Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(64,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("315.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.d (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: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.350464.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 64.5 | ||
Root | \(1.45161 - 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.64 |
Dual form | 315.2.d.e.64.2 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.90321i | 1.34577i | 0.739745 | + | 0.672887i | \(0.234946\pi\) | ||||
−0.739745 | + | 0.672887i | \(0.765054\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.62222 | −0.811108 | ||||||||
\(5\) | −0.311108 | + | 2.21432i | −0.139132 | + | 0.990274i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 1.00000i | − | 0.377964i | ||||||
\(8\) | 0.719004i | 0.254206i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.21432 | − | 0.592104i | −1.33268 | − | 0.187240i | ||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.42864i | 1.78298i | 0.453037 | + | 0.891492i | \(0.350341\pi\) | ||||
−0.453037 | + | 0.891492i | \(0.649659\pi\) | |||||||
\(14\) | 1.90321 | 0.508655 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.61285 | −1.15321 | ||||||||
\(17\) | − | 4.42864i | − | 1.07410i | −0.843550 | − | 0.537051i | \(-0.819538\pi\) | ||
0.843550 | − | 0.537051i | \(-0.180462\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.42864 | 0.557168 | 0.278584 | − | 0.960412i | \(-0.410135\pi\) | ||||
0.278584 | + | 0.960412i | \(0.410135\pi\) | |||||||
\(20\) | 0.504684 | − | 3.59210i | 0.112851 | − | 0.803219i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 3.80642i | − | 0.811532i | ||||||
\(23\) | 1.37778i | 0.287288i | 0.989629 | + | 0.143644i | \(0.0458820\pi\) | ||||
−0.989629 | + | 0.143644i | \(0.954118\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.80642 | − | 1.37778i | −0.961285 | − | 0.275557i | ||||
\(26\) | −12.2351 | −2.39949 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.62222i | 0.306570i | ||||||||
\(29\) | 0.755569 | 0.140306 | 0.0701528 | − | 0.997536i | \(-0.477651\pi\) | ||||
0.0701528 | + | 0.997536i | \(0.477651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.18421 | 0.931111 | 0.465556 | − | 0.885019i | \(-0.345855\pi\) | ||||
0.465556 | + | 0.885019i | \(0.345855\pi\) | |||||||
\(32\) | − | 7.34122i | − | 1.29776i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 8.42864 | 1.44550 | ||||||||
\(35\) | 2.21432 | + | 0.311108i | 0.374288 | + | 0.0525868i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.61285i | 1.25154i | 0.780006 | + | 0.625772i | \(0.215216\pi\) | ||||
−0.780006 | + | 0.625772i | \(0.784784\pi\) | |||||||
\(38\) | 4.62222i | 0.749822i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.59210 | − | 0.223688i | −0.251734 | − | 0.0353681i | ||||
\(41\) | 8.23506 | 1.28610 | 0.643050 | − | 0.765824i | \(-0.277669\pi\) | ||||
0.643050 | + | 0.765824i | \(0.277669\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 10.1017i | − | 1.54050i | −0.637744 | − | 0.770248i | \(-0.720132\pi\) | ||
0.637744 | − | 0.770248i | \(-0.279868\pi\) | |||||||
\(44\) | 3.24443 | 0.489116 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.62222 | −0.386625 | ||||||||
\(47\) | − | 2.75557i | − | 0.401941i | −0.979597 | − | 0.200971i | \(-0.935590\pi\) | ||
0.979597 | − | 0.200971i | \(-0.0644095\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 2.62222 | − | 9.14764i | 0.370837 | − | 1.29367i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 10.4286i | − | 1.44619i | ||||||
\(53\) | 9.18421i | 1.26155i | 0.775967 | + | 0.630774i | \(0.217263\pi\) | ||||
−0.775967 | + | 0.630774i | \(0.782737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.622216 | − | 4.42864i | 0.0838995 | − | 0.597158i | ||||
\(56\) | 0.719004 | 0.0960809 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.43801i | 0.188820i | ||||||||
\(59\) | 14.1017 | 1.83589 | 0.917943 | − | 0.396712i | \(-0.129849\pi\) | ||||
0.917943 | + | 0.396712i | \(0.129849\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.85728 | 0.877985 | 0.438992 | − | 0.898491i | \(-0.355336\pi\) | ||||
0.438992 | + | 0.898491i | \(0.355336\pi\) | |||||||
\(62\) | 9.86665i | 1.25307i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 4.74620 | 0.593275 | ||||||||
\(65\) | −14.2351 | − | 2.00000i | −1.76564 | − | 0.248069i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.75557i | 0.336646i | 0.985732 | + | 0.168323i | \(0.0538352\pi\) | ||||
−0.985732 | + | 0.168323i | \(0.946165\pi\) | |||||||
\(68\) | 7.18421i | 0.871213i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.592104 | + | 4.21432i | −0.0707700 | + | 0.503708i | ||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.57136i | 0.183914i | 0.995763 | + | 0.0919569i | \(0.0293122\pi\) | ||||
−0.995763 | + | 0.0919569i | \(0.970688\pi\) | |||||||
\(74\) | −14.4889 | −1.68430 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.93978 | −0.451923 | ||||||||
\(77\) | 2.00000i | 0.227921i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.85728 | 0.546487 | 0.273243 | − | 0.961945i | \(-0.411904\pi\) | ||||
0.273243 | + | 0.961945i | \(0.411904\pi\) | |||||||
\(80\) | 1.43509 | − | 10.2143i | 0.160448 | − | 1.14200i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 15.6731i | 1.73080i | ||||||||
\(83\) | 11.6128i | 1.27468i | 0.770585 | + | 0.637338i | \(0.219964\pi\) | ||||
−0.770585 | + | 0.637338i | \(0.780036\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.80642 | + | 1.37778i | 1.06366 | + | 0.149442i | ||||
\(86\) | 19.2257 | 2.07316 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 1.43801i | − | 0.153292i | ||||||
\(89\) | 4.62222 | 0.489954 | 0.244977 | − | 0.969529i | \(-0.421220\pi\) | ||||
0.244977 | + | 0.969529i | \(0.421220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.42864 | 0.673905 | ||||||||
\(92\) | − | 2.23506i | − | 0.233021i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 5.24443 | 0.540922 | ||||||||
\(95\) | −0.755569 | + | 5.37778i | −0.0775197 | + | 0.551749i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.9398i | − | 1.21230i | −0.795350 | − | 0.606150i | \(-0.792713\pi\) | ||
0.795350 | − | 0.606150i | \(-0.207287\pi\) | |||||||
\(98\) | − | 1.90321i | − | 0.192253i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.79706 | + | 2.23506i | 0.779706 | + | 0.223506i | ||||
\(101\) | −1.47949 | −0.147215 | −0.0736076 | − | 0.997287i | \(-0.523451\pi\) | ||||
−0.0736076 | + | 0.997287i | \(0.523451\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.85728i | 0.872734i | 0.899769 | + | 0.436367i | \(0.143735\pi\) | ||||
−0.899769 | + | 0.436367i | \(0.856265\pi\) | |||||||
\(104\) | −4.62222 | −0.453246 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −17.4795 | −1.69776 | ||||||||
\(107\) | − | 1.76494i | − | 0.170623i | −0.996354 | − | 0.0853114i | \(-0.972811\pi\) | ||
0.996354 | − | 0.0853114i | \(-0.0271885\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.61285 | −0.537613 | −0.268807 | − | 0.963194i | \(-0.586629\pi\) | ||||
−0.268807 | + | 0.963194i | \(0.586629\pi\) | |||||||
\(110\) | 8.42864 | + | 1.18421i | 0.803639 | + | 0.112910i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.61285i | 0.435873i | ||||||||
\(113\) | − | 11.2859i | − | 1.06169i | −0.847469 | − | 0.530845i | \(-0.821875\pi\) | ||
0.847469 | − | 0.530845i | \(-0.178125\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.05086 | − | 0.428639i | −0.284494 | − | 0.0399708i | ||||
