Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8,14,Mod(5,8)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8.5");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8 = 2^{3} \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 8.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: | \(8.57847431615\) |
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: | \( x^{10} - 5 x^{9} + 752 x^{8} + 708 x^{7} - 743866 x^{6} + 96647426 x^{5} + 2540283092 x^{4} - 180067834748 x^{3} + 15101451375489 x^{2} + \cdots + 31\!\cdots\!68 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{48}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 5.2 | ||
Root | \(-46.7129 + 17.5509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8.5 |
Dual form | 8.14.b.b.5.1 |
$q$-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 \(\left(\mathbb{Z}/8\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(7\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −83.4258 | + | 35.1018i | −0.921734 | + | 0.387823i | ||||
\(3\) | 622.159i | 0.492735i | 0.969177 | + | 0.246367i | \(0.0792370\pi\) | ||||
−0.969177 | + | 0.246367i | \(0.920763\pi\) | |||||||
\(4\) | 5727.73 | − | 5856.79i | 0.699186 | − | 0.714940i | ||||
\(5\) | − | 26675.4i | − | 0.763494i | −0.924267 | − | 0.381747i | \(-0.875323\pi\) | ||
0.924267 | − | 0.381747i | \(-0.124677\pi\) | |||||||
\(6\) | −21838.9 | − | 51904.1i | −0.191094 | − | 0.454170i | ||||
\(7\) | 50480.5 | 0.162176 | 0.0810880 | − | 0.996707i | \(-0.474161\pi\) | ||||
0.0810880 | + | 0.996707i | \(0.474161\pi\) | |||||||
\(8\) | −272257. | + | 689661.i | −0.367193 | + | 0.930145i | ||||
\(9\) | 1.20724e6 | 0.757213 | ||||||||
\(10\) | 936352. | + | 2.22541e6i | 0.296101 | + | 0.703738i | ||||
\(11\) | 9.06102e6i | 1.54214i | 0.636749 | + | 0.771071i | \(0.280279\pi\) | ||||
−0.636749 | + | 0.771071i | \(0.719721\pi\) | |||||||
\(12\) | 3.64385e6 | + | 3.56356e6i | 0.352276 | + | 0.344513i | ||||
\(13\) | 8.06792e6i | 0.463586i | 0.972765 | + | 0.231793i | \(0.0744592\pi\) | ||||
−0.972765 | + | 0.231793i | \(0.925541\pi\) | |||||||
\(14\) | −4.21138e6 | + | 1.77195e6i | −0.149483 | + | 0.0628956i | ||||
\(15\) | 1.65963e7 | 0.376200 | ||||||||
\(16\) | −1.49501e6 | − | 6.70922e7i | −0.0222773 | − | 0.999752i | ||||
\(17\) | 5.68106e7 | 0.570836 | 0.285418 | − | 0.958403i | \(-0.407868\pi\) | ||||
0.285418 | + | 0.958403i | \(0.407868\pi\) | |||||||
\(18\) | −1.00715e8 | + | 4.23763e7i | −0.697948 | + | 0.293665i | ||||
\(19\) | 1.06435e8i | 0.519022i | 0.965740 | + | 0.259511i | \(0.0835613\pi\) | ||||
−0.965740 | + | 0.259511i | \(0.916439\pi\) | |||||||
\(20\) | −1.56232e8 | − | 1.52789e8i | −0.545852 | − | 0.533824i | ||||
\(21\) | 3.14069e7i | 0.0799097i | ||||||||
\(22\) | −3.18058e8 | − | 7.55923e8i | −0.598079 | − | 1.42145i | ||||
\(23\) | 6.31214e8 | 0.889090 | 0.444545 | − | 0.895757i | \(-0.353365\pi\) | ||||
0.444545 | + | 0.895757i | \(0.353365\pi\) | |||||||
\(24\) | −4.29078e8 | − | 1.69387e8i | −0.458314 | − | 0.180929i | ||||
\(25\) | 5.09128e8 | 0.417078 | ||||||||
\(26\) | −2.83198e8 | − | 6.73073e8i | −0.179789 | − | 0.427303i | ||||
\(27\) | 1.74302e9i | 0.865839i | ||||||||
\(28\) | 2.89139e8 | − | 2.95653e8i | 0.113391 | − | 0.115946i | ||||
\(29\) | 4.06467e9i | 1.26893i | 0.772951 | + | 0.634465i | \(0.218780\pi\) | ||||
−0.772951 | + | 0.634465i | \(0.781220\pi\) | |||||||
\(30\) | −1.38456e9 | + | 5.82560e8i | −0.346756 | + | 0.145899i | ||||
\(31\) | 5.86986e9 | 1.18789 | 0.593946 | − | 0.804505i | \(-0.297569\pi\) | ||||
0.593946 | + | 0.804505i | \(0.297569\pi\) | |||||||
\(32\) | 2.47978e9 | + | 5.54474e9i | 0.408261 | + | 0.912865i | ||||
\(33\) | −5.63739e9 | −0.759867 | ||||||||
\(34\) | −4.73947e9 | + | 1.99415e9i | −0.526158 | + | 0.221383i | ||||
\(35\) | − | 1.34659e9i | − | 0.123820i | ||||||
\(36\) | 6.91476e9 | − | 7.07055e9i | 0.529433 | − | 0.541361i | ||||
\(37\) | − | 2.97403e10i | − | 1.90561i | −0.303581 | − | 0.952806i | \(-0.598182\pi\) | ||
0.303581 | − | 0.952806i | \(-0.401818\pi\) | |||||||
\(38\) | −3.73605e9 | − | 8.87941e9i | −0.201289 | − | 0.478400i | ||||
\(39\) | −5.01953e9 | −0.228425 | ||||||||
\(40\) | 1.83969e10 | + | 7.26256e9i | 0.710159 | + | 0.280350i | ||||
\(41\) | −5.32006e10 | −1.74913 | −0.874564 | − | 0.484910i | \(-0.838852\pi\) | ||||
−0.874564 | + | 0.484910i | \(0.838852\pi\) | |||||||
\(42\) | −1.10244e9 | − | 2.62015e9i | −0.0309908 | − | 0.0736555i | ||||
\(43\) | 8.32576e9i | 0.200853i | 0.994944 | + | 0.100427i | \(0.0320208\pi\) | ||||
−0.994944 | + | 0.100427i | \(0.967979\pi\) | |||||||
\(44\) | 5.30684e10 | + | 5.18991e10i | 1.10254 | + | 1.07824i | ||||
\(45\) | − | 3.22036e10i | − | 0.578127i | ||||||
\(46\) | −5.26595e10 | + | 2.21567e10i | −0.819504 | + | 0.344810i | ||||
\(47\) | 1.06617e11 | 1.44274 | 0.721372 | − | 0.692548i | \(-0.243512\pi\) | ||||
0.721372 | + | 0.692548i | \(0.243512\pi\) | |||||||
\(48\) | 4.17420e10 | − | 9.30131e8i | 0.492612 | − | 0.0109768i | ||||
\(49\) | −9.43407e10 | −0.973699 | ||||||||
\(50\) | −4.24744e10 | + | 1.78713e10i | −0.384435 | + | 0.161752i | ||||
\(51\) | 3.53452e10i | 0.281270i | ||||||||
\(52\) | 4.72521e10 | + | 4.62109e10i | 0.331436 | + | 0.324133i | ||||
\(53\) | 1.04708e11i | 0.648913i | 0.945901 | + | 0.324457i | \(0.105181\pi\) | ||||
−0.945901 | + | 0.324457i | \(0.894819\pi\) | |||||||
\(54\) | −6.11830e10 | − | 1.45413e11i | −0.335793 | − | 0.798073i | ||||
\(55\) | 2.41706e11 | 1.17742 | ||||||||
\(56\) | −1.37437e10 | + | 3.48144e10i | −0.0595499 | + | 0.150847i | ||||
\(57\) | −6.62194e10 | −0.255740 | ||||||||
\(58\) | −1.42677e11 | − | 3.39098e11i | −0.492121 | − | 1.16962i | ||||
\(59\) | 3.49274e11i | 1.07802i | 0.842298 | + | 0.539011i | \(0.181202\pi\) | ||||
−0.842298 | + | 0.539011i | \(0.818798\pi\) | |||||||
\(60\) | 9.50593e10 | − | 9.72010e10i | 0.263034 | − | 0.268960i | ||||
\(61\) | − | 2.73155e11i | − | 0.678836i | −0.940636 | − | 0.339418i | \(-0.889770\pi\) | ||
0.940636 | − | 0.339418i | \(-0.110230\pi\) | |||||||
\(62\) | −4.89698e11 | + | 2.06042e11i | −1.09492 | + | 0.460692i | ||||
\(63\) | 6.09422e10 | 0.122802 | ||||||||
\(64\) | −4.01508e11 | − | 3.75530e11i | −0.730338 | − | 0.683086i | ||||
\(65\) | 2.15215e11 | 0.353945 | ||||||||
\(66\) | 4.70304e11 | − | 1.97882e11i | 0.700395 | − | 0.294694i | ||||
\(67\) | − | 4.69722e11i | − | 0.634387i | −0.948361 | − | 0.317193i | \(-0.897260\pi\) | ||
0.948361 | − | 0.317193i | \(-0.102740\pi\) | |||||||
\(68\) | 3.25396e11 | − | 3.32727e11i | 0.399120 | − | 0.408113i | ||||
\(69\) | 3.92715e11i | 0.438085i | ||||||||
\(70\) | 4.72675e10 | + | 1.12340e11i | 0.0480204 | + | 0.114129i | ||||
\(71\) | −4.62545e11 | −0.428524 | −0.214262 | − | 0.976776i | \(-0.568735\pi\) | ||||
−0.214262 | + | 0.976776i | \(0.568735\pi\) | |||||||
\(72\) | −3.28680e11 | + | 8.32587e11i | −0.278043 | + | 0.704317i | ||||
\(73\) | 4.02036e11 | 0.310933 | 0.155466 | − | 0.987841i | \(-0.450312\pi\) | ||||
0.155466 | + | 0.987841i | \(0.450312\pi\) | |||||||
\(74\) | 1.04394e12 | + | 2.48111e12i | 0.739041 | + | 1.75647i | ||||
\(75\) | 3.16758e11i | 0.205509i | ||||||||
\(76\) | 6.23366e11 | + | 6.09630e11i | 0.371069 | + | 0.362893i | ||||
\(77\) | 4.57405e11i | 0.250098i | ||||||||
\(78\) | 4.18758e11 | − | 1.76194e11i | 0.210547 | − | 0.0885884i | ||||
\(79\) | −3.34144e12 | −1.54653 | −0.773264 | − | 0.634084i | \(-0.781377\pi\) | ||||
−0.773264 | + | 0.634084i | \(0.781377\pi\) | |||||||
\(80\) | −1.78971e12 | + | 3.98798e10i | −0.763304 | + | 0.0170086i | ||||
\(81\) | 8.40299e11 | 0.330583 | ||||||||
\(82\) | 4.43831e12 | − | 1.86744e12i | 1.61223 | − | 0.678353i | ||||
\(83\) | − | 4.78169e12i | − | 1.60537i | −0.596406 | − | 0.802683i | \(-0.703405\pi\) | ||
0.596406 | − | 0.802683i | \(-0.296595\pi\) | |||||||
\(84\) | 1.83943e11 | + | 1.79890e11i | 0.0571306 | + | 0.0558718i | ||||
\(85\) | − | 1.51544e12i | − | 0.435829i | ||||||
\(86\) | −2.92249e11 | − | 6.94583e11i | −0.0778956 | − | 0.185133i | ||||
\(87\) | −2.52887e12 | −0.625246 | ||||||||
\(88\) | −6.24903e12 | − | 2.46693e12i | −1.43442 | − | 0.566264i | ||||
\(89\) | 3.03971e12 | 0.648331 | 0.324166 | − | 0.946000i | \(-0.394917\pi\) | ||||
0.324166 | + | 0.946000i | \(0.394917\pi\) | |||||||
\(90\) | 1.13040e12 | + | 2.68661e12i | 0.224211 | + | 0.532879i | ||||
\(91\) | 4.07273e11i | 0.0751824i | ||||||||
\(92\) | 3.61543e12 | − | 3.69689e12i | 0.621639 | − | 0.635646i | ||||
\(93\) | 3.65199e12i | 0.585315i | ||||||||
\(94\) | −8.89459e12 | + | 3.74243e12i | −1.32983 | + | 0.559530i | ||||
\(95\) | 2.83919e12 | 0.396270 | ||||||||
\(96\) | −3.44971e12 | + | 1.54281e12i | −0.449800 | + | 0.201164i | ||||
\(97\) | 4.70760e12 | 0.573830 | 0.286915 | − | 0.957956i | \(-0.407370\pi\) | ||||
0.286915 | + | 0.957956i | \(0.407370\pi\) | |||||||
\(98\) | 7.87045e12 | − | 3.31153e12i | 0.897491 | − | 0.377623i | ||||
\(99\) | 1.09388e13i | 1.16773i | ||||||||
\(100\) | 2.91615e12 | − | 2.98185e12i | 0.291615 | − | 0.298185i | ||||
\(101\) | 1.03295e13i | 0.968260i | 0.874996 | + | 0.484130i | \(0.160864\pi\) | ||||
−0.874996 | + | 0.484130i | \(0.839136\pi\) | |||||||
\(102\) | −1.24068e12 | − | 2.94870e12i | −0.109083 | − | 0.259256i | ||||
\(103\) | 3.92826e12 | 0.324159 | 0.162079 | − | 0.986778i | \(-0.448180\pi\) | ||||
0.162079 | + | 0.986778i | \(0.448180\pi\) | |||||||
\(104\) | −5.56413e12 | − | 2.19655e12i | −0.431202 | − | 0.170226i | ||||
\(105\) | 8.37790e11 | 0.0610105 | ||||||||
\(106\) | −3.67543e12 | − | 8.73535e12i | −0.251664 | − | 0.598125i | ||||
\(107\) | 7.39245e12i | 0.476205i | 0.971240 | + | 0.238102i | \(0.0765254\pi\) | ||||
−0.971240 | + | 0.238102i | \(0.923475\pi\) | |||||||
