Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,10,Mod(4,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("15.4");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.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: | \(7.72553754246\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 939x^{6} + 217699x^{4} + 14559561x^{2} + 31136400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 3^{12}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 4.5 | ||
Root | \(10.9137i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.4 |
Dual form | 15.10.b.a.4.4 |
$q$-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 \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 14.3372i | 0.633619i | 0.948489 | + | 0.316810i | \(0.102612\pi\) | ||||
−0.948489 | + | 0.316810i | \(0.897388\pi\) | |||||||
\(3\) | 81.0000i | 0.577350i | ||||||||
\(4\) | 306.446 | 0.598526 | ||||||||
\(5\) | 1380.00 | − | 220.717i | 0.987450 | − | 0.157932i | ||||
\(6\) | −1161.31 | −0.365820 | ||||||||
\(7\) | 2878.61i | 0.453150i | 0.973994 | + | 0.226575i | \(0.0727529\pi\) | ||||
−0.973994 | + | 0.226575i | \(0.927247\pi\) | |||||||
\(8\) | 11734.2i | 1.01286i | ||||||||
\(9\) | −6561.00 | −0.333333 | ||||||||
\(10\) | 3164.45 | + | 19785.3i | 0.100069 | + | 0.625667i | ||||
\(11\) | −23286.0 | −0.479543 | −0.239772 | − | 0.970829i | \(-0.577073\pi\) | ||||
−0.239772 | + | 0.970829i | \(0.577073\pi\) | |||||||
\(12\) | 24822.1i | 0.345559i | ||||||||
\(13\) | 112501.i | 1.09247i | 0.837630 | + | 0.546237i | \(0.183940\pi\) | ||||
−0.837630 | + | 0.546237i | \(0.816060\pi\) | |||||||
\(14\) | −41271.2 | −0.287125 | ||||||||
\(15\) | 17878.0 | + | 111780.i | 0.0911820 | + | 0.570105i | ||||
\(16\) | −11335.0 | −0.0432396 | ||||||||
\(17\) | − | 115964.i | − | 0.336745i | −0.985723 | − | 0.168373i | \(-0.946149\pi\) | ||
0.985723 | − | 0.168373i | \(-0.0538512\pi\) | |||||||
\(18\) | − | 94066.2i | − | 0.211206i | ||||||
\(19\) | 213578. | 0.375980 | 0.187990 | − | 0.982171i | \(-0.439803\pi\) | ||||
0.187990 | + | 0.982171i | \(0.439803\pi\) | |||||||
\(20\) | 422896. | − | 67637.6i | 0.591015 | − | 0.0945264i | ||||
\(21\) | −233168. | −0.261627 | ||||||||
\(22\) | − | 333855.i | − | 0.303848i | ||||||
\(23\) | − | 1.83629e6i | − | 1.36825i | −0.729363 | − | 0.684127i | \(-0.760184\pi\) | ||
0.729363 | − | 0.684127i | \(-0.239816\pi\) | |||||||
\(24\) | −950470. | −0.584773 | ||||||||
\(25\) | 1.85569e6 | − | 609179.i | 0.950115 | − | 0.311900i | ||||
\(26\) | −1.61295e6 | −0.692213 | ||||||||
\(27\) | − | 531441.i | − | 0.192450i | ||||||
\(28\) | 882139.i | 0.271223i | ||||||||
\(29\) | −3.67540e6 | −0.964969 | −0.482485 | − | 0.875904i | \(-0.660266\pi\) | ||||
−0.482485 | + | 0.875904i | \(0.660266\pi\) | |||||||
\(30\) | −1.60261e6 | + | 256321.i | −0.361229 | + | 0.0577747i | ||||
\(31\) | 8.85139e6 | 1.72141 | 0.860704 | − | 0.509105i | \(-0.170024\pi\) | ||||
0.860704 | + | 0.509105i | \(0.170024\pi\) | |||||||
\(32\) | 5.84540e6i | 0.985460i | ||||||||
\(33\) | − | 1.88617e6i | − | 0.276864i | ||||||
\(34\) | 1.66259e6 | 0.213368 | ||||||||
\(35\) | 635358. | + | 3.97250e6i | 0.0715669 | + | 0.447463i | ||||
\(36\) | −2.01059e6 | −0.199509 | ||||||||
\(37\) | 9.17921e6i | 0.805188i | 0.915379 | + | 0.402594i | \(0.131891\pi\) | ||||
−0.915379 | + | 0.402594i | \(0.868109\pi\) | |||||||
\(38\) | 3.06210e6i | 0.238228i | ||||||||
\(39\) | −9.11258e6 | −0.630741 | ||||||||
\(40\) | 2.58993e6 | + | 1.61932e7i | 0.159963 | + | 1.00015i | ||||
\(41\) | −1.17626e7 | −0.650093 | −0.325046 | − | 0.945698i | \(-0.605380\pi\) | ||||
−0.325046 | + | 0.945698i | \(0.605380\pi\) | |||||||
\(42\) | − | 3.34297e6i | − | 0.165772i | ||||||
\(43\) | − | 3.93230e7i | − | 1.75403i | −0.480459 | − | 0.877017i | \(-0.659530\pi\) | ||
0.480459 | − | 0.877017i | \(-0.340470\pi\) | |||||||
\(44\) | −7.13589e6 | −0.287019 | ||||||||
\(45\) | −9.05420e6 | + | 1.44812e6i | −0.329150 | + | 0.0526440i | ||||
\(46\) | 2.63272e7 | 0.866952 | ||||||||
\(47\) | − | 3.26882e7i | − | 0.977126i | −0.872529 | − | 0.488563i | \(-0.837521\pi\) | ||
0.872529 | − | 0.488563i | \(-0.162479\pi\) | |||||||
\(48\) | − | 918134.i | − | 0.0249644i | ||||||
\(49\) | 3.20672e7 | 0.794655 | ||||||||
\(50\) | 8.73391e6 | + | 2.66054e7i | 0.197626 | + | 0.602011i | ||||
\(51\) | 9.39305e6 | 0.194420 | ||||||||
\(52\) | 3.44754e7i | 0.653875i | ||||||||
\(53\) | − | 1.04826e8i | − | 1.82486i | −0.409238 | − | 0.912428i | \(-0.634206\pi\) | ||
0.409238 | − | 0.912428i | \(-0.365794\pi\) | |||||||
\(54\) | 7.61936e6 | 0.121940 | ||||||||
\(55\) | −3.21348e7 | + | 5.13961e6i | −0.473525 | + | 0.0757352i | ||||
\(56\) | −3.37782e7 | −0.458977 | ||||||||
\(57\) | 1.72998e7i | 0.217072i | ||||||||
\(58\) | − | 5.26948e7i | − | 0.611423i | ||||||
\(59\) | 1.02836e8 | 1.10486 | 0.552432 | − | 0.833558i | \(-0.313700\pi\) | ||||
0.552432 | + | 0.833558i | \(0.313700\pi\) | |||||||
\(60\) | 5.47865e6 | + | 3.42546e7i | 0.0545749 | + | 0.341223i | ||||
\(61\) | −1.65686e8 | −1.53215 | −0.766074 | − | 0.642752i | \(-0.777792\pi\) | ||||
−0.766074 | + | 0.642752i | \(0.777792\pi\) | |||||||
\(62\) | 1.26904e8i | 1.09072i | ||||||||
\(63\) | − | 1.88866e7i | − | 0.151050i | ||||||
\(64\) | −8.96099e7 | −0.667646 | ||||||||
\(65\) | 2.48308e7 | + | 1.55252e8i | 0.172537 | + | 1.07876i | ||||
\(66\) | 2.70423e7 | 0.175427 | ||||||||
\(67\) | 1.76387e8i | 1.06937i | 0.845051 | + | 0.534686i | \(0.179570\pi\) | ||||
−0.845051 | + | 0.534686i | \(0.820430\pi\) | |||||||
\(68\) | − | 3.55365e7i | − | 0.201551i | ||||||
\(69\) | 1.48740e8 | 0.789962 | ||||||||
\(70\) | −5.69544e7 | + | 9.10923e6i | −0.283521 | + | 0.0453462i | ||||
\(71\) | 1.30237e8 | 0.608234 | 0.304117 | − | 0.952635i | \(-0.401639\pi\) | ||||
0.304117 | + | 0.952635i | \(0.401639\pi\) | |||||||
\(72\) | − | 7.69880e7i | − | 0.337619i | ||||||
\(73\) | − | 2.35713e8i | − | 0.971474i | −0.874105 | − | 0.485737i | \(-0.838551\pi\) | ||
0.874105 | − | 0.485737i | \(-0.161449\pi\) | |||||||
\(74\) | −1.31604e8 | −0.510183 | ||||||||
\(75\) | 4.93435e7 | + | 1.50311e8i | 0.180075 | + | 0.548549i | ||||
\(76\) | 6.54500e7 | 0.225034 | ||||||||
\(77\) | − | 6.70314e7i | − | 0.217305i | ||||||
\(78\) | − | 1.30649e8i | − | 0.399649i | ||||||
\(79\) | −1.56763e8 | −0.452815 | −0.226407 | − | 0.974033i | \(-0.572698\pi\) | ||||
−0.226407 | + | 0.974033i | \(0.572698\pi\) | |||||||
\(80\) | −1.56423e7 | + | 2.50182e6i | −0.0426969 | + | 0.00682891i | ||||
\(81\) | 4.30467e7 | 0.111111 | ||||||||
\(82\) | − | 1.68642e8i | − | 0.411911i | ||||||
\(83\) | − | 3.38241e7i | − | 0.0782303i | −0.999235 | − | 0.0391151i | \(-0.987546\pi\) | ||
0.999235 | − | 0.0391151i | \(-0.0124539\pi\) | |||||||
\(84\) | −7.14532e7 | −0.156590 | ||||||||
\(85\) | −2.55951e7 | − | 1.60030e8i | −0.0531828 | − | 0.332519i | ||||
\(86\) | 5.63780e8 | 1.11139 | ||||||||
\(87\) | − | 2.97707e8i | − | 0.557125i | ||||||
\(88\) | − | 2.73242e8i | − | 0.485709i | ||||||
\(89\) | −4.86766e8 | −0.822366 | −0.411183 | − | 0.911553i | \(-0.634884\pi\) | ||||
−0.411183 | + | 0.911553i | \(0.634884\pi\) | |||||||
\(90\) | −2.07620e7 | − | 1.29812e8i | −0.0333562 | − | 0.208556i | ||||
\(91\) | −3.23847e8 | −0.495055 | ||||||||
\(92\) | − | 5.62724e8i | − | 0.818936i | ||||||
\(93\) | 7.16963e8i | 0.993856i | ||||||||
\(94\) | 4.68656e8 | 0.619126 | ||||||||
\(95\) | 2.94738e8 | − | 4.71402e7i | 0.371262 | − | 0.0593793i | ||||
\(96\) | −4.73477e8 | −0.568956 | ||||||||
\(97\) | 1.40255e9i | 1.60859i | 0.594231 | + | 0.804294i | \(0.297456\pi\) | ||||
−0.594231 | + | 0.804294i | \(0.702544\pi\) | |||||||
\(98\) | 4.59753e8i | 0.503509i | ||||||||
\(99\) | 1.52779e8 | 0.159848 | ||||||||
\(100\) | 5.68669e8 | − | 1.86680e8i | 0.568669 | − | 0.186680i | ||||
\(101\) | −3.51675e8 | −0.336276 | −0.168138 | − | 0.985763i | \(-0.553775\pi\) | ||||
−0.168138 | + | 0.985763i | \(0.553775\pi\) | |||||||
\(102\) | 1.34670e8i | 0.123188i | ||||||||
\(103\) | 1.09902e9i | 0.962137i | 0.876683 | + | 0.481069i | \(0.159751\pi\) | ||||
−0.876683 | + | 0.481069i | \(0.840249\pi\) | |||||||
\(104\) | −1.32011e9 | −1.10652 | ||||||||
\(105\) | −3.21772e8 | + | 5.14640e7i | −0.258343 | + | 0.0413192i | ||||
\(106\) | 1.50291e9 | 1.15626 | ||||||||
\(107\) | − | 1.42345e8i | − | 0.104982i | −0.998621 | − | 0.0524910i | \(-0.983284\pi\) | ||
0.998621 | − | 0.0524910i | \(-0.0167161\pi\) | |||||||
\(108\) | − | 1.62858e8i | − | 0.115186i | ||||||
\(109\) | 1.23981e9 | 0.841273 | 0.420637 | − | 0.907229i | \(-0.361807\pi\) | ||||
0.420637 | + | 0.907229i | \(0.361807\pi\) | |||||||
