Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1,42,Mod(1,1)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1, base_ring=CyclotomicField(1))
chi = DirichletCharacter(H, H._module([]))
N = Newforms(chi, 42, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1.1");
S:= CuspForms(chi, 42);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1 \) |
Weight: | \( k \) | \(=\) | \( 42 \) |
Character orbit: | \([\chi]\) | \(=\) | 1.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: | \(10.6471670456\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 2784108376x + 1945534874860 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{3}\cdot 5\cdot 7 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(52412.2\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.40087e6 | 1.61903 | 0.809514 | − | 0.587100i | \(-0.199730\pi\) | ||||
0.809514 | + | 0.587100i | \(0.199730\pi\) | |||||||
\(3\) | −6.65953e9 | −1.10270 | −0.551351 | − | 0.834274i | \(-0.685887\pi\) | ||||
−0.551351 | + | 0.834274i | \(0.685887\pi\) | |||||||
\(4\) | 3.56518e12 | 1.62125 | ||||||||
\(5\) | −3.38080e14 | −1.58538 | −0.792691 | − | 0.609624i | \(-0.791321\pi\) | ||||
−0.792691 | + | 0.609624i | \(0.791321\pi\) | |||||||
\(6\) | −1.59887e16 | −1.78530 | ||||||||
\(7\) | −9.19453e16 | −0.435532 | −0.217766 | − | 0.976001i | \(-0.569877\pi\) | ||||
−0.217766 | + | 0.976001i | \(0.569877\pi\) | |||||||
\(8\) | 3.27996e18 | 1.00583 | ||||||||
\(9\) | 7.87633e18 | 0.215949 | ||||||||
\(10\) | −8.11687e20 | −2.56678 | ||||||||
\(11\) | 2.15850e21 | 0.967392 | 0.483696 | − | 0.875236i | \(-0.339294\pi\) | ||||
0.483696 | + | 0.875236i | \(0.339294\pi\) | |||||||
\(12\) | −2.37424e22 | −1.78776 | ||||||||
\(13\) | −8.71848e22 | −1.27234 | −0.636169 | − | 0.771550i | \(-0.719482\pi\) | ||||
−0.636169 | + | 0.771550i | \(0.719482\pi\) | |||||||
\(14\) | −2.20749e23 | −0.705138 | ||||||||
\(15\) | 2.25145e24 | 1.74820 | ||||||||
\(16\) | 3.48699e22 | 0.00721093 | ||||||||
\(17\) | 5.13467e24 | 0.306415 | 0.153207 | − | 0.988194i | \(-0.451040\pi\) | ||||
0.153207 | + | 0.988194i | \(0.451040\pi\) | |||||||
\(18\) | 1.89101e25 | 0.349628 | ||||||||
\(19\) | 4.11372e25 | 0.251065 | 0.125532 | − | 0.992090i | \(-0.459936\pi\) | ||||
0.125532 | + | 0.992090i | \(0.459936\pi\) | |||||||
\(20\) | −1.20531e27 | −2.57031 | ||||||||
\(21\) | 6.12312e26 | 0.480261 | ||||||||
\(22\) | 5.18229e27 | 1.56624 | ||||||||
\(23\) | 2.60656e27 | 0.316699 | 0.158350 | − | 0.987383i | \(-0.449383\pi\) | ||||
0.158350 | + | 0.987383i | \(0.449383\pi\) | |||||||
\(24\) | −2.18430e28 | −1.10913 | ||||||||
\(25\) | 6.88231e28 | 1.51344 | ||||||||
\(26\) | −2.09320e29 | −2.05995 | ||||||||
\(27\) | 1.90440e29 | 0.864573 | ||||||||
\(28\) | −3.27801e29 | −0.706107 | ||||||||
\(29\) | −4.19842e29 | −0.440480 | −0.220240 | − | 0.975446i | \(-0.570684\pi\) | ||||
−0.220240 | + | 0.975446i | \(0.570684\pi\) | |||||||
\(30\) | 5.40545e30 | 2.83039 | ||||||||
\(31\) | −2.68405e30 | −0.717589 | −0.358794 | − | 0.933417i | \(-0.616812\pi\) | ||||
−0.358794 | + | 0.933417i | \(0.616812\pi\) | |||||||
\(32\) | −7.12899e30 | −0.994154 | ||||||||
\(33\) | −1.43746e31 | −1.06674 | ||||||||
\(34\) | 1.23277e31 | 0.496094 | ||||||||
\(35\) | 3.10848e31 | 0.690484 | ||||||||
\(36\) | 2.80805e31 | 0.350109 | ||||||||
\(37\) | −1.06323e32 | −0.755947 | −0.377974 | − | 0.925816i | \(-0.623379\pi\) | ||||
−0.377974 | + | 0.925816i | \(0.623379\pi\) | |||||||
\(38\) | 9.87652e31 | 0.406481 | ||||||||
\(39\) | 5.80610e32 | 1.40301 | ||||||||
\(40\) | −1.10889e33 | −1.59462 | ||||||||
\(41\) | −1.44220e33 | −1.25013 | −0.625065 | − | 0.780573i | \(-0.714928\pi\) | ||||
−0.625065 | + | 0.780573i | \(0.714928\pi\) | |||||||
\(42\) | 1.47009e33 | 0.777557 | ||||||||
\(43\) | −7.60160e31 | −0.0248200 | −0.0124100 | − | 0.999923i | \(-0.503950\pi\) | ||||
−0.0124100 | + | 0.999923i | \(0.503950\pi\) | |||||||
\(44\) | 7.69544e33 | 1.56839 | ||||||||
\(45\) | −2.66283e33 | −0.342362 | ||||||||
\(46\) | 6.25802e33 | 0.512745 | ||||||||
\(47\) | −3.36927e34 | −1.77636 | −0.888179 | − | 0.459499i | \(-0.848029\pi\) | ||||
−0.888179 | + | 0.459499i | \(0.848029\pi\) | |||||||
\(48\) | −2.32217e32 | −0.00795151 | ||||||||
\(49\) | −3.61137e34 | −0.810312 | ||||||||
\(50\) | 1.65236e35 | 2.45030 | ||||||||
\(51\) | −3.41945e34 | −0.337884 | ||||||||
\(52\) | −3.10829e35 | −2.06278 | ||||||||
\(53\) | 3.75996e35 | 1.68861 | 0.844303 | − | 0.535866i | \(-0.180015\pi\) | ||||
0.844303 | + | 0.535866i | \(0.180015\pi\) | |||||||
\(54\) | 4.57223e35 | 1.39977 | ||||||||
\(55\) | −7.29746e35 | −1.53369 | ||||||||
\(56\) | −3.01577e35 | −0.438070 | ||||||||
\(57\) | −2.73954e35 | −0.276849 | ||||||||
\(58\) | −1.00799e36 | −0.713150 | ||||||||
\(59\) | −6.72854e34 | −0.0335316 | −0.0167658 | − | 0.999859i | \(-0.505337\pi\) | ||||
−0.0167658 | + | 0.999859i | \(0.505337\pi\) | |||||||
\(60\) | 8.02682e36 | 2.83428 | ||||||||
\(61\) | −2.74886e35 | −0.0691657 | −0.0345828 | − | 0.999402i | \(-0.511010\pi\) | ||||
−0.0345828 | + | 0.999402i | \(0.511010\pi\) | |||||||
\(62\) | −6.44406e36 | −1.16180 | ||||||||
\(63\) | −7.24191e35 | −0.0940528 | ||||||||
\(64\) | −1.71925e37 | −1.61677 | ||||||||
\(65\) | 2.94754e37 | 2.01714 | ||||||||
\(66\) | −3.45116e37 | −1.72709 | ||||||||
\(67\) | 2.47724e37 | 0.910824 | 0.455412 | − | 0.890281i | \(-0.349492\pi\) | ||||
0.455412 | + | 0.890281i | \(0.349492\pi\) | |||||||
\(68\) | 1.83060e37 | 0.496776 | ||||||||
\(69\) | −1.73585e37 | −0.349225 | ||||||||
\(70\) | 7.46308e37 | 1.11791 | ||||||||
\(71\) | −1.25628e38 | −1.40698 | −0.703491 | − | 0.710704i | \(-0.748377\pi\) | ||||
−0.703491 | + | 0.710704i | \(0.748377\pi\) | |||||||
\(72\) | 2.58340e37 | 0.217208 | ||||||||
\(73\) | 2.44972e38 | 1.55238 | 0.776189 | − | 0.630500i | \(-0.217150\pi\) | ||||
0.776189 | + | 0.630500i | \(0.217150\pi\) | |||||||
\(74\) | −2.55268e38 | −1.22390 | ||||||||
\(75\) | −4.58329e38 | −1.66887 | ||||||||
\(76\) | 1.46661e38 | 0.407040 | ||||||||
\(77\) | −1.98464e38 | −0.421330 | ||||||||
\(78\) | 1.39397e39 | 2.27151 | ||||||||
\(79\) | 6.92089e38 | 0.868574 | 0.434287 | − | 0.900775i | \(-0.357000\pi\) | ||||
0.434287 | + | 0.900775i | \(0.357000\pi\) | |||||||
\(80\) | −1.17888e37 | −0.0114321 | ||||||||
\(81\) | −1.55552e39 | −1.16932 | ||||||||
\(82\) | −3.46253e39 | −2.02400 | ||||||||
\(83\) | 1.80861e39 | 0.824600 | 0.412300 | − | 0.911048i | \(-0.364726\pi\) | ||||
0.412300 | + | 0.911048i | \(0.364726\pi\) | |||||||
\(84\) | 2.18300e39 | 0.778625 | ||||||||
\(85\) | −1.73593e39 | −0.485784 | ||||||||
\(86\) | −1.82505e38 | −0.0401843 | ||||||||
\(87\) | 2.79595e39 | 0.485718 | ||||||||
\(88\) | 7.07980e39 | 0.973031 | ||||||||
\(89\) | −7.15901e39 | −0.780473 | −0.390237 | − | 0.920715i | \(-0.627607\pi\) | ||||
−0.390237 | + | 0.920715i | \(0.627607\pi\) | |||||||
\(90\) | −6.39311e39 | −0.554295 | ||||||||
\(91\) | 8.01623e39 | 0.554143 | ||||||||
\(92\) | 9.29284e39 | 0.513450 | ||||||||
\(93\) | 1.78745e40 | 0.791286 | ||||||||
\(94\) | −8.08920e40 | −2.87597 | ||||||||
\(95\) | −1.39076e40 | −0.398034 | ||||||||
\(96\) | 4.74757e40 | 1.09625 | ||||||||
\(97\) | 7.50364e40 | 1.40104 | 0.700521 | − | 0.713632i | \(-0.252951\pi\) | ||||
0.700521 | + | 0.713632i | \(0.252951\pi\) | |||||||
\(98\) | −8.67045e40 | −1.31192 | ||||||||
\(99\) | 1.70011e40 | 0.208908 | ||||||||
\(100\) | 2.45366e41 | 2.45366 | ||||||||
\(101\) | −9.43857e40 | −0.769694 | −0.384847 | − | 0.922980i | \(-0.625746\pi\) | ||||
−0.384847 | + | 0.922980i | \(0.625746\pi\) | |||||||
\(102\) | −8.20967e40 | −0.547044 | ||||||||
