Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,22,Mod(1,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 22, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.1");
S:= CuspForms(chi, 22);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 22 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.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: | \(209.608008215\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2 x^{7} - 13701836 x^{6} + 201589162 x^{5} + 55078074399586 x^{4} + \cdots + 23\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{21}\cdot 3^{10}\cdot 5^{14}\cdot 7^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1237.86\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1154.86 | −0.797469 | −0.398734 | − | 0.917066i | \(-0.630550\pi\) | ||||
−0.398734 | + | 0.917066i | \(0.630550\pi\) | |||||||
\(3\) | −59049.0 | −0.577350 | ||||||||
\(4\) | −763454. | −0.364043 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.81932e7 | 0.460419 | ||||||||
\(7\) | −5.42271e7 | −0.0725583 | −0.0362791 | − | 0.999342i | \(-0.511551\pi\) | ||||
−0.0362791 | + | 0.999342i | \(0.511551\pi\) | |||||||
\(8\) | 3.30359e9 | 1.08778 | ||||||||
\(9\) | 3.48678e9 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −9.88393e10 | −1.14896 | −0.574482 | − | 0.818517i | \(-0.694797\pi\) | ||||
−0.574482 | + | 0.818517i | \(0.694797\pi\) | |||||||
\(12\) | 4.50812e10 | 0.210180 | ||||||||
\(13\) | −3.35334e10 | −0.0674640 | −0.0337320 | − | 0.999431i | \(-0.510739\pi\) | ||||
−0.0337320 | + | 0.999431i | \(0.510739\pi\) | |||||||
\(14\) | 6.26246e10 | 0.0578630 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.21411e12 | −0.503429 | ||||||||
\(17\) | −1.60047e13 | −1.92545 | −0.962727 | − | 0.270476i | \(-0.912819\pi\) | ||||
−0.962727 | + | 0.270476i | \(0.912819\pi\) | |||||||
\(18\) | −4.02674e12 | −0.265823 | ||||||||
\(19\) | −1.23391e13 | −0.461711 | −0.230855 | − | 0.972988i | \(-0.574152\pi\) | ||||
−0.230855 | + | 0.972988i | \(0.574152\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.20206e12 | 0.0418916 | ||||||||
\(22\) | 1.14145e14 | 0.916263 | ||||||||
\(23\) | 3.49309e14 | 1.75820 | 0.879100 | − | 0.476638i | \(-0.158145\pi\) | ||||
0.879100 | + | 0.476638i | \(0.158145\pi\) | |||||||
\(24\) | −1.95074e14 | −0.628031 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.87263e13 | 0.0538005 | ||||||||
\(27\) | −2.05891e14 | −0.192450 | ||||||||
\(28\) | 4.13999e13 | 0.0264144 | ||||||||
\(29\) | 9.02810e14 | 0.398490 | 0.199245 | − | 0.979950i | \(-0.436151\pi\) | ||||
0.199245 | + | 0.979950i | \(0.436151\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.33235e15 | −0.730218 | −0.365109 | − | 0.930965i | \(-0.618968\pi\) | ||||
−0.365109 | + | 0.930965i | \(0.618968\pi\) | |||||||
\(32\) | −4.37116e15 | −0.686313 | ||||||||
\(33\) | 5.83636e15 | 0.663355 | ||||||||
\(34\) | 1.84831e16 | 1.53549 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.66200e15 | −0.121348 | ||||||||
\(37\) | 4.76742e16 | 1.62992 | 0.814958 | − | 0.579520i | \(-0.196760\pi\) | ||||
0.814958 | + | 0.579520i | \(0.196760\pi\) | |||||||
\(38\) | 1.42499e16 | 0.368200 | ||||||||
\(39\) | 1.98011e15 | 0.0389504 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.62667e16 | 0.887369 | 0.443684 | − | 0.896183i | \(-0.353671\pi\) | ||||
0.443684 | + | 0.896183i | \(0.353671\pi\) | |||||||
\(42\) | −3.69792e15 | −0.0334072 | ||||||||
\(43\) | −1.86047e17 | −1.31282 | −0.656408 | − | 0.754406i | \(-0.727925\pi\) | ||||
−0.656408 | + | 0.754406i | \(0.727925\pi\) | |||||||
\(44\) | 7.54593e16 | 0.418273 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.03403e17 | −1.40211 | ||||||||
\(47\) | −1.66048e17 | −0.460474 | −0.230237 | − | 0.973135i | \(-0.573950\pi\) | ||||
−0.230237 | + | 0.973135i | \(0.573950\pi\) | |||||||
\(48\) | 1.30741e17 | 0.290655 | ||||||||
\(49\) | −5.55605e17 | −0.994735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.45060e17 | 1.11166 | ||||||||
\(52\) | 2.56012e16 | 0.0245598 | ||||||||
\(53\) | −1.04319e18 | −0.819345 | −0.409673 | − | 0.912233i | \(-0.634357\pi\) | ||||
−0.409673 | + | 0.912233i | \(0.634357\pi\) | |||||||
\(54\) | 2.37775e17 | 0.153473 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.79144e17 | −0.0789276 | ||||||||
\(57\) | 7.28610e17 | 0.266569 | ||||||||
\(58\) | −1.04262e18 | −0.317783 | ||||||||
\(59\) | −1.49458e18 | −0.380691 | −0.190345 | − | 0.981717i | \(-0.560961\pi\) | ||||
−0.190345 | + | 0.981717i | \(0.560961\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.01457e18 | −0.182105 | −0.0910523 | − | 0.995846i | \(-0.529023\pi\) | ||||
−0.0910523 | + | 0.995846i | \(0.529023\pi\) | |||||||
\(62\) | 3.84839e18 | 0.582326 | ||||||||
\(63\) | −1.89078e17 | −0.0241861 | ||||||||
\(64\) | 9.69139e18 | 1.05074 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.74017e18 | −0.529005 | ||||||||
\(67\) | −1.39620e19 | −0.935754 | −0.467877 | − | 0.883794i | \(-0.654981\pi\) | ||||
−0.467877 | + | 0.883794i | \(0.654981\pi\) | |||||||
\(68\) | 1.22188e19 | 0.700948 | ||||||||
\(69\) | −2.06264e19 | −1.01510 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.39714e19 | −0.509362 | −0.254681 | − | 0.967025i | \(-0.581970\pi\) | ||||
−0.254681 | + | 0.967025i | \(0.581970\pi\) | |||||||
\(72\) | 1.15189e19 | 0.362594 | ||||||||
\(73\) | −3.21010e19 | −0.874235 | −0.437118 | − | 0.899404i | \(-0.644001\pi\) | ||||
−0.437118 | + | 0.899404i | \(0.644001\pi\) | |||||||
\(74\) | −5.50570e19 | −1.29981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9.42032e18 | 0.168083 | ||||||||
\(77\) | 5.35977e18 | 0.0833669 | ||||||||
\(78\) | −2.28675e18 | −0.0310617 | ||||||||
\(79\) | 5.59225e19 | 0.664511 | 0.332255 | − | 0.943189i | \(-0.392190\pi\) | ||||
0.332255 | + | 0.943189i | \(0.392190\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.21577e19 | 0.111111 | ||||||||
\(82\) | −8.80772e19 | −0.707649 | ||||||||
\(83\) | −1.95969e20 | −1.38633 | −0.693167 | − | 0.720777i | \(-0.743785\pi\) | ||||
−0.693167 | + | 0.720777i | \(0.743785\pi\) | |||||||
\(84\) | −2.44462e18 | −0.0152503 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.14858e20 | 1.04693 | ||||||||
\(87\) | −5.33100e19 | −0.230068 | ||||||||
\(88\) | −3.26525e20 | −1.24982 | ||||||||
\(89\) | 4.40698e18 | 0.0149812 | 0.00749059 | − | 0.999972i | \(-0.497616\pi\) | ||||
0.00749059 | + | 0.999972i | \(0.497616\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.81842e18 | 0.00489508 | ||||||||
\(92\) | −2.66682e20 | −0.640061 | ||||||||
\(93\) | 1.96772e20 | 0.421591 | ||||||||
\(94\) | 1.91762e20 | 0.367214 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.58113e20 | 0.396243 | ||||||||
\(97\) | 6.20950e20 | 0.854975 | 0.427487 | − | 0.904021i | \(-0.359399\pi\) | ||||
0.427487 | + | 0.904021i | \(0.359399\pi\) | |||||||
\(98\) | 6.41645e20 | 0.793271 | ||||||||
\(99\) | −3.44631e20 | −0.382988 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.06357e21 | −0.958054 | −0.479027 | − | 0.877800i | \(-0.659010\pi\) | ||||
−0.479027 | + | 0.877800i | \(0.659010\pi\) | |||||||
\(102\) | −1.09141e21 | −0.886515 | ||||||||
\(103\) | −8.58566e20 | −0.629481 | −0.314741 | − | 0.949178i | \(-0.601918\pi\) | ||||
−0.314741 | + | 0.949178i | \(0.601918\pi\) | |||||||
