Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1088,2,Mod(1,1088)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1088, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1088.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1088 = 2^{6} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1088.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: | \(8.68772373992\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 136) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.61803\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1088.1 |
$q$-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 | ||||||||
\(3\) | −3.23607 | −1.86834 | −0.934172 | − | 0.356822i | \(-0.883860\pi\) | ||||
−0.934172 | + | 0.356822i | \(0.883860\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.00000 | −0.894427 | −0.447214 | − | 0.894427i | \(-0.647584\pi\) | ||||
−0.447214 | + | 0.894427i | \(0.647584\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.23607 | −1.22312 | −0.611559 | − | 0.791199i | \(-0.709457\pi\) | ||||
−0.611559 | + | 0.791199i | \(0.709457\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.47214 | 2.49071 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.23607 | 0.975711 | 0.487856 | − | 0.872924i | \(-0.337779\pi\) | ||||
0.487856 | + | 0.872924i | \(0.337779\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 6.47214 | 1.67110 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.47214 | 0.567147 | 0.283573 | − | 0.958951i | \(-0.408480\pi\) | ||||
0.283573 | + | 0.958951i | \(0.408480\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 10.4721 | 2.28521 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.23607 | −0.674767 | −0.337383 | − | 0.941367i | \(-0.609542\pi\) | ||||
−0.337383 | + | 0.941367i | \(0.609542\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −14.4721 | −2.78516 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.00000 | −0.371391 | −0.185695 | − | 0.982607i | \(-0.559454\pi\) | ||||
−0.185695 | + | 0.982607i | \(0.559454\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.23607 | 0.581215 | 0.290607 | − | 0.956842i | \(-0.406143\pi\) | ||||
0.290607 | + | 0.956842i | \(0.406143\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −10.4721 | −1.82296 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.47214 | 1.09399 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.94427 | −1.14163 | −0.570816 | − | 0.821078i | \(-0.693373\pi\) | ||||
−0.570816 | + | 0.821078i | \(0.693373\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −14.4721 | −2.31740 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.00000 | 0.312348 | 0.156174 | − | 0.987730i | \(-0.450084\pi\) | ||||
0.156174 | + | 0.987730i | \(0.450084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.4721 | −1.59699 | −0.798493 | − | 0.602004i | \(-0.794369\pi\) | ||||
−0.798493 | + | 0.602004i | \(0.794369\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.9443 | −2.22776 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.94427 | 0.721196 | 0.360598 | − | 0.932721i | \(-0.382573\pi\) | ||||
0.360598 | + | 0.932721i | \(0.382573\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.23607 | −0.453140 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.47214 | −0.872703 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.00000 | −1.05963 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.52786 | 0.719667 | 0.359833 | − | 0.933017i | \(-0.382834\pi\) | ||||
0.359833 | + | 0.933017i | \(0.382834\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.9443 | 1.40127 | 0.700635 | − | 0.713520i | \(-0.252900\pi\) | ||||
0.700635 | + | 0.713520i | \(0.252900\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −24.1803 | −3.04644 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.94427 | −1.10940 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.0000 | −1.46603 | −0.733017 | − | 0.680211i | \(-0.761888\pi\) | ||||
−0.733017 | + | 0.680211i | \(0.761888\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 10.4721 | 1.26070 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.76393 | −0.565375 | −0.282687 | − | 0.959212i | \(-0.591226\pi\) | ||||
−0.282687 | + | 0.959212i | \(0.591226\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −2.94427 | −0.344601 | −0.172300 | − | 0.985044i | \(-0.555120\pi\) | ||||
−0.172300 | + | 0.985044i | \(0.555120\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.23607 | 0.373669 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −10.4721 | −1.19341 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.70820 | 0.192188 | 0.0960940 | − | 0.995372i | \(-0.469365\pi\) | ||||
0.0960940 | + | 0.995372i | \(0.469365\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 24.4164 | 2.71293 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 10.4721 | 1.14947 | 0.574733 | − | 0.818341i | \(-0.305106\pi\) | ||||
0.574733 | + | 0.818341i | \(0.305106\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00000 | −0.216930 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.47214 | 0.693886 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.4721 | −1.74604 | −0.873021 | − | 0.487682i | \(-0.837843\pi\) | ||||
−0.873021 | + | 0.487682i | \(0.837843\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.4721 | −1.51709 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.4721 | −1.08591 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.94427 | −0.507272 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.00000 | 0.203069 | 0.101535 | − | 0.994832i | \(-0.467625\pi\) | ||||
0.101535 | + | 0.994832i | \(0.467625\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 24.1803 | 2.43022 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.4164 | −1.33498 | −0.667491 | − | 0.744618i | \(-0.732632\pi\) | ||||
−0.667491 | + | 0.744618i | \(0.732632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.00000 | 0.788263 | 0.394132 | − | 0.919054i | \(-0.371045\pi\) | ||||
0.394132 | + | 0.919054i | \(0.371045\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −20.9443 | −2.04395 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 9.70820 | 0.938527 | 0.469264 | − | 0.883058i | \(-0.344519\pi\) | ||||
0.469264 | + | 0.883058i | \(0.344519\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 22.4721 | 2.13296 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.94427 | −0.276974 | −0.138487 | − | 0.990364i | \(-0.544224\pi\) | ||||
