Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [144,3,Mod(31,144)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(144, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("144.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 144 = 2^{4} \cdot 3^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 144.o (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: | \(3.92371580679\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 8.0.856615824.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 11x^{6} + 36x^{4} + 32x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 79.4 | ||
Root | \(-2.33086i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 144.79 |
Dual form | 144.3.o.a.31.4 |
$q$-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 \(\left(\mathbb{Z}/144\mathbb{Z}\right)^\times\).
\(n\) | \(37\) | \(65\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.89248 | − | 0.795973i | 0.964159 | − | 0.265324i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.355304 | + | 0.615405i | 0.0710609 | + | 0.123081i | 0.899367 | − | 0.437195i | \(-0.144028\pi\) |
−0.828306 | + | 0.560277i | \(0.810695\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.70480 | + | 1.56162i | 0.386401 | + | 0.223088i | 0.680599 | − | 0.732656i | \(-0.261719\pi\) |
−0.294199 | + | 0.955744i | \(0.595053\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.73285 | − | 4.60467i | 0.859206 | − | 0.511630i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.3822 | + | 8.30359i | 1.30748 | + | 0.754872i | 0.981674 | − | 0.190566i | \(-0.0610325\pi\) |
0.325802 | + | 0.945438i | \(0.394366\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −9.17743 | − | 15.8958i | −0.705956 | − | 1.22275i | −0.966345 | − | 0.257248i | \(-0.917184\pi\) |
0.260389 | − | 0.965504i | \(-0.416149\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.51756 | + | 1.49723i | 0.101170 | + | 0.0998156i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −9.69321 | −0.570189 | −0.285095 | − | 0.958499i | \(-0.592025\pi\) | ||||
−0.285095 | + | 0.958499i | \(0.592025\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.20686i | 0.431940i | 0.976400 | + | 0.215970i | \(0.0692913\pi\) | ||||
−0.976400 | + | 0.215970i | \(0.930709\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.06659 | + | 2.36400i | 0.431742 | + | 0.112571i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.94815 | − | 1.12477i | 0.0847022 | − | 0.0489028i | −0.457051 | − | 0.889441i | \(-0.651094\pi\) |
0.541753 | + | 0.840538i | \(0.317761\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.2475 | − | 21.2133i | 0.489901 | − | 0.848533i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 18.7019 | − | 19.4740i | 0.692663 | − | 0.721261i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −20.8217 | + | 36.0642i | −0.717989 | + | 1.24359i | 0.243806 | + | 0.969824i | \(0.421604\pi\) |
−0.961795 | + | 0.273770i | \(0.911729\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −21.6298 | + | 12.4879i | −0.697734 | + | 0.402837i | −0.806503 | − | 0.591230i | \(-0.798642\pi\) |
0.108769 | + | 0.994067i | \(0.465309\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 48.2097 | + | 12.5701i | 1.46090 | + | 0.380911i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.21940i | 0.0634115i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −40.3888 | −1.09159 | −0.545794 | − | 0.837919i | \(-0.683772\pi\) | ||||
−0.545794 | + | 0.837919i | \(0.683772\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −39.1981 | − | 38.6732i | −1.00508 | − | 0.991620i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 25.6944 | + | 44.5040i | 0.626692 | + | 1.08546i | 0.988211 | + | 0.153098i | \(0.0489251\pi\) |
−0.361519 | + | 0.932365i | \(0.617742\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −56.6621 | − | 32.7139i | −1.31772 | − | 0.760787i | −0.334360 | − | 0.942445i | \(-0.608520\pi\) |
−0.983362 | + | 0.181658i | \(0.941854\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.58126 | + | 3.12278i | 0.124028 | + | 0.0693951i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 29.2894 | + | 16.9102i | 0.623179 | + | 0.359793i | 0.778106 | − | 0.628133i | \(-0.216181\pi\) |
−0.154927 | + | 0.987926i | \(0.549514\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −19.6227 | − | 33.9875i | −0.400463 | − | 0.693622i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −28.0374 | + | 7.71554i | −0.549753 | + | 0.151285i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −90.6691 | −1.71074 | −0.855369 | − | 0.518019i | \(-0.826670\pi\) | ||||
−0.855369 | + | 0.518019i | \(0.826670\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 11.8012i | 0.214567i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.53244 | + | 23.7382i | 0.114604 | + | 0.416459i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −66.2243 | + | 38.2346i | −1.12245 | + | 0.648045i | −0.942024 | − | 0.335545i | \(-0.891080\pi\) |
−0.180422 | + | 0.983589i | \(0.557746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.35822 | − | 2.35250i | 0.0222659 | − | 0.0385656i | −0.854678 | − | 0.519159i | \(-0.826245\pi\) |
0.876944 | + | 0.480593i | \(0.159579\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 28.1066 | − | 0.378955i | 0.446136 | − | 0.00601516i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.52157 | − | 11.2957i | 0.100332 | − | 0.173780i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −34.5422 | + | 19.9429i | −0.515555 | + | 0.297656i | −0.735114 | − | 0.677943i | \(-0.762871\pi\) |
0.219559 | + | 0.975599i | \(0.429538\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.73970 | − | 4.80403i | 0.0686913 | − | 0.0696237i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 102.923i | − | 1.44962i | −0.688950 | − | 0.724809i | \(-0.741928\pi\) | ||
0.688950 | − | 0.724809i | \(-0.258072\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 38.1741 | 0.522933 | 0.261466 | − | 0.965213i | \(-0.415794\pi\) | ||||
0.261466 | + | 0.965213i | \(0.415794\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 18.5404 | − | 71.1078i | 0.247206 | − | 0.948103i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 25.9341 | + | 44.9192i | 0.336806 | + | 0.583366i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 94.4994 | + | 54.5593i | 1.19620 | + | 0.690624i | 0.959705 | − | 0.281010i | \(-0.0906694\pi\) |
0.236491 | + | 0.971634i | \(0.424003\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 38.5940 | − | 71.2145i | 0.476470 | − | 0.879191i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 113.503 | + | 65.5311i | 1.36751 | + | 0.789531i | 0.990609 | − | 0.136723i | \(-0.0436570\pi\) |
0.376899 | + | 0.926254i | \(0.376990\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.44404 | − | 5.96526i | −0.0405181 | − | 0.0701795i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −31.5201 | + | 120.888i | −0.362300 | + | 1.38952i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 38.0903 | 0.427981 | 0.213991 | − | 0.976836i | \(-0.431354\pi\) | ||||
0.213991 | + | 0.976836i | \(0.431354\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 57.3266i | − | 0.629963i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −52.6235 | + | 53.3378i | −0.565844 | + | 0.573525i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.05055 | + | 2.91593i | −0.0531636 | + | 0.0306940i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −12.1961 | + | 21.1243i | −0.125733 | + | 0.217776i | −0.922019 | − | 0.387144i | \(-0.873462\pi\) |
0.796286 | + | 0.604920i | \(0.206795\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 149.451 | − | 2.01501i | 1.50961 | − | 0.0203537i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 98.1305 | − | 169.967i | 0.971589 | − | 1.68284i | 0.280829 | − | 0.959758i | \(-0.409391\pi\) |
0.690760 | − | 0.723084i | \(-0.257276\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 104.472 | − | 60.3172i | 1.01430 | − | 0.585604i | 0.101849 | − | 0.994800i | \(-0.467524\pi\) |
0.912446 | + | 0.409196i | \(0.134191\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.76658 | + | 6.41957i | 0.0168246 | + | 0.0611387i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.52440i | 0.0609757i | 0.999535 | + | 0.0304878i | \(0.00970609\pi\) | ||||
