Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3,42,Mod(1,3)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 42, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3.1");
S:= CuspForms(chi, 42);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3 \) |
Weight: | \( k \) | \(=\) | \( 42 \) |
Character orbit: | \([\chi]\) | \(=\) | 3.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: | \(31.9415011369\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 196497525461x^{2} + 10360343667016365x + 6095744045744274504000 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{13}\cdot 3^{10}\cdot 5^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(263663.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.59943e6 | −1.07857 | −0.539287 | − | 0.842122i | \(-0.681306\pi\) | ||||
−0.539287 | + | 0.842122i | \(0.681306\pi\) | |||||||
\(3\) | 3.48678e9 | 0.577350 | ||||||||
\(4\) | 3.59152e11 | 0.163323 | ||||||||
\(5\) | 3.20915e14 | 1.50489 | 0.752446 | − | 0.658654i | \(-0.228874\pi\) | ||||
0.752446 | + | 0.658654i | \(0.228874\pi\) | |||||||
\(6\) | −5.57687e15 | −0.622715 | ||||||||
\(7\) | 2.35480e17 | 1.11544 | 0.557718 | − | 0.830030i | \(-0.311677\pi\) | ||||
0.557718 | + | 0.830030i | \(0.311677\pi\) | |||||||
\(8\) | 2.94274e18 | 0.902418 | ||||||||
\(9\) | 1.21577e19 | 0.333333 | ||||||||
\(10\) | −5.13282e20 | −1.62314 | ||||||||
\(11\) | 4.09335e21 | 1.83455 | 0.917273 | − | 0.398260i | \(-0.130386\pi\) | ||||
0.917273 | + | 0.398260i | \(0.130386\pi\) | |||||||
\(12\) | 1.25229e21 | 0.0942948 | ||||||||
\(13\) | 2.26252e22 | 0.330183 | 0.165091 | − | 0.986278i | \(-0.447208\pi\) | ||||
0.165091 | + | 0.986278i | \(0.447208\pi\) | |||||||
\(14\) | −3.76634e23 | −1.20308 | ||||||||
\(15\) | 1.11896e24 | 0.868850 | ||||||||
\(16\) | −5.49650e24 | −1.13665 | ||||||||
\(17\) | −2.18147e25 | −1.30181 | −0.650904 | − | 0.759160i | \(-0.725610\pi\) | ||||
−0.650904 | + | 0.759160i | \(0.725610\pi\) | |||||||
\(18\) | −1.94453e25 | −0.359525 | ||||||||
\(19\) | −1.65269e26 | −1.00866 | −0.504328 | − | 0.863512i | \(-0.668260\pi\) | ||||
−0.504328 | + | 0.863512i | \(0.668260\pi\) | |||||||
\(20\) | 1.15257e26 | 0.245784 | ||||||||
\(21\) | 8.21069e26 | 0.643997 | ||||||||
\(22\) | −6.54702e27 | −1.97869 | ||||||||
\(23\) | 1.04809e28 | 1.27344 | 0.636718 | − | 0.771097i | \(-0.280292\pi\) | ||||
0.636718 | + | 0.771097i | \(0.280292\pi\) | |||||||
\(24\) | 1.02607e28 | 0.521011 | ||||||||
\(25\) | 5.75119e28 | 1.26470 | ||||||||
\(26\) | −3.61875e28 | −0.356127 | ||||||||
\(27\) | 4.23912e28 | 0.192450 | ||||||||
\(28\) | 8.45732e28 | 0.182177 | ||||||||
\(29\) | −1.48336e29 | −0.155628 | −0.0778140 | − | 0.996968i | \(-0.524794\pi\) | ||||
−0.0778140 | + | 0.996968i | \(0.524794\pi\) | |||||||
\(30\) | −1.78970e30 | −0.937120 | ||||||||
\(31\) | 2.32552e30 | 0.621734 | 0.310867 | − | 0.950453i | \(-0.399381\pi\) | ||||
0.310867 | + | 0.950453i | \(0.399381\pi\) | |||||||
\(32\) | 2.32010e30 | 0.323542 | ||||||||
\(33\) | 1.42726e31 | 1.05918 | ||||||||
\(34\) | 3.48911e31 | 1.40410 | ||||||||
\(35\) | 7.55692e31 | 1.67861 | ||||||||
\(36\) | 4.36645e30 | 0.0544411 | ||||||||
\(37\) | −5.37090e31 | −0.381867 | −0.190933 | − | 0.981603i | \(-0.561151\pi\) | ||||
−0.190933 | + | 0.981603i | \(0.561151\pi\) | |||||||
\(38\) | 2.64337e32 | 1.08791 | ||||||||
\(39\) | 7.88894e31 | 0.190631 | ||||||||
\(40\) | 9.44372e32 | 1.35804 | ||||||||
\(41\) | −9.27726e32 | −0.804176 | −0.402088 | − | 0.915601i | \(-0.631715\pi\) | ||||
−0.402088 | + | 0.915601i | \(0.631715\pi\) | |||||||
\(42\) | −1.31324e33 | −0.694599 | ||||||||
\(43\) | 4.47072e33 | 1.45973 | 0.729867 | − | 0.683589i | \(-0.239582\pi\) | ||||
0.729867 | + | 0.683589i | \(0.239582\pi\) | |||||||
\(44\) | 1.47013e33 | 0.299624 | ||||||||
\(45\) | 3.90158e33 | 0.501631 | ||||||||
\(46\) | −1.67634e34 | −1.37350 | ||||||||
\(47\) | −1.02491e34 | −0.540355 | −0.270177 | − | 0.962811i | \(-0.587082\pi\) | ||||
−0.270177 | + | 0.962811i | \(0.587082\pi\) | |||||||
\(48\) | −1.91651e34 | −0.656245 | ||||||||
\(49\) | 1.08833e34 | 0.244198 | ||||||||
\(50\) | −9.19863e34 | −1.36407 | ||||||||
\(51\) | −7.60632e34 | −0.751599 | ||||||||
\(52\) | 8.12590e33 | 0.0539266 | ||||||||
\(53\) | −2.32449e35 | −1.04393 | −0.521966 | − | 0.852966i | \(-0.674801\pi\) | ||||
−0.521966 | + | 0.852966i | \(0.674801\pi\) | |||||||
\(54\) | −6.78017e34 | −0.207572 | ||||||||
\(55\) | 1.31362e36 | 2.76079 | ||||||||
\(56\) | 6.92958e35 | 1.00659 | ||||||||
\(57\) | −5.76258e35 | −0.582348 | ||||||||
\(58\) | 2.37253e35 | 0.167856 | ||||||||
\(59\) | −1.00765e35 | −0.0502159 | −0.0251080 | − | 0.999685i | \(-0.507993\pi\) | ||||
−0.0251080 | + | 0.999685i | \(0.507993\pi\) | |||||||
\(60\) | 4.01878e35 | 0.141904 | ||||||||
\(61\) | 1.56573e36 | 0.393964 | 0.196982 | − | 0.980407i | \(-0.436886\pi\) | ||||
0.196982 | + | 0.980407i | \(0.436886\pi\) | |||||||
\(62\) | −3.71950e36 | −0.670587 | ||||||||
\(63\) | 2.86289e36 | 0.371812 | ||||||||
\(64\) | 8.37609e36 | 0.787684 | ||||||||
\(65\) | 7.26079e36 | 0.496890 | ||||||||
\(66\) | −2.28280e37 | −1.14240 | ||||||||
\(67\) | −5.00920e36 | −0.184177 | −0.0920883 | − | 0.995751i | \(-0.529354\pi\) | ||||
−0.0920883 | + | 0.995751i | \(0.529354\pi\) | |||||||
\(68\) | −7.83480e36 | −0.212616 | ||||||||
\(69\) | 3.65446e37 | 0.735218 | ||||||||
\(70\) | −1.20868e38 | −1.81051 | ||||||||
\(71\) | −7.95732e37 | −0.891191 | −0.445596 | − | 0.895234i | \(-0.647008\pi\) | ||||
−0.445596 | + | 0.895234i | \(0.647008\pi\) | |||||||
\(72\) | 3.57769e37 | 0.300806 | ||||||||
\(73\) | −1.56377e38 | −0.990955 | −0.495477 | − | 0.868621i | \(-0.665007\pi\) | ||||
−0.495477 | + | 0.868621i | \(0.665007\pi\) | |||||||
\(74\) | 8.59038e37 | 0.411872 | ||||||||
\(75\) | 2.00532e38 | 0.730175 | ||||||||
\(76\) | −5.93568e37 | −0.164737 | ||||||||
\(77\) | 9.63902e38 | 2.04632 | ||||||||
\(78\) | −1.26178e38 | −0.205610 | ||||||||
\(79\) | 1.20235e39 | 1.50895 | 0.754475 | − | 0.656329i | \(-0.227892\pi\) | ||||
0.754475 | + | 0.656329i | \(0.227892\pi\) | |||||||
\(80\) | −1.76391e39 | −1.71053 | ||||||||
\(81\) | 1.47809e38 | 0.111111 | ||||||||
\(82\) | 1.48383e39 | 0.867363 | ||||||||
\(83\) | 2.45813e39 | 1.12074 | 0.560369 | − | 0.828243i | \(-0.310659\pi\) | ||||
0.560369 | + | 0.828243i | \(0.310659\pi\) | |||||||
\(84\) | 2.94889e38 | 0.105180 | ||||||||
\(85\) | −7.00068e39 | −1.95908 | ||||||||
\(86\) | −7.15060e39 | −1.57443 | ||||||||
\(87\) | −5.17216e38 | −0.0898519 | ||||||||
\(88\) | 1.20457e40 | 1.65553 | ||||||||
\(89\) | −1.06301e40 | −1.15889 | −0.579443 | − | 0.815012i | \(-0.696730\pi\) | ||||
−0.579443 | + | 0.815012i | \(0.696730\pi\) | |||||||
\(90\) | −6.24030e39 | −0.541046 | ||||||||
\(91\) | 5.32780e39 | 0.368298 | ||||||||
\(92\) | 3.76423e39 | 0.207982 | ||||||||
\(93\) | 8.10858e39 | 0.358958 | ||||||||
\(94\) | 1.63927e40 | 0.582813 | ||||||||
\(95\) | −5.30374e40 | −1.51792 | ||||||||
\(96\) | 8.08967e39 | 0.186797 | ||||||||
\(97\) | 2.08674e40 | 0.389626 | 0.194813 | − | 0.980840i | \(-0.437590\pi\) | ||||
0.194813 | + | 0.980840i | \(0.437590\pi\) | |||||||
\(98\) | −1.74071e40 | −0.263386 | ||||||||
\(99\) | 4.97655e40 | 0.611515 | ||||||||
\(100\) | 2.06555e40 | 0.206555 | ||||||||
\(101\) | 1.04865e41 | 0.855146 | 0.427573 | − | 0.903981i | \(-0.359369\pi\) | ||||
0.427573 | + | 0.903981i | \(0.359369\pi\) | |||||||
\(102\) | 1.21658e41 | 0.810656 | ||||||||
\(103\) | −2.03937e41 | −1.11258 | −0.556292 | − | 0.830987i | \(-0.687777\pi\) | ||||
−0.556292 | + | 0.830987i | \(0.687777\pi\) | |||||||
\(104\) | 6.65803e40 | 0.297963 | ||||||||
