Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [43,11,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, 11, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("43.42");
S:= CuspForms(chi, 11);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 43 \) |
Weight: | \( k \) | \(=\) | \( 11 \) |
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: | \(27.3203618650\) |
Analytic rank: | \(0\) |
Dimension: | \(34\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 42.1 | ||
Character | \(\chi\) | \(=\) | 43.42 |
Dual form | 43.11.b.b.42.34 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 59.1014i | − | 1.84692i | −0.383696 | − | 0.923459i | \(-0.625349\pi\) | ||
0.383696 | − | 0.923459i | \(-0.374651\pi\) | |||||||
\(3\) | 419.853i | 1.72779i | 0.503670 | + | 0.863896i | \(0.331983\pi\) | ||||
−0.503670 | + | 0.863896i | \(0.668017\pi\) | |||||||
\(4\) | −2468.98 | −2.41111 | ||||||||
\(5\) | − | 832.528i | − | 0.266409i | −0.991089 | − | 0.133204i | \(-0.957473\pi\) | ||
0.991089 | − | 0.133204i | \(-0.0425267\pi\) | |||||||
\(6\) | 24813.9 | 3.19109 | ||||||||
\(7\) | − | 31219.1i | − | 1.85751i | −0.370696 | − | 0.928754i | \(-0.620881\pi\) | ||
0.370696 | − | 0.928754i | \(-0.379119\pi\) | |||||||
\(8\) | 85400.1i | 2.60621i | ||||||||
\(9\) | −117228. | −1.98527 | ||||||||
\(10\) | −49203.6 | −0.492036 | ||||||||
\(11\) | −30601.5 | −0.190011 | −0.0950056 | − | 0.995477i | \(-0.530287\pi\) | ||||
−0.0950056 | + | 0.995477i | \(0.530287\pi\) | |||||||
\(12\) | − | 1.03661e6i | − | 4.16590i | ||||||
\(13\) | −11019.9 | −0.0296797 | −0.0148398 | − | 0.999890i | \(-0.504724\pi\) | ||||
−0.0148398 | + | 0.999890i | \(0.504724\pi\) | |||||||
\(14\) | −1.84510e6 | −3.43067 | ||||||||
\(15\) | 349540. | 0.460299 | ||||||||
\(16\) | 2.51904e6 | 2.40234 | ||||||||
\(17\) | 1.14659e6 | 0.807539 | 0.403769 | − | 0.914861i | \(-0.367700\pi\) | ||||
0.403769 | + | 0.914861i | \(0.367700\pi\) | |||||||
\(18\) | 6.92834e6i | 3.66662i | ||||||||
\(19\) | 4.19962e6i | 1.69606i | 0.529946 | + | 0.848032i | \(0.322212\pi\) | ||||
−0.529946 | + | 0.848032i | \(0.677788\pi\) | |||||||
\(20\) | 2.05549e6i | 0.642341i | ||||||||
\(21\) | 1.31075e7 | 3.20939 | ||||||||
\(22\) | 1.80859e6i | 0.350935i | ||||||||
\(23\) | −6.78637e6 | −1.05438 | −0.527192 | − | 0.849746i | \(-0.676755\pi\) | ||||
−0.527192 | + | 0.849746i | \(0.676755\pi\) | |||||||
\(24\) | −3.58555e7 | −4.50298 | ||||||||
\(25\) | 9.07252e6 | 0.929026 | ||||||||
\(26\) | 651289.i | 0.0548160i | ||||||||
\(27\) | − | 2.44266e7i | − | 1.70233i | ||||||
\(28\) | 7.70793e7i | 4.47866i | ||||||||
\(29\) | 2.48741e7i | 1.21271i | 0.795193 | + | 0.606356i | \(0.207369\pi\) | ||||
−0.795193 | + | 0.606356i | \(0.792631\pi\) | |||||||
\(30\) | − | 2.06583e7i | − | 0.850136i | ||||||
\(31\) | −3.61300e6 | −0.126200 | −0.0631000 | − | 0.998007i | \(-0.520099\pi\) | ||||
−0.0631000 | + | 0.998007i | \(0.520099\pi\) | |||||||
\(32\) | − | 6.14288e7i | − | 1.83072i | ||||||
\(33\) | − | 1.28481e7i | − | 0.328300i | ||||||
\(34\) | − | 6.77651e7i | − | 1.49146i | ||||||
\(35\) | −2.59908e7 | −0.494857 | ||||||||
\(36\) | 2.89433e8 | 4.78669 | ||||||||
\(37\) | 1.01376e8i | 1.46193i | 0.682414 | + | 0.730966i | \(0.260930\pi\) | ||||
−0.682414 | + | 0.730966i | \(0.739070\pi\) | |||||||
\(38\) | 2.48203e8 | 3.13249 | ||||||||
\(39\) | − | 4.62673e6i | − | 0.0512803i | ||||||
\(40\) | 7.10980e7 | 0.694316 | ||||||||
\(41\) | −3.57321e7 | −0.308418 | −0.154209 | − | 0.988038i | \(-0.549283\pi\) | ||||
−0.154209 | + | 0.988038i | \(0.549283\pi\) | |||||||
\(42\) | − | 7.74670e8i | − | 5.92748i | ||||||
\(43\) | −1.34018e8 | + | 6.04208e7i | −0.911634 | + | 0.411002i | ||||
\(44\) | 7.55544e7 | 0.458138 | ||||||||
\(45\) | 9.75955e7i | 0.528892i | ||||||||
\(46\) | 4.01084e8i | 1.94736i | ||||||||
\(47\) | 2.71560e8 | 1.18407 | 0.592034 | − | 0.805913i | \(-0.298325\pi\) | ||||
0.592034 | + | 0.805913i | \(0.298325\pi\) | |||||||
\(48\) | 1.05763e9i | 4.15074i | ||||||||
\(49\) | −6.92160e8 | −2.45034 | ||||||||
\(50\) | − | 5.36199e8i | − | 1.71584i | ||||||
\(51\) | 4.81400e8i | 1.39526i | ||||||||
\(52\) | 2.72078e7 | 0.0715610 | ||||||||
\(53\) | 4.96941e8 | 1.18830 | 0.594149 | − | 0.804355i | \(-0.297489\pi\) | ||||
0.594149 | + | 0.804355i | \(0.297489\pi\) | |||||||
\(54\) | −1.44365e9 | −3.14407 | ||||||||
\(55\) | 2.54766e7i | 0.0506207i | ||||||||
\(56\) | 2.66612e9 | 4.84105 | ||||||||
\(57\) | −1.76323e9 | −2.93044 | ||||||||
\(58\) | 1.47010e9 | 2.23978 | ||||||||
\(59\) | −6.47645e8 | −0.905893 | −0.452946 | − | 0.891538i | \(-0.649627\pi\) | ||||
−0.452946 | + | 0.891538i | \(0.649627\pi\) | |||||||
\(60\) | −8.63005e8 | −1.10983 | ||||||||
\(61\) | − | 5.21284e8i | − | 0.617199i | −0.951192 | − | 0.308599i | \(-0.900140\pi\) | ||
0.951192 | − | 0.308599i | \(-0.0998602\pi\) | |||||||
\(62\) | 2.13533e8i | 0.233081i | ||||||||
\(63\) | 3.65976e9i | 3.68765i | ||||||||
\(64\) | −1.05104e9 | −0.978855 | ||||||||
\(65\) | 9.17434e6i | 0.00790693i | ||||||||
\(66\) | −7.59343e8 | −0.606343 | ||||||||
\(67\) | 1.81540e9 | 1.34461 | 0.672307 | − | 0.740272i | \(-0.265303\pi\) | ||||
0.672307 | + | 0.740272i | \(0.265303\pi\) | |||||||
\(68\) | −2.83090e9 | −1.94706 | ||||||||
\(69\) | − | 2.84928e9i | − | 1.82176i | ||||||
\(70\) | 1.53609e9i | 0.913961i | ||||||||
\(71\) | − | 6.55571e8i | − | 0.363353i | −0.983358 | − | 0.181676i | \(-0.941848\pi\) | ||
0.983358 | − | 0.181676i | \(-0.0581523\pi\) | |||||||
\(72\) | − | 1.00113e10i | − | 5.17401i | ||||||
\(73\) | 2.34267e9i | 1.13005i | 0.825074 | + | 0.565024i | \(0.191133\pi\) | ||||
−0.825074 | + | 0.565024i | \(0.808867\pi\) | |||||||
\(74\) | 5.99147e9 | 2.70007 | ||||||||
\(75\) | 3.80913e9i | 1.60516i | ||||||||
\(76\) | − | 1.03688e10i | − | 4.08939i | ||||||
\(77\) | 9.55352e8i | 0.352947i | ||||||||
\(78\) | −2.73446e8 | −0.0947106 | ||||||||
\(79\) | 3.31775e9 | 1.07822 | 0.539110 | − | 0.842235i | \(-0.318761\pi\) | ||||
0.539110 | + | 0.842235i | \(0.318761\pi\) | |||||||
\(80\) | − | 2.09717e9i | − | 0.640005i | ||||||
\(81\) | 3.33341e9 | 0.956013 | ||||||||
\(82\) | 2.11182e9i | 0.569622i | ||||||||
\(83\) | −3.83424e9 | −0.973393 | −0.486697 | − | 0.873571i | \(-0.661798\pi\) | ||||
−0.486697 | + | 0.873571i | \(0.661798\pi\) | |||||||
\(84\) | −3.23620e10 | −7.73819 | ||||||||
\(85\) | − | 9.54568e8i | − | 0.215136i | ||||||
\(86\) | 3.57095e9 | + | 7.92065e9i | 0.759087 | + | 1.68371i | ||||
\(87\) | −1.04435e10 | −2.09531 | ||||||||
\(88\) | − | 2.61337e9i | − | 0.495208i | ||||||
\(89\) | 7.01136e9i | 1.25560i | 0.778373 | + | 0.627802i | \(0.216045\pi\) | ||||
−0.778373 | + | 0.627802i | \(0.783955\pi\) | |||||||
\(90\) | 5.76803e9 | 0.976822 | ||||||||
\(91\) | 3.44031e8i | 0.0551303i | ||||||||
\(92\) | 1.67554e10 | 2.54223 | ||||||||
\(93\) | − | 1.51693e9i | − | 0.218047i | ||||||
\(94\) | − | 1.60496e10i | − | 2.18688i | ||||||
\(95\) | 3.49630e9 | 0.451846 | ||||||||
\(96\) | 2.57911e10 | 3.16311 | ||||||||
\(97\) | −5.78385e9 | −0.673532 | −0.336766 | − | 0.941588i | \(-0.609333\pi\) | ||||
−0.336766 | + | 0.941588i | \(0.609333\pi\) | |||||||
\(98\) | 4.09076e10i | 4.52557i | ||||||||
\(99\) | 3.58735e9 | 0.377223 | ||||||||
\(100\) | −2.23998e10 | −2.23998 | ||||||||
\(101\) | −3.51511e9 | −0.334451 | −0.167226 | − | 0.985919i | \(-0.553481\pi\) | ||||
−0.167226 | + | 0.985919i | \(0.553481\pi\) | |||||||
\(102\) | 2.84514e10 | 2.57693 | ||||||||
\(103\) | 1.15282e10 | 0.994430 | 0.497215 | − | 0.867627i | \(-0.334356\pi\) | ||||
0.497215 | + | 0.867627i | \(0.334356\pi\) | |||||||
\(104\) | − | 9.41097e8i | − | 0.0773513i | ||||||
\(105\) | − | 1.09123e10i | − | 0.855010i | ||||||
\(106\) | − | 2.93699e10i | − | 2.19469i | ||||||
\(107\) | 5.33567e9 | 0.380426 | 0.190213 | − | 0.981743i | \(-0.439082\pi\) | ||||
0.190213 | + | 0.981743i | \(0.439082\pi\) | |||||||
