Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [672,2,Mod(575,672)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(672, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("672.575");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 672 = 2^{5} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 672.h (of order \(2\), degree \(1\), 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: | \(5.36594701583\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 575.2 | ||
Root | \(-0.707107 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 672.575 |
Dual form | 672.2.h.d.575.1 |
$q$-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 \(\left(\mathbb{Z}/672\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(421\) | \(449\) | \(577\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.292893 | + | 1.70711i | 0.169102 | + | 0.985599i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.41421i | 1.52688i | 0.645877 | + | 0.763441i | \(0.276492\pi\) | ||||
−0.645877 | + | 0.763441i | \(0.723508\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | + | 1.00000i | −0.942809 | + | 0.333333i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.41421 | 0.946932 | 0.473466 | − | 0.880812i | \(-0.343003\pi\) | ||||
0.473466 | + | 0.880812i | \(0.343003\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.82843 | + | 1.00000i | −1.50489 | + | 0.258199i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.82843i | 1.17107i | 0.810649 | + | 0.585533i | \(0.199115\pi\) | ||||
−0.810649 | + | 0.585533i | \(0.800885\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.24264i | − | 1.43216i | −0.698018 | − | 0.716080i | \(-0.745935\pi\) | ||
0.698018 | − | 0.716080i | \(-0.254065\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.70711 | + | 0.292893i | −0.372521 | + | 0.0639145i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.00000 | −0.834058 | −0.417029 | − | 0.908893i | \(-0.636929\pi\) | ||||
−0.417029 | + | 0.908893i | \(0.636929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.65685 | −1.33137 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.53553 | − | 4.53553i | −0.487964 | − | 0.872864i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.82843i | 0.896616i | 0.893879 | + | 0.448308i | \(0.147973\pi\) | ||||
−0.893879 | + | 0.448308i | \(0.852027\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.17157i | 0.210421i | 0.994450 | + | 0.105210i | \(0.0335516\pi\) | ||||
−0.994450 | + | 0.105210i | \(0.966448\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.585786 | + | 3.41421i | 0.101972 | + | 0.594338i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.41421 | −0.577107 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.828427 | −0.136193 | −0.0680963 | − | 0.997679i | \(-0.521693\pi\) | ||||
−0.0680963 | + | 0.997679i | \(0.521693\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.00000 | + | 5.82843i | 0.160128 | + | 0.933295i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.0000i | − | 1.56174i | −0.624695 | − | 0.780869i | \(-0.714777\pi\) | ||
0.624695 | − | 0.780869i | \(-0.285223\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.4853i | − | 1.59899i | −0.600672 | − | 0.799495i | \(-0.705100\pi\) | ||
0.600672 | − | 0.799495i | \(-0.294900\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −3.41421 | − | 9.65685i | −0.508961 | − | 1.43956i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.65685 | 0.241677 | 0.120839 | − | 0.992672i | \(-0.461442\pi\) | ||||
0.120839 | + | 0.992672i | \(0.461442\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.24264 | + | 1.41421i | −1.15420 | + | 0.198030i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.3137i | 1.82878i | 0.404836 | + | 0.914389i | \(0.367329\pi\) | ||||
−0.404836 | + | 0.914389i | \(0.632671\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 6.82843i | 0.920745i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 10.6569 | − | 1.82843i | 1.41153 | − | 0.242181i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.24264 | −0.812723 | −0.406361 | − | 0.913712i | \(-0.633203\pi\) | ||||
−0.406361 | + | 0.913712i | \(0.633203\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14.2426 | 1.82358 | 0.911792 | − | 0.410653i | \(-0.134699\pi\) | ||||
0.911792 | + | 0.410653i | \(0.134699\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.00000 | − | 2.82843i | −0.125988 | − | 0.356348i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.6569i | 1.44585i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.31371i | 1.13785i | 0.822389 | + | 0.568925i | \(0.192641\pi\) | ||||
−0.822389 | + | 0.568925i | \(0.807359\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.17157 | − | 6.82843i | −0.141041 | − | 0.822046i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −0.343146 | −0.0407239 | −0.0203620 | − | 0.999793i | \(-0.506482\pi\) | ||||
−0.0203620 | + | 0.999793i | \(0.506482\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.17157 | −0.371205 | −0.185602 | − | 0.982625i | \(-0.559424\pi\) | ||||
−0.185602 | + | 0.982625i | \(0.559424\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.94975 | − | 11.3640i | −0.225137 | − | 1.31220i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.00000i | 0.450035i | 0.974355 | + | 0.225018i | \(0.0722440\pi\) | ||||
−0.974355 | + | 0.225018i | \(0.927756\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.00000 | − | 5.65685i | 0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 11.4142 | 1.25287 | 0.626436 | − | 0.779473i | \(-0.284513\pi\) | ||||
0.626436 | + | 0.779473i | \(0.284513\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −16.4853 | −1.78808 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −8.24264 | + | 1.41421i | −0.883704 | + | 0.151620i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.65685i | 0.811625i | 0.913956 | + | 0.405812i | \(0.133011\pi\) | ||||
−0.913956 | + | 0.405812i | \(0.866989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.41421i | 0.357907i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.00000 | + | 0.343146i | −0.207390 | + | 0.0355826i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.3137 | 2.18674 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.31371 | 0.539525 | 0.269763 | − | 0.962927i | \(-0.413055\pi\) | ||||
0.269763 | + | 0.962927i | \(0.413055\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.65685 | + | 2.00000i | −0.568535 | + | 0.201008i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 18.2426i | − | 1.81521i | −0.419825 | − | 0.907605i | \(-0.637908\pi\) | ||
0.419825 | − | 0.907605i | \(-0.362092\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.9706i | 1.67216i | 0.548608 | + | 0.836080i | \(0.315158\pi\) | ||||
−0.548608 | + | 0.836080i | \(0.684842\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.00000 | − | 5.82843i | −0.0975900 | − | 0.568796i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.4853 | 1.40035 | 0.700173 | − | 0.713974i | \(-0.253106\pi\) | ||||
0.700173 | + | 0.713974i | \(0.253106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.48528 | −0.238047 | −0.119023 | − | 0.992891i | \(-0.537976\pi\) | ||||
