Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(499,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.499");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.o (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 499.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.499 |
Dual form | 1050.2.o.j.949.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | + | 0.500000i | 0.612372 | + | 0.353553i | ||||
\(3\) | 0.866025 | − | 0.500000i | 0.500000 | − | 0.288675i | ||||
\(4\) | 0.500000 | + | 0.866025i | 0.250000 | + | 0.433013i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.500000 | + | 0.866025i | 0.150756 | + | 0.261116i | 0.931505 | − | 0.363727i | \(-0.118496\pi\) |
−0.780750 | + | 0.624844i | \(0.785163\pi\) | |||||||
\(12\) | 0.866025 | + | 0.500000i | 0.250000 | + | 0.144338i | ||||
\(13\) | 7.00000i | 1.94145i | 0.240192 | + | 0.970725i | \(0.422790\pi\) | ||||
−0.240192 | + | 0.970725i | \(0.577210\pi\) | |||||||
\(14\) | 2.50000 | − | 0.866025i | 0.668153 | − | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 3.46410 | − | 2.00000i | 0.840168 | − | 0.485071i | −0.0171533 | − | 0.999853i | \(-0.505460\pi\) |
0.857321 | + | 0.514782i | \(0.172127\pi\) | |||||||
\(18\) | 0.866025 | − | 0.500000i | 0.204124 | − | 0.117851i | ||||
\(19\) | 0.500000 | − | 0.866025i | 0.114708 | − | 0.198680i | −0.802955 | − | 0.596040i | \(-0.796740\pi\) |
0.917663 | + | 0.397360i | \(0.130073\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.500000 | − | 2.59808i | 0.109109 | − | 0.566947i | ||||
\(22\) | 1.00000i | 0.213201i | ||||||||
\(23\) | −0.866025 | − | 0.500000i | −0.180579 | − | 0.104257i | 0.406986 | − | 0.913434i | \(-0.366580\pi\) |
−0.587565 | + | 0.809177i | \(0.699913\pi\) | |||||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.50000 | + | 6.06218i | −0.686406 | + | 1.18889i | ||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 2.59808 | + | 0.500000i | 0.490990 | + | 0.0944911i | ||||
\(29\) | 8.00000 | 1.48556 | 0.742781 | − | 0.669534i | \(-0.233506\pi\) | ||||
0.742781 | + | 0.669534i | \(0.233506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.00000 | − | 5.19615i | −0.538816 | − | 0.933257i | −0.998968 | − | 0.0454165i | \(-0.985539\pi\) |
0.460152 | − | 0.887840i | \(-0.347795\pi\) | |||||||
\(32\) | −0.866025 | + | 0.500000i | −0.153093 | + | 0.0883883i | ||||
\(33\) | 0.866025 | + | 0.500000i | 0.150756 | + | 0.0870388i | ||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −2.59808 | − | 1.50000i | −0.427121 | − | 0.246598i | 0.270998 | − | 0.962580i | \(-0.412646\pi\) |
−0.698119 | + | 0.715981i | \(0.745980\pi\) | |||||||
\(38\) | 0.866025 | − | 0.500000i | 0.140488 | − | 0.0811107i | ||||
\(39\) | 3.50000 | + | 6.06218i | 0.560449 | + | 0.970725i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 9.00000 | 1.40556 | 0.702782 | − | 0.711405i | \(-0.251941\pi\) | ||||
0.702782 | + | 0.711405i | \(0.251941\pi\) | |||||||
\(42\) | 1.73205 | − | 2.00000i | 0.267261 | − | 0.308607i | ||||
\(43\) | − | 4.00000i | − | 0.609994i | −0.952353 | − | 0.304997i | \(-0.901344\pi\) | ||
0.952353 | − | 0.304997i | \(-0.0986555\pi\) | |||||||
\(44\) | −0.500000 | + | 0.866025i | −0.0753778 | + | 0.130558i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.500000 | − | 0.866025i | −0.0737210 | − | 0.127688i | ||||
\(47\) | −2.59808 | − | 1.50000i | −0.378968 | − | 0.218797i | 0.298401 | − | 0.954441i | \(-0.403547\pi\) |
−0.677369 | + | 0.735643i | \(0.736880\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.00000 | − | 3.46410i | 0.280056 | − | 0.485071i | ||||
\(52\) | −6.06218 | + | 3.50000i | −0.840673 | + | 0.485363i | ||||
\(53\) | −0.866025 | + | 0.500000i | −0.118958 | + | 0.0686803i | −0.558298 | − | 0.829640i | \(-0.688546\pi\) |
0.439340 | + | 0.898321i | \(0.355212\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.00000 | + | 1.73205i | 0.267261 | + | 0.231455i | ||||
\(57\) | − | 1.00000i | − | 0.132453i | ||||||
\(58\) | 6.92820 | + | 4.00000i | 0.909718 | + | 0.525226i | ||||
\(59\) | 6.00000 | + | 10.3923i | 0.781133 | + | 1.35296i | 0.931282 | + | 0.364299i | \(0.118692\pi\) |
−0.150148 | + | 0.988663i | \(0.547975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | − | 3.46410i | 0.256074 | − | 0.443533i | −0.709113 | − | 0.705095i | \(-0.750904\pi\) |
0.965187 | + | 0.261562i | \(0.0842377\pi\) | |||||||
\(62\) | − | 6.00000i | − | 0.762001i | ||||||
\(63\) | −0.866025 | − | 2.50000i | −0.109109 | − | 0.314970i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0.500000 | + | 0.866025i | 0.0615457 | + | 0.106600i | ||||
\(67\) | −10.3923 | + | 6.00000i | −1.26962 | + | 0.733017i | −0.974916 | − | 0.222571i | \(-0.928555\pi\) |
−0.294706 | + | 0.955588i | \(0.595222\pi\) | |||||||
\(68\) | 3.46410 | + | 2.00000i | 0.420084 | + | 0.242536i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14.0000 | −1.66149 | −0.830747 | − | 0.556650i | \(-0.812086\pi\) | ||||
−0.830747 | + | 0.556650i | \(0.812086\pi\) | |||||||
\(72\) | 0.866025 | + | 0.500000i | 0.102062 | + | 0.0589256i | ||||
\(73\) | −12.1244 | + | 7.00000i | −1.41905 | + | 0.819288i | −0.996215 | − | 0.0869195i | \(-0.972298\pi\) |
−0.422833 | + | 0.906208i | \(0.638964\pi\) | |||||||
\(74\) | −1.50000 | − | 2.59808i | −0.174371 | − | 0.302020i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | 2.59808 | + | 0.500000i | 0.296078 | + | 0.0569803i | ||||
\(78\) | 7.00000i | 0.792594i | ||||||||
\(79\) | 2.00000 | − | 3.46410i | 0.225018 | − | 0.389742i | −0.731307 | − | 0.682048i | \(-0.761089\pi\) |
0.956325 | + | 0.292306i | \(0.0944227\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 7.79423 | + | 4.50000i | 0.860729 | + | 0.496942i | ||||
\(83\) | 12.0000i | 1.31717i | 0.752506 | + | 0.658586i | \(0.228845\pi\) | ||||
−0.752506 | + | 0.658586i | \(0.771155\pi\) | |||||||
\(84\) | 2.50000 | − | 0.866025i | 0.272772 | − | 0.0944911i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 2.00000 | − | 3.46410i | 0.215666 | − | 0.373544i | ||||
\(87\) | 6.92820 | − | 4.00000i | 0.742781 | − | 0.428845i | ||||
\(88\) | −0.866025 | + | 0.500000i | −0.0923186 | + | 0.0533002i | ||||
\(89\) | −1.00000 | + | 1.73205i | −0.106000 | + | 0.183597i | −0.914146 | − | 0.405385i | \(-0.867138\pi\) |
0.808146 | + | 0.588982i | \(0.200471\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 14.0000 | + | 12.1244i | 1.46760 | + | 1.27098i | ||||
\(92\) | − | 1.00000i | − | 0.104257i | ||||||
\(93\) | −5.19615 | − | 3.00000i | −0.538816 | − | 0.311086i | ||||
\(94\) | −1.50000 | − | 2.59808i | −0.154713 | − | 0.267971i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −0.500000 | + | 0.866025i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | 16.0000i | 1.62455i | 0.583272 | + | 0.812277i | \(0.301772\pi\) | ||||
−0.583272 | + | 0.812277i | \(0.698228\pi\) | |||||||
\(98\) | 2.59808 | − | 6.50000i | 0.262445 | − | 0.656599i | ||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 3.46410 | − | 2.00000i | 0.342997 | − | 0.198030i | ||||
\(103\) | −13.8564 | − | 8.00000i | −1.36531 | − | 0.788263i | −0.374987 | − | 0.927030i | \(-0.622353\pi\) |
−0.990325 | + | 0.138767i | \(0.955686\pi\) | |||||||
\(104\) | −7.00000 | −0.686406 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | −15.5885 | − | 9.00000i | −1.50699 | − | 0.870063i | −0.999967 | − | 0.00813215i | \(-0.997411\pi\) |
−0.507026 | − | 0.861931i | \(-0.669255\pi\) | |||||||
\(108\) | 0.866025 | − | 0.500000i | 0.0833333 | − | 0.0481125i | ||||
\(109\) | −5.00000 | − | 8.66025i | −0.478913 | − | 0.829502i | 0.520794 | − | 0.853682i | \(-0.325636\pi\) |
−0.999708 | + | 0.0241802i | \(0.992302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.00000 | −0.284747 | ||||||||
\(112\) | 0.866025 | + | 2.50000i | 0.0818317 | + | 0.236228i | ||||
\(113\) | − | 6.00000i | − | 0.564433i | −0.959351 | − | 0.282216i | \(-0.908930\pi\) | ||
0.959351 | − | 0.282216i | \(-0.0910696\pi\) | |||||||
\(114\) | 0.500000 | − | 0.866025i | 0.0468293 | − | 0.0811107i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.00000 | + | 6.92820i | 0.371391 | + | 0.643268i | ||||
\(117\) | 6.06218 | + | 3.50000i | 0.560449 | + | 0.323575i | ||||
\(118\) | 12.0000i | 1.10469i | ||||||||
\(119\) | 2.00000 | − | 10.3923i | 0.183340 | − | 0.952661i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.00000 | − | 8.66025i | 0.454545 | − | 0.787296i | ||||
\(122\) | 3.46410 | − | 2.00000i | 0.313625 | − | 0.181071i | ||||
\(123\) | 7.79423 | − | 4.50000i | 0.702782 | − | 0.405751i | ||||
\(124\) | 3.00000 | − | 5.19615i | 0.269408 | − | 0.466628i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.500000 | − | 2.59808i | 0.0445435 | − | 0.231455i | ||||
\(127\) | − | 5.00000i | − | 0.443678i | −0.975083 | − | 0.221839i | \(-0.928794\pi\) | ||
0.975083 | − | 0.221839i | \(-0.0712060\pi\) | |||||||