\(116\) | −1.22570 | −0.113803 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 26.8385i | 2.47069i | ||||||||
\(119\) | −4.42864 | −0.405973 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 13.0509i | 1.18157i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.40990 | −0.755232 | ||||||||
\(125\) | 4.54617 | − | 10.2143i | 0.406622 | − | 0.913597i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 12.8573i | − | 1.14090i | −0.821333 | − | 0.570450i | \(-0.806769\pi\) | ||
0.821333 | − | 0.570450i | \(-0.193231\pi\) | |||||||
\(128\) | − | 5.64941i | − | 0.499342i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 3.80642 | − | 27.0923i | 0.333845 | − | 2.37616i | ||||
\(131\) | 2.10171 | 0.183627 | 0.0918136 | − | 0.995776i | \(-0.470734\pi\) | ||||
0.0918136 | + | 0.995776i | \(0.470734\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 2.42864i | − | 0.210590i | ||||||
\(134\) | −5.24443 | −0.453050 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.18421 | 0.273044 | ||||||||
\(137\) | − | 15.9398i | − | 1.36183i | −0.732364 | − | 0.680914i | \(-0.761583\pi\) | ||
0.732364 | − | 0.680914i | \(-0.238417\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6731 | −0.990097 | −0.495048 | − | 0.868865i | \(-0.664850\pi\) | ||||
−0.495048 | + | 0.868865i | \(0.664850\pi\) | |||||||
\(140\) | −3.59210 | − | 0.504684i | −0.303588 | − | 0.0426536i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 3.80642i | − | 0.319428i | ||||||
\(143\) | − | 12.8573i | − | 1.07518i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.235063 | + | 1.67307i | −0.0195209 | + | 0.138941i | ||||
\(146\) | −2.99063 | −0.247506 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 12.3497i | − | 1.01514i | ||||||
\(149\) | −21.2257 | −1.73888 | −0.869438 | − | 0.494041i | \(-0.835519\pi\) | ||||
−0.869438 | + | 0.494041i | \(0.835519\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 16.8573 | 1.37183 | 0.685913 | − | 0.727684i | \(-0.259403\pi\) | ||||
0.685913 | + | 0.727684i | \(0.259403\pi\) | |||||||
\(152\) | 1.74620i | 0.141636i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.80642 | −0.306730 | ||||||||
\(155\) | −1.61285 | + | 11.4795i | −0.129547 | + | 0.922055i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 10.4286i | − | 0.832296i | −0.909297 | − | 0.416148i | \(-0.863380\pi\) | ||
0.909297 | − | 0.416148i | \(-0.136620\pi\) | |||||||
\(158\) | 9.24443i | 0.735447i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 16.2558 | + | 2.28391i | 1.28513 | + | 0.180559i | ||||
\(161\) | 1.37778 | 0.108585 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 20.8573i | − | 1.63367i | −0.576873 | − | 0.816834i | \(-0.695727\pi\) | ||
0.576873 | − | 0.816834i | \(-0.304273\pi\) | |||||||
\(164\) | −13.3590 | −1.04317 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −22.1017 | −1.71543 | ||||||||
\(167\) | − | 15.3461i | − | 1.18752i | −0.804642 | − | 0.593760i | \(-0.797643\pi\) | ||
0.804642 | − | 0.593760i | \(-0.202357\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28.3274 | −2.17903 | ||||||||
\(170\) | −2.62222 | + | 18.6637i | −0.201115 | + | 1.43144i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 16.3872i | 1.24951i | ||||||||
\(173\) | 2.06022i | 0.156636i | 0.996928 | + | 0.0783179i | \(0.0249549\pi\) | ||||
−0.996928 | + | 0.0783179i | \(0.975045\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.37778 | + | 4.80642i | −0.104151 | + | 0.363331i | ||||
\(176\) | 9.22570 | 0.695413 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 8.79706i | 0.659367i | ||||||||
\(179\) | 10.0000 | 0.747435 | 0.373718 | − | 0.927543i | \(-0.378083\pi\) | ||||
0.373718 | + | 0.927543i | \(0.378083\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.1017 | −0.899513 | −0.449757 | − | 0.893151i | \(-0.648489\pi\) | ||||
−0.449757 | + | 0.893151i | \(0.648489\pi\) | |||||||
\(182\) | 12.2351i | 0.906923i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.990632 | −0.0730304 | ||||||||
\(185\) | −16.8573 | − | 2.36842i | −1.23937 | − | 0.174129i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.85728i | 0.647708i | ||||||||
\(188\) | 4.47013i | 0.326017i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.2351 | − | 1.43801i | −0.742530 | − | 0.104324i | ||||
\(191\) | −0.488863 | −0.0353729 | −0.0176864 | − | 0.999844i | \(-0.505630\pi\) | ||||
−0.0176864 | + | 0.999844i | \(0.505630\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 22.9590i | 1.65262i | 0.563212 | + | 0.826312i | \(0.309565\pi\) | ||||
−0.563212 | + | 0.826312i | \(0.690435\pi\) | |||||||
\(194\) | 22.7239 | 1.63148 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.62222 | 0.115873 | ||||||||
\(197\) | 1.18421i | 0.0843713i | 0.999110 | + | 0.0421857i | \(0.0134321\pi\) | ||||
−0.999110 | + | 0.0421857i | \(0.986568\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −8.79706 | −0.623607 | −0.311803 | − | 0.950147i | \(-0.600933\pi\) | ||||
−0.311803 | + | 0.950147i | \(0.600933\pi\) | |||||||
\(200\) | 0.990632 | − | 3.45584i | 0.0700483 | − | 0.244365i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 2.81579i | − | 0.198118i | ||||||
\(203\) | − | 0.755569i | − | 0.0530305i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.56199 | + | 18.2351i | −0.178937 | + | 1.27359i | ||||
\(206\) | −16.8573 | −1.17450 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 29.6543i | − | 2.05616i | ||||||
\(209\) | −4.85728 | −0.335985 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.2257 | 1.59892 | 0.799461 | − | 0.600717i | \(-0.205118\pi\) | ||||
0.799461 | + | 0.600717i | \(0.205118\pi\) | |||||||
\(212\) | − | 14.8988i | − | 1.02325i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 3.35905 | 0.229620 | ||||||||
\(215\) | 22.3684 | + | 3.14272i | 1.52551 | + | 0.214332i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5.18421i | − | 0.351927i | ||||||
\(218\) | − | 10.6824i | − | 0.723506i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.00937 | + | 7.18421i | −0.0680516 | + | 0.484359i | ||||
\(221\) | 28.4701 | 1.91511 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 15.2257i | 1.01959i | 0.860297 | + | 0.509794i | \(0.170278\pi\) | ||||
−0.860297 | + | 0.509794i | \(0.829722\pi\) | |||||||
\(224\) | −7.34122 | −0.490506 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.4795 | 1.42879 | ||||||||
\(227\) | 14.3684i | 0.953665i | 0.878994 | + | 0.476833i | \(0.158215\pi\) | ||||
−0.878994 | + | 0.476833i | \(0.841785\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.61285 | 0.370907 | 0.185454 | − | 0.982653i | \(-0.440625\pi\) | ||||
0.185454 | + | 0.982653i | \(0.440625\pi\) | |||||||
\(230\) | 0.815792 | − | 5.80642i | 0.0537917 | − | 0.382864i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0.543257i | 0.0356666i | ||||||||
\(233\) | 23.2859i | 1.52551i | 0.646687 | + | 0.762756i | \(0.276154\pi\) | ||||
−0.646687 | + | 0.762756i | \(0.723846\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.10171 | + | 0.857279i | 0.398032 | + | 0.0559227i | ||||
\(236\) | −22.8760 | −1.48910 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 8.42864i | − | 0.546348i | ||||||
\(239\) | −8.48886 | −0.549099 | −0.274549 | − | 0.961573i | \(-0.588529\pi\) | ||||
−0.274549 | + | 0.961573i | \(0.588529\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.24443 | −0.466655 | −0.233327 | − | 0.972398i | \(-0.574961\pi\) | ||||
−0.233327 | + | 0.972398i | \(0.574961\pi\) | |||||||
\(242\) | − | 13.3225i | − | 0.856402i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.1240 | −0.712140 | ||||||||
