Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(2645,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2646.2645");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.d (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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
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: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 378) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2645.6 | ||
Root | \(-0.965926 - 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2645 |
Dual form | 2646.2.d.d.2645.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −2.44949 | −1.09545 | −0.547723 | − | 0.836660i | \(-0.684505\pi\) | ||||
−0.547723 | + | 0.836660i | \(0.684505\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 2.44949i | − 0.774597i | ||||||||
\(11\) | 4.24264i | 1.27920i | 0.768706 | + | 0.639602i | \(0.220901\pi\) | ||||
−0.768706 | + | 0.639602i | \(0.779099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 4.18154i | − 1.15975i | −0.814705 | − | 0.579875i | \(-0.803101\pi\) | ||||
0.814705 | − | 0.579875i | \(-0.196899\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.44949 | −0.594089 | −0.297044 | − | 0.954864i | \(-0.596001\pi\) | ||||
−0.297044 | + | 0.954864i | \(0.596001\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 4.89898i | − 1.12390i | −0.827170 | − | 0.561951i | \(-0.810051\pi\) | ||||
0.827170 | − | 0.561951i | \(-0.189949\pi\) | |||||||
\(20\) | 2.44949 | 0.547723 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.24264 | −0.904534 | ||||||||
\(23\) | 6.00000i | 1.25109i | 0.780189 | + | 0.625543i | \(0.215123\pi\) | ||||
−0.780189 | + | 0.625543i | \(0.784877\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 4.18154 | 0.820068 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 10.2426i | − 1.90201i | −0.309175 | − | 0.951005i | \(-0.600053\pi\) | ||||
0.309175 | − | 0.951005i | \(-0.399947\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.61642i | 1.00874i | 0.863488 | + | 0.504369i | \(0.168275\pi\) | ||||
−0.863488 | + | 0.504369i | \(0.831725\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − 2.44949i | − 0.420084i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.24264 | −0.533087 | −0.266543 | − | 0.963823i | \(-0.585882\pi\) | ||||
−0.266543 | + | 0.963823i | \(0.585882\pi\) | |||||||
\(38\) | 4.89898 | 0.794719 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 2.44949i | 0.387298i | ||||||||
\(41\) | 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 | \(0.320784\pi\) | |||||||
\(44\) | − 4.24264i | − 0.639602i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −6.00000 | −0.884652 | ||||||||
\(47\) | 7.94282 | 1.15858 | 0.579289 | − | 0.815122i | \(-0.303330\pi\) | ||||
0.579289 | + | 0.815122i | \(0.303330\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.18154i | 0.579875i | ||||||||
\(53\) | − 2.48528i | − 0.341380i | −0.985325 | − | 0.170690i | \(-0.945400\pi\) | ||||
0.985325 | − | 0.170690i | \(-0.0545996\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 10.3923i | − 1.40130i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 10.2426 | 1.34492 | ||||||||
\(59\) | 2.44949 | 0.318896 | 0.159448 | − | 0.987206i | \(-0.449029\pi\) | ||||
0.159448 | + | 0.987206i | \(0.449029\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.717439i | 0.0918586i | 0.998945 | + | 0.0459293i | \(0.0146249\pi\) | ||||
−0.998945 | + | 0.0459293i | \(0.985375\pi\) | |||||||
\(62\) | −5.61642 | −0.713286 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 10.2426i | 1.27044i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.48528 | −0.425795 | −0.212897 | − | 0.977075i | \(-0.568290\pi\) | ||||
−0.212897 | + | 0.977075i | \(0.568290\pi\) | |||||||
\(68\) | 2.44949 | 0.297044 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.7279i | 1.51053i | 0.655422 | + | 0.755263i | \(0.272491\pi\) | ||||
−0.655422 | + | 0.755263i | \(0.727509\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 15.2913i | − 1.78971i | −0.446357 | − | 0.894855i | \(-0.647279\pi\) | ||||
0.446357 | − | 0.894855i | \(-0.352721\pi\) | |||||||
\(74\) | − 3.24264i | − 0.376949i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.89898i | 0.561951i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.24264 | 1.03988 | 0.519939 | − | 0.854203i | \(-0.325955\pi\) | ||||
0.519939 | + | 0.854203i | \(0.325955\pi\) | |||||||
\(80\) | −2.44949 | −0.273861 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 2.44949i | 0.270501i | ||||||||
\(83\) | 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 | ||||||||
\(86\) | 7.00000i | 0.754829i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.24264 | 0.452267 | ||||||||
\(89\) | 17.7408 | 1.88052 | 0.940259 | − | 0.340460i | \(-0.110583\pi\) | ||||
0.940259 | + | 0.340460i | \(0.110583\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 6.00000i | − 0.625543i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.94282i | 0.819239i | ||||||||
\(95\) | 12.0000i | 1.23117i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.63103i | 0.673279i | 0.941634 | + | 0.336640i | \(0.109290\pi\) | ||||
−0.941634 | + | 0.336640i | \(0.890710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | −7.34847 | −0.731200 | −0.365600 | − | 0.930772i | \(-0.619136\pi\) | ||||
−0.365600 | + | 0.930772i | \(0.619136\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6.21076i | − 0.611965i | −0.952037 | − | 0.305982i | \(-0.901015\pi\) | ||||
0.952037 | − | 0.305982i | \(-0.0989849\pi\) | |||||||
\(104\) | −4.18154 | −0.410034 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 2.48528 | 0.241392 | ||||||||
\(107\) | 14.4853i | 1.40035i | 0.713974 | + | 0.700173i | \(0.246894\pi\) | ||||
−0.713974 | + | 0.700173i | \(0.753106\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.72792 | 0.740201 | 0.370100 | − | 0.928992i | \(-0.379323\pi\) | ||||
0.370100 | + | 0.928992i | \(0.379323\pi\) | |||||||
\(110\) | 10.3923 | 0.990867 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.75736i | 0.165318i | 0.996578 | + | 0.0826592i | \(0.0263413\pi\) | ||||
