Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2916,3,Mod(1457,2916)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2916, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2916.1457");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2916 = 2^{2} \cdot 3^{6} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 2916.c (of order \(2\), degree \(1\), 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: | \(79.4552450875\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1457.4 | ||
Character | \(\chi\) | \(=\) | 2916.1457 |
Dual form | 2916.3.c.b.1457.33 |
$q$-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 \(\left(\mathbb{Z}/2916\mathbb{Z}\right)^\times\).
\(n\) | \(1459\) | \(2189\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 7.77099i | − 1.55420i | −0.629379 | − | 0.777099i | \(-0.716691\pi\) | ||||
0.629379 | − | 0.777099i | \(-0.283309\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 13.6742 | 1.95345 | 0.976727 | − | 0.214485i | \(-0.0688072\pi\) | ||||
0.976727 | + | 0.214485i | \(0.0688072\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 2.59394i | − 0.235813i | −0.993025 | − | 0.117906i | \(-0.962382\pi\) | ||||
0.993025 | − | 0.117906i | \(-0.0376183\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 8.76827 | 0.674482 | 0.337241 | − | 0.941418i | \(-0.390506\pi\) | ||||
0.337241 | + | 0.941418i | \(0.390506\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 17.6544i | − 1.03849i | −0.854624 | − | 0.519247i | \(-0.826213\pi\) | ||||
0.854624 | − | 0.519247i | \(-0.173787\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.93881 | −0.154674 | −0.0773372 | − | 0.997005i | \(-0.524642\pi\) | ||||
−0.0773372 | + | 0.997005i | \(0.524642\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 18.5107i | 0.804814i | 0.915461 | + | 0.402407i | \(0.131826\pi\) | ||||
−0.915461 | + | 0.402407i | \(0.868174\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −35.3882 | −1.41553 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.09899i | 0.106862i | 0.998572 | + | 0.0534308i | \(0.0170157\pi\) | ||||
−0.998572 | + | 0.0534308i | \(0.982984\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 40.0195 | 1.29095 | 0.645476 | − | 0.763781i | \(-0.276659\pi\) | ||||
0.645476 | + | 0.763781i | \(0.276659\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − 106.262i | − 3.03605i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 25.6409 | 0.692998 | 0.346499 | − | 0.938050i | \(-0.387370\pi\) | ||||
0.346499 | + | 0.938050i | \(0.387370\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 62.1311i | − 1.51539i | −0.652608 | − | 0.757696i | \(-0.726325\pi\) | ||||
0.652608 | − | 0.757696i | \(-0.273675\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.9177 | 0.765529 | 0.382764 | − | 0.923846i | \(-0.374972\pi\) | ||||
0.382764 | + | 0.923846i | \(0.374972\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 52.0015i | − 1.10641i | −0.833044 | − | 0.553207i | \(-0.813404\pi\) | ||||
0.833044 | − | 0.553207i | \(-0.186596\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 137.983 | 2.81599 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 53.2686i | − 1.00507i | −0.864557 | − | 0.502534i | \(-0.832401\pi\) | ||||
0.864557 | − | 0.502534i | \(-0.167599\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −20.1575 | −0.366500 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 103.991i | 1.76255i | 0.472601 | + | 0.881277i | \(0.343315\pi\) | ||||
−0.472601 | + | 0.881277i | \(0.656685\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.95342 | −0.0975970 | −0.0487985 | − | 0.998809i | \(-0.515539\pi\) | ||||
−0.0487985 | + | 0.998809i | \(0.515539\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − 68.1381i | − 1.04828i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 47.3318 | 0.706445 | 0.353222 | − | 0.935539i | \(-0.385086\pi\) | ||||
0.353222 | + | 0.935539i | \(0.385086\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 89.5061i | 1.26065i | 0.776331 | + | 0.630325i | \(0.217078\pi\) | ||||
−0.776331 | + | 0.630325i | \(0.782922\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −67.2043 | −0.920607 | −0.460303 | − | 0.887762i | \(-0.652259\pi\) | ||||
−0.460303 | + | 0.887762i | \(0.652259\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 35.4700i | − 0.460650i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −36.3221 | −0.459774 | −0.229887 | − | 0.973217i | \(-0.573836\pi\) | ||||
−0.229887 | + | 0.973217i | \(0.573836\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 20.2994i | 0.244571i | 0.992495 | + | 0.122286i | \(0.0390224\pi\) | ||||
−0.992495 | + | 0.122286i | \(0.960978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −137.192 | −1.61402 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 96.6488i | 1.08594i | 0.839752 | + | 0.542971i | \(0.182701\pi\) | ||||
−0.839752 | + | 0.542971i | \(0.817299\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 119.899 | 1.31757 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 22.8375i | 0.240395i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −67.2509 | −0.693308 | −0.346654 | − | 0.937993i | \(-0.612682\pi\) | ||||
