Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,2,Mod(165,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.x (of order \(12\), degree \(4\), 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: | \(6.26027151847\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 112) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 165.1 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.165 |
Dual form | 784.2.x.g.765.1 |
$q$-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 \(\left(\mathbb{Z}/784\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(687\) | \(689\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.36603 | + | 0.366025i | 0.965926 | + | 0.258819i | ||||
\(3\) | −0.732051 | − | 2.73205i | −0.422650 | − | 1.57735i | −0.769002 | − | 0.639246i | \(-0.779247\pi\) |
0.346353 | − | 0.938104i | \(-0.387420\pi\) | |||||||
\(4\) | 1.73205 | + | 1.00000i | 0.866025 | + | 0.500000i | ||||
\(5\) | −0.732051 | + | 2.73205i | −0.327383 | + | 1.22181i | 0.584511 | + | 0.811386i | \(0.301286\pi\) |
−0.911894 | + | 0.410425i | \(0.865380\pi\) | |||||||
\(6\) | − | 4.00000i | − | 1.63299i | ||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 2.00000 | + | 2.00000i | 0.707107 | + | 0.707107i | ||||
\(9\) | −4.33013 | + | 2.50000i | −1.44338 | + | 0.833333i | ||||
\(10\) | −2.00000 | + | 3.46410i | −0.632456 | + | 1.09545i | ||||
\(11\) | 4.09808 | − | 1.09808i | 1.23562 | − | 0.331082i | 0.418852 | − | 0.908054i | \(-0.362432\pi\) |
0.816764 | + | 0.576972i | \(0.195766\pi\) | |||||||
\(12\) | 1.46410 | − | 5.46410i | 0.422650 | − | 1.57735i | ||||
\(13\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 8.00000 | 2.06559 | ||||||||
\(16\) | 2.00000 | + | 3.46410i | 0.500000 | + | 0.866025i | ||||
\(17\) | 3.00000 | − | 5.19615i | 0.727607 | − | 1.26025i | −0.230285 | − | 0.973123i | \(-0.573966\pi\) |
0.957892 | − | 0.287129i | \(-0.0927008\pi\) | |||||||
\(18\) | −6.83013 | + | 1.83013i | −1.60988 | + | 0.431365i | ||||
\(19\) | 5.46410 | + | 1.46410i | 1.25355 | + | 0.335888i | 0.823707 | − | 0.567015i | \(-0.191902\pi\) |
0.429844 | + | 0.902903i | \(0.358569\pi\) | |||||||
\(20\) | −4.00000 | + | 4.00000i | −0.894427 | + | 0.894427i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6.00000 | 1.27920 | ||||||||
\(23\) | 1.73205 | − | 1.00000i | 0.361158 | − | 0.208514i | −0.308431 | − | 0.951247i | \(-0.599804\pi\) |
0.669588 | + | 0.742732i | \(0.266471\pi\) | |||||||
\(24\) | 4.00000 | − | 6.92820i | 0.816497 | − | 1.41421i | ||||
\(25\) | −2.59808 | − | 1.50000i | −0.519615 | − | 0.300000i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.00000 | + | 4.00000i | 0.769800 | + | 0.769800i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.00000 | + | 1.00000i | −0.185695 | + | 0.185695i | −0.793832 | − | 0.608137i | \(-0.791917\pi\) |
0.608137 | + | 0.793832i | \(0.291917\pi\) | |||||||
\(30\) | 10.9282 | + | 2.92820i | 1.99521 | + | 0.534614i | ||||
\(31\) | −2.00000 | + | 3.46410i | −0.359211 | + | 0.622171i | −0.987829 | − | 0.155543i | \(-0.950287\pi\) |
0.628619 | + | 0.777714i | \(0.283621\pi\) | |||||||
\(32\) | 1.46410 | + | 5.46410i | 0.258819 | + | 0.965926i | ||||
\(33\) | −6.00000 | − | 10.3923i | −1.04447 | − | 1.80907i | ||||
\(34\) | 6.00000 | − | 6.00000i | 1.02899 | − | 1.02899i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.0000 | −1.66667 | ||||||||
\(37\) | 1.09808 | − | 4.09808i | 0.180523 | − | 0.673720i | −0.815022 | − | 0.579430i | \(-0.803275\pi\) |
0.995545 | − | 0.0942898i | \(-0.0300580\pi\) | |||||||
\(38\) | 6.92820 | + | 4.00000i | 1.12390 | + | 0.648886i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.92820 | + | 4.00000i | −1.09545 | + | 0.632456i | ||||
\(41\) | 2.00000i | 0.312348i | 0.987730 | + | 0.156174i | \(0.0499160\pi\) | ||||
−0.987730 | + | 0.156174i | \(0.950084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | − | 5.00000i | −0.762493 | − | 0.762493i | 0.214280 | − | 0.976772i | \(-0.431260\pi\) |
−0.976772 | + | 0.214280i | \(0.931260\pi\) | |||||||
\(44\) | 8.19615 | + | 2.19615i | 1.23562 | + | 0.331082i | ||||
\(45\) | −3.66025 | − | 13.6603i | −0.545638 | − | 2.03635i | ||||
\(46\) | 2.73205 | − | 0.732051i | 0.402819 | − | 0.107935i | ||||
\(47\) | 4.00000 | + | 6.92820i | 0.583460 | + | 1.01058i | 0.995066 | + | 0.0992202i | \(0.0316348\pi\) |
−0.411606 | + | 0.911362i | \(0.635032\pi\) | |||||||
\(48\) | 8.00000 | − | 8.00000i | 1.15470 | − | 1.15470i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −3.00000 | − | 3.00000i | −0.424264 | − | 0.424264i | ||||
\(51\) | −16.3923 | − | 4.39230i | −2.29538 | − | 0.615046i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.56218 | + | 2.56218i | −1.31347 | + | 0.351942i | −0.846526 | − | 0.532347i | \(-0.821310\pi\) |
−0.466940 | + | 0.884289i | \(0.654644\pi\) | |||||||
\(54\) | 4.00000 | + | 6.92820i | 0.544331 | + | 0.942809i | ||||
\(55\) | 12.0000i | 1.61808i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 16.0000i | − | 2.11925i | ||||||
\(58\) | −1.73205 | + | 1.00000i | −0.227429 | + | 0.131306i | ||||
\(59\) | −2.73205 | + | 0.732051i | −0.355683 | + | 0.0953049i | −0.432236 | − | 0.901761i | \(-0.642275\pi\) |
0.0765531 | + | 0.997066i | \(0.475609\pi\) | |||||||
\(60\) | 13.8564 | + | 8.00000i | 1.78885 | + | 1.03280i | ||||
\(61\) | −8.19615 | − | 2.19615i | −1.04941 | − | 0.281189i | −0.307402 | − | 0.951580i | \(-0.599460\pi\) |
−0.742008 | + | 0.670391i | \(0.766126\pi\) | |||||||
\(62\) | −4.00000 | + | 4.00000i | −0.508001 | + | 0.508001i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.00000i | 1.00000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −4.39230 | − | 16.3923i | −0.540655 | − | 2.01775i | ||||
\(67\) | −1.83013 | − | 6.83013i | −0.223586 | − | 0.834433i | −0.982966 | − | 0.183786i | \(-0.941165\pi\) |
0.759381 | − | 0.650647i | \(-0.225502\pi\) | |||||||
\(68\) | 10.3923 | − | 6.00000i | 1.26025 | − | 0.727607i | ||||
\(69\) | −4.00000 | − | 4.00000i | −0.481543 | − | 0.481543i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 8.00000i | − | 0.949425i | −0.880141 | − | 0.474713i | \(-0.842552\pi\) | ||
0.880141 | − | 0.474713i | \(-0.157448\pi\) | |||||||
\(72\) | −13.6603 | − | 3.66025i | −1.60988 | − | 0.431365i | ||||
\(73\) | 8.66025 | + | 5.00000i | 1.01361 | + | 0.585206i | 0.912245 | − | 0.409644i | \(-0.134347\pi\) |
0.101361 | + | 0.994850i | \(0.467680\pi\) | |||||||
\(74\) | 3.00000 | − | 5.19615i | 0.348743 | − | 0.604040i | ||||
\(75\) | −2.19615 | + | 8.19615i | −0.253590 | + | 0.946410i | ||||
\(76\) | 8.00000 | + | 8.00000i | 0.917663 | + | 0.917663i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.00000 | + | 12.1244i | 0.787562 | + | 1.36410i | 0.927457 | + | 0.373930i | \(0.121990\pi\) |
−0.139895 | + | 0.990166i | \(0.544677\pi\) | |||||||
\(80\) | −10.9282 | + | 2.92820i | −1.22181 | + | 0.327383i | ||||
\(81\) | 0.500000 | − | 0.866025i | 0.0555556 | − | 0.0962250i | ||||
\(82\) | −0.732051 | + | 2.73205i | −0.0808415 | + | 0.301705i | ||||
\(83\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0000 | + | 12.0000i | 1.30158 | + | 1.30158i | ||||
\(86\) | −5.00000 | − | 8.66025i | −0.539164 | − | 0.933859i | ||||
\(87\) | 3.46410 | + | 2.00000i | 0.371391 | + | 0.214423i | ||||
\(88\) | 10.3923 | + | 6.00000i | 1.10782 | + | 0.639602i | ||||
\(89\) | 5.19615 | − | 3.00000i | 0.550791 | − | 0.317999i | −0.198650 | − | 0.980071i | \(-0.563656\pi\) |
0.749441 | + | 0.662071i | \(0.230322\pi\) | |||||||
\(90\) | − | 20.0000i | − | 2.10819i | ||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 10.9282 | + | 2.92820i | 1.13320 | + | 0.303641i | ||||
\(94\) | 2.92820 | + | 10.9282i | 0.302021 | + | 1.12716i | ||||
\(95\) | −8.00000 | + | 13.8564i | −0.820783 | + | 1.42164i | ||||
\(96\) | 13.8564 | − | 8.00000i | 1.41421 | − | 0.816497i | ||||
\(97\) | −6.00000 | −0.609208 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −15.0000 | + | 15.0000i | −1.50756 | + | 1.50756i | ||||
\(100\) | −3.00000 | − | 5.19615i | −0.300000 | − | 0.519615i | ||||
\(101\) | −2.73205 | + | 0.732051i | −0.271849 | + | 0.0728418i | −0.392168 | − | 0.919893i | \(-0.628275\pi\) |
0.120319 | + | 0.992735i | \(0.461608\pi\) | |||||||
\(102\) | −20.7846 | − | 12.0000i | −2.05798 | − | 1.18818i | ||||
\(103\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14.0000 | −1.35980 | ||||||||
\(107\) | 1.83013 | − | 6.83013i | 0.176925 | − | 0.660293i | −0.819291 | − | 0.573378i | \(-0.805633\pi\) |
0.996216 | − | 0.0869149i | \(-0.0277008\pi\) | |||||||
\(108\) | 2.92820 | + | 10.9282i | 0.281766 | + | 1.05157i | ||||
\(109\) | −1.09808 | − | 4.09808i | −0.105177 | − | 0.392525i | 0.893189 | − | 0.449682i | \(-0.148463\pi\) |
−0.998365 | + | 0.0571579i | \(0.981796\pi\) | |||||||
\(110\) | −4.39230 | + | 16.3923i | −0.418790 | + | 1.56294i | ||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.0000 | −1.12887 | −0.564433 | − | 0.825479i | \(-0.690905\pi\) | ||||
−0.564433 | + | 0.825479i | \(0.690905\pi\) | |||||||
\(114\) | 5.85641 | − | 21.8564i | 0.548503 | − | 2.04704i | ||||