−0.996578 | + | 0.0826592i | \(0.973659\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 14.6969i | − 1.37050i | ||||||||
\(116\) | 10.2426i | 0.951005i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2.44949i | 0.225494i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −0.717439 | −0.0649539 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 5.61642i | − 0.504369i | ||||||||
\(125\) | 9.79796 | 0.876356 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.7279 | 1.57310 | 0.786549 | − | 0.617527i | \(-0.211866\pi\) | ||||
0.786549 | + | 0.617527i | \(0.211866\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.2426 | −0.898339 | ||||||||
\(131\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 3.48528i | − 0.301082i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.44949i | 0.210042i | ||||||||
\(137\) | 6.00000i | 0.512615i | 0.966595 | + | 0.256307i | \(0.0825059\pi\) | ||||
−0.966595 | + | 0.256307i | \(0.917494\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.5300i | 0.977963i | 0.872294 | + | 0.488981i | \(0.162631\pi\) | ||||
−0.872294 | + | 0.488981i | \(0.837369\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.7279 | −1.06810 | ||||||||
\(143\) | 17.7408 | 1.48356 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.0892i | 2.08355i | ||||||||
\(146\) | 15.2913 | 1.26552 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.24264 | 0.266543 | ||||||||
\(149\) | 7.75736i | 0.635508i | 0.948173 | + | 0.317754i | \(0.102929\pi\) | ||||
−0.948173 | + | 0.317754i | \(0.897071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 17.2426 | 1.40319 | 0.701593 | − | 0.712578i | \(-0.252472\pi\) | ||||
0.701593 | + | 0.712578i | \(0.252472\pi\) | |||||||
\(152\) | −4.89898 | −0.397360 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 13.7574i | − 1.10502i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 10.3923i | − 0.829396i | −0.909959 | − | 0.414698i | \(-0.863887\pi\) | ||||
0.909959 | − | 0.414698i | \(-0.136113\pi\) | |||||||
\(158\) | 9.24264i | 0.735305i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 2.44949i | − 0.193649i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.48528 | 0.586292 | 0.293146 | − | 0.956068i | \(-0.405298\pi\) | ||||
0.293146 | + | 0.956068i | \(0.405298\pi\) | |||||||
\(164\) | −2.44949 | −0.191273 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 5.49333i | 0.426365i | ||||||||
\(167\) | −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 | ||||||||
\(170\) | 6.00000i | 0.460179i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.00000 | −0.533745 | ||||||||
\(173\) | 20.7846 | 1.58022 | 0.790112 | − | 0.612962i | \(-0.210022\pi\) | ||||
0.790112 | + | 0.612962i | \(0.210022\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.24264i | 0.319801i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 17.7408i | 1.32973i | ||||||||
\(179\) | 18.7279i | 1.39979i | 0.714245 | + | 0.699895i | \(0.246770\pi\) | ||||
−0.714245 | + | 0.699895i | \(0.753230\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 9.79796i | − 0.728277i | −0.931345 | − | 0.364138i | \(-0.881364\pi\) | ||||
0.931345 | − | 0.364138i | \(-0.118636\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.00000 | 0.442326 | ||||||||
\(185\) | 7.94282 | 0.583967 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 10.3923i | − 0.759961i | ||||||||
\(188\) | −7.94282 | −0.579289 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −12.0000 | −0.870572 | ||||||||
\(191\) | − 21.2132i | − 1.53493i | −0.641089 | − | 0.767467i | \(-0.721517\pi\) | ||||
0.641089 | − | 0.767467i | \(-0.278483\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.4853 | 1.11465 | 0.557327 | − | 0.830293i | \(-0.311827\pi\) | ||||
0.557327 | + | 0.830293i | \(0.311827\pi\) | |||||||
\(194\) | −6.63103 | −0.476080 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 16.9706i | − 1.20910i | −0.796566 | − | 0.604551i | \(-0.793352\pi\) | ||||
0.796566 | − | 0.604551i | \(-0.206648\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.58719i | 0.254289i | 0.991884 | + | 0.127145i | \(0.0405813\pi\) | ||||
−0.991884 | + | 0.127145i | \(0.959419\pi\) | |||||||
\(200\) | − 1.00000i | − 0.0707107i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 7.34847i | − 0.517036i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.00000 | −0.419058 | ||||||||
\(206\) | 6.21076 | 0.432724 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 4.18154i | − 0.289938i | ||||||||
\(209\) | 20.7846 | 1.43770 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −13.4853 | −0.928365 | −0.464183 | − | 0.885740i | \(-0.653652\pi\) | ||||
−0.464183 | + | 0.885740i | \(0.653652\pi\) | |||||||
\(212\) | 2.48528i | 0.170690i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −14.4853 | −0.990193 | ||||||||
\(215\) | −17.1464 | −1.16938 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 7.72792i | 0.523401i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.3923i | 0.700649i | ||||||||
\(221\) | 10.2426i | 0.688995i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.3923i | 0.695920i | 0.937509 | + | 0.347960i | \(0.113126\pi\) | ||||
−0.937509 | + | 0.347960i | \(0.886874\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.75736 | −0.116898 | ||||||||
\(227\) | 4.30463 | 0.285709 | 0.142854 | − | 0.989744i | \(-0.454372\pi\) | ||||
0.142854 | + | 0.989744i | \(0.454372\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 9.08052i | − 0.600058i | −0.953930 | − | 0.300029i | \(-0.903004\pi\) | ||||
0.953930 | − | 0.300029i | \(-0.0969963\pi\) | |||||||
\(230\) | 14.6969 | 0.969087 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.2426 | −0.672462 | ||||||||
\(233\) | 3.51472i | 0.230257i | 0.993351 | + | 0.115128i | \(0.0367280\pi\) | ||||
−0.993351 | + | 0.115128i | \(0.963272\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.4558 | −1.26916 | ||||||||
\(236\) | −2.44949 | −0.159448 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.75736i | 0.501782i | 0.968015 | + | 0.250891i | \(0.0807236\pi\) | ||||
−0.968015 | + | 0.250891i | \(0.919276\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.4582i | 1.18900i | 0.804096 | + | 0.594499i | \(0.202650\pi\) | ||||
