Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,34,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 34, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 34);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 34 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(172.457072203\) |
Analytic rank: | \(1\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} - 9680197848 x^{4} + 8052423720422 x^{3} + \cdots - 10\!\cdots\!50 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{5}\cdot 5^{6}\cdot 7\cdot 11^{2} \) |
Twist minimal: | no (minimal twist has level 5) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-21408.2\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 18258.4 | 0.197001 | 0.0985006 | − | 0.995137i | \(-0.468595\pi\) | ||||
0.0985006 | + | 0.995137i | \(0.468595\pi\) | |||||||
\(3\) | 3.67420e7 | 0.492791 | 0.246395 | − | 0.969169i | \(-0.420754\pi\) | ||||
0.246395 | + | 0.969169i | \(0.420754\pi\) | |||||||
\(4\) | −8.25656e9 | −0.961191 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.70852e11 | 0.0970803 | ||||||||
\(7\) | 1.51681e13 | 0.172510 | 0.0862550 | − | 0.996273i | \(-0.472510\pi\) | ||||
0.0862550 | + | 0.996273i | \(0.472510\pi\) | |||||||
\(8\) | −3.07591e14 | −0.386357 | ||||||||
\(9\) | −4.20908e15 | −0.757157 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.61480e17 | −1.71577 | −0.857887 | − | 0.513839i | \(-0.828223\pi\) | ||||
−0.857887 | + | 0.513839i | \(0.828223\pi\) | |||||||
\(12\) | −3.03363e17 | −0.473666 | ||||||||
\(13\) | 3.70714e17 | 0.154516 | 0.0772580 | − | 0.997011i | \(-0.475383\pi\) | ||||
0.0772580 | + | 0.997011i | \(0.475383\pi\) | |||||||
\(14\) | 2.76946e17 | 0.0339847 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.53072e19 | 0.885078 | ||||||||
\(17\) | 3.71730e20 | 1.85276 | 0.926382 | − | 0.376585i | \(-0.122902\pi\) | ||||
0.926382 | + | 0.376585i | \(0.122902\pi\) | |||||||
\(18\) | −7.68513e19 | −0.149161 | ||||||||
\(19\) | 1.42255e21 | 1.13145 | 0.565723 | − | 0.824595i | \(-0.308597\pi\) | ||||
0.565723 | + | 0.824595i | \(0.308597\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.57308e20 | 0.0850113 | ||||||||
\(22\) | −4.77422e21 | −0.338009 | ||||||||
\(23\) | 3.26990e22 | 1.11180 | 0.555898 | − | 0.831250i | \(-0.312374\pi\) | ||||
0.555898 | + | 0.831250i | \(0.312374\pi\) | |||||||
\(24\) | −1.13015e22 | −0.190393 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 6.76865e21 | 0.0304398 | ||||||||
\(27\) | −3.58901e23 | −0.865911 | ||||||||
\(28\) | −1.25237e23 | −0.165815 | ||||||||
\(29\) | 6.41343e23 | 0.475909 | 0.237954 | − | 0.971276i | \(-0.423523\pi\) | ||||
0.237954 | + | 0.971276i | \(0.423523\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.44554e23 | −0.0356914 | −0.0178457 | − | 0.999841i | \(-0.505681\pi\) | ||||
−0.0178457 | + | 0.999841i | \(0.505681\pi\) | |||||||
\(32\) | 3.83459e24 | 0.560718 | ||||||||
\(33\) | −9.60732e24 | −0.845517 | ||||||||
\(34\) | 6.78720e24 | 0.364997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.47526e25 | 0.727772 | ||||||||
\(37\) | −1.34909e26 | −1.79768 | −0.898842 | − | 0.438273i | \(-0.855590\pi\) | ||||
−0.898842 | + | 0.438273i | \(0.855590\pi\) | |||||||
\(38\) | 2.59736e25 | 0.222896 | ||||||||
\(39\) | 1.36208e25 | 0.0761440 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.37865e26 | 1.56241 | 0.781205 | − | 0.624275i | \(-0.214605\pi\) | ||||
0.781205 | + | 0.624275i | \(0.214605\pi\) | |||||||
\(42\) | 1.01756e25 | 0.0167473 | ||||||||
\(43\) | −3.37044e26 | −0.376233 | −0.188117 | − | 0.982147i | \(-0.560238\pi\) | ||||
−0.188117 | + | 0.982147i | \(0.560238\pi\) | |||||||
\(44\) | 2.15893e27 | 1.64919 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.97033e26 | 0.219025 | ||||||||
\(47\) | −3.12828e27 | −0.804807 | −0.402403 | − | 0.915462i | \(-0.631825\pi\) | ||||
−0.402403 | + | 0.915462i | \(0.631825\pi\) | |||||||
\(48\) | 2.39952e27 | 0.436158 | ||||||||
\(49\) | −7.50092e27 | −0.970240 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.36581e28 | 0.913025 | ||||||||
\(52\) | −3.06082e27 | −0.148519 | ||||||||
\(53\) | 4.06250e28 | 1.43960 | 0.719799 | − | 0.694182i | \(-0.244234\pi\) | ||||
0.719799 | + | 0.694182i | \(0.244234\pi\) | |||||||
\(54\) | −6.55298e27 | −0.170585 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −4.66557e27 | −0.0666504 | ||||||||
\(57\) | 5.22675e28 | 0.557566 | ||||||||
\(58\) | 1.17099e28 | 0.0937545 | ||||||||
\(59\) | −8.77955e28 | −0.530169 | −0.265084 | − | 0.964225i | \(-0.585400\pi\) | ||||
−0.265084 | + | 0.964225i | \(0.585400\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.84902e28 | −0.0644168 | −0.0322084 | − | 0.999481i | \(-0.510254\pi\) | ||||
−0.0322084 | + | 0.999481i | \(0.510254\pi\) | |||||||
\(62\) | −2.63933e27 | −0.00703124 | ||||||||
\(63\) | −6.38439e28 | −0.130617 | ||||||||
\(64\) | −4.90971e29 | −0.774616 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.75415e29 | −0.166568 | ||||||||
\(67\) | −7.69531e29 | −0.570154 | −0.285077 | − | 0.958505i | \(-0.592019\pi\) | ||||
−0.285077 | + | 0.958505i | \(0.592019\pi\) | |||||||
\(68\) | −3.06921e30 | −1.78086 | ||||||||
\(69\) | 1.20143e30 | 0.547883 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.72988e30 | 0.776929 | 0.388464 | − | 0.921464i | \(-0.373006\pi\) | ||||
0.388464 | + | 0.921464i | \(0.373006\pi\) | |||||||
\(72\) | 1.29468e30 | 0.292533 | ||||||||
\(73\) | −4.44452e30 | −0.799831 | −0.399915 | − | 0.916552i | \(-0.630960\pi\) | ||||
−0.399915 | + | 0.916552i | \(0.630960\pi\) | |||||||
\(74\) | −2.46323e30 | −0.354146 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.17454e31 | −1.08754 | ||||||||
\(77\) | −3.96617e30 | −0.295988 | ||||||||
\(78\) | 2.48694e29 | 0.0150005 | ||||||||
\(79\) | −1.16758e31 | −0.570743 | −0.285371 | − | 0.958417i | \(-0.592117\pi\) | ||||
−0.285371 | + | 0.958417i | \(0.592117\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.02118e31 | 0.330445 | ||||||||
\(82\) | 1.16464e31 | 0.307796 | ||||||||
\(83\) | 4.84088e31 | 1.04746 | 0.523728 | − | 0.851886i | \(-0.324541\pi\) | ||||
0.523728 | + | 0.851886i | \(0.324541\pi\) | |||||||
\(84\) | −4.60145e30 | −0.0817121 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −6.15390e30 | −0.0741184 | ||||||||
\(87\) | 2.35643e31 | 0.234523 | ||||||||
\(88\) | 8.04290e31 | 0.662901 | ||||||||
\(89\) | 1.18101e32 | 0.807831 | 0.403915 | − | 0.914796i | \(-0.367649\pi\) | ||||
0.403915 | + | 0.914796i | \(0.367649\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.62303e30 | 0.0266555 | ||||||||
\(92\) | −2.69981e32 | −1.06865 | ||||||||
\(93\) | −5.31122e30 | −0.0175884 | ||||||||
\(94\) | −5.71176e31 | −0.158548 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.40891e32 | 0.276317 | ||||||||
\(97\) | 2.71846e31 | 0.0449355 | 0.0224678 | − | 0.999748i | \(-0.492848\pi\) | ||||
0.0224678 | + | 0.999748i | \(0.492848\pi\) | |||||||
\(98\) | −1.36955e32 | −0.191138 | ||||||||
\(99\) | 1.10059e33 | 1.29911 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.30031e33 | −1.10343 | −0.551714 | − | 0.834033i | \(-0.686026\pi\) | ||||
−0.551714 | + | 0.834033i | \(0.686026\pi\) | |||||||
\(102\) | 2.49376e32 | 0.179867 | ||||||||
\(103\) | −1.73233e33 | −1.06369 | −0.531846 | − | 0.846841i | \(-0.678502\pi\) | ||||
