Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [576,3,Mod(271,576)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(576, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("576.271");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 576 = 2^{6} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 576.m (of order \(4\), 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: | \(15.6948632272\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 271.3 | ||
Root | \(-1.96679 - 0.362960i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 576.271 |
Dual form | 576.3.m.c.559.3 |
$q$-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 \(\left(\mathbb{Z}/576\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(325\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.69930 | − | 1.69930i | −0.339861 | − | 0.339861i | 0.516454 | − | 0.856315i | \(-0.327252\pi\) |
−0.856315 | + | 0.516454i | \(0.827252\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.74280 | 0.820400 | 0.410200 | − | 0.911996i | \(-0.365459\pi\) | ||||
0.410200 | + | 0.911996i | \(0.365459\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.59560 | + | 5.59560i | −0.508691 | + | 0.508691i | −0.914125 | − | 0.405434i | \(-0.867121\pi\) |
0.405434 | + | 0.914125i | \(0.367121\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −13.5782 | + | 13.5782i | −1.04447 | + | 1.04447i | −0.0455110 | + | 0.998964i | \(0.514492\pi\) |
−0.998964 | + | 0.0455110i | \(0.985508\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −19.7023 | −1.15896 | −0.579481 | − | 0.814986i | \(-0.696745\pi\) | ||||
−0.579481 | + | 0.814986i | \(0.696745\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.6943 | + | 21.6943i | 1.14181 | + | 1.14181i | 0.988120 | + | 0.153687i | \(0.0491147\pi\) |
0.153687 | + | 0.988120i | \(0.450885\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 24.9257 | 1.08373 | 0.541863 | − | 0.840467i | \(-0.317719\pi\) | ||||
0.541863 | + | 0.840467i | \(0.317719\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 19.2247i | − | 0.768989i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.50581 | + | 1.50581i | −0.0519245 | + | 0.0519245i | −0.732592 | − | 0.680668i | \(-0.761690\pi\) |
0.680668 | + | 0.732592i | \(0.261690\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 2.20037i | − | 0.0709796i | −0.999370 | − | 0.0354898i | \(-0.988701\pi\) | ||
0.999370 | − | 0.0354898i | \(-0.0112991\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −9.75877 | − | 9.75877i | −0.278822 | − | 0.278822i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 27.6956 | + | 27.6956i | 0.748530 | + | 0.748530i | 0.974203 | − | 0.225673i | \(-0.0724580\pi\) |
−0.225673 | + | 0.974203i | \(0.572458\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 51.3127i | 1.25153i | 0.780012 | + | 0.625764i | \(0.215213\pi\) | ||||
−0.780012 | + | 0.625764i | \(0.784787\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −21.4400 | + | 21.4400i | −0.498606 | + | 0.498606i | −0.911004 | − | 0.412398i | \(-0.864691\pi\) |
0.412398 | + | 0.911004i | \(0.364691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 76.5216i | 1.62812i | 0.580781 | + | 0.814060i | \(0.302747\pi\) | ||||
−0.580781 | + | 0.814060i | \(0.697253\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16.0202 | −0.326944 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 56.5145 | + | 56.5145i | 1.06631 | + | 1.06631i | 0.997639 | + | 0.0686712i | \(0.0218759\pi\) |
0.0686712 | + | 0.997639i | \(0.478124\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 19.0173 | 0.345768 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −48.0041 | + | 48.0041i | −0.813628 | + | 0.813628i | −0.985176 | − | 0.171547i | \(-0.945123\pi\) |
0.171547 | + | 0.985176i | \(0.445123\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −51.5587 | + | 51.5587i | −0.845224 | + | 0.845224i | −0.989533 | − | 0.144308i | \(-0.953904\pi\) |
0.144308 | + | 0.989533i | \(0.453904\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 46.1469 | 0.709952 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −63.4445 | − | 63.4445i | −0.946934 | − | 0.946934i | 0.0517277 | − | 0.998661i | \(-0.483527\pi\) |
−0.998661 | + | 0.0517277i | \(0.983527\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 43.4856 | 0.612473 | 0.306237 | − | 0.951955i | \(-0.400930\pi\) | ||||
0.306237 | + | 0.951955i | \(0.400930\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 73.9992i | − | 1.01369i | −0.862038 | − | 0.506844i | \(-0.830812\pi\) | ||
0.862038 | − | 0.506844i | \(-0.169188\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −32.1344 | + | 32.1344i | −0.417330 | + | 0.417330i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.12659i | − | 0.0522354i | −0.999659 | − | 0.0261177i | \(-0.991686\pi\) | ||
0.999659 | − | 0.0261177i | \(-0.00831446\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 38.4428 | + | 38.4428i | 0.463166 | + | 0.463166i | 0.899692 | − | 0.436526i | \(-0.143791\pi\) |
−0.436526 | + | 0.899692i | \(0.643791\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 33.4803 | + | 33.4803i | 0.393886 | + | 0.393886i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 52.9839i | − | 0.595325i | −0.954671 | − | 0.297662i | \(-0.903793\pi\) | ||
0.954671 | − | 0.297662i | \(-0.0962070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −77.9767 | + | 77.9767i | −0.856887 | + | 0.856887i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 73.7305i | − | 0.776111i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 23.1008 | 0.238153 | 0.119077 | − | 0.992885i | \(-0.462007\pi\) | ||||
0.119077 | + | 0.992885i | \(0.462007\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.1216 | − | 16.1216i | −0.159619 | − | 0.159619i | 0.622779 | − | 0.782398i | \(-0.286004\pi\) |