\(105\) | 2.63494e41 | 0.969147 | ||||||||
\(106\) | 3.71786e41 | 1.12596 | ||||||||
\(107\) | −7.60455e41 | −1.89979 | −0.949896 | − | 0.312567i | \(-0.898811\pi\) | ||||
−0.949896 | + | 0.312567i | \(0.898811\pi\) | |||||||
\(108\) | 1.52249e40 | 0.0314316 | ||||||||
\(109\) | 1.97252e41 | 0.337115 | 0.168557 | − | 0.985692i | \(-0.446089\pi\) | ||||
0.168557 | + | 0.985692i | \(0.446089\pi\) | |||||||
\(110\) | −2.10104e42 | −2.97772 | ||||||||
\(111\) | −1.87272e41 | −0.220471 | ||||||||
\(112\) | −1.29432e42 | −1.26786 | ||||||||
\(113\) | 7.19758e41 | 0.587595 | 0.293798 | − | 0.955868i | \(-0.405081\pi\) | ||||
0.293798 | + | 0.955868i | \(0.405081\pi\) | |||||||
\(114\) | 9.21685e41 | 0.628106 | ||||||||
\(115\) | 3.36347e42 | 1.91638 | ||||||||
\(116\) | −5.32752e40 | −0.0254177 | ||||||||
\(117\) | 2.75070e41 | 0.110061 | ||||||||
\(118\) | 1.61166e41 | 0.0541617 | ||||||||
\(119\) | −5.13694e42 | −1.45208 | ||||||||
\(120\) | 3.29282e42 | 0.784066 | ||||||||
\(121\) | 1.17770e43 | 2.36556 | ||||||||
\(122\) | −2.50428e42 | −0.424919 | ||||||||
\(123\) | −3.23478e42 | −0.464291 | ||||||||
\(124\) | 8.35214e41 | 0.101544 | ||||||||
\(125\) | 3.86292e42 | 0.398346 | ||||||||
\(126\) | −4.57899e42 | −0.401027 | ||||||||
\(127\) | −7.84129e42 | −0.583998 | −0.291999 | − | 0.956419i | \(-0.594320\pi\) | ||||
−0.291999 | + | 0.956419i | \(0.594320\pi\) | |||||||
\(128\) | −1.84989e43 | −1.17312 | ||||||||
\(129\) | 1.55884e43 | 0.842778 | ||||||||
\(130\) | −1.16131e43 | −0.535933 | ||||||||
\(131\) | 1.88589e43 | 0.743799 | 0.371899 | − | 0.928273i | \(-0.378707\pi\) | ||||
0.371899 | + | 0.928273i | \(0.378707\pi\) | |||||||
\(132\) | 5.12604e42 | 0.172988 | ||||||||
\(133\) | −3.89177e43 | −1.12509 | ||||||||
\(134\) | 8.01186e42 | 0.198648 | ||||||||
\(135\) | 1.36040e43 | 0.289617 | ||||||||
\(136\) | −6.41952e43 | −1.17477 | ||||||||
\(137\) | 4.38524e43 | 0.690592 | 0.345296 | − | 0.938494i | \(-0.387779\pi\) | ||||
0.345296 | + | 0.938494i | \(0.387779\pi\) | |||||||
\(138\) | −5.84504e43 | −0.792988 | ||||||||
\(139\) | 2.01750e43 | 0.236054 | 0.118027 | − | 0.993010i | \(-0.462343\pi\) | ||||
0.118027 | + | 0.993010i | \(0.462343\pi\) | |||||||
\(140\) | 2.71408e43 | 0.274157 | ||||||||
\(141\) | −3.57363e43 | −0.311974 | ||||||||
\(142\) | 1.27272e44 | 0.961216 | ||||||||
\(143\) | 9.26130e43 | 0.605736 | ||||||||
\(144\) | −6.68246e43 | −0.378883 | ||||||||
\(145\) | −4.76033e43 | −0.234203 | ||||||||
\(146\) | 2.50114e44 | 1.06882 | ||||||||
\(147\) | 3.79479e43 | 0.140988 | ||||||||
\(148\) | −1.92897e43 | −0.0623677 | ||||||||
\(149\) | 3.54704e44 | 0.998958 | 0.499479 | − | 0.866326i | \(-0.333525\pi\) | ||||
0.499479 | + | 0.866326i | \(0.333525\pi\) | |||||||
\(150\) | −3.20736e44 | −0.787549 | ||||||||
\(151\) | 7.36078e44 | 1.57724 | 0.788618 | − | 0.614884i | \(-0.210797\pi\) | ||||
0.788618 | + | 0.614884i | \(0.210797\pi\) | |||||||
\(152\) | −4.86345e44 | −0.910230 | ||||||||
\(153\) | −2.65216e44 | −0.433936 | ||||||||
\(154\) | −1.54169e45 | −2.20711 | ||||||||
\(155\) | 7.46294e44 | 0.935643 | ||||||||
\(156\) | 2.83333e43 | 0.0311345 | ||||||||
\(157\) | −1.20760e45 | −1.16407 | −0.582036 | − | 0.813163i | \(-0.697744\pi\) | ||||
−0.582036 | + | 0.813163i | \(0.697744\pi\) | |||||||
\(158\) | −1.92307e45 | −1.62752 | ||||||||
\(159\) | −8.10499e44 | −0.602714 | ||||||||
\(160\) | 7.44554e44 | 0.486897 | ||||||||
\(161\) | 2.46804e45 | 1.42044 | ||||||||
\(162\) | −2.36410e44 | −0.119842 | ||||||||
\(163\) | 3.84692e45 | 1.71897 | 0.859484 | − | 0.511163i | \(-0.170785\pi\) | ||||
0.859484 | + | 0.511163i | \(0.170785\pi\) | |||||||
\(164\) | −3.33195e44 | −0.131341 | ||||||||
\(165\) | 4.58030e45 | 1.59394 | ||||||||
\(166\) | −3.93160e45 | −1.20880 | ||||||||
\(167\) | −1.57930e45 | −0.429316 | −0.214658 | − | 0.976689i | \(-0.568864\pi\) | ||||
−0.214658 | + | 0.976689i | \(0.568864\pi\) | |||||||
\(168\) | 2.41620e45 | 0.581155 | ||||||||
\(169\) | −4.18355e45 | −0.890979 | ||||||||
\(170\) | 1.11971e46 | 2.11301 | ||||||||
\(171\) | −2.00929e45 | −0.336219 | ||||||||
\(172\) | 1.60567e45 | 0.238409 | ||||||||
\(173\) | −1.39579e46 | −1.84024 | −0.920122 | − | 0.391631i | \(-0.871911\pi\) | ||||
−0.920122 | + | 0.391631i | \(0.871911\pi\) | |||||||
\(174\) | 8.27250e44 | 0.0969120 | ||||||||
\(175\) | 1.35429e46 | 1.41069 | ||||||||
\(176\) | −2.24991e46 | −2.08523 | ||||||||
\(177\) | −3.51344e44 | −0.0289922 | ||||||||
\(178\) | 1.70021e46 | 1.24995 | ||||||||
\(179\) | −4.81309e45 | −0.315454 | −0.157727 | − | 0.987483i | \(-0.550417\pi\) | ||||
−0.157727 | + | 0.987483i | \(0.550417\pi\) | |||||||
\(180\) | 1.40126e45 | 0.0819280 | ||||||||
\(181\) | −1.02164e46 | −0.533199 | −0.266599 | − | 0.963807i | \(-0.585900\pi\) | ||||
−0.266599 | + | 0.963807i | \(0.585900\pi\) | |||||||
\(182\) | −8.52144e45 | −0.397237 | ||||||||
\(183\) | 5.45938e45 | 0.227455 | ||||||||
\(184\) | 3.08425e46 | 1.14917 | ||||||||
\(185\) | −1.72360e46 | −0.574668 | ||||||||
\(186\) | −1.29691e46 | −0.387164 | ||||||||
\(187\) | −8.92952e46 | −2.38822 | ||||||||
\(188\) | −3.68098e45 | −0.0882525 | ||||||||
\(189\) | 9.98228e45 | 0.214666 | ||||||||
\(190\) | 8.48297e46 | 1.63719 | ||||||||
\(191\) | 3.42603e46 | 0.593755 | 0.296878 | − | 0.954916i | \(-0.404055\pi\) | ||||
0.296878 | + | 0.954916i | \(0.404055\pi\) | |||||||
\(192\) | 2.92056e46 | 0.454770 | ||||||||
\(193\) | 1.60284e46 | 0.224370 | 0.112185 | − | 0.993687i | \(-0.464215\pi\) | ||||
0.112185 | + | 0.993687i | \(0.464215\pi\) | |||||||
\(194\) | −3.33759e46 | −0.420241 | ||||||||
\(195\) | 2.53168e46 | 0.286879 | ||||||||
\(196\) | 3.90877e45 | 0.0398833 | ||||||||
\(197\) | 1.67914e47 | 1.54358 | 0.771792 | − | 0.635875i | \(-0.219361\pi\) | ||||
0.771792 | + | 0.635875i | \(0.219361\pi\) | |||||||
\(198\) | −7.95965e46 | −0.659565 | ||||||||
\(199\) | −5.27435e46 | −0.394168 | −0.197084 | − | 0.980387i | \(-0.563147\pi\) | ||||
−0.197084 | + | 0.980387i | \(0.563147\pi\) | |||||||
\(200\) | 1.69243e47 | 1.14129 | ||||||||
\(201\) | −1.74660e46 | −0.106334 | ||||||||
\(202\) | −1.67723e47 | −0.922339 | ||||||||
\(203\) | −3.49302e46 | −0.173593 | ||||||||
\(204\) | −2.73183e46 | −0.122754 | ||||||||
\(205\) | −2.97722e47 | −1.21020 | ||||||||
\(206\) | 3.26183e47 | 1.20001 | ||||||||
\(207\) | 1.27423e47 | 0.424478 | ||||||||
\(208\) | −1.24360e47 | −0.375302 | ||||||||
\(209\) | −6.76504e47 | −1.85043 | ||||||||
\(210\) | −4.21440e47 | −1.04530 | ||||||||
\(211\) | −4.70265e47 | −1.05816 | −0.529081 | − | 0.848571i | \(-0.677463\pi\) | ||||
−0.529081 | + | 0.848571i | \(0.677463\pi\) | |||||||
\(212\) | −8.34844e46 | −0.170498 | ||||||||
\(213\) | −2.77455e47 | −0.514530 | ||||||||
\(214\) | 1.21629e48 | 2.04907 | ||||||||
\(215\) | 1.43472e48 | 2.19674 | ||||||||
\(216\) | 1.24746e47 | 0.173670 | ||||||||
\(217\) | 5.47614e47 | 0.693505 | ||||||||
\(218\) | −3.15490e47 | −0.363603 | ||||||||
\(219\) | −5.45252e47 | −0.572128 | ||||||||
\(220\) | 4.71788e47 | 0.450902 | ||||||||
\(221\) | −4.93564e47 | −0.429835 | ||||||||
\(222\) | 2.99528e47 | 0.237794 | ||||||||
\(223\) | 6.26777e47 | 0.453799 | 0.226899 | − | 0.973918i | \(-0.427141\pi\) | ||||
0.226899 | + | 0.973918i | \(0.427141\pi\) | |||||||
\(224\) | 5.46337e47 | 0.360891 | ||||||||
\(225\) | 6.99211e47 | 0.421567 | ||||||||
\(226\) | −1.15120e48 | −0.633766 | ||||||||
\(227\) | 1.14299e48 | 0.574794 | 0.287397 | − | 0.957812i | \(-0.407210\pi\) | ||||
0.287397 | + | 0.957812i | \(0.407210\pi\) | |||||||
\(228\) | −2.06964e47 | −0.0951110 | ||||||||
