Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(361,2646)]
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([2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.361");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.h (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 | 667.2 | ||
Root | \(-1.22474 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.667 |
Dual form | 2646.2.h.n.361.2 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | + | 0.866025i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 3.44949 | 1.54266 | 0.771329 | − | 0.636436i | \(-0.219592\pi\) | ||||
0.771329 | + | 0.636436i | \(0.219592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.72474 | + | 2.98735i | 0.545412 | + | 0.944682i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 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 | ||||
\(17\) | −1.00000 | − | 1.73205i | −0.242536 | − | 0.420084i | 0.718900 | − | 0.695113i | \(-0.244646\pi\) |
−0.961436 | + | 0.275029i | \(0.911312\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.72474 | − | 6.45145i | 0.854515 | − | 1.48006i | −0.0225791 | − | 0.999745i | \(-0.507188\pi\) |
0.877094 | − | 0.480318i | \(-0.159479\pi\) | |||||||
\(20\) | −1.72474 | + | 2.98735i | −0.385665 | + | 0.667991i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | − | 1.73205i | −0.213201 | − | 0.369274i | ||||
\(23\) | 1.00000 | 0.208514 | 0.104257 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 6.89898 | 1.37980 | ||||||||
\(26\) | 2.44949 | − | 4.24264i | 0.480384 | − | 0.832050i | ||||
\(27\) | 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 | −0.460152 | − | 0.887840i | \(-0.652205\pi\) |
0.998968 | − | 0.0454165i | \(-0.0144615\pi\) | |||||||
\(32\) | 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 | ||||||||
\(37\) | 3.89898 | − | 6.75323i | 0.640988 | − | 1.11022i | −0.344224 | − | 0.938887i | \(-0.611858\pi\) |
0.985213 | − | 0.171337i | \(-0.0548086\pi\) | |||||||
\(38\) | 7.44949 | 1.20847 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.44949 | −0.545412 | ||||||||
\(41\) | 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 | \(0.0957199\pi\) | |||||||
\(44\) | 1.00000 | − | 1.73205i | 0.150756 | − | 0.261116i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.500000 | + | 0.866025i | 0.0737210 | + | 0.127688i | ||||
\(47\) | 4.89898 | + | 8.48528i | 0.714590 | + | 1.23771i | 0.963118 | + | 0.269081i | \(0.0867199\pi\) |
−0.248528 | + | 0.968625i | \(0.579947\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 3.44949 | + | 5.97469i | 0.487832 | + | 0.844949i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.89898 | 0.679366 | ||||||||
\(53\) | −0.550510 | − | 0.953512i | −0.0756184 | − | 0.130975i | 0.825737 | − | 0.564056i | \(-0.190760\pi\) |
−0.901355 | + | 0.433081i | \(0.857426\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.89898 | −0.930258 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.89898 | 0.380655 | ||||||||
\(59\) | 1.00000 | − | 1.73205i | 0.130189 | − | 0.225494i | −0.793560 | − | 0.608492i | \(-0.791775\pi\) |
0.923749 | + | 0.382998i | \(0.125108\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.72474 | + | 9.91555i | 0.732978 | + | 1.26956i | 0.955605 | + | 0.294652i | \(0.0952037\pi\) |
−0.222626 | + | 0.974904i | \(0.571463\pi\) | |||||||
\(62\) | 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 | −0.755634 | − | 0.654994i | \(-0.772671\pi\) |
0.945059 | + | 0.326901i | \(0.106004\pi\) | |||||||
\(68\) | 2.00000 | 0.242536 | ||||||||
\(69\) | 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 | ||||||||
\(73\) | 1.44949 | + | 2.51059i | 0.169650 | + | 0.293842i | 0.938297 | − | 0.345831i | \(-0.112403\pi\) |
−0.768647 | + | 0.639673i | \(0.779070\pi\) | |||||||
\(74\) | 7.79796 | 0.906494 | ||||||||
\(75\) | 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 | 0.553655 | − | 0.832746i | \(-0.313233\pi\) |
−0.998007 | + | 0.0631057i | \(0.979899\pi\) | |||||||
\(80\) | −1.72474 | − | 2.98735i | −0.192832 | − | 0.333995i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.89898 | + | 8.48528i | −0.541002 | + | 0.937043i | ||||
\(83\) | −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 | ||||
\(86\) | 2.89898 | 0.312605 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | 3.55051 | − | 6.14966i | 0.376353 | − | 0.651863i | −0.614175 | − | 0.789170i | \(-0.710511\pi\) |
0.990529 | + | 0.137307i | \(0.0438445\pi\) | |||||||
\(90\) | 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 | ||||||||
\(100\) | −3.44949 | + | 5.97469i | −0.344949 | + | 0.597469i | ||||
\(101\) | 7.24745 | 0.721148 | 0.360574 | − | 0.932731i | \(-0.382581\pi\) | ||||
0.360574 | + | 0.932731i | \(0.382581\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.0000 | −1.37946 | −0.689730 | − | 0.724066i | \(-0.742271\pi\) | ||||
−0.689730 | + | 0.724066i | \(0.742271\pi\) | |||||||
\(104\) | 2.44949 | + | 4.24264i | 0.240192 | + | 0.416025i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.550510 | − | 0.953512i | 0.0534703 | − | 0.0926132i | ||||
\(107\) | −6.00000 | + | 10.3923i | −0.580042 | + | 1.00466i | 0.415432 | + | 0.909624i | \(0.363630\pi\) |
