Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,8,Mod(1,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.a (trivial) |
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: | yes |
Analytic conductor: | \(55.2921495107\) |
Analytic rank: | \(0\) |
Dimension: | \(18\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{18} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + 3375594921 x^{11} + 115310342333 x^{10} + \cdots + 51\!\cdots\!48 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{12}\cdot 3^{5} \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-20.5204\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −19.5204 | −1.72538 | −0.862688 | − | 0.505737i | \(-0.831221\pi\) | ||||
−0.862688 | + | 0.505737i | \(0.831221\pi\) | |||||||
\(3\) | 27.0000 | 0.577350 | ||||||||
\(4\) | 253.046 | 1.97692 | ||||||||
\(5\) | −49.6011 | −0.177458 | −0.0887292 | − | 0.996056i | \(-0.528281\pi\) | ||||
−0.0887292 | + | 0.996056i | \(0.528281\pi\) | |||||||
\(6\) | −527.051 | −0.996146 | ||||||||
\(7\) | −119.919 | −0.132143 | −0.0660714 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660714 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(8\) | −2440.94 | −1.68555 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 968.233 | 0.306182 | ||||||||
\(11\) | −5494.59 | −1.24469 | −0.622344 | − | 0.782744i | \(-0.713820\pi\) | ||||
−0.622344 | + | 0.782744i | \(0.713820\pi\) | |||||||
\(12\) | 6832.23 | 1.14137 | ||||||||
\(13\) | −12895.9 | −1.62798 | −0.813990 | − | 0.580879i | \(-0.802709\pi\) | ||||
−0.813990 | + | 0.580879i | \(0.802709\pi\) | |||||||
\(14\) | 2340.86 | 0.227996 | ||||||||
\(15\) | −1339.23 | −0.102456 | ||||||||
\(16\) | 15258.3 | 0.931291 | ||||||||
\(17\) | 25621.3 | 1.26482 | 0.632411 | − | 0.774633i | \(-0.282065\pi\) | ||||
0.632411 | + | 0.774633i | \(0.282065\pi\) | |||||||
\(18\) | −14230.4 | −0.575125 | ||||||||
\(19\) | −17560.8 | −0.587363 | −0.293681 | − | 0.955903i | \(-0.594880\pi\) | ||||
−0.293681 | + | 0.955903i | \(0.594880\pi\) | |||||||
\(20\) | −12551.3 | −0.350821 | ||||||||
\(21\) | −3237.80 | −0.0762927 | ||||||||
\(22\) | 107256. | 2.14755 | ||||||||
\(23\) | 63260.9 | 1.08415 | 0.542074 | − | 0.840331i | \(-0.317639\pi\) | ||||
0.542074 | + | 0.840331i | \(0.317639\pi\) | |||||||
\(24\) | −65905.4 | −0.973154 | ||||||||
\(25\) | −75664.7 | −0.968509 | ||||||||
\(26\) | 251733. | 2.80888 | ||||||||
\(27\) | 19683.0 | 0.192450 | ||||||||
\(28\) | −30344.9 | −0.261236 | ||||||||
\(29\) | −29622.4 | −0.225542 | −0.112771 | − | 0.993621i | \(-0.535973\pi\) | ||||
−0.112771 | + | 0.993621i | \(0.535973\pi\) | |||||||
\(30\) | 26142.3 | 0.176774 | ||||||||
\(31\) | 166521. | 1.00393 | 0.501963 | − | 0.864889i | \(-0.332611\pi\) | ||||
0.501963 | + | 0.864889i | \(0.332611\pi\) | |||||||
\(32\) | 14593.0 | 0.0787264 | ||||||||
\(33\) | −148354. | −0.718621 | ||||||||
\(34\) | −500138. | −2.18229 | ||||||||
\(35\) | 5948.10 | 0.0234498 | ||||||||
\(36\) | 184470. | 0.658973 | ||||||||
\(37\) | 107247. | 0.348080 | 0.174040 | − | 0.984739i | \(-0.444318\pi\) | ||||
0.174040 | + | 0.984739i | \(0.444318\pi\) | |||||||
\(38\) | 342794. | 1.01342 | ||||||||
\(39\) | −348189. | −0.939915 | ||||||||
\(40\) | 121073. | 0.299115 | ||||||||
\(41\) | 520929. | 1.18042 | 0.590208 | − | 0.807251i | \(-0.299046\pi\) | ||||
0.590208 | + | 0.807251i | \(0.299046\pi\) | |||||||
\(42\) | 63203.2 | 0.131633 | ||||||||
\(43\) | −943358. | −1.80941 | −0.904704 | − | 0.426040i | \(-0.859908\pi\) | ||||
−0.904704 | + | 0.426040i | \(0.859908\pi\) | |||||||
\(44\) | −1.39038e6 | −2.46065 | ||||||||
\(45\) | −36159.2 | −0.0591528 | ||||||||
\(46\) | −1.23488e6 | −1.87056 | ||||||||
\(47\) | −789984. | −1.10988 | −0.554939 | − | 0.831891i | \(-0.687259\pi\) | ||||
−0.554939 | + | 0.831891i | \(0.687259\pi\) | |||||||
\(48\) | 411973. | 0.537681 | ||||||||
\(49\) | −809163. | −0.982538 | ||||||||
\(50\) | 1.47701e6 | 1.67104 | ||||||||
\(51\) | 691775. | 0.730246 | ||||||||
\(52\) | −3.26325e6 | −3.21839 | ||||||||
\(53\) | −930361. | −0.858392 | −0.429196 | − | 0.903211i | \(-0.641203\pi\) | ||||
−0.429196 | + | 0.903211i | \(0.641203\pi\) | |||||||
\(54\) | −384220. | −0.332049 | ||||||||
\(55\) | 272538. | 0.220880 | ||||||||
\(56\) | 292714. | 0.222734 | ||||||||
\(57\) | −474141. | −0.339114 | ||||||||
\(58\) | 578240. | 0.389144 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | −338886. | −0.202546 | ||||||||
\(61\) | 2.19795e6 | 1.23983 | 0.619915 | − | 0.784669i | \(-0.287167\pi\) | ||||
0.619915 | + | 0.784669i | \(0.287167\pi\) | |||||||
\(62\) | −3.25055e6 | −1.73215 | ||||||||
\(63\) | −87420.7 | −0.0440476 | ||||||||
\(64\) | −2.23792e6 | −1.06712 | ||||||||
\(65\) | 639650. | 0.288899 | ||||||||
\(66\) | 2.89593e6 | 1.23989 | ||||||||
\(67\) | 1.13372e6 | 0.460513 | 0.230257 | − | 0.973130i | \(-0.426043\pi\) | ||||
0.230257 | + | 0.973130i | \(0.426043\pi\) | |||||||
\(68\) | 6.48336e6 | 2.50045 | ||||||||
\(69\) | 1.70805e6 | 0.625933 | ||||||||
\(70\) | −116109. | −0.0404598 | ||||||||
\(71\) | 2.46554e6 | 0.817537 | 0.408769 | − | 0.912638i | \(-0.365958\pi\) | ||||
0.408769 | + | 0.912638i | \(0.365958\pi\) | |||||||
\(72\) | −1.77945e6 | −0.561851 | ||||||||
\(73\) | 5.09118e6 | 1.53175 | 0.765876 | − | 0.642988i | \(-0.222306\pi\) | ||||
0.765876 | + | 0.642988i | \(0.222306\pi\) | |||||||
\(74\) | −2.09351e6 | −0.600569 | ||||||||
\(75\) | −2.04295e6 | −0.559169 | ||||||||
\(76\) | −4.44368e6 | −1.16117 | ||||||||
\(77\) | 658903. | 0.164477 | ||||||||
\(78\) | 6.79678e6 | 1.62171 | ||||||||
\(79\) | 4.40371e6 | 1.00490 | 0.502452 | − | 0.864605i | \(-0.332431\pi\) | ||||
0.502452 | + | 0.864605i | \(0.332431\pi\) | |||||||
\(80\) | −756827. | −0.165265 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | −1.01687e7 | −2.03666 | ||||||||
\(83\) | 172296. | 0.0330751 | 0.0165375 | − | 0.999863i | \(-0.494736\pi\) | ||||
0.0165375 | + | 0.999863i | \(0.494736\pi\) | |||||||
\(84\) | −819312. | −0.150824 | ||||||||
\(85\) | −1.27084e6 | −0.224453 | ||||||||
\(86\) | 1.84147e7 | 3.12191 | ||||||||
\(87\) | −799804. | −0.130217 | ||||||||
\(88\) | 1.34120e7 | 2.09799 | ||||||||
\(89\) | 8.28035e6 | 1.24504 | 0.622521 | − | 0.782603i | \(-0.286109\pi\) | ||||
0.622521 | + | 0.782603i | \(0.286109\pi\) | |||||||
\(90\) | 705842. | 0.102061 | ||||||||
\(91\) | 1.54646e6 | 0.215126 | ||||||||
\(92\) | 1.60079e7 | 2.14327 | ||||||||
\(93\) | 4.49606e6 | 0.579617 | ||||||||
\(94\) | 1.54208e7 | 1.91496 | ||||||||
\(95\) | 871035. | 0.104232 | ||||||||
\(96\) | 394012. | 0.0454527 | ||||||||
\(97\) | −6.60133e6 | −0.734396 | −0.367198 | − | 0.930143i | \(-0.619683\pi\) | ||||
−0.367198 | + | 0.930143i | \(0.619683\pi\) | |||||||
\(98\) | 1.57952e7 | 1.69525 | ||||||||
\(99\) | −4.00555e6 | −0.414896 | ||||||||
\(100\) | −1.91466e7 | −1.91466 | ||||||||
\(101\) | −1.77940e6 | −0.171849 | −0.0859247 | − | 0.996302i | \(-0.527384\pi\) | ||||
−0.0859247 | + | 0.996302i | \(0.527384\pi\) | |||||||
\(102\) | −1.35037e7 | −1.25995 | ||||||||
\(103\) | −6.76389e6 | −0.609911 | −0.304955 | − | 0.952367i | \(-0.598642\pi\) | ||||
−0.304955 | + | 0.952367i | \(0.598642\pi\) | |||||||
\(104\) | 3.14781e7 | 2.74405 | ||||||||
\(105\) | 160599. | 0.0135388 | ||||||||
\(106\) | 1.81610e7 | 1.48105 | ||||||||
\(107\) | 2.49224e7 | 1.96674 | 0.983371 | − | 0.181607i | \(-0.0581299\pi\) | ||||
0.983371 | + | 0.181607i | \(0.0581299\pi\) | |||||||
