Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,52,Mod(1,9)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 52, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 52);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 52 \) |
Character orbit: | \([\chi]\) | \(=\) | 9.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: | \(148.258218073\) |
Analytic rank: | \(1\) |
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: | \( x^{4} - 2x^{3} - 495735060514x^{2} - 23954614981416598x + 48979992255622025570313 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{23}\cdot 3^{14}\cdot 5^{3}\cdot 7^{2}\cdot 13\cdot 17 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-511801.\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.13381e7 | −1.08187 | −0.540935 | − | 0.841064i | \(-0.681930\pi\) | ||||
−0.540935 | + | 0.841064i | \(0.681930\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.83803e14 | 0.170443 | ||||||||
\(5\) | −4.84667e17 | −0.727291 | −0.363645 | − | 0.931537i | \(-0.618468\pi\) | ||||
−0.363645 | + | 0.931537i | \(0.618468\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.59004e21 | 0.729972 | 0.364986 | − | 0.931013i | \(-0.381074\pi\) | ||||
0.364986 | + | 0.931013i | \(0.381074\pi\) | |||||||
\(8\) | 9.58994e22 | 0.897473 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.48819e25 | 0.786834 | ||||||||
\(11\) | 4.45050e26 | 1.23850 | 0.619249 | − | 0.785194i | \(-0.287437\pi\) | ||||
0.619249 | + | 0.785194i | \(0.287437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.37117e28 | −0.538934 | −0.269467 | − | 0.963010i | \(-0.586847\pi\) | ||||
−0.269467 | + | 0.963010i | \(0.586847\pi\) | |||||||
\(14\) | −1.32968e29 | −0.789735 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −5.78755e30 | −1.14139 | ||||||||
\(17\) | −2.62484e31 | −1.10320 | −0.551601 | − | 0.834108i | \(-0.685983\pi\) | ||||
−0.551601 | + | 0.834108i | \(0.685983\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.11022e32 | 0.273647 | 0.136824 | − | 0.990595i | \(-0.456311\pi\) | ||||
0.136824 | + | 0.990595i | \(0.456311\pi\) | |||||||
\(20\) | −1.86017e32 | −0.123962 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.28480e34 | −1.33989 | ||||||||
\(23\) | −2.36137e34 | −0.445764 | −0.222882 | − | 0.974845i | \(-0.571546\pi\) | ||||
−0.222882 | + | 0.974845i | \(0.571546\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.09187e35 | −0.471048 | ||||||||
\(26\) | 7.03932e35 | 0.583056 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 9.94066e35 | 0.124419 | ||||||||
\(29\) | 2.25752e37 | 1.15474 | 0.577368 | − | 0.816484i | \(-0.304080\pi\) | ||||
0.577368 | + | 0.816484i | \(0.304080\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.11662e37 | −0.384431 | −0.192215 | − | 0.981353i | \(-0.561567\pi\) | ||||
−0.192215 | + | 0.981353i | \(0.561567\pi\) | |||||||
\(32\) | 8.11754e37 | 0.337365 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.34754e39 | 1.19352 | ||||||||
\(35\) | −1.25531e39 | −0.530902 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5.65183e39 | 0.579488 | 0.289744 | − | 0.957104i | \(-0.406430\pi\) | ||||
0.289744 | + | 0.957104i | \(0.406430\pi\) | |||||||
\(38\) | −5.69965e39 | −0.296051 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.64793e40 | −0.652724 | ||||||||
\(41\) | 5.54318e40 | 0.414735 | 0.207367 | − | 0.978263i | \(-0.433510\pi\) | ||||
0.207367 | + | 0.978263i | \(0.433510\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.70927e41 | −1.26805 | −0.634023 | − | 0.773314i | \(-0.718598\pi\) | ||||
−0.634023 | + | 0.773314i | \(0.718598\pi\) | |||||||
\(44\) | 1.70812e41 | 0.211093 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.21229e42 | 0.482259 | ||||||||
\(47\) | −1.49403e42 | −0.343449 | −0.171725 | − | 0.985145i | \(-0.554934\pi\) | ||||
−0.171725 | + | 0.985145i | \(0.554934\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.88095e42 | −0.467140 | ||||||||
\(50\) | 1.07393e43 | 0.509613 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −5.26259e42 | −0.0918574 | ||||||||
\(53\) | 1.42123e44 | 1.52626 | 0.763131 | − | 0.646244i | \(-0.223661\pi\) | ||||
0.763131 | + | 0.646244i | \(0.223661\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.15701e44 | −0.900749 | ||||||||
\(56\) | 2.48383e44 | 0.655131 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.15897e45 | −1.24927 | ||||||||
\(59\) | −2.24820e44 | −0.156714 | −0.0783572 | − | 0.996925i | \(-0.524967\pi\) | ||||
−0.0783572 | + | 0.996925i | \(0.524967\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.34137e44 | 0.0697524 | 0.0348762 | − | 0.999392i | \(-0.488896\pi\) | ||||
0.0348762 | + | 0.999392i | \(0.488896\pi\) | |||||||
\(62\) | 2.11340e45 | 0.415904 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.86500e45 | 0.776407 | ||||||||
\(65\) | 6.64560e45 | 0.391962 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.65209e45 | −0.0722240 | −0.0361120 | − | 0.999348i | \(-0.511497\pi\) | ||||
−0.0361120 | + | 0.999348i | \(0.511497\pi\) | |||||||
\(68\) | −1.00742e46 | −0.188033 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 6.44450e46 | 0.574367 | ||||||||
\(71\) | −7.64854e46 | −0.474778 | −0.237389 | − | 0.971415i | \(-0.576292\pi\) | ||||
−0.237389 | + | 0.971415i | \(0.576292\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.90560e47 | 1.80522 | 0.902611 | − | 0.430456i | \(-0.141647\pi\) | ||||
0.902611 | + | 0.430456i | \(0.141647\pi\) | |||||||
\(74\) | −2.90154e47 | −0.626931 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.26105e46 | 0.0466412 | ||||||||
\(77\) | 1.15270e48 | 0.904070 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 3.15804e48 | 1.28803 | 0.644017 | − | 0.765011i | \(-0.277267\pi\) | ||||
0.644017 | + | 0.765011i | \(0.277267\pi\) | |||||||
\(80\) | 2.80503e48 | 0.830124 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.84576e48 | −0.448689 | ||||||||
\(83\) | 1.40261e48 | 0.162348 | 0.0811739 | − | 0.996700i | \(-0.474133\pi\) | ||||
0.0811739 | + | 0.996700i | \(0.474133\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.27217e49 | 0.802348 | ||||||||
\(86\) | 2.93103e49 | 1.37186 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.26801e49 | 1.11152 | ||||||||
\(89\) | 1.71424e48 | 0.0334677 | 0.0167338 | − | 0.999860i | \(-0.494673\pi\) | ||||
0.0167338 | + | 0.999860i | \(0.494673\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.55138e49 | −0.393407 | ||||||||
\(92\) | −9.06303e48 | −0.0759773 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.67005e49 | 0.371568 | ||||||||
\(95\) | −5.38085e49 | −0.199021 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.68956e50 | 1.45451 | 0.727257 | − | 0.686365i | \(-0.240795\pi\) | ||||
0.727257 | + | 0.686365i | \(0.240795\pi\) | |||||||
\(98\) | 3.01917e50 | 0.505385 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.02868e49 | −0.0802868 | ||||||||
\(101\) | −2.03385e51 | −1.57806 | −0.789031 | − | 0.614354i | \(-0.789417\pi\) | ||||
