Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [912,2,Mod(49,912)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(912, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("912.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 912 = 2^{4} \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 912.q (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.28235666434\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 912.49 |
Dual form | 912.2.q.d.577.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/912\mathbb{Z}\right)^\times\).
\(n\) | \(97\) | \(229\) | \(305\) | \(799\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.00000 | − | 3.46410i | 0.894427 | − | 1.54919i | 0.0599153 | − | 0.998203i | \(-0.480917\pi\) |
0.834512 | − | 0.550990i | \(-0.185750\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.50000 | + | 6.06218i | 0.970725 | + | 1.68135i | 0.693375 | + | 0.720577i | \(0.256123\pi\) |
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.00000 | + | 3.46410i | 0.516398 | + | 0.894427i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.00000 | − | 1.73205i | 0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50000 | + | 2.59808i | −0.327327 | + | 0.566947i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.00000 | − | 3.46410i | −0.417029 | − | 0.722315i | 0.578610 | − | 0.815604i | \(-0.303595\pi\) |
−0.995639 | + | 0.0932891i | \(0.970262\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.50000 | − | 9.52628i | −1.10000 | − | 1.90526i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | − | 3.46410i | −0.371391 | − | 0.643268i | 0.618389 | − | 0.785872i | \(-0.287786\pi\) |
−0.989780 | + | 0.142605i | \(0.954452\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.00000 | −0.179605 | −0.0898027 | − | 0.995960i | \(-0.528624\pi\) | ||||
−0.0898027 | + | 0.995960i | \(0.528624\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.00000 | − | 1.73205i | 0.174078 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.00000 | − | 10.3923i | 1.01419 | − | 1.75662i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.00000 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −7.00000 | −1.12090 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.00000 | + | 3.46410i | −0.312348 | + | 0.541002i | −0.978870 | − | 0.204483i | \(-0.934449\pi\) |
0.666523 | + | 0.745485i | \(0.267782\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.50000 | − | 6.06218i | 0.533745 | − | 0.924473i | −0.465478 | − | 0.885059i | \(-0.654118\pi\) |
0.999223 | − | 0.0394140i | \(-0.0125491\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.00000 | −0.596285 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.00000 | + | 1.73205i | 0.145865 | + | 0.252646i | 0.929695 | − | 0.368329i | \(-0.120070\pi\) |
−0.783830 | + | 0.620975i | \(0.786737\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | + | 3.46410i | 0.274721 | + | 0.475831i | 0.970065 | − | 0.242846i | \(-0.0780811\pi\) |
−0.695344 | + | 0.718677i | \(0.744748\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.00000 | + | 6.92820i | −0.539360 | + | 0.934199i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.500000 | + | 4.33013i | −0.0662266 | + | 0.573539i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.00000 | + | 5.19615i | −0.390567 | + | 0.676481i | −0.992524 | − | 0.122047i | \(-0.961054\pi\) |
0.601958 | + | 0.798528i | \(0.294388\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.50000 | − | 2.59808i | −0.188982 | − | 0.327327i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 28.0000 | 3.47297 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.50000 | + | 2.59808i | 0.183254 | + | 0.317406i | 0.942987 | − | 0.332830i | \(-0.108004\pi\) |
−0.759733 | + | 0.650236i | \(0.774670\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.00000 | − | 1.73205i | 0.118678 | − | 0.205557i | −0.800566 | − | 0.599245i | \(-0.795468\pi\) |
0.919244 | + | 0.393688i | \(0.128801\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.50000 | − | 2.59808i | 0.175562 | − | 0.304082i | −0.764794 | − | 0.644275i | \(-0.777159\pi\) |
0.940356 | + | 0.340193i | \(0.110493\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 11.0000 | 1.27017 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −6.00000 | −0.683763 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.50000 | − | 4.33013i | 0.281272 | − | 0.487177i | −0.690426 | − | 0.723403i | \(-0.742577\pi\) |
0.971698 | + | 0.236225i | \(0.0759104\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.0000 | 1.31717 | 0.658586 | − | 0.752506i | \(-0.271155\pi\) | ||||
0.658586 | + | 0.752506i | \(0.271155\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.00000 | 0.428845 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.00000 | − | 15.5885i | −0.953998 | − | 1.65237i | −0.736644 | − | 0.676280i | \(-0.763591\pi\) |
−0.217354 | − | 0.976093i | \(-0.569742\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.5000 | + | 18.1865i | 1.10070 | + | 1.90647i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.500000 | − | 0.866025i | 0.0518476 | − | 0.0898027i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 2.00000 | − | 17.3205i | 0.205196 | − | 1.77705i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.00000 | + | 8.66025i | −0.507673 | + | 0.879316i | 0.492287 | + | 0.870433i | \(0.336161\pi\) |
−0.999961 | + | 0.00888289i | \(0.997172\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.00000 | + | 1.73205i | 0.100504 | + | 0.174078i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.00000 | − | 1.73205i | −0.0995037 | − | 0.172345i | 0.811976 | − | 0.583691i | \(-0.198392\pi\) |
−0.911479 | + | 0.411346i | \(0.865059\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −9.00000 | −0.886796 | −0.443398 | − | 0.896325i | \(-0.646227\pi\) | ||||
−0.443398 | + | 0.896325i | \(0.646227\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.00000 | + | 10.3923i | 0.585540 | + | 1.01419i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.00000 | −0.193347 | −0.0966736 | − | 0.995316i | \(-0.530820\pi\) | ||||
−0.0966736 | + | 0.995316i | \(0.530820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.00000 | + | 5.19615i | −0.287348 | + | 0.497701i | −0.973176 | − | 0.230063i | \(-0.926107\pi\) |
0.685828 | + | 0.727764i | \(0.259440\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.50000 | + | 6.06218i | −0.332205 | + | 0.575396i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.0000 | −1.49201 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.50000 | − | 6.06218i | 0.323575 | − | 0.560449i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.00000 | − | 3.46410i | −0.180334 | − | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −24.0000 | −2.14663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.50000 | + | 6.06218i | 0.308158 | + | 0.533745i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.0000 | − | 5.19615i | 1.04053 | − | 0.450564i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.00000 | − | 3.46410i | 0.172133 | − | 0.298142i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | + | 1.73205i | 0.0854358 | + | 0.147979i | 0.905577 | − | 0.424182i | \(-0.139438\pi\) |