−0.119023 | + | 0.992891i | \(0.537976\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.242641 | − | 1.41421i | −0.0230304 | − | 0.134231i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 5.31371i | − | 0.499872i | −0.968262 | − | 0.249936i | \(-0.919590\pi\) | ||
0.968262 | − | 0.249936i | \(-0.0804095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 13.6569i | − | 1.27351i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −9.65685 | + | 3.41421i | −0.892776 | + | 0.315644i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.82843 | −0.442621 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 17.0711 | − | 2.92893i | 1.53925 | − | 0.264093i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.65685i | − | 0.505964i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 2.00000i | − | 0.177471i | −0.996055 | − | 0.0887357i | \(-0.971717\pi\) | ||
0.996055 | − | 0.0887357i | \(-0.0282826\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 17.8995 | − | 3.07107i | 1.57596 | − | 0.270392i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21.5563 | 1.88339 | 0.941693 | − | 0.336472i | \(-0.109234\pi\) | ||||
0.941693 | + | 0.336472i | \(0.109234\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.24264 | 0.541306 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 15.4853 | − | 8.65685i | 1.33276 | − | 0.745063i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 11.3137i | 0.966595i | 0.875456 | + | 0.483298i | \(0.160561\pi\) | ||||
−0.875456 | + | 0.483298i | \(0.839439\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.75736i | 0.149057i | 0.997219 | + | 0.0745286i | \(0.0237452\pi\) | ||||
−0.997219 | + | 0.0745286i | \(0.976255\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.485281 | + | 2.82843i | 0.0408681 | + | 0.238197i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.82843 | 0.571022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.4853 | −1.36903 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.292893 | − | 1.70711i | −0.0241574 | − | 0.140800i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.65685i | 0.627274i | 0.949543 | + | 0.313637i | \(0.101547\pi\) | ||||
−0.949543 | + | 0.313637i | \(0.898453\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 18.0000i | − | 1.46482i | −0.680864 | − | 0.732410i | \(-0.738396\pi\) | ||
0.680864 | − | 0.732410i | \(-0.261604\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.82843 | − | 13.6569i | −0.390355 | − | 1.10409i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.00000 | −0.321288 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.24264 | 0.178982 | 0.0894911 | − | 0.995988i | \(-0.471476\pi\) | ||||
0.0894911 | + | 0.995988i | \(0.471476\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.7279 | + | 3.89949i | −1.80244 | + | 0.309250i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 4.00000i | − | 0.315244i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.14214i | 0.637741i | 0.947798 | + | 0.318871i | \(0.103304\pi\) | ||||
−0.947798 | + | 0.318871i | \(0.896696\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −11.6569 | + | 2.00000i | −0.907485 | + | 0.155700i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.8284 | −0.837929 | −0.418964 | − | 0.908003i | \(-0.637607\pi\) | ||||
−0.418964 | + | 0.908003i | \(0.637607\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.34315 | −0.103319 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.24264 | + | 17.6569i | 0.477387 | + | 1.35025i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 9.55635i | − | 0.726556i | −0.931681 | − | 0.363278i | \(-0.881658\pi\) | ||
0.931681 | − | 0.363278i | \(-0.118342\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6.65685i | − | 0.503211i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.82843 | − | 10.6569i | −0.137433 | − | 0.801018i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 6.48528 | 0.484733 | 0.242366 | − | 0.970185i | \(-0.422076\pi\) | ||||
0.242366 | + | 0.970185i | \(0.422076\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.3848 | 1.51519 | 0.757594 | − | 0.652726i | \(-0.226375\pi\) | ||||
0.757594 | + | 0.652726i | \(0.226375\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.17157 | + | 24.3137i | 0.308372 | + | 1.79732i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 2.82843i | − | 0.207950i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.65685i | 0.706179i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 4.53553 | − | 2.53553i | 0.329912 | − | 0.184433i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.65685 | −0.264601 | −0.132300 | − | 0.991210i | \(-0.542236\pi\) | ||||
−0.132300 | + | 0.991210i | \(0.542236\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 17.6569 | 1.27097 | 0.635484 | − | 0.772114i | \(-0.280801\pi\) | ||||
0.635484 | + | 0.772114i | \(0.280801\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.8995 | + | 3.41421i | −1.42503 | + | 0.244497i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 26.0000i | − | 1.85242i | −0.377004 | − | 0.926212i | \(-0.623046\pi\) | ||
0.377004 | − | 0.926212i | \(-0.376954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 7.31371i | − | 0.518455i | −0.965816 | − | 0.259228i | \(-0.916532\pi\) | ||
0.965816 | − | 0.259228i | \(-0.0834680\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −15.8995 | + | 2.72792i | −1.12146 | + | 0.192413i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −4.82843 | −0.338889 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 34.1421 | 2.38459 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 11.3137 | − | 4.00000i | 0.786357 | − | 0.278019i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 12.4853i | − | 0.863625i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 0.343146i | 0.0236231i | 0.999930 | + | 0.0118116i | \(0.00375982\pi\) | ||||
−0.999930 | + | 0.0118116i | \(0.996240\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.100505 | − | 0.585786i | −0.00688649 | − | 0.0401374i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 35.7990 | 2.44147 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.17157 | −0.0795315 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.928932 | − | 5.41421i | −0.0627714 | − | 0.365859i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.4853i | 1.10892i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.82843i | − | 0.189405i | −0.995506 | − | 0.0947027i | \(-0.969810\pi\) | ||
0.995506 | − | 0.0947027i | \(-0.0301901\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 18.8284 | − | 6.65685i | 1.25523 | − | 0.443790i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −23.8995 | −1.58627 | −0.793133 | − | 0.609049i | \(-0.791551\pi\) | ||||
−0.793133 | + | 0.609049i | \(0.791551\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.07107 | −0.0707782 | −0.0353891 | − | 0.999374i | \(-0.511267\pi\) | ||||
−0.0353891 | + | 0.999374i | \(0.511267\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.41421 | + | 0.585786i | −0.224639 | + | 0.0385419i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 8.97056i | 0.587681i | 0.955854 | + | 0.293841i | \(0.0949335\pi\) | ||||
