Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [9747,2,Mod(1,9747)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(9747, 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("9747.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 9747 = 3^{3} \cdot 19^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 9747.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: | \(77.8301868501\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 513) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.239123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 9747.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.239123 | −0.169086 | −0.0845428 | − | 0.996420i | \(-0.526943\pi\) | ||||
−0.0845428 | + | 0.996420i | \(0.526943\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.94282 | −0.971410 | ||||||||
\(5\) | 1.76088 | 0.787488 | 0.393744 | − | 0.919220i | \(-0.371180\pi\) | ||||
0.393744 | + | 0.919220i | \(0.371180\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.18194 | 1.20266 | 0.601331 | − | 0.799000i | \(-0.294637\pi\) | ||||
0.601331 | + | 0.799000i | \(0.294637\pi\) | |||||||
\(8\) | 0.942820 | 0.333337 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.421067 | −0.133153 | ||||||||
\(11\) | −0.181943 | −0.0548580 | −0.0274290 | − | 0.999624i | \(-0.508732\pi\) | ||||
−0.0274290 | + | 0.999624i | \(0.508732\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.18194 | 0.882512 | 0.441256 | − | 0.897381i | \(-0.354533\pi\) | ||||
0.441256 | + | 0.897381i | \(0.354533\pi\) | |||||||
\(14\) | −0.760877 | −0.203353 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.66019 | 0.915047 | ||||||||
\(17\) | 7.84213 | 1.90200 | 0.950998 | − | 0.309196i | \(-0.100060\pi\) | ||||
0.950998 | + | 0.309196i | \(0.100060\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −3.42107 | −0.764974 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.0435069 | 0.00927570 | ||||||||
\(23\) | 3.28263 | 0.684476 | 0.342238 | − | 0.939613i | \(-0.388815\pi\) | ||||
0.342238 | + | 0.939613i | \(0.388815\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.89931 | −0.379863 | ||||||||
\(26\) | −0.760877 | −0.149220 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −6.18194 | −1.16828 | ||||||||
\(29\) | −9.48865 | −1.76200 | −0.880999 | − | 0.473118i | \(-0.843128\pi\) | ||||
−0.880999 | + | 0.473118i | \(0.843128\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.18194 | −0.391889 | −0.195944 | − | 0.980615i | \(-0.562777\pi\) | ||||
−0.195944 | + | 0.980615i | \(0.562777\pi\) | |||||||
\(32\) | −2.76088 | −0.488059 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −1.87524 | −0.321600 | ||||||||
\(35\) | 5.60301 | 0.947082 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.42107 | 1.05562 | 0.527808 | − | 0.849363i | \(-0.323014\pi\) | ||||
0.527808 | + | 0.849363i | \(0.323014\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.66019 | 0.262499 | ||||||||
\(41\) | −1.76088 | −0.275003 | −0.137501 | − | 0.990502i | \(-0.543907\pi\) | ||||
−0.137501 | + | 0.990502i | \(0.543907\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9.16827 | 1.39815 | 0.699074 | − | 0.715049i | \(-0.253596\pi\) | ||||
0.699074 | + | 0.715049i | \(0.253596\pi\) | |||||||
\(44\) | 0.353483 | 0.0532896 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.784953 | −0.115735 | ||||||||
\(47\) | 9.00000 | 1.31278 | 0.656392 | − | 0.754420i | \(-0.272082\pi\) | ||||
0.656392 | + | 0.754420i | \(0.272082\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.12476 | 0.446395 | ||||||||
\(50\) | 0.454170 | 0.0642293 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.18194 | −0.857281 | ||||||||
\(53\) | 13.6706 | 1.87780 | 0.938900 | − | 0.344189i | \(-0.111846\pi\) | ||||
0.938900 | + | 0.344189i | \(0.111846\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.320380 | −0.0432000 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.26896 | 0.297929 | ||||||||
\(59\) | 8.78495 | 1.14370 | 0.571852 | − | 0.820357i | \(-0.306225\pi\) | ||||
