Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(79,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.79");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.79 |
Dual form | 546.2.i.d.235.1 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | 0.500000 | + | 0.866025i | 0.288675 | + | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −2.50000 | + | 0.866025i | −0.944911 | + | 0.327327i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | 0.500000 | − | 0.866025i | 0.144338 | − | 0.250000i | ||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 0.500000 | − | 2.59808i | 0.133631 | − | 0.694365i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | −3.50000 | − | 6.06218i | −0.848875 | − | 1.47029i | −0.882213 | − | 0.470850i | \(-0.843947\pi\) |
0.0333386 | − | 0.999444i | \(-0.489386\pi\) | |||||||
\(18\) | −0.500000 | − | 0.866025i | −0.117851 | − | 0.204124i | ||||
\(19\) | −3.50000 | + | 6.06218i | −0.802955 | + | 1.39076i | 0.114708 | + | 0.993399i | \(0.463407\pi\) |
−0.917663 | + | 0.397360i | \(0.869927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | − | 1.73205i | −0.436436 | − | 0.377964i | ||||
\(22\) | −5.00000 | −1.06600 | ||||||||
\(23\) | −1.00000 | + | 1.73205i | −0.208514 | + | 0.361158i | −0.951247 | − | 0.308431i | \(-0.900196\pi\) |
0.742732 | + | 0.669588i | \(0.233529\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 2.50000 | + | 4.33013i | 0.500000 | + | 0.866025i | ||||
\(26\) | 0.500000 | − | 0.866025i | 0.0980581 | − | 0.169842i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.00000 | + | 1.73205i | 0.377964 | + | 0.327327i | ||||
\(29\) | −9.00000 | −1.67126 | −0.835629 | − | 0.549294i | \(-0.814897\pi\) | ||||
−0.835629 | + | 0.549294i | \(0.814897\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −2.50000 | + | 4.33013i | −0.435194 | + | 0.753778i | ||||
\(34\) | 7.00000 | 1.20049 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.00000 | + | 3.46410i | −0.328798 | + | 0.569495i | −0.982274 | − | 0.187453i | \(-0.939977\pi\) |
0.653476 | + | 0.756948i | \(0.273310\pi\) | |||||||
\(38\) | −3.50000 | − | 6.06218i | −0.567775 | − | 0.983415i | ||||
\(39\) | −0.500000 | − | 0.866025i | −0.0800641 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.00000 | 0.624695 | 0.312348 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312348 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(42\) | 2.50000 | − | 0.866025i | 0.385758 | − | 0.133631i | ||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 2.50000 | − | 4.33013i | 0.376889 | − | 0.652791i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | − | 1.73205i | −0.147442 | − | 0.255377i | ||||
\(47\) | 1.50000 | − | 2.59808i | 0.218797 | − | 0.378968i | −0.735643 | − | 0.677369i | \(-0.763120\pi\) |
0.954441 | + | 0.298401i | \(0.0964533\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 5.50000 | − | 4.33013i | 0.785714 | − | 0.618590i | ||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | 3.50000 | − | 6.06218i | 0.490098 | − | 0.848875i | ||||
\(52\) | 0.500000 | + | 0.866025i | 0.0693375 | + | 0.120096i | ||||
\(53\) | −0.500000 | − | 0.866025i | −0.0686803 | − | 0.118958i | 0.829640 | − | 0.558298i | \(-0.188546\pi\) |
−0.898321 | + | 0.439340i | \(0.855212\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.50000 | + | 0.866025i | −0.334077 | + | 0.115728i | ||||
\(57\) | −7.00000 | −0.927173 | ||||||||
\(58\) | 4.50000 | − | 7.79423i | 0.590879 | − | 1.02343i | ||||
\(59\) | −3.50000 | − | 6.06218i | −0.455661 | − | 0.789228i | 0.543065 | − | 0.839691i | \(-0.317264\pi\) |
−0.998726 | + | 0.0504625i | \(0.983930\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.50000 | + | 11.2583i | −0.832240 | + | 1.44148i | 0.0640184 | + | 0.997949i | \(0.479608\pi\) |
−0.896258 | + | 0.443533i | \(0.853725\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.500000 | − | 2.59808i | 0.0629941 | − | 0.327327i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.50000 | − | 4.33013i | −0.307729 | − | 0.533002i | ||||
\(67\) | −1.50000 | − | 2.59808i | −0.183254 | − | 0.317406i | 0.759733 | − | 0.650236i | \(-0.225330\pi\) |
−0.942987 | + | 0.332830i | \(0.891996\pi\) | |||||||
\(68\) | −3.50000 | + | 6.06218i | −0.424437 | + | 0.735147i | ||||
\(69\) | −2.00000 | −0.240772 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.00000 | 1.06810 | 0.534052 | − | 0.845452i | \(-0.320669\pi\) | ||||
0.534052 | + | 0.845452i | \(0.320669\pi\) | |||||||
\(72\) | −0.500000 | + | 0.866025i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 5.00000 | + | 8.66025i | 0.585206 | + | 1.01361i | 0.994850 | + | 0.101361i | \(0.0323196\pi\) |
−0.409644 | + | 0.912245i | \(0.634347\pi\) | |||||||
\(74\) | −2.00000 | − | 3.46410i | −0.232495 | − | 0.402694i | ||||
\(75\) | −2.50000 | + | 4.33013i | −0.288675 | + | 0.500000i | ||||
\(76\) | 7.00000 | 0.802955 | ||||||||
\(77\) | −10.0000 | − | 8.66025i | −1.13961 | − | 0.986928i | ||||
\(78\) | 1.00000 | 0.113228 | ||||||||
\(79\) | −7.00000 | + | 12.1244i | −0.787562 | + | 1.36410i | 0.139895 | + | 0.990166i | \(0.455323\pi\) |
−0.927457 | + | 0.373930i | \(0.878010\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −2.00000 | + | 3.46410i | −0.220863 | + | 0.382546i | ||||
\(83\) | 16.0000 | 1.75623 | 0.878114 | − | 0.478451i | \(-0.158802\pi\) | ||||
0.878114 | + | 0.478451i | \(0.158802\pi\) | |||||||
\(84\) | −0.500000 | + | 2.59808i | −0.0545545 | + | 0.283473i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.00000 | + | 1.73205i | −0.107833 | + | 0.186772i | ||||
\(87\) | −4.50000 | − | 7.79423i | −0.482451 | − | 0.835629i | ||||
\(88\) | 2.50000 | + | 4.33013i | 0.266501 | + | 0.461593i | ||||
\(89\) | 6.00000 | − | 10.3923i | 0.635999 | − | 1.10158i | −0.350304 | − | 0.936636i | \(-0.613922\pi\) |
0.986303 | − | 0.164946i | \(-0.0527450\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.50000 | − | 0.866025i | 0.262071 | − | 0.0907841i | ||||
\(92\) | 2.00000 | 0.208514 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.50000 | + | 2.59808i | 0.154713 | + | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 1.00000 | + | 6.92820i | 0.101015 | + | 0.699854i | ||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | 2.50000 | − | 4.33013i | 0.250000 | − | 0.433013i | ||||
\(101\) | 3.00000 | + | 5.19615i | 0.298511 | + | 0.517036i | 0.975796 | − | 0.218685i | \(-0.0701767\pi\) |
−0.677284 | + | 0.735721i | \(0.736843\pi\) | |||||||
\(102\) | 3.50000 | + | 6.06218i | 0.346552 | + | 0.600245i | ||||
\(103\) | 5.00000 | − | 8.66025i | 0.492665 | − | 0.853320i | −0.507300 | − | 0.861770i | \(-0.669356\pi\) |
0.999964 | + | 0.00844953i | \(0.00268960\pi\) | |||||||
\(104\) | −1.00000 | −0.0980581 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.00000 | 0.0971286 | ||||||||
\(107\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(108\) | 0.500000 | + | 0.866025i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | −4.00000 | − | 6.92820i | −0.383131 | − | 0.663602i | 0.608377 | − | 0.793648i | \(-0.291821\pi\) |
−0.991508 | + | 0.130046i | \(0.958487\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.00000 | −0.379663 | ||||||||
\(112\) | 0.500000 | − | 2.59808i | 0.0472456 | − | 0.245495i | ||||
\(113\) | 1.00000 | 0.0940721 | 0.0470360 | − | 0.998893i | \(-0.485022\pi\) | ||||
0.0470360 | + | 0.998893i | \(0.485022\pi\) | |||||||
\(114\) | 3.50000 | − | 6.06218i | 0.327805 | − | 0.567775i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.50000 | + | 7.79423i | 0.417815 | + | 0.723676i | ||||
\(117\) | 0.500000 | − | 0.866025i | 0.0462250 | − | 0.0800641i | ||||
\(118\) | 7.00000 | 0.644402 | ||||||||
\(119\) | 14.0000 | + | 12.1244i | 1.28338 | + | 1.11144i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | −6.50000 | − | 11.2583i | −0.588482 | − | 1.01928i | ||||
\(123\) | 2.00000 | + | 3.46410i | 0.180334 | + | 0.312348i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.00000 | + | 1.73205i | 0.178174 | + | 0.154303i | ||||
\(127\) | 22.0000 | 1.95218 | 0.976092 | − | 0.217357i | \(-0.0697436\pi\) | ||||
0.976092 | + | 0.217357i | \(0.0697436\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 1.00000 | + | 1.73205i | 0.0880451 | + | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.00000 | + | 15.5885i | −0.786334 | + | 1.36197i | 0.141865 | + | 0.989886i | \(0.454690\pi\) |
−0.928199 | + | 0.372084i | \(0.878643\pi\) | |||||||
\(132\) | 5.00000 | 0.435194 | ||||||||