−0.346654 | + | 0.937993i | \(0.612682\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − 93.9271i | − 0.929971i | −0.885318 | − | 0.464985i | \(-0.846060\pi\) | ||||
0.885318 | − | 0.464985i | \(-0.153940\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.0359 | 0.155688 | 0.0778442 | − | 0.996966i | \(-0.475196\pi\) | ||||
0.0778442 | + | 0.996966i | \(0.475196\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 96.4400i | 0.901308i | 0.892699 | + | 0.450654i | \(0.148809\pi\) | ||||
−0.892699 | + | 0.450654i | \(0.851191\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −141.184 | −1.29527 | −0.647635 | − | 0.761951i | \(-0.724242\pi\) | ||||
−0.647635 | + | 0.761951i | \(0.724242\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 26.3337i | − 0.233042i | −0.993188 | − | 0.116521i | \(-0.962826\pi\) | ||||
0.993188 | − | 0.116521i | \(-0.0371742\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 143.847 | 1.25084 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − 241.409i | − 2.02865i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 114.271 | 0.944392 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 80.7268i | 0.645814i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 102.490 | 0.807010 | 0.403505 | − | 0.914977i | \(-0.367792\pi\) | ||||
0.403505 | + | 0.914977i | \(0.367792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 78.0185i | 0.595561i | 0.954634 | + | 0.297781i | \(0.0962464\pi\) | ||||
−0.954634 | + | 0.297781i | \(0.903754\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −40.1859 | −0.302149 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 54.9068i | 0.400779i | 0.979716 | + | 0.200390i | \(0.0642208\pi\) | ||||
−0.979716 | + | 0.200390i | \(0.935779\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −40.5682 | −0.291857 | −0.145929 | − | 0.989295i | \(-0.546617\pi\) | ||||
−0.145929 | + | 0.989295i | \(0.546617\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 22.7444i | − 0.159051i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 24.0822 | 0.166084 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 167.504i | − 1.12419i | −0.827073 | − | 0.562094i | \(-0.809996\pi\) | ||||
0.827073 | − | 0.562094i | \(-0.190004\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 275.526 | 1.82467 | 0.912336 | − | 0.409441i | \(-0.134276\pi\) | ||||
0.912336 | + | 0.409441i | \(0.134276\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 310.991i | − 2.00639i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −206.161 | −1.31313 | −0.656565 | − | 0.754270i | \(-0.727991\pi\) | ||||
−0.656565 | + | 0.754270i | \(0.727991\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 253.119i | 1.57217i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −85.6172 | −0.525259 | −0.262629 | − | 0.964897i | \(-0.584590\pi\) | ||||
−0.262629 | + | 0.964897i | \(0.584590\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 44.9509i | 0.269167i | 0.990902 | + | 0.134584i | \(0.0429697\pi\) | ||||
−0.990902 | + | 0.134584i | \(0.957030\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −92.1175 | −0.545074 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 169.446i | − 0.979456i | −0.871875 | − | 0.489728i | \(-0.837096\pi\) | ||||
0.871875 | − | 0.489728i | \(-0.162904\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −483.905 | −2.76517 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 140.618i | 0.785577i | 0.919629 | + | 0.392789i | \(0.128490\pi\) | ||||
−0.919629 | + | 0.392789i | \(0.871510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 69.3731 | 0.383277 | 0.191638 | − | 0.981466i | \(-0.438620\pi\) | ||||
0.191638 | + | 0.981466i | \(0.438620\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 199.255i | − 1.07706i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −45.7944 | −0.244890 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − 294.098i | − 1.53978i | −0.638175 | − | 0.769891i | \(-0.720310\pi\) | ||||
0.638175 | − | 0.769891i | \(-0.279690\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −104.946 | −0.543762 | −0.271881 | − | 0.962331i | \(-0.587646\pi\) | ||||
−0.271881 | + | 0.962331i | \(0.587646\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 66.6479i | 0.338314i | 0.985589 | + | 0.169157i | \(0.0541045\pi\) | ||||
−0.985589 | + | 0.169157i | \(0.945895\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −185.725 | −0.933294 | −0.466647 | − | 0.884444i | \(-0.654538\pi\) | ||||
−0.466647 | + | 0.884444i | \(0.654538\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 42.3761i | 0.208749i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −482.820 | −2.35522 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 7.62311i | 0.0364742i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.3483 | 0.110655 | 0.0553276 | − | 0.998468i | \(-0.482380\pi\) | ||||
0.0553276 | + | 0.998468i | \(0.482380\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 255.803i | − 1.18978i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 547.234 | 2.52181 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 154.798i | − 0.700445i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −184.646 | −0.828008 | −0.414004 | − | 0.910275i | \(-0.635870\pi\) | ||||
