||||
\(422\) | −1.63948e31 | − | 4.43014e30i | −0.513991 | − | 0.138889i | ||||
\(423\) | − | 3.24444e31i | − | 0.988680i | ||||||
\(424\) | 1.21377e31 | − | 1.19847e31i | 0.359538 | − | 0.355006i | ||||
\(425\) | −5.83173e31 | −1.67931 | ||||||||
\(426\) | 1.49739e30 | − | 5.54146e30i | 0.0419200 | − | 0.155135i | ||||
\(427\) | 7.02862e31i | 1.91309i | ||||||||
\(428\) | 8.83702e30 | − | 1.51578e31i | 0.233873 | − | 0.401153i | ||||
\(429\) | −1.58455e30 | −0.0407773 | ||||||||
\(430\) | −6.70883e31 | − | 1.81284e31i | −1.67890 | − | 0.453668i | ||||
\(431\) | 5.13923e31i | 1.25075i | 0.780324 | + | 0.625375i | \(0.215054\pi\) | ||||
−0.780324 | + | 0.625375i | \(0.784946\pi\) | |||||||
\(432\) | −2.50411e31 | + | 1.41765e31i | −0.592718 | + | 0.335554i | ||||
\(433\) | 4.38354e31 | 1.00918 | 0.504592 | − | 0.863358i | \(-0.331643\pi\) | ||||
0.504592 | + | 0.863358i | \(0.331643\pi\) | |||||||
\(434\) | 1.29683e31 | − | 4.79922e31i | 0.290407 | − | 1.07472i | ||||
\(435\) | 1.47239e30i | 0.0320739i | ||||||||
\(436\) | −2.46207e31 | − | 1.43539e31i | −0.521750 | − | 0.304181i | ||||
\(437\) | 8.85651e30 | 0.182594 | ||||||||
\(438\) | −1.86603e30 | − | 5.04233e29i | −0.0374308 | − | 0.0101144i | ||||
\(439\) | 3.05818e31i | 0.596882i | 0.954428 | + | 0.298441i | \(0.0964665\pi\) | ||||
−0.954428 | + | 0.298441i | \(0.903533\pi\) | |||||||
\(440\) | −1.30128e31 | − | 1.31789e31i | −0.247137 | − | 0.250293i | ||||
\(441\) | −1.03258e32 | −1.90836 | ||||||||
\(442\) | −8.78682e30 | + | 3.25177e31i | −0.158039 | + | 0.584860i | ||||
\(443\) | − | 5.66961e31i | − | 0.992449i | −0.868194 | − | 0.496225i | \(-0.834719\pi\) | ||
0.868194 | − | 0.496225i | \(-0.165281\pi\) | |||||||
\(444\) | 1.64220e29 | − | 2.81680e29i | 0.00279789 | − | 0.00479910i | ||||
\(445\) | 5.84871e31 | 0.969930 | ||||||||
\(446\) | 1.20657e31 | + | 3.26035e30i | 0.194775 | + | 0.0526316i | ||||
\(447\) | 1.14558e31i | 0.180026i | ||||||||
\(448\) | 1.16942e32 | + | 1.48370e30i | 1.78909 | + | 0.0226992i | ||||
\(449\) | 3.41900e31 | 0.509264 | 0.254632 | − | 0.967038i | \(-0.418046\pi\) | ||||
0.254632 | + | 0.967038i | \(0.418046\pi\) | |||||||
\(450\) | −2.10551e31 | + | 7.79194e31i | −0.305357 | + | 1.13004i | ||||
\(451\) | − | 6.50561e30i | − | 0.0918691i | ||||||
\(452\) | 5.99105e31 | + | 3.49280e31i | 0.823837 | + | 0.480299i | ||||
\(453\) | 4.83935e31 | 0.648050 | ||||||||
\(454\) | −4.69728e31 | − | 1.26928e31i | −0.612599 | − | 0.165535i | ||||
\(455\) | − | 1.05202e32i | − | 1.33625i | ||||||
\(456\) | −1.89203e31 | + | 1.86818e31i | −0.234072 | + | 0.231121i | ||||
\(457\) | 3.67398e30 | 0.0442734 | 0.0221367 | − | 0.999755i | \(-0.492953\pi\) | ||||
0.0221367 | + | 0.999755i | \(0.492953\pi\) | |||||||
\(458\) | 2.20407e31 | − | 8.15666e31i | 0.258725 | − | 0.957474i | ||||
\(459\) | − | 7.40743e31i | − | 0.847063i | ||||||
\(460\) | −1.40361e31 | + | 2.40756e31i | −0.156370 | + | 0.268215i | ||||
\(461\) | 4.41661e30 | 0.0479378 | 0.0239689 | − | 0.999713i | \(-0.492370\pi\) | ||||
0.0239689 | + | 0.999713i | \(0.492370\pi\) | |||||||
\(462\) | −1.36719e31 | − | 3.69438e30i | −0.144586 | − | 0.0390695i | ||||
\(463\) | 1.06447e32i | 1.09688i | 0.836189 | + | 0.548442i | \(0.184779\pi\) | ||||
−0.836189 | + | 0.548442i | \(0.815221\pi\) | |||||||
\(464\) | 2.81353e30 | + | 4.96979e30i | 0.0282512 | + | 0.0499025i | ||||
\(465\) | −3.55652e31 | −0.348008 | ||||||||
\(466\) | −5.37066e30 | + | 1.98754e31i | −0.0512150 | + | 0.189533i | ||||
\(467\) | − | 1.75777e32i | − | 1.63365i | −0.576883 | − | 0.816827i | \(-0.695731\pi\) | ||
0.576883 | − | 0.816827i | \(-0.304269\pi\) | |||||||
\(468\) | 4.02753e31 | + | 2.34806e31i | 0.364828 | + | 0.212696i | ||||
\(469\) | −2.00480e32 | −1.77010 | ||||||||
\(470\) | 1.96120e32 | + | 5.29950e31i | 1.68791 | + | 0.456101i | ||||
\(471\) | − | 2.62747e31i | − | 0.220438i | ||||||
\(472\) | −1.53493e32 | − | 1.55453e32i | −1.25541 | − | 1.27144i | ||||
\(473\) | 3.26410e31 | 0.260273 | ||||||||
\(474\) | −1.66250e31 | + | 6.15247e31i | −0.129247 | + | 0.478310i | ||||
\(475\) | 1.60615e32i | 1.21748i | ||||||||
\(476\) | −1.51630e32 | + | 2.60085e32i | −1.12073 | + | 1.92234i | ||||
\(477\) | 6.07729e31 | 0.438015 | ||||||||
\(478\) | 1.15193e32 | + | 3.11271e31i | 0.809640 | + | 0.218778i | ||||
\(479\) | − | 2.62105e31i | − | 0.179659i | −0.995957 | − | 0.0898296i | \(-0.971368\pi\) | ||
0.995957 | − | 0.0898296i | \(-0.0286322\pi\) | |||||||
\(480\) | −2.07990e31 | − | 8.10406e31i | −0.139043 | − | 0.541761i | ||||
\(481\) | −1.13761e30 | −0.00741744 | ||||||||
\(482\) | −5.85282e31 | + | 2.16597e32i | −0.372221 | + | 1.37749i | ||||
\(483\) | 2.13102e31i | 0.132197i | ||||||||
\(484\) | −1.35246e32 | − | 7.88487e31i | −0.818426 | − | 0.477145i | ||||
\(485\) | 9.11873e31 | 0.538311 | ||||||||
\(486\) | −1.51987e32 | − | 4.10696e31i | −0.875331 | − | 0.236529i | ||||
\(487\) | 1.67958e32i | 0.943744i | 0.881667 | + | 0.471872i | \(0.156422\pi\) | ||||
−0.881667 | + | 0.471872i | \(0.843578\pi\) | |||||||
\(488\) | 1.38780e32 | − | 1.37031e32i | 0.760834 | − | 0.751242i | ||||
\(489\) | 4.46673e31 | 0.238937 | ||||||||
\(490\) | 1.68662e32 | − | 6.24174e32i | 0.880369 | − | 3.25801i | ||||
\(491\) | 2.06726e32i | 1.05298i | 0.850183 | + | 0.526488i | \(0.176491\pi\) | ||||
−0.850183 | + | 0.526488i | \(0.823509\pi\) | |||||||
\(492\) | 1.48020e31 | − | 2.53893e31i | 0.0735766 | − | 0.126203i | ||||
\(493\) | −1.47012e31 | −0.0713164 | ||||||||