−0.955854 | + | 0.293841i | \(0.905067\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.65685i | 0.369012i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.82843 | + | 1.17157i | −0.443554 | + | 0.0761018i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.65685 | 0.235559 | 0.117779 | − | 0.993040i | \(-0.462422\pi\) | ||||
0.117779 | + | 0.993040i | \(0.462422\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.7071 | + | 10.2929i | 0.751011 | + | 0.660289i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 3.41421i | − | 0.218126i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 21.3137i | − | 1.35616i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.34315 | + | 19.4853i | 0.211863 | + | 1.23483i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −20.5858 | −1.29936 | −0.649682 | − | 0.760206i | \(-0.725098\pi\) | ||||
−0.649682 | + | 0.760206i | \(0.725098\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00000 | −0.502956 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.82843 | − | 28.1421i | −0.302368 | − | 1.76233i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 14.4853i | − | 0.903567i | −0.892128 | − | 0.451784i | \(-0.850788\pi\) | ||
0.892128 | − | 0.451784i | \(-0.149212\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 0.828427i | − | 0.0514760i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.82843 | − | 13.6569i | −0.298872 | − | 0.845338i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.31371 | −0.0810067 | −0.0405034 | − | 0.999179i | \(-0.512896\pi\) | ||||
−0.0405034 | + | 0.999179i | \(0.512896\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −45.4558 | −2.79233 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.0711 | + | 2.24264i | −0.799936 | + | 0.137247i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.7279i | 1.14186i | 0.820998 | + | 0.570931i | \(0.193418\pi\) | ||||
−0.820998 | + | 0.570931i | \(0.806582\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.4853i | 0.758427i | 0.925309 | + | 0.379213i | \(0.123805\pi\) | ||||
−0.925309 | + | 0.379213i | \(0.876195\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.82843 | + | 1.00000i | −0.352752 | + | 0.0605228i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −13.3137 | −0.802847 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.31371 | −0.0789331 | −0.0394665 | − | 0.999221i | \(-0.512566\pi\) | ||||
−0.0394665 | + | 0.999221i | \(0.512566\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.17157 | − | 3.31371i | −0.0701402 | − | 0.198387i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8.97056i | − | 0.535139i | −0.963539 | − | 0.267569i | \(-0.913780\pi\) | ||
0.963539 | − | 0.267569i | \(-0.0862205\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.2426i | 0.608862i | 0.952534 | + | 0.304431i | \(0.0984663\pi\) | ||||
−0.952534 | + | 0.304431i | \(0.901534\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.24264 | + | 36.3848i | 0.369782 | + | 2.15525i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 10.0000 | 0.590281 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.31371 | −0.371395 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.55635 | + | 9.07107i | 0.0912348 | + | 0.531755i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.27208i | 0.0743156i | 0.999309 | + | 0.0371578i | \(0.0118304\pi\) | ||||
−0.999309 | + | 0.0371578i | \(0.988170\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 21.3137i | − | 1.24093i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.07107 | − | 9.07107i | −0.294253 | − | 0.526357i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −13.6569 | −0.789796 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.4853 | 0.604362 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.1421 | − | 5.34315i | 1.78907 | − | 0.306956i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 48.6274i | 2.78440i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.55635i | − | 0.545410i | −0.962098 | − | 0.272705i | \(-0.912082\pi\) | ||
0.962098 | − | 0.272705i | \(-0.0879182\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −28.9706 | + | 4.97056i | −1.64808 | + | 0.282765i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −19.7990 | −1.12270 | −0.561349 | − | 0.827579i | \(-0.689717\pi\) | ||||
−0.561349 | + | 0.827579i | \(0.689717\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.82843 | −0.499012 | −0.249506 | − | 0.968373i | \(-0.580268\pi\) | ||||
−0.249506 | + | 0.968373i | \(0.580268\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9.65685 | − | 3.41421i | 0.544102 | − | 0.192369i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.0000i | 0.561656i | 0.959758 | + | 0.280828i | \(0.0906090\pi\) | ||||
−0.959758 | + | 0.280828i | \(0.909391\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.65685i | 0.540680i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.24264 | + | 24.7279i | 0.236801 | + | 1.38018i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 30.1421 | 1.67715 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −22.7279 | −1.26072 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −0.727922 | − | 4.24264i | −0.0402542 | − | 0.234619i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.65685i | 0.0913453i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.82843i | 0.265394i | 0.991157 | + | 0.132697i | \(0.0423638\pi\) | ||||
−0.991157 | + | 0.132697i | \(0.957636\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.34315 | − | 0.828427i | 0.128404 | − | 0.0453975i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −31.7990 | −1.73736 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 27.3137 | 1.48787 | 0.743936 | − | 0.668251i | \(-0.232957\pi\) | ||||
0.743936 | + | 0.668251i | \(0.232957\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.07107 | − | 1.55635i | 0.492673 | − | 0.0845293i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.34315i | 0.126888i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 23.3137 | − | 4.00000i | 1.25517 | − | 0.215353i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 0.343146 | 0.0184210 | 0.00921051 | − | 0.999958i | \(-0.497068\pi\) | ||||
0.00921051 | + | 0.999958i | \(0.497068\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 14.9289 | 0.799127 | 0.399564 | − | 0.916705i | \(-0.369162\pi\) | ||||
0.399564 | + | 0.916705i | \(0.369162\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.65685 | − | 15.4853i | −0.462069 | − | 0.826543i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 19.4558i | − | 1.03553i | −0.855523 | − | 0.517765i | \(-0.826764\pi\) | ||
0.855523 | − | 0.517765i | \(-0.173236\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 1.17157i | − | 0.0621806i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.41421 | − | 8.24264i | −0.0748481 | − | 0.436247i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −26.6274 | −1.40534 | −0.702671 | − | 0.711515i | \(-0.748009\pi\) | ||||
−0.702671 | + | 0.711515i | \(0.748009\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −19.9706 | −1.05108 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.05025 | − | 11.9497i | −0.107610 | − | 0.627199i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 10.8284i | − | 0.566786i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.1716i | 0.687551i | 0.939052 | + | 0.343775i | \(0.111706\pi\) | ||||