0.571852 | + | 0.820357i | \(0.306225\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.703697 | −0.0900991 | −0.0450496 | − | 0.998985i | \(-0.514345\pi\) | ||||
−0.0450496 | + | 0.998985i | \(0.514345\pi\) | |||||||
\(62\) | 0.521753 | 0.0662628 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.66019 | −0.832524 | ||||||||
\(65\) | 5.60301 | 0.694968 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.37756 | 0.779143 | 0.389571 | − | 0.920996i | \(-0.372623\pi\) | ||||
0.389571 | + | 0.920996i | \(0.372623\pi\) | |||||||
\(68\) | −15.2359 | −1.84762 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.33981 | −0.160138 | ||||||||
\(71\) | 3.22545 | 0.382791 | 0.191395 | − | 0.981513i | \(-0.438699\pi\) | ||||
0.191395 | + | 0.981513i | \(0.438699\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.88564 | −0.805903 | −0.402952 | − | 0.915221i | \(-0.632016\pi\) | ||||
−0.402952 | + | 0.915221i | \(0.632016\pi\) | |||||||
\(74\) | −1.53543 | −0.178490 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.578933 | −0.0659756 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.986327 | 0.110970 | 0.0554852 | − | 0.998460i | \(-0.482329\pi\) | ||||
0.0554852 | + | 0.998460i | \(0.482329\pi\) | |||||||
\(80\) | 6.44514 | 0.720589 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.421067 | 0.0464990 | ||||||||
\(83\) | −10.2930 | −1.12981 | −0.564904 | − | 0.825157i | \(-0.691087\pi\) | ||||
−0.564904 | + | 0.825157i | \(0.691087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 13.8090 | 1.49780 | ||||||||
\(86\) | −2.19235 | −0.236407 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.171540 | −0.0182862 | ||||||||
\(89\) | −7.58934 | −0.804468 | −0.402234 | − | 0.915537i | \(-0.631766\pi\) | ||||
−0.402234 | + | 0.915537i | \(0.631766\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.1248 | 1.06136 | ||||||||
\(92\) | −6.37756 | −0.664907 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.15211 | −0.221973 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −0.784953 | −0.0796999 | −0.0398500 | − | 0.999206i | \(-0.512688\pi\) | ||||
−0.0398500 | + | 0.999206i | \(0.512688\pi\) | |||||||
\(98\) | −0.747204 | −0.0754790 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.69002 | 0.369002 | ||||||||
\(101\) | −3.06758 | −0.305236 | −0.152618 | − | 0.988285i | \(-0.548770\pi\) | ||||
−0.152618 | + | 0.988285i | \(0.548770\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 19.0104 | 1.87315 | 0.936575 | − | 0.350466i | \(-0.113977\pi\) | ||||
0.936575 | + | 0.350466i | \(0.113977\pi\) | |||||||
\(104\) | 3.00000 | 0.294174 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.26896 | −0.317509 | ||||||||
\(107\) | 1.23912 | 0.119791 | 0.0598953 | − | 0.998205i | \(-0.480923\pi\) | ||||
0.0598953 | + | 0.998205i | \(0.480923\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.19562 | −0.114519 | −0.0572596 | − | 0.998359i | \(-0.518236\pi\) | ||||
−0.0572596 | + | 0.998359i | \(0.518236\pi\) | |||||||
\(110\) | 0.0766103 | 0.00730450 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 11.6465 | 1.10049 | ||||||||
\(113\) | −5.78495 | −0.544203 | −0.272101 | − | 0.962269i | \(-0.587719\pi\) | ||||
−0.272101 | + | 0.962269i | \(0.587719\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.78031 | 0.539016 | ||||||||
\(116\) | 18.4347 | 1.71162 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2.10069 | −0.193384 | ||||||||
\(119\) | 24.9532 | 2.28746 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9669 | −0.996991 | ||||||||
\(122\) | 0.168270 | 0.0152345 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.23912 | 0.380685 | ||||||||
\(125\) | −12.1488 | −1.08663 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.2060 | −1.08311 | −0.541555 | − | 0.840666i | \(-0.682164\pi\) | ||||
−0.541555 | + | 0.840666i | \(0.682164\pi\) | |||||||
\(128\) | 7.11436 | 0.628827 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.33981 | −0.117509 | ||||||||