\(108\) | 1.02085e13 | + | 9.98354e12i | 0.619023 | + | 0.605383i | ||||
\(109\) | − | 2.46418e13i | − | 1.40734i | −0.710525 | − | 0.703672i | \(-0.751542\pi\) | ||
0.710525 | − | 0.703672i | \(-0.248458\pi\) | |||||||
\(110\) | −2.01645e13 | + | 8.48431e12i | −1.08526 | + | 0.456629i | ||||
\(111\) | 1.85032e13 | 0.938961 | ||||||||
\(112\) | −7.54687e10 | − | 3.38685e12i | −0.00361285 | − | 0.162136i | ||||
\(113\) | −2.74600e13 | −1.24077 | −0.620384 | − | 0.784298i | \(-0.713023\pi\) | ||||
−0.620384 | + | 0.784298i | \(0.713023\pi\) | |||||||
\(114\) | 5.52440e12 | − | 2.32442e12i | 0.235724 | − | 0.0991819i | ||||
\(115\) | − | 1.68379e13i | − | 0.678814i | ||||||
\(116\) | 2.38059e13 | + | 2.32813e13i | 0.907209 | + | 0.887219i | ||||
\(117\) | 9.73993e12i | 0.351033i | ||||||||
\(118\) | −1.22601e13 | − | 2.91385e13i | −0.418082 | − | 0.993650i | ||||
\(119\) | 2.86783e12 | 0.0925758 | ||||||||
\(120\) | −4.51847e12 | + | 1.14458e13i | −0.138138 | + | 0.349920i | ||||
\(121\) | −4.75794e13 | −1.37820 | ||||||||
\(122\) | 9.58821e12 | + | 2.27881e13i | 0.263268 | + | 0.625706i | ||||
\(123\) | − | 3.30992e13i | − | 0.861856i | ||||||
\(124\) | 3.36210e13 | − | 3.43785e13i | 0.830558 | − | 0.849271i | ||||
\(125\) | − | 4.61439e13i | − | 1.08193i | ||||||
\(126\) | −5.08415e12 | + | 2.13918e12i | −0.113190 | + | 0.0476253i | ||||
\(127\) | −5.26162e12 | −0.111274 | −0.0556372 | − | 0.998451i | \(-0.517719\pi\) | ||||
−0.0556372 | + | 0.998451i | \(0.517719\pi\) | |||||||
\(128\) | 4.66779e13 | + | 1.72353e13i | 0.938094 | + | 0.346381i | ||||
\(129\) | −5.17994e12 | −0.0989673 | ||||||||
\(130\) | −1.79545e13 | + | 7.55442e12i | −0.326243 | + | 0.137268i | ||||
\(131\) | 8.17887e13i | 1.41394i | 0.707246 | + | 0.706968i | \(0.249937\pi\) | ||||
−0.707246 | + | 0.706968i | \(0.750063\pi\) | |||||||
\(132\) | −3.22895e13 | + | 3.30170e13i | −0.531289 | + | 0.543259i | ||||
\(133\) | 5.37288e12i | 0.0841728i | ||||||||
\(134\) | 1.64881e13 | + | 3.91869e13i | 0.246030 | + | 0.584736i | ||||
\(135\) | 4.64956e13 | 0.661063 | ||||||||
\(136\) | −1.54671e13 | + | 3.91800e13i | −0.209607 | + | 0.530960i | ||||
\(137\) | 4.43802e13 | 0.573464 | 0.286732 | − | 0.958011i | \(-0.407431\pi\) | ||||
0.286732 | + | 0.958011i | \(0.407431\pi\) | |||||||
\(138\) | −1.37850e13 | − | 3.27626e13i | −0.169900 | − | 0.403798i | ||||
\(139\) | 2.15053e13i | 0.252901i | 0.991973 | + | 0.126450i | \(0.0403584\pi\) | ||||
−0.991973 | + | 0.126450i | \(0.959642\pi\) | |||||||
\(140\) | −7.88666e12 | − | 7.71288e12i | −0.0885240 | − | 0.0865734i | ||||
\(141\) | 6.63325e13i | 0.710890i | ||||||||
\(142\) | 3.85882e13 | − | 1.62361e13i | 0.394985 | − | 0.166191i | ||||
\(143\) | −7.31036e13 | −0.714915 | ||||||||
\(144\) | −1.80483e12 | − | 8.09965e13i | −0.0168687 | − | 0.757025i | ||||
\(145\) | 1.08426e14 | 0.968820 | ||||||||
\(146\) | −3.35402e13 | + | 1.41122e13i | −0.286597 | + | 0.120587i | ||||
\(147\) | − | 5.86949e13i | − | 0.479775i | ||||||
\(148\) | −1.74183e14 | − | 1.70345e14i | −1.36240 | − | 1.33238i | ||||
\(149\) | 1.27918e13i | 0.0957679i | 0.998853 | + | 0.0478839i | \(0.0152478\pi\) | ||||
−0.998853 | + | 0.0478839i | \(0.984752\pi\) | |||||||
\(150\) | −1.11188e13 | − | 2.64258e13i | −0.0797010 | − | 0.189424i | ||||
\(151\) | −1.69973e13 | −0.116689 | −0.0583444 | − | 0.998297i | \(-0.518582\pi\) | ||||
−0.0583444 | + | 0.998297i | \(0.518582\pi\) | |||||||
\(152\) | −7.34039e13 | − | 2.89777e13i | −0.482765 | − | 0.190581i | ||||
\(153\) | 6.85841e13 | 0.432244 | ||||||||
\(154\) | −1.60557e13 | − | 3.81594e13i | −0.0969940 | − | 0.230524i | ||||
\(155\) | − | 1.56581e14i | − | 0.906948i | ||||||
\(156\) | −2.87505e13 | + | 2.93983e13i | −0.159711 | + | 0.163310i | ||||
\(157\) | 1.27151e14i | 0.677599i | 0.940859 | + | 0.338799i | \(0.110021\pi\) | ||||
−0.940859 | + | 0.338799i | \(0.889979\pi\) | |||||||
\(158\) | 2.78763e14 | − | 1.17291e14i | 1.42549 | − | 0.599780i | ||||
\(159\) | −6.51450e13 | −0.319742 | ||||||||
\(160\) | 1.47908e14 | − | 6.61489e13i | 0.696967 | − | 0.311704i | ||||
\(161\) | 3.18640e13 | 0.144189 | ||||||||
\(162\) | −7.01026e13 | + | 2.94960e13i | −0.304710 | + | 0.128208i | ||||
\(163\) | 8.50516e13i | 0.355192i | 0.984103 | + | 0.177596i | \(0.0568320\pi\) | ||||
−0.984103 | + | 0.177596i | \(0.943168\pi\) | |||||||
\(164\) | −3.04719e14 | + | 3.11585e14i | −1.22297 | + | 1.25052i | ||||
\(165\) | 1.50380e14i | 0.580154i | ||||||||
\(166\) | 1.67846e14 | + | 3.98917e14i | 0.622598 | + | 1.47972i | ||||
\(167\) | −3.22006e14 | −1.14870 | −0.574351 | − | 0.818609i | \(-0.694745\pi\) | ||||
−0.574351 | + | 0.818609i | \(0.694745\pi\) | |||||||
\(168\) | −2.16601e13 | − | 8.55076e12i | −0.0743276 | − | 0.0293423i | ||||
\(169\) | 2.37784e14 | 0.785088 | ||||||||
\(170\) | 5.31947e13 | + | 1.26427e14i | 0.169025 | + | 0.401719i | ||||
\(171\) | 1.28493e14i | 0.393010i | ||||||||
\(172\) | 4.87622e13 | + | 4.76877e13i | 0.143598 | + | 0.140434i | ||||
\(173\) | − | 5.68385e14i | − | 1.61192i | −0.591971 | − | 0.805959i | \(-0.701650\pi\) | ||
0.591971 | − | 0.805959i | \(-0.298350\pi\) | |||||||
\(174\) | 2.10973e14 | − | 8.87677e13i | 0.576310 | − | 0.242485i | ||||
\(175\) | 2.57010e13 | 0.0676400 | ||||||||
\(176\) | 6.07924e14 | − | 1.35463e13i | 1.54176 | − | 0.0343548i | ||||
\(177\) | −2.17304e14 | −0.531179 | ||||||||
\(178\) | −2.53590e14 | + | 1.06699e14i | −0.597589 | + | 0.251438i | ||||
\(179\) | − | 5.79456e14i | − | 1.31667i | −0.752726 | − | 0.658334i | \(-0.771262\pi\) | ||
0.752726 | − | 0.658334i | \(-0.228738\pi\) | |||||||
\(180\) | −1.88610e14 | − | 1.84454e14i | −0.413326 | − | 0.404218i | ||||
\(181\) | 1.23355e14i | 0.260763i | 0.991464 | + | 0.130381i | \(0.0416202\pi\) | ||||
−0.991464 | + | 0.130381i | \(0.958380\pi\) | |||||||
\(182\) | −1.42960e13 | − | 3.39771e13i | −0.0291575 | − | 0.0692982i | ||||
\(183\) | 1.69946e14 | 0.334486 | ||||||||
\(184\) | −1.71853e14 | + | 4.35323e14i | −0.326468 | + | 0.826982i | ||||
\(185\) | −7.93334e14 | −1.45492 | ||||||||
\(186\) | −1.28191e14 | − | 3.04670e14i | −0.226999 | − | 0.539505i | ||||
\(187\) | 5.14762e14i | 0.880310i | ||||||||
\(188\) | 6.10672e14 | − | 6.24431e14i | 1.00875 | − | 1.03147i | ||||
\(189\) | 8.79884e13i | 0.140418i | ||||||||
\(190\) | −2.36862e14 | + | 9.96605e13i | −0.365255 | + | 0.153683i | ||||
\(191\) | 7.14579e13 | 0.106496 | 0.0532480 | − | 0.998581i | \(-0.483043\pi\) | ||||
0.0532480 | + | 0.998581i | \(0.483043\pi\) | |||||||
\(192\) | 2.33640e14 | − | 2.49802e14i | 0.336580 | − | 0.359863i | ||||
\(193\) | 1.08856e14 | 0.151611 | 0.0758054 | − | 0.997123i | \(-0.475847\pi\) | ||||
0.0758054 | + | 0.997123i | \(0.475847\pi\) | |||||||
\(194\) | −3.92735e14 | + | 1.65245e14i | −0.528918 | + | 0.222545i | ||||
\(195\) | 1.33898e14i | 0.174401i | ||||||||
\(196\) | −5.40359e14 | + | 5.52533e14i | −0.680797 | + | 0.696136i | ||||
\(197\) | − | 7.97270e14i | − | 0.971796i | −0.874015 | − | 0.485898i | \(-0.838493\pi\) | ||
0.874015 | − | 0.485898i | \(-0.161507\pi\) | |||||||
\(198\) | −3.83972e14 | − | 9.12581e14i | −0.452873 | − | 1.07634i | ||||
\(199\) | 1.45222e15 | 1.65763 | 0.828817 | − | 0.559520i | \(-0.189015\pi\) | ||||
0.828817 | + | 0.559520i | \(0.189015\pi\) | |||||||
\(200\) | −1.38614e14 | + | 3.51126e14i | −0.153148 | + | 0.387943i | ||||
\(201\) | 2.92241e14 | 0.312584 | ||||||||
\(202\) | −3.62585e14 | − | 8.61750e14i | −0.375514 | − | 0.892478i | ||||
\(203\) | 2.05186e14i | 0.205790i | ||||||||
\(204\) | 2.07009e14 | + | 2.02448e14i | 0.201091 | + | 0.196660i | ||||
\(205\) | 1.41915e15i | 1.33545i | ||||||||
\(206\) | −3.27718e14 | + | 1.37889e14i | −0.298788 | + | 0.125716i | ||||
\(207\) | 7.62028e14 | 0.673230 | ||||||||
\(208\) | 5.41295e14 | − | 1.20616e13i | 0.463471 | − | 0.0103275i | ||||
\(209\) | −9.64408e14 | −0.800405 | ||||||||
\(210\) | −6.98933e13 | + | 2.94079e13i | −0.0562355 | + | 0.0236613i | ||||
\(211\) | 1.42871e15i | 1.11457i | 0.830320 | + | 0.557287i | \(0.188158\pi\) | ||||
−0.830320 | + | 0.557287i | \(0.811842\pi\) | |||||||
\(212\) | 6.13252e14 | + | 5.99739e14i | 0.463934 | + | 0.453711i | ||||
\(213\) | − | 2.87776e14i | − | 0.211148i | ||||||
\(214\) | −2.59488e14 | − | 6.16721e14i | −0.184683 | − | 0.438934i | ||||
\(215\) | 2.22093e14 | 0.153350 | ||||||||
\(216\) | −1.20209e15 | − | 4.74549e14i | −0.805356 | − | 0.317930i | ||||
\(217\) | 2.96314e14 | 0.192647 | ||||||||
\(218\) | 8.64971e14 | + | 2.05576e15i | 0.545801 | + | 1.29720i | ||||
\(219\) | 2.50130e14i | 0.153207i | ||||||||
\(220\) | 1.38443e15 | − | 1.41562e15i | 0.823233 | − | 0.841781i | ||||
\(221\) | 4.58343e14i | 0.264631i | ||||||||
\(222\) | −1.54364e15 | + | 6.49495e14i | −0.865472 | + | 0.364151i | ||||
\(223\) | −2.08322e15 | −1.13437 | −0.567183 | − | 0.823591i | \(-0.691967\pi\) | ||||
−0.567183 | + | 0.823591i | \(0.691967\pi\) | |||||||
\(224\) | 1.25180e14 | + | 2.79902e14i | 0.0662101 | + | 0.148045i | ||||
\(225\) | 6.14640e14 | 0.315816 | ||||||||
\(226\) | 2.29087e15 | − | 9.63895e14i | 1.14366 | − | 0.481199i | ||||
\(227\) | − | 2.90336e15i | − | 1.40842i | −0.709990 | − | 0.704212i | \(-0.751301\pi\) | ||
0.709990 | − | 0.704212i | \(-0.248699\pi\) | |||||||
\(228\) | −3.79287e14 | + | 3.87833e14i | −0.178810 | + | 0.182839i | ||||
\(229\) | − | 2.20366e15i | − | 1.00975i | −0.863192 | − | 0.504875i | \(-0.831539\pi\) | ||
0.863192 | − | 0.504875i | \(-0.168461\pi\) | |||||||
\(230\) | 5.91039e14 | + | 1.40471e15i | 0.263260 | + | 0.625686i | ||||
\(231\) | −2.84578e14 | −0.123232 | ||||||||
\(232\) | −2.80324e15 | − | 1.10664e15i | −1.18029 | − | 0.465943i | ||||