\(494\) | 8.95586e31 | + | 2.42002e31i | 0.424018 | + | 0.114577i | ||||
\(495\) | − | 6.59864e31i | − | 0.304924i | ||||||
\(496\) | −1.20044e32 | + | 6.79602e31i | −0.541452 | + | 0.306531i | ||||
\(497\) | −1.79003e32 | −0.788102 | ||||||||
\(498\) | −1.24057e31 | + | 4.59101e31i | −0.0533173 | + | 0.197313i | ||||
\(499\) | 7.08999e31i | 0.297467i | 0.988877 | + | 0.148734i | \(0.0475197\pi\) | ||||
−0.988877 | + | 0.148734i | \(0.952480\pi\) | |||||||
\(500\) | −1.13270e32 | − | 6.60369e31i | −0.463955 | − | 0.270487i | ||||
\(501\) | 8.64588e31 | 0.345746 | ||||||||
\(502\) | −7.68302e31 | − | 2.07608e31i | −0.299977 | − | 0.0810587i | ||||
\(503\) | − | 2.66560e32i | − | 1.01620i | −0.861298 | − | 0.508099i | \(-0.830348\pi\) | ||
0.861298 | − | 0.508099i | \(-0.169652\pi\) | |||||||
\(504\) | 2.92761e32 | + | 2.96499e32i | 1.08980 | + | 1.10372i | ||||
\(505\) | 4.73159e32 | 1.71993 | ||||||||
\(506\) | 3.41455e30 | − | 1.26363e31i | 0.0121207 | − | 0.0448555i | ||||
\(507\) | − | 8.02679e31i | − | 0.278257i | ||||||
\(508\) | 1.52204e32 | − | 2.61070e32i | 0.515303 | − | 0.883877i | ||||
\(509\) | −2.56748e30 | −0.00848973 | −0.00424487 | − | 0.999991i | \(-0.501351\pi\) | ||||
−0.00424487 | + | 0.999991i | \(0.501351\pi\) | |||||||
\(510\) | 2.07920e32 | + | 5.61835e31i | 0.671513 | + | 0.181454i | ||||
\(511\) | 6.02773e31i | 0.190153i | ||||||||
\(512\) | −2.25061e32 | − | 2.33794e32i | −0.693523 | − | 0.720434i | ||||
\(513\) | −2.04012e32 | −0.614112 | ||||||||
\(514\) | −1.13152e32 | + | 4.18746e32i | −0.332740 | + | 1.23138i | ||||
\(515\) | 3.93254e32i | 1.12976i | ||||||||
\(516\) | 1.27387e32 | + | 7.42671e31i | 0.357544 | + | 0.208449i | ||||
\(517\) | −9.54199e31 | −0.261669 | ||||||||
\(518\) | −9.81564e30 | − | 2.65235e30i | −0.0263004 | − | 0.00710680i | ||||
\(519\) | 2.31316e32i | 0.605616i | ||||||||
\(520\) | −2.07722e32 | + | 2.05103e32i | −0.531425 | + | 0.524725i | ||||
\(521\) | −4.01252e32 | −1.00315 | −0.501574 | − | 0.865115i | \(-0.667246\pi\) | ||||
−0.501574 | + | 0.865115i | \(0.667246\pi\) | |||||||
\(522\) | −5.30778e30 | + | 1.96427e31i | −0.0129678 | + | 0.0479904i | ||||
\(523\) | − | 7.13294e32i | − | 1.70313i | −0.524248 | − | 0.851566i | \(-0.675653\pi\) | ||
0.524248 | − | 0.851566i | \(-0.324347\pi\) | |||||||
\(524\) | −9.82165e31 | + | 1.68467e32i | −0.229197 | + | 0.393132i | ||||
\(525\) | −3.86465e32 | −0.881451 | ||||||||
\(526\) | −6.48864e32 | − | 1.75334e32i | −1.44652 | − | 0.390874i | ||||
\(527\) | − | 3.55104e32i | − | 0.773798i | ||||||
\(528\) | 1.93603e31 | + | 3.41978e31i | 0.0412388 | + | 0.0728436i | ||||
\(529\) | 4.60555e32 | 0.958988 | ||||||||
\(530\) | −9.92669e31 | + | 3.67360e32i | −0.202066 | + | 0.747794i | ||||
\(531\) | − | 7.78347e32i | − | 1.54895i | ||||||
\(532\) | 7.16313e32 | + | 4.17612e32i | 1.39368 | + | 0.812520i | ||||
\(533\) | −1.02539e32 | −0.195058 | ||||||||
\(534\) | −1.19803e32 | − | 3.23728e31i | −0.222829 | − | 0.0602122i | ||||
\(535\) | 3.91429e32i | 0.711881i | ||||||||
\(536\) | 3.90858e32 | + | 3.95848e32i | 0.695090 | + | 0.703965i | ||||
\(537\) | 2.64802e32 | 0.460500 | ||||||||
\(538\) | 1.03818e31 | − | 3.84203e31i | 0.0176557 | − | 0.0653391i | ||||
\(539\) | 3.03684e32i | 0.505076i | ||||||||
\(540\) | 3.23326e32 | − | 5.54587e32i | 0.525915 | − | 0.902080i | ||||
\(541\) | −9.97054e32 | −1.58618 | −0.793088 | − | 0.609107i | \(-0.791528\pi\) | ||||
−0.793088 | + | 0.609107i | \(0.791528\pi\) | |||||||
\(542\) | −1.71310e32 | − | 4.62908e31i | −0.266557 | − | 0.0720283i | ||||
\(543\) | − | 2.97702e32i | − | 0.453089i | ||||||
\(544\) | 8.09157e32 | − | 2.07670e32i | 1.20461 | − | 0.309162i | ||||
\(545\) | 6.35795e32 | 0.925890 | ||||||||
\(546\) | −5.82296e31 | + | 2.15492e32i | −0.0829530 | + | 0.306987i | ||||
\(547\) | 8.77146e32i | 1.22243i | 0.791464 | + | 0.611215i | \(0.209319\pi\) | ||||
−0.791464 | + | 0.611215i | \(0.790681\pi\) | |||||||
\(548\) | −8.30284e32 | − | 4.84058e32i | −1.13204 | − | 0.659979i | ||||
\(549\) | 6.94867e32 | 0.926901 | ||||||||
\(550\) | 2.29163e32 | + | 6.19237e31i | 0.299083 | + | 0.0808173i | ||||
\(551\) | 4.04893e31i | 0.0517037i | ||||||||
\(552\) | 4.20770e31 | − | 4.15465e31i | 0.0525746 | − | 0.0519118i | ||||
\(553\) | 1.98740e33 | 2.42987 | ||||||||
\(554\) | 3.46372e32 | − | 1.28183e33i | 0.414406 | − | 1.53361i | ||||
\(555\) | 7.27399e30i | 0.00851641i | ||||||||
\(556\) | 4.77473e32 | − | 8.18990e32i | 0.547081 | − | 0.938385i | ||||
\(557\) | −1.54101e33 | −1.72799 | −0.863997 | − | 0.503497i | \(-0.832047\pi\) | ||||
−0.863997 | + | 0.503497i | \(0.832047\pi\) | |||||||
\(558\) | −4.74464e32 | − | 1.28208e32i | −0.520706 | − | 0.140703i | ||||
\(559\) | − | 5.14477e32i | − | 0.552617i | ||||||
\(560\) | −2.27048e33 | + | 1.28538e33i | −2.38705 | + | 1.35137i | ||||
\(561\) | −1.01161e32 | −0.104102 | ||||||||
\(562\) | −3.88941e31 | + | 1.43937e32i | −0.0391785 | + | 0.144989i | ||||
\(563\) | 7.04341e32i | 0.694516i | 0.937770 | + | 0.347258i | \(0.112887\pi\) | ||||
−0.937770 | + | 0.347258i | \(0.887113\pi\) | |||||||
\(564\) | −3.72393e32 | − | 2.17106e32i | −0.359461 | − | 0.209567i | ||||
\(565\) | −1.54711e33 | −1.46197 | ||||||||
\(566\) | 1.26118e33 | + | 3.40791e32i | 1.16675 | + | 0.315276i | ||||
\(567\) | 1.22162e33i | 1.10647i | ||||||||
\(568\) | 3.48985e32 | + | 3.53441e32i | 0.309476 | + | 0.313427i | ||||
