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: | 8.0.170772624.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 5x^{6} - 6x^{5} + 6x^{4} - 12x^{3} + 20x^{2} - 24x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 107.7 | ||
Root | \(0.335728 + 1.37379i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 216.107 |
Dual form | 216.2.f.b.107.8 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.35760 | − | 0.396143i | 0.959966 | − | 0.280116i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.68614 | − | 1.07561i | 0.843070 | − | 0.537803i | ||||
\(5\) | −0.505408 | −0.226025 | −0.113013 | − | 0.993594i | \(-0.536050\pi\) | ||||
−0.113013 | + | 0.993594i | \(0.536050\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.42703i | − | 1.29530i | −0.761939 | − | 0.647649i | \(-0.775753\pi\) | ||
0.761939 | − | 0.647649i | \(-0.224247\pi\) | |||||||
\(8\) | 1.86301 | − | 2.12819i | 0.658672 | − | 0.752430i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.686141 | + | 0.200214i | −0.216977 | + | 0.0633133i | ||||
\(11\) | 3.31662i | 1.00000i | 0.866025 | + | 0.500000i | \(0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.55164i | 0.707698i | 0.935303 | + | 0.353849i | \(0.115127\pi\) | ||||
−0.935303 | + | 0.353849i | \(0.884873\pi\) | |||||||
\(14\) | −1.35760 | − | 4.65253i | −0.362833 | − | 1.24344i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.68614 | − | 3.62725i | 0.421535 | − | 0.906812i | ||||
\(17\) | 5.04868i | 1.22448i | 0.790671 | + | 0.612242i | \(0.209732\pi\) | ||||
−0.790671 | + | 0.612242i | \(0.790268\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.74456 | 1.08848 | 0.544239 | − | 0.838930i | \(-0.316819\pi\) | ||||
0.544239 | + | 0.838930i | \(0.316819\pi\) | |||||||
\(20\) | −0.852189 | + | 0.543620i | −0.190555 | + | 0.121557i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.31386 | + | 4.50264i | 0.280116 | + | 0.959966i | ||||
\(23\) | −6.44121 | −1.34308 | −0.671542 | − | 0.740966i | \(-0.734368\pi\) | ||||
−0.671542 | + | 0.740966i | \(0.734368\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.74456 | −0.948913 | ||||||||
\(26\) | 1.01082 | + | 3.46410i | 0.198237 | + | 0.679366i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −3.68614 | − | 5.77846i | −0.696615 | − | 1.09203i | ||||
\(29\) | −5.43039 | −1.00840 | −0.504199 | − | 0.863588i | \(-0.668212\pi\) | ||||
−0.504199 | + | 0.863588i | \(0.668212\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.97868i | − | 1.07380i | −0.843645 | − | 0.536901i | \(-0.819595\pi\) | ||
0.843645 | − | 0.536901i | \(-0.180405\pi\) | |||||||
\(32\) | 0.852189 | − | 5.59230i | 0.150647 | − | 0.988588i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.00000 | + | 6.85407i | 0.342997 | + | 1.17546i | ||||
\(35\) | 1.73205i | 0.292770i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.1565i | 1.83412i | 0.398753 | + | 0.917058i | \(0.369443\pi\) | ||||
−0.398753 | + | 0.917058i | \(0.630557\pi\) | |||||||
\(38\) | 6.44121 | − | 1.87953i | 1.04490 | − | 0.304900i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.941578 | + | 1.07561i | −0.148877 | + | 0.170068i | ||||
\(41\) | − | 1.87953i | − | 0.293533i | −0.989171 | − | 0.146766i | \(-0.953113\pi\) | ||
0.989171 | − | 0.146766i | \(-0.0468866\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −4.00000 | −0.609994 | −0.304997 | − | 0.952353i | \(-0.598656\pi\) | ||||
−0.304997 | + | 0.952353i | \(0.598656\pi\) | |||||||
\(44\) | 3.56738 | + | 5.59230i | 0.537803 | + | 0.843070i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.74456 | + | 2.55164i | −1.28932 | + | 0.376219i | ||||
\(47\) | 10.8608 | 1.58421 | 0.792104 | − | 0.610387i | \(-0.208986\pi\) | ||||
0.792104 | + | 0.610387i | \(0.208986\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.74456 | −0.677795 | ||||||||
\(50\) | −6.44121 | + | 1.87953i | −0.910924 | + | 0.265805i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.74456 | + | 4.30243i | 0.380602 | + | 0.596639i | ||||
\(53\) | 5.93580 | 0.815344 | 0.407672 | − | 0.913128i | \(-0.366341\pi\) | ||||
0.407672 | + | 0.913128i | \(0.366341\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.67625i | − | 0.226025i | ||||||
\(56\) | −7.29339 | − | 6.38458i | −0.974621 | − | 0.853176i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.37228 | + | 2.15121i | −0.968028 | + | 0.282468i | ||||
\(59\) | − | 6.63325i | − | 0.863576i | −0.901975 | − | 0.431788i | \(-0.857883\pi\) | ||
0.901975 | − | 0.431788i | \(-0.142117\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.10328i | 0.653408i | 0.945127 | + | 0.326704i | \(0.105938\pi\) | ||||
−0.945127 | + | 0.326704i | \(0.894062\pi\) | |||||||
\(62\) | −2.36841 | − | 8.11663i | −0.300789 | − | 1.03081i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.05842 | − | 7.92967i | −0.132303 | − | 0.991209i | ||||
\(65\) | − | 1.28962i | − | 0.159958i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | 5.43039 | + | 8.51278i | 0.658531 | + | 1.03233i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.686141 | + | 2.35143i | 0.0820095 | + | 0.281049i | ||||
\(71\) | −4.41957 | −0.524507 | −0.262253 | − | 0.964999i | \(-0.584466\pi\) | ||||
−0.262253 | + | 0.964999i | \(0.584466\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.74456 | 0.906432 | 0.453216 | − | 0.891401i | \(-0.350277\pi\) | ||||
0.453216 | + | 0.891401i | \(0.350277\pi\) | |||||||
\(74\) | 4.41957 | + | 15.1460i | 0.513765 | + | 1.76069i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.00000 | − | 5.10328i | 0.917663 | − | 0.585387i | ||||
\(77\) | 11.3662 | 1.29530 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.30243i | − | 0.484061i | −0.970269 | − | 0.242030i | \(-0.922187\pi\) | ||
0.970269 | − | 0.242030i | \(-0.0778134\pi\) | |||||||
\(80\) | −0.852189 | + | 1.83324i | −0.0952776 | + | 0.204963i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.744563 | − | 2.55164i | −0.0822232 | − | 0.281782i | ||||
\(83\) | − | 3.61158i | − | 0.396422i | −0.980159 | − | 0.198211i | \(-0.936487\pi\) | ||
0.980159 | − | 0.198211i | \(-0.0635132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 2.55164i | − | 0.276764i | ||||||
\(86\) | −5.43039 | + | 1.58457i | −0.585574 | + | 0.170869i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.05842 | + | 6.17889i | 0.752430 | + | 0.658672i | ||||
\(89\) | − | 17.0256i | − | 1.80471i | −0.430999 | − | 0.902353i | \(-0.641839\pi\) | ||
0.430999 | − | 0.902353i | \(-0.358161\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.74456 | 0.916679 | ||||||||
\(92\) | −10.8608 | + | 6.92820i | −1.13231 | + | 0.722315i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 14.7446 | − | 4.30243i | 1.52079 | − | 0.443761i | ||||
\(95\) | −2.39794 | −0.246023 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.00000 | −0.101535 | −0.0507673 | − | 0.998711i | \(-0.516167\pi\) | ||||
−0.0507673 | + | 0.998711i | \(0.516167\pi\) | |||||||
\(98\) | −6.44121 | + | 1.87953i | −0.650660 | + | 0.189861i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −8.00000 | + | 5.10328i | −0.800000 | + | 0.510328i | ||||
\(101\) | −15.7858 | −1.57074 | −0.785371 | − | 0.619026i | \(-0.787528\pi\) | ||||
−0.785371 | + | 0.619026i | \(0.787528\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.800857i | 0.0789107i | 0.999221 | + | 0.0394554i | \(0.0125623\pi\) | ||||
−0.999221 | + | 0.0394554i | \(0.987438\pi\) | |||||||
\(104\) | 5.43039 | + | 4.75372i | 0.532493 | + | 0.466141i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.05842 | − | 2.35143i | 0.782703 | − | 0.228391i | ||||
\(107\) | − | 4.90120i | − | 0.473817i | −0.971532 | − | 0.236908i | \(-0.923866\pi\) | ||
0.971532 | − | 0.236908i | \(-0.0761341\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 11.1565i | − | 1.06860i | −0.845295 | − | 0.534299i | \(-0.820576\pi\) | ||
0.845295 | − | 0.534299i | \(-0.179424\pi\) | |||||||
\(110\) | −0.664035 | − | 2.27567i | −0.0633133 | − | 0.216977i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.4307 | − | 5.77846i | −1.17459 | − | 0.546013i | ||||
\(113\) | 11.9769i | 1.12669i | 0.826222 | + | 0.563345i | \(0.190486\pi\) | ||||