\(104\) | −1.10781e20 | −0.0733862 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.20474e21 | 0.653402 | ||||||||
\(107\) | −3.42950e21 | −1.68539 | −0.842695 | − | 0.538391i | \(-0.819032\pi\) | ||||
−0.842695 | + | 0.538391i | \(0.819032\pi\) | |||||||
\(108\) | 1.57188e20 | 0.0700602 | ||||||||
\(109\) | 2.39482e21 | 0.968935 | 0.484467 | − | 0.874809i | \(-0.339013\pi\) | ||||
0.484467 | + | 0.874809i | \(0.339013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.81511e21 | −0.941033 | ||||||||
\(112\) | 1.20065e20 | 0.0365280 | ||||||||
\(113\) | −2.79687e21 | −0.775084 | −0.387542 | − | 0.921852i | \(-0.626676\pi\) | ||||
−0.387542 | + | 0.921852i | \(0.626676\pi\) | |||||||
\(114\) | −8.41442e20 | −0.212580 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −6.89254e20 | −0.145068 | ||||||||
\(117\) | −1.16924e20 | −0.0224880 | ||||||||
\(118\) | 1.72603e21 | 0.303589 | ||||||||
\(119\) | 8.67887e20 | 0.139708 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.36896e21 | 0.320119 | ||||||||
\(122\) | 1.17169e21 | 0.145223 | ||||||||
\(123\) | −4.50347e21 | −0.512323 | ||||||||
\(124\) | 2.54409e21 | 0.265831 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.18359e20 | 0.0192877 | ||||||||
\(127\) | −1.65628e22 | −1.34646 | −0.673232 | − | 0.739431i | \(-0.735095\pi\) | ||||
−0.673232 | + | 0.739431i | \(0.735095\pi\) | |||||||
\(128\) | −2.02519e21 | −0.151622 | ||||||||
\(129\) | 1.09859e22 | 0.757955 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.08415e22 | −1.22344 | −0.611718 | − | 0.791076i | \(-0.709521\pi\) | ||||
−0.611718 | + | 0.791076i | \(0.709521\pi\) | |||||||
\(132\) | −4.45580e21 | −0.241490 | ||||||||
\(133\) | 6.69113e20 | 0.0335009 | ||||||||
\(134\) | 1.61241e22 | 0.746235 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.28729e22 | −2.09447 | ||||||||
\(137\) | −7.17560e21 | −0.263204 | −0.131602 | − | 0.991303i | \(-0.542012\pi\) | ||||
−0.131602 | + | 0.991303i | \(0.542012\pi\) | |||||||
\(138\) | 2.38205e22 | 0.809508 | ||||||||
\(139\) | 2.49666e22 | 0.786511 | 0.393255 | − | 0.919429i | \(-0.371349\pi\) | ||||
0.393255 | + | 0.919429i | \(0.371349\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.80495e21 | 0.265855 | ||||||||
\(142\) | 1.61350e22 | 0.406200 | ||||||||
\(143\) | 3.31442e21 | 0.0775138 | ||||||||
\(144\) | −7.72011e21 | −0.167810 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.70721e22 | 0.697176 | ||||||||
\(147\) | 3.28079e22 | 0.574311 | ||||||||
\(148\) | −3.63971e22 | −0.593360 | ||||||||
\(149\) | 5.63800e22 | 0.856386 | 0.428193 | − | 0.903687i | \(-0.359150\pi\) | ||||
0.428193 | + | 0.903687i | \(0.359150\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.78403e22 | −0.631736 | −0.315868 | − | 0.948803i | \(-0.602296\pi\) | ||||
−0.315868 | + | 0.948803i | \(0.602296\pi\) | |||||||
\(152\) | −4.07633e22 | −0.502241 | ||||||||
\(153\) | −5.58048e22 | −0.641818 | ||||||||
\(154\) | −6.18978e21 | −0.0664825 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.51173e21 | −0.0141796 | ||||||||
\(157\) | −2.18796e23 | −1.91908 | −0.959540 | − | 0.281572i | \(-0.909144\pi\) | ||||
−0.959540 | + | 0.281572i | \(0.909144\pi\) | |||||||
\(158\) | −6.45825e22 | −0.529927 | ||||||||
\(159\) | 6.15993e22 | 0.473049 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.89420e22 | −0.127572 | ||||||||
\(162\) | −1.40404e22 | −0.0886077 | ||||||||
\(163\) | 1.51641e23 | 0.897114 | 0.448557 | − | 0.893754i | \(-0.351938\pi\) | ||||
0.448557 | + | 0.893754i | \(0.351938\pi\) | |||||||
\(164\) | −5.82261e22 | −0.323041 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.26317e23 | 1.10556 | ||||||||
\(167\) | 5.39750e22 | 0.247554 | 0.123777 | − | 0.992310i | \(-0.460499\pi\) | ||||
0.123777 | + | 0.992310i | \(0.460499\pi\) | |||||||
\(168\) | 1.05783e22 | 0.0455689 | ||||||||
\(169\) | −2.45940e23 | −0.995449 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.30237e22 | −0.153904 | ||||||||
\(172\) | 1.42038e23 | 0.477922 | ||||||||
\(173\) | −3.76178e23 | −1.19099 | −0.595496 | − | 0.803358i | \(-0.703045\pi\) | ||||
−0.595496 | + | 0.803358i | \(0.703045\pi\) | |||||||
\(174\) | 6.15655e22 | 0.183472 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.18841e23 | 0.578422 | ||||||||
\(177\) | 8.82533e22 | 0.219792 | ||||||||
\(178\) | −5.08944e21 | −0.0119470 | ||||||||
\(179\) | 1.10081e23 | 0.243643 | 0.121822 | − | 0.992552i | \(-0.461126\pi\) | ||||
0.121822 | + | 0.992552i | \(0.461126\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.38729e23 | 0.273238 | 0.136619 | − | 0.990624i | \(-0.456376\pi\) | ||||
0.136619 | + | 0.990624i | \(0.456376\pi\) | |||||||
\(182\) | −2.10002e21 | −0.00390367 | ||||||||
\(183\) | 5.99096e22 | 0.105138 | ||||||||
\(184\) | 1.15398e24 | 1.91254 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.27243e23 | −0.336206 | ||||||||
\(187\) | 1.58189e24 | 2.21228 | ||||||||
\(188\) | 1.26770e23 | 0.167633 | ||||||||
\(189\) | 1.11649e22 | 0.0139639 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.08029e23 | 0.680885 | 0.340443 | − | 0.940265i | \(-0.389423\pi\) | ||||
0.340443 | + | 0.940265i | \(0.389423\pi\) | |||||||
\(192\) | −5.72267e23 | −0.606646 | ||||||||
\(193\) | −1.31797e24 | −1.32299 | −0.661493 | − | 0.749951i | \(-0.730077\pi\) | ||||
−0.661493 | + | 0.749951i | \(0.730077\pi\) | |||||||
\(194\) | −7.17109e23 | −0.681816 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 4.24179e23 | 0.362127 | ||||||||
\(197\) | 6.55437e23 | 0.530439 | 0.265220 | − | 0.964188i | \(-0.414556\pi\) | ||||
0.265220 | + | 0.964188i | \(0.414556\pi\) | |||||||
\(198\) | 3.98000e23 | 0.305421 | ||||||||
\(199\) | −1.28284e24 | −0.933718 | −0.466859 | − | 0.884332i | \(-0.654615\pi\) | ||||
−0.466859 | + | 0.884332i | \(0.654615\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 8.24441e23 | 0.540258 | ||||||||
\(202\) | 1.22827e24 | 0.764018 | ||||||||
\(203\) | −4.89568e22 | −0.0289138 | ||||||||
\(204\) | −7.21510e23 | −0.404693 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.91522e23 | 0.501992 | ||||||||
\(207\) | 1.21797e24 | 0.586066 | ||||||||
\(208\) | 7.42465e22 | 0.0339634 | ||||||||
\(209\) | 1.21959e24 | 0.530489 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.46432e23 | −0.254423 | −0.127212 | − | 0.991876i | \(-0.540603\pi\) | ||||
−0.127212 | + | 0.991876i | \(0.540603\pi\) | |||||||
\(212\) | 7.96428e23 | 0.298277 | ||||||||
\(213\) | 8.24996e23 | 0.294080 | ||||||||
\(214\) | 3.96058e24 | 1.34405 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −6.80181e23 | −0.209344 | ||||||||
\(217\) | 1.80704e23 | 0.0529834 | ||||||||
\(218\) | −2.76568e24 | −0.772695 | ||||||||
\(219\) | 1.89553e24 | 0.504740 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.36691e23 | 0.129899 | ||||||||
\(222\) | 3.25106e24 | 0.750444 | ||||||||
\(223\) | 2.49752e24 | 0.549930 | 0.274965 | − | 0.961454i | \(-0.411334\pi\) | ||||
0.274965 | + | 0.961454i | \(0.411334\pi\) | |||||||
\(224\) | 2.37036e23 | 0.0497977 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.22999e24 | 0.618106 | ||||||||
\(227\) | 9.79134e24 | 1.78884 | 0.894418 | − | 0.447232i | \(-0.147590\pi\) | ||||
0.894418 | + | 0.447232i | \(0.147590\pi\) | |||||||
\(228\) | −5.56260e23 | −0.0970426 | ||||||||
\(229\) | 9.64103e24 | 1.60639 | 0.803195 | − | 0.595716i | \(-0.203132\pi\) | ||||