\(103\) | −2.03470e41 | −1.11003 | −0.555017 | − | 0.831839i | \(-0.687288\pi\) | ||||
−0.555017 | + | 0.831839i | \(0.687288\pi\) | |||||||
\(104\) | −2.85963e41 | −1.27975 | ||||||||
\(105\) | −2.07010e41 | −0.761397 | ||||||||
\(106\) | 9.02720e41 | 2.73390 | ||||||||
\(107\) | −1.95974e41 | −0.489589 | −0.244794 | − | 0.969575i | \(-0.578720\pi\) | ||||
−0.244794 | + | 0.969575i | \(0.578720\pi\) | |||||||
\(108\) | 6.78953e41 | 1.40169 | ||||||||
\(109\) | 1.27681e41 | 0.218214 | 0.109107 | − | 0.994030i | \(-0.465201\pi\) | ||||
0.109107 | + | 0.994030i | \(0.465201\pi\) | |||||||
\(110\) | −1.75203e42 | −2.48308 | ||||||||
\(111\) | 7.08060e41 | 0.833584 | ||||||||
\(112\) | −3.20613e39 | −0.00314059 | ||||||||
\(113\) | 1.47167e42 | 1.20144 | 0.600720 | − | 0.799460i | \(-0.294881\pi\) | ||||
0.600720 | + | 0.799460i | \(0.294881\pi\) | |||||||
\(114\) | −6.57730e41 | −0.448227 | ||||||||
\(115\) | −8.81225e41 | −0.502089 | ||||||||
\(116\) | −1.49681e42 | −0.714131 | ||||||||
\(117\) | −6.86696e41 | −0.274761 | ||||||||
\(118\) | −1.61544e41 | −0.0542886 | ||||||||
\(119\) | −4.72109e41 | −0.133453 | ||||||||
\(120\) | 7.38467e42 | 1.75839 | ||||||||
\(121\) | −3.19384e41 | −0.0641524 | ||||||||
\(122\) | −6.59966e41 | −0.111981 | ||||||||
\(123\) | 9.60435e42 | 1.37852 | ||||||||
\(124\) | −9.56910e42 | −1.16339 | ||||||||
\(125\) | −7.89360e42 | −0.813992 | ||||||||
\(126\) | −1.73869e42 | −0.152274 | ||||||||
\(127\) | −3.99623e42 | −0.297628 | −0.148814 | − | 0.988865i | \(-0.547546\pi\) | ||||
−0.148814 | + | 0.988865i | \(0.547546\pi\) | |||||||
\(128\) | −2.56002e43 | −1.62345 | ||||||||
\(129\) | 5.06230e41 | 0.0273690 | ||||||||
\(130\) | 7.07668e43 | 3.26581 | ||||||||
\(131\) | 1.69219e43 | 0.667404 | 0.333702 | − | 0.942679i | \(-0.391702\pi\) | ||||
0.333702 | + | 0.942679i | \(0.391702\pi\) | |||||||
\(132\) | −5.12480e43 | −1.72946 | ||||||||
\(133\) | −3.78237e42 | −0.109347 | ||||||||
\(134\) | 5.94754e43 | 1.47465 | ||||||||
\(135\) | −6.43840e43 | −1.37068 | ||||||||
\(136\) | 1.68415e43 | 0.308201 | ||||||||
\(137\) | −3.96792e43 | −0.624873 | −0.312436 | − | 0.949939i | \(-0.601145\pi\) | ||||
−0.312436 | + | 0.949939i | \(0.601145\pi\) | |||||||
\(138\) | −4.16755e43 | −0.565405 | ||||||||
\(139\) | −2.45873e43 | −0.287679 | −0.143839 | − | 0.989601i | \(-0.545945\pi\) | ||||
−0.143839 | + | 0.989601i | \(0.545945\pi\) | |||||||
\(140\) | 1.10823e44 | 1.11945 | ||||||||
\(141\) | 2.24378e44 | 1.95879 | ||||||||
\(142\) | −3.01616e44 | −2.27795 | ||||||||
\(143\) | −1.88189e44 | −1.23085 | ||||||||
\(144\) | 2.74647e41 | 0.00155720 | ||||||||
\(145\) | 1.41940e44 | 0.698330 | ||||||||
\(146\) | 5.88147e44 | 2.51334 | ||||||||
\(147\) | 2.40500e44 | 0.893532 | ||||||||
\(148\) | −3.79060e44 | −1.22558 | ||||||||
\(149\) | −2.54122e42 | −0.00715687 | −0.00357844 | − | 0.999994i | \(-0.501139\pi\) | ||||
−0.00357844 | + | 0.999994i | \(0.501139\pi\) | |||||||
\(150\) | −1.10039e45 | −2.70194 | ||||||||
\(151\) | 7.23871e43 | 0.155108 | 0.0775539 | − | 0.996988i | \(-0.475289\pi\) | ||||
0.0775539 | + | 0.996988i | \(0.475289\pi\) | |||||||
\(152\) | 1.34928e44 | 0.252528 | ||||||||
\(153\) | 4.04423e43 | 0.0661701 | ||||||||
\(154\) | −4.76488e44 | −0.682145 | ||||||||
\(155\) | 9.07422e44 | 1.13765 | ||||||||
\(156\) | 2.06998e45 | 2.27463 | ||||||||
\(157\) | −1.76934e45 | −1.70557 | −0.852783 | − | 0.522266i | \(-0.825087\pi\) | ||||
−0.852783 | + | 0.522266i | \(0.825087\pi\) | |||||||
\(158\) | 1.66162e45 | 1.40625 | ||||||||
\(159\) | −2.50396e45 | −1.86203 | ||||||||
\(160\) | 2.41017e45 | 1.57611 | ||||||||
\(161\) | −2.39661e44 | −0.137933 | ||||||||
\(162\) | −3.73460e45 | −1.89316 | ||||||||
\(163\) | 1.55154e45 | 0.693295 | 0.346648 | − | 0.937995i | \(-0.387320\pi\) | ||||
0.346648 | + | 0.937995i | \(0.387320\pi\) | |||||||
\(164\) | −5.14168e45 | −2.02678 | ||||||||
\(165\) | 4.85976e45 | 1.69120 | ||||||||
\(166\) | 4.34224e45 | 1.33505 | ||||||||
\(167\) | −5.53546e45 | −1.50476 | −0.752378 | − | 0.658732i | \(-0.771093\pi\) | ||||
−0.752378 | + | 0.658732i | \(0.771093\pi\) | |||||||
\(168\) | 2.00836e45 | 0.483060 | ||||||||
\(169\) | 2.90574e45 | 0.618842 | ||||||||
\(170\) | −4.16774e45 | −0.786499 | ||||||||
\(171\) | 3.24010e44 | 0.0542173 | ||||||||
\(172\) | −2.71010e44 | −0.0402395 | ||||||||
\(173\) | 6.50011e45 | 0.856990 | 0.428495 | − | 0.903544i | \(-0.359044\pi\) | ||||
0.428495 | + | 0.903544i | \(0.359044\pi\) | |||||||
\(174\) | 6.71272e45 | 0.786392 | ||||||||
\(175\) | −6.32796e45 | −0.659149 | ||||||||
\(176\) | 7.52669e43 | 0.00697580 | ||||||||
\(177\) | 4.48089e44 | 0.0369753 | ||||||||
\(178\) | −1.71879e46 | −1.26361 | ||||||||
\(179\) | −1.33774e46 | −0.876765 | −0.438383 | − | 0.898788i | \(-0.644449\pi\) | ||||
−0.438383 | + | 0.898788i | \(0.644449\pi\) | |||||||
\(180\) | −9.49344e45 | −0.555057 | ||||||||
\(181\) | 1.31888e46 | 0.688328 | 0.344164 | − | 0.938910i | \(-0.388162\pi\) | ||||
0.344164 | + | 0.938910i | \(0.388162\pi\) | |||||||
\(182\) | 1.92460e46 | 0.897173 | ||||||||
\(183\) | 1.83061e45 | 0.0762691 | ||||||||
\(184\) | 8.54941e45 | 0.318545 | ||||||||
\(185\) | 3.59456e46 | 1.19847 | ||||||||
\(186\) | 4.29144e46 | 1.28111 | ||||||||
\(187\) | 1.10832e46 | 0.296423 | ||||||||
\(188\) | −1.20121e47 | −2.87993 | ||||||||
\(189\) | −1.75101e46 | −0.376549 | ||||||||
\(190\) | −3.33905e46 | −0.644428 | ||||||||
\(191\) | −1.01788e47 | −1.76406 | −0.882031 | − | 0.471192i | \(-0.843824\pi\) | ||||
−0.882031 | + | 0.471192i | \(0.843824\pi\) | |||||||
\(192\) | 1.14494e47 | 1.78282 | ||||||||
\(193\) | 8.24135e46 | 1.15365 | 0.576824 | − | 0.816868i | \(-0.304292\pi\) | ||||
0.576824 | + | 0.816868i | \(0.304292\pi\) | |||||||
\(194\) | 1.80153e47 | 2.26833 | ||||||||
\(195\) | −1.96292e47 | −2.22430 | ||||||||
\(196\) | −1.28752e47 | −1.31372 | ||||||||
\(197\) | 2.27618e46 | 0.209242 | 0.104621 | − | 0.994512i | \(-0.466637\pi\) | ||||
0.104621 | + | 0.994512i | \(0.466637\pi\) | |||||||
\(198\) | 4.08174e46 | 0.338228 | ||||||||
\(199\) | 1.53840e47 | 1.14969 | 0.574846 | − | 0.818262i | \(-0.305062\pi\) | ||||
0.574846 | + | 0.818262i | \(0.305062\pi\) | |||||||
\(200\) | 2.25737e47 | 1.52226 | ||||||||
\(201\) | −1.64972e47 | −1.00437 | ||||||||
\(202\) | −2.26608e47 | −1.24616 | ||||||||
\(203\) | 3.86025e46 | 0.191843 | ||||||||
\(204\) | −1.21909e47 | −0.547796 | ||||||||
\(205\) | 4.87577e47 | 1.98193 | ||||||||
\(206\) | −4.88505e47 | −1.79718 | ||||||||
\(207\) | 2.05301e46 | 0.0683910 | ||||||||
\(208\) | −3.04013e45 | −0.00917474 | ||||||||
\(209\) | 8.87947e46 | 0.242878 | ||||||||
\(210\) | −4.97006e47 | −1.23272 | ||||||||
\(211\) | −7.00983e47 | −1.57731 | −0.788655 | − | 0.614836i | \(-0.789222\pi\) | ||||
−0.788655 | + | 0.614836i | \(0.789222\pi\) | |||||||
\(212\) | 1.34049e48 | 2.73766 | ||||||||
\(213\) | 8.36620e47 | 1.55148 | ||||||||
\(214\) | −4.70509e47 | −0.792658 | ||||||||
\(215\) | 2.56994e46 | 0.0393491 | ||||||||
\(216\) | 6.24637e47 | 0.869612 | ||||||||
\(217\) | 2.46786e47 | 0.312533 | ||||||||
\(218\) | 3.06546e47 | 0.353295 | ||||||||
\(219\) | −1.63140e48 | −1.71181 | ||||||||
\(220\) | −2.60167e48 | −2.48649 | ||||||||
\(221\) | −4.47665e47 | −0.389863 | ||||||||
\(222\) | 1.69996e48 | 1.34960 | ||||||||
\(223\) | −2.18317e47 | −0.158066 | −0.0790330 | − | 0.996872i | \(-0.525183\pi\) | ||||
−0.0790330 | + | 0.996872i | \(0.525183\pi\) | |||||||
\(224\) | 6.55477e47 | 0.432985 | ||||||||
\(225\) | 5.42073e47 | 0.326826 | ||||||||
\(226\) | 3.53329e48 | 1.94516 | ||||||||
\(227\) | −1.64330e48 | −0.826391 | −0.413196 | − | 0.910642i | \(-0.635587\pi\) | ||||
