Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,14,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, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
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: | \(189.798744245\) |
Analytic rank: | \(1\) |
Dimension: | \(30\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.22 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 76.7885 | 0.848401 | 0.424200 | − | 0.905568i | \(-0.360555\pi\) | ||||
0.424200 | + | 0.905568i | \(0.360555\pi\) | |||||||
\(3\) | 729.000 | 0.577350 | ||||||||
\(4\) | −2295.53 | −0.280217 | ||||||||
\(5\) | 8611.65 | 0.246480 | 0.123240 | − | 0.992377i | \(-0.460672\pi\) | ||||
0.123240 | + | 0.992377i | \(0.460672\pi\) | |||||||
\(6\) | 55978.8 | 0.489824 | ||||||||
\(7\) | 343688. | 1.10415 | 0.552074 | − | 0.833795i | \(-0.313837\pi\) | ||||
0.552074 | + | 0.833795i | \(0.313837\pi\) | |||||||
\(8\) | −805321. | −1.08614 | ||||||||
\(9\) | 531441. | 0.333333 | ||||||||
\(10\) | 661275. | 0.209114 | ||||||||
\(11\) | 2.10913e6 | 0.358963 | 0.179482 | − | 0.983761i | \(-0.442558\pi\) | ||||
0.179482 | + | 0.983761i | \(0.442558\pi\) | |||||||
\(12\) | −1.67344e6 | −0.161783 | ||||||||
\(13\) | 1.64154e7 | 0.943236 | 0.471618 | − | 0.881803i | \(-0.343670\pi\) | ||||
0.471618 | + | 0.881803i | \(0.343670\pi\) | |||||||
\(14\) | 2.63913e7 | 0.936760 | ||||||||
\(15\) | 6.27789e6 | 0.142305 | ||||||||
\(16\) | −4.30344e7 | −0.641262 | ||||||||
\(17\) | −1.54112e8 | −1.54852 | −0.774261 | − | 0.632867i | \(-0.781878\pi\) | ||||
−0.774261 | + | 0.632867i | \(0.781878\pi\) | |||||||
\(18\) | 4.08085e7 | 0.282800 | ||||||||
\(19\) | −1.40672e8 | −0.685975 | −0.342987 | − | 0.939340i | \(-0.611439\pi\) | ||||
−0.342987 | + | 0.939340i | \(0.611439\pi\) | |||||||
\(20\) | −1.97683e7 | −0.0690677 | ||||||||
\(21\) | 2.50549e8 | 0.637480 | ||||||||
\(22\) | 1.61957e8 | 0.304545 | ||||||||
\(23\) | −7.50683e8 | −1.05737 | −0.528683 | − | 0.848819i | \(-0.677314\pi\) | ||||
−0.528683 | + | 0.848819i | \(0.677314\pi\) | |||||||
\(24\) | −5.87079e8 | −0.627081 | ||||||||
\(25\) | −1.14654e9 | −0.939248 | ||||||||
\(26\) | 1.26052e9 | 0.800242 | ||||||||
\(27\) | 3.87420e8 | 0.192450 | ||||||||
\(28\) | −7.88948e8 | −0.309400 | ||||||||
\(29\) | −5.30324e9 | −1.65560 | −0.827798 | − | 0.561027i | \(-0.810406\pi\) | ||||
−0.827798 | + | 0.561027i | \(0.810406\pi\) | |||||||
\(30\) | 4.82070e8 | 0.120732 | ||||||||
\(31\) | 6.09654e9 | 1.23376 | 0.616882 | − | 0.787055i | \(-0.288395\pi\) | ||||
0.616882 | + | 0.787055i | \(0.288395\pi\) | |||||||
\(32\) | 3.29265e9 | 0.542089 | ||||||||
\(33\) | 1.53755e9 | 0.207248 | ||||||||
\(34\) | −1.18340e10 | −1.31377 | ||||||||
\(35\) | 2.95972e9 | 0.272150 | ||||||||
\(36\) | −1.21994e9 | −0.0934055 | ||||||||
\(37\) | 1.01295e10 | 0.649050 | 0.324525 | − | 0.945877i | \(-0.394796\pi\) | ||||
0.324525 | + | 0.945877i | \(0.394796\pi\) | |||||||
\(38\) | −1.08020e10 | −0.581981 | ||||||||
\(39\) | 1.19668e10 | 0.544578 | ||||||||
\(40\) | −6.93514e9 | −0.267711 | ||||||||
\(41\) | −2.18330e8 | −0.00717824 | −0.00358912 | − | 0.999994i | \(-0.501142\pi\) | ||||
−0.00358912 | + | 0.999994i | \(0.501142\pi\) | |||||||
\(42\) | 1.92392e10 | 0.540838 | ||||||||
\(43\) | 6.90652e9 | 0.166615 | 0.0833075 | − | 0.996524i | \(-0.473452\pi\) | ||||
0.0833075 | + | 0.996524i | \(0.473452\pi\) | |||||||
\(44\) | −4.84157e9 | −0.100587 | ||||||||
\(45\) | 4.57658e9 | 0.0821599 | ||||||||
\(46\) | −5.76438e10 | −0.897070 | ||||||||
\(47\) | −7.05108e10 | −0.954156 | −0.477078 | − | 0.878861i | \(-0.658304\pi\) | ||||
−0.477078 | + | 0.878861i | \(0.658304\pi\) | |||||||
\(48\) | −3.13721e10 | −0.370233 | ||||||||
\(49\) | 2.12325e10 | 0.219142 | ||||||||
\(50\) | −8.80412e10 | −0.796858 | ||||||||
\(51\) | −1.12347e11 | −0.894039 | ||||||||
\(52\) | −3.76822e10 | −0.264310 | ||||||||
\(53\) | 1.26195e11 | 0.782079 | 0.391039 | − | 0.920374i | \(-0.372116\pi\) | ||||
0.391039 | + | 0.920374i | \(0.372116\pi\) | |||||||
\(54\) | 2.97494e10 | 0.163275 | ||||||||
\(55\) | 1.81631e10 | 0.0884772 | ||||||||
\(56\) | −2.76779e11 | −1.19926 | ||||||||
\(57\) | −1.02550e11 | −0.396048 | ||||||||
\(58\) | −4.07227e11 | −1.40461 | ||||||||
\(59\) | 4.21805e10 | 0.130189 | ||||||||
\(60\) | −1.44111e10 | −0.0398763 | ||||||||
\(61\) | 3.47997e11 | 0.864831 | 0.432416 | − | 0.901674i | \(-0.357661\pi\) | ||||
0.432416 | + | 0.901674i | \(0.357661\pi\) | |||||||
\(62\) | 4.68144e11 | 1.04673 | ||||||||
\(63\) | 1.82650e11 | 0.368049 | ||||||||
\(64\) | 6.05375e11 | 1.10117 | ||||||||
\(65\) | 1.41364e11 | 0.232489 | ||||||||
\(66\) | 1.18066e11 | 0.175829 | ||||||||
\(67\) | 7.19021e11 | 0.971081 | 0.485541 | − | 0.874214i | \(-0.338623\pi\) | ||||
0.485541 | + | 0.874214i | \(0.338623\pi\) | |||||||
\(68\) | 3.53768e11 | 0.433921 | ||||||||
\(69\) | −5.47248e11 | −0.610471 | ||||||||
\(70\) | 2.27272e11 | 0.230892 | ||||||||
\(71\) | −1.79801e12 | −1.66576 | −0.832879 | − | 0.553455i | \(-0.813309\pi\) | ||||
−0.832879 | + | 0.553455i | \(0.813309\pi\) | |||||||
\(72\) | −4.27981e11 | −0.362045 | ||||||||
\(73\) | −6.59872e11 | −0.510342 | −0.255171 | − | 0.966896i | \(-0.582132\pi\) | ||||
−0.255171 | + | 0.966896i | \(0.582132\pi\) | |||||||
\(74\) | 7.77831e11 | 0.550654 | ||||||||
\(75\) | −8.35830e11 | −0.542275 | ||||||||
\(76\) | 3.22916e11 | 0.192221 | ||||||||
\(77\) | 7.24882e11 | 0.396349 | ||||||||
\(78\) | 9.18915e11 | 0.462020 | ||||||||
\(79\) | 6.24170e11 | 0.288886 | 0.144443 | − | 0.989513i | \(-0.453861\pi\) | ||||
0.144443 | + | 0.989513i | \(0.453861\pi\) | |||||||
\(80\) | −3.70597e11 | −0.158058 | ||||||||
\(81\) | 2.82430e11 | 0.111111 | ||||||||
\(82\) | −1.67652e10 | −0.00609003 | ||||||||
\(83\) | −3.14870e12 | −1.05712 | −0.528560 | − | 0.848896i | \(-0.677268\pi\) | ||||
−0.528560 | + | 0.848896i | \(0.677268\pi\) | |||||||
\(84\) | −5.75143e11 | −0.178632 | ||||||||
\(85\) | −1.32715e12 | −0.381679 | ||||||||
\(86\) | 5.30341e11 | 0.141356 | ||||||||
\(87\) | −3.86606e12 | −0.955858 | ||||||||
\(88\) | −1.69852e12 | −0.389883 | ||||||||
\(89\) | −5.10394e12 | −1.08861 | −0.544303 | − | 0.838889i | \(-0.683206\pi\) | ||||
−0.544303 | + | 0.838889i | \(0.683206\pi\) | |||||||
\(90\) | 3.51429e11 | 0.0697045 | ||||||||
\(91\) | 5.64179e12 | 1.04147 | ||||||||
\(92\) | 1.72322e12 | 0.296292 | ||||||||
\(93\) | 4.44438e12 | 0.712314 | ||||||||
\(94\) | −5.41441e12 | −0.809507 | ||||||||
\(95\) | −1.21141e12 | −0.169079 | ||||||||
\(96\) | 2.40034e12 | 0.312975 | ||||||||
\(97\) | 2.84901e12 | 0.347278 | 0.173639 | − | 0.984809i | \(-0.444447\pi\) | ||||
0.173639 | + | 0.984809i | \(0.444447\pi\) | |||||||
\(98\) | 1.63041e12 | 0.185920 | ||||||||
\(99\) | 1.12088e12 | 0.119654 | ||||||||
\(100\) | 2.63193e12 | 0.263193 | ||||||||
\(101\) | −1.38799e13 | −1.30106 | −0.650529 | − | 0.759481i | \(-0.725453\pi\) | ||||
−0.650529 | + | 0.759481i | \(0.725453\pi\) | |||||||
\(102\) | −8.62698e12 | −0.758504 | ||||||||
\(103\) | 4.18122e12 | 0.345033 | 0.172517 | − | 0.985007i | \(-0.444810\pi\) | ||||
0.172517 | + | 0.985007i | \(0.444810\pi\) | |||||||
\(104\) | −1.32197e13 | −1.02448 | ||||||||
\(105\) | 2.15764e12 | 0.157126 | ||||||||
\(106\) | 9.69035e12 | 0.663516 | ||||||||
\(107\) | −2.51194e13 | −1.61813 | −0.809067 | − | 0.587717i | \(-0.800027\pi\) | ||||
−0.809067 | + | 0.587717i | \(0.800027\pi\) | |||||||
\(108\) | −8.89337e11 | −0.0539277 | ||||||||
\(109\) | −2.51900e13 | −1.43865 | −0.719327 | − | 0.694672i | \(-0.755550\pi\) | ||||
−0.719327 | + | 0.694672i | \(0.755550\pi\) | |||||||
