Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1728,3,Mod(449,1728)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1728, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1728.449");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1728 = 2^{6} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1728.q (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: | \(47.0845896815\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.19269881856.9 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 15x^{6} - 2x^{5} + 133x^{4} - 84x^{3} + 276x^{2} + 144x + 144 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 72) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 449.1 | ||
Root | \(-1.41950 - 2.45865i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1728.449 |
Dual form | 1728.3.q.i.1601.1 |
$q$-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 \(\left(\mathbb{Z}/1728\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(703\) | \(1217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.20800 | − | 4.73889i | −1.64160 | − | 0.947779i | −0.980265 | − | 0.197688i | \(-0.936657\pi\) |
−0.661336 | − | 0.750090i | \(-0.730010\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.05671 | − | 1.83027i | −0.150958 | − | 0.261467i | 0.780622 | − | 0.625004i | \(-0.214903\pi\) |
−0.931580 | + | 0.363537i | \(0.881569\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −13.7064 | + | 7.91342i | −1.24604 | + | 0.719401i | −0.970317 | − | 0.241836i | \(-0.922250\pi\) |
−0.275723 | + | 0.961237i | \(0.588917\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.70337 | + | 8.14648i | −0.361798 | + | 0.626652i | −0.988257 | − | 0.152802i | \(-0.951170\pi\) |
0.626459 | + | 0.779454i | \(0.284504\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 11.6027i | 0.682513i | 0.939970 | + | 0.341256i | \(0.110852\pi\) | ||||
−0.939970 | + | 0.341256i | \(0.889148\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 12.9707 | 0.682667 | 0.341334 | − | 0.939942i | \(-0.389121\pi\) | ||||
0.341334 | + | 0.939942i | \(0.389121\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.27427 | − | 3.04510i | −0.229316 | − | 0.132396i | 0.380940 | − | 0.924600i | \(-0.375600\pi\) |
−0.610256 | + | 0.792204i | \(0.708934\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 32.4142 | + | 56.1431i | 1.29657 | + | 2.24572i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −24.7667 | + | 14.2991i | −0.854026 | + | 0.493072i | −0.862007 | − | 0.506896i | \(-0.830793\pi\) |
0.00798151 | + | 0.999968i | \(0.497459\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.75365 | + | 15.1618i | −0.282376 | + | 0.489089i | −0.971969 | − | 0.235107i | \(-0.924456\pi\) |
0.689594 | + | 0.724196i | \(0.257789\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 20.0305i | 0.572299i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15.6207 | 0.422181 | 0.211091 | − | 0.977467i | \(-0.432298\pi\) | ||||
0.211091 | + | 0.977467i | \(0.432298\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −14.8062 | − | 8.54836i | −0.361127 | − | 0.208497i | 0.308448 | − | 0.951241i | \(-0.400190\pi\) |
−0.669575 | + | 0.742745i | \(0.733524\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.7157 | − | 37.6127i | −0.505016 | − | 0.874714i | −0.999983 | − | 0.00580217i | \(-0.998153\pi\) |
0.494967 | − | 0.868912i | \(-0.335180\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 20.6696 | − | 11.9336i | 0.439778 | − | 0.253906i | −0.263726 | − | 0.964598i | \(-0.584951\pi\) |
0.703503 | + | 0.710692i | \(0.251618\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 22.2667 | − | 38.5671i | 0.454423 | − | 0.787084i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 14.1051i | − | 0.266134i | −0.991107 | − | 0.133067i | \(-0.957517\pi\) | ||
0.991107 | − | 0.133067i | \(-0.0424825\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 150.003 | 2.72733 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −38.5788 | − | 22.2735i | −0.653877 | − | 0.377516i | 0.136063 | − | 0.990700i | \(-0.456555\pi\) |
−0.789940 | + | 0.613184i | \(0.789888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.86057 | + | 3.22260i | 0.0305012 | + | 0.0528296i | 0.880873 | − | 0.473353i | \(-0.156956\pi\) |
−0.850372 | + | 0.526182i | \(0.823623\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 77.2105 | − | 44.5775i | 1.18785 | − | 0.685808i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 21.0090 | − | 36.3887i | 0.313568 | − | 0.543115i | −0.665564 | − | 0.746340i | \(-0.731809\pi\) |
0.979132 | + | 0.203225i | \(0.0651424\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 120.440i | 1.69634i | 0.529724 | + | 0.848170i | \(0.322295\pi\) | ||||
−0.529724 | + | 0.848170i | \(0.677705\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 5.48692 | 0.0751633 | 0.0375817 | − | 0.999294i | \(-0.488035\pi\) | ||||
0.0375817 | + | 0.999294i | \(0.488035\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 28.9674 | + | 16.7243i | 0.376200 | + | 0.217199i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −60.5480 | − | 104.872i | −0.766430 | − | 1.32750i | −0.939487 | − | 0.342585i | \(-0.888698\pi\) |
0.173056 | − | 0.984912i | \(-0.444636\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −46.5861 | + | 26.8965i | −0.561279 | + | 0.324054i | −0.753659 | − | 0.657266i | \(-0.771713\pi\) |
0.192380 | + | 0.981321i | \(0.438379\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 54.9840 | − | 95.2351i | 0.646871 | − | 1.12041i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 102.195i | − | 1.14825i | −0.818766 | − | 0.574127i | \(-0.805342\pi\) | ||
0.818766 | − | 0.574127i | \(-0.194658\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.8803 | 0.218465 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −106.463 | − | 61.4667i | −1.12067 | − | 0.647018i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −58.9377 | − | 102.083i | −0.607605 | − | 1.05240i | −0.991634 | − | 0.129081i | \(-0.958797\pi\) |
0.384029 | − | 0.923321i | \(-0.374536\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 118.181 | − | 68.2317i | 1.17011 | − | 0.675561i | 0.216401 | − | 0.976304i | \(-0.430568\pi\) |