−0.531846 | + | 0.846841i | \(0.678502\pi\) | |||||||
\(104\) | −1.14028e32 | −0.0596983 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.41749e32 | 0.283603 | ||||||||
\(107\) | −3.72062e32 | −0.121838 | −0.0609191 | − | 0.998143i | \(-0.519403\pi\) | ||||
−0.0609191 | + | 0.998143i | \(0.519403\pi\) | |||||||
\(108\) | 2.96329e33 | 0.832305 | ||||||||
\(109\) | −5.92448e33 | −1.42927 | −0.714633 | − | 0.699500i | \(-0.753406\pi\) | ||||
−0.714633 | + | 0.699500i | \(0.753406\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.95684e33 | −0.885882 | ||||||||
\(112\) | 9.90588e32 | 0.152685 | ||||||||
\(113\) | −2.74196e33 | −0.364978 | −0.182489 | − | 0.983208i | \(-0.558415\pi\) | ||||
−0.182489 | + | 0.983208i | \(0.558415\pi\) | |||||||
\(114\) | 9.54322e32 | 0.109841 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.29529e33 | −0.457439 | ||||||||
\(117\) | −1.56036e33 | −0.116993 | ||||||||
\(118\) | −1.60301e33 | −0.104444 | ||||||||
\(119\) | 5.63844e33 | 0.319620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.51469e34 | 1.94388 | ||||||||
\(122\) | −3.37602e32 | −0.0126902 | ||||||||
\(123\) | 2.34364e34 | 0.769941 | ||||||||
\(124\) | 1.19352e33 | 0.0343062 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.16569e33 | −0.0257317 | ||||||||
\(127\) | −7.72774e34 | −1.49724 | −0.748619 | − | 0.663000i | \(-0.769283\pi\) | ||||
−0.748619 | + | 0.663000i | \(0.769283\pi\) | |||||||
\(128\) | −4.19033e34 | −0.713318 | ||||||||
\(129\) | −1.23837e34 | −0.185404 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.77088e34 | −0.205690 | −0.102845 | − | 0.994697i | \(-0.532795\pi\) | ||||
−0.102845 | + | 0.994697i | \(0.532795\pi\) | |||||||
\(132\) | 7.93235e34 | 0.812703 | ||||||||
\(133\) | 2.15774e34 | 0.195186 | ||||||||
\(134\) | −1.40504e34 | −0.112321 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.14341e35 | −0.715828 | ||||||||
\(137\) | 1.26744e35 | 0.703133 | 0.351567 | − | 0.936163i | \(-0.385649\pi\) | ||||
0.351567 | + | 0.936163i | \(0.385649\pi\) | |||||||
\(138\) | 2.19362e34 | 0.107934 | ||||||||
\(139\) | 1.04160e35 | 0.454941 | 0.227471 | − | 0.973785i | \(-0.426954\pi\) | ||||
0.227471 | + | 0.973785i | \(0.426954\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.14940e35 | −0.396601 | ||||||||
\(142\) | 4.98434e34 | 0.153056 | ||||||||
\(143\) | −9.69344e34 | −0.265114 | ||||||||
\(144\) | −2.74884e35 | −0.670143 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.11501e34 | −0.157568 | ||||||||
\(147\) | −2.75599e35 | −0.478125 | ||||||||
\(148\) | 1.11389e36 | 1.72792 | ||||||||
\(149\) | −3.09463e35 | −0.429572 | −0.214786 | − | 0.976661i | \(-0.568905\pi\) | ||||
−0.214786 | + | 0.976661i | \(0.568905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.12720e36 | 1.25569 | 0.627844 | − | 0.778340i | \(-0.283938\pi\) | ||||
0.627844 | + | 0.778340i | \(0.283938\pi\) | |||||||
\(152\) | −4.37564e35 | −0.437142 | ||||||||
\(153\) | −1.56464e36 | −1.40283 | ||||||||
\(154\) | −7.24160e34 | −0.0583100 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.12461e35 | −0.0731889 | ||||||||
\(157\) | −1.58631e36 | −0.929061 | −0.464530 | − | 0.885557i | \(-0.653777\pi\) | ||||
−0.464530 | + | 0.885557i | \(0.653777\pi\) | |||||||
\(158\) | −2.13182e35 | −0.112437 | ||||||||
\(159\) | 1.49264e36 | 0.709421 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.95982e35 | 0.191796 | ||||||||
\(162\) | 1.86451e35 | 0.0650979 | ||||||||
\(163\) | 3.56599e36 | 1.12483 | 0.562413 | − | 0.826857i | \(-0.309873\pi\) | ||||
0.562413 | + | 0.826857i | \(0.309873\pi\) | |||||||
\(164\) | −5.26657e36 | −1.50177 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.83869e35 | 0.206350 | ||||||||
\(167\) | −6.77798e36 | −1.43311 | −0.716553 | − | 0.697532i | \(-0.754281\pi\) | ||||
−0.716553 | + | 0.697532i | \(0.754281\pi\) | |||||||
\(168\) | −1.71423e35 | −0.0328447 | ||||||||
\(169\) | −5.61870e36 | −0.976125 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.98764e36 | −0.856683 | ||||||||
\(172\) | 2.78283e36 | 0.361632 | ||||||||
\(173\) | −1.72200e36 | −0.203364 | −0.101682 | − | 0.994817i | \(-0.532422\pi\) | ||||
−0.101682 | + | 0.994817i | \(0.532422\pi\) | |||||||
\(174\) | 4.30247e35 | 0.0462014 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.70766e37 | −1.51859 | ||||||||
\(177\) | −3.22578e36 | −0.261262 | ||||||||
\(178\) | 2.15635e36 | 0.159144 | ||||||||
\(179\) | −6.69163e36 | −0.450253 | −0.225127 | − | 0.974330i | \(-0.572280\pi\) | ||||
−0.225127 | + | 0.974330i | \(0.572280\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.34636e37 | 0.754163 | 0.377082 | − | 0.926180i | \(-0.376928\pi\) | ||||
0.377082 | + | 0.926180i | \(0.376928\pi\) | |||||||
\(182\) | 1.02668e35 | 0.00525117 | ||||||||
\(183\) | −6.79367e35 | −0.0317440 | ||||||||
\(184\) | −1.00579e37 | −0.429550 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.69745e34 | −0.00346493 | ||||||||
\(187\) | −9.72001e37 | −3.17892 | ||||||||
\(188\) | 2.58289e37 | 0.773573 | ||||||||
\(189\) | −5.44386e36 | −0.149378 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.65942e36 | −0.153598 | −0.0767990 | − | 0.997047i | \(-0.524470\pi\) | ||||
−0.0767990 | + | 0.997047i | \(0.524470\pi\) | |||||||
\(192\) | −1.80393e37 | −0.381723 | ||||||||
\(193\) | 5.05982e37 | 0.982742 | 0.491371 | − | 0.870950i | \(-0.336496\pi\) | ||||
0.491371 | + | 0.870950i | \(0.336496\pi\) | |||||||
\(194\) | 4.96349e35 | 0.00885235 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 6.19318e37 | 0.932586 | ||||||||
\(197\) | −2.33016e37 | −0.322621 | −0.161311 | − | 0.986904i | \(-0.551572\pi\) | ||||
−0.161311 | + | 0.986904i | \(0.551572\pi\) | |||||||
\(198\) | 2.00951e37 | 0.255926 | ||||||||
\(199\) | −1.24079e38 | −1.45420 | −0.727100 | − | 0.686531i | \(-0.759132\pi\) | ||||
−0.727100 | + | 0.686531i | \(0.759132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.82742e37 | −0.280967 | ||||||||
\(202\) | −2.37416e37 | −0.217377 | ||||||||
\(203\) | 9.72798e36 | 0.0820990 | ||||||||
\(204\) | −1.12769e38 | −0.877591 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.16296e37 | −0.209549 | ||||||||
\(207\) | −1.37633e38 | −0.841805 | ||||||||
\(208\) | 2.42103e37 | 0.136759 | ||||||||
\(209\) | −3.71970e38 | −1.94130 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.15498e38 | −0.961133 | −0.480567 | − | 0.876958i | \(-0.659569\pi\) | ||||
−0.480567 | + | 0.876958i | \(0.659569\pi\) | |||||||
\(212\) | −3.35423e38 | −1.38373 | ||||||||
\(213\) | 1.00301e38 | 0.382863 | ||||||||
\(214\) | −6.79328e36 | −0.0240023 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.10395e38 | 0.334550 | ||||||||
\(217\) | −2.19262e36 | −0.00615711 | ||||||||
\(218\) | −1.08172e38 | −0.281567 | ||||||||
\(219\) | −1.63301e38 | −0.394149 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.37805e38 | 0.286282 | ||||||||
\(222\) | −9.05042e37 | −0.174520 | ||||||||
\(223\) | 1.94520e37 | 0.0348285 | 0.0174142 | − | 0.999848i | \(-0.494457\pi\) | ||||
0.0174142 | + | 0.999848i | \(0.494457\pi\) | |||||||
\(224\) | 5.81636e37 | 0.0967294 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.00639e37 | −0.0719011 | ||||||||
\(227\) | −1.37345e39 | −1.83395 | −0.916974 | − | 0.398947i | \(-0.869376\pi\) | ||||
−0.916974 | + | 0.398947i | \(0.869376\pi\) | |||||||
