Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1078,2,Mod(67,1078)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1078, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1078.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1078 = 2 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1078.e (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: | \(8.60787333789\) |
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: | no (minimal twist has level 154) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1078.67 |
Dual form | 1078.2.e.f.177.1 |
$q$-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 \(\left(\mathbb{Z}/1078\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(981\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | 1.50000 | − | 2.59808i | 0.866025 | − | 1.50000i | − | 1.00000i | \(-0.5\pi\) | |
0.866025 | − | 0.500000i | \(-0.166667\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 1.00000 | + | 1.73205i | 0.447214 | + | 0.774597i | 0.998203 | − | 0.0599153i | \(-0.0190830\pi\) |
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(6\) | −3.00000 | −1.22474 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −3.00000 | − | 5.19615i | −1.00000 | − | 1.73205i | ||||
\(10\) | 1.00000 | − | 1.73205i | 0.316228 | − | 0.547723i | ||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 1.50000 | + | 2.59808i | 0.433013 | + | 0.750000i | ||||
\(13\) | 7.00000 | 1.94145 | 0.970725 | − | 0.240192i | \(-0.0772105\pi\) | ||||
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.00000 | 1.54919 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.00000 | − | 1.73205i | 0.242536 | − | 0.420084i | −0.718900 | − | 0.695113i | \(-0.755354\pi\) |
0.961436 | + | 0.275029i | \(0.0886875\pi\) | |||||||
\(18\) | −3.00000 | + | 5.19615i | −0.707107 | + | 1.22474i | ||||
\(19\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | 4.00000 | + | 6.92820i | 0.834058 | + | 1.44463i | 0.894795 | + | 0.446476i | \(0.147321\pi\) |
−0.0607377 | + | 0.998154i | \(0.519345\pi\) | |||||||
\(24\) | 1.50000 | − | 2.59808i | 0.306186 | − | 0.530330i | ||||
\(25\) | 0.500000 | − | 0.866025i | 0.100000 | − | 0.173205i | ||||
\(26\) | −3.50000 | − | 6.06218i | −0.686406 | − | 1.18889i | ||||
\(27\) | −9.00000 | −1.73205 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −5.00000 | −0.928477 | −0.464238 | − | 0.885710i | \(-0.653672\pi\) | ||||
−0.464238 | + | 0.885710i | \(0.653672\pi\) | |||||||
\(30\) | −3.00000 | − | 5.19615i | −0.547723 | − | 0.948683i | ||||
\(31\) | 2.00000 | − | 3.46410i | 0.359211 | − | 0.622171i | −0.628619 | − | 0.777714i | \(-0.716379\pi\) |
0.987829 | + | 0.155543i | \(0.0497126\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | −1.50000 | − | 2.59808i | −0.261116 | − | 0.452267i | ||||
\(34\) | −2.00000 | −0.342997 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 1.00000 | ||||||||
\(37\) | −2.00000 | − | 3.46410i | −0.328798 | − | 0.569495i | 0.653476 | − | 0.756948i | \(-0.273310\pi\) |
−0.982274 | + | 0.187453i | \(0.939977\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 10.5000 | − | 18.1865i | 1.68135 | − | 2.91218i | ||||
\(40\) | 1.00000 | + | 1.73205i | 0.158114 | + | 0.273861i | ||||
\(41\) | −4.00000 | −0.624695 | −0.312348 | − | 0.949968i | \(-0.601115\pi\) | ||||
−0.312348 | + | 0.949968i | \(0.601115\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −8.00000 | −1.21999 | −0.609994 | − | 0.792406i | \(-0.708828\pi\) | ||||
−0.609994 | + | 0.792406i | \(0.708828\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 6.00000 | − | 10.3923i | 0.894427 | − | 1.54919i | ||||
\(46\) | 4.00000 | − | 6.92820i | 0.589768 | − | 1.02151i | ||||
\(47\) | 1.00000 | + | 1.73205i | 0.145865 | + | 0.252646i | 0.929695 | − | 0.368329i | \(-0.120070\pi\) |
−0.783830 | + | 0.620975i | \(0.786737\pi\) | |||||||
\(48\) | −3.00000 | −0.433013 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | −3.00000 | − | 5.19615i | −0.420084 | − | 0.727607i | ||||
\(52\) | −3.50000 | + | 6.06218i | −0.485363 | + | 0.840673i | ||||
\(53\) | 3.00000 | − | 5.19615i | 0.412082 | − | 0.713746i | −0.583036 | − | 0.812447i | \(-0.698135\pi\) |
0.995117 | + | 0.0987002i | \(0.0314685\pi\) | |||||||
\(54\) | 4.50000 | + | 7.79423i | 0.612372 | + | 1.06066i | ||||
\(55\) | 2.00000 | 0.269680 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.50000 | + | 4.33013i | 0.328266 | + | 0.568574i | ||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | −3.00000 | + | 5.19615i | −0.387298 | + | 0.670820i | ||||
\(61\) | 0.500000 | + | 0.866025i | 0.0640184 | + | 0.110883i | 0.896258 | − | 0.443533i | \(-0.146275\pi\) |
−0.832240 | + | 0.554416i | \(0.812942\pi\) | |||||||
\(62\) | −4.00000 | −0.508001 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 7.00000 | + | 12.1244i | 0.868243 | + | 1.50384i | ||||
\(66\) | −1.50000 | + | 2.59808i | −0.184637 | + | 0.319801i | ||||
\(67\) | −4.50000 | + | 7.79423i | −0.549762 | + | 0.952217i | 0.448528 | + | 0.893769i | \(0.351948\pi\) |
−0.998290 | + | 0.0584478i | \(0.981385\pi\) | |||||||
\(68\) | 1.00000 | + | 1.73205i | 0.121268 | + | 0.210042i | ||||
\(69\) | 24.0000 | 2.88926 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | −3.00000 | − | 5.19615i | −0.353553 | − | 0.612372i | ||||
\(73\) | 2.00000 | − | 3.46410i | 0.234082 | − | 0.405442i | −0.724923 | − | 0.688830i | \(-0.758125\pi\) |
0.959006 | + | 0.283387i | \(0.0914581\pi\) | |||||||
\(74\) | −2.00000 | + | 3.46410i | −0.232495 | + | 0.402694i | ||||
\(75\) | −1.50000 | − | 2.59808i | −0.173205 | − | 0.300000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −21.0000 | −2.37778 | ||||||||
\(79\) | −4.50000 | − | 7.79423i | −0.506290 | − | 0.876919i | −0.999974 | − | 0.00727784i | \(-0.997683\pi\) |
0.493684 | − | 0.869641i | \(-0.335650\pi\) | |||||||
\(80\) | 1.00000 | − | 1.73205i | 0.111803 | − | 0.193649i | ||||
\(81\) | −4.50000 | + | 7.79423i | −0.500000 | + | 0.866025i | ||||
\(82\) | 2.00000 | + | 3.46410i | 0.220863 | + | 0.382546i | ||||
\(83\) | −6.00000 | −0.658586 | −0.329293 | − | 0.944228i | \(-0.606810\pi\) | ||||
−0.329293 | + | 0.944228i | \(0.606810\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.00000 | 0.433861 | ||||||||
\(86\) | 4.00000 | + | 6.92820i | 0.431331 | + | 0.747087i | ||||
\(87\) | −7.50000 | + | 12.9904i | −0.804084 | + | 1.39272i | ||||
\(88\) | 0.500000 | − | 0.866025i | 0.0533002 | − | 0.0923186i | ||||
\(89\) | 3.00000 | + | 5.19615i | 0.317999 | + | 0.550791i | 0.980071 | − | 0.198650i | \(-0.0636557\pi\) |
−0.662071 | + | 0.749441i | \(0.730322\pi\) | |||||||
\(90\) | −12.0000 | −1.26491 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −8.00000 | −0.834058 | ||||||||
\(93\) | −6.00000 | − | 10.3923i | −0.622171 | − | 1.07763i | ||||
\(94\) | 1.00000 | − | 1.73205i | 0.103142 | − | 0.178647i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.50000 | + | 2.59808i | 0.153093 | + | 0.265165i | ||||
\(97\) | −7.00000 | −0.710742 | −0.355371 | − | 0.934725i | \(-0.615646\pi\) | ||||
−0.355371 | + | 0.934725i | \(0.615646\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | −0.603023 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | −4.50000 | + | 7.79423i | −0.447767 | + | 0.775555i | −0.998240 | − | 0.0592978i | \(-0.981114\pi\) |
0.550474 | + | 0.834853i | \(0.314447\pi\) | |||||||
\(102\) | −3.00000 | + | 5.19615i | −0.297044 | + | 0.514496i | ||||
\(103\) | 9.00000 | + | 15.5885i | 0.886796 | + | 1.53598i | 0.843641 | + | 0.536908i | \(0.180408\pi\) |
0.0431555 | + | 0.999068i | \(0.486259\pi\) | |||||||
\(104\) | 7.00000 | 0.686406 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | −0.582772 | ||||||||
\(107\) | −1.00000 | − | 1.73205i | −0.0966736 | − | 0.167444i | 0.813632 | − | 0.581380i | \(-0.197487\pi\) |
−0.910306 | + | 0.413936i | \(0.864154\pi\) | |||||||
\(108\) | 4.50000 | − | 7.79423i | 0.433013 | − | 0.750000i | ||||
\(109\) | 1.00000 | − | 1.73205i | 0.0957826 | − | 0.165900i | −0.814152 | − | 0.580651i | \(-0.802798\pi\) |
0.909935 | + | 0.414751i | \(0.136131\pi\) | |||||||
\(110\) | −1.00000 | − | 1.73205i | −0.0953463 | − | 0.165145i | ||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.00000 | 0.470360 | 0.235180 | − | 0.971952i | \(-0.424432\pi\) | ||||
0.235180 | + | 0.971952i | \(0.424432\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | + | 13.8564i | −0.746004 | + | 1.29212i | ||||
\(116\) | 2.50000 | − | 4.33013i | 0.232119 | − | 0.402042i | ||||
