Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2240,2,Mod(1791,2240)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2240, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2240.1791");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2240 = 2^{6} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2240.k (of order \(2\), degree \(1\), not 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: | \(17.8864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 140) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1791.4 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2240.1791 |
Dual form | 2240.2.k.b.1791.3 |
$q$-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 \(\left(\mathbb{Z}/2240\mathbb{Z}\right)^\times\).
\(n\) | \(897\) | \(1471\) | \(1541\) | \(1921\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.73205 | 1.00000 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.73205 | + | 2.00000i | −0.654654 | + | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 3.73205i | − | 1.12526i | −0.826710 | − | 0.562628i | \(-0.809790\pi\) | ||
0.826710 | − | 0.562628i | \(-0.190210\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 6.46410i | − | 1.79282i | −0.443227 | − | 0.896410i | \(-0.646166\pi\) | ||
0.443227 | − | 0.896410i | \(-0.353834\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.73205i | 0.447214i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.464102i | 0.112561i | 0.998415 | + | 0.0562806i | \(0.0179241\pi\) | ||||
−0.998415 | + | 0.0562806i | \(0.982076\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000 | 1.37649 | 0.688247 | − | 0.725476i | \(-0.258380\pi\) | ||||
0.688247 | + | 0.725476i | \(0.258380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | + | 3.46410i | −0.654654 | + | 0.755929i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 5.46410i | − | 1.13934i | −0.821872 | − | 0.569672i | \(-0.807070\pi\) | ||
0.821872 | − | 0.569672i | \(-0.192930\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5.92820 | 1.10084 | 0.550420 | − | 0.834888i | \(-0.314468\pi\) | ||||
0.550420 | + | 0.834888i | \(0.314468\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 6.46410i | − | 1.12526i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.00000 | − | 1.73205i | −0.338062 | − | 0.292770i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.53590 | 0.416899 | 0.208450 | − | 0.978033i | \(-0.433158\pi\) | ||||
0.208450 | + | 0.978033i | \(0.433158\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 11.1962i | − | 1.79282i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.73205 | 0.252646 | 0.126323 | − | 0.991989i | \(-0.459682\pi\) | ||||
0.126323 | + | 0.991989i | \(0.459682\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.803848i | 0.112561i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.00000 | −0.274721 | −0.137361 | − | 0.990521i | \(-0.543862\pi\) | ||||
−0.137361 | + | 0.990521i | \(0.543862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.73205 | 0.503230 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.3923 | 1.37649 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.46410 | 0.450988 | 0.225494 | − | 0.974245i | \(-0.427600\pi\) | ||||
0.225494 | + | 0.974245i | \(0.427600\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 2.53590i | − | 0.324689i | −0.986734 | − | 0.162344i | \(-0.948094\pi\) | ||
0.986734 | − | 0.162344i | \(-0.0519055\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.46410 | 0.801773 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.46410i | − | 0.423207i | −0.977356 | − | 0.211604i | \(-0.932131\pi\) | ||
0.977356 | − | 0.211604i | \(-0.0678686\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 9.46410i | − | 1.13934i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.535898i | 0.0635994i | 0.999494 | + | 0.0317997i | \(0.0101239\pi\) | ||||
−0.999494 | + | 0.0317997i | \(0.989876\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.928203i | − | 0.108638i | −0.998524 | − | 0.0543190i | \(-0.982701\pi\) | ||
0.998524 | − | 0.0543190i | \(-0.0172988\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.73205 | −0.200000 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.46410 | + | 6.46410i | 0.850613 | + | 0.736653i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 2.66025i | − | 0.299302i | −0.988739 | − | 0.149651i | \(-0.952185\pi\) | ||
0.988739 | − | 0.149651i | \(-0.0478150\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −1.00000 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.53590 | 0.936937 | 0.468468 | − | 0.883480i | \(-0.344806\pi\) | ||||
0.468468 | + | 0.883480i | \(0.344806\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.464102 | −0.0503389 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 10.2679 | 1.10084 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.46410i | 1.00319i | 0.865102 | + | 0.501596i | \(0.167254\pi\) | ||||
−0.865102 | + | 0.501596i | \(0.832746\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 12.9282 | + | 11.1962i | 1.35524 | + | 1.17368i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 10.3923 | 1.07763 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000i | 0.615587i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.39230i | 0.750575i | 0.926908 | + | 0.375287i | \(0.122456\pi\) | ||||
−0.926908 | + | 0.375287i | \(0.877544\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 8.53590i | 0.849354i | 0.905345 | + | 0.424677i | \(0.139612\pi\) | ||||
−0.905345 | + | 0.424677i | \(0.860388\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.1962 | 1.69439 | 0.847194 | − | 0.531284i | \(-0.178290\pi\) | ||||
0.847194 | + | 0.531284i | \(0.178290\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.46410 | − | 3.00000i | −0.338062 | − | 0.292770i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 18.3923i | − | 1.77805i | −0.457857 | − | 0.889026i | \(-0.651383\pi\) | ||
0.457857 | − | 0.889026i | \(-0.348617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −15.9282 | −1.52565 | −0.762823 | − | 0.646608i | \(-0.776187\pi\) | ||||
−0.762823 | + | 0.646608i | \(0.776187\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 4.39230 | 0.416899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.46410 | −0.137731 | −0.0688655 | − | 0.997626i | \(-0.521938\pi\) | ||||