\(229\) | −2.06328e48 | −0.866825 | −0.433413 | − | 0.901196i | \(-0.642691\pi\) | ||||
−0.433413 | + | 0.901196i | \(0.642691\pi\) | |||||||
\(230\) | −5.37964e48 | −2.06696 | ||||||||
\(231\) | 3.36092e48 | 1.18144 | ||||||||
\(232\) | −4.36515e47 | −0.140442 | ||||||||
\(233\) | −7.30911e47 | −0.215312 | −0.107656 | − | 0.994188i | \(-0.534335\pi\) | ||||
−0.107656 | + | 0.994188i | \(0.534335\pi\) | |||||||
\(234\) | −4.39955e47 | −0.118709 | ||||||||
\(235\) | −3.28909e48 | −0.813175 | ||||||||
\(236\) | −3.61898e46 | −0.00820144 | ||||||||
\(237\) | 4.19233e48 | 0.871193 | ||||||||
\(238\) | 8.21617e48 | 1.56618 | ||||||||
\(239\) | 3.57354e48 | 0.625089 | 0.312545 | − | 0.949903i | \(-0.398819\pi\) | ||||
0.312545 | + | 0.949903i | \(0.398819\pi\) | |||||||
\(240\) | −6.15037e48 | −0.987577 | ||||||||
\(241\) | 2.64837e47 | 0.0390507 | 0.0195254 | − | 0.999809i | \(-0.493784\pi\) | ||||
0.0195254 | + | 0.999809i | \(0.493784\pi\) | |||||||
\(242\) | −1.88364e49 | −2.55143 | ||||||||
\(243\) | 5.15378e47 | 0.0641500 | ||||||||
\(244\) | 5.62336e47 | 0.0643435 | ||||||||
\(245\) | 3.49263e48 | 0.367492 | ||||||||
\(246\) | 5.17381e48 | 0.500773 | ||||||||
\(247\) | −3.73926e48 | −0.333041 | ||||||||
\(248\) | 6.84340e48 | 0.561064 | ||||||||
\(249\) | 8.57097e48 | 0.647058 | ||||||||
\(250\) | −6.17847e48 | −0.429646 | ||||||||
\(251\) | 1.94890e48 | 0.124876 | 0.0624380 | − | 0.998049i | \(-0.480112\pi\) | ||||
0.0624380 | + | 0.998049i | \(0.480112\pi\) | |||||||
\(252\) | 1.02821e48 | 0.0607256 | ||||||||
\(253\) | 4.29018e49 | 2.33617 | ||||||||
\(254\) | 1.25416e49 | 0.629886 | ||||||||
\(255\) | −2.44099e49 | −1.13108 | ||||||||
\(256\) | 1.11685e49 | 0.477612 | ||||||||
\(257\) | 9.44017e48 | 0.372692 | 0.186346 | − | 0.982484i | \(-0.440335\pi\) | ||||
0.186346 | + | 0.982484i | \(0.440335\pi\) | |||||||
\(258\) | −2.49326e49 | −0.908999 | ||||||||
\(259\) | −1.26474e49 | −0.425948 | ||||||||
\(260\) | 2.60773e48 | 0.0811537 | ||||||||
\(261\) | −1.80342e48 | −0.0518760 | ||||||||
\(262\) | −3.01635e49 | −0.802243 | ||||||||
\(263\) | −5.72032e49 | −1.40711 | −0.703554 | − | 0.710641i | \(-0.748405\pi\) | ||||
−0.703554 | + | 0.710641i | \(0.748405\pi\) | |||||||
\(264\) | 4.20007e49 | 0.955819 | ||||||||
\(265\) | −7.45964e49 | −1.57100 | ||||||||
\(266\) | 6.22461e49 | 1.21350 | ||||||||
\(267\) | −3.70648e49 | −0.669084 | ||||||||
\(268\) | −1.79906e48 | −0.0300804 | ||||||||
\(269\) | −2.68077e49 | −0.415278 | −0.207639 | − | 0.978206i | \(-0.566578\pi\) | ||||
−0.207639 | + | 0.978206i | \(0.566578\pi\) | |||||||
\(270\) | −2.17586e49 | −0.312373 | ||||||||
\(271\) | −8.22411e49 | −1.09451 | −0.547253 | − | 0.836967i | \(-0.684327\pi\) | ||||
−0.547253 | + | 0.836967i | \(0.684327\pi\) | |||||||
\(272\) | 1.19905e50 | 1.47970 | ||||||||
\(273\) | 1.85769e49 | 0.212637 | ||||||||
\(274\) | −7.01388e49 | −0.744855 | ||||||||
\(275\) | 2.35416e50 | 2.32015 | ||||||||
\(276\) | 1.31250e49 | 0.120078 | ||||||||
\(277\) | 2.17515e49 | 0.184780 | 0.0923898 | − | 0.995723i | \(-0.470549\pi\) | ||||
0.0923898 | + | 0.995723i | \(0.470549\pi\) | |||||||
\(278\) | −3.22685e49 | −0.254601 | ||||||||
\(279\) | 2.82729e49 | 0.207245 | ||||||||
\(280\) | 2.22381e50 | 1.51481 | ||||||||
\(281\) | −1.76875e50 | −1.11992 | −0.559961 | − | 0.828519i | \(-0.689184\pi\) | ||||
−0.559961 | + | 0.828519i | \(0.689184\pi\) | |||||||
\(282\) | 5.71578e49 | 0.336487 | ||||||||
\(283\) | 1.98156e50 | 1.08489 | 0.542444 | − | 0.840092i | \(-0.317499\pi\) | ||||
0.542444 | + | 0.840092i | \(0.317499\pi\) | |||||||
\(284\) | −2.85789e49 | −0.145552 | ||||||||
\(285\) | −1.84930e50 | −0.876371 | ||||||||
\(286\) | −1.48128e50 | −0.653331 | ||||||||
\(287\) | −2.18461e50 | −0.897007 | ||||||||
\(288\) | 2.82069e49 | 0.107847 | ||||||||
\(289\) | 1.95077e50 | 0.694703 | ||||||||
\(290\) | 7.61382e49 | 0.252606 | ||||||||
\(291\) | 7.27601e49 | 0.224951 | ||||||||
\(292\) | −5.61630e49 | −0.161846 | ||||||||
\(293\) | −5.47637e50 | −1.47132 | −0.735659 | − | 0.677352i | \(-0.763128\pi\) | ||||
−0.735659 | + | 0.677352i | \(0.763128\pi\) | |||||||
\(294\) | −6.06949e49 | −0.152066 | ||||||||
\(295\) | −3.23369e49 | −0.0755696 | ||||||||
\(296\) | −1.58052e50 | −0.344603 | ||||||||
\(297\) | 1.73522e50 | 0.353058 | ||||||||
\(298\) | −5.67323e50 | −1.07745 | ||||||||
\(299\) | 2.37132e50 | 0.420467 | ||||||||
\(300\) | 7.20213e49 | 0.119255 | ||||||||
\(301\) | 1.05277e51 | 1.62824 | ||||||||
\(302\) | −1.17731e51 | −1.70117 | ||||||||
\(303\) | 3.65640e50 | 0.493719 | ||||||||
\(304\) | 9.08402e50 | 1.14649 | ||||||||
\(305\) | 5.02468e50 | 0.592873 | ||||||||
\(306\) | 4.24194e50 | 0.468032 | ||||||||
\(307\) | −1.15018e51 | −1.18694 | −0.593468 | − | 0.804857i | \(-0.702242\pi\) | ||||
−0.593468 | + | 0.804857i | \(0.702242\pi\) | |||||||
\(308\) | 3.46187e50 | 0.334212 | ||||||||
\(309\) | −7.11085e50 | −0.642351 | ||||||||
\(310\) | −1.19365e51 | −1.00916 | ||||||||
\(311\) | −9.25059e50 | −0.732119 | −0.366059 | − | 0.930592i | \(-0.619293\pi\) | ||||
−0.366059 | + | 0.930592i | \(0.619293\pi\) | |||||||
\(312\) | 2.32151e50 | 0.172029 | ||||||||
\(313\) | 1.36691e51 | 0.948597 | 0.474299 | − | 0.880364i | \(-0.342702\pi\) | ||||
0.474299 | + | 0.880364i | \(0.342702\pi\) | |||||||
\(314\) | 1.93147e51 | 1.25554 | ||||||||
\(315\) | 9.18746e50 | 0.559537 | ||||||||
\(316\) | 4.31826e50 | 0.246447 | ||||||||
\(317\) | 9.60481e49 | 0.0513776 | 0.0256888 | − | 0.999670i | \(-0.491822\pi\) | ||||
0.0256888 | + | 0.999670i | \(0.491822\pi\) | |||||||
\(318\) | 1.29634e51 | 0.650072 | ||||||||
\(319\) | −6.07191e50 | −0.285507 | ||||||||
\(320\) | 2.68802e51 | 1.18538 | ||||||||
\(321\) | −2.65154e51 | −1.09685 | ||||||||
\(322\) | −3.94746e51 | −1.53205 | ||||||||
\(323\) | 3.60530e51 | 1.31308 | ||||||||
\(324\) | 5.30858e49 | 0.0181470 | ||||||||
\(325\) | 1.30122e51 | 0.417583 | ||||||||
\(326\) | −6.15288e51 | −1.85404 | ||||||||
\(327\) | 6.87774e50 | 0.194633 | ||||||||
\(328\) | −2.73006e51 | −0.725703 | ||||||||
\(329\) | −2.41346e51 | −0.602731 | ||||||||
\(330\) | −7.32587e51 | −1.71919 | ||||||||
\(331\) | 4.43023e51 | 0.977130 | 0.488565 | − | 0.872527i | \(-0.337520\pi\) | ||||
0.488565 | + | 0.872527i | \(0.337520\pi\) | |||||||
\(332\) | 8.82842e50 | 0.183043 | ||||||||
\(333\) | −6.52976e50 | −0.127289 | ||||||||
\(334\) | 2.52598e51 | 0.463050 | ||||||||
\(335\) | −1.60753e51 | −0.277166 | ||||||||
\(336\) | −4.51300e51 | −0.731999 | ||||||||
\(337\) | −3.71004e50 | −0.0566194 | −0.0283097 | − | 0.999599i | \(-0.509012\pi\) | ||||
−0.0283097 | + | 0.999599i | \(0.509012\pi\) | |||||||
\(338\) | 6.69129e51 | 0.960988 | ||||||||
\(339\) | 2.50964e51 | 0.339248 | ||||||||
\(340\) | −2.51431e51 | −0.319964 | ||||||||
\(341\) | 9.51915e51 | 1.14060 | ||||||||
\(342\) | 3.21372e51 | 0.362637 | ||||||||
\(343\) | −7.93199e51 | −0.843049 | ||||||||
\(344\) | 1.31562e52 | 1.31729 | ||||||||
\(345\) | 1.17277e52 | 1.10642 | ||||||||
\(346\) | 2.23247e52 | 1.98484 | ||||||||
\(347\) | −2.30793e51 | −0.193405 | −0.0967025 | − | 0.995313i | \(-0.530830\pi\) | ||||
−0.0967025 | + | 0.995313i | \(0.530830\pi\) | |||||||
\(348\) | −1.85759e50 | −0.0146749 | ||||||||
\(349\) | −1.85442e52 | −1.38129 | −0.690647 | − | 0.723192i | \(-0.742674\pi\) | ||||
−0.690647 | + | 0.723192i | \(0.742674\pi\) | |||||||
\(350\) | −2.16610e52 | −1.52154 | ||||||||
\(351\) | 9.59110e50 | 0.0635437 | ||||||||
\(352\) | 9.49695e51 | 0.593553 | ||||||||
\(353\) | −5.30734e51 | −0.312965 | −0.156482 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156482 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(354\) | 5.61951e50 | 0.0312702 | ||||||||
