Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2166,2,Mod(1,2166)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2166, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2166.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2166 = 2 \cdot 3 \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2166.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: | \(17.2955970778\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\Q(\zeta_{18})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - 3x - 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 114) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-1.53209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2166.1 |
$q$-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 | ||||||||
\(5\) | 3.41147 | 1.52566 | 0.762829 | − | 0.646601i | \(-0.223810\pi\) | ||||
0.762829 | + | 0.646601i | \(0.223810\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | −4.87939 | −1.84423 | −0.922117 | − | 0.386911i | \(-0.873542\pi\) | ||||
−0.922117 | + | 0.386911i | \(0.873542\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.41147 | 1.07880 | ||||||||
\(11\) | −3.41147 | −1.02860 | −0.514299 | − | 0.857611i | \(-0.671948\pi\) | ||||
−0.514299 | + | 0.857611i | \(0.671948\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −2.71688 | −0.753527 | −0.376764 | − | 0.926309i | \(-0.622963\pi\) | ||||
−0.376764 | + | 0.926309i | \(0.622963\pi\) | |||||||
\(14\) | −4.87939 | −1.30407 | ||||||||
\(15\) | −3.41147 | −0.880839 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 1.18479 | 0.287354 | 0.143677 | − | 0.989625i | \(-0.454107\pi\) | ||||
0.143677 | + | 0.989625i | \(0.454107\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | 3.41147 | 0.762829 | ||||||||
\(21\) | 4.87939 | 1.06477 | ||||||||
\(22\) | −3.41147 | −0.727329 | ||||||||
\(23\) | −3.41147 | −0.711342 | −0.355671 | − | 0.934611i | \(-0.615748\pi\) | ||||
−0.355671 | + | 0.934611i | \(0.615748\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 6.63816 | 1.32763 | ||||||||
\(26\) | −2.71688 | −0.532824 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −4.87939 | −0.922117 | ||||||||
\(29\) | −3.77332 | −0.700688 | −0.350344 | − | 0.936621i | \(-0.613935\pi\) | ||||
−0.350344 | + | 0.936621i | \(0.613935\pi\) | |||||||
\(30\) | −3.41147 | −0.622847 | ||||||||
\(31\) | −6.61587 | −1.18824 | −0.594122 | − | 0.804375i | \(-0.702501\pi\) | ||||
−0.594122 | + | 0.804375i | \(0.702501\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.41147 | 0.593861 | ||||||||
\(34\) | 1.18479 | 0.203190 | ||||||||
\(35\) | −16.6459 | −2.81367 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −6.75877 | −1.11114 | −0.555568 | − | 0.831471i | \(-0.687499\pi\) | ||||
−0.555568 | + | 0.831471i | \(0.687499\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.71688 | 0.435049 | ||||||||
\(40\) | 3.41147 | 0.539401 | ||||||||
\(41\) | −6.55438 | −1.02362 | −0.511811 | − | 0.859098i | \(-0.671025\pi\) | ||||
−0.511811 | + | 0.859098i | \(0.671025\pi\) | |||||||
\(42\) | 4.87939 | 0.752905 | ||||||||
\(43\) | 4.17024 | 0.635956 | 0.317978 | − | 0.948098i | \(-0.396996\pi\) | ||||
0.317978 | + | 0.948098i | \(0.396996\pi\) | |||||||
\(44\) | −3.41147 | −0.514299 | ||||||||
\(45\) | 3.41147 | 0.508553 | ||||||||
\(46\) | −3.41147 | −0.502994 | ||||||||
\(47\) | 2.85710 | 0.416750 | 0.208375 | − | 0.978049i | \(-0.433182\pi\) | ||||
0.208375 | + | 0.978049i | \(0.433182\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | 16.8084 | 2.40120 | ||||||||
\(50\) | 6.63816 | 0.938777 | ||||||||
\(51\) | −1.18479 | −0.165904 | ||||||||
\(52\) | −2.71688 | −0.376764 | ||||||||
\(53\) | −0.630415 | −0.0865942 | −0.0432971 | − | 0.999062i | \(-0.513786\pi\) | ||||
−0.0432971 | + | 0.999062i | \(0.513786\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | −11.6382 | −1.56929 | ||||||||
\(56\) | −4.87939 | −0.652035 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3.77332 | −0.495461 | ||||||||
\(59\) | −11.6382 | −1.51516 | −0.757579 | − | 0.652743i | \(-0.773618\pi\) | ||||
−0.757579 | + | 0.652743i | \(0.773618\pi\) | |||||||
\(60\) | −3.41147 | −0.440419 | ||||||||
\(61\) | 6.90167 | 0.883669 | 0.441834 | − | 0.897097i | \(-0.354328\pi\) | ||||
0.441834 | + | 0.897097i | \(0.354328\pi\) | |||||||
\(62\) | −6.61587 | −0.840216 | ||||||||
\(63\) | −4.87939 | −0.614745 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −9.26857 | −1.14962 | ||||||||
\(66\) | 3.41147 | 0.419923 | ||||||||
\(67\) | −0.709141 | −0.0866353 | −0.0433177 | − | 0.999061i | \(-0.513793\pi\) | ||||
−0.0433177 | + | 0.999061i | \(0.513793\pi\) | |||||||
\(68\) | 1.18479 | 0.143677 | ||||||||
\(69\) | 3.41147 | 0.410693 | ||||||||
\(70\) | −16.6459 | −1.98957 | ||||||||
\(71\) | −7.95811 | −0.944454 | −0.472227 | − | 0.881477i | \(-0.656550\pi\) | ||||
−0.472227 | + | 0.881477i | \(0.656550\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −12.7442 | −1.49160 | −0.745799 | − | 0.666171i | \(-0.767932\pi\) | ||||
−0.745799 | + | 0.666171i | \(0.767932\pi\) | |||||||
\(74\) | −6.75877 | −0.785691 | ||||||||
\(75\) | −6.63816 | −0.766508 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 16.6459 | 1.89698 | ||||||||
\(78\) | 2.71688 | 0.307626 | ||||||||
\(79\) | −0.297667 | −0.0334901 | −0.0167450 | − | 0.999860i | \(-0.505330\pi\) | ||||
−0.0167450 | + | 0.999860i | \(0.505330\pi\) | |||||||
\(80\) | 3.41147 | 0.381414 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −6.55438 | −0.723810 | ||||||||
\(83\) | 15.6040 | 1.71276 | 0.856381 | − | 0.516344i | \(-0.172707\pi\) | ||||
0.856381 | + | 0.516344i | \(0.172707\pi\) | |||||||
\(84\) | 4.87939 | 0.532385 | ||||||||
\(85\) | 4.04189 | 0.438404 | ||||||||
\(86\) | 4.17024 | 0.449689 | ||||||||
\(87\) | 3.77332 | 0.404542 | ||||||||
\(88\) | −3.41147 | −0.363664 | ||||||||
\(89\) | −6.77332 | −0.717970 | −0.358985 | − | 0.933343i | \(-0.616877\pi\) | ||||
−0.358985 | + | 0.933343i | \(0.616877\pi\) | |||||||
\(90\) | 3.41147 | 0.359601 | ||||||||
\(91\) | 13.2567 | 1.38968 | ||||||||
\(92\) | −3.41147 | −0.355671 | ||||||||
\(93\) | 6.61587 | 0.686033 | ||||||||
\(94\) | 2.85710 | 0.294687 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | 7.12567 | 0.723502 | 0.361751 | − | 0.932275i | \(-0.382179\pi\) | ||||
0.361751 | + | 0.932275i | \(0.382179\pi\) | |||||||
\(98\) | 16.8084 | 1.69790 | ||||||||
\(99\) | −3.41147 | −0.342866 | ||||||||
\(100\) | 6.63816 | 0.663816 | ||||||||
\(101\) | −4.64590 | −0.462284 | −0.231142 | − | 0.972920i | \(-0.574246\pi\) | ||||
−0.231142 | + | 0.972920i | \(0.574246\pi\) | |||||||
\(102\) | −1.18479 | −0.117312 | ||||||||
\(103\) | 12.3824 | 1.22007 | 0.610036 | − | 0.792374i | \(-0.291155\pi\) | ||||
0.610036 | + | 0.792374i | \(0.291155\pi\) | |||||||
\(104\) | −2.71688 | −0.266412 | ||||||||
\(105\) | 16.6459 | 1.62447 | ||||||||
\(106\) | −0.630415 | −0.0612313 | ||||||||
\(107\) | −3.89899 | −0.376929 | −0.188465 | − | 0.982080i | \(-0.560351\pi\) | ||||
−0.188465 | + | 0.982080i | \(0.560351\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 11.5963 | 1.11072 | 0.555360 | − | 0.831610i | \(-0.312580\pi\) | ||||
0.555360 | + | 0.831610i | \(0.312580\pi\) | |||||||
