Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(298,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("429.298");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.b (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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} + 23x^{12} + 201x^{10} + 835x^{8} + 1695x^{6} + 1565x^{4} + 511x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 298.5 | ||
Root | \(-1.36814i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 429.298 |
Dual form | 429.2.b.b.298.10 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.36814i | − | 0.967420i | −0.875228 | − | 0.483710i | \(-0.839289\pi\) | ||
0.875228 | − | 0.483710i | \(-0.160711\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0.128197 | 0.0640985 | ||||||||
\(5\) | 2.18365i | 0.976558i | 0.872688 | + | 0.488279i | \(0.162375\pi\) | ||||
−0.872688 | + | 0.488279i | \(0.837625\pi\) | |||||||
\(6\) | − | 1.36814i | − | 0.558540i | ||||||
\(7\) | 4.27070i | 1.61417i | 0.590433 | + | 0.807087i | \(0.298957\pi\) | ||||
−0.590433 | + | 0.807087i | \(0.701043\pi\) | |||||||
\(8\) | − | 2.91167i | − | 1.02943i | ||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.98753 | 0.944741 | ||||||||
\(11\) | − | 1.00000i | − | 0.301511i | ||||||
\(12\) | 0.128197 | 0.0370073 | ||||||||
\(13\) | −0.922450 | + | 3.48555i | −0.255842 | + | 0.966719i | ||||
\(14\) | 5.84291 | 1.56158 | ||||||||
\(15\) | 2.18365i | 0.563816i | ||||||||
\(16\) | −3.72717 | −0.931793 | ||||||||
\(17\) | 3.79173 | 0.919629 | 0.459815 | − | 0.888015i | \(-0.347916\pi\) | ||||
0.459815 | + | 0.888015i | \(0.347916\pi\) | |||||||
\(18\) | − | 1.36814i | − | 0.322473i | ||||||
\(19\) | − | 3.17118i | − | 0.727519i | −0.931493 | − | 0.363760i | \(-0.881493\pi\) | ||
0.931493 | − | 0.363760i | \(-0.118507\pi\) | |||||||
\(20\) | 0.279937i | 0.0625959i | ||||||||
\(21\) | 4.27070i | 0.931943i | ||||||||
\(22\) | −1.36814 | −0.291688 | ||||||||
\(23\) | 4.94243 | 1.03057 | 0.515284 | − | 0.857020i | \(-0.327687\pi\) | ||||
0.515284 | + | 0.857020i | \(0.327687\pi\) | |||||||
\(24\) | − | 2.91167i | − | 0.594342i | ||||||
\(25\) | 0.231676 | 0.0463352 | ||||||||
\(26\) | 4.76872 | + | 1.26204i | 0.935223 | + | 0.247506i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.547491i | 0.103466i | ||||||||
\(29\) | −7.35483 | −1.36576 | −0.682879 | − | 0.730531i | \(-0.739272\pi\) | ||||
−0.682879 | + | 0.730531i | \(0.739272\pi\) | |||||||
\(30\) | 2.98753 | 0.545447 | ||||||||
\(31\) | 0.0727448i | 0.0130654i | 0.999979 | + | 0.00653268i | \(0.00207943\pi\) | ||||
−0.999979 | + | 0.00653268i | \(0.997921\pi\) | |||||||
\(32\) | − | 0.724050i | − | 0.127995i | ||||||
\(33\) | − | 1.00000i | − | 0.174078i | ||||||
\(34\) | − | 5.18761i | − | 0.889668i | ||||||
\(35\) | −9.32571 | −1.57633 | ||||||||
\(36\) | 0.128197 | 0.0213662 | ||||||||
\(37\) | − | 3.66658i | − | 0.602782i | −0.953501 | − | 0.301391i | \(-0.902549\pi\) | ||
0.953501 | − | 0.301391i | \(-0.0974510\pi\) | |||||||
\(38\) | −4.33862 | −0.703817 | ||||||||
\(39\) | −0.922450 | + | 3.48555i | −0.147710 | + | 0.558135i | ||||
\(40\) | 6.35806 | 1.00530 | ||||||||
\(41\) | − | 4.16722i | − | 0.650811i | −0.945575 | − | 0.325405i | \(-0.894499\pi\) | ||
0.945575 | − | 0.325405i | \(-0.105501\pi\) | |||||||
\(42\) | 5.84291 | 0.901581 | ||||||||
\(43\) | −7.11697 | −1.08533 | −0.542664 | − | 0.839950i | \(-0.682584\pi\) | ||||
−0.542664 | + | 0.839950i | \(0.682584\pi\) | |||||||
\(44\) | − | 0.128197i | − | 0.0193264i | ||||||
\(45\) | 2.18365i | 0.325519i | ||||||||
\(46\) | − | 6.76193i | − | 0.996992i | ||||||
\(47\) | − | 11.6337i | − | 1.69695i | −0.529232 | − | 0.848477i | \(-0.677520\pi\) | ||
0.529232 | − | 0.848477i | \(-0.322480\pi\) | |||||||
\(48\) | −3.72717 | −0.537971 | ||||||||
\(49\) | −11.2389 | −1.60556 | ||||||||
\(50\) | − | 0.316965i | − | 0.0448256i | ||||||
\(51\) | 3.79173 | 0.530948 | ||||||||
\(52\) | −0.118255 | + | 0.446838i | −0.0163991 | + | 0.0619652i | ||||
\(53\) | 5.11268 | 0.702281 | 0.351140 | − | 0.936323i | \(-0.385794\pi\) | ||||
0.351140 | + | 0.936323i | \(0.385794\pi\) | |||||||
\(54\) | − | 1.36814i | − | 0.186180i | ||||||
\(55\) | 2.18365 | 0.294443 | ||||||||
\(56\) | 12.4349 | 1.66168 | ||||||||
\(57\) | − | 3.17118i | − | 0.420034i | ||||||
\(58\) | 10.0624i | 1.32126i | ||||||||
\(59\) | − | 5.62765i | − | 0.732658i | −0.930485 | − | 0.366329i | \(-0.880614\pi\) | ||
0.930485 | − | 0.366329i | \(-0.119386\pi\) | |||||||
\(60\) | 0.279937i | 0.0361398i | ||||||||
\(61\) | −5.40800 | −0.692424 | −0.346212 | − | 0.938156i | \(-0.612532\pi\) | ||||
−0.346212 | + | 0.938156i | \(0.612532\pi\) | |||||||
\(62\) | 0.0995250 | 0.0126397 | ||||||||
\(63\) | 4.27070i | 0.538058i | ||||||||
\(64\) | −8.44494 | −1.05562 | ||||||||
\(65\) | −7.61123 | − | 2.01431i | −0.944057 | − | 0.249844i | ||||
\(66\) | −1.36814 | −0.168406 | ||||||||
\(67\) | 10.1145i | 1.23569i | 0.786302 | + | 0.617843i | \(0.211993\pi\) | ||||
−0.786302 | + | 0.617843i | \(0.788007\pi\) | |||||||
\(68\) | 0.486088 | 0.0589469 | ||||||||
\(69\) | 4.94243 | 0.594998 | ||||||||
\(70\) | 12.7589i | 1.52498i | ||||||||
\(71\) | 9.62239i | 1.14197i | 0.820961 | + | 0.570984i | \(0.193438\pi\) | ||||
−0.820961 | + | 0.570984i | \(0.806562\pi\) | |||||||
\(72\) | − | 2.91167i | − | 0.343143i | ||||||
\(73\) | − | 6.44736i | − | 0.754607i | −0.926090 | − | 0.377303i | \(-0.876851\pi\) | ||
0.926090 | − | 0.377303i | \(-0.123149\pi\) | |||||||
\(74\) | −5.01639 | −0.583144 | ||||||||
\(75\) | 0.231676 | 0.0267516 | ||||||||
\(76\) | − | 0.406536i | − | 0.0466329i | ||||||
\(77\) | 4.27070 | 0.486692 | ||||||||
\(78\) | 4.76872 | + | 1.26204i | 0.539951 | + | 0.142898i | ||||
\(79\) | 10.1209 | 1.13869 | 0.569347 | − | 0.822097i | \(-0.307196\pi\) | ||||
0.569347 | + | 0.822097i | \(0.307196\pi\) | |||||||
\(80\) | − | 8.13884i | − | 0.909949i | ||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −5.70134 | −0.629607 | ||||||||
\(83\) | − | 7.80918i | − | 0.857169i | −0.903502 | − | 0.428585i | \(-0.859012\pi\) | ||
0.903502 | − | 0.428585i | \(-0.140988\pi\) | |||||||
\(84\) | 0.547491i | 0.0597362i | ||||||||
\(85\) | 8.27981i | 0.898071i | ||||||||
\(86\) | 9.73700i | 1.04997i | ||||||||
\(87\) | −7.35483 | −0.788521 | ||||||||
\(88\) | −2.91167 | −0.310385 | ||||||||
\(89\) | − | 2.87912i | − | 0.305187i | −0.988289 | − | 0.152593i | \(-0.951238\pi\) | ||
0.988289 | − | 0.152593i | \(-0.0487624\pi\) | |||||||
\(90\) | 2.98753 | 0.314914 | ||||||||
\(91\) | −14.8858 | − | 3.93951i | −1.56045 | − | 0.412973i | ||||
\(92\) | 0.633605 | 0.0660579 | ||||||||
\(93\) | 0.0727448i | 0.00754329i | ||||||||
\(94\) | −15.9166 | −1.64167 | ||||||||
\(95\) | 6.92475 | 0.710465 | ||||||||
\(96\) | − | 0.724050i | − | 0.0738980i | ||||||
\(97\) | 3.79281i | 0.385101i | 0.981287 | + | 0.192551i | \(0.0616760\pi\) | ||||
−0.981287 | + | 0.192551i | \(0.938324\pi\) | |||||||
\(98\) | 15.3764i | 1.55325i | ||||||||
\(99\) | − | 1.00000i | − | 0.100504i | ||||||
\(100\) | 0.0297002 | 0.00297002 | ||||||||
\(101\) | −12.8641 | −1.28003 | −0.640014 | − | 0.768363i | \(-0.721072\pi\) | ||||
−0.640014 | + | 0.768363i | \(0.721072\pi\) | |||||||
\(102\) | − | 5.18761i | − | 0.513650i | ||||||
\(103\) | 16.9975 | 1.67482 | 0.837409 | − | 0.546577i | \(-0.184070\pi\) | ||||
0.837409 | + | 0.546577i | \(0.184070\pi\) | |||||||
\(104\) | 10.1488 | + | 2.68587i | 0.995169 | + | 0.263371i | ||||
\(105\) | −9.32571 | −0.910096 | ||||||||
\(106\) | − | 6.99486i | − | 0.679400i | ||||||
\(107\) | −12.6819 | −1.22600 | −0.613001 | − | 0.790082i | \(-0.710038\pi\) | ||||
−0.613001 | + | 0.790082i | \(0.710038\pi\) | |||||||
\(108\) | 0.128197 | 0.0123358 | ||||||||
\(109\) | 8.89607i | 0.852089i | 0.904702 | + | 0.426045i | \(0.140093\pi\) | ||||