\(108\) | 6.03088e10i | 4.10451i | ||||||||
\(109\) | −1.55469e10 | −1.01044 | −0.505221 | − | 0.862990i | \(-0.668589\pi\) | ||||
−0.505221 | + | 0.862990i | \(0.668589\pi\) | |||||||
\(110\) | 1.50570e9 | 0.0934923 | ||||||||
\(111\) | −4.25631e10 | −2.52591 | ||||||||
\(112\) | − | 7.86421e10i | − | 4.46237i | ||||||
\(113\) | − | 1.28377e10i | − | 0.696780i | −0.937350 | − | 0.348390i | \(-0.886728\pi\) | ||
0.937350 | − | 0.348390i | \(-0.113272\pi\) | |||||||
\(114\) | 1.04209e11i | 5.41229i | ||||||||
\(115\) | 5.64985e9i | 0.280897i | ||||||||
\(116\) | − | 6.14136e10i | − | 2.92398i | ||||||
\(117\) | 1.29184e9 | 0.0589220 | ||||||||
\(118\) | 3.82767e10i | 1.67311i | ||||||||
\(119\) | − | 3.57955e10i | − | 1.50001i | ||||||
\(120\) | 2.98507e10i | 1.19963i | ||||||||
\(121\) | −2.50010e10 | −0.963896 | ||||||||
\(122\) | −3.08086e10 | −1.13992 | ||||||||
\(123\) | − | 1.50022e10i | − | 0.532881i | ||||||
\(124\) | 8.92041e9 | 0.304282 | ||||||||
\(125\) | − | 1.56833e10i | − | 0.513910i | ||||||
\(126\) | 2.16297e11 | 6.81078 | ||||||||
\(127\) | 2.04030e10 | 0.617554 | 0.308777 | − | 0.951134i | \(-0.400080\pi\) | ||||
0.308777 | + | 0.951134i | \(0.400080\pi\) | |||||||
\(128\) | − | 7.85315e8i | − | 0.0228557i | ||||||
\(129\) | −2.53679e10 | − | 5.62679e10i | −0.710126 | − | 1.57511i | ||||
\(130\) | 5.42217e8 | 0.0146035 | ||||||||
\(131\) | 6.81112e10i | 1.76548i | 0.469864 | + | 0.882739i | \(0.344303\pi\) | ||||
−0.469864 | + | 0.882739i | \(0.655697\pi\) | |||||||
\(132\) | 3.17218e10i | 0.791567i | ||||||||
\(133\) | 1.31109e11 | 3.15045 | ||||||||
\(134\) | − | 1.07293e11i | − | 2.48339i | ||||||
\(135\) | −2.03358e10 | −0.453517 | ||||||||
\(136\) | 9.79189e10i | 2.10461i | ||||||||
\(137\) | 1.98461e10i | 0.411218i | 0.978634 | + | 0.205609i | \(0.0659175\pi\) | ||||
−0.978634 | + | 0.205609i | \(0.934083\pi\) | |||||||
\(138\) | −1.68397e11 | −3.36464 | ||||||||
\(139\) | −1.29281e10 | −0.249150 | −0.124575 | − | 0.992210i | \(-0.539757\pi\) | ||||
−0.124575 | + | 0.992210i | \(0.539757\pi\) | |||||||
\(140\) | 6.41707e10 | 1.19315 | ||||||||
\(141\) | 1.14016e11i | 2.04582i | ||||||||
\(142\) | −3.87452e10 | −0.671083 | ||||||||
\(143\) | 3.37224e8 | 0.00563947 | ||||||||
\(144\) | −2.95301e11 | −4.76928 | ||||||||
\(145\) | 2.07084e10 | 0.323077 | ||||||||
\(146\) | 1.38455e11 | 2.08711 | ||||||||
\(147\) | − | 2.90606e11i | − | 4.23367i | ||||||
\(148\) | − | 2.50295e11i | − | 3.52488i | ||||||
\(149\) | 8.07569e10i | 1.09963i | 0.835285 | + | 0.549817i | \(0.185303\pi\) | ||||
−0.835285 | + | 0.549817i | \(0.814697\pi\) | |||||||
\(150\) | 2.25125e11 | 2.96461 | ||||||||
\(151\) | − | 2.06213e10i | − | 0.262682i | −0.991337 | − | 0.131341i | \(-0.958072\pi\) | ||
0.991337 | − | 0.131341i | \(-0.0419283\pi\) | |||||||
\(152\) | −3.58648e11 | −4.42029 | ||||||||
\(153\) | −1.34412e11 | −1.60318 | ||||||||
\(154\) | 5.64627e10 | 0.651865 | ||||||||
\(155\) | 3.00792e9i | 0.0336208i | ||||||||
\(156\) | 1.14233e10i | 0.123642i | ||||||||
\(157\) | 5.75822e10i | 0.603656i | 0.953362 | + | 0.301828i | \(0.0975969\pi\) | ||||
−0.953362 | + | 0.301828i | \(0.902403\pi\) | |||||||
\(158\) | − | 1.96083e11i | − | 1.99139i | ||||||
\(159\) | 2.08642e11i | 2.05313i | ||||||||
\(160\) | −5.11412e10 | −0.487721 | ||||||||
\(161\) | 2.11865e11i | 1.95853i | ||||||||
\(162\) | − | 1.97009e11i | − | 1.76568i | ||||||
\(163\) | − | 1.01222e11i | − | 0.879707i | −0.898070 | − | 0.439853i | \(-0.855030\pi\) | ||
0.898070 | − | 0.439853i | \(-0.144970\pi\) | |||||||
\(164\) | 8.82217e10 | 0.743629 | ||||||||
\(165\) | −1.06964e10 | −0.0874620 | ||||||||
\(166\) | 2.26609e11i | 1.79778i | ||||||||
\(167\) | −1.61243e11 | −1.24136 | −0.620681 | − | 0.784063i | \(-0.713144\pi\) | ||||
−0.620681 | + | 0.784063i | \(0.713144\pi\) | |||||||
\(168\) | 1.11938e12i | 8.36432i | ||||||||
\(169\) | −1.37737e11 | −0.999119 | ||||||||
\(170\) | −5.64163e10 | −0.397338 | ||||||||
\(171\) | − | 4.92313e11i | − | 3.36714i | ||||||
\(172\) | 3.30887e11 | − | 1.49177e11i | 2.19805 | − | 0.990971i | ||||
\(173\) | −5.74774e10 | −0.370908 | −0.185454 | − | 0.982653i | \(-0.559376\pi\) | ||||
−0.185454 | + | 0.982653i | \(0.559376\pi\) | |||||||
\(174\) | 6.17225e11i | 3.86988i | ||||||||
\(175\) | − | 2.83236e11i | − | 1.72567i | ||||||
\(176\) | −7.70863e10 | −0.456472 | ||||||||
\(177\) | − | 2.71916e11i | − | 1.56519i | ||||||
\(178\) | 4.14381e11 | 2.31900 | ||||||||
\(179\) | − | 4.14002e10i | − | 0.225288i | −0.993635 | − | 0.112644i | \(-0.964068\pi\) | ||
0.993635 | − | 0.112644i | \(-0.0359319\pi\) | |||||||
\(180\) | − | 2.40961e11i | − | 1.27522i | ||||||
\(181\) | 1.16160e10 | 0.0597947 | 0.0298973 | − | 0.999553i | \(-0.490482\pi\) | ||||
0.0298973 | + | 0.999553i | \(0.490482\pi\) | |||||||
\(182\) | 2.03327e10 | 0.101821 | ||||||||
\(183\) | 2.18863e11 | 1.06639 | ||||||||
\(184\) | − | 5.79557e11i | − | 2.74794i | ||||||
\(185\) | 8.43985e10 | 0.389472 | ||||||||
\(186\) | −8.96527e10 | −0.402716 | ||||||||
\(187\) | −3.50874e10 | −0.153441 | ||||||||
\(188\) | −6.70476e11 | −2.85492 | ||||||||
\(189\) | −7.62578e11 | −3.16210 | ||||||||
\(190\) | − | 2.06636e11i | − | 0.834524i | ||||||
\(191\) | 1.75795e11i | 0.691575i | 0.938313 | + | 0.345787i | \(0.112388\pi\) | ||||
−0.938313 | + | 0.345787i | \(0.887612\pi\) | |||||||
\(192\) | − | 4.41282e11i | − | 1.69126i | ||||||
\(193\) | −8.33306e10 | −0.311184 | −0.155592 | − | 0.987821i | \(-0.549729\pi\) | ||||
−0.155592 | + | 0.987821i | \(0.549729\pi\) | |||||||
\(194\) | 3.41834e11i | 1.24396i | ||||||||
\(195\) | −3.85188e9 | −0.0136615 | ||||||||
\(196\) | 1.70893e12 | 5.90803 | ||||||||
\(197\) | 4.38324e10 | 0.147728 | 0.0738641 | − | 0.997268i | \(-0.476467\pi\) | ||||
0.0738641 | + | 0.997268i | \(0.476467\pi\) | |||||||
\(198\) | − | 2.12017e11i | − | 0.696700i | ||||||
\(199\) | − | 3.35527e11i | − | 1.07513i | −0.843221 | − | 0.537566i | \(-0.819344\pi\) | ||
0.843221 | − | 0.537566i | \(-0.180656\pi\) | |||||||
\(200\) | 7.74795e11i | 2.42123i | ||||||||
\(201\) | 7.62201e11i | 2.32321i | ||||||||
\(202\) | 2.07748e11i | 0.617704i | ||||||||
\(203\) | 7.76549e11 | 2.25262 | ||||||||
\(204\) | − | 1.18856e12i | − | 3.36412i | ||||||
\(205\) | 2.97480e10i | 0.0821652i | ||||||||
\(206\) | − | 6.81331e11i | − | 1.83663i | ||||||
\(207\) | 7.95553e11 | 2.09323 | ||||||||
\(208\) | −2.77594e10 | −0.0713007 | ||||||||
\(209\) | − | 1.28515e11i | − | 0.322271i | ||||||
\(210\) | −6.44934e11 | −1.57913 | ||||||||
\(211\) | 3.28767e11i | 0.786097i | 0.919518 | + | 0.393048i | \(0.128580\pi\) | ||||
−0.919518 | + | 0.393048i | \(0.871420\pi\) | |||||||
\(212\) | −1.22693e12 | −2.86512 | ||||||||
\(213\) | 2.75244e11 | 0.627798 | ||||||||
\(214\) | − | 3.15346e11i | − | 0.702616i | ||||||
\(215\) | 5.03020e10 | + | 1.11574e11i | 0.109495 | + | 0.242868i | ||||
\(216\) | 2.08604e12 | 4.43663 | ||||||||
\(217\) | 1.12795e11i | 0.234417i | ||||||||
\(218\) | 9.18844e11i | 1.86621i | ||||||||
\(219\) | −9.83579e11 | −1.95249 | ||||||||
\(220\) | − | 6.29011e10i | − | 0.122052i | ||||||
\(221\) | −1.26353e10 | −0.0239675 | ||||||||
\(222\) | 2.51554e12i | 4.66516i | ||||||||
\(223\) | − | 2.39669e11i | − | 0.434599i | −0.976105 | − | 0.217299i | \(-0.930275\pi\) | ||
0.976105 | − | 0.217299i | \(-0.0697248\pi\) | |||||||
\(224\) | −1.91776e12 | −3.40058 | ||||||||
\(225\) | −1.06355e12 | −1.84436 | ||||||||
\(226\) | −7.58728e11 | −1.28690 | ||||||||
\(227\) | − | 1.85715e11i | − | 0.308118i | −0.988062 | − | 0.154059i | \(-0.950765\pi\) | ||
0.988062 | − | 0.154059i | \(-0.0492346\pi\) | |||||||
\(228\) | 4.35336e12 | 7.06562 | ||||||||
\(229\) | 1.47897e11 | 0.234846 | 0.117423 | − | 0.993082i | \(-0.462537\pi\) | ||||
0.117423 | + | 0.993082i | \(0.462537\pi\) | |||||||
\(230\) | 3.33914e11 | 0.518795 | ||||||||
\(231\) | −4.01108e11 | −0.609820 | ||||||||
