Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,12,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, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
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: | \(135.996742959\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −33.1334 | −0.732152 | −0.366076 | − | 0.930585i | \(-0.619299\pi\) | ||||
−0.366076 | + | 0.930585i | \(0.619299\pi\) | |||||||
\(3\) | 243.000 | 0.577350 | ||||||||
\(4\) | −950.178 | −0.463954 | ||||||||
\(5\) | −7615.06 | −1.08978 | −0.544889 | − | 0.838508i | \(-0.683428\pi\) | ||||
−0.544889 | + | 0.838508i | \(0.683428\pi\) | |||||||
\(6\) | −8051.42 | −0.422708 | ||||||||
\(7\) | 31854.1 | 0.716350 | 0.358175 | − | 0.933654i | \(-0.383399\pi\) | ||||
0.358175 | + | 0.933654i | \(0.383399\pi\) | |||||||
\(8\) | 99339.8 | 1.07184 | ||||||||
\(9\) | 59049.0 | 0.333333 | ||||||||
\(10\) | 252313. | 0.797883 | ||||||||
\(11\) | −99167.3 | −0.185656 | −0.0928280 | − | 0.995682i | \(-0.529591\pi\) | ||||
−0.0928280 | + | 0.995682i | \(0.529591\pi\) | |||||||
\(12\) | −230893. | −0.267864 | ||||||||
\(13\) | −2.33849e6 | −1.74681 | −0.873406 | − | 0.486992i | \(-0.838094\pi\) | ||||
−0.873406 | + | 0.486992i | \(0.838094\pi\) | |||||||
\(14\) | −1.05543e6 | −0.524477 | ||||||||
\(15\) | −1.85046e6 | −0.629184 | ||||||||
\(16\) | −1.34550e6 | −0.320793 | ||||||||
\(17\) | 6.72361e6 | 1.14851 | 0.574253 | − | 0.818678i | \(-0.305292\pi\) | ||||
0.574253 | + | 0.818678i | \(0.305292\pi\) | |||||||
\(18\) | −1.95649e6 | −0.244051 | ||||||||
\(19\) | 1.10609e7 | 1.02482 | 0.512410 | − | 0.858741i | \(-0.328753\pi\) | ||||
0.512410 | + | 0.858741i | \(0.328753\pi\) | |||||||
\(20\) | 7.23566e6 | 0.505607 | ||||||||
\(21\) | 7.74054e6 | 0.413585 | ||||||||
\(22\) | 3.28575e6 | 0.135928 | ||||||||
\(23\) | −5.57179e7 | −1.80506 | −0.902531 | − | 0.430625i | \(-0.858293\pi\) | ||||
−0.902531 | + | 0.430625i | \(0.858293\pi\) | |||||||
\(24\) | 2.41396e7 | 0.618825 | ||||||||
\(25\) | 9.16098e6 | 0.187617 | ||||||||
\(26\) | 7.74820e7 | 1.27893 | ||||||||
\(27\) | 1.43489e7 | 0.192450 | ||||||||
\(28\) | −3.02670e7 | −0.332354 | ||||||||
\(29\) | 1.29094e8 | 1.16874 | 0.584369 | − | 0.811488i | \(-0.301342\pi\) | ||||
0.584369 | + | 0.811488i | \(0.301342\pi\) | |||||||
\(30\) | 6.13120e7 | 0.460658 | ||||||||
\(31\) | 2.79883e8 | 1.75585 | 0.877924 | − | 0.478800i | \(-0.158928\pi\) | ||||
0.877924 | + | 0.478800i | \(0.158928\pi\) | |||||||
\(32\) | −1.58867e8 | −0.836967 | ||||||||
\(33\) | −2.40977e7 | −0.107189 | ||||||||
\(34\) | −2.22776e8 | −0.840881 | ||||||||
\(35\) | −2.42570e8 | −0.780663 | ||||||||
\(36\) | −5.61070e7 | −0.154651 | ||||||||
\(37\) | −4.52016e8 | −1.07163 | −0.535814 | − | 0.844336i | \(-0.679995\pi\) | ||||
−0.535814 | + | 0.844336i | \(0.679995\pi\) | |||||||
\(38\) | −3.66487e8 | −0.750324 | ||||||||
\(39\) | −5.68252e8 | −1.00852 | ||||||||
\(40\) | −7.56479e8 | −1.16806 | ||||||||
\(41\) | −1.17503e9 | −1.58393 | −0.791965 | − | 0.610566i | \(-0.790942\pi\) | ||||
−0.791965 | + | 0.610566i | \(0.790942\pi\) | |||||||
\(42\) | −2.56470e8 | −0.302807 | ||||||||
\(43\) | −2.54829e8 | −0.264346 | −0.132173 | − | 0.991227i | \(-0.542195\pi\) | ||||
−0.132173 | + | 0.991227i | \(0.542195\pi\) | |||||||
\(44\) | 9.42266e7 | 0.0861358 | ||||||||
\(45\) | −4.49662e8 | −0.363259 | ||||||||
\(46\) | 1.84613e9 | 1.32158 | ||||||||
\(47\) | −5.43969e8 | −0.345968 | −0.172984 | − | 0.984925i | \(-0.555341\pi\) | ||||
−0.172984 | + | 0.984925i | \(0.555341\pi\) | |||||||
\(48\) | −3.26957e8 | −0.185210 | ||||||||
\(49\) | −9.62646e8 | −0.486842 | ||||||||
\(50\) | −3.03535e8 | −0.137364 | ||||||||
\(51\) | 1.63384e9 | 0.663091 | ||||||||
\(52\) | 2.22198e9 | 0.810441 | ||||||||
\(53\) | −1.96026e8 | −0.0643868 | −0.0321934 | − | 0.999482i | \(-0.510249\pi\) | ||||
−0.0321934 | + | 0.999482i | \(0.510249\pi\) | |||||||
\(54\) | −4.75428e8 | −0.140903 | ||||||||
\(55\) | 7.55165e8 | 0.202324 | ||||||||
\(56\) | 3.16438e9 | 0.767810 | ||||||||
\(57\) | 2.68781e9 | 0.591680 | ||||||||
\(58\) | −4.27732e9 | −0.855693 | ||||||||
\(59\) | 7.14924e8 | 0.130189 | ||||||||
\(60\) | 1.75826e9 | 0.291912 | ||||||||
\(61\) | 2.08702e8 | 0.0316383 | 0.0158191 | − | 0.999875i | \(-0.494964\pi\) | ||||
0.0158191 | + | 0.999875i | \(0.494964\pi\) | |||||||
\(62\) | −9.27347e9 | −1.28555 | ||||||||
\(63\) | 1.88095e9 | 0.238783 | ||||||||
\(64\) | 8.01939e9 | 0.933580 | ||||||||
\(65\) | 1.78077e10 | 1.90364 | ||||||||
\(66\) | 7.98438e8 | 0.0784783 | ||||||||
\(67\) | −1.67659e10 | −1.51711 | −0.758553 | − | 0.651612i | \(-0.774093\pi\) | ||||
−0.758553 | + | 0.651612i | \(0.774093\pi\) | |||||||
\(68\) | −6.38863e9 | −0.532854 | ||||||||
\(69\) | −1.35395e10 | −1.04215 | ||||||||
\(70\) | 8.03719e9 | 0.571564 | ||||||||
\(71\) | 1.37657e10 | 0.905476 | 0.452738 | − | 0.891644i | \(-0.350447\pi\) | ||||
0.452738 | + | 0.891644i | \(0.350447\pi\) | |||||||
\(72\) | 5.86592e9 | 0.357279 | ||||||||
\(73\) | 1.74137e10 | 0.983140 | 0.491570 | − | 0.870838i | \(-0.336423\pi\) | ||||
0.491570 | + | 0.870838i | \(0.336423\pi\) | |||||||
\(74\) | 1.49768e10 | 0.784595 | ||||||||
\(75\) | 2.22612e9 | 0.108321 | ||||||||
\(76\) | −1.05099e10 | −0.475469 | ||||||||
\(77\) | −3.15888e9 | −0.132995 | ||||||||
\(78\) | 1.88281e10 | 0.738392 | ||||||||
\(79\) | −4.30634e10 | −1.57456 | −0.787280 | − | 0.616596i | \(-0.788511\pi\) | ||||
−0.787280 | + | 0.616596i | \(0.788511\pi\) | |||||||
\(80\) | 1.02461e10 | 0.349593 | ||||||||
\(81\) | 3.48678e9 | 0.111111 | ||||||||
\(82\) | 3.89326e10 | 1.15968 | ||||||||
\(83\) | 1.24248e10 | 0.346227 | 0.173113 | − | 0.984902i | \(-0.444617\pi\) | ||||
0.173113 | + | 0.984902i | \(0.444617\pi\) | |||||||
\(84\) | −7.35488e9 | −0.191884 | ||||||||
\(85\) | −5.12007e10 | −1.25162 | ||||||||
\(86\) | 8.44337e9 | 0.193542 | ||||||||
\(87\) | 3.13698e10 | 0.674771 | ||||||||
\(88\) | −9.85127e9 | −0.198993 | ||||||||
\(89\) | −7.87224e10 | −1.49435 | −0.747177 | − | 0.664626i | \(-0.768591\pi\) | ||||
−0.747177 | + | 0.664626i | \(0.768591\pi\) | |||||||
\(90\) | 1.48988e10 | 0.265961 | ||||||||
\(91\) | −7.44903e10 | −1.25133 | ||||||||
\(92\) | 5.29419e10 | 0.837465 | ||||||||
\(93\) | 6.80115e10 | 1.01374 | ||||||||
\(94\) | 1.80236e10 | 0.253301 | ||||||||
\(95\) | −8.42298e10 | −1.11683 | ||||||||
\(96\) | −3.86046e10 | −0.483223 | ||||||||
\(97\) | 4.05929e9 | 0.0479960 | 0.0239980 | − | 0.999712i | \(-0.492360\pi\) | ||||
0.0239980 | + | 0.999712i | \(0.492360\pi\) | |||||||
\(98\) | 3.18957e10 | 0.356442 | ||||||||
\(99\) | −5.85573e9 | −0.0618853 | ||||||||
\(100\) | −8.70456e9 | −0.0870456 | ||||||||
\(101\) | −1.60174e9 | −0.0151644 | −0.00758218 | − | 0.999971i | \(-0.502414\pi\) | ||||
−0.00758218 | + | 0.999971i | \(0.502414\pi\) | |||||||
\(102\) | −5.41346e10 | −0.485483 | ||||||||
\(103\) | 5.39345e10 | 0.458418 | 0.229209 | − | 0.973377i | \(-0.426386\pi\) | ||||
0.229209 | + | 0.973377i | \(0.426386\pi\) | |||||||
\(104\) | −2.32305e11 | −1.87230 | ||||||||
\(105\) | −5.89446e10 | −0.450716 | ||||||||
\(106\) | 6.49501e9 | 0.0471409 | ||||||||
\(107\) | −1.13176e10 | −0.0780091 | −0.0390046 | − | 0.999239i | \(-0.512419\pi\) | ||||
−0.0390046 | + | 0.999239i | \(0.512419\pi\) | |||||||
\(108\) | −1.36340e10 | −0.0892880 | ||||||||
\(109\) | −1.07676e11 | −0.670308 | −0.335154 | − | 0.942163i | \(-0.608788\pi\) | ||||
−0.335154 | + | 0.942163i | \(0.608788\pi\) | |||||||
\(110\) | −2.50212e10 | −0.148132 | ||||||||
\(111\) | −1.09840e11 | −0.618705 | ||||||||
