Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,2,Mod(215,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.215");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.k (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.01834519640\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 269.2 | ||
Root | \(-0.258819 - 0.965926i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.269 |
Dual form | 378.2.k.d.215.2 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.866025 | + | 0.500000i | −0.612372 | + | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.22474 | + | 2.12132i | 0.547723 | + | 0.948683i | 0.998430 | + | 0.0560116i | \(0.0178384\pi\) |
−0.450708 | + | 0.892672i | \(0.648828\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | − | 2.44949i | −0.377964 | − | 0.925820i | ||||
\(8\) | 1.00000i | 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.12132 | − | 1.22474i | −0.670820 | − | 0.387298i | ||||
\(11\) | 3.67423 | + | 2.12132i | 1.10782 | + | 0.639602i | 0.938265 | − | 0.345918i | \(-0.112432\pi\) |
0.169559 | + | 0.985520i | \(0.445766\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.18154i | 1.15975i | 0.814705 | + | 0.579875i | \(0.196899\pi\) | ||||
−0.814705 | + | 0.579875i | \(0.803101\pi\) | |||||||
\(14\) | 2.09077 | + | 1.62132i | 0.558782 | + | 0.433316i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 1.22474 | − | 2.12132i | 0.297044 | − | 0.514496i | −0.678414 | − | 0.734680i | \(-0.737332\pi\) |
0.975458 | + | 0.220184i | \(0.0706658\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.24264 | − | 2.44949i | 0.973329 | − | 0.561951i | 0.0730792 | − | 0.997326i | \(-0.476717\pi\) |
0.900249 | + | 0.435375i | \(0.143384\pi\) | |||||||
\(20\) | 2.44949 | 0.547723 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.24264 | −0.904534 | ||||||||
\(23\) | −5.19615 | + | 3.00000i | −1.08347 | + | 0.625543i | −0.931831 | − | 0.362892i | \(-0.881789\pi\) |
−0.151642 | + | 0.988436i | \(0.548456\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.500000 | + | 0.866025i | −0.100000 | + | 0.173205i | ||||
\(26\) | −2.09077 | − | 3.62132i | −0.410034 | − | 0.710199i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.62132 | − | 0.358719i | −0.495383 | − | 0.0677916i | ||||
\(29\) | 10.2426i | 1.90201i | 0.309175 | + | 0.951005i | \(0.399947\pi\) | ||||
−0.309175 | + | 0.951005i | \(0.600053\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.86396 | + | 2.80821i | 0.873593 | + | 0.504369i | 0.868541 | − | 0.495618i | \(-0.165058\pi\) |
0.00505256 | + | 0.999987i | \(0.498392\pi\) | |||||||
\(32\) | 0.866025 | + | 0.500000i | 0.153093 | + | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.44949i | 0.420084i | ||||||||
\(35\) | 3.97141 | − | 5.12132i | 0.671290 | − | 0.865661i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.62132 | + | 2.80821i | 0.266543 | + | 0.461667i | 0.967967 | − | 0.251078i | \(-0.0807851\pi\) |
−0.701423 | + | 0.712745i | \(0.747452\pi\) | |||||||
\(38\) | −2.44949 | + | 4.24264i | −0.397360 | + | 0.688247i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.12132 | + | 1.22474i | −0.335410 | + | 0.193649i | ||||
\(41\) | 2.44949 | 0.382546 | 0.191273 | − | 0.981537i | \(-0.438738\pi\) | ||||
0.191273 | + | 0.981537i | \(0.438738\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.00000 | 1.06749 | 0.533745 | − | 0.845645i | \(-0.320784\pi\) | ||||
0.533745 | + | 0.845645i | \(0.320784\pi\) | |||||||
\(44\) | 3.67423 | − | 2.12132i | 0.553912 | − | 0.319801i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.00000 | − | 5.19615i | 0.442326 | − | 0.766131i | ||||
\(47\) | −3.97141 | − | 6.87868i | −0.579289 | − | 1.00336i | −0.995561 | − | 0.0941183i | \(-0.969997\pi\) |
0.416272 | − | 0.909240i | \(-0.363337\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.00000 | + | 4.89898i | −0.714286 | + | 0.699854i | ||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.62132 | + | 2.09077i | 0.502187 | + | 0.289938i | ||||
\(53\) | −2.15232 | − | 1.24264i | −0.295643 | − | 0.170690i | 0.344841 | − | 0.938661i | \(-0.387933\pi\) |
−0.640484 | + | 0.767971i | \(0.721266\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.3923i | 1.40130i | ||||||||
\(56\) | 2.44949 | − | 1.00000i | 0.327327 | − | 0.133631i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.12132 | − | 8.87039i | −0.672462 | − | 1.16474i | ||||
\(59\) | −1.22474 | + | 2.12132i | −0.159448 | + | 0.276172i | −0.934670 | − | 0.355517i | \(-0.884305\pi\) |
0.775222 | + | 0.631689i | \(0.217638\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.621320 | + | 0.358719i | −0.0795519 | + | 0.0459293i | −0.539248 | − | 0.842147i | \(-0.681292\pi\) |
0.459696 | + | 0.888076i | \(0.347958\pi\) | |||||||
\(62\) | −5.61642 | −0.713286 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −8.87039 | + | 5.12132i | −1.10024 | + | 0.635222i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.74264 | − | 3.01834i | 0.212897 | − | 0.368749i | −0.739723 | − | 0.672912i | \(-0.765043\pi\) |
0.952620 | + | 0.304163i | \(0.0983766\pi\) | |||||||
\(68\) | −1.22474 | − | 2.12132i | −0.148522 | − | 0.257248i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.878680 | + | 6.42090i | −0.105022 | + | 0.767444i | ||||
\(71\) | − | 12.7279i | − | 1.51053i | −0.655422 | − | 0.755263i | \(-0.727509\pi\) | ||
0.655422 | − | 0.755263i | \(-0.272491\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13.2426 | − | 7.64564i | −1.54993 | − | 0.894855i | −0.998146 | − | 0.0608704i | \(-0.980612\pi\) |
−0.551788 | − | 0.833984i | \(-0.686054\pi\) | |||||||
\(74\) | −2.80821 | − | 1.62132i | −0.326448 | − | 0.188475i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.89898i | − | 0.561951i | ||||||
\(77\) | 1.52192 | − | 11.1213i | 0.173439 | − | 1.26739i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.62132 | − | 8.00436i | −0.519939 | − | 0.900561i | −0.999731 | − | 0.0231789i | \(-0.992621\pi\) |
0.479792 | − | 0.877382i | \(-0.340712\pi\) | |||||||
\(80\) | 1.22474 | − | 2.12132i | 0.136931 | − | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.12132 | + | 1.22474i | −0.234261 | + | 0.135250i | ||||
\(83\) | 5.49333 | 0.602971 | 0.301485 | − | 0.953471i | \(-0.402518\pi\) | ||||
0.301485 | + | 0.953471i | \(0.402518\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.00000 | 0.650791 | ||||||||
\(86\) | −6.06218 | + | 3.50000i | −0.653701 | + | 0.377415i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.12132 | + | 3.67423i | −0.226134 | + | 0.391675i | ||||
\(89\) | −8.87039 | − | 15.3640i | −0.940259 | − | 1.62858i | −0.764976 | − | 0.644059i | \(-0.777249\pi\) |
−0.175283 | − | 0.984518i | \(-0.556084\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.2426 | − | 4.18154i | 1.07372 | − | 0.438345i | ||||
\(92\) | 6.00000i | 0.625543i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.87868 | + | 3.97141i | 0.709482 | + | 0.409619i | ||||
\(95\) | 10.3923 | + | 6.00000i | 1.06623 | + | 0.615587i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 6.63103i | − | 0.673279i | −0.941634 | − | 0.336640i | \(-0.890710\pi\) | ||
0.941634 | − | 0.336640i | \(-0.109290\pi\) | |||||||
\(98\) | 1.88064 | − | 6.74264i | 0.189973 | − | 0.681110i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.500000 | + | 0.866025i | 0.0500000 | + | 0.0866025i | ||||
\(101\) | 3.67423 | − | 6.36396i | 0.365600 | − | 0.633238i | −0.623272 | − | 0.782005i | \(-0.714197\pi\) |
0.988872 | + | 0.148767i | \(0.0475305\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.37868 | − | 3.10538i | 0.529977 | − | 0.305982i | −0.211030 | − | 0.977480i | \(-0.567682\pi\) |
0.741007 | + | 0.671497i | \(0.234348\pi\) | |||||||
\(104\) | −4.18154 | −0.410034 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.48528 | 0.241392 | ||||||||
\(107\) | −12.5446 | + | 7.24264i | −1.21273 | + | 0.700173i | −0.963354 | − | 0.268233i | \(-0.913560\pi\) |
−0.249380 | + | 0.968406i | \(0.580227\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.86396 | + | 6.69258i | −0.370100 | + | 0.641033i | −0.989581 | − | 0.143980i | \(-0.954010\pi\) |
0.619480 | + | 0.785012i | \(0.287343\pi\) | |||||||
\(110\) | −5.19615 | − | 9.00000i | −0.495434 | − | 0.858116i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.62132 | + | 2.09077i | −0.153200 | + | 0.197559i | ||||
\(113\) | − | 1.75736i | − | 0.165318i | −0.996578 | − | 0.0826592i | \(-0.973659\pi\) | ||