−0.804096 | + | 0.594499i | \(0.797350\pi\) | |||||||
\(242\) | − 7.00000i | − 0.449977i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 0.717439i | − 0.0459293i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −20.4853 | −1.30345 | ||||||||
\(248\) | 5.61642 | 0.356643 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.79796i | 0.619677i | ||||||||
\(251\) | −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 | ||||||||
\(254\) | 17.7279i | 1.11235i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.30463 | 0.268516 | 0.134258 | − | 0.990946i | \(-0.457135\pi\) | ||||
0.134258 | + | 0.990946i | \(0.457135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − 10.2426i | − 0.635222i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 18.7279i | − 1.15481i | −0.816457 | − | 0.577407i | \(-0.804065\pi\) | ||||
0.816457 | − | 0.577407i | \(-0.195935\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.08767i | 0.373963i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.48528 | 0.212897 | ||||||||
\(269\) | 9.79796 | 0.597392 | 0.298696 | − | 0.954348i | \(-0.403448\pi\) | ||||
0.298696 | + | 0.954348i | \(0.403448\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 15.4144i | − 0.936357i | −0.883634 | − | 0.468178i | \(-0.844910\pi\) | ||||
0.883634 | − | 0.468178i | \(-0.155090\pi\) | |||||||
\(272\) | −2.44949 | −0.148522 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −6.00000 | −0.362473 | ||||||||
\(275\) | 4.24264i | 0.255841i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.72792 | −0.103821 | −0.0519104 | − | 0.998652i | \(-0.516531\pi\) | ||||
−0.0519104 | + | 0.998652i | \(0.516531\pi\) | |||||||
\(278\) | −11.5300 | −0.691524 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 22.2426i | − 1.32688i | −0.748227 | − | 0.663442i | \(-0.769095\pi\) | ||||
0.748227 | − | 0.663442i | \(-0.230905\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 23.3572i | − 1.38844i | −0.719762 | − | 0.694220i | \(-0.755749\pi\) | ||||
0.719762 | − | 0.694220i | \(-0.244251\pi\) | |||||||
\(284\) | − 12.7279i | − 0.755263i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 17.7408i | 1.04903i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11.0000 | −0.647059 | ||||||||
\(290\) | −25.0892 | −1.47329 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 15.2913i | 0.894855i | ||||||||
\(293\) | −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 | ||||||||
\(296\) | 3.24264i | 0.188475i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −7.75736 | −0.449372 | ||||||||
\(299\) | 25.0892 | 1.45095 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 17.2426i | 0.992202i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − 4.89898i | − 0.280976i | ||||||||
\(305\) | − 1.75736i | − 0.100626i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.57258i | 0.146825i | 0.997302 | + | 0.0734125i | \(0.0233890\pi\) | ||||
−0.997302 | + | 0.0734125i | \(0.976611\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 13.7574 | 0.781366 | ||||||||
\(311\) | −17.1464 | −0.972285 | −0.486142 | − | 0.873880i | \(-0.661596\pi\) | ||||
−0.486142 | + | 0.873880i | \(0.661596\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.594346i | 0.0335944i | 0.999859 | + | 0.0167972i | \(0.00534697\pi\) | ||||
−0.999859 | + | 0.0167972i | \(0.994653\pi\) | |||||||
\(314\) | 10.3923 | 0.586472 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.24264 | −0.519939 | ||||||||
\(317\) | − 13.7574i | − 0.772690i | −0.922354 | − | 0.386345i | \(-0.873737\pi\) | ||||
0.922354 | − | 0.386345i | \(-0.126263\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 43.4558 | 2.43306 | ||||||||
\(320\) | 2.44949 | 0.136931 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.0000i | 0.667698i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 4.18154i | − 0.231950i | ||||||||
\(326\) | 7.48528i | 0.414571i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − 2.44949i | − 0.135250i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.0000 | 0.549650 | 0.274825 | − | 0.961494i | \(-0.411380\pi\) | ||||
0.274825 | + | 0.961494i | \(0.411380\pi\) | |||||||
\(332\) | −5.49333 | −0.301485 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 20.1903i | − 1.10476i | ||||||||
\(335\) | 8.53716 | 0.466435 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 29.4558 | 1.60456 | 0.802281 | − | 0.596947i | \(-0.203620\pi\) | ||||
0.802281 | + | 0.596947i | \(0.203620\pi\) | |||||||
\(338\) | − 4.48528i | − 0.243967i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.00000 | −0.325396 | ||||||||
\(341\) | −23.8284 | −1.29038 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − 7.00000i | − 0.377415i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.7846i | 1.11739i | ||||||||
\(347\) | − 28.9706i | − 1.55522i | −0.628746 | − | 0.777611i | \(-0.716432\pi\) | ||||
0.628746 | − | 0.777611i | \(-0.283568\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 24.3718i | − 1.30459i | −0.757964 | − | 0.652296i | \(-0.773806\pi\) | ||||
0.757964 | − | 0.652296i | \(-0.226194\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.24264 | −0.226134 | ||||||||
\(353\) | −30.5826 | −1.62775 | −0.813873 | − | 0.581043i | \(-0.802645\pi\) | ||||
−0.813873 | + | 0.581043i | \(0.802645\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 31.1769i | − 1.65470i | ||||||||
\(356\) | −17.7408 | −0.940259 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −18.7279 | −0.989801 | ||||||||
\(359\) | 2.48528i | 0.131168i | 0.997847 | + | 0.0655841i | \(0.0208911\pi\) | ||||
−0.997847 | + | 0.0655841i | \(0.979109\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.00000 | −0.263158 | ||||||||
\(362\) | 9.79796 | 0.514969 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 37.4558i | 1.96053i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.20361i | 0.480425i | 0.970720 | + | 0.240212i | \(0.0772171\pi\) | ||||
−0.970720 | + | 0.240212i | \(0.922783\pi\) | |||||||
\(368\) | 6.00000i | 0.312772i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 7.94282i | 0.412927i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −22.0000 | −1.13912 | −0.569558 | − | 0.821951i | \(-0.692886\pi\) | ||||