\(233\) | −1.29391e15 | −0.529772 | −0.264886 | − | 0.964280i | \(-0.585334\pi\) | ||||
−0.264886 | + | 0.964280i | \(0.585334\pi\) | |||||||
\(234\) | −3.41889e14 | − | 8.12562e14i | −0.136139 | − | 0.323559i | ||||
\(235\) | − | 2.84404e15i | − | 1.10153i | ||||||
\(236\) | 2.04562e15 | + | 2.00055e15i | 0.770721 | + | 0.753739i | ||||
\(237\) | − | 2.07891e15i | − | 0.762028i | ||||||
\(238\) | −2.39251e14 | + | 1.00666e14i | −0.0853302 | + | 0.0359030i | ||||
\(239\) | −4.34770e15 | −1.50895 | −0.754473 | − | 0.656332i | \(-0.772107\pi\) | ||||
−0.754473 | + | 0.656332i | \(0.772107\pi\) | |||||||
\(240\) | −2.48116e13 | − | 1.11348e15i | −0.00838072 | − | 0.376106i | ||||
\(241\) | 2.63820e15 | 0.867355 | 0.433677 | − | 0.901068i | \(-0.357216\pi\) | ||||
0.433677 | + | 0.901068i | \(0.357216\pi\) | |||||||
\(242\) | 3.96935e15 | − | 1.67012e15i | 1.27034 | − | 0.534500i | ||||
\(243\) | 3.30173e15i | 1.02873i | ||||||||
\(244\) | −1.59981e15 | − | 1.56456e15i | −0.485326 | − | 0.474632i | ||||
\(245\) | 2.51657e15i | 0.743413i | ||||||||
\(246\) | 1.16184e15 | + | 2.76133e15i | 0.334248 | + | 0.794402i | ||||
\(247\) | −8.58708e14 | −0.240611 | ||||||||
\(248\) | −1.59811e15 | + | 4.04821e15i | −0.436186 | + | 1.10491i | ||||
\(249\) | 2.97497e15 | 0.791020 | ||||||||
\(250\) | 1.61973e15 | + | 3.84959e15i | 0.419597 | + | 0.997251i | ||||
\(251\) | − | 1.18733e15i | − | 0.299704i | −0.988708 | − | 0.149852i | \(-0.952120\pi\) | ||
0.988708 | − | 0.149852i | \(-0.0478797\pi\) | |||||||
\(252\) | 3.49060e14 | − | 3.56925e14i | 0.0858612 | − | 0.0877958i | ||||
\(253\) | 5.71944e15i | 1.37110i | ||||||||
\(254\) | 4.38955e14 | − | 1.84692e14i | 0.102565 | − | 0.0431548i | ||||
\(255\) | 9.42846e14 | 0.214748 | ||||||||
\(256\) | −4.49913e15 | + | 2.00607e14i | −0.999007 | + | 0.0445436i | ||||
\(257\) | −8.62360e13 | −0.0186691 | −0.00933455 | − | 0.999956i | \(-0.502971\pi\) | ||||
−0.00933455 | + | 0.999956i | \(0.502971\pi\) | |||||||
\(258\) | 4.32141e14 | − | 1.81825e14i | 0.0912215 | − | 0.0383818i | ||||
\(259\) | − | 1.50131e15i | − | 0.309044i | ||||||
\(260\) | 1.23269e15 | − | 1.26047e15i | 0.247473 | − | 0.253049i | ||||
\(261\) | 4.90703e15i | 0.960850i | ||||||||
\(262\) | −2.87093e15 | − | 6.82328e15i | −0.548357 | − | 1.30327i | ||||
\(263\) | 3.35128e15 | 0.624452 | 0.312226 | − | 0.950008i | \(-0.398925\pi\) | ||||
0.312226 | + | 0.950008i | \(0.398925\pi\) | |||||||
\(264\) | 1.53482e15 | − | 3.88789e15i | 0.279018 | − | 0.706786i | ||||
\(265\) | 2.79312e15 | 0.495441 | ||||||||
\(266\) | −1.88598e14 | − | 4.48237e14i | −0.0326442 | − | 0.0775849i | ||||
\(267\) | 1.89118e15i | 0.319455i | ||||||||
\(268\) | −2.75106e15 | − | 2.69044e15i | −0.453548 | − | 0.443555i | ||||
\(269\) | − | 7.67954e15i | − | 1.23579i | −0.786260 | − | 0.617896i | \(-0.787985\pi\) | ||
0.786260 | − | 0.617896i | \(-0.212015\pi\) | |||||||
\(270\) | −3.87894e15 | + | 1.63208e15i | −0.609324 | + | 0.256376i | ||||
\(271\) | −2.08567e15 | −0.319849 | −0.159925 | − | 0.987129i | \(-0.551125\pi\) | ||||
−0.159925 | + | 0.987129i | \(0.551125\pi\) | |||||||
\(272\) | −8.49321e13 | − | 3.81155e15i | −0.0127167 | − | 0.570694i | ||||
\(273\) | −2.53388e14 | −0.0370450 | ||||||||
\(274\) | −3.70246e15 | + | 1.55782e15i | −0.528581 | + | 0.222403i | ||||
\(275\) | 4.61322e15i | 0.643193i | ||||||||
\(276\) | 2.30005e15 | + | 2.24937e15i | 0.313205 | + | 0.306303i | ||||
\(277\) | − | 4.24355e15i | − | 0.564431i | −0.959351 | − | 0.282215i | \(-0.908931\pi\) | ||
0.959351 | − | 0.282215i | \(-0.0910692\pi\) | |||||||
\(278\) | −7.54875e14 | − | 1.79410e15i | −0.0980807 | − | 0.233107i | ||||
\(279\) | 7.08634e15 | 0.899487 | ||||||||
\(280\) | 9.28687e14 | + | 3.66618e14i | 0.115171 | + | 0.0454660i | ||||
\(281\) | −2.75085e15 | −0.333331 | −0.166666 | − | 0.986013i | \(-0.553300\pi\) | ||||
−0.166666 | + | 0.986013i | \(0.553300\pi\) | |||||||
\(282\) | −2.32839e15 | − | 5.53384e15i | −0.275700 | − | 0.655251i | ||||
\(283\) | − | 8.54209e14i | − | 0.0988445i | −0.998778 | − | 0.0494223i | \(-0.984262\pi\) | ||
0.998778 | − | 0.0494223i | \(-0.0157380\pi\) | |||||||
\(284\) | −2.64933e15 | + | 2.70903e15i | −0.299618 | + | 0.306369i | ||||
\(285\) | 1.76643e15i | 0.195256i | ||||||||
\(286\) | 6.09873e15 | − | 2.56607e15i | 0.658962 | − | 0.277261i | ||||
\(287\) | −2.68559e15 | −0.283666 | ||||||||
\(288\) | 2.99369e15 | + | 6.69385e15i | 0.309140 | + | 0.691233i | ||||
\(289\) | −6.67714e15 | −0.674147 | ||||||||
\(290\) | −9.04556e15 | + | 3.80596e15i | −0.892994 | + | 0.375731i | ||||
\(291\) | 2.92887e15i | 0.282746i | ||||||||
\(292\) | 2.30275e15 | − | 2.35464e15i | 0.217400 | − | 0.222298i | ||||
\(293\) | − | 7.18596e15i | − | 0.663507i | −0.943366 | − | 0.331753i | \(-0.892360\pi\) | ||
0.943366 | − | 0.331753i | \(-0.107640\pi\) | |||||||
\(294\) | 2.06029e15 | + | 4.89667e15i | 0.186068 | + | 0.442225i | ||||
\(295\) | 9.31701e15 | 0.823064 | ||||||||
\(296\) | 2.05107e16 | + | 8.09702e15i | 1.77249 | + | 0.699728i | ||||
\(297\) | −1.57935e16 | −1.33525 | ||||||||
\(298\) | −4.49013e14 | − | 1.06716e15i | −0.0371410 | − | 0.0882725i | ||||
\(299\) | 5.09259e15i | 0.412169i | ||||||||
\(300\) | 1.85519e15 | + | 1.81431e15i | 0.146926 | + | 0.143689i | ||||
\(301\) | 4.20288e14i | 0.0325736i | ||||||||
\(302\) | 1.41801e15 | − | 5.96634e14i | 0.107556 | − | 0.0452546i | ||||
\(303\) | −6.42661e15 | −0.477095 | ||||||||
\(304\) | 7.14095e15 | − | 1.59121e14i | 0.518893 | − | 0.0115624i | ||||
\(305\) | −7.28650e15 | −0.518287 | ||||||||
\(306\) | −5.72168e15 | + | 2.40742e15i | −0.398414 | + | 0.167634i | ||||
\(307\) | − | 1.79040e16i | − | 1.22054i | −0.792195 | − | 0.610268i | \(-0.791062\pi\) | ||
0.792195 | − | 0.610268i | \(-0.208938\pi\) | |||||||
\(308\) | 2.67892e15 | + | 2.61989e15i | 0.178805 | + | 0.174865i | ||||
\(309\) | 2.44400e15i | 0.159724i | ||||||||
\(310\) | 5.49626e15 | + | 1.30629e16i | 0.351735 | + | 0.835964i | ||||
\(311\) | 2.77510e16 | 1.73915 | 0.869575 | − | 0.493802i | \(-0.164393\pi\) | ||||
0.869575 | + | 0.493802i | \(0.164393\pi\) | |||||||
\(312\) | 1.36660e15 | − | 3.46177e15i | 0.0838760 | − | 0.212468i | ||||
\(313\) | 8.26927e15 | 0.497083 | 0.248542 | − | 0.968621i | \(-0.420049\pi\) | ||||
0.248542 | + | 0.968621i | \(0.420049\pi\) | |||||||
\(314\) | −4.46323e15 | − | 1.06077e16i | −0.262789 | − | 0.624566i | ||||
\(315\) | − | 1.62565e15i | − | 0.0937583i | ||||||
\(316\) | −1.91389e16 | + | 1.95701e16i | −1.08131 | + | 1.10567i | ||||
\(317\) | − | 1.49970e15i | − | 0.0830079i | −0.999138 | − | 0.0415040i | \(-0.986785\pi\) | ||
0.999138 | − | 0.0415040i | \(-0.0132149\pi\) | |||||||
\(318\) | 5.43477e15 | − | 2.28670e15i | 0.294717 | − | 0.124003i | ||||
\(319\) | −3.68300e16 | −1.95687 | ||||||||
\(320\) | −1.00174e16 | + | 1.07104e16i | −0.521532 | + | 0.557608i | ||||
\(321\) | −4.59928e15 | −0.234643 | ||||||||
\(322\) | −2.65828e15 | + | 1.11848e15i | −0.132904 | + | 0.0559199i | ||||
\(323\) | 6.04662e15i | 0.296276i | ||||||||
\(324\) | 4.81301e15 | − | 4.92145e15i | 0.231139 | − | 0.236347i | ||||
\(325\) | 4.10761e15i | 0.193351i | ||||||||
\(326\) | −2.98546e15 | − | 7.09550e15i | −0.137752 | − | 0.327392i | ||||
\(327\) | 1.53311e16 | 0.693447 | ||||||||
\(328\) | 1.44843e16 | − | 3.66904e16i | 0.642268 | − | 1.62694i | ||||
\(329\) | 5.38206e15 | 0.233978 | ||||||||
\(330\) | −5.27859e15 | − | 1.25455e16i | −0.224997 | − | 0.534747i | ||||
\(331\) | 2.14800e16i | 0.897742i | 0.893597 | + | 0.448871i | \(0.148174\pi\) | ||||
−0.893597 | + | 0.448871i | \(0.851826\pi\) | |||||||
\(332\) | −2.80054e16 | − | 2.73883e16i | −1.14774 | − | 1.12245i | ||||
\(333\) | − | 3.59037e16i | − | 1.44295i | ||||||
\(334\) | 2.68636e16 | − | 1.13030e16i | 1.05880 | − | 0.445493i | ||||
\(335\) | −1.25300e16 | −0.484350 | ||||||||
\(336\) | 2.10716e15 | − | 4.69535e13i | 0.0798899 | − | 0.00178017i | ||||
\(337\) | 4.34776e16 | 1.61686 | 0.808428 | − | 0.588596i | \(-0.200319\pi\) | ||||
0.808428 | + | 0.588596i | \(0.200319\pi\) | |||||||
\(338\) | −1.98373e16 | + | 8.34663e15i | −0.723642 | + | 0.304476i | ||||
\(339\) | − | 1.70845e16i | − | 0.611370i | ||||||
\(340\) | −8.87562e15 | − | 8.68005e15i | −0.311592 | − | 0.304726i | ||||
\(341\) | 5.31869e16i | 1.83190i | ||||||||
\(342\) | −4.51031e15 | − | 1.07196e16i | −0.152418 | − | 0.362250i | ||||
\(343\) | −9.65337e15 | −0.320086 | ||||||||
\(344\) | −5.74195e15 | − | 2.26675e15i | −0.186823 | − | 0.0737520i | ||||
\(345\) | 1.04758e16 | 0.334475 | ||||||||
\(346\) | 1.99513e16 | + | 4.74180e16i | 0.625139 | + | 1.48576i | ||||
\(347\) | 1.66277e15i | 0.0511317i | 0.999673 | + | 0.0255658i | \(0.00813874\pi\) | ||||
−0.999673 | + | 0.0255658i | \(0.991861\pi\) | |||||||
\(348\) | −1.44847e16 | + | 1.48110e16i | −0.437163 | + | 0.447013i | ||||
\(349\) | 3.69674e16i | 1.09510i | 0.836773 | + | 0.547549i | \(0.184439\pi\) | ||||
−0.836773 | + | 0.547549i | \(0.815561\pi\) | |||||||
\(350\) | −2.14413e15 | + | 9.02152e14i | −0.0623460 | + | 0.0262324i | ||||
\(351\) | −1.40625e16 | −0.401391 | ||||||||
\(352\) | −5.02410e16 | + | 2.24693e16i | −1.40777 | + | 0.629596i | ||||
\(353\) | 2.09201e16 | 0.575478 | 0.287739 | − | 0.957709i | \(-0.407096\pi\) | ||||
0.287739 | + | 0.957709i | \(0.407096\pi\) | |||||||
\(354\) | 1.81287e16 | − | 7.62775e15i | 0.489606 | − | 0.206004i | ||||
\(355\) | 1.23386e16i | 0.327175i | ||||||||
\(356\) | 1.74106e16 | − | 1.78029e16i | 0.453304 | − | 0.463518i | ||||
\(357\) | 1.78424e15i | 0.0456153i | ||||||||
\(358\) | 2.03399e16 | + | 4.83416e16i | 0.510634 | + | 1.21362i | ||||
\(359\) | 3.51028e16 | 0.865423 | 0.432711 | − | 0.901533i | \(-0.357557\pi\) | ||||