\(115\) | 1.46410 | + | 5.46410i | 0.136528 | + | 0.509530i | ||||
\(116\) | −2.73205 | + | 0.732051i | −0.253665 | + | 0.0679692i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.00000 | −0.368230 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 16.0000 | + | 16.0000i | 1.46059 | + | 1.46059i | ||||
\(121\) | 6.06218 | − | 3.50000i | 0.551107 | − | 0.318182i | ||||
\(122\) | −10.3923 | − | 6.00000i | −0.940875 | − | 0.543214i | ||||
\(123\) | 5.46410 | − | 1.46410i | 0.492681 | − | 0.132014i | ||||
\(124\) | −6.92820 | + | 4.00000i | −0.622171 | + | 0.359211i | ||||
\(125\) | −4.00000 | + | 4.00000i | −0.357771 | + | 0.357771i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.00000 | 0.709885 | 0.354943 | − | 0.934888i | \(-0.384500\pi\) | ||||
0.354943 | + | 0.934888i | \(0.384500\pi\) | |||||||
\(128\) | −2.92820 | + | 10.9282i | −0.258819 | + | 0.965926i | ||||
\(129\) | −10.0000 | + | 17.3205i | −0.880451 | + | 1.52499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −16.3923 | − | 4.39230i | −1.43220 | − | 0.383757i | −0.542406 | − | 0.840116i | \(-0.682487\pi\) |
−0.889796 | + | 0.456359i | \(0.849153\pi\) | |||||||
\(132\) | − | 24.0000i | − | 2.08893i | ||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − | 10.0000i | − | 0.863868i | ||||||
\(135\) | −13.8564 | + | 8.00000i | −1.19257 | + | 0.688530i | ||||
\(136\) | 16.3923 | − | 4.39230i | 1.40563 | − | 0.376637i | ||||
\(137\) | −10.3923 | − | 6.00000i | −0.887875 | − | 0.512615i | −0.0146279 | − | 0.999893i | \(-0.504656\pi\) |
−0.873247 | + | 0.487278i | \(0.837990\pi\) | |||||||
\(138\) | −4.00000 | − | 6.92820i | −0.340503 | − | 0.589768i | ||||
\(139\) | −12.0000 | − | 12.0000i | −1.01783 | − | 1.01783i | −0.999838 | − | 0.0179885i | \(-0.994274\pi\) |
−0.0179885 | − | 0.999838i | \(-0.505726\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.0000 | − | 16.0000i | 1.34744 | − | 1.34744i | ||||
\(142\) | 2.92820 | − | 10.9282i | 0.245729 | − | 0.917074i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −17.3205 | − | 10.0000i | −1.44338 | − | 0.833333i | ||||
\(145\) | −2.00000 | − | 3.46410i | −0.166091 | − | 0.287678i | ||||
\(146\) | 10.0000 | + | 10.0000i | 0.827606 | + | 0.827606i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 6.00000 | − | 6.00000i | 0.493197 | − | 0.493197i | ||||
\(149\) | −4.75833 | + | 17.7583i | −0.389818 | + | 1.45482i | 0.440613 | + | 0.897697i | \(0.354761\pi\) |
−0.830431 | + | 0.557122i | \(0.811906\pi\) | |||||||
\(150\) | −6.00000 | + | 10.3923i | −0.489898 | + | 0.848528i | ||||
\(151\) | 5.19615 | + | 3.00000i | 0.422857 | + | 0.244137i | 0.696299 | − | 0.717752i | \(-0.254829\pi\) |
−0.273442 | + | 0.961888i | \(0.588162\pi\) | |||||||
\(152\) | 8.00000 | + | 13.8564i | 0.648886 | + | 1.12390i | ||||
\(153\) | 30.0000i | 2.42536i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.00000 | − | 8.00000i | −0.642575 | − | 0.642575i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0 | 0 | 0.965926 | − | 0.258819i | \(-0.0833333\pi\) | ||||
−0.965926 | + | 0.258819i | \(0.916667\pi\) | |||||||
\(158\) | 5.12436 | + | 19.1244i | 0.407672 | + | 1.52145i | ||||
\(159\) | 14.0000 | + | 24.2487i | 1.11027 | + | 1.92305i | ||||
\(160\) | −16.0000 | −1.26491 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000 | − | 1.00000i | 0.0785674 | − | 0.0785674i | ||||
\(163\) | 6.83013 | + | 1.83013i | 0.534977 | + | 0.143347i | 0.516185 | − | 0.856477i | \(-0.327352\pi\) |
0.0187913 | + | 0.999823i | \(0.494018\pi\) | |||||||
\(164\) | −2.00000 | + | 3.46410i | −0.156174 | + | 0.270501i | ||||
\(165\) | 32.7846 | − | 8.78461i | 2.55228 | − | 0.683881i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 13.0000i | 1.00000i | ||||||||
\(170\) | 12.0000 | + | 20.7846i | 0.920358 | + | 1.59411i | ||||
\(171\) | −27.3205 | + | 7.32051i | −2.08925 | + | 0.559813i | ||||
\(172\) | −3.66025 | − | 13.6603i | −0.279092 | − | 1.04158i | ||||
\(173\) | −21.8564 | − | 5.85641i | −1.66171 | − | 0.445254i | −0.698854 | − | 0.715264i | \(-0.746306\pi\) |
−0.962858 | + | 0.270010i | \(0.912973\pi\) | |||||||
\(174\) | 4.00000 | + | 4.00000i | 0.303239 | + | 0.303239i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0000 | + | 12.0000i | 0.904534 | + | 0.904534i | ||||
\(177\) | 4.00000 | + | 6.92820i | 0.300658 | + | 0.520756i | ||||
\(178\) | 8.19615 | − | 2.19615i | 0.614328 | − | 0.164609i | ||||
\(179\) | 1.83013 | + | 6.83013i | 0.136790 | + | 0.510508i | 0.999984 | + | 0.00563529i | \(0.00179378\pi\) |
−0.863194 | + | 0.504872i | \(0.831540\pi\) | |||||||
\(180\) | 7.32051 | − | 27.3205i | 0.545638 | − | 2.03635i | ||||
\(181\) | 4.00000 | + | 4.00000i | 0.297318 | + | 0.297318i | 0.839962 | − | 0.542645i | \(-0.182577\pi\) |
−0.542645 | + | 0.839962i | \(0.682577\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 24.0000i | 1.77413i | ||||||||
\(184\) | 5.46410 | + | 1.46410i | 0.402819 | + | 0.107935i | ||||
\(185\) | 10.3923 | + | 6.00000i | 0.764057 | + | 0.441129i | ||||
\(186\) | 13.8564 | + | 8.00000i | 1.01600 | + | 0.586588i | ||||
\(187\) | 6.58846 | − | 24.5885i | 0.481796 | − | 1.79809i | ||||
\(188\) | 16.0000i | 1.16692i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −16.0000 | + | 16.0000i | −1.16076 | + | 1.16076i | ||||
\(191\) | −11.0000 | − | 19.0526i | −0.795932 | − | 1.37859i | −0.922246 | − | 0.386604i | \(-0.873648\pi\) |
0.126314 | − | 0.991990i | \(-0.459685\pi\) | |||||||
\(192\) | 21.8564 | − | 5.85641i | 1.57735 | − | 0.422650i | ||||
\(193\) | 12.0000 | − | 20.7846i | 0.863779 | − | 1.49611i | −0.00447566 | − | 0.999990i | \(-0.501425\pi\) |
0.868255 | − | 0.496119i | \(-0.165242\pi\) | |||||||
\(194\) | −8.19615 | − | 2.19615i | −0.588449 | − | 0.157675i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −11.0000 | − | 11.0000i | −0.783718 | − | 0.783718i | 0.196738 | − | 0.980456i | \(-0.436965\pi\) |
−0.980456 | + | 0.196738i | \(0.936965\pi\) | |||||||
\(198\) | −25.9808 | + | 15.0000i | −1.84637 | + | 1.06600i | ||||
\(199\) | 17.3205 | + | 10.0000i | 1.22782 | + | 0.708881i | 0.966573 | − | 0.256391i | \(-0.0825336\pi\) |
0.261245 | + | 0.965272i | \(0.415867\pi\) | |||||||
\(200\) | −2.19615 | − | 8.19615i | −0.155291 | − | 0.579555i | ||||
\(201\) | −17.3205 | + | 10.0000i | −1.22169 | + | 0.705346i | ||||
\(202\) | −4.00000 | −0.281439 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −24.0000 | − | 24.0000i | −1.68034 | − | 1.68034i | ||||
\(205\) | −5.46410 | − | 1.46410i | −0.381629 | − | 0.102257i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.00000 | + | 8.66025i | −0.347524 | + | 0.601929i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 24.0000 | 1.66011 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.00000 | + | 9.00000i | −0.619586 | + | 0.619586i | −0.945425 | − | 0.325840i | \(-0.894353\pi\) |
0.325840 | + | 0.945425i | \(0.394353\pi\) | |||||||
\(212\) | −19.1244 | − | 5.12436i | −1.31347 | − | 0.351942i | ||||
\(213\) | −21.8564 | + | 5.85641i | −1.49758 | + | 0.401274i | ||||
\(214\) | 5.00000 | − | 8.66025i | 0.341793 | − | 0.592003i | ||||
\(215\) | 17.3205 | − | 10.0000i | 1.18125 | − | 0.681994i | ||||
\(216\) | 16.0000i | 1.08866i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | − | 6.00000i | − | 0.406371i | ||||||
\(219\) | 7.32051 | − | 27.3205i | 0.494674 | − | 1.84615i | ||||
\(220\) | −12.0000 | + | 20.7846i | −0.809040 | + | 1.40130i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −16.3923 | − | 4.39230i | −1.10018 | − | 0.294792i | ||||
\(223\) | 4.00000 | 0.267860 | 0.133930 | − | 0.990991i | \(-0.457240\pi\) | ||||
0.133930 | + | 0.990991i | \(0.457240\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 15.0000 | 1.00000 | ||||||||
\(226\) | −16.3923 | − | 4.39230i | −1.09040 | − | 0.292172i | ||||
\(227\) | 1.46410 | + | 5.46410i | 0.0971758 | + | 0.362665i | 0.997340 | − | 0.0728849i | \(-0.0232206\pi\) |
−0.900165 | + | 0.435550i | \(0.856554\pi\) | |||||||
\(228\) | 16.0000 | − | 27.7128i | 1.05963 | − | 1.83533i | ||||
\(229\) | 4.39230 | − | 16.3923i | 0.290252 | − | 1.08323i | −0.654664 | − | 0.755920i | \(-0.727190\pi\) |
0.944916 | − | 0.327314i | \(-0.106143\pi\) | |||||||
\(230\) | 8.00000i | 0.527504i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −4.00000 | −0.262613 | ||||||||
\(233\) | −6.92820 | + | 4.00000i | −0.453882 | + | 0.262049i | −0.709468 | − | 0.704737i | \(-0.751065\pi\) |
0.255586 | + | 0.966786i | \(0.417731\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −21.8564 | + | 5.85641i | −1.42575 | + | 0.382030i | ||||
\(236\) | −5.46410 | − | 1.46410i | −0.355683 | − | 0.0953049i | ||||
\(237\) | 28.0000 | − | 28.0000i | 1.81880 | − | 1.81880i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −8.00000 | −0.517477 | −0.258738 | − | 0.965947i | \(-0.583307\pi\) | ||||
−0.258738 | + | 0.965947i | \(0.583307\pi\) | |||||||
\(240\) | 16.0000 | + | 27.7128i | 1.03280 | + | 1.78885i | ||||
\(241\) | 11.0000 | − | 19.0526i | 0.708572 | − | 1.22728i | −0.256814 | − | 0.966461i | \(-0.582673\pi\) |
0.965387 | − | 0.260822i | \(-0.0839937\pi\) | |||||||