\(228\) | −4.31550e38 | −0.535927 | ||||||||
\(229\) | −3.69693e38 | −0.427126 | −0.213563 | − | 0.976929i | \(-0.568507\pi\) | ||||
−0.213563 | + | 0.976929i | \(0.568507\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.45725e38 | −0.145860 | ||||||||
\(232\) | −1.97271e38 | −0.183871 | ||||||||
\(233\) | 2.02428e39 | 1.75751 | 0.878754 | − | 0.477275i | \(-0.158375\pi\) | ||||
0.878754 | + | 0.477275i | \(0.158375\pi\) | |||||||
\(234\) | −2.84898e37 | −0.0230477 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 7.24889e38 | 0.509593 | ||||||||
\(237\) | −4.28994e38 | −0.281257 | ||||||||
\(238\) | 1.02949e38 | 0.0629655 | ||||||||
\(239\) | −6.31944e38 | −0.360673 | −0.180336 | − | 0.983605i | \(-0.557719\pi\) | ||||
−0.180336 | + | 0.983605i | \(0.557719\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.82829e39 | −0.909420 | −0.454710 | − | 0.890640i | \(-0.650257\pi\) | ||||
−0.454710 | + | 0.890640i | \(0.650257\pi\) | |||||||
\(242\) | 8.24311e38 | 0.382946 | ||||||||
\(243\) | 2.37036e39 | 1.02875 | ||||||||
\(244\) | 1.52665e38 | 0.0619168 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.27913e38 | 0.151679 | ||||||||
\(247\) | 5.27360e38 | 0.174826 | ||||||||
\(248\) | 4.44636e37 | 0.0137896 | ||||||||
\(249\) | 1.77864e39 | 0.516177 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.17903e39 | −0.554174 | −0.277087 | − | 0.960845i | \(-0.589369\pi\) | ||||
−0.277087 | + | 0.960845i | \(0.589369\pi\) | |||||||
\(252\) | 5.27131e38 | 0.125548 | ||||||||
\(253\) | −8.55015e39 | −1.90759 | ||||||||
\(254\) | −1.41096e39 | −0.294958 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 3.45232e39 | 0.634091 | ||||||||
\(257\) | 1.48926e39 | 0.256492 | 0.128246 | − | 0.991742i | \(-0.459065\pi\) | ||||
0.128246 | + | 0.991742i | \(0.459065\pi\) | |||||||
\(258\) | −2.26107e38 | −0.0365249 | ||||||||
\(259\) | −2.04632e39 | −0.310118 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.69947e39 | −0.360338 | ||||||||
\(262\) | −3.23335e38 | −0.0405211 | ||||||||
\(263\) | −1.17319e40 | −1.38069 | −0.690346 | − | 0.723479i | \(-0.742542\pi\) | ||||
−0.690346 | + | 0.723479i | \(0.742542\pi\) | |||||||
\(264\) | 2.95512e39 | 0.326671 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3.93970e38 | 0.0384518 | ||||||||
\(267\) | 4.33929e39 | 0.398091 | ||||||||
\(268\) | 6.35369e39 | 0.548027 | ||||||||
\(269\) | 2.30936e40 | 1.87318 | 0.936590 | − | 0.350428i | \(-0.113964\pi\) | ||||
0.936590 | + | 0.350428i | \(0.113964\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.16176e40 | 1.55172 | 0.775861 | − | 0.630903i | \(-0.217316\pi\) | ||||
0.775861 | + | 0.630903i | \(0.217316\pi\) | |||||||
\(272\) | 2.42766e40 | 1.63984 | ||||||||
\(273\) | 2.06602e38 | 0.0131356 | ||||||||
\(274\) | 2.31414e39 | 0.138518 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9.91967e39 | −0.526620 | ||||||||
\(277\) | 1.86721e40 | 0.933847 | 0.466924 | − | 0.884298i | \(-0.345362\pi\) | ||||
0.466924 | + | 0.884298i | \(0.345362\pi\) | |||||||
\(278\) | 1.90179e39 | 0.0896239 | ||||||||
\(279\) | 6.08441e38 | 0.0270240 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.80173e39 | −0.268513 | −0.134256 | − | 0.990947i | \(-0.542865\pi\) | ||||
−0.134256 | + | 0.990947i | \(0.542865\pi\) | |||||||
\(282\) | −2.09862e39 | −0.0781309 | ||||||||
\(283\) | 3.60211e40 | 1.26497 | 0.632485 | − | 0.774573i | \(-0.282035\pi\) | ||||
0.632485 | + | 0.774573i | \(0.282035\pi\) | |||||||
\(284\) | −2.25395e40 | −0.746777 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.76987e39 | −0.0522278 | ||||||||
\(287\) | 9.67521e39 | 0.269531 | ||||||||
\(288\) | −1.61401e40 | −0.424552 | ||||||||
\(289\) | 9.79285e40 | 2.43274 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 9.98819e38 | 0.0221438 | ||||||||
\(292\) | 3.66965e40 | 0.768790 | ||||||||
\(293\) | −6.02024e40 | −1.19206 | −0.596030 | − | 0.802962i | \(-0.703256\pi\) | ||||
−0.596030 | + | 0.802962i | \(0.703256\pi\) | |||||||
\(294\) | −5.03201e39 | −0.0941912 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 4.14968e40 | 0.694547 | ||||||||
\(297\) | 9.38457e40 | 1.48571 | ||||||||
\(298\) | −5.65032e39 | −0.0846261 | ||||||||
\(299\) | 1.21220e40 | 0.171790 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.11233e39 | −0.0649040 | ||||||||
\(302\) | 2.05809e40 | 0.247372 | ||||||||
\(303\) | −4.77760e40 | −0.543759 | ||||||||
\(304\) | 9.29029e40 | 1.00142 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −2.85679e40 | −0.276360 | ||||||||
\(307\) | −2.05983e41 | −1.88820 | −0.944098 | − | 0.329664i | \(-0.893064\pi\) | ||||
−0.944098 | + | 0.329664i | \(0.893064\pi\) | |||||||
\(308\) | 3.27469e40 | 0.284501 | ||||||||
\(309\) | −6.36493e40 | −0.524178 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.19843e41 | −0.887294 | −0.443647 | − | 0.896202i | \(-0.646316\pi\) | ||||
−0.443647 | + | 0.896202i | \(0.646316\pi\) | |||||||
\(312\) | −4.18962e39 | −0.0294188 | ||||||||
\(313\) | −2.13282e41 | −1.42060 | −0.710302 | − | 0.703897i | \(-0.751442\pi\) | ||||
−0.710302 | + | 0.703897i | \(0.751442\pi\) | |||||||
\(314\) | −2.89636e40 | −0.183026 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.64022e40 | 0.548593 | ||||||||
\(317\) | 2.31538e41 | 1.25068 | 0.625338 | − | 0.780354i | \(-0.284961\pi\) | ||||
0.625338 | + | 0.780354i | \(0.284961\pi\) | |||||||
\(318\) | 2.72534e40 | 0.139757 | ||||||||
\(319\) | −1.67699e41 | −0.816552 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.36703e40 | −0.0600407 | ||||||||
\(322\) | 9.05586e39 | 0.0377840 | ||||||||
\(323\) | 5.28805e41 | 2.09630 | ||||||||
\(324\) | −8.43142e40 | −0.317620 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 6.51094e40 | 0.221592 | ||||||||
\(327\) | −2.17677e41 | −0.704329 | ||||||||
\(328\) | −1.96201e41 | −0.603647 | ||||||||
\(329\) | −4.74502e40 | −0.138837 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.27790e40 | −0.0867830 | −0.0433915 | − | 0.999058i | \(-0.513816\pi\) | ||||
−0.0433915 | + | 0.999058i | \(0.513816\pi\) | |||||||
\(332\) | −3.99690e41 | −1.00680 | ||||||||
\(333\) | 5.67844e41 | 1.36113 | ||||||||
\(334\) | −1.23755e41 | −0.282324 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.63962e40 | 0.0752416 | ||||||||
\(337\) | −5.05149e41 | −0.994321 | −0.497160 | − | 0.867659i | \(-0.665624\pi\) | ||||
−0.497160 | + | 0.867659i | \(0.665624\pi\) | |||||||
\(338\) | −1.02589e41 | −0.192298 | ||||||||
\(339\) | −1.00745e41 | −0.179858 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.77981e40 | 0.0612383 | ||||||||
\(342\) | −1.09325e41 | −0.168767 | ||||||||
\(343\) | −2.31040e41 | −0.339886 | ||||||||
\(344\) | 1.03672e41 | 0.145360 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.14411e40 | −0.0400629 | ||||||||
\(347\) | −5.54748e40 | −0.0673999 | −0.0337000 | − | 0.999432i | \(-0.510729\pi\) | ||||
−0.0337000 | + | 0.999432i | \(0.510729\pi\) | |||||||
\(348\) | −1.94560e41 | −0.225422 | ||||||||
\(349\) | −4.36140e41 | −0.481955 | −0.240978 | − | 0.970531i | \(-0.577468\pi\) | ||||
−0.240978 | + | 0.970531i | \(0.577468\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.33050e41 | −0.133797 | ||||||||
\(352\) | −1.00267e42 | −0.962065 | ||||||||
\(353\) | −2.19124e41 | −0.200635 | −0.100318 | − | 0.994955i | \(-0.531986\pi\) | ||||