\(133\) | 3.50000 | − | 18.1865i | 0.303488 | − | 1.57697i | ||||
\(134\) | 3.00000 | 0.259161 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.50000 | − | 6.06218i | −0.300123 | − | 0.519827i | ||||
\(137\) | 6.00000 | + | 10.3923i | 0.512615 | + | 0.887875i | 0.999893 | + | 0.0146279i | \(0.00465636\pi\) |
−0.487278 | + | 0.873247i | \(0.662010\pi\) | |||||||
\(138\) | 1.00000 | − | 1.73205i | 0.0851257 | − | 0.147442i | ||||
\(139\) | 16.0000 | 1.35710 | 0.678551 | − | 0.734553i | \(-0.262608\pi\) | ||||
0.678551 | + | 0.734553i | \(0.262608\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.00000 | 0.252646 | ||||||||
\(142\) | −4.50000 | + | 7.79423i | −0.377632 | + | 0.654077i | ||||
\(143\) | −2.50000 | − | 4.33013i | −0.209061 | − | 0.362103i | ||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −10.0000 | −0.827606 | ||||||||
\(147\) | 6.50000 | + | 2.59808i | 0.536111 | + | 0.214286i | ||||
\(148\) | 4.00000 | 0.328798 | ||||||||
\(149\) | −5.00000 | + | 8.66025i | −0.409616 | + | 0.709476i | −0.994847 | − | 0.101391i | \(-0.967671\pi\) |
0.585231 | + | 0.810867i | \(0.301004\pi\) | |||||||
\(150\) | −2.50000 | − | 4.33013i | −0.204124 | − | 0.353553i | ||||
\(151\) | 8.50000 | + | 14.7224i | 0.691720 | + | 1.19809i | 0.971274 | + | 0.237964i | \(0.0764802\pi\) |
−0.279554 | + | 0.960130i | \(0.590186\pi\) | |||||||
\(152\) | −3.50000 | + | 6.06218i | −0.283887 | + | 0.491708i | ||||
\(153\) | 7.00000 | 0.565916 | ||||||||
\(154\) | 12.5000 | − | 4.33013i | 1.00728 | − | 0.348932i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.500000 | + | 0.866025i | −0.0400320 | + | 0.0693375i | ||||
\(157\) | −5.50000 | − | 9.52628i | −0.438948 | − | 0.760280i | 0.558661 | − | 0.829396i | \(-0.311315\pi\) |
−0.997609 | + | 0.0691164i | \(0.977982\pi\) | |||||||
\(158\) | −7.00000 | − | 12.1244i | −0.556890 | − | 0.964562i | ||||
\(159\) | 0.500000 | − | 0.866025i | 0.0396526 | − | 0.0686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.00000 | − | 5.19615i | 0.0788110 | − | 0.409514i | ||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −6.50000 | + | 11.2583i | −0.509119 | + | 0.881820i | 0.490825 | + | 0.871258i | \(0.336695\pi\) |
−0.999944 | + | 0.0105623i | \(0.996638\pi\) | |||||||
\(164\) | −2.00000 | − | 3.46410i | −0.156174 | − | 0.270501i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −8.00000 | + | 13.8564i | −0.620920 | + | 1.07547i | ||||
\(167\) | −5.00000 | −0.386912 | −0.193456 | − | 0.981109i | \(-0.561970\pi\) | ||||
−0.193456 | + | 0.981109i | \(0.561970\pi\) | |||||||
\(168\) | −2.00000 | − | 1.73205i | −0.154303 | − | 0.133631i | ||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.50000 | − | 6.06218i | −0.267652 | − | 0.463586i | ||||
\(172\) | −1.00000 | − | 1.73205i | −0.0762493 | − | 0.132068i | ||||
\(173\) | 6.50000 | − | 11.2583i | 0.494186 | − | 0.855955i | −0.505792 | − | 0.862656i | \(-0.668800\pi\) |
0.999978 | + | 0.00670064i | \(0.00213290\pi\) | |||||||
\(174\) | 9.00000 | 0.682288 | ||||||||
\(175\) | −10.0000 | − | 8.66025i | −0.755929 | − | 0.654654i | ||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | 3.50000 | − | 6.06218i | 0.263076 | − | 0.455661i | ||||
\(178\) | 6.00000 | + | 10.3923i | 0.449719 | + | 0.778936i | ||||
\(179\) | 5.00000 | + | 8.66025i | 0.373718 | + | 0.647298i | 0.990134 | − | 0.140122i | \(-0.0447496\pi\) |
−0.616417 | + | 0.787420i | \(0.711416\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.0000 | −0.817624 | −0.408812 | − | 0.912619i | \(-0.634057\pi\) | ||||
−0.408812 | + | 0.912619i | \(0.634057\pi\) | |||||||
\(182\) | −0.500000 | + | 2.59808i | −0.0370625 | + | 0.192582i | ||||
\(183\) | −13.0000 | −0.960988 | ||||||||
\(184\) | −1.00000 | + | 1.73205i | −0.0737210 | + | 0.127688i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.5000 | − | 30.3109i | 1.27973 | − | 2.21655i | ||||
\(188\) | −3.00000 | −0.218797 | ||||||||
\(189\) | 2.50000 | − | 0.866025i | 0.181848 | − | 0.0629941i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.00000 | − | 10.3923i | 0.434145 | − | 0.751961i | −0.563081 | − | 0.826402i | \(-0.690384\pi\) |
0.997225 | + | 0.0744412i | \(0.0237173\pi\) | |||||||
\(192\) | 0.500000 | + | 0.866025i | 0.0360844 | + | 0.0625000i | ||||
\(193\) | 4.00000 | + | 6.92820i | 0.287926 | + | 0.498703i | 0.973315 | − | 0.229475i | \(-0.0737008\pi\) |
−0.685388 | + | 0.728178i | \(0.740368\pi\) | |||||||
\(194\) | −3.00000 | + | 5.19615i | −0.215387 | + | 0.373062i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.50000 | − | 2.59808i | −0.464286 | − | 0.185577i | ||||
\(197\) | 22.0000 | 1.56744 | 0.783718 | − | 0.621117i | \(-0.213321\pi\) | ||||
0.783718 | + | 0.621117i | \(0.213321\pi\) | |||||||
\(198\) | 2.50000 | − | 4.33013i | 0.177667 | − | 0.307729i | ||||
\(199\) | −9.00000 | − | 15.5885i | −0.637993 | − | 1.10504i | −0.985873 | − | 0.167497i | \(-0.946431\pi\) |
0.347879 | − | 0.937539i | \(-0.386902\pi\) | |||||||
\(200\) | 2.50000 | + | 4.33013i | 0.176777 | + | 0.306186i | ||||
\(201\) | 1.50000 | − | 2.59808i | 0.105802 | − | 0.183254i | ||||
\(202\) | −6.00000 | −0.422159 | ||||||||
\(203\) | 22.5000 | − | 7.79423i | 1.57919 | − | 0.547048i | ||||
\(204\) | −7.00000 | −0.490098 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 5.00000 | + | 8.66025i | 0.348367 | + | 0.603388i | ||||
\(207\) | −1.00000 | − | 1.73205i | −0.0695048 | − | 0.120386i | ||||
\(208\) | 0.500000 | − | 0.866025i | 0.0346688 | − | 0.0600481i | ||||
\(209\) | −35.0000 | −2.42100 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.0000 | −1.78991 | −0.894957 | − | 0.446153i | \(-0.852794\pi\) | ||||
−0.894957 | + | 0.446153i | \(0.852794\pi\) | |||||||
\(212\) | −0.500000 | + | 0.866025i | −0.0343401 | + | 0.0594789i | ||||
\(213\) | 4.50000 | + | 7.79423i | 0.308335 | + | 0.534052i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 8.00000 | 0.541828 | ||||||||
\(219\) | −5.00000 | + | 8.66025i | −0.337869 | + | 0.585206i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.50000 | + | 6.06218i | 0.235435 | + | 0.407786i | ||||
\(222\) | 2.00000 | − | 3.46410i | 0.134231 | − | 0.232495i | ||||
\(223\) | −1.00000 | −0.0669650 | −0.0334825 | − | 0.999439i | \(-0.510660\pi\) | ||||
−0.0334825 | + | 0.999439i | \(0.510660\pi\) | |||||||
\(224\) | 2.00000 | + | 1.73205i | 0.133631 | + | 0.115728i | ||||
\(225\) | −5.00000 | −0.333333 | ||||||||
\(226\) | −0.500000 | + | 0.866025i | −0.0332595 | + | 0.0576072i | ||||
\(227\) | −6.00000 | − | 10.3923i | −0.398234 | − | 0.689761i | 0.595274 | − | 0.803523i | \(-0.297043\pi\) |
−0.993508 | + | 0.113761i | \(0.963710\pi\) | |||||||
\(228\) | 3.50000 | + | 6.06218i | 0.231793 | + | 0.401478i | ||||
\(229\) | −9.00000 | + | 15.5885i | −0.594737 | + | 1.03011i | 0.398847 | + | 0.917017i | \(0.369410\pi\) |
−0.993584 | + | 0.113097i | \(0.963923\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.50000 | − | 12.9904i | 0.164488 | − | 0.854704i | ||||
\(232\) | −9.00000 | −0.590879 | ||||||||
\(233\) | 1.50000 | − | 2.59808i | 0.0982683 | − | 0.170206i | −0.812700 | − | 0.582683i | \(-0.802003\pi\) |
0.910968 | + | 0.412477i | \(0.135336\pi\) | |||||||
\(234\) | 0.500000 | + | 0.866025i | 0.0326860 | + | 0.0566139i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.50000 | + | 6.06218i | −0.227831 | + | 0.394614i | ||||
\(237\) | −14.0000 | −0.909398 | ||||||||
\(238\) | −17.5000 | + | 6.06218i | −1.13436 | + | 0.392953i | ||||
\(239\) | −1.00000 | −0.0646846 | −0.0323423 | − | 0.999477i | \(-0.510297\pi\) | ||||
−0.0323423 | + | 0.999477i | \(0.510297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(242\) | −7.00000 | − | 12.1244i | −0.449977 | − | 0.779383i | ||||
\(243\) | 0.500000 | − | 0.866025i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | 13.0000 | 0.832240 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −4.00000 | −0.255031 | ||||||||
\(247\) | 3.50000 | − | 6.06218i | 0.222700 | − | 0.385727i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.00000 | + | 13.8564i | 0.506979 | + | 0.878114i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.0000 | 1.13615 | 0.568075 | − | 0.822977i | \(-0.307688\pi\) | ||||
0.568075 | + | 0.822977i | \(0.307688\pi\) | |||||||
\(252\) | −2.50000 | + | 0.866025i | −0.157485 | + | 0.0545545i | ||||
\(253\) | −10.0000 | −0.628695 | ||||||||
\(254\) | −11.0000 | + | 19.0526i | −0.690201 | + | 1.19546i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 7.00000 | − | 12.1244i | 0.436648 | − | 0.756297i | −0.560781 | − | 0.827964i | \(-0.689499\pi\) |