−0.789031 | + | 0.614354i | \(0.789417\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.62630e51 | −1.23593 | −0.617967 | − | 0.786204i | \(-0.712043\pi\) | ||||
−0.617967 | + | 0.786204i | \(0.712043\pi\) | |||||||
\(104\) | −1.31494e51 | −0.483679 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.29632e51 | −1.65122 | ||||||||
\(107\) | 4.29375e51 | 0.764804 | 0.382402 | − | 0.923996i | \(-0.375097\pi\) | ||||
0.382402 | + | 0.923996i | \(0.375097\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.62834e49 | −0.00514103 | −0.00257051 | − | 0.999997i | \(-0.500818\pi\) | ||||
−0.00257051 | + | 0.999997i | \(0.500818\pi\) | |||||||
\(110\) | 1.10737e52 | 0.974493 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.49900e52 | −0.833185 | ||||||||
\(113\) | −2.75611e52 | −1.22123 | −0.610613 | − | 0.791929i | \(-0.709077\pi\) | ||||
−0.610613 | + | 0.791929i | \(0.709077\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.14448e52 | 0.324200 | ||||||||
\(116\) | 8.66444e51 | 0.196817 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.15418e52 | 0.169545 | ||||||||
\(119\) | −6.79843e52 | −0.805307 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.89398e52 | 0.533880 | ||||||||
\(122\) | −1.20202e52 | −0.0754630 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.57997e52 | −0.0655235 | ||||||||
\(125\) | 3.16621e53 | 1.06988 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.01732e53 | 1.80732 | 0.903659 | − | 0.428254i | \(-0.140871\pi\) | ||||
0.903659 | + | 0.428254i | \(0.140871\pi\) | |||||||
\(128\) | −6.37903e53 | −1.17734 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.41173e53 | −0.424051 | ||||||||
\(131\) | 1.06837e54 | 1.09220 | 0.546102 | − | 0.837719i | \(-0.316111\pi\) | ||||
0.546102 | + | 0.837719i | \(0.316111\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.87551e53 | 0.199755 | ||||||||
\(134\) | 1.36153e53 | 0.0781369 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.51720e54 | −0.990094 | ||||||||
\(137\) | −1.78751e54 | −0.583274 | −0.291637 | − | 0.956529i | \(-0.594200\pi\) | ||||
−0.291637 | + | 0.956529i | \(0.594200\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.89879e54 | −1.33010 | −0.665052 | − | 0.746797i | \(-0.731591\pi\) | ||||
−0.665052 | + | 0.746797i | \(0.731591\pi\) | |||||||
\(140\) | −4.81790e53 | −0.0904885 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.92662e54 | 0.513648 | ||||||||
\(143\) | −6.10239e54 | −0.667469 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.09414e55 | −0.839829 | ||||||||
\(146\) | −3.03182e55 | −1.95302 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.16919e54 | 0.0987697 | ||||||||
\(149\) | −2.84854e55 | −1.09238 | −0.546188 | − | 0.837663i | \(-0.683922\pi\) | ||||
−0.546188 | + | 0.837663i | \(0.683922\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.60980e54 | 0.207712 | 0.103856 | − | 0.994592i | \(-0.466882\pi\) | ||||
0.103856 | + | 0.994592i | \(0.466882\pi\) | |||||||
\(152\) | 1.06469e55 | 0.245591 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −5.91774e55 | −0.978086 | ||||||||
\(155\) | 1.99519e55 | 0.279593 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.29871e56 | −1.31242 | −0.656209 | − | 0.754579i | \(-0.727841\pi\) | ||||
−0.656209 | + | 0.754579i | \(0.727841\pi\) | |||||||
\(158\) | −1.62128e56 | −1.39349 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.93430e55 | −0.245362 | ||||||||
\(161\) | −6.11605e55 | −0.325395 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.13179e56 | 1.60455 | 0.802277 | − | 0.596952i | \(-0.203622\pi\) | ||||
0.802277 | + | 0.596952i | \(0.203622\pi\) | |||||||
\(164\) | 2.12749e55 | 0.0706886 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.20075e55 | −0.175639 | ||||||||
\(167\) | −4.33151e56 | −0.906504 | −0.453252 | − | 0.891383i | \(-0.649736\pi\) | ||||
−0.453252 | + | 0.891383i | \(0.649736\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.59298e56 | −0.709550 | ||||||||
\(170\) | −6.53109e56 | −0.868037 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.19124e56 | −0.216130 | ||||||||
\(173\) | −4.65407e56 | −0.395966 | −0.197983 | − | 0.980205i | \(-0.563439\pi\) | ||||
−0.197983 | + | 0.980205i | \(0.563439\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −5.41804e56 | −0.343852 | ||||||||
\(176\) | −2.57575e57 | −1.41361 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.80057e55 | −0.0362077 | ||||||||
\(179\) | −5.11036e57 | −1.82263 | −0.911316 | − | 0.411708i | \(-0.864932\pi\) | ||||
−0.911316 | + | 0.411708i | \(0.864932\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.70440e57 | −1.26387 | −0.631933 | − | 0.775023i | \(-0.717738\pi\) | ||||
−0.631933 | + | 0.775023i | \(0.717738\pi\) | |||||||
\(182\) | 1.82321e57 | 0.425615 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.26454e57 | −0.400061 | ||||||||
\(185\) | −2.73925e57 | −0.421457 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.16818e58 | −1.36631 | ||||||||
\(188\) | −5.73412e56 | −0.0585385 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.76243e57 | 0.215315 | ||||||||
\(191\) | 2.06433e58 | 1.40743 | 0.703717 | − | 0.710481i | \(-0.251522\pi\) | ||||
0.703717 | + | 0.710481i | \(0.251522\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.31461e57 | 0.330092 | 0.165046 | − | 0.986286i | \(-0.447223\pi\) | ||||
0.165046 | + | 0.986286i | \(0.447223\pi\) | |||||||
\(194\) | −3.43429e58 | −1.57360 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2.25713e57 | −0.0796207 | ||||||||
\(197\) | 2.12414e58 | 0.658104 | 0.329052 | − | 0.944312i | \(-0.393271\pi\) | ||||
0.329052 | + | 0.944312i | \(0.393271\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5.17721e58 | 1.23977 | 0.619887 | − | 0.784691i | \(-0.287178\pi\) | ||||
0.619887 | + | 0.784691i | \(0.287178\pi\) | |||||||
\(200\) | −2.00610e58 | −0.422753 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.04414e59 | 1.70726 | ||||||||
\(203\) | 5.84707e58 | 0.842925 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.68659e58 | −0.301633 | ||||||||
\(206\) | 1.34829e59 | 1.33712 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.93570e58 | 0.615135 | ||||||||
\(209\) | 4.94103e58 | 0.338912 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.46281e57 | −0.0240107 | −0.0120054 | − | 0.999928i | \(-0.503822\pi\) | ||||
−0.0120054 | + | 0.999928i | \(0.503822\pi\) | |||||||
\(212\) | 5.45472e58 | 0.260140 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.20433e59 | −0.827419 | ||||||||
\(215\) | 2.76709e59 | 0.922238 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.06622e59 | −0.280624 | ||||||||
\(218\) | 2.37610e57 | 0.00556192 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −8.27868e58 | −0.153526 | ||||||||
\(221\) | 3.59910e59 | 0.594553 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.20757e57 | 0.00683694 | 0.00341847 | − | 0.999994i | \(-0.498912\pi\) | ||||
0.00341847 | + | 0.999994i | \(0.498912\pi\) | |||||||
\(224\) | 2.10248e59 | 0.246267 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.41493e60 | 1.32121 | ||||||||