−0.939052 | + | 0.343775i | \(0.888294\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 10.0000 | + | 28.2843i | 0.520579 | + | 1.47242i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.3137 | −0.691213 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.9706 | −1.18937 | −0.594685 | − | 0.803959i | \(-0.702723\pi\) | ||||
−0.594685 | + | 0.803959i | \(0.702723\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 9.65685 | − | 1.65685i | 0.498678 | − | 0.0855596i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 16.4853i | 0.849035i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.4853i | 1.77139i | 0.464268 | + | 0.885695i | \(0.346318\pi\) | ||||
−0.464268 | + | 0.885695i | \(0.653682\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.41421 | − | 0.585786i | 0.174915 | − | 0.0300107i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5.65685 | 0.289052 | 0.144526 | − | 0.989501i | \(-0.453834\pi\) | ||||
0.144526 | + | 0.989501i | \(0.453834\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.82843 | −0.348009 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.4853 | + | 29.6569i | 0.532997 | + | 1.50754i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.48528i | 0.328817i | 0.986392 | + | 0.164408i | \(0.0525715\pi\) | ||||
−0.986392 | + | 0.164408i | \(0.947429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 19.3137i | − | 0.976736i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.31371 | + | 36.7990i | 0.318484 | + | 1.85626i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −13.6569 | −0.687151 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.2426 | 0.915572 | 0.457786 | − | 0.889062i | \(-0.348643\pi\) | ||||
0.457786 | + | 0.889062i | \(0.348643\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.82843 | + | 10.6569i | 0.0915358 | + | 0.533510i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 31.6569i | − | 1.58087i | −0.612547 | − | 0.790434i | \(-0.709855\pi\) | ||
0.612547 | − | 0.790434i | \(-0.290145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000i | 0.199254i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 19.3137 | + | 23.8995i | 0.959706 | + | 1.18758i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.65685 | −0.0821272 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.4853 | 1.30961 | 0.654806 | − | 0.755797i | \(-0.272750\pi\) | ||||
0.654806 | + | 0.755797i | \(0.272750\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.3137 | + | 3.31371i | −0.952675 | + | 0.163453i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 6.24264i | − | 0.307180i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 38.9706i | 1.91299i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3.00000 | + | 0.514719i | −0.146911 | + | 0.0252059i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −18.7279 | −0.914919 | −0.457459 | − | 0.889230i | \(-0.651241\pi\) | ||||
−0.457459 | + | 0.889230i | \(0.651241\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −15.6569 | −0.763068 | −0.381534 | − | 0.924355i | \(-0.624604\pi\) | ||||
−0.381534 | + | 0.924355i | \(0.624604\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.68629 | + | 1.65685i | −0.227855 | + | 0.0805590i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 32.1421i | − | 1.55912i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 14.2426i | 0.689250i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.00000 | + | 11.6569i | 0.0965609 | + | 0.562798i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.0000 | −0.770693 | −0.385346 | − | 0.922772i | \(-0.625918\pi\) | ||||
−0.385346 | + | 0.922772i | \(0.625918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.9706 | 0.719439 | 0.359720 | − | 0.933060i | \(-0.382872\pi\) | ||||
0.359720 | + | 0.933060i | \(0.382872\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −4.82843 | − | 28.1421i | −0.231505 | − | 1.34931i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.9706i | 1.19450i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 40.2843i | − | 1.92266i | −0.275393 | − | 0.961332i | \(-0.588808\pi\) | ||
0.275393 | − | 0.961332i | \(-0.411192\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.82843 | − | 1.00000i | 0.134687 | − | 0.0476190i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 23.1716 | 1.10091 | 0.550457 | − | 0.834863i | \(-0.314453\pi\) | ||||
0.550457 | + | 0.834863i | \(0.314453\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −26.1421 | −1.23926 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −13.0711 | + | 2.24264i | −0.618240 | + | 0.106073i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18.3431i | 0.865667i | 0.901474 | + | 0.432833i | \(0.142486\pi\) | ||||
−0.901474 | + | 0.432833i | \(0.857514\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 20.0000i | − | 0.941763i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 30.7279 | − | 5.27208i | 1.44372 | − | 0.247704i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −11.6569 | −0.546482 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −24.0000 | −1.12267 | −0.561336 | − | 0.827588i | \(-0.689713\pi\) | ||||
−0.561336 | + | 0.827588i | \(0.689713\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 21.8995 | − | 12.2426i | 1.02218 | − | 0.571438i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 22.0416i | − | 1.02658i | −0.858215 | − | 0.513291i | \(-0.828426\pi\) | ||
0.858215 | − | 0.513291i | \(-0.171574\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.65685i | 0.0770005i | 0.999259 | + | 0.0385003i | \(0.0122580\pi\) | ||||
−0.999259 | + | 0.0385003i | \(0.987742\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.17157 | − | 6.82843i | −0.0543304 | − | 0.316661i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.0416 | 0.834867 | 0.417434 | − | 0.908707i | \(-0.362930\pi\) | ||||
0.417434 | + | 0.908707i | \(0.362930\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.31371 | −0.430067 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0.656854 | + | 3.82843i | 0.0302662 | + | 0.176405i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 20.9706i | − | 0.964228i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 41.5563i | 1.90674i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −13.3137 | − | 37.6569i | −0.609593 | − | 1.72419i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −11.3137 | −0.516937 | −0.258468 | − | 0.966020i | \(-0.583218\pi\) | ||||
−0.258468 | + | 0.966020i | \(0.583218\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.82843 | −0.128965 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 6.82843 | − | 1.17157i | 0.310704 | − | 0.0533084i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.1421i | 0.823792i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.0000i | − | 0.996915i | −0.866914 | − | 0.498458i | \(-0.833900\pi\) | ||
0.866914 | − | 0.498458i | \(-0.166100\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −13.8995 | + | 2.38478i | −0.628557 | + | 0.107843i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −7.17157 | −0.323649 | −0.161824 | − | 0.986820i | \(-0.551738\pi\) | ||||
