Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [29,12,Mod(1,29)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(29, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 12, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("29.1");
S:= CuspForms(chi, 12);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 29 \) |
Weight: | \( k \) | \(=\) | \( 12 \) |
Character orbit: | \([\chi]\) | \(=\) | 29.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: | \(22.2819522362\) |
Analytic rank: | \(1\) |
Dimension: | \(11\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{11} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{11} - x^{10} - 15790 x^{9} + 14666 x^{8} + 87206462 x^{7} - 14008334 x^{6} - 203974096304 x^{5} + \cdots - 75\!\cdots\!58 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-65.3340\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 29.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −68.3340 | −1.50998 | −0.754991 | − | 0.655735i | \(-0.772359\pi\) | ||||
−0.754991 | + | 0.655735i | \(0.772359\pi\) | |||||||
\(3\) | 537.644 | 1.27740 | 0.638702 | − | 0.769454i | \(-0.279472\pi\) | ||||
0.638702 | + | 0.769454i | \(0.279472\pi\) | |||||||
\(4\) | 2621.54 | 1.28005 | ||||||||
\(5\) | 8265.40 | 1.18285 | 0.591424 | − | 0.806361i | \(-0.298566\pi\) | ||||
0.591424 | + | 0.806361i | \(0.298566\pi\) | |||||||
\(6\) | −36739.4 | −1.92886 | ||||||||
\(7\) | −68659.4 | −1.54405 | −0.772024 | − | 0.635593i | \(-0.780756\pi\) | ||||
−0.772024 | + | 0.635593i | \(0.780756\pi\) | |||||||
\(8\) | −39192.0 | −0.422866 | ||||||||
\(9\) | 111914. | 0.631759 | ||||||||
\(10\) | −564808. | −1.78608 | ||||||||
\(11\) | −970140. | −1.81625 | −0.908123 | − | 0.418703i | \(-0.862485\pi\) | ||||
−0.908123 | + | 0.418703i | \(0.862485\pi\) | |||||||
\(12\) | 1.40945e6 | 1.63514 | ||||||||
\(13\) | 1.54127e6 | 1.15130 | 0.575651 | − | 0.817696i | \(-0.304749\pi\) | ||||
0.575651 | + | 0.817696i | \(0.304749\pi\) | |||||||
\(14\) | 4.69177e6 | 2.33149 | ||||||||
\(15\) | 4.44384e6 | 1.51097 | ||||||||
\(16\) | −2.69076e6 | −0.641527 | ||||||||
\(17\) | −3.34371e6 | −0.571162 | −0.285581 | − | 0.958355i | \(-0.592187\pi\) | ||||
−0.285581 | + | 0.958355i | \(0.592187\pi\) | |||||||
\(18\) | −7.64755e6 | −0.953945 | ||||||||
\(19\) | 5.46951e6 | 0.506762 | 0.253381 | − | 0.967367i | \(-0.418457\pi\) | ||||
0.253381 | + | 0.967367i | \(0.418457\pi\) | |||||||
\(20\) | 2.16680e7 | 1.51410 | ||||||||
\(21\) | −3.69143e7 | −1.97237 | ||||||||
\(22\) | 6.62936e7 | 2.74250 | ||||||||
\(23\) | −3.32547e7 | −1.07733 | −0.538667 | − | 0.842519i | \(-0.681072\pi\) | ||||
−0.538667 | + | 0.842519i | \(0.681072\pi\) | |||||||
\(24\) | −2.10714e7 | −0.540171 | ||||||||
\(25\) | 1.94887e7 | 0.399128 | ||||||||
\(26\) | −1.05321e8 | −1.73845 | ||||||||
\(27\) | −3.50720e7 | −0.470392 | ||||||||
\(28\) | −1.79993e8 | −1.97646 | ||||||||
\(29\) | 2.05111e7 | 0.185695 | ||||||||
\(30\) | −3.03666e8 | −2.28154 | ||||||||
\(31\) | −8.71995e7 | −0.547047 | −0.273523 | − | 0.961865i | \(-0.588189\pi\) | ||||
−0.273523 | + | 0.961865i | \(0.588189\pi\) | |||||||
\(32\) | 2.64136e8 | 1.39156 | ||||||||
\(33\) | −5.21590e8 | −2.32008 | ||||||||
\(34\) | 2.28489e8 | 0.862445 | ||||||||
\(35\) | −5.67498e8 | −1.82637 | ||||||||
\(36\) | 2.93387e8 | 0.808681 | ||||||||
\(37\) | −1.97918e8 | −0.469220 | −0.234610 | − | 0.972090i | \(-0.575381\pi\) | ||||
−0.234610 | + | 0.972090i | \(0.575381\pi\) | |||||||
\(38\) | −3.73754e8 | −0.765201 | ||||||||
\(39\) | 8.28652e8 | 1.47068 | ||||||||
\(40\) | −3.23938e8 | −0.500186 | ||||||||
\(41\) | 1.10998e9 | 1.49625 | 0.748123 | − | 0.663560i | \(-0.230955\pi\) | ||||
0.748123 | + | 0.663560i | \(0.230955\pi\) | |||||||
\(42\) | 2.52251e9 | 2.97825 | ||||||||
\(43\) | −9.82013e8 | −1.01869 | −0.509344 | − | 0.860563i | \(-0.670112\pi\) | ||||
−0.509344 | + | 0.860563i | \(0.670112\pi\) | |||||||
\(44\) | −2.54326e9 | −2.32488 | ||||||||
\(45\) | 9.25016e8 | 0.747275 | ||||||||
\(46\) | 2.27243e9 | 1.62675 | ||||||||
\(47\) | −2.38472e9 | −1.51670 | −0.758348 | − | 0.651850i | \(-0.773993\pi\) | ||||
−0.758348 | + | 0.651850i | \(0.773993\pi\) | |||||||
\(48\) | −1.44667e9 | −0.819488 | ||||||||
\(49\) | 2.73679e9 | 1.38409 | ||||||||
\(50\) | −1.33174e9 | −0.602676 | ||||||||
\(51\) | −1.79773e9 | −0.729604 | ||||||||
\(52\) | 4.04048e9 | 1.47372 | ||||||||
\(53\) | 2.86882e9 | 0.942293 | 0.471147 | − | 0.882055i | \(-0.343840\pi\) | ||||
0.471147 | + | 0.882055i | \(0.343840\pi\) | |||||||
\(54\) | 2.39661e9 | 0.710284 | ||||||||
\(55\) | −8.01859e9 | −2.14834 | ||||||||
\(56\) | 2.69090e9 | 0.652926 | ||||||||
\(57\) | 2.94065e9 | 0.647339 | ||||||||
\(58\) | −1.40161e9 | −0.280397 | ||||||||
\(59\) | −7.54410e9 | −1.37379 | −0.686896 | − | 0.726755i | \(-0.741027\pi\) | ||||
−0.686896 | + | 0.726755i | \(0.741027\pi\) | |||||||
\(60\) | 1.16497e10 | 1.93412 | ||||||||
\(61\) | −1.25957e10 | −1.90945 | −0.954723 | − | 0.297496i | \(-0.903849\pi\) | ||||
−0.954723 | + | 0.297496i | \(0.903849\pi\) | |||||||
\(62\) | 5.95869e9 | 0.826031 | ||||||||
\(63\) | −7.68397e9 | −0.975467 | ||||||||
\(64\) | −1.25388e10 | −1.45970 | ||||||||
\(65\) | 1.27392e10 | 1.36181 | ||||||||
\(66\) | 3.56423e10 | 3.50328 | ||||||||
\(67\) | −2.53077e8 | −0.0229003 | −0.0114502 | − | 0.999934i | \(-0.503645\pi\) | ||||
−0.0114502 | + | 0.999934i | \(0.503645\pi\) | |||||||
\(68\) | −8.76565e9 | −0.731114 | ||||||||
\(69\) | −1.78792e10 | −1.37619 | ||||||||
\(70\) | 3.87794e10 | 2.75779 | ||||||||
\(71\) | −7.66739e9 | −0.504344 | −0.252172 | − | 0.967682i | \(-0.581145\pi\) | ||||
−0.252172 | + | 0.967682i | \(0.581145\pi\) | |||||||
\(72\) | −4.38615e9 | −0.267150 | ||||||||
\(73\) | −1.59232e10 | −0.898991 | −0.449495 | − | 0.893283i | \(-0.648396\pi\) | ||||
−0.449495 | + | 0.893283i | \(0.648396\pi\) | |||||||
\(74\) | 1.35245e10 | 0.708513 | ||||||||
\(75\) | 1.04780e10 | 0.509848 | ||||||||
\(76\) | 1.43385e10 | 0.648679 | ||||||||
\(77\) | 6.66093e10 | 2.80437 | ||||||||
\(78\) | −5.66251e10 | −2.22070 | ||||||||
\(79\) | 1.03493e10 | 0.378411 | 0.189205 | − | 0.981938i | \(-0.439409\pi\) | ||||
0.189205 | + | 0.981938i | \(0.439409\pi\) | |||||||
\(80\) | −2.22402e10 | −0.758828 | ||||||||
\(81\) | −3.86815e10 | −1.23264 | ||||||||
\(82\) | −7.58492e10 | −2.25930 | ||||||||
\(83\) | 2.23246e10 | 0.622091 | 0.311046 | − | 0.950395i | \(-0.399321\pi\) | ||||
0.311046 | + | 0.950395i | \(0.399321\pi\) | |||||||
\(84\) | −9.67723e10 | −2.52473 | ||||||||
\(85\) | −2.76371e10 | −0.675598 | ||||||||
\(86\) | 6.71049e10 | 1.53820 | ||||||||
\(87\) | 1.10277e10 | 0.237208 | ||||||||
\(88\) | 3.80218e10 | 0.768029 | ||||||||
\(89\) | 7.10371e10 | 1.34847 | 0.674233 | − | 0.738518i | \(-0.264474\pi\) | ||||
0.674233 | + | 0.738518i | \(0.264474\pi\) | |||||||
\(90\) | −6.32100e10 | −1.12837 | ||||||||
\(91\) | −1.05822e11 | −1.77767 | ||||||||
\(92\) | −8.71784e10 | −1.37904 | ||||||||
\(93\) | −4.68823e10 | −0.698800 | ||||||||
\(94\) | 1.62957e11 | 2.29018 | ||||||||
\(95\) | 4.52077e10 | 0.599422 | ||||||||
\(96\) | 1.42011e11 | 1.77758 | ||||||||
\(97\) | −5.61657e9 | −0.0664090 | −0.0332045 | − | 0.999449i | \(-0.510571\pi\) | ||||
−0.0332045 | + | 0.999449i | \(0.510571\pi\) | |||||||
\(98\) | −1.87016e11 | −2.08995 | ||||||||
\(99\) | −1.08572e11 | −1.14743 | ||||||||
\(100\) | 5.10903e10 | 0.510903 | ||||||||
\(101\) | 1.50942e11 | 1.42904 | 0.714518 | − | 0.699617i | \(-0.246646\pi\) | ||||
0.714518 | + | 0.699617i | \(0.246646\pi\) | |||||||
\(102\) | 1.22846e11 | 1.10169 | ||||||||