\(227\) | 5.70910e59 | 0.476330 | 0.238165 | − | 0.971225i | \(-0.423454\pi\) | ||||
0.238165 | + | 0.971225i | \(0.423454\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.79988e60 | −1.20071 | −0.600354 | − | 0.799734i | \(-0.704974\pi\) | ||||
−0.600354 | + | 0.799734i | \(0.704974\pi\) | |||||||
\(230\) | −5.87554e59 | −0.350742 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.16495e60 | 1.03634 | ||||||||
\(233\) | −2.07611e60 | −0.890581 | −0.445290 | − | 0.895386i | \(-0.646900\pi\) | ||||
−0.445290 | + | 0.895386i | \(0.646900\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.24104e59 | 0.249787 | ||||||||
\(236\) | −8.62867e58 | −0.0267109 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.49019e60 | 0.871237 | ||||||||
\(239\) | 4.43052e60 | 0.993822 | 0.496911 | − | 0.867802i | \(-0.334468\pi\) | ||||
0.496911 | + | 0.867802i | \(0.334468\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.39407e60 | −0.796952 | −0.398476 | − | 0.917179i | \(-0.630461\pi\) | ||||
−0.398476 | + | 0.917179i | \(0.630461\pi\) | |||||||
\(242\) | −3.53924e60 | −0.577588 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 8.98625e58 | 0.0118888 | ||||||||
\(245\) | 2.85030e60 | 0.339747 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.52230e60 | −0.147478 | ||||||||
\(248\) | −3.94782e60 | −0.345016 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.62547e61 | −1.15747 | ||||||||
\(251\) | 2.03323e60 | 0.130770 | 0.0653849 | − | 0.997860i | \(-0.479172\pi\) | ||||
0.0653849 | + | 0.997860i | \(0.479172\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.05093e61 | −0.552078 | ||||||||
\(254\) | −4.11594e61 | −1.95528 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.27866e61 | 0.497318 | ||||||||
\(257\) | −3.10631e61 | −1.09383 | −0.546915 | − | 0.837188i | \(-0.684198\pi\) | ||||
−0.546915 | + | 0.837188i | \(0.684198\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.46385e61 | 0.423011 | ||||||||
\(260\) | 2.55060e60 | 0.0668071 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5.48481e61 | −1.18162 | ||||||||
\(263\) | −7.24647e61 | −1.41663 | −0.708313 | − | 0.705899i | \(-0.750543\pi\) | ||||
−0.708313 | + | 0.705899i | \(0.750543\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.88822e61 | −1.11004 | ||||||||
\(266\) | −1.47623e61 | −0.216109 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.01788e60 | −0.0123101 | ||||||||
\(269\) | 5.04207e61 | 0.554531 | 0.277265 | − | 0.960793i | \(-0.410572\pi\) | ||||
0.277265 | + | 0.960793i | \(0.410572\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5.33395e61 | 0.485660 | 0.242830 | − | 0.970069i | \(-0.421924\pi\) | ||||
0.242830 | + | 0.970069i | \(0.421924\pi\) | |||||||
\(272\) | 1.51914e62 | 1.25919 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.17672e61 | 0.631027 | ||||||||
\(275\) | −9.30990e61 | −0.583393 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.79274e62 | 0.933861 | 0.466931 | − | 0.884294i | \(-0.345360\pi\) | ||||
0.466931 | + | 0.884294i | \(0.345360\pi\) | |||||||
\(278\) | 3.02833e62 | 1.43900 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.20383e62 | −0.476470 | ||||||||
\(281\) | 1.23411e62 | 0.446006 | 0.223003 | − | 0.974818i | \(-0.428414\pi\) | ||||
0.223003 | + | 0.974818i | \(0.428414\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.28631e61 | 0.159440 | 0.0797202 | − | 0.996817i | \(-0.474597\pi\) | ||||
0.0797202 | + | 0.996817i | \(0.474597\pi\) | |||||||
\(284\) | −2.93553e61 | −0.0809225 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.13285e62 | 0.722115 | ||||||||
\(287\) | 1.43571e62 | 0.302745 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.22875e62 | 0.217054 | ||||||||
\(290\) | 5.61713e62 | 0.908586 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.26659e62 | 0.307687 | ||||||||
\(293\) | −3.24054e62 | −0.403174 | −0.201587 | − | 0.979471i | \(-0.564610\pi\) | ||||
−0.201587 | + | 0.979471i | \(0.564610\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.08963e62 | 0.113977 | ||||||||
\(296\) | 5.42007e62 | 0.520075 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.46239e63 | 1.18181 | ||||||||
\(299\) | 3.23784e62 | 0.240237 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.47872e63 | −0.925639 | ||||||||
\(302\) | −3.90673e62 | −0.224717 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −6.42543e62 | −0.312339 | ||||||||
\(305\) | −1.13478e62 | −0.0507303 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4.26649e63 | −1.61451 | −0.807257 | − | 0.590200i | \(-0.799049\pi\) | ||||
−0.807257 | + | 0.590200i | \(0.799049\pi\) | |||||||
\(308\) | 4.42409e62 | 0.154092 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.02429e63 | −0.302483 | ||||||||
\(311\) | −2.40513e63 | −0.654258 | −0.327129 | − | 0.944980i | \(-0.606081\pi\) | ||||
−0.327129 | + | 0.944980i | \(0.606081\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.21400e62 | −0.0973451 | −0.0486726 | − | 0.998815i | \(-0.515499\pi\) | ||||
−0.0486726 | + | 0.998815i | \(0.515499\pi\) | |||||||
\(314\) | 6.66736e63 | 1.41987 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.21207e63 | 0.219536 | ||||||||
\(317\) | −3.76818e63 | −0.629681 | −0.314840 | − | 0.949145i | \(-0.601951\pi\) | ||||
−0.314840 | + | 0.949145i | \(0.601951\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.00471e64 | 1.43014 | ||||||||
\(320\) | −4.29657e63 | −0.564674 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.13987e63 | 0.352036 | ||||||||
\(323\) | −2.91414e63 | −0.301888 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2.86831e63 | 0.253864 | ||||||||
\(326\) | −2.12118e64 | −1.73592 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.31588e63 | 0.372213 | ||||||||
\(329\) | −3.86959e63 | −0.250709 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.48200e64 | −1.93293 | −0.966463 | − | 0.256807i | \(-0.917330\pi\) | ||||
−0.966463 | + | 0.256807i | \(0.917330\pi\) | |||||||
\(332\) | 5.38328e62 | 0.0276710 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.22372e64 | 0.980719 | ||||||||
\(335\) | 1.28538e63 | 0.0525278 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.75434e64 | −1.31817 | −0.659085 | − | 0.752068i | \(-0.729056\pi\) | ||||
−0.659085 | + | 0.752068i | \(0.729056\pi\) | |||||||
\(338\) | 2.35795e64 | 0.767641 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.88263e63 | 0.136755 | ||||||||
\(341\) | −1.83210e64 | −0.476117 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.78386e64 | −1.07097 | ||||||||
\(344\) | −5.47516e64 | −1.13804 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.38931e64 | 0.428383 | ||||||||
\(347\) | −1.26312e63 | −0.0210399 | −0.0105200 | − | 0.999945i | \(-0.503349\pi\) | ||||
−0.0105200 | + | 0.999945i | \(0.503349\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.61603e64 | −0.951808 | −0.475904 | − | 0.879497i | \(-0.657879\pi\) | ||||
−0.475904 | + | 0.879497i | \(0.657879\pi\) | |||||||
\(350\) | 2.78152e64 | 0.372004 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.61271e64 | 0.417826 | ||||||||
