Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,2,Mod(307,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 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("900.307");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.k (of order \(4\), 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: | \(7.18653618192\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 307.1 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.307 |
Dual form | 900.2.k.l.343.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.22474 | − | 0.707107i | −0.866025 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | + | 1.73205i | 0.500000 | + | 0.866025i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.15660 | − | 3.15660i | 1.19308 | − | 1.19308i | 0.216884 | − | 0.976197i | \(-0.430411\pi\) |
0.976197 | − | 0.216884i | \(-0.0695893\pi\) | |||||||
\(8\) | − | 2.82843i | − | 1.00000i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.60368 | − | 1.60368i | 0.444781 | − | 0.444781i | −0.448834 | − | 0.893615i | \(-0.648160\pi\) |
0.893615 | + | 0.448834i | \(0.148160\pi\) | |||||||
\(14\) | −6.09808 | + | 1.63397i | −1.62978 | + | 0.436698i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.00000 | + | 3.46410i | −0.500000 | + | 0.866025i | ||||
\(17\) | −4.24264 | − | 4.24264i | −1.02899 | − | 1.02899i | −0.999567 | − | 0.0294245i | \(-0.990633\pi\) |
−0.0294245 | − | 0.999567i | \(-0.509367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.19615 | −0.733248 | −0.366624 | − | 0.930369i | \(-0.619486\pi\) | ||||
−0.366624 | + | 0.930369i | \(0.619486\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.41421 | + | 2.44949i | −0.301511 | + | 0.522233i | ||||
\(23\) | 5.27792 | + | 5.27792i | 1.10052 | + | 1.10052i | 0.994348 | + | 0.106174i | \(0.0338601\pi\) |
0.106174 | + | 0.994348i | \(0.466140\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.09808 | + | 0.830127i | −0.607583 | + | 0.162801i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 8.62398 | + | 2.31079i | 1.62978 | + | 0.436698i | ||||
\(29\) | − | 0.535898i | − | 0.0995138i | −0.998761 | − | 0.0497569i | \(-0.984155\pi\) | ||
0.998761 | − | 0.0497569i | \(-0.0158447\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.73205i | 0.670296i | 0.942165 | + | 0.335148i | \(0.108786\pi\) | ||||
−0.942165 | + | 0.335148i | \(0.891214\pi\) | |||||||
\(32\) | 4.89898 | − | 2.82843i | 0.866025 | − | 0.500000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.19615 | + | 8.19615i | 0.376637 | + | 1.40563i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.72741 | − | 7.72741i | −1.27038 | − | 1.27038i | −0.945890 | − | 0.324488i | \(-0.894808\pi\) |
−0.324488 | − | 0.945890i | \(-0.605192\pi\) | |||||||
\(38\) | 3.91447 | + | 2.26002i | 0.635011 | + | 0.366624i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.46410 | −0.228654 | −0.114327 | − | 0.993443i | \(-0.536471\pi\) | ||||
−0.114327 | + | 0.993443i | \(0.536471\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.15660 | − | 3.15660i | −0.481376 | − | 0.481376i | 0.424195 | − | 0.905571i | \(-0.360557\pi\) |
−0.905571 | + | 0.424195i | \(0.860557\pi\) | |||||||
\(44\) | 3.46410 | − | 2.00000i | 0.522233 | − | 0.301511i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −2.73205 | − | 10.1962i | −0.402819 | − | 1.50334i | ||||
\(47\) | 0.656339 | − | 0.656339i | 0.0957369 | − | 0.0957369i | −0.657616 | − | 0.753353i | \(-0.728435\pi\) |
0.753353 | + | 0.657616i | \(0.228435\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 12.9282i | − | 1.84689i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.38134 | + | 1.17398i | 0.607583 | + | 0.162801i | ||||
\(53\) | 3.86370 | − | 3.86370i | 0.530720 | − | 0.530720i | −0.390066 | − | 0.920787i | \(-0.627548\pi\) |
0.920787 | + | 0.390066i | \(0.127548\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.92820 | − | 8.92820i | −1.19308 | − | 1.19308i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.378937 | + | 0.656339i | −0.0497569 | + | 0.0861815i | ||||
\(59\) | 11.4641 | 1.49250 | 0.746249 | − | 0.665666i | \(-0.231853\pi\) | ||||
0.746249 | + | 0.665666i | \(0.231853\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.00000 | 0.384111 | 0.192055 | − | 0.981384i | \(-0.438485\pi\) | ||||
0.192055 | + | 0.981384i | \(0.438485\pi\) | |||||||
\(62\) | 2.63896 | − | 4.57081i | 0.335148 | − | 0.580493i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.00000 | −1.00000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.91447 | + | 3.91447i | −0.478229 | + | 0.478229i | −0.904565 | − | 0.426336i | \(-0.859804\pi\) |
0.426336 | + | 0.904565i | \(0.359804\pi\) | |||||||
\(68\) | 3.10583 | − | 11.5911i | 0.376637 | − | 1.40563i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.53590i | 0.300956i | 0.988613 | + | 0.150478i | \(0.0480812\pi\) | ||||
−0.988613 | + | 0.150478i | \(0.951919\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.82843 | + | 2.82843i | −0.331042 | + | 0.331042i | −0.852982 | − | 0.521940i | \(-0.825209\pi\) |
0.521940 | + | 0.852982i | \(0.325209\pi\) | |||||||
\(74\) | 4.00000 | + | 14.9282i | 0.464991 | + | 1.73537i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.19615 | − | 5.53590i | −0.366624 | − | 0.635011i | ||||
\(77\) | −6.31319 | − | 6.31319i | −0.719455 | − | 0.719455i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.46410 | 0.839777 | 0.419889 | − | 0.907576i | \(-0.362069\pi\) | ||||
0.419889 | + | 0.907576i | \(0.362069\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.79315 | + | 1.03528i | 0.198020 | + | 0.114327i | ||||
\(83\) | −9.14162 | − | 9.14162i | −1.00342 | − | 1.00342i | −0.999994 | − | 0.00342905i | \(-0.998908\pi\) |
−0.00342905 | − | 0.999994i | \(-0.501092\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.63397 | + | 6.09808i | 0.176196 | + | 0.657572i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −5.65685 | −0.603023 | ||||||||
\(89\) | − | 6.92820i | − | 0.734388i | −0.930144 | − | 0.367194i | \(-0.880318\pi\) | ||
0.930144 | − | 0.367194i | \(-0.119682\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10.1244i | − | 1.06132i | ||||||
\(92\) | −3.86370 | + | 14.4195i | −0.402819 | + | 1.50334i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.26795 | + | 0.339746i | −0.130779 | + | 0.0350421i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.88160 | − | 6.88160i | −0.698721 | − | 0.698721i | 0.265414 | − | 0.964135i | \(-0.414491\pi\) |
−0.964135 | + | 0.265414i | \(0.914491\pi\) | |||||||
\(98\) | −9.14162 | + | 15.8338i | −0.923443 | + | 1.59945i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.46410 | −0.543698 | −0.271849 | − | 0.962340i | \(-0.587635\pi\) | ||||
−0.271849 | + | 0.962340i | \(0.587635\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.89898 | + | 4.89898i | 0.482711 | + | 0.482711i | 0.905996 | − | 0.423286i | \(-0.139123\pi\) |
−0.423286 | + | 0.905996i | \(0.639123\pi\) | |||||||
\(104\) | −4.53590 | − | 4.53590i | −0.444781 | − | 0.444781i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.46410 | + | 2.00000i | −0.724978 | + | 0.194257i | ||||
\(107\) | 9.52056 | − | 9.52056i | 0.920387 | − | 0.920387i | −0.0766695 | − | 0.997057i | \(-0.524429\pi\) |
0.997057 | + | 0.0766695i | \(0.0244286\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.00000i | − | 0.670478i | −0.942133 | − | 0.335239i | \(-0.891183\pi\) | ||
0.942133 | − | 0.335239i | \(-0.108817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 4.62158 | + | 17.2480i | 0.436698 | + | 1.62978i | ||||