−0.782398 | + | 0.622779i | \(0.786004\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 98.8380 | 0.959592 | 0.479796 | − | 0.877380i | \(-0.340711\pi\) | ||||
0.479796 | + | 0.877380i | \(0.340711\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 15.6655 | − | 15.6655i | 0.146406 | − | 0.146406i | −0.630104 | − | 0.776511i | \(-0.716988\pi\) |
0.776511 | + | 0.630104i | \(0.216988\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 84.6938 | − | 84.6938i | 0.777008 | − | 0.777008i | −0.202313 | − | 0.979321i | \(-0.564846\pi\) |
0.979321 | + | 0.202313i | \(0.0648459\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −63.8537 | −0.565077 | −0.282538 | − | 0.959256i | \(-0.591176\pi\) | ||||
−0.282538 | + | 0.959256i | \(0.591176\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −42.3563 | − | 42.3563i | −0.368316 | − | 0.368316i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −113.147 | −0.950812 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 58.3785i | 0.482467i | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −75.1513 | + | 75.1513i | −0.601210 | + | 0.601210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.8901i | 0.290473i | 0.989397 | + | 0.145237i | \(0.0463944\pi\) | ||||
−0.989397 | + | 0.145237i | \(0.953606\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −40.4136 | − | 40.4136i | −0.308500 | − | 0.308500i | 0.535827 | − | 0.844328i | \(-0.320000\pi\) |
−0.844328 | + | 0.535827i | \(0.820000\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 124.586 | + | 124.586i | 0.936738 | + | 0.936738i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 253.499i | − | 1.85036i | −0.379531 | − | 0.925179i | \(-0.623915\pi\) | ||
0.379531 | − | 0.925179i | \(-0.376085\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −67.8065 | + | 67.8065i | −0.487816 | + | 0.487816i | −0.907617 | − | 0.419800i | \(-0.862100\pi\) |
0.419800 | + | 0.907617i | \(0.362100\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 151.956i | − | 1.06263i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.11766 | 0.0352942 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 43.9337 | + | 43.9337i | 0.294857 | + | 0.294857i | 0.838996 | − | 0.544138i | \(-0.183143\pi\) |
−0.544138 | + | 0.838996i | \(0.683143\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 223.084 | 1.47738 | 0.738688 | − | 0.674047i | \(-0.235446\pi\) | ||||
0.738688 | + | 0.674047i | \(0.235446\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.73909 | + | 3.73909i | −0.0241232 | + | 0.0241232i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −78.8526 | + | 78.8526i | −0.502246 | + | 0.502246i | −0.912135 | − | 0.409889i | \(-0.865567\pi\) |
0.409889 | + | 0.912135i | \(0.365567\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 143.143 | 0.889089 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −52.2425 | − | 52.2425i | −0.320506 | − | 0.320506i | 0.528455 | − | 0.848961i | \(-0.322772\pi\) |
−0.848961 | + | 0.528455i | \(0.822772\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 96.5201 | 0.577965 | 0.288982 | − | 0.957334i | \(-0.406683\pi\) | ||||
0.288982 | + | 0.957334i | \(0.406683\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 199.734i | − | 1.18186i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 46.3076 | − | 46.3076i | 0.267674 | − | 0.267674i | −0.560488 | − | 0.828162i | \(-0.689386\pi\) |
0.828162 | + | 0.560488i | \(0.189386\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 110.404i | − | 0.630879i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −93.5440 | − | 93.5440i | −0.522592 | − | 0.522592i | 0.395761 | − | 0.918353i | \(-0.370481\pi\) |
−0.918353 | + | 0.395761i | \(0.870481\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −115.810 | − | 115.810i | −0.639836 | − | 0.639836i | 0.310679 | − | 0.950515i | \(-0.399444\pi\) |
−0.950515 | + | 0.310679i | \(0.899444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 94.1266i | − | 0.508792i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 110.246 | − | 110.246i | 0.589553 | − | 0.589553i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 35.2964i | − | 0.184798i | −0.995722 | − | 0.0923991i | \(-0.970546\pi\) | ||
0.995722 | − | 0.0923991i | \(-0.0294535\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −364.339 | −1.88777 | −0.943884 | − | 0.330277i | \(-0.892858\pi\) | ||||
−0.943884 | + | 0.330277i | \(0.892858\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −130.582 | − | 130.582i | −0.662851 | − | 0.662851i | 0.293200 | − | 0.956051i | \(-0.405280\pi\) |
−0.956051 | + | 0.293200i | \(0.905280\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.7493 | 0.0640670 | 0.0320335 | − | 0.999487i | \(-0.489802\pi\) | ||||
0.0320335 | + | 0.999487i | \(0.489802\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −8.64756 | + | 8.64756i | −0.0425988 | + | 0.0425988i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 87.1958 | − | 87.1958i | 0.425346 | − | 0.425346i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −242.786 | −1.16165 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.59499 | − | 8.59499i | −0.0407345 | − | 0.0407345i | 0.686446 | − | 0.727181i | \(-0.259170\pi\) |
−0.727181 | + | 0.686446i | \(0.759170\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 72.8663 | 0.338913 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 12.6363i | − | 0.0582317i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 267.522 | − | 267.522i | 1.21051 | − | 1.21051i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 50.5909i | − | 0.226865i | −0.993546 | − | 0.113433i | \(-0.963815\pi\) | ||
0.993546 | − | 0.113433i | \(-0.0361846\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 31.7175 | + | 31.7175i | 0.139725 | + | 0.139725i | 0.773509 | − | 0.633785i | \(-0.218499\pi\) |
