Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [21,14,Mod(5,21)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(21, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 14, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("21.5");
S:= CuspForms(chi, 14);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 21 = 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 14 \) |
Character orbit: | \([\chi]\) | \(=\) | 21.g (of order \(6\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(22.5184950799\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{U}(1)[D_{6}]$ |
Embedding invariants
Embedding label | 5.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 21.5 |
Dual form | 21.14.g.a.17.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/21\mathbb{Z}\right)^\times\).
\(n\) | \(8\) | \(10\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(3\) | −1093.50 | + | 631.333i | −0.866025 | + | 0.500000i | ||||
\(4\) | −4096.00 | − | 7094.48i | −0.500000 | − | 0.866025i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 193284. | − | 243988.i | 0.620954 | − | 0.783847i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 797162. | − | 1.38072e6i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(12\) | 8.95795e6 | + | 5.17188e6i | 0.866025 | + | 0.500000i | ||||
\(13\) | 408541.i | 0.0234749i | 0.999931 | + | 0.0117374i | \(0.00373623\pi\) | ||||
−0.999931 | + | 0.0117374i | \(0.996264\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.35544e7 | + | 5.81180e7i | −0.500000 | + | 0.866025i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.20245e8 | − | 1.84894e8i | −1.56165 | − | 0.901621i | −0.997090 | − | 0.0762303i | \(-0.975712\pi\) |
−0.564563 | − | 0.825390i | \(-0.690955\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −5.73191e7 | + | 3.88828e8i | −0.145839 | + | 0.989308i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.10352e8 | + | 1.05716e9i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 2.01310e9i | 1.00000i | ||||||||
\(28\) | −2.52266e9 | − | 3.71878e8i | −0.989308 | − | 0.145839i | ||||
\(29\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.12279e9 | + | 4.11235e9i | −1.44145 | + | 0.832221i | −0.997947 | − | 0.0640519i | \(-0.979598\pi\) |
−0.443503 | + | 0.896273i | \(0.646264\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.30607e10 | −1.00000 | ||||||||
\(37\) | −1.36887e10 | + | 2.37095e10i | −0.877105 | + | 1.51919i | −0.0226010 | + | 0.999745i | \(0.507195\pi\) |
−0.854504 | + | 0.519445i | \(0.826139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.57925e8 | − | 4.46739e8i | −0.0117374 | − | 0.0203298i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.72188e10 | 1.86285 | 0.931426 | − | 0.363931i | \(-0.118566\pi\) | ||||
0.931426 | + | 0.363931i | \(0.118566\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(48\) | − | 8.47360e10i | − | 1.00000i | ||||||
\(49\) | −2.21712e10 | − | 9.43182e10i | −0.228831 | − | 0.973466i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.89838e9 | − | 1.67338e9i | 0.0203298 | − | 0.0117374i | ||||
\(53\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 4.66918e11 | 1.80324 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.12088e11 | − | 1.22449e11i | −0.527075 | − | 0.304307i | 0.212750 | − | 0.977107i | \(-0.431758\pi\) |
−0.739824 | + | 0.672800i | \(0.765091\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.82801e11 | − | 4.61370e11i | −0.368354 | − | 0.929686i | ||||
\(64\) | 5.49756e11 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.13436e11 | + | 1.96477e11i | 0.153202 | + | 0.265354i | 0.932403 | − | 0.361421i | \(-0.117708\pi\) |
−0.779201 | + | 0.626774i | \(0.784375\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.56615e12 | + | 9.04216e11i | −1.21125 | + | 0.699316i | −0.963032 | − | 0.269388i | \(-0.913179\pi\) |
−0.248219 | + | 0.968704i | \(0.579845\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.33484e12 | − | 7.70670e11i | −0.866025 | − | 0.500000i | ||||
\(76\) | 3.02930e12i | 1.80324i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.04227e12 | + | 3.53732e12i | −0.945229 | + | 1.63719i | −0.189938 | + | 0.981796i | \(0.560829\pi\) |