\(353\) | 1.20269e65 | 1.29390 | 0.646949 | − | 0.762533i | \(-0.276045\pi\) | ||||
0.646949 | + | 0.762533i | \(0.276045\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.70699e64 | 0.345302 | ||||||||
\(356\) | 6.57930e62 | 0.00570433 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.62356e65 | 1.97185 | ||||||||
\(359\) | −1.83244e63 | −0.0128269 | −0.00641344 | − | 0.999979i | \(-0.502041\pi\) | ||||
−0.00641344 | + | 0.999979i | \(0.502041\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.52276e65 | −0.925117 | ||||||||
\(362\) | 2.41515e65 | 1.36734 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.36303e64 | −0.0670534 | ||||||||
\(365\) | −2.86225e65 | −1.31292 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.73824e65 | 1.49170 | 0.745851 | − | 0.666112i | \(-0.232043\pi\) | ||||
0.745851 | + | 0.666112i | \(0.232043\pi\) | |||||||
\(368\) | 1.36666e65 | 0.508791 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.40628e65 | 0.455961 | ||||||||
\(371\) | 3.68104e65 | 1.11413 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.09981e65 | 1.08190 | 0.540952 | − | 0.841054i | \(-0.318064\pi\) | ||||
0.540952 | + | 0.841054i | \(0.318064\pi\) | |||||||
\(374\) | 5.99724e65 | 1.47817 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.43276e65 | −0.308236 | ||||||||
\(377\) | −3.09544e65 | −0.622326 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −3.52556e65 | −0.619338 | −0.309669 | − | 0.950844i | \(-0.600218\pi\) | ||||
−0.309669 | + | 0.950844i | \(0.600218\pi\) | |||||||
\(380\) | −2.06519e64 | −0.0339217 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.05979e66 | −1.52266 | ||||||||
\(383\) | 5.89561e65 | 0.792429 | 0.396214 | − | 0.918158i | \(-0.370324\pi\) | ||||
0.396214 | + | 0.918158i | \(0.370324\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.58674e65 | −0.657522 | ||||||||
\(386\) | −3.24180e65 | −0.357117 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.56747e65 | 0.247912 | ||||||||
\(389\) | −1.54980e66 | −1.40140 | −0.700698 | − | 0.713458i | \(-0.747128\pi\) | ||||
−0.700698 | + | 0.713458i | \(0.747128\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.19822e65 | 0.491768 | ||||||||
\(392\) | −5.63980e65 | −0.419246 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.09049e66 | −0.711983 | ||||||||
\(395\) | −1.53060e66 | −0.936775 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.73577e65 | −0.201012 | −0.100506 | − | 0.994936i | \(-0.532046\pi\) | ||||
−0.100506 | + | 0.994936i | \(0.532046\pi\) | |||||||
\(398\) | −2.65788e66 | −1.34127 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.21068e66 | 0.537651 | ||||||||
\(401\) | 2.11569e65 | 0.0881600 | 0.0440800 | − | 0.999028i | \(-0.485964\pi\) | ||||
0.0440800 | + | 0.999028i | \(0.485964\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.64459e65 | 0.207183 | ||||||||
\(404\) | −7.80598e65 | −0.268969 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.00177e66 | −0.911936 | ||||||||
\(407\) | 2.51535e66 | 0.717696 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.06566e66 | 0.268332 | 0.134166 | − | 0.990959i | \(-0.457164\pi\) | ||||
0.134166 | + | 0.990959i | \(0.457164\pi\) | |||||||
\(410\) | 1.37925e66 | 0.326328 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.00798e66 | −0.210656 | ||||||||
\(413\) | −5.82293e65 | −0.114397 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.79800e65 | −0.118074 | ||||||||
\(416\) | −1.11305e66 | −0.181817 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.53663e66 | −0.366659 | ||||||||
\(419\) | −5.15077e65 | −0.0700511 | −0.0350255 | − | 0.999386i | \(-0.511151\pi\) | ||||
−0.0350255 | + | 0.999386i | \(0.511151\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.05760e66 | 0.609187 | 0.304594 | − | 0.952482i | \(-0.401479\pi\) | ||||
0.304594 | + | 0.952482i | \(0.401479\pi\) | |||||||
\(422\) | 2.29112e65 | 0.0259765 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.36295e67 | 1.36978 | ||||||||
\(425\) | 5.49083e66 | 0.519661 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.06424e65 | 0.0509173 | ||||||||
\(428\) | 1.64795e66 | 0.130355 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.42057e67 | −0.997742 | ||||||||
\(431\) | 6.54142e66 | 0.433014 | 0.216507 | − | 0.976281i | \(-0.430534\pi\) | ||||
0.216507 | + | 0.976281i | \(0.430534\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.67034e66 | 0.215906 | 0.107953 | − | 0.994156i | \(-0.465570\pi\) | ||||
0.107953 | + | 0.994156i | \(0.465570\pi\) | |||||||
\(434\) | 5.47378e66 | 0.303598 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.77637e64 | −0.000876252 0 | ||||||||
\(437\) | −2.62164e66 | −0.121982 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.98143e66 | 0.330549 | 0.165274 | − | 0.986248i | \(-0.447149\pi\) | ||||
0.165274 | + | 0.986248i | \(0.447149\pi\) | |||||||
\(440\) | −2.06856e67 | −0.808398 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.84771e67 | −0.643229 | ||||||||
\(443\) | 1.14974e67 | 0.377836 | 0.188918 | − | 0.981993i | \(-0.439502\pi\) | ||||
0.188918 | + | 0.981993i | \(0.439502\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.30834e65 | −0.0243407 | ||||||||
\(446\) | −2.67347e65 | −0.00739668 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.29607e67 | 0.566756 | ||||||||
\(449\) | 7.25393e67 | 1.69158 | 0.845789 | − | 0.533518i | \(-0.179130\pi\) | ||||
0.845789 | + | 0.533518i | \(0.179130\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.46699e67 | 0.513649 | ||||||||
\(452\) | −1.05780e67 | −0.208149 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.93094e67 | −0.515327 | ||||||||
\(455\) | 1.72124e67 | 0.286121 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.92391e67 | −0.583251 | −0.291626 | − | 0.956533i | \(-0.594196\pi\) | ||||
−0.291626 | + | 0.956533i | \(0.594196\pi\) | |||||||
\(458\) | 9.24022e67 | 1.29901 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.39255e66 | 0.0552576 | ||||||||
\(461\) | 2.24623e67 | 0.267350 | 0.133675 | − | 0.991025i | \(-0.457322\pi\) | ||||
0.133675 | + | 0.991025i | \(0.457322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.68251e67 | 0.925401 | 0.462701 | − | 0.886515i | \(-0.346880\pi\) | ||||
0.462701 | + | 0.886515i | \(0.346880\pi\) | |||||||
\(464\) | −1.30655e68 | −1.31801 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.06583e68 | 0.963493 | ||||||||
\(467\) | −3.24322e67 | −0.277585 | −0.138792 | − | 0.990322i | \(-0.544322\pi\) | ||||
−0.138792 | + | 0.990322i | \(0.544322\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.86903e66 | −0.0527215 | ||||||||
\(470\) | −3.71742e67 | −0.270238 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.15601e67 | −0.140647 | ||||||||
\(473\) | −2.54091e68 | −1.57047 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.32244e67 | −0.128901 | ||||||||
\(476\) | −2.60926e67 | −0.137259 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.27455e68 | −1.07519 | ||||||||
