Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6080,2,Mod(1,6080)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6080, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6080.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6080 = 2^{6} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6080.a (trivial) |
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: | yes |
Analytic conductor: | \(48.5490444289\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.568.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 6x - 2 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 760) |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-0.363328\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6080.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 | 0 | ||||||||
\(3\) | 0.363328 | 0.209768 | 0.104884 | − | 0.994484i | \(-0.466553\pi\) | ||||
0.104884 | + | 0.994484i | \(0.466553\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.14134 | −0.431385 | −0.215692 | − | 0.976461i | \(-0.569201\pi\) | ||||
−0.215692 | + | 0.976461i | \(0.569201\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.86799 | −0.955998 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.72666 | −0.822118 | −0.411059 | − | 0.911609i | \(-0.634841\pi\) | ||||
−0.411059 | + | 0.911609i | \(0.634841\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.64600 | 1.28857 | 0.644284 | − | 0.764786i | \(-0.277155\pi\) | ||||
0.644284 | + | 0.764786i | \(0.277155\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.363328 | 0.0938109 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.858664 | −0.208257 | −0.104128 | − | 0.994564i | \(-0.533205\pi\) | ||||
−0.104128 | + | 0.994564i | \(0.533205\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.414680 | −0.0904905 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.41468 | 0.920524 | 0.460262 | − | 0.887783i | \(-0.347755\pi\) | ||||
0.460262 | + | 0.887783i | \(0.347755\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.13201 | −0.410305 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −9.42401 | −1.74999 | −0.874997 | − | 0.484128i | \(-0.839137\pi\) | ||||
−0.874997 | + | 0.484128i | \(0.839137\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2827 | 1.84682 | 0.923411 | − | 0.383812i | \(-0.125389\pi\) | ||||
0.923411 | + | 0.383812i | \(0.125389\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.990671 | −0.172454 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.14134 | −0.192921 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.77801 | −1.11430 | −0.557149 | − | 0.830413i | \(-0.688105\pi\) | ||||
−0.557149 | + | 0.830413i | \(0.688105\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.68802 | 0.270300 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.55602 | −1.18005 | −0.590026 | − | 0.807384i | \(-0.700882\pi\) | ||||
−0.590026 | + | 0.807384i | \(0.700882\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.29200 | 1.41702 | 0.708508 | − | 0.705702i | \(-0.249368\pi\) | ||||
0.708508 | + | 0.705702i | \(0.249368\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.86799 | −0.427535 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.00933 | 1.02242 | 0.511208 | − | 0.859457i | \(-0.329198\pi\) | ||||
0.511208 | + | 0.859457i | \(0.329198\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.69735 | −0.813907 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.311977 | −0.0436855 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.64600 | 1.18762 | 0.593810 | − | 0.804605i | \(-0.297623\pi\) | ||||
0.593810 | + | 0.804605i | \(0.297623\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.72666 | −0.367662 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.363328 | −0.0481240 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −5.14134 | −0.669345 | −0.334672 | − | 0.942335i | \(-0.608626\pi\) | ||||
−0.334672 | + | 0.942335i | \(0.608626\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −9.45331 | −1.21037 | −0.605186 | − | 0.796084i | \(-0.706901\pi\) | ||||
−0.605186 | + | 0.796084i | \(0.706901\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.27334 | 0.412403 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.64600 | 0.576265 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.6553 | −1.66826 | −0.834132 | − | 0.551565i | \(-0.814031\pi\) | ||||
−0.834132 | + | 0.551565i | \(0.814031\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.60398 | 0.193096 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.45331 | 0.647189 | 0.323595 | − | 0.946196i | \(-0.395109\pi\) | ||||
0.323595 | + | 0.946196i | \(0.395109\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.87732 | 0.804930 | 0.402465 | − | 0.915435i | \(-0.368154\pi\) | ||||
0.402465 | + | 0.915435i | \(0.368154\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.363328 | 0.0419535 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.11203 | 0.354649 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −17.2920 | −1.94550 | −0.972751 | − | 0.231852i | \(-0.925521\pi\) | ||||
−0.972751 | + | 0.231852i | \(0.925521\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.82936 | 0.869929 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.2827 | −1.56773 | −0.783863 | − | 0.620933i | \(-0.786754\pi\) | ||||
−0.783863 | + | 0.620933i | \(0.786754\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.858664 | −0.0931352 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.42401 | −0.367092 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.0093 | 1.37899 | 0.689493 | − | 0.724292i | \(-0.257833\pi\) | ||||
0.689493 | + | 0.724292i | \(0.257833\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −5.30265 | −0.555869 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.73599 | 0.387404 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.00000 | −0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.68463 | −0.983326 | −0.491663 | − | 0.870786i | \(-0.663611\pi\) | ||||
−0.491663 | + | 0.870786i | \(0.663611\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 7.82003 | 0.785943 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.45331 | −0.144610 | −0.0723050 | − | 0.997383i | \(-0.523036\pi\) | ||||
−0.0723050 | + | 0.997383i | \(0.523036\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.23132 | −0.219859 | −0.109929 | − | 0.993939i | \(-0.535062\pi\) | ||||
−0.109929 | + | 0.993939i | \(0.535062\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.414680 | −0.0404686 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.6553 | 1.32011 | 0.660055 | − | 0.751217i | \(-0.270533\pi\) | ||||
