Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2205,2,Mod(1324,2205)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2205, 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("2205.1324");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2205 = 3^{2} \cdot 5 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2205.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: | \(17.6070136457\) |
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: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1324.5 | ||
Root | \(1.45161 - 1.45161i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2205.1324 |
Dual form | 2205.2.d.l.1324.2 |
$q$-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 \(\left(\mathbb{Z}/2205\mathbb{Z}\right)^\times\).
\(n\) | \(442\) | \(1081\) | \(1226\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 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 | \(-0.649659\pi\) | ||
0.453037 | − | 0.891492i | \(-0.350341\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.61285 | −1.15321 | ||||||||
\(17\) | 4.42864i | 1.07410i | 0.843550 | + | 0.537051i | \(0.180462\pi\) | ||||
−0.843550 | + | 0.537051i | \(0.819538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.42864 | −0.557168 | −0.278584 | − | 0.960412i | \(-0.589865\pi\) | ||||
−0.278584 | + | 0.960412i | \(0.589865\pi\) | |||||||
\(20\) | −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 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 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 | \(-0.654145\pi\) | ||||
−0.465556 | + | 0.885019i | \(0.654145\pi\) | |||||||
\(32\) | − | 7.34122i | − | 1.29776i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −8.42864 | −1.44550 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 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 | \(-0.722331\pi\) | ||||
−0.643050 | + | 0.765824i | \(0.722331\pi\) | |||||||
\(42\) | 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 | \(0.0644095\pi\) | ||||
−0.979597 | + | 0.200971i | \(0.935590\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 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 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.43801i | 0.188820i | ||||||||
\(59\) | −14.1017 | −1.83589 | −0.917943 | − | 0.396712i | \(-0.870151\pi\) | ||||
−0.917943 | + | 0.396712i | \(0.870151\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.85728 | −0.877985 | −0.438992 | − | 0.898491i | \(-0.644664\pi\) | ||||
−0.438992 | + | 0.898491i | \(0.644664\pi\) | |||||||
\(62\) | − | 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 | 0 | ||||||||
\(71\) | −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 | \(-0.970688\pi\) | ||
0.995763 | − | 0.0919569i | \(-0.0293122\pi\) | |||||||
\(74\) | −14.4889 | −1.68430 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.93978 | 0.451923 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 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 | \(-0.780036\pi\) | ||
0.770585 | − | 0.637338i | \(-0.219964\pi\) | |||||||
\(84\) | 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 | \(-0.578780\pi\) | ||||
−0.244977 | + | 0.969529i | \(0.578780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 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 | \(0.207287\pi\) | ||||
−0.795350 | + | 0.606150i | \(0.792713\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.79706 | + | 2.23506i | 0.779706 | + | 0.223506i | ||||
\(101\) | 1.47949 | 0.147215 | 0.0736076 | − | 0.997287i | \(-0.476549\pi\) | ||||
0.0736076 | + | 0.997287i | \(0.476549\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.85728i | − | 0.872734i | −0.899769 | − | 0.436367i | \(-0.856265\pi\) | ||
0.899769 | − | 0.436367i | \(-0.143735\pi\) | |||||||
\(104\) | 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 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 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 | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 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 | \(-0.529266\pi\) | ||||
−0.0918136 | + | 0.995776i | \(0.529266\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −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 | \(-0.335150\pi\) | ||||
0.495048 | + | 0.868865i | \(0.335150\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 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 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.61285 | + | 11.4795i | −0.129547 | + | 0.922055i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.4286i | 0.832296i | 0.909297 | + | 0.416148i | \(0.136620\pi\) | ||||
−0.909297 | + | 0.416148i | \(0.863380\pi\) | |||||||
\(158\) | 9.24443i | 0.735447i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.2558 | − | 2.28391i | −1.28513 | − | 0.180559i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 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 | \(0.202357\pi\) | ||||
−0.804642 | + | 0.593760i | \(0.797643\pi\) | |||||||
\(168\) | 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 | \(-0.975045\pi\) | ||
