Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(883,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.883");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.f (of order \(3\), degree \(2\), 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 883.1 | ||
Root | \(-1.22474 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.883 |
Dual form | 2646.2.f.k.1765.1 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.72474 | − | 2.98735i | −0.771329 | − | 1.33598i | −0.936835 | − | 0.349773i | \(-0.886259\pi\) |
0.165505 | − | 0.986209i | \(-0.447075\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.44949 | −1.09082 | ||||||||
\(11\) | 1.00000 | − | 1.73205i | 0.301511 | − | 0.522233i | −0.674967 | − | 0.737848i | \(-0.735842\pi\) |
0.976478 | + | 0.215615i | \(0.0691756\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.44949 | − | 4.24264i | −0.679366 | − | 1.17670i | −0.975172 | − | 0.221449i | \(-0.928921\pi\) |
0.295806 | − | 0.955248i | \(-0.404412\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.44949 | −1.70903 | −0.854515 | − | 0.519427i | \(-0.826146\pi\) | ||||
−0.854515 | + | 0.519427i | \(0.826146\pi\) | |||||||
\(20\) | −1.72474 | + | 2.98735i | −0.385665 | + | 0.667991i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | − | 1.73205i | −0.213201 | − | 0.369274i | ||||
\(23\) | −0.500000 | − | 0.866025i | −0.104257 | − | 0.180579i | 0.809177 | − | 0.587565i | \(-0.199913\pi\) |
−0.913434 | + | 0.406986i | \(0.866580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.44949 | + | 5.97469i | −0.689898 | + | 1.19494i | ||||
\(26\) | −4.89898 | −0.960769 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.44949 | − | 2.51059i | 0.269163 | − | 0.466205i | −0.699483 | − | 0.714650i | \(-0.746586\pi\) |
0.968646 | + | 0.248445i | \(0.0799195\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | + | 5.19615i | 0.538816 | + | 0.933257i | 0.998968 | + | 0.0454165i | \(0.0144615\pi\) |
−0.460152 | + | 0.887840i | \(0.652205\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.00000 | − | 1.73205i | 0.171499 | − | 0.297044i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.79796 | −1.28198 | −0.640988 | − | 0.767551i | \(-0.721475\pi\) | ||||
−0.640988 | + | 0.767551i | \(0.721475\pi\) | |||||||
\(38\) | −3.72474 | + | 6.45145i | −0.604233 | + | 1.04656i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.72474 | + | 2.98735i | 0.272706 | + | 0.472341i | ||||
\(41\) | 4.89898 | + | 8.48528i | 0.765092 | + | 1.32518i | 0.940198 | + | 0.340629i | \(0.110640\pi\) |
−0.175106 | + | 0.984550i | \(0.556027\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.44949 | − | 2.51059i | 0.221045 | − | 0.382861i | −0.734080 | − | 0.679062i | \(-0.762387\pi\) |
0.955126 | + | 0.296201i | \(0.0957199\pi\) | |||||||
\(44\) | −2.00000 | −0.301511 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | 4.89898 | − | 8.48528i | 0.714590 | − | 1.23771i | −0.248528 | − | 0.968625i | \(-0.579947\pi\) |
0.963118 | − | 0.269081i | \(-0.0867199\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.44949 | + | 5.97469i | 0.487832 | + | 0.844949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.44949 | + | 4.24264i | −0.339683 | + | 0.588348i | ||||
\(53\) | 1.10102 | 0.151237 | 0.0756184 | − | 0.997137i | \(-0.475907\pi\) | ||||
0.0756184 | + | 0.997137i | \(0.475907\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.89898 | −0.930258 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.44949 | − | 2.51059i | −0.190327 | − | 0.329657i | ||||
\(59\) | 1.00000 | + | 1.73205i | 0.130189 | + | 0.225494i | 0.923749 | − | 0.382998i | \(-0.125108\pi\) |
−0.793560 | + | 0.608492i | \(0.791775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.72474 | − | 9.91555i | 0.732978 | − | 1.26956i | −0.222626 | − | 0.974904i | \(-0.571463\pi\) |
0.955605 | − | 0.294652i | \(-0.0952037\pi\) | |||||||
\(62\) | 6.00000 | 0.762001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −8.44949 | + | 14.6349i | −1.04803 | + | 1.81524i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.55051 | + | 2.68556i | 0.189425 | + | 0.328094i | 0.945059 | − | 0.326901i | \(-0.106004\pi\) |
−0.755634 | + | 0.654994i | \(0.772671\pi\) | |||||||
\(68\) | −1.00000 | − | 1.73205i | −0.121268 | − | 0.210042i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.89898 | −1.17479 | −0.587396 | − | 0.809299i | \(-0.699847\pi\) | ||||
−0.587396 | + | 0.809299i | \(0.699847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.89898 | −0.339300 | −0.169650 | − | 0.985504i | \(-0.554264\pi\) | ||||
−0.169650 | + | 0.985504i | \(0.554264\pi\) | |||||||
\(74\) | −3.89898 | + | 6.75323i | −0.453247 | + | 0.785047i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.72474 | + | 6.45145i | 0.427258 | + | 0.740032i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.94949 | + | 6.84072i | −0.444352 | + | 0.769641i | −0.998007 | − | 0.0631057i | \(-0.979899\pi\) |
0.553655 | + | 0.832746i | \(0.313233\pi\) | |||||||
\(80\) | 3.44949 | 0.385665 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 9.79796 | 1.08200 | ||||||||
\(83\) | −1.00000 | + | 1.73205i | −0.109764 | + | 0.190117i | −0.915675 | − | 0.401920i | \(-0.868343\pi\) |
0.805910 | + | 0.592037i | \(0.201676\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.44949 | − | 5.97469i | −0.374150 | − | 0.648046i | ||||
\(86\) | −1.44949 | − | 2.51059i | −0.156302 | − | 0.270724i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.00000 | + | 1.73205i | −0.106600 | + | 0.184637i | ||||
\(89\) | −7.10102 | −0.752707 | −0.376353 | − | 0.926476i | \(-0.622822\pi\) | ||||
−0.376353 | + | 0.926476i | \(0.622822\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.500000 | + | 0.866025i | −0.0521286 | + | 0.0902894i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.89898 | − | 8.48528i | −0.505291 | − | 0.875190i | ||||
\(95\) | 12.8485 | + | 22.2542i | 1.31823 | + | 2.28323i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.44949 | + | 5.97469i | −0.350243 | + | 0.606638i | −0.986292 | − | 0.165011i | \(-0.947234\pi\) |
0.636049 | + | 0.771649i | \(0.280568\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.89898 | 0.689898 | ||||||||
\(101\) | −3.62372 | + | 6.27647i | −0.360574 | + | 0.624533i | −0.988055 | − | 0.154099i | \(-0.950753\pi\) |
0.627481 | + | 0.778632i | \(0.284086\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | 2.44949 | + | 4.24264i | 0.240192 | + | 0.416025i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.550510 | − | 0.953512i | 0.0534703 | − | 0.0926132i | ||||
\(107\) | 12.0000 | 1.16008 | 0.580042 | − | 0.814587i | \(-0.303036\pi\) | ||||
0.580042 | + | 0.814587i | \(0.303036\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −16.6969 | −1.59928 | −0.799638 | − | 0.600482i | \(-0.794975\pi\) | ||||
−0.799638 | + | 0.600482i | \(0.794975\pi\) | |||||||
\(110\) | −3.44949 | + | 5.97469i | −0.328896 | + | 0.569664i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −7.94949 | − | 13.7689i | −0.747825 | − | 1.29527i | −0.948863 | − | 0.315688i | \(-0.897765\pi\) |
0.201038 | − | 0.979583i | \(-0.435569\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.72474 | + | 2.98735i | −0.160833 | + | 0.278571i | ||||