0.803195 | + | 0.595716i | \(0.203132\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.16489e23 | −0.0481319 | ||||||||
\(232\) | 2.98252e24 | 0.433470 | ||||||||
\(233\) | −4.53906e23 | −0.0630564 | −0.0315282 | − | 0.999503i | \(-0.510037\pi\) | ||||
−0.0315282 | + | 0.999503i | \(0.510037\pi\) | |||||||
\(234\) | 1.35030e23 | 0.0179335 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 1.14104e24 | 0.138588 | ||||||||
\(237\) | −3.30217e24 | −0.383655 | ||||||||
\(238\) | −1.00229e24 | −0.111412 | ||||||||
\(239\) | 1.44716e25 | 1.53936 | 0.769678 | − | 0.638432i | \(-0.220417\pi\) | ||||
0.769678 | + | 0.638432i | \(0.220417\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.14181e24 | 0.111280 | 0.0556399 | − | 0.998451i | \(-0.482280\pi\) | ||||
0.0556399 | + | 0.998451i | \(0.482280\pi\) | |||||||
\(242\) | −2.73582e24 | −0.255285 | ||||||||
\(243\) | −7.17898e23 | −0.0641500 | ||||||||
\(244\) | 7.74581e23 | 0.0662939 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 5.20087e24 | 0.408561 | ||||||||
\(247\) | 4.13771e23 | 0.0311489 | ||||||||
\(248\) | −1.10087e25 | −0.794318 | ||||||||
\(249\) | 1.15718e25 | 0.800401 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.09389e25 | 1.33162 | 0.665810 | − | 0.746121i | \(-0.268086\pi\) | ||||
0.665810 | + | 0.746121i | \(0.268086\pi\) | |||||||
\(252\) | 1.44353e23 | 0.00880479 | ||||||||
\(253\) | −3.45255e25 | −2.02011 | ||||||||
\(254\) | 1.91277e25 | 1.07376 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.79855e25 | −0.929829 | ||||||||
\(257\) | −1.80282e25 | −0.894653 | −0.447326 | − | 0.894371i | \(-0.647624\pi\) | ||||
−0.447326 | + | 0.894371i | \(0.647624\pi\) | |||||||
\(258\) | −1.26871e25 | −0.604445 | ||||||||
\(259\) | −2.58523e24 | −0.118264 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.14790e24 | 0.132830 | ||||||||
\(262\) | 2.40690e25 | 0.975652 | ||||||||
\(263\) | −2.96509e25 | −1.15479 | −0.577395 | − | 0.816465i | \(-0.695931\pi\) | ||||
−0.577395 | + | 0.816465i | \(0.695931\pi\) | |||||||
\(264\) | 1.92810e25 | 0.721586 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −7.72730e23 | −0.0267160 | ||||||||
\(267\) | −2.60228e23 | −0.00864939 | ||||||||
\(268\) | 1.06593e25 | 0.340655 | ||||||||
\(269\) | 5.52895e25 | 1.69920 | 0.849599 | − | 0.527430i | \(-0.176844\pi\) | ||||
0.849599 | + | 0.527430i | \(0.176844\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.65005e25 | 0.753490 | 0.376745 | − | 0.926317i | \(-0.377043\pi\) | ||||
0.376745 | + | 0.926317i | \(0.377043\pi\) | |||||||
\(272\) | 3.54360e25 | 0.969329 | ||||||||
\(273\) | −1.07376e23 | −0.00282617 | ||||||||
\(274\) | 8.28680e24 | 0.209897 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1.57473e25 | 0.369539 | ||||||||
\(277\) | −1.15811e25 | −0.261645 | −0.130822 | − | 0.991406i | \(-0.541762\pi\) | ||||
−0.130822 | + | 0.991406i | \(0.541762\pi\) | |||||||
\(278\) | −2.88329e25 | −0.627218 | ||||||||
\(279\) | −1.16192e25 | −0.243406 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.84037e25 | −1.52377 | −0.761887 | − | 0.647710i | \(-0.775727\pi\) | ||||
−0.761887 | + | 0.647710i | \(0.775727\pi\) | |||||||
\(282\) | −1.13233e25 | −0.212011 | ||||||||
\(283\) | −7.91685e25 | −1.42822 | −0.714109 | − | 0.700034i | \(-0.753168\pi\) | ||||
−0.714109 | + | 0.700034i | \(0.753168\pi\) | |||||||
\(284\) | 1.06665e25 | 0.185430 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.82768e24 | −0.0618148 | ||||||||
\(287\) | −4.13572e24 | −0.0643860 | ||||||||
\(288\) | −1.52413e25 | −0.228771 | ||||||||
\(289\) | 1.87058e26 | 2.70737 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.66665e25 | −0.493620 | ||||||||
\(292\) | 2.45076e25 | 0.318260 | ||||||||
\(293\) | 4.94119e25 | 0.619043 | 0.309522 | − | 0.950892i | \(-0.399831\pi\) | ||||
0.309522 | + | 0.950892i | \(0.399831\pi\) | |||||||
\(294\) | −3.78885e25 | −0.457995 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.57496e26 | 1.77299 | ||||||||
\(297\) | 2.03501e25 | 0.221118 | ||||||||
\(298\) | −6.51109e25 | −0.682941 | ||||||||
\(299\) | −1.17135e25 | −0.118615 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00888e25 | 0.0952557 | ||||||||
\(302\) | 5.52488e25 | 0.503790 | ||||||||
\(303\) | 6.28025e25 | 0.553132 | ||||||||
\(304\) | 2.73200e25 | 0.232439 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.44467e25 | 0.511830 | ||||||||
\(307\) | 1.81029e26 | 1.38930 | 0.694648 | − | 0.719350i | \(-0.255560\pi\) | ||||
0.694648 | + | 0.719350i | \(0.255560\pi\) | |||||||
\(308\) | −4.09194e24 | −0.0303492 | ||||||||
\(309\) | 5.06975e25 | 0.363431 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.12773e26 | 0.755473 | 0.377737 | − | 0.925913i | \(-0.376702\pi\) | ||||
0.377737 | + | 0.925913i | \(0.376702\pi\) | |||||||
\(312\) | 6.54149e24 | 0.0423695 | ||||||||
\(313\) | −2.07181e26 | −1.29758 | −0.648790 | − | 0.760967i | \(-0.724725\pi\) | ||||
−0.648790 | + | 0.760967i | \(0.724725\pi\) | |||||||
\(314\) | 2.52678e26 | 1.53041 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.26942e25 | −0.241911 | ||||||||
\(317\) | 1.12129e26 | 0.614604 | 0.307302 | − | 0.951612i | \(-0.400574\pi\) | ||||
0.307302 | + | 0.951612i | \(0.400574\pi\) | |||||||
\(318\) | −7.11385e25 | −0.377242 | ||||||||
\(319\) | −8.92331e25 | −0.457851 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.02508e26 | 0.973061 | ||||||||
\(322\) | 2.18754e25 | 0.101735 | ||||||||
\(323\) | 1.97483e26 | 0.889002 | ||||||||
\(324\) | −9.28182e24 | −0.0404493 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1.75124e26 | −0.715421 | ||||||||
\(327\) | −1.41412e26 | −0.559415 | ||||||||
\(328\) | 2.51954e26 | 0.965264 | ||||||||
\(329\) | 9.00429e24 | 0.0334112 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.52788e26 | −1.22834 | −0.614172 | − | 0.789172i | \(-0.710510\pi\) | ||||
−0.614172 | + | 0.789172i | \(0.710510\pi\) | |||||||
\(332\) | 1.49614e26 | 0.504686 | ||||||||
\(333\) | 1.66230e26 | 0.543306 | ||||||||
\(334\) | −6.23335e25 | −0.197417 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.08969e24 | −0.0210894 | ||||||||
\(337\) | 3.81011e26 | 1.09856 | 0.549279 | − | 0.835639i | \(-0.314902\pi\) | ||||
0.549279 | + | 0.835639i | \(0.314902\pi\) | |||||||
\(338\) | 2.84026e26 | 0.793839 | ||||||||
\(339\) | 1.65152e26 | 0.447495 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.29367e26 | 0.838994 | ||||||||
\(342\) | 4.96863e25 | 0.122733 | ||||||||
\(343\) | 6.04172e25 | 0.144735 | ||||||||
\(344\) | −6.14624e26 | −1.42806 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.34432e26 | 0.949780 | ||||||||
\(347\) | −3.94952e26 | −0.837692 | −0.418846 | − | 0.908057i | \(-0.637565\pi\) | ||||
−0.418846 | + | 0.908057i | \(0.637565\pi\) | |||||||
\(348\) | 4.06998e25 | 0.0837548 | ||||||||
\(349\) | −9.12481e26 | −1.82203 | −0.911017 | − | 0.412368i | \(-0.864702\pi\) | ||||
−0.911017 | + | 0.412368i | \(0.864702\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.90423e24 | 0.0129835 | ||||||||
\(352\) | 4.32043e26 | 0.788549 | ||||||||
\(353\) | −3.95907e26 | −0.701388 | −0.350694 | − | 0.936490i | \(-0.614054\pi\) | ||||
−0.350694 | + | 0.936490i | \(0.614054\pi\) | |||||||
\(354\) | −1.01920e26 | −0.175277 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.36453e24 | −0.00545380 | ||||||||