\(110\) | −7.36874e7 | − | 4.60721e8i | −0.0479873 | − | 0.300035i | ||||
\(111\) | −7.43516e8 | −0.464876 | ||||||||
\(112\) | − | 3.26291e7i | − | 0.0195940i | ||||||
\(113\) | 1.73091e9i | 0.998670i | 0.866409 | + | 0.499335i | \(0.166422\pi\) | ||||
−0.866409 | + | 0.499335i | \(0.833578\pi\) | |||||||
\(114\) | −2.48030e8 | −0.137541 | ||||||||
\(115\) | −4.05300e8 | − | 2.53409e9i | −0.216091 | − | 1.35108i | ||||
\(116\) | −1.12631e9 | −0.577560 | ||||||||
\(117\) | − | 7.38119e8i | − | 0.364158i | ||||||
\(118\) | 1.47437e9i | 0.700064i | ||||||||
\(119\) | 3.33814e8 | 0.152596 | ||||||||
\(120\) | −1.31165e9 | + | 2.09784e8i | −0.577435 | + | 0.0923544i | ||||
\(121\) | −1.81571e9 | −0.770038 | ||||||||
\(122\) | − | 2.37546e9i | − | 0.970799i | ||||||
\(123\) | − | 9.52769e8i | − | 0.375331i | ||||||
\(124\) | 2.71247e9 | 1.03031 | ||||||||
\(125\) | 2.42641e9 | − | 1.25025e9i | 0.888932 | − | 0.458039i | ||||
\(126\) | 2.70780e8 | 0.0957083 | ||||||||
\(127\) | − | 4.01797e9i | − | 1.37053i | −0.728292 | − | 0.685267i | \(-0.759685\pi\) | ||
0.728292 | − | 0.685267i | \(-0.240315\pi\) | |||||||
\(128\) | 1.70809e9i | 0.562426i | ||||||||
\(129\) | 3.18516e9 | 1.01269 | ||||||||
\(130\) | −2.22587e9 | + | 3.56004e8i | −0.683526 | + | 0.109323i | ||||
\(131\) | 1.65761e9 | 0.491768 | 0.245884 | − | 0.969299i | \(-0.420922\pi\) | ||||
0.245884 | + | 0.969299i | \(0.420922\pi\) | |||||||
\(132\) | − | 5.78007e8i | − | 0.165711i | ||||||
\(133\) | 6.14808e8i | 0.170376i | ||||||||
\(134\) | −2.52888e9 | −0.677575 | ||||||||
\(135\) | −1.17298e8 | − | 7.33390e8i | −0.0303940 | − | 0.190035i | ||||
\(136\) | 1.36074e9 | 0.341075 | ||||||||
\(137\) | 3.50673e9i | 0.850472i | 0.905083 | + | 0.425236i | \(0.139809\pi\) | ||||
−0.905083 | + | 0.425236i | \(0.860191\pi\) | |||||||
\(138\) | 2.13251e9i | 0.500535i | ||||||||
\(139\) | −2.92997e9 | −0.665729 | −0.332864 | − | 0.942975i | \(-0.608015\pi\) | ||||
−0.332864 | + | 0.942975i | \(0.608015\pi\) | |||||||
\(140\) | 1.94703e8 | + | 1.21735e9i | 0.0428347 | + | 0.267819i | ||||
\(141\) | 2.64774e9 | 0.564144 | ||||||||
\(142\) | 1.86722e9i | 0.385389i | ||||||||
\(143\) | − | 2.61970e9i | − | 0.523889i | ||||||
\(144\) | 7.43689e7 | 0.0144132 | ||||||||
\(145\) | −5.07206e9 | + | 8.11221e8i | −0.952859 | + | 0.152399i | ||||
\(146\) | 3.37946e9 | 0.615545 | ||||||||
\(147\) | 2.59744e9i | 0.458794i | ||||||||
\(148\) | 2.81293e9i | 0.481927i | ||||||||
\(149\) | −6.83881e9 | −1.13669 | −0.568345 | − | 0.822790i | \(-0.692416\pi\) | ||||
−0.568345 | + | 0.822790i | \(0.692416\pi\) | |||||||
\(150\) | −2.15504e9 | + | 7.07446e8i | −0.347571 | + | 0.114099i | ||||
\(151\) | −7.68746e9 | −1.20333 | −0.601667 | − | 0.798747i | \(-0.705497\pi\) | ||||
−0.601667 | + | 0.798747i | \(0.705497\pi\) | |||||||
\(152\) | 2.50616e9i | 0.380814i | ||||||||
\(153\) | 7.60837e8i | 0.112248i | ||||||||
\(154\) | 9.61041e8 | 0.137689 | ||||||||
\(155\) | 1.22149e10 | − | 1.95365e9i | 1.69980 | − | 0.271865i | ||||
\(156\) | −2.79251e9 | −0.377515 | ||||||||
\(157\) | 2.91924e9i | 0.383461i | 0.981448 | + | 0.191730i | \(0.0614099\pi\) | ||||
−0.981448 | + | 0.191730i | \(0.938590\pi\) | |||||||
\(158\) | − | 2.24753e9i | − | 0.286912i | ||||||
\(159\) | 8.49092e9 | 1.05358 | ||||||||
\(160\) | 1.29018e9 | + | 8.06666e9i | 0.155636 | + | 0.973092i | ||||
\(161\) | 5.28598e9 | 0.620025 | ||||||||
\(162\) | 6.17168e8i | 0.0704022i | ||||||||
\(163\) | − | 1.45510e10i | − | 1.61454i | −0.590181 | − | 0.807271i | \(-0.700943\pi\) | ||
0.590181 | − | 0.807271i | \(-0.299057\pi\) | |||||||
\(164\) | −3.60459e9 | −0.389098 | ||||||||
\(165\) | −4.16308e8 | − | 2.60291e9i | −0.0437257 | − | 0.273390i | ||||
\(166\) | 4.84942e8 | 0.0495682 | ||||||||
\(167\) | − | 3.12784e8i | − | 0.0311186i | −0.999879 | − | 0.0155593i | \(-0.995047\pi\) | ||
0.999879 | − | 0.0155593i | \(-0.00495289\pi\) | |||||||
\(168\) | − | 2.73604e9i | − | 0.264990i | ||||||
\(169\) | −2.05198e9 | −0.193501 | ||||||||
\(170\) | 2.29438e9 | − | 3.66961e8i | 0.210690 | − | 0.0336977i | ||||
\(171\) | −1.40128e9 | −0.125327 | ||||||||
\(172\) | − | 1.20503e10i | − | 1.04984i | ||||||
\(173\) | − | 7.25178e9i | − | 0.615513i | −0.951465 | − | 0.307756i | \(-0.900422\pi\) | ||
0.951465 | − | 0.307756i | \(-0.0995782\pi\) | |||||||
\(174\) | 4.26828e9 | 0.353005 | ||||||||
\(175\) | 1.75359e9 | + | 5.34183e9i | 0.141337 | + | 0.430545i | ||||
\(176\) | 2.63947e8 | 0.0207352 | ||||||||
\(177\) | 8.32968e9i | 0.637894i | ||||||||
\(178\) | − | 6.97885e9i | − | 0.521067i | ||||||
\(179\) | −2.55227e10 | −1.85818 | −0.929091 | − | 0.369851i | \(-0.879409\pi\) | ||||
−0.929091 | + | 0.369851i | \(0.879409\pi\) | |||||||
\(180\) | −2.77462e9 | + | 4.43770e8i | −0.197005 | + | 0.0315088i | ||||
\(181\) | −3.92246e9 | −0.271647 | −0.135823 | − | 0.990733i | \(-0.543368\pi\) | ||||
−0.135823 | + | 0.990733i | \(0.543368\pi\) | |||||||
\(182\) | − | 4.64305e9i | − | 0.313677i | ||||||
\(183\) | − | 1.34205e10i | − | 0.884586i | ||||||
\(184\) | 2.15474e10 | 1.38585 | ||||||||
\(185\) | 2.02600e9 | + | 1.26673e10i | 0.127165 | + | 0.795083i | ||||
\(186\) | −1.02792e10 | −0.629726 | ||||||||
\(187\) | 2.70033e9i | 0.161484i | ||||||||
\(188\) | − | 1.00171e10i | − | 0.584836i | ||||||
\(189\) | 1.52981e9 | 0.0872088 | ||||||||
\(190\) | 6.75857e8 | + | 4.22571e9i | 0.0376239 | + | 0.235239i | ||||
\(191\) | 1.92925e10 | 1.04891 | 0.524456 | − | 0.851438i | \(-0.324269\pi\) | ||||
0.524456 | + | 0.851438i | \(0.324269\pi\) | |||||||
\(192\) | − | 7.25840e9i | − | 0.385466i | ||||||
\(193\) | 2.10306e10i | 1.09105i | 0.838095 | + | 0.545525i | \(0.183670\pi\) | ||||
−0.838095 | + | 0.545525i | \(0.816330\pi\) | |||||||
\(194\) | −2.01086e10 | −1.01923 | ||||||||
\(195\) | −1.25754e10 | + | 2.01130e9i | −0.622825 | + | 0.0996141i | ||||
\(196\) | 9.82685e9 | 0.475622 | ||||||||
\(197\) | 4.12625e10i | 1.95190i | 0.217991 | + | 0.975951i | \(0.430050\pi\) | ||||
−0.217991 | + | 0.975951i | \(0.569950\pi\) | |||||||
\(198\) | 2.19042e9i | 0.101283i | ||||||||
\(199\) | 3.42528e10 | 1.54831 | 0.774154 | − | 0.632997i | \(-0.218175\pi\) | ||||
0.774154 | + | 0.632997i | \(0.218175\pi\) | |||||||
\(200\) | 7.14823e9 | + | 2.17751e10i | 0.315910 | + | 0.962331i | ||||
\(201\) | −1.42873e10 | −0.617402 | ||||||||
\(202\) | − | 5.04203e9i | − | 0.213071i | ||||||
\(203\) | − | 1.05801e10i | − | 0.437276i | ||||||
\(204\) | 2.87846e9 | 0.116365 | ||||||||
\(205\) | −1.62324e10 | + | 2.59620e9i | −0.641934 | + | 0.102670i | ||||
\(206\) | −1.57568e10 | −0.609629 | ||||||||
\(207\) | 1.20479e10i | 0.456084i | ||||||||
\(208\) | − | 1.27520e9i | − | 0.0472381i | ||||||
\(209\) | −4.97337e9 | −0.180299 | ||||||||
\(210\) | −7.37848e8 | − | 4.61330e9i | −0.0261806 | − | 0.163691i | ||||
\(211\) | 8.11815e9 | 0.281959 | 0.140979 | − | 0.990013i | \(-0.454975\pi\) | ||||
0.140979 | + | 0.990013i | \(0.454975\pi\) | |||||||
\(212\) | − | 3.21235e10i | − | 1.09222i | ||||||
\(213\) | 1.05492e10i | 0.351164i | ||||||||
\(214\) | 2.04082e9 | 0.0665187 | ||||||||
\(215\) | −8.67923e9 | − | 5.42658e10i | −0.277018 | − | 1.73202i | ||||
\(216\) | 6.23603e9 | 0.194924 | ||||||||
\(217\) | 2.54797e10i | 0.780057i | ||||||||
\(218\) | 1.77754e10i | 0.533047i | ||||||||
\(219\) | 1.90928e10 | 0.560881 | ||||||||
\(220\) | −9.84755e9 | + | 1.57501e9i | −0.283417 | + | 0.0453295i | ||||
\(221\) | 1.30460e10 | 0.367886 | ||||||||
\(222\) | − | 1.06599e10i | − | 0.294554i | ||||||
\(223\) | − | 1.23274e10i | − | 0.333811i | −0.985973 | − | 0.166906i | \(-0.946622\pi\) | ||
0.985973 | − | 0.166906i | \(-0.0533775\pi\) | |||||||
\(224\) | −1.68266e10 | −0.446562 | ||||||||
\(225\) | −1.21752e10 | + | 3.99682e9i | −0.316705 | + | 0.103967i | ||||
\(226\) | −2.48164e10 | −0.632777 | ||||||||
\(227\) | − | 1.29830e10i | − | 0.324532i | −0.986747 | − | 0.162266i | \(-0.948120\pi\) | ||
0.986747 | − | 0.162266i | \(-0.0518802\pi\) | |||||||
\(228\) | 5.30145e9i | 0.129924i | ||||||||
\(229\) | −1.23093e9 | −0.0295784 | −0.0147892 | − | 0.999891i | \(-0.504708\pi\) | ||||
−0.0147892 | + | 0.999891i | \(0.504708\pi\) | |||||||
\(230\) | 3.63317e10 | − | 5.81086e9i | 0.856072 | − | 0.136919i | ||||
\(231\) | 5.42954e9 | 0.125461 | ||||||||
\(232\) | − | 4.31278e10i | − | 0.977376i | ||||||
\(233\) | 1.54183e9i | 0.0342716i | 0.999853 | + | 0.0171358i | \(0.00545476\pi\) | ||||
−0.999853 | + | 0.0171358i | \(0.994545\pi\) | |||||||
\(234\) | 1.05825e10 | 0.230738 | ||||||||
\(235\) | −7.21482e9 | − | 4.51098e10i | −0.154319 | − | 0.964863i | ||||
\(236\) | 3.15135e10 | 0.661291 | ||||||||
\(237\) | − | 1.26978e10i | − | 0.261433i | ||||||