\(113\) | −9.79796 | + | 9.79796i | −0.921714 | + | 0.921714i | −0.997151 | − | 0.0754362i | \(-0.975965\pi\) |
0.0754362 | + | 0.997151i | \(0.475965\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.928203 | − | 0.535898i | 0.0861815 | − | 0.0497569i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −14.0406 | − | 8.10634i | −1.29254 | − | 0.746249i | ||||
\(119\) | −26.7846 | −2.45534 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −3.67423 | − | 2.12132i | −0.332650 | − | 0.192055i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.46410 | + | 3.73205i | −0.580493 | + | 0.335148i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.72741 | − | 7.72741i | 0.685696 | − | 0.685696i | −0.275581 | − | 0.961278i | \(-0.588870\pi\) |
0.961278 | + | 0.275581i | \(0.0888703\pi\) | |||||||
\(128\) | 9.79796 | + | 5.65685i | 0.866025 | + | 0.500000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 2.53590i | − | 0.221562i | −0.993845 | − | 0.110781i | \(-0.964665\pi\) | ||
0.993845 | − | 0.110781i | \(-0.0353353\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.0890 | + | 10.0890i | −0.874824 | + | 0.874824i | ||||
\(134\) | 7.56218 | − | 2.02628i | 0.653273 | − | 0.175044i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −12.0000 | + | 12.0000i | −1.02899 | + | 1.02899i | ||||
\(137\) | 10.9348 | + | 10.9348i | 0.934221 | + | 0.934221i | 0.997966 | − | 0.0637456i | \(-0.0203046\pi\) |
−0.0637456 | + | 0.997966i | \(0.520305\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.5359 | 1.06328 | 0.531641 | − | 0.846970i | \(-0.321576\pi\) | ||||
0.531641 | + | 0.846970i | \(0.321576\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.79315 | − | 3.10583i | 0.150478 | − | 0.260635i | ||||
\(143\) | −3.20736 | − | 3.20736i | −0.268213 | − | 0.268213i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.46410 | − | 1.46410i | 0.452212 | − | 0.121170i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5.65685 | − | 21.1117i | 0.464991 | − | 1.73537i | ||||
\(149\) | − | 11.8564i | − | 0.971315i | −0.874149 | − | 0.485657i | \(-0.838580\pi\) | ||
0.874149 | − | 0.485657i | \(-0.161420\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.73205i | 0.629225i | 0.949220 | + | 0.314613i | \(0.101875\pi\) | ||||
−0.949220 | + | 0.314613i | \(0.898125\pi\) | |||||||
\(152\) | 9.04008i | 0.733248i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.26795 | + | 12.1962i | 0.263339 | + | 0.982794i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.43211 | + | 4.43211i | 0.353721 | + | 0.353721i | 0.861492 | − | 0.507771i | \(-0.169530\pi\) |
−0.507771 | + | 0.861492i | \(0.669530\pi\) | |||||||
\(158\) | −9.14162 | − | 5.27792i | −0.727268 | − | 0.419889i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 33.3205 | 2.62602 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.32868 | + | 5.32868i | 0.417375 | + | 0.417375i | 0.884298 | − | 0.466923i | \(-0.154638\pi\) |
−0.466923 | + | 0.884298i | \(0.654638\pi\) | |||||||
\(164\) | −1.46410 | − | 2.53590i | −0.114327 | − | 0.198020i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.73205 | + | 17.6603i | 0.367278 | + | 1.37070i | ||||
\(167\) | −11.5911 | + | 11.5911i | −0.896947 | + | 0.896947i | −0.995165 | − | 0.0982179i | \(-0.968686\pi\) |
0.0982179 | + | 0.995165i | \(0.468686\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.85641i | 0.604339i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.31079 | − | 8.62398i | 0.176196 | − | 0.657572i | ||||
\(173\) | 3.48477 | − | 3.48477i | 0.264942 | − | 0.264942i | −0.562116 | − | 0.827058i | \(-0.690013\pi\) |
0.827058 | + | 0.562116i | \(0.190013\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.92820 | + | 4.00000i | 0.522233 | + | 0.301511i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −4.89898 | + | 8.48528i | −0.367194 | + | 0.635999i | ||||
\(179\) | 9.32051 | 0.696647 | 0.348324 | − | 0.937374i | \(-0.386751\pi\) | ||||
0.348324 | + | 0.937374i | \(0.386751\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.0717968 | −0.00533661 | −0.00266831 | − | 0.999996i | \(-0.500849\pi\) | ||||
−0.00266831 | + | 0.999996i | \(0.500849\pi\) | |||||||
\(182\) | −7.15900 | + | 12.3998i | −0.530660 | + | 0.919131i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 14.9282 | − | 14.9282i | 1.10052 | − | 1.10052i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.48528 | + | 8.48528i | −0.620505 | + | 0.620505i | ||||
\(188\) | 1.79315 | + | 0.480473i | 0.130779 | + | 0.0350421i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.07180i | 0.222267i | 0.993805 | + | 0.111134i | \(0.0354482\pi\) | ||||
−0.993805 | + | 0.111134i | \(0.964552\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.26054 | − | 7.26054i | 0.522625 | − | 0.522625i | −0.395738 | − | 0.918363i | \(-0.629511\pi\) |
0.918363 | + | 0.395738i | \(0.129511\pi\) | |||||||
\(194\) | 3.56218 | + | 13.2942i | 0.255749 | + | 0.954470i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 22.3923 | − | 12.9282i | 1.59945 | − | 0.923443i | ||||
\(197\) | −4.52004 | − | 4.52004i | −0.322040 | − | 0.322040i | 0.527509 | − | 0.849549i | \(-0.323126\pi\) |
−0.849549 | + | 0.527509i | \(0.823126\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.1244 | 0.717697 | 0.358848 | − | 0.933396i | \(-0.383170\pi\) | ||||
0.358848 | + | 0.933396i | \(0.383170\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 6.69213 | + | 3.86370i | 0.470857 | + | 0.271849i | ||||
\(203\) | −1.69161 | − | 1.69161i | −0.118728 | − | 0.118728i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.53590 | − | 9.46410i | −0.176684 | − | 0.659395i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.34795 | + | 8.76268i | 0.162801 | + | 0.607583i | ||||
\(209\) | 6.39230i | 0.442165i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.19615i | 0.220032i | 0.993930 | + | 0.110016i | \(0.0350902\pi\) | ||||
−0.993930 | + | 0.110016i | \(0.964910\pi\) | |||||||
\(212\) | 10.5558 | + | 2.82843i | 0.724978 | + | 0.194257i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.3923 | + | 4.92820i | −1.25727 | + | 0.336885i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 11.7806 | + | 11.7806i | 0.799718 | + | 0.799718i | ||||
\(218\) | −4.94975 | + | 8.57321i | −0.335239 | + | 0.580651i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −13.6077 | −0.915353 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.64136 | − | 6.64136i | −0.444739 | − | 0.444739i | 0.448862 | − | 0.893601i | \(-0.351829\pi\) |
−0.893601 | + | 0.448862i | \(0.851829\pi\) | |||||||
\(224\) | 6.53590 | − | 24.3923i | 0.436698 | − | 1.62978i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 18.9282 | − | 5.07180i | 1.25909 | − | 0.337371i | ||||
\(227\) | −5.93426 | + | 5.93426i | −0.393870 | + | 0.393870i | −0.876064 | − | 0.482194i | \(-0.839840\pi\) |
0.482194 | + | 0.876064i | \(0.339840\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 2.85641i | − | 0.188757i | −0.995536 | − | 0.0943783i | \(-0.969914\pi\) | ||
0.995536 | − | 0.0943783i | \(-0.0300863\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.51575 | −0.0995138 | ||||||||
\(233\) | 5.93426 | − | 5.93426i | 0.388766 | − | 0.388766i | −0.485481 | − | 0.874247i | \(-0.661356\pi\) |
0.874247 | + | 0.485481i | \(0.161356\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 11.4641 | + | 19.8564i | 0.746249 | + | 1.29254i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 32.8043 | + | 18.9396i | 2.12639 | + | 1.22767i | ||||
\(239\) | 10.5359 | 0.681511 | 0.340755 | − | 0.940152i | \(-0.389317\pi\) | ||||