\(110\) | 1.39471e12 | 0.0750641 | ||||||||
\(111\) | 7.38443e12 | 0.374729 | ||||||||
\(112\) | −1.47904e13 | −0.708048 | ||||||||
\(113\) | −3.23342e13 | −1.46101 | −0.730504 | − | 0.682909i | \(-0.760715\pi\) | ||||
−0.730504 | + | 0.682909i | \(0.760715\pi\) | |||||||
\(114\) | −7.87463e12 | −0.336007 | ||||||||
\(115\) | −6.46462e12 | −0.260619 | ||||||||
\(116\) | 1.21738e13 | 0.463925 | ||||||||
\(117\) | 8.72383e12 | 0.314412 | ||||||||
\(118\) | 3.23898e12 | 0.110452 | ||||||||
\(119\) | −5.29663e13 | −1.70980 | ||||||||
\(120\) | −5.05572e12 | −0.154563 | ||||||||
\(121\) | −3.00743e13 | −0.871145 | ||||||||
\(122\) | 2.67221e13 | 0.733723 | ||||||||
\(123\) | −1.59163e11 | −0.00414436 | ||||||||
\(124\) | −1.39948e13 | −0.345721 | ||||||||
\(125\) | −2.03859e13 | −0.477985 | ||||||||
\(126\) | 1.40254e13 | 0.312253 | ||||||||
\(127\) | 6.21896e13 | 1.31521 | 0.657603 | − | 0.753364i | \(-0.271570\pi\) | ||||
0.657603 | + | 0.753364i | \(0.271570\pi\) | |||||||
\(128\) | 1.95124e13 | 0.392145 | ||||||||
\(129\) | 5.03485e12 | 0.0961953 | ||||||||
\(130\) | 1.08551e13 | 0.197243 | ||||||||
\(131\) | −2.18425e13 | −0.377606 | −0.188803 | − | 0.982015i | \(-0.560461\pi\) | ||||
−0.188803 | + | 0.982015i | \(0.560461\pi\) | |||||||
\(132\) | −3.52951e12 | −0.0580742 | ||||||||
\(133\) | −4.83472e13 | −0.757417 | ||||||||
\(134\) | 5.52125e13 | 0.823866 | ||||||||
\(135\) | 3.33633e12 | 0.0474350 | ||||||||
\(136\) | 1.24109e14 | 1.68191 | ||||||||
\(137\) | 6.08541e13 | 0.786332 | 0.393166 | − | 0.919467i | \(-0.371380\pi\) | ||||
0.393166 | + | 0.919467i | \(0.371380\pi\) | |||||||
\(138\) | −4.20223e13 | −0.517924 | ||||||||
\(139\) | 3.74691e13 | 0.440633 | 0.220317 | − | 0.975428i | \(-0.429291\pi\) | ||||
0.220317 | + | 0.975428i | \(0.429291\pi\) | |||||||
\(140\) | −6.79414e12 | −0.0762609 | ||||||||
\(141\) | −5.14024e13 | −0.550882 | ||||||||
\(142\) | −1.38066e14 | −1.41323 | ||||||||
\(143\) | 3.46222e13 | 0.338587 | ||||||||
\(144\) | −2.28702e13 | −0.213754 | ||||||||
\(145\) | −4.56696e13 | −0.408071 | ||||||||
\(146\) | −5.06706e13 | −0.432974 | ||||||||
\(147\) | 1.54785e13 | 0.126522 | ||||||||
\(148\) | −2.32527e13 | −0.181875 | ||||||||
\(149\) | −1.78413e13 | −0.133572 | −0.0667861 | − | 0.997767i | \(-0.521275\pi\) | ||||
−0.0667861 | + | 0.997767i | \(0.521275\pi\) | |||||||
\(150\) | −6.41821e13 | −0.460066 | ||||||||
\(151\) | −1.23097e14 | −0.845080 | −0.422540 | − | 0.906344i | \(-0.638861\pi\) | ||||
−0.422540 | + | 0.906344i | \(0.638861\pi\) | |||||||
\(152\) | 1.13286e14 | 0.745062 | ||||||||
\(153\) | −8.19012e13 | −0.516174 | ||||||||
\(154\) | 5.56625e13 | 0.336262 | ||||||||
\(155\) | 5.25012e13 | 0.304098 | ||||||||
\(156\) | −2.74703e13 | −0.152600 | ||||||||
\(157\) | −8.41553e13 | −0.448470 | −0.224235 | − | 0.974535i | \(-0.571988\pi\) | ||||
−0.224235 | + | 0.974535i | \(0.571988\pi\) | |||||||
\(158\) | 4.79290e13 | 0.245091 | ||||||||
\(159\) | 9.19965e13 | 0.451533 | ||||||||
\(160\) | 2.83551e13 | 0.133614 | ||||||||
\(161\) | −2.58001e14 | −1.16749 | ||||||||
\(162\) | 2.16873e13 | 0.0942667 | ||||||||
\(163\) | 2.96776e14 | 1.23939 | 0.619697 | − | 0.784841i | \(-0.287256\pi\) | ||||
0.619697 | + | 0.784841i | \(0.287256\pi\) | |||||||
\(164\) | 5.01184e11 | 0.00201146 | ||||||||
\(165\) | 1.32409e13 | 0.0510823 | ||||||||
\(166\) | −2.41784e14 | −0.896861 | ||||||||
\(167\) | −7.20047e13 | −0.256864 | −0.128432 | − | 0.991718i | \(-0.540994\pi\) | ||||
−0.128432 | + | 0.991718i | \(0.540994\pi\) | |||||||
\(168\) | −2.01772e14 | −0.692390 | ||||||||
\(169\) | −3.34089e13 | −0.110306 | ||||||||
\(170\) | −1.01910e14 | −0.323817 | ||||||||
\(171\) | −7.47587e13 | −0.228658 | ||||||||
\(172\) | −1.58541e13 | −0.0466883 | ||||||||
\(173\) | 4.81605e12 | 0.0136581 | 0.00682907 | − | 0.999977i | \(-0.497826\pi\) | ||||
0.00682907 | + | 0.999977i | \(0.497826\pi\) | |||||||
\(174\) | −2.96869e14 | −0.810951 | ||||||||
\(175\) | −3.94053e14 | −1.03707 | ||||||||
\(176\) | −9.07649e13 | −0.230190 | ||||||||
\(177\) | 3.07496e13 | 0.0751646 | ||||||||
\(178\) | −3.91924e14 | −0.923574 | ||||||||
\(179\) | 7.75206e13 | 0.176146 | 0.0880729 | − | 0.996114i | \(-0.471929\pi\) | ||||
0.0880729 | + | 0.996114i | \(0.471929\pi\) | |||||||
\(180\) | −1.05057e13 | −0.0230226 | ||||||||
\(181\) | −6.20019e14 | −1.31067 | −0.655336 | − | 0.755337i | \(-0.727473\pi\) | ||||
−0.655336 | + | 0.755337i | \(0.727473\pi\) | |||||||
\(182\) | 4.33224e14 | 0.883585 | ||||||||
\(183\) | 2.53690e14 | 0.499311 | ||||||||
\(184\) | 6.04541e14 | 1.14844 | ||||||||
\(185\) | 8.72320e13 | 0.159978 | ||||||||
\(186\) | 3.41277e14 | 0.604328 | ||||||||
\(187\) | −3.25041e14 | −0.555863 | ||||||||
\(188\) | 1.61860e14 | 0.267370 | ||||||||
\(189\) | 1.33152e14 | 0.212493 | ||||||||
\(190\) | −9.30226e13 | −0.143447 | ||||||||
\(191\) | −1.03485e14 | −0.154228 | −0.0771139 | − | 0.997022i | \(-0.524571\pi\) | ||||
−0.0771139 | + | 0.997022i | \(0.524571\pi\) | |||||||
\(192\) | 4.41318e14 | 0.635761 | ||||||||
\(193\) | −7.29182e14 | −1.01558 | −0.507789 | − | 0.861481i | \(-0.669537\pi\) | ||||
−0.507789 | + | 0.861481i | \(0.669537\pi\) | |||||||
\(194\) | 2.18771e14 | 0.294631 | ||||||||
\(195\) | 1.03054e14 | 0.134227 | ||||||||
\(196\) | −4.87399e13 | −0.0614073 | ||||||||
\(197\) | 1.49693e15 | 1.82462 | 0.912308 | − | 0.409504i | \(-0.134298\pi\) | ||||
0.912308 | + | 0.409504i | \(0.134298\pi\) | |||||||
\(198\) | 8.60704e13 | 0.101515 | ||||||||
\(199\) | 8.30367e14 | 0.947819 | 0.473909 | − | 0.880574i | \(-0.342842\pi\) | ||||
0.473909 | + | 0.880574i | \(0.342842\pi\) | |||||||
\(200\) | 9.23335e14 | 1.02015 | ||||||||
\(201\) | 5.24167e14 | 0.560654 | ||||||||
\(202\) | −1.06581e15 | −1.10382 | ||||||||
\(203\) | −1.82266e15 | −1.82802 | ||||||||
\(204\) | 2.57897e14 | 0.250525 | ||||||||
\(205\) | −1.88018e12 | −0.00176929 | ||||||||
\(206\) | 3.21069e14 | 0.292727 | ||||||||
\(207\) | −3.98944e14 | −0.352455 | ||||||||
\(208\) | −7.06428e14 | −0.604862 | ||||||||
\(209\) | −2.96694e14 | −0.246240 | ||||||||
\(210\) | 1.65682e14 | 0.133306 | ||||||||
\(211\) | −1.71589e15 | −1.33861 | −0.669306 | − | 0.742987i | \(-0.733408\pi\) | ||||
−0.669306 | + | 0.742987i | \(0.733408\pi\) | |||||||
\(212\) | −2.89686e14 | −0.219151 | ||||||||
\(213\) | −1.31075e15 | −0.961726 | ||||||||
\(214\) | −1.92888e15 | −1.37283 | ||||||||
\(215\) | 5.94765e13 | 0.0410672 | ||||||||
\(216\) | −3.11998e14 | −0.209027 | ||||||||
\(217\) | 2.09531e15 | 1.36226 | ||||||||
\(218\) | −1.93430e15 | −1.22055 | ||||||||
\(219\) | −4.81047e14 | −0.294646 | ||||||||
\(220\) | −4.16939e13 | −0.0247928 | ||||||||
\(221\) | −2.52981e15 | −1.46062 | ||||||||
\(222\) | 5.67039e14 | 0.317921 | ||||||||
\(223\) | 4.75904e14 | 0.259142 | 0.129571 | − | 0.991570i | \(-0.458640\pi\) | ||||
0.129571 | + | 0.991570i | \(0.458640\pi\) | |||||||
\(224\) | 1.13164e15 | 0.598547 | ||||||||
\(225\) | −6.09320e14 | −0.313083 | ||||||||
\(226\) | −2.48289e15 | −1.23952 | ||||||||
\(227\) | 2.78931e14 | 0.135310 | 0.0676548 | − | 0.997709i | \(-0.478448\pi\) | ||||
0.0676548 | + | 0.997709i | \(0.478448\pi\) | |||||||
\(228\) | 2.35406e14 | 0.110979 | ||||||||
\(229\) | 3.77467e15 | 1.72961 | 0.864805 | − | 0.502107i | \(-0.167442\pi\) | ||||
0.864805 | + | 0.502107i | \(0.167442\pi\) | |||||||
\(230\) | −4.96408e14 | −0.221110 | ||||||||
\(231\) | 5.28439e14 | 0.228832 | ||||||||
\(232\) | 4.27081e15 | 1.79820 | ||||||||
\(233\) | 2.36280e15 | 0.967418 | 0.483709 | − | 0.875229i | \(-0.339289\pi\) | ||||