\(357\) | −5.12479e25 | −0.0806602 | ||||||||
\(358\) | −1.27128e26 | −0.194298 | ||||||||
\(359\) | 9.83596e26 | 1.45991 | 0.729953 | − | 0.683497i | \(-0.239542\pi\) | ||||
0.729953 | + | 0.683497i | \(0.239542\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.61957e26 | −0.786823 | ||||||||
\(362\) | −1.60212e26 | −0.217899 | ||||||||
\(363\) | −1.39885e26 | −0.184821 | ||||||||
\(364\) | −1.38828e24 | −0.00178202 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6.91871e25 | −0.0838444 | ||||||||
\(367\) | −9.56476e26 | −1.12637 | −0.563184 | − | 0.826331i | \(-0.690424\pi\) | ||||
−0.563184 | + | 0.826331i | \(0.690424\pi\) | |||||||
\(368\) | −7.73408e26 | −0.885129 | ||||||||
\(369\) | 2.65925e26 | 0.295790 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 5.65692e25 | 0.0594503 | ||||||||
\(372\) | −1.50226e26 | −0.153478 | ||||||||
\(373\) | −2.93918e26 | −0.291933 | −0.145967 | − | 0.989290i | \(-0.546629\pi\) | ||||
−0.145967 | + | 0.989290i | \(0.546629\pi\) | |||||||
\(374\) | −1.82686e27 | −1.76422 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.48555e26 | −0.500896 | ||||||||
\(377\) | −3.02743e25 | −0.0268837 | ||||||||
\(378\) | −1.28939e25 | −0.0111357 | ||||||||
\(379\) | −1.77322e27 | −1.48954 | −0.744769 | − | 0.667323i | \(-0.767440\pi\) | ||||
−0.744769 | + | 0.667323i | \(0.767440\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.78018e26 | 0.777382 | ||||||||
\(382\) | −7.02187e26 | −0.542985 | ||||||||
\(383\) | 1.95770e27 | 1.47285 | 0.736427 | − | 0.676517i | \(-0.236511\pi\) | ||||
0.736427 | + | 0.676517i | \(0.236511\pi\) | |||||||
\(384\) | 1.19585e26 | 0.0875387 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1.52207e27 | 1.05504 | ||||||||
\(387\) | −6.48706e26 | −0.437605 | ||||||||
\(388\) | −4.74067e26 | −0.311248 | ||||||||
\(389\) | −4.47898e26 | −0.286225 | −0.143113 | − | 0.989706i | \(-0.545711\pi\) | ||||
−0.143113 | + | 0.989706i | \(0.545711\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.59058e27 | −3.38533 | ||||||||
\(392\) | −1.83549e27 | −1.08206 | ||||||||
\(393\) | 1.23067e27 | 0.706351 | ||||||||
\(394\) | −7.56937e26 | −0.423009 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.63110e26 | 0.139424 | ||||||||
\(397\) | −3.07981e26 | −0.158936 | −0.0794682 | − | 0.996837i | \(-0.525322\pi\) | ||||
−0.0794682 | + | 0.996837i | \(0.525322\pi\) | |||||||
\(398\) | 1.48150e27 | 0.744611 | ||||||||
\(399\) | −3.95104e25 | −0.0193418 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.66508e27 | −0.773426 | −0.386713 | − | 0.922200i | \(-0.626390\pi\) | ||||
−0.386713 | + | 0.922200i | \(0.626390\pi\) | |||||||
\(402\) | −9.52113e26 | −0.430839 | ||||||||
\(403\) | 1.11745e26 | 0.0492634 | ||||||||
\(404\) | 8.11983e26 | 0.348773 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.65381e25 | 0.0230578 | ||||||||
\(407\) | −4.71209e27 | −1.87272 | ||||||||
\(408\) | 3.12209e27 | 1.20925 | ||||||||
\(409\) | 3.42658e27 | 1.29350 | 0.646749 | − | 0.762703i | \(-0.276128\pi\) | ||||
0.646749 | + | 0.762703i | \(0.276128\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.23712e26 | 0.151961 | ||||||||
\(412\) | 6.55476e26 | 0.229158 | ||||||||
\(413\) | 8.10466e25 | 0.0276223 | ||||||||
\(414\) | −1.40658e27 | −0.467370 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1.46580e26 | 0.0463015 | ||||||||
\(417\) | −1.47426e27 | −0.454092 | ||||||||
\(418\) | −1.40845e27 | −0.423049 | ||||||||
\(419\) | −5.73314e27 | −1.67937 | −0.839683 | − | 0.543077i | \(-0.817259\pi\) | ||||
−0.839683 | + | 0.543077i | \(0.817259\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.33038e26 | −0.0649330 | −0.0324665 | − | 0.999473i | \(-0.510336\pi\) | ||||
−0.0324665 | + | 0.999473i | \(0.510336\pi\) | |||||||
\(422\) | 7.46538e26 | 0.202895 | ||||||||
\(423\) | −5.78973e26 | −0.153491 | ||||||||
\(424\) | −3.44628e27 | −0.891269 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −9.52753e26 | −0.234520 | ||||||||
\(427\) | 5.50175e25 | 0.0132132 | ||||||||
\(428\) | 2.61826e27 | 0.613555 | ||||||||
\(429\) | −1.95713e26 | −0.0447526 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.70136e26 | 0.0806028 | 0.0403014 | − | 0.999188i | \(-0.487168\pi\) | ||||
0.0403014 | + | 0.999188i | \(0.487168\pi\) | |||||||
\(432\) | 4.55865e26 | 0.0968850 | ||||||||
\(433\) | 3.01062e27 | 0.624501 | 0.312251 | − | 0.950000i | \(-0.398917\pi\) | ||||
0.312251 | + | 0.950000i | \(0.398917\pi\) | |||||||
\(434\) | −2.08687e26 | −0.0422526 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.82833e27 | −0.352734 | ||||||||
\(437\) | −4.31016e27 | −0.811779 | ||||||||
\(438\) | −2.18907e27 | −0.402515 | ||||||||
\(439\) | −2.48833e27 | −0.446714 | −0.223357 | − | 0.974737i | \(-0.571702\pi\) | ||||
−0.223357 | + | 0.974737i | \(0.571702\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.93728e27 | −0.331578 | ||||||||
\(442\) | −6.19802e26 | −0.103590 | ||||||||
\(443\) | 5.05509e27 | 0.825069 | 0.412534 | − | 0.910942i | \(-0.364644\pi\) | ||||
0.412534 | + | 0.910942i | \(0.364644\pi\) | |||||||
\(444\) | 2.14921e27 | 0.342577 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −2.88428e27 | −0.438552 | ||||||||
\(447\) | −3.32918e27 | −0.494435 | ||||||||
\(448\) | −5.25536e26 | −0.0762401 | ||||||||
\(449\) | 4.22145e27 | 0.598240 | 0.299120 | − | 0.954216i | \(-0.403307\pi\) | ||||
0.299120 | + | 0.954216i | \(0.403307\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.53814e27 | −1.01956 | ||||||||
\(452\) | 2.13528e27 | 0.282164 | ||||||||
\(453\) | 2.82492e27 | 0.364733 | ||||||||
\(454\) | −1.13076e28 | −1.42654 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2.40703e27 | 0.289969 | ||||||||
\(457\) | 1.25255e28 | 1.47460 | 0.737299 | − | 0.675567i | \(-0.236101\pi\) | ||||
0.737299 | + | 0.675567i | \(0.236101\pi\) | |||||||
\(458\) | −1.11340e28 | −1.28105 | ||||||||
\(459\) | 3.29522e27 | 0.370554 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.17590e28 | 1.26331 | 0.631655 | − | 0.775250i | \(-0.282376\pi\) | ||||
0.631655 | + | 0.775250i | \(0.282376\pi\) | |||||||
\(462\) | 3.65500e26 | 0.0383837 | ||||||||
\(463\) | 3.41343e27 | 0.350421 | 0.175210 | − | 0.984531i | \(-0.443939\pi\) | ||||
0.175210 | + | 0.984531i | \(0.443939\pi\) | |||||||
\(464\) | −1.99892e27 | −0.200611 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.24198e26 | 0.0502855 | ||||||||
\(467\) | 1.81244e28 | 1.69995 | 0.849975 | − | 0.526823i | \(-0.176617\pi\) | ||||
0.849975 | + | 0.526823i | \(0.176617\pi\) | |||||||
\(468\) | 8.92659e25 | 0.00818661 | ||||||||
\(469\) | 7.57118e26 | 0.0678967 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.29197e28 | 1.10798 | ||||||||
\(472\) | −4.93748e27 | −0.414109 | ||||||||
\(473\) | 1.83888e28 | 1.50838 | ||||||||
\(474\) | 3.81353e27 | 0.305953 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.62592e26 | −0.0508596 | ||||||||
\(477\) | −3.63738e27 | −0.273115 | ||||||||
\(478\) | −1.67127e28 | −1.22759 | ||||||||
\(479\) | −2.72034e27 | −0.195479 | −0.0977397 | − | 0.995212i | \(-0.531161\pi\) | ||||
−0.0977397 | + | 0.995212i | \(0.531161\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.59868e27 | −0.109961 | ||||||||
\(482\) | −1.31863e27 | −0.0887422 | ||||||||