0.996578 | − | 0.0826592i | \(-0.0263413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.7279 | − | 7.34847i | −1.18688 | − | 0.685248i | ||||
\(116\) | 8.87039 | + | 5.12132i | 0.823595 | + | 0.475503i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 2.44949i | − | 0.225494i | ||||||
\(119\) | −6.42090 | − | 0.878680i | −0.588603 | − | 0.0805484i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.50000 | + | 6.06218i | 0.318182 | + | 0.551107i | ||||
\(122\) | 0.358719 | − | 0.621320i | 0.0324769 | − | 0.0562517i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.86396 | − | 2.80821i | 0.436797 | − | 0.252185i | ||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7279 | 1.57310 | 0.786549 | − | 0.617527i | \(-0.211866\pi\) | ||||
0.786549 | + | 0.617527i | \(0.211866\pi\) | |||||||
\(128\) | 0.866025 | − | 0.500000i | 0.0765466 | − | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.12132 | − | 8.87039i | 0.449170 | − | 0.777984i | ||||
\(131\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10.2426 | − | 7.94282i | −0.888150 | − | 0.688729i | ||||
\(134\) | 3.48528i | 0.301082i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.12132 | + | 1.22474i | 0.181902 | + | 0.105021i | ||||
\(137\) | 5.19615 | + | 3.00000i | 0.443937 | + | 0.256307i | 0.705266 | − | 0.708942i | \(-0.250827\pi\) |
−0.261329 | + | 0.965250i | \(0.584161\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 11.5300i | − | 0.977963i | −0.872294 | − | 0.488981i | \(-0.837369\pi\) | ||
0.872294 | − | 0.488981i | \(-0.162631\pi\) | |||||||
\(140\) | −2.44949 | − | 6.00000i | −0.207020 | − | 0.507093i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.36396 | + | 11.0227i | 0.534052 | + | 0.925005i | ||||
\(143\) | −8.87039 | + | 15.3640i | −0.741779 | + | 1.28480i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −21.7279 | + | 12.5446i | −1.80441 | + | 1.04177i | ||||
\(146\) | 15.2913 | 1.26552 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.24264 | 0.266543 | ||||||||
\(149\) | −6.71807 | + | 3.87868i | −0.550366 | + | 0.317754i | −0.749270 | − | 0.662265i | \(-0.769595\pi\) |
0.198904 | + | 0.980019i | \(0.436262\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.62132 | + | 14.9326i | −0.701593 | + | 1.21519i | 0.266314 | + | 0.963886i | \(0.414194\pi\) |
−0.967907 | + | 0.251309i | \(0.919139\pi\) | |||||||
\(152\) | 2.44949 | + | 4.24264i | 0.198680 | + | 0.344124i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.24264 | + | 10.3923i | 0.341882 | + | 0.837436i | ||||
\(155\) | 13.7574i | 1.10502i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.00000 | − | 5.19615i | −0.718278 | − | 0.414698i | 0.0958404 | − | 0.995397i | \(-0.469446\pi\) |
−0.814119 | + | 0.580699i | \(0.802779\pi\) | |||||||
\(158\) | 8.00436 | + | 4.62132i | 0.636793 | + | 0.367653i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.44949i | 0.193649i | ||||||||
\(161\) | 12.5446 | + | 9.72792i | 0.988655 | + | 0.766668i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −3.74264 | − | 6.48244i | −0.293146 | − | 0.507744i | 0.681406 | − | 0.731906i | \(-0.261369\pi\) |
−0.974552 | + | 0.224162i | \(0.928036\pi\) | |||||||
\(164\) | 1.22474 | − | 2.12132i | 0.0956365 | − | 0.165647i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.75736 | + | 2.74666i | −0.369243 | + | 0.213182i | ||||
\(167\) | −20.1903 | −1.56237 | −0.781185 | − | 0.624300i | \(-0.785384\pi\) | ||||
−0.781185 | + | 0.624300i | \(0.785384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.48528 | −0.345022 | ||||||||
\(170\) | −5.19615 | + | 3.00000i | −0.398527 | + | 0.230089i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.50000 | − | 6.06218i | 0.266872 | − | 0.462237i | ||||
\(173\) | −10.3923 | − | 18.0000i | −0.790112 | − | 1.36851i | −0.925897 | − | 0.377776i | \(-0.876689\pi\) |
0.135785 | − | 0.990738i | \(-0.456644\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.62132 | + | 0.358719i | 0.198153 | + | 0.0271166i | ||||
\(176\) | − | 4.24264i | − | 0.319801i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 15.3640 | + | 8.87039i | 1.15158 | + | 0.664864i | ||||
\(179\) | 16.2189 | + | 9.36396i | 1.21225 | + | 0.699895i | 0.963250 | − | 0.268607i | \(-0.0865633\pi\) |
0.249004 | + | 0.968502i | \(0.419897\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.79796i | 0.728277i | 0.931345 | + | 0.364138i | \(0.118636\pi\) | ||||
−0.931345 | + | 0.364138i | \(0.881364\pi\) | |||||||
\(182\) | −6.77962 | + | 8.74264i | −0.502539 | + | 0.648048i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.00000 | − | 5.19615i | −0.221163 | − | 0.383065i | ||||
\(185\) | −3.97141 | + | 6.87868i | −0.291984 | + | 0.505731i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 9.00000 | − | 5.19615i | 0.658145 | − | 0.379980i | ||||
\(188\) | −7.94282 | −0.579289 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | 18.3712 | − | 10.6066i | 1.32929 | − | 0.767467i | 0.344101 | − | 0.938933i | \(-0.388184\pi\) |
0.985190 | + | 0.171466i | \(0.0548503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.74264 | + | 13.4106i | −0.557327 | + | 0.965319i | 0.440391 | + | 0.897806i | \(0.354840\pi\) |
−0.997718 | + | 0.0675134i | \(0.978493\pi\) | |||||||
\(194\) | 3.31552 | + | 5.74264i | 0.238040 | + | 0.412298i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.74264 | + | 6.77962i | 0.124474 | + | 0.484258i | ||||
\(197\) | 16.9706i | 1.20910i | 0.796566 | + | 0.604551i | \(0.206648\pi\) | ||||
−0.796566 | + | 0.604551i | \(0.793352\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.10660 | + | 1.79360i | 0.220221 | + | 0.127145i | 0.606053 | − | 0.795425i | \(-0.292752\pi\) |
−0.385832 | + | 0.922569i | \(0.626085\pi\) | |||||||
\(200\) | −0.866025 | − | 0.500000i | −0.0612372 | − | 0.0353553i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 7.34847i | 0.517036i | ||||||||
\(203\) | 25.0892 | − | 10.2426i | 1.76092 | − | 0.718892i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | −3.10538 | + | 5.37868i | −0.216362 | + | 0.374750i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.62132 | − | 2.09077i | 0.251093 | − | 0.144969i | ||||
\(209\) | 20.7846 | 1.43770 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4853 | −0.928365 | −0.464183 | − | 0.885740i | \(-0.653652\pi\) | ||||
−0.464183 | + | 0.885740i | \(0.653652\pi\) | |||||||
\(212\) | −2.15232 | + | 1.24264i | −0.147822 | + | 0.0853449i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 7.24264 | − | 12.5446i | 0.495097 | − | 0.857533i | ||||
\(215\) | 8.57321 | + | 14.8492i | 0.584688 | + | 1.01271i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.01472 | − | 14.7224i | 0.136768 | − | 0.999424i | ||||
\(218\) | − | 7.72792i | − | 0.523401i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 9.00000 | + | 5.19615i | 0.606780 | + | 0.350325i | ||||
\(221\) | 8.87039 | + | 5.12132i | 0.596687 | + | 0.344497i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 10.3923i | − | 0.695920i | −0.937509 | − | 0.347960i | \(-0.886874\pi\) | ||
0.937509 | − | 0.347960i | \(-0.113126\pi\) | |||||||
\(224\) | 0.358719 | − | 2.62132i | 0.0239680 | − | 0.175144i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.878680 | + | 1.52192i | 0.0584489 | + | 0.101236i | ||||
\(227\) | −2.15232 | + | 3.72792i | −0.142854 | + | 0.247431i | −0.928570 | − | 0.371156i | \(-0.878961\pi\) |
0.785716 | + | 0.618587i | \(0.212295\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.86396 | − | 4.54026i | 0.519665 | − | 0.300029i | −0.217132 | − | 0.976142i | \(-0.569670\pi\) |
0.736798 | + | 0.676113i | \(0.236337\pi\) | |||||||
\(230\) | 14.6969 | 0.969087 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.2426 | −0.672462 | ||||||||
\(233\) | −3.04384 | + | 1.75736i | −0.199408 | + | 0.115128i | −0.596379 | − | 0.802703i | \(-0.703395\pi\) |
0.396971 | + | 0.917831i | \(0.370061\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 9.72792 | − | 16.8493i | 0.634580 | − | 1.09912i | ||||
\(236\) | 1.22474 | + | 2.12132i | 0.0797241 | + | 0.138086i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.00000 | − | 2.44949i | 0.388922 | − | 0.158777i | ||||
\(239\) | − | 7.75736i | − | 0.501782i | −0.968015 | − | 0.250891i | \(-0.919276\pi\) | ||
0.968015 | − | 0.250891i | \(-0.0807236\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.9853 | + | 9.22911i | 1.02970 | + | 0.594499i | 0.916899 | − | 0.399118i | \(-0.130684\pi\) |
0.112803 | + | 0.993617i | \(0.464017\pi\) | |||||||
