Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,9,Mod(42,43)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(43, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 9, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 9);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 9 \) |
Character orbit: | \([\chi]\) | \(=\) | 43.b (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.5172802326\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.25 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.9.b.b.42.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/43\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 24.2897i | 1.51810i | 0.651030 | + | 0.759052i | \(0.274337\pi\) | ||||
−0.651030 | + | 0.759052i | \(0.725663\pi\) | |||||||
\(3\) | 13.8077i | 0.170466i | 0.996361 | + | 0.0852330i | \(0.0271635\pi\) | ||||
−0.996361 | + | 0.0852330i | \(0.972837\pi\) | |||||||
\(4\) | −333.988 | −1.30464 | ||||||||
\(5\) | − | 427.967i | − | 0.684747i | −0.939564 | − | 0.342374i | \(-0.888769\pi\) | ||
0.939564 | − | 0.342374i | \(-0.111231\pi\) | |||||||
\(6\) | −335.386 | −0.258785 | ||||||||
\(7\) | − | 2563.83i | − | 1.06782i | −0.845542 | − | 0.533909i | \(-0.820722\pi\) | ||
0.845542 | − | 0.533909i | \(-0.179278\pi\) | |||||||
\(8\) | − | 1894.31i | − | 0.462478i | ||||||
\(9\) | 6370.35 | 0.970941 | ||||||||
\(10\) | 10395.2 | 1.03952 | ||||||||
\(11\) | 3299.24 | 0.225342 | 0.112671 | − | 0.993632i | \(-0.464059\pi\) | ||||
0.112671 | + | 0.993632i | \(0.464059\pi\) | |||||||
\(12\) | − | 4611.62i | − | 0.222397i | ||||||
\(13\) | 1783.00 | 0.0624278 | 0.0312139 | − | 0.999513i | \(-0.490063\pi\) | ||||
0.0312139 | + | 0.999513i | \(0.490063\pi\) | |||||||
\(14\) | 62274.6 | 1.62106 | ||||||||
\(15\) | 5909.26 | 0.116726 | ||||||||
\(16\) | −39488.8 | −0.602551 | ||||||||
\(17\) | 161819. | 1.93746 | 0.968732 | − | 0.248109i | \(-0.0798092\pi\) | ||||
0.968732 | + | 0.248109i | \(0.0798092\pi\) | |||||||
\(18\) | 154734.i | 1.47399i | ||||||||
\(19\) | − | 188274.i | − | 1.44470i | −0.691529 | − | 0.722349i | \(-0.743063\pi\) | ||
0.691529 | − | 0.722349i | \(-0.256937\pi\) | |||||||
\(20\) | 142936.i | 0.893350i | ||||||||
\(21\) | 35400.7 | 0.182027 | ||||||||
\(22\) | 80137.4i | 0.342093i | ||||||||
\(23\) | −430185. | −1.53725 | −0.768624 | − | 0.639701i | \(-0.779058\pi\) | ||||
−0.768624 | + | 0.639701i | \(0.779058\pi\) | |||||||
\(24\) | 26156.2 | 0.0788368 | ||||||||
\(25\) | 207469. | 0.531121 | ||||||||
\(26\) | 43308.5i | 0.0947720i | ||||||||
\(27\) | 178553.i | 0.335978i | ||||||||
\(28\) | 856290.i | 1.39312i | ||||||||
\(29\) | 1.23444e6i | 1.74533i | 0.488320 | + | 0.872665i | \(0.337610\pi\) | ||||
−0.488320 | + | 0.872665i | \(0.662390\pi\) | |||||||
\(30\) | 143534.i | 0.177202i | ||||||||
\(31\) | 819928. | 0.887828 | 0.443914 | − | 0.896069i | \(-0.353589\pi\) | ||||
0.443914 | + | 0.896069i | \(0.353589\pi\) | |||||||
\(32\) | − | 1.44411e6i | − | 1.37721i | ||||||
\(33\) | 45555.0i | 0.0384132i | ||||||||
\(34\) | 3.93053e6i | 2.94127i | ||||||||
\(35\) | −1.09724e6 | −0.731185 | ||||||||
\(36\) | −2.12762e6 | −1.26673 | ||||||||
\(37\) | − | 1.89464e6i | − | 1.01092i | −0.862849 | − | 0.505462i | \(-0.831322\pi\) | ||
0.862849 | − | 0.505462i | \(-0.168678\pi\) | |||||||
\(38\) | 4.57312e6 | 2.19320 | ||||||||
\(39\) | 24619.2i | 0.0106418i | ||||||||
\(40\) | −810703. | −0.316681 | ||||||||
\(41\) | 1.24331e6 | 0.439993 | 0.219996 | − | 0.975501i | \(-0.429395\pi\) | ||||
0.219996 | + | 0.975501i | \(0.429395\pi\) | |||||||
\(42\) | 859872.i | 0.276336i | ||||||||
\(43\) | 1.79787e6 | − | 2.90790e6i | 0.525877 | − | 0.850561i | ||||
\(44\) | −1.10191e6 | −0.293991 | ||||||||
\(45\) | − | 2.72630e6i | − | 0.664849i | ||||||
\(46\) | − | 1.04491e7i | − | 2.33370i | ||||||
\(47\) | 3.12874e6 | 0.641176 | 0.320588 | − | 0.947219i | \(-0.396119\pi\) | ||||
0.320588 | + | 0.947219i | \(0.396119\pi\) | |||||||
\(48\) | − | 545251.i | − | 0.102714i | ||||||
\(49\) | −808432. | −0.140236 | ||||||||
\(50\) | 5.03936e6i | 0.806298i | ||||||||
\(51\) | 2.23435e6i | 0.330272i | ||||||||
\(52\) | −595502. | −0.0814460 | ||||||||
\(53\) | 6.47469e6 | 0.820570 | 0.410285 | − | 0.911957i | \(-0.365429\pi\) | ||||
0.410285 | + | 0.911957i | \(0.365429\pi\) | |||||||
\(54\) | −4.33699e6 | −0.510050 | ||||||||
\(55\) | − | 1.41196e6i | − | 0.154303i | ||||||
\(56\) | −4.85670e6 | −0.493843 | ||||||||
\(57\) | 2.59964e6 | 0.246272 | ||||||||
\(58\) | −2.99841e7 | −2.64959 | ||||||||
\(59\) | −177535. | −0.0146513 | −0.00732565 | − | 0.999973i | \(-0.502332\pi\) | ||||
−0.00732565 | + | 0.999973i | \(0.502332\pi\) | |||||||
\(60\) | −1.97362e6 | −0.152286 | ||||||||
\(61\) | − | 1.30117e7i | − | 0.939753i | −0.882732 | − | 0.469876i | \(-0.844298\pi\) | ||
0.882732 | − | 0.469876i | \(-0.155702\pi\) | |||||||
\(62\) | 1.99158e7i | 1.34782i | ||||||||
\(63\) | − | 1.63325e7i | − | 1.03679i | ||||||
\(64\) | 2.49679e7 | 1.48820 | ||||||||
\(65\) | − | 763066.i | − | 0.0427473i | ||||||
\(66\) | −1.10652e6 | −0.0583153 | ||||||||
\(67\) | −1.94324e7 | −0.964335 | −0.482167 | − | 0.876079i | \(-0.660150\pi\) | ||||
−0.482167 | + | 0.876079i | \(0.660150\pi\) | |||||||
\(68\) | −5.40456e7 | −2.52770 | ||||||||
\(69\) | − | 5.93988e6i | − | 0.262048i | ||||||
\(70\) | − | 2.66515e7i | − | 1.11002i | ||||||
\(71\) | − | 1.97077e7i | − | 0.775536i | −0.921757 | − | 0.387768i | \(-0.873246\pi\) | ||
0.921757 | − | 0.387768i | \(-0.126754\pi\) | |||||||
\(72\) | − | 1.20674e7i | − | 0.449039i | ||||||
\(73\) | 4.15914e7i | 1.46458i | 0.680994 | + | 0.732289i | \(0.261548\pi\) | ||||
−0.680994 | + | 0.732289i | \(0.738452\pi\) | |||||||
\(74\) | 4.60201e7 | 1.53469 | ||||||||
\(75\) | 2.86468e6i | 0.0905381i | ||||||||
\(76\) | 6.28815e7i | 1.88481i | ||||||||
\(77\) | − | 8.45869e6i | − | 0.240625i | ||||||
\(78\) | −597993. | −0.0161554 | ||||||||
\(79\) | 8.29308e6 | 0.212916 | 0.106458 | − | 0.994317i | \(-0.466049\pi\) | ||||
0.106458 | + | 0.994317i | \(0.466049\pi\) | |||||||
\(80\) | 1.68999e7i | 0.412595i | ||||||||
\(81\) | 3.93304e7 | 0.913668 | ||||||||
\(82\) | 3.01997e7i | 0.667955i | ||||||||
\(83\) | 4.28237e7 | 0.902344 | 0.451172 | − | 0.892437i | \(-0.351006\pi\) | ||||
0.451172 | + | 0.892437i | \(0.351006\pi\) | |||||||
\(84\) | −1.18234e7 | −0.237480 | ||||||||
\(85\) | − | 6.92532e7i | − | 1.32667i | ||||||
\(86\) | 7.06319e7 | + | 4.36696e7i | 1.29124 | + | 0.798336i | ||||
\(87\) | −1.70448e7 | −0.297519 | ||||||||
\(88\) | − | 6.24978e6i | − | 0.104216i | ||||||
\(89\) | − | 2.70210e7i | − | 0.430666i | −0.976541 | − | 0.215333i | \(-0.930916\pi\) | ||
0.976541 | − | 0.215333i | \(-0.0690838\pi\) | |||||||
\(90\) | 6.62209e7 | 1.00931 | ||||||||
\(91\) | − | 4.57131e6i | − | 0.0666616i | ||||||
\(92\) | 1.43677e8 | 2.00556 | ||||||||
\(93\) | 1.13214e7i | 0.151345i | ||||||||
\(94\) | 7.59960e7i | 0.973373i | ||||||||
\(95\) | −8.05752e7 | −0.989252 | ||||||||
\(96\) | 1.99400e7 | 0.234768 | ||||||||
\(97\) | −1.00518e8 | −1.13542 | −0.567708 | − | 0.823230i | \(-0.692170\pi\) | ||||
−0.567708 | + | 0.823230i | \(0.692170\pi\) | |||||||
\(98\) | − | 1.96366e7i | − | 0.212893i | ||||||
\(99\) | 2.10173e7 | 0.218794 | ||||||||
\(100\) | −6.92923e7 | −0.692923 | ||||||||
\(101\) | −7.93058e7 | −0.762113 | −0.381057 | − | 0.924552i | \(-0.624440\pi\) | ||||
−0.381057 | + | 0.924552i | \(0.624440\pi\) | |||||||
\(102\) | −5.42717e7 | −0.501387 | ||||||||
\(103\) | 1.08221e8 | 0.961533 | 0.480767 | − | 0.876849i | \(-0.340358\pi\) | ||||
0.480767 | + | 0.876849i | \(0.340358\pi\) | |||||||
\(104\) | − | 3.37756e6i | − | 0.0288715i | ||||||
\(105\) | − | 1.51503e7i | − | 0.124642i | ||||||
\(106\) | 1.57268e8i | 1.24571i | ||||||||
\(107\) | −1.03278e8 | −0.787907 | −0.393953 | − | 0.919130i | \(-0.628893\pi\) | ||||
−0.393953 | + | 0.919130i | \(0.628893\pi\) | |||||||