0.660055 | + | 0.751217i | \(0.270533\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −20.1693 | −1.93187 | −0.965935 | − | 0.258784i | \(-0.916678\pi\) | ||||
−0.965935 | + | 0.258784i | \(0.916678\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.46264 | −0.233744 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.0514 | −0.945552 | −0.472776 | − | 0.881183i | \(-0.656748\pi\) | ||||
−0.472776 | + | 0.881183i | \(0.656748\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.41468 | 0.411671 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −13.3247 | −1.23187 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.980024 | 0.0898387 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.56534 | −0.324122 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −2.74531 | −0.247537 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.0700 | 1.24851 | 0.624256 | − | 0.781220i | \(-0.285402\pi\) | ||||
0.624256 | + | 0.781220i | \(0.285402\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.37605 | 0.297244 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.00000 | −0.349482 | −0.174741 | − | 0.984614i | \(-0.555909\pi\) | ||||
−0.174741 | + | 0.984614i | \(0.555909\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.14134 | 0.0989664 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.13201 | −0.183494 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −4.85866 | −0.415104 | −0.207552 | − | 0.978224i | \(-0.566550\pi\) | ||||
−0.207552 | + | 0.978224i | \(0.566550\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.17997 | −0.354540 | −0.177270 | − | 0.984162i | \(-0.556727\pi\) | ||||
−0.177270 | + | 0.984162i | \(0.556727\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.54669 | 0.214470 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −12.6680 | −1.05936 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.42401 | −0.782621 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −2.07001 | −0.170731 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.45331 | −0.119060 | −0.0595300 | − | 0.998227i | \(-0.518960\pi\) | ||||
−0.0595300 | + | 0.998227i | \(0.518960\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.27334 | −0.591896 | −0.295948 | − | 0.955204i | \(-0.595636\pi\) | ||||
−0.295948 | + | 0.955204i | \(0.595636\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.46264 | 0.199093 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.2827 | 0.825924 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.0093 | −1.35749 | −0.678746 | − | 0.734373i | \(-0.737476\pi\) | ||||
−0.678746 | + | 0.734373i | \(0.737476\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.14134 | 0.249124 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.03863 | −0.397100 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −10.1800 | −0.797357 | −0.398678 | − | 0.917091i | \(-0.630531\pi\) | ||||
−0.398678 | + | 0.917091i | \(0.630531\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.990671 | −0.0771237 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.07001 | −0.469711 | −0.234856 | − | 0.972030i | \(-0.575462\pi\) | ||||
−0.234856 | + | 0.972030i | \(0.575462\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.58532 | 0.660409 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.86799 | 0.219321 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.22199 | 0.397021 | 0.198510 | − | 0.980099i | \(-0.436390\pi\) | ||||
0.198510 | + | 0.980099i | \(0.436390\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.14134 | −0.0862769 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.86799 | −0.140407 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.55602 | −0.116302 | −0.0581510 | − | 0.998308i | \(-0.518520\pi\) | ||||
−0.0581510 | + | 0.998308i | \(0.518520\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −22.0000 | −1.63525 | −0.817624 | − | 0.575753i | \(-0.804709\pi\) | ||||
−0.817624 | + | 0.575753i | \(0.804709\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.43466 | −0.253897 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −6.77801 | −0.498329 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.34128 | 0.171211 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.43334 | 0.176999 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.03863 | 0.364583 | 0.182291 | − | 0.983245i | \(-0.441649\pi\) | ||||
0.182291 | + | 0.983245i | \(0.441649\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.68463 | −0.697115 | −0.348558 | − | 0.937287i | \(-0.613328\pi\) | ||||
−0.348558 | + | 0.937287i | \(0.613328\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.68802 | 0.120882 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.00000 | 0.142494 | 0.0712470 | − | 0.997459i | \(-0.477302\pi\) | ||||
0.0712470 | + | 0.997459i | \(0.477302\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −19.8867 | −1.40973 | −0.704864 | − | 0.709343i | \(-0.748992\pi\) | ||||
−0.704864 | + | 0.709343i | \(0.748992\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.96137 | −0.349948 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 10.7560 | 0.754920 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.55602 | −0.527735 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.6613 | −0.880019 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.72666 | 0.188607 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.31198 | 0.296849 | 0.148424 | − | 0.988924i | \(-0.452580\pi\) | ||||
0.148424 | + | 0.988924i | \(0.452580\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.98134 | 0.135759 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.29200 | 0.633709 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −11.7360 | −0.796691 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.49873 | 0.168848 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.98935 | −0.268353 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.5327 | 1.24104 | 0.620519 | − | 0.784191i | \(-0.286922\pi\) | ||||
0.620519 | + | 0.784191i | \(0.286922\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.86799 | −0.191200 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.82597 | 0.320311 | 0.160155 | − | 0.987092i | \(-0.448800\pi\) | ||||
0.160155 | + | 0.987092i | \(0.448800\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −23.7360 | −1.56852 | −0.784259 | − | 0.620434i | \(-0.786957\pi\) | ||||
−0.784259 | + | 0.620434i | \(0.786957\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.13069 | 0.0743939 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −14.5653 | −0.954207 | −0.477104 | − | 0.878847i | \(-0.658313\pi\) | ||||
