Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(101,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.101");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.bi (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 9 x^{14} - 18 x^{13} + 32 x^{12} - 36 x^{11} + 51 x^{9} - 167 x^{8} + 153 x^{7} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 101.3 | ||
Root | \(0.990987 + 1.42054i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.101 |
Dual form | 2100.2.bi.l.1601.3 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.990987 | + | 1.42054i | −0.572147 | + | 0.820151i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.64111 | − | 0.156656i | −0.998246 | − | 0.0592104i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.03589 | − | 2.81548i | −0.345297 | − | 0.938494i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.92449 | − | 2.84316i | −1.48479 | − | 0.857244i | −0.484940 | − | 0.874548i | \(-0.661158\pi\) |
−0.999850 | + | 0.0173038i | \(0.994492\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 1.43616i | − | 0.398318i | −0.979967 | − | 0.199159i | \(-0.936179\pi\) | ||
0.979967 | − | 0.199159i | \(-0.0638210\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.62414 | + | 2.81310i | −0.393913 | + | 0.682277i | −0.992962 | − | 0.118435i | \(-0.962212\pi\) |
0.599049 | + | 0.800712i | \(0.295545\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.43583 | − | 3.13838i | 1.24707 | − | 0.719994i | 0.276543 | − | 0.961002i | \(-0.410811\pi\) |
0.970523 | + | 0.241008i | \(0.0774779\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.83984 | − | 3.59657i | 0.619704 | − | 0.784835i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.884443 | − | 0.510633i | 0.184419 | − | 0.106474i | −0.404948 | − | 0.914340i | \(-0.632710\pi\) |
0.589367 | + | 0.807865i | \(0.299377\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.02607 | + | 1.31858i | 0.967267 | + | 0.253760i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.95680i | 0.920456i | 0.887801 | + | 0.460228i | \(0.152232\pi\) | ||||
−0.887801 | + | 0.460228i | \(0.847768\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.28384 | − | 1.31858i | −0.410190 | − | 0.236823i | 0.280681 | − | 0.959801i | \(-0.409440\pi\) |
−0.690871 | + | 0.722978i | \(0.742773\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.91893 | − | 4.17793i | 1.55259 | − | 0.727283i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.55098 | + | 7.88253i | 0.748176 | + | 1.29588i | 0.948696 | + | 0.316190i | \(0.102404\pi\) |
−0.200520 | + | 0.979690i | \(0.564263\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.04012 | + | 1.42321i | 0.326681 | + | 0.227896i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.203153 | −0.0317271 | −0.0158636 | − | 0.999874i | \(-0.505050\pi\) | ||||
−0.0158636 | + | 0.999874i | \(0.505050\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.91245 | −0.596642 | −0.298321 | − | 0.954466i | \(-0.596427\pi\) | ||||
−0.298321 | + | 0.954466i | \(0.596427\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.76577 | + | 9.98660i | 0.841024 | + | 1.45670i | 0.889030 | + | 0.457849i | \(0.151380\pi\) |
−0.0480062 | + | 0.998847i | \(0.515287\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.95092 | + | 0.827492i | 0.992988 | + | 0.118213i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.38663 | − | 5.09491i | −0.334195 | − | 0.713431i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.21721 | + | 5.32156i | 1.26608 | + | 0.730972i | 0.974244 | − | 0.225496i | \(-0.0724002\pi\) |
0.291837 | + | 0.956468i | \(0.405734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.928633 | + | 10.8319i | −0.123000 | + | 1.43472i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.739701 | + | 1.28120i | −0.0963009 | + | 0.166798i | −0.910151 | − | 0.414277i | \(-0.864034\pi\) |
0.813850 | + | 0.581075i | \(0.197368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.62492 | − | 4.40225i | 0.976271 | − | 0.563650i | 0.0751289 | − | 0.997174i | \(-0.476063\pi\) |
0.901142 | + | 0.433523i | \(0.142730\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.29484 | + | 7.59827i | 0.289122 | + | 0.957292i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.34108 | − | 4.05487i | 0.286008 | − | 0.495381i | −0.686845 | − | 0.726804i | \(-0.741005\pi\) |
0.972853 | + | 0.231423i | \(0.0743382\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.151094 | + | 1.76242i | −0.0181896 | + | 0.212171i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.08138i | 0.128336i | 0.997939 | + | 0.0641680i | \(0.0204394\pi\) | ||||
−0.997939 | + | 0.0641680i | \(0.979561\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.82857 | − | 4.51983i | −0.916265 | − | 0.529006i | −0.0338235 | − | 0.999428i | \(-0.510768\pi\) |
−0.882442 | + | 0.470422i | \(0.844102\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.5607 | + | 8.28054i | 1.43143 | + | 0.943655i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.80981 | − | 10.0629i | −0.653655 | − | 1.13216i | −0.982229 | − | 0.187685i | \(-0.939902\pi\) |
0.328575 | − | 0.944478i | \(-0.393432\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.85386 | + | 5.83306i | −0.761540 | + | 0.648117i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −10.1512 | −1.11424 | −0.557118 | − | 0.830433i | \(-0.688093\pi\) | ||||
−0.557118 | + | 0.830433i | \(0.688093\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.04136 | − | 4.91213i | −0.754913 | − | 0.526635i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 7.53465 | + | 13.0504i | 0.798672 | + | 1.38334i | 0.920481 | + | 0.390787i | \(0.127797\pi\) |
−0.121810 | + | 0.992553i | \(0.538870\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.224982 | + | 3.79304i | −0.0235846 | + | 0.397619i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.13636 | − | 1.93761i | 0.428920 | − | 0.200920i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 10.5540i | − | 1.07159i | −0.844347 | − | 0.535797i | \(-0.820011\pi\) | ||
0.844347 | − | 0.535797i | \(-0.179989\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.90362 | + | 16.8100i | −0.291825 | + | 1.68947i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.49149 | − | 12.9756i | 0.745431 | − | 1.29112i | −0.204562 | − | 0.978854i | \(-0.565577\pi\) |
0.949993 | − | 0.312271i | \(-0.101090\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.43283 | − | 1.98195i | 0.338247 | − | 0.195287i | −0.321249 | − | 0.946995i | \(-0.604103\pi\) |
0.659497 | + | 0.751708i | \(0.270769\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −8.28071 | + | 4.78087i | −0.800526 | + | 0.462184i | −0.843655 | − | 0.536885i | \(-0.819601\pi\) |
0.0431288 | + | 0.999070i | \(0.486267\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.03847 | + | 12.1910i | −0.674163 | + | 1.16769i | 0.302549 | + | 0.953134i | \(0.402162\pi\) |