−0.100318 | + | 0.994955i | \(0.531986\pi\) | |||||||
\(354\) | −5.88978e40 | −0.0514689 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −9.75113e41 | −0.776479 | ||||||||
\(357\) | 2.07168e41 | 0.157506 | ||||||||
\(358\) | −1.22179e41 | −0.0887004 | ||||||||
\(359\) | −1.83249e42 | −1.27053 | −0.635264 | − | 0.772295i | \(-0.719109\pi\) | ||||
−0.635264 | + | 0.772295i | \(0.719109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.42885e41 | 0.280170 | ||||||||
\(362\) | 2.45825e41 | 0.148571 | ||||||||
\(363\) | 1.65879e42 | 0.957925 | ||||||||
\(364\) | −4.64269e40 | −0.0256211 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.24042e40 | −0.00625360 | ||||||||
\(367\) | −2.46022e42 | −1.18572 | −0.592862 | − | 0.805304i | \(-0.702002\pi\) | ||||
−0.592862 | + | 0.805304i | \(0.702002\pi\) | |||||||
\(368\) | 2.13548e42 | 0.984026 | ||||||||
\(369\) | −2.68483e42 | −1.18299 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.16205e41 | 0.248345 | ||||||||
\(372\) | 4.38524e40 | 0.0169058 | ||||||||
\(373\) | −9.17264e41 | −0.338297 | −0.169149 | − | 0.985591i | \(-0.554102\pi\) | ||||
−0.169149 | + | 0.985591i | \(0.554102\pi\) | |||||||
\(374\) | −1.77472e42 | −0.626251 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.62231e41 | 0.310942 | ||||||||
\(377\) | 2.37755e41 | 0.0735355 | ||||||||
\(378\) | −9.93964e40 | −0.0294277 | ||||||||
\(379\) | 5.49346e42 | 1.55704 | 0.778518 | − | 0.627622i | \(-0.215972\pi\) | ||||
0.778518 | + | 0.627622i | \(0.215972\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.83933e42 | −0.737825 | ||||||||
\(382\) | −1.21591e41 | −0.0302590 | ||||||||
\(383\) | −2.70725e42 | −0.645281 | −0.322640 | − | 0.946522i | \(-0.604570\pi\) | ||||
−0.322640 | + | 0.946522i | \(0.604570\pi\) | |||||||
\(384\) | −1.53961e42 | −0.351517 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.23844e41 | 0.193601 | ||||||||
\(387\) | 1.41865e42 | 0.284868 | ||||||||
\(388\) | −2.24452e41 | −0.0431916 | ||||||||
\(389\) | 5.33079e42 | 0.983157 | 0.491579 | − | 0.870833i | \(-0.336420\pi\) | ||||
0.491579 | + | 0.870833i | \(0.336420\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.21552e43 | 2.05990 | ||||||||
\(392\) | 2.30721e42 | 0.374859 | ||||||||
\(393\) | −6.50657e41 | −0.101362 | ||||||||
\(394\) | −4.25451e41 | −0.0635568 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −9.08712e42 | −1.24869 | ||||||||
\(397\) | −8.08784e42 | −1.06608 | −0.533039 | − | 0.846091i | \(-0.678950\pi\) | ||||
−0.533039 | + | 0.846091i | \(0.678950\pi\) | |||||||
\(398\) | −2.26550e42 | −0.286479 | ||||||||
\(399\) | 7.92799e41 | 0.0961857 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.16113e43 | −1.29717 | −0.648587 | − | 0.761140i | \(-0.724640\pi\) | ||||
−0.648587 | + | 0.761140i | \(0.724640\pi\) | |||||||
\(402\) | −5.16242e41 | −0.0553507 | ||||||||
\(403\) | −5.35882e40 | −0.00551488 | ||||||||
\(404\) | 1.07361e43 | 1.06061 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.77618e41 | 0.0161736 | ||||||||
\(407\) | 3.52761e43 | 3.08442 | ||||||||
\(408\) | −4.20111e42 | −0.352753 | ||||||||
\(409\) | 4.40488e42 | 0.355222 | 0.177611 | − | 0.984101i | \(-0.443163\pi\) | ||||
0.177611 | + | 0.984101i | \(0.443163\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.65683e42 | 0.346498 | ||||||||
\(412\) | 1.43031e43 | 1.02241 | ||||||||
\(413\) | −1.33169e42 | −0.0914594 | ||||||||
\(414\) | −2.51296e42 | −0.165836 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.42154e42 | 0.0866399 | ||||||||
\(417\) | 3.82704e42 | 0.224191 | ||||||||
\(418\) | −6.79158e42 | −0.382439 | ||||||||
\(419\) | 2.34926e43 | 1.27174 | 0.635871 | − | 0.771796i | \(-0.280641\pi\) | ||||
0.635871 | + | 0.771796i | \(0.280641\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4.10149e42 | −0.205252 | −0.102626 | − | 0.994720i | \(-0.532724\pi\) | ||||
−0.102626 | + | 0.994720i | \(0.532724\pi\) | |||||||
\(422\) | −3.93466e42 | −0.189344 | ||||||||
\(423\) | 1.31672e43 | 0.609365 | ||||||||
\(424\) | −1.24959e43 | −0.556199 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 1.83135e42 | 0.0754245 | ||||||||
\(427\) | −2.80461e41 | −0.0111125 | ||||||||
\(428\) | 3.07196e42 | 0.117110 | ||||||||
\(429\) | −3.56157e42 | −0.130646 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 1.92923e43 | 0.655404 | 0.327702 | − | 0.944781i | \(-0.393726\pi\) | ||||
0.327702 | + | 0.944781i | \(0.393726\pi\) | |||||||
\(432\) | −2.34389e43 | −0.766398 | ||||||||
\(433\) | −1.20050e43 | −0.377843 | −0.188922 | − | 0.981992i | \(-0.560499\pi\) | ||||
−0.188922 | + | 0.981992i | \(0.560499\pi\) | |||||||
\(434\) | −4.00338e40 | −0.00121296 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.89159e43 | 1.37380 | ||||||||
\(437\) | 4.65160e43 | 1.25794 | ||||||||
\(438\) | −2.98162e42 | −0.0776478 | ||||||||
\(439\) | 3.55254e43 | 0.890993 | 0.445496 | − | 0.895284i | \(-0.353027\pi\) | ||||
0.445496 | + | 0.895284i | \(0.353027\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.15720e43 | 0.734625 | ||||||||
\(442\) | 2.51611e42 | 0.0563978 | ||||||||
\(443\) | −4.50074e43 | −0.971901 | −0.485951 | − | 0.873986i | \(-0.661526\pi\) | ||||
−0.485951 | + | 0.873986i | \(0.661526\pi\) | |||||||
\(444\) | 4.09265e43 | 0.851501 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.55163e41 | 0.00686124 | ||||||||
\(447\) | −1.13703e43 | −0.211689 | ||||||||
\(448\) | −7.44711e42 | −0.133629 | ||||||||
\(449\) | −4.48522e43 | −0.775745 | −0.387872 | − | 0.921713i | \(-0.626790\pi\) | ||||
−0.387872 | + | 0.921713i | \(0.626790\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.66789e44 | −2.68074 | ||||||||
\(452\) | 2.26392e43 | 0.350814 | ||||||||
\(453\) | 4.14156e43 | 0.618791 | ||||||||
\(454\) | −2.50771e43 | −0.361290 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.60770e43 | −0.215419 | ||||||||
\(457\) | −5.99465e43 | −0.774723 | −0.387362 | − | 0.921928i | \(-0.626614\pi\) | ||||
−0.387362 | + | 0.921928i | \(0.626614\pi\) | |||||||
\(458\) | −6.75002e42 | −0.0841442 | ||||||||
\(459\) | −1.33414e44 | −1.60433 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.64117e43 | 0.407546 | 0.203773 | − | 0.979018i | \(-0.434680\pi\) | ||||
0.203773 | + | 0.979018i | \(0.434680\pi\) | |||||||
\(462\) | −2.66071e42 | −0.0287346 | ||||||||
\(463\) | 4.93497e43 | 0.514278 | 0.257139 | − | 0.966374i | \(-0.417220\pi\) | ||||
0.257139 | + | 0.966374i | \(0.417220\pi\) | |||||||
\(464\) | 4.18844e43 | 0.421216 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.69601e43 | 0.346231 | ||||||||
\(467\) | −6.19636e43 | −0.560284 | −0.280142 | − | 0.959959i | \(-0.590381\pi\) | ||||
−0.280142 | + | 0.959959i | \(0.590381\pi\) | |||||||
\(468\) | 1.28833e43 | 0.112452 | ||||||||
\(469\) | −1.16723e43 | −0.0983572 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5.82843e43 | −0.457832 | ||||||||
\(472\) | 2.70051e43 | 0.204834 | ||||||||
\(473\) | 8.81305e43 | 0.645531 | ||||||||
\(474\) | −7.83275e42 | −0.0554079 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.65542e43 | −0.307216 | ||||||||
\(477\) | −1.70994e44 | −1.09000 | ||||||||
\(478\) | −1.15383e43 | −0.0710530 | ||||||||
\(479\) | 1.65648e44 | 0.985483 | 0.492741 | − | 0.870176i | \(-0.335995\pi\) | ||||
0.492741 | + | 0.870176i | \(0.335995\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.00127e43 | −0.277771 | ||||||||
