Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [600,2,Mod(293,600)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(600, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("600.293");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 600 = 2^{3} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 600.w (of order \(4\), 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: | \(4.79102412128\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.1 | ||
Root | \(-0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.293 |
Dual form | 600.2.w.f.557.1 |
$q$-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 \(\left(\mathbb{Z}/600\mathbb{Z}\right)^\times\).
\(n\) | \(151\) | \(301\) | \(401\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.366025 | + | 1.36603i | −0.258819 | + | 0.965926i | ||||
\(3\) | 1.73205i | 1.00000i | ||||||||
\(4\) | −1.73205 | − | 1.00000i | −0.866025 | − | 0.500000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.36603 | − | 0.633975i | −0.965926 | − | 0.258819i | ||||
\(7\) | 3.00000 | − | 3.00000i | 1.13389 | − | 1.13389i | 0.144370 | − | 0.989524i | \(-0.453885\pi\) |
0.989524 | − | 0.144370i | \(-0.0461154\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.707107 | − | 0.707107i | ||||
\(9\) | −3.00000 | −1.00000 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410 | 1.04447 | 0.522233 | − | 0.852803i | \(-0.325099\pi\) | ||||
0.522233 | + | 0.852803i | \(0.325099\pi\) | |||||||
\(12\) | 1.73205 | − | 3.00000i | 0.500000 | − | 0.866025i | ||||
\(13\) | 3.46410 | − | 3.46410i | 0.960769 | − | 0.960769i | −0.0384901 | − | 0.999259i | \(-0.512255\pi\) |
0.999259 | + | 0.0384901i | \(0.0122548\pi\) | |||||||
\(14\) | 3.00000 | + | 5.19615i | 0.801784 | + | 1.38873i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 4.00000 | + | 4.00000i | 0.970143 | + | 0.970143i | 0.999567 | − | 0.0294245i | \(-0.00936746\pi\) |
−0.0294245 | + | 0.999567i | \(0.509367\pi\) | |||||||
\(18\) | 1.09808 | − | 4.09808i | 0.258819 | − | 0.965926i | ||||
\(19\) | −3.46410 | −0.794719 | −0.397360 | − | 0.917663i | \(-0.630073\pi\) | ||||
−0.397360 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.19615 | + | 5.19615i | 1.13389 | + | 1.13389i | ||||
\(22\) | −1.26795 | + | 4.73205i | −0.270328 | + | 1.00888i | ||||
\(23\) | 1.00000 | − | 1.00000i | 0.208514 | − | 0.208514i | −0.595121 | − | 0.803636i | \(-0.702896\pi\) |
0.803636 | + | 0.595121i | \(0.202896\pi\) | |||||||
\(24\) | 3.46410 | + | 3.46410i | 0.707107 | + | 0.707107i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 3.46410 | + | 6.00000i | 0.679366 | + | 1.17670i | ||||
\(27\) | − | 5.19615i | − | 1.00000i | ||||||
\(28\) | −8.19615 | + | 2.19615i | −1.54893 | + | 0.415034i | ||||
\(29\) | − | 3.46410i | − | 0.643268i | −0.946864 | − | 0.321634i | \(-0.895768\pi\) | ||
0.946864 | − | 0.321634i | \(-0.104232\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | −5.46410 | + | 1.46410i | −0.965926 | + | 0.258819i | ||||
\(33\) | 6.00000i | 1.04447i | ||||||||
\(34\) | −6.92820 | + | 4.00000i | −1.18818 | + | 0.685994i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.19615 | + | 3.00000i | 0.866025 | + | 0.500000i | ||||
\(37\) | 0 | 0 | 0.707107 | − | 0.707107i | \(-0.250000\pi\) | ||||
−0.707107 | + | 0.707107i | \(0.750000\pi\) | |||||||
\(38\) | 1.26795 | − | 4.73205i | 0.205689 | − | 0.767640i | ||||
\(39\) | 6.00000 | + | 6.00000i | 0.960769 | + | 0.960769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 6.00000i | − | 0.937043i | −0.883452 | − | 0.468521i | \(-0.844787\pi\) | ||
0.883452 | − | 0.468521i | \(-0.155213\pi\) | |||||||
\(42\) | −9.00000 | + | 5.19615i | −1.38873 | + | 0.801784i | ||||
\(43\) | −1.73205 | + | 1.73205i | −0.264135 | + | 0.264135i | −0.826732 | − | 0.562596i | \(-0.809803\pi\) |
0.562596 | + | 0.826732i | \(0.309803\pi\) | |||||||
\(44\) | −6.00000 | − | 3.46410i | −0.904534 | − | 0.522233i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | + | 1.73205i | 0.147442 | + | 0.255377i | ||||
\(47\) | 5.00000 | + | 5.00000i | 0.729325 | + | 0.729325i | 0.970485 | − | 0.241160i | \(-0.0775280\pi\) |
−0.241160 | + | 0.970485i | \(0.577528\pi\) | |||||||
\(48\) | −6.00000 | + | 3.46410i | −0.866025 | + | 0.500000i | ||||
\(49\) | − | 11.0000i | − | 1.57143i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.92820 | + | 6.92820i | −0.970143 | + | 0.970143i | ||||
\(52\) | −9.46410 | + | 2.53590i | −1.31243 | + | 0.351666i | ||||
\(53\) | 3.46410 | + | 3.46410i | 0.475831 | + | 0.475831i | 0.903796 | − | 0.427965i | \(-0.140769\pi\) |
−0.427965 | + | 0.903796i | \(0.640769\pi\) | |||||||
\(54\) | 7.09808 | + | 1.90192i | 0.965926 | + | 0.258819i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 12.0000i | − | 1.60357i | ||||||
\(57\) | − | 6.00000i | − | 0.794719i | ||||||
\(58\) | 4.73205 | + | 1.26795i | 0.621349 | + | 0.166490i | ||||
\(59\) | 10.3923i | 1.35296i | 0.736460 | + | 0.676481i | \(0.236496\pi\) | ||||
−0.736460 | + | 0.676481i | \(0.763504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.46410i | − | 0.443533i | −0.975100 | − | 0.221766i | \(-0.928818\pi\) | ||
0.975100 | − | 0.221766i | \(-0.0711822\pi\) | |||||||
\(62\) | 1.46410 | − | 5.46410i | 0.185941 | − | 0.693942i | ||||
\(63\) | −9.00000 | + | 9.00000i | −1.13389 | + | 1.13389i | ||||
\(64\) | − | 8.00000i | − | 1.00000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.19615 | − | 2.19615i | −1.00888 | − | 0.270328i | ||||
\(67\) | −5.19615 | − | 5.19615i | −0.634811 | − | 0.634811i | 0.314460 | − | 0.949271i | \(-0.398177\pi\) |
−0.949271 | + | 0.314460i | \(0.898177\pi\) | |||||||
\(68\) | −2.92820 | − | 10.9282i | −0.355097 | − | 1.32524i | ||||
\(69\) | 1.73205 | + | 1.73205i | 0.208514 | + | 0.208514i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.0000i | 1.42414i | 0.702109 | + | 0.712069i | \(0.252242\pi\) | ||||
−0.702109 | + | 0.712069i | \(0.747758\pi\) | |||||||
\(72\) | −6.00000 | + | 6.00000i | −0.707107 | + | 0.707107i | ||||
\(73\) | 6.00000 | + | 6.00000i | 0.702247 | + | 0.702247i | 0.964892 | − | 0.262646i | \(-0.0845950\pi\) |
−0.262646 | + | 0.964892i | \(0.584595\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | + | 3.46410i | 0.688247 | + | 0.397360i | ||||
\(77\) | 10.3923 | − | 10.3923i | 1.18431 | − | 1.18431i | ||||
\(78\) | −10.3923 | + | 6.00000i | −1.17670 | + | 0.679366i | ||||
\(79\) | 8.00000i | 0.900070i | 0.893011 | + | 0.450035i | \(0.148589\pi\) | ||||
−0.893011 | + | 0.450035i | \(0.851411\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 1.00000 | ||||||||
\(82\) | 8.19615 | + | 2.19615i | 0.905114 | + | 0.242524i | ||||
\(83\) | −1.73205 | − | 1.73205i | −0.190117 | − | 0.190117i | 0.605629 | − | 0.795747i | \(-0.292921\pi\) |
−0.795747 | + | 0.605629i | \(0.792921\pi\) | |||||||
\(84\) | −3.80385 | − | 14.1962i | −0.415034 | − | 1.54893i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.73205 | − | 3.00000i | −0.186772 | − | 0.323498i | ||||
\(87\) | 6.00000 | 0.643268 | ||||||||
\(88\) | 6.92820 | − | 6.92820i | 0.738549 | − | 0.738549i | ||||
\(89\) | −12.0000 | −1.27200 | −0.635999 | − | 0.771690i | \(-0.719412\pi\) | ||||
−0.635999 | + | 0.771690i | \(0.719412\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 20.7846i | − | 2.17882i | ||||||
\(92\) | −2.73205 | + | 0.732051i | −0.284836 | + | 0.0763216i | ||||
\(93\) | − | 6.92820i | − | 0.718421i | ||||||
\(94\) | −8.66025 | + | 5.00000i | −0.893237 | + | 0.515711i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −2.53590 | − | 9.46410i | −0.258819 | − | 0.965926i | ||||
\(97\) | 6.00000 | − | 6.00000i | 0.609208 | − | 0.609208i | −0.333531 | − | 0.942739i | \(-0.608240\pi\) |
0.942739 | + | 0.333531i | \(0.108240\pi\) | |||||||
\(98\) | 15.0263 | + | 4.02628i | 1.51788 | + | 0.406716i | ||||
\(99\) | −10.3923 | −1.04447 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.46410 | −0.344691 | −0.172345 | − | 0.985037i | \(-0.555135\pi\) | ||||
−0.172345 | + | 0.985037i | \(0.555135\pi\) | |||||||
\(102\) | −6.92820 | − | 12.0000i | −0.685994 | − | 1.18818i | ||||
\(103\) | 3.00000 | + | 3.00000i | 0.295599 | + | 0.295599i | 0.839287 | − | 0.543688i | \(-0.182973\pi\) |
−0.543688 | + | 0.839287i | \(0.682973\pi\) | |||||||
\(104\) | − | 13.8564i | − | 1.35873i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | + | 3.46410i | −0.582772 | + | 0.336463i | ||||
\(107\) | −5.19615 | + | 5.19615i | −0.502331 | + | 0.502331i | −0.912162 | − | 0.409831i | \(-0.865588\pi\) |
0.409831 | + | 0.912162i | \(0.365588\pi\) | |||||||
\(108\) | −5.19615 | + | 9.00000i | −0.500000 | + | 0.866025i | ||||
\(109\) | 17.3205 | 1.65900 | 0.829502 | − | 0.558504i | \(-0.188624\pi\) | ||||
