Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1452,2,Mod(493,1452)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1452, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1452.493");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1452 = 2^{2} \cdot 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1452.i (of order \(5\), degree \(4\), 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: | \(11.5942783735\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 132) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 1213.1 | ||
Root | \(0.809017 + 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1452.1213 |
Dual form | 1452.2.i.d.565.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1452\mathbb{Z}\right)^\times\).
\(n\) | \(485\) | \(727\) | \(1333\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{4}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.309017 | + | 0.951057i | 0.178411 | + | 0.549093i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.61803 | − | 1.17557i | −0.723607 | − | 0.525731i | 0.163928 | − | 0.986472i | \(-0.447584\pi\) |
−0.887535 | + | 0.460741i | \(0.847584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.618034 | − | 1.90211i | 0.233595 | − | 0.718931i | −0.763710 | − | 0.645560i | \(-0.776624\pi\) |
0.997305 | − | 0.0733714i | \(-0.0233759\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.809017 | + | 0.587785i | −0.269672 | + | 0.195928i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.61803 | + | 1.17557i | −0.448762 | + | 0.326045i | −0.789107 | − | 0.614256i | \(-0.789456\pi\) |
0.340345 | + | 0.940301i | \(0.389456\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.618034 | − | 1.90211i | 0.159576 | − | 0.491123i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.23607 | + | 2.35114i | 0.784862 | + | 0.570235i | 0.906434 | − | 0.422347i | \(-0.138794\pi\) |
−0.121572 | + | 0.992583i | \(0.538794\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.85410 | + | 5.70634i | 0.425360 | + | 1.30912i | 0.902649 | + | 0.430377i | \(0.141620\pi\) |
−0.477289 | + | 0.878746i | \(0.658380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | 0.436436 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.309017 | − | 0.951057i | −0.0618034 | − | 0.190211i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.809017 | − | 0.587785i | −0.155695 | − | 0.113119i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.47214 | − | 7.60845i | 0.459064 | − | 1.41285i | −0.407233 | − | 0.913324i | \(-0.633506\pi\) |
0.866297 | − | 0.499530i | \(-0.166494\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.47214 | − | 4.70228i | 1.16243 | − | 0.844555i | 0.172347 | − | 0.985036i | \(-0.444865\pi\) |
0.990083 | + | 0.140482i | \(0.0448651\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.23607 | + | 2.35114i | −0.546995 | + | 0.397415i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.09017 | − | 9.51057i | 0.508021 | − | 1.56353i | −0.287611 | − | 0.957747i | \(-0.592861\pi\) |
0.795632 | − | 0.605780i | \(-0.207139\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.61803 | − | 1.17557i | −0.259093 | − | 0.188242i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.47214 | − | 7.60845i | −0.386083 | − | 1.18824i | −0.935692 | − | 0.352819i | \(-0.885223\pi\) |
0.549609 | − | 0.835422i | \(-0.314777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.00000 | 0.298142 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.47214 | − | 7.60845i | −0.360598 | − | 1.10981i | −0.952692 | − | 0.303938i | \(-0.901699\pi\) |
0.592094 | − | 0.805869i | \(-0.298301\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.42705 | + | 1.76336i | 0.346722 | + | 0.251908i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.23607 | + | 3.80423i | −0.173084 | + | 0.532698i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.61803 | − | 1.17557i | 0.222254 | − | 0.161477i | −0.471087 | − | 0.882087i | \(-0.656138\pi\) |
0.693341 | + | 0.720610i | \(0.256138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.85410 | + | 3.52671i | −0.642942 | + | 0.467124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.70820 | − | 11.4127i | 0.482767 | − | 1.48580i | −0.352422 | − | 0.935841i | \(-0.614642\pi\) |
0.835189 | − | 0.549963i | \(-0.185358\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 8.09017 | + | 5.87785i | 1.03584 | + | 0.752582i | 0.969469 | − | 0.245213i | \(-0.0788579\pi\) |
0.0663709 | + | 0.997795i | \(0.478858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.618034 | + | 1.90211i | 0.0778650 | + | 0.239644i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.00000 | 0.496139 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.0000 | 1.46603 | 0.733017 | − | 0.680211i | \(-0.238112\pi\) | ||||
0.733017 | + | 0.680211i | \(0.238112\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −6.47214 | − | 4.70228i | −0.768101 | − | 0.558058i | 0.133283 | − | 0.991078i | \(-0.457448\pi\) |
−0.901384 | + | 0.433020i | \(0.857448\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.85410 | + | 5.70634i | −0.217006 | + | 0.667876i | 0.781999 | + | 0.623280i | \(0.214200\pi\) |
−0.999005 | + | 0.0445966i | \(0.985800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.809017 | − | 0.587785i | 0.0934172 | − | 0.0678716i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.61803 | + | 1.17557i | −0.182043 | + | 0.132262i | −0.675075 | − | 0.737749i | \(-0.735889\pi\) |
0.493032 | + | 0.870011i | \(0.335889\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.309017 | − | 0.951057i | 0.0343352 | − | 0.105673i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.9443 | + | 9.40456i | 1.42082 | + | 1.03229i | 0.991636 | + | 0.129067i | \(0.0411983\pi\) |
0.429183 | + | 0.903218i | \(0.358802\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.47214 | − | 7.60845i | −0.268141 | − | 0.825253i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 8.00000 | 0.857690 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.0000 | −1.48400 | −0.741999 | − | 0.670402i | \(-0.766122\pi\) | ||||
−0.741999 | + | 0.670402i | \(0.766122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.23607 | + | 3.80423i | 0.129575 | + | 0.398791i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.47214 | + | 4.70228i | 0.671129 | + | 0.487604i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.70820 | − | 11.4127i | 0.380454 | − | 1.17092i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.61803 | − | 1.17557i | 0.164286 | − | 0.119361i | −0.502604 | − | 0.864517i | \(-0.667625\pi\) |
0.666891 | + | 0.745155i | \(0.267625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.9443 | + | 9.40456i | −1.28800 | + | 0.935789i | −0.999763 | − | 0.0217690i | \(-0.993070\pi\) |