\(116\) | −2.89898 | −0.269163 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000 | 0.184115 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | −5.72474 | − | 9.91555i | −0.518294 | − | 0.897712i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 3.00000 | − | 5.19615i | 0.269408 | − | 0.466628i | ||||
\(125\) | 6.55051 | 0.585895 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.00000 | −0.266207 | −0.133103 | − | 0.991102i | \(-0.542494\pi\) | ||||
−0.133103 | + | 0.991102i | \(0.542494\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 8.44949 | + | 14.6349i | 0.741069 | + | 1.28357i | ||||
\(131\) | 6.72474 | + | 11.6476i | 0.587544 | + | 1.01766i | 0.994553 | + | 0.104232i | \(0.0332383\pi\) |
−0.407009 | + | 0.913424i | \(0.633428\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.10102 | 0.267887 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.00000 | −0.171499 | ||||||||
\(137\) | −5.89898 | + | 10.2173i | −0.503984 | + | 0.872926i | 0.496006 | + | 0.868319i | \(0.334800\pi\) |
−0.999989 | + | 0.00460626i | \(0.998534\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.72474 | + | 8.18350i | 0.400748 | + | 0.694115i | 0.993816 | − | 0.111037i | \(-0.0354171\pi\) |
−0.593069 | + | 0.805152i | \(0.702084\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −4.94949 | + | 8.57277i | −0.415352 | + | 0.719411i | ||||
\(143\) | −9.79796 | −0.819346 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.0000 | −0.830455 | ||||||||
\(146\) | −1.44949 | + | 2.51059i | −0.119961 | + | 0.207778i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.89898 | + | 6.75323i | 0.320494 | + | 0.555112i | ||||
\(149\) | −3.00000 | − | 5.19615i | −0.245770 | − | 0.425685i | 0.716578 | − | 0.697507i | \(-0.245707\pi\) |
−0.962348 | + | 0.271821i | \(0.912374\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.50000 | − | 4.33013i | 0.203447 | − | 0.352381i | −0.746190 | − | 0.665733i | \(-0.768119\pi\) |
0.949637 | + | 0.313353i | \(0.101452\pi\) | |||||||
\(152\) | 7.44949 | 0.604233 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.3485 | − | 17.9241i | 0.831209 | − | 1.43970i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.17423 | + | 5.49794i | 0.253332 | + | 0.438783i | 0.964441 | − | 0.264298i | \(-0.0851403\pi\) |
−0.711109 | + | 0.703081i | \(0.751807\pi\) | |||||||
\(158\) | 3.94949 | + | 6.84072i | 0.314205 | + | 0.544218i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.72474 | − | 2.98735i | 0.136353 | − | 0.236170i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.202041 | −0.0158251 | −0.00791254 | − | 0.999969i | \(-0.502519\pi\) | ||||
−0.00791254 | + | 0.999969i | \(0.502519\pi\) | |||||||
\(164\) | 4.89898 | − | 8.48528i | 0.382546 | − | 0.662589i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.00000 | + | 1.73205i | 0.0776151 | + | 0.134433i | ||||
\(167\) | −9.34847 | − | 16.1920i | −0.723406 | − | 1.25298i | −0.959627 | − | 0.281277i | \(-0.909242\pi\) |
0.236220 | − | 0.971700i | \(-0.424091\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.50000 | + | 9.52628i | −0.423077 | + | 0.732791i | ||||
\(170\) | −6.89898 | −0.529128 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.89898 | −0.221045 | ||||||||
\(173\) | 6.44949 | − | 11.1708i | 0.490346 | − | 0.849304i | −0.509593 | − | 0.860416i | \(-0.670204\pi\) |
0.999938 | + | 0.0111123i | \(0.00353722\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | + | 1.73205i | 0.0753778 | + | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.55051 | + | 6.14966i | −0.266122 | + | 0.460937i | ||||
\(179\) | 8.69694 | 0.650040 | 0.325020 | − | 0.945707i | \(-0.394629\pi\) | ||||
0.325020 | + | 0.945707i | \(0.394629\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.34847 | −0.323219 | −0.161610 | − | 0.986855i | \(-0.551669\pi\) | ||||
−0.161610 | + | 0.986855i | \(0.551669\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0.500000 | + | 0.866025i | 0.0368605 | + | 0.0638442i | ||||
\(185\) | 13.4495 | + | 23.2952i | 0.988826 | + | 1.71270i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.00000 | − | 3.46410i | 0.146254 | − | 0.253320i | ||||
\(188\) | −9.79796 | −0.714590 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 25.6969 | 1.86425 | ||||||||
\(191\) | 6.94949 | − | 12.0369i | 0.502847 | − | 0.870957i | −0.497147 | − | 0.867666i | \(-0.665619\pi\) |
0.999995 | − | 0.00329106i | \(-0.00104758\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.05051 | + | 7.01569i | 0.291562 | + | 0.505000i | 0.974179 | − | 0.225776i | \(-0.0724917\pi\) |
−0.682617 | + | 0.730776i | \(0.739158\pi\) | |||||||
\(194\) | 3.44949 | + | 5.97469i | 0.247659 | + | 0.428958i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6969 | 0.904619 | 0.452310 | − | 0.891861i | \(-0.350600\pi\) | ||||
0.452310 | + | 0.891861i | \(0.350600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.89898 | −0.489056 | −0.244528 | − | 0.969642i | \(-0.578633\pi\) | ||||
−0.244528 | + | 0.969642i | \(0.578633\pi\) | |||||||
\(200\) | 3.44949 | − | 5.97469i | 0.243916 | − | 0.422474i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.62372 | + | 6.27647i | 0.254964 | + | 0.441611i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.8990 | − | 29.2699i | 1.18028 | − | 2.04430i | ||||
\(206\) | 14.0000 | 0.975426 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.89898 | 0.339683 | ||||||||
\(209\) | −7.44949 | + | 12.9029i | −0.515292 | + | 0.892512i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.55051 | − | 2.68556i | −0.106742 | − | 0.184882i | 0.807707 | − | 0.589584i | \(-0.200708\pi\) |
−0.914448 | + | 0.404703i | \(0.867375\pi\) | |||||||
\(212\) | −0.550510 | − | 0.953512i | −0.0378092 | − | 0.0654875i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 6.00000 | − | 10.3923i | 0.410152 | − | 0.710403i | ||||
\(215\) | −10.0000 | −0.681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −8.34847 | + | 14.4600i | −0.565430 | + | 0.979353i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.44949 | + | 5.97469i | 0.232565 | + | 0.402814i | ||||
\(221\) | −4.89898 | − | 8.48528i | −0.329541 | − | 0.570782i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.4495 | + | 18.0990i | −0.699750 | + | 1.21200i | 0.268804 | + | 0.963195i | \(0.413372\pi\) |
−0.968553 | + | 0.248807i | \(0.919962\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −15.8990 | −1.05758 | ||||||||
\(227\) | 0.275255 | − | 0.476756i | 0.0182693 | − | 0.0316434i | −0.856746 | − | 0.515738i | \(-0.827518\pi\) |
0.875016 | + | 0.484095i | \(0.160851\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.6237 | − | 20.1329i | −0.768117 | − | 1.33042i | −0.938583 | − | 0.345055i | \(-0.887860\pi\) |
0.170465 | − | 0.985364i | \(-0.445473\pi\) | |||||||
\(230\) | 1.72474 | + | 2.98735i | 0.113726 | + | 0.196980i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.44949 | + | 2.51059i | −0.0951637 | + | 0.164828i | ||||
\(233\) | 7.00000 | 0.458585 | 0.229293 | − | 0.973358i | \(-0.426359\pi\) | ||||
0.229293 | + | 0.973358i | \(0.426359\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −33.7980 | −2.20474 | ||||||||
\(236\) | 1.00000 | − | 1.73205i | 0.0650945 | − | 0.112747i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.39898 | − | 11.0834i | −0.413916 | − | 0.716923i | 0.581398 | − | 0.813619i | \(-0.302506\pi\) |
−0.995314 | + | 0.0966962i | \(0.969172\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.44949 | + | 7.70674i | −0.286617 | + | 0.496435i | −0.973000 | − | 0.230805i | \(-0.925864\pi\) |