−0.633785 | + | 0.773509i | \(0.718499\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −169.826 | − | 169.826i | −0.741599 | − | 0.741599i | 0.231287 | − | 0.972886i | \(-0.425706\pi\) |
−0.972886 | + | 0.231287i | \(0.925706\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 363.082i | 1.55829i | 0.626844 | + | 0.779145i | \(0.284346\pi\) | ||||
−0.626844 | + | 0.779145i | \(0.715654\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 130.033 | − | 130.033i | 0.553334 | − | 0.553334i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.6282i | 0.115599i | 0.998328 | + | 0.0577996i | \(0.0184084\pi\) | ||||
−0.998328 | + | 0.0577996i | \(0.981592\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 368.121 | 1.52747 | 0.763737 | − | 0.645527i | \(-0.223362\pi\) | ||||
0.763737 | + | 0.645527i | \(0.223362\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 27.2233 | + | 27.2233i | 0.111115 | + | 0.111115i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −589.139 | −2.38518 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 329.839 | − | 329.839i | 1.31410 | − | 1.31410i | 0.395734 | − | 0.918365i | \(-0.370490\pi\) |
0.918365 | − | 0.395734i | \(-0.129510\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −139.474 | + | 139.474i | −0.551281 | + | 0.551281i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −23.6762 | −0.0921252 | −0.0460626 | − | 0.998939i | \(-0.514667\pi\) | ||||
−0.0460626 | + | 0.998939i | \(0.514667\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 159.050 | + | 159.050i | 0.614094 | + | 0.614094i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 243.854 | 0.927202 | 0.463601 | − | 0.886044i | \(-0.346557\pi\) | ||||
0.463601 | + | 0.886044i | \(0.346557\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 192.071i | − | 0.724794i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −234.293 | + | 234.293i | −0.870976 | + | 0.870976i | −0.992579 | − | 0.121603i | \(-0.961197\pi\) |
0.121603 | + | 0.992579i | \(0.461197\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 30.9533i | − | 0.114219i | −0.998368 | − | 0.0571094i | \(-0.981812\pi\) | ||
0.998368 | − | 0.0571094i | \(-0.0181884\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 107.574 | + | 107.574i | 0.391178 | + | 0.391178i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −41.4479 | − | 41.4479i | −0.149631 | − | 0.149631i | 0.628322 | − | 0.777953i | \(-0.283742\pi\) |
−0.777953 | + | 0.628322i | \(0.783742\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 93.3971i | − | 0.332374i | −0.986094 | − | 0.166187i | \(-0.946854\pi\) | ||
0.986094 | − | 0.166187i | \(-0.0531455\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −40.0982 | + | 40.0982i | −0.141690 | + | 0.141690i | −0.774394 | − | 0.632704i | \(-0.781945\pi\) |
0.632704 | + | 0.774394i | \(0.281945\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 294.678i | 1.02675i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 99.1824 | 0.343192 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −141.326 | − | 141.326i | −0.482340 | − | 0.482340i | 0.423538 | − | 0.905878i | \(-0.360788\pi\) |
−0.905878 | + | 0.423538i | \(0.860788\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 163.147 | 0.553041 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −338.445 | + | 338.445i | −1.13192 | + | 1.13192i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −123.126 | + | 123.126i | −0.409056 | + | 0.409056i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 175.228 | 0.574517 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 285.548 | + | 285.548i | 0.930125 | + | 0.930125i | 0.997713 | − | 0.0675885i | \(-0.0215305\pi\) |
−0.0675885 | + | 0.997713i | \(0.521530\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −365.454 | −1.17509 | −0.587547 | − | 0.809190i | \(-0.699906\pi\) | ||||
−0.587547 | + | 0.809190i | \(0.699906\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 461.508i | 1.47447i | 0.675638 | + | 0.737234i | \(0.263868\pi\) | ||||
−0.675638 | + | 0.737234i | \(0.736132\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 319.216 | − | 319.216i | 1.00699 | − | 1.00699i | 0.00701388 | − | 0.999975i | \(-0.497767\pi\) |
0.999975 | − | 0.00701388i | \(-0.00223261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 16.8518i | − | 0.0528270i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −427.429 | − | 427.429i | −1.32331 | − | 1.32331i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 261.037 | + | 261.037i | 0.803190 | + | 0.803190i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 439.448i | 1.33571i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 85.7864 | − | 85.7864i | 0.259173 | − | 0.259173i | −0.565544 | − | 0.824718i | \(-0.691334\pi\) |
0.824718 | + | 0.565544i | \(0.191334\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 215.623i | 0.643651i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 258.256 | 0.766339 | 0.383170 | − | 0.923678i | \(-0.374832\pi\) | ||||
0.383170 | + | 0.923678i | \(0.374832\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.3124 | + | 12.3124i | 0.0361067 | + | 0.0361067i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −373.398 | −1.08862 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 27.7237 | − | 27.7237i | 0.0798953 | − | 0.0798953i | −0.666030 | − | 0.745925i | \(-0.732008\pi\) |
0.745925 | + | 0.666030i | \(0.232008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 321.089 | − | 321.089i | 0.920027 | − | 0.920027i | −0.0770037 | − | 0.997031i | \(-0.524535\pi\) |
0.997031 | + | 0.0770037i | \(0.0245353\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 241.363 | 0.683748 | 0.341874 | − | 0.939746i | \(-0.388938\pi\) | ||||
0.341874 | + | 0.939746i | \(0.388938\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −73.8953 | − | 73.8953i | −0.208156 | − | 0.208156i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −363.821 | −1.01343 | −0.506714 | − | 0.862114i | \(-0.669140\pi\) | ||||