−0.995474 | + | 0.0950377i | \(0.969703\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.34847 | + | 14.4600i | 0.799638 | + | 1.38501i | 0.919852 | + | 0.392266i | \(0.128309\pi\) |
−0.120213 | + | 0.992748i | \(0.538358\pi\) | |||||||
\(110\) | −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 | ||||||||
\(115\) | 3.44949 | 0.321667 | ||||||||
\(116\) | 1.44949 | + | 2.51059i | 0.134582 | + | 0.233102i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.00000 | 0.184115 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −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 | ||||
\(131\) | −13.4495 | −1.17509 | −0.587544 | − | 0.809192i | \(-0.699905\pi\) | ||||
−0.587544 | + | 0.809192i | \(0.699905\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 3.10102 | 0.267887 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.00000 | + | 1.73205i | 0.0857493 | + | 0.148522i | ||||
\(137\) | 11.7980 | 1.00797 | 0.503984 | − | 0.863713i | \(-0.331867\pi\) | ||||
0.503984 | + | 0.863713i | \(0.331867\pi\) | |||||||
\(138\) | 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 | ||||
\(143\) | 4.89898 | + | 8.48528i | 0.409673 | + | 0.709575i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.00000 | − | 8.66025i | 0.415227 | − | 0.719195i | ||||
\(146\) | −1.44949 | + | 2.51059i | −0.119961 | + | 0.207778i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.89898 | + | 6.75323i | 0.320494 | + | 0.555112i | ||||
\(149\) | 6.00000 | 0.491539 | 0.245770 | − | 0.969328i | \(-0.420959\pi\) | ||||
0.245770 | + | 0.969328i | \(0.420959\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00000 | −0.406894 | −0.203447 | − | 0.979086i | \(-0.565214\pi\) | ||||
−0.203447 | + | 0.979086i | \(0.565214\pi\) | |||||||
\(152\) | −3.72474 | + | 6.45145i | −0.302117 | + | 0.523281i | ||||
\(153\) | 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 | −0.711109 | − | 0.703081i | \(-0.751807\pi\) |
0.964441 | + | 0.264298i | \(0.0851403\pi\) | |||||||
\(158\) | 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 | ||||||||
\(163\) | 0.101021 | − | 0.174973i | 0.00791254 | − | 0.0137049i | −0.862042 | − | 0.506837i | \(-0.830815\pi\) |
0.869955 | + | 0.493132i | \(0.164148\pi\) | |||||||
\(164\) | −9.79796 | −0.765092 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | −0.155230 | ||||||||
\(167\) | −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 | ||||
\(170\) | 3.44949 | − | 5.97469i | 0.264564 | − | 0.458238i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.44949 | + | 2.51059i | 0.110523 | + | 0.191431i | ||||
\(173\) | 6.44949 | + | 11.1708i | 0.490346 | + | 0.849304i | 0.999938 | − | 0.0111123i | \(-0.00353722\pi\) |
−0.509593 | + | 0.860416i | \(0.670204\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.00000 | + | 1.73205i | 0.0753778 | + | 0.130558i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 7.10102 | 0.532244 | ||||||||
\(179\) | −4.34847 | − | 7.53177i | −0.325020 | − | 0.562951i | 0.656497 | − | 0.754329i | \(-0.272038\pi\) |
−0.981516 | + | 0.191378i | \(0.938704\pi\) | |||||||
\(180\) | 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 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 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 | 0.999995 | + | 0.00329106i | \(0.00104758\pi\) |
−0.497147 | + | 0.867666i | \(0.665619\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.05051 | − | 7.01569i | 0.291562 | − | 0.505000i | −0.682617 | − | 0.730776i | \(-0.739158\pi\) |
0.974179 | + | 0.225776i | \(0.0724917\pi\) | |||||||
\(194\) | −6.89898 | −0.495318 | ||||||||
\(195\) | 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 | ||||||||
\(199\) | 3.44949 | + | 5.97469i | 0.244528 | + | 0.423535i | 0.961999 | − | 0.273054i | \(-0.0880337\pi\) |
−0.717471 | + | 0.696588i | \(0.754700\pi\) | |||||||
\(200\) | −6.89898 | −0.487832 | ||||||||
\(201\) | 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 | ||||
\(206\) | −7.00000 | − | 12.1244i | −0.487713 | − | 0.844744i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.44949 | + | 4.24264i | −0.169842 | + | 0.294174i | ||||
\(209\) | −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 | \(0.867375\pi\) | |||||||
\(212\) | 1.10102 | 0.0756184 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.0000 | −0.820303 | ||||||||
\(215\) | 5.00000 | − | 8.66025i | 0.340997 | − | 0.590624i | ||||
\(216\) | 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 | ||||||||
\(226\) | 7.94949 | − | 13.7689i | 0.528792 | − | 0.915895i | ||||
\(227\) | −0.550510 | −0.0365386 | −0.0182693 | − | 0.999833i | \(-0.505816\pi\) | ||||
−0.0182693 | + | 0.999833i | \(0.505816\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.2474 | 1.53623 | 0.768117 | − | 0.640309i | \(-0.221194\pi\) | ||||
0.768117 | + | 0.640309i | \(0.221194\pi\) | |||||||
\(230\) | 1.72474 | + | 2.98735i | 0.113726 | + | 0.196980i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.44949 | + | 2.51059i | −0.0951637 | + | 0.164828i | ||||
\(233\) | −3.50000 | + | 6.06218i | −0.229293 | + | 0.397146i | −0.957599 | − | 0.288106i | \(-0.906975\pi\) |