0.686383 | + | 0.727240i | \(0.259197\pi\) | |||||||
\(242\) | 7.00000 | 0.449977 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.4495 | −0.732978 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.2474 | + | 31.6055i | 1.16106 | + | 2.01101i | ||||
\(248\) | −3.00000 | − | 5.19615i | −0.190500 | − | 0.329956i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 3.27526 | − | 5.67291i | 0.207145 | − | 0.358786i | ||||
\(251\) | 12.5505 | 0.792181 | 0.396091 | − | 0.918211i | \(-0.370367\pi\) | ||||
0.396091 | + | 0.918211i | \(0.370367\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.00000 | −0.125739 | ||||||||
\(254\) | −1.50000 | + | 2.59808i | −0.0941184 | + | 0.163018i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −13.8990 | − | 24.0737i | −0.866995 | − | 1.50168i | −0.865053 | − | 0.501680i | \(-0.832715\pi\) |
−0.00194150 | − | 0.999998i | \(-0.500618\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.8990 | 1.04803 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 13.4495 | 0.830912 | ||||||||
\(263\) | 8.05051 | − | 13.9439i | 0.496416 | − | 0.859817i | −0.503576 | − | 0.863951i | \(-0.667983\pi\) |
0.999991 | + | 0.00413383i | \(0.00131584\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.89898 | − | 3.28913i | −0.116653 | − | 0.202050i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.55051 | − | 2.68556i | 0.0947125 | − | 0.164047i | ||||
\(269\) | −3.65153 | −0.222638 | −0.111319 | − | 0.993785i | \(-0.535507\pi\) | ||||
−0.111319 | + | 0.993785i | \(0.535507\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −16.8990 | −1.02654 | −0.513270 | − | 0.858227i | \(-0.671566\pi\) | ||||
−0.513270 | + | 0.858227i | \(0.671566\pi\) | |||||||
\(272\) | −1.00000 | + | 1.73205i | −0.0606339 | + | 0.105021i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.89898 | + | 10.2173i | 0.356370 | + | 0.617252i | ||||
\(275\) | 6.89898 | + | 11.9494i | 0.416024 | + | 0.720575i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.34847 | + | 9.26382i | −0.321358 | + | 0.556609i | −0.980769 | − | 0.195174i | \(-0.937473\pi\) |
0.659410 | + | 0.751783i | \(0.270806\pi\) | |||||||
\(278\) | 9.44949 | 0.566743 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −9.50000 | + | 16.4545i | −0.566722 | + | 0.981592i | 0.430165 | + | 0.902750i | \(0.358455\pi\) |
−0.996887 | + | 0.0788417i | \(0.974878\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.2753 | − | 17.7973i | −0.610801 | − | 1.05794i | −0.991106 | − | 0.133077i | \(-0.957514\pi\) |
0.380305 | − | 0.924861i | \(-0.375819\pi\) | |||||||
\(284\) | 4.94949 | + | 8.57277i | 0.293698 | + | 0.508700i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.89898 | + | 8.48528i | −0.289683 | + | 0.501745i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | −5.00000 | + | 8.66025i | −0.293610 | + | 0.508548i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.44949 | + | 2.51059i | 0.0848250 | + | 0.146921i | ||||
\(293\) | −13.6237 | − | 23.5970i | −0.795906 | − | 1.37855i | −0.922262 | − | 0.386565i | \(-0.873661\pi\) |
0.126356 | − | 0.991985i | \(-0.459672\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.44949 | − | 5.97469i | 0.200837 | − | 0.347860i | ||||
\(296\) | 7.79796 | 0.453247 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −6.00000 | −0.347571 | ||||||||
\(299\) | −2.44949 | + | 4.24264i | −0.141658 | + | 0.245358i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −2.50000 | − | 4.33013i | −0.143859 | − | 0.249171i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.72474 | − | 6.45145i | 0.213629 | − | 0.370016i | ||||
\(305\) | −39.4949 | −2.26147 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.752551 | −0.0429504 | −0.0214752 | − | 0.999769i | \(-0.506836\pi\) | ||||
−0.0214752 | + | 0.999769i | \(0.506836\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −10.3485 | − | 17.9241i | −0.587754 | − | 1.01802i | ||||
\(311\) | −0.651531 | − | 1.12848i | −0.0369449 | − | 0.0639905i | 0.846962 | − | 0.531654i | \(-0.178429\pi\) |
−0.883907 | + | 0.467663i | \(0.845096\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3485 | − | 21.3882i | 0.697977 | − | 1.20893i | −0.271190 | − | 0.962526i | \(-0.587417\pi\) |
0.969167 | − | 0.246405i | \(-0.0792495\pi\) | |||||||
\(314\) | 6.34847 | 0.358265 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.89898 | 0.444352 | ||||||||
\(317\) | −4.34847 | + | 7.53177i | −0.244234 | + | 0.423026i | −0.961916 | − | 0.273345i | \(-0.911870\pi\) |
0.717682 | + | 0.696371i | \(0.245203\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.89898 | − | 5.02118i | −0.162312 | − | 0.281132i | ||||
\(320\) | −1.72474 | − | 2.98735i | −0.0964162 | − | 0.166998i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.8990 | −0.829001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 33.7980 | 1.87477 | ||||||||
\(326\) | −0.101021 | + | 0.174973i | −0.00559501 | + | 0.00969084i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.89898 | − | 8.48528i | −0.270501 | − | 0.468521i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.3485 | − | 21.3882i | 0.678733 | − | 1.17560i | −0.296629 | − | 0.954993i | \(-0.595863\pi\) |
0.975363 | − | 0.220608i | \(-0.0708041\pi\) | |||||||
\(332\) | 2.00000 | 0.109764 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −18.6969 | −1.02305 | ||||||||
\(335\) | 5.34847 | − | 9.26382i | 0.292218 | − | 0.506137i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −17.6969 | − | 30.6520i | −0.964014 | − | 1.66972i | −0.712242 | − | 0.701934i | \(-0.752320\pi\) |
−0.251772 | − | 0.967787i | \(-0.581013\pi\) | |||||||
\(338\) | 5.50000 | + | 9.52628i | 0.299161 | + | 0.518161i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −3.44949 | + | 5.97469i | −0.187075 | + | 0.324023i | ||||
\(341\) | 12.0000 | 0.649836 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −1.44949 | + | 2.51059i | −0.0781512 | + | 0.135362i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.44949 | − | 11.1708i | −0.346727 | − | 0.600548i | ||||
\(347\) | −9.79796 | − | 16.9706i | −0.525982 | − | 0.911028i | −0.999542 | − | 0.0302659i | \(-0.990365\pi\) |
0.473560 | − | 0.880762i | \(-0.342969\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.4495 | − | 18.0990i | 0.559348 | − | 0.968820i | −0.438203 | − | 0.898876i | \(-0.644385\pi\) |
0.997551 | − | 0.0699435i | \(-0.0222819\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.00000 | 0.106600 | ||||||||
\(353\) | 3.00000 | − | 5.19615i | 0.159674 | − | 0.276563i | −0.775077 | − | 0.631867i | \(-0.782289\pi\) |
0.934751 | + | 0.355303i | \(0.115622\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.0732 | + | 29.5717i | 0.906152 | + | 1.56950i | ||||
\(356\) | 3.55051 | + | 6.14966i | 0.188177 | + | 0.325932i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.34847 | − | 7.53177i | 0.229824 | − | 0.398066i | ||||
\(359\) | −10.7980 | −0.569894 | −0.284947 | − | 0.958543i | \(-0.591976\pi\) | ||||
−0.284947 | + | 0.958543i | \(0.591976\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 36.4949 | 1.92078 | ||||||||
\(362\) | −2.17423 | + | 3.76588i | −0.114275 | + | 0.197931i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.00000 | + | 8.66025i | 0.261712 | + | 0.453298i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.89898 | − | 5.02118i | 0.151325 | − | 0.262103i | −0.780389 | − | 0.625294i | \(-0.784979\pi\) |