0.340755 | + | 0.940152i | \(0.389317\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 12.8564 | 0.828154 | 0.414077 | − | 0.910242i | \(-0.364104\pi\) | ||||
0.414077 | + | 0.910242i | \(0.364104\pi\) | |||||||
\(242\) | −8.57321 | − | 4.94975i | −0.551107 | − | 0.318182i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.00000 | + | 5.19615i | 0.192055 | + | 0.332650i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.12561 | + | 5.12561i | −0.326135 | + | 0.326135i | ||||
\(248\) | 10.5558 | 0.670296 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 29.8564i | 1.88452i | 0.334883 | + | 0.942260i | \(0.391303\pi\) | ||||
−0.334883 | + | 0.942260i | \(0.608697\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 10.5558 | − | 10.5558i | 0.663640 | − | 0.663640i | ||||
\(254\) | −14.9282 | + | 4.00000i | −0.936679 | + | 0.250982i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −8.00000 | − | 13.8564i | −0.500000 | − | 0.866025i | ||||
\(257\) | 20.3538 | + | 20.3538i | 1.26963 | + | 1.26963i | 0.946277 | + | 0.323358i | \(0.104812\pi\) |
0.323358 | + | 0.946277i | \(0.395188\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −48.7846 | −3.03133 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.79315 | + | 3.10583i | −0.110781 | + | 0.191879i | ||||
\(263\) | 10.2784 | + | 10.2784i | 0.633795 | + | 0.633795i | 0.949018 | − | 0.315223i | \(-0.102079\pi\) |
−0.315223 | + | 0.949018i | \(0.602079\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 19.4904 | − | 5.22243i | 1.19503 | − | 0.320208i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.6945 | − | 2.86559i | −0.653273 | − | 0.175044i | ||||
\(269\) | 22.3923i | 1.36528i | 0.730753 | + | 0.682641i | \(0.239169\pi\) | ||||
−0.730753 | + | 0.682641i | \(0.760831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.2487i | 1.47300i | 0.676435 | + | 0.736502i | \(0.263524\pi\) | ||||
−0.676435 | + | 0.736502i | \(0.736476\pi\) | |||||||
\(272\) | 23.1822 | − | 6.21166i | 1.40563 | − | 0.376637i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.66025 | − | 21.1244i | −0.341948 | − | 1.27617i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.50266 | − | 6.50266i | −0.390707 | − | 0.390707i | 0.484232 | − | 0.874939i | \(-0.339099\pi\) |
−0.874939 | + | 0.484232i | \(0.839099\pi\) | |||||||
\(278\) | −15.3533 | − | 8.86422i | −0.920828 | − | 0.531641i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.39230 | −0.381333 | −0.190666 | − | 0.981655i | \(-0.561065\pi\) | ||||
−0.190666 | + | 0.981655i | \(0.561065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.429705 | − | 0.429705i | −0.0255433 | − | 0.0255433i | 0.694220 | − | 0.719763i | \(-0.255750\pi\) |
−0.719763 | + | 0.694220i | \(0.755750\pi\) | |||||||
\(284\) | −4.39230 | + | 2.53590i | −0.260635 | + | 0.150478i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.66025 | + | 6.19615i | 0.0981729 | + | 0.366386i | ||||
\(287\) | −4.62158 | + | 4.62158i | −0.272803 | + | 0.272803i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 19.0000i | 1.11765i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −7.72741 | − | 2.07055i | −0.452212 | − | 0.121170i | ||||
\(293\) | −13.7632 | + | 13.7632i | −0.804055 | + | 0.804055i | −0.983727 | − | 0.179672i | \(-0.942496\pi\) |
0.179672 | + | 0.983727i | \(0.442496\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −21.8564 | + | 21.8564i | −1.27038 | + | 1.27038i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.38375 | + | 14.5211i | −0.485657 | + | 0.841183i | ||||
\(299\) | 16.9282 | 0.978983 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19.9282 | −1.14864 | ||||||||
\(302\) | 5.46739 | − | 9.46979i | 0.314613 | − | 0.544925i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.39230 | − | 11.0718i | 0.366624 | − | 0.635011i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.22715 | + | 5.22715i | −0.298329 | + | 0.298329i | −0.840359 | − | 0.542030i | \(-0.817656\pi\) |
0.542030 | + | 0.840359i | \(0.317656\pi\) | |||||||
\(308\) | 4.62158 | − | 17.2480i | 0.263339 | − | 0.982794i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 20.5359i | − | 1.16448i | −0.813016 | − | 0.582242i | \(-0.802176\pi\) | ||
0.813016 | − | 0.582242i | \(-0.197824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.4016 | + | 11.4016i | −0.644459 | + | 0.644459i | −0.951648 | − | 0.307190i | \(-0.900611\pi\) |
0.307190 | + | 0.951648i | \(0.400611\pi\) | |||||||
\(314\) | −2.29423 | − | 8.56218i | −0.129471 | − | 0.483192i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.46410 | + | 12.9282i | 0.419889 | + | 0.727268i | ||||
\(317\) | −4.89898 | − | 4.89898i | −0.275154 | − | 0.275154i | 0.556017 | − | 0.831171i | \(-0.312329\pi\) |
−0.831171 | + | 0.556017i | \(0.812329\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.07180 | −0.0600091 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −40.8091 | − | 23.5612i | −2.27420 | − | 1.31301i | ||||
\(323\) | 13.5601 | + | 13.5601i | 0.754506 | + | 0.754506i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2.75833 | − | 10.2942i | −0.152770 | − | 0.570145i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.14110i | 0.228654i | ||||||||
\(329\) | − | 4.14359i | − | 0.228444i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 18.3923i | − | 1.01093i | −0.862846 | − | 0.505466i | \(-0.831321\pi\) | ||
0.862846 | − | 0.505466i | \(-0.168679\pi\) | |||||||
\(332\) | 6.69213 | − | 24.9754i | 0.367278 | − | 1.37070i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 22.3923 | − | 6.00000i | 1.22525 | − | 0.328305i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 20.2659 | + | 20.2659i | 1.10395 | + | 1.10395i | 0.993929 | + | 0.110023i | \(0.0350923\pi\) |
0.110023 | + | 0.993929i | \(0.464908\pi\) | |||||||
\(338\) | 5.55532 | − | 9.62209i | 0.302169 | − | 0.523373i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.46410 | 0.404204 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.7129 | − | 18.7129i | −1.01040 | − | 1.01040i | ||||
\(344\) | −8.92820 | + | 8.92820i | −0.481376 | + | 0.481376i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.73205 | + | 1.80385i | −0.361917 | + | 0.0969754i | ||||
\(347\) | 17.6269 | − | 17.6269i | 0.946262 | − | 0.946262i | −0.0523663 | − | 0.998628i | \(-0.516676\pi\) |
0.998628 | + | 0.0523663i | \(0.0166763\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.8564i | 1.27700i | 0.769620 | + | 0.638502i | \(0.220446\pi\) | ||||
−0.769620 | + | 0.638502i | \(0.779554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.65685 | − | 9.79796i | −0.301511 | − | 0.522233i | ||||
\(353\) | −8.38375 | + | 8.38375i | −0.446222 | + | 0.446222i | −0.894096 | − | 0.447875i | \(-0.852181\pi\) |
0.447875 | + | 0.894096i | \(0.352181\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 12.0000 | − | 6.92820i | 0.635999 | − | 0.367194i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.4152 | − | 6.59059i | −0.603314 | − | 0.348324i | ||||
\(359\) | −3.60770 | −0.190407 | −0.0952034 | − | 0.995458i | \(-0.530350\pi\) | ||||
−0.0952034 | + | 0.995458i | \(0.530350\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8.78461 | −0.462348 | ||||||||
\(362\) | 0.0879327 | + | 0.0507680i | 0.00462164 | + | 0.00266831i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 17.5359 | − | 10.1244i | 0.919131 | − | 0.530660i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.1977 | − | 22.1977i | 1.15871 | − | 1.15871i | 0.173958 | − | 0.984753i | \(-0.444344\pi\) |
0.984753 | − | 0.173958i | \(-0.0556557\pi\) | |||||||
