Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [114,2,Mod(7,114)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(114, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("114.7");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 114 = 2 \cdot 3 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 114.e (of order \(3\), degree \(2\), 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: | \(0.910294583043\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 7.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 114.7 |
Dual form | 114.2.e.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/114\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(97\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.00000 | + | 3.46410i | 0.894427 | + | 1.54919i | 0.834512 | + | 0.550990i | \(0.185750\pi\) |
0.0599153 | + | 0.998203i | \(0.480917\pi\) | |||||||
\(6\) | 0.500000 | − | 0.866025i | 0.204124 | − | 0.353553i | ||||
\(7\) | −3.00000 | −1.13389 | −0.566947 | − | 0.823754i | \(-0.691875\pi\) | ||||
−0.566947 | + | 0.823754i | \(0.691875\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 2.00000 | − | 3.46410i | 0.632456 | − | 1.09545i | ||||
\(11\) | 2.00000 | 0.603023 | 0.301511 | − | 0.953463i | \(-0.402509\pi\) | ||||
0.301511 | + | 0.953463i | \(0.402509\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 3.50000 | − | 6.06218i | 0.970725 | − | 1.68135i | 0.277350 | − | 0.960769i | \(-0.410544\pi\) |
0.693375 | − | 0.720577i | \(-0.256123\pi\) | |||||||
\(14\) | 1.50000 | + | 2.59808i | 0.400892 | + | 0.694365i | ||||
\(15\) | −2.00000 | + | 3.46410i | −0.516398 | + | 0.894427i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | −4.00000 | −0.894427 | ||||||||
\(21\) | −1.50000 | − | 2.59808i | −0.327327 | − | 0.566947i | ||||
\(22\) | −1.00000 | − | 1.73205i | −0.213201 | − | 0.369274i | ||||
\(23\) | 2.00000 | − | 3.46410i | 0.417029 | − | 0.722315i | −0.578610 | − | 0.815604i | \(-0.696405\pi\) |
0.995639 | + | 0.0932891i | \(0.0297381\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −5.50000 | + | 9.52628i | −1.10000 | + | 1.90526i | ||||
\(26\) | −7.00000 | −1.37281 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.50000 | − | 2.59808i | 0.283473 | − | 0.490990i | ||||
\(29\) | −2.00000 | + | 3.46410i | −0.371391 | + | 0.643268i | −0.989780 | − | 0.142605i | \(-0.954452\pi\) |
0.618389 | + | 0.785872i | \(0.287786\pi\) | |||||||
\(30\) | 4.00000 | 0.730297 | ||||||||
\(31\) | 1.00000 | 0.179605 | 0.0898027 | − | 0.995960i | \(-0.471376\pi\) | ||||
0.0898027 | + | 0.995960i | \(0.471376\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 1.00000 | + | 1.73205i | 0.174078 | + | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −6.00000 | − | 10.3923i | −1.01419 | − | 1.75662i | ||||
\(36\) | −0.500000 | − | 0.866025i | −0.0833333 | − | 0.144338i | ||||
\(37\) | 7.00000 | 1.15079 | 0.575396 | − | 0.817875i | \(-0.304848\pi\) | ||||
0.575396 | + | 0.817875i | \(0.304848\pi\) | |||||||
\(38\) | 0.500000 | + | 4.33013i | 0.0811107 | + | 0.702439i | ||||
\(39\) | 7.00000 | 1.12090 | ||||||||
\(40\) | 2.00000 | + | 3.46410i | 0.316228 | + | 0.547723i | ||||
\(41\) | −2.00000 | − | 3.46410i | −0.312348 | − | 0.541002i | 0.666523 | − | 0.745485i | \(-0.267782\pi\) |
−0.978870 | + | 0.204483i | \(0.934449\pi\) | |||||||
\(42\) | −1.50000 | + | 2.59808i | −0.231455 | + | 0.400892i | ||||
\(43\) | −3.50000 | − | 6.06218i | −0.533745 | − | 0.924473i | −0.999223 | − | 0.0394140i | \(-0.987451\pi\) |
0.465478 | − | 0.885059i | \(-0.345882\pi\) | |||||||
\(44\) | −1.00000 | + | 1.73205i | −0.150756 | + | 0.261116i | ||||
\(45\) | −4.00000 | −0.596285 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | −1.00000 | + | 1.73205i | −0.145865 | + | 0.252646i | −0.929695 | − | 0.368329i | \(-0.879930\pi\) |
0.783830 | + | 0.620975i | \(0.213263\pi\) | |||||||
\(48\) | 0.500000 | − | 0.866025i | 0.0721688 | − | 0.125000i | ||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 11.0000 | 1.55563 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.50000 | + | 6.06218i | 0.485363 | + | 0.840673i | ||||
\(53\) | 2.00000 | − | 3.46410i | 0.274721 | − | 0.475831i | −0.695344 | − | 0.718677i | \(-0.744748\pi\) |
0.970065 | + | 0.242846i | \(0.0780811\pi\) | |||||||
\(54\) | 0.500000 | + | 0.866025i | 0.0680414 | + | 0.117851i | ||||
\(55\) | 4.00000 | + | 6.92820i | 0.539360 | + | 0.934199i | ||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | −0.500000 | − | 4.33013i | −0.0662266 | − | 0.573539i | ||||
\(58\) | 4.00000 | 0.525226 | ||||||||
\(59\) | 3.00000 | + | 5.19615i | 0.390567 | + | 0.676481i | 0.992524 | − | 0.122047i | \(-0.0389457\pi\) |
−0.601958 | + | 0.798528i | \(0.705612\pi\) | |||||||
\(60\) | −2.00000 | − | 3.46410i | −0.258199 | − | 0.447214i | ||||
\(61\) | 0.500000 | − | 0.866025i | 0.0640184 | − | 0.110883i | −0.832240 | − | 0.554416i | \(-0.812942\pi\) |
0.896258 | + | 0.443533i | \(0.146275\pi\) | |||||||
\(62\) | −0.500000 | − | 0.866025i | −0.0635001 | − | 0.109985i | ||||
\(63\) | 1.50000 | − | 2.59808i | 0.188982 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 28.0000 | 3.47297 | ||||||||
\(66\) | 1.00000 | − | 1.73205i | 0.123091 | − | 0.213201i | ||||
\(67\) | −1.50000 | + | 2.59808i | −0.183254 | + | 0.317406i | −0.942987 | − | 0.332830i | \(-0.891996\pi\) |
0.759733 | + | 0.650236i | \(0.225330\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.00000 | 0.481543 | ||||||||
\(70\) | −6.00000 | + | 10.3923i | −0.717137 | + | 1.24212i | ||||
\(71\) | −1.00000 | − | 1.73205i | −0.118678 | − | 0.205557i | 0.800566 | − | 0.599245i | \(-0.204532\pi\) |
−0.919244 | + | 0.393688i | \(0.871199\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 1.50000 | + | 2.59808i | 0.175562 | + | 0.304082i | 0.940356 | − | 0.340193i | \(-0.110493\pi\) |
−0.764794 | + | 0.644275i | \(0.777159\pi\) | |||||||
\(74\) | −3.50000 | − | 6.06218i | −0.406867 | − | 0.704714i | ||||
\(75\) | −11.0000 | −1.27017 | ||||||||
\(76\) | 3.50000 | − | 2.59808i | 0.401478 | − | 0.298020i | ||||
\(77\) | −6.00000 | −0.683763 | ||||||||
\(78\) | −3.50000 | − | 6.06218i | −0.396297 | − | 0.686406i | ||||
\(79\) | −2.50000 | − | 4.33013i | −0.281272 | − | 0.487177i | 0.690426 | − | 0.723403i | \(-0.257423\pi\) |
−0.971698 | + | 0.236225i | \(0.924090\pi\) | |||||||
\(80\) | 2.00000 | − | 3.46410i | 0.223607 | − | 0.387298i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.00000 | + | 3.46410i | −0.220863 | + | 0.382546i | ||||
\(83\) | −12.0000 | −1.31717 | −0.658586 | − | 0.752506i | \(-0.728845\pi\) | ||||
−0.658586 | + | 0.752506i | \(0.728845\pi\) | |||||||
\(84\) | 3.00000 | 0.327327 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −3.50000 | + | 6.06218i | −0.377415 | + | 0.653701i | ||||
\(87\) | −4.00000 | −0.428845 | ||||||||
\(88\) | 2.00000 | 0.213201 | ||||||||
\(89\) | −9.00000 | + | 15.5885i | −0.953998 | + | 1.65237i | −0.217354 | + | 0.976093i | \(0.569742\pi\) |
−0.736644 | + | 0.676280i | \(0.763591\pi\) | |||||||
\(90\) | 2.00000 | + | 3.46410i | 0.210819 | + | 0.365148i | ||||
\(91\) | −10.5000 | + | 18.1865i | −1.10070 | + | 1.90647i | ||||
\(92\) | 2.00000 | + | 3.46410i | 0.208514 | + | 0.361158i | ||||
\(93\) | 0.500000 | + | 0.866025i | 0.0518476 | + | 0.0898027i | ||||
\(94\) | 2.00000 | 0.206284 | ||||||||
\(95\) | −2.00000 | − | 17.3205i | −0.205196 | − | 1.77705i | ||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −5.00000 | − | 8.66025i | −0.507673 | − | 0.879316i | −0.999961 | − | 0.00888289i | \(-0.997172\pi\) |
0.492287 | − | 0.870433i | \(-0.336161\pi\) | |||||||
\(98\) | −1.00000 | − | 1.73205i | −0.101015 | − | 0.174964i | ||||
\(99\) | −1.00000 | + | 1.73205i | −0.100504 | + | 0.174078i | ||||
\(100\) | −5.50000 | − | 9.52628i | −0.550000 | − | 0.952628i | ||||
\(101\) | −1.00000 | + | 1.73205i | −0.0995037 | + | 0.172345i | −0.911479 | − | 0.411346i | \(-0.865059\pi\) |
0.811976 | + | 0.583691i | \(0.198392\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.00000 | 0.886796 | 0.443398 | − | 0.896325i | \(-0.353773\pi\) | ||||
0.443398 | + | 0.896325i | \(0.353773\pi\) | |||||||
\(104\) | 3.50000 | − | 6.06218i | 0.343203 | − | 0.594445i | ||||
\(105\) | 6.00000 | − | 10.3923i | 0.585540 | − | 1.01419i | ||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | 2.00000 | 0.193347 | 0.0966736 | − | 0.995316i | \(-0.469180\pi\) | ||||
0.0966736 | + | 0.995316i | \(0.469180\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | −3.00000 | − | 5.19615i | −0.287348 | − | 0.497701i | 0.685828 | − | 0.727764i | \(-0.259440\pi\) |
−0.973176 | + | 0.230063i | \(0.926107\pi\) | |||||||
\(110\) | 4.00000 | − | 6.92820i | 0.381385 | − | 0.660578i | ||||
\(111\) | 3.50000 | + | 6.06218i | 0.332205 | + | 0.575396i | ||||
\(112\) | 1.50000 | + | 2.59808i | 0.141737 | + | 0.245495i | ||||
\(113\) | 2.00000 | 0.188144 | 0.0940721 | − | 0.995565i | \(-0.470012\pi\) | ||||
0.0940721 | + | 0.995565i | \(0.470012\pi\) | |||||||
\(114\) | −3.50000 | + | 2.59808i | −0.327805 | + | 0.243332i | ||||
\(115\) | 16.0000 | 1.49201 | ||||||||
\(116\) | −2.00000 | − | 3.46410i | −0.185695 | − | 0.321634i | ||||
