Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(253,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.02446026187\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.72339481600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{6} - 2x^{4} - 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 253.8 | ||
Root | \(1.38758 + 0.273147i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.253 |
Dual form | 504.2.c.e.253.7 |
$q$-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 \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38758 | + | 0.273147i | 0.981170 | + | 0.193144i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.85078 | + | 0.758030i | 0.925391 | + | 0.379015i | ||||
\(5\) | − | 3.66103i | − | 1.63726i | −0.574320 | − | 0.818631i | \(-0.694734\pi\) | ||
0.574320 | − | 0.818631i | \(-0.305266\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.36106 | + | 1.55737i | 0.834761 | + | 0.550612i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | − | 5.07999i | 0.316228 | − | 1.60643i | ||||
\(11\) | − | 2.56844i | − | 0.774413i | −0.921993 | − | 0.387207i | \(-0.873440\pi\) | ||
0.921993 | − | 0.387207i | \(-0.126560\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.03212i | 0.840959i | 0.907302 | + | 0.420479i | \(0.138138\pi\) | ||||
−0.907302 | + | 0.420479i | \(0.861862\pi\) | |||||||
\(14\) | −1.38758 | − | 0.273147i | −0.370848 | − | 0.0730017i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.85078 | + | 2.80590i | 0.712695 | + | 0.701474i | ||||
\(17\) | 7.49729 | 1.81836 | 0.909180 | − | 0.416403i | \(-0.136710\pi\) | ||||
0.909180 | + | 0.416403i | \(0.136710\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.12785i | − | 1.63524i | −0.575758 | − | 0.817620i | \(-0.695293\pi\) | ||
0.575758 | − | 0.817620i | \(-0.304707\pi\) | |||||||
\(20\) | 2.77517 | − | 6.77576i | 0.620547 | − | 1.51511i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.701562 | − | 3.56393i | 0.149574 | − | 0.759831i | ||||
\(23\) | −3.60338 | −0.751358 | −0.375679 | − | 0.926750i | \(-0.622590\pi\) | ||||
−0.375679 | + | 0.926750i | \(0.622590\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −8.40312 | −1.68062 | ||||||||
\(26\) | −0.828216 | + | 4.20732i | −0.162426 | + | 0.825124i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.85078 | − | 0.758030i | −0.349765 | − | 0.143254i | ||||
\(29\) | 6.22947i | 1.15678i | 0.815759 | + | 0.578391i | \(0.196319\pi\) | ||||
−0.815759 | + | 0.578391i | \(0.803681\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −5.40312 | −0.970430 | −0.485215 | − | 0.874395i | \(-0.661259\pi\) | ||||
−0.485215 | + | 0.874395i | \(0.661259\pi\) | |||||||
\(32\) | 3.18928 | + | 4.67210i | 0.563790 | + | 0.825918i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.4031 | + | 2.04787i | 1.78412 | + | 0.351206i | ||||
\(35\) | 3.66103i | 0.618827i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.12785i | 1.17181i | 0.810379 | + | 0.585906i | \(0.199261\pi\) | ||||
−0.810379 | + | 0.585906i | \(0.800739\pi\) | |||||||
\(38\) | 1.94695 | − | 9.89049i | 0.315838 | − | 1.60445i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 5.70156 | − | 8.64391i | 0.901496 | − | 1.36672i | ||||
\(41\) | 3.60338 | 0.562754 | 0.281377 | − | 0.959597i | \(-0.409209\pi\) | ||||
0.281377 | + | 0.959597i | \(0.409209\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.1600i | 1.54938i | 0.632341 | + | 0.774690i | \(0.282094\pi\) | ||||
−0.632341 | + | 0.774690i | \(0.717906\pi\) | |||||||
\(44\) | 1.94695 | − | 4.75362i | 0.293514 | − | 0.716635i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.00000 | − | 0.984255i | −0.737210 | − | 0.145120i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −11.6600 | − | 2.29529i | −1.64898 | − | 0.324603i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.29844 | + | 5.61179i | −0.318736 | + | 0.778215i | ||||
\(53\) | − | 8.41464i | − | 1.15584i | −0.816093 | − | 0.577920i | \(-0.803864\pi\) | ||
0.816093 | − | 0.577920i | \(-0.196136\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −9.40312 | −1.26792 | ||||||||
\(56\) | −2.36106 | − | 1.55737i | −0.315510 | − | 0.208112i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.70156 | + | 8.64391i | −0.223426 | + | 1.13500i | ||||
\(59\) | 2.18518i | 0.284486i | 0.989832 | + | 0.142243i | \(0.0454314\pi\) | ||||
−0.989832 | + | 0.142243i | \(0.954569\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.03212i | 0.388223i | 0.980979 | + | 0.194112i | \(0.0621824\pi\) | ||||
−0.980979 | + | 0.194112i | \(0.937818\pi\) | |||||||
\(62\) | −7.49729 | − | 1.47585i | −0.952157 | − | 0.187433i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 3.14922 | + | 7.35408i | 0.393652 | + | 0.919259i | ||||
\(65\) | 11.1007 | 1.37687 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.1600i | 1.24124i | 0.784112 | + | 0.620619i | \(0.213119\pi\) | ||||
−0.784112 | + | 0.620619i | \(0.786881\pi\) | |||||||
\(68\) | 13.8758 | + | 5.68317i | 1.68269 | + | 0.689186i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.00000 | + | 5.07999i | −0.119523 | + | 0.607174i | ||||
\(71\) | −7.49729 | −0.889765 | −0.444882 | − | 0.895589i | \(-0.646755\pi\) | ||||
−0.444882 | + | 0.895589i | \(0.646755\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | −1.94695 | + | 9.89049i | −0.226329 | + | 1.14975i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.40312 | − | 13.1921i | 0.619781 | − | 1.51324i | ||||
\(77\) | 2.56844i | 0.292701i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 10.2725 | − | 10.4368i | 1.14850 | − | 1.16687i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 5.00000 | + | 0.984255i | 0.552158 | + | 0.108693i | ||||
\(83\) | 7.32206i | 0.803700i | 0.915706 | + | 0.401850i | \(0.131633\pi\) | ||||
−0.915706 | + | 0.401850i | \(0.868367\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 27.4478i | − | 2.97713i | ||||||
\(86\) | −2.77517 | + | 14.0978i | −0.299254 | + | 1.52021i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.00000 | − | 6.06424i | 0.426401 | − | 0.646450i | ||||
\(89\) | −3.60338 | −0.381958 | −0.190979 | − | 0.981594i | \(-0.561166\pi\) | ||||
−0.190979 | + | 0.981594i | \(0.561166\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 3.03212i | − | 0.317853i | ||||||
\(92\) | −6.66908 | − | 2.73147i | −0.695299 | − | 0.284776i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −26.0953 | −2.67732 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.80625 | −0.894139 | −0.447070 | − | 0.894499i | \(-0.647532\pi\) | ||||
−0.447070 | + | 0.894499i | \(0.647532\pi\) | |||||||
\(98\) | 1.38758 | + | 0.273147i | 0.140167 | + | 0.0275920i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −15.5523 | − | 6.36982i | −1.55523 | − | 0.636982i | ||||
\(101\) | − | 5.84621i | − | 0.581719i | −0.956766 | − | 0.290860i | \(-0.906059\pi\) | ||
0.956766 | − | 0.290860i | \(-0.0939413\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 9.40312 | 0.926517 | 0.463259 | − | 0.886223i | \(-0.346680\pi\) | ||||
0.463259 | + | 0.886223i | \(0.346680\pi\) | |||||||
\(104\) | −4.72212 | + | 7.15902i | −0.463042 | + | 0.702000i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.29844 | − | 11.6760i | 0.223244 | − | 1.13408i | ||||
\(107\) | − | 7.70532i | − | 0.744901i | −0.928052 | − | 0.372450i | \(-0.878518\pi\) | ||
0.928052 | − | 0.372450i | \(-0.121482\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(110\) | −13.0476 | − | 2.56844i | −1.24404 | − | 0.244891i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.85078 | − | 2.80590i | −0.269373 | − | 0.265132i | ||||
\(113\) | −3.89391 | −0.366308 | −0.183154 | − | 0.983084i | \(-0.558631\pi\) | ||||
−0.183154 | + | 0.983084i | \(0.558631\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 13.1921i | 1.23017i | ||||||||