−0.138487 | + | 0.990364i | \(0.544224\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.47214 | 0.603530 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 33.4164 | 3.08935 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.23607 | −0.296650 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.527864 | −0.0479876 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −6.47214 | −0.583573 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0000 | 1.07331 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.47214 | 0.574309 | 0.287155 | − | 0.957884i | \(-0.407291\pi\) | ||||
0.287155 | + | 0.957884i | \(0.407291\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 33.8885 | 2.98372 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −21.1246 | −1.84567 | −0.922833 | − | 0.385200i | \(-0.874132\pi\) | ||||
−0.922833 | + | 0.385200i | \(0.874132\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 28.9443 | 2.49113 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.4721 | −1.40731 | −0.703655 | − | 0.710542i | \(-0.748450\pi\) | ||||
−0.703655 | + | 0.710542i | \(0.748450\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.2361 | −0.953031 | −0.476515 | − | 0.879166i | \(-0.658100\pi\) | ||||
−0.476515 | + | 0.879166i | \(0.658100\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.0000 | −1.34744 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.4721 | 1.21022 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.00000 | 0.332182 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.2361 | −0.926735 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.00000 | −0.491539 | −0.245770 | − | 0.969328i | \(-0.579041\pi\) | ||||
−0.245770 | + | 0.969328i | \(0.579041\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.4721 | −1.17773 | −0.588863 | − | 0.808233i | \(-0.700424\pi\) | ||||
−0.588863 | + | 0.808233i | \(0.700424\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.47214 | 0.604086 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.47214 | −0.519854 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −23.8885 | −1.90651 | −0.953257 | − | 0.302162i | \(-0.902292\pi\) | ||||
−0.953257 | + | 0.302162i | \(0.902292\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −6.47214 | −0.513274 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 10.4721 | 0.825320 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.180340 | 0.0141253 | 0.00706266 | − | 0.999975i | \(-0.497752\pi\) | ||||
0.00706266 | + | 0.999975i | \(0.497752\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 20.9443 | 1.63051 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 6.29180 | 0.486874 | 0.243437 | − | 0.969917i | \(-0.421725\pi\) | ||||
0.243437 | + | 0.969917i | \(0.421725\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.4721 | 1.41260 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.00000 | −0.152057 | −0.0760286 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760286 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.23607 | 0.244624 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −17.8885 | −1.34459 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.52786 | 0.413172 | 0.206586 | − | 0.978428i | \(-0.433765\pi\) | ||||
0.206586 | + | 0.978428i | \(0.433765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.0000 | −0.743294 | −0.371647 | − | 0.928374i | \(-0.621207\pi\) | ||||
−0.371647 | + | 0.928374i | \(0.621207\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −35.4164 | −2.61806 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 13.8885 | 1.02111 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.23607 | 0.236645 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 46.8328 | 3.40659 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −4.94427 | −0.357755 | −0.178877 | − | 0.983871i | \(-0.557247\pi\) | ||||
−0.178877 | + | 0.983871i | \(0.557247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.94427 | −0.211933 | −0.105967 | − | 0.994370i | \(-0.533794\pi\) | ||||
−0.105967 | + | 0.994370i | \(0.533794\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 28.9443 | 2.07274 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.9443 | 0.779747 | 0.389874 | − | 0.920868i | \(-0.372519\pi\) | ||||
0.389874 | + | 0.920868i | \(0.372519\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.180340 | 0.0127840 | 0.00639198 | − | 0.999980i | \(-0.497965\pi\) | ||||
0.00639198 | + | 0.999980i | \(0.497965\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 38.8328 | 2.73906 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.47214 | 0.454255 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.00000 | −0.279372 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −24.1803 | −1.68065 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.00000 | 0.553372 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.23607 | 0.222780 | 0.111390 | − | 0.993777i | \(-0.464470\pi\) | ||||
0.111390 | + | 0.993777i | \(0.464470\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.4164 | 1.05631 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 20.9443 | 1.42839 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.4721 | −0.710895 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 9.52786 | 0.643833 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.47214 | 0.300828 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.4721 | −0.969126 | −0.484563 | − | 0.874756i | \(-0.661021\pi\) | ||||
−0.484563 | + | 0.874756i | \(0.661021\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.47214 | −0.498142 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 3.23607 | 0.214785 | 0.107393 | − | 0.994217i | \(-0.465750\pi\) | ||||
0.107393 | + | 0.994217i | \(0.465750\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 15.5279 | 1.02611 | 0.513055 | − | 0.858356i | \(-0.328514\pi\) | ||||
0.513055 | + | 0.858356i | \(0.328514\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 33.8885 | 2.22970 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 11.8885 | 0.778844 | 0.389422 | − | 0.921059i | \(-0.372675\pi\) | ||||
0.389422 | + | 0.921059i | \(0.372675\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.88854 | −0.645057 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.52786 | −0.359073 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.8885 | 1.15711 | 0.578557 | − | 0.815642i | \(-0.303616\pi\) | ||||
0.578557 | + | 0.815642i | \(0.303616\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.9443 | −1.22031 | −0.610154 | − | 0.792283i | \(-0.708892\pi\) | ||||