\(368\) | −28.8391 | + | 7.72741i | −1.50334 | + | 0.402819i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 24.3923i | − | 1.26639i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.9227 | − | 25.9227i | 1.34223 | − | 1.34223i | 0.448388 | − | 0.893839i | \(-0.351998\pi\) |
0.893839 | − | 0.448388i | \(-0.148002\pi\) | |||||||
\(374\) | 16.3923 | − | 4.39230i | 0.847626 | − | 0.227121i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.85641 | − | 1.85641i | −0.0957369 | − | 0.0957369i | ||||
\(377\) | −0.859411 | − | 0.859411i | −0.0442619 | − | 0.0442619i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.2679 | −0.630162 | −0.315081 | − | 0.949065i | \(-0.602032\pi\) | ||||
−0.315081 | + | 0.949065i | \(0.602032\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.17209 | − | 3.76217i | 0.111134 | − | 0.192489i | ||||
\(383\) | −17.5254 | − | 17.5254i | −0.895504 | − | 0.895504i | 0.0995302 | − | 0.995035i | \(-0.468266\pi\) |
−0.995035 | + | 0.0995302i | \(0.968266\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.0263 | + | 3.75833i | −0.713919 | + | 0.191294i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.03768 | − | 18.8009i | 0.255749 | − | 0.954470i | ||||
\(389\) | 21.4641i | 1.08827i | 0.838997 | + | 0.544137i | \(0.183143\pi\) | ||||
−0.838997 | + | 0.544137i | \(0.816857\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 44.7846i | − | 2.26486i | ||||||
\(392\) | −36.5665 | −1.84689 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.33975 | + | 8.73205i | 0.117875 | + | 0.439914i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8.19428 | + | 8.19428i | 0.411259 | + | 0.411259i | 0.882177 | − | 0.470918i | \(-0.156077\pi\) |
−0.470918 | + | 0.882177i | \(0.656077\pi\) | |||||||
\(398\) | −12.3998 | − | 7.15900i | −0.621543 | − | 0.358848i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −29.1769 | −1.45703 | −0.728513 | − | 0.685032i | \(-0.759788\pi\) | ||||
−0.728513 | + | 0.685032i | \(0.759788\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.98502 | + | 5.98502i | 0.298135 | + | 0.298135i | ||||
\(404\) | −5.46410 | − | 9.46410i | −0.271849 | − | 0.470857i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.875644 | + | 3.26795i | 0.0434575 | + | 0.162186i | ||||
\(407\) | −15.4548 | + | 15.4548i | −0.766067 | + | 0.766067i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 13.7846i | − | 0.681605i | −0.940135 | − | 0.340803i | \(-0.889301\pi\) | ||
0.940135 | − | 0.340803i | \(-0.110699\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.58630 | + | 13.3843i | −0.176684 | + | 0.659395i | ||||
\(413\) | 36.1875 | − | 36.1875i | 1.78067 | − | 1.78067i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 3.32051 | − | 12.3923i | 0.162801 | − | 0.607583i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4.52004 | − | 7.82894i | 0.221082 | − | 0.382926i | ||||
\(419\) | −33.4641 | −1.63483 | −0.817414 | − | 0.576050i | \(-0.804593\pi\) | ||||
−0.817414 | + | 0.576050i | \(0.804593\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −34.7846 | −1.69530 | −0.847649 | − | 0.530557i | \(-0.821983\pi\) | ||||
−0.847649 | + | 0.530557i | \(0.821983\pi\) | |||||||
\(422\) | 2.26002 | − | 3.91447i | 0.110016 | − | 0.190553i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −10.9282 | − | 10.9282i | −0.530720 | − | 0.530720i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.46979 | − | 9.46979i | 0.458275 | − | 0.458275i | ||||
\(428\) | 26.0106 | + | 6.96953i | 1.25727 | + | 0.336885i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 29.7128i | − | 1.43122i | −0.698502 | − | 0.715608i | \(-0.746150\pi\) | ||
0.698502 | − | 0.715608i | \(-0.253850\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −25.1648 | + | 25.1648i | −1.20935 | + | 1.20935i | −0.238106 | + | 0.971239i | \(0.576526\pi\) |
−0.971239 | + | 0.238106i | \(0.923474\pi\) | |||||||
\(434\) | −6.09808 | − | 22.7583i | −0.292717 | − | 1.09243i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.1244 | − | 7.00000i | 0.580651 | − | 0.335239i | ||||
\(437\) | −16.8690 | − | 16.8690i | −0.806955 | − | 0.806955i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 23.9808 | 1.14454 | 0.572270 | − | 0.820066i | \(-0.306063\pi\) | ||||
0.572270 | + | 0.820066i | \(0.306063\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.6660 | + | 9.62209i | 0.792719 | + | 0.457676i | ||||
\(443\) | 20.3538 | + | 20.3538i | 0.967038 | + | 0.967038i | 0.999474 | − | 0.0324359i | \(-0.0103265\pi\) |
−0.0324359 | + | 0.999474i | \(0.510326\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.43782 | + | 12.8301i | 0.162786 | + | 0.607524i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −25.2528 | + | 25.2528i | −1.19308 | + | 1.19308i | ||||
\(449\) | 6.14359i | 0.289934i | 0.989436 | + | 0.144967i | \(0.0463076\pi\) | ||||
−0.989436 | + | 0.144967i | \(0.953692\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.92820i | 0.137884i | ||||||||
\(452\) | −26.7685 | − | 7.17260i | −1.25909 | − | 0.337371i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.4641 | − | 3.07180i | 0.538037 | − | 0.144167i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13.9391 | + | 13.9391i | 0.652042 | + | 0.652042i | 0.953484 | − | 0.301442i | \(-0.0974681\pi\) |
−0.301442 | + | 0.953484i | \(0.597468\pi\) | |||||||
\(458\) | −2.01978 | + | 3.49837i | −0.0943783 | + | 0.163468i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −36.3923 | −1.69496 | −0.847479 | − | 0.530828i | \(-0.821881\pi\) | ||||
−0.847479 | + | 0.530828i | \(0.821881\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 19.0411 | + | 19.0411i | 0.884916 | + | 0.884916i | 0.994029 | − | 0.109114i | \(-0.0348012\pi\) |
−0.109114 | + | 0.994029i | \(0.534801\pi\) | |||||||
\(464\) | 1.85641 | + | 1.07180i | 0.0861815 | + | 0.0497569i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −11.4641 | + | 3.07180i | −0.531064 | + | 0.142298i | ||||
\(467\) | −2.44949 | + | 2.44949i | −0.113349 | + | 0.113349i | −0.761506 | − | 0.648157i | \(-0.775540\pi\) |
0.648157 | + | 0.761506i | \(0.275540\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.7128i | 1.14113i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 32.4254i | − | 1.49250i | ||||||
\(473\) | −6.31319 | + | 6.31319i | −0.290281 | + | 0.290281i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −26.7846 | − | 46.3923i | −1.22767 | − | 2.12639i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −12.9038 | − | 7.45001i | −0.590206 | − | 0.340755i | ||||
\(479\) | 21.3205 | 0.974159 | 0.487079 | − | 0.873358i | \(-0.338062\pi\) | ||||
0.487079 | + | 0.873358i | \(0.338062\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.7846 | −1.13008 | ||||||||
\(482\) | −15.7458 | − | 9.09085i | −0.717202 | − | 0.414077i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | + | 12.1244i | 0.318182 | + | 0.551107i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −20.1272 | + | 20.1272i | −0.912049 | + | 0.912049i | −0.996433 | − | 0.0843846i | \(-0.973108\pi\) |
0.0843846 | + | 0.996433i | \(0.473108\pi\) | |||||||
\(488\) | − | 8.48528i | − | 0.384111i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 34.6410i | 1.56333i | 0.623700 | + | 0.781664i | \(0.285629\pi\) | ||||
−0.623700 | + | 0.781664i | \(0.714371\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.27362 | + | 2.27362i | −0.102399 | + | 0.102399i | ||||
\(494\) | 9.90192 | − | 2.65321i | 0.445509 | − | 0.119374i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −12.9282 | − | 7.46410i | −0.580493 | − | 0.335148i | ||||