0.931715 | + | 0.363190i | \(0.118313\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.8990 | 1.39841 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.44949 | − | 2.51059i | −0.0750517 | − | 0.129993i | 0.826057 | − | 0.563587i | \(-0.190579\pi\) |
−0.901109 | + | 0.433593i | \(0.857246\pi\) | |||||||
\(374\) | −2.00000 | − | 3.46410i | −0.103418 | − | 0.179124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.89898 | + | 8.48528i | −0.252646 | + | 0.437595i | ||||
\(377\) | −14.2020 | −0.731442 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.4949 | −1.36095 | −0.680476 | − | 0.732771i | \(-0.738227\pi\) | ||||
−0.680476 | + | 0.732771i | \(0.738227\pi\) | |||||||
\(380\) | 12.8485 | − | 22.2542i | 0.659113 | − | 1.14162i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.94949 | − | 12.0369i | −0.355567 | − | 0.615860i | ||||
\(383\) | −3.44949 | − | 5.97469i | −0.176261 | − | 0.305292i | 0.764336 | − | 0.644818i | \(-0.223067\pi\) |
−0.940597 | + | 0.339526i | \(0.889734\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.10102 | 0.412331 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.89898 | 0.350243 | ||||||||
\(389\) | −7.55051 | + | 13.0779i | −0.382826 | + | 0.663074i | −0.991465 | − | 0.130373i | \(-0.958382\pi\) |
0.608639 | + | 0.793447i | \(0.291716\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.00000 | − | 1.73205i | −0.0505722 | − | 0.0875936i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 6.34847 | − | 10.9959i | 0.319831 | − | 0.553964i | ||||
\(395\) | 27.2474 | 1.37097 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.30306 | −0.466907 | −0.233454 | − | 0.972368i | \(-0.575003\pi\) | ||||
−0.233454 | + | 0.972368i | \(0.575003\pi\) | |||||||
\(398\) | −3.44949 | + | 5.97469i | −0.172907 | + | 0.299484i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.44949 | − | 5.97469i | −0.172474 | − | 0.298735i | ||||
\(401\) | −5.05051 | − | 8.74774i | −0.252210 | − | 0.436841i | 0.711924 | − | 0.702257i | \(-0.247824\pi\) |
−0.964134 | + | 0.265416i | \(0.914491\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.6969 | − | 25.4558i | 0.732107 | − | 1.26805i | ||||
\(404\) | 7.24745 | 0.360574 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −7.79796 | + | 13.5065i | −0.386530 | + | 0.669490i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.89898 | + | 5.02118i | 0.143345 | + | 0.248281i | 0.928754 | − | 0.370696i | \(-0.120881\pi\) |
−0.785409 | + | 0.618977i | \(0.787547\pi\) | |||||||
\(410\) | −16.8990 | − | 29.2699i | −0.834581 | − | 1.44554i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.00000 | − | 12.1244i | 0.344865 | − | 0.597324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.89898 | 0.338658 | ||||||||
\(416\) | 2.44949 | − | 4.24264i | 0.120096 | − | 0.208013i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.44949 | + | 12.9029i | 0.364366 | + | 0.631101i | ||||
\(419\) | −12.2753 | − | 21.2614i | −0.599685 | − | 1.03869i | −0.992867 | − | 0.119225i | \(-0.961959\pi\) |
0.393182 | − | 0.919461i | \(-0.371374\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.55051 | + | 11.3458i | −0.319252 | + | 0.552961i | −0.980332 | − | 0.197354i | \(-0.936765\pi\) |
0.661080 | + | 0.750316i | \(0.270098\pi\) | |||||||
\(422\) | −3.10102 | −0.150955 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.10102 | −0.0534703 | ||||||||
\(425\) | −6.89898 | + | 11.9494i | −0.334650 | + | 0.579630i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −6.00000 | − | 10.3923i | −0.290021 | − | 0.502331i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.00000 | + | 8.66025i | −0.241121 | + | 0.417635i | ||||
\(431\) | 7.59592 | 0.365882 | 0.182941 | − | 0.983124i | \(-0.441438\pi\) | ||||
0.182941 | + | 0.983124i | \(0.441438\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.7980 | −0.566974 | −0.283487 | − | 0.958976i | \(-0.591491\pi\) | ||||
−0.283487 | + | 0.958976i | \(0.591491\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 8.34847 | + | 14.4600i | 0.399819 | + | 0.692507i | ||||
\(437\) | 3.72474 | + | 6.45145i | 0.178179 | + | 0.308615i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8990 | − | 18.8776i | 0.520180 | − | 0.900978i | −0.479545 | − | 0.877517i | \(-0.659198\pi\) |
0.999725 | − | 0.0234607i | \(-0.00746845\pi\) | |||||||
\(440\) | 6.89898 | 0.328896 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.79796 | −0.466041 | ||||||||
\(443\) | −2.55051 | + | 4.41761i | −0.121178 | + | 0.209887i | −0.920233 | − | 0.391372i | \(-0.872001\pi\) |
0.799054 | + | 0.601259i | \(0.205334\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.2474 | + | 21.2132i | 0.580585 | + | 1.00560i | ||||
\(446\) | 10.4495 | + | 18.0990i | 0.494798 | + | 0.857015i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.5959 | 0.877596 | 0.438798 | − | 0.898586i | \(-0.355404\pi\) | ||||
0.438798 | + | 0.898586i | \(0.355404\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 19.5959 | 0.922736 | ||||||||
\(452\) | −7.94949 | + | 13.7689i | −0.373913 | + | 0.647636i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −0.275255 | − | 0.476756i | −0.0129184 | − | 0.0223753i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −15.7474 | + | 27.2754i | −0.736635 | + | 1.27589i | 0.217368 | + | 0.976090i | \(0.430253\pi\) |
−0.954002 | + | 0.299799i | \(0.903080\pi\) | |||||||
\(458\) | −23.2474 | −1.08628 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.44949 | 0.160833 | ||||||||
\(461\) | −10.1742 | + | 17.6223i | −0.473861 | + | 0.820752i | −0.999552 | − | 0.0299238i | \(-0.990474\pi\) |
0.525691 | + | 0.850676i | \(0.323807\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.8485 | + | 22.2542i | 0.597119 | + | 1.03424i | 0.993244 | + | 0.116044i | \(0.0370213\pi\) |
−0.396125 | + | 0.918197i | \(0.629645\pi\) | |||||||
\(464\) | 1.44949 | + | 2.51059i | 0.0672909 | + | 0.116551i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 3.50000 | − | 6.06218i | 0.162134 | − | 0.280825i | ||||
\(467\) | 10.0000 | 0.462745 | 0.231372 | − | 0.972865i | \(-0.425678\pi\) | ||||
0.231372 | + | 0.972865i | \(0.425678\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −16.8990 | + | 29.2699i | −0.779492 | + | 1.35012i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.00000 | − | 1.73205i | −0.0460287 | − | 0.0797241i | ||||
\(473\) | −2.89898 | − | 5.02118i | −0.133295 | − | 0.230874i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 25.6969 | − | 44.5084i | 1.17906 | − | 2.04219i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.7980 | −0.585365 | ||||||||
\(479\) | 14.7980 | − | 25.6308i | 0.676136 | − | 1.17110i | −0.299999 | − | 0.953939i | \(-0.596987\pi\) |
0.976135 | − | 0.217163i | \(-0.0696802\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.1010 | + | 33.0839i | 0.870932 | + | 1.50850i | ||||
\(482\) | 4.44949 | + | 7.70674i | 0.202669 | + | 0.351032i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50000 | − | 6.06218i | 0.159091 | − | 0.275554i | ||||
\(485\) | 23.7980 | 1.08061 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.3939 | 1.01476 | 0.507382 | − | 0.861721i | \(-0.330613\pi\) | ||||
0.507382 | + | 0.861721i | \(0.330613\pi\) | |||||||