−0.477104 | + | 0.878847i | \(0.658313\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.00933 | 0.457238 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −6.28267 | −0.408103 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.43334 | −0.157399 | −0.0786997 | − | 0.996898i | \(-0.525077\pi\) | ||||
−0.0786997 | + | 0.996898i | \(0.525077\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.1986 | 1.17228 | 0.586138 | − | 0.810211i | \(-0.300648\pi\) | ||||
0.586138 | + | 0.810211i | \(0.300648\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 9.24065 | 0.592788 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −5.69735 | −0.363990 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.64600 | −0.295618 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −5.18930 | −0.328858 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −15.1120 | −0.953863 | −0.476931 | − | 0.878940i | \(-0.658251\pi\) | ||||
−0.476931 | + | 0.878940i | \(0.658251\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0373 | −0.756779 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.311977 | −0.0195367 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 12.2313 | 0.762969 | 0.381484 | − | 0.924375i | \(-0.375413\pi\) | ||||
0.381484 | + | 0.924375i | \(0.375413\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.73599 | 0.480691 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 27.0280 | 1.67299 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −22.5840 | −1.39259 | −0.696295 | − | 0.717756i | \(-0.745169\pi\) | ||||
−0.696295 | + | 0.717756i | \(0.745169\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.64600 | 0.531120 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4.72666 | 0.289267 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 13.1120 | 0.799455 | 0.399727 | − | 0.916634i | \(-0.369105\pi\) | ||||
0.399727 | + | 0.916634i | \(0.369105\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 20.8960 | 1.26934 | 0.634670 | − | 0.772783i | \(-0.281136\pi\) | ||||
0.634670 | + | 0.772783i | \(0.281136\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.92660 | −0.116603 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −2.72666 | −0.164424 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.1800 | 1.21250 | 0.606248 | − | 0.795275i | \(-0.292674\pi\) | ||||
0.606248 | + | 0.795275i | \(0.292674\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −29.4906 | −1.76556 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −22.4626 | −1.34001 | −0.670004 | − | 0.742357i | \(-0.733708\pi\) | ||||
−0.670004 | + | 0.742357i | \(0.733708\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.829359 | −0.0493003 | −0.0246501 | − | 0.999696i | \(-0.507847\pi\) | ||||
−0.0246501 | + | 0.999696i | \(0.507847\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.363328 | −0.0215217 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.62395 | 0.509056 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.2627 | −0.956629 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.51870 | −0.206270 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 31.2886 | 1.82790 | 0.913950 | − | 0.405827i | \(-0.133016\pi\) | ||||
0.913950 | + | 0.405827i | \(0.133016\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.14134 | −0.299340 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.81325 | 0.337319 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 20.5106 | 1.18616 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −10.6053 | −0.611279 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.528030 | −0.0303345 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −9.45331 | −0.541295 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.11929 | −0.178027 | −0.0890136 | − | 0.996030i | \(-0.528371\pi\) | ||||
−0.0890136 | + | 0.996030i | \(0.528371\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −0.810702 | −0.0461192 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.4240 | 1.21484 | 0.607422 | − | 0.794379i | \(-0.292204\pi\) | ||||
0.607422 | + | 0.794379i | \(0.292204\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −12.1320 | −0.685742 | −0.342871 | − | 0.939383i | \(-0.611399\pi\) | ||||
−0.342871 | + | 0.939383i | \(0.611399\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.27334 | 0.184432 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −16.7487 | −0.940701 | −0.470350 | − | 0.882480i | \(-0.655872\pi\) | ||||
−0.470350 | + | 0.882480i | \(0.655872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 25.6960 | 1.43870 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4.96137 | 0.276916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.858664 | 0.0477773 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.64600 | 0.257714 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.32808 | −0.405244 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.00000 | −0.441054 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.97070 | −0.328179 | −0.164090 | − | 0.986445i | \(-0.552469\pi\) | ||||
−0.164090 | + | 0.986445i | \(0.552469\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 19.4393 | 1.06527 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −13.6553 | −0.746070 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −20.3340 | −1.10766 | −0.553832 | − | 0.832628i | \(-0.686835\pi\) | ||||
−0.553832 | + | 0.832628i | \(0.686835\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.65194 | −0.198346 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −28.0373 | −1.51831 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.4919 | 0.782492 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.60398 | 0.0863553 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 20.8294 | 1.11818 | 0.559089 | − | 0.829107i | \(-0.311151\pi\) | ||||
0.559089 | + | 0.829107i | \(0.311151\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.0187 | 1.07157 | 0.535787 | − | 0.844353i | \(-0.320015\pi\) | ||||
0.535787 | + | 0.844353i | \(0.320015\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9.90531 | −0.528706 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −27.1413 | −1.44459 | −0.722294 | − | 0.691586i | \(-0.756912\pi\) | ||||
−0.722294 | + | 0.691586i | \(0.756912\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.45331 | 0.289432 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.356070 | 0.0188452 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.59465 | 0.242496 | 0.121248 | − | 0.992622i | \(-0.461310\pi\) | ||||