0.728306 | + | 0.685252i | \(0.240308\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 16.8990 | + | 29.2699i | 1.10237 | + | 1.90936i | ||||
\(236\) | 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 | ||||||||
\(241\) | 8.89898 | 0.573234 | 0.286617 | − | 0.958045i | \(-0.407469\pi\) | ||||
0.286617 | + | 0.958045i | \(0.407469\pi\) | |||||||
\(242\) | −3.50000 | − | 6.06218i | −0.224989 | − | 0.389692i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.4495 | −0.732978 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −36.4949 | −2.32211 | ||||||||
\(248\) | −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 | ||||
\(257\) | 27.7980 | 1.73399 | 0.866995 | − | 0.498318i | \(-0.166049\pi\) | ||||
0.866995 | + | 0.498318i | \(0.166049\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 16.8990 | 1.04803 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.72474 | − | 11.6476i | −0.415456 | − | 0.719591i | ||||
\(263\) | −16.1010 | −0.992831 | −0.496416 | − | 0.868085i | \(-0.665351\pi\) | ||||
−0.496416 | + | 0.868085i | \(0.665351\pi\) | |||||||
\(264\) | 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 | ||||
\(269\) | 1.82577 | + | 3.16232i | 0.111319 | + | 0.192810i | 0.916302 | − | 0.400487i | \(-0.131159\pi\) |
−0.804983 | + | 0.593297i | \(0.797826\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.44949 | − | 14.6349i | 0.513270 | − | 0.889010i | −0.486612 | − | 0.873618i | \(-0.661767\pi\) |
0.999882 | − | 0.0153912i | \(-0.00489937\pi\) | |||||||
\(272\) | −1.00000 | + | 1.73205i | −0.0606339 | + | 0.105021i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.89898 | + | 10.2173i | 0.356370 | + | 0.617252i | ||||
\(275\) | −13.7980 | −0.832048 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.6969 | 0.642717 | 0.321358 | − | 0.946958i | \(-0.395861\pi\) | ||||
0.321358 | + | 0.946958i | \(0.395861\pi\) | |||||||
\(278\) | −4.72474 | + | 8.18350i | −0.283371 | + | 0.490814i | ||||
\(279\) | 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 | 0.380305 | + | 0.924861i | \(0.375819\pi\) |
−0.991106 | + | 0.133077i | \(0.957514\pi\) | |||||||
\(284\) | 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 | ||||||||
\(289\) | 6.50000 | − | 11.2583i | 0.382353 | − | 0.662255i | ||||
\(290\) | 10.0000 | 0.587220 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.89898 | −0.169650 | ||||||||
\(293\) | −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 | ||||
\(296\) | −3.89898 | + | 6.75323i | −0.226624 | + | 0.392524i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.00000 | + | 5.19615i | 0.173785 | + | 0.301005i | ||||
\(299\) | −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 | ||||||||
\(304\) | −7.44949 | −0.427258 | ||||||||
\(305\) | 19.7474 | + | 34.2036i | 1.13074 | + | 1.95849i | ||||
\(306\) | 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 | ||||||||
\(310\) | 20.6969 | 1.17551 | ||||||||
\(311\) | −0.651531 | + | 1.12848i | −0.0369449 | + | 0.0639905i | −0.883907 | − | 0.467663i | \(-0.845096\pi\) |
0.846962 | + | 0.531654i | \(0.178429\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.3485 | + | 21.3882i | 0.697977 | + | 1.20893i | 0.969167 | + | 0.246405i | \(0.0792495\pi\) |
−0.271190 | + | 0.962526i | \(0.587417\pi\) | |||||||
\(314\) | 6.34847 | 0.358265 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.89898 | 0.444352 | ||||||||
\(317\) | −4.34847 | − | 7.53177i | −0.244234 | − | 0.423026i | 0.717682 | − | 0.696371i | \(-0.245203\pi\) |
−0.961916 | + | 0.273345i | \(0.911870\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.89898 | + | 5.02118i | −0.162312 | + | 0.281132i | ||||
\(320\) | 3.44949 | 0.192832 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.8990 | −0.829001 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.8990 | − | 29.2699i | −0.937387 | − | 1.62360i | ||||
\(326\) | 0.202041 | 0.0111900 | ||||||||
\(327\) | 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 | 0.975363 | + | 0.220608i | \(0.0708041\pi\) |
−0.296629 | + | 0.954993i | \(0.595863\pi\) | |||||||
\(332\) | −1.00000 | − | 1.73205i | −0.0548821 | − | 0.0950586i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 9.34847 | − | 16.1920i | 0.511525 | − | 0.885988i | ||||
\(335\) | 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 | \(-0.581013\pi\) | |||||||
\(338\) | −11.0000 | −0.598321 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.89898 | 0.374150 | ||||||||
\(341\) | −6.00000 | + | 10.3923i | −0.324918 | + | 0.562775i | ||||
\(342\) | 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 | 0.473560 | + | 0.880762i | \(0.342969\pi\) |
−0.999542 | + | 0.0302659i | \(0.990365\pi\) | |||||||
\(348\) | 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 | ||||||||
\(352\) | −1.00000 | + | 1.73205i | −0.0533002 | + | 0.0923186i | ||||
\(353\) | −6.00000 | −0.319348 | −0.159674 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159674 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −34.1464 | −1.81230 | ||||||||
