Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(41,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bl (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 41.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.41 |
Dual form | 315.2.bl.e.146.1 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(3\) | −1.50000 | + | 0.866025i | −0.866025 | + | 0.500000i | ||||
\(4\) | −1.00000 | + | 1.73205i | −0.500000 | + | 0.866025i | ||||
\(5\) | −0.500000 | + | 0.866025i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.50000 | − | 0.866025i | −0.944911 | − | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.50000 | − | 2.59808i | 0.500000 | − | 0.866025i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.50000 | − | 0.866025i | 0.452267 | − | 0.261116i | −0.256520 | − | 0.966539i | \(-0.582576\pi\) |
0.708787 | + | 0.705422i | \(0.249243\pi\) | |||||||
\(12\) | − | 3.46410i | − | 1.00000i | ||||||
\(13\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 1.73205i | − | 0.447214i | ||||||
\(16\) | −2.00000 | − | 3.46410i | −0.500000 | − | 0.866025i | ||||
\(17\) | −6.00000 | −1.45521 | −0.727607 | − | 0.685994i | \(-0.759367\pi\) | ||||
−0.727607 | + | 0.685994i | \(0.759367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 6.92820i | − | 1.58944i | −0.606977 | − | 0.794719i | \(-0.707618\pi\) | ||
0.606977 | − | 0.794719i | \(-0.292382\pi\) | |||||||
\(20\) | −1.00000 | − | 1.73205i | −0.223607 | − | 0.387298i | ||||
\(21\) | 4.50000 | − | 0.866025i | 0.981981 | − | 0.188982i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.00000 | + | 1.73205i | 0.625543 | + | 0.361158i | 0.779024 | − | 0.626994i | \(-0.215715\pi\) |
−0.153481 | + | 0.988152i | \(0.549048\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | − | 0.866025i | −0.100000 | − | 0.173205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 1.00000i | ||||||||
\(28\) | 4.00000 | − | 3.46410i | 0.755929 | − | 0.654654i | ||||
\(29\) | −7.50000 | + | 4.33013i | −1.39272 | + | 0.804084i | −0.993615 | − | 0.112823i | \(-0.964011\pi\) |
−0.399100 | + | 0.916907i | \(0.630677\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.00000 | + | 1.73205i | 0.538816 | + | 0.311086i | 0.744599 | − | 0.667512i | \(-0.232641\pi\) |
−0.205783 | + | 0.978598i | \(0.565974\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.50000 | + | 2.59808i | −0.261116 | + | 0.452267i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.00000 | − | 1.73205i | 0.338062 | − | 0.292770i | ||||
\(36\) | 3.00000 | + | 5.19615i | 0.500000 | + | 0.866025i | ||||
\(37\) | −8.00000 | −1.31519 | −0.657596 | − | 0.753371i | \(-0.728427\pi\) | ||||
−0.657596 | + | 0.753371i | \(0.728427\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.00000 | + | 5.19615i | −0.468521 | + | 0.811503i | −0.999353 | − | 0.0359748i | \(-0.988546\pi\) |
0.530831 | + | 0.847477i | \(0.321880\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −5.00000 | − | 8.66025i | −0.762493 | − | 1.32068i | −0.941562 | − | 0.336840i | \(-0.890642\pi\) |
0.179069 | − | 0.983836i | \(-0.442691\pi\) | |||||||
\(44\) | 3.46410i | 0.522233i | ||||||||
\(45\) | 1.50000 | + | 2.59808i | 0.223607 | + | 0.387298i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.50000 | − | 7.79423i | −0.656392 | − | 1.13691i | −0.981543 | − | 0.191243i | \(-0.938748\pi\) |
0.325150 | − | 0.945662i | \(-0.394585\pi\) | |||||||
\(48\) | 6.00000 | + | 3.46410i | 0.866025 | + | 0.500000i | ||||
\(49\) | 5.50000 | + | 4.33013i | 0.785714 | + | 0.618590i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.00000 | − | 5.19615i | 1.26025 | − | 0.727607i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 13.8564i | 1.90332i | 0.307148 | + | 0.951662i | \(0.400625\pi\) | ||||
−0.307148 | + | 0.951662i | \(0.599375\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.73205i | 0.233550i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | + | 10.3923i | 0.794719 | + | 1.37649i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(60\) | 3.00000 | + | 1.73205i | 0.387298 | + | 0.223607i | ||||
\(61\) | 3.00000 | − | 1.73205i | 0.384111 | − | 0.221766i | −0.295495 | − | 0.955344i | \(-0.595484\pi\) |
0.679605 | + | 0.733578i | \(0.262151\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.00000 | + | 5.19615i | −0.755929 | + | 0.654654i | ||||
\(64\) | 8.00000 | 1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | + | 6.92820i | −0.488678 | + | 0.846415i | −0.999915 | − | 0.0130248i | \(-0.995854\pi\) |
0.511237 | + | 0.859440i | \(0.329187\pi\) | |||||||
\(68\) | 6.00000 | − | 10.3923i | 0.727607 | − | 1.26025i | ||||
\(69\) | −6.00000 | −0.722315 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 1.73205i | − | 0.205557i | −0.994704 | − | 0.102778i | \(-0.967227\pi\) | ||
0.994704 | − | 0.102778i | \(-0.0327732\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.66025i | − | 1.01361i | −0.862062 | − | 0.506803i | \(-0.830827\pi\) | ||
0.862062 | − | 0.506803i | \(-0.169173\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.50000 | + | 0.866025i | 0.173205 | + | 0.100000i | ||||
\(76\) | 12.0000 | + | 6.92820i | 1.37649 | + | 0.794719i | ||||
\(77\) | −4.50000 | + | 0.866025i | −0.512823 | + | 0.0986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.500000 | + | 0.866025i | 0.0562544 | + | 0.0974355i | 0.892781 | − | 0.450490i | \(-0.148751\pi\) |
−0.836527 | + | 0.547926i | \(0.815418\pi\) | |||||||
\(80\) | 4.00000 | 0.447214 | ||||||||
\(81\) | −4.50000 | − | 7.79423i | −0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.50000 | + | 7.79423i | 0.493939 | + | 0.855528i | 0.999976 | − | 0.00698436i | \(-0.00222321\pi\) |
−0.506036 | + | 0.862512i | \(0.668890\pi\) | |||||||
\(84\) | −3.00000 | + | 8.66025i | −0.327327 | + | 0.944911i | ||||
\(85\) | 3.00000 | − | 5.19615i | 0.325396 | − | 0.563602i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 7.50000 | − | 12.9904i | 0.804084 | − | 1.39272i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | + | 3.46410i | −0.625543 | + | 0.361158i | ||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.00000 | + | 3.46410i | 0.615587 | + | 0.355409i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.50000 | − | 0.866025i | 0.152302 | − | 0.0879316i | −0.421912 | − | 0.906637i | \(-0.638641\pi\) |
0.574214 | + | 0.818705i | \(0.305308\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 5.19615i | − | 0.522233i | ||||||
\(100\) | 2.00000 | 0.200000 | ||||||||
\(101\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −10.5000 | − | 6.06218i | −1.03460 | − | 0.597324i | −0.116298 | − | 0.993214i | \(-0.537103\pi\) |
−0.918298 | + | 0.395890i | \(0.870436\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.50000 | + | 4.33013i | −0.146385 | + | 0.422577i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.92820i | 0.669775i | 0.942258 | + | 0.334887i | \(0.108698\pi\) | ||||
−0.942258 | + | 0.334887i | \(0.891302\pi\) | |||||||
\(108\) | −9.00000 | − | 5.19615i | −0.866025 | − | 0.500000i | ||||
\(109\) | −11.0000 | −1.05361 | −0.526804 | − | 0.849987i | \(-0.676610\pi\) | ||||
−0.526804 | + | 0.849987i | \(0.676610\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.0000 | − | 6.92820i | 1.13899 | − | 0.657596i | ||||
\(112\) | 2.00000 | + | 10.3923i | 0.188982 | + | 0.981981i | ||||
\(113\) | −9.00000 | − | 5.19615i | −0.846649 | − | 0.488813i | 0.0128699 | − | 0.999917i | \(-0.495903\pi\) |
−0.859519 | + | 0.511104i | \(0.829237\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00000 | + | 1.73205i | −0.279751 | + | 0.161515i | ||||
\(116\) | − | 17.3205i | − | 1.60817i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.0000 | + | 5.19615i | 1.37505 | + | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | + | 6.92820i | −0.363636 | + | 0.629837i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 10.3923i | − | 0.937043i | ||||||