−0.904702 | + | 0.426045i | \(0.859907\pi\) | |||||||
\(110\) | − | 2.98753i | − | 0.284850i | ||||||
\(111\) | − | 3.66658i | − | 0.348017i | ||||||
\(112\) | − | 15.9176i | − | 1.50408i | ||||||
\(113\) | 1.36552 | 0.128457 | 0.0642287 | − | 0.997935i | \(-0.479541\pi\) | ||||
0.0642287 | + | 0.997935i | \(0.479541\pi\) | |||||||
\(114\) | −4.33862 | −0.406349 | ||||||||
\(115\) | 10.7925i | 1.00641i | ||||||||
\(116\) | −0.942868 | −0.0875431 | ||||||||
\(117\) | −0.922450 | + | 3.48555i | −0.0852805 | + | 0.322240i | ||||
\(118\) | −7.69941 | −0.708788 | ||||||||
\(119\) | 16.1933i | 1.48444i | ||||||||
\(120\) | 6.35806 | 0.580409 | ||||||||
\(121\) | −1.00000 | −0.0909091 | ||||||||
\(122\) | 7.39890i | 0.669865i | ||||||||
\(123\) | − | 4.16722i | − | 0.375746i | ||||||
\(124\) | 0.00932567i | 0.000837470i | ||||||||
\(125\) | 11.4241i | 1.02181i | ||||||||
\(126\) | 5.84291 | 0.520528 | ||||||||
\(127\) | −10.4027 | −0.923093 | −0.461546 | − | 0.887116i | \(-0.652705\pi\) | ||||
−0.461546 | + | 0.887116i | \(0.652705\pi\) | |||||||
\(128\) | 10.1058i | 0.893231i | ||||||||
\(129\) | −7.11697 | −0.626614 | ||||||||
\(130\) | −2.75585 | + | 10.4132i | −0.241704 | + | 0.913299i | ||||
\(131\) | −12.0678 | −1.05437 | −0.527183 | − | 0.849752i | \(-0.676752\pi\) | ||||
−0.527183 | + | 0.849752i | \(0.676752\pi\) | |||||||
\(132\) | − | 0.128197i | − | 0.0111581i | ||||||
\(133\) | 13.5432 | 1.17434 | ||||||||
\(134\) | 13.8381 | 1.19543 | ||||||||
\(135\) | 2.18365i | 0.187939i | ||||||||
\(136\) | − | 11.0403i | − | 0.946694i | ||||||
\(137\) | − | 3.96114i | − | 0.338423i | −0.985580 | − | 0.169211i | \(-0.945878\pi\) | ||
0.985580 | − | 0.169211i | \(-0.0541221\pi\) | |||||||
\(138\) | − | 6.76193i | − | 0.575613i | ||||||
\(139\) | 18.2437 | 1.54741 | 0.773703 | − | 0.633548i | \(-0.218402\pi\) | ||||
0.773703 | + | 0.633548i | \(0.218402\pi\) | |||||||
\(140\) | −1.19553 | −0.101041 | ||||||||
\(141\) | − | 11.6337i | − | 0.979737i | ||||||
\(142\) | 13.1648 | 1.10476 | ||||||||
\(143\) | 3.48555 | + | 0.922450i | 0.291477 | + | 0.0771391i | ||||
\(144\) | −3.72717 | −0.310598 | ||||||||
\(145\) | − | 16.0604i | − | 1.33374i | ||||||
\(146\) | −8.82089 | −0.730022 | ||||||||
\(147\) | −11.2389 | −0.926968 | ||||||||
\(148\) | − | 0.470045i | − | 0.0386375i | ||||||
\(149\) | 13.8984i | 1.13860i | 0.822131 | + | 0.569299i | \(0.192785\pi\) | ||||
−0.822131 | + | 0.569299i | \(0.807215\pi\) | |||||||
\(150\) | − | 0.316965i | − | 0.0258801i | ||||||
\(151\) | 2.29739i | 0.186959i | 0.995621 | + | 0.0934795i | \(0.0297990\pi\) | ||||
−0.995621 | + | 0.0934795i | \(0.970201\pi\) | |||||||
\(152\) | −9.23344 | −0.748931 | ||||||||
\(153\) | 3.79173 | 0.306543 | ||||||||
\(154\) | − | 5.84291i | − | 0.470835i | ||||||
\(155\) | −0.158849 | −0.0127591 | ||||||||
\(156\) | −0.118255 | + | 0.446838i | −0.00946801 | + | 0.0357756i | ||||
\(157\) | −15.6293 | −1.24736 | −0.623678 | − | 0.781682i | \(-0.714362\pi\) | ||||
−0.623678 | + | 0.781682i | \(0.714362\pi\) | |||||||
\(158\) | − | 13.8468i | − | 1.10160i | ||||||
\(159\) | 5.11268 | 0.405462 | ||||||||
\(160\) | 1.58107 | 0.124995 | ||||||||
\(161\) | 21.1076i | 1.66351i | ||||||||
\(162\) | − | 1.36814i | − | 0.107491i | ||||||
\(163\) | − | 1.25583i | − | 0.0983643i | −0.998790 | − | 0.0491822i | \(-0.984339\pi\) | ||
0.998790 | − | 0.0491822i | \(-0.0156615\pi\) | |||||||
\(164\) | − | 0.534226i | − | 0.0417160i | ||||||
\(165\) | 2.18365 | 0.169997 | ||||||||
\(166\) | −10.6840 | −0.829243 | ||||||||
\(167\) | − | 17.3823i | − | 1.34509i | −0.740058 | − | 0.672543i | \(-0.765202\pi\) | ||
0.740058 | − | 0.672543i | \(-0.234798\pi\) | |||||||
\(168\) | 12.4349 | 0.959371 | ||||||||
\(169\) | −11.2982 | − | 6.43050i | −0.869090 | − | 0.494654i | ||||
\(170\) | 11.3279 | 0.868812 | ||||||||
\(171\) | − | 3.17118i | − | 0.242506i | ||||||
\(172\) | −0.912375 | −0.0695679 | ||||||||
\(173\) | 12.0899 | 0.919178 | 0.459589 | − | 0.888132i | \(-0.347997\pi\) | ||||
0.459589 | + | 0.888132i | \(0.347997\pi\) | |||||||
\(174\) | 10.0624i | 0.762831i | ||||||||
\(175\) | 0.989418i | 0.0747930i | ||||||||
\(176\) | 3.72717i | 0.280946i | ||||||||
\(177\) | − | 5.62765i | − | 0.423000i | ||||||
\(178\) | −3.93904 | −0.295244 | ||||||||
\(179\) | 5.13094 | 0.383504 | 0.191752 | − | 0.981443i | \(-0.438583\pi\) | ||||
0.191752 | + | 0.981443i | \(0.438583\pi\) | |||||||
\(180\) | 0.279937i | 0.0208653i | ||||||||
\(181\) | 23.3170 | 1.73314 | 0.866568 | − | 0.499059i | \(-0.166321\pi\) | ||||
0.866568 | + | 0.499059i | \(0.166321\pi\) | |||||||
\(182\) | −5.38979 | + | 20.3658i | −0.399518 | + | 1.50961i | ||||
\(183\) | −5.40800 | −0.399771 | ||||||||
\(184\) | − | 14.3907i | − | 1.06090i | ||||||
\(185\) | 8.00653 | 0.588652 | ||||||||
\(186\) | 0.0995250 | 0.00729753 | ||||||||
\(187\) | − | 3.79173i | − | 0.277279i | ||||||
\(188\) | − | 1.49141i | − | 0.108772i | ||||||
\(189\) | 4.27070i | 0.310648i | ||||||||
\(190\) | − | 9.47402i | − | 0.687318i | ||||||
\(191\) | 11.1231 | 0.804838 | 0.402419 | − | 0.915456i | \(-0.368169\pi\) | ||||
0.402419 | + | 0.915456i | \(0.368169\pi\) | |||||||
\(192\) | −8.44494 | −0.609461 | ||||||||
\(193\) | − | 23.1664i | − | 1.66756i | −0.552099 | − | 0.833778i | \(-0.686173\pi\) | ||
0.552099 | − | 0.833778i | \(-0.313827\pi\) | |||||||
\(194\) | 5.18909 | 0.372555 | ||||||||
\(195\) | −7.61123 | − | 2.01431i | −0.545051 | − | 0.144248i | ||||
\(196\) | −1.44079 | −0.102914 | ||||||||
\(197\) | 9.18435i | 0.654358i | 0.944962 | + | 0.327179i | \(0.106098\pi\) | ||||
−0.944962 | + | 0.327179i | \(0.893902\pi\) | |||||||
\(198\) | −1.36814 | −0.0972294 | ||||||||
\(199\) | −6.38937 | −0.452930 | −0.226465 | − | 0.974019i | \(-0.572717\pi\) | ||||
−0.226465 | + | 0.974019i | \(0.572717\pi\) | |||||||
\(200\) | − | 0.674563i | − | 0.0476988i | ||||||
\(201\) | 10.1145i | 0.713423i | ||||||||
\(202\) | 17.5999i | 1.23833i | ||||||||
\(203\) | − | 31.4103i | − | 2.20457i | ||||||
\(204\) | 0.486088 | 0.0340330 | ||||||||
\(205\) | 9.09975 | 0.635554 | ||||||||
\(206\) | − | 23.2550i | − | 1.62025i | ||||||
\(207\) | 4.94243 | 0.343522 | ||||||||
\(208\) | 3.43813 | − | 12.9913i | 0.238391 | − | 0.900782i | ||||
\(209\) | −3.17118 | −0.219355 | ||||||||
\(210\) | 12.7589i | 0.880446i | ||||||||
\(211\) | 22.4436 | 1.54508 | 0.772541 | − | 0.634965i | \(-0.218985\pi\) | ||||
0.772541 | + | 0.634965i | \(0.218985\pi\) | |||||||
\(212\) | 0.655431 | 0.0450152 | ||||||||
\(213\) | 9.62239i | 0.659315i | ||||||||
\(214\) | 17.3505i | 1.18606i | ||||||||
\(215\) | − | 15.5410i | − | 1.05989i | ||||||
\(216\) | − | 2.91167i | − | 0.198114i | ||||||
\(217\) | −0.310671 | −0.0210897 | ||||||||
\(218\) | 12.1711 | 0.824328 | ||||||||
\(219\) | − | 6.44736i | − | 0.435673i | ||||||
\(220\) | 0.279937 | 0.0188734 | ||||||||
\(221\) | −3.49768 | + | 13.2163i | −0.235279 | + | 0.889023i | ||||
\(222\) | −5.01639 | −0.336678 | ||||||||
\(223\) | − | 16.5344i | − | 1.10722i | −0.832775 | − | 0.553611i | \(-0.813249\pi\) | ||
0.832775 | − | 0.553611i | \(-0.186751\pi\) | |||||||
\(224\) | 3.09220 | 0.206606 | ||||||||
\(225\) | 0.231676 | 0.0154451 | ||||||||
\(226\) | − | 1.86822i | − | 0.124272i | ||||||
\(227\) | − | 19.9826i | − | 1.32630i | −0.748489 | − | 0.663148i | \(-0.769220\pi\) | ||
0.748489 | − | 0.663148i | \(-0.230780\pi\) | |||||||
\(228\) | − | 0.406536i | − | 0.0269235i | ||||||
\(229\) | − | 15.8459i | − | 1.04713i | −0.851986 | − | 0.523564i | \(-0.824602\pi\) | ||
0.851986 | − | 0.523564i | \(-0.175398\pi\) | |||||||
\(230\) | 14.7657 | 0.973620 | ||||||||
\(231\) | 4.27070 | 0.280992 | ||||||||
\(232\) | 21.4148i | 1.40595i | ||||||||
\(233\) | −15.9195 | −1.04292 | −0.521460 | − | 0.853276i | \(-0.674612\pi\) | ||||