0.121248 | + | 0.992622i | \(0.461310\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.29539 | −0.0679904 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.87732 | 0.359975 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 34.1214 | 1.78112 | 0.890560 | − | 0.454865i | \(-0.150313\pi\) | ||||
0.890560 | + | 0.454865i | \(0.150313\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 21.6706 | 1.12813 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.86799 | −0.512321 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.81664 | 0.404730 | 0.202365 | − | 0.979310i | \(-0.435137\pi\) | ||||
0.202365 | + | 0.979310i | \(0.435137\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0.363328 | 0.0187622 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −43.7839 | −2.25499 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −23.0573 | −1.18437 | −0.592187 | − | 0.805801i | \(-0.701735\pi\) | ||||
−0.592187 | + | 0.805801i | \(0.701735\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.11203 | 0.261897 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.8807 | −0.862564 | −0.431282 | − | 0.902217i | \(-0.641939\pi\) | ||||
−0.431282 | + | 0.902217i | \(0.641939\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.11203 | 0.158604 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −26.6494 | −1.35466 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 18.3013 | 0.927914 | 0.463957 | − | 0.885858i | \(-0.346429\pi\) | ||||
0.463957 | + | 0.885858i | \(0.346429\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.79073 | −0.191705 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.45331 | −0.0733099 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.2920 | −0.870055 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −12.1800 | −0.611295 | −0.305648 | − | 0.952145i | \(-0.598873\pi\) | ||||
−0.305648 | + | 0.952145i | \(0.598873\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.414680 | 0.0207599 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.5840 | 0.828166 | 0.414083 | − | 0.910239i | \(-0.364102\pi\) | ||||
0.414083 | + | 0.910239i | \(0.364102\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 47.7733 | 2.37976 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 7.82936 | 0.389044 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.4813 | 0.916084 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.5653 | 0.917997 | 0.458999 | − | 0.888437i | \(-0.348208\pi\) | ||||
0.458999 | + | 0.888437i | \(0.348208\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.76529 | −0.0870753 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5.86799 | 0.288745 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.2827 | −0.701109 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1.51870 | −0.0743711 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.84802 | 0.139135 | 0.0695674 | − | 0.997577i | \(-0.477838\pi\) | ||||
0.0695674 | + | 0.997577i | \(0.477838\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −24.5360 | −1.19581 | −0.597907 | − | 0.801566i | \(-0.704001\pi\) | ||||
−0.597907 | + | 0.801566i | \(0.704001\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −20.1027 | −0.977427 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.858664 | −0.0416513 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 10.7894 | 0.522136 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.60266 | −0.222218 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.53736 | 0.363062 | 0.181531 | − | 0.983385i | \(-0.441895\pi\) | ||||
0.181531 | + | 0.983385i | \(0.441895\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.392633 | −0.0188687 | −0.00943437 | − | 0.999955i | \(-0.503003\pi\) | ||||
−0.00943437 | + | 0.999955i | \(0.503003\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.42401 | −0.164169 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.41468 | −0.211183 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.29200 | −0.252573 | −0.126287 | − | 0.991994i | \(-0.540306\pi\) | ||||
−0.126287 | + | 0.991994i | \(0.540306\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 16.3400 | 0.778093 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.0187 | −1.04614 | −0.523069 | − | 0.852290i | \(-0.675213\pi\) | ||||
−0.523069 | + | 0.852290i | \(0.675213\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.0093 | 0.616701 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −0.528030 | −0.0249749 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.90663 | −0.231558 | −0.115779 | − | 0.993275i | \(-0.536936\pi\) | ||||
−0.115779 | + | 0.993275i | \(0.536936\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6027 | 0.970141 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −2.64261 | −0.124161 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.30265 | −0.248592 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.9800 | 1.26207 | 0.631036 | − | 0.775753i | \(-0.282630\pi\) | ||||
0.631036 | + | 0.775753i | \(0.282630\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.83068 | 0.0854487 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 27.1307 | 1.26360 | 0.631801 | − | 0.775131i | \(-0.282316\pi\) | ||||
0.631801 | + | 0.775131i | \(0.282316\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.9253 | 0.786585 | 0.393292 | − | 0.919413i | \(-0.371336\pi\) | ||||
0.393292 | + | 0.919413i | \(0.371336\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.73599 | 0.173252 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −42.6213 | −1.97228 | −0.986140 | − | 0.165917i | \(-0.946942\pi\) | ||||
−0.986140 | + | 0.165917i | \(0.946942\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 15.5853 | 0.719663 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −6.17997 | −0.284758 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −25.3361 | −1.16495 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −24.7967 | −1.13536 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 25.3107 | 1.15647 | 0.578237 | − | 0.815869i | \(-0.303741\pi\) | ||||
0.578237 | + | 0.815869i | \(0.303741\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.4906 | −1.43585 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.83068 | −0.0832987 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −9.68463 | −0.439757 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.4020 | −1.15107 | −0.575536 | − | 0.817776i | \(-0.695207\pi\) | ||||