\(124\) | −6.00000 | + | 3.46410i | −0.538816 | + | 0.311086i | ||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.0000 | + | 8.66025i | 1.32068 | + | 0.762493i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.00000 | + | 5.19615i | −0.262111 | + | 0.453990i | −0.966803 | − | 0.255524i | \(-0.917752\pi\) |
0.704692 | + | 0.709514i | \(0.251085\pi\) | |||||||
\(132\) | −3.00000 | − | 5.19615i | −0.261116 | − | 0.452267i | ||||
\(133\) | −6.00000 | + | 17.3205i | −0.520266 | + | 1.50188i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −4.50000 | − | 2.59808i | −0.387298 | − | 0.223607i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 15.0000 | − | 8.66025i | 1.28154 | − | 0.739895i | 0.304407 | − | 0.952542i | \(-0.401542\pi\) |
0.977129 | + | 0.212647i | \(0.0682083\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.0000 | − | 8.66025i | −1.27228 | − | 0.734553i | −0.296866 | − | 0.954919i | \(-0.595942\pi\) |
−0.975417 | + | 0.220366i | \(0.929275\pi\) | |||||||
\(140\) | 1.00000 | + | 5.19615i | 0.0845154 | + | 0.439155i | ||||
\(141\) | 13.5000 | + | 7.79423i | 1.13691 | + | 0.656392i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −12.0000 | −1.00000 | ||||||||
\(145\) | − | 8.66025i | − | 0.719195i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −12.0000 | − | 1.73205i | −0.989743 | − | 0.142857i | ||||
\(148\) | 8.00000 | − | 13.8564i | 0.657596 | − | 1.13899i | ||||
\(149\) | 4.50000 | + | 2.59808i | 0.368654 | + | 0.212843i | 0.672870 | − | 0.739760i | \(-0.265061\pi\) |
−0.304216 | + | 0.952603i | \(0.598394\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.00000 | + | 6.92820i | 0.325515 | + | 0.563809i | 0.981617 | − | 0.190864i | \(-0.0611289\pi\) |
−0.656101 | + | 0.754673i | \(0.727796\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −9.00000 | + | 15.5885i | −0.727607 | + | 1.26025i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.00000 | + | 1.73205i | −0.240966 | + | 0.139122i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.50000 | + | 0.866025i | 0.119713 | + | 0.0691164i | 0.558661 | − | 0.829396i | \(-0.311315\pi\) |
−0.438948 | + | 0.898513i | \(0.644649\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.0000 | − | 20.7846i | −0.951662 | − | 1.64833i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −6.00000 | − | 6.92820i | −0.472866 | − | 0.546019i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.0000 | 1.09656 | 0.548282 | − | 0.836293i | \(-0.315282\pi\) | ||||
0.548282 | + | 0.836293i | \(0.315282\pi\) | |||||||
\(164\) | −6.00000 | − | 10.3923i | −0.468521 | − | 0.811503i | ||||
\(165\) | −1.50000 | − | 2.59808i | −0.116775 | − | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.50000 | − | 11.2583i | −0.500000 | − | 0.866025i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −18.0000 | − | 10.3923i | −1.37649 | − | 0.794719i | ||||
\(172\) | 20.0000 | 1.52499 | ||||||||
\(173\) | 1.50000 | + | 2.59808i | 0.114043 | + | 0.197528i | 0.917397 | − | 0.397974i | \(-0.130287\pi\) |
−0.803354 | + | 0.595502i | \(0.796953\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.500000 | + | 2.59808i | 0.0377964 | + | 0.196396i | ||||
\(176\) | −6.00000 | − | 3.46410i | −0.452267 | − | 0.261116i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 15.5885i | − | 1.16514i | −0.812782 | − | 0.582568i | \(-0.802048\pi\) | ||
0.812782 | − | 0.582568i | \(-0.197952\pi\) | |||||||
\(180\) | −6.00000 | −0.447214 | ||||||||
\(181\) | 20.7846i | 1.54491i | 0.635071 | + | 0.772454i | \(0.280971\pi\) | ||||
−0.635071 | + | 0.772454i | \(0.719029\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.00000 | + | 5.19615i | −0.221766 | + | 0.384111i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.00000 | − | 6.92820i | 0.294086 | − | 0.509372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | + | 5.19615i | −0.658145 | + | 0.379980i | ||||
\(188\) | 18.0000 | 1.31278 | ||||||||
\(189\) | 4.50000 | − | 12.9904i | 0.327327 | − | 0.944911i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.50000 | − | 0.866025i | 0.108536 | − | 0.0626634i | −0.444749 | − | 0.895655i | \(-0.646707\pi\) |
0.553285 | + | 0.832992i | \(0.313374\pi\) | |||||||
\(192\) | −12.0000 | + | 6.92820i | −0.866025 | + | 0.500000i | ||||
\(193\) | −2.00000 | + | 3.46410i | −0.143963 | + | 0.249351i | −0.928986 | − | 0.370116i | \(-0.879318\pi\) |
0.785022 | + | 0.619467i | \(0.212651\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −13.0000 | + | 5.19615i | −0.928571 | + | 0.371154i | ||||
\(197\) | − | 3.46410i | − | 0.246807i | −0.992357 | − | 0.123404i | \(-0.960619\pi\) | ||
0.992357 | − | 0.123404i | \(-0.0393809\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.3923i | 0.736691i | 0.929689 | + | 0.368345i | \(0.120076\pi\) | ||||
−0.929689 | + | 0.368345i | \(0.879924\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 13.8564i | − | 0.977356i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 22.5000 | − | 4.33013i | 1.57919 | − | 0.303915i | ||||
\(204\) | 20.7846i | 1.45521i | ||||||||
\(205\) | −3.00000 | − | 5.19615i | −0.209529 | − | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.00000 | − | 5.19615i | 0.625543 | − | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.00000 | − | 10.3923i | −0.415029 | − | 0.718851i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.500000 | + | 0.866025i | −0.0344214 | + | 0.0596196i | −0.882723 | − | 0.469894i | \(-0.844292\pi\) |
0.848301 | + | 0.529514i | \(0.177626\pi\) | |||||||
\(212\) | −24.0000 | − | 13.8564i | −1.64833 | − | 0.951662i | ||||
\(213\) | 1.50000 | + | 2.59808i | 0.102778 | + | 0.178017i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 10.0000 | 0.681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.00000 | − | 6.92820i | −0.407307 | − | 0.470317i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.50000 | + | 12.9904i | 0.506803 | + | 0.877809i | ||||
\(220\) | −3.00000 | − | 1.73205i | −0.202260 | − | 0.116775i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.00000 | − | 1.73205i | 0.200895 | − | 0.115987i | −0.396178 | − | 0.918174i | \(-0.629664\pi\) |
0.597073 | + | 0.802187i | \(0.296330\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | −0.200000 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.00000 | + | 10.3923i | 0.398234 | + | 0.689761i | 0.993508 | − | 0.113761i | \(-0.0362899\pi\) |
−0.595274 | + | 0.803523i | \(0.702957\pi\) | |||||||
\(228\) | −24.0000 | −1.58944 | ||||||||
\(229\) | 24.0000 | + | 13.8564i | 1.58596 | + | 0.915657i | 0.993962 | + | 0.109721i | \(0.0349957\pi\) |
0.592002 | + | 0.805936i | \(0.298338\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | − | 5.19615i | 0.394771 | − | 0.341882i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.46410i | 0.226941i | 0.993541 | + | 0.113470i | \(0.0361967\pi\) | ||||
−0.993541 | + | 0.113470i | \(0.963803\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.00000 | 0.587095 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.50000 | − | 0.866025i | −0.0974355 | − | 0.0562544i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.50000 | − | 4.33013i | −0.485135 | − | 0.280093i | 0.237419 | − | 0.971407i | \(-0.423699\pi\) |
−0.722554 | + | 0.691315i | \(0.757032\pi\) | |||||||
\(240\) | −6.00000 | + | 3.46410i | −0.387298 | + | 0.223607i | ||||
\(241\) | 9.00000 | − | 5.19615i | 0.579741 | − | 0.334714i | −0.181289 | − | 0.983430i | \(-0.558027\pi\) |
0.761030 | + | 0.648716i | \(0.224694\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 13.5000 | + | 7.79423i | 0.866025 | + | 0.500000i | ||||
\(244\) | 6.92820i | 0.443533i | ||||||||