−0.976713 | + | 0.214551i | \(0.931171\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.7074 | − | 1.34661i | −1.49088 | − | 0.127815i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.91796i | 0.556715i | 0.960478 | + | 0.278357i | \(0.0897900\pi\) | ||||
−0.960478 | + | 0.278357i | \(0.910210\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.04347 | + | 1.48770i | −0.373819 | + | 0.137538i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 4.73023 | − | 7.17527i | 0.433620 | − | 0.657756i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.6671 | + | 18.4759i | 0.969734 | + | 1.67963i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.201322 | − | 0.288587i | 0.0181526 | − | 0.0260210i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.35916 | 0.741756 | 0.370878 | − | 0.928682i | \(-0.379057\pi\) | ||||
0.370878 | + | 0.928682i | \(0.379057\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.87718 | − | 5.55780i | 0.341367 | − | 0.489337i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.27436 | − | 14.3316i | −0.722934 | − | 1.25216i | −0.959819 | − | 0.280620i | \(-0.909460\pi\) |
0.236885 | − | 0.971538i | \(-0.423874\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −14.8483 | + | 7.43725i | −1.28751 | + | 0.644891i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.96454 | + | 5.17568i | 0.765892 | + | 0.442188i | 0.831407 | − | 0.555663i | \(-0.187536\pi\) |
−0.0655150 | + | 0.997852i | \(0.520869\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9.17498i | 0.778212i | 0.921193 | + | 0.389106i | \(0.127216\pi\) | ||||
−0.921193 | + | 0.389106i | \(0.872784\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.9002 | − | 1.70607i | −1.67590 | − | 0.143677i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.08321 | + | 7.07233i | −0.341455 | + | 0.591418i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −8.06376 | + | 9.05405i | −0.665087 | + | 0.746765i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.71301 | − | 2.14370i | 0.304181 | − | 0.175619i | −0.340138 | − | 0.940375i | \(-0.610474\pi\) |
0.644320 | + | 0.764756i | \(0.277141\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.06606 | − | 10.5067i | 0.493649 | − | 0.855025i | −0.506324 | − | 0.862343i | \(-0.668996\pi\) |
0.999973 | + | 0.00731794i | \(0.00232939\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 9.60266 | + | 1.65868i | 0.776329 | + | 0.134097i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7317 | + | 6.19593i | 0.856480 | + | 0.494489i | 0.862832 | − | 0.505491i | \(-0.168689\pi\) |
−0.00635192 | + | 0.999980i | \(0.502022\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −16.6936 | + | 7.81986i | −1.32389 | + | 0.620155i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.41590 | + | 1.21009i | −0.190400 | + | 0.0953681i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2811 | + | 17.8074i | 0.805279 | + | 1.39478i | 0.916103 | + | 0.400944i | \(0.131318\pi\) |
−0.110824 | + | 0.993840i | \(0.535349\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.95678 | 0.306185 | 0.153093 | − | 0.988212i | \(-0.451077\pi\) | ||||
0.153093 | + | 0.988212i | \(0.451077\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.9375 | 0.841343 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −14.4670 | − | 12.0535i | −1.10632 | − | 0.921752i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 6.50547 | + | 11.2678i | 0.494602 | + | 0.856675i | 0.999981 | − | 0.00622220i | \(-0.00198060\pi\) |
−0.505379 | + | 0.862898i | \(0.668647\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.08697 | − | 2.32043i | −0.0817014 | − | 0.174414i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.2033 | + | 11.6644i | 1.51007 | + | 0.871837i | 0.999931 | + | 0.0117426i | \(0.00373787\pi\) |
0.510135 | + | 0.860094i | \(0.329595\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.770872i | − | 0.0572984i | −0.999590 | − | 0.0286492i | \(-0.990879\pi\) | ||
0.999590 | − | 0.0286492i | \(-0.00912058\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.30261 | + | 15.1941i | −0.0962915 | + | 1.12318i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 15.9962 | − | 9.23539i | 1.16976 | − | 0.675359i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −13.0678 | − | 4.26987i | −0.950545 | − | 0.310587i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.02156 | − | 1.16715i | 0.146275 | − | 0.0844517i | −0.425076 | − | 0.905157i | \(-0.639753\pi\) |
0.571351 | + | 0.820706i | \(0.306419\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.351009 | − | 0.607965i | 0.0252662 | − | 0.0437623i | −0.853116 | − | 0.521722i | \(-0.825290\pi\) |
0.878382 | + | 0.477959i | \(0.158623\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 19.3932i | − | 1.38171i | −0.722993 | − | 0.690855i | \(-0.757234\pi\) | ||
0.722993 | − | 0.690855i | \(-0.242766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.0457 | + | 9.26397i | 1.13745 | + | 0.656706i | 0.945797 | − | 0.324758i | \(-0.105283\pi\) |
0.191650 | + | 0.981463i | \(0.438616\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3.44014 | + | 7.34393i | 0.242649 | + | 0.518001i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.776514 | − | 13.0915i | 0.0545006 | − | 0.918841i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.35386 | − | 1.96117i | −0.163605 | − | 0.136311i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −35.6916 | −2.46884 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 22.5538 | 1.55267 | 0.776335 | − | 0.630321i | \(-0.217077\pi\) | ||||
0.776335 | + | 0.630321i | \(0.217077\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.53615 | − | 1.07163i | −0.105255 | − | 0.0734270i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.82532 | + | 3.84028i | 0.395448 | + | 0.260696i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.1786 | − | 6.64174i | 0.958103 | − | 0.448807i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.04005 | + | 2.33252i | 0.271763 | + | 0.156902i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 14.7072i | − | 0.984868i | −0.870350 | − | 0.492434i | \(-0.836107\pi\) | ||
0.870350 | − | 0.492434i | \(-0.163893\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.47751 | + | 14.6835i | −0.562672 | + | 0.974577i | 0.434590 | + | 0.900628i | \(0.356893\pi\) |
−0.997262 | + | 0.0739481i | \(0.976440\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.4690 | + | 11.2404i | −1.28655 | + | 0.742789i | −0.978037 | − | 0.208432i | \(-0.933164\pi\) |
−0.308511 | + | 0.951221i | \(0.599831\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −24.2104 | + | 9.63715i | −1.59293 | + | 0.634078i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.2249 | − | 12.8315i | 1.45600 | − | 0.840621i | 0.457188 | − | 0.889370i | \(-0.348857\pi\) |
0.998811 | + | 0.0487486i | \(0.0155233\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 20.0522 | + | 1.71910i | 1.30253 | + | 0.111667i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.58286i | 0.490494i | 0.969461 | + | 0.245247i | \(0.0788691\pi\) | ||||