−0.569558 | + | 0.821951i | \(0.692886\pi\) | |||||||
\(374\) | 10.3923 | 0.537373 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − 7.94282i | − 0.409619i | ||||||||
\(377\) | −42.8300 | −2.20586 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.48528 | 0.487226 | 0.243613 | − | 0.969872i | \(-0.421667\pi\) | ||||
0.243613 | + | 0.969872i | \(0.421667\pi\) | |||||||
\(380\) | − 12.0000i | − 0.615587i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 21.2132 | 1.08536 | ||||||||
\(383\) | −15.2913 | −0.781348 | −0.390674 | − | 0.920529i | \(-0.627758\pi\) | ||||
−0.390674 | + | 0.920529i | \(0.627758\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 15.4853i | 0.788180i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 6.63103i | − 0.336640i | ||||||||
\(389\) | − 32.4853i | − 1.64707i | −0.567266 | − | 0.823535i | \(-0.691999\pi\) | ||||
0.567266 | − | 0.823535i | \(-0.308001\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 14.6969i | − 0.743256i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.9706 | 0.854965 | ||||||||
\(395\) | −22.6398 | −1.13913 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.8651i | 1.49889i | 0.662068 | + | 0.749444i | \(0.269679\pi\) | ||||
−0.662068 | + | 0.749444i | \(0.730321\pi\) | |||||||
\(398\) | −3.58719 | −0.179810 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | − 28.2426i | − 1.41037i | −0.709023 | − | 0.705185i | \(-0.750864\pi\) | ||||
0.709023 | − | 0.705185i | \(-0.249136\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.4853 | 1.16989 | ||||||||
\(404\) | 7.34847 | 0.365600 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 13.7574i | − 0.681927i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − 13.5592i | − 0.670461i | −0.942136 | − | 0.335230i | \(-0.891186\pi\) | ||||
0.942136 | − | 0.335230i | \(-0.108814\pi\) | |||||||
\(410\) | − 6.00000i | − 0.296319i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 6.21076i | 0.305982i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −13.4558 | −0.660521 | ||||||||
\(416\) | 4.18154 | 0.205017 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 20.7846i | 1.01661i | ||||||||
\(419\) | −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 | \(0.266698\pi\) | |||||||
\(422\) | − 13.4853i | − 0.656453i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.48528 | −0.120696 | ||||||||
\(425\) | −2.44949 | −0.118818 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 14.4853i | − 0.700173i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − 17.1464i | − 0.826874i | ||||||||
\(431\) | − 10.2426i | − 0.493371i | −0.969096 | − | 0.246685i | \(-0.920659\pi\) | ||||
0.969096 | − | 0.246685i | \(-0.0793414\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 26.8213i | 1.28895i | 0.764626 | + | 0.644475i | \(0.222924\pi\) | ||||
−0.764626 | + | 0.644475i | \(0.777076\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −7.72792 | −0.370100 | ||||||||
\(437\) | 29.3939 | 1.40610 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.0892i | 1.19744i | 0.800957 | + | 0.598722i | \(0.204325\pi\) | ||||
−0.800957 | + | 0.598722i | \(0.795675\pi\) | |||||||
\(440\) | −10.3923 | −0.495434 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.2426 | −0.487193 | ||||||||
\(443\) | 25.4558i | 1.20944i | 0.796437 | + | 0.604722i | \(0.206716\pi\) | ||||
−0.796437 | + | 0.604722i | \(0.793284\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −43.4558 | −2.06000 | ||||||||
\(446\) | −10.3923 | −0.492090 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 30.7279i | 1.45014i | 0.688675 | + | 0.725070i | \(0.258193\pi\) | ||||
−0.688675 | + | 0.725070i | \(0.741807\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.3923i | 0.489355i | ||||||||
\(452\) | − 1.75736i | − 0.0826592i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.30463i | 0.202026i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −23.0000 | −1.07589 | −0.537947 | − | 0.842978i | \(-0.680800\pi\) | ||||
−0.537947 | + | 0.842978i | \(0.680800\pi\) | |||||||
\(458\) | 9.08052 | 0.424305 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14.6969i | 0.685248i | ||||||||
\(461\) | 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 | \(0.670804\pi\) | |||||||
\(464\) | − 10.2426i | − 0.475503i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.51472 | −0.162816 | ||||||||
\(467\) | −3.04384 | −0.140852 | −0.0704260 | − | 0.997517i | \(-0.522436\pi\) | ||||
−0.0704260 | + | 0.997517i | \(0.522436\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − 19.4558i | − 0.897431i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − 2.44949i | − 0.112747i | ||||||||
\(473\) | 29.6985i | 1.36554i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 4.89898i | − 0.224781i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −7.75736 | −0.354813 | ||||||||
\(479\) | 2.44949 | 0.111920 | 0.0559600 | − | 0.998433i | \(-0.482178\pi\) | ||||
0.0559600 | + | 0.998433i | \(0.482178\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.5592i | 0.618248i | ||||||||
\(482\) | −18.4582 | −0.840749 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | − 16.2426i | − 0.737540i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 22.0000 | 0.996915 | 0.498458 | − | 0.866914i | \(-0.333900\pi\) | ||||
0.498458 | + | 0.866914i | \(0.333900\pi\) | |||||||
\(488\) | 0.717439 | 0.0324769 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.02944i | 0.0464579i | 0.999730 | + | 0.0232289i | \(0.00739466\pi\) | ||||
−0.999730 | + | 0.0232289i | \(0.992605\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.0892i | 1.12996i | ||||||||
\(494\) | − 20.4853i | − 0.921676i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 5.61642i | 0.252185i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.4558 | 1.18433 | 0.592163 | − | 0.805818i | \(-0.298274\pi\) | ||||
0.592163 | + | 0.805818i | \(0.298274\pi\) | |||||||
\(500\) | −9.79796 | −0.438178 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − 5.49333i | − 0.245179i | ||||||||