\(108\) | − | 5.96345e7i | − | 0.438332i | ||||||
\(109\) | −2.51482e8 | −1.78156 | −0.890782 | − | 0.454431i | \(-0.849842\pi\) | ||||
−0.890782 | + | 0.454431i | \(0.849842\pi\) | |||||||
\(110\) | 3.42962e7 | 0.234247 | ||||||||
\(111\) | 2.61606e7 | 0.172328 | ||||||||
\(112\) | 1.01243e8i | 0.643415i | ||||||||
\(113\) | 2.85143e8i | 1.74884i | 0.485171 | + | 0.874419i | \(0.338757\pi\) | ||||
−0.485171 | + | 0.874419i | \(0.661243\pi\) | |||||||
\(114\) | 6.31445e7i | 0.373866i | ||||||||
\(115\) | 1.84105e8i | 1.05263i | ||||||||
\(116\) | − | 4.12288e8i | − | 2.27703i | ||||||
\(117\) | 1.13583e7 | 0.0606138 | ||||||||
\(118\) | − | 4.31227e6i | − | 0.0222422i | ||||||
\(119\) | − | 4.14877e8i | − | 2.06886i | ||||||
\(120\) | − | 1.11940e7i | − | 0.0539833i | ||||||
\(121\) | −2.03474e8 | −0.949221 | ||||||||
\(122\) | 3.16049e8 | 1.42664 | ||||||||
\(123\) | 1.71674e7i | 0.0750038i | ||||||||
\(124\) | −2.73846e8 | −1.15830 | ||||||||
\(125\) | − | 2.55965e8i | − | 1.04843i | ||||||
\(126\) | 3.96711e8 | 1.57395 | ||||||||
\(127\) | −7.89136e7 | −0.303345 | −0.151673 | − | 0.988431i | \(-0.548466\pi\) | ||||
−0.151673 | + | 0.988431i | \(0.548466\pi\) | |||||||
\(128\) | 2.36770e8i | 0.882036i | ||||||||
\(129\) | 4.01515e7 | + | 2.48245e7i | 0.144992 | + | 0.0896441i | ||||
\(130\) | 1.85346e7 | 0.0648948 | ||||||||
\(131\) | − | 2.16717e8i | − | 0.735882i | −0.929849 | − | 0.367941i | \(-0.880063\pi\) | ||
0.929849 | − | 0.367941i | \(-0.119937\pi\) | |||||||
\(132\) | − | 1.52148e7i | − | 0.0501155i | ||||||
\(133\) | −4.82704e8 | −1.54267 | ||||||||
\(134\) | − | 4.72007e8i | − | 1.46396i | ||||||
\(135\) | 7.64146e7 | 0.230060 | ||||||||
\(136\) | − | 3.06536e8i | − | 0.896035i | ||||||
\(137\) | − | 4.99384e8i | − | 1.41759i | −0.705412 | − | 0.708797i | \(-0.749238\pi\) | ||
0.705412 | − | 0.708797i | \(-0.250762\pi\) | |||||||
\(138\) | 1.44278e8 | 0.397817 | ||||||||
\(139\) | −1.46570e7 | −0.0392632 | −0.0196316 | − | 0.999807i | \(-0.506249\pi\) | ||||
−0.0196316 | + | 0.999807i | \(0.506249\pi\) | |||||||
\(140\) | 3.66464e8 | 0.953935 | ||||||||
\(141\) | 4.32008e7i | 0.109299i | ||||||||
\(142\) | 4.78693e8 | 1.17735 | ||||||||
\(143\) | 5.88255e6 | 0.0140676 | ||||||||
\(144\) | −2.51557e8 | −0.585042 | ||||||||
\(145\) | 5.28299e8 | 1.19511 | ||||||||
\(146\) | −1.01024e9 | −2.22338 | ||||||||
\(147\) | − | 1.11626e7i | − | 0.0239054i | ||||||
\(148\) | 6.32786e8i | 1.31889i | ||||||||
\(149\) | 7.39245e7i | 0.149983i | 0.997184 | + | 0.0749917i | \(0.0238930\pi\) | ||||
−0.997184 | + | 0.0749917i | \(0.976107\pi\) | |||||||
\(150\) | −6.95822e7 | −0.137446 | ||||||||
\(151\) | 7.14958e8i | 1.37522i | 0.726079 | + | 0.687611i | \(0.241340\pi\) | ||||
−0.726079 | + | 0.687611i | \(0.758660\pi\) | |||||||
\(152\) | −3.56650e8 | −0.668141 | ||||||||
\(153\) | 1.03084e9 | 1.88116 | ||||||||
\(154\) | 2.05459e8 | 0.365294 | ||||||||
\(155\) | − | 3.50902e8i | − | 0.607938i | ||||||
\(156\) | − | 8.22253e6i | − | 0.0138838i | ||||||
\(157\) | 1.90914e7i | 0.0314224i | 0.999877 | + | 0.0157112i | \(0.00500124\pi\) | ||||
−0.999877 | + | 0.0157112i | \(0.994999\pi\) | |||||||
\(158\) | 2.01436e8i | 0.323228i | ||||||||
\(159\) | 8.94008e7i | 0.139879i | ||||||||
\(160\) | −6.18033e8 | −0.943044 | ||||||||
\(161\) | 1.10292e9i | 1.64150i | ||||||||
\(162\) | 9.55323e8i | 1.38704i | ||||||||
\(163\) | − | 5.04417e8i | − | 0.714561i | −0.933997 | − | 0.357281i | \(-0.883704\pi\) | ||
0.933997 | − | 0.357281i | \(-0.116296\pi\) | |||||||
\(164\) | −4.15253e8 | −0.574033 | ||||||||
\(165\) | 1.94960e7 | 0.0263033 | ||||||||
\(166\) | 1.04017e9i | 1.36985i | ||||||||
\(167\) | −6.01163e8 | −0.772906 | −0.386453 | − | 0.922309i | \(-0.626300\pi\) | ||||
−0.386453 | + | 0.922309i | \(0.626300\pi\) | |||||||
\(168\) | − | 6.70600e7i | − | 0.0841834i | ||||||
\(169\) | −8.12552e8 | −0.996103 | ||||||||
\(170\) | 1.68214e9 | 2.01403 | ||||||||
\(171\) | − | 1.19937e9i | − | 1.40272i | ||||||
\(172\) | −6.00467e8 | + | 9.71204e8i | −0.686081 | + | 1.10968i | ||||
\(173\) | −8.47715e7 | −0.0946380 | −0.0473190 | − | 0.998880i | \(-0.515068\pi\) | ||||
−0.0473190 | + | 0.998880i | \(0.515068\pi\) | |||||||
\(174\) | − | 4.14013e8i | − | 0.451665i | ||||||
\(175\) | − | 5.31916e8i | − | 0.567141i | ||||||
\(176\) | −1.30283e8 | −0.135780 | ||||||||
\(177\) | − | 2.45136e6i | − | 0.00249755i | ||||||
\(178\) | 6.56331e8 | 0.653797 | ||||||||
\(179\) | − | 1.43087e8i | − | 0.139376i | −0.997569 | − | 0.0696882i | \(-0.977800\pi\) | ||
0.997569 | − | 0.0696882i | \(-0.0222004\pi\) | |||||||
\(180\) | 9.10552e8i | 0.867390i | ||||||||
\(181\) | 8.57397e8 | 0.798854 | 0.399427 | − | 0.916765i | \(-0.369209\pi\) | ||||
0.399427 | + | 0.916765i | \(0.369209\pi\) | |||||||
\(182\) | 1.11036e8 | 0.101199 | ||||||||
\(183\) | 1.79662e8 | 0.160196 | ||||||||
\(184\) | 8.14904e8i | 0.710944i | ||||||||
\(185\) | −8.10842e8 | −0.692228 | ||||||||
\(186\) | −2.74992e8 | −0.229757 | ||||||||
\(187\) | 5.33879e8 | 0.436593 | ||||||||
\(188\) | −1.04496e9 | −0.836505 | ||||||||
\(189\) | 4.57779e8 | 0.358764 | ||||||||
\(190\) | − | 1.95715e9i | − | 1.50179i | ||||||
\(191\) | 1.26564e9i | 0.950990i | 0.879718 | + | 0.475495i | \(0.157731\pi\) | ||||
−0.879718 | + | 0.475495i | \(0.842269\pi\) | |||||||
\(192\) | 3.44751e8i | 0.253688i | ||||||||
\(193\) | 1.30174e9 | 0.938198 | 0.469099 | − | 0.883145i | \(-0.344579\pi\) | ||||
0.469099 | + | 0.883145i | \(0.344579\pi\) | |||||||
\(194\) | − | 2.44154e9i | − | 1.72368i | ||||||
\(195\) | 1.05362e7 | 0.00728695 | ||||||||
\(196\) | 2.70007e8 | 0.182958 | ||||||||
\(197\) | 2.06607e9 | 1.37177 | 0.685885 | − | 0.727710i | \(-0.259415\pi\) | ||||
0.685885 | + | 0.727710i | \(0.259415\pi\) | |||||||
\(198\) | 5.10503e8i | 0.332153i | ||||||||
\(199\) | 9.02872e8i | 0.575723i | 0.957672 | + | 0.287862i | \(0.0929443\pi\) | ||||
−0.957672 | + | 0.287862i | \(0.907056\pi\) | |||||||
\(200\) | − | 3.93012e8i | − | 0.245632i | ||||||
\(201\) | − | 2.68318e8i | − | 0.164386i | ||||||
\(202\) | − | 1.92631e9i | − | 1.15697i | ||||||
\(203\) | 3.16489e9 | 1.86370 | ||||||||
\(204\) | − | 7.46248e8i | − | 0.430886i | ||||||
\(205\) | − | 5.32098e8i | − | 0.301284i | ||||||
\(206\) | 2.62866e9i | 1.45971i | ||||||||
\(207\) | −2.74043e9 | −1.49258 | ||||||||
\(208\) | −7.04086e7 | −0.0376160 | ||||||||
\(209\) | − | 6.21162e8i | − | 0.325552i | ||||||
\(210\) | 3.67997e8 | 0.189220 | ||||||||
\(211\) | 2.34791e9i | 1.18454i | 0.805738 | + | 0.592272i | \(0.201769\pi\) | ||||
−0.805738 | + | 0.592272i | \(0.798231\pi\) | |||||||
\(212\) | −2.16247e9 | −1.07055 | ||||||||
\(213\) | 2.72119e8 | 0.132203 | ||||||||
\(214\) | − | 2.50860e9i | − | 1.19612i | ||||||
\(215\) | −1.24448e9 | − | 7.69428e8i | −0.582419 | − | 0.360093i | ||||
\(216\) | 3.38234e8 | 0.155383 | ||||||||
\(217\) | − | 2.10216e9i | − | 0.948039i | ||||||
\(218\) | − | 6.10842e9i | − | 2.70460i | ||||||
\(219\) | −5.74284e8 | −0.249661 | ||||||||
\(220\) | 4.71580e8i | 0.201310i | ||||||||
\(221\) | 2.88523e8 | 0.120952 | ||||||||
\(222\) | 6.35434e8i | 0.261612i | ||||||||
\(223\) | 2.77345e9i | 1.12150i | 0.827984 | + | 0.560752i | \(0.189488\pi\) | ||||
−0.827984 | + | 0.560752i | \(0.810512\pi\) | |||||||
\(224\) | −3.70247e9 | −1.47061 | ||||||||
\(225\) | 1.32165e9 | 0.515688 | ||||||||
\(226\) | −6.92604e9 | −2.65492 | ||||||||
\(227\) | 2.06840e8i | 0.0778989i | 0.999241 | + | 0.0389494i | \(0.0124011\pi\) | ||||
−0.999241 | + | 0.0389494i | \(0.987599\pi\) | |||||||
\(228\) | −8.68251e8 | −0.321296 | ||||||||
\(229\) | −2.78916e9 | −1.01422 | −0.507110 | − | 0.861881i | \(-0.669286\pi\) | ||||
−0.507110 | + | 0.861881i | \(0.669286\pi\) | |||||||
\(230\) | −4.47185e9 | −1.59800 | ||||||||
\(231\) | 1.16795e8 | 0.0410183 | ||||||||
\(232\) | 2.33841e9 | 0.807177 | ||||||||