−0.999535 | + | 0.0304878i | \(0.990294\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 38.0272 | 0.348873 | 0.174437 | − | 0.984668i | \(-0.444190\pi\) | ||||
0.174437 | + | 0.984668i | \(0.444190\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −116.824 | + | 32.1484i | −1.05247 | + | 0.289625i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −53.5086 | − | 92.6795i | −0.473527 | − | 0.820173i | 0.526014 | − | 0.850476i | \(-0.323686\pi\) |
−0.999541 | + | 0.0303032i | \(0.990353\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.38437 | + | 0.799268i | 0.0120380 | + | 0.00695016i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −144.163 | − | 80.6607i | −1.23216 | − | 0.689408i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −26.2182 | − | 15.1371i | −0.220321 | − | 0.127203i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 77.3992 | + | 134.059i | 0.639662 | + | 1.10793i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 109.744 | + | 108.275i | 0.892231 | + | 0.880282i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 35.1716 | 0.281373 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 101.437i | 0.798713i | 0.916796 | + | 0.399357i | \(0.130766\pi\) | ||||
−0.916796 | + | 0.399357i | \(0.869234\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −189.933 | − | 49.5226i | −1.47235 | − | 0.383896i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −162.820 | + | 94.0042i | −1.24290 | + | 0.717589i | −0.969684 | − | 0.244363i | \(-0.921421\pi\) |
−0.273217 | + | 0.961952i | \(0.588088\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.8160 | + | 22.1979i | −0.0963608 | + | 0.166902i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18.6293 | + | 4.59004i | 0.137995 | + | 0.0340003i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 31.3271 | − | 54.2601i | 0.228665 | − | 0.396059i | −0.728748 | − | 0.684782i | \(-0.759897\pi\) |
0.957413 | + | 0.288723i | \(0.0932307\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 40.5801 | − | 23.4289i | 0.291943 | − | 0.168553i | −0.346875 | − | 0.937911i | \(-0.612757\pi\) |
0.638818 | + | 0.769358i | \(0.279424\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 98.1791 | + | 25.5989i | 0.696305 | + | 0.181553i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 304.822i | − | 2.13163i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −29.5922 | −0.204084 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −83.8113 | − | 82.6889i | −0.570145 | − | 0.562510i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 53.9860 | + | 93.5064i | 0.362322 | + | 0.627560i | 0.988343 | − | 0.152247i | \(-0.0486508\pi\) |
−0.626021 | + | 0.779806i | \(0.715317\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.75240 | − | 1.58910i | −0.0182278 | − | 0.0105238i | 0.490858 | − | 0.871239i | \(-0.336683\pi\) |
−0.509086 | + | 0.860716i | \(0.670017\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −74.9562 | + | 44.6340i | −0.489910 | + | 0.291726i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.3703 | − | 8.87405i | −0.0991632 | − | 0.0572519i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 128.215 | + | 222.075i | 0.816656 | + | 1.41449i | 0.908133 | + | 0.418683i | \(0.137508\pi\) |
−0.0914764 | + | 0.995807i | \(0.529159\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −262.258 | + | 72.1702i | −1.64942 | + | 0.453901i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.02582 | 0.0436386 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 201.100i | − | 1.23374i | −0.787065 | − | 0.616870i | \(-0.788400\pi\) | ||
0.787065 | − | 0.616870i | \(-0.211600\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.39345 | + | 34.1347i | 0.0569300 | + | 0.206877i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −110.689 | + | 63.9062i | −0.662807 | + | 0.382672i | −0.793346 | − | 0.608771i | \(-0.791663\pi\) |
0.130538 | + | 0.991443i | \(0.458329\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −83.9505 | + | 145.407i | −0.496749 | + | 0.860394i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 37.7899 | + | 63.4624i | 0.220993 | + | 0.371125i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 100.718 | − | 174.448i | 0.582183 | − | 1.00837i | −0.413037 | − | 0.910714i | \(-0.635532\pi\) |
0.995220 | − | 0.0976562i | \(-0.0311346\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 66.2543 | − | 38.2519i | 0.378596 | − | 0.218582i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −161.119 | + | 163.306i | −0.910275 | + | 0.922630i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 5.83187i | − | 0.0325803i | −0.999867 | − | 0.0162901i | \(-0.994814\pi\) | ||
0.999867 | − | 0.0162901i | \(-0.00518554\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 132.737 | 0.733353 | 0.366677 | − | 0.930348i | \(-0.380496\pi\) | ||||
0.366677 | + | 0.930348i | \(0.380496\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.05608 | − | 7.88566i | 0.0112354 | − | 0.0430910i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.3503 | − | 24.8555i | −0.0775693 | − | 0.134354i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −139.410 | − | 80.4885i | −0.745509 | − | 0.430420i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 80.9960 | − | 23.4682i | 0.428551 | − | 0.124170i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −36.0843 | − | 20.8333i | −0.188923 | − | 0.109075i | 0.402555 | − | 0.915396i | \(-0.368122\pi\) |
−0.591478 | + | 0.806321i | \(0.701455\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −69.1927 | − | 119.845i | −0.358511 | − | 0.620960i | 0.629201 | − | 0.777242i | \(-0.283382\pi\) |
−0.987712 | + | 0.156283i | \(0.950049\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9.87242 | − | 37.8635i | 0.0506278 | − | 0.194172i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −109.421 | −0.555438 | −0.277719 | − | 0.960662i | \(-0.589578\pi\) | ||||
−0.277719 | + | 0.960662i | \(0.589578\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 87.0243i | 0.437308i | 0.975802 | + | 0.218654i | \(0.0701666\pi\) | ||||
−0.975802 | + | 0.218654i | \(0.929833\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −84.0385 | + | 85.1792i | −0.418102 | + | 0.423777i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −112.637 | + | 65.0311i | −0.554863 | + | 0.320350i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.2587 | + | 31.6249i | −0.0890666 | + | 0.154268i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.88559 | − | 17.6682i | 0.0477565 | − | 0.0853538i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −68.1464 | + | 118.033i | −0.326059 | + | 0.564751i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −244.383 | + | 141.095i | −1.15821 | + | 0.668695i | −0.950875 | − | 0.309574i | \(-0.899814\pi\) |
−0.207339 | + | 0.978269i | \(0.566480\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −81.9239 | − | 297.702i | −0.384619 | − | 1.39766i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 46.4935i | − | 0.216249i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −78.0057 | −0.359473 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 110.418 | − | 30.3855i | 0.504190 | − | 0.138747i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 88.9588 | + | 154.081i | 0.402529 | + | 0.697200i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 255.359 | + | 147.432i | 1.14511 | + | 0.661129i | 0.947691 | − | 0.319190i | \(-0.103411\pi\) |
0.197419 | + | 0.980319i | \(0.436744\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.97208 | − | 220.435i | −0.0132092 | − | 0.979712i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 124.390 | + | 71.8164i | 0.547972 | + | 0.316372i | 0.748304 | − | 0.663356i | \(-0.230869\pi\) |
−0.200332 | + | 0.979728i | \(0.564202\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −141.426 | − | 244.958i | −0.617583 | − | 1.06968i | −0.989925 | − | 0.141590i | \(-0.954779\pi\) |
0.372343 | − | 0.928095i | \(-0.378555\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 110.768 | + | 109.285i | 0.479516 | + | 0.473094i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −25.9127 | −0.111213 | −0.0556067 | − | 0.998453i | \(-0.517709\pi\) | ||||