0.432711 | + | 0.901533i | \(0.357557\pi\) | |||||||
\(360\) | 2.22096e16 | + | 8.76767e15i | 0.537742 | + | 0.212284i | ||||
\(361\) | 3.07246e16 | 0.730617 | ||||||||
\(362\) | −4.32998e15 | − | 1.02910e16i | −0.101130 | − | 0.240354i | ||||
\(363\) | − | 2.96019e16i | − | 0.679089i | ||||||
\(364\) | 2.38531e15 | + | 2.33275e15i | 0.0537509 | + | 0.0525665i | ||||
\(365\) | − | 1.07245e16i | − | 0.237395i | ||||||
\(366\) | −1.41778e16 | + | 5.96539e15i | −0.308307 | + | 0.129721i | ||||
\(367\) | −9.02016e16 | −1.92701 | −0.963507 | − | 0.267683i | \(-0.913742\pi\) | ||||
−0.963507 | + | 0.267683i | \(0.913742\pi\) | |||||||
\(368\) | −9.43669e14 | − | 4.23495e16i | −0.0198066 | − | 0.888869i | ||||
\(369\) | −6.42260e16 | −1.32446 | ||||||||
\(370\) | 6.61845e16 | − | 2.78474e16i | 1.34105 | − | 0.564253i | ||||
\(371\) | 5.28571e15i | 0.105238i | ||||||||
\(372\) | 2.13889e16 | + | 2.09176e16i | 0.418465 | + | 0.409244i | ||||
\(373\) | − | 5.62933e16i | − | 1.08230i | −0.840925 | − | 0.541152i | \(-0.817988\pi\) | ||
0.840925 | − | 0.541152i | \(-0.182012\pi\) | |||||||
\(374\) | −1.80690e16 | − | 4.29444e16i | −0.341405 | − | 0.811411i | ||||
\(375\) | 2.87088e16 | 0.533104 | ||||||||
\(376\) | −2.90272e16 | + | 7.35293e16i | −0.529766 | + | 1.34196i | ||||
\(377\) | −3.27934e16 | −0.588258 | ||||||||
\(378\) | −3.08855e15 | − | 7.34051e15i | −0.0544575 | − | 0.129428i | ||||
\(379\) | − | 8.75626e16i | − | 1.51762i | −0.651310 | − | 0.758811i | \(-0.725780\pi\) | ||
0.651310 | − | 0.758811i | \(-0.274220\pi\) | |||||||
\(380\) | 1.62621e16 | − | 1.66285e16i | 0.277066 | − | 0.283309i | ||||
\(381\) | − | 3.27356e15i | − | 0.0548288i | ||||||
\(382\) | −5.96144e15 | + | 2.50830e15i | −0.0981610 | + | 0.0413017i | ||||
\(383\) | −2.39043e16 | −0.386975 | −0.193488 | − | 0.981103i | \(-0.561980\pi\) | ||||
−0.193488 | + | 0.981103i | \(0.561980\pi\) | |||||||
\(384\) | −1.07231e16 | + | 2.90411e16i | −0.170674 | + | 0.462231i | ||||
\(385\) | 1.22014e16 | 0.190949 | ||||||||
\(386\) | −9.08140e15 | + | 3.82104e15i | −0.139745 | + | 0.0587982i | ||||
\(387\) | 1.00512e16i | 0.152089i | ||||||||
\(388\) | 2.69639e16 | − | 2.75714e16i | 0.401214 | − | 0.410254i | ||||
\(389\) | − | 6.79906e16i | − | 0.994893i | −0.867495 | − | 0.497447i | \(-0.834271\pi\) | ||
0.867495 | − | 0.497447i | \(-0.165729\pi\) | |||||||
\(390\) | −4.70005e15 | − | 1.11705e16i | −0.0676367 | − | 0.160751i | ||||
\(391\) | 3.58596e16 | 0.507524 | ||||||||
\(392\) | 2.56850e16 | − | 6.50631e16i | 0.357536 | − | 0.905681i | ||||
\(393\) | −5.08855e16 | −0.696695 | ||||||||
\(394\) | 2.79856e16 | + | 6.65129e16i | 0.376885 | + | 0.895737i | ||||
\(395\) | 8.91342e16i | 1.18076i | ||||||||
\(396\) | 6.40664e16 | + | 6.26547e16i | 0.834856 | + | 0.816461i | ||||
\(397\) | 7.25697e16i | 0.930287i | 0.885235 | + | 0.465144i | \(0.153997\pi\) | ||||
−0.885235 | + | 0.465144i | \(0.846003\pi\) | |||||||
\(398\) | −1.21153e17 | + | 5.09756e16i | −1.52790 | + | 0.642869i | ||||
\(399\) | −3.34279e15 | −0.0414749 | ||||||||
\(400\) | −7.61150e14 | − | 3.41585e16i | −0.00929138 | − | 0.416974i | ||||
\(401\) | −3.28988e16 | −0.395132 | −0.197566 | − | 0.980290i | \(-0.563304\pi\) | ||||
−0.197566 | + | 0.980290i | \(0.563304\pi\) | |||||||
\(402\) | −2.43805e16 | + | 1.02582e16i | −0.288120 | + | 0.121228i | ||||
\(403\) | 4.73576e16i | 0.550690i | ||||||||
\(404\) | 6.04979e16 | + | 5.91648e16i | 0.692247 | + | 0.676994i | ||||
\(405\) | − | 2.24153e16i | − | 0.252398i | ||||||
\(406\) | −7.20240e15 | − | 1.71178e16i | −0.0798101 | − | 0.189684i | ||||
\(407\) | 2.69478e17 | 2.93873 | ||||||||
\(408\) | −2.43762e16 | − | 9.62299e15i | −0.261622 | − | 0.103281i | ||||
\(409\) | 8.11813e15 | 0.0857540 | 0.0428770 | − | 0.999080i | \(-0.486348\pi\) | ||||
0.0428770 | + | 0.999080i | \(0.486348\pi\) | |||||||
\(410\) | −4.98145e16 | − | 1.18393e17i | −0.517918 | − | 1.23093i | ||||
\(411\) | 2.76115e16i | 0.282565i | ||||||||
\(412\) | 2.25000e16 | − | 2.30070e16i | 0.226647 | − | 0.231754i | ||||
\(413\) | 1.76315e16i | 0.174829i | ||||||||
\(414\) | −6.35728e16 | + | 2.67485e16i | −0.620539 | + | 0.261094i | ||||
\(415\) | −1.27553e17 | −1.22569 | ||||||||
\(416\) | −4.47346e16 | + | 2.00067e16i | −0.423191 | + | 0.189264i | ||||
\(417\) | −1.33797e16 | −0.124613 | ||||||||
\(418\) | 8.04565e16 | − | 3.38524e16i | 0.737761 | − | 0.310416i | ||||
\(419\) | 5.76432e16i | 0.520424i | 0.965552 | + | 0.260212i | \(0.0837924\pi\) | ||||
−0.965552 | + | 0.260212i | \(0.916208\pi\) | |||||||
\(420\) | 4.79864e15 | − | 4.90676e15i | 0.0426577 | − | 0.0436189i | ||||
\(421\) | 3.89380e16i | 0.340832i | 0.985372 | + | 0.170416i | \(0.0545112\pi\) | ||||
−0.985372 | + | 0.170416i | \(0.945489\pi\) | |||||||
\(422\) | −5.01503e16 | − | 1.19191e17i | −0.432257 | − | 1.02734i | ||||
\(423\) | 1.28712e17 | 1.09246 | ||||||||
\(424\) | −7.22130e16 | − | 2.85075e16i | −0.603583 | − | 0.238277i | ||||
\(425\) | 2.89238e16 | 0.238083 | ||||||||
\(426\) | 1.01015e16 | + | 2.40080e16i | 0.0818883 | + | 0.194623i | ||||
\(427\) | − | 1.37890e16i | − | 0.110091i | ||||||
\(428\) | 4.32960e16 | + | 4.23420e16i | 0.340458 | + | 0.332956i | ||||
\(429\) | − | 4.54821e16i | − | 0.352264i | ||||||
\(430\) | −1.85283e16 | + | 7.79584e15i | −0.141348 | + | 0.0594728i | ||||
\(431\) | −5.38838e16 | −0.404908 | −0.202454 | − | 0.979292i | \(-0.564892\pi\) | ||||
−0.202454 | + | 0.979292i | \(0.564892\pi\) | |||||||
\(432\) | 1.16943e17 | − | 2.60582e15i | 0.865625 | − | 0.0192886i | ||||
\(433\) | 5.06818e16 | 0.369557 | 0.184778 | − | 0.982780i | \(-0.440843\pi\) | ||||
0.184778 | + | 0.982780i | \(0.440843\pi\) | |||||||
\(434\) | −2.47202e16 | + | 1.04011e16i | −0.177570 | + | 0.0747132i | ||||
\(435\) | 6.74585e16i | 0.477371i | ||||||||
\(436\) | −1.44322e17 | − | 1.41142e17i | −1.00617 | − | 0.983996i | ||||
\(437\) | 6.71832e16i | 0.461457i | ||||||||
\(438\) | −8.78001e15 | − | 2.08673e16i | −0.0594173 | − | 0.141216i | ||||
\(439\) | −8.26240e16 | −0.550918 | −0.275459 | − | 0.961313i | \(-0.588830\pi\) | ||||
−0.275459 | + | 0.961313i | \(0.588830\pi\) | |||||||
\(440\) | −6.58062e16 | + | 1.66695e17i | −0.432339 | + | 1.09517i | ||||
\(441\) | −1.13892e17 | −0.737297 | ||||||||
\(442\) | −1.60887e16 | − | 3.82377e16i | −0.102630 | − | 0.243920i | ||||
\(443\) | − | 7.44258e16i | − | 0.467842i | −0.972256 | − | 0.233921i | \(-0.924844\pi\) | ||
0.972256 | − | 0.233921i | \(-0.0751557\pi\) | |||||||
\(444\) | 1.05981e17 | − | 1.08369e17i | 0.656508 | − | 0.671300i | ||||
\(445\) | − | 8.10853e16i | − | 0.494997i | ||||||
\(446\) | 1.73794e17 | − | 7.31247e16i | 1.04558 | − | 0.439934i | ||||
\(447\) | −7.95851e15 | −0.0471881 | ||||||||
\(448\) | −2.02683e16 | − | 1.89570e16i | −0.118443 | − | 0.110780i | ||||
\(449\) | −7.45593e16 | −0.429438 | −0.214719 | − | 0.976676i | \(-0.568884\pi\) | ||||
−0.214719 | + | 0.976676i | \(0.568884\pi\) | |||||||
\(450\) | −5.12769e16 | + | 2.15750e16i | −0.291099 | + | 0.122481i | ||||
\(451\) | − | 4.82052e17i | − | 2.69741i | ||||||
\(452\) | −1.57284e17 | + | 1.60827e17i | −0.867528 | + | 0.887075i | ||||
\(453\) | − | 1.05750e16i | − | 0.0574966i | ||||||
\(454\) | 1.01913e17 | + | 2.42215e17i | 0.546219 | + | 1.29819i | ||||
\(455\) | 1.08642e16 | 0.0574013 | ||||||||
\(456\) | 1.80287e16 | − | 4.56689e16i | 0.0939060 | − | 0.237875i | ||||
\(457\) | 2.69972e17 | 1.38632 | 0.693159 | − | 0.720785i | \(-0.256218\pi\) | ||||
0.693159 | + | 0.720785i | \(0.256218\pi\) | |||||||
\(458\) | 7.73523e16 | + | 1.83842e17i | 0.391605 | + | 0.930721i | ||||
\(459\) | 9.90218e16i | 0.494252i | ||||||||
\(460\) | −9.86158e16 | − | 9.64428e16i | −0.485311 | − | 0.474618i | ||||
\(461\) | 4.89036e16i | 0.237293i | 0.992937 | + | 0.118646i | \(0.0378555\pi\) | ||||
−0.992937 | + | 0.118646i | \(0.962145\pi\) | |||||||
\(462\) | 2.37412e16 | − | 9.98920e15i | 0.113587 | − | 0.0477923i | ||||
\(463\) | −4.05876e17 | −1.91477 | −0.957386 | − | 0.288813i | \(-0.906739\pi\) | ||||
−0.957386 | + | 0.288813i | \(0.906739\pi\) | |||||||
\(464\) | 2.72707e17 | − | 6.07670e15i | 1.26862 | − | 0.0282684i | ||||
\(465\) | 9.74181e16 | 0.446885 | ||||||||
\(466\) | 1.07945e17 | − | 4.54184e16i | 0.488309 | − | 0.205458i | ||||
\(467\) | 2.47217e17i | 1.10286i | 0.834223 | + | 0.551428i | \(0.185917\pi\) | ||||
−0.834223 | + | 0.551428i | \(0.814083\pi\) | |||||||
\(468\) | 5.70447e16 | + | 5.57877e16i | 0.250967 | + | 0.245437i | ||||
\(469\) | − | 2.37118e16i | − | 0.102882i | ||||||
\(470\) | 9.98308e16 | + | 2.37266e17i | 0.427197 | + | 1.01531i | ||||
\(471\) | −7.91082e16 | −0.333876 | ||||||||
\(472\) | −2.40880e17 | − | 9.50924e16i | −1.00272 | − | 0.395843i | ||||
\(473\) | −7.54399e16 | −0.309744 | ||||||||
\(474\) | 7.29733e16 | + | 1.73435e17i | 0.295532 | + | 0.702387i | ||||
\(475\) | 5.41890e16i | 0.216472i | ||||||||
\(476\) | 1.64261e16 | − | 1.67962e16i | 0.0647277 | − | 0.0661861i | ||||
\(477\) | 1.26408e17i | 0.491365i | ||||||||
\(478\) | 3.62711e17 | − | 1.52612e17i | 1.39085 | − | 0.585204i | ||||
\(479\) | −1.68600e17 | −0.637788 | −0.318894 | − | 0.947790i | \(-0.603311\pi\) | ||||
−0.318894 | + | 0.947790i | \(0.603311\pi\) | |||||||
\(480\) | 4.11551e16 | + | 9.20223e16i | 0.153588 | + | 0.343420i | ||||
\(481\) | 2.39943e17 | 0.883414 | ||||||||
\(482\) | −2.20094e17 | + | 9.26054e16i | −0.799470 | + | 0.336380i | ||||
\(483\) | 1.98245e16i | 0.0710469i | ||||||||
\(484\) | −2.72522e17 | + | 2.78662e17i | −0.963622 | + | 0.985333i | ||||
\(485\) | − | 1.25577e17i | − | 0.438115i | ||||||
\(486\) | −1.15897e17 | − | 2.75450e17i | −0.398965 | − | 0.948215i | ||||
\(487\) | 7.90235e16 | 0.268422 | 0.134211 | − | 0.990953i | \(-0.457150\pi\) | ||||