\(355\) | −2.55363e52 | −1.34115 | ||||||||
\(356\) | −3.81781e51 | −0.189273 | ||||||||
\(357\) | −1.79114e52 | −0.838361 | ||||||||
\(358\) | 7.69820e51 | 0.340241 | ||||||||
\(359\) | −6.85308e51 | −0.286055 | −0.143028 | − | 0.989719i | \(-0.545684\pi\) | ||||
−0.143028 | + | 0.989719i | \(0.545684\pi\) | |||||||
\(360\) | 1.14814e52 | 0.452681 | ||||||||
\(361\) | 4.66809e50 | 0.0173877 | ||||||||
\(362\) | 1.63405e52 | 0.575095 | ||||||||
\(363\) | 4.10637e52 | 1.36575 | ||||||||
\(364\) | 1.91349e51 | 0.0601517 | ||||||||
\(365\) | −5.01837e52 | −1.49128 | ||||||||
\(366\) | −8.73189e51 | −0.245327 | ||||||||
\(367\) | 3.14343e51 | 0.0835120 | 0.0417560 | − | 0.999128i | \(-0.486705\pi\) | ||||
0.0417560 | + | 0.999128i | \(0.486705\pi\) | |||||||
\(368\) | −5.76081e52 | −1.44745 | ||||||||
\(369\) | −1.12790e52 | −0.268059 | ||||||||
\(370\) | 2.75678e52 | 0.619822 | ||||||||
\(371\) | −5.47371e52 | −1.16444 | ||||||||
\(372\) | 2.91221e51 | 0.0586263 | ||||||||
\(373\) | 9.77187e52 | 1.86186 | 0.930929 | − | 0.365199i | \(-0.118999\pi\) | ||||
0.930929 | + | 0.365199i | \(0.118999\pi\) | |||||||
\(374\) | 1.42821e53 | 2.57588 | ||||||||
\(375\) | 1.34692e52 | 0.229985 | ||||||||
\(376\) | −3.01604e52 | −0.487626 | ||||||||
\(377\) | −3.35614e51 | −0.0513857 | ||||||||
\(378\) | −1.59660e52 | −0.231533 | ||||||||
\(379\) | −6.70476e52 | −0.921042 | −0.460521 | − | 0.887649i | \(-0.652337\pi\) | ||||
−0.460521 | + | 0.887649i | \(0.652337\pi\) | |||||||
\(380\) | −1.90485e52 | −0.247912 | ||||||||
\(381\) | −2.73409e52 | −0.337171 | ||||||||
\(382\) | −5.47970e52 | −0.640410 | ||||||||
\(383\) | 2.82438e52 | 0.312859 | 0.156429 | − | 0.987689i | \(-0.450002\pi\) | ||||
0.156429 | + | 0.987689i | \(0.450002\pi\) | |||||||
\(384\) | −6.45017e52 | −0.677300 | ||||||||
\(385\) | 3.09331e53 | 3.07949 | ||||||||
\(386\) | −2.56363e52 | −0.242000 | ||||||||
\(387\) | 5.43535e52 | 0.486578 | ||||||||
\(388\) | 7.49457e51 | 0.0636350 | ||||||||
\(389\) | −1.90072e52 | −0.153091 | −0.0765457 | − | 0.997066i | \(-0.524389\pi\) | ||||
−0.0765457 | + | 0.997066i | \(0.524389\pi\) | |||||||
\(390\) | −4.04925e52 | −0.309421 | ||||||||
\(391\) | −2.28637e53 | −1.65777 | ||||||||
\(392\) | 3.20269e52 | 0.220369 | ||||||||
\(393\) | 6.57570e52 | 0.429433 | ||||||||
\(394\) | −2.68567e53 | −1.66487 | ||||||||
\(395\) | 3.85852e53 | 2.27081 | ||||||||
\(396\) | 1.78734e52 | 0.0998747 | ||||||||
\(397\) | −1.59987e53 | −0.848947 | −0.424474 | − | 0.905440i | \(-0.639541\pi\) | ||||
−0.424474 | + | 0.905440i | \(0.639541\pi\) | |||||||
\(398\) | 8.43596e52 | 0.425139 | ||||||||
\(399\) | −1.35697e53 | −0.649572 | ||||||||
\(400\) | −3.16114e53 | −1.43752 | ||||||||
\(401\) | −2.13645e53 | −0.923067 | −0.461534 | − | 0.887123i | \(-0.652701\pi\) | ||||
−0.461534 | + | 0.887123i | \(0.652701\pi\) | |||||||
\(402\) | 2.79356e52 | 0.114690 | ||||||||
\(403\) | 5.26154e52 | 0.205286 | ||||||||
\(404\) | 3.76623e52 | 0.139665 | ||||||||
\(405\) | 4.74341e52 | 0.167210 | ||||||||
\(406\) | 5.58684e52 | 0.187233 | ||||||||
\(407\) | −2.19849e53 | −0.700551 | ||||||||
\(408\) | −2.23835e53 | −0.678257 | ||||||||
\(409\) | 2.66798e53 | 0.768872 | 0.384436 | − | 0.923152i | \(-0.374396\pi\) | ||||
0.384436 | + | 0.923152i | \(0.374396\pi\) | |||||||
\(410\) | 4.76185e53 | 1.30529 | ||||||||
\(411\) | 1.52904e53 | 0.398713 | ||||||||
\(412\) | −7.32444e52 | −0.181711 | ||||||||
\(413\) | −2.37281e52 | −0.0560127 | ||||||||
\(414\) | −2.03804e53 | −0.457832 | ||||||||
\(415\) | 7.88851e53 | 1.68659 | ||||||||
\(416\) | 5.24927e52 | 0.106828 | ||||||||
\(417\) | 7.03459e52 | 0.136286 | ||||||||
\(418\) | 1.08202e54 | 1.99582 | ||||||||
\(419\) | −4.29684e53 | −0.754678 | −0.377339 | − | 0.926075i | \(-0.623161\pi\) | ||||
−0.377339 | + | 0.926075i | \(0.623161\pi\) | |||||||
\(420\) | 9.46343e52 | 0.158284 | ||||||||
\(421\) | −2.09315e53 | −0.333439 | −0.166720 | − | 0.986004i | \(-0.553317\pi\) | ||||
−0.166720 | + | 0.986004i | \(0.553317\pi\) | |||||||
\(422\) | 7.52156e53 | 1.14131 | ||||||||
\(423\) | −1.24605e53 | −0.180118 | ||||||||
\(424\) | −6.84038e53 | −0.942063 | ||||||||
\(425\) | −1.25461e54 | −1.64640 | ||||||||
\(426\) | 4.43769e53 | 0.554959 | ||||||||
\(427\) | 3.68700e53 | 0.439442 | ||||||||
\(428\) | −2.73119e53 | −0.310280 | ||||||||
\(429\) | 3.22921e53 | 0.349722 | ||||||||
\(430\) | −2.29474e54 | −2.36935 | ||||||||
\(431\) | −1.17896e54 | −1.16069 | −0.580343 | − | 0.814372i | \(-0.697081\pi\) | ||||
−0.580343 | + | 0.814372i | \(0.697081\pi\) | |||||||
\(432\) | −2.33003e53 | −0.218748 | ||||||||
\(433\) | 9.09513e53 | 0.814342 | 0.407171 | − | 0.913352i | \(-0.366515\pi\) | ||||
0.407171 | + | 0.913352i | \(0.366515\pi\) | |||||||
\(434\) | −8.75869e53 | −0.747997 | ||||||||
\(435\) | −1.65983e53 | −0.135217 | ||||||||
\(436\) | 7.08433e52 | 0.0550587 | ||||||||
\(437\) | −1.73217e54 | −1.28446 | ||||||||
\(438\) | 8.72093e53 | 0.617083 | ||||||||
\(439\) | 2.37938e54 | 1.60673 | 0.803363 | − | 0.595490i | \(-0.203042\pi\) | ||||
0.803363 | + | 0.595490i | \(0.203042\pi\) | |||||||
\(440\) | 3.86564e54 | 2.49139 | ||||||||
\(441\) | 1.32316e53 | 0.0813994 | ||||||||
\(442\) | 7.89420e53 | 0.463609 | ||||||||
\(443\) | −2.17243e54 | −1.21806 | −0.609030 | − | 0.793147i | \(-0.708441\pi\) | ||||
−0.609030 | + | 0.793147i | \(0.708441\pi\) | |||||||
\(444\) | −6.72590e52 | −0.0360080 | ||||||||
\(445\) | −3.41135e54 | −1.74400 | ||||||||
\(446\) | −1.00249e54 | −0.489456 | ||||||||
\(447\) | 1.23677e54 | 0.576748 | ||||||||
\(448\) | 1.97241e54 | 0.878612 | ||||||||
\(449\) | 4.64070e54 | 1.97485 | 0.987423 | − | 0.158100i | \(-0.0505370\pi\) | ||||
0.987423 | + | 0.158100i | \(0.0505370\pi\) | |||||||
\(450\) | −1.11834e54 | −0.454691 | ||||||||
\(451\) | −3.79751e54 | −1.47530 | ||||||||
\(452\) | 2.58502e53 | 0.0959681 | ||||||||
\(453\) | 2.56655e54 | 0.910617 | ||||||||
\(454\) | −1.82813e54 | −0.619959 | ||||||||
\(455\) | 1.70977e54 | 0.554249 | ||||||||
\(456\) | −1.69578e54 | −0.525521 | ||||||||
\(457\) | 2.01271e54 | 0.596346 | 0.298173 | − | 0.954512i | \(-0.403623\pi\) | ||||
0.298173 | + | 0.954512i | \(0.403623\pi\) | |||||||
\(458\) | 3.30008e54 | 0.934936 | ||||||||
\(459\) | −9.24751e53 | −0.250533 | ||||||||
\(460\) | 1.20800e54 | 0.312990 | ||||||||
\(461\) | −4.15737e54 | −1.03027 | −0.515133 | − | 0.857110i | \(-0.672258\pi\) | ||||
−0.515133 | + | 0.857110i | \(0.672258\pi\) | |||||||
\(462\) | −5.37555e54 | −1.27427 | ||||||||
\(463\) | 5.22768e54 | 1.18549 | 0.592746 | − | 0.805390i | \(-0.298044\pi\) | ||||
0.592746 | + | 0.805390i | \(0.298044\pi\) | |||||||
\(464\) | 8.15329e53 | 0.176894 | ||||||||
\(465\) | 2.60217e54 | 0.540194 | ||||||||
\(466\) | 1.16904e54 | 0.232230 | ||||||||
\(467\) | −9.76914e54 | −1.85721 | −0.928604 | − | 0.371073i | \(-0.878990\pi\) | ||||
−0.928604 | + | 0.371073i | \(0.878990\pi\) | |||||||
\(468\) | 9.87920e52 | 0.0179755 | ||||||||
\(469\) | −1.17957e54 | −0.205437 | ||||||||
\(470\) | 5.26066e54 | 0.877070 | ||||||||
\(471\) | −4.21064e54 | −0.672077 | ||||||||
\(472\) | −2.96524e53 | −0.0453158 | ||||||||
\(473\) | 1.83002e55 | 2.67795 | ||||||||
\(474\) | −6.70533e54 | −0.939646 | ||||||||
\(475\) | −9.50495e54 | −1.27565 | ||||||||
\(476\) | −1.84494e54 | −0.237159 | ||||||||
\(477\) | −2.82603e54 | −0.347977 | ||||||||
\(478\) | −5.71563e54 | −0.674205 | ||||||||
\(479\) | −1.65944e55 | −1.87536 | −0.937678 | − | 0.347505i | \(-0.887029\pi\) | ||||
−0.937678 | + | 0.347505i | \(0.887029\pi\) | |||||||
\(480\) | 2.59610e54 | 0.281110 | ||||||||
