Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,2,Mod(255,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.255");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.n (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.70980888579\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 304) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 255.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.255 |
Dual form | 1216.2.n.a.639.1 |
$q$-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 \(\left(\mathbb{Z}/1216\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(705\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.500000 | + | 0.866025i | −0.288675 | + | 0.500000i | −0.973494 | − | 0.228714i | \(-0.926548\pi\) |
0.684819 | + | 0.728714i | \(0.259881\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | − | 2.59808i | 0.670820 | − | 1.16190i | −0.306851 | − | 0.951757i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673912\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.46410i | 1.30931i | 0.755929 | + | 0.654654i | \(0.227186\pi\) | ||||
−0.755929 | + | 0.654654i | \(0.772814\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | + | 1.73205i | 0.333333 | + | 0.577350i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.46410i | 1.04447i | 0.852803 | + | 0.522233i | \(0.174901\pi\) | ||||
−0.852803 | + | 0.522233i | \(0.825099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.50000 | − | 2.59808i | 1.24808 | − | 0.720577i | 0.277350 | − | 0.960769i | \(-0.410544\pi\) |
0.970725 | + | 0.240192i | \(0.0772105\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.50000 | + | 2.59808i | 0.387298 | + | 0.670820i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | + | 2.59808i | −0.363803 | + | 0.630126i | −0.988583 | − | 0.150675i | \(-0.951855\pi\) |
0.624780 | + | 0.780801i | \(0.285189\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.00000 | − | 1.73205i | −0.917663 | − | 0.397360i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.00000 | − | 1.73205i | −0.654654 | − | 0.377964i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.50000 | − | 2.59808i | 0.938315 | − | 0.541736i | 0.0488832 | − | 0.998805i | \(-0.484434\pi\) |
0.889432 | + | 0.457068i | \(0.151100\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −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 | ||||||||
\(31\) | −4.00000 | −0.718421 | −0.359211 | − | 0.933257i | \(-0.616954\pi\) | ||||
−0.359211 | + | 0.933257i | \(0.616954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.00000 | − | 1.73205i | −0.522233 | − | 0.301511i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 9.00000 | + | 5.19615i | 1.52128 | + | 0.878310i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.19615i | 0.832050i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.50000 | + | 4.33013i | 1.17130 | + | 0.676252i | 0.953987 | − | 0.299849i | \(-0.0969363\pi\) |
0.217317 | + | 0.976101i | \(0.430270\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.5000 | + | 6.06218i | 1.60123 | + | 0.924473i | 0.991241 | + | 0.132068i | \(0.0421616\pi\) |
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 6.00000 | 0.894427 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.50000 | + | 0.866025i | −0.218797 | + | 0.126323i | −0.605393 | − | 0.795926i | \(-0.706984\pi\) |
0.386596 | + | 0.922249i | \(0.373651\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | −0.714286 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.50000 | − | 2.59808i | −0.210042 | − | 0.363803i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.50000 | + | 0.866025i | −0.206041 | + | 0.118958i | −0.599470 | − | 0.800397i | \(-0.704622\pi\) |
0.393429 | + | 0.919355i | \(0.371289\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 9.00000 | + | 5.19615i | 1.21356 | + | 0.700649i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.50000 | − | 2.59808i | 0.463586 | − | 0.344124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.50000 | − | 2.59808i | 0.195283 | − | 0.338241i | −0.751710 | − | 0.659494i | \(-0.770771\pi\) |
0.946993 | + | 0.321253i | \(0.104104\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.50000 | + | 6.06218i | 0.448129 | + | 0.776182i | 0.998264 | − | 0.0588933i | \(-0.0187572\pi\) |
−0.550135 | + | 0.835076i | \(0.685424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.00000 | + | 3.46410i | −0.755929 | + | 0.436436i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 15.5885i | − | 1.93351i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.50000 | + | 4.33013i | 0.305424 | + | 0.529009i | 0.977356 | − | 0.211604i | \(-0.0678686\pi\) |
−0.671932 | + | 0.740613i | \(0.734535\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.19615i | 0.625543i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.50000 | − | 7.79423i | 0.534052 | − | 0.925005i | −0.465157 | − | 0.885228i | \(-0.654002\pi\) |
0.999209 | − | 0.0397765i | \(-0.0126646\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.50000 | + | 6.06218i | −0.409644 | + | 0.709524i | −0.994850 | − | 0.101361i | \(-0.967680\pi\) |
0.585206 | + | 0.810885i | \(0.301014\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −12.0000 | −1.36753 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.50000 | + | 6.06218i | −0.393781 | + | 0.682048i | −0.992945 | − | 0.118578i | \(-0.962166\pi\) |
0.599164 | + | 0.800626i | \(0.295500\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | + | 0.866025i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.46410i | − | 0.380235i | −0.981761 | − | 0.190117i | \(-0.939113\pi\) | ||
0.981761 | − | 0.190117i | \(-0.0608868\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.50000 | + | 7.79423i | 0.488094 | + | 0.845403i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 8.66025i | − | 0.928477i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.50000 | − | 4.33013i | 0.794998 | − | 0.458993i | −0.0467209 | − | 0.998908i | \(-0.514877\pi\) |
0.841719 | + | 0.539915i | \(0.181544\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.00000 | + | 15.5885i | 0.943456 | + | 1.63411i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | − | 3.46410i | 0.207390 | − | 0.359211i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −10.5000 | + | 7.79423i | −1.07728 | + | 0.799671i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.50000 | + | 4.33013i | 0.761510 | + | 0.439658i | 0.829837 | − | 0.558005i | \(-0.188433\pi\) |
−0.0683279 | + | 0.997663i | \(0.521766\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.00000 | + | 3.46410i | −0.603023 | + | 0.348155i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.50000 | + | 2.59808i | 0.149256 | + | 0.258518i | 0.930953 | − | 0.365140i | \(-0.118979\pi\) |
−0.781697 | + | 0.623658i | \(0.785646\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0000 | 1.57653 | 0.788263 | − | 0.615338i | \(-0.210980\pi\) | ||||
0.788263 | + | 0.615338i | \(0.210980\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −9.00000 | + | 5.19615i | −0.878310 | + | 0.507093i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −12.0000 | −1.16008 | −0.580042 | − | 0.814587i | \(-0.696964\pi\) | ||||
−0.580042 | + | 0.814587i | \(0.696964\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −13.5000 | − | 7.79423i | −1.29307 | − | 0.746552i | −0.313869 | − | 0.949466i | \(-0.601625\pi\) |
−0.979196 | + | 0.202915i | \(0.934959\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 6.92820i | − | 0.651751i | −0.945413 | − | 0.325875i | \(-0.894341\pi\) | ||