\(497\) | 8.00481 | + | 8.00481i | 0.359065 | + | 0.359065i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 30.1244 | 1.34855 | 0.674276 | − | 0.738480i | \(-0.264456\pi\) | ||||
0.674276 | + | 0.738480i | \(0.264456\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 21.1117 | − | 36.5665i | 0.942260 | − | 1.63204i | ||||
\(503\) | 0.277401 | + | 0.277401i | 0.0123687 | + | 0.0123687i | 0.713264 | − | 0.700895i | \(-0.247216\pi\) |
−0.700895 | + | 0.713264i | \(0.747216\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −20.3923 | + | 5.46410i | −0.906549 | + | 0.242909i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 21.1117 | + | 5.65685i | 0.936679 | + | 0.250982i | ||||
\(509\) | − | 24.9282i | − | 1.10492i | −0.833538 | − | 0.552462i | \(-0.813689\pi\) | ||
0.833538 | − | 0.552462i | \(-0.186311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.8564i | 0.789921i | ||||||||
\(512\) | 22.6274i | 1.00000i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.5359 | − | 39.3205i | −0.464719 | − | 1.73435i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.31268 | − | 1.31268i | −0.0577315 | − | 0.0577315i | ||||
\(518\) | 59.7487 | + | 34.4959i | 2.62521 | + | 1.51566i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.3923 | 1.68200 | 0.840999 | − | 0.541037i | \(-0.181968\pi\) | ||||
0.840999 | + | 0.541037i | \(0.181968\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.984508 | + | 0.984508i | 0.0430495 | + | 0.0430495i | 0.728304 | − | 0.685254i | \(-0.240309\pi\) |
−0.685254 | + | 0.728304i | \(0.740309\pi\) | |||||||
\(524\) | 4.39230 | − | 2.53590i | 0.191879 | − | 0.110781i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.32051 | − | 19.8564i | −0.231985 | − | 0.865780i | ||||
\(527\) | 15.8338 | − | 15.8338i | 0.689729 | − | 0.689729i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 32.7128i | 1.42230i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −27.5636 | − | 7.38563i | −1.19503 | − | 0.320208i | ||||
\(533\) | −2.34795 | + | 2.34795i | −0.101701 | + | 0.101701i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 11.0718 | + | 11.0718i | 0.478229 | + | 0.478229i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15.8338 | − | 27.4249i | 0.682641 | − | 1.18237i | ||||
\(539\) | −25.8564 | −1.11371 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.78461 | 0.334687 | 0.167343 | − | 0.985899i | \(-0.446481\pi\) | ||||
0.167343 | + | 0.985899i | \(0.446481\pi\) | |||||||
\(542\) | 17.1464 | − | 29.6985i | 0.736502 | − | 1.27566i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −32.7846 | − | 8.78461i | −1.40563 | − | 0.376637i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.8685 | + | 11.8685i | −0.507461 | + | 0.507461i | −0.913746 | − | 0.406285i | \(-0.866824\pi\) |
0.406285 | + | 0.913746i | \(0.366824\pi\) | |||||||
\(548\) | −8.00481 | + | 29.8744i | −0.341948 | + | 1.27617i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.71281i | 0.0729683i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 23.5612 | − | 23.5612i | 1.00192 | − | 1.00192i | ||||
\(554\) | 3.36603 | + | 12.5622i | 0.143009 | + | 0.533716i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.5359 | + | 21.7128i | 0.531641 | + | 0.920828i | ||||
\(557\) | −8.66115 | − | 8.66115i | −0.366985 | − | 0.366985i | 0.499392 | − | 0.866376i | \(-0.333557\pi\) |
−0.866376 | + | 0.499392i | \(0.833557\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.1244 | −0.428215 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.82894 | + | 4.52004i | 0.330244 | + | 0.190666i | ||||
\(563\) | −27.7023 | − | 27.7023i | −1.16751 | − | 1.16751i | −0.982791 | − | 0.184720i | \(-0.940862\pi\) |
−0.184720 | − | 0.982791i | \(-0.559138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0.222432 | + | 0.830127i | 0.00934951 | + | 0.0348928i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.17260 | 0.300956 | ||||||||
\(569\) | − | 17.3205i | − | 0.726113i | −0.931767 | − | 0.363057i | \(-0.881733\pi\) | ||
0.931767 | − | 0.363057i | \(-0.118267\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.1962i | 1.13812i | 0.822295 | + | 0.569062i | \(0.192693\pi\) | ||||
−0.822295 | + | 0.569062i | \(0.807307\pi\) | |||||||
\(572\) | 2.34795 | − | 8.76268i | 0.0981729 | − | 0.366386i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 8.92820 | − | 2.39230i | 0.372656 | − | 0.0998529i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −23.0943 | − | 23.0943i | −0.961428 | − | 0.961428i | 0.0378555 | − | 0.999283i | \(-0.487947\pi\) |
−0.999283 | + | 0.0378555i | \(0.987947\pi\) | |||||||
\(578\) | 13.4350 | − | 23.2702i | 0.558824 | − | 0.967911i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −57.7128 | −2.39433 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.72741 | − | 7.72741i | −0.320036 | − | 0.320036i | ||||
\(584\) | 8.00000 | + | 8.00000i | 0.331042 | + | 0.331042i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 26.5885 | − | 7.12436i | 1.09836 | − | 0.294304i | ||||
\(587\) | 10.8332 | − | 10.8332i | 0.447135 | − | 0.447135i | −0.447266 | − | 0.894401i | \(-0.647602\pi\) |
0.894401 | + | 0.447266i | \(0.147602\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.9282i | − | 0.491493i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 42.2233 | − | 11.3137i | 1.73537 | − | 0.464991i | ||||
\(593\) | 8.20788 | − | 8.20788i | 0.337057 | − | 0.337057i | −0.518201 | − | 0.855259i | \(-0.673398\pi\) |
0.855259 | + | 0.518201i | \(0.173398\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 20.5359 | − | 11.8564i | 0.841183 | − | 0.485657i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −20.7327 | − | 11.9700i | −0.847824 | − | 0.489492i | ||||
\(599\) | −22.6410 | −0.925087 | −0.462543 | − | 0.886597i | \(-0.653063\pi\) | ||||
−0.462543 | + | 0.886597i | \(0.653063\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 21.7846 | 0.888613 | 0.444306 | − | 0.895875i | \(-0.353450\pi\) | ||||
0.444306 | + | 0.895875i | \(0.353450\pi\) | |||||||
\(602\) | 24.4070 | + | 14.0914i | 0.994754 | + | 0.574321i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −13.3923 | + | 7.73205i | −0.544925 | + | 0.314613i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25.2528 | + | 25.2528i | −1.02498 | + | 1.02498i | −0.0252985 | + | 0.999680i | \(0.508054\pi\) |
−0.999680 | + | 0.0252985i | \(0.991946\pi\) | |||||||
\(608\) | −15.6579 | + | 9.04008i | −0.635011 | + | 0.366624i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2.10512i | − | 0.0851639i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(614\) | 10.0981 | − | 2.70577i | 0.407525 | − | 0.109196i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −17.8564 | + | 17.8564i | −0.719455 | + | 0.719455i | ||||
\(617\) | 24.2175 | + | 24.2175i | 0.974960 | + | 0.974960i | 0.999694 | − | 0.0247344i | \(-0.00787400\pi\) |
−0.0247344 | + | 0.999694i | \(0.507874\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 15.9808 | 0.642321 | 0.321161 | − | 0.947025i | \(-0.395927\pi\) | ||||
0.321161 | + | 0.947025i | \(0.395927\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14.5211 | + | 25.1512i | −0.582242 | + | 1.00847i | ||||
\(623\) | −21.8695 | − | 21.8695i | −0.876185 | − | 0.876185i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 22.0263 | − | 5.90192i | 0.880347 | − | 0.235888i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.24453 | + | 12.1087i | −0.129471 | + | 0.483192i | ||||