−0.413196 | + | 0.910642i | \(0.635587\pi\) | |||||||
\(228\) | −9.76695e47 | −0.448843 | ||||||||
\(229\) | 2.31385e48 | 0.972093 | 0.486047 | − | 0.873933i | \(-0.338438\pi\) | ||||
0.486047 | + | 0.873933i | \(0.338438\pi\) | |||||||
\(230\) | −2.11571e48 | −0.812897 | ||||||||
\(231\) | 1.32168e48 | 0.464601 | ||||||||
\(232\) | −1.37706e48 | −0.443048 | ||||||||
\(233\) | −5.25096e48 | −1.54683 | −0.773414 | − | 0.633901i | \(-0.781453\pi\) | ||||
−0.773414 | + | 0.633901i | \(0.781453\pi\) | |||||||
\(234\) | −1.64867e48 | −0.444845 | ||||||||
\(235\) | 1.13908e49 | 2.81620 | ||||||||
\(236\) | −2.39884e47 | −0.0543633 | ||||||||
\(237\) | −4.60899e48 | −0.957777 | ||||||||
\(238\) | −1.13347e48 | −0.216065 | ||||||||
\(239\) | −4.02474e48 | −0.704013 | −0.352007 | − | 0.935998i | \(-0.614501\pi\) | ||||
−0.352007 | + | 0.935998i | \(0.614501\pi\) | |||||||
\(240\) | 7.85080e46 | 0.0126062 | ||||||||
\(241\) | −2.82992e48 | −0.417277 | −0.208638 | − | 0.977993i | \(-0.566903\pi\) | ||||
−0.208638 | + | 0.977993i | \(0.566903\pi\) | |||||||
\(242\) | −7.66800e47 | −0.103865 | ||||||||
\(243\) | 3.41307e48 | 0.424832 | ||||||||
\(244\) | −9.80016e47 | −0.112135 | ||||||||
\(245\) | 1.22093e49 | 1.28465 | ||||||||
\(246\) | 2.30588e49 | 2.23186 | ||||||||
\(247\) | −3.58654e48 | −0.319439 | ||||||||
\(248\) | −8.80357e48 | −0.721771 | ||||||||
\(249\) | −1.20445e49 | −0.909287 | ||||||||
\(250\) | −1.89516e49 | −1.31788 | ||||||||
\(251\) | 2.68976e48 | 0.172346 | 0.0861732 | − | 0.996280i | \(-0.472536\pi\) | ||||
0.0861732 | + | 0.996280i | \(0.472536\pi\) | |||||||
\(252\) | −2.58187e48 | −0.152484 | ||||||||
\(253\) | 5.62627e48 | 0.306372 | ||||||||
\(254\) | −9.59444e48 | −0.481868 | ||||||||
\(255\) | 1.15605e49 | 0.535675 | ||||||||
\(256\) | −2.36562e49 | −1.01164 | ||||||||
\(257\) | −6.05982e48 | −0.239238 | −0.119619 | − | 0.992820i | \(-0.538167\pi\) | ||||
−0.119619 | + | 0.992820i | \(0.538167\pi\) | |||||||
\(258\) | 1.21540e48 | 0.0443112 | ||||||||
\(259\) | 9.77589e48 | 0.329239 | ||||||||
\(260\) | 1.05085e50 | 3.27030 | ||||||||
\(261\) | −3.30681e48 | −0.0951215 | ||||||||
\(262\) | 4.06275e49 | 1.08055 | ||||||||
\(263\) | −4.72993e49 | −1.16349 | −0.581743 | − | 0.813372i | \(-0.697629\pi\) | ||||
−0.581743 | + | 0.813372i | \(0.697629\pi\) | |||||||
\(264\) | −4.71482e49 | −1.07296 | ||||||||
\(265\) | −1.27117e50 | −2.67709 | ||||||||
\(266\) | −9.08100e48 | −0.177035 | ||||||||
\(267\) | 4.76757e49 | 0.860629 | ||||||||
\(268\) | 8.83179e49 | 1.47668 | ||||||||
\(269\) | 3.21338e49 | 0.497784 | 0.248892 | − | 0.968531i | \(-0.419934\pi\) | ||||
0.248892 | + | 0.968531i | \(0.419934\pi\) | |||||||
\(270\) | −1.54578e50 | −2.21917 | ||||||||
\(271\) | 1.33856e50 | 1.78142 | 0.890709 | − | 0.454574i | \(-0.150208\pi\) | ||||
0.890709 | + | 0.454574i | \(0.150208\pi\) | |||||||
\(272\) | 1.79046e47 | 0.00220954 | ||||||||
\(273\) | −5.33843e49 | −0.611054 | ||||||||
\(274\) | −9.52648e49 | −1.01169 | ||||||||
\(275\) | 1.48555e50 | 1.46409 | ||||||||
\(276\) | −6.18859e49 | −0.566182 | ||||||||
\(277\) | 5.53962e49 | 0.470592 | 0.235296 | − | 0.971924i | \(-0.424394\pi\) | ||||
0.235296 | + | 0.971924i | \(0.424394\pi\) | |||||||
\(278\) | −5.90310e49 | −0.465760 | ||||||||
\(279\) | −2.11404e49 | −0.154963 | ||||||||
\(280\) | 1.01957e50 | 0.694508 | ||||||||
\(281\) | −2.22399e49 | −0.140816 | −0.0704082 | − | 0.997518i | \(-0.522430\pi\) | ||||
−0.0704082 | + | 0.997518i | \(0.522430\pi\) | |||||||
\(282\) | 5.38703e50 | 3.17134 | ||||||||
\(283\) | −1.61973e50 | −0.886790 | −0.443395 | − | 0.896326i | \(-0.646226\pi\) | ||||
−0.443395 | + | 0.896326i | \(0.646226\pi\) | |||||||
\(284\) | −4.47884e50 | −2.28108 | ||||||||
\(285\) | 9.26184e49 | 0.438912 | ||||||||
\(286\) | −4.51817e50 | −1.99278 | ||||||||
\(287\) | 1.32603e50 | 0.544471 | ||||||||
\(288\) | −5.61503e49 | −0.214687 | ||||||||
\(289\) | −2.54441e50 | −0.906110 | ||||||||
\(290\) | 3.40780e50 | 1.13062 | ||||||||
\(291\) | −4.99707e50 | −1.54493 | ||||||||
\(292\) | 8.73367e50 | 2.51680 | ||||||||
\(293\) | 4.58527e49 | 0.123191 | 0.0615955 | − | 0.998101i | \(-0.480381\pi\) | ||||
0.0615955 | + | 0.998101i | \(0.480381\pi\) | |||||||
\(294\) | 5.77411e50 | 1.44665 | ||||||||
\(295\) | 2.27478e49 | 0.0531604 | ||||||||
\(296\) | −3.48735e50 | −0.760353 | ||||||||
\(297\) | 4.11066e50 | 0.836381 | ||||||||
\(298\) | −6.10115e48 | −0.0115872 | ||||||||
\(299\) | −2.27252e50 | −0.402948 | ||||||||
\(300\) | −1.63402e51 | −2.70566 | ||||||||
\(301\) | 6.98931e48 | 0.0108099 | ||||||||
\(302\) | 1.73792e50 | 0.251124 | ||||||||
\(303\) | 6.28564e50 | 0.848742 | ||||||||
\(304\) | 1.43445e48 | 0.00181041 | ||||||||
\(305\) | 9.29333e49 | 0.109654 | ||||||||
\(306\) | 9.70970e49 | 0.107131 | ||||||||
\(307\) | −1.04806e51 | −1.08156 | −0.540779 | − | 0.841165i | \(-0.681871\pi\) | ||||
−0.540779 | + | 0.841165i | \(0.681871\pi\) | |||||||
\(308\) | −7.07560e50 | −0.683083 | ||||||||
\(309\) | 1.35501e51 | 1.22404 | ||||||||
\(310\) | 2.17861e51 | 1.84189 | ||||||||
\(311\) | −1.45879e51 | −1.15453 | −0.577265 | − | 0.816557i | \(-0.695880\pi\) | ||||
−0.577265 | + | 0.816557i | \(0.695880\pi\) | |||||||
\(312\) | 1.90438e51 | 1.41118 | ||||||||
\(313\) | 5.50229e50 | 0.381843 | 0.190922 | − | 0.981605i | \(-0.438852\pi\) | ||||
0.190922 | + | 0.981605i | \(0.438852\pi\) | |||||||
\(314\) | −4.24796e51 | −2.76136 | ||||||||
\(315\) | 2.44834e50 | 0.149110 | ||||||||
\(316\) | 2.46742e51 | 1.40818 | ||||||||
\(317\) | 2.01228e51 | 1.07640 | 0.538199 | − | 0.842818i | \(-0.319105\pi\) | ||||
0.538199 | + | 0.842818i | \(0.319105\pi\) | |||||||
\(318\) | −6.01169e51 | −3.01468 | ||||||||
\(319\) | −9.06229e50 | −0.426117 | ||||||||
\(320\) | 5.81243e51 | 2.56320 | ||||||||
\(321\) | 1.30510e51 | 0.539870 | ||||||||
\(322\) | −5.75396e50 | −0.223317 | ||||||||
\(323\) | 2.11226e50 | 0.0769299 | ||||||||
\(324\) | −5.54569e51 | −1.89576 | ||||||||
\(325\) | −6.00033e51 | −1.92560 | ||||||||
\(326\) | 3.72506e51 | 1.12246 | ||||||||
\(327\) | −8.50295e50 | −0.240625 | ||||||||
\(328\) | −4.73035e51 | −1.25742 | ||||||||
\(329\) | 3.09789e51 | 0.773660 | ||||||||
\(330\) | 1.16677e52 | 2.73810 | ||||||||
\(331\) | 7.84661e51 | 1.73065 | 0.865323 | − | 0.501215i | \(-0.167113\pi\) | ||||
0.865323 | + | 0.501215i | \(0.167113\pi\) | |||||||
\(332\) | 6.44800e51 | 1.33689 | ||||||||
\(333\) | −8.37434e50 | −0.163246 | ||||||||
\(334\) | −1.32899e52 | −2.43624 | ||||||||
\(335\) | −8.37504e51 | −1.44400 | ||||||||
\(336\) | 2.13513e49 | 0.00346313 | ||||||||
\(337\) | 1.59637e51 | 0.243624 | 0.121812 | − | 0.992553i | \(-0.461129\pi\) | ||||
0.121812 | + | 0.992553i | \(0.461129\pi\) | |||||||
\(338\) | 6.97632e51 | 1.00192 | ||||||||
\(339\) | −9.80062e51 | −1.32483 | ||||||||
\(340\) | −6.18889e51 | −0.787580 | ||||||||
\(341\) | −5.79352e51 | −0.694190 | ||||||||
\(342\) | 7.77907e50 | 0.0877794 | ||||||||
\(343\) | 7.41827e51 | 0.788448 | ||||||||
\(344\) | −2.49329e50 | −0.0249646 | ||||||||
\(345\) | 5.86854e51 | 0.553654 | ||||||||
\(346\) | 1.56060e52 | 1.38749 | ||||||||
\(347\) | −3.39579e51 | −0.284568 | −0.142284 | − | 0.989826i | \(-0.545445\pi\) | ||||
−0.142284 | + | 0.989826i | \(0.545445\pi\) | |||||||
\(348\) | 9.96804e51 | 0.787473 | ||||||||
\(349\) | 9.21738e51 | 0.686572 | 0.343286 | − | 0.939231i | \(-0.388460\pi\) | ||||
0.343286 | + | 0.939231i | \(0.388460\pi\) | |||||||
\(350\) | −1.51926e52 | −1.06718 | ||||||||
\(351\) | −1.66035e52 | −1.10003 | ||||||||
\(352\) | −1.53879e52 | −0.961737 | ||||||||
\(353\) | 1.05771e52 | 0.623715 | 0.311857 | − | 0.950129i | \(-0.399049\pi\) | ||||