\(128\) | −0.866025 | − | 0.500000i | −0.0765466 | − | 0.0441942i | ||||
\(129\) | −2.00000 | − | 3.46410i | −0.176090 | − | 0.304997i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.50000 | − | 11.2583i | 0.567908 | − | 0.983645i | −0.428865 | − | 0.903369i | \(-0.641086\pi\) |
0.996773 | − | 0.0802763i | \(-0.0255803\pi\) | |||||||
\(132\) | 1.00000i | 0.0870388i | ||||||||
\(133\) | −0.866025 | − | 2.50000i | −0.0750939 | − | 0.216777i | ||||
\(134\) | −12.0000 | −1.03664 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.00000 | + | 3.46410i | 0.171499 | + | 0.297044i | ||||
\(137\) | 1.73205 | − | 1.00000i | 0.147979 | − | 0.0854358i | −0.424182 | − | 0.905577i | \(-0.639438\pi\) |
0.572161 | + | 0.820141i | \(0.306105\pi\) | |||||||
\(138\) | −0.866025 | − | 0.500000i | −0.0737210 | − | 0.0425628i | ||||
\(139\) | 4.00000 | 0.339276 | 0.169638 | − | 0.985506i | \(-0.445740\pi\) | ||||
0.169638 | + | 0.985506i | \(0.445740\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.00000 | −0.252646 | ||||||||
\(142\) | −12.1244 | − | 7.00000i | −1.01745 | − | 0.587427i | ||||
\(143\) | −6.06218 | + | 3.50000i | −0.506945 | + | 0.292685i | ||||
\(144\) | 0.500000 | + | 0.866025i | 0.0416667 | + | 0.0721688i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −14.0000 | −1.15865 | ||||||||
\(147\) | −4.33013 | − | 5.50000i | −0.357143 | − | 0.453632i | ||||
\(148\) | − | 3.00000i | − | 0.246598i | ||||||
\(149\) | −2.00000 | + | 3.46410i | −0.163846 | + | 0.283790i | −0.936245 | − | 0.351348i | \(-0.885723\pi\) |
0.772399 | + | 0.635138i | \(0.219057\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.00000 | + | 1.73205i | 0.0813788 | + | 0.140952i | 0.903842 | − | 0.427865i | \(-0.140734\pi\) |
−0.822464 | + | 0.568818i | \(0.807401\pi\) | |||||||
\(152\) | 0.866025 | + | 0.500000i | 0.0702439 | + | 0.0405554i | ||||
\(153\) | − | 4.00000i | − | 0.323381i | ||||||
\(154\) | 2.00000 | + | 1.73205i | 0.161165 | + | 0.139573i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −3.50000 | + | 6.06218i | −0.280224 | + | 0.485363i | ||||
\(157\) | −12.9904 | + | 7.50000i | −1.03675 | + | 0.598565i | −0.918910 | − | 0.394468i | \(-0.870929\pi\) |
−0.117836 | + | 0.993033i | \(0.537596\pi\) | |||||||
\(158\) | 3.46410 | − | 2.00000i | 0.275589 | − | 0.159111i | ||||
\(159\) | −0.500000 | + | 0.866025i | −0.0396526 | + | 0.0686803i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.50000 | + | 0.866025i | −0.197028 | + | 0.0682524i | ||||
\(162\) | − | 1.00000i | − | 0.0785674i | ||||||
\(163\) | −6.92820 | − | 4.00000i | −0.542659 | − | 0.313304i | 0.203497 | − | 0.979076i | \(-0.434769\pi\) |
−0.746156 | + | 0.665771i | \(0.768103\pi\) | |||||||
\(164\) | 4.50000 | + | 7.79423i | 0.351391 | + | 0.608627i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.00000 | + | 10.3923i | −0.465690 | + | 0.806599i | ||||
\(167\) | 5.00000i | 0.386912i | 0.981109 | + | 0.193456i | \(0.0619696\pi\) | ||||
−0.981109 | + | 0.193456i | \(0.938030\pi\) | |||||||
\(168\) | 2.59808 | + | 0.500000i | 0.200446 | + | 0.0385758i | ||||
\(169\) | −36.0000 | −2.76923 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.500000 | − | 0.866025i | −0.0382360 | − | 0.0662266i | ||||
\(172\) | 3.46410 | − | 2.00000i | 0.264135 | − | 0.152499i | ||||
\(173\) | 18.1865 | + | 10.5000i | 1.38270 | + | 0.798300i | 0.992478 | − | 0.122422i | \(-0.0390662\pi\) |
0.390218 | + | 0.920722i | \(0.372399\pi\) | |||||||
\(174\) | 8.00000 | 0.606478 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 10.3923 | + | 6.00000i | 0.781133 | + | 0.450988i | ||||
\(178\) | −1.73205 | + | 1.00000i | −0.129823 | + | 0.0749532i | ||||
\(179\) | 6.50000 | + | 11.2583i | 0.485833 | + | 0.841487i | 0.999867 | − | 0.0162823i | \(-0.00518305\pi\) |
−0.514035 | + | 0.857769i | \(0.671850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0000 | −0.891953 | −0.445976 | − | 0.895045i | \(-0.647144\pi\) | ||||
−0.445976 | + | 0.895045i | \(0.647144\pi\) | |||||||
\(182\) | 6.06218 | + | 17.5000i | 0.449359 | + | 1.29719i | ||||
\(183\) | − | 4.00000i | − | 0.295689i | ||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.00000 | − | 5.19615i | −0.219971 | − | 0.381000i | ||||
\(187\) | 3.46410 | + | 2.00000i | 0.253320 | + | 0.146254i | ||||
\(188\) | − | 3.00000i | − | 0.218797i | ||||||
\(189\) | −2.00000 | − | 1.73205i | −0.145479 | − | 0.125988i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.00000 | − | 8.66025i | 0.361787 | − | 0.626634i | −0.626468 | − | 0.779447i | \(-0.715500\pi\) |
0.988255 | + | 0.152813i | \(0.0488333\pi\) | |||||||
\(192\) | −0.866025 | + | 0.500000i | −0.0625000 | + | 0.0360844i | ||||
\(193\) | 22.5167 | − | 13.0000i | 1.62078 | − | 0.935760i | 0.634074 | − | 0.773272i | \(-0.281381\pi\) |
0.986710 | − | 0.162488i | \(-0.0519520\pi\) | |||||||
\(194\) | −8.00000 | + | 13.8564i | −0.574367 | + | 0.994832i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.50000 | − | 4.33013i | 0.392857 | − | 0.309295i | ||||
\(197\) | 3.00000i | 0.213741i | 0.994273 | + | 0.106871i | \(0.0340831\pi\) | ||||
−0.994273 | + | 0.106871i | \(0.965917\pi\) | |||||||
\(198\) | 0.866025 | + | 0.500000i | 0.0615457 | + | 0.0355335i | ||||
\(199\) | −6.00000 | − | 10.3923i | −0.425329 | − | 0.736691i | 0.571122 | − | 0.820865i | \(-0.306508\pi\) |
−0.996451 | + | 0.0841740i | \(0.973175\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6.00000 | + | 10.3923i | −0.423207 | + | 0.733017i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.8564 | − | 16.0000i | 0.972529 | − | 1.12298i | ||||
\(204\) | 4.00000 | 0.280056 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.00000 | − | 13.8564i | −0.557386 | − | 0.965422i | ||||
\(207\) | −0.866025 | + | 0.500000i | −0.0601929 | + | 0.0347524i | ||||
\(208\) | −6.06218 | − | 3.50000i | −0.420336 | − | 0.242681i | ||||
\(209\) | 1.00000 | 0.0691714 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.0000 | −1.03264 | −0.516321 | − | 0.856395i | \(-0.672699\pi\) | ||||
−0.516321 | + | 0.856395i | \(0.672699\pi\) | |||||||
\(212\) | −0.866025 | − | 0.500000i | −0.0594789 | − | 0.0343401i | ||||
\(213\) | −12.1244 | + | 7.00000i | −0.830747 | + | 0.479632i | ||||
\(214\) | −9.00000 | − | 15.5885i | −0.615227 | − | 1.06561i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | −15.5885 | − | 3.00000i | −1.05821 | − | 0.203653i | ||||
\(218\) | − | 10.0000i | − | 0.677285i | ||||||
\(219\) | −7.00000 | + | 12.1244i | −0.473016 | + | 0.819288i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.0000 | + | 24.2487i | 0.941742 | + | 1.63114i | ||||
\(222\) | −2.59808 | − | 1.50000i | −0.174371 | − | 0.100673i | ||||
\(223\) | − | 4.00000i | − | 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | −0.500000 | + | 2.59808i | −0.0334077 | + | 0.173591i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.00000 | − | 5.19615i | 0.199557 | − | 0.345643i | ||||
\(227\) | 17.3205 | − | 10.0000i | 1.14960 | − | 0.663723i | 0.200812 | − | 0.979630i | \(-0.435642\pi\) |
0.948790 | + | 0.315906i | \(0.102309\pi\) | |||||||
\(228\) | 0.866025 | − | 0.500000i | 0.0573539 | − | 0.0331133i | ||||
\(229\) | −11.0000 | + | 19.0526i | −0.726900 | + | 1.25903i | 0.231287 | + | 0.972886i | \(0.425707\pi\) |
−0.958187 | + | 0.286143i | \(0.907627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.50000 | − | 0.866025i | 0.164488 | − | 0.0569803i | ||||
\(232\) | 8.00000i | 0.525226i | ||||||||
\(233\) | −22.5167 | − | 13.0000i | −1.47512 | − | 0.851658i | −0.475509 | − | 0.879711i | \(-0.657736\pi\) |
−0.999606 | + | 0.0280525i | \(0.991069\pi\) | |||||||
\(234\) | 3.50000 | + | 6.06218i | 0.228802 | + | 0.396297i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −6.00000 | + | 10.3923i | −0.390567 | + | 0.676481i | ||||
\(237\) | − | 4.00000i | − | 0.259828i | ||||||
\(238\) | 6.92820 | − | 8.00000i | 0.449089 | − | 0.518563i | ||||
\(239\) | 6.00000 | 0.388108 | 0.194054 | − | 0.980991i | \(-0.437836\pi\) | ||||
0.194054 | + | 0.980991i | \(0.437836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.50000 | − | 6.06218i | −0.225455 | − | 0.390499i | 0.731001 | − | 0.682376i | \(-0.239053\pi\) |
−0.956456 | + | 0.291877i | \(0.905720\pi\) | |||||||
\(242\) | 8.66025 | − | 5.00000i | 0.556702 | − | 0.321412i | ||||
\(243\) | −0.866025 | − | 0.500000i | −0.0555556 | − | 0.0320750i | ||||
\(244\) | 4.00000 | 0.256074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 9.00000 | 0.573819 | ||||||||
\(247\) | 6.06218 | + | 3.50000i | 0.385727 | + | 0.222700i | ||||
\(248\) | 5.19615 | − | 3.00000i | 0.329956 | − | 0.190500i | ||||
\(249\) | 6.00000 | + | 10.3923i | 0.380235 | + | 0.658586i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.00000 | −0.189358 | −0.0946792 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946792 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(252\) | 1.73205 | − | 2.00000i | 0.109109 | − | 0.125988i | ||||