−0.969461 | + | 0.245247i | \(0.921131\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.34408 | + | 4.24011i | 0.473074 | + | 0.273129i | 0.717526 | − | 0.696532i | \(-0.245275\pi\) |
−0.244452 | + | 0.969661i | \(0.578608\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.49402 | − | 15.5167i | −0.0958417 | − | 0.995397i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.50720 | − | 7.80670i | −0.286786 | − | 0.496729i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.0597 | − | 14.4202i | 0.637506 | − | 0.913842i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.17721 | 0.0743051 | 0.0371526 | − | 0.999310i | \(-0.488171\pi\) | ||||
0.0371526 | + | 0.999310i | \(0.488171\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.80724 | −0.365098 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.66857 | − | 4.62211i | −0.166461 | − | 0.288319i | 0.770712 | − | 0.637184i | \(-0.219901\pi\) |
−0.937173 | + | 0.348864i | \(0.886567\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.7848 | − | 21.5316i | −0.670134 | − | 1.33791i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.9558 | − | 5.13470i | 0.863842 | − | 0.317830i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −13.2573 | − | 7.65408i | −0.817478 | − | 0.471971i | 0.0320683 | − | 0.999486i | \(-0.489791\pi\) |
−0.849546 | + | 0.527515i | \(0.823124\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −26.0054 | − | 2.22947i | −1.59151 | − | 0.136441i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.50096 | − | 6.06384i | 0.213457 | − | 0.369719i | −0.739337 | − | 0.673336i | \(-0.764861\pi\) |
0.952794 | + | 0.303617i | \(0.0981943\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.1722 | − | 6.45029i | 0.678665 | − | 0.391827i | −0.120687 | − | 0.992691i | \(-0.538510\pi\) |
0.799352 | + | 0.600863i | \(0.205176\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −5.16523 | − | 4.07845i | −0.312614 | − | 0.246839i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.56717 | + | 9.64261i | −0.334499 | + | 0.579369i | −0.983388 | − | 0.181514i | \(-0.941900\pi\) |
0.648890 | + | 0.760882i | \(0.275234\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1.34662 | + | 7.79602i | −0.0806200 | + | 0.466735i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.5391i | 1.34457i | 0.740291 | + | 0.672286i | \(0.234688\pi\) | ||||
−0.740291 | + | 0.672286i | \(0.765312\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.8420 | − | 9.14640i | −0.941710 | − | 0.543697i | −0.0512144 | − | 0.998688i | \(-0.516309\pi\) |
−0.890496 | + | 0.454991i | \(0.849643\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.536549 | + | 0.0318251i | 0.0316715 | + | 0.00187858i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.22431 | + | 5.58467i | 0.189665 | + | 0.328510i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.9924 | + | 10.4588i | 0.878869 | + | 0.613108i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −17.0413 | −0.995566 | −0.497783 | − | 0.867302i | \(-0.665852\pi\) | ||||
−0.497783 | + | 0.867302i | \(0.665852\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −21.0019 | − | 20.7832i | −1.21865 | − | 1.20596i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.733349 | − | 1.27020i | −0.0424106 | − | 0.0734574i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.3332 | + | 0.612909i | 0.595596 | + | 0.0353275i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 11.0085 | + | 23.5007i | 0.632422 | + | 1.35008i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.9629i | 0.968124i | 0.875034 | + | 0.484062i | \(0.160839\pi\) | ||||
−0.875034 | + | 0.484062i | \(0.839161\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.586450 | + | 6.84058i | −0.0333620 | + | 0.389147i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.7519 | + | 29.0151i | −0.949911 | + | 1.64529i | −0.204305 | + | 0.978907i | \(0.565493\pi\) |
−0.745606 | + | 0.666387i | \(0.767840\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.92768 | − | 3.42235i | 0.335052 | − | 0.193443i | −0.323030 | − | 0.946389i | \(-0.604701\pi\) |
0.658082 | + | 0.752946i | \(0.271368\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11.2908 | + | 6.51876i | −0.634156 | + | 0.366130i | −0.782360 | − | 0.622827i | \(-0.785984\pi\) |
0.148204 | + | 0.988957i | \(0.452651\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.0930 | − | 24.4097i | 0.789055 | − | 1.36668i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.41464 | − | 16.5009i | 0.0789574 | − | 0.920990i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 20.3887i | 1.13446i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −10.3428 | − | 22.0796i | −0.571958 | − | 1.22100i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −13.6636 | − | 27.2790i | −0.753297 | − | 1.50394i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.35727 | + | 5.81496i | 0.184532 | + | 0.319619i | 0.943419 | − | 0.331604i | \(-0.107590\pi\) |
−0.758887 | + | 0.651223i | \(0.774256\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 17.4788 | − | 20.9786i | 0.957832 | − | 1.14962i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.0783052 | 0.00426556 | 0.00213278 | − | 0.999998i | \(-0.499321\pi\) | ||||
0.00213278 | + | 0.999998i | \(0.499321\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −8.40672 | − | 5.86462i | −0.456590 | − | 0.318522i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.49784 | + | 12.9866i | 0.406031 | + | 0.703266i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −18.2285 | − | 3.27440i | −0.984247 | − | 0.176801i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −24.1913 | − | 13.9669i | −1.29866 | − | 0.749780i | −0.318485 | − | 0.947928i | \(-0.603174\pi\) |
−0.980172 | + | 0.198148i | \(0.936507\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 18.8292i | − | 1.00790i | −0.863732 | − | 0.503952i | \(-0.831879\pi\) | ||
0.863732 | − | 0.503952i | \(-0.168121\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.89368 | − | 7.21821i | 0.101077 | − | 0.385280i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 13.8890 | − | 24.0565i | 0.739239 | − | 1.28040i | −0.213600 | − | 0.976921i | \(-0.568519\pi\) |
0.952839 | − | 0.303477i | \(-0.0981477\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.50519 | + | 13.8301i | 0.291366 | + | 0.731967i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 24.6446 | − | 14.2286i | 1.30069 | − | 0.750954i | 0.320168 | − | 0.947361i | \(-0.396260\pi\) |
0.980523 | + | 0.196406i | \(0.0629271\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.1989 | − | 17.6650i | 0.536782 | − | 0.929734i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −36.8168 | − | 3.15634i | −1.93238 | − | 0.165665i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5818 | + | 7.84147i | 0.708966 | + | 0.409321i | 0.810678 | − | 0.585492i | \(-0.199099\pi\) |