−0.826222 | + | 0.563345i | \(0.809514\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 3.25544 | 0.303571 | ||||||||
\(116\) | −9.15640 | + | 5.84096i | −0.850150 | + | 0.542320i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.62772 | − | 9.00528i | −0.241901 | − | 0.829003i | ||||
\(119\) | 17.3020 | 1.58607 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 2.02163 | + | 6.92820i | 0.183030 | + | 0.627250i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.43070 | − | 10.0809i | −0.577494 | − | 0.905290i | ||||
\(125\) | 4.92498 | 0.440504 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.2811i | 0.912300i | 0.889903 | + | 0.456150i | \(0.150772\pi\) | ||||
−0.889903 | + | 0.456150i | \(0.849228\pi\) | |||||||
\(128\) | −4.57820 | − | 10.3460i | −0.404660 | − | 0.914467i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.510875 | − | 1.75079i | −0.0448067 | − | 0.153554i | ||||
\(131\) | 2.02700i | 0.177100i | 0.996072 | + | 0.0885501i | \(0.0282233\pi\) | ||||
−0.996072 | + | 0.0885501i | \(0.971777\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 16.2598i | − | 1.40990i | ||||||
\(134\) | −5.43039 | + | 1.58457i | −0.469114 | + | 0.136886i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 10.7446 | + | 9.40571i | 0.921339 | + | 0.806533i | ||||
\(137\) | − | 17.0256i | − | 1.45459i | −0.686324 | − | 0.727296i | \(-0.740777\pi\) | ||
0.686324 | − | 0.727296i | \(-0.259223\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.00000 | 0.678551 | 0.339276 | − | 0.940687i | \(-0.389818\pi\) | ||||
0.339276 | + | 0.940687i | \(0.389818\pi\) | |||||||
\(140\) | 1.86301 | + | 2.92048i | 0.157453 | + | 0.246826i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.00000 | + | 1.75079i | −0.503509 | + | 0.146923i | ||||
\(143\) | −8.46284 | −0.707698 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.74456 | 0.227924 | ||||||||
\(146\) | 10.5140 | − | 3.06796i | 0.870145 | − | 0.253906i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.0000 | + | 18.8114i | 0.986394 | + | 1.54629i | ||||
\(149\) | 18.8182 | 1.54165 | 0.770824 | − | 0.637048i | \(-0.219845\pi\) | ||||
0.770824 | + | 0.637048i | \(0.219845\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.72946i | 0.629015i | 0.949255 | + | 0.314507i | \(0.101839\pi\) | ||||
−0.949255 | + | 0.314507i | \(0.898161\pi\) | |||||||
\(152\) | 8.83915 | − | 10.0974i | 0.716949 | − | 0.819003i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 15.4307 | − | 4.50264i | 1.24344 | − | 0.362833i | ||||
\(155\) | 3.02167i | 0.242706i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.10328i | − | 0.407286i | −0.979045 | − | 0.203643i | \(-0.934722\pi\) | ||
0.979045 | − | 0.203643i | \(-0.0652782\pi\) | |||||||
\(158\) | −1.70438 | − | 5.84096i | −0.135593 | − | 0.464682i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.430703 | + | 2.82639i | −0.0340501 | + | 0.223446i | ||||
\(161\) | 22.0742i | 1.73969i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.2337 | −1.42817 | −0.714086 | − | 0.700058i | \(-0.753158\pi\) | ||||
−0.714086 | + | 0.700058i | \(0.753158\pi\) | |||||||
\(164\) | −2.02163 | − | 3.16915i | −0.157863 | − | 0.247469i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.43070 | − | 4.90307i | −0.111044 | − | 0.380552i | ||||
\(167\) | −2.02163 | −0.156439 | −0.0782193 | − | 0.996936i | \(-0.524923\pi\) | ||||
−0.0782193 | + | 0.996936i | \(0.524923\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.48913 | 0.499163 | ||||||||
\(170\) | −1.01082 | − | 3.46410i | −0.0775261 | − | 0.265684i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.74456 | + | 4.30243i | −0.514268 | + | 0.328057i | ||||
\(173\) | −11.3662 | −0.864155 | −0.432078 | − | 0.901836i | \(-0.642219\pi\) | ||||
−0.432078 | + | 0.901836i | \(0.642219\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 16.2598i | 1.22912i | ||||||||
\(176\) | 12.0302 | + | 5.59230i | 0.906812 | + | 0.421535i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −6.74456 | − | 23.1138i | −0.505526 | − | 1.73246i | ||||
\(179\) | − | 11.8294i | − | 0.884171i | −0.896973 | − | 0.442086i | \(-0.854239\pi\) | ||
0.896973 | − | 0.442086i | \(-0.145761\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(182\) | 11.8716 | − | 3.46410i | 0.879981 | − | 0.256776i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −12.0000 | + | 13.7081i | −0.884652 | + | 1.01058i | ||||
\(185\) | − | 5.63858i | − | 0.414557i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −16.7446 | −1.22448 | ||||||||
\(188\) | 18.3128 | − | 11.6819i | 1.33560 | − | 0.851992i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.25544 | + | 0.949929i | −0.236174 | + | 0.0689151i | ||||
\(191\) | −8.46284 | −0.612349 | −0.306175 | − | 0.951975i | \(-0.599049\pi\) | ||||
−0.306175 | + | 0.951975i | \(0.599049\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 13.2337 | 0.952582 | 0.476291 | − | 0.879288i | \(-0.341981\pi\) | ||||
0.476291 | + | 0.879288i | \(0.341981\pi\) | |||||||
\(194\) | −1.35760 | + | 0.396143i | −0.0974698 | + | 0.0284414i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.00000 | + | 5.10328i | −0.571429 | + | 0.364520i | ||||
\(197\) | −13.3878 | −0.953843 | −0.476921 | − | 0.878946i | \(-0.658247\pi\) | ||||
−0.476921 | + | 0.878946i | \(0.658247\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.77953i | 0.480588i | 0.970700 | + | 0.240294i | \(0.0772439\pi\) | ||||
−0.970700 | + | 0.240294i | \(0.922756\pi\) | |||||||
\(200\) | −8.83915 | + | 10.0974i | −0.625022 | + | 0.713991i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −21.4307 | + | 6.25343i | −1.50786 | + | 0.439990i | ||||
\(203\) | 18.6101i | 1.30617i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.949929i | 0.0663459i | ||||||||
\(206\) | 0.317254 | + | 1.08724i | 0.0221041 | + | 0.0757516i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.25544 | + | 4.30243i | 0.641749 | + | 0.298320i | ||||
\(209\) | 15.7359i | 1.08848i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.7446 | −0.877372 | −0.438686 | − | 0.898640i | \(-0.644556\pi\) | ||||
−0.438686 | + | 0.898640i | \(0.644556\pi\) | |||||||
\(212\) | 10.0086 | − | 6.38458i | 0.687393 | − | 0.438495i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.94158 | − | 6.65385i | −0.132724 | − | 0.454848i | ||||
\(215\) | 2.02163 | 0.137874 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −20.4891 | −1.39089 | ||||||||
\(218\) | −4.41957 | − | 15.1460i | −0.299331 | − | 1.02582i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.80298 | − | 2.82639i | −0.121557 | − | 0.190555i | ||||
\(221\) | −12.8824 | −0.866565 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.0106i | 1.20608i | 0.797712 | + | 0.603038i | \(0.206043\pi\) | ||||
−0.797712 | + | 0.603038i | \(0.793957\pi\) | |||||||
\(224\) | −19.1650 | − | 2.92048i | −1.28051 | − | 0.195133i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.74456 | + | 16.2598i | 0.315604 | + | 1.08158i | ||||
\(227\) | 23.6588i | 1.57029i | 0.619312 | + | 0.785145i | \(0.287412\pi\) | ||||
−0.619312 | + | 0.785145i | \(0.712588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 8.60485i | − | 0.568625i | −0.958732 | − | 0.284312i | \(-0.908235\pi\) | ||
0.958732 | − | 0.284312i | \(-0.0917653\pi\) | |||||||
\(230\) | 4.41957 | − | 1.28962i | 0.291418 | − | 0.0850350i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.1168 | + | 11.5569i | −0.664203 | + | 0.758749i | ||||
\(233\) | − | 0.589907i | − | 0.0386461i | −0.999813 | − | 0.0193231i | \(-0.993849\pi\) | ||
0.999813 | − | 0.0193231i | \(-0.00615110\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.48913 | −0.358071 | ||||||||
\(236\) | −7.13477 | − | 11.1846i | −0.464434 | − | 0.728055i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.4891 | − | 6.85407i | 1.52257 | − | 0.444283i | ||||
\(239\) | −15.2804 | −0.988404 | −0.494202 | − | 0.869347i | \(-0.664540\pi\) | ||||
−0.494202 | + | 0.869347i | \(0.664540\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.48913 | + | 8.60485i | 0.351405 | + | 0.550869i | ||||