0.996928 | − | 0.0783179i | \(-0.0249549\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 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 | \(-0.351511\pi\) | ||||
0.449757 | + | 0.893151i | \(0.351511\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 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 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 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 | \(-0.399067\pi\) | ||||
0.311803 | + | 0.950147i | \(0.399067\pi\) | |||||||
\(200\) | 0.990632 | − | 3.45584i | 0.0700483 | − | 0.244365i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.81579i | 0.198118i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 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 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 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 | \(-0.829722\pi\) | ||
0.860297 | − | 0.509794i | \(-0.170278\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 21.4795 | 1.42879 | ||||||||
\(227\) | − | 14.3684i | − | 0.953665i | −0.878994 | − | 0.476833i | \(-0.841785\pi\) | ||
0.878994 | − | 0.476833i | \(-0.158215\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.61285 | −0.370907 | −0.185454 | − | 0.982653i | \(-0.559375\pi\) | ||||
−0.185454 | + | 0.982653i | \(0.559375\pi\) | |||||||
\(230\) | −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 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −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 | \(-0.425039\pi\) | ||||
0.233327 | + | 0.972398i | \(0.425039\pi\) | |||||||
\(242\) | − | 13.3225i | − | 0.856402i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11.1240 | 0.712140 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 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 | \(-0.163178\pi\) | ||||
0.871454 | + | 0.490478i | \(0.163178\pi\) | |||||||
\(252\) | 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 | \(-0.995744\pi\) | ||
0.999911 | − | 0.0133689i | \(-0.00425558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 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 | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 4.47013i | − | 0.273056i | ||||||
\(269\) | −1.74620 | −0.106468 | −0.0532339 | − | 0.998582i | \(-0.516953\pi\) | ||||
−0.0532339 | + | 0.998582i | \(0.516953\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.69535 | 0.163731 | 0.0818653 | − | 0.996643i | \(-0.473912\pi\) | ||||
0.0818653 | + | 0.996643i | \(0.473912\pi\) | |||||||
\(272\) | − | 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 | 0 | ||||||||
\(281\) | −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 | \(0.0224256\pi\) | ||||
−0.997519 | + | 0.0703939i | \(0.977574\pi\) | |||||||
\(284\) | 3.24443 | 0.192522 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −24.4701 | −1.44695 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 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 | \(-0.920817\pi\) | ||
0.969218 | − | 0.246203i | \(-0.0791831\pi\) | |||||||
\(294\) | 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 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 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 | \(0.222777\pi\) | ||||
−0.764923 | + | 0.644121i | \(0.777223\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −21.8479 | − | 3.06959i | −1.24088 | − | 0.174341i | ||||
\(311\) | −24.0830 | −1.36562 | −0.682810 | − | 0.730596i | \(-0.739242\pi\) | ||||
−0.682810 | + | 0.730596i | \(0.739242\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 9.65433i | 0.545695i | 0.962057 | + | 0.272848i | \(0.0879655\pi\) | ||||
−0.962057 | + | 0.272848i | \(0.912035\pi\) | |||||||
\(314\) | −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 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 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 | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 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 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 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 | \(-0.644345\pi\) | ||||
−0.438091 | + | 0.898931i | \(0.644345\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 14.6824i | 0.782577i | ||||||||
\(353\) | − | 0.549086i | − | 0.0292249i | −0.999893 | − | 0.0146124i | \(-0.995349\pi\) | ||
0.999893 | − | 0.0146124i | \(-0.00465145\pi\) | |||||||
\(354\) | 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 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3.47949 | − | 0.488863i | −0.182125 | − | 0.0255882i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 1.71456i | − | 0.0894992i | −0.998998 | − | 0.0447496i | \(-0.985751\pi\) | ||
0.998998 | − | 0.0447496i | \(-0.0142490\pi\) | |||||||
\(368\) | − | 6.35551i | − | 0.331304i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −4.50760 | + | 32.0830i | −0.234339 | + | 1.66791i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 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 | \(0.0687411\pi\) | ||||
−0.976772 | + | 0.214282i | \(0.931259\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −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 | 0 | ||||||||
\(393\) | 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 | \(0.0203754\pi\) | ||||
