Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [216,2,Mod(107,216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("216.107");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 216 = 2^{3} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 216.f (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: | \(1.72476868366\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.23123460096.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 2x^{6} + 6x^{4} + 8x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.2 | ||
Root | \(1.08766 + 0.903873i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.107 |
Dual form | 216.2.f.a.107.1 |
$q$-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 \(\left(\mathbb{Z}/216\mathbb{Z}\right)^\times\).
\(n\) | \(55\) | \(109\) | \(137\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.08766 | + | 0.903873i | −0.769095 | + | 0.639135i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.366025 | − | 1.96622i | 0.183013 | − | 0.983111i | ||||
\(5\) | −1.59245 | −0.712165 | −0.356083 | − | 0.934454i | \(-0.615888\pi\) | ||||
−0.356083 | + | 0.934454i | \(0.615888\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.43937i | 0.544032i | 0.962293 | + | 0.272016i | \(0.0876904\pi\) | ||||
−0.962293 | + | 0.272016i | \(0.912310\pi\) | |||||||
\(8\) | 1.37910 | + | 2.46943i | 0.487586 | + | 0.873075i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.73205 | − | 1.43937i | 0.547723 | − | 0.455170i | ||||
\(11\) | 4.93886i | 1.48912i | 0.667555 | + | 0.744561i | \(0.267341\pi\) | ||||
−0.667555 | + | 0.744561i | \(0.732659\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.37182i | 1.48987i | 0.667135 | + | 0.744937i | \(0.267520\pi\) | ||||
−0.667135 | + | 0.744937i | \(0.732480\pi\) | |||||||
\(14\) | −1.30101 | − | 1.56555i | −0.347710 | − | 0.418412i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.73205 | − | 1.43937i | −0.933013 | − | 0.359843i | ||||
\(17\) | − | 1.32336i | − | 0.320963i | −0.987039 | − | 0.160481i | \(-0.948695\pi\) | ||
0.987039 | − | 0.160481i | \(-0.0513046\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.267949 | 0.0614718 | 0.0307359 | − | 0.999528i | \(-0.490215\pi\) | ||||
0.0307359 | + | 0.999528i | \(0.490215\pi\) | |||||||
\(20\) | −0.582877 | + | 3.13111i | −0.130335 | + | 0.700137i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.46410 | − | 5.37182i | −0.951750 | − | 1.14528i | ||||
\(23\) | 5.94311 | 1.23922 | 0.619612 | − | 0.784909i | \(-0.287290\pi\) | ||||
0.619612 | + | 0.784909i | \(0.287290\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.46410 | −0.492820 | ||||||||
\(26\) | −4.85544 | − | 5.84273i | −0.952231 | − | 1.14585i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.83013 | + | 0.526847i | 0.534844 | + | 0.0995648i | ||||
\(29\) | −8.70131 | −1.61579 | −0.807896 | − | 0.589324i | \(-0.799394\pi\) | ||||
−0.807896 | + | 0.589324i | \(0.799394\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.86488i | 1.41257i | 0.707925 | + | 0.706287i | \(0.249631\pi\) | ||||
−0.707925 | + | 0.706287i | \(0.750369\pi\) | |||||||
\(32\) | 5.36023 | − | 1.80775i | 0.947564 | − | 0.319568i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.19615 | + | 1.43937i | 0.205138 | + | 0.246851i | ||||
\(35\) | − | 2.29213i | − | 0.387441i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 2.49307i | − | 0.409858i | −0.978777 | − | 0.204929i | \(-0.934304\pi\) | ||
0.978777 | − | 0.204929i | \(-0.0656963\pi\) | |||||||
\(38\) | −0.291439 | + | 0.242192i | −0.0472776 | + | 0.0392888i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.19615 | − | 3.93244i | −0.347242 | − | 0.621774i | ||||
\(41\) | − | 9.87771i | − | 1.54264i | −0.636448 | − | 0.771320i | \(-0.719597\pi\) | ||
0.636448 | − | 0.771320i | \(-0.280403\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000 | 0.304997 | 0.152499 | − | 0.988304i | \(-0.451268\pi\) | ||||
0.152499 | + | 0.988304i | \(0.451268\pi\) | |||||||
\(44\) | 9.71088 | + | 1.80775i | 1.46397 | + | 0.272528i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.46410 | + | 5.37182i | −0.953080 | + | 0.792031i | ||||
\(47\) | 9.12801 | 1.33146 | 0.665728 | − | 0.746194i | \(-0.268121\pi\) | ||||
0.665728 | + | 0.746194i | \(0.268121\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.92820 | 0.704029 | ||||||||
\(50\) | 2.68011 | − | 2.22724i | 0.379025 | − | 0.314979i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 10.5622 | + | 1.96622i | 1.46471 | + | 0.272666i | ||||
\(53\) | 5.51641 | 0.757737 | 0.378869 | − | 0.925450i | \(-0.376313\pi\) | ||||
0.378869 | + | 0.925450i | \(0.376313\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 7.86488i | − | 1.06050i | ||||||
\(56\) | −3.55443 | + | 1.98504i | −0.474981 | + | 0.265263i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 9.46410 | − | 7.86488i | 1.24270 | − | 1.03271i | ||||
\(59\) | 4.93886i | 0.642984i | 0.946912 | + | 0.321492i | \(0.104184\pi\) | ||||
−0.946912 | + | 0.321492i | \(0.895816\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 5.37182i | − | 0.687791i | −0.939008 | − | 0.343895i | \(-0.888253\pi\) | ||
0.939008 | − | 0.343895i | \(-0.111747\pi\) | |||||||
\(62\) | −7.10886 | − | 8.55435i | −0.902826 | − | 1.08640i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.19615 | + | 6.81119i | −0.524519 | + | 0.851399i | ||||
\(65\) | − | 8.55435i | − | 1.06104i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.19615 | 0.146133 | 0.0730666 | − | 0.997327i | \(-0.476721\pi\) | ||||
0.0730666 | + | 0.997327i | \(0.476721\pi\) | |||||||
\(68\) | −2.60202 | − | 0.484384i | −0.315542 | − | 0.0587402i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.07180 | + | 2.49307i | 0.247627 | + | 0.297979i | ||||
\(71\) | −5.51641 | −0.654677 | −0.327339 | − | 0.944907i | \(-0.606152\pi\) | ||||
−0.327339 | + | 0.944907i | \(0.606152\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.92820 | −0.927926 | −0.463963 | − | 0.885855i | \(-0.653573\pi\) | ||||
−0.463963 | + | 0.885855i | \(0.653573\pi\) | |||||||
\(74\) | 2.25342 | + | 2.71162i | 0.261955 | + | 0.315219i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.0980762 | − | 0.526847i | 0.0112501 | − | 0.0604335i | ||||
\(77\) | −7.10886 | −0.810130 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 12.1830i | − | 1.37070i | −0.728216 | − | 0.685348i | \(-0.759650\pi\) | ||
0.728216 | − | 0.685348i | \(-0.240350\pi\) | |||||||
\(80\) | 5.94311 | + | 2.29213i | 0.664459 | + | 0.256268i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.92820 | + | 10.7436i | 0.985955 | + | 1.18644i | ||||
\(83\) | 7.23099i | 0.793704i | 0.917883 | + | 0.396852i | \(0.129897\pi\) | ||||
−0.917883 | + | 0.396852i | \(0.870103\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.10739i | 0.228578i | ||||||||
\(86\) | −2.17533 | + | 1.80775i | −0.234572 | + | 0.194934i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −12.1962 | + | 6.81119i | −1.30011 | + | 0.726075i | ||||
\(89\) | 15.7853i | 1.67324i | 0.547782 | + | 0.836621i | \(0.315472\pi\) | ||||
−0.547782 | + | 0.836621i | \(0.684528\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.73205 | −0.810539 | ||||||||
\(92\) | 2.17533 | − | 11.6855i | 0.226794 | − | 1.21829i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.92820 | + | 8.25056i | −1.02402 | + | 0.850981i | ||||
\(95\) | −0.426696 | −0.0437781 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.39230 | 0.953644 | 0.476822 | − | 0.879000i | \(-0.341789\pi\) | ||||
0.476822 | + | 0.879000i | \(0.341789\pi\) | |||||||
\(98\) | −5.36023 | + | 4.45447i | −0.541465 | + | 0.449970i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.901924 | + | 4.84497i | −0.0901924 | + | 0.484497i | ||||
\(101\) | −3.18490 | −0.316909 | −0.158455 | − | 0.987366i | \(-0.550651\pi\) | ||||
−0.158455 | + | 0.987366i | \(0.550651\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 1.43937i | − | 0.141826i | −0.997483 | − | 0.0709129i | \(-0.977409\pi\) | ||
0.997483 | − | 0.0709129i | \(-0.0225912\pi\) | |||||||
\(104\) | −13.2653 | + | 7.40828i | −1.30077 | + | 0.726442i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.00000 | + | 4.98614i | −0.582772 | + | 0.484296i | ||||
\(107\) | − | 12.1698i | − | 1.17650i | −0.808678 | − | 0.588252i | \(-0.799816\pi\) | ||