−0.161824 | + | 0.986820i | \(0.551738\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −23.3137 | −1.05000 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.82843 | − | 19.3137i | −0.306915 | − | 0.868087i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 0.343146i | − | 0.0153922i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 36.6274i | − | 1.63967i | −0.572601 | − | 0.819834i | \(-0.694066\pi\) | ||
0.572601 | − | 0.819834i | \(-0.305934\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.17157 | − | 18.4853i | −0.141695 | − | 0.825861i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.4558 | 1.13502 | 0.567510 | − | 0.823367i | \(-0.307907\pi\) | ||||
0.567510 | + | 0.823367i | \(0.307907\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 62.2843 | 2.77161 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −0.393398 | − | 2.29289i | −0.0174714 | − | 0.101831i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 20.8701i | − | 0.925049i | −0.886606 | − | 0.462525i | \(-0.846944\pi\) | ||
0.886606 | − | 0.462525i | \(-0.153056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 3.17157i | − | 0.140302i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −28.3137 | + | 15.8284i | −1.25008 | + | 0.698842i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −57.9411 | −2.55319 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.31371 | 0.145737 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.3137 | − | 2.79899i | 0.716092 | − | 0.122862i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 12.3431i | − | 0.540763i | −0.962753 | − | 0.270382i | \(-0.912850\pi\) | ||
0.962753 | − | 0.270382i | \(-0.0871498\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 39.8995i | − | 1.74468i | −0.488897 | − | 0.872342i | \(-0.662601\pi\) | ||
0.488897 | − | 0.872342i | \(-0.337399\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 11.3640 | − | 1.94975i | 0.495964 | − | 0.0850940i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.65685 | −0.246416 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17.6569 | − | 6.24264i | 0.766242 | − | 0.270908i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 34.1421i | − | 1.47886i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 49.4558i | 2.13816i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.89949 | + | 11.0711i | 0.0819693 | + | 0.477752i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.6274 | 0.542895 | 0.271448 | − | 0.962453i | \(-0.412498\pi\) | ||||
0.271448 | + | 0.962453i | \(0.412498\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 5.97056 | + | 34.7990i | 0.256221 | + | 1.49337i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 8.48528i | − | 0.363470i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.14214i | 0.348133i | 0.984734 | + | 0.174066i | \(0.0556907\pi\) | ||||
−0.984734 | + | 0.174066i | \(0.944309\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −40.2843 | + | 14.2426i | −1.71929 | + | 0.607861i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.1421 | 1.28410 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.00000 | −0.170097 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.82843 | − | 0.828427i | 0.204955 | − | 0.0351648i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 6.68629i | − | 0.283307i | −0.989916 | − | 0.141654i | \(-0.954758\pi\) | ||
0.989916 | − | 0.141654i | \(-0.0452419\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 35.7990i | − | 1.51414i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −16.4853 | + | 2.82843i | −0.696009 | + | 0.119416i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.21320 | −0.304000 | −0.152000 | − | 0.988380i | \(-0.548571\pi\) | ||||
−0.152000 | + | 0.988380i | \(0.548571\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 18.1421 | 0.763245 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.65685 | + | 7.00000i | 0.237566 | + | 0.293972i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 1.31371i | − | 0.0550735i | −0.999621 | − | 0.0275368i | \(-0.991234\pi\) | ||
0.999621 | − | 0.0275368i | \(-0.00876633\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 8.14214i | − | 0.340738i | −0.985380 | − | 0.170369i | \(-0.945504\pi\) | ||
0.985380 | − | 0.170369i | \(-0.0544959\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.07107 | − | 6.24264i | −0.0447445 | − | 0.260790i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.6274 | 1.11044 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 29.3137 | 1.22035 | 0.610173 | − | 0.792268i | \(-0.291100\pi\) | ||||
0.610173 | + | 0.792268i | \(0.291100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5.17157 | + | 30.1421i | 0.214923 | + | 1.25266i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.4142i | 0.473541i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 26.6274i | 1.10279i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −11.6569 | − | 32.9706i | −0.481952 | − | 1.36316i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 30.7279 | 1.26828 | 0.634139 | − | 0.773219i | \(-0.281355\pi\) | ||||
0.634139 | + | 0.773219i | \(0.281355\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.31371 | 0.301356 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 44.3848 | − | 7.61522i | 1.82575 | − | 0.313248i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 22.4853i | − | 0.923360i | −0.887047 | − | 0.461680i | \(-0.847247\pi\) | ||
0.887047 | − | 0.461680i | \(-0.152753\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 16.4853i | − | 0.675831i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.4853 | − | 2.14214i | 0.510989 | − | 0.0876718i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −16.6274 | −0.679378 | −0.339689 | − | 0.940538i | \(-0.610322\pi\) | ||||
−0.339689 | + | 0.940538i | \(0.610322\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.1421 | −0.658451 | −0.329226 | − | 0.944251i | \(-0.606788\pi\) | ||||
−0.329226 | + | 0.944251i | \(0.606788\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.31371 | − | 26.3431i | −0.379284 | − | 1.07278i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 23.8995i | − | 0.971653i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.14214i | − | 0.0869466i | −0.999055 | − | 0.0434733i | \(-0.986158\pi\) | ||
0.999055 | − | 0.0434733i | \(-0.0138423\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.41421 | − | 8.24264i | −0.0573068 | − | 0.334009i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.65685 | 0.228852 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.7696 | 1.08121 | 0.540606 | − | 0.841276i | \(-0.318195\pi\) | ||||
0.540606 | + | 0.841276i | \(0.318195\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.0000 | + | 58.2843i | 0.403239 | + | 2.35025i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.6274i | − | 1.15250i | −0.817275 | − | 0.576248i | \(-0.804516\pi\) | ||
0.817275 | − | 0.576248i | \(-0.195484\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 18.2426i | − | 0.733234i | −0.930372 | − | 0.366617i | \(-0.880516\pi\) | ||