−0.997952 | + | 0.0639675i | \(0.979625\pi\) | |||||||
\(398\) | 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 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 15.2257i | − | 0.754710i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −31.9813 | −1.58137 | −0.790686 | − | 0.612222i | \(-0.790276\pi\) | ||||
−0.790686 | + | 0.612222i | \(0.790276\pi\) | |||||||
\(410\) | −34.7052 | − | 4.87601i | −1.71397 | − | 0.240809i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 14.3684i | 0.707881i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 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 | \(-0.496345\pi\) | ||||
0.0114836 | + | 0.999934i | \(0.496345\pi\) | |||||||
\(420\) | 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 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 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 | \(-0.999539\pi\) | ||
0.999999 | − | 0.00144707i | \(-0.000460616\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.10525 | 0.436062 | ||||||||
\(437\) | − | 3.34614i | − | 0.160068i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.4286 | −1.07046 | −0.535230 | − | 0.844706i | \(-0.679775\pi\) | ||||
−0.535230 | + | 0.844706i | \(0.679775\pi\) | |||||||
\(440\) | −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 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 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 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 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 | \(-0.525064\pi\) | ||||
−0.0786596 | + | 0.996902i | \(0.525064\pi\) | |||||||
\(462\) | 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 | \(-0.892126\pi\) | ||
0.943122 | − | 0.332446i | \(-0.107874\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −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 | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | − | 16.1561i | − | 0.738963i | ||||||
\(479\) | −6.36842 | −0.290980 | −0.145490 | − | 0.989360i | \(-0.546476\pi\) | ||||
−0.145490 | + | 0.989360i | \(0.546476\pi\) | |||||||
\(480\) | 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 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −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 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 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 | \(-0.997253\pi\) | ||
0.999963 | − | 0.00863113i | \(-0.00274741\pi\) | |||||||
\(504\) | 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 | \(-0.268965\pi\) | ||||
0.663747 | + | 0.747957i | \(0.268965\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 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 | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.43801 | − | 10.2351i | 0.0630608 | − | 0.448837i | ||||
\(521\) | −18.5205 | −0.811398 | −0.405699 | − | 0.914007i | \(-0.632972\pi\) | ||||
−0.405699 | + | 0.914007i | \(0.632972\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 4.00000i | − | 0.174908i | −0.996169 | − | 0.0874539i | \(-0.972127\pi\) | ||
0.996169 | − | 0.0874539i | \(-0.0278730\pi\) | |||||||
\(524\) | 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 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 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 | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 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 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 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 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 45.6414i | − | 1.92527i | ||||||
\(563\) | 2.01874i | 0.0850796i | 0.999095 | + | 0.0425398i | \(0.0135449\pi\) | ||||
−0.999095 | + | 0.0425398i | \(0.986455\pi\) | |||||||
\(564\) | 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 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.89829 | − | 6.62222i | 0.0791642 | − | 0.276165i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 28.6766i | − | 1.19382i | −0.802307 | − | 0.596911i | \(-0.796394\pi\) | ||
0.802307 | − | 0.596911i | \(-0.203606\pi\) | |||||||
\(578\) | − | 4.97280i | − | 0.206841i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −0.381323 | + | 2.71408i | −0.0158336 | + | 0.112696i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 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 | \(0.382771\pi\) | ||||
−0.360018 | + | 0.932945i | \(0.617229\pi\) | |||||||
\(588\) | 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 | \(0.122357\pi\) | ||||
−0.927025 | + | 0.374999i | \(0.877643\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 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 | \(-0.503174\pi\) | ||||
−0.00997056 | + | 0.999950i | \(0.503174\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 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 | \(-0.865523\pi\) | ||
0.912078 | − | 0.410016i | \(-0.134477\pi\) | |||||||
\(608\) | 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 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 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 | \(-0.169134\pi\) | ||||