\(116\) | −4.72212 | + | 11.5294i | −0.438438 | + | 1.07048i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.596876 | + | 3.03212i | −0.0549469 | + | 0.279129i | ||||
\(119\) | −7.49729 | −0.687276 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.40312 | 0.400284 | ||||||||
\(122\) | −0.828216 | + | 4.20732i | −0.0749831 | + | 0.380913i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.0000 | − | 4.09573i | −0.898027 | − | 0.367807i | ||||
\(125\) | 12.4589i | 1.11436i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.8062 | 1.66878 | 0.834392 | − | 0.551171i | \(-0.185819\pi\) | ||||
0.834392 | + | 0.551171i | \(0.185819\pi\) | |||||||
\(128\) | 2.36106 | + | 11.0646i | 0.208690 | + | 0.977982i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 15.4031 | + | 3.03212i | 1.35094 | + | 0.265935i | ||||
\(131\) | − | 7.32206i | − | 0.639731i | −0.947463 | − | 0.319865i | \(-0.896362\pi\) | ||
0.947463 | − | 0.319865i | \(-0.103638\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.12785i | 0.618063i | ||||||||
\(134\) | −2.77517 | + | 14.0978i | −0.239738 | + | 1.21787i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17.7016 | + | 11.6760i | 1.51790 | + | 1.00121i | ||||
\(137\) | 7.20677 | 0.615716 | 0.307858 | − | 0.951432i | \(-0.400388\pi\) | ||||
0.307858 | + | 0.951432i | \(0.400388\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.19146i | − | 0.694791i | −0.937719 | − | 0.347395i | \(-0.887066\pi\) | ||
0.937719 | − | 0.347395i | \(-0.112934\pi\) | |||||||
\(140\) | −2.77517 | + | 6.77576i | −0.234545 | + | 0.572656i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.4031 | − | 2.04787i | −0.873011 | − | 0.171853i | ||||
\(143\) | 7.78781 | 0.651250 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 22.8062 | 1.89396 | ||||||||
\(146\) | −8.32551 | − | 1.63888i | −0.689024 | − | 0.135635i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.40312 | + | 13.1921i | −0.444134 | + | 1.08438i | ||||
\(149\) | − | 10.5998i | − | 0.868371i | −0.900823 | − | 0.434186i | \(-0.857036\pi\) | ||
0.900823 | − | 0.434186i | \(-0.142964\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.8062 | −1.53043 | −0.765215 | − | 0.643774i | \(-0.777368\pi\) | ||||
−0.765215 | + | 0.643774i | \(0.777368\pi\) | |||||||
\(152\) | 11.1007 | − | 16.8293i | 0.900384 | − | 1.36504i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.701562 | + | 3.56393i | −0.0565335 | + | 0.287189i | ||||
\(155\) | 19.7810i | 1.58885i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 3.03212i | − | 0.241990i | −0.992653 | − | 0.120995i | \(-0.961392\pi\) | ||
0.992653 | − | 0.120995i | \(-0.0386084\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 17.1047 | − | 11.6760i | 1.35224 | − | 0.923071i | ||||
\(161\) | 3.60338 | 0.283986 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 22.2885i | − | 1.74577i | −0.487929 | − | 0.872883i | \(-0.662248\pi\) | ||
0.487929 | − | 0.872883i | \(-0.337752\pi\) | |||||||
\(164\) | 6.66908 | + | 2.73147i | 0.520767 | + | 0.213292i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.00000 | + | 10.1600i | −0.155230 | + | 0.788567i | ||||
\(167\) | −14.9946 | −1.16032 | −0.580158 | − | 0.814504i | \(-0.697009\pi\) | ||||
−0.580158 | + | 0.814504i | \(0.697009\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.80625 | 0.292788 | ||||||||
\(170\) | 7.49729 | − | 38.0861i | 0.575016 | − | 2.92107i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.70156 | + | 18.8039i | −0.587239 | + | 1.43378i | ||||
\(173\) | 8.03139i | 0.610615i | 0.952254 | + | 0.305307i | \(0.0987592\pi\) | ||||
−0.952254 | + | 0.305307i | \(0.901241\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.40312 | 0.635216 | ||||||||
\(176\) | 7.20677 | − | 7.32206i | 0.543231 | − | 0.551921i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.00000 | − | 0.984255i | −0.374766 | − | 0.0737730i | ||||
\(179\) | 12.0757i | 0.902578i | 0.892378 | + | 0.451289i | \(0.149036\pi\) | ||||
−0.892378 | + | 0.451289i | \(0.850964\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 23.3521i | 1.73574i | 0.496787 | + | 0.867872i | \(0.334513\pi\) | ||||
−0.496787 | + | 0.867872i | \(0.665487\pi\) | |||||||
\(182\) | 0.828216 | − | 4.20732i | 0.0613914 | − | 0.311867i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −8.50781 | − | 5.61179i | −0.627204 | − | 0.413707i | ||||
\(185\) | 26.0953 | 1.91856 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 19.2563i | − | 1.40816i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −36.2094 | − | 7.12785i | −2.62690 | − | 0.517109i | ||||
\(191\) | −7.49729 | −0.542485 | −0.271242 | − | 0.962511i | \(-0.587435\pi\) | ||||
−0.271242 | + | 0.962511i | \(0.587435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 11.4031 | 0.820815 | 0.410407 | − | 0.911902i | \(-0.365386\pi\) | ||||
0.410407 | + | 0.911902i | \(0.365386\pi\) | |||||||
\(194\) | −12.2194 | − | 2.40540i | −0.877303 | − | 0.172698i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.85078 | + | 0.758030i | 0.132199 | + | 0.0541450i | ||||
\(197\) | − | 11.3663i | − | 0.809818i | −0.914357 | − | 0.404909i | \(-0.867303\pi\) | ||
0.914357 | − | 0.404909i | \(-0.132697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.8062 | 1.04959 | 0.524794 | − | 0.851230i | \(-0.324143\pi\) | ||||
0.524794 | + | 0.851230i | \(0.324143\pi\) | |||||||
\(200\) | −19.8403 | − | 13.0867i | −1.40292 | − | 0.925373i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.59688 | − | 8.11211i | 0.112356 | − | 0.570766i | ||||
\(203\) | − | 6.22947i | − | 0.437223i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 13.1921i | − | 0.921376i | ||||||
\(206\) | 13.0476 | + | 2.56844i | 0.909071 | + | 0.178952i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −8.50781 | + | 8.64391i | −0.589911 | + | 0.599347i | ||||
\(209\) | −18.3074 | −1.26635 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.09573i | 0.281962i | 0.990012 | + | 0.140981i | \(0.0450256\pi\) | ||||
−0.990012 | + | 0.140981i | \(0.954974\pi\) | |||||||
\(212\) | 6.37855 | − | 15.5737i | 0.438081 | − | 1.06960i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.10469 | − | 10.6918i | 0.143873 | − | 0.730875i | ||||
\(215\) | 37.1959 | 2.53674 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 5.40312 | 0.366788 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −17.4031 | − | 7.12785i | −1.17332 | − | 0.480560i | ||||
\(221\) | 22.7327i | 1.52917i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.8062 | −0.991500 | −0.495750 | − | 0.868465i | \(-0.665107\pi\) | ||||
−0.495750 | + | 0.868465i | \(0.665107\pi\) | |||||||
\(224\) | −3.18928 | − | 4.67210i | −0.213093 | − | 0.312168i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.40312 | − | 1.06361i | −0.359410 | − | 0.0707503i | ||||
\(227\) | − | 19.7810i | − | 1.31291i | −0.754365 | − | 0.656455i | \(-0.772055\pi\) | ||
0.754365 | − | 0.656455i | \(-0.227945\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.2236i | 0.741675i | 0.928698 | + | 0.370838i | \(0.120929\pi\) | ||||
−0.928698 | + | 0.370838i | \(0.879071\pi\) | |||||||
\(230\) | −3.60338 | + | 18.3051i | −0.237600 | + | 1.20701i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −9.70156 | + | 14.7082i | −0.636939 | + | 0.965637i | ||||
\(233\) | 18.8885 | 1.23743 | 0.618713 | − | 0.785617i | \(-0.287654\pi\) | ||||
0.618713 | + | 0.785617i | \(0.287654\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.65643 | + | 4.04429i | −0.107824 | + | 0.263261i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −10.4031 | − | 2.04787i | −0.674334 | − | 0.132743i | ||||
\(239\) | 14.7041 | 0.951127 | 0.475563 | − | 0.879682i | \(-0.342244\pi\) | ||||