\(108\) | 4.98070e6 | 0.380458 | ||||||||
\(109\) | −2.15957e7 | −1.59726 | −0.798630 | − | 0.601823i | \(-0.794441\pi\) | ||||
−0.798630 | + | 0.601823i | \(0.794441\pi\) | |||||||
\(110\) | −5.32004e6 | −0.381101 | ||||||||
\(111\) | 2.89567e6 | 0.200964 | ||||||||
\(112\) | −1.82975e6 | −0.123063 | ||||||||
\(113\) | −1.84076e7 | −1.20011 | −0.600056 | − | 0.799958i | \(-0.704855\pi\) | ||||
−0.600056 | + | 0.799958i | \(0.704855\pi\) | |||||||
\(114\) | 9.25543e6 | 0.585099 | ||||||||
\(115\) | −3.13781e6 | −0.192391 | ||||||||
\(116\) | −7.49582e6 | −0.445878 | ||||||||
\(117\) | −9.40109e6 | −0.542660 | ||||||||
\(118\) | −4.00908e6 | −0.224625 | ||||||||
\(119\) | −3.07247e6 | −0.167137 | ||||||||
\(120\) | 3.26898e6 | 0.172694 | ||||||||
\(121\) | 1.07033e7 | 0.549249 | ||||||||
\(122\) | −4.29047e7 | −2.13917 | ||||||||
\(123\) | 1.40651e7 | 0.681513 | ||||||||
\(124\) | 4.21373e7 | 1.98468 | ||||||||
\(125\) | 7.62814e6 | 0.349328 | ||||||||
\(126\) | 1.70649e6 | 0.0759986 | ||||||||
\(127\) | 2.65579e7 | 1.15049 | 0.575243 | − | 0.817983i | \(-0.304908\pi\) | ||||
0.575243 | + | 0.817983i | \(0.304908\pi\) | |||||||
\(128\) | 4.18172e7 | 1.76246 | ||||||||
\(129\) | −2.54707e7 | −1.04466 | ||||||||
\(130\) | −1.24862e7 | −0.498459 | ||||||||
\(131\) | 3.58406e7 | 1.39292 | 0.696460 | − | 0.717595i | \(-0.254757\pi\) | ||||
0.696460 | + | 0.717595i | \(0.254757\pi\) | |||||||
\(132\) | −3.75403e7 | −1.42066 | ||||||||
\(133\) | 2.10587e6 | 0.0776158 | ||||||||
\(134\) | −2.21306e7 | −0.794558 | ||||||||
\(135\) | −976299. | −0.0341519 | ||||||||
\(136\) | −6.25400e7 | −2.13193 | ||||||||
\(137\) | 3.94491e7 | 1.31074 | 0.655368 | − | 0.755310i | \(-0.272513\pi\) | ||||
0.655368 | + | 0.755310i | \(0.272513\pi\) | |||||||
\(138\) | −3.33417e7 | −1.07997 | ||||||||
\(139\) | −1.10784e7 | −0.349886 | −0.174943 | − | 0.984579i | \(-0.555974\pi\) | ||||
−0.174943 | + | 0.984579i | \(0.555974\pi\) | |||||||
\(140\) | 1.50514e6 | 0.0463584 | ||||||||
\(141\) | −2.13296e7 | −0.640789 | ||||||||
\(142\) | −4.81283e7 | −1.41056 | ||||||||
\(143\) | 7.08575e7 | 2.02633 | ||||||||
\(144\) | 1.11233e7 | 0.310430 | ||||||||
\(145\) | 1.46930e6 | 0.0400243 | ||||||||
\(146\) | −9.93819e7 | −2.64285 | ||||||||
\(147\) | −2.18474e7 | −0.567269 | ||||||||
\(148\) | 2.71384e7 | 0.688127 | ||||||||
\(149\) | 2.08170e7 | 0.515546 | 0.257773 | − | 0.966206i | \(-0.417011\pi\) | ||||
0.257773 | + | 0.966206i | \(0.417011\pi\) | |||||||
\(150\) | 3.98791e7 | 0.964776 | ||||||||
\(151\) | −2.65440e7 | −0.627403 | −0.313702 | − | 0.949522i | \(-0.601569\pi\) | ||||
−0.313702 | + | 0.949522i | \(0.601569\pi\) | |||||||
\(152\) | 4.28648e7 | 0.990031 | ||||||||
\(153\) | 1.86779e7 | 0.421608 | ||||||||
\(154\) | −1.28620e7 | −0.283784 | ||||||||
\(155\) | −8.25961e6 | −0.178155 | ||||||||
\(156\) | −8.81076e7 | −1.85814 | ||||||||
\(157\) | 5.98029e7 | 1.23331 | 0.616656 | − | 0.787232i | \(-0.288487\pi\) | ||||
0.616656 | + | 0.787232i | \(0.288487\pi\) | |||||||
\(158\) | −8.59622e7 | −1.73384 | ||||||||
\(159\) | −2.51197e7 | −0.495593 | ||||||||
\(160\) | −723831. | −0.0139707 | ||||||||
\(161\) | −7.58616e6 | −0.143262 | ||||||||
\(162\) | −1.03739e7 | −0.191708 | ||||||||
\(163\) | 9.55079e7 | 1.72736 | 0.863679 | − | 0.504042i | \(-0.168154\pi\) | ||||
0.863679 | + | 0.504042i | \(0.168154\pi\) | |||||||
\(164\) | 1.31819e8 | 2.33359 | ||||||||
\(165\) | 7.35852e6 | 0.127525 | ||||||||
\(166\) | −3.36328e6 | −0.0570669 | ||||||||
\(167\) | −1.67858e7 | −0.278890 | −0.139445 | − | 0.990230i | \(-0.544532\pi\) | ||||
−0.139445 | + | 0.990230i | \(0.544532\pi\) | |||||||
\(168\) | 7.90328e6 | 0.128595 | ||||||||
\(169\) | 1.03555e8 | 1.65032 | ||||||||
\(170\) | 2.48074e7 | 0.387266 | ||||||||
\(171\) | −1.28018e7 | −0.195788 | ||||||||
\(172\) | −2.38713e8 | −3.57706 | ||||||||
\(173\) | −7.07459e7 | −1.03882 | −0.519410 | − | 0.854525i | \(-0.673848\pi\) | ||||
−0.519410 | + | 0.854525i | \(0.673848\pi\) | |||||||
\(174\) | 1.56125e7 | 0.224672 | ||||||||
\(175\) | 9.07361e6 | 0.127981 | ||||||||
\(176\) | −8.38379e7 | −1.15917 | ||||||||
\(177\) | 5.54523e6 | 0.0751646 | ||||||||
\(178\) | −1.61636e8 | −2.14816 | ||||||||
\(179\) | −9.77537e6 | −0.127394 | −0.0636968 | − | 0.997969i | \(-0.520289\pi\) | ||||
−0.0636968 | + | 0.997969i | \(0.520289\pi\) | |||||||
\(180\) | −9.14993e6 | −0.116940 | ||||||||
\(181\) | 9.13710e7 | 1.14534 | 0.572668 | − | 0.819787i | \(-0.305908\pi\) | ||||
0.572668 | + | 0.819787i | \(0.305908\pi\) | |||||||
\(182\) | −3.01874e7 | −0.371173 | ||||||||
\(183\) | 5.93445e7 | 0.715817 | ||||||||
\(184\) | −1.54416e8 | −1.82739 | ||||||||
\(185\) | −5.31957e6 | −0.0617698 | ||||||||
\(186\) | −8.77648e7 | −1.00006 | ||||||||
\(187\) | −1.40778e8 | −1.57431 | ||||||||
\(188\) | −1.99902e8 | −2.19414 | ||||||||
\(189\) | −2.36036e6 | −0.0254309 | ||||||||
\(190\) | −1.70029e7 | −0.179840 | ||||||||
\(191\) | −1.44165e8 | −1.49707 | −0.748536 | − | 0.663094i | \(-0.769243\pi\) | ||||
−0.748536 | + | 0.663094i | \(0.769243\pi\) | |||||||
\(192\) | −6.04238e7 | −0.616104 | ||||||||
\(193\) | 5.46350e7 | 0.547042 | 0.273521 | − | 0.961866i | \(-0.411812\pi\) | ||||
0.273521 | + | 0.961866i | \(0.411812\pi\) | |||||||
\(194\) | 1.28861e8 | 1.26711 | ||||||||
\(195\) | 1.72705e7 | 0.166796 | ||||||||
\(196\) | −2.04755e8 | −1.94240 | ||||||||
\(197\) | 1.55456e8 | 1.44869 | 0.724347 | − | 0.689436i | \(-0.242141\pi\) | ||||
0.724347 | + | 0.689436i | \(0.242141\pi\) | |||||||
\(198\) | 7.81900e7 | 0.715852 | ||||||||
\(199\) | −2.03195e7 | −0.182780 | −0.0913898 | − | 0.995815i | \(-0.529131\pi\) | ||||
−0.0913898 | + | 0.995815i | \(0.529131\pi\) | |||||||
\(200\) | 1.84693e8 | 1.63247 | ||||||||
\(201\) | 3.06103e7 | 0.265878 | ||||||||
\(202\) | 3.47345e7 | 0.296505 | ||||||||
\(203\) | 3.55227e6 | 0.0298037 | ||||||||
\(204\) | 1.75051e8 | 1.44364 | ||||||||
\(205\) | −2.58386e7 | −0.209475 | ||||||||
\(206\) | 1.32034e8 | 1.05233 | ||||||||
\(207\) | 4.61172e7 | 0.361382 | ||||||||
\(208\) | −1.96769e8 | −1.51612 | ||||||||
\(209\) | 9.64893e7 | 0.731084 | ||||||||
\(210\) | −3.13495e6 | −0.0233595 | ||||||||
\(211\) | −1.34211e8 | −0.983557 | −0.491779 | − | 0.870720i | \(-0.663653\pi\) | ||||
−0.491779 | + | 0.870720i | \(0.663653\pi\) | |||||||
\(212\) | −2.35424e8 | −1.69697 | ||||||||
\(213\) | 6.65695e7 | 0.472005 | ||||||||
\(214\) | −4.86496e8 | −3.39337 | ||||||||
\(215\) | 4.67916e7 | 0.321095 | ||||||||
\(216\) | −4.80450e7 | −0.324385 | ||||||||
\(217\) | −1.99689e7 | −0.132662 | ||||||||
\(218\) | 4.21557e8 | 2.75587 | ||||||||
\(219\) | 1.37462e8 | 0.884358 | ||||||||
\(220\) | 6.89645e7 | 0.436663 | ||||||||
\(221\) | −3.30409e8 | −2.05911 | ||||||||
\(222\) | −5.65246e7 | −0.346739 | ||||||||
\(223\) | 1.58205e8 | 0.955328 | 0.477664 | − | 0.878543i | \(-0.341484\pi\) | ||||
0.477664 | + | 0.878543i | \(0.341484\pi\) | |||||||
\(224\) | −1.74998e6 | −0.0104031 | ||||||||
\(225\) | −5.51596e7 | −0.322836 | ||||||||
\(226\) | 3.59323e8 | 2.07064 | ||||||||
\(227\) | 2.48289e8 | 1.40886 | 0.704428 | − | 0.709775i | \(-0.251204\pi\) | ||||
0.704428 | + | 0.709775i | \(0.251204\pi\) | |||||||
\(228\) | −1.19979e8 | −0.670401 | ||||||||
\(229\) | 5.03600e6 | 0.0277116 | 0.0138558 | − | 0.999904i | \(-0.495589\pi\) | ||||
0.0138558 | + | 0.999904i | \(0.495589\pi\) | |||||||
\(230\) | 6.12513e7 | 0.331947 | ||||||||
\(231\) | 1.77904e7 | 0.0949606 | ||||||||
\(232\) | 7.23065e7 | 0.380162 | ||||||||