\(253\) | − | 1.00000i | − | 0.0628695i | ||||||
\(254\) | 2.50000 | − | 4.33013i | 0.156864 | − | 0.271696i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −6.92820 | − | 4.00000i | −0.432169 | − | 0.249513i | 0.268101 | − | 0.963391i | \(-0.413604\pi\) |
−0.700270 | + | 0.713878i | \(0.746937\pi\) | |||||||
\(258\) | − | 4.00000i | − | 0.249029i | ||||||
\(259\) | −7.50000 | + | 2.59808i | −0.466027 | + | 0.161437i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.00000 | − | 6.92820i | 0.247594 | − | 0.428845i | ||||
\(262\) | 11.2583 | − | 6.50000i | 0.695542 | − | 0.401571i | ||||
\(263\) | −13.8564 | + | 8.00000i | −0.854423 | + | 0.493301i | −0.862141 | − | 0.506669i | \(-0.830877\pi\) |
0.00771799 | + | 0.999970i | \(0.497543\pi\) | |||||||
\(264\) | −0.500000 | + | 0.866025i | −0.0307729 | + | 0.0533002i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.500000 | − | 2.59808i | 0.0306570 | − | 0.159298i | ||||
\(267\) | 2.00000i | 0.122398i | ||||||||
\(268\) | −10.3923 | − | 6.00000i | −0.634811 | − | 0.366508i | ||||
\(269\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.00000 | + | 13.8564i | −0.485965 | + | 0.841717i | −0.999870 | − | 0.0161307i | \(-0.994865\pi\) |
0.513905 | + | 0.857847i | \(0.328199\pi\) | |||||||
\(272\) | 4.00000i | 0.242536i | ||||||||
\(273\) | 18.1865 | + | 3.50000i | 1.10070 | + | 0.211830i | ||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.500000 | − | 0.866025i | −0.0300965 | − | 0.0521286i | ||||
\(277\) | 1.73205 | − | 1.00000i | 0.104069 | − | 0.0600842i | −0.447062 | − | 0.894503i | \(-0.647530\pi\) |
0.551131 | + | 0.834419i | \(0.314196\pi\) | |||||||
\(278\) | 3.46410 | + | 2.00000i | 0.207763 | + | 0.119952i | ||||
\(279\) | −6.00000 | −0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.00000 | 0.178965 | 0.0894825 | − | 0.995988i | \(-0.471479\pi\) | ||||
0.0894825 | + | 0.995988i | \(0.471479\pi\) | |||||||
\(282\) | −2.59808 | − | 1.50000i | −0.154713 | − | 0.0893237i | ||||
\(283\) | −1.73205 | + | 1.00000i | −0.102960 | + | 0.0594438i | −0.550596 | − | 0.834772i | \(-0.685599\pi\) |
0.447636 | + | 0.894216i | \(0.352266\pi\) | |||||||
\(284\) | −7.00000 | − | 12.1244i | −0.415374 | − | 0.719448i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7.00000 | −0.413919 | ||||||||
\(287\) | 15.5885 | − | 18.0000i | 0.920158 | − | 1.06251i | ||||
\(288\) | 1.00000i | 0.0589256i | ||||||||
\(289\) | −0.500000 | + | 0.866025i | −0.0294118 | + | 0.0509427i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.00000 | + | 13.8564i | 0.468968 | + | 0.812277i | ||||
\(292\) | −12.1244 | − | 7.00000i | −0.709524 | − | 0.409644i | ||||
\(293\) | 9.00000i | 0.525786i | 0.964825 | + | 0.262893i | \(0.0846766\pi\) | ||||
−0.964825 | + | 0.262893i | \(0.915323\pi\) | |||||||
\(294\) | −1.00000 | − | 6.92820i | −0.0583212 | − | 0.404061i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.50000 | − | 2.59808i | 0.0871857 | − | 0.151010i | ||||
\(297\) | 0.866025 | − | 0.500000i | 0.0502519 | − | 0.0290129i | ||||
\(298\) | −3.46410 | + | 2.00000i | −0.200670 | + | 0.115857i | ||||
\(299\) | 3.50000 | − | 6.06218i | 0.202410 | − | 0.350585i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.00000 | − | 6.92820i | −0.461112 | − | 0.399335i | ||||
\(302\) | 2.00000i | 0.115087i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.500000 | + | 0.866025i | 0.0286770 | + | 0.0496700i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.00000 | − | 3.46410i | 0.114332 | − | 0.198030i | ||||
\(307\) | − | 8.00000i | − | 0.456584i | −0.973593 | − | 0.228292i | \(-0.926686\pi\) | ||
0.973593 | − | 0.228292i | \(-0.0733141\pi\) | |||||||
\(308\) | 0.866025 | + | 2.50000i | 0.0493464 | + | 0.142451i | ||||
\(309\) | −16.0000 | −0.910208 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8.00000 | − | 13.8564i | −0.453638 | − | 0.785725i | 0.544970 | − | 0.838455i | \(-0.316541\pi\) |
−0.998609 | + | 0.0527306i | \(0.983208\pi\) | |||||||
\(312\) | −6.06218 | + | 3.50000i | −0.343203 | + | 0.198148i | ||||
\(313\) | 20.7846 | + | 12.0000i | 1.17482 | + | 0.678280i | 0.954810 | − | 0.297218i | \(-0.0960589\pi\) |
0.220006 | + | 0.975499i | \(0.429392\pi\) | |||||||
\(314\) | −15.0000 | −0.846499 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.00000 | 0.225018 | ||||||||
\(317\) | 8.66025 | + | 5.00000i | 0.486408 | + | 0.280828i | 0.723083 | − | 0.690761i | \(-0.242724\pi\) |
−0.236675 | + | 0.971589i | \(0.576058\pi\) | |||||||
\(318\) | −0.866025 | + | 0.500000i | −0.0485643 | + | 0.0280386i | ||||
\(319\) | 4.00000 | + | 6.92820i | 0.223957 | + | 0.387905i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −18.0000 | −1.00466 | ||||||||
\(322\) | −2.59808 | − | 0.500000i | −0.144785 | − | 0.0278639i | ||||
\(323\) | − | 4.00000i | − | 0.222566i | ||||||
\(324\) | 0.500000 | − | 0.866025i | 0.0277778 | − | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4.00000 | − | 6.92820i | −0.221540 | − | 0.383718i | ||||
\(327\) | −8.66025 | − | 5.00000i | −0.478913 | − | 0.276501i | ||||
\(328\) | 9.00000i | 0.496942i | ||||||||
\(329\) | −7.50000 | + | 2.59808i | −0.413488 | + | 0.143237i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.50000 | − | 7.79423i | 0.247342 | − | 0.428410i | −0.715445 | − | 0.698669i | \(-0.753776\pi\) |
0.962788 | + | 0.270259i | \(0.0871094\pi\) | |||||||
\(332\) | −10.3923 | + | 6.00000i | −0.570352 | + | 0.329293i | ||||
\(333\) | −2.59808 | + | 1.50000i | −0.142374 | + | 0.0821995i | ||||
\(334\) | −2.50000 | + | 4.33013i | −0.136794 | + | 0.236934i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.00000 | + | 1.73205i | 0.109109 | + | 0.0944911i | ||||
\(337\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(338\) | −31.1769 | − | 18.0000i | −1.69580 | − | 0.979071i | ||||
\(339\) | −3.00000 | − | 5.19615i | −0.162938 | − | 0.282216i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.00000 | − | 5.19615i | 0.162459 | − | 0.281387i | ||||
\(342\) | − | 1.00000i | − | 0.0540738i | ||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 4.00000 | 0.215666 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.5000 | + | 18.1865i | 0.564483 | + | 0.977714i | ||||
\(347\) | 29.4449 | − | 17.0000i | 1.58068 | − | 0.912608i | 0.585923 | − | 0.810366i | \(-0.300732\pi\) |
0.994760 | − | 0.102241i | \(-0.0326014\pi\) | |||||||
\(348\) | 6.92820 | + | 4.00000i | 0.371391 | + | 0.214423i | ||||
\(349\) | 28.0000 | 1.49881 | 0.749403 | − | 0.662114i | \(-0.230341\pi\) | ||||
0.749403 | + | 0.662114i | \(0.230341\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.00000 | 0.373632 | ||||||||
\(352\) | −0.866025 | − | 0.500000i | −0.0461593 | − | 0.0266501i | ||||
\(353\) | −6.92820 | + | 4.00000i | −0.368751 | + | 0.212899i | −0.672913 | − | 0.739722i | \(-0.734957\pi\) |
0.304162 | + | 0.952620i | \(0.401624\pi\) | |||||||
\(354\) | 6.00000 | + | 10.3923i | 0.318896 | + | 0.552345i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2.00000 | −0.106000 | ||||||||
\(357\) | −3.46410 | − | 10.0000i | −0.183340 | − | 0.529256i | ||||
\(358\) | 13.0000i | 0.687071i | ||||||||
\(359\) | 18.0000 | − | 31.1769i | 0.950004 | − | 1.64545i | 0.204595 | − | 0.978847i | \(-0.434412\pi\) |
0.745409 | − | 0.666608i | \(-0.232254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | + | 15.5885i | 0.473684 | + | 0.820445i | ||||
\(362\) | −10.3923 | − | 6.00000i | −0.546207 | − | 0.315353i | ||||
\(363\) | − | 10.0000i | − | 0.524864i | ||||||
\(364\) | −3.50000 | + | 18.1865i | −0.183450 | + | 0.953233i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2.00000 | − | 3.46410i | 0.104542 | − | 0.181071i | ||||
\(367\) | −16.4545 | + | 9.50000i | −0.858917 | + | 0.495896i | −0.863649 | − | 0.504093i | \(-0.831827\pi\) |
0.00473247 | + | 0.999989i | \(0.498494\pi\) | |||||||
\(368\) | 0.866025 | − | 0.500000i | 0.0451447 | − | 0.0260643i | ||||
\(369\) | 4.50000 | − | 7.79423i | 0.234261 | − | 0.405751i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.500000 | + | 2.59808i | −0.0259587 | + | 0.134885i | ||||
\(372\) | − | 6.00000i | − | 0.311086i | ||||||
\(373\) | −22.5167 | − | 13.0000i | −1.16587 | − | 0.673114i | −0.213165 | − | 0.977016i | \(-0.568377\pi\) |
−0.952703 | + | 0.303902i | \(0.901711\pi\) | |||||||
\(374\) | 2.00000 | + | 3.46410i | 0.103418 | + | 0.179124i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.50000 | − | 2.59808i | 0.0773566 | − | 0.133986i | ||||
\(377\) | 56.0000i | 2.88415i | ||||||||
\(378\) | −0.866025 | − | 2.50000i | −0.0445435 | − | 0.128586i | ||||
\(379\) | −1.00000 | −0.0513665 | −0.0256833 | − | 0.999670i | \(-0.508176\pi\) | ||||
−0.0256833 | + | 0.999670i | \(0.508176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.50000 | − | 4.33013i | −0.128079 | − | 0.221839i | ||||