0.997429 | + | 0.0716680i | \(0.0228322\pi\) | |||||||
\(258\) | −2.00000 | −0.124515 | ||||||||
\(259\) | 2.00000 | − | 10.3923i | 0.124274 | − | 0.645746i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.50000 | − | 7.79423i | 0.278543 | − | 0.482451i | ||||
\(262\) | −9.00000 | − | 15.5885i | −0.556022 | − | 0.963058i | ||||
\(263\) | 2.00000 | + | 3.46410i | 0.123325 | + | 0.213606i | 0.921077 | − | 0.389380i | \(-0.127311\pi\) |
−0.797752 | + | 0.602986i | \(0.793977\pi\) | |||||||
\(264\) | −2.50000 | + | 4.33013i | −0.153864 | + | 0.266501i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 14.0000 | + | 12.1244i | 0.858395 | + | 0.743392i | ||||
\(267\) | 12.0000 | 0.734388 | ||||||||
\(268\) | −1.50000 | + | 2.59808i | −0.0916271 | + | 0.158703i | ||||
\(269\) | −11.5000 | − | 19.9186i | −0.701167 | − | 1.21446i | −0.968057 | − | 0.250730i | \(-0.919329\pi\) |
0.266890 | − | 0.963727i | \(-0.414004\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.50000 | + | 2.59808i | −0.0911185 | + | 0.157822i | −0.907982 | − | 0.419009i | \(-0.862378\pi\) |
0.816864 | + | 0.576831i | \(0.195711\pi\) | |||||||
\(272\) | 7.00000 | 0.424437 | ||||||||
\(273\) | 2.00000 | + | 1.73205i | 0.121046 | + | 0.104828i | ||||
\(274\) | −12.0000 | −0.724947 | ||||||||
\(275\) | −12.5000 | + | 21.6506i | −0.753778 | + | 1.30558i | ||||
\(276\) | 1.00000 | + | 1.73205i | 0.0601929 | + | 0.104257i | ||||
\(277\) | −9.50000 | − | 16.4545i | −0.570800 | − | 0.988654i | −0.996484 | − | 0.0837823i | \(-0.973300\pi\) |
0.425684 | − | 0.904872i | \(-0.360033\pi\) | |||||||
\(278\) | −8.00000 | + | 13.8564i | −0.479808 | + | 0.831052i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −24.0000 | −1.43172 | −0.715860 | − | 0.698244i | \(-0.753965\pi\) | ||||
−0.715860 | + | 0.698244i | \(0.753965\pi\) | |||||||
\(282\) | −1.50000 | + | 2.59808i | −0.0893237 | + | 0.154713i | ||||
\(283\) | 5.00000 | + | 8.66025i | 0.297219 | + | 0.514799i | 0.975499 | − | 0.220005i | \(-0.0706075\pi\) |
−0.678280 | + | 0.734804i | \(0.737274\pi\) | |||||||
\(284\) | −4.50000 | − | 7.79423i | −0.267026 | − | 0.462502i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.00000 | 0.295656 | ||||||||
\(287\) | −10.0000 | + | 3.46410i | −0.590281 | + | 0.204479i | ||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −16.0000 | + | 27.7128i | −0.941176 | + | 1.63017i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.00000 | + | 5.19615i | 0.175863 | + | 0.304604i | ||||
\(292\) | 5.00000 | − | 8.66025i | 0.292603 | − | 0.506803i | ||||
\(293\) | −30.0000 | −1.75262 | −0.876309 | − | 0.481749i | \(-0.840002\pi\) | ||||
−0.876309 | + | 0.481749i | \(0.840002\pi\) | |||||||
\(294\) | −5.50000 | + | 4.33013i | −0.320767 | + | 0.252538i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −2.00000 | + | 3.46410i | −0.116248 | + | 0.201347i | ||||
\(297\) | −2.50000 | − | 4.33013i | −0.145065 | − | 0.251259i | ||||
\(298\) | −5.00000 | − | 8.66025i | −0.289642 | − | 0.501675i | ||||
\(299\) | 1.00000 | − | 1.73205i | 0.0578315 | − | 0.100167i | ||||
\(300\) | 5.00000 | 0.288675 | ||||||||
\(301\) | −5.00000 | + | 1.73205i | −0.288195 | + | 0.0998337i | ||||
\(302\) | −17.0000 | −0.978240 | ||||||||
\(303\) | −3.00000 | + | 5.19615i | −0.172345 | + | 0.298511i | ||||
\(304\) | −3.50000 | − | 6.06218i | −0.200739 | − | 0.347690i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3.50000 | + | 6.06218i | −0.200082 | + | 0.346552i | ||||
\(307\) | 19.0000 | 1.08439 | 0.542194 | − | 0.840254i | \(-0.317594\pi\) | ||||
0.542194 | + | 0.840254i | \(0.317594\pi\) | |||||||
\(308\) | −2.50000 | + | 12.9904i | −0.142451 | + | 0.740196i | ||||
\(309\) | 10.0000 | 0.568880 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −10.0000 | − | 17.3205i | −0.567048 | − | 0.982156i | −0.996856 | − | 0.0792356i | \(-0.974752\pi\) |
0.429808 | − | 0.902920i | \(-0.358581\pi\) | |||||||
\(312\) | −0.500000 | − | 0.866025i | −0.0283069 | − | 0.0490290i | ||||
\(313\) | 3.00000 | − | 5.19615i | 0.169570 | − | 0.293704i | −0.768699 | − | 0.639611i | \(-0.779095\pi\) |
0.938269 | + | 0.345907i | \(0.112429\pi\) | |||||||
\(314\) | 11.0000 | 0.620766 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0000 | 0.787562 | ||||||||
\(317\) | −13.0000 | + | 22.5167i | −0.730153 | + | 1.26466i | 0.226665 | + | 0.973973i | \(0.427218\pi\) |
−0.956818 | + | 0.290689i | \(0.906116\pi\) | |||||||
\(318\) | 0.500000 | + | 0.866025i | 0.0280386 | + | 0.0485643i | ||||
\(319\) | −22.5000 | − | 38.9711i | −1.25976 | − | 2.18197i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 4.00000 | + | 3.46410i | 0.222911 | + | 0.193047i | ||||
\(323\) | 49.0000 | 2.72643 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | −2.50000 | − | 4.33013i | −0.138675 | − | 0.240192i | ||||
\(326\) | −6.50000 | − | 11.2583i | −0.360002 | − | 0.623541i | ||||
\(327\) | 4.00000 | − | 6.92820i | 0.221201 | − | 0.383131i | ||||
\(328\) | 4.00000 | 0.220863 | ||||||||
\(329\) | −1.50000 | + | 7.79423i | −0.0826977 | + | 0.429710i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.00000 | + | 3.46410i | −0.109930 | + | 0.190404i | −0.915742 | − | 0.401768i | \(-0.868396\pi\) |
0.805812 | + | 0.592172i | \(0.201729\pi\) | |||||||
\(332\) | −8.00000 | − | 13.8564i | −0.439057 | − | 0.760469i | ||||
\(333\) | −2.00000 | − | 3.46410i | −0.109599 | − | 0.189832i | ||||
\(334\) | 2.50000 | − | 4.33013i | 0.136794 | − | 0.236934i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.50000 | − | 0.866025i | 0.136386 | − | 0.0472456i | ||||
\(337\) | −33.0000 | −1.79762 | −0.898812 | − | 0.438334i | \(-0.855569\pi\) | ||||
−0.898812 | + | 0.438334i | \(0.855569\pi\) | |||||||
\(338\) | −0.500000 | + | 0.866025i | −0.0271964 | + | 0.0471056i | ||||
\(339\) | 0.500000 | + | 0.866025i | 0.0271563 | + | 0.0470360i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.00000 | 0.378517 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | 2.00000 | 0.107833 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 6.50000 | + | 11.2583i | 0.349442 | + | 0.605252i | ||||
\(347\) | 8.00000 | + | 13.8564i | 0.429463 | + | 0.743851i | 0.996826 | − | 0.0796169i | \(-0.0253697\pi\) |
−0.567363 | + | 0.823468i | \(0.692036\pi\) | |||||||
\(348\) | −4.50000 | + | 7.79423i | −0.241225 | + | 0.417815i | ||||
\(349\) | 2.00000 | 0.107058 | 0.0535288 | − | 0.998566i | \(-0.482953\pi\) | ||||
0.0535288 | + | 0.998566i | \(0.482953\pi\) | |||||||
\(350\) | 12.5000 | − | 4.33013i | 0.668153 | − | 0.231455i | ||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 2.50000 | − | 4.33013i | 0.133250 | − | 0.230797i | ||||
\(353\) | −1.00000 | − | 1.73205i | −0.0532246 | − | 0.0921878i | 0.838186 | − | 0.545385i | \(-0.183617\pi\) |
−0.891410 | + | 0.453197i | \(0.850283\pi\) | |||||||
\(354\) | 3.50000 | + | 6.06218i | 0.186023 | + | 0.322201i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −12.0000 | −0.635999 | ||||||||
\(357\) | −3.50000 | + | 18.1865i | −0.185240 | + | 0.962533i | ||||
\(358\) | −10.0000 | −0.528516 | ||||||||
\(359\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | − | 25.9808i | −0.789474 | − | 1.36741i | ||||
\(362\) | 5.50000 | − | 9.52628i | 0.289074 | − | 0.500690i | ||||
\(363\) | −14.0000 | −0.734809 | ||||||||
\(364\) | −2.00000 | − | 1.73205i | −0.104828 | − | 0.0907841i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 6.50000 | − | 11.2583i | 0.339760 | − | 0.588482i | ||||
\(367\) | −1.00000 | − | 1.73205i | −0.0521996 | − | 0.0904123i | 0.838745 | − | 0.544524i | \(-0.183290\pi\) |
−0.890945 | + | 0.454112i | \(0.849957\pi\) | |||||||
\(368\) | −1.00000 | − | 1.73205i | −0.0521286 | − | 0.0902894i | ||||
\(369\) | −2.00000 | + | 3.46410i | −0.104116 | + | 0.180334i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.00000 | + | 1.73205i | 0.103835 | + | 0.0899236i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.5000 | − | 18.1865i | 0.543669 | − | 0.941663i | −0.455020 | − | 0.890481i | \(-0.650368\pi\) |
0.998689 | − | 0.0511818i | \(-0.0162988\pi\) | |||||||
\(374\) | 17.5000 | + | 30.3109i | 0.904903 | + | 1.56734i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.50000 | − | 2.59808i | 0.0773566 | − | 0.133986i | ||||
\(377\) | 9.00000 | 0.463524 | ||||||||
\(378\) | −0.500000 | + | 2.59808i | −0.0257172 | + | 0.133631i | ||||
\(379\) | −4.00000 | −0.205466 | −0.102733 | − | 0.994709i | \(-0.532759\pi\) | ||||