\(232\) | −2.12425e12 | −3.16058 | ||||||||
\(233\) | − | 2.30728e11i | − | 0.335985i | −0.985788 | − | 0.167992i | \(-0.946272\pi\) | ||
0.985788 | − | 0.167992i | \(-0.0537284\pi\) | |||||||
\(234\) | − | 7.63493e10i | − | 0.108824i | ||||||
\(235\) | − | 2.26082e11i | − | 0.315447i | ||||||
\(236\) | 1.59902e12 | 2.18421 | ||||||||
\(237\) | 1.39297e12i | 1.86294i | ||||||||
\(238\) | −2.11557e12 | −2.77040 | ||||||||
\(239\) | −4.08458e11 | −0.523791 | −0.261895 | − | 0.965096i | \(-0.584348\pi\) | ||||
−0.261895 | + | 0.965096i | \(0.584348\pi\) | |||||||
\(240\) | 8.80503e11 | 1.10580 | ||||||||
\(241\) | 8.99974e11i | 1.10699i | 0.832851 | + | 0.553497i | \(0.186707\pi\) | ||||
−0.832851 | + | 0.553497i | \(0.813293\pi\) | |||||||
\(242\) | 1.47759e12i | 1.78024i | ||||||||
\(243\) | − | 4.28238e10i | − | 0.0505421i | ||||||
\(244\) | 1.28704e12i | 1.48813i | ||||||||
\(245\) | 5.76242e11i | 0.652792i | ||||||||
\(246\) | −8.86654e11 | −0.984189 | ||||||||
\(247\) | − | 4.62792e10i | − | 0.0503386i | ||||||
\(248\) | − | 3.08550e11i | − | 0.328903i | ||||||
\(249\) | − | 1.60982e12i | − | 1.68182i | ||||||
\(250\) | −9.26904e11 | −0.949150 | ||||||||
\(251\) | −1.12564e12 | −1.12988 | −0.564939 | − | 0.825133i | \(-0.691100\pi\) | ||||
−0.564939 | + | 0.825133i | \(0.691100\pi\) | |||||||
\(252\) | − | 9.03585e12i | − | 8.89132i | ||||||
\(253\) | 2.07673e11 | 0.200345 | ||||||||
\(254\) | − | 1.20584e12i | − | 1.14057i | ||||||
\(255\) | 4.00779e11 | 0.371710 | ||||||||
\(256\) | −1.12268e12 | −1.02107 | ||||||||
\(257\) | 2.02956e12i | 1.81024i | 0.425154 | + | 0.905121i | \(0.360220\pi\) | ||||
−0.425154 | + | 0.905121i | \(0.639780\pi\) | |||||||
\(258\) | −3.32551e12 | + | 1.49928e12i | −2.90911 | + | 1.31155i | ||||
\(259\) | 3.16488e12 | 2.71555 | ||||||||
\(260\) | − | 2.26512e10i | − | 0.0190645i | ||||||
\(261\) | − | 2.91594e12i | − | 2.40756i | ||||||
\(262\) | 4.02547e12 | 3.26069 | ||||||||
\(263\) | 1.35423e12i | 1.07625i | 0.842866 | + | 0.538124i | \(0.180867\pi\) | ||||
−0.842866 | + | 0.538124i | \(0.819133\pi\) | |||||||
\(264\) | 1.09723e12 | 0.855617 | ||||||||
\(265\) | − | 4.13717e11i | − | 0.316573i | ||||||
\(266\) | − | 7.74870e12i | − | 5.81863i | ||||||
\(267\) | −2.94375e12 | −2.16942 | ||||||||
\(268\) | −4.48218e12 | −3.24201 | ||||||||
\(269\) | 1.52798e12 | 1.08482 | 0.542408 | − | 0.840115i | \(-0.317513\pi\) | ||||
0.542408 | + | 0.840115i | \(0.317513\pi\) | |||||||
\(270\) | 1.20188e12i | 0.837609i | ||||||||
\(271\) | −1.08870e12 | −0.744839 | −0.372420 | − | 0.928064i | \(-0.621472\pi\) | ||||
−0.372420 | + | 0.928064i | \(0.621472\pi\) | |||||||
\(272\) | 2.88830e12 | 1.93998 | ||||||||
\(273\) | −1.44442e11 | −0.0952536 | ||||||||
\(274\) | 1.17293e12 | 0.759486 | ||||||||
\(275\) | −2.77633e11 | −0.176525 | ||||||||
\(276\) | 7.03481e12i | 4.39245i | ||||||||
\(277\) | 1.26133e12i | 0.773448i | 0.922196 | + | 0.386724i | \(0.126393\pi\) | ||||
−0.922196 | + | 0.386724i | \(0.873607\pi\) | |||||||
\(278\) | 7.64070e11i | 0.460160i | ||||||||
\(279\) | 4.23544e11 | 0.250540 | ||||||||
\(280\) | − | 2.21962e12i | − | 1.28970i | ||||||
\(281\) | 9.77086e11 | 0.557701 | 0.278850 | − | 0.960335i | \(-0.410047\pi\) | ||||
0.278850 | + | 0.960335i | \(0.410047\pi\) | |||||||
\(282\) | 6.73848e12 | 3.77847 | ||||||||
\(283\) | 1.67181e12 | 0.920989 | 0.460494 | − | 0.887663i | \(-0.347672\pi\) | ||||
0.460494 | + | 0.887663i | \(0.347672\pi\) | |||||||
\(284\) | 1.61859e12i | 0.876083i | ||||||||
\(285\) | 1.46793e12i | 0.780697i | ||||||||
\(286\) | − | 1.99304e10i | − | 0.0104156i | ||||||
\(287\) | 1.11553e12i | 0.572888i | ||||||||
\(288\) | 7.20118e12i | 3.63447i | ||||||||
\(289\) | −7.01326e11 | −0.347881 | ||||||||
\(290\) | − | 1.22390e12i | − | 0.596698i | ||||||
\(291\) | − | 2.42837e12i | − | 1.16372i | ||||||
\(292\) | − | 5.78400e12i | − | 2.72467i | ||||||
\(293\) | 2.94397e12 | 1.36331 | 0.681656 | − | 0.731673i | \(-0.261260\pi\) | ||||
0.681656 | + | 0.731673i | \(0.261260\pi\) | |||||||
\(294\) | −1.71752e13 | −7.81925 | ||||||||
\(295\) | 5.39182e11i | 0.241338i | ||||||||
\(296\) | −8.65753e12 | −3.81009 | ||||||||
\(297\) | 7.47491e11i | 0.323462i | ||||||||
\(298\) | 4.77285e12 | 2.03094 | ||||||||
\(299\) | 7.47849e10 | 0.0312938 | ||||||||
\(300\) | − | 9.40465e12i | − | 3.87023i | ||||||
\(301\) | 1.88628e12 | + | 4.18393e12i | 0.763440 | + | 1.69337i | ||||
\(302\) | −1.21875e12 | −0.485152 | ||||||||
\(303\) | − | 1.47583e12i | − | 0.577862i | ||||||
\(304\) | 1.05790e13i | 4.07452i | ||||||||
\(305\) | −4.33983e11 | −0.164427 | ||||||||
\(306\) | 7.94396e12i | 2.96094i | ||||||||
\(307\) | −1.62167e11 | −0.0594661 | −0.0297330 | − | 0.999558i | \(-0.509466\pi\) | ||||
−0.0297330 | + | 0.999558i | \(0.509466\pi\) | |||||||
\(308\) | − | 2.35874e12i | − | 0.850995i | ||||||
\(309\) | 4.84014e12i | 1.71817i | ||||||||
\(310\) | 1.77772e11 | 0.0620949 | ||||||||
\(311\) | −1.80279e12 | −0.619646 | −0.309823 | − | 0.950794i | \(-0.600270\pi\) | ||||
−0.309823 | + | 0.950794i | \(0.600270\pi\) | |||||||
\(312\) | 3.95123e11 | 0.133647 | ||||||||
\(313\) | − | 4.74297e12i | − | 1.57881i | −0.613876 | − | 0.789403i | \(-0.710390\pi\) | ||
0.613876 | − | 0.789403i | \(-0.289610\pi\) | |||||||
\(314\) | 3.40319e12 | 1.11490 | ||||||||
\(315\) | 3.04685e12 | 0.982422 | ||||||||
\(316\) | −8.19144e12 | −2.59971 | ||||||||
\(317\) | 3.23655e12 | 1.01108 | 0.505541 | − | 0.862803i | \(-0.331293\pi\) | ||||
0.505541 | + | 0.862803i | \(0.331293\pi\) | |||||||
\(318\) | 1.23310e13 | 3.79197 | ||||||||
\(319\) | − | 7.61185e11i | − | 0.230429i | ||||||
\(320\) | 8.75018e11i | 0.260776i | ||||||||
\(321\) | 2.24020e12i | 0.657297i | ||||||||
\(322\) | 1.25215e13 | 3.61724 | ||||||||
\(323\) | 4.81524e12i | 1.36964i | ||||||||
\(324\) | −8.23011e12 | −2.30505 | ||||||||
\(325\) | −9.99779e10 | −0.0275732 | ||||||||
\(326\) | −5.98238e12 | −1.62475 | ||||||||
\(327\) | − | 6.52742e12i | − | 1.74583i | ||||||
\(328\) | − | 3.05153e12i | − | 0.803799i | ||||||
\(329\) | − | 8.47788e12i | − | 2.19942i | ||||||
\(330\) | 6.32175e11i | 0.161535i | ||||||||
\(331\) | − | 5.02102e12i | − | 1.26372i | −0.775081 | − | 0.631862i | \(-0.782291\pi\) | ||
0.775081 | − | 0.631862i | \(-0.217709\pi\) | |||||||
\(332\) | 9.46664e12 | 2.34696 | ||||||||
\(333\) | − | 1.18841e13i | − | 2.90232i | ||||||
\(334\) | 9.52969e12i | 2.29270i | ||||||||
\(335\) | − | 1.51137e12i | − | 0.358217i | ||||||
\(336\) | 3.30182e13 | 7.71004 | ||||||||
\(337\) | 3.22069e12 | 0.740967 | 0.370483 | − | 0.928839i | \(-0.379192\pi\) | ||||
0.370483 | + | 0.928839i | \(0.379192\pi\) | |||||||
\(338\) | 8.14045e12i | 1.84529i | ||||||||
\(339\) | 5.38996e12 | 1.20389 | ||||||||
\(340\) | 2.35681e12i | 0.518716i | ||||||||
\(341\) | 1.10563e11 | 0.0239794 | ||||||||
\(342\) | −2.90964e13 | −6.21883 | ||||||||
\(343\) | 1.27900e13i | 2.69401i | ||||||||
\(344\) | −5.15994e12 | − | 1.14452e13i | −1.07116 | − | 2.37591i | ||||
\(345\) | −2.37211e12 | −0.485332 | ||||||||
\(346\) | 3.39699e12i | 0.685037i | ||||||||
\(347\) | − | 1.79363e12i | − | 0.356521i | −0.983983 | − | 0.178260i | \(-0.942953\pi\) | ||
0.983983 | − | 0.178260i | \(-0.0570469\pi\) | |||||||
\(348\) | 2.57847e13 | 5.05203 | ||||||||
\(349\) | 1.98981e12i | 0.384312i | 0.981364 | + | 0.192156i | \(0.0615480\pi\) | ||||
−0.981364 | + | 0.192156i | \(0.938452\pi\) | |||||||
\(350\) | −1.67397e13 | −3.18718 | ||||||||
\(351\) | 2.69178e11i | 0.0505247i | ||||||||
\(352\) | 1.87981e12i | 0.347858i | ||||||||
\(353\) | −6.67536e12 | −1.21787 | −0.608935 | − | 0.793220i | \(-0.708403\pi\) | ||||
−0.608935 | + | 0.793220i | \(0.708403\pi\) | |||||||
\(354\) | −1.60706e13 | −2.89079 | ||||||||
\(355\) | −5.45782e11 | −0.0968004 | ||||||||
\(356\) | − | 1.73109e13i | − | 3.02740i | ||||||
\(357\) | 1.50289e13 | 2.59171 | ||||||||
\(358\) | −2.44681e12 | −0.416088 | ||||||||