−0.506714 | + | 0.862114i | \(0.669140\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 580.287i | 1.60744i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −125.747 | + | 125.747i | −0.344513 | + | 0.344513i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 411.402i | 1.12099i | 0.828159 | + | 0.560493i | \(0.189388\pi\) | ||||
−0.828159 | + | 0.560493i | \(0.810612\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 324.551 | + | 324.551i | 0.874801 | + | 0.874801i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −225.677 | − | 225.677i | −0.605033 | − | 0.605033i | 0.336611 | − | 0.941644i | \(-0.390719\pi\) |
−0.941644 | + | 0.336611i | \(0.890719\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 40.8923i | − | 0.108468i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 157.180 | − | 157.180i | 0.414724 | − | 0.414724i | −0.468656 | − | 0.883381i | \(-0.655262\pi\) |
0.883381 | + | 0.468656i | \(0.155262\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 703.356i | − | 1.83644i | −0.396072 | − | 0.918219i | \(-0.629627\pi\) | ||
0.396072 | − | 0.918219i | \(-0.370373\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 109.212 | 0.283668 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −10.7401 | − | 10.7401i | −0.0276095 | − | 0.0276095i | 0.693167 | − | 0.720777i | \(-0.256215\pi\) |
−0.720777 | + | 0.693167i | \(0.756215\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −491.095 | −1.25600 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.01234 | + | 7.01234i | −0.0177528 | + | 0.0177528i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 365.020 | − | 365.020i | 0.919446 | − | 0.919446i | −0.0775433 | − | 0.996989i | \(-0.524708\pi\) |
0.996989 | + | 0.0775433i | \(0.0247076\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −341.735 | −0.852207 | −0.426104 | − | 0.904674i | \(-0.640114\pi\) | ||||
−0.426104 | + | 0.904674i | \(0.640114\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 29.8770 | + | 29.8770i | 0.0741364 | + | 0.0741364i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −309.947 | −0.761541 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 368.259i | 0.900389i | 0.892931 | + | 0.450194i | \(0.148645\pi\) | ||||
−0.892931 | + | 0.450194i | \(0.851355\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −275.678 | + | 275.678i | −0.667501 | + | 0.667501i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 130.652i | − | 0.314824i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 407.140 | + | 407.140i | 0.971694 | + | 0.971694i | 0.999610 | − | 0.0279165i | \(-0.00888725\pi\) |
−0.0279165 | + | 0.999610i | \(0.508887\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 57.5576 | + | 57.5576i | 0.136716 | + | 0.136716i | 0.772153 | − | 0.635437i | \(-0.219180\pi\) |
−0.635437 | + | 0.772153i | \(0.719180\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 378.772i | 0.891229i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −296.091 | + | 296.091i | −0.693422 | + | 0.693422i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 796.565i | 1.84818i | 0.382177 | + | 0.924089i | \(0.375174\pi\) | ||||
−0.382177 | + | 0.924089i | \(0.624826\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −335.804 | −0.775529 | −0.387764 | − | 0.921758i | \(-0.626753\pi\) | ||||
−0.387764 | + | 0.921758i | \(0.626753\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 540.746 | + | 540.746i | 1.23741 | + | 1.23741i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 285.630 | 0.650638 | 0.325319 | − | 0.945604i | \(-0.394528\pi\) | ||||
0.325319 | + | 0.945604i | \(0.394528\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 111.596 | − | 111.596i | 0.251909 | − | 0.251909i | −0.569844 | − | 0.821753i | \(-0.692996\pi\) |
0.821753 | + | 0.569844i | \(0.192996\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −90.0358 | + | 90.0358i | −0.202328 | + | 0.202328i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 99.6741 | 0.221991 | 0.110996 | − | 0.993821i | \(-0.464596\pi\) | ||||
0.110996 | + | 0.993821i | \(0.464596\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −287.125 | − | 287.125i | −0.636641 | − | 0.636641i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 265.012 | 0.582445 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 32.1643i | − | 0.0703813i | −0.999381 | − | 0.0351907i | \(-0.988796\pi\) | ||
0.999381 | − | 0.0351907i | \(-0.0112039\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −165.361 | + | 165.361i | −0.358701 | + | 0.358701i | −0.863334 | − | 0.504633i | \(-0.831628\pi\) |
0.504633 | + | 0.863334i | \(0.331628\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 923.215i | 1.99398i | 0.0774991 | + | 0.996992i | \(0.475307\pi\) | ||||
−0.0774991 | + | 0.996992i | \(0.524693\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 507.842 | + | 507.842i | 1.08746 | + | 1.08746i | 0.995790 | + | 0.0916660i | \(0.0292192\pi\) |
0.0916660 | + | 0.995790i | \(0.470781\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −364.349 | − | 364.349i | −0.776864 | − | 0.776864i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 239.940i | − | 0.507272i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 417.068 | − | 417.068i | 0.878037 | − | 0.878037i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 52.3866i | 0.109367i | 0.998504 | + | 0.0546833i | \(0.0174149\pi\) | ||||
−0.998504 | + | 0.0546833i | \(0.982585\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −752.112 | −1.56364 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −39.2554 | − | 39.2554i | −0.0809389 | − | 0.0809389i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 715.733 | 1.46968 | 0.734839 | − | 0.678241i | \(-0.237258\pi\) | ||||