\(479\) | −2.10847e68 | −0.944959 | −0.472479 | − | 0.881342i | \(-0.656641\pi\) | ||||
−0.472479 | + | 0.881342i | \(0.656641\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.74961e67 | −0.312306 | ||||||||
\(482\) | 2.25583e68 | 0.862199 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.64593e67 | 0.0909960 | ||||||||
\(485\) | −3.24220e68 | −1.05785 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.64479e68 | −0.483195 | −0.241597 | − | 0.970377i | \(-0.577671\pi\) | ||||
−0.241597 | + | 0.970377i | \(0.577671\pi\) | |||||||
\(488\) | 2.24536e67 | 0.0626009 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.46329e68 | −0.367562 | ||||||||
\(491\) | 2.01454e68 | 0.480395 | 0.240197 | − | 0.970724i | \(-0.422788\pi\) | ||||
0.240197 | + | 0.970724i | \(0.422788\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.92562e68 | −1.27391 | ||||||||
\(494\) | 7.81518e67 | 0.159552 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.38251e68 | 0.438786 | ||||||||
\(497\) | −1.98100e68 | −0.346575 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.52023e68 | −0.555914 | −0.277957 | − | 0.960594i | \(-0.589657\pi\) | ||||
−0.277957 | + | 0.960594i | \(0.589657\pi\) | |||||||
\(500\) | 1.21520e68 | 0.182353 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.04382e68 | −0.141476 | ||||||||
\(503\) | −1.03779e69 | −1.33698 | −0.668492 | − | 0.743719i | \(-0.733060\pi\) | ||||
−0.668492 | + | 0.743719i | \(0.733060\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.85739e68 | 1.14771 | ||||||||
\(506\) | 5.39528e68 | 0.597277 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.07707e68 | 0.308044 | ||||||||
\(509\) | 1.43270e69 | 1.36411 | 0.682057 | − | 0.731299i | \(-0.261086\pi\) | ||||
0.682057 | + | 0.731299i | \(0.261086\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.52957e69 | 1.31776 | ||||||||
\(512\) | 7.79993e68 | 0.639303 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.59472e69 | 1.18338 | ||||||||
\(515\) | 1.27288e69 | 0.898883 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.64917e68 | −0.425362 | ||||||||
\(518\) | −7.51511e68 | −0.457642 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.37309e68 | 0.351775 | ||||||||
\(521\) | −7.41512e67 | −0.0389723 | −0.0194862 | − | 0.999810i | \(-0.506203\pi\) | ||||
−0.0194862 | + | 0.999810i | \(0.506203\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.30708e69 | −0.623030 | −0.311515 | − | 0.950241i | \(-0.600836\pi\) | ||||
−0.311515 | + | 0.950241i | \(0.600836\pi\) | |||||||
\(524\) | 4.10044e68 | 0.186158 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.72020e69 | 1.53260 | ||||||||
\(527\) | 1.08055e69 | 0.424104 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.24860e69 | −0.801294 | ||||||||
\(530\) | 3.53628e69 | 1.20091 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.10363e68 | 0.0340468 | ||||||||
\(533\) | −7.60064e68 | −0.223515 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.08104e69 | −0.556235 | ||||||||
\(536\) | −2.54334e68 | −0.0648191 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.58850e69 | −0.599930 | ||||||||
\(539\) | −2.61732e69 | −0.578553 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.56485e69 | −1.52149 | −0.760746 | − | 0.649049i | \(-0.775167\pi\) | ||||
−0.760746 | + | 0.649049i | \(0.775167\pi\) | |||||||
\(542\) | −2.73835e69 | −0.525421 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.13072e69 | −0.372182 | ||||||||
\(545\) | 2.24320e67 | 0.00373902 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.07662e68 | −0.0467087 | −0.0233543 | − | 0.999727i | \(-0.507435\pi\) | ||||
−0.0233543 | + | 0.999727i | \(0.507435\pi\) | |||||||
\(548\) | −6.86050e68 | −0.0994150 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.77953e69 | 0.631155 | ||||||||
\(551\) | 2.50634e69 | 0.315990 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.17946e69 | 0.940229 | ||||||||
\(554\) | −9.20357e69 | −1.01032 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −2.26398e69 | −0.226707 | ||||||||
\(557\) | −2.02206e70 | −1.93414 | −0.967068 | − | 0.254519i | \(-0.918083\pi\) | ||||
−0.967068 | + | 0.254519i | \(0.918083\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.82838e69 | 0.683393 | ||||||||
\(560\) | 7.26514e69 | 0.605967 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.33567e69 | −0.482521 | ||||||||
\(563\) | −1.22868e69 | −0.0894285 | −0.0447142 | − | 0.999000i | \(-0.514238\pi\) | ||||
−0.0447142 | + | 0.999000i | \(0.514238\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.33579e70 | 0.888186 | ||||||||
\(566\) | −2.71389e69 | −0.172494 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.33491e69 | −0.426100 | ||||||||
\(569\) | 5.32852e69 | 0.295967 | 0.147984 | − | 0.988990i | \(-0.452722\pi\) | ||||
0.147984 | + | 0.988990i | \(0.452722\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.57707e69 | −0.334050 | −0.167025 | − | 0.985953i | \(-0.553416\pi\) | ||||
−0.167025 | + | 0.985953i | \(0.553416\pi\) | |||||||
\(572\) | −2.34212e69 | −0.113765 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7.37064e69 | −0.327531 | ||||||||
\(575\) | 4.93970e69 | 0.209976 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.36043e70 | −1.69647 | −0.848235 | − | 0.529620i | \(-0.822335\pi\) | ||||
−0.848235 | + | 0.529620i | \(0.822335\pi\) | |||||||
\(578\) | −6.30816e69 | −0.234824 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −4.19936e69 | −0.143143 | ||||||||
\(581\) | 3.63282e69 | 0.118509 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.32518e70 | 1.89027 | ||||||||
\(584\) | 5.66343e70 | 1.62014 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.66363e70 | 0.436182 | ||||||||
\(587\) | −1.47836e70 | −0.371115 | −0.185557 | − | 0.982633i | \(-0.559409\pi\) | ||||
−0.185557 | + | 0.982633i | \(0.559409\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.57035e69 | −0.105198 | ||||||||
\(590\) | −5.59395e69 | −0.123308 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.27102e70 | −0.661424 | ||||||||
\(593\) | −4.45541e70 | −0.862964 | −0.431482 | − | 0.902122i | \(-0.642009\pi\) | ||||
−0.431482 | + | 0.902122i | \(0.642009\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.29497e70 | 0.585692 | ||||||||
\(596\) | −1.09328e70 | −0.186188 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.66225e70 | −0.259906 | ||||||||
\(599\) | 2.36232e70 | 0.353961 | 0.176980 | − | 0.984214i | \(-0.443367\pi\) | ||||
0.176980 | + | 0.984214i | \(0.443367\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.60000e70 | −1.04596 | −0.522979 | − | 0.852345i | \(-0.675180\pi\) | ||||
−0.522979 | + | 0.852345i | \(0.675180\pi\) | |||||||
\(602\) | 7.59149e70 | 1.00142 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 2.92067e69 | 0.0354030 | ||||||||
\(605\) | −3.34128e70 | −0.388286 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.81615e70 | 0.834990 | 0.417495 | − | 0.908679i | \(-0.362908\pi\) | ||||
0.417495 | + | 0.908679i | \(0.362908\pi\) | |||||||