\(482\) | −3.33818e43 | −0.179157 | ||||||||
\(483\) | 1.82234e43 | 0.0945152 | ||||||||
\(484\) | −3.72758e44 | −1.86844 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.32790e43 | 0.202665 | ||||||||
\(487\) | −3.41088e44 | −1.54397 | −0.771984 | − | 0.635642i | \(-0.780736\pi\) | ||||
−0.771984 | + | 0.635642i | \(0.780736\pi\) | |||||||
\(488\) | 5.68741e42 | 0.0248879 | ||||||||
\(489\) | 1.31022e44 | 0.554303 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4.35160e44 | 1.72109 | 0.860547 | − | 0.509371i | \(-0.170122\pi\) | ||||
0.860547 | + | 0.509371i | \(0.170122\pi\) | |||||||
\(492\) | −1.93505e44 | −0.740060 | ||||||||
\(493\) | 2.38406e44 | 0.881747 | ||||||||
\(494\) | 9.62876e42 | 0.0344410 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.44044e42 | −0.0315896 | ||||||||
\(497\) | 4.14072e43 | 0.134028 | ||||||||
\(498\) | 3.24751e43 | 0.101687 | ||||||||
\(499\) | −6.19626e44 | −1.87703 | −0.938514 | − | 0.345242i | \(-0.887797\pi\) | ||||
−0.938514 | + | 0.345242i | \(0.887797\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.49037e44 | −0.706222 | ||||||||
\(502\) | −3.97856e43 | −0.109173 | ||||||||
\(503\) | −5.28443e44 | −1.40322 | −0.701611 | − | 0.712560i | \(-0.747536\pi\) | ||||
−0.701611 | + | 0.712560i | \(0.747536\pi\) | |||||||
\(504\) | 1.96378e43 | 0.0504648 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.56112e44 | −0.375797 | ||||||||
\(507\) | −2.06443e44 | −0.481025 | ||||||||
\(508\) | 6.38046e44 | 1.43913 | ||||||||
\(509\) | −4.72823e43 | −0.103242 | −0.0516209 | − | 0.998667i | \(-0.516439\pi\) | ||||
−0.0516209 | + | 0.998667i | \(0.516439\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.74151e43 | −0.137979 | ||||||||
\(512\) | 4.22980e44 | 0.838235 | ||||||||
\(513\) | −5.10556e44 | −0.979731 | ||||||||
\(514\) | 2.71916e43 | 0.0505293 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.02247e44 | 0.178209 | ||||||||
\(517\) | 8.17985e44 | 1.38087 | ||||||||
\(518\) | −3.73626e43 | −0.0610937 | ||||||||
\(519\) | −6.32699e43 | −0.100216 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −4.38738e44 | −0.652203 | −0.326102 | − | 0.945335i | \(-0.605735\pi\) | ||||
−0.326102 | + | 0.945335i | \(0.605735\pi\) | |||||||
\(522\) | −4.92881e43 | −0.0709869 | ||||||||
\(523\) | 1.40016e44 | 0.195389 | 0.0976944 | − | 0.995216i | \(-0.468853\pi\) | ||||
0.0976944 | + | 0.995216i | \(0.468853\pi\) | |||||||
\(524\) | 1.46214e44 | 0.197707 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −2.14205e44 | −0.271998 | ||||||||
\(527\) | −5.37351e43 | −0.0661277 | ||||||||
\(528\) | −6.27428e44 | −0.748349 | ||||||||
\(529\) | 2.04220e44 | 0.236091 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.69539e44 | 0.401421 | ||||||||
\(532\) | −1.78156e44 | −0.187611 | ||||||||
\(533\) | 2.36465e44 | 0.241417 | ||||||||
\(534\) | 7.92286e43 | 0.0784244 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.36701e44 | 0.220283 | ||||||||
\(537\) | −2.45864e44 | −0.221881 | ||||||||
\(538\) | 4.21653e44 | 0.369018 | ||||||||
\(539\) | 1.96134e45 | 1.66471 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.56960e45 | 1.25324 | 0.626622 | − | 0.779324i | \(-0.284437\pi\) | ||||
0.626622 | + | 0.779324i | \(0.284437\pi\) | |||||||
\(542\) | 3.94704e44 | 0.305691 | ||||||||
\(543\) | 4.94681e44 | 0.371645 | ||||||||
\(544\) | 1.42543e45 | 1.03888 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.77222e42 | 0.00258773 | ||||||||
\(547\) | 2.11683e45 | 1.40895 | 0.704474 | − | 0.709730i | \(-0.251183\pi\) | ||||
0.704474 | + | 0.709730i | \(0.251183\pi\) | |||||||
\(548\) | −1.04647e45 | −0.675845 | ||||||||
\(549\) | 7.78267e43 | 0.0487736 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.12345e44 | 0.538465 | ||||||||
\(552\) | −3.69548e44 | −0.211678 | ||||||||
\(553\) | −1.77100e44 | −0.0984588 | ||||||||
\(554\) | 3.40922e44 | 0.183969 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.60001e44 | −0.437285 | ||||||||
\(557\) | 1.56733e45 | 0.773661 | 0.386830 | − | 0.922151i | \(-0.373570\pi\) | ||||
0.386830 | + | 0.922151i | \(0.373570\pi\) | |||||||
\(558\) | 1.11092e43 | 0.00532375 | ||||||||
\(559\) | −1.24947e44 | −0.0581341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.57133e45 | −1.56654 | ||||||||
\(562\) | −1.24189e44 | −0.0528974 | ||||||||
\(563\) | −1.29413e44 | −0.0535291 | −0.0267646 | − | 0.999642i | \(-0.508520\pi\) | ||||
−0.0267646 | + | 0.999642i | \(0.508520\pi\) | |||||||
\(564\) | 9.49006e44 | 0.381209 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.57688e44 | 0.249200 | ||||||||
\(567\) | 1.54894e44 | 0.0570050 | ||||||||
\(568\) | −8.39687e44 | −0.300172 | ||||||||
\(569\) | −2.93499e45 | −1.01919 | −0.509593 | − | 0.860415i | \(-0.670204\pi\) | ||||
−0.509593 | + | 0.860415i | \(0.670204\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.20277e44 | −0.301594 | −0.150797 | − | 0.988565i | \(-0.548184\pi\) | ||||
−0.150797 | + | 0.988565i | \(0.548184\pi\) | |||||||
\(572\) | 8.00345e44 | 0.254825 | ||||||||
\(573\) | −2.44681e44 | −0.0756917 | ||||||||
\(574\) | 1.76654e44 | 0.0530979 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 2.06654e45 | 0.586506 | ||||||||
\(577\) | 6.78370e45 | 1.87097 | 0.935483 | − | 0.353371i | \(-0.114965\pi\) | ||||
0.935483 | + | 0.353371i | \(0.114965\pi\) | |||||||
\(578\) | 1.78802e45 | 0.479251 | ||||||||
\(579\) | 1.85908e45 | 0.484286 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.34270e44 | 0.180697 | ||||||||
\(582\) | 1.82369e43 | 0.00436236 | ||||||||
\(583\) | −1.06226e46 | −2.47003 | ||||||||
\(584\) | 1.36709e45 | 0.309020 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.09920e45 | −0.234837 | ||||||||
\(587\) | −1.92291e45 | −0.399421 | −0.199710 | − | 0.979855i | \(-0.564000\pi\) | ||||
−0.199710 | + | 0.979855i | \(0.564000\pi\) | |||||||
\(588\) | 2.27550e45 | 0.459570 | ||||||||
\(589\) | −2.05636e44 | −0.0403828 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.56148e44 | −0.158985 | ||||||||
\(592\) | −8.81055e45 | −1.59109 | ||||||||
\(593\) | 3.84061e45 | 0.674524 | 0.337262 | − | 0.941411i | \(-0.390499\pi\) | ||||
0.337262 | + | 0.941411i | \(0.390499\pi\) | |||||||
\(594\) | 1.71348e45 | 0.292686 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.55510e45 | 0.412900 | ||||||||
\(597\) | −4.55893e45 | −0.716616 | ||||||||
\(598\) | 2.21328e44 | 0.0338429 | ||||||||
\(599\) | −1.48464e45 | −0.220840 | −0.110420 | − | 0.993885i | \(-0.535220\pi\) | ||||
−0.110420 | + | 0.993885i | \(0.535220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.01345e45 | 0.705843 | 0.352921 | − | 0.935653i | \(-0.385188\pi\) | ||||
0.352921 | + | 0.935653i | \(0.385188\pi\) | |||||||
\(602\) | −9.33431e43 | −0.0127862 | ||||||||
\(603\) | 3.23902e45 | 0.431696 | ||||||||
\(604\) | −9.30680e45 | −1.20695 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −8.72316e44 | −0.107121 | ||||||||
\(607\) | −3.29284e45 | −0.393511 | −0.196756 | − | 0.980453i | \(-0.563041\pi\) | ||||
−0.196756 | + | 0.980453i | \(0.563041\pi\) | |||||||
\(608\) | 5.45491e45 | 0.634422 | ||||||||
\(609\) | 3.57426e44 | 0.0404576 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.15970e45 | −0.124355 | ||||||||
\(612\) | 1.29186e46 | 1.34839 | ||||||||