\(569\) | 1.12962e32 | 0.0980813 | 0.0490406 | − | 0.998797i | \(-0.484384\pi\) | ||||
0.0490406 | + | 0.998797i | \(0.484384\pi\) | |||||||
\(570\) | 1.54738e32 | − | 5.72644e32i | 0.131552 | − | 0.486840i | ||||
\(571\) | 4.43464e32i | 0.369169i | 0.982817 | + | 0.184584i | \(0.0590939\pi\) | ||||
−0.982817 | + | 0.184584i | \(0.940906\pi\) | |||||||
\(572\) | 6.90571e31 | − | 1.18451e32i | 0.0562932 | − | 0.0965574i | ||||
\(573\) | 1.66463e32 | 0.132881 | ||||||||
\(574\) | −8.84736e32 | − | 2.39070e32i | −0.691625 | − | 0.186889i | ||||
\(575\) | − | 3.57192e32i | − | 0.273456i | ||||||
\(576\) | 1.46683e31 | − | 1.15612e33i | 0.0109979 | − | 0.866825i | ||||
\(577\) | 4.76894e32 | 0.350197 | 0.175098 | − | 0.984551i | \(-0.443976\pi\) | ||||
0.175098 | + | 0.984551i | \(0.443976\pi\) | |||||||
\(578\) | −1.98273e32 | + | 7.33757e32i | −0.142604 | + | 0.527737i | ||||
\(579\) | 9.04028e32i | 0.636853i | ||||||||
\(580\) | −1.10066e32 | − | 6.41690e31i | −0.0759484 | − | 0.0442781i | ||||
\(581\) | 1.48301e33 | 1.00237 | ||||||||
\(582\) | −1.86785e32 | − | 5.04724e31i | −0.123670 | − | 0.0334178i | ||||
\(583\) | − | 1.78735e32i | − | 0.115927i | ||||||
\(584\) | 1.19018e32 | − | 1.17517e32i | 0.0756237 | − | 0.0746703i | ||||
\(585\) | −1.04005e33 | −0.647420 | ||||||||
\(586\) | −3.34407e32 | + | 1.23755e33i | −0.203941 | + | 0.754730i | ||||
\(587\) | − | 1.12430e33i | − | 0.671778i | −0.941902 | − | 0.335889i | \(-0.890963\pi\) | ||
0.941902 | − | 0.335889i | \(-0.109037\pi\) | |||||||
\(588\) | −6.90963e32 | + | 1.18518e33i | −0.404508 | + | 0.693835i | ||||
\(589\) | −9.78010e32 | −0.560996 | ||||||||
\(590\) | 4.70496e33 | + | 1.27136e33i | 2.64443 | + | 0.714568i | ||||
\(591\) | − | 4.89029e32i | − | 0.269330i | ||||||
\(592\) | 1.38996e31 | + | 2.45521e31i | 0.00750139 | + | 0.0132504i | ||||
\(593\) | −9.54143e32 | −0.504612 | −0.252306 | − | 0.967648i | \(-0.581189\pi\) | ||||
−0.252306 | + | 0.967648i | \(0.581189\pi\) | |||||||
\(594\) | −7.86551e31 | + | 2.91082e32i | −0.0407652 | + | 0.150861i | ||||
\(595\) | − | 6.71633e33i | − | 3.41137i | ||||||
\(596\) | −8.56362e32 | − | 4.99262e32i | −0.426287 | − | 0.248527i | ||||
\(597\) | 1.31751e33 | 0.642779 | ||||||||
\(598\) | −1.99170e32 | − | 5.38190e31i | −0.0952378 | − | 0.0257349i | ||||
\(599\) | − | 4.00768e32i | − | 0.187833i | −0.995580 | − | 0.0939163i | \(-0.970061\pi\) | ||
0.995580 | − | 0.0939163i | \(-0.0299386\pi\) | |||||||
\(600\) | 7.53456e32 | + | 7.63076e32i | 0.346133 | + | 0.350552i | ||||
\(601\) | 6.35675e31 | 0.0286247 | 0.0143124 | − | 0.999898i | \(-0.495444\pi\) | ||||
0.0143124 | + | 0.999898i | \(0.495444\pi\) | |||||||
\(602\) | 1.19950e33 | − | 4.43904e33i | 0.529473 | − | 1.95944i | ||||
\(603\) | 1.98200e33i | 0.857620i | ||||||||
\(604\) | −2.10906e33 | + | 3.61759e33i | −0.894636 | + | 1.53453i | ||||
\(605\) | 3.49254e33 | 1.45237 | ||||||||
\(606\) | −9.69202e32 | − | 2.61895e32i | −0.395133 | − | 0.106771i | ||||
\(607\) | 1.65365e33i | 0.660966i | 0.943812 | + | 0.330483i | \(0.107212\pi\) | ||||
−0.943812 | + | 0.330483i | \(0.892788\pi\) | |||||||
\(608\) | −5.71954e32 | − | 2.22854e33i | −0.224139 | − | 0.873330i | ||||
\(609\) | −9.74237e31 | −0.0374332 | ||||||||
\(610\) | −1.13500e33 | + | 4.20034e33i | −0.427601 | + | 1.58244i | ||||
\(611\) | 1.50398e33i | 0.555580i | ||||||||
\(612\) | 2.57126e33 | + | 1.49905e33i | 0.931386 | + | 0.543000i | ||||
\(613\) | −5.09843e33 | −1.81097 | −0.905483 | − | 0.424382i | \(-0.860491\pi\) | ||||
−0.905483 | + | 0.424382i | \(0.860491\pi\) | |||||||
\(614\) | −9.19990e32 | − | 2.48597e32i | −0.320452 | − | 0.0865915i | ||||
\(615\) | 6.55643e32i | 0.223958i | ||||||||
\(616\) | 8.72012e32 | − | 8.61018e32i | 0.292115 | − | 0.288432i | ||||
\(617\) | −1.67729e31 | −0.00551044 | −0.00275522 | − | 0.999996i | \(-0.500877\pi\) | ||||
−0.00275522 | + | 0.999996i | \(0.500877\pi\) | |||||||
\(618\) | 2.17667e32 | − | 8.05527e32i | 0.0701343 | − | 0.259548i | ||||
\(619\) | 1.29014e32i | 0.0407709i | 0.999792 | + | 0.0203855i | \(0.00648934\pi\) | ||||
−0.999792 | + | 0.0203855i | \(0.993511\pi\) | |||||||
\(620\) | 1.54999e33 | − | 2.65863e33i | 0.480427 | − | 0.824056i | ||||
\(621\) | 4.53704e32 | 0.137935 | ||||||||
\(622\) | −1.32093e33 | − | 3.56939e32i | −0.393910 | − | 0.106441i | ||||
\(623\) | 3.86993e33i | 1.13200i | ||||||||
\(624\) | 5.39015e32 | − | 3.05151e32i | 0.154663 | − | 0.0875588i | ||||
\(625\) | −1.87220e33 | −0.526978 | ||||||||
\(626\) | −1.01736e33 | + | 3.76497e33i | −0.280920 | + | 1.03961i | ||||
\(627\) | 2.78613e32i | 0.0754729i | ||||||||
\(628\) | 1.96413e33 | + | 1.14509e33i | 0.521981 | + | 0.304316i | ||||
\(629\) | −7.26278e31 | −0.0189363 | ||||||||
\(630\) | −8.97387e33 | − | 2.42489e33i | −2.29559 | − | 0.620306i | ||||
\(631\) | − | 6.78727e33i | − | 1.70350i | −0.523947 | − | 0.851751i | \(-0.675541\pi\) | ||
0.523947 | − | 0.851751i | \(-0.324459\pi\) | |||||||
\(632\) | −3.87465e33 | − | 3.92412e33i | −0.954174 | − | 0.966356i | ||||
\(633\) | −8.03899e32 | −0.194248 | ||||||||
\(634\) | 1.54445e33 | − | 5.71559e33i | 0.366187 | − | 1.35516i | ||||
\(635\) | 6.74176e33i | 1.56852i | ||||||||
\(636\) | 4.06669e32 | − | 6.97543e32i | 0.0928445 | − | 0.159252i | ||||
\(637\) | 4.78656e33 | 1.07238 | ||||||||
\(638\) | 5.77696e31 | + | 1.56103e31i | 0.0127014 | + | 0.00343213i | ||||
\(639\) | 1.76967e33i | 0.381839i | ||||||||
\(640\) | 6.96454e33 | + | 1.97708e33i | 1.47480 | + | 0.418662i | ||||