0.953705 | + | 0.300743i | \(0.0972347\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −60.8511 | + | 105.397i | −0.590787 | + | 1.02327i | 0.403340 | + | 0.915050i | \(0.367849\pi\) |
−0.994127 | + | 0.108223i | \(0.965484\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 82.1437i | − | 0.767698i | −0.923396 | − | 0.383849i | \(-0.874598\pi\) | ||
0.923396 | − | 0.383849i | \(-0.125402\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 165.603 | 1.51929 | 0.759646 | − | 0.650337i | \(-0.225372\pi\) | ||||
0.759646 | + | 0.650337i | \(0.225372\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −68.7460 | − | 39.6905i | −0.608372 | − | 0.351244i | 0.163956 | − | 0.986468i | \(-0.447574\pi\) |
−0.772328 | + | 0.635224i | \(0.780908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 28.8608 | + | 49.9884i | 0.250964 | + | 0.434682i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.2361 | − | 12.2607i | 0.178455 | − | 0.103031i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 64.7443 | − | 112.140i | 0.535077 | − | 0.926781i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 377.485i | − | 3.01988i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −147.235 | −1.15933 | −0.579666 | − | 0.814854i | \(-0.696817\pi\) | ||||
−0.579666 | + | 0.814854i | \(0.696817\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 145.857 | + | 84.2103i | 1.11341 | + | 0.642827i | 0.939710 | − | 0.341972i | \(-0.111095\pi\) |
0.173699 | + | 0.984799i | \(0.444428\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.7062 | − | 23.7398i | −0.103054 | − | 0.178495i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 174.984 | − | 101.027i | 1.27726 | − | 0.737426i | 0.300915 | − | 0.953651i | \(-0.402708\pi\) |
0.976343 | + | 0.216225i | \(0.0693746\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −129.193 | + | 223.768i | −0.929443 | + | 1.60984i | −0.145189 | + | 0.989404i | \(0.546379\pi\) |
−0.784255 | + | 0.620439i | \(0.786954\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 148.879i | − | 1.04111i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 271.047 | 1.86929 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 68.6316 | + | 39.6245i | 0.460615 | + | 0.265936i | 0.712303 | − | 0.701872i | \(-0.247652\pi\) |
−0.251688 | + | 0.967808i | \(0.580986\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.73094 | − | 8.19422i | −0.0313307 | − | 0.0542664i | 0.849935 | − | 0.526888i | \(-0.176641\pi\) |
−0.881266 | + | 0.472621i | \(0.843308\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 143.700 | − | 82.9652i | 0.927096 | − | 0.535259i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −34.3561 | + | 59.5066i | −0.218829 | + | 0.379023i | −0.954450 | − | 0.298370i | \(-0.903557\pi\) |
0.735621 | + | 0.677393i | \(0.236890\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.8711i | 0.0799448i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 209.391 | 1.28461 | 0.642304 | − | 0.766450i | \(-0.277979\pi\) | ||||
0.642304 | + | 0.766450i | \(0.277979\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.3682 | + | 12.3369i | 0.127953 | + | 0.0738739i | 0.562610 | − | 0.826722i | \(-0.309797\pi\) |
−0.434657 | + | 0.900596i | \(0.643130\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 40.2566 | + | 69.7265i | 0.238205 | + | 0.412583i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 129.186 | − | 74.5855i | 0.746739 | − | 0.431130i | −0.0777754 | − | 0.996971i | \(-0.524782\pi\) |
0.824514 | + | 0.565841i | \(0.191448\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 68.5046 | − | 118.654i | 0.391455 | − | 0.678020i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 65.1600i | 0.364022i | 0.983296 | + | 0.182011i | \(0.0582607\pi\) | ||||
−0.983296 | + | 0.182011i | \(0.941739\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 95.5019 | 0.527635 | 0.263817 | − | 0.964573i | \(-0.415018\pi\) | ||||
0.263817 | + | 0.964573i | \(0.415018\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −128.215 | − | 74.0248i | −0.693053 | − | 0.400134i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −91.8171 | − | 159.032i | −0.491001 | − | 0.850438i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 160.947 | − | 92.9225i | 0.842652 | − | 0.486505i | −0.0155129 | − | 0.999880i | \(-0.504938\pi\) |
0.858165 | + | 0.513374i | \(0.171605\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −48.1579 | + | 83.4119i | −0.249523 | + | 0.432186i | −0.963393 | − | 0.268091i | \(-0.913607\pi\) |
0.713871 | + | 0.700277i | \(0.246940\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 126.121i | 0.640209i | 0.947382 | + | 0.320105i | \(0.103718\pi\) | ||||
−0.947382 | + | 0.320105i | \(0.896282\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −131.718 | −0.661899 | −0.330950 | − | 0.943648i | \(-0.607369\pi\) | ||||
−0.330950 | + | 0.943648i | \(0.607369\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 52.3424 | + | 30.2199i | 0.257844 | + | 0.148866i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 81.0195 | + | 140.330i | 0.395217 | + | 0.684536i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −177.782 | + | 102.642i | −0.850631 | + | 0.491112i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.15331 | + | 8.92579i | −0.0244233 | + | 0.0423023i | −0.877979 | − | 0.478700i | \(-0.841108\pi\) |
0.853555 | + | 0.521002i | \(0.174442\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 411.634i | 1.91457i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 37.0001 | 0.170508 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −94.5212 | − | 54.5718i | −0.427698 | − | 0.246931i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 86.4202 | + | 149.684i | 0.387535 | + | 0.671230i | 0.992117 | − | 0.125313i | \(-0.0399934\pi\) |
−0.604583 | + | 0.796542i | \(0.706660\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 173.974 | − | 100.444i | 0.766403 | − | 0.442483i | −0.0651869 | − | 0.997873i | \(-0.520764\pi\) |