−0.521460 | + | 0.853276i | \(0.674612\pi\) | |||||||
\(234\) | 4.76872 | + | 1.26204i | 0.311741 | + | 0.0825021i | ||||
\(235\) | 25.4040 | 1.65717 | ||||||||
\(236\) | − | 0.721449i | − | 0.0469623i | ||||||
\(237\) | 10.1209 | 0.657425 | ||||||||
\(238\) | 22.1547 | 1.43608 | ||||||||
\(239\) | 16.9898i | 1.09898i | 0.835500 | + | 0.549491i | \(0.185178\pi\) | ||||
−0.835500 | + | 0.549491i | \(0.814822\pi\) | |||||||
\(240\) | − | 8.13884i | − | 0.525360i | ||||||
\(241\) | 21.9883i | 1.41639i | 0.706015 | + | 0.708197i | \(0.250491\pi\) | ||||
−0.706015 | + | 0.708197i | \(0.749509\pi\) | |||||||
\(242\) | 1.36814i | 0.0879473i | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −0.693290 | −0.0443834 | ||||||||
\(245\) | − | 24.5418i | − | 1.56792i | ||||||
\(246\) | −5.70134 | −0.363504 | ||||||||
\(247\) | 11.0533 | + | 2.92526i | 0.703307 | + | 0.186130i | ||||
\(248\) | 0.211809 | 0.0134499 | ||||||||
\(249\) | − | 7.80918i | − | 0.494887i | ||||||
\(250\) | 15.6298 | 0.988516 | ||||||||
\(251\) | −11.9461 | −0.754029 | −0.377015 | − | 0.926207i | \(-0.623049\pi\) | ||||
−0.377015 | + | 0.926207i | \(0.623049\pi\) | |||||||
\(252\) | 0.547491i | 0.0344887i | ||||||||
\(253\) | − | 4.94243i | − | 0.310728i | ||||||
\(254\) | 14.2324i | 0.893019i | ||||||||
\(255\) | 8.27981i | 0.518502i | ||||||||
\(256\) | −3.06382 | −0.191489 | ||||||||
\(257\) | −28.3671 | −1.76949 | −0.884746 | − | 0.466074i | \(-0.845668\pi\) | ||||
−0.884746 | + | 0.466074i | \(0.845668\pi\) | |||||||
\(258\) | 9.73700i | 0.606199i | ||||||||
\(259\) | 15.6589 | 0.972995 | ||||||||
\(260\) | −0.975737 | − | 0.258228i | −0.0605126 | − | 0.0160146i | ||||
\(261\) | −7.35483 | −0.455253 | ||||||||
\(262\) | 16.5104i | 1.02001i | ||||||||
\(263\) | −1.37798 | −0.0849699 | −0.0424849 | − | 0.999097i | \(-0.513527\pi\) | ||||
−0.0424849 | + | 0.999097i | \(0.513527\pi\) | |||||||
\(264\) | −2.91167 | −0.179201 | ||||||||
\(265\) | 11.1643i | 0.685818i | ||||||||
\(266\) | − | 18.5289i | − | 1.13608i | ||||||
\(267\) | − | 2.87912i | − | 0.176200i | ||||||
\(268\) | 1.29665i | 0.0792056i | ||||||||
\(269\) | −14.6274 | −0.891847 | −0.445923 | − | 0.895071i | \(-0.647125\pi\) | ||||
−0.445923 | + | 0.895071i | \(0.647125\pi\) | |||||||
\(270\) | 2.98753 | 0.181816 | ||||||||
\(271\) | − | 13.3040i | − | 0.808158i | −0.914724 | − | 0.404079i | \(-0.867592\pi\) | ||
0.914724 | − | 0.404079i | \(-0.132408\pi\) | |||||||
\(272\) | −14.1324 | −0.856904 | ||||||||
\(273\) | −14.8858 | − | 3.93951i | −0.900927 | − | 0.238430i | ||||
\(274\) | −5.41938 | −0.327397 | ||||||||
\(275\) | − | 0.231676i | − | 0.0139706i | ||||||
\(276\) | 0.633605 | 0.0381385 | ||||||||
\(277\) | −22.1581 | −1.33135 | −0.665676 | − | 0.746241i | \(-0.731857\pi\) | ||||
−0.665676 | + | 0.746241i | \(0.731857\pi\) | |||||||
\(278\) | − | 24.9598i | − | 1.49699i | ||||||
\(279\) | 0.0727448i | 0.00435512i | ||||||||
\(280\) | 27.1534i | 1.62273i | ||||||||
\(281\) | 2.12589i | 0.126820i | 0.997988 | + | 0.0634100i | \(0.0201976\pi\) | ||||
−0.997988 | + | 0.0634100i | \(0.979802\pi\) | |||||||
\(282\) | −15.9166 | −0.947817 | ||||||||
\(283\) | 31.1036 | 1.84892 | 0.924458 | − | 0.381283i | \(-0.124518\pi\) | ||||
0.924458 | + | 0.381283i | \(0.124518\pi\) | |||||||
\(284\) | 1.23356i | 0.0731984i | ||||||||
\(285\) | 6.92475 | 0.410187 | ||||||||
\(286\) | 1.26204 | − | 4.76872i | 0.0746259 | − | 0.281980i | ||||
\(287\) | 17.7970 | 1.05052 | ||||||||
\(288\) | − | 0.724050i | − | 0.0426650i | ||||||
\(289\) | −2.62279 | −0.154282 | ||||||||
\(290\) | −21.9728 | −1.29029 | ||||||||
\(291\) | 3.79281i | 0.222338i | ||||||||
\(292\) | − | 0.826533i | − | 0.0483692i | ||||||
\(293\) | − | 16.9009i | − | 0.987363i | −0.869643 | − | 0.493682i | \(-0.835651\pi\) | ||
0.869643 | − | 0.493682i | \(-0.164349\pi\) | |||||||
\(294\) | 15.3764i | 0.896767i | ||||||||
\(295\) | 12.2888 | 0.715483 | ||||||||
\(296\) | −10.6759 | −0.620523 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | 19.0149 | 1.10150 | ||||||||
\(299\) | −4.55914 | + | 17.2271i | −0.263662 | + | 0.996269i | ||||
\(300\) | 0.0297002 | 0.00171474 | ||||||||
\(301\) | − | 30.3945i | − | 1.75191i | ||||||
\(302\) | 3.14315 | 0.180868 | ||||||||
\(303\) | −12.8641 | −0.739025 | ||||||||
\(304\) | 11.8195i | 0.677897i | ||||||||
\(305\) | − | 11.8092i | − | 0.676192i | ||||||
\(306\) | − | 5.18761i | − | 0.296556i | ||||||
\(307\) | 24.6110i | 1.40462i | 0.711869 | + | 0.702312i | \(0.247849\pi\) | ||||
−0.711869 | + | 0.702312i | \(0.752151\pi\) | |||||||
\(308\) | 0.547491 | 0.0311962 | ||||||||
\(309\) | 16.9975 | 0.966956 | ||||||||
\(310\) | 0.217328i | 0.0123434i | ||||||||
\(311\) | 1.00504 | 0.0569904 | 0.0284952 | − | 0.999594i | \(-0.490928\pi\) | ||||
0.0284952 | + | 0.999594i | \(0.490928\pi\) | |||||||
\(312\) | 10.1488 | + | 2.68587i | 0.574561 | + | 0.152057i | ||||
\(313\) | −13.8744 | −0.784227 | −0.392114 | − | 0.919917i | \(-0.628256\pi\) | ||||
−0.392114 | + | 0.919917i | \(0.628256\pi\) | |||||||
\(314\) | 21.3831i | 1.20672i | ||||||||
\(315\) | −9.32571 | −0.525444 | ||||||||
\(316\) | 1.29747 | 0.0729886 | ||||||||
\(317\) | 15.6405i | 0.878460i | 0.898375 | + | 0.439230i | \(0.144749\pi\) | ||||
−0.898375 | + | 0.439230i | \(0.855251\pi\) | |||||||
\(318\) | − | 6.99486i | − | 0.392252i | ||||||
\(319\) | 7.35483i | 0.411792i | ||||||||
\(320\) | − | 18.4408i | − | 1.03087i | ||||||
\(321\) | −12.6819 | −0.707832 | ||||||||
\(322\) | 28.8782 | 1.60932 | ||||||||
\(323\) | − | 12.0243i | − | 0.669048i | ||||||
\(324\) | 0.128197 | 0.00712206 | ||||||||
\(325\) | −0.213709 | + | 0.807519i | −0.0118545 | + | 0.0447931i | ||||
\(326\) | −1.71815 | −0.0951596 | ||||||||
\(327\) | 8.89607i | 0.491954i | ||||||||
\(328\) | −12.1336 | −0.669964 | ||||||||
\(329\) | 49.6842 | 2.73918 | ||||||||
\(330\) | − | 2.98753i | − | 0.164458i | ||||||
\(331\) | 23.1426i | 1.27203i | 0.771675 | + | 0.636017i | \(0.219419\pi\) | ||||
−0.771675 | + | 0.636017i | \(0.780581\pi\) | |||||||
\(332\) | − | 1.00111i | − | 0.0549433i | ||||||
\(333\) | − | 3.66658i | − | 0.200927i | ||||||
\(334\) | −23.7814 | −1.30126 | ||||||||
\(335\) | −22.0866 | −1.20672 | ||||||||
\(336\) | − | 15.9176i | − | 0.868378i | ||||||
\(337\) | −15.1946 | −0.827705 | −0.413853 | − | 0.910344i | \(-0.635817\pi\) | ||||
−0.413853 | + | 0.910344i | \(0.635817\pi\) | |||||||
\(338\) | −8.79781 | + | 15.4575i | −0.478538 | + | 0.840775i | ||||
\(339\) | 1.36552 | 0.0741650 | ||||||||
\(340\) | 1.06145i | 0.0575650i | ||||||||
\(341\) | 0.0727448 | 0.00393935 | ||||||||
\(342\) | −4.33862 | −0.234606 | ||||||||
\(343\) | − | 18.1030i | − | 0.977472i | ||||||
\(344\) | 20.7223i | 1.11727i | ||||||||
\(345\) | 10.7925i | 0.581050i | ||||||||
\(346\) | − | 16.5407i | − | 0.889231i | ||||||
\(347\) | 16.6545 | 0.894061 | 0.447030 | − | 0.894519i | \(-0.352482\pi\) | ||||
0.447030 | + | 0.894519i | \(0.352482\pi\) | |||||||
\(348\) | −0.942868 | −0.0505430 | ||||||||
\(349\) | 29.1080i | 1.55812i | 0.626952 | + | 0.779058i | \(0.284302\pi\) | ||||
−0.626952 | + | 0.779058i | \(0.715698\pi\) | |||||||
\(350\) | 1.35366 | 0.0723562 | ||||||||
\(351\) | −0.922450 | + | 3.48555i | −0.0492367 | + | 0.186045i | ||||
\(352\) | −0.724050 | −0.0385920 | ||||||||
\(353\) | 29.1723i | 1.55268i | 0.630312 | + | 0.776342i | \(0.282927\pi\) | ||||
−0.630312 | + | 0.776342i | \(0.717073\pi\) | |||||||
\(354\) | −7.69941 | −0.409219 | ||||||||
\(355\) | −21.0119 | −1.11520 | ||||||||
\(356\) | − | 0.369095i | − | 0.0195620i | ||||||
\(357\) | 16.1933i | 0.857043i | ||||||||
\(358\) | − | 7.01983i | − | 0.371010i | ||||||
\(359\) | 18.0809i | 0.954271i | 0.878830 | + | 0.477136i | \(0.158325\pi\) | ||||
−0.878830 | + | 0.477136i | \(0.841675\pi\) | |||||||