−0.414004 | + | 0.910275i | \(0.635870\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 198.608i | 0.874925i | 0.899237 | + | 0.437463i | \(0.144123\pi\) | ||||
−0.899237 | + | 0.437463i | \(0.855877\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −62.2729 | −0.271934 | −0.135967 | − | 0.990713i | \(-0.543414\pi\) | ||||
−0.135967 | + | 0.990713i | \(0.543414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 138.893i | − 0.596108i | −0.954549 | − | 0.298054i | \(-0.903662\pi\) | ||||
0.954549 | − | 0.298054i | \(-0.0963375\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −404.103 | −1.71959 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 394.203i | 1.64938i | 0.565583 | + | 0.824692i | \(0.308651\pi\) | ||||
−0.565583 | + | 0.824692i | \(0.691349\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.0515 | −0.0583051 | −0.0291526 | − | 0.999575i | \(-0.509281\pi\) | ||||
−0.0291526 | + | 0.999575i | \(0.509281\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 1072.27i | − 4.37660i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −25.7683 | −0.104325 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 137.653i | − 0.548417i | −0.961670 | − | 0.274208i | \(-0.911584\pi\) | ||||
0.961670 | − | 0.274208i | \(-0.0884158\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 48.0157 | 0.189786 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 449.614i | 1.74947i | 0.484600 | + | 0.874736i | \(0.338965\pi\) | ||||
−0.484600 | + | 0.874736i | \(0.661035\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 350.619 | 1.35374 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 5.84301i | − 0.0222168i | −0.999938 | − | 0.0111084i | \(-0.996464\pi\) | ||||
0.999938 | − | 0.0111084i | \(-0.00353598\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −413.950 | −1.56207 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 382.562i | − 1.42216i | −0.703109 | − | 0.711082i | \(-0.748206\pi\) | ||||
0.703109 | − | 0.711082i | \(-0.251794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 41.5492 | 0.153318 | 0.0766591 | − | 0.997057i | \(-0.475575\pi\) | ||||
0.0766591 | + | 0.997057i | \(0.475575\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 91.7950i | 0.333800i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 269.629 | 0.973391 | 0.486695 | − | 0.873572i | \(-0.338202\pi\) | ||||
0.486695 | + | 0.873572i | \(0.338202\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 280.532i | − 0.998335i | −0.866506 | − | 0.499167i | \(-0.833639\pi\) | ||||
0.866506 | − | 0.499167i | \(-0.166361\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 229.103 | 0.809553 | 0.404776 | − | 0.914416i | \(-0.367349\pi\) | ||||
0.404776 | + | 0.914416i | \(0.367349\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 849.591i | − 2.96025i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −22.6772 | −0.0784679 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 134.836i | − 0.460191i | −0.973168 | − | 0.230095i | \(-0.926096\pi\) | ||||
0.973168 | − | 0.230095i | \(-0.0739038\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 808.110 | 2.73936 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 162.307i | 0.542833i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 450.123 | 1.49543 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 46.2639i | 0.151685i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −394.389 | −1.28465 | −0.642327 | − | 0.766431i | \(-0.722031\pi\) | ||||
−0.642327 | + | 0.766431i | \(0.722031\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − 173.275i | − 0.557154i | −0.960414 | − | 0.278577i | \(-0.910137\pi\) | ||||
0.960414 | − | 0.278577i | \(-0.0898627\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −42.7576 | −0.136606 | −0.0683028 | − | 0.997665i | \(-0.521758\pi\) | ||||
−0.0683028 | + | 0.997665i | \(0.521758\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 233.172i | − 0.735560i | −0.929913 | − | 0.367780i | \(-0.880118\pi\) | ||||
0.929913 | − | 0.367780i | \(-0.119882\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.03859 | 0.0251993 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 51.8829i | 0.160628i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −310.293 | −0.954749 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − 711.078i | − 2.16133i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −373.782 | −1.12925 | −0.564626 | − | 0.825347i | \(-0.690979\pi\) | ||||
−0.564626 | + | 0.825347i | \(0.690979\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 367.815i | − 1.09795i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 204.899 | 0.608010 | 0.304005 | − | 0.952670i | \(-0.401676\pi\) | ||||
0.304005 | + | 0.952670i | \(0.401676\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 103.808i | − 0.304423i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1216.77 | 3.54744 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 535.122i | − 1.54214i | −0.636751 | − | 0.771070i | \(-0.719722\pi\) | ||||
0.636751 | − | 0.771070i | \(-0.280278\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −478.052 | −1.36978 | −0.684888 | − | 0.728648i | \(-0.740149\pi\) | ||||