\(117\) | 3.50000 | + | 6.06218i | 0.323575 | + | 0.560449i | ||||
\(118\) | 3.00000 | − | 5.19615i | 0.276172 | − | 0.478345i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.00000 | + | 3.46410i | −0.182574 | + | 0.316228i | ||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −1.00000 | −0.0905357 | ||||||||
\(123\) | 2.00000 | − | 3.46410i | 0.180334 | − | 0.312348i | ||||
\(124\) | −0.500000 | + | 0.866025i | −0.0449013 | + | 0.0777714i | ||||
\(125\) | −24.0000 | −2.14663 | ||||||||
\(126\) | −3.00000 | −0.267261 | ||||||||
\(127\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 3.50000 | − | 6.06218i | 0.308158 | − | 0.533745i | ||||
\(130\) | −14.0000 | − | 24.2487i | −1.22788 | − | 2.12675i | ||||
\(131\) | 9.00000 | + | 15.5885i | 0.786334 | + | 1.36197i | 0.928199 | + | 0.372084i | \(0.121357\pi\) |
−0.141865 | + | 0.989886i | \(0.545310\pi\) | |||||||
\(132\) | −2.00000 | −0.174078 | ||||||||
\(133\) | 12.0000 | + | 5.19615i | 1.04053 | + | 0.450564i | ||||
\(134\) | 3.00000 | 0.259161 | ||||||||
\(135\) | −2.00000 | − | 3.46410i | −0.172133 | − | 0.298142i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | − | 1.73205i | 0.0854358 | − | 0.147979i | −0.820141 | − | 0.572161i | \(-0.806105\pi\) |
0.905577 | + | 0.424182i | \(0.139438\pi\) | |||||||
\(138\) | −2.00000 | − | 3.46410i | −0.170251 | − | 0.294884i | ||||
\(139\) | −10.5000 | + | 18.1865i | −0.890598 | + | 1.54256i | −0.0514389 | + | 0.998676i | \(0.516381\pi\) |
−0.839159 | + | 0.543885i | \(0.816953\pi\) | |||||||
\(140\) | 12.0000 | 1.01419 | ||||||||
\(141\) | −2.00000 | −0.168430 | ||||||||
\(142\) | −1.00000 | + | 1.73205i | −0.0839181 | + | 0.145350i | ||||
\(143\) | 7.00000 | − | 12.1244i | 0.585369 | − | 1.01389i | ||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −16.0000 | −1.32873 | ||||||||
\(146\) | 1.50000 | − | 2.59808i | 0.124141 | − | 0.215018i | ||||
\(147\) | 1.00000 | + | 1.73205i | 0.0824786 | + | 0.142857i | ||||
\(148\) | −3.50000 | + | 6.06218i | −0.287698 | + | 0.498308i | ||||
\(149\) | 9.00000 | + | 15.5885i | 0.737309 | + | 1.27706i | 0.953703 | + | 0.300750i | \(0.0972370\pi\) |
−0.216394 | + | 0.976306i | \(0.569430\pi\) | |||||||
\(150\) | 5.50000 | + | 9.52628i | 0.449073 | + | 0.777817i | ||||
\(151\) | 20.0000 | 1.62758 | 0.813788 | − | 0.581161i | \(-0.197401\pi\) | ||||
0.813788 | + | 0.581161i | \(0.197401\pi\) | |||||||
\(152\) | −4.00000 | − | 1.73205i | −0.324443 | − | 0.140488i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.00000 | + | 5.19615i | 0.241747 | + | 0.418718i | ||||
\(155\) | 2.00000 | + | 3.46410i | 0.160644 | + | 0.278243i | ||||
\(156\) | −3.50000 | + | 6.06218i | −0.280224 | + | 0.485363i | ||||
\(157\) | −3.50000 | − | 6.06218i | −0.279330 | − | 0.483814i | 0.691888 | − | 0.722005i | \(-0.256779\pi\) |
−0.971219 | + | 0.238190i | \(0.923446\pi\) | |||||||
\(158\) | −2.50000 | + | 4.33013i | −0.198889 | + | 0.344486i | ||||
\(159\) | 4.00000 | 0.317221 | ||||||||
\(160\) | −4.00000 | −0.316228 | ||||||||
\(161\) | −6.00000 | + | 10.3923i | −0.472866 | + | 0.819028i | ||||
\(162\) | −0.500000 | + | 0.866025i | −0.0392837 | + | 0.0680414i | ||||
\(163\) | 11.0000 | 0.861586 | 0.430793 | − | 0.902451i | \(-0.358234\pi\) | ||||
0.430793 | + | 0.902451i | \(0.358234\pi\) | |||||||
\(164\) | 4.00000 | 0.312348 | ||||||||
\(165\) | −4.00000 | + | 6.92820i | −0.311400 | + | 0.539360i | ||||
\(166\) | 6.00000 | + | 10.3923i | 0.465690 | + | 0.806599i | ||||
\(167\) | −3.00000 | + | 5.19615i | −0.232147 | + | 0.402090i | −0.958440 | − | 0.285295i | \(-0.907908\pi\) |
0.726293 | + | 0.687386i | \(0.241242\pi\) | |||||||
\(168\) | −1.50000 | − | 2.59808i | −0.115728 | − | 0.200446i | ||||
\(169\) | −18.0000 | − | 31.1769i | −1.38462 | − | 2.39822i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.50000 | − | 2.59808i | 0.267652 | − | 0.198680i | ||||
\(172\) | 7.00000 | 0.533745 | ||||||||
\(173\) | −6.00000 | − | 10.3923i | −0.456172 | − | 0.790112i | 0.542583 | − | 0.840002i | \(-0.317446\pi\) |
−0.998755 | + | 0.0498898i | \(0.984113\pi\) | |||||||
\(174\) | 2.00000 | + | 3.46410i | 0.151620 | + | 0.262613i | ||||
\(175\) | 16.5000 | − | 28.5788i | 1.24728 | − | 2.16036i | ||||
\(176\) | −1.00000 | − | 1.73205i | −0.0753778 | − | 0.130558i | ||||
\(177\) | −3.00000 | + | 5.19615i | −0.225494 | + | 0.390567i | ||||
\(178\) | 18.0000 | 1.34916 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 2.00000 | − | 3.46410i | 0.149071 | − | 0.258199i | ||||
\(181\) | 1.00000 | − | 1.73205i | 0.0743294 | − | 0.128742i | −0.826465 | − | 0.562988i | \(-0.809652\pi\) |
0.900794 | + | 0.434246i | \(0.142985\pi\) | |||||||
\(182\) | 21.0000 | 1.55662 | ||||||||
\(183\) | 1.00000 | 0.0739221 | ||||||||
\(184\) | 2.00000 | − | 3.46410i | 0.147442 | − | 0.255377i | ||||
\(185\) | 14.0000 | + | 24.2487i | 1.02930 | + | 1.78280i | ||||
\(186\) | 0.500000 | − | 0.866025i | 0.0366618 | − | 0.0635001i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.00000 | − | 1.73205i | −0.0729325 | − | 0.126323i | ||||
\(189\) | 3.00000 | 0.218218 | ||||||||
\(190\) | −14.0000 | + | 10.3923i | −1.01567 | + | 0.753937i | ||||
\(191\) | −20.0000 | −1.44715 | −0.723575 | − | 0.690246i | \(-0.757502\pi\) | ||||
−0.723575 | + | 0.690246i | \(0.757502\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 10.5000 | + | 18.1865i | 0.755807 | + | 1.30910i | 0.944972 | + | 0.327150i | \(0.106088\pi\) |
−0.189166 | + | 0.981945i | \(0.560578\pi\) | |||||||
\(194\) | −5.00000 | + | 8.66025i | −0.358979 | + | 0.621770i | ||||
\(195\) | 14.0000 | + | 24.2487i | 1.00256 | + | 1.73649i | ||||
\(196\) | −1.00000 | + | 1.73205i | −0.0714286 | + | 0.123718i | ||||
\(197\) | −10.0000 | −0.712470 | −0.356235 | − | 0.934396i | \(-0.615940\pi\) | ||||
−0.356235 | + | 0.934396i | \(0.615940\pi\) | |||||||
\(198\) | 2.00000 | 0.142134 | ||||||||
\(199\) | 3.50000 | − | 6.06218i | 0.248108 | − | 0.429736i | −0.714893 | − | 0.699234i | \(-0.753524\pi\) |
0.963001 | + | 0.269498i | \(0.0868577\pi\) | |||||||
\(200\) | −5.50000 | + | 9.52628i | −0.388909 | + | 0.673610i | ||||
\(201\) | −3.00000 | −0.211604 | ||||||||
\(202\) | 2.00000 | 0.140720 | ||||||||
\(203\) | 6.00000 | − | 10.3923i | 0.421117 | − | 0.729397i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.00000 | − | 13.8564i | 0.558744 | − | 0.967773i | ||||
\(206\) | −4.50000 | − | 7.79423i | −0.313530 | − | 0.543050i | ||||
\(207\) | 2.00000 | + | 3.46410i | 0.139010 | + | 0.240772i | ||||
\(208\) | −7.00000 | −0.485363 | ||||||||
\(209\) | −8.00000 | − | 3.46410i | −0.553372 | − | 0.239617i | ||||
\(210\) | −12.0000 | −0.828079 | ||||||||
\(211\) | −4.50000 | − | 7.79423i | −0.309793 | − | 0.536577i | 0.668524 | − | 0.743690i | \(-0.266926\pi\) |
−0.978317 | + | 0.207114i | \(0.933593\pi\) | |||||||
\(212\) | 2.00000 | + | 3.46410i | 0.137361 | + | 0.237915i | ||||
\(213\) | 1.00000 | − | 1.73205i | 0.0685189 | − | 0.118678i | ||||
\(214\) | −1.00000 | − | 1.73205i | −0.0683586 | − | 0.118401i | ||||
\(215\) | 14.0000 | − | 24.2487i | 0.954792 | − | 1.65375i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −3.00000 | −0.203653 | ||||||||
\(218\) | −3.00000 | + | 5.19615i | −0.203186 | + | 0.351928i | ||||
\(219\) | −1.50000 | + | 2.59808i | −0.101361 | + | 0.175562i | ||||
\(220\) | −8.00000 | −0.539360 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 3.50000 | − | 6.06218i | 0.234905 | − | 0.406867i | ||||
\(223\) | −2.50000 | − | 4.33013i | −0.167412 | − | 0.289967i | 0.770097 | − | 0.637927i | \(-0.220208\pi\) |
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 1.50000 | − | 2.59808i | 0.100223 | − | 0.173591i | ||||
\(225\) | −5.50000 | − | 9.52628i | −0.366667 | − | 0.635085i | ||||
\(226\) | −1.00000 | − | 1.73205i | −0.0665190 | − | 0.115214i | ||||
\(227\) | 4.00000 | 0.265489 | 0.132745 | − | 0.991150i | \(-0.457621\pi\) | ||||
0.132745 | + | 0.991150i | \(0.457621\pi\) | |||||||
\(228\) | 4.00000 | + | 1.73205i | 0.264906 | + | 0.114708i | ||||
\(229\) | −7.00000 | −0.462573 | −0.231287 | − | 0.972886i | \(-0.574293\pi\) | ||||
−0.231287 | + | 0.972886i | \(0.574293\pi\) | |||||||
\(230\) | −8.00000 | − | 13.8564i | −0.527504 | − | 0.913664i | ||||
\(231\) | −3.00000 | − | 5.19615i | −0.197386 | − | 0.341882i | ||||
\(232\) | −2.00000 | + | 3.46410i | −0.131306 | + | 0.227429i | ||||
\(233\) | −3.00000 | − | 5.19615i | −0.196537 | − | 0.340411i | 0.750867 | − | 0.660454i | \(-0.229636\pi\) |
−0.947403 | + | 0.320043i | \(0.896303\pi\) | |||||||
\(234\) | 3.50000 | − | 6.06218i | 0.228802 | − | 0.396297i | ||||
\(235\) | −8.00000 | −0.521862 | ||||||||
\(236\) | −6.00000 | −0.390567 | ||||||||
\(237\) | 2.50000 | − | 4.33013i | 0.162392 | − | 0.281272i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 4.00000 | 0.258199 | ||||||||
\(241\) | −0.500000 | + | 0.866025i | −0.0322078 | + | 0.0557856i | −0.881680 | − | 0.471848i | \(-0.843587\pi\) |
0.849472 | + | 0.527633i | \(0.176921\pi\) | |||||||
\(242\) | 3.50000 | + | 6.06218i | 0.224989 | + | 0.389692i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 0.500000 | + | 0.866025i | 0.0320092 | + | 0.0554416i | ||||
\(245\) | 4.00000 | + | 6.92820i | 0.255551 | + | 0.442627i | ||||