\(242\) | 9.56218 | − | 2.56218i | 0.614680 | − | 0.164703i | ||||
\(243\) | 13.6603 | + | 3.66025i | 0.876306 | + | 0.234805i | ||||
\(244\) | −12.0000 | − | 12.0000i | −0.768221 | − | 0.768221i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 8.00000 | 0.510061 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.9282 | + | 2.92820i | −0.693942 | + | 0.185941i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.92820 | + | 4.00000i | −0.438178 | + | 0.252982i | ||||
\(251\) | 4.00000 | + | 4.00000i | 0.252478 | + | 0.252478i | 0.821986 | − | 0.569508i | \(-0.192866\pi\) |
−0.569508 | + | 0.821986i | \(0.692866\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.00000 | − | 6.00000i | 0.377217 | − | 0.377217i | ||||
\(254\) | 10.9282 | + | 2.92820i | 0.685696 | + | 0.183732i | ||||
\(255\) | 24.0000 | − | 41.5692i | 1.50294 | − | 2.60317i | ||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | 5.00000 | + | 8.66025i | 0.311891 | + | 0.540212i | 0.978772 | − | 0.204953i | \(-0.0657041\pi\) |
−0.666880 | + | 0.745165i | \(0.732371\pi\) | |||||||
\(258\) | −20.0000 | + | 20.0000i | −1.24515 | + | 1.24515i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.83013 | − | 6.83013i | 0.113282 | − | 0.422774i | ||||
\(262\) | −20.7846 | − | 12.0000i | −1.28408 | − | 0.741362i | ||||
\(263\) | −20.7846 | − | 12.0000i | −1.28163 | − | 0.739952i | −0.304487 | − | 0.952517i | \(-0.598485\pi\) |
−0.977147 | + | 0.212565i | \(0.931818\pi\) | |||||||
\(264\) | 8.78461 | − | 32.7846i | 0.540655 | − | 2.01775i | ||||
\(265\) | − | 28.0000i | − | 1.72003i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −12.0000 | − | 12.0000i | −0.734388 | − | 0.734388i | ||||
\(268\) | 3.66025 | − | 13.6603i | 0.223586 | − | 0.834433i | ||||
\(269\) | −5.85641 | − | 21.8564i | −0.357071 | − | 1.33261i | −0.877858 | − | 0.478922i | \(-0.841028\pi\) |
0.520786 | − | 0.853687i | \(-0.325639\pi\) | |||||||
\(270\) | −21.8564 | + | 5.85641i | −1.33014 | + | 0.356410i | ||||
\(271\) | −8.00000 | − | 13.8564i | −0.485965 | − | 0.841717i | 0.513905 | − | 0.857847i | \(-0.328199\pi\) |
−0.999870 | + | 0.0161307i | \(0.994865\pi\) | |||||||
\(272\) | 24.0000 | 1.45521 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.0000 | − | 12.0000i | −0.724947 | − | 0.724947i | ||||
\(275\) | −12.2942 | − | 3.29423i | −0.741370 | − | 0.198649i | ||||
\(276\) | −2.92820 | − | 10.9282i | −0.176257 | − | 0.657801i | ||||
\(277\) | −1.36603 | + | 0.366025i | −0.0820765 | + | 0.0219923i | −0.299624 | − | 0.954057i | \(-0.596861\pi\) |
0.217547 | + | 0.976050i | \(0.430194\pi\) | |||||||
\(278\) | −12.0000 | − | 20.7846i | −0.719712 | − | 1.24658i | ||||
\(279\) | − | 20.0000i | − | 1.19737i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.0000i | 1.43172i | 0.698244 | + | 0.715860i | \(0.253965\pi\) | ||||
−0.698244 | + | 0.715860i | \(0.746035\pi\) | |||||||
\(282\) | 27.7128 | − | 16.0000i | 1.65027 | − | 0.952786i | ||||
\(283\) | 8.19615 | − | 2.19615i | 0.487211 | − | 0.130548i | −0.00684749 | − | 0.999977i | \(-0.502180\pi\) |
0.494058 | + | 0.869429i | \(0.335513\pi\) | |||||||
\(284\) | 8.00000 | − | 13.8564i | 0.474713 | − | 0.822226i | ||||
\(285\) | 43.7128 | + | 11.7128i | 2.58932 | + | 0.693807i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −20.0000 | − | 20.0000i | −1.17851 | − | 1.17851i | ||||
\(289\) | −9.50000 | − | 16.4545i | −0.558824 | − | 0.967911i | ||||
\(290\) | −1.46410 | − | 5.46410i | −0.0859750 | − | 0.320863i | ||||
\(291\) | 4.39230 | + | 16.3923i | 0.257481 | + | 0.960934i | ||||
\(292\) | 10.0000 | + | 17.3205i | 0.585206 | + | 1.01361i | ||||
\(293\) | −10.0000 | − | 10.0000i | −0.584206 | − | 0.584206i | 0.351850 | − | 0.936056i | \(-0.385553\pi\) |
−0.936056 | + | 0.351850i | \(0.885553\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 8.00000i | − | 0.465778i | ||||||
\(296\) | 10.3923 | − | 6.00000i | 0.604040 | − | 0.348743i | ||||
\(297\) | 20.7846 | + | 12.0000i | 1.20605 | + | 0.696311i | ||||
\(298\) | −13.0000 | + | 22.5167i | −0.753070 | + | 1.30436i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −12.0000 | + | 12.0000i | −0.692820 | + | 0.692820i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 6.00000 | + | 6.00000i | 0.345261 | + | 0.345261i | ||||
\(303\) | 4.00000 | + | 6.92820i | 0.229794 | + | 0.398015i | ||||
\(304\) | 5.85641 | + | 21.8564i | 0.335888 | + | 1.25355i | ||||
\(305\) | 12.0000 | − | 20.7846i | 0.687118 | − | 1.19012i | ||||
\(306\) | −10.9808 | + | 40.9808i | −0.627728 | + | 2.34271i | ||||
\(307\) | −8.00000 | + | 8.00000i | −0.456584 | + | 0.456584i | −0.897532 | − | 0.440948i | \(-0.854642\pi\) |
0.440948 | + | 0.897532i | \(0.354642\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −8.00000 | − | 13.8564i | −0.454369 | − | 0.786991i | ||||
\(311\) | 3.46410 | + | 2.00000i | 0.196431 | + | 0.113410i | 0.594990 | − | 0.803733i | \(-0.297156\pi\) |
−0.398559 | + | 0.917143i | \(0.630489\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.73205 | + | 1.00000i | −0.0979013 | + | 0.0565233i | −0.548151 | − | 0.836379i | \(-0.684668\pi\) |
0.450250 | + | 0.892903i | \(0.351335\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 28.0000i | 1.57512i | ||||||||
\(317\) | 20.4904 | + | 5.49038i | 1.15085 | + | 0.308371i | 0.783307 | − | 0.621634i | \(-0.213531\pi\) |
0.367547 | + | 0.930005i | \(0.380198\pi\) | |||||||
\(318\) | 10.2487 | + | 38.2487i | 0.574719 | + | 2.14488i | ||||
\(319\) | −3.00000 | + | 5.19615i | −0.167968 | + | 0.290929i | ||||
\(320\) | −21.8564 | − | 5.85641i | −1.22181 | − | 0.327383i | ||||
\(321\) | −20.0000 | −1.11629 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 24.0000 | − | 24.0000i | 1.33540 | − | 1.33540i | ||||
\(324\) | 1.73205 | − | 1.00000i | 0.0962250 | − | 0.0555556i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 8.66025 | + | 5.00000i | 0.479647 | + | 0.276924i | ||||
\(327\) | −10.3923 | + | 6.00000i | −0.574696 | + | 0.331801i | ||||
\(328\) | −4.00000 | + | 4.00000i | −0.220863 | + | 0.220863i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 48.0000 | 2.64231 | ||||||||
\(331\) | −5.49038 | + | 20.4904i | −0.301779 | + | 1.12625i | 0.633904 | + | 0.773411i | \(0.281451\pi\) |
−0.935683 | + | 0.352842i | \(0.885215\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 5.49038 | + | 20.4904i | 0.300871 | + | 1.12287i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 20.0000 | 1.09272 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.00000 | −0.435788 | −0.217894 | − | 0.975972i | \(-0.569919\pi\) | ||||
−0.217894 | + | 0.975972i | \(0.569919\pi\) | |||||||
\(338\) | −4.75833 | + | 17.7583i | −0.258819 | + | 0.965926i | ||||
\(339\) | 8.78461 | + | 32.7846i | 0.477115 | + | 1.78062i | ||||
\(340\) | 8.78461 | + | 32.7846i | 0.476412 | + | 1.77800i | ||||
\(341\) | −4.39230 | + | 16.3923i | −0.237857 | + | 0.887693i | ||||
\(342\) | −40.0000 | −2.16295 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 20.0000i | − | 1.07833i | ||||||
\(345\) | 13.8564 | − | 8.00000i | 0.746004 | − | 0.430706i | ||||
\(346\) | −27.7128 | − | 16.0000i | −1.48985 | − | 0.860165i | ||||
\(347\) | 17.7583 | − | 4.75833i | 0.953317 | − | 0.255441i | 0.251548 | − | 0.967845i | \(-0.419060\pi\) |
0.701769 | + | 0.712404i | \(0.252394\pi\) | |||||||
\(348\) | 4.00000 | + | 6.92820i | 0.214423 | + | 0.371391i | ||||
\(349\) | 16.0000 | − | 16.0000i | 0.856460 | − | 0.856460i | −0.134459 | − | 0.990919i | \(-0.542930\pi\) |
0.990919 | + | 0.134459i | \(0.0429296\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.0000 | + | 20.7846i | 0.639602 | + | 1.10782i | ||||
\(353\) | −9.00000 | + | 15.5885i | −0.479022 | + | 0.829690i | −0.999711 | − | 0.0240566i | \(-0.992342\pi\) |
0.520689 | + | 0.853746i | \(0.325675\pi\) | |||||||
\(354\) | 2.92820 | + | 10.9282i | 0.155632 | + | 0.580827i | ||||
\(355\) | 21.8564 | + | 5.85641i | 1.16002 | + | 0.310826i | ||||
\(356\) | 12.0000 | 0.635999 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.0000i | 0.528516i | ||||||||
\(359\) | 19.0526 | − | 11.0000i | 1.00556 | − | 0.580558i | 0.0956683 | − | 0.995413i | \(-0.469501\pi\) |
0.909887 | + | 0.414855i | \(0.136168\pi\) | |||||||
\(360\) | 20.0000 | − | 34.6410i | 1.05409 | − | 1.82574i | ||||
\(361\) | 11.2583 | + | 6.50000i | 0.592544 | + | 0.342105i | ||||
\(362\) | 4.00000 | + | 6.92820i | 0.210235 | + | 0.364138i | ||||
\(363\) | −14.0000 | − | 14.0000i | −0.734809 | − | 0.734809i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −20.0000 | + | 20.0000i | −1.04685 | + | 1.04685i | ||||
\(366\) | −8.78461 | + | 32.7846i | −0.459179 | + | 1.71368i | ||||
\(367\) | 8.00000 | − | 13.8564i | 0.417597 | − | 0.723299i | −0.578101 | − | 0.815966i | \(-0.696206\pi\) |
0.995697 | + | 0.0926670i | \(0.0295392\pi\) | |||||||
\(368\) | 6.92820 | + | 4.00000i | 0.361158 | + | 0.208514i | ||||
\(369\) | −5.00000 | − | 8.66025i | −0.260290 | − | 0.450835i | ||||
\(370\) | 12.0000 | + | 12.0000i | 0.623850 | + | 0.623850i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 16.0000 | + | 16.0000i | 0.829561 | + | 0.829561i | ||||