\(359\) | −4.33742e12 | −0.727376 | −0.363688 | − | 0.931521i | \(-0.618483\pi\) | ||||
−0.363688 | + | 0.931521i | \(0.618483\pi\) | |||||||
\(360\) | −8.33467e12 | −1.37840 | ||||||||
\(361\) | −1.15057e13 | −1.87663 | ||||||||
\(362\) | − | 6.86520e11i | − | 0.110436i | ||||||
\(363\) | − | 1.04967e13i | − | 1.66541i | ||||||
\(364\) | − | 8.49403e11i | − | 0.132925i | ||||||
\(365\) | 1.95034e12 | 0.301055 | ||||||||
\(366\) | − | 1.29351e13i | − | 1.96954i | ||||||
\(367\) | −6.86650e12 | −1.03135 | −0.515674 | − | 0.856785i | \(-0.672458\pi\) | ||||
−0.515674 | + | 0.856785i | \(0.672458\pi\) | |||||||
\(368\) | −1.70951e13 | −2.53299 | ||||||||
\(369\) | 4.18880e12 | 0.612291 | ||||||||
\(370\) | − | 4.98807e12i | − | 0.719323i | ||||||
\(371\) | − | 1.55141e13i | − | 2.20727i | ||||||
\(372\) | 3.74526e12i | 0.525736i | ||||||||
\(373\) | 3.72115e12i | 0.515386i | 0.966227 | + | 0.257693i | \(0.0829623\pi\) | ||||
−0.966227 | + | 0.257693i | \(0.917038\pi\) | |||||||
\(374\) | 2.07371e12i | 0.283394i | ||||||||
\(375\) | 6.58468e12 | 0.887929 | ||||||||
\(376\) | 2.31913e13i | 3.08593i | ||||||||
\(377\) | − | 2.74109e11i | − | 0.0359929i | ||||||
\(378\) | 4.50694e13i | 5.84014i | ||||||||
\(379\) | 7.27747e12 | 0.930646 | 0.465323 | − | 0.885141i | \(-0.345938\pi\) | ||||
0.465323 | + | 0.885141i | \(0.345938\pi\) | |||||||
\(380\) | −8.63229e12 | −1.08945 | ||||||||
\(381\) | 8.56626e12i | 1.06700i | ||||||||
\(382\) | 1.03897e13 | 1.27728 | ||||||||
\(383\) | 1.39131e13i | 1.68822i | 0.536168 | + | 0.844112i | \(0.319872\pi\) | ||||
−0.536168 | + | 0.844112i | \(0.680128\pi\) | |||||||
\(384\) | 3.29717e11 | 0.0394899 | ||||||||
\(385\) | 7.95358e11 | 0.0940284 | ||||||||
\(386\) | 4.92496e12i | 0.574732i | ||||||||
\(387\) | 1.57106e13 | − | 7.08300e12i | 1.80984 | − | 0.815948i | ||||
\(388\) | 1.42802e13 | 1.62396 | ||||||||
\(389\) | 5.23131e12i | 0.587303i | 0.955912 | + | 0.293652i | \(0.0948706\pi\) | ||||
−0.955912 | + | 0.293652i | \(0.905129\pi\) | |||||||
\(390\) | 2.27651e11i | 0.0252318i | ||||||||
\(391\) | −7.78119e12 | −0.851456 | ||||||||
\(392\) | − | 5.91105e13i | − | 6.38608i | ||||||
\(393\) | −2.85967e13 | −3.05038 | ||||||||
\(394\) | − | 2.59055e12i | − | 0.272842i | ||||||
\(395\) | − | 2.76212e12i | − | 0.287248i | ||||||
\(396\) | −8.85708e12 | −0.909525 | ||||||||
\(397\) | −3.23534e12 | −0.328071 | −0.164035 | − | 0.986454i | \(-0.552451\pi\) | ||||
−0.164035 | + | 0.986454i | \(0.552451\pi\) | |||||||
\(398\) | −1.98301e13 | −1.98568 | ||||||||
\(399\) | 5.50464e13i | 5.44333i | ||||||||
\(400\) | 2.28540e13 | 2.23184 | ||||||||
\(401\) | 6.71315e12 | 0.647448 | 0.323724 | − | 0.946152i | \(-0.395065\pi\) | ||||
0.323724 | + | 0.946152i | \(0.395065\pi\) | |||||||
\(402\) | 4.50472e13 | 4.29079 | ||||||||
\(403\) | 3.98147e10 | 0.00374558 | ||||||||
\(404\) | 8.67873e12 | 0.806398 | ||||||||
\(405\) | − | 2.77516e12i | − | 0.254690i | ||||||
\(406\) | − | 4.58951e13i | − | 4.16041i | ||||||
\(407\) | − | 3.10226e12i | − | 0.277783i | ||||||
\(408\) | −4.11116e13 | −3.63633 | ||||||||
\(409\) | − | 3.76964e12i | − | 0.329369i | −0.986346 | − | 0.164685i | \(-0.947339\pi\) | ||
0.986346 | − | 0.164685i | \(-0.0526606\pi\) | |||||||
\(410\) | 1.75815e12 | 0.151752 | ||||||||
\(411\) | −8.33244e12 | −0.710499 | ||||||||
\(412\) | −2.84628e13 | −2.39768 | ||||||||
\(413\) | 2.02189e13i | 1.68270i | ||||||||
\(414\) | − | 4.70183e13i | − | 3.86603i | ||||||
\(415\) | 3.19211e12i | 0.259321i | ||||||||
\(416\) | 6.76937e11i | 0.0543353i | ||||||||
\(417\) | − | 5.42792e12i | − | 0.430480i | ||||||
\(418\) | −7.59540e12 | −0.595208 | ||||||||
\(419\) | 5.70342e12i | 0.441636i | 0.975315 | + | 0.220818i | \(0.0708728\pi\) | ||||
−0.975315 | + | 0.220818i | \(0.929127\pi\) | |||||||
\(420\) | 2.69423e13i | 2.06152i | ||||||||
\(421\) | − | 6.78163e12i | − | 0.512771i | −0.966575 | − | 0.256386i | \(-0.917468\pi\) | ||
0.966575 | − | 0.256386i | \(-0.0825317\pi\) | |||||||
\(422\) | 1.94306e13 | 1.45186 | ||||||||
\(423\) | −3.18345e13 | −2.35069 | ||||||||
\(424\) | 4.24388e13i | 3.09695i | ||||||||
\(425\) | 1.04025e13 | 0.750225 | ||||||||
\(426\) | − | 1.62673e13i | − | 1.15949i | ||||||
\(427\) | −1.62740e13 | −1.14645 | ||||||||
\(428\) | −1.31736e13 | −0.917249 | ||||||||
\(429\) | 1.41585e11i | 0.00974384i | ||||||||
\(430\) | 6.59416e12 | − | 2.97292e12i | 0.448557 | − | 0.202228i | ||||
\(431\) | 1.47502e13 | 0.991769 | 0.495884 | − | 0.868389i | \(-0.334844\pi\) | ||||
0.495884 | + | 0.868389i | \(0.334844\pi\) | |||||||
\(432\) | − | 6.15315e13i | − | 4.08958i | ||||||
\(433\) | 4.40794e12i | 0.289598i | 0.989461 | + | 0.144799i | \(0.0462536\pi\) | ||||
−0.989461 | + | 0.144799i | \(0.953746\pi\) | |||||||
\(434\) | 6.66632e12 | 0.432950 | ||||||||
\(435\) | 8.69450e12i | 0.558211i | ||||||||
\(436\) | 3.83850e13 | 2.43629 | ||||||||
\(437\) | − | 2.85002e13i | − | 1.78830i | ||||||
\(438\) | 5.81309e13i | 3.60609i | ||||||||
\(439\) | −2.34447e13 | −1.43788 | −0.718938 | − | 0.695074i | \(-0.755371\pi\) | ||||
−0.718938 | + | 0.695074i | \(0.755371\pi\) | |||||||
\(440\) | −2.17571e12 | −0.131928 | ||||||||
\(441\) | 8.11404e13 | 4.86457 | ||||||||
\(442\) | 7.46761e11i | 0.0442660i | ||||||||
\(443\) | −2.81507e13 | −1.64995 | −0.824975 | − | 0.565169i | \(-0.808811\pi\) | ||||
−0.824975 | + | 0.565169i | \(0.808811\pi\) | |||||||
\(444\) | 1.05087e14 | 6.09026 | ||||||||
\(445\) | 5.83716e12 | 0.334504 | ||||||||
\(446\) | −1.41648e13 | −0.802669 | ||||||||
\(447\) | −3.39061e13 | −1.89994 | ||||||||
\(448\) | 3.28125e13i | 1.81823i | ||||||||
\(449\) | 1.80546e13i | 0.989363i | 0.869074 | + | 0.494681i | \(0.164715\pi\) | ||||
−0.869074 | + | 0.494681i | \(0.835285\pi\) | |||||||
\(450\) | 6.28575e13i | 3.40639i | ||||||||
\(451\) | 1.09346e12 | 0.0586028 | ||||||||
\(452\) | 3.16960e13i | 1.68001i | ||||||||
\(453\) | 8.65791e12 | 0.453860 | ||||||||
\(454\) | −1.09760e13 | −0.569069 | ||||||||
\(455\) | 2.86415e11 | 0.0146872 | ||||||||
\(456\) | − | 1.50580e14i | − | 7.63734i | ||||||
\(457\) | − | 1.63525e13i | − | 0.820357i | −0.912005 | − | 0.410179i | \(-0.865466\pi\) | ||
0.912005 | − | 0.410179i | \(-0.134534\pi\) | |||||||
\(458\) | − | 8.74093e12i | − | 0.433741i | ||||||
\(459\) | − | 2.80073e13i | − | 1.37470i | ||||||
\(460\) | − | 1.39493e13i | − | 0.677274i | ||||||
\(461\) | −2.03281e13 | −0.976321 | −0.488161 | − | 0.872754i | \(-0.662332\pi\) | ||||
−0.488161 | + | 0.872754i | \(0.662332\pi\) | |||||||
\(462\) | 2.37060e13i | 1.12629i | ||||||||
\(463\) | − | 1.17169e13i | − | 0.550689i | −0.961346 | − | 0.275345i | \(-0.911208\pi\) | ||
0.961346 | − | 0.275345i | \(-0.0887919\pi\) | |||||||
\(464\) | 6.26588e13i | 2.91335i | ||||||||
\(465\) | −1.26289e12 | −0.0580898 | ||||||||
\(466\) | −1.36363e13 | −0.620537 | ||||||||
\(467\) | 2.71597e13i | 1.22276i | 0.791337 | + | 0.611380i | \(0.209385\pi\) | ||||
−0.791337 | + | 0.611380i | \(0.790615\pi\) | |||||||
\(468\) | −3.18951e12 | −0.142068 | ||||||||
\(469\) | − | 5.66752e13i | − | 2.49763i | ||||||
\(470\) | −1.33617e13 | −0.582604 | ||||||||
\(471\) | −2.41761e13 | −1.04299 | ||||||||
\(472\) | − | 5.53089e13i | − | 2.36094i | ||||||
\(473\) | 4.10115e12 | − | 1.84897e12i | 0.173221 | − | 0.0780950i | ||||
\(474\) | 8.23263e13 | 3.44070 | ||||||||
\(475\) | 3.81012e13i | 1.57569i | ||||||||
\(476\) | 8.83784e13i | 3.61669i | ||||||||
\(477\) | −5.82553e13 | −2.35909 | ||||||||
\(478\) | 2.41404e13i | 0.967399i | ||||||||
\(479\) | 3.61505e13 | 1.43363 | 0.716815 | − | 0.697263i | \(-0.245599\pi\) | ||||
0.716815 | + | 0.697263i | \(0.245599\pi\) | |||||||
\(480\) | − | 2.14718e13i | − | 0.842680i | ||||||
\(481\) | − | 1.11715e12i | − | 0.0433897i | ||||||
\(482\) | 5.31897e13 | 2.04453 | ||||||||
\(483\) | −8.89522e13 | −3.38393 | ||||||||
\(484\) | 6.17268e13 | 2.32406 | ||||||||