−0.0556067 | + | 0.998453i | \(0.517709\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 24.0331i | 0.102269i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 316.765 | + | 82.5925i | 1.33656 | + | 0.348491i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 310.807 | − | 179.444i | 1.30045 | − | 0.750813i | 0.319966 | − | 0.947429i | \(-0.396328\pi\) |
0.980481 | + | 0.196616i | \(0.0629951\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 87.7048 | − | 151.909i | 0.363920 | − | 0.630328i | −0.624682 | − | 0.780879i | \(-0.714771\pi\) |
0.988602 | + | 0.150551i | \(0.0481048\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 54.9476 | − | 236.706i | 0.226122 | − | 0.974099i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 13.9441 | − | 24.1518i | 0.0569145 | − | 0.0985789i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 130.454 | − | 75.3179i | 0.528156 | − | 0.304931i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 380.466 | + | 99.2017i | 1.52798 | + | 0.398401i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 410.044i | 1.63364i | 0.576891 | + | 0.816821i | \(0.304266\pi\) | ||||
−0.576891 | + | 0.816821i | \(0.695734\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 37.3583 | 0.147661 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.7100 | − | 14.5130i | −0.0576863 | − | 0.0569137i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −86.4280 | − | 149.698i | −0.336296 | − | 0.582481i | 0.647437 | − | 0.762119i | \(-0.275841\pi\) |
−0.983733 | + | 0.179638i | \(0.942507\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −109.244 | − | 63.0719i | −0.421790 | − | 0.243521i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.05276 | + | 374.756i | 0.0193592 | + | 1.43585i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 132.696 | + | 76.6118i | 0.504546 | + | 0.291300i | 0.730589 | − | 0.682818i | \(-0.239246\pi\) |
−0.226043 | + | 0.974117i | \(0.572579\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −32.2151 | − | 55.7983i | −0.121567 | − | 0.210559i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 110.175 | − | 30.3189i | 0.412642 | − | 0.113554i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 12.6752 | 0.0471198 | 0.0235599 | − | 0.999722i | \(-0.492500\pi\) | ||||
0.0235599 | + | 0.999722i | \(0.492500\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 40.7101i | 0.150222i | 0.997175 | + | 0.0751108i | \(0.0239311\pi\) | ||||
−0.997175 | + | 0.0751108i | \(0.976069\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −45.6305 | − | 165.816i | −0.167145 | − | 0.607385i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 352.293 | − | 203.397i | 1.28107 | − | 0.739624i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 184.143 | − | 318.945i | 0.664776 | − | 1.15143i | −0.314570 | − | 0.949234i | \(-0.601860\pi\) |
0.979346 | − | 0.202191i | \(-0.0648063\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −109.757 | + | 196.165i | −0.393394 | + | 0.703101i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −238.310 | + | 412.765i | −0.848078 | + | 1.46891i | 0.0348433 | + | 0.999393i | \(0.488907\pi\) |
−0.882921 | + | 0.469521i | \(0.844427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 150.052 | − | 86.6323i | 0.530217 | − | 0.306121i | −0.210888 | − | 0.977510i | \(-0.567635\pi\) |
0.741105 | + | 0.671389i | \(0.234302\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.2876 | + | 12.4544i | −0.0431143 | + | 0.0436995i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 160.499i | 0.559231i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −195.042 | −0.674884 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −18.4626 | + | 70.8094i | −0.0634455 | + | 0.243331i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2.91833 | − | 5.05470i | −0.00996017 | − | 0.0172515i | 0.861002 | − | 0.508601i | \(-0.169837\pi\) |
−0.870963 | + | 0.491349i | \(0.836504\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −47.0596 | − | 27.1699i | −0.159524 | − | 0.0921013i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 430.680 | − | 124.787i | 1.45010 | − | 0.420160i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −35.7580 | − | 20.6449i | −0.119592 | − | 0.0690465i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −102.173 | − | 176.969i | −0.339446 | − | 0.587937i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 148.551 | − | 569.735i | 0.490268 | − | 1.88031i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.93032 | 0.00632893 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 371.717i | 1.21080i | 0.795920 | + | 0.605402i | \(0.206988\pi\) | ||||
−0.795920 | + | 0.605402i | \(0.793012\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 254.173 | − | 257.623i | 0.822567 | − | 0.833733i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −193.964 | + | 111.985i | −0.623679 | + | 0.360081i | −0.778300 | − | 0.627892i | \(-0.783918\pi\) |
0.154621 | + | 0.987974i | \(0.450584\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 79.0960 | − | 136.998i | 0.252703 | − | 0.437694i | −0.711566 | − | 0.702619i | \(-0.752014\pi\) |
0.964269 | + | 0.264925i | \(0.0853472\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 10.2196 | + | 17.1623i | 0.0324432 | + | 0.0544835i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −206.428 | + | 357.543i | −0.651191 | + | 1.12790i | 0.331643 | + | 0.943405i | \(0.392397\pi\) |
−0.982834 | + | 0.184491i | \(0.940936\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −598.925 | + | 345.789i | −1.87751 | + | 1.08398i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.19325 | + | 18.8717i | 0.0161783 | + | 0.0587903i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 79.5508i | − | 0.246287i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −449.603 | −1.38339 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 109.993 | − | 30.2686i | 0.336370 | − | 0.0925646i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 52.8147 | + | 91.4778i | 0.160531 | + | 0.278048i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −126.937 | − | 73.2871i | −0.383495 | − | 0.221411i | 0.295843 | − | 0.955237i | \(-0.404400\pi\) |
−0.679338 | + | 0.733826i | \(0.737733\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −312.320 | + | 185.977i | −0.937899 | + | 0.558489i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −24.5460 | − | 14.1716i | −0.0732716 | − | 0.0423034i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −47.3499 | − | 82.0124i | −0.140504 | − | 0.243360i | 0.787182 | − | 0.616720i | \(-0.211539\pi\) |
−0.927687 | + | 0.373360i | \(0.878206\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −228.543 | − | 225.482i | −0.674167 | − | 0.665139i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −414.779 | −1.21636 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 275.611i | − | 0.803532i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 4.64046 | + | 1.20994i | 0.0134506 | + | 0.00350708i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −81.3438 | + | 46.9639i | −0.234420 | + | 0.135343i | −0.612609 | − | 0.790386i | \(-0.709880\pi\) |
0.378189 | + | 0.925728i | \(0.376547\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −115.579 | + | 200.188i | −0.331171 | + | 0.573605i | −0.982742 | − | 0.184983i | \(-0.940777\pi\) |
0.651571 | + | 0.758588i | \(0.274110\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −481.191 | − | 118.560i | −1.37091 | − | 0.337777i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −48.9623 | + | 84.8052i | −0.138703 | + | 0.240241i | −0.927006 | − | 0.375046i | \(-0.877627\pi\) |
0.788303 | + | 0.615288i | \(0.210960\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 63.3393 | − | 36.5690i | 0.178421 | − | 0.103011i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −87.8844 | − | 22.9147i | −0.246175 | − | 0.0641869i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 244.287i | 0.680465i | 0.940341 | + | 0.340233i | \(0.110506\pi\) | ||||
−0.940341 | + | 0.340233i | \(0.889494\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 293.647 | 0.813428 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 330.583 | + | 326.156i | 0.910697 | + | 0.898501i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 13.5634 | + | 23.4925i | 0.0371601 | + | 0.0643631i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −368.327 | − | 212.654i | −1.00362 | − | 0.579438i | −0.0942999 | − | 0.995544i | \(-0.530061\pi\) |