\(103\) | −4.18049e10 | −0.355322 | −0.177661 | − | 0.984092i | \(-0.556853\pi\) | ||||
−0.177661 | + | 0.984092i | \(0.556853\pi\) | |||||||
\(104\) | −6.04054e10 | −0.486847 | ||||||||
\(105\) | −3.05112e11 | −2.33302 | ||||||||
\(106\) | −1.96038e11 | −1.42285 | ||||||||
\(107\) | 3.91482e10 | 0.269837 | 0.134918 | − | 0.990857i | \(-0.456923\pi\) | ||||
0.134918 | + | 0.990857i | \(0.456923\pi\) | |||||||
\(108\) | −9.19426e10 | −0.602124 | ||||||||
\(109\) | −1.25846e11 | −0.783421 | −0.391710 | − | 0.920089i | \(-0.628116\pi\) | ||||
−0.391710 | + | 0.920089i | \(0.628116\pi\) | |||||||
\(110\) | 5.47943e11 | 3.24396 | ||||||||
\(111\) | −1.06410e11 | −0.599383 | ||||||||
\(112\) | 1.84746e11 | 0.990548 | ||||||||
\(113\) | 8.94509e10 | 0.456724 | 0.228362 | − | 0.973576i | \(-0.426663\pi\) | ||||
0.228362 | + | 0.973576i | \(0.426663\pi\) | |||||||
\(114\) | −2.00947e11 | −0.977471 | ||||||||
\(115\) | −2.74863e11 | −1.27432 | ||||||||
\(116\) | 5.37707e10 | 0.237699 | ||||||||
\(117\) | 1.72490e11 | 0.727345 | ||||||||
\(118\) | 5.15518e11 | 2.07440 | ||||||||
\(119\) | 2.29577e11 | 0.881902 | ||||||||
\(120\) | −1.74163e11 | −0.638940 | ||||||||
\(121\) | 6.55860e11 | 2.29875 | ||||||||
\(122\) | 8.60713e11 | 2.88323 | ||||||||
\(123\) | 5.96773e11 | 1.91131 | ||||||||
\(124\) | −2.28597e11 | −0.700246 | ||||||||
\(125\) | −2.42502e11 | −0.710740 | ||||||||
\(126\) | 5.25076e11 | 1.47294 | ||||||||
\(127\) | 1.50285e11 | 0.403642 | 0.201821 | − | 0.979422i | \(-0.435314\pi\) | ||||
0.201821 | + | 0.979422i | \(0.435314\pi\) | |||||||
\(128\) | 3.15875e11 | 0.812569 | ||||||||
\(129\) | −5.27974e11 | −1.30127 | ||||||||
\(130\) | −8.70519e11 | −2.05632 | ||||||||
\(131\) | −2.82004e11 | −0.638651 | −0.319326 | − | 0.947645i | \(-0.603456\pi\) | ||||
−0.319326 | + | 0.947645i | \(0.603456\pi\) | |||||||
\(132\) | −1.36737e12 | −2.96981 | ||||||||
\(133\) | −3.75534e11 | −0.782465 | ||||||||
\(134\) | 1.72938e10 | 0.0345791 | ||||||||
\(135\) | −2.89884e11 | −0.556402 | ||||||||
\(136\) | 1.31047e11 | 0.241525 | ||||||||
\(137\) | 3.90301e11 | 0.690933 | 0.345467 | − | 0.938431i | \(-0.387721\pi\) | ||||
0.345467 | + | 0.938431i | \(0.387721\pi\) | |||||||
\(138\) | 1.22176e12 | 2.07802 | ||||||||
\(139\) | −4.80262e10 | −0.0785049 | −0.0392524 | − | 0.999229i | \(-0.512498\pi\) | ||||
−0.0392524 | + | 0.999229i | \(0.512498\pi\) | |||||||
\(140\) | −1.48772e12 | −2.33785 | ||||||||
\(141\) | −1.28213e12 | −1.93743 | ||||||||
\(142\) | 5.23943e11 | 0.761550 | ||||||||
\(143\) | −1.49524e12 | −2.09105 | ||||||||
\(144\) | −3.01134e11 | −0.405290 | ||||||||
\(145\) | 1.69533e11 | 0.219649 | ||||||||
\(146\) | 1.08810e12 | 1.35746 | ||||||||
\(147\) | 1.47142e12 | 1.76804 | ||||||||
\(148\) | −5.18850e11 | −0.600623 | ||||||||
\(149\) | −7.91388e11 | −0.882805 | −0.441402 | − | 0.897309i | \(-0.645519\pi\) | ||||
−0.441402 | + | 0.897309i | \(0.645519\pi\) | |||||||
\(150\) | −7.16002e11 | −0.769861 | ||||||||
\(151\) | 1.31177e12 | 1.35983 | 0.679915 | − | 0.733291i | \(-0.262016\pi\) | ||||
0.679915 | + | 0.733291i | \(0.262016\pi\) | |||||||
\(152\) | −2.14361e11 | −0.214292 | ||||||||
\(153\) | −3.74209e11 | −0.360837 | ||||||||
\(154\) | −4.55168e12 | −4.23455 | ||||||||
\(155\) | −7.20738e11 | −0.647073 | ||||||||
\(156\) | 2.17234e12 | 1.88253 | ||||||||
\(157\) | −6.76641e11 | −0.566122 | −0.283061 | − | 0.959102i | \(-0.591350\pi\) | ||||
−0.283061 | + | 0.959102i | \(0.591350\pi\) | |||||||
\(158\) | −7.07211e11 | −0.571394 | ||||||||
\(159\) | 1.54240e12 | 1.20369 | ||||||||
\(160\) | 2.18319e12 | 1.64600 | ||||||||
\(161\) | 2.28325e12 | 1.66346 | ||||||||
\(162\) | 2.64326e12 | 1.86126 | ||||||||
\(163\) | 8.90844e11 | 0.606415 | 0.303207 | − | 0.952925i | \(-0.401943\pi\) | ||||
0.303207 | + | 0.952925i | \(0.401943\pi\) | |||||||
\(164\) | 2.90985e12 | 1.91527 | ||||||||
\(165\) | −4.31115e12 | −2.74430 | ||||||||
\(166\) | −1.52553e12 | −0.939347 | ||||||||
\(167\) | 7.38410e11 | 0.439903 | 0.219952 | − | 0.975511i | \(-0.429410\pi\) | ||||
0.219952 | + | 0.975511i | \(0.429410\pi\) | |||||||
\(168\) | 1.44675e12 | 0.834050 | ||||||||
\(169\) | 5.83339e11 | 0.325495 | ||||||||
\(170\) | 1.88855e12 | 1.02014 | ||||||||
\(171\) | 6.12116e11 | 0.320151 | ||||||||
\(172\) | −2.57438e12 | −1.30397 | ||||||||
\(173\) | −1.13157e12 | −0.555170 | −0.277585 | − | 0.960701i | \(-0.589534\pi\) | ||||
−0.277585 | + | 0.960701i | \(0.589534\pi\) | |||||||
\(174\) | −7.53567e11 | −0.358180 | ||||||||
\(175\) | −1.33808e12 | −0.616273 | ||||||||
\(176\) | 2.61041e12 | 1.16517 | ||||||||
\(177\) | −4.05604e12 | −1.75489 | ||||||||
\(178\) | −4.85425e12 | −2.03616 | ||||||||
\(179\) | 4.03407e12 | 1.64079 | 0.820393 | − | 0.571799i | \(-0.193754\pi\) | ||||
0.820393 | + | 0.571799i | \(0.193754\pi\) | |||||||
\(180\) | 2.42496e12 | 0.956547 | ||||||||
\(181\) | −3.88701e12 | −1.48725 | −0.743625 | − | 0.668597i | \(-0.766895\pi\) | ||||
−0.743625 | + | 0.668597i | \(0.766895\pi\) | |||||||
\(182\) | 7.23127e12 | 2.68424 | ||||||||
\(183\) | −6.77199e12 | −2.43913 | ||||||||
\(184\) | 1.30332e12 | 0.455568 | ||||||||
\(185\) | −1.63587e12 | −0.555015 | ||||||||
\(186\) | 3.20366e12 | 1.05518 | ||||||||
\(187\) | 3.24387e12 | 1.03737 | ||||||||
\(188\) | −6.25162e12 | −1.94144 | ||||||||
\(189\) | 2.40802e12 | 0.726308 | ||||||||
\(190\) | −3.08922e12 | −0.905117 | ||||||||
\(191\) | −2.12510e12 | −0.604916 | −0.302458 | − | 0.953163i | \(-0.597807\pi\) | ||||
−0.302458 | + | 0.953163i | \(0.597807\pi\) | |||||||
\(192\) | −6.74140e12 | −1.86463 | ||||||||
\(193\) | 1.38130e12 | 0.371298 | 0.185649 | − | 0.982616i | \(-0.440561\pi\) | ||||
0.185649 | + | 0.982616i | \(0.440561\pi\) | |||||||
\(194\) | 3.83803e11 | 0.100276 | ||||||||
\(195\) | 6.84914e12 | 1.73959 | ||||||||
\(196\) | 7.17460e12 | 1.77170 | ||||||||
\(197\) | 4.09906e12 | 0.984283 | 0.492142 | − | 0.870515i | \(-0.336214\pi\) | ||||
0.492142 | + | 0.870515i | \(0.336214\pi\) | |||||||
\(198\) | 7.41919e12 | 1.73260 | ||||||||
\(199\) | 2.67780e12 | 0.608255 | 0.304127 | − | 0.952631i | \(-0.401635\pi\) | ||||
0.304127 | + | 0.952631i | \(0.401635\pi\) | |||||||
\(200\) | −7.63801e11 | −0.168778 | ||||||||
\(201\) | −1.36065e11 | −0.0292529 | ||||||||
\(202\) | −1.03145e13 | −2.15782 | ||||||||
\(203\) | −1.40828e12 | −0.286723 | ||||||||
\(204\) | −4.71280e12 | −0.933928 | ||||||||
\(205\) | 9.17440e12 | 1.76983 | ||||||||
\(206\) | 2.85669e12 | 0.536530 | ||||||||
\(207\) | −3.72168e12 | −0.680615 | ||||||||
\(208\) | −4.14717e12 | −0.738590 | ||||||||
\(209\) | −5.30619e12 | −0.920404 | ||||||||
\(210\) | 2.08495e13 | 3.52281 | ||||||||
\(211\) | −4.90054e12 | −0.806660 | −0.403330 | − | 0.915055i | \(-0.632147\pi\) | ||||
−0.403330 | + | 0.915055i | \(0.632147\pi\) | |||||||
\(212\) | 7.52072e12 | 1.20618 | ||||||||
\(213\) | −4.12233e12 | −0.644250 | ||||||||
\(214\) | −2.67515e12 | −0.407449 | ||||||||
\(215\) | −8.11673e12 | −1.20495 | ||||||||
\(216\) | 1.37454e12 | 0.198913 | ||||||||
\(217\) | 5.98707e12 | 0.844667 | ||||||||
\(218\) | 8.59959e12 | 1.18295 | ||||||||
\(219\) | −8.56103e12 | −1.14837 | ||||||||
\(220\) | −2.10210e13 | −2.74998 | ||||||||
\(221\) | −5.15354e12 | −0.657580 | ||||||||
\(222\) | 7.27139e12 | 0.905057 | ||||||||
\(223\) | 1.59341e13 | 1.93487 | 0.967435 | − | 0.253120i | \(-0.0814566\pi\) | ||||
0.967435 | + | 0.253120i | \(0.0814566\pi\) | |||||||
\(224\) | −1.81354e13 | −2.14864 | ||||||||
\(225\) | 2.18106e12 | 0.252153 | ||||||||
\(226\) | −6.11254e12 | −0.689645 | ||||||||
\(227\) | 1.88453e12 | 0.207520 | 0.103760 | − | 0.994602i | \(-0.466913\pi\) | ||||
