Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6042,2,Mod(1,6042)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6042, 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("6042.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6042 = 2 \cdot 3 \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6042.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: | \(48.2456129013\) |
Analytic rank: | \(0\) |
Dimension: | \(9\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{9} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{9} - 4x^{8} - 11x^{7} + 51x^{6} + 25x^{5} - 180x^{4} + 29x^{3} + 119x^{2} - 8x - 14 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.690250\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6042.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.37472 | −1.95643 | −0.978216 | − | 0.207589i | \(-0.933438\pi\) | ||||
−0.978216 | + | 0.207589i | \(0.933438\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.773393 | −0.292315 | −0.146157 | − | 0.989261i | \(-0.546691\pi\) | ||||
−0.146157 | + | 0.989261i | \(0.546691\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.37472 | 1.38341 | ||||||||
\(11\) | 4.42079 | 1.33292 | 0.666460 | − | 0.745541i | \(-0.267809\pi\) | ||||
0.666460 | + | 0.745541i | \(0.267809\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | 0.648462 | 0.179851 | 0.0899255 | − | 0.995948i | \(-0.471337\pi\) | ||||
0.0899255 | + | 0.995948i | \(0.471337\pi\) | |||||||
\(14\) | 0.773393 | 0.206698 | ||||||||
\(15\) | 4.37472 | 1.12955 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.40302 | 1.55296 | 0.776480 | − | 0.630142i | \(-0.217003\pi\) | ||||
0.776480 | + | 0.630142i | \(0.217003\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −4.37472 | −0.978216 | ||||||||
\(21\) | 0.773393 | 0.168768 | ||||||||
\(22\) | −4.42079 | −0.942517 | ||||||||
\(23\) | 0.287580 | 0.0599645 | 0.0299823 | − | 0.999550i | \(-0.490455\pi\) | ||||
0.0299823 | + | 0.999550i | \(0.490455\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 14.1381 | 2.82763 | ||||||||
\(26\) | −0.648462 | −0.127174 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −0.773393 | −0.146157 | ||||||||
\(29\) | 0.347880 | 0.0645998 | 0.0322999 | − | 0.999478i | \(-0.489717\pi\) | ||||
0.0322999 | + | 0.999478i | \(0.489717\pi\) | |||||||
\(30\) | −4.37472 | −0.798710 | ||||||||
\(31\) | −3.57302 | −0.641733 | −0.320867 | − | 0.947124i | \(-0.603974\pi\) | ||||
−0.320867 | + | 0.947124i | \(0.603974\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.42079 | −0.769562 | ||||||||
\(34\) | −6.40302 | −1.09811 | ||||||||
\(35\) | 3.38337 | 0.571894 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −8.71669 | −1.43301 | −0.716507 | − | 0.697580i | \(-0.754260\pi\) | ||||
−0.716507 | + | 0.697580i | \(0.754260\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −0.648462 | −0.103837 | ||||||||
\(40\) | 4.37472 | 0.691703 | ||||||||
\(41\) | 8.14882 | 1.27263 | 0.636316 | − | 0.771429i | \(-0.280458\pi\) | ||||
0.636316 | + | 0.771429i | \(0.280458\pi\) | |||||||
\(42\) | −0.773393 | −0.119337 | ||||||||
\(43\) | 8.05514 | 1.22840 | 0.614199 | − | 0.789151i | \(-0.289479\pi\) | ||||
0.614199 | + | 0.789151i | \(0.289479\pi\) | |||||||
\(44\) | 4.42079 | 0.666460 | ||||||||
\(45\) | −4.37472 | −0.652144 | ||||||||
\(46\) | −0.287580 | −0.0424013 | ||||||||
\(47\) | 11.2879 | 1.64650 | 0.823252 | − | 0.567676i | \(-0.192157\pi\) | ||||
0.823252 | + | 0.567676i | \(0.192157\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −6.40186 | −0.914552 | ||||||||
\(50\) | −14.1381 | −1.99943 | ||||||||
\(51\) | −6.40302 | −0.896602 | ||||||||
\(52\) | 0.648462 | 0.0899255 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −19.3397 | −2.60777 | ||||||||
\(56\) | 0.773393 | 0.103349 | ||||||||
\(57\) | 1.00000 | 0.132453 | ||||||||
\(58\) | −0.347880 | −0.0456789 | ||||||||
\(59\) | −3.60190 | −0.468927 | −0.234463 | − | 0.972125i | \(-0.575333\pi\) | ||||
−0.234463 | + | 0.972125i | \(0.575333\pi\) | |||||||
\(60\) | 4.37472 | 0.564773 | ||||||||
\(61\) | 6.21492 | 0.795738 | 0.397869 | − | 0.917442i | \(-0.369750\pi\) | ||||
0.397869 | + | 0.917442i | \(0.369750\pi\) | |||||||
\(62\) | 3.57302 | 0.453774 | ||||||||
\(63\) | −0.773393 | −0.0974383 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.83684 | −0.351866 | ||||||||
\(66\) | 4.42079 | 0.544162 | ||||||||
\(67\) | −1.86347 | −0.227659 | −0.113830 | − | 0.993500i | \(-0.536312\pi\) | ||||
−0.113830 | + | 0.993500i | \(0.536312\pi\) | |||||||
\(68\) | 6.40302 | 0.776480 | ||||||||
\(69\) | −0.287580 | −0.0346205 | ||||||||
\(70\) | −3.38337 | −0.404390 | ||||||||
\(71\) | −1.42484 | −0.169097 | −0.0845487 | − | 0.996419i | \(-0.526945\pi\) | ||||
−0.0845487 | + | 0.996419i | \(0.526945\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | −8.80129 | −1.03011 | −0.515056 | − | 0.857156i | \(-0.672229\pi\) | ||||
−0.515056 | + | 0.857156i | \(0.672229\pi\) | |||||||
\(74\) | 8.71669 | 1.01329 | ||||||||
\(75\) | −14.1381 | −1.63253 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −3.41901 | −0.389632 | ||||||||
\(78\) | 0.648462 | 0.0734238 | ||||||||
\(79\) | −7.81384 | −0.879126 | −0.439563 | − | 0.898212i | \(-0.644867\pi\) | ||||
−0.439563 | + | 0.898212i | \(0.644867\pi\) | |||||||
\(80\) | −4.37472 | −0.489108 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −8.14882 | −0.899886 | ||||||||
\(83\) | 16.9311 | 1.85843 | 0.929216 | − | 0.369537i | \(-0.120484\pi\) | ||||
0.929216 | + | 0.369537i | \(0.120484\pi\) | |||||||
\(84\) | 0.773393 | 0.0843841 | ||||||||
\(85\) | −28.0114 | −3.03826 | ||||||||
\(86\) | −8.05514 | −0.868608 | ||||||||
\(87\) | −0.347880 | −0.0372967 | ||||||||
\(88\) | −4.42079 | −0.471258 | ||||||||
\(89\) | −17.7376 | −1.88019 | −0.940094 | − | 0.340917i | \(-0.889263\pi\) | ||||
−0.940094 | + | 0.340917i | \(0.889263\pi\) | |||||||
\(90\) | 4.37472 | 0.461136 | ||||||||
\(91\) | −0.501516 | −0.0525731 | ||||||||
\(92\) | 0.287580 | 0.0299823 | ||||||||
\(93\) | 3.57302 | 0.370505 | ||||||||
\(94\) | −11.2879 | −1.16425 | ||||||||
\(95\) | 4.37472 | 0.448836 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 9.18686 | 0.932785 | 0.466392 | − | 0.884578i | \(-0.345553\pi\) | ||||
0.466392 | + | 0.884578i | \(0.345553\pi\) | |||||||
\(98\) | 6.40186 | 0.646686 | ||||||||
\(99\) | 4.42079 | 0.444307 | ||||||||
\(100\) | 14.1381 | 1.41381 | ||||||||
\(101\) | 16.2939 | 1.62131 | 0.810654 | − | 0.585526i | \(-0.199112\pi\) | ||||
0.810654 | + | 0.585526i | \(0.199112\pi\) | |||||||
\(102\) | 6.40302 | 0.633994 | ||||||||
\(103\) | −8.42044 | −0.829690 | −0.414845 | − | 0.909892i | \(-0.636164\pi\) | ||||
−0.414845 | + | 0.909892i | \(0.636164\pi\) | |||||||
\(104\) | −0.648462 | −0.0635869 | ||||||||
\(105\) | −3.38337 | −0.330183 | ||||||||
\(106\) | −1.00000 | −0.0971286 | ||||||||
\(107\) | 0.329410 | 0.0318452 | 0.0159226 | − | 0.999873i | \(-0.494931\pi\) | ||||
0.0159226 | + | 0.999873i | \(0.494931\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | −0.493136 | −0.0472338 | −0.0236169 | − | 0.999721i | \(-0.507518\pi\) | ||||
−0.0236169 | + | 0.999721i | \(0.507518\pi\) | |||||||