\(629\) | 65.5692i | 2.61442i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 29.5885i | − | 1.17790i | −0.808170 | − | 0.588949i | \(-0.799542\pi\) | ||
0.808170 | − | 0.588949i | \(-0.200458\pi\) | |||||||
\(632\) | − | 21.1117i | − | 0.839777i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.53590 | + | 9.46410i | 0.100713 | + | 0.375867i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.7327 | − | 20.7327i | −0.821461 | − | 0.821461i | ||||
\(638\) | 1.31268 | + | 0.757875i | 0.0519694 | + | 0.0300045i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 44.7846 | 1.76889 | 0.884443 | − | 0.466648i | \(-0.154539\pi\) | ||||
0.884443 | + | 0.466648i | \(0.154539\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 21.8695 | + | 21.8695i | 0.862451 | + | 0.862451i | 0.991622 | − | 0.129172i | \(-0.0412318\pi\) |
−0.129172 | + | 0.991622i | \(0.541232\pi\) | |||||||
\(644\) | 33.3205 | + | 57.7128i | 1.31301 | + | 2.27420i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.01924 | − | 26.1962i | −0.276168 | − | 1.03067i | ||||
\(647\) | 13.3843 | − | 13.3843i | 0.526190 | − | 0.526190i | −0.393244 | − | 0.919434i | \(-0.628647\pi\) |
0.919434 | + | 0.393244i | \(0.128647\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 22.9282i | − | 0.900011i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.90087 | + | 14.5582i | −0.152770 | + | 0.570145i | ||||
\(653\) | 7.34847 | − | 7.34847i | 0.287568 | − | 0.287568i | −0.548550 | − | 0.836118i | \(-0.684820\pi\) |
0.836118 | + | 0.548550i | \(0.184820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.92820 | − | 5.07180i | 0.114327 | − | 0.198020i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.92996 | + | 5.07484i | −0.114222 | + | 0.197838i | ||||
\(659\) | 21.4641 | 0.836123 | 0.418061 | − | 0.908419i | \(-0.362710\pi\) | ||||
0.418061 | + | 0.908419i | \(0.362710\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 19.8564 | 0.772325 | 0.386162 | − | 0.922431i | \(-0.373800\pi\) | ||||
0.386162 | + | 0.922431i | \(0.373800\pi\) | |||||||
\(662\) | −13.0053 | + | 22.5259i | −0.505466 | + | 0.875493i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −25.8564 | + | 25.8564i | −1.00342 | + | 1.00342i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.82843 | − | 2.82843i | 0.109517 | − | 0.109517i | ||||
\(668\) | −31.6675 | − | 8.48528i | −1.22525 | − | 0.328305i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 6.00000i | − | 0.231627i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.82843 | − | 2.82843i | 0.109028 | − | 0.109028i | −0.650488 | − | 0.759516i | \(-0.725436\pi\) |
0.759516 | + | 0.650488i | \(0.225436\pi\) | |||||||
\(674\) | −10.4904 | − | 39.1506i | −0.404074 | − | 1.50803i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −13.6077 | + | 7.85641i | −0.523373 | + | 0.302169i | ||||
\(677\) | −23.0807 | − | 23.0807i | −0.887063 | − | 0.887063i | 0.107177 | − | 0.994240i | \(-0.465819\pi\) |
−0.994240 | + | 0.107177i | \(0.965819\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −43.4449 | −1.66726 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −9.14162 | − | 5.27792i | −0.350051 | − | 0.202102i | ||||
\(683\) | 13.3843 | + | 13.3843i | 0.512135 | + | 0.512135i | 0.915180 | − | 0.403045i | \(-0.132048\pi\) |
−0.403045 | + | 0.915180i | \(0.632048\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.68653 | + | 36.1506i | 0.369834 | + | 1.38024i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 17.2480 | − | 4.62158i | 0.657572 | − | 0.176196i | ||||
\(689\) | − | 12.3923i | − | 0.472109i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.32051i | 0.354569i | 0.984160 | + | 0.177284i | \(0.0567312\pi\) | ||||
−0.984160 | + | 0.177284i | \(0.943269\pi\) | |||||||
\(692\) | 9.52056 | + | 2.55103i | 0.361917 | + | 0.0969754i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −34.0526 | + | 9.12436i | −1.29262 | + | 0.346356i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.21166 | + | 6.21166i | 0.235283 | + | 0.235283i | ||||
\(698\) | 16.8690 | − | 29.2180i | 0.638502 | − | 1.10592i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.53590 | 0.322396 | 0.161198 | − | 0.986922i | \(-0.448464\pi\) | ||||
0.161198 | + | 0.986922i | \(0.448464\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 24.6980 | + | 24.6980i | 0.931502 | + | 0.931502i | ||||
\(704\) | 16.0000i | 0.603023i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16.1962 | − | 4.33975i | 0.609550 | − | 0.163328i | ||||
\(707\) | −17.2480 | + | 17.2480i | −0.648676 | + | 0.648676i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 2.85641i | − | 0.107275i | −0.998560 | − | 0.0536373i | \(-0.982919\pi\) | ||
0.998560 | − | 0.0536373i | \(-0.0170815\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −19.5959 | −0.734388 | ||||||||
\(713\) | −19.6975 | + | 19.6975i | −0.737675 | + | 0.737675i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.32051 | + | 16.1436i | 0.348324 | + | 0.603314i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.41851 | + | 2.55103i | 0.164897 | + | 0.0952034i | ||||
\(719\) | 0.928203 | 0.0346161 | 0.0173081 | − | 0.999850i | \(-0.494490\pi\) | ||||
0.0173081 | + | 0.999850i | \(0.494490\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 30.9282 | 1.15183 | ||||||||
\(722\) | 10.7589 | + | 6.21166i | 0.400405 | + | 0.231174i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.0717968 | − | 0.124356i | −0.00266831 | − | 0.00462164i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.5804 | − | 20.5804i | 0.763286 | − | 0.763286i | −0.213629 | − | 0.976915i | \(-0.568528\pi\) |
0.976915 | + | 0.213629i | \(0.0685284\pi\) | |||||||
\(728\) | −28.6360 | −1.06132 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.7846i | 0.990665i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −25.2528 | + | 25.2528i | −0.932732 | + | 0.932732i | −0.997876 | − | 0.0651435i | \(-0.979249\pi\) |
0.0651435 | + | 0.997876i | \(0.479249\pi\) | |||||||
\(734\) | −42.8827 | + | 11.4904i | −1.58283 | + | 0.424118i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 40.7846 | + | 10.9282i | 1.50334 | + | 0.402819i | ||||
\(737\) | 7.82894 | + | 7.82894i | 0.288383 | + | 0.288383i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.39230 | −0.235145 | −0.117572 | − | 0.993064i | \(-0.537511\pi\) | ||||
−0.117572 | + | 0.993064i | \(0.537511\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −17.2480 | + | 29.8744i | −0.633193 | + | 1.09672i | ||||
\(743\) | 12.0716 | + | 12.0716i | 0.442863 | + | 0.442863i | 0.892973 | − | 0.450110i | \(-0.148615\pi\) |
−0.450110 | + | 0.892973i | \(0.648615\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −50.0788 | + | 13.4186i | −1.83352 | + | 0.491289i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −23.1822 | − | 6.21166i | −0.847626 | − | 0.227121i | ||||
\(749\) | − | 60.1051i | − | 2.19619i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 4.53590i | − | 0.165517i | −0.996570 | − | 0.0827586i | \(-0.973627\pi\) | ||
0.996570 | − | 0.0827586i | \(-0.0263731\pi\) | |||||||
\(752\) | 0.960947 | + | 3.58630i | 0.0350421 | + | 0.130779i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.444864 | + | 1.66025i | 0.0162010 | + | 0.0604629i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.2963 | + | 13.2963i | 0.483263 | + | 0.483263i | 0.906172 | − | 0.422909i | \(-0.138991\pi\) |
−0.422909 | + | 0.906172i | \(0.638991\pi\) | |||||||
\(758\) | 15.0251 | + | 8.67475i | 0.545736 | + | 0.315081i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.6410 | 0.820736 | 0.410368 | − | 0.911920i | \(-0.365400\pi\) | ||||
