Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9,68,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, 68, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("9.1");
S:= CuspForms(chi, 68);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9 = 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 68 \) |
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: | \(255.861316737\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} + \cdots + 20\!\cdots\!00 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{40}\cdot 3^{20}\cdot 5^{4}\cdot 7^{2}\cdot 11\cdot 13\cdot 17 \) |
Twist minimal: | no (minimal twist has level 1) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-8.99335e8\) 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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.26950e10 | −1.86821 | −0.934105 | − | 0.356999i | \(-0.883800\pi\) | ||||
−0.934105 | + | 0.356999i | \(0.883800\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.67490e20 | 2.49021 | ||||||||
\(5\) | 1.61198e23 | 0.619247 | 0.309623 | − | 0.950859i | \(-0.399797\pi\) | ||||
0.309623 | + | 0.950859i | \(0.399797\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.93806e28 | 1.43641 | 0.718203 | − | 0.695834i | \(-0.244965\pi\) | ||||
0.718203 | + | 0.695834i | \(0.244965\pi\) | |||||||
\(8\) | −4.99099e30 | −2.78402 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.65838e33 | −1.15688 | ||||||||
\(11\) | −1.03989e35 | −1.34999 | −0.674995 | − | 0.737822i | \(-0.735854\pi\) | ||||
−0.674995 | + | 0.737822i | \(0.735854\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.30624e35 | −0.0448407 | −0.0224203 | − | 0.999749i | \(-0.507137\pi\) | ||||
−0.0224203 | + | 0.999749i | \(0.507137\pi\) | |||||||
\(14\) | −6.66794e38 | −2.68351 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.90387e40 | 2.71092 | ||||||||
\(17\) | −2.52116e41 | −1.51901 | −0.759506 | − | 0.650500i | \(-0.774559\pi\) | ||||
−0.759506 | + | 0.650500i | \(0.774559\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.10720e41 | −0.0596074 | −0.0298037 | − | 0.999556i | \(-0.509488\pi\) | ||||
−0.0298037 | + | 0.999556i | \(0.509488\pi\) | |||||||
\(20\) | 5.92385e43 | 1.54205 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.36002e45 | 2.52207 | ||||||||
\(23\) | 7.28152e44 | 0.175525 | 0.0877626 | − | 0.996141i | \(-0.472028\pi\) | ||||
0.0877626 | + | 0.996141i | \(0.472028\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.17779e46 | −0.616533 | ||||||||
\(26\) | 2.11205e46 | 0.0837718 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.07971e49 | 3.57695 | ||||||||
\(29\) | 8.66841e48 | 0.886353 | 0.443176 | − | 0.896434i | \(-0.353852\pi\) | ||||
0.443176 | + | 0.896434i | \(0.353852\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.42697e49 | 0.594211 | 0.297106 | − | 0.954845i | \(-0.403979\pi\) | ||||
0.297106 | + | 0.954845i | \(0.403979\pi\) | |||||||
\(32\) | −6.03344e50 | −2.28056 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 5.72177e51 | 2.83783 | ||||||||
\(35\) | 4.73609e51 | 0.889490 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.44090e52 | 0.712511 | 0.356255 | − | 0.934389i | \(-0.384053\pi\) | ||||
0.356255 | + | 0.934389i | \(0.384053\pi\) | |||||||
\(38\) | 9.32129e51 | 0.111359 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −8.04536e53 | −1.72399 | ||||||||
\(41\) | −8.84851e52 | −0.0829108 | −0.0414554 | − | 0.999140i | \(-0.513199\pi\) | ||||
−0.0414554 | + | 0.999140i | \(0.513199\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.35174e54 | −0.636909 | −0.318455 | − | 0.947938i | \(-0.603164\pi\) | ||||
−0.318455 | + | 0.947938i | \(0.603164\pi\) | |||||||
\(44\) | −3.82147e55 | −3.36176 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.65254e55 | −0.327918 | ||||||||
\(47\) | 1.34362e56 | 1.29718 | 0.648588 | − | 0.761140i | \(-0.275360\pi\) | ||||
0.648588 | + | 0.761140i | \(0.275360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.44845e56 | 1.06326 | ||||||||
\(50\) | 9.48151e56 | 1.15181 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.41995e56 | −0.111663 | ||||||||
\(53\) | 3.87432e57 | 0.668273 | 0.334136 | − | 0.942525i | \(-0.391555\pi\) | ||||
0.334136 | + | 0.942525i | \(0.391555\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.67627e58 | −0.835977 | ||||||||
\(56\) | −1.46639e59 | −3.99898 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.96730e59 | −1.65589 | ||||||||
\(59\) | 2.62052e59 | 1.24407 | 0.622035 | − | 0.782989i | \(-0.286306\pi\) | ||||
0.622035 | + | 0.782989i | \(0.286306\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.77635e59 | −0.742244 | −0.371122 | − | 0.928584i | \(-0.621027\pi\) | ||||
−0.371122 | + | 0.928584i | \(0.621027\pi\) | |||||||
\(62\) | −1.23165e60 | −1.11011 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.98032e60 | 1.54963 | ||||||||
\(65\) | −1.50015e59 | −0.0277674 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.36430e61 | −1.58561 | −0.792805 | − | 0.609476i | \(-0.791380\pi\) | ||||
−0.792805 | + | 0.609476i | \(0.791380\pi\) | |||||||
\(68\) | −9.26500e61 | −3.78265 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.07486e62 | −1.66175 | ||||||||
\(71\) | −2.36087e61 | −0.226943 | −0.113471 | − | 0.993541i | \(-0.536197\pi\) | ||||
−0.113471 | + | 0.993541i | \(0.536197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.86035e61 | 0.297938 | 0.148969 | − | 0.988842i | \(-0.452404\pi\) | ||||
0.148969 | + | 0.988842i | \(0.452404\pi\) | |||||||
\(74\) | −5.53962e62 | −1.33112 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.50935e62 | −0.148435 | ||||||||
\(77\) | −3.05525e63 | −1.93913 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.74602e63 | −0.738237 | −0.369118 | − | 0.929382i | \(-0.620340\pi\) | ||||
−0.369118 | + | 0.929382i | \(0.620340\pi\) | |||||||
\(80\) | 9.51690e63 | 1.67873 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.00817e63 | 0.154895 | ||||||||
\(83\) | −9.16622e63 | −0.471058 | −0.235529 | − | 0.971867i | \(-0.575682\pi\) | ||||
−0.235529 | + | 0.971867i | \(0.575682\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.06405e64 | −0.940643 | ||||||||
\(86\) | 7.60679e64 | 1.18988 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.19006e65 | 3.75840 | ||||||||
\(89\) | 3.36134e65 | 1.66704 | 0.833521 | − | 0.552488i | \(-0.186321\pi\) | ||||
0.833521 | + | 0.552488i | \(0.186321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.73423e64 | −0.0644094 | ||||||||
\(92\) | 2.67588e65 | 0.437094 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.04935e66 | −2.42340 | ||||||||
\(95\) | −6.62071e64 | −0.0369117 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.50306e66 | 1.80412 | 0.902059 | − | 0.431614i | \(-0.142056\pi\) | ||||
0.902059 | + | 0.431614i | \(0.142056\pi\) | |||||||
\(98\) | −1.00958e67 | −1.98639 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.53530e67 | −1.53530 | ||||||||
\(101\) | −1.99950e67 | −1.43270 | −0.716352 | − | 0.697739i | \(-0.754189\pi\) | ||||