−0.820141 | + | 0.572161i | \(0.806105\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.5000 | + | 18.1865i | 0.890598 | + | 1.54256i | 0.839159 | + | 0.543885i | \(0.183047\pi\) |
0.0514389 | + | 0.998676i | \(0.483619\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.00000 | − | 12.1244i | −0.585369 | − | 1.01389i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.0000 | −1.32873 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.00000 | + | 1.73205i | −0.0824786 | + | 0.142857i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 9.00000 | − | 15.5885i | 0.737309 | − | 1.27706i | −0.216394 | − | 0.976306i | \(-0.569430\pi\) |
0.953703 | − | 0.300750i | \(-0.0972370\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.00000 | + | 3.46410i | −0.160644 | + | 0.278243i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.50000 | + | 6.06218i | −0.279330 | + | 0.483814i | −0.971219 | − | 0.238190i | \(-0.923446\pi\) |
0.691888 | + | 0.722005i | \(0.256779\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.00000 | −0.317221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | − | 10.3923i | −0.472866 | − | 0.819028i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.0000 | −0.861586 | −0.430793 | − | 0.902451i | \(-0.641766\pi\) | ||||
−0.430793 | + | 0.902451i | \(0.641766\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.00000 | − | 6.92820i | −0.311400 | − | 0.539360i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.00000 | + | 5.19615i | 0.232147 | + | 0.402090i | 0.958440 | − | 0.285295i | \(-0.0920916\pi\) |
−0.726293 | + | 0.687386i | \(0.758758\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −18.0000 | + | 31.1769i | −1.38462 | + | 2.39822i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.50000 | − | 2.59808i | −0.267652 | − | 0.198680i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −6.00000 | + | 10.3923i | −0.456172 | + | 0.790112i | −0.998755 | − | 0.0498898i | \(-0.984113\pi\) |
0.542583 | + | 0.840002i | \(0.317446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −16.5000 | − | 28.5788i | −1.24728 | − | 2.16036i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −3.00000 | − | 5.19615i | −0.225494 | − | 0.390567i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1.00000 | + | 1.73205i | 0.0743294 | + | 0.128742i | 0.900794 | − | 0.434246i | \(-0.142985\pi\) |
−0.826465 | + | 0.562988i | \(0.809652\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.00000 | −0.0739221 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 14.0000 | − | 24.2487i | 1.02930 | − | 1.78280i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.00000 | 0.218218 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 20.0000 | 1.44715 | 0.723575 | − | 0.690246i | \(-0.242498\pi\) | ||||
0.723575 | + | 0.690246i | \(0.242498\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.5000 | − | 18.1865i | 0.755807 | − | 1.30910i | −0.189166 | − | 0.981945i | \(-0.560578\pi\) |
0.944972 | − | 0.327150i | \(-0.106088\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.0000 | + | 24.2487i | −1.00256 | + | 1.73649i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.50000 | − | 6.06218i | −0.248108 | − | 0.429736i | 0.714893 | − | 0.699234i | \(-0.246476\pi\) |
−0.963001 | + | 0.269498i | \(0.913142\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.00000 | −0.211604 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.00000 | − | 10.3923i | −0.421117 | − | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00000 | + | 13.8564i | 0.558744 | + | 0.967773i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.00000 | + | 3.46410i | −0.139010 | + | 0.240772i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −8.00000 | + | 3.46410i | −0.553372 | + | 0.239617i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.50000 | − | 7.79423i | 0.309793 | − | 0.536577i | −0.668524 | − | 0.743690i | \(-0.733074\pi\) |
0.978317 | + | 0.207114i | \(0.0664070\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.00000 | + | 1.73205i | 0.0685189 | + | 0.118678i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.0000 | − | 24.2487i | −0.954792 | − | 1.65375i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.50000 | + | 2.59808i | 0.101361 | + | 0.175562i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.50000 | − | 4.33013i | 0.167412 | − | 0.289967i | −0.770097 | − | 0.637927i | \(-0.779792\pi\) |
0.937509 | + | 0.347960i | \(0.113126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5.50000 | + | 9.52628i | −0.366667 | + | 0.635085i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.00000 | −0.265489 | −0.132745 | − | 0.991150i | \(-0.542379\pi\) | ||||
−0.132745 | + | 0.991150i | \(0.542379\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −7.00000 | −0.462573 | −0.231287 | − | 0.972886i | \(-0.574293\pi\) | ||||
−0.231287 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.00000 | − | 5.19615i | 0.197386 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.00000 | + | 5.19615i | −0.196537 | + | 0.340411i | −0.947403 | − | 0.320043i | \(-0.896303\pi\) |
0.750867 | + | 0.660454i | \(0.229636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.00000 | 0.521862 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2.50000 | + | 4.33013i | 0.162392 | + | 0.281272i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.500000 | − | 0.866025i | −0.0322078 | − | 0.0557856i | 0.849472 | − | 0.527633i | \(-0.176921\pi\) |
−0.881680 | + | 0.471848i | \(0.843587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | − | 0.866025i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.00000 | − | 6.92820i | 0.255551 | − | 0.442627i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 24.5000 | + | 18.1865i | 1.55890 | + | 1.15718i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −6.00000 | + | 10.3923i | −0.380235 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.00000 | + | 12.1244i | 0.441836 | + | 0.765283i | 0.997826 | − | 0.0659066i | \(-0.0209939\pi\) |
−0.555990 | + | 0.831189i | \(0.687661\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.00000 | + | 6.92820i | 0.251478 | + | 0.435572i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.0000 | + | 24.2487i | 0.873296 | + | 1.51259i | 0.858567 | + | 0.512702i | \(0.171355\pi\) |
0.0147291 | + | 0.999892i | \(0.495311\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 21.0000 | 1.30488 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.00000 | + | 3.46410i | −0.123797 | + | 0.214423i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.00000 | + | 15.5885i | −0.554964 | + | 0.961225i | 0.442943 | + | 0.896550i | \(0.353935\pi\) |
