Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5070,2,Mod(1,5070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5070, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5070.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5070 = 2 \cdot 3 \cdot 5 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5070.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: | \(40.4841538248\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 390) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 5070.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −2.00000 | −0.755929 | −0.377964 | − | 0.925820i | \(-0.623376\pi\) | ||||
−0.377964 | + | 0.925820i | \(0.623376\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −6.46410 | −1.94900 | −0.974500 | − | 0.224388i | \(-0.927962\pi\) | ||||
−0.974500 | + | 0.224388i | \(0.927962\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 2.00000 | 0.534522 | ||||||||
\(15\) | 1.00000 | 0.258199 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.00000 | 0.970143 | 0.485071 | − | 0.874475i | \(-0.338794\pi\) | ||||
0.485071 | + | 0.874475i | \(0.338794\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −7.46410 | −1.71238 | −0.856191 | − | 0.516659i | \(-0.827175\pi\) | ||||
−0.856191 | + | 0.516659i | \(0.827175\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 6.46410 | 1.37815 | ||||||||
\(23\) | −3.73205 | −0.778186 | −0.389093 | − | 0.921198i | \(-0.627212\pi\) | ||||
−0.389093 | + | 0.921198i | \(0.627212\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −2.00000 | −0.377964 | ||||||||
\(29\) | 0.267949 | 0.0497569 | 0.0248785 | − | 0.999690i | \(-0.492080\pi\) | ||||
0.0248785 | + | 0.999690i | \(0.492080\pi\) | |||||||
\(30\) | −1.00000 | −0.182574 | ||||||||
\(31\) | 1.73205 | 0.311086 | 0.155543 | − | 0.987829i | \(-0.450287\pi\) | ||||
0.155543 | + | 0.987829i | \(0.450287\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 6.46410 | 1.12526 | ||||||||
\(34\) | −4.00000 | −0.685994 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −9.19615 | −1.51184 | −0.755919 | − | 0.654665i | \(-0.772810\pi\) | ||||
−0.755919 | + | 0.654665i | \(0.772810\pi\) | |||||||
\(38\) | 7.46410 | 1.21084 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | −2.00000 | −0.308607 | ||||||||
\(43\) | −11.9282 | −1.81903 | −0.909517 | − | 0.415667i | \(-0.863548\pi\) | ||||
−0.909517 | + | 0.415667i | \(0.863548\pi\) | |||||||
\(44\) | −6.46410 | −0.974500 | ||||||||
\(45\) | −1.00000 | −0.149071 | ||||||||
\(46\) | 3.73205 | 0.550261 | ||||||||
\(47\) | −3.53590 | −0.515764 | −0.257882 | − | 0.966176i | \(-0.583025\pi\) | ||||
−0.257882 | + | 0.966176i | \(0.583025\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −4.00000 | −0.560112 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.928203 | 0.127499 | 0.0637493 | − | 0.997966i | \(-0.479694\pi\) | ||||
0.0637493 | + | 0.997966i | \(0.479694\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 6.46410 | 0.871619 | ||||||||
\(56\) | 2.00000 | 0.267261 | ||||||||
\(57\) | 7.46410 | 0.988644 | ||||||||
\(58\) | −0.267949 | −0.0351835 | ||||||||
\(59\) | 8.46410 | 1.10193 | 0.550966 | − | 0.834528i | \(-0.314259\pi\) | ||||
0.550966 | + | 0.834528i | \(0.314259\pi\) | |||||||
\(60\) | 1.00000 | 0.129099 | ||||||||
\(61\) | −10.3923 | −1.33060 | −0.665299 | − | 0.746577i | \(-0.731696\pi\) | ||||
−0.665299 | + | 0.746577i | \(0.731696\pi\) | |||||||
\(62\) | −1.73205 | −0.219971 | ||||||||
\(63\) | −2.00000 | −0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.46410 | −0.795676 | ||||||||
\(67\) | −11.4641 | −1.40056 | −0.700281 | − | 0.713867i | \(-0.746942\pi\) | ||||
−0.700281 | + | 0.713867i | \(0.746942\pi\) | |||||||
\(68\) | 4.00000 | 0.485071 | ||||||||
\(69\) | 3.73205 | 0.449286 | ||||||||
\(70\) | −2.00000 | −0.239046 | ||||||||
\(71\) | 12.3923 | 1.47070 | 0.735348 | − | 0.677690i | \(-0.237019\pi\) | ||||
0.735348 | + | 0.677690i | \(0.237019\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 2.00000 | 0.234082 | 0.117041 | − | 0.993127i | \(-0.462659\pi\) | ||||
0.117041 | + | 0.993127i | \(0.462659\pi\) | |||||||
\(74\) | 9.19615 | 1.06903 | ||||||||
\(75\) | −1.00000 | −0.115470 | ||||||||
\(76\) | −7.46410 | −0.856191 | ||||||||
\(77\) | 12.9282 | 1.47331 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.9282 | −1.56705 | −0.783523 | − | 0.621363i | \(-0.786579\pi\) | ||||
−0.783523 | + | 0.621363i | \(0.786579\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.00000 | −0.220863 | ||||||||
\(83\) | −8.92820 | −0.979998 | −0.489999 | − | 0.871723i | \(-0.663003\pi\) | ||||
−0.489999 | + | 0.871723i | \(0.663003\pi\) | |||||||
\(84\) | 2.00000 | 0.218218 | ||||||||
\(85\) | −4.00000 | −0.433861 | ||||||||
\(86\) | 11.9282 | 1.28625 | ||||||||
\(87\) | −0.267949 | −0.0287272 | ||||||||
\(88\) | 6.46410 | 0.689076 | ||||||||
\(89\) | 0.535898 | 0.0568051 | 0.0284026 | − | 0.999597i | \(-0.490958\pi\) | ||||
0.0284026 | + | 0.999597i | \(0.490958\pi\) | |||||||
\(90\) | 1.00000 | 0.105409 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −3.73205 | −0.389093 | ||||||||
\(93\) | −1.73205 | −0.179605 | ||||||||
\(94\) | 3.53590 | 0.364700 | ||||||||
\(95\) | 7.46410 | 0.765801 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | −0.535898 | −0.0544122 | −0.0272061 | − | 0.999630i | \(-0.508661\pi\) | ||||
−0.0272061 | + | 0.999630i | \(0.508661\pi\) | |||||||
\(98\) | 3.00000 | 0.303046 | ||||||||
\(99\) | −6.46410 | −0.649667 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −2.92820 | −0.291367 | −0.145684 | − | 0.989331i | \(-0.546538\pi\) | ||||
−0.145684 | + | 0.989331i | \(0.546538\pi\) | |||||||
\(102\) | 4.00000 | 0.396059 | ||||||||
\(103\) | 11.8564 | 1.16825 | 0.584123 | − | 0.811665i | \(-0.301438\pi\) | ||||
0.584123 | + | 0.811665i | \(0.301438\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.00000 | −0.195180 | ||||||||
\(106\) | −0.928203 | −0.0901551 | ||||||||
\(107\) | −7.85641 | −0.759507 | −0.379754 | − | 0.925088i | \(-0.623991\pi\) | ||||
−0.379754 | + | 0.925088i | \(0.623991\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 15.8564 | 1.51877 | 0.759384 | − | 0.650643i | \(-0.225500\pi\) | ||||
0.759384 | + | 0.650643i | \(0.225500\pi\) | |||||||
\(110\) | −6.46410 | −0.616328 | ||||||||
\(111\) | 9.19615 | 0.872860 | ||||||||
\(112\) | −2.00000 | −0.188982 | ||||||||
\(113\) | 0.803848 | 0.0756196 | 0.0378098 | − | 0.999285i | \(-0.487962\pi\) | ||||
0.0378098 | + | 0.999285i | \(0.487962\pi\) | |||||||
\(114\) | −7.46410 | −0.699077 | ||||||||
\(115\) | 3.73205 | 0.348016 | ||||||||
\(116\) | 0.267949 | 0.0248785 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −8.46410 | −0.779184 | ||||||||
\(119\) | −8.00000 | −0.733359 | ||||||||
\(120\) | −1.00000 | −0.0912871 | ||||||||
\(121\) | 30.7846 | 2.79860 | ||||||||
\(122\) | 10.3923 | 0.940875 | ||||||||
\(123\) | −2.00000 | −0.180334 | ||||||||
\(124\) | 1.73205 | 0.155543 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 2.00000 | 0.178174 | ||||||||