\(483\) | 1.11851e27 | 0.0736537 | ||||||||
\(484\) | −1.80859e27 | −0.116537 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 8.29071e26 | 0.0511577 | ||||||||
\(487\) | 8.83077e27 | 0.533267 | 0.266633 | − | 0.963798i | \(-0.414089\pi\) | ||||
0.266633 | + | 0.963798i | \(0.414089\pi\) | |||||||
\(488\) | −3.35174e27 | −0.198090 | ||||||||
\(489\) | −8.95427e27 | −0.517949 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.20139e27 | 0.454498 | 0.227249 | − | 0.973837i | \(-0.427027\pi\) | ||||
0.227249 | + | 0.973837i | \(0.427027\pi\) | |||||||
\(492\) | 3.43819e27 | 0.186508 | ||||||||
\(493\) | −1.44492e28 | −0.767274 | ||||||||
\(494\) | −4.77847e26 | −0.0248403 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.37817e27 | 0.367613 | ||||||||
\(497\) | 7.57627e26 | 0.0369584 | ||||||||
\(498\) | −1.33638e28 | −0.638295 | ||||||||
\(499\) | 1.79278e26 | 0.00838437 | 0.00419218 | − | 0.999991i | \(-0.498666\pi\) | ||||
0.00419218 | + | 0.999991i | \(0.498666\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.18717e27 | −0.142925 | ||||||||
\(502\) | −2.41815e28 | −1.06193 | ||||||||
\(503\) | −2.00700e28 | −0.863145 | −0.431572 | − | 0.902078i | \(-0.642041\pi\) | ||||
−0.431572 | + | 0.902078i | \(0.642041\pi\) | |||||||
\(504\) | −6.24638e26 | −0.0263092 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.98721e28 | 1.61097 | ||||||||
\(507\) | 1.45225e28 | 0.574723 | ||||||||
\(508\) | 1.26449e28 | 0.490172 | ||||||||
\(509\) | 1.92770e28 | 0.731988 | 0.365994 | − | 0.930617i | \(-0.380729\pi\) | ||||
0.365994 | + | 0.930617i | \(0.380729\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.74074e27 | 0.0634330 | ||||||||
\(512\) | 2.50178e28 | 0.893131 | ||||||||
\(513\) | 2.54051e27 | 0.0888563 | ||||||||
\(514\) | 2.08200e28 | 0.713458 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −8.38722e27 | −0.275928 | ||||||||
\(517\) | 1.64120e28 | 0.529069 | ||||||||
\(518\) | 2.98558e27 | 0.0943118 | ||||||||
\(519\) | 2.22129e28 | 0.687620 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.71956e28 | −0.808542 | −0.404271 | − | 0.914639i | \(-0.632475\pi\) | ||||
−0.404271 | + | 0.914639i | \(0.632475\pi\) | |||||||
\(522\) | −3.63538e27 | −0.105928 | ||||||||
\(523\) | 1.07341e28 | 0.306547 | 0.153273 | − | 0.988184i | \(-0.451018\pi\) | ||||
0.153273 | + | 0.988184i | \(0.451018\pi\) | |||||||
\(524\) | 1.59116e28 | 0.445383 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3.42426e28 | 0.920909 | ||||||||
\(527\) | 5.33331e28 | 1.40600 | ||||||||
\(528\) | −1.29223e28 | −0.333952 | ||||||||
\(529\) | 8.25455e28 | 2.09126 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.21127e27 | −0.126897 | ||||||||
\(532\) | −5.10837e26 | −0.0121958 | ||||||||
\(533\) | −2.55748e27 | −0.0598655 | ||||||||
\(534\) | 3.00526e26 | 0.00689762 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −4.61247e28 | −1.01790 | ||||||||
\(537\) | −6.50016e27 | −0.140668 | ||||||||
\(538\) | −6.38515e28 | −1.35506 | ||||||||
\(539\) | 5.49157e28 | 1.14292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.57220e28 | 0.314728 | 0.157364 | − | 0.987541i | \(-0.449700\pi\) | ||||
0.157364 | + | 0.987541i | \(0.449700\pi\) | |||||||
\(542\) | −3.06044e28 | −0.600885 | ||||||||
\(543\) | −8.19178e27 | −0.157754 | ||||||||
\(544\) | 6.99590e28 | 1.32146 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1.24004e26 | 0.00225379 | ||||||||
\(547\) | 8.57716e27 | 0.152924 | 0.0764622 | − | 0.997072i | \(-0.475638\pi\) | ||||
0.0764622 | + | 0.997072i | \(0.475638\pi\) | |||||||
\(548\) | 5.47824e27 | 0.0958175 | ||||||||
\(549\) | −3.53760e27 | −0.0607015 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.11398e28 | −0.183987 | ||||||||
\(552\) | −6.81412e28 | −1.10420 | ||||||||
\(553\) | −3.03251e27 | −0.0482158 | ||||||||
\(554\) | 1.33745e28 | 0.208653 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.90609e28 | −0.286324 | ||||||||
\(557\) | 1.39112e28 | 0.205062 | 0.102531 | − | 0.994730i | \(-0.467306\pi\) | ||||
0.102531 | + | 0.994730i | \(0.467306\pi\) | |||||||
\(558\) | 1.34185e28 | 0.194109 | ||||||||
\(559\) | 6.23879e27 | 0.0885679 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9.34091e28 | −1.27726 | ||||||||
\(562\) | 9.05452e28 | 1.21516 | ||||||||
\(563\) | 3.60324e28 | 0.474629 | 0.237315 | − | 0.971433i | \(-0.423733\pi\) | ||||
0.237315 | + | 0.971433i | \(0.423733\pi\) | |||||||
\(564\) | −7.48563e27 | −0.0967827 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.14284e28 | 1.13896 | ||||||||
\(567\) | −6.59275e26 | −0.00806203 | ||||||||
\(568\) | −4.61558e28 | −0.554075 | ||||||||
\(569\) | −7.59750e28 | −0.895348 | −0.447674 | − | 0.894197i | \(-0.647747\pi\) | ||||
−0.447674 | + | 0.894197i | \(0.647747\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.16584e27 | −0.0359592 | −0.0179796 | − | 0.999838i | \(-0.505723\pi\) | ||||
−0.0179796 | + | 0.999838i | \(0.505723\pi\) | |||||||
\(572\) | −2.53041e27 | −0.0282184 | ||||||||
\(573\) | −3.59035e28 | −0.393109 | ||||||||
\(574\) | 4.77617e27 | 0.0513458 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3.37918e28 | 0.350248 | ||||||||
\(577\) | −1.53123e29 | −1.55845 | −0.779227 | − | 0.626742i | \(-0.784388\pi\) | ||||
−0.779227 | + | 0.626742i | \(0.784388\pi\) | |||||||
\(578\) | −2.16025e29 | −2.15904 | ||||||||
\(579\) | 7.78251e28 | 0.763826 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.06269e28 | 0.100590 | ||||||||
\(582\) | 4.23446e28 | 0.393647 | ||||||||
\(583\) | 1.03108e29 | 0.941399 | ||||||||
\(584\) | −1.06049e29 | −0.950978 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.70637e28 | −0.493668 | ||||||||
\(587\) | 1.31923e29 | 1.12104 | 0.560519 | − | 0.828141i | \(-0.310602\pi\) | ||||
0.560519 | + | 0.828141i | \(0.310602\pi\) | |||||||
\(588\) | −2.50474e28 | −0.209074 | ||||||||
\(589\) | 4.11181e28 | 0.337149 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3.87029e28 | −0.306249 | ||||||||
\(592\) | −1.05556e29 | −0.820548 | ||||||||
\(593\) | 5.00314e28 | 0.382093 | 0.191046 | − | 0.981581i | \(-0.438812\pi\) | ||||
0.191046 | + | 0.981581i | \(0.438812\pi\) | |||||||
\(594\) | −2.35015e28 | −0.176335 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.30436e28 | −0.311761 | ||||||||
\(597\) | 7.57505e28 | 0.539083 | ||||||||
\(598\) | 1.35275e28 | 0.0945920 | ||||||||
\(599\) | 2.24144e29 | 1.54009 | 0.770043 | − | 0.637993i | \(-0.220235\pi\) | ||||
0.770043 | + | 0.637993i | \(0.220235\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2.91222e29 | 1.93215 | 0.966077 | − | 0.258255i | \(-0.0831475\pi\) | ||||
0.966077 | + | 0.258255i | \(0.0831475\pi\) | |||||||
\(602\) | −1.16511e28 | −0.0759635 | ||||||||
\(603\) | −4.86824e28 | −0.311918 | ||||||||
\(604\) | 3.65239e28 | 0.229979 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.25280e28 | −0.441106 | ||||||||
\(607\) | −2.63905e29 | −1.57749 | −0.788743 | − | 0.614723i | \(-0.789268\pi\) | ||||
−0.788743 | + | 0.614723i | \(0.789268\pi\) | |||||||
\(608\) | 5.39361e28 | 0.316878 | ||||||||
\(609\) | 2.89085e27 | 0.0166934 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.56815e27 | 0.0310655 | ||||||||
\(612\) | 4.26044e28 | 0.233649 | ||||||||
\(613\) | 2.31019e29 | 1.24541 | 0.622705 | − | 0.782457i | \(-0.286034\pi\) | ||||