−0.0688655 | + | 0.997626i | \(0.521938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.46410 | 0.509530 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.928203 | − | 0.803848i | −0.0850883 | − | 0.0736886i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.92820 | −0.266200 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.00000i | 0.541002i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 8.53590i | − | 0.757438i | −0.925512 | − | 0.378719i | \(-0.876365\pi\) | ||
0.925512 | − | 0.378719i | \(-0.123635\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 3.46410i | − | 0.304997i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.46410 | 0.826882 | 0.413441 | − | 0.910531i | \(-0.364327\pi\) | ||||
0.413441 | + | 0.910531i | \(0.364327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.3923 | + | 12.0000i | −0.901127 | + | 1.04053i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 5.19615i | − | 0.447214i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.392305 | −0.0335169 | −0.0167584 | − | 0.999860i | \(-0.505335\pi\) | ||||
−0.0167584 | + | 0.999860i | \(0.505335\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.92820 | −0.587643 | −0.293821 | − | 0.955860i | \(-0.594927\pi\) | ||||
−0.293821 | + | 0.955860i | \(0.594927\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −24.1244 | −2.01738 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.92820i | 0.492310i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.73205 | − | 12.0000i | −0.142857 | − | 0.989743i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.9282 | −1.38681 | −0.693406 | − | 0.720547i | \(-0.743891\pi\) | ||||
−0.693406 | + | 0.720547i | \(0.743891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.80385i | 0.390932i | 0.980711 | + | 0.195466i | \(0.0626219\pi\) | ||||
−0.980711 | + | 0.195466i | \(0.937378\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.00000i | 0.481932i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 19.8564i | 1.58471i | 0.610058 | + | 0.792357i | \(0.291146\pi\) | ||||
−0.610058 | + | 0.792357i | \(0.708854\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.46410 | −0.274721 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.9282 | + | 9.46410i | 0.861263 | + | 0.745876i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 20.7846i | − | 1.62798i | −0.580881 | − | 0.813988i | \(-0.697292\pi\) | ||
0.580881 | − | 0.813988i | \(-0.302708\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.46410 | 0.503230 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.19615 | −0.402090 | −0.201045 | − | 0.979582i | \(-0.564434\pi\) | ||||
−0.201045 | + | 0.979582i | \(0.564434\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28.7846 | −2.21420 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 20.3205i | − | 1.54494i | −0.635051 | − | 0.772470i | \(-0.719021\pi\) | ||
0.635051 | − | 0.772470i | \(-0.280979\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.73205 | − | 2.00000i | 0.130931 | − | 0.151186i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 6.00000 | 0.450988 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 14.3923i | − | 1.07573i | −0.843031 | − | 0.537866i | \(-0.819231\pi\) | ||
0.843031 | − | 0.537866i | \(-0.180769\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 12.9282i | − | 0.960946i | −0.877010 | − | 0.480473i | \(-0.840465\pi\) | ||
0.877010 | − | 0.480473i | \(-0.159535\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 4.39230i | − | 0.324689i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.53590i | 0.186443i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.73205 | 0.126660 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000 | − | 10.3923i | 0.654654 | − | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 3.19615i | − | 0.231265i | −0.993292 | − | 0.115633i | \(-0.963110\pi\) | ||
0.993292 | − | 0.115633i | \(-0.0368896\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.53590 | −0.182538 | −0.0912690 | − | 0.995826i | \(-0.529092\pi\) | ||||
−0.0912690 | + | 0.995826i | \(0.529092\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.1962 | 0.801773 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −21.3205 | −1.51902 | −0.759512 | − | 0.650494i | \(-0.774562\pi\) | ||||
−0.759512 | + | 0.650494i | \(0.774562\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.46410 | 0.245564 | 0.122782 | − | 0.992434i | \(-0.460818\pi\) | ||||
0.122782 | + | 0.992434i | \(0.460818\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 6.00000i | − | 0.423207i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10.2679 | + | 11.8564i | −0.720669 | + | 0.832157i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.46410 | −0.241943 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 22.3923i | − | 1.54891i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.19615i | 0.495404i | 0.968836 | + | 0.247702i | \(0.0796753\pi\) | ||||
−0.968836 | + | 0.247702i | \(0.920325\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.928203i | 0.0635994i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.00000 | 0.136399 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.3923 | + | 12.0000i | −0.705476 | + | 0.814613i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1.60770i | − | 0.108638i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | 0.201802 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.2679 | 0.687593 | 0.343796 | − | 0.939044i | \(-0.388287\pi\) | ||||
0.343796 | + | 0.939044i | \(0.388287\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.33975 | 0.221667 | 0.110833 | − | 0.993839i | \(-0.464648\pi\) | ||||
0.110833 | + | 0.993839i | \(0.464648\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.4641i | 1.02190i | 0.859611 | + | 0.510948i | \(0.170706\pi\) | ||||
−0.859611 | + | 0.510948i | \(0.829294\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 12.9282 | + | 11.1962i | 0.850613 | + | 0.736653i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −22.9282 | −1.50208 | −0.751038 | − | 0.660259i | \(-0.770447\pi\) | ||||
−0.751038 | + | 0.660259i | \(0.770447\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1.73205i | 0.112987i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 4.60770i | − | 0.299302i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.9808i | 1.80993i | 0.425491 | + | 0.904963i | \(0.360101\pi\) | ||||