−0.575536 | + | 0.817776i | \(0.695207\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.69867 | −0.167260 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.6240 | 0.930746 | 0.465373 | − | 0.885115i | \(-0.345920\pi\) | ||||
0.465373 | + | 0.885115i | \(0.345920\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8.09206 | 0.364448 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.82003 | 0.351484 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −6.22406 | −0.279187 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.3693 | 0.777555 | 0.388778 | − | 0.921332i | \(-0.372897\pi\) | ||||
0.388778 | + | 0.921332i | \(0.372897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.20541 | −0.0985303 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 14.9987 | 0.668758 | 0.334379 | − | 0.942439i | \(-0.391473\pi\) | ||||
0.334379 | + | 0.942439i | \(0.391473\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.45331 | −0.0646716 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.11929 | 0.138533 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 19.9160 | 0.882759 | 0.441380 | − | 0.897320i | \(-0.354489\pi\) | ||||
0.441380 | + | 0.897320i | \(0.354489\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7.84934 | −0.347234 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.13201 | 0.0941304 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −2.23132 | −0.0983237 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.1120 | −0.840546 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.89730 | 0.0832821 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.8294 | −0.649686 | −0.324843 | − | 0.945768i | \(-0.605311\pi\) | ||||
−0.324843 | + | 0.945768i | \(0.605311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9966 | 0.524575 | 0.262288 | − | 0.964990i | \(-0.415523\pi\) | ||||
0.262288 | + | 0.964990i | \(0.415523\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.414680 | −0.0180981 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.82936 | −0.384613 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.51060 | −0.152635 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.7453 | 0.639892 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −35.1053 | −1.52058 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 13.6553 | 0.590371 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.565344 | −0.0243964 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 15.5347 | 0.669128 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.01866 | 0.0867889 | 0.0433944 | − | 0.999058i | \(-0.486183\pi\) | ||||
0.0433944 | + | 0.999058i | \(0.486183\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −7.99322 | −0.343022 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −20.1693 | −0.863959 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.6940 | −0.799296 | −0.399648 | − | 0.916669i | \(-0.630868\pi\) | ||||
−0.399648 | + | 0.916669i | \(0.630868\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 27.1120 | 1.15711 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.42401 | 0.401476 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.7360 | 0.839259 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.46264 | −0.104533 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −11.0866 | −0.469754 | −0.234877 | − | 0.972025i | \(-0.575469\pi\) | ||||
−0.234877 | + | 0.972025i | \(0.575469\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 43.1706 | 1.82592 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.850654 | 0.0359146 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.69396 | 0.113537 | 0.0567685 | − | 0.998387i | \(-0.481920\pi\) | ||||
0.0567685 | + | 0.998387i | \(0.481920\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.0514 | −0.422864 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −8.93593 | −0.375274 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 29.4134 | 1.23307 | 0.616536 | − | 0.787327i | \(-0.288535\pi\) | ||||
0.616536 | + | 0.787327i | \(0.288535\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.0466 | −1.38296 | −0.691479 | − | 0.722396i | \(-0.743041\pi\) | ||||
−0.691479 | + | 0.722396i | \(0.743041\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.83068 | 0.0764777 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.41468 | 0.184105 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −0.396022 | −0.0164866 | −0.00824331 | − | 0.999966i | \(-0.502624\pi\) | ||||
−0.00824331 | + | 0.999966i | \(0.502624\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.51870 | −0.146232 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.3013 | 0.676293 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −23.5747 | −0.976363 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.3247 | −0.550908 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.0773 | −0.581031 | −0.290515 | − | 0.956870i | \(-0.593827\pi\) | ||||
−0.290515 | + | 0.956870i | \(0.593827\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.2827 | −0.423690 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.726656 | 0.0298907 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.43466 | 0.223175 | 0.111587 | − | 0.993755i | \(-0.464407\pi\) | ||||
0.111587 | + | 0.993755i | \(0.464407\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.980024 | 0.0401771 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.22538 | −0.295715 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −11.6333 | −0.475323 | −0.237662 | − | 0.971348i | \(-0.576381\pi\) | ||||
−0.237662 | + | 0.971348i | \(0.576381\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 8.12136 | 0.331277 | 0.165639 | − | 0.986187i | \(-0.447031\pi\) | ||||
0.165639 | + | 0.986187i | \(0.447031\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 39.1634 | 1.59486 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.56534 | −0.144952 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −10.5327 | −0.427507 | −0.213754 | − | 0.976888i | \(-0.568569\pi\) | ||||
−0.213754 | + | 0.976888i | \(0.568569\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.90794 | 0.158358 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 32.5653 | 1.31745 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −47.3293 | −1.91161 | −0.955807 | − | 0.293996i | \(-0.905015\pi\) | ||||
−0.955807 | + | 0.293996i | \(0.905015\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.74531 | −0.110702 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −33.3693 | −1.34340 | −0.671698 | − | 0.740825i | \(-0.734435\pi\) | ||||
−0.671698 | + | 0.740825i | \(0.734435\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −33.8760 | −1.36159 | −0.680796 | − | 0.732473i | \(-0.738366\pi\) | ||||