\(246\) | −4.00000 | −0.255031 | ||||||||
\(247\) | −24.5000 | + | 18.1865i | −1.55890 | + | 1.15718i | ||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −6.00000 | − | 10.3923i | −0.380235 | − | 0.658586i | ||||
\(250\) | 12.0000 | + | 20.7846i | 0.758947 | + | 1.31453i | ||||
\(251\) | −7.00000 | + | 12.1244i | −0.441836 | + | 0.765283i | −0.997826 | − | 0.0659066i | \(-0.979006\pi\) |
0.555990 | + | 0.831189i | \(0.312339\pi\) | |||||||
\(252\) | 1.50000 | + | 2.59808i | 0.0944911 | + | 0.163663i | ||||
\(253\) | 4.00000 | − | 6.92820i | 0.251478 | − | 0.435572i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 14.0000 | − | 24.2487i | 0.873296 | − | 1.51259i | 0.0147291 | − | 0.999892i | \(-0.495311\pi\) |
0.858567 | − | 0.512702i | \(-0.171355\pi\) | |||||||
\(258\) | −7.00000 | −0.435801 | ||||||||
\(259\) | −21.0000 | −1.30488 | ||||||||
\(260\) | −14.0000 | + | 24.2487i | −0.868243 | + | 1.50384i | ||||
\(261\) | −2.00000 | − | 3.46410i | −0.123797 | − | 0.214423i | ||||
\(262\) | 9.00000 | − | 15.5885i | 0.556022 | − | 0.963058i | ||||
\(263\) | 9.00000 | + | 15.5885i | 0.554964 | + | 0.961225i | 0.997906 | + | 0.0646755i | \(0.0206012\pi\) |
−0.442943 | + | 0.896550i | \(0.646065\pi\) | |||||||
\(264\) | 1.00000 | + | 1.73205i | 0.0615457 | + | 0.106600i | ||||
\(265\) | 16.0000 | 0.982872 | ||||||||
\(266\) | −1.50000 | − | 12.9904i | −0.0919709 | − | 0.796491i | ||||
\(267\) | −18.0000 | −1.10158 | ||||||||
\(268\) | −1.50000 | − | 2.59808i | −0.0916271 | − | 0.158703i | ||||
\(269\) | −9.00000 | − | 15.5885i | −0.548740 | − | 0.950445i | −0.998361 | − | 0.0572259i | \(-0.981774\pi\) |
0.449622 | − | 0.893219i | \(-0.351559\pi\) | |||||||
\(270\) | −2.00000 | + | 3.46410i | −0.121716 | + | 0.210819i | ||||
\(271\) | 4.00000 | + | 6.92820i | 0.242983 | + | 0.420858i | 0.961563 | − | 0.274586i | \(-0.0885408\pi\) |
−0.718580 | + | 0.695444i | \(0.755208\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −21.0000 | −1.27098 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | −11.0000 | + | 19.0526i | −0.663325 | + | 1.14891i | ||||
\(276\) | −2.00000 | + | 3.46410i | −0.120386 | + | 0.208514i | ||||
\(277\) | −26.0000 | −1.56219 | −0.781094 | − | 0.624413i | \(-0.785338\pi\) | ||||
−0.781094 | + | 0.624413i | \(0.785338\pi\) | |||||||
\(278\) | 21.0000 | 1.25950 | ||||||||
\(279\) | −0.500000 | + | 0.866025i | −0.0299342 | + | 0.0518476i | ||||
\(280\) | −6.00000 | − | 10.3923i | −0.358569 | − | 0.621059i | ||||
\(281\) | −2.00000 | + | 3.46410i | −0.119310 | + | 0.206651i | −0.919494 | − | 0.393103i | \(-0.871402\pi\) |
0.800184 | + | 0.599754i | \(0.204735\pi\) | |||||||
\(282\) | 1.00000 | + | 1.73205i | 0.0595491 | + | 0.103142i | ||||
\(283\) | 6.00000 | + | 10.3923i | 0.356663 | + | 0.617758i | 0.987401 | − | 0.158237i | \(-0.0505811\pi\) |
−0.630738 | + | 0.775996i | \(0.717248\pi\) | |||||||
\(284\) | 2.00000 | 0.118678 | ||||||||
\(285\) | 14.0000 | − | 10.3923i | 0.829288 | − | 0.615587i | ||||
\(286\) | −14.0000 | −0.827837 | ||||||||
\(287\) | 6.00000 | + | 10.3923i | 0.354169 | + | 0.613438i | ||||
\(288\) | −0.500000 | − | 0.866025i | −0.0294628 | − | 0.0510310i | ||||
\(289\) | 8.50000 | − | 14.7224i | 0.500000 | − | 0.866025i | ||||
\(290\) | 8.00000 | + | 13.8564i | 0.469776 | + | 0.813676i | ||||
\(291\) | 5.00000 | − | 8.66025i | 0.293105 | − | 0.507673i | ||||
\(292\) | −3.00000 | −0.175562 | ||||||||
\(293\) | −18.0000 | −1.05157 | −0.525786 | − | 0.850617i | \(-0.676229\pi\) | ||||
−0.525786 | + | 0.850617i | \(0.676229\pi\) | |||||||
\(294\) | 1.00000 | − | 1.73205i | 0.0583212 | − | 0.101015i | ||||
\(295\) | −12.0000 | + | 20.7846i | −0.698667 | + | 1.21013i | ||||
\(296\) | 7.00000 | 0.406867 | ||||||||
\(297\) | −2.00000 | −0.116052 | ||||||||
\(298\) | 9.00000 | − | 15.5885i | 0.521356 | − | 0.903015i | ||||
\(299\) | −14.0000 | − | 24.2487i | −0.809641 | − | 1.40234i | ||||
\(300\) | 5.50000 | − | 9.52628i | 0.317543 | − | 0.550000i | ||||
\(301\) | 10.5000 | + | 18.1865i | 0.605210 | + | 1.04825i | ||||
\(302\) | −10.0000 | − | 17.3205i | −0.575435 | − | 0.996683i | ||||
\(303\) | −2.00000 | −0.114897 | ||||||||
\(304\) | 0.500000 | + | 4.33013i | 0.0286770 | + | 0.248350i | ||||
\(305\) | 4.00000 | 0.229039 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.00000 | − | 10.3923i | −0.342438 | − | 0.593120i | 0.642447 | − | 0.766330i | \(-0.277919\pi\) |
−0.984885 | + | 0.173210i | \(0.944586\pi\) | |||||||
\(308\) | 3.00000 | − | 5.19615i | 0.170941 | − | 0.296078i | ||||
\(309\) | 4.50000 | + | 7.79423i | 0.255996 | + | 0.443398i | ||||
\(310\) | 2.00000 | − | 3.46410i | 0.113592 | − | 0.196748i | ||||
\(311\) | 34.0000 | 1.92796 | 0.963982 | − | 0.265969i | \(-0.0856919\pi\) | ||||
0.963982 | + | 0.265969i | \(0.0856919\pi\) | |||||||
\(312\) | 7.00000 | 0.396297 | ||||||||
\(313\) | −7.00000 | + | 12.1244i | −0.395663 | + | 0.685309i | −0.993186 | − | 0.116543i | \(-0.962819\pi\) |
0.597522 | + | 0.801852i | \(0.296152\pi\) | |||||||
\(314\) | −3.50000 | + | 6.06218i | −0.197516 | + | 0.342108i | ||||
\(315\) | 12.0000 | 0.676123 | ||||||||
\(316\) | 5.00000 | 0.281272 | ||||||||
\(317\) | 12.0000 | − | 20.7846i | 0.673987 | − | 1.16738i | −0.302777 | − | 0.953062i | \(-0.597914\pi\) |
0.976764 | − | 0.214318i | \(-0.0687530\pi\) | |||||||
\(318\) | −2.00000 | − | 3.46410i | −0.112154 | − | 0.194257i | ||||
\(319\) | −4.00000 | + | 6.92820i | −0.223957 | + | 0.387905i | ||||
\(320\) | 2.00000 | + | 3.46410i | 0.111803 | + | 0.193649i | ||||
\(321\) | 1.00000 | + | 1.73205i | 0.0558146 | + | 0.0966736i | ||||
\(322\) | 12.0000 | 0.668734 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 38.5000 | + | 66.6840i | 2.13560 | + | 3.69896i | ||||
\(326\) | −5.50000 | − | 9.52628i | −0.304617 | − | 0.527612i | ||||
\(327\) | 3.00000 | − | 5.19615i | 0.165900 | − | 0.287348i | ||||
\(328\) | −2.00000 | − | 3.46410i | −0.110432 | − | 0.191273i | ||||
\(329\) | 3.00000 | − | 5.19615i | 0.165395 | − | 0.286473i | ||||
\(330\) | 8.00000 | 0.440386 | ||||||||
\(331\) | 23.0000 | 1.26419 | 0.632097 | − | 0.774889i | \(-0.282194\pi\) | ||||
0.632097 | + | 0.774889i | \(0.282194\pi\) | |||||||
\(332\) | 6.00000 | − | 10.3923i | 0.329293 | − | 0.570352i | ||||
\(333\) | −3.50000 | + | 6.06218i | −0.191799 | + | 0.332205i | ||||
\(334\) | 6.00000 | 0.328305 | ||||||||
\(335\) | −12.0000 | −0.655630 | ||||||||
\(336\) | −1.50000 | + | 2.59808i | −0.0818317 | + | 0.141737i | ||||
\(337\) | −6.50000 | − | 11.2583i | −0.354078 | − | 0.613280i | 0.632882 | − | 0.774248i | \(-0.281872\pi\) |
−0.986960 | + | 0.160968i | \(0.948538\pi\) | |||||||
\(338\) | −18.0000 | + | 31.1769i | −0.979071 | + | 1.69580i | ||||
\(339\) | 1.00000 | + | 1.73205i | 0.0543125 | + | 0.0940721i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.00000 | 0.108306 | ||||||||
\(342\) | −4.00000 | − | 1.73205i | −0.216295 | − | 0.0936586i | ||||
\(343\) | 15.0000 | 0.809924 | ||||||||
\(344\) | −3.50000 | − | 6.06218i | −0.188707 | − | 0.326851i | ||||
\(345\) | 8.00000 | + | 13.8564i | 0.430706 | + | 0.746004i | ||||
\(346\) | −6.00000 | + | 10.3923i | −0.322562 | + | 0.558694i | ||||
\(347\) | −14.0000 | − | 24.2487i | −0.751559 | − | 1.30174i | −0.947067 | − | 0.321037i | \(-0.895969\pi\) |
0.195507 | − | 0.980702i | \(-0.437365\pi\) | |||||||
\(348\) | 2.00000 | − | 3.46410i | 0.107211 | − | 0.185695i | ||||
\(349\) | 31.0000 | 1.65939 | 0.829696 | − | 0.558216i | \(-0.188514\pi\) | ||||
0.829696 | + | 0.558216i | \(0.188514\pi\) | |||||||
\(350\) | −33.0000 | −1.76392 | ||||||||
\(351\) | −3.50000 | + | 6.06218i | −0.186816 | + | 0.323575i | ||||
\(352\) | −1.00000 | + | 1.73205i | −0.0533002 | + | 0.0923186i | ||||
\(353\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(354\) | 6.00000 | 0.318896 | ||||||||
\(355\) | 4.00000 | − | 6.92820i | 0.212298 | − | 0.367711i | ||||
\(356\) | −9.00000 | − | 15.5885i | −0.476999 | − | 0.826187i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.00000 | + | 10.3923i | 0.317110 | + | 0.549250i | ||||
\(359\) | 6.00000 | + | 10.3923i | 0.316668 | + | 0.548485i | 0.979791 | − | 0.200026i | \(-0.0641026\pi\) |
−0.663123 | + | 0.748511i | \(0.730769\pi\) | |||||||
\(360\) | −4.00000 | −0.210819 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | −2.00000 | −0.105118 | ||||||||
\(363\) | −3.50000 | − | 6.06218i | −0.183702 | − | 0.318182i | ||||
\(364\) | −10.5000 | − | 18.1865i | −0.550350 | − | 0.953233i | ||||
\(365\) | −6.00000 | + | 10.3923i | −0.314054 | + | 0.543958i | ||||
\(366\) | −0.500000 | − | 0.866025i | −0.0261354 | − | 0.0452679i | ||||
\(367\) | −9.50000 | + | 16.4545i | −0.495896 | + | 0.858917i | −0.999989 | − | 0.00473247i | \(-0.998494\pi\) |
0.504093 | + | 0.863649i | \(0.331827\pi\) | |||||||
\(368\) | −4.00000 | −0.208514 | ||||||||
\(369\) | 4.00000 | 0.208232 | ||||||||
\(370\) | 14.0000 | − | 24.2487i | 0.727825 | − | 1.26063i | ||||
\(371\) | −6.00000 | + | 10.3923i | −0.311504 | + | 0.539542i | ||||
\(372\) | −1.00000 | −0.0518476 | ||||||||
\(373\) | −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 | ||||
\(376\) | −1.00000 | + | 1.73205i | −0.0515711 | + | 0.0893237i | ||||