0.734839 | + | 0.678241i | \(0.237258\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −22.3258 | + | 22.3258i | −0.0454701 | + | 0.0454701i | −0.729476 | − | 0.684006i | \(-0.760236\pi\) |
0.684006 | + | 0.729476i | \(0.260236\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 29.6680 | − | 29.6680i | 0.0601784 | − | 0.0601784i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 249.729 | 0.502473 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −84.0984 | − | 84.0984i | −0.168534 | − | 0.168534i | 0.617801 | − | 0.786335i | \(-0.288024\pi\) |
−0.786335 | + | 0.617801i | \(0.788024\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 327.870 | 0.651829 | 0.325914 | − | 0.945399i | \(-0.394328\pi\) | ||||
0.325914 | + | 0.945399i | \(0.394328\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 54.7909i | 0.108497i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.6224 | + | 34.6224i | −0.0680205 | + | 0.0680205i | −0.740299 | − | 0.672278i | \(-0.765316\pi\) |
0.672278 | + | 0.740299i | \(0.265316\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 424.963i | − | 0.831630i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −167.956 | − | 167.956i | −0.326128 | − | 0.326128i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −428.184 | − | 428.184i | −0.828210 | − | 0.828210i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 235.719i | − | 0.452436i | −0.974077 | − | 0.226218i | \(-0.927364\pi\) | ||
0.974077 | − | 0.226218i | \(-0.0726362\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 185.851 | − | 185.851i | 0.355356 | − | 0.355356i | −0.506742 | − | 0.862098i | \(-0.669150\pi\) |
0.862098 | + | 0.506742i | \(0.169150\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 43.3524i | 0.0822626i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 92.2900 | 0.174461 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −696.732 | − | 696.732i | −1.30719 | − | 1.30719i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −53.2408 | −0.0995155 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 89.6428 | − | 89.6428i | 0.166313 | − | 0.166313i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −315.952 | + | 315.952i | −0.584015 | + | 0.584015i | −0.936004 | − | 0.351989i | \(-0.885506\pi\) |
0.351989 | + | 0.936004i | \(0.385506\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −287.841 | −0.528149 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 550.957 | + | 550.957i | 1.00723 | + | 1.00723i | 0.999974 | + | 0.00725954i | \(0.00231080\pi\) |
0.00725954 | + | 0.999974i | \(0.497689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −65.3350 | −0.118575 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 23.6982i | − | 0.0428539i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −2.35545 | + | 2.35545i | −0.00422882 | + | 0.00422882i | −0.709218 | − | 0.704989i | \(-0.750952\pi\) |
0.704989 | + | 0.709218i | \(0.250952\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 582.233i | − | 1.04156i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 269.210 | + | 269.210i | 0.478170 | + | 0.478170i | 0.904546 | − | 0.426376i | \(-0.140210\pi\) |
−0.426376 | + | 0.904546i | \(0.640210\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 108.507 | + | 108.507i | 0.192047 | + | 0.192047i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 342.558i | 0.602035i | 0.953619 | + | 0.301018i | \(0.0973263\pi\) | ||||
−0.953619 | + | 0.301018i | \(0.902674\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −153.948 | + | 153.948i | −0.269610 | + | 0.269610i | −0.828943 | − | 0.559333i | \(-0.811057\pi\) |
0.559333 | + | 0.828943i | \(0.311057\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 479.190i | − | 0.833373i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 563.693 | 0.976938 | 0.488469 | − | 0.872581i | \(-0.337556\pi\) | ||||
0.488469 | + | 0.872581i | \(0.337556\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 220.769 | + | 220.769i | 0.379981 | + | 0.379981i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −632.465 | −1.08484 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 176.603 | − | 176.603i | 0.300857 | − | 0.300857i | −0.540492 | − | 0.841349i | \(-0.681762\pi\) |
0.841349 | + | 0.540492i | \(0.181762\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 47.7355 | − | 47.7355i | 0.0810450 | − | 0.0810450i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 996.597 | 1.68060 | 0.840301 | − | 0.542120i | \(-0.182378\pi\) | ||||
0.840301 | + | 0.542120i | \(0.182378\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 192.271 | + | 192.271i | 0.323144 | + | 0.323144i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −854.031 | −1.42576 | −0.712880 | − | 0.701286i | \(-0.752610\pi\) | ||||
−0.712880 | + | 0.701286i | \(0.752610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 345.733i | − | 0.575263i | −0.957741 | − | 0.287631i | \(-0.907132\pi\) | ||
0.957741 | − | 0.287631i | \(-0.0928678\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 99.2029 | − | 99.2029i | 0.163972 | − | 0.163972i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 526.354i | − | 0.867141i | −0.901120 | − | 0.433570i | \(-0.857254\pi\) | ||
0.901120 | − | 0.433570i | \(-0.142746\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1039.02 | − | 1039.02i | −1.70053 | − | 1.70053i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 410.567 | + | 410.567i | 0.669767 | + | 0.669767i | 0.957662 | − | 0.287895i | \(-0.0929554\pi\) |
−0.287895 | + | 0.957662i | \(0.592955\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 514.755i | − | 0.834287i | −0.908841 | − | 0.417144i | \(-0.863031\pi\) | ||
0.908841 | − | 0.417144i | \(-0.136969\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −314.214 | + | 314.214i | −0.507615 | + | 0.507615i | −0.913794 | − | 0.406179i | \(-0.866861\pi\) |