\(233\) | 3.53341e9i | 1.19887i | 0.800425 | + | 0.599433i | \(0.204607\pi\) | ||||
−0.800425 | + | 0.599433i | \(0.795393\pi\) | |||||||
\(234\) | 2.75890e8i | 0.0920180i | ||||||||
\(235\) | − | 1.33900e9i | − | 0.439044i | ||||||
\(236\) | 5.92946e7 | 0.0191147 | ||||||||
\(237\) | 1.14509e8i | 0.0362949i | ||||||||
\(238\) | 1.00772e10 | 3.14075 | ||||||||
\(239\) | −2.07769e9 | −0.636781 | −0.318391 | − | 0.947960i | \(-0.603142\pi\) | ||||
−0.318391 | + | 0.947960i | \(0.603142\pi\) | |||||||
\(240\) | −2.33349e8 | −0.0703334 | ||||||||
\(241\) | 2.64446e8i | 0.0783916i | 0.999232 | + | 0.0391958i | \(0.0124796\pi\) | ||||
−0.999232 | + | 0.0391958i | \(0.987520\pi\) | |||||||
\(242\) | − | 4.94232e9i | − | 1.44102i | ||||||
\(243\) | 1.71455e9i | 0.491728i | ||||||||
\(244\) | 4.34575e9i | 1.22604i | ||||||||
\(245\) | 3.45982e8i | 0.0960261i | ||||||||
\(246\) | −4.16990e8 | −0.113864 | ||||||||
\(247\) | − | 3.35694e8i | − | 0.0901893i | ||||||
\(248\) | − | 1.55320e9i | − | 0.410602i | ||||||
\(249\) | 5.91299e8i | 0.153819i | ||||||||
\(250\) | 6.21730e9 | 1.59163 | ||||||||
\(251\) | 3.38964e9 | 0.854003 | 0.427001 | − | 0.904251i | \(-0.359570\pi\) | ||||
0.427001 | + | 0.904251i | \(0.359570\pi\) | |||||||
\(252\) | 5.45486e9i | 1.35264i | ||||||||
\(253\) | −1.41928e9 | −0.346407 | ||||||||
\(254\) | − | 1.91679e9i | − | 0.460510i | ||||||
\(255\) | 9.56230e8 | 0.226153 | ||||||||
\(256\) | 6.40731e8 | 0.149182 | ||||||||
\(257\) | 6.06881e9i | 1.39114i | 0.718458 | + | 0.695570i | \(0.244848\pi\) | ||||
−0.718458 | + | 0.695570i | \(0.755152\pi\) | |||||||
\(258\) | −6.02979e8 | + | 9.75267e8i | −0.136089 | + | 0.220112i | ||||
\(259\) | −4.85753e9 | −1.07948 | ||||||||
\(260\) | 2.54855e8i | 0.0557699i | ||||||||
\(261\) | 7.86380e9i | 1.69461i | ||||||||
\(262\) | 5.26399e9 | 1.11715 | ||||||||
\(263\) | − | 7.16640e9i | − | 1.49788i | −0.662635 | − | 0.748942i | \(-0.730562\pi\) | ||
0.662635 | − | 0.748942i | \(-0.269438\pi\) | |||||||
\(264\) | 8.62954e7 | 0.0177653 | ||||||||
\(265\) | − | 2.77095e9i | − | 0.561883i | ||||||
\(266\) | − | 1.17247e10i | − | 2.34194i | ||||||
\(267\) | 3.73099e8 | 0.0734140 | ||||||||
\(268\) | 6.49020e9 | 1.25811 | ||||||||
\(269\) | −1.04774e9 | −0.200098 | −0.100049 | − | 0.994982i | \(-0.531900\pi\) | ||||
−0.100049 | + | 0.994982i | \(0.531900\pi\) | |||||||
\(270\) | 1.85609e9i | 0.349256i | ||||||||
\(271\) | −8.61683e9 | −1.59761 | −0.798804 | − | 0.601591i | \(-0.794534\pi\) | ||||
−0.798804 | + | 0.601591i | \(0.794534\pi\) | |||||||
\(272\) | −6.39004e9 | −1.16742 | ||||||||
\(273\) | 6.31195e7 | 0.0113635 | ||||||||
\(274\) | 1.21299e10 | 2.15206 | ||||||||
\(275\) | 6.84491e8 | 0.119684 | ||||||||
\(276\) | 1.98385e9i | 0.341879i | ||||||||
\(277\) | 8.11515e9i | 1.37841i | 0.724568 | + | 0.689204i | \(0.242039\pi\) | ||||
−0.724568 | + | 0.689204i | \(0.757961\pi\) | |||||||
\(278\) | − | 3.56013e8i | − | 0.0596056i | ||||||
\(279\) | 5.22323e9 | 0.862029 | ||||||||
\(280\) | 2.07851e9i | 0.338158i | ||||||||
\(281\) | −3.10778e9 | −0.498454 | −0.249227 | − | 0.968445i | \(-0.580177\pi\) | ||||
−0.249227 | + | 0.968445i | \(0.580177\pi\) | |||||||
\(282\) | −1.04933e9 | −0.165927 | ||||||||
\(283\) | 9.84866e9 | 1.53544 | 0.767718 | − | 0.640788i | \(-0.221392\pi\) | ||||
0.767718 | + | 0.640788i | \(0.221392\pi\) | |||||||
\(284\) | 6.58214e9i | 1.01180i | ||||||||
\(285\) | − | 1.11256e9i | − | 0.168634i | ||||||
\(286\) | 1.42885e8i | 0.0213561i | ||||||||
\(287\) | − | 3.18765e9i | − | 0.469832i | ||||||
\(288\) | − | 9.19951e9i | − | 1.33719i | ||||||
\(289\) | 1.92096e10 | 2.75377 | ||||||||
\(290\) | 1.28322e10i | 1.81430i | ||||||||
\(291\) | − | 1.38792e9i | − | 0.193550i | ||||||
\(292\) | − | 1.38911e10i | − | 1.91075i | ||||||
\(293\) | −1.18065e10 | −1.60195 | −0.800977 | − | 0.598695i | \(-0.795686\pi\) | ||||
−0.800977 | + | 0.598695i | \(0.795686\pi\) | |||||||
\(294\) | 2.71136e8 | 0.0362910 | ||||||||
\(295\) | 7.59791e7i | 0.0100324i | ||||||||
\(296\) | −3.58903e9 | −0.467531 | ||||||||
\(297\) | 5.89088e8i | 0.0757102i | ||||||||
\(298\) | −1.79560e9 | −0.227690 | ||||||||
\(299\) | −7.67020e8 | −0.0959670 | ||||||||
\(300\) | − | 9.56771e8i | − | 0.118120i | ||||||
\(301\) | −7.45536e9 | − | 4.60943e9i | −0.908244 | − | 0.561541i | ||||
\(302\) | −1.73661e10 | −2.08773 | ||||||||
\(303\) | − | 1.09503e9i | − | 0.129914i | ||||||
\(304\) | 7.43473e9i | 0.870504i | ||||||||
\(305\) | −5.56856e9 | −0.643493 | ||||||||
\(306\) | 2.50388e10i | 2.85580i | ||||||||
\(307\) | −3.68250e9 | −0.414561 | −0.207281 | − | 0.978282i | \(-0.566461\pi\) | ||||
−0.207281 | + | 0.978282i | \(0.566461\pi\) | |||||||
\(308\) | 2.82510e9i | 0.313929i | ||||||||
\(309\) | 1.49429e9i | 0.163909i | ||||||||
\(310\) | 8.52330e9 | 0.922913 | ||||||||
\(311\) | 5.09479e9 | 0.544609 | 0.272305 | − | 0.962211i | \(-0.412214\pi\) | ||||
0.272305 | + | 0.962211i | \(0.412214\pi\) | |||||||
\(312\) | 4.66365e7 | 0.00492161 | ||||||||
\(313\) | 8.21077e9i | 0.855473i | 0.903903 | + | 0.427736i | \(0.140689\pi\) | ||||
−0.903903 | + | 0.427736i | \(0.859311\pi\) | |||||||
\(314\) | −4.63725e8 | −0.0477025 | ||||||||
\(315\) | −6.98977e9 | −0.709938 | ||||||||
\(316\) | −2.76979e9 | −0.277779 | ||||||||
\(317\) | 1.07248e10 | 1.06207 | 0.531034 | − | 0.847351i | \(-0.321804\pi\) | ||||
0.531034 | + | 0.847351i | \(0.321804\pi\) | |||||||
\(318\) | −2.17152e9 | −0.212351 | ||||||||
\(319\) | 4.07271e9i | 0.393297i | ||||||||
\(320\) | − | 1.06854e10i | − | 1.01904i | ||||||
\(321\) | − | 1.42604e9i | − | 0.134311i | ||||||
\(322\) | −2.67896e10 | −2.49197 | ||||||||
\(323\) | − | 3.04664e10i | − | 2.79905i | ||||||
\(324\) | −1.31359e10 | −1.19201 | ||||||||
\(325\) | 3.69918e8 | 0.0331568 | ||||||||
\(326\) | 1.22521e10 | 1.08478 | ||||||||
\(327\) | − | 3.47240e9i | − | 0.303696i | ||||||
\(328\) | − | 2.35523e9i | − | 0.203487i | ||||||
\(329\) | − | 8.02155e9i | − | 0.684660i | ||||||
\(330\) | 4.73553e8i | 0.0399312i | ||||||||
\(331\) | − | 2.06009e9i | − | 0.171623i | −0.996311 | − | 0.0858114i | \(-0.972652\pi\) | ||
0.996311 | − | 0.0858114i | \(-0.0273482\pi\) | |||||||
\(332\) | −1.43026e10 | −1.17724 | ||||||||
\(333\) | − | 1.20695e10i | − | 0.981549i | ||||||
\(334\) | − | 1.46021e10i | − | 1.17335i | ||||||
\(335\) | 8.31643e9i | 0.660325i | ||||||||
\(336\) | −1.39793e9 | −0.109680 | ||||||||
\(337\) | 1.19620e10 | 0.927436 | 0.463718 | − | 0.885983i | \(-0.346515\pi\) | ||||
0.463718 | + | 0.885983i | \(0.346515\pi\) | |||||||
\(338\) | − | 1.97366e10i | − | 1.51219i | ||||||
\(339\) | −3.93719e9 | −0.298117 | ||||||||
\(340\) | 2.31297e10i | 1.73083i | ||||||||
\(341\) | 2.70514e9 | 0.200065 | ||||||||
\(342\) | 2.91324e10 | 2.12947 | ||||||||
\(343\) | − | 1.27073e10i | − | 0.918072i | ||||||
\(344\) | −5.50846e9 | − | 3.40572e9i | −0.393366 | − | 0.243207i | ||||
\(345\) | −2.54207e9 | −0.179437 | ||||||||
\(346\) | − | 2.05907e9i | − | 0.143670i | ||||||
\(347\) | − | 3.44498e9i | − | 0.237612i | −0.992917 | − | 0.118806i | \(-0.962093\pi\) | ||
0.992917 | − | 0.118806i | \(-0.0379067\pi\) | |||||||
\(348\) | 5.69277e9 | 0.388156 | ||||||||
\(349\) | 8.41368e9i | 0.567132i | 0.958953 | + | 0.283566i | \(0.0915176\pi\) | ||||
−0.958953 | + | 0.283566i | \(0.908482\pi\) | |||||||
\(350\) | 1.29201e10 | 0.860980 | ||||||||
\(351\) | 3.18360e8i | 0.0209744i | ||||||||
\(352\) | − | 4.76448e9i | − | 0.310345i | ||||||
\(353\) | 1.58116e10 | 1.01830 | 0.509152 | − | 0.860677i | \(-0.329959\pi\) | ||||
0.509152 | + | 0.860677i | \(0.329959\pi\) | |||||||
\(354\) | 5.95427e7 | 0.00379154 | ||||||||
\(355\) | −8.43424e9 | −0.531046 | ||||||||
\(356\) | 9.02469e9i | 0.561865i | ||||||||
\(357\) | 5.72851e9 | 0.352670 | ||||||||
\(358\) | 3.47555e9 | 0.211588 | ||||||||
\(359\) | −1.75353e10 | −1.05568 | −0.527842 | − | 0.849342i | \(-0.676999\pi\) | ||||
−0.527842 | + | 0.849342i | \(0.676999\pi\) | |||||||
