Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,11,Mod(58,177)]
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, 1]))
N = Newforms(chi, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.58");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(112.458233723\) |
Analytic rank: | \(0\) |
Dimension: | \(100\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 58.15 | ||
Character | \(\chi\) | \(=\) | 177.58 |
Dual form | 177.11.c.a.58.86 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 48.0671i | − | 1.50210i | −0.660248 | − | 0.751048i | \(-0.729549\pi\) | ||
0.660248 | − | 0.751048i | \(-0.270451\pi\) | |||||||
\(3\) | −140.296 | −0.577350 | ||||||||
\(4\) | −1286.44 | −1.25629 | ||||||||
\(5\) | −1212.73 | −0.388073 | −0.194036 | − | 0.980994i | \(-0.562158\pi\) | ||||
−0.194036 | + | 0.980994i | \(0.562158\pi\) | |||||||
\(6\) | 6743.62i | 0.867235i | ||||||||
\(7\) | −4240.63 | −0.252313 | −0.126157 | − | 0.992010i | \(-0.540264\pi\) | ||||
−0.126157 | + | 0.992010i | \(0.540264\pi\) | |||||||
\(8\) | 12614.8i | 0.384974i | ||||||||
\(9\) | 19683.0 | 0.333333 | ||||||||
\(10\) | 58292.2i | 0.582922i | ||||||||
\(11\) | − | 33949.7i | − | 0.210801i | −0.994430 | − | 0.105401i | \(-0.966388\pi\) | ||
0.994430 | − | 0.105401i | \(-0.0336125\pi\) | |||||||
\(12\) | 180483. | 0.725320 | ||||||||
\(13\) | − | 413622.i | − | 1.11400i | −0.830511 | − | 0.557002i | \(-0.811952\pi\) | ||
0.830511 | − | 0.557002i | \(-0.188048\pi\) | |||||||
\(14\) | 203835.i | 0.378999i | ||||||||
\(15\) | 170141. | 0.224054 | ||||||||
\(16\) | −710959. | −0.678023 | ||||||||
\(17\) | −2.03662e6 | −1.43439 | −0.717193 | − | 0.696874i | \(-0.754573\pi\) | ||||
−0.717193 | + | 0.696874i | \(0.754573\pi\) | |||||||
\(18\) | − | 946104.i | − | 0.500699i | ||||||
\(19\) | 946849. | 0.382396 | 0.191198 | − | 0.981552i | \(-0.438763\pi\) | ||||
0.191198 | + | 0.981552i | \(0.438763\pi\) | |||||||
\(20\) | 1.56010e6 | 0.487532 | ||||||||
\(21\) | 594944. | 0.145673 | ||||||||
\(22\) | −1.63186e6 | −0.316643 | ||||||||
\(23\) | 2.44743e6i | 0.380251i | 0.981760 | + | 0.190126i | \(0.0608895\pi\) | ||||
−0.981760 | + | 0.190126i | \(0.939110\pi\) | |||||||
\(24\) | − | 1.76981e6i | − | 0.222265i | ||||||
\(25\) | −8.29492e6 | −0.849400 | ||||||||
\(26\) | −1.98816e7 | −1.67334 | ||||||||
\(27\) | −2.76145e6 | −0.192450 | ||||||||
\(28\) | 5.45533e6 | 0.316979 | ||||||||
\(29\) | −1.24602e7 | −0.607485 | −0.303743 | − | 0.952754i | \(-0.598236\pi\) | ||||
−0.303743 | + | 0.952754i | \(0.598236\pi\) | |||||||
\(30\) | − | 8.17817e6i | − | 0.336550i | ||||||
\(31\) | 3.60531e7i | 1.25931i | 0.776874 | + | 0.629657i | \(0.216804\pi\) | ||||
−0.776874 | + | 0.629657i | \(0.783196\pi\) | |||||||
\(32\) | 4.70913e7i | 1.40343i | ||||||||
\(33\) | 4.76302e6i | 0.121706i | ||||||||
\(34\) | 9.78945e7i | 2.15459i | ||||||||
\(35\) | 5.14273e6 | 0.0979159 | ||||||||
\(36\) | −2.53210e7 | −0.418764 | ||||||||
\(37\) | − | 1.04163e8i | − | 1.50212i | −0.660236 | − | 0.751058i | \(-0.729544\pi\) | ||
0.660236 | − | 0.751058i | \(-0.270456\pi\) | |||||||
\(38\) | − | 4.55123e7i | − | 0.574395i | ||||||
\(39\) | 5.80296e7i | 0.643171i | ||||||||
\(40\) | − | 1.52984e7i | − | 0.149398i | ||||||
\(41\) | 2.63018e7 | 0.227021 | 0.113510 | − | 0.993537i | \(-0.463790\pi\) | ||||
0.113510 | + | 0.993537i | \(0.463790\pi\) | |||||||
\(42\) | − | 2.85972e7i | − | 0.218815i | ||||||
\(43\) | 1.45679e8i | 0.990957i | 0.868620 | + | 0.495478i | \(0.165007\pi\) | ||||
−0.868620 | + | 0.495478i | \(0.834993\pi\) | |||||||
\(44\) | 4.36744e7i | 0.264828i | ||||||||
\(45\) | −2.38701e7 | −0.129358 | ||||||||
\(46\) | 1.17641e8 | 0.571174 | ||||||||
\(47\) | 2.23833e8i | 0.975968i | 0.872853 | + | 0.487984i | \(0.162268\pi\) | ||||
−0.872853 | + | 0.487984i | \(0.837732\pi\) | |||||||
\(48\) | 9.97448e7 | 0.391457 | ||||||||
\(49\) | −2.64492e8 | −0.936338 | ||||||||
\(50\) | 3.98712e8i | 1.27588i | ||||||||
\(51\) | 2.85730e8 | 0.828143 | ||||||||
\(52\) | 5.32101e8i | 1.39951i | ||||||||
\(53\) | −3.03978e8 | −0.726880 | −0.363440 | − | 0.931618i | \(-0.618398\pi\) | ||||
−0.363440 | + | 0.931618i | \(0.618398\pi\) | |||||||
\(54\) | 1.32735e8i | 0.289078i | ||||||||
\(55\) | 4.11717e7i | 0.0818061i | ||||||||
\(56\) | − | 5.34949e7i | − | 0.0971342i | ||||||
\(57\) | −1.32839e8 | −0.220776 | ||||||||
\(58\) | 5.98926e8i | 0.912501i | ||||||||
\(59\) | −3.68406e8 | − | 6.12694e8i | −0.515308 | − | 0.857005i | ||||
\(60\) | −2.18876e8 | −0.281477 | ||||||||
\(61\) | − | 1.36135e9i | − | 1.61183i | −0.592029 | − | 0.805917i | \(-0.701673\pi\) | ||
0.592029 | − | 0.805917i | \(-0.298327\pi\) | |||||||
\(62\) | 1.73296e9 | 1.89161 | ||||||||
\(63\) | −8.34684e7 | −0.0841045 | ||||||||
\(64\) | 1.53552e9 | 1.43006 | ||||||||
\(65\) | 5.01610e8i | 0.432314i | ||||||||
\(66\) | 2.28944e8 | 0.182814 | ||||||||
\(67\) | 2.43057e9i | 1.80025i | 0.435628 | + | 0.900127i | \(0.356526\pi\) | ||||
−0.435628 | + | 0.900127i | \(0.643474\pi\) | |||||||
\(68\) | 2.62000e9 | 1.80201 | ||||||||
\(69\) | − | 3.43365e8i | − | 0.219538i | ||||||
\(70\) | − | 2.47196e8i | − | 0.147079i | ||||||
\(71\) | 2.64328e9 | 1.46504 | 0.732522 | − | 0.680743i | \(-0.238343\pi\) | ||||
0.732522 | + | 0.680743i | \(0.238343\pi\) | |||||||
\(72\) | 2.48298e8i | 0.128325i | ||||||||
\(73\) | − | 8.53440e8i | − | 0.411679i | −0.978586 | − | 0.205839i | \(-0.934008\pi\) | ||
0.978586 | − | 0.205839i | \(-0.0659925\pi\) | |||||||
\(74\) | −5.00680e9 | −2.25632 | ||||||||
\(75\) | 1.16374e9 | 0.490401 | ||||||||
\(76\) | −1.21807e9 | −0.480400 | ||||||||
\(77\) | 1.43968e8i | 0.0531880i | ||||||||
\(78\) | 2.78931e9 | 0.966104 | ||||||||
\(79\) | 4.49737e7 | 0.0146158 | 0.00730792 | − | 0.999973i | \(-0.497674\pi\) | ||||
0.00730792 | + | 0.999973i | \(0.497674\pi\) | |||||||
\(80\) | 8.62199e8 | 0.263122 | ||||||||
\(81\) | 3.87420e8 | 0.111111 | ||||||||
\(82\) | − | 1.26425e9i | − | 0.341007i | ||||||
\(83\) | 1.00500e9i | 0.255138i | 0.991830 | + | 0.127569i | \(0.0407175\pi\) | ||||
−0.991830 | + | 0.127569i | \(0.959283\pi\) | |||||||
\(84\) | −7.65362e8 | −0.183008 | ||||||||
\(85\) | 2.46987e9 | 0.556646 | ||||||||
\(86\) | 7.00236e9 | 1.48851 | ||||||||
\(87\) | 1.74812e9 | 0.350732 | ||||||||
\(88\) | 4.28271e8 | 0.0811531 | ||||||||
\(89\) | − | 3.83266e9i | − | 0.686358i | −0.939270 | − | 0.343179i | \(-0.888496\pi\) | ||
0.939270 | − | 0.343179i | \(-0.111504\pi\) | |||||||
\(90\) | 1.14737e9i | 0.194307i | ||||||||
\(91\) | 1.75402e9i | 0.281078i | ||||||||
\(92\) | − | 3.14848e9i | − | 0.477707i | ||||||
\(93\) | − | 5.05810e9i | − | 0.727065i | ||||||
\(94\) | 1.07590e10 | 1.46600 | ||||||||
\(95\) | −1.14827e9 | −0.148397 | ||||||||
\(96\) | − | 6.60673e9i | − | 0.810271i | ||||||
\(97\) | 2.35025e9i | 0.273687i | 0.990593 | + | 0.136844i | \(0.0436958\pi\) | ||||
−0.990593 | + | 0.136844i | \(0.956304\pi\) | |||||||
\(98\) | 1.27134e10i | 1.40647i | ||||||||
\(99\) | − | 6.68233e8i | − | 0.0702670i | ||||||
\(100\) | 1.06709e10 | 1.06709 | ||||||||
\(101\) | 1.81712e9i | 0.172893i | 0.996256 | + | 0.0864466i | \(0.0275512\pi\) | ||||
−0.996256 | + | 0.0864466i | \(0.972449\pi\) | |||||||
\(102\) | − | 1.37342e10i | − | 1.24395i | ||||||
\(103\) | − | 1.59866e9i | − | 0.137901i | −0.997620 | − | 0.0689507i | \(-0.978035\pi\) | ||
0.997620 | − | 0.0689507i | \(-0.0219651\pi\) | |||||||
\(104\) | 5.21778e9 | 0.428863 | ||||||||
\(105\) | −7.21505e8 | −0.0565318 | ||||||||
\(106\) | 1.46113e10i | 1.09184i | ||||||||
\(107\) | 2.24233e10 | 1.59875 | 0.799376 | − | 0.600832i | \(-0.205164\pi\) | ||||
0.799376 | + | 0.600832i | \(0.205164\pi\) | |||||||
\(108\) | 3.55244e9 | 0.241773 | ||||||||
\(109\) | 2.20040e10i | 1.43011i | 0.699069 | + | 0.715054i | \(0.253598\pi\) | ||||
−0.699069 | + | 0.715054i | \(0.746402\pi\) | |||||||
\(110\) | 1.97900e9 | 0.122881 | ||||||||