−0.997906 | + | 0.0646755i | \(0.979399\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.0000 | 0.982872 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.00000 | + | 15.5885i | −0.548740 | + | 0.950445i | 0.449622 | + | 0.893219i | \(0.351559\pi\) |
−0.998361 | + | 0.0572259i | \(0.981774\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.00000 | + | 6.92820i | −0.242983 | + | 0.420858i | −0.961563 | − | 0.274586i | \(-0.911459\pi\) |
0.718580 | + | 0.695444i | \(0.244792\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.0000 | −1.27098 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.0000 | + | 19.0526i | 0.663325 | + | 1.14891i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.0000 | −1.56219 | −0.781094 | − | 0.624413i | \(-0.785338\pi\) | ||||
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0.500000 | + | 0.866025i | 0.0299342 | + | 0.0518476i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.00000 | − | 3.46410i | −0.119310 | − | 0.206651i | 0.800184 | − | 0.599754i | \(-0.204735\pi\) |
−0.919494 | + | 0.393103i | \(0.871402\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.00000 | + | 10.3923i | −0.356663 | + | 0.617758i | −0.987401 | − | 0.158237i | \(-0.949419\pi\) |
0.630738 | + | 0.775996i | \(0.282752\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 14.0000 | + | 10.3923i | 0.829288 | + | 0.615587i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.00000 | + | 10.3923i | −0.354169 | + | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.50000 | + | 14.7224i | 0.500000 | + | 0.866025i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −5.00000 | − | 8.66025i | −0.293105 | − | 0.507673i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.0000 | + | 20.7846i | 0.698667 | + | 1.21013i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.00000 | −0.116052 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 14.0000 | − | 24.2487i | 0.809641 | − | 1.40234i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.5000 | − | 18.1865i | 0.605210 | − | 1.04825i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.00000 | 0.114897 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.00000 | 0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.00000 | − | 10.3923i | 0.342438 | − | 0.593120i | −0.642447 | − | 0.766330i | \(-0.722081\pi\) |
0.984885 | + | 0.173210i | \(0.0554140\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.50000 | − | 7.79423i | 0.255996 | − | 0.443398i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −34.0000 | −1.92796 | −0.963982 | − | 0.265969i | \(-0.914308\pi\) | ||||
−0.963982 | + | 0.265969i | \(0.914308\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.00000 | − | 12.1244i | −0.395663 | − | 0.685309i | 0.597522 | − | 0.801852i | \(-0.296152\pi\) |
−0.993186 | + | 0.116543i | \(0.962819\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −12.0000 | −0.676123 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.0000 | + | 20.7846i | 0.673987 | + | 1.16738i | 0.976764 | + | 0.214318i | \(0.0687530\pi\) |
−0.302777 | + | 0.953062i | \(0.597914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.00000 | − | 1.73205i | 0.0558146 | − | 0.0966736i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 38.5000 | − | 66.6840i | 2.13560 | − | 3.69896i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.00000 | − | 5.19615i | −0.165900 | − | 0.287348i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.00000 | + | 5.19615i | 0.165395 | + | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.0000 | −1.26419 | −0.632097 | − | 0.774889i | \(-0.717806\pi\) | ||||
−0.632097 | + | 0.774889i | \(0.717806\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.50000 | − | 6.06218i | −0.191799 | − | 0.332205i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 12.0000 | 0.655630 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.50000 | + | 11.2583i | −0.354078 | + | 0.613280i | −0.986960 | − | 0.160968i | \(-0.948538\pi\) |
0.632882 | + | 0.774248i | \(0.281872\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −1.00000 | + | 1.73205i | −0.0543125 | + | 0.0940721i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 8.00000 | − | 13.8564i | 0.430706 | − | 0.746004i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 14.0000 | − | 24.2487i | 0.751559 | − | 1.30174i | −0.195507 | − | 0.980702i | \(-0.562635\pi\) |
0.947067 | − | 0.321037i | \(-0.104031\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 31.0000 | 1.65939 | 0.829696 | − | 0.558216i | \(-0.188514\pi\) | ||||
0.829696 | + | 0.558216i | \(0.188514\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.50000 | + | 6.06218i | 0.186816 | + | 0.323575i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.00000 | − | 6.92820i | −0.212298 | − | 0.367711i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −6.00000 | + | 10.3923i | −0.316668 | + | 0.548485i | −0.979791 | − | 0.200026i | \(-0.935897\pi\) |
0.663123 | + | 0.748511i | \(0.269231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | − | 13.8564i | 0.684211 | − | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.50000 | − | 6.06218i | 0.183702 | − | 0.318182i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −6.00000 | − | 10.3923i | −0.314054 | − | 0.543958i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.50000 | + | 16.4545i | 0.495896 | + | 0.858917i | 0.999989 | − | 0.00473247i | \(-0.00150640\pi\) |
−0.504093 | + | 0.863649i | \(0.668173\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.00000 | + | 10.3923i | 0.311504 | + | 0.539542i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.0000 | − | 20.7846i | 0.619677 | − | 1.07331i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 14.0000 | − | 24.2487i | 0.721037 | − | 1.24887i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0000 | 1.07870 | 0.539349 | − | 0.842082i | \(-0.318670\pi\) | ||||
0.539349 | + | 0.842082i | \(0.318670\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7.00000 | + | 12.1244i | −0.357683 | + | 0.619526i | −0.987573 | − | 0.157159i | \(-0.949767\pi\) |
0.629890 | + | 0.776684i | \(0.283100\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −12.0000 | + | 20.7846i | −0.611577 | + | 1.05928i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.00000 | −0.355830 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 12.0000 | + | 20.7846i | 0.608424 | + | 1.05382i | 0.991500 | + | 0.130105i | \(0.0415314\pi\) |
−0.383076 | + | 0.923717i | \(0.625135\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −9.00000 | − | 15.5885i | −0.453990 | − | 0.786334i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −10.0000 | − | 17.3205i | −0.503155 | − | 0.871489i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.50000 | − | 11.2583i | 0.326226 | − | 0.565039i | −0.655534 | − | 0.755166i | \(-0.727556\pi\) |