\(245\) | 2.39794 | 0.153199 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.1064i | 0.770313i | ||||||||
\(248\) | −12.7238 | − | 11.1383i | −0.807961 | − | 0.707283i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.68614 | − | 1.95100i | 0.422869 | − | 0.123392i | ||||
\(251\) | 9.80240i | 0.618722i | 0.950945 | + | 0.309361i | \(0.100115\pi\) | ||||
−0.950945 | + | 0.309361i | \(0.899885\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 21.3631i | − | 1.34308i | ||||||
\(254\) | 4.07279 | + | 13.9576i | 0.255550 | + | 0.875777i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.3139 | − | 12.2321i | −0.644616 | − | 0.764506i | ||||
\(257\) | 18.9051i | 1.17927i | 0.807671 | + | 0.589633i | \(0.200728\pi\) | ||||
−0.807671 | + | 0.589633i | \(0.799272\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.2337 | 2.37573 | ||||||||
\(260\) | −1.38712 | − | 2.17448i | −0.0860258 | − | 0.134856i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.802985 | + | 2.75186i | 0.0496086 | + | 0.170010i | ||||
\(263\) | 6.44121 | 0.397182 | 0.198591 | − | 0.980082i | \(-0.436364\pi\) | ||||
0.198591 | + | 0.980082i | \(0.436364\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3.00000 | −0.184289 | ||||||||
\(266\) | −6.44121 | − | 22.0742i | −0.394936 | − | 1.35346i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −6.74456 | + | 4.30243i | −0.411990 | + | 0.262813i | ||||
\(269\) | 7.45202 | 0.454358 | 0.227179 | − | 0.973853i | \(-0.427050\pi\) | ||||
0.227179 | + | 0.973853i | \(0.427050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 23.1884i | − | 1.40859i | −0.709905 | − | 0.704297i | \(-0.751262\pi\) | ||
0.709905 | − | 0.704297i | \(-0.248738\pi\) | |||||||
\(272\) | 18.3128 | + | 8.51278i | 1.11038 | + | 0.516163i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.74456 | − | 23.1138i | −0.407454 | − | 1.39636i | ||||
\(275\) | − | 15.7359i | − | 0.948913i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.10328i | 0.306627i | 0.988178 | + | 0.153313i | \(0.0489944\pi\) | ||||
−0.988178 | + | 0.153313i | \(0.951006\pi\) | |||||||
\(278\) | 10.8608 | − | 3.16915i | 0.651386 | − | 0.190073i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 3.68614 | + | 3.22682i | 0.220289 | + | 0.192839i | ||||
\(281\) | − | 8.80773i | − | 0.525425i | −0.964874 | − | 0.262713i | \(-0.915383\pi\) | ||
0.964874 | − | 0.262713i | \(-0.0846171\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 11.2554 | 0.669066 | 0.334533 | − | 0.942384i | \(-0.391421\pi\) | ||||
0.334533 | + | 0.942384i | \(0.391421\pi\) | |||||||
\(284\) | −7.45202 | + | 4.75372i | −0.442196 | + | 0.282082i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −11.4891 | + | 3.35250i | −0.679366 | + | 0.198237i | ||||
\(287\) | −6.44121 | −0.380212 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.48913 | −0.499360 | ||||||||
\(290\) | 3.72601 | − | 1.08724i | 0.218799 | − | 0.0638450i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.0584 | − | 8.33010i | 0.764186 | − | 0.487482i | ||||
\(293\) | −9.47365 | −0.553457 | −0.276728 | − | 0.960948i | \(-0.589250\pi\) | ||||
−0.276728 | + | 0.960948i | \(0.589250\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.35250i | 0.195190i | ||||||||
\(296\) | 23.7432 | + | 20.7846i | 1.38004 | + | 1.20808i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 25.5475 | − | 7.45471i | 1.47993 | − | 0.431840i | ||||
\(299\) | − | 16.4356i | − | 0.950498i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.7081i | 0.790124i | ||||||||
\(302\) | 3.06198 | + | 10.4935i | 0.176197 | + | 0.603833i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 8.00000 | − | 17.2097i | 0.458831 | − | 0.987044i | ||||
\(305\) | − | 2.57924i | − | 0.147687i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.25544 | −0.414090 | −0.207045 | − | 0.978331i | \(-0.566385\pi\) | ||||
−0.207045 | + | 0.978331i | \(0.566385\pi\) | |||||||
\(308\) | 19.1650 | − | 12.2255i | 1.09203 | − | 0.696615i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.19702 | + | 4.10221i | 0.0679859 | + | 0.232990i | ||||
\(311\) | 2.39794 | 0.135975 | 0.0679874 | − | 0.997686i | \(-0.478342\pi\) | ||||
0.0679874 | + | 0.997686i | \(0.478342\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 25.2337 | 1.42629 | 0.713146 | − | 0.701015i | \(-0.247270\pi\) | ||||
0.713146 | + | 0.701015i | \(0.247270\pi\) | |||||||
\(314\) | −2.02163 | − | 6.92820i | −0.114087 | − | 0.390981i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.62772 | − | 7.25450i | −0.260330 | − | 0.408097i | ||||
\(317\) | 7.95743 | 0.446934 | 0.223467 | − | 0.974712i | \(-0.428263\pi\) | ||||
0.223467 | + | 0.974712i | \(0.428263\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 18.0106i | − | 1.00840i | ||||||
\(320\) | 0.534935 | + | 4.00772i | 0.0299038 | + | 0.224038i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.74456 | + | 29.9679i | 0.487315 | + | 1.67005i | ||||
\(323\) | 23.9538i | 1.33282i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 12.1064i | − | 0.671544i | ||||||
\(326\) | −24.7540 | + | 7.22316i | −1.37100 | + | 0.400054i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.00000 | − | 3.50157i | −0.220863 | − | 0.193342i | ||||
\(329\) | − | 37.2203i | − | 2.05202i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.5109 | −0.577730 | −0.288865 | − | 0.957370i | \(-0.593278\pi\) | ||||
−0.288865 | + | 0.957370i | \(0.593278\pi\) | |||||||
\(332\) | −3.88464 | − | 6.08963i | −0.213197 | − | 0.334212i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.74456 | + | 0.800857i | −0.150176 | + | 0.0438209i | ||||
\(335\) | 2.02163 | 0.110454 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00000 | 0.108947 | 0.0544735 | − | 0.998515i | \(-0.482652\pi\) | ||||
0.0544735 | + | 0.998515i | \(0.482652\pi\) | |||||||
\(338\) | 8.80962 | − | 2.57062i | 0.479180 | − | 0.139824i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.74456 | − | 4.30243i | −0.148845 | − | 0.233332i | ||||
\(341\) | 19.8290 | 1.07380 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 7.72946i | − | 0.417352i | ||||||
\(344\) | −7.45202 | + | 8.51278i | −0.401786 | + | 0.458978i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −15.4307 | + | 4.50264i | −0.829560 | + | 0.242063i | ||||
\(347\) | − | 26.9754i | − | 1.44812i | −0.689739 | − | 0.724058i | \(-0.742275\pi\) | ||
0.689739 | − | 0.724058i | \(-0.257725\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 16.2598i | 0.870366i | 0.900342 | + | 0.435183i | \(0.143316\pi\) | ||||
−0.900342 | + | 0.435183i | \(0.856684\pi\) | |||||||
\(350\) | 6.44121 | + | 22.0742i | 0.344297 | + | 1.17992i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 18.5475 | + | 2.82639i | 0.988588 | + | 0.150647i | ||||
\(353\) | 28.4125i | 1.51225i | 0.654429 | + | 0.756123i | \(0.272909\pi\) | ||||
−0.654429 | + | 0.756123i | \(0.727091\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.23369 | 0.118552 | ||||||||
\(356\) | −18.3128 | − | 28.7075i | −0.970576 | − | 1.52149i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.68614 | − | 16.0596i | −0.247670 | − | 0.848774i | ||||
\(359\) | 23.7432 | 1.25312 | 0.626559 | − | 0.779374i | \(-0.284463\pi\) | ||||
0.626559 | + | 0.779374i | \(0.284463\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.51087 | 0.184783 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 14.7446 | − | 9.40571i | 0.772825 | − | 0.492993i | ||||
\(365\) | −3.91416 | −0.204877 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 11.0820i | − | 0.578474i | −0.957258 | − | 0.289237i | \(-0.906599\pi\) | ||
0.957258 | − | 0.289237i | \(-0.0934015\pi\) | |||||||
\(368\) | −10.8608 | + | 23.3639i | −0.566157 | + | 1.21792i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.23369 | − | 7.65492i | −0.116124 | − | 0.397961i | ||||
\(371\) | − | 20.3422i | − | 1.05611i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.55164i | 0.132119i | 0.997816 | + | 0.0660595i | \(0.0210427\pi\) | ||||
−0.997816 | + | 0.0660595i | \(0.978957\pi\) | |||||||
\(374\) | −22.7324 | + | 6.63325i | −1.17546 | + | 0.342997i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 20.2337 | − | 23.1138i | 1.04347 | − | 1.19201i | ||||