\(382\) | 8.66025 | − | 5.00000i | 0.443097 | − | 0.255822i | ||||
\(383\) | −11.2583 | − | 6.50000i | −0.575274 | − | 0.332134i | 0.183979 | − | 0.982930i | \(-0.441102\pi\) |
−0.759253 | + | 0.650796i | \(0.774435\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 26.0000 | 1.32337 | ||||||||
\(387\) | −3.46410 | − | 2.00000i | −0.176090 | − | 0.101666i | ||||
\(388\) | −13.8564 | + | 8.00000i | −0.703452 | + | 0.406138i | ||||
\(389\) | −7.00000 | − | 12.1244i | −0.354914 | − | 0.614729i | 0.632189 | − | 0.774814i | \(-0.282157\pi\) |
−0.987103 | + | 0.160085i | \(0.948823\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 6.92820 | − | 1.00000i | 0.349927 | − | 0.0505076i | ||||
\(393\) | − | 13.0000i | − | 0.655763i | ||||||
\(394\) | −1.50000 | + | 2.59808i | −0.0755689 | + | 0.130889i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0.500000 | + | 0.866025i | 0.0251259 | + | 0.0435194i | ||||
\(397\) | 15.5885 | + | 9.00000i | 0.782362 | + | 0.451697i | 0.837267 | − | 0.546795i | \(-0.184152\pi\) |
−0.0549046 | + | 0.998492i | \(0.517485\pi\) | |||||||
\(398\) | − | 12.0000i | − | 0.601506i | ||||||
\(399\) | −2.00000 | − | 1.73205i | −0.100125 | − | 0.0867110i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.50000 | − | 14.7224i | 0.424470 | − | 0.735203i | −0.571901 | − | 0.820323i | \(-0.693794\pi\) |
0.996371 | + | 0.0851195i | \(0.0271272\pi\) | |||||||
\(402\) | −10.3923 | + | 6.00000i | −0.518321 | + | 0.299253i | ||||
\(403\) | 36.3731 | − | 21.0000i | 1.81187 | − | 1.04608i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.0000 | − | 6.92820i | 0.992583 | − | 0.343841i | ||||
\(407\) | − | 3.00000i | − | 0.148704i | ||||||
\(408\) | 3.46410 | + | 2.00000i | 0.171499 | + | 0.0990148i | ||||
\(409\) | 5.00000 | + | 8.66025i | 0.247234 | + | 0.428222i | 0.962757 | − | 0.270367i | \(-0.0871450\pi\) |
−0.715523 | + | 0.698589i | \(0.753812\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.00000 | − | 1.73205i | 0.0493264 | − | 0.0854358i | ||||
\(412\) | − | 16.0000i | − | 0.788263i | ||||||
\(413\) | 31.1769 | + | 6.00000i | 1.53412 | + | 0.295241i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.50000 | − | 6.06218i | −0.171602 | − | 0.297223i | ||||
\(417\) | 3.46410 | − | 2.00000i | 0.169638 | − | 0.0979404i | ||||
\(418\) | 0.866025 | + | 0.500000i | 0.0423587 | + | 0.0244558i | ||||
\(419\) | −11.0000 | −0.537385 | −0.268693 | − | 0.963226i | \(-0.586592\pi\) | ||||
−0.268693 | + | 0.963226i | \(0.586592\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0000 | −0.682318 | −0.341159 | − | 0.940006i | \(-0.610819\pi\) | ||||
−0.341159 | + | 0.940006i | \(0.610819\pi\) | |||||||
\(422\) | −12.9904 | − | 7.50000i | −0.632362 | − | 0.365094i | ||||
\(423\) | −2.59808 | + | 1.50000i | −0.126323 | + | 0.0729325i | ||||
\(424\) | −0.500000 | − | 0.866025i | −0.0242821 | − | 0.0420579i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −14.0000 | −0.678302 | ||||||||
\(427\) | −3.46410 | − | 10.0000i | −0.167640 | − | 0.483934i | ||||
\(428\) | − | 18.0000i | − | 0.870063i | ||||||
\(429\) | −3.50000 | + | 6.06218i | −0.168982 | + | 0.292685i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.00000 | + | 10.3923i | 0.289010 | + | 0.500580i | 0.973574 | − | 0.228373i | \(-0.0733406\pi\) |
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(432\) | 0.866025 | + | 0.500000i | 0.0416667 | + | 0.0240563i | ||||
\(433\) | 40.0000i | 1.92228i | 0.276066 | + | 0.961139i | \(0.410969\pi\) | ||||
−0.276066 | + | 0.961139i | \(0.589031\pi\) | |||||||
\(434\) | −12.0000 | − | 10.3923i | −0.576018 | − | 0.498847i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.00000 | − | 8.66025i | 0.239457 | − | 0.414751i | ||||
\(437\) | −0.866025 | + | 0.500000i | −0.0414276 | + | 0.0239182i | ||||
\(438\) | −12.1244 | + | 7.00000i | −0.579324 | + | 0.334473i | ||||
\(439\) | 8.00000 | − | 13.8564i | 0.381819 | − | 0.661330i | −0.609503 | − | 0.792784i | \(-0.708631\pi\) |
0.991322 | + | 0.131453i | \(0.0419644\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.50000 | − | 2.59808i | −0.309524 | − | 0.123718i | ||||
\(442\) | 28.0000i | 1.33182i | ||||||||
\(443\) | 31.1769 | + | 18.0000i | 1.48126 | + | 0.855206i | 0.999774 | − | 0.0212481i | \(-0.00676401\pi\) |
0.481486 | + | 0.876454i | \(0.340097\pi\) | |||||||
\(444\) | −1.50000 | − | 2.59808i | −0.0711868 | − | 0.123299i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.00000 | − | 3.46410i | 0.0947027 | − | 0.164030i | ||||
\(447\) | 4.00000i | 0.189194i | ||||||||
\(448\) | −1.73205 | + | 2.00000i | −0.0818317 | + | 0.0944911i | ||||
\(449\) | 25.0000 | 1.17982 | 0.589911 | − | 0.807468i | \(-0.299163\pi\) | ||||
0.589911 | + | 0.807468i | \(0.299163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.50000 | + | 7.79423i | 0.211897 | + | 0.367016i | ||||
\(452\) | 5.19615 | − | 3.00000i | 0.244406 | − | 0.141108i | ||||
\(453\) | 1.73205 | + | 1.00000i | 0.0813788 | + | 0.0469841i | ||||
\(454\) | 20.0000 | 0.938647 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.00000 | 0.0468293 | ||||||||
\(457\) | 8.66025 | + | 5.00000i | 0.405110 | + | 0.233890i | 0.688686 | − | 0.725059i | \(-0.258188\pi\) |
−0.283577 | + | 0.958950i | \(0.591521\pi\) | |||||||
\(458\) | −19.0526 | + | 11.0000i | −0.890268 | + | 0.513996i | ||||
\(459\) | −2.00000 | − | 3.46410i | −0.0933520 | − | 0.161690i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −28.0000 | −1.30409 | −0.652045 | − | 0.758180i | \(-0.726089\pi\) | ||||
−0.652045 | + | 0.758180i | \(0.726089\pi\) | |||||||
\(462\) | 2.59808 | + | 0.500000i | 0.120873 | + | 0.0232621i | ||||
\(463\) | 33.0000i | 1.53364i | 0.641862 | + | 0.766820i | \(0.278162\pi\) | ||||
−0.641862 | + | 0.766820i | \(0.721838\pi\) | |||||||
\(464\) | −4.00000 | + | 6.92820i | −0.185695 | + | 0.321634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −13.0000 | − | 22.5167i | −0.602213 | − | 1.04306i | ||||
\(467\) | 10.3923 | + | 6.00000i | 0.480899 | + | 0.277647i | 0.720791 | − | 0.693153i | \(-0.243779\pi\) |
−0.239892 | + | 0.970799i | \(0.577112\pi\) | |||||||
\(468\) | 7.00000i | 0.323575i | ||||||||
\(469\) | −6.00000 | + | 31.1769i | −0.277054 | + | 1.43962i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.50000 | + | 12.9904i | −0.345582 | + | 0.598565i | ||||
\(472\) | −10.3923 | + | 6.00000i | −0.478345 | + | 0.276172i | ||||
\(473\) | 3.46410 | − | 2.00000i | 0.159280 | − | 0.0919601i | ||||
\(474\) | 2.00000 | − | 3.46410i | 0.0918630 | − | 0.159111i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.0000 | − | 3.46410i | 0.458349 | − | 0.158777i | ||||
\(477\) | 1.00000i | 0.0457869i | ||||||||
\(478\) | 5.19615 | + | 3.00000i | 0.237666 | + | 0.137217i | ||||
\(479\) | 13.0000 | + | 22.5167i | 0.593985 | + | 1.02881i | 0.993689 | + | 0.112168i | \(0.0357796\pi\) |
−0.399704 | + | 0.916644i | \(0.630887\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.5000 | − | 18.1865i | 0.478759 | − | 0.829235i | ||||
\(482\) | − | 7.00000i | − | 0.318841i | ||||||
\(483\) | −1.73205 | + | 2.00000i | −0.0788110 | + | 0.0910032i | ||||
\(484\) | 10.0000 | 0.454545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.500000 | − | 0.866025i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 6.92820 | − | 4.00000i | 0.313947 | − | 0.181257i | −0.334744 | − | 0.942309i | \(-0.608650\pi\) |
0.648691 | + | 0.761052i | \(0.275317\pi\) | |||||||
\(488\) | 3.46410 | + | 2.00000i | 0.156813 | + | 0.0905357i | ||||
\(489\) | −8.00000 | −0.361773 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −12.0000 | −0.541552 | −0.270776 | − | 0.962642i | \(-0.587280\pi\) | ||||
−0.270776 | + | 0.962642i | \(0.587280\pi\) | |||||||
\(492\) | 7.79423 | + | 4.50000i | 0.351391 | + | 0.202876i | ||||
\(493\) | 27.7128 | − | 16.0000i | 1.24812 | − | 0.720604i | ||||
\(494\) | 3.50000 | + | 6.06218i | 0.157472 | + | 0.272750i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | −24.2487 | + | 28.0000i | −1.08770 | + | 1.25597i | ||||
\(498\) | 12.0000i | 0.537733i | ||||||||
\(499\) | 12.0000 | − | 20.7846i | 0.537194 | − | 0.930447i | −0.461860 | − | 0.886953i | \(-0.652818\pi\) |
0.999054 | − | 0.0434940i | \(-0.0138489\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.50000 | + | 4.33013i | 0.111692 | + | 0.193456i | ||||
\(502\) | −2.59808 | − | 1.50000i | −0.115958 | − | 0.0669483i | ||||
\(503\) | 28.0000i | 1.24846i | 0.781241 | + | 0.624229i | \(0.214587\pi\) | ||||
−0.781241 | + | 0.624229i | \(0.785413\pi\) | |||||||
\(504\) | 2.50000 | − | 0.866025i | 0.111359 | − | 0.0385758i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.500000 | − | 0.866025i | 0.0222277 | − | 0.0384995i | ||||
\(507\) | −31.1769 | + | 18.0000i | −1.38462 | + | 0.799408i | ||||
\(508\) | 4.33013 | − | 2.50000i | 0.192118 | − | 0.110920i | ||||