−0.101712 | + | 0.994814i | \(0.532432\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.210444 | + | 0.571973i | 0.0109553 | + | 0.0297757i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −23.5100 | − | 15.4988i | −1.22058 | − | 0.804655i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.31769 | + | 2.28231i | 0.0682274 | + | 0.118173i | 0.898121 | − | 0.439748i | \(-0.144932\pi\) |
−0.829894 | + | 0.557922i | \(0.811599\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.11874 | 0.366634 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.3684 | 1.35445 | 0.677227 | − | 0.735774i | \(-0.263181\pi\) | ||||
0.677227 | + | 0.735774i | \(0.263181\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.28382 | + | 11.8746i | −0.424393 | + | 0.608352i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −8.95565 | − | 15.5116i | −0.457612 | − | 0.792607i | 0.541222 | − | 0.840880i | \(-0.317962\pi\) |
−0.998834 | + | 0.0482722i | \(0.984628\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.05286 | + | 11.0154i | 0.206019 | + | 0.559945i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −17.6243 | − | 10.1754i | −0.893590 | − | 0.515914i | −0.0184749 | − | 0.999829i | \(-0.505881\pi\) |
−0.875115 | + | 0.483915i | \(0.839214\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.31737i | 0.167767i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 28.5585 | + | 2.44835i | 1.44058 | + | 0.123503i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 14.3014 | − | 8.25692i | 0.717767 | − | 0.414403i | −0.0961632 | − | 0.995366i | \(-0.530657\pi\) |
0.813930 | + | 0.580963i | \(0.197324\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 4.14951 | − | 28.4629i | 0.207735 | − | 1.42492i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.0643 | − | 15.0482i | 1.30159 | − | 0.751473i | 0.320912 | − | 0.947109i | \(-0.396010\pi\) |
0.980677 | + | 0.195636i | \(0.0626772\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.89368 | + | 3.27995i | −0.0943310 | + | 0.163386i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 51.7566i | − | 2.56548i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.1623 | + | 11.0634i | 0.947515 | + | 0.547048i | 0.892308 | − | 0.451427i | \(-0.149085\pi\) |
0.0552067 | + | 0.998475i | \(0.482418\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.2360 | + | 7.60549i | −0.800864 | + | 0.375151i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 2.15434 | − | 3.26791i | 0.106008 | − | 0.160803i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −13.0335 | − | 9.09228i | −0.638251 | − | 0.445251i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.3632 | −1.19022 | −0.595111 | − | 0.803643i | \(-0.702892\pi\) | ||||
−0.595111 | + | 0.803643i | \(0.702892\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.6655 | −0.666018 | −0.333009 | − | 0.942924i | \(-0.608064\pi\) | ||||
−0.333009 | + | 0.942924i | \(0.608064\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 22.1444 | − | 26.5784i | 1.07670 | − | 1.29229i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.8279 | + | 10.4323i | −1.00793 | + | 0.504856i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.00015 | − | 12.8090i | −0.289690 | − | 0.618423i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.2369 | + | 10.5291i | 0.878439 | + | 0.507167i | 0.870143 | − | 0.492798i | \(-0.164026\pi\) |
0.00829574 | + | 0.999966i | \(0.497359\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.13627i | − | 0.102663i | −0.998682 | − | 0.0513313i | \(-0.983654\pi\) | ||
0.998682 | − | 0.0513313i | \(-0.0163465\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.20512 | − | 5.55144i | 0.153322 | − | 0.265561i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.0942 | − | 7.55996i | 0.624954 | − | 0.360817i | −0.153841 | − | 0.988096i | \(-0.549164\pi\) |
0.778795 | + | 0.627278i | \(0.215831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.87060 | − | 20.4274i | −0.231933 | − | 0.972732i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −12.8040 | + | 7.39238i | −0.608335 | + | 0.351223i | −0.772314 | − | 0.635241i | \(-0.780901\pi\) |
0.163978 | + | 0.986464i | \(0.447567\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.634313 | + | 7.39887i | −0.0300020 | + | 0.349955i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 24.2040i | 1.14226i | 0.820860 | + | 0.571130i | \(0.193495\pi\) | ||||
−0.820860 | + | 0.571130i | \(0.806505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.00042 | + | 0.577595i | 0.0471081 | + | 0.0271979i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8.91388 | + | 19.0291i | 0.418811 | + | 0.894067i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.19577 | + | 10.7314i | 0.289826 | + | 0.501993i | 0.973768 | − | 0.227543i | \(-0.0730693\pi\) |
−0.683942 | + | 0.729536i | \(0.739736\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.8723 | + | 11.9973i | −0.554154 | + | 0.559985i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.34732 | −0.155900 | −0.0779502 | − | 0.996957i | \(-0.524838\pi\) | ||||
−0.0779502 | + | 0.996957i | \(0.524838\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −12.8360 | −0.596542 | −0.298271 | − | 0.954481i | \(-0.596410\pi\) | ||||
−0.298271 | + | 0.954481i | \(0.596410\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −14.9741 | − | 25.9359i | −0.692918 | − | 1.20017i | −0.970878 | − | 0.239576i | \(-0.922991\pi\) |
0.277959 | − | 0.960593i | \(-0.410342\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −6.81827 | + | 10.3426i | −0.314838 | + | 0.477577i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.4365 | + | 9.10472i | −0.895588 | + | 0.419523i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.2668 | + | 11.1237i | 0.885889 | + | 0.511468i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.43473 | − | 31.4634i | 0.248839 | − | 1.44061i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10.0585 | − | 17.4218i | 0.459584 | − | 0.796023i | −0.539355 | − | 0.842079i | \(-0.681332\pi\) |
0.998939 | + | 0.0460557i | \(0.0146652\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.3205 | − | 6.53591i | 0.516172 | − | 0.298012i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.675150 | − | 4.63108i | 0.0307204 | − | 0.210721i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −12.4697 | + | 21.5981i | −0.565055 | + | 0.978704i | 0.431989 | + | 0.901879i | \(0.357812\pi\) |
−0.997045 | + | 0.0768256i | \(0.975522\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −35.4847 | − | 3.04214i | −1.60467 | − | 0.137570i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 11.2524i | 0.507814i | 0.967229 | + | 0.253907i | \(0.0817157\pi\) | ||||
−0.967229 | + | 0.253907i | \(0.918284\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.9440 | − | 8.05057i | −0.628006 | − | 0.362579i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0.169405 | − | 2.85604i | 0.00759883 | − | 0.128111i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.84476 | + | 4.92727i | 0.127349 | + | 0.220575i | 0.922649 | − | 0.385642i | \(-0.126020\pi\) |