−0.755292 | + | 0.655389i | \(0.772505\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.27093e12 | − | 2.20132e12i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(84\) | 2.99331e12 | − | 1.18599e12i | 0.929686 | − | 0.368354i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.96790e10 | + | 7.89646e10i | 0.0184007 | + | 0.0145768i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 5.19252e12 | − | 8.99370e12i | 0.832221 | − | 1.44145i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.07990e13i | 1.31634i | 0.752869 | + | 0.658171i | \(0.228670\pi\) | ||||
−0.752869 | + | 0.658171i | \(0.771330\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000e12 | − | 8.66025e12i | 0.500000 | − | 0.866025i | ||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.82813e12 | − | 1.63282e12i | −0.233377 | − | 0.134740i | 0.378752 | − | 0.925498i | \(-0.376353\pi\) |
−0.612129 | + | 0.790758i | \(0.709687\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(108\) | 1.42819e13 | − | 8.24564e12i | 0.866025 | − | 0.500000i | ||||
\(109\) | −3.47667e12 | − | 6.02178e12i | −0.198560 | − | 0.343916i | 0.749502 | − | 0.662002i | \(-0.230293\pi\) |
−0.948062 | + | 0.318086i | \(0.896960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 3.45685e13i | − | 1.75421i | ||||||
\(112\) | 7.69453e12 | + | 1.94202e13i | 0.368354 | + | 0.929686i | ||||
\(113\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.64082e11 | + | 3.25673e11i | 0.0203298 | + | 0.0117374i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.72614e13 | + | 2.98975e13i | −0.500000 | + | 0.866025i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.83499e13 | + | 3.36883e13i | 1.44145 | + | 0.832221i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −4.28486e13 | −0.906176 | −0.453088 | − | 0.891466i | \(-0.649678\pi\) | ||||
−0.453088 | + | 0.891466i | \(0.649678\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.44388e13 | + | 4.87508e13i | −1.61328 | + | 0.931426i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.07010e14 | + | 4.23989e13i | −1.67645 | + | 0.664231i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1.21296e14i | − | 1.42642i | −0.700948 | − | 0.713212i | \(-0.747240\pi\) | ||
0.700948 | − | 0.713212i | \(-0.252760\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 5.34966e13 | + | 9.26588e13i | 0.500000 | + | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.37904e13 | + | 8.91395e13i | 0.684907 | + | 0.728631i | ||||
\(148\) | 2.24276e14 | 1.75421 | ||||||||
\(149\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.23837e14 | − | 2.14492e14i | −0.850159 | − | 1.47252i | −0.881064 | − | 0.472997i | \(-0.843172\pi\) |
0.0309046 | − | 0.999522i | \(-0.490161\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −2.11292e12 | + | 3.65969e12i | −0.0117374 | + | 0.0203298i | ||||
\(157\) | 4.79171e13 | − | 2.76649e13i | 0.255354 | − | 0.147429i | −0.366859 | − | 0.930276i | \(-0.619567\pi\) |
0.622213 | + | 0.782848i | \(0.286234\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.01637e14 | − | 3.49246e14i | 0.842077 | − | 1.45852i | −0.0460587 | − | 0.998939i | \(-0.514666\pi\) |
0.888136 | − | 0.459581i | \(-0.152001\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.02708e14 | 0.999449 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −5.10575e14 | + | 2.94780e14i | −1.56165 | + | 0.901621i | ||||
\(172\) | −3.16288e14 | − | 5.47827e14i | −0.931426 | − | 1.61328i | ||||
\(173\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.75906e14 | + | 5.54142e13i | 0.989308 | + | 0.145839i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.09326e14i | 1.92225i | 0.276120 | + | 0.961123i | \(0.410951\pi\) | ||||
−0.276120 | + | 0.961123i | \(0.589049\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.09224e14 | 0.608613 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.91171e14 | + | 3.89100e14i | 0.783847 | + | 0.620954i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(192\) | −6.01158e14 | + | 3.47079e14i | −0.866025 | + | 0.500000i | ||||
\(193\) | −6.57636e14 | − | 1.13906e15i | −0.915932 | − | 1.58644i | −0.805531 | − | 0.592554i | \(-0.798120\pi\) |
−0.110402 | − | 0.993887i | \(-0.535214\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.78325e14 | + | 5.43620e14i | −0.728631 | + | 0.684907i | ||||
\(197\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.51676e15 | + | 8.75704e14i | −1.73130 | + | 0.999568i | −0.850950 | + | 0.525246i | \(0.823973\pi\) |