0.862123 | + | 0.506698i | \(0.169134\pi\) | |||||||
\(620\) | 2.61639 | − | 18.6222i | 0.105077 | − | 0.747886i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 45.8350i | − | 1.83782i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 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 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 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 | \(0.418477\pi\) | ||||
−0.253320 | + | 0.967383i | \(0.581523\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 20.4701 | 0.805386 | ||||||||
\(647\) | 15.3461i | 0.603319i | 0.953416 | + | 0.301660i | \(0.0975406\pi\) | ||||
−0.953416 | + | 0.301660i | \(0.902459\pi\) | |||||||
\(648\) | 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 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 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 | \(-0.879808\pi\) | ||||
−0.929554 | + | 0.368685i | \(0.879808\pi\) | |||||||
\(662\) | 25.7146i | 0.999425i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.34968 | 0.324030 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 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 | \(0.118973\pi\) | ||||
−0.930959 | + | 0.365124i | \(0.881027\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −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 | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 46.5977i | 1.77652i | ||||||||
\(689\) | 59.0420 | 2.24932 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.18421 | 0.0450494 | 0.0225247 | − | 0.999746i | \(-0.492830\pi\) | ||||
0.0225247 | + | 0.999746i | \(0.492830\pi\) | |||||||
\(692\) | 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 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 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 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 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 | \(-0.528870\pi\) | ||||
−0.0905730 | + | 0.995890i | \(0.528870\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 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 | \(0.127715\pi\) | ||||
−0.920582 | + | 0.390549i | \(0.872285\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 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 | \(-0.944157\pi\) | ||
0.984650 | − | 0.174539i | \(-0.0558434\pi\) | |||||||
\(734\) | 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 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 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 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 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 | \(-0.504764\pi\) | ||||
−0.0149646 | + | 0.999888i | \(0.504764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 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 | \(-0.374991\pi\) | ||||
0.382709 | + | 0.923869i | \(0.374991\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | − | 37.2444i | − | 1.34046i | ||||||
\(773\) | 29.4893i | 1.06066i | 0.847792 | + | 0.530329i | \(0.177932\pi\) | ||||
−0.847792 | + | 0.530329i | \(0.822068\pi\) | |||||||
\(774\) | 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 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.0923 | + | 3.24443i | 0.824201 | + | 0.115799i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 34.4514i | − | 1.22806i | −0.789283 | − | 0.614030i | \(-0.789547\pi\) | ||
0.789283 | − | 0.614030i | \(-0.210453\pi\) | |||||||
\(788\) | − | 1.92104i | − | 0.0684343i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 20.4701 | + | 2.87601i | 0.728294 | + | 0.102324i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 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 | \(-0.891248\pi\) | ||
0.942202 | − | 0.335046i | \(-0.108752\pi\) | |||||||
\(798\) | 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 | 0 | ||||||||
\(806\) | −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 | \(-0.376741\pi\) | ||||
0.377625 | + | 0.925958i | \(0.376741\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 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 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 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 | \(-0.419621\pi\) | ||||
0.249843 | + | 0.968286i | \(0.419621\pi\) | |||||||
\(830\) | 6.87601 | − | 48.9403i | 0.238670 | − | 1.69874i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 30.5116i | − | 1.05780i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 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 | \(-0.508304\pi\) | ||||
−0.0260851 | + | 0.999660i | \(0.508304\pi\) | |||||||
\(840\) | 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 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 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 | \(0.0849600\pi\) | ||||
−0.964591 | + | 0.263752i | \(0.915040\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.26900 | 0.0433734 | ||||||||
\(857\) | − | 19.8578i | − | 0.678328i | −0.940727 | − | 0.339164i | \(-0.889856\pi\) | ||
0.940727 | − | 0.339164i | \(-0.110144\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.42864 | 0.0828641 | 0.0414321 | − | 0.999141i | \(-0.486808\pi\) | ||||