\(110\) | −11.6382 | −1.10965 | ||||||||
\(111\) | 6.75877 | 0.641514 | ||||||||
\(112\) | −4.87939 | −0.461059 | ||||||||
\(113\) | −1.94087 | −0.182582 | −0.0912911 | − | 0.995824i | \(-0.529099\pi\) | ||||
−0.0912911 | + | 0.995824i | \(0.529099\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −11.6382 | −1.08526 | ||||||||
\(116\) | −3.77332 | −0.350344 | ||||||||
\(117\) | −2.71688 | −0.251176 | ||||||||
\(118\) | −11.6382 | −1.07138 | ||||||||
\(119\) | −5.78106 | −0.529949 | ||||||||
\(120\) | −3.41147 | −0.311424 | ||||||||
\(121\) | 0.638156 | 0.0580142 | ||||||||
\(122\) | 6.90167 | 0.624848 | ||||||||
\(123\) | 6.55438 | 0.590988 | ||||||||
\(124\) | −6.61587 | −0.594122 | ||||||||
\(125\) | 5.58853 | 0.499853 | ||||||||
\(126\) | −4.87939 | −0.434690 | ||||||||
\(127\) | 6.08378 | 0.539848 | 0.269924 | − | 0.962882i | \(-0.413001\pi\) | ||||
0.269924 | + | 0.962882i | \(0.413001\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −4.17024 | −0.367170 | ||||||||
\(130\) | −9.26857 | −0.812907 | ||||||||
\(131\) | −18.6040 | −1.62544 | −0.812720 | − | 0.582655i | \(-0.802014\pi\) | ||||
−0.812720 | + | 0.582655i | \(0.802014\pi\) | |||||||
\(132\) | 3.41147 | 0.296931 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.709141 | −0.0612604 | ||||||||
\(135\) | −3.41147 | −0.293613 | ||||||||
\(136\) | 1.18479 | 0.101595 | ||||||||
\(137\) | 4.54664 | 0.388445 | 0.194223 | − | 0.980957i | \(-0.437782\pi\) | ||||
0.194223 | + | 0.980957i | \(0.437782\pi\) | |||||||
\(138\) | 3.41147 | 0.290404 | ||||||||
\(139\) | −3.01455 | −0.255691 | −0.127845 | − | 0.991794i | \(-0.540806\pi\) | ||||
−0.127845 | + | 0.991794i | \(0.540806\pi\) | |||||||
\(140\) | −16.6459 | −1.40684 | ||||||||
\(141\) | −2.85710 | −0.240611 | ||||||||
\(142\) | −7.95811 | −0.667830 | ||||||||
\(143\) | 9.26857 | 0.775077 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −12.8726 | −1.06901 | ||||||||
\(146\) | −12.7442 | −1.05472 | ||||||||
\(147\) | −16.8084 | −1.38633 | ||||||||
\(148\) | −6.75877 | −0.555568 | ||||||||
\(149\) | 1.18479 | 0.0970620 | 0.0485310 | − | 0.998822i | \(-0.484546\pi\) | ||||
0.0485310 | + | 0.998822i | \(0.484546\pi\) | |||||||
\(150\) | −6.63816 | −0.542003 | ||||||||
\(151\) | 3.63816 | 0.296069 | 0.148034 | − | 0.988982i | \(-0.452705\pi\) | ||||
0.148034 | + | 0.988982i | \(0.452705\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.18479 | 0.0957848 | ||||||||
\(154\) | 16.6459 | 1.34136 | ||||||||
\(155\) | −22.5699 | −1.81285 | ||||||||
\(156\) | 2.71688 | 0.217525 | ||||||||
\(157\) | 6.27126 | 0.500501 | 0.250250 | − | 0.968181i | \(-0.419487\pi\) | ||||
0.250250 | + | 0.968181i | \(0.419487\pi\) | |||||||
\(158\) | −0.297667 | −0.0236811 | ||||||||
\(159\) | 0.630415 | 0.0499952 | ||||||||
\(160\) | 3.41147 | 0.269701 | ||||||||
\(161\) | 16.6459 | 1.31188 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −19.2986 | −1.51158 | −0.755792 | − | 0.654812i | \(-0.772748\pi\) | ||||
−0.755792 | + | 0.654812i | \(0.772748\pi\) | |||||||
\(164\) | −6.55438 | −0.511811 | ||||||||
\(165\) | 11.6382 | 0.906029 | ||||||||
\(166\) | 15.6040 | 1.21111 | ||||||||
\(167\) | 7.72193 | 0.597541 | 0.298771 | − | 0.954325i | \(-0.403423\pi\) | ||||
0.298771 | + | 0.954325i | \(0.403423\pi\) | |||||||
\(168\) | 4.87939 | 0.376453 | ||||||||
\(169\) | −5.61856 | −0.432197 | ||||||||
\(170\) | 4.04189 | 0.309999 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.17024 | 0.317978 | ||||||||
\(173\) | 14.4953 | 1.10205 | 0.551027 | − | 0.834488i | \(-0.314236\pi\) | ||||
0.551027 | + | 0.834488i | \(0.314236\pi\) | |||||||
\(174\) | 3.77332 | 0.286055 | ||||||||
\(175\) | −32.3901 | −2.44846 | ||||||||
\(176\) | −3.41147 | −0.257150 | ||||||||
\(177\) | 11.6382 | 0.874777 | ||||||||
\(178\) | −6.77332 | −0.507682 | ||||||||
\(179\) | 9.82295 | 0.734202 | 0.367101 | − | 0.930181i | \(-0.380350\pi\) | ||||
0.367101 | + | 0.930181i | \(0.380350\pi\) | |||||||
\(180\) | 3.41147 | 0.254276 | ||||||||
\(181\) | −18.9145 | −1.40590 | −0.702951 | − | 0.711239i | \(-0.748135\pi\) | ||||
−0.702951 | + | 0.711239i | \(0.748135\pi\) | |||||||
\(182\) | 13.2567 | 0.982653 | ||||||||
\(183\) | −6.90167 | −0.510186 | ||||||||
\(184\) | −3.41147 | −0.251497 | ||||||||
\(185\) | −23.0574 | −1.69521 | ||||||||
\(186\) | 6.61587 | 0.485099 | ||||||||
\(187\) | −4.04189 | −0.295572 | ||||||||
\(188\) | 2.85710 | 0.208375 | ||||||||
\(189\) | 4.87939 | 0.354923 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −10.0915 | −0.730197 | −0.365098 | − | 0.930969i | \(-0.618965\pi\) | ||||
−0.365098 | + | 0.930969i | \(0.618965\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −2.52435 | −0.181707 | −0.0908533 | − | 0.995864i | \(-0.528959\pi\) | ||||
−0.0908533 | + | 0.995864i | \(0.528959\pi\) | |||||||
\(194\) | 7.12567 | 0.511593 | ||||||||
\(195\) | 9.26857 | 0.663736 | ||||||||
\(196\) | 16.8084 | 1.20060 | ||||||||
\(197\) | 14.8571 | 1.05852 | 0.529262 | − | 0.848458i | \(-0.322469\pi\) | ||||
0.529262 | + | 0.848458i | \(0.322469\pi\) | |||||||
\(198\) | −3.41147 | −0.242443 | ||||||||
\(199\) | 8.06923 | 0.572013 | 0.286006 | − | 0.958228i | \(-0.407672\pi\) | ||||
0.286006 | + | 0.958228i | \(0.407672\pi\) | |||||||
\(200\) | 6.63816 | 0.469388 | ||||||||
\(201\) | 0.709141 | 0.0500189 | ||||||||
\(202\) | −4.64590 | −0.326884 | ||||||||
\(203\) | 18.4115 | 1.29223 | ||||||||
\(204\) | −1.18479 | −0.0829521 | ||||||||
\(205\) | −22.3601 | −1.56170 | ||||||||
\(206\) | 12.3824 | 0.862721 | ||||||||
\(207\) | −3.41147 | −0.237114 | ||||||||
\(208\) | −2.71688 | −0.188382 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 16.6459 | 1.14868 | ||||||||
\(211\) | −7.94356 | −0.546857 | −0.273429 | − | 0.961892i | \(-0.588158\pi\) | ||||
−0.273429 | + | 0.961892i | \(0.588158\pi\) | |||||||
\(212\) | −0.630415 | −0.0432971 | ||||||||
\(213\) | 7.95811 | 0.545281 | ||||||||
\(214\) | −3.89899 | −0.266529 | ||||||||
\(215\) | 14.2267 | 0.970252 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 32.2814 | 2.19140 | ||||||||
\(218\) | 11.5963 | 0.785398 | ||||||||
\(219\) | 12.7442 | 0.861175 | ||||||||
\(220\) | −11.6382 | −0.784644 | ||||||||
\(221\) | −3.21894 | −0.216529 | ||||||||
\(222\) | 6.75877 | 0.453619 | ||||||||
\(223\) | −11.9682 | −0.801451 | −0.400726 | − | 0.916198i | \(-0.631242\pi\) | ||||
−0.400726 | + | 0.916198i | \(0.631242\pi\) | |||||||
\(224\) | −4.87939 | −0.326018 | ||||||||
\(225\) | 6.63816 | 0.442544 | ||||||||
\(226\) | −1.94087 | −0.129105 | ||||||||
\(227\) | −26.5945 | −1.76514 | −0.882570 | − | 0.470181i | \(-0.844189\pi\) | ||||
−0.882570 | + | 0.470181i | \(0.844189\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −19.9026 | −1.31520 | −0.657601 | − | 0.753367i | \(-0.728429\pi\) | ||||
−0.657601 | + | 0.753367i | \(0.728429\pi\) | |||||||
\(230\) | −11.6382 | −0.767397 | ||||||||
\(231\) | −16.6459 | −1.09522 | ||||||||
\(232\) | −3.77332 | −0.247730 | ||||||||
\(233\) | −4.31046 | −0.282388 | −0.141194 | − | 0.989982i | \(-0.545094\pi\) | ||||
−0.141194 | + | 0.989982i | \(0.545094\pi\) | |||||||
\(234\) | −2.71688 | −0.177608 | ||||||||
\(235\) | 9.74691 | 0.635818 | ||||||||