−0.716352 | + | 0.697739i | \(0.754189\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.01461e67 | 0.748417 | 0.374209 | − | 0.927345i | \(-0.377914\pi\) | ||||
0.374209 | + | 0.927345i | \(0.377914\pi\) | |||||||
\(104\) | 4.64474e66 | 0.124837 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.79277e67 | −1.24847 | ||||||||
\(107\) | 3.65427e67 | 0.378830 | 0.189415 | − | 0.981897i | \(-0.439341\pi\) | ||||
0.189415 | + | 0.981897i | \(0.439341\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.60552e67 | −0.312484 | −0.156242 | − | 0.987719i | \(-0.549938\pi\) | ||||
−0.156242 | + | 0.987719i | \(0.549938\pi\) | |||||||
\(110\) | 3.80430e68 | 1.56178 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.73460e69 | 3.89399 | ||||||||
\(113\) | 9.31318e66 | 0.0155228 | 0.00776140 | − | 0.999970i | \(-0.497529\pi\) | ||||
0.00776140 | + | 0.999970i | \(0.497529\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.17376e68 | 0.108693 | ||||||||
\(116\) | 3.18555e69 | 2.20720 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −5.94727e69 | −2.32418 | ||||||||
\(119\) | −7.40733e69 | −2.18192 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.88014e69 | 0.822474 | ||||||||
\(122\) | 1.08399e70 | 1.38667 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.99436e70 | 1.47971 | ||||||||
\(125\) | −1.76577e70 | −1.00103 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.79868e70 | 0.932243 | 0.466121 | − | 0.884721i | \(-0.345651\pi\) | ||||
0.466121 | + | 0.884721i | \(0.345651\pi\) | |||||||
\(128\) | −2.39907e70 | −0.614480 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.40458e69 | 0.0518754 | ||||||||
\(131\) | 2.72280e70 | 0.320943 | 0.160471 | − | 0.987040i | \(-0.448699\pi\) | ||||
0.160471 | + | 0.987040i | \(0.448699\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.20672e70 | −0.0856204 | ||||||||
\(134\) | 5.36578e71 | 2.96225 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.25831e72 | 4.22896 | ||||||||
\(137\) | −3.57817e70 | −0.0940853 | −0.0470427 | − | 0.998893i | \(-0.514980\pi\) | ||||
−0.0470427 | + | 0.998893i | \(0.514980\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.45641e71 | 1.20652 | 0.603259 | − | 0.797545i | \(-0.293869\pi\) | ||||
0.603259 | + | 0.797545i | \(0.293869\pi\) | |||||||
\(140\) | 1.74047e72 | 2.21501 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 5.35799e71 | 0.423977 | ||||||||
\(143\) | 9.67743e70 | 0.0605345 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.39733e72 | 0.548871 | ||||||||
\(146\) | −1.78391e72 | −0.556611 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 8.97004e72 | 1.77430 | ||||||||
\(149\) | −1.30102e72 | −0.205373 | −0.102686 | − | 0.994714i | \(-0.532744\pi\) | ||||
−0.102686 | + | 0.994714i | \(0.532744\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.36349e73 | −1.37697 | −0.688486 | − | 0.725250i | \(-0.741724\pi\) | ||||
−0.688486 | + | 0.725250i | \(0.741724\pi\) | |||||||
\(152\) | 2.04990e72 | 0.165948 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 6.93390e73 | 3.62271 | ||||||||
\(155\) | 8.74816e72 | 0.367963 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.66635e73 | −0.456171 | −0.228085 | − | 0.973641i | \(-0.573247\pi\) | ||||
−0.228085 | + | 0.973641i | \(0.573247\pi\) | |||||||
\(158\) | 6.23209e73 | 1.37918 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −9.72577e73 | −1.41223 | ||||||||
\(161\) | 2.13936e73 | 0.252125 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.35739e70 | −0.000729239 0 | −0.000364620 | − | 1.00000i | \(-0.500116\pi\) | ||||
−0.000364620 | 1.00000i | \(0.500116\pi\) | ||||||||
\(164\) | −3.25174e73 | −0.206465 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.08027e74 | 0.880035 | ||||||||
\(167\) | −4.79288e74 | −1.65804 | −0.829019 | − | 0.559220i | \(-0.811101\pi\) | ||||
−0.829019 | + | 0.559220i | \(0.811101\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.29863e74 | −0.997989 | ||||||||
\(170\) | 9.22337e74 | 1.75732 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.23173e75 | −1.58604 | ||||||||
\(173\) | −1.22221e75 | −1.29599 | −0.647995 | − | 0.761645i | \(-0.724392\pi\) | ||||
−0.647995 | + | 0.761645i | \(0.724392\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.22746e75 | −0.885592 | ||||||||
\(176\) | −6.13935e75 | −3.65972 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −7.62856e75 | −3.11438 | ||||||||
\(179\) | 1.85195e75 | 0.626689 | 0.313344 | − | 0.949640i | \(-0.398551\pi\) | ||||
0.313344 | + | 0.949640i | \(0.398551\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.04550e75 | 0.943497 | 0.471748 | − | 0.881733i | \(-0.343623\pi\) | ||||
0.471748 | + | 0.881733i | \(0.343623\pi\) | |||||||
\(182\) | 6.20535e74 | 0.120330 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.63420e75 | −0.488666 | ||||||||
\(185\) | 3.93467e75 | 0.441220 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.62172e76 | 2.05065 | ||||||||
\(188\) | 4.93767e76 | 3.23024 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.50257e75 | 0.0689587 | ||||||||
\(191\) | −8.00578e74 | −0.0308167 | −0.0154083 | − | 0.999881i | \(-0.504905\pi\) | ||||
−0.0154083 | + | 0.999881i | \(0.504905\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.34503e76 | −1.45138 | −0.725688 | − | 0.688024i | \(-0.758478\pi\) | ||||
−0.725688 | + | 0.688024i | \(0.758478\pi\) | |||||||
\(194\) | −1.47587e77 | −3.37047 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.63476e77 | 2.64774 | ||||||||
\(197\) | −2.95191e75 | −0.0403166 | −0.0201583 | − | 0.999797i | \(-0.506417\pi\) | ||||
−0.0201583 | + | 0.999797i | \(0.506417\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.57308e77 | −1.53170 | −0.765850 | − | 0.643019i | \(-0.777682\pi\) | ||||
−0.765850 | + | 0.643019i | \(0.777682\pi\) | |||||||
\(200\) | 2.08513e77 | 1.71644 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.53788e77 | 2.67659 | ||||||||
\(203\) | 2.54684e77 | 1.27316 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.42636e76 | −0.0513422 | ||||||||
\(206\) | −4.57216e77 | −1.39820 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −5.49428e76 | −0.121560 | ||||||||
\(209\) | 4.27102e76 | 0.0804694 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.28985e77 | 1.27217 | 0.636087 | − | 0.771618i | \(-0.280552\pi\) | ||||
0.636087 | + | 0.771618i | \(0.280552\pi\) | |||||||
\(212\) | 1.42377e78 | 1.66414 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.29337e77 | −0.707734 | ||||||||
\(215\) | −5.40294e77 | −0.394404 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.59448e78 | 0.853528 | ||||||||
\(218\) | 1.27217e78 | 0.583786 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.16013e78 | −2.08176 | ||||||||
\(221\) | 2.34625e77 | 0.0681135 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.42241e78 | −1.37875 | −0.689374 | − | 0.724406i | \(-0.742114\pi\) | ||||
−0.689374 | + | 0.724406i | \(0.742114\pi\) | |||||||
\(224\) | −1.77266e79 | −3.27580 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.11363e77 | −0.0289999 | ||||||||
