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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 293.2 | ||
Root | \(0.866025 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 600.293 |
Dual form | 600.2.w.e.557.2 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | − | 0.366025i | 0.965926 | − | 0.258819i | ||||
\(3\) | −1.73205 | −1.00000 | ||||||||
\(4\) | 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 | \(0.546115\pi\) |
−0.989524 | + | 0.144370i | \(0.953885\pi\) | |||||||
\(8\) | 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 | \(0.325099\pi\) | |||||||
\(12\) | −3.00000 | + | 1.73205i | −0.866025 | + | 0.500000i | ||||
\(13\) | 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 | \(0.509367\pi\) | |||||||
\(18\) | 4.09808 | − | 1.09808i | 0.965926 | − | 0.258819i | ||||
\(19\) | 3.46410 | 0.794719 | 0.397360 | − | 0.917663i | \(-0.369927\pi\) | ||||
0.397360 | + | 0.917663i | \(0.369927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.19615 | − | 5.19615i | 1.13389 | − | 1.13389i | ||||
\(22\) | 4.73205 | − | 1.26795i | 1.00888 | − | 0.270328i | ||||
\(23\) | 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 | ||||
\(27\) | −5.19615 | −1.00000 | ||||||||
\(28\) | −2.19615 | + | 8.19615i | −0.415034 | + | 1.54893i | ||||
\(29\) | − | 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 | \(0.616954\pi\) | |||||||
\(32\) | 1.46410 | − | 5.46410i | 0.258819 | − | 0.965926i | ||||
\(33\) | −6.00000 | −1.04447 | ||||||||
\(34\) | 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 | \(0.750000\pi\) | |||||||
\(38\) | 4.73205 | − | 1.26795i | 0.767640 | − | 0.205689i | ||||
\(39\) | −6.00000 | + | 6.00000i | −0.960769 | + | 0.960769i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.00000i | 0.937043i | 0.883452 | + | 0.468521i | \(0.155213\pi\) | ||||
−0.883452 | + | 0.468521i | \(0.844787\pi\) | |||||||
\(42\) | 5.19615 | − | 9.00000i | 0.801784 | − | 1.38873i | ||||
\(43\) | −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 | \(0.577528\pi\) | |||||||
\(48\) | −3.46410 | + | 6.00000i | −0.500000 | + | 0.866025i | ||||
\(49\) | − | 11.0000i | − | 1.57143i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.92820 | − | 6.92820i | −0.970143 | − | 0.970143i | ||||
\(52\) | 2.53590 | − | 9.46410i | 0.351666 | − | 1.31243i | ||||
\(53\) | −3.46410 | − | 3.46410i | −0.475831 | − | 0.475831i | 0.427965 | − | 0.903796i | \(-0.359231\pi\) |
−0.903796 | + | 0.427965i | \(0.859231\pi\) | |||||||
\(54\) | −7.09808 | + | 1.90192i | −0.965926 | + | 0.258819i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.0000i | 1.60357i | ||||||||
\(57\) | −6.00000 | −0.794719 | ||||||||
\(58\) | −1.26795 | − | 4.73205i | −0.166490 | − | 0.621349i | ||||
\(59\) | 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 | \(0.0711822\pi\) | ||||
−0.975100 | + | 0.221766i | \(0.928818\pi\) | |||||||
\(62\) | −5.46410 | + | 1.46410i | −0.693942 | + | 0.185941i | ||||
\(63\) | −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 | \(0.898177\pi\) | |||||||
\(68\) | 10.9282 | + | 2.92820i | 1.32524 | + | 0.355097i | ||||
\(69\) | −1.73205 | + | 1.73205i | −0.208514 | + | 0.208514i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 12.0000i | − | 1.42414i | −0.702109 | − | 0.712069i | \(-0.747758\pi\) | ||
0.702109 | − | 0.712069i | \(-0.252242\pi\) | |||||||
\(72\) | 6.00000 | − | 6.00000i | 0.707107 | − | 0.707107i | ||||
\(73\) | −6.00000 | − | 6.00000i | −0.702247 | − | 0.702247i | 0.262646 | − | 0.964892i | \(-0.415405\pi\) |
−0.964892 | + | 0.262646i | \(0.915405\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.00000 | − | 3.46410i | 0.688247 | − | 0.397360i | ||||
\(77\) | −10.3923 | + | 10.3923i | −1.18431 | + | 1.18431i | ||||
\(78\) | −6.00000 | + | 10.3923i | −0.679366 | + | 1.17670i | ||||
\(79\) | 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 | ||||||||
\(82\) | 2.19615 | + | 8.19615i | 0.242524 | + | 0.905114i | ||||
\(83\) | 1.73205 | + | 1.73205i | 0.190117 | + | 0.190117i | 0.795747 | − | 0.605629i | \(-0.207079\pi\) |
−0.605629 | + | 0.795747i | \(0.707079\pi\) | |||||||
\(84\) | 3.80385 | − | 14.1962i | 0.415034 | − | 1.54893i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.73205 | + | 3.00000i | −0.186772 | + | 0.323498i | ||||
\(87\) | 6.00000i | 0.643268i | ||||||||
\(88\) | 6.92820 | − | 6.92820i | 0.738549 | − | 0.738549i | ||||
\(89\) | 12.0000 | 1.27200 | 0.635999 | − | 0.771690i | \(-0.280588\pi\) | ||||
0.635999 | + | 0.771690i | \(0.280588\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 20.7846i | 2.17882i | ||||||||
\(92\) | 0.732051 | − | 2.73205i | 0.0763216 | − | 0.284836i | ||||
\(93\) | 6.92820 | 0.718421 | ||||||||
\(94\) | 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 | −0.942739 | − | 0.333531i | \(-0.891760\pi\) |
0.333531 | + | 0.942739i | \(0.391760\pi\) | |||||||
\(98\) | −4.02628 | − | 15.0263i | −0.406716 | − | 1.51788i | ||||
\(99\) | 10.3923 | 1.04447 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.46410 | −0.344691 | −0.172345 | − | 0.985037i | \(-0.555135\pi\) | ||||
−0.172345 | + | 0.985037i | \(0.555135\pi\) | |||||||
\(102\) | −12.0000 | − | 6.92820i | −1.18818 | − | 0.685994i | ||||
\(103\) | −3.00000 | − | 3.00000i | −0.295599 | − | 0.295599i | 0.543688 | − | 0.839287i | \(-0.317027\pi\) |