\(641\) | 8.81260e33 | 1.83150 | 0.915751 | − | 0.401745i | \(-0.131596\pi\) | ||||
0.915751 | + | 0.401745i | \(0.131596\pi\) | |||||||
\(642\) | 2.16657e32 | − | 8.01789e32i | 0.0441928 | − | 0.163546i | ||||
\(643\) | 5.83164e33i | 1.16751i | 0.811931 | + | 0.583753i | \(0.198416\pi\) | ||||
−0.811931 | + | 0.583753i | \(0.801584\pi\) | |||||||
\(644\) | −1.59301e33 | − | 9.28730e32i | −0.313032 | − | 0.182498i | ||||
\(645\) | −3.28960e33 | −0.634493 | ||||||||
\(646\) | 5.71762e33 | + | 1.54500e33i | 1.08249 | + | 0.292508i | ||||
\(647\) | − | 2.33961e33i | − | 0.434803i | −0.976082 | − | 0.217401i | \(-0.930242\pi\) | ||
0.976082 | − | 0.217401i | \(-0.0697580\pi\) | |||||||
\(648\) | 2.41209e33 | − | 2.38168e33i | 0.440041 | − | 0.434493i | ||||
\(649\) | −2.28914e33 | −0.409954 | ||||||||
\(650\) | 9.76020e32 | − | 3.61199e33i | 0.171593 | − | 0.635018i | ||||
\(651\) | − | 2.35325e33i | − | 0.406158i | ||||||
\(652\) | −1.94667e33 | + | 3.33905e33i | −0.329854 | + | 0.565785i | ||||
\(653\) | 1.66590e32 | 0.0277135 | 0.0138567 | − | 0.999904i | \(-0.495589\pi\) | ||||
0.0138567 | + | 0.999904i | \(0.495589\pi\) | |||||||
\(654\) | −1.30234e33 | − | 3.51914e32i | −0.212712 | − | 0.0574783i | ||||
\(655\) | − | 4.35042e33i | − | 0.697647i | ||||||
\(656\) | 1.25284e33 | + | 2.21301e33i | 0.197266 | + | 0.348447i | ||||
\(657\) | 5.95917e32 | 0.0921301 | ||||||||
\(658\) | −3.50653e33 | + | 1.29767e34i | −0.532312 | + | 1.96994i | ||||
\(659\) | − | 1.15981e34i | − | 1.72887i | −0.502743 | − | 0.864436i | \(-0.667676\pi\) | ||
0.502743 | − | 0.864436i | \(-0.332324\pi\) | |||||||
\(660\) | −7.57383e32 | − | 4.41556e32i | −0.110863 | − | 0.0646337i | ||||
\(661\) | 5.94550e33 | 0.854616 | 0.427308 | − | 0.904106i | \(-0.359462\pi\) | ||||
0.427308 | + | 0.904106i | \(0.359462\pi\) | |||||||
\(662\) | 6.24752e33 | + | 1.68819e33i | 0.881885 | + | 0.238300i | ||||
\(663\) | 1.59447e33i | 0.221031i | ||||||||
\(664\) | −2.89129e33 | − | 2.92820e33i | −0.393617 | − | 0.398643i | ||||
\(665\) | −1.84978e34 | −2.47321 | ||||||||
\(666\) | −2.62218e31 | + | 9.70400e31i | −0.00344328 | + | 0.0127427i | ||||
\(667\) | − | 9.00445e31i | − | 0.0116131i | ||||||
\(668\) | −3.76801e33 | + | 6.46311e33i | −0.477304 | + | 0.818699i | ||||
\(669\) | 5.91628e32 | 0.0736097 | ||||||||
\(670\) | −1.19808e34 | − | 3.23741e33i | −1.46416 | − | 0.395640i | ||||
\(671\) | − | 2.04362e33i | − | 0.245319i | ||||||
\(672\) | 5.36223e33 | − | 1.37621e33i | 0.632286 | − | 0.162276i | ||||
\(673\) | −9.95537e33 | −1.15313 | −0.576563 | − | 0.817053i | \(-0.695606\pi\) | ||||
−0.576563 | + | 0.817053i | \(0.695606\pi\) | |||||||
\(674\) | 1.55737e33 | − | 5.76340e33i | 0.177203 | − | 0.655783i | ||||
\(675\) | 8.22802e33i | 0.919708i | ||||||||
\(676\) | 6.00031e33 | + | 3.49820e33i | 0.658891 | + | 0.384135i | ||||
\(677\) | 5.92405e33 | 0.639080 | 0.319540 | − | 0.947573i | \(-0.396472\pi\) | ||||
0.319540 | + | 0.947573i | \(0.396472\pi\) | |||||||
\(678\) | 3.16904e33 | + | 8.56326e32i | 0.335870 | + | 0.0907576i | ||||
\(679\) | 6.03360e33i | 0.628260i | ||||||||
\(680\) | −1.32614e34 | + | 1.30942e34i | −1.35670 | + | 1.33959i | ||||
\(681\) | −2.30326e33 | −0.231514 | ||||||||
\(682\) | −3.77063e32 | + | 1.39541e33i | −0.0372393 | + | 0.137813i | ||||
\(683\) | − | 1.31966e34i | − | 1.28060i | −0.768125 | − | 0.640300i | \(-0.778810\pi\) | ||
0.768125 | − | 0.640300i | \(-0.221190\pi\) | |||||||
\(684\) | 4.12862e33 | − | 7.08165e33i | 0.393670 | − | 0.675245i | ||||
\(685\) | 2.14409e34 | 2.00889 | ||||||||
\(686\) | 2.25389e34 | + | 6.09038e33i | 2.07512 | + | 0.560731i | ||||
\(687\) | − | 3.99953e33i | − | 0.361849i | ||||||
\(688\) | −1.11035e34 | + | 6.28598e33i | −0.987182 | + | 0.558871i | ||||
\(689\) | −2.81715e33 | −0.246139 | ||||||||
\(690\) | −3.44123e32 | + | 1.27351e33i | −0.0295477 | + | 0.109348i | ||||
\(691\) | − | 1.13536e34i | − | 0.958069i | −0.877796 | − | 0.479035i | \(-0.840987\pi\) | ||
0.877796 | − | 0.479035i | \(-0.159013\pi\) | |||||||
\(692\) | −1.72917e34 | − | 1.00811e34i | −1.43405 | − | 0.836056i | ||||
\(693\) | 4.36613e33 | 0.355875 | ||||||||
\(694\) | 6.59619e33 | + | 1.78240e33i | 0.528420 | + | 0.142788i | ||||
\(695\) | 2.11493e34i | 1.66524i | ||||||||
\(696\) | 1.89938e32 | + | 1.92363e32i | 0.0146995 | + | 0.0148872i | ||||
\(697\) | −6.54633e33 | −0.497971 | ||||||||
\(698\) | 1.43682e33 | − | 5.31727e33i | 0.107433 | − | 0.397579i | ||||
\(699\) | 9.74567e32i | 0.0716284i | ||||||||
\(700\) | 1.68427e34 | − | 2.88896e34i | 1.21685 | − | 2.08721i | ||||
\(701\) | −1.04847e34 | −0.744632 | −0.372316 | − | 0.928106i | \(-0.621436\pi\) | ||||
−0.372316 | + | 0.928106i | \(0.621436\pi\) | |||||||
\(702\) | 4.58793e33 | + | 1.23974e33i | 0.320311 | + | 0.0865533i | ||||
\(703\) | 2.00028e32i | 0.0137286i | ||||||||
\(704\) | −3.40017e33 | − | 4.31397e31i | −0.229418 | − | 0.00291075i | ||||
\(705\) | 9.61654e33 | 0.637895 | ||||||||
\(706\) | 6.18887e33 | − | 2.29033e34i | 0.403603 | − | 1.49363i | ||||
\(707\) | 3.13076e34i | 2.00732i | ||||||||
\(708\) | −8.93376e33 | − | 5.20841e33i | −0.563164 | − | 0.328326i | ||||
\(709\) | 1.25348e34 | 0.776893 | 0.388446 | − | 0.921471i | \(-0.373012\pi\) | ||||
0.388446 | + | 0.921471i | \(0.373012\pi\) | |||||||
\(710\) | −1.06973e34 | − | 2.89059e33i | −0.651889 | − | 0.176151i | ||||
\(711\) | − | 1.96479e34i | − | 1.17728i | ||||||
\(712\) | 7.64118e33 | − | 7.54485e33i | 0.450195 | − | 0.444519i | ||||