−0.610154 | + | 0.792283i | \(0.708892\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −35.5967 | −2.28353 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −6.94427 | −0.443653 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 11.0557 | 0.703459 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −33.8885 | −2.14760 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.94427 | 0.564557 | 0.282279 | − | 0.959332i | \(-0.408910\pi\) | ||||
0.282279 | + | 0.959332i | \(0.408910\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −10.4721 | −0.658378 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 6.47214 | 0.405301 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.3607 | 1.39482 | 0.697410 | − | 0.716672i | \(-0.254335\pi\) | ||||
0.697410 | + | 0.716672i | \(0.254335\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 22.4721 | 1.39635 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −14.9443 | −0.925027 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −11.4164 | −0.703966 | −0.351983 | − | 0.936006i | \(-0.614492\pi\) | ||||
−0.351983 | + | 0.936006i | \(0.614492\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.00000 | −0.245718 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 53.3050 | 3.26221 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.9443 | 1.15505 | 0.577526 | − | 0.816372i | \(-0.304018\pi\) | ||||
0.577526 | + | 0.816372i | \(0.304018\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −17.8885 | −1.08665 | −0.543326 | − | 0.839522i | \(-0.682835\pi\) | ||||
−0.543326 | + | 0.839522i | \(0.682835\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 46.8328 | 2.83445 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −3.23607 | −0.195142 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −32.8328 | −1.97273 | −0.986366 | − | 0.164564i | \(-0.947378\pi\) | ||||
−0.986366 | + | 0.164564i | \(0.947378\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 24.1803 | 1.44764 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −15.8885 | −0.947831 | −0.473916 | − | 0.880570i | \(-0.657160\pi\) | ||||
−0.473916 | + | 0.880570i | \(0.657160\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.23607 | 0.192364 | 0.0961821 | − | 0.995364i | \(-0.469337\pi\) | ||||
0.0961821 | + | 0.995364i | \(0.469337\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 16.0000 | 0.947758 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.47214 | −0.382038 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.47214 | −0.379403 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.0000 | 0.584206 | 0.292103 | − | 0.956387i | \(-0.405645\pi\) | ||||
0.292103 | + | 0.956387i | \(0.405645\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.0557 | −0.643689 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −46.8328 | −2.71752 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.4721 | −0.836945 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 33.8885 | 1.95330 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 43.4164 | 2.49421 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −21.8885 | −1.25333 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.8885 | −1.70583 | −0.852915 | − | 0.522050i | \(-0.825167\pi\) | ||||
−0.852915 | + | 0.522050i | \(0.825167\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −25.8885 | −1.47275 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 19.2361 | 1.09078 | 0.545389 | − | 0.838183i | \(-0.316382\pi\) | ||||
0.545389 | + | 0.838183i | \(0.316382\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 27.8885 | 1.57635 | 0.788177 | − | 0.615449i | \(-0.211025\pi\) | ||||
0.788177 | + | 0.615449i | \(0.211025\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 48.3607 | 2.72482 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −19.8885 | −1.11705 | −0.558526 | − | 0.829487i | \(-0.688633\pi\) | ||||
−0.558526 | + | 0.829487i | \(0.688633\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.47214 | −0.362370 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31.4164 | −1.75349 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2.47214 | 0.137553 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.47214 | −0.248069 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 32.3607 | 1.78955 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0000 | −0.882109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −10.4721 | −0.575601 | −0.287800 | − | 0.957690i | \(-0.592924\pi\) | ||||
−0.287800 | + | 0.957690i | \(0.592924\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −51.8885 | −2.84347 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 24.0000 | 1.31126 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −23.8885 | −1.30129 | −0.650646 | − | 0.759381i | \(-0.725502\pi\) | ||||
−0.650646 | + | 0.759381i | \(0.725502\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.52786 | 0.517483 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.4721 | 0.567098 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 11.4164 | 0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −20.9443 | −1.12760 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.76393 | −0.255741 | −0.127871 | − | 0.991791i | \(-0.540814\pi\) | ||||
−0.127871 | + | 0.991791i | \(0.540814\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.00000 | −0.321173 | −0.160586 | − | 0.987022i | \(-0.551338\pi\) | ||||
−0.160586 | + | 0.987022i | \(0.551338\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −64.7214 | −3.45457 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −23.8885 | −1.27146 | −0.635729 | − | 0.771912i | \(-0.719301\pi\) | ||||
−0.635729 | + | 0.771912i | \(0.719301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.52786 | 0.505687 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.4721 | 0.554244 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −22.4721 | −1.18603 | −0.593017 | − | 0.805190i | \(-0.702063\pi\) | ||||
−0.593017 | + | 0.805190i | \(0.702063\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.8885 | −0.678344 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.70820 | 0.0896575 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.88854 | 0.308220 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −19.2361 | −1.00411 | −0.502057 | − | 0.864834i | \(-0.667423\pi\) | ||||
−0.502057 | + | 0.864834i | \(0.667423\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 14.9443 | 0.777968 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.47214 | −0.336017 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.52786 | −0.182666 | −0.0913329 | − | 0.995820i | \(-0.529113\pi\) | ||||