\(233\) | 2.76994e8 | 1.43458 | 0.717291 | − | 0.696774i | \(-0.245382\pi\) | ||||
0.717291 | + | 0.696774i | \(0.245382\pi\) | |||||||
\(234\) | 1.83513e8 | 0.936292 | ||||||||
\(235\) | 3.91841e7 | 0.196957 | ||||||||
\(236\) | 5.19703e7 | 0.257373 | ||||||||
\(237\) | 1.18900e8 | 0.580181 | ||||||||
\(238\) | 5.99758e7 | 0.288374 | ||||||||
\(239\) | 3.80453e8 | 1.80264 | 0.901319 | − | 0.433157i | \(-0.142600\pi\) | ||||
0.901319 | + | 0.433157i | \(0.142600\pi\) | |||||||
\(240\) | −2.04343e7 | −0.0954160 | ||||||||
\(241\) | 6.73805e7 | 0.310080 | 0.155040 | − | 0.987908i | \(-0.450449\pi\) | ||||
0.155040 | + | 0.987908i | \(0.450449\pi\) | |||||||
\(242\) | −2.08933e8 | −0.947661 | ||||||||
\(243\) | 1.43489e7 | 0.0641500 | ||||||||
\(244\) | 5.56181e8 | 2.45105 | ||||||||
\(245\) | 4.01354e7 | 0.174360 | ||||||||
\(246\) | −2.74556e8 | −1.17587 | ||||||||
\(247\) | 2.26462e8 | 0.956215 | ||||||||
\(248\) | −4.06467e8 | −1.69217 | ||||||||
\(249\) | 4.65198e6 | 0.0190959 | ||||||||
\(250\) | −1.48904e8 | −0.602722 | ||||||||
\(251\) | −1.44862e8 | −0.578225 | −0.289113 | − | 0.957295i | \(-0.593360\pi\) | ||||
−0.289113 | + | 0.957295i | \(0.593360\pi\) | |||||||
\(252\) | −2.21214e7 | −0.0870785 | ||||||||
\(253\) | −3.47593e8 | −1.34943 | ||||||||
\(254\) | −5.18421e8 | −1.98502 | ||||||||
\(255\) | −3.43128e7 | −0.129588 | ||||||||
\(256\) | −5.29834e8 | −1.97378 | ||||||||
\(257\) | 5.53323e7 | 0.203335 | 0.101668 | − | 0.994818i | \(-0.467582\pi\) | ||||
0.101668 | + | 0.994818i | \(0.467582\pi\) | |||||||
\(258\) | 4.97197e8 | 1.80244 | ||||||||
\(259\) | −1.28609e7 | −0.0459963 | ||||||||
\(260\) | 1.61861e8 | 0.571129 | ||||||||
\(261\) | −2.15947e7 | −0.0751806 | ||||||||
\(262\) | −6.99623e8 | −2.40331 | ||||||||
\(263\) | 1.21289e8 | 0.411128 | 0.205564 | − | 0.978644i | \(-0.434097\pi\) | ||||
0.205564 | + | 0.978644i | \(0.434097\pi\) | |||||||
\(264\) | 3.62123e8 | 1.21127 | ||||||||
\(265\) | 4.61469e7 | 0.152329 | ||||||||
\(266\) | −4.11073e7 | −0.133916 | ||||||||
\(267\) | 2.23569e8 | 0.718825 | ||||||||
\(268\) | 2.86882e8 | 0.910398 | ||||||||
\(269\) | −5.24972e8 | −1.64438 | −0.822191 | − | 0.569211i | \(-0.807249\pi\) | ||||
−0.822191 | + | 0.569211i | \(0.807249\pi\) | |||||||
\(270\) | 1.90577e7 | 0.0589248 | ||||||||
\(271\) | 1.03625e8 | 0.316280 | 0.158140 | − | 0.987417i | \(-0.449450\pi\) | ||||
0.158140 | + | 0.987417i | \(0.449450\pi\) | |||||||
\(272\) | 3.90936e8 | 1.17792 | ||||||||
\(273\) | 4.17543e7 | 0.124203 | ||||||||
\(274\) | −7.70062e8 | −2.26151 | ||||||||
\(275\) | 4.15746e8 | 1.20549 | ||||||||
\(276\) | 4.32213e8 | 1.23742 | ||||||||
\(277\) | 1.95179e8 | 0.551765 | 0.275883 | − | 0.961191i | \(-0.411030\pi\) | ||||
0.275883 | + | 0.961191i | \(0.411030\pi\) | |||||||
\(278\) | 2.16255e8 | 0.603684 | ||||||||
\(279\) | 1.21394e8 | 0.334642 | ||||||||
\(280\) | −1.45189e7 | −0.0395259 | ||||||||
\(281\) | 2.55753e8 | 0.687621 | 0.343811 | − | 0.939039i | \(-0.388282\pi\) | ||||
0.343811 | + | 0.939039i | \(0.388282\pi\) | |||||||
\(282\) | 4.16361e8 | 1.10560 | ||||||||
\(283\) | −1.42799e8 | −0.374518 | −0.187259 | − | 0.982311i | \(-0.559960\pi\) | ||||
−0.187259 | + | 0.982311i | \(0.559960\pi\) | |||||||
\(284\) | 6.23894e8 | 1.61621 | ||||||||
\(285\) | 2.35179e7 | 0.0601786 | ||||||||
\(286\) | −1.38317e9 | −3.49618 | ||||||||
\(287\) | −6.24691e7 | −0.155983 | ||||||||
\(288\) | 1.06383e7 | 0.0262421 | ||||||||
\(289\) | 2.46112e8 | 0.599777 | ||||||||
\(290\) | −2.86814e7 | −0.0690569 | ||||||||
\(291\) | −1.78236e8 | −0.424004 | ||||||||
\(292\) | 1.28830e9 | 3.02815 | ||||||||
\(293\) | −3.51565e8 | −0.816524 | −0.408262 | − | 0.912865i | \(-0.633865\pi\) | ||||
−0.408262 | + | 0.912865i | \(0.633865\pi\) | |||||||
\(294\) | 4.26470e8 | 0.978751 | ||||||||
\(295\) | −1.01870e7 | −0.0231031 | ||||||||
\(296\) | −2.61784e8 | −0.586708 | ||||||||
\(297\) | −1.08150e8 | −0.239540 | ||||||||
\(298\) | −4.06357e8 | −0.889510 | ||||||||
\(299\) | −8.15805e8 | −1.76497 | ||||||||
\(300\) | −5.16959e8 | −1.10543 | ||||||||
\(301\) | 1.13126e8 | 0.239100 | ||||||||
\(302\) | 5.18149e8 | 1.08251 | ||||||||
\(303\) | −4.80437e7 | −0.0992172 | ||||||||
\(304\) | −2.67947e8 | −0.547006 | ||||||||
\(305\) | −1.09021e8 | −0.220018 | ||||||||
\(306\) | −3.64600e8 | −0.727431 | ||||||||
\(307\) | −6.10924e8 | −1.20504 | −0.602522 | − | 0.798102i | \(-0.705837\pi\) | ||||
−0.602522 | + | 0.798102i | \(0.705837\pi\) | |||||||
\(308\) | 1.66733e8 | 0.325157 | ||||||||
\(309\) | −1.82625e8 | −0.352132 | ||||||||
\(310\) | 1.61231e8 | 0.307384 | ||||||||
\(311\) | −5.80323e8 | −1.09398 | −0.546988 | − | 0.837140i | \(-0.684226\pi\) | ||||
−0.546988 | + | 0.837140i | \(0.684226\pi\) | |||||||
\(312\) | 8.49908e8 | 1.58428 | ||||||||
\(313\) | 8.00376e8 | 1.47533 | 0.737664 | − | 0.675168i | \(-0.235929\pi\) | ||||
0.737664 | + | 0.675168i | \(0.235929\pi\) | |||||||
\(314\) | −1.16738e9 | −2.12793 | ||||||||
\(315\) | 4.33616e6 | 0.00781661 | ||||||||
\(316\) | 1.11434e9 | 1.98661 | ||||||||
\(317\) | −6.06744e8 | −1.06979 | −0.534895 | − | 0.844919i | \(-0.679649\pi\) | ||||
−0.534895 | + | 0.844919i | \(0.679649\pi\) | |||||||
\(318\) | 4.90347e8 | 0.855084 | ||||||||
\(319\) | 1.62763e8 | 0.280729 | ||||||||
\(320\) | 1.11003e8 | 0.189370 | ||||||||
\(321\) | 6.72906e8 | 1.13550 | ||||||||
\(322\) | 1.48085e8 | 0.247181 | ||||||||
\(323\) | −4.49930e8 | −0.742910 | ||||||||
\(324\) | 1.34479e8 | 0.219658 | ||||||||
\(325\) | 9.75763e8 | 1.57671 | ||||||||
\(326\) | −1.86435e9 | −2.98034 | ||||||||
\(327\) | −5.83085e8 | −0.922178 | ||||||||
\(328\) | −1.27156e9 | −1.98965 | ||||||||
\(329\) | 9.47337e7 | 0.146662 | ||||||||
\(330\) | −1.43641e8 | −0.220029 | ||||||||
\(331\) | −4.95371e8 | −0.750814 | −0.375407 | − | 0.926860i | \(-0.622497\pi\) | ||||
−0.375407 | + | 0.926860i | \(0.622497\pi\) | |||||||
\(332\) | 4.35987e7 | 0.0653868 | ||||||||
\(333\) | 7.81831e7 | 0.116027 | ||||||||
\(334\) | 3.27665e8 | 0.481191 | ||||||||
\(335\) | −5.62335e7 | −0.0817219 | ||||||||
\(336\) | −4.94033e7 | −0.0710507 | ||||||||
\(337\) | −5.35635e8 | −0.762367 | −0.381183 | − | 0.924499i | \(-0.624483\pi\) | ||||
−0.381183 | + | 0.924499i | \(0.624483\pi\) | |||||||
\(338\) | −2.02144e9 | −2.84742 | ||||||||
\(339\) | −4.97004e8 | −0.692885 | ||||||||
\(340\) | −3.21582e8 | −0.443726 | ||||||||
\(341\) | −9.14962e8 | −1.24958 | ||||||||
\(342\) | 2.49896e8 | 0.337807 | ||||||||
\(343\) | 1.95792e8 | 0.261978 | ||||||||
\(344\) | 2.30268e9 | 3.04985 | ||||||||
\(345\) | −8.47209e7 | −0.111077 | ||||||||
\(346\) | 1.38099e9 | 1.79235 | ||||||||
\(347\) | 1.06614e9 | 1.36981 | 0.684905 | − | 0.728633i | \(-0.259844\pi\) | ||||
0.684905 | + | 0.728633i | \(0.259844\pi\) | |||||||
\(348\) | −2.02387e8 | −0.257428 | ||||||||
\(349\) | 9.40691e8 | 1.18456 | 0.592282 | − | 0.805731i | \(-0.298227\pi\) | ||||
0.592282 | + | 0.805731i | \(0.298227\pi\) | |||||||
\(350\) | −1.77120e8 | −0.220816 | ||||||||
\(351\) | −2.53830e8 | −0.313305 | ||||||||
\(352\) | −8.01827e7 | −0.0979899 | ||||||||
\(353\) | −6.36948e8 | −0.770713 | −0.385357 | − | 0.922768i | \(-0.625922\pi\) | ||||
−0.385357 | + | 0.922768i | \(0.625922\pi\) | |||||||
\(354\) | −1.08245e8 | −0.129687 | ||||||||
\(355\) | −1.22293e8 | −0.145079 | ||||||||
\(356\) | 2.09531e9 | 2.46135 | ||||||||
\(357\) | −8.29567e7 | −0.0964967 | ||||||||
\(358\) | 1.90819e8 | 0.219802 | ||||||||