\(373\) | 1.83013 | − | 6.83013i | 0.0947604 | − | 0.353651i | −0.902223 | − | 0.431271i | \(-0.858065\pi\) |
0.996983 | + | 0.0776200i | \(0.0247321\pi\) | |||||||
\(374\) | 18.0000 | − | 31.1769i | 0.930758 | − | 1.61212i | ||||
\(375\) | 13.8564 | + | 8.00000i | 0.715542 | + | 0.413118i | ||||
\(376\) | −5.85641 | + | 21.8564i | −0.302021 | + | 1.12716i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 17.0000 | + | 17.0000i | 0.873231 | + | 0.873231i | 0.992823 | − | 0.119592i | \(-0.0381586\pi\) |
−0.119592 | + | 0.992823i | \(0.538159\pi\) | |||||||
\(380\) | −27.7128 | + | 16.0000i | −1.42164 | + | 0.820783i | ||||
\(381\) | −5.85641 | − | 21.8564i | −0.300033 | − | 1.11974i | ||||
\(382\) | −8.05256 | − | 30.0526i | −0.412005 | − | 1.53762i | ||||
\(383\) | 8.00000 | + | 13.8564i | 0.408781 | + | 0.708029i | 0.994753 | − | 0.102302i | \(-0.0326207\pi\) |
−0.585973 | + | 0.810331i | \(0.699287\pi\) | |||||||
\(384\) | 32.0000 | 1.63299 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 24.0000 | − | 24.0000i | 1.22157 | − | 1.22157i | ||||
\(387\) | 34.1506 | + | 9.15064i | 1.73597 | + | 0.465153i | ||||
\(388\) | −10.3923 | − | 6.00000i | −0.527589 | − | 0.304604i | ||||
\(389\) | −25.9545 | + | 6.95448i | −1.31594 | + | 0.352606i | −0.847457 | − | 0.530864i | \(-0.821868\pi\) |
−0.468487 | + | 0.883470i | \(0.655201\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 12.0000i | − | 0.606866i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 48.0000i | 2.42128i | ||||||||
\(394\) | −11.0000 | − | 19.0526i | −0.554172 | − | 0.959854i | ||||
\(395\) | −38.2487 | + | 10.2487i | −1.92450 | + | 0.515669i | ||||
\(396\) | −40.9808 | + | 10.9808i | −2.05936 | + | 0.551804i | ||||
\(397\) | 0 | 0 | 0.258819 | − | 0.965926i | \(-0.416667\pi\) | ||||
−0.258819 | + | 0.965926i | \(0.583333\pi\) | |||||||
\(398\) | 20.0000 | + | 20.0000i | 1.00251 | + | 1.00251i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 12.0000i | − | 0.600000i | ||||||
\(401\) | 2.00000 | + | 3.46410i | 0.0998752 | + | 0.172989i | 0.911633 | − | 0.411005i | \(-0.134822\pi\) |
−0.811758 | + | 0.583994i | \(0.801489\pi\) | |||||||
\(402\) | −27.3205 | + | 7.32051i | −1.36262 | + | 0.365114i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −5.46410 | − | 1.46410i | −0.271849 | − | 0.0728418i | ||||
\(405\) | 2.00000 | + | 2.00000i | 0.0993808 | + | 0.0993808i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 18.0000i | − | 0.892227i | ||||||
\(408\) | −24.0000 | − | 41.5692i | −1.18818 | − | 2.05798i | ||||
\(409\) | −8.66025 | − | 5.00000i | −0.428222 | − | 0.247234i | 0.270367 | − | 0.962757i | \(-0.412855\pi\) |
−0.698589 | + | 0.715523i | \(0.746188\pi\) | |||||||
\(410\) | −6.92820 | − | 4.00000i | −0.342160 | − | 0.197546i | ||||
\(411\) | −8.78461 | + | 32.7846i | −0.433313 | + | 1.61715i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −10.0000 | + | 10.0000i | −0.491473 | + | 0.491473i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −24.0000 | + | 41.5692i | −1.17529 | + | 2.03565i | ||||
\(418\) | 32.7846 | + | 8.78461i | 1.60355 | + | 0.429669i | ||||
\(419\) | −10.0000 | + | 10.0000i | −0.488532 | + | 0.488532i | −0.907843 | − | 0.419311i | \(-0.862272\pi\) |
0.419311 | + | 0.907843i | \(0.362272\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −25.0000 | − | 25.0000i | −1.21843 | − | 1.21843i | −0.968183 | − | 0.250242i | \(-0.919490\pi\) |
−0.250242 | − | 0.968183i | \(-0.580510\pi\) | |||||||
\(422\) | −15.5885 | + | 9.00000i | −0.758834 | + | 0.438113i | ||||
\(423\) | −34.6410 | − | 20.0000i | −1.68430 | − | 0.972433i | ||||
\(424\) | −24.2487 | − | 14.0000i | −1.17762 | − | 0.679900i | ||||
\(425\) | −15.5885 | + | 9.00000i | −0.756151 | + | 0.436564i | ||||
\(426\) | −32.0000 | −1.55041 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.0000 | − | 10.0000i | 0.483368 | − | 0.483368i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 27.3205 | − | 7.32051i | 1.31751 | − | 0.353026i | ||||
\(431\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(432\) | −5.85641 | + | 21.8564i | −0.281766 | + | 1.05157i | ||||
\(433\) | −2.00000 | −0.0961139 | −0.0480569 | − | 0.998845i | \(-0.515303\pi\) | ||||
−0.0480569 | + | 0.998845i | \(0.515303\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8.00000 | + | 8.00000i | −0.383571 | + | 0.383571i | ||||
\(436\) | 2.19615 | − | 8.19615i | 0.105177 | − | 0.392525i | ||||
\(437\) | 10.9282 | − | 2.92820i | 0.522767 | − | 0.140075i | ||||
\(438\) | 20.0000 | − | 34.6410i | 0.955637 | − | 1.65521i | ||||
\(439\) | −20.7846 | + | 12.0000i | −0.991995 | + | 0.572729i | −0.905870 | − | 0.423556i | \(-0.860782\pi\) |
−0.0861252 | + | 0.996284i | \(0.527448\pi\) | |||||||
\(440\) | −24.0000 | + | 24.0000i | −1.14416 | + | 1.14416i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6.22243 | + | 23.2224i | −0.295637 | + | 1.10333i | 0.645074 | + | 0.764120i | \(0.276827\pi\) |
−0.940710 | + | 0.339211i | \(0.889840\pi\) | |||||||
\(444\) | −20.7846 | − | 12.0000i | −0.986394 | − | 0.569495i | ||||
\(445\) | 4.39230 | + | 16.3923i | 0.208215 | + | 0.777070i | ||||
\(446\) | 5.46410 | + | 1.46410i | 0.258733 | + | 0.0693272i | ||||
\(447\) | 52.0000 | 2.45952 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 34.0000 | 1.60456 | 0.802280 | − | 0.596948i | \(-0.203620\pi\) | ||||
0.802280 | + | 0.596948i | \(0.203620\pi\) | |||||||
\(450\) | 20.4904 | + | 5.49038i | 0.965926 | + | 0.258819i | ||||
\(451\) | 2.19615 | + | 8.19615i | 0.103413 | + | 0.385942i | ||||
\(452\) | −20.7846 | − | 12.0000i | −0.977626 | − | 0.564433i | ||||
\(453\) | 4.39230 | − | 16.3923i | 0.206368 | − | 0.770178i | ||||
\(454\) | 8.00000i | 0.375459i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 32.0000 | − | 32.0000i | 1.49854 | − | 1.49854i | ||||
\(457\) | −22.5167 | + | 13.0000i | −1.05328 | + | 0.608114i | −0.923567 | − | 0.383437i | \(-0.874740\pi\) |
−0.129718 | + | 0.991551i | \(0.541407\pi\) | |||||||
\(458\) | 12.0000 | − | 20.7846i | 0.560723 | − | 0.971201i | ||||
\(459\) | 32.7846 | − | 8.78461i | 1.53025 | − | 0.410030i | ||||
\(460\) | −2.92820 | + | 10.9282i | −0.136528 | + | 0.509530i | ||||
\(461\) | −28.0000 | + | 28.0000i | −1.30409 | + | 1.30409i | −0.378481 | + | 0.925609i | \(0.623553\pi\) |
−0.925609 | + | 0.378481i | \(0.876447\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 14.0000 | 0.650635 | 0.325318 | − | 0.945605i | \(-0.394529\pi\) | ||||
0.325318 | + | 0.945605i | \(0.394529\pi\) | |||||||
\(464\) | −5.46410 | − | 1.46410i | −0.253665 | − | 0.0679692i | ||||
\(465\) | −16.0000 | + | 27.7128i | −0.741982 | + | 1.28515i | ||||
\(466\) | −10.9282 | + | 2.92820i | −0.506239 | + | 0.135646i | ||||
\(467\) | 21.8564 | + | 5.85641i | 1.01139 | + | 0.271002i | 0.726212 | − | 0.687471i | \(-0.241279\pi\) |
0.285182 | + | 0.958473i | \(0.407946\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −32.0000 | −1.47605 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.92820 | − | 4.00000i | −0.318896 | − | 0.184115i | ||||
\(473\) | −25.9808 | − | 15.0000i | −1.19460 | − | 0.689701i | ||||
\(474\) | 48.4974 | − | 28.0000i | 2.22756 | − | 1.28608i | ||||
\(475\) | −12.0000 | − | 12.0000i | −0.550598 | − | 0.550598i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 35.0000 | − | 35.0000i | 1.60254 | − | 1.60254i | ||||
\(478\) | −10.9282 | − | 2.92820i | −0.499844 | − | 0.133933i | ||||
\(479\) | 4.00000 | − | 6.92820i | 0.182765 | − | 0.316558i | −0.760056 | − | 0.649857i | \(-0.774829\pi\) |
0.942821 | + | 0.333300i | \(0.108162\pi\) | |||||||
\(480\) | 11.7128 | + | 43.7128i | 0.534614 | + | 1.99521i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 22.0000 | − | 22.0000i | 1.00207 | − | 1.00207i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 14.0000 | 0.636364 | ||||||||
\(485\) | 4.39230 | − | 16.3923i | 0.199444 | − | 0.744336i | ||||
\(486\) | 17.3205 | + | 10.0000i | 0.785674 | + | 0.453609i | ||||
\(487\) | 1.73205 | + | 1.00000i | 0.0784867 | + | 0.0453143i | 0.538730 | − | 0.842479i | \(-0.318904\pi\) |
−0.460243 | + | 0.887793i | \(0.652238\pi\) | |||||||
\(488\) | −12.0000 | − | 20.7846i | −0.543214 | − | 0.940875i | ||||
\(489\) | − | 20.0000i | − | 0.904431i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.0000 | − | 11.0000i | −0.496423 | − | 0.496423i | 0.413900 | − | 0.910323i | \(-0.364166\pi\) |
−0.910323 | + | 0.413900i | \(0.864166\pi\) | |||||||
\(492\) | 10.9282 | + | 2.92820i | 0.492681 | + | 0.132014i | ||||
\(493\) | 2.19615 | + | 8.19615i | 0.0989097 | + | 0.369136i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −30.0000 | − | 51.9615i | −1.34840 | − | 2.33550i | ||||
\(496\) | −16.0000 | −0.718421 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.4904 | + | 5.49038i | 0.917275 | + | 0.245783i | 0.686420 | − | 0.727205i | \(-0.259181\pi\) |
0.230855 | + | 0.972988i | \(0.425848\pi\) | |||||||
\(500\) | −10.9282 | + | 2.92820i | −0.488724 | + | 0.130953i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.00000 | + | 6.92820i | 0.178529 | + | 0.309221i | ||||