0.483709 | + | 0.875229i | \(0.339289\pi\) | |||||||
\(234\) | 6.69889e14 | 0.266747 | ||||||||
\(235\) | −6.07214e14 | −0.235180 | ||||||||
\(236\) | −9.68268e13 | −0.0364811 | ||||||||
\(237\) | 4.55020e14 | 0.166788 | ||||||||
\(238\) | −4.06720e15 | −1.45059 | ||||||||
\(239\) | −3.91248e15 | −1.35789 | −0.678947 | − | 0.734187i | \(-0.737564\pi\) | ||||
−0.678947 | + | 0.734187i | \(0.737564\pi\) | |||||||
\(240\) | −2.70165e14 | −0.0912549 | ||||||||
\(241\) | −1.97175e15 | −0.648248 | −0.324124 | − | 0.946015i | \(-0.605070\pi\) | ||||
−0.324124 | + | 0.946015i | \(0.605070\pi\) | |||||||
\(242\) | −2.30936e15 | −0.739080 | ||||||||
\(243\) | 2.05891e14 | 0.0641500 | ||||||||
\(244\) | −7.98839e14 | −0.242340 | ||||||||
\(245\) | 1.82847e14 | 0.0540141 | ||||||||
\(246\) | −1.22218e13 | −0.00351608 | ||||||||
\(247\) | −2.30918e15 | −0.647036 | ||||||||
\(248\) | −4.90967e15 | −1.34004 | ||||||||
\(249\) | −2.29541e15 | −0.610328 | ||||||||
\(250\) | −1.56540e15 | −0.405523 | ||||||||
\(251\) | −1.67742e15 | −0.423412 | −0.211706 | − | 0.977333i | \(-0.567902\pi\) | ||||
−0.211706 | + | 0.977333i | \(0.567902\pi\) | |||||||
\(252\) | −4.19279e14 | −0.103133 | ||||||||
\(253\) | −1.58328e15 | −0.379556 | ||||||||
\(254\) | 4.77545e15 | 1.11582 | ||||||||
\(255\) | −9.67496e14 | −0.220363 | ||||||||
\(256\) | −3.46090e15 | −0.768475 | ||||||||
\(257\) | 6.30357e15 | 1.36465 | 0.682325 | − | 0.731049i | \(-0.260969\pi\) | ||||
0.682325 | + | 0.731049i | \(0.260969\pi\) | |||||||
\(258\) | 3.86619e14 | 0.0816121 | ||||||||
\(259\) | 3.48140e15 | 0.716647 | ||||||||
\(260\) | −3.24506e14 | −0.0651471 | ||||||||
\(261\) | −2.81836e15 | −0.551865 | ||||||||
\(262\) | −1.67725e15 | −0.320361 | ||||||||
\(263\) | 2.60734e15 | 0.485832 | 0.242916 | − | 0.970047i | \(-0.421896\pi\) | ||||
0.242916 | + | 0.970047i | \(0.421896\pi\) | |||||||
\(264\) | −1.23822e15 | −0.225099 | ||||||||
\(265\) | 1.08675e15 | 0.192767 | ||||||||
\(266\) | −3.71250e15 | −0.642593 | ||||||||
\(267\) | −3.72077e15 | −0.628507 | ||||||||
\(268\) | −1.65054e15 | −0.272113 | ||||||||
\(269\) | −1.09355e15 | −0.175974 | −0.0879868 | − | 0.996122i | \(-0.528043\pi\) | ||||
−0.0879868 | + | 0.996122i | \(0.528043\pi\) | |||||||
\(270\) | 2.56192e14 | 0.0402439 | ||||||||
\(271\) | 8.18155e15 | 1.25469 | 0.627343 | − | 0.778743i | \(-0.284142\pi\) | ||||
0.627343 | + | 0.778743i | \(0.284142\pi\) | |||||||
\(272\) | 6.63210e15 | 0.993008 | ||||||||
\(273\) | 4.11286e15 | 0.601294 | ||||||||
\(274\) | 4.67289e15 | 0.667125 | ||||||||
\(275\) | −2.41820e15 | −0.337156 | ||||||||
\(276\) | 1.25623e15 | 0.171064 | ||||||||
\(277\) | −6.43750e15 | −0.856247 | −0.428123 | − | 0.903720i | \(-0.640825\pi\) | ||||
−0.428123 | + | 0.903720i | \(0.640825\pi\) | |||||||
\(278\) | 2.87720e15 | 0.373834 | ||||||||
\(279\) | 3.23995e15 | 0.411255 | ||||||||
\(280\) | −2.38353e15 | −0.295592 | ||||||||
\(281\) | −9.95467e15 | −1.20625 | −0.603123 | − | 0.797648i | \(-0.706077\pi\) | ||||
−0.603123 | + | 0.797648i | \(0.706077\pi\) | |||||||
\(282\) | −3.94711e15 | −0.467369 | ||||||||
\(283\) | 3.16274e14 | 0.0365976 | 0.0182988 | − | 0.999833i | \(-0.494175\pi\) | ||||
0.0182988 | + | 0.999833i | \(0.494175\pi\) | |||||||
\(284\) | 4.12739e15 | 0.466773 | ||||||||
\(285\) | −8.83121e14 | −0.0976177 | ||||||||
\(286\) | 2.65859e15 | 0.287258 | ||||||||
\(287\) | −7.50374e13 | −0.00792584 | ||||||||
\(288\) | 1.74985e15 | 0.180696 | ||||||||
\(289\) | 1.38458e16 | 1.39792 | ||||||||
\(290\) | −3.50690e15 | −0.346207 | ||||||||
\(291\) | 2.07693e15 | 0.200501 | ||||||||
\(292\) | 1.51476e15 | 0.143006 | ||||||||
\(293\) | −1.80488e16 | −1.66652 | −0.833258 | − | 0.552885i | \(-0.813527\pi\) | ||||
−0.833258 | + | 0.552885i | \(0.813527\pi\) | |||||||
\(294\) | 1.18857e15 | 0.107341 | ||||||||
\(295\) | 3.63244e14 | 0.0320889 | ||||||||
\(296\) | −8.15753e15 | −0.704957 | ||||||||
\(297\) | 8.17119e14 | 0.0690825 | ||||||||
\(298\) | −1.37001e15 | −0.113323 | ||||||||
\(299\) | −1.23228e16 | −0.997346 | ||||||||
\(300\) | 1.91868e15 | 0.151954 | ||||||||
\(301\) | 2.37369e15 | 0.183968 | ||||||||
\(302\) | −9.45244e15 | −0.716966 | ||||||||
\(303\) | −1.01184e16 | −0.751166 | ||||||||
\(304\) | 6.05372e15 | 0.439890 | ||||||||
\(305\) | 2.99683e15 | 0.213163 | ||||||||
\(306\) | −6.28907e15 | −0.437922 | ||||||||
\(307\) | −9.77787e15 | −0.666568 | −0.333284 | − | 0.942826i | \(-0.608157\pi\) | ||||
−0.333284 | + | 0.942826i | \(0.608157\pi\) | |||||||
\(308\) | −1.66399e15 | −0.111063 | ||||||||
\(309\) | 3.04811e15 | 0.199205 | ||||||||
\(310\) | 4.03149e15 | 0.257997 | ||||||||
\(311\) | 9.68949e15 | 0.607237 | 0.303618 | − | 0.952794i | \(-0.401805\pi\) | ||||
0.303618 | + | 0.952794i | \(0.401805\pi\) | |||||||
\(312\) | −9.63716e15 | −0.591485 | ||||||||
\(313\) | −2.56809e16 | −1.54373 | −0.771867 | − | 0.635785i | \(-0.780677\pi\) | ||||
−0.771867 | + | 0.635785i | \(0.780677\pi\) | |||||||
\(314\) | −6.46215e15 | −0.380482 | ||||||||
\(315\) | 1.57292e15 | 0.0907167 | ||||||||
\(316\) | −1.43280e15 | −0.0809506 | ||||||||
\(317\) | 2.06363e15 | 0.114221 | 0.0571105 | − | 0.998368i | \(-0.481811\pi\) | ||||
0.0571105 | + | 0.998368i | \(0.481811\pi\) | |||||||
\(318\) | 7.06427e15 | 0.383081 | ||||||||
\(319\) | −1.11852e16 | −0.594298 | ||||||||
\(320\) | 5.21328e15 | 0.271416 | ||||||||
\(321\) | −1.83120e16 | −0.934230 | ||||||||
\(322\) | −1.98115e16 | −0.990498 | ||||||||
\(323\) | 2.16791e16 | 1.06225 | ||||||||
\(324\) | −6.48327e14 | −0.0311352 | ||||||||
\(325\) | −1.88210e16 | −0.885932 | ||||||||
\(326\) | 2.27890e16 | 1.05150 | ||||||||
\(327\) | −1.83635e16 | −0.830607 | ||||||||
\(328\) | 1.75826e14 | 0.00779655 | ||||||||
\(329\) | −2.42337e16 | −1.05353 | ||||||||
\(330\) | 1.01675e15 | 0.0433383 | ||||||||
\(331\) | −3.78462e16 | −1.58176 | −0.790879 | − | 0.611972i | \(-0.790376\pi\) | ||||
−0.790879 | + | 0.611972i | \(0.790376\pi\) | |||||||
\(332\) | 7.22796e15 | 0.296222 | ||||||||
\(333\) | 5.38325e15 | 0.216350 | ||||||||
\(334\) | −5.52913e15 | −0.217924 | ||||||||
\(335\) | 6.19196e15 | 0.239352 | ||||||||
\(336\) | −1.07822e16 | −0.408792 | ||||||||
\(337\) | −4.52293e16 | −1.68200 | −0.840999 | − | 0.541037i | \(-0.818032\pi\) | ||||
−0.840999 | + | 0.541037i | \(0.818032\pi\) | |||||||
\(338\) | −2.56542e15 | −0.0935837 | ||||||||
\(339\) | −2.35716e16 | −0.843513 | ||||||||
\(340\) | 3.04653e15 | 0.106953 | ||||||||
\(341\) | 1.28584e16 | 0.442876 | ||||||||
\(342\) | −5.74060e15 | −0.193994 | ||||||||
\(343\) | −2.60022e16 | −0.862182 | ||||||||
\(344\) | −5.56197e15 | −0.180967 | ||||||||
\(345\) | −4.71270e15 | −0.150469 | ||||||||
\(346\) | 3.69817e14 | 0.0115876 | ||||||||
\(347\) | 4.54759e16 | 1.39843 | 0.699213 | − | 0.714914i | \(-0.253534\pi\) | ||||
0.699213 | + | 0.714914i | \(0.253534\pi\) | |||||||
\(348\) | 8.87467e15 | 0.267847 | ||||||||
\(349\) | 1.79338e16 | 0.531259 | 0.265629 | − | 0.964075i | \(-0.414420\pi\) | ||||
0.265629 | + | 0.964075i | \(0.414420\pi\) | |||||||
\(350\) | −3.02587e16 | −0.879849 | ||||||||
\(351\) | 6.35967e15 | 0.181526 | ||||||||
\(352\) | 6.94462e15 | 0.194590 | ||||||||
\(353\) | 5.08417e16 | 1.39857 | 0.699285 | − | 0.714843i | \(-0.253502\pi\) | ||||
0.699285 | + | 0.714843i | \(0.253502\pi\) | |||||||
\(354\) | 2.36121e15 | 0.0637697 | ||||||||
\(355\) | −1.54838e16 | −0.410576 | ||||||||
\(356\) | 1.17163e16 | 0.305045 | ||||||||
\(357\) | −3.86124e16 | −0.987152 | ||||||||
\(358\) | 5.95268e15 | 0.149442 | ||||||||
\(359\) | 3.52166e16 | 0.868227 | 0.434113 | − | 0.900858i | \(-0.357062\pi\) | ||||