\(377\) | 14.0000 | + | 24.2487i | 0.721037 | + | 1.24887i | ||||
\(378\) | −1.50000 | − | 2.59808i | −0.0771517 | − | 0.133631i | ||||
\(379\) | −21.0000 | −1.07870 | −0.539349 | − | 0.842082i | \(-0.681330\pi\) | ||||
−0.539349 | + | 0.842082i | \(0.681330\pi\) | |||||||
\(380\) | 16.0000 | + | 6.92820i | 0.820783 | + | 0.355409i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 10.0000 | + | 17.3205i | 0.511645 | + | 0.886194i | ||||
\(383\) | 7.00000 | + | 12.1244i | 0.357683 | + | 0.619526i | 0.987573 | − | 0.157159i | \(-0.0502334\pi\) |
−0.629890 | + | 0.776684i | \(0.716900\pi\) | |||||||
\(384\) | 0.500000 | − | 0.866025i | 0.0255155 | − | 0.0441942i | ||||
\(385\) | −12.0000 | − | 20.7846i | −0.611577 | − | 1.05928i | ||||
\(386\) | 10.5000 | − | 18.1865i | 0.534436 | − | 0.925670i | ||||
\(387\) | 7.00000 | 0.355830 | ||||||||
\(388\) | 10.0000 | 0.507673 | ||||||||
\(389\) | 12.0000 | − | 20.7846i | 0.608424 | − | 1.05382i | −0.383076 | − | 0.923717i | \(-0.625135\pi\) |
0.991500 | − | 0.130105i | \(-0.0415314\pi\) | |||||||
\(390\) | 14.0000 | − | 24.2487i | 0.708918 | − | 1.22788i | ||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 2.00000 | 0.101015 | ||||||||
\(393\) | −9.00000 | + | 15.5885i | −0.453990 | + | 0.786334i | ||||
\(394\) | 5.00000 | + | 8.66025i | 0.251896 | + | 0.436297i | ||||
\(395\) | 10.0000 | − | 17.3205i | 0.503155 | − | 0.871489i | ||||
\(396\) | −1.00000 | − | 1.73205i | −0.0502519 | − | 0.0870388i | ||||
\(397\) | 6.50000 | + | 11.2583i | 0.326226 | + | 0.565039i | 0.981760 | − | 0.190126i | \(-0.0608897\pi\) |
−0.655534 | + | 0.755166i | \(0.727556\pi\) | |||||||
\(398\) | −7.00000 | −0.350878 | ||||||||
\(399\) | 1.50000 | + | 12.9904i | 0.0750939 | + | 0.650332i | ||||
\(400\) | 11.0000 | 0.550000 | ||||||||
\(401\) | −5.00000 | − | 8.66025i | −0.249688 | − | 0.432472i | 0.713751 | − | 0.700399i | \(-0.246995\pi\) |
−0.963439 | + | 0.267927i | \(0.913661\pi\) | |||||||
\(402\) | 1.50000 | + | 2.59808i | 0.0748132 | + | 0.129580i | ||||
\(403\) | 3.50000 | − | 6.06218i | 0.174347 | − | 0.301979i | ||||
\(404\) | −1.00000 | − | 1.73205i | −0.0497519 | − | 0.0861727i | ||||
\(405\) | 2.00000 | − | 3.46410i | 0.0993808 | − | 0.172133i | ||||
\(406\) | −12.0000 | −0.595550 | ||||||||
\(407\) | 14.0000 | 0.693954 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.00000 | + | 8.66025i | −0.247234 | + | 0.428222i | −0.962757 | − | 0.270367i | \(-0.912855\pi\) |
0.715523 | + | 0.698589i | \(0.246188\pi\) | |||||||
\(410\) | −16.0000 | −0.790184 | ||||||||
\(411\) | 2.00000 | 0.0986527 | ||||||||
\(412\) | −4.50000 | + | 7.79423i | −0.221699 | + | 0.383994i | ||||
\(413\) | −9.00000 | − | 15.5885i | −0.442861 | − | 0.767058i | ||||
\(414\) | 2.00000 | − | 3.46410i | 0.0982946 | − | 0.170251i | ||||
\(415\) | −24.0000 | − | 41.5692i | −1.17811 | − | 2.04055i | ||||
\(416\) | 3.50000 | + | 6.06218i | 0.171602 | + | 0.297223i | ||||
\(417\) | −21.0000 | −1.02837 | ||||||||
\(418\) | 1.00000 | + | 8.66025i | 0.0489116 | + | 0.423587i | ||||
\(419\) | 30.0000 | 1.46560 | 0.732798 | − | 0.680446i | \(-0.238214\pi\) | ||||
0.732798 | + | 0.680446i | \(0.238214\pi\) | |||||||
\(420\) | 6.00000 | + | 10.3923i | 0.292770 | + | 0.507093i | ||||
\(421\) | −13.0000 | − | 22.5167i | −0.633581 | − | 1.09739i | −0.986814 | − | 0.161859i | \(-0.948251\pi\) |
0.353233 | − | 0.935536i | \(-0.385082\pi\) | |||||||
\(422\) | −4.50000 | + | 7.79423i | −0.219057 | + | 0.379417i | ||||
\(423\) | −1.00000 | − | 1.73205i | −0.0486217 | − | 0.0842152i | ||||
\(424\) | 2.00000 | − | 3.46410i | 0.0971286 | − | 0.168232i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2.00000 | −0.0969003 | ||||||||
\(427\) | −1.50000 | + | 2.59808i | −0.0725901 | + | 0.125730i | ||||
\(428\) | −1.00000 | + | 1.73205i | −0.0483368 | + | 0.0837218i | ||||
\(429\) | 14.0000 | 0.675926 | ||||||||
\(430\) | −28.0000 | −1.35028 | ||||||||
\(431\) | −3.00000 | + | 5.19615i | −0.144505 | + | 0.250290i | −0.929188 | − | 0.369607i | \(-0.879492\pi\) |
0.784683 | + | 0.619897i | \(0.212826\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −11.5000 | + | 19.9186i | −0.552655 | + | 0.957226i | 0.445427 | + | 0.895318i | \(0.353052\pi\) |
−0.998082 | + | 0.0619079i | \(0.980282\pi\) | |||||||
\(434\) | 1.50000 | + | 2.59808i | 0.0720023 | + | 0.124712i | ||||
\(435\) | −8.00000 | − | 13.8564i | −0.383571 | − | 0.664364i | ||||
\(436\) | 6.00000 | 0.287348 | ||||||||
\(437\) | −14.0000 | + | 10.3923i | −0.669711 | + | 0.497131i | ||||
\(438\) | 3.00000 | 0.143346 | ||||||||
\(439\) | −11.5000 | − | 19.9186i | −0.548865 | − | 0.950662i | −0.998353 | − | 0.0573756i | \(-0.981727\pi\) |
0.449488 | − | 0.893287i | \(-0.351607\pi\) | |||||||
\(440\) | 4.00000 | + | 6.92820i | 0.190693 | + | 0.330289i | ||||
\(441\) | −1.00000 | + | 1.73205i | −0.0476190 | + | 0.0824786i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.00000 | + | 3.46410i | −0.0950229 | + | 0.164584i | −0.909618 | − | 0.415445i | \(-0.863626\pi\) |
0.814595 | + | 0.580030i | \(0.196959\pi\) | |||||||
\(444\) | −7.00000 | −0.332205 | ||||||||
\(445\) | −72.0000 | −3.41313 | ||||||||
\(446\) | −2.50000 | + | 4.33013i | −0.118378 | + | 0.205037i | ||||
\(447\) | −9.00000 | + | 15.5885i | −0.425685 | + | 0.737309i | ||||
\(448\) | −3.00000 | −0.141737 | ||||||||
\(449\) | 16.0000 | 0.755087 | 0.377543 | − | 0.925992i | \(-0.376769\pi\) | ||||
0.377543 | + | 0.925992i | \(0.376769\pi\) | |||||||
\(450\) | −5.50000 | + | 9.52628i | −0.259272 | + | 0.449073i | ||||
\(451\) | −4.00000 | − | 6.92820i | −0.188353 | − | 0.326236i | ||||
\(452\) | −1.00000 | + | 1.73205i | −0.0470360 | + | 0.0814688i | ||||
\(453\) | 10.0000 | + | 17.3205i | 0.469841 | + | 0.813788i | ||||
\(454\) | −2.00000 | − | 3.46410i | −0.0938647 | − | 0.162578i | ||||
\(455\) | −84.0000 | −3.93798 | ||||||||
\(456\) | −0.500000 | − | 4.33013i | −0.0234146 | − | 0.202777i | ||||
\(457\) | 29.0000 | 1.35656 | 0.678281 | − | 0.734802i | \(-0.262725\pi\) | ||||
0.678281 | + | 0.734802i | \(0.262725\pi\) | |||||||
\(458\) | 3.50000 | + | 6.06218i | 0.163544 | + | 0.283267i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.00000 | + | 13.8564i | −0.373002 | + | 0.646058i | ||||
\(461\) | 17.0000 | + | 29.4449i | 0.791769 | + | 1.37138i | 0.924871 | + | 0.380282i | \(0.124173\pi\) |
−0.133102 | + | 0.991102i | \(0.542494\pi\) | |||||||
\(462\) | −3.00000 | + | 5.19615i | −0.139573 | + | 0.241747i | ||||
\(463\) | 19.0000 | 0.883005 | 0.441502 | − | 0.897260i | \(-0.354446\pi\) | ||||
0.441502 | + | 0.897260i | \(0.354446\pi\) | |||||||
\(464\) | 4.00000 | 0.185695 | ||||||||
\(465\) | −2.00000 | + | 3.46410i | −0.0927478 | + | 0.160644i | ||||
\(466\) | −3.00000 | + | 5.19615i | −0.138972 | + | 0.240707i | ||||
\(467\) | −8.00000 | −0.370196 | −0.185098 | − | 0.982720i | \(-0.559260\pi\) | ||||
−0.185098 | + | 0.982720i | \(0.559260\pi\) | |||||||
\(468\) | −7.00000 | −0.323575 | ||||||||
\(469\) | 4.50000 | − | 7.79423i | 0.207791 | − | 0.359904i | ||||
\(470\) | 4.00000 | + | 6.92820i | 0.184506 | + | 0.319574i | ||||
\(471\) | 3.50000 | − | 6.06218i | 0.161271 | − | 0.279330i | ||||
\(472\) | 3.00000 | + | 5.19615i | 0.138086 | + | 0.239172i | ||||
\(473\) | −7.00000 | − | 12.1244i | −0.321860 | − | 0.557478i | ||||
\(474\) | −5.00000 | −0.229658 | ||||||||
\(475\) | 38.5000 | − | 28.5788i | 1.76650 | − | 1.31129i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 2.00000 | + | 3.46410i | 0.0915737 | + | 0.158610i | ||||
\(478\) | −12.0000 | − | 20.7846i | −0.548867 | − | 0.950666i | ||||
\(479\) | −17.0000 | + | 29.4449i | −0.776750 | + | 1.34537i | 0.157056 | + | 0.987590i | \(0.449800\pi\) |
−0.933806 | + | 0.357780i | \(0.883534\pi\) | |||||||
\(480\) | −2.00000 | − | 3.46410i | −0.0912871 | − | 0.158114i | ||||
\(481\) | 24.5000 | − | 42.4352i | 1.11710 | − | 1.93488i | ||||
\(482\) | 1.00000 | 0.0455488 | ||||||||
\(483\) | −12.0000 | −0.546019 | ||||||||
\(484\) | 3.50000 | − | 6.06218i | 0.159091 | − | 0.275554i | ||||
\(485\) | 20.0000 | − | 34.6410i | 0.908153 | − | 1.57297i | ||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 16.0000 | 0.725029 | 0.362515 | − | 0.931978i | \(-0.381918\pi\) | ||||
0.362515 | + | 0.931978i | \(0.381918\pi\) | |||||||
\(488\) | 0.500000 | − | 0.866025i | 0.0226339 | − | 0.0392031i | ||||
\(489\) | 5.50000 | + | 9.52628i | 0.248719 | + | 0.430793i | ||||
\(490\) | 4.00000 | − | 6.92820i | 0.180702 | − | 0.312984i | ||||
\(491\) | −13.0000 | − | 22.5167i | −0.586682 | − | 1.01616i | −0.994663 | − | 0.103173i | \(-0.967101\pi\) |
0.407982 | − | 0.912990i | \(-0.366233\pi\) | |||||||
\(492\) | 2.00000 | + | 3.46410i | 0.0901670 | + | 0.156174i | ||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 28.0000 | + | 12.1244i | 1.25978 | + | 0.545501i | ||||
\(495\) | −8.00000 | −0.359573 | ||||||||
\(496\) | −0.500000 | − | 0.866025i | −0.0224507 | − | 0.0388857i | ||||
\(497\) | 3.00000 | + | 5.19615i | 0.134568 | + | 0.233079i | ||||
\(498\) | −6.00000 | + | 10.3923i | −0.268866 | + | 0.465690i | ||||
\(499\) | 5.50000 | + | 9.52628i | 0.246214 | + | 0.426455i | 0.962472 | − | 0.271380i | \(-0.0874801\pi\) |