0.134211 | + | 0.990953i | \(0.457150\pi\) | |||||||
\(488\) | 1.88384e17 | + | 7.43683e16i | 0.631415 | + | 0.249264i | ||||
\(489\) | −5.29156e16 | −0.175015 | ||||||||
\(490\) | −8.83362e16 | − | 2.09947e17i | −0.288313 | − | 0.685229i | ||||
\(491\) | − | 1.92491e17i | − | 0.619984i | −0.950739 | − | 0.309992i | \(-0.899674\pi\) | ||
0.950739 | − | 0.309992i | \(-0.100326\pi\) | |||||||
\(492\) | −1.93855e17 | − | 1.89584e17i | −0.616175 | − | 0.602598i | ||||
\(493\) | 2.30916e17i | 0.724351i | ||||||||
\(494\) | 7.16384e16 | − | 3.01422e16i | 0.221779 | − | 0.0933145i | ||||
\(495\) | 2.91798e17 | 0.891554 | ||||||||
\(496\) | −8.77548e15 | − | 3.93822e17i | −0.0264631 | − | 1.18760i | ||||
\(497\) | −2.33495e16 | −0.0694962 | ||||||||
\(498\) | −2.48190e17 | + | 1.04427e17i | −0.729109 | + | 0.306776i | ||||
\(499\) | − | 2.23025e17i | − | 0.646697i | −0.946280 | − | 0.323349i | \(-0.895191\pi\) | ||
0.946280 | − | 0.323349i | \(-0.104809\pi\) | |||||||
\(500\) | −2.70255e17 | − | 2.64300e17i | −0.773514 | − | 0.756470i | ||||
\(501\) | − | 2.00339e17i | − | 0.566005i | ||||||
\(502\) | 4.16774e16 | + | 9.90539e16i | 0.116232 | + | 0.276247i | ||||
\(503\) | 9.72300e16 | 0.267675 | 0.133838 | − | 0.991003i | \(-0.457270\pi\) | ||||
0.133838 | + | 0.991003i | \(0.457270\pi\) | |||||||
\(504\) | −1.65920e16 | + | 4.20294e16i | −0.0450919 | + | 0.114223i | ||||
\(505\) | 2.75544e17 | 0.739260 | ||||||||
\(506\) | −2.00762e17 | − | 4.77149e17i | −0.531746 | − | 1.26379i | ||||
\(507\) | 1.47939e17i | 0.386840i | ||||||||
\(508\) | −3.01372e16 | + | 3.08162e16i | −0.0778016 | + | 0.0795545i | ||||
\(509\) | − | 2.69652e17i | − | 0.687287i | −0.939100 | − | 0.343643i | \(-0.888339\pi\) | ||
0.939100 | − | 0.343643i | \(-0.111661\pi\) | |||||||
\(510\) | −7.86577e16 | + | 3.30955e16i | −0.197941 | + | 0.0832843i | ||||
\(511\) | 2.02950e16 | 0.0504258 | ||||||||
\(512\) | 3.68302e17 | − | 1.74663e17i | 0.903544 | − | 0.428496i | ||||
\(513\) | −1.85518e17 | −0.449389 | ||||||||
\(514\) | 7.19431e15 | − | 3.02704e15i | 0.0172079 | − | 0.00724031i | ||||
\(515\) | − | 1.04788e17i | − | 0.247493i | ||||||
\(516\) | −2.96693e16 | + | 3.03378e16i | −0.0691966 | + | 0.0707557i | ||||
\(517\) | 9.66056e17i | 2.22492i | ||||||||
\(518\) | 5.26985e16 | + | 1.25248e17i | 0.119855 | + | 0.284857i | ||||
\(519\) | 3.53626e17 | 0.794248 | ||||||||
\(520\) | −5.85938e16 | + | 1.48425e17i | −0.129966 | + | 0.329220i | ||||
\(521\) | −6.40373e17 | −1.40277 | −0.701387 | − | 0.712781i | \(-0.747436\pi\) | ||||
−0.701387 | + | 0.712781i | \(0.747436\pi\) | |||||||
\(522\) | −1.72245e17 | − | 4.09373e17i | −0.372640 | − | 0.885648i | ||||
\(523\) | 8.02434e17i | 1.71454i | 0.514864 | + | 0.857272i | \(0.327842\pi\) | ||||
−0.514864 | + | 0.857272i | \(0.672158\pi\) | |||||||
\(524\) | 4.79019e17 | + | 4.68464e17i | 1.01088 | + | 0.988604i | ||||
\(525\) | 1.59901e16i | 0.0333285i | ||||||||
\(526\) | −2.79584e17 | + | 1.17636e17i | −0.575578 | + | 0.242177i | ||||
\(527\) | 3.33470e17 | 0.678091 | ||||||||
\(528\) | 8.42794e15 | + | 3.78225e17i | 0.0169278 | + | 0.759679i | ||||
\(529\) | −1.05605e17 | −0.209519 | ||||||||
\(530\) | −2.33019e17 | + | 9.80436e16i | −0.456665 | + | 0.192144i | ||||
\(531\) | 4.21658e17i | 0.816293i | ||||||||
\(532\) | 3.14678e16 | + | 3.07744e16i | 0.0601785 | + | 0.0588525i | ||||
\(533\) | − | 4.29219e17i | − | 0.810871i | ||||||
\(534\) | −6.63838e16 | − | 1.57773e17i | −0.123892 | − | 0.294453i | ||||
\(535\) | 1.97196e17 | 0.363579 | ||||||||
\(536\) | 3.23948e17 | + | 1.27885e17i | 0.590072 | + | 0.232943i | ||||
\(537\) | 3.60514e17 | 0.648768 | ||||||||
\(538\) | 2.69565e17 | + | 6.40672e17i | 0.479269 | + | 1.13907i | ||||
\(539\) | − | 8.54823e17i | − | 1.50158i | ||||||
\(540\) | 2.66315e17 | − | 2.72315e17i | 0.462206 | − | 0.472620i | ||||
\(541\) | − | 1.00333e18i | − | 1.72053i | −0.509848 | − | 0.860265i | \(-0.670298\pi\) | ||
0.509848 | − | 0.860265i | \(-0.329702\pi\) | |||||||
\(542\) | 1.73999e17 | − | 7.32107e16i | 0.294816 | − | 0.124045i | ||||
\(543\) | −7.67464e16 | −0.128487 | ||||||||
\(544\) | 1.40877e17 | + | 3.15000e17i | 0.233050 | + | 0.521096i | ||||
\(545\) | −6.57329e17 | −1.07450 | ||||||||
\(546\) | 2.11391e16 | − | 8.89438e15i | 0.0341456 | − | 0.0143669i | ||||
\(547\) | 8.57926e17i | 1.36941i | 0.728822 | + | 0.684703i | \(0.240068\pi\) | ||||
−0.728822 | + | 0.684703i | \(0.759932\pi\) | |||||||
\(548\) | 2.54198e17 | − | 2.59925e17i | 0.400958 | − | 0.409992i | ||||
\(549\) | − | 3.29764e17i | − | 0.514023i | ||||||
\(550\) | −1.61932e17 | − | 3.84862e17i | −0.249445 | − | 0.592853i | ||||
\(551\) | −4.32622e17 | −0.658602 | ||||||||
\(552\) | −2.70840e17 | − | 1.06920e17i | −0.407483 | − | 0.160862i | ||||
\(553\) | −1.68678e17 | −0.250810 | ||||||||
\(554\) | 1.48956e17 | + | 3.54021e17i | 0.218899 | + | 0.520255i | ||||
\(555\) | − | 4.93580e17i | − | 0.716890i | ||||||
\(556\) | 1.25952e17 | + | 1.23177e17i | 0.180809 | + | 0.176825i | ||||
\(557\) | − | 1.46708e17i | − | 0.208160i | −0.994569 | − | 0.104080i | \(-0.966810\pi\) | ||
0.994569 | − | 0.104080i | \(-0.0331897\pi\) | |||||||
\(558\) | −5.91184e17 | + | 2.48743e17i | −0.829087 | + | 0.348842i | ||||
\(559\) | −6.71716e16 | −0.0931127 | ||||||||
\(560\) | −9.03454e16 | + | 2.01315e15i | −0.123790 | + | 0.00275839i | ||||
\(561\) | −3.20263e17 | −0.433759 | ||||||||
\(562\) | 2.29492e17 | − | 9.65597e16i | 0.307242 | − | 0.129274i | ||||
\(563\) | − | 7.50214e17i | − | 0.992843i | −0.868082 | − | 0.496422i | \(-0.834647\pi\) | ||
0.868082 | − | 0.496422i | \(-0.165353\pi\) | |||||||
\(564\) | 3.88495e17 | + | 3.79935e17i | 0.508243 | + | 0.497044i | ||||
\(565\) | 7.32506e17i | 0.947319i | ||||||||
\(566\) | 2.99843e16 | + | 7.12631e16i | 0.0383342 | + | 0.0911083i | ||||
\(567\) | 4.24187e16 | 0.0536127 | ||||||||
\(568\) | 1.25931e17 | − | 3.18999e17i | 0.157351 | − | 0.398589i | ||||
\(569\) | −5.82283e17 | −0.719291 | −0.359645 | − | 0.933089i | \(-0.617102\pi\) | ||||
−0.359645 | + | 0.933089i | \(0.617102\pi\) | |||||||
\(570\) | −6.20047e16 | − | 1.47366e17i | −0.0757247 | − | 0.179974i | ||||
\(571\) | − | 6.73020e17i | − | 0.812630i | −0.913733 | − | 0.406315i | \(-0.866814\pi\) | ||
0.913733 | − | 0.406315i | \(-0.133186\pi\) | |||||||
\(572\) | −4.18718e17 | + | 4.28152e17i | −0.499859 | + | 0.511121i | ||||
\(573\) | 4.44582e16i | 0.0524743i | ||||||||
\(574\) | 2.24048e17 | − | 9.42691e16i | 0.261465 | − | 0.110012i | ||||
\(575\) | 3.21369e17 | 0.370820 | ||||||||
\(576\) | −4.84717e17 | − | 4.53356e17i | −0.553021 | − | 0.517241i | ||||
\(577\) | 9.35938e17 | 1.05585 | 0.527927 | − | 0.849290i | \(-0.322969\pi\) | ||||
0.527927 | + | 0.849290i | \(0.322969\pi\) | |||||||
\(578\) | 5.57046e17 | − | 2.34379e17i | 0.621384 | − | 0.261450i | ||||
\(579\) | 6.77257e16i | 0.0747039i | ||||||||
\(580\) | 6.21038e17 | − | 6.35030e17i | 0.677386 | − | 0.692648i | ||||
\(581\) | − | 2.41382e17i | − | 0.260352i | ||||||
\(582\) | −1.02809e17 | − | 2.44344e17i | −0.109655 | − | 0.260616i | ||||
\(583\) | −9.48761e17 | −1.00072 | ||||||||
\(584\) | −1.09457e17 | + | 2.77268e17i | −0.114172 | + | 0.289212i | ||||
\(585\) | 2.59816e17 | 0.268011 | ||||||||
\(586\) | 2.52240e17 | + | 5.99495e17i | 0.257323 | + | 0.611576i | ||||
\(587\) | 1.30002e18i | 1.31160i | 0.754935 | + | 0.655799i | \(0.227668\pi\) | ||||
−0.754935 | + | 0.655799i | \(0.772332\pi\) | |||||||
\(588\) | −3.43764e17 | − | 3.36189e17i | −0.343010 | − | 0.335452i | ||||
\(589\) | 6.24758e17i | 0.616541i | ||||||||
\(590\) | −7.77279e17 | + | 3.27043e17i | −0.758645 | + | 0.319203i | ||||
\(591\) | 4.96029e17 | 0.478838 | ||||||||
\(592\) | −1.99534e18 | + | 4.44620e16i | −1.90514 | + | 0.0424519i | ||||
\(593\) | 1.33010e18 | 1.25611 | 0.628057 | − | 0.778168i | \(-0.283851\pi\) | ||||
0.628057 | + | 0.778168i | \(0.283851\pi\) | |||||||
\(594\) | 1.31759e18 | − | 5.54380e17i | 1.23074 | − | 0.517840i | ||||
\(595\) | − | 7.65003e16i | − | 0.0706810i | ||||||
\(596\) | 7.49186e16 | + | 7.32678e16i | 0.0684682 | + | 0.0669596i | ||||
\(597\) | 9.03514e17i | 0.816773i | ||||||||
\(598\) | −1.78759e17 | − | 4.24853e17i | −0.159849 | − | 0.379910i | ||||
\(599\) | −1.69219e18 | −1.49684 | −0.748418 | − | 0.663227i | \(-0.769186\pi\) | ||||
−0.748418 | + | 0.663227i | \(0.769186\pi\) | |||||||
\(600\) | −2.18456e17 | − | 8.62398e16i | −0.191153 | − | 0.0754614i | ||||
\(601\) | 1.09369e18 | 0.946695 | 0.473347 | − | 0.880876i | \(-0.343046\pi\) | ||||
0.473347 | + | 0.880876i | \(0.343046\pi\) | |||||||
\(602\) | −1.47529e16 | − | 3.50629e16i | −0.0126328 | − | 0.0300241i | ||||
\(603\) | − | 5.67067e17i | − | 0.480366i | ||||||
\(604\) | −9.73558e16 | + | 9.95493e16i | −0.0815871 | + | 0.0834254i | ||||
\(605\) | 1.26920e18i | 1.05225i | ||||||||
\(606\) | 5.36145e17 | − | 2.25585e17i | 0.439755 | − | 0.185029i | ||||
\(607\) | 1.88846e18 | 1.53243 | 0.766214 | − | 0.642585i | \(-0.222138\pi\) | ||||
0.766214 | + | 0.642585i | \(0.222138\pi\) | |||||||
\(608\) | −5.90154e17 | + | 2.63935e17i | −0.473797 | + | 0.211896i | ||||
\(609\) | −1.27658e17 | −0.101400 | ||||||||
\(610\) | 6.07882e17 | − | 2.55769e17i | 0.477722 | − | 0.201004i | ||||
\(611\) | 8.60176e17i | 0.668835i | ||||||||
\(612\) | 3.92831e17 | − | 4.01682e17i | 0.302219 | − | 0.309028i | ||||
\(613\) | − | 9.88263e17i | − | 0.752280i | −0.926563 | − | 0.376140i | \(-0.877251\pi\) | ||
0.926563 | − | 0.376140i | \(-0.122749\pi\) | |||||||
\(614\) | 6.28462e17 | + | 1.49366e18i | 0.473353 | + | 1.12501i | ||||
\(615\) | −8.82934e17 | −0.658021 | ||||||||
\(616\) | −3.15454e17 | − | 1.24532e17i | −0.232628 | − | 0.0918345i | ||||