0.930372 | − | 0.366617i | \(-0.119484\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 10.1421 | + | 18.1421i | 0.406990 | + | 0.728019i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −7.65685 | −0.306765 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13.9706 | −0.558823 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 21.3137 | − | 3.65685i | 0.851188 | − | 0.146041i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 4.00000i | − | 0.159490i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.97056i | 0.357112i | 0.983930 | + | 0.178556i | \(0.0571426\pi\) | ||||
−0.983930 | + | 0.178556i | \(0.942857\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −0.585786 | + | 0.100505i | −0.0232829 | + | 0.00399472i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 6.82843 | 0.270978 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.41421 | −0.135276 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0.970563 | − | 0.343146i | 0.0383949 | − | 0.0135746i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 4.34315i | 0.171544i | 0.996315 | + | 0.0857720i | \(0.0273357\pi\) | ||||
−0.996315 | + | 0.0857720i | \(0.972664\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 37.7574i | − | 1.48900i | −0.667620 | − | 0.744502i | \(-0.732687\pi\) | ||
0.667620 | − | 0.744502i | \(-0.267313\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.4853 | + | 61.1127i | 0.412858 | + | 2.40631i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.4558 | 0.843516 | 0.421758 | − | 0.906708i | \(-0.361413\pi\) | ||||
0.421758 | + | 0.906708i | \(0.361413\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.4853 | −0.490090 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −0.343146 | − | 2.00000i | −0.0134489 | − | 0.0783862i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 2.48528i | − | 0.0972566i | −0.998817 | − | 0.0486283i | \(-0.984515\pi\) | ||
0.998817 | − | 0.0486283i | \(-0.0154850\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 73.5980i | 2.87571i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.97056 | − | 3.17157i | 0.349975 | − | 0.123735i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.9706 | −0.583170 | −0.291585 | − | 0.956545i | \(-0.594183\pi\) | ||||
−0.291585 | + | 0.956545i | \(0.594183\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.1838 | 1.56297 | 0.781484 | − | 0.623926i | \(-0.214463\pi\) | ||||
0.781484 | + | 0.623926i | \(0.214463\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −28.1421 | + | 4.82843i | −1.09295 | + | 0.187521i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 21.3137i | 0.826510i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 19.3137i | − | 0.747830i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.82843 | − | 0.828427i | 0.186678 | − | 0.0320288i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 28.4853 | 1.09966 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.00000 | 0.0770943 | 0.0385472 | − | 0.999257i | \(-0.487727\pi\) | ||||
0.0385472 | + | 0.999257i | \(0.487727\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 16.8787 | + | 30.1924i | 0.649661 | + | 1.16211i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 4.87006i | − | 0.187172i | −0.995611 | − | 0.0935858i | \(-0.970167\pi\) | ||
0.995611 | − | 0.0935858i | \(-0.0298329\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.31371i | 0.203921i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.00000 | − | 40.7990i | −0.268241 | − | 1.56342i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.5147 | 1.12935 | 0.564675 | − | 0.825314i | \(-0.309002\pi\) | ||||
0.564675 | + | 0.825314i | \(0.309002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −38.6274 | −1.47588 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.313708 | − | 1.82843i | −0.0119687 | − | 0.0697588i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 45.4558i | 1.73173i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.0416i | 0.838503i | 0.907870 | + | 0.419252i | \(0.137707\pi\) | ||||
−0.907870 | + | 0.419252i | \(0.862293\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.00000 | − | 5.65685i | −0.0759737 | − | 0.214886i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.00000 | −0.227593 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 48.2843 | 1.82890 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −15.3137 | + | 2.62742i | −0.579218 | + | 0.0993780i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 28.1421i | 1.06291i | 0.847085 | + | 0.531457i | \(0.178355\pi\) | ||||
−0.847085 | + | 0.531457i | \(0.821645\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 5.17157i | 0.195050i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −9.65685 | + | 1.65685i | −0.363698 | + | 0.0624007i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 18.2426 | 0.686085 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.51472 | 0.207110 | 0.103555 | − | 0.994624i | \(-0.466978\pi\) | ||||
0.103555 | + | 0.994624i | \(0.466978\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.00000 | − | 11.3137i | −0.150012 | − | 0.424297i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 4.68629i | − | 0.175503i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 23.3137i | 0.871883i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.31371 | − | 19.3137i | −0.123753 | − | 0.721284i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.6863 | −0.771468 | −0.385734 | − | 0.922610i | \(-0.626052\pi\) | ||||
−0.385734 | + | 0.922610i | \(0.626052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −16.9706 | −0.632017 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.07107 | + | 6.24264i | 0.0398334 | + | 0.232166i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 32.1421i | − | 1.19373i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.6274i | 0.394149i | 0.980389 | + | 0.197075i | \(0.0631441\pi\) | ||||
−0.980389 | + | 0.197075i | \(0.936856\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14.1421 | + | 23.0000i | −0.523783 | + | 0.851852i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.6274 | 1.87252 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.384776 | 0.0142120 | 0.00710602 | − | 0.999975i | \(-0.497738\pi\) | ||||
0.00710602 | + | 0.999975i | \(0.497738\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 5.82843 | − | 1.00000i | 0.214985 | − | 0.0368856i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18.6274i | 0.686150i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.8579i | 0.436199i | 0.975927 | + | 0.218099i | \(0.0699857\pi\) | ||||
−0.975927 | + | 0.218099i | \(0.930014\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 36.3848 | − | 6.24264i | 1.33663 | − | 0.229329i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.9411 | 0.804942 | 0.402471 | − | 0.915433i | \(-0.368151\pi\) | ||||
0.402471 | + | 0.915433i | \(0.368151\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.1421 | −0.957774 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −32.2843 | + | 11.4142i | −1.18122 | + | 0.417624i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.4853i | 0.529281i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 30.2843i | − | 1.10509i | −0.833483 | − | 0.552544i | \(-0.813657\pi\) | ||