0.475563 | + | 0.879682i | \(0.342244\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −0.806248 | −0.0519350 | −0.0259675 | − | 0.999663i | \(-0.508267\pi\) | ||||
−0.0259675 | + | 0.999663i | \(0.508267\pi\) | |||||||
\(242\) | 6.10971 | + | 1.20270i | 0.392747 | + | 0.0773126i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2.29844 | + | 5.61179i | −0.147142 | + | 0.359258i | ||||
\(245\) | − | 3.66103i | − | 0.233894i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.6125 | 1.37517 | ||||||||
\(248\) | −12.7571 | − | 8.41464i | −0.810077 | − | 0.534330i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.40312 | + | 17.2878i | −0.215232 | + | 1.09338i | ||||
\(251\) | − | 9.50723i | − | 0.600091i | −0.953925 | − | 0.300046i | \(-0.902998\pi\) | ||
0.953925 | − | 0.300046i | \(-0.0970019\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.25507i | 0.581861i | ||||||||
\(254\) | 26.0953 | + | 5.13688i | 1.63736 | + | 0.322316i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.253905 | + | 15.9980i | 0.0158691 | + | 0.999874i | ||||
\(257\) | −18.5980 | −1.16011 | −0.580055 | − | 0.814578i | \(-0.696969\pi\) | ||||
−0.580055 | + | 0.814578i | \(0.696969\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 7.12785i | − | 0.442903i | ||||||
\(260\) | 20.5449 | + | 8.41464i | 1.27414 | + | 0.521854i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.00000 | − | 10.1600i | 0.123560 | − | 0.627685i | ||||
\(263\) | 11.3912 | 0.702411 | 0.351206 | − | 0.936298i | \(-0.385772\pi\) | ||||
0.351206 | + | 0.936298i | \(0.385772\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −30.8062 | −1.89241 | ||||||||
\(266\) | −1.94695 | + | 9.89049i | −0.119375 | + | 0.606425i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.70156 | + | 18.8039i | −0.470448 | + | 1.14863i | ||||
\(269\) | − | 19.0717i | − | 1.16282i | −0.813611 | − | 0.581410i | \(-0.802501\pi\) | ||
0.813611 | − | 0.581410i | \(-0.197499\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.59688 | −0.400732 | −0.200366 | − | 0.979721i | \(-0.564213\pi\) | ||||
−0.200366 | + | 0.979721i | \(0.564213\pi\) | |||||||
\(272\) | 21.3731 | + | 21.0366i | 1.29594 | + | 1.27553i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 10.0000 | + | 1.96851i | 0.604122 | + | 0.118922i | ||||
\(275\) | 21.5829i | 1.30150i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 1.06361i | − | 0.0639061i | −0.999489 | − | 0.0319531i | \(-0.989827\pi\) | ||
0.999489 | − | 0.0319531i | \(-0.0101727\pi\) | |||||||
\(278\) | 2.23748 | − | 11.3663i | 0.134195 | − | 0.681708i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −5.70156 | + | 8.64391i | −0.340734 | + | 0.516572i | ||||
\(281\) | −33.3020 | −1.98663 | −0.993316 | − | 0.115425i | \(-0.963177\pi\) | ||||
−0.993316 | + | 0.115425i | \(0.963177\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.06361i | 0.0632251i | 0.999500 | + | 0.0316125i | \(0.0100643\pi\) | ||||
−0.999500 | + | 0.0316125i | \(0.989936\pi\) | |||||||
\(284\) | −13.8758 | − | 5.68317i | −0.823380 | − | 0.337234i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.8062 | + | 2.12722i | 0.638987 | + | 0.125785i | ||||
\(287\) | −3.60338 | −0.212701 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 39.2094 | 2.30643 | ||||||||
\(290\) | 31.6456 | + | 6.22947i | 1.85829 | + | 0.365807i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −11.1047 | − | 4.54818i | −0.649853 | − | 0.266162i | ||||
\(293\) | − | 21.2568i | − | 1.24184i | −0.783875 | − | 0.620919i | \(-0.786760\pi\) | ||
0.783875 | − | 0.620919i | \(-0.213240\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000 | 0.465778 | ||||||||
\(296\) | −11.1007 | + | 16.8293i | −0.645214 | + | 0.978183i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.89531 | − | 14.7082i | 0.167721 | − | 0.852020i | ||||
\(299\) | − | 10.9259i | − | 0.631861i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 10.1600i | − | 0.585611i | ||||||
\(302\) | −26.0953 | − | 5.13688i | −1.50161 | − | 0.295594i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 20.0000 | − | 20.3199i | 1.14708 | − | 1.16543i | ||||
\(305\) | 11.1007 | 0.635623 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.12785i | 0.406808i | 0.979095 | + | 0.203404i | \(0.0652005\pi\) | ||||
−0.979095 | + | 0.203404i | \(0.934800\pi\) | |||||||
\(308\) | −1.94695 | + | 4.75362i | −0.110938 | + | 0.270862i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −5.40312 | + | 27.4478i | −0.306877 | + | 1.55893i | ||||
\(311\) | −22.2014 | −1.25892 | −0.629462 | − | 0.777032i | \(-0.716724\pi\) | ||||
−0.629462 | + | 0.777032i | \(0.716724\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −14.0000 | −0.791327 | −0.395663 | − | 0.918396i | \(-0.629485\pi\) | ||||
−0.395663 | + | 0.918396i | \(0.629485\pi\) | |||||||
\(314\) | 0.828216 | − | 4.20732i | 0.0467389 | − | 0.237433i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6.22947i | − | 0.349882i | −0.984579 | − | 0.174941i | \(-0.944027\pi\) | ||
0.984579 | − | 0.174941i | \(-0.0559734\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.0000 | 0.895828 | ||||||||
\(320\) | 26.9235 | − | 11.5294i | 1.50507 | − | 0.644512i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.00000 | + | 0.984255i | 0.278639 | + | 0.0548504i | ||||
\(323\) | − | 53.4396i | − | 2.97346i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 25.4793i | − | 1.41334i | ||||||
\(326\) | 6.08803 | − | 30.9271i | 0.337185 | − | 1.71289i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.50781 | + | 5.61179i | 0.469765 | + | 0.309859i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 22.2885i | 1.22508i | 0.790438 | + | 0.612542i | \(0.209853\pi\) | ||||
−0.790438 | + | 0.612542i | \(0.790147\pi\) | |||||||
\(332\) | −5.55034 | + | 13.5515i | −0.304614 | + | 0.743736i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −20.8062 | − | 4.09573i | −1.13847 | − | 0.224108i | ||||
\(335\) | 37.1959 | 2.03223 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 28.8062 | 1.56918 | 0.784588 | − | 0.620017i | \(-0.212874\pi\) | ||||
0.784588 | + | 0.620017i | \(0.212874\pi\) | |||||||
\(338\) | 5.28149 | + | 1.03967i | 0.287275 | + | 0.0565504i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 20.8062 | − | 50.7999i | 1.12838 | − | 2.75501i | ||||
\(341\) | 13.8776i | 0.751514i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −15.8228 | + | 23.9883i | −0.853108 | + | 1.29336i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.19375 | + | 11.1442i | −0.117937 | + | 0.599117i | ||||
\(347\) | 26.7198i | 1.43439i | 0.696871 | + | 0.717197i | \(0.254575\pi\) | ||||
−0.696871 | + | 0.717197i | \(0.745425\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 5.15934i | − | 0.276173i | −0.990420 | − | 0.138087i | \(-0.955905\pi\) | ||
0.990420 | − | 0.138087i | \(-0.0440952\pi\) | |||||||
\(350\) | 11.6600 | + | 2.29529i | 0.623256 | + | 0.122688i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 12.0000 | − | 8.19146i | 0.639602 | − | 0.436606i | ||||
\(353\) | −3.60338 | −0.191789 | −0.0958944 | − | 0.995392i | \(-0.530571\pi\) | ||||
−0.0958944 | + | 0.995392i | \(0.530571\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.4478i | 1.45678i | ||||||||
\(356\) | −6.66908 | − | 2.73147i | −0.353460 | − | 0.144768i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.29844 | + | 16.7560i | −0.174328 | + | 0.885583i | ||||
\(359\) | 7.49729 | 0.395692 | 0.197846 | − | 0.980233i | \(-0.436605\pi\) | ||||
0.197846 | + | 0.980233i | \(0.436605\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −31.8062 | −1.67401 | ||||||||
\(362\) | −6.37855 | + | 32.4030i | −0.335249 | + | 1.70306i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.29844 | − | 5.61179i | 0.120471 | − | 0.294138i | ||||