\(377\) | − | 13.8564i | − | 0.713641i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.48913 | −0.487424 | −0.243712 | − | 0.969848i | \(-0.578365\pi\) | ||||
−0.243712 | + | 0.969848i | \(0.578365\pi\) | |||||||
\(380\) | −4.04326 | + | 2.57924i | −0.207415 | + | 0.132312i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −11.4891 | + | 3.35250i | −0.587835 | + | 0.171529i | ||||
\(383\) | 26.1411 | 1.33575 | 0.667875 | − | 0.744274i | \(-0.267204\pi\) | ||||
0.667875 | + | 0.744274i | \(0.267204\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.74456 | −0.292770 | ||||||||
\(386\) | 17.9660 | − | 5.24244i | 0.914446 | − | 0.266833i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.68614 | + | 1.07561i | −0.0856008 | + | 0.0546057i | ||||
\(389\) | 22.8615 | 1.15912 | 0.579561 | − | 0.814929i | \(-0.303224\pi\) | ||||
0.579561 | + | 0.814929i | \(0.303224\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 32.5196i | − | 1.64458i | ||||||
\(392\) | −8.83915 | + | 10.0974i | −0.446444 | + | 0.509993i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −18.1753 | + | 5.30350i | −0.915657 | + | 0.267186i | ||||
\(395\) | 2.17448i | 0.109410i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.9679i | 1.50405i | 0.659137 | + | 0.752023i | \(0.270922\pi\) | ||||
−0.659137 | + | 0.752023i | \(0.729078\pi\) | |||||||
\(398\) | 2.68567 | + | 9.20387i | 0.134620 | + | 0.461349i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.00000 | + | 17.2097i | −0.400000 | + | 0.860485i | ||||
\(401\) | 3.75906i | 0.187718i | 0.995585 | + | 0.0938591i | \(0.0299203\pi\) | ||||
−0.995585 | + | 0.0938591i | \(0.970080\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.2554 | 0.759927 | ||||||||
\(404\) | −26.6170 | + | 16.9793i | −1.32425 | + | 0.844750i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.37228 | + | 25.2651i | 0.365880 | + | 1.25388i | ||||
\(407\) | −37.0019 | −1.83412 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 11.0000 | 0.543915 | 0.271957 | − | 0.962309i | \(-0.412329\pi\) | ||||
0.271957 | + | 0.962309i | \(0.412329\pi\) | |||||||
\(410\) | 0.376308 | + | 1.28962i | 0.0185845 | + | 0.0636898i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.861407 | + | 1.35036i | 0.0424385 | + | 0.0665273i | ||||
\(413\) | −22.7324 | −1.11859 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.82532i | 0.0896015i | ||||||||
\(416\) | 14.2695 | + | 2.17448i | 0.699622 | + | 0.106613i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.23369 | + | 21.3631i | 0.304900 | + | 1.04490i | ||||
\(419\) | 7.22316i | 0.352874i | 0.984312 | + | 0.176437i | \(0.0564572\pi\) | ||||
−0.984312 | + | 0.176437i | \(0.943543\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4163i | 1.33619i | 0.744077 | + | 0.668094i | \(0.232889\pi\) | ||||
−0.744077 | + | 0.668094i | \(0.767111\pi\) | |||||||
\(422\) | −17.3020 | + | 5.04868i | −0.842247 | + | 0.245766i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 11.0584 | − | 12.6325i | 0.537044 | − | 0.613490i | ||||
\(425\) | − | 23.9538i | − | 1.16193i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 17.4891 | 0.846358 | ||||||||
\(428\) | −5.27176 | − | 8.26411i | −0.254820 | − | 0.399461i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.74456 | − | 0.800857i | 0.132355 | − | 0.0386207i | ||||
\(431\) | 14.9040 | 0.717902 | 0.358951 | − | 0.933356i | \(-0.383134\pi\) | ||||
0.358951 | + | 0.933356i | \(0.383134\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4891 | −0.888531 | −0.444265 | − | 0.895895i | \(-0.646535\pi\) | ||||
−0.444265 | + | 0.895895i | \(0.646535\pi\) | |||||||
\(434\) | −27.8160 | + | 8.11663i | −1.33521 | + | 0.389611i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.0000 | − | 18.8114i | −0.574696 | − | 0.900904i | ||||
\(437\) | −30.5607 | −1.46192 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 18.7369i | − | 0.894263i | −0.894468 | − | 0.447131i | \(-0.852446\pi\) | ||
0.894468 | − | 0.447131i | \(-0.147554\pi\) | |||||||
\(440\) | −3.56738 | − | 3.12286i | −0.170068 | − | 0.148877i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.4891 | + | 5.10328i | −0.831873 | + | 0.242738i | ||||
\(443\) | − | 6.63325i | − | 0.315155i | −0.987507 | − | 0.157578i | \(-0.949632\pi\) | ||
0.987507 | − | 0.157578i | \(-0.0503684\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.60485i | 0.407909i | ||||||||
\(446\) | 7.13477 | + | 24.4511i | 0.337841 | + | 1.15779i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −27.1753 | + | 3.62725i | −1.28391 | + | 0.171371i | ||||
\(449\) | − | 4.45877i | − | 0.210422i | −0.994450 | − | 0.105211i | \(-0.966448\pi\) | ||
0.994450 | − | 0.105211i | \(-0.0335518\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.23369 | 0.293533 | ||||||||
\(452\) | 12.8824 | + | 20.1947i | 0.605938 | + | 0.949879i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.37228 | + | 32.1191i | 0.439863 | + | 1.50743i | ||||
\(455\) | −4.41957 | −0.207193 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −41.4674 | −1.93976 | −0.969881 | − | 0.243579i | \(-0.921678\pi\) | ||||
−0.969881 | + | 0.243579i | \(0.921678\pi\) | |||||||
\(458\) | −3.40876 | − | 11.6819i | −0.159281 | − | 0.545861i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.48913 | − | 3.50157i | 0.255932 | − | 0.163262i | ||||
\(461\) | 34.4749 | 1.60565 | 0.802827 | − | 0.596212i | \(-0.203328\pi\) | ||||
0.802827 | + | 0.596212i | \(0.203328\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 31.6442i | 1.47063i | 0.677726 | + | 0.735314i | \(0.262966\pi\) | ||||
−0.677726 | + | 0.735314i | \(0.737034\pi\) | |||||||
\(464\) | −9.15640 | + | 19.6974i | −0.425075 | + | 0.914427i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.233688 | − | 0.800857i | −0.0108254 | − | 0.0370990i | ||||
\(467\) | − | 31.3244i | − | 1.44952i | −0.689001 | − | 0.724760i | \(-0.741951\pi\) | ||
0.689001 | − | 0.724760i | \(-0.258049\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.7081i | 0.632983i | ||||||||
\(470\) | −7.45202 | + | 2.17448i | −0.343736 | + | 0.100301i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −14.1168 | − | 12.3578i | −0.649780 | − | 0.568813i | ||||
\(473\) | − | 13.2665i | − | 0.609994i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −22.5109 | −1.03287 | ||||||||
\(476\) | 29.1736 | − | 18.6101i | 1.33717 | − | 0.852994i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −20.7446 | + | 6.05321i | −0.948834 | + | 0.276867i | ||||
\(479\) | 2.02163 | 0.0923707 | 0.0461854 | − | 0.998933i | \(-0.485294\pi\) | ||||
0.0461854 | + | 0.998933i | \(0.485294\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28.4674 | −1.29800 | ||||||||
\(482\) | 2.71519 | − | 0.792287i | 0.123674 | − | 0.0360877i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.505408 | 0.0229494 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 9.40571i | − | 0.426213i | −0.977029 | − | 0.213107i | \(-0.931642\pi\) | ||
0.977029 | − | 0.213107i | \(-0.0683582\pi\) | |||||||
\(488\) | 10.8608 | + | 9.50744i | 0.491644 | + | 0.430382i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3.25544 | − | 0.949929i | 0.147066 | − | 0.0429134i | ||||
\(491\) | 27.9701i | 1.26227i | 0.775672 | + | 0.631136i | \(0.217411\pi\) | ||||
−0.775672 | + | 0.631136i | \(0.782589\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 27.4163i | − | 1.23477i | ||||||
\(494\) | 4.79588 | + | 16.4356i | 0.215777 | + | 0.739475i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −21.6861 | − | 10.0809i | −0.973736 | − | 0.452645i | ||||
\(497\) | 15.1460i | 0.679392i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.0000 | −1.25345 | −0.626726 | − | 0.779240i | \(-0.715605\pi\) | ||||
−0.626726 | + | 0.779240i | \(0.715605\pi\) | |||||||
\(500\) | 8.30421 | − | 5.29734i | 0.371376 | − | 0.236904i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.88316 | + | 13.3077i | 0.173314 | + | 0.593952i | ||||
\(503\) | −19.3236 | −0.861597 | −0.430799 | − | 0.902448i | \(-0.641768\pi\) | ||||