\(227\) | −1.17887e79 | −1.39509 | −0.697543 | − | 0.716543i | \(-0.745723\pi\) | ||||
−0.697543 | + | 0.716543i | \(0.745723\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.55534e79 | −1.37194 | −0.685972 | − | 0.727628i | \(-0.740623\pi\) | ||||
−0.685972 | + | 0.727628i | \(0.740623\pi\) | |||||||
\(230\) | −2.66386e78 | −0.203062 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.32640e79 | −2.46762 | ||||||||
\(233\) | −1.81926e79 | −0.898403 | −0.449201 | − | 0.893431i | \(-0.648291\pi\) | ||||
−0.449201 | + | 0.893431i | \(0.648291\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.16589e79 | 0.803272 | ||||||||
\(236\) | 9.63014e79 | 3.09799 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.68109e80 | 4.07628 | ||||||||
\(239\) | 2.13612e79 | 0.450087 | 0.225043 | − | 0.974349i | \(-0.427748\pi\) | ||||
0.225043 | + | 0.974349i | \(0.427748\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.27834e79 | −0.522497 | −0.261248 | − | 0.965272i | \(-0.584134\pi\) | ||||
−0.261248 | + | 0.965272i | \(0.584134\pi\) | |||||||
\(242\) | −1.10755e80 | −1.53655 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.75526e80 | −1.84834 | ||||||||
\(245\) | 7.17080e79 | 0.658421 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.82226e77 | 0.00267283 | ||||||||
\(248\) | −2.70860e80 | −1.65430 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.00742e80 | 1.87014 | ||||||||
\(251\) | 2.97257e80 | 1.21356 | 0.606782 | − | 0.794868i | \(-0.292460\pi\) | ||||
0.606782 | + | 0.794868i | \(0.292460\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −7.57195e79 | −0.236957 | ||||||||
\(254\) | −6.35161e80 | −1.74162 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.90498e80 | −0.401653 | ||||||||
\(257\) | −2.91395e80 | −0.539166 | −0.269583 | − | 0.962977i | \(-0.586886\pi\) | ||||
−0.269583 | + | 0.962977i | \(0.586886\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.17151e80 | 1.02345 | ||||||||
\(260\) | −5.51288e79 | −0.0691467 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.17940e80 | −0.599588 | ||||||||
\(263\) | −8.50029e79 | −0.0725966 | −0.0362983 | − | 0.999341i | \(-0.511557\pi\) | ||||
−0.0362983 | + | 0.999341i | \(0.511557\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.24531e80 | 0.413826 | ||||||||
\(266\) | 2.73866e80 | 0.159957 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −8.68855e81 | −3.94850 | ||||||||
\(269\) | 1.19177e81 | 0.478070 | 0.239035 | − | 0.971011i | \(-0.423169\pi\) | ||||
0.239035 | + | 0.971011i | \(0.423169\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.56294e81 | 1.11516 | 0.557580 | − | 0.830123i | \(-0.311730\pi\) | ||||
0.557580 | + | 0.830123i | \(0.311730\pi\) | |||||||
\(272\) | −1.48846e82 | −4.11793 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8.12066e80 | 0.175771 | ||||||||
\(275\) | 4.34443e81 | 0.832314 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.14305e82 | −1.71787 | −0.858937 | − | 0.512081i | \(-0.828875\pi\) | ||||
−0.858937 | + | 0.512081i | \(0.828875\pi\) | |||||||
\(278\) | −1.69223e82 | −2.25403 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.36378e82 | −2.47636 | ||||||||
\(281\) | −1.56122e82 | −1.45145 | −0.725727 | − | 0.687983i | \(-0.758496\pi\) | ||||
−0.725727 | + | 0.687983i | \(0.758496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.49072e81 | −0.695751 | −0.347875 | − | 0.937541i | \(-0.613097\pi\) | ||||
−0.347875 | + | 0.937541i | \(0.613097\pi\) | |||||||
\(284\) | −8.67594e81 | −0.565135 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.19629e81 | −0.113091 | ||||||||
\(287\) | −2.59975e81 | −0.119094 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.60152e82 | 1.30740 | ||||||||
\(290\) | −3.17124e82 | −1.02541 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.88860e82 | 0.741928 | ||||||||
\(293\) | 8.72184e82 | 1.99776 | 0.998879 | − | 0.0473268i | \(-0.0150702\pi\) | ||||
0.998879 | + | 0.0473268i | \(0.0150702\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.22422e82 | 0.770387 | ||||||||
\(296\) | −1.21825e83 | −1.98364 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.95266e82 | 0.383679 | ||||||||
\(299\) | −6.77636e80 | −0.00787067 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.84764e82 | −0.914860 | ||||||||
\(302\) | 3.09445e83 | 2.57247 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −2.42484e82 | −0.161591 | ||||||||
\(305\) | −7.69937e82 | −0.459632 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.53054e83 | 0.734021 | 0.367010 | − | 0.930217i | \(-0.380381\pi\) | ||||
0.367010 | + | 0.930217i | \(0.380381\pi\) | |||||||
\(308\) | −1.12277e84 | −4.82884 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.98540e83 | −0.687433 | ||||||||
\(311\) | 5.46579e82 | 0.169895 | 0.0849473 | − | 0.996385i | \(-0.472928\pi\) | ||||
0.0849473 | + | 0.996385i | \(0.472928\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.36258e83 | 0.843214 | 0.421607 | − | 0.906779i | \(-0.361466\pi\) | ||||
0.421607 | + | 0.906779i | \(0.361466\pi\) | |||||||
\(314\) | 3.78178e83 | 0.852222 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.00913e84 | −1.83836 | ||||||||
\(317\) | −6.50933e83 | −1.06672 | −0.533360 | − | 0.845888i | \(-0.679071\pi\) | ||||
−0.533360 | + | 0.845888i | \(0.679071\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.01416e83 | −1.19657 | ||||||||
\(320\) | 8.02817e83 | 0.959604 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.85528e83 | −0.471023 | ||||||||
\(323\) | 1.03549e83 | 0.0905443 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.88796e82 | 0.0276458 | ||||||||
\(326\) | 2.12366e81 | 0.00136237 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.41628e83 | 0.230825 | ||||||||
\(329\) | 3.94765e84 | 1.86327 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.75141e84 | −1.06003 | −0.530014 | − | 0.847989i | \(-0.677813\pi\) | ||||
−0.530014 | + | 0.847989i | \(0.677813\pi\) | |||||||
\(332\) | −3.36849e84 | −1.17303 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.08774e85 | 3.09756 | ||||||||
\(335\) | −3.81119e84 | −0.981883 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.52892e83 | 0.180008 | 0.0900041 | − | 0.995941i | \(-0.471312\pi\) | ||||
0.0900041 | + | 0.995941i | \(0.471312\pi\) | |||||||
\(338\) | 9.75576e84 | 1.86445 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.49350e85 | −2.34240 | ||||||||
\(341\) | −5.64343e84 | −0.802180 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.77614e83 | 0.0908681 | ||||||||
\(344\) | 1.67285e85 | 1.77317 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.77381e85 | 2.42118 | ||||||||
\(347\) | −1.21189e84 | −0.0960340 | −0.0480170 | − | 0.998847i | \(-0.515290\pi\) | ||||
−0.0480170 | + | 0.998847i | \(0.515290\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.49172e85 | 0.975067 | 0.487534 | − | 0.873104i | \(-0.337897\pi\) | ||||
0.487534 | + | 0.873104i | \(0.337897\pi\) | |||||||