−0.839287 | + | 0.543688i | \(0.817027\pi\) | |||||||
\(104\) | − | 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 | −0.409831 | − | 0.912162i | \(-0.634412\pi\) |
0.912162 | + | 0.409831i | \(0.134412\pi\) | |||||||
\(108\) | −9.00000 | + | 5.19615i | −0.866025 | + | 0.500000i | ||||
\(109\) | −17.3205 | −1.65900 | −0.829502 | − | 0.558504i | \(-0.811376\pi\) | ||||
−0.829502 | + | 0.558504i | \(0.811376\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.39230 | + | 16.3923i | 0.415034 | + | 1.54893i | ||||
\(113\) | 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 | ||||
\(118\) | 3.80385 | + | 14.1962i | 0.350173 | + | 1.30686i | ||||
\(119\) | −24.0000 | −2.20008 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 1.26795 | + | 4.73205i | 0.114795 | + | 0.428420i | ||||
\(123\) | − | 10.3923i | − | 0.937043i | ||||||
\(124\) | −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 | −0.561363 | − | 0.827570i | \(-0.689723\pi\) |
0.827570 | + | 0.561363i | \(0.189723\pi\) | |||||||
\(128\) | −2.92820 | − | 10.9282i | −0.258819 | − | 0.965926i | ||||
\(129\) | 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 | \(0.773165\pi\) | |||||||
\(132\) | −10.3923 | + | 6.00000i | −0.904534 | + | 0.522233i | ||||
\(133\) | −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 | \(0.543524\pi\) | |||||||
\(138\) | −1.73205 | + | 3.00000i | −0.147442 | + | 0.255377i | ||||
\(139\) | −10.3923 | −0.881464 | −0.440732 | − | 0.897639i | \(-0.645281\pi\) | ||||
−0.440732 | + | 0.897639i | \(0.645281\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −8.66025 | − | 8.66025i | −0.729325 | − | 0.729325i | ||||
\(142\) | −4.39230 | − | 16.3923i | −0.368594 | − | 1.37561i | ||||
\(143\) | 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 | ||||
\(147\) | 19.0526i | 1.57143i | ||||||||
\(148\) | 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 | \(0.877864\pi\) | |||||||
\(158\) | 2.92820 | + | 10.9282i | 0.232955 | + | 0.869401i | ||||
\(159\) | 6.00000 | + | 6.00000i | 0.475831 | + | 0.475831i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 6.00000i | 0.472866i | ||||||||
\(162\) | 12.2942 | − | 3.29423i | 0.965926 | − | 0.258819i | ||||
\(163\) | 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 | \(-0.501906\pi\) | |||||||
\(168\) | − | 20.7846i | − | 1.60357i | ||||||
\(169\) | − | 11.0000i | − | 0.846154i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.3923 | 0.794719 | ||||||||
\(172\) | −1.26795 | + | 4.73205i | −0.0966802 | + | 0.360815i | ||||
\(173\) | −6.92820 | − | 6.92820i | −0.526742 | − | 0.526742i | 0.392858 | − | 0.919599i | \(-0.371486\pi\) |
−0.919599 | + | 0.392858i | \(0.871486\pi\) | |||||||
\(174\) | 2.19615 | + | 8.19615i | 0.166490 | + | 0.621349i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.92820 | − | 12.0000i | 0.522233 | − | 0.904534i | ||||
\(177\) | − | 18.0000i | − | 1.35296i | ||||||
\(178\) | 16.3923 | − | 4.39230i | 1.22866 | − | 0.329217i | ||||
\(179\) | − | 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 | \(0.172197\pi\) | ||||
−0.857209 | + | 0.514969i | \(0.827803\pi\) | |||||||
\(182\) | 7.60770 | + | 28.3923i | 0.563920 | + | 2.10458i | ||||
\(183\) | − | 6.00000i | − | 0.443533i | ||||||
\(184\) | − | 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 | ||||
\(188\) | 13.6603 | + | 3.66025i | 0.996276 | + | 0.266951i | ||||
\(189\) | 15.5885 | − | 15.5885i | 1.13389 | − | 1.13389i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 12.0000i | 0.868290i | 0.900843 | + | 0.434145i | \(0.142949\pi\) | ||||
−0.900843 | + | 0.434145i | \(0.857051\pi\) | |||||||
\(192\) | 13.8564i | 1.00000i | ||||||||
\(193\) | 18.0000 | + | 18.0000i | 1.29567 | + | 1.29567i | 0.931226 | + | 0.364442i | \(0.118740\pi\) |
0.364442 | + | 0.931226i | \(0.381260\pi\) | |||||||
\(194\) | −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 | −0.572852 | − | 0.819659i | \(-0.694163\pi\) |
0.819659 | + | 0.572852i | \(0.194163\pi\) | |||||||
\(198\) | 14.1962 | − | 3.80385i | 1.00888 | − | 0.270328i | ||||
\(199\) | 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 | ||||
\(202\) | −4.73205 | + | 1.26795i | −0.332946 | + | 0.0892126i | ||||
\(203\) | 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 | ||||
\(208\) | −5.07180 | − | 18.9282i | −0.351666 | − | 1.31243i | ||||
\(209\) | 12.0000 | 0.830057 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 3.46410i | − | 0.238479i | −0.992866 | − | 0.119239i | \(-0.961954\pi\) | ||
0.992866 | − | 0.119239i | \(-0.0380456\pi\) | |||||||
\(212\) | −9.46410 | − | 2.53590i | −0.649997 | − | 0.174166i | ||||
\(213\) | 20.7846i | 1.42414i | ||||||||
\(214\) | 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 | ||||
\(218\) | −23.6603 | + | 6.33975i | −1.60247 | + | 0.429382i | ||||
\(219\) | 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 | 0.800383 | − | 0.599489i | \(-0.204629\pi\) |
−0.599489 | + | 0.800383i | \(0.704629\pi\) | |||||||
\(224\) | 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 | \(-0.397759\pi\) |
0.948857 | − | 0.315706i | \(-0.102241\pi\) | |||||||
\(228\) | −10.3923 | + | 6.00000i | −0.688247 | + | 0.397360i | ||||
\(229\) | −13.8564 | −0.915657 | −0.457829 | − | 0.889041i | \(-0.651373\pi\) | ||||
−0.457829 | + | 0.889041i | \(0.651373\pi\) | |||||||
\(230\) | 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 | ||||