\(117\) | −21.0000 | − | 36.3731i | −1.94145 | − | 3.36269i | ||||
\(118\) | −3.00000 | −0.276172 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 6.00000 | 0.547723 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 0.500000 | − | 0.866025i | 0.0452679 | − | 0.0784063i | ||||
\(123\) | −6.00000 | + | 10.3923i | −0.541002 | + | 0.937043i | ||||
\(124\) | 2.00000 | + | 3.46410i | 0.179605 | + | 0.311086i | ||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −19.0000 | −1.68598 | −0.842989 | − | 0.537931i | \(-0.819206\pi\) | ||||
−0.842989 | + | 0.537931i | \(0.819206\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | −12.0000 | + | 20.7846i | −1.05654 | + | 1.82998i | ||||
\(130\) | 7.00000 | − | 12.1244i | 0.613941 | − | 1.06338i | ||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 3.00000 | 0.261116 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 9.00000 | 0.777482 | ||||||||
\(135\) | −9.00000 | − | 15.5885i | −0.774597 | − | 1.34164i | ||||
\(136\) | 1.00000 | − | 1.73205i | 0.0857493 | − | 0.148522i | ||||
\(137\) | −1.50000 | + | 2.59808i | −0.128154 | + | 0.221969i | −0.922961 | − | 0.384893i | \(-0.874238\pi\) |
0.794808 | + | 0.606861i | \(0.207572\pi\) | |||||||
\(138\) | −12.0000 | − | 20.7846i | −1.02151 | − | 1.76930i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.00000 | 0.505291 | ||||||||
\(142\) | 1.00000 | + | 1.73205i | 0.0839181 | + | 0.145350i | ||||
\(143\) | 3.50000 | − | 6.06218i | 0.292685 | − | 0.506945i | ||||
\(144\) | −3.00000 | + | 5.19615i | −0.250000 | + | 0.433013i | ||||
\(145\) | −5.00000 | − | 8.66025i | −0.415227 | − | 0.719195i | ||||
\(146\) | −4.00000 | −0.331042 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | 5.00000 | + | 8.66025i | 0.409616 | + | 0.709476i | 0.994847 | − | 0.101391i | \(-0.0323294\pi\) |
−0.585231 | + | 0.810867i | \(0.698996\pi\) | |||||||
\(150\) | −1.50000 | + | 2.59808i | −0.122474 | + | 0.212132i | ||||
\(151\) | 1.50000 | − | 2.59808i | 0.122068 | − | 0.211428i | −0.798515 | − | 0.601975i | \(-0.794381\pi\) |
0.920583 | + | 0.390547i | \(0.127714\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.0000 | −0.970143 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 8.00000 | 0.642575 | ||||||||
\(156\) | 10.5000 | + | 18.1865i | 0.840673 | + | 1.45609i | ||||
\(157\) | 8.00000 | − | 13.8564i | 0.638470 | − | 1.10586i | −0.347299 | − | 0.937754i | \(-0.612901\pi\) |
0.985769 | − | 0.168107i | \(-0.0537655\pi\) | |||||||
\(158\) | −4.50000 | + | 7.79423i | −0.358001 | + | 0.620076i | ||||
\(159\) | −9.00000 | − | 15.5885i | −0.713746 | − | 1.23625i | ||||
\(160\) | −2.00000 | −0.158114 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.00000 | 0.707107 | ||||||||
\(163\) | 8.50000 | + | 14.7224i | 0.665771 | + | 1.15315i | 0.979076 | + | 0.203497i | \(0.0652307\pi\) |
−0.313304 | + | 0.949653i | \(0.601436\pi\) | |||||||
\(164\) | 2.00000 | − | 3.46410i | 0.156174 | − | 0.270501i | ||||
\(165\) | 3.00000 | − | 5.19615i | 0.233550 | − | 0.404520i | ||||
\(166\) | 3.00000 | + | 5.19615i | 0.232845 | + | 0.403300i | ||||
\(167\) | −19.0000 | −1.47026 | −0.735132 | − | 0.677924i | \(-0.762880\pi\) | ||||
−0.735132 | + | 0.677924i | \(0.762880\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.0000 | 2.76923 | ||||||||
\(170\) | −2.00000 | − | 3.46410i | −0.153393 | − | 0.265684i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.00000 | − | 6.92820i | 0.304997 | − | 0.528271i | ||||
\(173\) | 12.5000 | + | 21.6506i | 0.950357 | + | 1.64607i | 0.744652 | + | 0.667453i | \(0.232616\pi\) |
0.205706 | + | 0.978614i | \(0.434051\pi\) | |||||||
\(174\) | 15.0000 | 1.13715 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | −4.50000 | − | 7.79423i | −0.338241 | − | 0.585850i | ||||
\(178\) | 3.00000 | − | 5.19615i | 0.224860 | − | 0.389468i | ||||
\(179\) | −9.50000 | + | 16.4545i | −0.710063 | + | 1.22987i | 0.254770 | + | 0.967002i | \(0.418000\pi\) |
−0.964833 | + | 0.262864i | \(0.915333\pi\) | |||||||
\(180\) | 6.00000 | + | 10.3923i | 0.447214 | + | 0.774597i | ||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.00000 | 0.221766 | ||||||||
\(184\) | 4.00000 | + | 6.92820i | 0.294884 | + | 0.510754i | ||||
\(185\) | 4.00000 | − | 6.92820i | 0.294086 | − | 0.509372i | ||||
\(186\) | −6.00000 | + | 10.3923i | −0.439941 | + | 0.762001i | ||||
\(187\) | −1.00000 | − | 1.73205i | −0.0731272 | − | 0.126660i | ||||
\(188\) | −2.00000 | −0.145865 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.00000 | − | 1.73205i | −0.0723575 | − | 0.125327i | 0.827577 | − | 0.561353i | \(-0.189719\pi\) |
−0.899934 | + | 0.436026i | \(0.856386\pi\) | |||||||
\(192\) | 1.50000 | − | 2.59808i | 0.108253 | − | 0.187500i | ||||
\(193\) | −4.00000 | + | 6.92820i | −0.287926 | + | 0.498703i | −0.973315 | − | 0.229475i | \(-0.926299\pi\) |
0.685388 | + | 0.728178i | \(0.259632\pi\) | |||||||
\(194\) | 3.50000 | + | 6.06218i | 0.251285 | + | 0.435239i | ||||
\(195\) | 42.0000 | 3.00768 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.0000 | 1.06871 | 0.534353 | − | 0.845262i | \(-0.320555\pi\) | ||||
0.534353 | + | 0.845262i | \(0.320555\pi\) | |||||||
\(198\) | 3.00000 | + | 5.19615i | 0.213201 | + | 0.369274i | ||||
\(199\) | 2.00000 | − | 3.46410i | 0.141776 | − | 0.245564i | −0.786389 | − | 0.617731i | \(-0.788052\pi\) |
0.928166 | + | 0.372168i | \(0.121385\pi\) | |||||||
\(200\) | 0.500000 | − | 0.866025i | 0.0353553 | − | 0.0612372i | ||||
\(201\) | 13.5000 | + | 23.3827i | 0.952217 | + | 1.64929i | ||||
\(202\) | 9.00000 | 0.633238 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.00000 | 0.420084 | ||||||||
\(205\) | −4.00000 | − | 6.92820i | −0.279372 | − | 0.483887i | ||||
\(206\) | 9.00000 | − | 15.5885i | 0.627060 | − | 1.08610i | ||||
\(207\) | 24.0000 | − | 41.5692i | 1.66812 | − | 2.88926i | ||||
\(208\) | −3.50000 | − | 6.06218i | −0.242681 | − | 0.420336i | ||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 3.00000 | + | 5.19615i | 0.206041 | + | 0.356873i | ||||
\(213\) | −3.00000 | + | 5.19615i | −0.205557 | + | 0.356034i | ||||
\(214\) | −1.00000 | + | 1.73205i | −0.0683586 | + | 0.118401i | ||||
\(215\) | −8.00000 | − | 13.8564i | −0.545595 | − | 0.944999i | ||||
\(216\) | −9.00000 | −0.612372 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.00000 | −0.135457 | ||||||||
\(219\) | −6.00000 | − | 10.3923i | −0.405442 | − | 0.702247i | ||||
\(220\) | −1.00000 | + | 1.73205i | −0.0674200 | + | 0.116775i | ||||
\(221\) | 7.00000 | − | 12.1244i | 0.470871 | − | 0.815572i | ||||
\(222\) | 6.00000 | + | 10.3923i | 0.402694 | + | 0.697486i | ||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.00000 | −0.400000 | ||||||||
\(226\) | −2.50000 | − | 4.33013i | −0.166298 | − | 0.288036i | ||||
\(227\) | −1.00000 | + | 1.73205i | −0.0663723 | + | 0.114960i | −0.897302 | − | 0.441417i | \(-0.854476\pi\) |
0.830930 | + | 0.556378i | \(0.187809\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −14.0000 | − | 24.2487i | −0.925146 | − | 1.60240i | −0.791326 | − | 0.611394i | \(-0.790609\pi\) |
−0.133820 | − | 0.991006i | \(-0.542724\pi\) | |||||||
\(230\) | 16.0000 | 1.05501 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.00000 | −0.328266 | ||||||||
\(233\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(234\) | −21.0000 | + | 36.3731i | −1.37281 | + | 2.37778i | ||||
\(235\) | −2.00000 | + | 3.46410i | −0.130466 | + | 0.225973i | ||||
\(236\) | 1.50000 | + | 2.59808i | 0.0976417 | + | 0.169120i | ||||
\(237\) | −27.0000 | −1.75384 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.00000 | −0.323423 | −0.161712 | − | 0.986838i | \(-0.551701\pi\) | ||||
−0.161712 | + | 0.986838i | \(0.551701\pi\) | |||||||
\(240\) | −3.00000 | − | 5.19615i | −0.193649 | − | 0.335410i | ||||
\(241\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(242\) | −0.500000 | + | 0.866025i | −0.0321412 | + | 0.0556702i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.00000 | −0.0640184 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 12.0000 | 0.765092 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2.00000 | − | 3.46410i | 0.127000 | − | 0.219971i | ||||
\(249\) | −9.00000 | + | 15.5885i | −0.570352 | + | 0.987878i | ||||
\(250\) | −6.00000 | − | 10.3923i | −0.379473 | − | 0.657267i | ||||
\(251\) | 24.0000 | 1.51487 | 0.757433 | − | 0.652913i | \(-0.226453\pi\) | ||||
0.757433 | + | 0.652913i | \(0.226453\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.00000 | 0.502956 | ||||||||