0.434113 | + | 0.900858i | \(0.357062\pi\) | |||||||
\(360\) | −3.68562e15 | −0.0892369 | ||||||||
\(361\) | −2.22645e16 | −0.529439 | ||||||||
\(362\) | −4.76103e16 | −1.11197 | ||||||||
\(363\) | −2.19242e16 | −0.502956 | ||||||||
\(364\) | −1.29509e16 | −0.291838 | ||||||||
\(365\) | −5.68259e15 | −0.125789 | ||||||||
\(366\) | 1.94804e16 | 0.423615 | ||||||||
\(367\) | −2.18731e15 | −0.0467283 | −0.0233642 | − | 0.999727i | \(-0.507438\pi\) | ||||
−0.0233642 | + | 0.999727i | \(0.507438\pi\) | |||||||
\(368\) | 3.23052e16 | 0.678049 | ||||||||
\(369\) | −1.16029e14 | −0.00239275 | ||||||||
\(370\) | 6.69841e15 | 0.135725 | ||||||||
\(371\) | 4.33719e16 | 0.863530 | ||||||||
\(372\) | −1.02022e16 | −0.199602 | ||||||||
\(373\) | 3.93006e16 | 0.755600 | 0.377800 | − | 0.925887i | \(-0.376681\pi\) | ||||
0.377800 | + | 0.925887i | \(0.376681\pi\) | |||||||
\(374\) | −2.49594e16 | −0.471594 | ||||||||
\(375\) | −1.48613e16 | −0.275965 | ||||||||
\(376\) | 5.67839e16 | 1.03634 | ||||||||
\(377\) | −8.70549e16 | −1.56162 | ||||||||
\(378\) | 1.02245e16 | 0.180279 | ||||||||
\(379\) | −1.24895e15 | −0.0216467 | −0.0108234 | − | 0.999941i | \(-0.503445\pi\) | ||||
−0.0108234 | + | 0.999941i | \(0.503445\pi\) | |||||||
\(380\) | 2.78084e15 | 0.0473787 | ||||||||
\(381\) | 4.53363e16 | 0.759335 | ||||||||
\(382\) | −7.94649e15 | −0.130847 | ||||||||
\(383\) | 1.51746e15 | 0.0245655 | 0.0122827 | − | 0.999925i | \(-0.496090\pi\) | ||||
0.0122827 | + | 0.999925i | \(0.496090\pi\) | |||||||
\(384\) | 1.42246e16 | 0.226405 | ||||||||
\(385\) | 6.24243e15 | 0.0976919 | ||||||||
\(386\) | −5.59928e16 | −0.861617 | ||||||||
\(387\) | 3.67041e15 | 0.0555384 | ||||||||
\(388\) | −6.54000e15 | −0.0973132 | ||||||||
\(389\) | 2.38298e16 | 0.348697 | 0.174349 | − | 0.984684i | \(-0.444218\pi\) | ||||
0.174349 | + | 0.984684i | \(0.444218\pi\) | |||||||
\(390\) | 7.91338e15 | 0.113879 | ||||||||
\(391\) | 1.15689e17 | 1.63735 | ||||||||
\(392\) | −1.70990e16 | −0.238018 | ||||||||
\(393\) | −1.59232e16 | −0.218011 | ||||||||
\(394\) | 1.14947e17 | 1.54801 | ||||||||
\(395\) | 5.37513e15 | 0.0712046 | ||||||||
\(396\) | −2.57301e15 | −0.0335292 | ||||||||
\(397\) | −3.87404e16 | −0.496622 | −0.248311 | − | 0.968680i | \(-0.579876\pi\) | ||||
−0.248311 | + | 0.968680i | \(0.579876\pi\) | |||||||
\(398\) | 6.37626e16 | 0.804130 | ||||||||
\(399\) | −3.52451e16 | −0.437295 | ||||||||
\(400\) | 4.93407e16 | 0.602304 | ||||||||
\(401\) | 7.83431e16 | 0.940941 | 0.470470 | − | 0.882416i | \(-0.344084\pi\) | ||||
0.470470 | + | 0.882416i | \(0.344084\pi\) | |||||||
\(402\) | 4.02499e16 | 0.475659 | ||||||||
\(403\) | 1.00077e17 | 1.16373 | ||||||||
\(404\) | 3.18617e16 | 0.364578 | ||||||||
\(405\) | 2.43218e15 | 0.0273866 | ||||||||
\(406\) | −1.39959e17 | −1.55089 | ||||||||
\(407\) | 2.13645e16 | 0.232985 | ||||||||
\(408\) | 9.04757e16 | 0.971049 | ||||||||
\(409\) | −1.07399e17 | −1.13448 | −0.567241 | − | 0.823552i | \(-0.691989\pi\) | ||||
−0.567241 | + | 0.823552i | \(0.691989\pi\) | |||||||
\(410\) | −1.44376e14 | −0.00150107 | ||||||||
\(411\) | 4.43626e16 | 0.453989 | ||||||||
\(412\) | −9.59813e15 | −0.0966841 | ||||||||
\(413\) | 1.44969e16 | 0.143748 | ||||||||
\(414\) | −3.06343e16 | −0.299023 | ||||||||
\(415\) | −2.71155e16 | −0.260559 | ||||||||
\(416\) | 5.40503e16 | 0.511318 | ||||||||
\(417\) | 2.73150e16 | 0.254400 | ||||||||
\(418\) | −2.27827e16 | −0.208910 | ||||||||
\(419\) | −1.78230e17 | −1.60912 | −0.804562 | − | 0.593869i | \(-0.797600\pi\) | ||||
−0.804562 | + | 0.593869i | \(0.797600\pi\) | |||||||
\(420\) | −4.95293e15 | −0.0440293 | ||||||||
\(421\) | 1.71934e16 | 0.150497 | 0.0752484 | − | 0.997165i | \(-0.476025\pi\) | ||||
0.0752484 | + | 0.997165i | \(0.476025\pi\) | |||||||
\(422\) | −1.31761e17 | −1.13568 | ||||||||
\(423\) | −3.74723e16 | −0.318052 | ||||||||
\(424\) | −1.01628e17 | −0.849444 | ||||||||
\(425\) | 1.76696e17 | 1.45445 | ||||||||
\(426\) | −1.00650e17 | −0.815929 | ||||||||
\(427\) | 1.19602e17 | 0.954902 | ||||||||
\(428\) | 5.76624e16 | 0.453428 | ||||||||
\(429\) | 2.52396e16 | 0.195483 | ||||||||
\(430\) | 4.56711e15 | 0.0348415 | ||||||||
\(431\) | 1.08757e17 | 0.817248 | 0.408624 | − | 0.912703i | \(-0.366009\pi\) | ||||
0.408624 | + | 0.912703i | \(0.366009\pi\) | |||||||
\(432\) | −1.66724e16 | −0.123411 | ||||||||
\(433\) | 7.20835e16 | 0.525611 | 0.262805 | − | 0.964849i | \(-0.415352\pi\) | ||||
0.262805 | + | 0.964849i | \(0.415352\pi\) | |||||||
\(434\) | 1.60895e17 | 1.15574 | ||||||||
\(435\) | −3.32932e16 | −0.235600 | ||||||||
\(436\) | 5.78245e16 | 0.403135 | ||||||||
\(437\) | 1.05600e17 | 0.725326 | ||||||||
\(438\) | −3.69388e16 | −0.249978 | ||||||||
\(439\) | 9.77140e16 | 0.651534 | 0.325767 | − | 0.945450i | \(-0.394377\pi\) | ||||
0.325767 | + | 0.945450i | \(0.394377\pi\) | |||||||
\(440\) | −1.46271e16 | −0.0960983 | ||||||||
\(441\) | 1.12838e16 | 0.0730474 | ||||||||
\(442\) | −1.94260e17 | −1.23919 | ||||||||
\(443\) | 3.97269e16 | 0.249724 | 0.124862 | − | 0.992174i | \(-0.460151\pi\) | ||||
0.124862 | + | 0.992174i | \(0.460151\pi\) | |||||||
\(444\) | −1.69512e16 | −0.105005 | ||||||||
\(445\) | −4.39533e16 | −0.268319 | ||||||||
\(446\) | 3.65440e16 | 0.219856 | ||||||||
\(447\) | −1.30063e16 | −0.0771179 | ||||||||
\(448\) | 2.08060e17 | 1.21586 | ||||||||
\(449\) | 1.91140e17 | 1.10091 | 0.550453 | − | 0.834866i | \(-0.314455\pi\) | ||||
0.550453 | + | 0.834866i | \(0.314455\pi\) | |||||||
\(450\) | −4.67887e16 | −0.265619 | ||||||||
\(451\) | −4.60485e14 | −0.00257673 | ||||||||
\(452\) | 7.42243e16 | 0.409399 | ||||||||
\(453\) | −8.97378e16 | −0.487907 | ||||||||
\(454\) | 2.14187e16 | 0.114797 | ||||||||
\(455\) | 4.85851e16 | 0.256702 | ||||||||
\(456\) | 8.25854e16 | 0.430162 | ||||||||
\(457\) | 2.69665e17 | 1.38474 | 0.692372 | − | 0.721540i | \(-0.256566\pi\) | ||||
0.692372 | + | 0.721540i | \(0.256566\pi\) | |||||||
\(458\) | 2.89851e17 | 1.46740 | ||||||||
\(459\) | −5.97060e16 | −0.298013 | ||||||||
\(460\) | 1.48397e16 | 0.0730299 | ||||||||
\(461\) | −8.41504e15 | −0.0408320 | −0.0204160 | − | 0.999792i | \(-0.506499\pi\) | ||||
−0.0204160 | + | 0.999792i | \(0.506499\pi\) | |||||||
\(462\) | 4.05780e16 | 0.194141 | ||||||||
\(463\) | 5.63024e16 | 0.265614 | 0.132807 | − | 0.991142i | \(-0.457601\pi\) | ||||
0.132807 | + | 0.991142i | \(0.457601\pi\) | |||||||
\(464\) | 2.28222e17 | 1.06167 | ||||||||
\(465\) | 3.82734e16 | 0.175571 | ||||||||
\(466\) | 1.81436e17 | 0.820758 | ||||||||
\(467\) | 3.93932e17 | 1.75736 | 0.878681 | − | 0.477410i | \(-0.158424\pi\) | ||||
0.878681 | + | 0.477410i | \(0.158424\pi\) | |||||||
\(468\) | −2.00258e16 | −0.0881034 | ||||||||
\(469\) | 2.47119e17 | 1.07222 | ||||||||
\(470\) | −4.66270e16 | −0.199527 | ||||||||
\(471\) | −6.13492e16 | −0.258924 | ||||||||
\(472\) | −3.39689e16 | −0.141403 | ||||||||
\(473\) | 1.45667e16 | 0.0598087 | ||||||||
\(474\) | 3.49403e16 | 0.141503 | ||||||||
\(475\) | 1.61286e17 | 0.644300 | ||||||||
\(476\) | 1.21586e17 | 0.479113 | ||||||||
\(477\) | 6.70654e16 | 0.260693 | ||||||||
\(478\) | −3.00433e17 | −1.15204 | ||||||||
\(479\) | −1.30163e17 | −0.492387 | −0.246193 | − | 0.969221i | \(-0.579180\pi\) | ||||
−0.246193 | + | 0.969221i | \(0.579180\pi\) | |||||||
\(480\) | 2.06709e16 | 0.0771421 | ||||||||
\(481\) | 1.66281e17 | 0.612207 | ||||||||
\(482\) | −1.51408e17 | −0.549974 | ||||||||
\(483\) | −1.88083e17 | −0.674050 | ||||||||
\(484\) | 6.90366e16 | 0.244109 | ||||||||
\(485\) | 2.45347e16 | 0.0855971 | ||||||||