\(365\) | 21.9662i | 1.14976i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −22.8062 | −1.19048 | −0.595238 | − | 0.803549i | \(-0.702942\pi\) | ||||
−0.595238 | + | 0.803549i | \(0.702942\pi\) | |||||||
\(368\) | −10.2725 | − | 10.1107i | −0.535489 | − | 0.527058i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 36.2094 | + | 7.12785i | 1.88244 | + | 0.370559i | ||||
\(371\) | 8.41464i | 0.436867i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 6.06424i | − | 0.313994i | −0.987599 | − | 0.156997i | \(-0.949819\pi\) | ||
0.987599 | − | 0.156997i | \(-0.0501814\pi\) | |||||||
\(374\) | 5.25982 | − | 26.7198i | 0.271979 | − | 1.38165i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −18.8885 | −0.972807 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 16.2242i | − | 0.833382i | −0.909048 | − | 0.416691i | \(-0.863190\pi\) | ||
0.909048 | − | 0.416691i | \(-0.136810\pi\) | |||||||
\(380\) | −48.2966 | − | 19.7810i | −2.47756 | − | 1.01474i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.4031 | − | 2.04787i | −0.532270 | − | 0.104778i | ||||
\(383\) | 29.4081 | 1.50268 | 0.751342 | − | 0.659913i | \(-0.229407\pi\) | ||||
0.751342 | + | 0.659913i | \(0.229407\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9.40312 | 0.479228 | ||||||||
\(386\) | 15.8228 | + | 3.11473i | 0.805359 | + | 0.158536i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −16.2984 | − | 6.67540i | −0.827428 | − | 0.338892i | ||||
\(389\) | 10.5998i | 0.537432i | 0.963219 | + | 0.268716i | \(0.0865994\pi\) | ||||
−0.963219 | + | 0.268716i | \(0.913401\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −27.0156 | −1.36624 | ||||||||
\(392\) | 2.36106 | + | 1.55737i | 0.119252 | + | 0.0786589i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.10469 | − | 15.7718i | 0.156412 | − | 0.794570i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 29.4163i | − | 1.47636i | −0.674603 | − | 0.738181i | \(-0.735685\pi\) | ||
0.674603 | − | 0.738181i | \(-0.264315\pi\) | |||||||
\(398\) | 20.5449 | + | 4.04429i | 1.02982 | + | 0.202722i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −23.9555 | − | 23.5783i | −1.19777 | − | 1.17891i | ||||
\(401\) | 7.20677 | 0.359889 | 0.179944 | − | 0.983677i | \(-0.442408\pi\) | ||||
0.179944 | + | 0.983677i | \(0.442408\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 16.3829i | − | 0.816091i | ||||||
\(404\) | 4.43160 | − | 10.8200i | 0.220480 | − | 0.538318i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.70156 | − | 8.64391i | 0.0844471 | − | 0.428990i | ||||
\(407\) | 18.3074 | 0.907466 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −10.0000 | −0.494468 | −0.247234 | − | 0.968956i | \(-0.579522\pi\) | ||||
−0.247234 | + | 0.968956i | \(0.579522\pi\) | |||||||
\(410\) | 3.60338 | − | 18.3051i | 0.177958 | − | 0.904026i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 17.4031 | + | 7.12785i | 0.857390 | + | 0.351164i | ||||
\(413\) | − | 2.18518i | − | 0.107526i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 26.8062 | 1.31587 | ||||||||
\(416\) | −14.1664 | + | 9.67027i | −0.694563 | + | 0.474124i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −25.4031 | − | 5.00063i | −1.24251 | − | 0.244589i | ||||
\(419\) | − | 2.18518i | − | 0.106753i | −0.998574 | − | 0.0533765i | \(-0.983002\pi\) | ||
0.998574 | − | 0.0533765i | \(-0.0169983\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.1921i | 0.642943i | 0.946919 | + | 0.321472i | \(0.104177\pi\) | ||||
−0.946919 | + | 0.321472i | \(0.895823\pi\) | |||||||
\(422\) | −1.11874 | + | 5.68317i | −0.0544593 | + | 0.276652i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.1047 | − | 19.8675i | 0.636420 | − | 0.964851i | ||||
\(425\) | −63.0007 | −3.05598 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 3.03212i | − | 0.146735i | ||||||
\(428\) | 5.84086 | − | 14.2609i | 0.282329 | − | 0.689324i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 51.6125 | + | 10.1600i | 2.48898 | + | 0.489957i | ||||
\(431\) | −26.3858 | −1.27096 | −0.635479 | − | 0.772118i | \(-0.719197\pi\) | ||||
−0.635479 | + | 0.772118i | \(0.719197\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.19375 | 0.153482 | 0.0767410 | − | 0.997051i | \(-0.475549\pi\) | ||||
0.0767410 | + | 0.997051i | \(0.475549\pi\) | |||||||
\(434\) | 7.49729 | + | 1.47585i | 0.359881 | + | 0.0708430i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 25.6844i | 1.22865i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.0000 | 0.763638 | 0.381819 | − | 0.924237i | \(-0.375298\pi\) | ||||
0.381819 | + | 0.924237i | \(0.375298\pi\) | |||||||
\(440\) | −22.2014 | − | 14.6441i | −1.05841 | − | 0.698131i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6.20937 | + | 31.5435i | −0.295350 | + | 1.50037i | ||||
\(443\) | − | 6.93880i | − | 0.329672i | −0.986321 | − | 0.164836i | \(-0.947290\pi\) | ||
0.986321 | − | 0.164836i | \(-0.0527095\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.1921i | 0.625365i | ||||||||
\(446\) | −20.5449 | − | 4.04429i | −0.972830 | − | 0.191503i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.14922 | − | 7.35408i | −0.148787 | − | 0.347447i | ||||
\(449\) | −18.3074 | −0.863982 | −0.431991 | − | 0.901878i | \(-0.642189\pi\) | ||||
−0.431991 | + | 0.901878i | \(0.642189\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 9.25507i | − | 0.435804i | ||||||
\(452\) | −7.20677 | − | 2.95170i | −0.338978 | − | 0.138836i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.40312 | − | 27.4478i | 0.253581 | − | 1.28819i | ||||
\(455\) | −11.1007 | −0.520408 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.0000 | −1.02912 | −0.514558 | − | 0.857455i | \(-0.672044\pi\) | ||||
−0.514558 | + | 0.857455i | \(0.672044\pi\) | |||||||
\(458\) | −3.06569 | + | 15.5737i | −0.143250 | + | 0.727710i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −10.0000 | + | 24.4157i | −0.466252 | + | 1.13839i | ||||
\(461\) | − | 11.7496i | − | 0.547234i | −0.961839 | − | 0.273617i | \(-0.911780\pi\) | ||
0.961839 | − | 0.273617i | \(-0.0882200\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −24.0000 | −1.11537 | −0.557687 | − | 0.830051i | \(-0.688311\pi\) | ||||
−0.557687 | + | 0.830051i | \(0.688311\pi\) | |||||||
\(464\) | −17.4792 | + | 17.7588i | −0.811453 | + | 0.824434i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.2094 | + | 5.15934i | 1.21413 | + | 0.239002i | ||||
\(467\) | 40.3285i | 1.86618i | 0.359643 | + | 0.933090i | \(0.382899\pi\) | ||||
−0.359643 | + | 0.933090i | \(0.617101\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 10.1600i | − | 0.469144i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −3.40312 | + | 5.15934i | −0.156641 | + | 0.237478i | ||||
\(473\) | 26.0953 | 1.19986 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 59.8962i | 2.74823i | ||||||||
\(476\) | −13.8758 | − | 5.68317i | −0.635998 | − | 0.260488i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 20.4031 | + | 4.01637i | 0.933217 | + | 0.183705i | ||||
\(479\) | 14.4135 | 0.658571 | 0.329286 | − | 0.944230i | \(-0.393192\pi\) | ||||
0.329286 | + | 0.944230i | \(0.393192\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.6125 | −0.985445 | ||||||||
\(482\) | −1.11874 | − | 0.220225i | −0.0509571 | − | 0.0100310i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 8.14922 | + | 3.33770i | 0.370419 | + | 0.151714i | ||||
\(485\) | 32.2399i | 1.46394i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.00000 | −0.362515 | −0.181257 | − | 0.983436i | \(-0.558017\pi\) | ||||
−0.181257 | + | 0.983436i | \(0.558017\pi\) | |||||||
\(488\) | −4.72212 | + | 7.15902i | −0.213760 | + | 0.324074i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.00000 | − | 5.07999i | 0.0451754 | − | 0.229490i | ||||