\(713\) | 2.17500e33 | 0.126004 | ||||||||
\(714\) | −3.71750e33 | + | 1.37575e34i | −0.211774 | + | 0.783719i | ||||
\(715\) | 3.05883e33i | 0.171349i | ||||||||
\(716\) | −1.15405e34 | + | 1.97949e34i | −0.635722 | + | 1.09043i | ||||
\(717\) | 5.64836e33 | 0.305980 | ||||||||
\(718\) | −2.92673e34 | − | 7.90850e33i | −1.55915 | − | 0.421309i | ||||
\(719\) | 1.61198e34i | 0.844527i | 0.906473 | + | 0.422263i | \(0.138764\pi\) | ||||
−0.906473 | + | 0.422263i | \(0.861236\pi\) | |||||||
\(720\) | 1.27076e34 | + | 2.24465e34i | 0.654747 | + | 1.15654i | ||||
\(721\) | −2.60205e34 | −1.31854 | ||||||||
\(722\) | −9.79105e32 | + | 3.62341e33i | −0.0487959 | + | 0.180580i | ||||
\(723\) | 1.06206e34i | 0.520582i | ||||||||
\(724\) | 2.22543e34 | + | 1.29743e34i | 1.07288 | + | 0.625491i | ||||
\(725\) | 1.63298e33 | 0.0774326 | ||||||||
\(726\) | −7.15399e33 | − | 1.93313e33i | −0.333664 | − | 0.0901615i | ||||
\(727\) | 2.04682e33i | 0.0939004i | 0.998897 | + | 0.0469502i | \(0.0149502\pi\) | ||||
−0.998897 | + | 0.0469502i | \(0.985050\pi\) | |||||||
\(728\) | −1.35711e34 | − | 1.37444e34i | −0.612404 | − | 0.620223i | ||||
\(729\) | 6.47906e33 | 0.287595 | ||||||||
\(730\) | −9.73376e32 | + | 3.60221e33i | −0.0425017 | + | 0.157287i | ||||
\(731\) | − | 3.28453e34i | − | 1.41080i | ||||||
\(732\) | 4.64979e33 | − | 7.97559e33i | 0.196472 | − | 0.337000i | ||||
\(733\) | −2.79486e34 | −1.16175 | −0.580875 | − | 0.813993i | \(-0.697290\pi\) | ||||
−0.580875 | + | 0.813993i | \(0.697290\pi\) | |||||||
\(734\) | 2.62823e34 | + | 7.10191e33i | 1.07476 | + | 0.290417i | ||||
\(735\) | − | 3.06056e34i | − | 1.23127i | ||||||
\(736\) | 1.27197e33 | + | 4.95607e33i | 0.0503435 | + | 0.196157i | ||||
\(737\) | 5.82910e33 | 0.226982 | ||||||||
\(738\) | −2.36351e33 | + | 8.74673e33i | −0.0905485 | + | 0.335096i | ||||
\(739\) | 2.97126e34i | 1.11997i | 0.828502 | + | 0.559986i | \(0.189193\pi\) | ||||
−0.828502 | + | 0.559986i | \(0.810807\pi\) | |||||||
\(740\) | −5.43757e32 | − | 3.17012e32i | −0.0201662 | − | 0.0117570i | ||||
\(741\) | 4.39140e33 | 0.160245 | ||||||||
\(742\) | −2.43072e34 | − | 6.56821e33i | −0.872745 | − | 0.235830i | ||||
\(743\) | − | 6.03085e33i | − | 0.213065i | −0.994309 | − | 0.106533i | \(-0.966025\pi\) | ||
0.994309 | − | 0.106533i | \(-0.0339749\pi\) | |||||||
\(744\) | −4.64649e33 | + | 4.58791e33i | −0.161529 | + | 0.159492i | ||||
\(745\) | 2.21144e34 | 0.756484 | ||||||||
\(746\) | −5.54666e33 | + | 2.05267e34i | −0.186709 | + | 0.690961i | ||||
\(747\) | − | 1.46614e34i | − | 0.485655i | ||||||
\(748\) | 4.40876e33 | − | 7.56215e33i | 0.143713 | − | 0.246505i | ||||
\(749\) | −2.58997e34 | −0.830832 | ||||||||
\(750\) | −5.99156e33 | − | 1.61902e33i | −0.189149 | − | 0.0511114i | ||||
\(751\) | − | 2.60544e33i | − | 0.0809471i | −0.999181 | − | 0.0404735i | \(-0.987113\pi\) | ||
0.999181 | − | 0.0404735i | \(-0.0128866\pi\) | |||||||
\(752\) | 3.24589e34 | − | 1.83759e34i | 0.992476 | − | 0.561868i | ||||
\(753\) | −3.76728e33 | −0.113367 | ||||||||
\(754\) | 2.46045e32 | − | 9.10545e32i | 0.00728715 | − | 0.0269678i | ||||
\(755\) | − | 9.34193e34i | − | 2.72316i | ||||||
\(756\) | 3.66954e34 | + | 2.13935e34i | 1.05281 | + | 0.613792i | ||||
\(757\) | 3.47764e34 | 0.982052 | 0.491026 | − | 0.871145i | \(-0.336622\pi\) | ||||
0.491026 | + | 0.871145i | \(0.336622\pi\) | |||||||
\(758\) | 3.28141e34 | + | 8.86692e33i | 0.912074 | + | 0.246458i | ||||
\(759\) | − | 6.19609e32i | − | 0.0169518i | ||||||
\(760\) | 3.60635e34 | + | 3.65240e34i | 0.971191 | + | 0.983592i | ||||
\(761\) | 2.59400e34 | 0.687629 | 0.343814 | − | 0.939038i | \(-0.388281\pi\) | ||||
0.343814 | + | 0.939038i | \(0.388281\pi\) | |||||||
\(762\) | 3.73158e33 | − | 1.38096e34i | 0.0973718 | − | 0.360347i | ||||
\(763\) | 4.20688e34i | 1.08060i | ||||||||
\(764\) | −7.25474e33 | + | 1.24437e34i | −0.183443 | + | 0.314652i | ||||
\(765\) | −6.63994e34 | −1.65282 | ||||||||
\(766\) | −4.00475e34 | − | 1.08215e34i | −0.981364 | − | 0.265181i | ||||
\(767\) | 3.60806e34i | 0.870422i | ||||||||
\(768\) | −1.31716e34 | − | 7.90465e33i | −0.312826 | − | 0.187736i | ||||
\(769\) | 4.77229e34 | 1.11586 | 0.557932 | − | 0.829887i | \(-0.311595\pi\) | ||||
0.557932 | + | 0.829887i | \(0.311595\pi\) | |||||||
\(770\) | −7.13167e33 | + | 2.63924e34i | −0.164173 | + | 0.607561i | ||||
\(771\) | 2.05327e34i | 0.465365i | ||||||||
\(772\) | −6.75794e34 | − | 3.93989e34i | −1.50802 | − | 0.879178i | ||||
\(773\) | −4.82828e33 | −0.106081 | −0.0530406 | − | 0.998592i | \(-0.516891\pi\) | ||||
−0.0530406 | + | 0.998592i | \(0.516891\pi\) | |||||||
\(774\) | −4.38855e34 | − | 1.18586e34i | −0.949357 | − | 0.256532i | ||||
\(775\) | 3.94441e34i | 0.840160i | ||||||||
\(776\) | 1.19134e34 | − | 1.17632e34i | 0.249858 | − | 0.246708i | ||||
\(777\) | −4.81299e32 | −0.00993946 | ||||||||
\(778\) | 9.37951e33 | − | 3.47111e34i | 0.190733 | − | 0.705851i | ||||
\(779\) | 1.80296e34i | 0.361024i | ||||||||
\(780\) | −6.95966e33 | + | 1.19376e34i | −0.137231 | + | 0.235387i | ||||
\(781\) | 5.20463e33 | 0.101060 | ||||||||
\(782\) | −1.27154e34 | − | 3.43592e33i | −0.243137 | − | 0.0656996i | ||||
\(783\) | 2.07420e33i | 0.0390579i | ||||||||
\(784\) | −5.84832e34 | − | 1.03304e35i | −1.08452 | − | 1.91569i | ||||
\(785\) | −5.07210e34 | −0.926300 | ||||||||
\(786\) | −2.40797e33 | + | 8.91124e33i | −0.0433092 | + | 0.160276i | ||||