−0.716258 | + | 0.697835i | \(0.754147\pi\) | |||||||
\(500\) | 12.0000 | − | 20.7846i | 0.536656 | − | 0.929516i | ||||
\(501\) | −6.00000 | −0.268060 | ||||||||
\(502\) | 14.0000 | 0.624851 | ||||||||
\(503\) | 6.00000 | − | 10.3923i | 0.267527 | − | 0.463370i | −0.700696 | − | 0.713460i | \(-0.747127\pi\) |
0.968223 | + | 0.250090i | \(0.0804603\pi\) | |||||||
\(504\) | 1.50000 | − | 2.59808i | 0.0668153 | − | 0.115728i | ||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | −8.00000 | −0.355643 | ||||||||
\(507\) | 18.0000 | − | 31.1769i | 0.799408 | − | 1.38462i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.00000 | − | 5.19615i | 0.132973 | − | 0.230315i | −0.791849 | − | 0.610718i | \(-0.790881\pi\) |
0.924821 | + | 0.380402i | \(0.124214\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.50000 | − | 7.79423i | −0.199068 | − | 0.344796i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 4.00000 | + | 1.73205i | 0.176604 | + | 0.0764719i | ||||
\(514\) | −28.0000 | −1.23503 | ||||||||
\(515\) | 18.0000 | + | 31.1769i | 0.793175 | + | 1.37382i | ||||
\(516\) | 3.50000 | + | 6.06218i | 0.154079 | + | 0.266872i | ||||
\(517\) | −2.00000 | + | 3.46410i | −0.0879599 | + | 0.152351i | ||||
\(518\) | 10.5000 | + | 18.1865i | 0.461344 | + | 0.799070i | ||||
\(519\) | 6.00000 | − | 10.3923i | 0.263371 | − | 0.456172i | ||||
\(520\) | 28.0000 | 1.22788 | ||||||||
\(521\) | 38.0000 | 1.66481 | 0.832405 | − | 0.554168i | \(-0.186963\pi\) | ||||
0.832405 | + | 0.554168i | \(0.186963\pi\) | |||||||
\(522\) | −2.00000 | + | 3.46410i | −0.0875376 | + | 0.151620i | ||||
\(523\) | −14.5000 | + | 25.1147i | −0.634041 | + | 1.09819i | 0.352677 | + | 0.935745i | \(0.385272\pi\) |
−0.986718 | + | 0.162446i | \(0.948062\pi\) | |||||||
\(524\) | −18.0000 | −0.786334 | ||||||||
\(525\) | 33.0000 | 1.44024 | ||||||||
\(526\) | 9.00000 | − | 15.5885i | 0.392419 | − | 0.679689i | ||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 1.00000 | − | 1.73205i | 0.0435194 | − | 0.0753778i | ||||
\(529\) | 3.50000 | + | 6.06218i | 0.152174 | + | 0.263573i | ||||
\(530\) | −8.00000 | − | 13.8564i | −0.347498 | − | 0.601884i | ||||
\(531\) | −6.00000 | −0.260378 | ||||||||
\(532\) | −10.5000 | + | 7.79423i | −0.455233 | + | 0.337923i | ||||
\(533\) | −28.0000 | −1.21281 | ||||||||
\(534\) | 9.00000 | + | 15.5885i | 0.389468 | + | 0.674579i | ||||
\(535\) | 4.00000 | + | 6.92820i | 0.172935 | + | 0.299532i | ||||
\(536\) | −1.50000 | + | 2.59808i | −0.0647901 | + | 0.112220i | ||||
\(537\) | −6.00000 | − | 10.3923i | −0.258919 | − | 0.448461i | ||||
\(538\) | −9.00000 | + | 15.5885i | −0.388018 | + | 0.672066i | ||||
\(539\) | 4.00000 | 0.172292 | ||||||||
\(540\) | 4.00000 | 0.172133 | ||||||||
\(541\) | 9.50000 | − | 16.4545i | 0.408437 | − | 0.707433i | −0.586278 | − | 0.810110i | \(-0.699407\pi\) |
0.994715 | + | 0.102677i | \(0.0327407\pi\) | |||||||
\(542\) | 4.00000 | − | 6.92820i | 0.171815 | − | 0.297592i | ||||
\(543\) | 2.00000 | 0.0858282 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.0000 | − | 20.7846i | 0.514024 | − | 0.890315i | ||||
\(546\) | 10.5000 | + | 18.1865i | 0.449359 | + | 0.778312i | ||||
\(547\) | 14.5000 | − | 25.1147i | 0.619975 | − | 1.07383i | −0.369514 | − | 0.929225i | \(-0.620476\pi\) |
0.989490 | − | 0.144604i | \(-0.0461907\pi\) | |||||||
\(548\) | 1.00000 | + | 1.73205i | 0.0427179 | + | 0.0739895i | ||||
\(549\) | 0.500000 | + | 0.866025i | 0.0213395 | + | 0.0369611i | ||||
\(550\) | 22.0000 | 0.938083 | ||||||||
\(551\) | 14.0000 | − | 10.3923i | 0.596420 | − | 0.442727i | ||||
\(552\) | 4.00000 | 0.170251 | ||||||||
\(553\) | 7.50000 | + | 12.9904i | 0.318932 | + | 0.552407i | ||||
\(554\) | 13.0000 | + | 22.5167i | 0.552317 | + | 0.956641i | ||||
\(555\) | −14.0000 | + | 24.2487i | −0.594267 | + | 1.02930i | ||||
\(556\) | −10.5000 | − | 18.1865i | −0.445299 | − | 0.771281i | ||||
\(557\) | −11.0000 | + | 19.0526i | −0.466085 | + | 0.807283i | −0.999250 | − | 0.0387286i | \(-0.987669\pi\) |
0.533165 | + | 0.846011i | \(0.321003\pi\) | |||||||
\(558\) | 1.00000 | 0.0423334 | ||||||||
\(559\) | −49.0000 | −2.07248 | ||||||||
\(560\) | −6.00000 | + | 10.3923i | −0.253546 | + | 0.439155i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.00000 | 0.168730 | ||||||||
\(563\) | −42.0000 | −1.77009 | −0.885044 | − | 0.465506i | \(-0.845872\pi\) | ||||
−0.885044 | + | 0.465506i | \(0.845872\pi\) | |||||||
\(564\) | 1.00000 | − | 1.73205i | 0.0421076 | − | 0.0729325i | ||||
\(565\) | 4.00000 | + | 6.92820i | 0.168281 | + | 0.291472i | ||||
\(566\) | 6.00000 | − | 10.3923i | 0.252199 | − | 0.436821i | ||||
\(567\) | 1.50000 | + | 2.59808i | 0.0629941 | + | 0.109109i | ||||
\(568\) | −1.00000 | − | 1.73205i | −0.0419591 | − | 0.0726752i | ||||
\(569\) | 16.0000 | 0.670755 | 0.335377 | − | 0.942084i | \(-0.391136\pi\) | ||||
0.335377 | + | 0.942084i | \(0.391136\pi\) | |||||||
\(570\) | −16.0000 | − | 6.92820i | −0.670166 | − | 0.290191i | ||||
\(571\) | −7.00000 | −0.292941 | −0.146470 | − | 0.989215i | \(-0.546791\pi\) | ||||
−0.146470 | + | 0.989215i | \(0.546791\pi\) | |||||||
\(572\) | 7.00000 | + | 12.1244i | 0.292685 | + | 0.506945i | ||||
\(573\) | −10.0000 | − | 17.3205i | −0.417756 | − | 0.723575i | ||||
\(574\) | 6.00000 | − | 10.3923i | 0.250435 | − | 0.433766i | ||||
\(575\) | 22.0000 | + | 38.1051i | 0.917463 | + | 1.58909i | ||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 2.00000 | 0.0832611 | 0.0416305 | − | 0.999133i | \(-0.486745\pi\) | ||||
0.0416305 | + | 0.999133i | \(0.486745\pi\) | |||||||
\(578\) | −17.0000 | −0.707107 | ||||||||
\(579\) | −10.5000 | + | 18.1865i | −0.436365 | + | 0.755807i | ||||
\(580\) | 8.00000 | − | 13.8564i | 0.332182 | − | 0.575356i | ||||
\(581\) | 36.0000 | 1.49353 | ||||||||
\(582\) | −10.0000 | −0.414513 | ||||||||
\(583\) | 4.00000 | − | 6.92820i | 0.165663 | − | 0.286937i | ||||
\(584\) | 1.50000 | + | 2.59808i | 0.0620704 | + | 0.107509i | ||||
\(585\) | −14.0000 | + | 24.2487i | −0.578829 | + | 1.00256i | ||||
\(586\) | 9.00000 | + | 15.5885i | 0.371787 | + | 0.643953i | ||||
\(587\) | 9.00000 | + | 15.5885i | 0.371470 | + | 0.643404i | 0.989792 | − | 0.142520i | \(-0.0455206\pi\) |
−0.618322 | + | 0.785925i | \(0.712187\pi\) | |||||||
\(588\) | −2.00000 | −0.0824786 | ||||||||
\(589\) | −4.00000 | − | 1.73205i | −0.164817 | − | 0.0713679i | ||||
\(590\) | 24.0000 | 0.988064 | ||||||||
\(591\) | −5.00000 | − | 8.66025i | −0.205673 | − | 0.356235i | ||||
\(592\) | −3.50000 | − | 6.06218i | −0.143849 | − | 0.249154i | ||||
\(593\) | −17.0000 | + | 29.4449i | −0.698106 | + | 1.20916i | 0.271016 | + | 0.962575i | \(0.412640\pi\) |
−0.969122 | + | 0.246581i | \(0.920693\pi\) | |||||||
\(594\) | 1.00000 | + | 1.73205i | 0.0410305 | + | 0.0710669i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −18.0000 | −0.737309 | ||||||||
\(597\) | 7.00000 | 0.286491 | ||||||||
\(598\) | −14.0000 | + | 24.2487i | −0.572503 | + | 0.991604i | ||||
\(599\) | −15.0000 | + | 25.9808i | −0.612883 | + | 1.06155i | 0.377869 | + | 0.925859i | \(0.376657\pi\) |
−0.990752 | + | 0.135686i | \(0.956676\pi\) | |||||||
\(600\) | −11.0000 | −0.449073 | ||||||||
\(601\) | 19.0000 | 0.775026 | 0.387513 | − | 0.921864i | \(-0.373334\pi\) | ||||
0.387513 | + | 0.921864i | \(0.373334\pi\) | |||||||
\(602\) | 10.5000 | − | 18.1865i | 0.427948 | − | 0.741228i | ||||
\(603\) | −1.50000 | − | 2.59808i | −0.0610847 | − | 0.105802i | ||||
\(604\) | −10.0000 | + | 17.3205i | −0.406894 | + | 0.704761i | ||||
\(605\) | −14.0000 | − | 24.2487i | −0.569181 | − | 0.985850i | ||||
\(606\) | 1.00000 | + | 1.73205i | 0.0406222 | + | 0.0703598i | ||||
\(607\) | 41.0000 | 1.66414 | 0.832069 | − | 0.554672i | \(-0.187156\pi\) | ||||
0.832069 | + | 0.554672i | \(0.187156\pi\) | |||||||
\(608\) | 3.50000 | − | 2.59808i | 0.141944 | − | 0.105366i | ||||
\(609\) | 12.0000 | 0.486265 | ||||||||
\(610\) | −2.00000 | − | 3.46410i | −0.0809776 | − | 0.140257i | ||||
\(611\) | 7.00000 | + | 12.1244i | 0.283190 | + | 0.490499i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 19.0000 | + | 32.9090i | 0.767403 | + | 1.32918i | 0.938967 | + | 0.344008i | \(0.111785\pi\) |
−0.171564 | + | 0.985173i | \(0.554882\pi\) | |||||||
\(614\) | −6.00000 | + | 10.3923i | −0.242140 | + | 0.419399i | ||||
\(615\) | 16.0000 | 0.645182 | ||||||||
\(616\) | −6.00000 | −0.241747 | ||||||||
\(617\) | −9.00000 | + | 15.5885i | −0.362326 | + | 0.627568i | −0.988343 | − | 0.152242i | \(-0.951351\pi\) |
0.626017 | + | 0.779809i | \(0.284684\pi\) | |||||||
\(618\) | 4.50000 | − | 7.79423i | 0.181017 | − | 0.313530i | ||||
\(619\) | −23.0000 | −0.924448 | −0.462224 | − | 0.886763i | \(-0.652948\pi\) | ||||
−0.462224 | + | 0.886763i | \(0.652948\pi\) | |||||||
\(620\) | −4.00000 | −0.160644 | ||||||||
\(621\) | −2.00000 | + | 3.46410i | −0.0802572 | + | 0.139010i | ||||
\(622\) | −17.0000 | − | 29.4449i | −0.681638 | − | 1.18063i | ||||
\(623\) | 27.0000 | − | 46.7654i | 1.08173 | − | 1.87362i | ||||
\(624\) | −3.50000 | − | 6.06218i | −0.140112 | − | 0.242681i | ||||
\(625\) | −20.5000 | − | 35.5070i | −0.820000 | − | 1.42028i | ||||
\(626\) | 14.0000 | 0.559553 | ||||||||