\(503\) | 8.00000i | 0.356702i | 0.983967 | + | 0.178351i | \(0.0570763\pi\) | ||||
−0.983967 | + | 0.178351i | \(0.942924\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 8.00000i | − | 0.355995i | ||||||
\(506\) | 10.3923 | − | 6.00000i | 0.461994 | − | 0.266733i | ||||
\(507\) | 35.5167 | − | 9.51666i | 1.57735 | − | 0.422650i | ||||
\(508\) | 13.8564 | + | 8.00000i | 0.614779 | + | 0.354943i | ||||
\(509\) | 16.3923 | + | 4.39230i | 0.726576 | + | 0.194685i | 0.603104 | − | 0.797663i | \(-0.293930\pi\) |
0.123472 | + | 0.992348i | \(0.460597\pi\) | |||||||
\(510\) | 48.0000 | − | 48.0000i | 2.12548 | − | 2.12548i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −16.0000 | + | 16.0000i | −0.707107 | + | 0.707107i | ||||
\(513\) | 16.0000 | + | 27.7128i | 0.706417 | + | 1.22355i | ||||
\(514\) | 3.66025 | + | 13.6603i | 0.161447 | + | 0.602528i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −34.6410 | + | 20.0000i | −1.52499 | + | 0.880451i | ||||
\(517\) | 24.0000 | + | 24.0000i | 1.05552 | + | 1.05552i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 64.0000i | 2.80929i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.19615 | − | 3.00000i | −0.227648 | − | 0.131432i | 0.381839 | − | 0.924229i | \(-0.375291\pi\) |
−0.609486 | + | 0.792797i | \(0.708624\pi\) | |||||||
\(522\) | 5.00000 | − | 8.66025i | 0.218844 | − | 0.379049i | ||||
\(523\) | 9.51666 | − | 35.5167i | 0.416135 | − | 1.55304i | −0.366418 | − | 0.930450i | \(-0.619416\pi\) |
0.782552 | − | 0.622585i | \(-0.213917\pi\) | |||||||
\(524\) | −24.0000 | − | 24.0000i | −1.04844 | − | 1.04844i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −24.0000 | − | 24.0000i | −1.04645 | − | 1.04645i | ||||
\(527\) | 12.0000 | + | 20.7846i | 0.522728 | + | 0.905392i | ||||
\(528\) | 24.0000 | − | 41.5692i | 1.04447 | − | 1.80907i | ||||
\(529\) | −9.50000 | + | 16.4545i | −0.413043 | + | 0.715412i | ||||
\(530\) | 10.2487 | − | 38.2487i | 0.445176 | − | 1.66142i | ||||
\(531\) | 10.0000 | − | 10.0000i | 0.433963 | − | 0.433963i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −12.0000 | − | 20.7846i | −0.519291 | − | 0.899438i | ||||
\(535\) | 17.3205 | + | 10.0000i | 0.748831 | + | 0.432338i | ||||
\(536\) | 10.0000 | − | 17.3205i | 0.431934 | − | 0.748132i | ||||
\(537\) | 17.3205 | − | 10.0000i | 0.747435 | − | 0.431532i | ||||
\(538\) | − | 32.0000i | − | 1.37962i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −32.0000 | −1.37706 | ||||||||
\(541\) | 39.6147 | + | 10.6147i | 1.70317 | + | 0.456363i | 0.973735 | − | 0.227686i | \(-0.0731160\pi\) |
0.729436 | + | 0.684049i | \(0.239783\pi\) | |||||||
\(542\) | −5.85641 | − | 21.8564i | −0.251554 | − | 0.938813i | ||||
\(543\) | 8.00000 | − | 13.8564i | 0.343313 | − | 0.594635i | ||||
\(544\) | 32.7846 | + | 8.78461i | 1.40563 | + | 0.376637i | ||||
\(545\) | 12.0000 | 0.514024 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 19.0000 | − | 19.0000i | 0.812381 | − | 0.812381i | −0.172609 | − | 0.984990i | \(-0.555220\pi\) |
0.984990 | + | 0.172609i | \(0.0552197\pi\) | |||||||
\(548\) | −12.0000 | − | 20.7846i | −0.512615 | − | 0.887875i | ||||
\(549\) | 40.9808 | − | 10.9808i | 1.74902 | − | 0.468648i | ||||
\(550\) | −15.5885 | − | 9.00000i | −0.664694 | − | 0.383761i | ||||
\(551\) | −6.92820 | + | 4.00000i | −0.295151 | + | 0.170406i | ||||
\(552\) | − | 16.0000i | − | 0.681005i | ||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −2.00000 | −0.0849719 | ||||||||
\(555\) | 8.78461 | − | 32.7846i | 0.372886 | − | 1.39163i | ||||
\(556\) | −8.78461 | − | 32.7846i | −0.372550 | − | 1.39038i | ||||
\(557\) | 5.49038 | + | 20.4904i | 0.232635 | + | 0.868205i | 0.979201 | + | 0.202894i | \(0.0650346\pi\) |
−0.746566 | + | 0.665312i | \(0.768299\pi\) | |||||||
\(558\) | 7.32051 | − | 27.3205i | 0.309902 | − | 1.15657i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −72.0000 | −3.03984 | ||||||||
\(562\) | −8.78461 | + | 32.7846i | −0.370556 | + | 1.38294i | ||||
\(563\) | −8.05256 | − | 30.0526i | −0.339375 | − | 1.26656i | −0.899048 | − | 0.437851i | \(-0.855740\pi\) |
0.559673 | − | 0.828714i | \(-0.310927\pi\) | |||||||
\(564\) | 43.7128 | − | 11.7128i | 1.84064 | − | 0.493198i | ||||
\(565\) | 8.78461 | − | 32.7846i | 0.369571 | − | 1.37926i | ||||
\(566\) | 12.0000 | 0.504398 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.0000 | − | 16.0000i | 0.671345 | − | 0.671345i | ||||
\(569\) | −39.8372 | + | 23.0000i | −1.67006 | + | 0.964210i | −0.702461 | + | 0.711722i | \(0.747915\pi\) |
−0.967600 | + | 0.252488i | \(0.918751\pi\) | |||||||
\(570\) | 55.4256 | + | 32.0000i | 2.32152 | + | 1.34033i | ||||
\(571\) | 28.6865 | − | 7.68653i | 1.20049 | − | 0.321671i | 0.397468 | − | 0.917616i | \(-0.369889\pi\) |
0.803026 | + | 0.595944i | \(0.203222\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −44.0000 | + | 44.0000i | −1.83813 | + | 1.83813i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −6.00000 | −0.250217 | ||||||||
\(576\) | −20.0000 | − | 34.6410i | −0.833333 | − | 1.44338i | ||||
\(577\) | 13.0000 | − | 22.5167i | 0.541197 | − | 0.937381i | −0.457639 | − | 0.889138i | \(-0.651305\pi\) |
0.998836 | − | 0.0482425i | \(-0.0153620\pi\) | |||||||
\(578\) | −6.95448 | − | 25.9545i | −0.289268 | − | 1.07956i | ||||
\(579\) | −65.5692 | − | 17.5692i | −2.72496 | − | 0.730152i | ||||
\(580\) | − | 8.00000i | − | 0.332182i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 24.0000i | 0.994832i | ||||||||
\(583\) | −36.3731 | + | 21.0000i | −1.50642 | + | 0.869731i | ||||
\(584\) | 7.32051 | + | 27.3205i | 0.302925 | + | 1.13053i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.0000 | − | 17.3205i | −0.413096 | − | 0.715504i | ||||
\(587\) | 8.00000 | + | 8.00000i | 0.330195 | + | 0.330195i | 0.852661 | − | 0.522465i | \(-0.174988\pi\) |
−0.522465 | + | 0.852661i | \(0.674988\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.0000 | + | 16.0000i | −0.659269 | + | 0.659269i | ||||
\(590\) | 2.92820 | − | 10.9282i | 0.120552 | − | 0.449907i | ||||
\(591\) | −22.0000 | + | 38.1051i | −0.904959 | + | 1.56744i | ||||
\(592\) | 16.3923 | − | 4.39230i | 0.673720 | − | 0.180523i | ||||
\(593\) | 11.0000 | + | 19.0526i | 0.451716 | + | 0.782395i | 0.998493 | − | 0.0548835i | \(-0.0174787\pi\) |
−0.546777 | + | 0.837278i | \(0.684145\pi\) | |||||||
\(594\) | 24.0000 | + | 24.0000i | 0.984732 | + | 0.984732i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −26.0000 | + | 26.0000i | −1.06500 | + | 1.06500i | ||||
\(597\) | 14.6410 | − | 54.6410i | 0.599217 | − | 2.23631i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 6.92820 | + | 4.00000i | 0.283079 | + | 0.163436i | 0.634816 | − | 0.772663i | \(-0.281076\pi\) |
−0.351738 | + | 0.936099i | \(0.614409\pi\) | |||||||
\(600\) | −20.7846 | + | 12.0000i | −0.848528 | + | 0.489898i | ||||
\(601\) | − | 10.0000i | − | 0.407909i | −0.978980 | − | 0.203954i | \(-0.934621\pi\) | ||
0.978980 | − | 0.203954i | \(-0.0653794\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 25.0000 | + | 25.0000i | 1.01808 | + | 1.01808i | ||||
\(604\) | 6.00000 | + | 10.3923i | 0.244137 | + | 0.422857i | ||||
\(605\) | 5.12436 | + | 19.1244i | 0.208335 | + | 0.777516i | ||||
\(606\) | 2.92820 | + | 10.9282i | 0.118950 | + | 0.443928i | ||||
\(607\) | −10.0000 | − | 17.3205i | −0.405887 | − | 0.703018i | 0.588537 | − | 0.808470i | \(-0.299704\pi\) |
−0.994424 | + | 0.105453i | \(0.966371\pi\) | |||||||
\(608\) | 32.0000i | 1.29777i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 24.0000 | − | 24.0000i | 0.971732 | − | 0.971732i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −30.0000 | + | 51.9615i | −1.21268 | + | 2.10042i | ||||
\(613\) | 20.4904 | − | 5.49038i | 0.827599 | − | 0.221754i | 0.179933 | − | 0.983679i | \(-0.442412\pi\) |
0.647666 | + | 0.761924i | \(0.275745\pi\) | |||||||
\(614\) | −13.8564 | + | 8.00000i | −0.559199 | + | 0.322854i | ||||
\(615\) | 16.0000i | 0.645182i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 6.00000i | − | 0.241551i | −0.992680 | − | 0.120775i | \(-0.961462\pi\) | ||
0.992680 | − | 0.120775i | \(-0.0385381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.5885 | + | 6.58846i | −0.988294 | + | 0.264812i | −0.716534 | − | 0.697553i | \(-0.754272\pi\) |
−0.271760 | + | 0.962365i | \(0.587606\pi\) | |||||||
\(620\) | −5.85641 | − | 21.8564i | −0.235199 | − | 0.877774i | ||||
\(621\) | 10.9282 | + | 2.92820i | 0.438534 | + | 0.117505i | ||||
\(622\) | 4.00000 | + | 4.00000i | 0.160385 | + | 0.160385i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −15.5000 | − | 26.8468i | −0.620000 | − | 1.07387i | ||||
\(626\) | −2.73205 | + | 0.732051i | −0.109195 | + | 0.0292586i | ||||
\(627\) | −17.5692 | − | 65.5692i | −0.701647 | − | 2.61858i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −18.0000 | − | 18.0000i | −0.717707 | − | 0.717707i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(632\) | −10.2487 | + | 38.2487i | −0.407672 | + | 1.52145i | ||||
\(633\) | 31.1769 | + | 18.0000i | 1.23917 | + | 0.715436i | ||||
\(634\) | 25.9808 | + | 15.0000i | 1.03183 | + | 0.595726i | ||||