\(238\) | 4.78595e9i | 0.0966879i | ||||||||
\(239\) | −6.33257e9 | −0.125542 | −0.0627711 | − | 0.998028i | \(-0.519994\pi\) | ||||
−0.0627711 | + | 0.998028i | \(0.519994\pi\) | |||||||
\(240\) | −2.02647e8 | − | 1.26703e9i | −0.00394267 | − | 0.0246511i | ||||
\(241\) | −7.59959e7 | −0.00145115 | −0.000725577 | − | 1.00000i | \(-0.500231\pi\) | ||||
−0.000725577 | 1.00000i | \(0.500231\pi\) | ||||||||
\(242\) | − | 2.60321e10i | − | 0.487911i | ||||||
\(243\) | 3.48678e9i | 0.0641500i | ||||||||
\(244\) | −5.07736e10 | −0.917031 | ||||||||
\(245\) | 4.42528e10 | − | 7.07776e9i | 0.784682 | − | 0.125501i | ||||
\(246\) | 1.36600e10 | 0.237817 | ||||||||
\(247\) | 2.40277e10i | 0.410749i | ||||||||
\(248\) | 1.03864e11i | 1.74354i | ||||||||
\(249\) | 2.73975e9 | 0.0451663 | ||||||||
\(250\) | 1.79251e10 | + | 3.47878e10i | 0.290222 | + | 0.563245i | ||||
\(251\) | −6.53735e10 | −1.03961 | −0.519804 | − | 0.854285i | \(-0.673995\pi\) | ||||
−0.519804 | + | 0.854285i | \(0.673995\pi\) | |||||||
\(252\) | − | 5.78771e9i | − | 0.0904075i | ||||||
\(253\) | 4.27599e10i | 0.656137i | ||||||||
\(254\) | 5.76063e10 | 0.868397 | ||||||||
\(255\) | 1.29624e10 | − | 2.07320e9i | 0.191980 | − | 0.0307051i | ||||
\(256\) | −7.03695e10 | −1.02401 | ||||||||
\(257\) | 1.09014e9i | 0.0155878i | 0.999970 | + | 0.00779389i | \(0.00248090\pi\) | ||||
−0.999970 | + | 0.00779389i | \(0.997519\pi\) | |||||||
\(258\) | 4.56662e10i | 0.641662i | ||||||||
\(259\) | −2.64234e10 | −0.364871 | ||||||||
\(260\) | 7.60930e9 | + | 4.75762e10i | 0.103268 | + | 0.645669i | ||||
\(261\) | 2.41143e10 | 0.321656 | ||||||||
\(262\) | 2.37654e10i | 0.311594i | ||||||||
\(263\) | 3.67524e10i | 0.473680i | 0.971549 | + | 0.236840i | \(0.0761117\pi\) | ||||
−0.971549 | + | 0.236840i | \(0.923888\pi\) | |||||||
\(264\) | 2.21326e10 | 0.280424 | ||||||||
\(265\) | −2.31369e10 | − | 1.44660e11i | −0.288203 | − | 1.80195i | ||||
\(266\) | −8.81461e9 | −0.107953 | ||||||||
\(267\) | − | 3.94280e10i | − | 0.474793i | ||||||
\(268\) | 5.40529e10i | 0.640048i | ||||||||
\(269\) | −8.87738e10 | −1.03371 | −0.516856 | − | 0.856072i | \(-0.672898\pi\) | ||||
−0.516856 | + | 0.856072i | \(0.672898\pi\) | |||||||
\(270\) | 1.05147e10 | − | 1.68172e9i | 0.120410 | − | 0.0192582i | ||||
\(271\) | 5.79559e10 | 0.652733 | 0.326367 | − | 0.945243i | \(-0.394176\pi\) | ||||
0.326367 | + | 0.945243i | \(0.394176\pi\) | |||||||
\(272\) | 1.31445e9i | 0.0145607i | ||||||||
\(273\) | − | 2.62316e10i | − | 0.285820i | ||||||
\(274\) | −5.02766e10 | −0.538875 | ||||||||
\(275\) | −4.32117e10 | + | 1.41853e10i | −0.455621 | + | 0.149569i | ||||
\(276\) | 4.55806e10 | 0.472813 | ||||||||
\(277\) | 4.41915e10i | 0.451004i | 0.974243 | + | 0.225502i | \(0.0724022\pi\) | ||||
−0.974243 | + | 0.225502i | \(0.927598\pi\) | |||||||
\(278\) | − | 4.20075e10i | − | 0.421819i | ||||||
\(279\) | −5.80740e10 | −0.573803 | ||||||||
\(280\) | −4.66141e10 | + | 7.45541e9i | −0.453217 | + | 0.0724871i | ||||
\(281\) | 1.47398e11 | 1.41030 | 0.705151 | − | 0.709058i | \(-0.250879\pi\) | ||||
0.705151 | + | 0.709058i | \(0.250879\pi\) | |||||||
\(282\) | 3.79611e10i | 0.357452i | ||||||||
\(283\) | − | 1.63060e10i | − | 0.151115i | −0.997141 | − | 0.0755574i | \(-0.975926\pi\) | ||
0.997141 | − | 0.0755574i | \(-0.0240736\pi\) | |||||||
\(284\) | 3.99104e10 | 0.364044 | ||||||||
\(285\) | 3.81835e9 | + | 2.38738e10i | 0.0342826 | + | 0.214348i | ||||
\(286\) | 3.75591e10 | 0.331946 | ||||||||
\(287\) | − | 3.38599e10i | − | 0.294590i | ||||||
\(288\) | − | 3.83516e10i | − | 0.328487i | ||||||
\(289\) | 1.05140e11 | 0.886603 | ||||||||
\(290\) | −1.16306e10 | − | 7.27190e10i | −0.0965632 | − | 0.603750i | ||||
\(291\) | −1.13606e11 | −0.928719 | ||||||||
\(292\) | − | 7.22333e10i | − | 0.581453i | ||||||
\(293\) | − | 1.20226e11i | − | 0.952999i | −0.879175 | − | 0.476499i | \(-0.841905\pi\) | ||
0.879175 | − | 0.476499i | \(-0.158095\pi\) | |||||||
\(294\) | −3.72400e10 | −0.290701 | ||||||||
\(295\) | 1.41913e11 | − | 2.26975e10i | 1.09100 | − | 0.174493i | ||||
\(296\) | −1.07711e11 | −0.815541 | ||||||||
\(297\) | 1.23751e10i | 0.0922881i | ||||||||
\(298\) | − | 9.80491e10i | − | 0.720229i | ||||||
\(299\) | 2.06585e11 | 1.49478 | ||||||||
\(300\) | 1.51211e10 | + | 4.60622e10i | 0.107780 | + | 0.328321i | ||||
\(301\) | 1.13196e11 | 0.794842 | ||||||||
\(302\) | − | 1.10216e11i | − | 0.762456i | ||||||
\(303\) | − | 2.84857e10i | − | 0.194149i | ||||||
\(304\) | −2.42090e9 | −0.0162572 | ||||||||
\(305\) | −2.28647e11 | + | 3.65696e10i | −1.51292 | + | 0.241975i | ||||
\(306\) | −1.09082e10 | −0.0711227 | ||||||||
\(307\) | 1.80341e11i | 1.15870i | 0.815078 | + | 0.579351i | \(0.196694\pi\) | ||||
−0.815078 | + | 0.579351i | \(0.803306\pi\) | |||||||
\(308\) | − | 2.05415e10i | − | 0.130063i | ||||||
\(309\) | −8.90204e10 | −0.555490 | ||||||||
\(310\) | 2.80098e10 | + | 1.75128e11i | 0.172259 | + | 1.07703i | ||||
\(311\) | −2.27029e11 | −1.37613 | −0.688066 | − | 0.725648i | \(-0.741540\pi\) | ||||
−0.688066 | + | 0.725648i | \(0.741540\pi\) | |||||||
\(312\) | − | 1.06929e11i | − | 0.638850i | ||||||
\(313\) | − | 1.04403e11i | − | 0.614839i | −0.951574 | − | 0.307420i | \(-0.900534\pi\) | ||
0.951574 | − | 0.307420i | \(-0.0994655\pi\) | |||||||
\(314\) | −4.18536e10 | −0.242968 | ||||||||
\(315\) | −4.16858e9 | − | 2.60636e10i | −0.0238556 | − | 0.149154i | ||||
\(316\) | −4.80392e10 | −0.271022 | ||||||||
\(317\) | 2.18268e11i | 1.21401i | 0.794697 | + | 0.607006i | \(0.207630\pi\) | ||||
−0.794697 | + | 0.607006i | \(0.792370\pi\) | |||||||
\(318\) | 1.21736e11i | 0.667569i | ||||||||
\(319\) | 8.55853e10 | 0.462744 | ||||||||
\(320\) | −1.23662e11 | + | 1.97784e10i | −0.659267 | + | 0.105443i | ||||
\(321\) | 1.15299e10 | 0.0606114 | ||||||||
\(322\) | 7.57860e10i | 0.392860i | ||||||||
\(323\) | − | 2.47672e10i | − | 0.126610i | ||||||
\(324\) | 1.31915e10 | 0.0665029 | ||||||||
\(325\) | 6.85333e10 | + | 2.08767e11i | 0.340743 | + | 1.03798i | ||||
\(326\) | 2.08621e11 | 1.02301 | ||||||||
\(327\) | 1.00425e11i | 0.485709i | ||||||||
\(328\) | − | 1.38024e11i | − | 0.658451i | ||||||
\(329\) | 9.40967e10 | 0.442785 | ||||||||
\(330\) | 3.73184e10 | − | 5.96868e9i | 0.173225 | − | 0.0277055i | ||||
\(331\) | −2.79244e10 | −0.127867 | −0.0639334 | − | 0.997954i | \(-0.520365\pi\) | ||||
−0.0639334 | + | 0.997954i | \(0.520365\pi\) | |||||||
\(332\) | − | 1.03652e10i | − | 0.0468229i | ||||||
\(333\) | − | 6.02248e10i | − | 0.268396i | ||||||
\(334\) | 4.48444e9 | 0.0197174 | ||||||||
\(335\) | 3.89314e10 | + | 2.43414e11i | 0.168888 | + | 1.05595i | ||||
\(336\) | 2.64295e9 | 0.0113126 | ||||||||
\(337\) | − | 1.72048e11i | − | 0.726631i | −0.931666 | − | 0.363316i | \(-0.881645\pi\) | ||
0.931666 | − | 0.363316i | \(-0.118355\pi\) | |||||||
\(338\) | − | 2.94196e10i | − | 0.122606i | ||||||
\(339\) | −1.40204e11 | −0.576583 | ||||||||
\(340\) | −7.84350e9 | − | 4.90405e10i | −0.0318313 | − | 0.199021i | ||||
\(341\) | −2.06113e11 | −0.825490 | ||||||||
\(342\) | − | 2.00905e10i | − | 0.0794095i | ||||||
\(343\) | 2.08472e11i | 0.813249i | ||||||||
\(344\) | 4.61423e11 | 1.77659 | ||||||||
\(345\) | 2.05261e11 | − | 3.28293e10i | 0.780047 | − | 0.124760i | ||||
\(346\) | 1.03970e11 | 0.390001 | ||||||||
\(347\) | 2.86901e11i | 1.06231i | 0.847276 | + | 0.531153i | \(0.178241\pi\) | ||||
−0.847276 | + | 0.531153i | \(0.821759\pi\) | |||||||
\(348\) | − | 9.12311e10i | − | 0.333454i | ||||||
\(349\) | −4.90957e11 | −1.77145 | −0.885725 | − | 0.464210i | \(-0.846338\pi\) | ||||
−0.885725 | + | 0.464210i | \(0.846338\pi\) | |||||||
\(350\) | −7.65867e10 | + | 2.51415e10i | −0.272802 | + | 0.0895542i | ||||
\(351\) | 5.97877e10 | 0.210247 | ||||||||
\(352\) | − | 1.36116e11i | − | 0.472571i | ||||||
\(353\) | − | 2.72119e11i | − | 0.932765i | −0.884583 | − | 0.466382i | \(-0.845557\pi\) | ||
0.884583 | − | 0.466382i | \(-0.154443\pi\) | |||||||
\(354\) | −1.19424e11 | −0.404182 | ||||||||
\(355\) | 1.79727e11 | − | 2.87454e10i | 0.600600 | − | 0.0960595i | ||||
\(356\) | −1.49167e11 | −0.492208 | ||||||||
\(357\) | 2.70390e10i | 0.0881014i | ||||||||
\(358\) | − | 3.65924e11i | − | 1.17738i | ||||||
\(359\) | −4.82246e10 | −0.153230 | −0.0766150 | − | 0.997061i | \(-0.524411\pi\) | ||||
−0.0766150 | + | 0.997061i | \(0.524411\pi\) | |||||||
\(360\) | −1.69925e10 | − | 1.06244e11i | −0.0533208 | − | 0.333382i | ||||
\(361\) | −2.77072e11 | −0.858639 | ||||||||
\(362\) | − | 5.62369e10i | − | 0.172121i | ||||||
\(363\) | − | 1.47073e11i | − | 0.444582i | ||||||
\(364\) | −9.92415e10 | −0.296304 | ||||||||