\(236\) | −11.6382 | −0.757579 | ||||||||
\(237\) | 0.297667 | 0.0193355 | ||||||||
\(238\) | −5.78106 | −0.374730 | ||||||||
\(239\) | 0.285807 | 0.0184873 | 0.00924366 | − | 0.999957i | \(-0.497058\pi\) | ||||
0.00924366 | + | 0.999957i | \(0.497058\pi\) | |||||||
\(240\) | −3.41147 | −0.220210 | ||||||||
\(241\) | −9.56624 | −0.616216 | −0.308108 | − | 0.951351i | \(-0.599696\pi\) | ||||
−0.308108 | + | 0.951351i | \(0.599696\pi\) | |||||||
\(242\) | 0.638156 | 0.0410222 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 6.90167 | 0.441834 | ||||||||
\(245\) | 57.3414 | 3.66341 | ||||||||
\(246\) | 6.55438 | 0.417892 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −6.61587 | −0.420108 | ||||||||
\(249\) | −15.6040 | −0.988864 | ||||||||
\(250\) | 5.58853 | 0.353449 | ||||||||
\(251\) | 29.6878 | 1.87388 | 0.936938 | − | 0.349495i | \(-0.113647\pi\) | ||||
0.936938 | + | 0.349495i | \(0.113647\pi\) | |||||||
\(252\) | −4.87939 | −0.307372 | ||||||||
\(253\) | 11.6382 | 0.731685 | ||||||||
\(254\) | 6.08378 | 0.381730 | ||||||||
\(255\) | −4.04189 | −0.253113 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.7965 | −0.985361 | −0.492681 | − | 0.870210i | \(-0.663983\pi\) | ||||
−0.492681 | + | 0.870210i | \(0.663983\pi\) | |||||||
\(258\) | −4.17024 | −0.259628 | ||||||||
\(259\) | 32.9786 | 2.04919 | ||||||||
\(260\) | −9.26857 | −0.574812 | ||||||||
\(261\) | −3.77332 | −0.233563 | ||||||||
\(262\) | −18.6040 | −1.14936 | ||||||||
\(263\) | 10.8648 | 0.669955 | 0.334977 | − | 0.942226i | \(-0.391271\pi\) | ||||
0.334977 | + | 0.942226i | \(0.391271\pi\) | |||||||
\(264\) | 3.41147 | 0.209962 | ||||||||
\(265\) | −2.15064 | −0.132113 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.77332 | 0.414520 | ||||||||
\(268\) | −0.709141 | −0.0433177 | ||||||||
\(269\) | 17.2935 | 1.05441 | 0.527203 | − | 0.849739i | \(-0.323241\pi\) | ||||
0.527203 | + | 0.849739i | \(0.323241\pi\) | |||||||
\(270\) | −3.41147 | −0.207616 | ||||||||
\(271\) | 1.44562 | 0.0878153 | 0.0439077 | − | 0.999036i | \(-0.486019\pi\) | ||||
0.0439077 | + | 0.999036i | \(0.486019\pi\) | |||||||
\(272\) | 1.18479 | 0.0718386 | ||||||||
\(273\) | −13.2567 | −0.802333 | ||||||||
\(274\) | 4.54664 | 0.274672 | ||||||||
\(275\) | −22.6459 | −1.36560 | ||||||||
\(276\) | 3.41147 | 0.205347 | ||||||||
\(277\) | 21.1908 | 1.27323 | 0.636615 | − | 0.771182i | \(-0.280334\pi\) | ||||
0.636615 | + | 0.771182i | \(0.280334\pi\) | |||||||
\(278\) | −3.01455 | −0.180801 | ||||||||
\(279\) | −6.61587 | −0.396082 | ||||||||
\(280\) | −16.6459 | −0.994783 | ||||||||
\(281\) | 24.3678 | 1.45366 | 0.726831 | − | 0.686816i | \(-0.240992\pi\) | ||||
0.726831 | + | 0.686816i | \(0.240992\pi\) | |||||||
\(282\) | −2.85710 | −0.170138 | ||||||||
\(283\) | −4.12567 | −0.245245 | −0.122623 | − | 0.992453i | \(-0.539131\pi\) | ||||
−0.122623 | + | 0.992453i | \(0.539131\pi\) | |||||||
\(284\) | −7.95811 | −0.472227 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.26857 | 0.548062 | ||||||||
\(287\) | 31.9813 | 1.88780 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | −15.5963 | −0.917427 | ||||||||
\(290\) | −12.8726 | −0.755904 | ||||||||
\(291\) | −7.12567 | −0.417714 | ||||||||
\(292\) | −12.7442 | −0.745799 | ||||||||
\(293\) | −2.78106 | −0.162471 | −0.0812356 | − | 0.996695i | \(-0.525887\pi\) | ||||
−0.0812356 | + | 0.996695i | \(0.525887\pi\) | |||||||
\(294\) | −16.8084 | −0.980286 | ||||||||
\(295\) | −39.7033 | −2.31161 | ||||||||
\(296\) | −6.75877 | −0.392846 | ||||||||
\(297\) | 3.41147 | 0.197954 | ||||||||
\(298\) | 1.18479 | 0.0686332 | ||||||||
\(299\) | 9.26857 | 0.536015 | ||||||||
\(300\) | −6.63816 | −0.383254 | ||||||||
\(301\) | −20.3482 | −1.17285 | ||||||||
\(302\) | 3.63816 | 0.209352 | ||||||||
\(303\) | 4.64590 | 0.266900 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 23.5449 | 1.34818 | ||||||||
\(306\) | 1.18479 | 0.0677301 | ||||||||
\(307\) | 25.0232 | 1.42815 | 0.714075 | − | 0.700069i | \(-0.246847\pi\) | ||||
0.714075 | + | 0.700069i | \(0.246847\pi\) | |||||||
\(308\) | 16.6459 | 0.948488 | ||||||||
\(309\) | −12.3824 | −0.704409 | ||||||||
\(310\) | −22.5699 | −1.28188 | ||||||||
\(311\) | 23.9736 | 1.35942 | 0.679709 | − | 0.733482i | \(-0.262106\pi\) | ||||
0.679709 | + | 0.733482i | \(0.262106\pi\) | |||||||
\(312\) | 2.71688 | 0.153813 | ||||||||
\(313\) | −12.6382 | −0.714351 | −0.357175 | − | 0.934037i | \(-0.616260\pi\) | ||||
−0.357175 | + | 0.934037i | \(0.616260\pi\) | |||||||
\(314\) | 6.27126 | 0.353908 | ||||||||
\(315\) | −16.6459 | −0.937890 | ||||||||
\(316\) | −0.297667 | −0.0167450 | ||||||||
\(317\) | 14.1334 | 0.793811 | 0.396906 | − | 0.917859i | \(-0.370084\pi\) | ||||
0.396906 | + | 0.917859i | \(0.370084\pi\) | |||||||
\(318\) | 0.630415 | 0.0353519 | ||||||||
\(319\) | 12.8726 | 0.720726 | ||||||||
\(320\) | 3.41147 | 0.190707 | ||||||||
\(321\) | 3.89899 | 0.217620 | ||||||||
\(322\) | 16.6459 | 0.927640 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −18.0351 | −1.00041 | ||||||||
\(326\) | −19.2986 | −1.06885 | ||||||||
\(327\) | −11.5963 | −0.641275 | ||||||||
\(328\) | −6.55438 | −0.361905 | ||||||||
\(329\) | −13.9409 | −0.768585 | ||||||||
\(330\) | 11.6382 | 0.640659 | ||||||||
\(331\) | −29.4979 | −1.62135 | −0.810677 | − | 0.585494i | \(-0.800901\pi\) | ||||
−0.810677 | + | 0.585494i | \(0.800901\pi\) | |||||||
\(332\) | 15.6040 | 0.856381 | ||||||||
\(333\) | −6.75877 | −0.370378 | ||||||||
\(334\) | 7.72193 | 0.422525 | ||||||||
\(335\) | −2.41921 | −0.132176 | ||||||||
\(336\) | 4.87939 | 0.266192 | ||||||||
\(337\) | 22.2490 | 1.21198 | 0.605989 | − | 0.795473i | \(-0.292777\pi\) | ||||
0.605989 | + | 0.795473i | \(0.292777\pi\) | |||||||
\(338\) | −5.61856 | −0.305609 | ||||||||
\(339\) | 1.94087 | 0.105414 | ||||||||
\(340\) | 4.04189 | 0.219202 | ||||||||
\(341\) | 22.5699 | 1.22223 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −47.8590 | −2.58414 | ||||||||
\(344\) | 4.17024 | 0.224845 | ||||||||
\(345\) | 11.6382 | 0.626577 | ||||||||
\(346\) | 14.4953 | 0.779270 | ||||||||
\(347\) | −14.0250 | −0.752900 | −0.376450 | − | 0.926437i | \(-0.622855\pi\) | ||||
−0.376450 | + | 0.926437i | \(0.622855\pi\) | |||||||
\(348\) | 3.77332 | 0.202271 | ||||||||
\(349\) | −34.1121 | −1.82598 | −0.912988 | − | 0.407986i | \(-0.866231\pi\) | ||||
−0.912988 | + | 0.407986i | \(0.866231\pi\) | |||||||
\(350\) | −32.3901 | −1.73132 | ||||||||
\(351\) | 2.71688 | 0.145016 | ||||||||
\(352\) | −3.41147 | −0.181832 | ||||||||
\(353\) | 30.4439 | 1.62036 | 0.810182 | − | 0.586179i | \(-0.199368\pi\) | ||||
0.810182 | + | 0.586179i | \(0.199368\pi\) | |||||||
\(354\) | 11.6382 | 0.618561 | ||||||||
\(355\) | −27.1489 | −1.44091 | ||||||||
\(356\) | −6.77332 | −0.358985 | ||||||||
\(357\) | 5.78106 | 0.305966 | ||||||||
\(358\) | 9.82295 | 0.519159 | ||||||||
\(359\) | 13.6459 | 0.720203 | 0.360101 | − | 0.932913i | \(-0.382742\pi\) | ||||
0.360101 | + | 0.932913i | \(0.382742\pi\) | |||||||
\(360\) | 3.41147 | 0.179800 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | −18.9145 | −0.994122 | ||||||||
\(363\) | −0.638156 | −0.0334945 | ||||||||
\(364\) | 13.2567 | 0.694840 | ||||||||