\(627\) | −1.00000 | − | 8.66025i | −0.0399362 | − | 0.345857i | ||||
\(628\) | 7.00000 | 0.279330 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −6.00000 | − | 10.3923i | −0.239046 | − | 0.414039i | ||||
\(631\) | 9.50000 | − | 16.4545i | 0.378189 | − | 0.655043i | −0.612610 | − | 0.790386i | \(-0.709880\pi\) |
0.990799 | + | 0.135343i | \(0.0432136\pi\) | |||||||
\(632\) | −2.50000 | − | 4.33013i | −0.0994447 | − | 0.172243i | ||||
\(633\) | 4.50000 | − | 7.79423i | 0.178859 | − | 0.309793i | ||||
\(634\) | −24.0000 | −0.953162 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2.00000 | + | 3.46410i | −0.0793052 | + | 0.137361i | ||||
\(637\) | 7.00000 | − | 12.1244i | 0.277350 | − | 0.480384i | ||||
\(638\) | 8.00000 | 0.316723 | ||||||||
\(639\) | 2.00000 | 0.0791188 | ||||||||
\(640\) | 2.00000 | − | 3.46410i | 0.0790569 | − | 0.136931i | ||||
\(641\) | −9.00000 | − | 15.5885i | −0.355479 | − | 0.615707i | 0.631721 | − | 0.775196i | \(-0.282349\pi\) |
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(642\) | 1.00000 | − | 1.73205i | 0.0394669 | − | 0.0683586i | ||||
\(643\) | −6.50000 | − | 11.2583i | −0.256335 | − | 0.443985i | 0.708922 | − | 0.705287i | \(-0.249182\pi\) |
−0.965257 | + | 0.261301i | \(0.915848\pi\) | |||||||
\(644\) | −6.00000 | − | 10.3923i | −0.236433 | − | 0.409514i | ||||
\(645\) | 28.0000 | 1.10250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −28.0000 | −1.10079 | −0.550397 | − | 0.834903i | \(-0.685524\pi\) | ||||
−0.550397 | + | 0.834903i | \(0.685524\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 6.00000 | + | 10.3923i | 0.235521 | + | 0.407934i | ||||
\(650\) | 38.5000 | − | 66.6840i | 1.51009 | − | 2.61556i | ||||
\(651\) | −1.50000 | − | 2.59808i | −0.0587896 | − | 0.101827i | ||||
\(652\) | −5.50000 | + | 9.52628i | −0.215397 | + | 0.373078i | ||||
\(653\) | −30.0000 | −1.17399 | −0.586995 | − | 0.809590i | \(-0.699689\pi\) | ||||
−0.586995 | + | 0.809590i | \(0.699689\pi\) | |||||||
\(654\) | −6.00000 | −0.234619 | ||||||||
\(655\) | −36.0000 | + | 62.3538i | −1.40664 | + | 2.43637i | ||||
\(656\) | −2.00000 | + | 3.46410i | −0.0780869 | + | 0.135250i | ||||
\(657\) | −3.00000 | −0.117041 | ||||||||
\(658\) | −6.00000 | −0.233904 | ||||||||
\(659\) | 5.00000 | − | 8.66025i | 0.194772 | − | 0.337356i | −0.752054 | − | 0.659102i | \(-0.770937\pi\) |
0.946826 | + | 0.321746i | \(0.104270\pi\) | |||||||
\(660\) | −4.00000 | − | 6.92820i | −0.155700 | − | 0.269680i | ||||
\(661\) | −5.00000 | + | 8.66025i | −0.194477 | + | 0.336845i | −0.946729 | − | 0.322031i | \(-0.895634\pi\) |
0.752252 | + | 0.658876i | \(0.228968\pi\) | |||||||
\(662\) | −11.5000 | − | 19.9186i | −0.446960 | − | 0.774158i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 6.00000 | + | 51.9615i | 0.232670 | + | 2.01498i | ||||
\(666\) | 7.00000 | 0.271244 | ||||||||
\(667\) | 8.00000 | + | 13.8564i | 0.309761 | + | 0.536522i | ||||
\(668\) | −3.00000 | − | 5.19615i | −0.116073 | − | 0.201045i | ||||
\(669\) | 2.50000 | − | 4.33013i | 0.0966556 | − | 0.167412i | ||||
\(670\) | 6.00000 | + | 10.3923i | 0.231800 | + | 0.401490i | ||||
\(671\) | 1.00000 | − | 1.73205i | 0.0386046 | − | 0.0668651i | ||||
\(672\) | 3.00000 | 0.115728 | ||||||||
\(673\) | −1.00000 | −0.0385472 | −0.0192736 | − | 0.999814i | \(-0.506135\pi\) | ||||
−0.0192736 | + | 0.999814i | \(0.506135\pi\) | |||||||
\(674\) | −6.50000 | + | 11.2583i | −0.250371 | + | 0.433655i | ||||
\(675\) | 5.50000 | − | 9.52628i | 0.211695 | − | 0.366667i | ||||
\(676\) | 36.0000 | 1.38462 | ||||||||
\(677\) | −38.0000 | −1.46046 | −0.730229 | − | 0.683202i | \(-0.760587\pi\) | ||||
−0.730229 | + | 0.683202i | \(0.760587\pi\) | |||||||
\(678\) | 1.00000 | − | 1.73205i | 0.0384048 | − | 0.0665190i | ||||
\(679\) | 15.0000 | + | 25.9808i | 0.575647 | + | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.00000 | + | 3.46410i | 0.0766402 | + | 0.132745i | ||||
\(682\) | −1.00000 | − | 1.73205i | −0.0382920 | − | 0.0663237i | ||||
\(683\) | 40.0000 | 1.53056 | 0.765279 | − | 0.643699i | \(-0.222601\pi\) | ||||
0.765279 | + | 0.643699i | \(0.222601\pi\) | |||||||
\(684\) | 0.500000 | + | 4.33013i | 0.0191180 | + | 0.165567i | ||||
\(685\) | 8.00000 | 0.305664 | ||||||||
\(686\) | −7.50000 | − | 12.9904i | −0.286351 | − | 0.495975i | ||||
\(687\) | −3.50000 | − | 6.06218i | −0.133533 | − | 0.231287i | ||||
\(688\) | −3.50000 | + | 6.06218i | −0.133436 | + | 0.231118i | ||||
\(689\) | −14.0000 | − | 24.2487i | −0.533358 | − | 0.923802i | ||||
\(690\) | 8.00000 | − | 13.8564i | 0.304555 | − | 0.527504i | ||||
\(691\) | 12.0000 | 0.456502 | 0.228251 | − | 0.973602i | \(-0.426699\pi\) | ||||
0.228251 | + | 0.973602i | \(0.426699\pi\) | |||||||
\(692\) | 12.0000 | 0.456172 | ||||||||
\(693\) | 3.00000 | − | 5.19615i | 0.113961 | − | 0.197386i | ||||
\(694\) | −14.0000 | + | 24.2487i | −0.531433 | + | 0.920468i | ||||
\(695\) | −84.0000 | −3.18630 | ||||||||
\(696\) | −4.00000 | −0.151620 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | −15.5000 | − | 26.8468i | −0.586684 | − | 1.01617i | ||||
\(699\) | 3.00000 | − | 5.19615i | 0.113470 | − | 0.196537i | ||||
\(700\) | 16.5000 | + | 28.5788i | 0.623641 | + | 1.08018i | ||||
\(701\) | −4.00000 | − | 6.92820i | −0.151078 | − | 0.261675i | 0.780546 | − | 0.625098i | \(-0.214941\pi\) |
−0.931624 | + | 0.363424i | \(0.881608\pi\) | |||||||
\(702\) | 7.00000 | 0.264198 | ||||||||
\(703\) | −28.0000 | − | 12.1244i | −1.05604 | − | 0.457279i | ||||
\(704\) | 2.00000 | 0.0753778 | ||||||||
\(705\) | −4.00000 | − | 6.92820i | −0.150649 | − | 0.260931i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3.00000 | − | 5.19615i | 0.112827 | − | 0.195421i | ||||
\(708\) | −3.00000 | − | 5.19615i | −0.112747 | − | 0.195283i | ||||
\(709\) | 1.50000 | − | 2.59808i | 0.0563337 | − | 0.0975728i | −0.836483 | − | 0.547992i | \(-0.815392\pi\) |
0.892817 | + | 0.450420i | \(0.148726\pi\) | |||||||
\(710\) | −8.00000 | −0.300235 | ||||||||
\(711\) | 5.00000 | 0.187515 | ||||||||
\(712\) | −9.00000 | + | 15.5885i | −0.337289 | + | 0.584202i | ||||
\(713\) | 2.00000 | − | 3.46410i | 0.0749006 | − | 0.129732i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 56.0000 | 2.09428 | ||||||||
\(716\) | 6.00000 | − | 10.3923i | 0.224231 | − | 0.388379i | ||||
\(717\) | 12.0000 | + | 20.7846i | 0.448148 | + | 0.776215i | ||||
\(718\) | 6.00000 | − | 10.3923i | 0.223918 | − | 0.387837i | ||||
\(719\) | −8.00000 | − | 13.8564i | −0.298350 | − | 0.516757i | 0.677409 | − | 0.735607i | \(-0.263103\pi\) |
−0.975759 | + | 0.218850i | \(0.929769\pi\) | |||||||
\(720\) | 2.00000 | + | 3.46410i | 0.0745356 | + | 0.129099i | ||||
\(721\) | −27.0000 | −1.00553 | ||||||||
\(722\) | 5.50000 | − | 18.1865i | 0.204689 | − | 0.676833i | ||||
\(723\) | −1.00000 | −0.0371904 | ||||||||
\(724\) | 1.00000 | + | 1.73205i | 0.0371647 | + | 0.0643712i | ||||
\(725\) | −22.0000 | − | 38.1051i | −0.817059 | − | 1.41519i | ||||
\(726\) | −3.50000 | + | 6.06218i | −0.129897 | + | 0.224989i | ||||
\(727\) | −18.5000 | − | 32.0429i | −0.686127 | − | 1.18841i | −0.973081 | − | 0.230463i | \(-0.925976\pi\) |
0.286954 | − | 0.957944i | \(-0.407357\pi\) | |||||||
\(728\) | −10.5000 | + | 18.1865i | −0.389156 | + | 0.674038i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 12.0000 | 0.444140 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.500000 | + | 0.866025i | −0.0184805 | + | 0.0320092i | ||||
\(733\) | 30.0000 | 1.10808 | 0.554038 | − | 0.832492i | \(-0.313086\pi\) | ||||
0.554038 | + | 0.832492i | \(0.313086\pi\) | |||||||
\(734\) | 19.0000 | 0.701303 | ||||||||
\(735\) | −4.00000 | + | 6.92820i | −0.147542 | + | 0.255551i | ||||
\(736\) | 2.00000 | + | 3.46410i | 0.0737210 | + | 0.127688i | ||||
\(737\) | −3.00000 | + | 5.19615i | −0.110506 | + | 0.191403i | ||||
\(738\) | −2.00000 | − | 3.46410i | −0.0736210 | − | 0.127515i | ||||
\(739\) | −17.5000 | − | 30.3109i | −0.643748 | − | 1.11500i | −0.984589 | − | 0.174883i | \(-0.944045\pi\) |
0.340841 | − | 0.940121i | \(-0.389288\pi\) | |||||||
\(740\) | −28.0000 | −1.02930 | ||||||||
\(741\) | −28.0000 | − | 12.1244i | −1.02861 | − | 0.445399i | ||||
\(742\) | 12.0000 | 0.440534 | ||||||||
\(743\) | −13.0000 | − | 22.5167i | −0.476924 | − | 0.826056i | 0.522727 | − | 0.852500i | \(-0.324915\pi\) |
−0.999650 | + | 0.0264443i | \(0.991582\pi\) | |||||||
\(744\) | 0.500000 | + | 0.866025i | 0.0183309 | + | 0.0317500i | ||||
\(745\) | −36.0000 | + | 62.3538i | −1.31894 | + | 2.28447i | ||||
\(746\) | 11.0000 | + | 19.0526i | 0.402739 | + | 0.697564i | ||||
\(747\) | 6.00000 | − | 10.3923i | 0.219529 | − | 0.380235i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.00000 | −0.219235 | ||||||||
\(750\) | −12.0000 | + | 20.7846i | −0.438178 | + | 0.758947i | ||||
\(751\) | 15.5000 | − | 26.8468i | 0.565603 | − | 0.979653i | −0.431390 | − | 0.902165i | \(-0.641977\pi\) |
0.996993 | − | 0.0774878i | \(-0.0246899\pi\) | |||||||
\(752\) | 2.00000 | 0.0729325 | ||||||||
\(753\) | −14.0000 | −0.510188 | ||||||||
\(754\) | 14.0000 | − | 24.2487i | 0.509850 | − | 0.883086i | ||||
\(755\) | 40.0000 | + | 69.2820i | 1.45575 | + | 2.52143i | ||||