\(491\) | 42.1304i | 1.90132i | 0.310236 | + | 0.950659i | \(0.399592\pi\) | ||||
−0.310236 | + | 0.950659i | \(0.600408\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 46.7041i | 2.10345i | ||||||||
\(494\) | 29.9892 | + | 5.90340i | 1.34928 | + | 0.265606i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.4031 | − | 15.1606i | −0.691621 | − | 0.680731i | ||||
\(497\) | 7.49729 | 0.336299 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.03275i | − | 0.359595i | −0.983704 | − | 0.179798i | \(-0.942456\pi\) | ||
0.983704 | − | 0.179798i | \(-0.0575443\pi\) | |||||||
\(500\) | −9.44424 | + | 23.0588i | −0.422359 | + | 1.03122i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.59688 | − | 13.1921i | 0.115904 | − | 0.588792i | ||||
\(503\) | 7.20677 | 0.321334 | 0.160667 | − | 0.987009i | \(-0.448635\pi\) | ||||
0.160667 | + | 0.987009i | \(0.448635\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.4031 | −0.952427 | ||||||||
\(506\) | −2.52800 | + | 12.8422i | −0.112383 | + | 0.570905i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 34.8062 | + | 14.2557i | 1.54428 | + | 0.632494i | ||||
\(509\) | − | 9.56442i | − | 0.423936i | −0.977277 | − | 0.211968i | \(-0.932013\pi\) | ||
0.977277 | − | 0.211968i | \(-0.0679872\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | 0.265424 | ||||||||
\(512\) | −4.01749 | + | 22.2679i | −0.177550 | + | 0.984112i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −25.8062 | − | 5.07999i | −1.13826 | − | 0.224069i | ||||
\(515\) | − | 34.4251i | − | 1.51695i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 1.94695 | − | 9.89049i | 0.0855442 | − | 0.434563i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 26.2094 | + | 17.2878i | 1.14936 | + | 0.758121i | ||||
\(521\) | −37.4865 | −1.64231 | −0.821156 | − | 0.570704i | \(-0.806670\pi\) | ||||
−0.821156 | + | 0.570704i | \(0.806670\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.5114i | 1.24672i | 0.781936 | + | 0.623358i | \(0.214232\pi\) | ||||
−0.781936 | + | 0.623358i | \(0.785768\pi\) | |||||||
\(524\) | 5.55034 | − | 13.5515i | 0.242468 | − | 0.592001i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.8062 | + | 3.11148i | 0.689185 | + | 0.135667i | ||||
\(527\) | −40.5088 | −1.76459 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.0156 | −0.435462 | ||||||||
\(530\) | −42.7463 | − | 8.41464i | −1.85678 | − | 0.365509i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.40312 | + | 13.1921i | −0.234255 | + | 0.571950i | ||||
\(533\) | 10.9259i | 0.473253i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −28.2094 | −1.21960 | ||||||||
\(536\) | −15.8228 | + | 23.9883i | −0.683441 | + | 1.03614i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.20937 | − | 26.4635i | 0.224592 | − | 1.14092i | ||||
\(539\) | − | 2.56844i | − | 0.110630i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 1.06361i | − | 0.0457282i | −0.999739 | − | 0.0228641i | \(-0.992722\pi\) | ||
0.999739 | − | 0.0228641i | \(-0.00727850\pi\) | |||||||
\(542\) | −9.15372 | − | 1.80192i | −0.393186 | − | 0.0773991i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 23.9109 | + | 35.0281i | 1.02517 | + | 1.50182i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 36.5442i | − | 1.56252i | −0.624209 | − | 0.781258i | \(-0.714579\pi\) | ||
0.624209 | − | 0.781258i | \(-0.285421\pi\) | |||||||
\(548\) | 13.3382 | + | 5.46295i | 0.569778 | + | 0.233366i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −5.89531 | + | 29.9481i | −0.251377 | + | 1.27699i | ||||
\(551\) | 44.4027 | 1.89162 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.290522 | − | 1.47585i | 0.0123431 | − | 0.0627028i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 6.20937 | − | 15.1606i | 0.263336 | − | 0.642953i | ||||
\(557\) | − | 42.0732i | − | 1.78270i | −0.453316 | − | 0.891350i | \(-0.649759\pi\) | ||
0.453316 | − | 0.891350i | \(-0.350241\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −30.8062 | −1.30297 | ||||||||
\(560\) | −10.2725 | + | 10.4368i | −0.434091 | + | 0.441035i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −46.2094 | − | 9.09636i | −1.94922 | − | 0.383707i | ||||
\(563\) | 16.8293i | 0.709270i | 0.935005 | + | 0.354635i | \(0.115395\pi\) | ||||
−0.935005 | + | 0.354635i | \(0.884605\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.2557i | 0.599742i | ||||||||
\(566\) | −0.290522 | + | 1.47585i | −0.0122116 | + | 0.0620346i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −17.7016 | − | 11.6760i | −0.742741 | − | 0.489915i | ||||
\(569\) | −26.6763 | −1.11833 | −0.559164 | − | 0.829057i | \(-0.688878\pi\) | ||||
−0.559164 | + | 0.829057i | \(0.688878\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10.1600i | − | 0.425182i | −0.977141 | − | 0.212591i | \(-0.931810\pi\) | ||
0.977141 | − | 0.212591i | \(-0.0681901\pi\) | |||||||
\(572\) | 14.4135 | + | 5.90340i | 0.602660 | + | 0.246833i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −5.00000 | − | 0.984255i | −0.208696 | − | 0.0410820i | ||||
\(575\) | 30.2797 | 1.26275 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.8062 | 1.19922 | 0.599610 | − | 0.800292i | \(-0.295322\pi\) | ||||
0.599610 | + | 0.800292i | \(0.295322\pi\) | |||||||
\(578\) | 54.4063 | + | 10.7099i | 2.26300 | + | 0.445475i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 42.2094 | + | 17.2878i | 1.75265 | + | 0.717838i | ||||
\(581\) | − | 7.32206i | − | 0.303770i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −21.6125 | −0.895098 | ||||||||
\(584\) | −14.1664 | − | 9.34420i | −0.586208 | − | 0.386666i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.80625 | − | 29.4957i | 0.239854 | − | 1.21845i | ||||
\(587\) | − | 38.7955i | − | 1.60126i | −0.599159 | − | 0.800630i | \(-0.704498\pi\) | ||
0.599159 | − | 0.800630i | \(-0.295502\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 38.5127i | 1.58689i | ||||||||
\(590\) | 11.1007 | + | 2.18518i | 0.457008 | + | 0.0899624i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −20.0000 | + | 20.3199i | −0.821995 | + | 0.835144i | ||||
\(593\) | −44.1122 | −1.81147 | −0.905735 | − | 0.423844i | \(-0.860680\pi\) | ||||
−0.905735 | + | 0.423844i | \(0.860680\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27.4478i | 1.12525i | ||||||||
\(596\) | 8.03498 | − | 19.6180i | 0.329126 | − | 0.803583i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.98438 | − | 15.1606i | 0.122040 | − | 0.619963i | ||||
\(599\) | 0.290522 | 0.0118704 | 0.00593521 | − | 0.999982i | \(-0.498111\pi\) | ||||
0.00593521 | + | 0.999982i | \(0.498111\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −39.6125 | −1.61583 | −0.807914 | − | 0.589301i | \(-0.799403\pi\) | ||||
−0.807914 | + | 0.589301i | \(0.799403\pi\) | |||||||
\(602\) | 2.77517 | − | 14.0978i | 0.113107 | − | 0.574584i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −34.8062 | − | 14.2557i | −1.41625 | − | 0.580056i | ||||
\(605\) | − | 16.1200i | − | 0.655370i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −22.8062 | −0.925677 | −0.462839 | − | 0.886443i | \(-0.653169\pi\) | ||||
−0.462839 | + | 0.886443i | \(0.653169\pi\) | |||||||
\(608\) | 33.3020 | − | 22.7327i | 1.35058 | − | 0.921932i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 15.4031 | + | 3.03212i | 0.623654 | + | 0.122767i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(614\) | −1.94695 | + | 9.89049i | −0.0785726 | + | 0.399148i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −4.00000 | + | 6.06424i | −0.161165 | + | 0.244335i | ||||
\(617\) | 14.9946 | 0.603659 | 0.301830 | − | 0.953362i | \(-0.402403\pi\) | ||||
0.301830 | + | 0.953362i | \(0.402403\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 40.6399i | − | 1.63345i | −0.577024 | − | 0.816727i | \(-0.695786\pi\) | ||