\(365\) | −43.4766 | −2.27567 | ||||||||
\(366\) | −6.90167 | −0.360756 | ||||||||
\(367\) | 23.7665 | 1.24060 | 0.620301 | − | 0.784364i | \(-0.287010\pi\) | ||||
0.620301 | + | 0.784364i | \(0.287010\pi\) | |||||||
\(368\) | −3.41147 | −0.177835 | ||||||||
\(369\) | −6.55438 | −0.341207 | ||||||||
\(370\) | −23.0574 | −1.19870 | ||||||||
\(371\) | 3.07604 | 0.159700 | ||||||||
\(372\) | 6.61587 | 0.343017 | ||||||||
\(373\) | 23.2344 | 1.20303 | 0.601516 | − | 0.798860i | \(-0.294563\pi\) | ||||
0.601516 | + | 0.798860i | \(0.294563\pi\) | |||||||
\(374\) | −4.04189 | −0.209001 | ||||||||
\(375\) | −5.58853 | −0.288590 | ||||||||
\(376\) | 2.85710 | 0.147344 | ||||||||
\(377\) | 10.2517 | 0.527987 | ||||||||
\(378\) | 4.87939 | 0.250968 | ||||||||
\(379\) | 4.50030 | 0.231165 | 0.115583 | − | 0.993298i | \(-0.463127\pi\) | ||||
0.115583 | + | 0.993298i | \(0.463127\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −6.08378 | −0.311681 | ||||||||
\(382\) | −10.0915 | −0.516327 | ||||||||
\(383\) | −4.36009 | −0.222790 | −0.111395 | − | 0.993776i | \(-0.535532\pi\) | ||||
−0.111395 | + | 0.993776i | \(0.535532\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 56.7870 | 2.89414 | ||||||||
\(386\) | −2.52435 | −0.128486 | ||||||||
\(387\) | 4.17024 | 0.211985 | ||||||||
\(388\) | 7.12567 | 0.361751 | ||||||||
\(389\) | −1.31046 | −0.0664429 | −0.0332215 | − | 0.999448i | \(-0.510577\pi\) | ||||
−0.0332215 | + | 0.999448i | \(0.510577\pi\) | |||||||
\(390\) | 9.26857 | 0.469332 | ||||||||
\(391\) | −4.04189 | −0.204407 | ||||||||
\(392\) | 16.8084 | 0.848952 | ||||||||
\(393\) | 18.6040 | 0.938448 | ||||||||
\(394\) | 14.8571 | 0.748490 | ||||||||
\(395\) | −1.01548 | −0.0510944 | ||||||||
\(396\) | −3.41147 | −0.171433 | ||||||||
\(397\) | −19.0128 | −0.954225 | −0.477112 | − | 0.878842i | \(-0.658317\pi\) | ||||
−0.477112 | + | 0.878842i | \(0.658317\pi\) | |||||||
\(398\) | 8.06923 | 0.404474 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 6.63816 | 0.331908 | ||||||||
\(401\) | −35.8631 | −1.79092 | −0.895458 | − | 0.445145i | \(-0.853152\pi\) | ||||
−0.895458 | + | 0.445145i | \(0.853152\pi\) | |||||||
\(402\) | 0.709141 | 0.0353687 | ||||||||
\(403\) | 17.9745 | 0.895375 | ||||||||
\(404\) | −4.64590 | −0.231142 | ||||||||
\(405\) | 3.41147 | 0.169518 | ||||||||
\(406\) | 18.4115 | 0.913746 | ||||||||
\(407\) | 23.0574 | 1.14291 | ||||||||
\(408\) | −1.18479 | −0.0586560 | ||||||||
\(409\) | 29.1088 | 1.43934 | 0.719668 | − | 0.694319i | \(-0.244294\pi\) | ||||
0.719668 | + | 0.694319i | \(0.244294\pi\) | |||||||
\(410\) | −22.3601 | −1.10429 | ||||||||
\(411\) | −4.54664 | −0.224269 | ||||||||
\(412\) | 12.3824 | 0.610036 | ||||||||
\(413\) | 56.7870 | 2.79431 | ||||||||
\(414\) | −3.41147 | −0.167665 | ||||||||
\(415\) | 53.2327 | 2.61309 | ||||||||
\(416\) | −2.71688 | −0.133206 | ||||||||
\(417\) | 3.01455 | 0.147623 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 13.1584 | 0.642829 | 0.321415 | − | 0.946939i | \(-0.395842\pi\) | ||||
0.321415 | + | 0.946939i | \(0.395842\pi\) | |||||||
\(420\) | 16.6459 | 0.812237 | ||||||||
\(421\) | 0.150644 | 0.00734195 | 0.00367098 | − | 0.999993i | \(-0.498831\pi\) | ||||
0.00367098 | + | 0.999993i | \(0.498831\pi\) | |||||||
\(422\) | −7.94356 | −0.386687 | ||||||||
\(423\) | 2.85710 | 0.138917 | ||||||||
\(424\) | −0.630415 | −0.0306157 | ||||||||
\(425\) | 7.86484 | 0.381501 | ||||||||
\(426\) | 7.95811 | 0.385572 | ||||||||
\(427\) | −33.6759 | −1.62969 | ||||||||
\(428\) | −3.89899 | −0.188465 | ||||||||
\(429\) | −9.26857 | −0.447491 | ||||||||
\(430\) | 14.2267 | 0.686072 | ||||||||
\(431\) | 30.7965 | 1.48342 | 0.741709 | − | 0.670722i | \(-0.234016\pi\) | ||||
0.741709 | + | 0.670722i | \(0.234016\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | 29.4338 | 1.41450 | 0.707248 | − | 0.706965i | \(-0.249936\pi\) | ||||
0.707248 | + | 0.706965i | \(0.249936\pi\) | |||||||
\(434\) | 32.2814 | 1.54956 | ||||||||
\(435\) | 12.8726 | 0.617193 | ||||||||
\(436\) | 11.5963 | 0.555360 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 12.7442 | 0.608943 | ||||||||
\(439\) | −19.8007 | −0.945034 | −0.472517 | − | 0.881322i | \(-0.656654\pi\) | ||||
−0.472517 | + | 0.881322i | \(0.656654\pi\) | |||||||
\(440\) | −11.6382 | −0.554827 | ||||||||
\(441\) | 16.8084 | 0.800400 | ||||||||
\(442\) | −3.21894 | −0.153109 | ||||||||
\(443\) | −18.5868 | −0.883084 | −0.441542 | − | 0.897241i | \(-0.645568\pi\) | ||||
−0.441542 | + | 0.897241i | \(0.645568\pi\) | |||||||
\(444\) | 6.75877 | 0.320757 | ||||||||
\(445\) | −23.1070 | −1.09538 | ||||||||
\(446\) | −11.9682 | −0.566711 | ||||||||
\(447\) | −1.18479 | −0.0560388 | ||||||||
\(448\) | −4.87939 | −0.230529 | ||||||||
\(449\) | −3.37908 | −0.159469 | −0.0797343 | − | 0.996816i | \(-0.525407\pi\) | ||||
−0.0797343 | + | 0.996816i | \(0.525407\pi\) | |||||||
\(450\) | 6.63816 | 0.312926 | ||||||||
\(451\) | 22.3601 | 1.05290 | ||||||||
\(452\) | −1.94087 | −0.0912911 | ||||||||
\(453\) | −3.63816 | −0.170935 | ||||||||
\(454\) | −26.5945 | −1.24814 | ||||||||
\(455\) | 45.2249 | 2.12018 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.7912 | 1.01935 | 0.509674 | − | 0.860368i | \(-0.329766\pi\) | ||||
0.509674 | + | 0.860368i | \(0.329766\pi\) | |||||||
\(458\) | −19.9026 | −0.929988 | ||||||||
\(459\) | −1.18479 | −0.0553014 | ||||||||
\(460\) | −11.6382 | −0.542632 | ||||||||
\(461\) | 11.7638 | 0.547896 | 0.273948 | − | 0.961745i | \(-0.411670\pi\) | ||||
0.273948 | + | 0.961745i | \(0.411670\pi\) | |||||||
\(462\) | −16.6459 | −0.774437 | ||||||||
\(463\) | 16.9932 | 0.789741 | 0.394870 | − | 0.918737i | \(-0.370790\pi\) | ||||
0.394870 | + | 0.918737i | \(0.370790\pi\) | |||||||
\(464\) | −3.77332 | −0.175172 | ||||||||
\(465\) | 22.5699 | 1.04665 | ||||||||
\(466\) | −4.31046 | −0.199678 | ||||||||
\(467\) | −11.7050 | −0.541644 | −0.270822 | − | 0.962629i | \(-0.587295\pi\) | ||||
−0.270822 | + | 0.962629i | \(0.587295\pi\) | |||||||
\(468\) | −2.71688 | −0.125588 | ||||||||
\(469\) | 3.46017 | 0.159776 | ||||||||
\(470\) | 9.74691 | 0.449591 | ||||||||
\(471\) | −6.27126 | −0.288964 | ||||||||
\(472\) | −11.6382 | −0.535690 | ||||||||
\(473\) | −14.2267 | −0.654144 | ||||||||
\(474\) | 0.297667 | 0.0136723 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −5.78106 | −0.264974 | ||||||||
\(477\) | −0.630415 | −0.0288647 | ||||||||
\(478\) | 0.285807 | 0.0130725 | ||||||||
\(479\) | 29.9796 | 1.36980 | 0.684901 | − | 0.728636i | \(-0.259845\pi\) | ||||
0.684901 | + | 0.728636i | \(0.259845\pi\) | |||||||
\(480\) | −3.41147 | −0.155712 | ||||||||
\(481\) | 18.3628 | 0.837271 | ||||||||
\(482\) | −9.56624 | −0.435730 | ||||||||
\(483\) | −16.6459 | −0.757415 | ||||||||
\(484\) | 0.638156 | 0.0290071 | ||||||||
\(485\) | 24.3090 | 1.10382 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −14.5107 | −0.657544 | −0.328772 | − | 0.944409i | \(-0.606635\pi\) | ||||
−0.328772 | + | 0.944409i | \(0.606635\pi\) | |||||||
\(488\) | 6.90167 | 0.312424 | ||||||||
\(489\) | 19.2986 | 0.872713 | ||||||||
\(490\) | 57.3414 | 2.59042 | ||||||||
\(491\) | −11.6554 | −0.526000 | −0.263000 | − | 0.964796i | \(-0.584712\pi\) | ||||