\(608\) | 9.01223e69 | 0.0923190 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.82577e69 | 0.0548836 | ||||||||
\(611\) | 2.04856e70 | 0.185096 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.82908e70 | 0.817091 | 0.408546 | − | 0.912738i | \(-0.366036\pi\) | ||||
0.408546 | + | 0.912738i | \(0.366036\pi\) | |||||||
\(614\) | 2.19033e71 | 1.74669 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.10543e71 | 0.811378 | ||||||||
\(617\) | −6.23909e68 | −0.00439389 | −0.00219695 | − | 0.999998i | \(-0.500699\pi\) | ||||
−0.00219695 | + | 0.999998i | \(0.500699\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −3.87928e70 | −0.251559 | −0.125779 | − | 0.992058i | \(-0.540143\pi\) | ||||
−0.125779 | + | 0.992058i | \(0.540143\pi\) | |||||||
\(620\) | 7.65760e69 | 0.0476546 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.23475e71 | 0.707822 | ||||||||
\(623\) | 4.43994e69 | 0.0244305 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.05579e70 | −0.307065 | ||||||||
\(626\) | 2.16339e70 | 0.105315 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.98451e70 | −0.223692 | ||||||||
\(629\) | −1.48351e71 | −0.639293 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.57404e71 | −1.81782 | −0.908911 | − | 0.416989i | \(-0.863085\pi\) | ||||
−0.908911 | + | 0.416989i | \(0.863085\pi\) | |||||||
\(632\) | 3.02855e71 | 1.15598 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.93451e71 | 0.681233 | ||||||||
\(635\) | −3.88573e71 | −1.31444 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.06377e70 | 0.251758 | ||||||||
\(638\) | −5.15799e71 | −1.54723 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 3.09170e71 | 0.856266 | ||||||||
\(641\) | 3.22553e71 | 0.858463 | 0.429231 | − | 0.903195i | \(-0.358784\pi\) | ||||
0.429231 | + | 0.903195i | \(0.358784\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7.02269e71 | −1.72633 | −0.863165 | − | 0.504922i | \(-0.831521\pi\) | ||||
−0.863165 | + | 0.504922i | \(0.831521\pi\) | |||||||
\(644\) | −2.34736e70 | −0.0554613 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.49606e71 | 0.326604 | ||||||||
\(647\) | −8.46993e71 | −1.77755 | −0.888773 | − | 0.458347i | \(-0.848442\pi\) | ||||
−0.888773 | + | 0.458347i | \(0.848442\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.00056e71 | −0.194091 | ||||||||
\(650\) | −1.47254e71 | −0.274648 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.58580e71 | 0.273485 | ||||||||
\(653\) | −7.34453e71 | −1.21809 | −0.609043 | − | 0.793137i | \(-0.708446\pi\) | ||||
−0.609043 | + | 0.793137i | \(0.708446\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.17803e71 | −0.794350 | ||||||||
\(656\) | −3.20814e71 | −0.473375 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.98657e71 | 0.271234 | ||||||||
\(659\) | −5.48627e70 | −0.0720608 | −0.0360304 | − | 0.999351i | \(-0.511471\pi\) | ||||
−0.0360304 | + | 0.999351i | \(0.511471\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9.86251e71 | −1.19909 | −0.599543 | − | 0.800343i | \(-0.704651\pi\) | ||||
−0.599543 | + | 0.800343i | \(0.704651\pi\) | |||||||
\(662\) | 1.78759e72 | 2.09117 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.34510e71 | 0.145703 | ||||||||
\(665\) | −1.39366e71 | −0.145280 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.33085e71 | −0.514740 | ||||||||
\(668\) | −1.66245e71 | −0.154507 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −6.59890e70 | −0.0568283 | ||||||||
\(671\) | 1.04203e71 | 0.0863883 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.21639e72 | 0.934739 | 0.467369 | − | 0.884062i | \(-0.345202\pi\) | ||||
0.467369 | + | 0.884062i | \(0.345202\pi\) | |||||||
\(674\) | 1.92741e72 | 1.42609 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.76280e71 | −0.120938 | ||||||||
\(677\) | 9.64935e71 | 0.637510 | 0.318755 | − | 0.947837i | \(-0.396735\pi\) | ||||
0.318755 | + | 0.947837i | \(0.396735\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.73262e72 | 1.06176 | ||||||||
\(680\) | 1.22000e72 | 0.720086 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.40568e71 | 0.515097 | ||||||||
\(683\) | −3.44340e72 | −1.81660 | −0.908299 | − | 0.418321i | \(-0.862619\pi\) | ||||
−0.908299 | + | 0.418321i | \(0.862619\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.66344e71 | 0.424210 | ||||||||
\(686\) | 2.45594e72 | 1.15865 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.30427e72 | 1.44734 | ||||||||
\(689\) | −1.94874e72 | −0.822554 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.61159e70 | −0.00631779 | −0.00315889 | − | 0.999995i | \(-0.501006\pi\) | ||||
−0.00315889 | + | 0.999995i | \(0.501006\pi\) | |||||||
\(692\) | −1.78625e71 | −0.0674895 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 6.48463e70 | 0.0227624 | ||||||||
\(695\) | 2.85895e72 | 0.967373 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.45499e72 | −0.457536 | ||||||||
\(698\) | 3.39655e72 | 1.02973 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.07946e71 | −0.0586072 | ||||||||
\(701\) | −7.31953e71 | −0.198918 | −0.0994589 | − | 0.995042i | \(-0.531711\pi\) | ||||
−0.0994589 | + | 0.995042i | \(0.531711\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.27476e71 | 0.158575 | ||||||||
\(704\) | 3.94537e72 | 0.961579 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.17440e72 | −1.39983 | ||||||||
\(707\) | −5.26775e72 | −1.15194 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.60802e72 | −0.937637 | −0.468819 | − | 0.883294i | \(-0.655320\pi\) | ||||
−0.468819 | + | 0.883294i | \(0.655320\pi\) | |||||||
\(710\) | −1.90310e72 | −0.373571 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.64394e71 | 0.0300364 | ||||||||
\(713\) | 9.72089e71 | 0.171365 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.95763e72 | 0.485444 | ||||||||
\(716\) | −1.96137e72 | −0.310655 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 9.40739e70 | 0.0138770 | ||||||||
\(719\) | −8.14014e72 | −1.15890 | −0.579449 | − | 0.815009i | \(-0.696732\pi\) | ||||
−0.579449 | + | 0.815009i | \(0.696732\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.80222e72 | −0.902197 | ||||||||
\(722\) | 7.81754e72 | 1.00086 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.80557e72 | −0.215417 | ||||||||
\(725\) | −4.72245e72 | −0.543937 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.09226e72 | −0.868845 | −0.434423 | − | 0.900709i | \(-0.643048\pi\) | ||||
−0.434423 | + | 0.900709i | \(0.643048\pi\) | |||||||
\(728\) | −3.40576e72 | −0.353072 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1.46942e73 | 1.42041 | ||||||||
\(731\) | 1.49859e73 | 1.39891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.72167e73 | 1.49899 | 0.749495 | − | 0.662010i | \(-0.230297\pi\) | ||||
0.749495 | + | 0.662010i | \(0.230297\pi\) | |||||||
\(734\) | −1.91914e73 | −1.61383 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.91685e72 | −0.150385 | ||||||||
\(737\) | −1.18031e72 | −0.0894493 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.89392e72 | −0.346118 | −0.173059 | − | 0.984911i | \(-0.555365\pi\) | ||||