\(509\) | 15.0000 | − | 25.9808i | 0.664863 | − | 1.15158i | −0.314459 | − | 0.949271i | \(-0.601823\pi\) |
0.979322 | − | 0.202306i | \(-0.0648436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.00000 | + | 36.3731i | −0.309662 | + | 1.60905i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | −0.866025 | − | 0.500000i | −0.0382360 | − | 0.0220755i | ||||
\(514\) | −4.00000 | − | 6.92820i | −0.176432 | − | 0.305590i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.00000 | − | 3.46410i | 0.0880451 | − | 0.152499i | ||||
\(517\) | − | 3.00000i | − | 0.131940i | ||||||
\(518\) | −7.79423 | − | 1.50000i | −0.342459 | − | 0.0659062i | ||||
\(519\) | 21.0000 | 0.921798 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.5000 | + | 18.1865i | 0.460013 | + | 0.796766i | 0.998961 | − | 0.0455727i | \(-0.0145113\pi\) |
−0.538948 | + | 0.842339i | \(0.681178\pi\) | |||||||
\(522\) | 6.92820 | − | 4.00000i | 0.303239 | − | 0.175075i | ||||
\(523\) | 12.1244 | + | 7.00000i | 0.530161 | + | 0.306089i | 0.741082 | − | 0.671414i | \(-0.234313\pi\) |
−0.210921 | + | 0.977503i | \(0.567646\pi\) | |||||||
\(524\) | 13.0000 | 0.567908 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.0000 | −0.697633 | ||||||||
\(527\) | −20.7846 | − | 12.0000i | −0.905392 | − | 0.522728i | ||||
\(528\) | −0.866025 | + | 0.500000i | −0.0376889 | + | 0.0217597i | ||||
\(529\) | −11.0000 | − | 19.0526i | −0.478261 | − | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.0000 | 0.520756 | ||||||||
\(532\) | 1.73205 | − | 2.00000i | 0.0750939 | − | 0.0867110i | ||||
\(533\) | 63.0000i | 2.72883i | ||||||||
\(534\) | −1.00000 | + | 1.73205i | −0.0432742 | + | 0.0749532i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.00000 | − | 10.3923i | −0.259161 | − | 0.448879i | ||||
\(537\) | 11.2583 | + | 6.50000i | 0.485833 | + | 0.280496i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 5.50000 | − | 4.33013i | 0.236902 | − | 0.186512i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.00000 | + | 1.73205i | −0.0429934 | + | 0.0744667i | −0.886721 | − | 0.462304i | \(-0.847023\pi\) |
0.843728 | + | 0.536771i | \(0.180356\pi\) | |||||||
\(542\) | −13.8564 | + | 8.00000i | −0.595184 | + | 0.343629i | ||||
\(543\) | −10.3923 | + | 6.00000i | −0.445976 | + | 0.257485i | ||||
\(544\) | −2.00000 | + | 3.46410i | −0.0857493 | + | 0.148522i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 14.0000 | + | 12.1244i | 0.599145 | + | 0.518875i | ||||
\(547\) | − | 36.0000i | − | 1.53925i | −0.638497 | − | 0.769624i | \(-0.720443\pi\) | ||
0.638497 | − | 0.769624i | \(-0.279557\pi\) | |||||||
\(548\) | 1.73205 | + | 1.00000i | 0.0739895 | + | 0.0427179i | ||||
\(549\) | −2.00000 | − | 3.46410i | −0.0853579 | − | 0.147844i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.00000 | − | 6.92820i | 0.170406 | − | 0.295151i | ||||
\(552\) | − | 1.00000i | − | 0.0425628i | ||||||
\(553\) | −3.46410 | − | 10.0000i | −0.147309 | − | 0.425243i | ||||
\(554\) | 2.00000 | 0.0849719 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.00000 | + | 3.46410i | 0.0848189 | + | 0.146911i | ||||
\(557\) | −38.9711 | + | 22.5000i | −1.65126 | + | 0.953356i | −0.674705 | + | 0.738087i | \(0.735729\pi\) |
−0.976555 | + | 0.215268i | \(0.930937\pi\) | |||||||
\(558\) | −5.19615 | − | 3.00000i | −0.219971 | − | 0.127000i | ||||
\(559\) | 28.0000 | 1.18427 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.00000 | 0.168880 | ||||||||
\(562\) | 2.59808 | + | 1.50000i | 0.109593 | + | 0.0632737i | ||||
\(563\) | 12.1244 | − | 7.00000i | 0.510981 | − | 0.295015i | −0.222256 | − | 0.974988i | \(-0.571342\pi\) |
0.733237 | + | 0.679974i | \(0.238009\pi\) | |||||||
\(564\) | −1.50000 | − | 2.59808i | −0.0631614 | − | 0.109399i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.00000 | −0.0840663 | ||||||||
\(567\) | −2.59808 | − | 0.500000i | −0.109109 | − | 0.0209980i | ||||
\(568\) | − | 14.0000i | − | 0.587427i | ||||||
\(569\) | −18.5000 | + | 32.0429i | −0.775560 | + | 1.34331i | 0.158919 | + | 0.987292i | \(0.449199\pi\) |
−0.934479 | + | 0.356018i | \(0.884134\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | + | 6.92820i | 0.167395 | + | 0.289936i | 0.937503 | − | 0.347977i | \(-0.113131\pi\) |
−0.770108 | + | 0.637913i | \(0.779798\pi\) | |||||||
\(572\) | −6.06218 | − | 3.50000i | −0.253472 | − | 0.146342i | ||||
\(573\) | − | 10.0000i | − | 0.417756i | ||||||
\(574\) | 22.5000 | − | 7.79423i | 0.939132 | − | 0.325325i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 12.1244 | − | 7.00000i | 0.504744 | − | 0.291414i | −0.225927 | − | 0.974144i | \(-0.572541\pi\) |
0.730670 | + | 0.682730i | \(0.239208\pi\) | |||||||
\(578\) | −0.866025 | + | 0.500000i | −0.0360219 | + | 0.0207973i | ||||
\(579\) | 13.0000 | − | 22.5167i | 0.540262 | − | 0.935760i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 24.0000 | + | 20.7846i | 0.995688 | + | 0.862291i | ||||
\(582\) | 16.0000i | 0.663221i | ||||||||
\(583\) | −0.866025 | − | 0.500000i | −0.0358671 | − | 0.0207079i | ||||
\(584\) | −7.00000 | − | 12.1244i | −0.289662 | − | 0.501709i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.50000 | + | 7.79423i | −0.185893 | + | 0.321977i | ||||
\(587\) | − | 42.0000i | − | 1.73353i | −0.498721 | − | 0.866763i | \(-0.666197\pi\) | ||
0.498721 | − | 0.866763i | \(-0.333803\pi\) | |||||||
\(588\) | 2.59808 | − | 6.50000i | 0.107143 | − | 0.268055i | ||||
\(589\) | −6.00000 | −0.247226 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.50000 | + | 2.59808i | 0.0617018 | + | 0.106871i | ||||
\(592\) | 2.59808 | − | 1.50000i | 0.106780 | − | 0.0616496i | ||||
\(593\) | −10.3923 | − | 6.00000i | −0.426761 | − | 0.246390i | 0.271205 | − | 0.962522i | \(-0.412578\pi\) |
−0.697966 | + | 0.716131i | \(0.745911\pi\) | |||||||
\(594\) | 1.00000 | 0.0410305 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.00000 | −0.163846 | ||||||||
\(597\) | −10.3923 | − | 6.00000i | −0.425329 | − | 0.245564i | ||||
\(598\) | 6.06218 | − | 3.50000i | 0.247901 | − | 0.143126i | ||||
\(599\) | 3.00000 | + | 5.19615i | 0.122577 | + | 0.212309i | 0.920783 | − | 0.390075i | \(-0.127551\pi\) |
−0.798206 | + | 0.602384i | \(0.794218\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0000 | 0.897399 | 0.448699 | − | 0.893683i | \(-0.351887\pi\) | ||||
0.448699 | + | 0.893683i | \(0.351887\pi\) | |||||||
\(602\) | −3.46410 | − | 10.0000i | −0.141186 | − | 0.407570i | ||||
\(603\) | 12.0000i | 0.488678i | ||||||||
\(604\) | −1.00000 | + | 1.73205i | −0.0406894 | + | 0.0704761i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 21.6506 | + | 12.5000i | 0.878772 | + | 0.507359i | 0.870253 | − | 0.492604i | \(-0.163955\pi\) |
0.00851879 | + | 0.999964i | \(0.497288\pi\) | |||||||
\(608\) | 1.00000i | 0.0405554i | ||||||||
\(609\) | 4.00000 | − | 20.7846i | 0.162088 | − | 0.842235i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.5000 | − | 18.1865i | 0.424785 | − | 0.735748i | ||||
\(612\) | 3.46410 | − | 2.00000i | 0.140028 | − | 0.0808452i | ||||
\(613\) | −12.9904 | + | 7.50000i | −0.524677 | + | 0.302922i | −0.738846 | − | 0.673874i | \(-0.764629\pi\) |
0.214169 | + | 0.976797i | \(0.431296\pi\) | |||||||
\(614\) | 4.00000 | − | 6.92820i | 0.161427 | − | 0.279600i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.500000 | + | 2.59808i | −0.0201456 | + | 0.104679i | ||||
\(617\) | − | 8.00000i | − | 0.322068i | −0.986949 | − | 0.161034i | \(-0.948517\pi\) | ||
0.986949 | − | 0.161034i | \(-0.0514829\pi\) | |||||||
\(618\) | −13.8564 | − | 8.00000i | −0.557386 | − | 0.321807i | ||||
\(619\) | −3.50000 | − | 6.06218i | −0.140677 | − | 0.243659i | 0.787075 | − | 0.616858i | \(-0.211595\pi\) |
−0.927752 | + | 0.373198i | \(0.878261\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | − | 16.0000i | − | 0.641542i | ||||||
\(623\) | 1.73205 | + | 5.00000i | 0.0693932 | + | 0.200321i | ||||
\(624\) | −7.00000 | −0.280224 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.0000 | + | 20.7846i | 0.479616 | + | 0.830720i | ||||
\(627\) | 0.866025 | − | 0.500000i | 0.0345857 | − | 0.0199681i | ||||
\(628\) | −12.9904 | − | 7.50000i | −0.518373 | − | 0.299283i | ||||
\(629\) | −12.0000 | −0.478471 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0000 | 0.557331 | 0.278666 | − | 0.960388i | \(-0.410108\pi\) | ||||
0.278666 | + | 0.960388i | \(0.410108\pi\) | |||||||
\(632\) | 3.46410 | + | 2.00000i | 0.137795 | + | 0.0795557i | ||||
\(633\) | −12.9904 | + | 7.50000i | −0.516321 | + | 0.298098i | ||||
\(634\) | 5.00000 | + | 8.66025i | 0.198575 | + | 0.343943i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | 48.4974 | − | 7.00000i | 1.92154 | − | 0.277350i | ||||
\(638\) | 8.00000i | 0.316723i | ||||||||