−0.263000 | + | 0.964796i | \(0.584712\pi\) | |||||||
\(492\) | 6.55438 | 0.295494 | ||||||||
\(493\) | −4.47060 | −0.201346 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.6382 | −0.523096 | ||||||||
\(496\) | −6.61587 | −0.297061 | ||||||||
\(497\) | 38.8307 | 1.74179 | ||||||||
\(498\) | −15.6040 | −0.699232 | ||||||||
\(499\) | −1.68685 | −0.0755139 | −0.0377569 | − | 0.999287i | \(-0.512021\pi\) | ||||
−0.0377569 | + | 0.999287i | \(0.512021\pi\) | |||||||
\(500\) | 5.58853 | 0.249926 | ||||||||
\(501\) | −7.72193 | −0.344991 | ||||||||
\(502\) | 29.6878 | 1.32503 | ||||||||
\(503\) | 17.2935 | 0.771081 | 0.385541 | − | 0.922691i | \(-0.374015\pi\) | ||||
0.385541 | + | 0.922691i | \(0.374015\pi\) | |||||||
\(504\) | −4.87939 | −0.217345 | ||||||||
\(505\) | −15.8494 | −0.705287 | ||||||||
\(506\) | 11.6382 | 0.517379 | ||||||||
\(507\) | 5.61856 | 0.249529 | ||||||||
\(508\) | 6.08378 | 0.269924 | ||||||||
\(509\) | −32.4424 | −1.43799 | −0.718993 | − | 0.695017i | \(-0.755397\pi\) | ||||
−0.718993 | + | 0.695017i | \(0.755397\pi\) | |||||||
\(510\) | −4.04189 | −0.178978 | ||||||||
\(511\) | 62.1840 | 2.75086 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −15.7965 | −0.696756 | ||||||||
\(515\) | 42.2422 | 1.86141 | ||||||||
\(516\) | −4.17024 | −0.183585 | ||||||||
\(517\) | −9.74691 | −0.428669 | ||||||||
\(518\) | 32.9786 | 1.44900 | ||||||||
\(519\) | −14.4953 | −0.636271 | ||||||||
\(520\) | −9.26857 | −0.406454 | ||||||||
\(521\) | −31.1644 | −1.36534 | −0.682668 | − | 0.730729i | \(-0.739180\pi\) | ||||
−0.682668 | + | 0.730729i | \(0.739180\pi\) | |||||||
\(522\) | −3.77332 | −0.165154 | ||||||||
\(523\) | 16.6604 | 0.728510 | 0.364255 | − | 0.931299i | \(-0.381324\pi\) | ||||
0.364255 | + | 0.931299i | \(0.381324\pi\) | |||||||
\(524\) | −18.6040 | −0.812720 | ||||||||
\(525\) | 32.3901 | 1.41362 | ||||||||
\(526\) | 10.8648 | 0.473729 | ||||||||
\(527\) | −7.83843 | −0.341447 | ||||||||
\(528\) | 3.41147 | 0.148465 | ||||||||
\(529\) | −11.3618 | −0.493993 | ||||||||
\(530\) | −2.15064 | −0.0934180 | ||||||||
\(531\) | −11.6382 | −0.505053 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 17.8075 | 0.771327 | ||||||||
\(534\) | 6.77332 | 0.293110 | ||||||||
\(535\) | −13.3013 | −0.575065 | ||||||||
\(536\) | −0.709141 | −0.0306302 | ||||||||
\(537\) | −9.82295 | −0.423892 | ||||||||
\(538\) | 17.2935 | 0.745578 | ||||||||
\(539\) | −57.3414 | −2.46987 | ||||||||
\(540\) | −3.41147 | −0.146806 | ||||||||
\(541\) | 36.2449 | 1.55829 | 0.779144 | − | 0.626845i | \(-0.215654\pi\) | ||||
0.779144 | + | 0.626845i | \(0.215654\pi\) | |||||||
\(542\) | 1.44562 | 0.0620948 | ||||||||
\(543\) | 18.9145 | 0.811697 | ||||||||
\(544\) | 1.18479 | 0.0507976 | ||||||||
\(545\) | 39.5604 | 1.69458 | ||||||||
\(546\) | −13.2567 | −0.567335 | ||||||||
\(547\) | 17.1976 | 0.735316 | 0.367658 | − | 0.929961i | \(-0.380160\pi\) | ||||
0.367658 | + | 0.929961i | \(0.380160\pi\) | |||||||
\(548\) | 4.54664 | 0.194223 | ||||||||
\(549\) | 6.90167 | 0.294556 | ||||||||
\(550\) | −22.6459 | −0.965624 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 3.41147 | 0.145202 | ||||||||
\(553\) | 1.45243 | 0.0617636 | ||||||||
\(554\) | 21.1908 | 0.900310 | ||||||||
\(555\) | 23.0574 | 0.978731 | ||||||||
\(556\) | −3.01455 | −0.127845 | ||||||||
\(557\) | −16.5699 | −0.702087 | −0.351044 | − | 0.936359i | \(-0.614173\pi\) | ||||
−0.351044 | + | 0.936359i | \(0.614173\pi\) | |||||||
\(558\) | −6.61587 | −0.280072 | ||||||||
\(559\) | −11.3301 | −0.479210 | ||||||||
\(560\) | −16.6459 | −0.703418 | ||||||||
\(561\) | 4.04189 | 0.170649 | ||||||||
\(562\) | 24.3678 | 1.02789 | ||||||||
\(563\) | 30.6973 | 1.29374 | 0.646868 | − | 0.762602i | \(-0.276078\pi\) | ||||
0.646868 | + | 0.762602i | \(0.276078\pi\) | |||||||
\(564\) | −2.85710 | −0.120305 | ||||||||
\(565\) | −6.62124 | −0.278558 | ||||||||
\(566\) | −4.12567 | −0.173415 | ||||||||
\(567\) | −4.87939 | −0.204915 | ||||||||
\(568\) | −7.95811 | −0.333915 | ||||||||
\(569\) | −13.4534 | −0.563994 | −0.281997 | − | 0.959415i | \(-0.590997\pi\) | ||||
−0.281997 | + | 0.959415i | \(0.590997\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −9.47565 | −0.396544 | −0.198272 | − | 0.980147i | \(-0.563533\pi\) | ||||
−0.198272 | + | 0.980147i | \(0.563533\pi\) | |||||||
\(572\) | 9.26857 | 0.387538 | ||||||||
\(573\) | 10.0915 | 0.421579 | ||||||||
\(574\) | 31.9813 | 1.33488 | ||||||||
\(575\) | −22.6459 | −0.944399 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −18.7638 | −0.781148 | −0.390574 | − | 0.920571i | \(-0.627723\pi\) | ||||
−0.390574 | + | 0.920571i | \(0.627723\pi\) | |||||||
\(578\) | −15.5963 | −0.648719 | ||||||||
\(579\) | 2.52435 | 0.104908 | ||||||||
\(580\) | −12.8726 | −0.534505 | ||||||||
\(581\) | −76.1380 | −3.15873 | ||||||||
\(582\) | −7.12567 | −0.295368 | ||||||||
\(583\) | 2.15064 | 0.0890706 | ||||||||
\(584\) | −12.7442 | −0.527360 | ||||||||
\(585\) | −9.26857 | −0.383208 | ||||||||
\(586\) | −2.78106 | −0.114884 | ||||||||
\(587\) | −18.1753 | −0.750175 | −0.375087 | − | 0.926989i | \(-0.622387\pi\) | ||||
−0.375087 | + | 0.926989i | \(0.622387\pi\) | |||||||
\(588\) | −16.8084 | −0.693167 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −39.7033 | −1.63456 | ||||||||
\(591\) | −14.8571 | −0.611139 | ||||||||
\(592\) | −6.75877 | −0.277784 | ||||||||
\(593\) | −32.6938 | −1.34257 | −0.671286 | − | 0.741198i | \(-0.734258\pi\) | ||||
−0.671286 | + | 0.741198i | \(0.734258\pi\) | |||||||
\(594\) | 3.41147 | 0.139974 | ||||||||
\(595\) | −19.7219 | −0.808520 | ||||||||
\(596\) | 1.18479 | 0.0485310 | ||||||||
\(597\) | −8.06923 | −0.330252 | ||||||||
\(598\) | 9.26857 | 0.379020 | ||||||||
\(599\) | −8.83069 | −0.360812 | −0.180406 | − | 0.983592i | \(-0.557741\pi\) | ||||
−0.180406 | + | 0.983592i | \(0.557741\pi\) | |||||||
\(600\) | −6.63816 | −0.271002 | ||||||||
\(601\) | −33.0523 | −1.34823 | −0.674116 | − | 0.738625i | \(-0.735475\pi\) | ||||
−0.674116 | + | 0.738625i | \(0.735475\pi\) | |||||||
\(602\) | −20.3482 | −0.829332 | ||||||||
\(603\) | −0.709141 | −0.0288784 | ||||||||
\(604\) | 3.63816 | 0.148034 | ||||||||
\(605\) | 2.17705 | 0.0885097 | ||||||||
\(606\) | 4.64590 | 0.188727 | ||||||||
\(607\) | −5.16250 | −0.209540 | −0.104770 | − | 0.994497i | \(-0.533411\pi\) | ||||
−0.104770 | + | 0.994497i | \(0.533411\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.4115 | −0.746071 | ||||||||
\(610\) | 23.5449 | 0.953304 | ||||||||
\(611\) | −7.76239 | −0.314033 | ||||||||
\(612\) | 1.18479 | 0.0478924 | ||||||||
\(613\) | −47.0883 | −1.90188 | −0.950940 | − | 0.309376i | \(-0.899880\pi\) | ||||
−0.950940 | + | 0.309376i | \(0.899880\pi\) | |||||||
\(614\) | 25.0232 | 1.00986 | ||||||||
\(615\) | 22.3601 | 0.901646 | ||||||||
\(616\) | 16.6459 | 0.670682 | ||||||||
\(617\) | −42.3851 | −1.70636 | −0.853179 | − | 0.521618i | \(-0.825329\pi\) | ||||
−0.853179 | + | 0.521618i | \(0.825329\pi\) | |||||||
\(618\) | −12.3824 | −0.498092 | ||||||||
\(619\) | −1.85616 | −0.0746055 | −0.0373027 | − | 0.999304i | \(-0.511877\pi\) | ||||
−0.0373027 | + | 0.999304i | \(0.511877\pi\) | |||||||