−0.173059 | + | 0.984911i | \(0.555365\pi\) | |||||||
\(740\) | −1.05133e72 | −0.0718343 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.88978e73 | −1.20534 | ||||||||
\(743\) | −1.78935e73 | −1.10276 | −0.551379 | − | 0.834255i | \(-0.685898\pi\) | ||||
−0.551379 | + | 0.834255i | \(0.685898\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.38059e73 | 0.794475 | ||||||||
\(746\) | −2.10477e73 | −1.17048 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.48353e72 | −0.232879 | ||||||||
\(749\) | 1.11210e73 | 0.558286 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.11871e73 | 0.524685 | 0.262343 | − | 0.964975i | \(-0.415505\pi\) | ||||
0.262343 | + | 0.964975i | \(0.415505\pi\) | |||||||
\(752\) | 8.64674e72 | 0.392010 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.58914e73 | 0.673276 | ||||||||
\(755\) | −3.68822e72 | −0.151067 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −7.85188e72 | −0.300628 | −0.150314 | − | 0.988638i | \(-0.548028\pi\) | ||||
−0.150314 | + | 0.988638i | \(0.548028\pi\) | |||||||
\(758\) | 1.80995e73 | 0.670043 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −5.16021e72 | −0.178616 | ||||||||
\(761\) | 3.37728e73 | 1.13047 | 0.565234 | − | 0.824931i | \(-0.308786\pi\) | ||||
0.565234 | + | 0.824931i | \(0.308786\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.19876e71 | −0.00375281 | ||||||||
\(764\) | 7.92296e72 | 0.239887 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.02670e73 | −0.857305 | ||||||||
\(767\) | 3.08266e72 | 0.0844587 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.30333e73 | −1.87240 | −0.936202 | − | 0.351464i | \(-0.885684\pi\) | ||||
−0.936202 | + | 0.351464i | \(0.885684\pi\) | |||||||
\(770\) | 2.86813e73 | 0.711353 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.42357e72 | 0.0562619 | ||||||||
\(773\) | −8.48856e73 | −1.90659 | −0.953294 | − | 0.302043i | \(-0.902331\pi\) | ||||
−0.953294 | + | 0.302043i | \(0.902331\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.61146e72 | 0.181085 | ||||||||
\(776\) | 6.41525e73 | 1.30539 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.95638e73 | 1.51613 | ||||||||
\(779\) | 6.15414e72 | 0.113491 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.40398e73 | −0.588012 | ||||||||
\(782\) | −3.18205e73 | −0.532029 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.40363e73 | 0.533190 | ||||||||
\(785\) | 6.29443e73 | 0.954510 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.38760e73 | 0.765667 | 0.382833 | − | 0.923817i | \(-0.374948\pi\) | ||||
0.382833 | + | 0.923817i | \(0.374948\pi\) | |||||||
\(788\) | 8.15252e72 | 0.112169 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.85780e73 | 1.01347 | ||||||||
\(791\) | −7.13843e73 | −0.891461 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.21041e72 | −0.0375919 | ||||||||
\(794\) | 1.91788e73 | 0.217469 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.98703e73 | 0.211311 | ||||||||
\(797\) | 6.28418e73 | 0.647234 | 0.323617 | − | 0.946188i | \(-0.395101\pi\) | ||||
0.323617 | + | 0.946188i | \(0.395101\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.92157e73 | 0.378894 | ||||||||
\(800\) | −1.69809e73 | −0.158915 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.08616e73 | −0.0953776 | ||||||||
\(803\) | 2.62829e74 | 2.23577 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.96425e73 | 0.236657 | ||||||||
\(806\) | −2.89782e73 | −0.224145 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.95045e74 | −1.41627 | ||||||||
\(809\) | −9.71872e73 | −0.683788 | −0.341894 | − | 0.939738i | \(-0.611068\pi\) | ||||
−0.341894 | + | 0.939738i | \(0.611068\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.93558e74 | 1.27873 | 0.639366 | − | 0.768903i | \(-0.279197\pi\) | ||||
0.639366 | + | 0.768903i | \(0.279197\pi\) | |||||||
\(812\) | 2.24412e73 | 0.143671 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.29133e74 | −0.776454 | ||||||||
\(815\) | −2.00254e74 | −1.16698 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.33853e73 | −0.346998 | ||||||||
\(818\) | −5.47088e73 | −0.290300 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.03112e73 | −0.0514112 | ||||||||
\(821\) | 8.81688e73 | 0.426152 | 0.213076 | − | 0.977036i | \(-0.431652\pi\) | ||||
0.213076 | + | 0.977036i | \(0.431652\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.57751e74 | −0.716600 | −0.358300 | − | 0.933606i | \(-0.616644\pi\) | ||||
−0.358300 | + | 0.933606i | \(0.616644\pi\) | |||||||
\(824\) | −2.51861e74 | −1.10922 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.98938e73 | 0.123763 | ||||||||
\(827\) | −4.29357e74 | −1.72357 | −0.861784 | − | 0.507276i | \(-0.830653\pi\) | ||||
−0.861784 | + | 0.507276i | \(0.830653\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.05215e74 | −1.52949 | −0.764743 | − | 0.644336i | \(-0.777134\pi\) | ||||
−0.764743 | + | 0.644336i | \(0.777134\pi\) | |||||||
\(830\) | 3.48996e73 | 0.127741 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.21554e74 | −0.418432 | ||||||||
\(833\) | 1.54365e74 | 0.515350 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.09934e74 | 0.659292 | ||||||||
\(836\) | 1.89638e73 | 0.0577651 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.64431e73 | 0.0757862 | ||||||||
\(839\) | −3.20891e73 | −0.0892128 | −0.0446064 | − | 0.999005i | \(-0.514203\pi\) | ||||
−0.0446064 | + | 0.999005i | \(0.514203\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.27433e74 | 0.333415 | ||||||||
\(842\) | −2.59647e74 | −0.659061 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.71284e72 | −0.00409246 | ||||||||
\(845\) | 2.22606e74 | 0.516049 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.78557e74 | 0.389717 | ||||||||
\(848\) | −8.22542e74 | −1.74206 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.81889e74 | −0.562206 | ||||||||
\(851\) | −1.33461e74 | −0.258315 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.28210e74 | −0.598345 | −0.299172 | − | 0.954199i | \(-0.596711\pi\) | ||||
−0.299172 | + | 0.954199i | \(0.596711\pi\) | |||||||
\(854\) | −3.11327e73 | −0.0550859 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.11768e74 | 0.686391 | ||||||||
\(857\) | 1.05278e75 | 1.70344 | 0.851719 | − | 0.523999i | \(-0.175560\pi\) | ||||
0.851719 | + | 0.523999i | \(0.175560\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.91408e74 | 1.20663 | 0.603316 | − | 0.797502i | \(-0.293846\pi\) | ||||
0.603316 | + | 0.797502i | \(0.293846\pi\) | |||||||
\(860\) | 1.06202e74 | 0.157189 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.35824e74 | −0.468465 | ||||||||
\(863\) | 9.98167e74 | 1.35185 | 0.675924 | − | 0.736971i | \(-0.263745\pi\) | ||||
0.675924 | + | 0.736971i | \(0.263745\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.25567e74 | 0.287982 | ||||||||
\(866\) | −1.88428e74 | −0.233582 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.09219e73 | −0.0478303 | ||||||||
\(869\) | 1.40549e75 | 1.59523 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.63647e73 | 0.0389239 | ||||||||