\(127\) | 4.92820 | 0.437307 | 0.218654 | − | 0.975803i | \(-0.429834\pi\) | ||||
0.218654 | + | 0.975803i | \(0.429834\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 11.9282 | 1.05022 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −18.6603 | −1.63035 | −0.815177 | − | 0.579212i | \(-0.803360\pi\) | ||||
−0.815177 | + | 0.579212i | \(0.803360\pi\) | |||||||
\(132\) | 6.46410 | 0.562628 | ||||||||
\(133\) | 14.9282 | 1.29444 | ||||||||
\(134\) | 11.4641 | 0.990348 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | −4.00000 | −0.342997 | ||||||||
\(137\) | −2.46410 | −0.210522 | −0.105261 | − | 0.994445i | \(-0.533568\pi\) | ||||
−0.105261 | + | 0.994445i | \(0.533568\pi\) | |||||||
\(138\) | −3.73205 | −0.317693 | ||||||||
\(139\) | −12.9282 | −1.09656 | −0.548278 | − | 0.836296i | \(-0.684716\pi\) | ||||
−0.548278 | + | 0.836296i | \(0.684716\pi\) | |||||||
\(140\) | 2.00000 | 0.169031 | ||||||||
\(141\) | 3.53590 | 0.297776 | ||||||||
\(142\) | −12.3923 | −1.03994 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −0.267949 | −0.0222520 | ||||||||
\(146\) | −2.00000 | −0.165521 | ||||||||
\(147\) | 3.00000 | 0.247436 | ||||||||
\(148\) | −9.19615 | −0.755919 | ||||||||
\(149\) | 13.5359 | 1.10890 | 0.554452 | − | 0.832216i | \(-0.312928\pi\) | ||||
0.554452 | + | 0.832216i | \(0.312928\pi\) | |||||||
\(150\) | 1.00000 | 0.0816497 | ||||||||
\(151\) | −10.3923 | −0.845714 | −0.422857 | − | 0.906196i | \(-0.638973\pi\) | ||||
−0.422857 | + | 0.906196i | \(0.638973\pi\) | |||||||
\(152\) | 7.46410 | 0.605419 | ||||||||
\(153\) | 4.00000 | 0.323381 | ||||||||
\(154\) | −12.9282 | −1.04178 | ||||||||
\(155\) | −1.73205 | −0.139122 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −5.00000 | −0.399043 | −0.199522 | − | 0.979893i | \(-0.563939\pi\) | ||||
−0.199522 | + | 0.979893i | \(0.563939\pi\) | |||||||
\(158\) | 13.9282 | 1.10807 | ||||||||
\(159\) | −0.928203 | −0.0736113 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 7.46410 | 0.588254 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 15.0526 | 1.17901 | 0.589504 | − | 0.807766i | \(-0.299323\pi\) | ||||
0.589504 | + | 0.807766i | \(0.299323\pi\) | |||||||
\(164\) | 2.00000 | 0.156174 | ||||||||
\(165\) | −6.46410 | −0.503230 | ||||||||
\(166\) | 8.92820 | 0.692963 | ||||||||
\(167\) | −16.3205 | −1.26292 | −0.631459 | − | 0.775409i | \(-0.717544\pi\) | ||||
−0.631459 | + | 0.775409i | \(0.717544\pi\) | |||||||
\(168\) | −2.00000 | −0.154303 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 4.00000 | 0.306786 | ||||||||
\(171\) | −7.46410 | −0.570794 | ||||||||
\(172\) | −11.9282 | −0.909517 | ||||||||
\(173\) | −10.9282 | −0.830856 | −0.415428 | − | 0.909626i | \(-0.636368\pi\) | ||||
−0.415428 | + | 0.909626i | \(0.636368\pi\) | |||||||
\(174\) | 0.267949 | 0.0203132 | ||||||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | −6.46410 | −0.487250 | ||||||||
\(177\) | −8.46410 | −0.636201 | ||||||||
\(178\) | −0.535898 | −0.0401673 | ||||||||
\(179\) | 19.7321 | 1.47484 | 0.737421 | − | 0.675433i | \(-0.236043\pi\) | ||||
0.737421 | + | 0.675433i | \(0.236043\pi\) | |||||||
\(180\) | −1.00000 | −0.0745356 | ||||||||
\(181\) | 2.92820 | 0.217652 | 0.108826 | − | 0.994061i | \(-0.465291\pi\) | ||||
0.108826 | + | 0.994061i | \(0.465291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.3923 | 0.768221 | ||||||||
\(184\) | 3.73205 | 0.275130 | ||||||||
\(185\) | 9.19615 | 0.676115 | ||||||||
\(186\) | 1.73205 | 0.127000 | ||||||||
\(187\) | −25.8564 | −1.89081 | ||||||||
\(188\) | −3.53590 | −0.257882 | ||||||||
\(189\) | 2.00000 | 0.145479 | ||||||||
\(190\) | −7.46410 | −0.541503 | ||||||||
\(191\) | 21.4641 | 1.55309 | 0.776544 | − | 0.630063i | \(-0.216971\pi\) | ||||
0.776544 | + | 0.630063i | \(0.216971\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −11.3205 | −0.814868 | −0.407434 | − | 0.913235i | \(-0.633576\pi\) | ||||
−0.407434 | + | 0.913235i | \(0.633576\pi\) | |||||||
\(194\) | 0.535898 | 0.0384753 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 4.39230 | 0.312939 | 0.156469 | − | 0.987683i | \(-0.449989\pi\) | ||||
0.156469 | + | 0.987683i | \(0.449989\pi\) | |||||||
\(198\) | 6.46410 | 0.459384 | ||||||||
\(199\) | 5.07180 | 0.359530 | 0.179765 | − | 0.983710i | \(-0.442466\pi\) | ||||
0.179765 | + | 0.983710i | \(0.442466\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 11.4641 | 0.808615 | ||||||||
\(202\) | 2.92820 | 0.206028 | ||||||||
\(203\) | −0.535898 | −0.0376127 | ||||||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | −11.8564 | −0.826075 | ||||||||
\(207\) | −3.73205 | −0.259395 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 48.2487 | 3.33743 | ||||||||
\(210\) | 2.00000 | 0.138013 | ||||||||
\(211\) | −11.3205 | −0.779336 | −0.389668 | − | 0.920955i | \(-0.627410\pi\) | ||||
−0.389668 | + | 0.920955i | \(0.627410\pi\) | |||||||
\(212\) | 0.928203 | 0.0637493 | ||||||||
\(213\) | −12.3923 | −0.849107 | ||||||||
\(214\) | 7.85641 | 0.537053 | ||||||||
\(215\) | 11.9282 | 0.813497 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −3.46410 | −0.235159 | ||||||||
\(218\) | −15.8564 | −1.07393 | ||||||||
\(219\) | −2.00000 | −0.135147 | ||||||||
\(220\) | 6.46410 | 0.435810 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −9.19615 | −0.617205 | ||||||||
\(223\) | −20.5359 | −1.37519 | −0.687593 | − | 0.726097i | \(-0.741333\pi\) | ||||
−0.687593 | + | 0.726097i | \(0.741333\pi\) | |||||||
\(224\) | 2.00000 | 0.133631 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | −0.803848 | −0.0534711 | ||||||||
\(227\) | 16.3923 | 1.08800 | 0.543998 | − | 0.839087i | \(-0.316910\pi\) | ||||
0.543998 | + | 0.839087i | \(0.316910\pi\) | |||||||
\(228\) | 7.46410 | 0.494322 | ||||||||
\(229\) | −7.85641 | −0.519166 | −0.259583 | − | 0.965721i | \(-0.583585\pi\) | ||||
−0.259583 | + | 0.965721i | \(0.583585\pi\) | |||||||
\(230\) | −3.73205 | −0.246084 | ||||||||
\(231\) | −12.9282 | −0.850613 | ||||||||
\(232\) | −0.267949 | −0.0175917 | ||||||||
\(233\) | −6.12436 | −0.401220 | −0.200610 | − | 0.979671i | \(-0.564292\pi\) | ||||
−0.200610 | + | 0.979671i | \(0.564292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.53590 | 0.230657 | ||||||||
\(236\) | 8.46410 | 0.550966 | ||||||||
\(237\) | 13.9282 | 0.904734 | ||||||||
\(238\) | 8.00000 | 0.518563 | ||||||||
\(239\) | 16.3923 | 1.06033 | 0.530165 | − | 0.847894i | \(-0.322130\pi\) | ||||
0.530165 | + | 0.847894i | \(0.322130\pi\) | |||||||
\(240\) | 1.00000 | 0.0645497 | ||||||||
\(241\) | 17.7321 | 1.14222 | 0.571111 | − | 0.820873i | \(-0.306513\pi\) | ||||
0.571111 | + | 0.820873i | \(0.306513\pi\) | |||||||
\(242\) | −30.7846 | −1.97891 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −10.3923 | −0.665299 | ||||||||
\(245\) | 3.00000 | 0.191663 | ||||||||
\(246\) | 2.00000 | 0.127515 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −1.73205 | −0.109985 | ||||||||
\(249\) | 8.92820 | 0.565802 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −15.7321 | −0.992998 | −0.496499 | − | 0.868037i | \(-0.665381\pi\) | ||||