\(111\) | 1.46136e10i | 0.867248i | ||||||||
\(112\) | 3.01491e9 | 0.171074 | ||||||||
\(113\) | − | 3.36947e10i | − | 1.82881i | −0.404796 | − | 0.914407i | \(-0.632658\pi\) | ||
0.404796 | − | 0.914407i | \(-0.367342\pi\) | |||||||
\(114\) | 6.38519e9i | 0.331627i | ||||||||
\(115\) | − | 2.96806e9i | − | 0.147565i | ||||||
\(116\) | 1.60294e10 | 0.763178 | ||||||||
\(117\) | − | 8.14132e9i | − | 0.371335i | ||||||
\(118\) | −2.94504e10 | + | 1.77082e10i | −1.28730 | + | 0.774041i | ||||
\(119\) | 8.63657e9 | 0.361915 | ||||||||
\(120\) | 2.14630e9i | 0.0862550i | ||||||||
\(121\) | 2.47848e10 | 0.955563 | ||||||||
\(122\) | −6.54360e10 | −2.42113 | ||||||||
\(123\) | −3.69004e9 | −0.131071 | ||||||||
\(124\) | − | 4.63802e10i | − | 1.58206i | ||||||
\(125\) | 2.19025e10 | 0.717701 | ||||||||
\(126\) | 4.01208e9i | 0.126333i | ||||||||
\(127\) | −5.61401e10 | −1.69924 | −0.849619 | − | 0.527396i | \(-0.823168\pi\) | ||||
−0.849619 | + | 0.527396i | \(0.823168\pi\) | |||||||
\(128\) | − | 2.55864e10i | − | 0.744662i | ||||||
\(129\) | − | 2.04382e10i | − | 0.572129i | ||||||
\(130\) | 2.41109e10 | 0.649378 | ||||||||
\(131\) | 2.34480e10i | 0.607785i | 0.952706 | + | 0.303892i | \(0.0982863\pi\) | ||||
−0.952706 | + | 0.303892i | \(0.901714\pi\) | |||||||
\(132\) | − | 6.12735e9i | − | 0.152898i | ||||||
\(133\) | −4.01524e9 | −0.0964835 | ||||||||
\(134\) | 1.16830e11 | 2.70415 | ||||||||
\(135\) | 3.34888e9 | 0.0746846 | ||||||||
\(136\) | − | 2.56917e10i | − | 0.552202i | ||||||
\(137\) | −1.20211e10 | −0.249082 | −0.124541 | − | 0.992214i | \(-0.539746\pi\) | ||||
−0.124541 | + | 0.992214i | \(0.539746\pi\) | |||||||
\(138\) | −1.65045e10 | −0.329767 | ||||||||
\(139\) | −9.25758e10 | −1.78412 | −0.892059 | − | 0.451920i | \(-0.850739\pi\) | ||||
−0.892059 | + | 0.451920i | \(0.850739\pi\) | |||||||
\(140\) | −6.61582e9 | −0.123011 | ||||||||
\(141\) | − | 3.14030e10i | − | 0.563475i | ||||||
\(142\) | − | 1.27054e11i | − | 2.20064i | ||||||
\(143\) | −1.40424e10 | −0.234833 | ||||||||
\(144\) | −1.39938e10 | −0.226008 | ||||||||
\(145\) | 1.51108e10 | 0.235748 | ||||||||
\(146\) | −4.10224e10 | −0.618381 | ||||||||
\(147\) | 3.71072e10 | 0.540595 | ||||||||
\(148\) | 1.33999e11i | 1.88710i | ||||||||
\(149\) | − | 6.09103e10i | − | 0.829391i | −0.909960 | − | 0.414696i | \(-0.863888\pi\) | ||
0.909960 | − | 0.414696i | \(-0.136112\pi\) | |||||||
\(150\) | − | 5.59378e10i | − | 0.736629i | ||||||
\(151\) | − | 8.17973e10i | − | 1.04197i | −0.853567 | − | 0.520984i | \(-0.825565\pi\) | ||
0.853567 | − | 0.520984i | \(-0.174435\pi\) | |||||||
\(152\) | 1.19444e10i | 0.147213i | ||||||||
\(153\) | −4.00869e10 | −0.478129 | ||||||||
\(154\) | 6.92014e9 | 0.0798934 | ||||||||
\(155\) | − | 4.37225e10i | − | 0.488705i | ||||||
\(156\) | − | 7.46517e10i | − | 0.808010i | ||||||
\(157\) | − | 6.19935e10i | − | 0.649902i | −0.945731 | − | 0.324951i | \(-0.894652\pi\) | ||
0.945731 | − | 0.324951i | \(-0.105348\pi\) | |||||||
\(158\) | − | 2.16176e9i | − | 0.0219544i | ||||||
\(159\) | 4.26469e10 | 0.419664 | ||||||||
\(160\) | − | 5.71089e10i | − | 0.544633i | ||||||
\(161\) | − | 1.03786e10i | − | 0.0959425i | ||||||
\(162\) | − | 1.86222e10i | − | 0.166900i | ||||||
\(163\) | −1.91119e11 | −1.66099 | −0.830493 | − | 0.557029i | \(-0.811941\pi\) | ||||
−0.830493 | + | 0.557029i | \(0.811941\pi\) | |||||||
\(164\) | −3.38357e10 | −0.285204 | ||||||||
\(165\) | − | 5.77624e9i | − | 0.0472308i | ||||||
\(166\) | 4.83074e10 | 0.383242 | ||||||||
\(167\) | 2.21143e11 | 1.70251 | 0.851257 | − | 0.524749i | \(-0.175841\pi\) | ||||
0.851257 | + | 0.524749i | \(0.175841\pi\) | |||||||
\(168\) | 7.50513e9i | 0.0560805i | ||||||||
\(169\) | −3.32246e10 | −0.241005 | ||||||||
\(170\) | − | 1.18719e11i | − | 0.836135i | ||||||
\(171\) | 1.86368e10 | 0.127465 | ||||||||
\(172\) | − | 1.87408e11i | − | 1.24493i | ||||||
\(173\) | − | 2.47462e11i | − | 1.59690i | −0.602062 | − | 0.798450i | \(-0.705654\pi\) | ||
0.602062 | − | 0.798450i | \(-0.294346\pi\) | |||||||
\(174\) | − | 8.40270e10i | − | 0.526833i | ||||||
\(175\) | 3.51757e10 | 0.214315 | ||||||||
\(176\) | 2.41369e10i | 0.142928i | ||||||||
\(177\) | 5.16859e10 | + | 8.59586e10i | 0.297513 | + | 0.494792i | ||||
\(178\) | −1.84225e11 | −1.03098 | ||||||||
\(179\) | − | 1.41480e11i | − | 0.769893i | −0.922939 | − | 0.384947i | \(-0.874220\pi\) | ||
0.922939 | − | 0.384947i | \(-0.125780\pi\) | |||||||
\(180\) | 3.07075e10 | 0.162511 | ||||||||
\(181\) | 4.38883e10 | 0.225920 | 0.112960 | − | 0.993600i | \(-0.463967\pi\) | ||||
0.112960 | + | 0.993600i | \(0.463967\pi\) | |||||||
\(182\) | 8.43105e10 | 0.422206 | ||||||||
\(183\) | 1.90992e11i | 0.930592i | ||||||||
\(184\) | −3.08739e10 | −0.146387 | ||||||||
\(185\) | 1.26321e11i | 0.582930i | ||||||||
\(186\) | −2.43128e11 | −1.09212 | ||||||||
\(187\) | 6.91428e10i | 0.302370i | ||||||||
\(188\) | − | 2.87949e11i | − | 1.22610i | ||||||
\(189\) | 1.17103e10 | 0.0485577 | ||||||||
\(190\) | 5.51939e10i | 0.222907i | ||||||||
\(191\) | 4.46656e11i | 1.75714i | 0.477612 | + | 0.878571i | \(0.341502\pi\) | ||||
−0.477612 | + | 0.878571i | \(0.658498\pi\) | |||||||
\(192\) | −2.15427e11 | −0.825647 | ||||||||
\(193\) | 2.57216e10 | 0.0960529 | 0.0480265 | − | 0.998846i | \(-0.484707\pi\) | ||||
0.0480265 | + | 0.998846i | \(0.484707\pi\) | |||||||
\(194\) | 1.12969e11 | 0.411105 | ||||||||
\(195\) | − | 7.03740e10i | − | 0.249597i | ||||||
\(196\) | 3.40254e11 | 1.17631 | ||||||||
\(197\) | 1.77712e11 | 0.598943 | 0.299471 | − | 0.954105i | \(-0.403190\pi\) | ||||
0.299471 | + | 0.954105i | \(0.403190\pi\) | |||||||
\(198\) | −3.21200e10 | −0.105548 | ||||||||
\(199\) | 5.37426e11 | 1.72208 | 0.861039 | − | 0.508539i | \(-0.169814\pi\) | ||||
0.861039 | + | 0.508539i | \(0.169814\pi\) | |||||||
\(200\) | − | 1.04639e11i | − | 0.326997i | ||||||
\(201\) | − | 3.40999e11i | − | 1.03938i | ||||||
\(202\) | 8.73439e10 | 0.259702 | ||||||||
\(203\) | 5.28392e10 | 0.153277 | ||||||||
\(204\) | −3.67576e11 | −1.04039 | ||||||||
\(205\) | −3.18969e10 | −0.0881006 | ||||||||
\(206\) | −7.68427e10 | −0.207141 | ||||||||
\(207\) | 4.81727e10i | 0.126750i | ||||||||
\(208\) | 2.94068e11i | 0.755321i | ||||||||
\(209\) | − | 3.21453e10i | − | 0.0806094i | ||||||
\(210\) | 3.46806e10i | 0.0849161i | ||||||||
\(211\) | − | 5.80157e11i | − | 1.38718i | −0.720370 | − | 0.693590i | \(-0.756028\pi\) | ||
0.720370 | − | 0.693590i | \(-0.243972\pi\) | |||||||
\(212\) | 3.91050e11 | 0.913173 | ||||||||
\(213\) | −3.70841e11 | −0.845844 | ||||||||
\(214\) | − | 1.07782e12i | − | 2.40148i | ||||||
\(215\) | − | 1.76669e11i | − | 0.384563i | ||||||
\(216\) | − | 3.48352e10i | − | 0.0740884i | ||||||
\(217\) | − | 1.52888e11i | − | 0.317742i | ||||||
\(218\) | 1.05767e12 | 2.14816 | ||||||||
\(219\) | 1.19734e11i | 0.237683i | ||||||||
\(220\) | − | 5.29651e10i | − | 0.102772i | ||||||
\(221\) | 8.42392e11i | 1.59791i | ||||||||
\(222\) | 7.02434e11 | 1.30269 | ||||||||
\(223\) | 6.90723e11 | 1.25250 | 0.626252 | − | 0.779620i | \(-0.284588\pi\) | ||||
0.626252 | + | 0.779620i | \(0.284588\pi\) | |||||||
\(224\) | − | 1.99697e11i | − | 0.354104i | ||||||
\(225\) | −1.63269e11 | −0.283133 | ||||||||
\(226\) | −1.61961e12 | −2.74705 | ||||||||
\(227\) | 9.05355e11i | 1.50207i | 0.660263 | + | 0.751034i | \(0.270445\pi\) | ||||
−0.660263 | + | 0.751034i | \(0.729555\pi\) | |||||||
\(228\) | 1.70890e11 | 0.277359 | ||||||||
\(229\) | − | 2.08438e10i | − | 0.0330978i | −0.999863 | − | 0.0165489i | \(-0.994732\pi\) | ||
0.999863 | − | 0.0165489i | \(-0.00526792\pi\) | |||||||
\(230\) | −1.42666e11 | −0.221657 | ||||||||
\(231\) | − | 2.01982e10i | − | 0.0307081i | ||||||
\(232\) | − | 1.57184e11i | − | 0.233866i | ||||||
\(233\) | 1.06421e12i | 1.54970i | 0.632144 | + | 0.774851i | \(0.282175\pi\) | ||||
−0.632144 | + | 0.774851i | \(0.717825\pi\) | |||||||