−0.684888 | + | 0.728648i | \(0.740149\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 77.0832i | 0.218366i | 0.994022 | + | 0.109183i | \(0.0348235\pi\) | ||||
−0.994022 | + | 0.109183i | \(0.965177\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 695.551 | 1.95930 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − 203.832i | − 0.567777i | −0.958857 | − | 0.283889i | \(-0.908375\pi\) | ||||
0.958857 | − | 0.283889i | \(-0.0916246\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −352.363 | −0.976076 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 522.244i | 1.43080i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −407.785 | −1.11113 | −0.555566 | − | 0.831473i | \(-0.687498\pi\) | ||||
−0.555566 | + | 0.831473i | \(0.687498\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 728.405i | − 1.96335i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 345.500 | 0.926274 | 0.463137 | − | 0.886287i | \(-0.346724\pi\) | ||||
0.463137 | + | 0.886287i | \(0.346724\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 27.1728i | 0.0720763i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −63.5579 | −0.167699 | −0.0838495 | − | 0.996478i | \(-0.526722\pi\) | ||||
−0.0838495 | + | 0.996478i | \(0.526722\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 490.175i | 1.27983i | 0.768446 | + | 0.639915i | \(0.221030\pi\) | ||||
−0.768446 | + | 0.639915i | \(0.778970\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −275.637 | −0.715940 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 86.6934i | − 0.222862i | −0.993772 | − | 0.111431i | \(-0.964457\pi\) | ||||
0.993772 | − | 0.111431i | \(-0.0355435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 326.795 | 0.835794 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 282.259i | 0.714579i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −531.427 | −1.33861 | −0.669304 | − | 0.742989i | \(-0.733408\pi\) | ||||
−0.669304 | + | 0.742989i | \(0.733408\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 531.451i | 1.32531i | 0.748923 | + | 0.662657i | \(0.230571\pi\) | ||||
−0.748923 | + | 0.662657i | \(0.769429\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 350.902 | 0.870723 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 66.5110i | − 0.163418i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −212.013 | −0.518370 | −0.259185 | − | 0.965828i | \(-0.583454\pi\) | ||||
−0.259185 | + | 0.965828i | \(0.583454\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1421.99i | 3.44307i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 157.746 | 0.380112 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 9.74283i | − 0.0232526i | −0.999932 | − | 0.0116263i | \(-0.996299\pi\) | ||||
0.999932 | − | 0.0116263i | \(-0.00370085\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.7083 | −0.0254354 | −0.0127177 | − | 0.999919i | \(-0.504048\pi\) | ||||
−0.0127177 | + | 0.999919i | \(0.504048\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 624.757i | 1.47002i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −81.4082 | −0.190651 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 65.8369i | 0.152754i | 0.997079 | + | 0.0763769i | \(0.0243352\pi\) | ||||
−0.997079 | + | 0.0763769i | \(0.975665\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 6.63250 | 0.0153176 | 0.00765878 | − | 0.999971i | \(-0.497562\pi\) | ||||
0.00765878 | + | 0.999971i | \(0.497562\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 54.3996i | − 0.124484i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 87.6058 | 0.199558 | 0.0997788 | − | 0.995010i | \(-0.468186\pi\) | ||||
0.0997788 | + | 0.995010i | \(0.468186\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 587.210i | − 1.32553i | −0.748827 | − | 0.662765i | \(-0.769383\pi\) | ||||
0.748827 | − | 0.662765i | \(-0.230617\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 751.056 | 1.68777 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 235.351i | 0.524168i | 0.965045 | + | 0.262084i | \(0.0844097\pi\) | ||||
−0.965045 | + | 0.262084i | \(0.915590\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −161.164 | −0.357349 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − 931.733i | − 2.04776i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 609.689 | 1.33411 | 0.667056 | − | 0.745008i | \(-0.267554\pi\) | ||||
0.667056 | + | 0.745008i | \(0.267554\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 904.652i | − 1.96237i | −0.193071 | − | 0.981185i | \(-0.561845\pi\) | ||||
0.193071 | − | 0.981185i | \(-0.438155\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −69.6790 | −0.150495 | −0.0752473 | − | 0.997165i | \(-0.523975\pi\) | ||||
−0.0752473 | + | 0.997165i | \(0.523975\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 110.122i | − 0.235808i | −0.993025 | − | 0.117904i | \(-0.962383\pi\) | ||||
0.993025 | − | 0.117904i | \(-0.0376175\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 647.224 | 1.38001 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 85.3867i | − 0.180522i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 103.999 | 0.218946 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 166.090i | 0.346744i | 0.984856 | + | 0.173372i | \(0.0554663\pi\) | ||||