0.833483 | − | 0.552544i | \(-0.186343\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6.02944 | − | 35.1421i | −0.219725 | − | 1.28065i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 61.4558 | 2.23661 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.1127 | −1.78503 | −0.892516 | − | 0.451016i | \(-0.851062\pi\) | ||||
−0.892516 | + | 0.451016i | \(0.851062\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.34315 | − | 13.6569i | −0.0850508 | − | 0.495712i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.02944i | 0.0373171i | 0.999826 | + | 0.0186585i | \(0.00593954\pi\) | ||||
−0.999826 | + | 0.0186585i | \(0.994060\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 2.48528i | − | 0.0899732i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 46.6274 | − | 16.4853i | 1.68582 | − | 0.596027i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −21.3137 | −0.769593 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8.34315 | 0.300862 | 0.150431 | − | 0.988621i | \(-0.451934\pi\) | ||||
0.150431 | + | 0.988621i | \(0.451934\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 24.7279 | − | 4.24264i | 0.890554 | − | 0.152795i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1.27208i | − | 0.0457535i | −0.999738 | − | 0.0228767i | \(-0.992717\pi\) | ||
0.999738 | − | 0.0228767i | \(-0.00728253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 7.79899i | − | 0.280148i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.41421 | − | 0.242641i | 0.0507346 | − | 0.00870469i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −62.4264 | −2.23666 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.686292 | −0.0245574 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 21.8995 | − | 12.2426i | 0.782624 | − | 0.437516i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.65685i | 0.273285i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 33.7574i | − | 1.20332i | −0.798752 | − | 0.601660i | \(-0.794506\pi\) | ||
0.798752 | − | 0.601660i | \(-0.205494\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.384776 | − | 2.24264i | −0.0136984 | − | 0.0798401i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 5.31371 | 0.188934 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.6274 | 1.72681 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.3137 | − | 77.5980i | −0.472189 | − | 2.75212i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 12.1005i | − | 0.428622i | −0.976765 | − | 0.214311i | \(-0.931249\pi\) | ||
0.976765 | − | 0.214311i | \(-0.0687506\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8.00000i | 0.283020i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −7.65685 | − | 21.6569i | −0.270542 | − | 0.765207i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −6.34315 | −0.223845 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 13.6569 | 0.481341 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −31.9706 | + | 5.48528i | −1.12542 | + | 0.193091i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 10.6863i | − | 0.375710i | −0.982197 | − | 0.187855i | \(-0.939846\pi\) | ||
0.982197 | − | 0.187855i | \(-0.0601535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.5563i | 1.03786i | 0.854816 | + | 0.518932i | \(0.173670\pi\) | ||||
−0.854816 | + | 0.518932i | \(0.826330\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −21.3137 | + | 3.65685i | −0.747504 | + | 0.128251i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.7990 | −0.973756 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −65.4558 | −2.29001 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −3.41421 | − | 9.65685i | −0.119302 | − | 0.337438i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 26.9706i | − | 0.941279i | −0.882326 | − | 0.470640i | \(-0.844023\pi\) | ||
0.882326 | − | 0.470640i | \(-0.155977\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 32.9706i | − | 1.14928i | −0.818406 | − | 0.574641i | \(-0.805142\pi\) | ||
0.818406 | − | 0.574641i | \(-0.194858\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.89949 | − | 22.7279i | −0.135763 | − | 0.791285i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.45584 | 0.120171 | 0.0600857 | − | 0.998193i | \(-0.480863\pi\) | ||||
0.0600857 | + | 0.998193i | \(0.480863\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24.3848 | −0.846918 | −0.423459 | − | 0.905915i | \(-0.639184\pi\) | ||||
−0.423459 | + | 0.905915i | \(0.639184\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.384776 | − | 2.24264i | −0.0133477 | − | 0.0777963i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 4.82843i | − | 0.167295i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 36.9706i | − | 1.27942i | ||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.31371 | − | 2.97056i | 0.183669 | − | 0.102678i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.17157 | 0.0404472 | 0.0202236 | − | 0.999795i | \(-0.493562\pi\) | ||||
0.0202236 | + | 0.999795i | \(0.493562\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.68629 | 0.196079 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.3137 | − | 2.62742i | 0.527432 | − | 0.0904930i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 4.58579i | − | 0.157756i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 7.00000i | − | 0.240523i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.4853 | + | 3.00000i | −0.600093 | + | 0.102960i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.31371 | 0.113592 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.58579 | 0.157014 | 0.0785072 | − | 0.996914i | \(-0.474985\pi\) | ||||
0.0785072 | + | 0.996914i | \(0.474985\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −60.2843 | + | 21.3137i | −2.06168 | + | 0.728913i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 38.0000i | 1.29806i | 0.760765 | + | 0.649028i | \(0.224824\pi\) | ||||
−0.760765 | + | 0.649028i | \(0.775176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.5858i | 0.838856i | 0.907789 | + | 0.419428i | \(0.137769\pi\) | ||||
−0.907789 | + | 0.419428i | \(0.862231\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.92893 | + | 17.0711i | 0.0998177 | + | 0.581780i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.3726 | −0.387127 | −0.193564 | − | 0.981088i | \(-0.562005\pi\) | ||||
−0.193564 | + | 0.981088i | \(0.562005\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.6274 | 1.10937 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.84924 | − | 10.7782i | −0.0628036 | − | 0.366046i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.00000i | 0.271381i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.7990i | 1.07747i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −15.0294 | + | 5.31371i | −0.508669 | + | 0.179842i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.65685 | 0.191237 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −57.7990 | −1.95173 | −0.975867 | − | 0.218368i | \(-0.929927\pi\) | ||||
−0.975867 | + | 0.218368i | \(0.929927\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.17157 | + | 0.372583i | −0.0732453 | + | 0.0125669i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 7.85786i | − | 0.264738i | −0.991200 | − | 0.132369i | \(-0.957742\pi\) | ||