\(360\) | −5.16446e9 | −0.307478 | ||||||||
\(361\) | −1.84637e10 | −1.08715 | ||||||||
\(362\) | 2.08259e10i | 1.21274i | ||||||||
\(363\) | − | 2.80952e9i | − | 0.161810i | ||||||
\(364\) | 1.52677e9i | 0.0869695i | ||||||||
\(365\) | 1.77998e10 | 1.00287 | ||||||||
\(366\) | 4.36393e9i | 0.243194i | ||||||||
\(367\) | 1.96675e10 | 1.08414 | 0.542069 | − | 0.840334i | \(-0.317641\pi\) | ||||
0.542069 | + | 0.840334i | \(0.317641\pi\) | |||||||
\(368\) | 1.69875e10 | 0.926271 | ||||||||
\(369\) | 7.92034e9 | 0.427207 | ||||||||
\(370\) | − | 1.96951e10i | − | 1.05087i | ||||||
\(371\) | − | 1.66000e10i | − | 0.876219i | ||||||
\(372\) | − | 3.78120e9i | − | 0.197450i | ||||||
\(373\) | 2.22528e10i | 1.14961i | 0.818291 | + | 0.574804i | \(0.194922\pi\) | ||||
−0.818291 | + | 0.574804i | \(0.805078\pi\) | |||||||
\(374\) | 1.29678e10i | 0.662794i | ||||||||
\(375\) | 3.53429e9 | 0.178722 | ||||||||
\(376\) | − | 5.92680e9i | − | 0.296530i | ||||||
\(377\) | 2.20101e9i | 0.108957i | ||||||||
\(378\) | 1.11193e10i | 0.544641i | ||||||||
\(379\) | −2.22479e10 | −1.07828 | −0.539141 | − | 0.842215i | \(-0.681251\pi\) | ||||
−0.539141 | + | 0.842215i | \(0.681251\pi\) | |||||||
\(380\) | 2.69112e10 | 1.29062 | ||||||||
\(381\) | − | 1.08962e9i | − | 0.0517100i | ||||||
\(382\) | −3.07419e10 | −1.44370 | ||||||||
\(383\) | 1.88396e10i | 0.875542i | 0.899087 | + | 0.437771i | \(0.144232\pi\) | ||||
−0.899087 | + | 0.437771i | \(0.855768\pi\) | |||||||
\(384\) | −3.26925e9 | −0.150357 | ||||||||
\(385\) | −3.62004e9 | −0.164767 | ||||||||
\(386\) | 3.16188e10i | 1.42428i | ||||||||
\(387\) | 1.14530e10 | − | 1.85243e10i | 0.510596 | − | 0.825845i | ||||
\(388\) | 3.35717e10 | 1.48131 | ||||||||
\(389\) | − | 7.04839e9i | − | 0.307816i | −0.988085 | − | 0.153908i | \(-0.950814\pi\) | ||
0.988085 | − | 0.153908i | \(-0.0491860\pi\) | |||||||
\(390\) | 2.55921e8i | 0.0110624i | ||||||||
\(391\) | −6.96121e10 | −2.97836 | ||||||||
\(392\) | 1.53142e9i | 0.0648561i | ||||||||
\(393\) | 2.99237e9 | 0.125443 | ||||||||
\(394\) | 5.01843e10i | 2.08249i | ||||||||
\(395\) | − | 3.54917e9i | − | 0.145793i | ||||||
\(396\) | −7.01953e9 | −0.285448 | ||||||||
\(397\) | −7.77464e9 | −0.312981 | −0.156491 | − | 0.987679i | \(-0.550018\pi\) | ||||
−0.156491 | + | 0.987679i | \(0.550018\pi\) | |||||||
\(398\) | −2.19305e10 | −0.874008 | ||||||||
\(399\) | − | 6.66505e9i | − | 0.262973i | ||||||
\(400\) | −8.19271e9 | −0.320028 | ||||||||
\(401\) | 1.87199e9 | 0.0723980 | 0.0361990 | − | 0.999345i | \(-0.488475\pi\) | ||||
0.0361990 | + | 0.999345i | \(0.488475\pi\) | |||||||
\(402\) | 6.51735e9 | 0.249555 | ||||||||
\(403\) | 1.46193e9 | 0.0554252 | ||||||||
\(404\) | 2.64872e10 | 0.994285 | ||||||||
\(405\) | − | 1.68321e10i | − | 0.625632i | ||||||
\(406\) | 7.68742e10i | 2.82928i | ||||||||
\(407\) | − | 6.25085e9i | − | 0.227804i | ||||||
\(408\) | 4.23256e9 | 0.152744 | ||||||||
\(409\) | 1.64058e10i | 0.586278i | 0.956070 | + | 0.293139i | \(0.0946999\pi\) | ||||
−0.956070 | + | 0.293139i | \(0.905300\pi\) | |||||||
\(410\) | 1.29245e10 | 0.457380 | ||||||||
\(411\) | 6.89536e9 | 0.241652 | ||||||||
\(412\) | −3.61447e10 | −1.25446 | ||||||||
\(413\) | 4.55170e8i | 0.0156449i | ||||||||
\(414\) | − | 6.65641e10i | − | 2.26589i | ||||||
\(415\) | − | 1.83271e10i | − | 0.617877i | ||||||
\(416\) | − | 2.57486e9i | − | 0.0859765i | ||||||
\(417\) | − | 2.02380e8i | − | 0.00669304i | ||||||
\(418\) | 1.50878e10 | 0.494221 | ||||||||
\(419\) | 4.87108e10i | 1.58041i | 0.612844 | + | 0.790204i | \(0.290025\pi\) | ||||
−0.612844 | + | 0.790204i | \(0.709975\pi\) | |||||||
\(420\) | 5.06004e9i | 0.162613i | ||||||||
\(421\) | − | 9.06047e9i | − | 0.288418i | −0.989547 | − | 0.144209i | \(-0.953936\pi\) | ||
0.989547 | − | 0.144209i | \(-0.0460638\pi\) | |||||||
\(422\) | −5.70299e10 | −1.79826 | ||||||||
\(423\) | 1.99311e10 | 0.622545 | ||||||||
\(424\) | − | 1.22651e10i | − | 0.379496i | ||||||
\(425\) | 3.35725e10 | 1.02903 | ||||||||
\(426\) | 6.60967e9i | 0.200697i | ||||||||
\(427\) | −3.33597e10 | −1.00349 | ||||||||
\(428\) | 3.44938e10 | 1.02794 | ||||||||
\(429\) | 8.12247e7i | 0.00239805i | ||||||||
\(430\) | 1.86892e10 | − | 3.02281e10i | 0.546658 | − | 0.884173i | ||||
\(431\) | −4.56887e9 | −0.132404 | −0.0662019 | − | 0.997806i | \(-0.521088\pi\) | ||||
−0.0662019 | + | 0.997806i | \(0.521088\pi\) | |||||||
\(432\) | − | 7.05083e9i | − | 0.202444i | ||||||
\(433\) | − | 1.09451e10i | − | 0.311363i | −0.987807 | − | 0.155681i | \(-0.950243\pi\) | ||
0.987807 | − | 0.155681i | \(-0.0497573\pi\) | |||||||
\(434\) | 5.10607e10 | 1.43922 | ||||||||
\(435\) | 7.29461e9i | 0.203725i | ||||||||
\(436\) | 8.39921e10 | 2.32430 | ||||||||
\(437\) | 8.09928e10i | 2.22086i | ||||||||
\(438\) | − | 1.39492e10i | − | 0.379011i | ||||||
\(439\) | −8.95525e9 | −0.241112 | −0.120556 | − | 0.992706i | \(-0.538468\pi\) | ||||
−0.120556 | + | 0.992706i | \(0.538468\pi\) | |||||||
\(440\) | −2.67470e9 | −0.0713616 | ||||||||
\(441\) | −5.14999e9 | −0.136161 | ||||||||
\(442\) | 7.00814e9i | 0.183617i | ||||||||
\(443\) | 2.28878e10 | 0.594277 | 0.297139 | − | 0.954834i | \(-0.403968\pi\) | ||||
0.297139 | + | 0.954834i | \(0.403968\pi\) | |||||||
\(444\) | −8.73735e9 | −0.224827 | ||||||||
\(445\) | −1.15641e10 | −0.294898 | ||||||||
\(446\) | −6.73662e10 | −1.70256 | ||||||||
\(447\) | −1.02073e9 | −0.0255671 | ||||||||
\(448\) | − | 6.40136e10i | − | 1.58913i | ||||||
\(449\) | − | 1.64061e10i | − | 0.403664i | −0.979420 | − | 0.201832i | \(-0.935311\pi\) | ||
0.979420 | − | 0.201832i | \(-0.0646894\pi\) | |||||||
\(450\) | 3.21025e10i | 0.782868i | ||||||||
\(451\) | 4.10199e9 | 0.0991490 | ||||||||
\(452\) | − | 9.52346e10i | − | 2.28161i | ||||||
\(453\) | −9.87196e9 | −0.234428 | ||||||||
\(454\) | −5.02408e9 | −0.118259 | ||||||||
\(455\) | −1.95637e9 | −0.0456463 | ||||||||
\(456\) | − | 4.92454e9i | − | 0.113895i | ||||||
\(457\) | − | 6.73001e9i | − | 0.154295i | −0.997020 | − | 0.0771473i | \(-0.975419\pi\) | ||
0.997020 | − | 0.0771473i | \(-0.0245812\pi\) | |||||||
\(458\) | − | 6.77479e10i | − | 1.53969i | ||||||
\(459\) | 2.88932e10i | 0.650946i | ||||||||
\(460\) | − | 6.14889e10i | − | 1.37330i | ||||||
\(461\) | 9.84296e9 | 0.217932 | 0.108966 | − | 0.994045i | \(-0.465246\pi\) | ||||
0.108966 | + | 0.994045i | \(0.465246\pi\) | |||||||
\(462\) | 2.83692e9i | 0.0622701i | ||||||||
\(463\) | − | 6.34452e10i | − | 1.38062i | −0.723513 | − | 0.690311i | \(-0.757474\pi\) | ||
0.723513 | − | 0.690311i | \(-0.242526\pi\) | |||||||
\(464\) | − | 4.87465e10i | − | 1.05165i | ||||||
\(465\) | 4.84517e9 | 0.103633 | ||||||||
\(466\) | −8.58254e10 | −1.82000 | ||||||||
\(467\) | − | 3.63255e10i | − | 0.763738i | −0.924217 | − | 0.381869i | \(-0.875281\pi\) | ||
0.924217 | − | 0.381869i | \(-0.124719\pi\) | |||||||
\(468\) | −3.79355e9 | −0.0790793 | ||||||||
\(469\) | 4.98215e10i | 1.02973i | ||||||||
\(470\) | 3.25238e10 | 0.666514 | ||||||||
\(471\) | −2.63610e8 | −0.00535645 | ||||||||
\(472\) | 3.36307e8i | 0.00677591i | ||||||||
\(473\) | 5.93160e9 | − | 9.59385e9i | 0.118502 | − | 0.191667i | ||||
\(474\) | −2.78138e9 | −0.0550994 | ||||||||
\(475\) | − | 3.90612e10i | − | 0.767310i | ||||||
\(476\) | 1.38564e11i | 2.69912i | ||||||||
\(477\) | 4.12460e10 | 0.796725 | ||||||||
\(478\) | − | 5.04665e10i | − | 0.966700i | ||||||
\(479\) | −6.24570e10 | −1.18642 | −0.593211 | − | 0.805047i | \(-0.702140\pi\) | ||||
−0.593211 | + | 0.805047i | \(0.702140\pi\) | |||||||
\(480\) | − | 8.53364e9i | − | 0.160757i | ||||||
\(481\) | − | 3.37814e9i | − | 0.0631098i | ||||||
\(482\) | −6.42332e9 | −0.119007 | ||||||||
\(483\) | −1.52289e10 | −0.279820 | ||||||||
\(484\) | 6.79579e10 | 1.23839 | ||||||||
\(485\) | 4.30182e10i | 0.777473i | ||||||||
\(486\) | −4.16458e10 | −0.746494 | ||||||||