−0.496499 | + | 0.868037i | \(0.665381\pi\) | |||||||
\(252\) | −2.00000 | −0.125988 | ||||||||
\(253\) | 24.1244 | 1.51669 | ||||||||
\(254\) | −4.92820 | −0.309223 | ||||||||
\(255\) | 4.00000 | 0.250490 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 5.33975 | 0.333084 | 0.166542 | − | 0.986034i | \(-0.446740\pi\) | ||||
0.166542 | + | 0.986034i | \(0.446740\pi\) | |||||||
\(258\) | −11.9282 | −0.742617 | ||||||||
\(259\) | 18.3923 | 1.14284 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.267949 | 0.0165856 | ||||||||
\(262\) | 18.6603 | 1.15283 | ||||||||
\(263\) | 6.12436 | 0.377644 | 0.188822 | − | 0.982011i | \(-0.439533\pi\) | ||||
0.188822 | + | 0.982011i | \(0.439533\pi\) | |||||||
\(264\) | −6.46410 | −0.397838 | ||||||||
\(265\) | −0.928203 | −0.0570191 | ||||||||
\(266\) | −14.9282 | −0.915307 | ||||||||
\(267\) | −0.535898 | −0.0327964 | ||||||||
\(268\) | −11.4641 | −0.700281 | ||||||||
\(269\) | 12.0000 | 0.731653 | 0.365826 | − | 0.930683i | \(-0.380786\pi\) | ||||
0.365826 | + | 0.930683i | \(0.380786\pi\) | |||||||
\(270\) | −1.00000 | −0.0608581 | ||||||||
\(271\) | −1.19615 | −0.0726611 | −0.0363305 | − | 0.999340i | \(-0.511567\pi\) | ||||
−0.0363305 | + | 0.999340i | \(0.511567\pi\) | |||||||
\(272\) | 4.00000 | 0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.46410 | 0.148862 | ||||||||
\(275\) | −6.46410 | −0.389800 | ||||||||
\(276\) | 3.73205 | 0.224643 | ||||||||
\(277\) | 3.92820 | 0.236023 | 0.118011 | − | 0.993012i | \(-0.462348\pi\) | ||||
0.118011 | + | 0.993012i | \(0.462348\pi\) | |||||||
\(278\) | 12.9282 | 0.775382 | ||||||||
\(279\) | 1.73205 | 0.103695 | ||||||||
\(280\) | −2.00000 | −0.119523 | ||||||||
\(281\) | −8.92820 | −0.532612 | −0.266306 | − | 0.963889i | \(-0.585803\pi\) | ||||
−0.266306 | + | 0.963889i | \(0.585803\pi\) | |||||||
\(282\) | −3.53590 | −0.210560 | ||||||||
\(283\) | 9.92820 | 0.590170 | 0.295085 | − | 0.955471i | \(-0.404652\pi\) | ||||
0.295085 | + | 0.955471i | \(0.404652\pi\) | |||||||
\(284\) | 12.3923 | 0.735348 | ||||||||
\(285\) | −7.46410 | −0.442135 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.00000 | −0.236113 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −1.00000 | −0.0588235 | ||||||||
\(290\) | 0.267949 | 0.0157345 | ||||||||
\(291\) | 0.535898 | 0.0314149 | ||||||||
\(292\) | 2.00000 | 0.117041 | ||||||||
\(293\) | −31.8564 | −1.86107 | −0.930536 | − | 0.366202i | \(-0.880658\pi\) | ||||
−0.930536 | + | 0.366202i | \(0.880658\pi\) | |||||||
\(294\) | −3.00000 | −0.174964 | ||||||||
\(295\) | −8.46410 | −0.492799 | ||||||||
\(296\) | 9.19615 | 0.534516 | ||||||||
\(297\) | 6.46410 | 0.375085 | ||||||||
\(298\) | −13.5359 | −0.784114 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −1.00000 | −0.0577350 | ||||||||
\(301\) | 23.8564 | 1.37506 | ||||||||
\(302\) | 10.3923 | 0.598010 | ||||||||
\(303\) | 2.92820 | 0.168221 | ||||||||
\(304\) | −7.46410 | −0.428096 | ||||||||
\(305\) | 10.3923 | 0.595062 | ||||||||
\(306\) | −4.00000 | −0.228665 | ||||||||
\(307\) | 19.4641 | 1.11087 | 0.555437 | − | 0.831558i | \(-0.312551\pi\) | ||||
0.555437 | + | 0.831558i | \(0.312551\pi\) | |||||||
\(308\) | 12.9282 | 0.736653 | ||||||||
\(309\) | −11.8564 | −0.674487 | ||||||||
\(310\) | 1.73205 | 0.0983739 | ||||||||
\(311\) | 28.3923 | 1.60998 | 0.804990 | − | 0.593288i | \(-0.202171\pi\) | ||||
0.804990 | + | 0.593288i | \(0.202171\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −28.0000 | −1.58265 | −0.791327 | − | 0.611393i | \(-0.790609\pi\) | ||||
−0.791327 | + | 0.611393i | \(0.790609\pi\) | |||||||
\(314\) | 5.00000 | 0.282166 | ||||||||
\(315\) | 2.00000 | 0.112687 | ||||||||
\(316\) | −13.9282 | −0.783523 | ||||||||
\(317\) | −14.5359 | −0.816417 | −0.408209 | − | 0.912889i | \(-0.633846\pi\) | ||||
−0.408209 | + | 0.912889i | \(0.633846\pi\) | |||||||
\(318\) | 0.928203 | 0.0520511 | ||||||||
\(319\) | −1.73205 | −0.0969762 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 7.85641 | 0.438502 | ||||||||
\(322\) | −7.46410 | −0.415958 | ||||||||
\(323\) | −29.8564 | −1.66125 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −15.0526 | −0.833684 | ||||||||
\(327\) | −15.8564 | −0.876861 | ||||||||
\(328\) | −2.00000 | −0.110432 | ||||||||
\(329\) | 7.07180 | 0.389881 | ||||||||
\(330\) | 6.46410 | 0.355837 | ||||||||
\(331\) | 16.7846 | 0.922566 | 0.461283 | − | 0.887253i | \(-0.347389\pi\) | ||||
0.461283 | + | 0.887253i | \(0.347389\pi\) | |||||||
\(332\) | −8.92820 | −0.489999 | ||||||||
\(333\) | −9.19615 | −0.503946 | ||||||||
\(334\) | 16.3205 | 0.893018 | ||||||||
\(335\) | 11.4641 | 0.626351 | ||||||||
\(336\) | 2.00000 | 0.109109 | ||||||||
\(337\) | −9.32051 | −0.507720 | −0.253860 | − | 0.967241i | \(-0.581700\pi\) | ||||
−0.253860 | + | 0.967241i | \(0.581700\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.803848 | −0.0436590 | ||||||||
\(340\) | −4.00000 | −0.216930 | ||||||||
\(341\) | −11.1962 | −0.606306 | ||||||||
\(342\) | 7.46410 | 0.403612 | ||||||||
\(343\) | 20.0000 | 1.07990 | ||||||||
\(344\) | 11.9282 | 0.643126 | ||||||||
\(345\) | −3.73205 | −0.200927 | ||||||||
\(346\) | 10.9282 | 0.587504 | ||||||||
\(347\) | 1.60770 | 0.0863056 | 0.0431528 | − | 0.999068i | \(-0.486260\pi\) | ||||
0.0431528 | + | 0.999068i | \(0.486260\pi\) | |||||||
\(348\) | −0.267949 | −0.0143636 | ||||||||
\(349\) | −21.4641 | −1.14895 | −0.574474 | − | 0.818523i | \(-0.694793\pi\) | ||||
−0.574474 | + | 0.818523i | \(0.694793\pi\) | |||||||
\(350\) | 2.00000 | 0.106904 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 6.46410 | 0.344538 | ||||||||
\(353\) | 2.00000 | 0.106449 | 0.0532246 | − | 0.998583i | \(-0.483050\pi\) | ||||
0.0532246 | + | 0.998583i | \(0.483050\pi\) | |||||||
\(354\) | 8.46410 | 0.449862 | ||||||||
\(355\) | −12.3923 | −0.657715 | ||||||||
\(356\) | 0.535898 | 0.0284026 | ||||||||
\(357\) | 8.00000 | 0.423405 | ||||||||
\(358\) | −19.7321 | −1.04287 | ||||||||
\(359\) | 5.07180 | 0.267679 | 0.133840 | − | 0.991003i | \(-0.457269\pi\) | ||||
0.133840 | + | 0.991003i | \(0.457269\pi\) | |||||||
\(360\) | 1.00000 | 0.0527046 | ||||||||
\(361\) | 36.7128 | 1.93225 | ||||||||
\(362\) | −2.92820 | −0.153903 | ||||||||
\(363\) | −30.7846 | −1.61577 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.00000 | −0.104685 | ||||||||
\(366\) | −10.3923 | −0.543214 | ||||||||
\(367\) | 15.6077 | 0.814715 | 0.407358 | − | 0.913269i | \(-0.366450\pi\) | ||||
0.407358 | + | 0.913269i | \(0.366450\pi\) | |||||||
\(368\) | −3.73205 | −0.194547 | ||||||||
\(369\) | 2.00000 | 0.104116 | ||||||||
\(370\) | −9.19615 | −0.478085 | ||||||||
\(371\) | −1.85641 | −0.0963798 | ||||||||
\(372\) | −1.73205 | −0.0898027 | ||||||||
\(373\) | −15.7846 | −0.817296 | −0.408648 | − | 0.912692i | \(-0.634000\pi\) | ||||
−0.408648 | + | 0.912692i | \(0.634000\pi\) | |||||||
\(374\) | 25.8564 | 1.33700 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 3.53590 | 0.182350 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.00000 | −0.102869 | ||||||||