\(359\) | 1.13966e9 | 1.30001 | 0.650003 | − | 0.759932i | \(-0.274768\pi\) | ||||
0.650003 | + | 0.759932i | \(0.274768\pi\) | |||||||
\(360\) | 8.82625e7 | 0.0997051 | ||||||||
\(361\) | −5.85490e8 | −0.655005 | ||||||||
\(362\) | −1.78360e9 | −1.97614 | ||||||||
\(363\) | 2.88990e8 | 0.317109 | ||||||||
\(364\) | 3.91324e8 | 0.425286 | ||||||||
\(365\) | −2.52528e8 | −0.271822 | ||||||||
\(366\) | −1.15843e9 | −1.23505 | ||||||||
\(367\) | −3.66527e8 | −0.387057 | −0.193529 | − | 0.981095i | \(-0.561993\pi\) | ||||
−0.193529 | + | 0.981095i | \(0.561993\pi\) | |||||||
\(368\) | 9.65252e8 | 1.00966 | ||||||||
\(369\) | 3.79757e8 | 0.393472 | ||||||||
\(370\) | 1.03840e8 | 0.106576 | ||||||||
\(371\) | 1.11568e8 | 0.113430 | ||||||||
\(372\) | 1.13771e9 | 1.14586 | ||||||||
\(373\) | 1.84626e9 | 1.84209 | 0.921047 | − | 0.389452i | \(-0.127336\pi\) | ||||
0.921047 | + | 0.389452i | \(0.127336\pi\) | |||||||
\(374\) | 2.74805e9 | 2.71628 | ||||||||
\(375\) | 2.05960e8 | 0.201685 | ||||||||
\(376\) | 1.92830e9 | 1.87076 | ||||||||
\(377\) | 3.82007e8 | 0.367178 | ||||||||
\(378\) | 4.60751e7 | 0.0438778 | ||||||||
\(379\) | −1.89436e8 | −0.178742 | −0.0893708 | − | 0.995998i | \(-0.528486\pi\) | ||||
−0.0893708 | + | 0.995998i | \(0.528486\pi\) | |||||||
\(380\) | 2.20412e8 | 0.206059 | ||||||||
\(381\) | 7.17064e8 | 0.664233 | ||||||||
\(382\) | 2.81415e9 | 2.58301 | ||||||||
\(383\) | 9.23938e8 | 0.840325 | 0.420162 | − | 0.907449i | \(-0.361973\pi\) | ||||
0.420162 | + | 0.907449i | \(0.361973\pi\) | |||||||
\(384\) | 1.12906e9 | 1.01756 | ||||||||
\(385\) | −3.26823e7 | −0.0291877 | ||||||||
\(386\) | −1.06650e9 | −0.943852 | ||||||||
\(387\) | −6.87708e8 | −0.603136 | ||||||||
\(388\) | −1.67044e9 | −1.45184 | ||||||||
\(389\) | 1.32165e8 | 0.113839 | 0.0569197 | − | 0.998379i | \(-0.481872\pi\) | ||||
0.0569197 | + | 0.998379i | \(0.481872\pi\) | |||||||
\(390\) | −3.37128e8 | −0.287785 | ||||||||
\(391\) | 1.62083e9 | 1.37125 | ||||||||
\(392\) | 1.97512e9 | 1.65612 | ||||||||
\(393\) | 9.67697e8 | 0.804203 | ||||||||
\(394\) | −3.03457e9 | −2.49954 | ||||||||
\(395\) | −2.18429e8 | −0.178328 | ||||||||
\(396\) | −1.01359e9 | −0.820216 | ||||||||
\(397\) | −3.45223e8 | −0.276907 | −0.138453 | − | 0.990369i | \(-0.544213\pi\) | ||||
−0.138453 | + | 0.990369i | \(0.544213\pi\) | |||||||
\(398\) | 3.96645e8 | 0.315363 | ||||||||
\(399\) | 5.68584e7 | 0.0448115 | ||||||||
\(400\) | −1.15451e9 | −0.901963 | ||||||||
\(401\) | 1.50851e9 | 1.16827 | 0.584135 | − | 0.811656i | \(-0.301434\pi\) | ||||
0.584135 | + | 0.811656i | \(0.301434\pi\) | |||||||
\(402\) | −5.97525e8 | −0.458738 | ||||||||
\(403\) | −2.14743e9 | −1.63437 | ||||||||
\(404\) | −4.50268e8 | −0.339732 | ||||||||
\(405\) | −2.63601e7 | −0.0197176 | ||||||||
\(406\) | −6.93418e7 | −0.0514226 | ||||||||
\(407\) | −5.89279e8 | −0.433252 | ||||||||
\(408\) | −1.68858e9 | −1.23087 | ||||||||
\(409\) | −8.44043e8 | −0.610004 | −0.305002 | − | 0.952352i | \(-0.598657\pi\) | ||||
−0.305002 | + | 0.952352i | \(0.598657\pi\) | |||||||
\(410\) | 5.04381e8 | 0.361422 | ||||||||
\(411\) | 1.06513e9 | 0.756754 | ||||||||
\(412\) | −1.71157e9 | −1.20574 | ||||||||
\(413\) | −2.46288e7 | −0.0172035 | ||||||||
\(414\) | −9.00226e8 | −0.623520 | ||||||||
\(415\) | −8.54605e6 | −0.00586945 | ||||||||
\(416\) | −1.88190e8 | −0.128165 | ||||||||
\(417\) | −2.99118e8 | −0.202007 | ||||||||
\(418\) | −1.88351e9 | −1.26139 | ||||||||
\(419\) | −1.19941e9 | −0.796563 | −0.398281 | − | 0.917263i | \(-0.630393\pi\) | ||||
−0.398281 | + | 0.917263i | \(0.630393\pi\) | |||||||
\(420\) | 4.06388e7 | 0.0267651 | ||||||||
\(421\) | 6.99371e8 | 0.456794 | 0.228397 | − | 0.973568i | \(-0.426652\pi\) | ||||
0.228397 | + | 0.973568i | \(0.426652\pi\) | |||||||
\(422\) | 2.61985e9 | 1.69701 | ||||||||
\(423\) | −5.75898e8 | −0.369960 | ||||||||
\(424\) | 2.27095e9 | 1.44686 | ||||||||
\(425\) | −1.93863e9 | −1.22499 | ||||||||
\(426\) | −1.29946e9 | −0.814386 | ||||||||
\(427\) | −2.63575e8 | −0.163835 | ||||||||
\(428\) | 6.30652e9 | 3.88809 | ||||||||
\(429\) | 1.91315e9 | 1.16990 | ||||||||
\(430\) | −9.13390e8 | −0.554009 | ||||||||
\(431\) | 1.57533e9 | 0.947768 | 0.473884 | − | 0.880587i | \(-0.342852\pi\) | ||||
0.473884 | + | 0.880587i | \(0.342852\pi\) | |||||||
\(432\) | 3.00328e8 | 0.179227 | ||||||||
\(433\) | 1.94780e9 | 1.15302 | 0.576511 | − | 0.817090i | \(-0.304414\pi\) | ||||
0.576511 | + | 0.817090i | \(0.304414\pi\) | |||||||
\(434\) | 3.89801e8 | 0.228891 | ||||||||
\(435\) | 3.96712e7 | 0.0231080 | ||||||||
\(436\) | −5.46471e9 | −3.15765 | ||||||||
\(437\) | −1.11091e9 | −0.636788 | ||||||||
\(438\) | −2.68331e9 | −1.52585 | ||||||||
\(439\) | −1.26243e9 | −0.712167 | −0.356084 | − | 0.934454i | \(-0.615888\pi\) | ||||
−0.356084 | + | 0.934454i | \(0.615888\pi\) | |||||||
\(440\) | −6.65248e8 | −0.372305 | ||||||||
\(441\) | −5.89879e8 | −0.327513 | ||||||||
\(442\) | 6.44971e9 | 3.55273 | ||||||||
\(443\) | −2.40199e9 | −1.31268 | −0.656339 | − | 0.754466i | \(-0.727896\pi\) | ||||
−0.656339 | + | 0.754466i | \(0.727896\pi\) | |||||||
\(444\) | 7.32737e8 | 0.397290 | ||||||||
\(445\) | −4.10715e8 | −0.220943 | ||||||||
\(446\) | −3.08822e9 | −1.64830 | ||||||||
\(447\) | 5.62060e8 | 0.297650 | ||||||||
\(448\) | 2.68368e8 | 0.141013 | ||||||||
\(449\) | 7.69955e8 | 0.401424 | 0.200712 | − | 0.979650i | \(-0.435675\pi\) | ||||
0.200712 | + | 0.979650i | \(0.435675\pi\) | |||||||
\(450\) | 1.07674e9 | 0.557014 | ||||||||
\(451\) | −2.86229e9 | −1.46925 | ||||||||
\(452\) | −4.65795e9 | −2.37252 | ||||||||
\(453\) | −7.16687e8 | −0.362231 | ||||||||
\(454\) | −4.84669e9 | −2.43081 | ||||||||
\(455\) | −7.67059e7 | −0.0381759 | ||||||||
\(456\) | 1.15735e9 | 0.571595 | ||||||||
\(457\) | 7.07638e8 | 0.346820 | 0.173410 | − | 0.984850i | \(-0.444521\pi\) | ||||
0.173410 | + | 0.984850i | \(0.444521\pi\) | |||||||
\(458\) | −9.83046e7 | −0.0478129 | ||||||||
\(459\) | 5.04304e8 | 0.243415 | ||||||||
\(460\) | −7.94010e8 | −0.380341 | ||||||||
\(461\) | 1.84947e8 | 0.0879212 | 0.0439606 | − | 0.999033i | \(-0.486002\pi\) | ||||
0.0439606 | + | 0.999033i | \(0.486002\pi\) | |||||||
\(462\) | −3.47275e8 | −0.163843 | ||||||||
\(463\) | 2.34876e9 | 1.09978 | 0.549890 | − | 0.835237i | \(-0.314670\pi\) | ||||
0.549890 | + | 0.835237i | \(0.314670\pi\) | |||||||
\(464\) | −4.51986e8 | −0.210045 | ||||||||
\(465\) | −2.23009e8 | −0.102858 | ||||||||
\(466\) | −5.40704e9 | −2.47519 | ||||||||
\(467\) | −2.14573e9 | −0.974912 | −0.487456 | − | 0.873147i | \(-0.662075\pi\) | ||||
−0.487456 | + | 0.873147i | \(0.662075\pi\) | |||||||
\(468\) | −2.37891e9 | −1.07280 | ||||||||
\(469\) | −1.35954e8 | −0.0608535 | ||||||||
\(470\) | −7.64888e8 | −0.339825 | ||||||||
\(471\) | 1.61468e9 | 0.712053 | ||||||||
\(472\) | −5.01318e8 | −0.219440 | ||||||||
\(473\) | 5.18336e9 | 2.25215 | ||||||||
\(474\) | −2.32098e9 | −1.00103 | ||||||||
\(475\) | 1.32873e9 | 0.568866 | ||||||||
\(476\) | −7.77475e8 | −0.330417 | ||||||||
\(477\) | −6.78233e8 | −0.286131 | ||||||||
\(478\) | −7.42659e9 | −3.11023 | ||||||||
\(479\) | −4.02137e8 | −0.167186 | −0.0835931 | − | 0.996500i | \(-0.526640\pi\) | ||||
−0.0835931 | + | 0.996500i | \(0.526640\pi\) | |||||||
\(480\) | −1.95434e7 | −0.00806597 | ||||||||
\(481\) | −1.38305e9 | −0.566668 | ||||||||
\(482\) | −1.31529e9 | −0.535005 | ||||||||
\(483\) | −2.04826e8 | −0.0827125 | ||||||||
\(484\) | 2.70843e9 | 1.08582 | ||||||||