\(350\) | 2.78573e85 | 1.65447 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.27409e85 | 3.07873 | ||||||||
\(353\) | −3.26597e84 | −0.145734 | −0.0728668 | − | 0.997342i | \(-0.523215\pi\) | ||||
−0.0728668 | + | 0.997342i | \(0.523215\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.80566e84 | −0.140534 | ||||||||
\(356\) | 1.23526e86 | 4.15128 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.20300e85 | −1.17079 | ||||||||
\(359\) | −2.09151e85 | −0.530636 | −0.265318 | − | 0.964161i | \(-0.585477\pi\) | ||||
−0.265318 | + | 0.964161i | \(0.585477\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.73092e85 | −0.996447 | ||||||||
\(362\) | −9.18128e85 | −1.76265 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.00480e85 | −0.160393 | ||||||||
\(365\) | 1.26707e85 | 0.184497 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.55910e85 | 0.916552 | 0.458276 | − | 0.888810i | \(-0.348467\pi\) | ||||
0.458276 | + | 0.888810i | \(0.348467\pi\) | |||||||
\(368\) | 4.29892e85 | 0.475836 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −8.92974e85 | −0.824292 | ||||||||
\(371\) | 1.13830e86 | 0.959911 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.75561e86 | 1.23647 | 0.618233 | − | 0.785995i | \(-0.287849\pi\) | ||||
0.618233 | + | 0.785995i | \(0.287849\pi\) | |||||||
\(374\) | −5.94999e86 | −3.83105 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −6.70600e86 | −3.61136 | ||||||||
\(377\) | −8.06703e84 | −0.0397446 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.06583e86 | −0.852475 | −0.426237 | − | 0.904611i | \(-0.640161\pi\) | ||||
−0.426237 | + | 0.904611i | \(0.640161\pi\) | |||||||
\(380\) | −2.43304e85 | −0.0919177 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.81691e85 | 0.0575720 | ||||||||
\(383\) | −1.50230e86 | −0.436111 | −0.218055 | − | 0.975936i | \(-0.569971\pi\) | ||||
−0.218055 | + | 0.975936i | \(0.569971\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.92500e86 | −1.20080 | ||||||||
\(386\) | 1.21305e87 | 2.71147 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 2.38981e87 | 4.49263 | ||||||||
\(389\) | 6.44644e86 | 1.11175 | 0.555876 | − | 0.831265i | \(-0.312383\pi\) | ||||
0.555876 | + | 0.831265i | \(0.312383\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.83579e86 | −0.266625 | ||||||||
\(392\) | −2.22022e87 | −2.96014 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.69936e85 | 0.0753199 | ||||||||
\(395\) | −4.42652e86 | −0.457151 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.17131e87 | 1.02139 | 0.510694 | − | 0.859762i | \(-0.329388\pi\) | ||||
0.510694 | + | 0.859762i | \(0.329388\pi\) | |||||||
\(398\) | 3.57012e87 | 2.86154 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.46651e87 | −1.67138 | ||||||||
\(401\) | −2.38898e87 | −1.48894 | −0.744469 | − | 0.667657i | \(-0.767297\pi\) | ||||
−0.744469 | + | 0.667657i | \(0.767297\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.05047e85 | −0.0266448 | ||||||||
\(404\) | −7.34797e87 | −3.56773 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.78005e87 | −2.37853 | ||||||||
\(407\) | −2.53825e87 | −0.961883 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.85528e87 | 0.918159 | 0.459079 | − | 0.888395i | \(-0.348179\pi\) | ||||
0.459079 | + | 0.888395i | \(0.348179\pi\) | |||||||
\(410\) | 3.23713e86 | 0.0959181 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.40348e87 | 1.86371 | ||||||||
\(413\) | 7.69926e87 | 1.78699 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.47757e87 | −0.291701 | ||||||||
\(416\) | 5.61486e86 | 0.102262 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −9.69308e86 | −0.150334 | ||||||||
\(419\) | 3.71561e87 | 0.531937 | 0.265969 | − | 0.963982i | \(-0.414308\pi\) | ||||
0.265969 | + | 0.963982i | \(0.414308\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.25851e87 | −1.00798 | −0.503990 | − | 0.863710i | \(-0.668135\pi\) | ||||
−0.503990 | + | 0.863710i | \(0.668135\pi\) | |||||||
\(422\) | −2.10833e88 | −2.37669 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.93367e88 | −1.86048 | ||||||||
\(425\) | 1.05329e88 | 0.936522 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.40332e88 | −1.06616 | ||||||||
\(428\) | 1.34291e88 | 0.943365 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.22620e88 | 0.736830 | ||||||||
\(431\) | −2.02458e88 | −1.12550 | −0.562750 | − | 0.826627i | \(-0.690257\pi\) | ||||
−0.562750 | + | 0.826627i | \(0.690257\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.20914e88 | 1.05167 | 0.525835 | − | 0.850587i | \(-0.323753\pi\) | ||||
0.525835 | + | 0.850587i | \(0.323753\pi\) | |||||||
\(434\) | −3.61867e88 | −1.59457 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.05997e88 | −0.778151 | ||||||||
\(437\) | −2.99067e86 | −0.0104626 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.98644e86 | 0.0149703 | 0.00748513 | − | 0.999972i | \(-0.497617\pi\) | ||||
0.00748513 | + | 0.999972i | \(0.497617\pi\) | |||||||
\(440\) | 8.36626e88 | 2.32738 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.32482e87 | −0.127250 | ||||||||
\(443\) | −4.20816e88 | −0.932324 | −0.466162 | − | 0.884699i | \(-0.654364\pi\) | ||||
−0.466162 | + | 0.884699i | \(0.654364\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.41840e88 | 1.03231 | ||||||||
\(446\) | 1.45757e89 | 2.57579 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.46325e89 | 2.22590 | ||||||||
\(449\) | 5.36803e88 | 0.757814 | 0.378907 | − | 0.925435i | \(-0.376300\pi\) | ||||
0.378907 | + | 0.925435i | \(0.376300\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.20144e87 | 0.111929 | ||||||||
\(452\) | 3.42250e87 | 0.0386550 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.67546e89 | 2.60631 | ||||||||
\(455\) | −4.40752e87 | −0.0398853 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.47901e89 | −1.93680 | −0.968401 | − | 0.249399i | \(-0.919767\pi\) | ||||
−0.968401 | + | 0.249399i | \(0.919767\pi\) | |||||||
\(458\) | 3.52984e89 | 2.56308 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.31347e88 | 0.270669 | ||||||||
\(461\) | −1.39269e89 | −0.812593 | −0.406297 | − | 0.913741i | \(-0.633180\pi\) | ||||
−0.406297 | + | 0.913741i | \(0.633180\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.69968e89 | 1.36254 | 0.681271 | − | 0.732032i | \(-0.261428\pi\) | ||||
0.681271 | + | 0.732032i | \(0.261428\pi\) | |||||||
\(464\) | 5.11772e89 | 2.40283 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 4.12881e89 | 1.67840 | ||||||||
\(467\) | −3.76688e89 | −1.42517 | −0.712584 | − | 0.701586i | \(-0.752475\pi\) | ||||
−0.712584 | + | 0.701586i | \(0.752475\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.94646e89 | −2.27758 | ||||||||
\(470\) | −4.91549e89 | −1.50068 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.30790e90 | −3.46352 | ||||||||
\(473\) | 3.48543e89 | 0.859822 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.71590e88 | 0.0367499 | ||||||||
\(476\) | −2.72212e90 | −5.43343 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.84793e89 | −0.840857 | ||||||||