0.991200 | − | 0.132369i | \(-0.0422584\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.31371i | 0.313431i | 0.987644 | + | 0.156716i | \(0.0500906\pi\) | ||||
−0.987644 | + | 0.156716i | \(0.949909\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 36.3848 | − | 6.24264i | 1.22306 | − | 0.209844i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.82843 | −0.0949693 | −0.0474846 | − | 0.998872i | \(-0.515121\pi\) | ||||
−0.0474846 | + | 0.998872i | \(0.515121\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.00000 | 0.0670778 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 14.0000 | − | 11.3137i | 0.469018 | − | 0.379023i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 10.3431i | − | 0.346120i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 22.1421i | 0.740130i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −4.00000 | − | 23.3137i | −0.133556 | − | 0.778422i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.65685 | −0.188667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −64.2843 | −2.14162 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.07107 | + | 17.8995i | 0.102199 | + | 0.595658i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 69.5980i | 2.31352i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 37.5980i | − | 1.24842i | −0.781256 | − | 0.624210i | \(-0.785421\pi\) | ||
0.781256 | − | 0.624210i | \(-0.214579\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.2426 | + | 51.5980i | 0.605070 | + | 1.71140i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −16.9706 | −0.562260 | −0.281130 | − | 0.959670i | \(-0.590709\pi\) | ||||
−0.281130 | + | 0.959670i | \(0.590709\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 22.8284 | 0.755511 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −83.0122 | + | 14.2426i | −2.74430 | + | 0.470847i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 21.5563i | 0.711853i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 29.6569i | 0.978289i | 0.872203 | + | 0.489145i | \(0.162691\pi\) | ||||
−0.872203 | + | 0.489145i | \(0.837309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.3137 | − | 2.79899i | 0.537555 | − | 0.0922299i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.17157 | −0.0385628 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.51472 | 0.181323 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −16.9706 | − | 48.0000i | −0.557386 | − | 1.57653i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 33.7990i | − | 1.10891i | −0.832214 | − | 0.554454i | \(-0.812927\pi\) | ||
0.832214 | − | 0.554454i | \(-0.187073\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.24264i | 0.204594i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.79899 | − | 33.7990i | −0.189850 | − | 1.10653i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −32.9706 | −1.07825 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 21.5147 | 0.702855 | 0.351428 | − | 0.936215i | \(-0.385696\pi\) | ||||
0.351428 | + | 0.936215i | \(0.385696\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.58579 | − | 15.0711i | −0.0843840 | − | 0.491826i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.6985i | 0.511756i | 0.966709 | + | 0.255878i | \(0.0823645\pi\) | ||||
−0.966709 | + | 0.255878i | \(0.917635\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 40.0000i | 1.30258i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 8.65685 | + | 15.4853i | 0.281607 | + | 0.503736i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −57.3137 | −1.86245 | −0.931223 | − | 0.364451i | \(-0.881257\pi\) | ||||
−0.931223 | + | 0.364451i | \(0.881257\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.8284 | −0.351506 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −17.0711 | + | 2.92893i | −0.553567 | + | 0.0949771i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 0.686292i | 0.0222312i | 0.999938 | + | 0.0111156i | \(0.00353827\pi\) | ||||
−0.999938 | + | 0.0111156i | \(0.996462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 12.4853i | − | 0.404014i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −16.4853 | + | 2.82843i | −0.532893 | + | 0.0914301i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.3137 | −0.365339 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 29.6274 | 0.955723 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −40.9706 | + | 14.4853i | −1.32026 | + | 0.466782i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 60.2843i | 1.94062i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 27.6569i | − | 0.889384i | −0.895683 | − | 0.444692i | \(-0.853313\pi\) | ||
0.895683 | − | 0.444692i | \(-0.146687\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8.82843 | + | 51.4558i | 0.283610 | + | 1.65300i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 43.6985 | 1.40235 | 0.701176 | − | 0.712989i | \(-0.252659\pi\) | ||||
0.701176 | + | 0.712989i | \(0.252659\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.75736 | −0.0563384 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −6.65685 | − | 38.7990i | −0.213190 | − | 1.24256i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 44.0000i | − | 1.40768i | −0.710356 | − | 0.703842i | \(-0.751466\pi\) | ||
0.710356 | − | 0.703842i | \(-0.248534\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.3137i | 0.489428i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 7.02944 | − | 2.48528i | 0.224433 | − | 0.0793489i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.4558 | 0.556755 | 0.278377 | − | 0.960472i | \(-0.410203\pi\) | ||||
0.278377 | + | 0.960472i | \(0.410203\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 88.7696 | 2.82843 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.82843 | + | 0.485281i | −0.0900298 | + | 0.0154467i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.9411i | 1.33365i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 45.9411i | − | 1.45937i | −0.683785 | − | 0.729684i | \(-0.739667\pi\) | ||
0.683785 | − | 0.729684i | \(-0.260333\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −8.24264 | + | 1.41421i | −0.261572 | + | 0.0448787i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 24.9706 | 0.791620 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.95837 | 0.315385 | 0.157692 | − | 0.987488i | \(-0.449595\pi\) | ||||
0.157692 | + | 0.987488i | \(0.449595\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.10051 | + | 3.75736i | 0.0664570 | + | 0.118878i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 672.2.h.d.575.2 | yes | 4 | |
3.2 | odd | 2 | 672.2.h.a.575.4 | yes | 4 | ||
4.3 | odd | 2 | 672.2.h.a.575.3 | ✓ | 4 | ||
8.3 | odd | 2 | 1344.2.h.e.575.2 | 4 | |||
8.5 | even | 2 | 1344.2.h.a.575.3 | 4 | |||
12.11 | even | 2 | inner | 672.2.h.d.575.1 | yes | 4 | |
24.5 | odd | 2 | 1344.2.h.e.575.1 | 4 | |||
24.11 | even | 2 | 1344.2.h.a.575.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.2.h.a.575.3 | ✓ | 4 | 4.3 | odd | 2 | ||
672.2.h.a.575.4 | yes | 4 | 3.2 | odd | 2 | ||
672.2.h.d.575.1 | yes | 4 | 12.11 | even | 2 | inner | |
672.2.h.d.575.2 | yes | 4 | 1.1 | even | 1 | trivial | |
1344.2.h.a.575.3 | 4 | 8.5 | even | 2 | |||
1344.2.h.a.575.4 | 4 | 24.11 | even | 2 | |||
1344.2.h.e.575.1 | 4 | 24.5 | odd | 2 | |||
1344.2.h.e.575.2 | 4 | 8.3 | odd | 2 |