\(112\) | −4.28597e10 | −0.229800 | ||||||||
\(113\) | 2.25571e11 | 1.15173 | 0.575865 | − | 0.817545i | \(-0.304665\pi\) | ||||
0.575865 | + | 0.817545i | \(0.304665\pi\) | |||||||
\(114\) | −8.90563e10 | −0.433200 | ||||||||
\(115\) | 4.24295e11 | 1.96712 | ||||||||
\(116\) | −1.22662e11 | −0.542240 | ||||||||
\(117\) | −1.38085e11 | −0.582271 | ||||||||
\(118\) | −2.36879e10 | −0.0953180 | ||||||||
\(119\) | 2.14174e11 | 0.822733 | ||||||||
\(120\) | −1.83824e11 | −0.674382 | ||||||||
\(121\) | −2.75478e11 | −0.965532 | ||||||||
\(122\) | −6.91501e9 | −0.0231640 | ||||||||
\(123\) | −2.85531e11 | −0.914483 | ||||||||
\(124\) | −2.65938e11 | −0.814632 | ||||||||
\(125\) | 3.02068e11 | 0.885317 | ||||||||
\(126\) | −6.23223e10 | −0.174826 | ||||||||
\(127\) | 3.37316e11 | 0.905976 | 0.452988 | − | 0.891517i | \(-0.350358\pi\) | ||||
0.452988 | + | 0.891517i | \(0.350358\pi\) | |||||||
\(128\) | 5.96496e10 | 0.153445 | ||||||||
\(129\) | −6.19236e10 | −0.152620 | ||||||||
\(130\) | −5.90030e11 | −1.39375 | ||||||||
\(131\) | 8.15888e11 | 1.84773 | 0.923864 | − | 0.382720i | \(-0.125013\pi\) | ||||
0.923864 | + | 0.382720i | \(0.125013\pi\) | |||||||
\(132\) | 2.28971e10 | 0.0497305 | ||||||||
\(133\) | 3.52336e11 | 0.734130 | ||||||||
\(134\) | 5.55512e11 | 1.11075 | ||||||||
\(135\) | −1.09268e11 | −0.209728 | ||||||||
\(136\) | 6.67923e11 | 1.23101 | ||||||||
\(137\) | −2.76493e8 | −0.000489465 0 | −0.000244732 | − | 1.00000i | \(-0.500078\pi\) | ||||
−0.000244732 | 1.00000i | \(0.500078\pi\) | ||||||||
\(138\) | 4.48608e11 | 0.763014 | ||||||||
\(139\) | 1.88096e11 | 0.307467 | 0.153734 | − | 0.988112i | \(-0.450870\pi\) | ||||
0.153734 | + | 0.988112i | \(0.450870\pi\) | |||||||
\(140\) | 2.30485e11 | 0.362192 | ||||||||
\(141\) | −1.32185e11 | −0.199745 | ||||||||
\(142\) | −4.56104e11 | −0.662946 | ||||||||
\(143\) | 2.31901e11 | 0.324306 | ||||||||
\(144\) | −7.94506e10 | −0.106931 | ||||||||
\(145\) | −9.83058e11 | −1.27366 | ||||||||
\(146\) | −5.76975e11 | −0.719808 | ||||||||
\(147\) | −2.33923e11 | −0.281078 | ||||||||
\(148\) | 4.29495e11 | 0.497186 | ||||||||
\(149\) | −2.65066e11 | −0.295685 | −0.147843 | − | 0.989011i | \(-0.547233\pi\) | ||||
−0.147843 | + | 0.989011i | \(0.547233\pi\) | |||||||
\(150\) | −7.37589e10 | −0.0793072 | ||||||||
\(151\) | 1.28494e12 | 1.33202 | 0.666009 | − | 0.745944i | \(-0.268001\pi\) | ||||
0.666009 | + | 0.745944i | \(0.268001\pi\) | |||||||
\(152\) | 1.09879e12 | 1.09844 | ||||||||
\(153\) | 3.97023e11 | 0.382836 | ||||||||
\(154\) | 1.04665e11 | 0.0973723 | ||||||||
\(155\) | −2.13132e12 | −1.91348 | ||||||||
\(156\) | 5.39940e11 | 0.467908 | ||||||||
\(157\) | −4.16613e11 | −0.348566 | −0.174283 | − | 0.984696i | \(-0.555761\pi\) | ||||
−0.174283 | + | 0.984696i | \(0.555761\pi\) | |||||||
\(158\) | 1.42684e12 | 1.15282 | ||||||||
\(159\) | −4.76343e10 | −0.0371737 | ||||||||
\(160\) | 1.20978e12 | 0.912109 | ||||||||
\(161\) | −1.77484e12 | −1.29306 | ||||||||
\(162\) | −1.15529e11 | −0.0813502 | ||||||||
\(163\) | 3.78137e11 | 0.257405 | 0.128703 | − | 0.991683i | \(-0.458919\pi\) | ||||
0.128703 | + | 0.991683i | \(0.458919\pi\) | |||||||
\(164\) | 1.11648e12 | 0.734871 | ||||||||
\(165\) | 1.83505e11 | 0.116812 | ||||||||
\(166\) | −4.11677e11 | −0.253490 | ||||||||
\(167\) | 3.30555e12 | 1.96926 | 0.984630 | − | 0.174655i | \(-0.0558809\pi\) | ||||
0.984630 | + | 0.174655i | \(0.0558809\pi\) | |||||||
\(168\) | 7.68943e11 | 0.443296 | ||||||||
\(169\) | 3.67636e12 | 2.05136 | ||||||||
\(170\) | 1.69645e12 | 0.916374 | ||||||||
\(171\) | 6.53138e11 | 0.341607 | ||||||||
\(172\) | 2.42133e11 | 0.122644 | ||||||||
\(173\) | 4.89191e11 | 0.240008 | 0.120004 | − | 0.992773i | \(-0.461709\pi\) | ||||
0.120004 | + | 0.992773i | \(0.461709\pi\) | |||||||
\(174\) | −1.03939e12 | −0.494035 | ||||||||
\(175\) | 2.91814e11 | 0.134399 | ||||||||
\(176\) | 1.33430e11 | 0.0595571 | ||||||||
\(177\) | 1.73727e11 | 0.0751646 | ||||||||
\(178\) | 2.60834e12 | 1.09409 | ||||||||
\(179\) | −3.03678e12 | −1.23516 | −0.617578 | − | 0.786510i | \(-0.711886\pi\) | ||||
−0.617578 | + | 0.786510i | \(0.711886\pi\) | |||||||
\(180\) | 4.27258e11 | 0.168536 | ||||||||
\(181\) | −3.34218e11 | −0.127879 | −0.0639393 | − | 0.997954i | \(-0.520366\pi\) | ||||
−0.0639393 | + | 0.997954i | \(0.520366\pi\) | |||||||
\(182\) | 2.46812e12 | 0.916163 | ||||||||
\(183\) | 5.07146e10 | 0.0182664 | ||||||||
\(184\) | −5.53501e12 | −1.93473 | ||||||||
\(185\) | 3.44213e12 | 1.16784 | ||||||||
\(186\) | −2.25345e12 | −0.742211 | ||||||||
\(187\) | −6.66763e11 | −0.213227 | ||||||||
\(188\) | 5.16867e11 | 0.160513 | ||||||||
\(189\) | 4.57071e11 | 0.137862 | ||||||||
\(190\) | 2.79082e12 | 0.817686 | ||||||||
\(191\) | 3.03727e12 | 0.864571 | 0.432285 | − | 0.901737i | \(-0.357707\pi\) | ||||
0.432285 | + | 0.901737i | \(0.357707\pi\) | |||||||
\(192\) | 1.94871e12 | 0.539003 | ||||||||
\(193\) | 5.70463e12 | 1.53342 | 0.766712 | − | 0.641991i | \(-0.221891\pi\) | ||||
0.766712 | + | 0.641991i | \(0.221891\pi\) | |||||||
\(194\) | −1.34498e11 | −0.0351404 | ||||||||
\(195\) | 4.32727e12 | 1.09907 | ||||||||
\(196\) | 9.14685e11 | 0.225872 | ||||||||
\(197\) | 4.35600e11 | 0.104598 | 0.0522991 | − | 0.998631i | \(-0.483345\pi\) | ||||
0.0522991 | + | 0.998631i | \(0.483345\pi\) | |||||||
\(198\) | 1.94020e11 | 0.0453094 | ||||||||
\(199\) | 3.56600e12 | 0.810009 | 0.405004 | − | 0.914315i | \(-0.367270\pi\) | ||||
0.405004 | + | 0.914315i | \(0.367270\pi\) | |||||||
\(200\) | 9.10051e11 | 0.201095 | ||||||||
\(201\) | −4.07412e12 | −0.875901 | ||||||||
\(202\) | 5.30710e10 | 0.0111026 | ||||||||
\(203\) | 4.11217e12 | 0.837226 | ||||||||
\(204\) | −1.55244e12 | −0.307644 | ||||||||
\(205\) | 8.94789e12 | 1.72613 | ||||||||
\(206\) | −1.78703e12 | −0.335632 | ||||||||
\(207\) | −3.29009e12 | −0.601687 | ||||||||
\(208\) | 3.14644e12 | 0.560365 | ||||||||
\(209\) | −1.09688e12 | −0.190264 | ||||||||
\(210\) | 1.95304e12 | 0.329993 | ||||||||
\(211\) | −7.12598e12 | −1.17298 | −0.586491 | − | 0.809956i | \(-0.699491\pi\) | ||||
−0.586491 | + | 0.809956i | \(0.699491\pi\) | |||||||
\(212\) | 1.86260e11 | 0.0298725 | ||||||||
\(213\) | 3.34506e12 | 0.522777 | ||||||||
\(214\) | 3.74992e11 | 0.0571145 | ||||||||
\(215\) | 1.94054e12 | 0.288079 | ||||||||
\(216\) | 1.42542e12 | 0.206275 | ||||||||
\(217\) | 8.91540e12 | 1.25780 | ||||||||
\(218\) | 3.56768e12 | 0.490767 | ||||||||
\(219\) | 4.23153e12 | 0.567616 | ||||||||
\(220\) | −7.17541e11 | −0.0938689 | ||||||||
\(221\) | −1.57231e13 | −2.00623 | ||||||||
\(222\) | 3.63937e12 | 0.452986 | ||||||||
\(223\) | 2.54932e11 | 0.0309562 | 0.0154781 | − | 0.999880i | \(-0.495073\pi\) | ||||
0.0154781 | + | 0.999880i | \(0.495073\pi\) | |||||||
\(224\) | −5.06055e12 | −0.599562 | ||||||||
\(225\) | 5.40947e11 | 0.0625390 | ||||||||
\(226\) | −7.47392e12 | −0.843242 | ||||||||
\(227\) | −6.88194e12 | −0.757824 | −0.378912 | − | 0.925433i | \(-0.623702\pi\) | ||||
−0.378912 | + | 0.925433i | \(0.623702\pi\) | |||||||
\(228\) | −2.55390e12 | −0.274512 | ||||||||
\(229\) | 1.08908e11 | 0.0114279 | 0.00571394 | − | 0.999984i | \(-0.498181\pi\) | ||||
0.00571394 | + | 0.999984i | \(0.498181\pi\) | |||||||
\(230\) | −1.40584e13 | −1.44023 | ||||||||
\(231\) | −7.67608e11 | −0.0767845 | ||||||||
\(232\) | 1.28242e13 | 1.25270 | ||||||||
\(233\) | 1.00418e13 | 0.957971 | 0.478985 | − | 0.877823i | \(-0.341005\pi\) | ||||
0.478985 | + | 0.877823i | \(0.341005\pi\) | |||||||
\(234\) | 4.57524e12 | 0.426311 | ||||||||