−0.430799 | + | 0.902448i | \(0.641768\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7.97825 | 0.355027 | ||||||||
\(506\) | −8.46284 | − | 29.0024i | −0.376219 | − | 1.28932i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 11.0584 | + | 17.3354i | 0.490638 | + | 0.769133i | ||||
\(509\) | 23.2378 | 1.03000 | 0.514998 | − | 0.857191i | \(-0.327793\pi\) | ||||
0.514998 | + | 0.857191i | \(0.327793\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 26.5409i | − | 1.17410i | ||||||
\(512\) | −18.8477 | − | 12.5205i | −0.832960 | − | 0.553333i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.48913 | + | 25.6655i | 0.330331 | + | 1.13206i | ||||
\(515\) | − | 0.404759i | − | 0.0178358i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 36.0211i | 1.58421i | ||||||||
\(518\) | 51.9060 | − | 15.1460i | 2.28062 | − | 0.665478i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.74456 | − | 2.40257i | −0.120357 | − | 0.105360i | ||||
\(521\) | 5.04868i | 0.221186i | 0.993866 | + | 0.110593i | \(0.0352751\pi\) | ||||
−0.993866 | + | 0.110593i | \(0.964725\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 34.2337 | 1.49693 | 0.748467 | − | 0.663172i | \(-0.230790\pi\) | ||||
0.748467 | + | 0.663172i | \(0.230790\pi\) | |||||||
\(524\) | 2.18026 | + | 3.41781i | 0.0952451 | + | 0.149308i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 8.74456 | − | 2.55164i | 0.381281 | − | 0.111257i | ||||
\(527\) | 30.1844 | 1.31485 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.4891 | 0.803875 | ||||||||
\(530\) | −4.07279 | + | 1.18843i | −0.176911 | + | 0.0516221i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.4891 | − | 27.4163i | −0.758250 | − | 1.18865i | ||||
\(533\) | 4.79588 | 0.207733 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.47711i | 0.107095i | ||||||||
\(536\) | −7.45202 | + | 8.51278i | −0.321878 | + | 0.367696i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 10.1168 | − | 2.95207i | 0.436168 | − | 0.127273i | ||||
\(539\) | − | 15.7359i | − | 0.677795i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 37.6228i | 1.61753i | 0.588130 | + | 0.808766i | \(0.299864\pi\) | ||||
−0.588130 | + | 0.808766i | \(0.700136\pi\) | |||||||
\(542\) | −9.18593 | − | 31.4805i | −0.394569 | − | 1.35220i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 28.2337 | + | 4.30243i | 1.21051 | + | 0.184465i | ||||
\(545\) | 5.63858i | 0.241530i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5.76631 | 0.246550 | 0.123275 | − | 0.992373i | \(-0.460660\pi\) | ||||
0.123275 | + | 0.992373i | \(0.460660\pi\) | |||||||
\(548\) | −18.3128 | − | 28.7075i | −0.782284 | − | 1.22632i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.23369 | − | 21.3631i | −0.265805 | − | 0.910924i | ||||
\(551\) | −25.7648 | −1.09762 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.7446 | −0.627003 | ||||||||
\(554\) | 2.02163 | + | 6.92820i | 0.0858909 | + | 0.294351i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13.4891 | − | 8.60485i | 0.572066 | − | 0.364927i | ||||
\(557\) | −8.96825 | −0.379997 | −0.189998 | − | 0.981784i | \(-0.560848\pi\) | ||||
−0.189998 | + | 0.981784i | \(0.560848\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10.2066i | − | 0.431692i | ||||||
\(560\) | 6.28258 | + | 2.92048i | 0.265487 | + | 0.123413i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3.48913 | − | 11.9574i | −0.147180 | − | 0.504390i | ||||
\(563\) | 12.8241i | 0.540470i | 0.962794 | + | 0.270235i | \(0.0871014\pi\) | ||||
−0.962794 | + | 0.270235i | \(0.912899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 6.05321i | − | 0.254661i | ||||||
\(566\) | 15.2804 | − | 4.45877i | 0.642281 | − | 0.187416i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.23369 | + | 9.40571i | −0.345478 | + | 0.394655i | ||||
\(569\) | − | 7.51811i | − | 0.315176i | −0.987505 | − | 0.157588i | \(-0.949628\pi\) | ||
0.987505 | − | 0.157588i | \(-0.0503717\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 34.2337 | 1.43264 | 0.716318 | − | 0.697774i | \(-0.245826\pi\) | ||||
0.716318 | + | 0.697774i | \(0.245826\pi\) | |||||||
\(572\) | −14.2695 | + | 9.10268i | −0.596639 | + | 0.380602i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.74456 | + | 2.55164i | −0.364991 | + | 0.106503i | ||||
\(575\) | 30.5607 | 1.27447 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.9783 | 1.53942 | 0.769712 | − | 0.638391i | \(-0.220400\pi\) | ||||
0.769712 | + | 0.638391i | \(0.220400\pi\) | |||||||
\(578\) | −11.5248 | + | 3.36291i | −0.479369 | + | 0.139879i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.62772 | − | 2.95207i | 0.192156 | − | 0.122578i | ||||
\(581\) | −12.3770 | −0.513485 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.6868i | 0.815344i | ||||||||
\(584\) | 14.4282 | − | 16.4819i | 0.597042 | − | 0.682027i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.8614 | + | 3.75293i | −0.531300 | + | 0.155032i | ||||
\(587\) | 39.2473i | 1.61991i | 0.586494 | + | 0.809954i | \(0.300508\pi\) | ||||
−0.586494 | + | 0.809954i | \(0.699492\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 28.3662i | − | 1.16881i | ||||||
\(590\) | 1.32807 | + | 4.55134i | 0.0546758 | + | 0.187376i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 40.4674 | + | 18.8114i | 1.66320 | + | 0.773145i | ||||
\(593\) | 13.2665i | 0.544790i | 0.962186 | + | 0.272395i | \(0.0878157\pi\) | ||||
−0.962186 | + | 0.272395i | \(0.912184\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.74456 | −0.358492 | ||||||||
\(596\) | 31.7301 | − | 20.2410i | 1.29972 | − | 0.829103i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.51087 | − | 22.3130i | −0.266249 | − | 0.912446i | ||||
\(599\) | 27.7865 | 1.13532 | 0.567662 | − | 0.823262i | \(-0.307848\pi\) | ||||
0.567662 | + | 0.823262i | \(0.307848\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.23369 | −0.131905 | −0.0659524 | − | 0.997823i | \(-0.521009\pi\) | ||||
−0.0659524 | + | 0.997823i | \(0.521009\pi\) | |||||||
\(602\) | 5.43039 | + | 18.6101i | 0.221326 | + | 0.758492i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.31386 | + | 13.0330i | 0.338286 | + | 0.530304i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 36.8220i | − | 1.49456i | −0.664510 | − | 0.747279i | \(-0.731360\pi\) | ||
0.664510 | − | 0.747279i | \(-0.268640\pi\) | |||||||
\(608\) | 4.04326 | − | 26.5330i | 0.163976 | − | 1.07606i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.02175 | − | 3.50157i | −0.0413694 | − | 0.141774i | ||||
\(611\) | 27.7128i | 1.12114i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 34.1213i | − | 1.37815i | −0.724692 | − | 0.689073i | \(-0.758018\pi\) | ||
0.724692 | − | 0.689073i | \(-0.241982\pi\) | |||||||
\(614\) | −9.84996 | + | 2.87419i | −0.397512 | + | 0.115993i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 21.1753 | − | 24.1895i | 0.853176 | − | 0.974621i | ||||
\(617\) | 28.4125i | 1.14385i | 0.820308 | + | 0.571923i | \(0.193802\pi\) | ||||
−0.820308 | + | 0.571923i | \(0.806198\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.2337 | −1.69752 | −0.848758 | − | 0.528782i | \(-0.822649\pi\) | ||||
−0.848758 | + | 0.528782i | \(0.822649\pi\) | |||||||
\(620\) | 3.25013 | + | 5.09496i | 0.130528 | + | 0.204619i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.25544 | − | 0.949929i | 0.130531 | − | 0.0380887i | ||||
\(623\) | −58.3472 | −2.33763 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 21.2337 | 0.849348 | ||||||||
\(626\) | 34.2572 | − | 9.99616i | 1.36919 | − | 0.399527i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −5.48913 | − | 8.60485i | −0.219040 | − | 0.343371i | ||||
\(629\) | −56.3255 | −2.24585 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 13.7827i | 0.548680i | 0.961633 | + | 0.274340i | \(0.0884593\pi\) | ||||
−0.961633 | + | 0.274340i | \(0.911541\pi\) | |||||||
\(632\) | −9.15640 | − | 8.01544i | −0.364222 | − | 0.318837i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 10.8030 | − | 3.15228i | 0.429041 | − | 0.125193i | ||||
\(635\) | − | 5.19615i | − | 0.206203i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 12.1064i | − | 0.479674i | ||||||