\(242\) | −6.06218 | − | 3.50000i | −0.389692 | − | 0.224989i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.717439i | 0.0459293i | ||||||||
\(245\) | −16.5160 | − | 4.60660i | −1.05517 | − | 0.294305i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.2426 | + | 17.7408i | 0.651724 | + | 1.12882i | ||||
\(248\) | −2.80821 | + | 4.86396i | −0.178321 | + | 0.308862i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −8.48528 | + | 4.89898i | −0.536656 | + | 0.309839i | ||||
\(251\) | −5.49333 | −0.346736 | −0.173368 | − | 0.984857i | \(-0.555465\pi\) | ||||
−0.173368 | + | 0.984857i | \(0.555465\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −25.4558 | −1.60040 | ||||||||
\(254\) | −15.3528 | + | 8.86396i | −0.963322 | + | 0.556174i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −2.15232 | − | 3.72792i | −0.134258 | − | 0.232541i | 0.791056 | − | 0.611744i | \(-0.209532\pi\) |
−0.925314 | + | 0.379203i | \(0.876198\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 5.25736 | − | 6.77962i | 0.326676 | − | 0.421265i | ||||
\(260\) | 10.2426i | 0.635222i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.2189 | − | 9.36396i | −1.00010 | − | 0.577407i | −0.0918204 | − | 0.995776i | \(-0.529269\pi\) |
−0.908277 | + | 0.418369i | \(0.862602\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 6.08767i | − | 0.373963i | ||||||
\(266\) | 12.8418 | + | 1.75736i | 0.787381 | + | 0.107751i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.74264 | − | 3.01834i | −0.106449 | − | 0.184375i | ||||
\(269\) | −4.89898 | + | 8.48528i | −0.298696 | + | 0.517357i | −0.975838 | − | 0.218496i | \(-0.929885\pi\) |
0.677142 | + | 0.735853i | \(0.263218\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 13.3492 | − | 7.70719i | 0.810909 | − | 0.468178i | −0.0363626 | − | 0.999339i | \(-0.511577\pi\) |
0.847271 | + | 0.531160i | \(0.178244\pi\) | |||||||
\(272\) | −2.44949 | −0.148522 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | −3.67423 | + | 2.12132i | −0.221565 | + | 0.127920i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.863961 | − | 1.49642i | 0.0519104 | − | 0.0899114i | −0.838903 | − | 0.544282i | \(-0.816802\pi\) |
0.890813 | + | 0.454370i | \(0.150136\pi\) | |||||||
\(278\) | 5.76500 | + | 9.98528i | 0.345762 | + | 0.598877i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.12132 | + | 3.97141i | 0.306057 | + | 0.237337i | ||||
\(281\) | 22.2426i | 1.32688i | 0.748227 | + | 0.663442i | \(0.230905\pi\) | ||||
−0.748227 | + | 0.663442i | \(0.769095\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.2279 | − | 11.6786i | −1.20243 | − | 0.694220i | −0.241331 | − | 0.970443i | \(-0.577584\pi\) |
−0.961094 | + | 0.276222i | \(0.910917\pi\) | |||||||
\(284\) | −11.0227 | − | 6.36396i | −0.654077 | − | 0.377632i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 17.7408i | − | 1.04903i | ||||||
\(287\) | −2.44949 | − | 6.00000i | −0.144589 | − | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.50000 | + | 9.52628i | 0.323529 | + | 0.560369i | ||||
\(290\) | 12.5446 | − | 21.7279i | 0.736646 | − | 1.27591i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −13.2426 | + | 7.64564i | −0.774967 | + | 0.447427i | ||||
\(293\) | −7.94282 | −0.464024 | −0.232012 | − | 0.972713i | \(-0.574531\pi\) | ||||
−0.232012 | + | 0.972713i | \(0.574531\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6.00000 | −0.349334 | ||||||||
\(296\) | −2.80821 | + | 1.62132i | −0.163224 | + | 0.0942373i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.87868 | − | 6.71807i | 0.224686 | − | 0.389167i | ||||
\(299\) | −12.5446 | − | 21.7279i | −0.725474 | − | 1.25656i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7.00000 | − | 17.1464i | −0.403473 | − | 0.988304i | ||||
\(302\) | − | 17.2426i | − | 0.992202i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −4.24264 | − | 2.44949i | −0.243332 | − | 0.140488i | ||||
\(305\) | −1.52192 | − | 0.878680i | −0.0871448 | − | 0.0503131i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 2.57258i | − | 0.146825i | −0.997302 | − | 0.0734125i | \(-0.976611\pi\) | ||
0.997302 | − | 0.0734125i | \(-0.0233890\pi\) | |||||||
\(308\) | −8.87039 | − | 6.87868i | −0.505437 | − | 0.391949i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.87868 | − | 11.9142i | −0.390683 | − | 0.676682i | ||||
\(311\) | 8.57321 | − | 14.8492i | 0.486142 | − | 0.842023i | −0.513731 | − | 0.857951i | \(-0.671737\pi\) |
0.999873 | + | 0.0159282i | \(0.00507031\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.514719 | + | 0.297173i | −0.0290936 | + | 0.0167972i | −0.514476 | − | 0.857505i | \(-0.672014\pi\) |
0.485383 | + | 0.874302i | \(0.338680\pi\) | |||||||
\(314\) | 10.3923 | 0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.24264 | −0.519939 | ||||||||
\(317\) | 11.9142 | − | 6.87868i | 0.669169 | − | 0.386345i | −0.126592 | − | 0.991955i | \(-0.540404\pi\) |
0.795762 | + | 0.605610i | \(0.207071\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −21.7279 | + | 37.6339i | −1.21653 | + | 2.10709i | ||||
\(320\) | −1.22474 | − | 2.12132i | −0.0684653 | − | 0.118585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.7279 | − | 2.15232i | −0.876483 | − | 0.119944i | ||||
\(323\) | − | 12.0000i | − | 0.667698i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.62132 | − | 2.09077i | −0.200875 | − | 0.115975i | ||||
\(326\) | 6.48244 | + | 3.74264i | 0.359029 | + | 0.207286i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.44949i | 0.135250i | ||||||||
\(329\) | −12.8778 | + | 16.6066i | −0.709979 | + | 0.915552i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.00000 | − | 8.66025i | −0.274825 | − | 0.476011i | 0.695266 | − | 0.718752i | \(-0.255287\pi\) |
−0.970091 | + | 0.242742i | \(0.921953\pi\) | |||||||
\(332\) | 2.74666 | − | 4.75736i | 0.150743 | − | 0.261094i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 17.4853 | − | 10.0951i | 0.956752 | − | 0.552381i | ||||
\(335\) | 8.53716 | 0.466435 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.4558 | 1.60456 | 0.802281 | − | 0.596947i | \(-0.203620\pi\) | ||||
0.802281 | + | 0.596947i | \(0.203620\pi\) | |||||||
\(338\) | 3.88437 | − | 2.24264i | 0.211282 | − | 0.121984i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.00000 | − | 5.19615i | 0.162698 | − | 0.281801i | ||||
\(341\) | 11.9142 | + | 20.6360i | 0.645191 | + | 1.11750i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.0000 | + | 7.34847i | 0.917914 | + | 0.396780i | ||||
\(344\) | 7.00000i | 0.377415i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.0000 | + | 10.3923i | 0.967686 | + | 0.558694i | ||||
\(347\) | −25.0892 | − | 14.4853i | −1.34686 | − | 0.777611i | −0.359058 | − | 0.933315i | \(-0.616902\pi\) |
−0.987804 | + | 0.155705i | \(0.950235\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.3718i | 1.30459i | 0.757964 | + | 0.652296i | \(0.226194\pi\) | ||||
−0.757964 | + | 0.652296i | \(0.773806\pi\) | |||||||
\(350\) | −2.44949 | + | 1.00000i | −0.130931 | + | 0.0534522i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.12132 | + | 3.67423i | 0.113067 | + | 0.195837i | ||||
\(353\) | 15.2913 | − | 26.4853i | 0.813873 | − | 1.40967i | −0.0962614 | − | 0.995356i | \(-0.530688\pi\) |
0.910134 | − | 0.414313i | \(-0.135978\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 27.0000 | − | 15.5885i | 1.43301 | − | 0.827349i | ||||
\(356\) | −17.7408 | −0.940259 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.7279 | −0.989801 | ||||||||
\(359\) | −2.15232 | + | 1.24264i | −0.113595 | + | 0.0655841i | −0.555721 | − | 0.831369i | \(-0.687558\pi\) |
0.442126 | + | 0.896953i | \(0.354224\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.50000 | − | 4.33013i | 0.131579 | − | 0.227901i | ||||
\(362\) | −4.89898 | − | 8.48528i | −0.257485 | − | 0.445976i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.50000 | − | 10.9612i | 0.0786214 | − | 0.574521i | ||||
\(365\) | − | 37.4558i | − | 1.96053i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 7.97056 | + | 4.60181i | 0.416060 | + | 0.240212i | 0.693390 | − | 0.720562i | \(-0.256116\pi\) |
−0.277330 | + | 0.960775i | \(0.589450\pi\) | |||||||
\(368\) | 5.19615 | + | 3.00000i | 0.270868 | + | 0.156386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − | 7.94282i | − | 0.412927i | ||||||
\(371\) | −0.891519 | + | 6.51472i | −0.0462854 | + | 0.338227i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.0000 | + | 19.0526i | 0.569558 | + | 0.986504i | 0.996610 | + | 0.0822766i | \(0.0262191\pi\) |