\(488\) | −5.72474 | + | 9.91555i | −0.259147 | + | 0.448856i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.89898 | − | 3.28913i | −0.0856997 | − | 0.148436i | 0.819989 | − | 0.572379i | \(-0.193979\pi\) |
−0.905689 | + | 0.423942i | \(0.860646\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.89898 | − | 5.02118i | 0.130563 | − | 0.226143i | ||||
\(494\) | 36.4949 | 1.64198 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −16.6969 | − | 28.9199i | −0.747458 | − | 1.29463i | −0.949038 | − | 0.315163i | \(-0.897941\pi\) |
0.201580 | − | 0.979472i | \(-0.435392\pi\) | |||||||
\(500\) | −3.27526 | − | 5.67291i | −0.146474 | − | 0.253700i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 6.27526 | − | 10.8691i | 0.280078 | − | 0.485110i | ||||
\(503\) | 24.4949 | 1.09217 | 0.546087 | − | 0.837729i | \(-0.316117\pi\) | ||||
0.546087 | + | 0.837729i | \(0.316117\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 25.0000 | 1.11249 | ||||||||
\(506\) | −1.00000 | + | 1.73205i | −0.0444554 | + | 0.0769991i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.50000 | + | 2.59808i | 0.0665517 | + | 0.115271i | ||||
\(509\) | 8.44949 | + | 14.6349i | 0.374517 | + | 0.648683i | 0.990255 | − | 0.139269i | \(-0.0444752\pi\) |
−0.615738 | + | 0.787951i | \(0.711142\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −27.7980 | −1.22612 | ||||||||
\(515\) | 24.1464 | − | 41.8228i | 1.06402 | − | 1.84293i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.79796 | − | 16.9706i | −0.430914 | − | 0.746364i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 8.44949 | − | 14.6349i | 0.370535 | − | 0.641785i | ||||
\(521\) | −38.6969 | −1.69534 | −0.847672 | − | 0.530521i | \(-0.821996\pi\) | ||||
−0.847672 | + | 0.530521i | \(0.821996\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −0.348469 | −0.0152375 | −0.00761875 | − | 0.999971i | \(-0.502425\pi\) | ||||
−0.00761875 | + | 0.999971i | \(0.502425\pi\) | |||||||
\(524\) | 6.72474 | − | 11.6476i | 0.293772 | − | 0.508828i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.05051 | − | 13.9439i | −0.351019 | − | 0.607983i | ||||
\(527\) | 6.00000 | + | 10.3923i | 0.261364 | + | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | −3.79796 | −0.164973 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 24.0000 | − | 41.5692i | 1.03956 | − | 1.80056i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.6969 | − | 35.8481i | −0.894807 | − | 1.54985i | ||||
\(536\) | −1.55051 | − | 2.68556i | −0.0669718 | − | 0.115999i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.82577 | + | 3.16232i | −0.0787143 | + | 0.136337i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.4949 | 1.31108 | 0.655539 | − | 0.755161i | \(-0.272441\pi\) | ||||
0.655539 | + | 0.755161i | \(0.272441\pi\) | |||||||
\(542\) | −8.44949 | + | 14.6349i | −0.362937 | + | 0.628625i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.00000 | + | 1.73205i | 0.0428746 | + | 0.0742611i | ||||
\(545\) | 28.7980 | + | 49.8795i | 1.23357 | + | 2.13660i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15.7980 | + | 27.3629i | −0.675472 | + | 1.16995i | 0.300859 | + | 0.953669i | \(0.402727\pi\) |
−0.976331 | + | 0.216283i | \(0.930607\pi\) | |||||||
\(548\) | 11.7980 | 0.503984 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 13.7980 | 0.588347 | ||||||||
\(551\) | −10.7980 | + | 18.7026i | −0.460009 | + | 0.796758i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 5.34847 | + | 9.26382i | 0.227235 | + | 0.393582i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 4.72474 | − | 8.18350i | 0.200374 | − | 0.347058i | ||||
\(557\) | 3.10102 | 0.131394 | 0.0656972 | − | 0.997840i | \(-0.479073\pi\) | ||||
0.0656972 | + | 0.997840i | \(0.479073\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.2020 | −0.600682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9.50000 | + | 16.4545i | 0.400733 | + | 0.694090i | ||||
\(563\) | −6.97219 | − | 12.0762i | −0.293843 | − | 0.508951i | 0.680872 | − | 0.732402i | \(-0.261601\pi\) |
−0.974715 | + | 0.223451i | \(0.928268\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.4217 | + | 47.4957i | −1.15364 | + | 1.99816i | ||||
\(566\) | −20.5505 | −0.863802 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.89898 | 0.415352 | ||||||||
\(569\) | −15.0000 | + | 25.9808i | −0.628833 | + | 1.08917i | 0.358954 | + | 0.933355i | \(0.383134\pi\) |
−0.987786 | + | 0.155815i | \(0.950200\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.10102 | − | 12.2993i | −0.297168 | − | 0.514711i | 0.678319 | − | 0.734768i | \(-0.262709\pi\) |
−0.975487 | + | 0.220057i | \(0.929376\pi\) | |||||||
\(572\) | 4.89898 | + | 8.48528i | 0.204837 | + | 0.354787i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.89898 | 0.287707 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.5959 | −0.982311 | −0.491155 | − | 0.871072i | \(-0.663425\pi\) | ||||
−0.491155 | + | 0.871072i | \(0.663425\pi\) | |||||||
\(578\) | −6.50000 | + | 11.2583i | −0.270364 | + | 0.468285i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.00000 | + | 8.66025i | 0.207614 | + | 0.359597i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.10102 | − | 1.90702i | 0.0455996 | − | 0.0789808i | ||||
\(584\) | 2.89898 | 0.119961 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −27.2474 | −1.12558 | ||||||||
\(587\) | 9.07321 | − | 15.7153i | 0.374492 | − | 0.648639i | −0.615759 | − | 0.787934i | \(-0.711151\pi\) |
0.990251 | + | 0.139296i | \(0.0444839\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.3485 | − | 38.7087i | −0.920853 | − | 1.59496i | ||||
\(590\) | −3.44949 | − | 5.97469i | −0.142013 | − | 0.245974i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.89898 | − | 6.75323i | 0.160247 | − | 0.277556i | ||||
\(593\) | −14.6969 | −0.603531 | −0.301765 | − | 0.953382i | \(-0.597576\pi\) | ||||
−0.301765 | + | 0.953382i | \(0.597576\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.00000 | + | 5.19615i | −0.122885 | + | 0.212843i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.44949 | + | 4.24264i | 0.100167 | + | 0.173494i | ||||
\(599\) | −7.10102 | − | 12.2993i | −0.290140 | − | 0.502537i | 0.683703 | − | 0.729761i | \(-0.260368\pi\) |
−0.973843 | + | 0.227224i | \(0.927035\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.34847 | + | 10.9959i | −0.258959 | + | 0.448531i | −0.965963 | − | 0.258679i | \(-0.916713\pi\) |
0.707004 | + | 0.707210i | \(0.250046\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.00000 | −0.203447 | ||||||||
\(605\) | 12.0732 | − | 20.9114i | 0.490846 | − | 0.850170i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4.34847 | − | 7.53177i | −0.176499 | − | 0.305705i | 0.764180 | − | 0.645003i | \(-0.223144\pi\) |
−0.940679 | + | 0.339298i | \(0.889811\pi\) | |||||||
\(608\) | −3.72474 | − | 6.45145i | −0.151058 | − | 0.261641i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.7474 | + | 34.2036i | −0.799551 | + | 1.38486i | ||||
\(611\) | −48.0000 | −1.94187 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.6969 | 0.593604 | 0.296802 | − | 0.954939i | \(-0.404080\pi\) | ||||
0.296802 | + | 0.954939i | \(0.404080\pi\) | |||||||
\(614\) | −0.376276 | + | 0.651729i | −0.0151852 | + | 0.0263016i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6969 | + | 37.5802i | 0.873486 | + | 1.51292i | 0.858367 | + | 0.513036i | \(0.171479\pi\) |