\(235\) | 4.14236e12 | 0.377029 | ||||||||
\(236\) | −6.79305e11 | −0.0604016 | ||||||||
\(237\) | −1.04644e13 | −0.909072 | ||||||||
\(238\) | −7.09632e12 | −0.602366 | ||||||||
\(239\) | 1.63667e13 | 1.35760 | 0.678802 | − | 0.734322i | \(-0.262500\pi\) | ||||
0.678802 | + | 0.734322i | \(0.262500\pi\) | |||||||
\(240\) | 2.48980e12 | 0.201838 | ||||||||
\(241\) | 2.87914e12 | 0.228123 | 0.114062 | − | 0.993474i | \(-0.463614\pi\) | ||||
0.114062 | + | 0.993474i | \(0.463614\pi\) | |||||||
\(242\) | 9.12751e12 | 0.706916 | ||||||||
\(243\) | 8.47289e11 | 0.0641500 | ||||||||
\(244\) | −1.98304e11 | −0.0146787 | ||||||||
\(245\) | 7.33060e12 | 0.530550 | ||||||||
\(246\) | 9.46062e12 | 0.669540 | ||||||||
\(247\) | −2.58659e13 | −1.79017 | ||||||||
\(248\) | 2.78035e13 | 1.88198 | ||||||||
\(249\) | 3.01923e12 | 0.199894 | ||||||||
\(250\) | −1.00085e13 | −0.648187 | ||||||||
\(251\) | 9.79800e12 | 0.620772 | 0.310386 | − | 0.950611i | \(-0.399542\pi\) | ||||
0.310386 | + | 0.950611i | \(0.399542\pi\) | |||||||
\(252\) | −1.78724e12 | −0.110785 | ||||||||
\(253\) | 5.52540e12 | 0.335120 | ||||||||
\(254\) | −1.11764e13 | −0.663312 | ||||||||
\(255\) | −1.24418e13 | −0.722622 | ||||||||
\(256\) | −1.84001e13 | −1.04593 | ||||||||
\(257\) | −6.46536e12 | −0.359717 | −0.179858 | − | 0.983693i | \(-0.557564\pi\) | ||||
−0.179858 | + | 0.983693i | \(0.557564\pi\) | |||||||
\(258\) | 2.05174e12 | 0.111741 | ||||||||
\(259\) | −1.43985e13 | −0.767662 | ||||||||
\(260\) | −1.69205e13 | −0.883201 | ||||||||
\(261\) | 7.62287e12 | 0.389579 | ||||||||
\(262\) | −2.70331e13 | −1.35282 | ||||||||
\(263\) | 3.52320e13 | 1.72656 | 0.863278 | − | 0.504729i | \(-0.168408\pi\) | ||||
0.863278 | + | 0.504729i | \(0.168408\pi\) | |||||||
\(264\) | −2.39386e12 | −0.114889 | ||||||||
\(265\) | 1.49275e12 | 0.0701673 | ||||||||
\(266\) | −1.16741e13 | −0.537495 | ||||||||
\(267\) | −1.91295e13 | −0.862765 | ||||||||
\(268\) | 1.59306e13 | 0.703867 | ||||||||
\(269\) | 3.95151e13 | 1.71051 | 0.855255 | − | 0.518207i | \(-0.173400\pi\) | ||||
0.855255 | + | 0.518207i | \(0.173400\pi\) | |||||||
\(270\) | 3.62041e12 | 0.153553 | ||||||||
\(271\) | −3.21606e13 | −1.33657 | −0.668286 | − | 0.743904i | \(-0.732972\pi\) | ||||
−0.668286 | + | 0.743904i | \(0.732972\pi\) | |||||||
\(272\) | −9.04664e12 | −0.368433 | ||||||||
\(273\) | −1.81011e13 | −0.722456 | ||||||||
\(274\) | 9.16116e9 | 0.000358362 0 | ||||||||
\(275\) | −9.08470e11 | −0.0348322 | ||||||||
\(276\) | 1.28649e13 | 0.483511 | ||||||||
\(277\) | 3.18499e13 | 1.17346 | 0.586731 | − | 0.809782i | \(-0.300415\pi\) | ||||
0.586731 | + | 0.809782i | \(0.300415\pi\) | |||||||
\(278\) | −6.23227e12 | −0.225113 | ||||||||
\(279\) | 1.65268e13 | 0.585282 | ||||||||
\(280\) | −2.40969e13 | −0.836743 | ||||||||
\(281\) | 2.48402e13 | 0.845806 | 0.422903 | − | 0.906175i | \(-0.361011\pi\) | ||||
0.422903 | + | 0.906175i | \(0.361011\pi\) | |||||||
\(282\) | 4.37972e12 | 0.146244 | ||||||||
\(283\) | −2.30183e13 | −0.753787 | −0.376893 | − | 0.926257i | \(-0.623008\pi\) | ||||
−0.376893 | + | 0.926257i | \(0.623008\pi\) | |||||||
\(284\) | −1.30799e13 | −0.420099 | ||||||||
\(285\) | −2.04678e13 | −0.644800 | ||||||||
\(286\) | −7.68369e12 | −0.237441 | ||||||||
\(287\) | −3.74293e13 | −1.13465 | ||||||||
\(288\) | −9.38093e12 | −0.278989 | ||||||||
\(289\) | 1.09351e13 | 0.319068 | ||||||||
\(290\) | 3.25721e13 | 0.932516 | ||||||||
\(291\) | 9.86406e11 | 0.0277105 | ||||||||
\(292\) | −1.65461e13 | −0.456132 | ||||||||
\(293\) | 4.00130e13 | 1.08250 | 0.541252 | − | 0.840861i | \(-0.317951\pi\) | ||||
0.541252 | + | 0.840861i | \(0.317951\pi\) | |||||||
\(294\) | 7.75066e12 | 0.205792 | ||||||||
\(295\) | −5.44419e12 | −0.141877 | ||||||||
\(296\) | −4.49032e13 | −1.14861 | ||||||||
\(297\) | −1.42294e12 | −0.0357295 | ||||||||
\(298\) | 8.78254e12 | 0.216486 | ||||||||
\(299\) | 1.30296e14 | 3.15310 | ||||||||
\(300\) | −2.11521e12 | −0.0502558 | ||||||||
\(301\) | −8.11735e12 | −0.189365 | ||||||||
\(302\) | −4.25745e13 | −0.975239 | ||||||||
\(303\) | −3.89222e11 | −0.00875515 | ||||||||
\(304\) | −1.48825e13 | −0.328755 | ||||||||
\(305\) | −1.58928e12 | −0.0344787 | ||||||||
\(306\) | −1.31547e13 | −0.280294 | ||||||||
\(307\) | −7.35835e13 | −1.54000 | −0.769998 | − | 0.638046i | \(-0.779743\pi\) | ||||
−0.769998 | + | 0.638046i | \(0.779743\pi\) | |||||||
\(308\) | 3.00150e12 | 0.0617034 | ||||||||
\(309\) | 1.31061e13 | 0.264668 | ||||||||
\(310\) | 7.06180e13 | 1.40096 | ||||||||
\(311\) | −3.87432e13 | −0.755115 | −0.377557 | − | 0.925986i | \(-0.623236\pi\) | ||||
−0.377557 | + | 0.925986i | \(0.623236\pi\) | |||||||
\(312\) | −5.64501e13 | −1.08097 | ||||||||
\(313\) | −6.86342e13 | −1.29136 | −0.645679 | − | 0.763609i | \(-0.723426\pi\) | ||||
−0.645679 | + | 0.763609i | \(0.723426\pi\) | |||||||
\(314\) | 1.38038e13 | 0.255203 | ||||||||
\(315\) | −1.43235e13 | −0.260221 | ||||||||
\(316\) | 4.09178e13 | 0.730523 | ||||||||
\(317\) | 7.94681e13 | 1.39433 | 0.697167 | − | 0.716909i | \(-0.254444\pi\) | ||||
0.697167 | + | 0.716909i | \(0.254444\pi\) | |||||||
\(318\) | 1.57829e12 | 0.0272168 | ||||||||
\(319\) | −1.28019e13 | −0.216983 | ||||||||
\(320\) | −6.10681e13 | −1.01740 | ||||||||
\(321\) | −2.75019e12 | −0.0450386 | ||||||||
\(322\) | 5.88066e13 | 0.946714 | ||||||||
\(323\) | 7.43695e13 | 1.17701 | ||||||||
\(324\) | −3.31306e12 | −0.0515504 | ||||||||
\(325\) | −2.14228e13 | −0.327732 | ||||||||
\(326\) | −1.25290e13 | −0.188460 | ||||||||
\(327\) | −2.61653e13 | −0.387002 | ||||||||
\(328\) | −1.16727e14 | −1.69771 | ||||||||
\(329\) | −1.73276e13 | −0.247834 | ||||||||
\(330\) | −6.08015e12 | −0.0855239 | ||||||||
\(331\) | 1.06800e14 | 1.47747 | 0.738734 | − | 0.673997i | \(-0.235424\pi\) | ||||
0.738734 | + | 0.673997i | \(0.235424\pi\) | |||||||
\(332\) | −1.18058e13 | −0.160633 | ||||||||
\(333\) | −2.66911e13 | −0.357210 | ||||||||
\(334\) | −1.09524e14 | −1.44180 | ||||||||
\(335\) | 1.27673e14 | 1.65331 | ||||||||
\(336\) | −1.04149e13 | −0.132675 | ||||||||
\(337\) | 1.17087e14 | 1.46738 | 0.733691 | − | 0.679483i | \(-0.237796\pi\) | ||||
0.733691 | + | 0.679483i | \(0.237796\pi\) | |||||||
\(338\) | −1.21810e14 | −1.50190 | ||||||||
\(339\) | 5.48136e13 | 0.664952 | ||||||||
\(340\) | 4.86498e13 | 0.580693 | ||||||||
\(341\) | −2.77552e13 | −0.325984 | ||||||||
\(342\) | −2.16407e13 | −0.250108 | ||||||||
\(343\) | −9.36501e13 | −1.06510 | ||||||||
\(344\) | −2.53147e13 | −0.283336 | ||||||||
\(345\) | 1.03104e14 | 1.13572 | ||||||||
\(346\) | −1.62086e13 | −0.175722 | ||||||||
\(347\) | 3.75321e13 | 0.400489 | 0.200244 | − | 0.979746i | \(-0.435826\pi\) | ||||
0.200244 | + | 0.979746i | \(0.435826\pi\) | |||||||
\(348\) | −2.98069e13 | −0.313063 | ||||||||
\(349\) | −5.49071e13 | −0.567660 | −0.283830 | − | 0.958875i | \(-0.591605\pi\) | ||||
−0.283830 | + | 0.958875i | \(0.591605\pi\) | |||||||
\(350\) | −9.66881e12 | −0.0984008 | ||||||||
\(351\) | −3.35547e13 | −0.336174 | ||||||||
\(352\) | 1.57544e13 | 0.155388 | ||||||||
\(353\) | 2.81865e13 | 0.273704 | 0.136852 | − | 0.990592i | \(-0.456302\pi\) | ||||
0.136852 | + | 0.990592i | \(0.456302\pi\) | |||||||
\(354\) | −5.75615e12 | −0.0550319 | ||||||||
\(355\) | −1.04827e14 | −0.986769 | ||||||||
\(356\) | 7.48002e13 | 0.693311 | ||||||||
\(357\) | 5.20444e13 | 0.475005 | ||||||||
\(358\) | 1.00619e14 | 0.904321 | ||||||||
\(359\) | −2.43931e13 | −0.215898 | −0.107949 | − | 0.994156i | \(-0.534428\pi\) | ||||
−0.107949 | + | 0.994156i | \(0.534428\pi\) | |||||||