0.622705 | + | 0.782457i | \(0.286034\pi\) | |||||||
\(614\) | −2.09063e29 | −1.10792 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.77065e28 | 0.0906850 | ||||||||
\(617\) | 3.69003e29 | 1.85796 | 0.928978 | − | 0.370136i | \(-0.120689\pi\) | ||||
0.928978 | + | 0.370136i | \(0.120689\pi\) | |||||||
\(618\) | −5.85484e28 | −0.289825 | ||||||||
\(619\) | −1.15989e29 | −0.564501 | −0.282251 | − | 0.959341i | \(-0.591081\pi\) | ||||
−0.282251 | + | 0.959341i | \(0.591081\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.19197e28 | −0.338366 | ||||||||
\(622\) | −1.30236e29 | −0.602467 | ||||||||
\(623\) | −2.38978e26 | −0.00108701 | ||||||||
\(624\) | −4.38418e27 | −0.0196088 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 2.39265e29 | 1.03478 | ||||||||
\(627\) | −7.20153e28 | −0.306278 | ||||||||
\(628\) | 1.67041e29 | 0.698628 | ||||||||
\(629\) | −7.63010e29 | −3.13833 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.06645e27 | 0.0201556 | 0.0100778 | − | 0.999949i | \(-0.496792\pi\) | ||||
0.0100778 | + | 0.999949i | \(0.496792\pi\) | |||||||
\(632\) | 1.84745e29 | 0.722843 | ||||||||
\(633\) | 3.81712e28 | 0.146891 | ||||||||
\(634\) | −1.29493e29 | −0.490128 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −4.70283e28 | −0.172210 | ||||||||
\(637\) | 1.86313e28 | 0.0671089 | ||||||||
\(638\) | 1.03052e29 | 0.365122 | ||||||||
\(639\) | −4.87152e28 | −0.169787 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.31381e28 | 0.314136 | 0.157068 | − | 0.987588i | \(-0.449796\pi\) | ||||
0.157068 | + | 0.987588i | \(0.449796\pi\) | |||||||
\(642\) | −2.33868e29 | −0.775986 | ||||||||
\(643\) | −2.35019e29 | −0.767164 | −0.383582 | − | 0.923507i | \(-0.625310\pi\) | ||||
−0.383582 | + | 0.923507i | \(0.625310\pi\) | |||||||
\(644\) | 1.44614e28 | 0.0464417 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.28065e29 | −0.708952 | ||||||||
\(647\) | −2.34044e29 | −0.715817 | −0.357909 | − | 0.933757i | \(-0.616510\pi\) | ||||
−0.357909 | + | 0.933757i | \(0.616510\pi\) | |||||||
\(648\) | 4.01640e28 | 0.120865 | ||||||||
\(649\) | 1.47723e29 | 0.437400 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.06704e28 | −0.0305900 | ||||||||
\(652\) | −1.15771e29 | −0.326588 | ||||||||
\(653\) | 4.42897e29 | 1.22946 | 0.614730 | − | 0.788738i | \(-0.289265\pi\) | ||||
0.614730 | + | 0.788738i | \(0.289265\pi\) | |||||||
\(654\) | 1.63310e29 | 0.446116 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.68862e29 | −0.446727 | ||||||||
\(657\) | −1.11929e29 | −0.291412 | ||||||||
\(658\) | −1.03987e28 | −0.0266444 | ||||||||
\(659\) | −2.44989e29 | −0.617803 | −0.308901 | − | 0.951094i | \(-0.599961\pi\) | ||||
−0.308901 | + | 0.951094i | \(0.599961\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.68385e28 | −0.114416 | −0.0572082 | − | 0.998362i | \(-0.518220\pi\) | ||||
−0.0572082 | + | 0.998362i | \(0.518220\pi\) | |||||||
\(662\) | 4.07420e29 | 0.979567 | ||||||||
\(663\) | −3.16911e28 | −0.0749972 | ||||||||
\(664\) | −6.47403e29 | −1.50803 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.91972e29 | −0.433269 | ||||||||
\(667\) | 3.15360e29 | 0.700625 | ||||||||
\(668\) | −4.12074e28 | −0.0901203 | ||||||||
\(669\) | −1.47476e29 | −0.317502 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.00280e29 | 0.209232 | ||||||||
\(672\) | −1.39967e28 | −0.0287507 | ||||||||
\(673\) | 6.92309e29 | 1.40004 | 0.700022 | − | 0.714121i | \(-0.253174\pi\) | ||||
0.700022 | + | 0.714121i | \(0.253174\pi\) | |||||||
\(674\) | −4.40013e29 | −0.876066 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.87764e29 | 0.362386 | ||||||||
\(677\) | 4.53998e28 | 0.0862726 | 0.0431363 | − | 0.999069i | \(-0.486265\pi\) | ||||
0.0431363 | + | 0.999069i | \(0.486265\pi\) | |||||||
\(678\) | −1.90728e29 | −0.356863 | ||||||||
\(679\) | −3.36723e28 | −0.0620355 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.78169e29 | −1.03279 | ||||||||
\(682\) | −3.80372e29 | −0.669072 | ||||||||
\(683\) | 7.04765e29 | 1.22075 | 0.610375 | − | 0.792112i | \(-0.291019\pi\) | ||||
0.610375 | + | 0.792112i | \(0.291019\pi\) | |||||||
\(684\) | 3.28466e28 | 0.0560276 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −6.97733e28 | −0.115421 | ||||||||
\(687\) | −5.69293e29 | −0.927450 | ||||||||
\(688\) | 4.11928e29 | 0.660910 | ||||||||
\(689\) | 3.49817e28 | 0.0552763 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.53737e29 | −1.15532 | −0.577658 | − | 0.816279i | \(-0.696033\pi\) | ||||
−0.577658 | + | 0.816279i | \(0.696033\pi\) | |||||||
\(692\) | 2.87195e29 | 0.433573 | ||||||||
\(693\) | 1.86884e28 | 0.0277890 | ||||||||
\(694\) | 4.56113e29 | 0.668033 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.76115e29 | −0.250264 | ||||||||
\(697\) | −1.22062e30 | −1.70859 | ||||||||
\(698\) | 1.05379e30 | 1.45302 | ||||||||
\(699\) | 2.68027e28 | 0.0364056 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.61496e29 | −0.871943 | −0.435971 | − | 0.899961i | \(-0.643595\pi\) | ||||
−0.435971 | + | 0.899961i | \(0.643595\pi\) | |||||||
\(702\) | −7.97341e27 | −0.0103539 | ||||||||
\(703\) | −5.88256e29 | −0.752550 | ||||||||
\(704\) | −9.57890e29 | −1.20727 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.57216e29 | 0.559335 | ||||||||
\(707\) | 5.76741e28 | 0.0695147 | ||||||||
\(708\) | −6.73774e28 | −0.0800138 | ||||||||
\(709\) | 1.51806e30 | 1.77625 | 0.888125 | − | 0.459601i | \(-0.152008\pi\) | ||||
0.888125 | + | 0.459601i | \(0.152008\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.94990e29 | 0.221504 | ||||||||
\(712\) | 1.45589e28 | 0.0162963 | ||||||||
\(713\) | −1.16402e30 | −1.28387 | ||||||||
\(714\) | 5.91840e28 | 0.0643240 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.40416e28 | −0.0886967 | ||||||||
\(717\) | −8.54535e29 | −0.888748 | ||||||||
\(718\) | −1.13591e30 | −1.16423 | ||||||||
\(719\) | −7.62329e29 | −0.769997 | −0.384999 | − | 0.922917i | \(-0.625798\pi\) | ||||
−0.384999 | + | 0.922917i | \(0.625798\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.65575e28 | 0.0456741 | ||||||||
\(722\) | 6.48980e29 | 0.627467 | ||||||||
\(723\) | −6.74230e28 | −0.0642474 | ||||||||
\(724\) | −1.05913e29 | −0.0994704 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.61547e29 | 0.147389 | ||||||||
\(727\) | −1.25316e30 | −1.12692 | −0.563461 | − | 0.826142i | \(-0.690531\pi\) | ||||
−0.563461 | + | 0.826142i | \(0.690531\pi\) | |||||||
\(728\) | 6.00732e27 | 0.00532478 | ||||||||
\(729\) | 4.23912e28 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.97762e30 | 2.52777 | ||||||||
\(732\) | −4.57382e28 | −0.0382748 | ||||||||
\(733\) | −9.66845e29 | −0.797563 | −0.398782 | − | 0.917046i | \(-0.630567\pi\) | ||||
−0.398782 | + | 0.917046i | \(0.630567\pi\) | |||||||
\(734\) | 1.10459e30 | 0.898244 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.52689e30 | −1.20667 | ||||||||
\(737\) | 1.37999e30 | 1.07515 | ||||||||
\(738\) | −3.07106e29 | −0.235883 | ||||||||
\(739\) | −1.13028e30 | −0.855892 | −0.427946 | − | 0.903804i | \(-0.640763\pi\) | ||||
−0.427946 | + | 0.903804i | \(0.640763\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.44328e28 | −0.0179838 | ||||||||
\(742\) | −6.53294e28 | −0.0474098 | ||||||||
\(743\) | 1.52259e30 | 1.08943 | 0.544717 | − | 0.838620i | \(-0.316637\pi\) | ||||