0.831590 | + | 0.555390i | \(0.187431\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 130.630 | − | 226.259i | 0.570439 | − | 0.988029i | −0.426082 | − | 0.904684i | \(-0.640107\pi\) |
0.996521 | − | 0.0833443i | \(-0.0265601\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 130.530i | − | 0.560214i | −0.959969 | − | 0.280107i | \(-0.909630\pi\) | ||
0.959969 | − | 0.280107i | \(-0.0903700\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −226.208 | −0.962586 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −231.586 | − | 133.706i | −0.968981 | − | 0.559441i | −0.0700553 | − | 0.997543i | \(-0.522318\pi\) |
−0.898925 | + | 0.438102i | \(0.855651\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −50.8188 | − | 88.0207i | −0.210866 | − | 0.365231i | 0.741120 | − | 0.671373i | \(-0.234295\pi\) |
−0.951986 | + | 0.306142i | \(0.900962\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −365.531 | + | 211.039i | −1.49196 | + | 0.861385i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −61.0059 | + | 105.665i | −0.246987 | + | 0.427795i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 137.033i | 0.545946i | 0.962022 | + | 0.272973i | \(0.0880070\pi\) | ||||
−0.962022 | + | 0.272973i | \(0.911993\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 96.3886 | 0.380983 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 217.737 | + | 125.711i | 0.847226 | + | 0.489146i | 0.859714 | − | 0.510776i | \(-0.170642\pi\) |
−0.0124876 | + | 0.999922i | \(0.503975\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −16.5065 | − | 28.5901i | −0.0637317 | − | 0.110387i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 416.538 | − | 240.488i | 1.58379 | − | 0.914404i | 0.589496 | − | 0.807771i | \(-0.299326\pi\) |
0.994298 | − | 0.106633i | \(-0.0340069\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −66.8425 | + | 115.775i | −0.252236 | + | 0.436885i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 182.939i | 0.680071i | 0.940413 | + | 0.340036i | \(0.110439\pi\) | ||||
−0.940413 | + | 0.340036i | \(0.889561\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.0146 | 0.114445 | 0.0572225 | − | 0.998361i | \(-0.481776\pi\) | ||||
0.0572225 | + | 0.998361i | \(0.481776\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −888.567 | − | 513.014i | −3.23115 | − | 1.86551i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 206.382 | + | 357.464i | 0.745060 | + | 1.29048i | 0.950167 | + | 0.311743i | \(0.100913\pi\) |
−0.205106 | + | 0.978740i | \(0.565754\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 107.255 | − | 61.9236i | 0.381690 | − | 0.220369i | −0.296863 | − | 0.954920i | \(-0.595941\pi\) |
0.678553 | + | 0.734551i | \(0.262607\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4.23689 | + | 7.33850i | −0.0149713 | + | 0.0259311i | −0.873414 | − | 0.486978i | \(-0.838099\pi\) |
0.858443 | + | 0.512910i | \(0.171432\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 36.1324i | 0.125897i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 154.377 | 0.534177 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −93.2120 | − | 53.8160i | −0.318130 | − | 0.183672i | 0.332429 | − | 0.943128i | \(-0.392132\pi\) |
−0.650559 | + | 0.759456i | \(0.725465\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 211.103 | + | 365.641i | 0.715604 | + | 1.23946i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 49.6137 | − | 28.6445i | 0.165932 | − | 0.0958009i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −45.8943 | + | 79.4912i | −0.152473 | + | 0.264090i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 35.2682i | − | 0.115633i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −530.715 | −1.72871 | −0.864357 | − | 0.502878i | \(-0.832274\pi\) | ||||
−0.864357 | + | 0.502878i | \(0.832274\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 142.535 | + | 82.2926i | 0.458312 | + | 0.264606i | 0.711334 | − | 0.702854i | \(-0.248091\pi\) |
−0.253022 | + | 0.967460i | \(0.581425\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 273.833 | + | 474.293i | 0.874866 | + | 1.51531i | 0.856905 | + | 0.515474i | \(0.172384\pi\) |
0.0179611 | + | 0.999839i | \(0.494283\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 67.7106 | − | 39.0928i | 0.213598 | − | 0.123321i | −0.389384 | − | 0.921075i | \(-0.627312\pi\) |
0.602983 | + | 0.797754i | \(0.293979\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 226.309 | − | 391.979i | 0.709433 | − | 1.22877i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 150.495i | 0.465929i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −609.824 | −1.87638 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −43.6833 | − | 25.2206i | −0.132776 | − | 0.0766583i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 274.898 | + | 476.137i | 0.830507 | + | 1.43848i | 0.897637 | + | 0.440736i | \(0.145283\pi\) |
−0.0671297 | + | 0.997744i | \(0.521384\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −344.884 | + | 199.119i | −1.02951 | + | 0.594385i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 36.8057 | − | 63.7494i | 0.109216 | − | 0.189167i | −0.806237 | − | 0.591593i | \(-0.798499\pi\) |
0.915453 | + | 0.402425i | \(0.131833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 277.085i | − | 0.812566i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −197.675 | −0.576312 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 367.796 | + | 212.347i | 1.05993 | + | 0.611951i | 0.925413 | − | 0.378960i | \(-0.123718\pi\) |
0.134517 | + | 0.990911i | \(0.457052\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −267.361 | − | 463.082i | −0.766077 | − | 1.32688i | −0.939676 | − | 0.342067i | \(-0.888873\pi\) |
0.173599 | − | 0.984816i | \(-0.444460\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 155.165 | − | 89.5845i | 0.439561 | − | 0.253781i | −0.263851 | − | 0.964564i | \(-0.584993\pi\) |
0.703411 | + | 0.710783i | \(0.251659\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 570.753 | − | 988.573i | 1.60775 | − | 2.78471i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 351.534i | − | 0.979204i | −0.871946 | − | 0.489602i | \(-0.837142\pi\) | ||