0.981760 | + | 0.190126i | \(0.0608897\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.50000 | + | 12.9904i | −0.0750939 | + | 0.650332i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.00000 | + | 8.66025i | −0.249688 | + | 0.432472i | −0.963439 | − | 0.267927i | \(-0.913661\pi\) |
0.713751 | + | 0.700399i | \(0.246995\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.50000 | − | 6.06218i | −0.174347 | − | 0.301979i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.00000 | + | 3.46410i | 0.0993808 | + | 0.172133i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −14.0000 | −0.693954 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | − | 8.66025i | −0.247234 | − | 0.428222i | 0.715523 | − | 0.698589i | \(-0.246188\pi\) |
−0.962757 | + | 0.270367i | \(0.912855\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00000 | −0.0986527 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.00000 | + | 15.5885i | −0.442861 | + | 0.767058i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 24.0000 | − | 41.5692i | 1.17811 | − | 2.04055i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.0000 | −1.02837 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −30.0000 | −1.46560 | −0.732798 | − | 0.680446i | \(-0.761786\pi\) | ||||
−0.732798 | + | 0.680446i | \(0.761786\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0000 | + | 22.5167i | −0.633581 | + | 1.09739i | 0.353233 | + | 0.935536i | \(0.385082\pi\) |
−0.986814 | + | 0.161859i | \(0.948251\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1.00000 | − | 1.73205i | 0.0486217 | − | 0.0842152i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.50000 | + | 2.59808i | 0.0725901 | + | 0.125730i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 14.0000 | 0.675926 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.00000 | + | 5.19615i | 0.144505 | + | 0.250290i | 0.929188 | − | 0.369607i | \(-0.120508\pi\) |
−0.784683 | + | 0.619897i | \(0.787174\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.5000 | − | 19.9186i | −0.552655 | − | 0.957226i | −0.998082 | − | 0.0619079i | \(-0.980282\pi\) |
0.445427 | − | 0.895318i | \(-0.353052\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 8.00000 | − | 13.8564i | 0.383571 | − | 0.664364i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −14.0000 | − | 10.3923i | −0.669711 | − | 0.497131i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 11.5000 | − | 19.9186i | 0.548865 | − | 0.950662i | −0.449488 | − | 0.893287i | \(-0.648393\pi\) |
0.998353 | − | 0.0573756i | \(-0.0182733\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.00000 | − | 1.73205i | −0.0476190 | − | 0.0824786i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.00000 | + | 3.46410i | 0.0950229 | + | 0.164584i | 0.909618 | − | 0.415445i | \(-0.136374\pi\) |
−0.814595 | + | 0.580030i | \(0.803041\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −72.0000 | −3.41313 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.00000 | + | 15.5885i | 0.425685 | + | 0.737309i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.0000 | 0.755087 | 0.377543 | − | 0.925992i | \(-0.376769\pi\) | ||||
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.00000 | − | 6.92820i | 0.188353 | − | 0.326236i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.0000 | − | 17.3205i | 0.469841 | − | 0.813788i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 84.0000 | 3.93798 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.0000 | 1.35656 | 0.678281 | − | 0.734802i | \(-0.262725\pi\) | ||||
0.678281 | + | 0.734802i | \(0.262725\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17.0000 | − | 29.4449i | 0.791769 | − | 1.37138i | −0.133102 | − | 0.991102i | \(-0.542494\pi\) |
0.924871 | − | 0.380282i | \(-0.124173\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.0000 | −0.883005 | −0.441502 | − | 0.897260i | \(-0.645554\pi\) | ||||
−0.441502 | + | 0.897260i | \(0.645554\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2.00000 | − | 3.46410i | −0.0927478 | − | 0.160644i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 8.00000 | 0.370196 | 0.185098 | − | 0.982720i | \(-0.440740\pi\) | ||||
0.185098 | + | 0.982720i | \(0.440740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.50000 | + | 7.79423i | 0.207791 | + | 0.359904i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.50000 | − | 6.06218i | −0.161271 | − | 0.279330i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.00000 | + | 12.1244i | −0.321860 | + | 0.557478i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −38.5000 | − | 28.5788i | −1.76650 | − | 1.31129i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | − | 3.46410i | 0.0915737 | − | 0.158610i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.0000 | + | 29.4449i | 0.776750 | + | 1.34537i | 0.933806 | + | 0.357780i | \(0.116466\pi\) |
−0.157056 | + | 0.987590i | \(0.550200\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24.5000 | + | 42.4352i | 1.11710 | + | 1.93488i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 12.0000 | 0.546019 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.0000 | + | 34.6410i | 0.908153 | + | 1.57297i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.50000 | − | 9.52628i | 0.248719 | − | 0.430793i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.0000 | − | 22.5167i | 0.586682 | − | 1.01616i | −0.407982 | − | 0.912990i | \(-0.633767\pi\) |
0.994663 | − | 0.103173i | \(-0.0328994\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 8.00000 | 0.359573 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3.00000 | − | 5.19615i | 0.134568 | − | 0.233079i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.50000 | + | 9.52628i | −0.246214 | + | 0.426455i | −0.962472 | − | 0.271380i | \(-0.912520\pi\) |
0.716258 | + | 0.697835i | \(0.245853\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.00000 | − | 10.3923i | −0.267527 | − | 0.463370i | 0.700696 | − | 0.713460i | \(-0.252873\pi\) |
−0.968223 | + | 0.250090i | \(0.919540\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −18.0000 | − | 31.1769i | −0.799408 | − | 1.38462i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00000 | + | 5.19615i | 0.132973 | + | 0.230315i | 0.924821 | − | 0.380402i | \(-0.124214\pi\) |
−0.791849 | + | 0.610718i | \(0.790881\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.50000 | − | 7.79423i | 0.199068 | − | 0.344796i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 4.00000 | − | 1.73205i | 0.176604 | − | 0.0764719i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.0000 | + | 31.1769i | −0.793175 | + | 1.37382i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.00000 | − | 3.46410i | −0.0879599 | − | 0.152351i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.00000 | − | 10.3923i | −0.263371 | − | 0.456172i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.0000 | 1.66481 | 0.832405 | − | 0.554168i | \(-0.186963\pi\) | ||||