\(131\) | 7.50808 | 0.655984 | 0.327992 | − | 0.944680i | \(-0.393628\pi\) | ||||
0.327992 | + | 0.944680i | \(0.393628\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.52502 | −0.131742 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.39372 | 0.634006 | ||||||||
\(137\) | −12.2255 | −1.04449 | −0.522245 | − | 0.852795i | \(-0.674905\pi\) | ||||
−0.522245 | + | 0.852795i | \(0.674905\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.40739 | 0.373830 | 0.186915 | − | 0.982376i | \(-0.440151\pi\) | ||||
0.186915 | + | 0.982376i | \(0.440151\pi\) | |||||||
\(140\) | −10.8856 | −0.920005 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.771280 | −0.0647244 | ||||||||
\(143\) | −0.578933 | −0.0484128 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −16.7083 | −1.38755 | ||||||||
\(146\) | 1.64652 | 0.136267 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −12.4750 | −1.02544 | ||||||||
\(149\) | −2.45417 | −0.201053 | −0.100527 | − | 0.994934i | \(-0.532053\pi\) | ||||
−0.100527 | + | 0.994934i | \(0.532053\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.5127 | −1.58792 | −0.793962 | − | 0.607968i | \(-0.791985\pi\) | ||||
−0.793962 | + | 0.607968i | \(0.791985\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.138436 | 0.0111555 | ||||||||
\(155\) | −3.84213 | −0.308608 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −15.4991 | −1.23696 | −0.618480 | − | 0.785801i | \(-0.712251\pi\) | ||||
−0.618480 | + | 0.785801i | \(0.712251\pi\) | |||||||
\(158\) | −0.235854 | −0.0187635 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −4.86156 | −0.384340 | ||||||||
\(161\) | 10.4451 | 0.823193 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.2391 | 1.03697 | 0.518484 | − | 0.855087i | \(-0.326497\pi\) | ||||
0.518484 | + | 0.855087i | \(0.326497\pi\) | |||||||
\(164\) | 3.42107 | 0.267140 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.46130 | 0.191034 | ||||||||
\(167\) | −3.21505 | −0.248788 | −0.124394 | − | 0.992233i | \(-0.539699\pi\) | ||||
−0.124394 | + | 0.992233i | \(0.539699\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.87524 | −0.221172 | ||||||||
\(170\) | −3.30206 | −0.253256 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −17.8123 | −1.35818 | ||||||||
\(173\) | 10.9863 | 0.835275 | 0.417637 | − | 0.908614i | \(-0.362858\pi\) | ||||
0.417637 | + | 0.908614i | \(0.362858\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.04351 | −0.456846 | ||||||||
\(176\) | −0.665947 | −0.0501977 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.81479 | 0.136024 | ||||||||
\(179\) | −3.61668 | −0.270324 | −0.135162 | − | 0.990824i | \(-0.543155\pi\) | ||||
−0.135162 | + | 0.990824i | \(0.543155\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.38332 | −0.251480 | −0.125740 | − | 0.992063i | \(-0.540131\pi\) | ||||
−0.125740 | + | 0.992063i | \(0.540131\pi\) | |||||||
\(182\) | −2.42107 | −0.179461 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.09493 | 0.228161 | ||||||||
\(185\) | 11.3067 | 0.831286 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.42682 | −0.104340 | ||||||||
\(188\) | −17.4854 | −1.27525 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.1111 | −0.803970 | −0.401985 | − | 0.915646i | \(-0.631680\pi\) | ||||
−0.401985 | + | 0.915646i | \(0.631680\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.54583 | −0.543161 | −0.271580 | − | 0.962416i | \(-0.587546\pi\) | ||||
−0.271580 | + | 0.962416i | \(0.587546\pi\) | |||||||
\(194\) | 0.187701 | 0.0134761 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.07085 | −0.433632 | ||||||||
\(197\) | −12.4016 | −0.883580 | −0.441790 | − | 0.897118i | \(-0.645656\pi\) | ||||
−0.441790 | + | 0.897118i | \(0.645656\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.8960 | −1.33951 | −0.669753 | − | 0.742584i | \(-0.733600\pi\) | ||||
−0.669753 | + | 0.742584i | \(0.733600\pi\) | |||||||
\(200\) | −1.79071 | −0.126622 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.733531 | 0.0516110 | ||||||||