\(503\) | 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 | ||||||||
\(506\) | − 25.4558i | − 1.13165i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −17.7279 | −0.786549 | ||||||||
\(509\) | −29.9882 | −1.32920 | −0.664602 | − | 0.747197i | \(-0.731399\pi\) | ||||
−0.664602 | + | 0.747197i | \(0.731399\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.30463i | 0.189869i | ||||||||
\(515\) | 15.2132i | 0.670374i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 33.6985i | 1.48206i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.2426 | 0.449170 | ||||||||
\(521\) | −9.20361 | −0.403218 | −0.201609 | − | 0.979466i | \(-0.564617\pi\) | ||||
−0.201609 | + | 0.979466i | \(0.564617\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 17.6177i | − 0.770367i | −0.922840 | − | 0.385184i | \(-0.874138\pi\) | ||||
0.922840 | − | 0.385184i | \(-0.125862\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 18.7279 | 0.816576 | ||||||||
\(527\) | − 13.7574i | − 0.599280i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13.0000 | −0.565217 | ||||||||
\(530\) | −6.08767 | −0.264432 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 10.2426i | − 0.443658i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 35.4815i | − 1.53400i | ||||||||
\(536\) | 3.48528i | 0.150541i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.79796i | 0.422420i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 45.4558 | 1.95430 | 0.977150 | − | 0.212552i | \(-0.0681776\pi\) | ||||
0.977150 | + | 0.212552i | \(0.0681776\pi\) | |||||||
\(542\) | 15.4144 | 0.662104 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − 2.44949i | − 0.105021i | ||||||||
\(545\) | −18.9295 | −0.810849 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.02944 | 0.257800 | 0.128900 | − | 0.991658i | \(-0.458855\pi\) | ||||
0.128900 | + | 0.991658i | \(0.458855\pi\) | |||||||
\(548\) | − 6.00000i | − 0.256307i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.24264 | −0.180907 | ||||||||
\(551\) | −50.1785 | −2.13768 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − 1.72792i | − 0.0734124i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 11.5300i | − 0.488981i | ||||||||
\(557\) | − 21.2132i | − 0.898832i | −0.893323 | − | 0.449416i | \(-0.851632\pi\) | ||||
0.893323 | − | 0.449416i | \(-0.148368\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 29.2708i | − 1.23802i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 22.2426 | 0.938249 | ||||||||
\(563\) | 16.4800 | 0.694548 | 0.347274 | − | 0.937764i | \(-0.387107\pi\) | ||||
0.347274 | + | 0.937764i | \(0.387107\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 4.30463i | − 0.181097i | ||||||||
\(566\) | 23.3572 | 0.981776 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12.7279 | 0.534052 | ||||||||
\(569\) | − 1.75736i | − 0.0736723i | −0.999321 | − | 0.0368362i | \(-0.988272\pi\) | ||||
0.999321 | − | 0.0368362i | \(-0.0117280\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.0000 | −0.920671 | −0.460336 | − | 0.887745i | \(-0.652271\pi\) | ||||
−0.460336 | + | 0.887745i | \(0.652271\pi\) | |||||||
\(572\) | −17.7408 | −0.741779 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.00000i | 0.250217i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 17.6177i | 0.733434i | 0.930333 | + | 0.366717i | \(0.119518\pi\) | ||||
−0.930333 | + | 0.366717i | \(0.880482\pi\) | |||||||
\(578\) | − 11.0000i | − 0.457540i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 25.0892i | − 1.04177i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 10.5442 | 0.436694 | ||||||||
\(584\) | −15.2913 | −0.632758 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 7.94282i | − 0.328115i | ||||||||
\(587\) | 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 | ||||||||
\(590\) | − 6.00000i | − 0.247016i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3.24264 | −0.133272 | ||||||||
\(593\) | −22.6398 | −0.929703 | −0.464852 | − | 0.885389i | \(-0.653892\pi\) | ||||
−0.464852 | + | 0.885389i | \(0.653892\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 7.75736i | − 0.317754i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 25.0892i | 1.02598i | ||||||||
\(599\) | − 20.4853i | − 0.837006i | −0.908215 | − | 0.418503i | \(-0.862555\pi\) | ||||
0.908215 | − | 0.418503i | \(-0.137445\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2695i | 0.704438i | 0.935918 | + | 0.352219i | \(0.114573\pi\) | ||||
−0.935918 | + | 0.352219i | \(0.885427\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −17.2426 | −0.701593 | ||||||||
\(605\) | 17.1464 | 0.697101 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 26.2779i | − 1.06659i | −0.845930 | − | 0.533294i | \(-0.820954\pi\) | ||||
0.845930 | − | 0.533294i | \(-0.179046\pi\) | |||||||
\(608\) | 4.89898 | 0.198680 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.75736 | 0.0711534 | ||||||||
\(611\) | − 33.2132i | − 1.34366i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 14.2132 | 0.574066 | 0.287033 | − | 0.957921i | \(-0.407331\pi\) | ||||
0.287033 | + | 0.957921i | \(0.407331\pi\) | |||||||
\(614\) | −2.57258 | −0.103821 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 4.24264i | − 0.170802i | −0.996347 | − | 0.0854011i | \(-0.972783\pi\) | ||||
0.996347 | − | 0.0854011i | \(-0.0272172\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 32.3146i | − 1.29883i | −0.760432 | − | 0.649417i | \(-0.775013\pi\) | ||||
0.760432 | − | 0.649417i | \(-0.224987\pi\) | |||||||
\(620\) | 13.7574i | 0.552509i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 17.1464i | − 0.687509i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | −0.594346 | −0.0237548 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.3923i | 0.414698i | ||||||||
\(629\) | 7.94282 | 0.316701 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.2426 | −0.925275 | −0.462637 | − | 0.886548i | \(-0.653097\pi\) | ||||
−0.462637 | + | 0.886548i | \(0.653097\pi\) | |||||||
\(632\) | − 9.24264i | − 0.367653i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 13.7574 | 0.546375 | ||||||||