\(360\) | −4.46693e13 | −0.389355 | ||||||||
\(361\) | 5.85431e12 | 0.0502558 | ||||||||
\(362\) | 1.10738e13 | 0.0936265 | ||||||||
\(363\) | −6.69410e13 | −0.557450 | ||||||||
\(364\) | 7.07790e13 | 0.580559 | ||||||||
\(365\) | −1.32606e14 | −1.07141 | ||||||||
\(366\) | −1.68035e12 | −0.0133737 | ||||||||
\(367\) | 4.60549e13 | 0.361088 | 0.180544 | − | 0.983567i | \(-0.442214\pi\) | ||||
0.180544 | + | 0.983567i | \(0.442214\pi\) | |||||||
\(368\) | 7.49687e13 | 0.579051 | ||||||||
\(369\) | −6.93841e13 | −0.527977 | ||||||||
\(370\) | −1.14049e14 | −0.855034 | ||||||||
\(371\) | −6.24423e12 | −0.0461235 | ||||||||
\(372\) | −6.46230e13 | −0.470328 | ||||||||
\(373\) | 1.15238e14 | 0.826416 | 0.413208 | − | 0.910637i | \(-0.364408\pi\) | ||||
0.413208 | + | 0.910637i | \(0.364408\pi\) | |||||||
\(374\) | 2.20921e13 | 0.156115 | ||||||||
\(375\) | 7.34024e13 | 0.511138 | ||||||||
\(376\) | −5.40378e13 | −0.370821 | ||||||||
\(377\) | −3.01885e14 | −2.04157 | ||||||||
\(378\) | −1.51443e13 | −0.100936 | ||||||||
\(379\) | 1.20190e14 | 0.789503 | 0.394752 | − | 0.918788i | \(-0.370831\pi\) | ||||
0.394752 | + | 0.918788i | \(0.370831\pi\) | |||||||
\(380\) | 8.00332e13 | 0.518156 | ||||||||
\(381\) | 8.19678e13 | 0.523065 | ||||||||
\(382\) | −1.00635e14 | −0.632997 | ||||||||
\(383\) | −7.39307e13 | −0.458386 | −0.229193 | − | 0.973381i | \(-0.573609\pi\) | ||||
−0.229193 | + | 0.973381i | \(0.573609\pi\) | |||||||
\(384\) | 1.44949e13 | 0.0885916 | ||||||||
\(385\) | 2.40551e13 | 0.144935 | ||||||||
\(386\) | −1.89014e14 | −1.12270 | ||||||||
\(387\) | −1.50474e13 | −0.0881154 | ||||||||
\(388\) | −3.85704e12 | −0.0222679 | ||||||||
\(389\) | −3.62478e13 | −0.206329 | −0.103164 | − | 0.994664i | \(-0.532897\pi\) | ||||
−0.103164 | + | 0.994664i | \(0.532897\pi\) | |||||||
\(390\) | −1.43377e14 | −0.804683 | ||||||||
\(391\) | −3.74626e14 | −2.07313 | ||||||||
\(392\) | −9.56291e13 | −0.521815 | ||||||||
\(393\) | 1.98261e14 | 1.06679 | ||||||||
\(394\) | −1.44329e13 | −0.0765817 | ||||||||
\(395\) | 3.27930e14 | 1.71592 | ||||||||
\(396\) | 5.56399e12 | 0.0287119 | ||||||||
\(397\) | −1.65352e14 | −0.841515 | −0.420758 | − | 0.907173i | \(-0.638236\pi\) | ||||
−0.420758 | + | 0.907173i | \(0.638236\pi\) | |||||||
\(398\) | −1.18154e14 | −0.593049 | ||||||||
\(399\) | 8.56177e13 | 0.423850 | ||||||||
\(400\) | −1.23261e13 | −0.0601862 | ||||||||
\(401\) | 7.97032e13 | 0.383868 | 0.191934 | − | 0.981408i | \(-0.438524\pi\) | ||||
0.191934 | + | 0.981408i | \(0.438524\pi\) | |||||||
\(402\) | 1.34989e14 | 0.641293 | ||||||||
\(403\) | −6.54502e14 | −3.06714 | ||||||||
\(404\) | 1.52194e12 | 0.00703556 | ||||||||
\(405\) | −2.65521e13 | −0.121086 | ||||||||
\(406\) | −1.36250e14 | −0.612976 | ||||||||
\(407\) | 4.48252e13 | 0.198954 | ||||||||
\(408\) | 1.62305e14 | 0.710725 | ||||||||
\(409\) | −2.79151e14 | −1.20604 | −0.603019 | − | 0.797727i | \(-0.706036\pi\) | ||||
−0.603019 | + | 0.797727i | \(0.706036\pi\) | |||||||
\(410\) | −2.96474e14 | −1.26379 | ||||||||
\(411\) | −6.71878e10 | −0.000282593 0 | ||||||||
\(412\) | −5.12474e13 | −0.212685 | ||||||||
\(413\) | 2.27732e13 | 0.0932609 | ||||||||
\(414\) | 1.09012e14 | 0.440526 | ||||||||
\(415\) | −9.46157e13 | −0.377310 | ||||||||
\(416\) | 3.71508e14 | 1.46203 | ||||||||
\(417\) | 4.57074e13 | 0.177516 | ||||||||
\(418\) | 3.63435e13 | 0.139302 | ||||||||
\(419\) | 3.51450e14 | 1.32950 | 0.664748 | − | 0.747068i | \(-0.268539\pi\) | ||||
0.664748 | + | 0.747068i | \(0.268539\pi\) | |||||||
\(420\) | 5.60079e13 | 0.209111 | ||||||||
\(421\) | 1.33484e14 | 0.491900 | 0.245950 | − | 0.969282i | \(-0.420900\pi\) | ||||
0.245950 | + | 0.969282i | \(0.420900\pi\) | |||||||
\(422\) | 2.36108e14 | 0.858800 | ||||||||
\(423\) | −3.21208e13 | −0.115323 | ||||||||
\(424\) | −1.94732e13 | −0.0690121 | ||||||||
\(425\) | 6.15949e13 | 0.215479 | ||||||||
\(426\) | −1.10833e14 | −0.382752 | ||||||||
\(427\) | 6.64801e12 | 0.0226641 | ||||||||
\(428\) | 1.07538e13 | 0.0361926 | ||||||||
\(429\) | 5.63521e13 | 0.187238 | ||||||||
\(430\) | −6.42967e13 | −0.210917 | ||||||||
\(431\) | 1.79025e14 | 0.579815 | 0.289907 | − | 0.957055i | \(-0.406376\pi\) | ||||
0.289907 | + | 0.957055i | \(0.406376\pi\) | |||||||
\(432\) | −1.93065e13 | −0.0617366 | ||||||||
\(433\) | 1.72864e14 | 0.545786 | 0.272893 | − | 0.962044i | \(-0.412020\pi\) | ||||
0.272893 | + | 0.962044i | \(0.412020\pi\) | |||||||
\(434\) | −2.95398e14 | −0.920902 | ||||||||
\(435\) | −2.38883e14 | −0.735351 | ||||||||
\(436\) | 1.02312e14 | 0.310992 | ||||||||
\(437\) | −6.16293e14 | −1.84986 | ||||||||
\(438\) | −1.40205e14 | −0.415581 | ||||||||
\(439\) | −5.80238e14 | −1.69844 | −0.849222 | − | 0.528037i | \(-0.822928\pi\) | ||||
−0.849222 | + | 0.528037i | \(0.822928\pi\) | |||||||
\(440\) | 7.50180e13 | 0.216858 | ||||||||
\(441\) | −5.68433e13 | −0.162281 | ||||||||
\(442\) | 5.20959e14 | 1.46886 | ||||||||
\(443\) | 3.25451e14 | 0.906286 | 0.453143 | − | 0.891438i | \(-0.350303\pi\) | ||||
0.453143 | + | 0.891438i | \(0.350303\pi\) | |||||||
\(444\) | 1.04367e14 | 0.287051 | ||||||||
\(445\) | 5.99476e14 | 1.62851 | ||||||||
\(446\) | −8.44675e12 | −0.0226646 | ||||||||
\(447\) | −6.44111e13 | −0.170714 | ||||||||
\(448\) | 2.55450e14 | 0.668770 | ||||||||
\(449\) | −1.18005e14 | −0.305172 | −0.152586 | − | 0.988290i | \(-0.548760\pi\) | ||||
−0.152586 | + | 0.988290i | \(0.548760\pi\) | |||||||
\(450\) | −1.79234e13 | −0.0457880 | ||||||||
\(451\) | 1.16524e14 | 0.294066 | ||||||||
\(452\) | −2.14332e14 | −0.534350 | ||||||||
\(453\) | 3.12241e14 | 0.769041 | ||||||||
\(454\) | 2.28022e14 | 0.554842 | ||||||||
\(455\) | 5.67248e14 | 1.36367 | ||||||||
\(456\) | 2.67007e14 | 0.634184 | ||||||||
\(457\) | −1.55221e14 | −0.364261 | −0.182130 | − | 0.983274i | \(-0.558299\pi\) | ||||
−0.182130 | + | 0.983274i | \(0.558299\pi\) | |||||||
\(458\) | −3.60850e12 | −0.00836694 | ||||||||
\(459\) | 9.64765e13 | 0.221030 | ||||||||
\(460\) | −4.03156e14 | −0.912652 | ||||||||
\(461\) | 4.11776e14 | 0.921097 | 0.460549 | − | 0.887634i | \(-0.347653\pi\) | ||||
0.460549 | + | 0.887634i | \(0.347653\pi\) | |||||||
\(462\) | 2.54335e13 | 0.0562179 | ||||||||
\(463\) | −1.06071e14 | −0.231687 | −0.115844 | − | 0.993267i | \(-0.536957\pi\) | ||||
−0.115844 | + | 0.993267i | \(0.536957\pi\) | |||||||
\(464\) | −1.73696e14 | −0.374923 | ||||||||
\(465\) | −5.17912e14 | −1.10475 | ||||||||
\(466\) | −3.32718e14 | −0.701380 | ||||||||
\(467\) | −6.90002e14 | −1.43750 | −0.718749 | − | 0.695270i | \(-0.755285\pi\) | ||||
−0.718749 | + | 0.695270i | \(0.755285\pi\) | |||||||
\(468\) | 1.31206e14 | 0.270147 | ||||||||
\(469\) | −5.34062e14 | −1.08678 | ||||||||
\(470\) | −1.37250e14 | −0.276042 | ||||||||
\(471\) | −1.01237e14 | −0.201245 | ||||||||
\(472\) | 7.10205e13 | 0.139541 | ||||||||
\(473\) | 2.52708e13 | 0.0490775 | ||||||||
\(474\) | 3.46721e14 | 0.665579 | ||||||||
\(475\) | 1.01329e14 | 0.192274 | ||||||||
\(476\) | −2.03504e14 | −0.381710 | ||||||||
\(477\) | −1.15751e13 | −0.0214623 | ||||||||
\(478\) | −5.42285e14 | −0.993971 | ||||||||
\(479\) | −9.23453e14 | −1.67328 | −0.836641 | − | 0.547751i | \(-0.815484\pi\) | ||||
−0.836641 | + | 0.547751i | \(0.815484\pi\) | |||||||
\(480\) | 2.93977e14 | 0.526606 | ||||||||
\(481\) | 1.05703e15 | 1.87193 | ||||||||
\(482\) | −9.53957e13 | −0.167021 | ||||||||
\(483\) | −4.31287e14 | −0.746547 | ||||||||
\(484\) | 2.61753e14 | 0.447962 | ||||||||
\(485\) | −3.09117e13 | −0.0523050 | ||||||||
\(486\) | −2.80736e13 | −0.0469676 | ||||||||