\(254\) | 9.50000 | + | 16.4545i | 0.596083 | + | 1.03245i | ||||
\(255\) | 6.00000 | − | 10.3923i | 0.375735 | − | 0.650791i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 1.50000 | + | 2.59808i | 0.0935674 | + | 0.162064i | 0.909010 | − | 0.416775i | \(-0.136840\pi\) |
−0.815442 | + | 0.578838i | \(0.803506\pi\) | |||||||
\(258\) | 24.0000 | 1.49417 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −14.0000 | −0.868243 | ||||||||
\(261\) | 15.0000 | + | 25.9808i | 0.928477 | + | 1.60817i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.5000 | + | 23.3827i | −0.832446 | + | 1.44184i | 0.0636476 | + | 0.997972i | \(0.479727\pi\) |
−0.896093 | + | 0.443866i | \(0.853607\pi\) | |||||||
\(264\) | −1.50000 | − | 2.59808i | −0.0923186 | − | 0.159901i | ||||
\(265\) | 12.0000 | 0.737154 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 18.0000 | 1.10158 | ||||||||
\(268\) | −4.50000 | − | 7.79423i | −0.274881 | − | 0.476108i | ||||
\(269\) | −12.0000 | + | 20.7846i | −0.731653 | + | 1.26726i | 0.224523 | + | 0.974469i | \(0.427917\pi\) |
−0.956176 | + | 0.292791i | \(0.905416\pi\) | |||||||
\(270\) | −9.00000 | + | 15.5885i | −0.547723 | + | 0.948683i | ||||
\(271\) | −5.50000 | − | 9.52628i | −0.334101 | − | 0.578680i | 0.649211 | − | 0.760609i | \(-0.275099\pi\) |
−0.983312 | + | 0.181928i | \(0.941766\pi\) | |||||||
\(272\) | −2.00000 | −0.121268 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.00000 | 0.181237 | ||||||||
\(275\) | −0.500000 | − | 0.866025i | −0.0301511 | − | 0.0522233i | ||||
\(276\) | −12.0000 | + | 20.7846i | −0.722315 | + | 1.25109i | ||||
\(277\) | 4.50000 | − | 7.79423i | 0.270379 | − | 0.468310i | −0.698580 | − | 0.715532i | \(-0.746184\pi\) |
0.968959 | + | 0.247222i | \(0.0795177\pi\) | |||||||
\(278\) | −2.00000 | − | 3.46410i | −0.119952 | − | 0.207763i | ||||
\(279\) | −24.0000 | −1.43684 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.0000 | −1.67034 | −0.835170 | − | 0.549992i | \(-0.814631\pi\) | ||||
−0.835170 | + | 0.549992i | \(0.814631\pi\) | |||||||
\(282\) | −3.00000 | − | 5.19615i | −0.178647 | − | 0.309426i | ||||
\(283\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(284\) | 1.00000 | − | 1.73205i | 0.0593391 | − | 0.102778i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.00000 | −0.413919 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 6.00000 | 0.353553 | ||||||||
\(289\) | 6.50000 | + | 11.2583i | 0.382353 | + | 0.662255i | ||||
\(290\) | −5.00000 | + | 8.66025i | −0.293610 | + | 0.508548i | ||||
\(291\) | −10.5000 | + | 18.1865i | −0.615521 | + | 1.06611i | ||||
\(292\) | 2.00000 | + | 3.46410i | 0.117041 | + | 0.202721i | ||||
\(293\) | 18.0000 | 1.05157 | 0.525786 | − | 0.850617i | \(-0.323771\pi\) | ||||
0.525786 | + | 0.850617i | \(0.323771\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.00000 | 0.349334 | ||||||||
\(296\) | −2.00000 | − | 3.46410i | −0.116248 | − | 0.201347i | ||||
\(297\) | −4.50000 | + | 7.79423i | −0.261116 | + | 0.452267i | ||||
\(298\) | 5.00000 | − | 8.66025i | 0.289642 | − | 0.501675i | ||||
\(299\) | 28.0000 | + | 48.4974i | 1.61928 | + | 2.80468i | ||||
\(300\) | 3.00000 | 0.173205 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.00000 | −0.172631 | ||||||||
\(303\) | 13.5000 | + | 23.3827i | 0.775555 | + | 1.34330i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.00000 | + | 1.73205i | −0.0572598 | + | 0.0991769i | ||||
\(306\) | 6.00000 | + | 10.3923i | 0.342997 | + | 0.594089i | ||||
\(307\) | −2.00000 | −0.114146 | −0.0570730 | − | 0.998370i | \(-0.518177\pi\) | ||||
−0.0570730 | + | 0.998370i | \(0.518177\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 54.0000 | 3.07195 | ||||||||
\(310\) | −4.00000 | − | 6.92820i | −0.227185 | − | 0.393496i | ||||
\(311\) | −5.00000 | + | 8.66025i | −0.283524 | + | 0.491078i | −0.972250 | − | 0.233944i | \(-0.924837\pi\) |
0.688726 | + | 0.725022i | \(0.258170\pi\) | |||||||
\(312\) | 10.5000 | − | 18.1865i | 0.594445 | − | 1.02961i | ||||
\(313\) | 0.500000 | + | 0.866025i | 0.0282617 | + | 0.0489506i | 0.879810 | − | 0.475325i | \(-0.157669\pi\) |
−0.851549 | + | 0.524276i | \(0.824336\pi\) | |||||||
\(314\) | −16.0000 | −0.902932 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.00000 | 0.506290 | ||||||||
\(317\) | 6.00000 | + | 10.3923i | 0.336994 | + | 0.583690i | 0.983866 | − | 0.178908i | \(-0.0572566\pi\) |
−0.646872 | + | 0.762598i | \(0.723923\pi\) | |||||||
\(318\) | −9.00000 | + | 15.5885i | −0.504695 | + | 0.874157i | ||||
\(319\) | −2.50000 | + | 4.33013i | −0.139973 | + | 0.242441i | ||||
\(320\) | 1.00000 | + | 1.73205i | 0.0559017 | + | 0.0968246i | ||||
\(321\) | −6.00000 | −0.334887 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −4.50000 | − | 7.79423i | −0.250000 | − | 0.433013i | ||||
\(325\) | 3.50000 | − | 6.06218i | 0.194145 | − | 0.336269i | ||||
\(326\) | 8.50000 | − | 14.7224i | 0.470771 | − | 0.815400i | ||||
\(327\) | −3.00000 | − | 5.19615i | −0.165900 | − | 0.287348i | ||||
\(328\) | −4.00000 | −0.220863 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.00000 | −0.330289 | ||||||||
\(331\) | −6.50000 | − | 11.2583i | −0.357272 | − | 0.618814i | 0.630232 | − | 0.776407i | \(-0.282960\pi\) |
−0.987504 | + | 0.157593i | \(0.949627\pi\) | |||||||
\(332\) | 3.00000 | − | 5.19615i | 0.164646 | − | 0.285176i | ||||
\(333\) | −12.0000 | + | 20.7846i | −0.657596 | + | 1.13899i | ||||
\(334\) | 9.50000 | + | 16.4545i | 0.519817 | + | 0.900349i | ||||
\(335\) | −18.0000 | −0.983445 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0000 | −0.653682 | −0.326841 | − | 0.945079i | \(-0.605984\pi\) | ||||
−0.326841 | + | 0.945079i | \(0.605984\pi\) | |||||||
\(338\) | −18.0000 | − | 31.1769i | −0.979071 | − | 1.69580i | ||||
\(339\) | 7.50000 | − | 12.9904i | 0.407344 | − | 0.705541i | ||||
\(340\) | −2.00000 | + | 3.46410i | −0.108465 | + | 0.187867i | ||||
\(341\) | −2.00000 | − | 3.46410i | −0.108306 | − | 0.187592i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −8.00000 | −0.431331 | ||||||||
\(345\) | 24.0000 | + | 41.5692i | 1.29212 | + | 2.23801i | ||||
\(346\) | 12.5000 | − | 21.6506i | 0.672004 | − | 1.16395i | ||||
\(347\) | 11.0000 | − | 19.0526i | 0.590511 | − | 1.02279i | −0.403653 | − | 0.914912i | \(-0.632260\pi\) |
0.994164 | − | 0.107883i | \(-0.0344071\pi\) | |||||||
\(348\) | −7.50000 | − | 12.9904i | −0.402042 | − | 0.696358i | ||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −63.0000 | −3.36269 | ||||||||
\(352\) | 0.500000 | + | 0.866025i | 0.0266501 | + | 0.0461593i | ||||
\(353\) | −9.00000 | + | 15.5885i | −0.479022 | + | 0.829690i | −0.999711 | − | 0.0240566i | \(-0.992342\pi\) |
0.520689 | + | 0.853746i | \(0.325675\pi\) | |||||||
\(354\) | −4.50000 | + | 7.79423i | −0.239172 | + | 0.414259i | ||||
\(355\) | −2.00000 | − | 3.46410i | −0.106149 | − | 0.183855i | ||||
\(356\) | −6.00000 | −0.317999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 19.0000 | 1.00418 | ||||||||
\(359\) | 9.50000 | + | 16.4545i | 0.501391 | + | 0.868434i | 0.999999 | + | 0.00160673i | \(0.000511438\pi\) |
−0.498608 | + | 0.866828i | \(0.666155\pi\) | |||||||
\(360\) | 6.00000 | − | 10.3923i | 0.316228 | − | 0.547723i | ||||
\(361\) | 9.50000 | − | 16.4545i | 0.500000 | − | 0.866025i | ||||
\(362\) | −11.0000 | − | 19.0526i | −0.578147 | − | 1.00138i | ||||
\(363\) | −3.00000 | −0.157459 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.00000 | 0.418739 | ||||||||
\(366\) | −1.50000 | − | 2.59808i | −0.0784063 | − | 0.135804i | ||||
\(367\) | 2.00000 | − | 3.46410i | 0.104399 | − | 0.180825i | −0.809093 | − | 0.587680i | \(-0.800041\pi\) |
0.913493 | + | 0.406855i | \(0.133375\pi\) | |||||||
\(368\) | 4.00000 | − | 6.92820i | 0.208514 | − | 0.361158i | ||||
\(369\) | 12.0000 | + | 20.7846i | 0.624695 | + | 1.08200i | ||||
\(370\) | −8.00000 | −0.415900 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 12.0000 | 0.622171 | ||||||||
\(373\) | −5.50000 | − | 9.52628i | −0.284779 | − | 0.493252i | 0.687776 | − | 0.725923i | \(-0.258587\pi\) |
−0.972556 | + | 0.232671i | \(0.925254\pi\) | |||||||
\(374\) | −1.00000 | + | 1.73205i | −0.0517088 | + | 0.0895622i | ||||
\(375\) | 18.0000 | − | 31.1769i | 0.929516 | − | 1.60997i | ||||
\(376\) | 1.00000 | + | 1.73205i | 0.0515711 | + | 0.0893237i | ||||
\(377\) | −35.0000 | −1.80259 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00000 | 0.0513665 | 0.0256833 | − | 0.999670i | \(-0.491824\pi\) | ||||