−0.880352 | + | 0.474322i | \(0.842693\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.48084e14 | − | 1.43232e14i | −0.265354 | − | 0.153202i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.37436e13 | − | 1.37083e13i | −0.0203298 | − | 0.0117374i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.46966e15 | 1.92664 | 0.963321 | − | 0.268352i | \(-0.0864791\pi\) | ||||
0.963321 | + | 0.268352i | \(0.0864791\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.73363e14 | + | 2.53273e15i | −0.242741 | + | 1.64665i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.14172e15 | − | 1.97752e15i | 0.699316 | − | 1.21125i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.65730e15i | − | 1.99149i | −0.0921315 | − | 0.995747i | \(-0.529368\pi\) | ||
0.0921315 | − | 0.995747i | \(-0.470632\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.94620e15 | 1.00000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(228\) | −1.91250e15 | − | 3.31254e15i | −0.901621 | − | 1.56165i | ||||
\(229\) | 3.75822e15 | + | 2.16981e15i | 1.72207 | + | 0.994239i | 0.914630 | + | 0.404291i | \(0.132482\pi\) |
0.807442 | + | 0.589947i | \(0.200851\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 5.15741e15i | − | 1.89046i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.16120e15 | + | 2.97982e15i | −1.69684 | + | 0.979669i | −0.748108 | + | 0.663577i | \(0.769038\pi\) |
−0.948728 | + | 0.316093i | \(0.897629\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.77953e15 | + | 1.60476e15i | 0.866025 | + | 0.500000i | ||||
\(244\) | 2.00620e15i | 0.608613i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.55366e13 | − | 1.30833e14i | 0.0211654 | − | 0.0366596i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | −2.52443e15 | + | 3.18665e15i | −0.620954 | + | 0.783847i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.25180e15 | − | 3.90023e15i | −0.500000 | − | 0.866025i | ||||
\(257\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.13903e15 | + | 7.92257e15i | 0.646170 | + | 1.63086i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 9.29267e14 | − | 1.60954e15i | 0.153202 | − | 0.265354i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.97557e15 | − | 5.18205e15i | −1.37645 | − | 0.794696i | −0.384723 | − | 0.923032i | \(-0.625703\pi\) |
−0.991731 | + | 0.128336i | \(0.959036\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.58852e14 | − | 2.34172e13i | −0.0232239 | − | 0.00342355i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.00623e15 | + | 1.74284e15i | 0.133838 | + | 0.231814i | 0.925153 | − | 0.379595i | \(-0.123937\pi\) |
−0.791315 | + | 0.611408i | \(0.790603\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.31128e16i | 1.66444i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.36857e16 | + | 7.90142e15i | −1.58363 | + | 0.914310i | −0.589308 | + | 0.807908i | \(0.700600\pi\) |
−0.994323 | + | 0.106401i | \(0.966067\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.95229e15 | − | 8.57762e15i | 0.500000 | − | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.81778e15 | − | 1.18087e16i | −0.658171 | − | 1.13999i | ||||
\(292\) | 1.28299e16 | + | 7.40734e15i | 1.21125 | + | 0.699316i | ||||
\(293\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 1.26267e16i | 1.00000i | ||||||||
\(301\) | 1.49252e16 | − | 1.88405e16i | 1.15675 | − | 1.46019i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.14913e16 | − | 1.24080e16i | 1.56165 | − | 0.901621i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 1.75865e16i | − | 1.19889i | −0.800415 | − | 0.599446i | \(-0.795388\pi\) | ||
0.800415 | − | 0.599446i | \(-0.204612\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.12341e15 | 0.269480 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.71138e16 | − | 1.56542e16i | −1.62987 | − | 0.941005i | −0.984131 | − | 0.177446i | \(-0.943217\pi\) |
−0.645738 | − | 0.763559i | \(-0.723450\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.34606e16 | 1.89046 | ||||||||
\(317\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −1.04115e16 | + | 1.80332e16i | −0.500000 | + | 0.866025i | ||||
\(325\) | −4.31893e14 | + | 2.49353e14i | −0.0203298 | + | 0.0117374i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.60349e15 | + | 4.38988e15i | 0.343916 | + | 0.198560i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.36864e15 | + | 1.44949e16i | −0.349762 | + | 0.605806i | −0.986207 | − | 0.165516i | \(-0.947071\pi\) |
