Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [462,2,Mod(67,462)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(462, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 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("462.67");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 462 = 2 \cdot 3 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 462.i (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: | \(3.68908857338\) |
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 | 67.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 462.67 |
Dual form | 462.2.i.d.331.1 |
$q$-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 \(\left(\mathbb{Z}/462\mathbb{Z}\right)^\times\).
\(n\) | \(155\) | \(199\) | \(211\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||
\(3\) | 0.500000 | − | 0.866025i | 0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 2.00000 | − | 1.73205i | 0.755929 | − | 0.654654i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | − | 0.866025i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | − | 0.866025i | 0.150756 | − | 0.261116i | ||||
\(12\) | 0.500000 | + | 0.866025i | 0.144338 | + | 0.250000i | ||||
\(13\) | 4.00000 | 1.10940 | 0.554700 | − | 0.832050i | \(-0.312833\pi\) | ||||
0.554700 | + | 0.832050i | \(0.312833\pi\) | |||||||
\(14\) | 2.50000 | + | 0.866025i | 0.668153 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.500000 | − | 0.866025i | 0.121268 | − | 0.210042i | −0.799000 | − | 0.601331i | \(-0.794637\pi\) |
0.920268 | + | 0.391289i | \(0.127971\pi\) | |||||||
\(18\) | 0.500000 | − | 0.866025i | 0.117851 | − | 0.204124i | ||||
\(19\) | 1.50000 | + | 2.59808i | 0.344124 | + | 0.596040i | 0.985194 | − | 0.171442i | \(-0.0548427\pi\) |
−0.641071 | + | 0.767482i | \(0.721509\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.500000 | − | 2.59808i | −0.109109 | − | 0.566947i | ||||
\(22\) | 1.00000 | 0.213201 | ||||||||
\(23\) | 0.500000 | + | 0.866025i | 0.104257 | + | 0.180579i | 0.913434 | − | 0.406986i | \(-0.133420\pi\) |
−0.809177 | + | 0.587565i | \(0.800087\pi\) | |||||||
\(24\) | −0.500000 | + | 0.866025i | −0.102062 | + | 0.176777i | ||||
\(25\) | 2.50000 | − | 4.33013i | 0.500000 | − | 0.866025i | ||||
\(26\) | 2.00000 | + | 3.46410i | 0.392232 | + | 0.679366i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0.500000 | + | 2.59808i | 0.0944911 | + | 0.490990i | ||||
\(29\) | −1.00000 | −0.185695 | −0.0928477 | − | 0.995680i | \(-0.529597\pi\) | ||||
−0.0928477 | + | 0.995680i | \(0.529597\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | + | 5.19615i | −0.538816 | + | 0.933257i | 0.460152 | + | 0.887840i | \(0.347795\pi\) |
−0.998968 | + | 0.0454165i | \(0.985539\pi\) | |||||||
\(32\) | 0.500000 | − | 0.866025i | 0.0883883 | − | 0.153093i | ||||
\(33\) | −0.500000 | − | 0.866025i | −0.0870388 | − | 0.150756i | ||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 1.50000 | + | 2.59808i | 0.246598 | + | 0.427121i | 0.962580 | − | 0.270998i | \(-0.0873538\pi\) |
−0.715981 | + | 0.698119i | \(0.754020\pi\) | |||||||
\(38\) | −1.50000 | + | 2.59808i | −0.243332 | + | 0.421464i | ||||
\(39\) | 2.00000 | − | 3.46410i | 0.320256 | − | 0.554700i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.00000 | −0.937043 | −0.468521 | − | 0.883452i | \(-0.655213\pi\) | ||||
−0.468521 | + | 0.883452i | \(0.655213\pi\) | |||||||
\(42\) | 2.00000 | − | 1.73205i | 0.308607 | − | 0.267261i | ||||
\(43\) | 1.00000 | 0.152499 | 0.0762493 | − | 0.997089i | \(-0.475706\pi\) | ||||
0.0762493 | + | 0.997089i | \(0.475706\pi\) | |||||||
\(44\) | 0.500000 | + | 0.866025i | 0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.500000 | + | 0.866025i | −0.0737210 | + | 0.127688i | ||||
\(47\) | 0.500000 | + | 0.866025i | 0.0729325 | + | 0.126323i | 0.900185 | − | 0.435507i | \(-0.143431\pi\) |
−0.827253 | + | 0.561830i | \(0.810098\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 1.00000 | − | 6.92820i | 0.142857 | − | 0.989743i | ||||
\(50\) | 5.00000 | 0.707107 | ||||||||
\(51\) | −0.500000 | − | 0.866025i | −0.0700140 | − | 0.121268i | ||||
\(52\) | −2.00000 | + | 3.46410i | −0.277350 | + | 0.480384i | ||||
\(53\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(54\) | −0.500000 | − | 0.866025i | −0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | + | 1.73205i | −0.267261 | + | 0.231455i | ||||
\(57\) | 3.00000 | 0.397360 | ||||||||
\(58\) | −0.500000 | − | 0.866025i | −0.0656532 | − | 0.113715i | ||||
\(59\) | −3.50000 | + | 6.06218i | −0.455661 | + | 0.789228i | −0.998726 | − | 0.0504625i | \(-0.983930\pi\) |
0.543065 | + | 0.839691i | \(0.317264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.00000 | − | 5.19615i | −0.384111 | − | 0.665299i | 0.607535 | − | 0.794293i | \(-0.292159\pi\) |
−0.991645 | + | 0.128994i | \(0.958825\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | −2.50000 | − | 0.866025i | −0.314970 | − | 0.109109i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.500000 | − | 0.866025i | 0.0615457 | − | 0.106600i | ||||
\(67\) | 2.00000 | − | 3.46410i | 0.244339 | − | 0.423207i | −0.717607 | − | 0.696449i | \(-0.754762\pi\) |
0.961946 | + | 0.273241i | \(0.0880957\pi\) | |||||||
\(68\) | 0.500000 | + | 0.866025i | 0.0606339 | + | 0.105021i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15.0000 | −1.78017 | −0.890086 | − | 0.455792i | \(-0.849356\pi\) | ||||
−0.890086 | + | 0.455792i | \(0.849356\pi\) | |||||||
\(72\) | 0.500000 | + | 0.866025i | 0.0589256 | + | 0.102062i | ||||
\(73\) | −6.00000 | + | 10.3923i | −0.702247 | + | 1.21633i | 0.265429 | + | 0.964130i | \(0.414486\pi\) |
−0.967676 | + | 0.252197i | \(0.918847\pi\) | |||||||
\(74\) | −1.50000 | + | 2.59808i | −0.174371 | + | 0.302020i | ||||
\(75\) | −2.50000 | − | 4.33013i | −0.288675 | − | 0.500000i | ||||
\(76\) | −3.00000 | −0.344124 | ||||||||
\(77\) | −0.500000 | − | 2.59808i | −0.0569803 | − | 0.296078i | ||||
\(78\) | 4.00000 | 0.452911 | ||||||||
\(79\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −3.00000 | − | 5.19615i | −0.331295 | − | 0.573819i | ||||
\(83\) | −16.0000 | −1.75623 | −0.878114 | − | 0.478451i | \(-0.841198\pi\) | ||||
−0.878114 | + | 0.478451i | \(0.841198\pi\) | |||||||
\(84\) | 2.50000 | + | 0.866025i | 0.272772 | + | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.500000 | + | 0.866025i | 0.0539164 | + | 0.0933859i | ||||
\(87\) | −0.500000 | + | 0.866025i | −0.0536056 | + | 0.0928477i | ||||
\(88\) | −0.500000 | + | 0.866025i | −0.0533002 | + | 0.0923186i | ||||
\(89\) | 4.00000 | + | 6.92820i | 0.423999 | + | 0.734388i | 0.996326 | − | 0.0856373i | \(-0.0272926\pi\) |
−0.572327 | + | 0.820025i | \(0.693959\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.00000 | − | 6.92820i | 0.838628 | − | 0.726273i | ||||
\(92\) | −1.00000 | −0.104257 | ||||||||
\(93\) | 3.00000 | + | 5.19615i | 0.311086 | + | 0.538816i | ||||
\(94\) | −0.500000 | + | 0.866025i | −0.0515711 | + | 0.0893237i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | − | 0.866025i | −0.0510310 | − | 0.0883883i | ||||
\(97\) | 7.00000 | 0.710742 | 0.355371 | − | 0.934725i | \(-0.384354\pi\) | ||||
0.355371 | + | 0.934725i | \(0.384354\pi\) | |||||||
\(98\) | 6.50000 | − | 2.59808i | 0.656599 | − | 0.262445i | ||||
\(99\) | −1.00000 | −0.100504 | ||||||||
\(100\) | 2.50000 | + | 4.33013i | 0.250000 | + | 0.433013i | ||||
\(101\) | −7.50000 | + | 12.9904i | −0.746278 | + | 1.29259i | 0.203317 | + | 0.979113i | \(0.434828\pi\) |
−0.949595 | + | 0.313478i | \(0.898506\pi\) | |||||||
\(102\) | 0.500000 | − | 0.866025i | 0.0495074 | − | 0.0857493i | ||||
\(103\) | −2.00000 | − | 3.46410i | −0.197066 | − | 0.341328i | 0.750510 | − | 0.660859i | \(-0.229808\pi\) |
−0.947576 | + | 0.319531i | \(0.896475\pi\) | |||||||
\(104\) | −4.00000 | −0.392232 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.00000 | − | 1.73205i | −0.0966736 | − | 0.167444i | 0.813632 | − | 0.581380i | \(-0.197487\pi\) |
−0.910306 | + | 0.413936i | \(0.864154\pi\) | |||||||
\(108\) | 0.500000 | − | 0.866025i | 0.0481125 | − | 0.0833333i | ||||
\(109\) | 9.00000 | − | 15.5885i | 0.862044 | − | 1.49310i | −0.00790932 | − | 0.999969i | \(-0.502518\pi\) |
0.869953 | − | 0.493135i | \(-0.164149\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.00000 | 0.284747 | ||||||||
\(112\) | −2.50000 | − | 0.866025i | −0.236228 | − | 0.0818317i | ||||
\(113\) | 4.00000 | 0.376288 | 0.188144 | − | 0.982141i | \(-0.439753\pi\) | ||||
0.188144 | + | 0.982141i | \(0.439753\pi\) | |||||||
\(114\) | 1.50000 | + | 2.59808i | 0.140488 | + | 0.243332i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.500000 | − | 0.866025i | 0.0464238 | − | 0.0804084i | ||||