0.945413 | − | 0.325875i | \(-0.105659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 15.5885i | − | 1.45363i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.00000 | + | 5.19615i | 0.832050 | + | 0.480384i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.00000 | − | 5.19615i | −0.825029 | − | 0.476331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.50000 | + | 4.33013i | −0.676252 | + | 0.390434i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 3.00000 | 0.268328 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.50000 | + | 6.06218i | 0.310575 | + | 0.537931i | 0.978487 | − | 0.206309i | \(-0.0661452\pi\) |
−0.667912 | + | 0.744240i | \(0.732812\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.5000 | + | 6.06218i | −0.924473 | + | 0.533745i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.50000 | + | 2.59808i | 0.393167 | + | 0.226995i | 0.683531 | − | 0.729921i | \(-0.260443\pi\) |
−0.290365 | + | 0.956916i | \(0.593777\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.00000 | − | 13.8564i | 0.520266 | − | 1.20150i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −7.50000 | + | 12.9904i | −0.645497 | + | 1.11803i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.50000 | − | 2.59808i | −0.128154 | − | 0.221969i | 0.794808 | − | 0.606861i | \(-0.207572\pi\) |
−0.922961 | + | 0.384893i | \(0.874238\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −16.5000 | + | 9.52628i | −1.39951 | + | 0.808008i | −0.994341 | − | 0.106233i | \(-0.966121\pi\) |
−0.405170 | + | 0.914241i | \(0.632788\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 1.73205i | − | 0.145865i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.00000 | + | 15.5885i | 0.752618 | + | 1.30357i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.9808i | 2.15758i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.50000 | − | 4.33013i | 0.206197 | − | 0.357143i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.50000 | − | 12.9904i | 0.614424 | − | 1.06421i | −0.376061 | − | 0.926595i | \(-0.622722\pi\) |
0.990485 | − | 0.137619i | \(-0.0439449\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.00000 | −0.485071 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.00000 | + | 10.3923i | −0.481932 | + | 0.834730i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.50000 | + | 4.33013i | −0.199522 | + | 0.345582i | −0.948373 | − | 0.317156i | \(-0.897272\pi\) |
0.748852 | + | 0.662738i | \(0.230606\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 1.73205i | − | 0.137361i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 9.00000 | + | 15.5885i | 0.709299 | + | 1.22854i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 10.3923i | − | 0.813988i | −0.913431 | − | 0.406994i | \(-0.866577\pi\) | ||
0.913431 | − | 0.406994i | \(-0.133423\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −9.00000 | + | 5.19615i | −0.700649 | + | 0.404520i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.5000 | − | 18.1865i | −0.812514 | − | 1.40732i | −0.911099 | − | 0.412188i | \(-0.864765\pi\) |
0.0985846 | − | 0.995129i | \(-0.468568\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | − | 12.1244i | 0.538462 | − | 0.932643i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | − | 8.66025i | −0.0764719 | − | 0.662266i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −7.50000 | − | 4.33013i | −0.570214 | − | 0.329213i | 0.187021 | − | 0.982356i | \(-0.440117\pi\) |
−0.757235 | + | 0.653143i | \(0.773450\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 12.0000 | − | 6.92820i | 0.907115 | − | 0.523723i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.50000 | + | 2.59808i | 0.112747 | + | 0.195283i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.0000 | 0.896922 | 0.448461 | − | 0.893802i | \(-0.351972\pi\) | ||||
0.448461 | + | 0.893802i | \(0.351972\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.50000 | + | 0.866025i | −0.111494 | + | 0.0643712i | −0.554710 | − | 0.832044i | \(-0.687171\pi\) |
0.443216 | + | 0.896415i | \(0.353837\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −7.00000 | −0.517455 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.00000 | − | 5.19615i | −0.658145 | − | 0.379980i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 17.3205i | − | 1.25988i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 24.2487i | − | 1.75458i | −0.479965 | − | 0.877288i | \(-0.659351\pi\) | ||
0.479965 | − | 0.877288i | \(-0.340649\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.5000 | − | 6.06218i | −0.755807 | − | 0.436365i | 0.0719816 | − | 0.997406i | \(-0.477068\pi\) |
−0.827788 | + | 0.561041i | \(0.810401\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.5000 | + | 7.79423i | 0.966755 | + | 0.558156i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.0000 | −1.28245 | −0.641223 | − | 0.767354i | \(-0.721573\pi\) | ||||
−0.641223 | + | 0.767354i | \(0.721573\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.5000 | − | 6.06218i | 0.744325 | − | 0.429736i | −0.0793146 | − | 0.996850i | \(-0.525273\pi\) |
0.823640 | + | 0.567113i | \(0.191940\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.00000 | −0.352673 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.0000 | − | 25.9808i | −1.05279 | − | 1.82349i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 22.5000 | − | 12.9904i | 1.57147 | − | 0.907288i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.00000 | + | 5.19615i | 0.625543 | + | 0.361158i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 6.00000 | − | 13.8564i | 0.415029 | − | 0.958468i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.5000 | − | 19.9186i | 0.791693 | − | 1.37125i | −0.133226 | − | 0.991086i | \(-0.542533\pi\) |
0.924918 | − | 0.380166i | \(-0.124133\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.50000 | + | 7.79423i | 0.308335 | + | 0.534052i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 31.5000 | − | 18.1865i | 2.14828 | − | 1.24031i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 13.8564i | − | 0.940634i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.50000 | − | 6.06218i | −0.236508 | − | 0.409644i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 15.5885i | 1.04859i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.50000 | + | 16.4545i | −0.636167 | + | 1.10187i | 0.350100 | + | 0.936713i | \(0.386148\pi\) |
−0.986267 | + | 0.165161i | \(0.947186\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.00000 | − | 6.92820i | 0.266667 | − | 0.461880i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 12.0000 | 0.796468 | 0.398234 | − | 0.917284i | \(-0.369623\pi\) | ||||
0.398234 | + | 0.917284i | \(0.369623\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 22.0000 | 1.45380 | 0.726900 | − | 0.686743i | \(-0.240960\pi\) | ||||
0.726900 | + | 0.686743i | \(0.240960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00000 | − | 10.3923i | 0.394771 | − | 0.683763i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −13.5000 | + | 23.3827i | −0.884414 | + | 1.53185i | −0.0380310 | + | 0.999277i | \(0.512109\pi\) |
−0.846383 | + | 0.532574i | \(0.821225\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.19615i | 0.338960i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.50000 | − | 6.06218i | −0.227349 | − | 0.393781i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 17.3205i | − | 1.12037i | −0.828367 | − | 0.560185i | \(-0.810730\pi\) | ||
0.828367 | − | 0.560185i | \(-0.189270\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.5000 | − | 11.2583i | 1.25611 | − | 0.725213i | 0.283790 | − | 0.958886i | \(-0.408408\pi\) |