−0.288240 | + | 0.957558i | \(0.593070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.23607 | − | 3.80423i | 0.121793 | − | 0.374842i | −0.871510 | − | 0.490378i | \(-0.836859\pi\) |
0.993303 | + | 0.115536i | \(0.0368587\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −3.23607 | − | 2.35114i | −0.315808 | − | 0.229448i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 10.0000 | 0.949158 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.85410 | + | 5.70634i | 0.174419 | + | 0.536807i | 0.999606 | − | 0.0280521i | \(-0.00893043\pi\) |
−0.825187 | + | 0.564859i | \(0.808930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.618034 | − | 1.90211i | 0.0571373 | − | 0.175850i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.47214 | − | 4.70228i | 0.593300 | − | 0.431057i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.47214 | − | 4.70228i | 0.583573 | − | 0.423990i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3.70820 | + | 11.4127i | −0.331672 | + | 1.02078i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.09017 | − | 5.87785i | −0.717886 | − | 0.521575i | 0.167822 | − | 0.985817i | \(-0.446327\pi\) |
−0.885708 | + | 0.464242i | \(0.846327\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.618034 | + | 1.90211i | 0.0544149 | + | 0.167472i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −12.0000 | −1.04844 | −0.524222 | − | 0.851581i | \(-0.675644\pi\) | ||||
−0.524222 | + | 0.851581i | \(0.675644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | 1.04053 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0.618034 | + | 1.90211i | 0.0531919 | + | 0.163708i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.61803 | + | 1.17557i | 0.138238 | + | 0.100436i | 0.654755 | − | 0.755841i | \(-0.272772\pi\) |
−0.516517 | + | 0.856277i | \(0.672772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.85410 | − | 5.70634i | 0.157263 | − | 0.484005i | −0.841120 | − | 0.540848i | \(-0.818103\pi\) |
0.998383 | + | 0.0568428i | \(0.0181034\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.47214 | − | 4.70228i | 0.545052 | − | 0.396004i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.9443 | + | 9.40456i | −1.07496 | + | 0.781007i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.927051 | + | 2.85317i | −0.0764619 | + | 0.235325i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 16.1803 | + | 11.7557i | 1.32555 | + | 0.963065i | 0.999845 | + | 0.0175917i | \(0.00559989\pi\) |
0.325700 | + | 0.945473i | \(0.394400\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.09017 | + | 9.51057i | 0.251474 | + | 0.773959i | 0.994504 | + | 0.104700i | \(0.0333882\pi\) |
−0.743029 | + | 0.669259i | \(0.766612\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −16.0000 | −1.28515 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.85410 | + | 5.70634i | 0.147973 | + | 0.455415i | 0.997381 | − | 0.0723214i | \(-0.0230407\pi\) |
−0.849408 | + | 0.527737i | \(0.823041\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.61803 | + | 1.17557i | 0.128318 | + | 0.0932288i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.9443 | + | 9.40456i | −1.01387 | + | 0.736622i | −0.965018 | − | 0.262184i | \(-0.915557\pi\) |
−0.0488556 | + | 0.998806i | \(0.515557\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.70820 | − | 7.05342i | 0.751243 | − | 0.545810i | −0.144969 | − | 0.989436i | \(-0.546308\pi\) |
0.896212 | + | 0.443626i | \(0.146308\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.78115 | + | 8.55951i | −0.213935 | + | 0.658424i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.85410 | − | 3.52671i | −0.371202 | − | 0.269694i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.00000 | −0.151186 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 12.0000 | 0.901975 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.70820 | − | 11.4127i | −0.277164 | − | 0.853024i | −0.988639 | − | 0.150312i | \(-0.951972\pi\) |
0.711474 | − | 0.702712i | \(-0.248028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.09017 | + | 5.87785i | 0.601338 | + | 0.436897i | 0.846353 | − | 0.532622i | \(-0.178793\pi\) |
−0.245016 | + | 0.969519i | \(0.578793\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.09017 | + | 9.51057i | −0.228432 | + | 0.703041i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −16.1803 | + | 11.7557i | −1.18960 | + | 0.864297i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.61803 | + | 1.17557i | −0.117695 | + | 0.0855102i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.94427 | − | 15.2169i | 0.357755 | − | 1.10106i | −0.596640 | − | 0.802509i | \(-0.703498\pi\) |
0.954395 | − | 0.298547i | \(-0.0965021\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −17.7984 | − | 12.9313i | −1.28115 | − | 0.930814i | −0.281568 | − | 0.959541i | \(-0.590854\pi\) |
−0.999587 | + | 0.0287278i | \(0.990854\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.23607 | + | 3.80423i | 0.0885167 | + | 0.272426i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −24.0000 | −1.70993 | −0.854965 | − | 0.518686i | \(-0.826421\pi\) | ||||
−0.854965 | + | 0.518686i | \(0.826421\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.0000 | −1.13421 | −0.567105 | − | 0.823646i | \(-0.691937\pi\) | ||||
−0.567105 | + | 0.823646i | \(0.691937\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.70820 | + | 11.4127i | 0.261557 | + | 0.804988i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.9443 | − | 9.40456i | −0.908510 | − | 0.660071i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.94427 | + | 15.2169i | −0.345323 | + | 1.06279i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.5623 | − | 10.5801i | 1.00251 | − | 0.728366i | 0.0398855 | − | 0.999204i | \(-0.487301\pi\) |
0.962625 | + | 0.270838i | \(0.0873007\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 2.47214 | − | 7.60845i | 0.169388 | − | 0.521323i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −3.23607 | − | 2.35114i | −0.220698 | − | 0.160346i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.94427 | − | 15.2169i | −0.335639 | − | 1.03299i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −6.00000 | −0.405442 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.00000 | −0.538138 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.23607 | − | 3.80423i | −0.0827732 | − | 0.254750i | 0.901102 | − | 0.433608i | \(-0.142760\pi\) |
−0.983875 | + | 0.178858i | \(0.942760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.809017 | + | 0.587785i | 0.0539345 | + | 0.0391857i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.41641 | − | 22.8254i | 0.492244 | − | 1.51497i | −0.328963 | − | 0.944343i | \(-0.606699\pi\) |
0.821208 | − | 0.570629i | \(-0.193301\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.3262 | − | 8.22899i | 0.748459 | − | 0.543787i | −0.146890 | − | 0.989153i | \(-0.546926\pi\) |