0.0256833 | + | 0.999670i | \(0.491824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.5000 | + | 49.3634i | −1.46010 | + | 2.52897i | ||||
\(382\) | −1.00000 | + | 1.73205i | −0.0511645 | + | 0.0886194i | ||||
\(383\) | 13.0000 | + | 22.5167i | 0.664269 | + | 1.15055i | 0.979483 | + | 0.201527i | \(0.0645904\pi\) |
−0.315214 | + | 0.949021i | \(0.602076\pi\) | |||||||
\(384\) | −3.00000 | −0.153093 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | 24.0000 | + | 41.5692i | 1.21999 | + | 2.11308i | ||||
\(388\) | 3.50000 | − | 6.06218i | 0.177686 | − | 0.307760i | ||||
\(389\) | −9.00000 | + | 15.5885i | −0.456318 | + | 0.790366i | −0.998763 | − | 0.0497253i | \(-0.984165\pi\) |
0.542445 | + | 0.840091i | \(0.317499\pi\) | |||||||
\(390\) | −21.0000 | − | 36.3731i | −1.06338 | − | 1.84182i | ||||
\(391\) | 16.0000 | 0.809155 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.50000 | − | 12.9904i | −0.377845 | − | 0.654446i | ||||
\(395\) | 9.00000 | − | 15.5885i | 0.452839 | − | 0.784340i | ||||
\(396\) | 3.00000 | − | 5.19615i | 0.150756 | − | 0.261116i | ||||
\(397\) | 3.00000 | + | 5.19615i | 0.150566 | + | 0.260787i | 0.931436 | − | 0.363906i | \(-0.118557\pi\) |
−0.780870 | + | 0.624694i | \(0.785224\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 4.50000 | + | 7.79423i | 0.224719 | + | 0.389225i | 0.956235 | − | 0.292599i | \(-0.0945202\pi\) |
−0.731516 | + | 0.681824i | \(0.761187\pi\) | |||||||
\(402\) | 13.5000 | − | 23.3827i | 0.673319 | − | 1.16622i | ||||
\(403\) | 14.0000 | − | 24.2487i | 0.697390 | − | 1.20791i | ||||
\(404\) | −4.50000 | − | 7.79423i | −0.223883 | − | 0.387777i | ||||
\(405\) | −18.0000 | −0.894427 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.00000 | −0.198273 | ||||||||
\(408\) | −3.00000 | − | 5.19615i | −0.148522 | − | 0.257248i | ||||
\(409\) | 11.0000 | − | 19.0526i | 0.543915 | − | 0.942088i | −0.454759 | − | 0.890614i | \(-0.650275\pi\) |
0.998674 | − | 0.0514740i | \(-0.0163919\pi\) | |||||||
\(410\) | −4.00000 | + | 6.92820i | −0.197546 | + | 0.342160i | ||||
\(411\) | 4.50000 | + | 7.79423i | 0.221969 | + | 0.384461i | ||||
\(412\) | −18.0000 | −0.886796 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −48.0000 | −2.35907 | ||||||||
\(415\) | −6.00000 | − | 10.3923i | −0.294528 | − | 0.510138i | ||||
\(416\) | −3.50000 | + | 6.06218i | −0.171602 | + | 0.297223i | ||||
\(417\) | 6.00000 | − | 10.3923i | 0.293821 | − | 0.508913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.0000 | −0.781651 | −0.390826 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390826 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.0000 | −0.974740 | −0.487370 | − | 0.873195i | \(-0.662044\pi\) | ||||
−0.487370 | + | 0.873195i | \(0.662044\pi\) | |||||||
\(422\) | 10.0000 | + | 17.3205i | 0.486792 | + | 0.843149i | ||||
\(423\) | 6.00000 | − | 10.3923i | 0.291730 | − | 0.505291i | ||||
\(424\) | 3.00000 | − | 5.19615i | 0.145693 | − | 0.252347i | ||||
\(425\) | −1.00000 | − | 1.73205i | −0.0485071 | − | 0.0840168i | ||||
\(426\) | 6.00000 | 0.290701 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 2.00000 | 0.0966736 | ||||||||
\(429\) | −10.5000 | − | 18.1865i | −0.506945 | − | 0.878054i | ||||
\(430\) | −8.00000 | + | 13.8564i | −0.385794 | + | 0.668215i | ||||
\(431\) | −12.5000 | + | 21.6506i | −0.602104 | + | 1.04287i | 0.390398 | + | 0.920646i | \(0.372337\pi\) |
−0.992502 | + | 0.122228i | \(0.960996\pi\) | |||||||
\(432\) | 4.50000 | + | 7.79423i | 0.216506 | + | 0.375000i | ||||
\(433\) | 34.0000 | 1.63394 | 0.816968 | − | 0.576683i | \(-0.195653\pi\) | ||||
0.816968 | + | 0.576683i | \(0.195653\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −30.0000 | −1.43839 | ||||||||
\(436\) | 1.00000 | + | 1.73205i | 0.0478913 | + | 0.0829502i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −6.00000 | + | 10.3923i | −0.286691 | + | 0.496564i | ||||
\(439\) | −2.50000 | − | 4.33013i | −0.119318 | − | 0.206666i | 0.800179 | − | 0.599761i | \(-0.204738\pi\) |
−0.919498 | + | 0.393095i | \(0.871404\pi\) | |||||||
\(440\) | 2.00000 | 0.0953463 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.0000 | −0.665912 | ||||||||
\(443\) | −18.0000 | − | 31.1769i | −0.855206 | − | 1.48126i | −0.876454 | − | 0.481486i | \(-0.840097\pi\) |
0.0212481 | − | 0.999774i | \(-0.493236\pi\) | |||||||
\(444\) | 6.00000 | − | 10.3923i | 0.284747 | − | 0.493197i | ||||
\(445\) | −6.00000 | + | 10.3923i | −0.284427 | + | 0.492642i | ||||
\(446\) | 2.00000 | + | 3.46410i | 0.0947027 | + | 0.164030i | ||||
\(447\) | 30.0000 | 1.41895 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.00000 | −0.283158 | −0.141579 | − | 0.989927i | \(-0.545218\pi\) | ||||
−0.141579 | + | 0.989927i | \(0.545218\pi\) | |||||||
\(450\) | 3.00000 | + | 5.19615i | 0.141421 | + | 0.244949i | ||||
\(451\) | −2.00000 | + | 3.46410i | −0.0941763 | + | 0.163118i | ||||
\(452\) | −2.50000 | + | 4.33013i | −0.117590 | + | 0.203672i | ||||
\(453\) | −4.50000 | − | 7.79423i | −0.211428 | − | 0.366205i | ||||
\(454\) | 2.00000 | 0.0938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.00000 | − | 12.1244i | −0.327446 | − | 0.567153i | 0.654558 | − | 0.756012i | \(-0.272855\pi\) |
−0.982004 | + | 0.188858i | \(0.939521\pi\) | |||||||
\(458\) | −14.0000 | + | 24.2487i | −0.654177 | + | 1.13307i | ||||
\(459\) | −9.00000 | + | 15.5885i | −0.420084 | + | 0.727607i | ||||
\(460\) | −8.00000 | − | 13.8564i | −0.373002 | − | 0.646058i | ||||
\(461\) | −27.0000 | −1.25752 | −0.628758 | − | 0.777601i | \(-0.716436\pi\) | ||||
−0.628758 | + | 0.777601i | \(0.716436\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.00000 | −0.0929479 | −0.0464739 | − | 0.998920i | \(-0.514798\pi\) | ||||
−0.0464739 | + | 0.998920i | \(0.514798\pi\) | |||||||
\(464\) | 2.50000 | + | 4.33013i | 0.116060 | + | 0.201021i | ||||
\(465\) | 12.0000 | − | 20.7846i | 0.556487 | − | 0.963863i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 6.00000 | + | 10.3923i | 0.277647 | + | 0.480899i | 0.970799 | − | 0.239892i | \(-0.0771121\pi\) |
−0.693153 | + | 0.720791i | \(0.743779\pi\) | |||||||
\(468\) | 42.0000 | 1.94145 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.00000 | 0.184506 | ||||||||
\(471\) | −24.0000 | − | 41.5692i | −1.10586 | − | 1.91541i | ||||
\(472\) | 1.50000 | − | 2.59808i | 0.0690431 | − | 0.119586i | ||||
\(473\) | −4.00000 | + | 6.92820i | −0.183920 | + | 0.318559i | ||||
\(474\) | 13.5000 | + | 23.3827i | 0.620076 | + | 1.07400i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −36.0000 | −1.64833 | ||||||||
\(478\) | 2.50000 | + | 4.33013i | 0.114347 | + | 0.198055i | ||||
\(479\) | −0.500000 | + | 0.866025i | −0.0228456 | + | 0.0395697i | −0.877222 | − | 0.480085i | \(-0.840606\pi\) |
0.854377 | + | 0.519654i | \(0.173939\pi\) | |||||||
\(480\) | −3.00000 | + | 5.19615i | −0.136931 | + | 0.237171i | ||||
\(481\) | −14.0000 | − | 24.2487i | −0.638345 | − | 1.10565i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | −7.00000 | − | 12.1244i | −0.317854 | − | 0.550539i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.0000 | − | 34.6410i | 0.906287 | − | 1.56973i | 0.0871056 | − | 0.996199i | \(-0.472238\pi\) |
0.819181 | − | 0.573535i | \(-0.194428\pi\) | |||||||
\(488\) | 0.500000 | + | 0.866025i | 0.0226339 | + | 0.0392031i | ||||
\(489\) | 51.0000 | 2.30630 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 30.0000 | 1.35388 | 0.676941 | − | 0.736038i | \(-0.263305\pi\) | ||||
0.676941 | + | 0.736038i | \(0.263305\pi\) | |||||||
\(492\) | −6.00000 | − | 10.3923i | −0.270501 | − | 0.468521i | ||||
\(493\) | −5.00000 | + | 8.66025i | −0.225189 | + | 0.390038i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.00000 | − | 10.3923i | −0.269680 | − | 0.467099i | ||||
\(496\) | −4.00000 | −0.179605 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 18.0000 | 0.806599 | ||||||||
\(499\) | −10.0000 | − | 17.3205i | −0.447661 | − | 0.775372i | 0.550572 | − | 0.834788i | \(-0.314410\pi\) |
−0.998233 | + | 0.0594153i | \(0.981076\pi\) | |||||||
\(500\) | −6.00000 | + | 10.3923i | −0.268328 | + | 0.464758i | ||||
\(501\) | −28.5000 | + | 49.3634i | −1.27329 | + | 2.20540i | ||||
\(502\) | −12.0000 | − | 20.7846i | −0.535586 | − | 0.927663i | ||||
\(503\) | −3.00000 | −0.133763 | −0.0668817 | − | 0.997761i | \(-0.521305\pi\) | ||||
−0.0668817 | + | 0.997761i | \(0.521305\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.0000 | −0.800989 | ||||||||