\(487\) | 1.07267e15 | 1.77443 | 0.887214 | − | 0.461357i | \(-0.152637\pi\) | ||||
0.887214 | + | 0.461357i | \(0.152637\pi\) | |||||||
\(488\) | 2.07324e13 | 0.0339110 | ||||||||
\(489\) | 9.18873e13 | 0.148613 | ||||||||
\(490\) | −2.42888e14 | −0.388443 | ||||||||
\(491\) | −7.62052e13 | −0.120514 | −0.0602568 | − | 0.998183i | \(-0.519192\pi\) | ||||
−0.0602568 | + | 0.998183i | \(0.519192\pi\) | |||||||
\(492\) | 2.71305e14 | 0.424278 | ||||||||
\(493\) | 8.67978e14 | 1.34230 | ||||||||
\(494\) | 8.57025e14 | 1.31068 | ||||||||
\(495\) | 4.45917e13 | 0.0674413 | ||||||||
\(496\) | −3.76583e14 | −0.563263 | ||||||||
\(497\) | 4.38493e14 | 0.648638 | ||||||||
\(498\) | −1.00037e14 | −0.146353 | ||||||||
\(499\) | −8.39544e14 | −1.21476 | −0.607380 | − | 0.794411i | \(-0.707779\pi\) | ||||
−0.607380 | + | 0.794411i | \(0.707779\pi\) | |||||||
\(500\) | −2.87018e14 | −0.410746 | ||||||||
\(501\) | 8.03248e14 | 1.13695 | ||||||||
\(502\) | −3.24641e14 | −0.454499 | ||||||||
\(503\) | 3.99968e14 | 0.553862 | 0.276931 | − | 0.960890i | \(-0.410683\pi\) | ||||
0.276931 | + | 0.960890i | \(0.410683\pi\) | |||||||
\(504\) | 1.86853e14 | 0.255937 | ||||||||
\(505\) | 1.21973e13 | 0.0165258 | ||||||||
\(506\) | −1.83075e14 | −0.245359 | ||||||||
\(507\) | 8.93355e14 | 1.18435 | ||||||||
\(508\) | −3.20510e14 | −0.420331 | ||||||||
\(509\) | −4.77020e14 | −0.618855 | −0.309428 | − | 0.950923i | \(-0.600137\pi\) | ||||
−0.309428 | + | 0.950923i | \(0.600137\pi\) | |||||||
\(510\) | 4.12238e14 | 0.529069 | ||||||||
\(511\) | 5.54697e14 | 0.704273 | ||||||||
\(512\) | 4.87496e14 | 0.612331 | ||||||||
\(513\) | 1.58713e14 | 0.197227 | ||||||||
\(514\) | 2.14219e14 | 0.263367 | ||||||||
\(515\) | −4.10714e14 | −0.499574 | ||||||||
\(516\) | 5.88384e13 | 0.0708088 | ||||||||
\(517\) | 5.39440e13 | 0.0642311 | ||||||||
\(518\) | 4.77073e14 | 0.562045 | ||||||||
\(519\) | 1.18873e14 | 0.138568 | ||||||||
\(520\) | 1.76901e15 | 2.04039 | ||||||||
\(521\) | −9.56053e14 | −1.09113 | −0.545563 | − | 0.838070i | \(-0.683684\pi\) | ||||
−0.545563 | + | 0.838070i | \(0.683684\pi\) | |||||||
\(522\) | −2.52572e14 | −0.285231 | ||||||||
\(523\) | −1.61755e15 | −1.80758 | −0.903792 | − | 0.427972i | \(-0.859228\pi\) | ||||
−0.903792 | + | 0.427972i | \(0.859228\pi\) | |||||||
\(524\) | −7.75238e14 | −0.857261 | ||||||||
\(525\) | 7.09109e13 | 0.0775956 | ||||||||
\(526\) | −1.16736e15 | −1.26410 | ||||||||
\(527\) | 1.88182e15 | 2.01660 | ||||||||
\(528\) | 3.24235e13 | 0.0343853 | ||||||||
\(529\) | 2.15168e15 | 2.25825 | ||||||||
\(530\) | −4.94599e13 | −0.0513731 | ||||||||
\(531\) | 4.22156e13 | 0.0433963 | ||||||||
\(532\) | −3.34782e14 | −0.340603 | ||||||||
\(533\) | 2.74778e15 | 2.76683 | ||||||||
\(534\) | 6.33827e14 | 0.631675 | ||||||||
\(535\) | 8.61845e13 | 0.0850126 | ||||||||
\(536\) | −1.66552e15 | −1.62609 | ||||||||
\(537\) | −7.37937e14 | −0.713117 | ||||||||
\(538\) | −1.30927e15 | −1.25235 | ||||||||
\(539\) | 9.54630e13 | 0.0903851 | ||||||||
\(540\) | 1.03824e14 | 0.0973041 | ||||||||
\(541\) | −1.86689e15 | −1.73194 | −0.865972 | − | 0.500092i | \(-0.833300\pi\) | ||||
−0.865972 | + | 0.500092i | \(0.833300\pi\) | |||||||
\(542\) | 1.06559e15 | 0.978574 | ||||||||
\(543\) | −8.12150e13 | −0.0738307 | ||||||||
\(544\) | −1.06816e15 | −0.961263 | ||||||||
\(545\) | 8.19961e14 | 0.730487 | ||||||||
\(546\) | 5.99752e14 | 0.528947 | ||||||||
\(547\) | −1.39540e15 | −1.21834 | −0.609169 | − | 0.793041i | \(-0.708497\pi\) | ||||
−0.609169 | + | 0.793041i | \(0.708497\pi\) | |||||||
\(548\) | 2.62718e11 | 0.000227089 0 | ||||||||
\(549\) | 1.23236e13 | 0.0105461 | ||||||||
\(550\) | 3.01007e13 | 0.0255025 | ||||||||
\(551\) | 1.42790e15 | 1.19775 | ||||||||
\(552\) | −1.34501e15 | −1.11702 | ||||||||
\(553\) | −1.37174e15 | −1.12794 | ||||||||
\(554\) | −1.05529e15 | −0.859152 | ||||||||
\(555\) | 8.36437e14 | 0.674251 | ||||||||
\(556\) | −1.78725e14 | −0.142651 | ||||||||
\(557\) | 1.41602e15 | 1.11909 | 0.559546 | − | 0.828800i | \(-0.310976\pi\) | ||||
0.559546 | + | 0.828800i | \(0.310976\pi\) | |||||||
\(558\) | −5.47589e14 | −0.428516 | ||||||||
\(559\) | 5.95915e14 | 0.461763 | ||||||||
\(560\) | 3.26379e14 | 0.250431 | ||||||||
\(561\) | −1.62023e14 | −0.123107 | ||||||||
\(562\) | −8.23041e14 | −0.619258 | ||||||||
\(563\) | −1.01719e15 | −0.757887 | −0.378944 | − | 0.925420i | \(-0.623713\pi\) | ||||
−0.378944 | + | 0.925420i | \(0.623713\pi\) | |||||||
\(564\) | 1.25599e14 | 0.0926724 | ||||||||
\(565\) | −1.71773e15 | −1.25513 | ||||||||
\(566\) | 7.62676e14 | 0.551886 | ||||||||
\(567\) | 1.11068e14 | 0.0795945 | ||||||||
\(568\) | 1.36748e15 | 0.970522 | ||||||||
\(569\) | −1.92682e14 | −0.135433 | −0.0677163 | − | 0.997705i | \(-0.521571\pi\) | ||||
−0.0677163 | + | 0.997705i | \(0.521571\pi\) | |||||||
\(570\) | 6.78169e14 | 0.472092 | ||||||||
\(571\) | 4.49619e14 | 0.309989 | 0.154994 | − | 0.987915i | \(-0.450464\pi\) | ||||
0.154994 | + | 0.987915i | \(0.450464\pi\) | |||||||
\(572\) | −2.20348e14 | −0.150463 | ||||||||
\(573\) | 7.38058e14 | 0.499160 | ||||||||
\(574\) | 1.24016e15 | 0.830736 | ||||||||
\(575\) | −5.10431e14 | −0.338660 | ||||||||
\(576\) | 4.73537e14 | 0.311193 | ||||||||
\(577\) | −5.79595e13 | −0.0377275 | −0.0188637 | − | 0.999822i | \(-0.506005\pi\) | ||||
−0.0188637 | + | 0.999822i | \(0.506005\pi\) | |||||||
\(578\) | −3.62316e14 | −0.233606 | ||||||||
\(579\) | 1.38623e15 | 0.885323 | ||||||||
\(580\) | 9.34080e14 | 0.590922 | ||||||||
\(581\) | 3.95781e14 | 0.248020 | ||||||||
\(582\) | −3.26830e13 | −0.0202883 | ||||||||
\(583\) | 1.94394e13 | 0.0119538 | ||||||||
\(584\) | 1.72987e15 | 1.05377 | ||||||||
\(585\) | 1.05153e15 | 0.634546 | ||||||||
\(586\) | −1.32577e15 | −0.792557 | ||||||||
\(587\) | 1.51047e15 | 0.894545 | 0.447272 | − | 0.894398i | \(-0.352395\pi\) | ||||
0.447272 | + | 0.894398i | \(0.352395\pi\) | |||||||
\(588\) | 2.22268e14 | 0.130407 | ||||||||
\(589\) | 3.09577e15 | 1.79943 | ||||||||
\(590\) | 1.80385e14 | 0.103876 | ||||||||
\(591\) | 1.05851e14 | 0.0603898 | ||||||||
\(592\) | 6.08189e14 | 0.343771 | ||||||||
\(593\) | 1.43311e15 | 0.802561 | 0.401280 | − | 0.915955i | \(-0.368565\pi\) | ||||
0.401280 | + | 0.915955i | \(0.368565\pi\) | |||||||
\(594\) | 4.71469e13 | 0.0261594 | ||||||||
\(595\) | −1.63095e15 | −0.896597 | ||||||||
\(596\) | 2.51860e14 | 0.137184 | ||||||||
\(597\) | 8.66539e14 | 0.467659 | ||||||||
\(598\) | −4.31714e15 | −2.30855 | ||||||||
\(599\) | −1.05399e15 | −0.558457 | −0.279228 | − | 0.960225i | \(-0.590079\pi\) | ||||
−0.279228 | + | 0.960225i | \(0.590079\pi\) | |||||||
\(600\) | 2.21142e14 | 0.116102 | ||||||||
\(601\) | 2.55566e15 | 1.32952 | 0.664758 | − | 0.747059i | \(-0.268535\pi\) | ||||
0.664758 | + | 0.747059i | \(0.268535\pi\) | |||||||
\(602\) | 2.68956e14 | 0.138644 | ||||||||
\(603\) | −9.90010e14 | −0.505702 | ||||||||
\(604\) | −1.22092e15 | −0.617995 | ||||||||
\(605\) | 2.09778e15 | 1.05222 | ||||||||
\(606\) | 1.28963e13 | 0.00641010 | ||||||||
\(607\) | −4.23249e14 | −0.208477 | −0.104238 | − | 0.994552i | \(-0.533241\pi\) | ||||
−0.104238 | + | 0.994552i | \(0.533241\pi\) | |||||||
\(608\) | −1.75722e15 | −0.857741 | ||||||||
\(609\) | 9.99257e14 | 0.483372 | ||||||||
\(610\) | 5.26582e13 | 0.0252436 | ||||||||
\(611\) | 1.27206e15 | 0.604342 | ||||||||
\(612\) | −3.77242e14 | −0.177618 | ||||||||
\(613\) | 3.17218e15 | 1.48021 | 0.740107 | − | 0.672489i | \(-0.234775\pi\) | ||||
0.740107 | + | 0.672489i | \(0.234775\pi\) | |||||||
\(614\) | 2.43807e15 | 1.12751 | ||||||||