0.832405 | + | 0.554168i | \(0.186963\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 14.5000 | + | 25.1147i | 0.634041 | + | 1.09819i | 0.986718 | + | 0.162446i | \(0.0519382\pi\) |
−0.352677 | + | 0.935745i | \(0.614728\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 33.0000 | 1.44024 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.50000 | − | 6.06218i | 0.152174 | − | 0.263573i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.0000 | −1.21281 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | + | 6.92820i | −0.172935 | + | 0.299532i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −4.00000 | −0.172292 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.50000 | + | 16.4545i | 0.408437 | + | 0.707433i | 0.994715 | − | 0.102677i | \(-0.0327407\pi\) |
−0.586278 | + | 0.810110i | \(0.699407\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −2.00000 | −0.0858282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | + | 20.7846i | 0.514024 | + | 0.890315i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −14.5000 | − | 25.1147i | −0.619975 | − | 1.07383i | −0.989490 | − | 0.144604i | \(-0.953809\pi\) |
0.369514 | − | 0.929225i | \(-0.379524\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.500000 | − | 0.866025i | 0.0213395 | − | 0.0369611i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −14.0000 | − | 10.3923i | −0.596420 | − | 0.442727i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.50000 | − | 12.9904i | 0.318932 | − | 0.552407i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 14.0000 | + | 24.2487i | 0.594267 | + | 1.02930i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.0000 | − | 19.0526i | −0.466085 | − | 0.807283i | 0.533165 | − | 0.846011i | \(-0.321003\pi\) |
−0.999250 | + | 0.0387286i | \(0.987669\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 49.0000 | 2.07248 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 42.0000 | 1.77009 | 0.885044 | − | 0.465506i | \(-0.154128\pi\) | ||||
0.885044 | + | 0.465506i | \(0.154128\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.00000 | − | 6.92820i | 0.168281 | − | 0.291472i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.50000 | + | 2.59808i | −0.0629941 | + | 0.109109i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 16.0000 | 0.670755 | 0.335377 | − | 0.942084i | \(-0.391136\pi\) | ||||
0.335377 | + | 0.942084i | \(0.391136\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.00000 | 0.292941 | 0.146470 | − | 0.989215i | \(-0.453209\pi\) | ||||
0.146470 | + | 0.989215i | \(0.453209\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.0000 | + | 17.3205i | −0.417756 | + | 0.723575i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −22.0000 | + | 38.1051i | −0.917463 | + | 1.58909i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.5000 | + | 18.1865i | 0.436365 | + | 0.755807i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 36.0000 | 1.49353 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.00000 | − | 6.92820i | −0.165663 | − | 0.286937i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.0000 | − | 24.2487i | −0.578829 | − | 1.00256i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −9.00000 | + | 15.5885i | −0.371470 | + | 0.643404i | −0.989792 | − | 0.142520i | \(-0.954479\pi\) |
0.618322 | + | 0.785925i | \(0.287813\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.00000 | + | 1.73205i | −0.164817 | + | 0.0713679i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.00000 | − | 8.66025i | 0.205673 | − | 0.356235i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −17.0000 | − | 29.4449i | −0.698106 | − | 1.20916i | −0.969122 | − | 0.246581i | \(-0.920693\pi\) |
0.271016 | − | 0.962575i | \(-0.412640\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.00000 | 0.286491 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.0000 | + | 25.9808i | 0.612883 | + | 1.06155i | 0.990752 | + | 0.135686i | \(0.0433238\pi\) |
−0.377869 | + | 0.925859i | \(0.623343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 19.0000 | 0.775026 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.50000 | − | 2.59808i | 0.0610847 | − | 0.105802i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.0000 | + | 24.2487i | −0.569181 | + | 0.985850i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −41.0000 | −1.66414 | −0.832069 | − | 0.554672i | \(-0.812844\pi\) | ||||
−0.832069 | + | 0.554672i | \(0.812844\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 12.0000 | 0.486265 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.00000 | + | 12.1244i | −0.283190 | + | 0.490499i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.0000 | − | 32.9090i | 0.767403 | − | 1.32918i | −0.171564 | − | 0.985173i | \(-0.554882\pi\) |
0.938967 | − | 0.344008i | \(-0.111785\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −16.0000 | −0.645182 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00000 | − | 15.5885i | −0.362326 | − | 0.627568i | 0.626017 | − | 0.779809i | \(-0.284684\pi\) |
−0.988343 | + | 0.152242i | \(0.951351\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23.0000 | 0.924448 | 0.462224 | − | 0.886763i | \(-0.347052\pi\) | ||||
0.462224 | + | 0.886763i | \(0.347052\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −2.00000 | − | 3.46410i | −0.0802572 | − | 0.139010i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −27.0000 | − | 46.7654i | −1.08173 | − | 1.87362i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.5000 | + | 35.5070i | −0.820000 | + | 1.42028i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1.00000 | − | 8.66025i | 0.0399362 | − | 0.345857i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.50000 | − | 16.4545i | −0.378189 | − | 0.655043i | 0.612610 | − | 0.790386i | \(-0.290120\pi\) |
−0.990799 | + | 0.135343i | \(0.956786\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.50000 | + | 7.79423i | 0.178859 | + | 0.309793i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 7.00000 | + | 12.1244i | 0.277350 | + | 0.480384i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.00000 | −0.0791188 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | + | 15.5885i | −0.355479 | + | 0.615707i | −0.987200 | − | 0.159489i | \(-0.949015\pi\) |
0.631721 | + | 0.775196i | \(0.282349\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.50000 | − | 11.2583i | 0.256335 | − | 0.443985i | −0.708922 | − | 0.705287i | \(-0.750818\pi\) |
0.965257 | + | 0.261301i | \(0.0841516\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 28.0000 | 1.10250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 28.0000 | 1.10079 | 0.550397 | − | 0.834903i | \(-0.314476\pi\) | ||||