\(117\) | −2.00000 | − | 3.46410i | −0.184900 | − | 0.320256i | ||||
\(118\) | −7.00000 | −0.644402 | ||||||||
\(119\) | −0.500000 | − | 2.59808i | −0.0458349 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.500000 | − | 0.866025i | −0.0454545 | − | 0.0787296i | ||||
\(122\) | 3.00000 | − | 5.19615i | 0.271607 | − | 0.470438i | ||||
\(123\) | −3.00000 | + | 5.19615i | −0.270501 | + | 0.468521i | ||||
\(124\) | −3.00000 | − | 5.19615i | −0.269408 | − | 0.466628i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.500000 | − | 2.59808i | −0.0445435 | − | 0.231455i | ||||
\(127\) | −7.00000 | −0.621150 | −0.310575 | − | 0.950549i | \(-0.600522\pi\) | ||||
−0.310575 | + | 0.950549i | \(0.600522\pi\) | |||||||
\(128\) | 0.500000 | + | 0.866025i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0.500000 | − | 0.866025i | 0.0440225 | − | 0.0762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.00000 | + | 1.73205i | 0.0873704 | + | 0.151330i | 0.906399 | − | 0.422423i | \(-0.138820\pi\) |
−0.819028 | + | 0.573753i | \(0.805487\pi\) | |||||||
\(132\) | 1.00000 | 0.0870388 | ||||||||
\(133\) | 7.50000 | + | 2.59808i | 0.650332 | + | 0.225282i | ||||
\(134\) | 4.00000 | 0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.500000 | + | 0.866025i | −0.0428746 | + | 0.0742611i | ||||
\(137\) | 2.00000 | − | 3.46410i | 0.170872 | − | 0.295958i | −0.767853 | − | 0.640626i | \(-0.778675\pi\) |
0.938725 | + | 0.344668i | \(0.112008\pi\) | |||||||
\(138\) | 0.500000 | + | 0.866025i | 0.0425628 | + | 0.0737210i | ||||
\(139\) | −17.0000 | −1.44192 | −0.720961 | − | 0.692976i | \(-0.756299\pi\) | ||||
−0.720961 | + | 0.692976i | \(0.756299\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.00000 | 0.0842152 | ||||||||
\(142\) | −7.50000 | − | 12.9904i | −0.629386 | − | 1.09013i | ||||
\(143\) | 2.00000 | − | 3.46410i | 0.167248 | − | 0.289683i | ||||
\(144\) | −0.500000 | + | 0.866025i | −0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −12.0000 | −0.993127 | ||||||||
\(147\) | −5.50000 | − | 4.33013i | −0.453632 | − | 0.357143i | ||||
\(148\) | −3.00000 | −0.246598 | ||||||||
\(149\) | −0.500000 | − | 0.866025i | −0.0409616 | − | 0.0709476i | 0.844818 | − | 0.535054i | \(-0.179709\pi\) |
−0.885779 | + | 0.464107i | \(0.846375\pi\) | |||||||
\(150\) | 2.50000 | − | 4.33013i | 0.204124 | − | 0.353553i | ||||
\(151\) | −5.50000 | + | 9.52628i | −0.447584 | + | 0.775238i | −0.998228 | − | 0.0595022i | \(-0.981049\pi\) |
0.550645 | + | 0.834740i | \(0.314382\pi\) | |||||||
\(152\) | −1.50000 | − | 2.59808i | −0.121666 | − | 0.210732i | ||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 2.00000 | − | 1.73205i | 0.161165 | − | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.00000 | + | 3.46410i | 0.160128 | + | 0.277350i | ||||
\(157\) | 4.50000 | − | 7.79423i | 0.359139 | − | 0.622047i | −0.628678 | − | 0.777666i | \(-0.716404\pi\) |
0.987817 | + | 0.155618i | \(0.0497370\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.50000 | + | 0.866025i | 0.197028 | + | 0.0682524i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 9.00000 | + | 15.5885i | 0.704934 | + | 1.22098i | 0.966715 | + | 0.255855i | \(0.0823569\pi\) |
−0.261781 | + | 0.965127i | \(0.584310\pi\) | |||||||
\(164\) | 3.00000 | − | 5.19615i | 0.234261 | − | 0.405751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.00000 | − | 13.8564i | −0.620920 | − | 1.07547i | ||||
\(167\) | −12.0000 | −0.928588 | −0.464294 | − | 0.885681i | \(-0.653692\pi\) | ||||
−0.464294 | + | 0.885681i | \(0.653692\pi\) | |||||||
\(168\) | 0.500000 | + | 2.59808i | 0.0385758 | + | 0.200446i | ||||
\(169\) | 3.00000 | 0.230769 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.50000 | − | 2.59808i | 0.114708 | − | 0.198680i | ||||
\(172\) | −0.500000 | + | 0.866025i | −0.0381246 | + | 0.0660338i | ||||
\(173\) | 3.00000 | + | 5.19615i | 0.228086 | + | 0.395056i | 0.957241 | − | 0.289292i | \(-0.0934200\pi\) |
−0.729155 | + | 0.684349i | \(0.760087\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | −2.50000 | − | 12.9904i | −0.188982 | − | 0.981981i | ||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 3.50000 | + | 6.06218i | 0.263076 | + | 0.455661i | ||||
\(178\) | −4.00000 | + | 6.92820i | −0.299813 | + | 0.519291i | ||||
\(179\) | 12.5000 | − | 21.6506i | 0.934294 | − | 1.61824i | 0.158406 | − | 0.987374i | \(-0.449365\pi\) |
0.775888 | − | 0.630870i | \(-0.217302\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 22.0000 | 1.63525 | 0.817624 | − | 0.575753i | \(-0.195291\pi\) | ||||
0.817624 | + | 0.575753i | \(0.195291\pi\) | |||||||
\(182\) | 10.0000 | + | 3.46410i | 0.741249 | + | 0.256776i | ||||
\(183\) | −6.00000 | −0.443533 | ||||||||
\(184\) | −0.500000 | − | 0.866025i | −0.0368605 | − | 0.0638442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | + | 5.19615i | −0.219971 | + | 0.381000i | ||||
\(187\) | −0.500000 | − | 0.866025i | −0.0365636 | − | 0.0633300i | ||||
\(188\) | −1.00000 | −0.0729325 | ||||||||
\(189\) | −2.00000 | + | 1.73205i | −0.145479 | + | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000 | + | 20.7846i | 0.868290 | + | 1.50392i | 0.863743 | + | 0.503932i | \(0.168114\pi\) |
0.00454614 | + | 0.999990i | \(0.498553\pi\) | |||||||
\(192\) | 0.500000 | − | 0.866025i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | −7.00000 | + | 12.1244i | −0.503871 | + | 0.872730i | 0.496119 | + | 0.868255i | \(0.334758\pi\) |
−0.999990 | + | 0.00447566i | \(0.998575\pi\) | |||||||
\(194\) | 3.50000 | + | 6.06218i | 0.251285 | + | 0.435239i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | + | 4.33013i | 0.392857 | + | 0.309295i | ||||
\(197\) | 27.0000 | 1.92367 | 0.961835 | − | 0.273629i | \(-0.0882242\pi\) | ||||
0.961835 | + | 0.273629i | \(0.0882242\pi\) | |||||||
\(198\) | −0.500000 | − | 0.866025i | −0.0355335 | − | 0.0615457i | ||||
\(199\) | −2.00000 | + | 3.46410i | −0.141776 | + | 0.245564i | −0.928166 | − | 0.372168i | \(-0.878615\pi\) |
0.786389 | + | 0.617731i | \(0.211948\pi\) | |||||||
\(200\) | −2.50000 | + | 4.33013i | −0.176777 | + | 0.306186i | ||||
\(201\) | −2.00000 | − | 3.46410i | −0.141069 | − | 0.244339i | ||||
\(202\) | −15.0000 | −1.05540 | ||||||||
\(203\) | −2.00000 | + | 1.73205i | −0.140372 | + | 0.121566i | ||||
\(204\) | 1.00000 | 0.0700140 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 2.00000 | − | 3.46410i | 0.139347 | − | 0.241355i | ||||
\(207\) | 0.500000 | − | 0.866025i | 0.0347524 | − | 0.0601929i | ||||
\(208\) | −2.00000 | − | 3.46410i | −0.138675 | − | 0.240192i | ||||
\(209\) | 3.00000 | 0.207514 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.50000 | + | 12.9904i | −0.513892 | + | 0.890086i | ||||
\(214\) | 1.00000 | − | 1.73205i | 0.0683586 | − | 0.118401i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 3.00000 | + | 15.5885i | 0.203653 | + | 1.05821i | ||||
\(218\) | 18.0000 | 1.21911 | ||||||||
\(219\) | 6.00000 | + | 10.3923i | 0.405442 | + | 0.702247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.00000 | − | 3.46410i | 0.134535 | − | 0.233021i | ||||
\(222\) | 1.50000 | + | 2.59808i | 0.100673 | + | 0.174371i | ||||
\(223\) | 16.0000 | 1.07144 | 0.535720 | − | 0.844396i | \(-0.320040\pi\) | ||||
0.535720 | + | 0.844396i | \(0.320040\pi\) | |||||||
\(224\) | −0.500000 | − | 2.59808i | −0.0334077 | − | 0.173591i | ||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | 2.00000 | + | 3.46410i | 0.133038 | + | 0.230429i | ||||
\(227\) | 1.00000 | − | 1.73205i | 0.0663723 | − | 0.114960i | −0.830930 | − | 0.556378i | \(-0.812191\pi\) |
0.897302 | + | 0.441417i | \(0.145524\pi\) | |||||||
\(228\) | −1.50000 | + | 2.59808i | −0.0993399 | + | 0.172062i | ||||
\(229\) | 3.00000 | + | 5.19615i | 0.198246 | + | 0.343371i | 0.947960 | − | 0.318390i | \(-0.103142\pi\) |
−0.749714 | + | 0.661762i | \(0.769809\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.50000 | − | 0.866025i | −0.164488 | − | 0.0569803i | ||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | 5.50000 | + | 9.52628i | 0.360317 | + | 0.624087i | 0.988013 | − | 0.154371i | \(-0.0493352\pi\) |
−0.627696 | + | 0.778459i | \(0.716002\pi\) | |||||||
\(234\) | 2.00000 | − | 3.46410i | 0.130744 | − | 0.226455i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.50000 | − | 6.06218i | −0.227831 | − | 0.394614i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 2.00000 | − | 1.73205i | 0.129641 | − | 0.112272i | ||||
\(239\) | 16.0000 | 1.03495 | 0.517477 | − | 0.855697i | \(-0.326871\pi\) | ||||
0.517477 | + | 0.855697i | \(0.326871\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | − | 3.46410i | 0.128831 | − | 0.223142i | −0.794393 | − | 0.607404i | \(-0.792211\pi\) |
0.923224 | + | 0.384262i | \(0.125544\pi\) | |||||||