\(615\) | 2.17434e15 | 0.996584 | ||||||||
\(616\) | −3.13803e14 | −0.142549 | ||||||||
\(617\) | 5.88656e13 | 0.0265029 | 0.0132514 | − | 0.999912i | \(-0.495782\pi\) | ||||
0.0132514 | + | 0.999912i | \(0.495782\pi\) | |||||||
\(618\) | −4.34249e14 | −0.193777 | ||||||||
\(619\) | 6.94566e14 | 0.307195 | 0.153598 | − | 0.988133i | \(-0.450914\pi\) | ||||
0.153598 | + | 0.988133i | \(0.450914\pi\) | |||||||
\(620\) | 2.02514e15 | 0.887769 | ||||||||
\(621\) | −7.99492e14 | −0.347384 | ||||||||
\(622\) | 1.28369e15 | 0.552859 | ||||||||
\(623\) | −2.50763e15 | −1.07048 | ||||||||
\(624\) | 7.64585e14 | 0.323527 | ||||||||
\(625\) | −2.74758e15 | −1.15242 | ||||||||
\(626\) | 2.27409e15 | 0.945470 | ||||||||
\(627\) | −2.66543e14 | −0.109849 | ||||||||
\(628\) | 3.95856e14 | 0.161718 | ||||||||
\(629\) | −3.03918e15 | −1.23077 | ||||||||
\(630\) | 4.74588e14 | 0.190521 | ||||||||
\(631\) | 2.97858e14 | 0.118535 | 0.0592677 | − | 0.998242i | \(-0.481123\pi\) | ||||
0.0592677 | + | 0.998242i | \(0.481123\pi\) | |||||||
\(632\) | −4.27791e15 | −1.68767 | ||||||||
\(633\) | −1.73161e15 | −0.677221 | ||||||||
\(634\) | −2.63305e15 | −1.02086 | ||||||||
\(635\) | −2.56868e15 | −0.987313 | ||||||||
\(636\) | 4.52611e13 | 0.0172469 | ||||||||
\(637\) | 2.25113e15 | 0.850422 | ||||||||
\(638\) | 4.24171e14 | 0.158865 | ||||||||
\(639\) | 8.12850e14 | 0.301825 | ||||||||
\(640\) | −4.54235e14 | −0.167221 | ||||||||
\(641\) | −1.37938e15 | −0.503458 | −0.251729 | − | 0.967798i | \(-0.580999\pi\) | ||||
−0.251729 | + | 0.967798i | \(0.580999\pi\) | |||||||
\(642\) | 9.11231e13 | 0.0329751 | ||||||||
\(643\) | 3.94278e15 | 1.41463 | 0.707313 | − | 0.706900i | \(-0.249907\pi\) | ||||
0.707313 | + | 0.706900i | \(0.249907\pi\) | |||||||
\(644\) | 1.68642e15 | 0.599919 | ||||||||
\(645\) | 4.71552e14 | 0.166322 | ||||||||
\(646\) | −2.46412e15 | −0.861752 | ||||||||
\(647\) | 2.88189e15 | 0.999317 | 0.499658 | − | 0.866222i | \(-0.333459\pi\) | ||||
0.499658 | + | 0.866222i | \(0.333459\pi\) | |||||||
\(648\) | 3.46377e14 | 0.119093 | ||||||||
\(649\) | −7.08971e13 | −0.0241703 | ||||||||
\(650\) | 7.09811e14 | 0.239949 | ||||||||
\(651\) | 2.16644e15 | 0.726192 | ||||||||
\(652\) | −3.59297e14 | −0.119424 | ||||||||
\(653\) | 2.74822e15 | 0.905794 | 0.452897 | − | 0.891563i | \(-0.350390\pi\) | ||||
0.452897 | + | 0.891563i | \(0.350390\pi\) | |||||||
\(654\) | 8.66946e14 | 0.283344 | ||||||||
\(655\) | −6.21303e15 | −2.01362 | ||||||||
\(656\) | 1.58100e15 | 0.508114 | ||||||||
\(657\) | 1.02826e15 | 0.327713 | ||||||||
\(658\) | 5.74123e14 | 0.181452 | ||||||||
\(659\) | 3.87276e15 | 1.21381 | 0.606905 | − | 0.794774i | \(-0.292411\pi\) | ||||
0.606905 | + | 0.794774i | \(0.292411\pi\) | |||||||
\(660\) | −1.74362e14 | −0.0541953 | ||||||||
\(661\) | 2.71094e15 | 0.835625 | 0.417812 | − | 0.908533i | \(-0.362797\pi\) | ||||
0.417812 | + | 0.908533i | \(0.362797\pi\) | |||||||
\(662\) | −3.53866e15 | −1.08173 | ||||||||
\(663\) | −3.82071e15 | −1.15830 | ||||||||
\(664\) | 1.23428e15 | 0.371098 | ||||||||
\(665\) | −2.68306e15 | −0.800039 | ||||||||
\(666\) | 8.84367e14 | 0.261532 | ||||||||
\(667\) | −7.19285e15 | −2.10964 | ||||||||
\(668\) | −3.14086e15 | −0.913646 | ||||||||
\(669\) | 6.19484e13 | 0.0178725 | ||||||||
\(670\) | −4.23025e15 | −1.21047 | ||||||||
\(671\) | −2.06964e13 | −0.00587383 | ||||||||
\(672\) | −1.22971e15 | −0.346157 | ||||||||
\(673\) | −4.09696e14 | −0.114388 | −0.0571938 | − | 0.998363i | \(-0.518215\pi\) | ||||
−0.0571938 | + | 0.998363i | \(0.518215\pi\) | |||||||
\(674\) | −3.87948e15 | −1.07435 | ||||||||
\(675\) | 1.31450e14 | 0.0361069 | ||||||||
\(676\) | −3.49319e15 | −0.951734 | ||||||||
\(677\) | 5.60783e15 | 1.51551 | 0.757753 | − | 0.652542i | \(-0.226297\pi\) | ||||
0.757753 | + | 0.652542i | \(0.226297\pi\) | |||||||
\(678\) | −1.81616e15 | −0.486846 | ||||||||
\(679\) | 1.29305e14 | 0.0343820 | ||||||||
\(680\) | −5.08627e15 | −1.34153 | ||||||||
\(681\) | −1.67231e15 | −0.437530 | ||||||||
\(682\) | 9.19625e14 | 0.238669 | ||||||||
\(683\) | −5.41015e15 | −1.39282 | −0.696411 | − | 0.717643i | \(-0.745221\pi\) | ||||
−0.696411 | + | 0.717643i | \(0.745221\pi\) | |||||||
\(684\) | −6.20597e14 | −0.158490 | ||||||||
\(685\) | 2.10551e12 | 0.000533408 0 | ||||||||
\(686\) | 3.10294e15 | 0.779815 | ||||||||
\(687\) | 2.64647e13 | 0.00659789 | ||||||||
\(688\) | 3.42874e14 | 0.0848004 | ||||||||
\(689\) | 4.58404e14 | 0.112472 | ||||||||
\(690\) | −3.41618e15 | −0.831516 | ||||||||
\(691\) | −4.09841e15 | −0.989660 | −0.494830 | − | 0.868990i | \(-0.664770\pi\) | ||||
−0.494830 | + | 0.868990i | \(0.664770\pi\) | |||||||
\(692\) | −4.64818e14 | −0.111352 | ||||||||
\(693\) | −1.86529e14 | −0.0443316 | ||||||||
\(694\) | −1.24357e15 | −0.293219 | ||||||||
\(695\) | −1.43236e15 | −0.335071 | ||||||||
\(696\) | 3.11627e15 | 0.723244 | ||||||||
\(697\) | −7.90042e15 | −1.81916 | ||||||||
\(698\) | 1.81926e15 | 0.415614 | ||||||||
\(699\) | 2.44015e15 | 0.553085 | ||||||||
\(700\) | −2.77276e14 | −0.0623552 | ||||||||
\(701\) | 4.69655e15 | 1.04793 | 0.523963 | − | 0.851741i | \(-0.324453\pi\) | ||||
0.523963 | + | 0.851741i | \(0.324453\pi\) | |||||||
\(702\) | 1.11178e15 | 0.246131 | ||||||||
\(703\) | −4.99973e15 | −1.09823 | ||||||||
\(704\) | −7.95262e14 | −0.173325 | ||||||||
\(705\) | 1.00659e15 | 0.217678 | ||||||||
\(706\) | −9.33916e14 | −0.200393 | ||||||||
\(707\) | −5.10219e13 | −0.0108630 | ||||||||
\(708\) | −1.65071e14 | −0.0348729 | ||||||||
\(709\) | −7.16964e13 | −0.0150294 | −0.00751472 | − | 0.999972i | \(-0.502392\pi\) | ||||
−0.00751472 | + | 0.999972i | \(0.502392\pi\) | |||||||
\(710\) | 3.47326e15 | 0.722464 | ||||||||
\(711\) | −2.54285e15 | −0.524853 | ||||||||
\(712\) | −7.82027e15 | −1.60170 | ||||||||
\(713\) | −1.55945e16 | −3.16941 | ||||||||
\(714\) | −1.72441e15 | −0.347776 | ||||||||
\(715\) | −1.76594e15 | −0.353422 | ||||||||
\(716\) | 2.88548e15 | 0.573055 | ||||||||
\(717\) | 3.97711e15 | 0.783813 | ||||||||
\(718\) | 8.08227e14 | 0.158070 | ||||||||
\(719\) | 2.70106e14 | 0.0524234 | 0.0262117 | − | 0.999656i | \(-0.491656\pi\) | ||||
0.0262117 | + | 0.999656i | \(0.491656\pi\) | |||||||
\(720\) | 6.05021e14 | 0.116531 | ||||||||
\(721\) | 1.71803e15 | 0.328388 | ||||||||
\(722\) | −1.93973e14 | −0.0367949 | ||||||||
\(723\) | 6.99631e14 | 0.131707 | ||||||||
\(724\) | 3.17567e14 | 0.0593298 | ||||||||
\(725\) | 1.18263e15 | 0.219275 | ||||||||
\(726\) | 2.21798e15 | 0.408138 | ||||||||
\(727\) | 4.20851e15 | 0.768579 | 0.384290 | − | 0.923213i | \(-0.374446\pi\) | ||||
0.384290 | + | 0.923213i | \(0.374446\pi\) | |||||||
\(728\) | −7.39985e15 | −1.34122 | ||||||||
\(729\) | 2.05891e14 | 0.0370370 | ||||||||
\(730\) | 4.39370e15 | 0.784431 | ||||||||
\(731\) | −1.71337e15 | −0.303604 | ||||||||
\(732\) | −4.81879e13 | −0.00847475 | ||||||||
\(733\) | 5.46692e15 | 0.954269 | 0.477134 | − | 0.878830i | \(-0.341675\pi\) | ||||
0.477134 | + | 0.878830i | \(0.341675\pi\) | |||||||
\(734\) | −1.52596e15 | −0.264371 | ||||||||
\(735\) | 1.78134e15 | 0.306313 | ||||||||
\(736\) | 8.85174e15 | 1.51078 | ||||||||
\(737\) | 1.66263e15 | 0.281660 | ||||||||
\(738\) | 2.29893e15 | 0.386559 | ||||||||
\(739\) | −9.20087e15 | −1.53562 | −0.767811 | − | 0.640676i | \(-0.778654\pi\) | ||||
−0.767811 | + | 0.640676i | \(0.778654\pi\) | |||||||
\(740\) | −3.27063e15 | −0.541823 | ||||||||
\(741\) | −6.28541e15 | −1.03355 | ||||||||
\(742\) | 2.06892e14 | 0.0337694 | ||||||||