−0.909316 | + | 0.416106i | \(0.863395\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 403.617 | + | 225.829i | 1.09381 | + | 0.612002i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −245.242 | − | 141.591i | −0.661030 | − | 0.381646i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 44.8567 | + | 77.6941i | 0.120259 | + | 0.208295i | 0.919870 | − | 0.392224i | \(-0.128294\pi\) |
−0.799611 | + | 0.600519i | \(0.794961\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 101.733 | − | 27.9957i | 0.271288 | − | 0.0746551i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 764.359 | 2.02748 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 406.140i | − | 1.07161i | −0.844342 | − | 0.535805i | \(-0.820008\pi\) | ||
0.844342 | − | 0.535805i | \(-0.179992\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 80.7408 | + | 293.403i | 0.211918 | + | 0.770087i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 280.901 | − | 162.178i | 0.733423 | − | 0.423442i | −0.0862502 | − | 0.996274i | \(-0.527488\pi\) |
0.819673 | + | 0.572832i | \(0.194155\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.4290 | + | 31.9200i | −0.0478675 | + | 0.0829090i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −588.796 | + | 7.93860i | −1.52144 | + | 0.0205132i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −28.6761 | + | 49.6685i | −0.0737176 | + | 0.127683i | −0.900528 | − | 0.434798i | \(-0.856820\pi\) |
0.826810 | + | 0.562481i | \(0.190153\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −18.8838 | + | 10.9026i | −0.0482963 | + | 0.0278839i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −396.128 | + | 401.505i | −1.00796 | + | 1.02164i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 77.5406i | 0.196305i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 194.475 | 0.489861 | 0.244931 | − | 0.969541i | \(-0.421235\pi\) | ||||
0.244931 | + | 0.969541i | \(0.421235\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −19.4010 | + | 74.4082i | −0.0486240 | + | 0.186487i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −163.943 | − | 283.958i | −0.408836 | − | 0.708124i | 0.585924 | − | 0.810366i | \(-0.300732\pi\) |
−0.994760 | + | 0.102242i | \(0.967398\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 397.011 | + | 229.215i | 0.985140 | + | 0.568771i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 57.5384 | − | 1.55184i | 0.142070 | − | 0.00383170i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −580.881 | − | 335.372i | −1.42723 | − | 0.824009i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −36.6786 | − | 63.5292i | −0.0896787 | − | 0.155328i | 0.817697 | − | 0.575649i | \(-0.195251\pi\) |
−0.907375 | + | 0.420321i | \(0.861917\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 47.4233 | − | 181.882i | 0.115385 | − | 0.442534i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −238.832 | −0.578285 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 93.1340i | 0.224419i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 98.7282 | − | 100.068i | 0.236758 | − | 0.239972i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 557.390 | − | 321.809i | 1.33029 | − | 0.768041i | 0.344943 | − | 0.938624i | \(-0.387898\pi\) |
0.985343 | + | 0.170582i | \(0.0545649\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −280.151 | + | 485.236i | −0.665441 | + | 1.15258i | 0.313724 | + | 0.949514i | \(0.398423\pi\) |
−0.979165 | + | 0.203064i | \(0.934910\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 304.357 | − | 4.10358i | 0.719520 | − | 0.00970112i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −118.718 | + | 205.625i | −0.279336 | + | 0.483824i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.34742 | − | 4.24204i | 0.0172071 | − | 0.00993451i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −242.631 | − | 881.692i | −0.565572 | − | 2.05523i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 536.437i | 1.24463i | 0.782765 | + | 0.622317i | \(0.213809\pi\) | ||||
−0.782765 | + | 0.622317i | \(0.786191\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 281.999 | 0.651268 | 0.325634 | − | 0.945496i | \(-0.394422\pi\) | ||||
0.325634 | + | 0.945496i | \(0.394422\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −85.5947 | + | 23.5546i | −0.196769 | + | 0.0541484i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 9.23079 | + | 15.9882i | 0.0211231 | + | 0.0365863i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 87.2604 | + | 50.3798i | 0.198771 | + | 0.114760i | 0.596082 | − | 0.802924i | \(-0.296723\pi\) |
−0.397311 | + | 0.917684i | \(0.630057\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −308.241 | − | 172.464i | −0.698958 | − | 0.391076i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −519.799 | − | 300.106i | −1.17336 | − | 0.677440i | −0.218891 | − | 0.975749i | \(-0.570244\pi\) |
−0.954469 | + | 0.298309i | \(0.903577\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5337 | + | 23.4410i | 0.0304127 | + | 0.0526764i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 230.582 | + | 227.494i | 0.515843 | + | 0.508935i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 639.843 | 1.42504 | 0.712520 | − | 0.701651i | \(-0.247554\pi\) | ||||
0.712520 | + | 0.701651i | \(0.247554\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 853.422i | 1.89229i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.22612 | − | 2.40559i | −0.0203667 | − | 0.00531036i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 35.2791 | − | 20.3684i | 0.0775365 | − | 0.0447657i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 86.7721 | − | 150.294i | 0.189873 | − | 0.328870i | −0.755334 | − | 0.655339i | \(-0.772526\pi\) |
0.945208 | + | 0.326469i | \(0.105859\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −181.282 | + | 188.766i | −0.394949 | + | 0.411255i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 361.655 | − | 626.406i | 0.784502 | − | 1.35880i | −0.144794 | − | 0.989462i | \(-0.546252\pi\) |
0.929296 | − | 0.369336i | \(-0.120415\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 643.880 | − | 371.744i | 1.39067 | − | 0.802903i | 0.397280 | − | 0.917698i | \(-0.369954\pi\) |
0.993389 | + | 0.114794i | \(0.0366210\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −51.5217 | − | 13.4336i | −0.110799 | − | 0.0288895i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 98.0700i | − | 0.210000i | −0.994472 | − | 0.105000i | \(-0.966516\pi\) | ||
0.994472 | − | 0.105000i | \(-0.0334842\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −124.573 | −0.265614 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 547.625 | + | 540.291i | 1.16269 | + | 1.14711i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −543.285 | − | 940.997i | −1.14859 | − | 1.98942i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 174.095 | + | 100.514i | 0.366515 | + | 0.211608i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −701.131 | + | 417.501i | −1.46988 | + | 0.875265i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 293.648 | + | 169.538i | 0.613043 | + | 0.353941i | 0.774156 | − | 0.632995i | \(-0.218175\pi\) |
−0.161112 | + | 0.986936i | \(0.551508\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 370.665 | + | 642.011i | 0.770614 | + | 1.33474i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 20.3220 | − | 5.59236i | 0.0420746 | − | 0.0115784i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −17.3334 | −0.0357389 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 777.718i | − | 1.59696i | −0.602023 | − | 0.798479i | \(-0.705638\pi\) | ||
0.602023 | − | 0.798479i | \(-0.294362\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −160.070 | − | 581.676i | −0.327341 | − | 1.18952i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −52.0054 | + | 30.0254i | −0.105917 | + | 0.0611514i | −0.552023 | − | 0.833829i | \(-0.686144\pi\) |
0.446106 | + | 0.894980i | \(0.352811\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 201.829 | − | 349.578i | 0.409390 | − | 0.709084i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 54.3407 | + | 91.2570i | 0.109779 | + | 0.184358i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 160.726 | − | 278.386i | 0.323393 | − | 0.560133i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 250.110 | − | 144.401i | 0.501222 | − | 0.289381i | −0.227996 | − | 0.973662i | \(-0.573217\pi\) |