\(365\) | −5.20258e10 | − | 3.25285e11i | −0.153427 | − | 0.959282i | ||||
\(366\) | 1.92413e11 | 0.560491 | ||||||||
\(367\) | − | 1.87794e11i | − | 0.540360i | −0.962810 | − | 0.270180i | \(-0.912917\pi\) | ||
0.962810 | − | 0.270180i | \(-0.0870832\pi\) | |||||||
\(368\) | 2.08144e10i | 0.0591627i | ||||||||
\(369\) | 7.71743e10 | 0.216698 | ||||||||
\(370\) | −1.81614e11 | + | 2.90472e10i | −0.503780 | + | 0.0805742i | ||||
\(371\) | 3.01754e11 | 0.826934 | ||||||||
\(372\) | 2.19710e11i | 0.594849i | ||||||||
\(373\) | 7.83850e10i | 0.209673i | 0.994489 | + | 0.104837i | \(0.0334320\pi\) | ||||
−0.994489 | + | 0.104837i | \(0.966568\pi\) | |||||||
\(374\) | −3.87150e10 | −0.102319 | ||||||||
\(375\) | 1.01270e11 | + | 1.96539e11i | 0.264449 | + | 0.513225i | ||||
\(376\) | 3.83569e11 | 0.989689 | ||||||||
\(377\) | − | 4.13486e11i | − | 1.05420i | ||||||
\(378\) | 2.19332e10i | 0.0552572i | ||||||||
\(379\) | −2.25464e11 | −0.561307 | −0.280654 | − | 0.959809i | \(-0.590551\pi\) | ||||
−0.280654 | + | 0.959809i | \(0.590551\pi\) | |||||||
\(380\) | 9.03212e10 | − | 1.44459e10i | 0.222210 | − | 0.0355401i | ||||
\(381\) | 3.25456e11 | 0.791278 | ||||||||
\(382\) | 2.76600e11i | 0.664611i | ||||||||
\(383\) | 9.28094e10i | 0.220393i | 0.993910 | + | 0.110196i | \(0.0351480\pi\) | ||||
−0.993910 | + | 0.110196i | \(0.964852\pi\) | |||||||
\(384\) | −1.38355e11 | −0.324717 | ||||||||
\(385\) | −1.47949e10 | − | 9.25036e10i | −0.0343194 | − | 0.214578i | ||||
\(386\) | −3.01520e11 | −0.691310 | ||||||||
\(387\) | 2.57998e11i | 0.584678i | ||||||||
\(388\) | 4.29805e11i | 0.962783i | ||||||||
\(389\) | 8.47593e11 | 1.87678 | 0.938392 | − | 0.345573i | \(-0.112316\pi\) | ||||
0.938392 | + | 0.345573i | \(0.112316\pi\) | |||||||
\(390\) | −2.88363e10 | − | 1.80296e11i | −0.0631174 | − | 0.394634i | ||||
\(391\) | −2.12943e11 | −0.460753 | ||||||||
\(392\) | 3.76283e11i | 0.804872i | ||||||||
\(393\) | 1.34266e11i | 0.283923i | ||||||||
\(394\) | −5.91588e11 | −1.23676 | ||||||||
\(395\) | −2.16333e11 | + | 3.46001e10i | −0.447132 | + | 0.0715139i | ||||
\(396\) | 4.68186e10 | 0.0956731 | ||||||||
\(397\) | − | 7.37467e11i | − | 1.49000i | −0.667066 | − | 0.744999i | \(-0.732450\pi\) | ||
0.667066 | − | 0.744999i | \(-0.267550\pi\) | |||||||
\(398\) | 4.91089e11i | 0.981038i | ||||||||
\(399\) | −4.97995e10 | −0.0983664 | ||||||||
\(400\) | −2.10343e10 | + | 6.90504e9i | −0.0410825 | + | 0.0134864i | ||||
\(401\) | 2.85026e11 | 0.550471 | 0.275235 | − | 0.961377i | \(-0.411244\pi\) | ||||
0.275235 | + | 0.961377i | \(0.411244\pi\) | |||||||
\(402\) | − | 2.04840e11i | − | 0.391198i | ||||||
\(403\) | 9.95791e11i | 1.88060i | ||||||||
\(404\) | −1.07769e11 | −0.201270 | ||||||||
\(405\) | 5.94046e10 | − | 9.50112e9i | 0.109717 | − | 0.0175480i | ||||
\(406\) | 1.51688e11 | 0.277067 | ||||||||
\(407\) | − | 2.13747e11i | − | 0.386123i | ||||||
\(408\) | 1.10220e11i | 0.196920i | ||||||||
\(409\) | −1.41255e11 | −0.249603 | −0.124801 | − | 0.992182i | \(-0.539829\pi\) | ||||
−0.124801 | + | 0.992182i | \(0.539829\pi\) | |||||||
\(410\) | −3.72221e10 | − | 2.32727e11i | −0.0650540 | − | 0.406742i | ||||
\(411\) | −2.84045e11 | −0.491020 | ||||||||
\(412\) | 3.36789e11i | 0.575865i | ||||||||
\(413\) | 2.96024e11i | 0.500670i | ||||||||
\(414\) | −1.72733e11 | −0.288984 | ||||||||
\(415\) | −7.46554e9 | − | 4.66774e10i | −0.0123551 | − | 0.0772485i | ||||
\(416\) | −6.57613e11 | −1.07659 | ||||||||
\(417\) | − | 2.37328e11i | − | 0.384359i | ||||||
\(418\) | − | 7.13041e10i | − | 0.114241i | ||||||
\(419\) | 6.90309e10 | 0.109416 | 0.0547080 | − | 0.998502i | \(-0.482577\pi\) | ||||
0.0547080 | + | 0.998502i | \(0.482577\pi\) | |||||||
\(420\) | −9.86057e10 | + | 1.57709e10i | −0.154625 | + | 0.0247306i | ||||
\(421\) | −1.47198e11 | −0.228367 | −0.114184 | − | 0.993460i | \(-0.536425\pi\) | ||||
−0.114184 | + | 0.993460i | \(0.536425\pi\) | |||||||
\(422\) | 1.16391e11i | 0.178655i | ||||||||
\(423\) | 2.14467e11i | 0.325709i | ||||||||
\(424\) | 1.23005e12 | 1.84832 | ||||||||
\(425\) | −7.06426e10 | − | 2.15193e11i | −0.105031 | − | 0.319947i | ||||
\(426\) | −1.51245e11 | −0.222504 | ||||||||
\(427\) | − | 4.76945e11i | − | 0.694294i | ||||||
\(428\) | − | 4.36210e10i | − | 0.0628345i | ||||||
\(429\) | 2.12196e11 | 0.302467 | ||||||||
\(430\) | 7.78018e11 | − | 1.24436e11i | 1.09744 | − | 0.175524i | ||||
\(431\) | −4.72940e11 | −0.660173 | −0.330087 | − | 0.943951i | \(-0.607078\pi\) | ||||
−0.330087 | + | 0.943951i | \(0.607078\pi\) | |||||||
\(432\) | 6.02388e9i | 0.00832146i | ||||||||
\(433\) | − | 6.97304e11i | − | 0.953294i | −0.879095 | − | 0.476647i | \(-0.841852\pi\) | ||
0.879095 | − | 0.476647i | \(-0.158148\pi\) | |||||||
\(434\) | −3.65307e11 | −0.494259 | ||||||||
\(435\) | −6.57089e10 | − | 4.10837e11i | −0.0879879 | − | 0.550133i | ||||
\(436\) | 3.79935e11 | 0.503524 | ||||||||
\(437\) | − | 3.92191e11i | − | 0.514436i | ||||||
\(438\) | 2.73736e11i | 0.355385i | ||||||||
\(439\) | 9.99909e11 | 1.28490 | 0.642451 | − | 0.766327i | \(-0.277918\pi\) | ||||
0.642451 | + | 0.766327i | \(0.277918\pi\) | |||||||
\(440\) | −6.03091e10 | − | 3.77075e11i | −0.0767089 | − | 0.479613i | ||||
\(441\) | −2.10393e11 | −0.264885 | ||||||||
\(442\) | 1.87043e11i | 0.233099i | ||||||||
\(443\) | 2.04701e11i | 0.252524i | 0.991997 | + | 0.126262i | \(0.0402980\pi\) | ||||
−0.991997 | + | 0.126262i | \(0.959702\pi\) | |||||||
\(444\) | −2.27847e11 | −0.278240 | ||||||||
\(445\) | −6.71739e11 | + | 1.07437e11i | −0.812045 | + | 0.129878i | ||||
\(446\) | 1.76741e11 | 0.211509 | ||||||||
\(447\) | − | 5.53943e11i | − | 0.656268i | ||||||
\(448\) | − | 2.57952e11i | − | 0.302544i | ||||||
\(449\) | −1.14845e11 | −0.133354 | −0.0666769 | − | 0.997775i | \(-0.521240\pi\) | ||||
−0.0666769 | + | 0.997775i | \(0.521240\pi\) | |||||||
\(450\) | −5.73032e10 | − | 1.74558e11i | −0.0658752 | − | 0.200670i | ||||
\(451\) | 2.73903e11 | 0.311748 | ||||||||
\(452\) | 5.30430e11i | 0.597731i | ||||||||
\(453\) | − | 6.22684e11i | − | 0.694746i | ||||||
\(454\) | 1.86139e11 | 0.205630 | ||||||||
\(455\) | −4.46910e11 | + | 7.14784e10i | −0.488842 | + | 0.0781850i | ||||
\(456\) | −2.02999e11 | −0.219863 | ||||||||
\(457\) | 1.42783e11i | 0.153128i | 0.997065 | + | 0.0765639i | \(0.0243949\pi\) | ||||
−0.997065 | + | 0.0765639i | \(0.975605\pi\) | |||||||
\(458\) | − | 1.76481e10i | − | 0.0187414i | ||||||
\(459\) | −6.16278e10 | −0.0648066 | ||||||||
\(460\) | −1.24202e11 | − | 7.76560e11i | −0.129336 | − | 0.808658i | ||||
\(461\) | 9.88626e11 | 1.01948 | 0.509739 | − | 0.860329i | \(-0.329742\pi\) | ||||
0.509739 | + | 0.860329i | \(0.329742\pi\) | |||||||
\(462\) | 7.78443e10i | 0.0794947i | ||||||||
\(463\) | 4.74513e11i | 0.479881i | 0.970788 | + | 0.239940i | \(0.0771279\pi\) | ||||
−0.970788 | + | 0.239940i | \(0.922872\pi\) | |||||||
\(464\) | 4.16606e10 | 0.0417248 | ||||||||
\(465\) | 1.58246e11 | + | 9.89411e11i | 0.156962 | + | 0.981383i | ||||
\(466\) | −2.21054e10 | −0.0217151 | ||||||||
\(467\) | − | 8.43343e11i | − | 0.820499i | −0.911973 | − | 0.410250i | \(-0.865442\pi\) | ||
0.911973 | − | 0.410250i | \(-0.134558\pi\) | |||||||
\(468\) | − | 2.26193e11i | − | 0.217958i | ||||||
\(469\) | −5.07749e11 | −0.484587 | ||||||||
\(470\) | 6.46747e11 | − | 1.03440e11i | 0.611356 | − | 0.0977797i | ||||
\(471\) | −2.36458e11 | −0.221391 | ||||||||
\(472\) | 1.20669e12i | 1.11907i | ||||||||
\(473\) | 9.15674e11i | 0.841135i | ||||||||
\(474\) | 1.82050e11 | 0.165649 | ||||||||
\(475\) | 3.96335e11 | − | 1.30107e11i | 0.357224 | − | 0.117268i | ||||
\(476\) | 1.02296e11 | 0.0913329 | ||||||||
\(477\) | 6.87765e11i | 0.608285i | ||||||||
\(478\) | − | 9.07911e10i | − | 0.0795459i | ||||||
\(479\) | −2.16057e12 | −1.87525 | −0.937623 | − | 0.347655i | \(-0.886978\pi\) | ||||
−0.937623 | + | 0.347655i | \(0.886978\pi\) | |||||||
\(480\) | −6.53400e11 | + | 1.04504e11i | −0.561815 | + | 0.0898562i | ||||
\(481\) | −1.03267e12 | −0.879648 | ||||||||
\(482\) | − | 1.08957e9i | − | 0.000919479i | ||||||
\(483\) | 4.28164e11i | 0.357971i | ||||||||
\(484\) | −5.56416e11 | −0.460888 | ||||||||
\(485\) | 3.09566e11 | + | 1.93552e12i | 0.254047 | + | 1.58840i | ||||
\(486\) | −4.99906e10 | −0.0406467 | ||||||||
\(487\) | 1.03201e12i | 0.831387i | 0.909505 | + | 0.415694i | \(0.136461\pi\) | ||||
−0.909505 | + | 0.415694i | \(0.863539\pi\) | |||||||
\(488\) | − | 1.94419e12i | − | 1.55185i | ||||||
\(489\) | 1.17863e12 | 0.932157 | ||||||||
\(490\) | 1.01475e11 | + | 6.34460e11i | 0.0795201 | + | 0.497190i | ||||
\(491\) | 1.34186e12 | 1.04193 | 0.520966 | − | 0.853578i | \(-0.325572\pi\) | ||||