\(743\) | 3.25954e15 | 0.528102 | 0.264051 | − | 0.964509i | \(-0.414941\pi\) | ||||
0.264051 | + | 0.964509i | \(0.414941\pi\) | |||||||
\(744\) | 6.75625e15 | 1.08656 | ||||||||
\(745\) | 2.01849e15 | 0.322231 | ||||||||
\(746\) | −3.81824e15 | −0.605062 | ||||||||
\(747\) | 7.33673e14 | 0.115409 | ||||||||
\(748\) | 6.33543e14 | 0.0989276 | ||||||||
\(749\) | −3.60513e14 | −0.0558818 | ||||||||
\(750\) | −2.43207e15 | −0.374231 | ||||||||
\(751\) | −2.18002e15 | −0.332998 | −0.166499 | − | 0.986042i | \(-0.553246\pi\) | ||||
−0.166499 | + | 0.986042i | \(0.553246\pi\) | |||||||
\(752\) | 7.31912e14 | 0.110984 | ||||||||
\(753\) | 2.38091e15 | 0.358403 | ||||||||
\(754\) | 1.00025e16 | 1.49474 | ||||||||
\(755\) | −9.78490e15 | −1.45160 | ||||||||
\(756\) | −4.34298e14 | −0.0639615 | ||||||||
\(757\) | 1.25029e16 | 1.82804 | 0.914018 | − | 0.405675i | \(-0.132963\pi\) | ||||
0.914018 | + | 0.405675i | \(0.132963\pi\) | |||||||
\(758\) | −3.98232e15 | −0.578036 | ||||||||
\(759\) | 1.34267e15 | 0.193482 | ||||||||
\(760\) | −8.36737e15 | −1.19706 | ||||||||
\(761\) | 6.18184e15 | 0.878015 | 0.439008 | − | 0.898483i | \(-0.355330\pi\) | ||||
0.439008 | + | 0.898483i | \(0.355330\pi\) | |||||||
\(762\) | −2.71587e15 | −0.382963 | ||||||||
\(763\) | −3.42993e15 | −0.480175 | ||||||||
\(764\) | −2.88595e15 | −0.401121 | ||||||||
\(765\) | −3.02335e15 | −0.417206 | ||||||||
\(766\) | 2.44958e15 | 0.335608 | ||||||||
\(767\) | −1.67184e15 | −0.227416 | ||||||||
\(768\) | −4.47123e15 | −0.603865 | ||||||||
\(769\) | −1.63012e15 | −0.218587 | −0.109293 | − | 0.994010i | \(-0.534859\pi\) | ||||
−0.109293 | + | 0.994010i | \(0.534859\pi\) | |||||||
\(770\) | −7.97026e14 | −0.106114 | ||||||||
\(771\) | −1.57108e15 | −0.207683 | ||||||||
\(772\) | −5.42041e15 | −0.711438 | ||||||||
\(773\) | 1.65012e15 | 0.215045 | 0.107522 | − | 0.994203i | \(-0.465708\pi\) | ||||
0.107522 | + | 0.994203i | \(0.465708\pi\) | |||||||
\(774\) | 4.98572e14 | 0.0645139 | ||||||||
\(775\) | 2.56400e15 | 0.329427 | ||||||||
\(776\) | 4.03249e14 | 0.0514439 | ||||||||
\(777\) | −3.49885e15 | −0.443210 | ||||||||
\(778\) | 1.20101e15 | 0.151064 | ||||||||
\(779\) | −1.29969e16 | −1.62324 | ||||||||
\(780\) | −4.11168e15 | −0.509916 | ||||||||
\(781\) | −1.36511e15 | −0.168107 | ||||||||
\(782\) | 1.24126e16 | 1.51784 | ||||||||
\(783\) | 1.85236e15 | 0.224924 | ||||||||
\(784\) | 1.29524e15 | 0.156176 | ||||||||
\(785\) | 3.17253e15 | 0.379859 | ||||||||
\(786\) | −6.56905e15 | −0.781050 | ||||||||
\(787\) | −6.17546e15 | −0.729136 | −0.364568 | − | 0.931177i | \(-0.618783\pi\) | ||||
−0.364568 | + | 0.931177i | \(0.618783\pi\) | |||||||
\(788\) | −4.13898e14 | −0.0485287 | ||||||||
\(789\) | 8.56138e15 | 0.996828 | ||||||||
\(790\) | −1.08654e16 | −1.25631 | ||||||||
\(791\) | 7.18534e15 | 0.825043 | ||||||||
\(792\) | −5.81707e14 | −0.0663309 | ||||||||
\(793\) | −4.88047e14 | −0.0552661 | ||||||||
\(794\) | 5.47868e15 | 0.616117 | ||||||||
\(795\) | 3.62738e14 | 0.0405111 | ||||||||
\(796\) | −3.38834e15 | −0.375807 | ||||||||
\(797\) | 5.51112e15 | 0.607043 | 0.303521 | − | 0.952825i | \(-0.401838\pi\) | ||||
0.303521 | + | 0.952825i | \(0.401838\pi\) | |||||||
\(798\) | −2.83680e15 | −0.310323 | ||||||||
\(799\) | −3.65744e15 | −0.397347 | ||||||||
\(800\) | −1.45538e15 | −0.157029 | ||||||||
\(801\) | −4.64848e15 | −0.498118 | ||||||||
\(802\) | −2.64084e15 | −0.281049 | ||||||||
\(803\) | −1.72687e15 | −0.182526 | ||||||||
\(804\) | 3.87113e15 | 0.406378 | ||||||||
\(805\) | 1.35155e16 | 1.40915 | ||||||||
\(806\) | 2.16859e16 | 2.24561 | ||||||||
\(807\) | 9.60218e15 | 0.987564 | ||||||||
\(808\) | −1.59116e14 | −0.0162537 | ||||||||
\(809\) | 1.51244e16 | 1.53448 | 0.767238 | − | 0.641363i | \(-0.221631\pi\) | ||||
0.767238 | + | 0.641363i | \(0.221631\pi\) | |||||||
\(810\) | 8.79760e14 | 0.0886537 | ||||||||
\(811\) | −1.71215e15 | −0.171367 | −0.0856835 | − | 0.996322i | \(-0.527307\pi\) | ||||
−0.0856835 | + | 0.996322i | \(0.527307\pi\) | |||||||
\(812\) | −3.90729e15 | −0.388434 | ||||||||
\(813\) | −7.81501e15 | −0.771670 | ||||||||
\(814\) | −1.48521e15 | −0.145665 | ||||||||
\(815\) | −2.87953e15 | −0.280515 | ||||||||
\(816\) | −2.19833e15 | −0.212715 | ||||||||
\(817\) | −2.81866e15 | −0.270907 | ||||||||
\(818\) | 9.24922e15 | 0.883003 | ||||||||
\(819\) | −4.39858e15 | −0.417110 | ||||||||
\(820\) | −8.50208e15 | −0.800846 | ||||||||
\(821\) | 6.05932e14 | 0.0566939 | 0.0283469 | − | 0.999598i | \(-0.490976\pi\) | ||||
0.0283469 | + | 0.999598i | \(0.490976\pi\) | |||||||
\(822\) | 2.22616e12 | 0.000206901 0 | ||||||||
\(823\) | 8.30271e14 | 0.0766515 | 0.0383257 | − | 0.999265i | \(-0.487798\pi\) | ||||
0.0383257 | + | 0.999265i | \(0.487798\pi\) | |||||||
\(824\) | 5.35785e15 | 0.491349 | ||||||||
\(825\) | −2.20758e14 | −0.0201104 | ||||||||
\(826\) | −7.54555e14 | −0.0682811 | ||||||||
\(827\) | 1.05517e16 | 0.948507 | 0.474254 | − | 0.880388i | \(-0.342718\pi\) | ||||
0.474254 | + | 0.880388i | \(0.342718\pi\) | |||||||
\(828\) | 3.12617e15 | 0.279155 | ||||||||
\(829\) | −1.06911e15 | −0.0948357 | −0.0474179 | − | 0.998875i | \(-0.515099\pi\) | ||||
−0.0474179 | + | 0.998875i | \(0.515099\pi\) | |||||||
\(830\) | 3.13494e15 | 0.276248 | ||||||||
\(831\) | 7.73952e15 | 0.677498 | ||||||||
\(832\) | −1.87532e16 | −1.63079 | ||||||||
\(833\) | −6.47246e15 | −0.559142 | ||||||||
\(834\) | −1.51444e15 | −0.129969 | ||||||||
\(835\) | −2.51719e16 | −2.14606 | ||||||||
\(836\) | 1.04224e15 | 0.0882737 | ||||||||
\(837\) | 4.01601e15 | 0.337913 | ||||||||
\(838\) | −1.16448e16 | −0.973393 | ||||||||
\(839\) | 1.83086e16 | 1.52042 | 0.760211 | − | 0.649676i | \(-0.225096\pi\) | ||||
0.760211 | + | 0.649676i | \(0.225096\pi\) | |||||||
\(840\) | −5.85555e15 | −0.483094 | ||||||||
\(841\) | 4.46475e15 | 0.365948 | ||||||||
\(842\) | −4.42277e15 | −0.360146 | ||||||||
\(843\) | 6.03618e15 | 0.488326 | ||||||||
\(844\) | 6.77095e15 | 0.544209 | ||||||||
\(845\) | −2.79957e16 | −2.23552 | ||||||||
\(846\) | 1.06427e15 | 0.0844337 | ||||||||
\(847\) | −8.77508e15 | −0.691659 | ||||||||
\(848\) | 2.63754e14 | 0.0206548 | ||||||||
\(849\) | −5.59346e15 | −0.435199 | ||||||||
\(850\) | −2.04085e15 | −0.157764 | ||||||||
\(851\) | 2.51854e16 | 1.93436 | ||||||||
\(852\) | −3.17840e15 | −0.242544 | ||||||||
\(853\) | 1.27200e16 | 0.964420 | 0.482210 | − | 0.876056i | \(-0.339834\pi\) | ||||
0.482210 | + | 0.876056i | \(0.339834\pi\) | |||||||
\(854\) | −2.20271e14 | −0.0165935 | ||||||||
\(855\) | −4.97368e15 | −0.372276 | ||||||||
\(856\) | −1.12429e15 | −0.0836130 | ||||||||
\(857\) | −3.18318e15 | −0.235216 | −0.117608 | − | 0.993060i | \(-0.537523\pi\) | ||||
−0.117608 | + | 0.993060i | \(0.537523\pi\) | |||||||
\(858\) | −1.86714e15 | −0.137087 | ||||||||
\(859\) | −1.56173e16 | −1.13931 | −0.569656 | − | 0.821883i | \(-0.692924\pi\) | ||||
−0.569656 | + | 0.821883i | \(0.692924\pi\) | |||||||
\(860\) | −1.84386e15 | −0.133655 | ||||||||
\(861\) | −9.09533e15 | −0.655090 | ||||||||
\(862\) | −5.93171e15 | −0.424512 | ||||||||
\(863\) | 1.20362e16 | 0.855911 | 0.427955 | − | 0.903800i | \(-0.359234\pi\) | ||||
0.427955 | + | 0.903800i | \(0.359234\pi\) | |||||||
\(864\) | −2.27957e15 | −0.161074 | ||||||||
\(865\) | −3.72522e15 | −0.261555 | ||||||||
\(866\) | −5.72759e15 | −0.399598 | ||||||||
\(867\) | 2.65722e15 | 0.184214 | ||||||||
\(868\) | −8.47121e15 | −0.583562 | ||||||||
\(869\) | 4.27048e15 | 0.292326 | ||||||||
\(870\) | 7.91501e15 | 0.538388 | ||||||||
\(871\) | 3.92069e16 | 2.65010 | ||||||||
\(872\) | −1.06965e16 | −0.718460 | ||||||||