\(110\) | 19.3397 | 1.84397 | ||||||||
\(111\) | 8.71669 | 0.827351 | ||||||||
\(112\) | −0.773393 | −0.0730787 | ||||||||
\(113\) | −17.2506 | −1.62280 | −0.811400 | − | 0.584492i | \(-0.801294\pi\) | ||||
−0.811400 | + | 0.584492i | \(0.801294\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | −1.25808 | −0.117317 | ||||||||
\(116\) | 0.347880 | 0.0322999 | ||||||||
\(117\) | 0.648462 | 0.0599503 | ||||||||
\(118\) | 3.60190 | 0.331581 | ||||||||
\(119\) | −4.95205 | −0.453954 | ||||||||
\(120\) | −4.37472 | −0.399355 | ||||||||
\(121\) | 8.54342 | 0.776675 | ||||||||
\(122\) | −6.21492 | −0.562672 | ||||||||
\(123\) | −8.14882 | −0.734754 | ||||||||
\(124\) | −3.57302 | −0.320867 | ||||||||
\(125\) | −39.9768 | −3.57563 | ||||||||
\(126\) | 0.773393 | 0.0688993 | ||||||||
\(127\) | −10.8921 | −0.966521 | −0.483261 | − | 0.875476i | \(-0.660548\pi\) | ||||
−0.483261 | + | 0.875476i | \(0.660548\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −8.05514 | −0.709216 | ||||||||
\(130\) | 2.83684 | 0.248807 | ||||||||
\(131\) | 4.64018 | 0.405414 | 0.202707 | − | 0.979239i | \(-0.435026\pi\) | ||||
0.202707 | + | 0.979239i | \(0.435026\pi\) | |||||||
\(132\) | −4.42079 | −0.384781 | ||||||||
\(133\) | 0.773393 | 0.0670617 | ||||||||
\(134\) | 1.86347 | 0.160979 | ||||||||
\(135\) | 4.37472 | 0.376516 | ||||||||
\(136\) | −6.40302 | −0.549054 | ||||||||
\(137\) | −18.5932 | −1.58853 | −0.794263 | − | 0.607574i | \(-0.792143\pi\) | ||||
−0.794263 | + | 0.607574i | \(0.792143\pi\) | |||||||
\(138\) | 0.287580 | 0.0244804 | ||||||||
\(139\) | −20.2541 | −1.71793 | −0.858965 | − | 0.512035i | \(-0.828892\pi\) | ||||
−0.858965 | + | 0.512035i | \(0.828892\pi\) | |||||||
\(140\) | 3.38337 | 0.285947 | ||||||||
\(141\) | −11.2879 | −0.950610 | ||||||||
\(142\) | 1.42484 | 0.119570 | ||||||||
\(143\) | 2.86672 | 0.239727 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −1.52188 | −0.126385 | ||||||||
\(146\) | 8.80129 | 0.728400 | ||||||||
\(147\) | 6.40186 | 0.528017 | ||||||||
\(148\) | −8.71669 | −0.716507 | ||||||||
\(149\) | 3.94550 | 0.323228 | 0.161614 | − | 0.986854i | \(-0.448330\pi\) | ||||
0.161614 | + | 0.986854i | \(0.448330\pi\) | |||||||
\(150\) | 14.1381 | 1.15437 | ||||||||
\(151\) | −6.27644 | −0.510770 | −0.255385 | − | 0.966839i | \(-0.582202\pi\) | ||||
−0.255385 | + | 0.966839i | \(0.582202\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 6.40302 | 0.517654 | ||||||||
\(154\) | 3.41901 | 0.275512 | ||||||||
\(155\) | 15.6309 | 1.25551 | ||||||||
\(156\) | −0.648462 | −0.0519185 | ||||||||
\(157\) | 9.71418 | 0.775276 | 0.387638 | − | 0.921812i | \(-0.373291\pi\) | ||||
0.387638 | + | 0.921812i | \(0.373291\pi\) | |||||||
\(158\) | 7.81384 | 0.621636 | ||||||||
\(159\) | −1.00000 | −0.0793052 | ||||||||
\(160\) | 4.37472 | 0.345852 | ||||||||
\(161\) | −0.222412 | −0.0175285 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 19.7130 | 1.54404 | 0.772021 | − | 0.635597i | \(-0.219246\pi\) | ||||
0.772021 | + | 0.635597i | \(0.219246\pi\) | |||||||
\(164\) | 8.14882 | 0.636316 | ||||||||
\(165\) | 19.3397 | 1.50560 | ||||||||
\(166\) | −16.9311 | −1.31411 | ||||||||
\(167\) | −12.8412 | −0.993683 | −0.496842 | − | 0.867841i | \(-0.665507\pi\) | ||||
−0.496842 | + | 0.867841i | \(0.665507\pi\) | |||||||
\(168\) | −0.773393 | −0.0596685 | ||||||||
\(169\) | −12.5795 | −0.967654 | ||||||||
\(170\) | 28.0114 | 2.14838 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 8.05514 | 0.614199 | ||||||||
\(173\) | 10.3472 | 0.786683 | 0.393341 | − | 0.919393i | \(-0.371319\pi\) | ||||
0.393341 | + | 0.919393i | \(0.371319\pi\) | |||||||
\(174\) | 0.347880 | 0.0263727 | ||||||||
\(175\) | −10.9343 | −0.826558 | ||||||||
\(176\) | 4.42079 | 0.333230 | ||||||||
\(177\) | 3.60190 | 0.270735 | ||||||||
\(178\) | 17.7376 | 1.32949 | ||||||||
\(179\) | 9.63680 | 0.720288 | 0.360144 | − | 0.932897i | \(-0.382728\pi\) | ||||
0.360144 | + | 0.932897i | \(0.382728\pi\) | |||||||
\(180\) | −4.37472 | −0.326072 | ||||||||
\(181\) | 20.7568 | 1.54284 | 0.771420 | − | 0.636326i | \(-0.219547\pi\) | ||||
0.771420 | + | 0.636326i | \(0.219547\pi\) | |||||||
\(182\) | 0.501516 | 0.0371748 | ||||||||
\(183\) | −6.21492 | −0.459420 | ||||||||
\(184\) | −0.287580 | −0.0212007 | ||||||||
\(185\) | 38.1330 | 2.80360 | ||||||||
\(186\) | −3.57302 | −0.261986 | ||||||||
\(187\) | 28.3064 | 2.06997 | ||||||||
\(188\) | 11.2879 | 0.823252 | ||||||||
\(189\) | 0.773393 | 0.0562560 | ||||||||
\(190\) | −4.37472 | −0.317375 | ||||||||
\(191\) | 2.13393 | 0.154406 | 0.0772030 | − | 0.997015i | \(-0.475401\pi\) | ||||
0.0772030 | + | 0.997015i | \(0.475401\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | 5.01259 | 0.360814 | 0.180407 | − | 0.983592i | \(-0.442259\pi\) | ||||
0.180407 | + | 0.983592i | \(0.442259\pi\) | |||||||
\(194\) | −9.18686 | −0.659578 | ||||||||
\(195\) | 2.83684 | 0.203150 | ||||||||
\(196\) | −6.40186 | −0.457276 | ||||||||
\(197\) | 16.1361 | 1.14965 | 0.574825 | − | 0.818276i | \(-0.305070\pi\) | ||||
0.574825 | + | 0.818276i | \(0.305070\pi\) | |||||||
\(198\) | −4.42079 | −0.314172 | ||||||||
\(199\) | 13.0215 | 0.923069 | 0.461535 | − | 0.887122i | \(-0.347299\pi\) | ||||
0.461535 | + | 0.887122i | \(0.347299\pi\) | |||||||
\(200\) | −14.1381 | −0.999717 | ||||||||
\(201\) | 1.86347 | 0.131439 | ||||||||
\(202\) | −16.2939 | −1.14644 | ||||||||
\(203\) | −0.269048 | −0.0188835 | ||||||||
\(204\) | −6.40302 | −0.448301 | ||||||||
\(205\) | −35.6488 | −2.48982 | ||||||||
\(206\) | 8.42044 | 0.586680 | ||||||||
\(207\) | 0.287580 | 0.0199882 | ||||||||
\(208\) | 0.648462 | 0.0449627 | ||||||||
\(209\) | −4.42079 | −0.305793 | ||||||||
\(210\) | 3.38337 | 0.233475 | ||||||||
\(211\) | −4.52168 | −0.311285 | −0.155643 | − | 0.987813i | \(-0.549745\pi\) | ||||
−0.155643 | + | 0.987813i | \(0.549745\pi\) | |||||||
\(212\) | 1.00000 | 0.0686803 | ||||||||
\(213\) | 1.42484 | 0.0976285 | ||||||||
\(214\) | −0.329410 | −0.0225180 | ||||||||
\(215\) | −35.2389 | −2.40328 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.76335 | 0.187588 | ||||||||
\(218\) | 0.493136 | 0.0333994 | ||||||||
\(219\) | 8.80129 | 0.594736 | ||||||||
\(220\) | −19.3397 | −1.30388 | ||||||||
\(221\) | 4.15211 | 0.279301 | ||||||||
\(222\) | −8.71669 | −0.585026 | ||||||||
\(223\) | −20.1908 | −1.35207 | −0.676037 | − | 0.736868i | \(-0.736304\pi\) | ||||
−0.676037 | + | 0.736868i | \(0.736304\pi\) | |||||||
\(224\) | 0.773393 | 0.0516745 | ||||||||
\(225\) | 14.1381 | 0.942543 | ||||||||
\(226\) | 17.2506 | 1.14749 | ||||||||
\(227\) | 17.1876 | 1.14078 | 0.570392 | − | 0.821373i | \(-0.306791\pi\) | ||||
0.570392 | + | 0.821373i | \(0.306791\pi\) | |||||||
\(228\) | 1.00000 | 0.0662266 | ||||||||
\(229\) | 19.9182 | 1.31623 | 0.658114 | − | 0.752918i | \(-0.271354\pi\) | ||||
0.658114 | + | 0.752918i | \(0.271354\pi\) | |||||||
\(230\) | 1.25808 | 0.0829553 | ||||||||
\(231\) | 3.41901 | 0.224954 | ||||||||
\(232\) | −0.347880 | −0.0228395 | ||||||||
\(233\) | 21.1819 | 1.38767 | 0.693836 | − | 0.720133i | \(-0.255919\pi\) | ||||
0.693836 | + | 0.720133i | \(0.255919\pi\) | |||||||