\(620\) | −22.5699 | −0.906427 | ||||||||
\(621\) | 3.41147 | 0.136898 | ||||||||
\(622\) | 23.9736 | 0.961253 | ||||||||
\(623\) | 33.0496 | 1.32411 | ||||||||
\(624\) | 2.71688 | 0.108762 | ||||||||
\(625\) | −14.1257 | −0.565027 | ||||||||
\(626\) | −12.6382 | −0.505122 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.27126 | 0.250250 | ||||||||
\(629\) | −8.00774 | −0.319290 | ||||||||
\(630\) | −16.6459 | −0.663188 | ||||||||
\(631\) | 24.6483 | 0.981232 | 0.490616 | − | 0.871376i | \(-0.336772\pi\) | ||||
0.490616 | + | 0.871376i | \(0.336772\pi\) | |||||||
\(632\) | −0.297667 | −0.0118405 | ||||||||
\(633\) | 7.94356 | 0.315728 | ||||||||
\(634\) | 14.1334 | 0.561309 | ||||||||
\(635\) | 20.7547 | 0.823623 | ||||||||
\(636\) | 0.630415 | 0.0249976 | ||||||||
\(637\) | −45.6664 | −1.80937 | ||||||||
\(638\) | 12.8726 | 0.509630 | ||||||||
\(639\) | −7.95811 | −0.314818 | ||||||||
\(640\) | 3.41147 | 0.134850 | ||||||||
\(641\) | −17.6382 | −0.696665 | −0.348333 | − | 0.937371i | \(-0.613252\pi\) | ||||
−0.348333 | + | 0.937371i | \(0.613252\pi\) | |||||||
\(642\) | 3.89899 | 0.153881 | ||||||||
\(643\) | 29.8485 | 1.17711 | 0.588556 | − | 0.808457i | \(-0.299697\pi\) | ||||
0.588556 | + | 0.808457i | \(0.299697\pi\) | |||||||
\(644\) | 16.6459 | 0.655940 | ||||||||
\(645\) | −14.2267 | −0.560175 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 23.9391 | 0.941144 | 0.470572 | − | 0.882362i | \(-0.344048\pi\) | ||||
0.470572 | + | 0.882362i | \(0.344048\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | 39.7033 | 1.55849 | ||||||||
\(650\) | −18.0351 | −0.707394 | ||||||||
\(651\) | −32.2814 | −1.26521 | ||||||||
\(652\) | −19.2986 | −0.755792 | ||||||||
\(653\) | −26.4861 | −1.03648 | −0.518240 | − | 0.855235i | \(-0.673413\pi\) | ||||
−0.518240 | + | 0.855235i | \(0.673413\pi\) | |||||||
\(654\) | −11.5963 | −0.453450 | ||||||||
\(655\) | −63.4671 | −2.47986 | ||||||||
\(656\) | −6.55438 | −0.255905 | ||||||||
\(657\) | −12.7442 | −0.497199 | ||||||||
\(658\) | −13.9409 | −0.543472 | ||||||||
\(659\) | 5.29355 | 0.206207 | 0.103104 | − | 0.994671i | \(-0.467123\pi\) | ||||
0.103104 | + | 0.994671i | \(0.467123\pi\) | |||||||
\(660\) | 11.6382 | 0.453015 | ||||||||
\(661\) | −46.1070 | −1.79335 | −0.896677 | − | 0.442685i | \(-0.854026\pi\) | ||||
−0.896677 | + | 0.442685i | \(0.854026\pi\) | |||||||
\(662\) | −29.4979 | −1.14647 | ||||||||
\(663\) | 3.21894 | 0.125013 | ||||||||
\(664\) | 15.6040 | 0.605553 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6.75877 | −0.261897 | ||||||||
\(667\) | 12.8726 | 0.498428 | ||||||||
\(668\) | 7.72193 | 0.298771 | ||||||||
\(669\) | 11.9682 | 0.462718 | ||||||||
\(670\) | −2.41921 | −0.0934624 | ||||||||
\(671\) | −23.5449 | −0.908940 | ||||||||
\(672\) | 4.87939 | 0.188226 | ||||||||
\(673\) | −2.38144 | −0.0917979 | −0.0458990 | − | 0.998946i | \(-0.514615\pi\) | ||||
−0.0458990 | + | 0.998946i | \(0.514615\pi\) | |||||||
\(674\) | 22.2490 | 0.856998 | ||||||||
\(675\) | −6.63816 | −0.255503 | ||||||||
\(676\) | −5.61856 | −0.216098 | ||||||||
\(677\) | −15.9486 | −0.612955 | −0.306478 | − | 0.951878i | \(-0.599150\pi\) | ||||
−0.306478 | + | 0.951878i | \(0.599150\pi\) | |||||||
\(678\) | 1.94087 | 0.0745388 | ||||||||
\(679\) | −34.7689 | −1.33431 | ||||||||
\(680\) | 4.04189 | 0.154999 | ||||||||
\(681\) | 26.5945 | 1.01910 | ||||||||
\(682\) | 22.5699 | 0.864245 | ||||||||
\(683\) | 1.26083 | 0.0482443 | 0.0241222 | − | 0.999709i | \(-0.492321\pi\) | ||||
0.0241222 | + | 0.999709i | \(0.492321\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 15.5107 | 0.592635 | ||||||||
\(686\) | −47.8590 | −1.82726 | ||||||||
\(687\) | 19.9026 | 0.759332 | ||||||||
\(688\) | 4.17024 | 0.158989 | ||||||||
\(689\) | 1.71276 | 0.0652511 | ||||||||
\(690\) | 11.6382 | 0.443057 | ||||||||
\(691\) | −8.10876 | −0.308472 | −0.154236 | − | 0.988034i | \(-0.549292\pi\) | ||||
−0.154236 | + | 0.988034i | \(0.549292\pi\) | |||||||
\(692\) | 14.4953 | 0.551027 | ||||||||
\(693\) | 16.6459 | 0.632325 | ||||||||
\(694\) | −14.0250 | −0.532381 | ||||||||
\(695\) | −10.2841 | −0.390096 | ||||||||
\(696\) | 3.77332 | 0.143027 | ||||||||
\(697\) | −7.76558 | −0.294142 | ||||||||
\(698\) | −34.1121 | −1.29116 | ||||||||
\(699\) | 4.31046 | 0.163037 | ||||||||
\(700\) | −32.3901 | −1.22423 | ||||||||
\(701\) | 10.2284 | 0.386323 | 0.193161 | − | 0.981167i | \(-0.438126\pi\) | ||||
0.193161 | + | 0.981167i | \(0.438126\pi\) | |||||||
\(702\) | 2.71688 | 0.102542 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | −3.41147 | −0.128575 | ||||||||
\(705\) | −9.74691 | −0.367090 | ||||||||
\(706\) | 30.4439 | 1.14577 | ||||||||
\(707\) | 22.6691 | 0.852560 | ||||||||
\(708\) | 11.6382 | 0.437389 | ||||||||
\(709\) | 0.204393 | 0.00767614 | 0.00383807 | − | 0.999993i | \(-0.498778\pi\) | ||||
0.00383807 | + | 0.999993i | \(0.498778\pi\) | |||||||
\(710\) | −27.1489 | −1.01888 | ||||||||
\(711\) | −0.297667 | −0.0111634 | ||||||||
\(712\) | −6.77332 | −0.253841 | ||||||||
\(713\) | 22.5699 | 0.845248 | ||||||||
\(714\) | 5.78106 | 0.216351 | ||||||||
\(715\) | 31.6195 | 1.18250 | ||||||||
\(716\) | 9.82295 | 0.367101 | ||||||||
\(717\) | −0.285807 | −0.0106737 | ||||||||
\(718\) | 13.6459 | 0.509260 | ||||||||
\(719\) | 15.9394 | 0.594441 | 0.297220 | − | 0.954809i | \(-0.403940\pi\) | ||||
0.297220 | + | 0.954809i | \(0.403940\pi\) | |||||||
\(720\) | 3.41147 | 0.127138 | ||||||||
\(721\) | −60.4184 | −2.25010 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.56624 | 0.355772 | ||||||||
\(724\) | −18.9145 | −0.702951 | ||||||||
\(725\) | −25.0479 | −0.930255 | ||||||||
\(726\) | −0.638156 | −0.0236842 | ||||||||
\(727\) | −30.9632 | −1.14836 | −0.574180 | − | 0.818729i | \(-0.694679\pi\) | ||||
−0.574180 | + | 0.818729i | \(0.694679\pi\) | |||||||
\(728\) | 13.2567 | 0.491326 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −43.4766 | −1.60914 | ||||||||
\(731\) | 4.94087 | 0.182745 | ||||||||
\(732\) | −6.90167 | −0.255093 | ||||||||
\(733\) | 3.95811 | 0.146196 | 0.0730981 | − | 0.997325i | \(-0.476711\pi\) | ||||
0.0730981 | + | 0.997325i | \(0.476711\pi\) | |||||||
\(734\) | 23.7665 | 0.877238 | ||||||||
\(735\) | −57.3414 | −2.11507 | ||||||||
\(736\) | −3.41147 | −0.125749 | ||||||||
\(737\) | 2.41921 | 0.0891129 | ||||||||
\(738\) | −6.55438 | −0.241270 | ||||||||
\(739\) | −25.8033 | −0.949191 | −0.474596 | − | 0.880204i | \(-0.657406\pi\) | ||||
−0.474596 | + | 0.880204i | \(0.657406\pi\) | |||||||
\(740\) | −23.0574 | −0.847606 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.07604 | 0.112925 | ||||||||
\(743\) | −31.9145 | −1.17083 | −0.585414 | − | 0.810734i | \(-0.699068\pi\) | ||||
−0.585414 | + | 0.810734i | \(0.699068\pi\) | |||||||
\(744\) | 6.61587 | 0.242549 | ||||||||
\(745\) | 4.04189 | 0.148083 | ||||||||
\(746\) | 23.2344 | 0.850673 | ||||||||
\(747\) | 15.6040 | 0.570921 | ||||||||
\(748\) | −4.04189 | −0.147786 | ||||||||
\(749\) | 19.0247 | 0.695146 | ||||||||
\(750\) | −5.58853 | −0.204064 | ||||||||
\(751\) | 0.508045 | 0.0185388 | 0.00926942 | − | 0.999957i | \(-0.497049\pi\) | ||||
0.00926942 | + | 0.999957i | \(0.497049\pi\) | |||||||
