Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,10,Mod(1,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.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: | \(148.845356651\) |
Analytic rank: | \(1\) |
Dimension: | \(7\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{7} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{7} - x^{6} - 2986x^{5} + 8252x^{4} + 2252056x^{3} - 10388768x^{2} - 243559296x - 675998208 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 17) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-4.12962\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 4.12962 | 0.182505 | 0.0912526 | − | 0.995828i | \(-0.470913\pi\) | ||||
0.0912526 | + | 0.995828i | \(0.470913\pi\) | |||||||
\(3\) | 254.074 | 1.81099 | 0.905493 | − | 0.424360i | \(-0.139501\pi\) | ||||
0.905493 | + | 0.424360i | \(0.139501\pi\) | |||||||
\(4\) | −494.946 | −0.966692 | ||||||||
\(5\) | −151.544 | −0.108436 | −0.0542179 | − | 0.998529i | \(-0.517267\pi\) | ||||
−0.0542179 | + | 0.998529i | \(0.517267\pi\) | |||||||
\(6\) | 1049.23 | 0.330514 | ||||||||
\(7\) | −9407.97 | −1.48100 | −0.740499 | − | 0.672057i | \(-0.765411\pi\) | ||||
−0.740499 | + | 0.672057i | \(0.765411\pi\) | |||||||
\(8\) | −4158.31 | −0.358931 | ||||||||
\(9\) | 44870.8 | 2.27967 | ||||||||
\(10\) | −625.818 | −0.0197901 | ||||||||
\(11\) | 56967.2 | 1.17316 | 0.586581 | − | 0.809891i | \(-0.300474\pi\) | ||||
0.586581 | + | 0.809891i | \(0.300474\pi\) | |||||||
\(12\) | −125753. | −1.75067 | ||||||||
\(13\) | −60874.5 | −0.591140 | −0.295570 | − | 0.955321i | \(-0.595510\pi\) | ||||
−0.295570 | + | 0.955321i | \(0.595510\pi\) | |||||||
\(14\) | −38851.3 | −0.270290 | ||||||||
\(15\) | −38503.4 | −0.196376 | ||||||||
\(16\) | 236240. | 0.901185 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 185299. | 0.416052 | ||||||||
\(19\) | 1.00994e6 | 1.77789 | 0.888947 | − | 0.458010i | \(-0.151438\pi\) | ||||
0.888947 | + | 0.458010i | \(0.151438\pi\) | |||||||
\(20\) | 75006.0 | 0.104824 | ||||||||
\(21\) | −2.39032e6 | −2.68207 | ||||||||
\(22\) | 235253. | 0.214108 | ||||||||
\(23\) | −1.35979e6 | −1.01320 | −0.506602 | − | 0.862180i | \(-0.669099\pi\) | ||||
−0.506602 | + | 0.862180i | \(0.669099\pi\) | |||||||
\(24\) | −1.05652e6 | −0.650020 | ||||||||
\(25\) | −1.93016e6 | −0.988242 | ||||||||
\(26\) | −251388. | −0.107886 | ||||||||
\(27\) | 6.39958e6 | 2.31747 | ||||||||
\(28\) | 4.65644e6 | 1.43167 | ||||||||
\(29\) | −3.12503e6 | −0.820472 | −0.410236 | − | 0.911979i | \(-0.634554\pi\) | ||||
−0.410236 | + | 0.911979i | \(0.634554\pi\) | |||||||
\(30\) | −159004. | −0.0358396 | ||||||||
\(31\) | −2.97426e6 | −0.578431 | −0.289216 | − | 0.957264i | \(-0.593394\pi\) | ||||
−0.289216 | + | 0.957264i | \(0.593394\pi\) | |||||||
\(32\) | 3.10463e6 | 0.523402 | ||||||||
\(33\) | 1.44739e7 | 2.12458 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.42572e6 | 0.160593 | ||||||||
\(36\) | −2.22086e7 | −2.20374 | ||||||||
\(37\) | −681625. | −0.0597913 | −0.0298956 | − | 0.999553i | \(-0.509517\pi\) | ||||
−0.0298956 | + | 0.999553i | \(0.509517\pi\) | |||||||
\(38\) | 4.17068e6 | 0.324475 | ||||||||
\(39\) | −1.54666e7 | −1.07055 | ||||||||
\(40\) | 630165. | 0.0389210 | ||||||||
\(41\) | 4.09135e6 | 0.226120 | 0.113060 | − | 0.993588i | \(-0.463935\pi\) | ||||
0.113060 | + | 0.993588i | \(0.463935\pi\) | |||||||
\(42\) | −9.87113e6 | −0.489491 | ||||||||
\(43\) | 1.00085e7 | 0.446436 | 0.223218 | − | 0.974769i | \(-0.428344\pi\) | ||||
0.223218 | + | 0.974769i | \(0.428344\pi\) | |||||||
\(44\) | −2.81957e7 | −1.13409 | ||||||||
\(45\) | −6.79989e6 | −0.247198 | ||||||||
\(46\) | −5.61542e6 | −0.184915 | ||||||||
\(47\) | 2.54570e7 | 0.760970 | 0.380485 | − | 0.924787i | \(-0.375757\pi\) | ||||
0.380485 | + | 0.924787i | \(0.375757\pi\) | |||||||
\(48\) | 6.00226e7 | 1.63203 | ||||||||
\(49\) | 4.81562e7 | 1.19336 | ||||||||
\(50\) | −7.97082e6 | −0.180359 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.01296e7 | 0.571450 | ||||||||
\(53\) | −3.14563e7 | −0.547603 | −0.273801 | − | 0.961786i | \(-0.588281\pi\) | ||||
−0.273801 | + | 0.961786i | \(0.588281\pi\) | |||||||
\(54\) | 2.64278e7 | 0.422951 | ||||||||
\(55\) | −8.63302e6 | −0.127213 | ||||||||
\(56\) | 3.91212e7 | 0.531577 | ||||||||
\(57\) | 2.56601e8 | 3.21974 | ||||||||
\(58\) | −1.29052e7 | −0.149740 | ||||||||
\(59\) | −9.03573e7 | −0.970798 | −0.485399 | − | 0.874293i | \(-0.661326\pi\) | ||||
−0.485399 | + | 0.874293i | \(0.661326\pi\) | |||||||
\(60\) | 1.90571e7 | 0.189835 | ||||||||
\(61\) | −9.87113e7 | −0.912815 | −0.456408 | − | 0.889771i | \(-0.650864\pi\) | ||||
−0.456408 | + | 0.889771i | \(0.650864\pi\) | |||||||
\(62\) | −1.22826e7 | −0.105567 | ||||||||
\(63\) | −4.22143e8 | −3.37619 | ||||||||
\(64\) | −1.08134e8 | −0.805661 | ||||||||
\(65\) | 9.22514e6 | 0.0641007 | ||||||||
\(66\) | 5.97717e7 | 0.387747 | ||||||||
\(67\) | 1.32700e8 | 0.804516 | 0.402258 | − | 0.915526i | \(-0.368225\pi\) | ||||
0.402258 | + | 0.915526i | \(0.368225\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.45488e8 | −1.83490 | ||||||||
\(70\) | 5.88767e6 | 0.0293091 | ||||||||
\(71\) | −4.18554e8 | −1.95474 | −0.977369 | − | 0.211541i | \(-0.932152\pi\) | ||||
−0.977369 | + | 0.211541i | \(0.932152\pi\) | |||||||
\(72\) | −1.86587e8 | −0.818246 | ||||||||
\(73\) | −4.80282e7 | −0.197944 | −0.0989721 | − | 0.995090i | \(-0.531555\pi\) | ||||
−0.0989721 | + | 0.995090i | \(0.531555\pi\) | |||||||
\(74\) | −2.81485e6 | −0.0109122 | ||||||||
\(75\) | −4.90404e8 | −1.78969 | ||||||||
\(76\) | −4.99868e8 | −1.71868 | ||||||||
\(77\) | −5.35945e8 | −1.73745 | ||||||||
\(78\) | −6.38714e7 | −0.195380 | ||||||||
\(79\) | −3.49030e7 | −0.100819 | −0.0504093 | − | 0.998729i | \(-0.516053\pi\) | ||||
−0.0504093 | + | 0.998729i | \(0.516053\pi\) | |||||||
\(80\) | −3.58007e7 | −0.0977207 | ||||||||
\(81\) | 7.42778e8 | 1.91724 | ||||||||
\(82\) | 1.68957e7 | 0.0412681 | ||||||||
\(83\) | −2.05650e8 | −0.475638 | −0.237819 | − | 0.971309i | \(-0.576433\pi\) | ||||
−0.237819 | + | 0.971309i | \(0.576433\pi\) | |||||||
\(84\) | 1.18308e9 | 2.59273 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.13311e7 | 0.0814769 | ||||||||
\(87\) | −7.93991e8 | −1.48586 | ||||||||
\(88\) | −2.36887e8 | −0.421084 | ||||||||
\(89\) | −2.03866e8 | −0.344422 | −0.172211 | − | 0.985060i | \(-0.555091\pi\) | ||||
−0.172211 | + | 0.985060i | \(0.555091\pi\) | |||||||
\(90\) | −2.80810e7 | −0.0451150 | ||||||||
\(91\) | 5.72705e8 | 0.875477 | ||||||||
\(92\) | 6.73023e8 | 0.979456 | ||||||||
\(93\) | −7.55684e8 | −1.04753 | ||||||||
\(94\) | 1.05128e8 | 0.138881 | ||||||||
\(95\) | −1.53050e8 | −0.192787 | ||||||||
\(96\) | 7.88808e8 | 0.947875 | ||||||||
\(97\) | −1.24300e9 | −1.42560 | −0.712798 | − | 0.701369i | \(-0.752573\pi\) | ||||
−0.712798 | + | 0.701369i | \(0.752573\pi\) | |||||||
\(98\) | 1.98867e8 | 0.217794 | ||||||||
\(99\) | 2.55616e9 | 2.67443 | ||||||||
\(100\) | 9.55325e8 | 0.955325 | ||||||||
\(101\) | −2.02496e9 | −1.93629 | −0.968144 | − | 0.250395i | \(-0.919440\pi\) | ||||
−0.968144 | + | 0.250395i | \(0.919440\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.16276e9 | 1.01794 | 0.508970 | − | 0.860785i | \(-0.330027\pi\) | ||||
0.508970 | + | 0.860785i | \(0.330027\pi\) | |||||||
\(104\) | 2.53135e8 | 0.212179 | ||||||||
\(105\) | 3.62238e8 | 0.290832 | ||||||||
\(106\) | −1.29902e8 | −0.0999403 | ||||||||
\(107\) | −1.31593e9 | −0.970520 | −0.485260 | − | 0.874370i | \(-0.661275\pi\) | ||||