−0.102733 | + | 0.994709i | \(0.532759\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 11.0000 | + | 19.0526i | 0.563547 | + | 0.976092i | ||||
\(382\) | 6.00000 | + | 10.3923i | 0.306987 | + | 0.531717i | ||||
\(383\) | −4.00000 | + | 6.92820i | −0.204390 | + | 0.354015i | −0.949938 | − | 0.312437i | \(-0.898855\pi\) |
0.745548 | + | 0.666452i | \(0.232188\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −8.00000 | −0.407189 | ||||||||
\(387\) | −1.00000 | + | 1.73205i | −0.0508329 | + | 0.0880451i | ||||
\(388\) | −3.00000 | − | 5.19615i | −0.152302 | − | 0.263795i | ||||
\(389\) | 11.5000 | + | 19.9186i | 0.583073 | + | 1.00991i | 0.995113 | + | 0.0987463i | \(0.0314832\pi\) |
−0.412039 | + | 0.911166i | \(0.635183\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.0000 | 0.708010 | ||||||||
\(392\) | 5.50000 | − | 4.33013i | 0.277792 | − | 0.218704i | ||||
\(393\) | −18.0000 | −0.907980 | ||||||||
\(394\) | −11.0000 | + | 19.0526i | −0.554172 | + | 0.959854i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 2.50000 | + | 4.33013i | 0.125630 | + | 0.217597i | ||||
\(397\) | 1.00000 | − | 1.73205i | 0.0501886 | − | 0.0869291i | −0.839840 | − | 0.542834i | \(-0.817351\pi\) |
0.890028 | + | 0.455905i | \(0.150684\pi\) | |||||||
\(398\) | 18.0000 | 0.902258 | ||||||||
\(399\) | 17.5000 | − | 6.06218i | 0.876096 | − | 0.303488i | ||||
\(400\) | −5.00000 | −0.250000 | ||||||||
\(401\) | 19.0000 | − | 32.9090i | 0.948815 | − | 1.64340i | 0.200888 | − | 0.979614i | \(-0.435617\pi\) |
0.747927 | − | 0.663781i | \(-0.231049\pi\) | |||||||
\(402\) | 1.50000 | + | 2.59808i | 0.0748132 | + | 0.129580i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 3.00000 | − | 5.19615i | 0.149256 | − | 0.258518i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.50000 | + | 23.3827i | −0.223331 | + | 1.16046i | ||||
\(407\) | −20.0000 | −0.991363 | ||||||||
\(408\) | 3.50000 | − | 6.06218i | 0.173276 | − | 0.300123i | ||||
\(409\) | 2.00000 | + | 3.46410i | 0.0988936 | + | 0.171289i | 0.911227 | − | 0.411905i | \(-0.135136\pi\) |
−0.812333 | + | 0.583193i | \(0.801803\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.00000 | + | 10.3923i | −0.295958 | + | 0.512615i | ||||
\(412\) | −10.0000 | −0.492665 | ||||||||
\(413\) | 14.0000 | + | 12.1244i | 0.688895 | + | 0.596601i | ||||
\(414\) | 2.00000 | 0.0982946 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.500000 | + | 0.866025i | 0.0245145 | + | 0.0424604i | ||||
\(417\) | 8.00000 | + | 13.8564i | 0.391762 | + | 0.678551i | ||||
\(418\) | 17.5000 | − | 30.3109i | 0.855953 | − | 1.48255i | ||||
\(419\) | 26.0000 | 1.27018 | 0.635092 | − | 0.772437i | \(-0.280962\pi\) | ||||
0.635092 | + | 0.772437i | \(0.280962\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.0000 | 1.85201 | 0.926003 | − | 0.377515i | \(-0.123221\pi\) | ||||
0.926003 | + | 0.377515i | \(0.123221\pi\) | |||||||
\(422\) | 13.0000 | − | 22.5167i | 0.632830 | − | 1.09609i | ||||
\(423\) | 1.50000 | + | 2.59808i | 0.0729325 | + | 0.126323i | ||||
\(424\) | −0.500000 | − | 0.866025i | −0.0242821 | − | 0.0420579i | ||||
\(425\) | 17.5000 | − | 30.3109i | 0.848875 | − | 1.47029i | ||||
\(426\) | −9.00000 | −0.436051 | ||||||||
\(427\) | 6.50000 | − | 33.7750i | 0.314557 | − | 1.63449i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.50000 | − | 4.33013i | 0.120701 | − | 0.209061i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.00000 | + | 13.8564i | 0.385346 | + | 0.667440i | 0.991817 | − | 0.127666i | \(-0.0407486\pi\) |
−0.606471 | + | 0.795106i | \(0.707415\pi\) | |||||||
\(432\) | 0.500000 | − | 0.866025i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | −11.0000 | −0.528626 | −0.264313 | − | 0.964437i | \(-0.585145\pi\) | ||||
−0.264313 | + | 0.964437i | \(0.585145\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −4.00000 | + | 6.92820i | −0.191565 | + | 0.331801i | ||||
\(437\) | −7.00000 | − | 12.1244i | −0.334855 | − | 0.579987i | ||||
\(438\) | −5.00000 | − | 8.66025i | −0.238909 | − | 0.413803i | ||||
\(439\) | 11.0000 | − | 19.0526i | 0.525001 | − | 0.909329i | −0.474575 | − | 0.880215i | \(-0.657398\pi\) |
0.999576 | − | 0.0291138i | \(-0.00926853\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | + | 6.92820i | 0.0476190 | + | 0.329914i | ||||
\(442\) | −7.00000 | −0.332956 | ||||||||
\(443\) | 2.00000 | − | 3.46410i | 0.0950229 | − | 0.164584i | −0.814595 | − | 0.580030i | \(-0.803041\pi\) |
0.909618 | + | 0.415445i | \(0.136374\pi\) | |||||||
\(444\) | 2.00000 | + | 3.46410i | 0.0949158 | + | 0.164399i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0.500000 | − | 0.866025i | 0.0236757 | − | 0.0410075i | ||||
\(447\) | −10.0000 | −0.472984 | ||||||||
\(448\) | −2.50000 | + | 0.866025i | −0.118114 | + | 0.0409159i | ||||
\(449\) | 4.00000 | 0.188772 | 0.0943858 | − | 0.995536i | \(-0.469911\pi\) | ||||
0.0943858 | + | 0.995536i | \(0.469911\pi\) | |||||||
\(450\) | 2.50000 | − | 4.33013i | 0.117851 | − | 0.204124i | ||||
\(451\) | 10.0000 | + | 17.3205i | 0.470882 | + | 0.815591i | ||||
\(452\) | −0.500000 | − | 0.866025i | −0.0235180 | − | 0.0407344i | ||||
\(453\) | −8.50000 | + | 14.7224i | −0.399365 | + | 0.691720i | ||||
\(454\) | 12.0000 | 0.563188 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.00000 | −0.327805 | ||||||||
\(457\) | 5.00000 | − | 8.66025i | 0.233890 | − | 0.405110i | −0.725059 | − | 0.688686i | \(-0.758188\pi\) |
0.958950 | + | 0.283577i | \(0.0915211\pi\) | |||||||
\(458\) | −9.00000 | − | 15.5885i | −0.420542 | − | 0.728401i | ||||
\(459\) | 3.50000 | + | 6.06218i | 0.163366 | + | 0.282958i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.00000 | −0.372597 | −0.186299 | − | 0.982493i | \(-0.559649\pi\) | ||||
−0.186299 | + | 0.982493i | \(0.559649\pi\) | |||||||
\(462\) | 10.0000 | + | 8.66025i | 0.465242 | + | 0.402911i | ||||
\(463\) | 32.0000 | 1.48717 | 0.743583 | − | 0.668644i | \(-0.233125\pi\) | ||||
0.743583 | + | 0.668644i | \(0.233125\pi\) | |||||||
\(464\) | 4.50000 | − | 7.79423i | 0.208907 | − | 0.361838i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.50000 | + | 2.59808i | 0.0694862 | + | 0.120354i | ||||
\(467\) | 3.00000 | − | 5.19615i | 0.138823 | − | 0.240449i | −0.788228 | − | 0.615383i | \(-0.789001\pi\) |
0.927052 | + | 0.374934i | \(0.122335\pi\) | |||||||
\(468\) | −1.00000 | −0.0462250 | ||||||||
\(469\) | 6.00000 | + | 5.19615i | 0.277054 | + | 0.239936i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.50000 | − | 9.52628i | 0.253427 | − | 0.438948i | ||||
\(472\) | −3.50000 | − | 6.06218i | −0.161101 | − | 0.279034i | ||||
\(473\) | 5.00000 | + | 8.66025i | 0.229900 | + | 0.398199i | ||||
\(474\) | 7.00000 | − | 12.1244i | 0.321521 | − | 0.556890i | ||||
\(475\) | −35.0000 | −1.60591 | ||||||||
\(476\) | 3.50000 | − | 18.1865i | 0.160422 | − | 0.833578i | ||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | 0.500000 | − | 0.866025i | 0.0228695 | − | 0.0396111i | ||||
\(479\) | 5.50000 | + | 9.52628i | 0.251301 | + | 0.435267i | 0.963884 | − | 0.266321i | \(-0.0858081\pi\) |
−0.712583 | + | 0.701588i | \(0.752475\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.00000 | − | 3.46410i | 0.0911922 | − | 0.157949i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 5.00000 | − | 1.73205i | 0.227508 | − | 0.0788110i | ||||
\(484\) | 14.0000 | 0.636364 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 2.50000 | + | 4.33013i | 0.113286 | + | 0.196217i | 0.917093 | − | 0.398673i | \(-0.130529\pi\) |
−0.803807 | + | 0.594890i | \(0.797196\pi\) | |||||||
\(488\) | −6.50000 | + | 11.2583i | −0.294241 | + | 0.509641i | ||||
\(489\) | −13.0000 | −0.587880 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.0000 | −0.992846 | −0.496423 | − | 0.868081i | \(-0.665354\pi\) | ||||
−0.496423 | + | 0.868081i | \(0.665354\pi\) | |||||||
\(492\) | 2.00000 | − | 3.46410i | 0.0901670 | − | 0.156174i | ||||
\(493\) | 31.5000 | + | 54.5596i | 1.41869 | + | 2.45724i | ||||
\(494\) | 3.50000 | + | 6.06218i | 0.157472 | + | 0.272750i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.5000 | + | 7.79423i | −1.00926 | + | 0.349619i | ||||
\(498\) | −16.0000 | −0.716977 | ||||||||
\(499\) | −20.0000 | + | 34.6410i | −0.895323 | + | 1.55074i | −0.0619186 | + | 0.998081i | \(0.519722\pi\) |
−0.833404 | + | 0.552664i | \(0.813611\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.50000 | − | 4.33013i | −0.111692 | − | 0.193456i | ||||
\(502\) | −9.00000 | + | 15.5885i | −0.401690 | + | 0.695747i | ||||