−0.680796 | + | 0.732473i | \(0.738366\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −9.41213 | −0.377696 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −14.8480 | −0.594873 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.990671 | 0.0395636 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.82003 | 0.232060 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −27.8573 | −1.10898 | −0.554492 | − | 0.832189i | \(-0.687087\pi\) | ||||
−0.554492 | + | 0.832189i | \(0.687087\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.56666 | 0.0622693 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.0700 | 0.558351 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −26.4699 | −1.04878 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −15.6401 | −0.618711 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.74531 | −0.187429 | −0.0937143 | − | 0.995599i | \(-0.529874\pi\) | ||||
−0.0937143 | + | 0.995599i | \(0.529874\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.28267 | −0.247764 | −0.123882 | − | 0.992297i | \(-0.539534\pi\) | ||||
−0.123882 | + | 0.992297i | \(0.539534\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3.37605 | 0.132932 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16.1507 | −0.634948 | −0.317474 | − | 0.948267i | \(-0.602835\pi\) | ||||
−0.317474 | + | 0.948267i | \(0.602835\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.0187 | 0.550280 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −4.26401 | −0.167120 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −29.8760 | −1.16914 | −0.584569 | − | 0.811344i | \(-0.698736\pi\) | ||||
−0.584569 | + | 0.811344i | \(0.698736\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00000 | −0.156293 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.7241 | −0.769511 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −17.4427 | −0.679470 | −0.339735 | − | 0.940521i | \(-0.610337\pi\) | ||||
−0.339735 | + | 0.940521i | \(0.610337\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.87732 | 0.111915 | 0.0559574 | − | 0.998433i | \(-0.482179\pi\) | ||||
0.0559574 | + | 0.998433i | \(0.482179\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.44944 | −0.0562918 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.14134 | 0.0442591 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −41.6040 | −1.61091 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.73344 | 0.260330 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.7759 | 0.995069 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.9393 | 0.421680 | 0.210840 | − | 0.977521i | \(-0.432380\pi\) | ||||
0.210840 | + | 0.977521i | \(0.432380\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.13201 | −0.0820610 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −19.0900 | −0.733688 | −0.366844 | − | 0.930283i | \(-0.619562\pi\) | ||||
−0.366844 | + | 0.930283i | \(0.619562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 11.0534 | 0.424191 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.75341 | 0.0671909 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25.7687 | 0.986011 | 0.493006 | − | 0.870026i | \(-0.335898\pi\) | ||||
0.493006 | + | 0.870026i | \(0.335898\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.85866 | −0.185640 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −8.62395 | −0.329024 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 40.1693 | 1.53033 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −27.2334 | −1.03601 | −0.518004 | − | 0.855378i | \(-0.673325\pi\) | ||||
−0.518004 | + | 0.855378i | \(0.673325\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8.92528 | −0.339043 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.17997 | −0.158555 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6.48808 | 0.245753 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.29200 | −0.200162 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −49.6960 | −1.87699 | −0.938497 | − | 0.345288i | \(-0.887781\pi\) | ||||
−0.938497 | + | 0.345288i | \(0.887781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.77801 | 0.255637 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.54669 | 0.0959138 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.65872 | 0.0623825 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.64006 | −0.211817 | −0.105908 | − | 0.994376i | \(-0.533775\pi\) | ||||
−0.105908 | + | 0.994376i | \(0.533775\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 49.5933 | 1.85990 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 45.3947 | 1.70005 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12.6680 | −0.473758 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −0.884100 | −0.0330173 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.4240 | 1.24651 | 0.623253 | − | 0.782021i | \(-0.285811\pi\) | ||||
0.623253 | + | 0.782021i | \(0.285811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.54669 | 0.0948436 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 6.61208 | 0.245906 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −9.42401 | −0.349999 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.3306 | 0.531494 | 0.265747 | − | 0.964043i | \(-0.414381\pi\) | ||||
0.265747 | + | 0.964043i | \(0.414381\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −20.1307 | −0.745581 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.97871 | −0.295103 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.8853 | 1.51013 | 0.755067 | − | 0.655648i | \(-0.227604\pi\) | ||||
0.755067 | + | 0.655648i | \(0.227604\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −2.07001 | −0.0763534 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 37.2334 | 1.37151 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −28.8294 | −1.06051 | −0.530253 | − | 0.847840i | \(-0.677903\pi\) | ||||
−0.530253 | + | 0.847840i | \(0.677903\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.68802 | −0.0620111 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.05135 | 0.295375 | 0.147688 | − | 0.989034i | \(-0.452817\pi\) | ||||
0.147688 | + | 0.989034i | \(0.452817\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.45331 | −0.0532453 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 40.9626 | 1.49874 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15.5853 | −0.569475 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −47.3107 | −1.72639 | −0.863195 | − | 0.504870i | \(-0.831540\pi\) | ||||