−0.485260 | + | 0.874370i | \(0.661275\pi\) | |||||||
\(108\) | −3.16745e9 | −2.24028 | ||||||||
\(109\) | 1.79000e8 | 0.121460 | 0.0607302 | − | 0.998154i | \(-0.480657\pi\) | ||||
0.0607302 | + | 0.998154i | \(0.480657\pi\) | |||||||
\(110\) | −3.56511e7 | −0.0232170 | ||||||||
\(111\) | −1.73184e8 | −0.108281 | ||||||||
\(112\) | −2.22254e9 | −1.33465 | ||||||||
\(113\) | −2.53572e9 | −1.46301 | −0.731506 | − | 0.681835i | \(-0.761182\pi\) | ||||
−0.731506 | + | 0.681835i | \(0.761182\pi\) | |||||||
\(114\) | 1.05966e9 | 0.587619 | ||||||||
\(115\) | 2.06068e8 | 0.109868 | ||||||||
\(116\) | 1.54672e9 | 0.793144 | ||||||||
\(117\) | −2.73149e9 | −1.34761 | ||||||||
\(118\) | −3.73141e8 | −0.177176 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 1.60109e8 | 0.0704854 | ||||||||
\(121\) | 8.87314e8 | 0.376308 | ||||||||
\(122\) | −4.07640e8 | −0.166593 | ||||||||
\(123\) | 1.03951e9 | 0.409500 | ||||||||
\(124\) | 1.47210e9 | 0.559165 | ||||||||
\(125\) | 5.88487e8 | 0.215597 | ||||||||
\(126\) | −1.74329e9 | −0.616172 | ||||||||
\(127\) | 4.05326e9 | 1.38257 | 0.691287 | − | 0.722581i | \(-0.257044\pi\) | ||||
0.691287 | + | 0.722581i | \(0.257044\pi\) | |||||||
\(128\) | −2.03613e9 | −0.670440 | ||||||||
\(129\) | 2.54289e9 | 0.808490 | ||||||||
\(130\) | 3.80963e7 | 0.0116987 | ||||||||
\(131\) | 2.93543e9 | 0.870865 | 0.435432 | − | 0.900221i | \(-0.356595\pi\) | ||||
0.435432 | + | 0.900221i | \(0.356595\pi\) | |||||||
\(132\) | −7.16381e9 | −2.05381 | ||||||||
\(133\) | −9.50151e9 | −2.63306 | ||||||||
\(134\) | 5.48001e8 | 0.146828 | ||||||||
\(135\) | −9.69816e8 | −0.251297 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.82610e9 | −1.17045 | −0.585226 | − | 0.810870i | \(-0.698994\pi\) | ||||
−0.585226 | + | 0.810870i | \(0.698994\pi\) | |||||||
\(138\) | −1.42673e9 | −0.334879 | ||||||||
\(139\) | −2.65630e9 | −0.603546 | −0.301773 | − | 0.953380i | \(-0.597579\pi\) | ||||
−0.301773 | + | 0.953380i | \(0.597579\pi\) | |||||||
\(140\) | −7.05653e8 | −0.155244 | ||||||||
\(141\) | 6.46798e9 | 1.37811 | ||||||||
\(142\) | −1.72847e9 | −0.356750 | ||||||||
\(143\) | −3.46785e9 | −0.693502 | ||||||||
\(144\) | 1.06003e10 | 2.05441 | ||||||||
\(145\) | 4.73579e8 | 0.0889685 | ||||||||
\(146\) | −1.98338e8 | −0.0361259 | ||||||||
\(147\) | 1.22353e10 | 2.16115 | ||||||||
\(148\) | 3.37368e8 | 0.0577998 | ||||||||
\(149\) | −2.85114e9 | −0.473894 | −0.236947 | − | 0.971523i | \(-0.576147\pi\) | ||||
−0.236947 | + | 0.971523i | \(0.576147\pi\) | |||||||
\(150\) | −2.02518e9 | −0.326628 | ||||||||
\(151\) | −8.37259e9 | −1.31058 | −0.655290 | − | 0.755378i | \(-0.727454\pi\) | ||||
−0.655290 | + | 0.755378i | \(0.727454\pi\) | |||||||
\(152\) | −4.19965e9 | −0.638142 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.21325e9 | −0.317094 | ||||||||
\(155\) | 4.50731e8 | 0.0627227 | ||||||||
\(156\) | 7.65516e9 | 1.03489 | ||||||||
\(157\) | 8.37311e9 | 1.09986 | 0.549931 | − | 0.835210i | \(-0.314654\pi\) | ||||
0.549931 | + | 0.835210i | \(0.314654\pi\) | |||||||
\(158\) | −1.44136e8 | −0.0183999 | ||||||||
\(159\) | −7.99223e9 | −0.991702 | ||||||||
\(160\) | −4.70488e8 | −0.0567555 | ||||||||
\(161\) | 1.27929e10 | 1.50055 | ||||||||
\(162\) | 3.06739e9 | 0.349906 | ||||||||
\(163\) | 2.12079e8 | 0.0235317 | 0.0117659 | − | 0.999931i | \(-0.496255\pi\) | ||||
0.0117659 | + | 0.999931i | \(0.496255\pi\) | |||||||
\(164\) | −2.02500e9 | −0.218588 | ||||||||
\(165\) | −2.19343e9 | −0.230381 | ||||||||
\(166\) | −8.49256e8 | −0.0868064 | ||||||||
\(167\) | 9.27756e9 | 0.923017 | 0.461509 | − | 0.887136i | \(-0.347308\pi\) | ||||
0.461509 | + | 0.887136i | \(0.347308\pi\) | |||||||
\(168\) | 9.93969e9 | 0.962678 | ||||||||
\(169\) | −6.89880e9 | −0.650554 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 4.53170e10 | 4.05302 | ||||||||
\(172\) | −4.95365e9 | −0.431566 | ||||||||
\(173\) | 1.29744e10 | 1.10123 | 0.550617 | − | 0.834758i | \(-0.314392\pi\) | ||||
0.550617 | + | 0.834758i | \(0.314392\pi\) | |||||||
\(174\) | −3.27888e9 | −0.271178 | ||||||||
\(175\) | 1.81589e10 | 1.46358 | ||||||||
\(176\) | 1.34579e10 | 1.05724 | ||||||||
\(177\) | −2.29575e10 | −1.75810 | ||||||||
\(178\) | −8.41890e8 | −0.0628587 | ||||||||
\(179\) | 2.58172e10 | 1.87962 | 0.939812 | − | 0.341692i | \(-0.111000\pi\) | ||||
0.939812 | + | 0.341692i | \(0.111000\pi\) | |||||||
\(180\) | 3.36558e9 | 0.238965 | ||||||||
\(181\) | −2.61713e9 | −0.181248 | −0.0906238 | − | 0.995885i | \(-0.528886\pi\) | ||||
−0.0906238 | + | 0.995885i | \(0.528886\pi\) | |||||||
\(182\) | 2.36505e9 | 0.159779 | ||||||||
\(183\) | −2.50800e10 | −1.65310 | ||||||||
\(184\) | 5.65443e9 | 0.363671 | ||||||||
\(185\) | 1.03296e8 | 0.00648352 | ||||||||
\(186\) | −3.12069e9 | −0.191180 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.25999e10 | −0.735623 | ||||||||
\(189\) | −6.02070e10 | −3.43217 | ||||||||
\(190\) | −6.32040e8 | −0.0351847 | ||||||||
\(191\) | 8.25575e8 | 0.0448855 | 0.0224428 | − | 0.999748i | \(-0.492856\pi\) | ||||
0.0224428 | + | 0.999748i | \(0.492856\pi\) | |||||||
\(192\) | −2.74741e10 | −1.45904 | ||||||||
\(193\) | −1.88810e10 | −0.979530 | −0.489765 | − | 0.871855i | \(-0.662917\pi\) | ||||
−0.489765 | + | 0.871855i | \(0.662917\pi\) | |||||||
\(194\) | −5.13310e9 | −0.260179 | ||||||||
\(195\) | 2.34387e9 | 0.116086 | ||||||||
\(196\) | −2.38347e10 | −1.15361 | ||||||||
\(197\) | −1.73273e10 | −0.819659 | −0.409829 | − | 0.912162i | \(-0.634412\pi\) | ||||
−0.409829 | + | 0.912162i | \(0.634412\pi\) | |||||||
\(198\) | 1.05560e10 | 0.488096 | ||||||||
\(199\) | −2.14638e10 | −0.970216 | −0.485108 | − | 0.874454i | \(-0.661220\pi\) | ||||
−0.485108 | + | 0.874454i | \(0.661220\pi\) | |||||||
\(200\) | 8.02619e9 | 0.354711 | ||||||||
\(201\) | 3.37157e10 | 1.45697 | ||||||||
\(202\) | −8.36231e9 | −0.353382 | ||||||||
\(203\) | 2.94002e10 | 1.21512 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.20018e8 | −0.0245195 | ||||||||
\(206\) | 4.80175e9 | 0.185779 | ||||||||
\(207\) | −6.10149e10 | −2.30977 | ||||||||
\(208\) | −1.43810e10 | −0.532726 | ||||||||
\(209\) | 5.75336e10 | 2.08576 | ||||||||
\(210\) | 1.49591e9 | 0.0530784 | ||||||||
\(211\) | −7.73227e9 | −0.268557 | −0.134278 | − | 0.990944i | \(-0.542872\pi\) | ||||
−0.134278 | + | 0.990944i | \(0.542872\pi\) | |||||||
\(212\) | 1.55692e10 | 0.529363 | ||||||||
\(213\) | −1.06344e11 | −3.54001 | ||||||||
\(214\) | −5.43427e9 | −0.177125 | ||||||||
\(215\) | −1.51672e9 | −0.0484096 | ||||||||
\(216\) | −2.66114e10 | −0.831814 | ||||||||
\(217\) | 2.79818e10 | 0.856656 | ||||||||
\(218\) | 7.39204e8 | 0.0221672 | ||||||||
\(219\) | −1.22027e10 | −0.358475 | ||||||||
\(220\) | 4.27288e9 | 0.122975 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7.15182e8 | −0.0197619 | ||||||||
\(223\) | 9.27651e9 | 0.251196 | 0.125598 | − | 0.992081i | \(-0.459915\pi\) | ||||
0.125598 | + | 0.992081i | \(0.459915\pi\) | |||||||
\(224\) | −2.92083e10 | −0.775158 | ||||||||
\(225\) | −8.66078e10 | −2.25287 | ||||||||
\(226\) | −1.04715e10 | −0.267007 | ||||||||
\(227\) | 1.00921e10 | 0.252270 | 0.126135 | − | 0.992013i | \(-0.459743\pi\) | ||||
0.126135 | + | 0.992013i | \(0.459743\pi\) | |||||||
\(228\) | −1.27004e11 | −3.11250 | ||||||||
\(229\) | −2.70436e10 | −0.649837 | −0.324918 | − | 0.945742i | \(-0.605337\pi\) | ||||
−0.324918 | + | 0.945742i | \(0.605337\pi\) | |||||||
\(230\) | 8.50981e8 | 0.0200514 | ||||||||
\(231\) | −1.36170e11 | −3.14650 | ||||||||