0.103760 | + | 0.994602i | \(0.466913\pi\) | |||||||
\(228\) | 7.70903e12 | 0.828625 | ||||||||
\(229\) | −4.25535e12 | −0.446519 | −0.223259 | − | 0.974759i | \(-0.571670\pi\) | ||||
−0.223259 | + | 0.974759i | \(0.571670\pi\) | |||||||
\(230\) | 1.87825e13 | 1.92420 | ||||||||
\(231\) | 3.58121e13 | 3.58232 | ||||||||
\(232\) | −8.03874e11 | −0.0785243 | ||||||||
\(233\) | 6.22697e12 | 0.594045 | 0.297022 | − | 0.954871i | \(-0.404006\pi\) | ||||
0.297022 | + | 0.954871i | \(0.404006\pi\) | |||||||
\(234\) | −1.17869e13 | −1.09828 | ||||||||
\(235\) | −1.97106e13 | −1.79402 | ||||||||
\(236\) | −1.97771e13 | −1.75852 | ||||||||
\(237\) | 5.56426e12 | 0.483383 | ||||||||
\(238\) | −1.56879e13 | −1.33166 | ||||||||
\(239\) | 1.79781e13 | 1.49127 | 0.745633 | − | 0.666357i | \(-0.232147\pi\) | ||||
0.745633 | + | 0.666357i | \(0.232147\pi\) | |||||||
\(240\) | −1.19573e13 | −0.969329 | ||||||||
\(241\) | −1.00728e13 | −0.798097 | −0.399048 | − | 0.916930i | \(-0.630659\pi\) | ||||
−0.399048 | + | 0.916930i | \(0.630659\pi\) | |||||||
\(242\) | −4.48176e13 | −3.47107 | ||||||||
\(243\) | −1.45840e13 | −1.10419 | ||||||||
\(244\) | −3.30200e13 | −2.44418 | ||||||||
\(245\) | 2.26207e13 | 1.63716 | ||||||||
\(246\) | −4.07799e13 | −2.88604 | ||||||||
\(247\) | 8.42997e12 | 0.583436 | ||||||||
\(248\) | 3.41753e12 | 0.231328 | ||||||||
\(249\) | 1.20027e13 | 0.794661 | ||||||||
\(250\) | 1.65711e13 | 1.07320 | ||||||||
\(251\) | 1.15166e13 | 0.729654 | 0.364827 | − | 0.931075i | \(-0.381128\pi\) | ||||
0.364827 | + | 0.931075i | \(0.381128\pi\) | |||||||
\(252\) | −2.01438e13 | −1.24864 | ||||||||
\(253\) | 3.22617e13 | 1.95670 | ||||||||
\(254\) | −1.02696e13 | −0.609493 | ||||||||
\(255\) | −1.48589e13 | −0.863011 | ||||||||
\(256\) | 4.09441e12 | 0.232740 | ||||||||
\(257\) | −3.13280e13 | −1.74301 | −0.871506 | − | 0.490384i | \(-0.836857\pi\) | ||||
−0.871506 | + | 0.490384i | \(0.836857\pi\) | |||||||
\(258\) | 3.60786e13 | 1.96490 | ||||||||
\(259\) | 1.35890e13 | 0.724498 | ||||||||
\(260\) | 3.33962e13 | 1.74319 | ||||||||
\(261\) | 2.29549e12 | 0.117315 | ||||||||
\(262\) | 1.92705e13 | 0.964352 | ||||||||
\(263\) | 9.17362e12 | 0.449556 | 0.224778 | − | 0.974410i | \(-0.427834\pi\) | ||||
0.224778 | + | 0.974410i | \(0.427834\pi\) | |||||||
\(264\) | 2.04422e13 | 0.981083 | ||||||||
\(265\) | 2.37119e13 | 1.11459 | ||||||||
\(266\) | 2.56617e13 | 1.18151 | ||||||||
\(267\) | 3.81927e13 | 1.72254 | ||||||||
\(268\) | −6.63450e11 | −0.0293135 | ||||||||
\(269\) | −2.94832e13 | −1.27625 | −0.638127 | − | 0.769931i | \(-0.720291\pi\) | ||||
−0.638127 | + | 0.769931i | \(0.720291\pi\) | |||||||
\(270\) | 1.98089e13 | 0.840157 | ||||||||
\(271\) | −8.20600e12 | −0.341036 | −0.170518 | − | 0.985355i | \(-0.554544\pi\) | ||||
−0.170518 | + | 0.985355i | \(0.554544\pi\) | |||||||
\(272\) | 8.99711e12 | 0.366416 | ||||||||
\(273\) | −5.68948e13 | −2.27080 | ||||||||
\(274\) | −2.66708e13 | −1.04330 | ||||||||
\(275\) | −1.89067e13 | −0.724915 | ||||||||
\(276\) | −4.68710e13 | −1.76159 | ||||||||
\(277\) | 2.31768e13 | 0.853915 | 0.426958 | − | 0.904272i | \(-0.359585\pi\) | ||||
0.426958 | + | 0.904272i | \(0.359585\pi\) | |||||||
\(278\) | 3.28182e12 | 0.118541 | ||||||||
\(279\) | −9.75886e12 | −0.345602 | ||||||||
\(280\) | 2.22414e13 | 0.772312 | ||||||||
\(281\) | 4.19264e13 | 1.42759 | 0.713793 | − | 0.700357i | \(-0.246976\pi\) | ||||
0.713793 | + | 0.700357i | \(0.246976\pi\) | |||||||
\(282\) | 8.76130e13 | 2.92549 | ||||||||
\(283\) | −1.71390e13 | −0.561254 | −0.280627 | − | 0.959817i | \(-0.590542\pi\) | ||||
−0.280627 | + | 0.959817i | \(0.590542\pi\) | |||||||
\(284\) | −2.01003e13 | −0.645584 | ||||||||
\(285\) | 2.43057e13 | 0.765703 | ||||||||
\(286\) | 1.02176e14 | 3.15744 | ||||||||
\(287\) | −7.62104e13 | −2.31028 | ||||||||
\(288\) | 2.95605e13 | 0.879131 | ||||||||
\(289\) | −2.30915e13 | −0.673774 | ||||||||
\(290\) | −1.15849e13 | −0.331667 | ||||||||
\(291\) | −3.01972e12 | −0.0848310 | ||||||||
\(292\) | −4.17433e13 | −1.15075 | ||||||||
\(293\) | 6.88609e13 | 1.86295 | 0.931474 | − | 0.363807i | \(-0.118523\pi\) | ||||
0.931474 | + | 0.363807i | \(0.118523\pi\) | |||||||
\(294\) | −1.00548e14 | −2.66971 | ||||||||
\(295\) | −6.23550e13 | −1.62499 | ||||||||
\(296\) | 7.75682e12 | 0.198417 | ||||||||
\(297\) | 3.40248e13 | 0.854348 | ||||||||
\(298\) | 5.40787e13 | 1.33302 | ||||||||
\(299\) | −5.12543e13 | −1.24034 | ||||||||
\(300\) | 2.74684e13 | 0.652629 | ||||||||
\(301\) | 6.74245e13 | 1.57290 | ||||||||
\(302\) | −8.96386e13 | −2.05332 | ||||||||
\(303\) | 8.11532e13 | 1.82545 | ||||||||
\(304\) | −1.47171e13 | −0.325101 | ||||||||
\(305\) | −1.04108e14 | −2.25858 | ||||||||
\(306\) | 2.55712e13 | 0.544857 | ||||||||
\(307\) | −3.43334e13 | −0.718547 | −0.359273 | − | 0.933232i | \(-0.616975\pi\) | ||||
−0.359273 | + | 0.933232i | \(0.616975\pi\) | |||||||
\(308\) | 1.74619e14 | 3.58973 | ||||||||
\(309\) | −2.24761e13 | −0.453890 | ||||||||
\(310\) | 4.92509e13 | 0.977069 | ||||||||
\(311\) | −7.11998e13 | −1.38770 | −0.693852 | − | 0.720118i | \(-0.744088\pi\) | ||||
−0.693852 | + | 0.720118i | \(0.744088\pi\) | |||||||
\(312\) | −3.24766e13 | −0.621899 | ||||||||
\(313\) | −8.48846e13 | −1.59711 | −0.798555 | − | 0.601922i | \(-0.794402\pi\) | ||||
−0.798555 | + | 0.601922i | \(0.794402\pi\) | |||||||
\(314\) | 4.62376e13 | 0.854834 | ||||||||
\(315\) | −6.35111e13 | −1.15383 | ||||||||
\(316\) | 2.71312e13 | 0.484384 | ||||||||
\(317\) | 6.68644e13 | 1.17319 | 0.586595 | − | 0.809880i | \(-0.300468\pi\) | ||||
0.586595 | + | 0.809880i | \(0.300468\pi\) | |||||||
\(318\) | −1.05399e14 | −1.81755 | ||||||||
\(319\) | −1.98987e13 | −0.337268 | ||||||||
\(320\) | −1.03638e14 | −1.72661 | ||||||||
\(321\) | 2.10478e13 | 0.344690 | ||||||||
\(322\) | −1.56024e14 | −2.51179 | ||||||||
\(323\) | −1.82885e13 | −0.289443 | ||||||||
\(324\) | −1.01405e14 | −1.57784 | ||||||||
\(325\) | 3.00372e13 | 0.459517 | ||||||||
\(326\) | −6.08749e13 | −0.915675 | ||||||||
\(327\) | −6.76606e13 | −1.00074 | ||||||||
\(328\) | −4.35023e13 | −0.632712 | ||||||||
\(329\) | 1.63733e14 | 2.34185 | ||||||||
\(330\) | 2.94598e14 | 4.14384 | ||||||||
\(331\) | −1.01165e13 | −0.139951 | −0.0699755 | − | 0.997549i | \(-0.522292\pi\) | ||||
−0.0699755 | + | 0.997549i | \(0.522292\pi\) | |||||||
\(332\) | 5.85247e13 | 0.796306 | ||||||||
\(333\) | −2.21499e13 | −0.296434 | ||||||||
\(334\) | −5.04585e13 | −0.664246 | ||||||||
\(335\) | −2.09178e12 | −0.0270876 | ||||||||
\(336\) | 9.93275e13 | 1.26533 | ||||||||
\(337\) | −1.36391e14 | −1.70931 | −0.854653 | − | 0.519199i | \(-0.826230\pi\) | ||||
−0.854653 | + | 0.519199i | \(0.826230\pi\) | |||||||
\(338\) | −3.98619e13 | −0.491492 | ||||||||
\(339\) | 4.80928e13 | 0.583420 | ||||||||
\(340\) | −7.24516e13 | −0.864797 | ||||||||
\(341\) | 8.45957e13 | 0.993572 | ||||||||
\(342\) | −4.18284e13 | −0.483423 | ||||||||
\(343\) | −5.21445e13 | −0.593049 | ||||||||
\(344\) | 3.84871e13 | 0.430768 | ||||||||
\(345\) | −1.47779e14 | −1.62782 | ||||||||
\(346\) | 7.73244e13 | 0.838297 | ||||||||
\(347\) | 1.51964e14 | 1.62154 | 0.810769 | − | 0.585366i | \(-0.199049\pi\) | ||||
0.810769 | + | 0.585366i | \(0.199049\pi\) | |||||||
\(348\) | 2.89095e13 | 0.303637 | ||||||||
\(349\) | −3.81552e13 | −0.394470 | −0.197235 | − | 0.980356i | \(-0.563196\pi\) | ||||
−0.197235 | + | 0.980356i | \(0.563196\pi\) | |||||||
\(350\) | 9.14365e13 | 0.930562 | ||||||||
\(351\) | −5.40553e13 | −0.541563 | ||||||||
\(352\) | −2.56248e14 | −2.52742 | ||||||||