0.636445 | + | 0.771322i | \(0.280404\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.18242e16 | + | 3.78007e16i | 0.877105 | + | 1.51919i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.06746e16 | − | 1.63782e16i | −0.783847 | − | 0.620954i | ||||
\(337\) | −5.26531e16 | −1.95808 | −0.979039 | − | 0.203675i | \(-0.934711\pi\) | ||||
−0.979039 | + | 0.203675i | \(0.934711\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.72978e16 | − | 1.28207e16i | −0.905142 | − | 0.425110i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.86957e16i | 0.553830i | 0.960894 | + | 0.276915i | \(0.0893121\pi\) | ||||
−0.960894 | + | 0.276915i | \(0.910688\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.22431e14 | −0.0234749 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.73449e16 | + | 8.20038e16i | 1.12584 | + | 1.95001i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 4.35906e16i | − | 1.00000i | ||||||
\(364\) | 1.51927e14 | − | 1.03061e15i | 0.00342355 | − | 0.0232239i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.01591e16 | − | 3.47329e16i | 1.28520 | − | 0.742013i | 0.307409 | − | 0.951577i | \(-0.400538\pi\) |
0.977795 | + | 0.209565i | \(0.0672047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −8.50742e16 | −1.66444 | ||||||||
\(373\) | −5.03951e16 | + | 8.72870e16i | −0.968905 | + | 1.67819i | −0.270170 | + | 0.962813i | \(0.587080\pi\) |
−0.698735 | + | 0.715381i | \(0.746253\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.47585e16 | −1.12238 | −0.561192 | − | 0.827686i | \(-0.689657\pi\) | ||||
−0.561192 | + | 0.827686i | \(0.689657\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.68550e16 | − | 2.70517e16i | 0.784772 | − | 0.453088i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.15559e16 | − | 1.06618e17i | 0.931426 | − | 1.61328i | ||||
\(388\) | 7.66135e16 | − | 4.42328e16i | 1.13999 | − | 0.658171i | ||||
\(389\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.64904e16 | + | 1.52943e16i | 0.339587 | + | 0.196061i | 0.660089 | − | 0.751187i | \(-0.270518\pi\) |
−0.320502 | + | 0.947248i | \(0.603852\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.02480e16 | − | 1.13922e17i | 1.11973 | − | 1.41346i | ||||
\(400\) | −8.19200e16 | −1.00000 | ||||||||
\(401\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.68006e15 | − | 2.90995e15i | −0.0195363 | − | 0.0338378i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.04425e17 | − | 6.02900e16i | 1.10307 | − | 0.636860i | 0.166047 | − | 0.986118i | \(-0.446900\pi\) |
0.937027 | + | 0.349258i | \(0.113566\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.67521e16i | 0.269480i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.65778e16 | + | 1.32637e17i | 0.713212 | + | 1.23532i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.77139e15 | 0.0505181 | 0.0252590 | − | 0.999681i | \(-0.491959\pi\) | ||||
0.0252590 | + | 0.999681i | \(0.491959\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.08694e16 | + | 2.80794e16i | −0.565819 | + | 0.224185i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(432\) | −1.16997e17 | − | 6.75483e16i | −0.866025 | − | 0.500000i | ||||
\(433\) | 2.50198e17i | 1.82437i | 0.409783 | + | 0.912183i | \(0.365604\pi\) | ||||
−0.409783 | + | 0.912183i | \(0.634396\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.84809e16 | + | 4.93304e16i | −0.198560 | + | 0.343916i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.58756e17 | − | 1.49393e17i | −1.72532 | − | 0.996116i | −0.906686 | − | 0.421806i | \(-0.861396\pi\) |
−0.818638 | − | 0.574310i | \(-0.805270\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.47901e17 | − | 4.45745e16i | −0.957462 | − | 0.288560i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(444\) | −2.45246e17 | + | 1.41593e17i | −1.51919 | + | 0.877105i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.06259e17 | − | 1.34134e17i | 0.620954 | − | 0.783847i | ||||
\(449\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.70832e17 | + | 1.56365e17i | 1.47252 | + | 0.850159i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.61143e17 | + | 2.79109e17i | −0.827480 | + | 1.43324i | 0.0725294 | + | 0.997366i | \(0.476893\pi\) |