0.406179 | + | 0.913794i | \(0.366861\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 304.276i | − | 0.488404i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −225.209 | −0.360334 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −545.669 | − | 545.669i | −0.867518 | − | 0.867518i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 230.081 | 0.364629 | 0.182315 | − | 0.983240i | \(-0.441641\pi\) | ||||
0.182315 | + | 0.983240i | \(0.441641\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 62.6875 | − | 62.6875i | 0.0987205 | − | 0.0987205i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 217.526 | − | 217.526i | 0.341484 | − | 0.341484i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −746.825 | −1.16509 | −0.582547 | − | 0.812797i | \(-0.697944\pi\) | ||||
−0.582547 | + | 0.812797i | \(0.697944\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −548.092 | − | 548.092i | −0.852398 | − | 0.852398i | 0.138030 | − | 0.990428i | \(-0.455923\pi\) |
−0.990428 | + | 0.138030i | \(0.955923\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1055.00 | 1.63060 | 0.815302 | − | 0.579036i | \(-0.196571\pi\) | ||||
0.815302 | + | 0.579036i | \(0.196571\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 537.223i | − | 0.827771i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 854.888 | − | 854.888i | 1.30917 | − | 1.30917i | 0.387155 | − | 0.922015i | \(-0.373458\pi\) |
0.922015 | − | 0.387155i | \(-0.126542\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 137.350i | 0.209694i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −768.766 | − | 768.766i | −1.16656 | − | 1.16656i | −0.983009 | − | 0.183556i | \(-0.941239\pi\) |
−0.183556 | − | 0.983009i | \(-0.558761\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 312.323 | + | 312.323i | 0.472500 | + | 0.472500i | 0.902723 | − | 0.430223i | \(-0.141565\pi\) |
−0.430223 | + | 0.902723i | \(0.641565\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 423.420i | − | 0.636721i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −37.5333 | + | 37.5333i | −0.0562719 | + | 0.0562719i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 577.004i | − | 0.859916i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 740.565 | 1.10039 | 0.550197 | − | 0.835035i | \(-0.314553\pi\) | ||||
0.550197 | + | 0.835035i | \(0.314553\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 547.118 | + | 547.118i | 0.808151 | + | 0.808151i | 0.984354 | − | 0.176203i | \(-0.0563814\pi\) |
−0.176203 | + | 0.984354i | \(0.556381\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 132.664 | 0.195381 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −407.623 | + | 407.623i | −0.596813 | + | 0.596813i | −0.939463 | − | 0.342650i | \(-0.888676\pi\) |
0.342650 | + | 0.939463i | \(0.388676\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −430.772 | + | 430.772i | −0.628864 | + | 0.628864i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1534.73 | −2.22747 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −17.6037 | − | 17.6037i | −0.0254757 | − | 0.0254757i | 0.694254 | − | 0.719730i | \(-0.255734\pi\) |
−0.719730 | + | 0.694254i | \(0.755734\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 230.448 | 0.331579 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 1010.98i | − | 1.45047i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −164.273 | + | 164.273i | −0.234341 | + | 0.234341i | −0.814502 | − | 0.580161i | \(-0.802990\pi\) |
0.580161 | + | 0.814502i | \(0.302990\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1201.68i | 1.70935i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −92.5829 | − | 92.5829i | −0.130952 | − | 0.130952i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 422.796 | + | 422.796i | 0.596327 | + | 0.596327i | 0.939333 | − | 0.343006i | \(-0.111445\pi\) |
−0.343006 | + | 0.939333i | \(0.611445\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 54.8457i | − | 0.0769224i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −258.220 | + | 258.220i | −0.361146 | + | 0.361146i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1029.00i | 1.43115i | 0.698534 | + | 0.715577i | \(0.253836\pi\) | ||||
−0.698534 | + | 0.715577i | \(0.746164\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 567.607 | 0.787250 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 28.9488 | + | 28.9488i | 0.0399293 | + | 0.0399293i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 475.001 | 0.653372 | 0.326686 | − | 0.945133i | \(-0.394068\pi\) | ||||
0.326686 | + | 0.945133i | \(0.394068\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 422.419 | − | 422.419i | 0.577865 | − | 0.577865i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −344.939 | + | 344.939i | −0.470586 | + | 0.470586i | −0.902104 | − | 0.431519i | \(-0.857978\pi\) |
0.431519 | + | 0.902104i | \(0.357978\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 710.021 | 0.963393 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −363.340 | − | 363.340i | −0.491665 | − | 0.491665i | 0.417166 | − | 0.908831i | \(-0.363024\pi\) |
−0.908831 | + | 0.417166i | \(0.863024\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 271.667 | 0.365636 | 0.182818 | − | 0.983147i | \(-0.441478\pi\) | ||||
0.182818 | + | 0.983147i | \(0.441478\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 149.314i | − | 0.200421i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 89.9637 | − | 89.9637i | 0.120112 | − | 0.120112i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 1105.27i | − | 1.47173i | −0.677128 | − | 0.735866i | \(-0.736776\pi\) | ||
0.677128 | − | 0.735866i | \(-0.263224\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −379.087 | − | 379.087i | −0.502102 | − | 0.502102i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 554.565 | + | 554.565i | 0.732583 | + | 0.732583i | 0.971131 | − | 0.238548i | \(-0.0766713\pi\) |