0.577024 | − | 0.816727i | \(-0.304214\pi\) | |||||||
\(620\) | −14.9946 | + | 36.6103i | −0.602197 | + | 1.47030i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −30.8062 | − | 6.06424i | −1.23522 | − | 0.243154i | ||||
\(623\) | 3.60338 | 0.144367 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 3.59688 | 0.143875 | ||||||||
\(626\) | −19.4262 | − | 3.82406i | −0.776426 | − | 0.152840i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.29844 | − | 5.61179i | 0.0917177 | − | 0.223935i | ||||
\(629\) | 53.4396i | 2.13078i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.8062 | 0.430190 | 0.215095 | − | 0.976593i | \(-0.430994\pi\) | ||||
0.215095 | + | 0.976593i | \(0.430994\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.70156 | − | 8.64391i | 0.0675777 | − | 0.343294i | ||||
\(635\) | − | 68.8502i | − | 2.73224i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.03212i | 0.120137i | ||||||||
\(638\) | 22.2014 | + | 4.37036i | 0.878960 | + | 0.173024i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 40.5078 | − | 8.64391i | 1.60121 | − | 0.341681i | ||||
\(641\) | 14.9946 | 0.592250 | 0.296125 | − | 0.955149i | \(-0.404305\pi\) | ||||
0.296125 | + | 0.955149i | \(0.404305\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 15.3193i | − | 0.604135i | −0.953287 | − | 0.302067i | \(-0.902323\pi\) | ||
0.953287 | − | 0.302067i | \(-0.0976767\pi\) | |||||||
\(644\) | 6.66908 | + | 2.73147i | 0.262798 | + | 0.107635i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 14.5969 | − | 74.1519i | 0.574306 | − | 2.91747i | ||||
\(647\) | −22.7824 | −0.895668 | −0.447834 | − | 0.894117i | \(-0.647805\pi\) | ||||
−0.447834 | + | 0.894117i | \(0.647805\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.61250 | 0.220310 | ||||||||
\(650\) | 6.95960 | − | 35.3547i | 0.272978 | − | 1.38672i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 16.8953 | − | 41.2510i | 0.661672 | − | 1.61552i | ||||
\(653\) | − | 17.9219i | − | 0.701337i | −0.936500 | − | 0.350669i | \(-0.885954\pi\) | ||
0.936500 | − | 0.350669i | \(-0.114046\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −26.8062 | −1.04741 | ||||||||
\(656\) | 10.2725 | + | 10.1107i | 0.401072 | + | 0.394757i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 25.9533i | − | 1.01100i | −0.862828 | − | 0.505498i | \(-0.831309\pi\) | ||
0.862828 | − | 0.505498i | \(-0.168691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 39.7350i | 1.54551i | 0.634703 | + | 0.772756i | \(0.281122\pi\) | ||||
−0.634703 | + | 0.772756i | \(0.718878\pi\) | |||||||
\(662\) | −6.08803 | + | 30.9271i | −0.236618 | + | 1.20202i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −11.4031 | + | 17.2878i | −0.442527 | + | 0.670898i | ||||
\(665\) | 26.0953 | 1.01193 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 22.4472i | − | 0.869158i | ||||||
\(668\) | −27.7517 | − | 11.3663i | −1.07375 | − | 0.439777i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 51.6125 | + | 10.1600i | 1.99396 | + | 0.392514i | ||||
\(671\) | 7.78781 | 0.300645 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.5969 | 0.793951 | 0.396976 | − | 0.917829i | \(-0.370060\pi\) | ||||
0.396976 | + | 0.917829i | \(0.370060\pi\) | |||||||
\(674\) | 39.9711 | + | 7.86835i | 1.53963 | + | 0.303078i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.04453 | + | 2.88525i | 0.270944 | + | 0.110971i | ||||
\(677\) | 29.9976i | 1.15290i | 0.817133 | + | 0.576450i | \(0.195562\pi\) | ||||
−0.817133 | + | 0.576450i | \(0.804438\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8.80625 | 0.337953 | ||||||||
\(680\) | 42.7463 | − | 64.8059i | 1.63924 | − | 2.48519i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −3.79063 | + | 19.2563i | −0.145151 | + | 0.737363i | ||||
\(683\) | − | 8.47183i | − | 0.324166i | −0.986777 | − | 0.162083i | \(-0.948179\pi\) | ||
0.986777 | − | 0.162083i | \(-0.0518212\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 26.3842i | − | 1.00809i | ||||||
\(686\) | −1.38758 | − | 0.273147i | −0.0529782 | − | 0.0104288i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −28.5078 | + | 28.9639i | −1.08685 | + | 1.10424i | ||||
\(689\) | 25.5142 | 0.972014 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 8.19146i | − | 0.311618i | −0.987787 | − | 0.155809i | \(-0.950202\pi\) | ||
0.987787 | − | 0.155809i | \(-0.0497984\pi\) | |||||||
\(692\) | −6.08803 | + | 14.8643i | −0.231432 | + | 0.565057i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.29844 | + | 37.0760i | −0.277045 | + | 1.40738i | ||||
\(695\) | −29.9892 | −1.13755 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 27.0156 | 1.02329 | ||||||||
\(698\) | 1.40926 | − | 7.15902i | 0.0533413 | − | 0.270973i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 15.5523 | + | 6.36982i | 0.587823 | + | 0.240757i | ||||
\(701\) | − | 40.6546i | − | 1.53550i | −0.640748 | − | 0.767751i | \(-0.721376\pi\) | ||
0.640748 | − | 0.767751i | \(-0.278624\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 50.8062 | 1.91619 | ||||||||
\(704\) | 18.8885 | − | 8.08857i | 0.711887 | − | 0.304850i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.00000 | − | 0.984255i | −0.188177 | − | 0.0370429i | ||||
\(707\) | 5.84621i | 0.219869i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 40.6399i | − | 1.52626i | −0.646243 | − | 0.763131i | \(-0.723661\pi\) | ||
0.646243 | − | 0.763131i | \(-0.276339\pi\) | |||||||
\(710\) | −7.49729 | + | 38.0861i | −0.281368 | + | 1.42935i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.50781 | − | 5.61179i | −0.318844 | − | 0.210311i | ||||
\(713\) | 19.4695 | 0.729140 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 28.5114i | − | 1.06627i | ||||||
\(716\) | −9.15372 | + | 22.3494i | −0.342091 | + | 0.835237i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10.4031 | + | 2.04787i | 0.388241 | + | 0.0764256i | ||||
\(719\) | 29.4081 | 1.09674 | 0.548369 | − | 0.836237i | \(-0.315249\pi\) | ||||
0.548369 | + | 0.836237i | \(0.315249\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9.40312 | −0.350191 | ||||||||
\(722\) | −44.1339 | − | 8.68779i | −1.64249 | − | 0.323326i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −17.7016 | + | 43.2196i | −0.657873 | + | 1.60624i | ||||
\(725\) | − | 52.3470i | − | 1.94412i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 39.0156 | 1.44701 | 0.723505 | − | 0.690320i | \(-0.242530\pi\) | ||||
0.723505 | + | 0.690320i | \(0.242530\pi\) | |||||||
\(728\) | 4.72212 | − | 7.15902i | 0.175013 | − | 0.265331i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.00000 | + | 30.4799i | −0.222070 | + | 1.12811i | ||||
\(731\) | 76.1723i | 2.81733i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 19.4150i | − | 0.717111i | −0.933508 | − | 0.358555i | \(-0.883269\pi\) | ||
0.933508 | − | 0.358555i | \(-0.116731\pi\) | |||||||
\(734\) | −31.6456 | − | 6.22947i | −1.16806 | − | 0.229934i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −11.4922 | − | 16.8354i | −0.423608 | − | 0.620560i | ||||
\(737\) | 26.0953 | 0.961231 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 46.8628i | 1.72388i | 0.507013 | + | 0.861939i | \(0.330750\pi\) | ||||
−0.507013 | + | 0.861939i | \(0.669250\pi\) | |||||||
\(740\) | 48.2966 | + | 19.7810i | 1.77542 | + | 0.727164i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.29844 | + | 11.6760i | −0.0843783 | + | 0.428641i | ||||
\(743\) | 37.4865 | 1.37524 | 0.687622 | − | 0.726069i | \(-0.258655\pi\) | ||||
0.687622 | + | 0.726069i | \(0.258655\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.8062 | −1.42175 | ||||||||
\(746\) | 1.65643 | − | 8.41464i | 0.0606462 | − | 0.308082i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 14.5969 | − | 35.6393i | 0.533715 | − | 1.30310i | ||||