0.311857 | + | 0.950129i | \(0.399049\pi\) | |||||||
\(354\) | 1.07581e51 | 0.0598641 | ||||||||
\(355\) | 4.24721e52 | 2.23060 | ||||||||
\(356\) | −2.55231e52 | −1.26535 | ||||||||
\(357\) | 3.14402e51 | 0.147159 | ||||||||
\(358\) | −3.21174e52 | −1.41951 | ||||||||
\(359\) | 1.47439e52 | 0.615428 | 0.307714 | − | 0.951479i | \(-0.400436\pi\) | ||||
0.307714 | + | 0.951479i | \(0.400436\pi\) | |||||||
\(360\) | −8.73396e51 | −0.344358 | ||||||||
\(361\) | −2.51548e52 | −0.936966 | ||||||||
\(362\) | 3.16647e52 | 1.11442 | ||||||||
\(363\) | 2.12694e51 | 0.0707409 | ||||||||
\(364\) | 2.85793e52 | 0.898407 | ||||||||
\(365\) | −8.28200e52 | −2.46111 | ||||||||
\(366\) | 4.39506e51 | 0.123482 | ||||||||
\(367\) | 5.60693e52 | 1.48960 | 0.744802 | − | 0.667285i | \(-0.232544\pi\) | ||||
0.744802 | + | 0.667285i | \(0.232544\pi\) | |||||||
\(368\) | 9.08906e49 | 0.00228370 | ||||||||
\(369\) | −1.13592e52 | −0.269965 | ||||||||
\(370\) | 8.63009e52 | 1.94035 | ||||||||
\(371\) | −3.45711e52 | −0.735442 | ||||||||
\(372\) | 6.37257e52 | 1.28288 | ||||||||
\(373\) | −8.78610e52 | −1.67404 | −0.837018 | − | 0.547175i | \(-0.815703\pi\) | ||||
−0.837018 | + | 0.547175i | \(0.815703\pi\) | |||||||
\(374\) | 2.66094e52 | 0.479918 | ||||||||
\(375\) | 5.25677e52 | 0.897590 | ||||||||
\(376\) | −1.10511e53 | −1.78671 | ||||||||
\(377\) | 3.66038e52 | 0.560440 | ||||||||
\(378\) | −4.20395e52 | −0.609644 | ||||||||
\(379\) | −2.73345e52 | −0.375498 | −0.187749 | − | 0.982217i | \(-0.560119\pi\) | ||||
−0.187749 | + | 0.982217i | \(0.560119\pi\) | |||||||
\(380\) | −4.95832e52 | −0.645314 | ||||||||
\(381\) | 2.66130e52 | 0.328195 | ||||||||
\(382\) | −2.44381e53 | −2.85607 | ||||||||
\(383\) | 2.55810e52 | 0.283362 | 0.141681 | − | 0.989912i | \(-0.454749\pi\) | ||||
0.141681 | + | 0.989912i | \(0.454749\pi\) | |||||||
\(384\) | 1.70485e53 | 1.79018 | ||||||||
\(385\) | 6.70967e52 | 0.667969 | ||||||||
\(386\) | 1.97864e53 | 1.86779 | ||||||||
\(387\) | −5.98726e50 | −0.00535986 | ||||||||
\(388\) | 2.67518e53 | 2.27145 | ||||||||
\(389\) | 1.34317e53 | 1.08185 | 0.540923 | − | 0.841072i | \(-0.318075\pi\) | ||||
0.540923 | + | 0.841072i | \(0.318075\pi\) | |||||||
\(390\) | −4.71273e53 | −3.60121 | ||||||||
\(391\) | 1.33838e52 | 0.0970413 | ||||||||
\(392\) | −1.18452e53 | −0.815035 | ||||||||
\(393\) | −1.12692e53 | −0.735947 | ||||||||
\(394\) | 5.46483e52 | 0.338770 | ||||||||
\(395\) | −2.33981e53 | −1.37702 | ||||||||
\(396\) | 6.06118e52 | 0.338693 | ||||||||
\(397\) | 6.36376e52 | 0.337683 | 0.168841 | − | 0.985643i | \(-0.445997\pi\) | ||||
0.168841 | + | 0.985643i | \(0.445997\pi\) | |||||||
\(398\) | 3.69351e53 | 1.86138 | ||||||||
\(399\) | 2.51888e52 | 0.120577 | ||||||||
\(400\) | 2.39986e51 | 0.0109133 | ||||||||
\(401\) | −1.74531e53 | −0.754071 | −0.377036 | − | 0.926199i | \(-0.623057\pi\) | ||||
−0.377036 | + | 0.926199i | \(0.623057\pi\) | |||||||
\(402\) | −3.96078e53 | −1.62610 | ||||||||
\(403\) | 2.34008e53 | 0.913015 | ||||||||
\(404\) | −3.36501e53 | −1.24787 | ||||||||
\(405\) | 5.25888e53 | 1.85381 | ||||||||
\(406\) | 9.26797e52 | 0.310600 | ||||||||
\(407\) | −2.29498e53 | −0.731298 | ||||||||
\(408\) | −1.12157e53 | −0.339853 | ||||||||
\(409\) | −2.90188e53 | −0.836279 | −0.418140 | − | 0.908383i | \(-0.637318\pi\) | ||||
−0.418140 | + | 0.908383i | \(0.637318\pi\) | |||||||
\(410\) | 1.17061e54 | 3.20881 | ||||||||
\(411\) | 2.64245e53 | 0.689048 | ||||||||
\(412\) | −7.25405e53 | −1.79965 | ||||||||
\(413\) | 6.18657e51 | 0.0146041 | ||||||||
\(414\) | 4.92902e52 | 0.110727 | ||||||||
\(415\) | −6.11453e53 | −1.30731 | ||||||||
\(416\) | 6.21540e53 | 1.26490 | ||||||||
\(417\) | 1.63740e53 | 0.317223 | ||||||||
\(418\) | 2.13185e53 | 0.393227 | ||||||||
\(419\) | −1.59662e53 | −0.280424 | −0.140212 | − | 0.990121i | \(-0.544778\pi\) | ||||
−0.140212 | + | 0.990121i | \(0.544778\pi\) | |||||||
\(420\) | −7.38028e53 | −1.23442 | ||||||||
\(421\) | −4.06387e53 | −0.647377 | −0.323688 | − | 0.946164i | \(-0.604923\pi\) | ||||
−0.323688 | + | 0.946164i | \(0.604923\pi\) | |||||||
\(422\) | −1.68297e54 | −2.55371 | ||||||||
\(423\) | −2.65375e53 | −0.383603 | ||||||||
\(424\) | 1.23325e54 | 1.69845 | ||||||||
\(425\) | 3.53384e53 | 0.463739 | ||||||||
\(426\) | 2.00862e54 | 2.51189 | ||||||||
\(427\) | 2.52744e52 | 0.0301238 | ||||||||
\(428\) | −6.98682e53 | −0.793748 | ||||||||
\(429\) | 1.25325e54 | 1.35726 | ||||||||
\(430\) | 6.17011e52 | 0.0637074 | ||||||||
\(431\) | −9.52197e53 | −0.937438 | −0.468719 | − | 0.883347i | \(-0.655284\pi\) | ||||
−0.468719 | + | 0.883347i | \(0.655284\pi\) | |||||||
\(432\) | 6.64064e51 | 0.00623438 | ||||||||
\(433\) | 4.92132e53 | 0.440636 | 0.220318 | − | 0.975428i | \(-0.429291\pi\) | ||||
0.220318 | + | 0.975428i | \(0.429291\pi\) | |||||||
\(434\) | 5.92501e53 | 0.505999 | ||||||||
\(435\) | −9.45253e53 | −0.770049 | ||||||||
\(436\) | 4.55205e53 | 0.353780 | ||||||||
\(437\) | 1.07227e53 | 0.0795120 | ||||||||
\(438\) | −3.91678e54 | −2.77147 | ||||||||
\(439\) | 1.37566e54 | 0.928940 | 0.464470 | − | 0.885589i | \(-0.346245\pi\) | ||||
0.464470 | + | 0.885589i | \(0.346245\pi\) | |||||||
\(440\) | −2.39354e54 | −1.54263 | ||||||||
\(441\) | −2.84443e53 | −0.174987 | ||||||||
\(442\) | −1.07479e54 | −0.631199 | ||||||||
\(443\) | 2.53462e54 | 1.42114 | 0.710570 | − | 0.703626i | \(-0.248437\pi\) | ||||
0.710570 | + | 0.703626i | \(0.248437\pi\) | |||||||
\(444\) | 2.52436e54 | 1.35145 | ||||||||
\(445\) | 2.42032e54 | 1.23735 | ||||||||
\(446\) | −5.24152e53 | −0.255913 | ||||||||
\(447\) | 1.69233e52 | 0.00789189 | ||||||||
\(448\) | 1.58077e54 | 0.704156 | ||||||||
\(449\) | −3.83879e54 | −1.63359 | −0.816797 | − | 0.576926i | \(-0.804252\pi\) | ||||
−0.816797 | + | 0.576926i | \(0.804252\pi\) | |||||||
\(450\) | 1.30145e54 | 0.529140 | ||||||||
\(451\) | −3.11298e54 | −1.20937 | ||||||||
\(452\) | 5.24676e54 | 1.94784 | ||||||||
\(453\) | −4.82064e53 | −0.171038 | ||||||||
\(454\) | −3.94535e54 | −1.33795 | ||||||||
\(455\) | −2.71013e54 | −0.878528 | ||||||||
\(456\) | −8.98559e53 | −0.278463 | ||||||||
\(457\) | 5.46700e54 | 1.61982 | 0.809910 | − | 0.586554i | \(-0.199516\pi\) | ||||
0.809910 | + | 0.586554i | \(0.199516\pi\) | |||||||
\(458\) | 5.55527e54 | 1.57385 | ||||||||
\(459\) | 9.77848e53 | 0.264918 | ||||||||
\(460\) | −3.14172e54 | −0.814014 | ||||||||
\(461\) | −6.86605e54 | −1.70152 | −0.850762 | − | 0.525551i | \(-0.823859\pi\) | ||||
−0.850762 | + | 0.525551i | \(0.823859\pi\) | |||||||
\(462\) | 3.17318e54 | 0.752202 | ||||||||
\(463\) | 2.69469e54 | 0.611082 | 0.305541 | − | 0.952179i | \(-0.401163\pi\) | ||||
0.305541 | + | 0.952179i | \(0.401163\pi\) | |||||||
\(464\) | −1.46399e52 | −0.00317628 | ||||||||
\(465\) | −6.04300e54 | −1.25449 | ||||||||
\(466\) | −1.26069e55 | −2.50436 | ||||||||
\(467\) | −1.01233e54 | −0.192453 | −0.0962267 | − | 0.995359i | \(-0.530677\pi\) | ||||
−0.0962267 | + | 0.995359i | \(0.530677\pi\) | |||||||
\(468\) | −2.44819e54 | −0.445457 | ||||||||
\(469\) | −2.27770e54 | −0.396693 | ||||||||
\(470\) | 2.73480e55 | 4.55952 | ||||||||
\(471\) | 1.17830e55 | 1.88073 | ||||||||
\(472\) | −2.20693e53 | −0.0337271 | ||||||||
\(473\) | −1.64081e53 | −0.0240107 | ||||||||
\(474\) | −1.10656e55 | −1.55067 | ||||||||
\(475\) | 2.83119e54 | 0.379970 | ||||||||
\(476\) | −1.68315e54 | −0.216362 | ||||||||
\(477\) | 2.96147e54 | 0.364654 | ||||||||
\(478\) | −9.66289e54 | −1.13982 | ||||||||
\(479\) | 8.03512e54 | 0.908060 | 0.454030 | − | 0.890986i | \(-0.349986\pi\) | ||||
0.454030 | + | 0.890986i | \(0.349986\pi\) | |||||||