\(242\) | 0.500000 | − | 0.866025i | 0.0321412 | − | 0.0556702i | ||||
\(243\) | 0.500000 | + | 0.866025i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 6.00000 | 0.384111 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.00000 | −0.382546 | ||||||||
\(247\) | 6.00000 | + | 10.3923i | 0.381771 | + | 0.661247i | ||||
\(248\) | 3.00000 | − | 5.19615i | 0.190500 | − | 0.329956i | ||||
\(249\) | −8.00000 | + | 13.8564i | −0.506979 | + | 0.878114i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7.00000 | −0.441836 | −0.220918 | − | 0.975292i | \(-0.570905\pi\) | ||||
−0.220918 | + | 0.975292i | \(0.570905\pi\) | |||||||
\(252\) | 2.00000 | − | 1.73205i | 0.125988 | − | 0.109109i | ||||
\(253\) | 1.00000 | 0.0628695 | ||||||||
\(254\) | −3.50000 | − | 6.06218i | −0.219610 | − | 0.380375i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | 6.00000 | + | 10.3923i | 0.374270 | + | 0.648254i | 0.990217 | − | 0.139533i | \(-0.0445601\pi\) |
−0.615948 | + | 0.787787i | \(0.711227\pi\) | |||||||
\(258\) | 1.00000 | 0.0622573 | ||||||||
\(259\) | 7.50000 | + | 2.59808i | 0.466027 | + | 0.161437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.500000 | + | 0.866025i | 0.0309492 | + | 0.0536056i | ||||
\(262\) | −1.00000 | + | 1.73205i | −0.0617802 | + | 0.107006i | ||||
\(263\) | 7.00000 | − | 12.1244i | 0.431638 | − | 0.747620i | −0.565376 | − | 0.824833i | \(-0.691269\pi\) |
0.997015 | + | 0.0772134i | \(0.0246023\pi\) | |||||||
\(264\) | 0.500000 | + | 0.866025i | 0.0307729 | + | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.50000 | + | 7.79423i | 0.0919709 | + | 0.477895i | ||||
\(267\) | 8.00000 | 0.489592 | ||||||||
\(268\) | 2.00000 | + | 3.46410i | 0.122169 | + | 0.211604i | ||||
\(269\) | 9.00000 | − | 15.5885i | 0.548740 | − | 0.950445i | −0.449622 | − | 0.893219i | \(-0.648441\pi\) |
0.998361 | − | 0.0572259i | \(-0.0182255\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | + | 13.8564i | 0.485965 | + | 0.841717i | 0.999870 | − | 0.0161307i | \(-0.00513477\pi\) |
−0.513905 | + | 0.857847i | \(0.671801\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −2.00000 | − | 10.3923i | −0.121046 | − | 0.628971i | ||||
\(274\) | 4.00000 | 0.241649 | ||||||||
\(275\) | −2.50000 | − | 4.33013i | −0.150756 | − | 0.261116i | ||||
\(276\) | −0.500000 | + | 0.866025i | −0.0300965 | + | 0.0521286i | ||||
\(277\) | 8.00000 | − | 13.8564i | 0.480673 | − | 0.832551i | −0.519081 | − | 0.854725i | \(-0.673726\pi\) |
0.999754 | + | 0.0221745i | \(0.00705893\pi\) | |||||||
\(278\) | −8.50000 | − | 14.7224i | −0.509796 | − | 0.882993i | ||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −27.0000 | −1.61068 | −0.805342 | − | 0.592810i | \(-0.798019\pi\) | ||||
−0.805342 | + | 0.592810i | \(0.798019\pi\) | |||||||
\(282\) | 0.500000 | + | 0.866025i | 0.0297746 | + | 0.0515711i | ||||
\(283\) | −10.0000 | + | 17.3205i | −0.594438 | + | 1.02960i | 0.399188 | + | 0.916869i | \(0.369292\pi\) |
−0.993626 | + | 0.112728i | \(0.964041\pi\) | |||||||
\(284\) | 7.50000 | − | 12.9904i | 0.445043 | − | 0.770837i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | −12.0000 | + | 10.3923i | −0.708338 | + | 0.613438i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 8.00000 | + | 13.8564i | 0.470588 | + | 0.815083i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.50000 | − | 6.06218i | 0.205174 | − | 0.355371i | ||||
\(292\) | −6.00000 | − | 10.3923i | −0.351123 | − | 0.608164i | ||||
\(293\) | −15.0000 | −0.876309 | −0.438155 | − | 0.898900i | \(-0.644368\pi\) | ||||
−0.438155 | + | 0.898900i | \(0.644368\pi\) | |||||||
\(294\) | 1.00000 | − | 6.92820i | 0.0583212 | − | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.50000 | − | 2.59808i | −0.0871857 | − | 0.151010i | ||||
\(297\) | −0.500000 | + | 0.866025i | −0.0290129 | + | 0.0502519i | ||||
\(298\) | 0.500000 | − | 0.866025i | 0.0289642 | − | 0.0501675i | ||||
\(299\) | 2.00000 | + | 3.46410i | 0.115663 | + | 0.200334i | ||||
\(300\) | 5.00000 | 0.288675 | ||||||||
\(301\) | 2.00000 | − | 1.73205i | 0.115278 | − | 0.0998337i | ||||
\(302\) | −11.0000 | −0.632979 | ||||||||
\(303\) | 7.50000 | + | 12.9904i | 0.430864 | + | 0.746278i | ||||
\(304\) | 1.50000 | − | 2.59808i | 0.0860309 | − | 0.149010i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −0.500000 | − | 0.866025i | −0.0285831 | − | 0.0495074i | ||||
\(307\) | −20.0000 | −1.14146 | −0.570730 | − | 0.821138i | \(-0.693340\pi\) | ||||
−0.570730 | + | 0.821138i | \(0.693340\pi\) | |||||||
\(308\) | 2.50000 | + | 0.866025i | 0.142451 | + | 0.0493464i | ||||
\(309\) | −4.00000 | −0.227552 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.5000 | − | 26.8468i | 0.878924 | − | 1.52234i | 0.0264017 | − | 0.999651i | \(-0.491595\pi\) |
0.852523 | − | 0.522690i | \(-0.175072\pi\) | |||||||
\(312\) | −2.00000 | + | 3.46410i | −0.113228 | + | 0.196116i | ||||
\(313\) | 16.5000 | + | 28.5788i | 0.932635 | + | 1.61537i | 0.778798 | + | 0.627275i | \(0.215830\pi\) |
0.153838 | + | 0.988096i | \(0.450837\pi\) | |||||||
\(314\) | 9.00000 | 0.507899 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −6.00000 | − | 10.3923i | −0.336994 | − | 0.583690i | 0.646872 | − | 0.762598i | \(-0.276077\pi\) |
−0.983866 | + | 0.178908i | \(0.942743\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.500000 | + | 0.866025i | −0.0279946 | + | 0.0484881i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.00000 | −0.111629 | ||||||||
\(322\) | 0.500000 | + | 2.59808i | 0.0278639 | + | 0.144785i | ||||
\(323\) | 3.00000 | 0.166924 | ||||||||
\(324\) | −0.500000 | − | 0.866025i | −0.0277778 | − | 0.0481125i | ||||
\(325\) | 10.0000 | − | 17.3205i | 0.554700 | − | 0.960769i | ||||
\(326\) | −9.00000 | + | 15.5885i | −0.498464 | + | 0.863365i | ||||
\(327\) | −9.00000 | − | 15.5885i | −0.497701 | − | 0.862044i | ||||
\(328\) | 6.00000 | 0.331295 | ||||||||
\(329\) | 2.50000 | + | 0.866025i | 0.137829 | + | 0.0477455i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | − | 8.66025i | −0.274825 | − | 0.476011i | 0.695266 | − | 0.718752i | \(-0.255287\pi\) |
−0.970091 | + | 0.242742i | \(0.921953\pi\) | |||||||
\(332\) | 8.00000 | − | 13.8564i | 0.439057 | − | 0.760469i | ||||
\(333\) | 1.50000 | − | 2.59808i | 0.0821995 | − | 0.142374i | ||||
\(334\) | −6.00000 | − | 10.3923i | −0.328305 | − | 0.568642i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.00000 | + | 1.73205i | −0.109109 | + | 0.0944911i | ||||
\(337\) | −26.0000 | −1.41631 | −0.708155 | − | 0.706057i | \(-0.750472\pi\) | ||||
−0.708155 | + | 0.706057i | \(0.750472\pi\) | |||||||
\(338\) | 1.50000 | + | 2.59808i | 0.0815892 | + | 0.141317i | ||||
\(339\) | 2.00000 | − | 3.46410i | 0.108625 | − | 0.188144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | + | 5.19615i | 0.162459 | + | 0.281387i | ||||
\(342\) | 3.00000 | 0.162221 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | −1.00000 | −0.0539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.00000 | + | 5.19615i | −0.161281 | + | 0.279347i | ||||
\(347\) | 10.0000 | − | 17.3205i | 0.536828 | − | 0.929814i | −0.462244 | − | 0.886753i | \(-0.652956\pi\) |
0.999072 | − | 0.0430610i | \(-0.0137110\pi\) | |||||||
\(348\) | −0.500000 | − | 0.866025i | −0.0268028 | − | 0.0464238i | ||||
\(349\) | 32.0000 | 1.71292 | 0.856460 | − | 0.516213i | \(-0.172659\pi\) | ||||
0.856460 | + | 0.516213i | \(0.172659\pi\) | |||||||
\(350\) | 10.0000 | − | 8.66025i | 0.534522 | − | 0.462910i | ||||
\(351\) | −4.00000 | −0.213504 | ||||||||
\(352\) | −0.500000 | − | 0.866025i | −0.0266501 | − | 0.0461593i | ||||
\(353\) | 4.00000 | − | 6.92820i | 0.212899 | − | 0.368751i | −0.739722 | − | 0.672913i | \(-0.765043\pi\) |
0.952620 | + | 0.304162i | \(0.0983763\pi\) | |||||||
\(354\) | −3.50000 | + | 6.06218i | −0.186023 | + | 0.322201i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8.00000 | −0.423999 | ||||||||
\(357\) | −2.50000 | − | 0.866025i | −0.132314 | − | 0.0458349i | ||||
\(358\) | 25.0000 | 1.32129 | ||||||||
\(359\) | −1.00000 | − | 1.73205i | −0.0527780 | − | 0.0914141i | 0.838429 | − | 0.545010i | \(-0.183474\pi\) |
−0.891207 | + | 0.453596i | \(0.850141\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.00000 | − | 8.66025i | 0.263158 | − | 0.455803i | ||||
\(362\) | 11.0000 | + | 19.0526i | 0.578147 | + | 1.00138i | ||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | 2.00000 | + | 10.3923i | 0.104828 | + | 0.544705i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.00000 | − | 5.19615i | −0.156813 | − | 0.271607i | ||||
\(367\) | −10.0000 | + | 17.3205i | −0.521996 | + | 0.904123i | 0.477677 | + | 0.878536i | \(0.341479\pi\) |
−0.999673 | + | 0.0255875i | \(0.991854\pi\) | |||||||