\(479\) | 6.97444e89 | 1.12790 | 0.563949 | − | 0.825810i | \(-0.309282\pi\) | ||||
0.563949 | + | 0.825810i | \(0.309282\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.27156e88 | −0.0319495 | ||||||||
\(482\) | 7.44020e89 | 0.976133 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.79340e90 | 2.04813 | ||||||||
\(485\) | 1.04828e90 | 1.11719 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.50021e89 | 0.232143 | 0.116072 | − | 0.993241i | \(-0.462970\pi\) | ||||
0.116072 | + | 0.993241i | \(0.462970\pi\) | |||||||
\(488\) | 2.38387e90 | 2.06642 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.62741e90 | −1.23007 | ||||||||
\(491\) | −2.37132e90 | −1.67402 | −0.837009 | − | 0.547189i | \(-0.815698\pi\) | ||||
−0.837009 | + | 0.547189i | \(0.815698\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.18544e90 | −1.34638 | ||||||||
\(494\) | −8.67462e87 | −0.00499341 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.20401e90 | 1.61086 | ||||||||
\(497\) | −6.93638e89 | −0.325982 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.70263e90 | 1.52104 | 0.760522 | − | 0.649312i | \(-0.224943\pi\) | ||||
0.760522 | + | 0.649312i | \(0.224943\pi\) | |||||||
\(500\) | −6.48902e90 | −2.49278 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.74626e90 | −2.26719 | ||||||||
\(503\) | −3.39121e90 | −1.06617 | −0.533086 | − | 0.846061i | \(-0.678968\pi\) | ||||
−0.533086 | + | 0.846061i | \(0.678968\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.22316e90 | −0.887197 | ||||||||
\(506\) | 1.71846e90 | 0.442686 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.02849e91 | 2.32148 | ||||||||
\(509\) | 6.34938e89 | 0.134179 | 0.0670897 | − | 0.997747i | \(-0.478629\pi\) | ||||
0.0670897 | + | 0.997747i | \(0.478629\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.30942e90 | 0.427960 | ||||||||
\(512\) | 7.86374e90 | 1.36485 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 6.61321e90 | 1.00727 | ||||||||
\(515\) | 3.24750e90 | 0.463455 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.39721e91 | −1.75117 | ||||||||
\(518\) | −1.62758e91 | −1.91203 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 7.48721e89 | 0.0773051 | ||||||||
\(521\) | 6.72297e90 | 0.650874 | 0.325437 | − | 0.945564i | \(-0.394489\pi\) | ||||
0.325437 | + | 0.945564i | \(0.394489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.61652e90 | −0.307953 | −0.153977 | − | 0.988075i | \(-0.549208\pi\) | ||||
−0.153977 | + | 0.988075i | \(0.549208\pi\) | |||||||
\(524\) | 1.00060e91 | 0.799214 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.92914e90 | 0.135626 | ||||||||
\(527\) | −1.36823e91 | −0.902614 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.66792e91 | −0.969191 | ||||||||
\(530\) | −1.41738e91 | −0.773113 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.43458e90 | −0.213212 | ||||||||
\(533\) | 8.23464e88 | 0.00371777 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.89060e90 | 0.234589 | ||||||||
\(536\) | 1.18002e92 | 4.41437 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.70473e91 | −0.893135 | ||||||||
\(539\) | −4.62588e91 | −1.43539 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.31972e91 | −1.45808 | −0.729039 | − | 0.684472i | \(-0.760033\pi\) | ||||
−0.729039 | + | 0.684472i | \(0.760033\pi\) | |||||||
\(542\) | −8.08610e91 | −2.08335 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.52113e92 | 3.46419 | ||||||||
\(545\) | −9.03597e90 | −0.193505 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.75688e90 | −0.0332788 | −0.0166394 | − | 0.999862i | \(-0.505297\pi\) | ||||
−0.0166394 | + | 0.999862i | \(0.505297\pi\) | |||||||
\(548\) | −1.31494e91 | −0.234292 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.85968e91 | −1.55494 | ||||||||
\(551\) | −3.56029e90 | −0.0528331 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.06798e91 | −1.06041 | ||||||||
\(554\) | 2.59414e92 | 3.20935 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.74015e92 | 3.00448 | ||||||||
\(557\) | −4.64449e91 | −0.479500 | −0.239750 | − | 0.970835i | \(-0.577065\pi\) | ||||
−0.239750 | + | 0.970835i | \(0.577065\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.11921e90 | 0.0285594 | ||||||||
\(560\) | 2.79613e92 | 2.41134 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.54320e92 | 2.71162 | ||||||||
\(563\) | −8.66238e90 | −0.0624606 | −0.0312303 | − | 0.999512i | \(-0.509943\pi\) | ||||
−0.0312303 | + | 0.999512i | \(0.509943\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.50126e90 | 0.00961245 | ||||||||
\(566\) | 2.15392e92 | 1.29981 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.17831e92 | 0.631813 | ||||||||
\(569\) | −1.65010e92 | −0.834162 | −0.417081 | − | 0.908869i | \(-0.636947\pi\) | ||||
−0.417081 | + | 0.908869i | \(0.636947\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.09486e92 | −1.39101 | −0.695507 | − | 0.718519i | \(-0.744820\pi\) | ||||
−0.695507 | + | 0.718519i | \(0.744820\pi\) | |||||||
\(572\) | 3.55636e91 | 0.150743 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.90014e91 | 0.222492 | ||||||||
\(575\) | −3.04207e91 | −0.108217 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.88740e92 | −1.54771 | −0.773853 | − | 0.633366i | \(-0.781673\pi\) | ||||
−0.773853 | + | 0.633366i | \(0.781673\pi\) | |||||||
\(578\) | −8.17365e92 | −2.44249 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.13504e92 | 1.36680 | ||||||||
\(581\) | −2.69309e92 | −0.676630 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.02885e92 | −0.902162 | ||||||||
\(584\) | −3.92310e92 | −0.829466 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.97942e93 | −3.73223 | ||||||||
\(587\) | 4.93586e92 | 0.878995 | 0.439498 | − | 0.898244i | \(-0.355157\pi\) | ||||
0.439498 | + | 0.898244i | \(0.355157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.22896e91 | −0.0354194 | ||||||||
\(590\) | −9.58687e92 | −1.43924 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.44107e93 | 1.93156 | ||||||||
\(593\) | −8.91235e92 | −1.12891 | −0.564456 | − | 0.825463i | \(-0.690914\pi\) | ||||
−0.564456 | + | 0.825463i | \(0.690914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.19404e93 | −1.35115 | ||||||||
\(596\) | −4.78110e92 | −0.511420 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1.53790e91 | 0.0147041 | ||||||||
\(599\) | −1.27437e92 | −0.115212 | −0.0576059 | − | 0.998339i | \(-0.518347\pi\) | ||||
−0.0576059 | + | 0.998339i | \(0.518347\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.93861e93 | 1.56746 | 0.783728 | − | 0.621104i | \(-0.213316\pi\) | ||||
0.783728 | + | 0.621104i | \(0.213316\pi\) | |||||||
\(602\) | 2.23492e93 | 1.70915 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.01069e93 | −3.42894 | ||||||||
\(605\) | 7.86668e92 | 0.509315 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.21833e92 | 0.244523 | 0.122261 | − | 0.992498i | \(-0.460985\pi\) | ||||
0.122261 | + | 0.992498i | \(0.460985\pi\) | |||||||