0.829502 | + | 0.558504i | \(0.188624\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.3923 | + | 4.39230i | 1.54893 | + | 0.415034i | ||||
\(113\) | 2.00000 | − | 2.00000i | 0.188144 | − | 0.188144i | −0.606749 | − | 0.794893i | \(-0.707527\pi\) |
0.794893 | + | 0.606749i | \(0.207527\pi\) | |||||||
\(114\) | 8.19615 | + | 2.19615i | 0.767640 | + | 0.205689i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.46410 | + | 6.00000i | −0.321634 | + | 0.557086i | ||||
\(117\) | −10.3923 | + | 10.3923i | −0.960769 | + | 0.960769i | ||||
\(118\) | −14.1962 | − | 3.80385i | −1.30686 | − | 0.350173i | ||||
\(119\) | 24.0000 | 2.20008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 4.73205 | + | 1.26795i | 0.428420 | + | 0.114795i | ||||
\(123\) | 10.3923 | 0.937043 | ||||||||
\(124\) | 6.92820 | + | 4.00000i | 0.622171 | + | 0.359211i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −9.00000 | − | 15.5885i | −0.801784 | − | 1.38873i | ||||
\(127\) | −3.00000 | + | 3.00000i | −0.266207 | + | 0.266207i | −0.827570 | − | 0.561363i | \(-0.810277\pi\) |
0.561363 | + | 0.827570i | \(0.310277\pi\) | |||||||
\(128\) | 10.9282 | + | 2.92820i | 0.965926 | + | 0.258819i | ||||
\(129\) | −3.00000 | − | 3.00000i | −0.264135 | − | 0.264135i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.3205 | −1.51330 | −0.756650 | − | 0.653820i | \(-0.773165\pi\) | ||||
−0.756650 | + | 0.653820i | \(0.773165\pi\) | |||||||
\(132\) | 6.00000 | − | 10.3923i | 0.522233 | − | 0.904534i | ||||
\(133\) | −10.3923 | + | 10.3923i | −0.901127 | + | 0.901127i | ||||
\(134\) | 9.00000 | − | 5.19615i | 0.777482 | − | 0.448879i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 16.0000 | 1.37199 | ||||||||
\(137\) | 10.0000 | + | 10.0000i | 0.854358 | + | 0.854358i | 0.990666 | − | 0.136309i | \(-0.0435239\pi\) |
−0.136309 | + | 0.990666i | \(0.543524\pi\) | |||||||
\(138\) | −3.00000 | + | 1.73205i | −0.255377 | + | 0.147442i | ||||
\(139\) | 10.3923 | 0.881464 | 0.440732 | − | 0.897639i | \(-0.354719\pi\) | ||||
0.440732 | + | 0.897639i | \(0.354719\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.66025 | + | 8.66025i | −0.729325 | + | 0.729325i | ||||
\(142\) | −16.3923 | − | 4.39230i | −1.37561 | − | 0.368594i | ||||
\(143\) | 12.0000 | − | 12.0000i | 1.00349 | − | 1.00349i | ||||
\(144\) | −6.00000 | − | 10.3923i | −0.500000 | − | 0.866025i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.3923 | + | 6.00000i | −0.860073 | + | 0.496564i | ||||
\(147\) | 19.0526 | 1.57143 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 13.8564i | − | 1.13516i | −0.823318 | − | 0.567581i | \(-0.807880\pi\) | ||
0.823318 | − | 0.567581i | \(-0.192120\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.0000 | −1.62758 | −0.813788 | − | 0.581161i | \(-0.802599\pi\) | ||||
−0.813788 | + | 0.581161i | \(0.802599\pi\) | |||||||
\(152\) | −6.92820 | + | 6.92820i | −0.561951 | + | 0.561951i | ||||
\(153\) | −12.0000 | − | 12.0000i | −0.970143 | − | 0.970143i | ||||
\(154\) | 10.3923 | + | 18.0000i | 0.837436 | + | 1.45048i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.39230 | − | 16.3923i | −0.351666 | − | 1.31243i | ||||
\(157\) | −6.92820 | − | 6.92820i | −0.552931 | − | 0.552931i | 0.374355 | − | 0.927286i | \(-0.377864\pi\) |
−0.927286 | + | 0.374355i | \(0.877864\pi\) | |||||||
\(158\) | −10.9282 | − | 2.92820i | −0.869401 | − | 0.232955i | ||||
\(159\) | −6.00000 | + | 6.00000i | −0.475831 | + | 0.475831i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 6.00000i | − | 0.472866i | ||||||
\(162\) | −3.29423 | + | 12.2942i | −0.258819 | + | 0.965926i | ||||
\(163\) | 8.66025 | − | 8.66025i | 0.678323 | − | 0.678323i | −0.281297 | − | 0.959621i | \(-0.590765\pi\) |
0.959621 | + | 0.281297i | \(0.0907647\pi\) | |||||||
\(164\) | −6.00000 | + | 10.3923i | −0.468521 | + | 0.811503i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.00000 | − | 1.73205i | 0.232845 | − | 0.134433i | ||||
\(167\) | −13.0000 | − | 13.0000i | −1.00597 | − | 1.00597i | −0.999982 | − | 0.00598813i | \(-0.998094\pi\) |
−0.00598813 | − | 0.999982i | \(-0.501906\pi\) | |||||||
\(168\) | 20.7846 | 1.60357 | ||||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3923 | 0.794719 | ||||||||
\(172\) | 4.73205 | − | 1.26795i | 0.360815 | − | 0.0966802i | ||||
\(173\) | 6.92820 | + | 6.92820i | 0.526742 | + | 0.526742i | 0.919599 | − | 0.392858i | \(-0.128514\pi\) |
−0.392858 | + | 0.919599i | \(0.628514\pi\) | |||||||
\(174\) | −2.19615 | + | 8.19615i | −0.166490 | + | 0.621349i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.92820 | + | 12.0000i | 0.522233 | + | 0.904534i | ||||
\(177\) | −18.0000 | −1.35296 | ||||||||
\(178\) | 4.39230 | − | 16.3923i | 0.329217 | − | 1.22866i | ||||
\(179\) | − | 10.3923i | − | 0.776757i | −0.921500 | − | 0.388379i | \(-0.873035\pi\) | ||
0.921500 | − | 0.388379i | \(-0.126965\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 13.8564i | − | 1.02994i | −0.857209 | − | 0.514969i | \(-0.827803\pi\) | ||
0.857209 | − | 0.514969i | \(-0.172197\pi\) | |||||||
\(182\) | 28.3923 | + | 7.60770i | 2.10458 | + | 0.563920i | ||||
\(183\) | 6.00000 | 0.443533 | ||||||||
\(184\) | − | 4.00000i | − | 0.294884i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 9.46410 | + | 2.53590i | 0.693942 | + | 0.185941i | ||||
\(187\) | 13.8564 | + | 13.8564i | 1.01328 | + | 1.01328i | ||||
\(188\) | −3.66025 | − | 13.6603i | −0.266951 | − | 0.996276i | ||||
\(189\) | −15.5885 | − | 15.5885i | −1.13389 | − | 1.13389i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 12.0000i | − | 0.868290i | −0.900843 | − | 0.434145i | \(-0.857051\pi\) | ||
0.900843 | − | 0.434145i | \(-0.142949\pi\) | |||||||
\(192\) | 13.8564 | 1.00000 | ||||||||
\(193\) | −18.0000 | − | 18.0000i | −1.29567 | − | 1.29567i | −0.931226 | − | 0.364442i | \(-0.881260\pi\) |
−0.364442 | − | 0.931226i | \(-0.618740\pi\) | |||||||
\(194\) | 6.00000 | + | 10.3923i | 0.430775 | + | 0.746124i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −11.0000 | + | 19.0526i | −0.785714 | + | 1.36090i | ||||
\(197\) | −3.46410 | + | 3.46410i | −0.246807 | + | 0.246807i | −0.819659 | − | 0.572852i | \(-0.805837\pi\) |
0.572852 | + | 0.819659i | \(0.305837\pi\) | |||||||
\(198\) | 3.80385 | − | 14.1962i | 0.270328 | − | 1.00888i | ||||
\(199\) | 4.00000i | 0.283552i | 0.989899 | + | 0.141776i | \(0.0452813\pi\) | ||||
−0.989899 | + | 0.141776i | \(0.954719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 9.00000 | − | 9.00000i | 0.634811 | − | 0.634811i | ||||
\(202\) | 1.26795 | − | 4.73205i | 0.0892126 | − | 0.332946i | ||||
\(203\) | −10.3923 | − | 10.3923i | −0.729397 | − | 0.729397i | ||||
\(204\) | 18.9282 | − | 5.07180i | 1.32524 | − | 0.355097i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.19615 | + | 3.00000i | −0.362033 | + | 0.209020i | ||||
\(207\) | −3.00000 | + | 3.00000i | −0.208514 | + | 0.208514i | ||||
\(208\) | 18.9282 | + | 5.07180i | 1.31243 | + | 0.351666i | ||||
\(209\) | −12.0000 | −0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.46410i | 0.238479i | 0.992866 | + | 0.119239i | \(0.0380456\pi\) | ||||
−0.992866 | + | 0.119239i | \(0.961954\pi\) | |||||||
\(212\) | −2.53590 | − | 9.46410i | −0.174166 | − | 0.649997i | ||||
\(213\) | −20.7846 | −1.42414 | ||||||||
\(214\) | −5.19615 | − | 9.00000i | −0.355202 | − | 0.615227i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.3923 | − | 10.3923i | −0.707107 | − | 0.707107i | ||||
\(217\) | −12.0000 | + | 12.0000i | −0.814613 | + | 0.814613i | ||||
\(218\) | −6.33975 | + | 23.6603i | −0.429382 | + | 1.60247i | ||||
\(219\) | −10.3923 | + | 10.3923i | −0.702247 | + | 0.702247i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 27.7128 | 1.86417 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.00000 | − | 3.00000i | −0.200895 | − | 0.200895i | 0.599489 | − | 0.800383i | \(-0.295371\pi\) |
−0.800383 | + | 0.599489i | \(0.795371\pi\) | |||||||
\(224\) | −12.0000 | + | 20.7846i | −0.801784 | + | 1.38873i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.00000 | + | 3.46410i | 0.133038 | + | 0.230429i | ||||
\(227\) | −19.0526 | + | 19.0526i | −1.26456 | + | 1.26456i | −0.315706 | + | 0.948857i | \(0.602241\pi\) |
−0.948857 | + | 0.315706i | \(0.897759\pi\) | |||||||
\(228\) | −6.00000 | + | 10.3923i | −0.397360 | + | 0.688247i | ||||
\(229\) | 13.8564 | 0.915657 | 0.457829 | − | 0.889041i | \(-0.348627\pi\) | ||||
0.457829 | + | 0.889041i | \(0.348627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.0000 | + | 18.0000i | 1.18431 | + | 1.18431i | ||||
\(232\) | −6.92820 | − | 6.92820i | −0.454859 | − | 0.454859i | ||||
\(233\) | −4.00000 | + | 4.00000i | −0.262049 | + | 0.262049i | −0.825886 | − | 0.563837i | \(-0.809325\pi\) |