\(234\) | −3.91329e11 | −0.557780 | ||||||||
\(235\) | − | 2.71449e11i | − | 0.378746i | ||||||
\(236\) | 4.73933e11 | + | 7.88195e11i | 0.647377 | + | 1.07665i | ||||
\(237\) | −6.30964e9 | −0.00843846 | ||||||||
\(238\) | − | 4.15135e11i | − | 0.543631i | ||||||
\(239\) | 5.41434e11 | 0.694314 | 0.347157 | − | 0.937807i | \(-0.387147\pi\) | ||||
0.347157 | + | 0.937807i | \(0.387147\pi\) | |||||||
\(240\) | −1.20963e11 | −0.151914 | ||||||||
\(241\) | 6.09091e11 | 0.749199 | 0.374599 | − | 0.927187i | \(-0.377780\pi\) | ||||
0.374599 | + | 0.927187i | \(0.377780\pi\) | |||||||
\(242\) | − | 1.19133e12i | − | 1.43535i | ||||||
\(243\) | −5.43536e10 | −0.0641500 | ||||||||
\(244\) | 1.75130e12i | 2.02493i | ||||||||
\(245\) | 3.20757e11 | 0.363367 | ||||||||
\(246\) | 1.77369e11i | 0.196881i | ||||||||
\(247\) | − | 3.91638e11i | − | 0.425990i | ||||||
\(248\) | −4.54804e11 | −0.484803 | ||||||||
\(249\) | − | 1.40998e11i | − | 0.147304i | ||||||
\(250\) | − | 1.05279e12i | − | 1.07806i | ||||||
\(251\) | 1.61926e12 | 1.62536 | 0.812678 | − | 0.582713i | \(-0.198009\pi\) | ||||
0.812678 | + | 0.582713i | \(0.198009\pi\) | |||||||
\(252\) | 1.07377e11 | 0.105660 | ||||||||
\(253\) | 8.30895e10 | 0.0801574 | ||||||||
\(254\) | 2.69849e12i | 2.55242i | ||||||||
\(255\) | −3.46513e11 | −0.321380 | ||||||||
\(256\) | 3.42509e11 | 0.311510 | ||||||||
\(257\) | 1.41412e12 | 1.26130 | 0.630652 | − | 0.776066i | \(-0.282787\pi\) | ||||
0.630652 | + | 0.776066i | \(0.282787\pi\) | |||||||
\(258\) | −9.82404e11 | −0.859393 | ||||||||
\(259\) | 4.41716e11i | 0.379004i | ||||||||
\(260\) | − | 6.45293e11i | − | 0.543113i | ||||||
\(261\) | −2.45254e11 | −0.202495 | ||||||||
\(262\) | 1.12708e12 | 0.912951 | ||||||||
\(263\) | 1.67899e11 | 0.133434 | 0.0667172 | − | 0.997772i | \(-0.478747\pi\) | ||||
0.0667172 | + | 0.997772i | \(0.478747\pi\) | |||||||
\(264\) | −6.00847e10 | −0.0468537 | ||||||||
\(265\) | 3.68642e11 | 0.282082 | ||||||||
\(266\) | 1.93001e11i | 0.144928i | ||||||||
\(267\) | 5.37708e11i | 0.396269i | ||||||||
\(268\) | − | 3.12679e12i | − | 2.26164i | ||||||
\(269\) | 5.89368e10i | 0.0418432i | 0.999781 | + | 0.0209216i | \(0.00666004\pi\) | ||||
−0.999781 | + | 0.0209216i | \(0.993340\pi\) | |||||||
\(270\) | − | 1.60971e11i | − | 0.112183i | ||||||
\(271\) | −1.49409e12 | −1.02219 | −0.511093 | − | 0.859525i | \(-0.670759\pi\) | ||||
−0.511093 | + | 0.859525i | \(0.670759\pi\) | |||||||
\(272\) | 1.44796e12 | 0.972547 | ||||||||
\(273\) | − | 2.46082e11i | − | 0.162281i | ||||||
\(274\) | 5.77819e11i | 0.374144i | ||||||||
\(275\) | 2.81610e11i | 0.179054i | ||||||||
\(276\) | 4.41719e11i | 0.275804i | ||||||||
\(277\) | −1.48765e12 | −0.912224 | −0.456112 | − | 0.889922i | \(-0.650758\pi\) | ||||
−0.456112 | + | 0.889922i | \(0.650758\pi\) | |||||||
\(278\) | 4.44985e12i | 2.67992i | ||||||||
\(279\) | 7.09632e11i | 0.419771i | ||||||||
\(280\) | 6.48747e10i | 0.0376951i | ||||||||
\(281\) | 2.32124e12 | 1.32492 | 0.662458 | − | 0.749099i | \(-0.269513\pi\) | ||||
0.662458 | + | 0.749099i | \(0.269513\pi\) | |||||||
\(282\) | −1.50945e12 | −0.846394 | ||||||||
\(283\) | − | 1.72438e12i | − | 0.949948i | −0.880000 | − | 0.474974i | \(-0.842458\pi\) | ||
0.880000 | − | 0.474974i | \(-0.157542\pi\) | |||||||
\(284\) | −3.40042e12 | −1.84052 | ||||||||
\(285\) | 1.61098e11 | 0.0856772 | ||||||||
\(286\) | 6.74975e11i | 0.352742i | ||||||||
\(287\) | −1.11536e11 | −0.0572804 | ||||||||
\(288\) | 9.26898e11i | 0.467810i | ||||||||
\(289\) | 2.13184e12 | 1.05746 | ||||||||
\(290\) | − | 7.26334e11i | − | 0.354117i | ||||||
\(291\) | − | 3.29730e11i | − | 0.158013i | ||||||
\(292\) | 1.09790e12i | 0.517189i | ||||||||
\(293\) | −2.39530e12 | −1.10923 | −0.554615 | − | 0.832107i | \(-0.687134\pi\) | ||||
−0.554615 | + | 0.832107i | \(0.687134\pi\) | |||||||
\(294\) | − | 1.78364e12i | − | 0.812025i | ||||||
\(295\) | 4.46776e11 | + | 7.43030e11i | 0.199977 | + | 0.332580i | ||||
\(296\) | 1.31400e12 | 0.578277 | ||||||||
\(297\) | 9.37504e10i | 0.0405687i | ||||||||
\(298\) | −2.92778e12 | −1.24582 | ||||||||
\(299\) | 1.01231e12 | 0.423602 | ||||||||
\(300\) | −1.49709e12 | −0.616087 | ||||||||
\(301\) | − | 6.17771e11i | − | 0.250032i | ||||||
\(302\) | −3.93176e12 | −1.56514 | ||||||||
\(303\) | − | 2.54936e11i | − | 0.0998199i | ||||||
\(304\) | −6.73171e11 | −0.259273 | ||||||||
\(305\) | 1.65094e12i | 0.625508i | ||||||||
\(306\) | 1.92686e12i | 0.718195i | ||||||||
\(307\) | −2.92215e12 | −1.07154 | −0.535772 | − | 0.844363i | \(-0.679979\pi\) | ||||
−0.535772 | + | 0.844363i | \(0.679979\pi\) | |||||||
\(308\) | − | 1.85207e11i | − | 0.0668196i | ||||||
\(309\) | 2.24285e11i | 0.0796174i | ||||||||
\(310\) | −2.10161e12 | −0.734081 | ||||||||
\(311\) | 3.22319e12 | 1.10786 | 0.553928 | − | 0.832565i | \(-0.313128\pi\) | ||||
0.553928 | + | 0.832565i | \(0.313128\pi\) | |||||||
\(312\) | −7.32034e11 | −0.247604 | ||||||||
\(313\) | 1.49286e12i | 0.496931i | 0.968641 | + | 0.248465i | \(0.0799262\pi\) | ||||
−0.968641 | + | 0.248465i | \(0.920074\pi\) | |||||||
\(314\) | −2.97985e12 | −0.976215 | ||||||||
\(315\) | 1.01224e11 | 0.0326386 | ||||||||
\(316\) | −5.78561e10 | −0.0183617 | ||||||||
\(317\) | −4.43107e12 | −1.38424 | −0.692122 | − | 0.721781i | \(-0.743324\pi\) | ||||
−0.692122 | + | 0.721781i | \(0.743324\pi\) | |||||||
\(318\) | − | 2.04991e12i | − | 0.630376i | ||||||
\(319\) | 4.23021e11i | 0.128059i | ||||||||
\(320\) | −1.86216e12 | −0.554968 | ||||||||
\(321\) | −3.14590e12 | −0.923039 | ||||||||
\(322\) | −4.98871e11 | −0.144115 | ||||||||
\(323\) | −1.92838e12 | −0.548503 | ||||||||
\(324\) | −4.98394e11 | −0.139588 | ||||||||
\(325\) | 3.43096e12i | 0.946235i | ||||||||
\(326\) | 9.18654e12i | 2.49496i | ||||||||
\(327\) | − | 3.08707e12i | − | 0.825673i | ||||||
\(328\) | 3.31793e11i | 0.0873972i | ||||||||
\(329\) | − | 9.49195e11i | − | 0.246250i | ||||||
\(330\) | −2.77647e11 | −0.0709452 | ||||||||
\(331\) | 4.35658e12 | 1.09649 | 0.548246 | − | 0.836317i | \(-0.315296\pi\) | ||||
0.548246 | + | 0.836317i | \(0.315296\pi\) | |||||||
\(332\) | − | 1.29288e12i | − | 0.320528i | ||||||
\(333\) | − | 2.05024e12i | − | 0.500706i | ||||||
\(334\) | − | 1.06297e13i | − | 2.55734i | ||||||
\(335\) | − | 2.94761e12i | − | 0.698629i | ||||||
\(336\) | −4.22981e11 | −0.0987698 | ||||||||
\(337\) | 4.08576e12i | 0.939989i | 0.882669 | + | 0.469995i | \(0.155744\pi\) | ||||
−0.882669 | + | 0.469995i | \(0.844256\pi\) | |||||||
\(338\) | 1.59701e12i | 0.362013i | ||||||||
\(339\) | 4.72724e12i | 1.05587i | ||||||||
\(340\) | −3.17734e12 | −0.699310 | ||||||||
\(341\) | 1.22399e12 | 0.265465 | ||||||||
\(342\) | − | 8.95818e11i | − | 0.191465i | ||||||
\(343\) | 2.31949e12 | 0.488564 | ||||||||
\(344\) | −1.83772e12 | −0.381493 | ||||||||
\(345\) | 4.16407e11i | 0.0851967i | ||||||||
\(346\) | −1.18948e13 | −2.39870 | ||||||||
\(347\) | − | 4.87568e12i | − | 0.969144i | −0.874751 | − | 0.484572i | \(-0.838975\pi\) | ||
0.874751 | − | 0.484572i | \(-0.161025\pi\) | |||||||
\(348\) | −2.24886e12 | −0.440621 | ||||||||
\(349\) | 4.70800e12i | 0.909305i | 0.890669 | + | 0.454652i | \(0.150237\pi\) | ||||
−0.890669 | + | 0.454652i | \(0.849763\pi\) | |||||||
\(350\) | − | 1.69079e12i | − | 0.321922i | ||||||
\(351\) | 1.14220e12i | 0.214390i | ||||||||
\(352\) | 1.59874e12 | 0.295845 | ||||||||
\(353\) | 4.05744e12i | 0.740250i | 0.928982 | + | 0.370125i | \(0.120685\pi\) | ||||
−0.928982 | + | 0.370125i | \(0.879315\pi\) | |||||||
\(354\) | 4.13178e12 | − | 2.48439e12i | 0.743225 | − | 0.446893i | ||||
\(355\) | −3.20557e12 | −0.568543 | ||||||||
\(356\) | 4.93050e12i | 0.862266i | ||||||||
\(357\) | −1.21168e12 | −0.208952 | ||||||||
\(358\) | −6.80054e12 | −1.15645 | ||||||||
\(359\) | 8.17182e12 | 1.37040 | 0.685199 | − | 0.728356i | \(-0.259715\pi\) | ||||