−0.0913329 | + | 0.995820i | \(0.529113\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −38.8328 | −2.00532 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −8.94427 | −0.460653 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.34752 | −0.0692177 | −0.0346088 | − | 0.999401i | \(-0.511019\pi\) | ||||
−0.0346088 | + | 0.999401i | \(0.511019\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −20.9443 | −1.07301 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −3.41641 | −0.174570 | −0.0872851 | − | 0.996183i | \(-0.527819\pi\) | ||||
−0.0872851 | + | 0.996183i | \(0.527819\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.9443 | 1.06742 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −78.2492 | −3.97763 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 25.4164 | 1.28866 | 0.644332 | − | 0.764746i | \(-0.277136\pi\) | ||||
0.644332 | + | 0.764746i | \(0.277136\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.23607 | −0.163655 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 68.3607 | 3.44834 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3.41641 | −0.171898 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −30.9443 | −1.55305 | −0.776524 | − | 0.630087i | \(-0.783019\pi\) | ||||
−0.776524 | + | 0.630087i | \(0.783019\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 25.8885 | 1.29605 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13.0557 | 0.651972 | 0.325986 | − | 0.945375i | \(-0.394304\pi\) | ||||
0.325986 | + | 0.945375i | \(0.394304\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 14.4721 | 0.720908 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −48.8328 | −2.42652 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −22.4721 | −1.11390 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.00000 | −0.296681 | −0.148340 | − | 0.988936i | \(-0.547393\pi\) | ||||
−0.148340 | + | 0.988936i | \(0.547393\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 53.3050 | 2.62934 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −17.8885 | −0.880238 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.9443 | −1.02811 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 36.3607 | 1.78059 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −20.7639 | −1.01438 | −0.507192 | − | 0.861833i | \(-0.669317\pi\) | ||||
−0.507192 | + | 0.861833i | \(0.669317\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.3607 | 1.86959 | 0.934793 | − | 0.355194i | \(-0.115585\pi\) | ||||
0.934793 | + | 0.355194i | \(0.115585\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 36.9443 | 1.79629 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.00000 | −0.0485071 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −35.4164 | −1.71392 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −46.8328 | −2.26111 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 11.5967 | 0.558596 | 0.279298 | − | 0.960205i | \(-0.409898\pi\) | ||||
0.279298 | + | 0.960205i | \(0.409898\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −19.5279 | −0.938449 | −0.469225 | − | 0.883079i | \(-0.655467\pi\) | ||||
−0.469225 | + | 0.883079i | \(0.655467\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.9443 | −0.620630 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8.00000 | −0.382692 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −30.6525 | −1.46296 | −0.731481 | − | 0.681861i | \(-0.761171\pi\) | ||||
−0.731481 | + | 0.681861i | \(0.761171\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 25.9443 | 1.23544 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.9443 | 1.56171 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 19.4164 | 0.918365 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.8885 | 1.31614 | 0.658071 | − | 0.752956i | \(-0.271373\pi\) | ||||
0.658071 | + | 0.752956i | \(0.271373\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.47214 | 0.304761 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 46.8328 | 2.20040 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 28.9443 | 1.35693 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5836 | 0.495080 | 0.247540 | − | 0.968878i | \(-0.420378\pi\) | ||||
0.247540 | + | 0.968878i | \(0.420378\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −14.4721 | −0.675501 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.88854 | 0.181108 | 0.0905538 | − | 0.995892i | \(-0.471136\pi\) | ||||
0.0905538 | + | 0.995892i | \(0.471136\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.8328 | 1.06113 | 0.530565 | − | 0.847644i | \(-0.321980\pi\) | ||||
0.530565 | + | 0.847644i | \(0.321980\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 20.9443 | 0.971267 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 41.3050 | 1.91137 | 0.955683 | − | 0.294399i | \(-0.0951194\pi\) | ||||
0.955683 | + | 0.294399i | \(0.0951194\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 38.8328 | 1.79313 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 77.3050 | 3.56202 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −33.8885 | −1.55820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.47214 | −0.113429 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 14.9443 | 0.684251 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −33.7082 | −1.54017 | −0.770084 | − | 0.637943i | \(-0.779786\pi\) | ||||
−0.770084 | + | 0.637943i | \(0.779786\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −31.0557 | −1.41602 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −33.8885 | −1.54198 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −4.00000 | −0.181631 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −43.2361 | −1.95921 | −0.979607 | − | 0.200925i | \(-0.935605\pi\) | ||||
−0.979607 | + | 0.200925i | \(0.935605\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.583592 | −0.0263909 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 10.4721 | 0.472601 | 0.236300 | − | 0.971680i | \(-0.424065\pi\) | ||||
0.236300 | + | 0.971680i | \(0.424065\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.00000 | −0.0900755 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −48.3607 | −2.17365 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15.4164 | 0.691520 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.8197 | −0.708185 | −0.354093 | − | 0.935210i | \(-0.615210\pi\) | ||||
−0.354093 | + | 0.935210i | \(0.615210\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.3607 | −0.909648 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.2918 | −0.637240 | −0.318620 | − | 0.947883i | \(-0.603219\pi\) | ||||