\(379\) | 27.8564 | 1.43089 | 0.715444 | − | 0.698670i | \(-0.246225\pi\) | ||||
0.715444 | + | 0.698670i | \(0.246225\pi\) | |||||||
\(380\) | 7.46410 | 0.382900 | ||||||||
\(381\) | −4.92820 | −0.252479 | ||||||||
\(382\) | −21.4641 | −1.09820 | ||||||||
\(383\) | −25.3923 | −1.29749 | −0.648743 | − | 0.761007i | \(-0.724705\pi\) | ||||
−0.648743 | + | 0.761007i | \(0.724705\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −12.9282 | −0.658882 | ||||||||
\(386\) | 11.3205 | 0.576199 | ||||||||
\(387\) | −11.9282 | −0.606345 | ||||||||
\(388\) | −0.535898 | −0.0272061 | ||||||||
\(389\) | 23.7321 | 1.20326 | 0.601631 | − | 0.798774i | \(-0.294518\pi\) | ||||
0.601631 | + | 0.798774i | \(0.294518\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14.9282 | −0.754952 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | 18.6603 | 0.941285 | ||||||||
\(394\) | −4.39230 | −0.221281 | ||||||||
\(395\) | 13.9282 | 0.700804 | ||||||||
\(396\) | −6.46410 | −0.324833 | ||||||||
\(397\) | 12.1244 | 0.608504 | 0.304252 | − | 0.952592i | \(-0.401594\pi\) | ||||
0.304252 | + | 0.952592i | \(0.401594\pi\) | |||||||
\(398\) | −5.07180 | −0.254226 | ||||||||
\(399\) | −14.9282 | −0.747345 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 32.0000 | 1.59800 | 0.799002 | − | 0.601329i | \(-0.205362\pi\) | ||||
0.799002 | + | 0.601329i | \(0.205362\pi\) | |||||||
\(402\) | −11.4641 | −0.571777 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −2.92820 | −0.145684 | ||||||||
\(405\) | −1.00000 | −0.0496904 | ||||||||
\(406\) | 0.535898 | 0.0265962 | ||||||||
\(407\) | 59.4449 | 2.94657 | ||||||||
\(408\) | 4.00000 | 0.198030 | ||||||||
\(409\) | −4.00000 | −0.197787 | −0.0988936 | − | 0.995098i | \(-0.531530\pi\) | ||||
−0.0988936 | + | 0.995098i | \(0.531530\pi\) | |||||||
\(410\) | 2.00000 | 0.0987730 | ||||||||
\(411\) | 2.46410 | 0.121545 | ||||||||
\(412\) | 11.8564 | 0.584123 | ||||||||
\(413\) | −16.9282 | −0.832982 | ||||||||
\(414\) | 3.73205 | 0.183420 | ||||||||
\(415\) | 8.92820 | 0.438268 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.9282 | 0.633097 | ||||||||
\(418\) | −48.2487 | −2.35992 | ||||||||
\(419\) | 22.3923 | 1.09394 | 0.546968 | − | 0.837154i | \(-0.315782\pi\) | ||||
0.546968 | + | 0.837154i | \(0.315782\pi\) | |||||||
\(420\) | −2.00000 | −0.0975900 | ||||||||
\(421\) | −4.39230 | −0.214068 | −0.107034 | − | 0.994255i | \(-0.534135\pi\) | ||||
−0.107034 | + | 0.994255i | \(0.534135\pi\) | |||||||
\(422\) | 11.3205 | 0.551074 | ||||||||
\(423\) | −3.53590 | −0.171921 | ||||||||
\(424\) | −0.928203 | −0.0450775 | ||||||||
\(425\) | 4.00000 | 0.194029 | ||||||||
\(426\) | 12.3923 | 0.600409 | ||||||||
\(427\) | 20.7846 | 1.00584 | ||||||||
\(428\) | −7.85641 | −0.379754 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.9282 | −0.575229 | ||||||||
\(431\) | 28.3923 | 1.36761 | 0.683805 | − | 0.729665i | \(-0.260324\pi\) | ||||
0.683805 | + | 0.729665i | \(0.260324\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −19.3205 | −0.928484 | −0.464242 | − | 0.885708i | \(-0.653673\pi\) | ||||
−0.464242 | + | 0.885708i | \(0.653673\pi\) | |||||||
\(434\) | 3.46410 | 0.166282 | ||||||||
\(435\) | 0.267949 | 0.0128472 | ||||||||
\(436\) | 15.8564 | 0.759384 | ||||||||
\(437\) | 27.8564 | 1.33255 | ||||||||
\(438\) | 2.00000 | 0.0955637 | ||||||||
\(439\) | 17.8564 | 0.852240 | 0.426120 | − | 0.904667i | \(-0.359880\pi\) | ||||
0.426120 | + | 0.904667i | \(0.359880\pi\) | |||||||
\(440\) | −6.46410 | −0.308164 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.3923 | 0.778822 | 0.389411 | − | 0.921064i | \(-0.372679\pi\) | ||||
0.389411 | + | 0.921064i | \(0.372679\pi\) | |||||||
\(444\) | 9.19615 | 0.436430 | ||||||||
\(445\) | −0.535898 | −0.0254040 | ||||||||
\(446\) | 20.5359 | 0.972403 | ||||||||
\(447\) | −13.5359 | −0.640226 | ||||||||
\(448\) | −2.00000 | −0.0944911 | ||||||||
\(449\) | −15.7128 | −0.741533 | −0.370767 | − | 0.928726i | \(-0.620905\pi\) | ||||
−0.370767 | + | 0.928726i | \(0.620905\pi\) | |||||||
\(450\) | −1.00000 | −0.0471405 | ||||||||
\(451\) | −12.9282 | −0.608765 | ||||||||
\(452\) | 0.803848 | 0.0378098 | ||||||||
\(453\) | 10.3923 | 0.488273 | ||||||||
\(454\) | −16.3923 | −0.769329 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.46410 | −0.349539 | ||||||||
\(457\) | 24.5359 | 1.14774 | 0.573870 | − | 0.818946i | \(-0.305441\pi\) | ||||
0.573870 | + | 0.818946i | \(0.305441\pi\) | |||||||
\(458\) | 7.85641 | 0.367106 | ||||||||
\(459\) | −4.00000 | −0.186704 | ||||||||
\(460\) | 3.73205 | 0.174008 | ||||||||
\(461\) | −0.464102 | −0.0216154 | −0.0108077 | − | 0.999942i | \(-0.503440\pi\) | ||||
−0.0108077 | + | 0.999942i | \(0.503440\pi\) | |||||||
\(462\) | 12.9282 | 0.601474 | ||||||||
\(463\) | 7.07180 | 0.328654 | 0.164327 | − | 0.986406i | \(-0.447455\pi\) | ||||
0.164327 | + | 0.986406i | \(0.447455\pi\) | |||||||
\(464\) | 0.267949 | 0.0124392 | ||||||||
\(465\) | 1.73205 | 0.0803219 | ||||||||
\(466\) | 6.12436 | 0.283705 | ||||||||
\(467\) | 15.8564 | 0.733747 | 0.366873 | − | 0.930271i | \(-0.380428\pi\) | ||||
0.366873 | + | 0.930271i | \(0.380428\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 22.9282 | 1.05873 | ||||||||
\(470\) | −3.53590 | −0.163099 | ||||||||
\(471\) | 5.00000 | 0.230388 | ||||||||
\(472\) | −8.46410 | −0.389592 | ||||||||
\(473\) | 77.1051 | 3.54530 | ||||||||
\(474\) | −13.9282 | −0.639744 | ||||||||
\(475\) | −7.46410 | −0.342476 | ||||||||
\(476\) | −8.00000 | −0.366679 | ||||||||
\(477\) | 0.928203 | 0.0424995 | ||||||||
\(478\) | −16.3923 | −0.749767 | ||||||||
\(479\) | −5.46410 | −0.249661 | −0.124831 | − | 0.992178i | \(-0.539839\pi\) | ||||
−0.124831 | + | 0.992178i | \(0.539839\pi\) | |||||||
\(480\) | −1.00000 | −0.0456435 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −17.7321 | −0.807673 | ||||||||
\(483\) | −7.46410 | −0.339628 | ||||||||
\(484\) | 30.7846 | 1.39930 | ||||||||
\(485\) | 0.535898 | 0.0243339 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −23.1769 | −1.05025 | −0.525123 | − | 0.851026i | \(-0.675981\pi\) | ||||
−0.525123 | + | 0.851026i | \(0.675981\pi\) | |||||||
\(488\) | 10.3923 | 0.470438 | ||||||||
\(489\) | −15.0526 | −0.680700 | ||||||||
\(490\) | −3.00000 | −0.135526 | ||||||||
\(491\) | 17.3205 | 0.781664 | 0.390832 | − | 0.920462i | \(-0.372187\pi\) | ||||
0.390832 | + | 0.920462i | \(0.372187\pi\) | |||||||
\(492\) | −2.00000 | −0.0901670 | ||||||||
\(493\) | 1.07180 | 0.0482713 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 6.46410 | 0.290540 | ||||||||
\(496\) | 1.73205 | 0.0777714 | ||||||||
\(497\) | −24.7846 | −1.11174 | ||||||||
\(498\) | −8.92820 | −0.400082 | ||||||||
\(499\) | −6.53590 | −0.292587 | −0.146293 | − | 0.989241i | \(-0.546734\pi\) | ||||
−0.146293 | + | 0.989241i | \(0.546734\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 16.3205 | 0.729147 | ||||||||
\(502\) | 15.7321 | 0.702156 | ||||||||
\(503\) | −31.1769 | −1.39011 | −0.695055 | − | 0.718957i | \(-0.744620\pi\) | ||||
−0.695055 | + | 0.718957i | \(0.744620\pi\) | |||||||