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(374\) | −5.19615 | + | 9.00000i | −0.268687 | + | 0.465379i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.87868 | − | 3.97141i | 0.354741 | − | 0.204810i | ||||
\(377\) | −42.8300 | −2.20586 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.48528 | 0.487226 | 0.243613 | − | 0.969872i | \(-0.421667\pi\) | ||||
0.243613 | + | 0.969872i | \(0.421667\pi\) | |||||||
\(380\) | 10.3923 | − | 6.00000i | 0.533114 | − | 0.307794i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −10.6066 | + | 18.3712i | −0.542681 | + | 0.939951i | ||||
\(383\) | 7.64564 | + | 13.2426i | 0.390674 | + | 0.676667i | 0.992539 | − | 0.121931i | \(-0.0389086\pi\) |
−0.601865 | + | 0.798598i | \(0.705575\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 25.4558 | − | 10.3923i | 1.29735 | − | 0.529641i | ||||
\(386\) | − | 15.4853i | − | 0.788180i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.74264 | − | 3.31552i | −0.291538 | − | 0.168320i | ||||
\(389\) | −28.1331 | − | 16.2426i | −1.42640 | − | 0.823535i | −0.429569 | − | 0.903034i | \(-0.641334\pi\) |
−0.996835 | + | 0.0794995i | \(0.974668\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 14.6969i | 0.743256i | ||||||||
\(392\) | −4.89898 | − | 5.00000i | −0.247436 | − | 0.252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.48528 | − | 14.6969i | −0.427482 | − | 0.740421i | ||||
\(395\) | 11.3199 | − | 19.6066i | 0.569565 | − | 0.986515i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −25.8640 | + | 14.9326i | −1.29807 | + | 0.749444i | −0.980071 | − | 0.198646i | \(-0.936346\pi\) |
−0.318004 | + | 0.948090i | \(0.603012\pi\) | |||||||
\(398\) | −3.58719 | −0.179810 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 24.4588 | − | 14.1213i | 1.22142 | − | 0.705185i | 0.256197 | − | 0.966625i | \(-0.417531\pi\) |
0.965220 | + | 0.261440i | \(0.0841972\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.7426 | + | 20.3389i | −0.584943 | + | 1.01315i | ||||
\(404\) | −3.67423 | − | 6.36396i | −0.182800 | − | 0.316619i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16.6066 | + | 21.4150i | −0.824172 | + | 1.06281i | ||||
\(407\) | 13.7574i | 0.681927i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.7426 | − | 6.77962i | −0.580636 | − | 0.335230i | 0.180750 | − | 0.983529i | \(-0.442148\pi\) |
−0.761386 | + | 0.648299i | \(0.775481\pi\) | |||||||
\(410\) | −5.19615 | − | 3.00000i | −0.256620 | − | 0.148159i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 6.21076i | − | 0.305982i | ||||||
\(413\) | 6.42090 | + | 0.878680i | 0.315952 | + | 0.0432370i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.72792 | + | 11.6531i | 0.330261 | + | 0.572028i | ||||
\(416\) | −2.09077 | + | 3.62132i | −0.102508 | + | 0.177550i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −18.0000 | + | 10.3923i | −0.880409 | + | 0.508304i | ||||
\(419\) | −12.8418 | −0.627363 | −0.313681 | − | 0.949528i | \(-0.601562\pi\) | ||||
−0.313681 | + | 0.949528i | \(0.601562\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.4558 | 1.33812 | 0.669058 | − | 0.743210i | \(-0.266698\pi\) | ||||
0.669058 | + | 0.743210i | \(0.266698\pi\) | |||||||
\(422\) | 11.6786 | − | 6.74264i | 0.568505 | − | 0.328227i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.24264 | − | 2.15232i | 0.0603480 | − | 0.104526i | ||||
\(425\) | 1.22474 | + | 2.12132i | 0.0594089 | + | 0.102899i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.50000 | + | 1.16320i | 0.0725901 | + | 0.0562911i | ||||
\(428\) | 14.4853i | 0.700173i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −14.8492 | − | 8.57321i | −0.716094 | − | 0.413437i | ||||
\(431\) | −8.87039 | − | 5.12132i | −0.427272 | − | 0.246685i | 0.270912 | − | 0.962604i | \(-0.412675\pi\) |
−0.698184 | + | 0.715919i | \(0.746008\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.8213i | − | 1.28895i | −0.764626 | − | 0.644475i | \(-0.777076\pi\) | ||
0.764626 | − | 0.644475i | \(-0.222924\pi\) | |||||||
\(434\) | 5.61642 | + | 13.7574i | 0.269597 | + | 0.660374i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.86396 | + | 6.69258i | 0.185050 | + | 0.320516i | ||||
\(437\) | −14.6969 | + | 25.4558i | −0.703050 | + | 1.21772i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −21.7279 | + | 12.5446i | −1.03702 | + | 0.598722i | −0.918987 | − | 0.394288i | \(-0.870991\pi\) |
−0.118030 | + | 0.993010i | \(0.537658\pi\) | |||||||
\(440\) | −10.3923 | −0.495434 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.2426 | −0.487193 | ||||||||
\(443\) | −22.0454 | + | 12.7279i | −1.04741 | + | 0.604722i | −0.921923 | − | 0.387374i | \(-0.873382\pi\) |
−0.125486 | + | 0.992095i | \(0.540049\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.7279 | − | 37.6339i | 1.03000 | − | 1.78402i | ||||
\(446\) | 5.19615 | + | 9.00000i | 0.246045 | + | 0.426162i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | + | 2.44949i | 0.0472456 | + | 0.115728i | ||||
\(449\) | − | 30.7279i | − | 1.45014i | −0.688675 | − | 0.725070i | \(-0.741807\pi\) | ||
0.688675 | − | 0.725070i | \(-0.258193\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 9.00000 | + | 5.19615i | 0.423793 | + | 0.244677i | ||||
\(452\) | −1.52192 | − | 0.878680i | −0.0715850 | − | 0.0413296i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 4.30463i | − | 0.202026i | ||||||
\(455\) | 21.4150 | + | 16.6066i | 1.00395 | + | 0.778529i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.5000 | + | 19.9186i | 0.537947 | + | 0.931752i | 0.999014 | + | 0.0443868i | \(0.0141334\pi\) |
−0.461067 | + | 0.887365i | \(0.652533\pi\) | |||||||
\(458\) | −4.54026 | + | 7.86396i | −0.212152 | + | 0.367459i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −12.7279 | + | 7.34847i | −0.593442 | + | 0.342624i | ||||
\(461\) | 42.2357 | 1.96711 | 0.983556 | − | 0.180605i | \(-0.0578056\pi\) | ||||
0.983556 | + | 0.180605i | \(0.0578056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −22.0000 | −1.02243 | −0.511213 | − | 0.859454i | \(-0.670804\pi\) | ||||
−0.511213 | + | 0.859454i | \(0.670804\pi\) | |||||||
\(464\) | 8.87039 | − | 5.12132i | 0.411797 | − | 0.237751i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.75736 | − | 3.04384i | 0.0814081 | − | 0.141003i | ||||
\(467\) | 1.52192 | + | 2.63604i | 0.0704260 | + | 0.121981i | 0.899088 | − | 0.437768i | \(-0.144231\pi\) |
−0.828662 | + | 0.559749i | \(0.810897\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.13604 | − | 1.25024i | −0.421863 | − | 0.0577306i | ||||
\(470\) | 19.4558i | 0.897431i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.12132 | − | 1.22474i | −0.0976417 | − | 0.0563735i | ||||
\(473\) | 25.7196 | + | 14.8492i | 1.18259 | + | 0.682769i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 4.89898i | 0.224781i | ||||||||
\(476\) | −3.97141 | + | 5.12132i | −0.182029 | + | 0.234735i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 3.87868 | + | 6.71807i | 0.177407 | + | 0.307277i | ||||
\(479\) | −1.22474 | + | 2.12132i | −0.0559600 | + | 0.0969256i | −0.892648 | − | 0.450754i | \(-0.851155\pi\) |
0.836688 | + | 0.547679i | \(0.184489\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.7426 | + | 6.77962i | −0.535418 | + | 0.309124i | ||||
\(482\) | −18.4582 | −0.840749 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 14.0665 | − | 8.12132i | 0.638729 | − | 0.368770i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.0000 | + | 19.0526i | −0.498458 | + | 0.863354i | −0.999998 | − | 0.00178012i | \(-0.999433\pi\) |
0.501541 | + | 0.865134i | \(0.332767\pi\) | |||||||
\(488\) | −0.358719 | − | 0.621320i | −0.0162385 | − | 0.0281259i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 16.6066 | − | 4.26858i | 0.750210 | − | 0.192835i | ||||
\(491\) | − | 1.02944i | − | 0.0464579i | −0.999730 | − | 0.0232289i | \(-0.992605\pi\) | ||
0.999730 | − | 0.0232289i | \(-0.00739466\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.7279 | + | 12.5446i | 0.978576 | + | 0.564981i | ||||
\(494\) | −17.7408 | − | 10.2426i | −0.798195 | − | 0.460838i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 5.61642i | − | 0.252185i | ||||||
\(497\) | −31.1769 | + | 12.7279i | −1.39848 | + | 0.570925i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.2279 | − | 22.9114i | −0.592163 | − | 1.02566i | −0.993941 | − | 0.109919i | \(-0.964941\pi\) |