\(638\) | −7.13477 | − | 24.4511i | −0.282468 | − | 0.968028i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.31386 | + | 5.22896i | 0.0914633 | + | 0.206693i | ||||
\(641\) | − | 1.87953i | − | 0.0742369i | −0.999311 | − | 0.0371184i | \(-0.988182\pi\) | ||
0.999311 | − | 0.0371184i | \(-0.0118179\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −44.4674 | −1.75362 | −0.876811 | − | 0.480835i | \(-0.840334\pi\) | ||||
−0.876811 | + | 0.480835i | \(0.840334\pi\) | |||||||
\(644\) | 23.7432 | + | 37.2203i | 0.935613 | + | 1.46668i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 9.48913 | + | 32.5196i | 0.373345 | + | 1.27946i | ||||
\(647\) | −29.8081 | −1.17188 | −0.585938 | − | 0.810356i | \(-0.699274\pi\) | ||||
−0.585938 | + | 0.810356i | \(0.699274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 22.0000 | 0.863576 | ||||||||
\(650\) | −4.79588 | − | 16.4356i | −0.188110 | − | 0.644659i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −30.7446 | + | 19.6123i | −1.20405 | + | 0.768076i | ||||
\(653\) | −41.9269 | −1.64073 | −0.820363 | − | 0.571843i | \(-0.806229\pi\) | ||||
−0.820363 | + | 0.571843i | \(0.806229\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.02446i | − | 0.0400291i | ||||||
\(656\) | −6.81751 | − | 3.16915i | −0.266179 | − | 0.123734i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −14.7446 | − | 50.5301i | −0.574803 | − | 1.96987i | ||||
\(659\) | − | 39.5422i | − | 1.54035i | −0.637835 | − | 0.770173i | \(-0.720170\pi\) | ||
0.637835 | − | 0.770173i | \(-0.279830\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 16.2598i | − | 0.632432i | −0.948687 | − | 0.316216i | \(-0.897588\pi\) | ||
0.948687 | − | 0.316216i | \(-0.102412\pi\) | |||||||
\(662\) | −14.2695 | + | 4.16381i | −0.554601 | + | 0.161831i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.68614 | − | 6.72839i | −0.298280 | − | 0.261112i | ||||
\(665\) | 8.21782i | 0.318674i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.9783 | 1.35436 | ||||||||
\(668\) | −3.40876 | + | 2.17448i | −0.131889 | + | 0.0841332i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.74456 | − | 0.800857i | 0.106032 | − | 0.0309398i | ||||
\(671\) | −16.9257 | −0.653408 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.51087 | −0.289523 | −0.144761 | − | 0.989467i | \(-0.546241\pi\) | ||||
−0.144761 | + | 0.989467i | \(0.546241\pi\) | |||||||
\(674\) | 2.71519 | − | 0.792287i | 0.104585 | − | 0.0305178i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.9416 | − | 6.97975i | 0.420830 | − | 0.268452i | ||||
\(677\) | 42.0560 | 1.61634 | 0.808171 | − | 0.588947i | \(-0.200457\pi\) | ||||
0.808171 | + | 0.588947i | \(0.200457\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.42703i | 0.131517i | ||||||||
\(680\) | −5.43039 | − | 4.75372i | −0.208246 | − | 0.182297i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 26.9198 | − | 7.85514i | 1.03081 | − | 0.300789i | ||||
\(683\) | 9.80240i | 0.375078i | 0.982257 | + | 0.187539i | \(0.0600512\pi\) | ||||
−0.982257 | + | 0.187539i | \(0.939949\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.60485i | 0.328775i | ||||||||
\(686\) | −3.06198 | − | 10.4935i | −0.116907 | − | 0.400643i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −6.74456 | + | 14.5090i | −0.257134 | + | 0.553150i | ||||
\(689\) | 15.1460i | 0.577018i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.4891 | 1.88266 | 0.941328 | − | 0.337494i | \(-0.109579\pi\) | ||||
0.941328 | + | 0.337494i | \(0.109579\pi\) | |||||||
\(692\) | −19.1650 | + | 12.2255i | −0.728544 | + | 0.464746i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −10.6861 | − | 36.6218i | −0.405640 | − | 1.39014i | ||||
\(695\) | −4.04326 | −0.153370 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.48913 | 0.359426 | ||||||||
\(698\) | 6.44121 | + | 22.0742i | 0.243803 | + | 0.835522i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 17.4891 | + | 27.4163i | 0.661027 | + | 1.03624i | ||||
\(701\) | 10.3554 | 0.391117 | 0.195558 | − | 0.980692i | \(-0.437348\pi\) | ||||
0.195558 | + | 0.980692i | \(0.437348\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 52.9327i | 1.99639i | ||||||||
\(704\) | 26.2998 | − | 3.51039i | 0.991209 | − | 0.132303i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.2554 | + | 38.5728i | 0.423604 | + | 1.45171i | ||||
\(707\) | 54.0983i | 2.03458i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12.1064i | 0.454666i | 0.973817 | + | 0.227333i | \(0.0730006\pi\) | ||||
−0.973817 | + | 0.227333i | \(0.926999\pi\) | |||||||
\(710\) | 3.03245 | − | 0.884861i | 0.113806 | − | 0.0332082i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −36.2337 | − | 31.7187i | −1.35791 | − | 1.18871i | ||||
\(713\) | 38.5099i | 1.44221i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.27719 | 0.159958 | ||||||||
\(716\) | −12.7238 | − | 19.9460i | −0.475510 | − | 0.745418i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 32.2337 | − | 9.40571i | 1.20295 | − | 0.351018i | ||||
\(719\) | −8.83915 | −0.329645 | −0.164822 | − | 0.986323i | \(-0.552705\pi\) | ||||
−0.164822 | + | 0.986323i | \(0.552705\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.74456 | 0.102213 | ||||||||
\(722\) | 4.76635 | − | 1.39081i | 0.177385 | − | 0.0517606i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 25.7648 | 0.956881 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 10.4302i | − | 0.386834i | −0.981117 | − | 0.193417i | \(-0.938043\pi\) | ||
0.981117 | − | 0.193417i | \(-0.0619570\pi\) | |||||||
\(728\) | 16.2912 | − | 18.6101i | 0.603791 | − | 0.689737i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5.31386 | + | 1.55057i | −0.196675 | + | 0.0573892i | ||||
\(731\) | − | 20.1947i | − | 0.746928i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 38.5728i | − | 1.42472i | −0.701815 | − | 0.712359i | \(-0.747627\pi\) | ||
0.701815 | − | 0.712359i | \(-0.252373\pi\) | |||||||
\(734\) | −4.39005 | − | 15.0448i | −0.162040 | − | 0.555315i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.48913 | + | 36.0211i | −0.202332 | + | 1.32776i | ||||
\(737\) | − | 13.2665i | − | 0.488678i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.25544 | −0.266896 | −0.133448 | − | 0.991056i | \(-0.542605\pi\) | ||||
−0.133448 | + | 0.991056i | \(0.542605\pi\) | |||||||
\(740\) | −6.06490 | − | 9.50744i | −0.222950 | − | 0.349501i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.05842 | − | 27.6165i | −0.295834 | − | 1.01383i | ||||
\(743\) | 17.3020 | 0.634748 | 0.317374 | − | 0.948300i | \(-0.397199\pi\) | ||||
0.317374 | + | 0.948300i | \(0.397199\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.51087 | −0.348451 | ||||||||
\(746\) | 1.01082 | + | 3.46410i | 0.0370086 | + | 0.126830i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −28.2337 | + | 18.0106i | −1.03233 | + | 0.658531i | ||||
\(749\) | −16.7966 | −0.613734 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.02446i | 0.0373832i | 0.999825 | + | 0.0186916i | \(0.00595007\pi\) | ||||
−0.999825 | + | 0.0186916i | \(0.994050\pi\) | |||||||
\(752\) | 18.3128 | − | 39.3947i | 0.667799 | − | 1.43658i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5.48913 | − | 18.8114i | −0.199902 | − | 0.685071i | ||||
\(755\) | − | 3.90653i | − | 0.142173i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 34.1213i | − | 1.24016i | −0.784539 | − | 0.620079i | \(-0.787100\pi\) | ||
0.784539 | − | 0.620079i | \(-0.212900\pi\) | |||||||
\(758\) | −12.8824 | + | 3.75906i | −0.467910 | + | 0.136535i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.46738 | + | 5.10328i | −0.162049 | + | 0.185116i | ||||
\(761\) | − | 12.6766i | − | 0.459526i | −0.973247 | − | 0.229763i | \(-0.926205\pi\) | ||
0.973247 | − | 0.229763i | \(-0.0737951\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −38.2337 | −1.38415 | ||||||||
\(764\) | −14.2695 | + | 9.10268i | −0.516254 | + | 0.329324i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 35.4891 | − | 10.3556i | 1.28227 | − | 0.374164i | ||||
\(767\) | 16.9257 | 0.611151 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −21.7446 | −0.784129 | −0.392064 | − | 0.919938i | \(-0.628239\pi\) | ||||