\(356\) | 3.55051 | + | 6.14966i | 0.188177 | + | 0.325932i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4.34847 | − | 7.53177i | 0.229824 | − | 0.398066i | ||||
\(359\) | 5.39898 | − | 9.35131i | 0.284947 | − | 0.493543i | −0.687649 | − | 0.726043i | \(-0.741357\pi\) |
0.972596 | + | 0.232500i | \(0.0746906\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2474 | − | 31.6055i | −0.960392 | − | 1.66345i | ||||
\(362\) | −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 | ||||||||
\(367\) | −5.79796 | −0.302651 | −0.151325 | − | 0.988484i | \(-0.548354\pi\) | ||||
−0.151325 | + | 0.988484i | \(0.548354\pi\) | |||||||
\(368\) | −0.500000 | − | 0.866025i | −0.0260643 | − | 0.0451447i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 26.8990 | 1.39841 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.89898 | 0.150103 | 0.0750517 | − | 0.997180i | \(-0.476088\pi\) | ||||
0.0750517 | + | 0.997180i | \(0.476088\pi\) | |||||||
\(374\) | −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 | ||||
\(383\) | 6.89898 | 0.352521 | 0.176261 | − | 0.984344i | \(-0.443600\pi\) | ||||
0.176261 | + | 0.984344i | \(0.443600\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.10102 | 0.412331 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.44949 | − | 5.97469i | −0.175121 | − | 0.303319i | ||||
\(389\) | 15.1010 | 0.765652 | 0.382826 | − | 0.923820i | \(-0.374951\pi\) | ||||
0.382826 | + | 0.923820i | \(0.374951\pi\) | |||||||
\(390\) | 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 | ||||
\(395\) | −13.6237 | − | 23.5970i | −0.685484 | − | 1.18729i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.65153 | − | 8.05669i | 0.233454 | − | 0.404354i | −0.725369 | − | 0.688361i | \(-0.758331\pi\) |
0.958822 | + | 0.284007i | \(0.0916640\pi\) | |||||||
\(398\) | −3.44949 | + | 5.97469i | −0.172907 | + | 0.299484i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.44949 | − | 5.97469i | −0.172474 | − | 0.298735i | ||||
\(401\) | 10.1010 | 0.504421 | 0.252210 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252210 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.3939 | −1.46421 | ||||||||
\(404\) | −3.62372 | + | 6.27647i | −0.180287 | + | 0.312266i | ||||
\(405\) | 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 | −0.785409 | − | 0.618977i | \(-0.787547\pi\) |
0.928754 | + | 0.370696i | \(0.120881\pi\) | |||||||
\(410\) | −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 | ||||||||
\(415\) | −3.44949 | + | 5.97469i | −0.169329 | + | 0.293286i | ||||
\(416\) | −4.89898 | −0.240192 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −14.8990 | −0.728733 | ||||||||
\(419\) | −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 | \(0.270098\pi\) | |||||||
\(422\) | 1.55051 | − | 2.68556i | 0.0754777 | − | 0.130731i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0.550510 | + | 0.953512i | 0.0267351 | + | 0.0463066i | ||||
\(425\) | −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 | ||||||||
\(430\) | 10.0000 | 0.482243 | ||||||||
\(431\) | −3.79796 | − | 6.57826i | −0.182941 | − | 0.316864i | 0.759940 | − | 0.649994i | \(-0.225228\pi\) |
−0.942881 | + | 0.333130i | \(0.891895\pi\) | |||||||
\(432\) | 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 | ||||||||
\(436\) | −16.6969 | −0.799638 | ||||||||
\(437\) | 3.72474 | − | 6.45145i | 0.178179 | − | 0.308615i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.8990 | + | 18.8776i | 0.520180 | + | 0.900978i | 0.999725 | + | 0.0234607i | \(0.00746845\pi\) |
−0.479545 | + | 0.877517i | \(0.659198\pi\) | |||||||
\(440\) | 6.89898 | 0.328896 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −9.79796 | −0.466041 | ||||||||
\(443\) | −2.55051 | − | 4.41761i | −0.121178 | − | 0.209887i | 0.799054 | − | 0.601259i | \(-0.205334\pi\) |
−0.920233 | + | 0.391372i | \(0.872001\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.2474 | − | 21.2132i | 0.580585 | − | 1.00560i | ||||
\(446\) | −20.8990 | −0.989595 | ||||||||
\(447\) | 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 | ||||||||
\(451\) | −9.79796 | − | 16.9706i | −0.461368 | − | 0.799113i | ||||
\(452\) | 15.8990 | 0.747825 | ||||||||
\(453\) | 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 | −0.954002 | − | 0.299799i | \(-0.903080\pi\) |
0.217368 | − | 0.976090i | \(-0.430253\pi\) | |||||||
\(458\) | 11.6237 | + | 20.1329i | 0.543141 | + | 0.940748i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −1.72474 | + | 2.98735i | −0.0804166 | + | 0.139286i | ||||
\(461\) | −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 | \(0.629645\pi\) | |||||||
\(464\) | −2.89898 | −0.134582 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.00000 | −0.324269 | ||||||||
\(467\) | −5.00000 | + | 8.66025i | −0.231372 | + | 0.400749i | −0.958212 | − | 0.286058i | \(-0.907655\pi\) |
0.726840 | + | 0.686807i | \(0.240988\pi\) | |||||||
\(468\) | 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 | ||||||||
\(478\) | 6.39898 | − | 11.0834i | 0.292683 | − | 0.506941i | ||||
\(479\) | −29.5959 | −1.35227 | −0.676136 | − | 0.736777i | \(-0.736347\pi\) | ||||
−0.676136 | + | 0.736777i | \(0.736347\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −38.2020 | −1.74186 | ||||||||