0.895349 | + | 0.445366i | \(0.146926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 19.4164 | − | 14.1068i | 1.27201 | − | 0.924170i | 0.272730 | − | 0.962090i | \(-0.412073\pi\) |
0.999281 | + | 0.0379203i | \(0.0120733\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.94427 | + | 15.2169i | −0.322529 | + | 0.992641i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.61803 | − | 1.17557i | −0.105103 | − | 0.0763615i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.23607 | − | 3.80423i | −0.0799546 | − | 0.246075i | 0.903087 | − | 0.429458i | \(-0.141295\pi\) |
−0.983042 | + | 0.183383i | \(0.941295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.0000 | 1.15948 | 0.579741 | − | 0.814801i | \(-0.303154\pi\) | ||||
0.579741 | + | 0.814801i | \(0.303154\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.85410 | − | 5.70634i | −0.118454 | − | 0.364565i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −9.70820 | − | 7.05342i | −0.617718 | − | 0.448799i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −4.94427 | + | 15.2169i | −0.313331 | + | 0.964332i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.23607 | + | 2.35114i | −0.204259 | + | 0.148403i | −0.685212 | − | 0.728343i | \(-0.740291\pi\) |
0.480953 | + | 0.876746i | \(0.340291\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.47214 | − | 4.70228i | 0.405301 | − | 0.294468i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −9.27051 | + | 28.5317i | −0.578279 | + | 1.77976i | 0.0464552 | + | 0.998920i | \(0.485208\pi\) |
−0.624734 | + | 0.780838i | \(0.714792\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.1803 | − | 11.7557i | −1.00540 | − | 0.730464i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.47214 | + | 7.60845i | 0.153021 | + | 0.470951i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.00000 | 0.246651 | 0.123325 | − | 0.992366i | \(-0.460644\pi\) | ||||
0.123325 | + | 0.992366i | \(0.460644\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4.32624 | − | 13.3148i | −0.264761 | − | 0.814852i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.61803 | + | 1.17557i | 0.0986533 | + | 0.0716758i | 0.636018 | − | 0.771674i | \(-0.280580\pi\) |
−0.537365 | + | 0.843350i | \(0.680580\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.09017 | + | 9.51057i | −0.187714 | + | 0.577726i | −0.999985 | − | 0.00555577i | \(-0.998232\pi\) |
0.812270 | + | 0.583281i | \(0.198232\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.23607 | + | 2.35114i | −0.195856 | + | 0.142298i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.3262 | − | 8.22899i | 0.680528 | − | 0.494432i | −0.193005 | − | 0.981198i | \(-0.561823\pi\) |
0.873533 | + | 0.486765i | \(0.161823\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.47214 | + | 7.60845i | −0.148003 | + | 0.455506i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.47214 | − | 4.70228i | −0.386095 | − | 0.280515i | 0.377758 | − | 0.925904i | \(-0.376695\pi\) |
−0.763854 | + | 0.645390i | \(0.776695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.03444 | + | 24.7275i | 0.477598 | + | 1.46990i | 0.842422 | + | 0.538819i | \(0.181129\pi\) |
−0.364824 | + | 0.931077i | \(0.618871\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.0000 | 0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −16.0000 | −0.944450 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.309017 | − | 0.951057i | −0.0181775 | − | 0.0559445i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.61803 | + | 1.17557i | 0.0948508 | + | 0.0689132i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.18034 | + | 19.0211i | −0.361059 | + | 1.11123i | 0.591353 | + | 0.806413i | \(0.298594\pi\) |
−0.952412 | + | 0.304813i | \(0.901406\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −19.4164 | + | 14.1068i | −1.13047 | + | 0.821332i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.23607 | − | 3.80423i | 0.0712458 | − | 0.219272i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −12.9443 | − | 9.40456i | −0.743629 | − | 0.540278i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.18034 | − | 19.0211i | −0.353885 | − | 1.08915i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.00000 | 0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.94427 | − | 15.2169i | −0.280364 | − | 0.862871i | −0.987750 | − | 0.156044i | \(-0.950126\pi\) |
0.707386 | − | 0.706827i | \(-0.249874\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 14.5623 | + | 10.5801i | 0.823110 | + | 0.598025i | 0.917602 | − | 0.397501i | \(-0.130123\pi\) |
−0.0944915 | + | 0.995526i | \(0.530123\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.23607 | − | 3.80423i | 0.0696445 | − | 0.214344i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 11.3262 | − | 8.22899i | 0.636145 | − | 0.462186i | −0.222379 | − | 0.974960i | \(-0.571382\pi\) |
0.858524 | + | 0.512774i | \(0.171382\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.41641 | + | 22.8254i | −0.412660 | + | 1.27004i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.61803 | + | 1.17557i | 0.0897524 | + | 0.0652089i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.09017 | + | 9.51057i | 0.170887 | + | 0.525935i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0000 | −0.882109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.00000 | 0.439720 | 0.219860 | − | 0.975531i | \(-0.429440\pi\) | ||||
0.219860 | + | 0.975531i | \(0.429440\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.09017 | + | 9.51057i | 0.169340 | + | 0.521176i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −19.4164 | − | 14.1068i | −1.06083 | − | 0.770739i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.32624 | + | 13.3148i | −0.235665 | + | 0.725303i | 0.761367 | + | 0.648321i | \(0.224528\pi\) |
−0.997032 | + | 0.0769821i | \(0.975472\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.85410 | + | 3.52671i | −0.263639 | + | 0.191545i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1803 | − | 11.7557i | 0.873656 | − | 0.634748i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.32624 | + | 13.3148i | 0.231578 | + | 0.712724i | 0.997557 | + | 0.0698585i | \(0.0222548\pi\) |
−0.765979 | + | 0.642866i | \(0.777745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.00000 | 0.106752 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.94427 | + | 15.2169i | 0.262415 | + | 0.807629i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.47214 | + | 4.70228i | 0.342542 | + | 0.248871i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.47214 | − | 7.60845i | 0.130474 | − | 0.401559i | −0.864384 | − | 0.502832i | \(-0.832292\pi\) |