0.544717 | + | 0.838620i | \(0.316637\pi\) | |||||||
\(744\) | 6.50054e29 | 0.458600 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 3.39434e29 | 0.232808 | ||||||||
\(747\) | −6.83303e29 | −0.462112 | ||||||||
\(748\) | −1.20770e30 | −0.805365 | ||||||||
\(749\) | 1.85972e29 | 0.122289 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.27958e30 | −1.45759 | −0.728796 | − | 0.684731i | \(-0.759920\pi\) | ||||
−0.728796 | + | 0.684731i | \(0.759920\pi\) | |||||||
\(752\) | 3.67647e29 | 0.231816 | ||||||||
\(753\) | −1.23642e30 | −0.768811 | ||||||||
\(754\) | 3.49625e28 | 0.0214390 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −8.52387e27 | −0.00508345 | ||||||||
\(757\) | −2.33908e30 | −1.37575 | −0.687874 | − | 0.725830i | \(-0.741456\pi\) | ||||
−0.687874 | + | 0.725830i | \(0.741456\pi\) | |||||||
\(758\) | 2.04782e30 | 1.18786 | ||||||||
\(759\) | 2.03870e30 | 1.16631 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.09867e30 | 1.16790 | 0.583951 | − | 0.811789i | \(-0.301506\pi\) | ||||
0.583951 | + | 0.811789i | \(0.301506\pi\) | |||||||
\(762\) | −1.12947e30 | −0.619938 | ||||||||
\(763\) | −1.29864e29 | −0.0703043 | ||||||||
\(764\) | −4.64202e29 | −0.247872 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.26087e30 | −1.17456 | ||||||||
\(767\) | 5.01183e28 | 0.0256829 | ||||||||
\(768\) | 1.06203e30 | 0.536837 | ||||||||
\(769\) | −1.66515e29 | −0.0830286 | −0.0415143 | − | 0.999138i | \(-0.513218\pi\) | ||||
−0.0415143 | + | 0.999138i | \(0.513218\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.06455e30 | 0.516528 | ||||||||
\(772\) | 1.00621e30 | 0.481624 | ||||||||
\(773\) | −3.54312e30 | −1.67302 | −0.836509 | − | 0.547953i | \(-0.815407\pi\) | ||||
−0.836509 | + | 0.547953i | \(0.815407\pi\) | |||||||
\(774\) | 7.49163e29 | 0.348977 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.05137e30 | 0.930026 | ||||||||
\(777\) | 1.52656e29 | 0.0682797 | ||||||||
\(778\) | 5.17259e29 | 0.228256 | ||||||||
\(779\) | −9.41060e29 | −0.409708 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.38092e30 | 0.585239 | ||||||||
\(782\) | 6.45633e30 | 2.69970 | ||||||||
\(783\) | −1.85881e29 | −0.0766894 | ||||||||
\(784\) | 1.23017e30 | 0.500779 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −1.42125e30 | −0.563293 | ||||||||
\(787\) | 4.26632e30 | 1.66847 | 0.834236 | − | 0.551408i | \(-0.185909\pi\) | ||||
0.834236 | + | 0.551408i | \(0.185909\pi\) | |||||||
\(788\) | −5.00396e29 | −0.193103 | ||||||||
\(789\) | 1.75086e30 | 0.666718 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.51666e29 | 0.0562388 | ||||||||
\(792\) | −1.13852e30 | −0.416608 | ||||||||
\(793\) | 3.40221e28 | 0.0122855 | ||||||||
\(794\) | 3.55674e29 | 0.126747 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 9.79391e29 | 0.339914 | ||||||||
\(797\) | 2.93870e30 | 1.00657 | 0.503284 | − | 0.864121i | \(-0.332125\pi\) | ||||
0.503284 | + | 0.864121i | \(0.332125\pi\) | |||||||
\(798\) | 4.56289e28 | 0.0154245 | ||||||||
\(799\) | 2.65754e30 | 0.886622 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.53662e28 | 0.00499373 | ||||||||
\(802\) | 1.92293e30 | 0.616784 | ||||||||
\(803\) | 3.17284e30 | 1.00447 | ||||||||
\(804\) | −6.29423e29 | −0.196677 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.29050e29 | −0.0392861 | ||||||||
\(807\) | −3.26479e30 | −0.981032 | ||||||||
\(808\) | −3.51359e30 | −1.04215 | ||||||||
\(809\) | 2.08466e30 | 0.610345 | 0.305172 | − | 0.952297i | \(-0.401286\pi\) | ||||
0.305172 | + | 0.952297i | \(0.401286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.65885e29 | 0.247025 | 0.123513 | − | 0.992343i | \(-0.460584\pi\) | ||||
0.123513 | + | 0.992343i | \(0.460584\pi\) | |||||||
\(812\) | 3.73763e28 | 0.0105259 | ||||||||
\(813\) | −1.56483e30 | −0.435027 | ||||||||
\(814\) | 5.44179e30 | 1.49343 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.09246e30 | −0.559643 | ||||||||
\(817\) | 2.29565e30 | 0.606141 | ||||||||
\(818\) | −3.95721e30 | −1.03152 | ||||||||
\(819\) | 6.34044e27 | 0.00163169 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 7.71132e30 | 1.93431 | 0.967154 | − | 0.254190i | \(-0.0818090\pi\) | ||||
0.967154 | + | 0.254190i | \(0.0818090\pi\) | |||||||
\(822\) | −4.89327e29 | −0.121184 | ||||||||
\(823\) | −7.28859e30 | −1.78215 | −0.891077 | − | 0.453852i | \(-0.850049\pi\) | ||||
−0.891077 | + | 0.453852i | \(0.850049\pi\) | |||||||
\(824\) | −2.83635e30 | −0.684738 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −9.35974e28 | −0.0220279 | ||||||||
\(827\) | 7.57300e30 | 1.75979 | 0.879894 | − | 0.475170i | \(-0.157614\pi\) | ||||
0.879894 | + | 0.475170i | \(0.157614\pi\) | |||||||
\(828\) | −9.29862e29 | −0.213354 | ||||||||
\(829\) | −1.01498e30 | −0.229951 | −0.114975 | − | 0.993368i | \(-0.536679\pi\) | ||||
−0.114975 | + | 0.993368i | \(0.536679\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.83852e29 | 0.151061 | ||||||||
\(832\) | −3.24985e29 | −0.0708873 | ||||||||
\(833\) | 8.89228e30 | 1.91532 | ||||||||
\(834\) | 1.70256e30 | 0.362125 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.31098e29 | −0.193121 | ||||||||
\(837\) | 6.86101e29 | 0.140530 | ||||||||
\(838\) | 6.62097e30 | 1.33924 | ||||||||
\(839\) | −4.31459e30 | −0.861865 | −0.430933 | − | 0.902384i | \(-0.641815\pi\) | ||||
−0.430933 | + | 0.902384i | \(0.641815\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.31778e30 | −0.841206 | ||||||||
\(842\) | 2.69126e29 | 0.0517821 | ||||||||
\(843\) | 4.62966e30 | 0.879751 | ||||||||
\(844\) | 4.93521e29 | 0.0926212 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.68631e29 | 0.122405 | ||||||||
\(847\) | −1.28462e29 | −0.0232273 | ||||||||
\(848\) | 2.30973e30 | 0.412482 | ||||||||
\(849\) | 4.67482e30 | 0.824582 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.66531e31 | 2.86572 | ||||||||
\(852\) | −6.29846e29 | −0.107058 | ||||||||
\(853\) | −4.19489e30 | −0.704297 | −0.352149 | − | 0.935944i | \(-0.614549\pi\) | ||||
−0.352149 | + | 0.935944i | \(0.614549\pi\) | |||||||
\(854\) | −6.35374e28 | −0.0105371 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.13297e31 | −1.83334 | ||||||||
\(857\) | 5.58348e30 | 0.892497 | 0.446248 | − | 0.894909i | \(-0.352760\pi\) | ||||
0.446248 | + | 0.894909i | \(0.352760\pi\) | |||||||
\(858\) | 2.26021e29 | 0.0356888 | ||||||||
\(859\) | 4.37363e30 | 0.682203 | 0.341102 | − | 0.940026i | \(-0.389200\pi\) | ||||
0.341102 | + | 0.940026i | \(0.389200\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.44210e29 | 0.0371733 | ||||||||
\(862\) | −4.27455e29 | −0.0642782 | ||||||||
\(863\) | −3.15953e30 | −0.469363 | −0.234682 | − | 0.972072i | \(-0.575405\pi\) | ||||
−0.234682 | + | 0.972072i | \(0.575405\pi\) | |||||||
\(864\) | 8.99984e29 | 0.132081 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −3.47684e30 | −0.498020 | ||||||||
\(867\) | −1.10456e31 | −1.56310 | ||||||||
\(868\) | −1.37959e29 | −0.0192882 | ||||||||
\(869\) | −5.52734e30 | −0.763499 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.68193e29 | 0.0631297 | ||||||||
\(872\) | 7.91151e30 | 1.05399 | ||||||||
\(873\) | 2.16512e30 | 0.284992 | ||||||||
\(874\) | 4.97762e30 | 0.647369 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.44715e30 | −0.183747 | ||||||||