−0.392064 | + | 0.919938i | \(0.628239\pi\) | |||||||
\(770\) | −7.79880 | + | 2.27567i | −0.281049 | + | 0.0820095i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 22.3139 | − | 14.2342i | 0.803093 | − | 0.512302i | ||||
\(773\) | 33.9695 | 1.22180 | 0.610898 | − | 0.791709i | \(-0.290808\pi\) | ||||
0.610898 | + | 0.791709i | \(0.290808\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 28.3662i | 1.01894i | ||||||||
\(776\) | −1.86301 | + | 2.12819i | −0.0668780 | + | 0.0763977i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 31.0367 | − | 9.05642i | 1.11272 | − | 0.324689i | ||||
\(779\) | − | 8.91754i | − | 0.319504i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 14.6581i | − | 0.524507i | ||||||
\(782\) | −12.8824 | − | 44.1485i | −0.460674 | − | 1.57875i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −8.00000 | + | 17.2097i | −0.285714 | + | 0.614632i | ||||
\(785\) | 2.57924i | 0.0920570i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.48913 | 0.0530816 | 0.0265408 | − | 0.999648i | \(-0.491551\pi\) | ||||
0.0265408 | + | 0.999648i | \(0.491551\pi\) | |||||||
\(788\) | −22.5737 | + | 14.4000i | −0.804156 | + | 0.512980i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.861407 | + | 2.95207i | 0.0306475 | + | 0.105030i | ||||
\(791\) | 41.0452 | 1.45940 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.0217 | −0.462416 | ||||||||
\(794\) | 11.8716 | + | 40.6844i | 0.421307 | + | 1.44383i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.29211 | + | 11.4312i | 0.258462 | + | 0.405170i | ||||
\(797\) | −15.4095 | −0.545831 | −0.272915 | − | 0.962038i | \(-0.587988\pi\) | ||||
−0.272915 | + | 0.962038i | \(0.587988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 54.8325i | 1.93984i | ||||||||
\(800\) | −4.04326 | + | 26.5330i | −0.142951 | + | 0.938083i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.48913 | + | 5.10328i | 0.0525828 | + | 0.180203i | ||||
\(803\) | 25.6858i | 0.906432i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 11.1565i | − | 0.393215i | ||||||
\(806\) | 20.7107 | − | 6.04334i | 0.729505 | − | 0.212868i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −29.4090 | + | 33.5952i | −1.03460 | + | 1.18187i | ||||
\(809\) | − | 49.8968i | − | 1.75428i | −0.480235 | − | 0.877140i | \(-0.659449\pi\) | ||
0.480235 | − | 0.877140i | \(-0.340551\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.74456 | 0.166604 | 0.0833021 | − | 0.996524i | \(-0.473453\pi\) | ||||
0.0833021 | + | 0.996524i | \(0.473453\pi\) | |||||||
\(812\) | 20.0172 | + | 31.3793i | 0.702465 | + | 1.10120i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −50.2337 | + | 14.6581i | −1.76069 | + | 0.513765i | ||||
\(815\) | 9.21545 | 0.322803 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −18.9783 | −0.663965 | ||||||||
\(818\) | 14.9336 | − | 4.35758i | 0.522140 | − | 0.152359i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.02175 | + | 1.60171i | 0.0356810 | + | 0.0559342i | ||||
\(821\) | −35.2385 | −1.22983 | −0.614916 | − | 0.788593i | \(-0.710810\pi\) | ||||
−0.614916 | + | 0.788593i | \(0.710810\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 50.4556i | 1.75877i | 0.476110 | + | 0.879386i | \(0.342046\pi\) | ||||
−0.476110 | + | 0.879386i | \(0.657954\pi\) | |||||||
\(824\) | 1.70438 | + | 1.49200i | 0.0593748 | + | 0.0519763i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −30.8614 | + | 9.00528i | −1.07381 | + | 0.313334i | ||||
\(827\) | − | 6.63325i | − | 0.230661i | −0.993327 | − | 0.115330i | \(-0.963207\pi\) | ||
0.993327 | − | 0.115330i | \(-0.0367927\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.50157i | 0.121615i | 0.998150 | + | 0.0608073i | \(0.0193675\pi\) | ||||
−0.998150 | + | 0.0608073i | \(0.980632\pi\) | |||||||
\(830\) | 0.723089 | + | 2.47805i | 0.0250988 | + | 0.0860144i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 20.2337 | − | 2.70071i | 0.701477 | − | 0.0936304i | ||||
\(833\) | − | 23.9538i | − | 0.829949i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.02175 | 0.0353591 | ||||||||
\(836\) | 16.9257 | + | 26.5330i | 0.585387 | + | 0.917663i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.86141 | + | 9.80614i | 0.0988457 | + | 0.338747i | ||||
\(839\) | 12.5061 | 0.431759 | 0.215879 | − | 0.976420i | \(-0.430738\pi\) | ||||
0.215879 | + | 0.976420i | \(0.430738\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.489125 | 0.0168664 | ||||||||
\(842\) | 10.8608 | + | 37.2203i | 0.374287 | + | 1.28269i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −21.4891 | + | 13.7081i | −0.739686 | + | 0.471854i | ||||
\(845\) | −3.27966 | −0.112824 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 10.0086 | − | 21.5306i | 0.343696 | − | 0.739364i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −9.48913 | − | 32.5196i | −0.325474 | − | 1.11541i | ||||
\(851\) | − | 71.8613i | − | 2.46337i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 6.70500i | − | 0.229575i | −0.993390 | − | 0.114787i | \(-0.963381\pi\) | ||
0.993390 | − | 0.114787i | \(-0.0366187\pi\) | |||||||
\(854\) | 23.7432 | − | 6.92820i | 0.812475 | − | 0.237078i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.4307 | − | 9.13096i | −0.356514 | − | 0.312090i | ||||
\(857\) | 2.46943i | 0.0843543i | 0.999110 | + | 0.0421771i | \(0.0134294\pi\) | ||||
−0.999110 | + | 0.0421771i | \(0.986571\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −20.4674 | −0.698338 | −0.349169 | − | 0.937060i | \(-0.613536\pi\) | ||||
−0.349169 | + | 0.937060i | \(0.613536\pi\) | |||||||
\(860\) | 3.40876 | − | 2.17448i | 0.116238 | − | 0.0741492i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 20.2337 | − | 5.90414i | 0.689162 | − | 0.201096i | ||||
\(863\) | −26.5174 | −0.902664 | −0.451332 | − | 0.892356i | \(-0.649051\pi\) | ||||
−0.451332 | + | 0.892356i | \(0.649051\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.74456 | 0.195321 | ||||||||
\(866\) | −25.1008 | + | 7.32435i | −0.852959 | + | 0.248891i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −34.5475 | + | 22.0382i | −1.17262 | + | 0.748027i | ||||
\(869\) | 14.2695 | 0.484061 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 10.2066i | − | 0.345836i | ||||||
\(872\) | −23.7432 | − | 20.7846i | −0.804046 | − | 0.703856i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −41.4891 | + | 12.1064i | −1.40339 | + | 0.409506i | ||||
\(875\) | − | 16.8781i | − | 0.570583i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 13.7081i | 0.462891i | 0.972848 | + | 0.231445i | \(0.0743455\pi\) | ||||
−0.972848 | + | 0.231445i | \(0.925655\pi\) | |||||||
\(878\) | −7.42249 | − | 25.4371i | −0.250497 | − | 0.858462i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.08017 | − | 2.82639i | −0.204963 | − | 0.0952776i | ||||
\(881\) | 7.62792i | 0.256991i | 0.991710 | + | 0.128496i | \(0.0410148\pi\) | ||||
−0.991710 | + | 0.128496i | \(0.958985\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −23.7228 | −0.798336 | −0.399168 | − | 0.916878i | \(-0.630701\pi\) | ||||
−0.399168 | + | 0.916878i | \(0.630701\pi\) | |||||||
\(884\) | −21.7216 | + | 13.8564i | −0.730575 | + | 0.466041i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.62772 | − | 9.00528i | −0.0882799 | − | 0.302538i | ||||
\(887\) | −9.21545 | −0.309425 | −0.154712 | − | 0.987960i | \(-0.549445\pi\) | ||||
−0.154712 | + | 0.987960i | \(0.549445\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 35.2337 | 1.18170 | ||||||||
\(890\) | 3.40876 | + | 11.6819i | 0.114262 | + | 0.391579i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.3723 | + | 30.3683i | 0.648632 | + | 1.01681i | ||||
\(893\) | 51.5296 | 1.72437 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.97868i | 0.199845i | ||||||||
\(896\) | −35.4562 | + | 15.6896i | −1.18451 | + | 0.524154i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1.76631 | − | 6.05321i | −0.0589426 | − | 0.201998i | ||||
\(899\) | 32.4665i | 1.08282i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 29.9679i | 0.998376i | ||||||||