\(368\) | 0.500000 | − | 0.866025i | 0.0260643 | − | 0.0451447i | ||||
\(369\) | 3.00000 | + | 5.19615i | 0.156174 | + | 0.270501i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | −17.0000 | − | 29.4449i | −0.880227 | − | 1.52460i | −0.851089 | − | 0.525022i | \(-0.824057\pi\) |
−0.0291379 | − | 0.999575i | \(-0.509276\pi\) | |||||||
\(374\) | 0.500000 | − | 0.866025i | 0.0258544 | − | 0.0447811i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −0.500000 | − | 0.866025i | −0.0257855 | − | 0.0446619i | ||||
\(377\) | −4.00000 | −0.206010 | ||||||||
\(378\) | −2.50000 | − | 0.866025i | −0.128586 | − | 0.0445435i | ||||
\(379\) | −22.0000 | −1.13006 | −0.565032 | − | 0.825069i | \(-0.691136\pi\) | ||||
−0.565032 | + | 0.825069i | \(0.691136\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.50000 | + | 6.06218i | −0.179310 | + | 0.310575i | ||||
\(382\) | −12.0000 | + | 20.7846i | −0.613973 | + | 1.06343i | ||||
\(383\) | −14.5000 | − | 25.1147i | −0.740915 | − | 1.28330i | −0.952079 | − | 0.305852i | \(-0.901059\pi\) |
0.211164 | − | 0.977451i | \(-0.432275\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0000 | −0.712581 | ||||||||
\(387\) | −0.500000 | − | 0.866025i | −0.0254164 | − | 0.0440225i | ||||
\(388\) | −3.50000 | + | 6.06218i | −0.177686 | + | 0.307760i | ||||
\(389\) | 14.0000 | − | 24.2487i | 0.709828 | − | 1.22946i | −0.255092 | − | 0.966917i | \(-0.582106\pi\) |
0.964921 | − | 0.262542i | \(-0.0845608\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00000 | 0.0505722 | ||||||||
\(392\) | −1.00000 | + | 6.92820i | −0.0505076 | + | 0.349927i | ||||
\(393\) | 2.00000 | 0.100887 | ||||||||
\(394\) | 13.5000 | + | 23.3827i | 0.680120 | + | 1.17800i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.500000 | − | 0.866025i | 0.0251259 | − | 0.0435194i | ||||
\(397\) | −11.5000 | − | 19.9186i | −0.577168 | − | 0.999685i | −0.995802 | − | 0.0915300i | \(-0.970824\pi\) |
0.418634 | − | 0.908155i | \(-0.362509\pi\) | |||||||
\(398\) | −4.00000 | −0.200502 | ||||||||
\(399\) | 6.00000 | − | 5.19615i | 0.300376 | − | 0.260133i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | −1.00000 | − | 1.73205i | −0.0499376 | − | 0.0864945i | 0.839976 | − | 0.542623i | \(-0.182569\pi\) |
−0.889914 | + | 0.456129i | \(0.849236\pi\) | |||||||
\(402\) | 2.00000 | − | 3.46410i | 0.0997509 | − | 0.172774i | ||||
\(403\) | −12.0000 | + | 20.7846i | −0.597763 | + | 1.03536i | ||||
\(404\) | −7.50000 | − | 12.9904i | −0.373139 | − | 0.646296i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.50000 | − | 0.866025i | −0.124073 | − | 0.0429801i | ||||
\(407\) | 3.00000 | 0.148704 | ||||||||
\(408\) | 0.500000 | + | 0.866025i | 0.0247537 | + | 0.0428746i | ||||
\(409\) | −3.00000 | + | 5.19615i | −0.148340 | + | 0.256933i | −0.930614 | − | 0.366002i | \(-0.880726\pi\) |
0.782274 | + | 0.622935i | \(0.214060\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.00000 | − | 3.46410i | −0.0986527 | − | 0.170872i | ||||
\(412\) | 4.00000 | 0.197066 | ||||||||
\(413\) | 3.50000 | + | 18.1865i | 0.172224 | + | 0.894901i | ||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.00000 | − | 3.46410i | 0.0980581 | − | 0.169842i | ||||
\(417\) | −8.50000 | + | 14.7224i | −0.416247 | + | 0.720961i | ||||
\(418\) | 1.50000 | + | 2.59808i | 0.0733674 | + | 0.127076i | ||||
\(419\) | −17.0000 | −0.830504 | −0.415252 | − | 0.909706i | \(-0.636307\pi\) | ||||
−0.415252 | + | 0.909706i | \(0.636307\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.00000 | −0.146211 | −0.0731055 | − | 0.997324i | \(-0.523291\pi\) | ||||
−0.0731055 | + | 0.997324i | \(0.523291\pi\) | |||||||
\(422\) | −10.0000 | − | 17.3205i | −0.486792 | − | 0.843149i | ||||
\(423\) | 0.500000 | − | 0.866025i | 0.0243108 | − | 0.0421076i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.50000 | − | 4.33013i | −0.121268 | − | 0.210042i | ||||
\(426\) | −15.0000 | −0.726752 | ||||||||
\(427\) | −15.0000 | − | 5.19615i | −0.725901 | − | 0.251459i | ||||
\(428\) | 2.00000 | 0.0966736 | ||||||||
\(429\) | −2.00000 | − | 3.46410i | −0.0965609 | − | 0.167248i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0000 | − | 24.2487i | 0.674356 | − | 1.16802i | −0.302300 | − | 0.953213i | \(-0.597755\pi\) |
0.976657 | − | 0.214807i | \(-0.0689121\pi\) | |||||||
\(432\) | 0.500000 | + | 0.866025i | 0.0240563 | + | 0.0416667i | ||||
\(433\) | −19.0000 | −0.913082 | −0.456541 | − | 0.889702i | \(-0.650912\pi\) | ||||
−0.456541 | + | 0.889702i | \(0.650912\pi\) | |||||||
\(434\) | −12.0000 | + | 10.3923i | −0.576018 | + | 0.498847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.00000 | + | 15.5885i | 0.431022 | + | 0.746552i | ||||
\(437\) | −1.50000 | + | 2.59808i | −0.0717547 | + | 0.124283i | ||||
\(438\) | −6.00000 | + | 10.3923i | −0.286691 | + | 0.496564i | ||||
\(439\) | 5.50000 | + | 9.52628i | 0.262501 | + | 0.454665i | 0.966906 | − | 0.255134i | \(-0.0821195\pi\) |
−0.704405 | + | 0.709798i | \(0.748786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | + | 2.59808i | −0.309524 | + | 0.123718i | ||||
\(442\) | 4.00000 | 0.190261 | ||||||||
\(443\) | 1.50000 | + | 2.59808i | 0.0712672 | + | 0.123438i | 0.899457 | − | 0.437009i | \(-0.143962\pi\) |
−0.828190 | + | 0.560448i | \(0.810629\pi\) | |||||||
\(444\) | −1.50000 | + | 2.59808i | −0.0711868 | + | 0.123299i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8.00000 | + | 13.8564i | 0.378811 | + | 0.656120i | ||||
\(447\) | −1.00000 | −0.0472984 | ||||||||
\(448\) | 2.00000 | − | 1.73205i | 0.0944911 | − | 0.0818317i | ||||
\(449\) | −8.00000 | −0.377543 | −0.188772 | − | 0.982021i | \(-0.560451\pi\) | ||||
−0.188772 | + | 0.982021i | \(0.560451\pi\) | |||||||
\(450\) | −2.50000 | − | 4.33013i | −0.117851 | − | 0.204124i | ||||
\(451\) | −3.00000 | + | 5.19615i | −0.141264 | + | 0.244677i | ||||
\(452\) | −2.00000 | + | 3.46410i | −0.0940721 | + | 0.162938i | ||||
\(453\) | 5.50000 | + | 9.52628i | 0.258413 | + | 0.447584i | ||||
\(454\) | 2.00000 | 0.0938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −9.00000 | − | 15.5885i | −0.421002 | − | 0.729197i | 0.575036 | − | 0.818128i | \(-0.304988\pi\) |
−0.996038 | + | 0.0889312i | \(0.971655\pi\) | |||||||
\(458\) | −3.00000 | + | 5.19615i | −0.140181 | + | 0.242800i | ||||
\(459\) | −0.500000 | + | 0.866025i | −0.0233380 | + | 0.0404226i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.0000 | 0.978068 | 0.489034 | − | 0.872265i | \(-0.337349\pi\) | ||||
0.489034 | + | 0.872265i | \(0.337349\pi\) | |||||||
\(462\) | −0.500000 | − | 2.59808i | −0.0232621 | − | 0.120873i | ||||
\(463\) | −32.0000 | −1.48717 | −0.743583 | − | 0.668644i | \(-0.766875\pi\) | ||||
−0.743583 | + | 0.668644i | \(0.766875\pi\) | |||||||
\(464\) | 0.500000 | + | 0.866025i | 0.0232119 | + | 0.0402042i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.50000 | + | 9.52628i | −0.254783 | + | 0.441296i | ||||
\(467\) | 11.5000 | + | 19.9186i | 0.532157 | + | 0.921722i | 0.999295 | + | 0.0375381i | \(0.0119516\pi\) |
−0.467139 | + | 0.884184i | \(0.654715\pi\) | |||||||
\(468\) | 4.00000 | 0.184900 | ||||||||
\(469\) | −2.00000 | − | 10.3923i | −0.0923514 | − | 0.479872i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −4.50000 | − | 7.79423i | −0.207349 | − | 0.359139i | ||||
\(472\) | 3.50000 | − | 6.06218i | 0.161101 | − | 0.279034i | ||||
\(473\) | 0.500000 | − | 0.866025i | 0.0229900 | − | 0.0398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.0000 | 0.688247 | ||||||||
\(476\) | 2.50000 | + | 0.866025i | 0.114587 | + | 0.0396942i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.00000 | + | 13.8564i | 0.365911 | + | 0.633777i | ||||
\(479\) | −5.00000 | + | 8.66025i | −0.228456 | + | 0.395697i | −0.957351 | − | 0.288929i | \(-0.906701\pi\) |
0.728895 | + | 0.684626i | \(0.240034\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.00000 | + | 10.3923i | 0.273576 | + | 0.473848i | ||||
\(482\) | 4.00000 | 0.182195 | ||||||||
\(483\) | 2.00000 | − | 1.73205i | 0.0910032 | − | 0.0788110i | ||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | + | 0.866025i | −0.0226805 | + | 0.0392837i | ||||
\(487\) | −10.0000 | + | 17.3205i | −0.453143 | + | 0.784867i | −0.998579 | − | 0.0532853i | \(-0.983031\pi\) |
0.545436 | + | 0.838152i | \(0.316364\pi\) | |||||||
\(488\) | 3.00000 | + | 5.19615i | 0.135804 | + | 0.235219i | ||||
\(489\) | 18.0000 | 0.813988 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 12.0000 | 0.541552 | 0.270776 | − | 0.962642i | \(-0.412720\pi\) | ||||
0.270776 | + | 0.962642i | \(0.412720\pi\) | |||||||
\(492\) | −3.00000 | − | 5.19615i | −0.135250 | − | 0.234261i | ||||
\(493\) | −0.500000 | + | 0.866025i | −0.0225189 | + | 0.0390038i | ||||