0.729218 | + | 0.684281i | \(0.239884\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −269.297 | + | 272.953i | −0.537520 | + | 0.544816i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 567.389i | 1.12801i | 0.825772 | + | 0.564005i | \(0.190740\pi\) | ||||
−0.825772 | + | 0.564005i | \(0.809260\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 139.465 | 0.276168 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −127.085 | + | 487.408i | −0.250661 | + | 0.961357i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 158.283 | + | 274.155i | 0.310970 | + | 0.538615i | 0.978573 | − | 0.205902i | \(-0.0660130\pi\) |
−0.667603 | + | 0.744517i | \(0.732680\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 103.253 | + | 59.6134i | 0.202061 | + | 0.116660i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 159.821 | + | 153.484i | 0.311541 | + | 0.299189i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 74.2390 | + | 42.8619i | 0.144153 | + | 0.0832271i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 280.831 | + | 486.414i | 0.543194 | + | 0.940840i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 152.468 | − | 584.756i | 0.293772 | − | 1.12670i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 597.419 | 1.14668 | 0.573339 | − | 0.819318i | \(-0.305648\pi\) | ||||
0.573339 | + | 0.819318i | \(0.305648\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 630.846i | − | 1.20621i | −0.797663 | − | 0.603103i | \(-0.793931\pi\) | ||
0.797663 | − | 0.603103i | \(-0.206069\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 161.191 | − | 163.379i | 0.307031 | − | 0.311199i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 209.662 | − | 121.048i | 0.397840 | − | 0.229693i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −261.970 | + | 453.745i | −0.495217 | + | 0.857741i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −336.045 | + | 600.604i | −0.632853 | + | 1.13108i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 471.617 | − | 816.865i | 0.884835 | − | 1.53258i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.01515 | + | 2.31815i | −0.00750495 | + | 0.00433299i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −4.64201 | − | 16.8685i | −0.00864434 | − | 0.0314126i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 651.755i | − | 1.20919i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −144.808 | −0.267667 | −0.133834 | − | 0.991004i | \(-0.542729\pi\) | ||||
−0.133834 | + | 0.991004i | \(0.542729\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 383.939 | − | 105.655i | 0.707069 | − | 0.194577i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 13.5112 | + | 23.4022i | 0.0247913 | + | 0.0429397i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 679.104 | + | 392.081i | 1.24151 | + | 0.716784i | 0.969401 | − | 0.245484i | \(-0.0789468\pi\) |
0.272105 | + | 0.962268i | \(0.412280\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −0.329596 | − | 24.4457i | −0.000600357 | − | 0.0445277i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −295.974 | − | 170.881i | −0.537158 | − | 0.310128i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 170.402 | + | 295.144i | 0.308140 | + | 0.533715i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −61.2923 | − | 60.4714i | −0.110436 | − | 0.108958i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 92.1884 | 0.165509 | 0.0827544 | − | 0.996570i | \(-0.473628\pi\) | ||||
0.0827544 | + | 0.996570i | \(0.473628\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1200.92i | 2.14833i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −467.307 | − | 121.844i | −0.832990 | − | 0.217191i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 141.939 | − | 81.9485i | 0.252112 | − | 0.145557i | −0.368619 | − | 0.929581i | \(-0.620169\pi\) |
0.620731 | + | 0.784024i | \(0.286836\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 38.0237 | − | 65.8589i | 0.0672985 | − | 0.116564i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 215.599 | − | 132.352i | 0.380245 | − | 0.233425i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −352.219 | + | 610.061i | −0.619014 | + | 1.07216i | 0.370652 | + | 0.928772i | \(0.379134\pi\) |
−0.989666 | + | 0.143392i | \(0.954199\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 413.817 | − | 238.917i | 0.724723 | − | 0.418419i | −0.0917653 | − | 0.995781i | \(-0.529251\pi\) |
0.816489 | + | 0.577361i | \(0.195918\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −120.956 | − | 31.5377i | −0.211092 | − | 0.0550396i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 55.1023i | − | 0.0958301i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21.5525 | −0.0373527 | −0.0186764 | − | 0.999826i | \(-0.505945\pi\) | ||||
−0.0186764 | + | 0.999826i | \(0.505945\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −295.532 | − | 291.574i | −0.510418 | − | 0.503582i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 204.669 | + | 354.498i | 0.352271 | + | 0.610151i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1304.02 | − | 752.879i | −2.23675 | − | 1.29139i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.58257 | − | 117.378i | −0.00270526 | − | 0.200645i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −686.177 | − | 396.164i | −1.16896 | − | 0.674897i | −0.215522 | − | 0.976499i | \(-0.569145\pi\) |
−0.953434 | + | 0.301602i | \(0.902479\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −102.487 | − | 177.512i | −0.174001 | − | 0.301379i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −316.498 | + | 87.0964i | −0.535530 | + | 0.147371i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −571.777 | −0.964211 | −0.482105 | − | 0.876113i | \(-0.660128\pi\) | ||||
−0.482105 | + | 0.876113i | \(0.660128\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 21.5131i | − | 0.0361565i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 69.2690 | + | 251.716i | 0.116028 | + | 0.421635i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −803.662 | + | 463.994i | −1.34167 | + | 0.774615i | −0.987053 | − | 0.160396i | \(-0.948723\pi\) |
−0.354620 | + | 0.935011i | \(0.615390\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −66.4316 | + | 115.063i | −0.110535 | + | 0.191452i | −0.915986 | − | 0.401210i | \(-0.868590\pi\) |
0.805451 | + | 0.592662i | \(0.201923\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −175.279 | + | 313.271i | −0.290678 | + | 0.519521i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −55.0005 | + | 95.2637i | −0.0909100 | + | 0.157461i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −480.102 | + | 277.187i | −0.790942 | + | 0.456651i | −0.840294 | − | 0.542131i | \(-0.817618\pi\) |
0.0493520 | + | 0.998781i | \(0.484284\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −274.037 | + | 277.757i | −0.449979 | + | 0.456087i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 620.771i | − | 1.01599i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1096.88 | 1.78937 | 0.894684 | − | 0.446700i | \(-0.147401\pi\) | ||||
0.894684 | + | 0.446700i | \(0.147401\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −27.6402 | + | 106.008i | −0.0449434 | + | 0.172370i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −311.636 | − | 539.770i | −0.505083 | − | 0.874829i | −0.999983 | − | 0.00587917i | \(-0.998129\pi\) |
0.494900 | − | 0.868950i | \(-0.335205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 613.432 | + | 354.165i | 0.991005 | + | 0.572157i | 0.905575 | − | 0.424187i | \(-0.139440\pi\) |
0.0854305 | + | 0.996344i | \(0.472773\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 14.5304 | − | 58.9736i | 0.0233984 | − | 0.0949656i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 103.027 | + | 59.4826i | 0.165372 | + | 0.0954777i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −293.691 | − | 508.688i | −0.469906 | − | 0.813901i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −103.161 | + | 395.650i | −0.164531 | + | 0.631021i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 391.497 | 0.622412 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 1142.86i | − | 1.81119i | −0.424139 | − | 0.905597i | \(-0.639423\pi\) | ||