\(487\) | −7.05965e10 | −1.25507 | −0.627534 | − | 0.778589i | \(-0.715936\pi\) | ||||
−0.627534 | + | 0.778589i | \(0.715936\pi\) | |||||||
\(488\) | −2.46482e10 | −0.434615 | ||||||||
\(489\) | 6.96486e9 | 0.121808 | ||||||||
\(490\) | −8.40380e9 | −0.145778 | ||||||||
\(491\) | 4.83027e10i | 0.831085i | 0.909574 | + | 0.415542i | \(0.136408\pi\) | ||||
−0.909574 | + | 0.415542i | \(0.863592\pi\) | |||||||
\(492\) | − | 5.73370e9i | − | 0.0978531i | ||||||
\(493\) | 1.99756e11i | 3.38151i | ||||||||
\(494\) | 8.15389e9 | 0.136917 | ||||||||
\(495\) | − | 8.99470e9i | − | 0.149819i | ||||||
\(496\) | −3.23780e10 | −0.534962 | ||||||||
\(497\) | −5.05272e10 | −0.828132 | ||||||||
\(498\) | −1.43625e10 | −0.233513 | ||||||||
\(499\) | − | 6.67014e10i | − | 1.07580i | −0.843008 | − | 0.537901i | \(-0.819217\pi\) | ||
0.843008 | − | 0.537901i | \(-0.180783\pi\) | |||||||
\(500\) | 8.54892e10i | 1.36783i | ||||||||
\(501\) | − | 8.30071e9i | − | 0.131754i | ||||||
\(502\) | 8.23333e10i | 1.29647i | ||||||||
\(503\) | − | 1.08689e11i | − | 1.69791i | −0.528468 | − | 0.848954i | \(-0.677233\pi\) | ||
0.528468 | − | 0.848954i | \(-0.322767\pi\) | |||||||
\(504\) | −3.09388e10 | −0.479493 | ||||||||
\(505\) | 3.39403e10i | 0.521855i | ||||||||
\(506\) | − | 3.44739e10i | − | 0.525882i | ||||||
\(507\) | − | 1.12195e10i | − | 0.169802i | ||||||
\(508\) | 2.63562e10 | 0.395757 | ||||||||
\(509\) | 2.21280e10 | 0.329664 | 0.164832 | − | 0.986322i | \(-0.447292\pi\) | ||||
0.164832 | + | 0.986322i | \(0.447292\pi\) | |||||||
\(510\) | 2.32265e10i | 0.343323i | ||||||||
\(511\) | 1.06633e11 | 1.56390 | ||||||||
\(512\) | 7.61762e10i | 1.10851i | ||||||||
\(513\) | 3.36169e10 | 0.485387 | ||||||||
\(514\) | −1.47409e11 | −2.11190 | ||||||||
\(515\) | − | 4.63152e10i | − | 0.658407i | ||||||
\(516\) | −1.34101e10 | − | 8.29109e9i | −0.189162 | − | 0.116953i | ||||
\(517\) | 1.03224e10 | 0.144484 | ||||||||
\(518\) | − | 1.17988e11i | − | 1.63877i | ||||||
\(519\) | − | 1.17050e9i | − | 0.0161326i | ||||||
\(520\) | −1.44548e9 | −0.0197697 | ||||||||
\(521\) | 8.18254e10i | 1.11055i | 0.831668 | + | 0.555274i | \(0.187387\pi\) | ||||
−0.831668 | + | 0.555274i | \(0.812613\pi\) | |||||||
\(522\) | −1.91009e11 | −2.57260 | ||||||||
\(523\) | 1.35833e10i | 0.181552i | 0.995871 | + | 0.0907758i | \(0.0289347\pi\) | ||||
−0.995871 | + | 0.0907758i | \(0.971065\pi\) | |||||||
\(524\) | 7.23810e10i | 0.960063i | ||||||||
\(525\) | 7.34456e9 | 0.0966783 | ||||||||
\(526\) | 1.74070e11 | 2.27395 | ||||||||
\(527\) | 1.32680e11 | 1.72014 | ||||||||
\(528\) | − | 1.79891e9i | − | 0.0231459i | ||||||
\(529\) | 1.06748e11 | 1.36313 | ||||||||
\(530\) | 6.73056e10 | 0.852997 | ||||||||
\(531\) | −1.13096e9 | −0.0142255 | ||||||||
\(532\) | 1.61217e11 | 2.01264 | ||||||||
\(533\) | 2.21683e9 | 0.0274678 | ||||||||
\(534\) | 9.06244e9i | 0.111450i | ||||||||
\(535\) | 4.41998e10i | 0.539517i | ||||||||
\(536\) | 3.68111e10i | 0.445984i | ||||||||
\(537\) | 1.97571e9 | 0.0237589 | ||||||||
\(538\) | − | 2.54492e10i | − | 0.303770i | ||||||
\(539\) | −2.66721e9 | −0.0316011 | ||||||||
\(540\) | −2.55216e10 | −0.300146 | ||||||||
\(541\) | −2.54665e10 | −0.297289 | −0.148645 | − | 0.988891i | \(-0.547491\pi\) | ||||
−0.148645 | + | 0.988891i | \(0.547491\pi\) | |||||||
\(542\) | − | 2.09300e11i | − | 2.42534i | ||||||
\(543\) | 1.18387e10i | 0.136177i | ||||||||
\(544\) | − | 2.33685e11i | − | 2.66830i | ||||||
\(545\) | 1.07626e11i | 1.21992i | ||||||||
\(546\) | 1.53315e9i | 0.0172510i | ||||||||
\(547\) | −1.06228e11 | −1.18656 | −0.593278 | − | 0.804998i | \(-0.702167\pi\) | ||||
−0.593278 | + | 0.804998i | \(0.702167\pi\) | |||||||
\(548\) | 1.66788e11i | 1.84945i | ||||||||
\(549\) | − | 8.28888e10i | − | 0.912445i | ||||||
\(550\) | 1.66261e10i | 0.181693i | ||||||||
\(551\) | 2.32413e11 | 2.52147 | ||||||||
\(552\) | −1.12520e10 | −0.121192 | ||||||||
\(553\) | − | 2.12621e10i | − | 0.227355i | ||||||
\(554\) | −1.97114e11 | −2.09257 | ||||||||
\(555\) | − | 1.11959e10i | − | 0.118001i | ||||||
\(556\) | 4.89526e9 | 0.0512244 | ||||||||
\(557\) | −5.50843e10 | −0.572278 | −0.286139 | − | 0.958188i | \(-0.592372\pi\) | ||||
−0.286139 | + | 0.958188i | \(0.592372\pi\) | |||||||
\(558\) | 1.26870e11i | 1.30865i | ||||||||
\(559\) | 3.20560e9 | − | 5.18479e9i | 0.0328293 | − | 0.0530987i | ||||
\(560\) | 4.33285e10 | 0.440577 | ||||||||
\(561\) | 7.37167e9i | 0.0744242i | ||||||||
\(562\) | − | 7.54871e10i | − | 0.756706i | ||||||
\(563\) | 1.49411e11 | 1.48713 | 0.743564 | − | 0.668664i | \(-0.233134\pi\) | ||||
0.743564 | + | 0.668664i | \(0.233134\pi\) | |||||||
\(564\) | − | 1.44286e10i | − | 0.142596i | ||||||
\(565\) | 1.22032e11 | 1.19751 | ||||||||
\(566\) | 2.39221e11i | 2.33095i | ||||||||
\(567\) | − | 1.00837e11i | − | 0.975632i | ||||||
\(568\) | −3.73325e10 | −0.358669 | ||||||||
\(569\) | −1.27794e11 | −1.21916 | −0.609582 | − | 0.792723i | \(-0.708663\pi\) | ||||
−0.609582 | + | 0.792723i | \(0.708663\pi\) | |||||||
\(570\) | 2.70238e10 | 0.256004 | ||||||||
\(571\) | 1.25011e11i | 1.17599i | 0.808865 | + | 0.587995i | \(0.200082\pi\) | ||||
−0.808865 | + | 0.587995i | \(0.799918\pi\) | |||||||
\(572\) | −1.96470e9 | −0.0183532 | ||||||||
\(573\) | −1.74756e10 | −0.162111 | ||||||||
\(574\) | 7.74270e10 | 0.713255 | ||||||||
\(575\) | −8.92502e10 | −0.816465 | ||||||||
\(576\) | 1.59054e11 | 1.44496 | ||||||||
\(577\) | − | 1.59101e11i | − | 1.43539i | −0.696360 | − | 0.717693i | \(-0.745198\pi\) | ||
0.696360 | − | 0.717693i | \(-0.254802\pi\) | |||||||
\(578\) | 4.66595e11i | 4.18051i | ||||||||
\(579\) | 1.79741e10i | 0.159931i | ||||||||
\(580\) | −1.76446e11 | −1.55919 | ||||||||
\(581\) | − | 1.09793e11i | − | 0.963539i | ||||||
\(582\) | 3.37122e10 | 0.293829 | ||||||||
\(583\) | 2.13615e10 | 0.184909 | ||||||||
\(584\) | 7.87871e10 | 0.677336 | ||||||||
\(585\) | − | 4.86099e9i | − | 0.0415051i | ||||||
\(586\) | − | 2.86776e11i | − | 2.43193i | ||||||
\(587\) | − | 1.39779e10i | − | 0.117731i | −0.998266 | − | 0.0588654i | \(-0.981252\pi\) | ||
0.998266 | − | 0.0588654i | \(-0.0187483\pi\) | |||||||
\(588\) | 3.72819e9i | 0.0311880i | ||||||||
\(589\) | − | 1.54372e11i | − | 1.28264i | ||||||
\(590\) | −1.84551e9 | −0.0152303 | ||||||||
\(591\) | 2.85278e10i | 0.233840i | ||||||||
\(592\) | 7.48169e10i | 0.609134i | ||||||||
\(593\) | 8.73992e10i | 0.706787i | 0.935475 | + | 0.353394i | \(0.114972\pi\) | ||||
−0.935475 | + | 0.353394i | \(0.885028\pi\) | |||||||
\(594\) | −1.43088e10 | −0.114936 | ||||||||
\(595\) | −1.77553e11 | −1.41665 | ||||||||
\(596\) | − | 2.46899e10i | − | 0.195675i | ||||||
\(597\) | −1.24666e10 | −0.0981412 | ||||||||
\(598\) | − | 1.86307e10i | − | 0.145688i | ||||||
\(599\) | −1.57778e11 | −1.22557 | −0.612785 | − | 0.790250i | \(-0.709951\pi\) | ||||
−0.612785 | + | 0.790250i | \(0.709951\pi\) | |||||||
\(600\) | 5.42660e9 | 0.0418719 | ||||||||
\(601\) | 1.08858e11i | 0.834381i | 0.908819 | + | 0.417190i | \(0.136985\pi\) | ||||
−0.908819 | + | 0.417190i | \(0.863015\pi\) | |||||||
\(602\) | 1.11962e11 | − | 1.81088e11i | 0.852478 | − | 1.37881i | ||||
\(603\) | −1.23791e11 | −0.936312 | ||||||||
\(604\) | − | 2.38788e11i | − | 1.79417i | ||||||
\(605\) | 8.70801e10i | 0.649976i | ||||||||
\(606\) | 2.65980e10 | 0.197224 | ||||||||
\(607\) | 2.80501e10i | 0.206624i | 0.994649 | + | 0.103312i | \(0.0329440\pi\) | ||||
−0.994649 | + | 0.103312i | \(0.967056\pi\) | |||||||
\(608\) | −2.71890e11 | −1.98966 | ||||||||
\(609\) | 4.37000e10i | 0.317697i | ||||||||
\(610\) | − | 1.35259e11i | − | 0.976890i | ||||||
\(611\) | 5.57854e9 | 0.0400272 | ||||||||
\(612\) | −3.44289e11 | −2.45425 | ||||||||
\(613\) | 9.06755e10 | 0.642167 | 0.321084 | − | 0.947051i | \(-0.395953\pi\) | ||||
0.321084 | + | 0.947051i | \(0.395953\pi\) | |||||||
\(614\) | − | 8.94466e10i | − | 0.629348i | ||||||
\(615\) | 7.34707e9 | 0.0513586 | ||||||||