−0.984856 | + | 0.173372i | \(0.944534\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 224.826 | 0.467415 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 522.606i | 1.07754i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 492.594 | 1.01149 | 0.505743 | − | 0.862684i | \(-0.331218\pi\) | ||||
0.505743 | + | 0.862684i | \(0.331218\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 601.147i | − 1.22433i | −0.790730 | − | 0.612166i | \(-0.790299\pi\) | ||||
0.790730 | − | 0.612166i | \(-0.209701\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 54.7107 | 0.110975 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1223.92i | 2.46262i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −577.732 | −1.15778 | −0.578889 | − | 0.815406i | \(-0.696514\pi\) | ||||
−0.578889 | + | 0.815406i | \(0.696514\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 463.653i | 0.921775i | 0.887459 | + | 0.460887i | \(0.152469\pi\) | ||||
−0.887459 | + | 0.460887i | \(0.847531\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −729.906 | −1.44536 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 762.823i | 1.49867i | 0.662191 | + | 0.749335i | \(0.269627\pi\) | ||||
−0.662191 | + | 0.749335i | \(0.730373\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −918.964 | −1.79836 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 124.615i | − 0.241971i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −134.889 | −0.260907 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − 275.133i | − 0.528086i | −0.964511 | − | 0.264043i | \(-0.914944\pi\) | ||||
0.964511 | − | 0.264043i | \(-0.0850561\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −185.838 | −0.355331 | −0.177665 | − | 0.984091i | \(-0.556854\pi\) | ||||
−0.177665 | + | 0.984091i | \(0.556854\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − 706.519i | − 1.34064i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 186.353 | 0.352274 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 544.782i | − 1.02210i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 749.434 | 1.40081 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 357.920i | − 0.664045i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 745.728 | 1.37843 | 0.689213 | − | 0.724559i | \(-0.257956\pi\) | ||||
0.689213 | + | 0.724559i | \(0.257956\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1097.14i | 2.01310i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 44.4985 | 0.0813502 | 0.0406751 | − | 0.999172i | \(-0.487049\pi\) | ||||
0.0406751 | + | 0.999172i | \(0.487049\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 9.10735i | − 0.0165288i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −496.675 | −0.898147 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 973.545i | 1.74784i | 0.486073 | + | 0.873918i | \(0.338429\pi\) | ||||
−0.486073 | + | 0.873918i | \(0.661571\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 288.632 | 0.516335 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 180.589i | 0.320763i | 0.987055 | + | 0.160381i | \(0.0512724\pi\) | ||||
−0.987055 | + | 0.160381i | \(0.948728\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −204.639 | −0.362193 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 913.212i | 1.60494i | 0.596691 | + | 0.802471i | \(0.296482\pi\) | ||||
−0.596691 | + | 0.802471i | \(0.703518\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −25.3524 | −0.0444000 | −0.0222000 | − | 0.999754i | \(-0.507067\pi\) | ||||
−0.0222000 | + | 0.999754i | \(0.507067\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 655.062i | − 1.13924i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −208.508 | −0.361365 | −0.180683 | − | 0.983541i | \(-0.557831\pi\) | ||||
−0.180683 | + | 0.983541i | \(0.557831\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 277.578i | 0.477759i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −138.176 | −0.237008 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 573.400i | 0.976831i | 0.872611 | + | 0.488416i | \(0.162425\pi\) | ||||
−0.872611 | + | 0.488416i | \(0.837575\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −117.610 | −0.199677 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 875.654i | 1.47665i | 0.674445 | + | 0.738325i | \(0.264383\pi\) | ||||
−0.674445 | + | 0.738325i | \(0.735617\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1875.99 | −3.15292 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 474.655i | 0.792413i | 0.918161 | + | 0.396206i | \(0.129674\pi\) | ||||
−0.918161 | + | 0.396206i | \(0.870326\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 618.401 | 1.02895 | 0.514476 | − | 0.857505i | \(-0.327986\pi\) | ||||
0.514476 | + | 0.857505i | \(0.327986\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − 888.002i | − 1.46777i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −370.800 | −0.610873 | −0.305437 | − | 0.952212i | \(-0.598802\pi\) | ||||
−0.305437 | + | 0.952212i | \(0.598802\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 455.963i | − 0.746256i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 330.774 | 0.539598 | 0.269799 | − | 0.962917i | \(-0.413043\pi\) | ||||