\(232\) | 1.29948e10 | 0.294493 | ||||||||
\(233\) | −6.83620e10 | −1.51954 | −0.759771 | − | 0.650191i | \(-0.774689\pi\) | ||||
−0.759771 | + | 0.650191i | \(0.774689\pi\) | |||||||
\(234\) | −1.12800e10 | −0.245945 | ||||||||
\(235\) | −3.85785e9 | −0.0825164 | ||||||||
\(236\) | 4.47220e10 | 0.938463 | ||||||||
\(237\) | −8.86795e9 | −0.182581 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.57344e10 | −0.510179 | −0.255090 | − | 0.966917i | \(-0.582105\pi\) | ||||
−0.255090 | + | 0.966917i | \(0.582105\pi\) | |||||||
\(240\) | −9.09605e9 | −0.176971 | ||||||||
\(241\) | 1.97738e10 | 0.377584 | 0.188792 | − | 0.982017i | \(-0.439543\pi\) | ||||
0.188792 | + | 0.982017i | \(0.439543\pi\) | |||||||
\(242\) | 3.66427e9 | 0.0686781 | ||||||||
\(243\) | 6.27578e10 | 1.15462 | ||||||||
\(244\) | 4.88568e10 | 0.882411 | ||||||||
\(245\) | −7.29777e9 | −0.129402 | ||||||||
\(246\) | 4.29277e9 | 0.0747359 | ||||||||
\(247\) | −6.14798e10 | −1.05098 | ||||||||
\(248\) | 1.23679e10 | 0.207617 | ||||||||
\(249\) | −5.22504e10 | −0.861375 | ||||||||
\(250\) | 2.43023e9 | 0.0393475 | ||||||||
\(251\) | 3.35205e10 | 0.533063 | 0.266532 | − | 0.963826i | \(-0.414122\pi\) | ||||
0.266532 | + | 0.963826i | \(0.414122\pi\) | |||||||
\(252\) | 2.08938e11 | 3.26374 | ||||||||
\(253\) | −7.74635e10 | −1.18865 | ||||||||
\(254\) | 1.67384e10 | 0.252327 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 4.69562e10 | 0.683303 | ||||||||
\(257\) | −9.22091e10 | −1.31848 | −0.659242 | − | 0.751931i | \(-0.729123\pi\) | ||||
−0.659242 | + | 0.751931i | \(0.729123\pi\) | |||||||
\(258\) | 1.05012e10 | 0.147554 | ||||||||
\(259\) | 6.41271e9 | 0.0885508 | ||||||||
\(260\) | −4.56595e9 | −0.0619656 | ||||||||
\(261\) | −1.40223e11 | −1.87041 | ||||||||
\(262\) | 1.21222e10 | 0.158937 | ||||||||
\(263\) | 1.83512e10 | 0.236518 | 0.118259 | − | 0.992983i | \(-0.462269\pi\) | ||||
0.118259 | + | 0.992983i | \(0.462269\pi\) | |||||||
\(264\) | −6.01869e10 | −0.762578 | ||||||||
\(265\) | 4.76700e9 | 0.0593798 | ||||||||
\(266\) | −3.92376e10 | −0.480546 | ||||||||
\(267\) | −5.17972e10 | −0.623743 | ||||||||
\(268\) | −6.56795e10 | −0.777719 | ||||||||
\(269\) | 9.60172e10 | 1.11806 | 0.559029 | − | 0.829148i | \(-0.311174\pi\) | ||||
0.559029 | + | 0.829148i | \(0.311174\pi\) | |||||||
\(270\) | −4.00497e9 | −0.0458630 | ||||||||
\(271\) | −1.61081e11 | −1.81419 | −0.907097 | − | 0.420922i | \(-0.861706\pi\) | ||||
−0.907097 | + | 0.420922i | \(0.861706\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.45510e11 | 1.58548 | ||||||||
\(274\) | −1.99300e10 | −0.213614 | ||||||||
\(275\) | −1.09956e11 | −1.15937 | ||||||||
\(276\) | 1.70998e11 | 1.77378 | ||||||||
\(277\) | −5.34317e10 | −0.545305 | −0.272653 | − | 0.962113i | \(-0.587901\pi\) | ||||
−0.272653 | + | 0.962113i | \(0.587901\pi\) | |||||||
\(278\) | −1.09695e10 | −0.110150 | ||||||||
\(279\) | −1.33458e11 | −1.31863 | ||||||||
\(280\) | −5.92857e9 | −0.0576419 | ||||||||
\(281\) | 1.48954e11 | 1.42520 | 0.712599 | − | 0.701572i | \(-0.247518\pi\) | ||||
0.712599 | + | 0.701572i | \(0.247518\pi\) | |||||||
\(282\) | 2.67103e10 | 0.251511 | ||||||||
\(283\) | 5.51543e10 | 0.511140 | 0.255570 | − | 0.966790i | \(-0.417737\pi\) | ||||
0.255570 | + | 0.966790i | \(0.417737\pi\) | |||||||
\(284\) | 2.07162e11 | 1.88963 | ||||||||
\(285\) | −3.88862e10 | −0.349135 | ||||||||
\(286\) | −1.43209e10 | −0.126568 | ||||||||
\(287\) | −3.84913e10 | −0.334883 | ||||||||
\(288\) | 1.39307e11 | 1.19319 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | 1.95570e9 | 0.0162372 | ||||||||
\(291\) | −3.15813e11 | −2.58174 | ||||||||
\(292\) | 2.37714e10 | 0.191351 | ||||||||
\(293\) | −1.58399e11 | −1.25559 | −0.627794 | − | 0.778379i | \(-0.716042\pi\) | ||||
−0.627794 | + | 0.778379i | \(0.716042\pi\) | |||||||
\(294\) | 5.05270e10 | 0.394421 | ||||||||
\(295\) | 1.36931e10 | 0.105269 | ||||||||
\(296\) | 2.83441e9 | 0.0214610 | ||||||||
\(297\) | 3.64566e11 | 2.71877 | ||||||||
\(298\) | −1.17741e10 | −0.0864880 | ||||||||
\(299\) | 8.27766e10 | 0.598945 | ||||||||
\(300\) | 2.42724e11 | 1.73008 | ||||||||
\(301\) | −9.41592e10 | −0.661171 | ||||||||
\(302\) | −3.45756e10 | −0.239188 | ||||||||
\(303\) | −5.14490e11 | −3.50659 | ||||||||
\(304\) | 2.38589e11 | 1.60221 | ||||||||
\(305\) | 1.49591e10 | 0.0989818 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.33754e11 | 1.50188 | 0.750942 | − | 0.660368i | \(-0.229600\pi\) | ||||
0.750942 | + | 0.660368i | \(0.229600\pi\) | |||||||
\(308\) | 2.65264e11 | 1.67958 | ||||||||
\(309\) | 2.95427e11 | 1.84347 | ||||||||
\(310\) | 1.86135e9 | 0.0114472 | ||||||||
\(311\) | 2.24488e11 | 1.36073 | 0.680363 | − | 0.732875i | \(-0.261822\pi\) | ||||
0.680363 | + | 0.732875i | \(0.261822\pi\) | |||||||
\(312\) | 6.43150e10 | 0.384253 | ||||||||
\(313\) | 2.83464e10 | 0.166935 | 0.0834676 | − | 0.996510i | \(-0.473401\pi\) | ||||
0.0834676 | + | 0.996510i | \(0.473401\pi\) | |||||||
\(314\) | 3.45777e10 | 0.200730 | ||||||||
\(315\) | 6.39731e10 | 0.366100 | ||||||||
\(316\) | 1.72751e10 | 0.0974604 | ||||||||
\(317\) | 1.13413e11 | 0.630807 | 0.315404 | − | 0.948958i | \(-0.397860\pi\) | ||||
0.315404 | + | 0.948958i | \(0.397860\pi\) | |||||||
\(318\) | −3.30049e10 | −0.180991 | ||||||||
\(319\) | −1.78024e11 | −0.962546 | ||||||||
\(320\) | 1.63870e10 | 0.0873626 | ||||||||
\(321\) | −3.34343e11 | −1.75760 | ||||||||
\(322\) | 5.28297e10 | 0.273859 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −3.67635e11 | −1.85338 | ||||||||
\(325\) | 1.17497e11 | 0.584189 | ||||||||
\(326\) | 8.75807e8 | 0.00429466 | ||||||||
\(327\) | 4.54794e10 | 0.219963 | ||||||||
\(328\) | −1.70131e10 | −0.0811616 | ||||||||
\(329\) | −2.39499e11 | −1.12699 | ||||||||
\(330\) | −9.05803e9 | −0.0420456 | ||||||||
\(331\) | −4.08556e10 | −0.187079 | −0.0935397 | − | 0.995616i | \(-0.529818\pi\) | ||||
−0.0935397 | + | 0.995616i | \(0.529818\pi\) | |||||||
\(332\) | 1.01786e11 | 0.459796 | ||||||||
\(333\) | −3.05851e10 | −0.136305 | ||||||||
\(334\) | 3.83128e10 | 0.168455 | ||||||||
\(335\) | −2.01099e10 | −0.0872384 | ||||||||
\(336\) | −5.64691e11 | −2.41704 | ||||||||
\(337\) | −1.14143e11 | −0.482075 | −0.241037 | − | 0.970516i | \(-0.577488\pi\) | ||||
−0.241037 | + | 0.970516i | \(0.577488\pi\) | |||||||
\(338\) | −2.84894e10 | −0.118729 | ||||||||
\(339\) | −6.44261e11 | −2.64949 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.69435e11 | −0.678593 | ||||||||
\(342\) | 1.87142e11 | 0.739697 | ||||||||
\(343\) | −7.34065e10 | −0.286359 | ||||||||
\(344\) | −4.16182e10 | −0.160240 | ||||||||
\(345\) | 5.23565e10 | 0.198969 | ||||||||
\(346\) | 5.35793e10 | 0.200981 | ||||||||
\(347\) | 1.30233e11 | 0.482213 | 0.241106 | − | 0.970499i | \(-0.422490\pi\) | ||||
0.241106 | + | 0.970499i | \(0.422490\pi\) | |||||||
\(348\) | 3.92983e11 | 1.43637 | ||||||||
\(349\) | 1.52443e11 | 0.550039 | 0.275020 | − | 0.961439i | \(-0.411316\pi\) | ||||
0.275020 | + | 0.961439i | \(0.411316\pi\) | |||||||
\(350\) | 7.49892e10 | 0.267112 | ||||||||
\(351\) | −3.89571e11 | −1.36995 | ||||||||
\(352\) | 1.76862e11 | 0.614035 | ||||||||
\(353\) | 4.83570e11 | 1.65757 | 0.828787 | − | 0.559565i | \(-0.189032\pi\) | ||||
0.828787 | + | 0.559565i | \(0.189032\pi\) | |||||||
\(354\) | −9.48056e10 | −0.320863 | ||||||||
\(355\) | 6.34292e10 | 0.211964 | ||||||||
\(356\) | 1.00903e11 | 0.332950 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.06615e11 | 0.343041 | ||||||||