0.808678 | − | 0.588252i | \(-0.200184\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 13.6224i | − | 1.30479i | −0.757880 | − | 0.652394i | \(-0.773765\pi\) | ||
0.757880 | − | 0.652394i | \(-0.226235\pi\) | |||||||
\(110\) | 7.10886 | + | 8.55435i | 0.677803 | + | 0.815625i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.07180 | − | 5.37182i | 0.195766 | − | 0.507589i | ||||
\(113\) | 11.2011i | 1.05371i | 0.849956 | + | 0.526854i | \(0.176629\pi\) | ||||
−0.849956 | + | 0.526854i | \(0.823371\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −9.46410 | −0.882532 | ||||||||
\(116\) | −3.18490 | + | 17.1087i | −0.295711 | + | 1.58850i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.46410 | − | 5.37182i | −0.410954 | − | 0.494516i | ||||
\(119\) | 1.90481 | 0.174614 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −13.3923 | −1.21748 | ||||||||
\(122\) | 4.85544 | + | 5.84273i | 0.439591 | + | 0.528976i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 15.4641 | + | 2.87875i | 1.38872 | + | 0.258519i | ||||
\(125\) | 11.8862 | 1.06314 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(128\) | −1.59245 | − | 11.2011i | −0.140754 | − | 0.990045i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 7.73205 | + | 9.30426i | 0.678146 | + | 0.816037i | ||||
\(131\) | 7.23099i | 0.631774i | 0.948797 | + | 0.315887i | \(0.102302\pi\) | ||||
−0.948797 | + | 0.315887i | \(0.897698\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.385679i | 0.0334426i | ||||||||
\(134\) | −1.30101 | + | 1.08117i | −0.112390 | + | 0.0933989i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.26795 | − | 1.82505i | 0.280224 | − | 0.156497i | ||||
\(137\) | − | 5.90763i | − | 0.504722i | −0.967633 | − | 0.252361i | \(-0.918793\pi\) | ||
0.967633 | − | 0.252361i | \(-0.0812071\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.19615 | 0.610370 | 0.305185 | − | 0.952293i | \(-0.401282\pi\) | ||||
0.305185 | + | 0.952293i | \(0.401282\pi\) | |||||||
\(140\) | −4.50684 | − | 0.838978i | −0.380897 | − | 0.0709066i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.00000 | − | 4.98614i | 0.503509 | − | 0.418427i | ||||
\(143\) | −26.5306 | −2.21860 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 13.8564 | 1.15071 | ||||||||
\(146\) | 8.62322 | − | 7.16609i | 0.713663 | − | 0.593070i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.90192 | − | 0.912526i | −0.402936 | − | 0.0750092i | ||||
\(149\) | 3.18490 | 0.260917 | 0.130459 | − | 0.991454i | \(-0.458355\pi\) | ||||
0.130459 | + | 0.991454i | \(0.458355\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.42551i | 0.522901i | 0.965217 | + | 0.261450i | \(0.0842008\pi\) | ||||
−0.965217 | + | 0.261450i | \(0.915799\pi\) | |||||||
\(152\) | 0.369529 | + | 0.661681i | 0.0299728 | + | 0.0536694i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 7.73205 | − | 6.42551i | 0.623066 | − | 0.517782i | ||||
\(155\) | − | 12.5244i | − | 1.00599i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.10739i | − | 0.168188i | −0.996458 | − | 0.0840940i | \(-0.973200\pi\) | ||
0.996458 | − | 0.0840940i | \(-0.0267996\pi\) | |||||||
\(158\) | 11.0119 | + | 13.2510i | 0.876059 | + | 1.05419i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −8.53590 | + | 2.87875i | −0.674822 | + | 0.227585i | ||||
\(161\) | 8.55435i | 0.674177i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.1962 | 1.50356 | 0.751779 | − | 0.659415i | \(-0.229196\pi\) | ||||
0.751779 | + | 0.659415i | \(0.229196\pi\) | |||||||
\(164\) | −19.4218 | − | 3.61549i | −1.51659 | − | 0.282323i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.53590 | − | 7.86488i | −0.507284 | − | 0.610433i | ||||
\(167\) | −5.08971 | −0.393854 | −0.196927 | − | 0.980418i | \(-0.563096\pi\) | ||||
−0.196927 | + | 0.980418i | \(0.563096\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −15.8564 | −1.21972 | ||||||||
\(170\) | −1.90481 | − | 2.29213i | −0.146093 | − | 0.175798i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0.732051 | − | 3.93244i | 0.0558184 | − | 0.299846i | ||||
\(173\) | 11.8862 | 0.903692 | 0.451846 | − | 0.892096i | \(-0.350766\pi\) | ||||
0.451846 | + | 0.892096i | \(0.350766\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 3.54676i | − | 0.268110i | ||||||
\(176\) | 7.10886 | − | 18.4321i | 0.535851 | − | 1.38937i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −14.2679 | − | 17.1691i | −1.06943 | − | 1.28688i | ||||
\(179\) | − | 9.87771i | − | 0.738295i | −0.929371 | − | 0.369147i | \(-0.879650\pi\) | ||
0.929371 | − | 0.369147i | \(-0.120350\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.1154i | 1.19785i | 0.800804 | + | 0.598926i | \(0.204406\pi\) | ||||
−0.800804 | + | 0.598926i | \(0.795594\pi\) | |||||||
\(182\) | 8.40987 | − | 6.98880i | 0.623381 | − | 0.518044i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 8.19615 | + | 14.6761i | 0.604228 | + | 1.08193i | ||||
\(185\) | 3.97009i | 0.291887i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 6.53590 | 0.477952 | ||||||||
\(188\) | 3.34108 | − | 17.9477i | 0.243673 | − | 1.30897i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.464102 | − | 0.385679i | 0.0336695 | − | 0.0279801i | ||||
\(191\) | 9.12801 | 0.660479 | 0.330240 | − | 0.943897i | \(-0.392870\pi\) | ||||
0.330240 | + | 0.943897i | \(0.392870\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.3923 | 1.10796 | 0.553981 | − | 0.832529i | \(-0.313108\pi\) | ||||
0.553981 | + | 0.832529i | \(0.313108\pi\) | |||||||
\(194\) | −10.2157 | + | 8.48946i | −0.733442 | + | 0.609507i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.80385 | − | 9.68994i | 0.128846 | − | 0.692138i | ||||
\(197\) | 19.8485 | 1.41414 | 0.707072 | − | 0.707141i | \(-0.250016\pi\) | ||||
0.707072 | + | 0.707141i | \(0.250016\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.2904i | 1.01302i | 0.862234 | + | 0.506510i | \(0.169065\pi\) | ||||
−0.862234 | + | 0.506510i | \(0.830935\pi\) | |||||||
\(200\) | −3.39825 | − | 6.08492i | −0.240292 | − | 0.430269i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 3.46410 | − | 2.87875i | 0.243733 | − | 0.202548i | ||||
\(203\) | − | 12.5244i | − | 0.879043i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.7298i | 1.09861i | ||||||||
\(206\) | 1.30101 | + | 1.56555i | 0.0906458 | + | 0.109077i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.73205 | − | 20.0479i | 0.536121 | − | 1.39007i | ||||
\(209\) | 1.32336i | 0.0915389i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −17.0526 | −1.17395 | −0.586973 | − | 0.809606i | \(-0.699681\pi\) | ||||
−0.586973 | + | 0.809606i | \(0.699681\pi\) | |||||||
\(212\) | 2.01915 | − | 10.8465i | 0.138676 | − | 0.744939i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 11.0000 | + | 13.2367i | 0.751945 | + | 0.904842i | ||||
\(215\) | −3.18490 | −0.217208 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.3205 | −0.768486 | ||||||||
\(218\) | 12.3129 | + | 14.8166i | 0.833935 | + | 1.00350i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −15.4641 | − | 2.87875i | −1.04259 | − | 0.194085i | ||||
\(221\) | 7.10886 | 0.478194 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 19.3799i | 1.29777i | 0.760885 | + | 0.648886i | \(0.224765\pi\) | ||||
−0.760885 | + | 0.648886i | \(0.775235\pi\) | |||||||
\(224\) | 2.60202 | + | 7.71537i | 0.173855 | + | 0.515505i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.1244 | − | 12.1830i | −0.673462 | − | 0.810401i | ||||
\(227\) | − | 9.87771i | − | 0.655607i | −0.944746 | − | 0.327803i | \(-0.893692\pi\) | ||
0.944746 | − | 0.327803i | \(-0.106308\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.7298i | − | 1.03945i | −0.854333 | − | 0.519726i | \(-0.826034\pi\) | ||
0.854333 | − | 0.519726i | \(-0.173966\pi\) | |||||||
\(230\) | 10.2938 | − | 8.55435i | 0.678751 | − | 0.564057i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −12.0000 | − | 21.4873i | −0.787839 | − | 1.41071i | ||||
\(233\) | 2.64673i | 0.173393i | 0.996235 | + | 0.0866964i | \(0.0276310\pi\) | ||||
−0.996235 | + | 0.0866964i | \(0.972369\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −14.5359 | −0.948217 | ||||||||
\(236\) | 9.71088 | + | 1.80775i | 0.632125 | + | 0.117674i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.07180 | + | 1.72171i | −0.134295 | + | 0.111602i | ||||