−0.318620 | + | 0.947883i | \(0.603219\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 26.8328 | 1.19404 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −22.6525 | −1.00603 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.00000 | 0.0886484 | 0.0443242 | − | 0.999017i | \(-0.485887\pi\) | ||||
0.0443242 | + | 0.999017i | \(0.485887\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9.52786 | 0.421488 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −35.7771 | −1.57960 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −16.0000 | −0.705044 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0000 | 0.703679 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.47214 | 0.284095 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.8885 | 0.520847 | 0.260423 | − | 0.965495i | \(-0.416138\pi\) | ||||
0.260423 | + | 0.965495i | \(0.416138\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.05573 | −0.308525 | −0.154263 | − | 0.988030i | \(-0.549300\pi\) | ||||
−0.154263 | + | 0.988030i | \(0.549300\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −10.4721 | −0.457041 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.23607 | 0.140965 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.5279 | −0.544690 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 41.3050 | 1.79248 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 8.94427 | 0.387419 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.4164 | −0.839445 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −17.8885 | −0.771948 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11.2361 | 0.483972 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 30.0000 | 1.28980 | 0.644900 | − | 0.764267i | \(-0.276899\pi\) | ||||
0.644900 | + | 0.764267i | \(0.276899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 32.3607 | 1.38873 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 20.0000 | 0.856706 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.70820 | 0.0730375 | 0.0365188 | − | 0.999333i | \(-0.488373\pi\) | ||||
0.0365188 | + | 0.999333i | \(0.488373\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 81.7771 | 3.49016 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.94427 | −0.210633 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.52786 | −0.235069 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −44.9443 | −1.90778 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −21.4164 | −0.907442 | −0.453721 | − | 0.891144i | \(-0.649904\pi\) | ||||
−0.453721 | + | 0.891144i | \(0.649904\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −46.8328 | −1.98082 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.4721 | −0.442134 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 20.3607 | 0.858100 | 0.429050 | − | 0.903281i | \(-0.358848\pi\) | ||||
0.429050 | + | 0.903281i | \(0.358848\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.88854 | 0.247733 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −79.0132 | −3.31824 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 35.8885 | 1.50453 | 0.752263 | − | 0.658863i | \(-0.228962\pi\) | ||||
0.752263 | + | 0.658863i | \(0.228962\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.23607 | 0.135425 | 0.0677126 | − | 0.997705i | \(-0.478430\pi\) | ||||
0.0677126 | + | 0.997705i | \(0.478430\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.0000 | 0.668410 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.23607 | 0.134953 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −8.47214 | −0.352700 | −0.176350 | − | 0.984328i | \(-0.556429\pi\) | ||||
−0.176350 | + | 0.984328i | \(0.556429\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.52786 | 0.395965 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −33.8885 | −1.40593 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.47214 | 0.268048 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −66.8328 | −2.76320 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −12.3607 | −0.510180 | −0.255090 | − | 0.966917i | \(-0.582105\pi\) | ||||
−0.255090 | + | 0.966917i | \(0.582105\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.00000 | 0.329634 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −35.4164 | −1.45684 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.8885 | 0.488204 | 0.244102 | − | 0.969750i | \(-0.421507\pi\) | ||||
0.244102 | + | 0.969750i | \(0.421507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 6.47214 | 0.265332 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −0.583592 | −0.0238848 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −46.8328 | −1.91354 | −0.956768 | − | 0.290851i | \(-0.906062\pi\) | ||||
−0.956768 | + | 0.290851i | \(0.906062\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 38.9443 | 1.58857 | 0.794285 | − | 0.607545i | \(-0.207846\pi\) | ||||
0.794285 | + | 0.607545i | \(0.207846\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −89.6656 | −3.65147 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.05573 | 0.0429215 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.29180 | 0.255376 | 0.127688 | − | 0.991814i | \(-0.459244\pi\) | ||||
0.127688 | + | 0.991814i | \(0.459244\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −20.9443 | −0.848705 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 22.1115 | 0.894534 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.00000 | −0.242338 | −0.121169 | − | 0.992632i | \(-0.538664\pi\) | ||||
−0.121169 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 12.9443 | 0.521963 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 34.0000 | 1.36879 | 0.684394 | − | 0.729112i | \(-0.260067\pi\) | ||||
0.684394 | + | 0.729112i | \(0.260067\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.34752 | 0.0541616 | 0.0270808 | − | 0.999633i | \(-0.491379\pi\) | ||||
0.0270808 | + | 0.999633i | \(0.491379\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 46.8328 | 1.87934 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 53.3050 | 2.13562 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −25.8885 | −1.03389 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.94427 | −0.276886 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 29.3050 | 1.16661 | 0.583306 | − | 0.812253i | \(-0.301759\pi\) | ||||