0.424139 | − | 0.905597i | \(-0.360577\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −594.565 | + | 602.636i | −0.939282 | + | 0.952031i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −62.4246 | + | 36.0409i | −0.0983065 | + | 0.0567573i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −360.172 | + | 623.836i | −0.565419 | + | 0.979334i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −473.926 | − | 795.888i | −0.741668 | − | 1.24552i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −138.542 | + | 239.961i | −0.216134 | + | 0.374354i | −0.953623 | − | 0.301005i | \(-0.902678\pi\) |
0.737489 | + | 0.675359i | \(0.236011\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −737.236 | + | 425.644i | −1.14656 | + | 0.661965i | −0.948046 | − | 0.318133i | \(-0.896944\pi\) |
−0.198511 | + | 0.980099i | \(0.563611\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37.0076 | − | 134.481i | −0.0573761 | − | 0.208498i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 706.622i | 1.09215i | 0.837736 | + | 0.546076i | \(0.183879\pi\) | ||||
−0.837736 | + | 0.546076i | \(0.816121\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1269.94 | −1.95676 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −225.630 | + | 62.0904i | −0.346589 | + | 0.0953770i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −390.342 | − | 676.092i | −0.597767 | − | 1.03536i | −0.993150 | − | 0.116846i | \(-0.962722\pi\) |
0.395383 | − | 0.918516i | \(-0.370612\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −115.701 | − | 66.8002i | −0.176643 | − | 0.101985i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 295.195 | − | 175.779i | 0.449307 | − | 0.267548i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 491.322 | + | 283.665i | 0.745557 | + | 0.430447i | 0.824086 | − | 0.566465i | \(-0.191689\pi\) |
−0.0785296 | + | 0.996912i | \(0.525023\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 46.9164 | + | 81.2615i | 0.0709778 | + | 0.122937i | 0.899330 | − | 0.437270i | \(-0.144055\pi\) |
−0.828352 | + | 0.560208i | \(0.810721\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 379.956 | + | 374.868i | 0.573086 | + | 0.565411i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −18.2143 | −0.0273899 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 93.6780i | 0.140447i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 855.973 | + | 223.184i | 1.27948 | + | 0.333608i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.0684 | − | 22.5562i | 0.0582241 | − | 0.0336157i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 100.742 | − | 174.490i | 0.149691 | − | 0.259272i | −0.781422 | − | 0.624003i | \(-0.785505\pi\) |
0.931113 | + | 0.364730i | \(0.118839\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −184.057 | − | 635.238i | −0.272677 | − | 0.941094i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −336.988 | + | 583.680i | −0.497766 | + | 0.862157i | −0.999997 | − | 0.00257723i | \(-0.999180\pi\) |
0.502230 | + | 0.864734i | \(0.332513\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −65.9763 | + | 38.0914i | −0.0971668 | + | 0.0560993i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 416.958 | + | 108.716i | 0.612273 | + | 0.159642i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 155.633i | 0.227867i | 0.993488 | + | 0.113933i | \(0.0363450\pi\) | ||||
−0.993488 | + | 0.113933i | \(0.963655\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 44.5226 | 0.0649965 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −604.053 | − | 595.963i | −0.879262 | − | 0.867487i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 832.110 | + | 1441.26i | 1.20771 | + | 2.09181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −693.263 | − | 400.255i | −1.00327 | − | 0.579241i | −0.0940588 | − | 0.995567i | \(-0.529984\pi\) |
−0.909215 | + | 0.416326i | \(0.863318\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 407.382 | + | 227.935i | 0.587853 | + | 0.328911i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 28.8366 | + | 16.6488i | 0.0414915 | + | 0.0239551i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −249.061 | − | 431.387i | −0.357333 | − | 0.618919i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −74.9520 | + | 20.6258i | −0.107228 | + | 0.0295077i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −488.317 | −0.696601 | −0.348300 | − | 0.937383i | \(-0.613241\pi\) | ||||
−0.348300 | + | 0.937383i | \(0.613241\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 331.465i | − | 0.471501i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.1297 | + | 69.5153i | 0.0271344 | + | 0.0986033i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 530.848 | − | 306.485i | 0.750845 | − | 0.433501i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 358.633 | − | 621.170i | 0.505829 | − | 0.876121i | −0.494149 | − | 0.869377i | \(-0.664520\pi\) |
0.999977 | − | 0.00674353i | \(-0.00214655\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 981.978 | − | 13.2398i | 1.38112 | − | 0.0186214i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −28.0920 | + | 48.6568i | −0.0393997 | + | 0.0682423i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 187.589 | − | 108.305i | 0.262363 | − | 0.151475i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 756.169 | − | 766.433i | 1.05463 | − | 1.06894i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 512.219i | − | 0.712404i | −0.934409 | − | 0.356202i | \(-0.884071\pi\) | ||
0.934409 | − | 0.356202i | \(-0.115929\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 376.770 | 0.522566 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 132.768 | − | 509.204i | 0.183636 | − | 0.704294i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 510.028 | + | 883.394i | 0.703487 | + | 1.21848i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 574.499 | + | 331.687i | 0.790232 | + | 0.456241i | 0.840044 | − | 0.542518i | \(-0.182529\pi\) |
−0.0498122 | + | 0.998759i | \(0.515862\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −29.4770 | − | 728.404i | −0.0404349 | − | 0.999182i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 549.237 | + | 317.102i | 0.751351 | + | 0.433793i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −146.883 | − | 254.408i | −0.200386 | − | 0.347078i | 0.748267 | − | 0.663398i | \(-0.230886\pi\) |
−0.948653 | + | 0.316320i | \(0.897553\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.1087 | − | 80.9577i | 0.0287193 | − | 0.110147i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −662.392 | −0.898768 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1335.27i | 1.80686i | 0.428736 | + | 0.903430i | \(0.358959\pi\) | ||||
−0.428736 | + | 0.903430i | \(0.641041\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 317.385 | − | 321.694i | 0.428320 | − | 0.434134i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −488.188 | + | 281.855i | −0.657050 | + | 0.379348i | −0.791152 | − | 0.611620i | \(-0.790518\pi\) |
0.134102 | + | 0.990968i | \(0.457185\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.3629 | + | 66.4465i | −0.0514938 | + | 0.0891899i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1179.45 | − | 15.9023i | 1.57892 | − | 0.0212882i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −10.1886 | + | 17.6472i | −0.0136030 | + | 0.0235610i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −591.407 | + | 341.449i | −0.787493 | + | 0.454659i | −0.839079 | − | 0.544009i | \(-0.816906\pi\) |
0.0515861 | + | 0.998669i | \(0.483572\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 326.384 | + | 1186.04i | 0.433445 | + | 1.57509i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 2.25845i | − | 0.00299133i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −534.746 | −0.706401 | −0.353201 | − | 0.935548i | \(-0.614907\pi\) | ||||
−0.353201 | + | 0.935548i | \(0.614907\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 108.058 | − | 29.7362i | 0.142369 | − | 0.0391782i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −416.191 | − | 720.863i | −0.546900 | − | 0.947258i | −0.998485 | − | 0.0550300i | \(-0.982475\pi\) |