\(353\) | 5.20789e13 | 0.505710 | 0.252855 | − | 0.967504i | \(-0.418631\pi\) | ||||
0.252855 | + | 0.967504i | \(0.418631\pi\) | |||||||
\(354\) | 2.77165e14 | 2.64985 | ||||||||
\(355\) | −6.33740e13 | −0.596562 | ||||||||
\(356\) | 1.86226e14 | 1.72610 | ||||||||
\(357\) | 1.23431e14 | 1.12654 | ||||||||
\(358\) | −2.75664e14 | −2.47756 | ||||||||
\(359\) | −1.56134e14 | −1.38190 | −0.690950 | − | 0.722902i | \(-0.742808\pi\) | ||||
−0.690950 | + | 0.722902i | \(0.742808\pi\) | |||||||
\(360\) | −3.62533e13 | −0.315997 | ||||||||
\(361\) | −8.65747e13 | −0.743192 | ||||||||
\(362\) | 2.65615e14 | 2.24572 | ||||||||
\(363\) | 3.52619e14 | 2.93643 | ||||||||
\(364\) | −2.77417e14 | −2.27550 | ||||||||
\(365\) | −1.31612e14 | −1.06337 | ||||||||
\(366\) | 4.62757e14 | 3.68305 | ||||||||
\(367\) | −1.58571e14 | −1.24326 | −0.621629 | − | 0.783312i | \(-0.713529\pi\) | ||||
−0.621629 | + | 0.783312i | \(0.713529\pi\) | |||||||
\(368\) | 8.94803e13 | 0.691138 | ||||||||
\(369\) | 1.24222e14 | 0.945267 | ||||||||
\(370\) | 1.11786e14 | 0.838063 | ||||||||
\(371\) | −1.96972e14 | −1.45495 | ||||||||
\(372\) | −1.22904e14 | −0.894496 | ||||||||
\(373\) | 1.84813e14 | 1.32536 | 0.662682 | − | 0.748901i | \(-0.269418\pi\) | ||||
0.662682 | + | 0.748901i | \(0.269418\pi\) | |||||||
\(374\) | −2.21666e14 | −1.56641 | ||||||||
\(375\) | −1.30380e14 | −0.907901 | ||||||||
\(376\) | 9.34619e13 | 0.641360 | ||||||||
\(377\) | 3.16131e13 | 0.213791 | ||||||||
\(378\) | −1.64550e14 | −1.09671 | ||||||||
\(379\) | −5.17503e13 | −0.339936 | −0.169968 | − | 0.985450i | \(-0.554366\pi\) | ||||
−0.169968 | + | 0.985450i | \(0.554366\pi\) | |||||||
\(380\) | 1.18514e14 | 0.767288 | ||||||||
\(381\) | 8.08001e13 | 0.515614 | ||||||||
\(382\) | 1.45216e14 | 0.913413 | ||||||||
\(383\) | 1.91406e14 | 1.18676 | 0.593379 | − | 0.804923i | \(-0.297793\pi\) | ||||
0.593379 | + | 0.804923i | \(0.297793\pi\) | |||||||
\(384\) | 1.69828e14 | 1.03798 | ||||||||
\(385\) | 5.50552e14 | 3.31715 | ||||||||
\(386\) | −9.43897e13 | −0.560653 | ||||||||
\(387\) | −1.09901e14 | −0.643565 | ||||||||
\(388\) | −1.47240e13 | −0.0850066 | ||||||||
\(389\) | 7.30496e12 | 0.0415810 | 0.0207905 | − | 0.999784i | \(-0.493382\pi\) | ||||
0.0207905 | + | 0.999784i | \(0.493382\pi\) | |||||||
\(390\) | −4.68029e14 | −2.62674 | ||||||||
\(391\) | 1.11194e14 | 0.615332 | ||||||||
\(392\) | −1.07260e14 | −0.585284 | ||||||||
\(393\) | −1.51618e14 | −0.815815 | ||||||||
\(394\) | −2.80105e14 | −1.48625 | ||||||||
\(395\) | 8.55414e13 | 0.447602 | ||||||||
\(396\) | −2.84627e14 | −1.46876 | ||||||||
\(397\) | 2.82104e13 | 0.143569 | 0.0717846 | − | 0.997420i | \(-0.477131\pi\) | ||||
0.0717846 | + | 0.997420i | \(0.477131\pi\) | |||||||
\(398\) | −1.82985e14 | −0.918454 | ||||||||
\(399\) | −2.01904e14 | −0.999523 | ||||||||
\(400\) | −5.24393e13 | −0.256051 | ||||||||
\(401\) | −1.73909e14 | −0.837585 | −0.418793 | − | 0.908082i | \(-0.637547\pi\) | ||||
−0.418793 | + | 0.908082i | \(0.637547\pi\) | |||||||
\(402\) | 9.29789e12 | 0.0441714 | ||||||||
\(403\) | −1.34398e14 | −0.629816 | ||||||||
\(404\) | 3.95700e14 | 1.82923 | ||||||||
\(405\) | −3.19718e14 | −1.45802 | ||||||||
\(406\) | 9.62337e13 | 0.432946 | ||||||||
\(407\) | 1.92008e14 | 0.852218 | ||||||||
\(408\) | 7.04565e13 | 0.308525 | ||||||||
\(409\) | −1.51365e14 | −0.653953 | −0.326977 | − | 0.945032i | \(-0.606030\pi\) | ||||
−0.326977 | + | 0.945032i | \(0.606030\pi\) | |||||||
\(410\) | −6.26924e14 | −2.67241 | ||||||||
\(411\) | 2.09843e14 | 0.882600 | ||||||||
\(412\) | −1.09593e14 | −0.454829 | ||||||||
\(413\) | 5.17974e14 | 2.12120 | ||||||||
\(414\) | 2.54317e14 | 1.02772 | ||||||||
\(415\) | 1.84522e14 | 0.735839 | ||||||||
\(416\) | 4.07103e14 | 1.60211 | ||||||||
\(417\) | −2.58210e13 | −0.100282 | ||||||||
\(418\) | 3.62594e14 | 1.38979 | ||||||||
\(419\) | 1.96755e14 | 0.744303 | 0.372151 | − | 0.928172i | \(-0.378620\pi\) | ||||
0.372151 | + | 0.928172i | \(0.378620\pi\) | |||||||
\(420\) | −7.99862e14 | −2.98637 | ||||||||
\(421\) | 1.30439e14 | 0.480681 | 0.240340 | − | 0.970689i | \(-0.422741\pi\) | ||||
0.240340 | + | 0.970689i | \(0.422741\pi\) | |||||||
\(422\) | 3.34874e14 | 1.21804 | ||||||||
\(423\) | −2.66884e14 | −0.958187 | ||||||||
\(424\) | −1.12435e14 | −0.398464 | ||||||||
\(425\) | −6.51645e13 | −0.227967 | ||||||||
\(426\) | 2.81695e14 | 0.972806 | ||||||||
\(427\) | 8.64812e14 | 2.94828 | ||||||||
\(428\) | 1.02628e14 | 0.345404 | ||||||||
\(429\) | −8.03909e14 | −2.67111 | ||||||||
\(430\) | 5.54649e14 | 1.81946 | ||||||||
\(431\) | −3.01242e14 | −0.975642 | −0.487821 | − | 0.872944i | \(-0.662208\pi\) | ||||
−0.487821 | + | 0.872944i | \(0.662208\pi\) | |||||||
\(432\) | 9.43703e13 | 0.301769 | ||||||||
\(433\) | −4.01236e14 | −1.26682 | −0.633412 | − | 0.773815i | \(-0.718346\pi\) | ||||
−0.633412 | + | 0.773815i | \(0.718346\pi\) | |||||||
\(434\) | −4.09120e14 | −1.27543 | ||||||||
\(435\) | 9.11483e13 | 0.280581 | ||||||||
\(436\) | −3.29911e14 | −1.00282 | ||||||||
\(437\) | −1.81887e14 | −0.545951 | ||||||||
\(438\) | 5.85009e14 | 1.73402 | ||||||||
\(439\) | 1.67628e14 | 0.490673 | 0.245337 | − | 0.969438i | \(-0.421102\pi\) | ||||
0.245337 | + | 0.969438i | \(0.421102\pi\) | |||||||
\(440\) | 3.14265e14 | 0.908461 | ||||||||
\(441\) | 3.06286e14 | 0.874410 | ||||||||
\(442\) | 3.52162e14 | 0.992934 | ||||||||
\(443\) | 2.50447e14 | 0.697421 | 0.348710 | − | 0.937231i | \(-0.386620\pi\) | ||||
0.348710 | + | 0.937231i | \(0.386620\pi\) | |||||||
\(444\) | −2.78957e14 | −0.767238 | ||||||||
\(445\) | 5.87150e14 | 1.59503 | ||||||||
\(446\) | −1.08884e15 | −2.92162 | ||||||||
\(447\) | −4.25485e14 | −1.12770 | ||||||||
\(448\) | 8.60905e14 | 2.25386 | ||||||||
\(449\) | −5.39495e14 | −1.39519 | −0.697593 | − | 0.716494i | \(-0.745746\pi\) | ||||
−0.697593 | + | 0.716494i | \(0.745746\pi\) | |||||||
\(450\) | −1.49041e14 | −0.380746 | ||||||||
\(451\) | −1.07683e15 | −2.71755 | ||||||||
\(452\) | 2.34499e14 | 0.584628 | ||||||||
\(453\) | 7.05266e14 | 1.73705 | ||||||||
\(454\) | −1.28777e14 | −0.313352 | ||||||||
\(455\) | −8.74665e14 | −2.10271 | ||||||||
\(456\) | −1.15250e14 | −0.273738 | ||||||||
\(457\) | 1.34613e14 | 0.315899 | 0.157949 | − | 0.987447i | \(-0.449512\pi\) | ||||
0.157949 | + | 0.987447i | \(0.449512\pi\) | |||||||
\(458\) | 2.90785e14 | 0.674236 | ||||||||
\(459\) | 1.17271e14 | 0.268670 | ||||||||
\(460\) | −7.20564e14 | −1.63119 | ||||||||
\(461\) | −7.83557e14 | −1.75273 | −0.876367 | − | 0.481645i | \(-0.840040\pi\) | ||||
−0.876367 | + | 0.481645i | \(0.840040\pi\) | |||||||
\(462\) | −2.44718e15 | −5.40923 | ||||||||
\(463\) | −1.86516e14 | −0.407401 | −0.203700 | − | 0.979033i | \(-0.565297\pi\) | ||||
−0.203700 | + | 0.979033i | \(0.565297\pi\) | |||||||
\(464\) | −5.51905e13 | −0.119128 | ||||||||
\(465\) | −3.87501e14 | −0.826573 | ||||||||
\(466\) | −4.25514e14 | −0.896997 | ||||||||
\(467\) | −6.06343e14 | −1.26321 | −0.631605 | − | 0.775290i | \(-0.717604\pi\) | ||||
−0.631605 | + | 0.775290i | \(0.717604\pi\) | |||||||
\(468\) | 4.52188e14 | 0.931036 | ||||||||
\(469\) | 1.73761e13 | 0.0353592 | ||||||||
\(470\) | 1.34691e15 | 2.70894 | ||||||||
\(471\) | −3.63792e14 | −0.723166 | ||||||||
\(472\) | 2.95669e14 | 0.580931 | ||||||||
\(473\) | 9.52690e14 | 1.85019 | ||||||||
\(474\) | −3.80228e14 | −0.729900 | ||||||||
\(475\) | 1.06594e14 | 0.202263 | ||||||||
\(476\) | 6.01845e14 | 1.12888 | ||||||||
\(477\) | 3.21062e14 | 0.595302 | ||||||||
\(478\) | −1.22851e15 | −2.25179 | ||||||||
\(479\) | 6.70378e14 | 1.21471 | 0.607357 | − | 0.794429i | \(-0.292230\pi\) | ||||