\(787\) | 6.83022e34i | 1.20987i | 0.796276 | + | 0.604934i | \(0.206800\pi\) | ||||
−0.796276 | + | 0.604934i | \(0.793200\pi\) | |||||||
\(788\) | 3.65567e34 | + | 2.13126e34i | 0.637753 | + | 0.371811i | ||||
\(789\) | −3.18163e34 | −0.546671 | ||||||||
\(790\) | 1.18768e35 | + | 3.20931e34i | 2.00990 | + | 0.543108i | ||||
\(791\) | − | 1.02368e35i | − | 1.70626i | ||||||
\(792\) | −8.51225e33 | − | 8.62093e33i | −0.139747 | − | 0.141531i | ||||
\(793\) | −3.22109e34 | −0.520864 | ||||||||
\(794\) | 1.09361e34 | − | 4.04717e34i | 0.174188 | − | 0.644623i | ||||
\(795\) | 1.80131e34i | 0.282607i | ||||||||
\(796\) | −5.74192e34 | + | 9.84887e34i | −0.887360 | + | 1.52205i | ||||
\(797\) | 5.98073e34 | 0.910447 | 0.455223 | − | 0.890377i | \(-0.349559\pi\) | ||||
0.455223 | + | 0.890377i | \(0.349559\pi\) | |||||||
\(798\) | 3.78902e34 | + | 1.02386e34i | 0.568189 | + | 0.153534i | ||||
\(799\) | 9.60171e34i | 1.41836i | ||||||||
\(800\) | −8.98794e34 | + | 2.30675e34i | −1.30792 | + | 0.335676i | ||||
\(801\) | 3.82591e34 | 0.548459 | ||||||||
\(802\) | 2.66974e34 | − | 9.87999e34i | 0.377030 | − | 1.39529i | ||||
\(803\) | − | 1.75261e33i | − | 0.0243836i | ||||||
\(804\) | 2.27491e34 | + | 1.32628e34i | 0.311811 | + | 0.181787i | ||||
\(805\) | 4.11374e34 | 0.555502 | ||||||||
\(806\) | 2.19940e34 | + | 5.94314e33i | 0.292606 | + | 0.0790671i | ||||
\(807\) | − | 1.88389e33i | − | 0.0246930i | ||||||
\(808\) | 6.18169e34 | − | 6.10376e34i | 0.798309 | − | 0.788245i | ||||
\(809\) | 1.45996e35 | 1.85763 | 0.928817 | − | 0.370539i | \(-0.120827\pi\) | ||||
0.928817 | + | 0.370539i | \(0.120827\pi\) | |||||||
\(810\) | −1.97270e34 | + | 7.30045e34i | −0.247310 | + | 0.915228i | ||||
\(811\) | − | 5.68147e34i | − | 0.701796i | −0.936414 | − | 0.350898i | \(-0.885876\pi\) | ||
0.936414 | − | 0.350898i | \(-0.114124\pi\) | |||||||
\(812\) | 4.24588e33 | − | 7.28278e33i | 0.0516768 | − | 0.0886390i | ||||
\(813\) | −8.39998e33 | −0.100738 | ||||||||
\(814\) | 2.85397e32 | + | 7.71191e31i | 0.00337254 | + | 0.000911316i | ||||
\(815\) | − | 8.62263e34i | − | 1.00403i | ||||||
\(816\) | 3.44119e34 | − | 1.94815e34i | 0.394845 | − | 0.223533i | ||||
\(817\) | −9.04610e34 | −1.02281 | ||||||||
\(818\) | 2.28250e34 | − | 8.44693e34i | 0.254315 | − | 0.941151i | ||||
\(819\) | − | 6.88174e34i | − | 0.755599i | ||||||
\(820\) | −4.90117e34 | − | 2.85740e34i | −0.530315 | − | 0.309175i | ||||
\(821\) | −1.67574e35 | −1.78685 | −0.893425 | − | 0.449211i | \(-0.851705\pi\) | ||||
−0.893425 | + | 0.449211i | \(0.851705\pi\) | |||||||
\(822\) | −4.39188e34 | − | 1.18676e34i | −0.461519 | − | 0.124710i | ||||
\(823\) | − | 1.19678e35i | − | 1.23942i | −0.784833 | − | 0.619708i | \(-0.787251\pi\) | ||
0.784833 | − | 0.619708i | \(-0.212749\pi\) | |||||||
\(824\) | 5.07298e34 | + | 5.13775e34i | 0.517770 | + | 0.524381i | ||||
\(825\) | 1.12367e34 | 0.113030 | ||||||||
\(826\) | −8.41221e34 | + | 3.11313e35i | −0.833968 | + | 3.08629i | ||||
\(827\) | 1.56867e35i | 1.53273i | 0.642406 | + | 0.766365i | \(0.277936\pi\) | ||||
−0.642406 | + | 0.766365i | \(0.722064\pi\) | |||||||
\(828\) | −9.18167e33 | + | 1.57489e34i | −0.0884214 | + | 0.151666i | ||||
\(829\) | −1.52219e35 | −1.44482 | −0.722412 | − | 0.691463i | \(-0.756967\pi\) | ||||
−0.722412 | + | 0.691463i | \(0.756967\pi\) | |||||||
\(830\) | 8.86253e34 | + | 2.39480e34i | 0.829126 | + | 0.224044i | ||||
\(831\) | − | 6.28532e34i | − | 0.579582i | ||||||
\(832\) | −6.79954e32 | + | 5.35923e34i | −0.00618016 | + | 0.487105i | ||||
\(833\) | 3.05585e35 | 2.73774 | ||||||||
\(834\) | 1.17062e34 | − | 4.33214e34i | 0.103377 | − | 0.382569i | ||||
\(835\) | − | 1.66901e35i | − | 1.45285i | ||||||
\(836\) | −2.08273e34 | − | 1.21424e34i | −0.178714 | − | 0.104191i | ||||
\(837\) | −5.01017e34 | −0.423786 | ||||||||
\(838\) | −6.24792e34 | − | 1.68829e34i | −0.520964 | − | 0.140773i | ||||
\(839\) | 9.92113e34i | 0.815488i | 0.913096 | + | 0.407744i | \(0.133684\pi\) | ||||
−0.913096 | + | 0.407744i | \(0.866316\pi\) | |||||||
\(840\) | −8.78824e34 | + | 8.67745e34i | −0.712116 | + | 0.703138i | ||||
\(841\) | −1.24773e35 | −0.996712 | ||||||||
\(842\) | −1.24723e33 | + | 4.61565e33i | −0.00982200 | + | 0.0363486i | ||||
\(843\) | 7.05777e33i | 0.0547945i | ||||||||
\(844\) | 3.50352e34 | − | 6.00944e34i | 0.268161 | − | 0.459965i | ||||
\(845\) | −1.54950e35 | −1.16926 | ||||||||
\(846\) | 1.28291e35 | + | 3.46664e34i | 0.954448 | + | 0.257908i | ||||
\(847\) | 2.31091e35i | 1.69505i | ||||||||
\(848\) | 3.44206e34 | + | 6.08000e34i | 0.248925 | + | 0.439697i | ||||
\(849\) | 6.18403e34 | 0.440940 | ||||||||
\(850\) | 6.23113e34 | − | 2.30597e35i | 0.438066 | − | 1.62117i | ||||
\(851\) | − | 4.44843e32i | − | 0.00308356i | ||||||
\(852\) | 2.03120e34 | + | 1.18419e34i | 0.138828 | + | 0.0809371i | ||||
\(853\) | 1.95119e35 | 1.31496 | 0.657478 | − | 0.753474i | \(-0.271623\pi\) | ||||
0.657478 | + | 0.753474i | \(0.271623\pi\) | |||||||
\(854\) | −2.77924e35 | − | 7.50998e34i | −1.84685 | − | 0.499050i | ||||
\(855\) | 1.82874e35i | 1.19828i | ||||||||
\(856\) | 5.04944e34 | + | 5.11391e34i | 0.326255 | + | 0.330421i | ||||
\(857\) | −1.51242e35 | −0.963612 | −0.481806 | − | 0.876278i | \(-0.660019\pi\) | ||||
−0.481806 | + | 0.876278i | \(0.660019\pi\) | |||||||
\(858\) | 1.69307e33 | − | 6.26559e33i | 0.0106372 | − | 0.0393654i | ||||
\(859\) | − | 2.46051e35i | − | 1.52443i | −0.647325 | − | 0.762214i | \(-0.724112\pi\) | ||