\(245\) | −6.50000 | + | 2.59808i | −0.415270 | + | 0.165985i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.5000 | − | 7.79423i | −0.855528 | − | 0.493939i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.0000 | −1.13615 | −0.568075 | − | 0.822977i | \(-0.692312\pi\) | ||||
−0.568075 | + | 0.822977i | \(0.692312\pi\) | |||||||
\(252\) | −3.00000 | − | 15.5885i | −0.188982 | − | 0.981981i | ||||
\(253\) | 6.00000 | 0.377217 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 10.3923i | 0.650791i | ||||||||
\(256\) | −8.00000 | + | 13.8564i | −0.500000 | + | 0.866025i | ||||
\(257\) | −1.50000 | + | 2.59808i | −0.0935674 | + | 0.162064i | −0.909010 | − | 0.416775i | \(-0.863160\pi\) |
0.815442 | + | 0.578838i | \(0.196494\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.0000 | + | 6.92820i | 1.24274 | + | 0.430498i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 25.9808i | 1.60817i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.0000 | − | 8.66025i | 0.924940 | − | 0.534014i | 0.0397320 | − | 0.999210i | \(-0.487350\pi\) |
0.885208 | + | 0.465196i | \(0.154016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −12.0000 | − | 6.92820i | −0.737154 | − | 0.425596i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.00000 | − | 5.19615i | 0.550791 | − | 0.317999i | ||||
\(268\) | −8.00000 | − | 13.8564i | −0.488678 | − | 0.846415i | ||||
\(269\) | 24.0000 | 1.46331 | 0.731653 | − | 0.681677i | \(-0.238749\pi\) | ||||
0.731653 | + | 0.681677i | \(0.238749\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 17.3205i | − | 1.05215i | −0.850439 | − | 0.526073i | \(-0.823664\pi\) | ||
0.850439 | − | 0.526073i | \(-0.176336\pi\) | |||||||
\(272\) | 12.0000 | + | 20.7846i | 0.727607 | + | 1.26025i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.50000 | − | 0.866025i | −0.0904534 | − | 0.0522233i | ||||
\(276\) | 6.00000 | − | 10.3923i | 0.361158 | − | 0.625543i | ||||
\(277\) | 5.00000 | + | 8.66025i | 0.300421 | + | 0.520344i | 0.976231 | − | 0.216731i | \(-0.0695395\pi\) |
−0.675810 | + | 0.737075i | \(0.736206\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 9.00000 | − | 5.19615i | 0.538816 | − | 0.311086i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.5000 | + | 11.2583i | −1.16327 | + | 0.671616i | −0.952086 | − | 0.305830i | \(-0.901066\pi\) |
−0.211186 | + | 0.977446i | \(0.567733\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −10.5000 | − | 6.06218i | −0.624160 | − | 0.360359i | 0.154327 | − | 0.988020i | \(-0.450679\pi\) |
−0.778487 | + | 0.627661i | \(0.784012\pi\) | |||||||
\(284\) | 3.00000 | + | 1.73205i | 0.178017 | + | 0.102778i | ||||
\(285\) | −12.0000 | −0.710819 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 12.0000 | − | 10.3923i | 0.708338 | − | 0.613438i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000 | 1.11765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.50000 | + | 2.59808i | −0.0879316 | + | 0.152302i | ||||
\(292\) | 15.0000 | + | 8.66025i | 0.877809 | + | 0.506803i | ||||
\(293\) | 4.50000 | − | 7.79423i | 0.262893 | − | 0.455344i | −0.704117 | − | 0.710084i | \(-0.748657\pi\) |
0.967009 | + | 0.254741i | \(0.0819901\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.50000 | + | 7.79423i | 0.261116 | + | 0.452267i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −3.00000 | + | 1.73205i | −0.173205 | + | 0.100000i | ||||
\(301\) | 5.00000 | + | 25.9808i | 0.288195 | + | 1.49751i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −24.0000 | + | 13.8564i | −1.37649 | + | 0.794719i | ||||
\(305\) | 3.46410i | 0.198354i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.46410i | − | 0.197707i | −0.995102 | − | 0.0988534i | \(-0.968483\pi\) | ||
0.995102 | − | 0.0988534i | \(-0.0315175\pi\) | |||||||
\(308\) | 3.00000 | − | 8.66025i | 0.170941 | − | 0.493464i | ||||
\(309\) | 21.0000 | 1.19465 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.00000 | + | 15.5885i | −0.510343 | + | 0.883940i | 0.489585 | + | 0.871956i | \(0.337148\pi\) |
−0.999928 | + | 0.0119847i | \(0.996185\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.5000 | + | 7.79423i | −0.763065 | + | 0.440556i | −0.830395 | − | 0.557175i | \(-0.811885\pi\) |
0.0673300 | + | 0.997731i | \(0.478552\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.50000 | − | 7.79423i | −0.0845154 | − | 0.439155i | ||||
\(316\) | −2.00000 | −0.112509 | ||||||||
\(317\) | 3.00000 | − | 1.73205i | 0.168497 | − | 0.0972817i | −0.413380 | − | 0.910559i | \(-0.635652\pi\) |
0.581877 | + | 0.813277i | \(0.302319\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.50000 | + | 12.9904i | −0.419919 | + | 0.727322i | ||||
\(320\) | −4.00000 | + | 6.92820i | −0.223607 | + | 0.387298i | ||||
\(321\) | −6.00000 | − | 10.3923i | −0.334887 | − | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 41.5692i | 2.31297i | ||||||||
\(324\) | 18.0000 | 1.00000 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 16.5000 | − | 9.52628i | 0.912452 | − | 0.526804i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 4.50000 | + | 23.3827i | 0.248093 | + | 1.28913i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.50000 | + | 14.7224i | 0.467202 | + | 0.809218i | 0.999298 | − | 0.0374662i | \(-0.0119287\pi\) |
−0.532096 | + | 0.846684i | \(0.678595\pi\) | |||||||
\(332\) | −18.0000 | −0.987878 | ||||||||
\(333\) | −12.0000 | + | 20.7846i | −0.657596 | + | 1.13899i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.00000 | − | 6.92820i | −0.218543 | − | 0.378528i | ||||
\(336\) | −12.0000 | − | 13.8564i | −0.654654 | − | 0.755929i | ||||
\(337\) | 13.0000 | − | 22.5167i | 0.708155 | − | 1.22656i | −0.257386 | − | 0.966309i | \(-0.582861\pi\) |
0.965541 | − | 0.260252i | \(-0.0838056\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 18.0000 | 0.977626 | ||||||||
\(340\) | 6.00000 | + | 10.3923i | 0.325396 | + | 0.563602i | ||||
\(341\) | 6.00000 | 0.324918 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | − | 15.5885i | −0.539949 | − | 0.841698i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.00000 | − | 5.19615i | 0.161515 | − | 0.279751i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 24.0000 | + | 13.8564i | 1.28839 | + | 0.743851i | 0.978367 | − | 0.206879i | \(-0.0663306\pi\) |
0.310021 | + | 0.950730i | \(0.399664\pi\) | |||||||
\(348\) | 15.0000 | + | 25.9808i | 0.804084 | + | 1.39272i | ||||
\(349\) | 15.0000 | − | 8.66025i | 0.802932 | − | 0.463573i | −0.0415636 | − | 0.999136i | \(-0.513234\pi\) |
0.844495 | + | 0.535563i | \(0.179901\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.5000 | + | 18.1865i | 0.558859 | + | 0.967972i | 0.997592 | + | 0.0693543i | \(0.0220939\pi\) |
−0.438733 | + | 0.898617i | \(0.644573\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.50000 | + | 0.866025i | 0.0796117 | + | 0.0459639i | ||||
\(356\) | 6.00000 | − | 10.3923i | 0.317999 | − | 0.550791i | ||||
\(357\) | −27.0000 | + | 5.19615i | −1.42899 | + | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 31.1769i | − | 1.64545i | −0.568436 | − | 0.822727i | \(-0.692451\pi\) | ||
0.568436 | − | 0.822727i | \(-0.307549\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −29.0000 | −1.52632 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 13.8564i | − | 0.727273i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.50000 | + | 4.33013i | 0.392568 | + | 0.226649i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.00000 | − | 5.19615i | 0.469796 | − | 0.271237i | −0.246358 | − | 0.969179i | \(-0.579234\pi\) |
0.716154 | + | 0.697942i | \(0.245901\pi\) | |||||||
\(368\) | − | 13.8564i | − | 0.722315i | ||||||
\(369\) | 9.00000 | + | 15.5885i | 0.468521 | + | 0.811503i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.0000 | − | 34.6410i | 0.623009 | − | 1.79847i | ||||
\(372\) | 6.00000 | − | 10.3923i | 0.311086 | − | 0.538816i | ||||