0.607357 | + | 0.794429i | \(0.292230\pi\) | |||||||
\(480\) | 1.17378e15 | 2.10261 | ||||||||
\(481\) | −3.05044e14 | −0.540213 | ||||||||
\(482\) | 6.88313e14 | 1.20511 | ||||||||
\(483\) | 1.22758e15 | 2.12490 | ||||||||
\(484\) | 1.71936e15 | 2.94251 | ||||||||
\(485\) | −4.64232e13 | −0.0785517 | ||||||||
\(486\) | 9.96583e14 | 1.66730 | ||||||||
\(487\) | 3.36789e14 | 0.557120 | 0.278560 | − | 0.960419i | \(-0.410143\pi\) | ||||
0.278560 | + | 0.960419i | \(0.410143\pi\) | |||||||
\(488\) | 4.93650e14 | 0.807440 | ||||||||
\(489\) | 4.78957e14 | 0.774636 | ||||||||
\(490\) | −1.54576e15 | −2.47209 | ||||||||
\(491\) | 3.28879e14 | 0.520102 | 0.260051 | − | 0.965595i | \(-0.416261\pi\) | ||||
0.260051 | + | 0.965595i | \(0.416261\pi\) | |||||||
\(492\) | 1.56446e15 | 2.44657 | ||||||||
\(493\) | −6.85833e13 | −0.106062 | ||||||||
\(494\) | −5.76054e14 | −0.880978 | ||||||||
\(495\) | −8.97395e14 | −1.35723 | ||||||||
\(496\) | 2.34633e14 | 0.350945 | ||||||||
\(497\) | 5.26439e14 | 0.778731 | ||||||||
\(498\) | −8.20191e14 | −1.19992 | ||||||||
\(499\) | −1.89240e14 | −0.273817 | −0.136908 | − | 0.990584i | \(-0.543717\pi\) | ||||
−0.136908 | + | 0.990584i | \(0.543717\pi\) | |||||||
\(500\) | −6.35728e14 | −0.909780 | ||||||||
\(501\) | 3.97002e14 | 0.561934 | ||||||||
\(502\) | −7.86972e14 | −1.10176 | ||||||||
\(503\) | 1.64969e14 | 0.228444 | 0.114222 | − | 0.993455i | \(-0.463563\pi\) | ||||
0.114222 | + | 0.993455i | \(0.463563\pi\) | |||||||
\(504\) | 3.01150e14 | 0.412492 | ||||||||
\(505\) | 1.24760e15 | 1.69033 | ||||||||
\(506\) | −2.20457e15 | −2.95459 | ||||||||
\(507\) | 3.13629e14 | 0.415788 | ||||||||
\(508\) | 3.93979e14 | 0.516681 | ||||||||
\(509\) | 7.09880e14 | 0.920952 | 0.460476 | − | 0.887672i | \(-0.347679\pi\) | ||||
0.460476 | + | 0.887672i | \(0.347679\pi\) | |||||||
\(510\) | 1.01537e15 | 1.30313 | ||||||||
\(511\) | 1.09328e15 | 1.38809 | ||||||||
\(512\) | −9.26699e14 | −1.16400 | ||||||||
\(513\) | −1.91827e14 | −0.238377 | ||||||||
\(514\) | 2.14077e15 | 2.63192 | ||||||||
\(515\) | −3.45534e14 | −0.420292 | ||||||||
\(516\) | −1.38410e15 | −1.66569 | ||||||||
\(517\) | 2.31351e15 | 2.75469 | ||||||||
\(518\) | −9.28587e14 | −1.09398 | ||||||||
\(519\) | −6.08379e14 | −0.709176 | ||||||||
\(520\) | −4.99274e14 | −0.575865 | ||||||||
\(521\) | −2.38844e14 | −0.272588 | −0.136294 | − | 0.990668i | \(-0.543519\pi\) | ||||
−0.136294 | + | 0.990668i | \(0.543519\pi\) | |||||||
\(522\) | −1.56860e14 | −0.177143 | ||||||||
\(523\) | −5.08191e13 | −0.0567895 | −0.0283948 | − | 0.999597i | \(-0.509040\pi\) | ||||
−0.0283948 | + | 0.999597i | \(0.509040\pi\) | |||||||
\(524\) | −7.39285e14 | −0.817504 | ||||||||
\(525\) | −7.19412e14 | −0.787230 | ||||||||
\(526\) | −6.26870e14 | −0.678822 | ||||||||
\(527\) | 2.91570e14 | 0.312452 | ||||||||
\(528\) | 1.40347e15 | 1.48839 | ||||||||
\(529\) | 1.53066e14 | 0.160647 | ||||||||
\(530\) | −1.62033e15 | −1.68301 | ||||||||
\(531\) | −8.44292e14 | −0.867906 | ||||||||
\(532\) | −9.84475e14 | −1.00159 | ||||||||
\(533\) | 1.71077e15 | 1.72263 | ||||||||
\(534\) | −2.60986e15 | −2.60100 | ||||||||
\(535\) | 3.23575e14 | 0.319176 | ||||||||
\(536\) | 9.91860e12 | 0.00968376 | ||||||||
\(537\) | 2.16890e15 | 2.09595 | ||||||||
\(538\) | 2.01471e15 | 1.92712 | ||||||||
\(539\) | −2.65507e15 | −2.51384 | ||||||||
\(540\) | −7.59942e14 | −0.712221 | ||||||||
\(541\) | −1.83247e15 | −1.70001 | −0.850007 | − | 0.526771i | \(-0.823402\pi\) | ||||
−0.850007 | + | 0.526771i | \(0.823402\pi\) | |||||||
\(542\) | 5.60749e14 | 0.514959 | ||||||||
\(543\) | −2.08983e15 | −1.89982 | ||||||||
\(544\) | −8.83192e14 | −0.794806 | ||||||||
\(545\) | −1.04017e15 | −0.926667 | ||||||||
\(546\) | 3.88785e15 | 3.42886 | ||||||||
\(547\) | 3.76524e14 | 0.328747 | 0.164374 | − | 0.986398i | \(-0.447440\pi\) | ||||
0.164374 | + | 0.986398i | \(0.447440\pi\) | |||||||
\(548\) | 1.02319e15 | 0.884427 | ||||||||
\(549\) | −1.40964e15 | −1.20631 | ||||||||
\(550\) | 1.29197e15 | 1.09461 | ||||||||
\(551\) | 1.12186e14 | 0.0941033 | ||||||||
\(552\) | 7.00722e14 | 0.581944 | ||||||||
\(553\) | −7.10580e14 | −0.584285 | ||||||||
\(554\) | −1.58376e15 | −1.28940 | ||||||||
\(555\) | −8.79517e14 | −0.708978 | ||||||||
\(556\) | −1.25902e14 | −0.100490 | ||||||||
\(557\) | −7.28798e14 | −0.575975 | −0.287987 | − | 0.957634i | \(-0.592986\pi\) | ||||
−0.287987 | + | 0.957634i | \(0.592986\pi\) | |||||||
\(558\) | 6.66862e14 | 0.521853 | ||||||||
\(559\) | −1.51354e15 | −1.17282 | ||||||||
\(560\) | 1.52700e15 | 1.17167 | ||||||||
\(561\) | 1.74405e15 | 1.32514 | ||||||||
\(562\) | −2.86500e15 | −2.15563 | ||||||||
\(563\) | −2.20017e15 | −1.63930 | −0.819652 | − | 0.572862i | \(-0.805833\pi\) | ||||
−0.819652 | + | 0.572862i | \(0.805833\pi\) | |||||||
\(564\) | −3.36115e15 | −2.48001 | ||||||||
\(565\) | 7.39348e14 | 0.540234 | ||||||||
\(566\) | 1.17117e15 | 0.847483 | ||||||||
\(567\) | 2.65585e15 | 1.90326 | ||||||||
\(568\) | 3.00501e14 | 0.213270 | ||||||||
\(569\) | −1.15616e15 | −0.812643 | −0.406321 | − | 0.913730i | \(-0.633189\pi\) | ||||
−0.406321 | + | 0.913730i | \(0.633189\pi\) | |||||||
\(570\) | −1.66090e15 | −1.15620 | ||||||||
\(571\) | 1.61701e15 | 1.11485 | 0.557423 | − | 0.830229i | \(-0.311790\pi\) | ||||
0.557423 | + | 0.830229i | \(0.311790\pi\) | |||||||
\(572\) | −3.91984e15 | −2.67664 | ||||||||
\(573\) | −1.14255e15 | −0.772722 | ||||||||
\(574\) | 5.20776e15 | 3.48848 | ||||||||
\(575\) | −6.48090e14 | −0.429994 | ||||||||
\(576\) | −1.40327e15 | −0.922182 | ||||||||
\(577\) | 1.33066e15 | 0.866163 | 0.433081 | − | 0.901355i | \(-0.357426\pi\) | ||||
0.433081 | + | 0.901355i | \(0.357426\pi\) | |||||||
\(578\) | 1.57794e15 | 1.01739 | ||||||||
\(579\) | 7.42647e14 | 0.474297 | ||||||||
\(580\) | 4.44436e14 | 0.281161 | ||||||||
\(581\) | −1.53279e15 | −0.960539 | ||||||||
\(582\) | 2.06349e14 | 0.128093 | ||||||||
\(583\) | −2.78316e15 | −1.71144 | ||||||||
\(584\) | 6.24064e14 | 0.380153 | ||||||||
\(585\) | 1.42569e15 | 0.860338 | ||||||||
\(586\) | −4.70554e15 | −2.81302 | ||||||||
\(587\) | 2.02127e15 | 1.19706 | 0.598530 | − | 0.801101i | \(-0.295752\pi\) | ||||
0.598530 | + | 0.801101i | \(0.295752\pi\) | |||||||
\(588\) | 3.85738e15 | 2.26317 | ||||||||
\(589\) | −4.76939e14 | −0.277222 | ||||||||
\(590\) | 4.26097e15 | 2.45370 | ||||||||
\(591\) | 2.20384e15 | 1.25733 | ||||||||
\(592\) | 5.32550e14 | 0.301017 | ||||||||
\(593\) | 1.76241e15 | 0.986973 | 0.493486 | − | 0.869754i | \(-0.335722\pi\) | ||||
0.493486 | + | 0.869754i | \(0.335722\pi\) | |||||||
\(594\) | −2.32505e15 | −1.29005 | ||||||||
\(595\) | 1.89755e15 | 1.04316 | ||||||||
\(596\) | −2.07465e15 | −1.13003 | ||||||||
\(597\) | 1.43970e15 | 0.776987 | ||||||||
\(598\) | 3.50241e15 | 1.87288 | ||||||||
\(599\) | −3.33607e15 | −1.76761 | −0.883807 | − | 0.467851i | \(-0.845028\pi\) | ||||
−0.883807 | + | 0.467851i | \(0.845028\pi\) | |||||||
\(600\) | −4.10653e14 | −0.215597 | ||||||||
\(601\) | −9.06258e14 | −0.471457 | −0.235729 | − | 0.971819i | \(-0.575748\pi\) | ||||
−0.235729 | + | 0.971819i | \(0.575748\pi\) | |||||||
\(602\) | −4.60738e15 | −2.37506 | ||||||||
\(603\) | −2.83229e13 | −0.0144675 | ||||||||
\(604\) | 3.43886e15 | 1.74065 | ||||||||
\(605\) | 5.42095e15 | 2.71907 | ||||||||
\(606\) | −5.54552e15 | −2.75640 | ||||||||
\(607\) | 1.31379e15 | 0.647125 | 0.323562 | − | 0.946207i | \(-0.395119\pi\) | ||||
0.323562 | + | 0.946207i | \(0.395119\pi\) | |||||||
\(608\) | 1.44469e15 | 0.705189 | ||||||||
\(609\) | −7.57156e14 | −0.366260 | ||||||||
\(610\) | 7.11414e15 | 3.41042 | ||||||||