\(635\) | −5.85641 | + | 21.8564i | −0.232404 | + | 0.867345i | ||||
\(636\) | 56.0000i | 2.22054i | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −6.00000 | + | 6.00000i | −0.237542 | + | 0.237542i | ||||
\(639\) | 20.0000 | + | 34.6410i | 0.791188 | + | 1.37038i | ||||
\(640\) | −27.7128 | − | 16.0000i | −1.09545 | − | 0.632456i | ||||
\(641\) | −22.0000 | + | 38.1051i | −0.868948 | + | 1.50506i | −0.00587459 | + | 0.999983i | \(0.501870\pi\) |
−0.863073 | + | 0.505079i | \(0.831463\pi\) | |||||||
\(642\) | −27.3205 | − | 7.32051i | −1.07825 | − | 0.288917i | ||||
\(643\) | 26.0000 | − | 26.0000i | 1.02534 | − | 1.02534i | 0.0256694 | − | 0.999670i | \(-0.491828\pi\) |
0.999670 | − | 0.0256694i | \(-0.00817173\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.0000 | − | 40.0000i | −1.57500 | − | 1.57500i | ||||
\(646\) | 41.5692 | − | 24.0000i | 1.63552 | − | 0.944267i | ||||
\(647\) | 20.7846 | + | 12.0000i | 0.817127 | + | 0.471769i | 0.849425 | − | 0.527710i | \(-0.176949\pi\) |
−0.0322975 | + | 0.999478i | \(0.510282\pi\) | |||||||
\(648\) | 2.73205 | − | 0.732051i | 0.107325 | − | 0.0287577i | ||||
\(649\) | −10.3923 | + | 6.00000i | −0.407934 | + | 0.235521i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.0000 | + | 10.0000i | 0.391630 | + | 0.391630i | ||||
\(653\) | −34.1506 | − | 9.15064i | −1.33642 | − | 0.358092i | −0.481314 | − | 0.876548i | \(-0.659840\pi\) |
−0.855104 | + | 0.518456i | \(0.826507\pi\) | |||||||
\(654\) | −16.3923 | + | 4.39230i | −0.640990 | + | 0.171753i | ||||
\(655\) | 24.0000 | − | 41.5692i | 0.937758 | − | 1.62424i | ||||
\(656\) | −6.92820 | + | 4.00000i | −0.270501 | + | 0.156174i | ||||
\(657\) | −50.0000 | −1.95069 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 17.0000 | − | 17.0000i | 0.662226 | − | 0.662226i | −0.293678 | − | 0.955904i | \(-0.594879\pi\) |
0.955904 | + | 0.293678i | \(0.0948794\pi\) | |||||||
\(660\) | 65.5692 | + | 17.5692i | 2.55228 | + | 0.683881i | ||||
\(661\) | −40.9808 | + | 10.9808i | −1.59397 | + | 0.427102i | −0.943214 | − | 0.332187i | \(-0.892213\pi\) |
−0.650753 | + | 0.759289i | \(0.725547\pi\) | |||||||
\(662\) | −15.0000 | + | 25.9808i | −0.582992 | + | 1.00977i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 30.0000i | 1.16248i | ||||||||
\(667\) | −0.732051 | + | 2.73205i | −0.0283451 | + | 0.105785i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −2.92820 | − | 10.9282i | −0.113211 | − | 0.422509i | ||||
\(670\) | 27.3205 | + | 7.32051i | 1.05548 | + | 0.282816i | ||||
\(671\) | −36.0000 | −1.38976 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 26.0000 | 1.00223 | 0.501113 | − | 0.865382i | \(-0.332924\pi\) | ||||
0.501113 | + | 0.865382i | \(0.332924\pi\) | |||||||
\(674\) | −10.9282 | − | 2.92820i | −0.420939 | − | 0.112790i | ||||
\(675\) | −4.39230 | − | 16.3923i | −0.169060 | − | 0.630940i | ||||
\(676\) | −13.0000 | + | 22.5167i | −0.500000 | + | 0.866025i | ||||
\(677\) | 2.92820 | − | 10.9282i | 0.112540 | − | 0.420005i | −0.886551 | − | 0.462631i | \(-0.846906\pi\) |
0.999091 | + | 0.0426257i | \(0.0135723\pi\) | |||||||
\(678\) | 48.0000i | 1.84343i | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 48.0000i | 1.84072i | ||||||||
\(681\) | 13.8564 | − | 8.00000i | 0.530979 | − | 0.306561i | ||||
\(682\) | −12.0000 | + | 20.7846i | −0.459504 | + | 0.795884i | ||||
\(683\) | −6.83013 | + | 1.83013i | −0.261348 | + | 0.0700279i | −0.387113 | − | 0.922032i | \(-0.626528\pi\) |
0.125766 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(684\) | −54.6410 | − | 14.6410i | −2.08925 | − | 0.559813i | ||||
\(685\) | 24.0000 | − | 24.0000i | 0.916993 | − | 0.916993i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.0000 | −1.83131 | ||||||||
\(688\) | 7.32051 | − | 27.3205i | 0.279092 | − | 1.04158i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 21.8564 | − | 5.85641i | 0.832059 | − | 0.222950i | ||||
\(691\) | −16.3923 | − | 4.39230i | −0.623593 | − | 0.167091i | −0.0668322 | − | 0.997764i | \(-0.521289\pi\) |
−0.556760 | + | 0.830673i | \(0.687956\pi\) | |||||||
\(692\) | −32.0000 | − | 32.0000i | −1.21646 | − | 1.21646i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 26.0000 | 0.986947 | ||||||||
\(695\) | 41.5692 | − | 24.0000i | 1.57681 | − | 0.910372i | ||||
\(696\) | 2.92820 | + | 10.9282i | 0.110993 | + | 0.414232i | ||||
\(697\) | 10.3923 | + | 6.00000i | 0.393637 | + | 0.227266i | ||||
\(698\) | 27.7128 | − | 16.0000i | 1.04895 | − | 0.605609i | ||||
\(699\) | 16.0000 | + | 16.0000i | 0.605176 | + | 0.605176i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.0000 | − | 13.0000i | 0.491003 | − | 0.491003i | −0.417619 | − | 0.908622i | \(-0.637135\pi\) |
0.908622 | + | 0.417619i | \(0.137135\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.0000 | − | 20.7846i | 0.452589 | − | 0.783906i | ||||
\(704\) | 8.78461 | + | 32.7846i | 0.331082 | + | 1.23562i | ||||
\(705\) | 32.0000 | + | 55.4256i | 1.20519 | + | 2.08745i | ||||
\(706\) | −18.0000 | + | 18.0000i | −0.677439 | + | 0.677439i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 16.0000i | 0.601317i | ||||||||
\(709\) | −11.3468 | + | 42.3468i | −0.426138 | + | 1.59037i | 0.335289 | + | 0.942115i | \(0.391166\pi\) |
−0.761426 | + | 0.648252i | \(0.775501\pi\) | |||||||
\(710\) | 27.7128 | + | 16.0000i | 1.04004 | + | 0.600469i | ||||
\(711\) | −60.6218 | − | 35.0000i | −2.27349 | − | 1.31260i | ||||
\(712\) | 16.3923 | + | 4.39230i | 0.614328 | + | 0.164609i | ||||
\(713\) | 8.00000i | 0.299602i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.66025 | + | 13.6603i | −0.136790 | + | 0.510508i | ||||
\(717\) | 5.85641 | + | 21.8564i | 0.218712 | + | 0.816242i | ||||
\(718\) | 30.0526 | − | 8.05256i | 1.12155 | − | 0.300519i | ||||
\(719\) | 4.00000 | + | 6.92820i | 0.149175 | + | 0.258378i | 0.930923 | − | 0.365216i | \(-0.119005\pi\) |
−0.781748 | + | 0.623595i | \(0.785672\pi\) | |||||||
\(720\) | 40.0000 | − | 40.0000i | 1.49071 | − | 1.49071i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 13.0000 | + | 13.0000i | 0.483810 | + | 0.483810i | ||||
\(723\) | −60.1051 | − | 16.1051i | −2.23533 | − | 0.598956i | ||||
\(724\) | 2.92820 | + | 10.9282i | 0.108826 | + | 0.406143i | ||||
\(725\) | 4.09808 | − | 1.09808i | 0.152199 | − | 0.0407815i | ||||
\(726\) | −14.0000 | − | 24.2487i | −0.519589 | − | 0.899954i | ||||
\(727\) | 44.0000i | 1.63187i | 0.578144 | + | 0.815935i | \(0.303777\pi\) | ||||
−0.578144 | + | 0.815935i | \(0.696223\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 43.0000i | − | 1.59259i | ||||||
\(730\) | −34.6410 | + | 20.0000i | −1.28212 | + | 0.740233i | ||||
\(731\) | −40.9808 | + | 10.9808i | −1.51573 | + | 0.406138i | ||||
\(732\) | −24.0000 | + | 41.5692i | −0.887066 | + | 1.53644i | ||||
\(733\) | 2.73205 | + | 0.732051i | 0.100911 | + | 0.0270389i | 0.308921 | − | 0.951088i | \(-0.400032\pi\) |
−0.208010 | + | 0.978127i | \(0.566699\pi\) | |||||||
\(734\) | 16.0000 | − | 16.0000i | 0.590571 | − | 0.590571i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 8.00000 | + | 8.00000i | 0.294884 | + | 0.294884i | ||||
\(737\) | −15.0000 | − | 25.9808i | −0.552532 | − | 0.957014i | ||||
\(738\) | −3.66025 | − | 13.6603i | −0.134736 | − | 0.502841i | ||||
\(739\) | −1.83013 | − | 6.83013i | −0.0673223 | − | 0.251250i | 0.924061 | − | 0.382246i | \(-0.124849\pi\) |
−0.991383 | + | 0.130996i | \(0.958183\pi\) | |||||||
\(740\) | 12.0000 | + | 20.7846i | 0.441129 | + | 0.764057i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 6.00000i | − | 0.220119i | −0.993925 | − | 0.110059i | \(-0.964896\pi\) | ||
0.993925 | − | 0.110059i | \(-0.0351041\pi\) | |||||||
\(744\) | 16.0000 | + | 27.7128i | 0.586588 | + | 1.01600i | ||||
\(745\) | −45.0333 | − | 26.0000i | −1.64989 | − | 0.952566i | ||||
\(746\) | 5.00000 | − | 8.66025i | 0.183063 | − | 0.317074i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 36.0000 | − | 36.0000i | 1.31629 | − | 1.31629i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 16.0000 | + | 16.0000i | 0.584237 | + | 0.584237i | ||||
\(751\) | −20.0000 | − | 34.6410i | −0.729810 | − | 1.26407i | −0.956963 | − | 0.290209i | \(-0.906275\pi\) |
0.227153 | − | 0.973859i | \(-0.427058\pi\) | |||||||
\(752\) | −16.0000 | + | 27.7128i | −0.583460 | + | 1.01058i | ||||
\(753\) | 8.00000 | − | 13.8564i | 0.291536 | − | 0.504956i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | + | 12.0000i | −0.436725 | + | 0.436725i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 33.0000 | + | 33.0000i | 1.19941 | + | 1.19941i | 0.974345 | + | 0.225061i | \(0.0722580\pi\) |
0.225061 | + | 0.974345i | \(0.427742\pi\) | |||||||
\(758\) | 17.0000 | + | 29.4449i | 0.617468 | + | 1.06949i | ||||
\(759\) | −20.7846 | − | 12.0000i | −0.754434 | − | 0.435572i | ||||
\(760\) | −43.7128 | + | 11.7128i | −1.58563 | + | 0.424868i | ||||
\(761\) | 15.5885 | − | 9.00000i | 0.565081 | − | 0.326250i | −0.190101 | − | 0.981764i | \(-0.560882\pi\) |
0.755182 | + | 0.655515i | \(0.227548\pi\) | |||||||