−0.425491 | + | 0.904963i | \(0.639899\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.39230i | − | 0.282933i | −0.989943 | − | 0.141467i | \(-0.954818\pi\) | ||
0.989943 | − | 0.141467i | \(-0.0451818\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.92820 | − | 1.00000i | 0.442627 | − | 0.0638877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 38.7846i | − | 2.46781i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.7846 | 0.936937 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.85641 | 0.117175 | 0.0585877 | − | 0.998282i | \(-0.481340\pi\) | ||||
0.0585877 | + | 0.998282i | \(0.481340\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −20.3923 | −1.28205 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.803848 | −0.0503389 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.00000i | 0.374270i | 0.982334 | + | 0.187135i | \(0.0599201\pi\) | ||||
−0.982334 | + | 0.187135i | \(0.940080\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.39230 | + | 5.07180i | −0.272925 | + | 0.315146i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.53590i | − | 0.279695i | −0.990173 | − | 0.139848i | \(-0.955339\pi\) | ||
0.990173 | − | 0.139848i | \(-0.0446613\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2.00000i | − | 0.122859i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.3923i | 1.00319i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.0000i | 0.731653i | 0.930683 | + | 0.365826i | \(0.119214\pi\) | ||||
−0.930683 | + | 0.365826i | \(0.880786\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.53590 | −0.154045 | −0.0770224 | − | 0.997029i | \(-0.524541\pi\) | ||||
−0.0770224 | + | 0.997029i | \(0.524541\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 22.3923 | + | 19.3923i | 1.35524 | + | 1.17368i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3.73205i | 0.225051i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 24.7846 | 1.48916 | 0.744581 | − | 0.667532i | \(-0.232649\pi\) | ||||
0.744581 | + | 0.667532i | \(0.232649\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.92820 | 0.353647 | 0.176823 | − | 0.984243i | \(-0.443418\pi\) | ||||
0.176823 | + | 0.984243i | \(0.443418\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.1244 | −0.720718 | −0.360359 | − | 0.932814i | \(-0.617346\pi\) | ||||
−0.360359 | + | 0.932814i | \(0.617346\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.3923i | 0.615587i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.92820 | − | 6.00000i | −0.408959 | − | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7846 | 0.987330 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.8038i | 0.750575i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.3205i | 0.836613i | 0.908306 | + | 0.418307i | \(0.137376\pi\) | ||||
−0.908306 | + | 0.418307i | \(0.862624\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.46410i | 0.201688i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 19.3923i | 1.12526i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −35.3205 | −2.04264 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 3.46410i | 0.230556 | + | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 14.7846i | 0.849354i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.53590 | 0.145205 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.73205 | −0.0988534 | −0.0494267 | − | 0.998778i | \(-0.515739\pi\) | ||||
−0.0494267 | + | 0.998778i | \(0.515739\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 29.7846 | 1.69439 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.8564 | 1.12595 | 0.562977 | − | 0.826473i | \(-0.309656\pi\) | ||||
0.562977 | + | 0.826473i | \(0.309656\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 24.4641i | − | 1.38279i | −0.722476 | − | 0.691396i | \(-0.756996\pi\) | ||
0.722476 | − | 0.691396i | \(-0.243004\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.9282 | 0.950783 | 0.475391 | − | 0.879774i | \(-0.342306\pi\) | ||||
0.475391 | + | 0.879774i | \(0.342306\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 22.1244i | − | 1.23873i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 31.8564i | − | 1.77805i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.78461i | 0.154940i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.46410i | 0.358564i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.5885 | −1.52565 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00000 | + | 3.46410i | −0.165395 | + | 0.190982i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.60770i | 0.308227i | 0.988053 | + | 0.154113i | \(0.0492521\pi\) | ||||
−0.988053 | + | 0.154113i | \(0.950748\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.46410 | 0.189264 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.53590 | −0.137731 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 22.3923i | − | 1.21261i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.5885 | + | 10.0000i | 0.841698 | + | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 9.46410 | 0.509530 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.2487i | 0.764911i | 0.923974 | + | 0.382455i | \(0.124921\pi\) | ||||
−0.923974 | + | 0.382455i | \(0.875079\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 29.3205i | − | 1.56949i | −0.619818 | − | 0.784745i | \(-0.712794\pi\) | ||
0.619818 | − | 0.784745i | \(-0.287206\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 33.5885i | 1.79282i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.3923i | 0.712800i | 0.934333 | + | 0.356400i | \(0.115996\pi\) | ||||
−0.934333 | + | 0.356400i | \(0.884004\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.535898 | −0.0284425 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.60770 | − | 1.39230i | −0.0850883 | − | 0.0736886i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 9.32051i | − | 0.491918i | −0.969280 | − | 0.245959i | \(-0.920897\pi\) | ||
0.969280 | − | 0.245959i | \(-0.0791028\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.0000 | 0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −5.07180 | −0.266200 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.928203 | 0.0485844 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −36.1244 | −1.88568 | −0.942838 | − | 0.333251i | \(-0.891854\pi\) | ||||