\(752\) | 2.85710 | 0.104188 | ||||||||
\(753\) | −29.6878 | −1.08188 | ||||||||
\(754\) | 10.2517 | 0.373343 | ||||||||
\(755\) | 12.4115 | 0.451700 | ||||||||
\(756\) | 4.87939 | 0.177462 | ||||||||
\(757\) | −48.1694 | −1.75075 | −0.875374 | − | 0.483447i | \(-0.839385\pi\) | ||||
−0.875374 | + | 0.483447i | \(0.839385\pi\) | |||||||
\(758\) | 4.50030 | 0.163458 | ||||||||
\(759\) | −11.6382 | −0.422438 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.15064 | 0.186711 | 0.0933554 | − | 0.995633i | \(-0.470241\pi\) | ||||
0.0933554 | + | 0.995633i | \(0.470241\pi\) | |||||||
\(762\) | −6.08378 | −0.220392 | ||||||||
\(763\) | −56.5827 | −2.04843 | ||||||||
\(764\) | −10.0915 | −0.365098 | ||||||||
\(765\) | 4.04189 | 0.146135 | ||||||||
\(766\) | −4.36009 | −0.157536 | ||||||||
\(767\) | 31.6195 | 1.14171 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 19.5725 | 0.705804 | 0.352902 | − | 0.935660i | \(-0.385195\pi\) | ||||
0.352902 | + | 0.935660i | \(0.385195\pi\) | |||||||
\(770\) | 56.7870 | 2.04646 | ||||||||
\(771\) | 15.7965 | 0.568899 | ||||||||
\(772\) | −2.52435 | −0.0908533 | ||||||||
\(773\) | −22.3946 | −0.805476 | −0.402738 | − | 0.915315i | \(-0.631941\pi\) | ||||
−0.402738 | + | 0.915315i | \(0.631941\pi\) | |||||||
\(774\) | 4.17024 | 0.149896 | ||||||||
\(775\) | −43.9172 | −1.57755 | ||||||||
\(776\) | 7.12567 | 0.255797 | ||||||||
\(777\) | −32.9786 | −1.18310 | ||||||||
\(778\) | −1.31046 | −0.0469823 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 9.26857 | 0.331868 | ||||||||
\(781\) | 27.1489 | 0.971464 | ||||||||
\(782\) | −4.04189 | −0.144538 | ||||||||
\(783\) | 3.77332 | 0.134847 | ||||||||
\(784\) | 16.8084 | 0.600300 | ||||||||
\(785\) | 21.3942 | 0.763593 | ||||||||
\(786\) | 18.6040 | 0.663583 | ||||||||
\(787\) | −33.6887 | −1.20087 | −0.600437 | − | 0.799672i | \(-0.705007\pi\) | ||||
−0.600437 | + | 0.799672i | \(0.705007\pi\) | |||||||
\(788\) | 14.8571 | 0.529262 | ||||||||
\(789\) | −10.8648 | −0.386798 | ||||||||
\(790\) | −1.01548 | −0.0361292 | ||||||||
\(791\) | 9.47028 | 0.336724 | ||||||||
\(792\) | −3.41147 | −0.121221 | ||||||||
\(793\) | −18.7510 | −0.665869 | ||||||||
\(794\) | −19.0128 | −0.674739 | ||||||||
\(795\) | 2.15064 | 0.0762755 | ||||||||
\(796\) | 8.06923 | 0.286006 | ||||||||
\(797\) | 47.8631 | 1.69540 | 0.847699 | − | 0.530478i | \(-0.177988\pi\) | ||||
0.847699 | + | 0.530478i | \(0.177988\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.38507 | 0.119755 | ||||||||
\(800\) | 6.63816 | 0.234694 | ||||||||
\(801\) | −6.77332 | −0.239323 | ||||||||
\(802\) | −35.8631 | −1.26637 | ||||||||
\(803\) | 43.4766 | 1.53426 | ||||||||
\(804\) | 0.709141 | 0.0250095 | ||||||||
\(805\) | 56.7870 | 2.00148 | ||||||||
\(806\) | 17.9745 | 0.633126 | ||||||||
\(807\) | −17.2935 | −0.608762 | ||||||||
\(808\) | −4.64590 | −0.163442 | ||||||||
\(809\) | −3.67406 | −0.129173 | −0.0645865 | − | 0.997912i | \(-0.520573\pi\) | ||||
−0.0645865 | + | 0.997912i | \(0.520573\pi\) | |||||||
\(810\) | 3.41147 | 0.119867 | ||||||||
\(811\) | 18.7050 | 0.656822 | 0.328411 | − | 0.944535i | \(-0.393487\pi\) | ||||
0.328411 | + | 0.944535i | \(0.393487\pi\) | |||||||
\(812\) | 18.4115 | 0.646116 | ||||||||
\(813\) | −1.44562 | −0.0507002 | ||||||||
\(814\) | 23.0574 | 0.808160 | ||||||||
\(815\) | −65.8367 | −2.30616 | ||||||||
\(816\) | −1.18479 | −0.0414760 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 29.1088 | 1.01776 | ||||||||
\(819\) | 13.2567 | 0.463227 | ||||||||
\(820\) | −22.3601 | −0.780848 | ||||||||
\(821\) | −22.3164 | −0.778849 | −0.389425 | − | 0.921058i | \(-0.627326\pi\) | ||||
−0.389425 | + | 0.921058i | \(0.627326\pi\) | |||||||
\(822\) | −4.54664 | −0.158582 | ||||||||
\(823\) | −26.4037 | −0.920376 | −0.460188 | − | 0.887821i | \(-0.652218\pi\) | ||||
−0.460188 | + | 0.887821i | \(0.652218\pi\) | |||||||
\(824\) | 12.3824 | 0.431361 | ||||||||
\(825\) | 22.6459 | 0.788429 | ||||||||
\(826\) | 56.7870 | 1.97587 | ||||||||
\(827\) | −29.6705 | −1.03175 | −0.515873 | − | 0.856665i | \(-0.672532\pi\) | ||||
−0.515873 | + | 0.856665i | \(0.672532\pi\) | |||||||
\(828\) | −3.41147 | −0.118557 | ||||||||
\(829\) | −1.76827 | −0.0614144 | −0.0307072 | − | 0.999528i | \(-0.509776\pi\) | ||||
−0.0307072 | + | 0.999528i | \(0.509776\pi\) | |||||||
\(830\) | 53.2327 | 1.84773 | ||||||||
\(831\) | −21.1908 | −0.735100 | ||||||||
\(832\) | −2.71688 | −0.0941909 | ||||||||
\(833\) | 19.9145 | 0.689995 | ||||||||
\(834\) | 3.01455 | 0.104385 | ||||||||
\(835\) | 26.3432 | 0.911643 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6.61587 | 0.228678 | ||||||||
\(838\) | 13.1584 | 0.454549 | ||||||||
\(839\) | −26.7142 | −0.922276 | −0.461138 | − | 0.887328i | \(-0.652559\pi\) | ||||
−0.461138 | + | 0.887328i | \(0.652559\pi\) | |||||||
\(840\) | 16.6459 | 0.574338 | ||||||||
\(841\) | −14.7621 | −0.509037 | ||||||||
\(842\) | 0.150644 | 0.00519154 | ||||||||
\(843\) | −24.3678 | −0.839273 | ||||||||
\(844\) | −7.94356 | −0.273429 | ||||||||
\(845\) | −19.1676 | −0.659384 | ||||||||
\(846\) | 2.85710 | 0.0982290 | ||||||||
\(847\) | −3.11381 | −0.106992 | ||||||||
\(848\) | −0.630415 | −0.0216485 | ||||||||
\(849\) | 4.12567 | 0.141593 | ||||||||
\(850\) | 7.86484 | 0.269762 | ||||||||
\(851\) | 23.0574 | 0.790396 | ||||||||
\(852\) | 7.95811 | 0.272640 | ||||||||
\(853\) | 13.9263 | 0.476828 | 0.238414 | − | 0.971164i | \(-0.423372\pi\) | ||||
0.238414 | + | 0.971164i | \(0.423372\pi\) | |||||||
\(854\) | −33.6759 | −1.15237 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −3.89899 | −0.133265 | ||||||||
\(857\) | 19.6691 | 0.671884 | 0.335942 | − | 0.941883i | \(-0.390945\pi\) | ||||
0.335942 | + | 0.941883i | \(0.390945\pi\) | |||||||
\(858\) | −9.26857 | −0.316424 | ||||||||
\(859\) | −43.3979 | −1.48072 | −0.740358 | − | 0.672213i | \(-0.765344\pi\) | ||||
−0.740358 | + | 0.672213i | \(0.765344\pi\) | |||||||
\(860\) | 14.2267 | 0.485126 | ||||||||
\(861\) | −31.9813 | −1.08992 | ||||||||
\(862\) | 30.7965 | 1.04893 | ||||||||
\(863\) | 29.4192 | 1.00144 | 0.500721 | − | 0.865609i | \(-0.333068\pi\) | ||||
0.500721 | + | 0.865609i | \(0.333068\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 49.4502 | 1.68136 | ||||||||
\(866\) | 29.4338 | 1.00020 | ||||||||
\(867\) | 15.5963 | 0.529677 | ||||||||
\(868\) | 32.2814 | 1.09570 | ||||||||
\(869\) | 1.01548 | 0.0344479 | ||||||||
\(870\) | 12.8726 | 0.436421 | ||||||||
\(871\) | 1.92665 | 0.0652821 | ||||||||
\(872\) | 11.5963 | 0.392699 | ||||||||
\(873\) | 7.12567 | 0.241167 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −27.2686 | −0.921846 | ||||||||
\(876\) | 12.7442 | 0.430587 | ||||||||
\(877\) | 26.1652 | 0.883536 | 0.441768 | − | 0.897129i | \(-0.354351\pi\) | ||||
0.441768 | + | 0.897129i | \(0.354351\pi\) | |||||||
\(878\) | −19.8007 | −0.668240 | ||||||||
\(879\) | 2.78106 | 0.0938028 | ||||||||
\(880\) | −11.6382 | −0.392322 | ||||||||
\(881\) | 22.6287 | 0.762379 | 0.381189 | − | 0.924497i | \(-0.375515\pi\) | ||||
0.381189 | + | 0.924497i | \(0.375515\pi\) | |||||||
\(882\) | 16.8084 | 0.565968 | ||||||||
\(883\) | −8.28169 | −0.278701 | −0.139350 | − | 0.990243i | \(-0.544501\pi\) | ||||