\(360\) | 6.35806 | 0.335099 | ||||||||
\(361\) | 8.94359 | 0.470715 | ||||||||
\(362\) | − | 31.9008i | − | 1.67667i | ||||||
\(363\) | −1.00000 | −0.0524864 | ||||||||
\(364\) | −1.90831 | − | 0.505033i | −0.100023 | − | 0.0264709i | ||||
\(365\) | 14.0788 | 0.736917 | ||||||||
\(366\) | 7.39890i | 0.386747i | ||||||||
\(367\) | 18.1338 | 0.946578 | 0.473289 | − | 0.880907i | \(-0.343067\pi\) | ||||
0.473289 | + | 0.880907i | \(0.343067\pi\) | |||||||
\(368\) | −18.4213 | −0.960275 | ||||||||
\(369\) | − | 4.16722i | − | 0.216937i | ||||||
\(370\) | − | 10.9540i | − | 0.569474i | ||||||
\(371\) | 21.8347i | 1.13360i | ||||||||
\(372\) | 0.00932567i | 0.000483513i | ||||||||
\(373\) | −15.8564 | −0.821012 | −0.410506 | − | 0.911858i | \(-0.634648\pi\) | ||||
−0.410506 | + | 0.911858i | \(0.634648\pi\) | |||||||
\(374\) | −5.18761 | −0.268245 | ||||||||
\(375\) | 11.4241i | 0.589940i | ||||||||
\(376\) | −33.8736 | −1.74690 | ||||||||
\(377\) | 6.78447 | − | 25.6357i | 0.349418 | − | 1.32030i | ||||
\(378\) | 5.84291 | 0.300527 | ||||||||
\(379\) | − | 18.3431i | − | 0.942224i | −0.882073 | − | 0.471112i | \(-0.843853\pi\) | ||
0.882073 | − | 0.471112i | \(-0.156147\pi\) | |||||||
\(380\) | 0.887733 | 0.0455397 | ||||||||
\(381\) | −10.4027 | −0.532948 | ||||||||
\(382\) | − | 15.2179i | − | 0.778617i | ||||||
\(383\) | 16.1019i | 0.822768i | 0.911462 | + | 0.411384i | \(0.134954\pi\) | ||||
−0.911462 | + | 0.411384i | \(0.865046\pi\) | |||||||
\(384\) | 10.1058i | 0.515707i | ||||||||
\(385\) | 9.32571i | 0.475282i | ||||||||
\(386\) | −31.6949 | −1.61323 | ||||||||
\(387\) | −7.11697 | −0.361776 | ||||||||
\(388\) | 0.486227i | 0.0246844i | ||||||||
\(389\) | −32.7166 | −1.65880 | −0.829400 | − | 0.558655i | \(-0.811317\pi\) | ||||
−0.829400 | + | 0.558655i | \(0.811317\pi\) | |||||||
\(390\) | −2.75585 | + | 10.4132i | −0.139548 | + | 0.527294i | ||||
\(391\) | 18.7403 | 0.947740 | ||||||||
\(392\) | 32.7239i | 1.65281i | ||||||||
\(393\) | −12.0678 | −0.608738 | ||||||||
\(394\) | 12.5655 | 0.633039 | ||||||||
\(395\) | 22.1006i | 1.11200i | ||||||||
\(396\) | − | 0.128197i | − | 0.00644214i | ||||||
\(397\) | − | 3.51685i | − | 0.176506i | −0.996098 | − | 0.0882529i | \(-0.971872\pi\) | ||
0.996098 | − | 0.0882529i | \(-0.0281284\pi\) | |||||||
\(398\) | 8.74154i | 0.438174i | ||||||||
\(399\) | 13.5432 | 0.678007 | ||||||||
\(400\) | −0.863496 | −0.0431748 | ||||||||
\(401\) | 18.6231i | 0.929992i | 0.885313 | + | 0.464996i | \(0.153944\pi\) | ||||
−0.885313 | + | 0.464996i | \(0.846056\pi\) | |||||||
\(402\) | 13.8381 | 0.690180 | ||||||||
\(403\) | −0.253556 | − | 0.0671034i | −0.0126305 | − | 0.00334266i | ||||
\(404\) | −1.64914 | −0.0820480 | ||||||||
\(405\) | 2.18365i | 0.108506i | ||||||||
\(406\) | −42.9736 | −2.13275 | ||||||||
\(407\) | −3.66658 | −0.181746 | ||||||||
\(408\) | − | 11.0403i | − | 0.546574i | ||||||
\(409\) | 17.6809i | 0.874262i | 0.899398 | + | 0.437131i | \(0.144005\pi\) | ||||
−0.899398 | + | 0.437131i | \(0.855995\pi\) | |||||||
\(410\) | − | 12.4497i | − | 0.614848i | ||||||
\(411\) | − | 3.96114i | − | 0.195388i | ||||||
\(412\) | 2.17903 | 0.107353 | ||||||||
\(413\) | 24.0340 | 1.18264 | ||||||||
\(414\) | − | 6.76193i | − | 0.332331i | ||||||
\(415\) | 17.0525 | 0.837075 | ||||||||
\(416\) | 2.52371 | + | 0.667900i | 0.123735 | + | 0.0327465i | ||||
\(417\) | 18.2437 | 0.893395 | ||||||||
\(418\) | 4.33862i | 0.212209i | ||||||||
\(419\) | −1.93036 | −0.0943044 | −0.0471522 | − | 0.998888i | \(-0.515015\pi\) | ||||
−0.0471522 | + | 0.998888i | \(0.515015\pi\) | |||||||
\(420\) | −1.19553 | −0.0583358 | ||||||||
\(421\) | − | 7.21742i | − | 0.351756i | −0.984412 | − | 0.175878i | \(-0.943724\pi\) | ||
0.984412 | − | 0.175878i | \(-0.0562764\pi\) | |||||||
\(422\) | − | 30.7060i | − | 1.49474i | ||||||
\(423\) | − | 11.6337i | − | 0.565651i | ||||||
\(424\) | − | 14.8864i | − | 0.722949i | ||||||
\(425\) | 0.878452 | 0.0426112 | ||||||||
\(426\) | 13.1648 | 0.637835 | ||||||||
\(427\) | − | 23.0960i | − | 1.11769i | ||||||
\(428\) | −1.62578 | −0.0785849 | ||||||||
\(429\) | 3.48555 | + | 0.922450i | 0.168284 | + | 0.0445363i | ||||
\(430\) | −21.2622 | −1.02535 | ||||||||
\(431\) | − | 29.7876i | − | 1.43482i | −0.696653 | − | 0.717408i | \(-0.745328\pi\) | ||
0.696653 | − | 0.717408i | \(-0.254672\pi\) | |||||||
\(432\) | −3.72717 | −0.179324 | ||||||||
\(433\) | 25.2468 | 1.21329 | 0.606643 | − | 0.794975i | \(-0.292516\pi\) | ||||
0.606643 | + | 0.794975i | \(0.292516\pi\) | |||||||
\(434\) | 0.425041i | 0.0204026i | ||||||||
\(435\) | − | 16.0604i | − | 0.770036i | ||||||
\(436\) | 1.14045i | 0.0546177i | ||||||||
\(437\) | − | 15.6733i | − | 0.749758i | ||||||
\(438\) | −8.82089 | −0.421478 | ||||||||
\(439\) | 9.07110 | 0.432940 | 0.216470 | − | 0.976289i | \(-0.430546\pi\) | ||||
0.216470 | + | 0.976289i | \(0.430546\pi\) | |||||||
\(440\) | − | 6.35806i | − | 0.303109i | ||||||
\(441\) | −11.2389 | −0.535185 | ||||||||
\(442\) | 18.0817 | + | 4.78531i | 0.860059 | + | 0.227614i | ||||
\(443\) | −12.0753 | −0.573715 | −0.286858 | − | 0.957973i | \(-0.592611\pi\) | ||||
−0.286858 | + | 0.957973i | \(0.592611\pi\) | |||||||
\(444\) | − | 0.470045i | − | 0.0223074i | ||||||
\(445\) | 6.28700 | 0.298032 | ||||||||
\(446\) | −22.6213 | −1.07115 | ||||||||
\(447\) | 13.8984i | 0.657370i | ||||||||
\(448\) | − | 36.0658i | − | 1.70395i | ||||||
\(449\) | − | 8.94438i | − | 0.422111i | −0.977474 | − | 0.211056i | \(-0.932310\pi\) | ||
0.977474 | − | 0.211056i | \(-0.0676901\pi\) | |||||||
\(450\) | − | 0.316965i | − | 0.0149419i | ||||||
\(451\) | −4.16722 | −0.196227 | ||||||||
\(452\) | 0.175056 | 0.00823394 | ||||||||
\(453\) | 2.29739i | 0.107941i | ||||||||
\(454\) | −27.3390 | −1.28308 | ||||||||
\(455\) | 8.60250 | − | 32.5053i | 0.403292 | − | 1.52387i | ||||
\(456\) | −9.23344 | −0.432395 | ||||||||
\(457\) | − | 28.4975i | − | 1.33305i | −0.745481 | − | 0.666527i | \(-0.767780\pi\) | ||
0.745481 | − | 0.666527i | \(-0.232220\pi\) | |||||||
\(458\) | −21.6794 | −1.01301 | ||||||||
\(459\) | 3.79173 | 0.176983 | ||||||||
\(460\) | 1.38357i | 0.0645093i | ||||||||
\(461\) | − | 19.2580i | − | 0.896932i | −0.893800 | − | 0.448466i | \(-0.851970\pi\) | ||
0.893800 | − | 0.448466i | \(-0.148030\pi\) | |||||||
\(462\) | − | 5.84291i | − | 0.271837i | ||||||
\(463\) | − | 36.3639i | − | 1.68997i | −0.534787 | − | 0.844987i | \(-0.679608\pi\) | ||
0.534787 | − | 0.844987i | \(-0.320392\pi\) | |||||||
\(464\) | 27.4127 | 1.27260 | ||||||||
\(465\) | −0.158849 | −0.00736645 | ||||||||
\(466\) | 21.7801i | 1.00894i | ||||||||
\(467\) | −1.70345 | −0.0788264 | −0.0394132 | − | 0.999223i | \(-0.512549\pi\) | ||||
−0.0394132 | + | 0.999223i | \(0.512549\pi\) | |||||||
\(468\) | −0.118255 | + | 0.446838i | −0.00546636 | + | 0.0206551i | ||||
\(469\) | −43.1961 | −1.99461 | ||||||||
\(470\) | − | 34.7562i | − | 1.60318i | ||||||
\(471\) | −15.6293 | −0.720161 | ||||||||
\(472\) | −16.3859 | −0.754220 | ||||||||
\(473\) | 7.11697i | 0.327239i | ||||||||
\(474\) | − | 13.8468i | − | 0.636006i | ||||||
\(475\) | − | 0.734687i | − | 0.0337097i | ||||||
\(476\) | 2.07594i | 0.0951505i | ||||||||
\(477\) | 5.11268 | 0.234094 | ||||||||
\(478\) | 23.2444 | 1.06318 | ||||||||
\(479\) | 24.5812i | 1.12314i | 0.827429 | + | 0.561571i | \(0.189803\pi\) | ||||
−0.827429 | + | 0.561571i | \(0.810197\pi\) | |||||||
\(480\) | 1.58107 | 0.0721657 | ||||||||
\(481\) | 12.7801 | + | 3.38224i | 0.582721 | + | 0.154217i | ||||
\(482\) | 30.0831 | 1.37025 | ||||||||
\(483\) | 21.1076i | 0.960431i | ||||||||
\(484\) | −0.128197 | −0.00582714 | ||||||||
\(485\) | −8.28216 | −0.376074 | ||||||||
\(486\) | − | 1.36814i | − | 0.0620600i | ||||||