\(359\) | −3.20450e11 | −1.01820 | −0.509102 | − | 0.860706i | \(-0.670023\pi\) | ||||
−0.509102 | + | 0.860706i | \(0.670023\pi\) | |||||||
\(360\) | 2.82760e10 | 0.0887272 | ||||||||
\(361\) | 6.97298e11 | 2.16091 | ||||||||
\(362\) | −1.08078e10 | −0.0330786 | ||||||||
\(363\) | 2.25444e11 | 0.681488 | ||||||||
\(364\) | −2.83458e11 | −0.846316 | ||||||||
\(365\) | 7.27836e9 | 0.0214642 | ||||||||
\(366\) | −1.03571e11 | −0.301699 | ||||||||
\(367\) | 1.77614e11 | 0.511070 | 0.255535 | − | 0.966800i | \(-0.417748\pi\) | ||||
0.255535 | + | 0.966800i | \(0.417748\pi\) | |||||||
\(368\) | −3.21237e11 | −0.913084 | ||||||||
\(369\) | 1.83582e11 | 0.515480 | ||||||||
\(370\) | 4.26573e8 | 0.00118328 | ||||||||
\(371\) | 2.95939e11 | 0.810999 | ||||||||
\(372\) | 3.74023e11 | 1.01264 | ||||||||
\(373\) | 4.80280e11 | 1.28471 | 0.642355 | − | 0.766407i | \(-0.277958\pi\) | ||||
0.642355 | + | 0.766407i | \(0.277958\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.49520e11 | 0.390443 | ||||||||
\(376\) | −1.05858e11 | −0.273136 | ||||||||
\(377\) | 1.90235e11 | 0.485014 | ||||||||
\(378\) | −2.48632e11 | −0.626389 | ||||||||
\(379\) | −3.81929e11 | −0.950837 | −0.475419 | − | 0.879760i | \(-0.657703\pi\) | ||||
−0.475419 | + | 0.879760i | \(0.657703\pi\) | |||||||
\(380\) | 7.57518e10 | 0.186366 | ||||||||
\(381\) | 1.02983e12 | 2.50382 | ||||||||
\(382\) | 3.40931e9 | 0.00819184 | ||||||||
\(383\) | 3.63419e11 | 0.863004 | 0.431502 | − | 0.902112i | \(-0.357984\pi\) | ||||
0.431502 | + | 0.902112i | \(0.357984\pi\) | |||||||
\(384\) | −5.17327e11 | −1.21416 | ||||||||
\(385\) | 8.12191e10 | 0.188402 | ||||||||
\(386\) | −7.79714e10 | −0.178769 | ||||||||
\(387\) | 4.49088e11 | 1.01773 | ||||||||
\(388\) | 6.15216e11 | 1.37811 | ||||||||
\(389\) | −6.51726e11 | −1.44308 | −0.721542 | − | 0.692370i | \(-0.756566\pi\) | ||||
−0.721542 | + | 0.692370i | \(0.756566\pi\) | |||||||
\(390\) | 9.67930e9 | 0.0211862 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −2.00248e11 | −0.428333 | ||||||||
\(393\) | 7.45818e11 | 1.57713 | ||||||||
\(394\) | −7.15552e10 | −0.149592 | ||||||||
\(395\) | 5.28932e9 | 0.0109323 | ||||||||
\(396\) | −1.26516e12 | −2.58535 | ||||||||
\(397\) | −2.04054e11 | −0.412276 | −0.206138 | − | 0.978523i | \(-0.566090\pi\) | ||||
−0.206138 | + | 0.978523i | \(0.566090\pi\) | |||||||
\(398\) | −8.86375e10 | −0.177069 | ||||||||
\(399\) | −2.41409e12 | −4.76843 | ||||||||
\(400\) | −4.55981e11 | −0.890589 | ||||||||
\(401\) | 2.48041e11 | 0.479042 | 0.239521 | − | 0.970891i | \(-0.423010\pi\) | ||||
0.239521 | + | 0.970891i | \(0.423010\pi\) | |||||||
\(402\) | 1.39233e11 | 0.265904 | ||||||||
\(403\) | 1.81057e11 | 0.341934 | ||||||||
\(404\) | 1.00225e12 | 1.87179 | ||||||||
\(405\) | −1.12563e11 | −0.207897 | ||||||||
\(406\) | 1.21412e11 | 0.221765 | ||||||||
\(407\) | −3.88303e10 | −0.0701448 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.59982e11 | −0.459397 | −0.229698 | − | 0.973262i | \(-0.573774\pi\) | ||||
−0.229698 | + | 0.973262i | \(0.573774\pi\) | |||||||
\(410\) | −2.56044e9 | −0.00447494 | ||||||||
\(411\) | −1.22619e12 | −2.11967 | ||||||||
\(412\) | −5.75503e11 | −0.984033 | ||||||||
\(413\) | 8.50078e11 | 1.43775 | ||||||||
\(414\) | −2.51968e11 | −0.421546 | ||||||||
\(415\) | 3.11649e10 | 0.0515762 | ||||||||
\(416\) | −1.88993e11 | −0.309404 | ||||||||
\(417\) | −6.74898e11 | −1.09301 | ||||||||
\(418\) | 2.37592e11 | 0.380661 | ||||||||
\(419\) | 5.23470e11 | 0.829714 | 0.414857 | − | 0.909887i | \(-0.363832\pi\) | ||||
0.414857 | + | 0.909887i | \(0.363832\pi\) | |||||||
\(420\) | −1.79288e11 | −0.281145 | ||||||||
\(421\) | 4.04503e11 | 0.627555 | 0.313778 | − | 0.949497i | \(-0.398405\pi\) | ||||
0.313778 | + | 0.949497i | \(0.398405\pi\) | |||||||
\(422\) | −3.19313e10 | −0.0490130 | ||||||||
\(423\) | 1.14228e12 | 1.73476 | ||||||||
\(424\) | 1.30805e11 | 0.196552 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.39159e11 | −0.646069 | ||||||||
\(427\) | 9.28673e11 | 1.35188 | ||||||||
\(428\) | 6.51313e11 | 0.938194 | ||||||||
\(429\) | −8.81092e11 | −1.25592 | ||||||||
\(430\) | −6.26347e9 | −0.00883501 | ||||||||
\(431\) | 5.97189e11 | 0.833612 | 0.416806 | − | 0.908995i | \(-0.363149\pi\) | ||||
0.416806 | + | 0.908995i | \(0.363149\pi\) | |||||||
\(432\) | 1.51184e12 | 2.08847 | ||||||||
\(433\) | −8.45782e11 | −1.15628 | −0.578140 | − | 0.815938i | \(-0.696221\pi\) | ||||
−0.578140 | + | 0.815938i | \(0.696221\pi\) | |||||||
\(434\) | 1.15554e11 | 0.156344 | ||||||||
\(435\) | 1.20324e11 | 0.161121 | ||||||||
\(436\) | −8.85956e10 | −0.117415 | ||||||||
\(437\) | −1.37331e12 | −1.80137 | ||||||||
\(438\) | −5.03926e10 | −0.0654234 | ||||||||
\(439\) | −4.42347e11 | −0.568424 | −0.284212 | − | 0.958761i | \(-0.591732\pi\) | ||||
−0.284212 | + | 0.958761i | \(0.591732\pi\) | |||||||
\(440\) | 3.58987e10 | 0.0456606 | ||||||||
\(441\) | 2.16081e12 | 2.72046 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.05741e11 | −0.253807 | −0.126903 | − | 0.991915i | \(-0.540504\pi\) | ||||
−0.126903 | + | 0.991915i | \(0.540504\pi\) | |||||||
\(444\) | 8.57165e10 | 0.104675 | ||||||||
\(445\) | 3.08946e10 | 0.0373476 | ||||||||
\(446\) | 3.83085e10 | 0.0458446 | ||||||||
\(447\) | −7.24403e11 | −0.858215 | ||||||||
\(448\) | 1.01732e12 | 1.19318 | ||||||||
\(449\) | −1.29191e12 | −1.50012 | −0.750059 | − | 0.661371i | \(-0.769975\pi\) | ||||
−0.750059 | + | 0.661371i | \(0.769975\pi\) | |||||||
\(450\) | −3.57657e11 | −0.411160 | ||||||||
\(451\) | 2.33073e11 | 0.265275 | ||||||||
\(452\) | 1.25504e12 | 1.41428 | ||||||||
\(453\) | −2.12726e12 | −2.37344 | ||||||||
\(454\) | 4.16766e10 | 0.0460406 | ||||||||
\(455\) | −8.67898e10 | −0.0949330 | ||||||||
\(456\) | −1.06702e12 | −1.15567 | ||||||||
\(457\) | −2.65686e11 | −0.284935 | −0.142467 | − | 0.989799i | \(-0.545504\pi\) | ||||
−0.142467 | + | 0.989799i | \(0.545504\pi\) | |||||||
\(458\) | −1.11680e11 | −0.118599 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.01992e11 | −0.106208 | ||||||||
\(461\) | 4.14119e11 | 0.427043 | 0.213521 | − | 0.976938i | \(-0.431507\pi\) | ||||
0.213521 | + | 0.976938i | \(0.431507\pi\) | |||||||
\(462\) | −5.62330e11 | −0.574252 | ||||||||
\(463\) | 5.26394e11 | 0.532349 | 0.266175 | − | 0.963925i | \(-0.414240\pi\) | ||||
0.266175 | + | 0.963925i | \(0.414240\pi\) | |||||||
\(464\) | −7.38259e11 | −0.739397 | ||||||||
\(465\) | 1.14519e11 | 0.113590 | ||||||||
\(466\) | −2.82309e11 | −0.277324 | ||||||||
\(467\) | 5.24754e11 | 0.510540 | 0.255270 | − | 0.966870i | \(-0.417836\pi\) | ||||
0.255270 | + | 0.966870i | \(0.417836\pi\) | |||||||
\(468\) | 1.35194e12 | 1.30272 | ||||||||
\(469\) | −1.24844e12 | −1.19149 | ||||||||
\(470\) | −1.59315e10 | −0.0150597 | ||||||||
\(471\) | 2.12739e12 | 1.99184 | ||||||||
\(472\) | 3.75733e11 | 0.348450 | ||||||||
\(473\) | 5.70154e11 | 0.523741 | ||||||||
\(474\) | −3.66213e10 | −0.0333220 | ||||||||
\(475\) | −1.94935e12 | −1.75699 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.41147e12 | −1.24836 | ||||||||
\(478\) | −1.06273e11 | −0.0931103 | ||||||||
\(479\) | 6.90731e11 | 0.599514 | 0.299757 | − | 0.954016i | \(-0.403094\pi\) | ||||
0.299757 | + | 0.954016i | \(0.403094\pi\) | |||||||
\(480\) | −1.19539e11 | −0.102784 | ||||||||
\(481\) | 4.14936e10 | 0.0353450 | ||||||||
\(482\) | 8.16582e10 | 0.0689109 | ||||||||
\(483\) | 3.25034e12 | 2.71748 | ||||||||
\(484\) | −4.39173e11 | −0.363774 | ||||||||
\(485\) | 1.88368e11 | 0.154586 | ||||||||