\(203\) | −30.1923 | −2.11909 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.10069 | −0.216561 | ||||||||
\(206\) | −4.54583 | −0.316723 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 11.6465 | 0.807541 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7576 | 0.809427 | 0.404714 | − | 0.914444i | \(-0.367371\pi\) | ||||
0.404714 | + | 0.914444i | \(0.367371\pi\) | |||||||
\(212\) | −26.5595 | −1.82411 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.296303 | −0.0202549 | ||||||||
\(215\) | 16.1442 | 1.10102 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.94282 | −0.471309 | ||||||||
\(218\) | 0.285900 | 0.0193636 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.622440 | 0.0419649 | ||||||||
\(221\) | 24.9532 | 1.67854 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −10.1923 | −0.682530 | −0.341265 | − | 0.939967i | \(-0.610855\pi\) | ||||
−0.341265 | + | 0.939967i | \(0.610855\pi\) | |||||||
\(224\) | −8.78495 | −0.586969 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.38332 | 0.0920169 | ||||||||
\(227\) | −22.7141 | −1.50759 | −0.753794 | − | 0.657111i | \(-0.771778\pi\) | ||||
−0.753794 | + | 0.657111i | \(0.771778\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.8960 | 0.918276 | 0.459138 | − | 0.888365i | \(-0.348158\pi\) | ||||
0.459138 | + | 0.888365i | \(0.348158\pi\) | |||||||
\(230\) | −1.38221 | −0.0911400 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −8.94609 | −0.587340 | ||||||||
\(233\) | 27.4750 | 1.79995 | 0.899973 | − | 0.435946i | \(-0.143586\pi\) | ||||
0.899973 | + | 0.435946i | \(0.143586\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.8479 | 1.03380 | ||||||||
\(236\) | −17.0676 | −1.11101 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −5.96690 | −0.386776 | ||||||||
\(239\) | 18.4692 | 1.19467 | 0.597337 | − | 0.801990i | \(-0.296225\pi\) | ||||
0.597337 | + | 0.801990i | \(0.296225\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.1248 | 1.23193 | 0.615967 | − | 0.787772i | \(-0.288765\pi\) | ||||
0.615967 | + | 0.787772i | \(0.288765\pi\) | |||||||
\(242\) | 2.62244 | 0.168577 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.36716 | 0.0875232 | ||||||||
\(245\) | 5.50232 | 0.351531 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −2.05718 | −0.130631 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 2.90507 | 0.183733 | ||||||||
\(251\) | −19.7472 | −1.24643 | −0.623216 | − | 0.782050i | \(-0.714174\pi\) | ||||
−0.623216 | + | 0.782050i | \(0.714174\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.597253 | −0.0375490 | ||||||||
\(254\) | 2.91874 | 0.183138 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 11.6192 | 0.726198 | ||||||||
\(257\) | 16.4692 | 1.02732 | 0.513661 | − | 0.857993i | \(-0.328289\pi\) | ||||
0.513661 | + | 0.857993i | \(0.328289\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.4315 | 1.26955 | ||||||||
\(260\) | −10.8856 | −0.675099 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.79536 | −0.110918 | ||||||||
\(263\) | 19.4451 | 1.19904 | 0.599519 | − | 0.800360i | \(-0.295358\pi\) | ||||
0.599519 | + | 0.800360i | \(0.295358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.0722 | 1.47875 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −12.3905 | −0.756867 | ||||||||
\(269\) | −14.1546 | −0.863021 | −0.431511 | − | 0.902108i | \(-0.642019\pi\) | ||||
−0.431511 | + | 0.902108i | \(0.642019\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.75512 | 0.288853 | 0.144426 | − | 0.989516i | \(-0.453866\pi\) | ||||
0.144426 | + | 0.989516i | \(0.453866\pi\) | |||||||
\(272\) | 28.7037 | 1.74042 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.92339 | 0.176608 | ||||||||
\(275\) | 0.345567 | 0.0208385 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −25.4854 | −1.53127 | −0.765634 | − | 0.643276i | \(-0.777575\pi\) | ||||
−0.765634 | + | 0.643276i | \(0.777575\pi\) | |||||||
\(278\) | −1.05391 | −0.0632093 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.28263 | 0.315698 | ||||||||