\(485\) | 3.27433e8 | 0.130325 | ||||||||
\(486\) | −2.80096e8 | −0.110683 | ||||||||
\(487\) | 3.29797e9 | 1.29389 | 0.646943 | − | 0.762538i | \(-0.276047\pi\) | ||||
0.646943 | + | 0.762538i | \(0.276047\pi\) | |||||||
\(488\) | −5.36505e9 | −2.08980 | ||||||||
\(489\) | 2.57871e9 | 0.997291 | ||||||||
\(490\) | −7.83458e8 | −0.300836 | ||||||||
\(491\) | 1.59461e9 | 0.607953 | 0.303977 | − | 0.952680i | \(-0.401686\pi\) | ||||
0.303977 | + | 0.952680i | \(0.401686\pi\) | |||||||
\(492\) | 3.55911e9 | 1.34730 | ||||||||
\(493\) | −7.58963e8 | −0.285270 | ||||||||
\(494\) | −4.42062e9 | −1.64983 | ||||||||
\(495\) | 1.98680e8 | 0.0736268 | ||||||||
\(496\) | 2.54082e9 | 0.934948 | ||||||||
\(497\) | −2.95664e8 | −0.108032 | ||||||||
\(498\) | −9.08085e7 | −0.0329476 | ||||||||
\(499\) | −4.65147e9 | −1.67586 | −0.837931 | − | 0.545776i | \(-0.816235\pi\) | ||||
−0.837931 | + | 0.545776i | \(0.816235\pi\) | |||||||
\(500\) | 1.93027e9 | 0.690594 | ||||||||
\(501\) | −4.53216e8 | −0.161017 | ||||||||
\(502\) | 2.82777e9 | 0.997656 | ||||||||
\(503\) | −6.98423e8 | −0.244698 | −0.122349 | − | 0.992487i | \(-0.539043\pi\) | ||||
−0.122349 | + | 0.992487i | \(0.539043\pi\) | |||||||
\(504\) | 2.13389e8 | 0.0742445 | ||||||||
\(505\) | 8.82600e7 | 0.0304961 | ||||||||
\(506\) | 6.78515e9 | 2.32827 | ||||||||
\(507\) | 2.79599e9 | 0.952813 | ||||||||
\(508\) | 6.72037e9 | 2.27442 | ||||||||
\(509\) | −1.07682e9 | −0.361935 | −0.180967 | − | 0.983489i | \(-0.557923\pi\) | ||||
−0.180967 | + | 0.983489i | \(0.557923\pi\) | |||||||
\(510\) | 6.69799e8 | 0.223588 | ||||||||
\(511\) | −6.10527e8 | −0.202410 | ||||||||
\(512\) | 4.98996e9 | 1.64306 | ||||||||
\(513\) | −3.45649e8 | −0.113038 | ||||||||
\(514\) | −1.08011e9 | −0.350830 | ||||||||
\(515\) | 3.35497e8 | 0.108234 | ||||||||
\(516\) | −6.44524e9 | −2.06521 | ||||||||
\(517\) | 4.34063e9 | 1.38145 | ||||||||
\(518\) | 2.51050e8 | 0.0793609 | ||||||||
\(519\) | −1.91014e9 | −0.599763 | ||||||||
\(520\) | −1.56135e9 | −0.486954 | ||||||||
\(521\) | −3.06506e9 | −0.949527 | −0.474763 | − | 0.880114i | \(-0.657466\pi\) | ||||
−0.474763 | + | 0.880114i | \(0.657466\pi\) | |||||||
\(522\) | 4.21537e8 | 0.129715 | ||||||||
\(523\) | −5.83979e9 | −1.78501 | −0.892506 | − | 0.451036i | \(-0.851055\pi\) | ||||
−0.892506 | + | 0.451036i | \(0.851055\pi\) | |||||||
\(524\) | 9.06932e9 | 2.75369 | ||||||||
\(525\) | 2.44987e8 | 0.0738901 | ||||||||
\(526\) | −2.36762e9 | −0.709351 | ||||||||
\(527\) | 4.26647e9 | 1.26979 | ||||||||
\(528\) | −2.26362e9 | −0.669245 | ||||||||
\(529\) | 5.97121e8 | 0.175375 | ||||||||
\(530\) | −9.00806e8 | −0.262824 | ||||||||
\(531\) | 1.49721e8 | 0.0433963 | ||||||||
\(532\) | 5.32880e8 | 0.153440 | ||||||||
\(533\) | −6.71783e9 | −1.92169 | ||||||||
\(534\) | −4.36416e9 | −1.24024 | ||||||||
\(535\) | −1.23618e9 | −0.349015 | ||||||||
\(536\) | −2.76733e9 | −0.776219 | ||||||||
\(537\) | −2.63935e8 | −0.0735507 | ||||||||
\(538\) | 1.02477e10 | 2.83718 | ||||||||
\(539\) | 4.44601e9 | 1.22295 | ||||||||
\(540\) | −2.47048e8 | −0.0675155 | ||||||||
\(541\) | −4.19074e9 | −1.13789 | −0.568945 | − | 0.822375i | \(-0.692648\pi\) | ||||
−0.568945 | + | 0.822375i | \(0.692648\pi\) | |||||||
\(542\) | −2.02280e9 | −0.545701 | ||||||||
\(543\) | 2.46702e9 | 0.661261 | ||||||||
\(544\) | 3.73892e8 | 0.0995750 | ||||||||
\(545\) | 1.07117e9 | 0.283447 | ||||||||
\(546\) | −8.15060e8 | −0.214297 | ||||||||
\(547\) | 1.83917e9 | 0.480470 | 0.240235 | − | 0.970715i | \(-0.422775\pi\) | ||||
0.240235 | + | 0.970715i | \(0.422775\pi\) | |||||||
\(548\) | 9.98243e9 | 2.59122 | ||||||||
\(549\) | 1.60230e9 | 0.413277 | ||||||||
\(550\) | −8.11553e9 | −2.07992 | ||||||||
\(551\) | 5.20192e8 | 0.132475 | ||||||||
\(552\) | −4.16924e9 | −1.05504 | ||||||||
\(553\) | −5.28087e8 | −0.132791 | ||||||||
\(554\) | −3.80997e9 | −0.952002 | ||||||||
\(555\) | −1.43629e8 | −0.0356628 | ||||||||
\(556\) | −2.80335e9 | −0.691696 | ||||||||
\(557\) | −3.81190e9 | −0.934648 | −0.467324 | − | 0.884086i | \(-0.654782\pi\) | ||||
−0.467324 | + | 0.884086i | \(0.654782\pi\) | |||||||
\(558\) | −2.36965e9 | −0.577383 | ||||||||
\(559\) | 1.21654e10 | 2.94568 | ||||||||
\(560\) | 9.07576e7 | 0.0218386 | ||||||||
\(561\) | −3.80102e9 | −0.908929 | ||||||||
\(562\) | −4.99241e9 | −1.18640 | ||||||||
\(563\) | −6.18376e9 | −1.46041 | −0.730203 | − | 0.683231i | \(-0.760574\pi\) | ||||
−0.730203 | + | 0.683231i | \(0.760574\pi\) | |||||||
\(564\) | −5.39735e9 | −1.26679 | ||||||||
\(565\) | 9.13035e8 | 0.212970 | ||||||||
\(566\) | 2.78749e9 | 0.646184 | ||||||||
\(567\) | −6.37297e7 | −0.0146825 | ||||||||
\(568\) | −6.01823e9 | −1.37800 | ||||||||
\(569\) | −5.12814e9 | −1.16699 | −0.583495 | − | 0.812117i | \(-0.698315\pi\) | ||||
−0.583495 | + | 0.812117i | \(0.698315\pi\) | |||||||
\(570\) | −4.59079e8 | −0.103831 | ||||||||
\(571\) | 6.26225e8 | 0.140768 | 0.0703840 | − | 0.997520i | \(-0.477578\pi\) | ||||
0.0703840 | + | 0.997520i | \(0.477578\pi\) | |||||||
\(572\) | 1.79302e10 | 4.00589 | ||||||||
\(573\) | −3.89245e9 | −0.864335 | ||||||||
\(574\) | 1.21942e9 | 0.269130 | ||||||||
\(575\) | −4.78662e9 | −1.05001 | ||||||||
\(576\) | −1.63144e9 | −0.355708 | ||||||||
\(577\) | −2.62762e9 | −0.569440 | −0.284720 | − | 0.958611i | \(-0.591901\pi\) | ||||
−0.284720 | + | 0.958611i | \(0.591901\pi\) | |||||||
\(578\) | −4.80419e9 | −1.03484 | ||||||||
\(579\) | 1.47515e9 | 0.315835 | ||||||||
\(580\) | 3.71801e8 | 0.0791247 | ||||||||
\(581\) | −2.06614e7 | −0.00437063 | ||||||||
\(582\) | 3.47924e9 | 0.731566 | ||||||||
\(583\) | 5.11195e9 | 1.06843 | ||||||||
\(584\) | −1.24273e10 | −2.58185 | ||||||||
\(585\) | 4.66305e8 | 0.0962996 | ||||||||
\(586\) | 6.86269e9 | 1.40881 | ||||||||
\(587\) | −1.62680e9 | −0.331972 | −0.165986 | − | 0.986128i | \(-0.553081\pi\) | ||||
−0.165986 | + | 0.986128i | \(0.553081\pi\) | |||||||
\(588\) | −5.52839e9 | −1.12144 | ||||||||
\(589\) | −2.92423e9 | −0.589669 | ||||||||
\(590\) | 1.98855e8 | 0.0398615 | ||||||||
\(591\) | 4.19732e9 | 0.836404 | ||||||||
\(592\) | 1.63640e9 | 0.324164 | ||||||||
\(593\) | 2.05047e8 | 0.0403797 | 0.0201898 | − | 0.999796i | \(-0.493573\pi\) | ||||
0.0201898 | + | 0.999796i | \(0.493573\pi\) | |||||||
\(594\) | 2.11113e9 | 0.413297 | ||||||||
\(595\) | 1.52398e8 | 0.0296599 | ||||||||
\(596\) | 5.26766e9 | 1.01919 | ||||||||
\(597\) | −5.48627e8 | −0.105528 | ||||||||
\(598\) | 1.59248e10 | 3.04524 | ||||||||
\(599\) | −2.72889e9 | −0.518790 | −0.259395 | − | 0.965771i | \(-0.583523\pi\) | ||||
−0.259395 | + | 0.965771i | \(0.583523\pi\) | |||||||
\(600\) | 4.98671e9 | 0.942508 | ||||||||
\(601\) | 1.75593e9 | 0.329949 | 0.164974 | − | 0.986298i | \(-0.447246\pi\) | ||||
0.164974 | + | 0.986298i | \(0.447246\pi\) | |||||||
\(602\) | −2.20827e9 | −0.412538 | ||||||||
\(603\) | 8.26479e8 | 0.153504 | ||||||||
\(604\) | −6.71684e9 | −1.24033 | ||||||||
\(605\) | −5.30896e8 | −0.0974689 | ||||||||
\(606\) | 9.37832e8 | 0.171187 | ||||||||
\(607\) | 3.28692e9 | 0.596526 | 0.298263 | − | 0.954484i | \(-0.403593\pi\) | ||||
0.298263 | + | 0.954484i | \(0.403593\pi\) | |||||||
\(608\) | −2.56265e8 | −0.0462410 | ||||||||
\(609\) | 9.59114e7 | 0.0172072 | ||||||||
\(610\) | 2.12812e9 | 0.379614 | ||||||||
\(611\) | 1.01875e10 | 1.80686 | ||||||||
\(612\) | 4.72637e9 | 0.833484 | ||||||||
\(613\) | 5.79734e9 | 1.01652 | 0.508261 | − | 0.861203i | \(-0.330289\pi\) | ||||
0.508261 | + | 0.861203i | \(0.330289\pi\) | |||||||