−0.900009 | + | 0.435871i | \(0.856440\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.67094e17 | 1.73181 | 0.865906 | − | 0.500206i | \(-0.166743\pi\) | ||||
0.865906 | + | 0.500206i | \(0.166743\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(468\) | − | 5.33582e15i | − | 0.0234749i | ||||||
\(469\) | 6.98634e16 | + | 1.02989e16i | 0.303128 | + | 0.0446857i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.49316e16 | + | 6.05032e16i | −0.147429 | + | 0.255354i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 4.51401e17i | − | 1.80324i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.68631e15 | − | 5.59239e15i | −0.0356628 | − | 0.0205899i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.82810e17 | 1.00000 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.94302e17 | − | 5.09746e17i | −0.999667 | − | 1.73147i | −0.522191 | − | 0.852828i | \(-0.674885\pi\) |
−0.477475 | − | 0.878645i | \(-0.658448\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.09201e17i | 1.68415i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.51950e17i | − | 1.66444i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.13307e17 | − | 5.42664e17i | 0.908483 | − | 1.57354i | 0.0923099 | − | 0.995730i | \(-0.470575\pi\) |
0.816173 | − | 0.577808i | \(-0.196092\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.31011e17 | + | 1.91110e17i | −0.865548 | + | 0.499724i | ||||
\(508\) | 1.75508e17 | + | 3.03989e17i | 0.453088 | + | 0.784772i | ||||
\(509\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.20943e16 | + | 5.56892e17i | −0.203975 | + | 1.38368i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.72209e17 | − | 6.44685e17i | 0.901621 | − | 1.56165i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 6.91723e17 | + | 3.99366e17i | 1.61328 | + | 0.931426i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.64546e17 | − | 1.52736e17i | −0.565250 | − | 0.326347i | 0.190000 | − | 0.981784i | \(-0.439151\pi\) |
−0.755250 | + | 0.655437i | \(0.772484\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.46038e17 | + | 1.76726e17i | −0.929686 | + | 0.368354i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2.52018e17 | − | 4.36508e17i | −0.500000 | − | 0.866025i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.39112e17 | + | 5.85517e17i | 1.41346 | + | 1.11973i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.64242e17 | + | 6.30886e17i | −0.624609 | + | 1.08185i | 0.364008 | + | 0.931396i | \(0.381408\pi\) |
−0.988616 | + | 0.150458i | \(0.951925\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −5.74087e17 | − | 9.94348e17i | −0.961123 | − | 1.66471i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −8.71581e17 | −1.39120 | −0.695601 | − | 0.718428i | \(-0.744862\pi\) | ||||
−0.695601 | + | 0.718428i | \(0.744862\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −3.38137e17 | + | 1.95223e17i | −0.527075 | + | 0.304307i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.68323e17 | + | 1.18200e18i | 0.696358 | + | 1.75753i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.60529e17 | + | 4.96827e17i | −1.23532 | + | 0.713212i | ||||
\(557\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.15470e16i | 0.0437302i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.82747e17 | − | 1.15389e17i | −0.989308 | − | 0.145839i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.04237e17 | + | 3.53750e17i | 0.246604 | + | 0.427131i | 0.962581 | − | 0.270993i | \(-0.0873519\pi\) |
−0.715977 | + | 0.698124i | \(0.754019\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 4.38244e17 | − | 7.59061e17i | 0.500000 | − | 0.866025i | ||||
\(577\) | −5.76940e17 | + | 3.33096e17i | −0.650860 | + | 0.375774i | −0.788786 | − | 0.614668i | \(-0.789290\pi\) |
0.137926 | + | 0.990443i | \(0.455957\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.43825e18 | + | 8.30375e17i | 1.58644 | + | 0.915932i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(588\) | 2.89193e17 | − | 9.59564e17i | 0.288560 | − | 0.957462i | ||||
\(589\) | 3.04139e18 | 3.00139 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.18634e17 | − | 1.59112e18i | −0.877105 | − | 1.51919i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.10572e18 | − | 1.91516e18i | 0.999568 | − | 1.73130i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 1.02438e18i | − | 0.886700i | −0.896349 | − | 0.443350i | \(-0.853790\pi\) | ||