\(762\) | − | 32.0000i | − | 1.15924i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 44.0000i | − | 1.59186i | ||||||
\(765\) | −81.9615 | − | 21.9615i | −2.96333 | − | 0.794021i | ||||
\(766\) | 5.85641 | + | 21.8564i | 0.211601 | + | 0.789704i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 43.7128 | + | 11.7128i | 1.57735 | + | 0.422650i | ||||
\(769\) | −30.0000 | −1.08183 | −0.540914 | − | 0.841078i | \(-0.681921\pi\) | ||||
−0.540914 | + | 0.841078i | \(0.681921\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 20.0000 | − | 20.0000i | 0.720282 | − | 0.720282i | ||||
\(772\) | 41.5692 | − | 24.0000i | 1.49611 | − | 0.863779i | ||||
\(773\) | 40.9808 | − | 10.9808i | 1.47398 | − | 0.394951i | 0.569683 | − | 0.821864i | \(-0.307066\pi\) |
0.904292 | + | 0.426914i | \(0.140399\pi\) | |||||||
\(774\) | 43.3013 | + | 25.0000i | 1.55643 | + | 0.898606i | ||||
\(775\) | 10.3923 | − | 6.00000i | 0.373303 | − | 0.215526i | ||||
\(776\) | −12.0000 | − | 12.0000i | −0.430775 | − | 0.430775i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −38.0000 | −1.36237 | ||||||||
\(779\) | −2.92820 | + | 10.9282i | −0.104914 | + | 0.391544i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.78461 | − | 32.7846i | −0.314338 | − | 1.17313i | ||||
\(782\) | 4.39230 | − | 16.3923i | 0.157069 | − | 0.586188i | ||||
\(783\) | −8.00000 | −0.285897 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17.5692 | + | 65.5692i | −0.626673 | + | 2.33878i | ||||
\(787\) | −4.39230 | − | 16.3923i | −0.156569 | − | 0.584323i | −0.998966 | − | 0.0454654i | \(-0.985523\pi\) |
0.842397 | − | 0.538857i | \(-0.181144\pi\) | |||||||
\(788\) | −8.05256 | − | 30.0526i | −0.286861 | − | 1.07058i | ||||
\(789\) | −17.5692 | + | 65.5692i | −0.625481 | + | 2.33433i | ||||
\(790\) | −56.0000 | −1.99239 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −60.0000 | −2.13201 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −76.4974 | + | 20.4974i | −2.71308 | + | 0.726969i | ||||
\(796\) | 20.0000 | + | 34.6410i | 0.708881 | + | 1.22782i | ||||
\(797\) | 8.00000 | − | 8.00000i | 0.283375 | − | 0.283375i | −0.551079 | − | 0.834453i | \(-0.685784\pi\) |
0.834453 | + | 0.551079i | \(0.185784\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 48.0000 | 1.69812 | ||||||||
\(800\) | 4.39230 | − | 16.3923i | 0.155291 | − | 0.579555i | ||||
\(801\) | −15.0000 | + | 25.9808i | −0.529999 | + | 0.917985i | ||||
\(802\) | 1.46410 | + | 5.46410i | 0.0516992 | + | 0.192944i | ||||
\(803\) | 40.9808 | + | 10.9808i | 1.44618 | + | 0.387503i | ||||
\(804\) | −40.0000 | −1.41069 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −55.4256 | + | 32.0000i | −1.95107 | + | 1.12645i | ||||
\(808\) | −6.92820 | − | 4.00000i | −0.243733 | − | 0.140720i | ||||
\(809\) | −32.9090 | − | 19.0000i | −1.15702 | − | 0.668004i | −0.206430 | − | 0.978461i | \(-0.566185\pi\) |
−0.950587 | + | 0.310457i | \(0.899518\pi\) | |||||||
\(810\) | 2.00000 | + | 3.46410i | 0.0702728 | + | 0.121716i | ||||
\(811\) | 30.0000 | + | 30.0000i | 1.05344 | + | 1.05344i | 0.998489 | + | 0.0549536i | \(0.0175011\pi\) |
0.0549536 | + | 0.998489i | \(0.482499\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −32.0000 | + | 32.0000i | −1.12229 | + | 1.12229i | ||||
\(814\) | 6.58846 | − | 24.5885i | 0.230925 | − | 0.861825i | ||||
\(815\) | −10.0000 | + | 17.3205i | −0.350285 | + | 0.606711i | ||||
\(816\) | −17.5692 | − | 65.5692i | −0.615046 | − | 2.29538i | ||||
\(817\) | −20.0000 | − | 34.6410i | −0.699711 | − | 1.21194i | ||||
\(818\) | −10.0000 | − | 10.0000i | −0.349642 | − | 0.349642i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.00000 | − | 8.00000i | −0.279372 | − | 0.279372i | ||||
\(821\) | −2.56218 | + | 9.56218i | −0.0894206 | + | 0.333722i | −0.996115 | − | 0.0880668i | \(-0.971931\pi\) |
0.906694 | + | 0.421789i | \(0.138598\pi\) | |||||||
\(822\) | −24.0000 | + | 41.5692i | −0.837096 | + | 1.44989i | ||||
\(823\) | 34.6410 | + | 20.0000i | 1.20751 | + | 0.697156i | 0.962215 | − | 0.272292i | \(-0.0877817\pi\) |
0.245295 | + | 0.969448i | \(0.421115\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 36.0000i | 1.25336i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.0000 | − | 13.0000i | −0.452054 | − | 0.452054i | 0.443982 | − | 0.896036i | \(-0.353566\pi\) |
−0.896036 | + | 0.443982i | \(0.853566\pi\) | |||||||
\(828\) | −17.3205 | + | 10.0000i | −0.601929 | + | 0.347524i | ||||
\(829\) | −0.732051 | − | 2.73205i | −0.0254252 | − | 0.0948880i | 0.952047 | − | 0.305951i | \(-0.0989743\pi\) |
−0.977473 | + | 0.211063i | \(0.932308\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.00000 | + | 3.46410i | 0.0693792 | + | 0.120168i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −48.0000 | + | 48.0000i | −1.66210 | + | 1.66210i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 41.5692 | + | 24.0000i | 1.43770 | + | 0.830057i | ||||
\(837\) | −21.8564 | + | 5.85641i | −0.755468 | + | 0.202427i | ||||
\(838\) | −17.3205 | + | 10.0000i | −0.598327 | + | 0.345444i | ||||
\(839\) | − | 24.0000i | − | 0.828572i | −0.910147 | − | 0.414286i | \(-0.864031\pi\) | ||
0.910147 | − | 0.414286i | \(-0.135969\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 27.0000i | 0.931034i | ||||||||
\(842\) | −25.0000 | − | 43.3013i | −0.861557 | − | 1.49226i | ||||
\(843\) | 65.5692 | − | 17.5692i | 2.25832 | − | 0.605116i | ||||
\(844\) | −24.5885 | + | 6.58846i | −0.846370 | + | 0.226784i | ||||
\(845\) | −35.5167 | − | 9.51666i | −1.22181 | − | 0.327383i | ||||
\(846\) | −40.0000 | − | 40.0000i | −1.37523 | − | 1.37523i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −28.0000 | − | 28.0000i | −0.961524 | − | 0.961524i | ||||
\(849\) | −12.0000 | − | 20.7846i | −0.411839 | − | 0.713326i | ||||
\(850\) | −24.5885 | + | 6.58846i | −0.843377 | + | 0.225982i | ||||
\(851\) | −2.19615 | − | 8.19615i | −0.0752831 | − | 0.280960i | ||||
\(852\) | −43.7128 | − | 11.7128i | −1.49758 | − | 0.401274i | ||||
\(853\) | −4.00000 | − | 4.00000i | −0.136957 | − | 0.136957i | 0.635304 | − | 0.772262i | \(-0.280875\pi\) |
−0.772262 | + | 0.635304i | \(0.780875\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 80.0000i | − | 2.73594i | ||||||
\(856\) | 17.3205 | − | 10.0000i | 0.592003 | − | 0.341793i | ||||
\(857\) | 15.5885 | + | 9.00000i | 0.532492 | + | 0.307434i | 0.742030 | − | 0.670366i | \(-0.233863\pi\) |
−0.209539 | + | 0.977800i | \(0.567196\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.46410 | + | 5.46410i | −0.0499545 | + | 0.186433i | −0.986395 | − | 0.164395i | \(-0.947433\pi\) |
0.936440 | + | 0.350827i | \(0.114100\pi\) | |||||||
\(860\) | 40.0000 | 1.36399 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.00000 | − | 5.19615i | −0.102121 | − | 0.176879i | 0.810437 | − | 0.585826i | \(-0.199230\pi\) |
−0.912558 | + | 0.408946i | \(0.865896\pi\) | |||||||
\(864\) | −16.0000 | + | 27.7128i | −0.544331 | + | 0.942809i | ||||
\(865\) | 32.0000 | − | 55.4256i | 1.08803 | − | 1.88453i | ||||
\(866\) | −2.73205 | − | 0.732051i | −0.0928389 | − | 0.0248761i | ||||
\(867\) | −38.0000 | + | 38.0000i | −1.29055 | + | 1.29055i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 42.0000 | + | 42.0000i | 1.42475 | + | 1.42475i | ||||
\(870\) | −13.8564 | + | 8.00000i | −0.469776 | + | 0.271225i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 6.00000 | − | 10.3923i | 0.203186 | − | 0.351928i | ||||
\(873\) | 25.9808 | − | 15.0000i | 0.879316 | − | 0.507673i | ||||
\(874\) | 16.0000 | 0.541208 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 40.0000 | − | 40.0000i | 1.35147 | − | 1.35147i | ||||
\(877\) | 28.6865 | + | 7.68653i | 0.968675 | + | 0.259556i | 0.708268 | − | 0.705943i | \(-0.249477\pi\) |
0.260407 | + | 0.965499i | \(0.416143\pi\) | |||||||
\(878\) | −32.7846 | + | 8.78461i | −1.10643 | + | 0.296466i | ||||
\(879\) | −20.0000 | + | 34.6410i | −0.674583 | + | 1.16841i | ||||
\(880\) | −41.5692 | + | 24.0000i | −1.40130 | + | 0.809040i | ||||
\(881\) | 30.0000 | 1.01073 | 0.505363 | − | 0.862907i | \(-0.331359\pi\) | ||||
0.505363 | + | 0.862907i | \(0.331359\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −17.0000 | + | 17.0000i | −0.572096 | + | 0.572096i | −0.932714 | − | 0.360618i | \(-0.882566\pi\) |
0.360618 | + | 0.932714i | \(0.382566\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −21.8564 | + | 5.85641i | −0.734695 | + | 0.196861i | ||||
\(886\) | −17.0000 | + | 29.4449i | −0.571126 | + | 0.989220i | ||||
\(887\) | −20.7846 | + | 12.0000i | −0.697879 | + | 0.402921i | −0.806557 | − | 0.591156i | \(-0.798672\pi\) |
0.108678 | + | 0.994077i | \(0.465338\pi\) | |||||||
\(888\) | −24.0000 | − | 24.0000i | −0.805387 | − | 0.805387i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 24.0000i | 0.804482i | ||||||||
\(891\) | 1.09808 | − | 4.09808i | 0.0367869 | − | 0.137291i | ||||
\(892\) | 6.92820 | + | 4.00000i | 0.231973 | + | 0.133930i | ||||
\(893\) | 11.7128 | + | 43.7128i | 0.391954 | + | 1.46279i | ||||
\(894\) | 71.0333 | + | 19.0333i | 2.37571 | + | 0.636569i | ||||