\(608\) | 2.47805e92 | 0.135938 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.74737e93 | 0.858690 | ||||||||
\(611\) | −1.25041e92 | −0.0581662 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.48939e92 | −0.353957 | −0.176979 | − | 0.984215i | \(-0.556632\pi\) | ||||
−0.176979 | + | 0.984215i | \(0.556632\pi\) | |||||||
\(614\) | −3.47356e93 | −1.37130 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.52487e94 | 5.39859 | ||||||||
\(617\) | −5.31064e93 | −1.78071 | −0.890357 | − | 0.455263i | \(-0.849545\pi\) | ||||
−0.890357 | + | 0.455263i | \(0.849545\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.93673e93 | −1.78612 | −0.893060 | − | 0.449937i | \(-0.851446\pi\) | ||||
−0.893060 | + | 0.449937i | \(0.851446\pi\) | |||||||
\(620\) | 3.21486e93 | 0.916305 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.24046e93 | −0.317399 | ||||||||
\(623\) | 9.87582e93 | 2.39455 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.53972e91 | −0.00335322 | ||||||||
\(626\) | −7.63139e93 | −1.57530 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.12366e93 | −1.13596 | ||||||||
\(629\) | −6.15389e93 | −1.08231 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.19002e93 | −0.662572 | −0.331286 | − | 0.943530i | \(-0.607482\pi\) | ||||
−0.331286 | + | 0.943530i | \(0.607482\pi\) | |||||||
\(632\) | 1.37053e94 | 2.05527 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.47729e94 | 1.99286 | ||||||||
\(635\) | 4.51141e93 | 0.577288 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −4.13983e92 | −0.0476773 | ||||||||
\(638\) | 2.04576e94 | 2.23544 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.86724e93 | −0.380515 | ||||||||
\(641\) | −1.17710e94 | −1.09919 | −0.549593 | − | 0.835433i | \(-0.685217\pi\) | ||||
−0.549593 | + | 0.835433i | \(0.685217\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.15010e94 | 1.80880 | 0.904400 | − | 0.426686i | \(-0.140319\pi\) | ||||
0.904400 | + | 0.426686i | \(0.140319\pi\) | |||||||
\(644\) | 7.86192e93 | 0.627845 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.35004e93 | −0.169156 | ||||||||
\(647\) | 5.59785e93 | 0.382585 | 0.191292 | − | 0.981533i | \(-0.438732\pi\) | ||||
0.191292 | + | 0.981533i | \(0.438732\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.72504e94 | −1.67948 | ||||||||
\(650\) | −8.82372e92 | −0.0516481 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.43875e91 | −0.00181596 | ||||||||
\(653\) | −3.65193e94 | −1.83202 | −0.916012 | − | 0.401150i | \(-0.868611\pi\) | ||||
−0.916012 | + | 0.401150i | \(0.868611\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.38909e93 | 0.198743 | ||||||||
\(656\) | −5.22405e93 | −0.224765 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −8.95919e94 | −3.48098 | ||||||||
\(659\) | 2.31946e94 | 0.856497 | 0.428249 | − | 0.903661i | \(-0.359131\pi\) | ||||
0.428249 | + | 0.903661i | \(0.359131\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.29957e94 | 0.433563 | 0.216782 | − | 0.976220i | \(-0.430444\pi\) | ||||
0.216782 | + | 0.976220i | \(0.430444\pi\) | |||||||
\(662\) | 6.24433e94 | 1.98035 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.57485e94 | 1.31143 | ||||||||
\(665\) | −1.94521e93 | −0.0530201 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.31192e93 | 0.155577 | ||||||||
\(668\) | −1.76133e95 | −4.12886 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.64951e94 | 1.83436 | ||||||||
\(671\) | 4.96686e94 | 1.00202 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.32902e94 | 0.607872 | 0.303936 | − | 0.952693i | \(-0.401699\pi\) | ||||
0.303936 | + | 0.952693i | \(0.401699\pi\) | |||||||
\(674\) | −1.93564e94 | −0.336293 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.57970e95 | −2.48520 | ||||||||
\(677\) | 7.15153e94 | 1.07073 | 0.535364 | − | 0.844622i | \(-0.320175\pi\) | ||||
0.535364 | + | 0.844622i | \(0.320175\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.91064e95 | 2.59144 | ||||||||
\(680\) | 2.02836e95 | 2.61877 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.28078e95 | 1.49864 | ||||||||
\(683\) | 4.63147e94 | 0.515971 | 0.257985 | − | 0.966149i | \(-0.416941\pi\) | ||||
0.257985 | + | 0.966149i | \(0.416941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.76793e93 | −0.0582620 | ||||||||
\(686\) | −1.76480e94 | −0.169761 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.97883e95 | −1.72661 | ||||||||
\(689\) | −3.60554e93 | −0.0299658 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.93163e94 | 0.296523 | 0.148261 | − | 0.988948i | \(-0.452632\pi\) | ||||
0.148261 | + | 0.988948i | \(0.452632\pi\) | |||||||
\(692\) | −4.49150e95 | −3.22728 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.75038e94 | 0.179412 | ||||||||
\(695\) | 1.20196e95 | 0.747132 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.23085e94 | 0.125942 | ||||||||
\(698\) | −3.38545e95 | −1.82163 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.51080e95 | −2.20531 | ||||||||
\(701\) | 2.12972e95 | 0.992588 | 0.496294 | − | 0.868154i | \(-0.334694\pi\) | ||||
0.496294 | + | 0.868154i | \(0.334694\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.00252e94 | −0.0424709 | ||||||||
\(704\) | −5.17897e95 | −2.09199 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.41213e94 | 0.272261 | ||||||||
\(707\) | −5.87467e95 | −2.05794 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.82912e94 | −0.153893 | −0.0769466 | − | 0.997035i | \(-0.524517\pi\) | ||||
−0.0769466 | + | 0.997035i | \(0.524517\pi\) | |||||||
\(710\) | 8.63695e94 | 0.262546 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −1.67764e96 | −4.64108 | ||||||||
\(713\) | 3.95166e94 | 0.104299 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.55998e94 | 0.0374858 | ||||||||
\(716\) | 6.80571e95 | 1.56059 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.74669e95 | 0.991339 | ||||||||
\(719\) | 3.57892e93 | 0.00713401 | 0.00356700 | − | 0.999994i | \(-0.498865\pi\) | ||||
0.00356700 | + | 0.999994i | \(0.498865\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.91905e95 | 1.07503 | ||||||||
\(722\) | 1.07368e96 | 1.86157 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.48668e96 | 2.34950 | ||||||||
\(725\) | −3.62148e95 | −0.546466 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.13472e96 | 1.56129 | 0.780646 | − | 0.624973i | \(-0.214890\pi\) | ||||
0.780646 | + | 0.624973i | \(0.214890\pi\) | |||||||
\(728\) | 1.36465e95 | 0.179317 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.87562e95 | −0.344680 | ||||||||
\(731\) | 8.45028e95 | 0.967473 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.88530e95 | −0.823826 | −0.411913 | − | 0.911223i | \(-0.635139\pi\) | ||||
−0.411913 | + | 0.911223i | \(0.635139\pi\) | |||||||
\(734\) | −1.71554e96 | −1.71231 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.39326e95 | −0.400295 | ||||||||
\(737\) | 2.45860e96 | 2.14056 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.22688e95 | 0.654104 | 0.327052 | − | 0.945006i | \(-0.393945\pi\) | ||||