0.994859 | + | 0.101273i | \(0.0322915\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.7533 | + | 9.99235i | −0.723857 | + | 0.525913i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.70820 | − | 7.05342i | 0.508151 | − | 0.369193i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.23607 | + | 3.80423i | −0.0645222 | + | 0.198579i | −0.978121 | − | 0.208039i | \(-0.933292\pi\) |
0.913598 | + | 0.406618i | \(0.133292\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 6.47214 | + | 4.70228i | 0.336926 | + | 0.244791i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.23607 | − | 3.80423i | −0.0641735 | − | 0.197506i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −34.0000 | −1.76045 | −0.880227 | − | 0.474554i | \(-0.842610\pi\) | ||||
−0.880227 | + | 0.474554i | \(0.842610\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −12.0000 | −0.619677 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.94427 | + | 15.2169i | 0.254643 | + | 0.783710i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.9443 | − | 9.40456i | −0.664903 | − | 0.483080i | 0.203412 | − | 0.979093i | \(-0.434797\pi\) |
−0.868315 | + | 0.496013i | \(0.834797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.09017 | − | 9.51057i | 0.158314 | − | 0.487241i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 0 | 0 | −0.587785 | − | 0.809017i | \(-0.700000\pi\) | ||||
0.587785 | + | 0.809017i | \(0.300000\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.61803 | + | 1.17557i | −0.0822493 | + | 0.0597576i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.32624 | + | 13.3148i | −0.219349 | + | 0.675087i | 0.779467 | + | 0.626443i | \(0.215490\pi\) |
−0.998816 | + | 0.0486437i | \(0.984510\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.70820 | − | 11.4127i | −0.187054 | − | 0.575693i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.00000 | 0.201262 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0000 | 0.903394 | 0.451697 | − | 0.892171i | \(-0.350819\pi\) | ||||
0.451697 | + | 0.892171i | \(0.350819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.70820 | + | 11.4127i | 0.185642 | + | 0.571349i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.5623 | + | 10.5801i | 0.727207 | + | 0.528347i | 0.888679 | − | 0.458531i | \(-0.151624\pi\) |
−0.161472 | + | 0.986877i | \(0.551624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.94427 | + | 15.2169i | −0.246292 | + | 0.758008i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.61803 | + | 1.17557i | −0.0804008 | + | 0.0584146i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8.09017 | + | 5.87785i | −0.400033 | + | 0.290641i | −0.769554 | − | 0.638581i | \(-0.779522\pi\) |
0.369521 | + | 0.929222i | \(0.379522\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.618034 | + | 1.90211i | −0.0304854 | + | 0.0938243i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.4164 | − | 14.1068i | −0.955419 | − | 0.694153i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.88854 | − | 30.4338i | −0.485410 | − | 1.49394i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | 0.293821 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −12.0000 | −0.586238 | −0.293119 | − | 0.956076i | \(-0.594693\pi\) | ||||
−0.293119 | + | 0.956076i | \(0.594693\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.85410 | + | 5.70634i | 0.0903634 | + | 0.278110i | 0.986018 | − | 0.166641i | \(-0.0532921\pi\) |
−0.895654 | + | 0.444751i | \(0.853292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.47214 | + | 4.70228i | 0.314686 | + | 0.228633i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.23607 | − | 3.80423i | 0.0599581 | − | 0.184532i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 16.1803 | − | 11.7557i | 0.783022 | − | 0.568898i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.23607 | + | 2.35114i | −0.155876 | + | 0.113250i | −0.662989 | − | 0.748629i | \(-0.730713\pi\) |
0.507113 | + | 0.861879i | \(0.330713\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −5.56231 | + | 17.1190i | −0.267307 | + | 0.822687i | 0.723845 | + | 0.689962i | \(0.242373\pi\) |
−0.991153 | + | 0.132725i | \(0.957627\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.9443 | − | 9.40456i | −0.620630 | − | 0.450914i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −34.0000 | −1.62273 | −0.811366 | − | 0.584539i | \(-0.801275\pi\) | ||||
−0.811366 | + | 0.584539i | \(0.801275\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.70820 | + | 11.4127i | 0.176182 | + | 0.542233i | 0.999685 | − | 0.0250786i | \(-0.00798361\pi\) |
−0.823503 | + | 0.567311i | \(0.807984\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 22.6525 | + | 16.4580i | 1.07383 | + | 0.780183i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6.18034 | + | 19.0211i | −0.292320 | + | 0.899669i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.9787 | + | 24.6870i | −1.60355 | + | 1.16505i | −0.723319 | + | 0.690514i | \(0.757384\pi\) |
−0.880236 | + | 0.474536i | \(0.842616\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −8.09017 | + | 5.87785i | −0.380109 | + | 0.276166i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.47214 | − | 7.60845i | 0.115896 | − | 0.356690i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.7984 | + | 12.9313i | 0.832573 | + | 0.604900i | 0.920286 | − | 0.391246i | \(-0.127956\pi\) |
−0.0877132 | + | 0.996146i | \(0.527956\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.23607 | − | 3.80423i | −0.0576947 | − | 0.177566i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.0000 | −0.558896 | −0.279448 | − | 0.960161i | \(-0.590151\pi\) | ||||
−0.279448 | + | 0.960161i | \(0.590151\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.00000 | 0.185896 | 0.0929479 | − | 0.995671i | \(-0.470371\pi\) | ||||
0.0929479 | + | 0.995671i | \(0.470371\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.94427 | − | 15.2169i | −0.229285 | − | 0.705667i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.1803 | + | 11.7557i | 0.748737 | + | 0.543989i | 0.895435 | − | 0.445192i | \(-0.146865\pi\) |
−0.146698 | + | 0.989181i | \(0.546865\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.41641 | − | 22.8254i | 0.342458 | − | 1.05398i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.85410 | + | 3.52671i | −0.223665 | + | 0.162502i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.85410 | − | 3.52671i | 0.222721 | − | 0.161817i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −0.618034 | + | 1.90211i | −0.0282978 | + | 0.0870918i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.6525 | + | 16.4580i | 1.03502 | + | 0.751985i | 0.969307 | − | 0.245854i | \(-0.0790684\pi\) |
0.0657112 | + | 0.997839i | \(0.479068\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.18034 | + | 19.0211i | 0.281799 | + | 0.867289i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.00000 | −0.181631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.47214 | − | 7.60845i | −0.112023 | − | 0.344772i | 0.879291 | − | 0.476284i | \(-0.158017\pi\) |