\(639\) | −7.00000 | + | 12.1244i | −0.276916 | + | 0.479632i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.5000 | + | 19.9186i | 0.454223 | + | 0.786737i | 0.998643 | − | 0.0520757i | \(-0.0165837\pi\) |
−0.544420 | + | 0.838812i | \(0.683250\pi\) | |||||||
\(642\) | −15.5885 | − | 9.00000i | −0.615227 | − | 0.355202i | ||||
\(643\) | 26.0000i | 1.02534i | 0.858586 | + | 0.512670i | \(0.171344\pi\) | ||||
−0.858586 | + | 0.512670i | \(0.828656\pi\) | |||||||
\(644\) | −2.00000 | − | 1.73205i | −0.0788110 | − | 0.0682524i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.00000 | − | 3.46410i | 0.0786889 | − | 0.136293i | ||||
\(647\) | 12.9904 | − | 7.50000i | 0.510705 | − | 0.294855i | −0.222419 | − | 0.974951i | \(-0.571395\pi\) |
0.733123 | + | 0.680096i | \(0.238062\pi\) | |||||||
\(648\) | 0.866025 | − | 0.500000i | 0.0340207 | − | 0.0196419i | ||||
\(649\) | −6.00000 | + | 10.3923i | −0.235521 | + | 0.407934i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −15.0000 | + | 5.19615i | −0.587896 | + | 0.203653i | ||||
\(652\) | − | 8.00000i | − | 0.313304i | ||||||
\(653\) | −25.1147 | − | 14.5000i | −0.982816 | − | 0.567429i | −0.0796966 | − | 0.996819i | \(-0.525395\pi\) |
−0.903119 | + | 0.429390i | \(0.858728\pi\) | |||||||
\(654\) | −5.00000 | − | 8.66025i | −0.195515 | − | 0.338643i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −4.50000 | + | 7.79423i | −0.175695 | + | 0.304314i | ||||
\(657\) | 14.0000i | 0.546192i | ||||||||
\(658\) | −7.79423 | − | 1.50000i | −0.303851 | − | 0.0584761i | ||||
\(659\) | 12.0000 | 0.467454 | 0.233727 | − | 0.972302i | \(-0.424908\pi\) | ||||
0.233727 | + | 0.972302i | \(0.424908\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −4.00000 | − | 6.92820i | −0.155582 | − | 0.269476i | 0.777689 | − | 0.628649i | \(-0.216392\pi\) |
−0.933271 | + | 0.359174i | \(0.883059\pi\) | |||||||
\(662\) | 7.79423 | − | 4.50000i | 0.302931 | − | 0.174897i | ||||
\(663\) | 24.2487 | + | 14.0000i | 0.941742 | + | 0.543715i | ||||
\(664\) | −12.0000 | −0.465690 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −3.00000 | −0.116248 | ||||||||
\(667\) | −6.92820 | − | 4.00000i | −0.268261 | − | 0.154881i | ||||
\(668\) | −4.33013 | + | 2.50000i | −0.167538 | + | 0.0967279i | ||||
\(669\) | −2.00000 | − | 3.46410i | −0.0773245 | − | 0.133930i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4.00000 | 0.154418 | ||||||||
\(672\) | 0.866025 | + | 2.50000i | 0.0334077 | + | 0.0964396i | ||||
\(673\) | − | 12.0000i | − | 0.462566i | −0.972887 | − | 0.231283i | \(-0.925708\pi\) | ||
0.972887 | − | 0.231283i | \(-0.0742923\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −18.0000 | − | 31.1769i | −0.692308 | − | 1.19911i | ||||
\(677\) | 0.866025 | + | 0.500000i | 0.0332841 | + | 0.0192166i | 0.516550 | − | 0.856257i | \(-0.327216\pi\) |
−0.483266 | + | 0.875474i | \(0.660549\pi\) | |||||||
\(678\) | − | 6.00000i | − | 0.230429i | ||||||
\(679\) | 32.0000 | + | 27.7128i | 1.22805 | + | 1.06352i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 10.0000 | − | 17.3205i | 0.383201 | − | 0.663723i | ||||
\(682\) | 5.19615 | − | 3.00000i | 0.198971 | − | 0.114876i | ||||
\(683\) | 10.3923 | − | 6.00000i | 0.397650 | − | 0.229584i | −0.287819 | − | 0.957685i | \(-0.592930\pi\) |
0.685470 | + | 0.728101i | \(0.259597\pi\) | |||||||
\(684\) | 0.500000 | − | 0.866025i | 0.0191180 | − | 0.0331133i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.50000 | − | 16.4545i | −0.324532 | − | 0.628235i | ||||
\(687\) | 22.0000i | 0.839352i | ||||||||
\(688\) | 3.46410 | + | 2.00000i | 0.132068 | + | 0.0762493i | ||||
\(689\) | −3.50000 | − | 6.06218i | −0.133339 | − | 0.230951i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.00000 | + | 10.3923i | −0.228251 | + | 0.395342i | −0.957290 | − | 0.289130i | \(-0.906634\pi\) |
0.729039 | + | 0.684472i | \(0.239967\pi\) | |||||||
\(692\) | 21.0000i | 0.798300i | ||||||||
\(693\) | 1.73205 | − | 2.00000i | 0.0657952 | − | 0.0759737i | ||||
\(694\) | 34.0000 | 1.29062 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.00000 | + | 6.92820i | 0.151620 | + | 0.262613i | ||||
\(697\) | 31.1769 | − | 18.0000i | 1.18091 | − | 0.681799i | ||||
\(698\) | 24.2487 | + | 14.0000i | 0.917827 | + | 0.529908i | ||||
\(699\) | −26.0000 | −0.983410 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00000 | 0.226617 | 0.113308 | − | 0.993560i | \(-0.463855\pi\) | ||||
0.113308 | + | 0.993560i | \(0.463855\pi\) | |||||||
\(702\) | 6.06218 | + | 3.50000i | 0.228802 | + | 0.132099i | ||||
\(703\) | −2.59808 | + | 1.50000i | −0.0979883 | + | 0.0565736i | ||||
\(704\) | −0.500000 | − | 0.866025i | −0.0188445 | − | 0.0326396i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −8.00000 | −0.301084 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 12.0000i | 0.450988i | ||||||||
\(709\) | 2.00000 | − | 3.46410i | 0.0751116 | − | 0.130097i | −0.826023 | − | 0.563636i | \(-0.809402\pi\) |
0.901135 | + | 0.433539i | \(0.142735\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.00000 | − | 3.46410i | −0.0750059 | − | 0.129914i | ||||
\(712\) | −1.73205 | − | 1.00000i | −0.0649113 | − | 0.0374766i | ||||
\(713\) | 6.00000i | 0.224702i | ||||||||
\(714\) | 2.00000 | − | 10.3923i | 0.0748481 | − | 0.388922i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6.50000 | + | 11.2583i | −0.242916 | + | 0.420744i | ||||
\(717\) | 5.19615 | − | 3.00000i | 0.194054 | − | 0.112037i | ||||
\(718\) | 31.1769 | − | 18.0000i | 1.16351 | − | 0.671754i | ||||
\(719\) | 13.0000 | − | 22.5167i | 0.484818 | − | 0.839730i | −0.515030 | − | 0.857172i | \(-0.672219\pi\) |
0.999848 | + | 0.0174426i | \(0.00555244\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −40.0000 | + | 13.8564i | −1.48968 | + | 0.516040i | ||||
\(722\) | 18.0000i | 0.669891i | ||||||||
\(723\) | −6.06218 | − | 3.50000i | −0.225455 | − | 0.130166i | ||||
\(724\) | −6.00000 | − | 10.3923i | −0.222988 | − | 0.386227i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.00000 | − | 8.66025i | 0.185567 | − | 0.321412i | ||||
\(727\) | − | 17.0000i | − | 0.630495i | −0.949009 | − | 0.315248i | \(-0.897912\pi\) | ||
0.949009 | − | 0.315248i | \(-0.102088\pi\) | |||||||
\(728\) | −12.1244 | + | 14.0000i | −0.449359 | + | 0.518875i | ||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | − | 13.8564i | −0.295891 | − | 0.512498i | ||||
\(732\) | 3.46410 | − | 2.00000i | 0.128037 | − | 0.0739221i | ||||
\(733\) | −32.0429 | − | 18.5000i | −1.18353 | − | 0.683313i | −0.226704 | − | 0.973964i | \(-0.572795\pi\) |
−0.956829 | + | 0.290651i | \(0.906128\pi\) | |||||||
\(734\) | −19.0000 | −0.701303 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −10.3923 | − | 6.00000i | −0.382805 | − | 0.221013i | ||||
\(738\) | 7.79423 | − | 4.50000i | 0.286910 | − | 0.165647i | ||||
\(739\) | 20.5000 | + | 35.5070i | 0.754105 | + | 1.30615i | 0.945818 | + | 0.324697i | \(0.105262\pi\) |
−0.191714 | + | 0.981451i | \(0.561404\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 7.00000 | 0.257151 | ||||||||
\(742\) | −1.73205 | + | 2.00000i | −0.0635856 | + | 0.0734223i | ||||
\(743\) | − | 9.00000i | − | 0.330178i | −0.986279 | − | 0.165089i | \(-0.947209\pi\) | ||
0.986279 | − | 0.165089i | \(-0.0527911\pi\) | |||||||
\(744\) | 3.00000 | − | 5.19615i | 0.109985 | − | 0.190500i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −13.0000 | − | 22.5167i | −0.475964 | − | 0.824394i | ||||
\(747\) | 10.3923 | + | 6.00000i | 0.380235 | + | 0.219529i | ||||
\(748\) | 4.00000i | 0.146254i | ||||||||
\(749\) | −45.0000 | + | 15.5885i | −1.64426 | + | 0.569590i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 13.0000 | − | 22.5167i | 0.474377 | − | 0.821645i | −0.525193 | − | 0.850983i | \(-0.676007\pi\) |
0.999570 | + | 0.0293387i | \(0.00934013\pi\) | |||||||
\(752\) | 2.59808 | − | 1.50000i | 0.0947421 | − | 0.0546994i | ||||
\(753\) | −2.59808 | + | 1.50000i | −0.0946792 | + | 0.0546630i | ||||
\(754\) | −28.0000 | + | 48.4974i | −1.01970 | + | 1.76617i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0.500000 | − | 2.59808i | 0.0181848 | − | 0.0944911i | ||||
\(757\) | 2.00000i | 0.0726912i | 0.999339 | + | 0.0363456i | \(0.0115717\pi\) | ||||
−0.999339 | + | 0.0363456i | \(0.988428\pi\) | |||||||
\(758\) | −0.866025 | − | 0.500000i | −0.0314555 | − | 0.0181608i | ||||
\(759\) | −0.500000 | − | 0.866025i | −0.0181489 | − | 0.0314347i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.50000 | − | 14.7224i | 0.308125 | − | 0.533688i | −0.669827 | − | 0.742517i | \(-0.733632\pi\) |
0.977952 | + | 0.208829i | \(0.0669652\pi\) | |||||||
\(762\) | − | 5.00000i | − | 0.181131i | ||||||
\(763\) | −25.9808 | − | 5.00000i | −0.940567 | − | 0.181012i | ||||
\(764\) | 10.0000 | 0.361787 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.50000 | − | 11.2583i | −0.234855 | − | 0.406780i | ||||
\(767\) | −72.7461 | + | 42.0000i | −2.62671 | + | 1.51653i | ||||