\(494\) | −6.00000 | + | 10.3923i | −0.269953 | + | 0.467572i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | −30.0000 | + | 25.9808i | −1.34568 | + | 1.16540i | ||||
\(498\) | −16.0000 | −0.716977 | ||||||||
\(499\) | −5.00000 | − | 8.66025i | −0.223831 | − | 0.387686i | 0.732137 | − | 0.681157i | \(-0.238523\pi\) |
−0.955968 | + | 0.293471i | \(0.905190\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.00000 | + | 10.3923i | −0.268060 | + | 0.464294i | ||||
\(502\) | −3.50000 | − | 6.06218i | −0.156213 | − | 0.270568i | ||||
\(503\) | 2.00000 | 0.0891756 | 0.0445878 | − | 0.999005i | \(-0.485803\pi\) | ||||
0.0445878 | + | 0.999005i | \(0.485803\pi\) | |||||||
\(504\) | 2.50000 | + | 0.866025i | 0.111359 | + | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.500000 | + | 0.866025i | 0.0222277 | + | 0.0384995i | ||||
\(507\) | 1.50000 | − | 2.59808i | 0.0666173 | − | 0.115385i | ||||
\(508\) | 3.50000 | − | 6.06218i | 0.155287 | − | 0.268966i | ||||
\(509\) | −2.00000 | − | 3.46410i | −0.0886484 | − | 0.153544i | 0.818292 | − | 0.574803i | \(-0.194921\pi\) |
−0.906940 | + | 0.421260i | \(0.861588\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | + | 31.1769i | 0.265424 | + | 1.37919i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | −1.50000 | − | 2.59808i | −0.0662266 | − | 0.114708i | ||||
\(514\) | −6.00000 | + | 10.3923i | −0.264649 | + | 0.458385i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.500000 | + | 0.866025i | 0.0220113 | + | 0.0381246i | ||||
\(517\) | 1.00000 | 0.0439799 | ||||||||
\(518\) | 1.50000 | + | 7.79423i | 0.0659062 | + | 0.342459i | ||||
\(519\) | 6.00000 | 0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.00000 | + | 15.5885i | −0.394297 | + | 0.682943i | −0.993011 | − | 0.118020i | \(-0.962345\pi\) |
0.598714 | + | 0.800963i | \(0.295679\pi\) | |||||||
\(522\) | −0.500000 | + | 0.866025i | −0.0218844 | + | 0.0379049i | ||||
\(523\) | −22.0000 | − | 38.1051i | −0.961993 | − | 1.66622i | −0.717486 | − | 0.696573i | \(-0.754707\pi\) |
−0.244507 | − | 0.969648i | \(-0.578626\pi\) | |||||||
\(524\) | −2.00000 | −0.0873704 | ||||||||
\(525\) | −12.5000 | − | 4.33013i | −0.545545 | − | 0.188982i | ||||
\(526\) | 14.0000 | 0.610429 | ||||||||
\(527\) | 3.00000 | + | 5.19615i | 0.130682 | + | 0.226348i | ||||
\(528\) | −0.500000 | + | 0.866025i | −0.0217597 | + | 0.0376889i | ||||
\(529\) | 11.0000 | − | 19.0526i | 0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.00000 | 0.303774 | ||||||||
\(532\) | −6.00000 | + | 5.19615i | −0.260133 | + | 0.225282i | ||||
\(533\) | −24.0000 | −1.03956 | ||||||||
\(534\) | 4.00000 | + | 6.92820i | 0.173097 | + | 0.299813i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −2.00000 | + | 3.46410i | −0.0863868 | + | 0.149626i | ||||
\(537\) | −12.5000 | − | 21.6506i | −0.539415 | − | 0.934294i | ||||
\(538\) | 18.0000 | 0.776035 | ||||||||
\(539\) | −5.50000 | − | 4.33013i | −0.236902 | − | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.0000 | − | 17.3205i | −0.429934 | − | 0.744667i | 0.566933 | − | 0.823764i | \(-0.308130\pi\) |
−0.996867 | + | 0.0790969i | \(0.974796\pi\) | |||||||
\(542\) | −8.00000 | + | 13.8564i | −0.343629 | + | 0.595184i | ||||
\(543\) | 11.0000 | − | 19.0526i | 0.472055 | − | 0.817624i | ||||
\(544\) | −0.500000 | − | 0.866025i | −0.0214373 | − | 0.0371305i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8.00000 | − | 6.92820i | 0.342368 | − | 0.296500i | ||||
\(547\) | 7.00000 | 0.299298 | 0.149649 | − | 0.988739i | \(-0.452186\pi\) | ||||
0.149649 | + | 0.988739i | \(0.452186\pi\) | |||||||
\(548\) | 2.00000 | + | 3.46410i | 0.0854358 | + | 0.147979i | ||||
\(549\) | −3.00000 | + | 5.19615i | −0.128037 | + | 0.221766i | ||||
\(550\) | 2.50000 | − | 4.33013i | 0.106600 | − | 0.184637i | ||||
\(551\) | −1.50000 | − | 2.59808i | −0.0639021 | − | 0.110682i | ||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 16.0000 | 0.679775 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.50000 | − | 14.7224i | 0.360480 | − | 0.624370i | ||||
\(557\) | 1.50000 | − | 2.59808i | 0.0635570 | − | 0.110084i | −0.832496 | − | 0.554031i | \(-0.813089\pi\) |
0.896053 | + | 0.443947i | \(0.146422\pi\) | |||||||
\(558\) | 3.00000 | + | 5.19615i | 0.127000 | + | 0.219971i | ||||
\(559\) | 4.00000 | 0.169182 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.00000 | −0.0422200 | ||||||||
\(562\) | −13.5000 | − | 23.3827i | −0.569463 | − | 0.986339i | ||||
\(563\) | −6.00000 | + | 10.3923i | −0.252870 | + | 0.437983i | −0.964315 | − | 0.264758i | \(-0.914708\pi\) |
0.711445 | + | 0.702742i | \(0.248041\pi\) | |||||||
\(564\) | −0.500000 | + | 0.866025i | −0.0210538 | + | 0.0364662i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −20.0000 | −0.840663 | ||||||||
\(567\) | 0.500000 | + | 2.59808i | 0.0209980 | + | 0.109109i | ||||
\(568\) | 15.0000 | 0.629386 | ||||||||
\(569\) | −19.5000 | − | 33.7750i | −0.817483 | − | 1.41592i | −0.907532 | − | 0.419984i | \(-0.862036\pi\) |
0.0900490 | − | 0.995937i | \(-0.471298\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.50000 | + | 6.06218i | −0.146470 | + | 0.253694i | −0.929921 | − | 0.367760i | \(-0.880125\pi\) |
0.783450 | + | 0.621455i | \(0.213458\pi\) | |||||||
\(572\) | 2.00000 | + | 3.46410i | 0.0836242 | + | 0.144841i | ||||
\(573\) | 24.0000 | 1.00261 | ||||||||
\(574\) | −15.0000 | − | 5.19615i | −0.626088 | − | 0.216883i | ||||
\(575\) | 5.00000 | 0.208514 | ||||||||
\(576\) | −0.500000 | − | 0.866025i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 11.0000 | − | 19.0526i | 0.457936 | − | 0.793168i | −0.540916 | − | 0.841077i | \(-0.681922\pi\) |
0.998852 | + | 0.0479084i | \(0.0152556\pi\) | |||||||
\(578\) | −8.00000 | + | 13.8564i | −0.332756 | + | 0.576351i | ||||
\(579\) | 7.00000 | + | 12.1244i | 0.290910 | + | 0.503871i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −32.0000 | + | 27.7128i | −1.32758 | + | 1.14972i | ||||
\(582\) | 7.00000 | 0.290159 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 6.00000 | − | 10.3923i | 0.248282 | − | 0.430037i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7.50000 | − | 12.9904i | −0.309822 | − | 0.536628i | ||||
\(587\) | 4.00000 | 0.165098 | 0.0825488 | − | 0.996587i | \(-0.473694\pi\) | ||||
0.0825488 | + | 0.996587i | \(0.473694\pi\) | |||||||
\(588\) | 6.50000 | − | 2.59808i | 0.268055 | − | 0.107143i | ||||
\(589\) | −18.0000 | −0.741677 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13.5000 | − | 23.3827i | 0.555316 | − | 0.961835i | ||||
\(592\) | 1.50000 | − | 2.59808i | 0.0616496 | − | 0.106780i | ||||
\(593\) | 9.50000 | + | 16.4545i | 0.390118 | + | 0.675705i | 0.992465 | − | 0.122530i | \(-0.0391008\pi\) |
−0.602347 | + | 0.798235i | \(0.705767\pi\) | |||||||
\(594\) | −1.00000 | −0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 2.00000 | + | 3.46410i | 0.0818546 | + | 0.141776i | ||||
\(598\) | −2.00000 | + | 3.46410i | −0.0817861 | + | 0.141658i | ||||
\(599\) | 20.0000 | − | 34.6410i | 0.817178 | − | 1.41539i | −0.0905757 | − | 0.995890i | \(-0.528871\pi\) |
0.907754 | − | 0.419504i | \(-0.137796\pi\) | |||||||
\(600\) | 2.50000 | + | 4.33013i | 0.102062 | + | 0.176777i | ||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | 2.50000 | + | 0.866025i | 0.101892 | + | 0.0352966i | ||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | −5.50000 | − | 9.52628i | −0.223792 | − | 0.387619i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −7.50000 | + | 12.9904i | −0.304667 | + | 0.527698i | ||||
\(607\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(608\) | 3.00000 | 0.121666 | ||||||||
\(609\) | 0.500000 | + | 2.59808i | 0.0202610 | + | 0.105279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.00000 | + | 3.46410i | 0.0809113 | + | 0.140143i | ||||
\(612\) | 0.500000 | − | 0.866025i | 0.0202113 | − | 0.0350070i | ||||
\(613\) | −20.0000 | + | 34.6410i | −0.807792 | + | 1.39914i | 0.106597 | + | 0.994302i | \(0.466004\pi\) |
−0.914390 | + | 0.404835i | \(0.867329\pi\) | |||||||
\(614\) | −10.0000 | − | 17.3205i | −0.403567 | − | 0.698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.500000 | + | 2.59808i | 0.0201456 | + | 0.104679i | ||||
\(617\) | 26.0000 | 1.04672 | 0.523360 | − | 0.852111i | \(-0.324678\pi\) | ||||
0.523360 | + | 0.852111i | \(0.324678\pi\) | |||||||
\(618\) | −2.00000 | − | 3.46410i | −0.0804518 | − | 0.139347i | ||||
\(619\) | 15.0000 | − | 25.9808i | 0.602901 | − | 1.04425i | −0.389479 | − | 0.921036i | \(-0.627345\pi\) |
0.992379 | − | 0.123219i | \(-0.0393219\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.500000 | − | 0.866025i | −0.0200643 | − | 0.0347524i | ||||