0.410368 | + | 0.911920i | \(0.365400\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −22.0962 | − | 22.0962i | −0.799935 | − | 0.799935i | ||||
\(764\) | −5.32051 | + | 3.07180i | −0.192489 | + | 0.111134i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.07180 | + | 33.8564i | 0.327777 | + | 1.22328i | ||||
\(767\) | 18.3848 | − | 18.3848i | 0.663836 | − | 0.663836i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 16.0718i | − | 0.579564i | −0.957093 | − | 0.289782i | \(-0.906417\pi\) | ||
0.957093 | − | 0.289782i | \(-0.0935828\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 19.8362 | + | 5.31508i | 0.713919 | + | 0.191294i | ||||
\(773\) | 20.6312 | − | 20.6312i | 0.742052 | − | 0.742052i | −0.230920 | − | 0.972973i | \(-0.574174\pi\) |
0.972973 | + | 0.230920i | \(0.0741736\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −19.4641 | + | 19.4641i | −0.698721 | + | 0.698721i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 15.1774 | − | 26.2880i | 0.544137 | − | 0.942472i | ||||
\(779\) | 4.67949 | 0.167660 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.07180 | 0.181483 | ||||||||
\(782\) | −31.6675 | + | 54.8497i | −1.13243 | + | 1.96142i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 44.7846 | + | 25.8564i | 1.59945 | + | 0.923443i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 34.0662 | − | 34.0662i | 1.21433 | − | 1.21433i | 0.244741 | − | 0.969588i | \(-0.421297\pi\) |
0.969588 | − | 0.244741i | \(-0.0787030\pi\) | |||||||
\(788\) | 3.30890 | − | 12.3490i | 0.117875 | − | 0.439914i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.8564i | 2.19936i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.81105 | − | 4.81105i | 0.170845 | − | 0.170845i | ||||
\(794\) | −4.24167 | − | 15.8301i | −0.150531 | − | 0.561790i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 10.1244 | + | 17.5359i | 0.358848 | + | 0.621543i | ||||
\(797\) | 9.79796 | + | 9.79796i | 0.347062 | + | 0.347062i | 0.859014 | − | 0.511952i | \(-0.171078\pi\) |
−0.511952 | + | 0.859014i | \(0.671078\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.56922 | −0.197025 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35.7343 | + | 20.6312i | 1.26182 | + | 0.728513i | ||||
\(803\) | 5.65685 | + | 5.65685i | 0.199626 | + | 0.199626i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.09808 | − | 11.5622i | −0.109125 | − | 0.407260i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 15.4548i | 0.543698i | ||||||||
\(809\) | 13.1769i | 0.463276i | 0.972802 | + | 0.231638i | \(0.0744084\pi\) | ||||
−0.972802 | + | 0.231638i | \(0.925592\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.87564i | 0.0658628i | 0.999458 | + | 0.0329314i | \(0.0104843\pi\) | ||||
−0.999458 | + | 0.0329314i | \(0.989516\pi\) | |||||||
\(812\) | 1.23835 | − | 4.62158i | 0.0434575 | − | 0.162186i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 29.8564 | − | 8.00000i | 1.04647 | − | 0.280400i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.0890 | + | 10.0890i | 0.352968 | + | 0.352968i | ||||
\(818\) | −9.74719 | + | 16.8826i | −0.340803 | + | 0.590287i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 27.5692 | 0.962172 | 0.481086 | − | 0.876673i | \(-0.340242\pi\) | ||||
0.481086 | + | 0.876673i | \(0.340242\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.8145 | − | 18.8145i | −0.655832 | − | 0.655832i | 0.298559 | − | 0.954391i | \(-0.403494\pi\) |
−0.954391 | + | 0.298559i | \(0.903494\pi\) | |||||||
\(824\) | 13.8564 | − | 13.8564i | 0.482711 | − | 0.482711i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −69.9090 | + | 18.7321i | −2.43244 | + | 0.651771i | ||||
\(827\) | −34.9764 | + | 34.9764i | −1.21625 | + | 1.21625i | −0.247313 | + | 0.968936i | \(0.579548\pi\) |
−0.968936 | + | 0.247313i | \(0.920452\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 37.7128i | − | 1.30982i | −0.755707 | − | 0.654910i | \(-0.772706\pi\) | ||
0.755707 | − | 0.654910i | \(-0.227294\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −12.8295 | + | 12.8295i | −0.444781 | + | 0.444781i | ||||
\(833\) | −54.8497 | + | 54.8497i | −1.90043 | + | 1.90043i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −11.0718 | + | 6.39230i | −0.382926 | + | 0.221082i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 40.9850 | + | 23.6627i | 1.41580 | + | 0.817414i | ||||
\(839\) | 28.6410 | 0.988798 | 0.494399 | − | 0.869235i | \(-0.335388\pi\) | ||||
0.494399 | + | 0.869235i | \(0.335388\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.7128 | 0.990097 | ||||||||
\(842\) | 42.6023 | + | 24.5964i | 1.46817 | + | 0.847649i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.53590 | + | 3.19615i | −0.190553 | + | 0.110016i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.0962 | − | 22.0962i | 0.759234 | − | 0.759234i | ||||
\(848\) | 5.65685 | + | 21.1117i | 0.194257 | + | 0.724978i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 81.5692i | − | 2.79616i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −11.0227 | + | 11.0227i | −0.377410 | + | 0.377410i | −0.870167 | − | 0.492757i | \(-0.835989\pi\) |
0.492757 | + | 0.870167i | \(0.335989\pi\) | |||||||
\(854\) | −18.2942 | + | 4.90192i | −0.626016 | + | 0.167740i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −26.9282 | − | 26.9282i | −0.920387 | − | 0.920387i | ||||
\(857\) | 5.45378 | + | 5.45378i | 0.186298 | + | 0.186298i | 0.794093 | − | 0.607796i | \(-0.207946\pi\) |
−0.607796 | + | 0.794093i | \(0.707946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 42.3923 | 1.44641 | 0.723203 | − | 0.690635i | \(-0.242669\pi\) | ||||
0.723203 | + | 0.690635i | \(0.242669\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −21.0101 | + | 36.3906i | −0.715608 | + | 1.23947i | ||||
\(863\) | 21.6665 | + | 21.6665i | 0.737535 | + | 0.737535i | 0.972100 | − | 0.234565i | \(-0.0753666\pi\) |
−0.234565 | + | 0.972100i | \(0.575367\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 48.6147 | − | 13.0263i | 1.65200 | − | 0.442651i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.62398 | + | 32.1851i | −0.292717 | + | 1.09243i | ||||
\(869\) | − | 14.9282i | − | 0.506405i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.5551i | 0.425415i | ||||||||
\(872\) | −19.7990 | −0.670478 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 8.73205 | + | 32.5885i | 0.295366 | + | 1.10232i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −33.8260 | − | 33.8260i | −1.14222 | − | 1.14222i | −0.988043 | − | 0.154180i | \(-0.950727\pi\) |
−0.154180 | − | 0.988043i | \(-0.549273\pi\) | |||||||
\(878\) | −29.3703 | − | 16.9570i | −0.991200 | − | 0.572270i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 37.0718 | 1.24898 | 0.624490 | − | 0.781033i | \(-0.285307\pi\) | ||||
0.624490 | + | 0.781033i | \(0.285307\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.7525 | − | 22.7525i | −0.765683 | − | 0.765683i | 0.211660 | − | 0.977343i | \(-0.432113\pi\) |
−0.977343 | + | 0.211660i | \(0.932113\pi\) | |||||||
\(884\) | −13.6077 | − | 23.5692i | −0.457676 | − | 0.792719i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −10.5359 | − | 39.3205i | −0.353960 | − | 1.32100i | ||||
\(887\) | −14.0406 | + | 14.0406i | −0.471437 | + | 0.471437i | −0.902379 | − | 0.430942i | \(-0.858181\pi\) |
0.430942 | + | 0.902379i | \(0.358181\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 48.7846i | − | 1.63618i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.86181 | − | 18.1445i | 0.162786 | − | 0.607524i | ||||