\(237\) | − | 13.8564i | − | 0.900070i | ||||||
\(238\) | −32.7846 | + | 8.78461i | −2.12511 | + | 0.569422i | ||||
\(239\) | 24.0000 | 1.55243 | 0.776215 | − | 0.630468i | \(-0.217137\pi\) | ||||
0.776215 | + | 0.630468i | \(0.217137\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.00000 | −0.515325 | −0.257663 | − | 0.966235i | \(-0.582952\pi\) | ||||
−0.257663 | + | 0.966235i | \(0.582952\pi\) | |||||||
\(242\) | 1.36603 | − | 0.366025i | 0.0878114 | − | 0.0235290i | ||||
\(243\) | −15.5885 | −1.00000 | ||||||||
\(244\) | 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 | \(0.465131\pi\) | |||||||
\(252\) | −6.58846 | + | 24.5885i | −0.415034 | + | 1.54893i | ||||
\(253\) | 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 | \(0.895405\pi\) | |||||||
\(258\) | 3.00000 | − | 5.19615i | 0.186772 | − | 0.323498i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 10.3923i | − | 0.643268i | ||||||
\(262\) | −23.6603 | + | 6.33975i | −1.46174 | + | 0.391671i | ||||
\(263\) | −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 | ||||
\(267\) | −20.7846 | −1.27200 | ||||||||
\(268\) | −14.1962 | − | 3.80385i | −0.867168 | − | 0.232357i | ||||
\(269\) | 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 | \(0.421874\pi\) | |||||||
\(272\) | 21.8564 | − | 5.85641i | 1.32524 | − | 0.355097i | ||||
\(273\) | − | 36.0000i | − | 2.17882i | ||||||
\(274\) | 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 | \(0.405484\pi\) | |||||||
\(278\) | −14.1962 | + | 3.80385i | −0.851429 | + | 0.228140i | ||||
\(279\) | −12.0000 | −0.718421 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 18.0000i | − | 1.07379i | −0.843649 | − | 0.536895i | \(-0.819597\pi\) | ||
0.843649 | − | 0.536895i | \(-0.180403\pi\) | |||||||
\(282\) | −15.0000 | − | 8.66025i | −0.893237 | − | 0.515711i | ||||
\(283\) | −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 | ||||
\(288\) | 4.39230 | − | 16.3923i | 0.258819 | − | 0.965926i | ||||
\(289\) | 15.0000i | 0.882353i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.3923 | − | 10.3923i | 0.609208 | − | 0.609208i | ||||
\(292\) | −16.3923 | − | 4.39230i | −0.959287 | − | 0.257040i | ||||
\(293\) | 6.92820 | + | 6.92820i | 0.404750 | + | 0.404750i | 0.879903 | − | 0.475153i | \(-0.157607\pi\) |
−0.475153 | + | 0.879903i | \(0.657607\pi\) | |||||||
\(294\) | 6.97372 | + | 26.0263i | 0.406716 | + | 1.51788i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −18.0000 | −1.04447 | ||||||||
\(298\) | −5.07180 | − | 18.9282i | −0.293801 | − | 1.09648i | ||||
\(299\) | − | 6.92820i | − | 0.400668i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 10.3923i | − | 0.599002i | ||||||
\(302\) | −27.3205 | + | 7.32051i | −1.57212 | + | 0.421248i | ||||
\(303\) | 6.00000 | 0.344691 | ||||||||
\(304\) | 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 | \(0.772268\pi\) | |||||||
\(308\) | −7.60770 | + | 28.3923i | −0.433489 | + | 1.61780i | ||||
\(309\) | 5.19615 | + | 5.19615i | 0.295599 | + | 0.295599i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 24.0000i | 1.35873i | ||||||||
\(313\) | −12.0000 | − | 12.0000i | −0.678280 | − | 0.678280i | 0.281331 | − | 0.959611i | \(-0.409224\pi\) |
−0.959611 | + | 0.281331i | \(0.909224\pi\) | |||||||
\(314\) | −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 | \(0.663188\pi\) |
−0.871438 | + | 0.490505i | \(0.836812\pi\) | |||||||
\(318\) | 10.3923 | + | 6.00000i | 0.582772 | + | 0.336463i | ||||
\(319\) | − | 12.0000i | − | 0.671871i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −9.00000 | + | 9.00000i | −0.502331 | + | 0.502331i | ||||
\(322\) | 2.19615 | + | 8.19615i | 0.122387 | + | 0.456754i | ||||
\(323\) | 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 | ||||
\(327\) | 30.0000 | 1.65900 | ||||||||
\(328\) | 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 | \(-0.907805\pi\) | ||
0.958347 | − | 0.285606i | \(-0.0921950\pi\) | |||||||
\(332\) | 4.73205 | + | 1.26795i | 0.259705 | + | 0.0695878i | ||||
\(333\) | 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 | \(0.250000\pi\) | |||||||
\(338\) | −4.02628 | − | 15.0263i | −0.219001 | − | 0.817322i | ||||
\(339\) | −3.46410 | + | 3.46410i | −0.188144 | + | 0.188144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.8564 | −0.750366 | ||||||||
\(342\) | 14.1962 | − | 3.80385i | 0.767640 | − | 0.205689i | ||||
\(343\) | 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 | −0.151608 | − | 0.988441i | \(-0.548445\pi\) |
0.988441 | + | 0.151608i | \(0.0484453\pi\) | |||||||
\(348\) | 6.00000 | + | 10.3923i | 0.321634 | + | 0.557086i | ||||
\(349\) | 27.7128 | 1.48343 | 0.741716 | − | 0.670714i | \(-0.234012\pi\) | ||||
0.741716 | + | 0.670714i | \(0.234012\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −18.0000 | + | 18.0000i | −0.960769 | + | 0.960769i | ||||
\(352\) | 5.07180 | − | 18.9282i | 0.270328 | − | 1.00888i | ||||
\(353\) | −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 | ||||
\(357\) | 41.5692 | 2.20008 | ||||||||
\(358\) | −3.80385 | − | 14.1962i | −0.201040 | − | 0.750290i | ||||
\(359\) | −12.0000 | −0.633336 | −0.316668 | − | 0.948536i | \(-0.602564\pi\) | ||||
−0.316668 | + | 0.948536i | \(0.602564\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −7.00000 | −0.368421 | ||||||||