\(617\) | 1.64690e18 | 1.20175 | 0.600873 | − | 0.799345i | \(-0.294820\pi\) | ||||
0.600873 | + | 0.799345i | \(0.294820\pi\) | |||||||
\(618\) | −8.57887e16 | − | 2.03893e17i | −0.0619448 | − | 0.147223i | ||||
\(619\) | 2.50056e17i | 0.178669i | 0.996002 | + | 0.0893343i | \(0.0284740\pi\) | ||||
−0.996002 | + | 0.0893343i | \(0.971526\pi\) | |||||||
\(620\) | −9.17060e17 | − | 8.96853e17i | −0.648413 | − | 0.634125i | ||||
\(621\) | 1.10022e18i | 0.769809i | ||||||||
\(622\) | −2.31515e18 | + | 9.74111e17i | −1.60303 | + | 0.674483i | ||||
\(623\) | 1.53446e17 | 0.105144 | ||||||||
\(624\) | 7.50423e15 | + | 3.36771e17i | 0.00508869 | + | 0.228368i | ||||
\(625\) | −6.09411e17 | −0.408969 | ||||||||
\(626\) | −6.89871e17 | + | 2.90266e17i | −0.458178 | + | 0.192780i | ||||
\(627\) | − | 6.00015e17i | − | 0.394387i | ||||||
\(628\) | 7.44697e17 | + | 7.28288e17i | 0.484442 | + | 0.473768i | ||||
\(629\) | − | 1.68956e18i | − | 1.08779i | ||||||
\(630\) | 5.70633e16 | + | 1.35622e17i | 0.0363616 | + | 0.0864202i | ||||
\(631\) | −1.79473e18 | −1.13190 | −0.565949 | − | 0.824440i | \(-0.691490\pi\) | ||||
−0.565949 | + | 0.824440i | \(0.691490\pi\) | |||||||
\(632\) | 9.09733e17 | − | 2.30446e18i | 0.567875 | − | 1.43850i | ||||
\(633\) | −8.88885e17 | −0.549189 | ||||||||
\(634\) | 5.26421e16 | + | 1.25114e17i | 0.0321924 | + | 0.0765112i | ||||
\(635\) | 1.40356e17i | 0.0849573i | ||||||||
\(636\) | −3.73133e17 | + | 3.81540e17i | −0.223559 | + | 0.228596i | ||||
\(637\) | − | 7.61134e17i | − | 0.451393i | ||||||
\(638\) | 3.07257e18 | − | 1.29280e18i | 1.80371 | − | 0.758920i | ||||
\(639\) | −5.58404e17 | −0.324484 | ||||||||
\(640\) | 4.59758e17 | − | 1.24515e18i | 0.264460 | − | 0.716229i | ||||
\(641\) | −8.87296e16 | −0.0505233 | −0.0252616 | − | 0.999681i | \(-0.508042\pi\) | ||||
−0.0252616 | + | 0.999681i | \(0.508042\pi\) | |||||||
\(642\) | 3.83698e17 | − | 1.61443e17i | 0.216278 | − | 0.0909999i | ||||
\(643\) | − | 3.35822e18i | − | 1.87386i | −0.349511 | − | 0.936932i | \(-0.613652\pi\) | ||
0.349511 | − | 0.936932i | \(-0.386348\pi\) | |||||||
\(644\) | 1.82509e17 | − | 1.86621e17i | 0.100815 | − | 0.103086i | ||||
\(645\) | 1.38177e17i | 0.0755609i | ||||||||
\(646\) | −2.12247e17 | − | 5.04444e17i | −0.114903 | − | 0.273088i | ||||
\(647\) | −4.29076e16 | −0.0229962 | −0.0114981 | − | 0.999934i | \(-0.503660\pi\) | ||||
−0.0114981 | + | 0.999934i | \(0.503660\pi\) | |||||||
\(648\) | −2.28778e17 | + | 5.79521e17i | −0.121388 | + | 0.307490i | ||||
\(649\) | −3.16478e18 | −1.66247 | ||||||||
\(650\) | −1.44184e17 | − | 3.42680e17i | −0.0749861 | − | 0.178218i | ||||
\(651\) | 1.84354e17i | 0.0949241i | ||||||||
\(652\) | 4.98129e17 | + | 4.87153e17i | 0.253941 | + | 0.248345i | ||||
\(653\) | − | 6.77971e17i | − | 0.342197i | −0.985254 | − | 0.171098i | \(-0.945268\pi\) | ||
0.985254 | − | 0.171098i | \(-0.0547316\pi\) | |||||||
\(654\) | −1.27901e18 | + | 5.38149e17i | −0.639174 | + | 0.268935i | ||||
\(655\) | 2.18174e18 | 1.07953 | ||||||||
\(656\) | 7.95353e16 | + | 3.56935e18i | 0.0389659 | + | 1.74869i | ||||
\(657\) | 4.85354e17 | 0.235442 | ||||||||
\(658\) | −4.49003e17 | + | 1.88920e17i | −0.215666 | + | 0.0907422i | ||||
\(659\) | 1.20273e18i | 0.572021i | 0.958227 | + | 0.286010i | \(0.0923292\pi\) | ||||
−0.958227 | + | 0.286010i | \(0.907671\pi\) | |||||||
\(660\) | 8.80741e17 | + | 8.61334e17i | 0.414775 | + | 0.405635i | ||||
\(661\) | − | 1.00191e18i | − | 0.467217i | −0.972331 | − | 0.233608i | \(-0.924947\pi\) | ||
0.972331 | − | 0.233608i | \(-0.0750534\pi\) | |||||||
\(662\) | −7.53985e17 | − | 1.79198e18i | −0.348165 | − | 0.827479i | ||||
\(663\) | −2.85162e17 | −0.130393 | ||||||||
\(664\) | 3.29775e18 | + | 1.30185e18i | 1.49322 | + | 0.589480i | ||||
\(665\) | 1.43324e17 | 0.0642654 | ||||||||
\(666\) | 1.26028e18 | + | 2.99530e18i | 0.559611 | + | 1.33002i | ||||
\(667\) | 2.56567e18i | 1.12819i | ||||||||
\(668\) | −1.84437e18 | + | 1.88592e18i | −0.803156 | + | 0.821252i | ||||
\(669\) | − | 1.29609e18i | − | 0.558942i | ||||||
\(670\) | 1.04532e18 | − | 4.39825e17i | 0.446442 | − | 0.187842i | ||||
\(671\) | 2.47506e18 | 1.04686 | ||||||||
\(672\) | −1.74143e17 | + | 7.78821e16i | −0.0729468 | + | 0.0326240i | ||||
\(673\) | −3.10962e18 | −1.29006 | −0.645029 | − | 0.764158i | \(-0.723155\pi\) | ||||
−0.645029 | + | 0.764158i | \(0.723155\pi\) | |||||||
\(674\) | −3.62715e18 | + | 1.52614e18i | −1.49031 | + | 0.627054i | ||||
\(675\) | 8.87419e17i | 0.361122i | ||||||||
\(676\) | 1.36196e18 | − | 1.39265e18i | 0.548923 | − | 0.561291i | ||||
\(677\) | 3.32505e18i | 1.32731i | 0.748040 | + | 0.663653i | \(0.230995\pi\) | ||||
−0.748040 | + | 0.663653i | \(0.769005\pi\) | |||||||
\(678\) | 5.99695e17 | + | 1.42529e18i | 0.237103 | + | 0.563520i | ||||
\(679\) | 2.37642e17 | 0.0930614 | ||||||||
\(680\) | 1.04514e18 | + | 4.12590e17i | 0.405384 | + | 0.160034i | ||||
\(681\) | 1.80635e18 | 0.693979 | ||||||||
\(682\) | −1.86695e18 | − | 4.43716e18i | −0.710453 | − | 1.68852i | ||||
\(683\) | − | 1.67034e18i | − | 0.629607i | −0.949157 | − | 0.314804i | \(-0.898061\pi\) | ||
0.949157 | − | 0.314804i | \(-0.101939\pi\) | |||||||
\(684\) | 7.52553e17 | + | 7.35971e17i | 0.280978 | + | 0.274787i | ||||
\(685\) | − | 1.18386e18i | − | 0.437836i | ||||||
\(686\) | 8.05341e17 | − | 3.38850e17i | 0.295035 | − | 0.124137i | ||||
\(687\) | 1.37103e18 | 0.497539 | ||||||||
\(688\) | 5.58593e17 | − | 1.24471e16i | 0.200803 | − | 0.00447447i | ||||
\(689\) | −8.44776e17 | −0.300827 | ||||||||
\(690\) | −8.73954e17 | + | 3.67720e17i | −0.308297 | + | 0.129717i | ||||
\(691\) | 1.34749e18i | 0.470890i | 0.971888 | + | 0.235445i | \(0.0756547\pi\) | ||||
−0.971888 | + | 0.235445i | \(0.924345\pi\) | |||||||
\(692\) | −3.32891e18 | − | 3.25556e18i | −1.15242 | − | 1.12703i | ||||
\(693\) | 5.52198e17i | 0.189378i | ||||||||
\(694\) | −5.83661e16 | − | 1.38718e17i | −0.0198301 | − | 0.0471298i | ||||
\(695\) | 5.73662e17 | 0.193088 | ||||||||
\(696\) | 6.88503e17 | − | 1.74406e18i | 0.229586 | − | 0.581569i | ||||
\(697\) | −3.02236e18 | −0.998465 | ||||||||
\(698\) | −1.29762e18 | − | 3.08403e18i | −0.424705 | − | 1.00939i | ||||
\(699\) | − | 8.05015e17i | − | 0.261037i | ||||||
\(700\) | 1.47209e17 | − | 1.50525e17i | 0.0472929 | − | 0.0483585i | ||||
\(701\) | 3.66094e18i | 1.16527i | 0.812735 | + | 0.582634i | \(0.197978\pi\) | ||||
−0.812735 | + | 0.582634i | \(0.802022\pi\) | |||||||
\(702\) | 1.17318e18 | − | 4.93620e17i | 0.369975 | − | 0.155669i | ||||
\(703\) | 3.16541e18 | 0.989053 | ||||||||
\(704\) | 3.40269e18 | − | 3.63807e18i | 1.05342 | − | 1.12629i | ||||
\(705\) | 1.76944e18 | 0.542760 | ||||||||
\(706\) | −1.74528e18 | + | 7.34334e17i | −0.530438 | + | 0.223184i | ||||
\(707\) | 5.21440e17i | 0.157028i | ||||||||
\(708\) | −1.24466e18 | + | 1.27270e18i | −0.371393 | + | 0.379761i | ||||
\(709\) | − | 5.56977e18i | − | 1.64678i | −0.567473 | − | 0.823392i | \(-0.692079\pi\) | ||
0.567473 | − | 0.823392i | \(-0.307921\pi\) | |||||||
\(710\) | −4.33105e17 | − | 1.02935e18i | −0.126886 | − | 0.301568i | ||||
\(711\) | −4.03393e18 | −1.17105 | ||||||||
\(712\) | −8.27583e17 | + | 2.09637e18i | −0.238063 | + | 0.603042i | ||||
\(713\) | 3.70514e18 | 1.05614 | ||||||||
\(714\) | −6.26301e16 | − | 1.48852e17i | −0.0176907 | − | 0.0420452i | ||||
\(715\) | 1.95007e18i | 0.545833i | ||||||||
\(716\) | −3.39375e18 | − | 3.31897e18i | −0.941338 | − | 0.920596i | ||||
\(717\) | − | 2.70496e18i | − | 0.743510i | ||||||
\(718\) | −2.92848e18 | + | 1.23217e18i | −0.797689 | + | 0.335631i | ||||
\(719\) | 2.56260e18 | 0.691740 | 0.345870 | − | 0.938282i | \(-0.387584\pi\) | ||||
0.345870 | + | 0.938282i | \(0.387584\pi\) | |||||||
\(720\) | −2.16061e18 | + | 4.81446e16i | −0.577983 | + | 0.0128791i | ||||
\(721\) | 1.98300e17 | 0.0525708 | ||||||||
\(722\) | −2.56323e18 | + | 1.07849e18i | −0.673434 | + | 0.283350i | ||||
\(723\) | 1.64138e18i | 0.427376i | ||||||||
\(724\) | 7.22464e17 | + | 7.06544e17i | 0.186430 | + | 0.182322i | ||||
\(725\) | 2.06943e18i | 0.529242i | ||||||||
\(726\) | 1.03908e18 | + | 2.46956e18i | 0.263367 | + | 0.625939i | ||||
\(727\) | −1.47166e18 | −0.369688 | −0.184844 | − | 0.982768i | \(-0.559178\pi\) | ||||
−0.184844 | + | 0.982768i | \(0.559178\pi\) | |||||||
\(728\) | −2.80880e17 | − | 1.10883e17i | −0.0699306 | − | 0.0276065i | ||||
\(729\) | −7.14494e17 | −0.176307 | ||||||||
\(730\) | 3.76447e17 | + | 8.94696e17i | 0.0920673 | + | 0.218815i | ||||
\(731\) | 4.72991e17i | 0.114654i | ||||||||
\(732\) | 9.73403e17 | − | 9.95334e17i | 0.233868 | − | 0.239137i | ||||
\(733\) | 5.45589e18i | 1.29924i | 0.760259 | + | 0.649620i | \(0.225072\pi\) | ||||
−0.760259 | + | 0.649620i | \(0.774928\pi\) | |||||||
\(734\) | 7.52514e18 | − | 3.16623e18i | 1.77619 | − | 0.747341i | ||||
\(735\) | −1.56571e18 | −0.366305 | ||||||||
\(736\) | 1.56527e18 | + | 3.49992e18i | 0.362981 | + | 0.811619i | ||||
\(737\) | 4.25616e18 | 0.978315 | ||||||||
\(738\) | 5.35811e18 | − | 2.25445e18i | 1.22080 | − | 0.513657i | ||||
\(739\) | − | 3.33360e18i | − | 0.752878i | −0.926441 | − | 0.376439i | \(-0.877148\pi\) | ||
0.926441 | − | 0.376439i | \(-0.122852\pi\) | |||||||
\(740\) | −4.54400e18 | + | 4.64639e18i | −1.01726 | + | 1.04018i | ||||
\(741\) | − | 5.34253e17i | − | 0.118557i | ||||||
\(742\) | −1.85538e17 | − | 4.40965e17i | −0.0408138 | − | 0.0970015i | ||||
\(743\) | −7.19594e18 | −1.56913 | −0.784567 | − | 0.620044i | \(-0.787115\pi\) | ||||
−0.784567 | + | 0.620044i | \(0.787115\pi\) | |||||||
\(744\) | −2.51863e18 | − | 9.94280e17i | −0.544428 | − | 0.214924i | ||||
\(745\) | 3.41225e17 | 0.0731181 | ||||||||