\(749\) | 7.70532i | 0.281546i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −26.2094 | − | 5.15934i | −0.954489 | − | 0.187892i | ||||
\(755\) | 68.8502i | 2.50572i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.5114i | 1.03626i | 0.855301 | + | 0.518132i | \(0.173372\pi\) | ||||
−0.855301 | + | 0.518132i | \(0.826628\pi\) | |||||||
\(758\) | 4.43160 | − | 22.5125i | 0.160963 | − | 0.817689i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −61.6125 | − | 40.6399i | −2.23492 | − | 1.47416i | ||||
\(761\) | 7.49729 | 0.271777 | 0.135888 | − | 0.990724i | \(-0.456611\pi\) | ||||
0.135888 | + | 0.990724i | \(0.456611\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −13.8758 | − | 5.68317i | −0.502010 | − | 0.205610i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 40.8062 | + | 8.03275i | 1.47439 | + | 0.290235i | ||||
\(767\) | −6.62572 | −0.239241 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16.8062 | 0.606049 | 0.303024 | − | 0.952983i | \(-0.402004\pi\) | ||||
0.303024 | + | 0.952983i | \(0.402004\pi\) | |||||||
\(770\) | 13.0476 | + | 2.56844i | 0.470204 | + | 0.0925601i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 21.1047 | + | 8.64391i | 0.759574 | + | 0.311101i | ||||
\(773\) | 33.7158i | 1.21267i | 0.795209 | + | 0.606336i | \(0.207361\pi\) | ||||
−0.795209 | + | 0.606336i | \(0.792639\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.4031 | 1.63093 | ||||||||
\(776\) | −20.7921 | − | 13.7146i | −0.746393 | − | 0.492324i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.89531 | + | 14.7082i | −0.103802 | + | 0.527313i | ||||
\(779\) | − | 25.6844i | − | 0.920239i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 19.2563i | 0.689046i | ||||||||
\(782\) | −37.4865 | − | 7.37925i | −1.34051 | − | 0.263881i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.85078 | + | 2.80590i | 0.101814 | + | 0.100211i | ||||
\(785\) | −11.1007 | −0.396200 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 8.19146i | 0.291994i | 0.989285 | + | 0.145997i | \(0.0466390\pi\) | ||||
−0.989285 | + | 0.145997i | \(0.953361\pi\) | |||||||
\(788\) | 8.61603 | − | 21.0366i | 0.306933 | − | 0.749398i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3.89391 | 0.138451 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −9.19375 | −0.326480 | ||||||||
\(794\) | 8.03498 | − | 40.8176i | 0.285151 | − | 1.44856i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 27.4031 | + | 11.2236i | 0.971278 | + | 0.397809i | ||||
\(797\) | 9.56442i | 0.338789i | 0.985548 | + | 0.169395i | \(0.0541812\pi\) | ||||
−0.985548 | + | 0.169395i | \(0.945819\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −26.7999 | − | 39.2602i | −0.947519 | − | 1.38806i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 10.0000 | + | 1.96851i | 0.353112 | + | 0.0695105i | ||||
\(803\) | 15.4106i | 0.543829i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 13.1921i | − | 0.464960i | ||||||
\(806\) | 4.47495 | − | 22.7327i | 0.157623 | − | 0.800725i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.10469 | − | 13.8033i | 0.320302 | − | 0.485597i | ||||
\(809\) | 3.89391 | 0.136902 | 0.0684512 | − | 0.997654i | \(-0.478194\pi\) | ||||
0.0684512 | + | 0.997654i | \(0.478194\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 12.1285i | − | 0.425889i | −0.977064 | − | 0.212944i | \(-0.931695\pi\) | ||
0.977064 | − | 0.212944i | \(-0.0683053\pi\) | |||||||
\(812\) | 4.72212 | − | 11.5294i | 0.165714 | − | 0.404602i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 25.4031 | + | 5.00063i | 0.890379 | + | 0.175272i | ||||
\(815\) | −81.5986 | −2.85828 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 72.4187 | 2.53361 | ||||||||
\(818\) | −13.8758 | − | 2.73147i | −0.485158 | − | 0.0955037i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.0000 | − | 24.4157i | 0.349215 | − | 0.852632i | ||||
\(821\) | 1.85911i | 0.0648833i | 0.999474 | + | 0.0324417i | \(0.0103283\pi\) | ||||
−0.999474 | + | 0.0324417i | \(0.989672\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.19375 | −0.181043 | −0.0905214 | − | 0.995895i | \(-0.528853\pi\) | ||||
−0.0905214 | + | 0.995895i | \(0.528853\pi\) | |||||||
\(824\) | 22.2014 | + | 14.6441i | 0.773421 | + | 0.510152i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.596876 | − | 3.03212i | 0.0207680 | − | 0.105501i | ||||
\(827\) | 20.8164i | 0.723857i | 0.932206 | + | 0.361928i | \(0.117882\pi\) | ||||
−0.932206 | + | 0.361928i | \(0.882118\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 29.4163i | − | 1.02167i | −0.859679 | − | 0.510835i | \(-0.829336\pi\) | ||
0.859679 | − | 0.510835i | \(-0.170664\pi\) | |||||||
\(830\) | 37.1959 | + | 7.32206i | 1.29109 | + | 0.254152i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −22.2984 | + | 9.54881i | −0.773059 | + | 0.331045i | ||||
\(833\) | 7.49729 | 0.259766 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 54.8956i | 1.89974i | ||||||||
\(836\) | −33.8831 | − | 13.8776i | −1.17187 | − | 0.479967i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0.596876 | − | 3.03212i | 0.0206187 | − | 0.104743i | ||||
\(839\) | 44.9837 | 1.55301 | 0.776506 | − | 0.630110i | \(-0.216990\pi\) | ||||
0.776506 | + | 0.630110i | \(0.216990\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.80625 | −0.338146 | ||||||||
\(842\) | −3.60338 | + | 18.3051i | −0.124181 | + | 0.630837i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −3.10469 | + | 7.58030i | −0.106868 | + | 0.260925i | ||||
\(845\) | − | 13.9348i | − | 0.479371i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.40312 | −0.151293 | ||||||||
\(848\) | 23.6106 | − | 23.9883i | 0.810792 | − | 0.823762i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −87.4187 | − | 17.2085i | −2.99844 | − | 0.590245i | ||||
\(851\) | − | 25.6844i | − | 0.880449i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 51.8635i | − | 1.77577i | −0.460064 | − | 0.887886i | \(-0.652174\pi\) | ||
0.460064 | − | 0.887886i | \(-0.347826\pi\) | |||||||
\(854\) | 0.828216 | − | 4.20732i | 0.0283410 | − | 0.143972i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 12.0000 | − | 18.1927i | 0.410152 | − | 0.621814i | ||||
\(857\) | 29.6986 | 1.01449 | 0.507243 | − | 0.861803i | \(-0.330665\pi\) | ||||
0.507243 | + | 0.861803i | \(0.330665\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 9.25507i | − | 0.315779i | −0.987457 | − | 0.157889i | \(-0.949531\pi\) | ||
0.987457 | − | 0.157889i | \(-0.0504690\pi\) | |||||||
\(860\) | 68.8415 | + | 28.1956i | 2.34748 | + | 0.961463i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −36.6125 | − | 7.20721i | −1.24703 | − | 0.245478i | ||||
\(863\) | −0.290522 | −0.00988949 | −0.00494475 | − | 0.999988i | \(-0.501574\pi\) | ||||
−0.00494475 | + | 0.999988i | \(0.501574\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 29.4031 | 0.999736 | ||||||||
\(866\) | 4.43160 | + | 0.872365i | 0.150592 | + | 0.0296442i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 10.0000 | + | 4.09573i | 0.339422 | + | 0.139018i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30.8062 | −1.04383 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −7.01562 | + | 35.6393i | −0.237307 | + | 1.20552i | ||||
\(875\) | − | 12.4589i | − | 0.421189i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.3829i | 0.553212i | 0.960983 | + | 0.276606i | \(0.0892097\pi\) | ||||
−0.960983 | + | 0.276606i | \(0.910790\pi\) | |||||||
\(878\) | 22.2014 | + | 4.37036i | 0.749259 | + | 0.147492i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −26.8062 | − | 26.3842i | −0.903638 | − | 0.889411i | ||||
\(881\) | 6.91625 | 0.233014 | 0.116507 | − | 0.993190i | \(-0.462830\pi\) | ||||