0.563837 | + | 0.825886i | \(0.309325\pi\) | |||||||
\(234\) | −10.3923 | − | 18.0000i | −0.679366 | − | 1.17670i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 10.3923 | − | 18.0000i | 0.676481 | − | 1.17170i | ||||
\(237\) | −13.8564 | −0.900070 | ||||||||
\(238\) | −8.78461 | + | 32.7846i | −0.569422 | + | 2.12511i | ||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | −0.366025 | + | 1.36603i | −0.0235290 | + | 0.0878114i | ||||
\(243\) | 15.5885i | 1.00000i | ||||||||
\(244\) | −3.46410 | + | 6.00000i | −0.221766 | + | 0.384111i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.80385 | + | 14.1962i | −0.242524 | + | 0.905114i | ||||
\(247\) | −12.0000 | + | 12.0000i | −0.763542 | + | 0.763542i | ||||
\(248\) | −8.00000 | + | 8.00000i | −0.508001 | + | 0.508001i | ||||
\(249\) | 3.00000 | − | 3.00000i | 0.190117 | − | 0.190117i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.46410 | 0.218652 | 0.109326 | − | 0.994006i | \(-0.465131\pi\) | ||||
0.109326 | + | 0.994006i | \(0.465131\pi\) | |||||||
\(252\) | 24.5885 | − | 6.58846i | 1.54893 | − | 0.415034i | ||||
\(253\) | 3.46410 | − | 3.46410i | 0.217786 | − | 0.217786i | ||||
\(254\) | −3.00000 | − | 5.19615i | −0.188237 | − | 0.326036i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −10.0000 | − | 10.0000i | −0.623783 | − | 0.623783i | 0.322714 | − | 0.946497i | \(-0.395405\pi\) |
−0.946497 | + | 0.322714i | \(0.895405\pi\) | |||||||
\(258\) | 5.19615 | − | 3.00000i | 0.323498 | − | 0.186772i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 10.3923i | 0.643268i | ||||||||
\(262\) | 6.33975 | − | 23.6603i | 0.391671 | − | 1.46174i | ||||
\(263\) | −7.00000 | + | 7.00000i | −0.431638 | + | 0.431638i | −0.889185 | − | 0.457547i | \(-0.848728\pi\) |
0.457547 | + | 0.889185i | \(0.348728\pi\) | |||||||
\(264\) | 12.0000 | + | 12.0000i | 0.738549 | + | 0.738549i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.3923 | − | 18.0000i | −0.637193 | − | 1.10365i | ||||
\(267\) | − | 20.7846i | − | 1.27200i | ||||||
\(268\) | 3.80385 | + | 14.1962i | 0.232357 | + | 0.867168i | ||||
\(269\) | 27.7128i | 1.68968i | 0.535019 | + | 0.844840i | \(0.320304\pi\) | ||||
−0.535019 | + | 0.844840i | \(0.679696\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | −5.85641 | + | 21.8564i | −0.355097 | + | 1.32524i | ||||
\(273\) | 36.0000 | 2.17882 | ||||||||
\(274\) | −17.3205 | + | 10.0000i | −1.04637 | + | 0.604122i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.26795 | − | 4.73205i | −0.0763216 | − | 0.284836i | ||||
\(277\) | 20.7846 | + | 20.7846i | 1.24883 | + | 1.24883i | 0.956239 | + | 0.292587i | \(0.0945162\pi\) |
0.292587 | + | 0.956239i | \(0.405484\pi\) | |||||||
\(278\) | −3.80385 | + | 14.1962i | −0.228140 | + | 0.851429i | ||||
\(279\) | 12.0000 | 0.718421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.0000i | 1.07379i | 0.843649 | + | 0.536895i | \(0.180403\pi\) | ||||
−0.843649 | + | 0.536895i | \(0.819597\pi\) | |||||||
\(282\) | −8.66025 | − | 15.0000i | −0.515711 | − | 0.893237i | ||||
\(283\) | −5.19615 | + | 5.19615i | −0.308879 | + | 0.308879i | −0.844475 | − | 0.535595i | \(-0.820087\pi\) |
0.535595 | + | 0.844475i | \(0.320087\pi\) | |||||||
\(284\) | 12.0000 | − | 20.7846i | 0.712069 | − | 1.23334i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 12.0000 | + | 20.7846i | 0.709575 | + | 1.22902i | ||||
\(287\) | −18.0000 | − | 18.0000i | −1.06251 | − | 1.06251i | ||||
\(288\) | 16.3923 | − | 4.39230i | 0.965926 | − | 0.258819i | ||||
\(289\) | 15.0000i | 0.882353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3923 | + | 10.3923i | 0.609208 | + | 0.609208i | ||||
\(292\) | −4.39230 | − | 16.3923i | −0.257040 | − | 0.959287i | ||||
\(293\) | −6.92820 | − | 6.92820i | −0.404750 | − | 0.404750i | 0.475153 | − | 0.879903i | \(-0.342393\pi\) |
−0.879903 | + | 0.475153i | \(0.842393\pi\) | |||||||
\(294\) | −6.97372 | + | 26.0263i | −0.406716 | + | 1.51788i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 18.0000i | − | 1.04447i | ||||||
\(298\) | 18.9282 | + | 5.07180i | 1.09648 | + | 0.293801i | ||||
\(299\) | − | 6.92820i | − | 0.400668i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3923i | 0.599002i | ||||||||
\(302\) | 7.32051 | − | 27.3205i | 0.421248 | − | 1.57212i | ||||
\(303\) | − | 6.00000i | − | 0.344691i | ||||||
\(304\) | −6.92820 | − | 12.0000i | −0.397360 | − | 0.688247i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 20.7846 | − | 12.0000i | 1.18818 | − | 0.685994i | ||||
\(307\) | −1.73205 | − | 1.73205i | −0.0988534 | − | 0.0988534i | 0.655951 | − | 0.754804i | \(-0.272268\pi\) |
−0.754804 | + | 0.655951i | \(0.772268\pi\) | |||||||
\(308\) | −28.3923 | + | 7.60770i | −1.61780 | + | 0.433489i | ||||
\(309\) | −5.19615 | + | 5.19615i | −0.295599 | + | 0.295599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 24.0000 | 1.35873 | ||||||||
\(313\) | 12.0000 | + | 12.0000i | 0.678280 | + | 0.678280i | 0.959611 | − | 0.281331i | \(-0.0907758\pi\) |
−0.281331 | + | 0.959611i | \(0.590776\pi\) | |||||||
\(314\) | 12.0000 | − | 6.92820i | 0.677199 | − | 0.390981i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.00000 | − | 13.8564i | 0.450035 | − | 0.779484i | ||||
\(317\) | 24.2487 | − | 24.2487i | 1.36194 | − | 1.36194i | 0.490505 | − | 0.871438i | \(-0.336812\pi\) |
0.871438 | − | 0.490505i | \(-0.163188\pi\) | |||||||
\(318\) | −6.00000 | − | 10.3923i | −0.336463 | − | 0.582772i | ||||
\(319\) | − | 12.0000i | − | 0.671871i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | − | 9.00000i | −0.502331 | − | 0.502331i | ||||
\(322\) | 8.19615 | + | 2.19615i | 0.456754 | + | 0.122387i | ||||
\(323\) | −13.8564 | − | 13.8564i | −0.770991 | − | 0.770991i | ||||
\(324\) | −15.5885 | − | 9.00000i | −0.866025 | − | 0.500000i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.66025 | + | 15.0000i | 0.479647 | + | 0.830773i | ||||
\(327\) | 30.0000i | 1.65900i | ||||||||
\(328\) | −12.0000 | − | 12.0000i | −0.662589 | − | 0.662589i | ||||
\(329\) | 30.0000 | 1.65395 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.3923i | 0.571213i | 0.958347 | + | 0.285606i | \(0.0921950\pi\) | ||||
−0.958347 | + | 0.285606i | \(0.907805\pi\) | |||||||
\(332\) | 1.26795 | + | 4.73205i | 0.0695878 | + | 0.259705i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.5167 | − | 13.0000i | 1.23206 | − | 0.711328i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −7.60770 | + | 28.3923i | −0.415034 | + | 1.54893i | ||||
\(337\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(338\) | 15.0263 | + | 4.02628i | 0.817322 | + | 0.219001i | ||||
\(339\) | 3.46410 | + | 3.46410i | 0.188144 | + | 0.188144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.8564 | −0.750366 | ||||||||
\(342\) | −3.80385 | + | 14.1962i | −0.205689 | + | 0.767640i | ||||
\(343\) | −12.0000 | − | 12.0000i | −0.647939 | − | 0.647939i | ||||
\(344\) | 6.92820i | 0.373544i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.0000 | + | 6.92820i | −0.645124 | + | 0.372463i | ||||
\(347\) | −15.5885 | + | 15.5885i | −0.836832 | + | 0.836832i | −0.988441 | − | 0.151608i | \(-0.951555\pi\) |
0.151608 | + | 0.988441i | \(0.451555\pi\) | |||||||
\(348\) | −10.3923 | − | 6.00000i | −0.557086 | − | 0.321634i | ||||
\(349\) | −27.7128 | −1.48343 | −0.741716 | − | 0.670714i | \(-0.765988\pi\) | ||||
−0.741716 | + | 0.670714i | \(0.765988\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0000 | − | 18.0000i | −0.960769 | − | 0.960769i | ||||
\(352\) | −18.9282 | + | 5.07180i | −1.00888 | + | 0.270328i | ||||
\(353\) | −14.0000 | + | 14.0000i | −0.745145 | + | 0.745145i | −0.973563 | − | 0.228418i | \(-0.926645\pi\) |
0.228418 | + | 0.973563i | \(0.426645\pi\) | |||||||
\(354\) | 6.58846 | − | 24.5885i | 0.350173 | − | 1.30686i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 20.7846 | + | 12.0000i | 1.10158 | + | 0.635999i | ||||
\(357\) | 41.5692i | 2.20008i | ||||||||
\(358\) | 14.1962 | + | 3.80385i | 0.750290 | + | 0.201040i | ||||
\(359\) | 12.0000 | 0.633336 | 0.316668 | − | 0.948536i | \(-0.397436\pi\) | ||||
0.316668 | + | 0.948536i | \(0.397436\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | 18.9282 | + | 5.07180i | 0.994844 | + | 0.266568i | ||||
\(363\) | 1.73205i | 0.0909091i | ||||||||
\(364\) | −20.7846 | + | 36.0000i | −1.08941 | + | 1.88691i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −2.19615 | + | 8.19615i | −0.114795 | + | 0.428420i | ||||
\(367\) | 9.00000 | − | 9.00000i | 0.469796 | − | 0.469796i | −0.432052 | − | 0.901849i | \(-0.642210\pi\) |
0.901849 | + | 0.432052i | \(0.142210\pi\) | |||||||
\(368\) | 5.46410 | + | 1.46410i | 0.284836 | + | 0.0763216i | ||||