\(234\) | −0.648462 | −0.0423913 | ||||||||
\(235\) | −49.3812 | −3.22127 | ||||||||
\(236\) | −3.60190 | −0.234463 | ||||||||
\(237\) | 7.81384 | 0.507564 | ||||||||
\(238\) | 4.95205 | 0.320994 | ||||||||
\(239\) | −1.90069 | −0.122945 | −0.0614727 | − | 0.998109i | \(-0.519580\pi\) | ||||
−0.0614727 | + | 0.998109i | \(0.519580\pi\) | |||||||
\(240\) | 4.37472 | 0.282387 | ||||||||
\(241\) | −0.815676 | −0.0525423 | −0.0262712 | − | 0.999655i | \(-0.508363\pi\) | ||||
−0.0262712 | + | 0.999655i | \(0.508363\pi\) | |||||||
\(242\) | −8.54342 | −0.549192 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.21492 | 0.397869 | ||||||||
\(245\) | 28.0063 | 1.78926 | ||||||||
\(246\) | 8.14882 | 0.519550 | ||||||||
\(247\) | −0.648462 | −0.0412606 | ||||||||
\(248\) | 3.57302 | 0.226887 | ||||||||
\(249\) | −16.9311 | −1.07297 | ||||||||
\(250\) | 39.9768 | 2.52835 | ||||||||
\(251\) | −24.0194 | −1.51609 | −0.758045 | − | 0.652202i | \(-0.773845\pi\) | ||||
−0.758045 | + | 0.652202i | \(0.773845\pi\) | |||||||
\(252\) | −0.773393 | −0.0487192 | ||||||||
\(253\) | 1.27133 | 0.0799279 | ||||||||
\(254\) | 10.8921 | 0.683434 | ||||||||
\(255\) | 28.0114 | 1.75414 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 29.0813 | 1.81404 | 0.907020 | − | 0.421088i | \(-0.138352\pi\) | ||||
0.907020 | + | 0.421088i | \(0.138352\pi\) | |||||||
\(258\) | 8.05514 | 0.501491 | ||||||||
\(259\) | 6.74142 | 0.418892 | ||||||||
\(260\) | −2.83684 | −0.175933 | ||||||||
\(261\) | 0.347880 | 0.0215333 | ||||||||
\(262\) | −4.64018 | −0.286671 | ||||||||
\(263\) | 2.58074 | 0.159135 | 0.0795676 | − | 0.996829i | \(-0.474646\pi\) | ||||
0.0795676 | + | 0.996829i | \(0.474646\pi\) | |||||||
\(264\) | 4.42079 | 0.272081 | ||||||||
\(265\) | −4.37472 | −0.268737 | ||||||||
\(266\) | −0.773393 | −0.0474197 | ||||||||
\(267\) | 17.7376 | 1.08553 | ||||||||
\(268\) | −1.86347 | −0.113830 | ||||||||
\(269\) | 9.69784 | 0.591288 | 0.295644 | − | 0.955298i | \(-0.404466\pi\) | ||||
0.295644 | + | 0.955298i | \(0.404466\pi\) | |||||||
\(270\) | −4.37472 | −0.266237 | ||||||||
\(271\) | −24.3884 | −1.48149 | −0.740745 | − | 0.671786i | \(-0.765527\pi\) | ||||
−0.740745 | + | 0.671786i | \(0.765527\pi\) | |||||||
\(272\) | 6.40302 | 0.388240 | ||||||||
\(273\) | 0.501516 | 0.0303531 | ||||||||
\(274\) | 18.5932 | 1.12326 | ||||||||
\(275\) | 62.5018 | 3.76900 | ||||||||
\(276\) | −0.287580 | −0.0173103 | ||||||||
\(277\) | −10.8414 | −0.651399 | −0.325700 | − | 0.945473i | \(-0.605600\pi\) | ||||
−0.325700 | + | 0.945473i | \(0.605600\pi\) | |||||||
\(278\) | 20.2541 | 1.21476 | ||||||||
\(279\) | −3.57302 | −0.213911 | ||||||||
\(280\) | −3.38337 | −0.202195 | ||||||||
\(281\) | −9.00314 | −0.537082 | −0.268541 | − | 0.963268i | \(-0.586542\pi\) | ||||
−0.268541 | + | 0.963268i | \(0.586542\pi\) | |||||||
\(282\) | 11.2879 | 0.672182 | ||||||||
\(283\) | 18.4920 | 1.09924 | 0.549619 | − | 0.835416i | \(-0.314773\pi\) | ||||
0.549619 | + | 0.835416i | \(0.314773\pi\) | |||||||
\(284\) | −1.42484 | −0.0845487 | ||||||||
\(285\) | −4.37472 | −0.259136 | ||||||||
\(286\) | −2.86672 | −0.169512 | ||||||||
\(287\) | −6.30223 | −0.372009 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 23.9987 | 1.41169 | ||||||||
\(290\) | 1.52188 | 0.0893678 | ||||||||
\(291\) | −9.18686 | −0.538544 | ||||||||
\(292\) | −8.80129 | −0.515056 | ||||||||
\(293\) | 6.56376 | 0.383459 | 0.191729 | − | 0.981448i | \(-0.438590\pi\) | ||||
0.191729 | + | 0.981448i | \(0.438590\pi\) | |||||||
\(294\) | −6.40186 | −0.373364 | ||||||||
\(295\) | 15.7573 | 0.917424 | ||||||||
\(296\) | 8.71669 | 0.506647 | ||||||||
\(297\) | −4.42079 | −0.256521 | ||||||||
\(298\) | −3.94550 | −0.228557 | ||||||||
\(299\) | 0.186484 | 0.0107847 | ||||||||
\(300\) | −14.1381 | −0.816266 | ||||||||
\(301\) | −6.22979 | −0.359079 | ||||||||
\(302\) | 6.27644 | 0.361169 | ||||||||
\(303\) | −16.2939 | −0.936062 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −27.1885 | −1.55681 | ||||||||
\(306\) | −6.40302 | −0.366036 | ||||||||
\(307\) | 19.0958 | 1.08986 | 0.544928 | − | 0.838483i | \(-0.316557\pi\) | ||||
0.544928 | + | 0.838483i | \(0.316557\pi\) | |||||||
\(308\) | −3.41901 | −0.194816 | ||||||||
\(309\) | 8.42044 | 0.479022 | ||||||||
\(310\) | −15.6309 | −0.887778 | ||||||||
\(311\) | 22.8539 | 1.29593 | 0.647964 | − | 0.761671i | \(-0.275621\pi\) | ||||
0.647964 | + | 0.761671i | \(0.275621\pi\) | |||||||
\(312\) | 0.648462 | 0.0367119 | ||||||||
\(313\) | 28.4846 | 1.61004 | 0.805022 | − | 0.593244i | \(-0.202153\pi\) | ||||
0.805022 | + | 0.593244i | \(0.202153\pi\) | |||||||
\(314\) | −9.71418 | −0.548203 | ||||||||
\(315\) | 3.38337 | 0.190631 | ||||||||
\(316\) | −7.81384 | −0.439563 | ||||||||
\(317\) | 20.1541 | 1.13197 | 0.565983 | − | 0.824417i | \(-0.308497\pi\) | ||||
0.565983 | + | 0.824417i | \(0.308497\pi\) | |||||||
\(318\) | 1.00000 | 0.0560772 | ||||||||
\(319\) | 1.53791 | 0.0861063 | ||||||||
\(320\) | −4.37472 | −0.244554 | ||||||||
\(321\) | −0.329410 | −0.0183858 | ||||||||
\(322\) | 0.222412 | 0.0123945 | ||||||||
\(323\) | −6.40302 | −0.356274 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 9.16804 | 0.508551 | ||||||||
\(326\) | −19.7130 | −1.09180 | ||||||||
\(327\) | 0.493136 | 0.0272705 | ||||||||
\(328\) | −8.14882 | −0.449943 | ||||||||
\(329\) | −8.72995 | −0.481298 | ||||||||
\(330\) | −19.3397 | −1.06462 | ||||||||
\(331\) | 25.8195 | 1.41917 | 0.709584 | − | 0.704621i | \(-0.248883\pi\) | ||||
0.709584 | + | 0.704621i | \(0.248883\pi\) | |||||||
\(332\) | 16.9311 | 0.929216 | ||||||||
\(333\) | −8.71669 | −0.477672 | ||||||||
\(334\) | 12.8412 | 0.702640 | ||||||||
\(335\) | 8.15216 | 0.445400 | ||||||||
\(336\) | 0.773393 | 0.0421920 | ||||||||
\(337\) | 19.8224 | 1.07980 | 0.539899 | − | 0.841730i | \(-0.318463\pi\) | ||||
0.539899 | + | 0.841730i | \(0.318463\pi\) | |||||||
\(338\) | 12.5795 | 0.684234 | ||||||||
\(339\) | 17.2506 | 0.936924 | ||||||||
\(340\) | −28.0114 | −1.51913 | ||||||||
\(341\) | −15.7956 | −0.855379 | ||||||||
\(342\) | 1.00000 | 0.0540738 | ||||||||
\(343\) | 10.3649 | 0.559652 | ||||||||
\(344\) | −8.05514 | −0.434304 | ||||||||
\(345\) | 1.25808 | 0.0677327 | ||||||||
\(346\) | −10.3472 | −0.556269 | ||||||||
\(347\) | −21.0397 | −1.12947 | −0.564735 | − | 0.825272i | \(-0.691022\pi\) | ||||
−0.564735 | + | 0.825272i | \(0.691022\pi\) | |||||||
\(348\) | −0.347880 | −0.0186483 | ||||||||
\(349\) | −22.1208 | −1.18410 | −0.592049 | − | 0.805902i | \(-0.701681\pi\) | ||||
−0.592049 | + | 0.805902i | \(0.701681\pi\) | |||||||
\(350\) | 10.9343 | 0.584465 | ||||||||
\(351\) | −0.648462 | −0.0346123 | ||||||||
\(352\) | −4.42079 | −0.235629 | ||||||||
\(353\) | −35.6025 | −1.89493 | −0.947466 | − | 0.319857i | \(-0.896365\pi\) | ||||
−0.947466 | + | 0.319857i | \(0.896365\pi\) | |||||||
\(354\) | −3.60190 | −0.191439 | ||||||||
\(355\) | 6.23327 | 0.330828 | ||||||||
\(356\) | −17.7376 | −0.940094 | ||||||||
\(357\) | 4.95205 | 0.262090 | ||||||||
\(358\) | −9.63680 | −0.509321 | ||||||||
\(359\) | 2.14270 | 0.113087 | 0.0565437 | − | 0.998400i | \(-0.481992\pi\) | ||||