\(480\) | −1.60506e55 | −1.73798 | ||||||||
\(481\) | 9.26974e54 | 0.961820 | ||||||||
\(482\) | −6.79428e54 | −0.675583 | ||||||||
\(483\) | 1.59603e54 | 0.152098 | ||||||||
\(484\) | −1.13866e54 | −0.104007 | ||||||||
\(485\) | −2.53683e55 | −2.22119 | ||||||||
\(486\) | 8.19436e54 | 0.687815 | ||||||||
\(487\) | 3.58922e54 | 0.288839 | 0.144420 | − | 0.989517i | \(-0.453868\pi\) | ||||
0.144420 | + | 0.989517i | \(0.453868\pi\) | |||||||
\(488\) | −9.01614e53 | −0.0695688 | ||||||||
\(489\) | −1.03326e55 | −0.764497 | ||||||||
\(490\) | 2.93130e55 | 2.07989 | ||||||||
\(491\) | 8.12128e53 | 0.0552655 | 0.0276327 | − | 0.999618i | \(-0.491203\pi\) | ||||
0.0276327 | + | 0.999618i | \(0.491203\pi\) | |||||||
\(492\) | 3.42412e55 | 2.23493 | ||||||||
\(493\) | −2.15575e54 | −0.134970 | ||||||||
\(494\) | −8.61083e54 | −0.517181 | ||||||||
\(495\) | −5.74772e54 | −0.331199 | ||||||||
\(496\) | −9.35926e52 | −0.00517448 | ||||||||
\(497\) | 1.15509e55 | 0.612785 | ||||||||
\(498\) | −2.89173e55 | −1.47216 | ||||||||
\(499\) | −6.57141e54 | −0.321068 | −0.160534 | − | 0.987030i | \(-0.551322\pi\) | ||||
−0.160534 | + | 0.987030i | \(0.551322\pi\) | |||||||
\(500\) | −2.81421e55 | −1.31969 | ||||||||
\(501\) | 3.68636e55 | 1.65930 | ||||||||
\(502\) | 6.45777e54 | 0.279034 | ||||||||
\(503\) | −3.12409e55 | −1.29592 | −0.647962 | − | 0.761672i | \(-0.724379\pi\) | ||||
−0.647962 | + | 0.761672i | \(0.724379\pi\) | |||||||
\(504\) | −2.37532e54 | −0.0946010 | ||||||||
\(505\) | 3.19099e55 | 1.22026 | ||||||||
\(506\) | 1.35080e55 | 0.496026 | ||||||||
\(507\) | −1.93509e55 | −0.682397 | ||||||||
\(508\) | −1.42472e55 | −0.482530 | ||||||||
\(509\) | −2.10477e55 | −0.684684 | −0.342342 | − | 0.939575i | \(-0.611220\pi\) | ||||
−0.342342 | + | 0.939575i | \(0.611220\pi\) | |||||||
\(510\) | 2.77552e55 | 0.867273 | ||||||||
\(511\) | −2.25240e55 | −0.676110 | ||||||||
\(512\) | −5.00094e53 | −0.0144217 | ||||||||
\(513\) | 7.83418e54 | 0.217064 | ||||||||
\(514\) | −1.45489e55 | −0.387334 | ||||||||
\(515\) | 6.87889e55 | 1.75983 | ||||||||
\(516\) | 1.80480e54 | 0.0443721 | ||||||||
\(517\) | −7.27259e55 | −1.71843 | ||||||||
\(518\) | 2.34707e55 | 0.533047 | ||||||||
\(519\) | −4.32877e55 | −0.945004 | ||||||||
\(520\) | 9.66782e55 | 2.02890 | ||||||||
\(521\) | 1.04403e55 | 0.210639 | 0.105320 | − | 0.994438i | \(-0.466413\pi\) | ||||
0.105320 | + | 0.994438i | \(0.466413\pi\) | |||||||
\(522\) | −7.93924e54 | −0.154004 | ||||||||
\(523\) | 3.89473e55 | 0.726429 | 0.363215 | − | 0.931706i | \(-0.381679\pi\) | ||||
0.363215 | + | 0.931706i | \(0.381679\pi\) | |||||||
\(524\) | 6.03297e55 | 1.08203 | ||||||||
\(525\) | 4.21412e55 | 0.726844 | ||||||||
\(526\) | −1.13560e56 | −1.88372 | ||||||||
\(527\) | −1.37817e55 | −0.219880 | ||||||||
\(528\) | −5.01242e53 | −0.00769222 | ||||||||
\(529\) | −6.09452e55 | −0.899702 | ||||||||
\(530\) | −3.05191e56 | −4.33428 | ||||||||
\(531\) | −5.29962e53 | −0.00724114 | ||||||||
\(532\) | −1.34848e55 | −0.177279 | ||||||||
\(533\) | 1.25738e56 | 1.59059 | ||||||||
\(534\) | 1.14463e56 | 1.39338 | ||||||||
\(535\) | 6.62549e55 | 0.776185 | ||||||||
\(536\) | 8.12524e55 | 0.916132 | ||||||||
\(537\) | 8.90869e55 | 0.966810 | ||||||||
\(538\) | 7.71493e55 | 0.805926 | ||||||||
\(539\) | −7.79515e55 | −0.783890 | ||||||||
\(540\) | −2.29540e56 | −2.22222 | ||||||||
\(541\) | 7.83261e55 | 0.730067 | 0.365033 | − | 0.930994i | \(-0.381058\pi\) | ||||
0.365033 | + | 0.930994i | \(0.381058\pi\) | |||||||
\(542\) | 3.21370e56 | 2.88417 | ||||||||
\(543\) | −8.78314e55 | −0.759020 | ||||||||
\(544\) | −3.66050e55 | −0.304623 | ||||||||
\(545\) | −4.31663e55 | −0.345953 | ||||||||
\(546\) | −1.28169e56 | −0.989314 | ||||||||
\(547\) | −1.75108e56 | −1.30187 | −0.650933 | − | 0.759135i | \(-0.725622\pi\) | ||||
−0.650933 | + | 0.759135i | \(0.725622\pi\) | |||||||
\(548\) | −1.41463e56 | −1.01308 | ||||||||
\(549\) | −2.16509e54 | −0.0149363 | ||||||||
\(550\) | 3.56662e56 | 2.37040 | ||||||||
\(551\) | −1.72711e55 | −0.110589 | ||||||||
\(552\) | −5.69351e55 | −0.351260 | ||||||||
\(553\) | −6.36343e55 | −0.378291 | ||||||||
\(554\) | 1.32999e56 | 0.761902 | ||||||||
\(555\) | −2.39381e56 | −1.32155 | ||||||||
\(556\) | −8.76581e55 | −0.466400 | ||||||||
\(557\) | 2.17848e56 | 1.11718 | 0.558588 | − | 0.829445i | \(-0.311343\pi\) | ||||
0.558588 | + | 0.829445i | \(0.311343\pi\) | |||||||
\(558\) | −5.07555e55 | −0.250889 | ||||||||
\(559\) | 6.62744e54 | 0.0315794 | ||||||||
\(560\) | 1.08393e54 | 0.00497903 | ||||||||
\(561\) | −7.38089e55 | −0.326866 | ||||||||
\(562\) | −5.33952e55 | −0.227986 | ||||||||
\(563\) | 3.30210e56 | 1.35947 | 0.679733 | − | 0.733459i | \(-0.262095\pi\) | ||||
0.679733 | + | 0.733459i | \(0.262095\pi\) | |||||||
\(564\) | 7.99946e56 | 3.17570 | ||||||||
\(565\) | −4.97541e56 | −1.90474 | ||||||||
\(566\) | −3.88877e56 | −1.43574 | ||||||||
\(567\) | 1.43022e56 | 0.509274 | ||||||||
\(568\) | −4.12053e56 | −1.41518 | ||||||||
\(569\) | −8.68468e55 | −0.287708 | −0.143854 | − | 0.989599i | \(-0.545950\pi\) | ||||
−0.143854 | + | 0.989599i | \(0.545950\pi\) | |||||||
\(570\) | 2.22365e56 | 0.710611 | ||||||||
\(571\) | 4.87083e56 | 1.50163 | 0.750815 | − | 0.660512i | \(-0.229661\pi\) | ||||
0.750815 | + | 0.660512i | \(0.229661\pi\) | |||||||
\(572\) | −6.70926e56 | −1.99552 | ||||||||
\(573\) | 6.77862e56 | 1.94523 | ||||||||
\(574\) | 3.18363e56 | 0.881514 | ||||||||
\(575\) | 1.79391e56 | 0.479304 | ||||||||
\(576\) | −1.35414e56 | −0.349142 | ||||||||
\(577\) | −7.14972e56 | −1.77904 | −0.889518 | − | 0.456900i | \(-0.848960\pi\) | ||||
−0.889518 | + | 0.456900i | \(0.848960\pi\) | |||||||
\(578\) | −6.10880e56 | −1.46702 | ||||||||
\(579\) | −5.48835e56 | −1.27213 | ||||||||
\(580\) | 5.06041e56 | 1.13217 | ||||||||
\(581\) | −1.66293e56 | −0.359139 | ||||||||
\(582\) | −1.19973e57 | −2.50129 | ||||||||
\(583\) | 8.11589e56 | 1.63354 | ||||||||
\(584\) | 8.03498e56 | 1.56143 | ||||||||
\(585\) | 2.32158e56 | 0.435600 | ||||||||
\(586\) | 1.10087e56 | 0.199450 | ||||||||
\(587\) | 4.35978e56 | 0.762752 | 0.381376 | − | 0.924420i | \(-0.375450\pi\) | ||||
0.381376 | + | 0.924420i | \(0.375450\pi\) | |||||||
\(588\) | 8.57426e56 | 1.44864 | ||||||||
\(589\) | −1.10414e56 | −0.180161 | ||||||||
\(590\) | 5.46147e55 | 0.0860682 | ||||||||
\(591\) | −1.51583e56 | −0.230732 | ||||||||
\(592\) | −3.70747e54 | −0.00545109 | ||||||||
\(593\) | −8.14584e56 | −1.15695 | −0.578475 | − | 0.815700i | \(-0.696352\pi\) | ||||
−0.578475 | + | 0.815700i | \(0.696352\pi\) | |||||||
\(594\) | 9.86918e56 | 1.35413 | ||||||||
\(595\) | 1.59610e56 | 0.211574 | ||||||||
\(596\) | −9.05989e54 | −0.0116031 | ||||||||
\(597\) | −1.02450e57 | −1.26777 | ||||||||
\(598\) | −5.45605e56 | −0.652385 | ||||||||
\(599\) | −1.46611e57 | −1.69401 | −0.847004 | − | 0.531587i | \(-0.821596\pi\) | ||||
−0.847004 | + | 0.531587i | \(0.821596\pi\) | |||||||
\(600\) | −1.50330e57 | −1.67859 | ||||||||
\(601\) | 1.27455e57 | 1.37540 | 0.687700 | − | 0.725995i | \(-0.258620\pi\) | ||||
0.687700 | + | 0.725995i | \(0.258620\pi\) | |||||||
\(602\) | 1.67805e55 | 0.0175015 | ||||||||
\(603\) | 1.95115e56 | 0.196692 | ||||||||
\(604\) | 2.58073e56 | 0.251469 | ||||||||
\(605\) | 1.07977e56 | 0.101706 | ||||||||
\(606\) | 1.50910e57 | 1.37414 | ||||||||
\(607\) | 7.08566e56 | 0.623752 | 0.311876 | − | 0.950123i | \(-0.399043\pi\) | ||||
0.311876 | + | 0.950123i | \(0.399043\pi\) | |||||||
\(608\) | −2.93267e56 | −0.249597 | ||||||||
\(609\) | −2.57074e56 | −0.211546 | ||||||||
\(610\) | 2.23121e56 | 0.177533 | ||||||||
\(611\) | 2.93750e57 | 2.26012 | ||||||||