0.972315 | + | 0.233674i | \(0.0750747\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −8.00000 | − | 13.8564i | −0.513200 | − | 0.888889i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.50000 | + | 12.9904i | −0.479157 | + | 0.829925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.5000 | + | 2.59808i | −1.43164 | + | 0.165312i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.00000 | + | 1.73205i | 0.190117 | + | 0.109764i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.50000 | + | 2.59808i | −0.284037 | + | 0.163989i | −0.635250 | − | 0.772307i | \(-0.719103\pi\) |
0.351212 | + | 0.936296i | \(0.385770\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.00000 | + | 15.5885i | 0.565825 | + | 0.980038i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −9.00000 | −0.563602 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 13.5000 | − | 7.79423i | 0.842107 | − | 0.486191i | −0.0158730 | − | 0.999874i | \(-0.505053\pi\) |
0.857980 | + | 0.513683i | \(0.171719\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −15.0000 | − | 8.66025i | −0.928477 | − | 0.536056i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5000 | − | 6.06218i | −0.647458 | − | 0.373810i | 0.140024 | − | 0.990148i | \(-0.455282\pi\) |
−0.787482 | + | 0.616338i | \(0.788615\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.19615i | 0.319197i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.66025i | 0.529999i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 22.5000 | + | 12.9904i | 1.37185 | + | 0.792038i | 0.991161 | − | 0.132666i | \(-0.0423537\pi\) |
0.380688 | + | 0.924703i | \(0.375687\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.5000 | − | 6.06218i | −0.637830 | − | 0.368251i | 0.145948 | − | 0.989292i | \(-0.453377\pi\) |
−0.783778 | + | 0.621041i | \(0.786710\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −18.0000 | −1.08941 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 12.0000 | − | 6.92820i | 0.723627 | − | 0.417786i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.00000 | −0.120168 | −0.0600842 | − | 0.998193i | \(-0.519137\pi\) | ||||
−0.0600842 | + | 0.998193i | \(0.519137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −4.00000 | − | 6.92820i | −0.239474 | − | 0.414781i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.5000 | − | 7.79423i | 0.805342 | − | 0.464965i | −0.0399934 | − | 0.999200i | \(-0.512734\pi\) |
0.845336 | + | 0.534235i | \(0.179400\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.50000 | + | 2.59808i | 0.267497 | + | 0.154440i | 0.627750 | − | 0.778415i | \(-0.283976\pi\) |
−0.360252 | + | 0.932855i | \(0.617309\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1.50000 | − | 12.9904i | −0.0888523 | − | 0.769484i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.0000 | + | 25.9808i | −0.885422 | + | 1.53360i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.00000 | + | 6.92820i | 0.235294 | + | 0.407541i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.50000 | + | 4.33013i | −0.439658 | + | 0.253837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 13.8564i | − | 0.809500i | −0.914427 | − | 0.404750i | \(-0.867359\pi\) | ||
0.914427 | − | 0.404750i | \(-0.132641\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.50000 | − | 7.79423i | −0.262000 | − | 0.453798i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 17.3205i | − | 1.00504i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 13.5000 | − | 23.3827i | 0.780725 | − | 1.35226i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.0000 | + | 36.3731i | −1.21042 | + | 2.09651i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.00000 | −0.172345 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.0000 | 1.20246 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.50000 | + | 4.33013i | −0.142683 | + | 0.247133i | −0.928506 | − | 0.371318i | \(-0.878906\pi\) |
0.785823 | + | 0.618451i | \(0.212239\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −8.00000 | + | 13.8564i | −0.455104 | + | 0.788263i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 3.46410i | − | 0.196431i | −0.995165 | − | 0.0982156i | \(-0.968687\pi\) | ||
0.995165 | − | 0.0982156i | \(-0.0313135\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.50000 | − | 16.4545i | −0.536972 | − | 0.930062i | −0.999065 | − | 0.0432311i | \(-0.986235\pi\) |
0.462093 | − | 0.886831i | \(-0.347098\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 20.7846i | 1.17108i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.50000 | − | 2.59808i | 0.252745 | − | 0.145922i | −0.368275 | − | 0.929717i | \(-0.620052\pi\) |
0.621021 | + | 0.783794i | \(0.286718\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.0000 | − | 25.9808i | −0.839839 | − | 1.45464i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.00000 | − | 10.3923i | 0.334887 | − | 0.580042i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 10.5000 | − | 7.79423i | 0.584236 | − | 0.433682i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.0000 | − | 10.3923i | −0.998460 | − | 0.576461i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 13.5000 | − | 7.79423i | 0.746552 | − | 0.431022i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3.00000 | − | 5.19615i | −0.165395 | − | 0.286473i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −28.0000 | −1.53902 | −0.769510 | − | 0.638635i | \(-0.779499\pi\) | ||||
−0.769510 | + | 0.638635i | \(0.779499\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 15.0000 | 0.819538 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −28.5000 | − | 16.4545i | −1.55249 | − | 0.896333i | −0.997938 | − | 0.0641864i | \(-0.979555\pi\) |
−0.554556 | − | 0.832146i | \(-0.687112\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 6.00000 | + | 3.46410i | 0.325875 | + | 0.188144i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 13.8564i | − | 0.750366i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820i | 0.374088i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 13.5000 | + | 7.79423i | 0.726816 | + | 0.419627i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −13.5000 | − | 7.79423i | −0.724718 | − | 0.418416i | 0.0917687 | − | 0.995780i | \(-0.470748\pi\) |
−0.816487 | + | 0.577364i | \(0.804081\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.00000 | −0.107058 | −0.0535288 | − | 0.998566i | \(-0.517047\pi\) | ||||
−0.0535288 | + | 0.998566i | \(0.517047\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −22.5000 | + | 12.9904i | −1.20096 | + | 0.693375i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −18.0000 | −0.958043 | −0.479022 | − | 0.877803i | \(-0.659008\pi\) | ||||
−0.479022 | + | 0.877803i | \(0.659008\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.5000 | − | 23.3827i | −0.716506 | − | 1.24102i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.00000 | − | 5.19615i | 0.476331 | − | 0.275010i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 13.5000 | + | 7.79423i | 0.712503 | + | 0.411364i | 0.811987 | − | 0.583675i | \(-0.198386\pi\) |
−0.0994843 | + | 0.995039i | \(0.531719\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0000 | + | 13.8564i | 0.684211 | + | 0.729285i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0.500000 | − | 0.866025i | 0.0262432 | − | 0.0454545i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 10.5000 | + | 18.1865i | 0.549595 | + | 0.951927i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5000 | + | 7.79423i | −0.704694 | + | 0.406855i | −0.809093 | − | 0.587680i | \(-0.800041\pi\) |