0.550397 | + | 0.834903i | \(0.314476\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.00000 | − | 10.3923i | 0.235521 | − | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.50000 | − | 2.59808i | 0.0587896 | − | 0.101827i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −30.0000 | −1.17399 | −0.586995 | − | 0.809590i | \(-0.699689\pi\) | ||||
−0.586995 | + | 0.809590i | \(0.699689\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 36.0000 | + | 62.3538i | 1.40664 | + | 2.43637i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −3.00000 | −0.117041 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.00000 | − | 8.66025i | −0.194772 | − | 0.337356i | 0.752054 | − | 0.659102i | \(-0.229063\pi\) |
−0.946826 | + | 0.321746i | \(0.895730\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.00000 | − | 8.66025i | −0.194477 | − | 0.336845i | 0.752252 | − | 0.658876i | \(-0.228968\pi\) |
−0.946729 | + | 0.322031i | \(0.895634\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.00000 | − | 51.9615i | 0.232670 | − | 2.01498i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.00000 | + | 13.8564i | −0.309761 | + | 0.536522i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.50000 | + | 4.33013i | 0.0966556 | + | 0.167412i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.00000 | − | 1.73205i | −0.0386046 | − | 0.0668651i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.00000 | −0.0385472 | −0.0192736 | − | 0.999814i | \(-0.506135\pi\) | ||||
−0.0192736 | + | 0.999814i | \(0.506135\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.50000 | − | 9.52628i | −0.211695 | − | 0.366667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −38.0000 | −1.46046 | −0.730229 | − | 0.683202i | \(-0.760587\pi\) | ||||
−0.730229 | + | 0.683202i | \(0.760587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0000 | + | 25.9808i | −0.575647 | + | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.00000 | − | 3.46410i | 0.0766402 | − | 0.132745i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.0000 | −1.53056 | −0.765279 | − | 0.643699i | \(-0.777399\pi\) | ||||
−0.765279 | + | 0.643699i | \(0.777399\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.00000 | 0.305664 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.50000 | − | 6.06218i | 0.133533 | − | 0.231287i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −14.0000 | + | 24.2487i | −0.533358 | + | 0.923802i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0000 | −0.456502 | −0.228251 | − | 0.973602i | \(-0.573301\pi\) | ||||
−0.228251 | + | 0.973602i | \(0.573301\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.00000 | + | 5.19615i | 0.113961 | + | 0.197386i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 84.0000 | 3.18630 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.00000 | − | 5.19615i | −0.113470 | − | 0.196537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.00000 | + | 6.92820i | −0.151078 | + | 0.261675i | −0.931624 | − | 0.363424i | \(-0.881608\pi\) |
0.780546 | + | 0.625098i | \(0.214941\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 28.0000 | − | 12.1244i | 1.05604 | − | 0.457279i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.00000 | + | 6.92820i | −0.150649 | + | 0.260931i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −3.00000 | − | 5.19615i | −0.112827 | − | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.50000 | + | 2.59808i | 0.0563337 | + | 0.0975728i | 0.892817 | − | 0.450420i | \(-0.148726\pi\) |
−0.836483 | + | 0.547992i | \(0.815392\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.00000 | −0.187515 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.00000 | + | 3.46410i | 0.0749006 | + | 0.129732i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −56.0000 | −2.09428 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12.0000 | − | 20.7846i | 0.448148 | − | 0.776215i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.00000 | − | 13.8564i | 0.298350 | − | 0.516757i | −0.677409 | − | 0.735607i | \(-0.736897\pi\) |
0.975759 | + | 0.218850i | \(0.0702305\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −27.0000 | −1.00553 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.00000 | 0.0371904 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −22.0000 | + | 38.1051i | −0.817059 | + | 1.41519i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.5000 | − | 32.0429i | 0.686127 | − | 1.18841i | −0.286954 | − | 0.957944i | \(-0.592643\pi\) |
0.973081 | − | 0.230463i | \(-0.0740239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 30.0000 | 1.10808 | 0.554038 | − | 0.832492i | \(-0.313086\pi\) | ||||
0.554038 | + | 0.832492i | \(0.313086\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.00000 | + | 6.92820i | 0.147542 | + | 0.255551i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −3.00000 | − | 5.19615i | −0.110506 | − | 0.191403i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.5000 | − | 30.3109i | 0.643748 | − | 1.11500i | −0.340841 | − | 0.940121i | \(-0.610712\pi\) |
0.984589 | − | 0.174883i | \(-0.0559548\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −28.0000 | + | 12.1244i | −1.02861 | + | 0.445399i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 13.0000 | − | 22.5167i | 0.476924 | − | 0.826056i | −0.522727 | − | 0.852500i | \(-0.675085\pi\) |
0.999650 | + | 0.0264443i | \(0.00841845\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −36.0000 | − | 62.3538i | −1.31894 | − | 2.28447i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −6.00000 | − | 10.3923i | −0.219529 | − | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | −0.219235 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.5000 | − | 26.8468i | −0.565603 | − | 0.979653i | −0.996993 | − | 0.0774878i | \(-0.975310\pi\) |
0.431390 | − | 0.902165i | \(-0.358023\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −14.0000 | −0.510188 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −40.0000 | + | 69.2820i | −1.45575 | + | 2.52143i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 11.5000 | − | 19.9186i | 0.417975 | − | 0.723953i | −0.577761 | − | 0.816206i | \(-0.696073\pi\) |
0.995736 | + | 0.0922527i | \(0.0294068\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.00000 | −0.290382 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.0000 | −1.52250 | −0.761249 | − | 0.648459i | \(-0.775414\pi\) | ||||
−0.761249 | + | 0.648459i | \(0.775414\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −9.00000 | + | 15.5885i | −0.325822 | + | 0.564340i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −42.0000 | −1.51653 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.50000 | + | 4.33013i | 0.0901523 | + | 0.156148i | 0.907575 | − | 0.419890i | \(-0.137931\pi\) |