\(245\) | 0.311108 | − | 2.21432i | 0.0198759 | − | 0.141468i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.6128i | 0.993422i | ||||||||
\(248\) | 3.72746i | 0.236694i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 19.4400 | + | 8.65233i | 1.22949 | + | 0.547221i | ||||
\(251\) | −27.6128 | −1.74291 | −0.871454 | − | 0.490478i | \(-0.836822\pi\) | ||||
−0.871454 | + | 0.490478i | \(0.836822\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 2.75557i | − | 0.173241i | ||||||
\(254\) | 24.4701 | 1.53539 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 20.2444 | 1.26528 | ||||||||
\(257\) | 0.428639i | 0.0267378i | 0.999911 | + | 0.0133689i | \(0.00425558\pi\) | ||||
−0.999911 | + | 0.0133689i | \(0.995744\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.61285 | 0.473039 | ||||||||
\(260\) | 23.0923 | + | 3.24443i | 1.43213 | + | 0.201211i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 4.00000i | 0.247121i | ||||||||
\(263\) | − | 9.37778i | − | 0.578259i | −0.957290 | − | 0.289129i | \(-0.906634\pi\) | ||
0.957290 | − | 0.289129i | \(-0.0933658\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.3368 | − | 2.85728i | −1.24928 | − | 0.175521i | ||||
\(266\) | 4.62222 | 0.283406 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 4.47013i | − | 0.273056i | ||||||
\(269\) | 1.74620 | 0.106468 | 0.0532339 | − | 0.998582i | \(-0.483047\pi\) | ||||
0.0532339 | + | 0.998582i | \(0.483047\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.69535 | −0.163731 | −0.0818653 | − | 0.996643i | \(-0.526088\pi\) | ||||
−0.0818653 | + | 0.996643i | \(0.526088\pi\) | |||||||
\(272\) | 20.4286i | 1.23867i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 30.3368 | 1.83271 | ||||||||
\(275\) | 9.61285 | + | 2.75557i | 0.579677 | + | 0.166167i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 5.12399i | − | 0.307870i | −0.988081 | − | 0.153935i | \(-0.950805\pi\) | ||
0.988081 | − | 0.153935i | \(-0.0491947\pi\) | |||||||
\(278\) | − | 22.2163i | − | 1.33245i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.223688 | + | 1.59210i | −0.0133679 | + | 0.0951464i | ||||
\(281\) | −23.9813 | −1.43060 | −0.715301 | − | 0.698816i | \(-0.753710\pi\) | ||||
−0.715301 | + | 0.698816i | \(0.753710\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 2.36842i | − | 0.140788i | −0.997519 | − | 0.0703939i | \(-0.977574\pi\) | ||
0.997519 | − | 0.0703939i | \(-0.0224256\pi\) | |||||||
\(284\) | 3.24443 | 0.192522 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 24.4701 | 1.44695 | ||||||||
\(287\) | − | 8.23506i | − | 0.486100i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.61285 | −0.153697 | ||||||||
\(290\) | −3.18421 | − | 0.447375i | −0.186983 | − | 0.0262708i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 2.54909i | − | 0.149174i | ||||||
\(293\) | 8.42864i | 0.492406i | 0.969218 | + | 0.246203i | \(0.0791831\pi\) | ||||
−0.969218 | + | 0.246203i | \(0.920817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.38715 | + | 31.2257i | −0.255430 | + | 1.81803i | ||||
\(296\) | −5.47367 | −0.318150 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 40.3970i | − | 2.34014i | ||||||
\(299\) | −8.85728 | −0.512230 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.1017 | −0.582253 | ||||||||
\(302\) | 32.0830i | 1.84617i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −11.2029 | −0.642533 | ||||||||
\(305\) | −2.13335 | + | 15.1842i | −0.122155 | + | 0.869445i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 22.5718i | − | 1.28824i | −0.764923 | − | 0.644121i | \(-0.777223\pi\) | ||
0.764923 | − | 0.644121i | \(-0.222777\pi\) | |||||||
\(308\) | − | 3.24443i | − | 0.184869i | ||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −21.8479 | − | 3.06959i | −1.24088 | − | 0.174341i | ||||
\(311\) | 24.0830 | 1.36562 | 0.682810 | − | 0.730596i | \(-0.260758\pi\) | ||||
0.682810 | + | 0.730596i | \(0.260758\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 9.65433i | − | 0.545695i | −0.962057 | − | 0.272848i | \(-0.912035\pi\) | ||
0.962057 | − | 0.272848i | \(-0.0879655\pi\) | |||||||
\(314\) | 19.8479 | 1.12008 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.87955 | −0.443260 | ||||||||
\(317\) | 6.04149i | 0.339324i | 0.985502 | + | 0.169662i | \(0.0542676\pi\) | ||||
−0.985502 | + | 0.169662i | \(0.945732\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.51114 | −0.0846075 | ||||||||
\(320\) | −1.47658 | + | 10.5096i | −0.0825433 | + | 0.587505i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.62222i | 0.146130i | ||||||||
\(323\) | − | 10.7556i | − | 0.598456i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 8.85728 | − | 30.8988i | 0.491313 | − | 1.71396i | ||||
\(326\) | 39.6958 | 2.19855 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5.92104i | 0.326935i | ||||||||
\(329\) | −2.75557 | −0.151919 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.5111 | 0.742639 | 0.371320 | − | 0.928505i | \(-0.378905\pi\) | ||||
0.371320 | + | 0.928505i | \(0.378905\pi\) | |||||||
\(332\) | − | 18.8385i | − | 1.03390i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 29.2070 | 1.59813 | ||||||||
\(335\) | −6.10171 | − | 0.857279i | −0.333372 | − | 0.0468382i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 10.4889i | 0.571365i | 0.958324 | + | 0.285682i | \(0.0922202\pi\) | ||||
−0.958324 | + | 0.285682i | \(0.907780\pi\) | |||||||
\(338\) | − | 53.9131i | − | 2.93248i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15.9081 | − | 2.23506i | −0.862740 | − | 0.121213i | ||||
\(341\) | −10.3684 | −0.561481 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 7.26317 | 0.391604 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.92104 | −0.210796 | ||||||||
\(347\) | 16.7239i | 0.897787i | 0.893585 | + | 0.448894i | \(0.148182\pi\) | ||||
−0.893585 | + | 0.448894i | \(0.851818\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.3684 | 0.876181 | 0.438091 | − | 0.898931i | \(-0.355655\pi\) | ||||
0.438091 | + | 0.898931i | \(0.355655\pi\) | |||||||
\(350\) | −9.14764 | − | 2.62222i | −0.488962 | − | 0.140163i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.6824i | 0.782577i | ||||||||
\(353\) | 0.549086i | 0.0292249i | 0.999893 | + | 0.0146124i | \(0.00465145\pi\) | ||||
−0.999893 | + | 0.0146124i | \(0.995349\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.622216 | − | 4.42864i | 0.0330238 | − | 0.235048i | ||||
\(356\) | −7.49823 | −0.397405 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.0321i | 1.00588i | ||||||||
\(359\) | −0.285442 | −0.0150651 | −0.00753253 | − | 0.999972i | \(-0.502398\pi\) | ||||
−0.00753253 | + | 0.999972i | \(0.502398\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.1017 | −0.689564 | ||||||||
\(362\) | − | 23.0321i | − | 1.21054i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.4286 | −0.546609 | ||||||||
\(365\) | −3.47949 | − | 0.488863i | −0.182125 | − | 0.0255882i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.71456i | 0.0894992i | 0.998998 | + | 0.0447496i | \(0.0142490\pi\) | ||||
−0.998998 | + | 0.0447496i | \(0.985751\pi\) | |||||||
\(368\) | − | 6.35551i | − | 0.331304i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.50760 | − | 32.0830i | 0.234339 | − | 1.66791i | ||||
\(371\) | 9.18421 | 0.476820 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 16.0000i | − | 0.828449i | −0.910175 | − | 0.414224i | \(-0.864053\pi\) | ||
0.910175 | − | 0.414224i | \(-0.135947\pi\) | |||||||