\(611\) | −3.67548e15 | −1.74617 | ||||||||
\(612\) | −9.81001e14 | −0.461888 | ||||||||
\(613\) | −1.67634e15 | −0.782219 | −0.391110 | − | 0.920344i | \(-0.627909\pi\) | ||||
−0.391110 | + | 0.920344i | \(0.627909\pi\) | |||||||
\(614\) | 2.34614e15 | 1.08499 | ||||||||
\(615\) | 4.93257e15 | 2.26079 | ||||||||
\(616\) | −2.61055e15 | −1.18587 | ||||||||
\(617\) | −1.29504e15 | −0.583063 | −0.291532 | − | 0.956561i | \(-0.594165\pi\) | ||||
−0.291532 | + | 0.956561i | \(0.594165\pi\) | |||||||
\(618\) | 1.53589e15 | 0.685365 | ||||||||
\(619\) | −2.90800e15 | −1.28616 | −0.643082 | − | 0.765797i | \(-0.722345\pi\) | ||||
−0.643082 | + | 0.765797i | \(0.722345\pi\) | |||||||
\(620\) | −1.88944e15 | −0.828284 | ||||||||
\(621\) | 1.16631e15 | 0.506769 | ||||||||
\(622\) | 4.86537e15 | 2.09541 | ||||||||
\(623\) | −4.87737e15 | −2.08210 | ||||||||
\(624\) | −2.22970e15 | −0.943478 | ||||||||
\(625\) | −2.95597e15 | −1.23982 | ||||||||
\(626\) | 5.80050e15 | 2.41161 | ||||||||
\(627\) | −2.85284e15 | −1.17573 | ||||||||
\(628\) | −1.77384e15 | −0.724663 | ||||||||
\(629\) | 6.61781e14 | 0.268000 | ||||||||
\(630\) | 4.33997e15 | 1.74226 | ||||||||
\(631\) | −7.31735e14 | −0.291201 | −0.145600 | − | 0.989343i | \(-0.546511\pi\) | ||||
−0.145600 | + | 0.989343i | \(0.546511\pi\) | |||||||
\(632\) | −4.05612e14 | −0.160017 | ||||||||
\(633\) | −2.63475e15 | −1.03043 | ||||||||
\(634\) | −4.56911e15 | −1.77150 | ||||||||
\(635\) | 1.24217e15 | 0.477447 | ||||||||
\(636\) | 4.04347e15 | 1.54078 | ||||||||
\(637\) | 4.21812e15 | 1.59350 | ||||||||
\(638\) | 1.35976e15 | 0.509269 | ||||||||
\(639\) | −8.58090e14 | −0.318624 | ||||||||
\(640\) | 2.61083e15 | 0.961145 | ||||||||
\(641\) | −4.90606e15 | −1.79066 | −0.895331 | − | 0.445401i | \(-0.853061\pi\) | ||||
−0.895331 | + | 0.445401i | \(0.853061\pi\) | |||||||
\(642\) | −1.43828e15 | −0.520476 | ||||||||
\(643\) | −1.88025e15 | −0.674612 | −0.337306 | − | 0.941395i | \(-0.609516\pi\) | ||||
−0.337306 | + | 0.941395i | \(0.609516\pi\) | |||||||
\(644\) | 5.98562e15 | 2.12930 | ||||||||
\(645\) | −4.36391e15 | −1.53921 | ||||||||
\(646\) | 1.24972e15 | 0.437054 | ||||||||
\(647\) | −1.81526e15 | −0.629457 | −0.314728 | − | 0.949182i | \(-0.601913\pi\) | ||||
−0.314728 | + | 0.949182i | \(0.601913\pi\) | |||||||
\(648\) | 1.51601e15 | 0.521242 | ||||||||
\(649\) | 7.31883e15 | 2.49515 | ||||||||
\(650\) | −2.05256e15 | −0.693862 | ||||||||
\(651\) | 3.21891e15 | 1.07898 | ||||||||
\(652\) | 2.33538e15 | 0.776239 | ||||||||
\(653\) | 1.09915e15 | 0.362271 | 0.181135 | − | 0.983458i | \(-0.442023\pi\) | ||||
0.181135 | + | 0.983458i | \(0.442023\pi\) | |||||||
\(654\) | 4.62352e15 | 1.51111 | ||||||||
\(655\) | −2.33088e15 | −0.755427 | ||||||||
\(656\) | −2.98668e15 | −0.959881 | ||||||||
\(657\) | −1.78204e15 | −0.567946 | ||||||||
\(658\) | −1.11886e16 | −3.53616 | ||||||||
\(659\) | 4.07550e14 | 0.127735 | 0.0638677 | − | 0.997958i | \(-0.479656\pi\) | ||||
0.0638677 | + | 0.997958i | \(0.479656\pi\) | |||||||
\(660\) | −1.13018e16 | −3.51283 | ||||||||
\(661\) | −1.78308e15 | −0.549620 | −0.274810 | − | 0.961499i | \(-0.588615\pi\) | ||||
−0.274810 | + | 0.961499i | \(0.588615\pi\) | |||||||
\(662\) | 6.91300e14 | 0.211324 | ||||||||
\(663\) | −2.77077e15 | −0.839995 | ||||||||
\(664\) | −8.74946e14 | −0.263061 | ||||||||
\(665\) | −3.10394e15 | −0.925537 | ||||||||
\(666\) | 1.51359e15 | 0.447610 | ||||||||
\(667\) | −6.82092e14 | −0.200056 | ||||||||
\(668\) | 1.93577e15 | 0.563097 | ||||||||
\(669\) | 8.56690e15 | 2.47161 | ||||||||
\(670\) | 1.42940e14 | 0.0409017 | ||||||||
\(671\) | 1.22196e16 | 3.46802 | ||||||||
\(672\) | −9.75039e15 | −2.74468 | ||||||||
\(673\) | −2.92949e15 | −0.817917 | −0.408958 | − | 0.912553i | \(-0.634108\pi\) | ||||
−0.408958 | + | 0.912553i | \(0.634108\pi\) | |||||||
\(674\) | 9.32012e15 | 2.58102 | ||||||||
\(675\) | −6.83507e14 | −0.187747 | ||||||||
\(676\) | 1.52925e15 | 0.416649 | ||||||||
\(677\) | −5.65022e15 | −1.52696 | −0.763480 | − | 0.645831i | \(-0.776511\pi\) | ||||
−0.763480 | + | 0.645831i | \(0.776511\pi\) | |||||||
\(678\) | −3.28637e15 | −0.880954 | ||||||||
\(679\) | 3.85631e14 | 0.102539 | ||||||||
\(680\) | 1.08315e15 | 0.285687 | ||||||||
\(681\) | 1.01320e15 | 0.265087 | ||||||||
\(682\) | −5.78076e15 | −1.50028 | ||||||||
\(683\) | −1.87327e15 | −0.482266 | −0.241133 | − | 0.970492i | \(-0.577519\pi\) | ||||
−0.241133 | + | 0.970492i | \(0.577519\pi\) | |||||||
\(684\) | 1.60469e15 | 0.409809 | ||||||||
\(685\) | 3.22599e15 | 0.817268 | ||||||||
\(686\) | 3.56324e15 | 0.895494 | ||||||||
\(687\) | −2.28786e15 | −0.570385 | ||||||||
\(688\) | 2.64236e15 | 0.653515 | ||||||||
\(689\) | 4.42161e15 | 1.08486 | ||||||||
\(690\) | 1.00983e16 | 2.45798 | ||||||||
\(691\) | −4.71553e15 | −1.13868 | −0.569339 | − | 0.822103i | \(-0.692801\pi\) | ||||
−0.569339 | + | 0.822103i | \(0.692801\pi\) | |||||||
\(692\) | −2.96644e15 | −0.710644 | ||||||||
\(693\) | 7.45453e15 | 1.77169 | ||||||||
\(694\) | −1.03843e16 | −2.44849 | ||||||||
\(695\) | −3.96956e14 | −0.0928593 | ||||||||
\(696\) | −4.32198e14 | −0.100307 | ||||||||
\(697\) | −3.71144e15 | −0.854599 | ||||||||
\(698\) | 2.60730e15 | 0.595643 | ||||||||
\(699\) | 3.34789e15 | 0.758835 | ||||||||
\(700\) | −3.50783e15 | −0.788859 | ||||||||
\(701\) | −2.35508e15 | −0.525480 | −0.262740 | − | 0.964867i | \(-0.584626\pi\) | ||||
−0.262740 | + | 0.964867i | \(0.584626\pi\) | |||||||
\(702\) | 3.69381e15 | 0.817751 | ||||||||
\(703\) | −1.08252e15 | −0.237783 | ||||||||
\(704\) | 1.21644e16 | 2.65118 | ||||||||
\(705\) | −1.05973e16 | −2.29169 | ||||||||
\(706\) | −3.55876e15 | −0.763613 | ||||||||
\(707\) | −1.03636e16 | −2.20650 | ||||||||
\(708\) | −1.06331e16 | −2.24634 | ||||||||
\(709\) | 7.95473e15 | 1.66752 | 0.833760 | − | 0.552126i | \(-0.186183\pi\) | ||||
0.833760 | + | 0.552126i | \(0.186183\pi\) | |||||||
\(710\) | 4.33060e15 | 0.900797 | ||||||||
\(711\) | 1.15824e15 | 0.239064 | ||||||||
\(712\) | −2.78409e15 | −0.570221 | ||||||||
\(713\) | 2.89979e15 | 0.589352 | ||||||||
\(714\) | −8.43452e15 | −1.70106 | ||||||||
\(715\) | −1.23588e16 | −2.47339 | ||||||||
\(716\) | 1.05755e16 | 2.10028 | ||||||||
\(717\) | 9.66581e15 | 1.90495 | ||||||||
\(718\) | 1.06692e16 | 2.08665 | ||||||||
\(719\) | −1.98037e15 | −0.384360 | −0.192180 | − | 0.981360i | \(-0.561556\pi\) | ||||
−0.192180 | + | 0.981360i | \(0.561556\pi\) | |||||||
\(720\) | −2.48899e15 | −0.479397 | ||||||||
\(721\) | 2.87030e15 | 0.548635 | ||||||||
\(722\) | 5.91600e15 | 1.12221 | ||||||||
\(723\) | −5.41557e15 | −1.01949 | ||||||||
\(724\) | −1.01899e16 | −1.90375 | ||||||||
\(725\) | 3.99735e14 | 0.0741162 | ||||||||
\(726\) | −2.40959e16 | −4.43396 | ||||||||
\(727\) | 3.46705e15 | 0.633171 | 0.316585 | − | 0.948564i | \(-0.397464\pi\) | ||||
0.316585 | + | 0.948564i | \(0.397464\pi\) | |||||||
\(728\) | 4.14740e15 | 0.751715 | ||||||||
\(729\) | −9.88684e14 | −0.177851 | ||||||||
\(730\) | 8.99356e15 | 1.60567 | ||||||||
\(731\) | 3.28357e15 | 0.581835 | ||||||||
\(732\) | −1.77530e16 | −3.12220 | ||||||||
\(733\) | 4.26101e15 | 0.743774 | 0.371887 | − | 0.928278i | \(-0.378711\pi\) | ||||
0.371887 | + | 0.928278i | \(0.378711\pi\) | |||||||
\(734\) | 1.08358e16 | 1.87730 | ||||||||
\(735\) | 1.21619e16 | 2.09132 | ||||||||
\(736\) | −8.78375e15 | −1.49917 | ||||||||
\(737\) | 2.45520e14 | 0.0415926 | ||||||||
\(738\) | −8.48861e15 | −1.42734 | ||||||||
\(739\) | 4.74592e15 | 0.792093 | 0.396046 | − | 0.918230i | \(-0.370382\pi\) | ||||
0.396046 | + | 0.918230i | \(0.370382\pi\) | |||||||