0.0414321 | + | 0.999141i | \(0.486808\pi\) | |||||||
\(860\) | 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 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −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 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 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 | \(-0.512533\pi\) | ||||
−0.0393640 | + | 0.999225i | \(0.512533\pi\) | |||||||
\(882\) | 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 | \(-0.702621\pi\) | ||
0.594427 | − | 0.804150i | \(-0.297379\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −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 | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 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 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −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 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 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 | \(-0.723291\pi\) | ||||
−0.645357 | + | 0.763881i | \(0.723291\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 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 | \(-0.906232\pi\) | ||
0.956924 | − | 0.290338i | \(-0.0937679\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.89829 | − | 1.39069i | −0.322847 | − | 0.0453594i | ||||
\(941\) | 35.5812 | 1.15991 | 0.579957 | − | 0.814647i | \(-0.303069\pi\) | ||||
0.579957 | + | 0.814647i | \(0.303069\pi\) | |||||||
\(942\) | 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 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 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 | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 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 | \(-0.273662\pi\) | ||||
0.652638 | + | 0.757670i | \(0.273662\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −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 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 3.80642i | − | 0.121468i | ||||||
\(983\) | 24.0000i | 0.765481i | 0.923856 | + | 0.382741i | \(0.125020\pi\) | ||||
−0.923856 | + | 0.382741i | \(0.874980\pi\) | |||||||
\(984\) | 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 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 2.73683 | − | 19.4795i | 0.0867634 | − | 0.617541i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 28.6766i | − | 0.908197i | −0.890951 | − | 0.454099i | \(-0.849961\pi\) | ||
0.890951 | − | 0.454099i | \(-0.150039\pi\) | |||||||
\(998\) | − | 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 | 2205.2.d.l.1324.5 | 6 | ||
3.2 | odd | 2 | 735.2.d.b.589.2 | 6 | |||
5.4 | even | 2 | inner | 2205.2.d.l.1324.2 | 6 | ||
7.6 | odd | 2 | 315.2.d.e.64.5 | 6 | |||
15.2 | even | 4 | 3675.2.a.bi.1.3 | 3 | |||
15.8 | even | 4 | 3675.2.a.bj.1.1 | 3 | |||
15.14 | odd | 2 | 735.2.d.b.589.5 | 6 | |||
21.2 | odd | 6 | 735.2.q.f.214.2 | 12 | |||
21.5 | even | 6 | 735.2.q.e.214.2 | 12 | |||
21.11 | odd | 6 | 735.2.q.f.79.5 | 12 | |||
21.17 | even | 6 | 735.2.q.e.79.5 | 12 | |||
21.20 | even | 2 | 105.2.d.b.64.2 | ✓ | 6 | ||
28.27 | even | 2 | 5040.2.t.v.1009.4 | 6 | |||
35.13 | even | 4 | 1575.2.a.w.1.3 | 3 | |||
35.27 | even | 4 | 1575.2.a.x.1.1 | 3 | |||
35.34 | odd | 2 | 315.2.d.e.64.2 | 6 | |||
84.83 | odd | 2 | 1680.2.t.k.1009.2 | 6 | |||
105.44 | odd | 6 | 735.2.q.f.214.5 | 12 | |||
105.59 | even | 6 | 735.2.q.e.79.2 | 12 | |||
105.62 | odd | 4 | 525.2.a.j.1.3 | 3 | |||
105.74 | odd | 6 | 735.2.q.f.79.2 | 12 | |||
105.83 | odd | 4 | 525.2.a.k.1.1 | 3 | |||
105.89 | even | 6 | 735.2.q.e.214.5 | 12 | |||
105.104 | even | 2 | 105.2.d.b.64.5 | yes | 6 | ||
140.139 | even | 2 | 5040.2.t.v.1009.3 | 6 | |||
420.83 | even | 4 | 8400.2.a.dj.1.1 | 3 | |||
420.167 | even | 4 | 8400.2.a.dg.1.3 | 3 | |||
420.419 | odd | 2 | 1680.2.t.k.1009.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.2.d.b.64.2 | ✓ | 6 | 21.20 | even | 2 | ||
105.2.d.b.64.5 | yes | 6 | 105.104 | even | 2 | ||
315.2.d.e.64.2 | 6 | 35.34 | odd | 2 | |||
315.2.d.e.64.5 | 6 | 7.6 | odd | 2 | |||
525.2.a.j.1.3 | 3 | 105.62 | odd | 4 | |||
525.2.a.k.1.1 | 3 | 105.83 | odd | 4 | |||
735.2.d.b.589.2 | 6 | 3.2 | odd | 2 | |||
735.2.d.b.589.5 | 6 | 15.14 | odd | 2 | |||
735.2.q.e.79.2 | 12 | 105.59 | even | 6 | |||
735.2.q.e.79.5 | 12 | 21.17 | even | 6 | |||
735.2.q.e.214.2 | 12 | 21.5 | even | 6 | |||
735.2.q.e.214.5 | 12 | 105.89 | even | 6 | |||
735.2.q.f.79.2 | 12 | 105.74 | odd | 6 | |||
735.2.q.f.79.5 | 12 | 21.11 | odd | 6 | |||
735.2.q.f.214.2 | 12 | 21.2 | odd | 6 | |||
735.2.q.f.214.5 | 12 | 105.44 | odd | 6 | |||
1575.2.a.w.1.3 | 3 | 35.13 | even | 4 | |||
1575.2.a.x.1.1 | 3 | 35.27 | even | 4 | |||
1680.2.t.k.1009.2 | 6 | 84.83 | odd | 2 | |||
1680.2.t.k.1009.5 | 6 | 420.419 | odd | 2 | |||
2205.2.d.l.1324.2 | 6 | 5.4 | even | 2 | inner | ||
2205.2.d.l.1324.5 | 6 | 1.1 | even | 1 | trivial | ||
3675.2.a.bi.1.3 | 3 | 15.2 | even | 4 | |||
3675.2.a.bj.1.1 | 3 | 15.8 | even | 4 | |||
5040.2.t.v.1009.3 | 6 | 140.139 | even | 2 | |||
5040.2.t.v.1009.4 | 6 | 28.27 | even | 2 | |||
8400.2.a.dg.1.3 | 3 | 420.167 | even | 4 | |||
8400.2.a.dj.1.1 | 3 | 420.83 | even | 4 |