−0.139350 | + | 0.990243i | \(0.544501\pi\) | |||||||
\(884\) | −3.21894 | −0.108265 | ||||||||
\(885\) | 39.7033 | 1.33461 | ||||||||
\(886\) | −18.5868 | −0.624435 | ||||||||
\(887\) | −40.3569 | −1.35505 | −0.677526 | − | 0.735499i | \(-0.736948\pi\) | ||||
−0.677526 | + | 0.735499i | \(0.736948\pi\) | |||||||
\(888\) | 6.75877 | 0.226809 | ||||||||
\(889\) | −29.6851 | −0.995606 | ||||||||
\(890\) | −23.1070 | −0.774548 | ||||||||
\(891\) | −3.41147 | −0.114289 | ||||||||
\(892\) | −11.9682 | −0.400726 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −1.18479 | −0.0396254 | ||||||||
\(895\) | 33.5107 | 1.12014 | ||||||||
\(896\) | −4.87939 | −0.163009 | ||||||||
\(897\) | −9.26857 | −0.309469 | ||||||||
\(898\) | −3.37908 | −0.112761 | ||||||||
\(899\) | 24.9638 | 0.832588 | ||||||||
\(900\) | 6.63816 | 0.221272 | ||||||||
\(901\) | −0.746911 | −0.0248832 | ||||||||
\(902\) | 22.3601 | 0.744510 | ||||||||
\(903\) | 20.3482 | 0.677147 | ||||||||
\(904\) | −1.94087 | −0.0645525 | ||||||||
\(905\) | −64.5262 | −2.14492 | ||||||||
\(906\) | −3.63816 | −0.120870 | ||||||||
\(907\) | 19.2513 | 0.639230 | 0.319615 | − | 0.947547i | \(-0.396446\pi\) | ||||
0.319615 | + | 0.947547i | \(0.396446\pi\) | |||||||
\(908\) | −26.5945 | −0.882570 | ||||||||
\(909\) | −4.64590 | −0.154095 | ||||||||
\(910\) | 45.2249 | 1.49919 | ||||||||
\(911\) | 58.7684 | 1.94708 | 0.973542 | − | 0.228510i | \(-0.0733853\pi\) | ||||
0.973542 | + | 0.228510i | \(0.0733853\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −53.2327 | −1.76174 | ||||||||
\(914\) | 21.7912 | 0.720788 | ||||||||
\(915\) | −23.5449 | −0.778370 | ||||||||
\(916\) | −19.9026 | −0.657601 | ||||||||
\(917\) | 90.7761 | 2.99769 | ||||||||
\(918\) | −1.18479 | −0.0391040 | ||||||||
\(919\) | −53.7428 | −1.77281 | −0.886406 | − | 0.462909i | \(-0.846806\pi\) | ||||
−0.886406 | + | 0.462909i | \(0.846806\pi\) | |||||||
\(920\) | −11.6382 | −0.383699 | ||||||||
\(921\) | −25.0232 | −0.824543 | ||||||||
\(922\) | 11.7638 | 0.387421 | ||||||||
\(923\) | 21.6212 | 0.711672 | ||||||||
\(924\) | −16.6459 | −0.547610 | ||||||||
\(925\) | −44.8658 | −1.47518 | ||||||||
\(926\) | 16.9932 | 0.558431 | ||||||||
\(927\) | 12.3824 | 0.406691 | ||||||||
\(928\) | −3.77332 | −0.123865 | ||||||||
\(929\) | −31.0387 | −1.01835 | −0.509173 | − | 0.860664i | \(-0.670049\pi\) | ||||
−0.509173 | + | 0.860664i | \(0.670049\pi\) | |||||||
\(930\) | 22.5699 | 0.740095 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.31046 | −0.141194 | ||||||||
\(933\) | −23.9736 | −0.784860 | ||||||||
\(934\) | −11.7050 | −0.383000 | ||||||||
\(935\) | −13.7888 | −0.450942 | ||||||||
\(936\) | −2.71688 | −0.0888040 | ||||||||
\(937\) | −20.7428 | −0.677637 | −0.338819 | − | 0.940852i | \(-0.610027\pi\) | ||||
−0.338819 | + | 0.940852i | \(0.610027\pi\) | |||||||
\(938\) | 3.46017 | 0.112979 | ||||||||
\(939\) | 12.6382 | 0.412431 | ||||||||
\(940\) | 9.74691 | 0.317909 | ||||||||
\(941\) | 14.8631 | 0.484523 | 0.242261 | − | 0.970211i | \(-0.422111\pi\) | ||||
0.242261 | + | 0.970211i | \(0.422111\pi\) | |||||||
\(942\) | −6.27126 | −0.204329 | ||||||||
\(943\) | 22.3601 | 0.728145 | ||||||||
\(944\) | −11.6382 | −0.378790 | ||||||||
\(945\) | 16.6459 | 0.541491 | ||||||||
\(946\) | −14.2267 | −0.462549 | ||||||||
\(947\) | −25.1999 | −0.818888 | −0.409444 | − | 0.912335i | \(-0.634277\pi\) | ||||
−0.409444 | + | 0.912335i | \(0.634277\pi\) | |||||||
\(948\) | 0.297667 | 0.00966776 | ||||||||
\(949\) | 34.6245 | 1.12396 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −14.1334 | −0.458307 | ||||||||
\(952\) | −5.78106 | −0.187365 | ||||||||
\(953\) | 12.3851 | 0.401192 | 0.200596 | − | 0.979674i | \(-0.435712\pi\) | ||||
0.200596 | + | 0.979674i | \(0.435712\pi\) | |||||||
\(954\) | −0.630415 | −0.0204104 | ||||||||
\(955\) | −34.4270 | −1.11403 | ||||||||
\(956\) | 0.285807 | 0.00924366 | ||||||||
\(957\) | −12.8726 | −0.416111 | ||||||||
\(958\) | 29.9796 | 0.968596 | ||||||||
\(959\) | −22.1848 | −0.716384 | ||||||||
\(960\) | −3.41147 | −0.110105 | ||||||||
\(961\) | 12.7697 | 0.411926 | ||||||||
\(962\) | 18.3628 | 0.592040 | ||||||||
\(963\) | −3.89899 | −0.125643 | ||||||||
\(964\) | −9.56624 | −0.308108 | ||||||||
\(965\) | −8.61175 | −0.277222 | ||||||||
\(966\) | −16.6459 | −0.535573 | ||||||||
\(967\) | −3.40879 | −0.109619 | −0.0548096 | − | 0.998497i | \(-0.517455\pi\) | ||||
−0.0548096 | + | 0.998497i | \(0.517455\pi\) | |||||||
\(968\) | 0.638156 | 0.0205111 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 24.3090 | 0.780516 | ||||||||
\(971\) | 13.8972 | 0.445983 | 0.222992 | − | 0.974820i | \(-0.428418\pi\) | ||||
0.222992 | + | 0.974820i | \(0.428418\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 14.7091 | 0.471553 | ||||||||
\(974\) | −14.5107 | −0.464954 | ||||||||
\(975\) | 18.0351 | 0.577585 | ||||||||
\(976\) | 6.90167 | 0.220917 | ||||||||
\(977\) | −12.8402 | −0.410794 | −0.205397 | − | 0.978679i | \(-0.565849\pi\) | ||||
−0.205397 | + | 0.978679i | \(0.565849\pi\) | |||||||
\(978\) | 19.2986 | 0.617101 | ||||||||
\(979\) | 23.1070 | 0.738503 | ||||||||
\(980\) | 57.3414 | 1.83170 | ||||||||
\(981\) | 11.5963 | 0.370240 | ||||||||
\(982\) | −11.6554 | −0.371939 | ||||||||
\(983\) | 0.866592 | 0.0276400 | 0.0138200 | − | 0.999904i | \(-0.495601\pi\) | ||||
0.0138200 | + | 0.999904i | \(0.495601\pi\) | |||||||
\(984\) | 6.55438 | 0.208946 | ||||||||
\(985\) | 50.6846 | 1.61495 | ||||||||
\(986\) | −4.47060 | −0.142373 | ||||||||
\(987\) | 13.9409 | 0.443743 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −14.2267 | −0.452382 | ||||||||
\(990\) | −11.6382 | −0.369885 | ||||||||
\(991\) | 20.9709 | 0.666163 | 0.333081 | − | 0.942898i | \(-0.391912\pi\) | ||||
0.333081 | + | 0.942898i | \(0.391912\pi\) | |||||||
\(992\) | −6.61587 | −0.210054 | ||||||||
\(993\) | 29.4979 | 0.936089 | ||||||||
\(994\) | 38.8307 | 1.23163 | ||||||||
\(995\) | 27.5280 | 0.872695 | ||||||||
\(996\) | −15.6040 | −0.494432 | ||||||||
\(997\) | 39.7475 | 1.25882 | 0.629408 | − | 0.777075i | \(-0.283297\pi\) | ||||
0.629408 | + | 0.777075i | \(0.283297\pi\) | |||||||
\(998\) | −1.68685 | −0.0533964 | ||||||||
\(999\) | 6.75877 | 0.213838 |
(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 | 2166.2.a.s.1.3 | 3 | ||
3.2 | odd | 2 | 6498.2.a.bm.1.1 | 3 | |||
19.3 | odd | 18 | 114.2.i.a.85.1 | yes | 6 | ||
19.13 | odd | 18 | 114.2.i.a.55.1 | ✓ | 6 | ||
19.18 | odd | 2 | 2166.2.a.q.1.3 | 3 | |||
57.32 | even | 18 | 342.2.u.e.55.1 | 6 | |||
57.41 | even | 18 | 342.2.u.e.199.1 | 6 | |||
57.56 | even | 2 | 6498.2.a.br.1.1 | 3 | |||
76.3 | even | 18 | 912.2.bo.a.769.1 | 6 | |||
76.51 | even | 18 | 912.2.bo.a.625.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
114.2.i.a.55.1 | ✓ | 6 | 19.13 | odd | 18 | ||
114.2.i.a.85.1 | yes | 6 | 19.3 | odd | 18 | ||
342.2.u.e.55.1 | 6 | 57.32 | even | 18 | |||
342.2.u.e.199.1 | 6 | 57.41 | even | 18 | |||
912.2.bo.a.625.1 | 6 | 76.51 | even | 18 | |||
912.2.bo.a.769.1 | 6 | 76.3 | even | 18 | |||
2166.2.a.q.1.3 | 3 | 19.18 | odd | 2 | |||
2166.2.a.s.1.3 | 3 | 1.1 | even | 1 | trivial | ||
6498.2.a.bm.1.1 | 3 | 3.2 | odd | 2 | |||
6498.2.a.br.1.1 | 3 | 57.56 | even | 2 |