−0.942838 | + | 0.333251i | \(0.891854\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.46410 | − | 4.00000i | 0.179847 | − | 0.207670i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 24.3923 | 1.26299 | 0.631493 | − | 0.775382i | \(-0.282443\pi\) | ||||
0.631493 | + | 0.775382i | \(0.282443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1.73205i | − | 0.0894427i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 38.3205i | − | 1.97361i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 26.3923i | − | 1.35568i | −0.735209 | − | 0.677841i | \(-0.762916\pi\) | ||
0.735209 | − | 0.677841i | \(-0.237084\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 14.7846i | − | 0.757438i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −20.5359 | −1.04934 | −0.524668 | − | 0.851307i | \(-0.675810\pi\) | ||||
−0.524668 | + | 0.851307i | \(0.675810\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.46410 | + | 7.46410i | −0.329441 | + | 0.380406i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.85641 | −0.347634 | −0.173817 | − | 0.984778i | \(-0.555610\pi\) | ||||
−0.173817 | + | 0.984778i | \(0.555610\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.53590 | 0.128246 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 16.3923 | 0.826882 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.66025 | 0.133852 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 5.53590i | − | 0.277839i | −0.990304 | − | 0.138919i | \(-0.955637\pi\) | ||
0.990304 | − | 0.138919i | \(-0.0443629\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −18.0000 | + | 20.7846i | −0.901127 | + | 1.04053i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −23.9282 | −1.19492 | −0.597459 | − | 0.801900i | \(-0.703823\pi\) | ||||
−0.597459 | + | 0.801900i | \(0.703823\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 38.7846i | − | 1.93200i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 9.00000i | − | 0.447214i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 9.46410i | − | 0.469118i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.8564i | 1.57520i | 0.616188 | + | 0.787599i | \(0.288676\pi\) | ||||
−0.616188 | + | 0.787599i | \(0.711324\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.679492 | −0.0335169 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.00000 | + | 6.92820i | −0.295241 | + | 0.340915i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.53590i | 0.419011i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −12.0000 | −0.587643 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 24.2487 | 1.18463 | 0.592314 | − | 0.805708i | \(-0.298215\pi\) | ||||
0.592314 | + | 0.805708i | \(0.298215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.0000 | −0.926003 | −0.463002 | − | 0.886357i | \(-0.653228\pi\) | ||||
−0.463002 | + | 0.886357i | \(0.653228\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 0.464102i | − | 0.0225122i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.07180 | + | 4.39230i | 0.245441 | + | 0.212559i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −41.7846 | −2.01738 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.5885i | 0.847206i | 0.905848 | + | 0.423603i | \(0.139235\pi\) | ||||
−0.905848 | + | 0.423603i | \(0.860765\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.14359i | − | 0.199128i | −0.995031 | − | 0.0995642i | \(-0.968255\pi\) | ||
0.995031 | − | 0.0995642i | \(-0.0317449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 10.2679i | 0.492310i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 32.7846i | − | 1.56830i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.7128 | −0.749932 | −0.374966 | − | 0.927039i | \(-0.622346\pi\) | ||||
−0.374966 | + | 0.927039i | \(0.622346\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.0000i | 1.23530i | 0.786454 | + | 0.617649i | \(0.211915\pi\) | ||||
−0.786454 | + | 0.617649i | \(0.788085\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.46410 | −0.448641 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −29.3205 | −1.38681 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.92820 | −0.0909975 | −0.0454988 | − | 0.998964i | \(-0.514488\pi\) | ||||
−0.0454988 | + | 0.998964i | \(0.514488\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 12.9282 | 0.608765 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.32051i | 0.390932i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.1962 | + | 12.9282i | −0.524884 | + | 0.606084i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 27.4641 | 1.28472 | 0.642358 | − | 0.766405i | \(-0.277956\pi\) | ||||
0.642358 | + | 0.766405i | \(0.277956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 2.41154i | − | 0.112561i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.7128i | 1.29071i | 0.763881 | + | 0.645357i | \(0.223291\pi\) | ||||
−0.763881 | + | 0.645357i | \(0.776709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.39230i | 0.204128i | 0.994778 | + | 0.102064i | \(0.0325446\pi\) | ||||
−0.994778 | + | 0.102064i | \(0.967455\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 10.3923i | 0.481932i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −22.5167 | −1.04195 | −0.520973 | − | 0.853573i | \(-0.674431\pi\) | ||||
−0.520973 | + | 0.853573i | \(0.674431\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6.92820 | + | 6.00000i | 0.319915 | + | 0.277054i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 34.3923i | 1.58471i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.46410 | −0.343200 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | −0.275299 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 37.1769 | 1.69866 | 0.849328 | − | 0.527865i | \(-0.177007\pi\) | ||||
0.849328 | + | 0.527865i | \(0.177007\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 16.3923i | − | 0.747425i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 18.9282 | + | 16.3923i | 0.861263 | + | 0.745876i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.39230 | −0.335667 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.7846i | 1.30436i | 0.758066 | + | 0.652178i | \(0.226144\pi\) | ||||