\(504\) | 2.00000 | 0.0890871 | ||||||||
\(505\) | 2.92820 | 0.130303 | ||||||||
\(506\) | −24.1244 | −1.07246 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.92820 | 0.218654 | ||||||||
\(509\) | 1.39230 | 0.0617128 | 0.0308564 | − | 0.999524i | \(-0.490177\pi\) | ||||
0.0308564 | + | 0.999524i | \(0.490177\pi\) | |||||||
\(510\) | −4.00000 | −0.177123 | ||||||||
\(511\) | −4.00000 | −0.176950 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 7.46410 | 0.329548 | ||||||||
\(514\) | −5.33975 | −0.235526 | ||||||||
\(515\) | −11.8564 | −0.522456 | ||||||||
\(516\) | 11.9282 | 0.525110 | ||||||||
\(517\) | 22.8564 | 1.00522 | ||||||||
\(518\) | −18.3923 | −0.808111 | ||||||||
\(519\) | 10.9282 | 0.479695 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.3205 | −0.758825 | −0.379413 | − | 0.925228i | \(-0.623874\pi\) | ||||
−0.379413 | + | 0.925228i | \(0.623874\pi\) | |||||||
\(522\) | −0.267949 | −0.0117278 | ||||||||
\(523\) | 11.7846 | 0.515305 | 0.257653 | − | 0.966238i | \(-0.417051\pi\) | ||||
0.257653 | + | 0.966238i | \(0.417051\pi\) | |||||||
\(524\) | −18.6603 | −0.815177 | ||||||||
\(525\) | 2.00000 | 0.0872872 | ||||||||
\(526\) | −6.12436 | −0.267035 | ||||||||
\(527\) | 6.92820 | 0.301797 | ||||||||
\(528\) | 6.46410 | 0.281314 | ||||||||
\(529\) | −9.07180 | −0.394426 | ||||||||
\(530\) | 0.928203 | 0.0403186 | ||||||||
\(531\) | 8.46410 | 0.367311 | ||||||||
\(532\) | 14.9282 | 0.647220 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0.535898 | 0.0231906 | ||||||||
\(535\) | 7.85641 | 0.339662 | ||||||||
\(536\) | 11.4641 | 0.495174 | ||||||||
\(537\) | −19.7321 | −0.851501 | ||||||||
\(538\) | −12.0000 | −0.517357 | ||||||||
\(539\) | 19.3923 | 0.835286 | ||||||||
\(540\) | 1.00000 | 0.0430331 | ||||||||
\(541\) | 26.9282 | 1.15773 | 0.578867 | − | 0.815422i | \(-0.303495\pi\) | ||||
0.578867 | + | 0.815422i | \(0.303495\pi\) | |||||||
\(542\) | 1.19615 | 0.0513791 | ||||||||
\(543\) | −2.92820 | −0.125661 | ||||||||
\(544\) | −4.00000 | −0.171499 | ||||||||
\(545\) | −15.8564 | −0.679214 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.9282 | 0.980339 | 0.490170 | − | 0.871627i | \(-0.336935\pi\) | ||||
0.490170 | + | 0.871627i | \(0.336935\pi\) | |||||||
\(548\) | −2.46410 | −0.105261 | ||||||||
\(549\) | −10.3923 | −0.443533 | ||||||||
\(550\) | 6.46410 | 0.275630 | ||||||||
\(551\) | −2.00000 | −0.0852029 | ||||||||
\(552\) | −3.73205 | −0.158847 | ||||||||
\(553\) | 27.8564 | 1.18457 | ||||||||
\(554\) | −3.92820 | −0.166893 | ||||||||
\(555\) | −9.19615 | −0.390355 | ||||||||
\(556\) | −12.9282 | −0.548278 | ||||||||
\(557\) | −17.7128 | −0.750516 | −0.375258 | − | 0.926920i | \(-0.622446\pi\) | ||||
−0.375258 | + | 0.926920i | \(0.622446\pi\) | |||||||
\(558\) | −1.73205 | −0.0733236 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 25.8564 | 1.09166 | ||||||||
\(562\) | 8.92820 | 0.376614 | ||||||||
\(563\) | 4.67949 | 0.197217 | 0.0986085 | − | 0.995126i | \(-0.468561\pi\) | ||||
0.0986085 | + | 0.995126i | \(0.468561\pi\) | |||||||
\(564\) | 3.53590 | 0.148888 | ||||||||
\(565\) | −0.803848 | −0.0338181 | ||||||||
\(566\) | −9.92820 | −0.417314 | ||||||||
\(567\) | −2.00000 | −0.0839921 | ||||||||
\(568\) | −12.3923 | −0.519970 | ||||||||
\(569\) | −29.3205 | −1.22918 | −0.614590 | − | 0.788847i | \(-0.710678\pi\) | ||||
−0.614590 | + | 0.788847i | \(0.710678\pi\) | |||||||
\(570\) | 7.46410 | 0.312637 | ||||||||
\(571\) | 17.1769 | 0.718832 | 0.359416 | − | 0.933178i | \(-0.382976\pi\) | ||||
0.359416 | + | 0.933178i | \(0.382976\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −21.4641 | −0.896676 | ||||||||
\(574\) | 4.00000 | 0.166957 | ||||||||
\(575\) | −3.73205 | −0.155637 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 10.0000 | 0.416305 | 0.208153 | − | 0.978096i | \(-0.433255\pi\) | ||||
0.208153 | + | 0.978096i | \(0.433255\pi\) | |||||||
\(578\) | 1.00000 | 0.0415945 | ||||||||
\(579\) | 11.3205 | 0.470464 | ||||||||
\(580\) | −0.267949 | −0.0111260 | ||||||||
\(581\) | 17.8564 | 0.740809 | ||||||||
\(582\) | −0.535898 | −0.0222137 | ||||||||
\(583\) | −6.00000 | −0.248495 | ||||||||
\(584\) | −2.00000 | −0.0827606 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 31.8564 | 1.31598 | ||||||||
\(587\) | −2.39230 | −0.0987410 | −0.0493705 | − | 0.998781i | \(-0.515722\pi\) | ||||
−0.0493705 | + | 0.998781i | \(0.515722\pi\) | |||||||
\(588\) | 3.00000 | 0.123718 | ||||||||
\(589\) | −12.9282 | −0.532697 | ||||||||
\(590\) | 8.46410 | 0.348462 | ||||||||
\(591\) | −4.39230 | −0.180675 | ||||||||
\(592\) | −9.19615 | −0.377960 | ||||||||
\(593\) | 45.1051 | 1.85225 | 0.926123 | − | 0.377223i | \(-0.123121\pi\) | ||||
0.926123 | + | 0.377223i | \(0.123121\pi\) | |||||||
\(594\) | −6.46410 | −0.265225 | ||||||||
\(595\) | 8.00000 | 0.327968 | ||||||||
\(596\) | 13.5359 | 0.554452 | ||||||||
\(597\) | −5.07180 | −0.207575 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −10.3923 | −0.424618 | −0.212309 | − | 0.977203i | \(-0.568098\pi\) | ||||
−0.212309 | + | 0.977203i | \(0.568098\pi\) | |||||||
\(600\) | 1.00000 | 0.0408248 | ||||||||
\(601\) | −19.7846 | −0.807031 | −0.403516 | − | 0.914973i | \(-0.632212\pi\) | ||||
−0.403516 | + | 0.914973i | \(0.632212\pi\) | |||||||
\(602\) | −23.8564 | −0.972315 | ||||||||
\(603\) | −11.4641 | −0.466854 | ||||||||
\(604\) | −10.3923 | −0.422857 | ||||||||
\(605\) | −30.7846 | −1.25157 | ||||||||
\(606\) | −2.92820 | −0.118950 | ||||||||
\(607\) | −19.1769 | −0.778367 | −0.389183 | − | 0.921160i | \(-0.627243\pi\) | ||||
−0.389183 | + | 0.921160i | \(0.627243\pi\) | |||||||
\(608\) | 7.46410 | 0.302709 | ||||||||
\(609\) | 0.535898 | 0.0217157 | ||||||||
\(610\) | −10.3923 | −0.420772 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 4.00000 | 0.161690 | ||||||||
\(613\) | −39.0526 | −1.57732 | −0.788659 | − | 0.614831i | \(-0.789224\pi\) | ||||
−0.788659 | + | 0.614831i | \(0.789224\pi\) | |||||||
\(614\) | −19.4641 | −0.785507 | ||||||||
\(615\) | 2.00000 | 0.0806478 | ||||||||
\(616\) | −12.9282 | −0.520892 | ||||||||
\(617\) | 22.4641 | 0.904371 | 0.452185 | − | 0.891924i | \(-0.350645\pi\) | ||||
0.452185 | + | 0.891924i | \(0.350645\pi\) | |||||||
\(618\) | 11.8564 | 0.476935 | ||||||||
\(619\) | −24.2487 | −0.974638 | −0.487319 | − | 0.873224i | \(-0.662025\pi\) | ||||
−0.487319 | + | 0.873224i | \(0.662025\pi\) | |||||||
\(620\) | −1.73205 | −0.0695608 | ||||||||
\(621\) | 3.73205 | 0.149762 | ||||||||
\(622\) | −28.3923 | −1.13843 | ||||||||
\(623\) | −1.07180 | −0.0429406 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 28.0000 | 1.11911 | ||||||||
\(627\) | −48.2487 | −1.92687 | ||||||||
\(628\) | −5.00000 | −0.199522 | ||||||||
\(629\) | −36.7846 | −1.46670 | ||||||||
\(630\) | −2.00000 | −0.0796819 | ||||||||
\(631\) | 31.4641 | 1.25257 | 0.626283 | − | 0.779596i | \(-0.284575\pi\) | ||||
0.626283 | + | 0.779596i | \(0.284575\pi\) | |||||||
\(632\) | 13.9282 | 0.554034 | ||||||||
\(633\) | 11.3205 | 0.449950 | ||||||||