0.520966 | + | 0.853578i | \(0.325572\pi\) | |||||||
\(492\) | − | 2.91972e11i | − | 0.224646i | ||||||
\(493\) | 4.26212e11i | 0.324949i | ||||||||
\(494\) | −3.44490e11 | −0.260258 | ||||||||
\(495\) | 2.10836e11 | − | 3.37209e10i | 0.157842 | − | 0.0252451i | ||||
\(496\) | −1.00330e11 | −0.0744329 | ||||||||
\(497\) | 3.74901e11i | 0.275621i | ||||||||
\(498\) | 3.92803e10i | 0.0286182i | ||||||||
\(499\) | 3.08677e11 | 0.222870 | 0.111435 | − | 0.993772i | \(-0.464455\pi\) | ||||
0.111435 | + | 0.993772i | \(0.464455\pi\) | |||||||
\(500\) | 7.43562e11 | − | 3.83134e11i | 0.532049 | − | 0.274148i | ||||
\(501\) | 2.53355e10 | 0.0179664 | ||||||||
\(502\) | − | 9.37271e11i | − | 0.658716i | ||||||
\(503\) | − | 8.27354e11i | − | 0.576283i | −0.957588 | − | 0.288141i | \(-0.906963\pi\) | ||
0.957588 | − | 0.288141i | \(-0.0930373\pi\) | |||||||
\(504\) | 2.21619e11 | 0.152992 | ||||||||
\(505\) | −4.85313e11 | + | 7.76206e10i | −0.332056 | + | 0.0531087i | ||||
\(506\) | −6.13056e11 | −0.415741 | ||||||||
\(507\) | − | 1.66211e11i | − | 0.111718i | ||||||
\(508\) | − | 1.23129e12i | − | 0.820301i | ||||||
\(509\) | −9.83765e11 | −0.649623 | −0.324812 | − | 0.945779i | \(-0.605301\pi\) | ||||
−0.324812 | + | 0.945779i | \(0.605301\pi\) | |||||||
\(510\) | 2.97238e10 | + | 1.85845e11i | 0.0194553 | + | 0.121642i | ||||
\(511\) | 6.78528e11 | 0.440224 | ||||||||
\(512\) | − | 1.34357e11i | − | 0.0864063i | ||||||
\(513\) | − | 1.13504e11i | − | 0.0723574i | ||||||
\(514\) | −1.56296e10 | −0.00987672 | ||||||||
\(515\) | 2.42571e11 | + | 1.51665e12i | 0.151952 | + | 0.950062i | ||||
\(516\) | 9.76078e11 | 0.606123 | ||||||||
\(517\) | 7.61177e11i | 0.468574i | ||||||||
\(518\) | − | 3.78837e11i | − | 0.231190i | ||||||
\(519\) | 5.87394e11 | 0.355367 | ||||||||
\(520\) | −1.82175e12 | + | 2.91370e11i | −1.09263 | + | 0.174755i | ||||
\(521\) | 2.68426e12 | 1.59608 | 0.798041 | − | 0.602603i | \(-0.205870\pi\) | ||||
0.798041 | + | 0.602603i | \(0.205870\pi\) | |||||||
\(522\) | 3.45731e11i | 0.203808i | ||||||||
\(523\) | − | 2.53611e12i | − | 1.48221i | −0.671388 | − | 0.741106i | \(-0.734302\pi\) | ||
0.671388 | − | 0.741106i | \(-0.265698\pi\) | |||||||
\(524\) | 5.07966e11 | 0.294336 | ||||||||
\(525\) | −4.32688e11 | + | 1.42041e11i | −0.248575 | + | 0.0816012i | ||||
\(526\) | −5.26925e11 | −0.300133 | ||||||||
\(527\) | − | 1.02644e12i | − | 0.579676i | ||||||
\(528\) | 2.13797e10i | 0.0119715i | ||||||||
\(529\) | −1.57082e12 | −0.872118 | ||||||||
\(530\) | 2.07402e12 | − | 3.31717e11i | 1.14175 | − | 0.182611i | ||||
\(531\) | −6.74704e11 | −0.368288 | ||||||||
\(532\) | 1.88405e11i | 0.101974i | ||||||||
\(533\) | − | 1.32330e12i | − | 0.710210i | ||||||
\(534\) | 5.65287e11 | 0.300838 | ||||||||
\(535\) | −3.14179e10 | − | 1.96437e11i | −0.0165800 | − | 0.103665i | ||||
\(536\) | −2.06975e12 | −1.08312 | ||||||||
\(537\) | − | 2.06734e12i | − | 1.07282i | ||||||
\(538\) | − | 1.27276e12i | − | 0.654980i | ||||||
\(539\) | −7.46716e11 | −0.381071 | ||||||||
\(540\) | −3.59454e10 | − | 2.24744e11i | −0.0181916 | − | 0.113741i | ||||
\(541\) | −3.13311e12 | −1.57249 | −0.786246 | − | 0.617914i | \(-0.787978\pi\) | ||||
−0.786246 | + | 0.617914i | \(0.787978\pi\) | |||||||
\(542\) | 8.30923e11i | 0.413584i | ||||||||
\(543\) | − | 3.17719e11i | − | 0.156835i | ||||||
\(544\) | 6.77853e11 | 0.331849 | ||||||||
\(545\) | 1.71095e12 | − | 2.73647e11i | 0.830715 | − | 0.132864i | ||||
\(546\) | 3.76087e11 | 0.181101 | ||||||||
\(547\) | − | 9.13486e11i | − | 0.436274i | −0.975918 | − | 0.218137i | \(-0.930002\pi\) | ||
0.975918 | − | 0.218137i | \(-0.0699979\pi\) | |||||||
\(548\) | 1.07462e12i | 0.509030i | ||||||||
\(549\) | 1.08706e12 | 0.510716 | ||||||||
\(550\) | −2.03378e11 | − | 6.19533e11i | −0.0947701 | − | 0.288690i | ||||
\(551\) | −7.84984e11 | −0.362809 | ||||||||
\(552\) | 1.74534e12i | 0.800118i | ||||||||
\(553\) | − | 4.51259e11i | − | 0.205193i | ||||||
\(554\) | −6.33581e11 | −0.285765 | ||||||||
\(555\) | −1.02605e12 | + | 1.64106e11i | −0.459041 | + | 0.0734187i | ||||
\(556\) | −8.97878e11 | −0.398456 | ||||||||
\(557\) | 3.59154e12i | 1.58100i | 0.612461 | + | 0.790501i | \(0.290180\pi\) | ||||
−0.612461 | + | 0.790501i | \(0.709820\pi\) | |||||||
\(558\) | − | 8.32616e11i | − | 0.363573i | ||||||
\(559\) | 4.42387e12 | 1.91624 | ||||||||
\(560\) | −7.20178e9 | − | 4.50282e10i | −0.00309452 | − | 0.0193481i | ||||
\(561\) | −2.18726e11 | −0.0932327 | ||||||||
\(562\) | 2.11326e12i | 0.893594i | ||||||||
\(563\) | 2.56254e12i | 1.07494i | 0.843284 | + | 0.537468i | \(0.180619\pi\) | ||||
−0.843284 | + | 0.537468i | \(0.819381\pi\) | |||||||
\(564\) | 8.11389e11 | 0.337655 | ||||||||
\(565\) | 3.82041e11 | + | 2.38866e12i | 0.157722 | + | 0.986137i | ||||
\(566\) | 2.33781e11 | 0.0957493 | ||||||||
\(567\) | 1.23915e11i | 0.0503500i | ||||||||
\(568\) | 1.52822e12i | 0.616054i | ||||||||
\(569\) | −3.17224e12 | −1.26871 | −0.634353 | − | 0.773043i | \(-0.718733\pi\) | ||||
−0.634353 | + | 0.773043i | \(0.718733\pi\) | |||||||
\(570\) | −3.42283e11 | + | 5.47444e10i | −0.135815 | + | 0.0217221i | ||||
\(571\) | 3.57733e12 | 1.40830 | 0.704152 | − | 0.710050i | \(-0.251328\pi\) | ||||
0.704152 | + | 0.710050i | \(0.251328\pi\) | |||||||
\(572\) | − | 8.02795e11i | − | 0.313561i | ||||||
\(573\) | 1.56270e12i | 0.605590i | ||||||||
\(574\) | 4.85456e11 | 0.186658 | ||||||||
\(575\) | −1.11863e12 | − | 3.40760e12i | −0.426758 | − | 1.30000i | ||||
\(576\) | 5.87931e11 | 0.222549 | ||||||||
\(577\) | − | 7.07479e11i | − | 0.265719i | −0.991135 | − | 0.132859i | \(-0.957584\pi\) | ||
0.991135 | − | 0.132859i | \(-0.0424159\pi\) | |||||||
\(578\) | 1.50741e12i | 0.561769i | ||||||||
\(579\) | −1.70348e12 | −0.629918 | ||||||||
\(580\) | −1.55431e12 | + | 2.48595e11i | −0.570311 | + | 0.0912151i | ||||
\(581\) | 9.73665e10 | 0.0354501 | ||||||||
\(582\) | − | 1.62879e12i | − | 0.588454i | ||||||
\(583\) | 2.44098e12i | 0.875097i | ||||||||
\(584\) | 2.76591e12 | 0.983965 | ||||||||
\(585\) | −1.62915e11 | − | 1.01861e12i | −0.0575122 | − | 0.359588i | ||||
\(586\) | 1.72369e12 | 0.603838 | ||||||||
\(587\) | − | 3.20959e12i | − | 1.11578i | −0.829916 | − | 0.557889i | \(-0.811612\pi\) | ||
0.829916 | − | 0.557889i | \(-0.188388\pi\) | |||||||
\(588\) | 7.95975e11i | 0.274600i | ||||||||
\(589\) | 1.89046e12 | 0.647216 | ||||||||
\(590\) | 3.25418e11 | + | 2.03464e12i | 0.110562 | + | 0.691278i | ||||
\(591\) | −3.34227e12 | −1.12693 | ||||||||
\(592\) | − | 1.04046e11i | − | 0.0348160i | ||||||
\(593\) | − | 3.72506e12i | − | 1.23705i | −0.785765 | − | 0.618526i | \(-0.787730\pi\) | ||
0.785765 | − | 0.618526i | \(-0.212270\pi\) | |||||||
\(594\) | −1.77424e11 | −0.0584755 | ||||||||
\(595\) | 4.60665e11 | − | 7.36784e10i | 0.150681 | − | 0.0240998i | ||||
\(596\) | −2.09572e12 | −0.680339 | ||||||||
\(597\) | 2.77448e12i | 0.893916i | ||||||||
\(598\) | 2.96184e12i | 0.947123i | ||||||||
\(599\) | −2.35643e12 | −0.747883 | −0.373942 | − | 0.927452i | \(-0.621994\pi\) | ||||
−0.373942 | + | 0.927452i | \(0.621994\pi\) | |||||||
\(600\) | −1.76378e12 | + | 5.79006e11i | −0.555602 | + | 0.182391i | ||||
\(601\) | 2.11495e10 | 0.00661250 | 0.00330625 | − | 0.999995i | \(-0.498948\pi\) | ||||
0.00330625 | + | 0.999995i | \(0.498948\pi\) | |||||||
\(602\) | 1.62291e12i | 0.503627i | ||||||||
\(603\) | − | 1.15727e12i | − | 0.356457i | ||||||
\(604\) | −2.35579e12 | −0.720228 | ||||||||
\(605\) | −2.50569e12 | + | 4.00757e11i | −0.760374 | + | 0.121614i | ||||
\(606\) | 4.08404e11 | 0.123017 | ||||||||
\(607\) | − | 5.85975e12i | − | 1.75198i | −0.482326 | − | 0.875992i | \(-0.660208\pi\) | ||
0.482326 | − | 0.875992i | \(-0.339792\pi\) | |||||||
\(608\) | 1.24845e12i | 0.370513i | ||||||||
\(609\) | 8.56985e11 | 0.252462 | ||||||||
\(610\) | −5.24304e11 | − | 3.27815e12i | −0.153320 | − | 0.958615i | ||||
\(611\) | 3.67745e12 | 1.06749 | ||||||||
\(612\) | 2.33155e11i | 0.0671836i | ||||||||
\(613\) | 3.39524e12i | 0.971178i | 0.874187 | + | 0.485589i | \(0.161395\pi\) | ||||
−0.874187 | + | 0.485589i | \(0.838605\pi\) | |||||||
\(614\) | −2.58558e12 | −0.734177 | ||||||||
\(615\) | −2.10292e11 | − | 1.31482e12i | −0.0592768 | − | 0.370621i | ||||
\(616\) | 7.86560e11 | 0.220099 | ||||||||
\(617\) | − | 2.99293e12i | − | 0.831406i | −0.909500 | − | 0.415703i | \(-0.863536\pi\) | ||
0.909500 | − | 0.415703i | \(-0.136464\pi\) | |||||||
\(618\) | − | 1.27630e12i | − | 0.351969i | ||||||
\(619\) | 3.89410e12 | 1.06610 | 0.533052 | − | 0.846082i | \(-0.321045\pi\) | ||||
0.533052 | + | 0.846082i | \(0.321045\pi\) | |||||||