0.104399 | + | 0.994535i | \(0.466708\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 17.3205i | 0.901670i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.00000 | − | 5.19615i | −0.155752 | − | 0.269771i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.92820i | 0.358729i | 0.983783 | + | 0.179364i | \(0.0574041\pi\) | ||||
−0.983783 | + | 0.179364i | \(0.942596\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.50000 | + | 2.59808i | −0.0774597 | + | 0.134164i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −22.5000 | + | 38.9711i | −1.15881 | + | 2.00712i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.0000 | 1.02733 | 0.513665 | − | 0.857991i | \(-0.328287\pi\) | ||||
0.513665 | + | 0.857991i | \(0.328287\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.00000 | −0.358621 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5000 | − | 28.5788i | 0.843111 | − | 1.46031i | −0.0441413 | − | 0.999025i | \(-0.514055\pi\) |
0.887252 | − | 0.461285i | \(-0.152611\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.0000 | + | 31.1769i | −0.917365 | + | 1.58892i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 24.2487i | 1.23263i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.50000 | + | 12.9904i | 0.380265 | + | 0.658638i | 0.991100 | − | 0.133120i | \(-0.0424994\pi\) |
−0.610835 | + | 0.791758i | \(0.709166\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 15.5885i | 0.788342i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.50000 | + | 2.59808i | −0.226995 | + | 0.131056i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 10.5000 | + | 18.1865i | 0.528312 | + | 0.915064i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.50000 | − | 9.52628i | 0.276037 | − | 0.478110i | −0.694359 | − | 0.719629i | \(-0.744312\pi\) |
0.970396 | + | 0.241518i | \(0.0776454\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 9.00000 | + | 12.1244i | 0.450564 | + | 0.606977i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.50000 | − | 2.59808i | −0.224719 | − | 0.129742i | 0.383414 | − | 0.923576i | \(-0.374748\pi\) |
−0.608134 | + | 0.793835i | \(0.708081\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −18.0000 | + | 10.3923i | −0.896644 | + | 0.517678i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.50000 | + | 2.59808i | 0.0745356 | + | 0.129099i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.50000 | − | 0.866025i | 0.0741702 | − | 0.0428222i | −0.462456 | − | 0.886642i | \(-0.653032\pi\) |
0.536626 | + | 0.843820i | \(0.319698\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3.00000 | 0.147979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 9.00000 | + | 5.19615i | 0.442861 | + | 0.255686i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.00000 | − | 5.19615i | −0.441793 | − | 0.255069i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 19.0526i | − | 0.933008i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 24.2487i | − | 1.18463i | −0.805708 | − | 0.592314i | \(-0.798215\pi\) | ||
0.805708 | − | 0.592314i | \(-0.201785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −19.5000 | − | 11.2583i | −0.950372 | − | 0.548697i | −0.0571754 | − | 0.998364i | \(-0.518209\pi\) |
−0.893196 | + | 0.449667i | \(0.851543\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −3.00000 | − | 1.73205i | −0.145865 | − | 0.0842152i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 12.0000 | 0.582086 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −21.0000 | + | 12.1244i | −1.01626 | + | 0.586739i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −18.0000 | −0.869048 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.50000 | + | 12.9904i | 0.361262 | + | 0.625725i | 0.988169 | − | 0.153370i | \(-0.0490126\pi\) |
−0.626907 | + | 0.779094i | \(0.715679\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.50000 | − | 0.866025i | 0.0720854 | − | 0.0416185i | −0.463524 | − | 0.886084i | \(-0.653415\pi\) |
0.535609 | + | 0.844466i | \(0.320082\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −22.5000 | − | 12.9904i | −1.07879 | − | 0.622841i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −22.5000 | + | 2.59808i | −1.07632 | + | 0.124283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.50000 | − | 14.7224i | 0.405683 | − | 0.702663i | −0.588718 | − | 0.808339i | \(-0.700367\pi\) |
0.994401 | + | 0.105675i | \(0.0337004\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.00000 | − | 8.66025i | −0.238095 | − | 0.412393i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.5000 | − | 11.2583i | 0.926473 | − | 0.534899i | 0.0407786 | − | 0.999168i | \(-0.487016\pi\) |
0.885694 | + | 0.464269i | \(0.153683\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 25.9808i | − | 1.23161i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.50000 | + | 12.9904i | 0.354738 | + | 0.614424i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6.92820i | 0.326962i | 0.986546 | + | 0.163481i | \(0.0522723\pi\) | ||||
−0.986546 | + | 0.163481i | \(0.947728\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.0000 | + | 25.9808i | −0.706322 | + | 1.22339i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4.00000 | − | 6.92820i | 0.187936 | − | 0.325515i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 54.0000 | 2.53156 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0000 | 0.467780 | 0.233890 | − | 0.972263i | \(-0.424854\pi\) | ||||
0.233890 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.50000 | − | 12.9904i | 0.350070 | − | 0.606339i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.50000 | − | 12.9904i | 0.349310 | − | 0.605022i | −0.636817 | − | 0.771015i | \(-0.719749\pi\) |
0.986127 | + | 0.165992i | \(0.0530827\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.3923i | 0.482971i | 0.970404 | + | 0.241486i | \(0.0776347\pi\) | ||||
−0.970404 | + | 0.241486i | \(0.922365\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −6.00000 | − | 10.3923i | −0.278243 | − | 0.481932i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 17.3205i | 0.801498i | 0.916188 | + | 0.400749i | \(0.131250\pi\) | ||||
−0.916188 | + | 0.400749i | \(0.868750\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.0000 | + | 8.66025i | −0.692636 | + | 0.399893i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.50000 | − | 4.33013i | −0.115194 | − | 0.199522i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −21.0000 | + | 36.3731i | −0.965581 | + | 1.67244i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.00000 | + | 17.3205i | 0.0917663 | + | 0.794719i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3.00000 | − | 1.73205i | −0.137361 | − | 0.0793052i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −13.5000 | + | 7.79423i | −0.616831 | + | 0.356127i | −0.775634 | − | 0.631183i | \(-0.782570\pi\) |
0.158803 | + | 0.987310i | \(0.449236\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −18.0000 | −0.819028 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 22.5000 | − | 12.9904i | 1.02167 | − | 0.589863i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −16.0000 | −0.725029 | −0.362515 | − | 0.931978i | \(-0.618082\pi\) | ||||
−0.362515 | + | 0.931978i | \(0.618082\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.00000 | + | 5.19615i | 0.406994 | + | 0.234978i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.5000 | + | 9.52628i | 0.744635 | + | 0.429915i | 0.823752 | − | 0.566950i | \(-0.191877\pi\) |