\(746\) | 1.97599e18 | + | 4.69631e18i | 0.419743 | + | 0.997596i | ||||
\(747\) | − | 5.77266e18i | − | 1.21560i | ||||||
\(748\) | 3.01485e18 | + | 2.94842e18i | 0.629369 | + | 0.615501i | ||||
\(749\) | 3.73175e17i | 0.0772290i | ||||||||
\(750\) | −2.39506e18 | + | 1.00773e18i | −0.491380 | + | 0.206750i | ||||
\(751\) | 1.83541e18 | 0.373313 | 0.186656 | − | 0.982425i | \(-0.440235\pi\) | ||||
0.186656 | + | 0.982425i | \(0.440235\pi\) | |||||||
\(752\) | −1.59393e17 | − | 7.15315e18i | −0.0321405 | − | 1.44239i | ||||
\(753\) | 7.38708e17 | 0.147674 | ||||||||
\(754\) | 2.73582e18 | − | 1.15111e18i | 0.542217 | − | 0.228140i | ||||
\(755\) | 4.53408e17i | 0.0890911i | ||||||||
\(756\) | 5.15329e17 | + | 5.03974e17i | 0.100391 | + | 0.0981786i | ||||
\(757\) | 5.20889e17i | 0.100605i | 0.998734 | + | 0.0503027i | \(0.0160186\pi\) | ||||
−0.998734 | + | 0.0503027i | \(0.983981\pi\) | |||||||
\(758\) | 3.07360e18 | + | 7.30498e18i | 0.588570 | + | 1.39884i | ||||
\(759\) | −3.55840e18 | −0.675590 | ||||||||
\(760\) | −7.72990e17 | + | 1.95808e18i | −0.145508 | + | 0.368588i | ||||
\(761\) | 1.39388e18 | 0.260150 | 0.130075 | − | 0.991504i | \(-0.458478\pi\) | ||||
0.130075 | + | 0.991504i | \(0.458478\pi\) | |||||||
\(762\) | 1.14908e17 | + | 2.73100e17i | 0.0212639 | + | 0.0505375i | ||||
\(763\) | − | 1.24393e18i | − | 0.228237i | ||||||
\(764\) | 4.09292e17 | − | 4.18514e17i | 0.0744606 | − | 0.0761383i | ||||
\(765\) | − | 1.82950e18i | − | 0.330015i | ||||||
\(766\) | 1.99423e18 | − | 8.39081e17i | 0.356688 | − | 0.150078i | ||||
\(767\) | −2.81792e18 | −0.499756 | ||||||||
\(768\) | −1.24809e17 | − | 2.79917e18i | −0.0219482 | − | 0.492246i | ||||
\(769\) | −5.95951e18 | −1.03918 | −0.519589 | − | 0.854417i | \(-0.673915\pi\) | ||||
−0.519589 | + | 0.854417i | \(0.673915\pi\) | |||||||
\(770\) | −1.01792e18 | + | 4.28292e17i | −0.176004 | + | 0.0740543i | ||||
\(771\) | − | 5.36525e16i | − | 0.00919891i | ||||||
\(772\) | 6.23498e17 | − | 6.37546e17i | 0.106004 | − | 0.108393i | ||||
\(773\) | 4.69569e18i | 0.791649i | 0.918326 | + | 0.395824i | \(0.129541\pi\) | ||||
−0.918326 | + | 0.395824i | \(0.870459\pi\) | |||||||
\(774\) | −3.52815e17 | − | 8.38530e17i | −0.0589835 | − | 0.140185i | ||||
\(775\) | 2.98851e18 | 0.495443 | ||||||||
\(776\) | −1.28168e18 | + | 3.24665e18i | −0.210707 | + | 0.533745i | ||||
\(777\) | 9.34051e17 | 0.152277 | ||||||||
\(778\) | 2.38659e18 | + | 5.67217e18i | 0.385843 | + | 0.917027i | ||||
\(779\) | − | 5.66240e18i | − | 0.907835i | ||||||
\(780\) | 7.84211e17 | + | 7.66931e17i | 0.124686 | + | 0.121939i | ||||
\(781\) | − | 4.19113e18i | − | 0.660845i | ||||||
\(782\) | −2.99162e18 | + | 1.25874e18i | −0.467802 | + | 0.196830i | ||||
\(783\) | −7.08478e18 | −1.09869 | ||||||||
\(784\) | 1.41040e17 | + | 6.32953e18i | 0.0216914 | + | 0.973457i | ||||
\(785\) | 3.39180e18 | 0.517342 | ||||||||
\(786\) | 4.24517e18 | − | 1.78617e18i | 0.642167 | − | 0.270195i | ||||
\(787\) | 2.14395e17i | 0.0321646i | 0.999871 | + | 0.0160823i | \(0.00511938\pi\) | ||||
−0.999871 | + | 0.0160823i | \(0.994881\pi\) | |||||||
\(788\) | −4.66944e18 | − | 4.56655e18i | −0.694776 | − | 0.679467i | ||||
\(789\) | 2.08503e18i | 0.307689i | ||||||||
\(790\) | −3.12877e18 | − | 7.43610e18i | −0.457928 | − | 1.08835i | ||||
\(791\) | −1.38620e18 | −0.201223 | ||||||||
\(792\) | −7.54409e18 | − | 2.97818e18i | −1.08616 | − | 0.428783i | ||||
\(793\) | 2.20379e18 | 0.314698 | ||||||||
\(794\) | −2.54732e18 | − | 6.05419e18i | −0.360787 | − | 0.857477i | ||||
\(795\) | 1.73777e18i | 0.244121i | ||||||||
\(796\) | 8.31795e18 | − | 8.50536e18i | 1.15899 | − | 1.18511i | ||||
\(797\) | − | 9.62508e18i | − | 1.33022i | −0.746743 | − | 0.665112i | \(-0.768384\pi\) | ||
0.746743 | − | 0.665112i | \(-0.231616\pi\) | |||||||
\(798\) | 2.78875e17 | − | 1.17338e17i | 0.0382288 | − | 0.0160849i | ||||
\(799\) | 6.05695e18 | 0.823569 | ||||||||
\(800\) | 1.26252e18 | + | 2.82298e18i | 0.170276 | + | 0.380736i | ||||
\(801\) | 3.66966e18 | 0.490924 | ||||||||
\(802\) | 2.74461e18 | − | 1.15481e18i | 0.364206 | − | 0.153241i | ||||
\(803\) | 3.64286e18i | 0.479503i | ||||||||
\(804\) | 1.67388e18 | − | 1.71160e18i | 0.218555 | − | 0.223479i | ||||
\(805\) | − | 8.49984e17i | − | 0.110087i | ||||||
\(806\) | −1.66234e18 | − | 3.95085e18i | −0.213570 | − | 0.507589i | ||||
\(807\) | 4.77789e18 | 0.608918 | ||||||||
\(808\) | −7.12387e18 | − | 2.81229e18i | −0.900622 | − | 0.355538i | ||||
\(809\) | −4.22254e18 | −0.529552 | −0.264776 | − | 0.964310i | \(-0.585298\pi\) | ||||
−0.264776 | + | 0.964310i | \(0.585298\pi\) | |||||||
\(810\) | 7.86816e17 | + | 1.87001e18i | 0.0978860 | + | 0.232644i | ||||
\(811\) | 1.17498e19i | 1.45009i | 0.688700 | + | 0.725047i | \(0.258182\pi\) | ||||
−0.688700 | + | 0.725047i | \(0.741818\pi\) | |||||||
\(812\) | 1.20173e18 | + | 1.17525e18i | 0.147127 | + | 0.143886i | ||||
\(813\) | − | 1.29762e18i | − | 0.157601i | ||||||
\(814\) | −2.24814e19 | + | 9.45914e18i | −2.70872 | + | 1.13971i | ||||
\(815\) | 2.26878e18 | 0.271187 | ||||||||
\(816\) | 2.37139e18 | − | 5.28413e16i | 0.281201 | − | 0.00626595i | ||||
\(817\) | −8.86151e17 | −0.104247 | ||||||||
\(818\) | −6.77262e17 | + | 2.84961e17i | −0.0790424 | + | 0.0332574i | ||||
\(819\) | 4.91677e17i | 0.0569291i | ||||||||
\(820\) | 8.31163e18 | + | 8.12849e18i | 0.954765 | + | 0.933727i | ||||
\(821\) | 6.22920e18i | 0.709907i | 0.934884 | + | 0.354954i | \(0.115503\pi\) | ||||
−0.934884 | + | 0.354954i | \(0.884497\pi\) | |||||||
\(822\) | −9.69214e17 | − | 2.30352e18i | −0.109585 | − | 0.260450i | ||||
\(823\) | 1.11473e19 | 1.25047 | 0.625233 | − | 0.780438i | \(-0.285004\pi\) | ||||
0.625233 | + | 0.780438i | \(0.285004\pi\) | |||||||
\(824\) | −1.06950e18 | + | 2.70916e18i | −0.119029 | + | 0.301515i | ||||
\(825\) | −2.87015e18 | −0.316924 | ||||||||
\(826\) | −6.18897e17 | − | 1.47092e18i | −0.0678029 | − | 0.161146i | ||||
\(827\) | 2.50398e18i | 0.272173i | 0.990697 | + | 0.136087i | \(0.0434526\pi\) | ||||
−0.990697 | + | 0.136087i | \(0.956547\pi\) | |||||||
\(828\) | 4.36469e18 | − | 4.46303e18i | 0.470713 | − | 0.481319i | ||||
\(829\) | 1.14681e19i | 1.22712i | 0.789648 | + | 0.613561i | \(0.210263\pi\) | ||||
−0.789648 | + | 0.613561i | \(0.789737\pi\) | |||||||
\(830\) | 1.06412e19 | − | 4.47735e18i | 1.12976 | − | 0.475350i | ||||
\(831\) | 2.64016e18 | 0.278114 | ||||||||
\(832\) | 3.02975e18 | − | 3.23933e18i | 0.316669 | − | 0.338574i | ||||
\(833\) | −5.35955e18 | −0.555822 | ||||||||
\(834\) | 1.11621e18 | − | 4.69652e17i | 0.114860 | − | 0.0483278i | ||||
\(835\) | 8.58963e18i | 0.877026i | ||||||||
\(836\) | −5.52387e18 | + | 5.64833e18i | −0.559632 | + | 0.572242i | ||||
\(837\) | 1.02313e19i | 1.02852i | ||||||||
\(838\) | −2.02338e18 | − | 4.80893e18i | −0.201832 | − | 0.479692i | ||||
\(839\) | 1.07752e19 | 1.06653 | 0.533265 | − | 0.845948i | \(-0.320965\pi\) | ||||
0.533265 | + | 0.845948i | \(0.320965\pi\) | |||||||
\(840\) | −2.28095e17 | + | 5.77791e17i | −0.0224027 | + | 0.0567486i | ||||
\(841\) | −6.26087e18 | −0.610184 | ||||||||
\(842\) | −1.36679e18 | − | 3.24844e18i | −0.132183 | − | 0.314156i | ||||
\(843\) | − | 1.71147e18i | − | 0.164244i | ||||||
\(844\) | 8.36766e18 | + | 8.18328e18i | 0.796853 | + | 0.779294i | ||||
\(845\) | − | 6.34297e18i | − | 0.599410i | ||||||
\(846\) | −1.07379e19 | + | 4.51802e18i | −1.00696 | + | 0.423683i | ||||
\(847\) | −2.40183e18 | −0.223512 | ||||||||
\(848\) | 7.02509e18 | − | 1.56539e17i | 0.648752 | − | 0.0144561i | ||||
\(849\) | 5.31454e17 | 0.0487041 | ||||||||
\(850\) | −2.41300e18 | + | 1.01528e18i | −0.219449 | + | 0.0923340i | ||||
\(851\) | − | 1.87725e19i | − | 1.69426i | ||||||
\(852\) | −1.68545e18 | − | 1.64831e18i | −0.150958 | − | 0.147632i | ||||
\(853\) | − | 1.25200e19i | − | 1.11285i | −0.830898 | − | 0.556425i | \(-0.812173\pi\) | ||
0.830898 | − | 0.556425i | \(-0.187827\pi\) | |||||||
\(854\) | 4.84017e17 | + | 1.15036e18i | 0.0426958 | + | 0.101474i | ||||
\(855\) | 3.42759e18 | 0.300060 | ||||||||
\(856\) | −5.09828e18 | − | 2.01265e18i | −0.442939 | − | 0.174859i | ||||
\(857\) | −3.34010e17 | −0.0287994 | −0.0143997 | − | 0.999896i | \(-0.504584\pi\) | ||||
−0.0143997 | + | 0.999896i | \(0.504584\pi\) | |||||||
\(858\) | 1.59650e18 | + | 3.79438e18i | 0.136616 | + | 0.324693i | ||||
\(859\) | 4.56359e18i | 0.387571i | 0.981044 | + | 0.193785i | \(0.0620765\pi\) | ||||
−0.981044 | + | 0.193785i | \(0.937923\pi\) | |||||||
\(860\) | 1.27209e18 | − | 1.30075e18i | 0.107220 | − | 0.109636i | ||||
\(861\) | − | 1.67087e18i | − | 0.139772i | ||||||
\(862\) | 4.49530e18 | − | 1.89142e18i | 0.373217 | − | 0.157033i | ||||
\(863\) | −1.77062e19 | −1.45900 | −0.729499 | − | 0.683982i | \(-0.760247\pi\) | ||||
−0.729499 | + | 0.683982i | \(0.760247\pi\) | |||||||
\(864\) | −9.66459e18 | + | 4.32230e18i | −0.790395 | + | 0.353488i | ||||
\(865\) | −1.51619e19 | −1.23069 | ||||||||
\(866\) | −4.22817e18 | + | 1.77902e18i | −0.340633 | + | 0.143323i | ||||
\(867\) | − | 4.15424e18i | − | 0.332175i | ||||||
\(868\) | 1.69721e18 | − | 1.73545e18i | 0.134696 | − | 0.137731i | ||||
\(869\) | − | 3.02769e19i | − | 2.38497i | ||||||
\(870\) | −2.36791e18 | − | 5.62778e18i | −0.185136 | − | 0.440009i | ||||
\(871\) | 3.78968e18 | 0.294093 | ||||||||
\(872\) | 1.69945e19 | + | 6.70891e18i | 1.30903 | + | 0.516767i | ||||
\(873\) | 5.68321e18 | 0.434511 | ||||||||
\(874\) | −2.35825e18 | − | 5.60481e18i | −0.178964 | − | 0.425340i | ||||
\(875\) | − | 2.32937e18i | − | 0.175463i | ||||||
\(876\) | 1.46496e18 | + | 1.43268e18i | 0.109534 | + | 0.107120i | ||||