\(503\) | −24.0000 | −1.07011 | −0.535054 | − | 0.844818i | \(-0.679709\pi\) | ||||
−0.535054 | + | 0.844818i | \(0.679709\pi\) | |||||||
\(504\) | 0.500000 | − | 2.59808i | 0.0222718 | − | 0.115728i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.00000 | − | 8.66025i | 0.222277 | − | 0.384995i | ||||
\(507\) | 0.500000 | + | 0.866025i | 0.0222058 | + | 0.0384615i | ||||
\(508\) | −11.0000 | − | 19.0526i | −0.488046 | − | 0.845321i | ||||
\(509\) | −12.0000 | + | 20.7846i | −0.531891 | + | 0.921262i | 0.467416 | + | 0.884037i | \(0.345185\pi\) |
−0.999307 | + | 0.0372243i | \(0.988148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.0000 | − | 17.3205i | −0.884748 | − | 0.766214i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 3.50000 | − | 6.06218i | 0.154529 | − | 0.267652i | ||||
\(514\) | 7.00000 | + | 12.1244i | 0.308757 | + | 0.534782i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.00000 | − | 1.73205i | 0.0440225 | − | 0.0762493i | ||||
\(517\) | 15.0000 | 0.659699 | ||||||||
\(518\) | 8.00000 | + | 6.92820i | 0.351500 | + | 0.304408i | ||||
\(519\) | 13.0000 | 0.570637 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.0000 | + | 32.9090i | 0.832405 | + | 1.44177i | 0.896126 | + | 0.443800i | \(0.146370\pi\) |
−0.0637207 | + | 0.997968i | \(0.520297\pi\) | |||||||
\(522\) | 4.50000 | + | 7.79423i | 0.196960 | + | 0.341144i | ||||
\(523\) | −13.0000 | + | 22.5167i | −0.568450 | + | 0.984585i | 0.428269 | + | 0.903651i | \(0.359124\pi\) |
−0.996719 | + | 0.0809336i | \(0.974210\pi\) | |||||||
\(524\) | 18.0000 | 0.786334 | ||||||||
\(525\) | 2.50000 | − | 12.9904i | 0.109109 | − | 0.566947i | ||||
\(526\) | −4.00000 | −0.174408 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −2.50000 | − | 4.33013i | −0.108799 | − | 0.188445i | ||||
\(529\) | 9.50000 | + | 16.4545i | 0.413043 | + | 0.715412i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.00000 | 0.303774 | ||||||||
\(532\) | −17.5000 | + | 6.06218i | −0.758721 | + | 0.262829i | ||||
\(533\) | −4.00000 | −0.173259 | ||||||||
\(534\) | −6.00000 | + | 10.3923i | −0.259645 | + | 0.449719i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1.50000 | − | 2.59808i | −0.0647901 | − | 0.112220i | ||||
\(537\) | −5.00000 | + | 8.66025i | −0.215766 | + | 0.373718i | ||||
\(538\) | 23.0000 | 0.991600 | ||||||||
\(539\) | 32.5000 | + | 12.9904i | 1.39987 | + | 0.559535i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.00000 | + | 13.8564i | −0.343947 | + | 0.595733i | −0.985162 | − | 0.171628i | \(-0.945097\pi\) |
0.641215 | + | 0.767361i | \(0.278431\pi\) | |||||||
\(542\) | −1.50000 | − | 2.59808i | −0.0644305 | − | 0.111597i | ||||
\(543\) | −5.50000 | − | 9.52628i | −0.236028 | − | 0.408812i | ||||
\(544\) | −3.50000 | + | 6.06218i | −0.150061 | + | 0.259914i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.50000 | + | 0.866025i | −0.106990 | + | 0.0370625i | ||||
\(547\) | −38.0000 | −1.62476 | −0.812381 | − | 0.583127i | \(-0.801829\pi\) | ||||
−0.812381 | + | 0.583127i | \(0.801829\pi\) | |||||||
\(548\) | 6.00000 | − | 10.3923i | 0.256307 | − | 0.443937i | ||||
\(549\) | −6.50000 | − | 11.2583i | −0.277413 | − | 0.480494i | ||||
\(550\) | −12.5000 | − | 21.6506i | −0.533002 | − | 0.923186i | ||||
\(551\) | 31.5000 | − | 54.5596i | 1.34195 | − | 2.32432i | ||||
\(552\) | −2.00000 | −0.0851257 | ||||||||
\(553\) | 7.00000 | − | 36.3731i | 0.297670 | − | 1.54674i | ||||
\(554\) | 19.0000 | 0.807233 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.00000 | − | 13.8564i | −0.339276 | − | 0.587643i | ||||
\(557\) | −9.00000 | − | 15.5885i | −0.381342 | − | 0.660504i | 0.609912 | − | 0.792469i | \(-0.291205\pi\) |
−0.991254 | + | 0.131965i | \(0.957871\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.00000 | −0.0845910 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 35.0000 | 1.47770 | ||||||||
\(562\) | 12.0000 | − | 20.7846i | 0.506189 | − | 0.876746i | ||||
\(563\) | 6.00000 | + | 10.3923i | 0.252870 | + | 0.437983i | 0.964315 | − | 0.264758i | \(-0.0852922\pi\) |
−0.711445 | + | 0.702742i | \(0.751959\pi\) | |||||||
\(564\) | −1.50000 | − | 2.59808i | −0.0631614 | − | 0.109399i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −10.0000 | −0.420331 | ||||||||
\(567\) | 2.00000 | + | 1.73205i | 0.0839921 | + | 0.0727393i | ||||
\(568\) | 9.00000 | 0.377632 | ||||||||
\(569\) | 15.5000 | − | 26.8468i | 0.649794 | − | 1.12548i | −0.333378 | − | 0.942793i | \(-0.608189\pi\) |
0.983172 | − | 0.182683i | \(-0.0584781\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.0000 | + | 27.7128i | 0.669579 | + | 1.15975i | 0.978022 | + | 0.208502i | \(0.0668588\pi\) |
−0.308443 | + | 0.951243i | \(0.599808\pi\) | |||||||
\(572\) | −2.50000 | + | 4.33013i | −0.104530 | + | 0.181052i | ||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | 2.00000 | − | 10.3923i | 0.0834784 | − | 0.433766i | ||||
\(575\) | −10.0000 | −0.417029 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 7.00000 | + | 12.1244i | 0.291414 | + | 0.504744i | 0.974144 | − | 0.225927i | \(-0.0725410\pi\) |
−0.682730 | + | 0.730670i | \(0.739208\pi\) | |||||||
\(578\) | −16.0000 | − | 27.7128i | −0.665512 | − | 1.15270i | ||||
\(579\) | −4.00000 | + | 6.92820i | −0.166234 | + | 0.287926i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −40.0000 | + | 13.8564i | −1.65948 | + | 0.574861i | ||||
\(582\) | −6.00000 | −0.248708 | ||||||||
\(583\) | 2.50000 | − | 4.33013i | 0.103539 | − | 0.179336i | ||||
\(584\) | 5.00000 | + | 8.66025i | 0.206901 | + | 0.358364i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15.0000 | − | 25.9808i | 0.619644 | − | 1.07326i | ||||
\(587\) | −45.0000 | −1.85735 | −0.928674 | − | 0.370896i | \(-0.879051\pi\) | ||||
−0.928674 | + | 0.370896i | \(0.879051\pi\) | |||||||
\(588\) | −1.00000 | − | 6.92820i | −0.0412393 | − | 0.285714i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 11.0000 | + | 19.0526i | 0.452480 | + | 0.783718i | ||||
\(592\) | −2.00000 | − | 3.46410i | −0.0821995 | − | 0.142374i | ||||
\(593\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(594\) | 5.00000 | 0.205152 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 10.0000 | 0.409616 | ||||||||
\(597\) | 9.00000 | − | 15.5885i | 0.368345 | − | 0.637993i | ||||
\(598\) | 1.00000 | + | 1.73205i | 0.0408930 | + | 0.0708288i | ||||
\(599\) | 8.00000 | + | 13.8564i | 0.326871 | + | 0.566157i | 0.981889 | − | 0.189456i | \(-0.0606724\pi\) |
−0.655018 | + | 0.755613i | \(0.727339\pi\) | |||||||
\(600\) | −2.50000 | + | 4.33013i | −0.102062 | + | 0.176777i | ||||
\(601\) | 25.0000 | 1.01977 | 0.509886 | − | 0.860242i | \(-0.329688\pi\) | ||||
0.509886 | + | 0.860242i | \(0.329688\pi\) | |||||||
\(602\) | 1.00000 | − | 5.19615i | 0.0407570 | − | 0.211779i | ||||
\(603\) | 3.00000 | 0.122169 | ||||||||
\(604\) | 8.50000 | − | 14.7224i | 0.345860 | − | 0.599047i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.00000 | − | 5.19615i | −0.121867 | − | 0.211079i | ||||
\(607\) | 7.00000 | − | 12.1244i | 0.284121 | − | 0.492112i | −0.688274 | − | 0.725450i | \(-0.741632\pi\) |
0.972396 | + | 0.233338i | \(0.0749648\pi\) | |||||||
\(608\) | 7.00000 | 0.283887 | ||||||||
\(609\) | 18.0000 | + | 15.5885i | 0.729397 | + | 0.631676i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.50000 | + | 2.59808i | −0.0606835 | + | 0.105107i | ||||
\(612\) | −3.50000 | − | 6.06218i | −0.141479 | − | 0.245049i | ||||
\(613\) | −4.00000 | − | 6.92820i | −0.161558 | − | 0.279827i | 0.773869 | − | 0.633345i | \(-0.218319\pi\) |
−0.935428 | + | 0.353518i | \(0.884985\pi\) | |||||||
\(614\) | −9.50000 | + | 16.4545i | −0.383389 | + | 0.664049i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.0000 | − | 8.66025i | −0.402911 | − | 0.348932i | ||||
\(617\) | −6.00000 | −0.241551 | −0.120775 | − | 0.992680i | \(-0.538538\pi\) | ||||
−0.120775 | + | 0.992680i | \(0.538538\pi\) | |||||||
\(618\) | −5.00000 | + | 8.66025i | −0.201129 | + | 0.348367i | ||||
\(619\) | 10.0000 | + | 17.3205i | 0.401934 | + | 0.696170i | 0.993959 | − | 0.109749i | \(-0.0350048\pi\) |
−0.592025 | + | 0.805919i | \(0.701671\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.00000 | − | 1.73205i | 0.0401286 | − | 0.0695048i | ||||
\(622\) | 20.0000 | 0.801927 | ||||||||
\(623\) | −6.00000 | + | 31.1769i | −0.240385 | + | 1.24908i | ||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | −12.5000 | + | 21.6506i | −0.500000 | + | 0.866025i | ||||
\(626\) | 3.00000 | + | 5.19615i | 0.119904 | + | 0.207680i | ||||