\(616\) | −1.60234e10 | −0.111284 | ||||||||
\(617\) | 2.14084e11 | 1.47721 | 0.738607 | − | 0.674136i | \(-0.235484\pi\) | ||||
0.738607 | + | 0.674136i | \(0.235484\pi\) | |||||||
\(618\) | −3.62959e10 | −0.248831 | ||||||||
\(619\) | −4.84848e10 | −0.330250 | −0.165125 | − | 0.986273i | \(-0.552803\pi\) | ||||
−0.165125 | + | 0.986273i | \(0.552803\pi\) | |||||||
\(620\) | 1.17197e11i | 0.793141i | ||||||||
\(621\) | − | 7.68107e10i | − | 0.516482i | ||||||
\(622\) | 1.23751e11i | 0.826774i | ||||||||
\(623\) | −6.92772e10 | −0.459873 | ||||||||
\(624\) | − | 9.72183e8i | − | 0.00641224i | ||||||
\(625\) | −2.85017e10 | −0.186789 | ||||||||
\(626\) | −1.99437e11 | −1.29870 | ||||||||
\(627\) | 8.57685e9 | 0.0554955 | ||||||||
\(628\) | − | 6.37631e9i | − | 0.0409950i | ||||||
\(629\) | − | 3.06588e11i | − | 1.95863i | ||||||
\(630\) | − | 1.69779e11i | − | 1.07776i | ||||||
\(631\) | 1.62923e11i | 1.02770i | 0.857881 | + | 0.513848i | \(0.171780\pi\) | ||||
−0.857881 | + | 0.513848i | \(0.828220\pi\) | |||||||
\(632\) | − | 1.57097e10i | − | 0.0984689i | ||||||
\(633\) | −3.24193e10 | −0.201924 | ||||||||
\(634\) | 2.60502e11i | 1.61233i | ||||||||
\(635\) | 3.37724e10i | 0.207715i | ||||||||
\(636\) | − | 2.98588e10i | − | 0.182492i | ||||||
\(637\) | −1.44144e9 | −0.00875462 | ||||||||
\(638\) | −9.89247e10 | −0.597066 | ||||||||
\(639\) | − | 1.25545e11i | − | 0.753000i | ||||||
\(640\) | 1.01330e11 | 0.603971 | ||||||||
\(641\) | 1.93130e11i | 1.14398i | 0.820262 | + | 0.571988i | \(0.193828\pi\) | ||||
−0.820262 | + | 0.571988i | \(0.806172\pi\) | |||||||
\(642\) | 3.46381e10 | 0.203899 | ||||||||
\(643\) | −2.75508e11 | −1.61172 | −0.805861 | − | 0.592105i | \(-0.798297\pi\) | ||||
−0.805861 | + | 0.592105i | \(0.798297\pi\) | |||||||
\(644\) | − | 3.68363e11i | − | 2.14157i | ||||||
\(645\) | 1.06241e10 | − | 1.71835e10i | 0.0613835 | − | 0.0992826i | ||||
\(646\) | 7.40018e11 | 4.24925 | ||||||||
\(647\) | − | 1.84960e11i | − | 1.05550i | −0.849398 | − | 0.527752i | \(-0.823035\pi\) | ||
0.849398 | − | 0.527752i | \(-0.176965\pi\) | |||||||
\(648\) | − | 7.45041e10i | − | 0.422552i | ||||||
\(649\) | −5.85730e8 | −0.00330156 | ||||||||
\(650\) | 8.98519e9i | 0.0503354i | ||||||||
\(651\) | 2.90261e10 | 0.161608 | ||||||||
\(652\) | 1.68470e11i | 0.932247i | ||||||||
\(653\) | 2.03633e11i | 1.11994i | 0.828513 | + | 0.559970i | \(0.189187\pi\) | ||||
−0.828513 | + | 0.559970i | \(0.810813\pi\) | |||||||
\(654\) | 8.43435e10 | 0.461042 | ||||||||
\(655\) | −9.27478e10 | −0.503893 | ||||||||
\(656\) | −4.90970e10 | −0.265118 | ||||||||
\(657\) | 2.64952e11i | 1.42202i | ||||||||
\(658\) | 1.94841e11 | 1.03939 | ||||||||
\(659\) | 3.21214e11 | 1.70315 | 0.851575 | − | 0.524232i | \(-0.175648\pi\) | ||||
0.851575 | + | 0.524232i | \(0.175648\pi\) | |||||||
\(660\) | −6.51145e9 | −0.0343164 | ||||||||
\(661\) | −2.59186e11 | −1.35771 | −0.678853 | − | 0.734274i | \(-0.737523\pi\) | ||||
−0.678853 | + | 0.734274i | \(0.737523\pi\) | |||||||
\(662\) | 5.00390e10 | 0.260541 | ||||||||
\(663\) | 3.98386e9i | 0.0206181i | ||||||||
\(664\) | − | 8.11215e10i | − | 0.417315i | ||||||
\(665\) | 2.06581e11i | 1.05634i | ||||||||
\(666\) | 2.93164e11 | 1.49009 | ||||||||
\(667\) | − | 5.31037e11i | − | 2.68300i | ||||||
\(668\) | 2.00781e11 | 1.00837 | ||||||||
\(669\) | −3.82951e10 | −0.191178 | ||||||||
\(670\) | −2.02003e11 | −1.00244 | ||||||||
\(671\) | − | 4.29286e10i | − | 0.211766i | ||||||
\(672\) | − | 5.11227e10i | − | 0.250690i | ||||||
\(673\) | − | 1.82200e11i | − | 0.888153i | −0.895989 | − | 0.444077i | \(-0.853532\pi\) | ||
0.895989 | − | 0.444077i | \(-0.146468\pi\) | |||||||
\(674\) | 2.90553e11i | 1.40794i | ||||||||
\(675\) | 3.70442e10i | 0.178445i | ||||||||
\(676\) | 2.71383e11 | 1.29956 | ||||||||
\(677\) | − | 3.72816e11i | − | 1.77476i | −0.461040 | − | 0.887379i | \(-0.652524\pi\) | ||
0.461040 | − | 0.887379i | \(-0.347476\pi\) | |||||||
\(678\) | − | 9.56330e10i | − | 0.452573i | ||||||
\(679\) | 2.57710e11i | 1.21242i | ||||||||
\(680\) | −1.31187e11 | −0.613558 | ||||||||
\(681\) | −2.85599e9 | −0.0132791 | ||||||||
\(682\) | 6.57069e10i | 0.303720i | ||||||||
\(683\) | −5.95037e10 | −0.273439 | −0.136720 | − | 0.990610i | \(-0.543656\pi\) | ||||
−0.136720 | + | 0.990610i | \(0.543656\pi\) | |||||||
\(684\) | 4.00577e11i | 1.83004i | ||||||||
\(685\) | −2.13720e11 | −0.970694 | ||||||||
\(686\) | 3.08656e11 | 1.39373 | ||||||||
\(687\) | − | 3.85121e10i | − | 0.172890i | ||||||
\(688\) | −7.09957e10 | + | 1.14829e11i | −0.316868 | + | 0.512506i | ||||
\(689\) | 1.15444e10 | 0.0512264 | ||||||||
\(690\) | − | 6.17461e10i | − | 0.272404i | ||||||
\(691\) | 1.43990e11i | 0.631568i | 0.948831 | + | 0.315784i | \(0.102268\pi\) | ||||
−0.948831 | + | 0.315784i | \(0.897732\pi\) | |||||||
\(692\) | 2.83127e10 | 0.123469 | ||||||||
\(693\) | − | 5.38848e10i | − | 0.233633i | ||||||
\(694\) | 8.36775e10 | 0.360721 | ||||||||
\(695\) | 6.27271e9i | 0.0268854i | ||||||||
\(696\) | 3.22882e10i | 0.137596i | ||||||||
\(697\) | 2.01192e11 | 0.852470 | ||||||||
\(698\) | −2.04366e11 | −0.860966 | ||||||||
\(699\) | −4.87884e10 | −0.204366 | ||||||||
\(700\) | 1.77654e11i | 0.739916i | ||||||||
\(701\) | 3.56792e11 | 1.47755 | 0.738776 | − | 0.673951i | \(-0.235404\pi\) | ||||
0.738776 | + | 0.673951i | \(0.235404\pi\) | |||||||
\(702\) | −7.73285e9 | −0.0318413 | ||||||||
\(703\) | −3.56711e11 | −1.46048 | ||||||||
\(704\) | 8.23751e10 | 0.335356 | ||||||||
\(705\) | 1.84885e10 | 0.0748420 | ||||||||
\(706\) | 3.84059e11i | 1.54589i | ||||||||
\(707\) | 2.03327e11i | 0.813798i | ||||||||
\(708\) | 8.18725e8i | 0.00325840i | ||||||||
\(709\) | −1.69458e11 | −0.670622 | −0.335311 | − | 0.942107i | \(-0.608841\pi\) | ||||
−0.335311 | + | 0.942107i | \(0.608841\pi\) | |||||||
\(710\) | − | 2.04865e11i | − | 0.806184i | ||||||
\(711\) | 5.28298e10 | 0.206729 | ||||||||
\(712\) | −5.11861e10 | −0.199174 | ||||||||
\(713\) | −3.52721e11 | −1.36481 | ||||||||
\(714\) | 1.39144e11i | 0.535390i | ||||||||
\(715\) | − | 2.51753e9i | − | 0.00963277i | ||||||
\(716\) | 4.77895e10i | 0.181836i | ||||||||
\(717\) | − | 2.86883e10i | − | 0.108549i | ||||||
\(718\) | − | 4.25926e11i | − | 1.60264i | ||||||
\(719\) | −3.94401e11 | −1.47578 | −0.737892 | − | 0.674919i | \(-0.764179\pi\) | ||||
−0.737892 | + | 0.674919i | \(0.764179\pi\) | |||||||
\(720\) | 1.07658e11i | 0.400606i | ||||||||
\(721\) | − | 2.77462e11i | − | 1.02674i | ||||||
\(722\) | − | 4.48477e11i | − | 1.65041i | ||||||
\(723\) | −3.65141e9 | −0.0133631 | ||||||||
\(724\) | −2.86360e11 | −1.04222 | ||||||||
\(725\) | 2.56108e11i | 0.926982i | ||||||||
\(726\) | 6.82422e10 | 0.245644 | ||||||||
\(727\) | 4.40578e11i | 1.57720i | 0.614909 | + | 0.788598i | \(0.289193\pi\) | ||||
−0.614909 | + | 0.788598i | \(0.710807\pi\) | |||||||
\(728\) | −8.65949e9 | −0.0308295 | ||||||||
\(729\) | 2.34373e11 | 0.829846 | ||||||||
\(730\) | 4.32350e11i | 1.52245i | ||||||||
\(731\) | 2.90929e11 | − | 4.70553e11i | 1.01887 | − | 1.64793i | ||||
\(732\) | −6.00049e10 | −0.208998 | ||||||||
\(733\) | − | 9.56982e10i | − | 0.331503i | −0.986168 | − | 0.165752i | \(-0.946995\pi\) | ||
0.986168 | − | 0.165752i | \(-0.0530050\pi\) | |||||||
\(734\) | 4.77716e11i | 1.64583i | ||||||||
\(735\) | −4.77723e9 | −0.0163692 | ||||||||
\(736\) | 6.21236e11i | 2.11712i | ||||||||
\(737\) | −6.41122e10 | −0.217305 | ||||||||
\(738\) | 1.92383e11i | 0.648545i | ||||||||
\(739\) | − | 2.11867e10i | − | 0.0710373i | −0.999369 | − | 0.0355186i | \(-0.988692\pi\) | ||
0.999369 | − | 0.0355186i | \(-0.0113083\pi\) | |||||||
\(740\) | 2.70812e11 | 0.903110 | ||||||||
\(741\) | 4.63517e9 | 0.0153742 | ||||||||
\(742\) | 4.03209e11 | 1.33019 | ||||||||
\(743\) | − | 5.43058e10i | − | 0.178193i | −0.996023 | − | 0.0890965i | \(-0.971602\pi\) | ||