−0.991315 | + | 0.131512i | \(0.958017\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −12.9443 | − | 9.40456i | −0.585360 | − | 0.425289i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.8885 | − | 18.8091i | 1.16596 | − | 0.847121i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −12.9443 | + | 9.40456i | −0.580630 | + | 0.421852i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.23607 | − | 3.80423i | 0.0553340 | − | 0.170301i | −0.919570 | − | 0.392926i | \(-0.871463\pi\) |
0.974904 | + | 0.222626i | \(0.0714628\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.70820 | + | 7.05342i | 0.433731 | + | 0.315124i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 6.18034 | + | 19.0211i | 0.275568 | + | 0.848110i | 0.989069 | + | 0.147456i | \(0.0471085\pi\) |
−0.713501 | + | 0.700654i | \(0.752892\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 32.0000 | 1.42398 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −9.00000 | −0.399704 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.618034 | − | 1.90211i | −0.0273939 | − | 0.0843097i | 0.936425 | − | 0.350868i | \(-0.114113\pi\) |
−0.963819 | + | 0.266558i | \(0.914113\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.70820 | + | 7.05342i | 0.429466 | + | 0.312025i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.85410 | − | 5.70634i | 0.0818606 | − | 0.251941i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −6.47214 | + | 4.70228i | −0.285196 | + | 0.207207i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.85410 | − | 5.70634i | 0.0812297 | − | 0.249999i | −0.902191 | − | 0.431336i | \(-0.858042\pi\) |
0.983421 | + | 0.181337i | \(0.0580424\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −27.5066 | − | 19.9847i | −1.20278 | − | 0.873870i | −0.208224 | − | 0.978081i | \(-0.566768\pi\) |
−0.994555 | + | 0.104211i | \(0.966768\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.618034 | − | 1.90211i | −0.0269732 | − | 0.0830150i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 32.0000 | 1.39394 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −23.0000 | −1.00000 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.70820 | + | 11.4127i | 0.160922 | + | 0.495268i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.9443 | + | 9.40456i | 0.560679 | + | 0.407357i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.70820 | − | 7.05342i | 0.418940 | − | 0.304378i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −14.5623 | + | 10.5801i | −0.626082 | + | 0.454876i | −0.855041 | − | 0.518561i | \(-0.826468\pi\) |
0.228958 | + | 0.973436i | \(0.426468\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.09017 | + | 9.51057i | −0.132612 | + | 0.408137i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.1803 | − | 11.7557i | −0.693090 | − | 0.503559i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.618034 | + | 1.90211i | 0.0264252 | + | 0.0813285i | 0.963399 | − | 0.268070i | \(-0.0863859\pi\) |
−0.936974 | + | 0.349399i | \(0.886386\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −10.0000 | −0.426790 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 48.0000 | 2.04487 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.23607 | + | 3.80423i | 0.0525630 | + | 0.161772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −16.1803 | − | 11.7557i | −0.686817 | − | 0.499002i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −6.18034 | + | 19.0211i | −0.261869 | + | 0.805951i | 0.730529 | + | 0.682882i | \(0.239274\pi\) |
−0.992398 | + | 0.123069i | \(0.960726\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.23607 | + | 2.35114i | −0.136871 | + | 0.0994427i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.1246 | + | 21.1603i | −1.22746 | + | 0.891799i | −0.996697 | − | 0.0812119i | \(-0.974121\pi\) |
−0.230759 | + | 0.973011i | \(0.574121\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.70820 | − | 11.4127i | 0.156005 | − | 0.480135i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.61803 | − | 1.17557i | −0.0679510 | − | 0.0493693i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −6.18034 | − | 19.0211i | −0.259093 | − | 0.797407i | −0.992996 | − | 0.118152i | \(-0.962303\pi\) |
0.733902 | − | 0.679255i | \(-0.237697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 10.0000 | 0.418487 | 0.209243 | − | 0.977864i | \(-0.432900\pi\) | ||||
0.209243 | + | 0.977864i | \(0.432900\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −27.5066 | − | 19.9847i | −1.14511 | − | 0.831974i | −0.157290 | − | 0.987552i | \(-0.550276\pi\) |
−0.987824 | + | 0.155579i | \(0.950276\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.79837 | − | 20.9232i | 0.282531 | − | 0.869540i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 25.8885 | − | 18.8091i | 1.07404 | − | 0.780334i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −3.23607 | + | 2.35114i | −0.133795 | + | 0.0972077i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 13.5967 | − | 41.8465i | 0.561198 | − | 1.72719i | −0.117789 | − | 0.993039i | \(-0.537581\pi\) |
0.678987 | − | 0.734151i | \(-0.262419\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38.8328 | + | 28.2137i | 1.60008 | + | 1.16252i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −7.41641 | − | 22.8254i | −0.305070 | − | 0.938910i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 16.0000 | 0.657041 | 0.328521 | − | 0.944497i | \(-0.393450\pi\) | ||||
0.328521 | + | 0.944497i | \(0.393450\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.0000 | −0.655936 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −4.94427 | − | 15.2169i | −0.202356 | − | 0.622786i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.4164 | − | 14.1068i | −0.793333 | − | 0.576390i | 0.115618 | − | 0.993294i | \(-0.463115\pi\) |
−0.908951 | + | 0.416904i | \(0.863115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.27051 | − | 28.5317i | 0.378152 | − | 1.16383i | −0.563175 | − | 0.826337i | \(-0.690420\pi\) |
0.941327 | − | 0.337495i | \(-0.109580\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.70820 | + | 7.05342i | −0.395349 | + | 0.287238i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.3262 | − | 8.22899i | 0.459718 | − | 0.334005i | −0.333703 | − | 0.942678i | \(-0.608298\pi\) |
0.793421 | + | 0.608674i | \(0.208298\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.94427 | − | 15.2169i | 0.200352 | − | 0.616620i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.9443 | + | 9.40456i | 0.523669 | + | 0.380468i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −0.618034 | − | 1.90211i | −0.0249622 | − | 0.0768256i | 0.937799 | − | 0.347178i | \(-0.112860\pi\) |