−0.758066 | + | 0.652178i | \(0.773856\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 36.0000i | − | 1.62798i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.1244i | 1.54001i | 0.638037 | + | 0.770005i | \(0.279746\pi\) | ||||
−0.638037 | + | 0.770005i | \(0.720254\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.75129i | 0.123912i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.07180 | − | 0.928203i | −0.0480767 | − | 0.0416356i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.58846i | 0.250174i | 0.992146 | + | 0.125087i | \(0.0399210\pi\) | ||||
−0.992146 | + | 0.125087i | \(0.960079\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.00000 | −0.402090 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −15.5885 | −0.695055 | −0.347527 | − | 0.937670i | \(-0.612979\pi\) | ||||
−0.347527 | + | 0.937670i | \(0.612979\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.53590 | −0.379842 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −49.8564 | −2.21420 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.85641i | 0.0822838i | 0.999153 | + | 0.0411419i | \(0.0130996\pi\) | ||||
−0.999153 | + | 0.0411419i | \(0.986900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.85641 | + | 1.60770i | 0.0821226 | + | 0.0711202i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −31.1769 | −1.37649 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 17.1962i | 0.757753i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 6.46410i | − | 0.284291i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 35.1962i | − | 1.54494i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 34.3923i | 1.50675i | 0.657589 | + | 0.753377i | \(0.271576\pi\) | ||||
−0.657589 | + | 0.753377i | \(0.728424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.2487 | 1.06032 | 0.530161 | − | 0.847897i | \(-0.322131\pi\) | ||||
0.530161 | + | 0.847897i | \(0.322131\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 3.00000 | − | 3.46410i | 0.130931 | − | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.78461i | 0.121300i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.85641 | −0.298105 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 22.3923 | 0.969918 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 18.3923 | 0.795169 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 24.9282i | − | 1.07573i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −25.8564 | + | 3.73205i | −1.11371 | + | 0.160751i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 33.7846 | 1.45251 | 0.726257 | − | 0.687423i | \(-0.241258\pi\) | ||||
0.726257 | + | 0.687423i | \(0.241258\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 22.3923i | − | 0.960946i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 15.9282i | − | 0.682289i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.5359i | − | 0.621510i | −0.950490 | − | 0.310755i | \(-0.899418\pi\) | ||
0.950490 | − | 0.310755i | \(-0.100582\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 35.5692 | 1.51530 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.32051 | + | 4.60770i | 0.226251 | + | 0.195939i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.39230i | 0.186443i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.85641 | −0.248144 | −0.124072 | − | 0.992273i | \(-0.539595\pi\) | ||||
−0.124072 | + | 0.992273i | \(0.539595\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −12.9282 | −0.546805 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.00000 | 0.126660 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −43.1769 | −1.81969 | −0.909845 | − | 0.414948i | \(-0.863800\pi\) | ||||
−0.909845 | + | 0.414948i | \(0.863800\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 1.46410i | − | 0.0615952i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.5885 | − | 18.0000i | 0.654654 | − | 0.755929i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 20.9282 | 0.877356 | 0.438678 | − | 0.898644i | \(-0.355447\pi\) | ||||
0.438678 | + | 0.898644i | \(0.355447\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 41.3205i | 1.72921i | 0.502453 | + | 0.864605i | \(0.332431\pi\) | ||||
−0.502453 | + | 0.864605i | \(0.667569\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.53590i | − | 0.231265i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.46410i | 0.227869i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 1.39230i | − | 0.0579624i | −0.999580 | − | 0.0289812i | \(-0.990774\pi\) | ||
0.999580 | − | 0.0289812i | \(-0.00922630\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −4.39230 | −0.182538 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −14.7846 | + | 17.0718i | −0.613369 | + | 0.708257i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.46410i | 0.309132i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −27.4641 | −1.13356 | −0.566782 | − | 0.823868i | \(-0.691812\pi\) | ||||
−0.566782 | + | 0.823868i | \(0.691812\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 36.0000 | 1.48335 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.9282 | −1.51902 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 23.5359i | 0.966504i | 0.875481 | + | 0.483252i | \(0.160544\pi\) | ||||
−0.875481 | + | 0.483252i | \(0.839456\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.803848 | − | 0.928203i | 0.0329545 | − | 0.0380526i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6.00000 | 0.245564 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.1244i | 0.577106i | 0.957464 | + | 0.288553i | \(0.0931741\pi\) | ||||
−0.957464 | + | 0.288553i | \(0.906826\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 26.7846i | 1.09257i | 0.837600 | + | 0.546284i | \(0.183958\pi\) | ||||
−0.837600 | + | 0.546284i | \(0.816042\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 2.92820i | − | 0.119048i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.8038 | 0.763225 | 0.381612 | − | 0.924322i | \(-0.375369\pi\) | ||||
0.381612 | + | 0.924322i | \(0.375369\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −17.7846 | + | 20.5359i | −0.720669 | + | 0.832157i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 11.1962i | − | 0.452948i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.0000 | 0.403896 | 0.201948 | − | 0.979396i | \(-0.435273\pi\) | ||||