0.871946 | − | 0.489602i | \(-0.162858\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −192.761 | −0.533965 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −45.0367 | − | 26.0019i | −0.123388 | − | 0.0712382i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −41.9855 | − | 72.7210i | −0.114402 | − | 0.198150i | 0.803139 | − | 0.595792i | \(-0.203162\pi\) |
−0.917541 | + | 0.397642i | \(0.869829\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.8161 | + | 14.9050i | −0.0695853 | + | 0.0401751i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 218.337 | − | 378.171i | 0.585354 | − | 1.01386i | −0.409477 | − | 0.912320i | \(-0.634289\pi\) |
0.994831 | − | 0.101543i | \(-0.0323779\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 269.016i | − | 0.713569i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 273.455 | 0.721516 | 0.360758 | − | 0.932659i | \(-0.382518\pi\) | ||||
0.360758 | + | 0.932659i | \(0.382518\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −192.544 | − | 111.166i | −0.502727 | − | 0.290249i | 0.227112 | − | 0.973869i | \(-0.427072\pi\) |
−0.729839 | + | 0.683619i | \(0.760405\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −158.510 | − | 274.547i | −0.411713 | − | 0.713108i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 522.471 | − | 301.649i | 1.34311 | − | 0.775447i | 0.355851 | − | 0.934543i | \(-0.384191\pi\) |
0.987263 | + | 0.159096i | \(0.0508578\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 35.3314 | − | 61.1958i | 0.0903617 | − | 0.156511i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1147.72i | 2.90563i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 138.804 | 0.349633 | 0.174816 | − | 0.984601i | \(-0.444067\pi\) | ||||
0.174816 | + | 0.984601i | \(0.444067\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 281.903 | + | 162.757i | 0.702999 | + | 0.405877i | 0.808464 | − | 0.588546i | \(-0.200300\pi\) |
−0.105464 | + | 0.994423i | \(0.533633\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −82.3433 | − | 142.623i | −0.204326 | − | 0.353903i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −214.104 | + | 123.613i | −0.526055 | + | 0.303718i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 257.442 | − | 445.903i | 0.629443 | − | 1.09023i | −0.358220 | − | 0.933637i | \(-0.616616\pi\) |
0.987664 | − | 0.156591i | \(-0.0500504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 94.1461i | 0.227957i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 509.839 | 1.22853 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −107.340 | − | 61.9726i | −0.256181 | − | 0.147906i | 0.366410 | − | 0.930453i | \(-0.380587\pi\) |
−0.622591 | + | 0.782547i | \(0.713920\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −255.924 | − | 443.273i | −0.607895 | − | 1.05291i | −0.991587 | − | 0.129444i | \(-0.958681\pi\) |
0.383691 | − | 0.923461i | \(-0.374653\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −651.412 | + | 376.093i | −1.53273 | + | 0.884924i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.93216 | − | 6.81070i | 0.00920880 | − | 0.0159501i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 650.840i | 1.51007i | 0.655684 | + | 0.755035i | \(0.272380\pi\) | ||||
−0.655684 | + | 0.755035i | \(0.727620\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −432.455 | −0.998742 | −0.499371 | − | 0.866388i | \(-0.666435\pi\) | ||||
−0.499371 | + | 0.866388i | \(0.666435\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −68.4108 | − | 39.4970i | −0.156547 | − | 0.0903822i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −190.663 | − | 330.238i | −0.434312 | − | 0.752251i | 0.562927 | − | 0.826507i | \(-0.309675\pi\) |
−0.997239 | + | 0.0742559i | \(0.976342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 33.3781 | − | 19.2708i | 0.0753455 | − | 0.0435007i | −0.461854 | − | 0.886956i | \(-0.652816\pi\) |
0.537199 | + | 0.843455i | \(0.319482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −484.289 | + | 838.813i | −1.08829 | + | 1.88497i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 373.577i | 0.832019i | 0.909360 | + | 0.416010i | \(0.136572\pi\) | ||||
−0.909360 | + | 0.416010i | \(0.863428\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 270.587 | 0.599971 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −163.178 | − | 94.2108i | −0.358633 | − | 0.207057i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −121.482 | − | 210.414i | −0.265826 | − | 0.460423i | 0.701954 | − | 0.712222i | \(-0.252311\pi\) |
−0.967780 | + | 0.251799i | \(0.918978\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −116.211 | + | 67.0942i | −0.252084 | + | 0.145541i | −0.620718 | − | 0.784034i | \(-0.713159\pi\) |
0.368634 | + | 0.929574i | \(0.379825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 155.129 | − | 268.691i | 0.335051 | − | 0.580326i | −0.648443 | − | 0.761263i | \(-0.724580\pi\) |
0.983495 | + | 0.180937i | \(0.0579131\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 765.680i | − | 1.63957i | −0.572670 | − | 0.819786i | \(-0.694092\pi\) | ||
0.572670 | − | 0.819786i | \(-0.305908\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −88.8015 | −0.189342 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 595.290 | + | 343.691i | 1.25854 | + | 0.726619i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 420.434 | + | 728.214i | 0.885125 | + | 1.53308i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 442.124 | − | 255.260i | 0.923014 | − | 0.532902i | 0.0384186 | − | 0.999262i | \(-0.487768\pi\) |
0.884595 | + | 0.466359i | \(0.154435\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −73.4699 | + | 127.254i | −0.152744 | + | 0.264561i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1117.20i | 2.30350i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −669.532 | −1.37481 | −0.687405 | − | 0.726274i | \(-0.741250\pi\) | ||||
−0.687405 | + | 0.726274i | \(0.741250\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −640.537 | − | 369.814i | −1.30456 | − | 0.753186i | −0.323375 | − | 0.946271i | \(-0.604817\pi\) |