−0.863195 | + | 0.504870i | \(0.831540\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −5.49063 | −0.200090 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −7.27334 | −0.264704 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −6.20541 | −0.225539 | −0.112770 | − | 0.993621i | \(-0.535972\pi\) | ||||
−0.112770 | + | 0.993621i | \(0.535972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.37350 | −0.158748 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 43.8280 | 1.58877 | 0.794383 | − | 0.607418i | \(-0.207795\pi\) | ||||
0.794383 | + | 0.607418i | \(0.207795\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23.0200 | 0.833379 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 2.46264 | 0.0890370 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −23.8867 | −0.862497 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3.22538 | −0.116310 | −0.0581551 | − | 0.998308i | \(-0.518522\pi\) | ||||
−0.0581551 | + | 0.998308i | \(0.518522\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 4.44398 | 0.160046 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.16470 | −0.221729 | −0.110864 | − | 0.993836i | \(-0.535362\pi\) | ||||
−0.110864 | + | 0.993836i | \(0.535362\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.2827 | 0.369364 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.81070 | 0.100833 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 7.55602 | 0.270722 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −14.8693 | −0.532066 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 20.0921 | 0.718031 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −17.0093 | −0.607089 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 35.1527 | 1.25306 | 0.626530 | − | 0.779397i | \(-0.284475\pi\) | ||||
0.626530 | + | 0.779397i | \(0.284475\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.20541 | −0.292120 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.4720 | 0.407896 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −43.9201 | −1.55965 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.14134 | 0.111412 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 30.3420 | 1.07477 | 0.537385 | − | 0.843337i | \(-0.319412\pi\) | ||||
0.537385 | + | 0.843337i | \(0.319412\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.01866 | −0.212925 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −37.3107 | −1.31831 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −18.7521 | −0.661747 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.03863 | −0.177588 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 4.76397 | 0.167700 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −4.96137 | −0.174432 | −0.0872162 | − | 0.996189i | \(-0.527797\pi\) | ||||
−0.0872162 | + | 0.996189i | \(0.527797\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.8094 | 1.04675 | 0.523375 | − | 0.852103i | \(-0.324673\pi\) | ||||
0.523375 | + | 0.852103i | \(0.324673\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7.59210 | 0.266267 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −10.1800 | −0.356589 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.29200 | −0.325086 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 15.2080 | 0.531409 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11.1520 | 0.389207 | 0.194603 | − | 0.980882i | \(-0.437658\pi\) | ||||
0.194603 | + | 0.980882i | \(0.437658\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.1413 | 0.597509 | 0.298755 | − | 0.954330i | \(-0.403429\pi\) | ||||
0.298755 | + | 0.954330i | \(0.403429\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.990671 | −0.0344907 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.8633 | 0.864581 | 0.432291 | − | 0.901734i | \(-0.357705\pi\) | ||||
0.432291 | + | 0.901734i | \(0.357705\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.7746 | 0.652069 | 0.326035 | − | 0.945358i | \(-0.394287\pi\) | ||||
0.326035 | + | 0.945358i | \(0.394287\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.33195 | 0.254343 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.89211 | 0.169502 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −6.07001 | −0.210061 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −21.9227 | −0.757761 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −29.0280 | −1.00216 | −0.501079 | − | 0.865402i | \(-0.667063\pi\) | ||||
−0.501079 | + | 0.865402i | \(0.667063\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.8119 | 2.06248 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.16131 | −0.281091 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 8.58532 | 0.295344 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.06926 | 0.139821 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −0.301330 | −0.0103416 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −29.9227 | −1.02574 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −40.7894 | −1.39660 | −0.698301 | − | 0.715804i | \(-0.746060\pi\) | ||||
−0.698301 | + | 0.715804i | \(0.746060\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 2.86799 | 0.0980833 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −32.6354 | −1.11480 | −0.557401 | − | 0.830243i | \(-0.688201\pi\) | ||||
−0.557401 | + | 0.830243i | \(0.688201\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.4906 | 1.14269 | 0.571343 | − | 0.820712i | \(-0.306423\pi\) | ||||
0.571343 | + | 0.820712i | \(0.306423\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.13333 | 0.106783 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −5.13795 | −0.174898 | −0.0874489 | − | 0.996169i | \(-0.527871\pi\) | ||||
−0.0874489 | + | 0.996169i | \(0.527871\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.22199 | 0.177553 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −5.90870 | −0.200670 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 47.1493 | 1.59943 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −63.4427 | −2.14967 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 27.7755 | 0.940057 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.14134 | −0.0385842 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0220 | 0.541026 | 0.270513 | − | 0.962716i | \(-0.412807\pi\) | ||||
0.270513 | + | 0.962716i | \(0.412807\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 11.3680 | 0.383434 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.5306 | 0.388475 | 0.194238 | − | 0.980955i | \(-0.437777\pi\) | ||||
0.194238 | + | 0.980955i | \(0.437777\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.5161 | −1.32982 | −0.664911 | − | 0.746923i | \(-0.731530\pi\) | ||||