\(373\) | 11.0000 | − | 19.0526i | 0.569558 | − | 0.986504i | −0.427051 | − | 0.904227i | \(-0.640448\pi\) |
0.996610 | − | 0.0822766i | \(-0.0262191\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.50000 | + | 0.866025i | −0.0774597 | + | 0.0447214i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0000 | −1.18143 | −0.590715 | − | 0.806880i | \(-0.701154\pi\) | ||||
−0.590715 | + | 0.806880i | \(0.701154\pi\) | |||||||
\(380\) | −12.0000 | + | 6.92820i | −0.615587 | + | 0.355409i | ||||
\(381\) | −3.00000 | + | 1.73205i | −0.153695 | + | 0.0887357i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 7.50000 | − | 12.9904i | 0.383232 | − | 0.663777i | −0.608290 | − | 0.793715i | \(-0.708144\pi\) |
0.991522 | + | 0.129937i | \(0.0414776\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.50000 | − | 4.33013i | 0.0764471 | − | 0.220684i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −30.0000 | −1.52499 | ||||||||
\(388\) | 3.46410i | 0.175863i | ||||||||
\(389\) | −28.5000 | + | 16.4545i | −1.44501 | + | 0.834275i | −0.998178 | − | 0.0603436i | \(-0.980780\pi\) |
−0.446830 | + | 0.894619i | \(0.647447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.0000 | − | 10.3923i | −0.910299 | − | 0.525561i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 10.3923i | − | 0.524222i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.00000 | −0.0503155 | ||||||||
\(396\) | 9.00000 | + | 5.19615i | 0.452267 | + | 0.261116i | ||||
\(397\) | 29.4449i | 1.47780i | 0.673818 | + | 0.738898i | \(0.264653\pi\) | ||||
−0.673818 | + | 0.738898i | \(0.735347\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.00000 | − | 31.1769i | −0.300376 | − | 1.56080i | ||||
\(400\) | −2.00000 | + | 3.46410i | −0.100000 | + | 0.173205i | ||||
\(401\) | −22.5000 | − | 12.9904i | −1.12360 | − | 0.648709i | −0.181280 | − | 0.983432i | \(-0.558024\pi\) |
−0.942317 | + | 0.334723i | \(0.891357\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.00000 | 0.447214 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −12.0000 | + | 6.92820i | −0.594818 | + | 0.343418i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9.00000 | − | 5.19615i | −0.445021 | − | 0.256933i | 0.260704 | − | 0.965419i | \(-0.416045\pi\) |
−0.705725 | + | 0.708486i | \(0.749379\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −15.0000 | + | 25.9808i | −0.739895 | + | 1.28154i | ||||
\(412\) | 21.0000 | − | 12.1244i | 1.03460 | − | 0.597324i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | −0.441793 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 30.0000 | 1.46911 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.00000 | + | 10.3923i | −0.293119 | + | 0.507697i | −0.974546 | − | 0.224189i | \(-0.928027\pi\) |
0.681426 | + | 0.731887i | \(0.261360\pi\) | |||||||
\(420\) | −6.00000 | − | 6.92820i | −0.292770 | − | 0.338062i | ||||
\(421\) | −11.5000 | − | 19.9186i | −0.560476 | − | 0.970772i | −0.997455 | − | 0.0713008i | \(-0.977285\pi\) |
0.436979 | − | 0.899472i | \(-0.356048\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −27.0000 | −1.31278 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | + | 5.19615i | 0.145521 | + | 0.252050i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.00000 | + | 1.73205i | −0.435541 | + | 0.0838198i | ||||
\(428\) | −12.0000 | − | 6.92820i | −0.580042 | − | 0.334887i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 31.1769i | 1.50174i | 0.660451 | + | 0.750870i | \(0.270365\pi\) | ||||
−0.660451 | + | 0.750870i | \(0.729635\pi\) | |||||||
\(432\) | 18.0000 | − | 10.3923i | 0.866025 | − | 0.500000i | ||||
\(433\) | − | 6.92820i | − | 0.332948i | −0.986046 | − | 0.166474i | \(-0.946762\pi\) | ||
0.986046 | − | 0.166474i | \(-0.0532382\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 7.50000 | + | 12.9904i | 0.359597 | + | 0.622841i | ||||
\(436\) | 11.0000 | − | 19.0526i | 0.526804 | − | 0.912452i | ||||
\(437\) | 12.0000 | − | 20.7846i | 0.574038 | − | 0.994263i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.00000 | − | 1.73205i | 0.143182 | − | 0.0826663i | −0.426698 | − | 0.904394i | \(-0.640323\pi\) |
0.569880 | + | 0.821728i | \(0.306990\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 19.5000 | − | 7.79423i | 0.928571 | − | 0.371154i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(444\) | 27.7128i | 1.31519i | ||||||||
\(445\) | 3.00000 | − | 5.19615i | 0.142214 | − | 0.246321i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.00000 | −0.425685 | ||||||||
\(448\) | −20.0000 | − | 6.92820i | −0.944911 | − | 0.327327i | ||||
\(449\) | − | 5.19615i | − | 0.245222i | −0.992455 | − | 0.122611i | \(-0.960873\pi\) | ||
0.992455 | − | 0.122611i | \(-0.0391267\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3923i | 0.489355i | ||||||||
\(452\) | 18.0000 | − | 10.3923i | 0.846649 | − | 0.488813i | ||||
\(453\) | −12.0000 | − | 6.92820i | −0.563809 | − | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.00000 | − | 13.8564i | −0.374224 | − | 0.648175i | 0.615986 | − | 0.787757i | \(-0.288758\pi\) |
−0.990211 | + | 0.139581i | \(0.955424\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 31.1769i | − | 1.45521i | ||||||
\(460\) | − | 6.92820i | − | 0.323029i | ||||||
\(461\) | −12.0000 | − | 20.7846i | −0.558896 | − | 0.968036i | −0.997589 | − | 0.0693989i | \(-0.977892\pi\) |
0.438693 | − | 0.898637i | \(-0.355441\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00000 | − | 3.46410i | 0.0929479 | − | 0.160990i | −0.815802 | − | 0.578331i | \(-0.803704\pi\) |
0.908750 | + | 0.417340i | \(0.137038\pi\) | |||||||
\(464\) | 30.0000 | + | 17.3205i | 1.39272 | + | 0.804084i | ||||
\(465\) | 3.00000 | − | 5.19615i | 0.139122 | − | 0.240966i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −27.0000 | −1.24941 | −0.624705 | − | 0.780860i | \(-0.714781\pi\) | ||||
−0.624705 | + | 0.780860i | \(0.714781\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16.0000 | − | 13.8564i | 0.738811 | − | 0.639829i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.00000 | −0.138233 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −15.0000 | − | 8.66025i | −0.689701 | − | 0.398199i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −6.00000 | + | 3.46410i | −0.275299 | + | 0.158944i | ||||
\(476\) | −24.0000 | + | 20.7846i | −1.10004 | + | 0.952661i | ||||
\(477\) | 36.0000 | + | 20.7846i | 1.64833 | + | 0.951662i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −18.0000 | − | 31.1769i | −0.822441 | − | 1.42451i | −0.903859 | − | 0.427830i | \(-0.859278\pi\) |
0.0814184 | − | 0.996680i | \(-0.474055\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 15.0000 | + | 5.19615i | 0.682524 | + | 0.236433i | ||||
\(484\) | −8.00000 | − | 13.8564i | −0.363636 | − | 0.629837i | ||||
\(485\) | 1.73205i | 0.0786484i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.00000 | −0.0906287 | −0.0453143 | − | 0.998973i | \(-0.514429\pi\) | ||||
−0.0453143 | + | 0.998973i | \(0.514429\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −21.0000 | + | 12.1244i | −0.949653 | + | 0.548282i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.00000 | + | 1.73205i | 0.135388 | + | 0.0781664i | 0.566164 | − | 0.824292i | \(-0.308427\pi\) |
−0.430776 | + | 0.902459i | \(0.641760\pi\) | |||||||
\(492\) | 18.0000 | + | 10.3923i | 0.811503 | + | 0.468521i | ||||
\(493\) | 45.0000 | − | 25.9808i | 2.02670 | − | 1.17011i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.50000 | + | 2.59808i | 0.202260 | + | 0.116775i | ||||
\(496\) | − | 13.8564i | − | 0.622171i | ||||||
\(497\) | −1.50000 | + | 4.33013i | −0.0672842 | + | 0.194233i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.0000 | − | 17.3205i | 0.447661 | − | 0.775372i | −0.550572 | − | 0.834788i | \(-0.685590\pi\) |