\(877\) | 3.25336e18i | 0.241454i | 0.992686 | + | 0.120727i | \(0.0385226\pi\) | ||||
−0.992686 | + | 0.120727i | \(0.961477\pi\) | |||||||
\(878\) | 6.89298e18 | − | 2.90025e18i | 0.507800 | − | 0.213659i | ||||
\(879\) | 4.47081e18 | 0.326933 | ||||||||
\(880\) | −3.61352e17 | − | 1.62166e19i | −0.0262297 | − | 1.17712i | ||||
\(881\) | −1.09270e17 | −0.00787334 | −0.00393667 | − | 0.999992i | \(-0.501253\pi\) | ||||
−0.00393667 | + | 0.999992i | \(0.501253\pi\) | |||||||
\(882\) | 9.50154e18 | − | 3.99781e18i | 0.679592 | − | 0.285941i | ||||
\(883\) | − | 1.18999e19i | − | 0.844886i | −0.906389 | − | 0.422443i | \(-0.861173\pi\) | ||
0.906389 | − | 0.422443i | \(-0.138827\pi\) | |||||||
\(884\) | 2.68442e18 | + | 2.62527e18i | 0.189195 | + | 0.185026i | ||||
\(885\) | 5.79666e18i | 0.405552i | ||||||||
\(886\) | 2.61247e18 | + | 6.20903e18i | 0.181440 | + | 0.431226i | ||||
\(887\) | −1.07712e19 | −0.742612 | −0.371306 | − | 0.928511i | \(-0.621090\pi\) | ||||
−0.371306 | + | 0.928511i | \(0.621090\pi\) | |||||||
\(888\) | −5.03763e18 | + | 1.27609e19i | −0.344780 | + | 0.873369i | ||||
\(889\) | −2.65609e17 | −0.0180460 | ||||||||
\(890\) | 2.84624e18 | + | 6.76461e18i | 0.191971 | + | 0.456255i | ||||
\(891\) | 7.61396e18i | 0.509807i | ||||||||
\(892\) | −1.19321e19 | + | 1.22010e19i | −0.793134 | + | 0.811004i | ||||
\(893\) | 1.13477e19i | 0.748815i | ||||||||
\(894\) | 6.63945e17 | − | 2.79358e17i | 0.0434949 | − | 0.0183007i | ||||
\(895\) | −1.54572e19 | −1.00527 | ||||||||
\(896\) | 2.35632e18 | + | 8.70047e17i | 0.152136 | + | 0.0561747i | ||||
\(897\) | −3.16840e18 | −0.203090 | ||||||||
\(898\) | 6.22017e18 | − | 2.61716e18i | 0.395828 | − | 0.166546i | ||||
\(899\) | 2.38590e19i | 1.50735i | ||||||||
\(900\) | 3.52050e18 | − | 3.59982e18i | 0.220814 | − | 0.225790i | ||||
\(901\) | 5.94852e18i | 0.370423i | ||||||||
\(902\) | 1.69209e19 | + | 4.02156e19i | 1.04612 | + | 2.48629i | ||||
\(903\) | −2.61486e17 | −0.0160501 | ||||||||
\(904\) | 7.47619e18 | − | 1.89381e19i | 0.455602 | − | 1.15409i | ||||
\(905\) | 3.29054e18 | 0.199091 | ||||||||
\(906\) | 3.71201e17 | + | 8.82228e17i | 0.0222985 | + | 0.0529965i | ||||
\(907\) | − | 1.30063e19i | − | 0.775724i | −0.921717 | − | 0.387862i | \(-0.873214\pi\) | ||
0.921717 | − | 0.387862i | \(-0.126786\pi\) | |||||||
\(908\) | −1.70044e19 | − | 1.66297e19i | −1.00694 | − | 0.984750i | ||||
\(909\) | 1.24702e19i | 0.733178i | ||||||||
\(910\) | −9.06351e17 | + | 3.81351e17i | −0.0529087 | + | 0.0222616i | ||||
\(911\) | −1.98966e19 | −1.15321 | −0.576606 | − | 0.817022i | \(-0.695623\pi\) | ||||
−0.576606 | + | 0.817022i | \(0.695623\pi\) | |||||||
\(912\) | 9.89984e16 | + | 4.44280e18i | 0.00569720 | + | 0.255676i | ||||
\(913\) | 4.33270e19 | 2.47570 | ||||||||
\(914\) | −2.25226e19 | + | 9.47648e18i | −1.27782 | + | 0.537646i | ||||
\(915\) | − | 4.53336e18i | − | 0.255378i | ||||||
\(916\) | −1.29064e19 | − | 1.26220e19i | −0.721911 | − | 0.706003i | ||||
\(917\) | 4.12873e18i | 0.229306i | ||||||||
\(918\) | −3.47584e18 | − | 8.26098e18i | −0.191682 | − | 0.455569i | ||||
\(919\) | 2.17102e19 | 1.18881 | 0.594406 | − | 0.804165i | \(-0.297387\pi\) | ||||
0.594406 | + | 0.804165i | \(0.297387\pi\) | |||||||
\(920\) | 1.16124e19 | + | 4.58423e18i | 0.631396 | + | 0.249256i | ||||
\(921\) | 1.11391e19 | 0.601401 | ||||||||
\(922\) | −1.71660e18 | − | 4.07982e18i | −0.0920276 | − | 0.218721i | ||||
\(923\) | − | 3.73178e18i | − | 0.198657i | ||||||
\(924\) | −1.62999e18 | + | 1.66671e18i | −0.0861622 | + | 0.0881036i | ||||
\(925\) | − | 1.51416e19i | − | 0.794788i | ||||||
\(926\) | 3.38605e19 | − | 1.42470e19i | 1.76491 | − | 0.742593i | ||||
\(927\) | 4.74236e18 | 0.245457 | ||||||||
\(928\) | −2.25375e19 | + | 1.00795e19i | −1.15836 | + | 0.518055i | ||||
\(929\) | −7.48826e18 | −0.382189 | −0.191095 | − | 0.981572i | \(-0.561204\pi\) | ||||
−0.191095 | + | 0.981572i | \(0.561204\pi\) | |||||||
\(930\) | −8.12718e18 | + | 3.41955e18i | −0.411909 | + | 0.173312i | ||||
\(931\) | − | 1.00411e19i | − | 0.505371i | ||||||
\(932\) | −7.41115e18 | + | 7.57813e18i | −0.370409 | + | 0.378755i | ||||
\(933\) | 1.72656e19i | 0.856939i | ||||||||
\(934\) | −8.67775e18 | − | 2.06243e19i | −0.427713 | − | 1.01654i | ||||
\(935\) | 1.37315e19 | 0.672111 | ||||||||
\(936\) | −6.71725e18 | − | 2.65177e18i | −0.326511 | − | 0.128897i | ||||
\(937\) | 5.06673e18 | 0.244580 | 0.122290 | − | 0.992494i | \(-0.460976\pi\) | ||||
0.122290 | + | 0.992494i | \(0.460976\pi\) | |||||||
\(938\) | 8.32325e17 | + | 1.97817e18i | 0.0399002 | + | 0.0948301i | ||||
\(939\) | 5.14480e18i | 0.244930i | ||||||||
\(940\) | −1.66569e19 | − | 1.62899e19i | −0.787524 | − | 0.770171i | ||||
\(941\) | 2.40469e19i | 1.12909i | 0.825404 | + | 0.564543i | \(0.190947\pi\) | ||||
−0.825404 | + | 0.564543i | \(0.809053\pi\) | |||||||
\(942\) | 6.59967e18 | − | 2.77684e18i | 0.307745 | − | 0.129485i | ||||
\(943\) | −3.35810e19 | −1.55513 | ||||||||
\(944\) | 2.34336e19 | − | 5.22167e17i | 1.07776 | − | 0.0240155i | ||||
\(945\) | 2.34712e18 | 0.107208 | ||||||||
\(946\) | 6.29363e18 | − | 2.64807e18i | 0.285502 | − | 0.120126i | ||||
\(947\) | 1.41531e19i | 0.637643i | 0.947815 | + | 0.318822i | \(0.103287\pi\) | ||||
−0.947815 | + | 0.318822i | \(0.896713\pi\) | |||||||
\(948\) | −1.21757e19 | − | 1.19074e19i | −0.544804 | − | 0.532800i | ||||
\(949\) | 3.24360e18i | 0.144144i | ||||||||
\(950\) | −1.90213e18 | − | 4.52076e18i | −0.0839530 | − | 0.199530i | ||||
\(951\) | 9.33052e17 | 0.0409009 | ||||||||
\(952\) | −7.80787e17 | + | 1.97783e18i | −0.0339932 | + | 0.0861089i | ||||
\(953\) | 1.12693e18 | 0.0487295 | 0.0243648 | − | 0.999703i | \(-0.492244\pi\) | ||||
0.0243648 | + | 0.999703i | \(0.492244\pi\) | |||||||
\(954\) | −4.43714e18 | − | 1.05457e19i | −0.190563 | − | 0.452908i | ||||
\(955\) | − | 1.90617e18i | − | 0.0813091i | ||||||
\(956\) | −2.49025e19 | + | 2.54636e19i | −1.05503 | + | 1.07880i | ||||
\(957\) | − | 2.29141e19i | − | 0.964219i | ||||||
\(958\) | 1.40656e19 | − | 5.91815e18i | 0.587871 | − | 0.247349i | ||||
\(959\) | 2.24034e18 | 0.0930020 | ||||||||
\(960\) | −6.66355e18 | − | 6.23242e18i | −0.274753 | − | 0.256977i | ||||
\(961\) | 1.00377e19 | 0.411087 | ||||||||
\(962\) | −2.00174e19 | + | 8.42241e18i | −0.814273 | + | 0.342609i | ||||
\(963\) | 8.92447e18i | 0.360588i | ||||||||
\(964\) | 1.51109e19 | − | 1.54514e19i | 0.606442 | − | 0.620106i | ||||
\(965\) | − | 2.90377e18i | − | 0.115754i | ||||||
\(966\) | −6.95874e17 | − | 1.65387e18i | −0.0275536 | − | 0.0654863i | ||||
\(967\) | −5.95509e18 | −0.234216 | −0.117108 | − | 0.993119i | \(-0.537362\pi\) | ||||
−0.117108 | + | 0.993119i | \(0.537362\pi\) | |||||||
\(968\) | 1.29538e19 | − | 3.28136e19i | 0.506067 | − | 1.28193i | ||||
\(969\) | −3.76196e18 | −0.145985 | ||||||||
\(970\) | 4.40797e18 | + | 1.04764e19i | 0.169911 | + | 0.403826i | ||||
\(971\) | − | 4.01654e19i | − | 1.53790i | −0.639311 | − | 0.768948i | \(-0.720780\pi\) | ||
0.639311 | − | 0.768948i | \(-0.279220\pi\) | |||||||
\(972\) | 1.93375e19 | + | 1.89114e19i | 0.735479 | + | 0.719273i | ||||
\(973\) | 1.08560e18i | 0.0410144i | ||||||||
\(974\) | −6.59260e18 | + | 2.77386e18i | −0.247414 | + | 0.104100i | ||||
\(975\) | −2.55558e18 | −0.0952709 | ||||||||
\(976\) | −1.83265e19 | + | 4.08368e17i | −0.678667 | + | 0.0151226i | ||||
\(977\) | −2.45562e19 | −0.903331 | −0.451665 | − | 0.892187i | \(-0.649170\pi\) | ||||
−0.451665 | + | 0.892187i | \(0.649170\pi\) | |||||||
\(978\) | 4.41453e18 | − | 1.85743e18i | 0.161318 | − | 0.0678750i | ||||
\(979\) | 2.75429e19i | 0.999819i | ||||||||
\(980\) | 1.47390e19 | + | 1.44143e19i | 0.531495 | + | 0.519784i | ||||
\(981\) | − | 2.97486e19i | − | 1.06566i | ||||||
\(982\) | 6.75677e18 | + | 1.60587e19i | 0.240444 | + | 0.571461i | ||||
\(983\) | 4.37287e19 | 1.54586 | 0.772928 | − | 0.634494i | \(-0.218791\pi\) | ||||
0.772928 | + | 0.634494i | \(0.218791\pi\) | |||||||
\(984\) | 2.28272e19 | + | 9.01151e18i | 0.801651 | + | 0.316468i | ||||
\(985\) | −2.12675e19 | −0.741960 | ||||||||
\(986\) | −8.10555e18 | − | 1.92643e19i | −0.280920 | − | 0.667658i | ||||
\(987\) | 3.34850e18i | 0.115289i | ||||||||
\(988\) | −4.91845e18 | + | 5.02927e18i | −0.168232 | + | 0.172022i | ||||
\(989\) | 5.25534e18i | 0.178577i | ||||||||
\(990\) | −2.43434e19 | + | 1.02426e19i | −0.821776 | + | 0.345766i | ||||
\(991\) | −3.53628e19 | −1.18595 | −0.592976 | − | 0.805220i | \(-0.702047\pi\) | ||||
−0.592976 | + | 0.805220i | \(0.702047\pi\) | |||||||
\(992\) | 1.45559e19 | + | 3.25469e19i | 0.484970 | + | 1.08439i | ||||
\(993\) | −1.33639e19 | −0.442349 | ||||||||
\(994\) | 1.94795e18 | − | 8.19609e17i | 0.0640570 | − | 0.0269523i | ||||
\(995\) | − | 3.87386e19i | − | 1.26559i | ||||||
\(996\) | 1.70398e19 | − | 1.74238e19i | 0.553070 | − | 0.565531i | ||||
\(997\) | 1.42415e19i | 0.459238i | 0.973281 | + | 0.229619i | \(0.0737479\pi\) | ||||
−0.973281 | + | 0.229619i | \(0.926252\pi\) | |||||||
\(998\) | 7.82859e18 | + | 1.86061e19i | 0.250804 | + | 0.596082i | ||||
\(999\) | 5.18379e19 | 1.64995 |
(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 | 8.14.b.b.5.2 | yes | 10 | |
3.2 | odd | 2 | 72.14.d.c.37.9 | 10 | |||
4.3 | odd | 2 | 32.14.b.b.17.4 | 10 | |||
8.3 | odd | 2 | 32.14.b.b.17.7 | 10 | |||
8.5 | even | 2 | inner | 8.14.b.b.5.1 | ✓ | 10 | |
24.5 | odd | 2 | 72.14.d.c.37.10 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8.14.b.b.5.1 | ✓ | 10 | 8.5 | even | 2 | inner | |
8.14.b.b.5.2 | yes | 10 | 1.1 | even | 1 | trivial | |
32.14.b.b.17.4 | 10 | 4.3 | odd | 2 | |||
32.14.b.b.17.7 | 10 | 8.3 | odd | 2 | |||
72.14.d.c.37.9 | 10 | 3.2 | odd | 2 | |||
72.14.d.c.37.10 | 10 | 24.5 | odd | 2 |