0.685199 | + | 0.728356i | \(0.259715\pi\) | |||||||
\(360\) | − | 3.01118e11i | − | 0.0497993i | ||||||
\(361\) | −5.23454e12 | −0.853774 | ||||||||
\(362\) | − | 2.10958e12i | − | 0.339354i | ||||||
\(363\) | −3.47722e12 | −0.551694 | ||||||||
\(364\) | − | 2.25644e12i | − | 0.353116i | ||||||
\(365\) | 1.03499e12i | 0.159761i | ||||||||
\(366\) | 9.18042e12 | 1.39784 | ||||||||
\(367\) | 6.99731e12i | 1.05100i | 0.850795 | + | 0.525498i | \(0.176121\pi\) | ||||
−0.850795 | + | 0.525498i | \(0.823879\pi\) | |||||||
\(368\) | − | 1.74002e12i | − | 0.257819i | ||||||
\(369\) | 5.17698e11 | 0.0756736 | ||||||||
\(370\) | 6.07188e12 | 0.875617 | ||||||||
\(371\) | 1.28906e12 | 0.183402 | ||||||||
\(372\) | 6.50696e12i | 0.913405i | ||||||||
\(373\) | 1.07780e13 | 1.49278 | 0.746388 | − | 0.665511i | \(-0.231786\pi\) | ||||
0.746388 | + | 0.665511i | \(0.231786\pi\) | |||||||
\(374\) | 3.32349e12 | 0.454189 | ||||||||
\(375\) | −3.07284e12 | −0.414365 | ||||||||
\(376\) | −2.82362e12 | −0.375723 | ||||||||
\(377\) | 5.15382e12i | 0.676741i | ||||||||
\(378\) | − | 5.62879e11i | − | 0.0729384i | ||||||
\(379\) | −1.18081e13 | −1.51003 | −0.755015 | − | 0.655708i | \(-0.772370\pi\) | ||||
−0.755015 | + | 0.655708i | \(0.772370\pi\) | |||||||
\(380\) | 1.47718e12 | 0.186430 | ||||||||
\(381\) | 7.87624e12 | 0.981056 | ||||||||
\(382\) | 2.14695e13 | 2.63939 | ||||||||
\(383\) | −4.15695e12 | −0.504407 | −0.252204 | − | 0.967674i | \(-0.581155\pi\) | ||||
−0.252204 | + | 0.967674i | \(0.581155\pi\) | |||||||
\(384\) | 3.58967e12i | 0.429931i | ||||||||
\(385\) | − | 1.74594e11i | − | 0.0206408i | ||||||
\(386\) | − | 1.23636e12i | − | 0.144281i | ||||||
\(387\) | 2.86740e12i | 0.330319i | ||||||||
\(388\) | − | 3.02346e12i | − | 0.343831i | ||||||
\(389\) | 9.22414e11 | 0.103557 | 0.0517783 | − | 0.998659i | \(-0.483511\pi\) | ||||
0.0517783 | + | 0.998659i | \(0.483511\pi\) | |||||||
\(390\) | −3.38267e12 | −0.374918 | ||||||||
\(391\) | − | 4.98449e12i | − | 0.545427i | ||||||
\(392\) | − | 3.33653e12i | − | 0.360466i | ||||||
\(393\) | − | 3.28967e12i | − | 0.350905i | ||||||
\(394\) | − | 8.54209e12i | − | 0.899669i | ||||||
\(395\) | −5.45409e10 | −0.00567200 | ||||||||
\(396\) | 8.59643e11i | 0.0882759i | ||||||||
\(397\) | 6.05681e11i | 0.0614174i | 0.999528 | + | 0.0307087i | \(0.00977641\pi\) | ||||
−0.999528 | + | 0.0307087i | \(0.990224\pi\) | |||||||
\(398\) | − | 2.58325e13i | − | 2.58673i | ||||||
\(399\) | 5.63322e11 | 0.0557048 | ||||||||
\(400\) | 5.89735e12 | 0.575913 | ||||||||
\(401\) | 9.92611e11i | 0.0957321i | 0.998854 | + | 0.0478660i | \(0.0152421\pi\) | ||||
−0.998854 | + | 0.0478660i | \(0.984758\pi\) | |||||||
\(402\) | −1.63908e13 | −1.56124 | ||||||||
\(403\) | 1.49123e13 | 1.40288 | ||||||||
\(404\) | − | 2.33763e12i | − | 0.217204i | ||||||
\(405\) | −4.69835e11 | −0.0431192 | ||||||||
\(406\) | − | 2.53983e12i | − | 0.230236i | ||||||
\(407\) | −3.53630e12 | −0.316648 | ||||||||
\(408\) | 3.60444e12i | 0.318814i | ||||||||
\(409\) | 5.50739e12i | 0.481204i | 0.970624 | + | 0.240602i | \(0.0773449\pi\) | ||||
−0.970624 | + | 0.240602i | \(0.922655\pi\) | |||||||
\(410\) | 1.53319e12i | 0.132335i | ||||||||
\(411\) | 1.68651e12 | 0.143807 | ||||||||
\(412\) | 2.05658e12i | 0.173244i | ||||||||
\(413\) | 1.56227e12 | + | 2.59821e12i | 0.130019 | + | 0.216234i | ||||
\(414\) | 2.31552e12 | 0.190391 | ||||||||
\(415\) | − | 1.21879e12i | − | 0.0990122i | ||||||
\(416\) | 1.94780e13 | 1.56343 | ||||||||
\(417\) | 1.29880e13 | 1.03006 | ||||||||
\(418\) | −1.54513e12 | −0.121083 | ||||||||
\(419\) | 1.35032e13i | 1.04560i | 0.852454 | + | 0.522802i | \(0.175113\pi\) | ||||
−0.852454 | + | 0.522802i | \(0.824887\pi\) | |||||||
\(420\) | 9.28174e11 | 0.0710204 | ||||||||
\(421\) | − | 1.71630e13i | − | 1.29772i | −0.760906 | − | 0.648862i | \(-0.775245\pi\) | ||
0.760906 | − | 0.648862i | \(-0.224755\pi\) | |||||||
\(422\) | −2.78864e13 | −2.08368 | ||||||||
\(423\) | 4.40571e12i | 0.325323i | ||||||||
\(424\) | − | 3.83463e12i | − | 0.279830i | ||||||
\(425\) | 1.68936e13 | 1.21837 | ||||||||
\(426\) | 1.78253e13i | 1.27054i | ||||||||
\(427\) | 5.77298e12i | 0.406687i | ||||||||
\(428\) | −2.88463e13 | −2.00850 | ||||||||
\(429\) | 1.97009e12 | 0.135581 | ||||||||
\(430\) | −8.49195e12 | −0.577650 | ||||||||
\(431\) | 6.74475e11i | 0.0453502i | 0.999743 | + | 0.0226751i | \(0.00721833\pi\) | ||||
−0.999743 | + | 0.0226751i | \(0.992782\pi\) | |||||||
\(432\) | 1.96328e12 | 0.130486 | ||||||||
\(433\) | 1.25185e13 | 0.822454 | 0.411227 | − | 0.911533i | \(-0.365100\pi\) | ||||
0.411227 | + | 0.911533i | \(0.365100\pi\) | |||||||
\(434\) | −7.34887e12 | −0.477278 | ||||||||
\(435\) | −2.11999e12 | −0.136109 | ||||||||
\(436\) | − | 2.83069e13i | − | 1.79663i | ||||||
\(437\) | 2.31735e12i | 0.145406i | ||||||||
\(438\) | 5.75528e12 | 0.357023 | ||||||||
\(439\) | 2.48488e13 | 1.52399 | 0.761997 | − | 0.647581i | \(-0.224219\pi\) | ||||
0.761997 | + | 0.647581i | \(0.224219\pi\) | |||||||
\(440\) | −5.19375e11 | −0.0314933 | ||||||||
\(441\) | −5.20600e12 | −0.312113 | ||||||||
\(442\) | 4.04913e13 | 2.40022 | ||||||||
\(443\) | 1.48108e13i | 0.868079i | 0.900894 | + | 0.434040i | \(0.142912\pi\) | ||||
−0.900894 | + | 0.434040i | \(0.857088\pi\) | |||||||
\(444\) | − | 1.87996e13i | − | 1.08952i | ||||||
\(445\) | 4.64797e12i | 0.266357i | ||||||||
\(446\) | − | 3.32010e13i | − | 1.88138i | ||||||
\(447\) | 8.54548e12i | 0.478849i | ||||||||
\(448\) | −6.51157e12 | −0.360824 | ||||||||
\(449\) | 2.59038e12 | 0.141949 | 0.0709744 | − | 0.997478i | \(-0.477389\pi\) | ||||
0.0709744 | + | 0.997478i | \(0.477389\pi\) | |||||||
\(450\) | 7.84786e12i | 0.425293i | ||||||||
\(451\) | − | 8.92938e11i | − | 0.0478563i | ||||||
\(452\) | 4.33463e13i | 2.29752i | ||||||||
\(453\) | 1.14758e13i | 0.601580i | ||||||||
\(454\) | 4.35178e13 | 2.25625 | ||||||||
\(455\) | − | 2.12714e12i | − | 0.109079i | ||||||
\(456\) | − | 1.67575e12i | − | 0.0849932i | ||||||
\(457\) | 2.99458e12i | 0.150230i | 0.997175 | + | 0.0751148i | \(0.0239323\pi\) | ||||
−0.997175 | + | 0.0751148i | \(0.976068\pi\) | |||||||
\(458\) | −1.00190e12 | −0.0497161 | ||||||||
\(459\) | 5.62403e12 | 0.276048 | ||||||||
\(460\) | 3.81824e12i | 0.185385i | ||||||||
\(461\) | −1.22054e13 | −0.586201 | −0.293101 | − | 0.956082i | \(-0.594687\pi\) | ||||
−0.293101 | + | 0.956082i | \(0.594687\pi\) | |||||||
\(462\) | −9.70868e11 | −0.0461265 | ||||||||
\(463\) | 1.22561e13i | 0.576031i | 0.957626 | + | 0.288016i | \(0.0929955\pi\) | ||||
−0.957626 | + | 0.288016i | \(0.907004\pi\) | |||||||
\(464\) | 8.85870e12 | 0.411889 | ||||||||
\(465\) | 6.13410e12i | 0.282154i | ||||||||
\(466\) | 5.11535e13 | 2.32780 | ||||||||
\(467\) | 1.45069e13i | 0.653118i | 0.945177 | + | 0.326559i | \(0.105889\pi\) | ||||
−0.945177 | + | 0.326559i | \(0.894111\pi\) | |||||||
\(468\) | 1.04733e13i | 0.466505i | ||||||||
\(469\) | − | 1.03071e13i | − | 0.454228i | ||||||
\(470\) | −1.30477e13 | −0.568913 | ||||||||
\(471\) | 8.69745e12i | 0.375221i | ||||||||
\(472\) | 7.72904e12 | − | 4.64738e12i | 0.329925 | − | 0.198380i | ||||
\(473\) | 4.94576e12 | 0.208895 | ||||||||
\(474\) | 3.03286e11i | 0.0126754i | ||||||||
\(475\) | −7.85404e12 | −0.324807 | ||||||||
\(476\) | −1.11105e13 | −0.454671 | ||||||||
\(477\) | −5.98320e12 | −0.242293 | ||||||||
\(478\) | − | 2.60251e13i | − | 1.04293i | ||||||
\(479\) | −2.73650e13 | −1.08522 | −0.542610 | − | 0.839985i | \(-0.682564\pi\) | ||||
−0.542610 | + | 0.839985i | \(0.682564\pi\) | |||||||
\(480\) | 8.01215e12i | 0.314444i | ||||||||
\(481\) | −4.30840e13 | −1.67336 | ||||||||
\(482\) | − | 2.92772e13i | − | 1.12537i | ||||||
\(483\) | 1.45608e12i | 0.0553924i | ||||||||
\(484\) | −3.18843e13 | −1.20047 | ||||||||
\(485\) | − | 2.85021e12i | − | 0.106211i | ||||||
\(486\) | 2.61262e12i | 0.0963595i | ||||||||