\(486\) | 1.58101e16 | 0.0544249 | ||||||||
\(487\) | 1.78044e17 | 0.604768 | 0.302384 | − | 0.953186i | \(-0.402218\pi\) | ||||
0.302384 | + | 0.953186i | \(0.402218\pi\) | |||||||
\(488\) | −2.80249e17 | −0.939325 | ||||||||
\(489\) | 2.16350e17 | 0.715564 | ||||||||
\(490\) | 1.40405e16 | 0.0458256 | ||||||||
\(491\) | 2.01033e17 | 0.647498 | 0.323749 | − | 0.946143i | \(-0.395057\pi\) | ||||
0.323749 | + | 0.946143i | \(0.395057\pi\) | |||||||
\(492\) | 3.65363e14 | 0.00116132 | ||||||||
\(493\) | 8.17290e17 | 2.56373 | ||||||||
\(494\) | −1.77319e17 | −0.548946 | ||||||||
\(495\) | 9.65259e15 | 0.0294924 | ||||||||
\(496\) | −2.62361e17 | −0.791166 | ||||||||
\(497\) | −6.17954e17 | −1.83924 | ||||||||
\(498\) | −1.76261e17 | −0.517803 | ||||||||
\(499\) | −6.38814e17 | −1.85234 | −0.926170 | − | 0.377105i | \(-0.876920\pi\) | ||||
−0.926170 | + | 0.377105i | \(0.876920\pi\) | |||||||
\(500\) | 4.67965e16 | 0.133939 | ||||||||
\(501\) | −5.24915e16 | −0.148301 | ||||||||
\(502\) | −1.28807e17 | −0.359223 | ||||||||
\(503\) | 2.91620e17 | 0.802832 | 0.401416 | − | 0.915896i | \(-0.368518\pi\) | ||||
0.401416 | + | 0.915896i | \(0.368518\pi\) | |||||||
\(504\) | −1.47092e17 | −0.399752 | ||||||||
\(505\) | −1.19529e17 | −0.320684 | ||||||||
\(506\) | −1.21578e17 | −0.322015 | ||||||||
\(507\) | −2.43551e16 | −0.0636852 | ||||||||
\(508\) | −1.42758e17 | −0.368543 | ||||||||
\(509\) | 5.67017e17 | 1.44521 | 0.722604 | − | 0.691262i | \(-0.242945\pi\) | ||||
0.722604 | + | 0.691262i | \(0.242945\pi\) | |||||||
\(510\) | −7.42925e16 | −0.186956 | ||||||||
\(511\) | −2.26790e17 | −0.563493 | ||||||||
\(512\) | −4.25603e17 | −1.04412 | ||||||||
\(513\) | −5.44991e16 | −0.132016 | ||||||||
\(514\) | 4.84041e17 | 1.15777 | ||||||||
\(515\) | 3.60072e16 | 0.0850437 | ||||||||
\(516\) | −1.15577e16 | −0.0269555 | ||||||||
\(517\) | −1.48716e17 | −0.342507 | ||||||||
\(518\) | 2.67331e17 | 0.608004 | ||||||||
\(519\) | 3.51090e15 | 0.00788553 | ||||||||
\(520\) | −1.13843e17 | −0.252514 | ||||||||
\(521\) | −1.79693e16 | −0.0393629 | −0.0196814 | − | 0.999806i | \(-0.506265\pi\) | ||||
−0.0196814 | + | 0.999806i | \(0.506265\pi\) | |||||||
\(522\) | −2.16417e17 | −0.468203 | ||||||||
\(523\) | 4.87927e17 | 1.04254 | 0.521271 | − | 0.853391i | \(-0.325458\pi\) | ||||
0.521271 | + | 0.853391i | \(0.325458\pi\) | |||||||
\(524\) | 5.01402e16 | 0.105812 | ||||||||
\(525\) | −2.87265e17 | −0.598752 | ||||||||
\(526\) | 2.00214e17 | 0.412180 | ||||||||
\(527\) | −9.39547e17 | −1.91051 | ||||||||
\(528\) | −6.61676e16 | −0.132900 | ||||||||
\(529\) | 5.94882e16 | 0.118024 | ||||||||
\(530\) | 8.34499e16 | 0.163543 | ||||||||
\(531\) | 2.24165e16 | 0.0433963 | ||||||||
\(532\) | 1.10983e17 | 0.212241 | ||||||||
\(533\) | −3.58398e15 | −0.00677078 | ||||||||
\(534\) | −2.85712e17 | −0.533225 | ||||||||
\(535\) | −2.16319e17 | −0.398837 | ||||||||
\(536\) | −5.79043e17 | −1.05473 | ||||||||
\(537\) | 5.65125e16 | 0.101698 | ||||||||
\(538\) | −8.39718e16 | −0.149296 | ||||||||
\(539\) | 4.47820e16 | 0.0786641 | ||||||||
\(540\) | −7.65866e15 | −0.0132921 | ||||||||
\(541\) | −2.65595e17 | −0.455448 | −0.227724 | − | 0.973726i | \(-0.573128\pi\) | ||||
−0.227724 | + | 0.973726i | \(0.573128\pi\) | |||||||
\(542\) | 6.28249e17 | 1.06448 | ||||||||
\(543\) | −4.51994e17 | −0.756717 | ||||||||
\(544\) | −5.07436e17 | −0.839437 | ||||||||
\(545\) | −2.16928e17 | −0.354599 | ||||||||
\(546\) | 3.15820e17 | 0.510138 | ||||||||
\(547\) | 9.23920e17 | 1.47474 | 0.737372 | − | 0.675486i | \(-0.236066\pi\) | ||||
0.737372 | + | 0.675486i | \(0.236066\pi\) | |||||||
\(548\) | −1.39693e17 | −0.220343 | ||||||||
\(549\) | 1.84940e17 | 0.288277 | ||||||||
\(550\) | −1.85690e17 | −0.286043 | ||||||||
\(551\) | 7.46015e17 | 1.13570 | ||||||||
\(552\) | 4.40710e17 | 0.663054 | ||||||||
\(553\) | 2.14520e17 | 0.318973 | ||||||||
\(554\) | −4.94326e17 | −0.726440 | ||||||||
\(555\) | 6.35921e16 | 0.0923632 | ||||||||
\(556\) | −8.60117e16 | −0.123473 | ||||||||
\(557\) | −9.57495e17 | −1.35856 | −0.679278 | − | 0.733881i | \(-0.737707\pi\) | ||||
−0.679278 | + | 0.733881i | \(0.737707\pi\) | |||||||
\(558\) | 2.48791e17 | 0.348909 | ||||||||
\(559\) | 1.13373e17 | 0.157157 | ||||||||
\(560\) | −1.27370e17 | −0.174520 | ||||||||
\(561\) | −2.36955e17 | −0.320927 | ||||||||
\(562\) | −7.64404e17 | −1.02338 | ||||||||
\(563\) | −1.06753e18 | −1.41278 | −0.706388 | − | 0.707824i | \(-0.749677\pi\) | ||||
−0.706388 | + | 0.707824i | \(0.749677\pi\) | |||||||
\(564\) | 1.17996e17 | 0.154366 | ||||||||
\(565\) | −2.78451e17 | −0.360109 | ||||||||
\(566\) | 2.42862e16 | 0.0310494 | ||||||||
\(567\) | 9.70677e16 | 0.122683 | ||||||||
\(568\) | 1.44797e18 | 1.80924 | ||||||||
\(569\) | −3.70781e17 | −0.458023 | −0.229011 | − | 0.973424i | \(-0.573549\pi\) | ||||
−0.229011 | + | 0.973424i | \(0.573549\pi\) | |||||||
\(570\) | −6.78135e16 | −0.0828189 | ||||||||
\(571\) | 2.25137e17 | 0.271839 | 0.135919 | − | 0.990720i | \(-0.456601\pi\) | ||||
0.135919 | + | 0.990720i | \(0.456601\pi\) | |||||||
\(572\) | −7.94764e16 | −0.0948777 | ||||||||
\(573\) | −7.54409e16 | −0.0890434 | ||||||||
\(574\) | −5.76201e15 | −0.00672429 | ||||||||
\(575\) | 8.60690e17 | 0.993129 | ||||||||
\(576\) | 3.21721e17 | 0.367057 | ||||||||
\(577\) | −1.24891e18 | −1.40893 | −0.704464 | − | 0.709740i | \(-0.748813\pi\) | ||||
−0.704464 | + | 0.709740i | \(0.748813\pi\) | |||||||
\(578\) | 1.06320e18 | 1.18600 | ||||||||
\(579\) | −5.31574e17 | −0.586344 | ||||||||
\(580\) | 1.04836e17 | 0.114348 | ||||||||
\(581\) | −1.08217e18 | −1.16722 | ||||||||
\(582\) | 1.59484e17 | 0.170105 | ||||||||
\(583\) | 2.66162e17 | 0.280738 | ||||||||
\(584\) | 5.31409e17 | 0.554301 | ||||||||
\(585\) | 7.51265e16 | 0.0774962 | ||||||||
\(586\) | −1.38594e18 | −1.41387 | ||||||||
\(587\) | 6.44717e17 | 0.650461 | 0.325231 | − | 0.945635i | \(-0.394558\pi\) | ||||
0.325231 | + | 0.945635i | \(0.394558\pi\) | |||||||
\(588\) | −3.55314e16 | −0.0354535 | ||||||||
\(589\) | −8.57610e17 | −0.846331 | ||||||||
\(590\) | 2.78929e16 | 0.0272243 | ||||||||
\(591\) | 1.09126e18 | 1.05344 | ||||||||
\(592\) | −4.35918e17 | −0.416211 | ||||||||
\(593\) | −8.38047e17 | −0.791430 | −0.395715 | − | 0.918373i | \(-0.629503\pi\) | ||||
−0.395715 | + | 0.918373i | \(0.629503\pi\) | |||||||
\(594\) | 6.27453e16 | 0.0586097 | ||||||||
\(595\) | −4.56127e17 | −0.421430 | ||||||||
\(596\) | 4.09553e16 | 0.0374291 | ||||||||
\(597\) | 6.05338e17 | 0.547223 | ||||||||
\(598\) | −9.46247e17 | −0.846149 | ||||||||
\(599\) | 6.02182e17 | 0.532664 | 0.266332 | − | 0.963881i | \(-0.414188\pi\) | ||||
0.266332 | + | 0.963881i | \(0.414188\pi\) | |||||||
\(600\) | 6.73112e17 | 0.588985 | ||||||||
\(601\) | 1.32927e18 | 1.15061 | 0.575305 | − | 0.817939i | \(-0.304884\pi\) | ||||
0.575305 | + | 0.817939i | \(0.304884\pi\) | |||||||
\(602\) | 1.82272e17 | 0.156078 | ||||||||
\(603\) | 3.82117e17 | 0.323694 | ||||||||
\(604\) | 2.82574e17 | 0.236805 | ||||||||
\(605\) | −2.58989e17 | −0.214720 | ||||||||
\(606\) | −7.76979e17 | −0.637290 | ||||||||
\(607\) | 1.14934e18 | 0.932658 | 0.466329 | − | 0.884611i | \(-0.345576\pi\) | ||||
0.466329 | + | 0.884611i | \(0.345576\pi\) | |||||||
\(608\) | −4.63182e17 | −0.371859 | ||||||||
\(609\) | −1.32872e18 | −1.05541 | ||||||||
\(610\) | 2.30122e17 | 0.180848 | ||||||||
\(611\) | −1.15746e18 | −0.899995 | ||||||||
\(612\) | 1.88007e17 | 0.144640 | ||||||||
\(613\) | −2.29915e17 | −0.175015 | −0.0875073 | − | 0.996164i | \(-0.527890\pi\) | ||||
−0.0875073 | + | 0.996164i | \(0.527890\pi\) | |||||||