\(622\) | 31.0000 | 1.24299 | ||||||||
\(623\) | 20.0000 | + | 6.92820i | 0.801283 | + | 0.277573i | ||||
\(624\) | −4.00000 | −0.160128 | ||||||||
\(625\) | −12.5000 | − | 21.6506i | −0.500000 | − | 0.866025i | ||||
\(626\) | −16.5000 | + | 28.5788i | −0.659473 | + | 1.14224i | ||||
\(627\) | 1.50000 | − | 2.59808i | 0.0599042 | − | 0.103757i | ||||
\(628\) | 4.50000 | + | 7.79423i | 0.179570 | + | 0.311024i | ||||
\(629\) | 3.00000 | 0.119618 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 40.0000 | 1.59237 | 0.796187 | − | 0.605050i | \(-0.206847\pi\) | ||||
0.796187 | + | 0.605050i | \(0.206847\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.0000 | + | 17.3205i | −0.397464 | + | 0.688428i | ||||
\(634\) | 6.00000 | − | 10.3923i | 0.238290 | − | 0.412731i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.00000 | − | 27.7128i | 0.158486 | − | 1.09802i | ||||
\(638\) | −1.00000 | −0.0395904 | ||||||||
\(639\) | 7.50000 | + | 12.9904i | 0.296695 | + | 0.513892i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.0000 | + | 29.4449i | −0.671460 | + | 1.16300i | 0.306031 | + | 0.952022i | \(0.400999\pi\) |
−0.977490 | + | 0.210981i | \(0.932334\pi\) | |||||||
\(642\) | −1.00000 | − | 1.73205i | −0.0394669 | − | 0.0683586i | ||||
\(643\) | −10.0000 | −0.394362 | −0.197181 | − | 0.980367i | \(-0.563179\pi\) | ||||
−0.197181 | + | 0.980367i | \(0.563179\pi\) | |||||||
\(644\) | −2.00000 | + | 1.73205i | −0.0788110 | + | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.50000 | + | 2.59808i | 0.0590167 | + | 0.102220i | ||||
\(647\) | −4.00000 | + | 6.92820i | −0.157256 | + | 0.272376i | −0.933878 | − | 0.357591i | \(-0.883598\pi\) |
0.776622 | + | 0.629967i | \(0.216932\pi\) | |||||||
\(648\) | 0.500000 | − | 0.866025i | 0.0196419 | − | 0.0340207i | ||||
\(649\) | 3.50000 | + | 6.06218i | 0.137387 | + | 0.237961i | ||||
\(650\) | 20.0000 | 0.784465 | ||||||||
\(651\) | 15.0000 | + | 5.19615i | 0.587896 | + | 0.203653i | ||||
\(652\) | −18.0000 | −0.704934 | ||||||||
\(653\) | −24.0000 | − | 41.5692i | −0.939193 | − | 1.62673i | −0.766982 | − | 0.641669i | \(-0.778242\pi\) |
−0.172211 | − | 0.985060i | \(-0.555091\pi\) | |||||||
\(654\) | 9.00000 | − | 15.5885i | 0.351928 | − | 0.609557i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 3.00000 | + | 5.19615i | 0.117130 | + | 0.202876i | ||||
\(657\) | 12.0000 | 0.468165 | ||||||||
\(658\) | 0.500000 | + | 2.59808i | 0.0194920 | + | 0.101284i | ||||
\(659\) | 50.0000 | 1.94772 | 0.973862 | − | 0.227142i | \(-0.0729380\pi\) | ||||
0.973862 | + | 0.227142i | \(0.0729380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.5000 | − | 35.5070i | 0.797358 | − | 1.38106i | −0.123974 | − | 0.992286i | \(-0.539564\pi\) |
0.921331 | − | 0.388778i | \(-0.127103\pi\) | |||||||
\(662\) | 5.00000 | − | 8.66025i | 0.194331 | − | 0.336590i | ||||
\(663\) | −2.00000 | − | 3.46410i | −0.0776736 | − | 0.134535i | ||||
\(664\) | 16.0000 | 0.620920 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.00000 | 0.116248 | ||||||||
\(667\) | −0.500000 | − | 0.866025i | −0.0193601 | − | 0.0335326i | ||||
\(668\) | 6.00000 | − | 10.3923i | 0.232147 | − | 0.402090i | ||||
\(669\) | 8.00000 | − | 13.8564i | 0.309298 | − | 0.535720i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.00000 | −0.231627 | ||||||||
\(672\) | −2.50000 | − | 0.866025i | −0.0964396 | − | 0.0334077i | ||||
\(673\) | −28.0000 | −1.07932 | −0.539660 | − | 0.841883i | \(-0.681447\pi\) | ||||
−0.539660 | + | 0.841883i | \(0.681447\pi\) | |||||||
\(674\) | −13.0000 | − | 22.5167i | −0.500741 | − | 0.867309i | ||||
\(675\) | −2.50000 | + | 4.33013i | −0.0962250 | + | 0.166667i | ||||
\(676\) | −1.50000 | + | 2.59808i | −0.0576923 | + | 0.0999260i | ||||
\(677\) | 4.50000 | + | 7.79423i | 0.172949 | + | 0.299557i | 0.939450 | − | 0.342687i | \(-0.111337\pi\) |
−0.766501 | + | 0.642244i | \(0.778004\pi\) | |||||||
\(678\) | 4.00000 | 0.153619 | ||||||||
\(679\) | 14.0000 | − | 12.1244i | 0.537271 | − | 0.465290i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.00000 | − | 1.73205i | −0.0383201 | − | 0.0663723i | ||||
\(682\) | −3.00000 | + | 5.19615i | −0.114876 | + | 0.198971i | ||||
\(683\) | −19.5000 | + | 33.7750i | −0.746147 | + | 1.29236i | 0.203510 | + | 0.979073i | \(0.434765\pi\) |
−0.949657 | + | 0.313291i | \(0.898568\pi\) | |||||||
\(684\) | 1.50000 | + | 2.59808i | 0.0573539 | + | 0.0993399i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 8.50000 | − | 16.4545i | 0.324532 | − | 0.628235i | ||||
\(687\) | 6.00000 | 0.228914 | ||||||||
\(688\) | −0.500000 | − | 0.866025i | −0.0190623 | − | 0.0330169i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.0000 | + | 29.4449i | 0.646710 | + | 1.12014i | 0.983904 | + | 0.178700i | \(0.0571891\pi\) |
−0.337193 | + | 0.941435i | \(0.609478\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −2.00000 | + | 1.73205i | −0.0759737 | + | 0.0657952i | ||||
\(694\) | 20.0000 | 0.759190 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0.500000 | − | 0.866025i | 0.0189525 | − | 0.0328266i | ||||
\(697\) | −3.00000 | + | 5.19615i | −0.113633 | + | 0.196818i | ||||
\(698\) | 16.0000 | + | 27.7128i | 0.605609 | + | 1.04895i | ||||
\(699\) | 11.0000 | 0.416058 | ||||||||
\(700\) | 12.5000 | + | 4.33013i | 0.472456 | + | 0.163663i | ||||
\(701\) | 29.0000 | 1.09531 | 0.547657 | − | 0.836703i | \(-0.315520\pi\) | ||||
0.547657 | + | 0.836703i | \(0.315520\pi\) | |||||||
\(702\) | −2.00000 | − | 3.46410i | −0.0754851 | − | 0.130744i | ||||
\(703\) | −4.50000 | + | 7.79423i | −0.169721 | + | 0.293965i | ||||
\(704\) | 0.500000 | − | 0.866025i | 0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 8.00000 | 0.301084 | ||||||||
\(707\) | 7.50000 | + | 38.9711i | 0.282067 | + | 1.46566i | ||||
\(708\) | −7.00000 | −0.263076 | ||||||||
\(709\) | 4.50000 | + | 7.79423i | 0.169001 | + | 0.292718i | 0.938069 | − | 0.346449i | \(-0.112613\pi\) |
−0.769068 | + | 0.639167i | \(0.779279\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.00000 | − | 6.92820i | −0.149906 | − | 0.259645i | ||||
\(713\) | −6.00000 | −0.224702 | ||||||||
\(714\) | −0.500000 | − | 2.59808i | −0.0187120 | − | 0.0972306i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 12.5000 | + | 21.6506i | 0.467147 | + | 0.809122i | ||||
\(717\) | 8.00000 | − | 13.8564i | 0.298765 | − | 0.517477i | ||||
\(718\) | 1.00000 | − | 1.73205i | 0.0373197 | − | 0.0646396i | ||||
\(719\) | 18.5000 | + | 32.0429i | 0.689934 | + | 1.19500i | 0.971859 | + | 0.235564i | \(0.0756936\pi\) |
−0.281925 | + | 0.959436i | \(0.590973\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.0000 | − | 3.46410i | −0.372419 | − | 0.129010i | ||||
\(722\) | 10.0000 | 0.372161 | ||||||||
\(723\) | −2.00000 | − | 3.46410i | −0.0743808 | − | 0.128831i | ||||
\(724\) | −11.0000 | + | 19.0526i | −0.408812 | + | 0.708083i | ||||
\(725\) | −2.50000 | + | 4.33013i | −0.0928477 | + | 0.160817i | ||||
\(726\) | −0.500000 | − | 0.866025i | −0.0185567 | − | 0.0321412i | ||||
\(727\) | 14.0000 | 0.519231 | 0.259616 | − | 0.965712i | \(-0.416404\pi\) | ||||
0.259616 | + | 0.965712i | \(0.416404\pi\) | |||||||
\(728\) | −8.00000 | + | 6.92820i | −0.296500 | + | 0.256776i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0.500000 | − | 0.866025i | 0.0184932 | − | 0.0320311i | ||||
\(732\) | 3.00000 | − | 5.19615i | 0.110883 | − | 0.192055i | ||||
\(733\) | 5.00000 | + | 8.66025i | 0.184679 | + | 0.319874i | 0.943468 | − | 0.331463i | \(-0.107542\pi\) |
−0.758789 | + | 0.651336i | \(0.774209\pi\) | |||||||
\(734\) | −20.0000 | −0.738213 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −2.00000 | − | 3.46410i | −0.0736709 | − | 0.127602i | ||||
\(738\) | −3.00000 | + | 5.19615i | −0.110432 | + | 0.191273i | ||||
\(739\) | 10.0000 | − | 17.3205i | 0.367856 | − | 0.637145i | −0.621374 | − | 0.783514i | \(-0.713425\pi\) |
0.989230 | + | 0.146369i | \(0.0467586\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0000 | 0.440831 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.00000 | −0.220119 | −0.110059 | − | 0.993925i | \(-0.535104\pi\) | ||||
−0.110059 | + | 0.993925i | \(0.535104\pi\) | |||||||
\(744\) | −3.00000 | − | 5.19615i | −0.109985 | − | 0.190500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 17.0000 | − | 29.4449i | 0.622414 | − | 1.07805i | ||||
\(747\) | 8.00000 | + | 13.8564i | 0.292705 | + | 0.506979i | ||||
\(748\) | 1.00000 | 0.0365636 | ||||||||
\(749\) | −5.00000 | − | 1.73205i | −0.182696 | − | 0.0632878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.0000 | + | 29.4449i | 0.620339 | + | 1.07446i | 0.989423 | + | 0.145062i | \(0.0463382\pi\) |
−0.369084 | + | 0.929396i | \(0.620328\pi\) | |||||||