0.451585 | − | 0.892228i | \(-0.350859\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 102.856 | + | 59.3840i | 0.134805 | + | 0.0778296i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −54.1003 | − | 30.2698i | −0.0707194 | − | 0.0395683i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1215.54 | + | 701.791i | 1.58480 | + | 0.914982i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −351.020 | − | 607.985i | −0.456464 | − | 0.790618i | 0.542308 | − | 0.840180i | \(-0.317551\pi\) |
−0.998771 | + | 0.0495620i | \(0.984217\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −369.146 | − | 364.203i | −0.478789 | − | 0.472377i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −472.477 | −0.611225 | −0.305612 | − | 0.952156i | \(-0.598861\pi\) | ||||
−0.305612 | + | 0.952156i | \(0.598861\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 611.785i | 0.789400i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −366.189 | − | 95.4790i | −0.471285 | − | 0.122882i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −365.238 | + | 210.870i | −0.468855 | + | 0.270693i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 854.630 | − | 1480.26i | 1.09428 | − | 1.89534i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 312.911 | + | 1079.95i | 0.399631 | + | 1.37925i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −91.1107 | + | 157.808i | −0.116065 | + | 0.201030i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 556.186 | − | 321.114i | 0.706717 | − | 0.408023i | −0.103127 | − | 0.994668i | \(-0.532885\pi\) |
0.809844 | + | 0.586645i | \(0.199552\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 444.800 | + | 115.976i | 0.563752 | + | 0.146991i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 334.240i | − | 0.422554i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −49.8598 | −0.0628749 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −137.596 | − | 135.753i | −0.173076 | − | 0.170758i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.3167 | + | 73.2947i | 0.0530950 | + | 0.0919632i | 0.891351 | − | 0.453313i | \(-0.149758\pi\) |
−0.838256 | + | 0.545276i | \(0.816425\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −283.909 | − | 163.915i | −0.355330 | − | 0.205150i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 294.547 | − | 175.393i | 0.367724 | − | 0.218968i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 549.029 | + | 316.982i | 0.683722 | + | 0.394747i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.49630 | + | 4.32373i | 0.00310100 | + | 0.00537109i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 36.6628 | − | 10.0891i | 0.0454310 | − | 0.0125020i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1071.63 | −1.32464 | −0.662319 | − | 0.749222i | \(-0.730427\pi\) | ||||
−0.662319 | + | 0.749222i | \(0.730427\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 745.523i | − | 0.919264i | −0.888110 | − | 0.459632i | \(-0.847981\pi\) | ||
0.888110 | − | 0.459632i | \(-0.152019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 32.4041 | + | 117.753i | 0.0398575 | + | 0.144838i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 123.758 | − | 71.4516i | 0.151850 | − | 0.0876707i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 268.478 | − | 465.017i | 0.328614 | − | 0.569177i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −263.970 | − | 443.298i | −0.322308 | − | 0.541268i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 417.550 | − | 723.217i | 0.508587 | − | 0.880898i | −0.491364 | − | 0.870954i | \(-0.663501\pi\) |
0.999951 | − | 0.00994363i | \(-0.00316521\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 369.777 | − | 213.491i | 0.449304 | − | 0.259406i | −0.258232 | − | 0.966083i | \(-0.583140\pi\) |
0.707536 | + | 0.706677i | \(0.249807\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 857.102 | − | 868.736i | 1.03891 | − | 1.05301i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 235.457i | 0.284713i | 0.989815 | + | 0.142356i | \(0.0454679\pi\) | ||||
−0.989815 | + | 0.142356i | \(0.954532\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1336.05 | −1.61164 | −0.805819 | − | 0.592161i | \(-0.798275\pi\) | ||||
−0.805819 | + | 0.592161i | \(0.798275\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 278.758 | − | 1069.11i | 0.335448 | − | 1.28654i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 190.207 | + | 329.448i | 0.228340 | + | 0.395496i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −78.6565 | − | 45.4123i | −0.0941994 | − | 0.0543860i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −161.327 | + | 654.767i | −0.192744 | + | 0.782279i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1315.40 | + | 759.449i | 1.56782 | + | 0.905183i | 0.996422 | + | 0.0845127i | \(0.0269334\pi\) |
0.571401 | + | 0.820671i | \(0.306400\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −446.586 | − | 773.509i | −0.531017 | − | 0.919749i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −360.756 | + | 1383.60i | −0.427943 | + | 1.64128i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −119.312 | −0.141198 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 483.472i | 0.570805i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 365.064 | − | 370.019i | 0.429993 | − | 0.435829i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −78.6834 | + | 45.4279i | −0.0924599 | + | 0.0533818i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −219.635 | + | 380.418i | −0.257485 | + | 0.445977i | −0.965568 | − | 0.260153i | \(-0.916227\pi\) |
0.708083 | + | 0.706130i | \(0.249560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −25.6282 | + | 45.8046i | −0.0299745 | + | 0.0535726i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 42.9674 | − | 74.4218i | 0.0501370 | − | 0.0868399i | −0.839868 | − | 0.542791i | \(-0.817368\pi\) |
0.890005 | + | 0.455951i | \(0.150701\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −750.391 | + | 433.239i | −0.873564 | + | 0.504352i | −0.868531 | − | 0.495635i | \(-0.834935\pi\) |
−0.00503295 | + | 0.999987i | \(0.501602\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 127.753 | + | 464.241i | 0.148378 | + | 0.539188i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 651.682i | − | 0.755136i | −0.925982 | − | 0.377568i | \(-0.876760\pi\) | ||
0.925982 | − | 0.377568i | \(-0.123240\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 143.142 | 0.165482 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −564.153 | + | 155.248i | −0.650696 | + | 0.179063i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 906.076 | + | 1569.37i | 1.04266 | + | 1.80595i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 634.017 | + | 366.050i | 0.727919 | + | 0.420264i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2.95961 | + | 219.510i | 0.00339016 | + | 0.251444i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 95.1323 | + | 54.9247i | 0.108723 | + | 0.0627711i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −359.003 | − | 621.811i | −0.409353 | − | 0.709020i | 0.585464 | − | 0.810698i | \(-0.300912\pi\) |
−0.994817 | + | 0.101678i | \(0.967579\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.4646 | − | 12.2977i | −0.0141804 | − | 0.0139905i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 292.378 | 0.331870 | 0.165935 | − | 0.986137i | \(-0.446936\pi\) | ||||
0.165935 | + | 0.986137i | \(0.446936\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 507.123i | 0.574318i | 0.957883 | + | 0.287159i | \(0.0927109\pi\) | ||||
−0.957883 | + | 0.287159i | \(0.907289\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −157.745 | − | 41.1301i | −0.178243 | − | 0.0464746i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −222.320 | + | 128.356i | −0.250642 | + | 0.144708i | −0.620058 | − | 0.784556i | \(-0.712891\pi\) |