\(239\) | −6.36980 | −0.412028 | −0.206014 | − | 0.978549i | \(-0.566049\pi\) | ||||
−0.206014 | + | 0.978549i | \(0.566049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.3923 | 0.991506 | 0.495753 | − | 0.868464i | \(-0.334892\pi\) | ||||
0.495753 | + | 0.868464i | \(0.334892\pi\) | |||||||
\(242\) | 14.5663 | − | 12.1049i | 0.936359 | − | 0.778136i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −10.5622 | − | 1.96622i | −0.676174 | − | 0.125874i | ||||
\(245\) | −7.84792 | −0.501385 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.43937i | 0.0915852i | ||||||||
\(248\) | −19.4218 | + | 10.8465i | −1.23328 | + | 0.688752i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −12.9282 | + | 10.7436i | −0.817651 | + | 0.679487i | ||||
\(251\) | 2.64673i | 0.167060i | 0.996505 | + | 0.0835299i | \(0.0266194\pi\) | ||||
−0.996505 | + | 0.0835299i | \(0.973381\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 29.3521i | 1.84535i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.8564 | + | 10.7436i | 0.741025 | + | 0.671477i | ||||
\(257\) | − | 9.87771i | − | 0.616155i | −0.951361 | − | 0.308077i | \(-0.900314\pi\) | ||
0.951361 | − | 0.308077i | \(-0.0996856\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.58846 | 0.222976 | ||||||||
\(260\) | −16.8197 | − | 3.13111i | −1.04312 | − | 0.194183i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.53590 | − | 7.86488i | −0.403789 | − | 0.485894i | ||||
\(263\) | −23.7724 | −1.46587 | −0.732935 | − | 0.680298i | \(-0.761850\pi\) | ||||
−0.732935 | + | 0.680298i | \(0.761850\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −8.78461 | −0.539634 | ||||||||
\(266\) | −0.348605 | − | 0.419489i | −0.0213743 | − | 0.0257205i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.437822 | − | 2.35190i | 0.0267442 | − | 0.143665i | ||||
\(269\) | 0.739059 | 0.0450612 | 0.0225306 | − | 0.999746i | \(-0.492828\pi\) | ||||
0.0225306 | + | 0.999746i | \(0.492828\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.31812i | 0.262307i | 0.991362 | + | 0.131154i | \(0.0418681\pi\) | ||||
−0.991362 | + | 0.131154i | \(0.958132\pi\) | |||||||
\(272\) | −1.90481 | + | 4.93886i | −0.115496 | + | 0.299462i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.33975 | + | 6.42551i | 0.322586 | + | 0.388179i | ||||
\(275\) | − | 12.1698i | − | 0.733869i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.10739i | 0.126621i | 0.997994 | + | 0.0633104i | \(0.0201658\pi\) | ||||
−0.997994 | + | 0.0633104i | \(0.979834\pi\) | |||||||
\(278\) | −7.82700 | + | 6.50441i | −0.469432 | + | 0.390109i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.66025 | − | 3.16108i | 0.338265 | − | 0.188911i | ||||
\(281\) | 7.23099i | 0.431365i | 0.976464 | + | 0.215682i | \(0.0691975\pi\) | ||||
−0.976464 | + | 0.215682i | \(0.930802\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.143594 | 0.00853575 | 0.00426787 | − | 0.999991i | \(-0.498641\pi\) | ||||
0.00426787 | + | 0.999991i | \(0.498641\pi\) | |||||||
\(284\) | −2.01915 | + | 10.8465i | −0.119814 | + | 0.643620i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 28.8564 | − | 23.9803i | 1.70632 | − | 1.41799i | ||||
\(287\) | 14.2177 | 0.839246 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.2487 | 0.896983 | ||||||||
\(290\) | −15.0711 | + | 12.5244i | −0.885006 | + | 0.735460i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.90192 | + | 15.5886i | −0.169822 | + | 0.912254i | ||||
\(293\) | −7.10886 | −0.415304 | −0.207652 | − | 0.978203i | \(-0.566582\pi\) | ||||
−0.207652 | + | 0.978203i | \(0.566582\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.86488i | − | 0.457911i | ||||||
\(296\) | 6.15645 | − | 3.43820i | 0.357837 | − | 0.199841i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.46410 | + | 2.87875i | −0.200670 | + | 0.166761i | ||||
\(299\) | 31.9253i | 1.84629i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.87875i | 0.165928i | ||||||||
\(302\) | −5.80785 | − | 6.98880i | −0.334204 | − | 0.402160i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | − | 0.385679i | −0.0573539 | − | 0.0221202i | ||||
\(305\) | 8.55435i | 0.489821i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.07180 | 0.403609 | 0.201804 | − | 0.979426i | \(-0.435319\pi\) | ||||
0.201804 | + | 0.979426i | \(0.435319\pi\) | |||||||
\(308\) | −2.60202 | + | 13.9776i | −0.148264 | + | 0.796447i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 11.3205 | + | 13.6224i | 0.642962 | + | 0.773699i | ||||
\(311\) | 16.9759 | 0.962616 | 0.481308 | − | 0.876551i | \(-0.340162\pi\) | ||||
0.481308 | + | 0.876551i | \(0.340162\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.3923 | −0.643931 | −0.321966 | − | 0.946751i | \(-0.604344\pi\) | ||||
−0.321966 | + | 0.946751i | \(0.604344\pi\) | |||||||
\(314\) | 1.90481 | + | 2.29213i | 0.107495 | + | 0.129352i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −23.9545 | − | 4.45929i | −1.34754 | − | 0.250855i | ||||
\(317\) | 2.33151 | 0.130951 | 0.0654753 | − | 0.997854i | \(-0.479144\pi\) | ||||
0.0654753 | + | 0.997854i | \(0.479144\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 42.9745i | − | 2.40611i | ||||||
\(320\) | 6.68216 | − | 10.8465i | 0.373544 | − | 0.606337i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −7.73205 | − | 9.30426i | −0.430890 | − | 0.518506i | ||||
\(323\) | − | 0.354594i | − | 0.0197301i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 13.2367i | − | 0.734240i | ||||||
\(326\) | −20.8790 | + | 17.3509i | −1.15638 | + | 0.960977i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 24.3923 | − | 13.6224i | 1.34684 | − | 0.752170i | ||||
\(329\) | 13.1386i | 0.724355i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 26.1244 | 1.43592 | 0.717962 | − | 0.696082i | \(-0.245075\pi\) | ||||
0.717962 | + | 0.696082i | \(0.245075\pi\) | |||||||
\(332\) | 14.2177 | + | 2.64673i | 0.780299 | + | 0.145258i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.53590 | − | 4.60046i | 0.302911 | − | 0.251726i | ||||
\(335\) | −1.90481 | −0.104071 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.39230 | 0.511631 | 0.255816 | − | 0.966726i | \(-0.417656\pi\) | ||||
0.255816 | + | 0.966726i | \(0.417656\pi\) | |||||||
\(338\) | 17.2464 | − | 14.3322i | 0.938083 | − | 0.779568i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 4.14359 | + | 0.771358i | 0.224718 | + | 0.0418328i | ||||
\(341\) | −38.8435 | −2.10350 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.1691i | 0.927047i | ||||||||
\(344\) | 2.75821 | + | 4.93886i | 0.148712 | + | 0.266285i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −12.9282 | + | 10.7436i | −0.695025 | + | 0.577581i | ||||
\(347\) | 19.7554i | 1.06053i | 0.847833 | + | 0.530263i | \(0.177907\pi\) | ||||
−0.847833 | + | 0.530263i | \(0.822093\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 23.9803i | − | 1.28364i | −0.766856 | − | 0.641819i | \(-0.778180\pi\) | ||
0.766856 | − | 0.641819i | \(-0.221820\pi\) | |||||||
\(350\) | 3.20583 | + | 3.85769i | 0.171359 | + | 0.206202i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 8.92820 | + | 26.4734i | 0.475875 | + | 1.41104i | ||||
\(353\) | 19.7554i | 1.05148i | 0.850647 | + | 0.525738i | \(0.176211\pi\) | ||||
−0.850647 | + | 0.525738i | \(0.823789\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.78461 | 0.466239 | ||||||||
\(356\) | 31.0375 | + | 5.77783i | 1.64498 | + | 0.306225i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 8.92820 | + | 10.7436i | 0.471870 | + | 0.567819i | ||||
\(359\) | 6.79650 | 0.358705 | 0.179353 | − | 0.983785i | \(-0.442600\pi\) | ||||
0.179353 | + | 0.983785i | \(0.442600\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.9282 | −0.996221 | ||||||||
\(362\) | −14.5663 | − | 17.5282i | −0.765589 | − | 0.921261i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.83013 | + | 15.2029i | −0.148339 | + | 0.796850i | ||||
\(365\) | 12.6253 | 0.660837 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.3978i | 0.855957i | 0.903789 | + | 0.427979i | \(0.140774\pi\) | ||||
−0.903789 | + | 0.427979i | \(0.859226\pi\) | |||||||