\(634\) | 14.5359 | 0.577294 | ||||||||
\(635\) | −4.92820 | −0.195570 | ||||||||
\(636\) | −0.928203 | −0.0368057 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.73205 | 0.0685725 | ||||||||
\(639\) | 12.3923 | 0.490232 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −0.143594 | −0.00567160 | −0.00283580 | − | 0.999996i | \(-0.500903\pi\) | ||||
−0.00283580 | + | 0.999996i | \(0.500903\pi\) | |||||||
\(642\) | −7.85641 | −0.310068 | ||||||||
\(643\) | 20.5359 | 0.809857 | 0.404928 | − | 0.914348i | \(-0.367296\pi\) | ||||
0.404928 | + | 0.914348i | \(0.367296\pi\) | |||||||
\(644\) | 7.46410 | 0.294127 | ||||||||
\(645\) | −11.9282 | −0.469673 | ||||||||
\(646\) | 29.8564 | 1.17468 | ||||||||
\(647\) | 13.3205 | 0.523683 | 0.261842 | − | 0.965111i | \(-0.415670\pi\) | ||||
0.261842 | + | 0.965111i | \(0.415670\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −54.7128 | −2.14767 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.46410 | 0.135769 | ||||||||
\(652\) | 15.0526 | 0.589504 | ||||||||
\(653\) | 4.24871 | 0.166265 | 0.0831325 | − | 0.996539i | \(-0.473508\pi\) | ||||
0.0831325 | + | 0.996539i | \(0.473508\pi\) | |||||||
\(654\) | 15.8564 | 0.620035 | ||||||||
\(655\) | 18.6603 | 0.729116 | ||||||||
\(656\) | 2.00000 | 0.0780869 | ||||||||
\(657\) | 2.00000 | 0.0780274 | ||||||||
\(658\) | −7.07180 | −0.275687 | ||||||||
\(659\) | −0.267949 | −0.0104378 | −0.00521891 | − | 0.999986i | \(-0.501661\pi\) | ||||
−0.00521891 | + | 0.999986i | \(0.501661\pi\) | |||||||
\(660\) | −6.46410 | −0.251615 | ||||||||
\(661\) | 8.67949 | 0.337593 | 0.168797 | − | 0.985651i | \(-0.446012\pi\) | ||||
0.168797 | + | 0.985651i | \(0.446012\pi\) | |||||||
\(662\) | −16.7846 | −0.652352 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.92820 | 0.346481 | ||||||||
\(665\) | −14.9282 | −0.578891 | ||||||||
\(666\) | 9.19615 | 0.356344 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −16.3205 | −0.631459 | ||||||||
\(669\) | 20.5359 | 0.793964 | ||||||||
\(670\) | −11.4641 | −0.442897 | ||||||||
\(671\) | 67.1769 | 2.59334 | ||||||||
\(672\) | −2.00000 | −0.0771517 | ||||||||
\(673\) | −32.0000 | −1.23351 | −0.616755 | − | 0.787155i | \(-0.711553\pi\) | ||||
−0.616755 | + | 0.787155i | \(0.711553\pi\) | |||||||
\(674\) | 9.32051 | 0.359013 | ||||||||
\(675\) | −1.00000 | −0.0384900 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 32.3923 | 1.24494 | 0.622469 | − | 0.782645i | \(-0.286130\pi\) | ||||
0.622469 | + | 0.782645i | \(0.286130\pi\) | |||||||
\(678\) | 0.803848 | 0.0308716 | ||||||||
\(679\) | 1.07180 | 0.0411318 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | −16.3923 | −0.628154 | ||||||||
\(682\) | 11.1962 | 0.428723 | ||||||||
\(683\) | −40.7846 | −1.56058 | −0.780290 | − | 0.625418i | \(-0.784928\pi\) | ||||
−0.780290 | + | 0.625418i | \(0.784928\pi\) | |||||||
\(684\) | −7.46410 | −0.285397 | ||||||||
\(685\) | 2.46410 | 0.0941485 | ||||||||
\(686\) | −20.0000 | −0.763604 | ||||||||
\(687\) | 7.85641 | 0.299741 | ||||||||
\(688\) | −11.9282 | −0.454758 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 3.73205 | 0.142077 | ||||||||
\(691\) | −27.1769 | −1.03386 | −0.516929 | − | 0.856028i | \(-0.672925\pi\) | ||||
−0.516929 | + | 0.856028i | \(0.672925\pi\) | |||||||
\(692\) | −10.9282 | −0.415428 | ||||||||
\(693\) | 12.9282 | 0.491102 | ||||||||
\(694\) | −1.60770 | −0.0610273 | ||||||||
\(695\) | 12.9282 | 0.490395 | ||||||||
\(696\) | 0.267949 | 0.0101566 | ||||||||
\(697\) | 8.00000 | 0.303022 | ||||||||
\(698\) | 21.4641 | 0.812428 | ||||||||
\(699\) | 6.12436 | 0.231644 | ||||||||
\(700\) | −2.00000 | −0.0755929 | ||||||||
\(701\) | 0.267949 | 0.0101203 | 0.00506015 | − | 0.999987i | \(-0.498389\pi\) | ||||
0.00506015 | + | 0.999987i | \(0.498389\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 68.6410 | 2.58884 | ||||||||
\(704\) | −6.46410 | −0.243625 | ||||||||
\(705\) | −3.53590 | −0.133170 | ||||||||
\(706\) | −2.00000 | −0.0752710 | ||||||||
\(707\) | 5.85641 | 0.220253 | ||||||||
\(708\) | −8.46410 | −0.318100 | ||||||||
\(709\) | −22.9282 | −0.861087 | −0.430543 | − | 0.902570i | \(-0.641678\pi\) | ||||
−0.430543 | + | 0.902570i | \(0.641678\pi\) | |||||||
\(710\) | 12.3923 | 0.465075 | ||||||||
\(711\) | −13.9282 | −0.522348 | ||||||||
\(712\) | −0.535898 | −0.0200836 | ||||||||
\(713\) | −6.46410 | −0.242083 | ||||||||
\(714\) | −8.00000 | −0.299392 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 19.7321 | 0.737421 | ||||||||
\(717\) | −16.3923 | −0.612182 | ||||||||
\(718\) | −5.07180 | −0.189278 | ||||||||
\(719\) | 34.6410 | 1.29189 | 0.645946 | − | 0.763383i | \(-0.276463\pi\) | ||||
0.645946 | + | 0.763383i | \(0.276463\pi\) | |||||||
\(720\) | −1.00000 | −0.0372678 | ||||||||
\(721\) | −23.7128 | −0.883111 | ||||||||
\(722\) | −36.7128 | −1.36631 | ||||||||
\(723\) | −17.7321 | −0.659462 | ||||||||
\(724\) | 2.92820 | 0.108826 | ||||||||
\(725\) | 0.267949 | 0.00995138 | ||||||||
\(726\) | 30.7846 | 1.14252 | ||||||||
\(727\) | 31.7128 | 1.17616 | 0.588082 | − | 0.808802i | \(-0.299883\pi\) | ||||
0.588082 | + | 0.808802i | \(0.299883\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 2.00000 | 0.0740233 | ||||||||
\(731\) | −47.7128 | −1.76472 | ||||||||
\(732\) | 10.3923 | 0.384111 | ||||||||
\(733\) | 50.9282 | 1.88108 | 0.940538 | − | 0.339688i | \(-0.110322\pi\) | ||||
0.940538 | + | 0.339688i | \(0.110322\pi\) | |||||||
\(734\) | −15.6077 | −0.576091 | ||||||||
\(735\) | −3.00000 | −0.110657 | ||||||||
\(736\) | 3.73205 | 0.137565 | ||||||||
\(737\) | 74.1051 | 2.72970 | ||||||||
\(738\) | −2.00000 | −0.0736210 | ||||||||
\(739\) | 19.3205 | 0.710716 | 0.355358 | − | 0.934730i | \(-0.384359\pi\) | ||||
0.355358 | + | 0.934730i | \(0.384359\pi\) | |||||||
\(740\) | 9.19615 | 0.338057 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.85641 | 0.0681508 | ||||||||
\(743\) | −40.4641 | −1.48448 | −0.742242 | − | 0.670132i | \(-0.766237\pi\) | ||||
−0.742242 | + | 0.670132i | \(0.766237\pi\) | |||||||
\(744\) | 1.73205 | 0.0635001 | ||||||||
\(745\) | −13.5359 | −0.495917 | ||||||||
\(746\) | 15.7846 | 0.577916 | ||||||||
\(747\) | −8.92820 | −0.326666 | ||||||||
\(748\) | −25.8564 | −0.945404 | ||||||||
\(749\) | 15.7128 | 0.574134 | ||||||||
\(750\) | −1.00000 | −0.0365148 | ||||||||
\(751\) | −14.0718 | −0.513487 | −0.256744 | − | 0.966480i | \(-0.582650\pi\) | ||||
−0.256744 | + | 0.966480i | \(0.582650\pi\) | |||||||
\(752\) | −3.53590 | −0.128941 | ||||||||
\(753\) | 15.7321 | 0.573308 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 10.3923 | 0.378215 | ||||||||
\(756\) | 2.00000 | 0.0727393 | ||||||||
\(757\) | −18.0000 | −0.654221 | −0.327111 | − | 0.944986i | \(-0.606075\pi\) | ||||
−0.327111 | + | 0.944986i | \(0.606075\pi\) | |||||||
\(758\) | −27.8564 | −1.01179 | ||||||||
\(759\) | −24.1244 | −0.875659 | ||||||||
\(760\) | −7.46410 | −0.270751 | ||||||||
\(761\) | 5.07180 | 0.183852 | 0.0919262 | − | 0.995766i | \(-0.470698\pi\) | ||||
0.0919262 | + | 0.995766i | \(0.470698\pi\) | |||||||
\(762\) | 4.92820 | 0.178530 | ||||||||