−0.795300 | + | 0.606216i | \(0.792687\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.92112 | + | 5.62078i | −0.175183 | + | 0.251118i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.7975 | −1.01649 | −0.508245 | − | 0.861212i | \(-0.669706\pi\) | ||||
−0.508245 | + | 0.861212i | \(0.669706\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −10.8389 | + | 15.5371i | −0.481371 | + | 0.690029i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −8.17913 | − | 14.1667i | −0.362534 | − | 0.627927i | 0.625843 | − | 0.779949i | \(-0.284755\pi\) |
−0.988377 | + | 0.152022i | \(0.951422\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 19.9681 | + | 13.1638i | 0.883335 | + | 0.582330i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 31.4591 | − | 8.60614i | 1.38895 | − | 0.379971i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 65.5719i | − | 2.88385i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −22.4532 | − | 1.92494i | −0.985588 | − | 0.0844955i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8.67177 | − | 15.0199i | 0.379917 | − | 0.658036i | −0.611133 | − | 0.791528i | \(-0.709286\pi\) |
0.991050 | + | 0.133492i | \(0.0426192\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.1701 | − | 6.44905i | 0.488433 | − | 0.281997i | −0.235491 | − | 0.971877i | \(-0.575670\pi\) |
0.723924 | + | 0.689879i | \(0.242336\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.41858 | − | 4.28312i | 0.323158 | − | 0.186576i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.9785 | + | 19.0153i | −0.477326 | + | 0.826754i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.37344 | + | 0.755432i | 0.189791 | + | 0.0327830i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.291759i | 0.0126375i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −36.5910 | + | 17.1404i | −1.57902 | + | 0.739664i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −31.8770 | − | 23.8375i | −1.37304 | − | 1.02675i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.22594 | − | 3.85543i | −0.0957004 | − | 0.165758i | 0.814200 | − | 0.580584i | \(-0.197176\pi\) |
−0.909901 | + | 0.414826i | \(0.863842\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.09506 | + | 0.763924i | 0.0469934 | + | 0.0327831i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.58754 | −0.238906 | −0.119453 | − | 0.992840i | \(-0.538114\pi\) | ||||
−0.119453 | + | 0.992840i | \(0.538114\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −20.2930 | − | 16.9076i | −0.866086 | − | 0.721598i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 15.5563 | + | 26.9444i | 0.662722 | + | 1.14787i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.7679 | + | 27.4873i | 0.585472 | + | 1.16888i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −18.1594 | − | 10.4844i | −0.769440 | − | 0.444236i | 0.0632348 | − | 0.997999i | \(-0.479858\pi\) |
−0.832675 | + | 0.553762i | \(0.813192\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.61888i | 0.237653i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.73271 | + | 31.8754i | −0.115375 | + | 1.34578i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.14487 | + | 10.6432i | −0.258975 | + | 0.448559i | −0.965968 | − | 0.258663i | \(-0.916718\pi\) |
0.706992 | + | 0.707221i | \(0.250052\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.0156 | − | 14.3320i | 0.798580 | − | 0.601889i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 37.1989 | − | 21.4768i | 1.55946 | − | 0.900355i | 0.562153 | − | 0.827033i | \(-0.309973\pi\) |
0.997308 | − | 0.0733217i | \(-0.0233600\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.24932 | + | 5.62799i | −0.135980 | + | 0.235524i | −0.925971 | − | 0.377594i | \(-0.876752\pi\) |
0.789991 | + | 0.613118i | \(0.210085\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −0.345353 | + | 4.02834i | −0.0144273 | + | 0.168286i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.15551 | − | 0.667135i | −0.0481046 | − | 0.0277732i | 0.475755 | − | 0.879578i | \(-0.342175\pi\) |
−0.523859 | + | 0.851805i | \(0.675508\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0.515796 | + | 1.10111i | 0.0214357 | + | 0.0457605i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 26.8104 | + | 1.59024i | 1.11228 | + | 0.0659744i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −30.2600 | − | 52.4119i | −1.25324 | − | 2.17068i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20.5791 | 0.849391 | 0.424696 | − | 0.905336i | \(-0.360381\pi\) | ||||
0.424696 | + | 0.905336i | \(0.360381\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −16.5528 | −0.682046 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 27.5489 | + | 19.2184i | 1.13321 | + | 0.790541i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4.83181 | − | 8.36894i | −0.198419 | − | 0.343671i | 0.749597 | − | 0.661894i | \(-0.230247\pi\) |
−0.948016 | + | 0.318223i | \(0.896914\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −29.0609 | + | 13.6131i | −1.18938 | + | 0.557147i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 37.3444 | + | 21.5608i | 1.52585 | + | 0.880951i | 0.999530 | + | 0.0306663i | \(0.00976291\pi\) |
0.526323 | + | 0.850285i | \(0.323570\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0495i | 0.980999i | 0.871442 | + | 0.490499i | \(0.163186\pi\) | ||||
−0.871442 | + | 0.490499i | \(0.836814\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −13.8415 | − | 2.39087i | −0.563670 | − | 0.0973636i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.56417 | − | 3.78982i | 0.266431 | − | 0.153824i | −0.360833 | − | 0.932630i | \(-0.617508\pi\) |
0.627265 | + | 0.778806i | \(0.284174\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.8275 | + | 14.0765i | 0.722406 | + | 0.570410i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.3423 | − | 8.28054i | 0.580228 | − | 0.334995i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23.1986 | + | 40.1812i | −0.936983 | + | 1.62290i | −0.165925 | + | 0.986138i | \(0.553061\pi\) |
−0.771058 | + | 0.636764i | \(0.780272\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.36960i | 0.0551380i | 0.999620 | + | 0.0275690i | \(0.00877660\pi\) | ||||
−0.999620 | + | 0.0275690i | \(0.991223\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0178 | − | 7.51581i | −0.523228 | − | 0.302086i | 0.215026 | − | 0.976608i | \(-0.431016\pi\) |
−0.738255 | + | 0.674522i | \(0.764350\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.11858 | − | 1.40027i | 0.205401 | − | 0.0561910i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −17.8554 | − | 35.6479i | −0.715362 | − | 1.42820i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 35.3699 | − | 50.7015i | 1.41254 | − | 2.02482i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −29.5658 | −1.17886 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.30638 | 0.171434 | 0.0857172 | − | 0.996320i | \(-0.472682\pi\) | ||||