\(895\) | −20.0000 | −0.668526 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 46.4449 | + | 12.4449i | 1.54989 | + | 0.415290i | ||||
\(899\) | −1.46410 | − | 5.46410i | −0.0488305 | − | 0.182238i | ||||
\(900\) | 25.9808 | + | 15.0000i | 0.866025 | + | 0.500000i | ||||
\(901\) | −15.3731 | + | 57.3731i | −0.512151 | + | 1.91137i | ||||
\(902\) | 12.0000i | 0.399556i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −24.0000 | − | 24.0000i | −0.798228 | − | 0.798228i | ||||
\(905\) | −13.8564 | + | 8.00000i | −0.460603 | + | 0.265929i | ||||
\(906\) | 12.0000 | − | 20.7846i | 0.398673 | − | 0.690522i | ||||
\(907\) | 12.2942 | − | 3.29423i | 0.408223 | − | 0.109383i | −0.0488630 | − | 0.998805i | \(-0.515560\pi\) |
0.457086 | + | 0.889422i | \(0.348893\pi\) | |||||||
\(908\) | −2.92820 | + | 10.9282i | −0.0971758 | + | 0.362665i | ||||
\(909\) | 10.0000 | − | 10.0000i | 0.331679 | − | 0.331679i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(912\) | 55.4256 | − | 32.0000i | 1.83533 | − | 1.05963i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −35.5167 | + | 9.51666i | −1.17479 | + | 0.314783i | ||||
\(915\) | −65.5692 | − | 17.5692i | −2.16765 | − | 0.580820i | ||||
\(916\) | 24.0000 | − | 24.0000i | 0.792982 | − | 0.792982i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 48.0000 | 1.58424 | ||||||||
\(919\) | 48.4974 | − | 28.0000i | 1.59978 | − | 0.923635i | 0.608254 | − | 0.793742i | \(-0.291870\pi\) |
0.991528 | − | 0.129893i | \(-0.0414632\pi\) | |||||||
\(920\) | −8.00000 | + | 13.8564i | −0.263752 | + | 0.456832i | ||||
\(921\) | 27.7128 | + | 16.0000i | 0.913168 | + | 0.527218i | ||||
\(922\) | −48.4974 | + | 28.0000i | −1.59718 | + | 0.922131i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −9.00000 | + | 9.00000i | −0.295918 | + | 0.295918i | ||||
\(926\) | 19.1244 | + | 5.12436i | 0.628465 | + | 0.168397i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.92820 | − | 4.00000i | −0.227429 | − | 0.131306i | ||||
\(929\) | 15.0000 | + | 25.9808i | 0.492134 | + | 0.852401i | 0.999959 | − | 0.00905914i | \(-0.00288365\pi\) |
−0.507825 | + | 0.861460i | \(0.669550\pi\) | |||||||
\(930\) | −32.0000 | + | 32.0000i | −1.04932 | + | 1.04932i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −16.0000 | −0.524097 | ||||||||
\(933\) | 2.92820 | − | 10.9282i | 0.0958651 | − | 0.357773i | ||||
\(934\) | 27.7128 | + | 16.0000i | 0.906791 | + | 0.523536i | ||||
\(935\) | 62.3538 | + | 36.0000i | 2.03919 | + | 1.17733i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50.0000i | 1.63343i | 0.577042 | + | 0.816714i | \(0.304207\pi\) | ||||
−0.577042 | + | 0.816714i | \(0.695793\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.00000 | + | 4.00000i | 0.130535 | + | 0.130535i | ||||
\(940\) | −43.7128 | − | 11.7128i | −1.42575 | − | 0.382030i | ||||
\(941\) | 9.51666 | + | 35.5167i | 0.310234 | + | 1.15781i | 0.928345 | + | 0.371719i | \(0.121232\pi\) |
−0.618111 | + | 0.786091i | \(0.712102\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.00000 | + | 3.46410i | 0.0651290 | + | 0.112807i | ||||
\(944\) | −8.00000 | − | 8.00000i | −0.260378 | − | 0.260378i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −30.0000 | − | 30.0000i | −0.975384 | − | 0.975384i | ||||
\(947\) | −17.7583 | − | 4.75833i | −0.577068 | − | 0.154625i | −0.0415319 | − | 0.999137i | \(-0.513224\pi\) |
−0.535536 | + | 0.844512i | \(0.679890\pi\) | |||||||
\(948\) | 76.4974 | − | 20.4974i | 2.48452 | − | 0.665725i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | −12.0000 | − | 20.7846i | −0.389331 | − | 0.674342i | ||||
\(951\) | − | 60.0000i | − | 1.94563i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 16.0000i | − | 0.518291i | −0.965838 | − | 0.259145i | \(-0.916559\pi\) | ||
0.965838 | − | 0.259145i | \(-0.0834409\pi\) | |||||||
\(954\) | 60.6218 | − | 35.0000i | 1.96270 | − | 1.13317i | ||||
\(955\) | 60.1051 | − | 16.1051i | 1.94496 | − | 0.521149i | ||||
\(956\) | −13.8564 | − | 8.00000i | −0.448148 | − | 0.258738i | ||||
\(957\) | 16.3923 | + | 4.39230i | 0.529888 | + | 0.141983i | ||||
\(958\) | 8.00000 | − | 8.00000i | 0.258468 | − | 0.258468i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 64.0000i | 2.06559i | ||||||||
\(961\) | 7.50000 | + | 12.9904i | 0.241935 | + | 0.419045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.15064 | + | 34.1506i | 0.294875 | + | 1.10049i | ||||
\(964\) | 38.1051 | − | 22.0000i | 1.22728 | − | 0.708572i | ||||
\(965\) | 48.0000 | + | 48.0000i | 1.54517 | + | 1.54517i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38.0000i | − | 1.22200i | −0.791632 | − | 0.610999i | \(-0.790768\pi\) | ||
0.791632 | − | 0.610999i | \(-0.209232\pi\) | |||||||
\(968\) | 19.1244 | + | 5.12436i | 0.614680 | + | 0.164703i | ||||
\(969\) | −83.1384 | − | 48.0000i | −2.67079 | − | 1.54198i | ||||
\(970\) | 12.0000 | − | 20.7846i | 0.385297 | − | 0.667354i | ||||
\(971\) | 9.51666 | − | 35.5167i | 0.305404 | − | 1.13978i | −0.627193 | − | 0.778864i | \(-0.715796\pi\) |
0.932597 | − | 0.360920i | \(-0.117537\pi\) | |||||||
\(972\) | 20.0000 | + | 20.0000i | 0.641500 | + | 0.641500i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.00000 | + | 2.00000i | 0.0640841 | + | 0.0640841i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.78461 | − | 32.7846i | −0.281189 | − | 1.04941i | ||||
\(977\) | 17.0000 | − | 29.4449i | 0.543878 | − | 0.942025i | −0.454798 | − | 0.890594i | \(-0.650289\pi\) |
0.998677 | − | 0.0514302i | \(-0.0163780\pi\) | |||||||
\(978\) | 7.32051 | − | 27.3205i | 0.234084 | − | 0.873614i | ||||
\(979\) | 18.0000 | − | 18.0000i | 0.575282 | − | 0.575282i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.0000 | + | 15.0000i | 0.478913 | + | 0.478913i | ||||
\(982\) | −11.0000 | − | 19.0526i | −0.351024 | − | 0.607992i | ||||
\(983\) | −41.5692 | − | 24.0000i | −1.32585 | − | 0.765481i | −0.341197 | − | 0.939992i | \(-0.610832\pi\) |
−0.984655 | + | 0.174511i | \(0.944166\pi\) | |||||||
\(984\) | 13.8564 | + | 8.00000i | 0.441726 | + | 0.255031i | ||||
\(985\) | 38.1051 | − | 22.0000i | 1.21413 | − | 0.700978i | ||||
\(986\) | 12.0000i | 0.382158i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −13.6603 | − | 3.66025i | −0.434371 | − | 0.116389i | ||||
\(990\) | −21.9615 | − | 81.9615i | −0.697983 | − | 2.60491i | ||||
\(991\) | 5.00000 | − | 8.66025i | 0.158830 | − | 0.275102i | −0.775617 | − | 0.631204i | \(-0.782561\pi\) |
0.934447 | + | 0.356102i | \(0.115894\pi\) | |||||||
\(992\) | −21.8564 | − | 5.85641i | −0.693942 | − | 0.185941i | ||||
\(993\) | 60.0000 | 1.90404 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −40.0000 | + | 40.0000i | −1.26809 | + | 1.26809i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −40.9808 | + | 10.9808i | −1.29787 | + | 0.347764i | −0.840646 | − | 0.541585i | \(-0.817824\pi\) |
−0.457228 | + | 0.889350i | \(0.651158\pi\) | |||||||
\(998\) | 25.9808 | + | 15.0000i | 0.822407 | + | 0.474817i | ||||
\(999\) | 20.7846 | − | 12.0000i | 0.657596 | − | 0.379663i |
(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 | 784.2.x.g.165.1 | 4 | ||
7.2 | even | 3 | inner | 784.2.x.g.373.1 | 4 | ||
7.3 | odd | 6 | 784.2.m.c.197.1 | 2 | |||
7.4 | even | 3 | 112.2.m.a.85.1 | yes | 2 | ||
7.5 | odd | 6 | 784.2.x.b.373.1 | 4 | |||
7.6 | odd | 2 | 784.2.x.b.165.1 | 4 | |||
16.13 | even | 4 | inner | 784.2.x.g.557.1 | 4 | ||
28.11 | odd | 6 | 448.2.m.b.113.1 | 2 | |||
56.11 | odd | 6 | 896.2.m.a.225.1 | 2 | |||
56.53 | even | 6 | 896.2.m.d.225.1 | 2 | |||
112.11 | odd | 12 | 896.2.m.a.673.1 | 2 | |||
112.13 | odd | 4 | 784.2.x.b.557.1 | 4 | |||
112.45 | odd | 12 | 784.2.m.c.589.1 | 2 | |||
112.53 | even | 12 | 896.2.m.d.673.1 | 2 | |||
112.61 | odd | 12 | 784.2.x.b.765.1 | 4 | |||
112.67 | odd | 12 | 448.2.m.b.337.1 | 2 | |||
112.93 | even | 12 | inner | 784.2.x.g.765.1 | 4 | ||
112.109 | even | 12 | 112.2.m.a.29.1 | ✓ | 2 | ||
224.67 | odd | 24 | 7168.2.a.i.1.2 | 2 | |||
224.109 | even | 24 | 7168.2.a.q.1.2 | 2 | |||
224.179 | odd | 24 | 7168.2.a.i.1.1 | 2 | |||
224.221 | even | 24 | 7168.2.a.q.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
112.2.m.a.29.1 | ✓ | 2 | 112.109 | even | 12 | ||
112.2.m.a.85.1 | yes | 2 | 7.4 | even | 3 | ||
448.2.m.b.113.1 | 2 | 28.11 | odd | 6 | |||
448.2.m.b.337.1 | 2 | 112.67 | odd | 12 | |||
784.2.m.c.197.1 | 2 | 7.3 | odd | 6 | |||
784.2.m.c.589.1 | 2 | 112.45 | odd | 12 | |||
784.2.x.b.165.1 | 4 | 7.6 | odd | 2 | |||
784.2.x.b.373.1 | 4 | 7.5 | odd | 6 | |||
784.2.x.b.557.1 | 4 | 112.13 | odd | 4 | |||
784.2.x.b.765.1 | 4 | 112.61 | odd | 12 | |||
784.2.x.g.165.1 | 4 | 1.1 | even | 1 | trivial | ||
784.2.x.g.373.1 | 4 | 7.2 | even | 3 | inner | ||
784.2.x.g.557.1 | 4 | 16.13 | even | 4 | inner | ||
784.2.x.g.765.1 | 4 | 112.93 | even | 12 | inner | ||
896.2.m.a.225.1 | 2 | 56.11 | odd | 6 | |||
896.2.m.a.673.1 | 2 | 112.11 | odd | 12 | |||
896.2.m.d.225.1 | 2 | 56.53 | even | 6 | |||
896.2.m.d.673.1 | 2 | 112.53 | even | 12 | |||
7168.2.a.i.1.1 | 2 | 224.179 | odd | 24 | |||
7168.2.a.i.1.2 | 2 | 224.67 | odd | 24 | |||
7168.2.a.q.1.1 | 2 | 224.221 | even | 24 | |||
7168.2.a.q.1.2 | 2 | 224.109 | even | 24 |