\(627\) | −17.5000 | − | 30.3109i | −0.698883 | − | 1.21050i | ||||
\(628\) | −5.50000 | + | 9.52628i | −0.219474 | + | 0.380140i | ||||
\(629\) | 28.0000 | 1.11643 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.0000 | −0.636950 | −0.318475 | − | 0.947931i | \(-0.603171\pi\) | ||||
−0.318475 | + | 0.947931i | \(0.603171\pi\) | |||||||
\(632\) | −7.00000 | + | 12.1244i | −0.278445 | + | 0.482281i | ||||
\(633\) | −13.0000 | − | 22.5167i | −0.516704 | − | 0.894957i | ||||
\(634\) | −13.0000 | − | 22.5167i | −0.516296 | − | 0.894251i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | −5.50000 | + | 4.33013i | −0.217918 | + | 0.171566i | ||||
\(638\) | 45.0000 | 1.78157 | ||||||||
\(639\) | −4.50000 | + | 7.79423i | −0.178017 | + | 0.308335i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −9.00000 | − | 15.5885i | −0.355479 | − | 0.615707i | 0.631721 | − | 0.775196i | \(-0.282349\pi\) |
−0.987200 | + | 0.159489i | \(0.949015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −9.00000 | −0.354925 | −0.177463 | − | 0.984128i | \(-0.556789\pi\) | ||||
−0.177463 | + | 0.984128i | \(0.556789\pi\) | |||||||
\(644\) | −5.00000 | + | 1.73205i | −0.197028 | + | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −24.5000 | + | 42.4352i | −0.963940 | + | 1.66959i | ||||
\(647\) | 3.00000 | + | 5.19615i | 0.117942 | + | 0.204282i | 0.918952 | − | 0.394369i | \(-0.129037\pi\) |
−0.801010 | + | 0.598651i | \(0.795704\pi\) | |||||||
\(648\) | −0.500000 | − | 0.866025i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | 17.5000 | − | 30.3109i | 0.686935 | − | 1.18981i | ||||
\(650\) | 5.00000 | 0.196116 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.0000 | 0.509119 | ||||||||
\(653\) | 11.0000 | − | 19.0526i | 0.430463 | − | 0.745584i | −0.566450 | − | 0.824096i | \(-0.691684\pi\) |
0.996913 | + | 0.0785119i | \(0.0250169\pi\) | |||||||
\(654\) | 4.00000 | + | 6.92820i | 0.156412 | + | 0.270914i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.00000 | + | 3.46410i | −0.0780869 | + | 0.135250i | ||||
\(657\) | −10.0000 | −0.390137 | ||||||||
\(658\) | −6.00000 | − | 5.19615i | −0.233904 | − | 0.202567i | ||||
\(659\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.00000 | + | 3.46410i | 0.0777910 | + | 0.134738i | 0.902297 | − | 0.431116i | \(-0.141880\pi\) |
−0.824506 | + | 0.565854i | \(0.808547\pi\) | |||||||
\(662\) | −2.00000 | − | 3.46410i | −0.0777322 | − | 0.134636i | ||||
\(663\) | −3.50000 | + | 6.06218i | −0.135929 | + | 0.235435i | ||||
\(664\) | 16.0000 | 0.620920 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.00000 | 0.154997 | ||||||||
\(667\) | 9.00000 | − | 15.5885i | 0.348481 | − | 0.603587i | ||||
\(668\) | 2.50000 | + | 4.33013i | 0.0967279 | + | 0.167538i | ||||
\(669\) | −0.500000 | − | 0.866025i | −0.0193311 | − | 0.0334825i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −65.0000 | −2.50930 | ||||||||
\(672\) | −0.500000 | + | 2.59808i | −0.0192879 | + | 0.100223i | ||||
\(673\) | 22.0000 | 0.848038 | 0.424019 | − | 0.905653i | \(-0.360619\pi\) | ||||
0.424019 | + | 0.905653i | \(0.360619\pi\) | |||||||
\(674\) | 16.5000 | − | 28.5788i | 0.635556 | − | 1.10082i | ||||
\(675\) | −2.50000 | − | 4.33013i | −0.0962250 | − | 0.166667i | ||||
\(676\) | −0.500000 | − | 0.866025i | −0.0192308 | − | 0.0333087i | ||||
\(677\) | −12.5000 | + | 21.6506i | −0.480414 | + | 0.832102i | −0.999748 | − | 0.0224702i | \(-0.992847\pi\) |
0.519333 | + | 0.854572i | \(0.326180\pi\) | |||||||
\(678\) | −1.00000 | −0.0384048 | ||||||||
\(679\) | −15.0000 | + | 5.19615i | −0.575647 | + | 0.199410i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | − | 10.3923i | 0.229920 | − | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 20.0000 | + | 34.6410i | 0.765279 | + | 1.32550i | 0.940099 | + | 0.340901i | \(0.110732\pi\) |
−0.174820 | + | 0.984600i | \(0.555934\pi\) | |||||||
\(684\) | −3.50000 | + | 6.06218i | −0.133826 | + | 0.231793i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | −18.0000 | −0.686743 | ||||||||
\(688\) | −1.00000 | + | 1.73205i | −0.0381246 | + | 0.0660338i | ||||
\(689\) | 0.500000 | + | 0.866025i | 0.0190485 | + | 0.0329929i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.50000 | + | 4.33013i | −0.0951045 | + | 0.164726i | −0.909652 | − | 0.415371i | \(-0.863652\pi\) |
0.814548 | + | 0.580097i | \(0.196985\pi\) | |||||||
\(692\) | −13.0000 | −0.494186 | ||||||||
\(693\) | 12.5000 | − | 4.33013i | 0.474836 | − | 0.164488i | ||||
\(694\) | −16.0000 | −0.607352 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.50000 | − | 7.79423i | −0.170572 | − | 0.295439i | ||||
\(697\) | −14.0000 | − | 24.2487i | −0.530288 | − | 0.918485i | ||||
\(698\) | −1.00000 | + | 1.73205i | −0.0378506 | + | 0.0655591i | ||||
\(699\) | 3.00000 | 0.113470 | ||||||||
\(700\) | −2.50000 | + | 12.9904i | −0.0944911 | + | 0.490990i | ||||
\(701\) | −42.0000 | −1.58632 | −0.793159 | − | 0.609015i | \(-0.791565\pi\) | ||||
−0.793159 | + | 0.609015i | \(0.791565\pi\) | |||||||
\(702\) | −0.500000 | + | 0.866025i | −0.0188713 | + | 0.0326860i | ||||
\(703\) | −14.0000 | − | 24.2487i | −0.528020 | − | 0.914557i | ||||
\(704\) | 2.50000 | + | 4.33013i | 0.0942223 | + | 0.163198i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 2.00000 | 0.0752710 | ||||||||
\(707\) | −12.0000 | − | 10.3923i | −0.451306 | − | 0.390843i | ||||
\(708\) | −7.00000 | −0.263076 | ||||||||
\(709\) | 23.0000 | − | 39.8372i | 0.863783 | − | 1.49612i | −0.00446726 | − | 0.999990i | \(-0.501422\pi\) |
0.868250 | − | 0.496126i | \(-0.165245\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.00000 | − | 12.1244i | −0.262521 | − | 0.454699i | ||||
\(712\) | 6.00000 | − | 10.3923i | 0.224860 | − | 0.389468i | ||||
\(713\) | 0 | 0 | ||||||||
\(714\) | −14.0000 | − | 12.1244i | −0.523937 | − | 0.453743i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5.00000 | − | 8.66025i | 0.186859 | − | 0.323649i | ||||
\(717\) | −0.500000 | − | 0.866025i | −0.0186728 | − | 0.0323423i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −3.00000 | + | 5.19615i | −0.111881 | + | 0.193784i | −0.916529 | − | 0.399969i | \(-0.869021\pi\) |
0.804648 | + | 0.593753i | \(0.202354\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −5.00000 | + | 25.9808i | −0.186210 | + | 0.967574i | ||||
\(722\) | 30.0000 | 1.11648 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5.50000 | + | 9.52628i | 0.204406 | + | 0.354041i | ||||
\(725\) | −22.5000 | − | 38.9711i | −0.835629 | − | 1.44735i | ||||
\(726\) | 7.00000 | − | 12.1244i | 0.259794 | − | 0.449977i | ||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 2.50000 | − | 0.866025i | 0.0926562 | − | 0.0320970i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.00000 | − | 12.1244i | −0.258904 | − | 0.448435i | ||||
\(732\) | 6.50000 | + | 11.2583i | 0.240247 | + | 0.416120i | ||||
\(733\) | −7.00000 | + | 12.1244i | −0.258551 | + | 0.447823i | −0.965854 | − | 0.259087i | \(-0.916578\pi\) |
0.707303 | + | 0.706910i | \(0.249912\pi\) | |||||||
\(734\) | 2.00000 | 0.0738213 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.00000 | 0.0737210 | ||||||||
\(737\) | 7.50000 | − | 12.9904i | 0.276266 | − | 0.478507i | ||||
\(738\) | −2.00000 | − | 3.46410i | −0.0736210 | − | 0.127515i | ||||
\(739\) | 14.0000 | + | 24.2487i | 0.514998 | + | 0.892003i | 0.999849 | + | 0.0174060i | \(0.00554079\pi\) |
−0.484850 | + | 0.874597i | \(0.661126\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.00000 | 0.257151 | ||||||||
\(742\) | −2.50000 | + | 0.866025i | −0.0917779 | + | 0.0317928i | ||||
\(743\) | −5.00000 | −0.183432 | −0.0917161 | − | 0.995785i | \(-0.529235\pi\) | ||||
−0.0917161 | + | 0.995785i | \(0.529235\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 10.5000 | + | 18.1865i | 0.384432 | + | 0.665856i | ||||
\(747\) | −8.00000 | + | 13.8564i | −0.292705 | + | 0.506979i | ||||
\(748\) | −35.0000 | −1.27973 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.0000 | + | 27.7128i | −0.583848 | + | 1.01125i | 0.411170 | + | 0.911559i | \(0.365120\pi\) |
−0.995018 | + | 0.0996961i | \(0.968213\pi\) | |||||||
\(752\) | 1.50000 | + | 2.59808i | 0.0546994 | + | 0.0947421i | ||||
\(753\) | 9.00000 | + | 15.5885i | 0.327978 | + | 0.568075i | ||||
\(754\) | −4.50000 | + | 7.79423i | −0.163880 | + | 0.283849i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | − | 1.73205i | −0.0727393 | − | 0.0629941i | ||||
\(757\) | 29.0000 | 1.05402 | 0.527011 | − | 0.849858i | \(-0.323312\pi\) | ||||