\(487\) | 40.5270i | 1.83646i | 0.396053 | + | 0.918228i | \(0.370380\pi\) | ||||
−0.396053 | + | 0.918228i | \(0.629620\pi\) | |||||||
\(488\) | 15.7463i | 0.712802i | ||||||||
\(489\) | − | 1.25583i | − | 0.0567907i | ||||||
\(490\) | −33.5766 | −1.51683 | ||||||||
\(491\) | −16.8245 | −0.759277 | −0.379639 | − | 0.925135i | \(-0.623952\pi\) | ||||
−0.379639 | + | 0.925135i | \(0.623952\pi\) | |||||||
\(492\) | − | 0.534226i | − | 0.0240848i | ||||||
\(493\) | −27.8875 | −1.25599 | ||||||||
\(494\) | 4.00216 | − | 15.1225i | 0.180066 | − | 0.680393i | ||||
\(495\) | 2.18365 | 0.0981477 | ||||||||
\(496\) | − | 0.271132i | − | 0.0121742i | ||||||
\(497\) | −41.0943 | −1.84333 | ||||||||
\(498\) | −10.6840 | −0.478764 | ||||||||
\(499\) | 28.5150i | 1.27651i | 0.769826 | + | 0.638254i | \(0.220343\pi\) | ||||
−0.769826 | + | 0.638254i | \(0.779657\pi\) | |||||||
\(500\) | 1.46454i | 0.0654963i | ||||||||
\(501\) | − | 17.3823i | − | 0.776586i | ||||||
\(502\) | 16.3439i | 0.729463i | ||||||||
\(503\) | 27.4200 | 1.22260 | 0.611299 | − | 0.791400i | \(-0.290647\pi\) | ||||
0.611299 | + | 0.791400i | \(0.290647\pi\) | |||||||
\(504\) | 12.4349 | 0.553893 | ||||||||
\(505\) | − | 28.0908i | − | 1.25002i | ||||||
\(506\) | −6.76193 | −0.300604 | ||||||||
\(507\) | −11.2982 | − | 6.43050i | −0.501769 | − | 0.285588i | ||||
\(508\) | −1.33360 | −0.0591689 | ||||||||
\(509\) | − | 25.4659i | − | 1.12876i | −0.825516 | − | 0.564378i | \(-0.809116\pi\) | ||
0.825516 | − | 0.564378i | \(-0.190884\pi\) | |||||||
\(510\) | 11.3279 | 0.501609 | ||||||||
\(511\) | 27.5348 | 1.21807 | ||||||||
\(512\) | 24.4032i | 1.07848i | ||||||||
\(513\) | − | 3.17118i | − | 0.140011i | ||||||
\(514\) | 38.8101i | 1.71184i | ||||||||
\(515\) | 37.1167i | 1.63556i | ||||||||
\(516\) | −0.912375 | −0.0401651 | ||||||||
\(517\) | −11.6337 | −0.511651 | ||||||||
\(518\) | − | 21.4235i | − | 0.941295i | ||||||
\(519\) | 12.0899 | 0.530688 | ||||||||
\(520\) | −5.86499 | + | 22.1614i | −0.257197 | + | 0.971840i | ||||
\(521\) | 2.38806 | 0.104623 | 0.0523113 | − | 0.998631i | \(-0.483341\pi\) | ||||
0.0523113 | + | 0.998631i | \(0.483341\pi\) | |||||||
\(522\) | 10.0624i | 0.440421i | ||||||||
\(523\) | 45.6041 | 1.99413 | 0.997064 | − | 0.0765769i | \(-0.0243991\pi\) | ||||
0.997064 | + | 0.0765769i | \(0.0243991\pi\) | |||||||
\(524\) | −1.54705 | −0.0675833 | ||||||||
\(525\) | 0.989418i | 0.0431818i | ||||||||
\(526\) | 1.88527i | 0.0822015i | ||||||||
\(527\) | 0.275829i | 0.0120153i | ||||||||
\(528\) | 3.72717i | 0.162204i | ||||||||
\(529\) | 1.42760 | 0.0620694 | ||||||||
\(530\) | 15.2743 | 0.663474 | ||||||||
\(531\) | − | 5.62765i | − | 0.244219i | ||||||
\(532\) | 1.73620 | 0.0752736 | ||||||||
\(533\) | 14.5251 | + | 3.84405i | 0.629151 | + | 0.166504i | ||||
\(534\) | −3.93904 | −0.170459 | ||||||||
\(535\) | − | 27.6927i | − | 1.19726i | ||||||
\(536\) | 29.4501 | 1.27205 | ||||||||
\(537\) | 5.13094 | 0.221416 | ||||||||
\(538\) | 20.0123i | 0.862791i | ||||||||
\(539\) | 11.2389i | 0.484093i | ||||||||
\(540\) | 0.279937i | 0.0120466i | ||||||||
\(541\) | 29.4997i | 1.26829i | 0.773214 | + | 0.634145i | \(0.218648\pi\) | ||||
−0.773214 | + | 0.634145i | \(0.781352\pi\) | |||||||
\(542\) | −18.2017 | −0.781828 | ||||||||
\(543\) | 23.3170 | 1.00063 | ||||||||
\(544\) | − | 2.74540i | − | 0.117708i | ||||||
\(545\) | −19.4259 | −0.832114 | ||||||||
\(546\) | −5.38979 | + | 20.3658i | −0.230662 | + | 0.871575i | ||||
\(547\) | 7.75142 | 0.331427 | 0.165713 | − | 0.986174i | \(-0.447007\pi\) | ||||
0.165713 | + | 0.986174i | \(0.447007\pi\) | |||||||
\(548\) | − | 0.507806i | − | 0.0216924i | ||||||
\(549\) | −5.40800 | −0.230808 | ||||||||
\(550\) | −0.316965 | −0.0135154 | ||||||||
\(551\) | 23.3235i | 0.993616i | ||||||||
\(552\) | − | 14.3907i | − | 0.612509i | ||||||
\(553\) | 43.2235i | 1.83805i | ||||||||
\(554\) | 30.3153i | 1.28798i | ||||||||
\(555\) | 8.00653 | 0.339858 | ||||||||
\(556\) | 2.33878 | 0.0991865 | ||||||||
\(557\) | 20.2857i | 0.859534i | 0.902940 | + | 0.429767i | \(0.141404\pi\) | ||||
−0.902940 | + | 0.429767i | \(0.858596\pi\) | |||||||
\(558\) | 0.0995250 | 0.00421323 | ||||||||
\(559\) | 6.56505 | − | 24.8066i | 0.277672 | − | 1.04921i | ||||
\(560\) | 34.7585 | 1.46882 | ||||||||
\(561\) | − | 3.79173i | − | 0.160087i | ||||||
\(562\) | 2.90851 | 0.122688 | ||||||||
\(563\) | 32.7633 | 1.38081 | 0.690403 | − | 0.723425i | \(-0.257433\pi\) | ||||
0.690403 | + | 0.723425i | \(0.257433\pi\) | |||||||
\(564\) | − | 1.49141i | − | 0.0627997i | ||||||
\(565\) | 2.98182i | 0.125446i | ||||||||
\(566\) | − | 42.5540i | − | 1.78868i | ||||||
\(567\) | 4.27070i | 0.179353i | ||||||||
\(568\) | 28.0172 | 1.17558 | ||||||||
\(569\) | −27.8002 | −1.16545 | −0.582723 | − | 0.812671i | \(-0.698013\pi\) | ||||
−0.582723 | + | 0.812671i | \(0.698013\pi\) | |||||||
\(570\) | − | 9.47402i | − | 0.396823i | ||||||
\(571\) | −43.4425 | −1.81801 | −0.909007 | − | 0.416782i | \(-0.863158\pi\) | ||||
−0.909007 | + | 0.416782i | \(0.863158\pi\) | |||||||
\(572\) | 0.446838 | + | 0.118255i | 0.0186832 | + | 0.00494450i | ||||
\(573\) | 11.1231 | 0.464674 | ||||||||
\(574\) | − | 24.3487i | − | 1.01630i | ||||||
\(575\) | 1.14504 | 0.0477515 | ||||||||
\(576\) | −8.44494 | −0.351873 | ||||||||
\(577\) | 25.7084i | 1.07025i | 0.844772 | + | 0.535127i | \(0.179736\pi\) | ||||
−0.844772 | + | 0.535127i | \(0.820264\pi\) | |||||||
\(578\) | 3.58834i | 0.149255i | ||||||||
\(579\) | − | 23.1664i | − | 0.962764i | ||||||
\(580\) | − | 2.05889i | − | 0.0854909i | ||||||
\(581\) | 33.3507 | 1.38362 | ||||||||
\(582\) | 5.18909 | 0.215095 | ||||||||
\(583\) | − | 5.11268i | − | 0.211746i | ||||||
\(584\) | −18.7726 | −0.776815 | ||||||||
\(585\) | −7.61123 | − | 2.01431i | −0.314686 | − | 0.0832814i | ||||
\(586\) | −23.1228 | −0.955195 | ||||||||
\(587\) | 1.44805i | 0.0597673i | 0.999553 | + | 0.0298837i | \(0.00951368\pi\) | ||||
−0.999553 | + | 0.0298837i | \(0.990486\pi\) | |||||||
\(588\) | −1.44079 | −0.0594173 | ||||||||
\(589\) | 0.230687 | 0.00950530 | ||||||||
\(590\) | − | 16.8128i | − | 0.692173i | ||||||
\(591\) | 9.18435i | 0.377794i | ||||||||
\(592\) | 13.6660i | 0.561668i | ||||||||
\(593\) | − | 4.27539i | − | 0.175569i | −0.996139 | − | 0.0877845i | \(-0.972021\pi\) | ||
0.996139 | − | 0.0877845i | \(-0.0279787\pi\) | |||||||
\(594\) | −1.36814 | −0.0561354 | ||||||||
\(595\) | −35.3606 | −1.44964 | ||||||||
\(596\) | 1.78173i | 0.0729824i | ||||||||
\(597\) | −6.38937 | −0.261499 | ||||||||
\(598\) | 23.5691 | + | 6.23754i | 0.963810 | + | 0.255072i | ||||
\(599\) | 15.9807 | 0.652953 | 0.326476 | − | 0.945205i | \(-0.394139\pi\) | ||||
0.326476 | + | 0.945205i | \(0.394139\pi\) | |||||||
\(600\) | − | 0.674563i | − | 0.0275389i | ||||||
\(601\) | −25.2647 | −1.03057 | −0.515283 | − | 0.857020i | \(-0.672313\pi\) | ||||
−0.515283 | + | 0.857020i | \(0.672313\pi\) | |||||||
\(602\) | −41.5838 | −1.69483 | ||||||||
\(603\) | 10.1145i | 0.411895i | ||||||||
\(604\) | 0.294519i | 0.0119838i | ||||||||
\(605\) | − | 2.18365i | − | 0.0887780i | ||||||
\(606\) | 17.5999i | 0.714948i | ||||||||
\(607\) | 41.6506 | 1.69055 | 0.845273 | − | 0.534334i | \(-0.179437\pi\) | ||||
0.845273 | + | 0.534334i | \(0.179437\pi\) | |||||||
\(608\) | −2.29610 | −0.0931190 | ||||||||
\(609\) | − | 31.4103i | − | 1.27281i | ||||||
\(610\) | −16.1566 | −0.654162 | ||||||||
\(611\) | 40.5500 | + | 10.7315i | 1.64048 | + | 0.434151i | ||||
\(612\) | 0.486088 | 0.0196490 | ||||||||
\(613\) | 16.1620i | 0.652777i | 0.945236 | + | 0.326388i | \(0.105832\pi\) | ||||
−0.945236 | + | 0.326388i | \(0.894168\pi\) | |||||||
\(614\) | 33.6713 | 1.35886 | ||||||||
\(615\) | 9.09975 | 0.366937 | ||||||||
\(616\) | − | 12.4349i | − | 0.501015i | ||||||