\(620\) | 3.74322e12 | − | 5.98687e11i | 1.01738 | − | 0.162719i | ||||
\(621\) | −9.75881e11 | −0.263321 | ||||||||
\(622\) | − | 3.25496e12i | − | 0.871944i | ||||||
\(623\) | − | 1.40121e12i | − | 0.372655i | ||||||
\(624\) | 1.03291e11 | 0.0272729 | ||||||||
\(625\) | 3.07250e12 | − | 2.26090e12i | 0.805437 | − | 0.592681i | ||||
\(626\) | 1.49684e12 | 0.389574 | ||||||||
\(627\) | − | 4.02843e11i | − | 0.104096i | ||||||
\(628\) | 8.94587e11i | 0.229511i | ||||||||
\(629\) | 1.06445e12 | 0.271143 | ||||||||
\(630\) | 3.73678e11 | − | 5.97657e10i | 0.0945072 | − | 0.0151154i | ||||
\(631\) | 6.58750e11 | 0.165420 | 0.0827101 | − | 0.996574i | \(-0.473642\pi\) | ||||
0.0827101 | + | 0.996574i | \(0.473642\pi\) | |||||||
\(632\) | − | 1.83948e12i | − | 0.458637i | ||||||
\(633\) | 6.57570e11i | 0.162789i | ||||||||
\(634\) | −3.12934e12 | −0.769222 | ||||||||
\(635\) | −8.86832e11 | − | 5.54481e12i | −0.216451 | − | 1.35333i | ||||
\(636\) | 2.60201e12 | 0.630596 | ||||||||
\(637\) | 3.60759e12i | 0.868140i | ||||||||
\(638\) | 1.22705e12i | 0.293204i | ||||||||
\(639\) | −8.54482e11 | −0.202745 | ||||||||
\(640\) | 3.77004e11 | + | 2.35717e12i | 0.0888251 | + | 0.555368i | ||||
\(641\) | −2.24747e12 | −0.525814 | −0.262907 | − | 0.964821i | \(-0.584681\pi\) | ||||
−0.262907 | + | 0.964821i | \(0.584681\pi\) | |||||||
\(642\) | 1.65307e11i | 0.0384046i | ||||||||
\(643\) | 9.01721e11i | 0.208028i | 0.994576 | + | 0.104014i | \(0.0331687\pi\) | ||||
−0.994576 | + | 0.104014i | \(0.966831\pi\) | |||||||
\(644\) | 1.61986e12 | 0.371101 | ||||||||
\(645\) | 4.39553e12 | − | 7.03018e11i | 0.999983 | − | 0.159936i | ||||
\(646\) | 3.55092e11 | 0.0802222 | ||||||||
\(647\) | 3.78126e12i | 0.848334i | 0.905584 | + | 0.424167i | \(0.139433\pi\) | ||||
−0.905584 | + | 0.424167i | \(0.860567\pi\) | |||||||
\(648\) | 5.05119e11i | 0.112540i | ||||||||
\(649\) | −2.39463e12 | −0.529830 | ||||||||
\(650\) | −2.99313e12 | + | 9.82573e11i | −0.657682 | + | 0.215901i | ||||
\(651\) | −2.06386e12 | −0.450366 | ||||||||
\(652\) | − | 4.45910e12i | − | 0.966347i | ||||||
\(653\) | 8.17889e12i | 1.76029i | 0.474702 | + | 0.880146i | \(0.342556\pi\) | ||||
−0.474702 | + | 0.880146i | \(0.657444\pi\) | |||||||
\(654\) | −1.43981e12 | −0.307755 | ||||||||
\(655\) | 2.28750e12 | − | 3.65861e11i | 0.485597 | − | 0.0776659i | ||||
\(656\) | 1.33329e11 | 0.0281097 | ||||||||
\(657\) | 1.54652e12i | 0.323825i | ||||||||
\(658\) | 1.34908e12i | 0.280557i | ||||||||
\(659\) | −4.24425e12 | −0.876631 | −0.438315 | − | 0.898821i | \(-0.644425\pi\) | ||||
−0.438315 | + | 0.898821i | \(0.644425\pi\) | |||||||
\(660\) | −1.27576e11 | − | 7.97652e11i | −0.0261710 | − | 0.163631i | ||||
\(661\) | −6.21151e12 | −1.26558 | −0.632791 | − | 0.774322i | \(-0.718091\pi\) | ||||
−0.632791 | + | 0.774322i | \(0.718091\pi\) | |||||||
\(662\) | − | 4.00357e11i | − | 0.0810189i | ||||||
\(663\) | 1.05673e12i | 0.212399i | ||||||||
\(664\) | 3.96898e11 | 0.0792361 | ||||||||
\(665\) | 1.35698e11 | + | 8.48438e11i | 0.0269077 | + | 0.168237i | ||||
\(666\) | 8.63453e11 | 0.170061 | ||||||||
\(667\) | 6.74911e12i | 1.32032i | ||||||||
\(668\) | − | 9.58513e10i | − | 0.0186253i | ||||||
\(669\) | 9.98523e11 | 0.192726 | ||||||||
\(670\) | −3.48987e12 | + | 5.58167e11i | −0.669071 | + | 0.107011i | ||||
\(671\) | 3.85816e12 | 0.734731 | ||||||||
\(672\) | − | 1.36296e12i | − | 0.257822i | ||||||
\(673\) | − | 8.89347e12i | − | 1.67110i | −0.549412 | − | 0.835552i | \(-0.685148\pi\) | ||
0.549412 | − | 0.835552i | \(-0.314852\pi\) | |||||||
\(674\) | 2.46668e12 | 0.460408 | ||||||||
\(675\) | −3.23743e11 | − | 9.86192e11i | −0.0600251 | − | 0.182850i | ||||
\(676\) | −6.28821e11 | −0.115816 | ||||||||
\(677\) | 7.52635e12i | 1.37700i | 0.725234 | + | 0.688502i | \(0.241732\pi\) | ||||
−0.725234 | + | 0.688502i | \(0.758268\pi\) | |||||||
\(678\) | − | 2.01013e12i | − | 0.365334i | ||||||
\(679\) | −4.03740e12 | −0.728933 | ||||||||
\(680\) | 1.87782e12 | − | 3.00338e11i | 0.336794 | − | 0.0538666i | ||||
\(681\) | 1.05162e12 | 0.187369 | ||||||||
\(682\) | − | 2.95508e12i | − | 0.523046i | ||||||
\(683\) | 4.87406e12i | 0.857034i | 0.903534 | + | 0.428517i | \(0.140964\pi\) | ||||
−0.903534 | + | 0.428517i | \(0.859036\pi\) | |||||||
\(684\) | −4.29417e11 | −0.0750114 | ||||||||
\(685\) | 7.73994e11 | + | 4.83930e12i | 0.134317 | + | 0.839798i | ||||
\(686\) | −2.98889e12 | −0.515290 | ||||||||
\(687\) | − | 9.97055e10i | − | 0.0170771i | ||||||
\(688\) | 4.45725e11i | 0.0758437i | ||||||||
\(689\) | 1.17931e13 | 1.99361 | ||||||||
\(690\) | 4.70679e11 | + | 2.94287e12i | 0.0790504 | + | 0.494253i | ||||
\(691\) | −4.18834e12 | −0.698861 | −0.349430 | − | 0.936962i | \(-0.613625\pi\) | ||||
−0.349430 | + | 0.936962i | \(0.613625\pi\) | |||||||
\(692\) | − | 2.22228e12i | − | 0.368401i | ||||||
\(693\) | 4.39793e11i | 0.0724351i | ||||||||
\(694\) | −4.11335e12 | −0.673098 | ||||||||
\(695\) | −4.04337e12 | + | 6.46694e11i | −0.657374 | + | 0.105140i | ||||
\(696\) | 3.49335e12 | 0.564288 | ||||||||
\(697\) | 1.36403e12i | 0.218916i | ||||||||
\(698\) | − | 7.03893e12i | − | 1.12243i | ||||||
\(699\) | −1.24888e11 | −0.0197867 | ||||||||
\(700\) | 5.37381e11 | + | 1.63698e12i | 0.0845942 | + | 0.257693i | ||||
\(701\) | 2.63533e12 | 0.412195 | 0.206098 | − | 0.978531i | \(-0.433924\pi\) | ||||
0.206098 | + | 0.978531i | \(0.433924\pi\) | |||||||
\(702\) | 8.57186e11i | 0.133216i | ||||||||
\(703\) | 1.96048e12i | 0.302735i | ||||||||
\(704\) | 2.08666e12 | 0.320165 | ||||||||
\(705\) | 3.65389e12 | − | 5.84401e11i | 0.557064 | − | 0.0890963i | ||||
\(706\) | 3.90141e12 | 0.591018 | ||||||||
\(707\) | − | 1.01234e12i | − | 0.152384i | ||||||
\(708\) | 2.55259e12i | 0.381797i | ||||||||
\(709\) | −3.46943e12 | −0.515644 | −0.257822 | − | 0.966192i | \(-0.583005\pi\) | ||||
−0.257822 | + | 0.966192i | \(0.583005\pi\) | |||||||
\(710\) | 4.12127e11 | + | 2.57678e12i | 0.0608652 | + | 0.380552i | ||||
\(711\) | 1.02852e12 | 0.150938 | ||||||||
\(712\) | − | 5.71181e12i | − | 0.832939i | ||||||
\(713\) | − | 1.62537e13i | − | 2.35532i | ||||||
\(714\) | −3.87662e11 | −0.0558228 | ||||||||
\(715\) | −5.78211e11 | − | 3.61519e12i | −0.0827388 | − | 0.517314i | ||||
\(716\) | −7.82132e12 | −1.11217 | ||||||||
\(717\) | − | 5.12938e11i | − | 0.0724818i | ||||||
\(718\) | − | 6.91405e11i | − | 0.0970895i | ||||||
\(719\) | 8.98267e12 | 1.25350 | 0.626752 | − | 0.779219i | \(-0.284384\pi\) | ||||
0.626752 | + | 0.779219i | \(0.284384\pi\) | |||||||
\(720\) | 1.02629e11 | − | 1.64144e10i | 0.0142323 | − | 0.00227630i | ||||
\(721\) | −3.16365e12 | −0.435993 | ||||||||
\(722\) | − | 3.97243e12i | − | 0.544050i | ||||||
\(723\) | − | 6.15567e9i | − | 0.000837824i | ||||||
\(724\) | −1.20202e12 | −0.162588 | ||||||||
\(725\) | −6.82041e12 | + | 2.23898e12i | −0.916832 | + | 0.300974i | ||||
\(726\) | 2.10860e12 | 0.281696 | ||||||||
\(727\) | 5.78092e12i | 0.767524i | 0.923432 | + | 0.383762i | \(0.125372\pi\) | ||||
−0.923432 | + | 0.383762i | \(0.874628\pi\) | |||||||
\(728\) | − | 3.80008e12i | − | 0.501420i | ||||||
\(729\) | −2.82430e11 | −0.0370370 | ||||||||
\(730\) | 4.66367e12 | − | 7.45903e11i | 0.607820 | − | 0.0972142i | ||||
\(731\) | −4.56003e12 | −0.590663 | ||||||||
\(732\) | − | 4.11267e12i | − | 0.529448i | ||||||
\(733\) | − | 1.40487e13i | − | 1.79749i | −0.438469 | − | 0.898746i | \(-0.644479\pi\) | ||
0.438469 | − | 0.898746i | \(-0.355521\pi\) | |||||||
\(734\) | 2.69243e12 | 0.342383 | ||||||||
\(735\) | 5.73298e11 | + | 3.58448e12i | 0.0724582 | + | 0.453036i | ||||
\(736\) | 1.07339e13 | 1.34836 | ||||||||
\(737\) | − | 4.10734e12i | − | 0.512810i | ||||||
\(738\) | 1.10646e12i | 0.137304i | ||||||||
\(739\) | −3.93871e11 | −0.0485796 | −0.0242898 | − | 0.999705i | \(-0.507732\pi\) | ||||
−0.0242898 | + | 0.999705i | \(0.507732\pi\) | |||||||
\(740\) | 6.20860e11 | + | 3.88185e12i | 0.0761116 | + | 0.475878i | ||||
\(741\) | −1.94625e12 | −0.237146 | ||||||||
\(742\) | 4.32630e12i | 0.523961i | ||||||||
\(743\) | 7.69778e12i | 0.926651i | 0.886188 | + | 0.463325i | \(0.153344\pi\) | ||||
−0.886188 | + | 0.463325i | \(0.846656\pi\) | |||||||
\(744\) | −8.41298e12 | −1.00663 | ||||||||
\(745\) | −9.43758e12 | + | 1.50944e12i | −1.12242 | + | 0.179520i | ||||
\(746\) | −1.12382e12 | −0.132853 | ||||||||
\(747\) | 2.21920e11i | 0.0260768i | ||||||||
\(748\) | 8.27503e11i | 0.0966524i | ||||||||
\(749\) | 4.09756e11 | 0.0475727 | ||||||||
\(750\) | −2.81781e12 | + | 1.45193e12i | −0.325189 | + | 0.167560i | ||||
\(751\) | 7.71512e12 | 0.885040 | 0.442520 | − | 0.896759i | \(-0.354085\pi\) | ||||