\(481\) | −1.21518e54 | −0.126086 | ||||||||
\(482\) | −4.23588e53 | −0.0421191 | ||||||||
\(483\) | 8.60552e54 | 0.820089 | ||||||||
\(484\) | 4.22972e54 | 0.386351 | ||||||||
\(485\) | 6.69667e54 | 0.586345 | ||||||||
\(486\) | −8.24310e53 | −0.0691906 | ||||||||
\(487\) | 4.75101e54 | 0.382333 | 0.191167 | − | 0.981558i | \(-0.438773\pi\) | ||||
0.191167 | + | 0.981558i | \(0.438773\pi\) | |||||||
\(488\) | 4.60756e54 | 0.355520 | ||||||||
\(489\) | 1.34134e55 | 0.992447 | ||||||||
\(490\) | −5.58622e54 | −0.396368 | ||||||||
\(491\) | 1.29983e55 | 0.884538 | 0.442269 | − | 0.896883i | \(-0.354174\pi\) | ||||
0.442269 | + | 0.896883i | \(0.354174\pi\) | |||||||
\(492\) | −1.16178e54 | −0.0758296 | ||||||||
\(493\) | 3.23591e54 | 0.202598 | ||||||||
\(494\) | 5.98068e54 | 0.359210 | ||||||||
\(495\) | 1.59705e55 | 0.920264 | ||||||||
\(496\) | −1.27822e55 | −0.706694 | ||||||||
\(497\) | −1.87379e55 | −0.994067 | ||||||||
\(498\) | −1.37087e55 | −0.697900 | ||||||||
\(499\) | 3.12552e55 | 1.52708 | 0.763539 | − | 0.645762i | \(-0.223460\pi\) | ||||
0.763539 | + | 0.645762i | \(0.223460\pi\) | |||||||
\(500\) | 1.38737e54 | 0.0650592 | ||||||||
\(501\) | −5.50669e54 | −0.247866 | ||||||||
\(502\) | −3.11713e54 | −0.134688 | ||||||||
\(503\) | 1.38978e55 | 0.576504 | 0.288252 | − | 0.957555i | \(-0.406926\pi\) | ||||
0.288252 | + | 0.957555i | \(0.406926\pi\) | |||||||
\(504\) | 8.42476e54 | 0.335530 | ||||||||
\(505\) | 3.36526e55 | 1.28690 | ||||||||
\(506\) | −6.86185e55 | −2.51974 | ||||||||
\(507\) | −1.45871e55 | −0.514407 | ||||||||
\(508\) | −2.81622e54 | −0.0953806 | ||||||||
\(509\) | −4.24927e55 | −1.38229 | −0.691146 | − | 0.722715i | \(-0.742894\pi\) | ||||
−0.691146 | + | 0.722715i | \(0.742894\pi\) | |||||||
\(510\) | 3.90419e55 | 1.21995 | ||||||||
\(511\) | −3.68237e55 | −1.10535 | ||||||||
\(512\) | 2.28163e55 | 0.657978 | ||||||||
\(513\) | −7.00595e54 | −0.194116 | ||||||||
\(514\) | −1.50989e55 | −0.401977 | ||||||||
\(515\) | −6.54465e55 | −1.67432 | ||||||||
\(516\) | 5.59861e54 | 0.137645 | ||||||||
\(517\) | −4.19530e55 | −0.991305 | ||||||||
\(518\) | 2.02286e55 | 0.459417 | ||||||||
\(519\) | −4.86683e55 | −1.06247 | ||||||||
\(520\) | 2.13666e55 | 0.448402 | ||||||||
\(521\) | 7.63345e55 | 1.54009 | 0.770047 | − | 0.637987i | \(-0.220233\pi\) | ||||
0.770047 | + | 0.637987i | \(0.220233\pi\) | |||||||
\(522\) | 2.88444e54 | 0.0559521 | ||||||||
\(523\) | 8.49813e55 | 1.58504 | 0.792518 | − | 0.609849i | \(-0.208770\pi\) | ||||
0.792518 | + | 0.609849i | \(0.208770\pi\) | |||||||
\(524\) | 6.77322e54 | 0.121480 | ||||||||
\(525\) | 4.72213e55 | 0.814464 | ||||||||
\(526\) | 9.14925e55 | 1.51767 | ||||||||
\(527\) | −5.07305e55 | −0.809379 | ||||||||
\(528\) | −7.84494e55 | −1.20391 | ||||||||
\(529\) | 4.21094e55 | 0.621638 | ||||||||
\(530\) | 1.19312e56 | 1.69445 | ||||||||
\(531\) | −1.22506e54 | −0.0167386 | ||||||||
\(532\) | −1.39774e55 | −0.183754 | ||||||||
\(533\) | −2.09900e55 | −0.265525 | ||||||||
\(534\) | 5.92825e55 | 0.721657 | ||||||||
\(535\) | −2.44042e56 | −2.85898 | ||||||||
\(536\) | −1.47408e55 | −0.166204 | ||||||||
\(537\) | −1.67822e55 | −0.182128 | ||||||||
\(538\) | 4.28771e55 | 0.447908 | ||||||||
\(539\) | 4.45493e55 | 0.447993 | ||||||||
\(540\) | 4.88589e54 | 0.0473012 | ||||||||
\(541\) | 8.87529e54 | 0.0827254 | 0.0413627 | − | 0.999144i | \(-0.486830\pi\) | ||||
0.0413627 | + | 0.999144i | \(0.486830\pi\) | |||||||
\(542\) | 1.31539e56 | 1.18051 | ||||||||
\(543\) | −3.56226e55 | −0.307842 | ||||||||
\(544\) | −5.06122e55 | −0.421190 | ||||||||
\(545\) | 6.33011e55 | 0.507321 | ||||||||
\(546\) | −2.97124e55 | −0.229345 | ||||||||
\(547\) | −1.64997e56 | −1.22669 | −0.613345 | − | 0.789815i | \(-0.710177\pi\) | ||||
−0.613345 | + | 0.789815i | \(0.710177\pi\) | |||||||
\(548\) | 1.57497e55 | 0.112790 | ||||||||
\(549\) | 1.90357e55 | 0.131321 | ||||||||
\(550\) | −3.76532e56 | −2.50246 | ||||||||
\(551\) | 2.45154e55 | 0.156975 | ||||||||
\(552\) | 1.07541e56 | 0.663474 | ||||||||
\(553\) | 2.83129e56 | 1.68314 | ||||||||
\(554\) | −3.47900e55 | −0.199299 | ||||||||
\(555\) | −6.00984e55 | −0.331785 | ||||||||
\(556\) | 7.24590e54 | 0.0385531 | ||||||||
\(557\) | 2.56239e56 | 1.31405 | 0.657027 | − | 0.753867i | \(-0.271814\pi\) | ||||
0.657027 | + | 0.753867i | \(0.271814\pi\) | |||||||
\(558\) | −4.52205e55 | −0.223529 | ||||||||
\(559\) | 1.01151e56 | 0.481979 | ||||||||
\(560\) | −4.15366e56 | −1.90799 | ||||||||
\(561\) | −3.11353e56 | −1.37884 | ||||||||
\(562\) | 2.82900e56 | 1.20792 | ||||||||
\(563\) | −1.39228e55 | −0.0573196 | −0.0286598 | − | 0.999589i | \(-0.509124\pi\) | ||||
−0.0286598 | + | 0.999589i | \(0.509124\pi\) | |||||||
\(564\) | −1.28348e55 | −0.0509526 | ||||||||
\(565\) | 2.30981e56 | 0.884268 | ||||||||
\(566\) | −3.16936e56 | −1.17013 | ||||||||
\(567\) | 3.48061e55 | 0.123937 | ||||||||
\(568\) | −2.34164e56 | −0.804227 | ||||||||
\(569\) | −2.49708e56 | −0.827239 | −0.413620 | − | 0.910450i | \(-0.635736\pi\) | ||||
−0.413620 | + | 0.910450i | \(0.635736\pi\) | |||||||
\(570\) | 2.95783e56 | 0.945232 | ||||||||
\(571\) | −1.43957e56 | −0.443805 | −0.221902 | − | 0.975069i | \(-0.571227\pi\) | ||||
−0.221902 | + | 0.975069i | \(0.571227\pi\) | |||||||
\(572\) | 3.32621e55 | 0.0989308 | ||||||||
\(573\) | 1.19458e56 | 0.342805 | ||||||||
\(574\) | 3.49414e56 | 0.967489 | ||||||||
\(575\) | 6.02775e56 | 1.61051 | ||||||||
\(576\) | 1.01834e56 | 0.262561 | ||||||||
\(577\) | 7.48240e56 | 1.86181 | 0.930907 | − | 0.365255i | \(-0.119018\pi\) | ||||
0.930907 | + | 0.365255i | \(0.119018\pi\) | |||||||
\(578\) | −3.12011e56 | −0.749289 | ||||||||
\(579\) | 5.58876e55 | 0.129540 | ||||||||
\(580\) | −1.70968e55 | −0.0382509 | ||||||||
\(581\) | 5.78841e56 | 1.25011 | ||||||||
\(582\) | −1.16375e56 | −0.242626 | ||||||||
\(583\) | −9.51493e56 | −1.91514 | ||||||||
\(584\) | −4.60177e56 | −0.894255 | ||||||||
\(585\) | 8.82742e55 | 0.165630 | ||||||||
\(586\) | 8.75907e56 | 1.58693 | ||||||||
\(587\) | −5.43255e56 | −0.950435 | −0.475217 | − | 0.879868i | \(-0.657631\pi\) | ||||
−0.475217 | + | 0.879868i | \(0.657631\pi\) | |||||||
\(588\) | 1.36290e55 | 0.0230266 | ||||||||
\(589\) | −3.84337e56 | −0.627116 | ||||||||
\(590\) | 5.17206e55 | 0.0815074 | ||||||||
\(591\) | 5.85481e56 | 0.891188 | ||||||||
\(592\) | 2.95211e56 | 0.434048 | ||||||||
\(593\) | −9.45252e56 | −1.34254 | −0.671269 | − | 0.741214i | \(-0.734250\pi\) | ||||
−0.671269 | + | 0.741214i | \(0.734250\pi\) | |||||||
\(594\) | −2.77536e56 | −0.380800 | ||||||||
\(595\) | −1.64852e57 | −2.18523 | ||||||||
\(596\) | 1.27392e56 | 0.163153 | ||||||||
\(597\) | −1.83905e56 | −0.227573 | ||||||||
\(598\) | −3.79277e56 | −0.453505 | ||||||||
\(599\) | −3.47722e56 | −0.401775 | −0.200887 | − | 0.979614i | \(-0.564383\pi\) | ||||
−0.200887 | + | 0.979614i | \(0.564383\pi\) | |||||||
\(600\) | 5.90114e56 | 0.658923 | ||||||||
\(601\) | 6.30772e56 | 0.680684 | 0.340342 | − | 0.940302i | \(-0.389457\pi\) | ||||
0.340342 | + | 0.940302i | \(0.389457\pi\) | |||||||
\(602\) | −1.68382e57 | −1.75618 | ||||||||
\(603\) | −6.09001e55 | −0.0613922 | ||||||||
\(604\) | 2.64364e56 | 0.257599 | ||||||||
\(605\) | 3.77941e57 | 3.55991 | ||||||||
\(606\) | −5.84815e56 | −0.532513 | ||||||||
\(607\) | −3.56157e56 | −0.313526 | −0.156763 | − | 0.987636i | \(-0.550106\pi\) | ||||
−0.156763 | + | 0.987636i | \(0.550106\pi\) | |||||||
\(608\) | −3.83440e56 | −0.326343 | ||||||||
\(609\) | −1.21794e56 | −0.100224 | ||||||||
\(610\) | −8.03662e56 | −0.639458 | ||||||||
\(611\) | −2.31888e56 | −0.178416 | ||||||||