0.0565437 | + | 0.998400i | \(0.481992\pi\) | |||||||
\(360\) | 4.37472 | 0.230568 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −20.7568 | −1.09095 | ||||||||
\(363\) | −8.54342 | −0.448413 | ||||||||
\(364\) | −0.501516 | −0.0262866 | ||||||||
\(365\) | 38.5031 | 2.01535 | ||||||||
\(366\) | 6.21492 | 0.324859 | ||||||||
\(367\) | −20.6265 | −1.07670 | −0.538349 | − | 0.842722i | \(-0.680952\pi\) | ||||
−0.538349 | + | 0.842722i | \(0.680952\pi\) | |||||||
\(368\) | 0.287580 | 0.0149911 | ||||||||
\(369\) | 8.14882 | 0.424210 | ||||||||
\(370\) | −38.1330 | −1.98244 | ||||||||
\(371\) | −0.773393 | −0.0401525 | ||||||||
\(372\) | 3.57302 | 0.185252 | ||||||||
\(373\) | −31.0811 | −1.60932 | −0.804660 | − | 0.593735i | \(-0.797653\pi\) | ||||
−0.804660 | + | 0.593735i | \(0.797653\pi\) | |||||||
\(374\) | −28.3064 | −1.46369 | ||||||||
\(375\) | 39.9768 | 2.06439 | ||||||||
\(376\) | −11.2879 | −0.582127 | ||||||||
\(377\) | 0.225587 | 0.0116183 | ||||||||
\(378\) | −0.773393 | −0.0397790 | ||||||||
\(379\) | 20.7497 | 1.06584 | 0.532920 | − | 0.846165i | \(-0.321095\pi\) | ||||
0.532920 | + | 0.846165i | \(0.321095\pi\) | |||||||
\(380\) | 4.37472 | 0.224418 | ||||||||
\(381\) | 10.8921 | 0.558021 | ||||||||
\(382\) | −2.13393 | −0.109182 | ||||||||
\(383\) | 29.8122 | 1.52333 | 0.761667 | − | 0.647969i | \(-0.224381\pi\) | ||||
0.761667 | + | 0.647969i | \(0.224381\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 14.9572 | 0.762289 | ||||||||
\(386\) | −5.01259 | −0.255134 | ||||||||
\(387\) | 8.05514 | 0.409466 | ||||||||
\(388\) | 9.18686 | 0.466392 | ||||||||
\(389\) | 6.58436 | 0.333841 | 0.166920 | − | 0.985970i | \(-0.446618\pi\) | ||||
0.166920 | + | 0.985970i | \(0.446618\pi\) | |||||||
\(390\) | −2.83684 | −0.143649 | ||||||||
\(391\) | 1.84138 | 0.0931225 | ||||||||
\(392\) | 6.40186 | 0.323343 | ||||||||
\(393\) | −4.64018 | −0.234066 | ||||||||
\(394\) | −16.1361 | −0.812926 | ||||||||
\(395\) | 34.1833 | 1.71995 | ||||||||
\(396\) | 4.42079 | 0.222153 | ||||||||
\(397\) | 8.13941 | 0.408505 | 0.204253 | − | 0.978918i | \(-0.434524\pi\) | ||||
0.204253 | + | 0.978918i | \(0.434524\pi\) | |||||||
\(398\) | −13.0215 | −0.652709 | ||||||||
\(399\) | −0.773393 | −0.0387181 | ||||||||
\(400\) | 14.1381 | 0.706907 | ||||||||
\(401\) | 13.6896 | 0.683627 | 0.341813 | − | 0.939768i | \(-0.388959\pi\) | ||||
0.341813 | + | 0.939768i | \(0.388959\pi\) | |||||||
\(402\) | −1.86347 | −0.0929415 | ||||||||
\(403\) | −2.31697 | −0.115416 | ||||||||
\(404\) | 16.2939 | 0.810654 | ||||||||
\(405\) | −4.37472 | −0.217381 | ||||||||
\(406\) | 0.269048 | 0.0133526 | ||||||||
\(407\) | −38.5347 | −1.91009 | ||||||||
\(408\) | 6.40302 | 0.316997 | ||||||||
\(409\) | −16.8342 | −0.832397 | −0.416199 | − | 0.909274i | \(-0.636638\pi\) | ||||
−0.416199 | + | 0.909274i | \(0.636638\pi\) | |||||||
\(410\) | 35.6488 | 1.76057 | ||||||||
\(411\) | 18.5932 | 0.917136 | ||||||||
\(412\) | −8.42044 | −0.414845 | ||||||||
\(413\) | 2.78568 | 0.137074 | ||||||||
\(414\) | −0.287580 | −0.0141338 | ||||||||
\(415\) | −74.0688 | −3.63590 | ||||||||
\(416\) | −0.648462 | −0.0317934 | ||||||||
\(417\) | 20.2541 | 0.991847 | ||||||||
\(418\) | 4.42079 | 0.216228 | ||||||||
\(419\) | 17.1176 | 0.836248 | 0.418124 | − | 0.908390i | \(-0.362688\pi\) | ||||
0.418124 | + | 0.908390i | \(0.362688\pi\) | |||||||
\(420\) | −3.38337 | −0.165092 | ||||||||
\(421\) | −5.89560 | −0.287334 | −0.143667 | − | 0.989626i | \(-0.545889\pi\) | ||||
−0.143667 | + | 0.989626i | \(0.545889\pi\) | |||||||
\(422\) | 4.52168 | 0.220112 | ||||||||
\(423\) | 11.2879 | 0.548835 | ||||||||
\(424\) | −1.00000 | −0.0485643 | ||||||||
\(425\) | 90.5268 | 4.39119 | ||||||||
\(426\) | −1.42484 | −0.0690337 | ||||||||
\(427\) | −4.80657 | −0.232606 | ||||||||
\(428\) | 0.329410 | 0.0159226 | ||||||||
\(429\) | −2.86672 | −0.138406 | ||||||||
\(430\) | 35.2389 | 1.69937 | ||||||||
\(431\) | 1.84910 | 0.0890681 | 0.0445341 | − | 0.999008i | \(-0.485820\pi\) | ||||
0.0445341 | + | 0.999008i | \(0.485820\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 18.0909 | 0.869394 | 0.434697 | − | 0.900577i | \(-0.356856\pi\) | ||||
0.434697 | + | 0.900577i | \(0.356856\pi\) | |||||||
\(434\) | −2.76335 | −0.132645 | ||||||||
\(435\) | 1.52188 | 0.0729685 | ||||||||
\(436\) | −0.493136 | −0.0236169 | ||||||||
\(437\) | −0.287580 | −0.0137568 | ||||||||
\(438\) | −8.80129 | −0.420542 | ||||||||
\(439\) | −8.56484 | −0.408778 | −0.204389 | − | 0.978890i | \(-0.565521\pi\) | ||||
−0.204389 | + | 0.978890i | \(0.565521\pi\) | |||||||
\(440\) | 19.3397 | 0.921985 | ||||||||
\(441\) | −6.40186 | −0.304851 | ||||||||
\(442\) | −4.15211 | −0.197496 | ||||||||
\(443\) | 28.8514 | 1.37077 | 0.685385 | − | 0.728181i | \(-0.259634\pi\) | ||||
0.685385 | + | 0.728181i | \(0.259634\pi\) | |||||||
\(444\) | 8.71669 | 0.413676 | ||||||||
\(445\) | 77.5972 | 3.67846 | ||||||||
\(446\) | 20.1908 | 0.956060 | ||||||||
\(447\) | −3.94550 | −0.186616 | ||||||||
\(448\) | −0.773393 | −0.0365394 | ||||||||
\(449\) | −11.8345 | −0.558505 | −0.279253 | − | 0.960218i | \(-0.590087\pi\) | ||||
−0.279253 | + | 0.960218i | \(0.590087\pi\) | |||||||
\(450\) | −14.1381 | −0.666478 | ||||||||
\(451\) | 36.0242 | 1.69632 | ||||||||
\(452\) | −17.2506 | −0.811400 | ||||||||
\(453\) | 6.27644 | 0.294893 | ||||||||
\(454\) | −17.1876 | −0.806656 | ||||||||
\(455\) | 2.19399 | 0.102856 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | 6.35020 | 0.297050 | 0.148525 | − | 0.988909i | \(-0.452547\pi\) | ||||
0.148525 | + | 0.988909i | \(0.452547\pi\) | |||||||
\(458\) | −19.9182 | −0.930714 | ||||||||
\(459\) | −6.40302 | −0.298867 | ||||||||
\(460\) | −1.25808 | −0.0586583 | ||||||||
\(461\) | 9.51641 | 0.443223 | 0.221612 | − | 0.975135i | \(-0.428868\pi\) | ||||
0.221612 | + | 0.975135i | \(0.428868\pi\) | |||||||
\(462\) | −3.41901 | −0.159067 | ||||||||
\(463\) | −26.8266 | −1.24674 | −0.623369 | − | 0.781927i | \(-0.714237\pi\) | ||||
−0.623369 | + | 0.781927i | \(0.714237\pi\) | |||||||
\(464\) | 0.347880 | 0.0161499 | ||||||||
\(465\) | −15.6309 | −0.724868 | ||||||||
\(466\) | −21.1819 | −0.981232 | ||||||||
\(467\) | −9.63770 | −0.445980 | −0.222990 | − | 0.974821i | \(-0.571582\pi\) | ||||
−0.222990 | + | 0.974821i | \(0.571582\pi\) | |||||||
\(468\) | 0.648462 | 0.0299752 | ||||||||
\(469\) | 1.44120 | 0.0665482 | ||||||||
\(470\) | 49.3812 | 2.27778 | ||||||||
\(471\) | −9.71418 | −0.447606 | ||||||||
\(472\) | 3.60190 | 0.165791 | ||||||||
\(473\) | 35.6101 | 1.63735 | ||||||||
\(474\) | −7.81384 | −0.358902 | ||||||||
\(475\) | −14.1381 | −0.648702 | ||||||||
\(476\) | −4.95205 | −0.226977 | ||||||||
\(477\) | 1.00000 | 0.0457869 | ||||||||
\(478\) | 1.90069 | 0.0869355 | ||||||||
\(479\) | −20.1735 | −0.921750 | −0.460875 | − | 0.887465i | \(-0.652464\pi\) | ||||
−0.460875 | + | 0.887465i | \(0.652464\pi\) | |||||||
\(480\) | −4.37472 | −0.199678 | ||||||||
\(481\) | −5.65244 | −0.257729 | ||||||||
\(482\) | 0.815676 | 0.0371530 | ||||||||
\(483\) | 0.222412 | 0.0101201 | ||||||||
\(484\) | 8.54342 | 0.388337 | ||||||||