\(506\) | −4.00000 | − | 6.92820i | −0.177822 | − | 0.307996i | ||||
\(507\) | 54.0000 | − | 93.5307i | 2.39822 | − | 4.15385i | ||||
\(508\) | 9.50000 | − | 16.4545i | 0.421494 | − | 0.730050i | ||||
\(509\) | −11.0000 | − | 19.0526i | −0.487566 | − | 0.844490i | 0.512331 | − | 0.858788i | \(-0.328782\pi\) |
−0.999898 | + | 0.0142980i | \(0.995449\pi\) | |||||||
\(510\) | −12.0000 | −0.531369 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.50000 | − | 2.59808i | 0.0661622 | − | 0.114596i | ||||
\(515\) | −18.0000 | + | 31.1769i | −0.793175 | + | 1.37382i | ||||
\(516\) | −12.0000 | − | 20.7846i | −0.528271 | − | 0.914991i | ||||
\(517\) | 2.00000 | 0.0879599 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 75.0000 | 3.29213 | ||||||||
\(520\) | 7.00000 | + | 12.1244i | 0.306970 | + | 0.531688i | ||||
\(521\) | 5.00000 | − | 8.66025i | 0.219054 | − | 0.379413i | −0.735465 | − | 0.677563i | \(-0.763036\pi\) |
0.954519 | + | 0.298150i | \(0.0963696\pi\) | |||||||
\(522\) | 15.0000 | − | 25.9808i | 0.656532 | − | 1.13715i | ||||
\(523\) | −5.00000 | − | 8.66025i | −0.218635 | − | 0.378686i | 0.735756 | − | 0.677247i | \(-0.236827\pi\) |
−0.954391 | + | 0.298560i | \(0.903494\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 27.0000 | 1.17726 | ||||||||
\(527\) | −4.00000 | − | 6.92820i | −0.174243 | − | 0.301797i | ||||
\(528\) | −1.50000 | + | 2.59808i | −0.0652791 | + | 0.113067i | ||||
\(529\) | −20.5000 | + | 35.5070i | −0.891304 | + | 1.54378i | ||||
\(530\) | −6.00000 | − | 10.3923i | −0.260623 | − | 0.451413i | ||||
\(531\) | −18.0000 | −0.781133 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −28.0000 | −1.21281 | ||||||||
\(534\) | −9.00000 | − | 15.5885i | −0.389468 | − | 0.674579i | ||||
\(535\) | 2.00000 | − | 3.46410i | 0.0864675 | − | 0.149766i | ||||
\(536\) | −4.50000 | + | 7.79423i | −0.194370 | + | 0.336659i | ||||
\(537\) | 28.5000 | + | 49.3634i | 1.22987 | + | 2.13019i | ||||
\(538\) | 24.0000 | 1.03471 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 18.0000 | 0.774597 | ||||||||
\(541\) | −2.50000 | − | 4.33013i | −0.107483 | − | 0.186167i | 0.807267 | − | 0.590187i | \(-0.200946\pi\) |
−0.914750 | + | 0.404020i | \(0.867613\pi\) | |||||||
\(542\) | −5.50000 | + | 9.52628i | −0.236245 | + | 0.409189i | ||||
\(543\) | 33.0000 | − | 57.1577i | 1.41617 | − | 2.45287i | ||||
\(544\) | 1.00000 | + | 1.73205i | 0.0428746 | + | 0.0742611i | ||||
\(545\) | 4.00000 | 0.171341 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.0000 | 1.28271 | 0.641354 | − | 0.767245i | \(-0.278373\pi\) | ||||
0.641354 | + | 0.767245i | \(0.278373\pi\) | |||||||
\(548\) | −1.50000 | − | 2.59808i | −0.0640768 | − | 0.110984i | ||||
\(549\) | 3.00000 | − | 5.19615i | 0.128037 | − | 0.221766i | ||||
\(550\) | −0.500000 | + | 0.866025i | −0.0213201 | + | 0.0369274i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 24.0000 | 1.02151 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.00000 | −0.382373 | ||||||||
\(555\) | −12.0000 | − | 20.7846i | −0.509372 | − | 0.882258i | ||||
\(556\) | −2.00000 | + | 3.46410i | −0.0848189 | + | 0.146911i | ||||
\(557\) | −13.0000 | + | 22.5167i | −0.550828 | + | 0.954062i | 0.447387 | + | 0.894340i | \(0.352355\pi\) |
−0.998215 | + | 0.0597213i | \(0.980979\pi\) | |||||||
\(558\) | 12.0000 | + | 20.7846i | 0.508001 | + | 0.879883i | ||||
\(559\) | −56.0000 | −2.36855 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.00000 | −0.253320 | ||||||||
\(562\) | 14.0000 | + | 24.2487i | 0.590554 | + | 1.02287i | ||||
\(563\) | 10.0000 | − | 17.3205i | 0.421450 | − | 0.729972i | −0.574632 | − | 0.818412i | \(-0.694855\pi\) |
0.996082 | + | 0.0884397i | \(0.0281881\pi\) | |||||||
\(564\) | −3.00000 | + | 5.19615i | −0.126323 | + | 0.218797i | ||||
\(565\) | 5.00000 | + | 8.66025i | 0.210352 | + | 0.364340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.00000 | −0.0839181 | ||||||||
\(569\) | 6.00000 | + | 10.3923i | 0.251533 | + | 0.435668i | 0.963948 | − | 0.266090i | \(-0.0857319\pi\) |
−0.712415 | + | 0.701758i | \(0.752399\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.0000 | + | 19.0526i | −0.460336 | + | 0.797325i | −0.998978 | − | 0.0452101i | \(-0.985604\pi\) |
0.538642 | + | 0.842535i | \(0.318938\pi\) | |||||||
\(572\) | 3.50000 | + | 6.06218i | 0.146342 | + | 0.253472i | ||||
\(573\) | −6.00000 | −0.250654 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.00000 | 0.333623 | ||||||||
\(576\) | −3.00000 | − | 5.19615i | −0.125000 | − | 0.216506i | ||||
\(577\) | −21.5000 | + | 37.2391i | −0.895057 | + | 1.55028i | −0.0613223 | + | 0.998118i | \(0.519532\pi\) |
−0.833734 | + | 0.552166i | \(0.813802\pi\) | |||||||
\(578\) | 6.50000 | − | 11.2583i | 0.270364 | − | 0.468285i | ||||
\(579\) | 12.0000 | + | 20.7846i | 0.498703 | + | 0.863779i | ||||
\(580\) | 10.0000 | 0.415227 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 21.0000 | 0.870478 | ||||||||
\(583\) | −3.00000 | − | 5.19615i | −0.124247 | − | 0.215203i | ||||
\(584\) | 2.00000 | − | 3.46410i | 0.0827606 | − | 0.143346i | ||||
\(585\) | 42.0000 | − | 72.7461i | 1.73649 | − | 3.00768i | ||||
\(586\) | −9.00000 | − | 15.5885i | −0.371787 | − | 0.643953i | ||||
\(587\) | −27.0000 | −1.11441 | −0.557205 | − | 0.830375i | \(-0.688126\pi\) | ||||
−0.557205 | + | 0.830375i | \(0.688126\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.00000 | − | 5.19615i | −0.123508 | − | 0.213922i | ||||
\(591\) | 22.5000 | − | 38.9711i | 0.925526 | − | 1.60306i | ||||
\(592\) | −2.00000 | + | 3.46410i | −0.0821995 | + | 0.142374i | ||||
\(593\) | 3.00000 | + | 5.19615i | 0.123195 | + | 0.213380i | 0.921026 | − | 0.389501i | \(-0.127353\pi\) |
−0.797831 | + | 0.602881i | \(0.794019\pi\) | |||||||
\(594\) | 9.00000 | 0.369274 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −10.0000 | −0.409616 | ||||||||
\(597\) | −6.00000 | − | 10.3923i | −0.245564 | − | 0.425329i | ||||
\(598\) | 28.0000 | − | 48.4974i | 1.14501 | − | 1.98321i | ||||
\(599\) | −18.0000 | + | 31.1769i | −0.735460 | + | 1.27385i | 0.219061 | + | 0.975711i | \(0.429701\pi\) |
−0.954521 | + | 0.298143i | \(0.903633\pi\) | |||||||
\(600\) | −1.50000 | − | 2.59808i | −0.0612372 | − | 0.106066i | ||||
\(601\) | −26.0000 | −1.06056 | −0.530281 | − | 0.847822i | \(-0.677914\pi\) | ||||
−0.530281 | + | 0.847822i | \(0.677914\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 54.0000 | 2.19905 | ||||||||
\(604\) | 1.50000 | + | 2.59808i | 0.0610341 | + | 0.105714i | ||||
\(605\) | 1.00000 | − | 1.73205i | 0.0406558 | − | 0.0704179i | ||||
\(606\) | 13.5000 | − | 23.3827i | 0.548400 | − | 0.949857i | ||||
\(607\) | 4.00000 | + | 6.92820i | 0.162355 | + | 0.281207i | 0.935713 | − | 0.352763i | \(-0.114758\pi\) |
−0.773358 | + | 0.633970i | \(0.781424\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.00000 | 0.0809776 | ||||||||
\(611\) | 7.00000 | + | 12.1244i | 0.283190 | + | 0.490499i | ||||
\(612\) | 6.00000 | − | 10.3923i | 0.242536 | − | 0.420084i | ||||
\(613\) | 19.0000 | − | 32.9090i | 0.767403 | − | 1.32918i | −0.171564 | − | 0.985173i | \(-0.554882\pi\) |
0.938967 | − | 0.344008i | \(-0.111785\pi\) | |||||||
\(614\) | 1.00000 | + | 1.73205i | 0.0403567 | + | 0.0698999i | ||||
\(615\) | −24.0000 | −0.967773 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.0000 | −0.603877 | −0.301939 | − | 0.953327i | \(-0.597634\pi\) | ||||
−0.301939 | + | 0.953327i | \(0.597634\pi\) | |||||||
\(618\) | −27.0000 | − | 46.7654i | −1.08610 | − | 1.88118i | ||||
\(619\) | −14.0000 | + | 24.2487i | −0.562708 | + | 0.974638i | 0.434551 | + | 0.900647i | \(0.356907\pi\) |
−0.997259 | + | 0.0739910i | \(0.976426\pi\) | |||||||
\(620\) | −4.00000 | + | 6.92820i | −0.160644 | + | 0.278243i | ||||
\(621\) | −36.0000 | − | 62.3538i | −1.44463 | − | 2.50217i | ||||
\(622\) | 10.0000 | 0.400963 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −21.0000 | −0.840673 | ||||||||
\(625\) | 9.50000 | + | 16.4545i | 0.380000 | + | 0.658179i | ||||
\(626\) | 0.500000 | − | 0.866025i | 0.0199840 | − | 0.0346133i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 8.00000 | + | 13.8564i | 0.319235 | + | 0.552931i | ||||
\(629\) | −8.00000 | −0.318981 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −18.0000 | −0.716569 | −0.358284 | − | 0.933613i | \(-0.616638\pi\) | ||||
−0.358284 | + | 0.933613i | \(0.616638\pi\) | |||||||