0.647325 | − | 0.762214i | \(-0.275888\pi\) | |||||||
\(860\) | 1.43366e35 | − | 2.45910e35i | 0.875920 | − | 1.50243i | ||||
\(861\) | −4.33820e34 | −0.261380 | ||||||||
\(862\) | −2.03214e35 | − | 5.49119e34i | −1.20744 | − | 0.326272i | ||||
\(863\) | − | 7.16485e34i | − | 0.419834i | −0.977719 | − | 0.209917i | \(-0.932681\pi\) | ||
0.977719 | − | 0.209917i | \(-0.0673193\pi\) | |||||||
\(864\) | −2.93002e34 | − | 1.14164e35i | −0.169319 | − | 0.659729i | ||||
\(865\) | 4.46535e35 | 2.54485 | ||||||||
\(866\) | −4.68375e34 | + | 1.73333e35i | −0.263257 | + | 0.974243i | ||||
\(867\) | 3.59789e34i | 0.199443i | ||||||||
\(868\) | 1.75914e35 | + | 1.02558e35i | 0.961751 | + | 0.560704i | ||||
\(869\) | −5.77850e34 | −0.311586 | ||||||||
\(870\) | −5.82209e33 | − | 1.57323e33i | −0.0309634 | − | 0.00836682i | ||||
\(871\) | − | 9.18763e34i | − | 0.481932i | ||||||
\(872\) | 8.30649e34 | − | 8.20177e34i | 0.429754 | − | 0.424336i | ||||
\(873\) | 5.96497e34 | 0.304395 | ||||||||
\(874\) | −9.46306e33 | + | 3.50203e34i | −0.0476315 | + | 0.176272i | ||||
\(875\) | 1.93542e35i | 0.960901i | ||||||||
\(876\) | 3.98766e33 | − | 6.83986e33i | 0.0195285 | − | 0.0334964i | ||||
\(877\) | 3.63061e34 | 0.175382 | 0.0876909 | − | 0.996148i | \(-0.472051\pi\) | ||||
0.0876909 | + | 0.996148i | \(0.472051\pi\) | |||||||
\(878\) | −1.20926e35 | − | 3.26762e34i | −0.576215 | − | 0.155703i | ||||
\(879\) | 6.06819e34i | 0.285228i | ||||||||
\(880\) | 6.60158e34 | − | 3.73734e34i | 0.306095 | − | 0.173289i | ||||
\(881\) | −2.46130e35 | −1.12578 | −0.562890 | − | 0.826532i | \(-0.690311\pi\) | ||||
−0.562890 | + | 0.826532i | \(0.690311\pi\) | |||||||
\(882\) | 1.10330e35 | − | 4.08300e35i | 0.497816 | − | 1.84228i | ||||
\(883\) | 3.13688e35i | 1.39627i | 0.715966 | + | 0.698135i | \(0.245986\pi\) | ||||
−0.715966 | + | 0.698135i | \(0.754014\pi\) | |||||||
\(884\) | −1.19192e35 | − | 6.94893e34i | −0.523384 | − | 0.305134i | ||||
\(885\) | 2.30702e35 | 0.999384 | ||||||||
\(886\) | 2.24187e35 | + | 6.05790e34i | 0.958087 | + | 0.258891i | ||||
\(887\) | 2.52387e35i | 1.06410i | 0.846712 | + | 0.532052i | \(0.178579\pi\) | ||||
−0.846712 | + | 0.532052i | \(0.821421\pi\) | |||||||
\(888\) | 9.38345e32 | + | 9.50326e32i | 0.00390308 | + | 0.00395291i | ||||
\(889\) | −4.46083e35 | −1.83061 | ||||||||
\(890\) | −6.24927e34 | + | 2.31269e35i | −0.253017 | + | 0.936347i | ||||
\(891\) | − | 3.55194e34i | − | 0.141884i | ||||||
\(892\) | −2.57841e34 | + | 4.42263e34i | −0.101619 | + | 0.174302i | ||||
\(893\) | 2.64446e35 | 1.02830 | ||||||||
\(894\) | −4.52983e34 | − | 1.22404e34i | −0.173793 | − | 0.0469617i | ||||
\(895\) | − | 5.11176e35i | − | 1.93506i | ||||||
\(896\) | −1.30817e35 | + | 4.60823e35i | −0.488618 | + | 1.72123i | ||||
\(897\) | −9.76607e33 | −0.0359924 | ||||||||
\(898\) | −3.65316e34 | + | 1.35194e35i | −0.132847 | + | 0.491632i | ||||
\(899\) | 9.94346e33i | 0.0356797i | ||||||||
\(900\) | −2.85610e35 | − | 1.66512e35i | −1.01126 | − | 0.589569i | ||||
\(901\) | −1.79853e35 | −0.628378 | ||||||||
\(902\) | 2.57244e34 | + | 6.95115e33i | 0.0886882 | + | 0.0239650i | ||||
\(903\) | − | 2.17663e35i | − | 0.740513i | ||||||
\(904\) | −2.02125e35 | + | 1.99577e35i | −0.678577 | + | 0.670022i | ||||
\(905\) | −5.74686e35 | −1.90392 | ||||||||
\(906\) | −5.17078e34 | + | 1.91357e35i | −0.169051 | + | 0.625612i | ||||
\(907\) | − | 1.65415e35i | − | 0.533688i | −0.963740 | − | 0.266844i | \(-0.914019\pi\) | ||
0.963740 | − | 0.266844i | \(-0.0859809\pi\) | |||||||
\(908\) | 1.00380e35 | − | 1.72177e35i | 0.319606 | − | 0.548208i | ||||
\(909\) | 3.09515e35 | 0.972557 | ||||||||
\(910\) | 4.15988e35 | + | 1.12407e35i | 1.28998 | + | 0.348575i | ||||
\(911\) | − | 5.66140e35i | − | 1.73262i | −0.499508 | − | 0.866309i | \(-0.666486\pi\) | ||
0.499508 | − | 0.866309i | \(-0.333514\pi\) | |||||||
\(912\) | −5.36551e34 | − | 9.47756e34i | −0.162059 | − | 0.286259i | ||||
\(913\) | −4.31196e34 | −0.128536 | ||||||||
\(914\) | −3.92560e33 | + | 1.45276e34i | −0.0115492 | + | 0.0427405i | ||||
\(915\) | 2.05959e35i | 0.598036i | ||||||||
\(916\) | 2.98979e35 | + | 1.74306e35i | 0.856831 | + | 0.499535i | ||||
\(917\) | 2.87855e35 | 0.814219 | ||||||||
\(918\) | 2.92903e35 | + | 7.91474e34i | 0.817734 | + | 0.220966i | ||||
\(919\) | 3.94277e35i | 1.08646i | 0.839583 | + | 0.543231i | \(0.182799\pi\) | ||||
−0.839583 | + | 0.543231i | \(0.817201\pi\) | |||||||
\(920\) | −8.02018e34 | − | 8.12258e34i | −0.218137 | − | 0.220923i | ||||
\(921\) | −4.51107e34 | −0.121105 | ||||||||
\(922\) | −4.71909e33 | + | 1.74641e34i | −0.0125051 | + | 0.0462780i | ||||
\(923\) | − | 8.20336e34i | − | 0.214571i | ||||||
\(924\) | 2.92165e34 | − | 5.01138e34i | 0.0754336 | − | 0.129388i | ||||
\(925\) | 8.06733e33 | 0.0205603 | ||||||||
\(926\) | −4.20910e35 | − | 1.13737e35i | −1.05891 | − | 0.286134i | ||||
\(927\) | 2.57245e35i | 0.638837i | ||||||||
\(928\) | −2.26577e34 | + | 5.81508e33i | −0.0555443 | + | 0.0142554i | ||||
\(929\) | 5.30490e35 | 1.28377 | 0.641887 | − | 0.766800i | \(-0.278152\pi\) | ||||
0.641887 | + | 0.766800i | \(0.278152\pi\) | |||||||
\(930\) | 3.80009e34 | − | 1.40631e35i | 0.0907817 | − | 0.335959i | ||||
\(931\) | − | 8.41627e35i | − | 1.98483i | ||||||
\(932\) | −7.28524e34 | − | 4.24731e34i | −0.169611 | − | 0.0988834i | ||||
\(933\) | −6.47705e34 | −0.148867 | ||||||||
\(934\) | 6.95055e35 | + | 1.87815e35i | 1.57709 | + | 0.426156i | ||||