\(612\) | 1.44184e56 | 0.107279 | ||||||||
\(613\) | −1.17754e57 | −0.847298 | −0.423649 | − | 0.905827i | \(-0.639251\pi\) | ||||
−0.423649 | + | 0.905827i | \(0.639251\pi\) | |||||||
\(614\) | −2.51626e57 | −1.75107 | ||||||||
\(615\) | −3.24703e57 | −2.18548 | ||||||||
\(616\) | −6.50955e56 | −0.423786 | ||||||||
\(617\) | 1.61404e57 | 1.01641 | 0.508205 | − | 0.861236i | \(-0.330309\pi\) | ||||
0.508205 | + | 0.861236i | \(0.330309\pi\) | |||||||
\(618\) | 3.25321e57 | 1.98175 | ||||||||
\(619\) | −6.36804e56 | −0.375273 | −0.187637 | − | 0.982239i | \(-0.560083\pi\) | ||||
−0.187637 | + | 0.982239i | \(0.560083\pi\) | |||||||
\(620\) | 3.23512e57 | 1.84442 | ||||||||
\(621\) | 4.96394e56 | 0.273810 | ||||||||
\(622\) | −3.50238e57 | −1.86922 | ||||||||
\(623\) | 6.58238e56 | 0.339921 | ||||||||
\(624\) | 2.02458e55 | 0.0101170 | ||||||||
\(625\) | −4.61045e56 | −0.222948 | ||||||||
\(626\) | 1.32103e57 | 0.618215 | ||||||||
\(627\) | −5.91331e56 | −0.267822 | ||||||||
\(628\) | −6.30801e57 | −2.76516 | ||||||||
\(629\) | −5.45933e56 | −0.231633 | ||||||||
\(630\) | 5.87816e56 | 0.241413 | ||||||||
\(631\) | −2.73724e57 | −1.08820 | −0.544102 | − | 0.839019i | \(-0.683130\pi\) | ||||
−0.544102 | + | 0.839019i | \(0.683130\pi\) | |||||||
\(632\) | 2.27003e57 | 0.873636 | ||||||||
\(633\) | 4.66821e57 | 1.73930 | ||||||||
\(634\) | 4.83123e57 | 1.74272 | ||||||||
\(635\) | 1.35104e57 | 0.471854 | ||||||||
\(636\) | −8.92706e57 | −3.01882 | ||||||||
\(637\) | 3.14857e57 | 1.03099 | ||||||||
\(638\) | −2.17574e57 | −0.689896 | ||||||||
\(639\) | −9.89483e56 | −0.303837 | ||||||||
\(640\) | 8.65491e57 | 2.57379 | ||||||||
\(641\) | −2.81100e57 | −0.809602 | −0.404801 | − | 0.914405i | \(-0.632659\pi\) | ||||
−0.404801 | + | 0.914405i | \(0.632659\pi\) | |||||||
\(642\) | 3.13337e57 | 0.874065 | ||||||||
\(643\) | 1.13133e57 | 0.305679 | 0.152840 | − | 0.988251i | \(-0.451158\pi\) | ||||
0.152840 | + | 0.988251i | \(0.451158\pi\) | |||||||
\(644\) | −8.54433e56 | −0.223624 | ||||||||
\(645\) | −1.71146e56 | −0.0433903 | ||||||||
\(646\) | 5.07127e56 | 0.124552 | ||||||||
\(647\) | 2.99702e57 | 0.713102 | 0.356551 | − | 0.934276i | \(-0.383953\pi\) | ||||
0.356551 | + | 0.934276i | \(0.383953\pi\) | |||||||
\(648\) | −5.10203e57 | −1.17613 | ||||||||
\(649\) | −1.45236e56 | −0.0324382 | ||||||||
\(650\) | −1.44060e58 | −3.11760 | ||||||||
\(651\) | −1.64348e57 | −0.344630 | ||||||||
\(652\) | 5.53153e57 | 1.12401 | ||||||||
\(653\) | 1.36513e57 | 0.268815 | 0.134407 | − | 0.990926i | \(-0.457087\pi\) | ||||
0.134407 | + | 0.990926i | \(0.457087\pi\) | |||||||
\(654\) | −2.04145e57 | −0.389579 | ||||||||
\(655\) | −5.72096e57 | −1.05809 | ||||||||
\(656\) | −5.02893e55 | −0.00901461 | ||||||||
\(657\) | 1.92948e57 | 0.335235 | ||||||||
\(658\) | 7.43764e57 | 1.25258 | ||||||||
\(659\) | −8.45274e57 | −1.37990 | −0.689949 | − | 0.723858i | \(-0.742367\pi\) | ||||
−0.689949 | + | 0.723858i | \(0.742367\pi\) | |||||||
\(660\) | 1.73259e58 | 2.74186 | ||||||||
\(661\) | −1.12370e58 | −1.72393 | −0.861964 | − | 0.506970i | \(-0.830766\pi\) | ||||
−0.861964 | + | 0.506970i | \(0.830766\pi\) | |||||||
\(662\) | 1.88387e58 | 2.80197 | ||||||||
\(663\) | 2.98124e57 | 0.429902 | ||||||||
\(664\) | 5.93216e57 | 0.829406 | ||||||||
\(665\) | 1.27874e57 | 0.173356 | ||||||||
\(666\) | −2.01057e57 | −0.264301 | ||||||||
\(667\) | −1.09434e57 | −0.139500 | ||||||||
\(668\) | −1.97349e58 | −2.43959 | ||||||||
\(669\) | 1.45389e57 | 0.174300 | ||||||||
\(670\) | −2.01074e58 | −2.33788 | ||||||||
\(671\) | −5.93342e56 | −0.0669103 | ||||||||
\(672\) | −4.36517e57 | −0.477453 | ||||||||
\(673\) | 1.32183e58 | 1.40239 | 0.701193 | − | 0.712971i | \(-0.252651\pi\) | ||||
0.701193 | + | 0.712971i | \(0.252651\pi\) | |||||||
\(674\) | 3.83269e57 | 0.394435 | ||||||||
\(675\) | 1.31067e58 | 1.30848 | ||||||||
\(676\) | 1.03595e58 | 1.00330 | ||||||||
\(677\) | 4.87678e57 | 0.458211 | 0.229105 | − | 0.973402i | \(-0.426420\pi\) | ||||
0.229105 | + | 0.973402i | \(0.426420\pi\) | |||||||
\(678\) | −2.35301e58 | −2.14494 | ||||||||
\(679\) | −6.89924e57 | −0.610198 | ||||||||
\(680\) | −5.69377e57 | −0.488616 | ||||||||
\(681\) | 1.09436e58 | 0.911262 | ||||||||
\(682\) | −1.39095e58 | −1.12391 | ||||||||
\(683\) | 2.89510e57 | 0.227007 | 0.113504 | − | 0.993538i | \(-0.463793\pi\) | ||||
0.113504 | + | 0.993538i | \(0.463793\pi\) | |||||||
\(684\) | 1.15515e57 | 0.0879001 | ||||||||
\(685\) | 1.34147e58 | 0.990662 | ||||||||
\(686\) | 1.78103e58 | 1.27652 | ||||||||
\(687\) | −1.54092e58 | −1.07193 | ||||||||
\(688\) | −2.65067e54 | −0.000178975 0 | ||||||||
\(689\) | −3.27812e58 | −2.14848 | ||||||||
\(690\) | 1.40896e58 | 0.896382 | ||||||||
\(691\) | 6.99589e57 | 0.432059 | 0.216029 | − | 0.976387i | \(-0.430689\pi\) | ||||
0.216029 | + | 0.976387i | \(0.430689\pi\) | |||||||
\(692\) | 2.31740e58 | 1.38940 | ||||||||
\(693\) | −1.56317e57 | −0.0909860 | ||||||||
\(694\) | −8.15286e57 | −0.460724 | ||||||||
\(695\) | 8.31247e57 | 0.456080 | ||||||||
\(696\) | 9.17060e57 | 0.488549 | ||||||||
\(697\) | −7.40520e57 | −0.383058 | ||||||||
\(698\) | 2.21298e58 | 1.11158 | ||||||||
\(699\) | 3.49689e58 | 1.70569 | ||||||||
\(700\) | −2.25603e58 | −1.06865 | ||||||||
\(701\) | −6.70824e56 | −0.0308595 | −0.0154298 | − | 0.999881i | \(-0.504912\pi\) | ||||
−0.0154298 | + | 0.999881i | \(0.504912\pi\) | |||||||
\(702\) | −3.98629e58 | −1.78098 | ||||||||
\(703\) | −4.37383e57 | −0.189792 | ||||||||
\(704\) | −3.71100e58 | −1.56405 | ||||||||
\(705\) | −7.58576e58 | −3.10543 | ||||||||
\(706\) | 2.53943e58 | 1.00981 | ||||||||
\(707\) | 8.67832e57 | 0.335226 | ||||||||
\(708\) | 1.59752e57 | 0.0599464 | ||||||||
\(709\) | −1.26212e58 | −0.460102 | −0.230051 | − | 0.973179i | \(-0.573889\pi\) | ||||
−0.230051 | + | 0.973179i | \(0.573889\pi\) | |||||||
\(710\) | 1.01970e59 | 3.61141 | ||||||||
\(711\) | 5.45112e57 | 0.187568 | ||||||||
\(712\) | −2.34813e58 | −0.785022 | ||||||||
\(713\) | −6.99613e57 | −0.227260 | ||||||||
\(714\) | 7.54840e57 | 0.238255 | ||||||||
\(715\) | 6.36228e58 | 1.95137 | ||||||||
\(716\) | −4.76926e58 | −1.42146 | ||||||||
\(717\) | 2.68029e58 | 0.776316 | ||||||||
\(718\) | 3.53983e58 | 0.996396 | ||||||||
\(719\) | −3.64927e58 | −0.998307 | −0.499153 | − | 0.866514i | \(-0.666356\pi\) | ||||
−0.499153 | + | 0.866514i | \(0.666356\pi\) | |||||||
\(720\) | −9.28526e55 | −0.00246875 | ||||||||
\(721\) | 1.87081e58 | 0.483455 | ||||||||
\(722\) | −6.03936e58 | −1.51698 | ||||||||
\(723\) | 1.88459e58 | 0.460132 | ||||||||
\(724\) | 4.70205e58 | 1.11595 | ||||||||
\(725\) | −2.88948e58 | −0.666639 | ||||||||
\(726\) | 5.10653e57 | 0.114532 | ||||||||
\(727\) | −5.20217e58 | −1.13430 | −0.567152 | − | 0.823613i | \(-0.691955\pi\) | ||||
−0.567152 | + | 0.823613i | \(0.691955\pi\) | |||||||
\(728\) | 2.62929e58 | 0.557373 | ||||||||
\(729\) | 3.40049e58 | 0.700853 | ||||||||
\(730\) | −1.98840e59 | −3.98461 | ||||||||
\(731\) | −3.90317e56 | −0.00760521 | ||||||||
\(732\) | 6.52644e57 | 0.123652 | ||||||||
\(733\) | 2.57497e58 | 0.474396 | 0.237198 | − | 0.971461i | \(-0.423771\pi\) | ||||
0.237198 | + | 0.971461i | \(0.423771\pi\) | |||||||
\(734\) | 1.34615e59 | 2.41171 | ||||||||
\(735\) | −8.13082e58 | −1.41659 | ||||||||
\(736\) | −1.85821e58 | −0.314848 | ||||||||
\(737\) | 5.34713e58 | 0.881124 | ||||||||
\(738\) | −2.72720e58 | −0.437081 | ||||||||
\(739\) | 1.07870e59 | 1.68148 | 0.840738 | − | 0.541442i | \(-0.182121\pi\) | ||||
0.840738 | + | 0.541442i | \(0.182121\pi\) | |||||||
\(740\) | 1.28152e59 | 1.94302 | ||||||||
\(741\) | 2.38847e58 | 0.352246 | ||||||||