0.0151189 | + | 0.999886i | \(0.495187\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.07321 | + | 3.59091i | −0.0833295 | + | 0.144331i | −0.904678 | − | 0.426096i | \(-0.859889\pi\) |
0.821349 | + | 0.570426i | \(0.193222\pi\) | |||||||
\(620\) | −20.6969 | −0.831209 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.30306 | −0.0522480 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.94949 | + | 10.3048i | 0.237980 | + | 0.412193i | ||||
\(626\) | −12.3485 | − | 21.3882i | −0.493544 | − | 0.854843i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 3.17423 | − | 5.49794i | 0.126666 | − | 0.219392i | ||||
\(629\) | −15.5959 | −0.621850 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.1010 | 0.720590 | 0.360295 | − | 0.932838i | \(-0.382676\pi\) | ||||
0.360295 | + | 0.932838i | \(0.382676\pi\) | |||||||
\(632\) | 3.94949 | − | 6.84072i | 0.157102 | − | 0.272109i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.34847 | + | 7.53177i | 0.172700 | + | 0.299125i | ||||
\(635\) | 5.17423 | + | 8.96204i | 0.205333 | + | 0.355648i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.79796 | −0.229543 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.44949 | −0.136353 | ||||||||
\(641\) | 20.7474 | − | 35.9356i | 0.819475 | − | 1.41937i | −0.0865947 | − | 0.996244i | \(-0.527599\pi\) |
0.906070 | − | 0.423129i | \(-0.139068\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.69694 | + | 16.7956i | 0.382410 | + | 0.662353i | 0.991406 | − | 0.130820i | \(-0.0417609\pi\) |
−0.608996 | + | 0.793173i | \(0.708428\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.44949 | + | 12.9029i | −0.293096 | + | 0.507658i | ||||
\(647\) | −21.3031 | −0.837510 | −0.418755 | − | 0.908099i | \(-0.637533\pi\) | ||||
−0.418755 | + | 0.908099i | \(0.637533\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.00000 | 0.157014 | ||||||||
\(650\) | 16.8990 | − | 29.2699i | 0.662833 | − | 1.14806i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.101021 | + | 0.174973i | 0.00395627 | + | 0.00685246i | ||||
\(653\) | −4.89898 | − | 8.48528i | −0.191712 | − | 0.332055i | 0.754106 | − | 0.656753i | \(-0.228071\pi\) |
−0.945818 | + | 0.324698i | \(0.894737\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.1969 | − | 40.1783i | 0.906379 | − | 1.56990i | ||||
\(656\) | −9.79796 | −0.382546 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.34847 | − | 4.06767i | 0.0914834 | − | 0.158454i | −0.816652 | − | 0.577130i | \(-0.804172\pi\) |
0.908136 | + | 0.418676i | \(0.137506\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.72474 | + | 8.18350i | 0.183771 | + | 0.318301i | 0.943162 | − | 0.332334i | \(-0.107836\pi\) |
−0.759391 | + | 0.650635i | \(0.774503\pi\) | |||||||
\(662\) | −12.3485 | − | 21.3882i | −0.479937 | − | 0.831275i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.00000 | − | 1.73205i | 0.0388075 | − | 0.0672166i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.89898 | −0.112249 | ||||||||
\(668\) | −9.34847 | + | 16.1920i | −0.361703 | + | 0.626488i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.34847 | − | 9.26382i | −0.206629 | − | 0.357893i | ||||
\(671\) | −11.4495 | − | 19.8311i | −0.442003 | − | 0.765571i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.2980 | + | 26.4968i | −0.589693 | + | 1.02138i | 0.404579 | + | 0.914503i | \(0.367418\pi\) |
−0.994272 | + | 0.106875i | \(0.965915\pi\) | |||||||
\(674\) | −35.3939 | −1.36332 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 11.0000 | 0.423077 | ||||||||
\(677\) | 7.34847 | − | 12.7279i | 0.282425 | − | 0.489174i | −0.689557 | − | 0.724232i | \(-0.742195\pi\) |
0.971981 | + | 0.235058i | \(0.0755280\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.44949 | + | 5.97469i | 0.132282 | + | 0.229119i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 6.00000 | − | 10.3923i | 0.229752 | − | 0.397942i | ||||
\(683\) | −32.2020 | −1.23218 | −0.616088 | − | 0.787677i | \(-0.711284\pi\) | ||||
−0.616088 | + | 0.787677i | \(0.711284\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.6969 | 1.55495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.44949 | + | 2.51059i | 0.0552613 | + | 0.0957153i | ||||
\(689\) | −2.69694 | − | 4.67123i | −0.102745 | − | 0.177960i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.47730 | − | 6.02285i | 0.132283 | − | 0.229120i | −0.792274 | − | 0.610166i | \(-0.791103\pi\) |
0.924556 | + | 0.381046i | \(0.124436\pi\) | |||||||
\(692\) | −12.8990 | −0.490346 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −19.5959 | −0.743851 | ||||||||
\(695\) | 16.2980 | − | 28.2289i | 0.618217 | − | 1.07078i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.79796 | + | 16.9706i | 0.371124 | + | 0.642806i | ||||
\(698\) | −10.4495 | − | 18.0990i | −0.395519 | − | 0.685059i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −51.3939 | −1.94112 | −0.970560 | − | 0.240860i | \(-0.922571\pi\) | ||||
−0.970560 | + | 0.240860i | \(0.922571\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 58.0908 | 2.19094 | ||||||||
\(704\) | 1.00000 | − | 1.73205i | 0.0376889 | − | 0.0652791i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.00000 | − | 5.19615i | −0.112906 | − | 0.195560i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.79796 | − | 10.0424i | 0.217747 | − | 0.377149i | −0.736372 | − | 0.676577i | \(-0.763463\pi\) |
0.954119 | + | 0.299428i | \(0.0967959\pi\) | |||||||
\(710\) | 34.1464 | 1.28149 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.10102 | 0.266122 | ||||||||
\(713\) | 3.00000 | − | 5.19615i | 0.112351 | − | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.8990 | + | 29.2699i | 0.631986 | + | 1.09463i | ||||
\(716\) | −4.34847 | − | 7.53177i | −0.162510 | − | 0.281475i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.39898 | + | 9.35131i | −0.201488 | + | 0.348988i | ||||
\(719\) | −9.79796 | −0.365402 | −0.182701 | − | 0.983169i | \(-0.558484\pi\) | ||||
−0.182701 | + | 0.983169i | \(0.558484\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 18.2474 | − | 31.6055i | 0.679100 | − | 1.17624i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.17423 | + | 3.76588i | 0.0808048 | + | 0.139958i | ||||
\(725\) | 10.0000 | + | 17.3205i | 0.371391 | + | 0.643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.2474 | − | 35.0696i | 0.750936 | − | 1.30066i | −0.196433 | − | 0.980517i | \(-0.562936\pi\) |
0.947369 | − | 0.320143i | \(-0.103731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 10.0000 | 0.370117 | ||||||||
\(731\) | 2.89898 | − | 5.02118i | 0.107223 | − | 0.185715i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −6.27526 | − | 10.8691i | −0.231782 | − | 0.401458i | 0.726551 | − | 0.687113i | \(-0.241122\pi\) |
−0.958333 | + | 0.285655i | \(0.907789\pi\) | |||||||
\(734\) | −2.89898 | − | 5.02118i | −0.107003 | − | 0.185335i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | − | 0.866025i | 0.0184302 | − | 0.0319221i | ||||
\(737\) | 6.20204 | 0.228455 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −25.5959 | −0.941561 | −0.470781 | − | 0.882250i | \(-0.656028\pi\) | ||||
−0.470781 | + | 0.882250i | \(0.656028\pi\) | |||||||
\(740\) | 13.4495 | − | 23.2952i | 0.494413 | − | 0.856349i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18.0000 | + | 31.1769i | 0.660356 | + | 1.14377i | 0.980522 | + | 0.196409i | \(0.0629279\pi\) |