\(935\) | 1.95282e35i | 0.437445i | ||||||||
\(936\) | −1.35880e35 | + | 1.34167e35i | −0.300501 | + | 0.296713i | ||||
\(937\) | 5.17858e35 | 1.13067 | 0.565334 | − | 0.824862i | \(-0.308747\pi\) | ||||
0.565334 | + | 0.824862i | \(0.308747\pi\) | |||||||
\(938\) | 2.14210e35 | − | 7.92734e35i | 0.461749 | − | 1.70881i | ||||
\(939\) | 1.84611e35i | 0.392890i | ||||||||
\(940\) | −4.19104e35 | + | 7.18871e35i | −0.880617 | + | 1.51049i | ||||
\(941\) | −1.91164e35 | −0.396579 | −0.198290 | − | 0.980143i | \(-0.563539\pi\) | ||||
−0.198290 | + | 0.980143i | \(0.563539\pi\) | |||||||
\(942\) | 1.03895e35 | + | 2.80742e34i | 0.212806 | + | 0.0575037i | ||||
\(943\) | − | 4.00961e34i | − | 0.0810889i | ||||||
\(944\) | 7.78694e35 | − | 4.40840e35i | 1.55490 | − | 0.880273i | ||||
\(945\) | −9.47610e35 | −1.86831 | ||||||||
\(946\) | −3.48765e34 | + | 1.29068e35i | −0.0678952 | + | 0.251262i | ||||
\(947\) | 8.39380e35i | 1.61346i | 0.590918 | + | 0.806732i | \(0.298766\pi\) | ||||
−0.590918 | + | 0.806732i | \(0.701234\pi\) | |||||||
\(948\) | −2.25516e35 | − | 1.31477e35i | −0.428033 | − | 0.249545i | ||||
\(949\) | −2.76240e34 | −0.0517717 | ||||||||
\(950\) | −6.35100e35 | − | 1.71615e35i | −1.17533 | − | 0.317593i | ||||
\(951\) | − | 2.80258e35i | − | 0.512143i | ||||||
\(952\) | −8.66407e35 | − | 8.77470e35i | −1.56343 | − | 1.58339i | ||||
\(953\) | −5.98415e35 | −1.06632 | −0.533161 | − | 0.846014i | \(-0.678996\pi\) | ||||
−0.533161 | + | 0.846014i | \(0.678996\pi\) | |||||||
\(954\) | −6.49350e34 | + | 2.40307e35i | −0.114261 | + | 0.422849i | ||||
\(955\) | − | 3.21343e35i | − | 0.558378i | ||||||
\(956\) | −2.46165e35 | + | 4.22236e35i | −0.422407 | + | 0.724536i | ||||
\(957\) | 2.83267e33 | 0.00480012 | ||||||||
\(958\) | 1.03641e35 | + | 2.80056e34i | 0.173439 | + | 0.0468661i | ||||
\(959\) | 1.41869e36i | 2.34457i | ||||||||
\(960\) | 3.42673e35 | + | 4.34768e33i | 0.559274 | + | 0.00709582i | ||||
\(961\) | 3.80231e35 | 0.612868 | ||||||||
\(962\) | 1.21552e33 | − | 4.49833e33i | 0.00193492 | − | 0.00716062i | ||||
\(963\) | 2.56051e35i | 0.402542i | ||||||||
\(964\) | −7.93928e35 | − | 4.62862e35i | −1.23270 | − | 0.718666i | ||||
\(965\) | 1.74514e36 | 2.67611 | ||||||||
\(966\) | −8.42643e34 | − | 2.27696e34i | −0.127620 | − | 0.0344850i | ||||
\(967\) | 2.56168e35i | 0.383183i | 0.981475 | + | 0.191592i | \(0.0613649\pi\) | ||||
−0.981475 | + | 0.191592i | \(0.938635\pi\) | |||||||
\(968\) | 4.56290e35 | − | 4.50538e35i | 0.674120 | − | 0.665621i | ||||
\(969\) | 2.80357e35 | 0.409097 | ||||||||
\(970\) | −9.74324e34 | + | 3.60571e35i | −0.140424 | + | 0.519673i | ||||
\(971\) | − | 4.97178e33i | − | 0.00707752i | −0.999994 | − | 0.00353876i | \(-0.998874\pi\) | ||
0.999994 | − | 0.00353876i | \(-0.00112643\pi\) | |||||||
\(972\) | 3.24793e35 | − | 5.57104e35i | 0.456679 | − | 0.783323i | ||||
\(973\) | −1.39939e36 | −1.94350 | ||||||||
\(974\) | −6.64138e35 | − | 1.79461e35i | −0.911069 | − | 0.246186i | ||||
\(975\) | − | 1.77110e35i | − | 0.239987i | ||||||
\(976\) | 3.93559e35 | + | 6.95178e35i | 0.526759 | + | 0.930460i | ||||
\(977\) | −3.29818e35 | −0.436054 | −0.218027 | − | 0.975943i | \(-0.569962\pi\) | ||||
−0.218027 | + | 0.975943i | \(0.569962\pi\) | |||||||
\(978\) | −4.77264e34 | + | 1.76623e35i | −0.0623294 | + | 0.230664i | ||||
\(979\) | − | 1.12521e35i | − | 0.145158i | ||||||
\(980\) | 2.28788e36 | + | 1.33384e36i | 2.91555 | + | 1.69978i | ||||
\(981\) | 4.15902e35 | 0.523556 | ||||||||
\(982\) | −8.17434e35 | − | 2.20884e35i | −1.01652 | − | 0.274680i | ||||
\(983\) | − | 1.26798e36i | − | 1.55765i | −0.627243 | − | 0.778824i | \(-0.715817\pi\) | ||
0.627243 | − | 0.778824i | \(-0.284183\pi\) | |||||||
\(984\) | 8.45780e34 | + | 8.56579e34i | 0.102640 | + | 0.103950i | ||||
\(985\) | −9.44027e35 | −1.13175 | ||||||||
\(986\) | 1.57080e34 | − | 5.81312e34i | 0.0186037 | − | 0.0688472i | ||||
\(987\) | 6.36299e35i | 0.744483i | ||||||||
\(988\) | −1.91384e35 | + | 3.28273e35i | −0.221219 | + | 0.379448i | ||||
\(989\) | 2.01177e35 | 0.229732 | ||||||||
\(990\) | 2.60922e35 | + | 7.05055e34i | 0.294367 | + | 0.0795428i | ||||
\(991\) | − | 1.23594e36i | − | 1.37757i | −0.724967 | − | 0.688783i | \(-0.758145\pi\) | ||
0.724967 | − | 0.688783i | \(-0.241855\pi\) | |||||||
\(992\) | −1.40462e35 | − | 5.47290e35i | −0.154674 | − | 0.602667i | ||||
\(993\) | 3.06340e35 | 0.333283 | ||||||||
\(994\) | 1.91262e35 | − | 7.07809e35i | 0.205585 | − | 0.760815i | ||||
\(995\) | − | 2.54333e36i | − | 2.70101i | ||||||
\(996\) | −1.68282e35 | − | 9.81086e34i | −0.176573 | − | 0.102943i | ||||
\(997\) | 1.52773e36 | 1.58381 | 0.791906 | − | 0.610643i | \(-0.209089\pi\) | ||||
0.791906 | + | 0.610643i | \(0.209089\pi\) | |||||||
\(998\) | −2.80351e35 | − | 7.57556e34i | −0.287168 | − | 0.0775976i | ||||
\(999\) | 1.02471e34i | 0.0103709i |
(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 | 4.25.b.b.3.6 | yes | 10 | |
3.2 | odd | 2 | 36.25.d.b.19.5 | 10 | |||
4.3 | odd | 2 | inner | 4.25.b.b.3.5 | ✓ | 10 | |
8.3 | odd | 2 | 64.25.c.d.63.6 | 10 | |||
8.5 | even | 2 | 64.25.c.d.63.5 | 10 | |||
12.11 | even | 2 | 36.25.d.b.19.6 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4.25.b.b.3.5 | ✓ | 10 | 4.3 | odd | 2 | inner | |
4.25.b.b.3.6 | yes | 10 | 1.1 | even | 1 | trivial | |
36.25.d.b.19.5 | 10 | 3.2 | odd | 2 | |||
36.25.d.b.19.6 | 10 | 12.11 | even | 2 | |||
64.25.c.d.63.5 | 10 | 8.5 | even | 2 | |||
64.25.c.d.63.6 | 10 | 8.3 | odd | 2 |