0.896349 | − | 0.443350i | \(-0.146210\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.61707e17 | 0.306404 | ||||||||
\(604\) | −1.01447e18 | + | 1.75712e18i | −0.850159 | + | 1.47252i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.09302e18 | − | 1.20841e18i | −1.69843 | − | 0.980588i | −0.947254 | − | 0.320484i | \(-0.896154\pi\) |
−0.751174 | − | 0.660104i | \(-0.770512\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6.27610e17 | + | 1.08705e18i | 0.477746 | + | 0.827480i | 0.999675 | − | 0.0255091i | \(-0.00812068\pi\) |
−0.521929 | + | 0.852989i | \(0.674787\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.84883e18 | − | 1.06742e18i | 1.32101 | − | 0.762688i | 0.337124 | − | 0.941460i | \(-0.390546\pi\) |
0.983890 | + | 0.178772i | \(0.0572125\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 3.46181e16 | 0.0234749 | ||||||||
\(625\) | −7.45058e17 | + | 1.29048e18i | −0.500000 | + | 0.866025i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.92537e17 | − | 2.26631e17i | −0.255354 | − | 0.147429i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.06063e18 | 1.93028 | 0.965139 | − | 0.261736i | \(-0.0842951\pi\) | ||||
0.965139 | + | 0.261736i | \(0.0842951\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.70057e18 | + | 1.55918e18i | −1.66852 | + | 0.963321i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.85328e16 | − | 9.05784e15i | 0.0228520 | − | 0.00537178i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.14675e17i | 0.454583i | 0.973827 | + | 0.227291i | \(0.0729870\pi\) | ||||
−0.973827 | + | 0.227291i | \(0.927013\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.19072e18 | − | 3.00525e18i | −0.613104 | − | 1.54741i | ||||
\(652\) | −3.30363e18 | −1.68415 | ||||||||
\(653\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.88322e18i | 1.39863i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.82087e18 | − | 1.62863e18i | 1.31545 | − | 0.759473i | 0.332454 | − | 0.943120i | \(-0.392123\pi\) |
0.982992 | + | 0.183646i | \(0.0587902\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.30897e18 | + | 3.99926e18i | 0.995747 | + | 1.72468i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.76575e18 | −1.56226 | −0.781130 | − | 0.624369i | \(-0.785356\pi\) | ||||
−0.781130 | + | 0.624369i | \(0.785356\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.12816e18 | + | 1.22870e18i | −0.866025 | + | 0.500000i | ||||
\(676\) | −1.23989e18 | − | 2.14756e18i | −0.499724 | − | 0.865548i | ||||
\(677\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.63483e18 | + | 2.08729e18i | 1.03181 | + | 0.817388i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(684\) | 4.18263e18 | + | 2.41484e18i | 1.56165 | + | 0.901621i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.47948e18 | −1.98848 | ||||||||
\(688\) | −2.59103e18 | + | 4.48780e18i | −0.931426 | + | 1.61328i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.92727e18 | − | 2.84476e18i | −1.72186 | − | 0.994119i | −0.915079 | − | 0.403274i | \(-0.867872\pi\) |
−0.806785 | − | 0.590845i | \(-0.798794\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.14658e18 | − | 2.89383e18i | −0.368354 | − | 0.929686i | ||||
\(701\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.76749e18 | − | 5.06192e18i | 2.73947 | − | 1.58163i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.29769e18 | − | 3.97971e18i | 0.679345 | − | 1.17666i | −0.295834 | − | 0.955239i | \(-0.595598\pi\) |
0.975179 | − | 0.221420i | \(-0.0710691\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.25604e18 | + | 5.63962e18i | 0.945229 | + | 1.63719i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.45022e17 | + | 3.74430e17i | −0.250532 | + | 0.0992640i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.76252e18 | − | 6.51687e18i | 0.979669 | − | 1.69684i | ||||
\(724\) | 6.45120e18 | − | 3.72460e18i | 1.66471 | − | 0.961123i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 5.02783e18i | − | 1.26301i | −0.775371 | − | 0.631505i | \(-0.782437\pi\) | ||
0.775371 | − | 0.631505i | \(-0.217563\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.05256e18 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1.26658e18 | − | 2.19379e18i | −0.304307 | − | 0.527075i | ||||