0.998233 | + | 0.0594153i | \(0.0189236\pi\) | |||||||
\(500\) | −1.00000 | + | 1.73205i | −0.0447214 | + | 0.0774597i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −39.0000 | −1.73892 | −0.869462 | − | 0.494000i | \(-0.835534\pi\) | ||||
−0.869462 | + | 0.494000i | \(0.835534\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 19.5000 | + | 11.2583i | 0.866025 | + | 0.500000i | ||||
\(508\) | −2.00000 | + | 3.46410i | −0.0887357 | + | 0.153695i | ||||
\(509\) | −21.0000 | + | 36.3731i | −0.930809 | + | 1.61221i | −0.148866 | + | 0.988857i | \(0.547562\pi\) |
−0.781943 | + | 0.623350i | \(0.785771\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.50000 | + | 21.6506i | −0.331780 | + | 0.957768i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 36.0000 | 1.58944 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 10.5000 | − | 6.06218i | 0.462685 | − | 0.267131i | ||||
\(516\) | −30.0000 | + | 17.3205i | −1.32068 | + | 0.762493i | ||||
\(517\) | −13.5000 | − | 7.79423i | −0.593729 | − | 0.342790i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.50000 | − | 2.59808i | −0.197528 | − | 0.114043i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.0000 | −0.788594 | −0.394297 | − | 0.918983i | \(-0.629012\pi\) | ||||
−0.394297 | + | 0.918983i | \(0.629012\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 12.1244i | 0.530161i | 0.964226 | + | 0.265081i | \(0.0853985\pi\) | ||||
−0.964226 | + | 0.265081i | \(0.914601\pi\) | |||||||
\(524\) | −6.00000 | − | 10.3923i | −0.262111 | − | 0.453990i | ||||
\(525\) | −3.00000 | − | 3.46410i | −0.130931 | − | 0.151186i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.0000 | − | 10.3923i | −0.784092 | − | 0.452696i | ||||
\(528\) | 12.0000 | 0.522233 | ||||||||
\(529\) | −5.50000 | − | 9.52628i | −0.239130 | − | 0.414186i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −24.0000 | − | 27.7128i | −1.04053 | − | 1.20150i | ||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.00000 | − | 3.46410i | −0.259403 | − | 0.149766i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 13.5000 | + | 23.3827i | 0.582568 | + | 1.00904i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 12.0000 | + | 1.73205i | 0.516877 | + | 0.0746047i | ||||
\(540\) | 9.00000 | − | 5.19615i | 0.387298 | − | 0.223607i | ||||
\(541\) | −10.0000 | −0.429934 | −0.214967 | − | 0.976621i | \(-0.568964\pi\) | ||||
−0.214967 | + | 0.976621i | \(0.568964\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −18.0000 | − | 31.1769i | −0.772454 | − | 1.33793i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 5.50000 | − | 9.52628i | 0.235594 | − | 0.408061i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.00000 | − | 12.1244i | −0.299298 | − | 0.518400i | 0.676677 | − | 0.736280i | \(-0.263419\pi\) |
−0.975976 | + | 0.217880i | \(0.930086\pi\) | |||||||
\(548\) | 34.6410i | 1.47979i | ||||||||
\(549\) | − | 10.3923i | − | 0.443533i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 30.0000 | + | 51.9615i | 1.27804 | + | 2.21364i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −0.500000 | − | 2.59808i | −0.0212622 | − | 0.110481i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 13.8564i | 0.588172i | ||||||||
\(556\) | 30.0000 | − | 17.3205i | 1.27228 | − | 0.734553i | ||||
\(557\) | 10.3923i | 0.440336i | 0.975462 | + | 0.220168i | \(0.0706606\pi\) | ||||
−0.975462 | + | 0.220168i | \(0.929339\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −10.0000 | − | 3.46410i | −0.422577 | − | 0.146385i | ||||
\(561\) | 9.00000 | − | 15.5885i | 0.379980 | − | 0.658145i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.50000 | + | 12.9904i | −0.316087 | + | 0.547479i | −0.979668 | − | 0.200625i | \(-0.935703\pi\) |
0.663581 | + | 0.748105i | \(0.269036\pi\) | |||||||
\(564\) | −27.0000 | + | 15.5885i | −1.13691 | + | 0.656392i | ||||
\(565\) | 9.00000 | − | 5.19615i | 0.378633 | − | 0.218604i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 4.50000 | + | 23.3827i | 0.188982 | + | 0.981981i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −31.5000 | + | 18.1865i | −1.32055 | + | 0.762419i | −0.983816 | − | 0.179181i | \(-0.942655\pi\) |
−0.336733 | + | 0.941600i | \(0.609322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.50000 | − | 11.2583i | 0.272017 | − | 0.471146i | −0.697362 | − | 0.716720i | \(-0.745643\pi\) |
0.969378 | + | 0.245573i | \(0.0789761\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.50000 | + | 2.59808i | −0.0626634 | + | 0.108536i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 3.46410i | − | 0.144463i | ||||||
\(576\) | 12.0000 | − | 20.7846i | 0.500000 | − | 0.866025i | ||||
\(577\) | 39.8372i | 1.65844i | 0.558920 | + | 0.829222i | \(0.311216\pi\) | ||||
−0.558920 | + | 0.829222i | \(0.688784\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 6.92820i | − | 0.287926i | ||||||
\(580\) | 15.0000 | + | 8.66025i | 0.622841 | + | 0.359597i | ||||
\(581\) | −4.50000 | − | 23.3827i | −0.186691 | − | 0.970077i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 12.0000 | + | 20.7846i | 0.496989 | + | 0.860811i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.00000 | − | 10.3923i | −0.247647 | − | 0.428936i | 0.715226 | − | 0.698893i | \(-0.246324\pi\) |
−0.962872 | + | 0.269957i | \(0.912990\pi\) | |||||||
\(588\) | 15.0000 | − | 19.0526i | 0.618590 | − | 0.785714i | ||||
\(589\) | 12.0000 | − | 20.7846i | 0.494451 | − | 0.856415i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.00000 | + | 5.19615i | 0.123404 | + | 0.213741i | ||||
\(592\) | 16.0000 | + | 27.7128i | 0.657596 | + | 1.13899i | ||||
\(593\) | −3.00000 | −0.123195 | −0.0615976 | − | 0.998101i | \(-0.519620\pi\) | ||||
−0.0615976 | + | 0.998101i | \(0.519620\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −12.0000 | + | 10.3923i | −0.491952 | + | 0.426043i | ||||
\(596\) | −9.00000 | + | 5.19615i | −0.368654 | + | 0.212843i | ||||
\(597\) | −9.00000 | − | 15.5885i | −0.368345 | − | 0.637993i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.00000 | − | 5.19615i | −0.367730 | − | 0.212309i | 0.304736 | − | 0.952437i | \(-0.401432\pi\) |
−0.672466 | + | 0.740128i | \(0.734765\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.00000 | − | 1.73205i | 0.122373 | − | 0.0706518i | −0.437564 | − | 0.899187i | \(-0.644159\pi\) |
0.559937 | + | 0.828535i | \(0.310825\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.0000 | + | 20.7846i | 0.488678 | + | 0.846415i | ||||
\(604\) | −16.0000 | −0.651031 | ||||||||
\(605\) | −4.00000 | − | 6.92820i | −0.162623 | − | 0.281672i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.50000 | + | 0.866025i | 0.0608831 | + | 0.0351509i | 0.530133 | − | 0.847915i | \(-0.322142\pi\) |
−0.469249 | + | 0.883066i | \(0.655475\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −30.0000 | + | 25.9808i | −1.21566 | + | 1.05279i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −18.0000 | − | 31.1769i | −0.727607 | − | 1.26025i | ||||
\(613\) | −16.0000 | −0.646234 | −0.323117 | − | 0.946359i | \(-0.604731\pi\) | ||||
−0.323117 | + | 0.946359i | \(0.604731\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 9.00000 | + | 5.19615i | 0.362915 | + | 0.209529i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.0000 | + | 12.1244i | 0.845428 | + | 0.488108i | 0.859106 | − | 0.511798i | \(-0.171020\pi\) |
−0.0136775 | + | 0.999906i | \(0.504354\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.0000 | − | 13.8564i | 0.964641 | − | 0.556936i | 0.0670430 | − | 0.997750i | \(-0.478644\pi\) |
0.897598 | + | 0.440814i | \(0.145310\pi\) | |||||||
\(620\) | − | 6.92820i | − | 0.278243i | ||||||