\(368\) | −22.1800 | − | 8.55435i | −1.15621 | − | 0.445926i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3.58846 | − | 4.31812i | −0.186555 | − | 0.224488i | ||||
\(371\) | 7.94018i | 0.412233i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 18.2228i | − | 0.943543i | −0.881721 | − | 0.471771i | \(-0.843615\pi\) | ||
0.881721 | − | 0.471771i | \(-0.156385\pi\) | |||||||
\(374\) | −7.10886 | + | 5.90763i | −0.367590 | + | 0.305476i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 12.5885 | + | 22.5410i | 0.649200 | + | 1.16246i | ||||
\(377\) | − | 46.7418i | − | 2.40733i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −29.7321 | −1.52723 | −0.763616 | − | 0.645670i | \(-0.776578\pi\) | ||||
−0.763616 | + | 0.645670i | \(0.776578\pi\) | |||||||
\(380\) | −0.156182 | + | 0.838978i | −0.00801194 | + | 0.0430387i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −9.92820 | + | 8.25056i | −0.507971 | + | 0.422136i | ||||
\(383\) | −11.8862 | −0.607357 | −0.303679 | − | 0.952775i | \(-0.598215\pi\) | ||||
−0.303679 | + | 0.952775i | \(0.598215\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 11.3205 | 0.576947 | ||||||||
\(386\) | −16.7417 | + | 13.9127i | −0.852128 | + | 0.708138i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.43782 | − | 18.4673i | 0.174529 | − | 0.937538i | ||||
\(389\) | −7.96225 | −0.403702 | −0.201851 | − | 0.979416i | \(-0.564696\pi\) | ||||
−0.201851 | + | 0.979416i | \(0.564696\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 7.86488i | − | 0.397744i | ||||||
\(392\) | 6.79650 | + | 12.1698i | 0.343275 | + | 0.614670i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −21.5885 | + | 17.9405i | −1.08761 | + | 0.903829i | ||||
\(395\) | 19.4008i | 0.976162i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 13.6224i | − | 0.683688i | −0.939757 | − | 0.341844i | \(-0.888949\pi\) | ||
0.939757 | − | 0.341844i | \(-0.111051\pi\) | |||||||
\(398\) | −12.9167 | − | 15.5431i | −0.647456 | − | 0.779108i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 9.19615 | + | 3.54676i | 0.459808 | + | 0.177338i | ||||
\(401\) | − | 39.5109i | − | 1.97308i | −0.163527 | − | 0.986539i | \(-0.552287\pi\) | ||
0.163527 | − | 0.986539i | \(-0.447713\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −42.2487 | −2.10456 | ||||||||
\(404\) | −1.16575 | + | 6.26222i | −0.0579985 | + | 0.311557i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 11.3205 | + | 13.6224i | 0.561827 | + | 0.676067i | ||||
\(407\) | 12.3129 | 0.610328 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −29.3923 | −1.45336 | −0.726678 | − | 0.686978i | \(-0.758937\pi\) | ||||
−0.726678 | + | 0.686978i | \(0.758937\pi\) | |||||||
\(410\) | −14.2177 | − | 17.1087i | −0.702163 | − | 0.844939i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.83013 | − | 0.526847i | −0.139430 | − | 0.0259559i | ||||
\(413\) | −7.10886 | −0.349804 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 11.5150i | − | 0.565249i | ||||||
\(416\) | 9.71088 | + | 28.7942i | 0.476115 | + | 1.41175i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.19615 | − | 1.43937i | −0.0585057 | − | 0.0704021i | ||||
\(419\) | 0.354594i | 0.0173230i | 0.999962 | + | 0.00866152i | \(0.00275708\pi\) | ||||
−0.999962 | + | 0.00866152i | \(0.997243\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.2367i | 0.645117i | 0.946549 | + | 0.322559i | \(0.104543\pi\) | ||||
−0.946549 | + | 0.322559i | \(0.895457\pi\) | |||||||
\(422\) | 18.5475 | − | 15.4134i | 0.902876 | − | 0.750310i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7.60770 | + | 13.6224i | 0.369462 | + | 0.661561i | ||||
\(425\) | 3.26090i | 0.158177i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.73205 | 0.374180 | ||||||||
\(428\) | −23.9286 | − | 4.45447i | −1.15663 | − | 0.215315i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.46410 | − | 2.87875i | 0.167054 | − | 0.138826i | ||||
\(431\) | 38.4168 | 1.85047 | 0.925237 | − | 0.379390i | \(-0.123866\pi\) | ||||
0.925237 | + | 0.379390i | \(0.123866\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.4641 | 0.550930 | 0.275465 | − | 0.961311i | \(-0.411168\pi\) | ||||
0.275465 | + | 0.961311i | \(0.411168\pi\) | |||||||
\(434\) | 12.3129 | − | 10.2323i | 0.591038 | − | 0.491166i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −26.7846 | − | 4.98614i | −1.28275 | − | 0.238793i | ||||
\(437\) | 1.59245 | 0.0761772 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 35.1096i | − | 1.67569i | −0.545907 | − | 0.837846i | \(-0.683815\pi\) | ||
0.545907 | − | 0.837846i | \(-0.316185\pi\) | |||||||
\(440\) | 19.4218 | − | 10.8465i | 0.925896 | − | 0.517086i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −7.73205 | + | 6.42551i | −0.367776 | + | 0.305630i | ||||
\(443\) | − | 31.5707i | − | 1.49997i | −0.661456 | − | 0.749984i | \(-0.730061\pi\) | ||
0.661456 | − | 0.749984i | \(-0.269939\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 25.1374i | − | 1.19163i | ||||||
\(446\) | −17.5170 | − | 21.0788i | −0.829452 | − | 0.998110i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −9.80385 | − | 6.03983i | −0.463188 | − | 0.285355i | ||||
\(449\) | − | 23.0163i | − | 1.08621i | −0.839666 | − | 0.543104i | \(-0.817249\pi\) | ||
0.839666 | − | 0.543104i | \(-0.182751\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 48.7846 | 2.29718 | ||||||||
\(452\) | 22.0238 | + | 4.09988i | 1.03591 | + | 0.192842i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8.92820 | + | 10.7436i | 0.419021 | + | 0.504224i | ||||
\(455\) | 12.3129 | 0.577238 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.3923 | −0.673244 | −0.336622 | − | 0.941640i | \(-0.609284\pi\) | ||||
−0.336622 | + | 0.941640i | \(0.609284\pi\) | |||||||
\(458\) | 14.2177 | + | 17.1087i | 0.664350 | + | 0.799437i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.46410 | + | 18.6085i | −0.161515 | + | 0.867627i | ||||
\(461\) | −18.9951 | −0.884689 | −0.442344 | − | 0.896845i | \(-0.645853\pi\) | ||||
−0.442344 | + | 0.896845i | \(0.645853\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.7915i | 1.43100i | 0.698611 | + | 0.715502i | \(0.253802\pi\) | ||||
−0.698611 | + | 0.715502i | \(0.746198\pi\) | |||||||
\(464\) | 32.4737 | + | 12.5244i | 1.50756 | + | 0.581432i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.39230 | − | 2.87875i | −0.110821 | − | 0.133355i | ||||
\(467\) | 17.4633i | 0.808105i | 0.914736 | + | 0.404052i | \(0.132399\pi\) | ||||
−0.914736 | + | 0.404052i | \(0.867601\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.72171i | 0.0795012i | ||||||||
\(470\) | 15.8102 | − | 13.1386i | 0.729269 | − | 0.606039i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12.1962 | + | 6.81119i | −0.561373 | + | 0.313510i | ||||
\(473\) | 9.87771i | 0.454178i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.660254 | −0.0302945 | ||||||||
\(476\) | 0.697210 | − | 3.74528i | 0.0319566 | − | 0.171665i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.92820 | − | 5.75749i | 0.316889 | − | 0.263342i | ||||
\(479\) | −3.18490 | −0.145522 | −0.0727609 | − | 0.997349i | \(-0.523181\pi\) | ||||
−0.0727609 | + | 0.997349i | \(0.523181\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3923 | 0.610637 | ||||||||
\(482\) | −16.7417 | + | 13.9127i | −0.762561 | + | 0.633706i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.90192 | + | 26.3322i | −0.222815 | + | 1.19692i | ||||
\(485\) | −14.9568 | −0.679152 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 37.8850i | − | 1.71674i | −0.513035 | − | 0.858368i | \(-0.671479\pi\) | ||
0.513035 | − | 0.858368i | \(-0.328521\pi\) | |||||||
\(488\) | 13.2653 | − | 7.40828i | 0.600493 | − | 0.335357i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 8.53590 | − | 7.09353i | 0.385613 | − | 0.320453i | ||||
\(491\) | − | 16.7541i | − | 0.756102i | −0.925785 | − | 0.378051i | \(-0.876594\pi\) | ||
0.925785 | − | 0.378051i | \(-0.123406\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11.5150i | 0.518609i | ||||||||
\(494\) | −1.30101 | − | 1.56555i | −0.0585353 | − | 0.0704376i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 11.3205 | − | 29.3521i | 0.508306 | − | 1.31795i | ||||
\(497\) | − | 7.94018i | − | 0.356166i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −26.3923 | −1.18148 | −0.590741 | − | 0.806861i | \(-0.701164\pi\) | ||||