−0.320166 | + | 0.947361i | \(0.603739\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.3485 | + | 17.9241i | −0.379139 | + | 0.656687i | ||||
\(746\) | −2.89898 | −0.106139 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.2980 | − | 35.1571i | −0.740683 | − | 1.28290i | −0.952185 | − | 0.305523i | \(-0.901169\pi\) |
0.211502 | − | 0.977378i | \(-0.432165\pi\) | |||||||
\(752\) | 4.89898 | + | 8.48528i | 0.178647 | + | 0.309426i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.10102 | + | 12.2993i | −0.258604 | + | 0.447915i | ||||
\(755\) | −17.2474 | −0.627699 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 23.3939 | 0.850265 | 0.425132 | − | 0.905131i | \(-0.360228\pi\) | ||||
0.425132 | + | 0.905131i | \(0.360228\pi\) | |||||||
\(758\) | −13.2474 | + | 22.9453i | −0.481169 | + | 0.833409i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −12.8485 | − | 22.2542i | −0.466063 | − | 0.807245i | ||||
\(761\) | −1.00000 | − | 1.73205i | −0.0362500 | − | 0.0627868i | 0.847331 | − | 0.531065i | \(-0.178208\pi\) |
−0.883581 | + | 0.468278i | \(0.844875\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.8990 | −0.502847 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.89898 | −0.249270 | ||||||||
\(767\) | 4.89898 | − | 8.48528i | 0.176892 | − | 0.306386i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 27.0454 | + | 46.8440i | 0.975282 | + | 1.68924i | 0.679000 | + | 0.734138i | \(0.262414\pi\) |
0.296282 | + | 0.955100i | \(0.404253\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.05051 | − | 7.01569i | 0.145781 | − | 0.252500i | ||||
\(773\) | −19.9444 | −0.717350 | −0.358675 | − | 0.933463i | \(-0.616771\pi\) | ||||
−0.358675 | + | 0.933463i | \(0.616771\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −41.3939 | −1.48691 | ||||||||
\(776\) | 3.44949 | − | 5.97469i | 0.123829 | − | 0.214479i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.55051 | + | 13.0779i | 0.270699 | + | 0.468864i | ||||
\(779\) | −36.4949 | − | 63.2110i | −1.30757 | − | 2.26477i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.89898 | + | 17.1455i | −0.354213 | + | 0.613515i | ||||
\(782\) | −2.00000 | −0.0715199 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.9495 | − | 18.9651i | 0.390804 | − | 0.676892i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 23.6969 | + | 41.0443i | 0.844705 | + | 1.46307i | 0.885877 | + | 0.463919i | \(0.153557\pi\) |
−0.0411728 | + | 0.999152i | \(0.513109\pi\) | |||||||
\(788\) | −6.34847 | − | 10.9959i | −0.226155 | − | 0.391712i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 13.6237 | − | 23.5970i | 0.484710 | − | 0.839543i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −56.0908 | −1.99184 | ||||||||
\(794\) | −4.65153 | + | 8.05669i | −0.165077 | + | 0.285921i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.44949 | + | 5.97469i | 0.122264 | + | 0.211767i | ||||
\(797\) | −17.9722 | − | 31.1288i | −0.636608 | − | 1.10264i | −0.986172 | − | 0.165725i | \(-0.947004\pi\) |
0.349564 | − | 0.936912i | \(-0.386330\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 9.79796 | − | 16.9706i | 0.346627 | − | 0.600375i | ||||
\(800\) | −6.89898 | −0.243916 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −10.1010 | −0.356679 | ||||||||
\(803\) | −2.89898 | + | 5.02118i | −0.102303 | + | 0.177194i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −14.6969 | − | 25.4558i | −0.517678 | − | 0.896644i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 3.62372 | − | 6.27647i | 0.127482 | − | 0.220806i | ||||
\(809\) | 35.7980 | 1.25859 | 0.629295 | − | 0.777167i | \(-0.283344\pi\) | ||||
0.629295 | + | 0.777167i | \(0.283344\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.00000 | 0.0702295 | 0.0351147 | − | 0.999383i | \(-0.488820\pi\) | ||||
0.0351147 | + | 0.999383i | \(0.488820\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.79796 | + | 13.5065i | 0.273318 | + | 0.473401i | ||||
\(815\) | 0.348469 | + | 0.603566i | 0.0122063 | + | 0.0211420i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −10.7980 | + | 18.7026i | −0.377773 | + | 0.654322i | ||||
\(818\) | 5.79796 | 0.202721 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −33.7980 | −1.18028 | ||||||||
\(821\) | 19.7980 | − | 34.2911i | 0.690954 | − | 1.19677i | −0.280572 | − | 0.959833i | \(-0.590524\pi\) |
0.971526 | − | 0.236934i | \(-0.0761424\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.6969 | − | 39.3123i | −0.791166 | − | 1.37034i | −0.925246 | − | 0.379368i | \(-0.876141\pi\) |
0.134080 | − | 0.990970i | \(-0.457192\pi\) | |||||||
\(824\) | −7.00000 | − | 12.1244i | −0.243857 | − | 0.422372i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.4949 | −0.434490 | −0.217245 | − | 0.976117i | \(-0.569707\pi\) | ||||
−0.217245 | + | 0.976117i | \(0.569707\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −30.6969 | −1.06615 | −0.533074 | − | 0.846068i | \(-0.678963\pi\) | ||||
−0.533074 | + | 0.846068i | \(0.678963\pi\) | |||||||
\(830\) | 3.44949 | − | 5.97469i | 0.119734 | − | 0.207385i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.44949 | − | 4.24264i | −0.0849208 | − | 0.147087i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −32.2474 | + | 55.8542i | −1.11597 | + | 1.93291i | ||||
\(836\) | 14.8990 | 0.515292 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24.5505 | −0.848083 | ||||||||
\(839\) | 22.4495 | − | 38.8837i | 0.775042 | − | 1.34241i | −0.159728 | − | 0.987161i | \(-0.551062\pi\) |
0.934771 | − | 0.355252i | \(-0.115605\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10.2980 | + | 17.8366i | 0.355102 | + | 0.615055i | ||||
\(842\) | 6.55051 | + | 11.3458i | 0.225745 | + | 0.391003i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.55051 | + | 2.68556i | −0.0533708 | + | 0.0924409i | ||||
\(845\) | 37.9444 | 1.30533 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −0.550510 | + | 0.953512i | −0.0189046 | + | 0.0327437i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.89898 | + | 11.9494i | 0.236633 | + | 0.409860i | ||||
\(851\) | 3.89898 | + | 6.75323i | 0.133655 | + | 0.231498i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19.4217 | + | 33.6393i | −0.664986 | + | 1.15179i | 0.314303 | + | 0.949323i | \(0.398229\pi\) |
−0.979289 | + | 0.202467i | \(0.935104\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0000 | −0.410152 | ||||||||
\(857\) | 12.5505 | − | 21.7381i | 0.428717 | − | 0.742560i | −0.568042 | − | 0.822999i | \(-0.692299\pi\) |
0.996760 | + | 0.0804393i | \(0.0256323\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.00000 | − | 8.66025i | −0.170598 | − | 0.295484i | 0.768031 | − | 0.640412i | \(-0.221237\pi\) |
−0.938629 | + | 0.344928i | \(0.887903\pi\) | |||||||
\(860\) | 5.00000 | + | 8.66025i | 0.170499 | + | 0.295312i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.79796 | − | 6.57826i | 0.129359 | − | 0.224056i | ||||
\(863\) | −2.10102 | −0.0715196 | −0.0357598 | − | 0.999360i | \(-0.511385\pi\) | ||||
−0.0357598 | + | 0.999360i | \(0.511385\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −44.4949 | −1.51287 | ||||||||
\(866\) | −5.89898 | + | 10.2173i | −0.200455 | + | 0.347199i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.89898 | + | 13.6814i | 0.267955 | + | 0.464111i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.59592 | − | 13.1565i | 0.257378 | − | 0.445792i | ||||