\(374\) | −16.8573 | −0.871669 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.98126 | 0.102176 | ||||||||
\(377\) | 4.85728i | 0.250163i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.85728 | 0.249502 | 0.124751 | − | 0.992188i | \(-0.460187\pi\) | ||||
0.124751 | + | 0.992188i | \(0.460187\pi\) | |||||||
\(380\) | 1.22570 | − | 8.72393i | 0.0628768 | − | 0.447528i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 0.930409i | − | 0.0476039i | ||||||
\(383\) | − | 8.38715i | − | 0.428563i | −0.976772 | − | 0.214282i | \(-0.931259\pi\) | ||
0.976772 | − | 0.214282i | \(-0.0687411\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −4.42864 | − | 0.622216i | −0.225704 | − | 0.0317110i | ||||
\(386\) | −43.6958 | −2.22406 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 19.3689i | 0.983307i | ||||||||
\(389\) | 8.95899 | 0.454239 | 0.227119 | − | 0.973867i | \(-0.427069\pi\) | ||||
0.227119 | + | 0.973867i | \(0.427069\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.10171 | 0.308577 | ||||||||
\(392\) | − | 0.719004i | − | 0.0363152i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.25380 | −0.113545 | ||||||||
\(395\) | −1.51114 | + | 10.7556i | −0.0760336 | + | 0.541171i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2.54909i | − | 0.127935i | −0.997952 | − | 0.0639675i | \(-0.979625\pi\) | ||
0.997952 | − | 0.0639675i | \(-0.0203754\pi\) | |||||||
\(398\) | − | 16.7427i | − | 0.839234i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 22.1713 | + | 6.35551i | 1.10857 | + | 0.317775i | ||||
\(401\) | −0.958989 | −0.0478896 | −0.0239448 | − | 0.999713i | \(-0.507623\pi\) | ||||
−0.0239448 | + | 0.999713i | \(0.507623\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 33.3274i | 1.66016i | ||||||||
\(404\) | 2.40006 | 0.119407 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.43801 | 0.0713671 | ||||||||
\(407\) | − | 15.2257i | − | 0.754710i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.9813 | 1.58137 | 0.790686 | − | 0.612222i | \(-0.209724\pi\) | ||||
0.790686 | + | 0.612222i | \(0.209724\pi\) | |||||||
\(410\) | −34.7052 | − | 4.87601i | −1.71397 | − | 0.240809i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 14.3684i | − | 0.707881i | ||||||
\(413\) | − | 14.1017i | − | 0.693900i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −25.7146 | − | 3.61285i | −1.26228 | − | 0.177348i | ||||
\(416\) | 47.1941 | 2.31388 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 9.24443i | − | 0.452160i | ||||||
\(419\) | −0.470127 | −0.0229672 | −0.0114836 | − | 0.999934i | \(-0.503655\pi\) | ||||
−0.0114836 | + | 0.999934i | \(0.503655\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.6128 | −1.63819 | −0.819095 | − | 0.573658i | \(-0.805524\pi\) | ||||
−0.819095 | + | 0.573658i | \(0.805524\pi\) | |||||||
\(422\) | 44.2034i | 2.15179i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.60348 | −0.320693 | ||||||||
\(425\) | −6.10171 | + | 21.2859i | −0.295976 | + | 1.03252i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 6.85728i | − | 0.331847i | ||||||
\(428\) | 2.86311i | 0.138394i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −5.98126 | + | 42.5718i | −0.288442 | + | 2.05300i | ||||
\(431\) | −11.7146 | −0.564270 | −0.282135 | − | 0.959375i | \(-0.591043\pi\) | ||||
−0.282135 | + | 0.959375i | \(0.591043\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.0602231i | 0.00289414i | 0.999999 | + | 0.00144707i | \(0.000460616\pi\) | ||||
−0.999999 | + | 0.00144707i | \(0.999539\pi\) | |||||||
\(434\) | 9.86665 | 0.473614 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.10525 | 0.436062 | ||||||||
\(437\) | 3.34614i | 0.160068i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.4286 | 1.07046 | 0.535230 | − | 0.844706i | \(-0.320225\pi\) | ||||
0.535230 | + | 0.844706i | \(0.320225\pi\) | |||||||
\(440\) | 3.18421 | + | 0.447375i | 0.151801 | + | 0.0213278i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 54.1847i | 2.57730i | ||||||||
\(443\) | − | 23.9496i | − | 1.13788i | −0.822379 | − | 0.568940i | \(-0.807353\pi\) | ||
0.822379 | − | 0.568940i | \(-0.192647\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.43801 | + | 10.2351i | −0.0681681 | + | 0.485189i | ||||
\(446\) | −28.9777 | −1.37214 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 4.74620i | − | 0.224237i | ||||||
\(449\) | 29.4291 | 1.38885 | 0.694423 | − | 0.719567i | \(-0.255660\pi\) | ||||
0.694423 | + | 0.719567i | \(0.255660\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −16.4701 | −0.775548 | ||||||||
\(452\) | 18.3082i | 0.861145i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −27.3461 | −1.28342 | ||||||||
\(455\) | −2.00000 | + | 14.2351i | −0.0937614 | + | 0.667350i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.14272i | − | 0.147010i | −0.997295 | − | 0.0735051i | \(-0.976581\pi\) | ||
0.997295 | − | 0.0735051i | \(-0.0234185\pi\) | |||||||
\(458\) | 10.6824i | 0.499158i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.94914 | + | 0.695346i | 0.230755 | + | 0.0324207i | ||||
\(461\) | 3.37778 | 0.157319 | 0.0786596 | − | 0.996902i | \(-0.474936\pi\) | ||||
0.0786596 | + | 0.996902i | \(0.474936\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 20.8573i | − | 0.969320i | −0.874703 | − | 0.484660i | \(-0.838943\pi\) | ||
0.874703 | − | 0.484660i | \(-0.161057\pi\) | |||||||
\(464\) | −3.48532 | −0.161802 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −44.3180 | −2.05299 | ||||||||
\(467\) | 14.3684i | 0.664891i | 0.943122 | + | 0.332446i | \(0.107874\pi\) | ||||
−0.943122 | + | 0.332446i | \(0.892126\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.75557 | 0.127240 | ||||||||
\(470\) | −1.63158 | + | 11.6128i | −0.0752593 | + | 0.535661i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.1392i | 0.466694i | ||||||||
\(473\) | 20.2034i | 0.928954i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.6731 | − | 3.34614i | −0.535597 | − | 0.153532i | ||||
\(476\) | 7.18421 | 0.329288 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 16.1561i | − | 0.738963i | ||||||
\(479\) | 6.36842 | 0.290980 | 0.145490 | − | 0.989360i | \(-0.453524\pi\) | ||||
0.145490 | + | 0.989360i | \(0.453524\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −48.9403 | −2.23148 | ||||||||
\(482\) | − | 13.7877i | − | 0.628012i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 11.3555 | 0.516160 | ||||||||
\(485\) | 26.4385 | + | 3.71456i | 1.20051 | + | 0.168669i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.3274i | 0.785180i | 0.919714 | + | 0.392590i | \(0.128421\pi\) | ||||
−0.919714 | + | 0.392590i | \(0.871579\pi\) | |||||||
\(488\) | 4.93041i | 0.223189i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.21432 | + | 0.592104i | 0.190384 | + | 0.0267485i | ||||
\(491\) | −2.00000 | −0.0902587 | −0.0451294 | − | 0.998981i | \(-0.514370\pi\) | ||||
−0.0451294 | + | 0.998981i | \(0.514370\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 3.34614i | − | 0.150703i | ||||||
\(494\) | −29.7146 | −1.33692 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −23.9140 | −1.07377 | ||||||||
\(497\) | 2.00000i | 0.0897123i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −23.3461 | −1.04512 | −0.522558 | − | 0.852603i | \(-0.675022\pi\) | ||||
−0.522558 | + | 0.852603i | \(0.675022\pi\) | |||||||
\(500\) | −7.37487 | + | 16.5698i | −0.329814 | + | 0.741025i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 52.5531i | − | 2.34556i | ||||||
\(503\) | 0.387152i | 0.0172623i | 0.999963 | + | 0.00863113i | \(0.00274741\pi\) | ||||