\(752\) | 0.500000 | − | 0.866025i | 0.0182331 | − | 0.0315807i | ||||
\(753\) | −3.50000 | + | 6.06218i | −0.127547 | + | 0.220918i | ||||
\(754\) | −2.00000 | − | 3.46410i | −0.0728357 | − | 0.126155i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.500000 | − | 2.59808i | −0.0181848 | − | 0.0944911i | ||||
\(757\) | 29.0000 | 1.05402 | 0.527011 | − | 0.849858i | \(-0.323312\pi\) | ||||
0.527011 | + | 0.849858i | \(0.323312\pi\) | |||||||
\(758\) | −11.0000 | − | 19.0526i | −0.399538 | − | 0.692020i | ||||
\(759\) | 0.500000 | − | 0.866025i | 0.0181489 | − | 0.0314347i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.00000 | + | 15.5885i | 0.326250 | + | 0.565081i | 0.981764 | − | 0.190101i | \(-0.0608816\pi\) |
−0.655515 | + | 0.755182i | \(0.727548\pi\) | |||||||
\(762\) | −7.00000 | −0.253583 | ||||||||
\(763\) | −9.00000 | − | 46.7654i | −0.325822 | − | 1.69302i | ||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 14.5000 | − | 25.1147i | 0.523906 | − | 0.907432i | ||||
\(767\) | −14.0000 | + | 24.2487i | −0.505511 | + | 0.875570i | ||||
\(768\) | 0.500000 | + | 0.866025i | 0.0180422 | + | 0.0312500i | ||||
\(769\) | −22.0000 | −0.793340 | −0.396670 | − | 0.917961i | \(-0.629834\pi\) | ||||
−0.396670 | + | 0.917961i | \(0.629834\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 12.0000 | 0.432169 | ||||||||
\(772\) | −7.00000 | − | 12.1244i | −0.251936 | − | 0.436365i | ||||
\(773\) | −7.00000 | + | 12.1244i | −0.251773 | + | 0.436083i | −0.964014 | − | 0.265852i | \(-0.914347\pi\) |
0.712241 | + | 0.701935i | \(0.247680\pi\) | |||||||
\(774\) | 0.500000 | − | 0.866025i | 0.0179721 | − | 0.0311286i | ||||
\(775\) | 15.0000 | + | 25.9808i | 0.538816 | + | 0.933257i | ||||
\(776\) | −7.00000 | −0.251285 | ||||||||
\(777\) | 6.00000 | − | 5.19615i | 0.215249 | − | 0.186411i | ||||
\(778\) | 28.0000 | 1.00385 | ||||||||
\(779\) | −9.00000 | − | 15.5885i | −0.322458 | − | 0.558514i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.50000 | + | 12.9904i | −0.268371 | + | 0.464832i | ||||
\(782\) | 0.500000 | + | 0.866025i | 0.0178800 | + | 0.0309690i | ||||
\(783\) | 1.00000 | 0.0357371 | ||||||||
\(784\) | −6.50000 | + | 2.59808i | −0.232143 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.00000 | + | 1.73205i | 0.0356688 | + | 0.0617802i | ||||
\(787\) | 5.50000 | − | 9.52628i | 0.196054 | − | 0.339575i | −0.751192 | − | 0.660084i | \(-0.770521\pi\) |
0.947245 | + | 0.320509i | \(0.103854\pi\) | |||||||
\(788\) | −13.5000 | + | 23.3827i | −0.480918 | + | 0.832974i | ||||
\(789\) | −7.00000 | − | 12.1244i | −0.249207 | − | 0.431638i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8.00000 | − | 6.92820i | 0.284447 | − | 0.246339i | ||||
\(792\) | 1.00000 | 0.0355335 | ||||||||
\(793\) | −12.0000 | − | 20.7846i | −0.426132 | − | 0.738083i | ||||
\(794\) | 11.5000 | − | 19.9186i | 0.408120 | − | 0.706884i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.00000 | − | 3.46410i | −0.0708881 | − | 0.122782i | ||||
\(797\) | 42.0000 | 1.48772 | 0.743858 | − | 0.668338i | \(-0.232994\pi\) | ||||
0.743858 | + | 0.668338i | \(0.232994\pi\) | |||||||
\(798\) | 7.50000 | + | 2.59808i | 0.265497 | + | 0.0919709i | ||||
\(799\) | 1.00000 | 0.0353775 | ||||||||
\(800\) | −2.50000 | − | 4.33013i | −0.0883883 | − | 0.153093i | ||||
\(801\) | 4.00000 | − | 6.92820i | 0.141333 | − | 0.244796i | ||||
\(802\) | 1.00000 | − | 1.73205i | 0.0353112 | − | 0.0611608i | ||||
\(803\) | 6.00000 | + | 10.3923i | 0.211735 | + | 0.366736i | ||||
\(804\) | 4.00000 | 0.141069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.0000 | −0.845364 | ||||||||
\(807\) | −9.00000 | − | 15.5885i | −0.316815 | − | 0.548740i | ||||
\(808\) | 7.50000 | − | 12.9904i | 0.263849 | − | 0.457000i | ||||
\(809\) | −21.0000 | + | 36.3731i | −0.738321 | + | 1.27881i | 0.214930 | + | 0.976629i | \(0.431048\pi\) |
−0.953251 | + | 0.302180i | \(0.902286\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 20.0000 | 0.702295 | 0.351147 | − | 0.936320i | \(-0.385792\pi\) | ||||
0.351147 | + | 0.936320i | \(0.385792\pi\) | |||||||
\(812\) | −0.500000 | − | 2.59808i | −0.0175466 | − | 0.0911746i | ||||
\(813\) | 16.0000 | 0.561144 | ||||||||
\(814\) | 1.50000 | + | 2.59808i | 0.0525750 | + | 0.0910625i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −0.500000 | + | 0.866025i | −0.0175035 | + | 0.0303170i | ||||
\(817\) | 1.50000 | + | 2.59808i | 0.0524784 | + | 0.0908952i | ||||
\(818\) | −6.00000 | −0.209785 | ||||||||
\(819\) | −10.0000 | − | 3.46410i | −0.349428 | − | 0.121046i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.00000 | − | 8.66025i | −0.174501 | − | 0.302245i | 0.765487 | − | 0.643451i | \(-0.222498\pi\) |
−0.939989 | + | 0.341206i | \(0.889165\pi\) | |||||||
\(822\) | 2.00000 | − | 3.46410i | 0.0697580 | − | 0.120824i | ||||
\(823\) | −25.0000 | + | 43.3013i | −0.871445 | + | 1.50939i | −0.0109433 | + | 0.999940i | \(0.503483\pi\) |
−0.860502 | + | 0.509447i | \(0.829850\pi\) | |||||||
\(824\) | 2.00000 | + | 3.46410i | 0.0696733 | + | 0.120678i | ||||
\(825\) | −5.00000 | −0.174078 | ||||||||
\(826\) | −14.0000 | + | 12.1244i | −0.487122 | + | 0.421860i | ||||
\(827\) | 30.0000 | 1.04320 | 0.521601 | − | 0.853189i | \(-0.325335\pi\) | ||||
0.521601 | + | 0.853189i | \(0.325335\pi\) | |||||||
\(828\) | 0.500000 | + | 0.866025i | 0.0173762 | + | 0.0300965i | ||||
\(829\) | 3.50000 | − | 6.06218i | 0.121560 | − | 0.210548i | −0.798823 | − | 0.601566i | \(-0.794544\pi\) |
0.920383 | + | 0.391018i | \(0.127877\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.00000 | − | 13.8564i | −0.277517 | − | 0.480673i | ||||
\(832\) | 4.00000 | 0.138675 | ||||||||
\(833\) | −5.50000 | − | 4.33013i | −0.190564 | − | 0.150030i | ||||
\(834\) | −17.0000 | −0.588662 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.50000 | + | 2.59808i | −0.0518786 | + | 0.0898563i | ||||
\(837\) | 3.00000 | − | 5.19615i | 0.103695 | − | 0.179605i | ||||
\(838\) | −8.50000 | − | 14.7224i | −0.293628 | − | 0.508578i | ||||
\(839\) | −4.00000 | −0.138095 | −0.0690477 | − | 0.997613i | \(-0.521996\pi\) | ||||
−0.0690477 | + | 0.997613i | \(0.521996\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.0000 | −0.965517 | ||||||||
\(842\) | −1.50000 | − | 2.59808i | −0.0516934 | − | 0.0895356i | ||||
\(843\) | −13.5000 | + | 23.3827i | −0.464965 | + | 0.805342i | ||||
\(844\) | 10.0000 | − | 17.3205i | 0.344214 | − | 0.596196i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 1.00000 | 0.0343807 | ||||||||
\(847\) | −2.50000 | − | 0.866025i | −0.0859010 | − | 0.0297570i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 10.0000 | + | 17.3205i | 0.343199 | + | 0.594438i | ||||
\(850\) | 2.50000 | − | 4.33013i | 0.0857493 | − | 0.148522i | ||||
\(851\) | −1.50000 | + | 2.59808i | −0.0514193 | + | 0.0890609i | ||||
\(852\) | −7.50000 | − | 12.9904i | −0.256946 | − | 0.445043i | ||||
\(853\) | −36.0000 | −1.23262 | −0.616308 | − | 0.787505i | \(-0.711372\pi\) | ||||
−0.616308 | + | 0.787505i | \(0.711372\pi\) | |||||||
\(854\) | −3.00000 | − | 15.5885i | −0.102658 | − | 0.533426i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.00000 | + | 1.73205i | 0.0341793 | + | 0.0592003i | ||||
\(857\) | −25.5000 | + | 44.1673i | −0.871063 | + | 1.50873i | −0.0101655 | + | 0.999948i | \(0.503236\pi\) |
−0.860898 | + | 0.508778i | \(0.830097\pi\) | |||||||
\(858\) | 2.00000 | − | 3.46410i | 0.0682789 | − | 0.118262i | ||||
\(859\) | −4.00000 | − | 6.92820i | −0.136478 | − | 0.236387i | 0.789683 | − | 0.613515i | \(-0.210245\pi\) |
−0.926161 | + | 0.377128i | \(0.876912\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.00000 | + | 15.5885i | 0.102240 | + | 0.531253i | ||||
\(862\) | 28.0000 | 0.953684 | ||||||||
\(863\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(864\) | −0.500000 | + | 0.866025i | −0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.50000 | − | 16.4545i | −0.322823 | − | 0.559146i | ||||
\(867\) | 16.0000 | 0.543388 | ||||||||
\(868\) | −15.0000 | − | 5.19615i | −0.509133 | − | 0.176369i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.00000 | − | 13.8564i | 0.271070 | − | 0.469506i | ||||
\(872\) | −9.00000 | + | 15.5885i | −0.304778 | + | 0.527892i | ||||
\(873\) | −3.50000 | − | 6.06218i | −0.118457 | − | 0.205174i | ||||
\(874\) | −3.00000 | −0.101477 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −12.0000 | −0.405442 | ||||||||
\(877\) | −16.0000 | − | 27.7128i | −0.540282 | − | 0.935795i | −0.998888 | − | 0.0471555i | \(-0.984984\pi\) |
0.458606 | − | 0.888640i | \(-0.348349\pi\) | |||||||
\(878\) | −5.50000 | + | 9.52628i | −0.185616 | + | 0.321496i | ||||