\(362\) | 5.07180 | + | 18.9282i | 0.266568 | + | 0.994844i | ||||
\(363\) | −1.73205 | −0.0909091 | ||||||||
\(364\) | 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 | −0.901849 | − | 0.432052i | \(-0.857790\pi\) |
0.432052 | + | 0.901849i | \(0.357790\pi\) | |||||||
\(368\) | −1.46410 | − | 5.46410i | −0.0763216 | − | 0.284836i | ||||
\(369\) | 18.0000i | 0.937043i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 20.7846 | 1.07908 | ||||||||
\(372\) | 12.0000 | − | 6.92820i | 0.622171 | − | 0.359211i | ||||
\(373\) | 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 | ||||
\(378\) | 15.5885 | − | 27.0000i | 0.801784 | − | 1.38873i | ||||
\(379\) | 3.46410 | 0.177939 | 0.0889695 | − | 0.996034i | \(-0.471643\pi\) | ||||
0.0889695 | + | 0.996034i | \(0.471643\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.19615 | + | 5.19615i | −0.266207 | + | 0.266207i | ||||
\(382\) | 4.39230 | + | 16.3923i | 0.224730 | + | 0.838703i | ||||
\(383\) | 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 | ||||
\(388\) | −4.39230 | + | 16.3923i | −0.222985 | + | 0.832193i | ||||
\(389\) | 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 | ||||
\(393\) | 30.0000 | 1.51330 | ||||||||
\(394\) | 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 | \(0.960716\pi\) | |||||||
\(398\) | 1.46410 | + | 5.46410i | 0.0733888 | + | 0.273891i | ||||
\(399\) | 18.0000 | − | 18.0000i | 0.901127 | − | 0.901127i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 12.0000i | − | 0.599251i | −0.954057 | − | 0.299626i | \(-0.903138\pi\) | ||
0.954057 | − | 0.299626i | \(-0.0968618\pi\) | |||||||
\(402\) | 15.5885 | + | 9.00000i | 0.777482 | + | 0.448879i | ||||
\(403\) | −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 | ||||||||
\(408\) | −27.7128 | −1.37199 | ||||||||
\(409\) | 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 | ||||
\(412\) | −8.19615 | − | 2.19615i | −0.403795 | − | 0.108197i | ||||
\(413\) | −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 | ||||
\(417\) | 18.0000 | 0.881464 | ||||||||
\(418\) | 16.3923 | − | 4.39230i | 0.801774 | − | 0.214835i | ||||
\(419\) | 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 | \(-0.973098\pi\) | ||
0.996431 | − | 0.0844150i | \(-0.0269021\pi\) | |||||||
\(422\) | −1.26795 | − | 4.73205i | −0.0617228 | − | 0.230353i | ||||
\(423\) | 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 | ||||
\(428\) | 3.80385 | − | 14.1962i | 0.183866 | − | 0.686197i | ||||
\(429\) | −20.7846 | + | 20.7846i | −1.00349 | + | 1.00349i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.0000i | 0.578020i | 0.957326 | + | 0.289010i | \(0.0933260\pi\) | ||||
−0.957326 | + | 0.289010i | \(0.906674\pi\) | |||||||
\(432\) | −10.3923 | + | 18.0000i | −0.500000 | + | 0.866025i | ||||
\(433\) | 6.00000 | + | 6.00000i | 0.288342 | + | 0.288342i | 0.836424 | − | 0.548083i | \(-0.184642\pi\) |
−0.548083 | + | 0.836424i | \(0.684642\pi\) | |||||||
\(434\) | 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 | ||||
\(438\) | 18.0000 | + | 10.3923i | 0.860073 | + | 0.496564i | ||||
\(439\) | − | 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 | ||||||
\(442\) | 37.8564 | − | 10.1436i | 1.80065 | − | 0.482482i | ||||
\(443\) | −8.66025 | − | 8.66025i | −0.411461 | − | 0.411461i | 0.470786 | − | 0.882247i | \(-0.343970\pi\) |
−0.882247 | + | 0.470786i | \(0.843970\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 5.19615 | + | 3.00000i | 0.246045 | + | 0.142054i | ||||
\(447\) | 24.0000i | 1.13516i | ||||||||
\(448\) | 24.0000 | + | 24.0000i | 1.13389 | + | 1.13389i | ||||
\(449\) | −18.0000 | −0.849473 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.7846i | 0.978709i | ||||||||
\(452\) | 1.46410 | − | 5.46410i | 0.0688655 | − | 0.257010i | ||||
\(453\) | 34.6410 | 1.62758 | ||||||||
\(454\) | 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 | −0.368351 | − | 0.929687i | \(-0.620077\pi\) |
0.929687 | + | 0.368351i | \(0.120077\pi\) | |||||||
\(458\) | −18.9282 | + | 5.07180i | −0.884457 | + | 0.236989i | ||||
\(459\) | −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 | \(0.758635\pi\) | |||||||
\(462\) | 18.0000 | − | 31.1769i | 0.837436 | − | 1.45048i | ||||
\(463\) | −9.00000 | − | 9.00000i | −0.418265 | − | 0.418265i | 0.466340 | − | 0.884606i | \(-0.345572\pi\) |
−0.884606 | + | 0.466340i | \(0.845572\pi\) | |||||||
\(464\) | −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 | −0.878497 | − | 0.477748i | \(-0.841453\pi\) |
0.477748 | + | 0.878497i | \(0.341453\pi\) | |||||||
\(468\) | 7.60770 | − | 28.3923i | 0.351666 | − | 1.31243i | ||||
\(469\) | 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 | ||||
\(478\) | 32.7846 | − | 8.78461i | 1.49953 | − | 0.401799i | ||||
\(479\) | 36.0000 | 1.64488 | 0.822441 | − | 0.568850i | \(-0.192612\pi\) | ||||
0.822441 | + | 0.568850i | \(0.192612\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −10.9282 | + | 2.92820i | −0.497766 | + | 0.133376i | ||||
\(483\) | − | 10.3923i | − | 0.472866i | ||||||
\(484\) | 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 | −0.959936 | − | 0.280221i | \(-0.909592\pi\) |
0.280221 | + | 0.959936i | \(0.409592\pi\) | |||||||
\(488\) | 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 | \(0.575345\pi\) | |||||||
\(492\) | −10.3923 | − | 18.0000i | −0.468521 | − | 0.811503i | ||||