\(485\) | 4.81522e12i | 0.179435i | ||||||||
\(486\) | −2.53095e12 | −0.0933472 | ||||||||
\(487\) | −1.13607e13 | −0.414727 | −0.207363 | − | 0.978264i | \(-0.566488\pi\) | ||||
−0.207363 | + | 0.978264i | \(0.566488\pi\) | |||||||
\(488\) | 4.45177e13 | 1.60855 | ||||||||
\(489\) | 4.24985e13 | 1.51995 | ||||||||
\(490\) | 3.40567e13 | 1.20565 | ||||||||
\(491\) | − | 3.37611e13i | − | 1.18307i | −0.806280 | − | 0.591534i | \(-0.798523\pi\) | ||
0.806280 | − | 0.591534i | \(-0.201477\pi\) | |||||||
\(492\) | 3.70402e13i | 1.28484i | ||||||||
\(493\) | 2.85204e13i | 0.979312i | ||||||||
\(494\) | −2.73517e12 | −0.0929714 | ||||||||
\(495\) | − | 2.98657e12i | − | 0.100496i | ||||||
\(496\) | −9.10127e12 | −0.303175 | ||||||||
\(497\) | −2.04664e13 | −0.674931 | ||||||||
\(498\) | −9.51425e13 | −3.10619 | ||||||||
\(499\) | − | 1.56284e13i | − | 0.505142i | −0.967578 | − | 0.252571i | \(-0.918724\pi\) | ||
0.967578 | − | 0.252571i | \(-0.0812761\pi\) | |||||||
\(500\) | 3.87217e13i | 1.23909i | ||||||||
\(501\) | − | 6.76985e13i | − | 2.14482i | ||||||
\(502\) | 6.65269e13i | 2.08679i | ||||||||
\(503\) | 1.88419e13i | 0.585172i | 0.956239 | + | 0.292586i | \(0.0945158\pi\) | ||||
−0.956239 | + | 0.292586i | \(0.905484\pi\) | |||||||
\(504\) | −3.12544e14 | −9.61076 | ||||||||
\(505\) | 2.92643e12i | 0.0891008i | ||||||||
\(506\) | − | 1.22738e13i | − | 0.370020i | ||||||
\(507\) | − | 5.78294e13i | − | 1.72627i | ||||||
\(508\) | −5.03744e13 | −1.48899 | ||||||||
\(509\) | −3.67101e13 | −1.07448 | −0.537238 | − | 0.843431i | \(-0.680532\pi\) | ||||
−0.537238 | + | 0.843431i | \(0.680532\pi\) | |||||||
\(510\) | − | 2.36866e13i | − | 0.686517i | ||||||
\(511\) | 7.31362e13 | 2.09907 | ||||||||
\(512\) | 6.55476e13i | 1.86297i | ||||||||
\(513\) | 1.02583e14 | 2.88727 | ||||||||
\(514\) | 1.19950e14 | 3.34337 | ||||||||
\(515\) | − | 9.59752e12i | − | 0.264925i | ||||||
\(516\) | 6.26327e13 | + | 1.38924e14i | 1.71219 | + | 3.79777i | ||||
\(517\) | −8.31015e12 | −0.224986 | ||||||||
\(518\) | − | 1.87049e14i | − | 5.01540i | ||||||
\(519\) | − | 2.41321e13i | − | 0.640852i | ||||||
\(520\) | −7.83490e11 | −0.0206071 | ||||||||
\(521\) | 5.47337e13i | 1.42583i | 0.701253 | + | 0.712913i | \(0.252624\pi\) | ||||
−0.701253 | + | 0.712913i | \(0.747376\pi\) | |||||||
\(522\) | −1.72336e14 | −4.44656 | ||||||||
\(523\) | − | 8.36353e12i | − | 0.213738i | −0.994273 | − | 0.106869i | \(-0.965917\pi\) | ||
0.994273 | − | 0.106869i | \(-0.0340825\pi\) | |||||||
\(524\) | − | 1.68165e14i | − | 4.25676i | ||||||
\(525\) | 1.18918e14 | 2.98161 | ||||||||
\(526\) | 8.00367e13 | 1.98774 | ||||||||
\(527\) | −4.14263e12 | −0.101911 | ||||||||
\(528\) | − | 3.23649e13i | − | 0.788688i | ||||||
\(529\) | 4.62837e12 | 0.111725 | ||||||||
\(530\) | −2.44513e13 | −0.584685 | ||||||||
\(531\) | 7.59220e13 | 1.79844 | ||||||||
\(532\) | −3.23704e14 | −7.59608 | ||||||||
\(533\) | 3.93763e11 | 0.00915374 | ||||||||
\(534\) | 1.73980e14i | 4.00675i | ||||||||
\(535\) | − | 4.44210e12i | − | 0.101349i | ||||||
\(536\) | 1.55035e14i | 3.50434i | ||||||||
\(537\) | 1.73820e13 | 0.389251 | ||||||||
\(538\) | − | 9.03058e13i | − | 2.00357i | ||||||
\(539\) | 2.11811e13 | 0.465592 | ||||||||
\(540\) | 5.02087e13 | 1.09348 | ||||||||
\(541\) | −3.55836e13 | −0.767828 | −0.383914 | − | 0.923369i | \(-0.625424\pi\) | ||||
−0.383914 | + | 0.923369i | \(0.625424\pi\) | |||||||
\(542\) | 6.43438e13i | 1.37566i | ||||||||
\(543\) | 4.87700e12i | 0.103313i | ||||||||
\(544\) | − | 7.04337e13i | − | 1.47838i | ||||||
\(545\) | 1.29432e13i | 0.269191i | ||||||||
\(546\) | 8.53675e12i | 0.175926i | ||||||||
\(547\) | 7.88966e13 | 1.61110 | 0.805548 | − | 0.592530i | \(-0.201871\pi\) | ||||
0.805548 | + | 0.592530i | \(0.201871\pi\) | |||||||
\(548\) | − | 4.89995e13i | − | 0.991491i | ||||||
\(549\) | 6.11090e13i | 1.22530i | ||||||||
\(550\) | 1.64085e13i | 0.326028i | ||||||||
\(551\) | −1.04462e14 | −2.05684 | ||||||||
\(552\) | 2.43329e14 | 4.74787 | ||||||||
\(553\) | − | 1.03577e14i | − | 2.00280i | ||||||
\(554\) | 7.45466e13 | 1.42850 | ||||||||
\(555\) | 3.54350e13i | 0.672926i | ||||||||
\(556\) | 3.19192e13 | 0.600729 | ||||||||
\(557\) | −8.83010e13 | −1.64699 | −0.823493 | − | 0.567327i | \(-0.807978\pi\) | ||||
−0.823493 | + | 0.567327i | \(0.807978\pi\) | |||||||
\(558\) | − | 2.50321e13i | − | 0.462728i | ||||||
\(559\) | 1.47686e12 | − | 6.65828e11i | 0.0270570 | − | 0.0121984i | ||||
\(560\) | −6.54718e13 | −1.18881 | ||||||||
\(561\) | − | 1.47315e13i | − | 0.265115i | ||||||
\(562\) | − | 5.77472e13i | − | 1.03003i | ||||||
\(563\) | 3.50978e13 | 0.620495 | 0.310247 | − | 0.950656i | \(-0.399588\pi\) | ||||
0.310247 | + | 0.950656i | \(0.399588\pi\) | |||||||
\(564\) | − | 2.81502e14i | − | 4.93271i | ||||||
\(565\) | −1.06878e13 | −0.185629 | ||||||||
\(566\) | − | 9.88063e13i | − | 1.70099i | ||||||
\(567\) | − | 1.04066e14i | − | 1.77580i | ||||||
\(568\) | 5.59859e13 | 0.946971 | ||||||||
\(569\) | −3.13808e13 | −0.526141 | −0.263071 | − | 0.964777i | \(-0.584735\pi\) | ||||
−0.263071 | + | 0.964777i | \(0.584735\pi\) | |||||||
\(570\) | 8.67570e13 | 1.44188 | ||||||||
\(571\) | − | 8.66236e13i | − | 1.42710i | −0.700602 | − | 0.713552i | \(-0.747085\pi\) | ||
0.700602 | − | 0.713552i | \(-0.252915\pi\) | |||||||
\(572\) | −8.32598e11 | −0.0135974 | ||||||||
\(573\) | −7.38081e13 | −1.19490 | ||||||||
\(574\) | 6.59291e13 | 1.05808 | ||||||||
\(575\) | −6.15695e13 | −0.979550 | ||||||||
\(576\) | 1.23211e14 | 1.94329 | ||||||||
\(577\) | 4.60046e13i | 0.719321i | 0.933083 | + | 0.359660i | \(0.117107\pi\) | ||||
−0.933083 | + | 0.359660i | \(0.882893\pi\) | |||||||
\(578\) | 4.14494e13i | 0.642508i | ||||||||
\(579\) | − | 3.49866e13i | − | 0.537662i | ||||||
\(580\) | −5.11286e13 | −0.778975 | ||||||||
\(581\) | 1.19702e14i | 1.80809i | ||||||||
\(582\) | −1.43520e14 | −2.14930 | ||||||||
\(583\) | −1.52071e13 | −0.225790 | ||||||||
\(584\) | −2.00064e14 | −2.94514 | ||||||||
\(585\) | − | 1.07549e12i | − | 0.0156974i | ||||||
\(586\) | − | 1.73993e14i | − | 2.51793i | ||||||
\(587\) | 1.77739e12i | 0.0255031i | 0.999919 | + | 0.0127515i | \(0.00405905\pi\) | ||||
−0.999919 | + | 0.0127515i | \(0.995941\pi\) | |||||||
\(588\) | 7.17498e14i | 10.2079i | ||||||||
\(589\) | − | 1.51732e13i | − | 0.214043i | ||||||
\(590\) | 3.18664e13 | 0.445732 | ||||||||
\(591\) | 1.84032e13i | 0.255244i | ||||||||
\(592\) | 2.55370e14i | 3.51206i | ||||||||
\(593\) | 8.29707e12i | 0.113149i | 0.998398 | + | 0.0565746i | \(0.0180179\pi\) | ||||
−0.998398 | + | 0.0565746i | \(0.981982\pi\) | |||||||
\(594\) | 4.41778e13 | 0.597409 | ||||||||
\(595\) | −2.98008e13 | −0.399616 | ||||||||
\(596\) | − | 1.99387e14i | − | 2.65134i | ||||||
\(597\) | 1.40872e14 | 1.85761 | ||||||||
\(598\) | − | 4.41989e12i | − | 0.0577971i | ||||||
\(599\) | −6.78681e13 | −0.880100 | −0.440050 | − | 0.897973i | \(-0.645039\pi\) | ||||
−0.440050 | + | 0.897973i | \(0.645039\pi\) | |||||||
\(600\) | −3.25300e14 | −4.18339 | ||||||||
\(601\) | 1.16255e13i | 0.148265i | 0.997248 | + | 0.0741325i | \(0.0236188\pi\) | ||||
−0.997248 | + | 0.0741325i | \(0.976381\pi\) | |||||||
\(602\) | 2.47276e14 | − | 1.11482e14i | 3.12751 | − | 1.41001i | ||||
\(603\) | −2.12815e14 | −2.66942 | ||||||||
\(604\) | 5.09134e13i | 0.633355i | ||||||||
\(605\) | 2.08140e13i | 0.256790i | ||||||||
\(606\) | −8.72238e13 | −1.06726 | ||||||||
\(607\) | − | 3.16649e13i | − | 0.384269i | −0.981369 | − | 0.192134i | \(-0.938459\pi\) | ||
0.981369 | − | 0.192134i | \(-0.0615409\pi\) | |||||||
\(608\) | 2.57978e14 | 3.10502 | ||||||||
\(609\) | 3.26037e14i | 3.89206i | ||||||||
\(610\) | 2.56490e13i | 0.303684i | ||||||||
\(611\) | −2.99256e12 | −0.0351428 | ||||||||
\(612\) | 3.31861e14 | 3.86544 | ||||||||
\(613\) | 8.80871e13 | 1.01768 | 0.508839 | − | 0.860862i | \(-0.330075\pi\) | ||||