0.583306 | + | 0.812253i | \(0.301759\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −10.4721 | −0.416230 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −12.9443 | −0.513678 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 15.5279 | 0.615236 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −35.5967 | −1.40819 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.88854 | −0.311579 | −0.155789 | − | 0.987790i | \(-0.549792\pi\) | ||||
−0.155789 | + | 0.987790i | \(0.549792\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 48.5410 | 1.91427 | 0.957135 | − | 0.289641i | \(-0.0935358\pi\) | ||||
0.957135 | + | 0.289641i | \(0.0935358\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −67.7771 | −2.66872 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −32.0000 | −1.25805 | −0.629025 | − | 0.777385i | \(-0.716546\pi\) | ||||
−0.629025 | + | 0.777385i | \(0.716546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 17.8885 | 0.702187 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.8885 | 1.32820 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.8328 | 0.815251 | 0.407626 | − | 0.913149i | \(-0.366357\pi\) | ||||
0.407626 | + | 0.913149i | \(0.366357\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 42.2492 | 1.65081 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −22.0000 | −0.858302 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 18.8328 | 0.733622 | 0.366811 | − | 0.930295i | \(-0.380450\pi\) | ||||
0.366811 | + | 0.930295i | \(0.380450\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −39.8885 | −1.55148 | −0.775742 | − | 0.631050i | \(-0.782624\pi\) | ||||
−0.775742 | + | 0.631050i | \(0.782624\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −14.4721 | −0.562051 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 16.0000 | 0.620453 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.47214 | 0.250602 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 46.8328 | 1.81066 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 35.4164 | 1.36724 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 37.7771 | 1.45620 | 0.728100 | − | 0.685471i | \(-0.240404\pi\) | ||||
0.728100 | + | 0.685471i | \(0.240404\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 14.4721 | 0.557033 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −43.8885 | −1.68677 | −0.843387 | − | 0.537307i | \(-0.819442\pi\) | ||||
−0.843387 | + | 0.537307i | \(0.819442\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.47214 | −0.248378 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −10.4721 | −0.401293 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −50.0689 | −1.91583 | −0.957916 | − | 0.287048i | \(-0.907326\pi\) | ||||
−0.957916 | + | 0.287048i | \(0.907326\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.9443 | 1.25874 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −50.2492 | −1.91713 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8.94427 | 0.340750 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.5967 | −0.441161 | −0.220581 | − | 0.975369i | \(-0.570795\pi\) | ||||
−0.220581 | + | 0.975369i | \(0.570795\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −78.2492 | −2.97244 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 22.4721 | 0.852417 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.00000 | 0.0757554 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −38.4721 | −1.45515 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.3607 | 1.14671 | 0.573354 | − | 0.819308i | \(-0.305642\pi\) | ||||
0.573354 | + | 0.819308i | \(0.305642\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −17.1672 | −0.647473 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32.0000 | 1.20519 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 43.4164 | 1.63284 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2.94427 | 0.110574 | 0.0552872 | − | 0.998470i | \(-0.482393\pi\) | ||||
0.0552872 | + | 0.998470i | \(0.482393\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.7639 | 0.478685 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.4721 | −0.392185 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.9443 | −1.08245 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −57.8885 | −2.16189 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.6525 | −0.844795 | −0.422397 | − | 0.906411i | \(-0.638811\pi\) | ||||
−0.422397 | + | 0.906411i | \(0.638811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.8885 | −0.964140 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 61.3050 | 2.27996 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.00000 | 0.0742781 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.05573 | −0.113331 | −0.0566653 | − | 0.998393i | \(-0.518047\pi\) | ||||
−0.0566653 | + | 0.998393i | \(0.518047\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 41.9443 | 1.55349 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.4721 | −0.387326 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.111456 | 0.00411673 | 0.00205836 | − | 0.999998i | \(-0.499345\pi\) | ||||
0.00205836 | + | 0.999998i | \(0.499345\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 22.4721 | 0.828897 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −38.8328 | −1.43043 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.5836 | −0.610037 | −0.305019 | − | 0.952346i | \(-0.598663\pi\) | ||||
−0.305019 | + | 0.952346i | \(0.598663\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.7771 | −1.31430 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 17.3475 | 0.636419 | 0.318209 | − | 0.948020i | \(-0.396918\pi\) | ||||
0.318209 | + | 0.948020i | \(0.396918\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 12.0000 | 0.439646 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 78.2492 | 2.86299 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −31.4164 | −1.14793 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22.2918 | 0.813439 | 0.406720 | − | 0.913553i | \(-0.366673\pi\) | ||||
0.406720 | + | 0.913553i | \(0.366673\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −28.9443 | −1.05479 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 28.9443 | 1.05339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.4721 | −0.598690 | −0.299345 | − | 0.954145i | \(-0.596768\pi\) | ||||
−0.299345 | + | 0.954145i | \(0.596768\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 33.8885 | 1.23008 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.3607 | −0.375574 | −0.187787 | − | 0.982210i | \(-0.560132\pi\) | ||||
−0.187787 | + | 0.982210i | \(0.560132\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.3607 | 1.17154 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −14.9443 | −0.540311 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 24.7214 | 0.892637 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.52786 | 0.271462 | 0.135731 | − | 0.990746i | \(-0.456662\pi\) | ||||