\(482\) | 4.44949 | + | 7.70674i | 0.202669 | + | 0.351032i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.50000 | − | 6.06218i | 0.159091 | − | 0.275554i | ||||
\(485\) | −11.8990 | + | 20.6096i | −0.540305 | + | 0.935835i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.1969 | − | 19.3937i | −0.507382 | − | 0.878811i | −0.999963 | − | 0.00854475i | \(-0.997280\pi\) |
0.492582 | − | 0.870266i | \(-0.336053\pi\) | |||||||
\(488\) | −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 | ||||||||
\(493\) | −5.79796 | −0.261127 | ||||||||
\(494\) | −18.2474 | − | 31.6055i | −0.820992 | − | 1.42200i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.00000 | −0.269408 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.3939 | 1.49492 | 0.747458 | − | 0.664309i | \(-0.231274\pi\) | ||||
0.747458 | + | 0.664309i | \(0.231274\pi\) | |||||||
\(500\) | −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 | ||||
\(509\) | −16.8990 | −0.749034 | −0.374517 | − | 0.927220i | \(-0.622191\pi\) | ||||
−0.374517 | + | 0.927220i | \(0.622191\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.8990 | + | 24.0737i | 0.613058 | + | 1.06185i | ||||
\(515\) | −48.2929 | −2.12804 | ||||||||
\(516\) | 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 | ||||
\(521\) | 19.3485 | + | 33.5125i | 0.847672 | + | 1.46821i | 0.883281 | + | 0.468845i | \(0.155330\pi\) |
−0.0356087 | + | 0.999366i | \(0.511337\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.174235 | − | 0.301783i | 0.00761875 | − | 0.0131961i | −0.862191 | − | 0.506584i | \(-0.830908\pi\) |
0.869810 | + | 0.493387i | \(0.164242\pi\) | |||||||
\(524\) | 6.72474 | − | 11.6476i | 0.293772 | − | 0.508828i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.05051 | − | 13.9439i | −0.351019 | − | 0.607983i | ||||
\(527\) | −12.0000 | −0.522728 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 1.89898 | − | 3.28913i | 0.0824864 | − | 0.142871i | ||||
\(531\) | 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 | ||||||||
\(541\) | −15.2474 | + | 26.4094i | −0.655539 | + | 1.13543i | 0.326219 | + | 0.945294i | \(0.394225\pi\) |
−0.981758 | + | 0.190133i | \(0.939108\pi\) | |||||||
\(542\) | 16.8990 | 0.725873 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.00000 | −0.0857493 | ||||||||
\(545\) | 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 | \(0.930607\pi\) | |||||||
\(548\) | −5.89898 | + | 10.2173i | −0.251992 | + | 0.436463i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.89898 | − | 11.9494i | −0.294173 | − | 0.509523i | ||||
\(551\) | −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 | ||||||||
\(556\) | −9.44949 | −0.400748 | ||||||||
\(557\) | −1.55051 | − | 2.68556i | −0.0656972 | − | 0.113791i | 0.831306 | − | 0.555815i | \(-0.187594\pi\) |
−0.897003 | + | 0.442024i | \(0.854260\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.2020 | −0.600682 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −19.0000 | −0.801467 | ||||||||
\(563\) | −6.97219 | + | 12.0762i | −0.293843 | + | 0.508951i | −0.974715 | − | 0.223451i | \(-0.928268\pi\) |
0.680872 | + | 0.732402i | \(0.261601\pi\) | |||||||
\(564\) | 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 | −0.987786 | − | 0.155815i | \(-0.950200\pi\) |
0.358954 | − | 0.933355i | \(-0.383134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.10102 | + | 12.2993i | −0.297168 | + | 0.514711i | −0.975487 | − | 0.220057i | \(-0.929376\pi\) |
0.678319 | + | 0.734768i | \(0.262709\pi\) | |||||||
\(572\) | −9.79796 | −0.409673 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.89898 | 0.287707 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.7980 | + | 20.4347i | 0.491155 | + | 0.850706i | 0.999948 | − | 0.0101829i | \(-0.00324136\pi\) |
−0.508793 | + | 0.860889i | \(0.669908\pi\) | |||||||
\(578\) | 13.0000 | 0.540729 | ||||||||
\(579\) | 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 | ||||
\(584\) | −1.44949 | − | 2.51059i | −0.0599803 | − | 0.103889i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 13.6237 | − | 23.5970i | 0.562791 | − | 0.974782i | ||||
\(587\) | 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 | ||||
\(590\) | 6.89898 | 0.284026 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −7.79796 | −0.320494 | ||||||||
\(593\) | 7.34847 | − | 12.7279i | 0.301765 | − | 0.522673i | −0.674770 | − | 0.738028i | \(-0.735757\pi\) |
0.976536 | + | 0.215355i | \(0.0690907\pi\) | |||||||
\(594\) | 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 | −0.973843 | − | 0.227224i | \(-0.927035\pi\) |
0.683703 | + | 0.729761i | \(0.260368\pi\) | |||||||
\(600\) | 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 | ||||||||
\(604\) | 2.50000 | − | 4.33013i | 0.101724 | − | 0.176190i | ||||
\(605\) | −24.1464 | −0.981692 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.69694 | 0.352998 | 0.176499 | − | 0.984301i | \(-0.443523\pi\) | ||||
0.176499 | + | 0.984301i | \(0.443523\pi\) | |||||||
\(608\) | −3.72474 | − | 6.45145i | −0.151058 | − | 0.261641i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −19.7474 | + | 34.2036i | −0.799551 | + | 1.38486i | ||||