\(872\) | −4.43856e72 | −0.00461393 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.34590e74 | 0.131969 | ||||||||
\(875\) | 8.20062e74 | 0.780983 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8.86567e73 | 0.0796567 | 0.0398283 | − | 0.999207i | \(-0.487319\pi\) | ||||
0.0398283 | + | 0.999207i | \(0.487319\pi\) | |||||||
\(878\) | −4.09752e74 | −0.357611 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.24838e75 | 1.02811 | ||||||||
\(881\) | 4.12425e74 | 0.329958 | 0.164979 | − | 0.986297i | \(-0.447244\pi\) | ||||
0.164979 | + | 0.986297i | \(0.447244\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.74600e74 | −0.282859 | −0.141429 | − | 0.989948i | \(-0.545170\pi\) | ||||
−0.141429 | + | 0.989948i | \(0.545170\pi\) | |||||||
\(884\) | 1.38134e74 | 0.101337 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.90253e74 | −0.408770 | ||||||||
\(887\) | −7.25014e74 | −0.487859 | −0.243929 | − | 0.969793i | \(-0.578437\pi\) | ||||
−0.243929 | + | 0.969793i | \(0.578437\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.07652e75 | 1.31929 | ||||||||
\(890\) | 4.26534e73 | 0.0263335 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.99868e72 | 0.00116531 | ||||||||
\(893\) | −1.65869e74 | −0.0939840 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.47682e75 | 1.32558 | ||||||||
\(896\) | −1.65219e75 | −0.859423 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.72403e75 | −1.83007 | ||||||||
\(899\) | −9.29336e74 | −0.443916 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.73049e75 | −1.68377 | ||||||||
\(902\) | −1.26651e75 | −0.555701 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.64309e75 | −1.09602 | ||||||||
\(905\) | 2.28007e75 | 0.919198 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.49801e75 | 0.951936 | 0.475968 | − | 0.879463i | \(-0.342098\pi\) | ||||
0.475968 | + | 0.879463i | \(0.342098\pi\) | |||||||
\(908\) | 2.19117e74 | 0.0811871 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −8.83650e74 | −0.309546 | ||||||||
\(911\) | −4.96282e75 | −1.69048 | −0.845240 | − | 0.534387i | \(-0.820543\pi\) | ||||
−0.845240 | + | 0.534387i | \(0.820543\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.24233e74 | 0.201068 | ||||||||
\(914\) | 2.01446e75 | 0.631002 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.90798e74 | −0.204652 | ||||||||
\(917\) | 2.76712e75 | 0.797279 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.27126e74 | 0.225437 | 0.112719 | − | 0.993627i | \(-0.464044\pi\) | ||||
0.112719 | + | 0.993627i | \(0.464044\pi\) | |||||||
\(920\) | 1.09755e75 | 0.290961 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.15317e75 | −0.289238 | ||||||||
\(923\) | 1.04874e75 | 0.255874 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.18229e75 | −0.272967 | ||||||||
\(926\) | −4.45744e75 | −1.00116 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.83255e75 | 0.389567 | ||||||||
\(929\) | −6.26908e75 | −1.29659 | −0.648296 | − | 0.761389i | \(-0.724518\pi\) | ||||
−0.648296 | + | 0.761389i | \(0.724518\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.52913e74 | −0.127832 | ||||||||
\(932\) | −7.96816e74 | −0.151793 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.66501e75 | 0.300311 | ||||||||
\(935\) | 5.66180e75 | 0.993707 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.04271e75 | 0.671913 | 0.335956 | − | 0.941878i | \(-0.390941\pi\) | ||||
0.335956 | + | 0.941878i | \(0.390941\pi\) | |||||||
\(938\) | 3.52643e74 | 0.0570378 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.77914e74 | 0.0425745 | ||||||||
\(941\) | −5.70557e75 | −0.850675 | −0.425337 | − | 0.905035i | \(-0.639845\pi\) | ||||
−0.425337 | + | 0.905035i | \(0.639845\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.30895e75 | −0.184874 | ||||||||
\(944\) | 1.30116e75 | 0.178873 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.30446e76 | 1.69905 | ||||||||
\(947\) | −9.10957e75 | −1.15498 | −0.577489 | − | 0.816399i | \(-0.695967\pi\) | ||||
−0.577489 | + | 0.816399i | \(0.695967\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.09757e75 | −0.972896 | ||||||||
\(950\) | 1.19230e75 | 0.139454 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.51966e75 | −0.722741 | ||||||||
\(953\) | 8.74403e75 | 0.943719 | 0.471859 | − | 0.881674i | \(-0.343583\pi\) | ||||
0.471859 | + | 0.881674i | \(0.343583\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.00051e76 | −1.02361 | ||||||||
\(956\) | 1.70045e75 | 0.169390 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.08245e76 | 1.02232 | ||||||||
\(959\) | −4.62971e75 | −0.425774 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.77225e75 | −0.852213 | ||||||||
\(962\) | 3.97850e75 | 0.337874 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.68646e75 | −0.135835 | ||||||||
\(965\) | −3.06048e75 | −0.240073 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.14685e75 | 0.606198 | 0.303099 | − | 0.952959i | \(-0.401979\pi\) | ||||
0.303099 | + | 0.952959i | \(0.401979\pi\) | |||||||
\(968\) | 6.61129e75 | 0.479143 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 1.66449e76 | 1.14446 | ||||||||
\(971\) | 7.24090e75 | 0.484956 | 0.242478 | − | 0.970157i | \(-0.422040\pi\) | ||||
0.242478 | + | 0.970157i | \(0.422040\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.52781e76 | −0.970940 | ||||||||
\(974\) | 8.44405e75 | 0.522754 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.35508e75 | −0.0796148 | ||||||||
\(977\) | 2.93870e76 | 1.68207 | 0.841034 | − | 0.540982i | \(-0.181947\pi\) | ||||
0.841034 | + | 0.540982i | \(0.181947\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7.62922e74 | 0.0414497 | ||||||||
\(980\) | 1.09395e75 | 0.0579074 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.03423e76 | −0.519725 | ||||||||
\(983\) | −3.52481e76 | −1.72592 | −0.862961 | − | 0.505271i | \(-0.831393\pi\) | ||||
−0.862961 | + | 0.505271i | \(0.831393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.02950e76 | −0.478633 | ||||||||
\(986\) | 3.04210e76 | 1.37820 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.84262e74 | −0.0251365 | ||||||||
\(989\) | 1.34817e76 | 0.565249 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.68555e76 | 0.671218 | 0.335609 | − | 0.942001i | \(-0.391058\pi\) | ||||
0.335609 | + | 0.942001i | \(0.391058\pi\) | |||||||
\(992\) | −3.34169e75 | −0.129693 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.01701e76 | 0.374949 | ||||||||
\(995\) | −2.50922e76 | −0.901676 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.12879e75 | 0.277523 | 0.138762 | − | 0.990326i | \(-0.455688\pi\) | ||||
0.138762 | + | 0.990326i | \(0.455688\pi\) | |||||||
\(998\) | 1.80722e76 | 0.601426 | ||||||||
\(999\) | 0 | 0 |
(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 | 9.52.a.b.1.2 | 4 | ||
3.2 | odd | 2 | 1.52.a.a.1.3 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.52.a.a.1.3 | ✓ | 4 | 3.2 | odd | 2 | ||
9.52.a.b.1.2 | 4 | 1.1 | even | 1 | trivial |