0.0857172 | + | 0.996320i | \(0.472682\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −22.3505 | + | 32.0387i | −0.888354 | + | 1.27342i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.18841 | − | 9.98260i | 0.0470864 | − | 0.395525i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.04460 | − | 1.12019i | 0.120443 | − | 0.0443140i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.9310 | + | 6.31100i | 0.431747 | + | 0.249270i | 0.700091 | − | 0.714054i | \(-0.253143\pi\) |
−0.268343 | + | 0.963323i | \(0.586476\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 29.2411i | 1.15316i | 0.817042 | + | 0.576578i | \(0.195612\pi\) | ||||
−0.817042 | + | 0.576578i | \(0.804388\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.33150 | − | 12.6985i | 0.288231 | − | 0.499231i | −0.685157 | − | 0.728396i | \(-0.740266\pi\) |
0.973388 | + | 0.229165i | \(0.0735995\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7.28531 | − | 4.20617i | 0.285973 | − | 0.165107i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.2281 | + | 4.46944i | −0.440064 | + | 0.175171i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.7557 | − | 16.0248i | 1.08617 | − | 0.627098i | 0.153613 | − | 0.988131i | \(-0.450909\pi\) |
0.932553 | + | 0.361033i | \(0.117576\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.61595 | + | 26.7232i | −0.180085 | + | 1.04257i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.0951i | 1.71770i | 0.512225 | + | 0.858851i | \(0.328821\pi\) | ||||
−0.512225 | + | 0.858851i | \(0.671179\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −29.9096 | − | 17.2683i | −1.16335 | − | 0.671660i | −0.211245 | − | 0.977433i | \(-0.567752\pi\) |
−0.952104 | + | 0.305773i | \(0.901085\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −7.31709 | + | 3.42757i | −0.284172 | + | 0.133116i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.53111 | + | 4.38401i | 0.0980050 | + | 0.169750i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 20.8922 | + | 14.5747i | 0.807741 | + | 0.563489i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −50.0651 | −1.93274 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.0196 | −0.424773 | −0.212386 | − | 0.977186i | \(-0.568124\pi\) | ||||
−0.212386 | + | 0.977186i | \(0.568124\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3.78738 | − | 6.55993i | −0.145561 | − | 0.252119i | 0.784021 | − | 0.620734i | \(-0.213165\pi\) |
−0.929582 | + | 0.368615i | \(0.879832\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.65334 | + | 27.8742i | −0.0634495 | + | 1.06971i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −12.4574 | − | 26.5938i | −0.477369 | − | 1.01908i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.9945 | − | 12.6985i | −0.841596 | − | 0.485896i | 0.0162102 | − | 0.999869i | \(-0.494840\pi\) |
−0.857807 | + | 0.513973i | \(0.828173\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.32600 | − | 38.7957i | 0.126895 | − | 1.48015i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.64258 | − | 13.2373i | 0.291159 | − | 0.504303i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −2.43241 | + | 1.40435i | −0.0925332 | + | 0.0534241i | −0.545553 | − | 0.838077i | \(-0.683680\pi\) |
0.453019 | + | 0.891501i | \(0.350347\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.3022 | − | 43.9422i | 0.391347 | − | 1.66923i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.329949 | − | 0.571489i | 0.0124977 | − | 0.0216467i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.79679 | + | 44.2873i | −0.143608 | + | 1.67510i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 18.1659i | 0.686115i | 0.939314 | + | 0.343058i | \(0.111463\pi\) | ||||
−0.939314 | + | 0.343058i | \(0.888537\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 49.4767 | + | 28.5654i | 1.86605 | + | 1.07736i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −21.8186 | + | 33.0965i | −0.820571 | + | 1.24472i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.0139 | − | 26.0048i | −0.563858 | − | 0.976631i | −0.997155 | − | 0.0753797i | \(-0.975983\pi\) |
0.433297 | − | 0.901251i | \(-0.357350\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −22.3135 | + | 26.7814i | −0.836823 | + | 1.00438i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.69324 | −0.100863 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −10.7718 | − | 7.51451i | −0.402279 | − | 0.280635i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 0.687643 | + | 1.19103i | 0.0256447 | + | 0.0444180i | 0.878563 | − | 0.477627i | \(-0.158503\pi\) |
−0.852918 | + | 0.522045i | \(0.825169\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.37697 | + | 4.69677i | −0.349217 | + | 0.174917i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −13.3011 | + | 6.23070i | −0.494675 | + | 0.231722i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 33.6733i | 1.24887i | 0.781076 | + | 0.624436i | \(0.214671\pi\) | ||||
−0.781076 | + | 0.624436i | \(0.785329\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.5227 | + | 13.2545i | 0.871211 | + | 0.490908i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.35438 | − | 11.0061i | 0.235025 | − | 0.407075i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.5146 | + | 8.37999i | −0.536108 | + | 0.309522i | −0.743500 | − | 0.668736i | \(-0.766836\pi\) |
0.207392 | + | 0.978258i | \(0.433502\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −23.0572 | + | 13.3121i | −0.849325 | + | 0.490358i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −19.3091 | + | 33.4444i | −0.710298 | + | 1.23027i | 0.254448 | + | 0.967087i | \(0.418106\pi\) |
−0.964745 | + | 0.263185i | \(0.915227\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.5563 | + | 1.33366i | 0.571476 | + | 0.0489933i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.3068i | 1.07516i | 0.843212 | + | 0.537582i | \(0.180662\pi\) | ||||
−0.843212 | + | 0.537582i | \(0.819338\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 10.5155 | + | 28.5804i | 0.384742 | + | 1.04570i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 22.6192 | − | 11.3296i | 0.826488 | − | 0.413974i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.94534 | − | 10.2976i | −0.216949 | − | 0.375766i | 0.736925 | − | 0.675974i | \(-0.236277\pi\) |
−0.953874 | + | 0.300209i | \(0.902944\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.16660 | + | 1.67228i | −0.0425134 | + | 0.0609414i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.9755 | 1.63466 | 0.817332 | − | 0.576167i | \(-0.195452\pi\) | ||||
0.817332 | + | 0.576167i | \(0.195452\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.75490 | − | 8.24944i | 0.208890 | − | 0.299436i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.22673 | − | 2.12476i | −0.0444690 | − | 0.0770226i | 0.842934 | − | 0.538017i | \(-0.180826\pi\) |