0.369416 | + | 0.929264i | \(0.379558\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −158.405 | + | 274.366i | −0.178184 | + | 0.308623i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1146.40 | − | 703.754i | 1.28665 | − | 0.789848i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −138.780 | + | 240.374i | −0.155409 | + | 0.269176i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 3.58896 | − | 2.07209i | 0.00401001 | − | 0.00231518i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −119.862 | − | 31.2525i | −0.133626 | − | 0.0348411i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 1040.08i | − | 1.15693i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 878.875 | 0.975444 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −436.396 | − | 430.552i | −0.483274 | − | 0.476802i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 47.1620 | + | 81.6870i | 0.0521127 | + | 0.0902619i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1341.24 | − | 774.365i | −1.47877 | − | 0.853766i | −0.479054 | − | 0.877785i | \(-0.659020\pi\) |
−0.999711 | + | 0.0240198i | \(0.992354\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −23.8131 | − | 1766.19i | −0.0261971 | − | 1.94300i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −465.815 | − | 268.938i | −0.511322 | − | 0.295212i | 0.222055 | − | 0.975034i | \(-0.428724\pi\) |
−0.733377 | + | 0.679822i | \(0.762057\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1088.29 | + | 1884.97i | 1.19199 | + | 2.06459i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.58342 | − | 1.53649i | 0.00610209 | − | 0.00167922i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −587.195 | −0.640343 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 1099.66i | − | 1.19659i | −0.801277 | − | 0.598294i | \(-0.795845\pi\) | ||
0.801277 | − | 0.598294i | \(-0.204155\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 295.877 | + | 1075.18i | 0.321256 | + | 1.16741i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1636.04 | + | 944.568i | −1.77252 | + | 1.02337i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −494.662 | + | 856.780i | −0.534770 | + | 0.926249i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 530.129 | − | 947.485i | 0.571876 | − | 1.02210i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −97.6555 | + | 169.144i | −0.105119 | + | 0.182071i | −0.913787 | − | 0.406194i | \(-0.866856\pi\) |
0.808668 | + | 0.588265i | \(0.200189\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 278.931 | − | 161.041i | 0.299603 | − | 0.172976i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −471.900 | + | 478.305i | −0.505788 | + | 0.512653i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 114.392i | − | 0.122344i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1286.97 | 1.37350 | 0.686752 | − | 0.726892i | \(-0.259036\pi\) | ||||
0.686752 | + | 0.726892i | \(0.259036\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 119.736 | − | 459.223i | 0.127515 | − | 0.489055i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −505.685 | − | 875.873i | −0.537391 | − | 0.930789i | −0.999043 | − | 0.0437282i | \(-0.986076\pi\) |
0.461652 | − | 0.887061i | \(-0.347257\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 100.113 | + | 57.8003i | 0.106164 | + | 0.0612941i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 43.2207 | + | 41.5070i | 0.0457362 | + | 0.0439228i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −598.516 | − | 345.553i | −0.632013 | − | 0.364893i | 0.149519 | − | 0.988759i | \(-0.452228\pi\) |
−0.781531 | + | 0.623866i | \(0.785561\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −350.340 | − | 606.807i | −0.369168 | − | 0.639417i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −312.492 | + | 1198.50i | −0.328594 | + | 1.26025i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 659.310 | 0.691826 | 0.345913 | − | 0.938267i | \(-0.387569\pi\) | ||||
0.345913 | + | 0.938267i | \(0.387569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 29.6086i | − | 0.0310038i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1457.14 | + | 1476.92i | −1.52261 | + | 1.54328i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 169.467 | − | 97.8419i | 0.176712 | − | 0.102025i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −168.602 | + | 292.028i | −0.175445 | + | 0.303879i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 30.0427 | + | 50.4522i | 0.0311970 | + | 0.0523907i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 49.1689 | − | 85.1631i | 0.0509522 | − | 0.0882519i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −980.817 | + | 566.275i | −1.01429 | + | 0.585600i | −0.912444 | − | 0.409201i | \(-0.865808\pi\) |
−0.101844 | + | 0.994800i | \(0.532474\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −63.3203 | − | 230.099i | −0.0653461 | − | 0.237460i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 277.255i | 0.285536i | 0.989756 | + | 0.142768i | \(0.0456002\pi\) | ||||
−0.989756 | + | 0.142768i | \(0.954400\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 146.348 | 0.150409 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1300.47 | + | 357.872i | −1.33381 | + | 0.367048i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −166.546 | − | 288.467i | −0.170467 | − | 0.295257i | 0.768116 | − | 0.640310i | \(-0.221194\pi\) |
−0.938583 | + | 0.345053i | \(0.887861\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 547.824 | + | 316.286i | 0.559575 | + | 0.323071i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 294.059 | − | 175.103i | 0.299754 | − | 0.178494i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1287.12 | − | 743.121i | −1.30938 | − | 0.755973i | −0.327390 | − | 0.944889i | \(-0.606169\pi\) |
−0.981993 | + | 0.188916i | \(0.939503\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −38.8778 | − | 67.3384i | −0.0394699 | − | 0.0683639i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 225.579 | + | 222.558i | 0.228551 | + | 0.225490i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −147.182 | −0.148819 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 17.1782i | − | 0.0173343i | −0.999962 | − | 0.00866713i | \(-0.997241\pi\) | ||
0.999962 | − | 0.00866713i | \(-0.00275887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −425.497 | − | 110.943i | −0.428496 | − | 0.111725i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −53.5552 | + | 30.9201i | −0.0538243 | + | 0.0310755i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −737.655 | + | 1277.66i | −0.739874 | + | 1.28150i | 0.212677 | + | 0.977123i | \(0.431782\pi\) |
−0.952552 | + | 0.304377i | \(0.901552\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −755.347 | + | 786.533i | −0.756103 | + | 0.787320i |
(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 | 144.3.o.a.79.4 | yes | 8 | |
3.2 | odd | 2 | 432.3.o.b.127.2 | 8 | |||
4.3 | odd | 2 | 144.3.o.c.79.1 | yes | 8 | ||
8.3 | odd | 2 | 576.3.o.d.511.4 | 8 | |||
8.5 | even | 2 | 576.3.o.f.511.1 | 8 | |||
9.2 | odd | 6 | 1296.3.g.k.1135.5 | 8 | |||
9.4 | even | 3 | 144.3.o.c.31.1 | yes | 8 | ||
9.5 | odd | 6 | 432.3.o.a.415.2 | 8 | |||
9.7 | even | 3 | 1296.3.g.j.1135.3 | 8 | |||
12.11 | even | 2 | 432.3.o.a.127.2 | 8 | |||
24.5 | odd | 2 | 1728.3.o.f.127.3 | 8 | |||
24.11 | even | 2 | 1728.3.o.e.127.3 | 8 | |||
36.7 | odd | 6 | 1296.3.g.j.1135.4 | 8 | |||
36.11 | even | 6 | 1296.3.g.k.1135.6 | 8 | |||
36.23 | even | 6 | 432.3.o.b.415.2 | 8 | |||
36.31 | odd | 6 | inner | 144.3.o.a.31.4 | ✓ | 8 | |
72.5 | odd | 6 | 1728.3.o.e.1279.3 | 8 | |||
72.13 | even | 6 | 576.3.o.d.319.4 | 8 | |||
72.59 | even | 6 | 1728.3.o.f.1279.3 | 8 | |||
72.67 | odd | 6 | 576.3.o.f.319.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
144.3.o.a.31.4 | ✓ | 8 | 36.31 | odd | 6 | inner | |
144.3.o.a.79.4 | yes | 8 | 1.1 | even | 1 | trivial | |
144.3.o.c.31.1 | yes | 8 | 9.4 | even | 3 | ||
144.3.o.c.79.1 | yes | 8 | 4.3 | odd | 2 | ||
432.3.o.a.127.2 | 8 | 12.11 | even | 2 | |||
432.3.o.a.415.2 | 8 | 9.5 | odd | 6 | |||
432.3.o.b.127.2 | 8 | 3.2 | odd | 2 | |||
432.3.o.b.415.2 | 8 | 36.23 | even | 6 | |||
576.3.o.d.319.4 | 8 | 72.13 | even | 6 | |||
576.3.o.d.511.4 | 8 | 8.3 | odd | 2 | |||
576.3.o.f.319.1 | 8 | 72.67 | odd | 6 | |||
576.3.o.f.511.1 | 8 | 8.5 | even | 2 | |||
1296.3.g.j.1135.3 | 8 | 9.7 | even | 3 | |||
1296.3.g.j.1135.4 | 8 | 36.7 | odd | 6 | |||
1296.3.g.k.1135.5 | 8 | 9.2 | odd | 6 | |||
1296.3.g.k.1135.6 | 8 | 36.11 | even | 6 | |||
1728.3.o.e.127.3 | 8 | 24.11 | even | 2 | |||
1728.3.o.e.1279.3 | 8 | 72.5 | odd | 6 | |||
1728.3.o.f.127.3 | 8 | 24.5 | odd | 2 | |||
1728.3.o.f.1279.3 | 8 | 72.59 | even | 6 |