\(756\) | −1.50000 | + | 2.59808i | −0.0545545 | + | 0.0944911i | ||||
\(757\) | 11.5000 | + | 19.9186i | 0.417975 | + | 0.723953i | 0.995736 | − | 0.0922527i | \(-0.0294068\pi\) |
−0.577761 | + | 0.816206i | \(0.696073\pi\) | |||||||
\(758\) | 10.5000 | + | 18.1865i | 0.381377 | + | 0.660565i | ||||
\(759\) | 8.00000 | 0.290382 | ||||||||
\(760\) | −2.00000 | − | 17.3205i | −0.0725476 | − | 0.628281i | ||||
\(761\) | −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 | ||||
\(764\) | 10.0000 | − | 17.3205i | 0.361787 | − | 0.626634i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.00000 | − | 12.1244i | 0.252920 | − | 0.438071i | ||||
\(767\) | 42.0000 | 1.51653 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 2.50000 | − | 4.33013i | 0.0901523 | − | 0.156148i | −0.817423 | − | 0.576038i | \(-0.804598\pi\) |
0.907575 | + | 0.419890i | \(0.137931\pi\) | |||||||
\(770\) | −12.0000 | + | 20.7846i | −0.432450 | + | 0.749025i | ||||
\(771\) | 28.0000 | 1.00840 | ||||||||
\(772\) | −21.0000 | −0.755807 | ||||||||
\(773\) | −3.00000 | + | 5.19615i | −0.107903 | + | 0.186893i | −0.914920 | − | 0.403634i | \(-0.867747\pi\) |
0.807018 | + | 0.590527i | \(0.201080\pi\) | |||||||
\(774\) | −3.50000 | − | 6.06218i | −0.125805 | − | 0.217900i | ||||
\(775\) | −5.50000 | + | 9.52628i | −0.197566 | + | 0.342194i | ||||
\(776\) | −5.00000 | − | 8.66025i | −0.179490 | − | 0.310885i | ||||
\(777\) | −10.5000 | − | 18.1865i | −0.376685 | − | 0.652438i | ||||
\(778\) | −24.0000 | −0.860442 | ||||||||
\(779\) | 2.00000 | + | 17.3205i | 0.0716574 | + | 0.620572i | ||||
\(780\) | −28.0000 | −1.00256 | ||||||||
\(781\) | −2.00000 | − | 3.46410i | −0.0715656 | − | 0.123955i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.00000 | − | 3.46410i | 0.0714742 | − | 0.123797i | ||||
\(784\) | −1.00000 | − | 1.73205i | −0.0357143 | − | 0.0618590i | ||||
\(785\) | 14.0000 | − | 24.2487i | 0.499681 | − | 0.865474i | ||||
\(786\) | 18.0000 | 0.642039 | ||||||||
\(787\) | 49.0000 | 1.74666 | 0.873331 | − | 0.487128i | \(-0.161955\pi\) | ||||
0.873331 | + | 0.487128i | \(0.161955\pi\) | |||||||
\(788\) | 5.00000 | − | 8.66025i | 0.178118 | − | 0.308509i | ||||
\(789\) | −9.00000 | + | 15.5885i | −0.320408 | + | 0.554964i | ||||
\(790\) | −20.0000 | −0.711568 | ||||||||
\(791\) | −6.00000 | −0.213335 | ||||||||
\(792\) | −1.00000 | + | 1.73205i | −0.0355335 | + | 0.0615457i | ||||
\(793\) | −3.50000 | − | 6.06218i | −0.124289 | − | 0.215274i | ||||
\(794\) | 6.50000 | − | 11.2583i | 0.230676 | − | 0.399543i | ||||
\(795\) | 8.00000 | + | 13.8564i | 0.283731 | + | 0.491436i | ||||
\(796\) | 3.50000 | + | 6.06218i | 0.124054 | + | 0.214868i | ||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | 10.5000 | − | 7.79423i | 0.371696 | − | 0.275913i | ||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −5.50000 | − | 9.52628i | −0.194454 | − | 0.336805i | ||||
\(801\) | −9.00000 | − | 15.5885i | −0.317999 | − | 0.550791i | ||||
\(802\) | −5.00000 | + | 8.66025i | −0.176556 | + | 0.305804i | ||||
\(803\) | 3.00000 | + | 5.19615i | 0.105868 | + | 0.183368i | ||||
\(804\) | 1.50000 | − | 2.59808i | 0.0529009 | − | 0.0916271i | ||||
\(805\) | −48.0000 | −1.69178 | ||||||||
\(806\) | −7.00000 | −0.246564 | ||||||||
\(807\) | 9.00000 | − | 15.5885i | 0.316815 | − | 0.548740i | ||||
\(808\) | −1.00000 | + | 1.73205i | −0.0351799 | + | 0.0609333i | ||||
\(809\) | 36.0000 | 1.26569 | 0.632846 | − | 0.774277i | \(-0.281886\pi\) | ||||
0.632846 | + | 0.774277i | \(0.281886\pi\) | |||||||
\(810\) | −4.00000 | −0.140546 | ||||||||
\(811\) | −18.0000 | + | 31.1769i | −0.632065 | + | 1.09477i | 0.355063 | + | 0.934842i | \(0.384459\pi\) |
−0.987129 | + | 0.159927i | \(0.948874\pi\) | |||||||
\(812\) | 6.00000 | + | 10.3923i | 0.210559 | + | 0.364698i | ||||
\(813\) | −4.00000 | + | 6.92820i | −0.140286 | + | 0.242983i | ||||
\(814\) | −7.00000 | − | 12.1244i | −0.245350 | − | 0.424958i | ||||
\(815\) | 22.0000 | + | 38.1051i | 0.770626 | + | 1.33476i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.50000 | + | 30.3109i | 0.122449 | + | 1.06044i | ||||
\(818\) | 10.0000 | 0.349642 | ||||||||
\(819\) | −10.5000 | − | 18.1865i | −0.366900 | − | 0.635489i | ||||
\(820\) | 8.00000 | + | 13.8564i | 0.279372 | + | 0.483887i | ||||
\(821\) | −6.00000 | + | 10.3923i | −0.209401 | + | 0.362694i | −0.951526 | − | 0.307568i | \(-0.900485\pi\) |
0.742125 | + | 0.670262i | \(0.233818\pi\) | |||||||
\(822\) | −1.00000 | − | 1.73205i | −0.0348790 | − | 0.0604122i | ||||
\(823\) | −22.0000 | + | 38.1051i | −0.766872 | + | 1.32826i | 0.172379 | + | 0.985031i | \(0.444854\pi\) |
−0.939251 | + | 0.343230i | \(0.888479\pi\) | |||||||
\(824\) | 9.00000 | 0.313530 | ||||||||
\(825\) | −22.0000 | −0.765942 | ||||||||
\(826\) | −9.00000 | + | 15.5885i | −0.313150 | + | 0.542392i | ||||
\(827\) | −4.00000 | + | 6.92820i | −0.139094 | + | 0.240917i | −0.927154 | − | 0.374681i | \(-0.877752\pi\) |
0.788060 | + | 0.615598i | \(0.211086\pi\) | |||||||
\(828\) | −4.00000 | −0.139010 | ||||||||
\(829\) | 45.0000 | 1.56291 | 0.781457 | − | 0.623959i | \(-0.214477\pi\) | ||||
0.781457 | + | 0.623959i | \(0.214477\pi\) | |||||||
\(830\) | −24.0000 | + | 41.5692i | −0.833052 | + | 1.44289i | ||||
\(831\) | −13.0000 | − | 22.5167i | −0.450965 | − | 0.781094i | ||||
\(832\) | 3.50000 | − | 6.06218i | 0.121341 | − | 0.210168i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 10.5000 | + | 18.1865i | 0.363585 | + | 0.629748i | ||||
\(835\) | −24.0000 | −0.830554 | ||||||||
\(836\) | 7.00000 | − | 5.19615i | 0.242100 | − | 0.179713i | ||||
\(837\) | −1.00000 | −0.0345651 | ||||||||
\(838\) | −15.0000 | − | 25.9808i | −0.518166 | − | 0.897491i | ||||
\(839\) | 20.0000 | + | 34.6410i | 0.690477 | + | 1.19594i | 0.971682 | + | 0.236293i | \(0.0759325\pi\) |
−0.281205 | + | 0.959648i | \(0.590734\pi\) | |||||||
\(840\) | 6.00000 | − | 10.3923i | 0.207020 | − | 0.358569i | ||||
\(841\) | 6.50000 | + | 11.2583i | 0.224138 | + | 0.388218i | ||||
\(842\) | −13.0000 | + | 22.5167i | −0.448010 | + | 0.775975i | ||||
\(843\) | −4.00000 | −0.137767 | ||||||||
\(844\) | 9.00000 | 0.309793 | ||||||||
\(845\) | 72.0000 | − | 124.708i | 2.47688 | − | 4.29007i | ||||
\(846\) | −1.00000 | + | 1.73205i | −0.0343807 | + | 0.0595491i | ||||
\(847\) | 21.0000 | 0.721569 | ||||||||
\(848\) | −4.00000 | −0.137361 | ||||||||
\(849\) | −6.00000 | + | 10.3923i | −0.205919 | + | 0.356663i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.0000 | − | 24.2487i | 0.479914 | − | 0.831235i | ||||
\(852\) | 1.00000 | + | 1.73205i | 0.0342594 | + | 0.0593391i | ||||
\(853\) | 4.50000 | + | 7.79423i | 0.154077 | + | 0.266869i | 0.932723 | − | 0.360595i | \(-0.117426\pi\) |
−0.778646 | + | 0.627464i | \(0.784093\pi\) | |||||||
\(854\) | 3.00000 | 0.102658 | ||||||||
\(855\) | 16.0000 | + | 6.92820i | 0.547188 | + | 0.236940i | ||||
\(856\) | 2.00000 | 0.0683586 | ||||||||
\(857\) | 3.00000 | + | 5.19615i | 0.102478 | + | 0.177497i | 0.912705 | − | 0.408619i | \(-0.133990\pi\) |
−0.810227 | + | 0.586116i | \(0.800656\pi\) | |||||||
\(858\) | −7.00000 | − | 12.1244i | −0.238976 | − | 0.413919i | ||||
\(859\) | −3.50000 | + | 6.06218i | −0.119418 | + | 0.206839i | −0.919537 | − | 0.393003i | \(-0.871436\pi\) |
0.800119 | + | 0.599841i | \(0.204770\pi\) | |||||||
\(860\) | 14.0000 | + | 24.2487i | 0.477396 | + | 0.826874i | ||||
\(861\) | −6.00000 | + | 10.3923i | −0.204479 | + | 0.354169i | ||||
\(862\) | 6.00000 | 0.204361 | ||||||||
\(863\) | −6.00000 | −0.204242 | −0.102121 | − | 0.994772i | \(-0.532563\pi\) | ||||
−0.102121 | + | 0.994772i | \(0.532563\pi\) | |||||||
\(864\) | 0.500000 | − | 0.866025i | 0.0170103 | − | 0.0294628i | ||||
\(865\) | 24.0000 | − | 41.5692i | 0.816024 | − | 1.41340i | ||||
\(866\) | 23.0000 | 0.781572 | ||||||||
\(867\) | 17.0000 | 0.577350 | ||||||||
\(868\) | 1.50000 | − | 2.59808i | 0.0509133 | − | 0.0881845i | ||||
\(869\) | −5.00000 | − | 8.66025i | −0.169613 | − | 0.293779i | ||||
\(870\) | −8.00000 | + | 13.8564i | −0.271225 | + | 0.469776i | ||||
\(871\) | 10.5000 | + | 18.1865i | 0.355779 | + | 0.616227i | ||||
\(872\) | −3.00000 | − | 5.19615i | −0.101593 | − | 0.175964i | ||||
\(873\) | 10.0000 | 0.338449 | ||||||||
\(874\) | 16.0000 | + | 6.92820i | 0.541208 | + | 0.234350i | ||||
\(875\) | 72.0000 | 2.43404 | ||||||||
\(876\) | −1.50000 | − | 2.59808i | −0.0506803 | − | 0.0877809i | ||||
\(877\) | −9.50000 | − | 16.4545i | −0.320792 | − | 0.555628i | 0.659860 | − | 0.751389i | \(-0.270616\pi\) |
−0.980652 | + | 0.195761i | \(0.937282\pi\) | |||||||
\(878\) | −11.5000 | + | 19.9186i | −0.388106 | + | 0.672220i | ||||
\(879\) | −9.00000 | − | 15.5885i | −0.303562 | − | 0.525786i | ||||
\(880\) | 4.00000 | − | 6.92820i | 0.134840 | − | 0.233550i | ||||
\(881\) | −24.0000 | −0.808581 | −0.404290 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404290 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(882\) | 2.00000 | 0.0673435 | ||||||||
\(883\) | 20.5000 | − | 35.5070i | 0.689880 | − | 1.19491i | −0.281996 | − | 0.959415i | \(-0.590997\pi\) |
0.971876 | − | 0.235492i | \(-0.0756700\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −24.0000 | −0.806751 | ||||||||