−0.590741 | + | 0.806861i | \(0.701164\pi\) | |||||||
\(500\) | 4.35066 | − | 23.3709i | 0.194567 | − | 1.04518i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.39230 | − | 2.87875i | −0.106774 | − | 0.128485i | ||||
\(503\) | 34.3785 | 1.53286 | 0.766432 | − | 0.642326i | \(-0.222030\pi\) | ||||
0.766432 | + | 0.642326i | \(0.222030\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 5.07180 | 0.225692 | ||||||||
\(506\) | −26.5306 | − | 31.9253i | −1.17943 | − | 1.41925i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −22.1800 | −0.983110 | −0.491555 | − | 0.870847i | \(-0.663571\pi\) | ||||
−0.491555 | + | 0.870847i | \(0.663571\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 11.4116i | − | 0.504822i | ||||||
\(512\) | −22.6067 | − | 0.968769i | −0.999083 | − | 0.0428139i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.92820 | + | 10.7436i | 0.393806 | + | 0.473881i | ||||
\(515\) | 2.29213i | 0.101003i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 45.0819i | 1.98270i | ||||||||
\(518\) | −3.90304 | + | 3.24351i | −0.171490 | + | 0.142512i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 21.1244 | − | 11.7973i | 0.926364 | − | 0.517347i | ||||
\(521\) | − | 1.32336i | − | 0.0579776i | −0.999580 | − | 0.0289888i | \(-0.990771\pi\) | ||
0.999580 | − | 0.0289888i | \(-0.00922871\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.41154 | −0.280357 | −0.140179 | − | 0.990126i | \(-0.544768\pi\) | ||||
−0.140179 | + | 0.990126i | \(0.544768\pi\) | |||||||
\(524\) | 14.2177 | + | 2.64673i | 0.621104 | + | 0.115623i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 25.8564 | − | 21.4873i | 1.12739 | − | 0.936889i | ||||
\(527\) | 10.4081 | 0.453384 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12.3205 | 0.535674 | ||||||||
\(530\) | 9.55470 | − | 7.94018i | 0.415030 | − | 0.344899i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0.758330 | + | 0.141168i | 0.0328778 | + | 0.00612042i | ||||
\(533\) | 53.0613 | 2.29834 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 19.3799i | 0.837865i | ||||||||
\(536\) | 1.64962 | + | 2.95381i | 0.0712526 | + | 0.127585i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.803848 | + | 0.668016i | −0.0346563 | + | 0.0288002i | ||||
\(539\) | 24.3397i | 1.04838i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 12.4653i | − | 0.535927i | −0.963429 | − | 0.267963i | \(-0.913649\pi\) | ||
0.963429 | − | 0.267963i | \(-0.0863506\pi\) | |||||||
\(542\) | −3.90304 | − | 4.69666i | −0.167650 | − | 0.201739i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.39230 | − | 7.09353i | −0.102569 | − | 0.304132i | ||||
\(545\) | 21.6930i | 0.929224i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −0.411543 | −0.0175963 | −0.00879815 | − | 0.999961i | \(-0.502801\pi\) | ||||
−0.00879815 | + | 0.999961i | \(0.502801\pi\) | |||||||
\(548\) | −11.6157 | − | 2.16234i | −0.496198 | − | 0.0923706i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.0000 | + | 13.2367i | 0.469042 | + | 0.564415i | ||||
\(551\) | −2.33151 | −0.0993256 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.5359 | 0.745702 | ||||||||
\(554\) | −1.90481 | − | 2.29213i | −0.0809278 | − | 0.0973833i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.63397 | − | 14.1492i | 0.111705 | − | 0.600061i | ||||
\(557\) | −36.3977 | −1.54222 | −0.771110 | − | 0.636702i | \(-0.780298\pi\) | ||||
−0.771110 | + | 0.636702i | \(0.780298\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 10.7436i | 0.454407i | ||||||||
\(560\) | −3.29923 | + | 8.55435i | −0.139418 | + | 0.361487i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.53590 | − | 7.86488i | −0.275700 | − | 0.331760i | ||||
\(563\) | 11.8153i | 0.497953i | 0.968509 | + | 0.248977i | \(0.0800943\pi\) | ||||
−0.968509 | + | 0.248977i | \(0.919906\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 17.8372i | − | 0.750415i | ||||||
\(566\) | −0.156182 | + | 0.129790i | −0.00656480 | + | 0.00545550i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −7.60770 | − | 13.6224i | −0.319212 | − | 0.571582i | ||||
\(569\) | − | 35.5408i | − | 1.48995i | −0.667094 | − | 0.744973i | \(-0.732462\pi\) | ||
0.667094 | − | 0.744973i | \(-0.267538\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.19615 | 0.301150 | 0.150575 | − | 0.988599i | \(-0.451888\pi\) | ||||
0.150575 | + | 0.988599i | \(0.451888\pi\) | |||||||
\(572\) | −9.71088 | + | 52.1651i | −0.406032 | + | 2.18113i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −15.4641 | + | 12.8510i | −0.645459 | + | 0.536391i | ||||
\(575\) | −14.6444 | −0.610714 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.92820 | −0.0802722 | −0.0401361 | − | 0.999194i | \(-0.512779\pi\) | ||||
−0.0401361 | + | 0.999194i | \(0.512779\pi\) | |||||||
\(578\) | −16.5855 | + | 13.7829i | −0.689865 | + | 0.573293i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.07180 | − | 27.2448i | 0.210595 | − | 1.13128i | ||||
\(581\) | −10.4081 | −0.431801 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 27.2448i | 1.12836i | ||||||||
\(584\) | −10.9338 | − | 19.5781i | −0.452444 | − | 0.810149i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7.73205 | − | 6.42551i | 0.319408 | − | 0.265435i | ||||
\(587\) | − | 16.7541i | − | 0.691516i | −0.938324 | − | 0.345758i | \(-0.887622\pi\) | ||
0.938324 | − | 0.345758i | \(-0.112378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.10739i | 0.0868335i | ||||||||
\(590\) | 7.10886 | + | 8.55435i | 0.292667 | + | 0.352177i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.58846 | + | 9.30426i | −0.147485 | + | 0.382403i | ||||
\(593\) | − | 1.93754i | − | 0.0795651i | −0.999208 | − | 0.0397826i | \(-0.987333\pi\) | ||
0.999208 | − | 0.0397826i | \(-0.0126665\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.03332 | −0.124354 | ||||||||
\(596\) | 1.16575 | − | 6.26222i | 0.0477512 | − | 0.256510i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −28.8564 | − | 34.7240i | −1.18003 | − | 1.41997i | ||||
\(599\) | −43.5066 | −1.77763 | −0.888815 | − | 0.458267i | \(-0.848471\pi\) | ||||
−0.888815 | + | 0.458267i | \(0.848471\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.60770 | 0.391906 | 0.195953 | − | 0.980613i | \(-0.437220\pi\) | ||||
0.195953 | + | 0.980613i | \(0.437220\pi\) | |||||||
\(602\) | −2.60202 | − | 3.13111i | −0.106051 | − | 0.127615i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.6340 | + | 2.35190i | 0.514069 | + | 0.0956975i | ||||
\(605\) | 21.3266 | 0.867049 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27.1414i | 1.10164i | 0.834625 | + | 0.550818i | \(0.185684\pi\) | ||||
−0.834625 | + | 0.550818i | \(0.814316\pi\) | |||||||
\(608\) | 1.43627 | − | 0.484384i | 0.0582484 | − | 0.0196444i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −7.73205 | − | 9.30426i | −0.313062 | − | 0.376718i | ||||
\(611\) | 49.0340i | 1.98370i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.49307i | 0.100694i | 0.998732 | + | 0.0503470i | \(0.0160327\pi\) | ||||
−0.998732 | + | 0.0503470i | \(0.983967\pi\) | |||||||
\(614\) | −7.69174 | + | 6.39201i | −0.310413 | + | 0.257961i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.80385 | − | 17.5548i | −0.395008 | − | 0.707304i | ||||
\(617\) | 23.7255i | 0.955153i | 0.878590 | + | 0.477577i | \(0.158485\pi\) | ||||
−0.878590 | + | 0.477577i | \(0.841515\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 26.8038 | 1.07734 | 0.538669 | − | 0.842518i | \(-0.318927\pi\) | ||||
0.538669 | + | 0.842518i | \(0.318927\pi\) | |||||||
\(620\) | −24.6258 | − | 4.58426i | −0.988997 | − | 0.184108i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −18.4641 | + | 15.3441i | −0.740343 | + | 0.615242i | ||||
\(623\) | −22.7210 | −0.910298 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.60770 | −0.264308 | ||||||||
\(626\) | 12.3910 | − | 10.2972i | 0.495244 | − | 0.411559i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.14359 | − | 0.771358i | −0.165347 | − | 0.0307805i | ||||
\(629\) | −3.29923 | −0.131549 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.9405i | 0.714200i | 0.934066 | + | 0.357100i | \(0.116234\pi\) | ||||
−0.934066 | + | 0.357100i | \(0.883766\pi\) | |||||||