0.327052 | + | 0.945006i | \(0.393945\pi\) | |||||||
\(740\) | 1.44595e96 | 1.09873 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.58337e96 | −1.79331 | ||||||||
\(743\) | −1.18799e96 | −0.788293 | −0.394147 | − | 0.919048i | \(-0.628960\pi\) | ||||
−0.394147 | + | 0.919048i | \(0.628960\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.09721e95 | −0.127176 | ||||||||
\(746\) | −3.98436e96 | −2.30998 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.63454e96 | 5.10655 | ||||||||
\(749\) | 1.07365e96 | 0.544153 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.90797e96 | −1.34788 | −0.673941 | − | 0.738785i | \(-0.735400\pi\) | ||||
−0.673941 | + | 0.738785i | \(0.735400\pi\) | |||||||
\(752\) | 7.93257e96 | 3.51654 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.83081e95 | 0.0742513 | ||||||||
\(755\) | −2.19792e96 | −0.852685 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.73071e96 | 0.614487 | 0.307244 | − | 0.951631i | \(-0.400593\pi\) | ||||
0.307244 | + | 0.951631i | \(0.400593\pi\) | |||||||
\(758\) | 4.68841e96 | 1.59260 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.30439e95 | 0.102763 | ||||||||
\(761\) | −3.70707e96 | −1.10318 | −0.551588 | − | 0.834117i | \(-0.685978\pi\) | ||||
−0.551588 | + | 0.834117i | \(0.685978\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.64694e96 | −0.448854 | ||||||||
\(764\) | −2.94204e95 | −0.0767399 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.40947e96 | 0.814746 | ||||||||
\(767\) | −2.43872e95 | −0.0557849 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.72162e95 | −0.203801 | −0.101900 | − | 0.994795i | \(-0.532492\pi\) | ||||
−0.101900 | + | 0.994795i | \(0.532492\pi\) | |||||||
\(770\) | 1.11773e97 | 2.24335 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.96424e97 | −3.61423 | ||||||||
\(773\) | 7.27011e95 | 0.128094 | 0.0640469 | − | 0.997947i | \(-0.479599\pi\) | ||||
0.0640469 | + | 0.997947i | \(0.479599\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.26728e96 | −0.366351 | ||||||||
\(776\) | −3.24567e97 | −5.02270 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.46302e97 | −2.07699 | ||||||||
\(779\) | 3.63426e94 | 0.00494209 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.45503e96 | 0.306371 | ||||||||
\(782\) | 4.16632e96 | 0.498111 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.62631e97 | 2.88242 | ||||||||
\(785\) | −2.68611e96 | −0.282482 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.49904e96 | −0.144764 | −0.0723820 | − | 0.997377i | \(-0.523060\pi\) | ||||
−0.0723820 | + | 0.997377i | \(0.523060\pi\) | |||||||
\(788\) | −1.08480e96 | −0.100397 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.00460e97 | 0.854053 | ||||||||
\(791\) | 2.73627e95 | 0.0222970 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.44499e95 | 0.0332827 | ||||||||
\(794\) | −2.65830e97 | −1.90817 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −5.78092e97 | −3.81425 | ||||||||
\(797\) | −1.40542e97 | −0.889107 | −0.444553 | − | 0.895752i | \(-0.646638\pi\) | ||||
−0.444553 | + | 0.895752i | \(0.646638\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.38748e97 | −1.97043 | ||||||||
\(800\) | 2.52065e97 | 1.40604 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.42180e97 | 2.78165 | ||||||||
\(803\) | −8.17387e96 | −0.402214 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3.44860e96 | 0.156128 | ||||||||
\(806\) | 1.14621e96 | 0.0497781 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.97951e97 | 3.98867 | ||||||||
\(809\) | 1.72375e97 | 0.660996 | 0.330498 | − | 0.943807i | \(-0.392783\pi\) | ||||
0.330498 | + | 0.943807i | \(0.392783\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3.10291e97 | −1.09540 | −0.547698 | − | 0.836676i | \(-0.684496\pi\) | ||||
−0.547698 | + | 0.836676i | \(0.684496\pi\) | |||||||
\(812\) | 9.35936e97 | 3.17044 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.76057e97 | 1.79700 | ||||||||
\(815\) | −1.50839e94 | −0.000451579 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.37663e96 | 0.0379645 | ||||||||
\(818\) | −6.48006e97 | −1.71531 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.24173e96 | −0.127853 | ||||||||
\(821\) | 4.71160e97 | 1.10325 | 0.551623 | − | 0.834094i | \(-0.314009\pi\) | ||||
0.551623 | + | 0.834094i | \(0.314009\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.28396e97 | −0.708766 | −0.354383 | − | 0.935100i | \(-0.615309\pi\) | ||||
−0.354383 | + | 0.935100i | \(0.615309\pi\) | |||||||
\(824\) | −1.00549e98 | −2.08361 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.74735e98 | −3.33847 | ||||||||
\(827\) | −1.14554e97 | −0.210172 | −0.105086 | − | 0.994463i | \(-0.533512\pi\) | ||||
−0.105086 | + | 0.994463i | \(0.533512\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.31404e97 | 0.899183 | 0.449591 | − | 0.893234i | \(-0.351570\pi\) | ||||
0.449591 | + | 0.893234i | \(0.351570\pi\) | |||||||
\(830\) | 3.35336e97 | 0.544959 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.63481e96 | −0.0694865 | ||||||||
\(833\) | −1.12152e98 | −1.61511 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.72601e97 | −1.02673 | ||||||||
\(836\) | 1.56955e97 | 0.200385 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.43258e97 | −0.993770 | ||||||||
\(839\) | −8.20510e97 | −0.929091 | −0.464545 | − | 0.885549i | \(-0.653782\pi\) | ||||
−0.464545 | + | 0.885549i | \(0.653782\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.05045e97 | −0.214379 | ||||||||
\(842\) | 1.87427e98 | 1.88312 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.41392e98 | 3.16797 | ||||||||
\(845\) | −6.92930e97 | −0.618002 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.43382e98 | 1.18141 | ||||||||
\(848\) | 2.28735e98 | 1.81164 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.39044e98 | −1.74962 | ||||||||
\(851\) | 1.77734e97 | 0.125064 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.75788e97 | −0.179384 | −0.0896918 | − | 0.995970i | \(-0.528588\pi\) | ||||
−0.0896918 | + | 0.995970i | \(0.528588\pi\) | |||||||
\(854\) | 3.18484e98 | 1.99182 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.82384e98 | −1.05467 | ||||||||
\(857\) | 2.49466e98 | 1.38725 | 0.693624 | − | 0.720337i | \(-0.256013\pi\) | ||||
0.693624 | + | 0.720337i | \(0.256013\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.28515e97 | −0.271823 | −0.135912 | − | 0.990721i | \(-0.543396\pi\) | ||||
−0.135912 | + | 0.990721i | \(0.543396\pi\) | |||||||
\(860\) | −1.98552e98 | −0.982148 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.59478e98 | 2.10267 | ||||||||
\(863\) | 1.41322e96 | 0.00622084 | 0.00311042 | − | 0.999995i | \(-0.499010\pi\) | ||||
0.00311042 | + | 0.999995i | \(0.499010\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.97018e98 | −0.802537 | ||||||||
\(866\) | −5.01365e98 | −1.96474 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.85955e98 | 2.12546 | ||||||||
\(869\) | 2.85554e98 | 0.996613 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.20027e97 | 0.0710998 | ||||||||