0.269799 | + | 0.962917i | \(0.413043\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 545.705i | 0.884449i | 0.896904 | + | 0.442224i | \(0.145810\pi\) | ||||
−0.896904 | + | 0.442224i | \(0.854190\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −959.199 | −1.54959 | −0.774797 | − | 0.632210i | \(-0.782148\pi\) | ||||
−0.774797 | + | 0.632210i | \(0.782148\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1321.59i | 2.12134i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −257.379 | −0.411806 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 452.675i | − 0.719674i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 573.390 | 0.908700 | 0.454350 | − | 0.890823i | \(-0.349872\pi\) | ||||
0.454350 | + | 0.890823i | \(0.349872\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 796.451i | − 1.25425i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1209.87 | 1.89933 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − 895.044i | − 1.39633i | −0.715939 | − | 0.698163i | \(-0.754001\pi\) | ||||
0.715939 | − | 0.698163i | \(-0.245999\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −474.571 | −0.738058 | −0.369029 | − | 0.929418i | \(-0.620310\pi\) | ||||
−0.369029 | + | 0.929418i | \(0.620310\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 459.625i | 0.710394i | 0.934792 | + | 0.355197i | \(0.115586\pi\) | ||||
−0.934792 | + | 0.355197i | \(0.884414\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 269.746 | 0.415633 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 27.2561i | − 0.0417398i | −0.999782 | − | 0.0208699i | \(-0.993356\pi\) | ||||
0.999782 | − | 0.0208699i | \(-0.00664357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 606.281 | 0.925619 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 50.4027i | 0.0764836i | 0.999269 | + | 0.0382418i | \(0.0121757\pi\) | ||||
−0.999269 | + | 0.0382418i | \(0.987824\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −928.837 | −1.40520 | −0.702600 | − | 0.711585i | \(-0.747978\pi\) | ||||
−0.702600 | + | 0.711585i | \(0.747978\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 312.284i | 0.469600i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −57.3645 | −0.0860038 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.4428i | 0.0230146i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 212.941 | 0.316406 | 0.158203 | − | 0.987407i | \(-0.449430\pi\) | ||||
0.158203 | + | 0.987407i | \(0.449430\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 879.368i | 1.29892i | 0.760396 | + | 0.649459i | \(0.225005\pi\) | ||||
−0.760396 | + | 0.649459i | \(0.774995\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −919.601 | −1.35435 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − 1189.08i | − 1.74097i | −0.492199 | − | 0.870483i | \(-0.663807\pi\) | ||||
0.492199 | − | 0.870483i | \(-0.336193\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 426.680 | 0.622890 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 467.073i | − 0.677900i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 165.918 | 0.240114 | 0.120057 | − | 0.992767i | \(-0.461692\pi\) | ||||
0.120057 | + | 0.992767i | \(0.461692\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 315.255i | 0.453604i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1096.89 | −1.57372 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 256.999i | − 0.366617i | −0.983055 | − | 0.183309i | \(-0.941319\pi\) | ||||
0.983055 | − | 0.183309i | \(-0.0586808\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −75.3539 | −0.107189 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 1284.38i | − 1.81666i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1096.94 | 1.54716 | 0.773581 | − | 0.633698i | \(-0.218464\pi\) | ||||
0.773581 | + | 0.633698i | \(0.218464\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 740.790i | 1.03898i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −176.746 | −0.247197 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 997.306i | − 1.38707i | −0.720421 | − | 0.693537i | \(-0.756051\pi\) | ||||
0.720421 | − | 0.693537i | \(-0.243949\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 219.278 | 0.304130 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 109.668i | − 0.151266i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −994.798 | −1.36836 | −0.684180 | − | 0.729313i | \(-0.739840\pi\) | ||||
−0.684180 | + | 0.729313i | \(0.739840\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 581.142i | − 0.794996i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1203.78 | −1.64226 | −0.821131 | − | 0.570740i | \(-0.806656\pi\) | ||||
−0.821131 | + | 0.570740i | \(0.806656\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − 122.776i | − 0.166589i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 266.460 | 0.360568 | 0.180284 | − | 0.983615i | \(-0.442298\pi\) | ||||
0.180284 | + | 0.983615i | \(0.442298\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 349.670i | 0.470619i | 0.971921 | + | 0.235309i | \(0.0756103\pi\) | ||||