\(632\) | −4.50000 | − | 7.79423i | −0.179000 | − | 0.310038i | ||||
\(633\) | −30.0000 | + | 51.9615i | −1.19239 | + | 2.06529i | ||||
\(634\) | 6.00000 | − | 10.3923i | 0.238290 | − | 0.412731i | ||||
\(635\) | −19.0000 | − | 32.9090i | −0.753992 | − | 1.30595i | ||||
\(636\) | 18.0000 | 0.713746 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 5.00000 | 0.197952 | ||||||||
\(639\) | 6.00000 | + | 10.3923i | 0.237356 | + | 0.411113i | ||||
\(640\) | 1.00000 | − | 1.73205i | 0.0395285 | − | 0.0684653i | ||||
\(641\) | 13.5000 | − | 23.3827i | 0.533218 | − | 0.923561i | −0.466029 | − | 0.884769i | \(-0.654316\pi\) |
0.999247 | − | 0.0387913i | \(-0.0123508\pi\) | |||||||
\(642\) | 3.00000 | + | 5.19615i | 0.118401 | + | 0.205076i | ||||
\(643\) | −31.0000 | −1.22252 | −0.611260 | − | 0.791430i | \(-0.709337\pi\) | ||||
−0.611260 | + | 0.791430i | \(0.709337\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −48.0000 | −1.89000 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.0000 | − | 25.9808i | 0.589711 | − | 1.02141i | −0.404559 | − | 0.914512i | \(-0.632575\pi\) |
0.994270 | − | 0.106897i | \(-0.0340916\pi\) | |||||||
\(648\) | −4.50000 | + | 7.79423i | −0.176777 | + | 0.306186i | ||||
\(649\) | −1.50000 | − | 2.59808i | −0.0588802 | − | 0.101983i | ||||
\(650\) | −7.00000 | −0.274563 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −17.0000 | −0.665771 | ||||||||
\(653\) | −20.0000 | − | 34.6410i | −0.782660 | − | 1.35561i | −0.930387 | − | 0.366579i | \(-0.880529\pi\) |
0.147726 | − | 0.989028i | \(-0.452805\pi\) | |||||||
\(654\) | −3.00000 | + | 5.19615i | −0.117309 | + | 0.203186i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.00000 | + | 3.46410i | 0.0780869 | + | 0.135250i | ||||
\(657\) | −24.0000 | −0.936329 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 28.0000 | 1.09073 | 0.545363 | − | 0.838200i | \(-0.316392\pi\) | ||||
0.545363 | + | 0.838200i | \(0.316392\pi\) | |||||||
\(660\) | 3.00000 | + | 5.19615i | 0.116775 | + | 0.202260i | ||||
\(661\) | −11.0000 | + | 19.0526i | −0.427850 | + | 0.741059i | −0.996682 | − | 0.0813955i | \(-0.974062\pi\) |
0.568831 | + | 0.822454i | \(0.307396\pi\) | |||||||
\(662\) | −6.50000 | + | 11.2583i | −0.252630 | + | 0.437567i | ||||
\(663\) | −21.0000 | − | 36.3731i | −0.815572 | − | 1.41261i | ||||
\(664\) | −6.00000 | −0.232845 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 24.0000 | 0.929981 | ||||||||
\(667\) | −20.0000 | − | 34.6410i | −0.774403 | − | 1.34131i | ||||
\(668\) | 9.50000 | − | 16.4545i | 0.367566 | − | 0.636643i | ||||
\(669\) | −6.00000 | + | 10.3923i | −0.231973 | + | 0.401790i | ||||
\(670\) | 9.00000 | + | 15.5885i | 0.347700 | + | 0.602235i | ||||
\(671\) | 1.00000 | 0.0386046 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 34.0000 | 1.31060 | 0.655302 | − | 0.755367i | \(-0.272541\pi\) | ||||
0.655302 | + | 0.755367i | \(0.272541\pi\) | |||||||
\(674\) | 6.00000 | + | 10.3923i | 0.231111 | + | 0.400297i | ||||
\(675\) | −4.50000 | + | 7.79423i | −0.173205 | + | 0.300000i | ||||
\(676\) | −18.0000 | + | 31.1769i | −0.692308 | + | 1.19911i | ||||
\(677\) | 7.00000 | + | 12.1244i | 0.269032 | + | 0.465977i | 0.968612 | − | 0.248577i | \(-0.0799630\pi\) |
−0.699580 | + | 0.714554i | \(0.746630\pi\) | |||||||
\(678\) | −15.0000 | −0.576072 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 4.00000 | 0.153393 | ||||||||
\(681\) | 3.00000 | + | 5.19615i | 0.114960 | + | 0.199117i | ||||
\(682\) | −2.00000 | + | 3.46410i | −0.0765840 | + | 0.132647i | ||||
\(683\) | −10.5000 | + | 18.1865i | −0.401771 | + | 0.695888i | −0.993940 | − | 0.109926i | \(-0.964939\pi\) |
0.592168 | + | 0.805814i | \(0.298272\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.00000 | −0.229248 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −84.0000 | −3.20480 | ||||||||
\(688\) | 4.00000 | + | 6.92820i | 0.152499 | + | 0.264135i | ||||
\(689\) | 21.0000 | − | 36.3731i | 0.800036 | − | 1.38570i | ||||
\(690\) | 24.0000 | − | 41.5692i | 0.913664 | − | 1.58251i | ||||
\(691\) | 16.5000 | + | 28.5788i | 0.627690 | + | 1.08719i | 0.988014 | + | 0.154363i | \(0.0493326\pi\) |
−0.360325 | + | 0.932827i | \(0.617334\pi\) | |||||||
\(692\) | −25.0000 | −0.950357 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.0000 | −0.835109 | ||||||||
\(695\) | 4.00000 | + | 6.92820i | 0.151729 | + | 0.262802i | ||||
\(696\) | −7.50000 | + | 12.9904i | −0.284287 | + | 0.492399i | ||||
\(697\) | −4.00000 | + | 6.92820i | −0.151511 | + | 0.262424i | ||||
\(698\) | 1.00000 | + | 1.73205i | 0.0378506 | + | 0.0655591i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −27.0000 | −1.01978 | −0.509888 | − | 0.860241i | \(-0.670313\pi\) | ||||
−0.509888 | + | 0.860241i | \(0.670313\pi\) | |||||||
\(702\) | 31.5000 | + | 54.5596i | 1.18889 | + | 2.05922i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 6.00000 | + | 10.3923i | 0.225973 | + | 0.391397i | ||||
\(706\) | 18.0000 | 0.677439 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 9.00000 | 0.338241 | ||||||||
\(709\) | 24.0000 | + | 41.5692i | 0.901339 | + | 1.56116i | 0.825758 | + | 0.564025i | \(0.190748\pi\) |
0.0755813 | + | 0.997140i | \(0.475919\pi\) | |||||||
\(710\) | −2.00000 | + | 3.46410i | −0.0750587 | + | 0.130005i | ||||
\(711\) | −27.0000 | + | 46.7654i | −1.01258 | + | 1.75384i | ||||
\(712\) | 3.00000 | + | 5.19615i | 0.112430 | + | 0.194734i | ||||
\(713\) | 32.0000 | 1.19841 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 14.0000 | 0.523570 | ||||||||
\(716\) | −9.50000 | − | 16.4545i | −0.355032 | − | 0.614933i | ||||
\(717\) | −7.50000 | + | 12.9904i | −0.280093 | + | 0.485135i | ||||
\(718\) | 9.50000 | − | 16.4545i | 0.354537 | − | 0.614076i | ||||
\(719\) | −19.0000 | − | 32.9090i | −0.708580 | − | 1.22730i | −0.965384 | − | 0.260834i | \(-0.916003\pi\) |
0.256803 | − | 0.966464i | \(-0.417331\pi\) | |||||||
\(720\) | −12.0000 | −0.447214 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −19.0000 | −0.707107 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −11.0000 | + | 19.0526i | −0.408812 | + | 0.708083i | ||||
\(725\) | −2.50000 | + | 4.33013i | −0.0928477 | + | 0.160817i | ||||
\(726\) | 1.50000 | + | 2.59808i | 0.0556702 | + | 0.0964237i | ||||
\(727\) | 22.0000 | 0.815935 | 0.407967 | − | 0.912996i | \(-0.366238\pi\) | ||||
0.407967 | + | 0.912996i | \(0.366238\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | −4.00000 | − | 6.92820i | −0.148047 | − | 0.256424i | ||||
\(731\) | −8.00000 | + | 13.8564i | −0.295891 | + | 0.512498i | ||||
\(732\) | −1.50000 | + | 2.59808i | −0.0554416 | + | 0.0960277i | ||||
\(733\) | −9.50000 | − | 16.4545i | −0.350891 | − | 0.607760i | 0.635515 | − | 0.772088i | \(-0.280788\pi\) |
−0.986406 | + | 0.164328i | \(0.947454\pi\) | |||||||
\(734\) | −4.00000 | −0.147643 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.00000 | −0.294884 | ||||||||
\(737\) | 4.50000 | + | 7.79423i | 0.165760 | + | 0.287104i | ||||
\(738\) | 12.0000 | − | 20.7846i | 0.441726 | − | 0.765092i | ||||
\(739\) | −21.0000 | + | 36.3731i | −0.772497 | + | 1.33800i | 0.163693 | + | 0.986511i | \(0.447659\pi\) |
−0.936190 | + | 0.351494i | \(0.885674\pi\) | |||||||
\(740\) | 4.00000 | + | 6.92820i | 0.147043 | + | 0.254686i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.0000 | 0.440237 | 0.220119 | − | 0.975473i | \(-0.429356\pi\) | ||||
0.220119 | + | 0.975473i | \(0.429356\pi\) | |||||||
\(744\) | −6.00000 | − | 10.3923i | −0.219971 | − | 0.381000i | ||||
\(745\) | −10.0000 | + | 17.3205i | −0.366372 | + | 0.634574i | ||||
\(746\) | −5.50000 | + | 9.52628i | −0.201369 | + | 0.348782i | ||||
\(747\) | 18.0000 | + | 31.1769i | 0.658586 | + | 1.14070i | ||||
\(748\) | 2.00000 | 0.0731272 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −36.0000 | −1.31453 | ||||||||
\(751\) | −14.0000 | − | 24.2487i | −0.510867 | − | 0.884848i | −0.999921 | − | 0.0125942i | \(-0.995991\pi\) |
0.489053 | − | 0.872254i | \(-0.337342\pi\) | |||||||
\(752\) | 1.00000 | − | 1.73205i | 0.0364662 | − | 0.0631614i | ||||
\(753\) | 36.0000 | − | 62.3538i | 1.31191 | − | 2.27230i | ||||
\(754\) | 17.5000 | + | 30.3109i | 0.637312 | + | 1.10386i | ||||
\(755\) | 6.00000 | 0.218362 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | −0.500000 | − | 0.866025i | −0.0181608 | − | 0.0314555i | ||||
\(759\) | 12.0000 | − | 20.7846i | 0.435572 | − | 0.754434i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.00000 | − | 5.19615i | −0.108750 | − | 0.188360i | 0.806514 | − | 0.591215i | \(-0.201351\pi\) |