−0.981182 | + | 0.193085i | \(0.938151\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −165.908 | − | 287.361i | −0.336528 | − | 0.582883i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 220.438 | − | 127.270i | 0.443537 | − | 0.256076i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −461.405 | + | 799.176i | −0.924659 | + | 1.60156i | −0.132550 | + | 0.991176i | \(0.542316\pi\) |
−0.792109 | + | 0.610380i | \(0.791017\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 223.098i | 0.443534i | 0.975100 | + | 0.221767i | \(0.0711824\pi\) | ||||
−0.975100 | + | 0.221767i | \(0.928818\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1293.37 | −2.56113 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 125.233 | + | 72.3030i | 0.246036 | + | 0.142049i | 0.617948 | − | 0.786219i | \(-0.287964\pi\) |
−0.371912 | + | 0.928268i | \(0.621298\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.79807 | − | 10.0425i | −0.0113465 | − | 0.0196527i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 998.932 | − | 576.733i | 1.93967 | − | 1.11987i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −188.871 | + | 327.134i | −0.365320 | + | 0.632753i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 452.382i | 0.868296i | 0.900842 | + | 0.434148i | \(0.142950\pi\) | ||||
−0.900842 | + | 0.434148i | \(0.857050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −168.242 | −0.321686 | −0.160843 | − | 0.986980i | \(-0.551421\pi\) | ||||
−0.160843 | + | 0.986980i | \(0.551421\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −175.918 | − | 101.566i | −0.333809 | − | 0.192725i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −245.955 | − | 426.006i | −0.464943 | − | 0.805305i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 139.278 | − | 80.4122i | 0.261309 | − | 0.150867i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −389.270 | + | 674.235i | −0.727607 | + | 1.26025i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 704.824i | 1.30765i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 809.693 | 1.49666 | 0.748330 | − | 0.663327i | \(-0.230856\pi\) | ||||
0.748330 | + | 0.663327i | \(0.230856\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1359.27 | − | 784.774i | −2.49407 | − | 1.43995i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −468.105 | − | 810.781i | −0.855767 | − | 1.48223i | −0.875931 | − | 0.482436i | \(-0.839752\pi\) |
0.0201641 | − | 0.999797i | \(-0.493581\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −321.242 | + | 185.469i | −0.583015 | + | 0.336604i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −127.963 | + | 221.638i | −0.231398 | + | 0.400793i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 318.572i | 0.571942i | 0.958238 | + | 0.285971i | \(0.0923162\pi\) | ||||
−0.958238 | + | 0.285971i | \(0.907684\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 408.548 | 0.730855 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −700.038 | − | 404.167i | −1.24341 | − | 0.717882i | −0.273621 | − | 0.961838i | \(-0.588221\pi\) |
−0.969786 | + | 0.243956i | \(0.921555\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 376.178 | + | 651.560i | 0.665802 | + | 1.15320i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −895.501 | + | 517.017i | −1.57381 | + | 0.908642i | −0.578120 | + | 0.815952i | \(0.696213\pi\) |
−0.995695 | + | 0.0926904i | \(0.970453\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 24.0163 | − | 41.5974i | 0.0420600 | − | 0.0728500i | −0.844229 | − | 0.535983i | \(-0.819941\pi\) |
0.886289 | + | 0.463133i | \(0.153275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 394.818i | − | 0.686640i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 396.617 | 0.687378 | 0.343689 | − | 0.939084i | \(-0.388323\pi\) | ||||
0.343689 | + | 0.939084i | \(0.388323\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 98.4558 | + | 56.8435i | 0.169459 | + | 0.0978373i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 111.619 | + | 193.331i | 0.191457 | + | 0.331613i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 560.569 | − | 323.645i | 0.954973 | − | 0.551354i | 0.0603509 | − | 0.998177i | \(-0.480778\pi\) |
0.894622 | + | 0.446823i | \(0.147445\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −113.541 | + | 196.658i | −0.192769 | + | 0.333885i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 322.360i | 0.543609i | 0.962352 | + | 0.271805i | \(0.0876204\pi\) | ||||
−0.962352 | + | 0.271805i | \(0.912380\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −232.408 | −0.390602 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −286.437 | − | 165.374i | −0.478191 | − | 0.276084i | 0.241471 | − | 0.970408i | \(-0.422370\pi\) |
−0.719662 | + | 0.694324i | \(0.755703\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.29683 | − | 3.97823i | −0.00382169 | − | 0.00661936i | 0.864108 | − | 0.503306i | \(-0.167883\pi\) |
−0.867930 | + | 0.496687i | \(0.834550\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1062.84 | + | 613.633i | −1.75677 | + | 1.01427i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −100.896 | + | 174.756i | −0.166220 | + | 0.287902i | −0.937088 | − | 0.349093i | \(-0.886490\pi\) |
0.770868 | + | 0.636995i | \(0.219823\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 224.512i | 0.367450i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −594.531 | −0.969871 | −0.484936 | − | 0.874550i | \(-0.661157\pi\) | ||||
−0.484936 | + | 0.874550i | \(0.661157\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 562.741 | + | 324.899i | 0.912060 | + | 0.526578i | 0.881093 | − | 0.472942i | \(-0.156808\pi\) |
0.0309665 | + | 0.999520i | \(0.490141\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 114.275 | + | 197.931i | 0.184613 | + | 0.319759i | 0.943446 | − | 0.331526i | \(-0.107564\pi\) |
−0.758833 | + | 0.651285i | \(0.774230\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −187.044 | + | 107.990i | −0.300231 | + | 0.173338i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −978.507 | + | 1694.82i | −1.56561 | + | 2.71172i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 181.243i | 0.288144i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 555.448 | 0.880266 | 0.440133 | − | 0.897933i | \(-0.354931\pi\) | ||||