\(612\) | −9.52529e55 | −0.0708719 | ||||||||
\(613\) | −4.16993e56 | −0.300047 | −0.150023 | − | 0.988682i | \(-0.547935\pi\) | ||||
−0.150023 | + | 0.988682i | \(0.547935\pi\) | |||||||
\(614\) | 1.83963e57 | 1.28020 | ||||||||
\(615\) | −1.03809e57 | −0.698708 | ||||||||
\(616\) | 2.83652e57 | 1.84663 | ||||||||
\(617\) | 2.42342e57 | 1.52610 | 0.763051 | − | 0.646338i | \(-0.223701\pi\) | ||||
0.763051 | + | 0.646338i | \(0.223701\pi\) | |||||||
\(618\) | 1.13733e57 | 0.692824 | ||||||||
\(619\) | −1.32231e56 | −0.0779246 | −0.0389623 | − | 0.999241i | \(-0.512405\pi\) | ||||
−0.0389623 | + | 0.999241i | \(0.512405\pi\) | |||||||
\(620\) | 2.68033e56 | 0.152812 | ||||||||
\(621\) | 4.44296e56 | 0.245073 | ||||||||
\(622\) | 1.47957e57 | 0.789645 | ||||||||
\(623\) | −2.50317e57 | −1.29266 | ||||||||
\(624\) | −4.33615e56 | −0.216681 | ||||||||
\(625\) | −1.37567e57 | −0.665233 | ||||||||
\(626\) | −2.18628e57 | −1.02313 | ||||||||
\(627\) | −2.35882e57 | −1.06834 | ||||||||
\(628\) | −4.33711e56 | −0.190120 | ||||||||
\(629\) | 1.17165e57 | 0.497117 | ||||||||
\(630\) | −1.46947e57 | −0.603503 | ||||||||
\(631\) | 1.32515e57 | 0.526822 | 0.263411 | − | 0.964684i | \(-0.415153\pi\) | ||||
0.263411 | + | 0.964684i | \(0.415153\pi\) | |||||||
\(632\) | 3.53820e57 | 1.36170 | ||||||||
\(633\) | −1.63971e57 | −0.610930 | ||||||||
\(634\) | −1.53622e56 | −0.0554146 | ||||||||
\(635\) | −2.51639e57 | −0.878854 | ||||||||
\(636\) | −2.91092e56 | −0.0984373 | ||||||||
\(637\) | 2.46238e56 | 0.0806301 | ||||||||
\(638\) | 9.71159e56 | 0.307940 | ||||||||
\(639\) | −9.67425e56 | −0.297064 | ||||||||
\(640\) | −5.93659e57 | −1.76542 | ||||||||
\(641\) | −5.79020e56 | −0.166765 | −0.0833824 | − | 0.996518i | \(-0.526572\pi\) | ||||
−0.0833824 | + | 0.996518i | \(0.526572\pi\) | |||||||
\(642\) | 4.24095e57 | 1.18303 | ||||||||
\(643\) | 9.70178e56 | 0.262136 | 0.131068 | − | 0.991373i | \(-0.458159\pi\) | ||||
0.131068 | + | 0.991373i | \(0.458159\pi\) | |||||||
\(644\) | 8.86401e56 | 0.231990 | ||||||||
\(645\) | 5.00256e57 | 1.26829 | ||||||||
\(646\) | −5.76643e57 | −1.41625 | ||||||||
\(647\) | −2.04507e57 | −0.486598 | −0.243299 | − | 0.969951i | \(-0.578230\pi\) | ||||
−0.243299 | + | 0.969951i | \(0.578230\pi\) | |||||||
\(648\) | 4.34964e56 | 0.100269 | ||||||||
\(649\) | −4.12464e56 | −0.0921234 | ||||||||
\(650\) | −2.08121e57 | −0.450394 | ||||||||
\(651\) | 1.90941e57 | 0.400395 | ||||||||
\(652\) | 1.38163e57 | 0.280748 | ||||||||
\(653\) | −6.17960e56 | −0.121686 | −0.0608430 | − | 0.998147i | \(-0.519379\pi\) | ||||
−0.0608430 | + | 0.998147i | \(0.519379\pi\) | |||||||
\(654\) | −1.10005e57 | −0.209926 | ||||||||
\(655\) | 6.05212e57 | 1.11934 | ||||||||
\(656\) | 5.09925e57 | 0.914065 | ||||||||
\(657\) | −1.90118e57 | −0.330318 | ||||||||
\(658\) | 3.86015e57 | 0.650091 | ||||||||
\(659\) | 2.52320e57 | 0.411909 | 0.205955 | − | 0.978562i | \(-0.433970\pi\) | ||||
0.205955 | + | 0.978562i | \(0.433970\pi\) | |||||||
\(660\) | 1.64502e57 | 0.260328 | ||||||||
\(661\) | −4.49723e57 | −0.689946 | −0.344973 | − | 0.938613i | \(-0.612112\pi\) | ||||
−0.344973 | + | 0.938613i | \(0.612112\pi\) | |||||||
\(662\) | −7.08584e57 | −1.05391 | ||||||||
\(663\) | −1.72095e57 | −0.248165 | ||||||||
\(664\) | 7.23365e57 | 1.01137 | ||||||||
\(665\) | −1.24893e58 | −1.69314 | ||||||||
\(666\) | 1.04439e57 | 0.137291 | ||||||||
\(667\) | −1.55469e57 | −0.198182 | ||||||||
\(668\) | −5.67209e56 | −0.0701174 | ||||||||
\(669\) | 2.18544e57 | 0.262001 | ||||||||
\(670\) | 2.57113e57 | 0.298944 | ||||||||
\(671\) | 6.40909e57 | 0.722745 | ||||||||
\(672\) | 1.90496e57 | 0.208361 | ||||||||
\(673\) | 1.53837e58 | 1.63212 | 0.816061 | − | 0.577966i | \(-0.196153\pi\) | ||||
0.816061 | + | 0.577966i | \(0.196153\pi\) | |||||||
\(674\) | 5.93395e56 | 0.0610683 | ||||||||
\(675\) | 2.43800e57 | 0.243392 | ||||||||
\(676\) | −1.50253e57 | −0.145518 | ||||||||
\(677\) | 1.37721e58 | 1.29399 | 0.646997 | − | 0.762492i | \(-0.276024\pi\) | ||||
0.646997 | + | 0.762492i | \(0.276024\pi\) | |||||||
\(678\) | −4.01399e57 | −0.365905 | ||||||||
\(679\) | 4.91386e57 | 0.434603 | ||||||||
\(680\) | −2.06012e58 | −1.76791 | ||||||||
\(681\) | 3.98536e57 | 0.331858 | ||||||||
\(682\) | −1.52252e58 | −1.23022 | ||||||||
\(683\) | −1.94435e58 | −1.52458 | −0.762290 | − | 0.647236i | \(-0.775925\pi\) | ||||
−0.762290 | + | 0.647236i | \(0.775925\pi\) | |||||||
\(684\) | −7.21640e56 | −0.0549124 | ||||||||
\(685\) | 1.40729e58 | 1.03927 | ||||||||
\(686\) | 1.26867e58 | 0.909291 | ||||||||
\(687\) | −7.19423e57 | −0.500462 | ||||||||
\(688\) | −2.45733e58 | −1.65921 | ||||||||
\(689\) | −5.25921e57 | −0.344688 | ||||||||
\(690\) | −1.87576e58 | −1.19336 | ||||||||
\(691\) | −2.44962e58 | −1.51286 | −0.756430 | − | 0.654074i | \(-0.773058\pi\) | ||||
−0.756430 | + | 0.654074i | \(0.773058\pi\) | |||||||
\(692\) | −5.01301e57 | −0.300555 | ||||||||
\(693\) | 1.17188e58 | 0.682106 | ||||||||
\(694\) | 3.69137e57 | 0.208602 | ||||||||
\(695\) | 6.47447e57 | 0.355235 | ||||||||
\(696\) | −1.52203e57 | −0.0810840 | ||||||||
\(697\) | 2.02381e58 | 1.04688 | ||||||||
\(698\) | 2.96601e58 | 1.48983 | ||||||||
\(699\) | −2.54853e57 | −0.124310 | ||||||||
\(700\) | 4.86397e57 | 0.230399 | ||||||||
\(701\) | −1.67730e58 | −0.771599 | −0.385799 | − | 0.922583i | \(-0.626074\pi\) | ||||
−0.385799 | + | 0.922583i | \(0.626074\pi\) | |||||||
\(702\) | −1.53403e57 | −0.0685367 | ||||||||
\(703\) | 8.87644e57 | 0.385172 | ||||||||
\(704\) | 3.42863e58 | 1.44504 | ||||||||
\(705\) | −1.14683e58 | −0.469487 | ||||||||
\(706\) | 8.48872e57 | 0.337556 | ||||||||
\(707\) | 2.46935e58 | 0.953861 | ||||||||
\(708\) | −1.26186e56 | −0.00473510 | ||||||||
\(709\) | −4.58084e58 | −1.66993 | −0.834963 | − | 0.550306i | \(-0.814511\pi\) | ||||
−0.834963 | + | 0.550306i | \(0.814511\pi\) | |||||||
\(710\) | 4.08435e58 | 1.44653 | ||||||||
\(711\) | 1.46177e58 | 0.502983 | ||||||||
\(712\) | −3.12816e58 | −1.04580 | ||||||||
\(713\) | 2.43735e58 | 0.791739 | ||||||||
\(714\) | 2.86480e58 | 0.904235 | ||||||||
\(715\) | 2.97209e58 | 0.911567 | ||||||||
\(716\) | −1.72863e57 | −0.0515211 | ||||||||
\(717\) | 1.24602e58 | 0.360895 | ||||||||
\(718\) | 1.09610e58 | 0.308532 | ||||||||
\(719\) | −4.86766e58 | −1.33161 | −0.665807 | − | 0.746124i | \(-0.731912\pi\) | ||||
−0.665807 | + | 0.746124i | \(0.731912\pi\) | |||||||
\(720\) | −2.14450e58 | −0.570178 | ||||||||
\(721\) | −4.80232e58 | −1.24102 | ||||||||
\(722\) | −7.46628e56 | −0.0187539 | ||||||||
\(723\) | 9.23429e56 | 0.0225460 | ||||||||
\(724\) | −3.66926e57 | −0.0870838 | ||||||||
\(725\) | −8.53109e57 | −0.196823 | ||||||||
\(726\) | −6.56785e58 | −1.47307 | ||||||||
\(727\) | −1.73618e58 | −0.378563 | −0.189282 | − | 0.981923i | \(-0.560616\pi\) | ||||
−0.189282 | + | 0.981923i | \(0.560616\pi\) | |||||||
\(728\) | 1.56784e58 | 0.332359 | ||||||||
\(729\) | 1.79701e57 | 0.0370370 | ||||||||
\(730\) | 8.02653e58 | 1.60846 | ||||||||
\(731\) | −9.75274e58 | −1.90029 | ||||||||
\(732\) | 1.96075e57 | 0.0371487 | ||||||||
\(733\) | −2.87695e58 | −0.530031 | −0.265015 | − | 0.964244i | \(-0.585377\pi\) | ||||
−0.265015 | + | 0.964244i | \(0.585377\pi\) | |||||||
\(734\) | −5.02769e57 | −0.0900739 | ||||||||
\(735\) | 1.21781e58 | 0.212172 | ||||||||
\(736\) | 2.43166e58 | 0.412010 | ||||||||
\(737\) | −2.05044e58 | −0.337880 | ||||||||
\(738\) | 1.80399e58 | 0.289121 | ||||||||
\(739\) | −9.32596e57 | −0.145373 | −0.0726863 | − | 0.997355i | \(-0.523157\pi\) | ||||
−0.0726863 | + | 0.997355i | \(0.523157\pi\) | |||||||
\(740\) | −6.19036e57 | −0.0938567 | ||||||||