\(768\) | −0.866025 | − | 0.500000i | −0.0312500 | − | 0.0180422i | ||||
\(769\) | 29.0000 | 1.04577 | 0.522883 | − | 0.852404i | \(-0.324856\pi\) | ||||
0.522883 | + | 0.852404i | \(0.324856\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.00000 | −0.288113 | ||||||||
\(772\) | 22.5167 | + | 13.0000i | 0.810392 | + | 0.467880i | ||||
\(773\) | 37.2391 | − | 21.5000i | 1.33940 | − | 0.773301i | 0.352679 | − | 0.935744i | \(-0.385271\pi\) |
0.986718 | + | 0.162443i | \(0.0519374\pi\) | |||||||
\(774\) | −2.00000 | − | 3.46410i | −0.0718885 | − | 0.124515i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −16.0000 | −0.574367 | ||||||||
\(777\) | −5.19615 | + | 6.00000i | −0.186411 | + | 0.215249i | ||||
\(778\) | − | 14.0000i | − | 0.501924i | ||||||
\(779\) | 4.50000 | − | 7.79423i | 0.161229 | − | 0.279257i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.00000 | − | 12.1244i | −0.250480 | − | 0.433844i | ||||
\(782\) | −3.46410 | − | 2.00000i | −0.123876 | − | 0.0715199i | ||||
\(783\) | − | 8.00000i | − | 0.285897i | ||||||
\(784\) | 6.50000 | + | 2.59808i | 0.232143 | + | 0.0927884i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 6.50000 | − | 11.2583i | 0.231847 | − | 0.401571i | ||||
\(787\) | 19.0526 | − | 11.0000i | 0.679150 | − | 0.392108i | −0.120384 | − | 0.992727i | \(-0.538413\pi\) |
0.799535 | + | 0.600620i | \(0.205079\pi\) | |||||||
\(788\) | −2.59808 | + | 1.50000i | −0.0925526 | + | 0.0534353i | ||||
\(789\) | −8.00000 | + | 13.8564i | −0.284808 | + | 0.493301i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −12.0000 | − | 10.3923i | −0.426671 | − | 0.369508i | ||||
\(792\) | 1.00000i | 0.0355335i | ||||||||
\(793\) | 24.2487 | + | 14.0000i | 0.861097 | + | 0.497155i | ||||
\(794\) | 9.00000 | + | 15.5885i | 0.319398 | + | 0.553214i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 6.00000 | − | 10.3923i | 0.212664 | − | 0.368345i | ||||
\(797\) | 6.00000i | 0.212531i | 0.994338 | + | 0.106265i | \(0.0338893\pi\) | ||||
−0.994338 | + | 0.106265i | \(0.966111\pi\) | |||||||
\(798\) | −0.866025 | − | 2.50000i | −0.0306570 | − | 0.0884990i | ||||
\(799\) | −12.0000 | −0.424529 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.00000 | + | 1.73205i | 0.0353333 | + | 0.0611990i | ||||
\(802\) | 14.7224 | − | 8.50000i | 0.519867 | − | 0.300145i | ||||
\(803\) | −12.1244 | − | 7.00000i | −0.427859 | − | 0.247025i | ||||
\(804\) | −12.0000 | −0.423207 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 42.0000 | 1.47939 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 26.5000 | + | 45.8993i | 0.931690 | + | 1.61374i | 0.780432 | + | 0.625241i | \(0.214999\pi\) |
0.151259 | + | 0.988494i | \(0.451667\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.0000 | 1.29925 | 0.649623 | − | 0.760257i | \(-0.274927\pi\) | ||||
0.649623 | + | 0.760257i | \(0.274927\pi\) | |||||||
\(812\) | 20.7846 | + | 4.00000i | 0.729397 | + | 0.140372i | ||||
\(813\) | 16.0000i | 0.561144i | ||||||||
\(814\) | 1.50000 | − | 2.59808i | 0.0525750 | − | 0.0910625i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | −3.46410 | − | 2.00000i | −0.121194 | − | 0.0699711i | ||||
\(818\) | 10.0000i | 0.349642i | ||||||||
\(819\) | 17.5000 | − | 6.06218i | 0.611499 | − | 0.211830i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.0000 | + | 29.4449i | −0.593304 | + | 1.02763i | 0.400480 | + | 0.916306i | \(0.368843\pi\) |
−0.993784 | + | 0.111327i | \(0.964490\pi\) | |||||||
\(822\) | 1.73205 | − | 1.00000i | 0.0604122 | − | 0.0348790i | ||||
\(823\) | 41.5692 | − | 24.0000i | 1.44901 | − | 0.836587i | 0.450589 | − | 0.892731i | \(-0.351214\pi\) |
0.998423 | + | 0.0561440i | \(0.0178806\pi\) | |||||||
\(824\) | 8.00000 | − | 13.8564i | 0.278693 | − | 0.482711i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 24.0000 | + | 20.7846i | 0.835067 | + | 0.723189i | ||||
\(827\) | − | 10.0000i | − | 0.347734i | −0.984769 | − | 0.173867i | \(-0.944374\pi\) | ||
0.984769 | − | 0.173867i | \(-0.0556263\pi\) | |||||||
\(828\) | −0.866025 | − | 0.500000i | −0.0300965 | − | 0.0173762i | ||||
\(829\) | 6.00000 | + | 10.3923i | 0.208389 | + | 0.360940i | 0.951207 | − | 0.308553i | \(-0.0998448\pi\) |
−0.742818 | + | 0.669493i | \(0.766511\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.00000 | − | 1.73205i | 0.0346896 | − | 0.0600842i | ||||
\(832\) | − | 7.00000i | − | 0.242681i | ||||||
\(833\) | −17.3205 | − | 22.0000i | −0.600120 | − | 0.762255i | ||||
\(834\) | 4.00000 | 0.138509 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0.500000 | + | 0.866025i | 0.0172929 | + | 0.0299521i | ||||
\(837\) | −5.19615 | + | 3.00000i | −0.179605 | + | 0.103695i | ||||
\(838\) | −9.52628 | − | 5.50000i | −0.329080 | − | 0.189994i | ||||
\(839\) | −44.0000 | −1.51905 | −0.759524 | − | 0.650479i | \(-0.774568\pi\) | ||||
−0.759524 | + | 0.650479i | \(0.774568\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.0000 | 1.20690 | ||||||||
\(842\) | −12.1244 | − | 7.00000i | −0.417833 | − | 0.241236i | ||||
\(843\) | 2.59808 | − | 1.50000i | 0.0894825 | − | 0.0516627i | ||||
\(844\) | −7.50000 | − | 12.9904i | −0.258161 | − | 0.447147i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.00000 | −0.103142 | ||||||||
\(847\) | −8.66025 | − | 25.0000i | −0.297570 | − | 0.859010i | ||||
\(848\) | − | 1.00000i | − | 0.0343401i | ||||||
\(849\) | −1.00000 | + | 1.73205i | −0.0343199 | + | 0.0594438i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.50000 | + | 2.59808i | 0.0514193 | + | 0.0890609i | ||||
\(852\) | −12.1244 | − | 7.00000i | −0.415374 | − | 0.239816i | ||||
\(853\) | 1.00000i | 0.0342393i | 0.999853 | + | 0.0171197i | \(0.00544963\pi\) | ||||
−0.999853 | + | 0.0171197i | \(0.994550\pi\) | |||||||
\(854\) | 2.00000 | − | 10.3923i | 0.0684386 | − | 0.355617i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 9.00000 | − | 15.5885i | 0.307614 | − | 0.532803i | ||||
\(857\) | 19.0526 | − | 11.0000i | 0.650823 | − | 0.375753i | −0.137948 | − | 0.990439i | \(-0.544051\pi\) |
0.788771 | + | 0.614687i | \(0.210717\pi\) | |||||||
\(858\) | −6.06218 | + | 3.50000i | −0.206959 | + | 0.119488i | ||||
\(859\) | −10.0000 | + | 17.3205i | −0.341196 | + | 0.590968i | −0.984655 | − | 0.174512i | \(-0.944165\pi\) |
0.643459 | + | 0.765480i | \(0.277499\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.50000 | − | 23.3827i | 0.153360 | − | 0.796880i | ||||
\(862\) | 12.0000i | 0.408722i | ||||||||
\(863\) | −25.1147 | − | 14.5000i | −0.854916 | − | 0.493586i | 0.00739078 | − | 0.999973i | \(-0.497647\pi\) |
−0.862306 | + | 0.506387i | \(0.830981\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −20.0000 | + | 34.6410i | −0.679628 | + | 1.17715i | ||||
\(867\) | 1.00000i | 0.0339618i | ||||||||
\(868\) | −5.19615 | − | 15.0000i | −0.176369 | − | 0.509133i | ||||
\(869\) | 4.00000 | 0.135691 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −42.0000 | − | 72.7461i | −1.42312 | − | 2.46491i | ||||
\(872\) | 8.66025 | − | 5.00000i | 0.293273 | − | 0.169321i | ||||
\(873\) | 13.8564 | + | 8.00000i | 0.468968 | + | 0.270759i | ||||
\(874\) | −1.00000 | −0.0338255 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −14.0000 | −0.473016 | ||||||||
\(877\) | 19.9186 | + | 11.5000i | 0.672603 | + | 0.388327i | 0.797062 | − | 0.603897i | \(-0.206386\pi\) |
−0.124459 | + | 0.992225i | \(0.539720\pi\) | |||||||
\(878\) | 13.8564 | − | 8.00000i | 0.467631 | − | 0.269987i | ||||
\(879\) | 4.50000 | + | 7.79423i | 0.151781 | + | 0.262893i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.0000 | −0.842271 | −0.421136 | − | 0.906998i | \(-0.638368\pi\) | ||||
−0.421136 | + | 0.906998i | \(0.638368\pi\) | |||||||
\(882\) | −4.33013 | − | 5.50000i | −0.145803 | − | 0.185195i | ||||
\(883\) | − | 58.0000i | − | 1.95186i | −0.218094 | − | 0.975928i | \(-0.569984\pi\) | ||
0.218094 | − | 0.975928i | \(-0.430016\pi\) | |||||||
\(884\) | −14.0000 | + | 24.2487i | −0.470871 | + | 0.815572i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 18.0000 | + | 31.1769i | 0.604722 | + | 1.04741i | ||||
\(887\) | 17.3205 | + | 10.0000i | 0.581566 | + | 0.335767i | 0.761755 | − | 0.647865i | \(-0.224338\pi\) |
−0.180190 | + | 0.983632i | \(0.557671\pi\) | |||||||
\(888\) | − | 3.00000i | − | 0.100673i | ||||||
\(889\) | −10.0000 | − | 8.66025i | −0.335389 | − | 0.290456i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.500000 | − | 0.866025i | 0.0167506 | − | 0.0290129i | ||||
\(892\) | 3.46410 | − | 2.00000i | 0.115987 | − | 0.0669650i | ||||
\(893\) | −2.59808 | + | 1.50000i | −0.0869413 | + | 0.0501956i | ||||
\(894\) | −2.00000 | + | 3.46410i | −0.0668900 | + | 0.115857i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.50000 | + | 0.866025i | −0.0835191 | + | 0.0289319i | ||||
\(897\) | − | 7.00000i | − | 0.233723i | ||||||