0.201948 | + | 0.979396i | \(0.435273\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −6.00000 | −0.241943 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.07180 | −0.365217 | −0.182608 | − | 0.983186i | \(-0.558454\pi\) | ||||
−0.182608 | + | 0.983186i | \(0.558454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 35.3205 | 1.41965 | 0.709826 | − | 0.704378i | \(-0.248774\pi\) | ||||
0.709826 | + | 0.704378i | \(0.248774\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 28.3923i | 1.13934i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.9282 | − | 16.3923i | −0.758342 | − | 0.656744i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 38.7846i | − | 1.54891i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.17691i | 0.0469267i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 26.9090i | − | 1.07123i | −0.844463 | − | 0.535614i | \(-0.820080\pi\) | ||
0.844463 | − | 0.535614i | \(-0.179920\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.4641i | 0.495404i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 8.53590 | 0.338737 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −44.7846 | + | 6.46410i | −1.77443 | + | 0.256117i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.92820 | −0.194652 | −0.0973262 | − | 0.995253i | \(-0.531029\pi\) | ||||
−0.0973262 | + | 0.995253i | \(0.531029\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.0526 | −1.22459 | −0.612297 | − | 0.790628i | \(-0.709754\pi\) | ||||
−0.612297 | + | 0.790628i | \(0.709754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.46410 | 0.136399 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −10.3923 | −0.408564 | −0.204282 | − | 0.978912i | \(-0.565486\pi\) | ||||
−0.204282 | + | 0.978912i | \(0.565486\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 12.9282i | − | 0.507476i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.0000 | + | 20.7846i | −0.705476 | + | 0.814613i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −38.3923 | −1.50241 | −0.751203 | − | 0.660071i | \(-0.770526\pi\) | ||||
−0.751203 | + | 0.660071i | \(0.770526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 9.46410i | 0.369793i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.8038i | 0.810403i | 0.914227 | + | 0.405201i | \(0.132799\pi\) | ||||
−0.914227 | + | 0.405201i | \(0.867201\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.7128i | 0.611158i | 0.952167 | + | 0.305579i | \(0.0988499\pi\) | ||||
−0.952167 | + | 0.305579i | \(0.901150\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.19615 | 0.201802 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | − | 10.3923i | −0.465340 | − | 0.402996i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 32.3923i | − | 1.25424i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.7846 | 0.687593 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.46410 | −0.365358 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 49.1769 | 1.89563 | 0.947815 | − | 0.318820i | \(-0.103286\pi\) | ||||
0.947815 | + | 0.318820i | \(0.103286\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.19615 | 0.200000 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.60770i | 0.177088i | 0.996072 | + | 0.0885441i | \(0.0282214\pi\) | ||||
−0.996072 | + | 0.0885441i | \(0.971779\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.7846 | − | 12.8038i | −0.567381 | − | 0.491367i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.78461 | 0.221667 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.3205i | 1.04539i | 0.852520 | + | 0.522695i | \(0.175073\pi\) | ||||
−0.852520 | + | 0.522695i | \(0.824927\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 0.392305i | − | 0.0149892i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 26.7846i | 1.02190i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.9282i | 0.492525i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 46.6410 | 1.77431 | 0.887154 | − | 0.461474i | \(-0.152679\pi\) | ||||
0.887154 | + | 0.461474i | \(0.152679\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 6.92820i | − | 0.262802i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.60770 | −0.0608958 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −39.7128 | −1.50208 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.78461 | −0.142943 | −0.0714714 | − | 0.997443i | \(-0.522769\pi\) | ||||
−0.0714714 | + | 0.997443i | \(0.522769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.2154 | 0.573859 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.00000i | 0.112987i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −17.0718 | − | 14.7846i | −0.642051 | − | 0.556032i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −21.0000 | −0.788672 | −0.394336 | − | 0.918966i | \(-0.629025\pi\) | ||||
−0.394336 | + | 0.918966i | \(0.629025\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 32.7846i | − | 1.22779i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 24.1244i | − | 0.902200i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 48.4641i | 1.80993i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −45.4641 | −1.69552 | −0.847762 | − | 0.530376i | \(-0.822051\pi\) | ||||
−0.847762 | + | 0.530376i | \(0.822051\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.7846 | + | 34.3923i | −1.10924 | + | 1.28084i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 7.60770i | − | 0.282933i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.92820 | −0.220168 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.3923 | 1.27554 | 0.637770 | − | 0.770227i | \(-0.279857\pi\) | ||||
0.637770 | + | 0.770227i | \(0.279857\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.928203 | 0.0343308 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 18.4641i | − | 0.681987i | −0.940066 | − | 0.340994i | \(-0.889237\pi\) | ||
0.940066 | − | 0.340994i | \(-0.110763\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.0000 | − | 1.73205i | 0.442627 | − | 0.0638877i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.9282 | −0.476216 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 7.73205i | 0.284428i | 0.989836 | + | 0.142214i | \(0.0454221\pi\) | ||||
−0.989836 | + | 0.142214i | \(0.954578\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 67.1769i | − | 2.46781i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.60770i | 0.352472i | 0.984348 | + | 0.176236i | \(0.0563922\pi\) | ||||