\(613\) | 1.00399e46 | 1.02008 | 0.510038 | − | 0.860152i | \(-0.329631\pi\) | ||||
0.510038 | + | 0.860152i | \(0.329631\pi\) | |||||||
\(614\) | −3.76092e45 | −0.371977 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.21996e45 | 0.114357 | ||||||||
\(617\) | −1.43698e46 | −1.31144 | −0.655718 | − | 0.755006i | \(-0.727634\pi\) | ||||
−0.655718 | + | 0.755006i | \(0.727634\pi\) | |||||||
\(618\) | −1.16214e45 | −0.103264 | ||||||||
\(619\) | 1.61224e46 | 1.39487 | 0.697435 | − | 0.716648i | \(-0.254325\pi\) | ||||
0.697435 | + | 0.716648i | \(0.254325\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.17357e46 | −0.962716 | ||||||||
\(622\) | −2.18815e45 | −0.174798 | ||||||||
\(623\) | 1.79138e45 | 0.139359 | ||||||||
\(624\) | 8.89535e44 | 0.0673934 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −3.89420e45 | −0.279861 | ||||||||
\(627\) | −1.36669e46 | −0.956657 | ||||||||
\(628\) | 1.30975e46 | 0.893004 | ||||||||
\(629\) | −5.01498e46 | −3.33068 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.47683e46 | 1.56103 | 0.780516 | − | 0.625136i | \(-0.214957\pi\) | ||||
0.780516 | + | 0.625136i | \(0.214957\pi\) | |||||||
\(632\) | 3.59138e45 | 0.220510 | ||||||||
\(633\) | −7.91785e45 | −0.473638 | ||||||||
\(634\) | 4.22752e45 | 0.246384 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.23241e46 | −0.681889 | ||||||||
\(637\) | −2.78069e45 | −0.149918 | ||||||||
\(638\) | −3.06192e45 | −0.160862 | ||||||||
\(639\) | −1.14903e46 | −0.588257 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.57575e46 | −1.73864 | −0.869321 | − | 0.494249i | \(-0.835443\pi\) | ||||
−0.869321 | + | 0.494249i | \(0.835443\pi\) | |||||||
\(642\) | −2.49599e44 | −0.0118281 | ||||||||
\(643\) | −1.88292e46 | −0.869663 | −0.434831 | − | 0.900512i | \(-0.643192\pi\) | ||||
−0.434831 | + | 0.900512i | \(0.643192\pi\) | |||||||
\(644\) | −4.09511e45 | −0.184352 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.65515e45 | 0.412974 | ||||||||
\(647\) | −2.33501e46 | −0.973573 | −0.486787 | − | 0.873521i | \(-0.661831\pi\) | ||||
−0.486787 | + | 0.873521i | \(0.661831\pi\) | |||||||
\(648\) | −3.14105e45 | −0.127669 | ||||||||
\(649\) | 2.29568e46 | 0.909649 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.05612e43 | −0.00303417 | ||||||||
\(652\) | −2.94428e46 | −1.08117 | ||||||||
\(653\) | −2.35876e46 | −0.844531 | −0.422266 | − | 0.906472i | \(-0.638765\pi\) | ||||
−0.422266 | + | 0.906472i | \(0.638765\pi\) | |||||||
\(654\) | −3.97445e45 | −0.138754 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.16572e46 | 1.38285 | ||||||||
\(657\) | 1.87074e46 | 0.605598 | ||||||||
\(658\) | −8.66366e44 | −0.0273511 | ||||||||
\(659\) | 2.73242e46 | 0.841276 | 0.420638 | − | 0.907228i | \(-0.361806\pi\) | ||||
0.420638 | + | 0.907228i | \(0.361806\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.72690e46 | −0.798629 | −0.399315 | − | 0.916814i | \(-0.630752\pi\) | ||||
−0.399315 | + | 0.916814i | \(0.630752\pi\) | |||||||
\(662\) | −5.98494e44 | −0.0170963 | ||||||||
\(663\) | 5.06325e45 | 0.141077 | ||||||||
\(664\) | −1.48901e46 | −0.404692 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.03679e46 | 0.268144 | ||||||||
\(667\) | 2.09713e46 | 0.529114 | ||||||||
\(668\) | 5.59628e46 | 1.37749 | ||||||||
\(669\) | 7.14706e44 | 0.0171631 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.83482e45 | 0.110525 | ||||||||
\(672\) | 2.13705e45 | 0.0476674 | ||||||||
\(673\) | 1.12643e46 | 0.245163 | 0.122581 | − | 0.992458i | \(-0.460883\pi\) | ||||
0.122581 | + | 0.992458i | \(0.460883\pi\) | |||||||
\(674\) | −9.22324e45 | −0.195882 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.63912e46 | 0.938242 | ||||||||
\(677\) | 4.69606e46 | 0.926874 | 0.463437 | − | 0.886130i | \(-0.346616\pi\) | ||||
0.463437 | + | 0.886130i | \(0.346616\pi\) | |||||||
\(678\) | −1.83945e45 | −0.0354322 | ||||||||
\(679\) | 4.12340e44 | 0.00775183 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.04634e46 | −0.903753 | ||||||||
\(682\) | 6.90134e44 | 0.0120640 | ||||||||
\(683\) | 1.23577e46 | 0.210860 | 0.105430 | − | 0.994427i | \(-0.466378\pi\) | ||||
0.105430 | + | 0.994427i | \(0.466378\pi\) | |||||||
\(684\) | 4.94373e46 | 0.823435 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.21842e45 | −0.0669579 | ||||||||
\(687\) | −1.35833e46 | −0.210484 | ||||||||
\(688\) | −2.20114e46 | −0.332996 | ||||||||
\(689\) | 1.50602e46 | 0.222441 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3.45406e46 | −0.486342 | −0.243171 | − | 0.969983i | \(-0.578188\pi\) | ||||
−0.243171 | + | 0.969983i | \(0.578188\pi\) | |||||||
\(692\) | 1.42178e46 | 0.195471 | ||||||||
\(693\) | 1.66939e46 | 0.224109 | ||||||||
\(694\) | −1.01288e45 | −0.0132779 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.24815e45 | −0.0906097 | ||||||||
\(697\) | 2.37113e47 | 2.89478 | ||||||||
\(698\) | −7.96324e45 | −0.0949457 | ||||||||
\(699\) | 7.43761e46 | 0.866084 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.58600e46 | 0.509433 | 0.254716 | − | 0.967016i | \(-0.418018\pi\) | ||||
0.254716 | + | 0.967016i | \(0.418018\pi\) | |||||||
\(702\) | −2.42928e45 | −0.0263582 | ||||||||
\(703\) | −1.91915e47 | −2.03398 | ||||||||
\(704\) | 1.28379e47 | 1.32907 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.00086e45 | −0.0395254 | ||||||||
\(707\) | −1.97233e46 | −0.190352 | ||||||||
\(708\) | 2.66339e46 | 0.251123 | ||||||||
\(709\) | 1.01825e46 | 0.0937978 | 0.0468989 | − | 0.998900i | \(-0.485066\pi\) | ||||
0.0468989 | + | 0.998900i | \(0.485066\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.91445e46 | 0.432142 | ||||||||
\(712\) | −3.63269e46 | −0.312111 | ||||||||
\(713\) | −4.72678e45 | −0.0396815 | ||||||||
\(714\) | 3.78256e45 | 0.0310288 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.52498e46 | 0.432779 | ||||||||
\(717\) | −2.32189e46 | −0.177736 | ||||||||
\(718\) | −3.34585e46 | −0.250295 | ||||||||
\(719\) | −2.37751e46 | −0.173818 | −0.0869092 | − | 0.996216i | \(-0.527699\pi\) | ||||
−0.0869092 | + | 0.996216i | \(0.527699\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.62762e46 | −0.183498 | ||||||||
\(722\) | 8.08638e45 | 0.0551938 | ||||||||
\(723\) | −6.71752e46 | −0.448154 | ||||||||
\(724\) | −1.11163e47 | −0.724895 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3.02869e46 | 0.188712 | ||||||||
\(727\) | 7.60235e46 | 0.463053 | 0.231526 | − | 0.972829i | \(-0.425628\pi\) | ||||
0.231526 | + | 0.972829i | \(0.425628\pi\) | |||||||
\(728\) | −1.72959e45 | −0.0102985 | ||||||||
\(729\) | 3.03238e46 | 0.176514 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.25289e47 | −0.697072 | ||||||||
\(732\) | 5.60924e45 | 0.0305120 | ||||||||
\(733\) | 9.46431e46 | 0.503354 | 0.251677 | − | 0.967811i | \(-0.419018\pi\) | ||||
0.251677 | + | 0.967811i | \(0.419018\pi\) | |||||||
\(734\) | −4.49197e46 | −0.233589 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.25387e47 | 0.623404 | ||||||||
\(737\) | 2.01217e47 | 0.978255 | ||||||||
\(738\) | −4.90207e46 | −0.233050 | ||||||||
\(739\) | 1.36554e46 | 0.0634851 | 0.0317425 | − | 0.999496i | \(-0.489894\pi\) | ||||
0.0317425 | + | 0.999496i | \(0.489894\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.93763e46 | 0.0861529 | ||||||||
\(742\) | 1.12509e46 | 0.0489243 | ||||||||