\(486\) | 2.59166e11 | 0.210724 | ||||||||
\(487\) | −5.21019e11 | −0.419733 | −0.209867 | − | 0.977730i | \(-0.567303\pi\) | ||||
−0.209867 | + | 0.977730i | \(0.567303\pi\) | |||||||
\(488\) | 4.10472e11 | 0.327638 | ||||||||
\(489\) | 5.38839e10 | 0.0426157 | ||||||||
\(490\) | −3.01370e10 | −0.0236166 | ||||||||
\(491\) | 3.74675e11 | 0.290930 | 0.145465 | − | 0.989363i | \(-0.453532\pi\) | ||||
0.145465 | + | 0.989363i | \(0.453532\pi\) | |||||||
\(492\) | −5.14500e11 | −0.395861 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −2.53888e11 | −0.191810 | ||||||||
\(495\) | −3.87371e11 | −0.290003 | ||||||||
\(496\) | −7.02641e11 | −0.521274 | ||||||||
\(497\) | 3.93774e12 | 2.89496 | ||||||||
\(498\) | −2.15774e11 | −0.157205 | ||||||||
\(499\) | 1.96144e12 | 1.41619 | 0.708096 | − | 0.706116i | \(-0.249554\pi\) | ||||
0.708096 | + | 0.706116i | \(0.249554\pi\) | |||||||
\(500\) | −2.91269e11 | −0.208415 | ||||||||
\(501\) | 2.35719e12 | 1.67157 | ||||||||
\(502\) | 1.38427e11 | 0.0972868 | ||||||||
\(503\) | −7.20856e11 | −0.502103 | −0.251051 | − | 0.967974i | \(-0.580776\pi\) | ||||
−0.251051 | + | 0.967974i | \(0.580776\pi\) | |||||||
\(504\) | 1.75540e12 | 1.21182 | ||||||||
\(505\) | 3.06870e11 | 0.209963 | ||||||||
\(506\) | −3.19895e11 | −0.216935 | ||||||||
\(507\) | −1.75281e12 | −1.17814 | ||||||||
\(508\) | −2.00615e12 | −1.33652 | ||||||||
\(509\) | 4.96970e11 | 0.328171 | 0.164085 | − | 0.986446i | \(-0.447533\pi\) | ||||
0.164085 | + | 0.986446i | \(0.447533\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.51847e11 | 0.293155 | ||||||||
\(512\) | 1.23641e12 | 0.795146 | ||||||||
\(513\) | 6.46321e12 | 4.12022 | ||||||||
\(514\) | −3.80789e11 | −0.240630 | ||||||||
\(515\) | −1.76209e11 | −0.110381 | ||||||||
\(516\) | −1.25860e12 | −0.781560 | ||||||||
\(517\) | 1.45022e12 | 0.892740 | ||||||||
\(518\) | 2.64820e10 | 0.0161610 | ||||||||
\(519\) | 3.29646e12 | 1.99432 | ||||||||
\(520\) | −3.83609e10 | −0.0230078 | ||||||||
\(521\) | 7.85633e11 | 0.467143 | 0.233572 | − | 0.972340i | \(-0.424959\pi\) | ||||
0.233572 | + | 0.972340i | \(0.424959\pi\) | |||||||
\(522\) | −5.79067e11 | −0.341359 | ||||||||
\(523\) | −1.28047e12 | −0.748363 | −0.374182 | − | 0.927355i | \(-0.622076\pi\) | ||||
−0.374182 | + | 0.927355i | \(0.622076\pi\) | |||||||
\(524\) | −1.45288e12 | −0.841858 | ||||||||
\(525\) | 4.61371e12 | 2.65053 | ||||||||
\(526\) | 7.57835e10 | 0.0431657 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 3.41932e12 | 1.91464 | ||||||||
\(529\) | 4.78790e10 | 0.0265824 | ||||||||
\(530\) | 1.96859e10 | 0.0108371 | ||||||||
\(531\) | −4.05440e12 | −2.21310 | ||||||||
\(532\) | 4.70274e12 | 2.54535 | ||||||||
\(533\) | −2.49059e11 | −0.133669 | ||||||||
\(534\) | −2.13903e11 | −0.113836 | ||||||||
\(535\) | 1.99420e11 | 0.105239 | ||||||||
\(536\) | −5.51808e11 | −0.288766 | ||||||||
\(537\) | 6.55950e12 | 3.40397 | ||||||||
\(538\) | 3.96515e11 | 0.204051 | ||||||||
\(539\) | 2.74332e12 | 1.40000 | ||||||||
\(540\) | 4.80007e11 | 0.242927 | ||||||||
\(541\) | −2.82997e12 | −1.42035 | −0.710174 | − | 0.704026i | \(-0.751384\pi\) | ||||
−0.710174 | + | 0.704026i | \(0.751384\pi\) | |||||||
\(542\) | −6.65205e11 | −0.331100 | ||||||||
\(543\) | −6.64947e11 | −0.328237 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −2.71264e10 | −0.0131707 | ||||||||
\(546\) | 6.00900e11 | 0.289358 | ||||||||
\(547\) | −3.65687e12 | −1.74649 | −0.873247 | − | 0.487278i | \(-0.837990\pi\) | ||||
−0.873247 | + | 0.487278i | \(0.837990\pi\) | |||||||
\(548\) | 2.38866e12 | 1.13147 | ||||||||
\(549\) | −4.42926e12 | −2.08092 | ||||||||
\(550\) | −4.54076e11 | −0.211590 | ||||||||
\(551\) | −3.15611e12 | −1.45871 | ||||||||
\(552\) | 1.43665e12 | 0.658603 | ||||||||
\(553\) | 3.28366e11 | 0.149312 | ||||||||
\(554\) | −2.20652e11 | −0.0995210 | ||||||||
\(555\) | 2.62449e10 | 0.0117416 | ||||||||
\(556\) | 1.31473e12 | 0.583443 | ||||||||
\(557\) | −8.41201e11 | −0.370298 | −0.185149 | − | 0.982710i | \(-0.559277\pi\) | ||||
−0.185149 | + | 0.982710i | \(0.559277\pi\) | |||||||
\(558\) | −5.51129e11 | −0.240658 | ||||||||
\(559\) | −6.09260e11 | −0.263906 | ||||||||
\(560\) | 3.36812e11 | 0.144724 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 6.15125e11 | 0.260106 | ||||||||
\(563\) | 2.93812e12 | 1.23249 | 0.616243 | − | 0.787556i | \(-0.288654\pi\) | ||||
0.616243 | + | 0.787556i | \(0.288654\pi\) | |||||||
\(564\) | −3.20130e12 | −1.33220 | ||||||||
\(565\) | 3.84272e11 | 0.158643 | ||||||||
\(566\) | 2.27766e11 | 0.0932858 | ||||||||
\(567\) | −6.98803e12 | −2.83943 | ||||||||
\(568\) | 1.74047e12 | 0.701617 | ||||||||
\(569\) | −2.06188e12 | −0.824627 | −0.412313 | − | 0.911042i | \(-0.635279\pi\) | ||||
−0.412313 | + | 0.911042i | \(0.635279\pi\) | |||||||
\(570\) | −1.60585e11 | −0.0637190 | ||||||||
\(571\) | 2.23269e12 | 0.878955 | 0.439477 | − | 0.898254i | \(-0.355164\pi\) | ||||
0.439477 | + | 0.898254i | \(0.355164\pi\) | |||||||
\(572\) | 1.71640e12 | 0.670403 | ||||||||
\(573\) | 2.09757e11 | 0.0812871 | ||||||||
\(574\) | −1.58954e11 | −0.0611179 | ||||||||
\(575\) | 2.62461e12 | 1.00129 | ||||||||
\(576\) | −4.85206e12 | −1.83665 | ||||||||
\(577\) | −9.94350e11 | −0.373464 | −0.186732 | − | 0.982411i | \(-0.559790\pi\) | ||||
−0.186732 | + | 0.982411i | \(0.559790\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.79719e12 | −1.77392 | ||||||||
\(580\) | −2.34396e11 | −0.0860052 | ||||||||
\(581\) | 1.93475e12 | 0.704420 | ||||||||
\(582\) | −1.30419e12 | −0.471180 | ||||||||
\(583\) | −1.79198e12 | −0.642427 | ||||||||
\(584\) | 1.99716e11 | 0.0710484 | ||||||||
\(585\) | 4.13940e11 | 0.146129 | ||||||||
\(586\) | −6.54126e11 | −0.229151 | ||||||||
\(587\) | −4.22018e12 | −1.46710 | −0.733549 | − | 0.679636i | \(-0.762138\pi\) | ||||
−0.733549 | + | 0.679636i | \(0.762138\pi\) | |||||||
\(588\) | −6.05580e12 | −2.08917 | ||||||||
\(589\) | −3.00384e12 | −1.02839 | ||||||||
\(590\) | 5.65472e10 | 0.0192122 | ||||||||
\(591\) | −4.40243e12 | −1.48439 | ||||||||
\(592\) | −1.61027e11 | −0.0538830 | ||||||||
\(593\) | −4.49622e12 | −1.49314 | −0.746571 | − | 0.665305i | \(-0.768301\pi\) | ||||
−0.746571 | + | 0.665305i | \(0.768301\pi\) | |||||||
\(594\) | 1.50552e12 | 0.496189 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.41116e12 | 0.458109 | ||||||||
\(597\) | −5.45341e12 | −1.75705 | ||||||||
\(598\) | 3.41836e11 | 0.109311 | ||||||||
\(599\) | 1.61824e11 | 0.0513598 | 0.0256799 | − | 0.999670i | \(-0.491825\pi\) | ||||
0.0256799 | + | 0.999670i | \(0.491825\pi\) | |||||||
\(600\) | 2.03925e12 | 0.642377 | ||||||||
\(601\) | 3.79766e12 | 1.18735 | 0.593677 | − | 0.804703i | \(-0.297676\pi\) | ||||
0.593677 | + | 0.804703i | \(0.297676\pi\) | |||||||
\(602\) | −3.88842e11 | −0.120667 | ||||||||
\(603\) | 5.95437e12 | 1.83403 | ||||||||
\(604\) | 4.14398e12 | 1.26693 | ||||||||
\(605\) | −1.34467e11 | −0.0408052 | ||||||||
\(606\) | −2.12465e12 | −0.639971 | ||||||||
\(607\) | −9.59183e11 | −0.286782 | −0.143391 | − | 0.989666i | \(-0.545801\pi\) | ||||
−0.143391 | + | 0.989666i | \(0.545801\pi\) | |||||||
\(608\) | 3.13550e12 | 0.930554 | ||||||||
\(609\) | 7.46984e12 | 2.20056 | ||||||||
\(610\) | 6.17753e10 | 0.0180647 | ||||||||
\(611\) | −1.54968e12 | −0.449839 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.49059e12 | 0.712409 | 0.356205 | − | 0.934408i | \(-0.384071\pi\) | ||||
0.356205 | + | 0.934408i | \(0.384071\pi\) | |||||||
\(614\) | 9.65315e11 | 0.274102 | ||||||||