\(621\) | −9.00000 | + | 15.5885i | −0.361158 | + | 0.625543i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.0000 | + | 5.19615i | 0.600962 | + | 0.208179i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −0.500000 | + | 0.866025i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 18.0000 | + | 10.3923i | 0.718851 | + | 0.415029i | ||||
\(628\) | −3.00000 | + | 1.73205i | −0.119713 | + | 0.0691164i | ||||
\(629\) | 48.0000 | 1.91389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.00000 | 0.199047 | 0.0995234 | − | 0.995035i | \(-0.468268\pi\) | ||||
0.0995234 | + | 0.995035i | \(0.468268\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 1.73205i | − | 0.0688428i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.00000 | + | 1.73205i | −0.0396838 | + | 0.0687343i | ||||
\(636\) | 48.0000 | 1.90332 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.50000 | − | 2.59808i | −0.178017 | − | 0.102778i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18.0000 | − | 10.3923i | 0.710957 | − | 0.410471i | −0.100458 | − | 0.994941i | \(-0.532031\pi\) |
0.811415 | + | 0.584470i | \(0.198698\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.5000 | − | 7.79423i | −0.532388 | − | 0.307374i | 0.209600 | − | 0.977787i | \(-0.432784\pi\) |
−0.741988 | + | 0.670413i | \(0.766117\pi\) | |||||||
\(644\) | 18.0000 | − | 3.46410i | 0.709299 | − | 0.136505i | ||||
\(645\) | −15.0000 | + | 8.66025i | −0.590624 | + | 0.340997i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 24.0000 | 0.943537 | 0.471769 | − | 0.881722i | \(-0.343616\pi\) | ||||
0.471769 | + | 0.881722i | \(0.343616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 15.0000 | + | 5.19615i | 0.587896 | + | 0.203653i | ||||
\(652\) | −14.0000 | + | 24.2487i | −0.548282 | + | 0.949653i | ||||
\(653\) | 3.00000 | + | 1.73205i | 0.117399 | + | 0.0677804i | 0.557550 | − | 0.830144i | \(-0.311742\pi\) |
−0.440151 | + | 0.897924i | \(0.645075\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.00000 | − | 5.19615i | −0.117220 | − | 0.203030i | ||||
\(656\) | 24.0000 | 0.937043 | ||||||||
\(657\) | −22.5000 | − | 12.9904i | −0.877809 | − | 0.506803i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −21.0000 | + | 12.1244i | −0.818044 | + | 0.472298i | −0.849741 | − | 0.527200i | \(-0.823242\pi\) |
0.0316976 | + | 0.999498i | \(0.489909\pi\) | |||||||
\(660\) | 6.00000 | 0.233550 | ||||||||
\(661\) | −21.0000 | − | 12.1244i | −0.816805 | − | 0.471583i | 0.0325082 | − | 0.999471i | \(-0.489650\pi\) |
−0.849314 | + | 0.527889i | \(0.822984\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −12.0000 | − | 13.8564i | −0.465340 | − | 0.537328i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.0000 | −1.16160 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.00000 | + | 5.19615i | −0.115987 | + | 0.200895i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.00000 | − | 5.19615i | 0.115814 | − | 0.200595i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13.0000 | + | 22.5167i | 0.501113 | + | 0.867953i | 0.999999 | + | 0.00128586i | \(0.000409302\pi\) |
−0.498886 | + | 0.866668i | \(0.666257\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.50000 | − | 2.59808i | 0.173205 | − | 0.100000i | ||||
\(676\) | 26.0000 | 1.00000 | ||||||||
\(677\) | −21.0000 | − | 36.3731i | −0.807096 | − | 1.39793i | −0.914867 | − | 0.403755i | \(-0.867705\pi\) |
0.107772 | − | 0.994176i | \(-0.465628\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.50000 | + | 0.866025i | −0.172694 | + | 0.0332350i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −18.0000 | − | 10.3923i | −0.689761 | − | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 17.3205i | − | 0.662751i | −0.943499 | − | 0.331375i | \(-0.892487\pi\) | ||
0.943499 | − | 0.331375i | \(-0.107513\pi\) | |||||||
\(684\) | 36.0000 | − | 20.7846i | 1.37649 | − | 0.794719i | ||||
\(685\) | 17.3205i | 0.661783i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −48.0000 | −1.83131 | ||||||||
\(688\) | −20.0000 | + | 34.6410i | −0.762493 | + | 1.32068i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.0000 | − | 10.3923i | 0.684752 | − | 0.395342i | −0.116891 | − | 0.993145i | \(-0.537293\pi\) |
0.801643 | + | 0.597803i | \(0.203959\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −4.50000 | + | 12.9904i | −0.170941 | + | 0.493464i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 15.0000 | − | 8.66025i | 0.568982 | − | 0.328502i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 18.0000 | − | 31.1769i | 0.681799 | − | 1.18091i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.00000 | − | 5.19615i | −0.113470 | − | 0.196537i | ||||
\(700\) | −5.00000 | − | 1.73205i | −0.188982 | − | 0.0654654i | ||||
\(701\) | − | 13.8564i | − | 0.523349i | −0.965156 | − | 0.261675i | \(-0.915725\pi\) | ||
0.965156 | − | 0.261675i | \(-0.0842747\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 55.4256i | 2.09042i | ||||||||
\(704\) | 12.0000 | − | 6.92820i | 0.452267 | − | 0.261116i | ||||
\(705\) | −13.5000 | + | 7.79423i | −0.508439 | + | 0.293548i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17.5000 | + | 30.3109i | 0.657226 | + | 1.13835i | 0.981331 | + | 0.192328i | \(0.0616038\pi\) |
−0.324104 | + | 0.946021i | \(0.605063\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.00000 | 0.112509 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.00000 | + | 10.3923i | 0.224702 | + | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 27.0000 | + | 15.5885i | 1.00904 | + | 0.582568i | ||||
\(717\) | 15.0000 | 0.560185 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0000 | 0.447524 | 0.223762 | − | 0.974644i | \(-0.428166\pi\) | ||||
0.223762 | + | 0.974644i | \(0.428166\pi\) | |||||||
\(720\) | 6.00000 | − | 10.3923i | 0.223607 | − | 0.387298i | ||||
\(721\) | 21.0000 | + | 24.2487i | 0.782081 | + | 0.903069i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −9.00000 | + | 15.5885i | −0.334714 | + | 0.579741i | ||||
\(724\) | −36.0000 | − | 20.7846i | −1.33793 | − | 0.772454i | ||||
\(725\) | 7.50000 | + | 4.33013i | 0.278543 | + | 0.160817i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.50000 | − | 0.866025i | 0.0556319 | − | 0.0321191i | −0.471926 | − | 0.881638i | \(-0.656441\pi\) |
0.527558 | + | 0.849519i | \(0.323108\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.0000 | + | 51.9615i | 1.10959 | + | 1.92187i | ||||
\(732\) | −6.00000 | − | 10.3923i | −0.221766 | − | 0.384111i | ||||
\(733\) | 22.5000 | + | 12.9904i | 0.831056 | + | 0.479811i | 0.854214 | − | 0.519921i | \(-0.174039\pi\) |
−0.0231578 | + | 0.999732i | \(0.507372\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 7.50000 | − | 9.52628i | 0.276642 | − | 0.351382i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.8564i | 0.510407i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −31.0000 | −1.14035 | −0.570177 | − | 0.821522i | \(-0.693125\pi\) | ||||
−0.570177 | + | 0.821522i | \(0.693125\pi\) | |||||||
\(740\) | 8.00000 | + | 13.8564i | 0.294086 | + | 0.509372i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −33.0000 | − | 19.0526i | −1.21065 | − | 0.698971i | −0.247751 | − | 0.968824i | \(-0.579692\pi\) |
−0.962901 | + | 0.269853i | \(0.913025\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.50000 | + | 2.59808i | −0.164867 | + | 0.0951861i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 27.0000 | 0.987878 | ||||||||
\(748\) | − | 20.7846i | − | 0.759961i | ||||||
\(749\) | 6.00000 | − | 17.3205i | 0.219235 | − | 0.632878i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.50000 | − | 4.33013i | 0.0912263 | − | 0.158009i | −0.816801 | − | 0.576919i | \(-0.804255\pi\) |
0.908027 | + | 0.418911i | \(0.137588\pi\) | |||||||
\(752\) | −18.0000 | + | 31.1769i | −0.656392 | + | 1.13691i | ||||
\(753\) | 27.0000 | − | 15.5885i | 0.983935 | − | 0.568075i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8.00000 | −0.291150 | ||||||||