−0.984348 | + | 0.176236i | \(0.943608\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 16.9282i | − | 0.620201i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 36.7846 | + | 31.8564i | 1.34408 | + | 1.16401i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 5.58846i | 0.203926i | 0.994788 | + | 0.101963i | \(0.0325123\pi\) | ||||
−0.994788 | + | 0.101963i | \(0.967488\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.21539 | 0.117175 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −4.80385 | −0.174830 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1436 | −0.368675 | −0.184338 | − | 0.982863i | \(-0.559014\pi\) | ||||
−0.184338 | + | 0.982863i | \(0.559014\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −35.3205 | −1.28205 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.24871i | 0.226516i | 0.993566 | + | 0.113258i | \(0.0361286\pi\) | ||||
−0.993566 | + | 0.113258i | \(0.963871\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.5885 | − | 31.8564i | 0.998769 | − | 1.15328i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 22.3923i | − | 0.808539i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.0000i | 0.649097i | 0.945869 | + | 0.324548i | \(0.105212\pi\) | ||||
−0.945869 | + | 0.324548i | \(0.894788\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10.3923i | 0.374270i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12.4641i | 0.448303i | 0.974554 | + | 0.224151i | \(0.0719610\pi\) | ||||
−0.974554 | + | 0.224151i | \(0.928039\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.00000 | −0.215526 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.60770 | + | 8.78461i | −0.272925 | + | 0.315146i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 20.7846i | 0.744686i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00000 | 0.0715656 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −30.8038 | −1.10084 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −19.8564 | −0.708706 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15.3397 | 0.546803 | 0.273401 | − | 0.961900i | \(-0.411851\pi\) | ||||
0.273401 | + | 0.961900i | \(0.411851\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 7.85641i | − | 0.279695i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.53590 | − | 2.92820i | 0.0901662 | − | 0.104115i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −16.3923 | −0.582108 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − | 3.46410i | − | 0.122859i | ||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 40.1769i | − | 1.42314i | −0.702616 | − | 0.711570i | \(-0.747985\pi\) | ||
0.702616 | − | 0.711570i | \(-0.252015\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.803848i | 0.0284381i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.46410 | −0.122245 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.46410 | + | 10.9282i | −0.333566 | + | 0.385169i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 20.7846i | 0.731653i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.92820 | −0.208425 | −0.104212 | − | 0.994555i | \(-0.533232\pi\) | ||||
−0.104212 | + | 0.994555i | \(0.533232\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.9282 | 1.50741 | 0.753707 | − | 0.657211i | \(-0.228264\pi\) | ||||
0.753707 | + | 0.657211i | \(0.228264\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.39230 | −0.154045 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 20.7846 | 0.728053 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 12.0000i | − | 0.419827i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.7846 | 0.481086 | 0.240543 | − | 0.970638i | \(-0.422674\pi\) | ||||
0.240543 | + | 0.970638i | \(0.422674\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24.9282i | 0.868943i | 0.900686 | + | 0.434471i | \(0.143065\pi\) | ||||
−0.900686 | + | 0.434471i | \(0.856935\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.46410i | 0.225051i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 41.8564i | − | 1.45549i | −0.685848 | − | 0.727745i | \(-0.740568\pi\) | ||
0.685848 | − | 0.727745i | \(-0.259432\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 48.2487i | 1.67575i | 0.545864 | + | 0.837874i | \(0.316201\pi\) | ||||
−0.545864 | + | 0.837874i | \(0.683799\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 42.9282 | 1.48916 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.21539 | − | 0.464102i | 0.111407 | − | 0.0160802i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 5.19615i | − | 0.179820i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −31.1769 | −1.07763 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16.3923 | 0.565925 | 0.282963 | − | 0.959131i | \(-0.408683\pi\) | ||||
0.282963 | + | 0.959131i | \(0.408683\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.14359 | 0.211848 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 10.2679 | 0.353647 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 28.7846i | − | 0.990221i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5.07180 | − | 5.85641i | 0.174269 | − | 0.201229i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.0000 | −0.720718 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 13.8564i | − | 0.474991i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 38.7846i | − | 1.32796i | −0.747750 | − | 0.663980i | \(-0.768866\pi\) | ||
0.747750 | − | 0.663980i | \(-0.231134\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.28719i | 0.0781288i | 0.999237 | + | 0.0390644i | \(0.0124378\pi\) | ||||
−0.999237 | + | 0.0390644i | \(0.987562\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.7128 | −0.536114 | −0.268057 | − | 0.963403i | \(-0.586382\pi\) | ||||
−0.268057 | + | 0.963403i | \(0.586382\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.0000 | − | 10.3923i | −0.408959 | − | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 12.1436i | − | 0.413373i | −0.978407 | − | 0.206686i | \(-0.933732\pi\) | ||