−0.664911 | + | 0.746923i | \(0.731530\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.86799 | −0.0627919 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20.8153 | 0.698910 | 0.349455 | − | 0.936953i | \(-0.386367\pi\) | ||||
0.349455 | + | 0.936953i | \(0.386367\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −16.0586 | −0.538588 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21.3480 | −0.715184 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7.00933 | −0.234558 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.55602 | −0.0520119 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.45208 | 0.248818 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −96.9040 | −3.23193 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.42401 | −0.247330 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.85320 | −0.128227 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −22.0000 | −0.731305 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.0339 | 1.06367 | 0.531835 | − | 0.846848i | \(-0.321503\pi\) | ||||
0.531835 | + | 0.846848i | \(0.321503\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.16809 | 0.138247 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.12136 | 0.0702838 | 0.0351419 | − | 0.999382i | \(-0.488812\pi\) | ||||
0.0351419 | + | 0.999382i | \(0.488812\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 38.9439 | 1.28886 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −3.43466 | −0.113546 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4.56534 | 0.150761 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 26.4333 | 0.871955 | 0.435978 | − | 0.899957i | \(-0.356403\pi\) | ||||
0.435978 | + | 0.899957i | \(0.356403\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.13333 | −0.0373444 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 25.3361 | 0.833948 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.77801 | −0.222860 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 6.39941 | 0.210184 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.7907 | 0.583695 | 0.291847 | − | 0.956465i | \(-0.405730\pi\) | ||||
0.291847 | + | 0.956465i | \(0.405730\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.69735 | 0.186723 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.78395 | 0.254835 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.34128 | 0.0765681 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7.46396 | −0.243837 | −0.121918 | − | 0.992540i | \(-0.538905\pi\) | ||||
−0.121918 | + | 0.992540i | \(0.538905\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −4.40790 | −0.143846 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.67869 | 0.0873229 | 0.0436615 | − | 0.999046i | \(-0.486098\pi\) | ||||
0.0436615 | + | 0.999046i | \(0.486098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −33.3574 | −1.08627 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.43334 | 0.0791565 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 42.5840 | 1.38379 | 0.691897 | − | 0.721996i | \(-0.256775\pi\) | ||||
0.691897 | + | 0.721996i | \(0.256775\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.9520 | 1.03721 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6.08528 | −0.197329 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 60.0046 | 1.94374 | 0.971870 | − | 0.235517i | \(-0.0756784\pi\) | ||||
0.971870 | + | 0.235517i | \(0.0756784\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.03863 | 0.163046 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 9.33609 | 0.301793 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5.54537 | 0.179069 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 74.7333 | 2.41075 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −39.1634 | −1.26202 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9.68463 | −0.311759 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 61.1307 | 1.96583 | 0.982915 | − | 0.184059i | \(-0.0589237\pi\) | ||||
0.982915 | + | 0.184059i | \(0.0589237\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.311977 | 0.0100221 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.6213 | 1.75288 | 0.876441 | − | 0.481510i | \(-0.159911\pi\) | ||||
0.876441 | + | 0.481510i | \(0.159911\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.77075 | 0.152943 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 1.68802 | 0.0540600 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −19.3060 | −0.617655 | −0.308827 | − | 0.951118i | \(-0.599937\pi\) | ||||
−0.308827 | + | 0.951118i | \(0.599937\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −35.4720 | −1.13369 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 57.8455 | 1.84686 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −25.1820 | −0.803182 | −0.401591 | − | 0.915819i | \(-0.631543\pi\) | ||||
−0.401591 | + | 0.915819i | \(0.631543\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.00000 | 0.0637253 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.90663 | −0.0925189 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.0212 | 1.30440 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.82003 | 0.184879 | 0.0924397 | − | 0.995718i | \(-0.470533\pi\) | ||||
0.0924397 | + | 0.995718i | \(0.470533\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.16932 | −0.0688414 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −19.8867 | −0.630449 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.97201 | −0.284147 | −0.142073 | − | 0.989856i | \(-0.545377\pi\) | ||||
−0.142073 | + | 0.989856i | \(0.545377\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 14.4508 | 0.457202 |
(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 | 6080.2.a.bs.1.2 | 3 | ||
4.3 | odd | 2 | 6080.2.a.bw.1.2 | 3 | |||
8.3 | odd | 2 | 760.2.a.h.1.2 | ✓ | 3 | ||
8.5 | even | 2 | 1520.2.a.r.1.2 | 3 | |||
24.11 | even | 2 | 6840.2.a.bj.1.3 | 3 | |||
40.3 | even | 4 | 3800.2.d.k.3649.4 | 6 | |||
40.19 | odd | 2 | 3800.2.a.y.1.2 | 3 | |||
40.27 | even | 4 | 3800.2.d.k.3649.3 | 6 | |||
40.29 | even | 2 | 7600.2.a.bo.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
760.2.a.h.1.2 | ✓ | 3 | 8.3 | odd | 2 | ||
1520.2.a.r.1.2 | 3 | 8.5 | even | 2 | |||
3800.2.a.y.1.2 | 3 | 40.19 | odd | 2 | |||
3800.2.d.k.3649.3 | 6 | 40.27 | even | 4 | |||
3800.2.d.k.3649.4 | 6 | 40.3 | even | 4 | |||
6080.2.a.bs.1.2 | 3 | 1.1 | even | 1 | trivial | ||
6080.2.a.bw.1.2 | 3 | 4.3 | odd | 2 | |||
6840.2.a.bj.1.3 | 3 | 24.11 | even | 2 | |||
7600.2.a.bo.1.2 | 3 | 40.29 | even | 2 |