−0.971921 | + | 0.235309i | \(0.924390\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1301.67 | −1.74721 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1318.74i | 1.76066i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −313.122 | −0.416940 | −0.208470 | − | 0.978029i | \(-0.566848\pi\) | ||||
−0.208470 | + | 0.978029i | \(0.566848\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 2141.11i | − 2.83590i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −806.976 | −1.06602 | −0.533009 | − | 0.846109i | \(-0.678939\pi\) | ||||
−0.533009 | + | 0.846109i | \(0.678939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 866.633i | 1.13881i | 0.822058 | + | 0.569404i | \(0.192826\pi\) | ||||
−0.822058 | + | 0.569404i | \(0.807174\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1930.58 | −2.53025 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 911.818i | 1.18881i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1254.03 | 1.63073 | 0.815365 | − | 0.578947i | \(-0.196536\pi\) | ||||
0.815365 | + | 0.578947i | \(0.196536\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 1013.11i | − 1.31062i | −0.755361 | − | 0.655309i | \(-0.772538\pi\) | ||||
0.755361 | − | 0.655309i | \(-0.227462\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1416.22 | −1.82738 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 182.592i | 0.234392i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 232.174 | 0.297277 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1602.08i | 2.04086i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1225.56 | −1.55726 | −0.778630 | − | 0.627484i | \(-0.784085\pi\) | ||||
−0.778630 | + | 0.627484i | \(0.784085\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − 360.092i | − 0.455237i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −52.2012 | −0.0658275 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 369.326i | − 0.463395i | −0.972788 | − | 0.231697i | \(-0.925572\pi\) | ||||
0.972788 | − | 0.231697i | \(-0.0744279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −918.054 | −1.14900 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 174.324i | 0.217091i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1966.98 | 2.44346 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − 622.873i | − 0.769930i | −0.922931 | − | 0.384965i | \(-0.874214\pi\) | ||||
0.922931 | − | 0.384965i | \(-0.125786\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 899.290 | 1.10887 | 0.554433 | − | 0.832228i | \(-0.312935\pi\) | ||||
0.554433 | + | 0.832228i | \(0.312935\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 665.330i | 0.816356i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −96.7391 | −0.118408 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 965.532i | − 1.17604i | −0.808845 | − | 0.588022i | \(-0.799907\pi\) | ||||
0.808845 | − | 0.588022i | \(-0.200093\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 486.562 | 0.591205 | 0.295602 | − | 0.955311i | \(-0.404480\pi\) | ||||
0.295602 | + | 0.955311i | \(0.404480\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 237.282i | 0.286919i | 0.989656 | + | 0.143460i | \(0.0458227\pi\) | ||||
−0.989656 | + | 0.143460i | \(0.954177\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 414.083 | 0.499497 | 0.249748 | − | 0.968311i | \(-0.419652\pi\) | ||||
0.249748 | + | 0.968311i | \(0.419652\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − 2436.01i | − 2.92438i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 349.313 | 0.418339 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 315.279i | 0.375779i | 0.982190 | + | 0.187890i | \(0.0601647\pi\) | ||||
−0.982190 | + | 0.187890i | \(0.939835\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 831.396 | 0.988581 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 715.844i | 0.847153i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1562.57 | 1.84483 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 474.632i | 0.557735i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1084.36 | 1.27123 | 0.635615 | − | 0.772006i | \(-0.280746\pi\) | ||||
0.635615 | + | 0.772006i | \(0.280746\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1451.35i | 1.69353i | 0.531969 | + | 0.846764i | \(0.321452\pi\) | ||||
−0.531969 | + | 0.846764i | \(0.678548\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 59.3435 | 0.0690844 | 0.0345422 | − | 0.999403i | \(-0.489003\pi\) | ||||
0.0345422 | + | 0.999403i | \(0.489003\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 617.264i | − 0.715254i | −0.933865 | − | 0.357627i | \(-0.883586\pi\) | ||||
0.933865 | − | 0.357627i | \(-0.116414\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1316.76 | −1.52227 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 94.2174i | 0.108420i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 415.018 | 0.476484 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1103.87i | 1.26157i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −926.943 | −1.05695 | −0.528474 | − | 0.848950i | \(-0.677236\pi\) | ||||
−0.528474 | + | 0.848950i | \(0.677236\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1539.43i | 1.74737i | 0.486491 | + | 0.873686i | \(0.338277\pi\) | ||||