\(485\) | −40.1899 | −1.82493 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | −3.00738 | −0.136277 | −0.0681386 | − | 0.997676i | \(-0.521706\pi\) | ||||
−0.0681386 | + | 0.997676i | \(0.521706\pi\) | |||||||
\(488\) | −6.21492 | −0.281336 | ||||||||
\(489\) | −19.7130 | −0.891453 | ||||||||
\(490\) | −28.0063 | −1.26520 | ||||||||
\(491\) | −18.0303 | −0.813695 | −0.406847 | − | 0.913496i | \(-0.633372\pi\) | ||||
−0.406847 | + | 0.913496i | \(0.633372\pi\) | |||||||
\(492\) | −8.14882 | −0.367377 | ||||||||
\(493\) | 2.22749 | 0.100321 | ||||||||
\(494\) | 0.648462 | 0.0291757 | ||||||||
\(495\) | −19.3397 | −0.869256 | ||||||||
\(496\) | −3.57302 | −0.160433 | ||||||||
\(497\) | 1.10196 | 0.0494297 | ||||||||
\(498\) | 16.9311 | 0.758702 | ||||||||
\(499\) | 22.9499 | 1.02738 | 0.513689 | − | 0.857976i | \(-0.328278\pi\) | ||||
0.513689 | + | 0.857976i | \(0.328278\pi\) | |||||||
\(500\) | −39.9768 | −1.78782 | ||||||||
\(501\) | 12.8412 | 0.573703 | ||||||||
\(502\) | 24.0194 | 1.07204 | ||||||||
\(503\) | 19.0086 | 0.847551 | 0.423775 | − | 0.905767i | \(-0.360705\pi\) | ||||
0.423775 | + | 0.905767i | \(0.360705\pi\) | |||||||
\(504\) | 0.773393 | 0.0344496 | ||||||||
\(505\) | −71.2813 | −3.17198 | ||||||||
\(506\) | −1.27133 | −0.0565176 | ||||||||
\(507\) | 12.5795 | 0.558675 | ||||||||
\(508\) | −10.8921 | −0.483261 | ||||||||
\(509\) | −44.7135 | −1.98189 | −0.990945 | − | 0.134270i | \(-0.957131\pi\) | ||||
−0.990945 | + | 0.134270i | \(0.957131\pi\) | |||||||
\(510\) | −28.0114 | −1.24037 | ||||||||
\(511\) | 6.80685 | 0.301117 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.00000 | 0.0441511 | ||||||||
\(514\) | −29.0813 | −1.28272 | ||||||||
\(515\) | 36.8370 | 1.62323 | ||||||||
\(516\) | −8.05514 | −0.354608 | ||||||||
\(517\) | 49.9013 | 2.19466 | ||||||||
\(518\) | −6.74142 | −0.296201 | ||||||||
\(519\) | −10.3472 | −0.454191 | ||||||||
\(520\) | 2.83684 | 0.124403 | ||||||||
\(521\) | −15.0524 | −0.659457 | −0.329728 | − | 0.944076i | \(-0.606957\pi\) | ||||
−0.329728 | + | 0.944076i | \(0.606957\pi\) | |||||||
\(522\) | −0.347880 | −0.0152263 | ||||||||
\(523\) | 10.8505 | 0.474458 | 0.237229 | − | 0.971454i | \(-0.423761\pi\) | ||||
0.237229 | + | 0.971454i | \(0.423761\pi\) | |||||||
\(524\) | 4.64018 | 0.202707 | ||||||||
\(525\) | 10.9343 | 0.477213 | ||||||||
\(526\) | −2.58074 | −0.112526 | ||||||||
\(527\) | −22.8781 | −0.996586 | ||||||||
\(528\) | −4.42079 | −0.192390 | ||||||||
\(529\) | −22.9173 | −0.996404 | ||||||||
\(530\) | 4.37472 | 0.190026 | ||||||||
\(531\) | −3.60190 | −0.156309 | ||||||||
\(532\) | 0.773393 | 0.0335308 | ||||||||
\(533\) | 5.28419 | 0.228884 | ||||||||
\(534\) | −17.7376 | −0.767583 | ||||||||
\(535\) | −1.44107 | −0.0623030 | ||||||||
\(536\) | 1.86347 | 0.0804897 | ||||||||
\(537\) | −9.63680 | −0.415859 | ||||||||
\(538\) | −9.69784 | −0.418104 | ||||||||
\(539\) | −28.3013 | −1.21902 | ||||||||
\(540\) | 4.37472 | 0.188258 | ||||||||
\(541\) | −29.4066 | −1.26429 | −0.632144 | − | 0.774851i | \(-0.717825\pi\) | ||||
−0.632144 | + | 0.774851i | \(0.717825\pi\) | |||||||
\(542\) | 24.3884 | 1.04757 | ||||||||
\(543\) | −20.7568 | −0.890760 | ||||||||
\(544\) | −6.40302 | −0.274527 | ||||||||
\(545\) | 2.15733 | 0.0924098 | ||||||||
\(546\) | −0.501516 | −0.0214629 | ||||||||
\(547\) | −24.1790 | −1.03382 | −0.516910 | − | 0.856039i | \(-0.672918\pi\) | ||||
−0.516910 | + | 0.856039i | \(0.672918\pi\) | |||||||
\(548\) | −18.5932 | −0.794263 | ||||||||
\(549\) | 6.21492 | 0.265246 | ||||||||
\(550\) | −62.5018 | −2.66509 | ||||||||
\(551\) | −0.347880 | −0.0148202 | ||||||||
\(552\) | 0.287580 | 0.0122402 | ||||||||
\(553\) | 6.04317 | 0.256982 | ||||||||
\(554\) | 10.8414 | 0.460609 | ||||||||
\(555\) | −38.1330 | −1.61866 | ||||||||
\(556\) | −20.2541 | −0.858965 | ||||||||
\(557\) | −17.8091 | −0.754596 | −0.377298 | − | 0.926092i | \(-0.623147\pi\) | ||||
−0.377298 | + | 0.926092i | \(0.623147\pi\) | |||||||
\(558\) | 3.57302 | 0.151258 | ||||||||
\(559\) | 5.22345 | 0.220928 | ||||||||
\(560\) | 3.38337 | 0.142974 | ||||||||
\(561\) | −28.3064 | −1.19510 | ||||||||
\(562\) | 9.00314 | 0.379775 | ||||||||
\(563\) | 3.25383 | 0.137132 | 0.0685662 | − | 0.997647i | \(-0.478158\pi\) | ||||
0.0685662 | + | 0.997647i | \(0.478158\pi\) | |||||||
\(564\) | −11.2879 | −0.475305 | ||||||||
\(565\) | 75.4664 | 3.17490 | ||||||||
\(566\) | −18.4920 | −0.777278 | ||||||||
\(567\) | −0.773393 | −0.0324794 | ||||||||
\(568\) | 1.42484 | 0.0597850 | ||||||||
\(569\) | −13.8182 | −0.579290 | −0.289645 | − | 0.957134i | \(-0.593537\pi\) | ||||
−0.289645 | + | 0.957134i | \(0.593537\pi\) | |||||||
\(570\) | 4.37472 | 0.183237 | ||||||||
\(571\) | 21.5278 | 0.900911 | 0.450455 | − | 0.892799i | \(-0.351262\pi\) | ||||
0.450455 | + | 0.892799i | \(0.351262\pi\) | |||||||
\(572\) | 2.86672 | 0.119863 | ||||||||
\(573\) | −2.13393 | −0.0891463 | ||||||||
\(574\) | 6.30223 | 0.263050 | ||||||||
\(575\) | 4.06584 | 0.169557 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 37.9416 | 1.57953 | 0.789765 | − | 0.613409i | \(-0.210202\pi\) | ||||
0.789765 | + | 0.613409i | \(0.210202\pi\) | |||||||
\(578\) | −23.9987 | −0.998213 | ||||||||
\(579\) | −5.01259 | −0.208316 | ||||||||
\(580\) | −1.52188 | −0.0631925 | ||||||||
\(581\) | −13.0944 | −0.543247 | ||||||||
\(582\) | 9.18686 | 0.380808 | ||||||||
\(583\) | 4.42079 | 0.183091 | ||||||||
\(584\) | 8.80129 | 0.364200 | ||||||||
\(585\) | −2.83684 | −0.117289 | ||||||||
\(586\) | −6.56376 | −0.271146 | ||||||||
\(587\) | −26.4655 | −1.09235 | −0.546174 | − | 0.837672i | \(-0.683916\pi\) | ||||
−0.546174 | + | 0.837672i | \(0.683916\pi\) | |||||||
\(588\) | 6.40186 | 0.264008 | ||||||||
\(589\) | 3.57302 | 0.147224 | ||||||||
\(590\) | −15.7573 | −0.648717 | ||||||||
\(591\) | −16.1361 | −0.663751 | ||||||||
\(592\) | −8.71669 | −0.358254 | ||||||||
\(593\) | 14.7251 | 0.604685 | 0.302343 | − | 0.953199i | \(-0.402231\pi\) | ||||
0.302343 | + | 0.953199i | \(0.402231\pi\) | |||||||
\(594\) | 4.42079 | 0.181387 | ||||||||
\(595\) | 21.6638 | 0.888130 | ||||||||
\(596\) | 3.94550 | 0.161614 | ||||||||
\(597\) | −13.0215 | −0.532934 | ||||||||
\(598\) | −0.186484 | −0.00762592 | ||||||||
\(599\) | 45.3990 | 1.85495 | 0.927476 | − | 0.373882i | \(-0.121974\pi\) | ||||
0.927476 | + | 0.373882i | \(0.121974\pi\) | |||||||
\(600\) | 14.1381 | 0.577187 | ||||||||
\(601\) | 18.4301 | 0.751781 | 0.375891 | − | 0.926664i | \(-0.377337\pi\) | ||||
0.375891 | + | 0.926664i | \(0.377337\pi\) | |||||||
\(602\) | 6.22979 | 0.253907 | ||||||||
\(603\) | −1.86347 | −0.0758864 | ||||||||
\(604\) | −6.27644 | −0.255385 | ||||||||
\(605\) | −37.3751 | −1.51951 | ||||||||
\(606\) | 16.2939 | 0.661896 | ||||||||
\(607\) | 10.8395 | 0.439960 | 0.219980 | − | 0.975504i | \(-0.429401\pi\) | ||||
0.219980 | + | 0.975504i | \(0.429401\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0.269048 | 0.0109024 | ||||||||
\(610\) | 27.1885 | 1.10083 | ||||||||
\(611\) | 7.31975 | 0.296125 | ||||||||
\(612\) | 6.40302 | 0.258827 | ||||||||
\(613\) | −9.40916 | −0.380033 | −0.190016 | − | 0.981781i | \(-0.560854\pi\) | ||||
−0.190016 | + | 0.981781i | \(0.560854\pi\) | |||||||