\(615\) | −1.57531e11 | −0.0444045 | ||||||||
\(616\) | 2.22862e12 | 0.623625 | ||||||||
\(617\) | 1.31221e12 | 0.364519 | 0.182259 | − | 0.983250i | \(-0.441659\pi\) | ||||
0.182259 | + | 0.983250i | \(0.441659\pi\) | |||||||
\(618\) | 1.22000e12 | 0.336444 | ||||||||
\(619\) | −6.10985e12 | −1.67272 | −0.836359 | − | 0.548182i | \(-0.815320\pi\) | ||||
−0.836359 | + | 0.548182i | \(0.815320\pi\) | |||||||
\(620\) | −2.23087e11 | −0.0606335 | ||||||||
\(621\) | −8.70209e12 | −2.34807 | ||||||||
\(622\) | 9.27049e11 | 0.248340 | ||||||||
\(623\) | 1.91797e12 | 0.510088 | ||||||||
\(624\) | −3.65384e12 | −0.964760 | ||||||||
\(625\) | 3.68066e12 | 0.964863 | ||||||||
\(626\) | 1.17060e11 | 0.0304665 | ||||||||
\(627\) | 1.46178e13 | 3.77728 | ||||||||
\(628\) | −4.14424e12 | −1.06323 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 2.64185e11 | 0.0668152 | ||||||||
\(631\) | −2.63235e12 | −0.661016 | −0.330508 | − | 0.943803i | \(-0.607220\pi\) | ||||
−0.330508 | + | 0.943803i | \(0.607220\pi\) | |||||||
\(632\) | 1.45137e11 | 0.0361869 | ||||||||
\(633\) | −1.96457e12 | −0.486353 | ||||||||
\(634\) | 4.68353e11 | 0.115126 | ||||||||
\(635\) | −6.14247e11 | −0.149920 | ||||||||
\(636\) | 3.95573e12 | 0.958670 | ||||||||
\(637\) | −2.93148e12 | −0.705440 | ||||||||
\(638\) | −7.35173e11 | −0.175670 | ||||||||
\(639\) | −1.87808e13 | −4.45617 | ||||||||
\(640\) | 3.08562e11 | 0.0726997 | ||||||||
\(641\) | −4.56614e12 | −1.06829 | −0.534144 | − | 0.845394i | \(-0.679366\pi\) | ||||
−0.534144 | + | 0.845394i | \(0.679366\pi\) | |||||||
\(642\) | −1.38071e12 | −0.320771 | ||||||||
\(643\) | 6.83172e12 | 1.57609 | 0.788044 | − | 0.615618i | \(-0.211094\pi\) | ||||
0.788044 | + | 0.615618i | \(0.211094\pi\) | |||||||
\(644\) | −6.33178e12 | −1.45057 | ||||||||
\(645\) | −3.85359e11 | −0.0876692 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.87609e12 | −0.869609 | −0.434805 | − | 0.900525i | \(-0.643183\pi\) | ||||
−0.434805 | + | 0.900525i | \(0.643183\pi\) | |||||||
\(648\) | −3.08870e12 | −0.688157 | ||||||||
\(649\) | −5.14740e12 | −1.13890 | ||||||||
\(650\) | 4.85220e11 | 0.106617 | ||||||||
\(651\) | 7.10945e12 | 1.55139 | ||||||||
\(652\) | −1.04968e11 | −0.0227479 | ||||||||
\(653\) | −5.89438e12 | −1.26861 | −0.634306 | − | 0.773082i | \(-0.718714\pi\) | ||||
−0.634306 | + | 0.773082i | \(0.718714\pi\) | |||||||
\(654\) | 1.87813e11 | 0.0401444 | ||||||||
\(655\) | −4.44846e11 | −0.0944329 | ||||||||
\(656\) | 9.66541e11 | 0.203776 | ||||||||
\(657\) | −2.15506e12 | −0.451248 | ||||||||
\(658\) | −9.89039e11 | −0.205682 | ||||||||
\(659\) | 6.62732e12 | 1.36884 | 0.684421 | − | 0.729087i | \(-0.260055\pi\) | ||||
0.684421 | + | 0.729087i | \(0.260055\pi\) | |||||||
\(660\) | 1.08563e12 | 0.222707 | ||||||||
\(661\) | −1.51309e12 | −0.308288 | −0.154144 | − | 0.988048i | \(-0.549262\pi\) | ||||
−0.154144 | + | 0.988048i | \(0.549262\pi\) | |||||||
\(662\) | −1.68718e11 | −0.0341429 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.55155e11 | 0.170722 | ||||||||
\(665\) | 1.43989e12 | 0.285518 | ||||||||
\(666\) | −1.26305e11 | −0.0248763 | ||||||||
\(667\) | 4.24939e12 | 0.831306 | ||||||||
\(668\) | −4.59190e12 | −0.892273 | ||||||||
\(669\) | 2.35692e12 | 0.454913 | ||||||||
\(670\) | −8.30461e10 | −0.0159215 | ||||||||
\(671\) | −5.62331e12 | −1.07088 | ||||||||
\(672\) | −7.42108e12 | −1.40380 | ||||||||
\(673\) | 7.99861e10 | 0.0150296 | 0.00751479 | − | 0.999972i | \(-0.497608\pi\) | ||||
0.00751479 | + | 0.999972i | \(0.497608\pi\) | |||||||
\(674\) | −4.71367e11 | −0.0879811 | ||||||||
\(675\) | −1.23522e13 | −2.29022 | ||||||||
\(676\) | 3.41453e12 | 0.628885 | ||||||||
\(677\) | 1.28946e12 | 0.235917 | 0.117958 | − | 0.993019i | \(-0.462365\pi\) | ||||
0.117958 | + | 0.993019i | \(0.462365\pi\) | |||||||
\(678\) | −2.66055e12 | −0.483546 | ||||||||
\(679\) | 1.16941e13 | 2.11131 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.56415e12 | 0.456858 | ||||||||
\(682\) | −6.99704e11 | −0.123847 | ||||||||
\(683\) | 1.41260e12 | 0.248386 | 0.124193 | − | 0.992258i | \(-0.460366\pi\) | ||||
0.124193 | + | 0.992258i | \(0.460366\pi\) | |||||||
\(684\) | −2.24295e13 | −3.91802 | ||||||||
\(685\) | 7.31365e11 | 0.126919 | ||||||||
\(686\) | −3.03141e11 | −0.0522620 | ||||||||
\(687\) | −6.87108e12 | −1.17685 | ||||||||
\(688\) | 2.36440e12 | 0.402321 | ||||||||
\(689\) | 1.91488e12 | 0.323710 | ||||||||
\(690\) | 2.16213e11 | 0.0363128 | ||||||||
\(691\) | 2.52816e12 | 0.421846 | 0.210923 | − | 0.977503i | \(-0.432353\pi\) | ||||
0.210923 | + | 0.977503i | \(0.432353\pi\) | |||||||
\(692\) | −6.42163e12 | −1.06455 | ||||||||
\(693\) | −2.40483e13 | −3.96082 | ||||||||
\(694\) | 5.37813e11 | 0.0880063 | ||||||||
\(695\) | 4.02546e11 | 0.0654460 | ||||||||
\(696\) | 3.30166e12 | 0.533323 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 6.29532e11 | 0.100385 | ||||||||
\(699\) | −1.73690e13 | −2.75187 | ||||||||
\(700\) | −8.98767e12 | −1.41483 | ||||||||
\(701\) | 6.98644e12 | 1.09276 | 0.546380 | − | 0.837537i | \(-0.316005\pi\) | ||||
0.546380 | + | 0.837537i | \(0.316005\pi\) | |||||||
\(702\) | −1.60878e12 | −0.250023 | ||||||||
\(703\) | −6.88403e11 | −0.106303 | ||||||||
\(704\) | −6.16009e12 | −0.945171 | ||||||||
\(705\) | −9.80181e11 | −0.149436 | ||||||||
\(706\) | 1.99696e12 | 0.302516 | ||||||||
\(707\) | 1.90507e13 | 2.86764 | ||||||||
\(708\) | 1.13627e13 | 1.69954 | ||||||||
\(709\) | 4.48848e12 | 0.667100 | 0.333550 | − | 0.942732i | \(-0.391753\pi\) | ||||
0.333550 | + | 0.942732i | \(0.391753\pi\) | |||||||
\(710\) | 2.61938e11 | 0.0386844 | ||||||||
\(711\) | −1.56612e12 | −0.229833 | ||||||||
\(712\) | 8.47738e11 | 0.123624 | ||||||||
\(713\) | 4.04438e12 | 0.586069 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.25530e11 | 0.0752005 | ||||||||
\(716\) | −1.27781e13 | −1.81702 | ||||||||
\(717\) | −6.53844e12 | −0.923928 | ||||||||
\(718\) | −1.32334e12 | −0.185828 | ||||||||
\(719\) | 7.44881e12 | 1.03946 | 0.519729 | − | 0.854331i | \(-0.326033\pi\) | ||||
0.519729 | + | 0.854331i | \(0.326033\pi\) | |||||||
\(720\) | −1.60641e12 | −0.222771 | ||||||||
\(721\) | −1.09392e13 | −1.50757 | ||||||||
\(722\) | 2.87957e12 | 0.394376 | ||||||||
\(723\) | 5.02401e12 | 0.683799 | ||||||||
\(724\) | 1.29534e12 | 0.175211 | ||||||||
\(725\) | 6.03181e12 | 0.810825 | ||||||||
\(726\) | 9.30997e11 | 0.124375 | ||||||||
\(727\) | 3.94611e12 | 0.523920 | 0.261960 | − | 0.965079i | \(-0.415631\pi\) | ||||
0.261960 | + | 0.965079i | \(0.415631\pi\) | |||||||
\(728\) | −2.38148e12 | −0.314236 | ||||||||
\(729\) | 1.32507e12 | 0.173766 | ||||||||
\(730\) | 3.00569e10 | 0.00391734 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 1.24133e13 | 1.59803 | ||||||||
\(733\) | 8.83103e12 | 1.12991 | 0.564955 | − | 0.825122i | \(-0.308894\pi\) | ||||
0.564955 | + | 0.825122i | \(0.308894\pi\) | |||||||
\(734\) | 7.33479e11 | 0.0932729 | ||||||||
\(735\) | −1.85418e12 | −0.234346 | ||||||||
\(736\) | −4.22165e12 | −0.530313 | ||||||||
\(737\) | 7.55956e12 | 0.943828 | ||||||||
\(738\) | 7.58124e11 | 0.0940777 | ||||||||
\(739\) | −6.70494e12 | −0.826980 | −0.413490 | − | 0.910509i | \(-0.635690\pi\) | ||||
−0.413490 | + | 0.910509i | \(0.635690\pi\) | |||||||
\(740\) | −5.11260e10 | −0.00626756 | ||||||||
\(741\) | −1.56204e13 | −1.90332 | ||||||||
\(742\) | 1.22212e12 | 0.148011 | ||||||||
\(743\) | 8.35278e12 | 1.00550 | 0.502749 | − | 0.864432i | \(-0.332322\pi\) | ||||
0.502749 | + | 0.864432i | \(0.332322\pi\) | |||||||