\(879\) | −7.50000 | + | 12.9904i | −0.252969 | + | 0.438155i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.0000 | −0.404290 | −0.202145 | − | 0.979356i | \(-0.564791\pi\) | ||||
−0.202145 | + | 0.979356i | \(0.564791\pi\) | |||||||
\(882\) | −5.50000 | − | 4.33013i | −0.185195 | − | 0.145803i | ||||
\(883\) | 14.0000 | 0.471138 | 0.235569 | − | 0.971858i | \(-0.424305\pi\) | ||||
0.235569 | + | 0.971858i | \(0.424305\pi\) | |||||||
\(884\) | 2.00000 | + | 3.46410i | 0.0672673 | + | 0.116510i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.50000 | + | 2.59808i | −0.0503935 | + | 0.0872841i | ||||
\(887\) | −4.00000 | − | 6.92820i | −0.134307 | − | 0.232626i | 0.791026 | − | 0.611783i | \(-0.209547\pi\) |
−0.925332 | + | 0.379157i | \(0.876214\pi\) | |||||||
\(888\) | −3.00000 | −0.100673 | ||||||||
\(889\) | −14.0000 | + | 12.1244i | −0.469545 | + | 0.406638i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | + | 0.866025i | 0.0167506 | + | 0.0290129i | ||||
\(892\) | −8.00000 | + | 13.8564i | −0.267860 | + | 0.463947i | ||||
\(893\) | −1.50000 | + | 2.59808i | −0.0501956 | + | 0.0869413i | ||||
\(894\) | −0.500000 | − | 0.866025i | −0.0167225 | − | 0.0289642i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.50000 | + | 0.866025i | 0.0835191 | + | 0.0289319i | ||||
\(897\) | 4.00000 | 0.133556 | ||||||||
\(898\) | −4.00000 | − | 6.92820i | −0.133482 | − | 0.231197i | ||||
\(899\) | 3.00000 | − | 5.19615i | 0.100056 | − | 0.173301i | ||||
\(900\) | 2.50000 | − | 4.33013i | 0.0833333 | − | 0.144338i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −6.00000 | −0.199778 | ||||||||
\(903\) | −0.500000 | − | 2.59808i | −0.0166390 | − | 0.0864586i | ||||
\(904\) | −4.00000 | −0.133038 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.50000 | + | 9.52628i | −0.182725 | + | 0.316489i | ||||
\(907\) | 4.00000 | − | 6.92820i | 0.132818 | − | 0.230047i | −0.791944 | − | 0.610594i | \(-0.790931\pi\) |
0.924762 | + | 0.380547i | \(0.124264\pi\) | |||||||
\(908\) | 1.00000 | + | 1.73205i | 0.0331862 | + | 0.0574801i | ||||
\(909\) | 15.0000 | 0.497519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −21.0000 | −0.695761 | −0.347881 | − | 0.937539i | \(-0.613099\pi\) | ||||
−0.347881 | + | 0.937539i | \(0.613099\pi\) | |||||||
\(912\) | −1.50000 | − | 2.59808i | −0.0496700 | − | 0.0860309i | ||||
\(913\) | −8.00000 | + | 13.8564i | −0.264761 | + | 0.458580i | ||||
\(914\) | 9.00000 | − | 15.5885i | 0.297694 | − | 0.515620i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.00000 | −0.198246 | ||||||||
\(917\) | 5.00000 | + | 1.73205i | 0.165115 | + | 0.0571974i | ||||
\(918\) | −1.00000 | −0.0330049 | ||||||||
\(919\) | 16.5000 | + | 28.5788i | 0.544285 | + | 0.942729i | 0.998652 | + | 0.0519142i | \(0.0165322\pi\) |
−0.454367 | + | 0.890815i | \(0.650134\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −10.0000 | + | 17.3205i | −0.329511 | + | 0.570730i | ||||
\(922\) | 10.5000 | + | 18.1865i | 0.345799 | + | 0.598942i | ||||
\(923\) | −60.0000 | −1.97492 | ||||||||
\(924\) | 2.00000 | − | 1.73205i | 0.0657952 | − | 0.0569803i | ||||
\(925\) | 15.0000 | 0.493197 | ||||||||
\(926\) | −16.0000 | − | 27.7128i | −0.525793 | − | 0.910700i | ||||
\(927\) | −2.00000 | + | 3.46410i | −0.0656886 | + | 0.113776i | ||||
\(928\) | −0.500000 | + | 0.866025i | −0.0164133 | + | 0.0284287i | ||||
\(929\) | −27.0000 | − | 46.7654i | −0.885841 | − | 1.53432i | −0.844746 | − | 0.535167i | \(-0.820249\pi\) |
−0.0410949 | − | 0.999155i | \(-0.513085\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 19.5000 | − | 7.79423i | 0.639087 | − | 0.255446i | ||||
\(932\) | −11.0000 | −0.360317 | ||||||||
\(933\) | −15.5000 | − | 26.8468i | −0.507447 | − | 0.878924i | ||||
\(934\) | −11.5000 | + | 19.9186i | −0.376291 | + | 0.651756i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.00000 | + | 3.46410i | 0.0653720 | + | 0.113228i | ||||
\(937\) | 8.00000 | 0.261349 | 0.130674 | − | 0.991425i | \(-0.458286\pi\) | ||||
0.130674 | + | 0.991425i | \(0.458286\pi\) | |||||||
\(938\) | 8.00000 | − | 6.92820i | 0.261209 | − | 0.226214i | ||||
\(939\) | 33.0000 | 1.07691 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22.5000 | − | 38.9711i | 0.733479 | − | 1.27042i | −0.221908 | − | 0.975068i | \(-0.571229\pi\) |
0.955387 | − | 0.295355i | \(-0.0954381\pi\) | |||||||
\(942\) | 4.50000 | − | 7.79423i | 0.146618 | − | 0.253950i | ||||
\(943\) | −3.00000 | − | 5.19615i | −0.0976934 | − | 0.169210i | ||||
\(944\) | 7.00000 | 0.227831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.00000 | 0.0325128 | ||||||||
\(947\) | 25.5000 | + | 44.1673i | 0.828639 | + | 1.43524i | 0.899106 | + | 0.437730i | \(0.144217\pi\) |
−0.0704677 | + | 0.997514i | \(0.522449\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24.0000 | + | 41.5692i | −0.779073 | + | 1.34939i | ||||
\(950\) | 7.50000 | + | 12.9904i | 0.243332 | + | 0.421464i | ||||
\(951\) | −12.0000 | −0.389127 | ||||||||
\(952\) | 0.500000 | + | 2.59808i | 0.0162051 | + | 0.0842041i | ||||
\(953\) | 14.0000 | 0.453504 | 0.226752 | − | 0.973952i | \(-0.427189\pi\) | ||||
0.226752 | + | 0.973952i | \(0.427189\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −8.00000 | + | 13.8564i | −0.258738 | + | 0.448148i | ||||
\(957\) | 0.500000 | + | 0.866025i | 0.0161627 | + | 0.0279946i | ||||
\(958\) | −10.0000 | −0.323085 | ||||||||
\(959\) | −2.00000 | − | 10.3923i | −0.0645834 | − | 0.335585i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | − | 4.33013i | −0.0806452 | − | 0.139682i | ||||
\(962\) | −6.00000 | + | 10.3923i | −0.193448 | + | 0.335061i | ||||
\(963\) | −1.00000 | + | 1.73205i | −0.0322245 | + | 0.0558146i | ||||
\(964\) | 2.00000 | + | 3.46410i | 0.0644157 | + | 0.111571i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.50000 | + | 0.866025i | 0.0804362 | + | 0.0278639i | ||||
\(967\) | −35.0000 | −1.12552 | −0.562762 | − | 0.826619i | \(-0.690261\pi\) | ||||
−0.562762 | + | 0.826619i | \(0.690261\pi\) | |||||||
\(968\) | 0.500000 | + | 0.866025i | 0.0160706 | + | 0.0278351i | ||||
\(969\) | 1.50000 | − | 2.59808i | 0.0481869 | − | 0.0834622i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −34.0000 | + | 29.4449i | −1.08999 | + | 0.943959i | ||||
\(974\) | −20.0000 | −0.640841 | ||||||||
\(975\) | −10.0000 | − | 17.3205i | −0.320256 | − | 0.554700i | ||||
\(976\) | −3.00000 | + | 5.19615i | −0.0960277 | + | 0.166325i | ||||
\(977\) | −6.00000 | + | 10.3923i | −0.191957 | + | 0.332479i | −0.945899 | − | 0.324462i | \(-0.894817\pi\) |
0.753942 | + | 0.656941i | \(0.228150\pi\) | |||||||
\(978\) | 9.00000 | + | 15.5885i | 0.287788 | + | 0.498464i | ||||
\(979\) | 8.00000 | 0.255681 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.0000 | −0.574696 | ||||||||
\(982\) | 6.00000 | + | 10.3923i | 0.191468 | + | 0.331632i | ||||
\(983\) | −9.50000 | + | 16.4545i | −0.303003 | + | 0.524816i | −0.976815 | − | 0.214087i | \(-0.931323\pi\) |
0.673812 | + | 0.738903i | \(0.264656\pi\) | |||||||
\(984\) | 3.00000 | − | 5.19615i | 0.0956365 | − | 0.165647i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.00000 | −0.0318465 | ||||||||
\(987\) | 2.00000 | − | 1.73205i | 0.0636607 | − | 0.0551318i | ||||
\(988\) | −12.0000 | −0.381771 | ||||||||
\(989\) | 0.500000 | + | 0.866025i | 0.0158991 | + | 0.0275380i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(992\) | 3.00000 | + | 5.19615i | 0.0952501 | + | 0.164978i | ||||
\(993\) | −10.0000 | −0.317340 | ||||||||
\(994\) | −37.5000 | − | 12.9904i | −1.18943 | − | 0.412030i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.00000 | − | 13.8564i | −0.253490 | − | 0.439057i | ||||
\(997\) | 22.0000 | − | 38.1051i | 0.696747 | − | 1.20680i | −0.272841 | − | 0.962059i | \(-0.587963\pi\) |
0.969588 | − | 0.244742i | \(-0.0787033\pi\) | |||||||
\(998\) | 5.00000 | − | 8.66025i | 0.158272 | − | 0.274136i | ||||
\(999\) | −1.50000 | − | 2.59808i | −0.0474579 | − | 0.0821995i |
(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 | 462.2.i.d.67.1 | ✓ | 2 | |
3.2 | odd | 2 | 1386.2.k.f.991.1 | 2 | |||
7.2 | even | 3 | inner | 462.2.i.d.331.1 | yes | 2 | |
7.3 | odd | 6 | 3234.2.a.j.1.1 | 1 | |||
7.4 | even | 3 | 3234.2.a.c.1.1 | 1 | |||
21.2 | odd | 6 | 1386.2.k.f.793.1 | 2 | |||
21.11 | odd | 6 | 9702.2.a.bv.1.1 | 1 | |||
21.17 | even | 6 | 9702.2.a.bq.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.i.d.67.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
462.2.i.d.331.1 | yes | 2 | 7.2 | even | 3 | inner | |
1386.2.k.f.793.1 | 2 | 21.2 | odd | 6 | |||
1386.2.k.f.991.1 | 2 | 3.2 | odd | 2 | |||
3234.2.a.c.1.1 | 1 | 7.4 | even | 3 | |||
3234.2.a.j.1.1 | 1 | 7.3 | odd | 6 | |||
9702.2.a.bq.1.1 | 1 | 21.17 | even | 6 | |||
9702.2.a.bv.1.1 | 1 | 21.11 | odd | 6 |