0.508839 | + | 0.860862i | \(0.330075\pi\) | |||||||
\(614\) | 9.58427e12i | 0.109829i | ||||||||
\(615\) | −1.24898e13 | −0.141964 | ||||||||
\(616\) | −8.15872e13 | −0.919853 | ||||||||
\(617\) | −8.82304e12 | −0.0986717 | −0.0493358 | − | 0.998782i | \(-0.515710\pi\) | ||||
−0.0493358 | + | 0.998782i | \(0.515710\pi\) | |||||||
\(618\) | 2.86059e14 | 3.17332 | ||||||||
\(619\) | 5.83774e13 | 0.642380 | 0.321190 | − | 0.947015i | \(-0.395917\pi\) | ||||
0.321190 | + | 0.947015i | \(0.395917\pi\) | |||||||
\(620\) | − | 7.42649e12i | − | 0.0810634i | ||||||
\(621\) | 1.65768e14i | 1.79491i | ||||||||
\(622\) | 1.06548e14i | 1.14444i | ||||||||
\(623\) | 2.18889e14 | 2.33229 | ||||||||
\(624\) | − | 1.16549e13i | − | 0.123193i | ||||||
\(625\) | 7.55421e13 | 0.792116 | ||||||||
\(626\) | −2.80316e14 | −2.91593 | ||||||||
\(627\) | 5.39573e13 | 0.556817 | ||||||||
\(628\) | − | 1.42169e14i | − | 1.45548i | ||||||
\(629\) | 1.16237e14i | 1.18057i | ||||||||
\(630\) | − | 1.80073e14i | − | 1.81445i | ||||||
\(631\) | 6.00578e13i | 0.600375i | 0.953880 | + | 0.300188i | \(0.0970493\pi\) | ||||
−0.953880 | + | 0.300188i | \(0.902951\pi\) | |||||||
\(632\) | 2.83336e14i | 2.81006i | ||||||||
\(633\) | −1.38034e14 | −1.35821 | ||||||||
\(634\) | − | 1.91285e14i | − | 1.86739i | ||||||
\(635\) | − | 1.69860e13i | − | 0.164522i | ||||||
\(636\) | − | 5.15133e14i | − | 4.95032i | ||||||
\(637\) | 7.62750e12 | 0.0727252 | ||||||||
\(638\) | −4.49871e13 | −0.425584 | ||||||||
\(639\) | 7.68513e13i | 0.721351i | ||||||||
\(640\) | −6.53797e11 | −0.00608896 | ||||||||
\(641\) | 1.93396e14i | 1.78713i | 0.448933 | + | 0.893565i | \(0.351804\pi\) | ||||
−0.448933 | + | 0.893565i | \(0.648196\pi\) | |||||||
\(642\) | 1.32399e14 | 1.21397 | ||||||||
\(643\) | −9.91593e13 | −0.902150 | −0.451075 | − | 0.892486i | \(-0.648959\pi\) | ||||
−0.451075 | + | 0.892486i | \(0.648959\pi\) | |||||||
\(644\) | − | 5.23089e14i | − | 4.72222i | ||||||
\(645\) | −4.68446e13 | + | 2.11195e13i | −0.419625 | + | 0.189184i | ||||
\(646\) | 2.84588e14 | 2.52961 | ||||||||
\(647\) | − | 1.71080e14i | − | 1.50896i | −0.656324 | − | 0.754479i | \(-0.727889\pi\) | ||
0.656324 | − | 0.754479i | \(-0.272111\pi\) | |||||||
\(648\) | 2.84674e14i | 2.49157i | ||||||||
\(649\) | 1.98189e13 | 0.172130 | ||||||||
\(650\) | 5.90884e12i | 0.0509255i | ||||||||
\(651\) | −4.73572e13 | −0.405025 | ||||||||
\(652\) | 2.49915e14i | 2.12107i | ||||||||
\(653\) | 8.58206e13i | 0.722813i | 0.932408 | + | 0.361406i | \(0.117703\pi\) | ||||
−0.932408 | + | 0.361406i | \(0.882297\pi\) | |||||||
\(654\) | −3.85780e14 | −3.22441 | ||||||||
\(655\) | 5.67045e13 | 0.470339 | ||||||||
\(656\) | −9.00104e13 | −0.740924 | ||||||||
\(657\) | − | 2.74626e14i | − | 2.24345i | ||||||
\(658\) | −5.01055e14 | −4.06215 | ||||||||
\(659\) | 1.56412e14 | 1.25847 | 0.629235 | − | 0.777215i | \(-0.283368\pi\) | ||||
0.629235 | + | 0.777215i | \(0.283368\pi\) | |||||||
\(660\) | 2.64093e13 | 0.210881 | ||||||||
\(661\) | 1.56927e14 | 1.24363 | 0.621814 | − | 0.783165i | \(-0.286396\pi\) | ||||
0.621814 | + | 0.783165i | \(0.286396\pi\) | |||||||
\(662\) | −2.96749e14 | −2.33400 | ||||||||
\(663\) | − | 5.30496e12i | − | 0.0414109i | ||||||
\(664\) | − | 3.27444e14i | − | 2.53686i | ||||||
\(665\) | − | 1.09152e14i | − | 0.839309i | ||||||
\(666\) | −7.02368e14 | −5.36035 | ||||||||
\(667\) | − | 1.68805e14i | − | 1.27866i | ||||||
\(668\) | 3.98105e14 | 2.99306 | ||||||||
\(669\) | 1.00626e14 | 0.750896 | ||||||||
\(670\) | −8.93241e13 | −0.661599 | ||||||||
\(671\) | 1.59521e13i | 0.117275i | ||||||||
\(672\) | − | 8.05176e14i | − | 5.87550i | ||||||
\(673\) | 2.20542e14i | 1.59741i | 0.601725 | + | 0.798703i | \(0.294480\pi\) | ||||
−0.601725 | + | 0.798703i | \(0.705520\pi\) | |||||||
\(674\) | − | 1.90347e14i | − | 1.36851i | ||||||
\(675\) | − | 2.21611e14i | − | 1.58151i | ||||||
\(676\) | 3.40070e14 | 2.40899 | ||||||||
\(677\) | 1.53249e14i | 1.07759i | 0.842436 | + | 0.538796i | \(0.181121\pi\) | ||||
−0.842436 | + | 0.538796i | \(0.818879\pi\) | |||||||
\(678\) | − | 3.18554e14i | − | 2.22349i | ||||||
\(679\) | 1.80567e14i | 1.25109i | ||||||||
\(680\) | 8.15202e13 | 0.560687 | ||||||||
\(681\) | 7.79729e13 | 0.532363 | ||||||||
\(682\) | − | 6.53444e12i | − | 0.0442880i | ||||||
\(683\) | 5.29142e13 | 0.356015 | 0.178008 | − | 0.984029i | \(-0.443035\pi\) | ||||
0.178008 | + | 0.984029i | \(0.443035\pi\) | |||||||
\(684\) | 1.21551e15i | 8.11853i | ||||||||
\(685\) | 1.65224e13 | 0.109552 | ||||||||
\(686\) | 7.55907e14 | 4.97562 | ||||||||
\(687\) | 6.20952e13i | 0.405765i | ||||||||
\(688\) | −3.37596e14 | + | 1.52202e14i | −2.19006 | + | 0.987366i | ||||
\(689\) | −5.47622e12 | −0.0352683 | ||||||||
\(690\) | 1.40195e14i | 0.896369i | ||||||||
\(691\) | − | 2.26934e14i | − | 1.44049i | −0.693720 | − | 0.720245i | \(-0.744029\pi\) | ||
0.693720 | − | 0.720245i | \(-0.255971\pi\) | |||||||
\(692\) | 1.41910e14 | 0.894300 | ||||||||
\(693\) | − | 1.11994e14i | − | 0.700694i | ||||||
\(694\) | −1.06006e14 | −0.658465 | ||||||||
\(695\) | 1.07630e13i | 0.0663759i | ||||||||
\(696\) | − | 8.91875e14i | − | 5.46082i | ||||||
\(697\) | −4.09700e13 | −0.249059 | ||||||||
\(698\) | 1.17601e14 | 0.709794 | ||||||||
\(699\) | 9.68718e13 | 0.580512 | ||||||||
\(700\) | 6.99304e14i | 4.16079i | ||||||||
\(701\) | 2.48822e14 | 1.46994 | 0.734968 | − | 0.678102i | \(-0.237197\pi\) | ||||
0.734968 | + | 0.678102i | \(0.237197\pi\) | |||||||
\(702\) | 1.59088e13 | 0.0933151 | ||||||||
\(703\) | −4.25741e14 | −2.47953 | ||||||||
\(704\) | 3.21633e13 | 0.185993 | ||||||||
\(705\) | 9.49211e13 | 0.545026 | ||||||||
\(706\) | 3.94523e14i | 2.24931i | ||||||||
\(707\) | 1.09739e14i | 0.621246i | ||||||||
\(708\) | 6.71354e14i | 3.77385i | ||||||||
\(709\) | 1.36841e14 | 0.763811 | 0.381906 | − | 0.924201i | \(-0.375268\pi\) | ||||
0.381906 | + | 0.924201i | \(0.375268\pi\) | |||||||
\(710\) | 3.22565e13i | 0.178783i | ||||||||
\(711\) | −3.88933e14 | −2.14055 | ||||||||
\(712\) | −5.98771e14 | −3.27236 | ||||||||
\(713\) | 2.45192e13 | 0.133063 | ||||||||
\(714\) | − | 8.88228e14i | − | 4.78667i | ||||||
\(715\) | − | 2.80749e11i | − | 0.00150241i | ||||||
\(716\) | 1.02216e14i | 0.543194i | ||||||||
\(717\) | − | 1.71493e14i | − | 0.905002i | ||||||
\(718\) | 2.56347e14i | 1.34340i | ||||||||
\(719\) | 1.12409e14 | 0.585001 | 0.292500 | − | 0.956265i | \(-0.405513\pi\) | ||||
0.292500 | + | 0.956265i | \(0.405513\pi\) | |||||||
\(720\) | 2.45847e14i | 1.27058i | ||||||||
\(721\) | − | 3.59900e14i | − | 1.84716i | ||||||
\(722\) | 6.80006e14i | 3.46598i | ||||||||
\(723\) | −3.77857e14 | −1.91265 | ||||||||
\(724\) | −2.86795e13 | −0.144172 | ||||||||
\(725\) | 2.25671e14i | 1.12664i | ||||||||
\(726\) | −6.20372e14 | −3.07588 | ||||||||
\(727\) | − | 3.16879e13i | − | 0.156035i | −0.996952 | − | 0.0780173i | \(-0.975141\pi\) | ||
0.996952 | − | 0.0780173i | \(-0.0248589\pi\) | |||||||
\(728\) | −2.93803e13 | −0.143681 | ||||||||
\(729\) | 2.14814e14 | 1.04334 | ||||||||
\(730\) | − | 1.15268e14i | − | 0.556024i | ||||||
\(731\) | −1.53664e14 | + | 6.92778e13i | −0.736180 | + | 0.331900i | ||||
\(732\) | −5.40367e14 | −2.57119 | ||||||||
\(733\) | − | 1.08536e14i | − | 0.512924i | −0.966554 | − | 0.256462i | \(-0.917443\pi\) | ||
0.966554 | − | 0.256462i | \(-0.0825568\pi\) | |||||||
\(734\) | 4.05820e14i | 1.90482i | ||||||||
\(735\) | −2.41937e14 | −1.12789 | ||||||||
\(736\) | 4.16879e14i | 1.93028i | ||||||||
\(737\) | −5.55539e13 | −0.255492 | ||||||||
\(738\) | − | 2.47564e14i | − | 1.13085i | ||||||
\(739\) | − | 1.36188e14i | − | 0.617898i | −0.951079 | − | 0.308949i | \(-0.900023\pi\) | ||
0.951079 | − | 0.308949i | \(-0.0999773\pi\) | |||||||
\(740\) | −2.08378e14 | −0.939059 | ||||||||
\(741\) | 1.94305e13 | 0.0869747 | ||||||||
\(742\) | −9.16903e14 | −4.07665 | ||||||||