\(493\) | 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 | ||||
\(498\) | −5.19615 | − | 3.00000i | −0.232845 | − | 0.134433i | ||||
\(499\) | −24.2487 | −1.08552 | −0.542761 | − | 0.839887i | \(-0.682621\pi\) | ||||
−0.542761 | + | 0.839887i | \(0.682621\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 22.5167 | + | 22.5167i | 1.00597 | + | 1.00597i | ||||
\(502\) | 4.73205 | − | 1.26795i | 0.211202 | − | 0.0565913i | ||||
\(503\) | 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 | ||||
\(507\) | 19.0526i | 0.846154i | ||||||||
\(508\) | 2.19615 | − | 8.19615i | 0.0974385 | − | 0.363645i | ||||
\(509\) | − | 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 | ||||
\(513\) | −18.0000 | −0.794719 | ||||||||
\(514\) | −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 | \(0.176208\pi\) | ||||
−0.850652 | + | 0.525730i | \(0.823792\pi\) | |||||||
\(522\) | −3.80385 | − | 14.1962i | −0.166490 | − | 0.621349i | ||||
\(523\) | −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 | ||||
\(528\) | −12.0000 | + | 20.7846i | −0.522233 | + | 0.904534i | ||||
\(529\) | 21.0000i | 0.913043i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 31.1769i | 1.35296i | ||||||||
\(532\) | −7.60770 | + | 28.3923i | −0.329835 | + | 1.23096i | ||||
\(533\) | 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 | ||||||||
\(537\) | 18.0000i | 0.776757i | ||||||||
\(538\) | 10.1436 | + | 37.8564i | 0.437321 | + | 1.63211i | ||||
\(539\) | − | 38.1051i | − | 1.64130i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 41.5692i | 1.78720i | 0.448864 | + | 0.893600i | \(0.351829\pi\) | ||||
−0.448864 | + | 0.893600i | \(0.648171\pi\) | |||||||
\(542\) | 10.9282 | − | 2.92820i | 0.469407 | − | 0.125777i | ||||
\(543\) | − | 24.0000i | − | 1.02994i | ||||||
\(544\) | 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 | \(0.834326\pi\) | |||||||
\(548\) | 27.3205 | + | 7.32051i | 1.16707 | + | 0.312717i | ||||
\(549\) | 10.3923i | 0.443533i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 12.0000i | − | 0.511217i | ||||||
\(552\) | 6.92820i | 0.294884i | ||||||||
\(553\) | −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 | −0.993603 | − | 0.112931i | \(-0.963976\pi\) |
0.112931 | + | 0.993603i | \(0.463976\pi\) | |||||||
\(558\) | −16.3923 | + | 4.39230i | −0.693942 | + | 0.185941i | ||||
\(559\) | 12.0000i | 0.507546i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −24.0000 | − | 24.0000i | −1.01328 | − | 1.01328i | ||||
\(562\) | −6.58846 | − | 24.5885i | −0.277917 | − | 1.03720i | ||||
\(563\) | −5.19615 | − | 5.19615i | −0.218992 | − | 0.218992i | 0.589082 | − | 0.808073i | \(-0.299490\pi\) |
−0.808073 | + | 0.589082i | \(0.799490\pi\) | |||||||
\(564\) | −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 | \(-0.459861\pi\) | ||||
0.125767 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 45.0333i | − | 1.88459i | −0.334790 | − | 0.942293i | \(-0.608665\pi\) | ||
0.334790 | − | 0.942293i | \(-0.391335\pi\) | |||||||
\(572\) | 8.78461 | − | 32.7846i | 0.367303 | − | 1.37079i | ||||
\(573\) | − | 20.7846i | − | 0.868290i | ||||||
\(574\) | −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 | −1.00000 | 0.000866551i | \(-0.999724\pi\) | |
0.000866551 | 1.00000i | \(0.499724\pi\) | ||||||||
\(578\) | 5.49038 | + | 20.4904i | 0.228370 | + | 0.852287i | ||||
\(579\) | −31.1769 | − | 31.1769i | −1.29567 | − | 1.29567i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.3923 | −0.431145 | ||||||||
\(582\) | 10.3923 | − | 18.0000i | 0.430775 | − | 0.746124i | ||||
\(583\) | −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 | −0.741947 | − | 0.670458i | \(-0.766098\pi\) |
0.670458 | + | 0.741947i | \(0.266098\pi\) | |||||||
\(588\) | 19.0526 | + | 33.0000i | 0.785714 | + | 1.36090i | ||||
\(589\) | −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 | ||||
\(597\) | − | 6.92820i | − | 0.283552i | ||||||
\(598\) | −2.53590 | − | 9.46410i | −0.103701 | − | 0.387016i | ||||
\(599\) | 24.0000 | 0.980613 | 0.490307 | − | 0.871550i | \(-0.336885\pi\) | ||||
0.490307 | + | 0.871550i | \(0.336885\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −8.00000 | −0.326327 | −0.163163 | − | 0.986599i | \(-0.552170\pi\) | ||||
−0.163163 | + | 0.986599i | \(0.552170\pi\) | |||||||
\(602\) | −3.80385 | − | 14.1962i | −0.155033 | − | 0.578592i | ||||
\(603\) | −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 | −0.643598 | − | 0.765364i | \(-0.722559\pi\) |
0.765364 | + | 0.643598i | \(0.222559\pi\) | |||||||
\(608\) | 5.07180 | − | 18.9282i | 0.205689 | − | 0.767640i | ||||
\(609\) | −18.0000 | − | 18.0000i | −0.729397 | − | 0.729397i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.6410 | 1.40143 | ||||||||
\(612\) | 32.7846 | + | 8.78461i | 1.32524 | + | 0.355097i | ||||
\(613\) | −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 | \(0.676868\pi\) | |||||||
\(618\) | 9.00000 | + | 5.19615i | 0.362033 | + | 0.209020i | ||||
\(619\) | 31.1769 | 1.25311 | 0.626553 | − | 0.779379i | \(-0.284465\pi\) | ||||
0.626553 | + | 0.779379i | \(0.284465\pi\) | |||||||
\(620\) | 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 | ||||
\(627\) | −20.7846 | −0.830057 | ||||||||
\(628\) | −18.9282 | − | 5.07180i | −0.755318 | − | 0.202387i | ||||
\(629\) | 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 | ||||