−0.0791174 | + | 0.996865i | \(0.525210\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 25.9808i | − | 1.17011i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 20.7846i | 0.934199i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 27.0000 | + | 15.5885i | 1.21112 | + | 0.699238i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 10.5000 | + | 6.06218i | 0.470045 | + | 0.271380i | 0.716258 | − | 0.697835i | \(-0.245853\pi\) |
−0.246214 | + | 0.969216i | \(0.579187\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 21.0000 | 0.938211 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.50000 | + | 4.33013i | −0.334408 | + | 0.193071i | −0.657797 | − | 0.753196i | \(-0.728511\pi\) |
0.323388 | + | 0.946266i | \(0.395178\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9.00000 | 0.400495 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 7.00000 | + | 12.1244i | 0.310881 | + | 0.538462i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5000 | − | 9.52628i | 0.731350 | − | 0.422245i | −0.0875661 | − | 0.996159i | \(-0.527909\pi\) |
0.818916 | + | 0.573914i | \(0.194576\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.0000 | − | 12.1244i | −0.928985 | − | 0.536350i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 20.0000 | + | 8.66025i | 0.883022 | + | 0.382360i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.0000 | − | 41.5692i | 1.05757 | − | 1.83176i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.00000 | − | 5.19615i | −0.131940 | − | 0.228527i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 7.50000 | − | 4.33013i | 0.329213 | − | 0.190071i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 41.5692i | − | 1.82118i | −0.413310 | − | 0.910590i | \(-0.635627\pi\) | ||
0.413310 | − | 0.910590i | \(-0.364373\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 2.50000 | + | 4.33013i | 0.109317 | + | 0.189343i | 0.915494 | − | 0.402332i | \(-0.131800\pi\) |
−0.806177 | + | 0.591675i | \(0.798467\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 13.8564i | 0.604743i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.00000 | − | 10.3923i | 0.261364 | − | 0.452696i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.00000 | − | 3.46410i | 0.0869565 | − | 0.150613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.00000 | 0.260378 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 45.0000 | 1.94917 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.0000 | + | 31.1769i | −0.778208 | + | 1.34790i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.00000 | + | 10.3923i | −0.258919 | + | 0.448461i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 17.3205i | − | 0.746047i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.50000 | − | 4.33013i | −0.107483 | − | 0.186167i | 0.807267 | − | 0.590187i | \(-0.200946\pi\) |
−0.914750 | + | 0.404020i | \(0.867613\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 1.73205i | − | 0.0743294i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −40.5000 | + | 23.3827i | −1.73483 | + | 1.00160i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.500000 | + | 0.866025i | 0.0213785 | + | 0.0370286i | 0.876517 | − | 0.481371i | \(-0.159861\pi\) |
−0.855138 | + | 0.518400i | \(0.826528\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −7.00000 | + | 12.1244i | −0.298753 | + | 0.517455i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 37.5000 | − | 4.33013i | 1.59755 | − | 0.184470i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −21.0000 | − | 12.1244i | −0.893011 | − | 0.515580i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.50000 | − | 7.79423i | −0.190671 | − | 0.330252i | 0.754802 | − | 0.655953i | \(-0.227733\pi\) |
−0.945473 | + | 0.325701i | \(0.894400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 63.0000 | 2.66462 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.00000 | − | 5.19615i | 0.379980 | − | 0.219382i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.0000 | 0.505740 | 0.252870 | − | 0.967500i | \(-0.418626\pi\) | ||||
0.252870 | + | 0.967500i | \(0.418626\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −18.0000 | − | 10.3923i | −0.757266 | − | 0.437208i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.00000 | − | 1.73205i | −0.125988 | − | 0.0727393i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 20.7846i | − | 0.871336i | −0.900107 | − | 0.435668i | \(-0.856512\pi\) | ||
0.900107 | − | 0.435668i | \(-0.143488\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10.3923i | − | 0.434904i | −0.976071 | − | 0.217452i | \(-0.930225\pi\) | ||
0.976071 | − | 0.217452i | \(-0.0697746\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 21.0000 | + | 12.1244i | 0.877288 | + | 0.506502i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −18.0000 | − | 10.3923i | −0.750652 | − | 0.433389i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 46.0000 | 1.91501 | 0.957503 | − | 0.288425i | \(-0.0931316\pi\) | ||||
0.957503 | + | 0.288425i | \(0.0931316\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.5000 | − | 6.06218i | 0.436365 | − | 0.251936i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12.0000 | 0.497844 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.00000 | − | 5.19615i | −0.124247 | − | 0.215203i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 27.0000 | − | 15.5885i | 1.11631 | − | 0.644503i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 4.50000 | + | 2.59808i | 0.185735 | + | 0.107234i | 0.589984 | − | 0.807415i | \(-0.299134\pi\) |
−0.404249 | + | 0.914649i | \(0.632467\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 16.0000 | + | 6.92820i | 0.659269 | + | 0.285472i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.00000 | − | 15.5885i | 0.370211 | − | 0.641223i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1.50000 | − | 2.59808i | −0.0615976 | − | 0.106690i | 0.833582 | − | 0.552396i | \(-0.186286\pi\) |
−0.895180 | + | 0.445705i | \(0.852953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.0000 | + | 15.5885i | −1.10689 | + | 0.639064i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.1244i | 0.496217i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.50000 | − | 7.79423i | −0.183865 | − | 0.318464i | 0.759328 | − | 0.650708i | \(-0.225528\pi\) |
−0.943193 | + | 0.332244i | \(0.892194\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6.92820i | 0.282607i | 0.989966 | + | 0.141304i | \(0.0451294\pi\) | ||||
−0.989966 | + | 0.141304i | \(0.954871\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.00000 | + | 8.66025i | −0.203616 | + | 0.352673i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.50000 | + | 2.59808i | −0.0609837 | + | 0.105627i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.0000 | −1.62355 | −0.811775 | − | 0.583970i | \(-0.801498\pi\) | ||||
−0.811775 | + | 0.583970i | \(0.801498\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 30.0000 | 1.21566 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.50000 | + | 7.79423i | −0.182051 | + | 0.315321i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.50000 | + | 14.7224i | −0.343312 | + | 0.594633i | −0.985046 | − | 0.172294i | \(-0.944882\pi\) |
0.641734 | + | 0.766927i | \(0.278215\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 25.9808i | 1.04765i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −13.5000 | − | 23.3827i | −0.543490 | − | 0.941351i | −0.998700 | − | 0.0509678i | \(-0.983769\pi\) |
0.455211 | − | 0.890384i | \(-0.349564\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.1769i | 1.25311i | 0.779379 | + | 0.626553i | \(0.215535\pi\) | ||||