\(743\) | − | 3.99392e13i | − | 0.176383i | −0.996104 | − | 0.0881913i | \(-0.971891\pi\) | ||
0.996104 | − | 0.0881913i | \(-0.0281087\pi\) | |||||||
\(744\) | 1.29546e14 | 0.568276 | ||||||||
\(745\) | 6.72324e13 | 0.292952 | ||||||||
\(746\) | 2.19925e14 | 0.951876 | ||||||||
\(747\) | 4.49480e14 | 1.93244 | ||||||||
\(748\) | 8.66299e13 | 0.369964 | ||||||||
\(749\) | − | 1.66575e14i | − | 0.706644i | ||||||
\(750\) | − | 3.89164e14i | − | 1.63993i | ||||||
\(751\) | − | 1.85094e14i | − | 0.774806i | −0.921910 | − | 0.387403i | \(-0.873372\pi\) | ||
0.921910 | − | 0.387403i | \(-0.126628\pi\) | |||||||
\(752\) | 6.84070e14 | 2.84454 | ||||||||
\(753\) | − | 4.72604e14i | − | 1.95219i | ||||||
\(754\) | −1.62002e13 | −0.0664760 | ||||||||
\(755\) | −1.71678e13 | −0.0699809 | ||||||||
\(756\) | 1.88279e15 | 7.62417 | ||||||||
\(757\) | − | 4.67882e14i | − | 1.88216i | −0.338183 | − | 0.941080i | \(-0.609812\pi\) | ||
0.338183 | − | 0.941080i | \(-0.390188\pi\) | |||||||
\(758\) | − | 4.30109e14i | − | 1.71883i | ||||||
\(759\) | 8.71923e13i | 0.346154i | ||||||||
\(760\) | 2.98585e14i | 1.17760i | ||||||||
\(761\) | 6.00935e13i | 0.235453i | 0.993046 | + | 0.117726i | \(0.0375606\pi\) | ||||
−0.993046 | + | 0.117726i | \(0.962439\pi\) | |||||||
\(762\) | 5.06278e14 | 1.97067 | ||||||||
\(763\) | 4.85361e14i | 1.87691i | ||||||||
\(764\) | − | 4.34033e14i | − | 1.66746i | ||||||
\(765\) | 1.11902e14i | 0.427101i | ||||||||
\(766\) | 8.22283e14 | 3.11801 | ||||||||
\(767\) | 7.13695e12 | 0.0268866 | ||||||||
\(768\) | − | 4.71359e14i | − | 1.76419i | ||||||
\(769\) | 4.69428e14 | 1.74557 | 0.872785 | − | 0.488104i | \(-0.162311\pi\) | ||||
0.872785 | + | 0.488104i | \(0.162311\pi\) | |||||||
\(770\) | − | 4.70068e13i | − | 0.173663i | ||||||
\(771\) | −8.52118e14 | −3.12772 | ||||||||
\(772\) | 2.05741e14 | 0.750300 | ||||||||
\(773\) | − | 1.61620e14i | − | 0.585595i | −0.956174 | − | 0.292798i | \(-0.905414\pi\) | ||
0.956174 | − | 0.292798i | \(-0.0945862\pi\) | |||||||
\(774\) | −4.18615e14 | − | 9.28521e14i | −1.50699 | − | 3.34262i | ||||
\(775\) | −3.27790e13 | −0.117243 | ||||||||
\(776\) | − | 4.93942e14i | − | 1.75536i | ||||||
\(777\) | 1.32878e15i | 4.69191i | ||||||||
\(778\) | 3.09178e14 | 1.08470 | ||||||||
\(779\) | − | 1.50061e14i | − | 0.523096i | ||||||
\(780\) | 9.51020e12 | 0.0329395 | ||||||||
\(781\) | 2.00615e13i | 0.0690411i | ||||||||
\(782\) | 4.59879e14i | 1.57257i | ||||||||
\(783\) | 6.07591e14 | 2.06444 | ||||||||
\(784\) | −1.74358e15 | −5.88654 | ||||||||
\(785\) | 4.79388e13 | 0.160820 | ||||||||
\(786\) | 1.69011e15i | 5.63380i | ||||||||
\(787\) | −6.16446e13 | −0.204184 | −0.102092 | − | 0.994775i | \(-0.532554\pi\) | ||||
−0.102092 | + | 0.994775i | \(0.532554\pi\) | |||||||
\(788\) | −1.08221e14 | −0.356189 | ||||||||
\(789\) | −5.68577e14 | −1.85953 | ||||||||
\(790\) | −1.63245e14 | −0.530523 | ||||||||
\(791\) | −4.00783e14 | −1.29428 | ||||||||
\(792\) | 3.06360e14i | 0.983120i | ||||||||
\(793\) | 5.74447e12i | 0.0183183i | ||||||||
\(794\) | 1.91213e14i | 0.605920i | ||||||||
\(795\) | 1.73701e14 | 0.546972 | ||||||||
\(796\) | 8.28408e14i | 2.59226i | ||||||||
\(797\) | 2.44080e14 | 0.758999 | 0.379499 | − | 0.925192i | \(-0.376096\pi\) | ||||
0.379499 | + | 0.925192i | \(0.376096\pi\) | |||||||
\(798\) | 3.25332e15 | 10.0534 | ||||||||
\(799\) | 3.11368e14 | 0.956182 | ||||||||
\(800\) | − | 5.57314e14i | − | 1.70079i | ||||||
\(801\) | − | 8.21928e14i | − | 2.49271i | ||||||
\(802\) | − | 3.96757e14i | − | 1.19578i | ||||||
\(803\) | − | 7.16892e13i | − | 0.214722i | ||||||
\(804\) | − | 1.88186e15i | − | 5.60153i | ||||||
\(805\) | 1.76383e14 | 0.521769 | ||||||||
\(806\) | − | 2.35311e12i | − | 0.00691777i | ||||||
\(807\) | 6.41528e14i | 1.87434i | ||||||||
\(808\) | − | 3.00191e14i | − | 0.871648i | ||||||
\(809\) | 2.67926e14 | 0.773165 | 0.386583 | − | 0.922255i | \(-0.373655\pi\) | ||||
0.386583 | + | 0.922255i | \(0.373655\pi\) | |||||||
\(810\) | −1.64016e14 | −0.470393 | ||||||||
\(811\) | − | 2.27265e14i | − | 0.647781i | −0.946095 | − | 0.323890i | \(-0.895009\pi\) | ||
0.946095 | − | 0.323890i | \(-0.104991\pi\) | |||||||
\(812\) | −1.91728e15 | −5.43132 | ||||||||
\(813\) | − | 4.57095e14i | − | 1.28693i | ||||||
\(814\) | −1.83348e14 | −0.513043 | ||||||||
\(815\) | −8.42704e13 | −0.234362 | ||||||||
\(816\) | 1.21266e15i | 3.35189i | ||||||||
\(817\) | −2.53744e14 | − | 5.62825e14i | −0.697085 | − | 1.54619i | ||||
\(818\) | −2.22791e14 | −0.608318 | ||||||||
\(819\) | − | 4.03300e13i | − | 0.109448i | ||||||
\(820\) | − | 7.34470e13i | − | 0.198109i | ||||||
\(821\) | −1.33376e14 | −0.357572 | −0.178786 | − | 0.983888i | \(-0.557217\pi\) | ||||
−0.178786 | + | 0.983888i | \(0.557217\pi\) | |||||||
\(822\) | 4.92459e14i | 1.31223i | ||||||||
\(823\) | 4.07315e14 | 1.07878 | 0.539388 | − | 0.842057i | \(-0.318655\pi\) | ||||
0.539388 | + | 0.842057i | \(0.318655\pi\) | |||||||
\(824\) | 9.84507e14i | 2.59169i | ||||||||
\(825\) | − | 1.16565e14i | − | 0.304999i | ||||||
\(826\) | 1.19497e15 | 3.10782 | ||||||||
\(827\) | 5.89117e14 | 1.52291 | 0.761455 | − | 0.648218i | \(-0.224485\pi\) | ||||
0.761455 | + | 0.648218i | \(0.224485\pi\) | |||||||
\(828\) | −1.96420e15 | −5.04701 | ||||||||
\(829\) | 3.25159e13i | 0.0830469i | 0.999138 | + | 0.0415235i | \(0.0132211\pi\) | ||||
−0.999138 | + | 0.0415235i | \(0.986779\pi\) | |||||||
\(830\) | 1.88658e14 | 0.478944 | ||||||||
\(831\) | −5.29575e14 | −1.33636 | ||||||||
\(832\) | 1.15823e13 | 0.0290521 | ||||||||
\(833\) | −7.93623e14 | −1.97874 | ||||||||
\(834\) | −3.20797e14 | −0.795061 | ||||||||
\(835\) | 1.34239e14i | 0.330710i | ||||||||
\(836\) | 3.17300e14i | 0.777031i | ||||||||
\(837\) | 8.82533e13i | 0.214834i | ||||||||
\(838\) | 3.37080e14 | 0.815667 | ||||||||
\(839\) | − | 3.43628e14i | − | 0.826568i | −0.910602 | − | 0.413284i | \(-0.864382\pi\) | ||
0.910602 | − | 0.413284i | \(-0.135618\pi\) | |||||||
\(840\) | 9.31915e14 | 2.22833 | ||||||||
\(841\) | −1.98015e14 | −0.470671 | ||||||||
\(842\) | −4.00804e14 | −0.947047 | ||||||||
\(843\) | 4.10233e14i | 0.963591i | ||||||||
\(844\) | − | 8.11718e14i | − | 1.89537i | ||||||
\(845\) | 1.14670e14i | 0.266174i | ||||||||
\(846\) | 1.88146e15i | 4.34154i | ||||||||
\(847\) | 7.80509e14i | 1.79044i | ||||||||
\(848\) | 1.25181e15 | 2.85469 | ||||||||
\(849\) | 7.01915e14i | 1.59128i | ||||||||
\(850\) | − | 6.14800e14i | − | 1.38560i | ||||||
\(851\) | − | 6.87976e14i | − | 1.54144i | ||||||
\(852\) | −6.79571e14 | −1.51369 | ||||||||
\(853\) | −2.06413e14 | −0.457079 | −0.228539 | − | 0.973535i | \(-0.573395\pi\) | ||||
−0.228539 | + | 0.973535i | \(0.573395\pi\) | |||||||
\(854\) | 9.61818e14i | 2.11740i | ||||||||
\(855\) | −4.09864e14 | −0.897035 | ||||||||
\(856\) | 4.55667e14i | 0.991468i | ||||||||
\(857\) | −6.70424e14 | −1.45026 | −0.725130 | − | 0.688612i | \(-0.758220\pi\) | ||||
−0.725130 | + | 0.688612i | \(0.758220\pi\) | |||||||
\(858\) | 8.36786e12 | 0.0179961 | ||||||||
\(859\) | 2.44866e14i | 0.523556i | 0.965128 | + | 0.261778i | \(0.0843089\pi\) | ||||
−0.965128 | + | 0.261778i | \(0.915691\pi\) | |||||||
\(860\) | −1.24194e14 | − | 2.75473e14i | −0.264004 | − | 0.585580i | ||||
\(861\) | −4.68357e14 | −0.989832 | ||||||||
\(862\) | − | 8.71755e14i | − | 1.83172i | ||||||
\(863\) | − | 4.00211e14i | − | 0.836055i | −0.908434 | − | 0.418027i | \(-0.862722\pi\) | ||
0.908434 | − | 0.418027i | \(-0.137278\pi\) | |||||||
\(864\) | −1.50050e15 | −3.11650 | ||||||||
\(865\) | 4.78515e13i | 0.0988133i | ||||||||
\(866\) | 2.60515e14 | 0.534865 | ||||||||
\(867\) | − | 2.94454e14i | − | 0.601066i | ||||||
\(868\) | − | 2.78487e14i | − | 0.565206i | ||||||
\(869\) | −1.01528e14 | −0.204874 | ||||||||
\(870\) | 5.13857e14 | 1.03097 | ||||||||
\(871\) | −2.00054e13 | −0.0399077 | ||||||||
\(872\) | − | 1.32771e15i | − | 2.63342i | ||||||
\(873\) | 6.78029e14 | 1.33714 | ||||||||