0.401777 | − | 0.915737i | \(-0.368393\pi\) | |||||||
\(500\) | 4.89898 | − | 8.48528i | 0.219089 | − | 0.379473i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.75736 | − | 2.74666i | 0.212331 | − | 0.122590i | ||||
\(503\) | 20.1903 | 0.900239 | 0.450120 | − | 0.892968i | \(-0.351381\pi\) | ||||
0.450120 | + | 0.892968i | \(0.351381\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 18.0000 | 0.800989 | ||||||||
\(506\) | 22.0454 | − | 12.7279i | 0.980038 | − | 0.565825i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 8.86396 | − | 15.3528i | 0.393275 | − | 0.681172i | ||||
\(509\) | 14.9941 | + | 25.9706i | 0.664602 | + | 1.15112i | 0.979393 | + | 0.201964i | \(0.0647323\pi\) |
−0.314791 | + | 0.949161i | \(0.601934\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.48528 | + | 40.0834i | −0.242655 | + | 1.77318i | ||||
\(512\) | − | 1.00000i | − | 0.0441942i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.72792 | + | 2.15232i | 0.164432 | + | 0.0949346i | ||||
\(515\) | 13.1750 | + | 7.60660i | 0.580561 | + | 0.335187i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 33.6985i | − | 1.48206i | ||||||
\(518\) | −1.16320 | + | 8.50000i | −0.0511080 | + | 0.373469i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −5.12132 | − | 8.87039i | −0.224585 | − | 0.388992i | ||||
\(521\) | 4.60181 | − | 7.97056i | 0.201609 | − | 0.349197i | −0.747438 | − | 0.664331i | \(-0.768716\pi\) |
0.949047 | + | 0.315135i | \(0.102050\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.2574 | − | 8.80884i | 0.667158 | − | 0.385184i | −0.127841 | − | 0.991795i | \(-0.540805\pi\) |
0.794999 | + | 0.606611i | \(0.207471\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.7279 | 0.816576 | ||||||||
\(527\) | 11.9142 | − | 6.87868i | 0.518992 | − | 0.299640i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 6.50000 | − | 11.2583i | 0.282609 | − | 0.489493i | ||||
\(530\) | 3.04384 | + | 5.27208i | 0.132216 | + | 0.229004i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −12.0000 | + | 4.89898i | −0.520266 | + | 0.212398i | ||||
\(533\) | 10.2426i | 0.443658i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −30.7279 | − | 17.7408i | −1.32848 | − | 0.767001i | ||||
\(536\) | 3.01834 | + | 1.74264i | 0.130373 | + | 0.0752706i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 9.79796i | − | 0.422420i | ||||||
\(539\) | −28.7635 | + | 7.39340i | −1.23893 | + | 0.318456i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.7279 | − | 39.3659i | −0.977150 | − | 1.69247i | −0.672651 | − | 0.739960i | \(-0.734844\pi\) |
−0.304499 | − | 0.952513i | \(-0.598489\pi\) | |||||||
\(542\) | −7.70719 | + | 13.3492i | −0.331052 | + | 0.573399i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.12132 | − | 1.22474i | 0.0909509 | − | 0.0525105i | ||||
\(545\) | −18.9295 | −0.810849 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.02944 | 0.257800 | 0.128900 | − | 0.991658i | \(-0.458855\pi\) | ||||
0.128900 | + | 0.991658i | \(0.458855\pi\) | |||||||
\(548\) | 5.19615 | − | 3.00000i | 0.221969 | − | 0.128154i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.12132 | − | 3.67423i | 0.0904534 | − | 0.156670i | ||||
\(551\) | 25.0892 | + | 43.4558i | 1.06884 | + | 1.85128i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −14.9853 | + | 19.3242i | −0.637239 | + | 0.821750i | ||||
\(554\) | 1.72792i | 0.0734124i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −9.98528 | − | 5.76500i | −0.423470 | − | 0.244491i | ||||
\(557\) | −18.3712 | − | 10.6066i | −0.778412 | − | 0.449416i | 0.0574555 | − | 0.998348i | \(-0.481701\pi\) |
−0.835867 | + | 0.548932i | \(0.815035\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.2708i | 1.23802i | ||||||||
\(560\) | −6.42090 | − | 0.878680i | −0.271332 | − | 0.0371310i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.1213 | − | 19.2627i | −0.469125 | − | 0.812548i | ||||
\(563\) | −8.23999 | + | 14.2721i | −0.347274 | + | 0.601496i | −0.985764 | − | 0.168134i | \(-0.946226\pi\) |
0.638490 | + | 0.769630i | \(0.279559\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3.72792 | − | 2.15232i | 0.156835 | − | 0.0905486i | ||||
\(566\) | 23.3572 | 0.981776 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.7279 | 0.534052 | ||||||||
\(569\) | 1.52192 | − | 0.878680i | 0.0638021 | − | 0.0368362i | −0.467760 | − | 0.883856i | \(-0.654939\pi\) |
0.531562 | + | 0.847020i | \(0.321605\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 11.0000 | − | 19.0526i | 0.460336 | − | 0.797325i | −0.538642 | − | 0.842535i | \(-0.681062\pi\) |
0.998978 | + | 0.0452101i | \(0.0143957\pi\) | |||||||
\(572\) | 8.87039 | + | 15.3640i | 0.370890 | + | 0.642399i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 5.12132 | + | 3.97141i | 0.213760 | + | 0.165763i | ||||
\(575\) | − | 6.00000i | − | 0.250217i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 15.2574 | + | 8.80884i | 0.635172 | + | 0.366717i | 0.782752 | − | 0.622333i | \(-0.213815\pi\) |
−0.147580 | + | 0.989050i | \(0.547148\pi\) | |||||||
\(578\) | −9.52628 | − | 5.50000i | −0.396241 | − | 0.228770i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 25.0892i | 1.04177i | ||||||||
\(581\) | −5.49333 | − | 13.4558i | −0.227902 | − | 0.558242i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.27208 | − | 9.13151i | −0.218347 | − | 0.378188i | ||||
\(584\) | 7.64564 | − | 13.2426i | 0.316379 | − | 0.547984i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.87868 | − | 3.97141i | 0.284156 | − | 0.164057i | ||||
\(587\) | 11.6531 | 0.480975 | 0.240488 | − | 0.970652i | \(-0.422693\pi\) | ||||
0.240488 | + | 0.970652i | \(0.422693\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 27.5147 | 1.13372 | ||||||||
\(590\) | 5.19615 | − | 3.00000i | 0.213922 | − | 0.123508i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.62132 | − | 2.80821i | 0.0666359 | − | 0.115417i | ||||
\(593\) | 11.3199 | + | 19.6066i | 0.464852 | + | 0.805147i | 0.999195 | − | 0.0401210i | \(-0.0127743\pi\) |
−0.534343 | + | 0.845268i | \(0.679441\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.00000 | − | 14.6969i | −0.245976 | − | 0.602516i | ||||
\(596\) | 7.75736i | 0.317754i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 21.7279 | + | 12.5446i | 0.888521 | + | 0.512988i | ||||
\(599\) | −17.7408 | − | 10.2426i | −0.724868 | − | 0.418503i | 0.0916735 | − | 0.995789i | \(-0.470778\pi\) |
−0.816542 | + | 0.577286i | \(0.804112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 17.2695i | − | 0.704438i | −0.935918 | − | 0.352219i | \(-0.885427\pi\) | ||
0.935918 | − | 0.352219i | \(-0.114573\pi\) | |||||||
\(602\) | 14.6354 | + | 11.3492i | 0.596494 | + | 0.462561i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.62132 | + | 14.9326i | 0.350797 | + | 0.607597i | ||||
\(605\) | −8.57321 | + | 14.8492i | −0.348551 | + | 0.603708i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.7574 | − | 13.1390i | 0.923693 | − | 0.533294i | 0.0388815 | − | 0.999244i | \(-0.487621\pi\) |
0.884811 | + | 0.465950i | \(0.154287\pi\) | |||||||
\(608\) | 4.89898 | 0.198680 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.75736 | 0.0711534 | ||||||||
\(611\) | 28.7635 | − | 16.6066i | 1.16365 | − | 0.671831i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7.10660 | + | 12.3090i | −0.287033 | + | 0.497156i | −0.973100 | − | 0.230383i | \(-0.926002\pi\) |
0.686067 | + | 0.727538i | \(0.259336\pi\) | |||||||
\(614\) | 1.28629 | + | 2.22792i | 0.0519105 | + | 0.0899116i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.1213 | + | 1.52192i | 0.448091 | + | 0.0613198i | ||||
\(617\) | 4.24264i | 0.170802i | 0.996347 | + | 0.0854011i | \(0.0272172\pi\) | ||||
−0.996347 | + | 0.0854011i | \(0.972783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −27.9853 | − | 16.1573i | −1.12482 | − | 0.649417i | −0.182196 | − | 0.983262i | \(-0.558320\pi\) |
−0.942628 | + | 0.333845i | \(0.891654\pi\) | |||||||
\(620\) | 11.9142 | + | 6.87868i | 0.478487 | + | 0.276254i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.1464i | 0.687509i | ||||||||
\(623\) | −28.7635 | + | 37.0919i | −1.15238 | + | 1.48605i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | + | 25.1147i | 0.580000 | + | 1.00459i | ||||
\(626\) | 0.297173 | − | 0.514719i | 0.0118774 | − | 0.0205723i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −9.00000 | + | 5.19615i | −0.359139 | + | 0.207349i | ||||