\(369\) | 18.0000i | 0.937043i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.7846 | 1.07908 | ||||||||
\(372\) | −6.92820 | + | 12.0000i | −0.359211 | + | 0.622171i | ||||
\(373\) | 6.92820 | − | 6.92820i | 0.358729 | − | 0.358729i | −0.504615 | − | 0.863344i | \(-0.668366\pi\) |
0.863344 | + | 0.504615i | \(0.168366\pi\) | |||||||
\(374\) | −24.0000 | + | 13.8564i | −1.24101 | + | 0.716498i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.0000 | 1.03142 | ||||||||
\(377\) | −12.0000 | − | 12.0000i | −0.618031 | − | 0.618031i | ||||
\(378\) | 27.0000 | − | 15.5885i | 1.38873 | − | 0.801784i | ||||
\(379\) | −3.46410 | −0.177939 | −0.0889695 | − | 0.996034i | \(-0.528357\pi\) | ||||
−0.0889695 | + | 0.996034i | \(0.528357\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.19615 | − | 5.19615i | −0.266207 | − | 0.266207i | ||||
\(382\) | 16.3923 | + | 4.39230i | 0.838703 | + | 0.224730i | ||||
\(383\) | 1.00000 | − | 1.00000i | 0.0510976 | − | 0.0510976i | −0.681096 | − | 0.732194i | \(-0.738496\pi\) |
0.732194 | + | 0.681096i | \(0.238496\pi\) | |||||||
\(384\) | −5.07180 | + | 18.9282i | −0.258819 | + | 0.965926i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 31.1769 | − | 18.0000i | 1.58686 | − | 0.916176i | ||||
\(387\) | 5.19615 | − | 5.19615i | 0.264135 | − | 0.264135i | ||||
\(388\) | −16.3923 | + | 4.39230i | −0.832193 | + | 0.222985i | ||||
\(389\) | 13.8564i | 0.702548i | 0.936273 | + | 0.351274i | \(0.114251\pi\) | ||||
−0.936273 | + | 0.351274i | \(0.885749\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.00000 | 0.404577 | ||||||||
\(392\) | −22.0000 | − | 22.0000i | −1.11117 | − | 1.11117i | ||||
\(393\) | − | 30.0000i | − | 1.51330i | ||||||
\(394\) | −3.46410 | − | 6.00000i | −0.174519 | − | 0.302276i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 18.0000 | + | 10.3923i | 0.904534 | + | 0.522233i | ||||
\(397\) | −17.3205 | − | 17.3205i | −0.869291 | − | 0.869291i | 0.123103 | − | 0.992394i | \(-0.460716\pi\) |
−0.992394 | + | 0.123103i | \(0.960716\pi\) | |||||||
\(398\) | −5.46410 | − | 1.46410i | −0.273891 | − | 0.0733888i | ||||
\(399\) | −18.0000 | − | 18.0000i | −0.901127 | − | 0.901127i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.0000i | 0.599251i | 0.954057 | + | 0.299626i | \(0.0968618\pi\) | ||||
−0.954057 | + | 0.299626i | \(0.903138\pi\) | |||||||
\(402\) | 9.00000 | + | 15.5885i | 0.448879 | + | 0.777482i | ||||
\(403\) | −13.8564 | + | 13.8564i | −0.690237 | + | 0.690237i | ||||
\(404\) | 6.00000 | + | 3.46410i | 0.298511 | + | 0.172345i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 18.0000 | − | 10.3923i | 0.893325 | − | 0.515761i | ||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 27.7128i | 1.37199i | ||||||||
\(409\) | 4.00000i | 0.197787i | 0.995098 | + | 0.0988936i | \(0.0315304\pi\) | ||||
−0.995098 | + | 0.0988936i | \(0.968470\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −17.3205 | + | 17.3205i | −0.854358 | + | 0.854358i | ||||
\(412\) | −2.19615 | − | 8.19615i | −0.108197 | − | 0.403795i | ||||
\(413\) | 31.1769 | + | 31.1769i | 1.53412 | + | 1.53412i | ||||
\(414\) | −3.00000 | − | 5.19615i | −0.147442 | − | 0.255377i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −13.8564 | + | 24.0000i | −0.679366 | + | 1.17670i | ||||
\(417\) | 18.0000i | 0.881464i | ||||||||
\(418\) | 4.39230 | − | 16.3923i | 0.214835 | − | 0.801774i | ||||
\(419\) | 24.2487i | 1.18463i | 0.805708 | + | 0.592314i | \(0.201785\pi\) | ||||
−0.805708 | + | 0.592314i | \(0.798215\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.46410i | 0.168830i | 0.996431 | + | 0.0844150i | \(0.0269021\pi\) | ||||
−0.996431 | + | 0.0844150i | \(0.973098\pi\) | |||||||
\(422\) | −4.73205 | − | 1.26795i | −0.230353 | − | 0.0617228i | ||||
\(423\) | −15.0000 | − | 15.0000i | −0.729325 | − | 0.729325i | ||||
\(424\) | 13.8564 | 0.672927 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 7.60770 | − | 28.3923i | 0.368594 | − | 1.37561i | ||||
\(427\) | −10.3923 | − | 10.3923i | −0.502919 | − | 0.502919i | ||||
\(428\) | 14.1962 | − | 3.80385i | 0.686197 | − | 0.183866i | ||||
\(429\) | 20.7846 | + | 20.7846i | 1.00349 | + | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 12.0000i | − | 0.578020i | −0.957326 | − | 0.289010i | \(-0.906674\pi\) | ||
0.957326 | − | 0.289010i | \(-0.0933260\pi\) | |||||||
\(432\) | 18.0000 | − | 10.3923i | 0.866025 | − | 0.500000i | ||||
\(433\) | −6.00000 | − | 6.00000i | −0.288342 | − | 0.288342i | 0.548083 | − | 0.836424i | \(-0.315358\pi\) |
−0.836424 | + | 0.548083i | \(0.815358\pi\) | |||||||
\(434\) | −12.0000 | − | 20.7846i | −0.576018 | − | 0.997693i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −30.0000 | − | 17.3205i | −1.43674 | − | 0.829502i | ||||
\(437\) | −3.46410 | + | 3.46410i | −0.165710 | + | 0.165710i | ||||
\(438\) | −10.3923 | − | 18.0000i | −0.496564 | − | 0.860073i | ||||
\(439\) | − | 32.0000i | − | 1.52728i | −0.645644 | − | 0.763638i | \(-0.723411\pi\) | ||
0.645644 | − | 0.763638i | \(-0.276589\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 33.0000i | 1.57143i | ||||||||
\(442\) | −10.1436 | + | 37.8564i | −0.482482 | + | 1.80065i | ||||
\(443\) | 8.66025 | + | 8.66025i | 0.411461 | + | 0.411461i | 0.882247 | − | 0.470786i | \(-0.156030\pi\) |
−0.470786 | + | 0.882247i | \(0.656030\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.19615 | − | 3.00000i | 0.246045 | − | 0.142054i | ||||
\(447\) | 24.0000 | 1.13516 | ||||||||
\(448\) | −24.0000 | − | 24.0000i | −1.13389 | − | 1.13389i | ||||
\(449\) | 18.0000 | 0.849473 | 0.424736 | − | 0.905317i | \(-0.360367\pi\) | ||||
0.424736 | + | 0.905317i | \(0.360367\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 20.7846i | − | 0.978709i | ||||||
\(452\) | −5.46410 | + | 1.46410i | −0.257010 | + | 0.0688655i | ||||
\(453\) | − | 34.6410i | − | 1.62758i | ||||||
\(454\) | −19.0526 | − | 33.0000i | −0.894181 | − | 1.54877i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −12.0000 | − | 12.0000i | −0.561951 | − | 0.561951i | ||||
\(457\) | −12.0000 | + | 12.0000i | −0.561336 | + | 0.561336i | −0.929687 | − | 0.368351i | \(-0.879923\pi\) |
0.368351 | + | 0.929687i | \(0.379923\pi\) | |||||||
\(458\) | −5.07180 | + | 18.9282i | −0.236989 | + | 0.884457i | ||||
\(459\) | 20.7846 | − | 20.7846i | 0.970143 | − | 0.970143i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −31.1769 | −1.45205 | −0.726027 | − | 0.687666i | \(-0.758635\pi\) | ||||
−0.726027 | + | 0.687666i | \(0.758635\pi\) | |||||||
\(462\) | −31.1769 | + | 18.0000i | −1.45048 | + | 0.837436i | ||||
\(463\) | 9.00000 | + | 9.00000i | 0.418265 | + | 0.418265i | 0.884606 | − | 0.466340i | \(-0.154428\pi\) |
−0.466340 | + | 0.884606i | \(0.654428\pi\) | |||||||
\(464\) | 12.0000 | − | 6.92820i | 0.557086 | − | 0.321634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.00000 | − | 6.92820i | −0.185296 | − | 0.320943i | ||||
\(467\) | 8.66025 | − | 8.66025i | 0.400749 | − | 0.400749i | −0.477748 | − | 0.878497i | \(-0.658547\pi\) |
0.878497 | + | 0.477748i | \(0.158547\pi\) | |||||||
\(468\) | 28.3923 | − | 7.60770i | 1.31243 | − | 0.351666i | ||||
\(469\) | −31.1769 | −1.43962 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.0000 | − | 12.0000i | 0.552931 | − | 0.552931i | ||||
\(472\) | 20.7846 | + | 20.7846i | 0.956689 | + | 0.956689i | ||||
\(473\) | −6.00000 | + | 6.00000i | −0.275880 | + | 0.275880i | ||||
\(474\) | 5.07180 | − | 18.9282i | 0.232955 | − | 0.869401i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −41.5692 | − | 24.0000i | −1.90532 | − | 1.10004i | ||||
\(477\) | −10.3923 | − | 10.3923i | −0.475831 | − | 0.475831i | ||||
\(478\) | 8.78461 | − | 32.7846i | 0.401799 | − | 1.49953i | ||||
\(479\) | −36.0000 | −1.64488 | −0.822441 | − | 0.568850i | \(-0.807388\pi\) | ||||
−0.822441 | + | 0.568850i | \(0.807388\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 2.92820 | − | 10.9282i | 0.133376 | − | 0.497766i | ||||
\(483\) | 10.3923 | 0.472866 | ||||||||
\(484\) | −1.73205 | − | 1.00000i | −0.0787296 | − | 0.0454545i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −21.2942 | − | 5.70577i | −0.965926 | − | 0.258819i | ||||
\(487\) | 15.0000 | − | 15.0000i | 0.679715 | − | 0.679715i | −0.280221 | − | 0.959936i | \(-0.590408\pi\) |
0.959936 | + | 0.280221i | \(0.0904077\pi\) | |||||||
\(488\) | −6.92820 | − | 6.92820i | −0.313625 | − | 0.313625i | ||||
\(489\) | 15.0000 | + | 15.0000i | 0.678323 | + | 0.678323i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.3923 | −0.468998 | −0.234499 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234499 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(492\) | −18.0000 | − | 10.3923i | −0.811503 | − | 0.468521i | ||||