\(487\) | 2.31886e13 | 0.846504 | 0.423252 | − | 0.906012i | \(-0.360889\pi\) | ||||
0.423252 | + | 0.906012i | \(0.360889\pi\) | |||||||
\(488\) | 1.71732e13 | 0.620515 | ||||||||
\(489\) | 2.68133e13 | 0.958971 | ||||||||
\(490\) | − | 1.54178e13i | − | 0.545812i | ||||||
\(491\) | −2.44864e13 | −0.858058 | −0.429029 | − | 0.903291i | \(-0.641144\pi\) | ||||
−0.429029 | + | 0.903291i | \(0.641144\pi\) | |||||||
\(492\) | 4.74702e12 | 0.164663 | ||||||||
\(493\) | 2.53768e13 | 0.871368 | ||||||||
\(494\) | −1.88249e13 | −0.639878 | ||||||||
\(495\) | 8.10384e11i | 0.0272687i | ||||||||
\(496\) | − | 2.56322e13i | − | 0.853843i | ||||||
\(497\) | −1.12092e13 | −0.369650 | ||||||||
\(498\) | −6.77734e12 | −0.221265 | ||||||||
\(499\) | −1.95409e13 | −0.631601 | −0.315800 | − | 0.948826i | \(-0.602273\pi\) | ||||
−0.315800 | + | 0.948826i | \(0.602273\pi\) | |||||||
\(500\) | −2.81763e13 | −0.901642 | ||||||||
\(501\) | −3.10255e13 | −0.982947 | ||||||||
\(502\) | − | 7.78332e13i | − | 2.44144i | ||||||
\(503\) | − | 4.04475e13i | − | 1.25618i | −0.778141 | − | 0.628090i | \(-0.783837\pi\) | ||
0.778141 | − | 0.628090i | \(-0.216163\pi\) | |||||||
\(504\) | − | 1.05294e12i | − | 0.0323781i | ||||||
\(505\) | − | 2.20368e12i | − | 0.0670951i | ||||||
\(506\) | − | 3.99387e12i | − | 0.120404i | ||||||
\(507\) | 4.66129e12 | 0.139144 | ||||||||
\(508\) | 7.22210e13 | 2.13474 | ||||||||
\(509\) | 4.75133e13i | 1.39068i | 0.718682 | + | 0.695339i | \(0.244746\pi\) | ||||
−0.718682 | + | 0.695339i | \(0.755254\pi\) | |||||||
\(510\) | 1.66559e13i | 0.482743i | ||||||||
\(511\) | 3.61912e12i | 0.103872i | ||||||||
\(512\) | − | 4.26638e13i | − | 1.21258i | ||||||
\(513\) | −2.61468e12 | −0.0735921 | ||||||||
\(514\) | − | 6.79725e13i | − | 1.89460i | ||||||
\(515\) | 1.93873e12i | 0.0535157i | ||||||||
\(516\) | 2.62926e13i | 0.718761i | ||||||||
\(517\) | 7.59909e12 | 0.205735 | ||||||||
\(518\) | 2.12320e13 | 0.569301 | ||||||||
\(519\) | 3.47179e13i | 0.921970i | ||||||||
\(520\) | −6.32774e12 | −0.166430 | ||||||||
\(521\) | −4.64189e13 | −1.20922 | −0.604611 | − | 0.796521i | \(-0.706671\pi\) | ||||
−0.604611 | + | 0.796521i | \(0.706671\pi\) | |||||||
\(522\) | 1.17887e13i | 0.304167i | ||||||||
\(523\) | −1.77026e13 | −0.452407 | −0.226204 | − | 0.974080i | \(-0.572631\pi\) | ||||
−0.226204 | + | 0.974080i | \(0.572631\pi\) | |||||||
\(524\) | − | 3.01645e13i | − | 0.763555i | ||||||
\(525\) | −4.93501e12 | −0.123735 | ||||||||
\(526\) | − | 8.07039e12i | − | 0.200431i | ||||||
\(527\) | − | 7.34265e13i | − | 1.80634i | ||||||
\(528\) | − | 3.38631e12i | − | 0.0825195i | ||||||
\(529\) | 3.54366e13 | 0.855409 | ||||||||
\(530\) | − | 1.77195e13i | − | 0.423714i | ||||||
\(531\) | −7.25133e12 | − | 1.20597e13i | −0.171769 | − | 0.285668i | ||||
\(532\) | 5.16537e12 | 0.121211 | ||||||||
\(533\) | − | 1.08790e13i | − | 0.252902i | ||||||
\(534\) | 2.58460e13 | 0.595234 | ||||||||
\(535\) | −2.71933e13 | −0.620431 | ||||||||
\(536\) | −3.06612e13 | −0.693052 | ||||||||
\(537\) | 1.98491e13i | 0.444498i | ||||||||
\(538\) | 2.83292e12 | 0.0628525 | ||||||||
\(539\) | 8.97944e12i | 0.197381i | ||||||||
\(540\) | −4.30814e12 | −0.0938256 | ||||||||
\(541\) | − | 7.67384e13i | − | 1.65587i | −0.560824 | − | 0.827935i | \(-0.689516\pi\) | ||
0.560824 | − | 0.827935i | \(-0.310484\pi\) | |||||||
\(542\) | 7.18165e13i | 1.53542i | ||||||||
\(543\) | −6.15735e12 | −0.130435 | ||||||||
\(544\) | − | 9.59072e13i | − | 2.01306i | ||||||
\(545\) | − | 2.66848e13i | − | 0.554986i | ||||||
\(546\) | −1.18284e13 | −0.243761 | ||||||||
\(547\) | −5.33433e13 | −1.08929 | −0.544644 | − | 0.838667i | \(-0.683335\pi\) | ||||
−0.544644 | + | 0.838667i | \(0.683335\pi\) | |||||||
\(548\) | 1.54645e13 | 0.312919 | ||||||||
\(549\) | − | 2.67954e13i | − | 0.537278i | ||||||
\(550\) | 1.35362e13 | 0.268957 | ||||||||
\(551\) | −1.17979e13 | −0.232300 | ||||||||
\(552\) | 4.33149e12 | 0.0845166 | ||||||||
\(553\) | −1.90717e11 | −0.00368777 | ||||||||
\(554\) | 7.15069e13i | 1.37025i | ||||||||
\(555\) | − | 1.77223e13i | − | 0.336555i | ||||||
\(556\) | 1.19093e14 | 2.24137 | ||||||||
\(557\) | −8.38263e13 | −1.56352 | −0.781761 | − | 0.623578i | \(-0.785679\pi\) | ||||
−0.781761 | + | 0.623578i | \(0.785679\pi\) | |||||||
\(558\) | 3.41099e13 | 0.630536 | ||||||||
\(559\) | 6.02560e13 | 1.10393 | ||||||||
\(560\) | −3.65627e12 | −0.0663893 | ||||||||
\(561\) | − | 9.70047e12i | − | 0.174574i | ||||||
\(562\) | − | 1.11575e14i | − | 1.99015i | ||||||
\(563\) | 8.01858e13i | 1.41761i | 0.705407 | + | 0.708803i | \(0.250764\pi\) | ||||
−0.705407 | + | 0.708803i | \(0.749236\pi\) | |||||||
\(564\) | 4.03981e13i | 0.707889i | ||||||||
\(565\) | 4.08625e13i | 0.709712i | ||||||||
\(566\) | −8.28857e13 | −1.42691 | ||||||||
\(567\) | −1.64291e12 | −0.0280348 | ||||||||
\(568\) | 3.33445e13i | 0.564004i | ||||||||
\(569\) | − | 4.44464e13i | − | 0.745203i | −0.927991 | − | 0.372602i | \(-0.878466\pi\) | ||
0.927991 | − | 0.372602i | \(-0.121534\pi\) | |||||||
\(570\) | − | 7.74349e12i | − | 0.128695i | ||||||
\(571\) | − | 5.25658e12i | − | 0.0866009i | −0.999062 | − | 0.0433005i | \(-0.986213\pi\) | ||
0.999062 | − | 0.0433005i | \(-0.0137873\pi\) | |||||||
\(572\) | 1.80647e13 | 0.295019 | ||||||||
\(573\) | − | 6.26642e13i | − | 1.01449i | ||||||
\(574\) | 5.36121e12i | 0.0860407i | ||||||||
\(575\) | − | 2.03012e13i | − | 0.322985i | ||||||
\(576\) | 3.02236e13 | 0.476688 | ||||||||
\(577\) | −1.09977e14 | −1.71958 | −0.859790 | − | 0.510648i | \(-0.829405\pi\) | ||||
−0.859790 | + | 0.510648i | \(0.829405\pi\) | |||||||
\(578\) | − | 1.02471e14i | − | 1.58841i | ||||||
\(579\) | −3.60863e12 | −0.0554562 | ||||||||
\(580\) | −1.94392e13 | −0.296169 | ||||||||
\(581\) | − | 4.26184e12i | − | 0.0643748i | ||||||
\(582\) | −1.58492e13 | −0.237351 | ||||||||
\(583\) | 1.03200e13i | 0.153227i | ||||||||
\(584\) | 1.07660e13 | 0.158486 | ||||||||
\(585\) | 9.87320e12i | 0.144105i | ||||||||
\(586\) | 1.15135e14i | 1.66617i | ||||||||
\(587\) | 3.08123e13i | 0.442113i | 0.975261 | + | 0.221056i | \(0.0709505\pi\) | ||||
−0.975261 | + | 0.221056i | \(0.929050\pi\) | |||||||
\(588\) | −4.77363e13 | −0.679145 | ||||||||
\(589\) | 3.41368e13i | 0.481556i | ||||||||
\(590\) | 3.57153e13 | − | 2.14752e13i | 0.499567 | − | 0.300384i | ||||
\(591\) | −2.49323e13 | −0.345800 | ||||||||
\(592\) | 7.40554e13i | 1.01847i | ||||||||
\(593\) | 1.74470e13 | 0.237929 | 0.118964 | − | 0.992899i | \(-0.462043\pi\) | ||||
0.118964 | + | 0.992899i | \(0.462043\pi\) | |||||||
\(594\) | 4.50631e12 | 0.0609381 | ||||||||
\(595\) | −1.04738e13 | −0.140449 | ||||||||
\(596\) | 7.83576e13i | 1.04196i | ||||||||
\(597\) | −7.53987e13 | −0.994242 | ||||||||
\(598\) | − | 4.86588e13i | − | 0.636290i | ||||||
\(599\) | 2.40542e13 | 0.311929 | 0.155965 | − | 0.987763i | \(-0.450151\pi\) | ||||
0.155965 | + | 0.987763i | \(0.450151\pi\) | |||||||
\(600\) | 1.46805e13i | 0.188792i | ||||||||
\(601\) | − | 3.18260e13i | − | 0.405891i | −0.979190 | − | 0.202945i | \(-0.934949\pi\) | ||
0.979190 | − | 0.202945i | \(-0.0650514\pi\) | |||||||
\(602\) | −2.96944e13 | −0.375571 | ||||||||
\(603\) | 4.78409e13i | 0.600085i | ||||||||
\(604\) | 1.05228e14i | 1.30902i | ||||||||
\(605\) | −3.00572e13 | −0.370828 | ||||||||
\(606\) | −1.22540e13 | −0.149939 | ||||||||
\(607\) | −7.13963e13 | −0.866427 | −0.433214 | − | 0.901291i | \(-0.642620\pi\) | ||||
−0.433214 | + | 0.901291i | \(0.642620\pi\) | |||||||
\(608\) | 4.45884e13i | 0.536665i | ||||||||
\(609\) | −7.41314e12 | −0.0884943 | ||||||||
\(610\) | 7.93560e13 | 0.939573 | ||||||||
\(611\) | 9.25824e13 | 1.08723 | ||||||||
\(612\) | 5.15694e13 | 0.600669 | ||||||||
\(613\) | 2.52653e13i | 0.291892i | 0.989293 | + | 0.145946i | \(0.0466226\pi\) | ||||
−0.989293 | + | 0.145946i | \(0.953377\pi\) | |||||||
\(614\) | 1.40459e14i | 1.60956i | ||||||||