\(902\) | 8.46284 | − | 2.46943i | 0.281782 | − | 0.0822232i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 25.4891 | + | 22.3130i | 0.847756 | + | 0.742119i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −54.2337 | −1.80080 | −0.900400 | − | 0.435063i | \(-0.856726\pi\) | ||||
−0.900400 | + | 0.435063i | \(0.856726\pi\) | |||||||
\(908\) | 25.4476 | + | 39.8921i | 0.844507 | + | 1.32386i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −6.00000 | + | 1.75079i | −0.198898 | + | 0.0580380i | ||||
\(911\) | 10.8608 | 0.359834 | 0.179917 | − | 0.983682i | \(-0.442417\pi\) | ||||
0.179917 | + | 0.983682i | \(0.442417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 11.9783 | 0.396422 | ||||||||
\(914\) | −56.2960 | + | 16.4270i | −1.86211 | + | 0.543358i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.25544 | − | 14.5090i | −0.305808 | − | 0.479391i | ||||
\(917\) | 6.94661 | 0.229397 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 26.6900i | − | 0.880420i | −0.897895 | − | 0.440210i | \(-0.854904\pi\) | ||
0.897895 | − | 0.440210i | \(-0.145096\pi\) | |||||||
\(920\) | 6.06490 | − | 6.92820i | 0.199954 | − | 0.228416i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 46.8030 | − | 13.6570i | 1.54137 | − | 0.449769i | ||||
\(923\) | − | 11.2772i | − | 0.371192i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 52.9327i | − | 1.74042i | ||||||
\(926\) | 12.5356 | + | 42.9600i | 0.411946 | + | 1.41175i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −4.62772 | + | 30.3683i | −0.151912 | + | 0.996890i | ||||
\(929\) | − | 42.9686i | − | 1.40976i | −0.709329 | − | 0.704878i | \(-0.751002\pi\) | ||
0.709329 | − | 0.704878i | \(-0.248998\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −22.5109 | −0.737764 | ||||||||
\(932\) | −0.634508 | − | 0.994667i | −0.0207840 | − | 0.0325814i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −12.4090 | − | 42.5259i | −0.406033 | − | 1.39149i | ||||
\(935\) | 8.46284 | 0.276764 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 35.0000 | 1.14340 | 0.571700 | − | 0.820463i | \(-0.306284\pi\) | ||||
0.571700 | + | 0.820463i | \(0.306284\pi\) | |||||||
\(938\) | 5.43039 | + | 18.6101i | 0.177308 | + | 0.607642i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.25544 | + | 5.90414i | −0.301879 | + | 0.192572i | ||||
\(941\) | 3.91416 | 0.127598 | 0.0637991 | − | 0.997963i | \(-0.479678\pi\) | ||||
0.0637991 | + | 0.997963i | \(0.479678\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.1064i | 0.394239i | ||||||||
\(944\) | −24.0604 | − | 11.1846i | −0.783101 | − | 0.364027i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.25544 | − | 18.0106i | −0.170869 | − | 0.585574i | ||||
\(947\) | − | 11.8294i | − | 0.384404i | −0.981355 | − | 0.192202i | \(-0.938437\pi\) | ||
0.981355 | − | 0.192202i | \(-0.0615629\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.7613i | 0.641481i | ||||||||
\(950\) | −30.5607 | + | 8.91754i | −0.991520 | + | 0.289323i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 32.2337 | − | 36.8220i | 1.04470 | − | 1.19341i | ||||
\(953\) | 31.4719i | 1.01947i | 0.860330 | + | 0.509737i | \(0.170257\pi\) | ||||
−0.860330 | + | 0.509737i | \(0.829743\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.27719 | 0.138407 | ||||||||
\(956\) | −25.7648 | + | 16.4356i | −0.833294 | + | 0.531567i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.74456 | − | 0.800857i | 0.0886728 | − | 0.0258745i | ||||
\(959\) | −58.3472 | −1.88413 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.74456 | −0.153050 | ||||||||
\(962\) | −38.6472 | + | 11.2772i | −1.24604 | + | 0.363590i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 3.37228 | − | 2.15121i | 0.108614 | − | 0.0692859i | ||||
\(965\) | −6.68841 | −0.215308 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8327i | 0.412673i | 0.978481 | + | 0.206337i | \(0.0661542\pi\) | ||||
−0.978481 | + | 0.206337i | \(0.933846\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.686141 | − | 0.200214i | 0.0220306 | − | 0.00642849i | ||||
\(971\) | 14.5938i | 0.468337i | 0.972196 | + | 0.234169i | \(0.0752367\pi\) | ||||
−0.972196 | + | 0.234169i | \(0.924763\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 27.4163i | − | 0.878925i | ||||||
\(974\) | −3.72601 | − | 12.7692i | −0.119389 | − | 0.409150i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 18.5109 | + | 8.60485i | 0.592519 | + | 0.275435i | ||||
\(977\) | − | 47.3176i | − | 1.51382i | −0.653517 | − | 0.756912i | \(-0.726707\pi\) | ||
0.653517 | − | 0.756912i | \(-0.273293\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 56.4674 | 1.80471 | ||||||||
\(980\) | 4.04326 | − | 2.57924i | 0.129157 | − | 0.0823908i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11.0802 | + | 37.9721i | 0.353582 | + | 1.21174i | ||||
\(983\) | 28.5391 | 0.910255 | 0.455127 | − | 0.890426i | \(-0.349594\pi\) | ||||
0.455127 | + | 0.890426i | \(0.349594\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6.76631 | 0.215593 | ||||||||
\(986\) | −10.8608 | − | 37.2203i | −0.345878 | − | 1.18533i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 13.0217 | + | 20.4131i | 0.414277 | + | 0.649428i | ||||
\(989\) | 25.7648 | 0.819274 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 12.0319i | − | 0.382205i | −0.981570 | − | 0.191103i | \(-0.938794\pi\) | ||
0.981570 | − | 0.191103i | \(-0.0612064\pi\) | |||||||
\(992\) | −33.4345 | − | 5.09496i | −1.06155 | − | 0.161765i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.00000 | + | 20.5622i | 0.190308 | + | 0.652194i | ||||
\(995\) | − | 3.42643i | − | 0.108625i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 31.8678i | − | 1.00926i | −0.863335 | − | 0.504631i | \(-0.831628\pi\) | ||
0.863335 | − | 0.504631i | \(-0.168372\pi\) | |||||||
\(998\) | −38.0127 | + | 11.0920i | −1.20327 | + | 0.351112i | ||||
\(999\) | 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.b.107.7 | yes | 8 | |
3.2 | odd | 2 | inner | 216.2.f.b.107.2 | yes | 8 | |
4.3 | odd | 2 | 864.2.f.b.431.4 | 8 | |||
8.3 | odd | 2 | inner | 216.2.f.b.107.1 | ✓ | 8 | |
8.5 | even | 2 | 864.2.f.b.431.5 | 8 | |||
9.2 | odd | 6 | 648.2.l.d.539.4 | 8 | |||
9.4 | even | 3 | 648.2.l.d.107.3 | 8 | |||
9.5 | odd | 6 | 648.2.l.e.107.2 | 8 | |||
9.7 | even | 3 | 648.2.l.e.539.1 | 8 | |||
12.11 | even | 2 | 864.2.f.b.431.6 | 8 | |||
24.5 | odd | 2 | 864.2.f.b.431.3 | 8 | |||
24.11 | even | 2 | inner | 216.2.f.b.107.8 | yes | 8 | |
36.7 | odd | 6 | 2592.2.p.e.2159.3 | 8 | |||
36.11 | even | 6 | 2592.2.p.d.2159.2 | 8 | |||
36.23 | even | 6 | 2592.2.p.e.431.2 | 8 | |||
36.31 | odd | 6 | 2592.2.p.d.431.3 | 8 | |||
72.5 | odd | 6 | 2592.2.p.e.431.3 | 8 | |||
72.11 | even | 6 | 648.2.l.d.539.3 | 8 | |||
72.13 | even | 6 | 2592.2.p.d.431.2 | 8 | |||
72.29 | odd | 6 | 2592.2.p.d.2159.3 | 8 | |||
72.43 | odd | 6 | 648.2.l.e.539.2 | 8 | |||
72.59 | even | 6 | 648.2.l.e.107.1 | 8 | |||
72.61 | even | 6 | 2592.2.p.e.2159.2 | 8 | |||
72.67 | odd | 6 | 648.2.l.d.107.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.f.b.107.1 | ✓ | 8 | 8.3 | odd | 2 | inner | |
216.2.f.b.107.2 | yes | 8 | 3.2 | odd | 2 | inner | |
216.2.f.b.107.7 | yes | 8 | 1.1 | even | 1 | trivial | |
216.2.f.b.107.8 | yes | 8 | 24.11 | even | 2 | inner | |
648.2.l.d.107.3 | 8 | 9.4 | even | 3 | |||
648.2.l.d.107.4 | 8 | 72.67 | odd | 6 | |||
648.2.l.d.539.3 | 8 | 72.11 | even | 6 | |||
648.2.l.d.539.4 | 8 | 9.2 | odd | 6 | |||
648.2.l.e.107.1 | 8 | 72.59 | even | 6 | |||
648.2.l.e.107.2 | 8 | 9.5 | odd | 6 | |||
648.2.l.e.539.1 | 8 | 9.7 | even | 3 | |||
648.2.l.e.539.2 | 8 | 72.43 | odd | 6 | |||
864.2.f.b.431.3 | 8 | 24.5 | odd | 2 | |||
864.2.f.b.431.4 | 8 | 4.3 | odd | 2 | |||
864.2.f.b.431.5 | 8 | 8.5 | even | 2 | |||
864.2.f.b.431.6 | 8 | 12.11 | even | 2 | |||
2592.2.p.d.431.2 | 8 | 72.13 | even | 6 | |||
2592.2.p.d.431.3 | 8 | 36.31 | odd | 6 | |||
2592.2.p.d.2159.2 | 8 | 36.11 | even | 6 | |||
2592.2.p.d.2159.3 | 8 | 72.29 | odd | 6 | |||
2592.2.p.e.431.2 | 8 | 36.23 | even | 6 | |||
2592.2.p.e.431.3 | 8 | 72.5 | odd | 6 | |||
2592.2.p.e.2159.2 | 8 | 72.61 | even | 6 | |||
2592.2.p.e.2159.3 | 8 | 36.7 | odd | 6 |