\(493\) | 13.8564 | − | 13.8564i | 0.624061 | − | 0.624061i | ||||
\(494\) | −12.0000 | − | 20.7846i | −0.539906 | − | 0.935144i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.00000 | − | 13.8564i | −0.359211 | − | 0.622171i | ||||
\(497\) | 36.0000 | + | 36.0000i | 1.61482 | + | 1.61482i | ||||
\(498\) | 3.00000 | + | 5.19615i | 0.134433 | + | 0.232845i | ||||
\(499\) | 24.2487 | 1.08552 | 0.542761 | − | 0.839887i | \(-0.317379\pi\) | ||||
0.542761 | + | 0.839887i | \(0.317379\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.5167 | − | 22.5167i | 1.00597 | − | 1.00597i | ||||
\(502\) | −1.26795 | + | 4.73205i | −0.0565913 | + | 0.211202i | ||||
\(503\) | 5.00000 | − | 5.00000i | 0.222939 | − | 0.222939i | −0.586796 | − | 0.809735i | \(-0.699611\pi\) |
0.809735 | + | 0.586796i | \(0.199611\pi\) | |||||||
\(504\) | 36.0000i | 1.60357i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 3.46410 | + | 6.00000i | 0.153998 | + | 0.266733i | ||||
\(507\) | 19.0526 | 0.846154 | ||||||||
\(508\) | 8.19615 | − | 2.19615i | 0.363645 | − | 0.0974385i | ||||
\(509\) | − | 38.1051i | − | 1.68898i | −0.535572 | − | 0.844490i | \(-0.679904\pi\) | ||
0.535572 | − | 0.844490i | \(-0.320096\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 36.0000 | 1.59255 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.707107 | − | 0.707107i | ||||
\(513\) | 18.0000i | 0.794719i | ||||||||
\(514\) | 17.3205 | − | 10.0000i | 0.763975 | − | 0.441081i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.19615 | + | 8.19615i | 0.0966802 | + | 0.360815i | ||||
\(517\) | 17.3205 | + | 17.3205i | 0.761755 | + | 0.761755i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −12.0000 | + | 12.0000i | −0.526742 | + | 0.526742i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 24.0000i | − | 1.05146i | −0.850652 | − | 0.525730i | \(-0.823792\pi\) | ||
0.850652 | − | 0.525730i | \(-0.176208\pi\) | |||||||
\(522\) | −14.1962 | − | 3.80385i | −0.621349 | − | 0.166490i | ||||
\(523\) | −8.66025 | + | 8.66025i | −0.378686 | + | 0.378686i | −0.870628 | − | 0.491942i | \(-0.836287\pi\) |
0.491942 | + | 0.870628i | \(0.336287\pi\) | |||||||
\(524\) | 30.0000 | + | 17.3205i | 1.31056 | + | 0.756650i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −7.00000 | − | 12.1244i | −0.305215 | − | 0.528647i | ||||
\(527\) | −16.0000 | − | 16.0000i | −0.696971 | − | 0.696971i | ||||
\(528\) | −20.7846 | + | 12.0000i | −0.904534 | + | 0.522233i | ||||
\(529\) | 21.0000i | 0.913043i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 31.1769i | − | 1.35296i | ||||||
\(532\) | 28.3923 | − | 7.60770i | 1.23096 | − | 0.329835i | ||||
\(533\) | −20.7846 | − | 20.7846i | −0.900281 | − | 0.900281i | ||||
\(534\) | 28.3923 | + | 7.60770i | 1.22866 | + | 0.329217i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −20.7846 | −0.897758 | ||||||||
\(537\) | 18.0000 | 0.776757 | ||||||||
\(538\) | −37.8564 | − | 10.1436i | −1.63211 | − | 0.437321i | ||||
\(539\) | − | 38.1051i | − | 1.64130i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 41.5692i | − | 1.78720i | −0.448864 | − | 0.893600i | \(-0.648171\pi\) | ||
0.448864 | − | 0.893600i | \(-0.351829\pi\) | |||||||
\(542\) | −2.92820 | + | 10.9282i | −0.125777 | + | 0.469407i | ||||
\(543\) | 24.0000 | 1.02994 | ||||||||
\(544\) | −27.7128 | − | 16.0000i | −1.18818 | − | 0.685994i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.1769 | + | 49.1769i | −0.563920 | + | 2.10458i | ||||
\(547\) | −8.66025 | − | 8.66025i | −0.370286 | − | 0.370286i | 0.497296 | − | 0.867581i | \(-0.334326\pi\) |
−0.867581 | + | 0.497296i | \(0.834326\pi\) | |||||||
\(548\) | −7.32051 | − | 27.3205i | −0.312717 | − | 1.16707i | ||||
\(549\) | 10.3923i | 0.443533i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 12.0000i | 0.511217i | ||||||||
\(552\) | 6.92820 | 0.294884 | ||||||||
\(553\) | 24.0000 | + | 24.0000i | 1.02058 | + | 1.02058i | ||||
\(554\) | −36.0000 | + | 20.7846i | −1.52949 | + | 0.883053i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −18.0000 | − | 10.3923i | −0.763370 | − | 0.440732i | ||||
\(557\) | 20.7846 | − | 20.7846i | 0.880672 | − | 0.880672i | −0.112931 | − | 0.993603i | \(-0.536024\pi\) |
0.993603 | + | 0.112931i | \(0.0360238\pi\) | |||||||
\(558\) | −4.39230 | + | 16.3923i | −0.185941 | + | 0.693942i | ||||
\(559\) | 12.0000i | 0.507546i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | + | 24.0000i | −1.01328 | + | 1.01328i | ||||
\(562\) | −24.5885 | − | 6.58846i | −1.03720 | − | 0.277917i | ||||
\(563\) | 5.19615 | + | 5.19615i | 0.218992 | + | 0.218992i | 0.808073 | − | 0.589082i | \(-0.200510\pi\) |
−0.589082 | + | 0.808073i | \(0.700510\pi\) | |||||||
\(564\) | 23.6603 | − | 6.33975i | 0.996276 | − | 0.266951i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.19615 | − | 9.00000i | −0.218411 | − | 0.378298i | ||||
\(567\) | 27.0000 | − | 27.0000i | 1.13389 | − | 1.13389i | ||||
\(568\) | 24.0000 | + | 24.0000i | 1.00702 | + | 1.00702i | ||||
\(569\) | −6.00000 | −0.251533 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 45.0333i | 1.88459i | 0.334790 | + | 0.942293i | \(0.391335\pi\) | ||||
−0.334790 | + | 0.942293i | \(0.608665\pi\) | |||||||
\(572\) | −32.7846 | + | 8.78461i | −1.37079 | + | 0.367303i | ||||
\(573\) | 20.7846 | 0.868290 | ||||||||
\(574\) | 31.1769 | − | 18.0000i | 1.30130 | − | 0.751305i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.0000i | 1.00000i | ||||||||
\(577\) | 24.0000 | − | 24.0000i | 0.999133 | − | 0.999133i | −0.000866551 | − | 1.00000i | \(-0.500276\pi\) |
1.00000 | 0.000866551i | \(0.000275832\pi\) | ||||||||
\(578\) | −20.4904 | − | 5.49038i | −0.852287 | − | 0.228370i | ||||
\(579\) | 31.1769 | − | 31.1769i | 1.29567 | − | 1.29567i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3923 | −0.431145 | ||||||||
\(582\) | −18.0000 | + | 10.3923i | −0.746124 | + | 0.430775i | ||||
\(583\) | 12.0000 | + | 12.0000i | 0.496989 | + | 0.496989i | ||||
\(584\) | 24.0000 | 0.993127 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.0000 | − | 6.92820i | 0.495715 | − | 0.286201i | ||||
\(587\) | 1.73205 | − | 1.73205i | 0.0714894 | − | 0.0714894i | −0.670458 | − | 0.741947i | \(-0.733902\pi\) |
0.741947 | + | 0.670458i | \(0.233902\pi\) | |||||||
\(588\) | −33.0000 | − | 19.0526i | −1.36090 | − | 0.785714i | ||||
\(589\) | 13.8564 | 0.570943 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6.00000 | − | 6.00000i | −0.246807 | − | 0.246807i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −14.0000 | + | 14.0000i | −0.574911 | + | 0.574911i | −0.933497 | − | 0.358586i | \(-0.883259\pi\) |
0.358586 | + | 0.933497i | \(0.383259\pi\) | |||||||
\(594\) | 24.5885 | + | 6.58846i | 1.00888 | + | 0.270328i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −13.8564 | + | 24.0000i | −0.567581 | + | 0.983078i | ||||
\(597\) | −6.92820 | −0.283552 | ||||||||
\(598\) | 9.46410 | + | 2.53590i | 0.387016 | + | 0.103701i | ||||
\(599\) | −24.0000 | −0.980613 | −0.490307 | − | 0.871550i | \(-0.663115\pi\) | ||||
−0.490307 | + | 0.871550i | \(0.663115\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | −14.1962 | − | 3.80385i | −0.578592 | − | 0.155033i | ||||
\(603\) | 15.5885 | + | 15.5885i | 0.634811 | + | 0.634811i | ||||
\(604\) | 34.6410 | + | 20.0000i | 1.40952 | + | 0.813788i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 8.19615 | + | 2.19615i | 0.332946 | + | 0.0892126i | ||||
\(607\) | −3.00000 | + | 3.00000i | −0.121766 | + | 0.121766i | −0.765364 | − | 0.643598i | \(-0.777441\pi\) |
0.643598 | + | 0.765364i | \(0.277441\pi\) | |||||||
\(608\) | 18.9282 | − | 5.07180i | 0.767640 | − | 0.205689i | ||||
\(609\) | 18.0000 | − | 18.0000i | 0.729397 | − | 0.729397i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.6410 | 1.40143 | ||||||||
\(612\) | 8.78461 | + | 32.7846i | 0.355097 | + | 1.32524i | ||||
\(613\) | −24.2487 | + | 24.2487i | −0.979396 | + | 0.979396i | −0.999792 | − | 0.0203958i | \(-0.993507\pi\) |
0.0203958 | + | 0.999792i | \(0.493507\pi\) | |||||||
\(614\) | 3.00000 | − | 1.73205i | 0.121070 | − | 0.0698999i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 41.5692i | − | 1.67487i | ||||||
\(617\) | 8.00000 | + | 8.00000i | 0.322068 | + | 0.322068i | 0.849560 | − | 0.527492i | \(-0.176868\pi\) |
−0.527492 | + | 0.849560i | \(0.676868\pi\) | |||||||
\(618\) | −5.19615 | − | 9.00000i | −0.209020 | − | 0.362033i | ||||
\(619\) | −31.1769 | −1.25311 | −0.626553 | − | 0.779379i | \(-0.715535\pi\) | ||||
−0.626553 | + | 0.779379i | \(0.715535\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.19615 | − | 5.19615i | −0.208514 | − | 0.208514i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −36.0000 | + | 36.0000i | −1.44231 | + | 1.44231i | ||||