0.135731 | + | 0.990746i | \(0.456662\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −72.3607 | −2.60601 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 35.3050 | 1.26983 | 0.634915 | − | 0.772582i | \(-0.281035\pi\) | ||||
0.634915 | + | 0.772582i | \(0.281035\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.23607 | −0.116243 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −72.7214 | −2.60886 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 4.94427 | 0.177147 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.4164 | −0.551642 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 28.9443 | 1.03438 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 47.7771 | 1.70524 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.65248 | 0.237135 | 0.118568 | − | 0.992946i | \(-0.462170\pi\) | ||||
0.118568 | + | 0.992946i | \(0.462170\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 36.9443 | 1.31525 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 9.52786 | 0.338772 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 48.9443 | 1.73806 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 12.9443 | 0.459086 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 19.8885 | 0.704488 | 0.352244 | − | 0.935908i | \(-0.385419\pi\) | ||||
0.352244 | + | 0.935908i | \(0.385419\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.94427 | 0.174916 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −123.082 | −4.34889 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.52786 | −0.336231 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.9443 | −0.738189 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −61.3050 | −2.15804 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −25.0557 | −0.880912 | −0.440456 | − | 0.897774i | \(-0.645183\pi\) | ||||
−0.440456 | + | 0.897774i | \(0.645183\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.1246 | −0.460867 | −0.230434 | − | 0.973088i | \(-0.574014\pi\) | ||||
−0.230434 | + | 0.973088i | \(0.574014\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 57.8885 | 2.03024 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.360680 | −0.0126341 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −25.8885 | −0.905725 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −108.138 | −3.77864 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −50.0000 | −1.74501 | −0.872506 | − | 0.488603i | \(-0.837507\pi\) | ||||
−0.872506 | + | 0.488603i | \(0.837507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 51.5967 | 1.79855 | 0.899275 | − | 0.437384i | \(-0.144095\pi\) | ||||
0.899275 | + | 0.437384i | \(0.144095\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 10.4721 | 0.364593 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −20.7639 | −0.722033 | −0.361016 | − | 0.932559i | \(-0.617570\pi\) | ||||
−0.361016 | + | 0.932559i | \(0.617570\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 8.11146 | 0.281723 | 0.140861 | − | 0.990029i | \(-0.455013\pi\) | ||||
0.140861 | + | 0.990029i | \(0.455013\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 106.249 | 3.68574 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.47214 | 0.120302 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.5836 | −0.435473 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −46.8328 | −1.61878 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26.0689 | −0.899998 | −0.449999 | − | 0.893029i | \(-0.648576\pi\) | ||||
−0.449999 | + | 0.893029i | \(0.648576\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −25.0000 | −0.862069 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 51.4164 | 1.77088 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.0000 | −0.481615 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.70820 | 0.0586946 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.4721 | −0.359403 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.4721 | 0.770335 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.7771 | 1.15651 | 0.578253 | − | 0.815858i | \(-0.303735\pi\) | ||||
0.578253 | + | 0.815858i | \(0.303735\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −36.9443 | −1.26347 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 27.8885 | 0.952655 | 0.476327 | − | 0.879268i | \(-0.341968\pi\) | ||||
0.476327 | + | 0.879268i | \(0.341968\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30.2492 | −1.03209 | −0.516045 | − | 0.856561i | \(-0.672596\pi\) | ||||
−0.516045 | + | 0.856561i | \(0.672596\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 20.9443 | 0.713779 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −22.8328 | −0.777238 | −0.388619 | − | 0.921399i | \(-0.627048\pi\) | ||||
−0.388619 | + | 0.921399i | \(0.627048\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.00000 | 0.136004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −3.23607 | −0.109903 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5.52786 | 0.187520 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.6656 | −1.81839 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.9443 | 0.505787 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.8328 | −1.31279 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 31.8885 | 1.07680 | 0.538400 | − | 0.842690i | \(-0.319029\pi\) | ||||
0.538400 | + | 0.842690i | \(0.319029\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −32.3607 | −1.09150 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 27.8885 | 0.939589 | 0.469794 | − | 0.882776i | \(-0.344328\pi\) | ||||
0.469794 | + | 0.882776i | \(0.344328\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −37.8885 | −1.27505 | −0.637526 | − | 0.770429i | \(-0.720042\pi\) | ||||
−0.637526 | + | 0.770429i | \(0.720042\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 35.7771 | 1.20263 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 29.1246 | 0.977909 | 0.488954 | − | 0.872309i | \(-0.337378\pi\) | ||||
0.488954 | + | 0.872309i | \(0.337378\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.9443 | −0.702448 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 79.0132 | 2.64704 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 12.2229 | 0.409024 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.0557 | −0.369552 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 46.8328 | 1.56370 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.47214 | −0.215858 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.00000 | 0.0666297 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −109.666 | −3.64944 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 20.0000 | 0.664822 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.8754 | −0.626747 | −0.313373 | − | 0.949630i | \(-0.601459\pi\) | ||||