\(281\) | 30.2060 | 1.80194 | 0.900970 | − | 0.433881i | \(-0.142856\pi\) | ||||
0.900970 | + | 0.433881i | \(0.142856\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.7986 | −0.939131 | −0.469565 | − | 0.882898i | \(-0.655589\pi\) | ||||
−0.469565 | + | 0.882898i | \(0.655589\pi\) | |||||||
\(284\) | −6.26647 | −0.371847 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.138436 | 0.00818592 | ||||||||
\(287\) | −5.60301 | −0.330735 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 44.4991 | 2.61759 | ||||||||
\(290\) | 3.99535 | 0.234615 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.3776 | 0.782862 | ||||||||
\(293\) | 27.2632 | 1.59273 | 0.796367 | − | 0.604814i | \(-0.206753\pi\) | ||||
0.796367 | + | 0.604814i | \(0.206753\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.4692 | 0.900653 | ||||||||
\(296\) | 6.05391 | 0.351876 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.586849 | 0.0339953 | ||||||||
\(299\) | 10.4451 | 0.604058 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 29.1729 | 1.68150 | ||||||||
\(302\) | 4.66595 | 0.268495 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.23912 | −0.0709520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −29.5264 | −1.68516 | −0.842580 | − | 0.538571i | \(-0.818964\pi\) | ||||
−0.842580 | + | 0.538571i | \(0.818964\pi\) | |||||||
\(308\) | 1.12476 | 0.0640893 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.918743 | 0.0521811 | ||||||||
\(311\) | 17.8525 | 1.01232 | 0.506162 | − | 0.862438i | \(-0.331064\pi\) | ||||
0.506162 | + | 0.862438i | \(0.331064\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.97265 | −0.168024 | −0.0840122 | − | 0.996465i | \(-0.526773\pi\) | ||||
−0.0840122 | + | 0.996465i | \(0.526773\pi\) | |||||||
\(314\) | 3.70618 | 0.209152 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.91626 | −0.107798 | ||||||||
\(317\) | −17.1625 | −0.963943 | −0.481971 | − | 0.876187i | \(-0.660079\pi\) | ||||
−0.481971 | + | 0.876187i | \(0.660079\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.72640 | 0.0966597 | ||||||||
\(320\) | −11.7278 | −0.655602 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.49768 | −0.139190 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.04351 | −0.335233 | ||||||||
\(326\) | −3.16578 | −0.175336 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.66019 | −0.0916687 | ||||||||
\(329\) | 28.6375 | 1.57884 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.9669 | −1.31734 | −0.658670 | − | 0.752432i | \(-0.728881\pi\) | ||||
−0.658670 | + | 0.752432i | \(0.728881\pi\) | |||||||
\(332\) | 19.9975 | 1.09751 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.768793 | 0.0420665 | ||||||||
\(335\) | 11.2301 | 0.613566 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.53791 | 0.410616 | 0.205308 | − | 0.978697i | \(-0.434180\pi\) | ||||
0.205308 | + | 0.978697i | \(0.434180\pi\) | |||||||
\(338\) | 0.687536 | 0.0373970 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −26.8285 | −1.45498 | ||||||||
\(341\) | 0.396990 | 0.0214982 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.3308 | −0.665800 | ||||||||
\(344\) | 8.64403 | 0.466055 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −2.62709 | −0.141233 | ||||||||
\(347\) | 7.78822 | 0.418094 | 0.209047 | − | 0.977906i | \(-0.432964\pi\) | ||||
0.209047 | + | 0.977906i | \(0.432964\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −16.0137 | −0.857192 | −0.428596 | − | 0.903496i | \(-0.640992\pi\) | ||||
−0.428596 | + | 0.903496i | \(0.640992\pi\) | |||||||
\(350\) | 1.44514 | 0.0772462 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.502323 | 0.0267739 | ||||||||
\(353\) | 21.8090 | 1.16078 | 0.580389 | − | 0.814340i | \(-0.302901\pi\) | ||||
0.580389 | + | 0.814340i | \(0.302901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.67962 | 0.301443 | ||||||||
\(356\) | 14.7447 | 0.781468 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.864833 | 0.0457078 | ||||||||
\(359\) | 13.9942 | 0.738588 | 0.369294 | − | 0.929313i | \(-0.379600\pi\) | ||||