0.442520 | + | 0.896759i | \(0.354085\pi\) | |||||||
\(752\) | 3.70520e11i | 0.0422505i | ||||||||
\(753\) | − | 5.29525e12i | − | 0.600219i | ||||||
\(754\) | 5.92822e12 | 0.667964 | ||||||||
\(755\) | −1.06087e13 | + | 1.69675e12i | −1.18823 | + | 0.190045i | ||||
\(756\) | 4.68805e11 | 0.0521968 | ||||||||
\(757\) | 5.54873e12i | 0.614132i | 0.951688 | + | 0.307066i | \(0.0993473\pi\) | ||||
−0.951688 | + | 0.307066i | \(0.900653\pi\) | |||||||
\(758\) | − | 3.23252e12i | − | 0.355655i | ||||||
\(759\) | −3.46355e12 | −0.378821 | ||||||||
\(760\) | 5.53152e11 | + | 3.45851e12i | 0.0601427 | + | 0.376035i | ||||
\(761\) | 7.40605e12 | 0.800490 | 0.400245 | − | 0.916408i | \(-0.368925\pi\) | ||||
0.400245 | + | 0.916408i | \(0.368925\pi\) | |||||||
\(762\) | 4.66611e12i | 0.501369i | ||||||||
\(763\) | 3.56895e12i | 0.381223i | ||||||||
\(764\) | 5.91211e12 | 0.627802 | ||||||||
\(765\) | 1.67929e11 | + | 1.04996e12i | 0.0177276 | + | 0.110840i | ||||
\(766\) | −1.33062e12 | −0.139645 | ||||||||
\(767\) | 1.15691e13i | 1.20704i | ||||||||
\(768\) | − | 5.69993e12i | − | 0.591213i | ||||||
\(769\) | 2.19820e12 | 0.226672 | 0.113336 | − | 0.993557i | \(-0.463846\pi\) | ||||
0.113336 | + | 0.993557i | \(0.463846\pi\) | |||||||
\(770\) | 1.32624e12 | − | 2.12118e11i | 0.135961 | − | 0.0217455i | ||||
\(771\) | −8.83016e10 | −0.00899961 | ||||||||
\(772\) | 6.44474e12i | 0.653022i | ||||||||
\(773\) | − | 4.88091e12i | − | 0.491692i | −0.969309 | − | 0.245846i | \(-0.920934\pi\) | ||
0.969309 | − | 0.245846i | \(-0.0790658\pi\) | |||||||
\(774\) | −3.69896e12 | −0.370463 | ||||||||
\(775\) | 1.64255e13 | − | 5.39208e12i | 1.63554 | − | 0.536907i | ||||
\(776\) | −1.64578e13 | −1.62927 | ||||||||
\(777\) | − | 2.14030e12i | − | 0.210659i | ||||||
\(778\) | 1.21521e13i | 1.18917i | ||||||||
\(779\) | −2.51223e12 | −0.244422 | ||||||||
\(780\) | −3.85367e12 | + | 6.16353e11i | −0.372777 | + | 0.0596217i | ||||
\(781\) | −3.03269e12 | −0.291674 | ||||||||
\(782\) | − | 3.05300e12i | − | 0.291942i | ||||||
\(783\) | 1.95326e12i | 0.185708i | ||||||||
\(784\) | −3.63481e11 | −0.0343605 | ||||||||
\(785\) | 6.44324e11 | + | 4.02856e12i | 0.0605607 | + | 0.378648i | ||||
\(786\) | −1.92500e12 | −0.179899 | ||||||||
\(787\) | 5.55849e12i | 0.516500i | 0.966078 | + | 0.258250i | \(0.0831459\pi\) | ||||
−0.966078 | + | 0.258250i | \(0.916854\pi\) | |||||||
\(788\) | 1.26447e13i | 1.16826i | ||||||||
\(789\) | −2.97694e12 | −0.273479 | ||||||||
\(790\) | −4.96068e11 | − | 3.10160e12i | −0.0453126 | − | 0.283311i | ||||
\(791\) | −4.98263e12 | −0.452548 | ||||||||
\(792\) | 1.79274e12i | 0.161903i | ||||||||
\(793\) | − | 1.86398e13i | − | 1.67383i | ||||||
\(794\) | 1.05732e13 | 0.944091 | ||||||||
\(795\) | 1.17175e13 | − | 1.87409e12i | 1.04036 | − | 0.166394i | ||||
\(796\) | 1.04966e13 | 0.926704 | ||||||||
\(797\) | 4.50429e11i | 0.0395425i | 0.999805 | + | 0.0197712i | \(0.00629379\pi\) | ||||
−0.999805 | + | 0.0197712i | \(0.993706\pi\) | |||||||
\(798\) | − | 7.13984e11i | − | 0.0623269i | ||||||
\(799\) | −3.79064e12 | −0.329042 | ||||||||
\(800\) | 3.56089e12 | + | 1.08473e13i | 0.307365 | + | 0.936300i | ||||
\(801\) | 3.19367e12 | 0.274122 | ||||||||
\(802\) | 4.08646e12i | 0.348789i | ||||||||
\(803\) | 5.48882e12i | 0.465864i | ||||||||
\(804\) | −4.37828e12 | −0.369532 | ||||||||
\(805\) | 7.29467e12 | − | 1.16670e12i | 0.612243 | − | 0.0979217i | ||||
\(806\) | −1.42768e13 | −1.19158 | ||||||||
\(807\) | − | 7.19068e12i | − | 0.596814i | ||||||
\(808\) | − | 4.12663e12i | − | 0.340599i | ||||||
\(809\) | −8.43581e12 | −0.692402 | −0.346201 | − | 0.938160i | \(-0.612529\pi\) | ||||
−0.346201 | + | 0.938160i | \(0.612529\pi\) | |||||||
\(810\) | 1.36219e11 | + | 8.51694e11i | 0.0111187 | + | 0.0695186i | ||||
\(811\) | −1.79645e12 | −0.145821 | −0.0729106 | − | 0.997338i | \(-0.523229\pi\) | ||||
−0.0729106 | + | 0.997338i | \(0.523229\pi\) | |||||||
\(812\) | − | 3.24221e12i | − | 0.261721i | ||||||
\(813\) | 4.69443e12i | 0.376856i | ||||||||
\(814\) | 3.06453e12 | 0.244655 | ||||||||
\(815\) | −3.21165e12 | − | 2.00805e13i | −0.254988 | − | 1.59428i | ||||
\(816\) | −1.06470e11 | −0.00840663 | ||||||||
\(817\) | − | 8.39851e12i | − | 0.659482i | ||||||
\(818\) | − | 2.02520e12i | − | 0.158153i | ||||||
\(819\) | 2.12476e12 | 0.165018 | ||||||||
\(820\) | −4.97435e12 | + | 7.95593e11i | −0.384215 | + | 0.0614510i | ||||
\(821\) | 2.37074e13 | 1.82112 | 0.910561 | − | 0.413374i | \(-0.135650\pi\) | ||||
0.910561 | + | 0.413374i | \(0.135650\pi\) | |||||||
\(822\) | − | 4.07240e12i | − | 0.311120i | ||||||
\(823\) | 5.83064e12i | 0.443013i | 0.975159 | + | 0.221507i | \(0.0710974\pi\) | ||||
−0.975159 | + | 0.221507i | \(0.928903\pi\) | |||||||
\(824\) | −1.28961e13 | −0.974508 | ||||||||
\(825\) | −1.14901e12 | − | 3.50015e12i | −0.0863539 | − | 0.263053i | ||||
\(826\) | −4.24415e12 | −0.317234 | ||||||||
\(827\) | − | 1.53707e13i | − | 1.14266i | −0.820719 | − | 0.571332i | \(-0.806427\pi\) | ||
0.820719 | − | 0.571332i | \(-0.193573\pi\) | |||||||
\(828\) | 3.69203e12i | 0.272979i | ||||||||
\(829\) | −1.38823e13 | −1.02086 | −0.510430 | − | 0.859920i | \(-0.670514\pi\) | ||||
−0.510430 | + | 0.859920i | \(0.670514\pi\) | |||||||
\(830\) | 6.69221e11 | − | 1.07035e11i | 0.0489461 | − | 0.00782840i | ||||
\(831\) | −3.57951e12 | −0.260387 | ||||||||
\(832\) | − | 1.00812e13i | − | 0.729386i | ||||||
\(833\) | − | 3.71862e12i | − | 0.267596i | ||||||
\(834\) | 3.40261e12 | 0.243537 | ||||||||
\(835\) | −6.90367e10 | − | 4.31643e11i | −0.00491463 | − | 0.0307281i | ||||
\(836\) | −1.52407e12 | −0.107914 | ||||||||
\(837\) | − | 4.70399e12i | − | 0.331285i | ||||||
\(838\) | 9.89708e11i | 0.0693281i | ||||||||
\(839\) | 1.07137e13 | 0.746468 | 0.373234 | − | 0.927737i | \(-0.378249\pi\) | ||||
0.373234 | + | 0.927737i | \(0.378249\pi\) | |||||||
\(840\) | −6.03888e11 | − | 3.77574e12i | −0.0418504 | − | 0.261665i | ||||
\(841\) | −9.98592e11 | −0.0688345 | ||||||||
\(842\) | − | 2.11041e12i | − | 0.144698i | ||||||
\(843\) | 1.19392e13i | 0.814238i | ||||||||
\(844\) | 2.48777e12 | 0.168760 | ||||||||
\(845\) | −2.83174e12 | + | 4.52907e11i | −0.191073 | + | 0.0305600i | ||||
\(846\) | −3.07485e12 | −0.206375 | ||||||||
\(847\) | − | 5.22673e12i | − | 0.348943i | ||||||
\(848\) | 1.18820e12i | 0.0789059i | ||||||||
\(849\) | 1.32078e12 | 0.0872462 | ||||||||
\(850\) | 3.08526e12 | − | 1.01281e12i | 0.202724 | − | 0.0665495i | ||||
\(851\) | 1.68557e13 | 1.10170 | ||||||||
\(852\) | 3.23275e12i | 0.210181i | ||||||||
\(853\) | 1.35460e13i | 0.876076i | 0.898956 | + | 0.438038i | \(0.144327\pi\) | ||||
−0.898956 | + | 0.438038i | \(0.855673\pi\) | |||||||
\(854\) | 6.83805e12 | 0.439918 | ||||||||
\(855\) | −1.93378e12 | + | 3.09287e11i | −0.123754 | + | 0.0197931i | ||||
\(856\) | 1.67030e12 | 0.106332 | ||||||||
\(857\) | − | 5.74619e12i | − | 0.363887i | −0.983309 | − | 0.181943i | \(-0.941761\pi\) | ||
0.983309 | − | 0.181943i | \(-0.0582387\pi\) | |||||||
\(858\) | 3.04228e12i | 0.191649i | ||||||||
\(859\) | −1.42325e13 | −0.891890 | −0.445945 | − | 0.895060i | \(-0.647132\pi\) | ||||
−0.445945 | + | 0.895060i | \(0.647132\pi\) | |||||||
\(860\) | −2.65971e12 | − | 1.66295e13i | −0.165803 | − | 1.03666i | ||||
\(861\) | 2.74266e12 | 0.170082 | ||||||||
\(862\) | − | 6.78062e12i | − | 0.418299i | ||||||
\(863\) | 1.45815e13i | 0.894859i | 0.894319 | + | 0.447429i | \(0.147660\pi\) | ||||
−0.894319 | + | 0.447429i | \(0.852340\pi\) | |||||||
\(864\) | 3.10648e12 | 0.189652 | ||||||||
\(865\) | −1.60059e12 | − | 1.00075e13i | −0.0972091 | − | 0.607788i | ||||
\(866\) | 9.99737e12 | 0.604025 | ||||||||
\(867\) | 8.51637e12i | 0.511880i | ||||||||
\(868\) | 7.80815e12i | 0.466885i | ||||||||
\(869\) | 3.65037e12 | 0.217144 | ||||||||
\(870\) | 5.89024e12 | − | 9.42080e11i | 0.348575 | − | 0.0557508i | ||||
\(871\) | −1.98437e13 | −1.16826 | ||||||||
\(872\) | 1.45482e13i | 0.852090i | ||||||||
\(873\) | − | 9.20212e12i | − | 0.536196i | ||||||
\(874\) | 5.62291e12 | 0.325957 | ||||||||
\(875\) | 3.59899e12 | + | 6.98469e12i | 0.207561 | + | 0.402820i | ||||
\(876\) | 5.85090e12 | 0.335702 | ||||||||
\(877\) | 1.38120e13i | 0.788419i | 0.919021 | + | 0.394209i | \(0.128982\pi\) | ||||
−0.919021 | + | 0.394209i | \(0.871018\pi\) | |||||||
\(878\) | 1.43359e13i | 0.814139i | ||||||||
\(879\) | 9.73827e12 | 0.550214 | ||||||||
\(880\) | 3.64247e11 | − | 5.82574e10i | 0.0204750 | − | 0.00327476i | ||||
\(881\) | −9.98590e12 | −0.558465 | −0.279232 | − | 0.960224i | \(-0.590080\pi\) | ||||
−0.279232 | + | 0.960224i | \(0.590080\pi\) | |||||||