\(614\) | 1.19255e10 | 2.07915 | ||||||||
\(615\) | −6.97643e8 | −0.120940 | ||||||||
\(616\) | −1.60834e9 | −0.277234 | ||||||||
\(617\) | 1.42127e9 | 0.243600 | 0.121800 | − | 0.992555i | \(-0.461133\pi\) | ||||
0.121800 | + | 0.992555i | \(0.461133\pi\) | |||||||
\(618\) | 3.56491e9 | 0.607560 | ||||||||
\(619\) | 3.85999e9 | 0.654138 | 0.327069 | − | 0.945001i | \(-0.393939\pi\) | ||||
0.327069 | + | 0.945001i | \(0.393939\pi\) | |||||||
\(620\) | −2.09006e9 | −0.352198 | ||||||||
\(621\) | 1.24517e9 | 0.208644 | ||||||||
\(622\) | 1.13281e10 | 1.88752 | ||||||||
\(623\) | −9.92968e8 | −0.164523 | ||||||||
\(624\) | −5.31276e9 | −0.875334 | ||||||||
\(625\) | 5.53294e9 | 0.906517 | ||||||||
\(626\) | −1.56236e10 | −2.54549 | ||||||||
\(627\) | 2.60521e9 | 0.422091 | ||||||||
\(628\) | 1.51329e10 | 2.43816 | ||||||||
\(629\) | 2.74781e9 | 0.440260 | ||||||||
\(630\) | −8.46436e7 | −0.0134866 | ||||||||
\(631\) | −5.65956e9 | −0.896768 | −0.448384 | − | 0.893841i | \(-0.648000\pi\) | ||||
−0.448384 | + | 0.893841i | \(0.648000\pi\) | |||||||
\(632\) | −1.07492e10 | −1.69382 | ||||||||
\(633\) | −3.62370e9 | −0.567857 | ||||||||
\(634\) | 1.18439e10 | 1.84579 | ||||||||
\(635\) | −1.31730e9 | −0.204163 | ||||||||
\(636\) | −6.35644e9 | −0.979747 | ||||||||
\(637\) | 1.04349e10 | 1.59955 | ||||||||
\(638\) | −3.17719e9 | −0.484363 | ||||||||
\(639\) | 1.79738e9 | 0.272512 | ||||||||
\(640\) | −2.07418e9 | −0.312763 | ||||||||
\(641\) | −2.57457e9 | −0.386101 | −0.193051 | − | 0.981189i | \(-0.561838\pi\) | ||||
−0.193051 | + | 0.981189i | \(0.561838\pi\) | |||||||
\(642\) | −1.31354e10 | −1.95916 | ||||||||
\(643\) | 3.46249e9 | 0.513629 | 0.256815 | − | 0.966461i | \(-0.417327\pi\) | ||||
0.256815 | + | 0.966461i | \(0.417327\pi\) | |||||||
\(644\) | −1.91965e9 | −0.283218 | ||||||||
\(645\) | 1.26337e9 | 0.185384 | ||||||||
\(646\) | 8.78281e9 | 1.28180 | ||||||||
\(647\) | 1.17598e9 | 0.170701 | 0.0853506 | − | 0.996351i | \(-0.472799\pi\) | ||||
0.0853506 | + | 0.996351i | \(0.472799\pi\) | |||||||
\(648\) | −1.29722e9 | −0.187284 | ||||||||
\(649\) | −1.12847e9 | −0.162045 | ||||||||
\(650\) | −1.90473e10 | −2.72042 | ||||||||
\(651\) | −5.39161e8 | −0.0765923 | ||||||||
\(652\) | 2.41679e10 | 3.41485 | ||||||||
\(653\) | 9.71067e9 | 1.36475 | 0.682375 | − | 0.731002i | \(-0.260947\pi\) | ||||
0.682375 | + | 0.731002i | \(0.260947\pi\) | |||||||
\(654\) | 1.13820e10 | 1.59110 | ||||||||
\(655\) | −1.77774e9 | −0.247185 | ||||||||
\(656\) | 7.94847e9 | 1.09931 | ||||||||
\(657\) | 3.71147e9 | 0.510584 | ||||||||
\(658\) | −1.84924e9 | −0.253048 | ||||||||
\(659\) | −9.69880e9 | −1.32014 | −0.660069 | − | 0.751205i | \(-0.729473\pi\) | ||||
−0.660069 | + | 0.751205i | \(0.729473\pi\) | |||||||
\(660\) | 1.86204e9 | 0.252107 | ||||||||
\(661\) | −1.15769e10 | −1.55914 | −0.779572 | − | 0.626313i | \(-0.784563\pi\) | ||||
−0.779572 | + | 0.626313i | \(0.784563\pi\) | |||||||
\(662\) | 9.66984e9 | 1.29544 | ||||||||
\(663\) | −8.92104e9 | −1.18883 | ||||||||
\(664\) | −4.20563e8 | −0.0557498 | ||||||||
\(665\) | −1.04453e8 | −0.0137736 | ||||||||
\(666\) | −1.52617e9 | −0.200190 | ||||||||
\(667\) | −1.87394e9 | −0.244520 | ||||||||
\(668\) | −4.24757e9 | −0.551344 | ||||||||
\(669\) | 4.27153e9 | 0.551559 | ||||||||
\(670\) | 1.09770e9 | 0.141001 | ||||||||
\(671\) | −1.20768e10 | −1.54320 | ||||||||
\(672\) | −4.72494e7 | −0.00600625 | ||||||||
\(673\) | −1.00199e10 | −1.26710 | −0.633552 | − | 0.773700i | \(-0.718404\pi\) | ||||
−0.633552 | + | 0.773700i | \(0.718404\pi\) | |||||||
\(674\) | 1.04558e10 | 1.31537 | ||||||||
\(675\) | −1.48931e9 | −0.186390 | ||||||||
\(676\) | 2.62042e10 | 3.26255 | ||||||||
\(677\) | −2.76445e8 | −0.0342411 | −0.0171206 | − | 0.999853i | \(-0.505450\pi\) | ||||
−0.0171206 | + | 0.999853i | \(0.505450\pi\) | |||||||
\(678\) | 9.70171e9 | 1.19549 | ||||||||
\(679\) | 7.91622e8 | 0.0970452 | ||||||||
\(680\) | 3.10205e9 | 0.378328 | ||||||||
\(681\) | 6.70380e9 | 0.813403 | ||||||||
\(682\) | 1.78604e10 | 2.15599 | ||||||||
\(683\) | 1.25710e9 | 0.150973 | 0.0754864 | − | 0.997147i | \(-0.475949\pi\) | ||||
0.0754864 | + | 0.997147i | \(0.475949\pi\) | |||||||
\(684\) | −3.23944e9 | −0.387056 | ||||||||
\(685\) | −1.95672e9 | −0.232601 | ||||||||
\(686\) | −3.82193e9 | −0.452011 | ||||||||
\(687\) | 1.35972e8 | 0.0159993 | ||||||||
\(688\) | −1.43940e10 | −1.68509 | ||||||||
\(689\) | 1.19978e10 | 1.39745 | ||||||||
\(690\) | 1.65379e9 | 0.191649 | ||||||||
\(691\) | 1.23439e10 | 1.42325 | 0.711623 | − | 0.702562i | \(-0.247960\pi\) | ||||
0.711623 | + | 0.702562i | \(0.247960\pi\) | |||||||
\(692\) | −1.79020e10 | −2.05366 | ||||||||
\(693\) | 4.80340e8 | 0.0548255 | ||||||||
\(694\) | −2.08114e10 | −2.36343 | ||||||||
\(695\) | 5.49502e8 | 0.0620902 | ||||||||
\(696\) | 1.95227e9 | 0.219487 | ||||||||
\(697\) | 1.33469e10 | 1.49302 | ||||||||
\(698\) | −1.83627e10 | −2.04382 | ||||||||
\(699\) | 7.47885e9 | 0.828256 | ||||||||
\(700\) | 2.29604e9 | 0.253009 | ||||||||
\(701\) | 4.36020e9 | 0.478072 | 0.239036 | − | 0.971011i | \(-0.423169\pi\) | ||||
0.239036 | + | 0.971011i | \(0.423169\pi\) | |||||||
\(702\) | 4.95485e9 | 0.540569 | ||||||||
\(703\) | −1.88334e9 | −0.204449 | ||||||||
\(704\) | 1.22964e10 | 1.32824 | ||||||||
\(705\) | 1.05797e9 | 0.113713 | ||||||||
\(706\) | 1.24335e10 | 1.32977 | ||||||||
\(707\) | 2.13383e8 | 0.0227086 | ||||||||
\(708\) | 1.40320e9 | 0.148594 | ||||||||
\(709\) | −6.54244e9 | −0.689411 | −0.344705 | − | 0.938711i | \(-0.612021\pi\) | ||||
−0.344705 | + | 0.938711i | \(0.612021\pi\) | |||||||
\(710\) | 2.38722e9 | 0.250315 | ||||||||
\(711\) | 3.21031e9 | 0.334968 | ||||||||
\(712\) | −2.02118e10 | −2.09858 | ||||||||
\(713\) | 1.05342e10 | 1.08840 | ||||||||
\(714\) | 1.61935e9 | 0.166493 | ||||||||
\(715\) | −3.51461e9 | −0.359589 | ||||||||
\(716\) | −2.47361e9 | −0.251847 | ||||||||
\(717\) | 1.02722e10 | 1.04075 | ||||||||
\(718\) | −2.22466e10 | −2.24300 | ||||||||
\(719\) | 1.24076e9 | 0.124491 | 0.0622453 | − | 0.998061i | \(-0.480174\pi\) | ||||
0.0622453 | + | 0.998061i | \(0.480174\pi\) | |||||||
\(720\) | −5.51727e8 | −0.0550884 | ||||||||
\(721\) | 8.11117e8 | 0.0805953 | ||||||||
\(722\) | 1.14290e10 | 1.13013 | ||||||||
\(723\) | 1.81927e9 | 0.179025 | ||||||||
\(724\) | 2.31210e10 | 2.26424 | ||||||||
\(725\) | 2.24137e9 | 0.218439 | ||||||||
\(726\) | −5.64119e9 | −0.547133 | ||||||||
\(727\) | 8.74540e8 | 0.0844130 | 0.0422065 | − | 0.999109i | \(-0.486561\pi\) | ||||
0.0422065 | + | 0.999109i | \(0.486561\pi\) | |||||||
\(728\) | −3.77481e9 | −0.362606 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 4.92945e9 | 0.468995 | ||||||||
\(731\) | −2.41700e10 | −2.28858 | ||||||||
\(732\) | 1.50169e10 | 1.41511 | ||||||||
\(733\) | −1.87673e10 | −1.76010 | −0.880052 | − | 0.474878i | \(-0.842492\pi\) | ||||
−0.880052 | + | 0.474878i | \(0.842492\pi\) | |||||||
\(734\) | 7.15476e9 | 0.667819 | ||||||||
\(735\) | 1.08365e9 | 0.100667 | ||||||||
\(736\) | 9.23169e8 | 0.0853510 | ||||||||
\(737\) | −6.22930e9 | −0.573196 | ||||||||
\(738\) | −7.41301e9 | −0.678887 | ||||||||
\(739\) | 1.50202e10 | 1.36905 | 0.684525 | − | 0.728989i | \(-0.260010\pi\) | ||||
0.684525 | + | 0.728989i | \(0.260010\pi\) | |||||||
\(740\) | −1.34610e9 | −0.122114 | ||||||||
\(741\) | 6.11447e9 | 0.552071 | ||||||||
\(742\) | −2.17784e9 | −0.195710 | ||||||||
\(743\) | 4.97295e9 | 0.444788 | 0.222394 | − | 0.974957i | \(-0.428613\pi\) | ||||