−0.999963 | + | 0.00863113i | \(0.997253\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.460282 | − | 3.27607i | 0.0204823 | − | 0.145783i | ||||
\(506\) | 5.24443 | 0.233143 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.8573i | 0.925392i | ||||||||
\(509\) | −29.9496 | −1.32749 | −0.663747 | − | 0.747957i | \(-0.731035\pi\) | ||||
−0.663747 | + | 0.747957i | \(0.731035\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.57136 | 0.0695129 | ||||||||
\(512\) | 27.2306i | 1.20343i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.815792 | −0.0359830 | ||||||||
\(515\) | −19.6128 | − | 2.75557i | −0.864245 | − | 0.121425i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.51114i | 0.242380i | ||||||||
\(518\) | 14.4889i | 0.636604i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.43801 | − | 10.2351i | 0.0630608 | − | 0.448837i | ||||
\(521\) | 18.5205 | 0.811398 | 0.405699 | − | 0.914007i | \(-0.367028\pi\) | ||||
0.405699 | + | 0.914007i | \(0.367028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | −3.40943 | −0.148942 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.8479 | 0.778206 | ||||||||
\(527\) | − | 22.9590i | − | 1.00011i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.1017 | 0.917466 | ||||||||
\(530\) | 5.43801 | − | 38.7052i | 0.236212 | − | 1.68125i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.93978i | 0.170811i | ||||||||
\(533\) | 52.9403i | 2.29310i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.90813 | + | 0.549086i | 0.168963 | + | 0.0237390i | ||||
\(536\) | −1.98126 | −0.0855776 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.32339i | 0.143282i | ||||||||
\(539\) | 2.00000 | 0.0861461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.5906 | 0.627298 | 0.313649 | − | 0.949539i | \(-0.398449\pi\) | ||||
0.313649 | + | 0.949539i | \(0.398449\pi\) | |||||||
\(542\) | − | 5.12981i | − | 0.220344i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −32.5116 | −1.39392 | ||||||||
\(545\) | 1.74620 | − | 12.4286i | 0.0747990 | − | 0.532384i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 18.7556i | − | 0.801930i | −0.916093 | − | 0.400965i | \(-0.868675\pi\) | ||
0.916093 | − | 0.400965i | \(-0.131325\pi\) | |||||||
\(548\) | 25.8578i | 1.10459i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.24443 | + | 18.2953i | −0.223623 | + | 0.780114i | ||||
\(551\) | 1.83500 | 0.0781738 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 4.85728i | − | 0.206553i | ||||||
\(554\) | 9.75203 | 0.414324 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 18.9362 | 0.803075 | ||||||||
\(557\) | − | 31.8765i | − | 1.35065i | −0.737520 | − | 0.675325i | \(-0.764003\pi\) | ||
0.737520 | − | 0.675325i | \(-0.235997\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 64.9403 | 2.74668 | ||||||||
\(560\) | −10.2143 | − | 1.43509i | −0.431634 | − | 0.0606437i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 45.6414i | − | 1.92527i | ||||||
\(563\) | − | 2.01874i | − | 0.0850796i | −0.999095 | − | 0.0425398i | \(-0.986455\pi\) | ||
0.999095 | − | 0.0425398i | \(-0.0135449\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 24.9906 | + | 3.51114i | 1.05136 | + | 0.147715i | ||||
\(566\) | 4.50760 | 0.189468 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − | 1.43801i | − | 0.0603375i | ||||||
\(569\) | −28.9590 | −1.21402 | −0.607012 | − | 0.794693i | \(-0.707632\pi\) | ||||
−0.607012 | + | 0.794693i | \(0.707632\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 8.97773 | 0.375706 | 0.187853 | − | 0.982197i | \(-0.439847\pi\) | ||||
0.187853 | + | 0.982197i | \(0.439847\pi\) | |||||||
\(572\) | 20.8573i | 0.872087i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 15.6731 | 0.654181 | ||||||||
\(575\) | 1.89829 | − | 6.62222i | 0.0791642 | − | 0.276165i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.6766i | 1.19382i | 0.802307 | + | 0.596911i | \(0.203606\pi\) | ||||
−0.802307 | + | 0.596911i | \(0.796394\pi\) | |||||||
\(578\) | − | 4.97280i | − | 0.206841i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.381323 | − | 2.71408i | 0.0158336 | − | 0.112696i | ||||
\(581\) | 11.6128 | 0.481782 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 18.3684i | − | 0.760742i | ||||||
\(584\) | −1.12981 | −0.0467520 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −16.0415 | −0.662668 | ||||||||
\(587\) | − | 45.2070i | − | 1.86589i | −0.360018 | − | 0.932945i | \(-0.617229\pi\) | ||
0.360018 | − | 0.932945i | \(-0.382771\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.5906 | 0.518786 | ||||||||
\(590\) | −59.4291 | − | 8.34968i | −2.44666 | − | 0.343751i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 35.1169i | − | 1.44330i | ||||||
\(593\) | − | 18.2636i | − | 0.749998i | −0.927025 | − | 0.374999i | \(-0.877643\pi\) | ||
0.927025 | − | 0.374999i | \(-0.122357\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.37778 | − | 9.80642i | 0.0564837 | − | 0.402024i | ||||
\(596\) | 34.4327 | 1.41042 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 16.8573i | − | 0.689345i | ||||||
\(599\) | −22.7368 | −0.929002 | −0.464501 | − | 0.885573i | \(-0.653766\pi\) | ||||
−0.464501 | + | 0.885573i | \(0.653766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.488863 | 0.0199411 | 0.00997056 | − | 0.999950i | \(-0.496826\pi\) | ||||
0.00997056 | + | 0.999950i | \(0.496826\pi\) | |||||||
\(602\) | − | 19.2257i | − | 0.783581i | ||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −27.3461 | −1.11270 | ||||||||
\(605\) | 2.17775 | − | 15.5002i | 0.0885383 | − | 0.630174i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20.2034i | 0.820032i | 0.912078 | + | 0.410016i | \(0.134477\pi\) | ||||
−0.912078 | + | 0.410016i | \(0.865523\pi\) | |||||||
\(608\) | − | 17.8292i | − | 0.723069i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −28.8988 | − | 4.06022i | −1.17008 | − | 0.164394i | ||||
\(611\) | 17.7146 | 0.716654 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.3684i | 0.418776i | 0.977833 | + | 0.209388i | \(0.0671472\pi\) | ||||
−0.977833 | + | 0.209388i | \(0.932853\pi\) | |||||||
\(614\) | 42.9590 | 1.73368 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.43801 | −0.0579390 | ||||||||
\(617\) | − | 39.2859i | − | 1.58159i | −0.612080 | − | 0.790796i | \(-0.709667\pi\) | ||
0.612080 | − | 0.790796i | \(-0.290333\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.8988 | −1.72425 | −0.862123 | − | 0.506698i | \(-0.830866\pi\) | ||||
−0.862123 | + | 0.506698i | \(0.830866\pi\) | |||||||
\(620\) | 2.61639 | − | 18.6222i | 0.105077 | − | 0.747886i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 45.8350i | 1.83782i | ||||||||
\(623\) | − | 4.62222i | − | 0.185185i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2034 | + | 13.2444i | 0.848137 | + | 0.529777i | ||||
\(626\) | 18.3742 | 0.734383 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 16.9175i | 0.675082i | ||||||||
\(629\) | 33.7146 | 1.34429 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.3461 | 0.610920 | 0.305460 | − | 0.952205i | \(-0.401190\pi\) | ||||
0.305460 | + | 0.952205i | \(0.401190\pi\) | |||||||
\(632\) | 3.49240i | 0.138920i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −11.4982 | −0.456653 | ||||||||
\(635\) | 28.4701 | + | 4.00000i | 1.12980 | + | 0.158735i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 6.42864i | − | 0.254712i | ||||||
\(638\) | − | 2.87601i | − | 0.113863i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.5096 | + | 1.75758i | 0.494486 | + | 0.0694743i | ||||