\(740\) | −4.28850e15 | −0.710446 | ||||||||
\(741\) | 4.53233e15 | 0.745283 | ||||||||
\(742\) | 1.34599e16 | 2.19694 | ||||||||
\(743\) | 4.32897e15 | 0.701369 | 0.350685 | − | 0.936494i | \(-0.385949\pi\) | ||||
0.350685 | + | 0.936494i | \(0.385949\pi\) | |||||||
\(744\) | 1.83741e15 | 0.295499 | ||||||||
\(745\) | −6.54113e15 | −1.04422 | ||||||||
\(746\) | −1.26290e16 | −2.00128 | ||||||||
\(747\) | 2.49844e15 | 0.393012 | ||||||||
\(748\) | 8.50391e15 | 1.32788 | ||||||||
\(749\) | −2.68789e15 | −0.416641 | ||||||||
\(750\) | 8.90938e15 | 1.37092 | ||||||||
\(751\) | 1.89924e15 | 0.290108 | 0.145054 | − | 0.989424i | \(-0.453664\pi\) | ||||
0.145054 | + | 0.989424i | \(0.453664\pi\) | |||||||
\(752\) | 6.41669e15 | 0.973001 | ||||||||
\(753\) | 6.19181e15 | 0.932063 | ||||||||
\(754\) | −2.16025e15 | −0.322821 | ||||||||
\(755\) | 1.08423e16 | 1.60847 | ||||||||
\(756\) | 6.31273e15 | 0.929709 | ||||||||
\(757\) | −6.04958e15 | −0.884500 | −0.442250 | − | 0.896892i | \(-0.645820\pi\) | ||||
−0.442250 | + | 0.896892i | \(0.645820\pi\) | |||||||
\(758\) | 3.53631e15 | 0.513298 | ||||||||
\(759\) | 1.73453e16 | 2.49950 | ||||||||
\(760\) | −1.77178e15 | −0.253475 | ||||||||
\(761\) | −9.10355e15 | −1.29299 | −0.646495 | − | 0.762918i | \(-0.723766\pi\) | ||||
−0.646495 | + | 0.762918i | \(0.723766\pi\) | |||||||
\(762\) | −5.52139e15 | −0.778568 | ||||||||
\(763\) | 8.64054e15 | 1.20964 | ||||||||
\(764\) | −5.57102e15 | −0.774321 | ||||||||
\(765\) | −3.09298e15 | −0.426815 | ||||||||
\(766\) | −1.30795e16 | −1.79198 | ||||||||
\(767\) | −1.16275e16 | −1.58165 | ||||||||
\(768\) | 2.20134e15 | 0.297303 | ||||||||
\(769\) | −5.47973e15 | −0.734792 | −0.367396 | − | 0.930065i | \(-0.619751\pi\) | ||||
−0.367396 | + | 0.930065i | \(0.619751\pi\) | |||||||
\(770\) | −3.76214e16 | −5.00883 | ||||||||
\(771\) | −1.68433e16 | −2.22653 | ||||||||
\(772\) | 3.62113e15 | 0.475279 | ||||||||
\(773\) | 7.09370e15 | 0.924455 | 0.462228 | − | 0.886761i | \(-0.347050\pi\) | ||||
0.462228 | + | 0.886761i | \(0.347050\pi\) | |||||||
\(774\) | 7.50999e15 | 0.971772 | ||||||||
\(775\) | −1.69940e15 | −0.218342 | ||||||||
\(776\) | 2.20125e14 | 0.0280821 | ||||||||
\(777\) | 7.30602e15 | 0.925476 | ||||||||
\(778\) | −4.99177e14 | −0.0627866 | ||||||||
\(779\) | 6.07104e15 | 0.758240 | ||||||||
\(780\) | 1.79553e16 | 2.22675 | ||||||||
\(781\) | 7.43844e15 | 0.916012 | ||||||||
\(782\) | −7.59834e15 | −0.929140 | ||||||||
\(783\) | −7.19367e14 | −0.0873496 | ||||||||
\(784\) | −7.36404e15 | −0.887928 | ||||||||
\(785\) | −5.59271e15 | −0.669636 | ||||||||
\(786\) | 1.03607e16 | 1.23187 | ||||||||
\(787\) | −2.33437e15 | −0.275619 | −0.137810 | − | 0.990459i | \(-0.544006\pi\) | ||||
−0.137810 | + | 0.990459i | \(0.544006\pi\) | |||||||
\(788\) | 1.07458e16 | 1.25993 | ||||||||
\(789\) | 4.93214e15 | 0.574265 | ||||||||
\(790\) | −5.84538e15 | −0.675871 | ||||||||
\(791\) | −6.14165e15 | −0.705204 | ||||||||
\(792\) | 4.25518e15 | 0.485209 | ||||||||
\(793\) | −1.94133e16 | −2.19835 | ||||||||
\(794\) | −1.92773e15 | −0.216787 | ||||||||
\(795\) | 1.27486e16 | 1.42378 | ||||||||
\(796\) | 7.01994e15 | 0.778595 | ||||||||
\(797\) | −5.40712e13 | −0.00595587 | −0.00297793 | − | 0.999996i | \(-0.500948\pi\) | ||||
−0.00297793 | + | 0.999996i | \(0.500948\pi\) | |||||||
\(798\) | 1.37969e16 | 1.50926 | ||||||||
\(799\) | 7.97380e15 | 0.866279 | ||||||||
\(800\) | 5.14765e15 | 0.555411 | ||||||||
\(801\) | 7.95006e15 | 0.851906 | ||||||||
\(802\) | 1.18839e16 | 1.26474 | ||||||||
\(803\) | 1.54478e16 | 1.63279 | ||||||||
\(804\) | −3.56700e14 | −0.0374451 | ||||||||
\(805\) | 1.88720e16 | 1.96761 | ||||||||
\(806\) | 9.18392e15 | 0.951011 | ||||||||
\(807\) | −1.58515e16 | −1.63029 | ||||||||
\(808\) | −5.91573e15 | −0.604291 | ||||||||
\(809\) | 4.45684e15 | 0.452179 | 0.226090 | − | 0.974107i | \(-0.427406\pi\) | ||||
0.226090 | + | 0.974107i | \(0.427406\pi\) | |||||||
\(810\) | 2.18476e16 | 2.20159 | ||||||||
\(811\) | −5.02280e15 | −0.502726 | −0.251363 | − | 0.967893i | \(-0.580879\pi\) | ||||
−0.251363 | + | 0.967893i | \(0.580879\pi\) | |||||||
\(812\) | −3.69187e15 | −0.367019 | ||||||||
\(813\) | −4.41191e15 | −0.435641 | ||||||||
\(814\) | −1.31207e16 | −1.28683 | ||||||||
\(815\) | 7.36318e15 | 0.717296 | ||||||||
\(816\) | 4.83724e15 | 0.468060 | ||||||||
\(817\) | −5.37113e15 | −0.516232 | ||||||||
\(818\) | 1.03434e16 | 0.987458 | ||||||||
\(819\) | −1.18430e16 | −1.12306 | ||||||||
\(820\) | 2.40510e16 | 2.26547 | ||||||||
\(821\) | 1.69234e15 | 0.158343 | 0.0791716 | − | 0.996861i | \(-0.474772\pi\) | ||||
0.0791716 | + | 0.996861i | \(0.474772\pi\) | |||||||
\(822\) | −1.43394e16 | −1.33271 | ||||||||
\(823\) | −9.20529e15 | −0.849842 | −0.424921 | − | 0.905230i | \(-0.639698\pi\) | ||||
−0.424921 | + | 0.905230i | \(0.639698\pi\) | |||||||
\(824\) | 1.63842e15 | 0.150254 | ||||||||
\(825\) | −1.01651e16 | −0.926009 | ||||||||
\(826\) | −3.53952e16 | −3.20298 | ||||||||
\(827\) | 2.50113e15 | 0.224831 | 0.112415 | − | 0.993661i | \(-0.464141\pi\) | ||||
0.112415 | + | 0.993661i | \(0.464141\pi\) | |||||||
\(828\) | −9.75651e15 | −0.871219 | ||||||||
\(829\) | 4.39695e15 | 0.390033 | 0.195017 | − | 0.980800i | \(-0.437524\pi\) | ||||
0.195017 | + | 0.980800i | \(0.437524\pi\) | |||||||
\(830\) | −1.26091e16 | −1.11110 | ||||||||
\(831\) | 1.24609e16 | 1.09079 | ||||||||
\(832\) | −1.93256e16 | −1.68056 | ||||||||
\(833\) | −9.15104e15 | −0.790538 | ||||||||
\(834\) | 1.76445e15 | 0.151425 | ||||||||
\(835\) | 6.10326e15 | 0.520339 | ||||||||
\(836\) | −1.39104e16 | −1.17816 | ||||||||
\(837\) | 3.05826e15 | 0.257327 | ||||||||
\(838\) | −1.34451e16 | −1.12388 | ||||||||
\(839\) | 9.17137e15 | 0.761629 | 0.380814 | − | 0.924652i | \(-0.375644\pi\) | ||||
0.380814 | + | 0.924652i | \(0.375644\pi\) | |||||||
\(840\) | 1.19580e16 | 0.986554 | ||||||||
\(841\) | 4.20707e14 | 0.0344828 | ||||||||
\(842\) | −8.91344e15 | −0.725820 | ||||||||
\(843\) | 2.25415e16 | 1.82360 | ||||||||
\(844\) | −1.28469e16 | −1.03256 | ||||||||
\(845\) | 4.82153e15 | 0.385011 | ||||||||
\(846\) | 1.82372e16 | 1.44685 | ||||||||
\(847\) | −4.50310e16 | −3.54938 | ||||||||
\(848\) | −7.71930e15 | −0.604506 | ||||||||
\(849\) | −9.21467e15 | −0.716947 | ||||||||
\(850\) | 4.45295e15 | 0.344226 | ||||||||
\(851\) | 6.58171e15 | 0.505506 | ||||||||
\(852\) | −1.08068e16 | −0.824671 | ||||||||
\(853\) | 7.56207e15 | 0.573352 | 0.286676 | − | 0.958028i | \(-0.407450\pi\) | ||||
0.286676 | + | 0.958028i | \(0.407450\pi\) | |||||||
\(854\) | −5.90961e16 | −4.45185 | ||||||||
\(855\) | 5.05939e15 | 0.378690 | ||||||||
\(856\) | −1.53430e15 | −0.114105 | ||||||||
\(857\) | −9.34890e15 | −0.690821 | −0.345411 | − | 0.938452i | \(-0.612260\pi\) | ||||
−0.345411 | + | 0.938452i | \(0.612260\pi\) | |||||||
\(858\) | 5.49343e16 | 4.03333 | ||||||||
\(859\) | −1.20867e16 | −0.881749 | −0.440875 | − | 0.897569i | \(-0.645332\pi\) | ||||
−0.440875 | + | 0.897569i | \(0.645332\pi\) | |||||||
\(860\) | −2.12783e16 | −1.54239 | ||||||||
\(861\) | −4.09741e16 | −2.95115 | ||||||||
\(862\) | 2.05851e16 | 1.47320 | ||||||||
\(863\) | −5.66080e15 | −0.402549 | −0.201275 | − | 0.979535i | \(-0.564508\pi\) | ||||
−0.201275 | + | 0.979535i | \(0.564508\pi\) | |||||||
\(864\) | −9.26377e15 | −0.654579 | ||||||||
\(865\) | −9.35284e15 | −0.656681 | ||||||||
\(866\) | 2.74181e16 | 1.91288 | ||||||||
\(867\) | −1.24150e16 | −0.860681 | ||||||||
\(868\) | 1.56953e16 | 1.08121 | ||||||||
\(869\) | −1.00403e16 | −0.687287 | ||||||||
\(870\) | −6.22853e15 | −0.423672 | ||||||||
\(871\) | −3.90059e14 | −0.0263651 | ||||||||