\(763\) | −31.7128 | −1.14808 | ||||||||
\(764\) | 21.4641 | 0.776544 | ||||||||
\(765\) | −4.00000 | −0.144620 | ||||||||
\(766\) | 25.3923 | 0.917461 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | −11.5885 | −0.417890 | −0.208945 | − | 0.977927i | \(-0.567003\pi\) | ||||
−0.208945 | + | 0.977927i | \(0.567003\pi\) | |||||||
\(770\) | 12.9282 | 0.465900 | ||||||||
\(771\) | −5.33975 | −0.192306 | ||||||||
\(772\) | −11.3205 | −0.407434 | ||||||||
\(773\) | −27.7128 | −0.996761 | −0.498380 | − | 0.866959i | \(-0.666072\pi\) | ||||
−0.498380 | + | 0.866959i | \(0.666072\pi\) | |||||||
\(774\) | 11.9282 | 0.428750 | ||||||||
\(775\) | 1.73205 | 0.0622171 | ||||||||
\(776\) | 0.535898 | 0.0192376 | ||||||||
\(777\) | −18.3923 | −0.659820 | ||||||||
\(778\) | −23.7321 | −0.850835 | ||||||||
\(779\) | −14.9282 | −0.534858 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −80.1051 | −2.86639 | ||||||||
\(782\) | 14.9282 | 0.533831 | ||||||||
\(783\) | −0.267949 | −0.00957572 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 5.00000 | 0.178458 | ||||||||
\(786\) | −18.6603 | −0.665589 | ||||||||
\(787\) | 1.73205 | 0.0617409 | 0.0308705 | − | 0.999523i | \(-0.490172\pi\) | ||||
0.0308705 | + | 0.999523i | \(0.490172\pi\) | |||||||
\(788\) | 4.39230 | 0.156469 | ||||||||
\(789\) | −6.12436 | −0.218033 | ||||||||
\(790\) | −13.9282 | −0.495543 | ||||||||
\(791\) | −1.60770 | −0.0571631 | ||||||||
\(792\) | 6.46410 | 0.229692 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −12.1244 | −0.430277 | ||||||||
\(795\) | 0.928203 | 0.0329200 | ||||||||
\(796\) | 5.07180 | 0.179765 | ||||||||
\(797\) | 10.1436 | 0.359305 | 0.179652 | − | 0.983730i | \(-0.442503\pi\) | ||||
0.179652 | + | 0.983730i | \(0.442503\pi\) | |||||||
\(798\) | 14.9282 | 0.528453 | ||||||||
\(799\) | −14.1436 | −0.500364 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0.535898 | 0.0189350 | ||||||||
\(802\) | −32.0000 | −1.12996 | ||||||||
\(803\) | −12.9282 | −0.456226 | ||||||||
\(804\) | 11.4641 | 0.404308 | ||||||||
\(805\) | −7.46410 | −0.263075 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −12.0000 | −0.422420 | ||||||||
\(808\) | 2.92820 | 0.103014 | ||||||||
\(809\) | −42.7846 | −1.50423 | −0.752113 | − | 0.659034i | \(-0.770965\pi\) | ||||
−0.752113 | + | 0.659034i | \(0.770965\pi\) | |||||||
\(810\) | 1.00000 | 0.0351364 | ||||||||
\(811\) | −40.7846 | −1.43214 | −0.716071 | − | 0.698028i | \(-0.754061\pi\) | ||||
−0.716071 | + | 0.698028i | \(0.754061\pi\) | |||||||
\(812\) | −0.535898 | −0.0188063 | ||||||||
\(813\) | 1.19615 | 0.0419509 | ||||||||
\(814\) | −59.4449 | −2.08354 | ||||||||
\(815\) | −15.0526 | −0.527268 | ||||||||
\(816\) | −4.00000 | −0.140028 | ||||||||
\(817\) | 89.0333 | 3.11488 | ||||||||
\(818\) | 4.00000 | 0.139857 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −2.00000 | −0.0698430 | ||||||||
\(821\) | 14.6077 | 0.509812 | 0.254906 | − | 0.966966i | \(-0.417955\pi\) | ||||
0.254906 | + | 0.966966i | \(0.417955\pi\) | |||||||
\(822\) | −2.46410 | −0.0859454 | ||||||||
\(823\) | −39.1769 | −1.36562 | −0.682811 | − | 0.730595i | \(-0.739243\pi\) | ||||
−0.682811 | + | 0.730595i | \(0.739243\pi\) | |||||||
\(824\) | −11.8564 | −0.413037 | ||||||||
\(825\) | 6.46410 | 0.225051 | ||||||||
\(826\) | 16.9282 | 0.589008 | ||||||||
\(827\) | 17.3205 | 0.602293 | 0.301147 | − | 0.953578i | \(-0.402631\pi\) | ||||
0.301147 | + | 0.953578i | \(0.402631\pi\) | |||||||
\(828\) | −3.73205 | −0.129698 | ||||||||
\(829\) | −16.5359 | −0.574315 | −0.287158 | − | 0.957883i | \(-0.592710\pi\) | ||||
−0.287158 | + | 0.957883i | \(0.592710\pi\) | |||||||
\(830\) | −8.92820 | −0.309902 | ||||||||
\(831\) | −3.92820 | −0.136268 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −12.0000 | −0.415775 | ||||||||
\(834\) | −12.9282 | −0.447667 | ||||||||
\(835\) | 16.3205 | 0.564794 | ||||||||
\(836\) | 48.2487 | 1.66872 | ||||||||
\(837\) | −1.73205 | −0.0598684 | ||||||||
\(838\) | −22.3923 | −0.773529 | ||||||||
\(839\) | −43.5692 | −1.50418 | −0.752088 | − | 0.659062i | \(-0.770953\pi\) | ||||
−0.752088 | + | 0.659062i | \(0.770953\pi\) | |||||||
\(840\) | 2.00000 | 0.0690066 | ||||||||
\(841\) | −28.9282 | −0.997524 | ||||||||
\(842\) | 4.39230 | 0.151369 | ||||||||
\(843\) | 8.92820 | 0.307504 | ||||||||
\(844\) | −11.3205 | −0.389668 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 3.53590 | 0.121567 | ||||||||
\(847\) | −61.5692 | −2.11554 | ||||||||
\(848\) | 0.928203 | 0.0318746 | ||||||||
\(849\) | −9.92820 | −0.340735 | ||||||||
\(850\) | −4.00000 | −0.137199 | ||||||||
\(851\) | 34.3205 | 1.17649 | ||||||||
\(852\) | −12.3923 | −0.424553 | ||||||||
\(853\) | 43.8372 | 1.50096 | 0.750478 | − | 0.660895i | \(-0.229823\pi\) | ||||
0.750478 | + | 0.660895i | \(0.229823\pi\) | |||||||
\(854\) | −20.7846 | −0.711235 | ||||||||
\(855\) | 7.46410 | 0.255267 | ||||||||
\(856\) | 7.85641 | 0.268526 | ||||||||
\(857\) | −24.5167 | −0.837473 | −0.418737 | − | 0.908108i | \(-0.637527\pi\) | ||||
−0.418737 | + | 0.908108i | \(0.637527\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −35.1769 | −1.20022 | −0.600110 | − | 0.799917i | \(-0.704877\pi\) | ||||
−0.600110 | + | 0.799917i | \(0.704877\pi\) | |||||||
\(860\) | 11.9282 | 0.406748 | ||||||||
\(861\) | 4.00000 | 0.136320 | ||||||||
\(862\) | −28.3923 | −0.967046 | ||||||||
\(863\) | −35.5359 | −1.20966 | −0.604828 | − | 0.796356i | \(-0.706758\pi\) | ||||
−0.604828 | + | 0.796356i | \(0.706758\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 10.9282 | 0.371570 | ||||||||
\(866\) | 19.3205 | 0.656538 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −3.46410 | −0.117579 | ||||||||
\(869\) | 90.0333 | 3.05417 | ||||||||
\(870\) | −0.267949 | −0.00908433 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −15.8564 | −0.536966 | ||||||||
\(873\) | −0.535898 | −0.0181374 | ||||||||
\(874\) | −27.8564 | −0.942257 | ||||||||
\(875\) | 2.00000 | 0.0676123 | ||||||||
\(876\) | −2.00000 | −0.0675737 | ||||||||
\(877\) | 3.87564 | 0.130871 | 0.0654356 | − | 0.997857i | \(-0.479156\pi\) | ||||
0.0654356 | + | 0.997857i | \(0.479156\pi\) | |||||||
\(878\) | −17.8564 | −0.602625 | ||||||||
\(879\) | 31.8564 | 1.07449 | ||||||||
\(880\) | 6.46410 | 0.217905 | ||||||||
\(881\) | 14.0000 | 0.471672 | 0.235836 | − | 0.971793i | \(-0.424217\pi\) | ||||
0.235836 | + | 0.971793i | \(0.424217\pi\) | |||||||
\(882\) | 3.00000 | 0.101015 | ||||||||
\(883\) | −29.9282 | −1.00716 | −0.503582 | − | 0.863947i | \(-0.667985\pi\) | ||||
−0.503582 | + | 0.863947i | \(0.667985\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.46410 | 0.284518 | ||||||||
\(886\) | −16.3923 | −0.550710 | ||||||||
\(887\) | 14.1244 | 0.474249 | 0.237125 | − | 0.971479i | \(-0.423795\pi\) | ||||
0.237125 | + | 0.971479i | \(0.423795\pi\) | |||||||
\(888\) | −9.19615 | −0.308603 | ||||||||
\(889\) | −9.85641 | −0.330573 | ||||||||
\(890\) | 0.535898 | 0.0179634 | ||||||||
\(891\) | −6.46410 | −0.216556 | ||||||||
\(892\) | −20.5359 | −0.687593 | ||||||||