\(641\) | −30.6735 | −1.21153 | −0.605766 | − | 0.795643i | \(-0.707133\pi\) | ||||
−0.605766 | + | 0.795643i | \(0.707133\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 49.0607i | − | 1.93477i | −0.253320 | − | 0.967383i | \(-0.581523\pi\) | ||
0.253320 | − | 0.967383i | \(-0.418477\pi\) | |||||||
\(644\) | −2.23506 | −0.0880738 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.4701 | 0.805386 | ||||||||
\(647\) | − | 15.3461i | − | 0.603319i | −0.953416 | − | 0.301660i | \(-0.902459\pi\) | ||
0.953416 | − | 0.301660i | \(-0.0975406\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −28.2034 | −1.10708 | ||||||||
\(650\) | 58.8069 | + | 16.8573i | 2.30660 | + | 0.661197i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 33.8350i | 1.32508i | ||||||||
\(653\) | 19.4697i | 0.761906i | 0.924594 | + | 0.380953i | \(0.124404\pi\) | ||||
−0.924594 | + | 0.380953i | \(0.875596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −0.653858 | + | 4.65386i | −0.0255484 | + | 0.181841i | ||||
\(656\) | −37.9871 | −1.48315 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 5.24443i | − | 0.204449i | ||||||
\(659\) | 30.9403 | 1.20526 | 0.602631 | − | 0.798020i | \(-0.294119\pi\) | ||||
0.602631 | + | 0.798020i | \(0.294119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.7975 | 1.85911 | 0.929554 | − | 0.368685i | \(-0.120192\pi\) | ||||
0.929554 | + | 0.368685i | \(0.120192\pi\) | |||||||
\(662\) | 25.7146i | 0.999425i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.34968 | −0.324030 | ||||||||
\(665\) | 5.37778 | + | 0.755569i | 0.208542 | + | 0.0292997i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.04101i | 0.0403081i | ||||||||
\(668\) | 24.8948i | 0.963207i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.63158 | − | 11.6128i | 0.0630336 | − | 0.448643i | ||||
\(671\) | −13.7146 | −0.529445 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 27.8163i | 1.07224i | 0.844142 | + | 0.536119i | \(0.180110\pi\) | ||||
−0.844142 | + | 0.536119i | \(0.819890\pi\) | |||||||
\(674\) | −19.9625 | −0.768928 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 45.9532 | 1.76743 | ||||||||
\(677\) | − | 19.0005i | − | 0.730248i | −0.930959 | − | 0.365124i | \(-0.881027\pi\) | ||
0.930959 | − | 0.365124i | \(-0.118973\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.9398 | −0.458207 | ||||||||
\(680\) | −0.990632 | + | 7.05086i | −0.0379890 | + | 0.270388i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − | 19.7333i | − | 0.755627i | ||||||
\(683\) | − | 4.52051i | − | 0.172972i | −0.996253 | − | 0.0864862i | \(-0.972436\pi\) | ||
0.996253 | − | 0.0864862i | \(-0.0275638\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 35.2958 | + | 4.95899i | 1.34858 | + | 0.189473i | ||||
\(686\) | −1.90321 | −0.0726650 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 46.5977i | 1.77652i | ||||||||
\(689\) | −59.0420 | −2.24932 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.18421 | −0.0450494 | −0.0225247 | − | 0.999746i | \(-0.507170\pi\) | ||||
−0.0225247 | + | 0.999746i | \(0.507170\pi\) | |||||||
\(692\) | − | 3.34213i | − | 0.127049i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −31.8292 | −1.20822 | ||||||||
\(695\) | 3.63158 | − | 25.8479i | 0.137754 | − | 0.980467i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 36.4701i | − | 1.38140i | ||||||
\(698\) | 31.1526i | 1.17914i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.23506 | − | 7.79706i | 0.0844775 | − | 0.294701i | ||||
\(701\) | 26.6735 | 1.00745 | 0.503723 | − | 0.863865i | \(-0.331963\pi\) | ||||
0.503723 | + | 0.863865i | \(0.331963\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.4889i | 0.697321i | ||||||||
\(704\) | −9.49240 | −0.357758 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.04503 | −0.0393301 | ||||||||
\(707\) | 1.47949i | 0.0556421i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 18.2034 | 0.683644 | 0.341822 | − | 0.939765i | \(-0.388956\pi\) | ||||
0.341822 | + | 0.939765i | \(0.388956\pi\) | |||||||
\(710\) | 8.42864 | + | 1.18421i | 0.316321 | + | 0.0444425i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.32339i | 0.124549i | ||||||||
\(713\) | 7.14272i | 0.267497i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 28.4701 | + | 4.00000i | 1.06472 | + | 0.149592i | ||||
\(716\) | −16.2222 | −0.606250 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 0.543257i | − | 0.0202742i | ||||||
\(719\) | 4.85728 | 0.181146 | 0.0905730 | − | 0.995890i | \(-0.471130\pi\) | ||||
0.0905730 | + | 0.995890i | \(0.471130\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.85728 | 0.329862 | ||||||||
\(722\) | − | 24.9353i | − | 0.927997i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 19.6316 | 0.729602 | ||||||||
\(725\) | −3.63158 | − | 1.04101i | −0.134874 | − | 0.0386622i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 21.0607i | − | 0.781098i | −0.920582 | − | 0.390549i | \(-0.872285\pi\) | ||
0.920582 | − | 0.390549i | \(-0.127715\pi\) | |||||||
\(728\) | 4.62222i | 0.171311i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.930409 | − | 6.62222i | 0.0344360 | − | 0.245099i | ||||
\(731\) | −44.7368 | −1.65465 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 9.45091i | 0.349077i | 0.984650 | + | 0.174539i | \(0.0558434\pi\) | ||||
−0.984650 | + | 0.174539i | \(0.944157\pi\) | |||||||
\(734\) | −3.26317 | −0.120446 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.1146 | 0.372830 | ||||||||
\(737\) | − | 5.51114i | − | 0.203005i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.20342 | 0.301768 | 0.150884 | − | 0.988551i | \(-0.451788\pi\) | ||||
0.150884 | + | 0.988551i | \(0.451788\pi\) | |||||||
\(740\) | 27.3461 | + | 3.84208i | 1.00526 | + | 0.141238i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 17.4795i | 0.641692i | ||||||||
\(743\) | − | 8.33677i | − | 0.305847i | −0.988238 | − | 0.152923i | \(-0.951131\pi\) | ||
0.988238 | − | 0.152923i | \(-0.0488687\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 6.60348 | − | 47.0005i | 0.241933 | − | 1.72196i | ||||
\(746\) | 30.4514 | 1.11490 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 14.3684i | − | 0.525361i | ||||||
\(749\) | −1.76494 | −0.0644894 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.9180 | −0.945760 | −0.472880 | − | 0.881127i | \(-0.656786\pi\) | ||||
−0.472880 | + | 0.881127i | \(0.656786\pi\) | |||||||
\(752\) | 12.7110i | 0.463523i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.24443 | −0.336662 | ||||||||
\(755\) | −5.24443 | + | 37.3274i | −0.190864 | + | 1.35848i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 8.94025i | − | 0.324939i | −0.986714 | − | 0.162470i | \(-0.948054\pi\) | ||
0.986714 | − | 0.162470i | \(-0.0519459\pi\) | |||||||
\(758\) | 9.24443i | 0.335773i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.86665 | − | 0.543257i | −0.140258 | − | 0.0197060i | ||||
\(761\) | 0.825636 | 0.0299293 | 0.0149646 | − | 0.999888i | \(-0.495236\pi\) | ||||
0.0149646 | + | 0.999888i | \(0.495236\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.61285i | 0.203199i | ||||||||
\(764\) | 0.793040 | 0.0286912 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.9625 | 0.576750 | ||||||||
\(767\) | 90.6548i | 3.27336i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.2257 | −0.765418 | −0.382709 | − | 0.923869i | \(-0.625009\pi\) | ||||
−0.382709 | + | 0.923869i | \(0.625009\pi\) | |||||||
\(770\) | 1.18421 | − | 8.42864i | 0.0426759 | − | 0.303747i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 37.2444i | − | 1.34046i | ||||||