−0.817423 | + | 0.576038i | \(0.804598\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.0000 | −1.00840 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.00000 | − | 5.19615i | −0.107903 | − | 0.186893i | 0.807018 | − | 0.590527i | \(-0.201080\pi\) |
−0.914920 | + | 0.403634i | \(0.867747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.50000 | + | 9.52628i | 0.197566 | + | 0.342194i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.5000 | + | 18.1865i | −0.376685 | + | 0.652438i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.00000 | + | 17.3205i | −0.0716574 | + | 0.620572i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.00000 | + | 3.46410i | −0.0715656 | + | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2.00000 | − | 3.46410i | −0.0714742 | − | 0.123797i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0000 | + | 24.2487i | 0.499681 | + | 0.865474i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −49.0000 | −1.74666 | −0.873331 | − | 0.487128i | \(-0.838045\pi\) | ||||
−0.873331 | + | 0.487128i | \(0.838045\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.00000 | − | 15.5885i | −0.320408 | − | 0.554964i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.00000 | 0.213335 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.50000 | + | 6.06218i | −0.124289 | + | 0.215274i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −8.00000 | + | 13.8564i | −0.283731 | + | 0.491436i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00000 | + | 15.5885i | −0.317999 | + | 0.550791i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −3.00000 | + | 5.19615i | −0.105868 | + | 0.183368i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −48.0000 | −1.69178 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −9.00000 | − | 15.5885i | −0.316815 | − | 0.548740i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 36.0000 | 1.26569 | 0.632846 | − | 0.774277i | \(-0.281886\pi\) | ||||
0.632846 | + | 0.774277i | \(0.281886\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.0000 | + | 31.1769i | 0.632065 | + | 1.09477i | 0.987129 | + | 0.159927i | \(0.0511260\pi\) |
−0.355063 | + | 0.934842i | \(0.615541\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.00000 | − | 6.92820i | −0.140286 | − | 0.242983i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −22.0000 | + | 38.1051i | −0.770626 | + | 1.33476i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.50000 | − | 30.3109i | 0.122449 | − | 1.06044i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.5000 | − | 18.1865i | 0.366900 | − | 0.635489i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.00000 | − | 10.3923i | −0.209401 | − | 0.362694i | 0.742125 | − | 0.670262i | \(-0.233818\pi\) |
−0.951526 | + | 0.307568i | \(0.900485\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 22.0000 | + | 38.1051i | 0.766872 | + | 1.32826i | 0.939251 | + | 0.343230i | \(0.111521\pi\) |
−0.172379 | + | 0.985031i | \(0.555146\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −22.0000 | −0.765942 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.00000 | + | 6.92820i | 0.139094 | + | 0.240917i | 0.927154 | − | 0.374681i | \(-0.122248\pi\) |
−0.788060 | + | 0.615598i | \(0.788914\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 45.0000 | 1.56291 | 0.781457 | − | 0.623959i | \(-0.214477\pi\) | ||||
0.781457 | + | 0.623959i | \(0.214477\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13.0000 | − | 22.5167i | 0.450965 | − | 0.781094i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.0000 | 0.830554 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −20.0000 | + | 34.6410i | −0.690477 | + | 1.19594i | 0.281205 | + | 0.959648i | \(0.409266\pi\) |
−0.971682 | + | 0.236293i | \(0.924067\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 6.50000 | − | 11.2583i | 0.224138 | − | 0.388218i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.00000 | 0.137767 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 72.0000 | + | 124.708i | 2.47688 | + | 4.29007i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −21.0000 | −0.721569 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −6.00000 | − | 10.3923i | −0.205919 | − | 0.356663i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.0000 | − | 24.2487i | −0.479914 | − | 0.831235i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 4.50000 | − | 7.79423i | 0.154077 | − | 0.266869i | −0.778646 | − | 0.627464i | \(-0.784093\pi\) |
0.932723 | + | 0.360595i | \(0.117426\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −16.0000 | + | 6.92820i | −0.547188 | + | 0.236940i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.00000 | − | 5.19615i | 0.102478 | − | 0.177497i | −0.810227 | − | 0.586116i | \(-0.800656\pi\) |
0.912705 | + | 0.408619i | \(0.133990\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.50000 | + | 6.06218i | 0.119418 | + | 0.206839i | 0.919537 | − | 0.393003i | \(-0.128564\pi\) |
−0.800119 | + | 0.599841i | \(0.795230\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.00000 | − | 10.3923i | −0.204479 | − | 0.354169i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 6.00000 | 0.204242 | 0.102121 | − | 0.994772i | \(-0.467437\pi\) | ||||
0.102121 | + | 0.994772i | \(0.467437\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.0000 | + | 41.5692i | 0.816024 | + | 1.41340i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −17.0000 | −0.577350 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.00000 | + | 8.66025i | −0.169613 | + | 0.293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.5000 | + | 18.1865i | −0.355779 | + | 0.616227i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.0000 | 0.338449 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −72.0000 | −2.43404 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −9.50000 | + | 16.4545i | −0.320792 | + | 0.555628i | −0.980652 | − | 0.195761i | \(-0.937282\pi\) |
0.659860 | + | 0.751389i | \(0.270616\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 9.00000 | − | 15.5885i | 0.303562 | − | 0.525786i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −24.0000 | −0.808581 | −0.404290 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404290 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.5000 | − | 35.5070i | −0.689880 | − | 1.19491i | −0.971876 | − | 0.235492i | \(-0.924330\pi\) |
0.281996 | − | 0.959415i | \(-0.409003\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.0000 | −0.806751 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.00000 | + | 8.66025i | 0.167884 | + | 0.290783i | 0.937676 | − | 0.347512i | \(-0.112973\pi\) |