\(624\) | −8.78461 | + | 32.7846i | −0.351666 | + | 1.31243i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −20.7846 | + | 12.0000i | −0.830720 | + | 0.479616i | ||||
\(627\) | − | 20.7846i | − | 0.830057i | ||||||
\(628\) | 5.07180 | + | 18.9282i | 0.202387 | + | 0.755318i | ||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 16.0000 | + | 16.0000i | 0.636446 | + | 0.636446i | ||||
\(633\) | −6.00000 | −0.238479 | ||||||||
\(634\) | 24.2487 | + | 42.0000i | 0.963039 | + | 1.66803i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 16.3923 | − | 4.39230i | 0.649997 | − | 0.174166i | ||||
\(637\) | −38.1051 | − | 38.1051i | −1.50978 | − | 1.50978i | ||||
\(638\) | 16.3923 | + | 4.39230i | 0.648978 | + | 0.173893i | ||||
\(639\) | − | 36.0000i | − | 1.42414i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 6.00000i | − | 0.236986i | −0.992955 | − | 0.118493i | \(-0.962194\pi\) | ||
0.992955 | − | 0.118493i | \(-0.0378063\pi\) | |||||||
\(642\) | 15.5885 | − | 9.00000i | 0.615227 | − | 0.355202i | ||||
\(643\) | 19.0526 | − | 19.0526i | 0.751360 | − | 0.751360i | −0.223373 | − | 0.974733i | \(-0.571707\pi\) |
0.974733 | + | 0.223373i | \(0.0717069\pi\) | |||||||
\(644\) | −6.00000 | + | 10.3923i | −0.236433 | + | 0.409514i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.0000 | − | 13.8564i | 0.944267 | − | 0.545173i | ||||
\(647\) | 25.0000 | + | 25.0000i | 0.982851 | + | 0.982851i | 0.999855 | − | 0.0170040i | \(-0.00541280\pi\) |
−0.0170040 | + | 0.999855i | \(0.505413\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.707107 | − | 0.707107i | ||||
\(649\) | 36.0000i | 1.41312i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −20.7846 | − | 20.7846i | −0.814613 | − | 0.814613i | ||||
\(652\) | −23.6603 | + | 6.33975i | −0.926607 | + | 0.248284i | ||||
\(653\) | 17.3205 | + | 17.3205i | 0.677804 | + | 0.677804i | 0.959503 | − | 0.281699i | \(-0.0908980\pi\) |
−0.281699 | + | 0.959503i | \(0.590898\pi\) | |||||||
\(654\) | −40.9808 | − | 10.9808i | −1.60247 | − | 0.429382i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 20.7846 | − | 12.0000i | 0.811503 | − | 0.468521i | ||||
\(657\) | −18.0000 | − | 18.0000i | −0.702247 | − | 0.702247i | ||||
\(658\) | −10.9808 | + | 40.9808i | −0.428075 | + | 1.59760i | ||||
\(659\) | − | 10.3923i | − | 0.404827i | −0.979300 | − | 0.202413i | \(-0.935122\pi\) | ||
0.979300 | − | 0.202413i | \(-0.0648785\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 31.1769i | 1.21264i | 0.795220 | + | 0.606321i | \(0.207355\pi\) | ||||
−0.795220 | + | 0.606321i | \(0.792645\pi\) | |||||||
\(662\) | −14.1962 | − | 3.80385i | −0.551749 | − | 0.147841i | ||||
\(663\) | 48.0000i | 1.86417i | ||||||||
\(664\) | −6.92820 | −0.268866 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.46410 | − | 3.46410i | −0.134131 | − | 0.134131i | ||||
\(668\) | 9.51666 | + | 35.5167i | 0.368211 | + | 1.37418i | ||||
\(669\) | 5.19615 | − | 5.19615i | 0.200895 | − | 0.200895i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 12.0000i | − | 0.463255i | ||||||
\(672\) | −36.0000 | − | 20.7846i | −1.38873 | − | 0.801784i | ||||
\(673\) | −6.00000 | − | 6.00000i | −0.231283 | − | 0.231283i | 0.581945 | − | 0.813228i | \(-0.302292\pi\) |
−0.813228 | + | 0.581945i | \(0.802292\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | + | 19.0526i | −0.423077 | + | 0.732791i | ||||
\(677\) | −10.3923 | + | 10.3923i | −0.399409 | + | 0.399409i | −0.878024 | − | 0.478616i | \(-0.841139\pi\) |
0.478616 | + | 0.878024i | \(0.341139\pi\) | |||||||
\(678\) | −6.00000 | + | 3.46410i | −0.230429 | + | 0.133038i | ||||
\(679\) | − | 36.0000i | − | 1.38155i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.0000 | − | 33.0000i | −1.26456 | − | 1.26456i | ||||
\(682\) | 5.07180 | − | 18.9282i | 0.194209 | − | 0.724798i | ||||
\(683\) | −29.4449 | − | 29.4449i | −1.12668 | − | 1.12668i | −0.990714 | − | 0.135962i | \(-0.956587\pi\) |
−0.135962 | − | 0.990714i | \(-0.543413\pi\) | |||||||
\(684\) | −18.0000 | − | 10.3923i | −0.688247 | − | 0.397360i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.7846 | − | 12.0000i | 0.793560 | − | 0.458162i | ||||
\(687\) | 24.0000i | 0.915657i | ||||||||
\(688\) | −9.46410 | − | 2.53590i | −0.360815 | − | 0.0966802i | ||||
\(689\) | 24.0000 | 0.914327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.46410i | 0.131781i | 0.997827 | + | 0.0658903i | \(0.0209887\pi\) | ||||
−0.997827 | + | 0.0658903i | \(0.979011\pi\) | |||||||
\(692\) | −5.07180 | − | 18.9282i | −0.192801 | − | 0.719542i | ||||
\(693\) | −31.1769 | + | 31.1769i | −1.18431 | + | 1.18431i | ||||
\(694\) | −15.5885 | − | 27.0000i | −0.591730 | − | 1.02491i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 12.0000 | − | 12.0000i | 0.454859 | − | 0.454859i | ||||
\(697\) | 24.0000 | − | 24.0000i | 0.909065 | − | 0.909065i | ||||
\(698\) | 10.1436 | − | 37.8564i | 0.383941 | − | 1.43289i | ||||
\(699\) | −6.92820 | − | 6.92820i | −0.262049 | − | 0.262049i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.8564 | −0.523349 | −0.261675 | − | 0.965156i | \(-0.584275\pi\) | ||||
−0.261675 | + | 0.965156i | \(0.584275\pi\) | |||||||
\(702\) | 31.1769 | − | 18.0000i | 1.17670 | − | 0.679366i | ||||
\(703\) | 0 | 0 | ||||||||
\(704\) | − | 27.7128i | − | 1.04447i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.0000 | − | 24.2487i | −0.526897 | − | 0.912612i | ||||
\(707\) | −10.3923 | + | 10.3923i | −0.390843 | + | 0.390843i | ||||
\(708\) | 31.1769 | + | 18.0000i | 1.17170 | + | 0.676481i | ||||
\(709\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 24.0000i | − | 0.900070i | ||||||
\(712\) | −24.0000 | + | 24.0000i | −0.899438 | + | 0.899438i | ||||
\(713\) | −4.00000 | + | 4.00000i | −0.149801 | + | 0.149801i | ||||
\(714\) | −56.7846 | − | 15.2154i | −2.12511 | − | 0.569422i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.3923 | + | 18.0000i | −0.388379 | + | 0.672692i | ||||
\(717\) | − | 41.5692i | − | 1.55243i | ||||||
\(718\) | −4.39230 | + | 16.3923i | −0.163919 | + | 0.611755i | ||||
\(719\) | 12.0000 | 0.447524 | 0.223762 | − | 0.974644i | \(-0.428166\pi\) | ||||
0.223762 | + | 0.974644i | \(0.428166\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0000 | 0.670355 | ||||||||
\(722\) | 2.56218 | − | 9.56218i | 0.0953544 | − | 0.355867i | ||||
\(723\) | − | 13.8564i | − | 0.515325i | ||||||
\(724\) | −13.8564 | + | 24.0000i | −0.514969 | + | 0.891953i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.36603 | − | 0.633975i | −0.0878114 | − | 0.0235290i | ||||
\(727\) | −15.0000 | + | 15.0000i | −0.556319 | + | 0.556319i | −0.928257 | − | 0.371938i | \(-0.878693\pi\) |
0.371938 | + | 0.928257i | \(0.378693\pi\) | |||||||
\(728\) | −41.5692 | − | 41.5692i | −1.54066 | − | 1.54066i | ||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.8564 | −0.512498 | ||||||||
\(732\) | −10.3923 | − | 6.00000i | −0.384111 | − | 0.221766i | ||||
\(733\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(734\) | 9.00000 | + | 15.5885i | 0.332196 | + | 0.575380i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | + | 6.92820i | −0.147442 | + | 0.255377i | ||||
\(737\) | −18.0000 | − | 18.0000i | −0.663039 | − | 0.663039i | ||||
\(738\) | −24.5885 | − | 6.58846i | −0.905114 | − | 0.242524i | ||||
\(739\) | 3.46410 | 0.127429 | 0.0637145 | − | 0.997968i | \(-0.479705\pi\) | ||||
0.0637145 | + | 0.997968i | \(0.479705\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.7846 | − | 20.7846i | −0.763542 | − | 0.763542i | ||||
\(742\) | −7.60770 | + | 28.3923i | −0.279287 | + | 1.04231i | ||||
\(743\) | 25.0000 | − | 25.0000i | 0.917161 | − | 0.917161i | −0.0796610 | − | 0.996822i | \(-0.525384\pi\) |
0.996822 | + | 0.0796610i | \(0.0253838\pi\) | |||||||
\(744\) | −13.8564 | − | 13.8564i | −0.508001 | − | 0.508001i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 6.92820 | + | 12.0000i | 0.253660 | + | 0.439351i | ||||
\(747\) | 5.19615 | + | 5.19615i | 0.190117 | + | 0.190117i | ||||
\(748\) | −10.1436 | − | 37.8564i | −0.370887 | − | 1.38417i | ||||
\(749\) | 31.1769i | 1.13918i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0000 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(752\) | −7.32051 | + | 27.3205i | −0.266951 | + | 0.996276i | ||||
\(753\) | 6.00000i | 0.218652i | ||||||||
\(754\) | 20.7846 | − | 12.0000i | 0.756931 | − | 0.437014i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 11.4115 | + | 42.5885i | 0.415034 | + | 1.54893i | ||||
\(757\) | 27.7128 | + | 27.7128i | 1.00724 | + | 1.00724i | 0.999974 | + | 0.00726571i | \(0.00231277\pi\) |
0.00726571 | + | 0.999974i | \(0.497687\pi\) | |||||||
\(758\) | 1.26795 | − | 4.73205i | 0.0460540 | − | 0.171876i | ||||