\(773\) | − | 29.4893i | − | 1.06066i | −0.847792 | − | 0.530329i | \(-0.822068\pi\) | ||
0.847792 | − | 0.530329i | \(-0.177932\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.9175 | − | 7.14272i | −0.895063 | − | 0.256574i | ||||
\(776\) | 8.58474 | 0.308174 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.0509i | 0.611303i | ||||||||
\(779\) | 20.0000 | 0.716574 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.00000 | 0.143131 | ||||||||
\(782\) | 11.6128i | 0.415275i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 4.61285 | 0.164745 | ||||||||
\(785\) | 23.0923 | + | 3.24443i | 0.824201 | + | 0.115799i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.4514i | 1.22806i | 0.789283 | + | 0.614030i | \(0.210453\pi\) | ||||
−0.789283 | + | 0.614030i | \(0.789547\pi\) | |||||||
\(788\) | − | 1.92104i | − | 0.0684343i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −20.4701 | − | 2.87601i | −0.728294 | − | 0.102324i | ||||
\(791\) | −11.2859 | −0.401281 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 44.0830i | 1.56543i | ||||||||
\(794\) | 4.85145 | 0.172172 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.2707 | 0.505812 | ||||||||
\(797\) | 18.9175i | 0.670092i | 0.942202 | + | 0.335046i | \(0.108752\pi\) | ||||
−0.942202 | + | 0.335046i | \(0.891248\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.2034 | −0.431726 | ||||||||
\(800\) | −10.1146 | + | 35.2850i | −0.357606 | + | 1.24751i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 1.82516i | − | 0.0644486i | ||||||
\(803\) | − | 3.14272i | − | 0.110904i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.428639 | + | 3.05086i | −0.0151076 | + | 0.107529i | ||||
\(806\) | −63.4291 | −2.23420 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 1.06376i | − | 0.0374230i | ||||||
\(809\) | 21.2257 | 0.746256 | 0.373128 | − | 0.927780i | \(-0.378285\pi\) | ||||
0.373128 | + | 0.927780i | \(0.378285\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.5081 | −0.755251 | −0.377625 | − | 0.925958i | \(-0.623259\pi\) | ||||
−0.377625 | + | 0.925958i | \(0.623259\pi\) | |||||||
\(812\) | 1.22570i | 0.0430135i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 28.9777 | 1.01567 | ||||||||
\(815\) | 46.1847 | + | 6.48886i | 1.61778 | + | 0.227295i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 24.5334i | − | 0.858315i | ||||||
\(818\) | 60.8671i | 2.12817i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.15610 | − | 29.5812i | 0.145137 | − | 1.03302i | ||||
\(821\) | 46.2034 | 1.61251 | 0.806255 | − | 0.591568i | \(-0.201491\pi\) | ||||
0.806255 | + | 0.591568i | \(0.201491\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 17.8350i | − | 0.621689i | −0.950461 | − | 0.310845i | \(-0.899388\pi\) | ||
0.950461 | − | 0.310845i | \(-0.100612\pi\) | |||||||
\(824\) | −6.36842 | −0.221854 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 26.8385 | 0.933832 | ||||||||
\(827\) | 35.2128i | 1.22447i | 0.790676 | + | 0.612234i | \(0.209729\pi\) | ||||
−0.790676 | + | 0.612234i | \(0.790271\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.3872 | −0.499686 | −0.249843 | − | 0.968286i | \(-0.580379\pi\) | ||||
−0.249843 | + | 0.968286i | \(0.580379\pi\) | |||||||
\(830\) | 6.87601 | − | 48.9403i | 0.238670 | − | 1.69874i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 30.5116i | 1.05780i | ||||||||
\(833\) | 4.42864i | 0.153443i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 33.9813 | + | 4.77430i | 1.17597 | + | 0.165222i | ||||
\(836\) | 7.87955 | 0.272520 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 0.894751i | − | 0.0309087i | ||||||
\(839\) | 1.51114 | 0.0521703 | 0.0260851 | − | 0.999660i | \(-0.491696\pi\) | ||||
0.0260851 | + | 0.999660i | \(0.491696\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4291 | −0.980314 | ||||||||
\(842\) | − | 63.9724i | − | 2.20463i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −37.6771 | −1.29690 | ||||||||
\(845\) | 8.81288 | − | 62.7259i | 0.303172 | − | 2.15784i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.00000i | 0.240523i | ||||||||
\(848\) | − | 42.3654i | − | 1.45483i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −40.5116 | − | 11.6128i | −1.38954 | − | 0.398317i | ||||
\(851\) | −10.4889 | −0.359554 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 15.4064i | − | 0.527504i | −0.964591 | − | 0.263752i | \(-0.915040\pi\) | ||
0.964591 | − | 0.263752i | \(-0.0849600\pi\) | |||||||
\(854\) | 13.0509 | 0.446591 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.26900 | 0.0433734 | ||||||||
\(857\) | 19.8578i | 0.678328i | 0.940727 | + | 0.339164i | \(0.110144\pi\) | ||||
−0.940727 | + | 0.339164i | \(0.889856\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.42864 | −0.0828641 | −0.0414321 | − | 0.999141i | \(-0.513192\pi\) | ||||
−0.0414321 | + | 0.999141i | \(0.513192\pi\) | |||||||
\(860\) | −36.2864 | − | 5.09817i | −1.23736 | − | 0.173846i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | − | 22.2953i | − | 0.759380i | ||||||
\(863\) | 39.2958i | 1.33764i | 0.743423 | + | 0.668822i | \(0.233201\pi\) | ||||
−0.743423 | + | 0.668822i | \(0.766799\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.56199 | − | 0.640951i | −0.155112 | − | 0.0217930i | ||||
\(866\) | −0.114617 | −0.00389485 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.40990i | 0.285451i | ||||||||
\(869\) | −9.71456 | −0.329544 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −17.7146 | −0.600235 | ||||||||
\(872\) | − | 4.03566i | − | 0.136665i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −6.36842 | −0.215415 | ||||||||
\(875\) | −10.2143 | − | 4.54617i | −0.345307 | − | 0.153689i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 56.2864i | 1.90066i | 0.311249 | + | 0.950328i | \(0.399253\pi\) | ||||
−0.311249 | + | 0.950328i | \(0.600747\pi\) | |||||||
\(878\) | 42.6865i | 1.44060i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.87019 | + | 20.4286i | −0.0967539 | + | 0.688649i | ||||
\(881\) | 2.33677 | 0.0787279 | 0.0393640 | − | 0.999225i | \(-0.487467\pi\) | ||||
0.0393640 | + | 0.999225i | \(0.487467\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33.7146i | 1.13459i | 0.823516 | + | 0.567293i | \(0.192009\pi\) | ||||
−0.823516 | + | 0.567293i | \(0.807991\pi\) | |||||||
\(884\) | −46.1847 | −1.55336 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45.5812 | 1.53133 | ||||||||
\(887\) | 47.8992i | 1.60830i | 0.594427 | + | 0.804150i | \(0.297379\pi\) | ||||
−0.594427 | + | 0.804150i | \(0.702621\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.8573 | −0.431219 | ||||||||
\(890\) | −19.4795 | − | 2.73683i | −0.652954 | − | 0.0917388i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 24.6994i | − | 0.826996i | ||||||
\(893\) | − | 6.69228i | − | 0.223949i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.11108 | + | 22.1432i | −0.103992 | + | 0.740165i | ||||
\(896\) | −5.64941 | −0.188734 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 56.0098i | 1.86907i | ||||||||
\(899\) | 3.91703 | 0.130640 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.6735 | 1.35503 | ||||||||
\(902\) | − | 31.3461i | − | 1.04371i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.11462 | 0.269888 | ||||||||
\(905\) | 3.76494 | − | 26.7971i | 0.125151 | − | 0.890764i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 23.7591i | − | 0.788908i | −0.918916 | − | 0.394454i | \(-0.870934\pi\) | ||
0.918916 | − | 0.394454i | \(-0.129066\pi\) | |||||||