0.222394 | + | 0.974957i | \(0.428613\pi\) | |||||||
\(744\) | −1.09746e10 | −0.976975 | ||||||||
\(745\) | −1.03255e9 | −0.0914879 | ||||||||
\(746\) | −3.60397e10 | −3.17830 | ||||||||
\(747\) | 1.25603e8 | 0.0110250 | ||||||||
\(748\) | −3.56234e10 | −3.11228 | ||||||||
\(749\) | −2.98867e9 | −0.259891 | ||||||||
\(750\) | −4.02042e9 | −0.347982 | ||||||||
\(751\) | −1.94834e10 | −1.67851 | −0.839255 | − | 0.543737i | \(-0.817009\pi\) | ||||
−0.839255 | + | 0.543737i | \(0.817009\pi\) | |||||||
\(752\) | −1.20538e10 | −1.03362 | ||||||||
\(753\) | −3.91128e9 | −0.333839 | ||||||||
\(754\) | −7.45692e9 | −0.633519 | ||||||||
\(755\) | 1.31661e9 | 0.111338 | ||||||||
\(756\) | −5.97278e8 | −0.0502748 | ||||||||
\(757\) | 5.89170e9 | 0.493634 | 0.246817 | − | 0.969062i | \(-0.420615\pi\) | ||||
0.246817 | + | 0.969062i | \(0.420615\pi\) | |||||||
\(758\) | 3.69787e9 | 0.308396 | ||||||||
\(759\) | −9.38500e9 | −0.779091 | ||||||||
\(760\) | −2.12614e9 | −0.175689 | ||||||||
\(761\) | 1.46780e10 | 1.20731 | 0.603656 | − | 0.797245i | \(-0.293710\pi\) | ||||
0.603656 | + | 0.797245i | \(0.293710\pi\) | |||||||
\(762\) | −1.39974e10 | −1.14605 | ||||||||
\(763\) | 2.58973e9 | 0.211066 | ||||||||
\(764\) | −3.64803e10 | −2.95959 | ||||||||
\(765\) | −9.26445e8 | −0.0748178 | ||||||||
\(766\) | −1.80356e10 | −1.44988 | ||||||||
\(767\) | −2.64854e9 | −0.211945 | ||||||||
\(768\) | −1.43055e10 | −1.13956 | ||||||||
\(769\) | −2.45703e10 | −1.94835 | −0.974177 | − | 0.225784i | \(-0.927506\pi\) | ||||
−0.974177 | + | 0.225784i | \(0.927506\pi\) | |||||||
\(770\) | 6.37972e8 | 0.0503598 | ||||||||
\(771\) | 1.49397e9 | 0.117396 | ||||||||
\(772\) | 1.38252e10 | 1.08146 | ||||||||
\(773\) | −1.40761e10 | −1.09611 | −0.548057 | − | 0.836441i | \(-0.684632\pi\) | ||||
−0.548057 | + | 0.836441i | \(0.684632\pi\) | |||||||
\(774\) | 1.34243e10 | 1.04064 | ||||||||
\(775\) | −1.25997e10 | −0.972312 | ||||||||
\(776\) | 1.61135e10 | 1.23786 | ||||||||
\(777\) | −3.47245e8 | −0.0265560 | ||||||||
\(778\) | −2.57991e9 | −0.196416 | ||||||||
\(779\) | −9.14792e9 | −0.693332 | ||||||||
\(780\) | 4.37024e9 | 0.329742 | ||||||||
\(781\) | −1.35471e10 | −1.01758 | ||||||||
\(782\) | −3.16392e10 | −2.36593 | ||||||||
\(783\) | −5.83057e8 | −0.0434055 | ||||||||
\(784\) | −1.23464e10 | −0.915029 | ||||||||
\(785\) | −2.96629e9 | −0.218862 | ||||||||
\(786\) | −1.88898e10 | −1.38755 | ||||||||
\(787\) | 7.50211e9 | 0.548620 | 0.274310 | − | 0.961641i | \(-0.411551\pi\) | ||||
0.274310 | + | 0.961641i | \(0.411551\pi\) | |||||||
\(788\) | 3.93376e10 | 2.86395 | ||||||||
\(789\) | 3.27481e9 | 0.237365 | ||||||||
\(790\) | 4.26382e9 | 0.307683 | ||||||||
\(791\) | 2.20741e9 | 0.158586 | ||||||||
\(792\) | 9.77732e9 | 0.699329 | ||||||||
\(793\) | −2.83444e10 | −2.01842 | ||||||||
\(794\) | 6.73889e9 | 0.477768 | ||||||||
\(795\) | 1.24597e9 | 0.0879471 | ||||||||
\(796\) | −5.14177e9 | −0.361341 | ||||||||
\(797\) | 1.68153e10 | 1.17652 | 0.588260 | − | 0.808672i | \(-0.299813\pi\) | ||||
0.588260 | + | 0.808672i | \(0.299813\pi\) | |||||||
\(798\) | −1.10990e9 | −0.0773166 | ||||||||
\(799\) | −2.02404e10 | −1.40380 | ||||||||
\(800\) | −1.10418e9 | −0.0762472 | ||||||||
\(801\) | 6.03638e9 | 0.415014 | ||||||||
\(802\) | −2.94467e10 | −2.01570 | ||||||||
\(803\) | −2.79739e10 | −1.90655 | ||||||||
\(804\) | 7.74581e9 | 0.525618 | ||||||||
\(805\) | 3.76282e8 | 0.0254231 | ||||||||
\(806\) | 4.19187e10 | 2.81991 | ||||||||
\(807\) | −1.41742e10 | −0.949385 | ||||||||
\(808\) | 4.34340e9 | 0.289661 | ||||||||
\(809\) | −2.50538e10 | −1.66362 | −0.831810 | − | 0.555060i | \(-0.812695\pi\) | ||||
−0.831810 | + | 0.555060i | \(0.812695\pi\) | |||||||
\(810\) | 5.14559e8 | 0.0340202 | ||||||||
\(811\) | −7.70837e9 | −0.507446 | −0.253723 | − | 0.967277i | \(-0.581655\pi\) | ||||
−0.253723 | + | 0.967277i | \(0.581655\pi\) | |||||||
\(812\) | 8.98888e8 | 0.0589195 | ||||||||
\(813\) | 2.79787e9 | 0.182604 | ||||||||
\(814\) | 1.15029e10 | 0.747522 | ||||||||
\(815\) | −4.73730e9 | −0.306534 | ||||||||
\(816\) | 1.05553e10 | 0.680071 | ||||||||
\(817\) | 1.65661e10 | 1.06278 | ||||||||
\(818\) | 1.64760e10 | 1.05249 | ||||||||
\(819\) | 1.12737e9 | 0.0717086 | ||||||||
\(820\) | −6.53836e9 | −0.414114 | ||||||||
\(821\) | −1.50406e10 | −0.948558 | −0.474279 | − | 0.880375i | \(-0.657291\pi\) | ||||
−0.474279 | + | 0.880375i | \(0.657291\pi\) | |||||||
\(822\) | −2.07917e10 | −1.30568 | ||||||||
\(823\) | 3.00702e10 | 1.88034 | 0.940172 | − | 0.340700i | \(-0.110664\pi\) | ||||
0.940172 | + | 0.340700i | \(0.110664\pi\) | |||||||
\(824\) | 1.65103e10 | 1.02804 | ||||||||
\(825\) | 1.12252e10 | 0.695991 | ||||||||
\(826\) | 4.80763e8 | 0.0296825 | ||||||||
\(827\) | 1.24512e10 | 0.765494 | 0.382747 | − | 0.923853i | \(-0.374978\pi\) | ||||
0.382747 | + | 0.923853i | \(0.374978\pi\) | |||||||
\(828\) | 1.16698e10 | 0.714424 | ||||||||
\(829\) | 1.67317e10 | 1.02000 | 0.509999 | − | 0.860175i | \(-0.329646\pi\) | ||||
0.509999 | + | 0.860175i | \(0.329646\pi\) | |||||||
\(830\) | 1.66822e8 | 0.0101270 | ||||||||
\(831\) | 5.26984e9 | 0.318562 | ||||||||
\(832\) | 2.88599e10 | 1.73726 | ||||||||
\(833\) | −2.07318e10 | −1.24274 | ||||||||
\(834\) | 5.83889e9 | 0.348537 | ||||||||
\(835\) | 8.32593e8 | 0.0494914 | ||||||||
\(836\) | 2.44162e10 | 1.44529 | ||||||||
\(837\) | 3.27762e9 | 0.193206 | ||||||||
\(838\) | 2.34130e10 | 1.37437 | ||||||||
\(839\) | 1.49303e10 | 0.872773 | 0.436386 | − | 0.899759i | \(-0.356258\pi\) | ||||
0.436386 | + | 0.899759i | \(0.356258\pi\) | |||||||
\(840\) | −3.92012e8 | −0.0228203 | ||||||||
\(841\) | −1.63724e10 | −0.949131 | ||||||||
\(842\) | −1.36520e10 | −0.788140 | ||||||||
\(843\) | 6.90534e9 | 0.396998 | ||||||||
\(844\) | −3.39615e10 | −1.94441 | ||||||||
\(845\) | −5.13645e9 | −0.292863 | ||||||||
\(846\) | 1.12418e10 | 0.638319 | ||||||||
\(847\) | −1.28353e9 | −0.0725794 | ||||||||
\(848\) | −1.41957e10 | −0.799413 | ||||||||
\(849\) | −3.85557e9 | −0.216228 | ||||||||
\(850\) | 3.78428e10 | 2.11357 | ||||||||
\(851\) | 6.78455e9 | 0.377370 | ||||||||
\(852\) | 1.68451e10 | 0.933116 | ||||||||
\(853\) | −6.25227e9 | −0.344918 | −0.172459 | − | 0.985017i | \(-0.555171\pi\) | ||||
−0.172459 | + | 0.985017i | \(0.555171\pi\) | |||||||
\(854\) | 5.14508e9 | 0.282676 | ||||||||
\(855\) | 6.34984e8 | 0.0347441 | ||||||||
\(856\) | −6.08342e10 | −3.31505 | ||||||||
\(857\) | 2.79248e10 | 1.51550 | 0.757751 | − | 0.652543i | \(-0.226298\pi\) | ||||
0.757751 | + | 0.652543i | \(0.226298\pi\) | |||||||
\(858\) | −3.73455e10 | −2.01852 | ||||||||
\(859\) | 4.15604e9 | 0.223719 | 0.111860 | − | 0.993724i | \(-0.464319\pi\) | ||||
0.111860 | + | 0.993724i | \(0.464319\pi\) | |||||||
\(860\) | 1.18404e10 | 0.634778 | ||||||||
\(861\) | −1.68666e9 | −0.0900570 | ||||||||
\(862\) | −3.07511e10 | −1.63525 | ||||||||
\(863\) | 1.83670e10 | 0.972750 | 0.486375 | − | 0.873750i | \(-0.338319\pi\) | ||||
0.486375 | + | 0.873750i | \(0.338319\pi\) | |||||||
\(864\) | 2.87235e8 | 0.0151509 | ||||||||
\(865\) | 3.50908e9 | 0.184347 | ||||||||
\(866\) | −3.80219e10 | −1.98939 | ||||||||
\(867\) | 6.64501e9 | 0.346281 | ||||||||
\(868\) | −5.05305e9 | −0.262261 | ||||||||
\(869\) | −2.41966e10 | −1.25079 | ||||||||
\(870\) | −7.74397e8 | −0.0398700 | ||||||||
\(871\) | −1.46203e10 | −0.749707 | ||||||||
\(872\) | 5.27139e10 | 2.69226 | ||||||||
\(873\) | −4.81237e9 | −0.244799 | ||||||||