−0.313373 | + | 0.949630i | \(0.601459\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −100.249 | −3.32506 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.2918 | −0.473508 | −0.236754 | − | 0.971570i | \(-0.576084\pi\) | ||||
−0.236754 | + | 0.971570i | \(0.576084\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 33.8885 | 1.12155 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 70.8328 | 2.34166 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 68.3607 | 2.25747 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.11146 | 0.201598 | 0.100799 | − | 0.994907i | \(-0.467860\pi\) | ||||
0.100799 | + | 0.994907i | \(0.467860\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 96.7214 | 3.18708 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21.3050 | −0.701261 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 6.94427 | 0.228326 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 59.7771 | 1.96334 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.05573 | −0.297109 | −0.148554 | − | 0.988904i | \(-0.547462\pi\) | ||||
−0.148554 | + | 0.988904i | \(0.547462\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.58359 | 0.281316 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −62.2492 | −2.03795 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.47214 | −0.211661 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26.0000 | 0.849383 | 0.424691 | − | 0.905338i | \(-0.360383\pi\) | ||||
0.424691 | + | 0.905338i | \(0.360383\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −90.2492 | −2.94517 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −45.7771 | −1.49229 | −0.746145 | − | 0.665783i | \(-0.768098\pi\) | ||||
−0.746145 | + | 0.665783i | \(0.768098\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −6.47214 | −0.210762 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −93.6656 | −3.04694 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −39.0132 | −1.26776 | −0.633879 | − | 0.773433i | \(-0.718538\pi\) | ||||
−0.633879 | + | 0.773433i | \(0.718538\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −13.1672 | −0.427425 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 64.3607 | 2.08704 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −32.4721 | −1.05188 | −0.525938 | − | 0.850523i | \(-0.676286\pi\) | ||||
−0.525938 | + | 0.850523i | \(0.676286\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.88854 | 0.319986 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.9443 | 0.677032 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53.3050 | 1.72131 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.5279 | −0.662189 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 72.5410 | 2.33760 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 5.88854 | 0.189559 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.47214 | −0.208130 | −0.104065 | − | 0.994571i | \(-0.533185\pi\) | ||||
−0.104065 | + | 0.994571i | \(0.533185\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.00000 | −0.256997 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 18.4721 | 0.592799 | 0.296400 | − | 0.955064i | \(-0.404214\pi\) | ||||
0.296400 | + | 0.955064i | \(0.404214\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.3607 | 1.16567 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 14.4721 | 0.463479 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 34.0000 | 1.08776 | 0.543878 | − | 0.839164i | \(-0.316955\pi\) | ||||
0.543878 | + | 0.839164i | \(0.316955\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −53.3050 | −1.70363 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −74.7214 | −2.38567 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 11.2361 | 0.358375 | 0.179187 | − | 0.983815i | \(-0.442653\pi\) | ||||
0.179187 | + | 0.983815i | \(0.442653\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.8885 | −0.697427 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 51.7771 | 1.64808 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 33.8885 | 1.07759 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12.7639 | −0.405460 | −0.202730 | − | 0.979235i | \(-0.564981\pi\) | ||||
−0.202730 | + | 0.979235i | \(0.564981\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.8885 | 1.07542 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.360680 | −0.0114343 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −46.9443 | −1.48674 | −0.743370 | − | 0.668880i | \(-0.766774\pi\) | ||||
−0.743370 | + | 0.668880i | \(0.766774\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 100.498 | 3.17963 |
(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 | 1088.2.a.o.1.1 | 2 | ||
3.2 | odd | 2 | 9792.2.a.da.1.1 | 2 | |||
4.3 | odd | 2 | 1088.2.a.s.1.2 | 2 | |||
8.3 | odd | 2 | 136.2.a.c.1.1 | ✓ | 2 | ||
8.5 | even | 2 | 272.2.a.f.1.2 | 2 | |||
12.11 | even | 2 | 9792.2.a.db.1.2 | 2 | |||
24.5 | odd | 2 | 2448.2.a.u.1.1 | 2 | |||
24.11 | even | 2 | 1224.2.a.i.1.2 | 2 | |||
40.3 | even | 4 | 3400.2.e.f.2449.1 | 4 | |||
40.19 | odd | 2 | 3400.2.a.i.1.2 | 2 | |||
40.27 | even | 4 | 3400.2.e.f.2449.4 | 4 | |||
40.29 | even | 2 | 6800.2.a.bd.1.1 | 2 | |||
56.27 | even | 2 | 6664.2.a.i.1.2 | 2 | |||
136.67 | odd | 2 | 2312.2.a.m.1.2 | 2 | |||
136.101 | even | 2 | 4624.2.a.h.1.1 | 2 | |||
136.115 | odd | 4 | 2312.2.b.g.577.1 | 4 | |||
136.123 | odd | 4 | 2312.2.b.g.577.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.2.a.c.1.1 | ✓ | 2 | 8.3 | odd | 2 | ||
272.2.a.f.1.2 | 2 | 8.5 | even | 2 | |||
1088.2.a.o.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1088.2.a.s.1.2 | 2 | 4.3 | odd | 2 | |||
1224.2.a.i.1.2 | 2 | 24.11 | even | 2 | |||
2312.2.a.m.1.2 | 2 | 136.67 | odd | 2 | |||
2312.2.b.g.577.1 | 4 | 136.115 | odd | 4 | |||
2312.2.b.g.577.4 | 4 | 136.123 | odd | 4 | |||
2448.2.a.u.1.1 | 2 | 24.5 | odd | 2 | |||
3400.2.a.i.1.2 | 2 | 40.19 | odd | 2 | |||
3400.2.e.f.2449.1 | 4 | 40.3 | even | 4 | |||
3400.2.e.f.2449.4 | 4 | 40.27 | even | 4 | |||
4624.2.a.h.1.1 | 2 | 136.101 | even | 2 | |||
6664.2.a.i.1.2 | 2 | 56.27 | even | 2 | |||
6800.2.a.bd.1.1 | 2 | 40.29 | even | 2 | |||
9792.2.a.da.1.1 | 2 | 3.2 | odd | 2 | |||
9792.2.a.db.1.2 | 2 | 12.11 | even | 2 |