−0.887403 | + | 0.460994i | \(0.847493\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.4992 | − | 31.0951i | 0.742120 | − | 1.12572i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.84000 | + | 1.06233i | 0.0664386 | + | 0.0383584i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.4658i | 0.665894i | 0.942946 | + | 0.332947i | \(0.108043\pi\) | ||||
−0.942946 | + | 0.332947i | \(0.891957\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.21043 | + | 0.789620i | 0.331705 | + | 0.0284375i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 0.884443 | − | 1.53190i | 0.0318112 | − | 0.0550986i | −0.849682 | − | 0.527296i | \(-0.823206\pi\) |
0.881493 | + | 0.472198i | \(0.156539\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 41.2741 | + | 6.01722i | 1.48070 | + | 0.215867i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.10430 | + | 0.637571i | −0.0395658 | + | 0.0228433i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.07453 | − | 5.32524i | 0.110015 | − | 0.190552i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.53593 | + | 24.9132i | −0.233575 | + | 0.890326i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 46.0531 | + | 26.5888i | 1.64162 | + | 0.947788i | 0.980259 | + | 0.197718i | \(0.0633529\pi\) |
0.661358 | + | 0.750070i | \(0.269980\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.0107 | − | 11.2474i | 0.854805 | − | 0.400419i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.927084 | − | 15.6300i | 0.0329633 | − | 0.555738i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −6.32231 | − | 10.9506i | −0.224512 | − | 0.388866i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 33.8237 | 1.19810 | 0.599049 | − | 0.800713i | \(-0.295546\pi\) | ||||
0.599049 | + | 0.800713i | \(0.295546\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −37.4578 | −1.32516 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 28.9381 | − | 34.7325i | 1.02248 | − | 1.22721i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 25.7012 | + | 44.5157i | 0.906974 | + | 1.57093i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.14454 | + | 10.9825i | 0.181097 | + | 0.386601i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −23.8866 | − | 13.7909i | −0.839807 | − | 0.484863i | 0.0173917 | − | 0.999849i | \(-0.494464\pi\) |
−0.857199 | + | 0.514986i | \(0.827797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.97378i | 0.139538i | 0.997563 | + | 0.0697692i | \(0.0222263\pi\) | ||||
−0.997563 | + | 0.0697692i | \(0.977774\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −1.90861 | + | 22.2628i | −0.0669380 | + | 0.780790i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.2674 | + | 12.2787i | −0.744052 | + | 0.429579i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.9123 | − | 3.29574i | 0.381306 | − | 0.115163i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −45.8143 | + | 26.4509i | −1.59893 | + | 0.923143i | −0.607237 | + | 0.794521i | \(0.707722\pi\) |
−0.991694 | + | 0.128623i | \(0.958944\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.18936 | − | 8.98823i | 0.180890 | − | 0.313310i | −0.761294 | − | 0.648407i | \(-0.775436\pi\) |
0.942184 | + | 0.335097i | \(0.108769\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 50.8249i | 1.76736i | 0.468095 | + | 0.883678i | \(0.344941\pi\) | ||||
−0.468095 | + | 0.883678i | \(0.655059\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.33850 | − | 0.772785i | −0.0464881 | − | 0.0268399i | 0.476576 | − | 0.879133i | \(-0.341878\pi\) |
−0.523064 | + | 0.852293i | \(0.675211\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.18077 | − | 17.4641i | −0.283788 | − | 0.605823i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −13.6171 | + | 18.2097i | −0.471805 | + | 0.630927i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.74010 | − | 9.63868i | −0.336667 | − | 0.333162i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −24.0738 | −0.831118 | −0.415559 | − | 0.909566i | \(-0.636414\pi\) | ||||
−0.415559 | + | 0.909566i | \(0.636414\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.43009 | 0.152762 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −32.0178 | − | 22.3360i | −1.10275 | − | 0.769293i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.2785 | − | 50.4680i | −0.868581 | − | 1.73410i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 28.6921 | − | 13.4403i | 0.984710 | − | 0.461271i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 8.05016 | + | 4.64776i | 0.275956 | + | 0.159323i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 16.6929i | − | 0.571555i | −0.958296 | − | 0.285777i | \(-0.907748\pi\) | ||
0.958296 | − | 0.285777i | \(-0.0922518\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.0858 | − | 24.3974i | 0.481163 | − | 0.833398i | −0.518604 | − | 0.855015i | \(-0.673548\pi\) |
0.999766 | + | 0.0216164i | \(0.00688126\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 48.0897 | − | 27.7646i | 1.64080 | − | 0.947315i | 0.660248 | − | 0.751048i | \(-0.270451\pi\) |
0.980550 | − | 0.196268i | \(-0.0628821\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.576922 | + | 0.730653i | −0.0196614 | + | 0.0249006i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.3774 | − | 14.6517i | 0.863857 | − | 0.498748i | −0.00144510 | − | 0.999999i | \(-0.500460\pi\) |
0.865302 | + | 0.501251i | \(0.167127\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −11.1285 | − | 0.954060i | −0.377944 | − | 0.0324016i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 66.0728i | 2.24137i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.82342 | − | 3.36215i | −0.197319 | − | 0.113922i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −29.7145 | + | 10.9328i | −1.00568 | + | 0.370018i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24.9574 | − | 43.2276i | −0.842753 | − | 1.45969i | −0.887558 | − | 0.460695i | \(-0.847600\pi\) |
0.0448051 | − | 0.998996i | \(-0.485733\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 16.8878 | − | 24.2080i | 0.569610 | − | 0.816515i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −57.0594 | −1.92238 | −0.961191 | − | 0.275885i | \(-0.911029\pi\) | ||||
−0.961191 | + | 0.275885i | \(0.911029\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 39.2846 | 1.32203 | 0.661017 | − | 0.750371i | \(-0.270125\pi\) | ||||
0.661017 | + | 0.750371i | \(0.270125\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.89144 | − | 13.6684i | −0.264969 | − | 0.458939i | 0.702587 | − | 0.711598i | \(-0.252028\pi\) |
−0.967555 | + | 0.252659i | \(0.918695\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.0775 | − | 1.30951i | −0.740454 | − | 0.0439197i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 50.3361 | − | 9.23823i | 1.68632 | − | 0.309492i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 62.6835 | + | 36.1904i | 2.09762 | + | 1.21106i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.53111 | + | 0.216995i | 0.0845113 | + | 0.00724524i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.53593 | − | 11.3206i | 0.217985 | − | 0.377562i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −29.9402 | + | 17.2860i | −0.997451 | + | 0.575879i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11.1107 | + | 14.0714i | −0.369742 | + | 0.468266i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −23.0343 | + | 39.8965i | −0.764840 | + | 1.32474i | 0.175490 | + | 0.984481i | \(0.443849\pi\) |