\(615\) | 4.47501e12 | 0.0508649 | ||||||||
\(616\) | −1.81614e12 | −0.0204760 | ||||||||
\(617\) | 4.37750e13 | 0.489554 | 0.244777 | − | 0.969579i | \(-0.421285\pi\) | ||||
0.244777 | + | 0.969579i | \(0.421285\pi\) | |||||||
\(618\) | 1.07807e13 | 0.119593 | ||||||||
\(619\) | −1.60155e14 | −1.76233 | −0.881165 | − | 0.472809i | \(-0.843240\pi\) | ||||
−0.881165 | + | 0.472809i | \(0.843240\pi\) | |||||||
\(620\) | 5.62465e13i | 0.613956i | ||||||||
\(621\) | − | 6.75845e12i | − | 0.0731794i | ||||||
\(622\) | − | 1.54929e14i | − | 1.66411i | ||||||
\(623\) | 1.62529e13i | 0.173177i | ||||||||
\(624\) | − | 4.12566e13i | − | 0.436085i | ||||||
\(625\) | 5.44433e13 | 0.570880 | ||||||||
\(626\) | 7.17572e13 | 0.746438 | ||||||||
\(627\) | 4.50986e12i | 0.0465399i | ||||||||
\(628\) | 7.97511e13i | 0.816467i | ||||||||
\(629\) | 2.12140e14i | 2.15462i | ||||||||
\(630\) | − | 4.86556e12i | − | 0.0490264i | ||||||
\(631\) | −3.60007e13 | −0.359886 | −0.179943 | − | 0.983677i | \(-0.557591\pi\) | ||||
−0.179943 | + | 0.983677i | \(0.557591\pi\) | |||||||
\(632\) | 5.67337e11i | 0.00562672i | ||||||||
\(633\) | 8.13937e13i | 0.800889i | ||||||||
\(634\) | 2.12989e14i | 2.07927i | ||||||||
\(635\) | 6.80826e13 | 0.659428 | ||||||||
\(636\) | −5.48628e13 | −0.527221 | ||||||||
\(637\) | 1.09400e14i | 1.04308i | ||||||||
\(638\) | 2.03334e13 | 0.192356 | ||||||||
\(639\) | 5.20276e13 | 0.488348 | ||||||||
\(640\) | 3.10293e13i | 0.288983i | ||||||||
\(641\) | −1.24923e14 | −1.15439 | −0.577193 | − | 0.816608i | \(-0.695852\pi\) | ||||
−0.577193 | + | 0.816608i | \(0.695852\pi\) | |||||||
\(642\) | 1.51214e14i | 1.38649i | ||||||||
\(643\) | −1.32175e14 | −1.20253 | −0.601264 | − | 0.799050i | \(-0.705336\pi\) | ||||
−0.601264 | + | 0.799050i | \(0.705336\pi\) | |||||||
\(644\) | 1.33515e13i | 0.120532i | ||||||||
\(645\) | 2.47859e13i | 0.222028i | ||||||||
\(646\) | 9.26913e13i | 0.823904i | ||||||||
\(647\) | 2.26232e14 | 1.99541 | 0.997706 | − | 0.0676954i | \(-0.0215646\pi\) | ||||
0.997706 | + | 0.0676954i | \(0.0215646\pi\) | |||||||
\(648\) | 4.88725e12i | 0.0427749i | ||||||||
\(649\) | −2.08008e13 | + | 1.25073e13i | −0.180658 | + | 0.108627i | ||||
\(650\) | 1.64916e14 | 1.42134 | ||||||||
\(651\) | 2.14496e13i | 0.183448i | ||||||||
\(652\) | 2.45864e14 | 2.08668 | ||||||||
\(653\) | −1.61068e14 | −1.35657 | −0.678287 | − | 0.734797i | \(-0.737277\pi\) | ||||
−0.678287 | + | 0.734797i | \(0.737277\pi\) | |||||||
\(654\) | −1.48387e14 | −1.24024 | ||||||||
\(655\) | − | 2.84360e13i | − | 0.235865i | ||||||
\(656\) | −1.86995e13 | −0.153925 | ||||||||
\(657\) | − | 1.67983e13i | − | 0.137226i | ||||||
\(658\) | −4.56250e13 | −0.369891 | ||||||||
\(659\) | 9.82649e13i | 0.790627i | 0.918546 | + | 0.395313i | \(0.129364\pi\) | ||||
−0.918546 | + | 0.395313i | \(0.870636\pi\) | |||||||
\(660\) | 7.43080e12i | 0.0593356i | ||||||||
\(661\) | 1.24089e14 | 0.983393 | 0.491696 | − | 0.870767i | \(-0.336377\pi\) | ||||
0.491696 | + | 0.870767i | \(0.336377\pi\) | |||||||
\(662\) | − | 2.09408e14i | − | 1.64704i | ||||||
\(663\) | − | 1.18184e14i | − | 0.922555i | ||||||
\(664\) | −1.26779e13 | −0.0982217 | ||||||||
\(665\) | 4.86939e12 | 0.0374426 | ||||||||
\(666\) | −9.85488e13 | −0.752108 | ||||||||
\(667\) | − | 3.04955e13i | − | 0.230997i | ||||||
\(668\) | −2.84488e14 | −2.13885 | ||||||||
\(669\) | −9.69057e13 | −0.723134 | ||||||||
\(670\) | −1.41683e14 | −1.04941 | ||||||||
\(671\) | −4.62174e13 | −0.339776 | ||||||||
\(672\) | 2.80167e13i | 0.204442i | ||||||||
\(673\) | 1.05709e14i | 0.765662i | 0.923818 | + | 0.382831i | \(0.125051\pi\) | ||||
−0.923818 | + | 0.382831i | \(0.874949\pi\) | |||||||
\(674\) | 1.96390e14 | 1.41195 | ||||||||
\(675\) | 2.29060e13 | 0.163467 | ||||||||
\(676\) | 4.27416e13 | 0.302773 | ||||||||
\(677\) | 1.17787e14 | 0.828238 | 0.414119 | − | 0.910223i | \(-0.364090\pi\) | ||||
0.414119 | + | 0.910223i | \(0.364090\pi\) | |||||||
\(678\) | 2.27224e14 | 1.58601 | ||||||||
\(679\) | − | 9.96653e12i | − | 0.0690550i | ||||||
\(680\) | 3.11570e13i | 0.214294i | ||||||||
\(681\) | − | 1.27018e14i | − | 0.867219i | ||||||
\(682\) | − | 5.88337e13i | − | 0.398753i | ||||||
\(683\) | 1.82949e14i | 1.23091i | 0.788172 | + | 0.615455i | \(0.211028\pi\) | ||||
−0.788172 | + | 0.615455i | \(0.788972\pi\) | |||||||
\(684\) | −2.39752e13 | −0.160133 | ||||||||
\(685\) | 1.45783e13 | 0.0966617 | ||||||||
\(686\) | − | 1.11491e14i | − | 0.733870i | ||||||
\(687\) | 2.92430e12i | 0.0191090i | ||||||||
\(688\) | − | 1.03572e14i | − | 0.671891i | ||||||
\(689\) | 1.25732e14i | 0.809747i | ||||||||
\(690\) | 2.00155e13 | 0.127974 | ||||||||
\(691\) | − | 8.14976e13i | − | 0.517314i | −0.965969 | − | 0.258657i | \(-0.916720\pi\) | ||
0.965969 | − | 0.258657i | \(-0.0832800\pi\) | |||||||
\(692\) | 3.18345e14i | 2.00617i | ||||||||
\(693\) | 2.83373e12i | 0.0177293i | ||||||||
\(694\) | −2.34360e14 | −1.45575 | ||||||||
\(695\) | 1.12269e14 | 0.692367 | ||||||||
\(696\) | 2.20523e13i | 0.135023i | ||||||||
\(697\) | −5.35668e13 | −0.325636 | ||||||||
\(698\) | 2.26300e14 | 1.36586 | ||||||||
\(699\) | − | 1.49305e14i | − | 0.894721i | ||||||
\(700\) | −4.52515e13 | −0.269242 | ||||||||
\(701\) | − | 2.29407e14i | − | 1.35524i | −0.735412 | − | 0.677620i | \(-0.763012\pi\) | ||
0.735412 | − | 0.677620i | \(-0.236988\pi\) | |||||||
\(702\) | 5.49020e13 | 0.322035 | ||||||||
\(703\) | − | 9.86264e13i | − | 0.574403i | ||||||
\(704\) | − | 5.21304e13i | − | 0.301459i | ||||||
\(705\) | 3.80832e13i | 0.218669i | ||||||||
\(706\) | 1.95029e14 | 1.11193 | ||||||||
\(707\) | − | 7.70576e12i | − | 0.0436233i | ||||||
\(708\) | −6.64910e13 | − | 1.10581e14i | −0.373763 | − | 0.621603i | ||||
\(709\) | 9.37167e13 | 0.523101 | 0.261551 | − | 0.965190i | \(-0.415766\pi\) | ||||
0.261551 | + | 0.965190i | \(0.415766\pi\) | |||||||
\(710\) | 1.54082e14i | 0.854006i | ||||||||
\(711\) | 8.85218e11 | 0.00487194 | ||||||||
\(712\) | 4.83485e13 | 0.264230 | ||||||||
\(713\) | −8.82373e13 | −0.478855 | ||||||||
\(714\) | 5.82418e13i | 0.313865i | ||||||||
\(715\) | 1.70295e13 | 0.0911324 | ||||||||
\(716\) | 1.82006e14i | 0.967211i | ||||||||
\(717\) | −7.59610e13 | −0.400862 | ||||||||
\(718\) | − | 3.92795e14i | − | 2.05847i | ||||||
\(719\) | 6.45439e13i | 0.335900i | 0.985795 | + | 0.167950i | \(0.0537148\pi\) | ||||
−0.985795 | + | 0.167950i | \(0.946285\pi\) | |||||||
\(720\) | 1.69707e13 | 0.0877074 | ||||||||
\(721\) | 6.77931e12i | 0.0347944i | ||||||||
\(722\) | 2.51609e14i | 1.28245i | ||||||||
\(723\) | −8.54531e13 | −0.432550 | ||||||||
\(724\) | −5.64597e13 | −0.283822 | ||||||||
\(725\) | 1.03357e14 | 0.515998 | ||||||||
\(726\) | 1.67140e14i | 0.828698i | ||||||||
\(727\) | −2.81569e14 | −1.38648 | −0.693239 | − | 0.720708i | \(-0.743817\pi\) | ||||
−0.693239 | + | 0.720708i | \(0.743817\pi\) | |||||||
\(728\) | −2.21267e13 | −0.108208 | ||||||||
\(729\) | 7.62560e12 | 0.0370370 | ||||||||
\(730\) | 4.97489e13 | 0.239977 | ||||||||
\(731\) | − | 2.96693e14i | − | 1.42141i | ||||||
\(732\) | − | 2.45700e14i | − | 1.16910i | ||||||
\(733\) | −1.25097e13 | −0.0591188 | −0.0295594 | − | 0.999563i | \(-0.509410\pi\) | ||||
−0.0295594 | + | 0.999563i | \(0.509410\pi\) | |||||||
\(734\) | 3.36340e14 | 1.57870 | ||||||||
\(735\) | −4.50009e13 | −0.209790 | ||||||||
\(736\) | −1.15253e14 | −0.533656 | ||||||||
\(737\) | 8.25171e13 | 0.379496 | ||||||||
\(738\) | − | 2.48842e13i | − | 0.113669i | ||||||
\(739\) | 3.10630e14i | 1.40936i | 0.709526 | + | 0.704679i | \(0.248909\pi\) | ||||
−0.709526 | + | 0.704679i | \(0.751091\pi\) | |||||||
\(740\) | − | 1.62505e14i | − | 0.732330i | ||||||
\(741\) | 5.49452e13i | 0.245946i | ||||||||
\(742\) | − | 6.19613e13i | − | 0.275487i | ||||||
\(743\) | 1.22114e13 | 0.0539290 | 0.0269645 | − | 0.999636i | \(-0.491416\pi\) | ||||