\(614\) | −19.0958 | −0.770645 | ||||||||
\(615\) | 35.6488 | 1.43750 | ||||||||
\(616\) | 3.41901 | 0.137756 | ||||||||
\(617\) | 1.80538 | 0.0726820 | 0.0363410 | − | 0.999339i | \(-0.488430\pi\) | ||||
0.0363410 | + | 0.999339i | \(0.488430\pi\) | |||||||
\(618\) | −8.42044 | −0.338720 | ||||||||
\(619\) | −17.1871 | −0.690807 | −0.345403 | − | 0.938454i | \(-0.612258\pi\) | ||||
−0.345403 | + | 0.938454i | \(0.612258\pi\) | |||||||
\(620\) | 15.6309 | 0.627754 | ||||||||
\(621\) | −0.287580 | −0.0115402 | ||||||||
\(622\) | −22.8539 | −0.916359 | ||||||||
\(623\) | 13.7182 | 0.549607 | ||||||||
\(624\) | −0.648462 | −0.0259592 | ||||||||
\(625\) | 104.196 | 4.16785 | ||||||||
\(626\) | −28.4846 | −1.13847 | ||||||||
\(627\) | 4.42079 | 0.176550 | ||||||||
\(628\) | 9.71418 | 0.387638 | ||||||||
\(629\) | −55.8131 | −2.22542 | ||||||||
\(630\) | −3.38337 | −0.134797 | ||||||||
\(631\) | −35.7059 | −1.42143 | −0.710715 | − | 0.703480i | \(-0.751628\pi\) | ||||
−0.710715 | + | 0.703480i | \(0.751628\pi\) | |||||||
\(632\) | 7.81384 | 0.310818 | ||||||||
\(633\) | 4.52168 | 0.179721 | ||||||||
\(634\) | −20.1541 | −0.800421 | ||||||||
\(635\) | 47.6500 | 1.89093 | ||||||||
\(636\) | −1.00000 | −0.0396526 | ||||||||
\(637\) | −4.15136 | −0.164483 | ||||||||
\(638\) | −1.53791 | −0.0608864 | ||||||||
\(639\) | −1.42484 | −0.0563658 | ||||||||
\(640\) | 4.37472 | 0.172926 | ||||||||
\(641\) | 15.0696 | 0.595214 | 0.297607 | − | 0.954688i | \(-0.403811\pi\) | ||||
0.297607 | + | 0.954688i | \(0.403811\pi\) | |||||||
\(642\) | 0.329410 | 0.0130008 | ||||||||
\(643\) | 32.5585 | 1.28398 | 0.641992 | − | 0.766712i | \(-0.278108\pi\) | ||||
0.641992 | + | 0.766712i | \(0.278108\pi\) | |||||||
\(644\) | −0.222412 | −0.00876426 | ||||||||
\(645\) | 35.2389 | 1.38753 | ||||||||
\(646\) | 6.40302 | 0.251923 | ||||||||
\(647\) | −12.3081 | −0.483883 | −0.241942 | − | 0.970291i | \(-0.577784\pi\) | ||||
−0.241942 | + | 0.970291i | \(0.577784\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −15.9232 | −0.625042 | ||||||||
\(650\) | −9.16804 | −0.359600 | ||||||||
\(651\) | −2.76335 | −0.108304 | ||||||||
\(652\) | 19.7130 | 0.772021 | ||||||||
\(653\) | −19.4383 | −0.760678 | −0.380339 | − | 0.924847i | \(-0.624193\pi\) | ||||
−0.380339 | + | 0.924847i | \(0.624193\pi\) | |||||||
\(654\) | −0.493136 | −0.0192831 | ||||||||
\(655\) | −20.2995 | −0.793166 | ||||||||
\(656\) | 8.14882 | 0.318158 | ||||||||
\(657\) | −8.80129 | −0.343371 | ||||||||
\(658\) | 8.72995 | 0.340329 | ||||||||
\(659\) | −35.5229 | −1.38378 | −0.691888 | − | 0.722005i | \(-0.743221\pi\) | ||||
−0.691888 | + | 0.722005i | \(0.743221\pi\) | |||||||
\(660\) | 19.3397 | 0.752798 | ||||||||
\(661\) | −41.9544 | −1.63184 | −0.815918 | − | 0.578168i | \(-0.803768\pi\) | ||||
−0.815918 | + | 0.578168i | \(0.803768\pi\) | |||||||
\(662\) | −25.8195 | −1.00350 | ||||||||
\(663\) | −4.15211 | −0.161255 | ||||||||
\(664\) | −16.9311 | −0.657055 | ||||||||
\(665\) | −3.38337 | −0.131202 | ||||||||
\(666\) | 8.71669 | 0.337765 | ||||||||
\(667\) | 0.100043 | 0.00387369 | ||||||||
\(668\) | −12.8412 | −0.496842 | ||||||||
\(669\) | 20.1908 | 0.780620 | ||||||||
\(670\) | −8.15216 | −0.314945 | ||||||||
\(671\) | 27.4749 | 1.06066 | ||||||||
\(672\) | −0.773393 | −0.0298343 | ||||||||
\(673\) | 48.8542 | 1.88319 | 0.941596 | − | 0.336745i | \(-0.109326\pi\) | ||||
0.941596 | + | 0.336745i | \(0.109326\pi\) | |||||||
\(674\) | −19.8224 | −0.763532 | ||||||||
\(675\) | −14.1381 | −0.544177 | ||||||||
\(676\) | −12.5795 | −0.483827 | ||||||||
\(677\) | −24.5972 | −0.945349 | −0.472674 | − | 0.881237i | \(-0.656711\pi\) | ||||
−0.472674 | + | 0.881237i | \(0.656711\pi\) | |||||||
\(678\) | −17.2506 | −0.662505 | ||||||||
\(679\) | −7.10505 | −0.272667 | ||||||||
\(680\) | 28.0114 | 1.07419 | ||||||||
\(681\) | −17.1876 | −0.658632 | ||||||||
\(682\) | 15.7956 | 0.604844 | ||||||||
\(683\) | 32.6023 | 1.24749 | 0.623746 | − | 0.781627i | \(-0.285610\pi\) | ||||
0.623746 | + | 0.781627i | \(0.285610\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 81.3400 | 3.10784 | ||||||||
\(686\) | −10.3649 | −0.395734 | ||||||||
\(687\) | −19.9182 | −0.759925 | ||||||||
\(688\) | 8.05514 | 0.307099 | ||||||||
\(689\) | 0.648462 | 0.0247044 | ||||||||
\(690\) | −1.25808 | −0.0478943 | ||||||||
\(691\) | 12.1284 | 0.461385 | 0.230692 | − | 0.973027i | \(-0.425901\pi\) | ||||
0.230692 | + | 0.973027i | \(0.425901\pi\) | |||||||
\(692\) | 10.3472 | 0.393341 | ||||||||
\(693\) | −3.41901 | −0.129877 | ||||||||
\(694\) | 21.0397 | 0.798656 | ||||||||
\(695\) | 88.6059 | 3.36101 | ||||||||
\(696\) | 0.347880 | 0.0131864 | ||||||||
\(697\) | 52.1770 | 1.97635 | ||||||||
\(698\) | 22.1208 | 0.837284 | ||||||||
\(699\) | −21.1819 | −0.801173 | ||||||||
\(700\) | −10.9343 | −0.413279 | ||||||||
\(701\) | −0.917740 | −0.0346625 | −0.0173313 | − | 0.999850i | \(-0.505517\pi\) | ||||
−0.0173313 | + | 0.999850i | \(0.505517\pi\) | |||||||
\(702\) | 0.648462 | 0.0244746 | ||||||||
\(703\) | 8.71669 | 0.328756 | ||||||||
\(704\) | 4.42079 | 0.166615 | ||||||||
\(705\) | 49.3812 | 1.85980 | ||||||||
\(706\) | 35.6025 | 1.33992 | ||||||||
\(707\) | −12.6016 | −0.473932 | ||||||||
\(708\) | 3.60190 | 0.135368 | ||||||||
\(709\) | −13.7581 | −0.516696 | −0.258348 | − | 0.966052i | \(-0.583178\pi\) | ||||
−0.258348 | + | 0.966052i | \(0.583178\pi\) | |||||||
\(710\) | −6.23327 | −0.233931 | ||||||||
\(711\) | −7.81384 | −0.293042 | ||||||||
\(712\) | 17.7376 | 0.664747 | ||||||||
\(713\) | −1.02753 | −0.0384812 | ||||||||
\(714\) | −4.95205 | −0.185326 | ||||||||
\(715\) | −12.5411 | −0.469009 | ||||||||
\(716\) | 9.63680 | 0.360144 | ||||||||
\(717\) | 1.90069 | 0.0709825 | ||||||||
\(718\) | −2.14270 | −0.0799648 | ||||||||
\(719\) | 8.42431 | 0.314174 | 0.157087 | − | 0.987585i | \(-0.449790\pi\) | ||||
0.157087 | + | 0.987585i | \(0.449790\pi\) | |||||||
\(720\) | −4.37472 | −0.163036 | ||||||||
\(721\) | 6.51230 | 0.242531 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 0.815676 | 0.0303353 | ||||||||
\(724\) | 20.7568 | 0.771420 | ||||||||
\(725\) | 4.91838 | 0.182664 | ||||||||
\(726\) | 8.54342 | 0.317076 | ||||||||
\(727\) | 11.6726 | 0.432911 | 0.216456 | − | 0.976292i | \(-0.430550\pi\) | ||||
0.216456 | + | 0.976292i | \(0.430550\pi\) | |||||||
\(728\) | 0.501516 | 0.0185874 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −38.5031 | −1.42506 | ||||||||
\(731\) | 51.5772 | 1.90765 | ||||||||
\(732\) | −6.21492 | −0.229710 | ||||||||
\(733\) | 45.1855 | 1.66896 | 0.834482 | − | 0.551036i | \(-0.185767\pi\) | ||||
0.834482 | + | 0.551036i | \(0.185767\pi\) | |||||||
\(734\) | 20.6265 | 0.761340 | ||||||||
\(735\) | −28.0063 | −1.03303 | ||||||||
\(736\) | −0.287580 | −0.0106003 | ||||||||
\(737\) | −8.23803 | −0.303452 | ||||||||
\(738\) | −8.14882 | −0.299962 | ||||||||
\(739\) | 29.9073 | 1.10016 | 0.550080 | − | 0.835112i | \(-0.314597\pi\) | ||||
0.550080 | + | 0.835112i | \(0.314597\pi\) | |||||||
\(740\) | 38.1330 | 1.40180 | ||||||||
\(741\) | 0.648462 | 0.0238218 | ||||||||
\(742\) | 0.773393 | 0.0283921 | ||||||||