\(635\) | −43.4244 | −1.72324 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 43.4558i | 1.72043i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.44949i | 0.0968246i | ||||||||
\(641\) | 9.21320i | 0.363900i | 0.983308 | + | 0.181950i | \(0.0582408\pi\) | ||||
−0.983308 | + | 0.181950i | \(0.941759\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.73205i | 0.0683054i | 0.999417 | + | 0.0341527i | \(0.0108733\pi\) | ||||
−0.999417 | + | 0.0341527i | \(0.989127\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12.0000 | −0.472134 | ||||||||
\(647\) | −20.7846 | −0.817127 | −0.408564 | − | 0.912730i | \(-0.633970\pi\) | ||||
−0.408564 | + | 0.912730i | \(0.633970\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.3923i | 0.407934i | ||||||||
\(650\) | 4.18154 | 0.164014 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.48528 | −0.293146 | ||||||||
\(653\) | 14.4853i | 0.566853i | 0.958994 | + | 0.283426i | \(0.0914712\pi\) | ||||
−0.958994 | + | 0.283426i | \(0.908529\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.44949 | 0.0956365 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 13.7574i | 0.535911i | 0.963431 | + | 0.267955i | \(0.0863480\pi\) | ||||
−0.963431 | + | 0.267955i | \(0.913652\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.89898i | 0.190548i | 0.995451 | + | 0.0952741i | \(0.0303728\pi\) | ||||
−0.995451 | + | 0.0952741i | \(0.969627\pi\) | |||||||
\(662\) | 10.0000i | 0.388661i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − 5.49333i | − 0.213182i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 61.4558 | 2.37958 | ||||||||
\(668\) | 20.1903 | 0.781185 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.53716i | 0.329819i | ||||||||
\(671\) | −3.04384 | −0.117506 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.45584 | 0.210307 | 0.105154 | − | 0.994456i | \(-0.466467\pi\) | ||||
0.105154 | + | 0.994456i | \(0.466467\pi\) | |||||||
\(674\) | 29.4558i | 1.13460i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.48528 | 0.172511 | ||||||||
\(677\) | −14.6969 | −0.564849 | −0.282425 | − | 0.959289i | \(-0.591139\pi\) | ||||
−0.282425 | + | 0.959289i | \(0.591139\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − 6.00000i | − 0.230089i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 23.8284i | − 0.912438i | ||||||||
\(683\) | − 1.75736i | − 0.0672435i | −0.999435 | − | 0.0336217i | \(-0.989296\pi\) | ||||
0.999435 | − | 0.0336217i | \(-0.0107042\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 14.6969i | − 0.561541i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.00000 | 0.266872 | ||||||||
\(689\) | −10.3923 | −0.395915 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 26.8213i | 1.02033i | 0.860077 | + | 0.510165i | \(0.170416\pi\) | ||||
−0.860077 | + | 0.510165i | \(0.829584\pi\) | |||||||
\(692\) | −20.7846 | −0.790112 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 28.9706 | 1.09971 | ||||||||
\(695\) | − 28.2426i | − 1.07130i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −6.00000 | −0.227266 | ||||||||
\(698\) | 24.3718 | 0.922486 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.51472i | 0.132749i | 0.997795 | + | 0.0663745i | \(0.0211432\pi\) | ||||
−0.997795 | + | 0.0663745i | \(0.978857\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15.8856i | 0.599138i | ||||||||
\(704\) | − 4.24264i | − 0.159901i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 30.5826i | − 1.15099i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.2132 | −0.984458 | −0.492229 | − | 0.870466i | \(-0.663818\pi\) | ||||
−0.492229 | + | 0.870466i | \(0.663818\pi\) | |||||||
\(710\) | 31.1769 | 1.17005 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 17.7408i | − 0.664864i | ||||||||
\(713\) | −33.6985 | −1.26202 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −43.4558 | −1.62516 | ||||||||
\(716\) | − 18.7279i | − 0.699895i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −2.48528 | −0.0927499 | ||||||||
\(719\) | 11.0588 | 0.412422 | 0.206211 | − | 0.978508i | \(-0.433887\pi\) | ||||
0.206211 | + | 0.978508i | \(0.433887\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 5.00000i | − 0.186081i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 9.79796i | 0.364138i | ||||||||
\(725\) | − 10.2426i | − 0.380402i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 45.4026i | − 1.68389i | −0.539564 | − | 0.841945i | \(-0.681411\pi\) | ||||
0.539564 | − | 0.841945i | \(-0.318589\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −37.4558 | −1.38630 | ||||||||
\(731\) | −17.1464 | −0.634184 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 16.0087i | − 0.591296i | −0.955297 | − | 0.295648i | \(-0.904465\pi\) | ||||
0.955297 | − | 0.295648i | \(-0.0955355\pi\) | |||||||
\(734\) | −9.20361 | −0.339712 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.00000 | −0.221163 | ||||||||
\(737\) | − 14.7868i | − 0.544679i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 42.4558 | 1.56176 | 0.780882 | − | 0.624679i | \(-0.214770\pi\) | ||||
0.780882 | + | 0.624679i | \(0.214770\pi\) | |||||||
\(740\) | −7.94282 | −0.291984 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − 6.72792i | − 0.246824i | −0.992356 | − | 0.123412i | \(-0.960616\pi\) | ||||
0.992356 | − | 0.123412i | \(-0.0393836\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 19.0016i | − 0.696164i | ||||||||
\(746\) | − 22.0000i | − 0.805477i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 10.3923i | 0.379980i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.54416 | 0.0928376 | 0.0464188 | − | 0.998922i | \(-0.485219\pi\) | ||||
0.0464188 | + | 0.998922i | \(0.485219\pi\) | |||||||
\(752\) | 7.94282 | 0.289645 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − 42.8300i | − 1.55978i | ||||||||
\(755\) | −42.2357 | −1.53711 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 41.2426 | 1.49899 | 0.749495 | − | 0.662010i | \(-0.230297\pi\) | ||||
0.749495 | + | 0.662010i | \(0.230297\pi\) | |||||||
\(758\) | 9.48528i | 0.344521i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 12.0000 | 0.435286 | ||||||||
\(761\) | 24.4949 | 0.887939 | 0.443970 | − | 0.896042i | \(-0.353570\pi\) | ||||