0.0269645 | + | 0.999636i | \(0.491416\pi\) | |||||||
\(744\) | 6.38072e13 | 0.279901 | ||||||||
\(745\) | 7.38675e13i | 0.321864i | ||||||||
\(746\) | − | 5.18068e14i | − | 2.24229i | ||||||
\(747\) | 1.97814e13i | 0.0850461i | ||||||||
\(748\) | − | 8.89483e13i | − | 0.379865i | ||||||
\(749\) | −9.50890e13 | −0.403386 | ||||||||
\(750\) | 1.47702e14i | 0.622416i | ||||||||
\(751\) | 2.02817e14i | 0.848994i | 0.905429 | + | 0.424497i | \(0.139549\pi\) | ||||
−0.905429 | + | 0.424497i | \(0.860451\pi\) | |||||||
\(752\) | − | 1.59136e14i | − | 0.661729i | ||||||
\(753\) | −2.27176e14 | −0.938400 | ||||||||
\(754\) | 2.47729e14 | 1.01653 | ||||||||
\(755\) | 9.91978e13i | 0.404359i | ||||||||
\(756\) | −1.50646e13 | −0.0610027 | ||||||||
\(757\) | 1.52549e14 | 0.613663 | 0.306832 | − | 0.951764i | \(-0.400731\pi\) | ||||
0.306832 | + | 0.951764i | \(0.400731\pi\) | |||||||
\(758\) | 5.67583e14i | 2.26821i | ||||||||
\(759\) | −1.16571e13 | −0.0462789 | ||||||||
\(760\) | − | 1.44852e13i | − | 0.0571291i | ||||||
\(761\) | 2.28700e14 | 0.896072 | 0.448036 | − | 0.894016i | \(-0.352124\pi\) | ||||
0.448036 | + | 0.894016i | \(0.352124\pi\) | |||||||
\(762\) | − | 3.78587e14i | − | 1.47364i | ||||||
\(763\) | − | 9.33108e13i | − | 0.360836i | ||||||
\(764\) | − | 5.74598e14i | − | 2.20748i | ||||||
\(765\) | 4.86144e13 | 0.185549 | ||||||||
\(766\) | 1.99813e14i | 0.757668i | ||||||||
\(767\) | −2.53424e14 | + | 1.52381e14i | −0.954707 | + | 0.574055i | ||||
\(768\) | −4.80527e13 | −0.179850 | ||||||||
\(769\) | − | 4.33481e14i | − | 1.61190i | −0.591982 | − | 0.805951i | \(-0.701654\pi\) | ||
0.591982 | − | 0.805951i | \(-0.298346\pi\) | |||||||
\(770\) | −8.39223e12 | −0.0310044 | ||||||||
\(771\) | −1.98395e14 | −0.728214 | ||||||||
\(772\) | −3.30893e13 | −0.120670 | ||||||||
\(773\) | 1.19916e14i | 0.434492i | 0.976117 | + | 0.217246i | \(0.0697073\pi\) | ||||
−0.976117 | + | 0.217246i | \(0.930293\pi\) | |||||||
\(774\) | 1.37827e14 | 0.496171 | ||||||||
\(775\) | − | 2.99057e14i | − | 1.06966i | ||||||
\(776\) | −2.96480e13 | −0.105363 | ||||||||
\(777\) | − | 6.19710e13i | − | 0.218818i | ||||||
\(778\) | − | 4.43377e13i | − | 0.155552i | ||||||
\(779\) | 2.49038e13 | 0.0868118 | ||||||||
\(780\) | 9.05321e13i | 0.313566i | ||||||||
\(781\) | − | 8.97385e13i | − | 0.308833i | ||||||
\(782\) | −2.39590e14 | −0.819284 | ||||||||
\(783\) | 3.44083e13 | 0.116911 | ||||||||
\(784\) | 1.88043e14 | 0.634859 | ||||||||
\(785\) | 7.51812e13i | 0.252209i | ||||||||
\(786\) | −1.58125e14 | −0.527092 | ||||||||
\(787\) | −1.36664e14 | −0.452670 | −0.226335 | − | 0.974049i | \(-0.572674\pi\) | ||||
−0.226335 | + | 0.974049i | \(0.572674\pi\) | |||||||
\(788\) | −2.28616e14 | −0.752447 | ||||||||
\(789\) | −2.35555e13 | −0.0770384 | ||||||||
\(790\) | 2.62162e12i | 0.00851989i | ||||||||
\(791\) | 1.42887e14i | 0.461434i | ||||||||
\(792\) | 8.42965e12 | 0.0270510 | ||||||||
\(793\) | −5.63084e14 | −1.79559 | ||||||||
\(794\) | 2.91133e13 | 0.0922547 | ||||||||
\(795\) | −5.17191e13 | −0.162860 | ||||||||
\(796\) | −6.91367e14 | −2.16343 | ||||||||
\(797\) | 5.64804e14i | 1.75633i | 0.478358 | + | 0.878165i | \(0.341232\pi\) | ||||
−0.478358 | + | 0.878165i | \(0.658768\pi\) | |||||||
\(798\) | − | 2.70773e13i | − | 0.0836739i | ||||||
\(799\) | − | 4.55864e14i | − | 1.39992i | ||||||
\(800\) | − | 3.90619e14i | − | 1.19207i | ||||||
\(801\) | − | 7.54383e13i | − | 0.228786i | ||||||
\(802\) | 4.77119e13 | 0.143799 | ||||||||
\(803\) | −2.89741e13 | −0.0867824 | ||||||||
\(804\) | 4.38676e14i | 1.30576i | ||||||||
\(805\) | 1.25865e13i | 0.0372327i | ||||||||
\(806\) | − | 7.16792e14i | − | 2.10726i | ||||||
\(807\) | − | 8.26860e12i | − | 0.0241582i | ||||||
\(808\) | −2.29227e13 | −0.0665595 | ||||||||
\(809\) | 3.16395e14i | 0.913034i | 0.889715 | + | 0.456517i | \(0.150903\pi\) | ||||
−0.889715 | + | 0.456517i | \(0.849097\pi\) | |||||||
\(810\) | 2.25836e13i | 0.0647691i | ||||||||
\(811\) | − | 2.71723e14i | − | 0.774500i | −0.921975 | − | 0.387250i | \(-0.873425\pi\) | ||
0.921975 | − | 0.387250i | \(-0.126575\pi\) | |||||||
\(812\) | −6.79746e13 | −0.192560 | ||||||||
\(813\) | 2.09615e14 | 0.590160 | ||||||||
\(814\) | 1.69979e14i | 0.475636i | ||||||||
\(815\) | 2.31775e14 | 0.644583 | ||||||||
\(816\) | −2.03142e14 | −0.561500 | ||||||||
\(817\) | 1.37936e14i | 0.378937i | ||||||||
\(818\) | 2.64724e14 | 0.722815 | ||||||||
\(819\) | 3.45243e13i | 0.0936927i | ||||||||
\(820\) | 4.10335e13 | 0.110680 | ||||||||
\(821\) | − | 6.50932e13i | − | 0.174510i | −0.996186 | − | 0.0872550i | \(-0.972191\pi\) | ||
0.996186 | − | 0.0872550i | \(-0.0278095\pi\) | |||||||
\(822\) | − | 8.10658e13i | − | 0.216012i | ||||||
\(823\) | 7.25621e14i | 1.92181i | 0.276877 | + | 0.960905i | \(0.410701\pi\) | ||||
−0.276877 | + | 0.960905i | \(0.589299\pi\) | |||||||
\(824\) | 2.01668e13 | 0.0530885 | ||||||||
\(825\) | − | 3.95088e13i | − | 0.103377i | ||||||
\(826\) | 1.24888e14 | − | 7.50939e13i | 0.324804 | − | 0.195301i | ||||
\(827\) | −5.15427e14 | −1.33241 | −0.666207 | − | 0.745767i | \(-0.732083\pi\) | ||||
−0.666207 | + | 0.745767i | \(0.732083\pi\) | |||||||
\(828\) | − | 6.19714e13i | − | 0.159236i | ||||||
\(829\) | −4.15282e14 | −1.06065 | −0.530323 | − | 0.847795i | \(-0.677930\pi\) | ||||
−0.530323 | + | 0.847795i | \(0.677930\pi\) | |||||||
\(830\) | −5.85837e13 | −0.148726 | ||||||||
\(831\) | 2.08711e14 | 0.526673 | ||||||||
\(832\) | − | 6.35124e14i | − | 1.59310i | ||||||
\(833\) | 5.38671e14 | 1.34307 | ||||||||
\(834\) | − | 6.24296e14i | − | 1.54725i | ||||||
\(835\) | −2.68186e14 | −0.660699 | ||||||||
\(836\) | 4.13531e13i | 0.101269i | ||||||||
\(837\) | − | 9.95587e13i | − | 0.242355i | ||||||
\(838\) | 6.49060e14 | 1.57060 | ||||||||
\(839\) | 6.50012e14i | 1.56355i | 0.623561 | + | 0.781774i | \(0.285685\pi\) | ||||
−0.623561 | + | 0.781774i | \(0.714315\pi\) | |||||||
\(840\) | − | 9.10167e12i | − | 0.0217633i | ||||||
\(841\) | −2.65450e14 | −0.630962 | ||||||||
\(842\) | −8.24975e14 | −1.94931 | ||||||||
\(843\) | −3.25661e14 | −0.764940 | ||||||||
\(844\) | 7.46338e14i | 1.74270i | ||||||||
\(845\) | 4.02924e13 | 0.0935275 | ||||||||
\(846\) | 2.11770e14 | 0.488666 | ||||||||
\(847\) | −1.05103e14 | −0.241101 | ||||||||
\(848\) | 2.16116e14 | 0.492842 | ||||||||
\(849\) | 2.41923e14i | 0.548452i | ||||||||
\(850\) | − | 8.12027e14i | − | 1.83010i | ||||||
\(851\) | 2.54931e14 | 0.571182 | ||||||||
\(852\) | 4.77066e14 | 1.06263 | ||||||||
\(853\) | −5.77920e14 | −1.27974 | −0.639871 | − | 0.768482i | \(-0.721012\pi\) | ||||
−0.639871 | + | 0.768482i | \(0.721012\pi\) | |||||||
\(854\) | 2.77490e14 | 0.610883 | ||||||||
\(855\) | −2.26014e13 | −0.0494657 | ||||||||
\(856\) | 2.82867e14i | 0.615478i | ||||||||
\(857\) | 1.52316e14i | 0.329488i | 0.986336 | + | 0.164744i | \(0.0526799\pi\) | ||||
−0.986336 | + | 0.164744i | \(0.947320\pi\) | |||||||
\(858\) | − | 9.46963e13i | − | 0.203656i | ||||||
\(859\) | − | 2.44874e14i | − | 0.523573i | −0.965126 | − | 0.261786i | \(-0.915688\pi\) | ||
0.965126 | − | 0.261786i | \(-0.0843116\pi\) | |||||||
\(860\) | 2.27274e14i | 0.483123i | ||||||||
\(861\) | 1.56481e13 | 0.0330709 | ||||||||
\(862\) | 3.24200e13 | 0.0681204 | ||||||||
\(863\) | − | 4.22291e14i | − | 0.882180i | −0.897463 | − | 0.441090i | \(-0.854592\pi\) | ||
0.897463 | − | 0.441090i | \(-0.145408\pi\) | |||||||
\(864\) | − | 1.30040e14i | − | 0.270090i | ||||||
\(865\) | 3.00103e14i | 0.619713i | ||||||||
\(866\) | − | 6.01726e14i | − | 1.23540i | ||||||
\(867\) | −2.99089e14 | −0.610527 | ||||||||
\(868\) | 1.96681e14i | 0.399176i | ||||||||
\(869\) | − | 1.52685e12i | − | 0.00308103i | ||||||
\(870\) | 1.01902e14i | 0.204449i | ||||||||
\(871\) | 1.00534e15 | 2.00549 | ||||||||
\(872\) | −2.77577e14 | −0.550555 | ||||||||
\(873\) | 4.62599e13i | 0.0912291i | ||||||||
\(874\) | 1.11388e14 | 0.218414 | ||||||||