\(877\) | −1.26020e31 | −1.58104 | −0.790519 | − | 0.612438i | \(-0.790189\pi\) | ||||
−0.790519 | + | 0.612438i | \(0.790189\pi\) | |||||||
\(878\) | 2.87367e30 | 0.356241 | ||||||||
\(879\) | −2.91772e30 | −0.357405 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.94046e30 | 0.232091 | 0.116046 | − | 0.993244i | \(-0.462978\pi\) | ||||
0.116046 | + | 0.993244i | \(0.462978\pi\) | |||||||
\(882\) | 2.23728e30 | 0.264424 | ||||||||
\(883\) | −9.71752e30 | −1.13493 | −0.567464 | − | 0.823398i | \(-0.692075\pi\) | ||||
−0.567464 | + | 0.823398i | \(0.692075\pi\) | |||||||
\(884\) | −4.09739e29 | −0.0472888 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −5.83792e30 | −0.657967 | ||||||||
\(887\) | −1.21031e31 | −1.34803 | −0.674014 | − | 0.738719i | \(-0.735431\pi\) | ||||
−0.674014 | + | 0.738719i | \(0.735431\pi\) | |||||||
\(888\) | −9.30000e30 | −1.02364 | ||||||||
\(889\) | 8.98154e29 | 0.0976972 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.20166e30 | −0.127663 | ||||||||
\(892\) | −1.90674e30 | −0.200198 | ||||||||
\(893\) | 2.04888e30 | 0.212606 | ||||||||
\(894\) | 3.84474e30 | 0.394296 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.09820e29 | 0.0110014 | ||||||||
\(897\) | 6.91672e29 | 0.0684825 | ||||||||
\(898\) | −4.87518e30 | −0.477078 | ||||||||
\(899\) | −3.00848e30 | −0.290984 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.66959e31 | 1.57761 | ||||||||
\(902\) | 8.70549e30 | 0.813064 | ||||||||
\(903\) | −5.95733e29 | −0.0549959 | ||||||||
\(904\) | −9.23973e30 | −0.843123 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −3.26238e30 | −0.290863 | ||||||||
\(907\) | −1.16242e31 | −1.02444 | −0.512221 | − | 0.858854i | \(-0.671177\pi\) | ||||
−0.512221 | + | 0.858854i | \(0.671177\pi\) | |||||||
\(908\) | −7.47524e30 | −0.651214 | ||||||||
\(909\) | −3.70842e30 | −0.319351 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.25241e31 | −1.05391 | −0.526956 | − | 0.849893i | \(-0.676667\pi\) | ||||
−0.526956 | + | 0.849893i | \(0.676667\pi\) | |||||||
\(912\) | −1.61322e30 | −0.134199 | ||||||||
\(913\) | 1.93695e31 | 1.59285 | ||||||||
\(914\) | −1.44651e31 | −1.17595 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −7.36049e30 | −0.584796 | ||||||||
\(917\) | 1.13018e30 | 0.0887704 | ||||||||
\(918\) | −3.80551e30 | −0.295505 | ||||||||
\(919\) | −2.43739e30 | −0.187116 | −0.0935582 | − | 0.995614i | \(-0.529824\pi\) | ||||
−0.0935582 | + | 0.995614i | \(0.529824\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.06896e31 | −0.802110 | ||||||||
\(922\) | −1.35800e31 | −1.00745 | ||||||||
\(923\) | 4.68508e29 | 0.0343636 | ||||||||
\(924\) | 2.41625e29 | 0.0175221 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.94202e30 | −0.279450 | ||||||||
\(927\) | −2.99363e30 | −0.209827 | ||||||||
\(928\) | −3.94633e30 | −0.273489 | ||||||||
\(929\) | −1.07248e30 | −0.0734891 | −0.0367446 | − | 0.999325i | \(-0.511699\pi\) | ||||
−0.0367446 | + | 0.999325i | \(0.511699\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.85566e30 | 0.459280 | ||||||||
\(932\) | 3.46537e29 | 0.0229553 | ||||||||
\(933\) | −6.65910e30 | −0.436173 | ||||||||
\(934\) | −2.09311e31 | −1.35566 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.86269e29 | −0.0244621 | ||||||||
\(937\) | −1.98552e31 | −1.24339 | −0.621697 | − | 0.783258i | \(-0.713556\pi\) | ||||
−0.621697 | + | 0.783258i | \(0.713556\pi\) | |||||||
\(938\) | −8.74364e29 | −0.0541455 | ||||||||
\(939\) | 1.22338e31 | 0.749158 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.14059e31 | 0.683026 | 0.341513 | − | 0.939877i | \(-0.389061\pi\) | ||||
0.341513 | + | 0.939877i | \(0.389061\pi\) | |||||||
\(942\) | −1.49204e31 | −0.883581 | ||||||||
\(943\) | 2.66407e31 | 1.56017 | ||||||||
\(944\) | 3.30915e30 | 0.191651 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.12364e31 | −1.20289 | ||||||||
\(947\) | 3.85453e30 | 0.215922 | 0.107961 | − | 0.994155i | \(-0.465568\pi\) | ||||
0.107961 | + | 0.994155i | \(0.465568\pi\) | |||||||
\(948\) | 2.52105e30 | 0.139667 | ||||||||
\(949\) | 1.07646e30 | 0.0589795 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.62110e30 | −0.354842 | ||||||||
\(952\) | 2.86715e30 | 0.151971 | ||||||||
\(953\) | 3.66219e31 | 1.91984 | 0.959921 | − | 0.280271i | \(-0.0904242\pi\) | ||||
0.959921 | + | 0.280271i | \(0.0904242\pi\) | |||||||
\(954\) | 4.20066e30 | 0.217801 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.10484e31 | −0.560393 | ||||||||
\(957\) | 5.26913e30 | 0.264340 | ||||||||
\(958\) | 3.14161e30 | 0.155889 | ||||||||
\(959\) | 3.89112e29 | 0.0190976 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.72097e30 | −0.466782 | ||||||||
\(962\) | 1.84625e30 | 0.0876903 | ||||||||
\(963\) | −1.19579e31 | −0.561797 | ||||||||
\(964\) | −8.71723e29 | −0.0405107 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.29172e30 | −0.0587365 | ||||||||
\(967\) | 1.78235e31 | 0.801706 | 0.400853 | − | 0.916142i | \(-0.368714\pi\) | ||||
0.400853 | + | 0.916142i | \(0.368714\pi\) | |||||||
\(968\) | 7.82609e30 | 0.348220 | ||||||||
\(969\) | −1.16612e31 | −0.513266 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.90769e31 | −0.821684 | −0.410842 | − | 0.911707i | \(-0.634765\pi\) | ||||
−0.410842 | + | 0.911707i | \(0.634765\pi\) | |||||||
\(972\) | 5.48082e29 | 0.0233534 | ||||||||
\(973\) | −1.35387e30 | −0.0570679 | ||||||||
\(974\) | −1.01983e31 | −0.425264 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.24638e30 | 0.0916767 | ||||||||
\(977\) | 7.85849e29 | 0.0317282 | 0.0158641 | − | 0.999874i | \(-0.494950\pi\) | ||||
0.0158641 | + | 0.999874i | \(0.494950\pi\) | |||||||
\(978\) | 1.03409e31 | 0.413048 | ||||||||
\(979\) | −4.35583e29 | −0.0172128 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.35022e30 | 0.322978 | ||||||||
\(982\) | −9.47145e30 | −0.362448 | ||||||||
\(983\) | 1.71763e31 | 0.650307 | 0.325154 | − | 0.945661i | \(-0.394584\pi\) | ||||
0.325154 | + | 0.945661i | \(0.394584\pi\) | |||||||
\(984\) | −1.48776e31 | −0.557295 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.66868e31 | 0.611877 | ||||||||
\(987\) | −5.31694e29 | −0.0192900 | ||||||||
\(988\) | −3.15895e29 | −0.0113395 | ||||||||
\(989\) | −6.49880e31 | −2.30819 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.47902e31 | 1.55743 | 0.778716 | − | 0.627376i | \(-0.215871\pi\) | ||||
0.778716 | + | 0.627376i | \(0.215871\pi\) | |||||||
\(992\) | 1.45662e31 | 0.501158 | ||||||||
\(993\) | 2.08318e31 | 0.709185 | ||||||||
\(994\) | −8.74952e29 | −0.0294732 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.83453e30 | −0.291381 | ||||||||
\(997\) | −5.08780e31 | −1.66047 | −0.830235 | − | 0.557414i | \(-0.811794\pi\) | ||||
−0.830235 | + | 0.557414i | \(0.811794\pi\) | |||||||
\(998\) | −2.07040e29 | −0.00668627 | ||||||||
\(999\) | −9.81570e30 | −0.313678 |
(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 | 75.22.a.l.1.3 | yes | 8 | |
5.2 | odd | 4 | 75.22.b.j.49.6 | 16 | |||
5.3 | odd | 4 | 75.22.b.j.49.11 | 16 | |||
5.4 | even | 2 | 75.22.a.k.1.6 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.22.a.k.1.6 | ✓ | 8 | 5.4 | even | 2 | ||
75.22.a.l.1.3 | yes | 8 | 1.1 | even | 1 | trivial | |
75.22.b.j.49.6 | 16 | 5.2 | odd | 4 | |||
75.22.b.j.49.11 | 16 | 5.3 | odd | 4 |