\(744\) | 3.14237e12 | 0.375992 | ||||||||
\(745\) | 4.32073e11 | 0.0513870 | ||||||||
\(746\) | 1.98338e12 | 0.234466 | ||||||||
\(747\) | −9.22768e12 | −1.08430 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.23802e13 | 1.43734 | ||||||||
\(750\) | 6.17459e11 | 0.0712578 | ||||||||
\(751\) | 1.43369e13 | 1.64465 | 0.822327 | − | 0.569015i | \(-0.192675\pi\) | ||||
0.822327 | + | 0.569015i | \(0.192675\pi\) | |||||||
\(752\) | 6.01398e12 | 0.685775 | ||||||||
\(753\) | 8.51671e12 | 0.965371 | ||||||||
\(754\) | 7.85597e11 | 0.0885175 | ||||||||
\(755\) | 1.26881e12 | 0.142114 | ||||||||
\(756\) | 2.97992e13 | 3.31785 | ||||||||
\(757\) | −1.30485e13 | −1.44421 | −0.722105 | − | 0.691784i | \(-0.756825\pi\) | ||||
−0.722105 | + | 0.691784i | \(0.756825\pi\) | |||||||
\(758\) | −1.57722e12 | −0.173533 | ||||||||
\(759\) | −1.96815e13 | −2.15263 | ||||||||
\(760\) | 6.36431e11 | 0.0691974 | ||||||||
\(761\) | −3.25303e10 | −0.00351607 | −0.00175804 | − | 0.999998i | \(-0.500560\pi\) | ||||
−0.00175804 | + | 0.999998i | \(0.500560\pi\) | |||||||
\(762\) | 4.25281e12 | 0.456960 | ||||||||
\(763\) | −1.68403e12 | −0.179883 | ||||||||
\(764\) | −4.08615e11 | −0.0433905 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.50078e12 | 0.157503 | ||||||||
\(767\) | 5.50045e12 | 0.573877 | ||||||||
\(768\) | 1.19304e13 | 1.23745 | ||||||||
\(769\) | 1.79023e13 | 1.84603 | 0.923016 | − | 0.384761i | \(-0.125716\pi\) | ||||
0.923016 | + | 0.384761i | \(0.125716\pi\) | |||||||
\(770\) | 3.35404e11 | 0.0343843 | ||||||||
\(771\) | −2.34280e13 | −2.38776 | ||||||||
\(772\) | 9.34509e12 | 0.946903 | ||||||||
\(773\) | 2.45846e12 | 0.247660 | 0.123830 | − | 0.992303i | \(-0.460482\pi\) | ||||
0.123830 | + | 0.992303i | \(0.460482\pi\) | |||||||
\(774\) | 1.85456e12 | 0.185741 | ||||||||
\(775\) | 5.74080e12 | 0.571630 | ||||||||
\(776\) | 5.16875e12 | 0.511691 | ||||||||
\(777\) | 1.62930e12 | 0.160364 | ||||||||
\(778\) | −2.69138e12 | −0.263370 | ||||||||
\(779\) | 4.13203e12 | 0.402017 | ||||||||
\(780\) | −1.16009e12 | −0.112219 | ||||||||
\(781\) | −2.38438e13 | −2.29322 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.99989e13 | −1.90142 | ||||||||
\(784\) | 1.13764e13 | 1.07543 | ||||||||
\(785\) | −1.26889e12 | −0.119264 | ||||||||
\(786\) | 3.07994e12 | 0.287833 | ||||||||
\(787\) | 1.50623e13 | 1.39961 | 0.699803 | − | 0.714336i | \(-0.253271\pi\) | ||||
0.699803 | + | 0.714336i | \(0.253271\pi\) | |||||||
\(788\) | 8.57609e12 | 0.792358 | ||||||||
\(789\) | 4.66257e12 | 0.428331 | ||||||||
\(790\) | 2.18429e10 | 0.00199521 | ||||||||
\(791\) | 2.38559e13 | 2.16672 | ||||||||
\(792\) | −1.06293e13 | −0.959935 | ||||||||
\(793\) | 6.00900e12 | 0.539601 | ||||||||
\(794\) | −8.42666e11 | −0.0752425 | ||||||||
\(795\) | 1.21117e12 | 0.107536 | ||||||||
\(796\) | 1.06234e13 | 0.937900 | ||||||||
\(797\) | −1.58318e12 | −0.138985 | −0.0694924 | − | 0.997582i | \(-0.522138\pi\) | ||||
−0.0694924 | + | 0.997582i | \(0.522138\pi\) | |||||||
\(798\) | −9.96928e12 | −0.870263 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.99244e12 | −0.517248 | ||||||||
\(801\) | −9.14765e12 | −0.785169 | ||||||||
\(802\) | 1.02431e12 | 0.0874276 | ||||||||
\(803\) | −2.73603e12 | −0.232221 | ||||||||
\(804\) | −1.66875e13 | −1.40844 | ||||||||
\(805\) | −1.93868e12 | −0.162714 | ||||||||
\(806\) | 7.47695e11 | 0.0624047 | ||||||||
\(807\) | 2.43955e13 | 2.02479 | ||||||||
\(808\) | 8.42039e12 | 0.694994 | ||||||||
\(809\) | −1.09269e13 | −0.896871 | −0.448435 | − | 0.893815i | \(-0.648019\pi\) | ||||
−0.448435 | + | 0.893815i | \(0.648019\pi\) | |||||||
\(810\) | −4.64843e11 | −0.0379423 | ||||||||
\(811\) | 1.40564e13 | 1.14098 | 0.570492 | − | 0.821303i | \(-0.306753\pi\) | ||||
0.570492 | + | 0.821303i | \(0.306753\pi\) | |||||||
\(812\) | −1.45515e13 | −1.17464 | ||||||||
\(813\) | −4.09267e13 | −3.28548 | ||||||||
\(814\) | −1.60354e11 | −0.0128018 | ||||||||
\(815\) | −3.21393e10 | −0.00255168 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.01080e13 | 0.793716 | ||||||||
\(818\) | −1.07363e12 | −0.0838423 | ||||||||
\(819\) | 2.56977e13 | 1.99580 | ||||||||
\(820\) | 3.06875e11 | 0.0237028 | ||||||||
\(821\) | 8.17487e12 | 0.627967 | 0.313983 | − | 0.949429i | \(-0.398336\pi\) | ||||
0.313983 | + | 0.949429i | \(0.398336\pi\) | |||||||
\(822\) | −5.06369e12 | −0.386852 | ||||||||
\(823\) | −1.18003e13 | −0.896587 | −0.448294 | − | 0.893886i | \(-0.647968\pi\) | ||||
−0.448294 | + | 0.893886i | \(0.647968\pi\) | |||||||
\(824\) | −4.83510e12 | −0.365370 | ||||||||
\(825\) | −2.79370e13 | −2.09960 | ||||||||
\(826\) | 3.51050e12 | 0.262397 | ||||||||
\(827\) | −1.45470e13 | −1.08143 | −0.540716 | − | 0.841205i | \(-0.681847\pi\) | ||||
−0.540716 | + | 0.841205i | \(0.681847\pi\) | |||||||
\(828\) | 3.01991e13 | 2.23284 | ||||||||
\(829\) | −1.06246e13 | −0.781301 | −0.390650 | − | 0.920539i | \(-0.627750\pi\) | ||||
−0.390650 | + | 0.920539i | \(0.627750\pi\) | |||||||
\(830\) | 1.28699e11 | 0.00941293 | ||||||||
\(831\) | −1.35756e13 | −0.987541 | ||||||||
\(832\) | 6.58260e12 | 0.476258 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −2.78707e12 | −0.199481 | ||||||||
\(835\) | −1.40596e12 | −0.100088 | ||||||||
\(836\) | −2.84761e13 | −2.01628 | ||||||||
\(837\) | −1.90340e13 | −1.34050 | ||||||||
\(838\) | 2.16173e12 | 0.151427 | ||||||||
\(839\) | 5.78736e12 | 0.403229 | 0.201614 | − | 0.979465i | \(-0.435381\pi\) | ||||
0.201614 | + | 0.979465i | \(0.435381\pi\) | |||||||
\(840\) | −1.50630e12 | −0.104389 | ||||||||
\(841\) | −4.74131e12 | −0.326826 | ||||||||
\(842\) | 1.67044e12 | 0.114532 | ||||||||
\(843\) | 3.78455e13 | 2.58101 | ||||||||
\(844\) | 3.82706e12 | 0.259612 | ||||||||
\(845\) | 1.04547e12 | 0.0705433 | ||||||||
\(846\) | 4.71717e12 | 0.316603 | ||||||||
\(847\) | −8.34782e12 | −0.557311 | ||||||||
\(848\) | −7.43124e12 | −0.493492 | ||||||||
\(849\) | 1.40133e13 | 0.925669 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9.26868e11 | 0.0605808 | ||||||||
\(852\) | 5.26345e13 | 3.42209 | ||||||||
\(853\) | −1.49513e13 | −0.966958 | −0.483479 | − | 0.875356i | \(-0.660627\pi\) | ||||
−0.483479 | + | 0.875356i | \(0.660627\pi\) | |||||||
\(854\) | 3.83507e12 | 0.246725 | ||||||||
\(855\) | −6.86750e12 | −0.439492 | ||||||||
\(856\) | 5.47202e12 | 0.348350 | ||||||||
\(857\) | 1.61752e13 | 1.02432 | 0.512159 | − | 0.858890i | \(-0.328846\pi\) | ||||
0.512159 | + | 0.858890i | \(0.328846\pi\) | |||||||
\(858\) | −3.63857e12 | −0.229213 | ||||||||
\(859\) | −2.12735e13 | −1.33312 | −0.666562 | − | 0.745450i | \(-0.732235\pi\) | ||||
−0.666562 | + | 0.745450i | \(0.732235\pi\) | |||||||
\(860\) | 7.50694e11 | 0.0467972 | ||||||||
\(861\) | −9.77964e12 | −0.606469 | ||||||||
\(862\) | 2.46616e12 | 0.152139 | ||||||||
\(863\) | 1.58563e13 | 0.973093 | 0.486547 | − | 0.873655i | \(-0.338256\pi\) | ||||
0.486547 | + | 0.873655i | \(0.338256\pi\) | |||||||
\(864\) | 1.98684e13 | 1.21297 | ||||||||
\(865\) | −1.96619e12 | −0.119413 | ||||||||
\(866\) | −3.49276e12 | −0.211027 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.38495e13 | −0.828122 | ||||||||
\(869\) | −1.98832e12 | −0.118276 | ||||||||
\(870\) | 4.96894e11 | 0.0294054 | ||||||||
\(871\) | −8.07805e12 | −0.475582 | ||||||||
\(872\) | −7.44339e11 | −0.0435960 | ||||||||
\(873\) | −5.57742e13 | −3.24990 | ||||||||
\(874\) | −5.67126e12 | −0.328759 | ||||||||
\(875\) | −5.53647e12 | −0.319298 | ||||||||
\(876\) | 6.03969e12 | 0.346534 | ||||||||