\(632\) | 30.0851 | − | 16.8016i | 1.19672 | − | 0.668332i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.53590 | + | 2.10739i | −0.100713 | + | 0.0836951i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 26.4734i | 1.04891i | ||||||||
\(638\) | 38.8435 | + | 46.7418i | 1.53783 | + | 1.85053i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.53590 | + | 17.8372i | 0.100240 | + | 0.705076i | ||||
\(641\) | 11.8153i | 0.466674i | 0.972396 | + | 0.233337i | \(0.0749646\pi\) | ||||
−0.972396 | + | 0.233337i | \(0.925035\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22.7846 | 0.898537 | 0.449269 | − | 0.893397i | \(-0.351685\pi\) | ||||
0.449269 | + | 0.893397i | \(0.351685\pi\) | |||||||
\(644\) | 16.8197 | + | 3.13111i | 0.662791 | + | 0.123383i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0.320508 | + | 0.385679i | 0.0126102 | + | 0.0151743i | ||||
\(647\) | 1.47812 | 0.0581108 | 0.0290554 | − | 0.999578i | \(-0.490750\pi\) | ||||
0.0290554 | + | 0.999578i | \(0.490750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.3923 | −0.957482 | ||||||||
\(650\) | 11.9643 | + | 14.3971i | 0.469279 | + | 0.564700i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 7.02628 | − | 37.7439i | 0.275170 | − | 1.47816i | ||||
\(653\) | 27.8107 | 1.08832 | 0.544159 | − | 0.838982i | \(-0.316849\pi\) | ||||
0.544159 | + | 0.838982i | \(0.316849\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 11.5150i | − | 0.449928i | ||||||
\(656\) | −14.2177 | + | 36.8641i | −0.555109 | + | 1.43930i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −11.8756 | − | 14.2904i | −0.462961 | − | 0.557098i | ||||
\(659\) | − | 22.4022i | − | 0.872664i | −0.899786 | − | 0.436332i | \(-0.856277\pi\) | ||
0.899786 | − | 0.436332i | \(-0.143723\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 41.2528i | 1.60455i | 0.596956 | + | 0.802274i | \(0.296377\pi\) | ||||
−0.596956 | + | 0.802274i | \(0.703623\pi\) | |||||||
\(662\) | −28.4145 | + | 23.6131i | −1.10436 | + | 0.917750i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17.8564 | + | 9.97227i | −0.692963 | + | 0.386999i | ||||
\(665\) | − | 0.614175i | − | 0.0238167i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −51.7128 | −2.00233 | ||||||||
\(668\) | −1.86296 | + | 10.0075i | −0.0720803 | + | 0.387202i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.07180 | − | 1.72171i | 0.0800405 | − | 0.0665155i | ||||
\(671\) | 26.5306 | 1.02420 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.2487 | −0.510700 | −0.255350 | − | 0.966849i | \(-0.582191\pi\) | ||||
−0.255350 | + | 0.966849i | \(0.582191\pi\) | |||||||
\(674\) | −10.2157 | + | 8.48946i | −0.393493 | + | 0.327002i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.80385 | + | 31.1772i | −0.223225 | + | 1.19912i | ||||
\(677\) | −12.0005 | −0.461218 | −0.230609 | − | 0.973046i | \(-0.574072\pi\) | ||||
−0.230609 | + | 0.973046i | \(0.574072\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.5190i | 0.518813i | ||||||||
\(680\) | −5.20405 | + | 2.90631i | −0.199566 | + | 0.111452i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 42.2487 | − | 35.1096i | 1.61779 | − | 1.34442i | ||||
\(683\) | − | 34.9266i | − | 1.33643i | −0.743969 | − | 0.668214i | \(-0.767059\pi\) | ||
0.743969 | − | 0.668214i | \(-0.232941\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.40760i | 0.359446i | ||||||||
\(686\) | −15.5187 | − | 18.6743i | −0.592508 | − | 0.712986i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −7.46410 | − | 2.87875i | −0.284566 | − | 0.109751i | ||||
\(689\) | 29.6331i | 1.12893i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.8564 | −0.907540 | −0.453770 | − | 0.891119i | \(-0.649921\pi\) | ||||
−0.453770 | + | 0.891119i | \(0.649921\pi\) | |||||||
\(692\) | 4.35066 | − | 23.3709i | 0.165387 | − | 0.888429i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −17.8564 | − | 21.4873i | −0.677820 | − | 0.815645i | ||||
\(695\) | −11.4595 | −0.434684 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.0718 | −0.495130 | ||||||||
\(698\) | 21.6752 | + | 26.0825i | 0.820418 | + | 0.987239i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −6.97372 | − | 1.29821i | −0.263582 | − | 0.0490676i | ||||
\(701\) | −17.2883 | −0.652970 | −0.326485 | − | 0.945202i | \(-0.605864\pi\) | ||||
−0.326485 | + | 0.945202i | \(0.605864\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 0.668016i | − | 0.0251947i | ||||||
\(704\) | −33.6395 | − | 20.7242i | −1.26784 | − | 0.781072i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −17.8564 | − | 21.4873i | −0.672035 | − | 0.808684i | ||||
\(707\) | − | 4.58426i | − | 0.172409i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 27.6304i | − | 1.03768i | −0.854870 | − | 0.518841i | \(-0.826364\pi\) | ||
0.854870 | − | 0.518841i | \(-0.173636\pi\) | |||||||
\(710\) | −9.55470 | + | 7.94018i | −0.358582 | + | 0.297989i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −38.9808 | + | 21.7696i | −1.46087 | + | 0.815850i | ||||
\(713\) | 46.7418i | 1.75050i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 42.2487 | 1.58001 | ||||||||
\(716\) | −19.4218 | − | 3.61549i | −0.725826 | − | 0.135117i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.39230 | + | 6.14317i | −0.275878 | + | 0.229261i | ||||
\(719\) | 15.0711 | 0.562058 | 0.281029 | − | 0.959699i | \(-0.409324\pi\) | ||||
0.281029 | + | 0.959699i | \(0.409324\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.07180 | 0.0771577 | ||||||||
\(722\) | 20.5875 | − | 17.1087i | 0.766188 | − | 0.636720i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 31.6865 | + | 5.89866i | 1.17762 | + | 0.219222i | ||||
\(725\) | 21.4409 | 0.796296 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.3799i | 0.718760i | 0.933191 | + | 0.359380i | \(0.117012\pi\) | ||||
−0.933191 | + | 0.359380i | \(0.882988\pi\) | |||||||
\(728\) | −10.6633 | − | 19.0937i | −0.395208 | − | 0.707661i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −13.7321 | + | 11.4116i | −0.508246 | + | 0.422364i | ||||
\(731\) | − | 2.64673i | − | 0.0978927i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 45.0819i | 1.66514i | 0.553921 | + | 0.832569i | \(0.313131\pi\) | ||||
−0.553921 | + | 0.832569i | \(0.686869\pi\) | |||||||
\(734\) | −14.8215 | − | 17.8353i | −0.547072 | − | 0.658312i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 31.8564 | − | 10.7436i | 1.17424 | − | 0.396016i | ||||
\(737\) | 5.90763i | 0.217610i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 48.6410 | 1.78929 | 0.894644 | − | 0.446779i | \(-0.147429\pi\) | ||||
0.894644 | + | 0.446779i | \(0.147429\pi\) | |||||||
\(740\) | 7.80607 | + | 1.45315i | 0.286957 | + | 0.0534190i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −7.17691 | − | 8.63624i | −0.263473 | − | 0.317046i | ||||
\(743\) | −43.3085 | −1.58884 | −0.794418 | − | 0.607372i | \(-0.792224\pi\) | ||||
−0.794418 | + | 0.607372i | \(0.792224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.07180 | −0.185816 | ||||||||
\(746\) | 16.4711 | + | 19.8203i | 0.603051 | + | 0.725674i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.39230 | − | 12.8510i | 0.0874713 | − | 0.469880i | ||||
\(749\) | 17.5170 | 0.640056 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.19687i | 0.262617i | 0.991342 | + | 0.131309i | \(0.0419179\pi\) | ||||
−0.991342 | + | 0.131309i | \(0.958082\pi\) | |||||||
\(752\) | −34.0662 | − | 13.1386i | −1.24227 | − | 0.479116i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 42.2487 | + | 50.8394i | 1.53861 | + | 1.85146i | ||||
\(755\) | − | 10.2323i | − | 0.372392i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 36.0600i | − | 1.31062i | −0.755359 | − | 0.655311i | \(-0.772537\pi\) | ||
0.755359 | − | 0.655311i | \(-0.227463\pi\) | |||||||
\(758\) | 32.3385 | − | 26.8740i | 1.17459 | − | 0.976108i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.588457 | − | 1.05369i | −0.0213456 | − | 0.0382215i | ||||
\(761\) | − | 26.3722i | − | 0.955993i | −0.878362 | − | 0.477996i | \(-0.841363\pi\) | ||
0.878362 | − | 0.477996i | \(-0.158637\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 19.6077 | 0.709846 | ||||||||
\(764\) | 3.34108 | − | 17.9477i | 0.120876 | − | 0.649324i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 12.9282 | − | 10.7436i | 0.467115 | − | 0.388183i | ||||