\(633\) | 6.00000i | 0.238479i | ||||||||
\(634\) | −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 | ||||
\(638\) | −4.39230 | − | 16.3923i | −0.173893 | − | 0.648978i | ||||
\(639\) | − | 36.0000i | − | 1.42414i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.00000i | 0.236986i | 0.992955 | + | 0.118493i | \(0.0378063\pi\) | ||||
−0.992955 | + | 0.118493i | \(0.962194\pi\) | |||||||
\(642\) | −9.00000 | + | 15.5885i | −0.355202 | + | 0.615227i | ||||
\(643\) | 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 | ||||
\(652\) | 6.33975 | − | 23.6603i | 0.248284 | − | 0.926607i | ||||
\(653\) | −17.3205 | − | 17.3205i | −0.677804 | − | 0.677804i | 0.281699 | − | 0.959503i | \(-0.409102\pi\) |
−0.959503 | + | 0.281699i | \(0.909102\pi\) | |||||||
\(654\) | 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 | ||||
\(658\) | −40.9808 | + | 10.9808i | −1.59760 | + | 0.428075i | ||||
\(659\) | − | 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 | \(-0.792645\pi\) | ||
0.795220 | − | 0.606321i | \(-0.207355\pi\) | |||||||
\(662\) | −3.80385 | − | 14.1962i | −0.147841 | − | 0.551749i | ||||
\(663\) | −48.0000 | −1.86417 | ||||||||
\(664\) | 6.92820 | 0.268866 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.46410 | − | 3.46410i | −0.134131 | − | 0.134131i | ||||
\(668\) | −35.5167 | − | 9.51666i | −1.37418 | − | 0.368211i | ||||
\(669\) | −5.19615 | − | 5.19615i | −0.200895 | − | 0.200895i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12.0000i | 0.463255i | ||||||||
\(672\) | −20.7846 | − | 36.0000i | −0.801784 | − | 1.38873i | ||||
\(673\) | 6.00000 | + | 6.00000i | 0.231283 | + | 0.231283i | 0.813228 | − | 0.581945i | \(-0.197708\pi\) |
−0.581945 | + | 0.813228i | \(0.697708\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −11.0000 | − | 19.0526i | −0.423077 | − | 0.732791i | ||||
\(677\) | 10.3923 | − | 10.3923i | 0.399409 | − | 0.399409i | −0.478616 | − | 0.878024i | \(-0.658861\pi\) |
0.878024 | + | 0.478616i | \(0.158861\pi\) | |||||||
\(678\) | −3.46410 | + | 6.00000i | −0.133038 | + | 0.230429i | ||||
\(679\) | − | 36.0000i | − | 1.38155i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.0000 | + | 33.0000i | −1.26456 | + | 1.26456i | ||||
\(682\) | −18.9282 | + | 5.07180i | −0.724798 | + | 0.194209i | ||||
\(683\) | 29.4449 | + | 29.4449i | 1.12668 | + | 1.12668i | 0.990714 | + | 0.135962i | \(0.0434126\pi\) |
0.135962 | + | 0.990714i | \(0.456587\pi\) | |||||||
\(684\) | 18.0000 | − | 10.3923i | 0.688247 | − | 0.397360i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.7846 | + | 12.0000i | 0.793560 | + | 0.458162i | ||||
\(687\) | 24.0000 | 0.915657 | ||||||||
\(688\) | 2.53590 | + | 9.46410i | 0.0966802 | + | 0.360815i | ||||
\(689\) | −24.0000 | −0.914327 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 3.46410i | − | 0.131781i | −0.997827 | − | 0.0658903i | \(-0.979011\pi\) | ||
0.997827 | − | 0.0658903i | \(-0.0209887\pi\) | |||||||
\(692\) | −18.9282 | − | 5.07180i | −0.719542 | − | 0.192801i | ||||
\(693\) | −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 | ||||
\(698\) | 37.8564 | − | 10.1436i | 1.43289 | − | 0.383941i | ||||
\(699\) | 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 | \(0.584275\pi\) | |||||||
\(702\) | −18.0000 | + | 31.1769i | −0.679366 | + | 1.17670i | ||||
\(703\) | 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 | ||||
\(708\) | −18.0000 | − | 31.1769i | −0.676481 | − | 1.17170i | ||||
\(709\) | 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 | ||||
\(717\) | −41.5692 | −1.55243 | ||||||||
\(718\) | −16.3923 | + | 4.39230i | −0.611755 | + | 0.163919i | ||||
\(719\) | −12.0000 | −0.447524 | −0.223762 | − | 0.974644i | \(-0.571834\pi\) | ||||
−0.223762 | + | 0.974644i | \(0.571834\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.0000 | 0.670355 | ||||||||
\(722\) | −9.56218 | + | 2.56218i | −0.355867 | + | 0.0953544i | ||||
\(723\) | 13.8564 | 0.515325 | ||||||||
\(724\) | 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 | −0.371938 | − | 0.928257i | \(-0.621307\pi\) |
0.928257 | + | 0.371938i | \(0.121307\pi\) | |||||||
\(728\) | 41.5692 | + | 41.5692i | 1.54066 | + | 1.54066i | ||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.8564 | −0.512498 | ||||||||
\(732\) | −6.00000 | − | 10.3923i | −0.221766 | − | 0.384111i | ||||
\(733\) | 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 | ||||
\(738\) | 6.58846 | + | 24.5885i | 0.242524 | + | 0.905114i | ||||
\(739\) | −3.46410 | −0.127429 | −0.0637145 | − | 0.997968i | \(-0.520295\pi\) | ||||
−0.0637145 | + | 0.997968i | \(0.520295\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −20.7846 | + | 20.7846i | −0.763542 | + | 0.763542i | ||||
\(742\) | 28.3923 | − | 7.60770i | 1.04231 | − | 0.279287i | ||||
\(743\) | 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 | ||||
\(748\) | 37.8564 | + | 10.1436i | 1.38417 | + | 0.370887i | ||||
\(749\) | 31.1769i | 1.13918i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32.0000 | 1.16770 | 0.583848 | − | 0.811863i | \(-0.301546\pi\) | ||||
0.583848 | + | 0.811863i | \(0.301546\pi\) | |||||||
\(752\) | 27.3205 | − | 7.32051i | 0.996276 | − | 0.266951i | ||||
\(753\) | −6.00000 | −0.218652 | ||||||||
\(754\) | −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 | \(0.497687\pi\) | |||||||