0.440133 | + | 0.897933i | \(0.354931\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1208.51 | + | 697.732i | 1.90316 | + | 1.09879i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 209.457 | + | 362.791i | 0.328819 | + | 0.569530i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −374.507 | + | 216.222i | −0.584254 | + | 0.337319i | −0.762822 | − | 0.646608i | \(-0.776187\pi\) |
0.178568 | + | 0.983928i | \(0.442853\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 170.831 | − | 295.888i | 0.265678 | − | 0.460168i | −0.702063 | − | 0.712115i | \(-0.747738\pi\) |
0.967741 | + | 0.251947i | \(0.0810709\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1066.85i | 1.64891i | 0.565926 | + | 0.824456i | \(0.308519\pi\) | ||||
−0.565926 | + | 0.824456i | \(0.691481\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 705.037 | 1.08634 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 576.545 | + | 332.868i | 0.882917 | + | 0.509752i | 0.871619 | − | 0.490184i | \(-0.163070\pi\) |
0.0112977 | + | 0.999936i | \(0.496404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −798.128 | − | 1382.40i | −1.21852 | − | 2.11053i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −795.462 | + | 459.260i | −1.20707 | + | 0.696905i | −0.962119 | − | 0.272630i | \(-0.912107\pi\) |
−0.244955 | + | 0.969534i | \(0.578773\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −385.777 | + | 668.185i | −0.583626 | + | 1.01087i | 0.411420 | + | 0.911446i | \(0.365033\pi\) |
−0.995045 | + | 0.0994232i | \(0.968300\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 259.809i | 0.390690i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 174.169 | 0.261122 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −51.0036 | − | 29.4470i | −0.0760114 | − | 0.0438852i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 559.767 | + | 969.546i | 0.831750 | + | 1.44063i | 0.896650 | + | 0.442741i | \(0.145994\pi\) |
−0.0649002 | + | 0.997892i | \(0.520673\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −339.051 | + | 195.751i | −0.500815 | + | 0.289145i | −0.729050 | − | 0.684461i | \(-0.760038\pi\) |
0.228235 | + | 0.973606i | \(0.426704\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −124.560 | + | 215.744i | −0.183446 | + | 0.317737i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 661.278i | − | 0.968196i | −0.875014 | − | 0.484098i | \(-0.839148\pi\) | ||
0.875014 | − | 0.484098i | \(-0.160852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1915.03 | −2.79566 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 114.907 | + | 66.3415i | 0.166773 | + | 0.0962866i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −412.836 | − | 715.053i | −0.597447 | − | 1.03481i | −0.993197 | − | 0.116450i | \(-0.962849\pi\) |
0.395750 | − | 0.918358i | \(-0.370485\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2120.83 | − | 1224.46i | 3.05155 | − | 1.76181i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 99.1841 | − | 171.792i | 0.142301 | − | 0.246473i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 236.167i | 0.336900i | 0.985710 | + | 0.168450i | \(0.0538761\pi\) | ||||
−0.985710 | + | 0.168450i | \(0.946124\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 202.611 | 0.288209 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −249.765 | − | 144.202i | −0.353274 | − | 0.203963i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 247.969 | + | 429.496i | 0.349745 | + | 0.605777i | 0.986204 | − | 0.165534i | \(-0.0529348\pi\) |
−0.636459 | + | 0.771311i | \(0.719601\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 92.3381 | − | 53.3115i | 0.129507 | − | 0.0747706i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −705.521 | + | 1222.00i | −0.986743 | + | 1.70909i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 1065.13i | − | 1.48141i | −0.671830 | − | 0.740705i | \(-0.734492\pi\) | ||
0.671830 | − | 0.740705i | \(-0.265508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 257.207 | 0.356736 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1605.59 | − | 926.987i | −2.21460 | − | 1.27860i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 549.525 | + | 951.806i | 0.755881 | + | 1.30922i | 0.944935 | + | 0.327257i | \(0.106124\pi\) |
−0.189054 | + | 0.981967i | \(0.560542\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 436.409 | − | 251.961i | 0.597003 | − | 0.344680i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 720.569 | − | 1248.06i | 0.983041 | − | 1.70268i | 0.332706 | − | 0.943031i | \(-0.392038\pi\) |
0.650336 | − | 0.759647i | \(-0.274628\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 665.013i | 0.902324i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1095.72 | 1.48271 | 0.741356 | − | 0.671112i | \(-0.234183\pi\) | ||||
0.741356 | + | 0.671112i | \(0.234183\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 857.848 | + | 495.279i | 1.15457 | + | 0.666593i | 0.949997 | − | 0.312258i | \(-0.101085\pi\) |
0.204575 | + | 0.978851i | \(0.434419\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −375.552 | − | 650.476i | −0.504097 | − | 0.873122i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −150.345 | + | 86.8018i | −0.200728 | + | 0.115890i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −177.884 | + | 308.103i | −0.236862 | + | 0.410258i | −0.959812 | − | 0.280643i | \(-0.909452\pi\) |
0.722950 | + | 0.690900i | \(0.242786\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 89.6776i | 0.118778i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 231.917 | 0.306364 | 0.153182 | − | 0.988198i | \(-0.451048\pi\) | ||||
0.153182 | + | 0.988198i | \(0.451048\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 368.325 | + | 212.653i | 0.484002 | + | 0.279438i | 0.722083 | − | 0.691807i | \(-0.243185\pi\) |