\(756\) | 18.0000 | + | 20.7846i | 0.654654 | + | 0.755929i | ||||
\(757\) | 16.0000 | 0.581530 | 0.290765 | − | 0.956795i | \(-0.406090\pi\) | ||||
0.290765 | + | 0.956795i | \(0.406090\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −9.00000 | + | 5.19615i | −0.326679 | + | 0.188608i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 24.0000 | − | 41.5692i | 0.869999 | − | 1.50688i | 0.00800331 | − | 0.999968i | \(-0.497452\pi\) |
0.861996 | − | 0.506915i | \(-0.169214\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.5000 | + | 9.52628i | 0.995567 | + | 0.344874i | ||||
\(764\) | 3.46410i | 0.125327i | ||||||||
\(765\) | −9.00000 | − | 15.5885i | −0.325396 | − | 0.563602i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | − | 27.7128i | − | 1.00000i | ||||||
\(769\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 5.19615i | − | 0.187135i | ||||||
\(772\) | −4.00000 | − | 6.92820i | −0.143963 | − | 0.249351i | ||||
\(773\) | −9.00000 | −0.323708 | −0.161854 | − | 0.986815i | \(-0.551747\pi\) | ||||
−0.161854 | + | 0.986815i | \(0.551747\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 3.46410i | − | 0.124434i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −36.0000 | + | 6.92820i | −1.29149 | + | 0.248548i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.0000 | + | 20.7846i | 1.28983 | + | 0.744686i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.50000 | − | 2.59808i | −0.0536742 | − | 0.0929665i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −22.5000 | − | 38.9711i | −0.804084 | − | 1.39272i | ||||
\(784\) | 4.00000 | − | 27.7128i | 0.142857 | − | 0.989743i | ||||
\(785\) | −1.50000 | + | 0.866025i | −0.0535373 | + | 0.0309098i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −33.0000 | − | 19.0526i | −1.17632 | − | 0.679150i | −0.221162 | − | 0.975237i | \(-0.570985\pi\) |
−0.955161 | + | 0.296087i | \(0.904318\pi\) | |||||||
\(788\) | 6.00000 | + | 3.46410i | 0.213741 | + | 0.123404i | ||||
\(789\) | −15.0000 | + | 25.9808i | −0.534014 | + | 0.924940i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.0000 | + | 20.7846i | 0.640006 | + | 0.739016i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 24.0000 | 0.851192 | ||||||||
\(796\) | −18.0000 | − | 10.3923i | −0.637993 | − | 0.368345i | ||||
\(797\) | −3.00000 | + | 5.19615i | −0.106265 | + | 0.184057i | −0.914255 | − | 0.405140i | \(-0.867223\pi\) |
0.807989 | + | 0.589197i | \(0.200556\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 27.0000 | + | 46.7654i | 0.955191 | + | 1.65444i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.00000 | + | 15.5885i | −0.317999 | + | 0.550791i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −7.50000 | − | 12.9904i | −0.264669 | − | 0.458421i | ||||
\(804\) | 24.0000 | + | 13.8564i | 0.846415 | + | 0.488678i | ||||
\(805\) | 9.00000 | − | 1.73205i | 0.317208 | − | 0.0610468i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −36.0000 | + | 20.7846i | −1.26726 | + | 0.731653i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 6.92820i | − | 0.243583i | −0.992556 | − | 0.121791i | \(-0.961136\pi\) | ||
0.992556 | − | 0.121791i | \(-0.0388639\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 55.4256i | 1.94626i | 0.230263 | + | 0.973128i | \(0.426041\pi\) | ||||
−0.230263 | + | 0.973128i | \(0.573959\pi\) | |||||||
\(812\) | −15.0000 | + | 43.3013i | −0.526397 | + | 1.51958i | ||||
\(813\) | 15.0000 | + | 25.9808i | 0.526073 | + | 0.911185i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.00000 | + | 12.1244i | −0.245199 | + | 0.424698i | ||||
\(816\) | −36.0000 | − | 20.7846i | −1.26025 | − | 0.727607i | ||||
\(817\) | −60.0000 | + | 34.6410i | −2.09913 | + | 1.21194i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 12.0000 | 0.419058 | ||||||||
\(821\) | 12.0000 | − | 6.92820i | 0.418803 | − | 0.241796i | −0.275762 | − | 0.961226i | \(-0.588930\pi\) |
0.694565 | + | 0.719430i | \(0.255597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.00000 | + | 6.92820i | −0.139431 | + | 0.241502i | −0.927281 | − | 0.374365i | \(-0.877861\pi\) |
0.787850 | + | 0.615867i | \(0.211194\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.00000 | 0.104447 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 34.6410i | − | 1.20459i | −0.798275 | − | 0.602293i | \(-0.794254\pi\) | ||
0.798275 | − | 0.602293i | \(-0.205746\pi\) | |||||||
\(828\) | 20.7846i | 0.722315i | ||||||||
\(829\) | 45.0333i | 1.56407i | 0.623233 | + | 0.782036i | \(0.285819\pi\) | ||||
−0.623233 | + | 0.782036i | \(0.714181\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.0000 | − | 8.66025i | −0.520344 | − | 0.300421i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −33.0000 | − | 25.9808i | −1.14338 | − | 0.900180i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 24.0000 | 0.830057 | ||||||||
\(837\) | −9.00000 | + | 15.5885i | −0.311086 | + | 0.538816i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 24.0000 | + | 41.5692i | 0.828572 | + | 1.43513i | 0.899158 | + | 0.437623i | \(0.144180\pi\) |
−0.0705865 | + | 0.997506i | \(0.522487\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0000 | − | 39.8372i | 0.793103 | − | 1.37370i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 19.5000 | − | 33.7750i | 0.671616 | − | 1.16327i | ||||
\(844\) | −1.00000 | − | 1.73205i | −0.0344214 | − | 0.0596196i | ||||
\(845\) | 13.0000 | 0.447214 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.0000 | − | 13.8564i | 0.549767 | − | 0.476112i | ||||
\(848\) | 48.0000 | − | 27.7128i | 1.64833 | − | 0.951662i | ||||
\(849\) | 21.0000 | 0.720718 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −24.0000 | − | 13.8564i | −0.822709 | − | 0.474991i | ||||
\(852\) | −6.00000 | −0.205557 | ||||||||
\(853\) | 18.0000 | − | 10.3923i | 0.616308 | − | 0.355826i | −0.159122 | − | 0.987259i | \(-0.550866\pi\) |
0.775430 | + | 0.631433i | \(0.217533\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 18.0000 | − | 10.3923i | 0.615587 | − | 0.355409i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −25.5000 | − | 44.1673i | −0.871063 | − | 1.50873i | −0.860898 | − | 0.508778i | \(-0.830097\pi\) |
−0.0101655 | − | 0.999948i | \(-0.503236\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.00000 | + | 3.46410i | 0.204717 | + | 0.118194i | 0.598854 | − | 0.800858i | \(-0.295623\pi\) |
−0.394137 | + | 0.919052i | \(0.628956\pi\) | |||||||
\(860\) | −10.0000 | + | 17.3205i | −0.340997 | + | 0.590624i | ||||
\(861\) | −9.00000 | + | 25.9808i | −0.306719 | + | 0.885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 55.4256i | − | 1.88671i | −0.331785 | − | 0.943355i | \(-0.607651\pi\) | ||
0.331785 | − | 0.943355i | \(-0.392349\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.00000 | −0.102003 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −28.5000 | + | 16.4545i | −0.967911 | + | 0.558824i | ||||
\(868\) | 18.0000 | − | 3.46410i | 0.610960 | − | 0.117579i | ||||
\(869\) | 1.50000 | + | 0.866025i | 0.0508840 | + | 0.0293779i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 5.19615i | − | 0.175863i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.50000 | − | 0.866025i | −0.0845154 | − | 0.0292770i | ||||
\(876\) | −30.0000 | −1.01361 | ||||||||
\(877\) | −7.00000 | + | 12.1244i | −0.236373 | + | 0.409410i | −0.959671 | − | 0.281126i | \(-0.909292\pi\) |
0.723298 | + | 0.690536i | \(0.242625\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15.5885i | 0.525786i | ||||||||
\(880\) | 6.00000 | − | 3.46410i | 0.202260 | − | 0.116775i | ||||
\(881\) | −36.0000 | −1.21287 | −0.606435 | − | 0.795133i | \(-0.707401\pi\) | ||||
−0.606435 | + | 0.795133i | \(0.707401\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −44.0000 | −1.48072 | −0.740359 | − | 0.672212i | \(-0.765344\pi\) | ||||