\(886\) | 4.00000 | 0.134383 | ||||||||
\(887\) | −5.00000 | + | 8.66025i | −0.167884 | + | 0.290783i | −0.937676 | − | 0.347512i | \(-0.887027\pi\) |
0.769792 | + | 0.638295i | \(0.220360\pi\) | |||||||
\(888\) | 3.50000 | + | 6.06218i | 0.117452 | + | 0.203433i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 36.0000 | + | 62.3538i | 1.20672 | + | 2.09011i | ||||
\(891\) | −1.00000 | − | 1.73205i | −0.0335013 | − | 0.0580259i | ||||
\(892\) | 5.00000 | 0.167412 | ||||||||
\(893\) | 7.00000 | − | 5.19615i | 0.234246 | − | 0.173883i | ||||
\(894\) | 18.0000 | 0.602010 | ||||||||
\(895\) | −24.0000 | − | 41.5692i | −0.802232 | − | 1.38951i | ||||
\(896\) | 1.50000 | + | 2.59808i | 0.0501115 | + | 0.0867956i | ||||
\(897\) | 14.0000 | − | 24.2487i | 0.467446 | − | 0.809641i | ||||
\(898\) | −8.00000 | − | 13.8564i | −0.266963 | − | 0.462394i | ||||
\(899\) | −2.00000 | + | 3.46410i | −0.0667037 | + | 0.115534i | ||||
\(900\) | 11.0000 | 0.366667 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −4.00000 | + | 6.92820i | −0.133185 | + | 0.230684i | ||||
\(903\) | −10.5000 | + | 18.1865i | −0.349418 | + | 0.605210i | ||||
\(904\) | 2.00000 | 0.0665190 | ||||||||
\(905\) | 8.00000 | 0.265929 | ||||||||
\(906\) | 10.0000 | − | 17.3205i | 0.332228 | − | 0.575435i | ||||
\(907\) | −10.0000 | − | 17.3205i | −0.332045 | − | 0.575118i | 0.650868 | − | 0.759191i | \(-0.274405\pi\) |
−0.982913 | + | 0.184073i | \(0.941072\pi\) | |||||||
\(908\) | −2.00000 | + | 3.46410i | −0.0663723 | + | 0.114960i | ||||
\(909\) | −1.00000 | − | 1.73205i | −0.0331679 | − | 0.0574485i | ||||
\(910\) | 42.0000 | + | 72.7461i | 1.39229 | + | 2.41151i | ||||
\(911\) | −12.0000 | −0.397578 | −0.198789 | − | 0.980042i | \(-0.563701\pi\) | ||||
−0.198789 | + | 0.980042i | \(0.563701\pi\) | |||||||
\(912\) | −3.50000 | + | 2.59808i | −0.115897 | + | 0.0860309i | ||||
\(913\) | −24.0000 | −0.794284 | ||||||||
\(914\) | −14.5000 | − | 25.1147i | −0.479617 | − | 0.830722i | ||||
\(915\) | 2.00000 | + | 3.46410i | 0.0661180 | + | 0.114520i | ||||
\(916\) | 3.50000 | − | 6.06218i | 0.115643 | − | 0.200300i | ||||
\(917\) | −27.0000 | − | 46.7654i | −0.891619 | − | 1.54433i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.0000 | 0.362857 | 0.181428 | − | 0.983404i | \(-0.441928\pi\) | ||||
0.181428 | + | 0.983404i | \(0.441928\pi\) | |||||||
\(920\) | 16.0000 | 0.527504 | ||||||||
\(921\) | 6.00000 | − | 10.3923i | 0.197707 | − | 0.342438i | ||||
\(922\) | 17.0000 | − | 29.4449i | 0.559865 | − | 0.969715i | ||||
\(923\) | −14.0000 | −0.460816 | ||||||||
\(924\) | 6.00000 | 0.197386 | ||||||||
\(925\) | −38.5000 | + | 66.6840i | −1.26587 | + | 2.19255i | ||||
\(926\) | −9.50000 | − | 16.4545i | −0.312189 | − | 0.540728i | ||||
\(927\) | −4.50000 | + | 7.79423i | −0.147799 | + | 0.255996i | ||||
\(928\) | −2.00000 | − | 3.46410i | −0.0656532 | − | 0.113715i | ||||
\(929\) | −4.00000 | − | 6.92820i | −0.131236 | − | 0.227307i | 0.792917 | − | 0.609329i | \(-0.208561\pi\) |
−0.924153 | + | 0.382022i | \(0.875228\pi\) | |||||||
\(930\) | 4.00000 | 0.131165 | ||||||||
\(931\) | −8.00000 | − | 3.46410i | −0.262189 | − | 0.113531i | ||||
\(932\) | 6.00000 | 0.196537 | ||||||||
\(933\) | 17.0000 | + | 29.4449i | 0.556555 | + | 0.963982i | ||||
\(934\) | 4.00000 | + | 6.92820i | 0.130884 | + | 0.226698i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 3.50000 | + | 6.06218i | 0.114401 | + | 0.198148i | ||||
\(937\) | 12.5000 | − | 21.6506i | 0.408357 | − | 0.707295i | −0.586349 | − | 0.810059i | \(-0.699435\pi\) |
0.994706 | + | 0.102763i | \(0.0327685\pi\) | |||||||
\(938\) | −9.00000 | −0.293860 | ||||||||
\(939\) | −14.0000 | −0.456873 | ||||||||
\(940\) | 4.00000 | − | 6.92820i | 0.130466 | − | 0.225973i | ||||
\(941\) | −8.00000 | + | 13.8564i | −0.260793 | + | 0.451706i | −0.966453 | − | 0.256844i | \(-0.917317\pi\) |
0.705660 | + | 0.708550i | \(0.250651\pi\) | |||||||
\(942\) | −7.00000 | −0.228072 | ||||||||
\(943\) | −16.0000 | −0.521032 | ||||||||
\(944\) | 3.00000 | − | 5.19615i | 0.0976417 | − | 0.169120i | ||||
\(945\) | 6.00000 | + | 10.3923i | 0.195180 | + | 0.338062i | ||||
\(946\) | −7.00000 | + | 12.1244i | −0.227590 | + | 0.394197i | ||||
\(947\) | −27.0000 | − | 46.7654i | −0.877382 | − | 1.51967i | −0.854203 | − | 0.519939i | \(-0.825955\pi\) |
−0.0231788 | − | 0.999731i | \(-0.507379\pi\) | |||||||
\(948\) | 2.50000 | + | 4.33013i | 0.0811962 | + | 0.140636i | ||||
\(949\) | 21.0000 | 0.681689 | ||||||||
\(950\) | −44.0000 | − | 19.0526i | −1.42755 | − | 0.618147i | ||||
\(951\) | 24.0000 | 0.778253 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.00000 | + | 8.66025i | 0.161966 | + | 0.280533i | 0.935574 | − | 0.353132i | \(-0.114883\pi\) |
−0.773608 | + | 0.633665i | \(0.781550\pi\) | |||||||
\(954\) | 2.00000 | − | 3.46410i | 0.0647524 | − | 0.112154i | ||||
\(955\) | −40.0000 | − | 69.2820i | −1.29437 | − | 2.24191i | ||||
\(956\) | −12.0000 | + | 20.7846i | −0.388108 | + | 0.672222i | ||||
\(957\) | −8.00000 | −0.258603 | ||||||||
\(958\) | 34.0000 | 1.09849 | ||||||||
\(959\) | −3.00000 | + | 5.19615i | −0.0968751 | + | 0.167793i | ||||
\(960\) | −2.00000 | + | 3.46410i | −0.0645497 | + | 0.111803i | ||||
\(961\) | −30.0000 | −0.967742 | ||||||||
\(962\) | −49.0000 | −1.57982 | ||||||||
\(963\) | −1.00000 | + | 1.73205i | −0.0322245 | + | 0.0558146i | ||||
\(964\) | −0.500000 | − | 0.866025i | −0.0161039 | − | 0.0278928i | ||||
\(965\) | −42.0000 | + | 72.7461i | −1.35203 | + | 2.34178i | ||||
\(966\) | 6.00000 | + | 10.3923i | 0.193047 | + | 0.334367i | ||||
\(967\) | 4.50000 | + | 7.79423i | 0.144710 | + | 0.250645i | 0.929265 | − | 0.369414i | \(-0.120442\pi\) |
−0.784555 | + | 0.620060i | \(0.787108\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −40.0000 | −1.28432 | ||||||||
\(971\) | −7.00000 | − | 12.1244i | −0.224641 | − | 0.389089i | 0.731571 | − | 0.681765i | \(-0.238788\pi\) |
−0.956212 | + | 0.292676i | \(0.905454\pi\) | |||||||
\(972\) | 0.500000 | + | 0.866025i | 0.0160375 | + | 0.0277778i | ||||
\(973\) | 31.5000 | − | 54.5596i | 1.00984 | − | 1.74910i | ||||
\(974\) | −8.00000 | − | 13.8564i | −0.256337 | − | 0.443988i | ||||
\(975\) | −38.5000 | + | 66.6840i | −1.23299 | + | 2.13560i | ||||
\(976\) | −1.00000 | −0.0320092 | ||||||||
\(977\) | 14.0000 | 0.447900 | 0.223950 | − | 0.974601i | \(-0.428105\pi\) | ||||
0.223950 | + | 0.974601i | \(0.428105\pi\) | |||||||
\(978\) | 5.50000 | − | 9.52628i | 0.175871 | − | 0.304617i | ||||
\(979\) | −18.0000 | + | 31.1769i | −0.575282 | + | 0.996419i | ||||
\(980\) | −8.00000 | −0.255551 | ||||||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | −13.0000 | + | 22.5167i | −0.414847 | + | 0.718536i | ||||
\(983\) | −3.00000 | − | 5.19615i | −0.0956851 | − | 0.165732i | 0.814209 | − | 0.580572i | \(-0.197171\pi\) |
−0.909894 | + | 0.414840i | \(0.863838\pi\) | |||||||
\(984\) | 2.00000 | − | 3.46410i | 0.0637577 | − | 0.110432i | ||||
\(985\) | −20.0000 | − | 34.6410i | −0.637253 | − | 1.10375i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | 0.190982 | ||||||||
\(988\) | −3.50000 | − | 30.3109i | −0.111350 | − | 0.964318i | ||||
\(989\) | −28.0000 | −0.890348 | ||||||||
\(990\) | 4.00000 | + | 6.92820i | 0.127128 | + | 0.220193i | ||||
\(991\) | 14.5000 | + | 25.1147i | 0.460608 | + | 0.797796i | 0.998991 | − | 0.0449040i | \(-0.0142982\pi\) |
−0.538384 | + | 0.842700i | \(0.680965\pi\) | |||||||
\(992\) | −0.500000 | + | 0.866025i | −0.0158750 | + | 0.0274963i | ||||
\(993\) | 11.5000 | + | 19.9186i | 0.364941 | + | 0.632097i | ||||
\(994\) | 3.00000 | − | 5.19615i | 0.0951542 | − | 0.164812i | ||||
\(995\) | 28.0000 | 0.887660 | ||||||||
\(996\) | 12.0000 | 0.380235 | ||||||||
\(997\) | 26.5000 | − | 45.8993i | 0.839263 | − | 1.45365i | −0.0512480 | − | 0.998686i | \(-0.516320\pi\) |
0.890511 | − | 0.454961i | \(-0.150347\pi\) | |||||||
\(998\) | 5.50000 | − | 9.52628i | 0.174099 | − | 0.301549i | ||||
\(999\) | −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 | 114.2.e.a.7.1 | ✓ | 2 | |
3.2 | odd | 2 | 342.2.g.d.235.1 | 2 | |||
4.3 | odd | 2 | 912.2.q.d.577.1 | 2 | |||
12.11 | even | 2 | 2736.2.s.c.577.1 | 2 | |||
19.7 | even | 3 | 2166.2.a.f.1.1 | 1 | |||
19.11 | even | 3 | inner | 114.2.e.a.49.1 | yes | 2 | |
19.12 | odd | 6 | 2166.2.a.c.1.1 | 1 | |||
57.11 | odd | 6 | 342.2.g.d.163.1 | 2 | |||
57.26 | odd | 6 | 6498.2.a.l.1.1 | 1 | |||
57.50 | even | 6 | 6498.2.a.x.1.1 | 1 | |||
76.11 | odd | 6 | 912.2.q.d.49.1 | 2 | |||
228.11 | even | 6 | 2736.2.s.c.1873.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.e.a.7.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
114.2.e.a.49.1 | yes | 2 | 19.11 | even | 3 | inner | |
342.2.g.d.163.1 | 2 | 57.11 | odd | 6 | |||
342.2.g.d.235.1 | 2 | 3.2 | odd | 2 | |||
912.2.q.d.49.1 | 2 | 76.11 | odd | 6 | |||
912.2.q.d.577.1 | 2 | 4.3 | odd | 2 | |||
2166.2.a.c.1.1 | 1 | 19.12 | odd | 6 | |||
2166.2.a.f.1.1 | 1 | 19.7 | even | 3 | |||
2736.2.s.c.577.1 | 2 | 12.11 | even | 2 | |||
2736.2.s.c.1873.1 | 2 | 228.11 | even | 6 | |||
6498.2.a.l.1.1 | 1 | 57.26 | odd | 6 | |||
6498.2.a.x.1.1 | 1 | 57.50 | even | 6 |