\(767\) | −26.5306 | −0.957965 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 17.9282 | 0.646508 | 0.323254 | − | 0.946312i | \(-0.395223\pi\) | ||||
0.323254 | + | 0.946312i | \(0.395223\pi\) | |||||||
\(770\) | −12.3129 | + | 10.2323i | −0.443726 | + | 0.368747i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 5.63397 | − | 30.2647i | 0.202771 | − | 1.08925i | ||||
\(773\) | 34.1805 | 1.22939 | 0.614694 | − | 0.788766i | \(-0.289280\pi\) | ||||
0.614694 | + | 0.788766i | \(0.289280\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 19.3799i | − | 0.696146i | ||||||
\(776\) | 12.9530 | + | 23.1936i | 0.464984 | + | 0.832603i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.66025 | − | 7.19687i | 0.310485 | − | 0.258020i | ||||
\(779\) | − | 2.64673i | − | 0.0948288i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 27.2448i | − | 0.974894i | ||||||
\(782\) | 7.10886 | + | 8.55435i | 0.254212 | + | 0.305903i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −18.3923 | − | 7.09353i | −0.656868 | − | 0.253340i | ||||
\(785\) | 3.35591i | 0.119778i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −51.4449 | −1.83381 | −0.916906 | − | 0.399104i | \(-0.869321\pi\) | ||||
−0.916906 | + | 0.399104i | \(0.869321\pi\) | |||||||
\(788\) | 7.26504 | − | 39.0265i | 0.258806 | − | 1.39026i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −17.5359 | − | 21.1016i | −0.623899 | − | 0.750761i | ||||
\(791\) | −16.1225 | −0.573251 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.8564 | 1.02472 | ||||||||
\(794\) | 12.3129 | + | 14.8166i | 0.436969 | + | 0.525820i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 28.0981 | + | 5.23065i | 0.995910 | + | 0.185395i | ||||
\(797\) | −7.84792 | −0.277988 | −0.138994 | − | 0.990293i | \(-0.544387\pi\) | ||||
−0.138994 | + | 0.990293i | \(0.544387\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 12.0797i | − | 0.427348i | ||||||
\(800\) | −13.2081 | + | 4.45447i | −0.466979 | + | 0.157489i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 35.7128 | + | 42.9745i | 1.26106 | + | 1.51748i | ||||
\(803\) | − | 39.1563i | − | 1.38179i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 13.6224i | − | 0.480126i | ||||||
\(806\) | 45.9524 | − | 38.1875i | 1.61860 | − | 1.34510i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.39230 | − | 7.86488i | −0.154521 | − | 0.276686i | ||||
\(809\) | 2.64673i | 0.0930539i | 0.998917 | + | 0.0465270i | \(0.0148153\pi\) | ||||
−0.998917 | + | 0.0465270i | \(0.985185\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.9282 | −1.43718 | −0.718592 | − | 0.695432i | \(-0.755213\pi\) | ||||
−0.718592 | + | 0.695432i | \(0.755213\pi\) | |||||||
\(812\) | −24.6258 | − | 4.58426i | −0.864197 | − | 0.160876i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −13.3923 | + | 11.1293i | −0.469400 | + | 0.390082i | ||||
\(815\) | −30.5689 | −1.07078 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.535898 | 0.0187487 | ||||||||
\(818\) | 31.9689 | − | 26.5669i | 1.11777 | − | 0.928891i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 30.9282 | + | 5.75749i | 1.08006 | + | 0.201060i | ||||
\(821\) | 16.6636 | 0.581562 | 0.290781 | − | 0.956790i | \(-0.406085\pi\) | ||||
0.290781 | + | 0.956790i | \(0.406085\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 28.6841i | − | 0.999866i | −0.866064 | − | 0.499933i | \(-0.833358\pi\) | ||
0.866064 | − | 0.499933i | \(-0.166642\pi\) | |||||||
\(824\) | 3.55443 | − | 1.98504i | 0.123824 | − | 0.0691523i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 7.73205 | − | 6.42551i | 0.269032 | − | 0.223572i | ||||
\(827\) | − | 3.00132i | − | 0.104366i | −0.998638 | − | 0.0521830i | \(-0.983382\pi\) | ||
0.998638 | − | 0.0521830i | \(-0.0166179\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12.4653i | 0.432939i | 0.976289 | + | 0.216470i | \(0.0694542\pi\) | ||||
−0.976289 | + | 0.216470i | \(0.930546\pi\) | |||||||
\(830\) | 10.4081 | + | 12.5244i | 0.361270 | + | 0.434730i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −36.5885 | − | 22.5410i | −1.26848 | − | 0.781467i | ||||
\(833\) | − | 6.52180i | − | 0.225967i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8.10512 | 0.280489 | ||||||||
\(836\) | 2.60202 | + | 0.484384i | 0.0899929 | + | 0.0167528i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −0.320508 | − | 0.385679i | −0.0110718 | − | 0.0133231i | ||||
\(839\) | 57.0996 | 1.97130 | 0.985648 | − | 0.168815i | \(-0.0539942\pi\) | ||||
0.985648 | + | 0.168815i | \(0.0539942\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 46.7128 | 1.61079 | ||||||||
\(842\) | −11.9643 | − | 14.3971i | −0.412317 | − | 0.496156i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.24167 | + | 33.5291i | −0.214847 | + | 1.15412i | ||||
\(845\) | 25.2505 | 0.868645 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 19.2765i | − | 0.662349i | ||||||
\(848\) | −20.5875 | − | 7.94018i | −0.706978 | − | 0.272667i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.94744 | − | 3.54676i | −0.101096 | − | 0.121653i | ||||
\(851\) | − | 14.8166i | − | 0.507905i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 0.385679i | − | 0.0132054i | −0.999978 | − | 0.00660270i | \(-0.997898\pi\) | ||
0.999978 | − | 0.00660270i | \(-0.00210172\pi\) | |||||||
\(854\) | −8.40987 | + | 6.98880i | −0.287780 | + | 0.239152i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 30.0526 | − | 16.7835i | 1.02718 | − | 0.573647i | ||||
\(857\) | 36.8641i | 1.25925i | 0.776897 | + | 0.629627i | \(0.216792\pi\) | ||||
−0.776897 | + | 0.629627i | \(0.783208\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −19.5885 | −0.668350 | −0.334175 | − | 0.942511i | \(-0.608458\pi\) | ||||
−0.334175 | + | 0.942511i | \(0.608458\pi\) | |||||||
\(860\) | −1.16575 | + | 6.26222i | −0.0397519 | + | 0.213540i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −41.7846 | + | 34.7240i | −1.42319 | + | 1.18270i | ||||
\(863\) | −8.27462 | −0.281671 | −0.140836 | − | 0.990033i | \(-0.544979\pi\) | ||||
−0.140836 | + | 0.990033i | \(0.544979\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.9282 | −0.643578 | ||||||||
\(866\) | −12.4691 | + | 10.3621i | −0.423717 | + | 0.352118i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.14359 | + | 22.2586i | −0.140643 | + | 0.755507i | ||||
\(869\) | 60.1701 | 2.04113 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.42551i | 0.217720i | ||||||||
\(872\) | 33.6395 | − | 18.7867i | 1.13918 | − | 0.636197i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.73205 | + | 1.43937i | −0.0585875 | + | 0.0486875i | ||||
\(875\) | 17.1087i | 0.578380i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 21.8729i | − | 0.738597i | −0.929311 | − | 0.369298i | \(-0.879598\pi\) | ||
0.929311 | − | 0.369298i | \(-0.120402\pi\) | |||||||
\(878\) | 31.7347 | + | 38.1875i | 1.07099 | + | 1.28877i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −11.3205 | + | 29.3521i | −0.381614 | + | 0.989461i | ||||
\(881\) | − | 35.5408i | − | 1.19740i | −0.800974 | − | 0.598699i | \(-0.795684\pi\) | ||
0.800974 | − | 0.598699i | \(-0.204316\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 19.8756 | 0.668869 | 0.334434 | − | 0.942419i | \(-0.391455\pi\) | ||||
0.334434 | + | 0.942419i | \(0.391455\pi\) | |||||||
\(884\) | 2.60202 | − | 13.9776i | 0.0875155 | − | 0.470117i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 28.5359 | + | 34.3383i | 0.958682 | + | 1.15362i | ||||
\(887\) | 19.7341 | 0.662607 | 0.331304 | − | 0.943524i | \(-0.392512\pi\) | ||||
0.331304 | + | 0.943524i | \(0.392512\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 22.7210 | + | 27.3410i | 0.761610 | + | 0.916473i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 38.1051 | + | 7.09353i | 1.27585 | + | 0.237509i | ||||
\(893\) | 2.44584 | 0.0818470 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.7298i | 0.525788i | ||||||||
\(896\) | 16.1225 | − | 2.29213i | 0.538616 | − | 0.0765747i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 20.8038 | + | 25.0340i | 0.694233 | + | 0.835396i | ||||
\(899\) | − | 68.4348i | − | 2.28243i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7.30021i | − | 0.243205i | ||||||