\(758\) | 4.73205 | − | 1.26795i | 0.171876 | − | 0.0460540i | ||||
\(759\) | −6.00000 | + | 6.00000i | −0.217786 | + | 0.217786i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 48.0000i | − | 1.74000i | −0.493053 | − | 0.869999i | \(-0.664119\pi\) | ||
0.493053 | − | 0.869999i | \(-0.335881\pi\) | |||||||
\(762\) | −5.19615 | + | 9.00000i | −0.188237 | + | 0.326036i | ||||
\(763\) | 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 | ||||
\(768\) | 13.8564 | + | 24.0000i | 0.500000 | + | 0.866025i | ||||
\(769\) | − | 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 | ||||
\(772\) | 49.1769 | + | 13.1769i | 1.76992 | + | 0.474248i | ||||
\(773\) | −3.46410 | − | 3.46410i | −0.124595 | − | 0.124595i | 0.642060 | − | 0.766655i | \(-0.278080\pi\) |
−0.766655 | + | 0.642060i | \(0.778080\pi\) | |||||||
\(774\) | −5.19615 | + | 9.00000i | −0.186772 | + | 0.323498i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 24.0000i | 0.861550i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 5.07180 | + | 18.9282i | 0.181833 | + | 0.678609i | ||||
\(779\) | 20.7846i | 0.744686i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 41.5692i | − | 1.48746i | ||||||
\(782\) | 10.9282 | − | 2.92820i | 0.390792 | − | 0.104712i | ||||
\(783\) | 18.0000i | 0.643268i | ||||||||
\(784\) | −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 | \(0.483794\pi\) | |||||||
\(788\) | 2.53590 | − | 9.46410i | 0.0903376 | − | 0.337145i | ||||
\(789\) | 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 | −0.991213 | − | 0.132279i | \(-0.957770\pi\) |
0.132279 | + | 0.991213i | \(0.457770\pi\) | |||||||
\(798\) | 18.0000 | − | 31.1769i | 0.637193 | − | 1.10365i | ||||
\(799\) | 40.0000i | 1.41510i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 36.0000 | 1.27200 | ||||||||
\(802\) | −4.39230 | − | 16.3923i | −0.155098 | − | 0.578832i | ||||
\(803\) | −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 | ||||
\(807\) | − | 48.0000i | − | 1.68968i | ||||||
\(808\) | −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 | \(-0.815623\pi\) | ||
0.836881 | − | 0.547385i | \(-0.184377\pi\) | |||||||
\(812\) | 28.3923 | + | 7.60770i | 0.996375 | + | 0.266978i | ||||
\(813\) | −13.8564 | −0.485965 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −37.8564 | + | 10.1436i | −1.32524 | + | 0.355097i | ||||
\(817\) | −6.00000 | + | 6.00000i | −0.209913 | + | 0.209913i | ||||
\(818\) | 1.46410 | + | 5.46410i | 0.0511911 | + | 0.191048i | ||||
\(819\) | 62.3538i | 2.17882i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 41.5692 | 1.45078 | 0.725388 | − | 0.688340i | \(-0.241660\pi\) | ||||
0.725388 | + | 0.688340i | \(0.241660\pi\) | |||||||
\(822\) | −30.0000 | − | 17.3205i | −1.04637 | − | 0.604122i | ||||
\(823\) | 3.00000 | + | 3.00000i | 0.104573 | + | 0.104573i | 0.757458 | − | 0.652884i | \(-0.226441\pi\) |
−0.652884 | + | 0.757458i | \(0.726441\pi\) | |||||||
\(824\) | −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 | −0.841462 | − | 0.540316i | \(-0.818305\pi\) |
0.540316 | + | 0.841462i | \(0.318305\pi\) | |||||||
\(828\) | 2.19615 | − | 8.19615i | 0.0763216 | − | 0.284836i | ||||
\(829\) | 51.9615 | 1.80470 | 0.902349 | − | 0.431006i | \(-0.141841\pi\) | ||||
0.902349 | + | 0.431006i | \(0.141841\pi\) | |||||||
\(830\) | 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 | ||||
\(837\) | 20.7846 | 0.718421 | ||||||||
\(838\) | 8.87564 | + | 33.1244i | 0.306604 | + | 1.14426i | ||||
\(839\) | 12.0000 | 0.414286 | 0.207143 | − | 0.978311i | \(-0.433583\pi\) | ||||
0.207143 | + | 0.978311i | \(0.433583\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 17.0000 | 0.586207 | ||||||||
\(842\) | −1.26795 | − | 4.73205i | −0.0436964 | − | 0.163077i | ||||
\(843\) | 31.1769i | 1.07379i | ||||||||
\(844\) | −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 | ||||
\(848\) | −18.9282 | + | 5.07180i | −0.649997 | + | 0.174166i | ||||
\(849\) | 9.00000 | − | 9.00000i | 0.308879 | − | 0.308879i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 20.7846 | + | 36.0000i | 0.712069 | + | 1.23334i | ||||
\(853\) | −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 | \(0.533869\pi\) | |||||||
\(858\) | −20.7846 | + | 36.0000i | −0.709575 | + | 1.22902i | ||||
\(859\) | −24.2487 | −0.827355 | −0.413678 | − | 0.910423i | \(-0.635756\pi\) | ||||
−0.413678 | + | 0.910423i | \(0.635756\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 31.1769 | + | 31.1769i | 1.06251 | + | 1.06251i | ||||
\(862\) | 4.39230 | + | 16.3923i | 0.149602 | + | 0.558324i | ||||
\(863\) | 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 | ||||
\(867\) | − | 25.9808i | − | 0.882353i | ||||||
\(868\) | 8.78461 | − | 32.7846i | 0.298169 | − | 1.11278i | ||||
\(869\) | 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 | \(0.857337\pi\) | |||||||
\(878\) | −11.7128 | − | 43.7128i | −0.395288 | − | 1.47524i | ||||
\(879\) | −12.0000 | − | 12.0000i | −0.404750 | − | 0.404750i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 30.0000i | − | 1.01073i | −0.862907 | − | 0.505363i | \(-0.831359\pi\) | ||
0.862907 | − | 0.505363i | \(-0.168641\pi\) | |||||||
\(882\) | −12.0788 | − | 45.0788i | −0.406716 | − | 1.51788i | ||||
\(883\) | −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 | ||||||||
\(892\) | 8.19615 | + | 2.19615i | 0.274427 | + | 0.0735326i | ||||