\(617\) | 8.12561i | 0.327125i | 0.986533 | + | 0.163562i | \(0.0522985\pi\) | ||||
−0.986533 | + | 0.163562i | \(0.947701\pi\) | |||||||
\(618\) | − | 23.2550i | − | 0.935453i | ||||||
\(619\) | − | 7.09593i | − | 0.285209i | −0.989780 | − | 0.142605i | \(-0.954452\pi\) | ||
0.989780 | − | 0.142605i | \(-0.0455478\pi\) | |||||||
\(620\) | −0.0203640 | −0.000817838 | ||||||||
\(621\) | 4.94243 | 0.198333 | ||||||||
\(622\) | − | 1.37503i | − | 0.0551337i | ||||||
\(623\) | 12.2959 | 0.492624 | ||||||||
\(624\) | 3.43813 | − | 12.9913i | 0.137635 | − | 0.520066i | ||||
\(625\) | −23.7879 | −0.951518 | ||||||||
\(626\) | 18.9821i | 0.758677i | ||||||||
\(627\) | −3.17118 | −0.126645 | ||||||||
\(628\) | −2.00363 | −0.0799536 | ||||||||
\(629\) | − | 13.9027i | − | 0.554337i | ||||||
\(630\) | 12.7589i | 0.508325i | ||||||||
\(631\) | − | 3.62153i | − | 0.144171i | −0.997398 | − | 0.0720854i | \(-0.977035\pi\) | ||
0.997398 | − | 0.0720854i | \(-0.0229654\pi\) | |||||||
\(632\) | − | 29.4688i | − | 1.17221i | ||||||
\(633\) | 22.4436 | 0.892053 | ||||||||
\(634\) | 21.3984 | 0.849840 | ||||||||
\(635\) | − | 22.7159i | − | 0.901453i | ||||||
\(636\) | 0.655431 | 0.0259895 | ||||||||
\(637\) | 10.3673 | − | 39.1738i | 0.410768 | − | 1.55212i | ||||
\(638\) | 10.0624 | 0.398375 | ||||||||
\(639\) | 9.62239i | 0.380656i | ||||||||
\(640\) | −22.0674 | −0.872291 | ||||||||
\(641\) | 8.81244 | 0.348070 | 0.174035 | − | 0.984739i | \(-0.444319\pi\) | ||||
0.174035 | + | 0.984739i | \(0.444319\pi\) | |||||||
\(642\) | 17.3505i | 0.684771i | ||||||||
\(643\) | − | 47.2262i | − | 1.86242i | −0.364484 | − | 0.931210i | \(-0.618755\pi\) | ||
0.364484 | − | 0.931210i | \(-0.381245\pi\) | |||||||
\(644\) | 2.70594i | 0.106629i | ||||||||
\(645\) | − | 15.5410i | − | 0.611925i | ||||||
\(646\) | −16.4509 | −0.647251 | ||||||||
\(647\) | −41.0552 | −1.61405 | −0.807023 | − | 0.590520i | \(-0.798923\pi\) | ||||
−0.807023 | + | 0.590520i | \(0.798923\pi\) | |||||||
\(648\) | − | 2.91167i | − | 0.114381i | ||||||
\(649\) | −5.62765 | −0.220905 | ||||||||
\(650\) | 1.10480 | + | 0.292384i | 0.0433337 | + | 0.0114682i | ||||
\(651\) | −0.310671 | −0.0121762 | ||||||||
\(652\) | − | 0.160994i | − | 0.00630501i | ||||||
\(653\) | 36.9362 | 1.44542 | 0.722712 | − | 0.691149i | \(-0.242895\pi\) | ||||
0.722712 | + | 0.691149i | \(0.242895\pi\) | |||||||
\(654\) | 12.1711 | 0.475926 | ||||||||
\(655\) | − | 26.3518i | − | 1.02965i | ||||||
\(656\) | 15.5320i | 0.606421i | ||||||||
\(657\) | − | 6.44736i | − | 0.251536i | ||||||
\(658\) | − | 67.9748i | − | 2.64994i | ||||||
\(659\) | 39.7980 | 1.55031 | 0.775154 | − | 0.631772i | \(-0.217672\pi\) | ||||
0.775154 | + | 0.631772i | \(0.217672\pi\) | |||||||
\(660\) | 0.279937 | 0.0108965 | ||||||||
\(661\) | 21.8622i | 0.850342i | 0.905113 | + | 0.425171i | \(0.139786\pi\) | ||||
−0.905113 | + | 0.425171i | \(0.860214\pi\) | |||||||
\(662\) | 31.6623 | 1.23059 | ||||||||
\(663\) | −3.49768 | + | 13.2163i | −0.135839 | + | 0.513278i | ||||
\(664\) | −22.7378 | −0.882396 | ||||||||
\(665\) | 29.5736i | 1.14681i | ||||||||
\(666\) | −5.01639 | −0.194381 | ||||||||
\(667\) | −36.3507 | −1.40751 | ||||||||
\(668\) | − | 2.22836i | − | 0.0862180i | ||||||
\(669\) | − | 16.5344i | − | 0.639255i | ||||||
\(670\) | 30.2175i | 1.16740i | ||||||||
\(671\) | 5.40800i | 0.208774i | ||||||||
\(672\) | 3.09220 | 0.119284 | ||||||||
\(673\) | 32.3152 | 1.24566 | 0.622830 | − | 0.782357i | \(-0.285983\pi\) | ||||
0.622830 | + | 0.782357i | \(0.285983\pi\) | |||||||
\(674\) | 20.7884i | 0.800739i | ||||||||
\(675\) | 0.231676 | 0.00891721 | ||||||||
\(676\) | −1.44839 | − | 0.824371i | −0.0557074 | − | 0.0317066i | ||||
\(677\) | −21.1472 | −0.812753 | −0.406376 | − | 0.913706i | \(-0.633208\pi\) | ||||
−0.406376 | + | 0.913706i | \(0.633208\pi\) | |||||||
\(678\) | − | 1.86822i | − | 0.0717487i | ||||||
\(679\) | −16.1979 | −0.621620 | ||||||||
\(680\) | 24.1081 | 0.924502 | ||||||||
\(681\) | − | 19.9826i | − | 0.765737i | ||||||
\(682\) | − | 0.0995250i | − | 0.00381101i | ||||||
\(683\) | 24.7401i | 0.946654i | 0.880887 | + | 0.473327i | \(0.156947\pi\) | ||||
−0.880887 | + | 0.473327i | \(0.843053\pi\) | |||||||
\(684\) | − | 0.406536i | − | 0.0155443i | ||||||
\(685\) | 8.64973 | 0.330489 | ||||||||
\(686\) | −24.7675 | −0.945626 | ||||||||
\(687\) | − | 15.8459i | − | 0.604560i | ||||||
\(688\) | 26.5262 | 1.01130 | ||||||||
\(689\) | −4.71619 | + | 17.8205i | −0.179673 | + | 0.678908i | ||||
\(690\) | 14.7657 | 0.562120 | ||||||||
\(691\) | 22.7394i | 0.865047i | 0.901623 | + | 0.432523i | \(0.142377\pi\) | ||||
−0.901623 | + | 0.432523i | \(0.857623\pi\) | |||||||
\(692\) | 1.54989 | 0.0589180 | ||||||||
\(693\) | 4.27070 | 0.162231 | ||||||||
\(694\) | − | 22.7857i | − | 0.864932i | ||||||
\(695\) | 39.8377i | 1.51113i | ||||||||
\(696\) | 21.4148i | 0.811727i | ||||||||
\(697\) | − | 15.8010i | − | 0.598505i | ||||||
\(698\) | 39.8238 | 1.50735 | ||||||||
\(699\) | −15.9195 | −0.602130 | ||||||||
\(700\) | 0.126840i | 0.00479412i | ||||||||
\(701\) | 23.8173 | 0.899567 | 0.449783 | − | 0.893138i | \(-0.351501\pi\) | ||||
0.449783 | + | 0.893138i | \(0.351501\pi\) | |||||||
\(702\) | 4.76872 | + | 1.26204i | 0.179984 | + | 0.0476326i | ||||
\(703\) | −11.6274 | −0.438536 | ||||||||
\(704\) | 8.44494i | 0.318281i | ||||||||
\(705\) | 25.4040 | 0.956769 | ||||||||
\(706\) | 39.9117 | 1.50210 | ||||||||
\(707\) | − | 54.9389i | − | 2.06619i | ||||||
\(708\) | − | 0.721449i | − | 0.0271137i | ||||||
\(709\) | − | 15.8902i | − | 0.596770i | −0.954446 | − | 0.298385i | \(-0.903552\pi\) | ||
0.954446 | − | 0.298385i | \(-0.0964480\pi\) | |||||||
\(710\) | 28.7472i | 1.07886i | ||||||||
\(711\) | 10.1209 | 0.379565 | ||||||||
\(712\) | −8.38305 | −0.314168 | ||||||||
\(713\) | 0.359536i | 0.0134647i | ||||||||
\(714\) | 22.1547 | 0.829120 | ||||||||
\(715\) | −2.01431 | + | 7.61123i | −0.0753308 | + | 0.284644i | ||||
\(716\) | 0.657771 | 0.0245821 | ||||||||
\(717\) | 16.9898i | 0.634497i | ||||||||
\(718\) | 24.7371 | 0.923181 | ||||||||
\(719\) | −4.64051 | −0.173062 | −0.0865309 | − | 0.996249i | \(-0.527578\pi\) | ||||
−0.0865309 | + | 0.996249i | \(0.527578\pi\) | |||||||
\(720\) | − | 8.13884i | − | 0.303316i | ||||||
\(721\) | 72.5914i | 2.70345i | ||||||||
\(722\) | − | 12.2361i | − | 0.455379i | ||||||
\(723\) | 21.9883i | 0.817755i | ||||||||
\(724\) | 2.98917 | 0.111091 | ||||||||
\(725\) | −1.70394 | −0.0632826 | ||||||||
\(726\) | 1.36814i | 0.0507764i | ||||||||
\(727\) | 14.5583 | 0.539938 | 0.269969 | − | 0.962869i | \(-0.412987\pi\) | ||||
0.269969 | + | 0.962869i | \(0.412987\pi\) | |||||||
\(728\) | −11.4705 | + | 43.3424i | −0.425127 | + | 1.60638i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | − | 19.2617i | − | 0.712908i | ||||||
\(731\) | −26.9856 | −0.998100 | ||||||||
\(732\) | −0.693290 | −0.0256247 | ||||||||
\(733\) | 34.2475i | 1.26496i | 0.774576 | + | 0.632480i | \(0.217963\pi\) | ||||
−0.774576 | + | 0.632480i | \(0.782037\pi\) | |||||||
\(734\) | − | 24.8096i | − | 0.915738i | ||||||
\(735\) | − | 24.5418i | − | 0.905238i | ||||||
\(736\) | − | 3.57856i | − | 0.131908i | ||||||
\(737\) | 10.1145 | 0.372573 | ||||||||
\(738\) | −5.70134 | −0.209869 | ||||||||
\(739\) | 30.5325i | 1.12316i | 0.827424 | + | 0.561578i | \(0.189806\pi\) | ||||
−0.827424 | + | 0.561578i | \(0.810194\pi\) | |||||||
\(740\) | 1.02641 | 0.0377317 | ||||||||
\(741\) | 11.0533 | + | 2.92526i | 0.406054 | + | 0.107462i | ||||
\(742\) | 29.8729 | 1.09667 | ||||||||
\(743\) | 2.86476i | 0.105098i | 0.998618 | + | 0.0525490i | \(0.0167346\pi\) | ||||
−0.998618 | + | 0.0525490i | \(0.983265\pi\) | |||||||
\(744\) | 0.211809 | 0.00776529 | ||||||||
\(745\) | −30.3491 | −1.11191 | ||||||||
\(746\) | 21.6937i | 0.794263i | ||||||||