\(893\) | −2.09776 | + | 2.09776i | −0.0701988 | + | 0.0701988i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 48.7846 | − | 13.0718i | 1.62978 | − | 0.436698i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.34418 | − | 7.52433i | 0.144967 | − | 0.251090i | ||||
\(899\) | 2.00000 | 0.0667037 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −32.7846 | −1.09221 | ||||||||
\(902\) | 2.07055 | − | 3.58630i | 0.0689419 | − | 0.119411i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 27.7128 | + | 27.7128i | 0.921714 | + | 0.921714i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −12.6264 | + | 12.6264i | −0.419252 | + | 0.419252i | −0.884946 | − | 0.465694i | \(-0.845805\pi\) |
0.465694 | + | 0.884946i | \(0.345805\pi\) | |||||||
\(908\) | −16.2127 | − | 4.34418i | −0.538037 | − | 0.144167i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.60770i | 0.185791i | 0.995676 | + | 0.0928956i | \(0.0296123\pi\) | ||||
−0.995676 | + | 0.0928956i | \(0.970388\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.2832 | + | 18.2832i | −0.605087 | + | 0.605087i | ||||
\(914\) | −7.21539 | − | 26.9282i | −0.238664 | − | 0.890706i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 4.94744 | − | 2.85641i | 0.163468 | − | 0.0943783i | ||||
\(917\) | −8.00481 | − | 8.00481i | −0.264342 | − | 0.264342i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.6603 | 0.879441 | 0.439720 | − | 0.898135i | \(-0.355078\pi\) | ||||
0.439720 | + | 0.898135i | \(0.355078\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 44.5713 | + | 25.7332i | 1.46788 | + | 0.847479i | ||||
\(923\) | 4.06678 | + | 4.06678i | 0.133860 | + | 0.133860i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −9.85641 | − | 36.7846i | −0.323902 | − | 1.20882i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.51575 | − | 2.62536i | −0.0497569 | − | 0.0861815i | ||||
\(929\) | − | 0.535898i | − | 0.0175823i | −0.999961 | − | 0.00879113i | \(-0.997202\pi\) | ||
0.999961 | − | 0.00879113i | \(-0.00279834\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 41.3205i | 1.35422i | ||||||||
\(932\) | 16.2127 | + | 4.34418i | 0.531064 | + | 0.142298i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.73205 | − | 1.26795i | 0.154837 | − | 0.0414886i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.12802 | − | 9.12802i | −0.298199 | − | 0.298199i | 0.542109 | − | 0.840308i | \(-0.317626\pi\) |
−0.840308 | + | 0.542109i | \(0.817626\pi\) | |||||||
\(938\) | 17.4746 | − | 30.2669i | 0.570566 | − | 0.988249i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −11.0718 | −0.360930 | −0.180465 | − | 0.983581i | \(-0.557760\pi\) | ||||
−0.180465 | + | 0.983581i | \(0.557760\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −7.72741 | − | 7.72741i | −0.251639 | − | 0.251639i | ||||
\(944\) | −22.9282 | + | 39.7128i | −0.746249 | + | 1.29254i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.1962 | − | 3.26795i | 0.396531 | − | 0.106250i | ||||
\(947\) | −22.8033 | + | 22.8033i | −0.741007 | + | 0.741007i | −0.972772 | − | 0.231765i | \(-0.925550\pi\) |
0.231765 | + | 0.972772i | \(0.425550\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.07180i | 0.294483i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 75.7583i | 2.45534i | ||||||||
\(953\) | 28.0812 | − | 28.0812i | 0.909639 | − | 0.909639i | −0.0866036 | − | 0.996243i | \(-0.527601\pi\) |
0.996243 | + | 0.0866036i | \(0.0276014\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.5359 | + | 18.2487i | 0.340755 | + | 0.590206i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −26.1122 | − | 15.0759i | −0.843646 | − | 0.487079i | ||||
\(959\) | 69.0333 | 2.22920 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 17.0718 | 0.550703 | ||||||||
\(962\) | 30.3548 | + | 17.5254i | 0.978679 | + | 0.565040i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.8564 | + | 22.2679i | 0.414077 | + | 0.717202i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −33.9411 | + | 33.9411i | −1.09147 | + | 1.09147i | −0.0961015 | + | 0.995372i | \(0.530637\pi\) |
−0.995372 | + | 0.0961015i | \(0.969363\pi\) | |||||||
\(968\) | − | 19.7990i | − | 0.636364i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 43.1769i | − | 1.38561i | −0.721123 | − | 0.692807i | \(-0.756374\pi\) | ||
0.721123 | − | 0.692807i | \(-0.243626\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.5708 | − | 39.5708i | 1.26858 | − | 1.26858i | ||||
\(974\) | 38.8827 | − | 10.4186i | 1.24588 | − | 0.333833i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.00000 | + | 10.3923i | −0.192055 | + | 0.332650i | ||||
\(977\) | −16.3886 | − | 16.3886i | −0.524316 | − | 0.524316i | 0.394556 | − | 0.918872i | \(-0.370899\pi\) |
−0.918872 | + | 0.394556i | \(0.870899\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.8564 | −0.442853 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 24.4949 | − | 42.4264i | 0.781664 | − | 1.35388i | ||||
\(983\) | −1.31268 | − | 1.31268i | −0.0418679 | − | 0.0418679i | 0.685863 | − | 0.727731i | \(-0.259425\pi\) |
−0.727731 | + | 0.685863i | \(0.759425\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4.39230 | − | 1.17691i | 0.139879 | − | 0.0374806i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.0034 | − | 3.75221i | −0.445509 | − | 0.119374i | ||||
\(989\) | − | 33.3205i | − | 1.05953i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4115i | 0.838990i | 0.907758 | + | 0.419495i | \(0.137793\pi\) | ||||
−0.907758 | + | 0.419495i | \(0.862207\pi\) | |||||||
\(992\) | 10.5558 | + | 18.2832i | 0.335148 | + | 0.580493i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.14359 | − | 15.4641i | −0.131427 | − | 0.490492i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.5959 | − | 19.5959i | −0.620609 | − | 0.620609i | 0.325078 | − | 0.945687i | \(-0.394609\pi\) |
−0.945687 | + | 0.325078i | \(0.894609\pi\) | |||||||
\(998\) | −36.8947 | − | 21.3011i | −1.16788 | − | 0.674276i | ||||
\(999\) | 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 | 900.2.k.l.307.1 | 8 | ||
3.2 | odd | 2 | 300.2.j.c.7.4 | yes | 8 | ||
4.3 | odd | 2 | 900.2.k.g.307.1 | 8 | |||
5.2 | odd | 4 | 900.2.k.g.343.3 | 8 | |||
5.3 | odd | 4 | 900.2.k.g.343.2 | 8 | |||
5.4 | even | 2 | inner | 900.2.k.l.307.4 | 8 | ||
12.11 | even | 2 | 300.2.j.a.7.4 | yes | 8 | ||
15.2 | even | 4 | 300.2.j.a.43.2 | yes | 8 | ||
15.8 | even | 4 | 300.2.j.a.43.3 | yes | 8 | ||
15.14 | odd | 2 | 300.2.j.c.7.1 | yes | 8 | ||
20.3 | even | 4 | inner | 900.2.k.l.343.2 | 8 | ||
20.7 | even | 4 | inner | 900.2.k.l.343.3 | 8 | ||
20.19 | odd | 2 | 900.2.k.g.307.4 | 8 | |||
60.23 | odd | 4 | 300.2.j.c.43.3 | yes | 8 | ||
60.47 | odd | 4 | 300.2.j.c.43.2 | yes | 8 | ||
60.59 | even | 2 | 300.2.j.a.7.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.j.a.7.1 | ✓ | 8 | 60.59 | even | 2 | ||
300.2.j.a.7.4 | yes | 8 | 12.11 | even | 2 | ||
300.2.j.a.43.2 | yes | 8 | 15.2 | even | 4 | ||
300.2.j.a.43.3 | yes | 8 | 15.8 | even | 4 | ||
300.2.j.c.7.1 | yes | 8 | 15.14 | odd | 2 | ||
300.2.j.c.7.4 | yes | 8 | 3.2 | odd | 2 | ||
300.2.j.c.43.2 | yes | 8 | 60.47 | odd | 4 | ||
300.2.j.c.43.3 | yes | 8 | 60.23 | odd | 4 | ||
900.2.k.g.307.1 | 8 | 4.3 | odd | 2 | |||
900.2.k.g.307.4 | 8 | 20.19 | odd | 2 | |||
900.2.k.g.343.2 | 8 | 5.3 | odd | 4 | |||
900.2.k.g.343.3 | 8 | 5.2 | odd | 4 | |||
900.2.k.l.307.1 | 8 | 1.1 | even | 1 | trivial | ||
900.2.k.l.307.4 | 8 | 5.4 | even | 2 | inner | ||
900.2.k.l.343.2 | 8 | 20.3 | even | 4 | inner | ||
900.2.k.l.343.3 | 8 | 20.7 | even | 4 | inner |