\(902\) | −53.0613 | + | 44.0951i | −1.76675 | + | 1.46821i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −27.6603 | + | 15.4474i | −0.919966 | + | 0.513774i | ||||
\(905\) | − | 25.6631i | − | 0.853069i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26.3731 | 0.875703 | 0.437852 | − | 0.899047i | \(-0.355740\pi\) | ||||
0.437852 | + | 0.899047i | \(0.355740\pi\) | |||||||
\(908\) | −19.4218 | − | 3.61549i | −0.644534 | − | 0.119984i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −13.3923 | + | 11.1293i | −0.443951 | + | 0.368933i | ||||
\(911\) | −44.3599 | −1.46971 | −0.734855 | − | 0.678224i | \(-0.762750\pi\) | ||||
−0.734855 | + | 0.678224i | \(0.762750\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −35.7128 | −1.18192 | ||||||||
\(914\) | 15.6540 | − | 13.0088i | 0.517788 | − | 0.430294i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −30.9282 | − | 5.75749i | −1.02190 | − | 0.190233i | ||||
\(917\) | −10.4081 | −0.343706 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.8949i | − | 1.01913i | −0.860433 | − | 0.509564i | \(-0.829807\pi\) | ||
0.860433 | − | 0.509564i | \(-0.170193\pi\) | |||||||
\(920\) | −13.0520 | − | 23.3709i | −0.430311 | − | 0.770516i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.6603 | − | 17.1691i | 0.680409 | − | 0.565436i | ||||
\(923\) | − | 29.6331i | − | 0.975387i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.14317i | 0.201986i | ||||||||
\(926\) | −27.8316 | − | 33.4908i | −0.914604 | − | 1.10058i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −46.6410 | + | 15.7298i | −1.53107 | + | 0.516355i | ||||
\(929\) | − | 14.4620i | − | 0.474482i | −0.971451 | − | 0.237241i | \(-0.923757\pi\) | ||
0.971451 | − | 0.237241i | \(-0.0762431\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.32051 | 0.0432779 | ||||||||
\(932\) | 5.20405 | + | 0.968769i | 0.170464 | + | 0.0317331i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −15.7846 | − | 18.9942i | −0.516488 | − | 0.621509i | ||||
\(935\) | −10.4081 | −0.340381 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.60770 | −0.0851897 | −0.0425948 | − | 0.999092i | \(-0.513562\pi\) | ||||
−0.0425948 | + | 0.999092i | \(0.513562\pi\) | |||||||
\(938\) | −1.55621 | − | 1.87264i | −0.0508120 | − | 0.0611439i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.32051 | + | 28.5808i | −0.173536 | + | 0.932203i | ||||
\(941\) | −31.7347 | −1.03452 | −0.517260 | − | 0.855828i | \(-0.673048\pi\) | ||||
−0.517260 | + | 0.855828i | \(0.673048\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 58.7043i | − | 1.91167i | ||||||
\(944\) | 7.10886 | − | 18.4321i | 0.231374 | − | 0.599913i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.92820 | − | 10.7436i | −0.290281 | − | 0.349306i | ||||
\(947\) | 26.6318i | 0.865418i | 0.901534 | + | 0.432709i | \(0.142442\pi\) | ||||
−0.901534 | + | 0.432709i | \(0.857558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 42.5888i | − | 1.38249i | ||||||
\(950\) | 0.718134 | − | 0.596786i | 0.0232994 | − | 0.0193623i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.62693 | + | 4.70380i | 0.0851394 | + | 0.152451i | ||||
\(953\) | 57.9429i | 1.87696i | 0.345340 | + | 0.938478i | \(0.387764\pi\) | ||||
−0.345340 | + | 0.938478i | \(0.612236\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14.5359 | −0.470371 | ||||||||
\(956\) | −2.33151 | + | 12.5244i | −0.0754064 | + | 0.405069i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.46410 | − | 2.87875i | 0.111920 | − | 0.0930081i | ||||
\(959\) | 8.50328 | 0.274585 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8564 | −0.995368 | ||||||||
\(962\) | −14.5663 | + | 12.1049i | −0.469637 | + | 0.390279i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 5.63397 | − | 30.2647i | 0.181458 | − | 0.974760i | ||||
\(965\) | −24.5115 | −0.789053 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 6.42551i | − | 0.206630i | −0.994649 | − | 0.103315i | \(-0.967055\pi\) | ||
0.994649 | − | 0.103315i | \(-0.0329451\pi\) | |||||||
\(968\) | −18.4694 | − | 33.0713i | −0.593628 | − | 1.06295i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.2679 | − | 13.5190i | 0.522332 | − | 0.434070i | ||||
\(971\) | 42.5122i | 1.36428i | 0.731221 | + | 0.682140i | \(0.238951\pi\) | ||||
−0.731221 | + | 0.682140i | \(0.761049\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 10.3580i | 0.332061i | ||||||||
\(974\) | 34.2433 | + | 41.2062i | 1.09723 | + | 1.32033i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.73205 | + | 20.0479i | −0.247497 | + | 0.641717i | ||||
\(977\) | 41.4484i | 1.32605i | 0.748597 | + | 0.663026i | \(0.230728\pi\) | ||||
−0.748597 | + | 0.663026i | \(0.769272\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −77.9615 | −2.49166 | ||||||||
\(980\) | −2.87254 | + | 15.4307i | −0.0917599 | + | 0.492917i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 15.1436 | + | 18.2228i | 0.483251 | + | 0.581514i | ||||
\(983\) | −54.1127 | −1.72593 | −0.862963 | − | 0.505267i | \(-0.831394\pi\) | ||||
−0.862963 | + | 0.505267i | \(0.831394\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −31.6077 | −1.00710 | ||||||||
\(986\) | −10.4081 | − | 12.5244i | −0.331461 | − | 0.398859i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.83013 | + | 0.526847i | 0.0900383 | + | 0.0167612i | ||||
\(989\) | 11.8862 | 0.377960 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 0.668016i | 0.0212202i | 0.999944 | + | 0.0106101i | \(0.00337737\pi\) | ||||
−0.999944 | + | 0.0106101i | \(0.996623\pi\) | |||||||
\(992\) | 14.2177 | + | 42.1576i | 0.451413 | + | 1.33850i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 7.17691 | + | 8.63624i | 0.227638 | + | 0.273925i | ||||
\(995\) | − | 22.7567i | − | 0.721437i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29.3521i | 0.929592i | 0.885418 | + | 0.464796i | \(0.153872\pi\) | ||||
−0.885418 | + | 0.464796i | \(0.846128\pi\) | |||||||
\(998\) | 28.7060 | − | 23.8553i | 0.908671 | − | 0.755126i | ||||
\(999\) | 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 | 216.2.f.a.107.2 | yes | 8 | |
3.2 | odd | 2 | inner | 216.2.f.a.107.7 | yes | 8 | |
4.3 | odd | 2 | 864.2.f.a.431.3 | 8 | |||
8.3 | odd | 2 | inner | 216.2.f.a.107.8 | yes | 8 | |
8.5 | even | 2 | 864.2.f.a.431.6 | 8 | |||
9.2 | odd | 6 | 648.2.l.f.539.2 | 16 | |||
9.4 | even | 3 | 648.2.l.f.107.4 | 16 | |||
9.5 | odd | 6 | 648.2.l.f.107.5 | 16 | |||
9.7 | even | 3 | 648.2.l.f.539.7 | 16 | |||
12.11 | even | 2 | 864.2.f.a.431.5 | 8 | |||
24.5 | odd | 2 | 864.2.f.a.431.4 | 8 | |||
24.11 | even | 2 | inner | 216.2.f.a.107.1 | ✓ | 8 | |
36.7 | odd | 6 | 2592.2.p.f.2159.5 | 16 | |||
36.11 | even | 6 | 2592.2.p.f.2159.3 | 16 | |||
36.23 | even | 6 | 2592.2.p.f.431.4 | 16 | |||
36.31 | odd | 6 | 2592.2.p.f.431.6 | 16 | |||
72.5 | odd | 6 | 2592.2.p.f.431.5 | 16 | |||
72.11 | even | 6 | 648.2.l.f.539.4 | 16 | |||
72.13 | even | 6 | 2592.2.p.f.431.3 | 16 | |||
72.29 | odd | 6 | 2592.2.p.f.2159.6 | 16 | |||
72.43 | odd | 6 | 648.2.l.f.539.5 | 16 | |||
72.59 | even | 6 | 648.2.l.f.107.7 | 16 | |||
72.61 | even | 6 | 2592.2.p.f.2159.4 | 16 | |||
72.67 | odd | 6 | 648.2.l.f.107.2 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.f.a.107.1 | ✓ | 8 | 24.11 | even | 2 | inner | |
216.2.f.a.107.2 | yes | 8 | 1.1 | even | 1 | trivial | |
216.2.f.a.107.7 | yes | 8 | 3.2 | odd | 2 | inner | |
216.2.f.a.107.8 | yes | 8 | 8.3 | odd | 2 | inner | |
648.2.l.f.107.2 | 16 | 72.67 | odd | 6 | |||
648.2.l.f.107.4 | 16 | 9.4 | even | 3 | |||
648.2.l.f.107.5 | 16 | 9.5 | odd | 6 | |||
648.2.l.f.107.7 | 16 | 72.59 | even | 6 | |||
648.2.l.f.539.2 | 16 | 9.2 | odd | 6 | |||
648.2.l.f.539.4 | 16 | 72.11 | even | 6 | |||
648.2.l.f.539.5 | 16 | 72.43 | odd | 6 | |||
648.2.l.f.539.7 | 16 | 9.7 | even | 3 | |||
864.2.f.a.431.3 | 8 | 4.3 | odd | 2 | |||
864.2.f.a.431.4 | 8 | 24.5 | odd | 2 | |||
864.2.f.a.431.5 | 8 | 12.11 | even | 2 | |||
864.2.f.a.431.6 | 8 | 8.5 | even | 2 | |||
2592.2.p.f.431.3 | 16 | 72.13 | even | 6 | |||
2592.2.p.f.431.4 | 16 | 36.23 | even | 6 | |||
2592.2.p.f.431.5 | 16 | 72.5 | odd | 6 | |||
2592.2.p.f.431.6 | 16 | 36.31 | odd | 6 | |||
2592.2.p.f.2159.3 | 16 | 36.11 | even | 6 | |||
2592.2.p.f.2159.4 | 16 | 72.61 | even | 6 | |||
2592.2.p.f.2159.5 | 16 | 36.7 | odd | 6 | |||
2592.2.p.f.2159.6 | 16 | 72.29 | odd | 6 |