\(882\) | − | 3.01644e12i | − | 0.167836i | ||||||
\(883\) | 2.46582e13i | 1.36502i | 0.730878 | + | 0.682508i | \(0.239111\pi\) | ||||
−0.730878 | + | 0.682508i | \(0.760889\pi\) | |||||||
\(884\) | 3.99789e12 | 0.220189 | ||||||||
\(885\) | 1.83850e12 | + | 1.14950e13i | 0.100744 | + | 0.629889i | ||||
\(886\) | −2.93483e12 | −0.160004 | ||||||||
\(887\) | 7.28183e12i | 0.394988i | 0.980304 | + | 0.197494i | \(0.0632803\pi\) | ||||
−0.980304 | + | 0.197494i | \(0.936720\pi\) | |||||||
\(888\) | − | 8.72456e12i | − | 0.470853i | ||||||
\(889\) | 1.15662e13 | 0.621058 | ||||||||
\(890\) | −1.54035e12 | − | 9.63083e12i | −0.0822931 | − | 0.514528i | ||||
\(891\) | −1.00239e12 | −0.0532826 | ||||||||
\(892\) | − | 3.77769e12i | − | 0.199795i | ||||||
\(893\) | − | 6.98147e12i | − | 0.367380i | ||||||
\(894\) | 7.94198e12 | 0.415824 | ||||||||
\(895\) | −3.52214e13 | + | 5.63329e12i | −1.83486 | + | 0.293466i | ||||
\(896\) | −4.91693e12 | −0.254864 | ||||||||
\(897\) | 1.67334e13i | 0.863013i | ||||||||
\(898\) | − | 1.64656e12i | − | 0.0844955i | ||||||
\(899\) | −3.25324e13 | −1.66111 | ||||||||
\(900\) | −3.73104e12 | + | 1.22481e12i | −0.189556 | + | 0.0622268i | ||||
\(901\) | −1.21560e13 | −0.614511 | ||||||||
\(902\) | 3.92700e12i | 0.197529i | ||||||||
\(903\) | 9.16885e12i | 0.458902i | ||||||||
\(904\) | −2.03109e13 | −1.01151 | ||||||||
\(905\) | −5.41300e12 | + | 8.65751e11i | −0.268238 | + | 0.0429017i | ||||
\(906\) | 8.92753e12 | 0.440204 | ||||||||
\(907\) | − | 2.90933e13i | − | 1.42745i | −0.700428 | − | 0.713723i | \(-0.747007\pi\) | ||
0.700428 | − | 0.713723i | \(-0.252993\pi\) | |||||||
\(908\) | − | 3.97857e12i | − | 0.194241i | ||||||
\(909\) | 2.30734e12 | 0.112092 | ||||||||
\(910\) | −1.02480e12 | − | 6.40743e12i | −0.0495396 | − | 0.309740i | ||||
\(911\) | 2.72560e13 | 1.31108 | 0.655541 | − | 0.755160i | \(-0.272441\pi\) | ||||
0.655541 | + | 0.755160i | \(0.272441\pi\) | |||||||
\(912\) | − | 1.96093e11i | − | 0.00938611i | ||||||
\(913\) | 7.87628e11i | 0.0375148i | ||||||||
\(914\) | −2.04711e12 | −0.0970247 | ||||||||
\(915\) | −2.96214e12 | − | 1.85204e13i | −0.139704 | − | 0.873485i | ||||
\(916\) | −3.77214e11 | −0.0177034 | ||||||||
\(917\) | 4.77161e12i | 0.222845i | ||||||||
\(918\) | − | 8.83568e11i | − | 0.0410627i | ||||||
\(919\) | 2.72901e13 | 1.26208 | 0.631038 | − | 0.775752i | \(-0.282629\pi\) | ||||
0.631038 | + | 0.775752i | \(0.282629\pi\) | |||||||
\(920\) | 2.97355e13 | − | 4.75587e12i | 1.36845 | − | 0.218869i | ||||
\(921\) | −1.46076e13 | −0.668977 | ||||||||
\(922\) | 1.41741e13i | 0.645961i | ||||||||
\(923\) | 1.46518e13i | 0.664480i | ||||||||
\(924\) | 1.66386e12 | 0.0750919 | ||||||||
\(925\) | 5.59178e12 | + | 1.70338e13i | 0.251138 | + | 0.765021i | ||||
\(926\) | −6.80317e12 | −0.304062 | ||||||||
\(927\) | − | 7.21065e12i | − | 0.320712i | ||||||
\(928\) | − | 2.14842e13i | − | 0.950938i | ||||||
\(929\) | 2.46091e12 | 0.108399 | 0.0541994 | − | 0.998530i | \(-0.482739\pi\) | ||||
0.0541994 | + | 0.998530i | \(0.482739\pi\) | |||||||
\(930\) | −1.41854e13 | + | 2.26879e12i | −0.621823 | + | 0.0994539i | ||||
\(931\) | 6.84884e12 | 0.298774 | ||||||||
\(932\) | 4.72486e11i | 0.0205125i | ||||||||
\(933\) | − | 1.83894e13i | − | 0.794510i | ||||||
\(934\) | 1.20911e13 | 0.519884 | ||||||||
\(935\) | 5.96007e11 | + | 3.72646e12i | 0.0255035 | + | 0.159457i | ||||
\(936\) | 8.66123e12 | 0.368840 | ||||||||
\(937\) | − | 1.99170e13i | − | 0.844105i | −0.906571 | − | 0.422052i | \(-0.861310\pi\) | ||
0.906571 | − | 0.422052i | \(-0.138690\pi\) | |||||||
\(938\) | − | 7.27968e12i | − | 0.307043i | ||||||
\(939\) | 8.45661e12 | 0.354978 | ||||||||
\(940\) | −2.21095e12 | − | 1.38237e13i | −0.0923642 | − | 0.577496i | ||||
\(941\) | −4.95810e12 | −0.206140 | −0.103070 | − | 0.994674i | \(-0.532867\pi\) | ||||
−0.103070 | + | 0.994674i | \(0.532867\pi\) | |||||||
\(942\) | − | 3.39014e12i | − | 0.140278i | ||||||
\(943\) | 2.15995e13i | 0.889492i | ||||||||
\(944\) | −1.16564e12 | −0.0477739 | ||||||||
\(945\) | 2.11115e12 | − | 3.37655e11i | 0.0861144 | − | 0.0137731i | ||||
\(946\) | −1.31282e13 | −0.532960 | ||||||||
\(947\) | 1.51016e12i | 0.0610165i | 0.999535 | + | 0.0305083i | \(0.00971259\pi\) | ||||
−0.999535 | + | 0.0305083i | \(0.990287\pi\) | |||||||
\(948\) | − | 3.89118e12i | − | 0.156474i | ||||||
\(949\) | 2.65180e13 | 1.06131 | ||||||||
\(950\) | 1.86537e12 | + | 5.68232e12i | 0.0743034 | + | 0.226344i | ||||
\(951\) | −1.76797e13 | −0.700910 | ||||||||
\(952\) | 3.91704e12i | 0.154558i | ||||||||
\(953\) | − | 1.89236e13i | − | 0.743167i | −0.928399 | − | 0.371584i | \(-0.878815\pi\) | ||
0.928399 | − | 0.371584i | \(-0.121185\pi\) | |||||||
\(954\) | −9.86060e12 | −0.385421 | ||||||||
\(955\) | 2.66238e13 | − | 4.25818e12i | 1.03575 | − | 0.165657i | ||||
\(956\) | −1.94059e12 | −0.0751403 | ||||||||
\(957\) | 6.93241e12i | 0.267166i | ||||||||
\(958\) | − | 3.09764e13i | − | 1.18819i | ||||||
\(959\) | −1.00945e13 | −0.385392 | ||||||||
\(960\) | −1.60205e12 | − | 1.00166e13i | −0.0608773 | − | 0.380628i | ||||
\(961\) | 5.19075e13 | 1.96325 | ||||||||
\(962\) | − | 1.48056e13i | − | 0.557362i | ||||||
\(963\) | 9.33925e11i | 0.0349940i | ||||||||
\(964\) | −2.32886e10 | −0.000868554 | ||||||||
\(965\) | 4.64181e12 | + | 2.90223e13i | 0.172311 | + | 1.07736i | ||||
\(966\) | −6.13866e12 | −0.226818 | ||||||||
\(967\) | − | 2.37839e13i | − | 0.874708i | −0.899289 | − | 0.437354i | \(-0.855916\pi\) | ||
0.899289 | − | 0.437354i | \(-0.144084\pi\) | |||||||
\(968\) | − | 2.13059e13i | − | 0.779939i | ||||||
\(969\) | 2.00615e12 | 0.0730980 | ||||||||
\(970\) | −2.77499e13 | + | 4.43829e12i | −1.00644 | + | 0.160969i | ||||
\(971\) | −3.64444e13 | −1.31566 | −0.657831 | − | 0.753166i | \(-0.728526\pi\) | ||||
−0.657831 | + | 0.753166i | \(0.728526\pi\) | |||||||
\(972\) | 1.06851e12i | 0.0383955i | ||||||||
\(973\) | − | 8.43427e12i | − | 0.301675i | ||||||
\(974\) | −1.47961e13 | −0.526783 | ||||||||
\(975\) | −1.69102e13 | + | 5.55120e12i | −0.599276 | + | 0.196728i | ||||
\(976\) | 1.87805e12 | 0.0662494 | ||||||||
\(977\) | − | 1.56031e13i | − | 0.547878i | −0.961747 | − | 0.273939i | \(-0.911673\pi\) | ||
0.961747 | − | 0.273939i | \(-0.0883267\pi\) | |||||||
\(978\) | 1.68983e13i | 0.590632i | ||||||||
\(979\) | 1.13348e13 | 0.394360 | ||||||||
\(980\) | 1.35611e13 | − | 2.16895e12i | 0.469653 | − | 0.0751159i | ||||
\(981\) | −8.13442e12 | −0.280424 | ||||||||
\(982\) | 1.92384e13i | 0.660188i | ||||||||
\(983\) | − | 3.08484e13i | − | 1.05376i | −0.849939 | − | 0.526881i | \(-0.823361\pi\) | ||
0.849939 | − | 0.526881i | \(-0.176639\pi\) | |||||||
\(984\) | 1.11800e13 | 0.380157 | ||||||||
\(985\) | 9.10733e12 | + | 5.69424e13i | 0.308268 | + | 1.92741i | ||||
\(986\) | −6.11068e12 | −0.205894 | ||||||||
\(987\) | 7.62183e12i | 0.255642i | ||||||||
\(988\) | 7.36319e12i | 0.245844i | ||||||||
\(989\) | −7.22085e13 | −2.39996 | ||||||||
\(990\) | 4.83463e11 | + | 3.02279e12i | 0.0159958 | + | 0.100012i | ||||
\(991\) | −3.26910e13 | −1.07671 | −0.538353 | − | 0.842720i | \(-0.680953\pi\) | ||||
−0.538353 | + | 0.842720i | \(0.680953\pi\) | |||||||
\(992\) | 5.17399e13i | 1.69638i | ||||||||
\(993\) | − | 2.26188e12i | − | 0.0738239i | ||||||
\(994\) | −5.37502e12 | −0.174639 | ||||||||
\(995\) | 4.72690e13 | − | 7.56017e12i | 1.52888 | − | 0.244527i | ||||
\(996\) | 8.39585e11 | 0.0270332 | ||||||||
\(997\) | 4.13191e13i | 1.32441i | 0.749322 | + | 0.662206i | \(0.230379\pi\) | ||||
−0.749322 | + | 0.662206i | \(0.769621\pi\) | |||||||
\(998\) | 4.42556e12i | 0.141215i | ||||||||
\(999\) | 4.87821e12 | 0.154959 |
(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 | 15.10.b.a.4.5 | yes | 8 | |
3.2 | odd | 2 | 45.10.b.c.19.4 | 8 | |||
4.3 | odd | 2 | 240.10.f.c.49.4 | 8 | |||
5.2 | odd | 4 | 75.10.a.l.1.2 | 4 | |||
5.3 | odd | 4 | 75.10.a.i.1.3 | 4 | |||
5.4 | even | 2 | inner | 15.10.b.a.4.4 | ✓ | 8 | |
15.2 | even | 4 | 225.10.a.q.1.3 | 4 | |||
15.8 | even | 4 | 225.10.a.u.1.2 | 4 | |||
15.14 | odd | 2 | 45.10.b.c.19.5 | 8 | |||
20.19 | odd | 2 | 240.10.f.c.49.8 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.10.b.a.4.4 | ✓ | 8 | 5.4 | even | 2 | inner | |
15.10.b.a.4.5 | yes | 8 | 1.1 | even | 1 | trivial | |
45.10.b.c.19.4 | 8 | 3.2 | odd | 2 | |||
45.10.b.c.19.5 | 8 | 15.14 | odd | 2 | |||
75.10.a.i.1.3 | 4 | 5.3 | odd | 4 | |||
75.10.a.l.1.2 | 4 | 5.2 | odd | 4 | |||
225.10.a.q.1.3 | 4 | 15.2 | even | 4 | |||
225.10.a.u.1.2 | 4 | 15.8 | even | 4 | |||
240.10.f.c.49.4 | 8 | 4.3 | odd | 2 | |||
240.10.f.c.49.8 | 8 | 20.19 | odd | 2 |