\(629\) | 7.94282 | 0.316701 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2426 | −0.925275 | −0.462637 | − | 0.886548i | \(-0.653097\pi\) | ||||
−0.462637 | + | 0.886548i | \(0.653097\pi\) | |||||||
\(632\) | 8.00436 | − | 4.62132i | 0.318396 | − | 0.183826i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.87868 | + | 11.9142i | −0.273187 | + | 0.473174i | ||||
\(635\) | 21.7122 | + | 37.6066i | 0.861622 | + | 1.49237i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.4853 | − | 20.9077i | −0.811656 | − | 0.828393i | ||||
\(638\) | − | 43.4558i | − | 1.72043i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.12132 | + | 1.22474i | 0.0838525 | + | 0.0484123i | ||||
\(641\) | 7.97887 | + | 4.60660i | 0.315146 | + | 0.181950i | 0.649227 | − | 0.760595i | \(-0.275092\pi\) |
−0.334081 | + | 0.942544i | \(0.608426\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 1.73205i | − | 0.0683054i | −0.999417 | − | 0.0341527i | \(-0.989127\pi\) | ||
0.999417 | − | 0.0341527i | \(-0.0108733\pi\) | |||||||
\(644\) | 14.6969 | − | 6.00000i | 0.579141 | − | 0.236433i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.00000 | + | 10.3923i | 0.236067 | + | 0.408880i | ||||
\(647\) | 10.3923 | − | 18.0000i | 0.408564 | − | 0.707653i | −0.586165 | − | 0.810191i | \(-0.699363\pi\) |
0.994729 | + | 0.102538i | \(0.0326965\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | + | 5.19615i | −0.353281 | + | 0.203967i | ||||
\(650\) | 4.18154 | 0.164014 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.48528 | −0.293146 | ||||||||
\(653\) | −12.5446 | + | 7.24264i | −0.490909 | + | 0.283426i | −0.724951 | − | 0.688800i | \(-0.758138\pi\) |
0.234043 | + | 0.972226i | \(0.424805\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.22474 | − | 2.12132i | −0.0478183 | − | 0.0828236i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.84924 | − | 20.8207i | 0.111075 | − | 0.811674i | ||||
\(659\) | − | 13.7574i | − | 0.535911i | −0.963431 | − | 0.267955i | \(-0.913652\pi\) | ||
0.963431 | − | 0.267955i | \(-0.0863480\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.24264 | + | 2.44949i | 0.165020 | + | 0.0952741i | 0.580235 | − | 0.814449i | \(-0.302961\pi\) |
−0.415216 | + | 0.909723i | \(0.636294\pi\) | |||||||
\(662\) | 8.66025 | + | 5.00000i | 0.336590 | + | 0.194331i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 5.49333i | 0.213182i | ||||||||
\(665\) | 4.30463 | − | 31.4558i | 0.166927 | − | 1.21981i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −30.7279 | − | 53.2223i | −1.18979 | − | 2.06078i | ||||
\(668\) | −10.0951 | + | 17.4853i | −0.390592 | + | 0.676526i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −7.39340 | + | 4.26858i | −0.285632 | + | 0.164910i | ||||
\(671\) | −3.04384 | −0.117506 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.45584 | 0.210307 | 0.105154 | − | 0.994456i | \(-0.466467\pi\) | ||||
0.105154 | + | 0.994456i | \(0.466467\pi\) | |||||||
\(674\) | −25.5095 | + | 14.7279i | −0.982590 | + | 0.567298i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.24264 | + | 3.88437i | −0.0862554 | + | 0.149399i | ||||
\(677\) | 7.34847 | + | 12.7279i | 0.282425 | + | 0.489174i | 0.971981 | − | 0.235058i | \(-0.0755280\pi\) |
−0.689557 | + | 0.724232i | \(0.742195\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.2426 | + | 6.63103i | −0.623335 | + | 0.254476i | ||||
\(680\) | 6.00000i | 0.230089i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −20.6360 | − | 11.9142i | −0.790195 | − | 0.456219i | ||||
\(683\) | −1.52192 | − | 0.878680i | −0.0582346 | − | 0.0336217i | 0.470600 | − | 0.882347i | \(-0.344037\pi\) |
−0.528835 | + | 0.848725i | \(0.677371\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6969i | 0.561541i | ||||||||
\(686\) | −18.3967 | + | 2.13604i | −0.702388 | + | 0.0815543i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.50000 | − | 6.06218i | −0.133436 | − | 0.231118i | ||||
\(689\) | 5.19615 | − | 9.00000i | 0.197958 | − | 0.342873i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −23.2279 | + | 13.4106i | −0.883632 | + | 0.510165i | −0.871854 | − | 0.489766i | \(-0.837082\pi\) |
−0.0117776 | + | 0.999931i | \(0.503749\pi\) | |||||||
\(692\) | −20.7846 | −0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.9706 | 1.09971 | ||||||||
\(695\) | 24.4588 | − | 14.1213i | 0.927777 | − | 0.535652i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | − | 5.19615i | 0.113633 | − | 0.196818i | ||||
\(698\) | −12.1859 | − | 21.1066i | −0.461243 | − | 0.798897i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.62132 | − | 2.09077i | 0.0612801 | − | 0.0790237i | ||||
\(701\) | − | 3.51472i | − | 0.132749i | −0.997795 | − | 0.0663745i | \(-0.978857\pi\) | ||
0.997795 | − | 0.0663745i | \(-0.0211432\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.7574 | + | 7.94282i | 0.518869 | + | 0.299569i | ||||
\(704\) | −3.67423 | − | 2.12132i | −0.138478 | − | 0.0799503i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 30.5826i | 1.15099i | ||||||||
\(707\) | −19.2627 | − | 2.63604i | −0.724448 | − | 0.0991384i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.1066 | + | 22.7013i | 0.492229 | + | 0.852565i | 0.999960 | − | 0.00895033i | \(-0.00284902\pi\) |
−0.507731 | + | 0.861516i | \(0.669516\pi\) | |||||||
\(710\) | −15.5885 | + | 27.0000i | −0.585024 | + | 1.01329i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.3640 | − | 8.87039i | 0.575789 | − | 0.332432i | ||||
\(713\) | −33.6985 | −1.26202 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43.4558 | −1.62516 | ||||||||
\(716\) | 16.2189 | − | 9.36396i | 0.606127 | − | 0.349948i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.24264 | − | 2.15232i | 0.0463749 | − | 0.0803237i | ||||
\(719\) | −5.52938 | − | 9.57716i | −0.206211 | − | 0.357168i | 0.744307 | − | 0.667838i | \(-0.232780\pi\) |
−0.950518 | + | 0.310670i | \(0.899447\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −12.9853 | − | 10.0696i | −0.483597 | − | 0.375013i | ||||
\(722\) | 5.00000i | 0.186081i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 8.48528 | + | 4.89898i | 0.315353 | + | 0.182069i | ||||
\(725\) | −8.87039 | − | 5.12132i | −0.329438 | − | 0.190201i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 45.4026i | 1.68389i | 0.539564 | + | 0.841945i | \(0.318589\pi\) | ||||
−0.539564 | + | 0.841945i | \(0.681411\pi\) | |||||||
\(728\) | 4.18154 | + | 10.2426i | 0.154978 | + | 0.379618i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 18.7279 | + | 32.4377i | 0.693151 | + | 1.20057i | ||||
\(731\) | 8.57321 | − | 14.8492i | 0.317092 | − | 0.549219i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 13.8640 | − | 8.00436i | 0.512077 | − | 0.295648i | −0.221610 | − | 0.975135i | \(-0.571131\pi\) |
0.733687 | + | 0.679488i | \(0.237798\pi\) | |||||||
\(734\) | −9.20361 | −0.339712 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | 12.8057 | − | 7.39340i | 0.471706 | − | 0.272339i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.2279 | + | 36.7678i | −0.780882 | + | 1.35253i | 0.150547 | + | 0.988603i | \(0.451897\pi\) |
−0.931429 | + | 0.363924i | \(0.881437\pi\) | |||||||
\(740\) | 3.97141 | + | 6.87868i | 0.145992 | + | 0.252865i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.48528 | − | 6.08767i | −0.0912375 | − | 0.223485i | ||||
\(743\) | 6.72792i | 0.246824i | 0.992356 | + | 0.123412i | \(0.0393836\pi\) | ||||
−0.992356 | + | 0.123412i | \(0.960616\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16.4558 | − | 9.50079i | −0.602895 | − | 0.348082i | ||||
\(746\) | −19.0526 | − | 11.0000i | −0.697564 | − | 0.402739i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 10.3923i | − | 0.379980i | ||||||
\(749\) | 30.2854 | + | 23.4853i | 1.10660 | + | 0.858134i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.27208 | − | 2.20330i | −0.0464188 | − | 0.0803997i | 0.841882 | − | 0.539661i | \(-0.181448\pi\) |
−0.888301 | + | 0.459261i | \(0.848114\pi\) | |||||||
\(752\) | −3.97141 | + | 6.87868i | −0.144822 | + | 0.250840i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 37.0919 | − | 21.4150i | 1.35081 | − | 0.779889i | ||||
\(755\) | −42.2357 | −1.53711 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.2426 | 1.49899 | 0.749495 | − | 0.662010i | \(-0.230297\pi\) | ||||
0.749495 | + | 0.662010i | \(0.230297\pi\) | |||||||
\(758\) | −8.21449 | + | 4.74264i | −0.298364 | + | 0.172260i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.00000 | + | 10.3923i | −0.217643 | + | 0.376969i | ||||