\(733\) | 8.30992e17 | + | 4.79773e17i | 0.197889 | + | 0.114251i | 0.595670 | − | 0.803229i | \(-0.296887\pi\) |
−0.397782 | + | 0.917480i | \(0.630220\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4.32301e18 | + | 7.48767e18i | 0.976332 | + | 1.69106i | 0.675468 | + | 0.737389i | \(0.263942\pi\) |
0.300864 | + | 0.953667i | \(0.402725\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.90755e17i | 0.0423309i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.91634e18 | + | 8.51536e18i | −0.999960 | + | 1.73198i | −0.492256 | + | 0.870450i | \(0.663828\pi\) |
−0.507704 | + | 0.861532i | \(0.669506\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 7.48627e17 | − | 5.07836e18i | 0.145839 | − | 0.989308i | ||||
\(757\) | −1.18142e18 | −0.228182 | −0.114091 | − | 0.993470i | \(-0.536396\pi\) | ||||
−0.114091 | + | 0.993470i | \(0.536396\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.14123e18 | − | 3.15649e17i | −0.392874 | − | 0.0579156i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4.92469e18 | + | 2.84327e18i | 0.866025 | + | 0.500000i | ||||
\(769\) | − | 6.27137e17i | − | 0.109356i | −0.998504 | − | 0.0546778i | \(-0.982587\pi\) | ||
0.998504 | − | 0.0546778i | \(-0.0174132\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.38736e18 | + | 9.33118e18i | −0.915932 | + | 1.58644i | ||||
\(773\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −8.69482e18 | − | 5.01995e18i | −1.44145 | − | 0.832221i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.43430e18 | − | 6.68156e18i | −1.37503 | − | 1.08928i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.22552e18 | + | 1.87625e18i | 0.957462 | + | 0.288560i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.30716e18 | + | 4.79614e18i | −1.24628 | + | 0.719542i | −0.970366 | − | 0.241639i | \(-0.922315\pi\) |
−0.275918 | + | 0.961181i | \(0.588982\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.00254e16 | − | 8.66465e16i | 0.00714356 | − | 0.0123730i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.24253e19 | + | 7.17377e18i | 1.73130 | + | 0.999568i | ||||
\(797\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 2.34671e18i | 0.306404i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.11200e19i | 1.37237i | 0.727429 | + | 0.686183i | \(0.240715\pi\) | ||||
−0.727429 | + | 0.686183i | \(0.759285\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.30864e19 | 1.58939 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.47290e19 | − | 1.42773e19i | −2.90913 | − | 1.67959i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.88489e17 | − | 7.46817e16i | 0.0218243 | − | 0.00864706i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.30311e18 | + | 1.26494e19i | 0.819236 | + | 1.41896i | 0.906246 | + | 0.422751i | \(0.138935\pi\) |
−0.0870099 | + | 0.996207i | \(0.527731\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.16931e17 | + | 1.25245e17i | −0.0232123 | + | 0.0134016i | −0.511561 | − | 0.859247i | \(-0.670933\pi\) |
0.488349 | + | 0.872648i | \(0.337599\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.20062e18 | − | 1.27053e18i | −0.231814 | − | 0.133838i | ||||
\(832\) | 2.24598e17i | 0.0234749i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.27855e18 | − | 1.43389e19i | −0.832221 | − | 1.44145i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.02606e19 | 1.00000 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.01157e19 | − | 1.75209e19i | −0.963321 | − | 1.66852i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.95829e18 | + | 9.99029e18i | 0.368354 | + | 0.929686i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.97685e18 | − | 1.72804e19i | 0.914310 | − | 1.58363i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 1.07549e19i | − | 0.955958i | −0.878371 | − | 0.477979i | \(-0.841370\pi\) | ||
0.878371 | − | 0.477979i | \(-0.158630\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.40195e19 | + | 8.09414e18i | 1.19063 | + | 0.687409i | 0.958449 | − | 0.285264i | \(-0.0920814\pi\) |
0.232178 | + | 0.972673i | \(0.425415\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.25062e19i | 1.00000i | ||||||||
\(868\) | 1.94977e19 | − | 7.72524e18i | 1.54741 | − | 0.613104i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.02688e16 | + | 4.63432e16i | −0.00622915 | + | 0.00359640i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.49105e19 | + | 8.60857e18i | 1.13999 | + | 0.658171i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.87060e19 | −1.39863 | ||||||||