−0.238548 | + | 0.971131i | \(0.576671\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 188.496i | 0.247695i | 0.992301 | + | 0.123847i | \(0.0395234\pi\) | ||||
−0.992301 | + | 0.123847i | \(0.960477\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 486.380 | − | 486.380i | 0.637457 | − | 0.637457i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1303.62i | − | 1.69963i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −593.354 | −0.771592 | −0.385796 | − | 0.922584i | \(-0.626073\pi\) | ||||
−0.385796 | + | 0.922584i | \(0.626073\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −514.720 | − | 514.720i | −0.665873 | − | 0.665873i | 0.290885 | − | 0.956758i | \(-0.406050\pi\) |
−0.956758 | + | 0.290885i | \(0.906050\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −42.3015 | −0.0545826 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1113.19 | + | 1113.19i | −1.42900 | + | 1.42900i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −243.328 | + | 243.328i | −0.311560 | + | 0.311560i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 267.989 | 0.341387 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −96.1835 | − | 96.1835i | −0.122215 | − | 0.122215i | 0.643354 | − | 0.765569i | \(-0.277542\pi\) |
−0.765569 | + | 0.643354i | \(0.777542\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −366.699 | −0.463589 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 1400.15i | − | 1.76563i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 664.410 | − | 664.410i | 0.833639 | − | 0.833639i | −0.154374 | − | 0.988013i | \(-0.549336\pi\) |
0.988013 | + | 0.154374i | \(0.0493359\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1507.66i | − | 1.88693i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 414.070 | + | 414.070i | 0.515654 | + | 0.515654i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −243.244 | − | 243.244i | −0.302166 | − | 0.302166i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 1371.63i | − | 1.69547i | −0.530422 | − | 0.847734i | \(-0.677966\pi\) | ||
0.530422 | − | 0.847734i | \(-0.322034\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −809.783 | + | 809.783i | −0.998500 | + | 0.998500i | −0.999999 | − | 0.00149916i | \(-0.999523\pi\) |
0.00149916 | + | 0.999999i | \(0.499523\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 177.552i | 0.217855i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −930.255 | −1.13862 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1144.74 | + | 1144.74i | 1.39432 | + | 1.39432i | 0.815342 | + | 0.578980i | \(0.196549\pi\) |
0.578980 | + | 0.815342i | \(0.303451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −439.361 | −0.533853 | −0.266926 | − | 0.963717i | \(-0.586008\pi\) | ||||
−0.266926 | + | 0.963717i | \(0.586008\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 911.996 | − | 911.996i | 1.10278 | − | 1.10278i | 0.108701 | − | 0.994074i | \(-0.465331\pi\) |
0.994074 | − | 0.108701i | \(-0.0346693\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 470.575 | − | 470.575i | 0.567642 | − | 0.567642i | −0.363825 | − | 0.931467i | \(-0.618529\pi\) |
0.931467 | + | 0.363825i | \(0.118529\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 315.636 | 0.378915 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −164.017 | − | 164.017i | −0.196428 | − | 0.196428i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1432.91 | 1.70787 | 0.853937 | − | 0.520376i | \(-0.174208\pi\) | ||||
0.853937 | + | 0.520376i | \(0.174208\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 836.465i | 0.994608i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −339.408 | + | 339.408i | −0.401666 | + | 0.401666i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 335.256i | 0.395816i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 690.332 | + | 690.332i | 0.811201 | + | 0.811201i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 211.443 | + | 211.443i | 0.247881 | + | 0.247881i | 0.820101 | − | 0.572219i | \(-0.193917\pi\) |
−0.572219 | + | 0.820101i | \(0.693917\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 710.925i | 0.829551i | 0.909924 | + | 0.414775i | \(0.136140\pi\) | ||||
−0.909924 | + | 0.414775i | \(0.863860\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −348.557 | + | 348.557i | −0.405771 | + | 0.405771i | −0.880261 | − | 0.474490i | \(-0.842632\pi\) |
0.474490 | + | 0.880261i | \(0.342632\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1493.19i | 1.73023i | 0.501571 | + | 0.865116i | \(0.332755\pi\) | ||||
−0.501571 | + | 0.865116i | \(0.667245\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −157.382 | −0.181944 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.0908 | + | 23.0908i | 0.0265717 | + | 0.0265717i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1722.92 | 1.97810 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −431.579 | + | 431.579i | −0.493233 | + | 0.493233i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −332.929 | + | 332.929i | −0.379623 | + | 0.379623i | −0.870966 | − | 0.491343i | \(-0.836506\pi\) |
0.491343 | + | 0.870966i | \(0.336506\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 637.491 | 0.723599 | 0.361799 | − | 0.932256i | \(-0.382162\pi\) | ||||
0.361799 | + | 0.932256i | \(0.382162\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −134.646 | − | 134.646i | −0.152487 | − | 0.152487i | 0.626741 | − | 0.779228i | \(-0.284388\pi\) |
−0.779228 | + | 0.626741i | \(0.784388\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3.90891 | 0.00440688 | 0.00220344 | − | 0.999998i | \(-0.499299\pi\) | ||||