−0.779379 | + | 0.626553i | \(0.784465\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −22.5000 | + | 12.9904i | −0.902894 | + | 0.521286i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 15.0000 | + | 25.9808i | 0.600962 | + | 1.04090i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 9.00000 | + | 12.1244i | 0.359425 | + | 0.484200i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.5000 | + | 7.79423i | −0.537427 | + | 0.310283i | −0.744035 | − | 0.668140i | \(-0.767091\pi\) |
0.206609 | + | 0.978424i | \(0.433757\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.5000 | + | 19.9186i | 0.457084 | + | 0.791693i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 21.0000 | 0.833360 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.5000 | + | 12.9904i | −0.891482 | + | 0.514698i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.0000 | 0.712069 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −34.5000 | − | 19.9186i | −1.36267 | − | 0.786737i | −0.372690 | − | 0.927956i | \(-0.621564\pi\) |
−0.989978 | + | 0.141219i | \(0.954898\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.50000 | − | 0.866025i | −0.0591542 | − | 0.0341527i | 0.470131 | − | 0.882597i | \(-0.344207\pi\) |
−0.529285 | + | 0.848444i | \(0.677540\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 36.3731i | 1.43219i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.46410i | 0.136188i | 0.997679 | + | 0.0680939i | \(0.0216918\pi\) | ||||
−0.997679 | + | 0.0680939i | \(0.978308\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.00000 | + | 5.19615i | 0.353281 | + | 0.203967i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.0000 | + | 6.92820i | 0.470317 | + | 0.271538i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −18.0000 | −0.704394 | −0.352197 | − | 0.935926i | \(-0.614565\pi\) | ||||
−0.352197 | + | 0.935926i | \(0.614565\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.5000 | − | 7.79423i | 0.527489 | − | 0.304546i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −14.0000 | −0.546192 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 22.5000 | + | 38.9711i | 0.876476 | + | 1.51810i | 0.855183 | + | 0.518327i | \(0.173445\pi\) |
0.0212930 | + | 0.999773i | \(0.493222\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.5000 | + | 11.2583i | −0.758462 | + | 0.437898i | −0.828743 | − | 0.559629i | \(-0.810944\pi\) |
0.0702812 | + | 0.997527i | \(0.477610\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −13.5000 | − | 7.79423i | −0.524297 | − | 0.302703i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −27.0000 | − | 36.3731i | −1.04702 | − | 1.41049i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.5000 | + | 38.9711i | −0.871203 | + | 1.50897i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9.50000 | − | 16.4545i | −0.367291 | − | 0.636167i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −21.0000 | + | 12.1244i | −0.810696 | + | 0.468056i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 48.4974i | − | 1.86944i | −0.355387 | − | 0.934719i | \(-0.615651\pi\) | ||
0.355387 | − | 0.934719i | \(-0.384349\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 10.0000 | + | 17.3205i | 0.384900 | + | 0.666667i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 41.5692i | − | 1.59763i | −0.601574 | − | 0.798817i | \(-0.705459\pi\) | ||
0.601574 | − | 0.798817i | \(-0.294541\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −15.0000 | + | 25.9808i | −0.575647 | + | 0.997050i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.00000 | + | 10.3923i | −0.229920 | + | 0.398234i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.00000 | −0.343872 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −11.0000 | + | 19.0526i | −0.419676 | + | 0.726900i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.50000 | + | 7.79423i | −0.171436 | + | 0.296936i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 10.3923i | − | 0.395342i | −0.980268 | − | 0.197671i | \(-0.936662\pi\) | ||
0.980268 | − | 0.197671i | \(-0.0633378\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.0000 | − | 20.7846i | −0.455842 | − | 0.789542i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 57.1577i | 2.16811i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −22.5000 | + | 12.9904i | −0.852248 | + | 0.492046i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.5000 | − | 23.3827i | −0.510617 | − | 0.884414i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −16.5000 | + | 28.5788i | −0.623196 | + | 1.07941i | 0.365690 | + | 0.930737i | \(0.380833\pi\) |
−0.988887 | + | 0.148671i | \(0.952500\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.50000 | − | 2.59808i | −0.169480 | − | 0.0978492i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −9.00000 | + | 5.19615i | −0.338480 | + | 0.195421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15.5000 | + | 26.8468i | 0.582115 | + | 1.00825i | 0.995228 | + | 0.0975728i | \(0.0311079\pi\) |
−0.413114 | + | 0.910679i | \(0.635559\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.0000 | −0.525041 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −18.0000 | + | 10.3923i | −0.674105 | + | 0.389195i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 54.0000 | 2.01949 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 15.0000 | + | 8.66025i | 0.560185 | + | 0.323423i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.50000 | + | 0.866025i | 0.0559406 | + | 0.0322973i | 0.527709 | − | 0.849425i | \(-0.323051\pi\) |
−0.471769 | + | 0.881722i | \(0.656384\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 55.4256i | 2.06416i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 22.5167i | 0.837404i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.0000 | + | 17.3205i | 1.11417 | + | 0.643268i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.50000 | + | 0.866025i | 0.0556319 | + | 0.0321191i | 0.527558 | − | 0.849519i | \(-0.323108\pi\) |
−0.471926 | + | 0.881638i | \(0.656441\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −31.5000 | + | 18.1865i | −1.16507 | + | 0.672653i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10.0000 | −0.369358 | −0.184679 | − | 0.982799i | \(-0.559125\pi\) | ||||
−0.184679 | + | 0.982799i | \(0.559125\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −7.50000 | − | 12.9904i | −0.276642 | − | 0.479157i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.0000 | + | 8.66025i | −0.552532 | + | 0.319005i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.50000 | − | 0.866025i | −0.0551784 | − | 0.0318573i | 0.472157 | − | 0.881514i | \(-0.343476\pi\) |
−0.527335 | + | 0.849657i | \(0.676809\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 9.00000 | − | 20.7846i | 0.330623 | − | 0.763542i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.50000 | + | 2.59808i | −0.0550297 | + | 0.0953142i | −0.892228 | − | 0.451585i | \(-0.850859\pi\) |
0.837198 | + | 0.546899i | \(0.184192\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.5000 | − | 38.9711i | −0.824336 | − | 1.42779i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 6.00000 | − | 3.46410i | 0.219529 | − | 0.126745i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 41.5692i | − | 1.51891i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.5000 | + | 19.9186i | 0.419641 | + | 0.726839i | 0.995903 | − | 0.0904254i | \(-0.0288227\pi\) |
−0.576262 | + | 0.817265i | \(0.695489\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 5.19615i | − | 0.189358i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −12.0000 | + | 20.7846i | −0.436725 | + | 0.756429i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.50000 | + | 11.2583i | −0.236247 | + | 0.409191i | −0.959634 | − | 0.281251i | \(-0.909251\pi\) |