−0.962762 | + | 0.270352i | \(0.912860\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.0000 | −0.645182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.0000 | −0.402585 | −0.201292 | − | 0.979531i | \(-0.564514\pi\) | ||||
−0.201292 | + | 0.979531i | \(0.564514\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.88854 | − | 30.4338i | −0.397454 | − | 1.22324i | −0.927034 | − | 0.374978i | \(-0.877650\pi\) |
0.529580 | − | 0.848260i | \(-0.322350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −8.65248 | + | 26.6296i | −0.346654 | + | 1.06689i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15.3713 | − | 11.1679i | 0.614853 | − | 0.446717i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 32.3607 | − | 23.5114i | 1.29030 | − | 0.937461i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.5623 | + | 10.5801i | 0.578800 | + | 0.420523i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.18034 | + | 19.0211i | 0.245259 | + | 0.754831i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.00000 | −0.237729 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.00000 | 0.316475 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.85410 | − | 5.70634i | −0.0732326 | − | 0.225387i | 0.907740 | − | 0.419533i | \(-0.137806\pi\) |
−0.980973 | + | 0.194147i | \(0.937806\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.9443 | + | 9.40456i | 0.510472 | + | 0.370880i | 0.813003 | − | 0.582260i | \(-0.197831\pi\) |
−0.302530 | + | 0.953140i | \(0.597831\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.23607 | − | 3.80423i | 0.0486701 | − | 0.149791i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.9443 | − | 9.40456i | 0.508892 | − | 0.369732i | −0.303511 | − | 0.952828i | \(-0.598159\pi\) |
0.812403 | + | 0.583096i | \(0.198159\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.9443 | − | 9.40456i | 0.507326 | − | 0.368594i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.85410 | − | 5.70634i | 0.0725566 | − | 0.223306i | −0.908201 | − | 0.418533i | \(-0.862544\pi\) |
0.980758 | + | 0.195227i | \(0.0625443\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 19.4164 | + | 14.1068i | 0.758662 | + | 0.551200i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.85410 | − | 5.70634i | −0.0723354 | − | 0.222625i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 20.0000 | 0.779089 | 0.389545 | − | 0.921008i | \(-0.372632\pi\) | ||||
0.389545 | + | 0.921008i | \(0.372632\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30.0000 | 1.16686 | 0.583432 | − | 0.812162i | \(-0.301709\pi\) | ||||
0.583432 | + | 0.812162i | \(0.301709\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −2.47214 | − | 7.60845i | −0.0960098 | − | 0.295488i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.4164 | − | 14.1068i | −0.752936 | − | 0.547040i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0 | 0 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.23607 | − | 2.35114i | 0.125114 | − | 0.0909004i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.7984 | + | 12.9313i | −0.686077 | + | 0.498464i | −0.875368 | − | 0.483457i | \(-0.839381\pi\) |
0.189291 | + | 0.981921i | \(0.439381\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.309017 | + | 0.951057i | −0.0118941 | + | 0.0366062i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6.47214 | + | 4.70228i | 0.248744 | + | 0.180723i | 0.705170 | − | 0.709038i | \(-0.250871\pi\) |
−0.456426 | + | 0.889761i | \(0.650871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.23607 | − | 3.80423i | −0.0474359 | − | 0.145993i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 24.0000 | 0.919682 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.0000 | 1.68361 | 0.841807 | − | 0.539779i | \(-0.181492\pi\) | ||||
0.841807 | + | 0.539779i | \(0.181492\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.23607 | − | 3.80423i | −0.0472277 | − | 0.145352i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.3262 | + | 8.22899i | 0.432123 | + | 0.313956i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.23607 | + | 3.80423i | −0.0470904 | + | 0.144929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.47214 | − | 4.70228i | 0.246212 | − | 0.178883i | −0.457835 | − | 0.889037i | \(-0.651375\pi\) |
0.704046 | + | 0.710154i | \(0.251375\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −9.70820 | + | 7.05342i | −0.368253 | + | 0.267552i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.88854 | − | 30.4338i | 0.374555 | − | 1.15276i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 19.4164 | + | 14.1068i | 0.734396 | + | 0.533570i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11.1246 | + | 34.2380i | 0.420171 | + | 1.29315i | 0.907543 | + | 0.419959i | \(0.137955\pi\) |
−0.487372 | + | 0.873194i | \(0.662045\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 60.0000 | 2.26294 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −16.0000 | −0.602595 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.88854 | + | 30.4338i | 0.371897 | + | 1.14458i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −27.5066 | − | 19.9847i | −1.03303 | − | 0.750541i | −0.0641181 | − | 0.997942i | \(-0.520423\pi\) |
−0.968913 | + | 0.247401i | \(0.920423\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.618034 | − | 1.90211i | 0.0231781 | − | 0.0713348i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 0 | 0 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.23607 | − | 2.35114i | 0.120853 | − | 0.0878050i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.3607 | − | 38.0423i | 0.460976 | − | 1.41874i | −0.402999 | − | 0.915201i | \(-0.632032\pi\) |
0.863974 | − | 0.503536i | \(-0.167968\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.47214 | − | 4.70228i | −0.241035 | − | 0.175122i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.56231 | + | 17.1190i | 0.206864 | + | 0.636663i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.00000 | −0.297113 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.309017 | + | 0.951057i | 0.0114451 | + | 0.0352243i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.47214 | + | 4.70228i | 0.239381 | + | 0.173920i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8.03444 | − | 24.7275i | 0.296759 | − | 0.913330i | −0.685866 | − | 0.727728i | \(-0.740576\pi\) |
0.982625 | − | 0.185602i | \(-0.0594236\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.85410 | − | 3.52671i | 0.179046 | − | 0.130085i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.5066 | + | 19.9847i | −1.01185 | + | 0.735149i | −0.964595 | − | 0.263734i | \(-0.915046\pi\) |
−0.0472504 | + | 0.998883i | \(0.515046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.70820 | − | 11.4127i | 0.136224 | − | 0.419255i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −32.3607 | − | 23.5114i | −1.18720 | − | 0.862550i | −0.194233 | − | 0.980955i | \(-0.562222\pi\) |