\(893\) | 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 | ||||
\(897\) | 12.0000i | 0.400668i | ||||||||
\(898\) | −24.5885 | + | 6.58846i | −0.820527 | + | 0.219860i | ||||
\(899\) | 13.8564i | 0.462137i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 27.7128i | − | 0.923248i | ||||||
\(902\) | 7.60770 | + | 28.3923i | 0.253309 | + | 0.945360i | ||||
\(903\) | 18.0000i | 0.599002i | ||||||||
\(904\) | − | 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 | \(0.897627\pi\) | |||||||
\(908\) | 13.9474 | − | 52.0526i | 0.462862 | − | 1.72742i | ||||
\(909\) | −10.3923 | −0.344691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12.0000i | − | 0.397578i | −0.980042 | − | 0.198789i | \(-0.936299\pi\) | ||
0.980042 | − | 0.198789i | \(-0.0637008\pi\) | |||||||
\(912\) | −12.0000 | + | 20.7846i | −0.397360 | + | 0.688247i | ||||
\(913\) | 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 | ||||
\(918\) | −36.0000 | − | 20.7846i | −1.18818 | − | 0.685994i | ||||
\(919\) | 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 | ||||
\(922\) | −42.5885 | + | 11.4115i | −1.40258 | + | 0.375819i | ||||
\(923\) | −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 | ||||
\(928\) | −18.9282 | − | 5.07180i | −0.621349 | − | 0.166490i | ||||
\(929\) | −6.00000 | −0.196854 | −0.0984268 | − | 0.995144i | \(-0.531381\pi\) | ||||
−0.0984268 | + | 0.995144i | \(0.531381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 38.1051i | − | 1.24884i | ||||||
\(932\) | −2.92820 | + | 10.9282i | −0.0959165 | + | 0.357965i | ||||
\(933\) | 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 | −0.349064 | − | 0.937099i | \(-0.613501\pi\) |
0.937099 | + | 0.349064i | \(0.113501\pi\) | |||||||
\(938\) | 42.5885 | − | 11.4115i | 1.39056 | − | 0.372600i | ||||
\(939\) | 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 | \(0.408897\pi\) | |||||||
\(942\) | 20.7846 | + | 12.0000i | 0.677199 | + | 0.390981i | ||||
\(943\) | 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 | −0.833675 | − | 0.552255i | \(-0.813768\pi\) |
0.552255 | + | 0.833675i | \(0.313768\pi\) | |||||||
\(948\) | −13.8564 | − | 24.0000i | −0.450035 | − | 0.779484i | ||||
\(949\) | −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 | ||||
\(957\) | 20.7846i | 0.671871i | ||||||||
\(958\) | 49.1769 | − | 13.1769i | 1.58883 | − | 0.425727i | ||||
\(959\) | −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 | \(0.597092\pi\) |
−0.953840 | + | 0.300316i | \(0.902908\pi\) | |||||||
\(968\) | 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 | \(0.627210\pi\) | |||||||
\(972\) | −27.0000 | + | 15.5885i | −0.866025 | + | 0.500000i | ||||
\(973\) | 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 | \(0.867891\pi\) | |||||||
\(978\) | −15.0000 | + | 25.9808i | −0.479647 | + | 0.830773i | ||||
\(979\) | 41.5692 | 1.32856 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −51.9615 | −1.65900 | ||||||||
\(982\) | −14.1962 | + | 3.80385i | −0.453017 | + | 0.121386i | ||||
\(983\) | 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 | ||||
\(987\) | 51.9615 | 1.65395 | ||||||||
\(988\) | 8.78461 | − | 32.7846i | 0.279476 | − | 1.04302i | ||||
\(989\) | 3.46410i | 0.110152i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.0000 | 0.635321 | 0.317660 | − | 0.948205i | \(-0.397103\pi\) | ||||
0.317660 | + | 0.948205i | \(0.397103\pi\) | |||||||
\(992\) | −5.85641 | + | 21.8564i | −0.185941 | + | 0.693942i | ||||
\(993\) | 18.0000i | 0.571213i | ||||||||
\(994\) | 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 | \(0.774718\pi\) | |||||||
\(998\) | −33.1244 | + | 8.87564i | −1.04853 | + | 0.280954i | ||||
\(999\) | 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.e.293.2 | yes | 4 | |
3.2 | odd | 2 | 600.2.w.c.293.1 | ✓ | 4 | ||
5.2 | odd | 4 | 600.2.w.c.557.2 | yes | 4 | ||
5.3 | odd | 4 | 600.2.w.f.557.1 | yes | 4 | ||
5.4 | even | 2 | 600.2.w.d.293.1 | yes | 4 | ||
8.5 | even | 2 | inner | 600.2.w.e.293.1 | yes | 4 | |
15.2 | even | 4 | inner | 600.2.w.e.557.1 | yes | 4 | |
15.8 | even | 4 | 600.2.w.d.557.2 | yes | 4 | ||
15.14 | odd | 2 | 600.2.w.f.293.2 | yes | 4 | ||
24.5 | odd | 2 | 600.2.w.c.293.2 | yes | 4 | ||
40.13 | odd | 4 | 600.2.w.f.557.2 | yes | 4 | ||
40.29 | even | 2 | 600.2.w.d.293.2 | yes | 4 | ||
40.37 | odd | 4 | 600.2.w.c.557.1 | yes | 4 | ||
120.29 | odd | 2 | 600.2.w.f.293.1 | yes | 4 | ||
120.53 | even | 4 | 600.2.w.d.557.1 | yes | 4 | ||
120.77 | even | 4 | inner | 600.2.w.e.557.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
600.2.w.c.293.1 | ✓ | 4 | 3.2 | odd | 2 | ||
600.2.w.c.293.2 | yes | 4 | 24.5 | odd | 2 | ||
600.2.w.c.557.1 | yes | 4 | 40.37 | odd | 4 | ||
600.2.w.c.557.2 | yes | 4 | 5.2 | odd | 4 | ||
600.2.w.d.293.1 | yes | 4 | 5.4 | even | 2 | ||
600.2.w.d.293.2 | yes | 4 | 40.29 | even | 2 | ||
600.2.w.d.557.1 | yes | 4 | 120.53 | even | 4 | ||
600.2.w.d.557.2 | yes | 4 | 15.8 | even | 4 | ||
600.2.w.e.293.1 | yes | 4 | 8.5 | even | 2 | inner | |
600.2.w.e.293.2 | yes | 4 | 1.1 | even | 1 | trivial | |
600.2.w.e.557.1 | yes | 4 | 15.2 | even | 4 | inner | |
600.2.w.e.557.2 | yes | 4 | 120.77 | even | 4 | inner | |
600.2.w.f.293.1 | yes | 4 | 120.29 | odd | 2 | ||
600.2.w.f.293.2 | yes | 4 | 15.14 | odd | 2 | ||
600.2.w.f.557.1 | yes | 4 | 5.3 | odd | 4 | ||
600.2.w.f.557.2 | yes | 4 | 40.13 | odd | 4 |