0.723388 | + | 0.690442i | \(0.242584\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −18.0000 | −0.653359 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30.0000 | 1.08750 | 0.543750 | − | 0.839248i | \(-0.317004\pi\) | ||||
0.543750 | + | 0.839248i | \(0.317004\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 27.0000 | − | 46.7654i | 0.977466 | − | 1.69302i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.00000 | + | 15.5885i | −0.325396 | + | 0.563602i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 15.5885i | − | 0.562867i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20.5000 | + | 35.5070i | 0.739249 | + | 1.28042i | 0.952834 | + | 0.303492i | \(0.0981526\pi\) |
−0.213585 | + | 0.976924i | \(0.568514\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 15.5885i | 0.561405i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −37.5000 | + | 21.6506i | −1.34878 | + | 0.778719i | −0.988077 | − | 0.153961i | \(-0.950797\pi\) |
−0.360704 | + | 0.932680i | \(0.617464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.00000 | + | 13.8564i | 0.287368 | + | 0.497737i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −22.5000 | − | 30.3109i | −0.806146 | − | 1.08600i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | + | 15.5885i | 0.966136 | + | 0.557799i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 37.5000 | − | 21.6506i | 1.34014 | − | 0.773731i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 7.50000 | + | 12.9904i | 0.267686 | + | 0.463647i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.0000 | 0.998092 | 0.499046 | − | 0.866575i | \(-0.333684\pi\) | ||||
0.499046 | + | 0.866575i | \(0.333684\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 10.5000 | − | 6.06218i | 0.373810 | − | 0.215819i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 24.0000 | 0.853342 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31.5000 | + | 18.1865i | 1.11860 | + | 0.645823i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −4.50000 | − | 2.59808i | −0.159599 | − | 0.0921443i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.8564i | 0.490819i | 0.969419 | + | 0.245410i | \(0.0789224\pi\) | ||||
−0.969419 | + | 0.245410i | \(0.921078\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.19615i | − | 0.183827i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 15.0000 | + | 8.66025i | 0.529999 | + | 0.305995i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −21.0000 | − | 12.1244i | −0.741074 | − | 0.427859i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 54.0000 | 1.90325 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −22.5000 | + | 12.9904i | −0.792038 | + | 0.457283i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 6.00000 | 0.210949 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.50000 | + | 11.2583i | 0.228246 | + | 0.395333i | 0.957288 | − | 0.289135i | \(-0.0933677\pi\) |
−0.729042 | + | 0.684468i | \(0.760034\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.5000 | − | 6.06218i | 0.368251 | − | 0.212610i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −27.0000 | − | 15.5885i | −0.945769 | − | 0.546040i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −31.5000 | − | 42.4352i | −1.10205 | − | 1.48462i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −18.0000 | + | 31.1769i | −0.628971 | + | 1.08941i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −22.5000 | − | 38.9711i | −0.785255 | − | 1.36010i | −0.928846 | − | 0.370465i | \(-0.879198\pi\) |
0.143591 | − | 0.989637i | \(-0.454135\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.50000 | + | 0.866025i | −0.0522867 | + | 0.0301877i | −0.525915 | − | 0.850537i | \(-0.676277\pi\) |
0.473629 | + | 0.880725i | \(0.342944\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13.8564i | 0.482418i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −19.5000 | − | 33.7750i | −0.678081 | − | 1.17447i | −0.975558 | − | 0.219742i | \(-0.929478\pi\) |
0.297477 | − | 0.954729i | \(-0.403855\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6.92820i | 0.240626i | 0.992736 | + | 0.120313i | \(0.0383899\pi\) | ||||
−0.992736 | + | 0.120313i | \(0.961610\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.00000 | − | 1.73205i | 0.0346896 | − | 0.0600842i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.50000 | − | 12.9904i | 0.259860 | − | 0.450090i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −63.0000 | −2.18020 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 20.0000 | 0.691301 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 10.5000 | − | 18.1865i | 0.362500 | − | 0.627869i | −0.625871 | − | 0.779926i | \(-0.715257\pi\) |
0.988372 | + | 0.152057i | \(0.0485899\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.0000 | − | 39.8372i | 0.793103 | − | 1.37370i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.5885i | 0.536895i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.0000 | − | 36.3731i | −0.722422 | − | 1.25127i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 3.46410i | − | 0.119028i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.50000 | + | 2.59808i | −0.154440 | + | 0.0891657i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 0 | 0 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 17.5000 | − | 30.3109i | 0.599189 | − | 1.03783i | −0.393753 | − | 0.919216i | \(-0.628823\pi\) |
0.992941 | − | 0.118609i | \(-0.0378434\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −24.0000 | − | 10.3923i | −0.820783 | − | 0.355409i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 37.5000 | + | 21.6506i | 1.28098 | + | 0.739572i | 0.977027 | − | 0.213117i | \(-0.0683615\pi\) |
0.303949 | + | 0.952688i | \(0.401695\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 49.5000 | − | 28.5788i | 1.68892 | − | 0.975097i | 0.733571 | − | 0.679613i | \(-0.237852\pi\) |
0.955348 | − | 0.295484i | \(-0.0954809\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −15.0000 | − | 25.9808i | −0.511199 | − | 0.885422i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −12.0000 | −0.408485 | −0.204242 | − | 0.978920i | \(-0.565473\pi\) | ||||
−0.204242 | + | 0.978920i | \(0.565473\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.5000 | + | 12.9904i | −0.765023 | + | 0.441686i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −8.00000 | −0.271694 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −21.0000 | − | 12.1244i | −0.712376 | − | 0.411291i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.5000 | + | 12.9904i | 0.762383 | + | 0.440162i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 17.3205i | 0.586210i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.3923i | 0.351324i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.5000 | + | 12.9904i | 0.759771 | + | 0.438654i | 0.829214 | − | 0.558932i | \(-0.188789\pi\) |
−0.0694425 | + | 0.997586i | \(0.522122\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 12.0000 | + | 6.92820i | 0.404750 | + | 0.233682i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −18.0000 | −0.606435 | −0.303218 | − | 0.952921i | \(-0.598061\pi\) | ||||
−0.303218 | + | 0.952921i | \(0.598061\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −4.50000 | + | 2.59808i | −0.151437 | + | 0.0874322i | −0.573804 | − | 0.818993i | \(-0.694533\pi\) |
0.422367 | + | 0.906425i | \(0.361199\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 9.00000 | 0.302532 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.50000 | + | 2.59808i | 0.0503651 | + | 0.0872349i | 0.890109 | − | 0.455748i | \(-0.150628\pi\) |