\(898\) | 21.6506 | + | 12.5000i | 0.722491 | + | 0.417130i | ||||
\(899\) | −24.0000 | − | 41.5692i | −0.800445 | − | 1.38641i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.00000 | + | 3.46410i | −0.0666297 | + | 0.115406i | ||||
\(902\) | 9.00000i | 0.299667i | ||||||||
\(903\) | −10.3923 | − | 2.00000i | −0.345834 | − | 0.0665558i | ||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 1.00000 | + | 1.73205i | 0.0332228 | + | 0.0575435i | ||||
\(907\) | −39.8372 | + | 23.0000i | −1.32277 | + | 0.763702i | −0.984170 | − | 0.177227i | \(-0.943287\pi\) |
−0.338602 | + | 0.940930i | \(0.609954\pi\) | |||||||
\(908\) | 17.3205 | + | 10.0000i | 0.574801 | + | 0.331862i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −58.0000 | −1.92163 | −0.960813 | − | 0.277198i | \(-0.910594\pi\) | ||||
−0.960813 | + | 0.277198i | \(0.910594\pi\) | |||||||
\(912\) | 0.866025 | + | 0.500000i | 0.0286770 | + | 0.0165567i | ||||
\(913\) | −10.3923 | + | 6.00000i | −0.343935 | + | 0.198571i | ||||
\(914\) | 5.00000 | + | 8.66025i | 0.165385 | + | 0.286456i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.0000 | −0.726900 | ||||||||
\(917\) | −11.2583 | − | 32.5000i | −0.371783 | − | 1.07324i | ||||
\(918\) | − | 4.00000i | − | 0.132020i | ||||||
\(919\) | −22.0000 | + | 38.1051i | −0.725713 | + | 1.25697i | 0.232967 | + | 0.972485i | \(0.425157\pi\) |
−0.958680 | + | 0.284487i | \(0.908177\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.00000 | − | 6.92820i | −0.131804 | − | 0.228292i | ||||
\(922\) | −24.2487 | − | 14.0000i | −0.798589 | − | 0.461065i | ||||
\(923\) | − | 98.0000i | − | 3.22571i | ||||||
\(924\) | 2.00000 | + | 1.73205i | 0.0657952 | + | 0.0569803i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −16.5000 | + | 28.5788i | −0.542224 | + | 0.939159i | ||||
\(927\) | −13.8564 | + | 8.00000i | −0.455104 | + | 0.262754i | ||||
\(928\) | −6.92820 | + | 4.00000i | −0.227429 | + | 0.131306i | ||||
\(929\) | 15.5000 | − | 26.8468i | 0.508539 | − | 0.880815i | −0.491413 | − | 0.870927i | \(-0.663519\pi\) |
0.999951 | − | 0.00988764i | \(-0.00314738\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.50000 | − | 2.59808i | −0.213029 | − | 0.0851485i | ||||
\(932\) | − | 26.0000i | − | 0.851658i | ||||||
\(933\) | −13.8564 | − | 8.00000i | −0.453638 | − | 0.261908i | ||||
\(934\) | 6.00000 | + | 10.3923i | 0.196326 | + | 0.340047i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −3.50000 | + | 6.06218i | −0.114401 | + | 0.198148i | ||||
\(937\) | − | 16.0000i | − | 0.522697i | −0.965244 | − | 0.261349i | \(-0.915833\pi\) | ||
0.965244 | − | 0.261349i | \(-0.0841672\pi\) | |||||||
\(938\) | −20.7846 | + | 24.0000i | −0.678642 | + | 0.783628i | ||||
\(939\) | 24.0000 | 0.783210 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 15.0000 | + | 25.9808i | 0.488986 | + | 0.846949i | 0.999920 | − | 0.0126715i | \(-0.00403357\pi\) |
−0.510934 | + | 0.859620i | \(0.670700\pi\) | |||||||
\(942\) | −12.9904 | + | 7.50000i | −0.423249 | + | 0.244363i | ||||
\(943\) | −7.79423 | − | 4.50000i | −0.253815 | − | 0.146540i | ||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.00000 | 0.130051 | ||||||||
\(947\) | 39.8372 | + | 23.0000i | 1.29453 | + | 0.747400i | 0.979454 | − | 0.201666i | \(-0.0646354\pi\) |
0.315080 | + | 0.949065i | \(0.397969\pi\) | |||||||
\(948\) | 3.46410 | − | 2.00000i | 0.112509 | − | 0.0649570i | ||||
\(949\) | −49.0000 | − | 84.8705i | −1.59061 | − | 2.75501i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 10.0000 | 0.324272 | ||||||||
\(952\) | 10.3923 | + | 2.00000i | 0.336817 | + | 0.0648204i | ||||
\(953\) | 44.0000i | 1.42530i | 0.701520 | + | 0.712650i | \(0.252505\pi\) | ||||
−0.701520 | + | 0.712650i | \(0.747495\pi\) | |||||||
\(954\) | −0.500000 | + | 0.866025i | −0.0161881 | + | 0.0280386i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 3.00000 | + | 5.19615i | 0.0970269 | + | 0.168056i | ||||
\(957\) | 6.92820 | + | 4.00000i | 0.223957 | + | 0.129302i | ||||
\(958\) | 26.0000i | 0.840022i | ||||||||
\(959\) | 1.00000 | − | 5.19615i | 0.0322917 | − | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.50000 | + | 4.33013i | −0.0806452 | + | 0.139682i | ||||
\(962\) | 18.1865 | − | 10.5000i | 0.586357 | − | 0.338534i | ||||
\(963\) | −15.5885 | + | 9.00000i | −0.502331 | + | 0.290021i | ||||
\(964\) | 3.50000 | − | 6.06218i | 0.112727 | − | 0.195250i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −2.50000 | + | 0.866025i | −0.0804362 | + | 0.0278639i | ||||
\(967\) | 20.0000i | 0.643157i | 0.946883 | + | 0.321578i | \(0.104213\pi\) | ||||
−0.946883 | + | 0.321578i | \(0.895787\pi\) | |||||||
\(968\) | 8.66025 | + | 5.00000i | 0.278351 | + | 0.160706i | ||||
\(969\) | −2.00000 | − | 3.46410i | −0.0642493 | − | 0.111283i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.5000 | + | 37.2391i | −0.689968 | + | 1.19506i | 0.281880 | + | 0.959450i | \(0.409042\pi\) |
−0.971848 | + | 0.235610i | \(0.924291\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 6.92820 | − | 8.00000i | 0.222108 | − | 0.256468i | ||||
\(974\) | 8.00000 | 0.256337 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | + | 3.46410i | 0.0640184 | + | 0.110883i | ||||
\(977\) | −15.5885 | + | 9.00000i | −0.498719 | + | 0.287936i | −0.728184 | − | 0.685381i | \(-0.759636\pi\) |
0.229465 | + | 0.973317i | \(0.426302\pi\) | |||||||
\(978\) | −6.92820 | − | 4.00000i | −0.221540 | − | 0.127906i | ||||
\(979\) | −2.00000 | −0.0639203 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −10.0000 | −0.319275 | ||||||||
\(982\) | −10.3923 | − | 6.00000i | −0.331632 | − | 0.191468i | ||||
\(983\) | −28.5788 | + | 16.5000i | −0.911523 | + | 0.526268i | −0.880921 | − | 0.473263i | \(-0.843076\pi\) |
−0.0306024 | + | 0.999532i | \(0.509743\pi\) | |||||||
\(984\) | 4.50000 | + | 7.79423i | 0.143455 | + | 0.248471i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 32.0000 | 1.01909 | ||||||||
\(987\) | −5.19615 | + | 6.00000i | −0.165395 | + | 0.190982i | ||||
\(988\) | 7.00000i | 0.222700i | ||||||||
\(989\) | −2.00000 | + | 3.46410i | −0.0635963 | + | 0.110152i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.00000 | − | 8.66025i | −0.158830 | − | 0.275102i | 0.775617 | − | 0.631204i | \(-0.217439\pi\) |
−0.934447 | + | 0.356102i | \(0.884106\pi\) | |||||||
\(992\) | 5.19615 | + | 3.00000i | 0.164978 | + | 0.0952501i | ||||
\(993\) | − | 9.00000i | − | 0.285606i | ||||||
\(994\) | −35.0000 | + | 12.1244i | −1.11013 | + | 0.384561i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −6.00000 | + | 10.3923i | −0.190117 | + | 0.329293i | ||||
\(997\) | −8.66025 | + | 5.00000i | −0.274273 | + | 0.158352i | −0.630828 | − | 0.775923i | \(-0.717285\pi\) |
0.356555 | + | 0.934274i | \(0.383951\pi\) | |||||||
\(998\) | 20.7846 | − | 12.0000i | 0.657925 | − | 0.379853i | ||||
\(999\) | −1.50000 | + | 2.59808i | −0.0474579 | + | 0.0821995i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1050.2.o.j.499.2 | 4 | ||
5.2 | odd | 4 | 210.2.i.a.121.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1050.2.i.s.751.1 | 2 | |||
5.4 | even | 2 | inner | 1050.2.o.j.499.1 | 4 | ||
7.4 | even | 3 | inner | 1050.2.o.j.949.1 | 4 | ||
15.2 | even | 4 | 630.2.k.h.541.1 | 2 | |||
20.7 | even | 4 | 1680.2.bg.k.961.1 | 2 | |||
35.2 | odd | 12 | 1470.2.a.r.1.1 | 1 | |||
35.4 | even | 6 | inner | 1050.2.o.j.949.2 | 4 | ||
35.12 | even | 12 | 1470.2.a.k.1.1 | 1 | |||
35.17 | even | 12 | 1470.2.i.i.361.1 | 2 | |||
35.18 | odd | 12 | 1050.2.i.s.151.1 | 2 | |||
35.23 | odd | 12 | 7350.2.a.j.1.1 | 1 | |||
35.27 | even | 4 | 1470.2.i.i.961.1 | 2 | |||
35.32 | odd | 12 | 210.2.i.a.151.1 | yes | 2 | ||
35.33 | even | 12 | 7350.2.a.ba.1.1 | 1 | |||
105.2 | even | 12 | 4410.2.a.g.1.1 | 1 | |||
105.32 | even | 12 | 630.2.k.h.361.1 | 2 | |||
105.47 | odd | 12 | 4410.2.a.q.1.1 | 1 | |||
140.67 | even | 12 | 1680.2.bg.k.1201.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.i.a.121.1 | ✓ | 2 | 5.2 | odd | 4 | ||
210.2.i.a.151.1 | yes | 2 | 35.32 | odd | 12 | ||
630.2.k.h.361.1 | 2 | 105.32 | even | 12 | |||
630.2.k.h.541.1 | 2 | 15.2 | even | 4 | |||
1050.2.i.s.151.1 | 2 | 35.18 | odd | 12 | |||
1050.2.i.s.751.1 | 2 | 5.3 | odd | 4 | |||
1050.2.o.j.499.1 | 4 | 5.4 | even | 2 | inner | ||
1050.2.o.j.499.2 | 4 | 1.1 | even | 1 | trivial | ||
1050.2.o.j.949.1 | 4 | 7.4 | even | 3 | inner | ||
1050.2.o.j.949.2 | 4 | 35.4 | even | 6 | inner | ||
1470.2.a.k.1.1 | 1 | 35.12 | even | 12 | |||
1470.2.a.r.1.1 | 1 | 35.2 | odd | 12 | |||
1470.2.i.i.361.1 | 2 | 35.17 | even | 12 | |||
1470.2.i.i.961.1 | 2 | 35.27 | even | 4 | |||
1680.2.bg.k.961.1 | 2 | 20.7 | even | 4 | |||
1680.2.bg.k.1201.1 | 2 | 140.67 | even | 12 | |||
4410.2.a.g.1.1 | 1 | 105.2 | even | 12 | |||
4410.2.a.q.1.1 | 1 | 105.47 | odd | 12 | |||
7350.2.a.j.1.1 | 1 | 35.23 | odd | 12 | |||
7350.2.a.ba.1.1 | 1 | 35.33 | even | 12 |