0.443970 | + | 0.896042i | \(0.353570\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 21.2132i | 0.767467i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 15.2913i | − 0.552497i | ||||||||
\(767\) | − 10.2426i | − 0.369840i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.18869i | 0.0428653i | 0.999770 | + | 0.0214327i | \(0.00682275\pi\) | ||||
−0.999770 | + | 0.0214327i | \(0.993177\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −15.4853 | −0.557327 | ||||||||
\(773\) | −9.79796 | −0.352408 | −0.176204 | − | 0.984354i | \(-0.556382\pi\) | ||||
−0.176204 | + | 0.984354i | \(0.556382\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.61642i | 0.201748i | ||||||||
\(776\) | 6.63103 | 0.238040 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 32.4853 | 1.16465 | ||||||||
\(779\) | − 12.0000i | − 0.429945i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −54.0000 | −1.93227 | ||||||||
\(782\) | 14.6969 | 0.525561 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 25.4558i | 0.908558i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.9357i | 0.389814i | 0.980822 | + | 0.194907i | \(0.0624406\pi\) | ||||
−0.980822 | + | 0.194907i | \(0.937559\pi\) | |||||||
\(788\) | 16.9706i | 0.604551i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − 22.6398i | − 0.805486i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.00000 | 0.106533 | ||||||||
\(794\) | −29.8651 | −1.05987 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − 3.58719i | − 0.127145i | ||||||||
\(797\) | 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 | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 28.2426 | 0.997282 | ||||||||
\(803\) | 64.8754 | 2.28940 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 23.4853i | 0.827234i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 7.34847i | 0.258518i | ||||||||
\(809\) | 2.48528i | 0.0873778i | 0.999045 | + | 0.0436889i | \(0.0139110\pi\) | ||||
−0.999045 | + | 0.0436889i | \(0.986089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.7574 | 0.482195 | ||||||||
\(815\) | −18.3351 | −0.642251 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 34.2929i | − 1.19976i | ||||||||
\(818\) | 13.5592 | 0.474087 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.00000 | 0.209529 | ||||||||
\(821\) | − 10.9706i | − 0.382875i | −0.981505 | − | 0.191438i | \(-0.938685\pi\) | ||||
0.981505 | − | 0.191438i | \(-0.0613150\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.2426 | −0.391894 | −0.195947 | − | 0.980615i | \(-0.562778\pi\) | ||||
−0.195947 | + | 0.980615i | \(0.562778\pi\) | |||||||
\(824\) | −6.21076 | −0.216362 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 20.4853i | − 0.712343i | −0.934421 | − | 0.356172i | \(-0.884082\pi\) | ||||
0.934421 | − | 0.356172i | \(-0.115918\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 9.79796i | − 0.340297i | −0.985418 | − | 0.170149i | \(-0.945575\pi\) | ||||
0.985418 | − | 0.170149i | \(-0.0544248\pi\) | |||||||
\(830\) | − 13.4558i | − 0.467059i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.18154i | 0.144969i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 49.4558 | 1.71149 | ||||||||
\(836\) | −20.7846 | −0.718851 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 12.8418i | − 0.443612i | ||||||||
\(839\) | −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 | ||||||||
\(842\) | 27.4558i | 0.946191i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 13.4853 | 0.464183 | ||||||||
\(845\) | 10.9867 | 0.377952 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 2.48528i | − 0.0853449i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | − 2.44949i | − 0.0840168i | ||||||||
\(851\) | − 19.4558i | − 0.666938i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 51.3672i | − 1.75878i | −0.476103 | − | 0.879389i | \(-0.657951\pi\) | ||||
0.476103 | − | 0.879389i | \(-0.342049\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14.4853 | 0.495097 | ||||||||
\(857\) | −6.75412 | −0.230716 | −0.115358 | − | 0.993324i | \(-0.536802\pi\) | ||||
−0.115358 | + | 0.993324i | \(0.536802\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.9357i | 0.373120i | 0.982444 | + | 0.186560i | \(0.0597339\pi\) | ||||
−0.982444 | + | 0.186560i | \(0.940266\pi\) | |||||||
\(860\) | 17.1464 | 0.584688 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 10.2426 | 0.348866 | ||||||||
\(863\) | − 13.4558i | − 0.458042i | −0.973421 | − | 0.229021i | \(-0.926448\pi\) | ||||
0.973421 | − | 0.229021i | \(-0.0735525\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −50.9117 | −1.73105 | ||||||||
\(866\) | −26.8213 | −0.911425 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.2132i | 1.33022i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.5738i | 0.493816i | ||||||||
\(872\) | − 7.72792i | − 0.261700i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 29.3939i | 0.994263i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.78680 | −0.127871 | −0.0639355 | − | 0.997954i | \(-0.520365\pi\) | ||||
−0.0639355 | + | 0.997954i | \(0.520365\pi\) | |||||||
\(878\) | −25.0892 | −0.846721 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − 10.3923i | − 0.350325i | ||||||||
\(881\) | −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 | \(0.510714\pi\) | |||||||
\(884\) | − 10.2426i | − 0.344497i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −25.4558 | −0.855206 | ||||||||
\(887\) | 29.9882 | 1.00691 | 0.503453 | − | 0.864023i | \(-0.332063\pi\) | ||||
0.503453 | + | 0.864023i | \(0.332063\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 43.4558i | − 1.45664i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 10.3923i | − 0.347960i | ||||||||
\(893\) | − 38.9117i | − 1.30213i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 45.8739i | − 1.53339i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −30.7279 | −1.02540 | ||||||||
\(899\) | 57.5270 | 1.91863 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.08767i | 0.202810i | ||||||||
\(902\) | −10.3923 | −0.346026 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.75736 | 0.0584489 | ||||||||