\(893\) | 26.3923 | 0.883185 | ||||||||
\(894\) | 13.5359 | 0.452708 | ||||||||
\(895\) | −19.7321 | −0.659570 | ||||||||
\(896\) | 2.00000 | 0.0668153 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.7128 | 0.524343 | ||||||||
\(899\) | 0.464102 | 0.0154787 | ||||||||
\(900\) | 1.00000 | 0.0333333 | ||||||||
\(901\) | 3.71281 | 0.123692 | ||||||||
\(902\) | 12.9282 | 0.430462 | ||||||||
\(903\) | −23.8564 | −0.793891 | ||||||||
\(904\) | −0.803848 | −0.0267356 | ||||||||
\(905\) | −2.92820 | −0.0973368 | ||||||||
\(906\) | −10.3923 | −0.345261 | ||||||||
\(907\) | 20.8564 | 0.692526 | 0.346263 | − | 0.938138i | \(-0.387451\pi\) | ||||
0.346263 | + | 0.938138i | \(0.387451\pi\) | |||||||
\(908\) | 16.3923 | 0.543998 | ||||||||
\(909\) | −2.92820 | −0.0971224 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 24.2487 | 0.803396 | 0.401698 | − | 0.915772i | \(-0.368420\pi\) | ||||
0.401698 | + | 0.915772i | \(0.368420\pi\) | |||||||
\(912\) | 7.46410 | 0.247161 | ||||||||
\(913\) | 57.7128 | 1.91002 | ||||||||
\(914\) | −24.5359 | −0.811575 | ||||||||
\(915\) | −10.3923 | −0.343559 | ||||||||
\(916\) | −7.85641 | −0.259583 | ||||||||
\(917\) | 37.3205 | 1.23243 | ||||||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | 14.6410 | 0.482963 | 0.241481 | − | 0.970405i | \(-0.422367\pi\) | ||||
0.241481 | + | 0.970405i | \(0.422367\pi\) | |||||||
\(920\) | −3.73205 | −0.123042 | ||||||||
\(921\) | −19.4641 | −0.641364 | ||||||||
\(922\) | 0.464102 | 0.0152844 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −12.9282 | −0.425307 | ||||||||
\(925\) | −9.19615 | −0.302368 | ||||||||
\(926\) | −7.07180 | −0.232394 | ||||||||
\(927\) | 11.8564 | 0.389415 | ||||||||
\(928\) | −0.267949 | −0.00879586 | ||||||||
\(929\) | 6.14359 | 0.201565 | 0.100782 | − | 0.994908i | \(-0.467865\pi\) | ||||
0.100782 | + | 0.994908i | \(0.467865\pi\) | |||||||
\(930\) | −1.73205 | −0.0567962 | ||||||||
\(931\) | 22.3923 | 0.733878 | ||||||||
\(932\) | −6.12436 | −0.200610 | ||||||||
\(933\) | −28.3923 | −0.929522 | ||||||||
\(934\) | −15.8564 | −0.518837 | ||||||||
\(935\) | 25.8564 | 0.845595 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −24.6410 | −0.804987 | −0.402493 | − | 0.915423i | \(-0.631856\pi\) | ||||
−0.402493 | + | 0.915423i | \(0.631856\pi\) | |||||||
\(938\) | −22.9282 | −0.748632 | ||||||||
\(939\) | 28.0000 | 0.913745 | ||||||||
\(940\) | 3.53590 | 0.115328 | ||||||||
\(941\) | 14.7846 | 0.481965 | 0.240982 | − | 0.970530i | \(-0.422530\pi\) | ||||
0.240982 | + | 0.970530i | \(0.422530\pi\) | |||||||
\(942\) | −5.00000 | −0.162909 | ||||||||
\(943\) | −7.46410 | −0.243065 | ||||||||
\(944\) | 8.46410 | 0.275483 | ||||||||
\(945\) | −2.00000 | −0.0650600 | ||||||||
\(946\) | −77.1051 | −2.50690 | ||||||||
\(947\) | −9.46410 | −0.307542 | −0.153771 | − | 0.988107i | \(-0.549142\pi\) | ||||
−0.153771 | + | 0.988107i | \(0.549142\pi\) | |||||||
\(948\) | 13.9282 | 0.452367 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 7.46410 | 0.242167 | ||||||||
\(951\) | 14.5359 | 0.471359 | ||||||||
\(952\) | 8.00000 | 0.259281 | ||||||||
\(953\) | 12.2679 | 0.397398 | 0.198699 | − | 0.980061i | \(-0.436328\pi\) | ||||
0.198699 | + | 0.980061i | \(0.436328\pi\) | |||||||
\(954\) | −0.928203 | −0.0300517 | ||||||||
\(955\) | −21.4641 | −0.694562 | ||||||||
\(956\) | 16.3923 | 0.530165 | ||||||||
\(957\) | 1.73205 | 0.0559893 | ||||||||
\(958\) | 5.46410 | 0.176537 | ||||||||
\(959\) | 4.92820 | 0.159140 | ||||||||
\(960\) | 1.00000 | 0.0322749 | ||||||||
\(961\) | −28.0000 | −0.903226 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.85641 | −0.253169 | ||||||||
\(964\) | 17.7321 | 0.571111 | ||||||||
\(965\) | 11.3205 | 0.364420 | ||||||||
\(966\) | 7.46410 | 0.240154 | ||||||||
\(967\) | 41.4641 | 1.33340 | 0.666698 | − | 0.745328i | \(-0.267707\pi\) | ||||
0.666698 | + | 0.745328i | \(0.267707\pi\) | |||||||
\(968\) | −30.7846 | −0.989455 | ||||||||
\(969\) | 29.8564 | 0.959126 | ||||||||
\(970\) | −0.535898 | −0.0172067 | ||||||||
\(971\) | 4.53590 | 0.145564 | 0.0727820 | − | 0.997348i | \(-0.476812\pi\) | ||||
0.0727820 | + | 0.997348i | \(0.476812\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 25.8564 | 0.828918 | ||||||||
\(974\) | 23.1769 | 0.742636 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −10.3923 | −0.332650 | ||||||||
\(977\) | 12.6077 | 0.403356 | 0.201678 | − | 0.979452i | \(-0.435361\pi\) | ||||
0.201678 | + | 0.979452i | \(0.435361\pi\) | |||||||
\(978\) | 15.0526 | 0.481328 | ||||||||
\(979\) | −3.46410 | −0.110713 | ||||||||
\(980\) | 3.00000 | 0.0958315 | ||||||||
\(981\) | 15.8564 | 0.506256 | ||||||||
\(982\) | −17.3205 | −0.552720 | ||||||||
\(983\) | −36.6077 | −1.16760 | −0.583802 | − | 0.811896i | \(-0.698436\pi\) | ||||
−0.583802 | + | 0.811896i | \(0.698436\pi\) | |||||||
\(984\) | 2.00000 | 0.0637577 | ||||||||
\(985\) | −4.39230 | −0.139950 | ||||||||
\(986\) | −1.07180 | −0.0341330 | ||||||||
\(987\) | −7.07180 | −0.225098 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 44.5167 | 1.41555 | ||||||||
\(990\) | −6.46410 | −0.205443 | ||||||||
\(991\) | −52.8564 | −1.67904 | −0.839520 | − | 0.543329i | \(-0.817163\pi\) | ||||
−0.839520 | + | 0.543329i | \(0.817163\pi\) | |||||||
\(992\) | −1.73205 | −0.0549927 | ||||||||
\(993\) | −16.7846 | −0.532643 | ||||||||
\(994\) | 24.7846 | 0.786120 | ||||||||
\(995\) | −5.07180 | −0.160787 | ||||||||
\(996\) | 8.92820 | 0.282901 | ||||||||
\(997\) | 35.5692 | 1.12649 | 0.563244 | − | 0.826290i | \(-0.309553\pi\) | ||||
0.563244 | + | 0.826290i | \(0.309553\pi\) | |||||||
\(998\) | 6.53590 | 0.206890 | ||||||||
\(999\) | 9.19615 | 0.290953 |
(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 | 5070.2.a.y.1.1 | 2 | ||
13.2 | odd | 12 | 390.2.bb.b.121.1 | ✓ | 4 | ||
13.5 | odd | 4 | 5070.2.b.o.1351.3 | 4 | |||
13.7 | odd | 12 | 390.2.bb.b.361.1 | yes | 4 | ||
13.8 | odd | 4 | 5070.2.b.o.1351.2 | 4 | |||
13.12 | even | 2 | 5070.2.a.bg.1.2 | 2 | |||
39.2 | even | 12 | 1170.2.bs.e.901.2 | 4 | |||
39.20 | even | 12 | 1170.2.bs.e.361.2 | 4 | |||
65.2 | even | 12 | 1950.2.y.f.199.1 | 4 | |||
65.7 | even | 12 | 1950.2.y.c.49.2 | 4 | |||
65.28 | even | 12 | 1950.2.y.c.199.2 | 4 | |||
65.33 | even | 12 | 1950.2.y.f.49.1 | 4 | |||
65.54 | odd | 12 | 1950.2.bc.b.901.2 | 4 | |||
65.59 | odd | 12 | 1950.2.bc.b.751.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
390.2.bb.b.121.1 | ✓ | 4 | 13.2 | odd | 12 | ||
390.2.bb.b.361.1 | yes | 4 | 13.7 | odd | 12 | ||
1170.2.bs.e.361.2 | 4 | 39.20 | even | 12 | |||
1170.2.bs.e.901.2 | 4 | 39.2 | even | 12 | |||
1950.2.y.c.49.2 | 4 | 65.7 | even | 12 | |||
1950.2.y.c.199.2 | 4 | 65.28 | even | 12 | |||
1950.2.y.f.49.1 | 4 | 65.33 | even | 12 | |||
1950.2.y.f.199.1 | 4 | 65.2 | even | 12 | |||
1950.2.bc.b.751.2 | 4 | 65.59 | odd | 12 | |||
1950.2.bc.b.901.2 | 4 | 65.54 | odd | 12 | |||
5070.2.a.y.1.1 | 2 | 1.1 | even | 1 | trivial | ||
5070.2.a.bg.1.2 | 2 | 13.12 | even | 2 | |||
5070.2.b.o.1351.2 | 4 | 13.8 | odd | 4 | |||
5070.2.b.o.1351.3 | 4 | 13.5 | odd | 4 |