\(743\) | −26.4670 | −0.970978 | −0.485489 | − | 0.874243i | \(-0.661358\pi\) | ||||
−0.485489 | + | 0.874243i | \(0.661358\pi\) | |||||||
\(744\) | −3.57302 | −0.130993 | ||||||||
\(745\) | −17.2604 | −0.632373 | ||||||||
\(746\) | 31.0811 | 1.13796 | ||||||||
\(747\) | 16.9311 | 0.619477 | ||||||||
\(748\) | 28.3064 | 1.03499 | ||||||||
\(749\) | −0.254763 | −0.00930884 | ||||||||
\(750\) | −39.9768 | −1.45975 | ||||||||
\(751\) | −33.5132 | −1.22291 | −0.611457 | − | 0.791277i | \(-0.709416\pi\) | ||||
−0.611457 | + | 0.791277i | \(0.709416\pi\) | |||||||
\(752\) | 11.2879 | 0.411626 | ||||||||
\(753\) | 24.0194 | 0.875315 | ||||||||
\(754\) | −0.225587 | −0.00821540 | ||||||||
\(755\) | 27.4577 | 0.999286 | ||||||||
\(756\) | 0.773393 | 0.0281280 | ||||||||
\(757\) | −33.1757 | −1.20579 | −0.602896 | − | 0.797820i | \(-0.705987\pi\) | ||||
−0.602896 | + | 0.797820i | \(0.705987\pi\) | |||||||
\(758\) | −20.7497 | −0.753663 | ||||||||
\(759\) | −1.27133 | −0.0461464 | ||||||||
\(760\) | −4.37472 | −0.158688 | ||||||||
\(761\) | −13.1685 | −0.477357 | −0.238678 | − | 0.971099i | \(-0.576714\pi\) | ||||
−0.238678 | + | 0.971099i | \(0.576714\pi\) | |||||||
\(762\) | −10.8921 | −0.394581 | ||||||||
\(763\) | 0.381388 | 0.0138072 | ||||||||
\(764\) | 2.13393 | 0.0772030 | ||||||||
\(765\) | −28.0114 | −1.01275 | ||||||||
\(766\) | −29.8122 | −1.07716 | ||||||||
\(767\) | −2.33569 | −0.0843369 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 37.5952 | 1.35572 | 0.677860 | − | 0.735191i | \(-0.262908\pi\) | ||||
0.677860 | + | 0.735191i | \(0.262908\pi\) | |||||||
\(770\) | −14.9572 | −0.539020 | ||||||||
\(771\) | −29.0813 | −1.04734 | ||||||||
\(772\) | 5.01259 | 0.180407 | ||||||||
\(773\) | 15.8778 | 0.571084 | 0.285542 | − | 0.958366i | \(-0.407826\pi\) | ||||
0.285542 | + | 0.958366i | \(0.407826\pi\) | |||||||
\(774\) | −8.05514 | −0.289536 | ||||||||
\(775\) | −50.5158 | −1.81458 | ||||||||
\(776\) | −9.18686 | −0.329789 | ||||||||
\(777\) | −6.74142 | −0.241847 | ||||||||
\(778\) | −6.58436 | −0.236061 | ||||||||
\(779\) | −8.14882 | −0.291962 | ||||||||
\(780\) | 2.83684 | 0.101575 | ||||||||
\(781\) | −6.29893 | −0.225393 | ||||||||
\(782\) | −1.84138 | −0.0658476 | ||||||||
\(783\) | −0.347880 | −0.0124322 | ||||||||
\(784\) | −6.40186 | −0.228638 | ||||||||
\(785\) | −42.4968 | −1.51677 | ||||||||
\(786\) | 4.64018 | 0.165510 | ||||||||
\(787\) | 32.1823 | 1.14718 | 0.573588 | − | 0.819144i | \(-0.305551\pi\) | ||||
0.573588 | + | 0.819144i | \(0.305551\pi\) | |||||||
\(788\) | 16.1361 | 0.574825 | ||||||||
\(789\) | −2.58074 | −0.0918768 | ||||||||
\(790\) | −34.1833 | −1.21619 | ||||||||
\(791\) | 13.3415 | 0.474369 | ||||||||
\(792\) | −4.42079 | −0.157086 | ||||||||
\(793\) | 4.03013 | 0.143114 | ||||||||
\(794\) | −8.13941 | −0.288857 | ||||||||
\(795\) | 4.37472 | 0.155155 | ||||||||
\(796\) | 13.0215 | 0.461535 | ||||||||
\(797\) | −4.13282 | −0.146392 | −0.0731961 | − | 0.997318i | \(-0.523320\pi\) | ||||
−0.0731961 | + | 0.997318i | \(0.523320\pi\) | |||||||
\(798\) | 0.773393 | 0.0273778 | ||||||||
\(799\) | 72.2764 | 2.55696 | ||||||||
\(800\) | −14.1381 | −0.499859 | ||||||||
\(801\) | −17.7376 | −0.626729 | ||||||||
\(802\) | −13.6896 | −0.483397 | ||||||||
\(803\) | −38.9087 | −1.37306 | ||||||||
\(804\) | 1.86347 | 0.0657196 | ||||||||
\(805\) | 0.972990 | 0.0342934 | ||||||||
\(806\) | 2.31697 | 0.0816116 | ||||||||
\(807\) | −9.69784 | −0.341380 | ||||||||
\(808\) | −16.2939 | −0.573219 | ||||||||
\(809\) | −30.8579 | −1.08491 | −0.542454 | − | 0.840086i | \(-0.682505\pi\) | ||||
−0.542454 | + | 0.840086i | \(0.682505\pi\) | |||||||
\(810\) | 4.37472 | 0.153712 | ||||||||
\(811\) | 10.5909 | 0.371896 | 0.185948 | − | 0.982560i | \(-0.440464\pi\) | ||||
0.185948 | + | 0.982560i | \(0.440464\pi\) | |||||||
\(812\) | −0.269048 | −0.00944174 | ||||||||
\(813\) | 24.3884 | 0.855339 | ||||||||
\(814\) | 38.5347 | 1.35064 | ||||||||
\(815\) | −86.2388 | −3.02081 | ||||||||
\(816\) | −6.40302 | −0.224151 | ||||||||
\(817\) | −8.05514 | −0.281814 | ||||||||
\(818\) | 16.8342 | 0.588594 | ||||||||
\(819\) | −0.501516 | −0.0175244 | ||||||||
\(820\) | −35.6488 | −1.24491 | ||||||||
\(821\) | 47.3101 | 1.65114 | 0.825568 | − | 0.564303i | \(-0.190855\pi\) | ||||
0.825568 | + | 0.564303i | \(0.190855\pi\) | |||||||
\(822\) | −18.5932 | −0.648513 | ||||||||
\(823\) | 6.83735 | 0.238335 | 0.119168 | − | 0.992874i | \(-0.461977\pi\) | ||||
0.119168 | + | 0.992874i | \(0.461977\pi\) | |||||||
\(824\) | 8.42044 | 0.293340 | ||||||||
\(825\) | −62.5018 | −2.17603 | ||||||||
\(826\) | −2.78568 | −0.0969262 | ||||||||
\(827\) | 18.7924 | 0.653474 | 0.326737 | − | 0.945115i | \(-0.394051\pi\) | ||||
0.326737 | + | 0.945115i | \(0.394051\pi\) | |||||||
\(828\) | 0.287580 | 0.00999409 | ||||||||
\(829\) | 40.4699 | 1.40558 | 0.702789 | − | 0.711398i | \(-0.251938\pi\) | ||||
0.702789 | + | 0.711398i | \(0.251938\pi\) | |||||||
\(830\) | 74.0688 | 2.57097 | ||||||||
\(831\) | 10.8414 | 0.376086 | ||||||||
\(832\) | 0.648462 | 0.0224814 | ||||||||
\(833\) | −40.9913 | −1.42026 | ||||||||
\(834\) | −20.2541 | −0.701342 | ||||||||
\(835\) | 56.1767 | 1.94407 | ||||||||
\(836\) | −4.42079 | −0.152896 | ||||||||
\(837\) | 3.57302 | 0.123502 | ||||||||
\(838\) | −17.1176 | −0.591317 | ||||||||
\(839\) | −45.6022 | −1.57436 | −0.787182 | − | 0.616721i | \(-0.788461\pi\) | ||||
−0.787182 | + | 0.616721i | \(0.788461\pi\) | |||||||
\(840\) | 3.38337 | 0.116737 | ||||||||
\(841\) | −28.8790 | −0.995827 | ||||||||
\(842\) | 5.89560 | 0.203176 | ||||||||
\(843\) | 9.00314 | 0.310085 | ||||||||
\(844\) | −4.52168 | −0.155643 | ||||||||
\(845\) | 55.0317 | 1.89315 | ||||||||
\(846\) | −11.2879 | −0.388085 | ||||||||
\(847\) | −6.60742 | −0.227034 | ||||||||
\(848\) | 1.00000 | 0.0343401 | ||||||||
\(849\) | −18.4920 | −0.634645 | ||||||||
\(850\) | −90.5268 | −3.10504 | ||||||||
\(851\) | −2.50674 | −0.0859300 | ||||||||
\(852\) | 1.42484 | 0.0488142 | ||||||||
\(853\) | −32.1482 | −1.10073 | −0.550367 | − | 0.834923i | \(-0.685512\pi\) | ||||
−0.550367 | + | 0.834923i | \(0.685512\pi\) | |||||||
\(854\) | 4.80657 | 0.164477 | ||||||||
\(855\) | 4.37472 | 0.149612 | ||||||||
\(856\) | −0.329410 | −0.0112590 | ||||||||
\(857\) | 21.1875 | 0.723750 | 0.361875 | − | 0.932227i | \(-0.382137\pi\) | ||||
0.361875 | + | 0.932227i | \(0.382137\pi\) | |||||||
\(858\) | 2.86672 | 0.0978681 | ||||||||
\(859\) | 12.7865 | 0.436270 | 0.218135 | − | 0.975919i | \(-0.430003\pi\) | ||||
0.218135 | + | 0.975919i | \(0.430003\pi\) | |||||||
\(860\) | −35.2389 | −1.20164 | ||||||||
\(861\) | 6.30223 | 0.214780 | ||||||||
\(862\) | −1.84910 | −0.0629807 | ||||||||
\(863\) | 40.3087 | 1.37213 | 0.686063 | − | 0.727542i | \(-0.259338\pi\) | ||||
0.686063 | + | 0.727542i | \(0.259338\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | −45.2660 | −1.53909 | ||||||||
\(866\) | −18.0909 | −0.614754 | ||||||||
\(867\) | −23.9987 | −0.815038 | ||||||||
\(868\) | 2.76335 | 0.0937941 | ||||||||
\(869\) | −34.5434 | −1.17180 | ||||||||
\(870\) | −1.52188 | −0.0515965 | ||||||||
\(871\) | −1.20839 | −0.0409447 | ||||||||
\(872\) | 0.493136 | 0.0166997 | ||||||||