0.996023 | − | 0.0890965i | \(-0.0283980\pi\) | |||||||
\(744\) | 2.14462e10 | 0.0699936 | ||||||||
\(745\) | 3.16372e10 | 0.102701 | ||||||||
\(746\) | −5.40514e11 | −1.74523 | ||||||||
\(747\) | 2.72802e11 | 0.876123 | ||||||||
\(748\) | −1.78309e11 | −0.569597 | ||||||||
\(749\) | 2.64789e11i | 0.841341i | ||||||||
\(750\) | 8.58468e10i | 0.271318i | ||||||||
\(751\) | − | 1.24175e11i | − | 0.390367i | −0.980767 | − | 0.195183i | \(-0.937470\pi\) | ||
0.980767 | − | 0.195183i | \(-0.0625302\pi\) | |||||||
\(752\) | −1.23550e11 | −0.386342 | ||||||||
\(753\) | 4.68033e10i | 0.145578i | ||||||||
\(754\) | −5.34617e10 | −0.165408 | ||||||||
\(755\) | 3.05978e11 | 0.941679 | ||||||||
\(756\) | −1.52893e11 | −0.468058 | ||||||||
\(757\) | − | 2.64168e11i | − | 0.804447i | −0.915542 | − | 0.402223i | \(-0.868238\pi\) | ||
0.915542 | − | 0.402223i | \(-0.131762\pi\) | |||||||
\(758\) | − | 5.40395e11i | − | 1.63695i | ||||||
\(759\) | − | 1.95971e10i | − | 0.0590506i | ||||||
\(760\) | 1.52635e11i | 0.457508i | ||||||||
\(761\) | − | 2.13908e11i | − | 0.637806i | −0.947787 | − | 0.318903i | \(-0.896686\pi\) | ||
0.947787 | − | 0.318903i | \(-0.103314\pi\) | |||||||
\(762\) | 2.64665e10 | 0.0785012 | ||||||||
\(763\) | 6.44758e11i | 1.90239i | ||||||||
\(764\) | − | 4.22708e11i | − | 1.24070i | ||||||
\(765\) | − | 4.41167e11i | − | 1.28812i | ||||||
\(766\) | −4.57608e11 | −1.32916 | ||||||||
\(767\) | −3.16545e8 | −0.000914649 | ||||||||
\(768\) | 8.84705e9i | 0.0254304i | ||||||||
\(769\) | 1.42773e11 | 0.408263 | 0.204132 | − | 0.978943i | \(-0.434563\pi\) | ||||
0.204132 | + | 0.978943i | \(0.434563\pi\) | |||||||
\(770\) | − | 8.79296e10i | − | 0.250134i | ||||||
\(771\) | −8.37966e10 | −0.237142 | ||||||||
\(772\) | −4.34766e11 | −1.22401 | ||||||||
\(773\) | 6.20070e9i | 0.0173669i | 0.999962 | + | 0.00868346i | \(0.00276407\pi\) | ||||
−0.999962 | + | 0.00868346i | \(0.997236\pi\) | |||||||
\(774\) | 4.49950e11 | + | 2.78191e11i | 1.25372 | + | 0.775138i | ||||
\(775\) | 1.70110e11 | 0.471545 | ||||||||
\(776\) | 1.90412e11i | 0.525106i | ||||||||
\(777\) | − | 6.70715e10i | − | 0.184015i | ||||||
\(778\) | 1.71203e11 | 0.467297 | ||||||||
\(779\) | − | 2.34084e11i | − | 0.635657i | ||||||
\(780\) | −3.51897e9 | −0.00950687 | ||||||||
\(781\) | − | 6.50203e10i | − | 0.174761i | ||||||
\(782\) | − | 1.69085e12i | − | 4.52147i | ||||||
\(783\) | −2.20412e11 | −0.586393 | ||||||||
\(784\) | 3.19240e10 | 0.0844993 | ||||||||
\(785\) | 8.17050e9 | 0.0215164 | ||||||||
\(786\) | 7.26838e10i | 0.190435i | ||||||||
\(787\) | 1.45567e11 | 0.379458 | 0.189729 | − | 0.981836i | \(-0.439239\pi\) | ||||
0.189729 | + | 0.981836i | \(0.439239\pi\) | |||||||
\(788\) | −6.90045e11 | −1.78967 | ||||||||
\(789\) | 9.89519e10 | 0.255338 | ||||||||
\(790\) | 8.62081e10 | 0.221330 | ||||||||
\(791\) | 7.31060e11 | 1.86744 | ||||||||
\(792\) | − | 3.98133e10i | − | 0.101188i | ||||||
\(793\) | − | 2.31998e10i | − | 0.0586667i | ||||||
\(794\) | − | 1.88844e11i | − | 0.475138i | ||||||
\(795\) | 3.82606e10 | 0.0957819 | ||||||||
\(796\) | − | 3.01549e11i | − | 0.751113i | ||||||
\(797\) | −7.57891e11 | −1.87834 | −0.939168 | − | 0.343458i | \(-0.888402\pi\) | ||||
−0.939168 | + | 0.343458i | \(0.888402\pi\) | |||||||
\(798\) | 1.61892e11 | 0.399221 | ||||||||
\(799\) | 5.06289e11 | 1.24226 | ||||||||
\(800\) | − | 2.99609e11i | − | 0.731468i | ||||||
\(801\) | − | 1.72133e11i | − | 0.418152i | ||||||
\(802\) | 4.54701e10i | 0.109908i | ||||||||
\(803\) | 1.37220e11i | 0.330031i | ||||||||
\(804\) | 8.96150e10i | 0.214465i | ||||||||
\(805\) | 4.72014e11 | 1.12401 | ||||||||
\(806\) | 3.55099e10i | 0.0841413i | ||||||||
\(807\) | − | 1.44669e10i | − | 0.0341099i | ||||||
\(808\) | 1.50230e11i | 0.352461i | ||||||||
\(809\) | −4.18797e11 | −0.977709 | −0.488854 | − | 0.872365i | \(-0.662585\pi\) | ||||
−0.488854 | + | 0.872365i | \(0.662585\pi\) | |||||||
\(810\) | 4.08847e11 | 0.949775 | ||||||||
\(811\) | − | 2.57888e11i | − | 0.596139i | −0.954544 | − | 0.298069i | \(-0.903657\pi\) | ||
0.954544 | − | 0.298069i | \(-0.0963426\pi\) | |||||||
\(812\) | −1.05704e12 | −2.43145 | ||||||||
\(813\) | − | 1.18979e11i | − | 0.272338i | ||||||
\(814\) | 1.51831e11 | 0.345831 | ||||||||
\(815\) | −2.15874e11 | −0.489294 | ||||||||
\(816\) | − | 8.82320e10i | − | 0.199006i | ||||||
\(817\) | −5.47483e11 | − | 3.38493e11i | −1.22880 | − | 0.759733i | ||||
\(818\) | −3.98491e11 | −0.890032 | ||||||||
\(819\) | − | 2.91209e10i | − | 0.0647245i | ||||||
\(820\) | 1.77714e11i | 0.393068i | ||||||||
\(821\) | 6.01891e11 | 1.32478 | 0.662392 | − | 0.749158i | \(-0.269541\pi\) | ||||
0.662392 | + | 0.749158i | \(0.269541\pi\) | |||||||
\(822\) | 1.67486e11i | 0.366853i | ||||||||
\(823\) | 8.61186e10 | 0.187714 | 0.0938572 | − | 0.995586i | \(-0.470080\pi\) | ||||
0.0938572 | + | 0.995586i | \(0.470080\pi\) | |||||||
\(824\) | − | 2.05005e11i | − | 0.444688i | ||||||
\(825\) | 9.45127e9i | 0.0204021i | ||||||||
\(826\) | −1.10559e10 | −0.0237506 | ||||||||
\(827\) | 8.32732e11 | 1.78026 | 0.890129 | − | 0.455708i | \(-0.150614\pi\) | ||||
0.890129 | + | 0.455708i | \(0.150614\pi\) | |||||||
\(828\) | 9.15271e11 | 1.94728 | ||||||||
\(829\) | 3.87262e11i | 0.819949i | 0.912097 | + | 0.409975i | \(0.134462\pi\) | ||||
−0.912097 | + | 0.409975i | \(0.865538\pi\) | |||||||
\(830\) | 4.45160e11 | 0.938003 | ||||||||
\(831\) | −1.12052e11 | −0.234971 | ||||||||
\(832\) | 4.45178e10 | 0.0929054 | ||||||||
\(833\) | −1.30820e11 | −0.271702 | ||||||||
\(834\) | 4.91574e9 | 0.0101607 | ||||||||
\(835\) | 2.57278e11i | 0.529245i | ||||||||
\(836\) | 2.07461e11i | 0.424728i | ||||||||
\(837\) | 1.46400e11i | 0.298291i | ||||||||
\(838\) | −1.18317e12 | −2.39922 | ||||||||
\(839\) | 4.89599e11i | 0.988081i | 0.869439 | + | 0.494040i | \(0.164481\pi\) | ||||
−0.869439 | + | 0.494040i | \(0.835519\pi\) | |||||||
\(840\) | −2.86995e10 | −0.0576443 | ||||||||
\(841\) | −1.02359e12 | −2.04618 | ||||||||
\(842\) | 2.20076e11 | 0.437849 | ||||||||
\(843\) | − | 4.29115e10i | − | 0.0849695i | ||||||
\(844\) | − | 7.84174e11i | − | 1.54541i | ||||||
\(845\) | 3.47745e11i | 0.682078i | ||||||||
\(846\) | 4.84121e11i | 0.945088i | ||||||||
\(847\) | 5.21673e11i | 1.01360i | ||||||||
\(848\) | −2.55678e11 | −0.494435 | ||||||||
\(849\) | 1.35988e11i | 0.261739i | ||||||||
\(850\) | 8.15464e11i | 1.56217i | ||||||||
\(851\) | 8.15044e11i | 1.55404i | ||||||||
\(852\) | −9.08844e10 | −0.172477 | ||||||||
\(853\) | 5.16576e11 | 0.975749 | 0.487875 | − | 0.872914i | \(-0.337772\pi\) | ||||
0.487875 | + | 0.872914i | \(0.337772\pi\) | |||||||
\(854\) | − | 8.10297e11i | − | 1.52340i | ||||||
\(855\) | −5.13292e11 | −0.960506 | ||||||||
\(856\) | 1.95642e11i | 0.364390i | ||||||||
\(857\) | 5.30011e11 | 0.982565 | 0.491282 | − | 0.871000i | \(-0.336528\pi\) | ||||
0.491282 | + | 0.871000i | \(0.336528\pi\) | |||||||
\(858\) | −1.97292e9 | −0.00364050 | ||||||||
\(859\) | − | 9.23019e11i | − | 1.69527i | −0.530583 | − | 0.847633i | \(-0.678027\pi\) | ||
0.530583 | − | 0.847633i | \(-0.321973\pi\) | |||||||
\(860\) | 4.15643e11 | + | 2.56980e11i | 0.759848 | + | 0.469792i | ||||
\(861\) | 4.40142e10 | 0.0800904 | ||||||||
\(862\) | − | 1.10976e11i | − | 0.201003i | ||||||
\(863\) | − | 4.53159e11i | − | 0.816972i | −0.912765 | − | 0.408486i | \(-0.866057\pi\) | ||
0.912765 | − | 0.408486i | \(-0.133943\pi\) | |||||||
\(864\) | 2.57850e11 | 0.462714 | ||||||||
\(865\) | 3.62794e10i | 0.0648031i | ||||||||
\(866\) | 2.65852e11 | 0.472681 | ||||||||
\(867\) | 2.65241e11i | 0.469424i | ||||||||
\(868\) | 7.02096e11i | 1.23685i | ||||||||
\(869\) | 2.73609e10 | 0.0479789 | ||||||||
\(870\) | −1.77184e11 | −0.309277 | ||||||||
\(871\) | −3.46480e10 | −0.0602013 | ||||||||
\(872\) | 4.76386e11i | 0.823935i | ||||||||
\(873\) | −6.40332e11 | −1.10242 | ||||||||
\(874\) | −1.96729e12 | −3.37150 | ||||||||