\(743\) | −2.14591e47 | −0.912632 | −0.456316 | − | 0.889818i | \(-0.650831\pi\) | ||||
−0.456316 | + | 0.889818i | \(0.650831\pi\) | |||||||
\(744\) | 1.63368e45 | 0.00679538 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1.67478e46 | −0.0666449 | ||||||||
\(747\) | −2.03757e47 | −0.793089 | ||||||||
\(748\) | 8.02539e47 | 3.05555 | ||||||||
\(749\) | −5.64349e45 | −0.0210183 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.00124e47 | −1.06965 | −0.534825 | − | 0.844963i | \(-0.679622\pi\) | ||||
−0.534825 | + | 0.844963i | \(0.679622\pi\) | |||||||
\(752\) | −2.04300e47 | −0.712317 | ||||||||
\(753\) | −8.00619e46 | −0.273092 | ||||||||
\(754\) | 4.34103e45 | 0.0144866 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 4.49476e46 | 0.143581 | ||||||||
\(757\) | −3.75997e47 | −1.17517 | −0.587587 | − | 0.809161i | \(-0.699922\pi\) | ||||
−0.587587 | + | 0.809161i | \(0.699922\pi\) | |||||||
\(758\) | 1.00302e47 | 0.306738 | ||||||||
\(759\) | −3.14150e47 | −0.940043 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.05125e47 | 0.587723 | 0.293861 | − | 0.955848i | \(-0.405060\pi\) | ||||
0.293861 | + | 0.955848i | \(0.405060\pi\) | |||||||
\(762\) | −5.18417e46 | −0.145352 | ||||||||
\(763\) | −8.98632e46 | −0.246563 | ||||||||
\(764\) | 5.49839e46 | 0.147637 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.94302e46 | −0.127121 | ||||||||
\(767\) | −3.25470e46 | −0.0819195 | ||||||||
\(768\) | 1.26845e47 | 0.312474 | ||||||||
\(769\) | −3.91739e47 | −0.944522 | −0.472261 | − | 0.881459i | \(-0.656562\pi\) | ||||
−0.472261 | + | 0.881459i | \(0.656562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.47185e46 | 0.126397 | ||||||||
\(772\) | −4.17767e47 | −0.944602 | ||||||||
\(773\) | −6.18683e47 | −1.36933 | −0.684663 | − | 0.728860i | \(-0.740051\pi\) | ||||
−0.684663 | + | 0.728860i | \(0.740051\pi\) | |||||||
\(774\) | 2.59023e46 | 0.0561193 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −8.36174e45 | −0.0173611 | ||||||||
\(777\) | −7.51860e46 | −0.152823 | ||||||||
\(778\) | 9.73319e46 | 0.193683 | ||||||||
\(779\) | 9.07396e47 | 1.76778 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.13811e47 | −1.33303 | ||||||||
\(782\) | 2.21935e47 | 0.405802 | ||||||||
\(783\) | −2.30179e47 | −0.412095 | ||||||||
\(784\) | −4.89864e47 | −0.858738 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.18800e46 | −0.0199684 | ||||||||
\(787\) | −2.50651e45 | −0.00412559 | −0.00206280 | − | 0.999998i | \(-0.500657\pi\) | ||||
−0.00206280 | + | 0.999998i | \(0.500657\pi\) | |||||||
\(788\) | 1.92391e47 | 0.310101 | ||||||||
\(789\) | −4.31052e47 | −0.680392 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.15904e46 | −0.0629624 | ||||||||
\(792\) | −3.38532e47 | −0.501920 | ||||||||
\(793\) | −6.85457e45 | −0.00995342 | ||||||||
\(794\) | −1.47671e47 | −0.210019 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.02447e48 | 1.39776 | ||||||||
\(797\) | −7.37335e47 | −0.985378 | −0.492689 | − | 0.870206i | \(-0.663986\pi\) | ||||
−0.492689 | + | 0.870206i | \(0.663986\pi\) | |||||||
\(798\) | 1.44753e46 | 0.0189487 | ||||||||
\(799\) | −1.16288e48 | −1.49112 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.97099e47 | −0.611655 | ||||||||
\(802\) | −2.12004e47 | −0.255545 | ||||||||
\(803\) | 1.16216e48 | 1.37233 | ||||||||
\(804\) | 2.33447e47 | 0.270062 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −9.78438e44 | −0.00108644 | ||||||||
\(807\) | 8.48506e47 | 0.923085 | ||||||||
\(808\) | 3.99963e47 | 0.426317 | ||||||||
\(809\) | −9.92771e47 | −1.03681 | −0.518404 | − | 0.855136i | \(-0.673474\pi\) | ||||
−0.518404 | + | 0.855136i | \(0.673474\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.07185e47 | 0.107470 | 0.0537351 | − | 0.998555i | \(-0.482887\pi\) | ||||
0.0537351 | + | 0.998555i | \(0.482887\pi\) | |||||||
\(812\) | −8.03197e46 | −0.0789128 | ||||||||
\(813\) | 7.94274e47 | 0.764674 | ||||||||
\(814\) | 6.44087e47 | 0.607634 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 8.91973e47 | 0.808098 | ||||||||
\(817\) | −4.79463e47 | −0.425688 | ||||||||
\(818\) | 8.04262e46 | 0.0699791 | ||||||||
\(819\) | −2.36678e46 | −0.0201824 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.20939e48 | −0.990610 | −0.495305 | − | 0.868719i | \(-0.664944\pi\) | ||||
−0.495305 | + | 0.868719i | \(0.664944\pi\) | |||||||
\(822\) | 8.50264e46 | 0.0682604 | ||||||||
\(823\) | −2.45743e48 | −1.93367 | −0.966837 | − | 0.255396i | \(-0.917794\pi\) | ||||
−0.966837 | + | 0.255396i | \(0.917794\pi\) | |||||||
\(824\) | 5.32848e47 | 0.410965 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.43146e46 | −0.0180176 | ||||||||
\(827\) | 1.80057e48 | 1.30789 | 0.653943 | − | 0.756544i | \(-0.273114\pi\) | ||||
0.653943 | + | 0.756544i | \(0.273114\pi\) | |||||||
\(828\) | 1.13637e48 | 0.809135 | ||||||||
\(829\) | 6.57735e47 | 0.459094 | 0.229547 | − | 0.973298i | \(-0.426276\pi\) | ||||
0.229547 | + | 0.973298i | \(0.426276\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.86049e47 | 0.460191 | ||||||||
\(832\) | −1.82010e47 | −0.119691 | ||||||||
\(833\) | −2.78832e48 | −1.79763 | ||||||||
\(834\) | 6.98757e46 | 0.0441658 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 3.07119e48 | 1.86596 | ||||||||
\(837\) | 5.18807e46 | 0.0309055 | ||||||||
\(838\) | 4.28937e47 | 0.250534 | ||||||||
\(839\) | 6.26140e47 | 0.358591 | 0.179295 | − | 0.983795i | \(-0.442618\pi\) | ||||
0.179295 | + | 0.983795i | \(0.442618\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.40475e48 | −0.773511 | ||||||||
\(842\) | −7.48868e46 | −0.0404348 | ||||||||
\(843\) | −2.49910e47 | −0.132321 | ||||||||
\(844\) | 1.77928e48 | 0.923832 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.40413e47 | 0.120046 | ||||||||
\(847\) | 6.84793e47 | 0.335338 | ||||||||
\(848\) | 2.65311e48 | 1.27416 | ||||||||
\(849\) | 1.32349e48 | 0.623365 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.41140e48 | −1.99866 | ||||||||
\(852\) | −8.28145e47 | −0.368005 | ||||||||
\(853\) | −3.16331e48 | −1.37874 | −0.689370 | − | 0.724410i | \(-0.742112\pi\) | ||||
−0.689370 | + | 0.724410i | \(0.742112\pi\) | |||||||
\(854\) | −5.12079e45 | −0.00218918 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.14443e47 | 0.0470730 | ||||||||
\(857\) | 3.13666e48 | 1.26556 | 0.632782 | − | 0.774330i | \(-0.281913\pi\) | ||||
0.632782 | + | 0.774330i | \(0.281913\pi\) | |||||||
\(858\) | −6.50286e46 | −0.0257374 | ||||||||
\(859\) | 2.20270e48 | 0.855202 | 0.427601 | − | 0.903968i | \(-0.359359\pi\) | ||||
0.427601 | + | 0.903968i | \(0.359359\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.55487e47 | 0.132822 | ||||||||
\(862\) | 3.52247e47 | 0.129115 | ||||||||
\(863\) | −5.00806e47 | −0.180091 | −0.0900453 | − | 0.995938i | \(-0.528701\pi\) | ||||
−0.0900453 | + | 0.995938i | \(0.528701\pi\) | |||||||
\(864\) | −1.37624e48 | −0.485532 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −2.19192e47 | −0.0744356 | ||||||||
\(867\) | 3.59809e48 | 1.19883 | ||||||||
\(868\) | 1.81035e46 | 0.00591816 | ||||||||
\(869\) | 3.05300e48 | 0.979266 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.85276e47 | −0.0880979 | ||||||||
\(872\) | 1.82232e48 | 0.552207 | ||||||||
\(873\) | −1.14422e47 | −0.0340233 | ||||||||
\(874\) | 8.49310e47 | 0.247815 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.34830e48 | 0.378852 | ||||||||