0.369294 | + | 0.929313i | \(0.379600\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 0.809030 | 0.0425217 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −19.6706 | −1.03102 | ||||||||
\(365\) | −12.1248 | −0.634639 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −28.6328 | −1.49462 | −0.747311 | − | 0.664474i | \(-0.768656\pi\) | ||||
−0.747311 | + | 0.664474i | \(0.768656\pi\) | |||||||
\(368\) | 12.0150 | 0.626328 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −2.70370 | −0.140559 | ||||||||
\(371\) | 43.4991 | 2.25836 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.2197 | 0.891602 | 0.445801 | − | 0.895132i | \(-0.352919\pi\) | ||||
0.445801 | + | 0.895132i | \(0.352919\pi\) | |||||||
\(374\) | 0.341187 | 0.0176423 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 8.48538 | 0.437600 | ||||||||
\(377\) | −30.1923 | −1.55498 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −9.01040 | −0.462833 | −0.231417 | − | 0.972855i | \(-0.574336\pi\) | ||||
−0.231417 | + | 0.972855i | \(0.574336\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.65692 | 0.135940 | ||||||||
\(383\) | −20.3639 | −1.04055 | −0.520273 | − | 0.854000i | \(-0.674170\pi\) | ||||
−0.520273 | + | 0.854000i | \(0.674170\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.01943 | −0.0519550 | ||||||||
\(386\) | 1.80438 | 0.0918407 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.52502 | 0.0774213 | ||||||||
\(389\) | −10.1327 | −0.513747 | −0.256874 | − | 0.966445i | \(-0.582692\pi\) | ||||
−0.256874 | + | 0.966445i | \(0.582692\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.7428 | 1.30187 | ||||||||
\(392\) | 2.94609 | 0.148800 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.96552 | 0.149401 | ||||||||
\(395\) | 1.73680 | 0.0873879 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.3250 | 1.52197 | 0.760985 | − | 0.648770i | \(-0.224716\pi\) | ||||
0.760985 | + | 0.648770i | \(0.224716\pi\) | |||||||
\(398\) | 4.51848 | 0.226491 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.95185 | −0.347592 | ||||||||
\(401\) | 31.5893 | 1.57750 | 0.788748 | − | 0.614717i | \(-0.210730\pi\) | ||||
0.788748 | + | 0.614717i | \(0.210730\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.94282 | −0.345847 | ||||||||
\(404\) | 5.95976 | 0.296509 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.21969 | 0.358307 | ||||||||
\(407\) | −1.16827 | −0.0579090 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.6192 | −1.61291 | −0.806457 | − | 0.591293i | \(-0.798618\pi\) | ||||
−0.806457 | + | 0.591293i | \(0.798618\pi\) | |||||||
\(410\) | 0.741446 | 0.0366174 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −36.9338 | −1.81960 | ||||||||
\(413\) | 27.9532 | 1.37549 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.1248 | −0.889710 | ||||||||
\(416\) | −8.78495 | −0.430718 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −27.0345 | −1.32072 | −0.660360 | − | 0.750949i | \(-0.729596\pi\) | ||||
−0.660360 | + | 0.750949i | \(0.729596\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.4315 | 1.62935 | 0.814675 | − | 0.579918i | \(-0.196915\pi\) | ||||
0.814675 | + | 0.579918i | \(0.196915\pi\) | |||||||
\(422\) | −2.81152 | −0.136863 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 12.8889 | 0.625941 | ||||||||
\(425\) | −14.8947 | −0.722497 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.23912 | −0.108359 | ||||||||
\(428\) | −2.40739 | −0.116366 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.86045 | −0.186168 | ||||||||
\(431\) | 12.1157 | 0.583594 | 0.291797 | − | 0.956480i | \(-0.405747\pi\) | ||||
0.291797 | + | 0.956480i | \(0.405747\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.1021 | 0.869930 | 0.434965 | − | 0.900447i | \(-0.356761\pi\) | ||||
0.434965 | + | 0.900447i | \(0.356761\pi\) | |||||||
\(434\) | 1.66019 | 0.0796917 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.32287 | 0.111245 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.2495 | 0.632365 | 0.316183 | − | 0.948698i | \(-0.397599\pi\) | ||||