\(874\) | −1.68440e15 | −3.30285 | ||||||||
\(875\) | −4.89619e14 | −0.954592 | ||||||||
\(876\) | 2.42843e15 | 4.70766 | ||||||||
\(877\) | 1.65134e14 | 0.318302 | 0.159151 | − | 0.987254i | \(-0.449124\pi\) | ||||
0.159151 | + | 0.987254i | \(0.449124\pi\) | |||||||
\(878\) | 1.38561e15i | 2.65564i | ||||||||
\(879\) | 1.23604e15i | 2.35552i | ||||||||
\(880\) | 6.41765e13i | 0.121608i | ||||||||
\(881\) | 6.20546e14 | 1.16921 | 0.584607 | − | 0.811316i | \(-0.301249\pi\) | ||||
0.584607 | + | 0.811316i | \(0.301249\pi\) | |||||||
\(882\) | − | 4.79551e15i | − | 8.98447i | ||||||
\(883\) | −7.21211e14 | −1.34357 | −0.671783 | − | 0.740748i | \(-0.734471\pi\) | ||||
−0.671783 | + | 0.740748i | \(0.734471\pi\) | |||||||
\(884\) | 3.11961e13 | 0.0577883 | ||||||||
\(885\) | −2.26378e14 | −0.416982 | ||||||||
\(886\) | 1.66375e15i | 3.04732i | ||||||||
\(887\) | − | 2.10658e14i | − | 0.383672i | −0.981427 | − | 0.191836i | \(-0.938556\pi\) | ||
0.981427 | − | 0.191836i | \(-0.0614441\pi\) | |||||||
\(888\) | − | 3.63490e15i | − | 6.58305i | ||||||
\(889\) | − | 6.36963e14i | − | 1.14711i | ||||||
\(890\) | − | 3.44984e14i | − | 0.617802i | ||||||
\(891\) | −1.02007e14 | −0.181653 | ||||||||
\(892\) | 5.91738e14i | 1.04787i | ||||||||
\(893\) | 1.14045e15i | 2.00826i | ||||||||
\(894\) | 2.00390e15i | 3.50903i | ||||||||
\(895\) | −3.44669e13 | −0.0600187 | ||||||||
\(896\) | −2.45169e13 | −0.0424546 | ||||||||
\(897\) | 3.13987e13i | 0.0540691i | ||||||||
\(898\) | 1.06705e15 | 1.82727 | ||||||||
\(899\) | − | 8.98702e13i | − | 0.153044i | ||||||
\(900\) | 2.62589e15 | 4.44696 | ||||||||
\(901\) | 5.69787e14 | 0.959596 | ||||||||
\(902\) | − | 6.46248e13i | − | 0.108235i | ||||||
\(903\) | −1.75664e15 | + | 7.91963e14i | −2.92579 | + | 1.31906i | ||||
\(904\) | 1.09634e15 | 1.81595 | ||||||||
\(905\) | − | 9.67062e12i | − | 0.0159298i | ||||||
\(906\) | − | 5.11694e14i | − | 0.838243i | ||||||
\(907\) | 5.78575e14 | 0.942592 | 0.471296 | − | 0.881975i | \(-0.343786\pi\) | ||||
0.471296 | + | 0.881975i | \(0.343786\pi\) | |||||||
\(908\) | 4.58525e14i | 0.742906i | ||||||||
\(909\) | 4.12070e14 | 0.663974 | ||||||||
\(910\) | − | 1.69275e13i | − | 0.0271261i | ||||||
\(911\) | − | 1.30023e14i | − | 0.207218i | −0.994618 | − | 0.103609i | \(-0.966961\pi\) | ||
0.994618 | − | 0.103609i | \(-0.0330391\pi\) | |||||||
\(912\) | −4.44163e15 | −7.03992 | ||||||||
\(913\) | 1.17333e14 | 0.184956 | ||||||||
\(914\) | −9.66455e14 | −1.51513 | ||||||||
\(915\) | − | 1.82209e14i | − | 0.284096i | ||||||
\(916\) | −3.65155e14 | −0.566239 | ||||||||
\(917\) | 2.12637e15 | 3.27939 | ||||||||
\(918\) | −1.65527e15 | −2.53896 | ||||||||
\(919\) | 2.06256e14 | 0.314651 | 0.157326 | − | 0.987547i | \(-0.449713\pi\) | ||||
0.157326 | + | 0.987547i | \(0.449713\pi\) | |||||||
\(920\) | −4.82498e14 | −0.732076 | ||||||||
\(921\) | − | 6.80862e13i | − | 0.102745i | ||||||
\(922\) | 1.20142e15i | 1.80319i | ||||||||
\(923\) | 7.22431e12i | 0.0107842i | ||||||||
\(924\) | 9.90326e14 | 1.47034 | ||||||||
\(925\) | 9.19737e14i | 1.35817i | ||||||||
\(926\) | −6.92483e14 | −1.01708 | ||||||||
\(927\) | −1.35142e15 | −1.97421 | ||||||||
\(928\) | 1.52799e15 | 2.22014 | ||||||||
\(929\) | − | 3.31265e14i | − | 0.478737i | −0.970929 | − | 0.239368i | \(-0.923060\pi\) | ||
0.970929 | − | 0.239368i | \(-0.0769404\pi\) | |||||||
\(930\) | 7.46384e13i | 0.107287i | ||||||||
\(931\) | − | 2.90681e15i | − | 4.15593i | ||||||
\(932\) | 5.69661e14i | 0.810097i | ||||||||
\(933\) | − | 7.56908e14i | − | 1.07062i | ||||||
\(934\) | 1.60518e15 | 2.25834 | ||||||||
\(935\) | 2.92112e13i | 0.0408782i | ||||||||
\(936\) | 1.10323e14i | 0.153563i | ||||||||
\(937\) | − | 1.13419e15i | − | 1.57032i | −0.619291 | − | 0.785161i | \(-0.712580\pi\) | ||
0.619291 | − | 0.785161i | \(-0.287420\pi\) | |||||||
\(938\) | −3.34958e15 | −4.61293 | ||||||||
\(939\) | 1.99135e15 | 2.72785 | ||||||||
\(940\) | 5.58190e14i | 0.760576i | ||||||||
\(941\) | −4.36022e14 | −0.590962 | −0.295481 | − | 0.955349i | \(-0.595480\pi\) | ||||
−0.295481 | + | 0.955349i | \(0.595480\pi\) | |||||||
\(942\) | 1.42884e15i | 1.92632i | ||||||||
\(943\) | 2.42491e14 | 0.325190 | ||||||||
\(944\) | −1.63144e15 | −2.17626 | ||||||||
\(945\) | 6.34868e14i | 0.842411i | ||||||||
\(946\) | −1.09276e14 | − | 2.42384e14i | −0.144235 | − | 0.319925i | ||||
\(947\) | −1.13238e15 | −1.48676 | −0.743381 | − | 0.668868i | \(-0.766779\pi\) | ||||
−0.743381 | + | 0.668868i | \(0.766779\pi\) | |||||||
\(948\) | − | 3.43920e15i | − | 4.49176i | ||||||
\(949\) | − | 2.58159e13i | − | 0.0335395i | ||||||
\(950\) | 2.25183e15 | 2.91017 | ||||||||
\(951\) | 1.35888e15i | 1.74694i | ||||||||
\(952\) | 3.05694e15 | 3.90933 | ||||||||
\(953\) | 1.16938e15i | 1.48762i | 0.668393 | + | 0.743808i | \(0.266982\pi\) | ||||
−0.668393 | + | 0.743808i | \(0.733018\pi\) | |||||||
\(954\) | 3.44297e15i | 4.35704i | ||||||||
\(955\) | 1.46354e14 | 0.184242 | ||||||||
\(956\) | 1.00847e15 | 1.26292 | ||||||||
\(957\) | 3.19586e14 | 0.398133 | ||||||||
\(958\) | − | 2.13655e15i | − | 2.64780i | ||||||
\(959\) | 6.19578e14 | 0.763840 | ||||||||
\(960\) | −3.67380e14 | −0.450566 | ||||||||
\(961\) | −8.06575e14 | −0.984074 | ||||||||
\(962\) | −6.60252e13 | −0.0801372 | ||||||||
\(963\) | −6.25490e14 | −0.755246 | ||||||||
\(964\) | − | 2.22202e15i | − | 2.66908i | ||||||
\(965\) | 6.93751e13i | 0.0829023i | ||||||||
\(966\) | 5.25720e15i | 6.24984i | ||||||||
\(967\) | −1.58671e15 | −1.87657 | −0.938284 | − | 0.345865i | \(-0.887585\pi\) | ||||
−0.938284 | + | 0.345865i | \(0.887585\pi\) | |||||||
\(968\) | − | 2.13509e15i | − | 2.51211i | ||||||
\(969\) | −2.02170e15 | −2.36645 | ||||||||
\(970\) | 2.84586e14 | 0.331402 | ||||||||
\(971\) | 3.24791e14 | 0.376278 | 0.188139 | − | 0.982142i | \(-0.439755\pi\) | ||||
0.188139 | + | 0.982142i | \(0.439755\pi\) | |||||||
\(972\) | 1.05731e14i | 0.121863i | ||||||||
\(973\) | 4.03605e14i | 0.462799i | ||||||||
\(974\) | 6.71436e14i | 0.765967i | ||||||||
\(975\) | − | 4.19761e13i | − | 0.0476408i | ||||||
\(976\) | − | 1.31313e15i | − | 1.48272i | ||||||
\(977\) | −8.18240e14 | −0.919196 | −0.459598 | − | 0.888127i | \(-0.652006\pi\) | ||||
−0.459598 | + | 0.888127i | \(0.652006\pi\) | |||||||
\(978\) | − | 2.51172e15i | − | 2.80723i | ||||||
\(979\) | − | 2.14558e14i | − | 0.238579i | ||||||
\(980\) | − | 1.42273e15i | − | 1.57395i | ||||||
\(981\) | 1.82253e15 | 2.00600 | ||||||||
\(982\) | −1.99533e15 | −2.18503 | ||||||||
\(983\) | 3.27838e14i | 0.357183i | 0.983923 | + | 0.178592i | \(0.0571541\pi\) | ||||
−0.983923 | + | 0.178592i | \(0.942846\pi\) | |||||||
\(984\) | 1.28119e15 | 1.38880 | ||||||||
\(985\) | − | 3.64917e13i | − | 0.0393561i | ||||||
\(986\) | 1.68560e15 | 1.80871 | ||||||||
\(987\) | 3.55947e15 | 3.80014 | ||||||||
\(988\) | 1.14262e14i | 0.121372i | ||||||||
\(989\) | 9.09496e14 | − | 4.10038e14i | 0.961212 | − | 0.433354i | ||||
\(990\) | −1.76510e14 | −0.185607 | ||||||||
\(991\) | 1.84522e14i | 0.193054i | 0.995330 | + | 0.0965271i | \(0.0307734\pi\) | ||||
−0.995330 | + | 0.0965271i | \(0.969227\pi\) | |||||||
\(992\) | 2.21942e14i | 0.231037i | ||||||||
\(993\) | 2.10809e15 | 2.18345 | ||||||||
\(994\) | 1.20959e15i | 1.24654i | ||||||||
\(995\) | −2.79336e14 | −0.286425 | ||||||||
\(996\) | 3.97460e15i | 4.05506i | ||||||||
\(997\) | − | 8.17869e14i | − | 0.830248i | −0.909765 | − | 0.415124i | \(-0.863738\pi\) | ||
0.909765 | − | 0.415124i | \(-0.136262\pi\) | |||||||
\(998\) | −9.23663e14 | −0.932956 | ||||||||
\(999\) | 2.47628e15 | 2.48870 |
(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 | 43.11.b.b.42.1 | ✓ | 34 | |
43.42 | odd | 2 | inner | 43.11.b.b.42.34 | yes | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
43.11.b.b.42.1 | ✓ | 34 | 1.1 | even | 1 | trivial | |
43.11.b.b.42.34 | yes | 34 | 43.42 | odd | 2 | inner |