\(614\) | −7.50827e17 | −0.565517 | ||||||||
\(615\) | −1.37065e15 | −0.00102150 | ||||||||
\(616\) | −5.83763e17 | −0.430489 | ||||||||
\(617\) | 7.07545e17 | 0.516298 | 0.258149 | − | 0.966105i | \(-0.416887\pi\) | ||||
0.258149 | + | 0.966105i | \(0.416887\pi\) | |||||||
\(618\) | 2.34060e17 | 0.169006 | ||||||||
\(619\) | 3.24098e17 | 0.231573 | 0.115786 | − | 0.993274i | \(-0.463061\pi\) | ||||
0.115786 | + | 0.993274i | \(0.463061\pi\) | |||||||
\(620\) | −1.20518e17 | −0.0852133 | ||||||||
\(621\) | −2.90830e17 | −0.203490 | ||||||||
\(622\) | 7.44041e17 | 0.515180 | ||||||||
\(623\) | −1.75416e18 | −1.20198 | ||||||||
\(624\) | −5.14986e17 | −0.349217 | ||||||||
\(625\) | 1.22403e18 | 0.821434 | ||||||||
\(626\) | −1.97200e18 | −1.30970 | ||||||||
\(627\) | −2.16290e17 | −0.142167 | ||||||||
\(628\) | 1.93181e17 | 0.125669 | ||||||||
\(629\) | −1.56108e18 | −1.00507 | ||||||||
\(630\) | 1.20782e17 | 0.0769641 | ||||||||
\(631\) | 1.56666e18 | 0.988059 | 0.494029 | − | 0.869445i | \(-0.335524\pi\) | ||||
0.494029 | + | 0.869445i | \(0.335524\pi\) | |||||||
\(632\) | −5.02657e17 | −0.313770 | ||||||||
\(633\) | −1.25089e18 | −0.772848 | ||||||||
\(634\) | 1.58463e17 | 0.0969051 | ||||||||
\(635\) | 5.35555e17 | 0.324172 | ||||||||
\(636\) | −2.11181e17 | −0.126527 | ||||||||
\(637\) | 3.48540e17 | 0.206703 | ||||||||
\(638\) | −8.58894e17 | −0.504203 | ||||||||
\(639\) | −9.55535e17 | −0.555253 | ||||||||
\(640\) | 1.68034e17 | 0.0966558 | ||||||||
\(641\) | −8.52146e17 | −0.485218 | −0.242609 | − | 0.970124i | \(-0.578003\pi\) | ||||
−0.242609 | + | 0.970124i | \(0.578003\pi\) | |||||||
\(642\) | −1.40615e18 | −0.792601 | ||||||||
\(643\) | 2.59198e17 | 0.144630 | 0.0723152 | − | 0.997382i | \(-0.476961\pi\) | ||||
0.0723152 | + | 0.997382i | \(0.476961\pi\) | |||||||
\(644\) | 5.92249e17 | 0.327150 | ||||||||
\(645\) | 4.33584e16 | 0.0237102 | ||||||||
\(646\) | 1.66471e18 | 0.901211 | ||||||||
\(647\) | 2.06094e18 | 1.10456 | 0.552278 | − | 0.833660i | \(-0.313759\pi\) | ||||
0.552278 | + | 0.833660i | \(0.313759\pi\) | |||||||
\(648\) | −2.27447e17 | −0.120682 | ||||||||
\(649\) | 8.89641e16 | 0.0467331 | ||||||||
\(650\) | −1.44523e18 | −0.751625 | ||||||||
\(651\) | 1.52748e18 | 0.786500 | ||||||||
\(652\) | −6.81259e17 | −0.347299 | ||||||||
\(653\) | −3.70684e18 | −1.87098 | −0.935488 | − | 0.353358i | \(-0.885040\pi\) | ||||
−0.935488 | + | 0.353358i | \(0.885040\pi\) | |||||||
\(654\) | −1.41011e18 | −0.704688 | ||||||||
\(655\) | −1.88100e17 | −0.0930723 | ||||||||
\(656\) | 9.39569e15 | 0.00460314 | ||||||||
\(657\) | −3.50683e17 | −0.170114 | ||||||||
\(658\) | −1.86087e18 | −0.893815 | ||||||||
\(659\) | 4.20177e18 | 1.99838 | 0.999189 | − | 0.0402739i | \(-0.0128230\pi\) | ||||
0.999189 | + | 0.0402739i | \(0.0128230\pi\) | |||||||
\(660\) | −3.03949e16 | −0.0143141 | ||||||||
\(661\) | 1.35612e18 | 0.632395 | 0.316197 | − | 0.948693i | \(-0.397594\pi\) | ||||
0.316197 | + | 0.948693i | \(0.397594\pi\) | |||||||
\(662\) | −2.90615e18 | −1.34196 | ||||||||
\(663\) | −1.84423e18 | −0.843290 | ||||||||
\(664\) | 2.53572e18 | 1.14818 | ||||||||
\(665\) | −4.16349e17 | −0.186688 | ||||||||
\(666\) | 4.13371e17 | 0.183551 | ||||||||
\(667\) | 3.98105e18 | 1.75057 | ||||||||
\(668\) | 1.65289e17 | 0.0719777 | ||||||||
\(669\) | 3.46934e17 | 0.149616 | ||||||||
\(670\) | 4.75471e17 | 0.203066 | ||||||||
\(671\) | 7.33969e17 | 0.310443 | ||||||||
\(672\) | 8.24969e17 | 0.345571 | ||||||||
\(673\) | −2.87276e18 | −1.19179 | −0.595897 | − | 0.803061i | \(-0.703203\pi\) | ||||
−0.595897 | + | 0.803061i | \(0.703203\pi\) | |||||||
\(674\) | −3.47309e18 | −1.42701 | ||||||||
\(675\) | −4.44194e17 | −0.180758 | ||||||||
\(676\) | 7.66913e16 | 0.0309096 | ||||||||
\(677\) | −1.07415e18 | −0.428783 | −0.214391 | − | 0.976748i | \(-0.568777\pi\) | ||||
−0.214391 | + | 0.976748i | \(0.568777\pi\) | |||||||
\(678\) | −1.81003e18 | −0.715637 | ||||||||
\(679\) | 9.79171e17 | 0.383447 | ||||||||
\(680\) | 1.06879e18 | 0.414556 | ||||||||
\(681\) | 2.03341e17 | 0.0781211 | ||||||||
\(682\) | 9.87374e17 | 0.375736 | ||||||||
\(683\) | −3.44874e18 | −1.29995 | −0.649973 | − | 0.759957i | \(-0.725220\pi\) | ||||
−0.649973 | + | 0.759957i | \(0.725220\pi\) | |||||||
\(684\) | 1.71611e17 | 0.0640738 | ||||||||
\(685\) | 5.24054e17 | 0.193815 | ||||||||
\(686\) | −1.99667e18 | −0.731476 | ||||||||
\(687\) | 2.75173e18 | 0.998591 | ||||||||
\(688\) | −2.97218e17 | −0.106844 | ||||||||
\(689\) | 2.07155e18 | 0.737685 | ||||||||
\(690\) | −3.61881e17 | −0.127658 | ||||||||
\(691\) | −7.16038e17 | −0.250224 | −0.125112 | − | 0.992143i | \(-0.539929\pi\) | ||||
−0.125112 | + | 0.992143i | \(0.539929\pi\) | |||||||
\(692\) | −1.10554e16 | −0.00382724 | ||||||||
\(693\) | 3.85232e17 | 0.132116 | ||||||||
\(694\) | 3.49202e18 | 1.18642 | ||||||||
\(695\) | 3.22671e17 | 0.108607 | ||||||||
\(696\) | 3.11342e18 | 1.03819 | ||||||||
\(697\) | 3.36472e16 | 0.0111157 | ||||||||
\(698\) | 1.37711e18 | 0.450720 | ||||||||
\(699\) | 1.72248e18 | 0.558539 | ||||||||
\(700\) | 9.04562e17 | 0.290604 | ||||||||
\(701\) | 4.24864e18 | 1.35233 | 0.676165 | − | 0.736750i | \(-0.263641\pi\) | ||||
0.676165 | + | 0.736750i | \(0.263641\pi\) | |||||||
\(702\) | 4.88349e17 | 0.154007 | ||||||||
\(703\) | −1.42494e18 | −0.445232 | ||||||||
\(704\) | 1.27681e18 | 0.395280 | ||||||||
\(705\) | −4.42659e17 | −0.135781 | ||||||||
\(706\) | 3.90406e18 | 1.18655 | ||||||||
\(707\) | −4.77035e18 | −1.43656 | ||||||||
\(708\) | −7.05868e16 | −0.0210624 | ||||||||
\(709\) | −1.51425e16 | −0.00447709 | −0.00223855 | − | 0.999997i | \(-0.500713\pi\) | ||||
−0.00223855 | + | 0.999997i | \(0.500713\pi\) | |||||||
\(710\) | −1.18898e18 | −0.348333 | ||||||||
\(711\) | 3.31709e17 | 0.0962954 | ||||||||
\(712\) | 4.11031e18 | 1.18237 | ||||||||
\(713\) | −4.57657e18 | −1.30454 | ||||||||
\(714\) | −2.96499e18 | −0.837500 | ||||||||
\(715\) | 2.98154e17 | 0.0834549 | ||||||||
\(716\) | −1.77951e17 | −0.0493590 | ||||||||
\(717\) | −2.85220e18 | −0.783981 | ||||||||
\(718\) | 2.70423e18 | 0.736604 | ||||||||
\(719\) | −5.69358e18 | −1.53691 | −0.768453 | − | 0.639906i | \(-0.778973\pi\) | ||||
−0.768453 | + | 0.639906i | \(0.778973\pi\) | |||||||
\(720\) | −1.96950e17 | −0.0526860 | ||||||||
\(721\) | 1.43704e18 | 0.380968 | ||||||||
\(722\) | −1.70966e18 | −0.449176 | ||||||||
\(723\) | −1.43741e18 | −0.374266 | ||||||||
\(724\) | 1.42327e18 | 0.367272 | ||||||||
\(725\) | 6.08039e18 | 1.55501 | ||||||||
\(726\) | −1.68352e18 | −0.426708 | ||||||||
\(727\) | 3.11211e18 | 0.781773 | 0.390887 | − | 0.920439i | \(-0.372168\pi\) | ||||
0.390887 | + | 0.920439i | \(0.372168\pi\) | |||||||
\(728\) | −4.54345e18 | −1.13118 | ||||||||
\(729\) | 1.50095e17 | 0.0370370 | ||||||||
\(730\) | −4.36357e17 | −0.106719 | ||||||||
\(731\) | −1.06437e18 | −0.258007 | ||||||||
\(732\) | −5.82353e17 | −0.139915 | ||||||||
\(733\) | 4.51504e18 | 1.07519 | 0.537596 | − | 0.843203i | \(-0.319333\pi\) | ||||
0.537596 | + | 0.843203i | \(0.319333\pi\) | |||||||
\(734\) | −1.67960e17 | −0.0396443 | ||||||||
\(735\) | 1.33295e17 | 0.0311851 | ||||||||
\(736\) | −2.47174e18 | −0.573187 | ||||||||
\(737\) | 1.51651e18 | 0.348583 | ||||||||
\(738\) | −8.90972e15 | −0.00203001 | ||||||||
\(739\) | −7.27367e18 | −1.64272 | −0.821362 | − | 0.570408i | \(-0.806785\pi\) | ||||
−0.821362 | + | 0.570408i | \(0.806785\pi\) | |||||||
\(740\) | −2.00244e17 | −0.0448284 | ||||||||
\(741\) | −1.68340e18 | −0.373566 | ||||||||
\(742\) | 3.33046e18 | 0.732620 | ||||||||