\(872\) | 16.6969 | 0.565430 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.44949 | 0.251983 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.2474 | + | 22.9453i | 0.447335 | + | 0.774806i | 0.998212 | − | 0.0597803i | \(-0.0190400\pi\) |
−0.550877 | + | 0.834586i | \(0.685707\pi\) | |||||||
\(878\) | −10.8990 | − | 18.8776i | −0.367823 | − | 0.637088i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.44949 | − | 5.97469i | 0.116282 | − | 0.201407i | ||||
\(881\) | −19.5959 | −0.660203 | −0.330102 | − | 0.943945i | \(-0.607083\pi\) | ||||
−0.330102 | + | 0.943945i | \(0.607083\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −0.202041 | −0.00679922 | −0.00339961 | − | 0.999994i | \(-0.501082\pi\) | ||||
−0.00339961 | + | 0.999994i | \(0.501082\pi\) | |||||||
\(884\) | −4.89898 | + | 8.48528i | −0.164771 | + | 0.285391i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.55051 | + | 4.41761i | 0.0856861 | + | 0.148413i | ||||
\(887\) | 16.8990 | + | 29.2699i | 0.567412 | + | 0.982787i | 0.996821 | + | 0.0796764i | \(0.0253887\pi\) |
−0.429409 | + | 0.903110i | \(0.641278\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.4949 | 0.821071 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.8990 | 0.699750 | ||||||||
\(893\) | −36.4949 | + | 63.2110i | −1.22126 | + | 2.11528i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.0000 | − | 25.9808i | −0.501395 | − | 0.868441i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.29796 | − | 16.1045i | 0.310277 | − | 0.537415i | ||||
\(899\) | 17.3939 | 0.580118 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.20204 | 0.0733606 | ||||||||
\(902\) | 9.79796 | − | 16.9706i | 0.326236 | − | 0.565058i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.94949 | + | 13.7689i | 0.264396 | + | 0.457947i | ||||
\(905\) | 7.50000 | + | 12.9904i | 0.249308 | + | 0.431815i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 13.3485 | − | 23.1202i | 0.443229 | − | 0.767695i | −0.554698 | − | 0.832052i | \(-0.687166\pi\) |
0.997927 | + | 0.0643570i | \(0.0204996\pi\) | |||||||
\(908\) | −0.550510 | −0.0182693 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −22.9949 | + | 39.8283i | −0.761855 | + | 1.31957i | 0.180038 | + | 0.983660i | \(0.442378\pi\) |
−0.941893 | + | 0.335912i | \(0.890956\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.00000 | + | 3.46410i | 0.0661903 | + | 0.114645i | ||||
\(914\) | 15.7474 | + | 27.2754i | 0.520879 | + | 0.902189i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.6237 | + | 20.1329i | −0.384059 | + | 0.665209i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.69694 | 0.121951 | 0.0609754 | − | 0.998139i | \(-0.480579\pi\) | ||||
0.0609754 | + | 0.998139i | \(0.480579\pi\) | |||||||
\(920\) | 1.72474 | − | 2.98735i | 0.0568632 | − | 0.0984899i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10.1742 | + | 17.6223i | 0.335071 | + | 0.580359i | ||||
\(923\) | 24.2474 | + | 41.9978i | 0.798114 | + | 1.38237i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.8990 | − | 46.5904i | 0.884433 | − | 1.53188i | ||||
\(926\) | 25.6969 | 0.844454 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.89898 | 0.0951637 | ||||||||
\(929\) | 17.1464 | − | 29.6985i | 0.562556 | − | 0.974376i | −0.434716 | − | 0.900567i | \(-0.643151\pi\) |
0.997272 | − | 0.0738083i | \(-0.0235153\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.50000 | − | 6.06218i | −0.114646 | − | 0.198573i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.00000 | − | 8.66025i | 0.163605 | − | 0.283372i | ||||
\(935\) | −13.7980 | −0.451242 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.40408 | −0.209212 | −0.104606 | − | 0.994514i | \(-0.533358\pi\) | ||||
−0.104606 | + | 0.994514i | \(0.533358\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 16.8990 | + | 29.2699i | 0.551184 | + | 0.954679i | ||||
\(941\) | −1.72474 | − | 2.98735i | −0.0562251 | − | 0.0973847i | 0.836543 | − | 0.547901i | \(-0.184573\pi\) |
−0.892768 | + | 0.450517i | \(0.851240\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.89898 | − | 8.48528i | 0.159533 | − | 0.276319i | ||||
\(944\) | −2.00000 | −0.0650945 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.79796 | −0.188508 | ||||||||
\(947\) | 1.75255 | − | 3.03551i | 0.0569503 | − | 0.0986408i | −0.836145 | − | 0.548509i | \(-0.815196\pi\) |
0.893095 | + | 0.449868i | \(0.148529\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.10102 | + | 12.2993i | 0.230509 | + | 0.399253i | ||||
\(950\) | −25.6969 | − | 44.5084i | −0.833719 | − | 1.44404i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −55.3939 | −1.79438 | −0.897192 | − | 0.441641i | \(-0.854396\pi\) | ||||
−0.897192 | + | 0.441641i | \(0.854396\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −47.9444 | −1.55144 | ||||||||
\(956\) | −6.39898 | + | 11.0834i | −0.206958 | + | 0.358461i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −14.7980 | − | 25.6308i | −0.478100 | − | 0.828094i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 38.2020 | 1.23168 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.89898 | 0.286617 | ||||||||
\(965\) | 13.9722 | − | 24.2005i | 0.449781 | − | 0.779043i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.29796 | + | 12.6404i | 0.234687 | + | 0.406489i | 0.959182 | − | 0.282791i | \(-0.0912603\pi\) |
−0.724495 | + | 0.689280i | \(0.757927\pi\) | |||||||
\(968\) | −3.50000 | − | 6.06218i | −0.112494 | − | 0.194846i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 11.8990 | − | 20.6096i | 0.382053 | − | 0.661736i | ||||
\(971\) | −53.9444 | −1.73116 | −0.865579 | − | 0.500773i | \(-0.833049\pi\) | ||||
−0.865579 | + | 0.500773i | \(0.833049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.1969 | − | 19.3937i | 0.358773 | − | 0.621413i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.72474 | + | 9.91555i | 0.183245 | + | 0.317389i | ||||
\(977\) | 0.797959 | + | 1.38211i | 0.0255290 | + | 0.0442175i | 0.878508 | − | 0.477728i | \(-0.158540\pi\) |
−0.852979 | + | 0.521946i | \(0.825206\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.10102 | + | 12.2993i | −0.226950 | + | 0.393088i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −3.79796 | −0.121198 | ||||||||
\(983\) | −22.5959 | + | 39.1373i | −0.720698 | + | 1.24829i | 0.240023 | + | 0.970767i | \(0.422845\pi\) |
−0.960720 | + | 0.277518i | \(0.910488\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.8990 | − | 37.9301i | −0.697760 | − | 1.20855i | ||||
\(986\) | −2.89898 | − | 5.02118i | −0.0923223 | − | 0.159907i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.2474 | − | 31.6055i | 0.580529 | − | 1.00551i | ||||
\(989\) | −2.89898 | −0.0921822 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7980 | 0.565371 | 0.282685 | − | 0.959213i | \(-0.408775\pi\) | ||||
0.282685 | + | 0.959213i | \(0.408775\pi\) | |||||||
\(992\) | −3.00000 | + | 5.19615i | −0.0952501 | + | 0.164978i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 11.8990 | + | 20.6096i | 0.377223 | + | 0.653369i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 8.92679 | − | 15.4616i | 0.282714 | − | 0.489675i | −0.689338 | − | 0.724440i | \(-0.742099\pi\) |
0.972052 | + | 0.234764i | \(0.0754319\pi\) | |||||||
\(998\) | −33.3939 | −1.05706 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))