0.527011 | + | 0.849858i | \(0.323312\pi\) | |||||||
\(758\) | 2.00000 | − | 3.46410i | 0.0726433 | − | 0.125822i | ||||
\(759\) | −5.00000 | − | 8.66025i | −0.181489 | − | 0.314347i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.00000 | − | 6.92820i | 0.145000 | − | 0.251147i | −0.784373 | − | 0.620289i | \(-0.787015\pi\) |
0.929373 | + | 0.369142i | \(0.120348\pi\) | |||||||
\(762\) | −22.0000 | −0.796976 | ||||||||
\(763\) | 16.0000 | + | 13.8564i | 0.579239 | + | 0.501636i | ||||
\(764\) | −12.0000 | −0.434145 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −4.00000 | − | 6.92820i | −0.144526 | − | 0.250326i | ||||
\(767\) | 3.50000 | + | 6.06218i | 0.126378 | + | 0.218893i | ||||
\(768\) | 0.500000 | − | 0.866025i | 0.0180422 | − | 0.0312500i | ||||
\(769\) | 2.00000 | 0.0721218 | 0.0360609 | − | 0.999350i | \(-0.488519\pi\) | ||||
0.0360609 | + | 0.999350i | \(0.488519\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.0000 | 0.504198 | ||||||||
\(772\) | 4.00000 | − | 6.92820i | 0.143963 | − | 0.249351i | ||||
\(773\) | 17.0000 | + | 29.4449i | 0.611448 | + | 1.05906i | 0.990997 | + | 0.133887i | \(0.0427458\pi\) |
−0.379549 | + | 0.925172i | \(0.623921\pi\) | |||||||
\(774\) | −1.00000 | − | 1.73205i | −0.0359443 | − | 0.0622573i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 6.00000 | 0.215387 | ||||||||
\(777\) | 10.0000 | − | 3.46410i | 0.358748 | − | 0.124274i | ||||
\(778\) | −23.0000 | −0.824590 | ||||||||
\(779\) | −14.0000 | + | 24.2487i | −0.501602 | + | 0.868800i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 22.5000 | + | 38.9711i | 0.805113 | + | 1.39450i | ||||
\(782\) | −7.00000 | + | 12.1244i | −0.250319 | + | 0.433566i | ||||
\(783\) | 9.00000 | 0.321634 | ||||||||
\(784\) | 1.00000 | + | 6.92820i | 0.0357143 | + | 0.247436i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 9.00000 | − | 15.5885i | 0.321019 | − | 0.556022i | ||||
\(787\) | −8.50000 | − | 14.7224i | −0.302992 | − | 0.524798i | 0.673820 | − | 0.738896i | \(-0.264652\pi\) |
−0.976812 | + | 0.214097i | \(0.931319\pi\) | |||||||
\(788\) | −11.0000 | − | 19.0526i | −0.391859 | − | 0.678719i | ||||
\(789\) | −2.00000 | + | 3.46410i | −0.0712019 | + | 0.123325i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.50000 | + | 0.866025i | −0.0888898 | + | 0.0307923i | ||||
\(792\) | −5.00000 | −0.177667 | ||||||||
\(793\) | 6.50000 | − | 11.2583i | 0.230822 | − | 0.399795i | ||||
\(794\) | 1.00000 | + | 1.73205i | 0.0354887 | + | 0.0614682i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.00000 | + | 15.5885i | −0.318997 | + | 0.552518i | ||||
\(797\) | 6.00000 | 0.212531 | 0.106265 | − | 0.994338i | \(-0.466111\pi\) | ||||
0.106265 | + | 0.994338i | \(0.466111\pi\) | |||||||
\(798\) | −3.50000 | + | 18.1865i | −0.123899 | + | 0.643796i | ||||
\(799\) | −21.0000 | −0.742927 | ||||||||
\(800\) | 2.50000 | − | 4.33013i | 0.0883883 | − | 0.153093i | ||||
\(801\) | 6.00000 | + | 10.3923i | 0.212000 | + | 0.367194i | ||||
\(802\) | 19.0000 | + | 32.9090i | 0.670913 | + | 1.16206i | ||||
\(803\) | −25.0000 | + | 43.3013i | −0.882231 | + | 1.52807i | ||||
\(804\) | −3.00000 | −0.105802 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.5000 | − | 19.9186i | 0.404819 | − | 0.701167i | ||||
\(808\) | 3.00000 | + | 5.19615i | 0.105540 | + | 0.182800i | ||||
\(809\) | −12.5000 | − | 21.6506i | −0.439477 | − | 0.761196i | 0.558173 | − | 0.829725i | \(-0.311503\pi\) |
−0.997649 | + | 0.0685291i | \(0.978169\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 12.0000 | 0.421377 | 0.210688 | − | 0.977553i | \(-0.432429\pi\) | ||||
0.210688 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(812\) | −18.0000 | − | 15.5885i | −0.631676 | − | 0.547048i | ||||
\(813\) | −3.00000 | −0.105215 | ||||||||
\(814\) | 10.0000 | − | 17.3205i | 0.350500 | − | 0.607083i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.50000 | + | 6.06218i | 0.122525 | + | 0.212219i | ||||
\(817\) | −7.00000 | + | 12.1244i | −0.244899 | + | 0.424178i | ||||
\(818\) | −4.00000 | −0.139857 | ||||||||
\(819\) | −0.500000 | + | 2.59808i | −0.0174714 | + | 0.0907841i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.0000 | − | 17.3205i | 0.349002 | − | 0.604490i | −0.637070 | − | 0.770806i | \(-0.719854\pi\) |
0.986073 | + | 0.166316i | \(0.0531872\pi\) | |||||||
\(822\) | −6.00000 | − | 10.3923i | −0.209274 | − | 0.362473i | ||||
\(823\) | −8.00000 | − | 13.8564i | −0.278862 | − | 0.483004i | 0.692240 | − | 0.721668i | \(-0.256624\pi\) |
−0.971102 | + | 0.238664i | \(0.923291\pi\) | |||||||
\(824\) | 5.00000 | − | 8.66025i | 0.174183 | − | 0.301694i | ||||
\(825\) | −25.0000 | −0.870388 | ||||||||
\(826\) | −17.5000 | + | 6.06218i | −0.608903 | + | 0.210930i | ||||
\(827\) | 21.0000 | 0.730242 | 0.365121 | − | 0.930960i | \(-0.381028\pi\) | ||||
0.365121 | + | 0.930960i | \(0.381028\pi\) | |||||||
\(828\) | −1.00000 | + | 1.73205i | −0.0347524 | + | 0.0601929i | ||||
\(829\) | 20.5000 | + | 35.5070i | 0.711994 | + | 1.23321i | 0.964107 | + | 0.265513i | \(0.0855412\pi\) |
−0.252113 | + | 0.967698i | \(0.581125\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.50000 | − | 16.4545i | 0.329551 | − | 0.570800i | ||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −45.5000 | − | 18.1865i | −1.57648 | − | 0.630126i | ||||
\(834\) | −16.0000 | −0.554035 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.5000 | + | 30.3109i | 0.605250 | + | 1.04832i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.0000 | + | 22.5167i | −0.449078 | + | 0.777825i | ||||
\(839\) | 5.00000 | 0.172619 | 0.0863096 | − | 0.996268i | \(-0.472493\pi\) | ||||
0.0863096 | + | 0.996268i | \(0.472493\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 52.0000 | 1.79310 | ||||||||
\(842\) | −19.0000 | + | 32.9090i | −0.654783 | + | 1.13412i | ||||
\(843\) | −12.0000 | − | 20.7846i | −0.413302 | − | 0.715860i | ||||
\(844\) | 13.0000 | + | 22.5167i | 0.447478 | + | 0.775055i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | 7.00000 | − | 36.3731i | 0.240523 | − | 1.24979i | ||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | −5.00000 | + | 8.66025i | −0.171600 | + | 0.297219i | ||||
\(850\) | 17.5000 | + | 30.3109i | 0.600245 | + | 1.03965i | ||||
\(851\) | −4.00000 | − | 6.92820i | −0.137118 | − | 0.237496i | ||||
\(852\) | 4.50000 | − | 7.79423i | 0.154167 | − | 0.267026i | ||||
\(853\) | −10.0000 | −0.342393 | −0.171197 | − | 0.985237i | \(-0.554763\pi\) | ||||
−0.171197 | + | 0.985237i | \(0.554763\pi\) | |||||||
\(854\) | 26.0000 | + | 22.5167i | 0.889702 | + | 0.770504i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −6.50000 | − | 11.2583i | −0.222036 | − | 0.384577i | 0.733390 | − | 0.679808i | \(-0.237937\pi\) |
−0.955426 | + | 0.295231i | \(0.904604\pi\) | |||||||
\(858\) | 2.50000 | + | 4.33013i | 0.0853486 | + | 0.147828i | ||||
\(859\) | 4.00000 | − | 6.92820i | 0.136478 | − | 0.236387i | −0.789683 | − | 0.613515i | \(-0.789755\pi\) |
0.926161 | + | 0.377128i | \(0.123088\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.00000 | − | 6.92820i | −0.272639 | − | 0.236113i | ||||
\(862\) | −16.0000 | −0.544962 | ||||||||
\(863\) | −6.00000 | + | 10.3923i | −0.204242 | + | 0.353758i | −0.949891 | − | 0.312581i | \(-0.898806\pi\) |
0.745649 | + | 0.666339i | \(0.232140\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 5.50000 | − | 9.52628i | 0.186898 | − | 0.323716i | ||||
\(867\) | −32.0000 | −1.08678 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −70.0000 | −2.37459 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.50000 | + | 2.59808i | 0.0508256 | + | 0.0880325i | ||||
\(872\) | −4.00000 | − | 6.92820i | −0.135457 | − | 0.234619i | ||||
\(873\) | −3.00000 | + | 5.19615i | −0.101535 | + | 0.175863i | ||||
\(874\) | 14.0000 | 0.473557 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.0000 | 0.337869 | ||||||||
\(877\) | 6.00000 | − | 10.3923i | 0.202606 | − | 0.350923i | −0.746762 | − | 0.665092i | \(-0.768392\pi\) |
0.949367 | + | 0.314169i | \(0.101726\pi\) | |||||||
\(878\) | 11.0000 | + | 19.0526i | 0.371232 | + | 0.642993i | ||||
\(879\) | −15.0000 | − | 25.9808i | −0.505937 | − | 0.876309i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14.0000 | −0.471672 | −0.235836 | − | 0.971793i | \(-0.575783\pi\) | ||||
−0.235836 | + | 0.971793i | \(0.575783\pi\) | |||||||
\(882\) | −6.50000 | − | 2.59808i | −0.218866 | − | 0.0874818i | ||||