\(761\) | −12.2474 | − | 21.2132i | −0.443970 | − | 0.768978i | 0.554010 | − | 0.832510i | \(-0.313097\pi\) |
−0.997980 | + | 0.0635319i | \(0.979764\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.2574 | + | 2.77216i | 0.733366 | + | 0.100359i | ||||
\(764\) | − | 21.2132i | − | 0.767467i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −13.2426 | − | 7.64564i | −0.478476 | − | 0.276248i | ||||
\(767\) | −8.87039 | − | 5.12132i | −0.320291 | − | 0.184920i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 1.18869i | − | 0.0428653i | −0.999770 | − | 0.0214327i | \(-0.993177\pi\) | ||
0.999770 | − | 0.0214327i | \(-0.00682275\pi\) | |||||||
\(770\) | −16.8493 | + | 21.7279i | −0.607205 | + | 0.783020i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.74264 | + | 13.4106i | 0.278664 | + | 0.482660i | ||||
\(773\) | 4.89898 | − | 8.48528i | 0.176204 | − | 0.305194i | −0.764373 | − | 0.644774i | \(-0.776951\pi\) |
0.940577 | + | 0.339580i | \(0.110285\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −4.86396 | + | 2.80821i | −0.174719 | + | 0.100874i | ||||
\(776\) | 6.63103 | 0.238040 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.4853 | 1.16465 | ||||||||
\(779\) | 10.3923 | − | 6.00000i | 0.372343 | − | 0.214972i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.0000 | − | 46.7654i | 0.966136 | − | 1.67340i | ||||
\(782\) | −7.34847 | − | 12.7279i | −0.262781 | − | 0.455150i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6.74264 | + | 1.88064i | 0.240809 | + | 0.0671656i | ||||
\(785\) | − | 25.4558i | − | 0.908558i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 9.47056 | + | 5.46783i | 0.337589 | + | 0.194907i | 0.659205 | − | 0.751963i | \(-0.270893\pi\) |
−0.321616 | + | 0.946870i | \(0.604226\pi\) | |||||||
\(788\) | 14.6969 | + | 8.48528i | 0.523557 | + | 0.302276i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 22.6398i | 0.805486i | ||||||||
\(791\) | −4.30463 | + | 1.75736i | −0.153055 | + | 0.0624845i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.50000 | − | 2.59808i | −0.0532666 | − | 0.0922604i | ||||
\(794\) | 14.9326 | − | 25.8640i | 0.529937 | − | 0.917878i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.10660 | − | 1.79360i | 0.110111 | − | 0.0635724i | ||||
\(797\) | 3.04384 | 0.107818 | 0.0539091 | − | 0.998546i | \(-0.482832\pi\) | ||||
0.0539091 | + | 0.998546i | \(0.482832\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −19.4558 | −0.688298 | ||||||||
\(800\) | −0.866025 | + | 0.500000i | −0.0306186 | + | 0.0176777i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.1213 | + | 24.4588i | −0.498641 | + | 0.863672i | ||||
\(803\) | −32.4377 | − | 56.1838i | −1.14470 | − | 1.98268i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.27208 | + | 38.5254i | −0.185816 | + | 1.35784i | ||||
\(806\) | − | 23.4853i | − | 0.827234i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6.36396 | + | 3.67423i | 0.223883 | + | 0.129259i | ||||
\(809\) | 2.15232 | + | 1.24264i | 0.0756714 | + | 0.0436889i | 0.537358 | − | 0.843354i | \(-0.319422\pi\) |
−0.461687 | + | 0.887043i | \(0.652756\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 3.67423 | − | 26.8492i | 0.128940 | − | 0.942224i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −6.87868 | − | 11.9142i | −0.241098 | − | 0.417593i | ||||
\(815\) | 9.16756 | − | 15.8787i | 0.321126 | − | 0.556206i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.6985 | − | 17.1464i | 1.03902 | − | 0.599878i | ||||
\(818\) | 13.5592 | 0.474087 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | 9.50079 | − | 5.48528i | 0.331580 | − | 0.191438i | −0.324963 | − | 0.945727i | \(-0.605352\pi\) |
0.656542 | + | 0.754289i | \(0.272018\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.62132 | − | 9.73641i | 0.195947 | − | 0.339390i | −0.751264 | − | 0.660002i | \(-0.770555\pi\) |
0.947211 | + | 0.320612i | \(0.103889\pi\) | |||||||
\(824\) | 3.10538 | + | 5.37868i | 0.108181 | + | 0.187375i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.00000 | + | 2.44949i | −0.208767 | + | 0.0852286i | ||||
\(827\) | 20.4853i | 0.712343i | 0.934421 | + | 0.356172i | \(0.115918\pi\) | ||||
−0.934421 | + | 0.356172i | \(0.884082\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.48528 | − | 4.89898i | −0.294706 | − | 0.170149i | 0.345356 | − | 0.938472i | \(-0.387758\pi\) |
−0.640062 | + | 0.768323i | \(0.721091\pi\) | |||||||
\(830\) | −11.6531 | − | 6.72792i | −0.404485 | − | 0.233530i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.18154i | − | 0.144969i | ||||||
\(833\) | 4.26858 | + | 16.6066i | 0.147898 | + | 0.575385i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −24.7279 | − | 42.8300i | −0.855745 | − | 1.48219i | ||||
\(836\) | 10.3923 | − | 18.0000i | 0.359425 | − | 0.622543i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.1213 | − | 6.42090i | 0.384180 | − | 0.221806i | ||||
\(839\) | −5.49333 | −0.189651 | −0.0948253 | − | 0.995494i | \(-0.530229\pi\) | ||||
−0.0948253 | + | 0.995494i | \(0.530229\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −75.9117 | −2.61764 | ||||||||
\(842\) | −23.7775 | + | 13.7279i | −0.819425 | + | 0.473095i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −6.74264 | + | 11.6786i | −0.232091 | + | 0.401994i | ||||
\(845\) | −5.49333 | − | 9.51472i | −0.188976 | − | 0.327316i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 11.3492 | − | 14.6354i | 0.389965 | − | 0.502878i | ||||
\(848\) | 2.48528i | 0.0853449i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.12132 | − | 1.22474i | −0.0727607 | − | 0.0420084i | ||||
\(851\) | −16.8493 | − | 9.72792i | −0.577585 | − | 0.333469i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 51.3672i | 1.75878i | 0.476103 | + | 0.879389i | \(0.342049\pi\) | ||||
−0.476103 | + | 0.879389i | \(0.657951\pi\) | |||||||
\(854\) | −1.88064 | − | 0.257359i | −0.0643541 | − | 0.00880665i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.24264 | − | 12.5446i | −0.247548 | − | 0.428766i | ||||
\(857\) | 3.37706 | − | 5.84924i | 0.115358 | − | 0.199806i | −0.802565 | − | 0.596565i | \(-0.796532\pi\) |
0.917923 | + | 0.396759i | \(0.129865\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.47056 | + | 5.46783i | −0.323131 | + | 0.186560i | −0.652787 | − | 0.757541i | \(-0.726401\pi\) |
0.329656 | + | 0.944101i | \(0.393067\pi\) | |||||||
\(860\) | 17.1464 | 0.584688 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.2426 | 0.348866 | ||||||||
\(863\) | 11.6531 | − | 6.72792i | 0.396676 | − | 0.229021i | −0.288373 | − | 0.957518i | \(-0.593114\pi\) |
0.685049 | + | 0.728497i | \(0.259781\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.4558 | − | 44.0908i | 0.865525 | − | 1.49913i | ||||
\(866\) | 13.4106 | + | 23.2279i | 0.455712 | + | 0.789317i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.7426 | − | 9.10601i | −0.398571 | − | 0.309078i | ||||
\(869\) | − | 39.2132i | − | 1.33022i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.6213 | + | 7.28692i | 0.427657 | + | 0.246908i | ||||
\(872\) | −6.69258 | − | 3.86396i | −0.226639 | − | 0.130850i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 29.3939i | − | 0.994263i | ||||||
\(875\) | −9.79796 | − | 24.0000i | −0.331231 | − | 0.811348i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.89340 | + | 3.27946i | 0.0639355 | + | 0.110740i | 0.896221 | − | 0.443607i | \(-0.146301\pi\) |
−0.832286 | + | 0.554347i | \(0.812968\pi\) | |||||||
\(878\) | 12.5446 | − | 21.7279i | 0.423360 | − | 0.733282i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 9.00000 | − | 5.19615i | 0.303390 | − | 0.175162i | ||||
\(881\) | −4.30463 | −0.145027 | −0.0725134 | − | 0.997367i | \(-0.523102\pi\) | ||||
−0.0725134 | + | 0.997367i | \(0.523102\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.00000 | −0.0673054 | −0.0336527 | − | 0.999434i | \(-0.510714\pi\) | ||||
−0.0336527 | + | 0.999434i | \(0.510714\pi\) | |||||||
\(884\) | 8.87039 | − | 5.12132i | 0.298343 | − | 0.172249i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 12.7279 | − | 22.0454i | 0.427603 | − | 0.740630i | ||||
\(887\) | −14.9941 | − | 25.9706i | −0.503453 | − | 0.872006i | −0.999992 | − | 0.00399177i | \(-0.998729\pi\) |
0.496539 | − | 0.868014i | \(-0.334604\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −17.7279 | − | 43.4244i | −0.594575 | − | 1.45641i | ||||