\(759\) | 6.00000 | + | 6.00000i | 0.217786 | + | 0.217786i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 48.0000i | 1.74000i | 0.493053 | + | 0.869999i | \(0.335881\pi\) | ||||
−0.493053 | + | 0.869999i | \(0.664119\pi\) | |||||||
\(762\) | 9.00000 | − | 5.19615i | 0.326036 | − | 0.188237i | ||||
\(763\) | 51.9615 | − | 51.9615i | 1.88113 | − | 1.88113i | ||||
\(764\) | −12.0000 | + | 20.7846i | −0.434145 | + | 0.751961i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.00000 | + | 1.73205i | 0.0361315 | + | 0.0625815i | ||||
\(767\) | 36.0000 | + | 36.0000i | 1.29988 | + | 1.29988i | ||||
\(768\) | −24.0000 | − | 13.8564i | −0.866025 | − | 0.500000i | ||||
\(769\) | − | 14.0000i | − | 0.504853i | −0.967616 | − | 0.252426i | \(-0.918771\pi\) | ||
0.967616 | − | 0.252426i | \(-0.0812286\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.3205 | − | 17.3205i | 0.623783 | − | 0.623783i | ||||
\(772\) | 13.1769 | + | 49.1769i | 0.474248 | + | 1.76992i | ||||
\(773\) | 3.46410 | + | 3.46410i | 0.124595 | + | 0.124595i | 0.766655 | − | 0.642060i | \(-0.221920\pi\) |
−0.642060 | + | 0.766655i | \(0.721920\pi\) | |||||||
\(774\) | 5.19615 | + | 9.00000i | 0.186772 | + | 0.323498i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 24.0000i | − | 0.861550i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.9282 | − | 5.07180i | −0.678609 | − | 0.181833i | ||||
\(779\) | 20.7846i | 0.744686i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 41.5692i | 1.48746i | ||||||||
\(782\) | −2.92820 | + | 10.9282i | −0.104712 | + | 0.390792i | ||||
\(783\) | −18.0000 | −0.643268 | ||||||||
\(784\) | 38.1051 | − | 22.0000i | 1.36090 | − | 0.785714i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 40.9808 | + | 10.9808i | 1.46174 | + | 0.391671i | ||||
\(787\) | 29.4449 | + | 29.4449i | 1.04960 | + | 1.04960i | 0.998704 | + | 0.0508919i | \(0.0162064\pi\) |
0.0508919 | + | 0.998704i | \(0.483794\pi\) | |||||||
\(788\) | 9.46410 | − | 2.53590i | 0.337145 | − | 0.0903376i | ||||
\(789\) | −12.1244 | − | 12.1244i | −0.431638 | − | 0.431638i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 12.0000i | − | 0.426671i | ||||||
\(792\) | −20.7846 | + | 20.7846i | −0.738549 | + | 0.738549i | ||||
\(793\) | −12.0000 | − | 12.0000i | −0.426132 | − | 0.426132i | ||||
\(794\) | 30.0000 | − | 17.3205i | 1.06466 | − | 0.614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.00000 | − | 6.92820i | 0.141776 | − | 0.245564i | ||||
\(797\) | 24.2487 | − | 24.2487i | 0.858933 | − | 0.858933i | −0.132279 | − | 0.991213i | \(-0.542230\pi\) |
0.991213 | + | 0.132279i | \(0.0422295\pi\) | |||||||
\(798\) | 31.1769 | − | 18.0000i | 1.10365 | − | 0.637193i | ||||
\(799\) | 40.0000i | 1.41510i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.0000 | 1.27200 | ||||||||
\(802\) | −16.3923 | − | 4.39230i | −0.578832 | − | 0.155098i | ||||
\(803\) | 20.7846 | + | 20.7846i | 0.733473 | + | 0.733473i | ||||
\(804\) | −24.5885 | + | 6.58846i | −0.867168 | + | 0.232357i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.8564 | − | 24.0000i | −0.488071 | − | 0.845364i | ||||
\(807\) | −48.0000 | −1.68968 | ||||||||
\(808\) | −6.92820 | + | 6.92820i | −0.243733 | + | 0.243733i | ||||
\(809\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 31.1769i | 1.09477i | 0.836881 | + | 0.547385i | \(0.184377\pi\) | ||||
−0.836881 | + | 0.547385i | \(0.815623\pi\) | |||||||
\(812\) | 7.60770 | + | 28.3923i | 0.266978 | + | 0.996375i | ||||
\(813\) | 13.8564i | 0.485965i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −37.8564 | − | 10.1436i | −1.32524 | − | 0.355097i | ||||
\(817\) | 6.00000 | − | 6.00000i | 0.209913 | − | 0.209913i | ||||
\(818\) | −5.46410 | − | 1.46410i | −0.191048 | − | 0.0511911i | ||||
\(819\) | 62.3538i | 2.17882i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.5692 | 1.45078 | 0.725388 | − | 0.688340i | \(-0.241660\pi\) | ||||
0.725388 | + | 0.688340i | \(0.241660\pi\) | |||||||
\(822\) | −17.3205 | − | 30.0000i | −0.604122 | − | 1.04637i | ||||
\(823\) | −3.00000 | − | 3.00000i | −0.104573 | − | 0.104573i | 0.652884 | − | 0.757458i | \(-0.273559\pi\) |
−0.757458 | + | 0.652884i | \(0.773559\pi\) | |||||||
\(824\) | 12.0000 | 0.418040 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −54.0000 | + | 31.1769i | −1.87890 | + | 1.08478i | ||||
\(827\) | 8.66025 | − | 8.66025i | 0.301147 | − | 0.301147i | −0.540316 | − | 0.841462i | \(-0.681695\pi\) |
0.841462 | + | 0.540316i | \(0.181695\pi\) | |||||||
\(828\) | 8.19615 | − | 2.19615i | 0.284836 | − | 0.0763216i | ||||
\(829\) | −51.9615 | −1.80470 | −0.902349 | − | 0.431006i | \(-0.858159\pi\) | ||||
−0.902349 | + | 0.431006i | \(0.858159\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −36.0000 | + | 36.0000i | −1.24883 | + | 1.24883i | ||||
\(832\) | −27.7128 | − | 27.7128i | −0.960769 | − | 0.960769i | ||||
\(833\) | 44.0000 | − | 44.0000i | 1.52451 | − | 1.52451i | ||||
\(834\) | −24.5885 | − | 6.58846i | −0.851429 | − | 0.228140i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 20.7846 | + | 12.0000i | 0.718851 | + | 0.415029i | ||||
\(837\) | 20.7846i | 0.718421i | ||||||||
\(838\) | −33.1244 | − | 8.87564i | −1.14426 | − | 0.306604i | ||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0000 | 0.586207 | ||||||||
\(842\) | −4.73205 | − | 1.26795i | −0.163077 | − | 0.0436964i | ||||
\(843\) | −31.1769 | −1.07379 | ||||||||
\(844\) | 3.46410 | − | 6.00000i | 0.119239 | − | 0.206529i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 25.9808 | − | 15.0000i | 0.893237 | − | 0.515711i | ||||
\(847\) | 3.00000 | − | 3.00000i | 0.103081 | − | 0.103081i | ||||
\(848\) | −5.07180 | + | 18.9282i | −0.174166 | + | 0.649997i | ||||
\(849\) | −9.00000 | − | 9.00000i | −0.308879 | − | 0.308879i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 36.0000 | + | 20.7846i | 1.23334 | + | 0.712069i | ||||
\(853\) | −3.46410 | + | 3.46410i | −0.118609 | + | 0.118609i | −0.763920 | − | 0.645311i | \(-0.776728\pi\) |
0.645311 | + | 0.763920i | \(0.276728\pi\) | |||||||
\(854\) | 18.0000 | − | 10.3923i | 0.615947 | − | 0.355617i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 20.7846i | 0.710403i | ||||||||
\(857\) | 26.0000 | + | 26.0000i | 0.888143 | + | 0.888143i | 0.994345 | − | 0.106202i | \(-0.0338689\pi\) |
−0.106202 | + | 0.994345i | \(0.533869\pi\) | |||||||
\(858\) | −36.0000 | + | 20.7846i | −1.22902 | + | 0.709575i | ||||
\(859\) | 24.2487 | 0.827355 | 0.413678 | − | 0.910423i | \(-0.364244\pi\) | ||||
0.413678 | + | 0.910423i | \(0.364244\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.1769 | − | 31.1769i | 1.06251 | − | 1.06251i | ||||
\(862\) | 16.3923 | + | 4.39230i | 0.558324 | + | 0.149602i | ||||
\(863\) | 23.0000 | − | 23.0000i | 0.782929 | − | 0.782929i | −0.197395 | − | 0.980324i | \(-0.563248\pi\) |
0.980324 | + | 0.197395i | \(0.0632481\pi\) | |||||||
\(864\) | 7.60770 | + | 28.3923i | 0.258819 | + | 0.965926i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 10.3923 | − | 6.00000i | 0.353145 | − | 0.203888i | ||||
\(867\) | −25.9808 | −0.882353 | ||||||||
\(868\) | 32.7846 | − | 8.78461i | 1.11278 | − | 0.298169i | ||||
\(869\) | 27.7128i | 0.940093i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −36.0000 | −1.21981 | ||||||||
\(872\) | 34.6410 | − | 34.6410i | 1.17309 | − | 1.17309i | ||||
\(873\) | −18.0000 | + | 18.0000i | −0.609208 | + | 0.609208i | ||||
\(874\) | −3.46410 | − | 6.00000i | −0.117175 | − | 0.202953i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 28.3923 | − | 7.60770i | 0.959287 | − | 0.257040i | ||||
\(877\) | −13.8564 | − | 13.8564i | −0.467898 | − | 0.467898i | 0.433335 | − | 0.901233i | \(-0.357337\pi\) |
−0.901233 | + | 0.433335i | \(0.857337\pi\) | |||||||
\(878\) | 43.7128 | + | 11.7128i | 1.47524 | + | 0.395288i | ||||
\(879\) | 12.0000 | − | 12.0000i | 0.404750 | − | 0.404750i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 30.0000i | 1.01073i | 0.862907 | + | 0.505363i | \(0.168641\pi\) | ||||
−0.862907 | + | 0.505363i | \(0.831359\pi\) | |||||||
\(882\) | −45.0788 | − | 12.0788i | −1.51788 | − | 0.406716i | ||||
\(883\) | −15.5885 | + | 15.5885i | −0.524593 | + | 0.524593i | −0.918955 | − | 0.394362i | \(-0.870966\pi\) |
0.394362 | + | 0.918955i | \(0.370966\pi\) | |||||||
\(884\) | −48.0000 | − | 27.7128i | −1.61441 | − | 0.932083i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.0000 | + | 8.66025i | −0.503935 | + | 0.290947i | ||||
\(887\) | −17.0000 | − | 17.0000i | −0.570804 | − | 0.570804i | 0.361549 | − | 0.932353i | \(-0.382248\pi\) |
−0.932353 | + | 0.361549i | \(0.882248\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18.0000i | 0.603701i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 31.1769 | 1.04447 | ||||||||