−0.238081 | + | 0.971245i | \(0.576518\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −174.994 | − | 303.098i | −0.229350 | − | 0.397245i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 362.900 | − | 209.521i | 0.473143 | − | 0.273169i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 422.147 | − | 731.179i | 0.548955 | − | 0.950819i | −0.449391 | − | 0.893335i | \(-0.648359\pi\) |
0.998346 | − | 0.0574834i | \(-0.0183076\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 816.503i | − | 1.05628i | −0.849158 | − | 0.528139i | \(-0.822890\pi\) | ||
0.849158 | − | 0.528139i | \(-0.177110\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1134.97 | −1.46448 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −192.046 | − | 110.878i | −0.246529 | − | 0.142334i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −953.093 | − | 1650.81i | −1.22035 | − | 2.11371i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 563.991 | − | 325.620i | 0.718459 | − | 0.414803i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −178.111 | + | 308.497i | −0.226316 | + | 0.391991i | −0.956713 | − | 0.291031i | \(-0.906002\pi\) |
0.730397 | + | 0.683022i | \(0.239335\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 167.765i | 0.212092i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −35.0038 | −0.0441410 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 561.666 | + | 324.278i | 0.704725 | + | 0.406873i | 0.809105 | − | 0.587664i | \(-0.199952\pi\) |
−0.104380 | + | 0.994537i | \(0.533286\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 138.462 | + | 239.823i | 0.173294 | + | 0.300154i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −75.2062 | + | 43.4203i | −0.0936565 | + | 0.0540726i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 60.9948 | − | 105.646i | 0.0757700 | − | 0.131237i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 445.244i | − | 0.550363i | −0.961392 | − | 0.275182i | \(-0.911262\pi\) | ||
0.961392 | − | 0.275182i | \(-0.0887380\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −373.366 | −0.460377 | −0.230189 | − | 0.973146i | \(-0.573934\pi\) | ||||
−0.230189 | + | 0.973146i | \(0.573934\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −1718.68 | − | 992.282i | −2.10881 | − | 1.21752i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −281.667 | − | 487.862i | −0.344758 | − | 0.597139i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −42.7001 | + | 24.6529i | −0.0520099 | + | 0.0300279i | −0.525779 | − | 0.850621i | \(-0.676226\pi\) |
0.473770 | + | 0.880649i | \(0.342893\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −289.224 | + | 500.950i | −0.351426 | + | 0.608688i | −0.986500 | − | 0.163764i | \(-0.947636\pi\) |
0.635074 | + | 0.772452i | \(0.280970\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 665.710i | 0.804970i | 0.915427 | + | 0.402485i | \(0.131853\pi\) | ||||
−0.915427 | + | 0.402485i | \(0.868147\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −133.042 | −0.160485 | −0.0802423 | − | 0.996775i | \(-0.525569\pi\) | ||||
−0.0802423 | + | 0.996775i | \(0.525569\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 447.483 | + | 258.355i | 0.537195 | + | 0.310150i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −116.927 | − | 202.523i | −0.140032 | − | 0.242543i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −707.636 | + | 408.554i | −0.843428 | + | 0.486954i | −0.858428 | − | 0.512934i | \(-0.828559\pi\) |
0.0149998 | + | 0.999887i | \(0.495225\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.5724 | + | 20.0439i | −0.0137602 | + | 0.0238334i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 763.087i | − | 0.903062i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −273.663 | −0.323097 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −82.3878 | − | 47.5666i | −0.0968129 | − | 0.0558950i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.2616 | + | 24.7018i | 0.0167193 | + | 0.0289587i | 0.874264 | − | 0.485451i | \(-0.161344\pi\) |
−0.857545 | + | 0.514409i | \(0.828011\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1218.49 | − | 703.496i | 1.42181 | − | 0.820883i | 0.425357 | − | 0.905026i | \(-0.360149\pi\) |
0.996454 | + | 0.0841433i | \(0.0268154\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −296.573 | + | 513.680i | −0.345254 | + | 0.597998i | −0.985400 | − | 0.170256i | \(-0.945541\pi\) |
0.640146 | + | 0.768254i | \(0.278874\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 549.058i | 0.636220i | 0.948054 | + | 0.318110i | \(0.103048\pi\) | ||||
−0.948054 | + | 0.318110i | \(0.896952\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1413.81 | −1.63446 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1659.80 | + | 958.283i | 1.91001 | + | 1.10274i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 197.626 | + | 342.299i | 0.226896 | + | 0.392996i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −690.900 | + | 398.891i | −0.789600 | + | 0.455876i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 481.413 | − | 833.831i | 0.548931 | − | 0.950776i | −0.449417 | − | 0.893322i | \(-0.648368\pi\) |
0.998348 | − | 0.0574544i | \(-0.0182984\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 485.913i | − | 0.551547i | −0.961223 | − | 0.275774i | \(-0.911066\pi\) | ||
0.961223 | − | 0.275774i | \(-0.0889340\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1020.25 | 1.15544 | 0.577720 | − | 0.816235i | \(-0.303943\pi\) | ||||
0.577720 | + | 0.816235i | \(0.303943\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 896.965 | + | 517.863i | 1.01123 | + | 0.583836i | 0.911553 | − | 0.411183i | \(-0.134884\pi\) |
0.0996814 | + | 0.995019i | \(0.468218\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 155.584 | + | 269.480i | 0.175011 | + | 0.303127i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 268.098 | − | 154.787i | 0.300222 | − | 0.173333i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 308.786 | − | 534.834i | 0.345013 | − | 0.597580i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 500.676i | − | 0.556926i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 163.657 | 0.181640 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −783.880 | − | 452.573i | −0.866165 | − | 0.500081i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −794.936 | − | 1376.87i | −0.876445 | − | 1.51805i | −0.855215 | − | 0.518273i | \(-0.826575\pi\) |