−0.940331 | + | 0.340261i | \(0.889484\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −44.2930 | − | 7.65081i | −1.46911 | − | 0.253761i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 26.6500i | − | 0.882953i | −0.897273 | − | 0.441477i | \(-0.854455\pi\) | ||
0.897273 | − | 0.441477i | \(-0.145545\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 49.9893 | + | 28.8614i | 1.65441 | + | 0.955172i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 19.6083 | + | 39.1476i | 0.647525 | + | 1.29277i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.65362 | − | 2.86415i | −0.0545478 | − | 0.0944795i | 0.837462 | − | 0.546495i | \(-0.184038\pi\) |
−0.892010 | + | 0.452016i | \(0.850705\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.0966 | − | 16.8100i | −0.794009 | − | 0.553909i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.55303 | 0.0511185 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.13617 | − | 7.61200i | −0.300071 | − | 0.250011i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11.3962 | + | 19.7388i | 0.373898 | + | 0.647610i | 0.990161 | − | 0.139930i | \(-0.0446878\pi\) |
−0.616264 | + | 0.787540i | \(0.711354\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 40.3810 | − | 17.3165i | 1.32343 | − | 0.567526i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.6163 | − | 52.5503i | −0.805902 | − | 1.72042i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 33.2636i | − | 1.08667i | −0.839515 | − | 0.543336i | \(-0.817161\pi\) | ||
0.839515 | − | 0.543336i | \(-0.182839\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.01266 | + | 11.8120i | −0.0330468 | + | 0.385471i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 23.1677 | − | 40.1277i | 0.755246 | − | 1.30812i | −0.190006 | − | 0.981783i | \(-0.560851\pi\) |
0.945252 | − | 0.326341i | \(-0.105816\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.179677 | + | 0.103737i | −0.00585109 | + | 0.00337813i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −36.1553 | + | 20.8743i | −1.17489 | + | 0.678322i | −0.954826 | − | 0.297164i | \(-0.903959\pi\) |
−0.220062 | + | 0.975486i | \(0.570626\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.49117 | + | 11.2430i | −0.210712 | + | 0.364965i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.92887 | − | 22.4991i | 0.0625480 | − | 0.729584i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.47667i | 0.177407i | 0.996058 | + | 0.0887034i | \(0.0282723\pi\) | ||||
−0.996058 | + | 0.0887034i | \(0.971728\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.7092 | + | 44.2094i | 0.669432 | + | 1.42909i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −22.8655 | − | 15.0739i | −0.738366 | − | 0.486761i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.0227 | − | 20.8239i | −0.387829 | − | 0.671740i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 22.0383 | + | 18.3617i | 0.710176 | + | 0.591698i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −60.2148 | −1.93638 | −0.968188 | − | 0.250223i | \(-0.919496\pi\) | ||||
−0.968188 | + | 0.250223i | \(0.919496\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −28.9631 | − | 20.2050i | −0.930428 | − | 0.649077i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.2636 | − | 22.9732i | −0.425650 | − | 0.737247i | 0.570831 | − | 0.821067i | \(-0.306621\pi\) |
−0.996481 | + | 0.0838207i | \(0.973288\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.43732 | − | 24.2321i | 0.0460782 | − | 0.776846i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −5.32572 | − | 3.07480i | −0.170385 | − | 0.0983717i | 0.412383 | − | 0.911011i | \(-0.364697\pi\) |
−0.582767 | + | 0.812639i | \(0.698030\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 85.6888i | − | 2.73863i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 41.6146 | + | 7.18816i | 1.32865 | + | 0.229500i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 22.7982 | − | 39.4877i | 0.727150 | − | 1.25946i | −0.230932 | − | 0.972970i | \(-0.574178\pi\) |
0.958083 | − | 0.286492i | \(-0.0924890\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 52.2914 | + | 7.62340i | 1.66445 | + | 0.242655i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.46033 | + | 1.99783i | −0.110032 | + | 0.0635271i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 11.0880 | − | 19.2049i | 0.352221 | − | 0.610065i | −0.634417 | − | 0.772991i | \(-0.718760\pi\) |
0.986638 | + | 0.162926i | \(0.0520931\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −11.5874 | − | 0.993401i | −0.367715 | − | 0.0315246i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 10.1188 | + | 5.84211i | 0.320466 | + | 0.185021i | 0.651600 | − | 0.758562i | \(-0.274098\pi\) |
−0.331134 | + | 0.943584i | \(0.607431\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.4798 | + | 45.6189i | 0.394844 | + | 1.44332i |
(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 | 2100.2.bi.l.101.3 | ✓ | 16 | |
3.2 | odd | 2 | inner | 2100.2.bi.l.101.7 | yes | 16 | |
5.2 | odd | 4 | 2100.2.bo.i.1949.12 | 32 | |||
5.3 | odd | 4 | 2100.2.bo.i.1949.5 | 32 | |||
5.4 | even | 2 | 2100.2.bi.m.101.6 | yes | 16 | ||
7.5 | odd | 6 | inner | 2100.2.bi.l.1601.7 | yes | 16 | |
15.2 | even | 4 | 2100.2.bo.i.1949.3 | 32 | |||
15.8 | even | 4 | 2100.2.bo.i.1949.14 | 32 | |||
15.14 | odd | 2 | 2100.2.bi.m.101.2 | yes | 16 | ||
21.5 | even | 6 | inner | 2100.2.bi.l.1601.3 | yes | 16 | |
35.12 | even | 12 | 2100.2.bo.i.1349.14 | 32 | |||
35.19 | odd | 6 | 2100.2.bi.m.1601.2 | yes | 16 | ||
35.33 | even | 12 | 2100.2.bo.i.1349.3 | 32 | |||
105.47 | odd | 12 | 2100.2.bo.i.1349.5 | 32 | |||
105.68 | odd | 12 | 2100.2.bo.i.1349.12 | 32 | |||
105.89 | even | 6 | 2100.2.bi.m.1601.6 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.bi.l.101.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
2100.2.bi.l.101.7 | yes | 16 | 3.2 | odd | 2 | inner | |
2100.2.bi.l.1601.3 | yes | 16 | 21.5 | even | 6 | inner | |
2100.2.bi.l.1601.7 | yes | 16 | 7.5 | odd | 6 | inner | |
2100.2.bi.m.101.2 | yes | 16 | 15.14 | odd | 2 | ||
2100.2.bi.m.101.6 | yes | 16 | 5.4 | even | 2 | ||
2100.2.bi.m.1601.2 | yes | 16 | 35.19 | odd | 6 | ||
2100.2.bi.m.1601.6 | yes | 16 | 105.89 | even | 6 | ||
2100.2.bo.i.1349.3 | 32 | 35.33 | even | 12 | |||
2100.2.bo.i.1349.5 | 32 | 105.47 | odd | 12 | |||
2100.2.bo.i.1349.12 | 32 | 105.68 | odd | 12 | |||
2100.2.bo.i.1349.14 | 32 | 35.12 | even | 12 | |||
2100.2.bo.i.1949.3 | 32 | 15.2 | even | 4 | |||
2100.2.bo.i.1949.5 | 32 | 5.3 | odd | 4 | |||
2100.2.bo.i.1949.12 | 32 | 5.2 | odd | 4 | |||
2100.2.bo.i.1949.14 | 32 | 15.8 | even | 4 |