−0.992965 | + | 0.118405i | \(0.962222\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −12.3607 | − | 38.0423i | −0.452860 | − | 1.39376i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −16.0000 | −0.585409 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.88854 | − | 30.4338i | −0.360838 | − | 1.11055i | −0.952546 | − | 0.304393i | \(-0.901546\pi\) |
0.591708 | − | 0.806152i | \(-0.298454\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.23607 | − | 2.35114i | −0.117929 | − | 0.0856803i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.18034 | − | 19.0211i | 0.224926 | − | 0.692250i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −43.6869 | + | 31.7404i | −1.58783 | + | 1.15362i | −0.680869 | + | 0.732405i | \(0.738398\pi\) |
−0.906959 | + | 0.421220i | \(0.861602\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.1803 | + | 11.7557i | −0.586537 | + | 0.426144i | −0.841075 | − | 0.540919i | \(-0.818077\pi\) |
0.254538 | + | 0.967063i | \(0.418077\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.18034 | − | 19.0211i | 0.223743 | − | 0.688611i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 6.47214 | + | 4.70228i | 0.234001 | + | 0.170011i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.41641 | + | 22.8254i | 0.267791 | + | 0.824176i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −34.0000 | −1.22607 | −0.613036 | − | 0.790055i | \(-0.710052\pi\) | ||||
−0.613036 | + | 0.790055i | \(0.710052\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −30.0000 | −1.08042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −0.618034 | − | 1.90211i | −0.0222291 | − | 0.0684143i | 0.939327 | − | 0.343024i | \(-0.111451\pi\) |
−0.961556 | + | 0.274610i | \(0.911451\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.47214 | − | 4.70228i | −0.232486 | − | 0.168911i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 6.18034 | − | 19.0211i | 0.221718 | − | 0.682379i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 38.8328 | − | 28.2137i | 1.39133 | − | 1.01086i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.47214 | + | 4.70228i | −0.231295 | + | 0.168046i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.70820 | − | 11.4127i | 0.132351 | − | 0.407336i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.3262 | + | 8.22899i | 0.403737 | + | 0.293332i | 0.771061 | − | 0.636761i | \(-0.219726\pi\) |
−0.367325 | + | 0.930093i | \(0.619726\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.23607 | + | 3.80423i | 0.0440052 | + | 0.135434i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.0000 | 0.426671 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −20.0000 | −0.710221 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.23607 | − | 3.80423i | −0.0438388 | − | 0.134922i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.7426 | + | 22.3358i | 1.08896 | + | 0.791176i | 0.979223 | − | 0.202785i | \(-0.0649991\pi\) |
0.109737 | + | 0.993961i | \(0.464999\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.88854 | − | 30.4338i | 0.349832 | − | 1.07667i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 11.3262 | − | 8.22899i | 0.400193 | − | 0.290757i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.618034 | + | 1.90211i | −0.0217558 | + | 0.0669575i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −16.1803 | − | 11.7557i | −0.568870 | − | 0.413309i | 0.265824 | − | 0.964022i | \(-0.414356\pi\) |
−0.834695 | + | 0.550713i | \(0.814356\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −5.56231 | − | 17.1190i | −0.195319 | − | 0.601130i | −0.999973 | − | 0.00738566i | \(-0.997649\pi\) |
0.804654 | − | 0.593744i | \(-0.202351\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −10.0000 | −0.350715 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 32.0000 | 1.12091 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.70820 | + | 11.4127i | 0.129734 | + | 0.399279i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.23607 | − | 2.35114i | −0.113077 | − | 0.0821555i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −4.94427 | + | 15.2169i | −0.172556 | + | 0.531074i | −0.999513 | − | 0.0311913i | \(-0.990070\pi\) |
0.826957 | + | 0.562265i | \(0.190070\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.70820 | − | 7.05342i | 0.338407 | − | 0.245867i | −0.405583 | − | 0.914058i | \(-0.632931\pi\) |
0.743989 | + | 0.668192i | \(0.232931\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.8328 | + | 28.2137i | −1.35035 | + | 0.981086i | −0.351355 | + | 0.936242i | \(0.614279\pi\) |
−0.998994 | + | 0.0448440i | \(0.985721\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.56231 | − | 17.1190i | 0.193187 | − | 0.594568i | −0.806806 | − | 0.590816i | \(-0.798806\pi\) |
0.999993 | − | 0.00375172i | \(-0.00119421\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.3262 | + | 8.22899i | 0.392903 | + | 0.285461i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.70820 | + | 11.4127i | 0.128482 | + | 0.395426i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.0000 | −0.830554 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −8.00000 | −0.276520 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3156 | − | 20.5725i | −0.976400 | − | 0.709396i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.47214 | − | 7.60845i | 0.0851449 | − | 0.262049i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14.5623 | − | 10.5801i | 0.500959 | − | 0.363968i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −21.0344 | + | 15.2824i | −0.721900 | + | 0.524491i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.85410 | − | 3.52671i | −0.166201 | − | 0.120752i | 0.501576 | − | 0.865114i | \(-0.332754\pi\) |
−0.667777 | + | 0.744362i | \(0.732754\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.70820 | + | 11.4127i | 0.126818 | + | 0.390305i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 28.0000 | 0.956462 | 0.478231 | − | 0.878234i | \(-0.341278\pi\) | ||||
0.478231 | + | 0.878234i | \(0.341278\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.00000 | −0.272956 | −0.136478 | − | 0.990643i | \(-0.543578\pi\) | ||||
−0.136478 | + | 0.990643i | \(0.543578\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.94427 | − | 15.2169i | −0.168500 | − | 0.518591i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.8328 | + | 28.2137i | 1.32188 | + | 0.960405i | 0.999907 | + | 0.0136580i | \(0.00434761\pi\) |