\(743\) | 4.41522e18 | 0.962775 | 0.481388 | − | 0.876508i | \(-0.340133\pi\) | ||||
0.481388 | + | 0.876508i | \(0.340133\pi\) | |||||||
\(744\) | −3.57915e18 | −0.773670 | ||||||||
\(745\) | −1.53643e17 | −0.0329228 | ||||||||
\(746\) | 3.01783e18 | 0.641052 | ||||||||
\(747\) | −1.67335e18 | −0.352373 | ||||||||
\(748\) | 7.46142e17 | 0.155762 | ||||||||
\(749\) | −8.63323e18 | −1.78666 | ||||||||
\(750\) | −1.14118e18 | −0.234129 | ||||||||
\(751\) | 4.39874e18 | 0.894683 | 0.447341 | − | 0.894363i | \(-0.352371\pi\) | ||||
0.447341 | + | 0.894363i | \(0.352371\pi\) | |||||||
\(752\) | 3.03439e18 | 0.611864 | ||||||||
\(753\) | −1.22284e18 | −0.244457 | ||||||||
\(754\) | −6.68481e18 | −1.32488 | ||||||||
\(755\) | −1.06007e18 | −0.208295 | ||||||||
\(756\) | −3.05654e17 | −0.0595441 | ||||||||
\(757\) | 4.09692e18 | 0.791288 | 0.395644 | − | 0.918404i | \(-0.370521\pi\) | ||||
0.395644 | + | 0.918404i | \(0.370521\pi\) | |||||||
\(758\) | −9.59053e16 | −0.0183651 | ||||||||
\(759\) | −1.15421e18 | −0.219137 | ||||||||
\(760\) | 9.75578e17 | 0.183643 | ||||||||
\(761\) | 2.07652e18 | 0.387556 | 0.193778 | − | 0.981045i | \(-0.437926\pi\) | ||||
0.193778 | + | 0.981045i | \(0.437926\pi\) | |||||||
\(762\) | 3.48130e18 | 0.644220 | ||||||||
\(763\) | −8.65751e18 | −1.58849 | ||||||||
\(764\) | 2.37554e17 | 0.0432172 | ||||||||
\(765\) | −7.05304e17 | −0.127226 | ||||||||
\(766\) | 1.16523e17 | 0.0208414 | ||||||||
\(767\) | 6.92411e17 | 0.122799 | ||||||||
\(768\) | −2.52300e18 | −0.443679 | ||||||||
\(769\) | 4.09552e18 | 0.714147 | 0.357074 | − | 0.934076i | \(-0.383774\pi\) | ||||
0.357074 | + | 0.934076i | \(0.383774\pi\) | |||||||
\(770\) | 4.79346e17 | 0.0828819 | ||||||||
\(771\) | 4.59530e18 | 0.787881 | ||||||||
\(772\) | 1.67386e18 | 0.284582 | ||||||||
\(773\) | −6.34771e18 | −1.07016 | −0.535082 | − | 0.844800i | \(-0.679719\pi\) | ||||
−0.535082 | + | 0.844800i | \(0.679719\pi\) | |||||||
\(774\) | 2.81845e17 | 0.0471188 | ||||||||
\(775\) | −6.98994e18 | −1.15881 | ||||||||
\(776\) | −2.29437e18 | −0.377192 | ||||||||
\(777\) | 2.53794e18 | 0.413756 | ||||||||
\(778\) | 1.82986e18 | 0.295835 | ||||||||
\(779\) | 3.07128e16 | 0.00492409 | ||||||||
\(780\) | −2.36565e17 | −0.0376127 | ||||||||
\(781\) | −3.79222e18 | −0.597946 | ||||||||
\(782\) | 8.88357e18 | 1.38913 | ||||||||
\(783\) | −2.05458e18 | −0.318619 | ||||||||
\(784\) | −9.13726e17 | −0.140528 | ||||||||
\(785\) | −7.24716e17 | −0.110539 | ||||||||
\(786\) | −1.22272e18 | −0.184961 | ||||||||
\(787\) | −9.40418e18 | −1.41086 | −0.705432 | − | 0.708778i | \(-0.749247\pi\) | ||||
−0.705432 | + | 0.708778i | \(0.749247\pi\) | |||||||
\(788\) | −3.43626e18 | −0.511288 | ||||||||
\(789\) | 1.90075e18 | 0.280495 | ||||||||
\(790\) | 4.12748e17 | 0.0604100 | ||||||||
\(791\) | −1.11129e19 | −1.61317 | ||||||||
\(792\) | −9.02666e17 | −0.129961 | ||||||||
\(793\) | 5.71252e18 | 0.815740 | ||||||||
\(794\) | −2.97482e18 | −0.421335 | ||||||||
\(795\) | 7.92241e17 | 0.111294 | ||||||||
\(796\) | −1.90614e18 | −0.265594 | ||||||||
\(797\) | −1.07134e17 | −0.0148064 | −0.00740320 | − | 0.999973i | \(-0.502357\pi\) | ||||
−0.00740320 | + | 0.999973i | \(0.502357\pi\) | |||||||
\(798\) | −2.70641e18 | −0.371001 | ||||||||
\(799\) | 1.08665e19 | 1.47753 | ||||||||
\(800\) | −3.77516e18 | −0.509156 | ||||||||
\(801\) | −2.71244e18 | −0.362869 | ||||||||
\(802\) | 6.01585e18 | 0.798295 | ||||||||
\(803\) | −1.39175e18 | −0.183194 | ||||||||
\(804\) | −1.20324e18 | −0.157105 | ||||||||
\(805\) | −2.22181e18 | −0.287762 | ||||||||
\(806\) | 7.68478e18 | 0.987310 | ||||||||
\(807\) | −7.97196e17 | −0.101598 | ||||||||
\(808\) | 1.11778e19 | 1.41313 | ||||||||
\(809\) | −2.53947e18 | −0.318477 | −0.159238 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159238 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(810\) | 1.86764e17 | 0.0232348 | ||||||||
\(811\) | −1.10168e19 | −1.35963 | −0.679813 | − | 0.733385i | \(-0.737939\pi\) | ||||
−0.679813 | + | 0.733385i | \(0.737939\pi\) | |||||||
\(812\) | 4.18398e18 | 0.512242 | ||||||||
\(813\) | 5.96435e18 | 0.724394 | ||||||||
\(814\) | 1.64054e18 | 0.197665 | ||||||||
\(815\) | 2.55573e18 | 0.305485 | ||||||||
\(816\) | 4.83480e18 | 0.573314 | ||||||||
\(817\) | −9.71551e17 | −0.114294 | ||||||||
\(818\) | −8.24698e18 | −0.962495 | ||||||||
\(819\) | 2.99828e18 | 0.347157 | ||||||||
\(820\) | 4.31602e15 | 0.000495785 0 | ||||||||
\(821\) | −9.54149e18 | −1.08739 | −0.543695 | − | 0.839283i | \(-0.682975\pi\) | ||||
−0.543695 | + | 0.839283i | \(0.682975\pi\) | |||||||
\(822\) | 3.40654e18 | 0.385165 | ||||||||
\(823\) | 9.44397e16 | 0.0105939 | 0.00529695 | − | 0.999986i | \(-0.498314\pi\) | ||||
0.00529695 | + | 0.999986i | \(0.498314\pi\) | |||||||
\(824\) | −3.36723e18 | −0.374753 | ||||||||
\(825\) | −1.76287e18 | −0.194657 | ||||||||
\(826\) | 1.11320e18 | 0.121956 | ||||||||
\(827\) | 1.47888e18 | 0.160749 | 0.0803744 | − | 0.996765i | \(-0.474388\pi\) | ||||
0.0803744 | + | 0.996765i | \(0.474388\pi\) | |||||||
\(828\) | 9.15788e17 | 0.0987638 | ||||||||
\(829\) | 8.97164e18 | 0.959992 | 0.479996 | − | 0.877271i | \(-0.340638\pi\) | ||||
0.479996 | + | 0.877271i | \(0.340638\pi\) | |||||||
\(830\) | −2.08216e18 | −0.221058 | ||||||||
\(831\) | −4.69294e18 | −0.494354 | ||||||||
\(832\) | 9.93749e18 | 1.03866 | ||||||||
\(833\) | −3.27217e18 | −0.339347 | ||||||||
\(834\) | 2.09748e18 | 0.215833 | ||||||||
\(835\) | −6.20079e17 | −0.0633119 | ||||||||
\(836\) | 6.81072e17 | 0.0690005 | ||||||||
\(837\) | 2.36192e18 | 0.237438 | ||||||||
\(838\) | −1.36860e19 | −1.36518 | ||||||||
\(839\) | 1.97263e19 | 1.95251 | 0.976255 | − | 0.216623i | \(-0.0695041\pi\) | ||||
0.976255 | + | 0.216623i | \(0.0695041\pi\) | |||||||
\(840\) | −1.73759e18 | −0.170660 | ||||||||
\(841\) | 1.78637e19 | 1.74100 | ||||||||
\(842\) | 1.32025e18 | 0.127682 | ||||||||
\(843\) | −7.25695e18 | −0.696426 | ||||||||
\(844\) | 3.93889e18 | 0.375101 | ||||||||
\(845\) | −2.87706e17 | −0.0271882 | ||||||||
\(846\) | −2.87744e18 | −0.269836 | ||||||||
\(847\) | −1.03362e19 | −0.961873 | ||||||||
\(848\) | −5.43074e18 | −0.501517 | ||||||||
\(849\) | 2.30564e17 | 0.0211296 | ||||||||
\(850\) | 1.35682e19 | 1.23395 | ||||||||
\(851\) | −7.60407e18 | −0.686284 | ||||||||
\(852\) | 3.00886e18 | 0.269492 | ||||||||
\(853\) | −3.16030e18 | −0.280905 | −0.140453 | − | 0.990087i | \(-0.544856\pi\) | ||||
−0.140453 | + | 0.990087i | \(0.544856\pi\) | |||||||
\(854\) | 9.18408e18 | 0.810139 | ||||||||
\(855\) | −6.43795e17 | −0.0563596 | ||||||||
\(856\) | 2.02292e19 | 1.75751 | ||||||||
\(857\) | −1.46970e19 | −1.26722 | −0.633612 | − | 0.773651i | \(-0.718429\pi\) | ||||
−0.633612 | + | 0.773651i | \(0.718429\pi\) | |||||||
\(858\) | 1.93811e18 | 0.165848 | ||||||||
\(859\) | −7.87423e17 | −0.0668732 | −0.0334366 | − | 0.999441i | \(-0.510645\pi\) | ||||
−0.0334366 | + | 0.999441i | \(0.510645\pi\) | |||||||
\(860\) | −1.36530e17 | −0.0115077 | ||||||||
\(861\) | −5.47023e16 | −0.00457599 | ||||||||
\(862\) | 8.35126e18 | 0.693354 | ||||||||
\(863\) | 1.47985e19 | 1.21940 | 0.609701 | − | 0.792632i | \(-0.291290\pi\) | ||||
0.609701 | + | 0.792632i | \(0.291290\pi\) | |||||||
\(864\) | 1.27564e18 | 0.104325 | ||||||||
\(865\) | 4.14742e16 | 0.00336646 | ||||||||
\(866\) | 5.53518e18 | 0.445929 | ||||||||
\(867\) | 1.00936e19 | 0.807089 | ||||||||
\(868\) | −4.80985e18 | −0.381727 | ||||||||
\(869\) | 1.31645e18 | 0.103700 | ||||||||
\(870\) | −2.55653e18 | −0.199883 | ||||||||
\(871\) | 1.18030e19 | 0.915959 | ||||||||