−0.486491 | + | 0.873686i | \(0.661723\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.0095 | −0.0441784 | −0.0220892 | − | 0.999756i | \(-0.507032\pi\) | ||||
−0.0220892 | + | 0.999756i | \(0.507032\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 766.276i | 0.863897i | 0.901898 | + | 0.431948i | \(0.142174\pi\) | ||||
−0.901898 | + | 0.431948i | \(0.857826\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1401.47 | 1.57646 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 152.823i | 0.171134i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1092.74 | 1.22094 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 124.020i | 0.137953i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −940.424 | −1.04376 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 539.097i | − 0.595687i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 463.758 | 0.511310 | 0.255655 | − | 0.966768i | \(-0.417709\pi\) | ||||
0.255655 | + | 0.966768i | \(0.417709\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1237.16i | − 1.35802i | −0.734128 | − | 0.679011i | \(-0.762409\pi\) | ||||
0.734128 | − | 0.679011i | \(-0.237591\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 52.6555 | 0.0576730 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1066.84i | 1.16340i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1781.60 | 1.93863 | 0.969315 | − | 0.245823i | \(-0.0790581\pi\) | ||||
0.969315 | + | 0.245823i | \(0.0790581\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 784.814i | 0.850286i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −907.387 | −0.980959 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1101.20i | 1.18536i | 0.805439 | + | 0.592678i | \(0.201929\pi\) | ||||
−0.805439 | + | 0.592678i | \(0.798071\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −405.507 | −0.435561 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 355.868i | 0.380607i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1408.82 | 1.50354 | 0.751771 | − | 0.659425i | \(-0.229200\pi\) | ||||
0.751771 | + | 0.659425i | \(0.229200\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 169.230i | 0.179841i | 0.995949 | + | 0.0899203i | \(0.0286612\pi\) | ||||
−0.995949 | + | 0.0899203i | \(0.971339\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1150.09 | 1.21961 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 1377.82i | 1.45494i | 0.686141 | + | 0.727468i | \(0.259303\pi\) | ||||
−0.686141 | + | 0.727468i | \(0.740697\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −589.265 | −0.620933 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 810.833i | 0.850821i | 0.905000 | + | 0.425411i | \(0.139870\pi\) | ||||
−0.905000 | + | 0.425411i | \(0.860130\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2285.44 | −2.39313 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 750.805i | 0.782904i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 640.559 | 0.666555 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 815.534i | 0.845113i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 947.710 | 0.980051 | 0.490026 | − | 0.871708i | \(-0.336987\pi\) | ||||
0.490026 | + | 0.871708i | \(0.336987\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1197.72i | 1.23349i | 0.787162 | + | 0.616747i | \(0.211550\pi\) | ||||
−0.787162 | + | 0.616747i | \(0.788450\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −554.737 | −0.570130 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 233.702i | 0.239204i | 0.992822 | + | 0.119602i | \(0.0381619\pi\) | ||||
−0.992822 | + | 0.119602i | \(0.961838\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 250.701 | 0.256079 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1128.07i | 1.14758i | 0.819003 | + | 0.573789i | \(0.194527\pi\) | ||||
−0.819003 | + | 0.573789i | \(0.805473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 517.920 | 0.525807 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 609.331i | 0.616109i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 550.092 | 0.555088 | 0.277544 | − | 0.960713i | \(-0.410480\pi\) | ||||
0.277544 | + | 0.960713i | \(0.410480\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1443.27i | 1.45052i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −999.986 | −1.00299 | −0.501497 | − | 0.865159i | \(-0.667217\pi\) | ||||
−0.501497 | + | 0.865159i | \(0.667217\pi\) | |||||||
\(998\) | 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 | 2916.3.c.b.1457.4 | 36 | ||
3.2 | odd | 2 | inner | 2916.3.c.b.1457.33 | 36 | ||
27.2 | odd | 18 | 324.3.k.a.17.6 | 36 | |||
27.13 | even | 9 | 324.3.k.a.305.6 | 36 | |||
27.14 | odd | 18 | 108.3.k.a.101.6 | yes | 36 | ||
27.25 | even | 9 | 108.3.k.a.77.6 | ✓ | 36 | ||
108.79 | odd | 18 | 432.3.bc.b.401.1 | 36 | |||
108.95 | even | 18 | 432.3.bc.b.209.1 | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.3.k.a.77.6 | ✓ | 36 | 27.25 | even | 9 | ||
108.3.k.a.101.6 | yes | 36 | 27.14 | odd | 18 | ||
324.3.k.a.17.6 | 36 | 27.2 | odd | 18 | |||
324.3.k.a.305.6 | 36 | 27.13 | even | 9 | |||
432.3.bc.b.209.1 | 36 | 108.95 | even | 18 | |||
432.3.bc.b.401.1 | 36 | 108.79 | odd | 18 | |||
2916.3.c.b.1457.4 | 36 | 1.1 | even | 1 | trivial | ||
2916.3.c.b.1457.33 | 36 | 3.2 | odd | 2 | inner |