\(877\) | 1.77120e48 | 0.488400 | 0.244200 | − | 0.969725i | \(-0.421475\pi\) | ||||
0.244200 | + | 0.969725i | \(0.421475\pi\) | |||||||
\(878\) | 6.48638e47 | 0.175527 | ||||||||
\(879\) | −2.21196e48 | −0.587436 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.59935e48 | 0.409111 | 0.204555 | − | 0.978855i | \(-0.434425\pi\) | ||||
0.204555 | + | 0.978855i | \(0.434425\pi\) | |||||||
\(882\) | 5.76455e47 | 0.144722 | ||||||||
\(883\) | 2.38704e48 | 0.588177 | 0.294089 | − | 0.955778i | \(-0.404984\pi\) | ||||
0.294089 | + | 0.955778i | \(0.404984\pi\) | |||||||
\(884\) | −1.13780e48 | −0.275171 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.21764e47 | −0.191466 | ||||||||
\(887\) | −5.13361e48 | −1.17404 | −0.587020 | − | 0.809572i | \(-0.699699\pi\) | ||||
−0.587020 | + | 0.809572i | \(0.699699\pi\) | |||||||
\(888\) | 1.52468e48 | 0.342266 | ||||||||
\(889\) | −1.17215e48 | −0.258289 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −2.67018e48 | −0.566968 | ||||||||
\(892\) | −1.60607e47 | −0.0334768 | ||||||||
\(893\) | −4.45015e48 | −0.910595 | ||||||||
\(894\) | −2.07604e47 | −0.0417030 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −6.35594e47 | −0.123054 | ||||||||
\(897\) | 4.45386e47 | 0.0846566 | ||||||||
\(898\) | −8.18931e47 | −0.152823 | ||||||||
\(899\) | −9.27089e46 | −0.0169858 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.51015e49 | 2.66724 | ||||||||
\(902\) | −3.04531e48 | −0.528109 | ||||||||
\(903\) | −1.87837e47 | −0.0319841 | ||||||||
\(904\) | 8.43402e47 | 0.141012 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 7.56185e47 | 0.121903 | ||||||||
\(907\) | −5.18589e48 | −0.820924 | −0.410462 | − | 0.911878i | \(-0.634632\pi\) | ||||
−0.410462 | + | 0.911878i | \(0.634632\pi\) | |||||||
\(908\) | 1.13400e49 | 1.76277 | ||||||||
\(909\) | 5.47311e48 | 0.835469 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.63747e48 | −0.977123 | −0.488562 | − | 0.872529i | \(-0.662478\pi\) | ||||
−0.488562 | + | 0.872529i | \(0.662478\pi\) | |||||||
\(912\) | 3.41344e48 | 0.493489 | ||||||||
\(913\) | −1.26580e49 | −1.79720 | ||||||||
\(914\) | −1.09453e48 | −0.152621 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.05239e48 | 0.410549 | ||||||||
\(917\) | −2.68609e47 | −0.0354835 | ||||||||
\(918\) | −2.43594e48 | −0.316054 | ||||||||
\(919\) | −7.10984e48 | −0.906054 | −0.453027 | − | 0.891497i | \(-0.649656\pi\) | ||||
−0.453027 | + | 0.891497i | \(0.649656\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −7.56822e48 | −0.930486 | ||||||||
\(922\) | 6.64821e47 | 0.0802869 | ||||||||
\(923\) | 1.01200e48 | 0.120048 | ||||||||
\(924\) | 1.20319e48 | 0.140199 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.01048e47 | 0.101313 | ||||||||
\(927\) | 7.29151e48 | 0.805382 | ||||||||
\(928\) | 2.45929e48 | 0.266851 | ||||||||
\(929\) | −1.17316e49 | −1.25054 | −0.625272 | − | 0.780407i | \(-0.715012\pi\) | ||||
−0.625272 | + | 0.780407i | \(0.715012\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.06705e49 | −1.09777 | ||||||||
\(932\) | −1.67136e49 | −1.68930 | ||||||||
\(933\) | −4.40329e48 | −0.437250 | ||||||||
\(934\) | −1.13136e48 | −0.110376 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.79954e47 | 0.0452010 | ||||||||
\(937\) | −7.60807e48 | −0.703998 | −0.351999 | − | 0.936000i | \(-0.614498\pi\) | ||||
−0.351999 | + | 0.936000i | \(0.614498\pi\) | |||||||
\(938\) | −2.13119e47 | −0.0193765 | ||||||||
\(939\) | −7.83643e48 | −0.700061 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −5.90432e48 | −0.509262 | −0.254631 | − | 0.967038i | \(-0.581954\pi\) | ||||
−0.254631 | + | 0.967038i | \(0.581954\pi\) | |||||||
\(942\) | −1.06418e48 | −0.0901935 | ||||||||
\(943\) | 2.08575e49 | 1.73708 | ||||||||
\(944\) | −5.73368e48 | −0.469241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.60912e48 | 0.127170 | ||||||||
\(947\) | 7.50195e47 | 0.0582639 | 0.0291319 | − | 0.999576i | \(-0.490726\pi\) | ||||
0.0291319 | + | 0.999576i | \(0.490726\pi\) | |||||||
\(948\) | 3.54201e48 | 0.270341 | ||||||||
\(949\) | −1.64765e48 | −0.123587 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.50718e48 | 0.616321 | ||||||||
\(952\) | −1.73433e48 | −0.123487 | ||||||||
\(953\) | 1.06031e49 | 0.741993 | 0.370997 | − | 0.928634i | \(-0.379016\pi\) | ||||
0.370997 | + | 0.928634i | \(0.379016\pi\) | |||||||
\(954\) | −3.12208e48 | −0.214732 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.21769e48 | 0.346675 | ||||||||
\(957\) | −6.16159e48 | −0.402389 | ||||||||
\(958\) | 3.02447e48 | 0.194141 | ||||||||
\(959\) | 1.92247e48 | 0.121297 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.63826e49 | −0.998726 | ||||||||
\(962\) | −9.13154e47 | −0.0547212 | ||||||||
\(963\) | 1.56604e48 | 0.0922507 | ||||||||
\(964\) | 1.50954e49 | 0.874126 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 3.32731e47 | 0.0186196 | ||||||||
\(967\) | 3.31961e48 | 0.182621 | 0.0913104 | − | 0.995822i | \(-0.470894\pi\) | ||||
0.0913104 | + | 0.995822i | \(0.470894\pi\) | |||||||
\(968\) | −1.38868e49 | −0.751030 | ||||||||
\(969\) | 1.94294e49 | 1.03304 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.67736e49 | 0.862003 | 0.431001 | − | 0.902351i | \(-0.358160\pi\) | ||||
0.431001 | + | 0.902351i | \(0.358160\pi\) | |||||||
\(972\) | −1.95710e49 | −0.988826 | ||||||||
\(973\) | 1.57991e48 | 0.0784819 | ||||||||
\(974\) | −6.22773e48 | −0.304164 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.20754e48 | −0.0570139 | ||||||||
\(977\) | −2.50785e49 | −1.16424 | −0.582118 | − | 0.813104i | \(-0.697776\pi\) | ||||
−0.582118 | + | 0.813104i | \(0.697776\pi\) | |||||||
\(978\) | 2.39225e48 | 0.109198 | ||||||||
\(979\) | −3.08812e49 | −1.38605 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.49366e49 | 1.08218 | ||||||||
\(982\) | 7.94535e48 | 0.339058 | ||||||||
\(983\) | −1.24304e49 | −0.521616 | −0.260808 | − | 0.965391i | \(-0.583989\pi\) | ||||
−0.260808 | + | 0.965391i | \(0.583989\pi\) | |||||||
\(984\) | −7.20883e48 | −0.297472 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.35293e48 | 0.173705 | ||||||||
\(987\) | −1.74342e48 | −0.0684177 | ||||||||
\(988\) | −4.35418e48 | −0.168042 | ||||||||
\(989\) | −1.10210e49 | −0.418295 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.48644e49 | −0.912774 | −0.456387 | − | 0.889781i | \(-0.650857\pi\) | ||||
−0.456387 | + | 0.889781i | \(0.650857\pi\) | |||||||
\(992\) | −5.54307e47 | −0.0200128 | ||||||||
\(993\) | −1.20437e48 | −0.0427658 | ||||||||
\(994\) | 7.56031e47 | 0.0264037 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.46854e49 | −0.496144 | ||||||||
\(997\) | 2.01041e49 | 0.668058 | 0.334029 | − | 0.942563i | \(-0.391592\pi\) | ||||
0.334029 | + | 0.942563i | \(0.391592\pi\) | |||||||
\(998\) | −1.13134e49 | −0.369777 | ||||||||
\(999\) | 4.84191e49 | 1.55663 |
(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 | 25.34.a.c.1.4 | 6 | ||
5.2 | odd | 4 | 25.34.b.c.24.7 | 12 | |||
5.3 | odd | 4 | 25.34.b.c.24.6 | 12 | |||
5.4 | even | 2 | 5.34.a.b.1.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5.34.a.b.1.3 | ✓ | 6 | 5.4 | even | 2 | ||
25.34.a.c.1.4 | 6 | 1.1 | even | 1 | trivial | ||
25.34.b.c.24.6 | 12 | 5.3 | odd | 4 | |||
25.34.b.c.24.7 | 12 | 5.2 | odd | 4 |