\(742\) | −8.30009e58 | −1.19070 | ||||||||
\(743\) | −1.21669e59 | −1.69788 | −0.848942 | − | 0.528487i | \(-0.822760\pi\) | ||||
−0.848942 | + | 0.528487i | \(0.822760\pi\) | |||||||
\(744\) | 5.86276e58 | 0.795898 | ||||||||
\(745\) | 8.59134e56 | 0.0113464 | ||||||||
\(746\) | −2.10943e59 | −2.71031 | ||||||||
\(747\) | 1.42452e58 | 0.178072 | ||||||||
\(748\) | 3.95136e58 | 0.480577 | ||||||||
\(749\) | 1.80189e58 | 0.213231 | ||||||||
\(750\) | 1.26208e59 | 1.45322 | ||||||||
\(751\) | 6.80995e58 | 0.763001 | 0.381500 | − | 0.924369i | \(-0.375408\pi\) | ||||
0.381500 | + | 0.924369i | \(0.375408\pi\) | |||||||
\(752\) | −1.17486e57 | −0.0128092 | ||||||||
\(753\) | −1.79125e58 | −0.190046 | ||||||||
\(754\) | 8.78812e58 | 0.907368 | ||||||||
\(755\) | −2.44726e58 | −0.245905 | ||||||||
\(756\) | −6.24266e58 | −0.610482 | ||||||||
\(757\) | −2.77019e58 | −0.263660 | −0.131830 | − | 0.991272i | \(-0.542085\pi\) | ||||
−0.131830 | + | 0.991272i | \(0.542085\pi\) | |||||||
\(758\) | −6.56267e58 | −0.607942 | ||||||||
\(759\) | −3.74683e58 | −0.337837 | ||||||||
\(760\) | −4.56165e58 | −0.400353 | ||||||||
\(761\) | −7.33770e57 | −0.0626866 | −0.0313433 | − | 0.999509i | \(-0.509979\pi\) | ||||
−0.0313433 | + | 0.999509i | \(0.509979\pi\) | |||||||
\(762\) | 6.38944e58 | 0.531356 | ||||||||
\(763\) | −1.17397e58 | −0.0950391 | ||||||||
\(764\) | −3.62893e59 | −2.85999 | ||||||||
\(765\) | −1.36727e58 | −0.104905 | ||||||||
\(766\) | 6.14167e58 | 0.458772 | ||||||||
\(767\) | 5.86626e57 | 0.0426635 | ||||||||
\(768\) | 1.57539e59 | 1.11554 | ||||||||
\(769\) | 7.07782e58 | 0.487988 | 0.243994 | − | 0.969777i | \(-0.421542\pi\) | ||||
0.243994 | + | 0.969777i | \(0.421542\pi\) | |||||||
\(770\) | 1.61091e59 | 1.08146 | ||||||||
\(771\) | 4.03555e58 | 0.263808 | ||||||||
\(772\) | 2.93819e59 | 1.87036 | ||||||||
\(773\) | −6.55116e57 | −0.0406105 | −0.0203053 | − | 0.999794i | \(-0.506464\pi\) | ||||
−0.0203053 | + | 0.999794i | \(0.506464\pi\) | |||||||
\(774\) | −1.43747e57 | −0.00867777 | ||||||||
\(775\) | −1.84724e59 | −1.08602 | ||||||||
\(776\) | 2.46116e59 | 1.40921 | ||||||||
\(777\) | −6.51028e58 | −0.363052 | ||||||||
\(778\) | 3.22479e59 | 1.75154 | ||||||||
\(779\) | −5.93279e58 | −0.313864 | ||||||||
\(780\) | −6.99817e59 | −3.60616 | ||||||||
\(781\) | −2.71167e59 | −1.36110 | ||||||||
\(782\) | 3.21329e58 | 0.157113 | ||||||||
\(783\) | −7.99548e58 | −0.380828 | ||||||||
\(784\) | −1.25928e57 | −0.00584311 | ||||||||
\(785\) | 5.98178e59 | 2.70397 | ||||||||
\(786\) | −2.70560e59 | −1.19152 | ||||||||
\(787\) | −3.33588e59 | −1.43129 | −0.715647 | − | 0.698462i | \(-0.753868\pi\) | ||||
−0.715647 | + | 0.698462i | \(0.753868\pi\) | |||||||
\(788\) | 8.11500e58 | 0.339235 | ||||||||
\(789\) | 3.14991e59 | 1.28298 | ||||||||
\(790\) | −5.61760e59 | −2.22944 | ||||||||
\(791\) | −1.35313e59 | −0.523265 | ||||||||
\(792\) | 5.57628e58 | 0.210125 | ||||||||
\(793\) | 2.39659e58 | 0.0880020 | ||||||||
\(794\) | 1.52786e59 | 0.546718 | ||||||||
\(795\) | 8.46538e59 | 2.95203 | ||||||||
\(796\) | 5.48467e59 | 1.86394 | ||||||||
\(797\) | −1.53090e59 | −0.507050 | −0.253525 | − | 0.967329i | \(-0.581590\pi\) | ||||
−0.253525 | + | 0.967329i | \(0.581590\pi\) | |||||||
\(798\) | 6.04752e58 | 0.195217 | ||||||||
\(799\) | −1.73001e59 | −0.544302 | ||||||||
\(800\) | −4.90639e59 | −1.50459 | ||||||||
\(801\) | −5.63867e58 | −0.168543 | ||||||||
\(802\) | −4.19027e59 | −1.22086 | ||||||||
\(803\) | 5.28772e59 | 1.50176 | ||||||||
\(804\) | −5.88156e59 | −1.62833 | ||||||||
\(805\) | 8.10245e58 | 0.218676 | ||||||||
\(806\) | 5.61824e59 | 1.47820 | ||||||||
\(807\) | −2.13996e59 | −0.548907 | ||||||||
\(808\) | −3.09581e59 | −0.774180 | ||||||||
\(809\) | −1.38621e59 | −0.337974 | −0.168987 | − | 0.985618i | \(-0.554050\pi\) | ||||
−0.168987 | + | 0.985618i | \(0.554050\pi\) | |||||||
\(810\) | 1.26259e60 | 3.00137 | ||||||||
\(811\) | 8.92972e58 | 0.206971 | 0.103486 | − | 0.994631i | \(-0.467000\pi\) | ||||
0.103486 | + | 0.994631i | \(0.467000\pi\) | |||||||
\(812\) | 1.37625e59 | 0.311026 | ||||||||
\(813\) | −8.91415e59 | −1.96437 | ||||||||
\(814\) | −5.50997e59 | −1.18399 | ||||||||
\(815\) | −5.24545e59 | −1.09914 | ||||||||
\(816\) | −1.19236e57 | −0.00243646 | ||||||||
\(817\) | −3.12708e57 | −0.00623142 | ||||||||
\(818\) | −6.96705e59 | −1.35396 | ||||||||
\(819\) | 6.31385e58 | 0.119667 | ||||||||
\(820\) | 1.73830e60 | 3.21322 | ||||||||
\(821\) | 5.66077e59 | 1.02057 | 0.510283 | − | 0.860007i | \(-0.329541\pi\) | ||||
0.510283 | + | 0.860007i | \(0.329541\pi\) | |||||||
\(822\) | 6.34419e59 | 1.11559 | ||||||||
\(823\) | −9.70422e59 | −1.66442 | −0.832212 | − | 0.554458i | \(-0.812926\pi\) | ||||
−0.832212 | + | 0.554458i | \(0.812926\pi\) | |||||||
\(824\) | −6.67372e59 | −1.11650 | ||||||||
\(825\) | −9.89305e59 | −1.61445 | ||||||||
\(826\) | 1.48532e58 | 0.0236444 | ||||||||
\(827\) | 1.07249e60 | 1.66545 | 0.832725 | − | 0.553687i | \(-0.186780\pi\) | ||||
0.832725 | + | 0.553687i | \(0.186780\pi\) | |||||||
\(828\) | 7.31934e58 | 0.110879 | ||||||||
\(829\) | 6.30712e59 | 0.932101 | 0.466051 | − | 0.884758i | \(-0.345676\pi\) | ||||
0.466051 | + | 0.884758i | \(0.345676\pi\) | |||||||
\(830\) | −1.46802e60 | −2.11657 | ||||||||
\(831\) | −3.68913e59 | −0.518923 | ||||||||
\(832\) | 1.49892e60 | 2.05708 | ||||||||
\(833\) | −1.85432e59 | −0.248292 | ||||||||
\(834\) | 3.93119e59 | 0.513594 | ||||||||
\(835\) | 1.87143e60 | 2.38561 | ||||||||
\(836\) | 3.16569e59 | 0.393767 | ||||||||
\(837\) | −5.11151e59 | −0.620408 | ||||||||
\(838\) | −3.83330e59 | −0.454015 | ||||||||
\(839\) | 6.10677e59 | 0.705815 | 0.352908 | − | 0.935658i | \(-0.385193\pi\) | ||||
0.352908 | + | 0.935658i | \(0.385193\pi\) | |||||||
\(840\) | −6.78986e59 | −0.765835 | ||||||||
\(841\) | −7.32218e59 | −0.805977 | ||||||||
\(842\) | −9.75685e59 | −1.04812 | ||||||||
\(843\) | 1.48107e59 | 0.155278 | ||||||||
\(844\) | −2.49913e60 | −2.55722 | ||||||||
\(845\) | −9.82372e59 | −0.981100 | ||||||||
\(846\) | −6.37132e59 | −0.621065 | ||||||||
\(847\) | 2.93658e58 | 0.0279404 | ||||||||
\(848\) | 1.31110e58 | 0.0121764 | ||||||||
\(849\) | 1.07866e60 | 0.977864 | ||||||||
\(850\) | 8.48430e59 | 0.750807 | ||||||||
\(851\) | −2.77137e59 | −0.239408 | ||||||||
\(852\) | 2.98270e60 | 2.51535 | ||||||||
\(853\) | 1.07715e60 | 0.886788 | 0.443394 | − | 0.896327i | \(-0.353774\pi\) | ||||
0.443394 | + | 0.896327i | \(0.353774\pi\) | |||||||
\(854\) | 6.06808e58 | 0.0487714 | ||||||||
\(855\) | −1.09541e59 | −0.0859552 | ||||||||
\(856\) | −6.42788e59 | −0.492442 | ||||||||
\(857\) | −2.94243e59 | −0.220090 | −0.110045 | − | 0.993927i | \(-0.535099\pi\) | ||||
−0.110045 | + | 0.993927i | \(0.535099\pi\) | |||||||
\(858\) | 3.00889e60 | 2.19744 | ||||||||
\(859\) | 1.39886e59 | 0.0997504 | 0.0498752 | − | 0.998755i | \(-0.484118\pi\) | ||||
0.0498752 | + | 0.998755i | \(0.484118\pi\) | |||||||
\(860\) | 9.16230e58 | 0.0637950 | ||||||||
\(861\) | −8.83074e59 | −0.600389 | ||||||||
\(862\) | −2.28610e60 | −1.51774 | ||||||||
\(863\) | −3.64782e59 | −0.236490 | −0.118245 | − | 0.992984i | \(-0.537727\pi\) | ||||
−0.118245 | + | 0.992984i | \(0.537727\pi\) | |||||||
\(864\) | −1.35765e60 | −0.859519 | ||||||||
\(865\) | −2.19756e60 | −1.35866 | ||||||||
\(866\) | 1.18155e60 | 0.713402 | ||||||||
\(867\) | 1.69446e60 | 0.999168 | ||||||||
\(868\) | 8.79834e59 | 0.506695 | ||||||||
\(869\) | 1.49388e60 | 0.840251 | ||||||||
\(870\) | −2.26943e60 | −1.24673 | ||||||||
\(871\) | −2.15978e60 | −1.15887 | ||||||||
\(872\) | 4.18788e59 | 0.219486 | ||||||||
\(873\) | 5.91011e59 | 0.302554 | ||||||||