\(611\) | 24.0000 | − | 41.5692i | 0.970936 | − | 1.68171i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.34847 | − | 12.7279i | −0.296802 | − | 0.514076i | 0.678601 | − | 0.734508i | \(-0.262587\pi\) |
−0.975402 | + | 0.220432i | \(0.929253\pi\) | |||||||
\(614\) | −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 | ||||||||
\(619\) | 4.14643 | 0.166659 | 0.0833295 | − | 0.996522i | \(-0.473445\pi\) | ||||
0.0833295 | + | 0.996522i | \(0.473445\pi\) | |||||||
\(620\) | 10.3485 | + | 17.9241i | 0.415605 | + | 0.719848i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.30306 | −0.0522480 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.8990 | −0.475959 | ||||||||
\(626\) | −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 | ||||
\(635\) | −10.3485 | −0.410666 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.79796 | −0.229543 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.72474 | + | 2.98735i | 0.0681765 | + | 0.118085i | ||||
\(641\) | −41.4949 | −1.63895 | −0.819475 | − | 0.573115i | \(-0.805735\pi\) | ||||
−0.819475 | + | 0.573115i | \(0.805735\pi\) | |||||||
\(642\) | 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 | ||||
\(647\) | 10.6515 | + | 18.4490i | 0.418755 | + | 0.725305i | 0.995815 | − | 0.0913973i | \(-0.0291333\pi\) |
−0.577060 | + | 0.816702i | \(0.695800\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.00000 | + | 3.46410i | −0.0785069 | + | 0.135978i | ||||
\(650\) | 16.8990 | − | 29.2699i | 0.662833 | − | 1.14806i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0.101021 | + | 0.174973i | 0.00395627 | + | 0.00685246i | ||||
\(653\) | 9.79796 | 0.383424 | 0.191712 | − | 0.981451i | \(-0.438596\pi\) | ||||
0.191712 | + | 0.981451i | \(0.438596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −46.3939 | −1.81276 | ||||||||
\(656\) | 4.89898 | − | 8.48528i | 0.191273 | − | 0.331295i | ||||
\(657\) | 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 | −0.759391 | − | 0.650635i | \(-0.774503\pi\) |
0.943162 | + | 0.332334i | \(0.107836\pi\) | |||||||
\(662\) | −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 | ||||||||
\(667\) | 1.44949 | − | 2.51059i | 0.0561245 | − | 0.0972104i | ||||
\(668\) | 18.6969 | 0.723406 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.6969 | 0.413259 | ||||||||
\(671\) | −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 | \(0.965915\pi\) | |||||||
\(674\) | 17.6969 | − | 30.6520i | 0.681661 | − | 1.18067i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.50000 | − | 9.52628i | −0.211538 | − | 0.366395i | ||||
\(677\) | 7.34847 | + | 12.7279i | 0.282425 | + | 0.489174i | 0.971981 | − | 0.235058i | \(-0.0755280\pi\) |
−0.689557 | + | 0.724232i | \(0.742195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 3.44949 | + | 5.97469i | 0.132282 | + | 0.229119i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.0000 | −0.459504 | ||||||||
\(683\) | 16.1010 | + | 27.8878i | 0.616088 | + | 1.06710i | 0.990193 | + | 0.139710i | \(0.0446169\pi\) |
−0.374104 | + | 0.927387i | \(0.622050\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 40.6969 | 1.55495 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.89898 | −0.110523 | ||||||||
\(689\) | −2.69694 | + | 4.67123i | −0.102745 | + | 0.177960i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.47730 | + | 6.02285i | 0.132283 | + | 0.229120i | 0.924556 | − | 0.381046i | \(-0.124436\pi\) |
−0.792274 | + | 0.610166i | \(0.791103\pi\) | |||||||
\(692\) | −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 | ||||
\(698\) | 20.8990 | 0.791038 | ||||||||
\(699\) | 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 | ||||||||
\(703\) | −29.0454 | − | 50.3081i | −1.09547 | − | 1.89741i | ||||
\(704\) | −2.00000 | −0.0753778 | ||||||||
\(705\) | 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 | 0.954119 | − | 0.299428i | \(-0.0967959\pi\) |
−0.736372 | + | 0.676577i | \(0.763463\pi\) | |||||||
\(710\) | −17.0732 | − | 29.5717i | −0.640746 | − | 1.10981i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −3.55051 | + | 6.14966i | −0.133061 | + | 0.230468i | ||||
\(713\) | 3.00000 | − | 5.19615i | 0.112351 | − | 0.194597i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.8990 | + | 29.2699i | 0.631986 | + | 1.09463i | ||||
\(716\) | 8.69694 | 0.325020 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.7980 | 0.402976 | ||||||||
\(719\) | 4.89898 | − | 8.48528i | 0.182701 | − | 0.316448i | −0.760098 | − | 0.649808i | \(-0.774849\pi\) |
0.942799 | + | 0.333360i | \(0.108183\pi\) | |||||||
\(720\) | 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 | ||||||||
\(730\) | −5.00000 | + | 8.66025i | −0.185058 | + | 0.320530i | ||||
\(731\) | −5.79796 | −0.214445 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.5505 | 0.463564 | 0.231782 | − | 0.972768i | \(-0.425544\pi\) | ||||
0.231782 | + | 0.972768i | \(0.425544\pi\) | |||||||
\(734\) | −2.89898 | − | 5.02118i | −0.107003 | − | 0.185335i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.500000 | − | 0.866025i | 0.0184302 | − | 0.0319221i | ||||