\(873\) | 9.18686 | 0.310928 | ||||||||
\(874\) | 0.287580 | 0.00972753 | ||||||||
\(875\) | 30.9177 | 1.04521 | ||||||||
\(876\) | 8.80129 | 0.297368 | ||||||||
\(877\) | 38.1296 | 1.28754 | 0.643772 | − | 0.765217i | \(-0.277369\pi\) | ||||
0.643772 | + | 0.765217i | \(0.277369\pi\) | |||||||
\(878\) | 8.56484 | 0.289049 | ||||||||
\(879\) | −6.56376 | −0.221390 | ||||||||
\(880\) | −19.3397 | −0.651942 | ||||||||
\(881\) | −4.82124 | −0.162432 | −0.0812159 | − | 0.996697i | \(-0.525880\pi\) | ||||
−0.0812159 | + | 0.996697i | \(0.525880\pi\) | |||||||
\(882\) | 6.40186 | 0.215562 | ||||||||
\(883\) | −10.2507 | −0.344964 | −0.172482 | − | 0.985013i | \(-0.555179\pi\) | ||||
−0.172482 | + | 0.985013i | \(0.555179\pi\) | |||||||
\(884\) | 4.15211 | 0.139651 | ||||||||
\(885\) | −15.7573 | −0.529675 | ||||||||
\(886\) | −28.8514 | −0.969281 | ||||||||
\(887\) | 23.8066 | 0.799346 | 0.399673 | − | 0.916658i | \(-0.369124\pi\) | ||||
0.399673 | + | 0.916658i | \(0.369124\pi\) | |||||||
\(888\) | −8.71669 | −0.292513 | ||||||||
\(889\) | 8.42390 | 0.282529 | ||||||||
\(890\) | −77.5972 | −2.60106 | ||||||||
\(891\) | 4.42079 | 0.148102 | ||||||||
\(892\) | −20.1908 | −0.676037 | ||||||||
\(893\) | −11.2879 | −0.377734 | ||||||||
\(894\) | 3.94550 | 0.131957 | ||||||||
\(895\) | −42.1583 | −1.40920 | ||||||||
\(896\) | 0.773393 | 0.0258372 | ||||||||
\(897\) | −0.186484 | −0.00622653 | ||||||||
\(898\) | 11.8345 | 0.394923 | ||||||||
\(899\) | −1.24298 | −0.0414558 | ||||||||
\(900\) | 14.1381 | 0.471271 | ||||||||
\(901\) | 6.40302 | 0.213316 | ||||||||
\(902\) | −36.0242 | −1.19948 | ||||||||
\(903\) | 6.22979 | 0.207314 | ||||||||
\(904\) | 17.2506 | 0.573746 | ||||||||
\(905\) | −90.8051 | −3.01846 | ||||||||
\(906\) | −6.27644 | −0.208521 | ||||||||
\(907\) | 51.8686 | 1.72227 | 0.861134 | − | 0.508378i | \(-0.169755\pi\) | ||||
0.861134 | + | 0.508378i | \(0.169755\pi\) | |||||||
\(908\) | 17.1876 | 0.570392 | ||||||||
\(909\) | 16.2939 | 0.540436 | ||||||||
\(910\) | −2.19399 | −0.0727300 | ||||||||
\(911\) | 21.0121 | 0.696162 | 0.348081 | − | 0.937464i | \(-0.386833\pi\) | ||||
0.348081 | + | 0.937464i | \(0.386833\pi\) | |||||||
\(912\) | 1.00000 | 0.0331133 | ||||||||
\(913\) | 74.8490 | 2.47714 | ||||||||
\(914\) | −6.35020 | −0.210046 | ||||||||
\(915\) | 27.1885 | 0.898824 | ||||||||
\(916\) | 19.9182 | 0.658114 | ||||||||
\(917\) | −3.58868 | −0.118509 | ||||||||
\(918\) | 6.40302 | 0.211331 | ||||||||
\(919\) | 29.2886 | 0.966142 | 0.483071 | − | 0.875581i | \(-0.339521\pi\) | ||||
0.483071 | + | 0.875581i | \(0.339521\pi\) | |||||||
\(920\) | 1.25808 | 0.0414777 | ||||||||
\(921\) | −19.0958 | −0.629229 | ||||||||
\(922\) | −9.51641 | −0.313406 | ||||||||
\(923\) | −0.923954 | −0.0304123 | ||||||||
\(924\) | 3.41901 | 0.112477 | ||||||||
\(925\) | −123.238 | −4.05203 | ||||||||
\(926\) | 26.8266 | 0.881578 | ||||||||
\(927\) | −8.42044 | −0.276563 | ||||||||
\(928\) | −0.347880 | −0.0114197 | ||||||||
\(929\) | 28.6935 | 0.941404 | 0.470702 | − | 0.882292i | \(-0.344001\pi\) | ||||
0.470702 | + | 0.882292i | \(0.344001\pi\) | |||||||
\(930\) | 15.6309 | 0.512559 | ||||||||
\(931\) | 6.40186 | 0.209813 | ||||||||
\(932\) | 21.1819 | 0.693836 | ||||||||
\(933\) | −22.8539 | −0.748204 | ||||||||
\(934\) | 9.63770 | 0.315355 | ||||||||
\(935\) | −123.833 | −4.04976 | ||||||||
\(936\) | −0.648462 | −0.0211956 | ||||||||
\(937\) | 15.0827 | 0.492730 | 0.246365 | − | 0.969177i | \(-0.420764\pi\) | ||||
0.246365 | + | 0.969177i | \(0.420764\pi\) | |||||||
\(938\) | −1.44120 | −0.0470567 | ||||||||
\(939\) | −28.4846 | −0.929560 | ||||||||
\(940\) | −49.3812 | −1.61064 | ||||||||
\(941\) | −8.37048 | −0.272870 | −0.136435 | − | 0.990649i | \(-0.543564\pi\) | ||||
−0.136435 | + | 0.990649i | \(0.543564\pi\) | |||||||
\(942\) | 9.71418 | 0.316505 | ||||||||
\(943\) | 2.34343 | 0.0763127 | ||||||||
\(944\) | −3.60190 | −0.117232 | ||||||||
\(945\) | −3.38337 | −0.110061 | ||||||||
\(946\) | −35.6101 | −1.15778 | ||||||||
\(947\) | 20.9380 | 0.680394 | 0.340197 | − | 0.940354i | \(-0.389506\pi\) | ||||
0.340197 | + | 0.940354i | \(0.389506\pi\) | |||||||
\(948\) | 7.81384 | 0.253782 | ||||||||
\(949\) | −5.70730 | −0.185267 | ||||||||
\(950\) | 14.1381 | 0.458702 | ||||||||
\(951\) | −20.1541 | −0.653541 | ||||||||
\(952\) | 4.95205 | 0.160497 | ||||||||
\(953\) | 8.10083 | 0.262412 | 0.131206 | − | 0.991355i | \(-0.458115\pi\) | ||||
0.131206 | + | 0.991355i | \(0.458115\pi\) | |||||||
\(954\) | −1.00000 | −0.0323762 | ||||||||
\(955\) | −9.33535 | −0.302085 | ||||||||
\(956\) | −1.90069 | −0.0614727 | ||||||||
\(957\) | −1.53791 | −0.0497135 | ||||||||
\(958\) | 20.1735 | 0.651776 | ||||||||
\(959\) | 14.3799 | 0.464350 | ||||||||
\(960\) | 4.37472 | 0.141193 | ||||||||
\(961\) | −18.2335 | −0.588179 | ||||||||
\(962\) | 5.65244 | 0.182242 | ||||||||
\(963\) | 0.329410 | 0.0106151 | ||||||||
\(964\) | −0.815676 | −0.0262712 | ||||||||
\(965\) | −21.9286 | −0.705908 | ||||||||
\(966\) | −0.222412 | −0.00715599 | ||||||||
\(967\) | −14.2848 | −0.459370 | −0.229685 | − | 0.973265i | \(-0.573770\pi\) | ||||
−0.229685 | + | 0.973265i | \(0.573770\pi\) | |||||||
\(968\) | −8.54342 | −0.274596 | ||||||||
\(969\) | 6.40302 | 0.205695 | ||||||||
\(970\) | 40.1899 | 1.29042 | ||||||||
\(971\) | 38.9676 | 1.25053 | 0.625266 | − | 0.780412i | \(-0.284991\pi\) | ||||
0.625266 | + | 0.780412i | \(0.284991\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 15.6644 | 0.502176 | ||||||||
\(974\) | 3.00738 | 0.0963626 | ||||||||
\(975\) | −9.16804 | −0.293612 | ||||||||
\(976\) | 6.21492 | 0.198935 | ||||||||
\(977\) | −44.3004 | −1.41729 | −0.708647 | − | 0.705563i | \(-0.750694\pi\) | ||||
−0.708647 | + | 0.705563i | \(0.750694\pi\) | |||||||
\(978\) | 19.7130 | 0.630352 | ||||||||
\(979\) | −78.4145 | −2.50614 | ||||||||
\(980\) | 28.0063 | 0.894630 | ||||||||
\(981\) | −0.493136 | −0.0157446 | ||||||||
\(982\) | 18.0303 | 0.575369 | ||||||||
\(983\) | 51.2218 | 1.63372 | 0.816861 | − | 0.576834i | \(-0.195712\pi\) | ||||
0.816861 | + | 0.576834i | \(0.195712\pi\) | |||||||
\(984\) | 8.14882 | 0.259775 | ||||||||
\(985\) | −70.5909 | −2.24921 | ||||||||
\(986\) | −2.22749 | −0.0709376 | ||||||||
\(987\) | 8.72995 | 0.277877 | ||||||||
\(988\) | −0.648462 | −0.0206303 | ||||||||
\(989\) | 2.31650 | 0.0736603 | ||||||||
\(990\) | 19.3397 | 0.614657 | ||||||||
\(991\) | 43.4662 | 1.38075 | 0.690375 | − | 0.723452i | \(-0.257446\pi\) | ||||
0.690375 | + | 0.723452i | \(0.257446\pi\) | |||||||
\(992\) | 3.57302 | 0.113443 | ||||||||
\(993\) | −25.8195 | −0.819357 | ||||||||
\(994\) | −1.10196 | −0.0349521 | ||||||||
\(995\) | −56.9653 | −1.80592 | ||||||||
\(996\) | −16.9311 | −0.536483 | ||||||||
\(997\) | 29.5124 | 0.934668 | 0.467334 | − | 0.884081i | \(-0.345215\pi\) | ||||
0.467334 | + | 0.884081i | \(0.345215\pi\) | |||||||
\(998\) | −22.9499 | −0.726466 | ||||||||
\(999\) | 8.71669 | 0.275784 |
(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 | 6042.2.a.z.1.1 | ✓ | 9 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6042.2.a.z.1.1 | ✓ | 9 | 1.1 | even | 1 | trivial |