\(875\) | −6.56250e11 | −1.11953 | ||||||||
\(876\) | 1.91804e11 | 0.325718 | ||||||||
\(877\) | 1.41919e10 | 0.0239907 | 0.0119953 | − | 0.999928i | \(-0.496182\pi\) | ||||
0.0119953 | + | 0.999928i | \(0.496182\pi\) | |||||||
\(878\) | − | 2.17520e11i | − | 0.366034i | ||||||
\(879\) | − | 1.63021e11i | − | 0.273079i | ||||||
\(880\) | 5.57568e10i | 0.0929752i | ||||||||
\(881\) | 3.79321e11 | 0.629656 | 0.314828 | − | 0.949149i | \(-0.398053\pi\) | ||||
0.314828 | + | 0.949149i | \(0.398053\pi\) | |||||||
\(882\) | − | 1.25092e11i | − | 0.206706i | ||||||
\(883\) | 9.27615e11 | 1.52590 | 0.762948 | − | 0.646459i | \(-0.223751\pi\) | ||||
0.762948 | + | 0.646459i | \(0.223751\pi\) | |||||||
\(884\) | −9.63634e10 | −0.157799 | ||||||||
\(885\) | −1.04910e9 | −0.00171019 | ||||||||
\(886\) | 5.55937e11i | 0.902175i | ||||||||
\(887\) | 1.16557e12i | 1.88297i | 0.337058 | + | 0.941484i | \(0.390568\pi\) | ||||
−0.337058 | + | 0.941484i | \(0.609432\pi\) | |||||||
\(888\) | − | 4.95564e10i | − | 0.0796981i | ||||||
\(889\) | 2.02321e11i | 0.323918i | ||||||||
\(890\) | − | 2.80888e11i | − | 0.447685i | ||||||
\(891\) | 1.29760e11 | 0.205888 | ||||||||
\(892\) | − | 9.26299e11i | − | 1.46316i | ||||||
\(893\) | − | 5.89061e11i | − | 0.926306i | ||||||
\(894\) | − | 2.47932e10i | − | 0.0388135i | ||||||
\(895\) | −6.12367e10 | −0.0954376 | ||||||||
\(896\) | 6.07038e11 | 0.941854 | ||||||||
\(897\) | − | 1.05908e10i | − | 0.0163591i | ||||||
\(898\) | 3.98498e11 | 0.612804 | ||||||||
\(899\) | 1.01215e12i | 1.54955i | ||||||||
\(900\) | −4.41416e11 | −0.672788 | ||||||||
\(901\) | 1.04773e12 | 1.58982 | ||||||||
\(902\) | 9.96360e10i | 0.150519i | ||||||||
\(903\) | 6.36458e10 | − | 1.02942e11i | 0.0957236 | − | 0.154825i | ||||
\(904\) | 5.40151e11 | 0.808800 | ||||||||
\(905\) | − | 3.66937e11i | − | 0.547013i | ||||||
\(906\) | − | 2.39787e11i | − | 0.355887i | ||||||
\(907\) | −9.10561e11 | −1.34549 | −0.672744 | − | 0.739876i | \(-0.734884\pi\) | ||||
−0.672744 | + | 0.739876i | \(0.734884\pi\) | |||||||
\(908\) | − | 6.90822e10i | − | 0.101630i | ||||||
\(909\) | −5.05205e11 | −0.739967 | ||||||||
\(910\) | − | 4.75196e10i | − | 0.0692959i | ||||||
\(911\) | 6.72912e11i | 0.976978i | 0.872570 | + | 0.488489i | \(0.162452\pi\) | ||||
−0.872570 | + | 0.488489i | \(0.837548\pi\) | |||||||
\(912\) | −1.02657e11 | −0.148391 | ||||||||
\(913\) | 1.41286e11 | 0.203336 | ||||||||
\(914\) | 1.63470e11 | 0.234235 | ||||||||
\(915\) | − | 7.68893e10i | − | 0.109694i | ||||||
\(916\) | 9.31548e11 | 1.32319 | ||||||||
\(917\) | −5.55626e11 | −0.785788 | ||||||||
\(918\) | −7.01807e11 | −0.988204 | ||||||||
\(919\) | 1.19782e12 | 1.67930 | 0.839652 | − | 0.543125i | \(-0.182759\pi\) | ||||
0.839652 | + | 0.543125i | \(0.182759\pi\) | |||||||
\(920\) | 3.48752e11 | 0.486817 | ||||||||
\(921\) | − | 5.08470e10i | − | 0.0706686i | ||||||
\(922\) | 2.39082e11i | 0.330844i | ||||||||
\(923\) | − | 3.51388e10i | − | 0.0484151i | ||||||
\(924\) | −3.90083e10 | −0.0535142 | ||||||||
\(925\) | − | 3.93079e11i | − | 0.536924i | ||||||
\(926\) | 1.54106e12 | 2.09593 | ||||||||
\(927\) | 6.89408e11 | 0.933593 | ||||||||
\(928\) | 1.78267e12 | 2.40369 | ||||||||
\(929\) | 3.59469e11i | 0.482612i | 0.970449 | + | 0.241306i | \(0.0775758\pi\) | ||||
−0.970449 | + | 0.241306i | \(0.922424\pi\) | |||||||
\(930\) | 1.17688e11i | 0.157325i | ||||||||
\(931\) | 1.52207e11i | 0.202598i | ||||||||
\(932\) | − | 1.18012e12i | − | 1.56409i | ||||||
\(933\) | 7.03476e10i | 0.0928373i | ||||||||
\(934\) | 8.82335e11 | 1.15943 | ||||||||
\(935\) | − | 2.28483e11i | − | 0.298956i | ||||||
\(936\) | − | 2.15162e10i | − | 0.0280326i | ||||||
\(937\) | − | 6.42002e11i | − | 0.832871i | −0.909165 | − | 0.416436i | \(-0.863279\pi\) | ||
0.909165 | − | 0.416436i | \(-0.136721\pi\) | |||||||
\(938\) | −1.21015e12 | −1.56324 | ||||||||
\(939\) | −1.13372e11 | −0.145829 | ||||||||
\(940\) | 4.47209e11i | 0.572795i | ||||||||
\(941\) | −1.25177e12 | −1.59650 | −0.798248 | − | 0.602329i | \(-0.794239\pi\) | ||||
−0.798248 | + | 0.602329i | \(0.794239\pi\) | |||||||
\(942\) | − | 6.40299e9i | − | 0.00813166i | ||||||
\(943\) | −5.34855e11 | −0.676378 | ||||||||
\(944\) | 7.01065e9 | 0.00882816 | ||||||||
\(945\) | − | 1.95914e11i | − | 0.245663i | ||||||
\(946\) | 2.33031e11 | + | 1.44077e11i | 0.290971 | + | 0.179899i | ||||
\(947\) | 5.56633e11 | 0.692101 | 0.346050 | − | 0.938216i | \(-0.387523\pi\) | ||||
0.346050 | + | 0.938216i | \(0.387523\pi\) | |||||||
\(948\) | − | 3.82446e10i | − | 0.0473518i | ||||||
\(949\) | 7.41576e10i | 0.0914304i | ||||||||
\(950\) | 9.48783e11 | 1.16486 | ||||||||
\(951\) | 1.48085e11i | 0.181046i | ||||||||
\(952\) | −7.85905e11 | −0.956803 | ||||||||
\(953\) | 8.41007e11i | 1.01960i | 0.860294 | + | 0.509798i | \(0.170280\pi\) | ||||
−0.860294 | + | 0.509798i | \(0.829720\pi\) | |||||||
\(954\) | 1.00185e12i | 1.20951i | ||||||||
\(955\) | 5.41651e11 | 0.651188 | ||||||||
\(956\) | 6.93926e11 | 0.830771 | ||||||||
\(957\) | −5.62349e10 | −0.0670437 | ||||||||
\(958\) | − | 1.51706e12i | − | 1.80111i | ||||||
\(959\) | −1.28034e12 | −1.51373 | ||||||||
\(960\) | 1.47542e11 | 0.173712 | ||||||||
\(961\) | −1.80609e11 | −0.211761 | ||||||||
\(962\) | 8.20539e10 | 0.0958073 | ||||||||
\(963\) | −6.57920e11 | −0.765011 | ||||||||
\(964\) | − | 8.83220e10i | − | 0.102273i | ||||||
\(965\) | − | 5.57101e11i | − | 0.642429i | ||||||
\(966\) | − | 3.69904e11i | − | 0.424796i | ||||||
\(967\) | 3.17275e11 | 0.362853 | 0.181426 | − | 0.983405i | \(-0.441929\pi\) | ||||
0.181426 | + | 0.983405i | \(0.441929\pi\) | |||||||
\(968\) | 3.85443e11i | 0.438994i | ||||||||
\(969\) | 4.20672e11 | 0.477143 | ||||||||
\(970\) | −1.04490e12 | −1.18029 | ||||||||
\(971\) | −9.75359e11 | −1.09720 | −0.548602 | − | 0.836084i | \(-0.684840\pi\) | ||||
−0.548602 | + | 0.836084i | \(0.684840\pi\) | |||||||
\(972\) | − | 5.72639e11i | − | 0.641529i | ||||||
\(973\) | 3.75781e10i | 0.0419259i | ||||||||
\(974\) | − | 1.71477e12i | − | 1.90533i | ||||||
\(975\) | 5.10773e9i | 0.00565210i | ||||||||
\(976\) | 5.13815e11i | 0.566249i | ||||||||
\(977\) | 6.48624e11 | 0.711893 | 0.355947 | − | 0.934506i | \(-0.384158\pi\) | ||||
0.355947 | + | 0.934506i | \(0.384158\pi\) | |||||||
\(978\) | 1.69174e11i | 0.184918i | ||||||||
\(979\) | − | 8.91486e10i | − | 0.0970474i | ||||||
\(980\) | − | 1.15554e11i | − | 0.125280i | ||||||
\(981\) | −1.60203e12 | −1.72979 | ||||||||
\(982\) | −1.17326e12 | −1.26167 | ||||||||
\(983\) | 1.10400e12i | 1.18238i | 0.806533 | + | 0.591189i | \(0.201341\pi\) | ||||
−0.806533 | + | 0.591189i | \(0.798659\pi\) | |||||||
\(984\) | 3.25203e10 | 0.0346876 | ||||||||
\(985\) | − | 8.84212e11i | − | 0.939315i | ||||||
\(986\) | −4.85200e12 | −5.13349 | ||||||||
\(987\) | 1.10760e11 | 0.116711 | ||||||||
\(988\) | 1.12118e11i | 0.117665i | ||||||||
\(989\) | −7.73416e11 | + | 1.25093e12i | −0.808403 | + | 1.30752i | ||||
\(990\) | 2.18478e11 | 0.227441 | ||||||||
\(991\) | 8.40020e11i | 0.870954i | 0.900200 | + | 0.435477i | \(0.143420\pi\) | ||||
−0.900200 | + | 0.435477i | \(0.856580\pi\) | |||||||
\(992\) | − | 1.18407e12i | − | 1.22273i | ||||||
\(993\) | 2.84452e10 | 0.0292558 | ||||||||
\(994\) | − | 1.22729e12i | − | 1.25719i | ||||||
\(995\) | 3.86399e11 | 0.394225 | ||||||||
\(996\) | − | 1.97487e11i | − | 0.200679i | ||||||
\(997\) | − | 1.03692e12i | − | 1.04946i | −0.851270 | − | 0.524728i | \(-0.824167\pi\) | ||
0.851270 | − | 0.524728i | \(-0.175833\pi\) | |||||||
\(998\) | 1.62015e12 | 1.63318 | ||||||||
\(999\) | 3.38292e11 | 0.339649 |
(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 | 43.9.b.b.42.25 | yes | 28 | |
43.42 | odd | 2 | inner | 43.9.b.b.42.4 | ✓ | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.9.b.b.42.4 | ✓ | 28 | 43.42 | odd | 2 | inner | |
43.9.b.b.42.25 | yes | 28 | 1.1 | even | 1 | trivial |