\(747\) | − | 7.80918i | − | 0.285723i | ||||||
\(748\) | − | 0.486088i | − | 0.0177732i | ||||||
\(749\) | − | 54.1604i | − | 1.97898i | ||||||
\(750\) | 15.6298 | 0.570720 | ||||||||
\(751\) | −38.1810 | −1.39324 | −0.696621 | − | 0.717439i | \(-0.745314\pi\) | ||||
−0.696621 | + | 0.717439i | \(0.745314\pi\) | |||||||
\(752\) | 43.3609i | 1.58121i | ||||||||
\(753\) | −11.9461 | −0.435339 | ||||||||
\(754\) | −35.0731 | − | 9.28209i | −1.27729 | − | 0.338034i | ||||
\(755\) | −5.01670 | −0.182576 | ||||||||
\(756\) | 0.547491i | 0.0199121i | ||||||||
\(757\) | −38.9456 | −1.41550 | −0.707750 | − | 0.706463i | \(-0.750290\pi\) | ||||
−0.707750 | + | 0.706463i | \(0.750290\pi\) | |||||||
\(758\) | −25.0960 | −0.911526 | ||||||||
\(759\) | − | 4.94243i | − | 0.179399i | ||||||
\(760\) | − | 20.1626i | − | 0.731374i | ||||||
\(761\) | 26.9359i | 0.976427i | 0.872724 | + | 0.488214i | \(0.162351\pi\) | ||||
−0.872724 | + | 0.488214i | \(0.837649\pi\) | |||||||
\(762\) | 14.2324i | 0.515585i | ||||||||
\(763\) | −37.9925 | −1.37542 | ||||||||
\(764\) | 1.42595 | 0.0515889 | ||||||||
\(765\) | 8.27981i | 0.299357i | ||||||||
\(766\) | 22.0296 | 0.795962 | ||||||||
\(767\) | 19.6155 | + | 5.19123i | 0.708274 | + | 0.187444i | ||||
\(768\) | −3.06382 | −0.110556 | ||||||||
\(769\) | 3.83575i | 0.138321i | 0.997606 | + | 0.0691603i | \(0.0220320\pi\) | ||||
−0.997606 | + | 0.0691603i | \(0.977968\pi\) | |||||||
\(770\) | 12.7589 | 0.459798 | ||||||||
\(771\) | −28.3671 | −1.02162 | ||||||||
\(772\) | − | 2.96987i | − | 0.106888i | ||||||
\(773\) | 21.7215i | 0.781267i | 0.920546 | + | 0.390633i | \(0.127744\pi\) | ||||
−0.920546 | + | 0.390633i | \(0.872256\pi\) | |||||||
\(774\) | 9.73700i | 0.349989i | ||||||||
\(775\) | 0.0168532i | 0.000605385i | ||||||||
\(776\) | 11.0434 | 0.396435 | ||||||||
\(777\) | 15.6589 | 0.561759 | ||||||||
\(778\) | 44.7609i | 1.60476i | ||||||||
\(779\) | −13.2150 | −0.473478 | ||||||||
\(780\) | −0.975737 | − | 0.258228i | −0.0349370 | − | 0.00924605i | ||||
\(781\) | 9.62239 | 0.344316 | ||||||||
\(782\) | − | 25.6394i | − | 0.916863i | ||||||
\(783\) | −7.35483 | −0.262840 | ||||||||
\(784\) | 41.8893 | 1.49605 | ||||||||
\(785\) | − | 34.1290i | − | 1.21811i | ||||||
\(786\) | 16.5104i | 0.588905i | ||||||||
\(787\) | − | 32.8705i | − | 1.17171i | −0.810417 | − | 0.585853i | \(-0.800760\pi\) | ||
0.810417 | − | 0.585853i | \(-0.199240\pi\) | |||||||
\(788\) | 1.17741i | 0.0419434i | ||||||||
\(789\) | −1.37798 | −0.0490574 | ||||||||
\(790\) | 30.2366 | 1.07577 | ||||||||
\(791\) | 5.83174i | 0.207353i | ||||||||
\(792\) | −2.91167 | −0.103462 | ||||||||
\(793\) | 4.98861 | − | 18.8499i | 0.177151 | − | 0.669379i | ||||
\(794\) | −4.81154 | −0.170755 | ||||||||
\(795\) | 11.1643i | 0.395957i | ||||||||
\(796\) | −0.819098 | −0.0290322 | ||||||||
\(797\) | 2.27867 | 0.0807147 | 0.0403573 | − | 0.999185i | \(-0.487150\pi\) | ||||
0.0403573 | + | 0.999185i | \(0.487150\pi\) | |||||||
\(798\) | − | 18.5289i | − | 0.655918i | ||||||
\(799\) | − | 44.1120i | − | 1.56057i | ||||||
\(800\) | − | 0.167745i | − | 0.00593068i | ||||||
\(801\) | − | 2.87912i | − | 0.101729i | ||||||
\(802\) | 25.4789 | 0.899693 | ||||||||
\(803\) | −6.44736 | −0.227523 | ||||||||
\(804\) | 1.29665i | 0.0457294i | ||||||||
\(805\) | −46.0917 | −1.62452 | ||||||||
\(806\) | −0.0918068 | + | 0.346900i | −0.00323376 | + | 0.0122190i | ||||
\(807\) | −14.6274 | −0.514908 | ||||||||
\(808\) | 37.4561i | 1.31770i | ||||||||
\(809\) | 25.3935 | 0.892786 | 0.446393 | − | 0.894837i | \(-0.352708\pi\) | ||||
0.446393 | + | 0.894837i | \(0.352708\pi\) | |||||||
\(810\) | 2.98753 | 0.104971 | ||||||||
\(811\) | − | 32.7178i | − | 1.14888i | −0.818548 | − | 0.574439i | \(-0.805220\pi\) | ||
0.818548 | − | 0.574439i | \(-0.194780\pi\) | |||||||
\(812\) | − | 4.02671i | − | 0.141310i | ||||||
\(813\) | − | 13.3040i | − | 0.466590i | ||||||
\(814\) | 5.01639i | 0.175824i | ||||||||
\(815\) | 2.74230 | 0.0960584 | ||||||||
\(816\) | −14.1324 | −0.494734 | ||||||||
\(817\) | 22.5692i | 0.789597i | ||||||||
\(818\) | 24.1899 | 0.845779 | ||||||||
\(819\) | −14.8858 | − | 3.93951i | −0.520151 | − | 0.137658i | ||||
\(820\) | 1.16656 | 0.0407381 | ||||||||
\(821\) | − | 31.2361i | − | 1.09015i | −0.838388 | − | 0.545073i | \(-0.816502\pi\) | ||
0.838388 | − | 0.545073i | \(-0.183498\pi\) | |||||||
\(822\) | −5.41938 | −0.189023 | ||||||||
\(823\) | −8.94424 | −0.311777 | −0.155888 | − | 0.987775i | \(-0.549824\pi\) | ||||
−0.155888 | + | 0.987775i | \(0.549824\pi\) | |||||||
\(824\) | − | 49.4912i | − | 1.72411i | ||||||
\(825\) | − | 0.231676i | − | 0.00806592i | ||||||
\(826\) | − | 32.8819i | − | 1.14411i | ||||||
\(827\) | 28.6667i | 0.996838i | 0.866936 | + | 0.498419i | \(0.166086\pi\) | ||||
−0.866936 | + | 0.498419i | \(0.833914\pi\) | |||||||
\(828\) | 0.633605 | 0.0220193 | ||||||||
\(829\) | −39.5515 | −1.37368 | −0.686839 | − | 0.726809i | \(-0.741002\pi\) | ||||
−0.686839 | + | 0.726809i | \(0.741002\pi\) | |||||||
\(830\) | − | 23.3302i | − | 0.809803i | ||||||
\(831\) | −22.1581 | −0.768656 | ||||||||
\(832\) | 7.79004 | − | 29.4353i | 0.270071 | − | 1.02049i | ||||
\(833\) | −42.6148 | −1.47652 | ||||||||
\(834\) | − | 24.9598i | − | 0.864289i | ||||||
\(835\) | 37.9569 | 1.31355 | ||||||||
\(836\) | −0.406536 | −0.0140604 | ||||||||
\(837\) | 0.0727448i | 0.00251443i | ||||||||
\(838\) | 2.64100i | 0.0912320i | ||||||||
\(839\) | − | 45.1833i | − | 1.55990i | −0.625840 | − | 0.779951i | \(-0.715244\pi\) | ||
0.625840 | − | 0.779951i | \(-0.284756\pi\) | |||||||
\(840\) | 27.1534i | 0.936881i | ||||||||
\(841\) | 25.0936 | 0.865296 | ||||||||
\(842\) | −9.87443 | −0.340295 | ||||||||
\(843\) | 2.12589i | 0.0732195i | ||||||||
\(844\) | 2.87720 | 0.0990375 | ||||||||
\(845\) | 14.0420 | − | 24.6712i | 0.483058 | − | 0.848717i | ||||
\(846\) | −15.9166 | −0.547222 | ||||||||
\(847\) | − | 4.27070i | − | 0.146743i | ||||||
\(848\) | −19.0558 | −0.654380 | ||||||||
\(849\) | 31.1036 | 1.06747 | ||||||||
\(850\) | − | 1.20184i | − | 0.0412229i | ||||||
\(851\) | − | 18.1218i | − | 0.621208i | ||||||
\(852\) | 1.23356i | 0.0422611i | ||||||||
\(853\) | 13.2579i | 0.453943i | 0.973901 | + | 0.226972i | \(0.0728825\pi\) | ||||
−0.973901 | + | 0.226972i | \(0.927118\pi\) | |||||||
\(854\) | −31.5985 | −1.08128 | ||||||||
\(855\) | 6.92475 | 0.236822 | ||||||||
\(856\) | 36.9254i | 1.26208i | ||||||||
\(857\) | −38.9268 | −1.32971 | −0.664857 | − | 0.746971i | \(-0.731507\pi\) | ||||
−0.664857 | + | 0.746971i | \(0.731507\pi\) | |||||||
\(858\) | 1.26204 | − | 4.76872i | 0.0430853 | − | 0.162801i | ||||
\(859\) | −21.2750 | −0.725893 | −0.362947 | − | 0.931810i | \(-0.618229\pi\) | ||||
−0.362947 | + | 0.931810i | \(0.618229\pi\) | |||||||
\(860\) | − | 1.99231i | − | 0.0679371i | ||||||
\(861\) | 17.7970 | 0.606519 | ||||||||
\(862\) | −40.7535 | −1.38807 | ||||||||
\(863\) | − | 8.94497i | − | 0.304490i | −0.988343 | − | 0.152245i | \(-0.951350\pi\) | ||
0.988343 | − | 0.152245i | \(-0.0486504\pi\) | |||||||
\(864\) | − | 0.724050i | − | 0.0246327i | ||||||
\(865\) | 26.4001i | 0.897630i | ||||||||
\(866\) | − | 34.5412i | − | 1.17376i | ||||||
\(867\) | −2.62279 | −0.0890746 | ||||||||
\(868\) | −0.0398271 | −0.00135182 | ||||||||
\(869\) | − | 10.1209i | − | 0.343329i | ||||||
\(870\) | −21.9728 | −0.744948 | ||||||||
\(871\) | −35.2547 | − | 9.33014i | −1.19456 | − | 0.316140i | ||||
\(872\) | 25.9024 | 0.877166 | ||||||||
\(873\) | 3.79281i | 0.128367i | ||||||||
\(874\) | −21.4433 | −0.725331 | ||||||||
\(875\) | −48.7891 | −1.64937 | ||||||||
\(876\) | − | 0.826533i | − | 0.0279260i | ||||||
\(877\) | 11.5696i | 0.390679i | 0.980736 | + | 0.195340i | \(0.0625809\pi\) | ||||
−0.980736 | + | 0.195340i | \(0.937419\pi\) | |||||||