\(872\) | 4.93218e15 | 0.331282 | ||||||||
\(873\) | −6.28574e14 | −0.0419545 | ||||||||
\(874\) | 1.24291e16 | 0.824377 | ||||||||
\(875\) | 1.66501e16 | 1.09742 | ||||||||
\(876\) | −2.24430e16 | −1.46997 | ||||||||
\(877\) | −8.61237e15 | −0.560564 | −0.280282 | − | 0.959918i | \(-0.590428\pi\) | ||||
−0.280282 | + | 0.959918i | \(0.590428\pi\) | |||||||
\(878\) | −1.14547e16 | −0.740908 | ||||||||
\(879\) | 3.70227e16 | 2.37974 | ||||||||
\(880\) | 2.15761e16 | 1.37822 | ||||||||
\(881\) | 7.82338e15 | 0.496623 | 0.248312 | − | 0.968680i | \(-0.420124\pi\) | ||||
0.248312 | + | 0.968680i | \(0.420124\pi\) | |||||||
\(882\) | −2.09298e16 | −1.32034 | ||||||||
\(883\) | 2.57988e16 | 1.61739 | 0.808696 | − | 0.588226i | \(-0.200174\pi\) | ||||
0.808696 | + | 0.588226i | \(0.200174\pi\) | |||||||
\(884\) | −1.35102e16 | −0.841733 | ||||||||
\(885\) | −3.35248e16 | −2.07576 | ||||||||
\(886\) | −1.71140e16 | −1.05309 | ||||||||
\(887\) | 1.53064e16 | 0.936035 | 0.468017 | − | 0.883719i | \(-0.344968\pi\) | ||||
0.468017 | + | 0.883719i | \(0.344968\pi\) | |||||||
\(888\) | 4.17041e15 | 0.253459 | ||||||||
\(889\) | −1.03185e16 | −0.623243 | ||||||||
\(890\) | −4.01223e16 | −2.40847 | ||||||||
\(891\) | 3.75265e16 | 2.23878 | ||||||||
\(892\) | 4.17719e16 | 2.47672 | ||||||||
\(893\) | −1.30432e16 | −0.768604 | ||||||||
\(894\) | 2.90751e16 | 1.70280 | ||||||||
\(895\) | 3.33432e16 | 1.94080 | ||||||||
\(896\) | −2.16878e16 | −1.25465 | ||||||||
\(897\) | −2.75566e16 | −1.58441 | ||||||||
\(898\) | 3.68658e16 | 2.10671 | ||||||||
\(899\) | −1.78856e15 | −0.101584 | ||||||||
\(900\) | 5.71773e15 | 0.322767 | ||||||||
\(901\) | −9.59250e15 | −0.538202 | ||||||||
\(902\) | 7.35844e16 | 4.10345 | ||||||||
\(903\) | 3.62504e16 | 2.00923 | ||||||||
\(904\) | −3.50577e15 | −0.193133 | ||||||||
\(905\) | −3.21277e16 | −1.75919 | ||||||||
\(906\) | −4.81937e16 | −2.62292 | ||||||||
\(907\) | 3.15987e15 | 0.170934 | 0.0854672 | − | 0.996341i | \(-0.472762\pi\) | ||||
0.0854672 | + | 0.996341i | \(0.472762\pi\) | |||||||
\(908\) | 4.94036e15 | 0.265635 | ||||||||
\(909\) | 1.68926e16 | 0.902806 | ||||||||
\(910\) | 5.97693e16 | 3.17505 | ||||||||
\(911\) | −2.95195e16 | −1.55868 | −0.779342 | − | 0.626599i | \(-0.784446\pi\) | ||||
−0.779342 | + | 0.626599i | \(0.784446\pi\) | |||||||
\(912\) | −7.91258e15 | −0.415285 | ||||||||
\(913\) | −2.16580e16 | −1.12987 | ||||||||
\(914\) | −9.19864e15 | −0.477001 | ||||||||
\(915\) | −5.59732e16 | −2.88512 | ||||||||
\(916\) | −1.11555e16 | −0.571565 | ||||||||
\(917\) | 1.93623e16 | 0.986109 | ||||||||
\(918\) | −8.01357e15 | −0.405687 | ||||||||
\(919\) | 2.89215e16 | 1.45541 | 0.727704 | − | 0.685891i | \(-0.240587\pi\) | ||||
0.727704 | + | 0.685891i | \(0.240587\pi\) | |||||||
\(920\) | 1.07725e16 | 0.538867 | ||||||||
\(921\) | −1.84591e16 | −0.917874 | ||||||||
\(922\) | 5.35436e16 | 2.64660 | ||||||||
\(923\) | −1.18175e16 | −0.580652 | ||||||||
\(924\) | 9.38827e16 | 4.58553 | ||||||||
\(925\) | −3.85716e15 | −0.187279 | ||||||||
\(926\) | 1.27454e16 | 0.615168 | ||||||||
\(927\) | −4.67856e15 | −0.224478 | ||||||||
\(928\) | 5.41772e15 | 0.258406 | ||||||||
\(929\) | 1.99050e16 | 0.943792 | 0.471896 | − | 0.881654i | \(-0.343570\pi\) | ||||
0.471896 | + | 0.881654i | \(0.343570\pi\) | |||||||
\(930\) | 2.64795e16 | 1.24811 | ||||||||
\(931\) | 1.49689e16 | 0.701402 | ||||||||
\(932\) | 1.63242e16 | 0.760405 | ||||||||
\(933\) | −3.82802e16 | −1.77266 | ||||||||
\(934\) | 4.14339e16 | 1.90743 | ||||||||
\(935\) | 2.68118e16 | 1.22705 | ||||||||
\(936\) | −6.76022e15 | −0.307570 | ||||||||
\(937\) | 2.81833e16 | 1.27475 | 0.637373 | − | 0.770556i | \(-0.280021\pi\) | ||||
0.637373 | + | 0.770556i | \(0.280021\pi\) | |||||||
\(938\) | −1.18738e15 | −0.0533917 | ||||||||
\(939\) | −4.56377e16 | −2.04015 | ||||||||
\(940\) | −5.16722e16 | −2.29643 | ||||||||
\(941\) | 1.92625e16 | 0.851079 | 0.425540 | − | 0.904940i | \(-0.360084\pi\) | ||||
0.425540 | + | 0.904940i | \(0.360084\pi\) | |||||||
\(942\) | 2.48594e16 | 1.09197 | ||||||||
\(943\) | −3.69120e16 | −1.61196 | ||||||||
\(944\) | 2.02993e16 | 0.881325 | ||||||||
\(945\) | 1.99033e16 | 0.859112 | ||||||||
\(946\) | −6.51012e16 | −2.79375 | ||||||||
\(947\) | −1.32271e16 | −0.564339 | −0.282170 | − | 0.959365i | \(-0.591054\pi\) | ||||
−0.282170 | + | 0.959365i | \(0.591054\pi\) | |||||||
\(948\) | 1.45869e16 | 0.618753 | ||||||||
\(949\) | −2.45419e16 | −1.03501 | ||||||||
\(950\) | −7.28397e15 | −0.305413 | ||||||||
\(951\) | 3.59492e16 | 1.49864 | ||||||||
\(952\) | −8.99760e15 | −0.372927 | ||||||||
\(953\) | −7.28946e15 | −0.300389 | −0.150195 | − | 0.988656i | \(-0.547990\pi\) | ||||
−0.150195 | + | 0.988656i | \(0.547990\pi\) | |||||||
\(954\) | −2.19394e16 | −0.898896 | ||||||||
\(955\) | −1.75648e16 | −0.715523 | ||||||||
\(956\) | 4.71302e16 | 1.90889 | ||||||||
\(957\) | −1.06984e16 | −0.430828 | ||||||||
\(958\) | −4.58096e16 | −1.83420 | ||||||||
\(959\) | −2.67978e16 | −1.06683 | ||||||||
\(960\) | −5.57203e16 | −2.20557 | ||||||||
\(961\) | −1.78047e16 | −0.700740 | ||||||||
\(962\) | 2.08449e16 | 0.815713 | ||||||||
\(963\) | 4.38124e15 | 0.170472 | ||||||||
\(964\) | −2.64062e16 | −1.02160 | ||||||||
\(965\) | 1.14170e16 | 0.439189 | ||||||||
\(966\) | −8.38852e16 | −3.20857 | ||||||||
\(967\) | −1.90917e16 | −0.726104 | −0.363052 | − | 0.931769i | \(-0.618265\pi\) | ||||
−0.363052 | + | 0.931769i | \(0.618265\pi\) | |||||||
\(968\) | −2.57045e16 | −0.972064 | ||||||||
\(969\) | −9.83268e15 | −0.369736 | ||||||||
\(970\) | 3.17228e15 | 0.118612 | ||||||||
\(971\) | 1.19393e16 | 0.443888 | 0.221944 | − | 0.975059i | \(-0.428760\pi\) | ||||
0.221944 | + | 0.975059i | \(0.428760\pi\) | |||||||
\(972\) | −3.82325e16 | −1.41341 | ||||||||
\(973\) | 3.29745e15 | 0.121215 | ||||||||
\(974\) | −2.30141e16 | −0.841241 | ||||||||
\(975\) | 1.61493e16 | 0.586988 | ||||||||
\(976\) | 3.38919e16 | 1.22496 | ||||||||
\(977\) | 4.01267e16 | 1.44216 | 0.721080 | − | 0.692852i | \(-0.243646\pi\) | ||||
0.721080 | + | 0.692852i | \(0.243646\pi\) | |||||||
\(978\) | −3.27290e16 | −1.16969 | ||||||||
\(979\) | −6.89160e16 | −2.44915 | ||||||||
\(980\) | 5.93009e16 | 2.09565 | ||||||||
\(981\) | −1.40840e16 | −0.494933 | ||||||||
\(982\) | −2.24736e16 | −0.785344 | ||||||||
\(983\) | −3.80717e16 | −1.32299 | −0.661497 | − | 0.749948i | \(-0.730078\pi\) | ||||
−0.661497 | + | 0.749948i | \(0.730078\pi\) | |||||||
\(984\) | −2.33887e16 | −0.808228 | ||||||||
\(985\) | 3.38804e16 | 1.16426 | ||||||||
\(986\) | 4.68657e15 | 0.160152 | ||||||||
\(987\) | 8.80303e16 | 2.99149 | ||||||||
\(988\) | 2.20995e16 | 0.746825 | ||||||||
\(989\) | 3.26566e16 | 1.09747 | ||||||||
\(990\) | 6.13226e16 | 2.04940 | ||||||||
\(991\) | −2.32664e16 | −0.773257 | −0.386629 | − | 0.922236i | \(-0.626360\pi\) | ||||
−0.386629 | + | 0.922236i | \(0.626360\pi\) | |||||||
\(992\) | −2.30325e16 | −0.761249 | ||||||||
\(993\) | −5.43907e15 | −0.178774 | ||||||||
\(994\) | −3.59737e16 | −1.17587 | ||||||||
\(995\) | 2.21331e16 | 0.719473 | ||||||||
\(996\) | 3.14655e16 | 1.01720 | ||||||||
\(997\) | 6.76473e14 | 0.0217484 | 0.0108742 | − | 0.999941i | \(-0.496539\pi\) | ||||
0.0108742 | + | 0.999941i | \(0.496539\pi\) | |||||||
\(998\) | 1.29315e16 | 0.413459 | ||||||||
\(999\) | 6.94139e15 | 0.220717 |
(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 | 29.12.a.a.1.2 | ✓ | 11 | |
3.2 | odd | 2 | 261.12.a.a.1.10 | 11 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
29.12.a.a.1.2 | ✓ | 11 | 1.1 | even | 1 | trivial | |
261.12.a.a.1.10 | 11 | 3.2 | odd | 2 |