\(890\) | 43.4558i | 1.45664i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −9.00000 | − | 5.19615i | −0.301342 | − | 0.173980i | ||||
\(893\) | −33.6985 | − | 19.4558i | −1.12768 | − | 0.651065i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.8739i | 1.53339i | ||||||||
\(896\) | −2.09077 | − | 1.62132i | −0.0698477 | − | 0.0541645i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 15.3640 | + | 26.6112i | 0.512702 | + | 0.888026i | ||||
\(899\) | −28.7635 | + | 49.8198i | −0.959316 | + | 1.66158i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.27208 | + | 3.04384i | −0.175638 | + | 0.101405i | ||||
\(902\) | −10.3923 | −0.346026 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.75736 | 0.0584489 | ||||||||
\(905\) | −20.7846 | + | 12.0000i | −0.690904 | + | 0.398893i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −1.74264 | + | 3.01834i | −0.0578634 | + | 0.100222i | −0.893506 | − | 0.449051i | \(-0.851762\pi\) |
0.835643 | + | 0.549273i | \(0.185095\pi\) | |||||||
\(908\) | 2.15232 | + | 3.72792i | 0.0714271 | + | 0.123715i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −26.8492 | − | 3.67423i | −0.890044 | − | 0.121800i | ||||
\(911\) | 1.75736i | 0.0582239i | 0.999576 | + | 0.0291120i | \(0.00926793\pi\) | ||||
−0.999576 | + | 0.0291120i | \(0.990732\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.1838 | + | 11.6531i | 0.667985 | + | 0.385661i | ||||
\(914\) | −19.9186 | − | 11.5000i | −0.658848 | − | 0.380386i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 9.08052i | − | 0.300029i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −0.136039 | − | 0.235626i | −0.00448751 | − | 0.00777260i | 0.863773 | − | 0.503881i | \(-0.168095\pi\) |
−0.868260 | + | 0.496109i | \(0.834762\pi\) | |||||||
\(920\) | 7.34847 | − | 12.7279i | 0.242272 | − | 0.419627i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −36.5772 | + | 21.1178i | −1.20460 | + | 0.695479i | ||||
\(923\) | 53.2223 | 1.75183 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.24264 | −0.106617 | ||||||||
\(926\) | 19.0526 | − | 11.0000i | 0.626106 | − | 0.361482i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.12132 | + | 8.87039i | −0.168116 | + | 0.291185i | ||||
\(929\) | 16.8132 | + | 29.1213i | 0.551623 | + | 0.955440i | 0.998158 | + | 0.0606731i | \(0.0193247\pi\) |
−0.446534 | + | 0.894766i | \(0.647342\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.21320 | + | 33.0321i | −0.301951 | + | 1.08258i | ||||
\(932\) | 3.51472i | 0.115128i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −2.63604 | − | 1.52192i | −0.0862538 | − | 0.0497987i | ||||
\(935\) | 22.0454 | + | 12.7279i | 0.720962 | + | 0.416248i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 53.0992i | − | 1.73468i | −0.497719 | − | 0.867338i | \(-0.665829\pi\) | ||
0.497719 | − | 0.867338i | \(-0.334171\pi\) | |||||||
\(938\) | 8.53716 | − | 3.48528i | 0.278748 | − | 0.113798i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.72792 | − | 16.8493i | −0.317290 | − | 0.549562i | ||||
\(941\) | −10.7255 | + | 18.5772i | −0.349642 | + | 0.605598i | −0.986186 | − | 0.165643i | \(-0.947030\pi\) |
0.636544 | + | 0.771241i | \(0.280364\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.7279 | + | 7.34847i | −0.414478 | + | 0.239299i | ||||
\(944\) | 2.44949 | 0.0797241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.6985 | −0.965581 | ||||||||
\(947\) | 6.71807 | − | 3.87868i | 0.218308 | − | 0.126040i | −0.386859 | − | 0.922139i | \(-0.626440\pi\) |
0.605167 | + | 0.796099i | \(0.293107\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.9706 | − | 55.3746i | 1.03781 | − | 1.79754i | ||||
\(950\) | −2.44949 | − | 4.24264i | −0.0794719 | − | 0.137649i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.878680 | − | 6.42090i | 0.0284782 | − | 0.208102i | ||||
\(953\) | 34.9706i | 1.13281i | 0.824128 | + | 0.566404i | \(0.191666\pi\) | ||||
−0.824128 | + | 0.566404i | \(0.808334\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 45.0000 | + | 25.9808i | 1.45617 | + | 0.840718i | ||||
\(956\) | −6.71807 | − | 3.87868i | −0.217278 | − | 0.125445i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 2.44949i | − | 0.0791394i | ||||||
\(959\) | 2.15232 | − | 15.7279i | 0.0695019 | − | 0.507881i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.272078 | + | 0.471253i | 0.00877671 | + | 0.0152017i | ||||
\(962\) | 6.77962 | − | 11.7426i | 0.218584 | − | 0.378598i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 15.9853 | − | 9.22911i | 0.514851 | − | 0.297250i | ||||
\(965\) | −37.9310 | −1.22104 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.6985 | 0.536987 | 0.268494 | − | 0.963281i | \(-0.413474\pi\) | ||||
0.268494 | + | 0.963281i | \(0.413474\pi\) | |||||||
\(968\) | −6.06218 | + | 3.50000i | −0.194846 | + | 0.112494i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.12132 | + | 14.0665i | −0.260760 | + | 0.451649i | ||||
\(971\) | −0.594346 | − | 1.02944i | −0.0190735 | − | 0.0330362i | 0.856331 | − | 0.516427i | \(-0.172738\pi\) |
−0.875405 | + | 0.483391i | \(0.839405\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −28.2426 | + | 11.5300i | −0.905417 | + | 0.369635i | ||||
\(974\) | − | 22.0000i | − | 0.704925i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.621320 | + | 0.358719i | 0.0198880 | + | 0.0114823i | ||||
\(977\) | 5.19615 | + | 3.00000i | 0.166240 | + | 0.0959785i | 0.580812 | − | 0.814038i | \(-0.302735\pi\) |
−0.414572 | + | 0.910017i | \(0.636069\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 75.2677i | − | 2.40557i | ||||||
\(980\) | −12.2474 | + | 12.0000i | −0.391230 | + | 0.383326i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0.514719 | + | 0.891519i | 0.0164253 | + | 0.0284495i | ||||
\(983\) | 9.16756 | − | 15.8787i | 0.292400 | − | 0.506451i | −0.681977 | − | 0.731374i | \(-0.738880\pi\) |
0.974377 | + | 0.224922i | \(0.0722129\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −36.0000 | + | 20.7846i | −1.14706 | + | 0.662253i | ||||
\(986\) | −25.0892 | −0.799004 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.4853 | 0.651724 | ||||||||
\(989\) | −36.3731 | + | 21.0000i | −1.15660 | + | 0.667761i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11.1066 | + | 19.2372i | −0.352813 | + | 0.611090i | −0.986741 | − | 0.162302i | \(-0.948108\pi\) |
0.633928 | + | 0.773392i | \(0.281441\pi\) | |||||||
\(992\) | 2.80821 | + | 4.86396i | 0.0891607 | + | 0.154431i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 20.6360 | − | 26.6112i | 0.654535 | − | 0.844055i | ||||
\(995\) | 8.78680i | 0.278560i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.13604 | + | 2.38794i | 0.130990 | + | 0.0756269i | 0.564063 | − | 0.825732i | \(-0.309238\pi\) |
−0.433073 | + | 0.901359i | \(0.642571\pi\) | |||||||
\(998\) | 22.9114 | + | 13.2279i | 0.725249 | + | 0.418723i | ||||
\(999\) | 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 | 378.2.k.d.269.2 | yes | 8 | |
3.2 | odd | 2 | inner | 378.2.k.d.269.3 | yes | 8 | |
7.3 | odd | 6 | 2646.2.d.d.2645.3 | 8 | |||
7.4 | even | 3 | 2646.2.d.d.2645.1 | 8 | |||
7.5 | odd | 6 | inner | 378.2.k.d.215.3 | yes | 8 | |
9.2 | odd | 6 | 1134.2.t.f.1025.2 | 8 | |||
9.4 | even | 3 | 1134.2.l.e.269.2 | 8 | |||
9.5 | odd | 6 | 1134.2.l.e.269.3 | 8 | |||
9.7 | even | 3 | 1134.2.t.f.1025.3 | 8 | |||
21.5 | even | 6 | inner | 378.2.k.d.215.2 | ✓ | 8 | |
21.11 | odd | 6 | 2646.2.d.d.2645.8 | 8 | |||
21.17 | even | 6 | 2646.2.d.d.2645.6 | 8 | |||
63.5 | even | 6 | 1134.2.t.f.593.3 | 8 | |||
63.40 | odd | 6 | 1134.2.t.f.593.2 | 8 | |||
63.47 | even | 6 | 1134.2.l.e.215.4 | 8 | |||
63.61 | odd | 6 | 1134.2.l.e.215.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.d.215.2 | ✓ | 8 | 21.5 | even | 6 | inner | |
378.2.k.d.215.3 | yes | 8 | 7.5 | odd | 6 | inner | |
378.2.k.d.269.2 | yes | 8 | 1.1 | even | 1 | trivial | |
378.2.k.d.269.3 | yes | 8 | 3.2 | odd | 2 | inner | |
1134.2.l.e.215.1 | 8 | 63.61 | odd | 6 | |||
1134.2.l.e.215.4 | 8 | 63.47 | even | 6 | |||
1134.2.l.e.269.2 | 8 | 9.4 | even | 3 | |||
1134.2.l.e.269.3 | 8 | 9.5 | odd | 6 | |||
1134.2.t.f.593.2 | 8 | 63.40 | odd | 6 | |||
1134.2.t.f.593.3 | 8 | 63.5 | even | 6 | |||
1134.2.t.f.1025.2 | 8 | 9.2 | odd | 6 | |||
1134.2.t.f.1025.3 | 8 | 9.7 | even | 3 | |||
2646.2.d.d.2645.1 | 8 | 7.4 | even | 3 | |||
2646.2.d.d.2645.3 | 8 | 7.3 | odd | 6 | |||
2646.2.d.d.2645.6 | 8 | 21.17 | even | 6 | |||
2646.2.d.d.2645.8 | 8 | 21.11 | odd | 6 |