0.978407 | − | 0.206686i | \(-0.0662680\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 20.3205 | 0.690918 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 29.0718 | 0.987330 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.92820 | −0.336791 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −22.3923 | −0.758734 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 2.00000 | + | 1.73205i | 0.0676123 | + | 0.0585540i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.39230 | −0.0807824 | −0.0403912 | − | 0.999184i | \(-0.512860\pi\) | ||||
−0.0403912 | + | 0.999184i | \(0.512860\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.8038i | 0.836613i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 42.9282i | − | 1.44629i | −0.690697 | − | 0.723144i | \(-0.742696\pi\) | ||
0.690697 | − | 0.723144i | \(-0.257304\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.3923i | 1.49392i | 0.664869 | + | 0.746960i | \(0.268487\pi\) | ||||
−0.664869 | + | 0.746960i | \(0.731513\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.00000i | 0.201688i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 15.4641 | 0.519234 | 0.259617 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259617 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 17.0718 | + | 14.7846i | 0.572570 | + | 0.495860i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 33.5885i | 1.12526i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.3923 | 0.347765 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14.3923 | 0.481082 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −61.1769 | −2.04264 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.5692 | 1.18630 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 0.928203i | − | 0.0309229i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 6.92820 | + | 6.00000i | 0.230556 | + | 0.199667i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.9282 | 0.429748 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.6077i | 0.385427i | 0.981255 | + | 0.192714i | \(0.0617288\pi\) | ||||
−0.981255 | + | 0.192714i | \(0.938271\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.2487i | 0.935922i | 0.883749 | + | 0.467961i | \(0.155011\pi\) | ||||
−0.883749 | + | 0.467961i | \(0.844989\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 31.8564i | − | 1.05429i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 4.39230 | 0.145205 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16.3923 | + | 18.9282i | −0.541322 | + | 0.625064i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 37.5885i | − | 1.23993i | −0.784630 | − | 0.619964i | \(-0.787147\pi\) | ||
0.784630 | − | 0.619964i | \(-0.212853\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.00000 | −0.0988534 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.46410 | 0.114022 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.53590 | −0.0833798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 42.4974i | 1.39430i | 0.716928 | + | 0.697148i | \(0.245548\pi\) | ||||
−0.716928 | + | 0.697148i | \(0.754452\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.00000 | − | 41.5692i | −0.196642 | − | 1.36238i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 34.3923 | 1.12595 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.73205i | 0.0566441i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 4.60770i | − | 0.150527i | −0.997164 | − | 0.0752634i | \(-0.976020\pi\) | ||
0.997164 | − | 0.0752634i | \(-0.0239798\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 42.3731i | − | 1.38279i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.0333i | 1.66364i | 0.555046 | + | 0.831819i | \(0.312700\pi\) | ||||
−0.555046 | + | 0.831819i | \(0.687300\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 18.9282 | 0.616387 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 10.3923 | + | 9.00000i | 0.338062 | + | 0.292770i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 18.7846i | 0.610418i | 0.952285 | + | 0.305209i | \(0.0987263\pi\) | ||||
−0.952285 | + | 0.305209i | \(0.901274\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.00000 | −0.194768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.3205 | 0.950783 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −13.3205 | −0.431494 | −0.215747 | − | 0.976449i | \(-0.569219\pi\) | ||||
−0.215747 | + | 0.976449i | \(0.569219\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.19615 | 0.103425 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 38.3205i | − | 1.23873i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.679492 | − | 0.784610i | 0.0219419 | − | 0.0253364i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 2.53590i | − | 0.0816335i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 31.1769i | − | 1.00258i | −0.865279 | − | 0.501291i | \(-0.832859\pi\) | ||
0.865279 | − | 0.501291i | \(-0.167141\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 4.82309i | 0.154940i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26.7846 | −0.859559 | −0.429780 | − | 0.902934i | \(-0.641409\pi\) | ||||
−0.429780 | + | 0.902934i | \(0.641409\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | − | 13.8564i | 0.384702 | − | 0.444216i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 11.1962i | 0.358564i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.2487 | 1.41564 | 0.707821 | − | 0.706392i | \(-0.249678\pi\) | ||||
0.707821 | + | 0.706392i | \(0.249678\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 35.3205 | 1.12885 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3.58846 | −0.114454 | −0.0572270 | − | 0.998361i | \(-0.518226\pi\) | ||||
−0.0572270 | + | 0.998361i | \(0.518226\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 21.3205i | − | 0.679328i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −5.19615 | + | 6.00000i | −0.165395 | + | 0.190982i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −10.9282 | −0.347497 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 15.1769i | − | 0.482111i | −0.970511 | − | 0.241055i | \(-0.922506\pi\) | ||
0.970511 | − | 0.241055i | \(-0.0774935\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 9.71281i | 0.308227i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 3.46410i | 0.109819i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 12.4641i | − | 0.394742i | −0.980329 | − | 0.197371i | \(-0.936760\pi\) | ||
0.980329 | − | 0.197371i | \(-0.0632404\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.1769 | −0.416899 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))