−0.839744 | + | 0.542983i | \(0.817295\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −21.0000 | + | 12.1244i | −0.704317 | + | 0.406638i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.00000 | − | 1.73205i | −0.100504 | − | 0.0580259i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 7.50000 | − | 0.866025i | 0.250978 | − | 0.0289804i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.0000 | − | 31.1769i | 0.601674 | − | 1.04213i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 13.5000 | + | 23.3827i | 0.450752 | + | 0.780725i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.0000 | − | 17.3205i | 1.00056 | − | 0.577671i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 5.19615i | − | 0.173109i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −21.0000 | − | 36.3731i | −0.698836 | − | 1.21042i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 5.19615i | 0.172726i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −6.50000 | + | 11.2583i | −0.215829 | + | 0.373827i | −0.953529 | − | 0.301302i | \(-0.902579\pi\) |
0.737700 | + | 0.675129i | \(0.235912\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.00000 | + | 5.19615i | −0.0995037 | + | 0.172345i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 48.0000 | 1.59031 | 0.795155 | − | 0.606406i | \(-0.207389\pi\) | ||||
0.795155 | + | 0.606406i | \(0.207389\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.0000 | 0.397142 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −10.5000 | + | 18.1865i | −0.347119 | + | 0.601228i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −9.00000 | + | 15.5885i | −0.297206 | + | 0.514776i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 38.1051i | − | 1.25697i | −0.777821 | − | 0.628486i | \(-0.783675\pi\) | ||
0.777821 | − | 0.628486i | \(-0.216325\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −2.50000 | − | 4.33013i | −0.0823778 | − | 0.142683i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 46.7654i | − | 1.53930i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 16.0000 | + | 27.7128i | 0.525509 | + | 0.910208i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −19.5000 | + | 33.7750i | −0.639774 | + | 1.10812i | 0.345708 | + | 0.938342i | \(0.387639\pi\) |
−0.985482 | + | 0.169779i | \(0.945695\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.0000 | + | 8.66025i | 0.655474 | + | 0.283828i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.00000 | + | 1.73205i | 0.0982156 | + | 0.0567048i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −27.0000 | + | 15.5885i | −0.882994 | + | 0.509797i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.5000 | + | 42.4352i | 0.800380 | + | 1.38630i | 0.919366 | + | 0.393403i | \(0.128702\pi\) |
−0.118986 | + | 0.992896i | \(0.537964\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 19.0000 | 0.620042 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −13.5000 | + | 7.79423i | −0.440087 | + | 0.254085i | −0.703635 | − | 0.710562i | \(-0.748441\pi\) |
0.263547 | + | 0.964646i | \(0.415107\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.0000 | 1.46540 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −45.0000 | − | 25.9808i | −1.46385 | − | 0.845154i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.5000 | − | 14.7224i | −0.828639 | − | 0.478415i | 0.0247477 | − | 0.999694i | \(-0.492122\pi\) |
−0.853386 | + | 0.521279i | \(0.825455\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 36.3731i | 1.18072i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.19615i | 0.168497i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −10.5000 | − | 6.06218i | −0.340128 | − | 0.196373i | 0.320200 | − | 0.947350i | \(-0.396250\pi\) |
−0.660329 | + | 0.750977i | \(0.729583\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −63.0000 | − | 36.3731i | −2.03863 | − | 1.17700i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 30.0000 | 0.969762 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 9.00000 | − | 5.19615i | 0.290625 | − | 0.167793i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.0000 | −0.483871 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.0000 | − | 20.7846i | −0.386695 | − | 0.669775i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31.5000 | + | 18.1865i | −1.01402 | + | 0.585445i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.5000 | + | 25.1147i | 1.39887 | + | 0.807635i | 0.994274 | − | 0.106862i | \(-0.0340803\pi\) |
0.404592 | + | 0.914497i | \(0.367414\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.50000 | + | 12.9904i | 0.0481869 | + | 0.417311i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13.5000 | − | 23.3827i | 0.433236 | − | 0.750386i | −0.563914 | − | 0.825833i | \(-0.690705\pi\) |
0.997150 | + | 0.0754473i | \(0.0240385\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33.0000 | − | 57.1577i | −1.05793 | − | 1.83239i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 18.0000 | − | 10.3923i | 0.576461 | − | 0.332820i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 6.92820i | 0.221653i | 0.993840 | + | 0.110826i | \(0.0353498\pi\) | ||||
−0.993840 | + | 0.110826i | \(0.964650\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.0000 | + | 25.9808i | 0.479402 | + | 0.830349i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 31.1769i | − | 0.995402i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.50000 | − | 7.79423i | 0.143528 | − | 0.248597i | −0.785295 | − | 0.619122i | \(-0.787489\pi\) |
0.928823 | + | 0.370525i | \(0.120822\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27.0000 | + | 46.7654i | −0.860292 | + | 1.49007i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.00000 | 0.190982 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 63.0000 | 2.00328 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.5000 | − | 21.6506i | 0.397076 | − | 0.687755i | −0.596288 | − | 0.802771i | \(-0.703358\pi\) |
0.993364 | + | 0.115015i | \(0.0366917\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 14.0000 | − | 24.2487i | 0.444277 | − | 0.769510i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 36.3731i | − | 1.15310i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 15.5000 | + | 26.8468i | 0.490890 | + | 0.850246i | 0.999945 | − | 0.0104877i | \(-0.00333839\pi\) |
−0.509055 | + | 0.860734i | \(0.670005\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1216.2.n.a.255.1 | 2 | ||
4.3 | odd | 2 | 1216.2.n.b.255.1 | 2 | |||
8.3 | odd | 2 | 304.2.n.a.255.1 | yes | 2 | ||
8.5 | even | 2 | 304.2.n.b.255.1 | yes | 2 | ||
19.12 | odd | 6 | 1216.2.n.b.639.1 | 2 | |||
24.5 | odd | 2 | 2736.2.bm.h.559.1 | 2 | |||
24.11 | even | 2 | 2736.2.bm.g.559.1 | 2 | |||
76.31 | even | 6 | inner | 1216.2.n.a.639.1 | 2 | ||
152.69 | odd | 6 | 304.2.n.a.31.1 | ✓ | 2 | ||
152.107 | even | 6 | 304.2.n.b.31.1 | yes | 2 | ||
456.107 | odd | 6 | 2736.2.bm.h.1855.1 | 2 | |||
456.221 | even | 6 | 2736.2.bm.g.1855.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
304.2.n.a.31.1 | ✓ | 2 | 152.69 | odd | 6 | ||
304.2.n.a.255.1 | yes | 2 | 8.3 | odd | 2 | ||
304.2.n.b.31.1 | yes | 2 | 152.107 | even | 6 | ||
304.2.n.b.255.1 | yes | 2 | 8.5 | even | 2 | ||
1216.2.n.a.255.1 | 2 | 1.1 | even | 1 | trivial | ||
1216.2.n.a.639.1 | 2 | 76.31 | even | 6 | inner | ||
1216.2.n.b.255.1 | 2 | 4.3 | odd | 2 | |||
1216.2.n.b.639.1 | 2 | 19.12 | odd | 6 | |||
2736.2.bm.g.559.1 | 2 | 24.11 | even | 2 | |||
2736.2.bm.g.1855.1 | 2 | 456.221 | even | 6 | |||
2736.2.bm.h.559.1 | 2 | 24.5 | odd | 2 | |||
2736.2.bm.h.1855.1 | 2 | 456.107 | odd | 6 |