0.116507 | + | 0.993190i | \(0.462830\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.09573i | 0.137832i | 0.997622 | + | 0.0689161i | \(0.0219541\pi\) | ||||
−0.997622 | + | 0.0689161i | \(0.978046\pi\) | |||||||
\(884\) | −17.2321 | + | 42.0732i | −0.579577 | + | 1.41508i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.89531 | − | 9.62817i | 0.0636743 | − | 0.323465i | ||||
\(887\) | −37.1959 | −1.24892 | −0.624459 | − | 0.781058i | \(-0.714680\pi\) | ||||
−0.624459 | + | 0.781058i | \(0.714680\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −18.8062 | −0.630741 | ||||||||
\(890\) | −3.60338 | + | 18.3051i | −0.120786 | + | 0.613590i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −27.4031 | − | 11.2236i | −0.917524 | − | 0.375793i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 44.2094 | 1.47776 | ||||||||
\(896\) | −2.36106 | − | 11.0646i | −0.0788775 | − | 0.369642i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −25.4031 | − | 5.00063i | −0.847713 | − | 0.166873i | ||||
\(899\) | − | 33.6586i | − | 1.12258i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 63.0870i | − | 2.10173i | ||||||
\(902\) | 2.52800 | − | 12.8422i | 0.0841731 | − | 0.427598i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.19375 | − | 6.06424i | −0.305780 | − | 0.201694i | ||||
\(905\) | 85.4925 | 2.84187 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.22295i | 0.206630i | 0.994649 | + | 0.103315i | \(0.0329449\pi\) | ||||
−0.994649 | + | 0.103315i | \(0.967055\pi\) | |||||||
\(908\) | 14.9946 | − | 36.6103i | 0.497613 | − | 1.21495i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −15.4031 | − | 3.03212i | −0.510609 | − | 0.100514i | ||||
\(911\) | 18.0169 | 0.596927 | 0.298464 | − | 0.954421i | \(-0.403526\pi\) | ||||
0.298464 | + | 0.954421i | \(0.403526\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 18.8062 | 0.622396 | ||||||||
\(914\) | −30.5269 | − | 6.00924i | −1.00974 | − | 0.198768i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −8.50781 | + | 20.7724i | −0.281106 | + | 0.686339i | ||||
\(917\) | 7.32206i | 0.241796i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | −20.5449 | + | 31.1473i | −0.677346 | + | 1.02690i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.20937 | − | 16.3036i | 0.105695 | − | 0.536929i | ||||
\(923\) | − | 22.7327i | − | 0.748255i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 59.8962i | − | 1.96938i | ||||||
\(926\) | −33.3020 | − | 6.55554i | −1.09437 | − | 0.215428i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −29.1047 | + | 19.8675i | −0.955408 | + | 0.652182i | ||||
\(929\) | −41.3804 | −1.35765 | −0.678823 | − | 0.734302i | \(-0.737510\pi\) | ||||
−0.678823 | + | 0.734302i | \(0.737510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 7.12785i | − | 0.233606i | ||||||
\(932\) | 34.9585 | + | 14.3180i | 1.14510 | + | 0.469003i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −11.0156 | + | 55.9592i | −0.360442 | + | 1.83104i | ||||
\(935\) | −70.4980 | −2.30553 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.61250 | 0.118015 | 0.0590076 | − | 0.998258i | \(-0.481206\pi\) | ||||
0.0590076 | + | 0.998258i | \(0.481206\pi\) | |||||||
\(938\) | 2.77517 | − | 14.0978i | 0.0906125 | − | 0.460310i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.7013i | 0.479249i | 0.970866 | + | 0.239624i | \(0.0770243\pi\) | ||||
−0.970866 | + | 0.239624i | \(0.922976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.9844 | −0.422830 | ||||||||
\(944\) | −6.13138 | + | 6.22947i | −0.199559 | + | 0.202752i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 36.2094 | + | 7.12785i | 1.17727 | + | 0.231746i | ||||
\(947\) | 40.5974i | 1.31924i | 0.751600 | + | 0.659619i | \(0.229282\pi\) | ||||
−0.751600 | + | 0.659619i | \(0.770718\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 18.1927i | − | 0.590561i | ||||||
\(950\) | −16.3605 | + | 83.1110i | −0.530804 | + | 2.69648i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −17.7016 | − | 11.6760i | −0.573711 | − | 0.378422i | ||||
\(953\) | 22.2014 | 0.719172 | 0.359586 | − | 0.933112i | \(-0.382918\pi\) | ||||
0.359586 | + | 0.933112i | \(0.382918\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.4478i | 0.888190i | ||||||||
\(956\) | 27.2140 | + | 11.1461i | 0.880164 | + | 0.360491i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 20.0000 | + | 3.93702i | 0.646171 | + | 0.127199i | ||||
\(959\) | −7.20677 | −0.232719 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.80625 | −0.0582661 | ||||||||
\(962\) | −29.9892 | − | 5.90340i | −0.966889 | − | 0.190333i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.49219 | − | 0.611161i | −0.0480602 | − | 0.0196842i | ||||
\(965\) | − | 41.7472i | − | 1.34389i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.8062 | 1.37656 | 0.688278 | − | 0.725447i | \(-0.258367\pi\) | ||||
0.688278 | + | 0.725447i | \(0.258367\pi\) | |||||||
\(968\) | 10.3960 | + | 6.85728i | 0.334142 | + | 0.220401i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.80625 | + | 44.7356i | −0.282752 | + | 1.43637i | ||||
\(971\) | − | 38.0289i | − | 1.22041i | −0.792245 | − | 0.610203i | \(-0.791088\pi\) | ||
0.792245 | − | 0.610203i | \(-0.208912\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.19146i | 0.262606i | ||||||||
\(974\) | −11.1007 | − | 2.18518i | −0.355689 | − | 0.0700176i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.50781 | + | 8.64391i | −0.272328 | + | 0.276685i | ||||
\(977\) | 55.5034 | 1.77571 | 0.887855 | − | 0.460123i | \(-0.152195\pi\) | ||||
0.887855 | + | 0.460123i | \(0.152195\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.25507i | 0.295793i | ||||||||
\(980\) | 2.77517 | − | 6.77576i | 0.0886495 | − | 0.216444i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −11.5078 | + | 58.4595i | −0.367229 | + | 1.86552i | ||||
\(983\) | −14.4135 | −0.459720 | −0.229860 | − | 0.973224i | \(-0.573827\pi\) | ||||
−0.229860 | + | 0.973224i | \(0.573827\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.6125 | −1.32588 | ||||||||
\(986\) | −12.7571 | + | 64.8059i | −0.406269 | + | 2.06384i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 40.0000 | + | 16.3829i | 1.27257 | + | 0.521210i | ||||
\(989\) | − | 36.6103i | − | 1.16414i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 21.1938 | 0.673242 | 0.336621 | − | 0.941640i | \(-0.390716\pi\) | ||||
0.336621 | + | 0.941640i | \(0.390716\pi\) | |||||||
\(992\) | −17.2321 | − | 25.2439i | −0.547118 | − | 0.801496i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 10.4031 | + | 2.04787i | 0.329967 | + | 0.0649543i | ||||
\(995\) | − | 54.2061i | − | 1.71845i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 23.3521i | 0.739567i | 0.929118 | + | 0.369784i | \(0.120568\pi\) | ||||
−0.929118 | + | 0.369784i | \(0.879432\pi\) | |||||||
\(998\) | 2.19412 | − | 11.1461i | 0.0694538 | − | 0.352824i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 504.2.c.e.253.8 | yes | 8 | |
3.2 | odd | 2 | inner | 504.2.c.e.253.1 | ✓ | 8 | |
4.3 | odd | 2 | 2016.2.c.f.1009.2 | 8 | |||
8.3 | odd | 2 | 2016.2.c.f.1009.7 | 8 | |||
8.5 | even | 2 | inner | 504.2.c.e.253.7 | yes | 8 | |
12.11 | even | 2 | 2016.2.c.f.1009.8 | 8 | |||
24.5 | odd | 2 | inner | 504.2.c.e.253.2 | yes | 8 | |
24.11 | even | 2 | 2016.2.c.f.1009.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
504.2.c.e.253.1 | ✓ | 8 | 3.2 | odd | 2 | inner | |
504.2.c.e.253.2 | yes | 8 | 24.5 | odd | 2 | inner | |
504.2.c.e.253.7 | yes | 8 | 8.5 | even | 2 | inner | |
504.2.c.e.253.8 | yes | 8 | 1.1 | even | 1 | trivial | |
2016.2.c.f.1009.1 | 8 | 24.11 | even | 2 | |||
2016.2.c.f.1009.2 | 8 | 4.3 | odd | 2 | |||
2016.2.c.f.1009.7 | 8 | 8.3 | odd | 2 | |||
2016.2.c.f.1009.8 | 8 | 12.11 | even | 2 |