\(741\) | −1.30380e58 | −0.192281 | ||||||||
\(742\) | 8.75482e58 | 1.25593 | ||||||||
\(743\) | 6.98846e58 | 0.975239 | 0.487619 | − | 0.873056i | \(-0.337865\pi\) | ||||
0.487619 | + | 0.873056i | \(0.337865\pi\) | |||||||
\(744\) | 2.38615e58 | 0.323931 | ||||||||
\(745\) | 1.13830e59 | 1.50332 | ||||||||
\(746\) | −1.56294e59 | −2.00815 | ||||||||
\(747\) | 2.98851e58 | 0.373579 | ||||||||
\(748\) | −3.20705e58 | −0.390053 | ||||||||
\(749\) | −1.79072e59 | −2.11910 | ||||||||
\(750\) | −2.15430e58 | −0.248056 | ||||||||
\(751\) | 1.15523e58 | 0.129434 | 0.0647172 | − | 0.997904i | \(-0.479385\pi\) | ||||
0.0647172 | + | 0.997904i | \(0.479385\pi\) | |||||||
\(752\) | 5.63340e58 | 0.614193 | ||||||||
\(753\) | 6.79541e57 | 0.0720972 | ||||||||
\(754\) | 5.36791e57 | 0.0554233 | ||||||||
\(755\) | 2.36219e59 | 2.37357 | ||||||||
\(756\) | 3.58516e57 | 0.0350599 | ||||||||
\(757\) | −8.37064e58 | −0.796697 | −0.398348 | − | 0.917234i | \(-0.630417\pi\) | ||||
−0.398348 | + | 0.917234i | \(0.630417\pi\) | |||||||
\(758\) | 1.07238e59 | 0.993412 | ||||||||
\(759\) | 1.49589e59 | 1.34879 | ||||||||
\(760\) | −1.56076e59 | −1.36980 | ||||||||
\(761\) | −2.09392e58 | −0.178885 | −0.0894425 | − | 0.995992i | \(-0.528509\pi\) | ||||
−0.0894425 | + | 0.995992i | \(0.528509\pi\) | |||||||
\(762\) | 4.37298e58 | 0.363665 | ||||||||
\(763\) | 4.64489e58 | 0.376030 | ||||||||
\(764\) | 1.23047e58 | 0.0969741 | ||||||||
\(765\) | −8.51119e58 | −0.653027 | ||||||||
\(766\) | −4.51740e58 | −0.337441 | ||||||||
\(767\) | −2.27982e57 | −0.0165805 | ||||||||
\(768\) | 3.89421e58 | 0.275749 | ||||||||
\(769\) | 1.28539e59 | 0.886229 | 0.443114 | − | 0.896465i | \(-0.353874\pi\) | ||||
0.443114 | + | 0.896465i | \(0.353874\pi\) | |||||||
\(770\) | −4.94753e59 | −3.32146 | ||||||||
\(771\) | 3.29158e58 | 0.215174 | ||||||||
\(772\) | 5.75663e57 | 0.0366449 | ||||||||
\(773\) | 1.59781e59 | 0.990478 | 0.495239 | − | 0.868757i | \(-0.335080\pi\) | ||||
0.495239 | + | 0.868757i | \(0.335080\pi\) | |||||||
\(774\) | −8.69346e58 | −0.524811 | ||||||||
\(775\) | 1.33745e59 | 0.786308 | ||||||||
\(776\) | 6.14074e58 | 0.351605 | ||||||||
\(777\) | −4.40988e58 | −0.245921 | ||||||||
\(778\) | 3.04006e58 | 0.165120 | ||||||||
\(779\) | 1.53325e59 | 0.811137 | ||||||||
\(780\) | 9.09258e57 | 0.0468541 | ||||||||
\(781\) | −3.25721e59 | −1.63493 | ||||||||
\(782\) | 3.65689e59 | 1.78803 | ||||||||
\(783\) | −6.28814e57 | −0.0299506 | ||||||||
\(784\) | −5.98203e58 | −0.277568 | ||||||||
\(785\) | −3.87537e59 | −1.75180 | ||||||||
\(786\) | −1.05174e59 | −0.463175 | ||||||||
\(787\) | 7.76783e58 | 0.333286 | 0.166643 | − | 0.986017i | \(-0.446707\pi\) | ||||
0.166643 | + | 0.986017i | \(0.446707\pi\) | |||||||
\(788\) | 6.03068e58 | 0.252103 | ||||||||
\(789\) | −1.99455e59 | −0.812395 | ||||||||
\(790\) | −6.17143e59 | −2.44923 | ||||||||
\(791\) | 1.69489e59 | 0.655425 | ||||||||
\(792\) | 1.46447e59 | 0.551842 | ||||||||
\(793\) | 3.54251e58 | 0.130080 | ||||||||
\(794\) | 2.55889e59 | 0.915653 | ||||||||
\(795\) | −2.60102e59 | −0.907020 | ||||||||
\(796\) | −1.89429e58 | −0.0643768 | ||||||||
\(797\) | 1.52749e58 | 0.0505920 | 0.0252960 | − | 0.999680i | \(-0.491947\pi\) | ||||
0.0252960 | + | 0.999680i | \(0.491947\pi\) | |||||||
\(798\) | 2.17039e59 | 0.700612 | ||||||||
\(799\) | 2.23581e59 | 0.703438 | ||||||||
\(800\) | 1.33433e59 | 0.409184 | ||||||||
\(801\) | −1.29237e59 | −0.386296 | ||||||||
\(802\) | 3.41710e59 | 0.995597 | ||||||||
\(803\) | −6.40104e59 | −1.81795 | ||||||||
\(804\) | −6.27294e57 | −0.0173669 | ||||||||
\(805\) | 7.92032e59 | 2.13760 | ||||||||
\(806\) | −8.41546e58 | −0.221416 | ||||||||
\(807\) | −9.34728e58 | −0.239761 | ||||||||
\(808\) | 3.08589e59 | 0.771699 | ||||||||
\(809\) | 5.87620e59 | 1.43269 | 0.716345 | − | 0.697747i | \(-0.245814\pi\) | ||||
0.716345 | + | 0.697747i | \(0.245814\pi\) | |||||||
\(810\) | −7.58675e58 | −0.180349 | ||||||||
\(811\) | −2.60886e59 | −0.604676 | −0.302338 | − | 0.953201i | \(-0.597767\pi\) | ||||
−0.302338 | + | 0.953201i | \(0.597767\pi\) | |||||||
\(812\) | −1.25453e58 | −0.0283518 | ||||||||
\(813\) | −2.86757e59 | −0.631914 | ||||||||
\(814\) | 3.51634e59 | 0.755597 | ||||||||
\(815\) | 1.23454e60 | 2.58686 | ||||||||
\(816\) | 4.18081e59 | 0.854304 | ||||||||
\(817\) | −7.38872e59 | −1.47237 | ||||||||
\(818\) | −4.26724e59 | −0.829286 | ||||||||
\(819\) | 6.47736e58 | 0.122766 | ||||||||
\(820\) | −1.06927e59 | −0.197654 | ||||||||
\(821\) | −2.68738e59 | −0.484502 | −0.242251 | − | 0.970214i | \(-0.577886\pi\) | ||||
−0.242251 | + | 0.970214i | \(0.577886\pi\) | |||||||
\(822\) | −2.44559e59 | −0.430042 | ||||||||
\(823\) | −6.91646e59 | −1.18628 | −0.593140 | − | 0.805099i | \(-0.702112\pi\) | ||||
−0.593140 | + | 0.805099i | \(0.702112\pi\) | |||||||
\(824\) | −6.00135e59 | −1.00402 | ||||||||
\(825\) | 8.20846e59 | 1.33954 | ||||||||
\(826\) | 3.79514e58 | 0.0604139 | ||||||||
\(827\) | −1.66543e58 | −0.0258621 | −0.0129310 | − | 0.999916i | \(-0.504116\pi\) | ||||
−0.0129310 | + | 0.999916i | \(0.504116\pi\) | |||||||
\(828\) | 4.57642e58 | 0.0693273 | ||||||||
\(829\) | −8.91805e59 | −1.31796 | −0.658980 | − | 0.752161i | \(-0.729012\pi\) | ||||
−0.658980 | + | 0.752161i | \(0.729012\pi\) | |||||||
\(830\) | −1.26171e60 | −1.81911 | ||||||||
\(831\) | 7.58428e58 | 0.106683 | ||||||||
\(832\) | 1.89511e59 | 0.260080 | ||||||||
\(833\) | −2.37417e59 | −0.317899 | ||||||||
\(834\) | −1.12513e59 | −0.146994 | ||||||||
\(835\) | −5.06822e59 | −0.646075 | ||||||||
\(836\) | −2.42968e59 | −0.302218 | ||||||||
\(837\) | 9.85814e58 | 0.119653 | ||||||||
\(838\) | 6.87250e59 | 0.813977 | ||||||||
\(839\) | 6.04271e59 | 0.698411 | 0.349206 | − | 0.937046i | \(-0.386451\pi\) | ||||
0.349206 | + | 0.937046i | \(0.386451\pi\) | |||||||
\(840\) | 7.75395e59 | 0.874576 | ||||||||
\(841\) | −8.86482e59 | −0.975780 | ||||||||
\(842\) | 3.34784e59 | 0.359639 | ||||||||
\(843\) | −6.16727e59 | −0.646588 | ||||||||
\(844\) | −1.68897e59 | −0.172823 | ||||||||
\(845\) | −1.34257e60 | −1.34083 | ||||||||
\(846\) | 1.99297e59 | 0.194271 | ||||||||
\(847\) | 2.77324e60 | 2.63863 | ||||||||
\(848\) | 1.27765e60 | 1.18658 | ||||||||
\(849\) | 6.90927e59 | 0.626361 | ||||||||
\(850\) | 2.00666e60 | 1.77576 | ||||||||
\(851\) | −5.62917e59 | −0.486282 | ||||||||
\(852\) | −9.96484e58 | −0.0840347 | ||||||||
\(853\) | 1.07100e60 | 0.881727 | 0.440863 | − | 0.897574i | \(-0.354672\pi\) | ||||
0.440863 | + | 0.897574i | \(0.354672\pi\) | |||||||
\(854\) | −5.89709e59 | −0.473971 | ||||||||
\(855\) | −6.44811e59 | −0.505973 | ||||||||
\(856\) | −2.23782e60 | −1.71441 | ||||||||
\(857\) | −1.09608e59 | −0.0819855 | −0.0409927 | − | 0.999159i | \(-0.513052\pi\) | ||||
−0.0409927 | + | 0.999159i | \(0.513052\pi\) | |||||||
\(858\) | −5.16490e59 | −0.377201 | ||||||||
\(859\) | 1.21084e60 | 0.863430 | 0.431715 | − | 0.902010i | \(-0.357909\pi\) | ||||
0.431715 | + | 0.902010i | \(0.357909\pi\) | |||||||
\(860\) | 5.15283e59 | 0.358779 | ||||||||
\(861\) | −7.61728e59 | −0.517887 | ||||||||
\(862\) | 1.88566e60 | 1.25189 | ||||||||
\(863\) | −1.35388e60 | −0.877728 | −0.438864 | − | 0.898554i | \(-0.644619\pi\) | ||||
−0.438864 | + | 0.898554i | \(0.644619\pi\) | |||||||
\(864\) | 9.83515e58 | 0.0622658 | ||||||||
\(865\) | −4.47931e60 | −2.76937 | ||||||||
\(866\) | −1.45470e60 | −0.878329 | ||||||||
\(867\) | 6.80190e59 | 0.401087 | ||||||||
\(868\) | 1.96676e59 | 0.113266 | ||||||||
\(869\) | 4.92163e60 | 2.76824 | ||||||||
\(870\) | 2.65477e59 | 0.145842 | ||||||||
\(871\) | −1.13334e59 | −0.0608120 | ||||||||