\(873\) | 2.39697e14 | 0.0159987 | ||||||||
\(874\) | 2.04199e16 | 1.35438 | ||||||||
\(875\) | 9.62208e15 | 0.634198 | ||||||||
\(876\) | −4.02071e15 | −0.263348 | ||||||||
\(877\) | −4.22997e14 | −0.0275321 | −0.0137660 | − | 0.999905i | \(-0.504382\pi\) | ||||
−0.0137660 | + | 0.999905i | \(0.504382\pi\) | |||||||
\(878\) | 1.92252e16 | 1.24352 | ||||||||
\(879\) | 9.72316e15 | 0.624984 | ||||||||
\(880\) | −1.01608e15 | −0.0649041 | ||||||||
\(881\) | −1.62941e16 | −1.03434 | −0.517171 | − | 0.855882i | \(-0.673015\pi\) | ||||
−0.517171 | + | 0.855882i | \(0.673015\pi\) | |||||||
\(882\) | 1.88341e15 | 0.118814 | ||||||||
\(883\) | 2.22431e16 | 1.39448 | 0.697240 | − | 0.716838i | \(-0.254411\pi\) | ||||
0.697240 | + | 0.716838i | \(0.254411\pi\) | |||||||
\(884\) | 1.49397e16 | 0.930797 | ||||||||
\(885\) | −1.32294e15 | −0.0819128 | ||||||||
\(886\) | −1.07833e16 | −0.663539 | ||||||||
\(887\) | −2.87196e15 | −0.175630 | −0.0878148 | − | 0.996137i | \(-0.527988\pi\) | ||||
−0.0878148 | + | 0.996137i | \(0.527988\pi\) | |||||||
\(888\) | −1.09115e16 | −0.663151 | ||||||||
\(889\) | 1.07449e16 | 0.648996 | ||||||||
\(890\) | −1.98627e16 | −1.19232 | ||||||||
\(891\) | −3.45775e14 | −0.0206284 | ||||||||
\(892\) | −2.42230e14 | −0.0143622 | ||||||||
\(893\) | −6.01682e15 | −0.354555 | ||||||||
\(894\) | 2.13416e15 | 0.124989 | ||||||||
\(895\) | 2.31252e16 | 1.34605 | ||||||||
\(896\) | 1.90008e15 | 0.109920 | ||||||||
\(897\) | 3.16618e16 | 1.82045 | ||||||||
\(898\) | 3.90990e15 | 0.223432 | ||||||||
\(899\) | 3.61312e16 | 2.05212 | ||||||||
\(900\) | −5.13996e14 | −0.0290152 | ||||||||
\(901\) | −1.31800e15 | −0.0739486 | ||||||||
\(902\) | −3.86084e15 | −0.215301 | ||||||||
\(903\) | −1.97252e15 | −0.109330 | ||||||||
\(904\) | 2.24081e16 | 1.23447 | ||||||||
\(905\) | 2.54509e15 | 0.139359 | ||||||||
\(906\) | −1.03456e16 | −0.563055 | ||||||||
\(907\) | 4.89137e15 | 0.264600 | 0.132300 | − | 0.991210i | \(-0.457764\pi\) | ||||
0.132300 | + | 0.991210i | \(0.457764\pi\) | |||||||
\(908\) | 6.53906e15 | 0.351595 | ||||||||
\(909\) | −9.45811e13 | −0.00505479 | ||||||||
\(910\) | −1.87948e16 | −0.998415 | ||||||||
\(911\) | 1.87122e16 | 0.988039 | 0.494020 | − | 0.869451i | \(-0.335527\pi\) | ||||
0.494020 | + | 0.869451i | \(0.335527\pi\) | |||||||
\(912\) | −3.61646e15 | −0.189807 | ||||||||
\(913\) | −1.23214e15 | −0.0642790 | ||||||||
\(914\) | 5.14302e15 | 0.266694 | ||||||||
\(915\) | −3.86195e14 | −0.0199063 | ||||||||
\(916\) | −1.03482e14 | −0.00530201 | ||||||||
\(917\) | 2.59893e16 | 1.32362 | ||||||||
\(918\) | −3.19659e15 | −0.161828 | ||||||||
\(919\) | 9.46234e15 | 0.476171 | 0.238086 | − | 0.971244i | \(-0.423480\pi\) | ||||
0.238086 | + | 0.971244i | \(0.423480\pi\) | |||||||
\(920\) | 4.21494e16 | 2.10843 | ||||||||
\(921\) | −1.78808e16 | −0.889117 | ||||||||
\(922\) | −1.36435e16 | −0.674383 | ||||||||
\(923\) | −3.21909e16 | −1.58170 | ||||||||
\(924\) | 7.29364e14 | 0.0356245 | ||||||||
\(925\) | −4.14091e15 | −0.201056 | ||||||||
\(926\) | 3.51450e15 | 0.169630 | ||||||||
\(927\) | 3.18478e15 | 0.152806 | ||||||||
\(928\) | −2.05088e16 | −0.978195 | ||||||||
\(929\) | 1.29084e16 | 0.612047 | 0.306023 | − | 0.952024i | \(-0.401001\pi\) | ||||
0.306023 | + | 0.952024i | \(0.401001\pi\) | |||||||
\(930\) | 1.71602e16 | 0.808845 | ||||||||
\(931\) | −1.06478e16 | −0.498926 | ||||||||
\(932\) | −9.54145e15 | −0.444454 | ||||||||
\(933\) | −9.41459e15 | −0.435966 | ||||||||
\(934\) | 2.28621e16 | 1.05247 | ||||||||
\(935\) | 5.07744e15 | 0.232370 | ||||||||
\(936\) | −1.37174e16 | −0.624099 | ||||||||
\(937\) | 2.51683e16 | 1.13838 | 0.569190 | − | 0.822206i | \(-0.307257\pi\) | ||||
0.569190 | + | 0.822206i | \(0.307257\pi\) | |||||||
\(938\) | 1.76953e16 | 0.795687 | ||||||||
\(939\) | −1.66781e16 | −0.745566 | ||||||||
\(940\) | −3.93598e15 | −0.174924 | ||||||||
\(941\) | 3.46430e16 | 1.53064 | 0.765319 | − | 0.643651i | \(-0.222581\pi\) | ||||
0.765319 | + | 0.643651i | \(0.222581\pi\) | |||||||
\(942\) | 3.35432e15 | 0.147342 | ||||||||
\(943\) | 6.54700e16 | 2.85909 | ||||||||
\(944\) | −9.61933e14 | −0.0417637 | ||||||||
\(945\) | −3.48062e15 | −0.150239 | ||||||||
\(946\) | −8.37306e14 | −0.0359321 | ||||||||
\(947\) | −4.03973e16 | −1.72356 | −0.861781 | − | 0.507280i | \(-0.830651\pi\) | ||||
−0.861781 | + | 0.507280i | \(0.830651\pi\) | |||||||
\(948\) | 9.94304e15 | 0.421768 | ||||||||
\(949\) | −4.07217e16 | −1.71736 | ||||||||
\(950\) | −3.35738e15 | −0.140773 | ||||||||
\(951\) | 1.93107e16 | 0.805019 | ||||||||
\(952\) | 2.12760e16 | 0.881836 | ||||||||
\(953\) | 2.98955e16 | 1.23196 | 0.615978 | − | 0.787763i | \(-0.288761\pi\) | ||||
0.615978 | + | 0.787763i | \(0.288761\pi\) | |||||||
\(954\) | 3.83524e14 | 0.0157136 | ||||||||
\(955\) | −2.31290e16 | −0.942190 | ||||||||
\(956\) | −1.55513e16 | −0.629865 | ||||||||
\(957\) | −3.11086e15 | −0.125275 | ||||||||
\(958\) | 3.05971e16 | 1.22510 | ||||||||
\(959\) | −8.80743e12 | −0.000350628 0 | ||||||||
\(960\) | −1.48396e16 | −0.587393 | ||||||||
\(961\) | 5.29259e16 | 2.08300 | ||||||||
\(962\) | −3.50231e16 | −1.37054 | ||||||||
\(963\) | −6.68296e14 | −0.0260030 | ||||||||
\(964\) | −2.73569e15 | −0.105839 | ||||||||
\(965\) | −4.34411e16 | −1.67109 | ||||||||
\(966\) | 1.42900e16 | 0.546585 | ||||||||
\(967\) | 3.83561e16 | 1.45878 | 0.729388 | − | 0.684100i | \(-0.239805\pi\) | ||||
0.729388 | + | 0.684100i | \(0.239805\pi\) | |||||||
\(968\) | −2.73659e16 | −1.03489 | ||||||||
\(969\) | 1.80718e16 | 0.679549 | ||||||||
\(970\) | 1.02421e15 | 0.0382952 | ||||||||
\(971\) | 4.08201e16 | 1.51764 | 0.758819 | − | 0.651301i | \(-0.225777\pi\) | ||||
0.758819 | + | 0.651301i | \(0.225777\pi\) | |||||||
\(972\) | −8.05075e14 | −0.0297627 | ||||||||
\(973\) | 5.99163e15 | 0.220254 | ||||||||
\(974\) | −3.55414e16 | −1.29915 | ||||||||
\(975\) | −5.20575e15 | −0.189216 | ||||||||
\(976\) | −2.80809e14 | −0.0101493 | ||||||||
\(977\) | −5.42928e16 | −1.95129 | −0.975646 | − | 0.219351i | \(-0.929606\pi\) | ||||
−0.975646 | + | 0.219351i | \(0.929606\pi\) | |||||||
\(978\) | −3.04454e15 | −0.108807 | ||||||||
\(979\) | 7.80669e15 | 0.277436 | ||||||||
\(980\) | −6.96538e15 | −0.246151 | ||||||||
\(981\) | −6.35817e15 | −0.223436 | ||||||||
\(982\) | 2.52494e15 | 0.0882343 | ||||||||
\(983\) | −4.45529e16 | −1.54822 | −0.774108 | − | 0.633053i | \(-0.781801\pi\) | ||||
−0.774108 | + | 0.633053i | \(0.781801\pi\) | |||||||
\(984\) | −2.83646e16 | −0.980176 | ||||||||
\(985\) | −3.31712e15 | −0.113989 | ||||||||
\(986\) | −2.87591e16 | −0.982770 | ||||||||
\(987\) | −4.21061e15 | −0.143087 | ||||||||
\(988\) | 2.45772e16 | 0.830556 | ||||||||
\(989\) | 1.41986e16 | 0.477161 | ||||||||
\(990\) | −1.47748e15 | −0.0493773 | ||||||||
\(991\) | 2.11566e16 | 0.703140 | 0.351570 | − | 0.936162i | \(-0.385648\pi\) | ||||
0.351570 | + | 0.936162i | \(0.385648\pi\) | |||||||
\(992\) | −4.44641e16 | −1.46959 | ||||||||
\(993\) | 2.59525e16 | 0.853017 | ||||||||
\(994\) | −1.45288e16 | −0.474902 | ||||||||
\(995\) | −2.71553e16 | −0.882730 | ||||||||
\(996\) | −2.86881e15 | −0.0927416 | ||||||||
\(997\) | −4.98712e16 | −1.60334 | −0.801671 | − | 0.597766i | \(-0.796055\pi\) | ||||
−0.801671 | + | 0.597766i | \(0.796055\pi\) | |||||||
\(998\) | 2.78170e16 | 0.889389 | ||||||||
\(999\) | −6.48594e15 | −0.206235 |
(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 | 177.12.a.d.1.11 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.12.a.d.1.11 | ✓ | 28 | 1.1 | even | 1 | trivial |