\(905\) | 24.0000i | 0.797787i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3.48528 | 0.115727 | 0.0578634 | − | 0.998325i | \(-0.481571\pi\) | ||||
0.0578634 | + | 0.998325i | \(0.481571\pi\) | |||||||
\(908\) | −4.30463 | −0.142854 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 1.75736i | − 0.0582239i | −0.999576 | − | 0.0291120i | \(-0.990732\pi\) | ||||
0.999576 | − | 0.0291120i | \(-0.00926793\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 23.3062i | 0.771323i | ||||||||
\(914\) | − 23.0000i | − 0.760772i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.08052i | 0.300029i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.272078 | 0.00897502 | 0.00448751 | − | 0.999990i | \(-0.498572\pi\) | ||||
0.00448751 | + | 0.999990i | \(0.498572\pi\) | |||||||
\(920\) | −14.6969 | −0.484544 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 42.2357i | 1.39096i | ||||||||
\(923\) | 53.2223 | 1.75183 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.24264 | −0.106617 | ||||||||
\(926\) | − 22.0000i | − 0.722965i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 10.2426 | 0.336231 | ||||||||
\(929\) | −33.6264 | −1.10325 | −0.551623 | − | 0.834093i | \(-0.685991\pi\) | ||||
−0.551623 | + | 0.834093i | \(0.685991\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − 3.51472i | − 0.115128i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 3.04384i | − 0.0995973i | ||||||||
\(935\) | 25.4558i | 0.832495i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.0992i | 1.73468i | 0.497719 | + | 0.867338i | \(0.334171\pi\) | ||||
−0.497719 | + | 0.867338i | \(0.665829\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 19.4558 | 0.634580 | ||||||||
\(941\) | 21.4511 | 0.699285 | 0.349642 | − | 0.936883i | \(-0.386303\pi\) | ||||
0.349642 | + | 0.936883i | \(0.386303\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 14.6969i | 0.478598i | ||||||||
\(944\) | 2.44949 | 0.0797241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.6985 | −0.965581 | ||||||||
\(947\) | − 7.75736i | − 0.252080i | −0.992025 | − | 0.126040i | \(-0.959773\pi\) | ||||
0.992025 | − | 0.126040i | \(-0.0402268\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −63.9411 | −2.07562 | ||||||||
\(950\) | 4.89898 | 0.158944 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 34.9706i | − 1.13281i | −0.824128 | − | 0.566404i | \(-0.808334\pi\) | ||||
0.824128 | − | 0.566404i | \(-0.191666\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 51.9615i | 1.68144i | ||||||||
\(956\) | − 7.75736i | − 0.250891i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.44949i | 0.0791394i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.544156 | −0.0175534 | ||||||||
\(962\) | −13.5592 | −0.437167 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 18.4582i | − 0.594499i | ||||||||
\(965\) | −37.9310 | −1.22104 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16.6985 | 0.536987 | 0.268494 | − | 0.963281i | \(-0.413474\pi\) | ||||
0.268494 | + | 0.963281i | \(0.413474\pi\) | |||||||
\(968\) | 7.00000i | 0.224989i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 16.2426 | 0.521520 | ||||||||
\(971\) | 1.18869 | 0.0381469 | 0.0190735 | − | 0.999818i | \(-0.493928\pi\) | ||||
0.0190735 | + | 0.999818i | \(0.493928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 22.0000i | 0.704925i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.717439i | 0.0229647i | ||||||||
\(977\) | 6.00000i | 0.191957i | 0.995383 | + | 0.0959785i | \(0.0305980\pi\) | ||||
−0.995383 | + | 0.0959785i | \(0.969402\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 75.2677i | 2.40557i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.02944 | −0.0328507 | ||||||||
\(983\) | −18.3351 | −0.584800 | −0.292400 | − | 0.956296i | \(-0.594454\pi\) | ||||
−0.292400 | + | 0.956296i | \(0.594454\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.5692i | 1.32451i | ||||||||
\(986\) | −25.0892 | −0.799004 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 20.4853 | 0.651724 | ||||||||
\(989\) | 42.0000i | 1.33552i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22.2132 | 0.705626 | 0.352813 | − | 0.935694i | \(-0.385225\pi\) | ||||
0.352813 | + | 0.935694i | \(0.385225\pi\) | |||||||
\(992\) | −5.61642 | −0.178321 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 8.78680i | − 0.278560i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.77589i | 0.151254i | 0.997136 | + | 0.0756269i | \(0.0240958\pi\) | ||||
−0.997136 | + | 0.0756269i | \(0.975904\pi\) | |||||||
\(998\) | 26.4558i | 0.837445i | ||||||||
\(999\) | 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 | 2646.2.d.d.2645.6 | 8 | ||
3.2 | odd | 2 | inner | 2646.2.d.d.2645.3 | 8 | ||
7.4 | even | 3 | 378.2.k.d.215.2 | ✓ | 8 | ||
7.5 | odd | 6 | 378.2.k.d.269.3 | yes | 8 | ||
7.6 | odd | 2 | inner | 2646.2.d.d.2645.8 | 8 | ||
21.5 | even | 6 | 378.2.k.d.269.2 | yes | 8 | ||
21.11 | odd | 6 | 378.2.k.d.215.3 | yes | 8 | ||
21.20 | even | 2 | inner | 2646.2.d.d.2645.1 | 8 | ||
63.4 | even | 3 | 1134.2.t.f.593.3 | 8 | |||
63.5 | even | 6 | 1134.2.l.e.269.2 | 8 | |||
63.11 | odd | 6 | 1134.2.l.e.215.1 | 8 | |||
63.25 | even | 3 | 1134.2.l.e.215.4 | 8 | |||
63.32 | odd | 6 | 1134.2.t.f.593.2 | 8 | |||
63.40 | odd | 6 | 1134.2.l.e.269.3 | 8 | |||
63.47 | even | 6 | 1134.2.t.f.1025.3 | 8 | |||
63.61 | odd | 6 | 1134.2.t.f.1025.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
378.2.k.d.215.2 | ✓ | 8 | 7.4 | even | 3 | ||
378.2.k.d.215.3 | yes | 8 | 21.11 | odd | 6 | ||
378.2.k.d.269.2 | yes | 8 | 21.5 | even | 6 | ||
378.2.k.d.269.3 | yes | 8 | 7.5 | odd | 6 | ||
1134.2.l.e.215.1 | 8 | 63.11 | odd | 6 | |||
1134.2.l.e.215.4 | 8 | 63.25 | even | 3 | |||
1134.2.l.e.269.2 | 8 | 63.5 | even | 6 | |||
1134.2.l.e.269.3 | 8 | 63.40 | odd | 6 | |||
1134.2.t.f.593.2 | 8 | 63.32 | odd | 6 | |||
1134.2.t.f.593.3 | 8 | 63.4 | even | 3 | |||
1134.2.t.f.1025.2 | 8 | 63.61 | odd | 6 | |||
1134.2.t.f.1025.3 | 8 | 63.47 | even | 6 | |||
2646.2.d.d.2645.1 | 8 | 21.20 | even | 2 | inner | ||
2646.2.d.d.2645.3 | 8 | 3.2 | odd | 2 | inner | ||
2646.2.d.d.2645.6 | 8 | 1.1 | even | 1 | trivial | ||
2646.2.d.d.2645.8 | 8 | 7.6 | odd | 2 | inner |