\(878\) | − | 12.4105i | − | 0.418835i | ||||||
\(879\) | − | 16.9009i | − | 0.570055i | ||||||
\(880\) | −8.13884 | −0.274360 | ||||||||
\(881\) | 13.2958 | 0.447947 | 0.223974 | − | 0.974595i | \(-0.428097\pi\) | ||||
0.223974 | + | 0.974595i | \(0.428097\pi\) | |||||||
\(882\) | 15.3764i | 0.517749i | ||||||||
\(883\) | 18.7422 | 0.630726 | 0.315363 | − | 0.948971i | \(-0.397874\pi\) | ||||
0.315363 | + | 0.948971i | \(0.397874\pi\) | |||||||
\(884\) | −0.448392 | + | 1.69429i | −0.0150811 | + | 0.0569851i | ||||
\(885\) | 12.2888 | 0.413084 | ||||||||
\(886\) | 16.5207i | 0.555024i | ||||||||
\(887\) | 41.6306 | 1.39782 | 0.698910 | − | 0.715210i | \(-0.253669\pi\) | ||||
0.698910 | + | 0.715210i | \(0.253669\pi\) | |||||||
\(888\) | −10.6759 | −0.358259 | ||||||||
\(889\) | − | 44.4269i | − | 1.49003i | ||||||
\(890\) | − | 8.60148i | − | 0.288322i | ||||||
\(891\) | − | 1.00000i | − | 0.0335013i | ||||||
\(892\) | − | 2.11966i | − | 0.0709713i | ||||||
\(893\) | −36.8927 | −1.23457 | ||||||||
\(894\) | 19.0149 | 0.635953 | ||||||||
\(895\) | 11.2042i | 0.374514i | ||||||||
\(896\) | −43.1586 | −1.44183 | ||||||||
\(897\) | −4.55914 | + | 17.2271i | −0.152225 | + | 0.575196i | ||||
\(898\) | −12.2372 | −0.408359 | ||||||||
\(899\) | − | 0.535026i | − | 0.0178441i | ||||||
\(900\) | 0.0297002 | 0.000990005 | ||||||||
\(901\) | 19.3859 | 0.645838 | ||||||||
\(902\) | 5.70134i | 0.189834i | ||||||||
\(903\) | − | 30.3945i | − | 1.01146i | ||||||
\(904\) | − | 3.97595i | − | 0.132238i | ||||||
\(905\) | 50.9161i | 1.69251i | ||||||||
\(906\) | 3.14315 | 0.104424 | ||||||||
\(907\) | −37.0540 | −1.23036 | −0.615179 | − | 0.788387i | \(-0.710916\pi\) | ||||
−0.615179 | + | 0.788387i | \(0.710916\pi\) | |||||||
\(908\) | − | 2.56172i | − | 0.0850136i | ||||||
\(909\) | −12.8641 | −0.426676 | ||||||||
\(910\) | −44.4717 | − | 11.7694i | −1.47422 | − | 0.390152i | ||||
\(911\) | −43.8739 | −1.45361 | −0.726804 | − | 0.686845i | \(-0.758995\pi\) | ||||
−0.726804 | + | 0.686845i | \(0.758995\pi\) | |||||||
\(912\) | 11.8195i | 0.391384i | ||||||||
\(913\) | −7.80918 | −0.258446 | ||||||||
\(914\) | −38.9885 | −1.28962 | ||||||||
\(915\) | − | 11.8092i | − | 0.390400i | ||||||
\(916\) | − | 2.03140i | − | 0.0671194i | ||||||
\(917\) | − | 51.5378i | − | 1.70193i | ||||||
\(918\) | − | 5.18761i | − | 0.171217i | ||||||
\(919\) | −30.1561 | −0.994759 | −0.497380 | − | 0.867533i | \(-0.665704\pi\) | ||||
−0.497380 | + | 0.867533i | \(0.665704\pi\) | |||||||
\(920\) | 31.4243 | 1.03603 | ||||||||
\(921\) | 24.6110i | 0.810961i | ||||||||
\(922\) | −26.3475 | −0.867710 | ||||||||
\(923\) | −33.5393 | − | 8.87617i | −1.10396 | − | 0.292163i | ||||
\(924\) | 0.547491 | 0.0180111 | ||||||||
\(925\) | − | 0.849459i | − | 0.0279300i | ||||||
\(926\) | −49.7508 | −1.63491 | ||||||||
\(927\) | 16.9975 | 0.558272 | ||||||||
\(928\) | 5.32527i | 0.174810i | ||||||||
\(929\) | − | 29.2684i | − | 0.960264i | −0.877196 | − | 0.480132i | \(-0.840589\pi\) | ||
0.877196 | − | 0.480132i | \(-0.159411\pi\) | |||||||
\(930\) | 0.217328i | 0.00712645i | ||||||||
\(931\) | 35.6406i | 1.16807i | ||||||||
\(932\) | −2.04083 | −0.0668496 | ||||||||
\(933\) | 1.00504 | 0.0329034 | ||||||||
\(934\) | 2.33056i | 0.0762583i | ||||||||
\(935\) | 8.27981 | 0.270779 | ||||||||
\(936\) | 10.1488 | + | 2.68587i | 0.331723 | + | 0.0877904i | ||||
\(937\) | −14.7979 | −0.483427 | −0.241713 | − | 0.970348i | \(-0.577709\pi\) | ||||
−0.241713 | + | 0.970348i | \(0.577709\pi\) | |||||||
\(938\) | 59.0983i | 1.92963i | ||||||||
\(939\) | −13.8744 | −0.452774 | ||||||||
\(940\) | 3.25672 | 0.106222 | ||||||||
\(941\) | 17.5021i | 0.570553i | 0.958445 | + | 0.285276i | \(0.0920854\pi\) | ||||
−0.958445 | + | 0.285276i | \(0.907915\pi\) | |||||||
\(942\) | 21.3831i | 0.696698i | ||||||||
\(943\) | − | 20.5962i | − | 0.670704i | ||||||
\(944\) | 20.9752i | 0.682686i | ||||||||
\(945\) | −9.32571 | −0.303365 | ||||||||
\(946\) | 9.73700 | 0.316577 | ||||||||
\(947\) | − | 32.5998i | − | 1.05935i | −0.848201 | − | 0.529675i | \(-0.822314\pi\) | ||
0.848201 | − | 0.529675i | \(-0.177686\pi\) | |||||||
\(948\) | 1.29747 | 0.0421400 | ||||||||
\(949\) | 22.4726 | + | 5.94737i | 0.729493 | + | 0.193060i | ||||
\(950\) | −1.00515 | −0.0326115 | ||||||||
\(951\) | 15.6405i | 0.507179i | ||||||||
\(952\) | 47.1496 | 1.52813 | ||||||||
\(953\) | 44.8368 | 1.45241 | 0.726204 | − | 0.687479i | \(-0.241283\pi\) | ||||
0.726204 | + | 0.687479i | \(0.241283\pi\) | |||||||
\(954\) | − | 6.99486i | − | 0.226467i | ||||||
\(955\) | 24.2889i | 0.785971i | ||||||||
\(956\) | 2.17805i | 0.0704431i | ||||||||
\(957\) | 7.35483i | 0.237748i | ||||||||
\(958\) | 33.6304 | 1.08655 | ||||||||
\(959\) | 16.9168 | 0.546273 | ||||||||
\(960\) | − | 18.4408i | − | 0.595174i | ||||||
\(961\) | 30.9947 | 0.999829 | ||||||||
\(962\) | 4.62737 | − | 17.4849i | 0.149192 | − | 0.563736i | ||||
\(963\) | −12.6819 | −0.408667 | ||||||||
\(964\) | 2.81884i | 0.0907887i | ||||||||
\(965\) | 50.5874 | 1.62847 | ||||||||
\(966\) | 28.8782 | 0.929140 | ||||||||
\(967\) | 21.7225i | 0.698550i | 0.937020 | + | 0.349275i | \(0.113572\pi\) | ||||
−0.937020 | + | 0.349275i | \(0.886428\pi\) | |||||||
\(968\) | 2.91167i | 0.0935846i | ||||||||
\(969\) | − | 12.0243i | − | 0.386275i | ||||||
\(970\) | 11.3311i | 0.363821i | ||||||||
\(971\) | −28.7521 | −0.922699 | −0.461349 | − | 0.887219i | \(-0.652635\pi\) | ||||
−0.461349 | + | 0.887219i | \(0.652635\pi\) | |||||||
\(972\) | 0.128197 | 0.00411192 | ||||||||
\(973\) | 77.9132i | 2.49778i | ||||||||
\(974\) | 55.4466 | 1.77662 | ||||||||
\(975\) | −0.213709 | + | 0.807519i | −0.00684418 | + | 0.0258613i | ||||
\(976\) | 20.1566 | 0.645196 | ||||||||
\(977\) | 13.7868i | 0.441077i | 0.975378 | + | 0.220539i | \(0.0707815\pi\) | ||||
−0.975378 | + | 0.220539i | \(0.929218\pi\) | |||||||
\(978\) | −1.71815 | −0.0549404 | ||||||||
\(979\) | −2.87912 | −0.0920172 | ||||||||
\(980\) | − | 3.14619i | − | 0.100501i | ||||||
\(981\) | 8.89607i | 0.284030i | ||||||||
\(982\) | 23.0182i | 0.734540i | ||||||||
\(983\) | 32.5478i | 1.03811i | 0.854740 | + | 0.519056i | \(0.173716\pi\) | ||||
−0.854740 | + | 0.519056i | \(0.826284\pi\) | |||||||
\(984\) | −12.1336 | −0.386804 | ||||||||
\(985\) | −20.0554 | −0.639018 | ||||||||
\(986\) | 38.1540i | 1.21507i | ||||||||
\(987\) | 49.6842 | 1.58146 | ||||||||
\(988\) | 1.41700 | + | 0.375009i | 0.0450809 | + | 0.0119306i | ||||
\(989\) | −35.1751 | −1.11850 | ||||||||
\(990\) | − | 2.98753i | − | 0.0949501i | ||||||
\(991\) | −3.97937 | −0.126409 | −0.0632044 | − | 0.998001i | \(-0.520132\pi\) | ||||
−0.0632044 | + | 0.998001i | \(0.520132\pi\) | |||||||
\(992\) | 0.0526709 | 0.00167230 | ||||||||
\(993\) | 23.1426i | 0.734409i | ||||||||
\(994\) | 56.2227i | 1.78328i | ||||||||
\(995\) | − | 13.9521i | − | 0.442312i | ||||||
\(996\) | − | 1.00111i | − | 0.0317215i | ||||||
\(997\) | −24.9767 | −0.791021 | −0.395511 | − | 0.918461i | \(-0.629432\pi\) | ||||
−0.395511 | + | 0.918461i | \(0.629432\pi\) | |||||||
\(998\) | 39.0125 | 1.23492 | ||||||||
\(999\) | − | 3.66658i | − | 0.116006i |
(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 | 429.2.b.b.298.5 | ✓ | 14 | |
3.2 | odd | 2 | 1287.2.b.c.298.10 | 14 | |||
13.5 | odd | 4 | 5577.2.a.y.1.2 | 7 | |||
13.8 | odd | 4 | 5577.2.a.x.1.6 | 7 | |||
13.12 | even | 2 | inner | 429.2.b.b.298.10 | yes | 14 | |
39.38 | odd | 2 | 1287.2.b.c.298.5 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.b.b.298.5 | ✓ | 14 | 1.1 | even | 1 | trivial | |
429.2.b.b.298.10 | yes | 14 | 13.12 | even | 2 | inner | |
1287.2.b.c.298.5 | 14 | 39.38 | odd | 2 | |||
1287.2.b.c.298.10 | 14 | 3.2 | odd | 2 | |||
5577.2.a.x.1.6 | 7 | 13.8 | odd | 4 | |||
5577.2.a.y.1.2 | 7 | 13.5 | odd | 4 |