\(877\) | 1.59980e13 | 0.913203 | 0.456601 | − | 0.889671i | \(-0.349067\pi\) | ||||
0.456601 | + | 0.889671i | \(0.349067\pi\) | |||||||
\(878\) | −1.82672e12 | −0.103740 | ||||||||
\(879\) | −4.02451e13 | −2.27385 | ||||||||
\(880\) | −2.03947e12 | −0.114642 | ||||||||
\(881\) | −1.84519e13 | −1.03193 | −0.515963 | − | 0.856611i | \(-0.672566\pi\) | ||||
−0.515963 | + | 0.856611i | \(0.672566\pi\) | |||||||
\(882\) | 8.92332e12 | 0.496498 | ||||||||
\(883\) | 2.67143e11 | 0.0147884 | 0.00739420 | − | 0.999973i | \(-0.497646\pi\) | ||||
0.00739420 | + | 0.999973i | \(0.497646\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.47906e12 | 0.190641 | ||||||||
\(886\) | −8.49630e11 | −0.0463210 | ||||||||
\(887\) | −2.38695e13 | −1.29475 | −0.647377 | − | 0.762170i | \(-0.724134\pi\) | ||||
−0.647377 | + | 0.762170i | \(0.724134\pi\) | |||||||
\(888\) | 7.20150e11 | 0.0388655 | ||||||||
\(889\) | −3.81330e13 | −2.04759 | ||||||||
\(890\) | 1.27583e11 | 0.00681614 | ||||||||
\(891\) | 4.23140e13 | 2.24923 | ||||||||
\(892\) | −4.59138e12 | −0.242829 | ||||||||
\(893\) | 2.57102e13 | 1.35292 | ||||||||
\(894\) | −2.99151e12 | −0.156629 | ||||||||
\(895\) | −3.91244e12 | −0.203819 | ||||||||
\(896\) | 1.91558e13 | 0.992920 | ||||||||
\(897\) | 2.10314e13 | 1.08468 | ||||||||
\(898\) | −5.33512e12 | −0.273779 | ||||||||
\(899\) | 9.29467e12 | 0.474587 | ||||||||
\(900\) | 4.28662e13 | 2.17783 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 9.62501e11 | 0.0484141 | ||||||||
\(903\) | −2.39235e13 | −1.19737 | ||||||||
\(904\) | 1.05443e13 | 0.525121 | ||||||||
\(905\) | 3.96610e11 | 0.0196537 | ||||||||
\(906\) | −8.78478e12 | −0.433166 | ||||||||
\(907\) | 2.77628e13 | 1.36217 | 0.681085 | − | 0.732205i | \(-0.261508\pi\) | ||||
0.681085 | + | 0.732205i | \(0.261508\pi\) | |||||||
\(908\) | −4.99505e12 | −0.243867 | ||||||||
\(909\) | −9.08615e13 | −4.41410 | ||||||||
\(910\) | −3.58409e11 | −0.0173258 | ||||||||
\(911\) | −2.28307e13 | −1.09821 | −0.549106 | − | 0.835753i | \(-0.685032\pi\) | ||||
−0.549106 | + | 0.835753i | \(0.685032\pi\) | |||||||
\(912\) | 6.06194e13 | 2.90158 | ||||||||
\(913\) | −1.17153e13 | −0.558001 | ||||||||
\(914\) | −1.09718e12 | −0.0520021 | ||||||||
\(915\) | 3.80072e12 | 0.179255 | ||||||||
\(916\) | 1.33851e13 | 0.628192 | ||||||||
\(917\) | −2.76164e13 | −1.28975 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −5.88802e11 | −0.0272301 | −0.0136150 | − | 0.999907i | \(-0.504334\pi\) | ||||
−0.0136150 | + | 0.999907i | \(0.504334\pi\) | |||||||
\(920\) | −8.56892e11 | −0.0394349 | ||||||||
\(921\) | 5.93909e13 | 2.71989 | ||||||||
\(922\) | 1.71015e12 | 0.0779375 | ||||||||
\(923\) | 2.54792e13 | 1.15552 | ||||||||
\(924\) | 6.73968e13 | 3.04170 | ||||||||
\(925\) | 1.31565e12 | 0.0590882 | ||||||||
\(926\) | 2.17381e12 | 0.0971565 | ||||||||
\(927\) | 5.21739e13 | 2.32057 | ||||||||
\(928\) | −9.70209e12 | −0.429437 | ||||||||
\(929\) | −3.31307e13 | −1.45935 | −0.729676 | − | 0.683793i | \(-0.760329\pi\) | ||||
−0.729676 | + | 0.683793i | \(0.760329\pi\) | |||||||
\(930\) | 4.72921e11 | 0.0207307 | ||||||||
\(931\) | 4.86350e13 | 2.12166 | ||||||||
\(932\) | 3.38355e13 | 1.46893 | ||||||||
\(933\) | 5.70366e13 | 2.46426 | ||||||||
\(934\) | 2.16703e12 | 0.0931761 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.13584e13 | 0.483698 | ||||||||
\(937\) | −1.19627e13 | −0.506993 | −0.253496 | − | 0.967336i | \(-0.581581\pi\) | ||||
−0.253496 | + | 0.967336i | \(0.581581\pi\) | |||||||
\(938\) | −5.15558e12 | −0.217453 | ||||||||
\(939\) | 7.20208e12 | 0.302317 | ||||||||
\(940\) | 1.90943e12 | 0.0797679 | ||||||||
\(941\) | 2.09786e13 | 0.872213 | 0.436106 | − | 0.899895i | \(-0.356357\pi\) | ||||
0.436106 | + | 0.899895i | \(0.356357\pi\) | |||||||
\(942\) | 8.78532e12 | 0.363520 | ||||||||
\(943\) | −5.56338e12 | −0.229106 | ||||||||
\(944\) | −2.13460e13 | −0.874869 | ||||||||
\(945\) | 9.12399e12 | 0.372170 | ||||||||
\(946\) | 2.35452e12 | 0.0955855 | ||||||||
\(947\) | −2.72802e13 | −1.10223 | −0.551115 | − | 0.834429i | \(-0.685797\pi\) | ||||
−0.551115 | + | 0.834429i | \(0.685797\pi\) | |||||||
\(948\) | 4.38916e12 | 0.176500 | ||||||||
\(949\) | 2.92369e12 | 0.117013 | ||||||||
\(950\) | −8.05008e12 | −0.320659 | ||||||||
\(951\) | 2.88154e13 | 1.14238 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.60893e13 | −0.631858 | −0.315929 | − | 0.948783i | \(-0.602316\pi\) | ||||
−0.315929 | + | 0.948783i | \(0.602316\pi\) | |||||||
\(954\) | −5.82883e12 | −0.227831 | ||||||||
\(955\) | −1.25111e11 | −0.00486720 | ||||||||
\(956\) | 1.27371e13 | 0.493186 | ||||||||
\(957\) | −4.52315e13 | −1.74316 | ||||||||
\(958\) | 2.85246e12 | 0.109414 | ||||||||
\(959\) | 4.54038e13 | 1.73344 | ||||||||
\(960\) | 4.16353e12 | 0.158212 | ||||||||
\(961\) | −1.75934e13 | −0.665417 | ||||||||
\(962\) | 1.71353e11 | 0.00645065 | ||||||||
\(963\) | −5.90467e13 | −2.21247 | ||||||||
\(964\) | −9.78696e12 | −0.365007 | ||||||||
\(965\) | 2.86130e12 | 0.106216 | ||||||||
\(966\) | 1.34227e13 | 0.495955 | ||||||||
\(967\) | −5.02741e13 | −1.84895 | −0.924475 | − | 0.381242i | \(-0.875497\pi\) | ||||
−0.924475 | + | 0.381242i | \(0.875497\pi\) | |||||||
\(968\) | −3.68972e12 | −0.135069 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 7.77888e11 | 0.0282127 | ||||||||
\(971\) | 3.00761e13 | 1.08576 | 0.542881 | − | 0.839810i | \(-0.317333\pi\) | ||||
0.542881 | + | 0.839810i | \(0.317333\pi\) | |||||||
\(972\) | −3.10618e13 | −1.11616 | ||||||||
\(973\) | 2.49904e13 | 0.893851 | ||||||||
\(974\) | −2.15161e12 | −0.0766035 | ||||||||
\(975\) | 2.98531e13 | 1.05796 | ||||||||
\(976\) | −2.33196e13 | −0.822615 | ||||||||
\(977\) | −4.15719e13 | −1.45974 | −0.729868 | − | 0.683588i | \(-0.760419\pi\) | ||||
−0.729868 | + | 0.683588i | \(0.760419\pi\) | |||||||
\(978\) | 2.22520e11 | 0.00777758 | ||||||||
\(979\) | −1.16137e13 | −0.404062 | ||||||||
\(980\) | 3.61200e12 | 0.125092 | ||||||||
\(981\) | 8.03190e12 | 0.276890 | ||||||||
\(982\) | 1.54727e12 | 0.0530962 | ||||||||
\(983\) | 3.65566e12 | 0.124875 | 0.0624375 | − | 0.998049i | \(-0.480113\pi\) | ||||
0.0624375 | + | 0.998049i | \(0.480113\pi\) | |||||||
\(984\) | −4.32259e12 | −0.146983 | ||||||||
\(985\) | 2.62584e12 | 0.0888804 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.08505e13 | −2.04097 | ||||||||
\(988\) | 3.04292e13 | 1.01598 | ||||||||
\(989\) | −1.36094e13 | −0.452331 | ||||||||
\(990\) | −1.59969e12 | −0.0529271 | ||||||||
\(991\) | 5.35178e13 | 1.76265 | 0.881326 | − | 0.472509i | \(-0.156652\pi\) | ||||
0.881326 | + | 0.472509i | \(0.156652\pi\) | |||||||
\(992\) | −9.23400e12 | −0.302752 | ||||||||
\(993\) | −1.03804e13 | −0.338798 | ||||||||
\(994\) | 1.62614e13 | 0.528346 | ||||||||
\(995\) | 3.25271e12 | 0.105206 | ||||||||
\(996\) | 2.58611e13 | 0.832684 | ||||||||
\(997\) | −6.71487e11 | −0.0215233 | −0.0107617 | − | 0.999942i | \(-0.503426\pi\) | ||||
−0.0107617 | + | 0.999942i | \(0.503426\pi\) | |||||||
\(998\) | 8.09999e12 | 0.258462 | ||||||||
\(999\) | −4.36212e12 | −0.138565 |
(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 | 289.10.a.b.1.4 | 7 | ||
17.16 | even | 2 | 17.10.a.b.1.4 | ✓ | 7 | ||
51.50 | odd | 2 | 153.10.a.f.1.4 | 7 | |||
68.67 | odd | 2 | 272.10.a.g.1.7 | 7 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
17.10.a.b.1.4 | ✓ | 7 | 17.16 | even | 2 | ||
153.10.a.f.1.4 | 7 | 51.50 | odd | 2 | |||
272.10.a.g.1.7 | 7 | 68.67 | odd | 2 | |||
289.10.a.b.1.4 | 7 | 1.1 | even | 1 | trivial |