\(883\) | 44.0000 | 1.48072 | 0.740359 | − | 0.672212i | \(-0.234656\pi\) | ||||
0.740359 | + | 0.672212i | \(0.234656\pi\) | |||||||
\(884\) | 3.50000 | − | 6.06218i | 0.117718 | − | 0.203893i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.00000 | + | 3.46410i | 0.0671913 | + | 0.116379i | ||||
\(887\) | −21.0000 | + | 36.3731i | −0.705111 | + | 1.22129i | 0.261540 | + | 0.965193i | \(0.415770\pi\) |
−0.966651 | + | 0.256096i | \(0.917564\pi\) | |||||||
\(888\) | −4.00000 | −0.134231 | ||||||||
\(889\) | −55.0000 | + | 19.0526i | −1.84464 | + | 0.639002i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.50000 | − | 4.33013i | 0.0837532 | − | 0.145065i | ||||
\(892\) | 0.500000 | + | 0.866025i | 0.0167412 | + | 0.0289967i | ||||
\(893\) | 10.5000 | + | 18.1865i | 0.351369 | + | 0.608589i | ||||
\(894\) | 5.00000 | − | 8.66025i | 0.167225 | − | 0.289642i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.500000 | − | 2.59808i | 0.0167038 | − | 0.0867956i | ||||
\(897\) | 2.00000 | 0.0667781 | ||||||||
\(898\) | −2.00000 | + | 3.46410i | −0.0667409 | + | 0.115599i | ||||
\(899\) | 0 | 0 | ||||||||
\(900\) | 2.50000 | + | 4.33013i | 0.0833333 | + | 0.144338i | ||||
\(901\) | −3.50000 | + | 6.06218i | −0.116602 | + | 0.201960i | ||||
\(902\) | −20.0000 | −0.665927 | ||||||||
\(903\) | −4.00000 | − | 3.46410i | −0.133112 | − | 0.115278i | ||||
\(904\) | 1.00000 | 0.0332595 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −8.50000 | − | 14.7224i | −0.282394 | − | 0.489120i | ||||
\(907\) | −27.0000 | − | 46.7654i | −0.896520 | − | 1.55282i | −0.831912 | − | 0.554908i | \(-0.812753\pi\) |
−0.0646086 | − | 0.997911i | \(-0.520580\pi\) | |||||||
\(908\) | −6.00000 | + | 10.3923i | −0.199117 | + | 0.344881i | ||||
\(909\) | −6.00000 | −0.199007 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −30.0000 | −0.993944 | −0.496972 | − | 0.867766i | \(-0.665555\pi\) | ||||
−0.496972 | + | 0.867766i | \(0.665555\pi\) | |||||||
\(912\) | 3.50000 | − | 6.06218i | 0.115897 | − | 0.200739i | ||||
\(913\) | 40.0000 | + | 69.2820i | 1.32381 | + | 2.29290i | ||||
\(914\) | 5.00000 | + | 8.66025i | 0.165385 | + | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.0000 | 0.594737 | ||||||||
\(917\) | 9.00000 | − | 46.7654i | 0.297206 | − | 1.54433i | ||||
\(918\) | −7.00000 | −0.231034 | ||||||||
\(919\) | 7.00000 | − | 12.1244i | 0.230909 | − | 0.399946i | −0.727167 | − | 0.686461i | \(-0.759163\pi\) |
0.958076 | + | 0.286515i | \(0.0924968\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.50000 | + | 16.4545i | 0.313036 | + | 0.542194i | ||||
\(922\) | 4.00000 | − | 6.92820i | 0.131733 | − | 0.228168i | ||||
\(923\) | −9.00000 | −0.296239 | ||||||||
\(924\) | −12.5000 | + | 4.33013i | −0.411220 | + | 0.142451i | ||||
\(925\) | −20.0000 | −0.657596 | ||||||||
\(926\) | −16.0000 | + | 27.7128i | −0.525793 | + | 0.910700i | ||||
\(927\) | 5.00000 | + | 8.66025i | 0.164222 | + | 0.284440i | ||||
\(928\) | 4.50000 | + | 7.79423i | 0.147720 | + | 0.255858i | ||||
\(929\) | −9.00000 | + | 15.5885i | −0.295280 | + | 0.511441i | −0.975050 | − | 0.221985i | \(-0.928746\pi\) |
0.679770 | + | 0.733426i | \(0.262080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.00000 | + | 48.4974i | 0.229416 | + | 1.58944i | ||||
\(932\) | −3.00000 | −0.0982683 | ||||||||
\(933\) | 10.0000 | − | 17.3205i | 0.327385 | − | 0.567048i | ||||
\(934\) | 3.00000 | + | 5.19615i | 0.0981630 | + | 0.170023i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0.500000 | − | 0.866025i | 0.0163430 | − | 0.0283069i | ||||
\(937\) | −1.00000 | −0.0326686 | −0.0163343 | − | 0.999867i | \(-0.505200\pi\) | ||||
−0.0163343 | + | 0.999867i | \(0.505200\pi\) | |||||||
\(938\) | −7.50000 | + | 2.59808i | −0.244884 | + | 0.0848302i | ||||
\(939\) | 6.00000 | 0.195803 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.00000 | + | 6.92820i | 0.130396 | + | 0.225853i | 0.923829 | − | 0.382804i | \(-0.125042\pi\) |
−0.793433 | + | 0.608657i | \(0.791708\pi\) | |||||||
\(942\) | 5.50000 | + | 9.52628i | 0.179200 | + | 0.310383i | ||||
\(943\) | −4.00000 | + | 6.92820i | −0.130258 | + | 0.225613i | ||||
\(944\) | 7.00000 | 0.227831 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10.0000 | −0.325128 | ||||||||
\(947\) | 2.50000 | − | 4.33013i | 0.0812391 | − | 0.140710i | −0.822543 | − | 0.568702i | \(-0.807446\pi\) |
0.903782 | + | 0.427992i | \(0.140779\pi\) | |||||||
\(948\) | 7.00000 | + | 12.1244i | 0.227349 | + | 0.393781i | ||||
\(949\) | −5.00000 | − | 8.66025i | −0.162307 | − | 0.281124i | ||||
\(950\) | 17.5000 | − | 30.3109i | 0.567775 | − | 0.983415i | ||||
\(951\) | −26.0000 | −0.843108 | ||||||||
\(952\) | 14.0000 | + | 12.1244i | 0.453743 | + | 0.392953i | ||||
\(953\) | 9.00000 | 0.291539 | 0.145769 | − | 0.989319i | \(-0.453434\pi\) | ||||
0.145769 | + | 0.989319i | \(0.453434\pi\) | |||||||
\(954\) | −0.500000 | + | 0.866025i | −0.0161881 | + | 0.0280386i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0.500000 | + | 0.866025i | 0.0161712 | + | 0.0280093i | ||||
\(957\) | 22.5000 | − | 38.9711i | 0.727322 | − | 1.25976i | ||||
\(958\) | −11.0000 | −0.355394 | ||||||||
\(959\) | −24.0000 | − | 20.7846i | −0.775000 | − | 0.671170i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.5000 | − | 26.8468i | 0.500000 | − | 0.866025i | ||||
\(962\) | 2.00000 | + | 3.46410i | 0.0644826 | + | 0.111687i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.00000 | + | 5.19615i | −0.0321745 | + | 0.167183i | ||||
\(967\) | 1.00000 | 0.0321578 | 0.0160789 | − | 0.999871i | \(-0.494882\pi\) | ||||
0.0160789 | + | 0.999871i | \(0.494882\pi\) | |||||||
\(968\) | −7.00000 | + | 12.1244i | −0.224989 | + | 0.389692i | ||||
\(969\) | 24.5000 | + | 42.4352i | 0.787053 | + | 1.36322i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.0000 | − | 31.1769i | 0.577647 | − | 1.00051i | −0.418101 | − | 0.908401i | \(-0.637304\pi\) |
0.995748 | − | 0.0921142i | \(-0.0293625\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | −40.0000 | + | 13.8564i | −1.28234 | + | 0.444216i | ||||
\(974\) | −5.00000 | −0.160210 | ||||||||
\(975\) | 2.50000 | − | 4.33013i | 0.0800641 | − | 0.138675i | ||||
\(976\) | −6.50000 | − | 11.2583i | −0.208060 | − | 0.360370i | ||||
\(977\) | −1.00000 | − | 1.73205i | −0.0319928 | − | 0.0554132i | 0.849586 | − | 0.527451i | \(-0.176852\pi\) |
−0.881579 | + | 0.472037i | \(0.843519\pi\) | |||||||
\(978\) | 6.50000 | − | 11.2583i | 0.207847 | − | 0.360002i | ||||
\(979\) | 60.0000 | 1.91761 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.00000 | 0.255420 | ||||||||
\(982\) | 11.0000 | − | 19.0526i | 0.351024 | − | 0.607992i | ||||
\(983\) | −29.5000 | − | 51.0955i | −0.940904 | − | 1.62969i | −0.763752 | − | 0.645510i | \(-0.776645\pi\) |
−0.177152 | − | 0.984184i | \(-0.556688\pi\) | |||||||
\(984\) | 2.00000 | + | 3.46410i | 0.0637577 | + | 0.110432i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −63.0000 | −2.00633 | ||||||||
\(987\) | −7.50000 | + | 2.59808i | −0.238728 | + | 0.0826977i | ||||
\(988\) | −7.00000 | −0.222700 | ||||||||
\(989\) | −2.00000 | + | 3.46410i | −0.0635963 | + | 0.110152i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | + | 27.7128i | 0.508257 | + | 0.880327i | 0.999954 | + | 0.00956046i | \(0.00304324\pi\) |
−0.491698 | + | 0.870766i | \(0.663623\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.00000 | −0.126936 | ||||||||
\(994\) | 4.50000 | − | 23.3827i | 0.142731 | − | 0.741654i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 8.00000 | − | 13.8564i | 0.253490 | − | 0.439057i | ||||
\(997\) | −10.5000 | − | 18.1865i | −0.332538 | − | 0.575973i | 0.650471 | − | 0.759532i | \(-0.274572\pi\) |
−0.983009 | + | 0.183558i | \(0.941238\pi\) | |||||||
\(998\) | −20.0000 | − | 34.6410i | −0.633089 | − | 1.09654i | ||||
\(999\) | 2.00000 | − | 3.46410i | 0.0632772 | − | 0.109599i |
(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 | 546.2.i.d.79.1 | ✓ | 2 | |
3.2 | odd | 2 | 1638.2.j.i.1171.1 | 2 | |||
7.2 | even | 3 | 3822.2.a.u.1.1 | 1 | |||
7.4 | even | 3 | inner | 546.2.i.d.235.1 | yes | 2 | |
7.5 | odd | 6 | 3822.2.a.bf.1.1 | 1 | |||
21.11 | odd | 6 | 1638.2.j.i.235.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.i.d.79.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
546.2.i.d.235.1 | yes | 2 | 7.4 | even | 3 | inner | |
1638.2.j.i.235.1 | 2 | 21.11 | odd | 6 | |||
1638.2.j.i.1171.1 | 2 | 3.2 | odd | 2 | |||
3822.2.a.u.1.1 | 1 | 7.2 | even | 3 | |||
3822.2.a.bf.1.1 | 1 | 7.5 | odd | 6 |