\(872\) | 2.79771e98 | 0.869962 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.78732e96 | 0.0195463 | ||||||||
\(875\) | −5.18794e98 | −1.43789 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.90704e98 | 1.25989 | 0.629946 | − | 0.776639i | \(-0.283077\pi\) | ||||
0.629946 | + | 0.776639i | \(0.283077\pi\) | |||||||
\(878\) | −1.13167e97 | −0.0279676 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −9.89649e98 | −2.26627 | ||||||||
\(881\) | 1.83004e98 | 0.403430 | 0.201715 | − | 0.979444i | \(-0.435349\pi\) | ||||
0.201715 | + | 0.979444i | \(0.435349\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.47514e98 | 0.301404 | 0.150702 | − | 0.988579i | \(-0.451847\pi\) | ||||
0.150702 | + | 0.988579i | \(0.451847\pi\) | |||||||
\(884\) | 8.62223e97 | 0.169617 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.55042e98 | 1.74178 | ||||||||
\(887\) | 4.64176e98 | 0.815157 | 0.407579 | − | 0.913170i | \(-0.366373\pi\) | ||||
0.407579 | + | 0.913170i | \(0.366373\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.22271e98 | 1.33908 | ||||||||
\(890\) | −1.22971e99 | −1.92857 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.36017e99 | −3.43337 | ||||||||
\(893\) | −5.51852e97 | −0.0773212 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.98530e98 | 0.388075 | ||||||||
\(896\) | −7.04861e98 | −0.882643 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.21828e99 | −1.41576 | ||||||||
\(899\) | 4.70432e98 | 0.526681 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −9.76777e98 | −1.01511 | ||||||||
\(902\) | −2.08827e98 | −0.209106 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.64820e97 | −0.0432158 | ||||||||
\(905\) | 6.52126e98 | 0.584257 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 8.33172e98 | 0.693251 | 0.346626 | − | 0.938004i | \(-0.387327\pi\) | ||||
0.346626 | + | 0.938004i | \(0.387327\pi\) | |||||||
\(908\) | −4.33224e99 | −3.47405 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.00029e98 | 0.0745141 | ||||||||
\(911\) | −1.45347e99 | −1.04362 | −0.521809 | − | 0.853062i | \(-0.674743\pi\) | ||||
−0.521809 | + | 0.853062i | \(0.674743\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 9.53182e98 | 0.635924 | ||||||||
\(914\) | 5.62611e99 | 3.61835 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.71571e99 | −3.41643 | ||||||||
\(917\) | 7.99977e98 | 0.461004 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.11251e99 | 0.595984 | 0.297992 | − | 0.954568i | \(-0.403683\pi\) | ||||
0.297992 | + | 0.954568i | \(0.403683\pi\) | |||||||
\(920\) | −5.85825e98 | −0.302605 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.16071e99 | 1.51809 | ||||||||
\(923\) | 2.19708e97 | 0.0101763 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.01976e99 | −0.439287 | ||||||||
\(926\) | −6.12694e99 | −2.54551 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.23003e99 | −2.02138 | ||||||||
\(929\) | −3.66789e99 | −1.36738 | −0.683692 | − | 0.729771i | \(-0.739627\pi\) | ||||
−0.683692 | + | 0.729771i | \(0.739627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.82707e98 | −0.0633782 | ||||||||
\(932\) | −6.68559e99 | −2.23721 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.54894e99 | 2.66251 | ||||||||
\(935\) | 4.22615e99 | 1.26986 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.86027e98 | 0.0520354 | 0.0260177 | − | 0.999661i | \(-0.491717\pi\) | ||||
0.0260177 | + | 0.999661i | \(0.491717\pi\) | |||||||
\(938\) | 1.57650e100 | 4.25499 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.95941e99 | 2.00031 | ||||||||
\(941\) | −4.09124e99 | −0.992208 | −0.496104 | − | 0.868263i | \(-0.665237\pi\) | ||||
−0.496104 | + | 0.868263i | \(0.665237\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.44306e97 | −0.0145529 | ||||||||
\(944\) | 1.54712e100 | 3.37258 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.91019e99 | −1.60633 | ||||||||
\(947\) | 4.63796e99 | 0.909082 | 0.454541 | − | 0.890726i | \(-0.349803\pi\) | ||||
0.454541 | + | 0.890726i | \(0.349803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.31504e97 | −0.0133598 | ||||||||
\(950\) | −3.89424e98 | −0.0686566 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 3.69699e100 | 6.07450 | ||||||||
\(953\) | 2.75137e99 | 0.436452 | 0.218226 | − | 0.975898i | \(-0.429973\pi\) | ||||
0.218226 | + | 0.975898i | \(0.429973\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.29051e98 | −0.0190831 | ||||||||
\(956\) | 7.85003e99 | 1.12081 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.58285e100 | −2.10715 | ||||||||
\(959\) | −1.05129e99 | −0.135145 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −5.39609e99 | −0.646913 | ||||||||
\(962\) | 5.15530e98 | 0.0596883 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.20476e100 | −1.30112 | ||||||||
\(965\) | −8.61606e99 | −0.898760 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.36496e99 | 0.424809 | 0.212404 | − | 0.977182i | \(-0.431871\pi\) | ||||
0.212404 | + | 0.977182i | \(0.431871\pi\) | |||||||
\(968\) | −2.43567e100 | −2.28978 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.37907e100 | −2.08715 | ||||||||
\(971\) | −6.33150e99 | −0.536614 | −0.268307 | − | 0.963333i | \(-0.586464\pi\) | ||||
−0.268307 | + | 0.963333i | \(0.586464\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.19074e100 | 1.73305 | ||||||||
\(974\) | −5.67423e99 | −0.433692 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.81990e100 | −2.01217 | ||||||||
\(977\) | −1.58929e100 | −1.09581 | −0.547905 | − | 0.836540i | \(-0.684575\pi\) | ||||
−0.547905 | + | 0.836540i | \(0.684575\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.49541e100 | −2.25049 | ||||||||
\(980\) | 2.63519e100 | 1.63960 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 5.38171e100 | 3.12742 | ||||||||
\(983\) | −4.62180e97 | −0.00259578 | −0.00129789 | − | 0.999999i | \(-0.500413\pi\) | ||||
−0.00129789 | + | 0.999999i | \(0.500413\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.75841e98 | −0.0249659 | ||||||||
\(986\) | 4.95987e100 | 2.51532 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.40464e98 | 0.00665591 | ||||||||
\(989\) | −2.44058e99 | −0.111794 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.58345e100 | −1.96212 | −0.981059 | − | 0.193708i | \(-0.937948\pi\) | ||||
−0.981059 | + | 0.193708i | \(0.937948\pi\) | |||||||
\(992\) | −3.27433e100 | −1.35513 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.57421e100 | 0.609003 | ||||||||
\(995\) | −2.53578e100 | −0.948501 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.49091e100 | −1.57053 | −0.785266 | − | 0.619159i | \(-0.787474\pi\) | ||||
−0.785266 | + | 0.619159i | \(0.787474\pi\) | |||||||
\(998\) | −8.40312e100 | −2.84163 | ||||||||
\(999\) | 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 | 9.68.a.a.1.1 | 5 | ||
3.2 | odd | 2 | 1.68.a.a.1.5 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1.68.a.a.1.5 | ✓ | 5 | 3.2 | odd | 2 | ||
9.68.a.a.1.1 | 5 | 1.1 | even | 1 | trivial |