\(908\) | − | 23.3087i | − | 0.773525i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −27.0923 | − | 3.80642i | −0.898102 | − | 0.126182i | ||||
\(911\) | −22.9403 | −0.760045 | −0.380022 | − | 0.924977i | \(-0.624084\pi\) | ||||
−0.380022 | + | 0.924977i | \(0.624084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 23.2257i | − | 0.768658i | ||||||
\(914\) | 5.98126 | 0.197843 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.10525 | −0.300846 | ||||||||
\(917\) | − | 2.10171i | − | 0.0694046i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.9777 | −0.560043 | −0.280022 | − | 0.959994i | \(-0.590342\pi\) | ||||
−0.280022 | + | 0.959994i | \(0.590342\pi\) | |||||||
\(920\) | 0.308193 | − | 2.19358i | 0.0101608 | − | 0.0723201i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.42864i | 0.211716i | ||||||||
\(923\) | − | 12.8573i | − | 0.423202i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 10.4889 | − | 36.5906i | 0.344872 | − | 1.20309i | ||||
\(926\) | 39.6958 | 1.30449 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 5.54680i | − | 0.182082i | ||||||
\(929\) | 39.3403 | 1.29071 | 0.645357 | − | 0.763881i | \(-0.276709\pi\) | ||||
0.645357 | + | 0.763881i | \(0.276709\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.42864 | −0.0795954 | ||||||||
\(932\) | − | 37.7748i | − | 1.23735i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −27.3461 | −0.894793 | ||||||||
\(935\) | −19.6128 | − | 2.75557i | −0.641409 | − | 0.0901167i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 17.7748i | 0.580677i | 0.956924 | + | 0.290338i | \(0.0937679\pi\) | ||||
−0.956924 | + | 0.290338i | \(0.906232\pi\) | |||||||
\(938\) | 5.24443i | 0.171237i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.89829 | − | 1.39069i | −0.322847 | − | 0.0453594i | ||||
\(941\) | −35.5812 | −1.15991 | −0.579957 | − | 0.814647i | \(-0.696931\pi\) | ||||
−0.579957 | + | 0.814647i | \(0.696931\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.3461i | 0.369481i | ||||||||
\(944\) | −65.0490 | −2.11717 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −38.4514 | −1.25016 | ||||||||
\(947\) | 30.5018i | 0.991174i | 0.868558 | + | 0.495587i | \(0.165047\pi\) | ||||
−0.868558 | + | 0.495587i | \(0.834953\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.1017 | −0.327915 | ||||||||
\(950\) | 6.36842 | − | 22.2163i | 0.206619 | − | 0.720793i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | − | 3.18421i | − | 0.103201i | ||||||
\(953\) | 51.1655i | 1.65741i | 0.559684 | + | 0.828706i | \(0.310923\pi\) | ||||
−0.559684 | + | 0.828706i | \(0.689077\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.152089 | − | 1.08250i | 0.00492148 | − | 0.0350288i | ||||
\(956\) | 13.7708 | 0.445378 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 12.1204i | 0.391594i | ||||||||
\(959\) | −15.9398 | −0.514722 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.12399 | −0.133032 | ||||||||
\(962\) | − | 93.1437i | − | 3.00307i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.7520 | 0.378507 | ||||||||
\(965\) | −50.8385 | − | 7.14272i | −1.63655 | − | 0.229932i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 47.8992i | − | 1.54034i | −0.637841 | − | 0.770168i | \(-0.720172\pi\) | ||
0.637841 | − | 0.770168i | \(-0.279828\pi\) | |||||||
\(968\) | − | 5.03303i | − | 0.161768i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.06959 | + | 50.3180i | −0.226991 | + | 1.61561i | ||||
\(971\) | −40.6735 | −1.30528 | −0.652638 | − | 0.757670i | \(-0.726338\pi\) | ||||
−0.652638 | + | 0.757670i | \(0.726338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.6731i | 0.374221i | ||||||||
\(974\) | −32.9777 | −1.05667 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −31.6316 | −1.01250 | ||||||||
\(977\) | − | 27.4893i | − | 0.879462i | −0.898130 | − | 0.439731i | \(-0.855074\pi\) | ||
0.898130 | − | 0.439731i | \(-0.144926\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.24443 | −0.295453 | ||||||||
\(980\) | −0.504684 | + | 3.59210i | −0.0161215 | + | 0.114746i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 3.80642i | − | 0.121468i | ||||||
\(983\) | − | 24.0000i | − | 0.765481i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.62222 | − | 0.368416i | −0.0835507 | − | 0.0117387i | ||||
\(986\) | 6.36842 | 0.202812 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 25.3274i | − | 0.805772i | ||||||
\(989\) | 13.9180 | 0.442566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −34.6923 | −1.10204 | −0.551018 | − | 0.834493i | \(-0.685761\pi\) | ||||
−0.551018 | + | 0.834493i | \(0.685761\pi\) | |||||||
\(992\) | − | 38.0584i | − | 1.20836i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −3.80642 | −0.120732 | ||||||||
\(995\) | 2.73683 | − | 19.4795i | 0.0867634 | − | 0.617541i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6766i | 0.908197i | 0.890951 | + | 0.454099i | \(0.150039\pi\) | ||||
−0.890951 | + | 0.454099i | \(0.849961\pi\) | |||||||
\(998\) | − | 44.4327i | − | 1.40649i | ||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 315.2.d.e.64.5 | 6 | ||
3.2 | odd | 2 | 105.2.d.b.64.2 | ✓ | 6 | ||
4.3 | odd | 2 | 5040.2.t.v.1009.4 | 6 | |||
5.2 | odd | 4 | 1575.2.a.x.1.1 | 3 | |||
5.3 | odd | 4 | 1575.2.a.w.1.3 | 3 | |||
5.4 | even | 2 | inner | 315.2.d.e.64.2 | 6 | ||
7.6 | odd | 2 | 2205.2.d.l.1324.5 | 6 | |||
12.11 | even | 2 | 1680.2.t.k.1009.2 | 6 | |||
15.2 | even | 4 | 525.2.a.j.1.3 | 3 | |||
15.8 | even | 4 | 525.2.a.k.1.1 | 3 | |||
15.14 | odd | 2 | 105.2.d.b.64.5 | yes | 6 | ||
20.19 | odd | 2 | 5040.2.t.v.1009.3 | 6 | |||
21.2 | odd | 6 | 735.2.q.e.214.2 | 12 | |||
21.5 | even | 6 | 735.2.q.f.214.2 | 12 | |||
21.11 | odd | 6 | 735.2.q.e.79.5 | 12 | |||
21.17 | even | 6 | 735.2.q.f.79.5 | 12 | |||
21.20 | even | 2 | 735.2.d.b.589.2 | 6 | |||
35.34 | odd | 2 | 2205.2.d.l.1324.2 | 6 | |||
60.23 | odd | 4 | 8400.2.a.dj.1.1 | 3 | |||
60.47 | odd | 4 | 8400.2.a.dg.1.3 | 3 | |||
60.59 | even | 2 | 1680.2.t.k.1009.5 | 6 | |||
105.44 | odd | 6 | 735.2.q.e.214.5 | 12 | |||
105.59 | even | 6 | 735.2.q.f.79.2 | 12 | |||
105.62 | odd | 4 | 3675.2.a.bi.1.3 | 3 | |||
105.74 | odd | 6 | 735.2.q.e.79.2 | 12 | |||
105.83 | odd | 4 | 3675.2.a.bj.1.1 | 3 | |||
105.89 | even | 6 | 735.2.q.f.214.5 | 12 | |||
105.104 | even | 2 | 735.2.d.b.589.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.2 | ✓ | 6 | 3.2 | odd | 2 | ||
105.2.d.b.64.5 | yes | 6 | 15.14 | odd | 2 | ||
315.2.d.e.64.2 | 6 | 5.4 | even | 2 | inner | ||
315.2.d.e.64.5 | 6 | 1.1 | even | 1 | trivial | ||
525.2.a.j.1.3 | 3 | 15.2 | even | 4 | |||
525.2.a.k.1.1 | 3 | 15.8 | even | 4 | |||
735.2.d.b.589.2 | 6 | 21.20 | even | 2 | |||
735.2.d.b.589.5 | 6 | 105.104 | even | 2 | |||
735.2.q.e.79.2 | 12 | 105.74 | odd | 6 | |||
735.2.q.e.79.5 | 12 | 21.11 | odd | 6 | |||
735.2.q.e.214.2 | 12 | 21.2 | odd | 6 | |||
735.2.q.e.214.5 | 12 | 105.44 | odd | 6 | |||
735.2.q.f.79.2 | 12 | 105.59 | even | 6 | |||
735.2.q.f.79.5 | 12 | 21.17 | even | 6 | |||
735.2.q.f.214.2 | 12 | 21.5 | even | 6 | |||
735.2.q.f.214.5 | 12 | 105.89 | even | 6 | |||
1575.2.a.w.1.3 | 3 | 5.3 | odd | 4 | |||
1575.2.a.x.1.1 | 3 | 5.2 | odd | 4 | |||
1680.2.t.k.1009.2 | 6 | 12.11 | even | 2 | |||
1680.2.t.k.1009.5 | 6 | 60.59 | even | 2 | |||
2205.2.d.l.1324.2 | 6 | 35.34 | odd | 2 | |||
2205.2.d.l.1324.5 | 6 | 7.6 | odd | 2 | |||
3675.2.a.bi.1.3 | 3 | 105.62 | odd | 4 | |||
3675.2.a.bj.1.1 | 3 | 105.83 | odd | 4 | |||
5040.2.t.v.1009.3 | 6 | 20.19 | odd | 2 | |||
5040.2.t.v.1009.4 | 6 | 4.3 | odd | 2 | |||
8400.2.a.dg.1.3 | 3 | 60.47 | odd | 4 | |||
8400.2.a.dj.1.1 | 3 | 60.23 | odd | 4 |