\(874\) | 2.57437e59 | 0.128732 | ||||||||
\(875\) | 7.25780e59 | 0.354519 | ||||||||
\(876\) | −5.81622e60 | −2.77528 | ||||||||
\(877\) | 3.99235e60 | 1.86096 | 0.930480 | − | 0.366341i | \(-0.119390\pi\) | ||||
0.930480 | + | 0.366341i | \(0.119390\pi\) | |||||||
\(878\) | 3.30278e60 | 1.50398 | ||||||||
\(879\) | −3.05358e59 | −0.135843 | ||||||||
\(880\) | −2.54462e58 | −0.0110593 | ||||||||
\(881\) | 1.50864e60 | 0.640589 | 0.320295 | − | 0.947318i | \(-0.396218\pi\) | ||||
0.320295 | + | 0.947318i | \(0.396218\pi\) | |||||||
\(882\) | −6.82913e59 | −0.283308 | ||||||||
\(883\) | −4.31876e60 | −1.75051 | −0.875254 | − | 0.483663i | \(-0.839306\pi\) | ||||
−0.875254 | + | 0.483663i | \(0.839306\pi\) | |||||||
\(884\) | −1.59601e60 | −0.632067 | ||||||||
\(885\) | −1.51490e59 | −0.0586200 | ||||||||
\(886\) | 6.08531e60 | 2.30087 | ||||||||
\(887\) | −4.39179e60 | −1.62259 | −0.811293 | − | 0.584640i | \(-0.801236\pi\) | ||||
−0.811293 | + | 0.584640i | \(0.801236\pi\) | |||||||
\(888\) | 2.32241e60 | 0.838442 | ||||||||
\(889\) | 3.67434e59 | 0.129626 | ||||||||
\(890\) | 5.81088e60 | 2.00330 | ||||||||
\(891\) | −3.35759e60 | −1.13119 | ||||||||
\(892\) | −7.78340e59 | −0.256265 | ||||||||
\(893\) | −1.38602e60 | −0.445981 | ||||||||
\(894\) | 4.06308e58 | 0.0127772 | ||||||||
\(895\) | 4.52261e60 | 1.39001 | ||||||||
\(896\) | 2.35382e60 | 0.707064 | ||||||||
\(897\) | 1.51339e60 | 0.444331 | ||||||||
\(898\) | −9.21644e60 | −2.64483 | ||||||||
\(899\) | 1.12688e60 | 0.316084 | ||||||||
\(900\) | 1.93259e60 | 0.529868 | ||||||||
\(901\) | 1.93062e60 | 0.517414 | ||||||||
\(902\) | −7.47388e60 | −1.95800 | ||||||||
\(903\) | −4.65455e58 | −0.0119201 | ||||||||
\(904\) | 4.82701e60 | 1.20844 | ||||||||
\(905\) | −4.45887e60 | −1.09126 | ||||||||
\(906\) | −1.15738e60 | −0.276915 | ||||||||
\(907\) | 1.38889e60 | 0.324875 | 0.162438 | − | 0.986719i | \(-0.448064\pi\) | ||||
0.162438 | + | 0.986719i | \(0.448064\pi\) | |||||||
\(908\) | −5.85864e60 | −1.33979 | ||||||||
\(909\) | −7.43412e59 | −0.166215 | ||||||||
\(910\) | −6.50667e60 | −1.42236 | ||||||||
\(911\) | 1.25104e60 | 0.267389 | 0.133694 | − | 0.991023i | \(-0.457316\pi\) | ||||
0.133694 | + | 0.991023i | \(0.457316\pi\) | |||||||
\(912\) | −9.55277e57 | −0.00199634 | ||||||||
\(913\) | 3.90388e60 | 0.797711 | ||||||||
\(914\) | 1.31256e61 | 2.62254 | ||||||||
\(915\) | −6.18892e59 | −0.120916 | ||||||||
\(916\) | 8.24929e60 | 1.57601 | ||||||||
\(917\) | −1.55589e60 | −0.290675 | ||||||||
\(918\) | 2.34769e60 | 0.428910 | ||||||||
\(919\) | −1.70510e60 | −0.304637 | −0.152319 | − | 0.988331i | \(-0.548674\pi\) | ||||
−0.152319 | + | 0.988331i | \(0.548674\pi\) | |||||||
\(920\) | −2.89038e60 | −0.505016 | ||||||||
\(921\) | 6.97959e60 | 1.19264 | ||||||||
\(922\) | −1.64845e61 | −2.75482 | ||||||||
\(923\) | 1.09528e61 | 1.79016 | ||||||||
\(924\) | 4.71201e60 | 0.753236 | ||||||||
\(925\) | −7.31747e60 | −1.14408 | ||||||||
\(926\) | 6.46962e60 | 0.989359 | ||||||||
\(927\) | −1.60259e60 | −0.239711 | ||||||||
\(928\) | 2.99305e60 | 0.437905 | ||||||||
\(929\) | −1.11160e60 | −0.159084 | −0.0795422 | − | 0.996832i | \(-0.525346\pi\) | ||||
−0.0795422 | + | 0.996832i | \(0.525346\pi\) | |||||||
\(930\) | −1.45085e61 | −2.03106 | ||||||||
\(931\) | −1.48562e60 | −0.203441 | ||||||||
\(932\) | −1.87206e61 | −2.50780 | ||||||||
\(933\) | 9.71487e60 | 1.27310 | ||||||||
\(934\) | −2.43048e60 | −0.311588 | ||||||||
\(935\) | −3.74700e60 | −0.469944 | ||||||||
\(936\) | −2.25234e60 | −0.276362 | ||||||||
\(937\) | −6.31851e60 | −0.758495 | −0.379248 | − | 0.925295i | \(-0.623817\pi\) | ||||
−0.379248 | + | 0.925295i | \(0.623817\pi\) | |||||||
\(938\) | −5.46848e60 | −0.642257 | ||||||||
\(939\) | −3.66427e60 | −0.421059 | ||||||||
\(940\) | 4.06103e61 | 4.56578 | ||||||||
\(941\) | −6.22380e59 | −0.0684650 | −0.0342325 | − | 0.999414i | \(-0.510899\pi\) | ||||
−0.0342325 | + | 0.999414i | \(0.510899\pi\) | |||||||
\(942\) | 2.82894e61 | 3.04495 | ||||||||
\(943\) | −3.75917e60 | −0.395915 | ||||||||
\(944\) | −2.34624e57 | −0.000241794 0 | ||||||||
\(945\) | 5.91981e60 | 0.596974 | ||||||||
\(946\) | −3.93937e59 | −0.0388739 | ||||||||
\(947\) | −1.79375e61 | −1.73216 | −0.866079 | − | 0.499907i | \(-0.833368\pi\) | ||||
−0.866079 | + | 0.499907i | \(0.833368\pi\) | |||||||
\(948\) | −1.64319e61 | −1.55280 | ||||||||
\(949\) | −2.13578e61 | −1.97515 | ||||||||
\(950\) | 6.79733e60 | 0.615183 | ||||||||
\(951\) | −1.34008e61 | −1.18695 | ||||||||
\(952\) | −1.54850e60 | −0.134231 | ||||||||
\(953\) | 1.46295e61 | 1.24116 | 0.620578 | − | 0.784145i | \(-0.286898\pi\) | ||||
0.620578 | + | 0.784145i | \(0.286898\pi\) | |||||||
\(954\) | 7.11012e60 | 0.590385 | ||||||||
\(955\) | 3.44125e61 | 2.79671 | ||||||||
\(956\) | −1.43489e61 | −1.14138 | ||||||||
\(957\) | 6.03506e60 | 0.469880 | ||||||||
\(958\) | 1.92913e61 | 1.47018 | ||||||||
\(959\) | 3.64832e60 | 0.272152 | ||||||||
\(960\) | −3.87081e61 | −2.82645 | ||||||||
\(961\) | −6.78626e60 | −0.485067 | ||||||||
\(962\) | 2.22555e61 | 1.55721 | ||||||||
\(963\) | −1.54356e60 | −0.105726 | ||||||||
\(964\) | −1.00892e61 | −0.676512 | ||||||||
\(965\) | −2.78623e61 | −1.82897 | ||||||||
\(966\) | 3.83186e60 | 0.246252 | ||||||||
\(967\) | 2.19658e61 | 1.38199 | 0.690993 | − | 0.722861i | \(-0.257173\pi\) | ||||
0.690993 | + | 0.722861i | \(0.257173\pi\) | |||||||
\(968\) | −1.04757e60 | −0.0645263 | ||||||||
\(969\) | −1.40666e60 | −0.0848307 | ||||||||
\(970\) | −6.09060e61 | −3.59617 | ||||||||
\(971\) | 8.01229e60 | 0.463193 | 0.231597 | − | 0.972812i | \(-0.425605\pi\) | ||||
0.231597 | + | 0.972812i | \(0.425605\pi\) | |||||||
\(972\) | 1.21682e61 | 0.688760 | ||||||||
\(973\) | 2.26069e60 | 0.125293 | ||||||||
\(974\) | 8.61726e60 | 0.467639 | ||||||||
\(975\) | 3.99594e61 | 2.12336 | ||||||||
\(976\) | −9.58525e57 | −0.000498749 0 | ||||||||
\(977\) | −1.53487e60 | −0.0782047 | −0.0391024 | − | 0.999235i | \(-0.512450\pi\) | ||||
−0.0391024 | + | 0.999235i | \(0.512450\pi\) | |||||||
\(978\) | −2.48072e61 | −1.23774 | ||||||||
\(979\) | −1.54528e61 | −0.755024 | ||||||||
\(980\) | 4.35283e61 | 2.08275 | ||||||||
\(981\) | 1.00566e60 | 0.0471232 | ||||||||
\(982\) | 1.94982e60 | 0.0894764 | ||||||||
\(983\) | 2.13980e61 | 0.961670 | 0.480835 | − | 0.876811i | \(-0.340334\pi\) | ||||
0.480835 | + | 0.876811i | \(0.340334\pi\) | |||||||
\(984\) | 3.15019e61 | 1.38655 | ||||||||
\(985\) | −7.69531e60 | −0.331729 | ||||||||
\(986\) | −5.17568e60 | −0.218520 | ||||||||
\(987\) | −2.06305e61 | −0.853115 | ||||||||
\(988\) | −1.27866e61 | −0.517892 | ||||||||
\(989\) | −1.98140e59 | −0.00786047 | ||||||||
\(990\) | −1.37995e61 | −0.536220 | ||||||||
\(991\) | 2.19295e61 | 0.834678 | 0.417339 | − | 0.908751i | \(-0.362963\pi\) | ||||
0.417339 | + | 0.908751i | \(0.362963\pi\) | |||||||
\(992\) | 1.91346e61 | 0.713393 | ||||||||
\(993\) | −5.22547e61 | −1.90838 | ||||||||
\(994\) | 2.77322e61 | 0.992117 | ||||||||
\(995\) | −5.20102e61 | −1.82270 | ||||||||
\(996\) | −4.29406e61 | −1.47419 | ||||||||
\(997\) | 1.15402e61 | 0.388116 | 0.194058 | − | 0.980990i | \(-0.437835\pi\) | ||||
0.194058 | + | 0.980990i | \(0.437835\pi\) | |||||||
\(998\) | −1.57771e61 | −0.519819 | ||||||||
\(999\) | −2.02482e61 | −0.653572 |
(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 | 1.42.a.a.1.3 | ✓ | 3 | |
3.2 | odd | 2 | 9.42.a.b.1.1 | 3 | |||
4.3 | odd | 2 | 16.42.a.c.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.42.a.a.1.3 | ✓ | 3 | 1.1 | even | 1 | trivial | |
9.42.a.b.1.1 | 3 | 3.2 | odd | 2 | |||
16.42.a.c.1.2 | 3 | 4.3 | odd | 2 |