0.321978 | + | 0.946747i | \(0.395652\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0.809017 | − | 0.587785i | 0.0274757 | − | 0.0199622i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.4164 | + | 14.1068i | −0.657900 | + | 0.477992i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −0.618034 | + | 1.90211i | −0.0209173 | + | 0.0643768i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 19.4164 | + | 14.1068i | 0.656394 | + | 0.476898i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.7426 | + | 36.1401i | 0.396521 | + | 1.22037i | 0.927771 | + | 0.373151i | \(0.121723\pi\) |
−0.531250 | + | 0.847215i | \(0.678277\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −20.0000 | −0.674583 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46.0000 | 1.54978 | 0.774890 | − | 0.632096i | \(-0.217805\pi\) | ||||
0.774890 | + | 0.632096i | \(0.217805\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.5967 | + | 41.8465i | 0.457567 | + | 1.40825i | 0.868095 | + | 0.496398i | \(0.165344\pi\) |
−0.410528 | + | 0.911848i | \(0.634656\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −19.4164 | − | 14.1068i | −0.652675 | − | 0.474196i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 14.8328 | − | 45.6507i | 0.498037 | − | 1.53280i | −0.314132 | − | 0.949379i | \(-0.601714\pi\) |
0.812169 | − | 0.583422i | \(-0.198286\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.1803 | + | 11.7557i | −0.542671 | + | 0.394274i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 38.8328 | − | 28.2137i | 1.29949 | − | 0.944135i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.41641 | + | 22.8254i | −0.247903 | + | 0.762968i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −19.7771 | − | 60.8676i | −0.659603 | − | 2.03005i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.00000 | 0.266519 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.00000 | 0.133112 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.18034 | − | 19.0211i | −0.205441 | − | 0.632284i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.94427 | − | 15.2169i | 0.163991 | − | 0.504713i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.47214 | + | 4.70228i | −0.214431 | + | 0.155794i | −0.689816 | − | 0.723984i | \(-0.742309\pi\) |
0.475385 | + | 0.879778i | \(0.342309\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 16.1803 | − | 11.7557i | 0.534906 | − | 0.388632i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.41641 | + | 22.8254i | −0.244911 | + | 0.753760i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.4508 | + | 29.3893i | 1.33435 | + | 0.969462i | 0.999632 | + | 0.0271443i | \(0.00864136\pi\) |
0.334719 | + | 0.942318i | \(0.391359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.618034 | − | 1.90211i | −0.0203649 | − | 0.0626768i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.0000 | 0.526646 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0000 | −0.328798 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1.23607 | + | 3.80423i | 0.0405978 | + | 0.124947i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.85410 | − | 3.52671i | −0.159258 | − | 0.115708i | 0.505302 | − | 0.862942i | \(-0.331381\pi\) |
−0.664560 | + | 0.747235i | \(0.731381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −5.56231 | + | 17.1190i | −0.182297 | + | 0.561053i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12.9443 | − | 9.40456i | 0.423776 | − | 0.307892i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.7426 | + | 22.3358i | −1.00432 | + | 0.729680i | −0.963010 | − | 0.269466i | \(-0.913153\pi\) |
−0.0413087 | + | 0.999146i | \(0.513153\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5.56231 | + | 17.1190i | −0.181519 | + | 0.558658i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −19.4164 | − | 14.1068i | −0.632957 | − | 0.459870i | 0.224467 | − | 0.974482i | \(-0.427936\pi\) |
−0.857423 | + | 0.514612i | \(0.827936\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0 | 0 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.00000 | 0.130120 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 52.0000 | 1.68977 | 0.844886 | − | 0.534946i | \(-0.179668\pi\) | ||||
0.844886 | + | 0.534946i | \(0.179668\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.70820 | − | 11.4127i | −0.120373 | − | 0.370471i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 11.3262 | + | 8.22899i | 0.367278 | + | 0.266843i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11.1246 | + | 34.2380i | −0.360362 | + | 1.10908i | 0.592473 | + | 0.805590i | \(0.298151\pi\) |
−0.952835 | + | 0.303489i | \(0.901849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −25.8885 | + | 18.8091i | −0.837734 | + | 0.608649i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.23607 | − | 2.35114i | 0.104498 | − | 0.0759223i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.1976 | − | 31.3849i | 0.328954 | − | 1.01242i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.5967 | + | 41.8465i | 0.437695 | + | 1.34709i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14.0000 | −0.450210 | −0.225105 | − | 0.974335i | \(-0.572272\pi\) | ||||
−0.225105 | + | 0.974335i | \(0.572272\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −24.0000 | −0.770991 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.18034 | + | 19.0211i | 0.198337 | + | 0.610417i | 0.999921 | + | 0.0125361i | \(0.00399048\pi\) |
−0.801585 | + | 0.597881i | \(0.796010\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −9.70820 | − | 7.05342i | −0.311231 | − | 0.226122i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −0.618034 | + | 1.90211i | −0.0197929 | + | 0.0609164i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −30.7426 | + | 22.3358i | −0.983544 | + | 0.714587i | −0.958498 | − | 0.285099i | \(-0.907973\pi\) |
−0.0250464 | + | 0.999686i | \(0.507973\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.09017 | + | 5.87785i | −0.258299 | + | 0.187665i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 2.47214 | − | 7.60845i | 0.0788489 | − | 0.242672i | −0.903860 | − | 0.427828i | \(-0.859279\pi\) |
0.982709 | + | 0.185156i | \(0.0592790\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 38.8328 | + | 28.2137i | 1.23732 | + | 0.898963i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −4.94427 | − | 15.2169i | −0.157378 | − | 0.484359i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −56.0000 | −1.77890 | −0.889449 | − | 0.457034i | \(-0.848912\pi\) | ||||
−0.889449 | + | 0.457034i | \(0.848912\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.47214 | + | 7.60845i | 0.0784509 | + | 0.241447i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.8885 | + | 18.8091i | 0.820722 | + | 0.596289i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.618034 | + | 1.90211i | −0.0195733 | + | 0.0602405i | −0.960366 | − | 0.278742i | \(-0.910083\pi\) |
0.940793 | + | 0.338982i | \(0.110083\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.09017 | + | 5.87785i | −0.255962 | + | 0.185967i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))