−0.915264 | + | 0.402854i | \(0.868018\pi\) | |||||||
\(762\) | 57.0000 | 2.06489 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.00000 | 0.0723575 | ||||||||
\(765\) | −12.0000 | − | 20.7846i | −0.433861 | − | 0.751469i | ||||
\(766\) | 13.0000 | − | 22.5167i | 0.469709 | − | 0.813560i | ||||
\(767\) | 10.5000 | − | 18.1865i | 0.379133 | − | 0.656678i | ||||
\(768\) | 1.50000 | + | 2.59808i | 0.0541266 | + | 0.0937500i | ||||
\(769\) | 14.0000 | 0.504853 | 0.252426 | − | 0.967616i | \(-0.418771\pi\) | ||||
0.252426 | + | 0.967616i | \(0.418771\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.00000 | 0.324127 | ||||||||
\(772\) | −4.00000 | − | 6.92820i | −0.143963 | − | 0.249351i | ||||
\(773\) | 12.0000 | − | 20.7846i | 0.431610 | − | 0.747570i | −0.565402 | − | 0.824815i | \(-0.691279\pi\) |
0.997012 | + | 0.0772449i | \(0.0246123\pi\) | |||||||
\(774\) | 24.0000 | − | 41.5692i | 0.862662 | − | 1.49417i | ||||
\(775\) | −2.00000 | − | 3.46410i | −0.0718421 | − | 0.124434i | ||||
\(776\) | −7.00000 | −0.251285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 18.0000 | 0.645331 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −21.0000 | + | 36.3731i | −0.751921 | + | 1.30236i | ||||
\(781\) | −1.00000 | + | 1.73205i | −0.0357828 | + | 0.0619777i | ||||
\(782\) | −8.00000 | − | 13.8564i | −0.286079 | − | 0.495504i | ||||
\(783\) | 45.0000 | 1.60817 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 32.0000 | 1.14213 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.0000 | + | 34.6410i | −0.712923 | + | 1.23482i | 0.250832 | + | 0.968031i | \(0.419296\pi\) |
−0.963755 | + | 0.266788i | \(0.914038\pi\) | |||||||
\(788\) | −7.50000 | + | 12.9904i | −0.267176 | + | 0.462763i | ||||
\(789\) | 40.5000 | + | 70.1481i | 1.44184 | + | 2.49734i | ||||
\(790\) | −18.0000 | −0.640411 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −6.00000 | −0.213201 | ||||||||
\(793\) | 3.50000 | + | 6.06218i | 0.124289 | + | 0.215274i | ||||
\(794\) | 3.00000 | − | 5.19615i | 0.106466 | − | 0.184405i | ||||
\(795\) | 18.0000 | − | 31.1769i | 0.638394 | − | 1.10573i | ||||
\(796\) | 2.00000 | + | 3.46410i | 0.0708881 | + | 0.122782i | ||||
\(797\) | −50.0000 | −1.77109 | −0.885545 | − | 0.464553i | \(-0.846215\pi\) | ||||
−0.885545 | + | 0.464553i | \(0.846215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.00000 | 0.141510 | ||||||||
\(800\) | 0.500000 | + | 0.866025i | 0.0176777 | + | 0.0306186i | ||||
\(801\) | 18.0000 | − | 31.1769i | 0.635999 | − | 1.10158i | ||||
\(802\) | 4.50000 | − | 7.79423i | 0.158901 | − | 0.275224i | ||||
\(803\) | −2.00000 | − | 3.46410i | −0.0705785 | − | 0.122245i | ||||
\(804\) | −27.0000 | −0.952217 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −28.0000 | −0.986258 | ||||||||
\(807\) | 36.0000 | + | 62.3538i | 1.26726 | + | 2.19496i | ||||
\(808\) | −4.50000 | + | 7.79423i | −0.158309 | + | 0.274200i | ||||
\(809\) | −6.00000 | + | 10.3923i | −0.210949 | + | 0.365374i | −0.952012 | − | 0.306062i | \(-0.900989\pi\) |
0.741063 | + | 0.671436i | \(0.234322\pi\) | |||||||
\(810\) | 9.00000 | + | 15.5885i | 0.316228 | + | 0.547723i | ||||
\(811\) | −8.00000 | −0.280918 | −0.140459 | − | 0.990086i | \(-0.544858\pi\) | ||||
−0.140459 | + | 0.990086i | \(0.544858\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −33.0000 | −1.15736 | ||||||||
\(814\) | 2.00000 | + | 3.46410i | 0.0701000 | + | 0.121417i | ||||
\(815\) | −17.0000 | + | 29.4449i | −0.595484 | + | 1.03141i | ||||
\(816\) | −3.00000 | + | 5.19615i | −0.105021 | + | 0.181902i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −22.0000 | −0.769212 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.00000 | 0.279372 | ||||||||
\(821\) | 22.5000 | + | 38.9711i | 0.785255 | + | 1.36010i | 0.928846 | + | 0.370465i | \(0.120802\pi\) |
−0.143591 | + | 0.989637i | \(0.545865\pi\) | |||||||
\(822\) | 4.50000 | − | 7.79423i | 0.156956 | − | 0.271855i | ||||
\(823\) | −13.0000 | + | 22.5167i | −0.453152 | + | 0.784881i | −0.998580 | − | 0.0532760i | \(-0.983034\pi\) |
0.545428 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(824\) | 9.00000 | + | 15.5885i | 0.313530 | + | 0.543050i | ||||
\(825\) | −3.00000 | −0.104447 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −4.00000 | −0.139094 | −0.0695468 | − | 0.997579i | \(-0.522155\pi\) | ||||
−0.0695468 | + | 0.997579i | \(0.522155\pi\) | |||||||
\(828\) | 24.0000 | + | 41.5692i | 0.834058 | + | 1.44463i | ||||
\(829\) | −1.00000 | + | 1.73205i | −0.0347314 | + | 0.0601566i | −0.882869 | − | 0.469620i | \(-0.844391\pi\) |
0.848137 | + | 0.529777i | \(0.177724\pi\) | |||||||
\(830\) | −6.00000 | + | 10.3923i | −0.208263 | + | 0.360722i | ||||
\(831\) | −13.5000 | − | 23.3827i | −0.468310 | − | 0.811136i | ||||
\(832\) | 7.00000 | 0.242681 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −12.0000 | −0.415526 | ||||||||
\(835\) | −19.0000 | − | 32.9090i | −0.657522 | − | 1.13886i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −18.0000 | + | 31.1769i | −0.622171 | + | 1.07763i | ||||
\(838\) | 8.00000 | + | 13.8564i | 0.276355 | + | 0.478662i | ||||
\(839\) | 18.0000 | 0.621429 | 0.310715 | − | 0.950503i | \(-0.399432\pi\) | ||||
0.310715 | + | 0.950503i | \(0.399432\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −4.00000 | −0.137931 | ||||||||
\(842\) | 10.0000 | + | 17.3205i | 0.344623 | + | 0.596904i | ||||
\(843\) | −42.0000 | + | 72.7461i | −1.44656 | + | 2.50551i | ||||
\(844\) | 10.0000 | − | 17.3205i | 0.344214 | − | 0.596196i | ||||
\(845\) | 36.0000 | + | 62.3538i | 1.23844 | + | 2.14504i | ||||
\(846\) | −12.0000 | −0.412568 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −6.00000 | −0.206041 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.00000 | + | 1.73205i | −0.0342997 | + | 0.0594089i | ||||
\(851\) | 16.0000 | − | 27.7128i | 0.548473 | − | 0.949983i | ||||
\(852\) | −3.00000 | − | 5.19615i | −0.102778 | − | 0.178017i | ||||
\(853\) | 10.0000 | 0.342393 | 0.171197 | − | 0.985237i | \(-0.445237\pi\) | ||||
0.171197 | + | 0.985237i | \(0.445237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.00000 | − | 1.73205i | −0.0341793 | − | 0.0592003i | ||||
\(857\) | 22.0000 | − | 38.1051i | 0.751506 | − | 1.30165i | −0.195587 | − | 0.980686i | \(-0.562661\pi\) |
0.947093 | − | 0.320960i | \(-0.104005\pi\) | |||||||
\(858\) | −10.5000 | + | 18.1865i | −0.358464 | + | 0.620878i | ||||
\(859\) | 6.50000 | + | 11.2583i | 0.221777 | + | 0.384129i | 0.955348 | − | 0.295484i | \(-0.0954809\pi\) |
−0.733571 | + | 0.679613i | \(0.762148\pi\) | |||||||
\(860\) | 16.0000 | 0.545595 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 25.0000 | 0.851503 | ||||||||
\(863\) | −2.00000 | − | 3.46410i | −0.0680808 | − | 0.117919i | 0.829976 | − | 0.557800i | \(-0.188354\pi\) |
−0.898056 | + | 0.439880i | \(0.855021\pi\) | |||||||
\(864\) | 4.50000 | − | 7.79423i | 0.153093 | − | 0.265165i | ||||
\(865\) | −25.0000 | + | 43.3013i | −0.850026 | + | 1.47229i | ||||
\(866\) | −17.0000 | − | 29.4449i | −0.577684 | − | 1.00058i | ||||
\(867\) | 39.0000 | 1.32451 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.00000 | −0.305304 | ||||||||
\(870\) | 15.0000 | + | 25.9808i | 0.508548 | + | 0.880830i | ||||
\(871\) | −31.5000 | + | 54.5596i | −1.06734 | + | 1.84868i | ||||
\(872\) | 1.00000 | − | 1.73205i | 0.0338643 | − | 0.0586546i | ||||
\(873\) | 21.0000 | + | 36.3731i | 0.710742 | + | 1.23104i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.0000 | 0.405442 | ||||||||
\(877\) | 14.5000 | + | 25.1147i | 0.489630 | + | 0.848064i | 0.999929 | − | 0.0119329i | \(-0.00379845\pi\) |
−0.510299 | + | 0.859997i | \(0.670465\pi\) | |||||||
\(878\) | −2.50000 | + | 4.33013i | −0.0843709 | + | 0.146135i | ||||
\(879\) | 27.0000 | − | 46.7654i | 0.910687 | − | 1.57736i | ||||
\(880\) | −1.00000 | − | 1.73205i | −0.0337100 | − | 0.0583874i | ||||
\(881\) | −21.0000 | −0.707508 | −0.353754 | − | 0.935339i | \(-0.615095\pi\) | ||||
−0.353754 | + | 0.935339i | \(0.615095\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −29.0000 | −0.975928 | −0.487964 | − | 0.872864i | \(-0.662260\pi\) | ||||
−0.487964 | + | 0.872864i | \(0.662260\pi\) | |||||||
\(884\) | 7.00000 | + | 12.1244i | 0.235435 | + | 0.407786i | ||||
\(885\) | 9.00000 | − | 15.5885i | 0.302532 | − | 0.524000i | ||||
\(886\) | −18.0000 | + | 31.1769i | −0.604722 | + | 1.04741i | ||||