−0.740359 | + | 0.672212i | \(0.765344\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0000 | − | 20.7846i | 0.402921 | − | 0.697879i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.994077 | + | 0.108678i | \(0.0346618\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.00000 | − | 1.73205i | −0.167695 | − | 0.0580911i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.5000 | − | 7.79423i | −0.452267 | − | 0.261116i | ||||
\(892\) | 6.92820i | 0.231973i | ||||||||
\(893\) | −54.0000 | + | 31.1769i | −1.80704 | + | 1.04330i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.5000 | + | 7.79423i | 0.451255 | + | 0.260532i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.0000 | −1.00056 | ||||||||
\(900\) | 3.00000 | − | 5.19615i | 0.100000 | − | 0.173205i | ||||
\(901\) | − | 83.1384i | − | 2.76974i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −30.0000 | − | 34.6410i | −0.998337 | − | 1.15278i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −18.0000 | − | 10.3923i | −0.598340 | − | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.00000 | + | 6.92820i | 0.132818 | + | 0.230047i | 0.924762 | − | 0.380547i | \(-0.124264\pi\) |
−0.791944 | + | 0.610594i | \(0.790931\pi\) | |||||||
\(908\) | −24.0000 | −0.796468 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.5000 | − | 25.1147i | 1.44122 | − | 0.832088i | 0.443288 | − | 0.896379i | \(-0.353812\pi\) |
0.997931 | + | 0.0642908i | \(0.0204785\pi\) | |||||||
\(912\) | 24.0000 | − | 41.5692i | 0.794719 | − | 1.37649i | ||||
\(913\) | 13.5000 | + | 7.79423i | 0.446785 | + | 0.257951i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.00000 | − | 5.19615i | −0.0991769 | − | 0.171780i | ||||
\(916\) | −48.0000 | + | 27.7128i | −1.58596 | + | 0.915657i | ||||
\(917\) | 12.0000 | − | 10.3923i | 0.396275 | − | 0.343184i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19.0000 | 0.626752 | 0.313376 | − | 0.949629i | \(-0.398540\pi\) | ||||
0.313376 | + | 0.949629i | \(0.398540\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.00000 | + | 5.19615i | 0.0988534 | + | 0.171219i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 3.00000 | + | 15.5885i | 0.0986928 | + | 0.512823i | ||||
\(925\) | 4.00000 | + | 6.92820i | 0.131519 | + | 0.227798i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −31.5000 | + | 18.1865i | −1.03460 | + | 0.597324i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −24.0000 | − | 41.5692i | −0.787414 | − | 1.36384i | −0.927546 | − | 0.373709i | \(-0.878086\pi\) |
0.140132 | − | 0.990133i | \(-0.455247\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.0000 | − | 38.1051i | 0.983210 | − | 1.24884i | ||||
\(932\) | −6.00000 | − | 3.46410i | −0.196537 | − | 0.113470i | ||||
\(933\) | − | 31.1769i | − | 1.02069i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 10.3923i | − | 0.339865i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 48.4974i | − | 1.58434i | −0.610299 | − | 0.792171i | \(-0.708951\pi\) | ||
0.610299 | − | 0.792171i | \(-0.291049\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 13.5000 | − | 23.3827i | 0.440556 | − | 0.763065i | ||||
\(940\) | −9.00000 | + | 15.5885i | −0.293548 | + | 0.508439i | ||||
\(941\) | 24.0000 | − | 41.5692i | 0.782378 | − | 1.35512i | −0.148176 | − | 0.988961i | \(-0.547340\pi\) |
0.930553 | − | 0.366157i | \(-0.119327\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −18.0000 | + | 10.3923i | −0.586161 | + | 0.338420i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 9.00000 | + | 10.3923i | 0.292770 | + | 0.338062i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 0 | 0 | −0.500000 | − | 0.866025i | \(-0.666667\pi\) | ||||
0.500000 | + | 0.866025i | \(0.333333\pi\) | |||||||
\(948\) | 3.00000 | − | 1.73205i | 0.0974355 | − | 0.0562544i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.00000 | + | 5.19615i | −0.0972817 | + | 0.168497i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.92820i | 0.224427i | 0.993684 | + | 0.112213i | \(0.0357940\pi\) | ||||
−0.993684 | + | 0.112213i | \(0.964206\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.73205i | 0.0560478i | ||||||||
\(956\) | 15.0000 | − | 8.66025i | 0.485135 | − | 0.280093i | ||||
\(957\) | − | 25.9808i | − | 0.839839i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −45.0000 | + | 8.66025i | −1.45313 | + | 0.279654i | ||||
\(960\) | − | 13.8564i | − | 0.447214i | ||||||
\(961\) | −9.50000 | − | 16.4545i | −0.306452 | − | 0.530790i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 18.0000 | + | 10.3923i | 0.580042 | + | 0.334887i | ||||
\(964\) | 20.7846i | 0.669427i | ||||||||
\(965\) | −2.00000 | − | 3.46410i | −0.0643823 | − | 0.111513i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.00000 | + | 1.73205i | −0.0321578 | + | 0.0556990i | −0.881656 | − | 0.471892i | \(-0.843571\pi\) |
0.849499 | + | 0.527591i | \(0.176905\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.0000 | − | 62.3538i | −1.15649 | − | 2.00309i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 42.0000 | 1.34784 | 0.673922 | − | 0.738802i | \(-0.264608\pi\) | ||||
0.673922 | + | 0.738802i | \(0.264608\pi\) | |||||||
\(972\) | −27.0000 | + | 15.5885i | −0.866025 | + | 0.500000i | ||||
\(973\) | 30.0000 | + | 34.6410i | 0.961756 | + | 1.11054i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.0000 | − | 6.92820i | −0.384111 | − | 0.221766i | ||||
\(977\) | 24.0000 | + | 13.8564i | 0.767828 | + | 0.443306i | 0.832099 | − | 0.554627i | \(-0.187139\pi\) |
−0.0642712 | + | 0.997932i | \(0.520472\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.00000 | + | 5.19615i | −0.287641 | + | 0.166070i | ||||
\(980\) | 2.00000 | − | 13.8564i | 0.0638877 | − | 0.442627i | ||||
\(981\) | −16.5000 | + | 28.5788i | −0.526804 | + | 0.912452i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.50000 | + | 12.9904i | 0.239213 | + | 0.414329i | 0.960489 | − | 0.278319i | \(-0.0897773\pi\) |
−0.721276 | + | 0.692648i | \(0.756444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.00000 | + | 1.73205i | 0.0955879 | + | 0.0551877i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −27.0000 | − | 31.1769i | −0.859419 | − | 0.992372i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 34.6410i | − | 1.10152i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.0000 | 1.17534 | 0.587672 | − | 0.809099i | \(-0.300045\pi\) | ||||
0.587672 | + | 0.809099i | \(0.300045\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −25.5000 | − | 14.7224i | −0.809218 | − | 0.467202i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −9.00000 | − | 5.19615i | −0.285319 | − | 0.164729i | ||||
\(996\) | 27.0000 | − | 15.5885i | 0.855528 | − | 0.493939i | ||||
\(997\) | 22.5000 | − | 12.9904i | 0.712582 | − | 0.411409i | −0.0994342 | − | 0.995044i | \(-0.531703\pi\) |
0.812016 | + | 0.583635i | \(0.198370\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | − | 41.5692i | − | 1.31519i |
(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 | 315.2.bl.e.41.1 | ✓ | 2 | |
3.2 | odd | 2 | 945.2.bl.c.881.1 | 2 | |||
7.6 | odd | 2 | 315.2.bl.h.41.1 | yes | 2 | ||
9.2 | odd | 6 | 315.2.bl.h.146.1 | yes | 2 | ||
9.7 | even | 3 | 945.2.bl.a.251.1 | 2 | |||
21.20 | even | 2 | 945.2.bl.a.881.1 | 2 | |||
63.20 | even | 6 | inner | 315.2.bl.e.146.1 | yes | 2 | |
63.34 | odd | 6 | 945.2.bl.c.251.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.bl.e.41.1 | ✓ | 2 | 1.1 | even | 1 | trivial | |
315.2.bl.e.146.1 | yes | 2 | 63.20 | even | 6 | inner | |
315.2.bl.h.41.1 | yes | 2 | 7.6 | odd | 2 | ||
315.2.bl.h.146.1 | yes | 2 | 9.2 | odd | 6 | ||
945.2.bl.a.251.1 | 2 | 9.7 | even | 3 | |||
945.2.bl.a.881.1 | 2 | 21.20 | even | 2 | |||
945.2.bl.c.251.1 | 2 | 63.34 | odd | 6 | |||
945.2.bl.c.881.1 | 2 | 3.2 | odd | 2 |