−0.769792 | + | 0.638295i | \(0.779640\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.00000 | − | 1.73205i | 0.0335013 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.00000 | + | 5.19615i | 0.234246 | + | 0.173883i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000 | − | 41.5692i | 0.802232 | − | 1.38951i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 14.0000 | + | 24.2487i | 0.467446 | + | 0.809641i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.00000 | + | 3.46410i | 0.0667037 | + | 0.115534i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10.5000 | + | 18.1865i | 0.349418 | + | 0.605210i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.00000 | 0.265929 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.0000 | − | 17.3205i | 0.332045 | − | 0.575118i | −0.650868 | − | 0.759191i | \(-0.725595\pi\) |
0.982913 | + | 0.184073i | \(0.0589282\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −1.00000 | + | 1.73205i | −0.0331679 | + | 0.0574485i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000 | 0.397578 | 0.198789 | − | 0.980042i | \(-0.436299\pi\) | ||||
0.198789 | + | 0.980042i | \(0.436299\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24.0000 | −0.794284 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.00000 | + | 3.46410i | −0.0661180 | + | 0.114520i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −27.0000 | + | 46.7654i | −0.891619 | + | 1.54433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.0000 | −0.362857 | −0.181428 | − | 0.983404i | \(-0.558072\pi\) | ||||
−0.181428 | + | 0.983404i | \(0.558072\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 6.00000 | + | 10.3923i | 0.197707 | + | 0.342438i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 14.0000 | 0.460816 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −38.5000 | − | 66.6840i | −1.26587 | − | 2.19255i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 4.50000 | + | 7.79423i | 0.147799 | + | 0.255996i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −4.00000 | + | 6.92820i | −0.131236 | + | 0.227307i | −0.924153 | − | 0.382022i | \(-0.875228\pi\) |
0.792917 | + | 0.609329i | \(0.208561\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.00000 | − | 3.46410i | 0.262189 | − | 0.113531i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 17.0000 | − | 29.4449i | 0.556555 | − | 0.963982i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 12.5000 | + | 21.6506i | 0.408357 | + | 0.707295i | 0.994706 | − | 0.102763i | \(-0.0327685\pi\) |
−0.586349 | + | 0.810059i | \(0.699435\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 14.0000 | 0.456873 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −8.00000 | − | 13.8564i | −0.260793 | − | 0.451706i | 0.705660 | − | 0.708550i | \(-0.250651\pi\) |
−0.966453 | + | 0.256844i | \(0.917317\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.0000 | 0.521032 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 6.00000 | − | 10.3923i | 0.195180 | − | 0.338062i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.0000 | − | 46.7654i | 0.877382 | − | 1.51967i | 0.0231788 | − | 0.999731i | \(-0.492621\pi\) |
0.854203 | − | 0.519939i | \(-0.174045\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.0000 | 0.681689 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −24.0000 | −0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.00000 | − | 8.66025i | 0.161966 | − | 0.280533i | −0.773608 | − | 0.633665i | \(-0.781550\pi\) |
0.935574 | + | 0.353132i | \(0.114883\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.0000 | − | 69.2820i | 1.29437 | − | 2.24191i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.00000 | −0.258603 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.00000 | + | 5.19615i | 0.0968751 | + | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.00000 | + | 1.73205i | 0.0322245 | + | 0.0558146i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −42.0000 | − | 72.7461i | −1.35203 | − | 2.34178i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −4.50000 | + | 7.79423i | −0.144710 | + | 0.250645i | −0.929265 | − | 0.369414i | \(-0.879558\pi\) |
0.784555 | + | 0.620060i | \(0.212892\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.00000 | − | 12.1244i | 0.224641 | − | 0.389089i | −0.731571 | − | 0.681765i | \(-0.761212\pi\) |
0.956212 | + | 0.292676i | \(0.0945458\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 31.5000 | + | 54.5596i | 1.00984 | + | 1.74910i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 38.5000 | + | 66.6840i | 1.23299 | + | 2.13560i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.0000 | 0.447900 | 0.223950 | − | 0.974601i | \(-0.428105\pi\) | ||||
0.223950 | + | 0.974601i | \(0.428105\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 18.0000 | + | 31.1769i | 0.575282 | + | 0.996419i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 3.00000 | − | 5.19615i | 0.0956851 | − | 0.165732i | −0.814209 | − | 0.580572i | \(-0.802829\pi\) |
0.909894 | + | 0.414840i | \(0.136162\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −20.0000 | + | 34.6410i | −0.637253 | + | 1.10375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.00000 | −0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −28.0000 | −0.890348 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −14.5000 | + | 25.1147i | −0.460608 | + | 0.797796i | −0.998991 | − | 0.0449040i | \(-0.985702\pi\) |
0.538384 | + | 0.842700i | \(0.319035\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.5000 | − | 19.9186i | 0.364941 | − | 0.632097i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −28.0000 | −0.887660 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 26.5000 | + | 45.8993i | 0.839263 | + | 1.45365i | 0.890511 | + | 0.454961i | \(0.150347\pi\) |
−0.0512480 | + | 0.998686i | \(0.516320\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.00000 | 0.221470 |
(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 | 912.2.q.d.49.1 | 2 | ||
3.2 | odd | 2 | 2736.2.s.c.1873.1 | 2 | |||
4.3 | odd | 2 | 114.2.e.a.49.1 | yes | 2 | ||
12.11 | even | 2 | 342.2.g.d.163.1 | 2 | |||
19.7 | even | 3 | inner | 912.2.q.d.577.1 | 2 | ||
57.26 | odd | 6 | 2736.2.s.c.577.1 | 2 | |||
76.7 | odd | 6 | 114.2.e.a.7.1 | ✓ | 2 | ||
76.11 | odd | 6 | 2166.2.a.f.1.1 | 1 | |||
76.27 | even | 6 | 2166.2.a.c.1.1 | 1 | |||
228.11 | even | 6 | 6498.2.a.l.1.1 | 1 | |||
228.83 | even | 6 | 342.2.g.d.235.1 | 2 | |||
228.179 | odd | 6 | 6498.2.a.x.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.e.a.7.1 | ✓ | 2 | 76.7 | odd | 6 | ||
114.2.e.a.49.1 | yes | 2 | 4.3 | odd | 2 | ||
342.2.g.d.163.1 | 2 | 12.11 | even | 2 | |||
342.2.g.d.235.1 | 2 | 228.83 | even | 6 | |||
912.2.q.d.49.1 | 2 | 1.1 | even | 1 | trivial | ||
912.2.q.d.577.1 | 2 | 19.7 | even | 3 | inner | ||
2166.2.a.c.1.1 | 1 | 76.27 | even | 6 | |||
2166.2.a.f.1.1 | 1 | 76.11 | odd | 6 | |||
2736.2.s.c.577.1 | 2 | 57.26 | odd | 6 | |||
2736.2.s.c.1873.1 | 2 | 3.2 | odd | 2 | |||
6498.2.a.l.1.1 | 1 | 228.11 | even | 6 | |||
6498.2.a.x.1.1 | 1 | 228.179 | odd | 6 |