\(887\) | −20.5000 | − | 35.5070i | −0.688323 | − | 1.19221i | −0.972380 | − | 0.233403i | \(-0.925014\pi\) |
0.284058 | − | 0.958807i | \(-0.408319\pi\) | |||||||
\(888\) | −12.0000 | −0.402694 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 12.0000 | 0.402241 | ||||||||
\(891\) | 4.50000 | + | 7.79423i | 0.150756 | + | 0.261116i | ||||
\(892\) | 2.00000 | − | 3.46410i | 0.0669650 | − | 0.115987i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −15.0000 | − | 25.9808i | −0.501675 | − | 0.868927i | ||||
\(895\) | −38.0000 | −1.27020 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 168.000 | 5.60936 | ||||||||
\(898\) | 3.00000 | + | 5.19615i | 0.100111 | + | 0.173398i | ||||
\(899\) | −10.0000 | + | 17.3205i | −0.333519 | + | 0.577671i | ||||
\(900\) | 3.00000 | − | 5.19615i | 0.100000 | − | 0.173205i | ||||
\(901\) | −6.00000 | − | 10.3923i | −0.199889 | − | 0.346218i | ||||
\(902\) | 4.00000 | 0.133185 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.00000 | 0.166298 | ||||||||
\(905\) | 22.0000 | + | 38.1051i | 0.731305 | + | 1.26666i | ||||
\(906\) | −4.50000 | + | 7.79423i | −0.149502 | + | 0.258946i | ||||
\(907\) | 14.0000 | − | 24.2487i | 0.464862 | − | 0.805165i | −0.534333 | − | 0.845274i | \(-0.679437\pi\) |
0.999195 | + | 0.0401089i | \(0.0127705\pi\) | |||||||
\(908\) | −1.00000 | − | 1.73205i | −0.0331862 | − | 0.0574801i | ||||
\(909\) | 54.0000 | 1.79107 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.0000 | 0.993944 | 0.496972 | − | 0.867766i | \(-0.334445\pi\) | ||||
0.496972 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.00000 | + | 5.19615i | −0.0992855 | + | 0.171968i | ||||
\(914\) | −7.00000 | + | 12.1244i | −0.231539 | + | 0.401038i | ||||
\(915\) | 3.00000 | + | 5.19615i | 0.0991769 | + | 0.171780i | ||||
\(916\) | 28.0000 | 0.925146 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 18.0000 | 0.594089 | ||||||||
\(919\) | −18.0000 | − | 31.1769i | −0.593765 | − | 1.02843i | −0.993720 | − | 0.111897i | \(-0.964307\pi\) |
0.399955 | − | 0.916535i | \(-0.369026\pi\) | |||||||
\(920\) | −8.00000 | + | 13.8564i | −0.263752 | + | 0.456832i | ||||
\(921\) | −3.00000 | + | 5.19615i | −0.0988534 | + | 0.171219i | ||||
\(922\) | 13.5000 | + | 23.3827i | 0.444599 | + | 0.770068i | ||||
\(923\) | −14.0000 | −0.460816 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 1.00000 | + | 1.73205i | 0.0328620 | + | 0.0569187i | ||||
\(927\) | 54.0000 | − | 93.5307i | 1.77359 | − | 3.07195i | ||||
\(928\) | 2.50000 | − | 4.33013i | 0.0820665 | − | 0.142143i | ||||
\(929\) | 7.50000 | + | 12.9904i | 0.246067 | + | 0.426201i | 0.962431 | − | 0.271526i | \(-0.0875283\pi\) |
−0.716364 | + | 0.697727i | \(0.754195\pi\) | |||||||
\(930\) | −24.0000 | −0.786991 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.0000 | + | 25.9808i | 0.491078 | + | 0.850572i | ||||
\(934\) | 6.00000 | − | 10.3923i | 0.196326 | − | 0.340047i | ||||
\(935\) | 2.00000 | − | 3.46410i | 0.0654070 | − | 0.113288i | ||||
\(936\) | −21.0000 | − | 36.3731i | −0.686406 | − | 1.18889i | ||||
\(937\) | 30.0000 | 0.980057 | 0.490029 | − | 0.871706i | \(-0.336986\pi\) | ||||
0.490029 | + | 0.871706i | \(0.336986\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 3.00000 | 0.0979013 | ||||||||
\(940\) | −2.00000 | − | 3.46410i | −0.0652328 | − | 0.112987i | ||||
\(941\) | −5.50000 | + | 9.52628i | −0.179295 | + | 0.310548i | −0.941639 | − | 0.336624i | \(-0.890715\pi\) |
0.762344 | + | 0.647172i | \(0.224048\pi\) | |||||||
\(942\) | −24.0000 | + | 41.5692i | −0.781962 | + | 1.35440i | ||||
\(943\) | −16.0000 | − | 27.7128i | −0.521032 | − | 0.902453i | ||||
\(944\) | −3.00000 | −0.0976417 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | 2.00000 | + | 3.46410i | 0.0649913 | + | 0.112568i | 0.896690 | − | 0.442659i | \(-0.145965\pi\) |
−0.831699 | + | 0.555227i | \(0.812631\pi\) | |||||||
\(948\) | 13.5000 | − | 23.3827i | 0.438460 | − | 0.759434i | ||||
\(949\) | 14.0000 | − | 24.2487i | 0.454459 | − | 0.787146i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 36.0000 | 1.16738 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 14.0000 | 0.453504 | 0.226752 | − | 0.973952i | \(-0.427189\pi\) | ||||
0.226752 | + | 0.973952i | \(0.427189\pi\) | |||||||
\(954\) | 18.0000 | + | 31.1769i | 0.582772 | + | 1.00939i | ||||
\(955\) | 2.00000 | − | 3.46410i | 0.0647185 | − | 0.112096i | ||||
\(956\) | 2.50000 | − | 4.33013i | 0.0808558 | − | 0.140046i | ||||
\(957\) | 7.50000 | + | 12.9904i | 0.242441 | + | 0.419919i | ||||
\(958\) | 1.00000 | 0.0323085 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6.00000 | 0.193649 | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | −14.0000 | + | 24.2487i | −0.451378 | + | 0.781810i | ||||
\(963\) | −6.00000 | + | 10.3923i | −0.193347 | + | 0.334887i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −16.0000 | −0.515058 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | −0.500000 | − | 0.866025i | −0.0160706 | − | 0.0278351i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.00000 | + | 12.1244i | −0.224756 | + | 0.389290i | ||||
\(971\) | 20.5000 | + | 35.5070i | 0.657876 | + | 1.13948i | 0.981164 | + | 0.193175i | \(0.0618784\pi\) |
−0.323288 | + | 0.946301i | \(0.604788\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −40.0000 | −1.28168 | ||||||||
\(975\) | −10.5000 | − | 18.1865i | −0.336269 | − | 0.582435i | ||||
\(976\) | 0.500000 | − | 0.866025i | 0.0160046 | − | 0.0277208i | ||||
\(977\) | 23.0000 | − | 39.8372i | 0.735835 | − | 1.27450i | −0.218521 | − | 0.975832i | \(-0.570123\pi\) |
0.954356 | − | 0.298672i | \(-0.0965435\pi\) | |||||||
\(978\) | −25.5000 | − | 44.1673i | −0.815400 | − | 1.41231i | ||||
\(979\) | 6.00000 | 0.191761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.0000 | −0.383131 | ||||||||
\(982\) | −15.0000 | − | 25.9808i | −0.478669 | − | 0.829079i | ||||
\(983\) | −9.00000 | + | 15.5885i | −0.287055 | + | 0.497195i | −0.973106 | − | 0.230360i | \(-0.926010\pi\) |
0.686050 | + | 0.727554i | \(0.259343\pi\) | |||||||
\(984\) | −6.00000 | + | 10.3923i | −0.191273 | + | 0.331295i | ||||
\(985\) | 15.0000 | + | 25.9808i | 0.477940 | + | 0.827816i | ||||
\(986\) | 10.0000 | 0.318465 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −32.0000 | − | 55.4256i | −1.01754 | − | 1.76243i | ||||
\(990\) | −6.00000 | + | 10.3923i | −0.190693 | + | 0.330289i | ||||
\(991\) | −5.00000 | + | 8.66025i | −0.158830 | + | 0.275102i | −0.934447 | − | 0.356102i | \(-0.884106\pi\) |
0.775617 | + | 0.631204i | \(0.217439\pi\) | |||||||
\(992\) | 2.00000 | + | 3.46410i | 0.0635001 | + | 0.109985i | ||||
\(993\) | −39.0000 | −1.23763 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.00000 | 0.253617 | ||||||||
\(996\) | −9.00000 | − | 15.5885i | −0.285176 | − | 0.493939i | ||||
\(997\) | −3.00000 | + | 5.19615i | −0.0950110 | + | 0.164564i | −0.909613 | − | 0.415456i | \(-0.863622\pi\) |
0.814602 | + | 0.580020i | \(0.196955\pi\) | |||||||
\(998\) | −10.0000 | + | 17.3205i | −0.316544 | + | 0.548271i | ||||
\(999\) | 18.0000 | + | 31.1769i | 0.569495 | + | 0.986394i |
(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 | 1078.2.e.f.67.1 | 2 | ||
7.2 | even | 3 | inner | 1078.2.e.f.177.1 | 2 | ||
7.3 | odd | 6 | 1078.2.a.m.1.1 | 1 | |||
7.4 | even | 3 | 1078.2.a.g.1.1 | 1 | |||
7.5 | odd | 6 | 154.2.e.a.23.1 | ✓ | 2 | ||
7.6 | odd | 2 | 154.2.e.a.67.1 | yes | 2 | ||
21.5 | even | 6 | 1386.2.k.o.793.1 | 2 | |||
21.11 | odd | 6 | 9702.2.a.y.1.1 | 1 | |||
21.17 | even | 6 | 9702.2.a.i.1.1 | 1 | |||
21.20 | even | 2 | 1386.2.k.o.991.1 | 2 | |||
28.3 | even | 6 | 8624.2.a.b.1.1 | 1 | |||
28.11 | odd | 6 | 8624.2.a.be.1.1 | 1 | |||
28.19 | even | 6 | 1232.2.q.e.177.1 | 2 | |||
28.27 | even | 2 | 1232.2.q.e.529.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
154.2.e.a.23.1 | ✓ | 2 | 7.5 | odd | 6 | ||
154.2.e.a.67.1 | yes | 2 | 7.6 | odd | 2 | ||
1078.2.a.g.1.1 | 1 | 7.4 | even | 3 | |||
1078.2.a.m.1.1 | 1 | 7.3 | odd | 6 | |||
1078.2.e.f.67.1 | 2 | 1.1 | even | 1 | trivial | ||
1078.2.e.f.177.1 | 2 | 7.2 | even | 3 | inner | ||
1232.2.q.e.177.1 | 2 | 28.19 | even | 6 | |||
1232.2.q.e.529.1 | 2 | 28.27 | even | 2 | |||
1386.2.k.o.793.1 | 2 | 21.5 | even | 6 | |||
1386.2.k.o.991.1 | 2 | 21.20 | even | 2 | |||
8624.2.a.b.1.1 | 1 | 28.3 | even | 6 | |||
8624.2.a.be.1.1 | 1 | 28.11 | odd | 6 | |||
9702.2.a.i.1.1 | 1 | 21.17 | even | 6 | |||
9702.2.a.y.1.1 | 1 | 21.11 | odd | 6 |