−0.0212301 | − | 0.999775i | \(-0.506758\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 362.743 | − | 209.430i | 0.398181 | − | 0.229890i | −0.287518 | − | 0.957775i | \(-0.592830\pi\) |
0.685699 | + | 0.727885i | \(0.259497\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 425.687 | − | 737.311i | 0.466250 | − | 0.807569i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 355.943i | − | 0.388160i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1499.57 | 1.63174 | 0.815872 | − | 0.578233i | \(-0.196257\pi\) | ||||
0.815872 | + | 0.578233i | \(0.196257\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −981.162 | − | 566.474i | −1.06301 | − | 0.613732i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 506.333 | + | 876.994i | 0.547387 | + | 0.948102i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1046.99 | − | 604.481i | 1.12701 | − | 0.650679i | 0.183829 | − | 0.982958i | \(-0.441151\pi\) |
0.943181 | + | 0.332279i | \(0.107817\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 288.815 | − | 500.242i | 0.310220 | − | 0.537317i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1740.45i | 1.86144i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 557.393 | 0.594870 | 0.297435 | − | 0.954742i | \(-0.403869\pi\) | ||||
0.297435 | + | 0.954742i | \(0.403869\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 465.315 | + | 268.650i | 0.494490 | + | 0.285494i | 0.726435 | − | 0.687235i | \(-0.241176\pi\) |
−0.231945 | + | 0.972729i | \(0.574509\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.0612 | + | 90.1727i | 0.0552081 | + | 0.0956232i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −515.416 | + | 297.575i | −0.544261 | + | 0.314229i | −0.746804 | − | 0.665044i | \(-0.768413\pi\) |
0.202543 | + | 0.979273i | \(0.435079\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −25.8070 | + | 44.6991i | −0.0271939 | + | 0.0471012i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 88.9834i | − | 0.0933718i | −0.998910 | − | 0.0466859i | \(-0.985134\pi\) | ||
0.998910 | − | 0.0466859i | \(-0.0148660\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1761.40 | −1.84440 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −369.814 | − | 213.512i | −0.385625 | − | 0.222641i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 327.247 | + | 566.809i | 0.340528 | + | 0.589812i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 790.560 | − | 456.430i | 0.819233 | − | 0.472985i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 658.074 | − | 1139.82i | 0.680532 | − | 1.17872i | −0.294287 | − | 0.955717i | \(-0.595082\pi\) |
0.974819 | − | 0.222998i | \(-0.0715845\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 361.433i | − | 0.372228i | −0.982528 | − | 0.186114i | \(-0.940411\pi\) | ||
0.982528 | − | 0.186114i | \(-0.0595893\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 546.075 | 0.561228 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −883.148 | − | 509.885i | −0.903938 | − | 0.521889i | −0.0254624 | − | 0.999676i | \(-0.508106\pi\) |
−0.878476 | + | 0.477787i | \(0.841439\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 808.708 | + | 1400.72i | 0.826056 | + | 1.43077i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1144.21 | + | 660.612i | −1.16400 | + | 0.672037i | −0.952260 | − | 0.305289i | \(-0.901247\pi\) |
−0.211742 | + | 0.977326i | \(0.567914\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 597.675 | − | 1035.20i | 0.606777 | − | 1.05097i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 264.506i | 0.267448i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.11587 | 0.00617141 | 0.00308571 | − | 0.999995i | \(-0.499018\pi\) | ||||
0.00308571 | + | 0.999995i | \(0.499018\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1081.14 | + | 624.197i | 1.08657 | + | 0.627334i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −315.180 | − | 545.908i | −0.316129 | − | 0.547551i | 0.663548 | − | 0.748134i | \(-0.269050\pi\) |
−0.979677 | + | 0.200583i | \(0.935716\pi\) | |||||||
\(998\) | 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 | 1728.3.q.i.449.1 | 8 | ||
3.2 | odd | 2 | 576.3.q.j.257.1 | 8 | |||
4.3 | odd | 2 | 1728.3.q.j.449.1 | 8 | |||
8.3 | odd | 2 | 216.3.m.b.17.4 | 8 | |||
8.5 | even | 2 | 432.3.q.e.17.4 | 8 | |||
9.2 | odd | 6 | inner | 1728.3.q.i.1601.1 | 8 | ||
9.7 | even | 3 | 576.3.q.j.65.1 | 8 | |||
12.11 | even | 2 | 576.3.q.i.257.4 | 8 | |||
24.5 | odd | 2 | 144.3.q.e.113.4 | 8 | |||
24.11 | even | 2 | 72.3.m.b.41.1 | ✓ | 8 | ||
36.7 | odd | 6 | 576.3.q.i.65.4 | 8 | |||
36.11 | even | 6 | 1728.3.q.j.1601.1 | 8 | |||
72.5 | odd | 6 | 1296.3.e.i.161.8 | 8 | |||
72.11 | even | 6 | 216.3.m.b.89.4 | 8 | |||
72.13 | even | 6 | 1296.3.e.i.161.1 | 8 | |||
72.29 | odd | 6 | 432.3.q.e.305.4 | 8 | |||
72.43 | odd | 6 | 72.3.m.b.65.1 | yes | 8 | ||
72.59 | even | 6 | 648.3.e.c.161.8 | 8 | |||
72.61 | even | 6 | 144.3.q.e.65.4 | 8 | |||
72.67 | odd | 6 | 648.3.e.c.161.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
72.3.m.b.41.1 | ✓ | 8 | 24.11 | even | 2 | ||
72.3.m.b.65.1 | yes | 8 | 72.43 | odd | 6 | ||
144.3.q.e.65.4 | 8 | 72.61 | even | 6 | |||
144.3.q.e.113.4 | 8 | 24.5 | odd | 2 | |||
216.3.m.b.17.4 | 8 | 8.3 | odd | 2 | |||
216.3.m.b.89.4 | 8 | 72.11 | even | 6 | |||
432.3.q.e.17.4 | 8 | 8.5 | even | 2 | |||
432.3.q.e.305.4 | 8 | 72.29 | odd | 6 | |||
576.3.q.i.65.4 | 8 | 36.7 | odd | 6 | |||
576.3.q.i.257.4 | 8 | 12.11 | even | 2 | |||
576.3.q.j.65.1 | 8 | 9.7 | even | 3 | |||
576.3.q.j.257.1 | 8 | 3.2 | odd | 2 | |||
648.3.e.c.161.1 | 8 | 72.67 | odd | 6 | |||
648.3.e.c.161.8 | 8 | 72.59 | even | 6 | |||
1296.3.e.i.161.1 | 8 | 72.13 | even | 6 | |||
1296.3.e.i.161.8 | 8 | 72.5 | odd | 6 | |||
1728.3.q.i.449.1 | 8 | 1.1 | even | 1 | trivial | ||
1728.3.q.i.1601.1 | 8 | 9.2 | odd | 6 | inner | ||
1728.3.q.j.449.1 | 8 | 4.3 | odd | 2 | |||
1728.3.q.j.1601.1 | 8 | 36.11 | even | 6 |