\(874\) | 2.16854e10 | 1.09870 | ||||||||
\(875\) | −9.14756e8 | −0.0461612 | ||||||||
\(876\) | 3.47841e10 | 1.74830 | ||||||||
\(877\) | −2.18727e10 | −1.09497 | −0.547487 | − | 0.836815i | \(-0.684415\pi\) | ||||
−0.547487 | + | 0.836815i | \(0.684415\pi\) | |||||||
\(878\) | 2.46432e10 | 1.22876 | ||||||||
\(879\) | −9.49225e9 | −0.471420 | ||||||||
\(880\) | 4.15845e9 | 0.205704 | ||||||||
\(881\) | 2.12719e10 | 1.04807 | 0.524035 | − | 0.851697i | \(-0.324426\pi\) | ||||
0.524035 | + | 0.851697i | \(0.324426\pi\) | |||||||
\(882\) | 1.15147e10 | 0.565082 | ||||||||
\(883\) | 2.46950e10 | 1.20711 | 0.603554 | − | 0.797322i | \(-0.293751\pi\) | ||||
0.603554 | + | 0.797322i | \(0.293751\pi\) | |||||||
\(884\) | −8.36086e10 | −4.07069 | ||||||||
\(885\) | −2.75050e8 | −0.0133386 | ||||||||
\(886\) | 4.68878e10 | 2.26486 | ||||||||
\(887\) | 2.50959e10 | 1.20745 | 0.603727 | − | 0.797191i | \(-0.293682\pi\) | ||||
0.603727 | + | 0.797191i | \(0.293682\pi\) | |||||||
\(888\) | −7.06816e9 | −0.338736 | ||||||||
\(889\) | −3.18479e9 | −0.152028 | ||||||||
\(890\) | 8.01731e9 | 0.381209 | ||||||||
\(891\) | −2.92005e9 | −0.138299 | ||||||||
\(892\) | 4.00330e10 | 1.88861 | ||||||||
\(893\) | 1.38727e10 | 0.651902 | ||||||||
\(894\) | −1.09716e10 | −0.513559 | ||||||||
\(895\) | 4.84869e8 | 0.0226071 | ||||||||
\(896\) | −5.01466e9 | −0.232897 | ||||||||
\(897\) | −2.20267e10 | −1.01901 | ||||||||
\(898\) | −1.50298e10 | −0.692606 | ||||||||
\(899\) | −4.93274e9 | −0.226427 | ||||||||
\(900\) | −1.39579e10 | −0.638221 | ||||||||
\(901\) | −2.38370e10 | −1.08571 | ||||||||
\(902\) | 5.58730e10 | 2.53501 | ||||||||
\(903\) | 3.05441e9 | 0.138045 | ||||||||
\(904\) | 4.49317e10 | 2.02285 | ||||||||
\(905\) | −4.53210e9 | −0.203250 | ||||||||
\(906\) | 1.39900e10 | 0.624985 | ||||||||
\(907\) | 1.03741e10 | 0.461662 | 0.230831 | − | 0.972994i | \(-0.425856\pi\) | ||||
0.230831 | + | 0.972994i | \(0.425856\pi\) | |||||||
\(908\) | 6.28284e10 | 2.78519 | ||||||||
\(909\) | −1.29718e9 | −0.0572831 | ||||||||
\(910\) | 1.49733e9 | 0.0658677 | ||||||||
\(911\) | −1.15863e10 | −0.507728 | −0.253864 | − | 0.967240i | \(-0.581702\pi\) | ||||
−0.253864 | + | 0.967240i | \(0.581702\pi\) | |||||||
\(912\) | −7.23458e9 | −0.315814 | ||||||||
\(913\) | −9.46693e8 | −0.0411682 | ||||||||
\(914\) | −1.38134e10 | −0.598395 | ||||||||
\(915\) | −2.94355e9 | −0.127028 | ||||||||
\(916\) | 1.27434e9 | 0.0547836 | ||||||||
\(917\) | −4.29796e9 | −0.184064 | ||||||||
\(918\) | −9.84421e9 | −0.419983 | ||||||||
\(919\) | −1.20996e10 | −0.514240 | −0.257120 | − | 0.966380i | \(-0.582774\pi\) | ||||
−0.257120 | + | 0.966380i | \(0.582774\pi\) | |||||||
\(920\) | 7.65921e9 | 0.324285 | ||||||||
\(921\) | −1.64949e10 | −0.695732 | ||||||||
\(922\) | −3.61024e9 | −0.151697 | ||||||||
\(923\) | −3.17953e10 | −1.33093 | ||||||||
\(924\) | 4.50178e9 | 0.187729 | ||||||||
\(925\) | −8.11482e9 | −0.337119 | ||||||||
\(926\) | −4.58488e10 | −1.89753 | ||||||||
\(927\) | −4.93088e9 | −0.203304 | ||||||||
\(928\) | −4.32280e8 | −0.0177561 | ||||||||
\(929\) | −2.16304e10 | −0.885134 | −0.442567 | − | 0.896735i | \(-0.645932\pi\) | ||||
−0.442567 | + | 0.896735i | \(0.645932\pi\) | |||||||
\(930\) | 4.35323e9 | 0.177469 | ||||||||
\(931\) | 1.42095e10 | 0.577107 | ||||||||
\(932\) | 7.00922e10 | 2.83605 | ||||||||
\(933\) | −1.56687e10 | −0.631608 | ||||||||
\(934\) | 4.18855e10 | 1.68209 | ||||||||
\(935\) | 6.98276e9 | 0.279374 | ||||||||
\(936\) | 2.29475e10 | 0.914682 | ||||||||
\(937\) | 1.59669e9 | 0.0634063 | 0.0317031 | − | 0.999497i | \(-0.489907\pi\) | ||||
0.0317031 | + | 0.999497i | \(0.489907\pi\) | |||||||
\(938\) | 2.65387e9 | 0.104995 | ||||||||
\(939\) | 2.16101e10 | 0.851781 | ||||||||
\(940\) | 9.91536e9 | 0.389369 | ||||||||
\(941\) | 3.39260e10 | 1.32730 | 0.663650 | − | 0.748043i | \(-0.269007\pi\) | ||||
0.663650 | + | 0.748043i | \(0.269007\pi\) | |||||||
\(942\) | −3.15191e10 | −1.22856 | ||||||||
\(943\) | 3.29544e10 | 1.27974 | ||||||||
\(944\) | 3.13373e9 | 0.121244 | ||||||||
\(945\) | 1.17076e8 | 0.00451292 | ||||||||
\(946\) | −1.01181e11 | −3.88580 | ||||||||
\(947\) | 2.74213e10 | 1.04921 | 0.524606 | − | 0.851345i | \(-0.324213\pi\) | ||||
0.524606 | + | 0.851345i | \(0.324213\pi\) | |||||||
\(948\) | 3.00872e10 | 1.14697 | ||||||||
\(949\) | −6.56553e10 | −2.49366 | ||||||||
\(950\) | −2.59374e10 | −0.981507 | ||||||||
\(951\) | −1.63821e10 | −0.617643 | ||||||||
\(952\) | 7.49971e9 | 0.281719 | ||||||||
\(953\) | −1.02794e10 | −0.384720 | −0.192360 | − | 0.981324i | \(-0.561614\pi\) | ||||
−0.192360 | + | 0.981324i | \(0.561614\pi\) | |||||||
\(954\) | 1.32394e10 | 0.493683 | ||||||||
\(955\) | 7.15074e9 | 0.265668 | ||||||||
\(956\) | 9.62720e10 | 3.56367 | ||||||||
\(957\) | 4.39459e9 | 0.162079 | ||||||||
\(958\) | 7.84988e9 | 0.288459 | ||||||||
\(959\) | −4.73068e9 | −0.173204 | ||||||||
\(960\) | 2.99709e9 | 0.109333 | ||||||||
\(961\) | 2.16493e8 | 0.00786887 | ||||||||
\(962\) | 2.69976e10 | 0.977715 | ||||||||
\(963\) | 1.81685e10 | 0.655581 | ||||||||
\(964\) | 1.70503e10 | 0.613004 | ||||||||
\(965\) | −2.70996e9 | −0.0970771 | ||||||||
\(966\) | 3.99829e9 | 0.142710 | ||||||||
\(967\) | −2.47735e10 | −0.881040 | −0.440520 | − | 0.897743i | \(-0.645206\pi\) | ||||
−0.440520 | + | 0.897743i | \(0.645206\pi\) | |||||||
\(968\) | −2.61262e10 | −0.925789 | ||||||||
\(969\) | −1.21481e10 | −0.428919 | ||||||||
\(970\) | −6.39163e9 | −0.224859 | ||||||||
\(971\) | 4.27396e10 | 1.49818 | 0.749088 | − | 0.662470i | \(-0.230492\pi\) | ||||
0.749088 | + | 0.662470i | \(0.230492\pi\) | |||||||
\(972\) | 3.63093e9 | 0.126819 | ||||||||
\(973\) | 1.32851e9 | 0.0462349 | ||||||||
\(974\) | −6.43778e10 | −2.23244 | ||||||||
\(975\) | 2.63456e10 | 0.910316 | ||||||||
\(976\) | 3.35368e10 | 1.15464 | ||||||||
\(977\) | 4.18609e8 | 0.0143608 | 0.00718039 | − | 0.999974i | \(-0.497714\pi\) | ||||
0.00718039 | + | 0.999974i | \(0.497714\pi\) | |||||||
\(978\) | −5.03375e10 | −1.72070 | ||||||||
\(979\) | −4.54971e10 | −1.54969 | ||||||||
\(980\) | 1.01561e10 | 0.344695 | ||||||||
\(981\) | −1.57433e10 | −0.532420 | ||||||||
\(982\) | −3.11275e10 | −1.04895 | ||||||||
\(983\) | −8.78167e9 | −0.294876 | −0.147438 | − | 0.989071i | \(-0.547103\pi\) | ||||
−0.147438 | + | 0.989071i | \(0.547103\pi\) | |||||||
\(984\) | −3.43320e10 | −1.14873 | ||||||||
\(985\) | −7.71081e9 | −0.257083 | ||||||||
\(986\) | 1.48153e10 | 0.492198 | ||||||||
\(987\) | 2.55781e9 | 0.0846756 | ||||||||
\(988\) | 5.73052e10 | 1.89036 | ||||||||
\(989\) | −5.96777e10 | −1.96167 | ||||||||
\(990\) | −3.87831e9 | −0.127034 | ||||||||
\(991\) | 3.19826e10 | 1.04389 | 0.521947 | − | 0.852978i | \(-0.325206\pi\) | ||||
0.521947 | + | 0.852978i | \(0.325206\pi\) | |||||||
\(992\) | 2.43004e9 | 0.0790356 | ||||||||
\(993\) | −1.33750e10 | −0.433483 | ||||||||
\(994\) | 5.77148e9 | 0.186395 | ||||||||
\(995\) | 1.00787e9 | 0.0324358 | ||||||||
\(996\) | 1.17716e9 | 0.0377511 | ||||||||
\(997\) | 1.39615e10 | 0.446170 | 0.223085 | − | 0.974799i | \(-0.428387\pi\) | ||||
0.223085 | + | 0.974799i | \(0.428387\pi\) | |||||||
\(998\) | 9.07985e10 | 2.89149 | ||||||||
\(999\) | 2.11094e9 | 0.0669881 |
(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 | 177.8.a.d.1.2 | ✓ | 18 | |
3.2 | odd | 2 | 531.8.a.e.1.17 | 18 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.d.1.2 | ✓ | 18 | 1.1 | even | 1 | trivial | |
531.8.a.e.1.17 | 18 | 3.2 | odd | 2 |