\(737\) | −3.10102 | + | 5.37113i | −0.114228 | + | 0.197848i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.7980 | + | 22.1667i | 0.470781 | + | 0.815416i | 0.999441 | − | 0.0334173i | \(-0.0106390\pi\) |
−0.528661 | + | 0.848833i | \(0.677306\pi\) | |||||||
\(740\) | 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 | ||||||||
\(745\) | 20.6969 | 0.758277 | ||||||||
\(746\) | 1.44949 | + | 2.51059i | 0.0530696 | + | 0.0919192i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.00000 | −0.146254 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.5959 | 1.48137 | 0.740683 | − | 0.671855i | \(-0.234502\pi\) | ||||
0.740683 | + | 0.671855i | \(0.234502\pi\) | |||||||
\(752\) | 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 | ||||
\(761\) | 2.00000 | 0.0724999 | 0.0362500 | − | 0.999343i | \(-0.488459\pi\) | ||||
0.0362500 | + | 0.999343i | \(0.488459\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.8990 | −0.502847 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.44949 | + | 5.97469i | 0.124635 | + | 0.215874i | ||||
\(767\) | −9.79796 | −0.353784 | ||||||||
\(768\) | 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 | ||||
\(773\) | 9.97219 | + | 17.2723i | 0.358675 | + | 0.621243i | 0.987740 | − | 0.156110i | \(-0.0498953\pi\) |
−0.629065 | + | 0.777353i | \(0.716562\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 20.6969 | − | 35.8481i | 0.743456 | − | 1.28770i | ||||
\(776\) | 3.44949 | − | 5.97469i | 0.123829 | − | 0.214479i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 7.55051 | + | 13.0779i | 0.270699 | + | 0.468864i | ||||
\(779\) | 72.9898 | 2.61513 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.7980 | 0.708427 | ||||||||
\(782\) | 1.00000 | − | 1.73205i | 0.0357599 | − | 0.0619380i | ||||
\(783\) | 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 | −0.0411728 | − | 0.999152i | \(-0.513109\pi\) |
0.885877 | − | 0.463919i | \(-0.153557\pi\) | |||||||
\(788\) | −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 | ||||||||
\(793\) | 28.0454 | − | 48.5761i | 0.995922 | − | 1.72499i | ||||
\(794\) | 9.30306 | 0.330153 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.89898 | −0.244528 | ||||||||
\(797\) | −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 | ||||
\(800\) | 3.44949 | − | 5.97469i | 0.121958 | − | 0.211237i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.05051 | + | 8.74774i | 0.178340 | + | 0.308893i | ||||
\(803\) | −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 | ||||||||
\(808\) | −7.24745 | −0.254964 | ||||||||
\(809\) | −17.8990 | − | 31.0019i | −0.629295 | − | 1.08997i | −0.987694 | − | 0.156402i | \(-0.950011\pi\) |
0.358399 | − | 0.933569i | \(-0.383323\pi\) | |||||||
\(810\) | 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 | ||||||||
\(814\) | −15.5959 | −0.546637 | ||||||||
\(815\) | 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 | 0.971526 | + | 0.236934i | \(0.0761424\pi\) |
−0.280572 | + | 0.959833i | \(0.590524\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.6969 | + | 39.3123i | −0.791166 | + | 1.37034i | 0.134080 | + | 0.990970i | \(0.457192\pi\) |
−0.925246 | + | 0.379368i | \(0.876141\pi\) | |||||||
\(824\) | 14.0000 | 0.487713 | ||||||||
\(825\) | 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 | ||||||||
\(829\) | 15.3485 | + | 26.5843i | 0.533074 | + | 0.923312i | 0.999254 | + | 0.0386218i | \(0.0122967\pi\) |
−0.466180 | + | 0.884690i | \(0.654370\pi\) | |||||||
\(830\) | −6.89898 | −0.239467 | ||||||||
\(831\) | 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 | ||||
\(836\) | −7.44949 | − | 12.9029i | −0.257646 | − | 0.446256i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.2753 | − | 21.2614i | 0.424042 | − | 0.734462i | ||||
\(839\) | 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 | ||||
\(842\) | −13.1010 | −0.451491 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.10102 | 0.106742 | ||||||||
\(845\) | −18.9722 | + | 32.8608i | −0.652663 | + | 1.13045i | ||||
\(846\) | 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 | ||||||||
\(856\) | 6.00000 | − | 10.3923i | 0.205076 | − | 0.355202i | ||||
\(857\) | −25.1010 | −0.857435 | −0.428717 | − | 0.903439i | \(-0.641034\pi\) | ||||
−0.428717 | + | 0.903439i | \(0.641034\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.0000 | 0.341196 | 0.170598 | − | 0.985341i | \(-0.445430\pi\) | ||||
0.170598 | + | 0.985341i | \(0.445430\pi\) | |||||||
\(860\) | 5.00000 | + | 8.66025i | 0.170499 | + | 0.295312i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.79796 | − | 6.57826i | 0.129359 | − | 0.224056i | ||||
\(863\) | 1.05051 | − | 1.81954i | 0.0357598 | − | 0.0619378i | −0.847592 | − | 0.530649i | \(-0.821948\pi\) |
0.883351 | + | 0.468711i | \(0.155282\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 22.2474 | + | 38.5337i | 0.756436 | + | 1.31019i | ||||
\(866\) | −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 | ||||||||
\(871\) | −15.1918 | −0.514756 | ||||||||