\(872\) | 2.02861e19 | 1.56257 | ||||||||
\(873\) | 1.51408e18 | 0.115759 | ||||||||
\(874\) | 8.10884e18 | 0.615367 | ||||||||
\(875\) | −7.00639e18 | −0.527766 | ||||||||
\(876\) | 1.10426e18 | 0.0825647 | ||||||||
\(877\) | 8.02347e18 | 0.595476 | 0.297738 | − | 0.954648i | \(-0.403768\pi\) | ||||
0.297738 | + | 0.954648i | \(0.403768\pi\) | |||||||
\(878\) | 7.50330e18 | 0.552762 | ||||||||
\(879\) | −1.31576e19 | −0.962163 | ||||||||
\(880\) | −7.81636e17 | −0.0567371 | ||||||||
\(881\) | −1.25518e19 | −0.904401 | −0.452201 | − | 0.891916i | \(-0.649361\pi\) | ||||
−0.452201 | + | 0.891916i | \(0.649361\pi\) | |||||||
\(882\) | 8.66466e17 | 0.0619735 | ||||||||
\(883\) | −2.91253e17 | −0.0206788 | −0.0103394 | − | 0.999947i | \(-0.503291\pi\) | ||||
−0.0103394 | + | 0.999947i | \(0.503291\pi\) | |||||||
\(884\) | 5.80726e18 | 0.409290 | ||||||||
\(885\) | 2.64805e17 | 0.0185266 | ||||||||
\(886\) | 3.05056e18 | 0.211866 | ||||||||
\(887\) | 1.57640e19 | 1.08684 | 0.543418 | − | 0.839462i | \(-0.317130\pi\) | ||||
0.543418 | + | 0.839462i | \(0.317130\pi\) | |||||||
\(888\) | −5.94684e18 | −0.407007 | ||||||||
\(889\) | 2.13738e19 | 1.45218 | ||||||||
\(890\) | −3.37511e18 | −0.227642 | ||||||||
\(891\) | 5.95680e17 | 0.0398848 | ||||||||
\(892\) | −1.09245e18 | −0.0726159 | ||||||||
\(893\) | 9.91887e18 | 0.654527 | ||||||||
\(894\) | −9.98735e17 | −0.0654269 | ||||||||
\(895\) | 6.67580e17 | 0.0434164 | ||||||||
\(896\) | 6.70619e18 | 0.432986 | ||||||||
\(897\) | −8.98330e18 | −0.575818 | ||||||||
\(898\) | 1.46773e19 | 0.934010 | ||||||||
\(899\) | −3.23314e19 | −2.04261 | ||||||||
\(900\) | 1.39871e18 | 0.0877309 | ||||||||
\(901\) | −1.94482e19 | −1.21107 | ||||||||
\(902\) | −3.53600e16 | −0.00218610 | ||||||||
\(903\) | 1.73042e18 | 0.106214 | ||||||||
\(904\) | 2.60394e19 | 1.58685 | ||||||||
\(905\) | −5.33938e18 | −0.323054 | ||||||||
\(906\) | −6.89083e18 | −0.413941 | ||||||||
\(907\) | −1.46154e18 | −0.0871691 | −0.0435846 | − | 0.999050i | \(-0.513878\pi\) | ||||
−0.0435846 | + | 0.999050i | \(0.513878\pi\) | |||||||
\(908\) | −6.40296e17 | −0.0379160 | ||||||||
\(909\) | −7.37634e18 | −0.433686 | ||||||||
\(910\) | 3.73077e18 | 0.217786 | ||||||||
\(911\) | 2.82120e19 | 1.63517 | 0.817587 | − | 0.575805i | \(-0.195311\pi\) | ||||
0.817587 | + | 0.575805i | \(0.195311\pi\) | |||||||
\(912\) | 4.41316e18 | 0.253970 | ||||||||
\(913\) | −6.64101e18 | −0.379467 | ||||||||
\(914\) | 2.07072e19 | 1.17482 | ||||||||
\(915\) | 2.18469e18 | 0.123070 | ||||||||
\(916\) | −8.66488e18 | −0.484666 | ||||||||
\(917\) | −7.50701e18 | −0.416933 | ||||||||
\(918\) | −4.58473e18 | −0.252835 | ||||||||
\(919\) | −3.13383e19 | −1.71603 | −0.858014 | − | 0.513626i | \(-0.828302\pi\) | ||||
−0.858014 | + | 0.513626i | \(0.828302\pi\) | |||||||
\(920\) | 5.20609e18 | 0.283068 | ||||||||
\(921\) | −7.12806e18 | −0.384843 | ||||||||
\(922\) | −6.46178e17 | −0.0346419 | ||||||||
\(923\) | −2.95150e19 | −1.57120 | ||||||||
\(924\) | −1.21305e18 | −0.0641225 | ||||||||
\(925\) | −1.16139e19 | −0.609619 | ||||||||
\(926\) | 4.32337e18 | 0.225347 | ||||||||
\(927\) | 2.22207e18 | 0.115011 | ||||||||
\(928\) | −1.74617e19 | −0.897480 | ||||||||
\(929\) | −8.09784e18 | −0.413301 | −0.206651 | − | 0.978415i | \(-0.566256\pi\) | ||||
−0.206651 | + | 0.978415i | \(0.566256\pi\) | |||||||
\(930\) | 2.93896e18 | 0.148955 | ||||||||
\(931\) | −2.98681e18 | −0.150326 | ||||||||
\(932\) | −5.42390e18 | −0.271087 | ||||||||
\(933\) | 7.06363e18 | 0.350588 | ||||||||
\(934\) | 3.02494e19 | 1.49095 | ||||||||
\(935\) | −2.79914e18 | −0.137009 | ||||||||
\(936\) | −7.02549e18 | −0.341494 | ||||||||
\(937\) | 1.90542e19 | 0.919779 | 0.459890 | − | 0.887976i | \(-0.347889\pi\) | ||||
0.459890 | + | 0.887976i | \(0.347889\pi\) | |||||||
\(938\) | 1.89759e19 | 0.909670 | ||||||||
\(939\) | −1.87214e19 | −0.891275 | ||||||||
\(940\) | 1.39388e18 | 0.0659014 | ||||||||
\(941\) | −2.66077e18 | −0.124932 | −0.0624662 | − | 0.998047i | \(-0.519897\pi\) | ||||
−0.0624662 | + | 0.998047i | \(0.519897\pi\) | |||||||
\(942\) | −4.71091e18 | −0.219672 | ||||||||
\(943\) | 1.63897e17 | 0.00759003 | ||||||||
\(944\) | −1.81521e18 | −0.0834852 | ||||||||
\(945\) | 1.14666e18 | 0.0523753 | ||||||||
\(946\) | 1.11856e18 | 0.0507418 | ||||||||
\(947\) | −9.21560e18 | −0.415192 | −0.207596 | − | 0.978215i | \(-0.566564\pi\) | ||||
−0.207596 | + | 0.978215i | \(0.566564\pi\) | |||||||
\(948\) | −1.04451e18 | −0.0467369 | ||||||||
\(949\) | −1.08321e19 | −0.481373 | ||||||||
\(950\) | 1.23849e19 | 0.546625 | ||||||||
\(951\) | 1.50438e18 | 0.0659455 | ||||||||
\(952\) | 4.26549e19 | 1.85707 | ||||||||
\(953\) | −1.78222e19 | −0.770652 | −0.385326 | − | 0.922780i | \(-0.625911\pi\) | ||||
−0.385326 | + | 0.922780i | \(0.625911\pi\) | |||||||
\(954\) | 5.14985e18 | 0.221172 | ||||||||
\(955\) | −8.91181e17 | −0.0380140 | ||||||||
\(956\) | 8.98123e18 | 0.380504 | ||||||||
\(957\) | −8.15401e18 | −0.343118 | ||||||||
\(958\) | −9.99500e18 | −0.417741 | ||||||||
\(959\) | 2.09148e19 | 0.868227 | ||||||||
\(960\) | 3.80048e18 | 0.156702 | ||||||||
\(961\) | 1.27502e19 | 0.522175 | ||||||||
\(962\) | 1.27684e19 | 0.519397 | ||||||||
\(963\) | −1.33495e19 | −0.539378 | ||||||||
\(964\) | 4.52622e18 | 0.181650 | ||||||||
\(965\) | −6.27946e18 | −0.250319 | ||||||||
\(966\) | −1.44426e19 | −0.571864 | ||||||||
\(967\) | 1.99762e19 | 0.785670 | 0.392835 | − | 0.919609i | \(-0.371494\pi\) | ||||
0.392835 | + | 0.919609i | \(0.371494\pi\) | |||||||
\(968\) | 2.42195e19 | 0.946183 | ||||||||
\(969\) | 1.58041e19 | 0.613288 | ||||||||
\(970\) | 1.88398e18 | 0.0726206 | ||||||||
\(971\) | 2.21119e19 | 0.846645 | 0.423322 | − | 0.905979i | \(-0.360864\pi\) | ||||
0.423322 | + | 0.905979i | \(0.360864\pi\) | |||||||
\(972\) | −4.72630e17 | −0.0179759 | ||||||||
\(973\) | 1.28777e19 | 0.486524 | ||||||||
\(974\) | 1.36717e19 | 0.513085 | ||||||||
\(975\) | −1.37205e19 | −0.511493 | ||||||||
\(976\) | −1.49758e19 | −0.554584 | ||||||||
\(977\) | −3.48798e19 | −1.28310 | −0.641548 | − | 0.767083i | \(-0.721707\pi\) | ||||
−0.641548 | + | 0.767083i | \(0.721707\pi\) | |||||||
\(978\) | 1.66132e19 | 0.607085 | ||||||||
\(979\) | −1.07649e19 | −0.390770 | ||||||||
\(980\) | −4.19731e17 | −0.0151357 | ||||||||
\(981\) | −1.33870e19 | −0.479551 | ||||||||
\(982\) | 1.54370e19 | 0.549337 | ||||||||
\(983\) | 1.62288e19 | 0.573703 | 0.286852 | − | 0.957975i | \(-0.407391\pi\) | ||||
0.286852 | + | 0.957975i | \(0.407391\pi\) | |||||||
\(984\) | 1.28177e17 | 0.00450134 | ||||||||
\(985\) | 1.28910e19 | 0.449731 | ||||||||
\(986\) | 6.27585e19 | 2.17507 | ||||||||
\(987\) | −1.76664e19 | −0.608256 | ||||||||
\(988\) | 5.30081e18 | 0.181310 | ||||||||
\(989\) | −5.18461e18 | −0.176173 | ||||||||
\(990\) | 7.41208e17 | 0.0250214 | ||||||||
\(991\) | 1.89013e18 | 0.0633889 | 0.0316945 | − | 0.999498i | \(-0.489910\pi\) | ||||
0.0316945 | + | 0.999498i | \(0.489910\pi\) | |||||||
\(992\) | 2.00738e19 | 0.668810 | ||||||||
\(993\) | −2.75899e19 | −0.913229 | ||||||||
\(994\) | −4.74517e19 | −1.56042 | ||||||||
\(995\) | 7.15083e18 | 0.233618 | ||||||||
\(996\) | 5.26918e18 | 0.171024 | ||||||||
\(997\) | 4.69666e19 | 1.51450 | 0.757252 | − | 0.653123i | \(-0.226541\pi\) | ||||
0.757252 | + | 0.653123i | \(0.226541\pi\) | |||||||
\(998\) | −4.90535e19 | −1.57153 | ||||||||
\(999\) | 3.92439e18 | 0.124910 |
(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 | 177.14.a.a.1.22 | ✓ | 30 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.14.a.a.1.22 | ✓ | 30 | 1.1 | even | 1 | trivial |