\(872\) | 5.80462e59 | 0.304218 | ||||||||
\(873\) | 2.53699e59 | 0.129875 | ||||||||
\(874\) | 2.77048e60 | 1.38538 | ||||||||
\(875\) | 9.09641e59 | 0.444329 | ||||||||
\(876\) | −1.95828e59 | −0.0934419 | ||||||||
\(877\) | 1.82892e60 | 0.852517 | 0.426259 | − | 0.904601i | \(-0.359831\pi\) | ||||
0.426259 | + | 0.904601i | \(0.359831\pi\) | |||||||
\(878\) | −3.80566e60 | −1.73297 | ||||||||
\(879\) | −1.90949e60 | −0.849466 | ||||||||
\(880\) | −7.22029e60 | −3.13805 | ||||||||
\(881\) | 9.73145e59 | 0.413210 | 0.206605 | − | 0.978424i | \(-0.433758\pi\) | ||||
0.206605 | + | 0.978424i | \(0.433758\pi\) | |||||||
\(882\) | −2.11630e59 | −0.0877954 | ||||||||
\(883\) | −2.26914e60 | −0.919742 | −0.459871 | − | 0.887986i | \(-0.652104\pi\) | ||||
−0.459871 | + | 0.887986i | \(0.652104\pi\) | |||||||
\(884\) | −1.77264e59 | −0.0702021 | ||||||||
\(885\) | −1.12752e59 | −0.0436301 | ||||||||
\(886\) | 3.47464e60 | 1.31377 | ||||||||
\(887\) | 9.48427e59 | 0.350404 | 0.175202 | − | 0.984532i | \(-0.443942\pi\) | ||||
0.175202 | + | 0.984532i | \(0.443942\pi\) | |||||||
\(888\) | −5.51093e59 | −0.198957 | ||||||||
\(889\) | −1.84647e60 | −0.651413 | ||||||||
\(890\) | 5.45622e60 | 1.88103 | ||||||||
\(891\) | 6.05033e59 | 0.203838 | ||||||||
\(892\) | 2.25108e59 | 0.0741160 | ||||||||
\(893\) | 1.69386e60 | 0.545032 | ||||||||
\(894\) | −1.97813e60 | −0.622066 | ||||||||
\(895\) | −1.54459e60 | −0.474725 | ||||||||
\(896\) | −4.35613e60 | −1.30854 | ||||||||
\(897\) | 8.26830e59 | 0.242757 | ||||||||
\(898\) | −7.42247e60 | −2.13002 | ||||||||
\(899\) | −3.44958e59 | −0.0967593 | ||||||||
\(900\) | 2.51123e59 | 0.0688517 | ||||||||
\(901\) | 5.07081e60 | 1.35900 | ||||||||
\(902\) | 6.07384e60 | 1.59122 | ||||||||
\(903\) | 3.67077e60 | 0.940065 | ||||||||
\(904\) | 2.11806e60 | 0.530257 | ||||||||
\(905\) | −3.27862e60 | −0.802407 | ||||||||
\(906\) | −4.10501e60 | −0.982169 | ||||||||
\(907\) | −6.87953e59 | −0.160920 | −0.0804599 | − | 0.996758i | \(-0.525639\pi\) | ||||
−0.0804599 | + | 0.996758i | \(0.525639\pi\) | |||||||
\(908\) | 4.10507e59 | 0.0938774 | ||||||||
\(909\) | 1.27491e60 | 0.285049 | ||||||||
\(910\) | −2.73466e60 | −0.597799 | ||||||||
\(911\) | −1.32323e60 | −0.282819 | −0.141409 | − | 0.989951i | \(-0.545163\pi\) | ||||
−0.141409 | + | 0.989951i | \(0.545163\pi\) | |||||||
\(912\) | 3.16740e60 | 0.661925 | ||||||||
\(913\) | 1.00620e61 | 2.05604 | ||||||||
\(914\) | −3.21918e60 | −0.643204 | ||||||||
\(915\) | 1.75200e60 | 0.342295 | ||||||||
\(916\) | −7.41032e59 | −0.141573 | ||||||||
\(917\) | 4.44091e60 | 0.829660 | ||||||||
\(918\) | 1.47907e60 | 0.270219 | ||||||||
\(919\) | −2.10890e60 | −0.376780 | −0.188390 | − | 0.982094i | \(-0.560327\pi\) | ||||
−0.188390 | + | 0.982094i | \(0.560327\pi\) | |||||||
\(920\) | 9.89784e60 | 1.72938 | ||||||||
\(921\) | −4.01042e60 | −0.685278 | ||||||||
\(922\) | 6.64942e60 | 1.11122 | ||||||||
\(923\) | −1.80036e60 | −0.294256 | ||||||||
\(924\) | 1.20708e60 | 0.192957 | ||||||||
\(925\) | −3.08891e60 | −0.482947 | ||||||||
\(926\) | −8.36130e60 | −1.27864 | ||||||||
\(927\) | −2.47940e60 | −0.370862 | ||||||||
\(928\) | −3.44154e59 | −0.0503523 | ||||||||
\(929\) | −8.23760e60 | −1.17890 | −0.589452 | − | 0.807803i | \(-0.700656\pi\) | ||||
−0.589452 | + | 0.807803i | \(0.700656\pi\) | |||||||
\(930\) | −4.16198e60 | −0.582639 | ||||||||
\(931\) | −1.79868e60 | −0.246312 | ||||||||
\(932\) | −2.62508e59 | −0.0351655 | ||||||||
\(933\) | −3.22548e60 | −0.422689 | ||||||||
\(934\) | 1.56251e61 | 2.00314 | ||||||||
\(935\) | −2.86562e61 | −3.59402 | ||||||||
\(936\) | 8.09461e59 | 0.0993210 | ||||||||
\(937\) | 1.44081e61 | 1.72960 | 0.864801 | − | 0.502115i | \(-0.167445\pi\) | ||||
0.864801 | + | 0.502115i | \(0.167445\pi\) | |||||||
\(938\) | 1.88663e60 | 0.221580 | ||||||||
\(939\) | 4.76613e60 | 0.547673 | ||||||||
\(940\) | −1.18128e60 | −0.132811 | ||||||||
\(941\) | −1.04517e61 | −1.14974 | −0.574870 | − | 0.818245i | \(-0.694947\pi\) | ||||
−0.574870 | + | 0.818245i | \(0.694947\pi\) | |||||||
\(942\) | 6.73462e60 | 0.724885 | ||||||||
\(943\) | −9.72339e60 | −1.02407 | ||||||||
\(944\) | 5.53852e59 | 0.0570779 | ||||||||
\(945\) | 3.20347e60 | 0.323049 | ||||||||
\(946\) | −2.92699e61 | −2.88837 | ||||||||
\(947\) | 9.09242e60 | 0.878021 | 0.439011 | − | 0.898482i | \(-0.355329\pi\) | ||||
0.439011 | + | 0.898482i | \(0.355329\pi\) | |||||||
\(948\) | 1.50568e60 | 0.142286 | ||||||||
\(949\) | −3.53806e60 | −0.327196 | ||||||||
\(950\) | 1.52025e61 | 1.37588 | ||||||||
\(951\) | 3.34899e59 | 0.0296629 | ||||||||
\(952\) | −1.51167e61 | −1.31039 | ||||||||
\(953\) | 8.38627e60 | 0.711483 | 0.355742 | − | 0.934584i | \(-0.384228\pi\) | ||||
0.355742 | + | 0.934584i | \(0.384228\pi\) | |||||||
\(954\) | 4.52004e60 | 0.375319 | ||||||||
\(955\) | 1.09947e61 | 0.893538 | ||||||||
\(956\) | 1.28344e60 | 0.102092 | ||||||||
\(957\) | −2.11714e60 | −0.164837 | ||||||||
\(958\) | 2.65416e61 | 2.02271 | ||||||||
\(959\) | 1.03264e61 | 0.770311 | ||||||||
\(960\) | 9.37254e60 | 0.684379 | ||||||||
\(961\) | −8.58235e60 | −0.613446 | ||||||||
\(962\) | 1.94359e60 | 0.135993 | ||||||||
\(963\) | −9.24535e60 | −0.633264 | ||||||||
\(964\) | 9.51167e58 | 0.00637790 | ||||||||
\(965\) | 5.14376e60 | 0.337653 | ||||||||
\(966\) | −1.37639e61 | −0.884527 | ||||||||
\(967\) | 2.28385e61 | 1.43689 | 0.718447 | − | 0.695581i | \(-0.244853\pi\) | ||||
0.718447 | + | 0.695581i | \(0.244853\pi\) | |||||||
\(968\) | 3.46566e61 | 2.13472 | ||||||||
\(969\) | 1.25709e61 | 0.758105 | ||||||||
\(970\) | −1.07109e61 | −0.632417 | ||||||||
\(971\) | −2.76347e61 | −1.59757 | −0.798786 | − | 0.601616i | \(-0.794524\pi\) | ||||
−0.798786 | + | 0.601616i | \(0.794524\pi\) | |||||||
\(972\) | 1.85099e59 | 0.0104772 | ||||||||
\(973\) | 4.75082e60 | 0.263303 | ||||||||
\(974\) | −7.59891e60 | −0.412375 | ||||||||
\(975\) | 4.53708e60 | 0.241091 | ||||||||
\(976\) | −8.60605e60 | −0.447799 | ||||||||
\(977\) | −2.22641e61 | −1.13440 | −0.567199 | − | 0.823581i | \(-0.691973\pi\) | ||||
−0.567199 | + | 0.823581i | \(0.691973\pi\) | |||||||
\(978\) | −2.14538e61 | −1.07043 | ||||||||
\(979\) | −4.35126e61 | −2.12603 | ||||||||
\(980\) | 1.25439e60 | 0.0600201 | ||||||||
\(981\) | 2.39812e60 | 0.112372 | ||||||||
\(982\) | −2.07899e61 | −0.954040 | ||||||||
\(983\) | 2.36280e61 | 1.06189 | 0.530945 | − | 0.847407i | \(-0.321837\pi\) | ||||
0.530945 | + | 0.847407i | \(0.321837\pi\) | |||||||
\(984\) | −9.51914e60 | −0.418985 | ||||||||
\(985\) | 5.38863e61 | 2.32293 | ||||||||
\(986\) | −5.17561e60 | −0.218517 | ||||||||
\(987\) | −8.41520e60 | −0.347987 | ||||||||
\(988\) | −1.34296e60 | −0.0543934 | ||||||||
\(989\) | 4.68570e61 | 1.85888 | ||||||||
\(990\) | −2.55437e61 | −0.992574 | ||||||||
\(991\) | −4.84850e61 | −1.84543 | −0.922716 | − | 0.385481i | \(-0.874035\pi\) | ||||
−0.922716 | + | 0.385481i | \(0.874035\pi\) | |||||||
\(992\) | 5.39542e60 | 0.201157 | ||||||||
\(993\) | 1.54473e61 | 0.564146 | ||||||||
\(994\) | 2.99700e61 | 1.07218 | ||||||||
\(995\) | −1.69262e61 | −0.593180 | ||||||||
\(996\) | 3.07828e60 | 0.105680 | ||||||||
\(997\) | 3.96621e60 | 0.133391 | 0.0666953 | − | 0.997773i | \(-0.478754\pi\) | ||||
0.0666953 | + | 0.997773i | \(0.478754\pi\) | |||||||
\(998\) | −4.99905e61 | −1.64707 | ||||||||
\(999\) | −2.27679e60 | −0.0734903 |
(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 | 3.42.a.b.1.2 | ✓ | 4 | |
3.2 | odd | 2 | 9.42.a.c.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.42.a.b.1.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
9.42.a.c.1.3 | 4 | 3.2 | odd | 2 |