\(875\) | −9.28805e13 | −0.181086 | ||||||||
\(876\) | − | 1.54031e14i | − | 0.298599i | ||||||
\(877\) | 8.12428e14 | 1.56598 | 0.782991 | − | 0.622033i | \(-0.213693\pi\) | ||||
0.782991 | + | 0.622033i | \(0.213693\pi\) | |||||||
\(878\) | − | 1.19441e15i | − | 2.28918i | ||||||
\(879\) | 3.36051e14 | 0.640414 | ||||||||
\(880\) | − | 2.92714e13i | − | 0.0554664i | ||||||
\(881\) | 1.13539e14i | 0.213927i | 0.994263 | + | 0.106963i | \(0.0341128\pi\) | ||||
−0.994263 | + | 0.106963i | \(0.965887\pi\) | |||||||
\(882\) | 2.50237e14i | 0.468823i | ||||||||
\(883\) | −1.36999e14 | −0.255219 | −0.127610 | − | 0.991824i | \(-0.540730\pi\) | ||||
−0.127610 | + | 0.991824i | \(0.540730\pi\) | |||||||
\(884\) | − | 1.08369e15i | − | 2.00744i | ||||||
\(885\) | −6.26809e13 | − | 1.04244e14i | −0.115457 | − | 0.192015i | ||||
\(886\) | 7.11911e14 | 1.30394 | ||||||||
\(887\) | 8.10100e14i | 1.47544i | 0.675109 | + | 0.737718i | \(0.264097\pi\) | ||||
−0.675109 | + | 0.737718i | \(0.735903\pi\) | |||||||
\(888\) | −1.84349e14 | −0.333868 | ||||||||
\(889\) | 2.38069e14 | 0.428741 | ||||||||
\(890\) | 2.23414e14 | 0.400093 | ||||||||
\(891\) | − | 1.31528e13i | − | 0.0234223i | ||||||
\(892\) | −8.88575e14 | −1.57351 | ||||||||
\(893\) | 2.11937e14i | 0.373206i | ||||||||
\(894\) | 4.10756e14 | 0.719277 | ||||||||
\(895\) | 1.71577e14i | 0.298774i | ||||||||
\(896\) | 1.08502e14i | 0.187888i | ||||||||
\(897\) | −1.42023e14 | −0.244566 | ||||||||
\(898\) | − | 1.24512e14i | − | 0.213221i | ||||||
\(899\) | − | 4.49229e14i | − | 0.765014i | ||||||
\(900\) | 2.10036e14 | 0.355698 | ||||||||
\(901\) | 6.19089e14 | 1.04263 | ||||||||
\(902\) | −4.29209e13 | −0.0718847 | ||||||||
\(903\) | 8.66709e13i | 0.144356i | ||||||||
\(904\) | 4.25053e14 | 0.704047 | ||||||||
\(905\) | −5.32245e13 | −0.0876735 | ||||||||
\(906\) | 5.51610e14 | 0.903631 | ||||||||
\(907\) | 6.54803e14 | 1.06678 | 0.533389 | − | 0.845870i | \(-0.320918\pi\) | ||||
0.533389 | + | 0.845870i | \(0.320918\pi\) | |||||||
\(908\) | − | 1.16469e15i | − | 1.88704i | ||||||
\(909\) | 3.57665e13i | 0.0576311i | ||||||||
\(910\) | −1.02246e14 | −0.163847 | ||||||||
\(911\) | 9.35781e14 | 1.49136 | 0.745680 | − | 0.666304i | \(-0.232125\pi\) | ||||
0.745680 | + | 0.666304i | \(0.232125\pi\) | |||||||
\(912\) | 9.44432e13 | 0.149691 | ||||||||
\(913\) | 3.41195e13 | 0.0537835 | ||||||||
\(914\) | 1.43941e14 | 0.225659 | ||||||||
\(915\) | − | 2.31621e14i | − | 0.361137i | ||||||
\(916\) | 2.68143e13i | 0.0415805i | ||||||||
\(917\) | − | 9.94344e13i | − | 0.153352i | ||||||
\(918\) | − | 2.70331e14i | − | 0.414650i | ||||||
\(919\) | 3.53276e14i | 0.538936i | 0.963009 | + | 0.269468i | \(0.0868478\pi\) | ||||
−0.963009 | + | 0.269468i | \(0.913152\pi\) | |||||||
\(920\) | 3.74416e13 | 0.0568088 | ||||||||
\(921\) | 4.09966e14 | 0.618656 | ||||||||
\(922\) | 5.86677e14i | 0.880531i | ||||||||
\(923\) | − | 1.09332e15i | − | 1.63207i | ||||||
\(924\) | 2.59838e13i | 0.0385783i | ||||||||
\(925\) | 8.64021e14i | 1.27590i | ||||||||
\(926\) | 5.89113e14 | 0.865254 | ||||||||
\(927\) | − | 3.14663e13i | − | 0.0459671i | ||||||
\(928\) | − | 5.86768e14i | − | 0.852563i | ||||||
\(929\) | 3.90298e14i | 0.564050i | 0.959407 | + | 0.282025i | \(0.0910061\pi\) | ||||
−0.959407 | + | 0.282025i | \(0.908994\pi\) | |||||||
\(930\) | 2.94848e14 | 0.423822 | ||||||||
\(931\) | −2.50434e14 | −0.358051 | ||||||||
\(932\) | − | 1.36905e15i | − | 1.94688i | ||||||
\(933\) | −4.52200e14 | −0.639621 | ||||||||
\(934\) | 6.97306e14 | 0.981045 | ||||||||
\(935\) | − | 8.38513e13i | − | 0.117342i | ||||||
\(936\) | 1.02701e14 | 0.142954 | ||||||||
\(937\) | 1.18889e15i | 1.64605i | 0.568007 | + | 0.823024i | \(0.307715\pi\) | ||||
−0.568007 | + | 0.823024i | \(0.692285\pi\) | |||||||
\(938\) | −4.95434e14 | −0.682294 | ||||||||
\(939\) | − | 2.09442e14i | − | 0.286903i | ||||||
\(940\) | 3.49203e14i | 0.475816i | ||||||||
\(941\) | − | 4.85054e13i | − | 0.0657419i | −0.999460 | − | 0.0328709i | \(-0.989535\pi\) | ||
0.999460 | − | 0.0328709i | \(-0.0104650\pi\) | |||||||
\(942\) | 4.18061e14 | 0.563618 | ||||||||
\(943\) | 6.43717e13i | 0.0863250i | ||||||||
\(944\) | 2.61921e14 | + | 4.35600e14i | 0.349391 | + | 0.581069i | ||||
\(945\) | −1.42014e13 | −0.0188439 | ||||||||
\(946\) | − | 2.37728e14i | − | 0.313780i | ||||||
\(947\) | 6.03885e14 | 0.792874 | 0.396437 | − | 0.918062i | \(-0.370246\pi\) | ||||
0.396437 | + | 0.918062i | \(0.370246\pi\) | |||||||
\(948\) | 8.11699e12 | 0.0106012 | ||||||||
\(949\) | −3.53002e14 | −0.458612 | ||||||||
\(950\) | 3.77521e14i | 0.487891i | ||||||||
\(951\) | 6.21662e14 | 0.799194 | ||||||||
\(952\) | 1.08949e14i | 0.139328i | ||||||||
\(953\) | 5.64065e14 | 0.717570 | 0.358785 | − | 0.933420i | \(-0.383191\pi\) | ||||
0.358785 | + | 0.933420i | \(0.383191\pi\) | |||||||
\(954\) | 2.87595e14i | 0.363948i | ||||||||
\(955\) | − | 5.41672e14i | − | 0.681898i | ||||||
\(956\) | −6.96523e14 | −0.872260 | ||||||||
\(957\) | − | 5.93482e13i | − | 0.0739347i | ||||||
\(958\) | 1.31535e15i | 1.63010i | ||||||||
\(959\) | 5.09771e13 | 0.0628466 | ||||||||
\(960\) | 2.61254e14 | 0.320411 | ||||||||
\(961\) | −4.80195e14 | −0.585869 | ||||||||
\(962\) | 2.07092e15i | 2.51355i | ||||||||
\(963\) | 4.41358e14 | 0.532917 | ||||||||
\(964\) | −7.83561e14 | −0.941212 | ||||||||
\(965\) | −3.11932e13 | −0.0372755 | ||||||||
\(966\) | 6.99896e13 | 0.0832047 | ||||||||
\(967\) | − | 1.21479e14i | − | 0.143671i | −0.997416 | − | 0.0718356i | \(-0.977114\pi\) | ||
0.997416 | − | 0.0718356i | \(-0.0228857\pi\) | |||||||
\(968\) | 3.12657e14i | 0.367867i | ||||||||
\(969\) | 2.70544e14 | 0.316678 | ||||||||
\(970\) | −1.37001e14 | −0.159538 | ||||||||
\(971\) | 7.06931e14 | 0.818994 | 0.409497 | − | 0.912311i | \(-0.365704\pi\) | ||||
0.409497 | + | 0.912311i | \(0.365704\pi\) | |||||||
\(972\) | 6.99228e13 | 0.0805911 | ||||||||
\(973\) | 3.92580e14 | 0.450157 | ||||||||
\(974\) | − | 1.11461e15i | − | 1.27153i | ||||||
\(975\) | − | 4.81350e14i | − | 0.546309i | ||||||
\(976\) | 9.67863e14i | 1.09286i | ||||||||
\(977\) | − | 1.21808e15i | − | 1.36837i | −0.729310 | − | 0.684183i | \(-0.760159\pi\) | ||
0.729310 | − | 0.684183i | \(-0.239841\pi\) | |||||||
\(978\) | − | 1.28884e15i | − | 1.44047i | ||||||
\(979\) | −1.30118e14 | −0.144685 | ||||||||
\(980\) | −4.12635e14 | −0.456495 | ||||||||
\(981\) | 4.33105e14i | 0.476703i | ||||||||
\(982\) | 1.17699e15i | 1.28889i | ||||||||
\(983\) | − | 7.48886e12i | − | 0.00815921i | −0.999992 | − | 0.00407961i | \(-0.998701\pi\) | ||
0.999992 | − | 0.00407961i | \(-0.00129858\pi\) | |||||||
\(984\) | − | 4.65492e13i | − | 0.0504588i | ||||||
\(985\) | −2.15516e14 | −0.232433 | ||||||||
\(986\) | − | 1.21979e15i | − | 1.30888i | ||||||
\(987\) | 1.33168e14i | 0.142172i | ||||||||
\(988\) | 5.03819e14i | 0.535168i | ||||||||
\(989\) | −3.56539e14 | −0.376813 | ||||||||
\(990\) | 3.89528e13 | 0.0409602 | ||||||||
\(991\) | − | 9.80875e13i | − | 0.102623i | −0.998683 | − | 0.0513116i | \(-0.983660\pi\) | ||
0.998683 | − | 0.0513116i | \(-0.0163402\pi\) | |||||||
\(992\) | −1.69779e15 | −1.76736 | ||||||||
\(993\) | −6.11211e14 | −0.633060 | ||||||||
\(994\) | 5.38791e14i | 0.555250i | ||||||||
\(995\) | −6.51750e14 | −0.668291 | ||||||||
\(996\) | 1.81385e14i | 0.185057i | ||||||||
\(997\) | −1.66006e15 | −1.68519 | −0.842595 | − | 0.538548i | \(-0.818973\pi\) | ||||
−0.842595 | + | 0.538548i | \(0.818973\pi\) | |||||||
\(998\) | 9.39275e14i | 0.948724i | ||||||||
\(999\) | 2.87640e14i | 0.289083i |
(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 | 177.11.c.a.58.15 | ✓ | 100 | |
59.58 | odd | 2 | inner | 177.11.c.a.58.86 | yes | 100 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.11.c.a.58.15 | ✓ | 100 | 1.1 | even | 1 | trivial | |
177.11.c.a.58.86 | yes | 100 | 59.58 | odd | 2 | inner |