0.00220344 | + | 0.999998i | \(0.499299\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 211.853i | 0.238304i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −1660.08 | + | 1660.08i | −1.85900 | + | 1.85900i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 317.919i | 0.355217i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.31333 | + | 3.31333i | 0.00368558 | + | 0.00368558i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1113.47 | − | 1113.47i | −1.23581 | − | 1.23581i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 393.594i | 0.434910i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −697.707 | + | 697.707i | −0.769247 | + | 0.769247i | −0.977974 | − | 0.208727i | \(-0.933068\pi\) |
0.208727 | + | 0.977974i | \(0.433068\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 796.856i | − | 0.874705i | −0.899290 | − | 0.437353i | \(-0.855916\pi\) | ||
0.899290 | − | 0.437353i | \(-0.144084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −430.221 | −0.471216 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −232.087 | − | 232.087i | −0.253094 | − | 0.253094i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −420.532 | −0.457597 | −0.228798 | − | 0.973474i | \(-0.573480\pi\) | ||||
−0.228798 | + | 0.973474i | \(0.573480\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −590.455 | + | 590.455i | −0.639713 | + | 0.639713i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 532.441 | − | 532.441i | 0.575612 | − | 0.575612i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1178.38 | −1.26843 | −0.634217 | − | 0.773155i | \(-0.718677\pi\) | ||||
−0.634217 | + | 0.773155i | \(0.718677\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −347.548 | − | 347.548i | −0.373306 | − | 0.373306i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −374.684 | −0.400732 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 405.962i | − | 0.433257i | −0.976254 | − | 0.216629i | \(-0.930494\pi\) | ||
0.976254 | − | 0.216629i | \(-0.0695061\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −429.859 | + | 429.859i | −0.456810 | + | 0.456810i | −0.897607 | − | 0.440797i | \(-0.854696\pi\) |
0.440797 | + | 0.897607i | \(0.354696\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1279.00i | 1.35631i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 661.681 | + | 661.681i | 0.698713 | + | 0.698713i | 0.964133 | − | 0.265420i | \(-0.0855107\pi\) |
−0.265420 | + | 0.964133i | \(0.585511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1004.77 | + | 1004.77i | 1.05877 | + | 1.05877i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 31.1854i | 0.0327234i | 0.999866 | + | 0.0163617i | \(0.00520833\pi\) | ||||
−0.999866 | + | 0.0163617i | \(0.994792\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −59.9794 | + | 59.9794i | −0.0628056 | + | 0.0628056i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1455.79i | − | 1.51803i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 956.158 | 0.994962 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 619.123 | + | 619.123i | 0.641578 | + | 0.641578i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1312.55 | 1.35734 | 0.678672 | − | 0.734442i | \(-0.262556\pi\) | ||||
0.678672 | + | 0.734442i | \(0.262556\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 318.758 | − | 318.758i | 0.328278 | − | 0.328278i | −0.523653 | − | 0.851931i | \(-0.675431\pi\) |
0.851931 | + | 0.523653i | \(0.175431\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −389.399 | + | 389.399i | −0.400205 | + | 0.400205i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 531.045 | 0.543546 | 0.271773 | − | 0.962361i | \(-0.412390\pi\) | ||||
0.271773 | + | 0.962361i | \(0.412390\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 296.477 | + | 296.477i | 0.302836 | + | 0.302836i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1796.17 | −1.82723 | −0.913614 | − | 0.406582i | \(-0.866721\pi\) | ||||
−0.913614 | + | 0.406582i | \(0.866721\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 443.796i | 0.450554i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −534.408 | + | 534.408i | −0.540352 | + | 0.540352i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 506.064i | − | 0.510660i | −0.966854 | − | 0.255330i | \(-0.917816\pi\) | ||
0.966854 | − | 0.255330i | \(-0.0821841\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −21.6650 | − | 21.6650i | −0.0217739 | − | 0.0217739i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −249.068 | − | 249.068i | −0.249817 | − | 0.249817i | 0.571078 | − | 0.820896i | \(-0.306525\pi\) |
−0.820896 | + | 0.571078i | \(0.806525\pi\) | |||||||
\(998\) | 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 | 576.3.m.c.271.3 | 16 | ||
3.2 | odd | 2 | 192.3.l.a.79.7 | 16 | |||
4.3 | odd | 2 | 144.3.m.c.91.1 | 16 | |||
8.3 | odd | 2 | 1152.3.m.f.415.6 | 16 | |||
8.5 | even | 2 | 1152.3.m.c.415.6 | 16 | |||
12.11 | even | 2 | 48.3.l.a.43.8 | yes | 16 | ||
16.3 | odd | 4 | inner | 576.3.m.c.559.3 | 16 | ||
16.5 | even | 4 | 1152.3.m.f.991.6 | 16 | |||
16.11 | odd | 4 | 1152.3.m.c.991.6 | 16 | |||
16.13 | even | 4 | 144.3.m.c.19.1 | 16 | |||
24.5 | odd | 2 | 384.3.l.b.31.2 | 16 | |||
24.11 | even | 2 | 384.3.l.a.31.6 | 16 | |||
48.5 | odd | 4 | 384.3.l.a.223.6 | 16 | |||
48.11 | even | 4 | 384.3.l.b.223.2 | 16 | |||
48.29 | odd | 4 | 48.3.l.a.19.8 | ✓ | 16 | ||
48.35 | even | 4 | 192.3.l.a.175.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.8 | ✓ | 16 | 48.29 | odd | 4 | ||
48.3.l.a.43.8 | yes | 16 | 12.11 | even | 2 | ||
144.3.m.c.19.1 | 16 | 16.13 | even | 4 | |||
144.3.m.c.91.1 | 16 | 4.3 | odd | 2 | |||
192.3.l.a.79.7 | 16 | 3.2 | odd | 2 | |||
192.3.l.a.175.7 | 16 | 48.35 | even | 4 | |||
384.3.l.a.31.6 | 16 | 24.11 | even | 2 | |||
384.3.l.a.223.6 | 16 | 48.5 | odd | 4 | |||
384.3.l.b.31.2 | 16 | 24.5 | odd | 2 | |||
384.3.l.b.223.2 | 16 | 48.11 | even | 4 | |||
576.3.m.c.271.3 | 16 | 1.1 | even | 1 | trivial | ||
576.3.m.c.559.3 | 16 | 16.3 | odd | 4 | inner | ||
1152.3.m.c.415.6 | 16 | 8.5 | even | 2 | |||
1152.3.m.c.991.6 | 16 | 16.11 | odd | 4 | |||
1152.3.m.f.415.6 | 16 | 8.3 | odd | 2 | |||
1152.3.m.f.991.6 | 16 | 16.5 | even | 4 |