\(892\) | 2.19615 | + | 8.19615i | 0.0735326 | + | 0.274427i | ||||
\(893\) | −17.3205 | − | 17.3205i | −0.579609 | − | 0.579609i | ||||
\(894\) | −8.78461 | + | 32.7846i | −0.293801 | + | 1.09648i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 41.5692 | − | 24.0000i | 1.38873 | − | 0.801784i | ||||
\(897\) | 12.0000 | 0.400668 | ||||||||
\(898\) | −6.58846 | + | 24.5885i | −0.219860 | + | 0.820527i | ||||
\(899\) | 13.8564i | 0.462137i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 27.7128i | 0.923248i | ||||||||
\(902\) | 28.3923 | + | 7.60770i | 0.945360 | + | 0.253309i | ||||
\(903\) | −18.0000 | −0.599002 | ||||||||
\(904\) | − | 8.00000i | − | 0.266076i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 47.3205 | + | 12.6795i | 1.57212 | + | 0.421248i | ||||
\(907\) | −19.0526 | − | 19.0526i | −0.632630 | − | 0.632630i | 0.316097 | − | 0.948727i | \(-0.397627\pi\) |
−0.948727 | + | 0.316097i | \(0.897627\pi\) | |||||||
\(908\) | 52.0526 | − | 13.9474i | 1.72742 | − | 0.462862i | ||||
\(909\) | 10.3923 | 0.344691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 12.0000i | 0.397578i | 0.980042 | + | 0.198789i | \(0.0637008\pi\) | ||||
−0.980042 | + | 0.198789i | \(0.936299\pi\) | |||||||
\(912\) | 20.7846 | − | 12.0000i | 0.688247 | − | 0.397360i | ||||
\(913\) | −6.00000 | − | 6.00000i | −0.198571 | − | 0.198571i | ||||
\(914\) | −12.0000 | − | 20.7846i | −0.396925 | − | 0.687494i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −24.0000 | − | 13.8564i | −0.792982 | − | 0.457829i | ||||
\(917\) | −51.9615 | + | 51.9615i | −1.71592 | + | 1.71592i | ||||
\(918\) | 20.7846 | + | 36.0000i | 0.685994 | + | 1.18818i | ||||
\(919\) | 40.0000i | 1.31948i | 0.751495 | + | 0.659739i | \(0.229333\pi\) | ||||
−0.751495 | + | 0.659739i | \(0.770667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.00000 | − | 3.00000i | 0.0988534 | − | 0.0988534i | ||||
\(922\) | 11.4115 | − | 42.5885i | 0.375819 | − | 1.40258i | ||||
\(923\) | 41.5692 | + | 41.5692i | 1.36827 | + | 1.36827i | ||||
\(924\) | −13.1769 | − | 49.1769i | −0.433489 | − | 1.61780i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −15.5885 | + | 9.00000i | −0.512268 | + | 0.295758i | ||||
\(927\) | −9.00000 | − | 9.00000i | −0.295599 | − | 0.295599i | ||||
\(928\) | 5.07180 | + | 18.9282i | 0.166490 | + | 0.621349i | ||||
\(929\) | 6.00000 | 0.196854 | 0.0984268 | − | 0.995144i | \(-0.468619\pi\) | ||||
0.0984268 | + | 0.995144i | \(0.468619\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 38.1051i | 1.24884i | ||||||||
\(932\) | 10.9282 | − | 2.92820i | 0.357965 | − | 0.0959165i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 8.66025 | + | 15.0000i | 0.283372 | + | 0.490815i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 41.5692i | 1.35873i | ||||||||
\(937\) | −18.0000 | + | 18.0000i | −0.588034 | + | 0.588034i | −0.937099 | − | 0.349064i | \(-0.886499\pi\) |
0.349064 | + | 0.937099i | \(0.386499\pi\) | |||||||
\(938\) | 11.4115 | − | 42.5885i | 0.372600 | − | 1.39056i | ||||
\(939\) | −20.7846 | + | 20.7846i | −0.678280 | + | 0.678280i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.3205 | 0.564632 | 0.282316 | − | 0.959321i | \(-0.408897\pi\) | ||||
0.282316 | + | 0.959321i | \(0.408897\pi\) | |||||||
\(942\) | 12.0000 | + | 20.7846i | 0.390981 | + | 0.677199i | ||||
\(943\) | −6.00000 | − | 6.00000i | −0.195387 | − | 0.195387i | ||||
\(944\) | −36.0000 | + | 20.7846i | −1.17170 | + | 0.676481i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6.00000 | − | 10.3923i | −0.195077 | − | 0.337883i | ||||
\(947\) | 8.66025 | − | 8.66025i | 0.281420 | − | 0.281420i | −0.552255 | − | 0.833675i | \(-0.686232\pi\) |
0.833675 | + | 0.552255i | \(0.186232\pi\) | |||||||
\(948\) | 24.0000 | + | 13.8564i | 0.779484 | + | 0.450035i | ||||
\(949\) | 41.5692 | 1.34939 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 42.0000 | + | 42.0000i | 1.36194 | + | 1.36194i | ||||
\(952\) | 48.0000 | − | 48.0000i | 1.55569 | − | 1.55569i | ||||
\(953\) | 10.0000 | − | 10.0000i | 0.323932 | − | 0.323932i | −0.526341 | − | 0.850273i | \(-0.676437\pi\) |
0.850273 | + | 0.526341i | \(0.176437\pi\) | |||||||
\(954\) | 18.0000 | − | 10.3923i | 0.582772 | − | 0.336463i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 41.5692 | + | 24.0000i | 1.34444 | + | 0.776215i | ||||
\(957\) | 20.7846 | 0.671871 | ||||||||
\(958\) | 13.1769 | − | 49.1769i | 0.425727 | − | 1.58883i | ||||
\(959\) | 60.0000 | 1.93750 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 15.5885 | − | 15.5885i | 0.502331 | − | 0.502331i | ||||
\(964\) | 13.8564 | + | 8.00000i | 0.446285 | + | 0.257663i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.80385 | + | 14.1962i | −0.122387 | + | 0.456754i | ||||
\(967\) | 39.0000 | − | 39.0000i | 1.25416 | − | 1.25416i | 0.300316 | − | 0.953840i | \(-0.402908\pi\) |
0.953840 | − | 0.300316i | \(-0.0970920\pi\) | |||||||
\(968\) | 2.00000 | − | 2.00000i | 0.0642824 | − | 0.0642824i | ||||
\(969\) | 24.0000 | − | 24.0000i | 0.770991 | − | 0.770991i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −24.2487 | −0.778178 | −0.389089 | − | 0.921200i | \(-0.627210\pi\) | ||||
−0.389089 | + | 0.921200i | \(0.627210\pi\) | |||||||
\(972\) | 15.5885 | − | 27.0000i | 0.500000 | − | 0.866025i | ||||
\(973\) | 31.1769 | − | 31.1769i | 0.999486 | − | 0.999486i | ||||
\(974\) | 15.0000 | + | 25.9808i | 0.480631 | + | 0.832477i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 12.0000 | − | 6.92820i | 0.384111 | − | 0.221766i | ||||
\(977\) | −16.0000 | − | 16.0000i | −0.511885 | − | 0.511885i | 0.403218 | − | 0.915104i | \(-0.367891\pi\) |
−0.915104 | + | 0.403218i | \(0.867891\pi\) | |||||||
\(978\) | −25.9808 | + | 15.0000i | −0.830773 | + | 0.479647i | ||||
\(979\) | −41.5692 | −1.32856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.9615 | −1.65900 | ||||||||
\(982\) | 3.80385 | − | 14.1962i | 0.121386 | − | 0.453017i | ||||
\(983\) | 11.0000 | − | 11.0000i | 0.350846 | − | 0.350846i | −0.509579 | − | 0.860424i | \(-0.670199\pi\) |
0.860424 | + | 0.509579i | \(0.170199\pi\) | |||||||
\(984\) | 20.7846 | − | 20.7846i | 0.662589 | − | 0.662589i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.8564 | + | 24.0000i | 0.441278 | + | 0.764316i | ||||
\(987\) | 51.9615i | 1.65395i | ||||||||
\(988\) | 32.7846 | − | 8.78461i | 1.04302 | − | 0.279476i | ||||
\(989\) | 3.46410i | 0.110152i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | 21.8564 | − | 5.85641i | 0.693942 | − | 0.185941i | ||||
\(993\) | −18.0000 | −0.571213 | ||||||||
\(994\) | −62.3538 | + | 36.0000i | −1.97774 | + | 1.14185i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −8.19615 | + | 2.19615i | −0.259705 | + | 0.0695878i | ||||
\(997\) | −3.46410 | − | 3.46410i | −0.109709 | − | 0.109709i | 0.650121 | − | 0.759830i | \(-0.274718\pi\) |
−0.759830 | + | 0.650121i | \(0.774718\pi\) | |||||||
\(998\) | −8.87564 | + | 33.1244i | −0.280954 | + | 1.04853i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 600.2.w.f.293.1 | yes | 4 | |
3.2 | odd | 2 | 600.2.w.d.293.2 | yes | 4 | ||
5.2 | odd | 4 | 600.2.w.d.557.1 | yes | 4 | ||
5.3 | odd | 4 | 600.2.w.e.557.2 | yes | 4 | ||
5.4 | even | 2 | 600.2.w.c.293.2 | yes | 4 | ||
8.5 | even | 2 | inner | 600.2.w.f.293.2 | yes | 4 | |
15.2 | even | 4 | inner | 600.2.w.f.557.2 | yes | 4 | |
15.8 | even | 4 | 600.2.w.c.557.1 | yes | 4 | ||
15.14 | odd | 2 | 600.2.w.e.293.1 | yes | 4 | ||
24.5 | odd | 2 | 600.2.w.d.293.1 | yes | 4 | ||
40.13 | odd | 4 | 600.2.w.e.557.1 | yes | 4 | ||
40.29 | even | 2 | 600.2.w.c.293.1 | ✓ | 4 | ||
40.37 | odd | 4 | 600.2.w.d.557.2 | yes | 4 | ||
120.29 | odd | 2 | 600.2.w.e.293.2 | yes | 4 | ||
120.53 | even | 4 | 600.2.w.c.557.2 | yes | 4 | ||
120.77 | even | 4 | inner | 600.2.w.f.557.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.2.w.c.293.1 | ✓ | 4 | 40.29 | even | 2 | ||
600.2.w.c.293.2 | yes | 4 | 5.4 | even | 2 | ||
600.2.w.c.557.1 | yes | 4 | 15.8 | even | 4 | ||
600.2.w.c.557.2 | yes | 4 | 120.53 | even | 4 | ||
600.2.w.d.293.1 | yes | 4 | 24.5 | odd | 2 | ||
600.2.w.d.293.2 | yes | 4 | 3.2 | odd | 2 | ||
600.2.w.d.557.1 | yes | 4 | 5.2 | odd | 4 | ||
600.2.w.d.557.2 | yes | 4 | 40.37 | odd | 4 | ||
600.2.w.e.293.1 | yes | 4 | 15.14 | odd | 2 | ||
600.2.w.e.293.2 | yes | 4 | 120.29 | odd | 2 | ||
600.2.w.e.557.1 | yes | 4 | 40.13 | odd | 4 | ||
600.2.w.e.557.2 | yes | 4 | 5.3 | odd | 4 | ||
600.2.w.f.293.1 | yes | 4 | 1.1 | even | 1 | trivial | |
600.2.w.f.293.2 | yes | 4 | 8.5 | even | 2 | inner | |
600.2.w.f.557.1 | yes | 4 | 120.77 | even | 4 | inner | |
600.2.w.f.557.2 | yes | 4 | 15.2 | even | 4 | inner |