\(877\) | 1.34136e19 | − | 2.32330e19i | 0.995513 | − | 1.72428i | 0.415805 | − | 0.909454i | \(-0.363500\pi\) |
0.579708 | − | 0.814825i | \(-0.303167\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.83204e19 | 1.30074 | 0.650369 | − | 0.759618i | \(-0.274614\pi\) | ||||
0.650369 | + | 0.759618i | \(0.274614\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.28197e18 | + | 1.04545e19i | −0.562694 | + | 0.710303i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.59466e19 | + | 1.49803e19i | −1.72468 | + | 0.995747i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0 | 0 | ||||||||
\(900\) | −7.97162e18 | − | 1.38072e19i | −0.500000 | − | 0.866025i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.42611e18 | + | 3.00248e19i | −0.271676 | + | 1.84293i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.46591e19 | − | 2.53903e19i | −0.874300 | − | 1.51433i | −0.857506 | − | 0.514473i | \(-0.827987\pi\) |
−0.0167938 | − | 0.999859i | \(-0.505346\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(912\) | −1.56672e19 | + | 2.71363e19i | −0.901621 | + | 1.56165i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 3.55501e19i | − | 1.98848i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.88591e18 | + | 6.73060e18i | −0.212786 | + | 0.368555i | −0.952585 | − | 0.304272i | \(-0.901587\pi\) |
0.739800 | + | 0.672827i | \(0.234920\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.11029e19 | + | 1.92308e19i | 0.599446 | + | 1.03827i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.34197e19 | −1.75421 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.50895e18 | + | 2.60324e18i | −0.233377 | + | 0.134740i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.03386e19 | + | 3.43043e19i | −0.520343 | + | 1.72653i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 2.38155e18i | 0.114961i | 0.998347 | + | 0.0574807i | \(0.0183068\pi\) | ||||
−0.998347 | + | 0.0574807i | \(0.981693\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.95320e19 | 1.88201 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(948\) | −3.65891e19 | + | 2.11247e19i | −1.63719 | + | 0.945229i | ||||
\(949\) | −3.69409e17 | − | 6.39835e17i | −0.0164164 | − | 0.0284340i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.16140e19 | − | 3.74366e19i | 0.885184 | − | 1.53318i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.22806e19 | + | 2.44107e19i | 1.69684 | + | 0.979669i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.22274e19 | 1.66082 | 0.830409 | − | 0.557154i | \(-0.188107\pi\) | ||||
0.830409 | + | 0.557154i | \(0.188107\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(972\) | − | 2.62924e19i | − | 1.00000i | ||||||
\(973\) | −2.95947e19 | − | 2.34445e19i | −1.11810 | − | 0.885744i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.14850e17 | − | 5.45336e17i | 0.0117374 | − | 0.0203298i | ||||
\(976\) | 1.42330e19 | − | 8.21742e18i | 0.527075 | − | 0.304307i | ||||
\(977\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1.10859e19 | −0.397120 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.23759e18 | −0.0423309 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.19587e19 | − | 2.07131e19i | −0.401057 | − | 0.694651i | 0.592797 | − | 0.805352i | \(-0.298024\pi\) |
−0.993854 | + | 0.110701i | \(0.964690\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 2.11336e19i | − | 0.699524i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.81081e19 | + | 1.62282e19i | −0.906386 | + | 0.523302i | −0.879267 | − | 0.476330i | \(-0.841967\pi\) |
−0.0271194 | + | 0.999632i | \(0.508633\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.77296e19 | − | 2.75567e19i | −1.51919 | − | 0.877105i |
(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 | 21.14.g.a.5.1 | ✓ | 2 | |
3.2 | odd | 2 | CM | 21.14.g.a.5.1 | ✓ | 2 | |
7.3 | odd | 6 | inner | 21.14.g.a.17.1 | yes | 2 | |
21.17 | even | 6 | inner | 21.14.g.a.17.1 | yes | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.14.g.a.5.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
21.14.g.a.5.1 | ✓ | 2 | 3.2 | odd | 2 | CM | |
21.14.g.a.17.1 | yes | 2 | 7.3 | odd | 6 | inner | |
21.14.g.a.17.1 | yes | 2 | 21.17 | even | 6 | inner |