\(872\) | −8.34847 | − | 14.4600i | −0.282715 | − | 0.489676i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.44949 | 0.251983 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.4949 | −0.894669 | −0.447335 | − | 0.894367i | \(-0.647627\pi\) | ||||
−0.447335 | + | 0.894367i | \(0.647627\pi\) | |||||||
\(878\) | −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 | ||||
\(887\) | −33.7980 | −1.13482 | −0.567412 | − | 0.823434i | \(-0.692055\pi\) | ||||
−0.567412 | + | 0.823434i | \(0.692055\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.4949 | 0.821071 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −10.4495 | − | 18.0990i | −0.349875 | − | 0.606001i | ||||
\(893\) | 72.9898 | 2.44251 | ||||||||
\(894\) | 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 | ||||
\(899\) | −8.69694 | − | 15.0635i | −0.290059 | − | 0.502397i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.10102 | + | 1.90702i | −0.0366803 | + | 0.0635322i | ||||
\(902\) | 9.79796 | − | 16.9706i | 0.326236 | − | 0.565058i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 7.94949 | + | 13.7689i | 0.264396 | + | 0.457947i | ||||
\(905\) | −15.0000 | −0.498617 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.6969 | −0.886457 | −0.443229 | − | 0.896409i | \(-0.646167\pi\) | ||||
−0.443229 | + | 0.896409i | \(0.646167\pi\) | |||||||
\(908\) | 0.275255 | − | 0.476756i | 0.00913466 | − | 0.0158217i | ||||
\(909\) | 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 | ||||||||
\(919\) | −1.84847 | + | 3.20164i | −0.0609754 | + | 0.105612i | −0.894902 | − | 0.446263i | \(-0.852754\pi\) |
0.833926 | + | 0.551876i | \(0.186088\pi\) | |||||||
\(920\) | −3.44949 | −0.113726 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −20.3485 | −0.670141 | ||||||||
\(923\) | 24.2474 | + | 41.9978i | 0.798114 | + | 1.38237i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26.8990 | − | 46.5904i | 0.884433 | − | 1.53188i | ||||
\(926\) | −12.8485 | + | 22.2542i | −0.422227 | + | 0.731318i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.44949 | − | 2.51059i | −0.0475818 | − | 0.0824142i | ||||
\(929\) | 17.1464 | + | 29.6985i | 0.562556 | + | 0.974376i | 0.997272 | + | 0.0738083i | \(0.0235153\pi\) |
−0.434716 | + | 0.900567i | \(0.643151\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −3.50000 | − | 6.06218i | −0.114646 | − | 0.198573i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −10.0000 | −0.327210 | ||||||||
\(935\) | 6.89898 | + | 11.9494i | 0.225621 | + | 0.390787i | ||||
\(936\) | 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 | ||||||||
\(940\) | −33.7980 | −1.10237 | ||||||||
\(941\) | −1.72474 | + | 2.98735i | −0.0562251 | + | 0.0973847i | −0.892768 | − | 0.450517i | \(-0.851240\pi\) |
0.836543 | + | 0.547901i | \(0.184573\pi\) | |||||||
\(942\) | 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 | 0.893095 | − | 0.449868i | \(-0.148529\pi\) |
−0.836145 | + | 0.548509i | \(0.815196\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.10102 | − | 12.2993i | 0.230509 | − | 0.399253i | ||||
\(950\) | 51.3939 | 1.66744 | ||||||||
\(951\) | 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 | ||||||||
\(955\) | 23.9722 | + | 41.5211i | 0.775722 | + | 1.34359i | ||||
\(956\) | 12.7980 | 0.413916 | ||||||||
\(957\) | 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 | ||||
\(962\) | −19.1010 | − | 33.0839i | −0.615842 | − | 1.06667i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.44949 | + | 7.70674i | −0.143308 | + | 0.248217i | ||||
\(965\) | 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 | \(0.757927\pi\) | |||||||
\(968\) | 7.00000 | 0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.7980 | −0.764106 | ||||||||
\(971\) | 26.9722 | − | 46.7172i | 0.865579 | − | 1.49923i | −0.000892350 | − | 1.00000i | \(-0.500284\pi\) |
0.866471 | − | 0.499227i | \(-0.166383\pi\) | |||||||
\(972\) | 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 | −0.852979 | − | 0.521946i | \(-0.825206\pi\) |
0.878508 | + | 0.477728i | \(0.158540\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.10102 | + | 12.2993i | −0.226950 | + | 0.393088i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.89898 | − | 3.28913i | 0.0605989 | − | 0.104960i | ||||
\(983\) | 45.1918 | 1.44140 | 0.720698 | − | 0.693249i | \(-0.243822\pi\) | ||||
0.720698 | + | 0.693249i | \(0.243822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 43.7980 | 1.39552 | ||||||||
\(986\) | −2.89898 | − | 5.02118i | −0.0923223 | − | 0.159907i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18.2474 | − | 31.6055i | 0.580529 | − | 1.00551i | ||||
\(989\) | 1.44949 | − | 2.51059i | 0.0460911 | − | 0.0798321i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.89898 | − | 15.4135i | −0.282685 | − | 0.489625i | 0.689360 | − | 0.724419i | \(-0.257892\pi\) |
−0.972045 | + | 0.234794i | \(0.924559\pi\) | |||||||
\(992\) | −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 | ||||||||
\(997\) | −17.8536 | −0.565428 | −0.282714 | − | 0.959204i | \(-0.591235\pi\) | ||||
−0.282714 | + | 0.959204i | \(0.591235\pi\) | |||||||
\(998\) | 16.6969 | + | 28.9199i | 0.528532 | + | 0.915445i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))