0.316183 | + | 0.948698i | \(0.397599\pi\) | |||||||
\(440\) | −0.302060 | −0.0144002 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.96690 | −0.283816 | ||||||||
\(443\) | 38.0553 | 1.80806 | 0.904031 | − | 0.427468i | \(-0.140594\pi\) | ||||
0.904031 | + | 0.427468i | \(0.140594\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.3639 | −0.633509 | ||||||||
\(446\) | 2.43723 | 0.115406 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.1923 | −1.00124 | ||||||||
\(449\) | 33.0837 | 1.56132 | 0.780659 | − | 0.624957i | \(-0.214883\pi\) | ||||
0.780659 | + | 0.624957i | \(0.214883\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.320380 | 0.0150861 | ||||||||
\(452\) | 11.2391 | 0.528644 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 5.43147 | 0.254912 | ||||||||
\(455\) | 17.8285 | 0.835811 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −22.9475 | −1.07344 | −0.536719 | − | 0.843761i | \(-0.680336\pi\) | ||||
−0.536719 | + | 0.843761i | \(0.680336\pi\) | |||||||
\(458\) | −3.32287 | −0.155267 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −11.2301 | −0.523606 | ||||||||
\(461\) | 7.33981 | 0.341849 | 0.170925 | − | 0.985284i | \(-0.445325\pi\) | ||||
0.170925 | + | 0.985284i | \(0.445325\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.6979 | −0.868967 | −0.434483 | − | 0.900680i | \(-0.643069\pi\) | ||||
−0.434483 | + | 0.900680i | \(0.643069\pi\) | |||||||
\(464\) | −34.7303 | −1.61231 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.56991 | −0.304345 | ||||||||
\(467\) | 23.0071 | 1.06464 | 0.532322 | − | 0.846542i | \(-0.321320\pi\) | ||||
0.532322 | + | 0.846542i | \(0.321320\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 20.2930 | 0.937045 | ||||||||
\(470\) | −3.78960 | −0.174801 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.28263 | 0.381239 | ||||||||
\(473\) | −1.66811 | −0.0766996 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −48.4796 | −2.22206 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.41642 | −0.202002 | ||||||||
\(479\) | −20.0482 | −0.916023 | −0.458012 | − | 0.888946i | \(-0.651438\pi\) | ||||
−0.458012 | + | 0.888946i | \(0.651438\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20.4315 | 0.931595 | ||||||||
\(482\) | −4.57318 | −0.208302 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.3067 | 0.968487 | ||||||||
\(485\) | −1.38221 | −0.0627627 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −3.47033 | −0.157256 | −0.0786278 | − | 0.996904i | \(-0.525054\pi\) | ||||
−0.0786278 | + | 0.996904i | \(0.525054\pi\) | |||||||
\(488\) | −0.663459 | −0.0300334 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.31573 | −0.0594388 | ||||||||
\(491\) | −26.7278 | −1.20621 | −0.603104 | − | 0.797663i | \(-0.706070\pi\) | ||||
−0.603104 | + | 0.797663i | \(0.706070\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −74.4113 | −3.35131 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.98633 | −0.358597 | ||||||||
\(497\) | 10.2632 | 0.460367 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −21.5322 | −0.963912 | −0.481956 | − | 0.876195i | \(-0.660073\pi\) | ||||
−0.481956 | + | 0.876195i | \(0.660073\pi\) | |||||||
\(500\) | 23.6030 | 1.05556 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.72202 | 0.210754 | ||||||||
\(503\) | 22.7220 | 1.01312 | 0.506562 | − | 0.862203i | \(-0.330916\pi\) | ||||
0.506562 | + | 0.862203i | \(0.330916\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.40164 | −0.240370 | ||||||||
\(506\) | 0.142817 | 0.00634899 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 23.7141 | 1.05214 | ||||||||
\(509\) | −18.1431 | −0.804178 | −0.402089 | − | 0.915601i | \(-0.631716\pi\) | ||||
−0.402089 | + | 0.915601i | \(0.631716\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −21.9097 | −0.969229 | ||||||||
\(512\) | −17.0071 | −0.751616 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.93817 | −0.173705 | ||||||||
\(515\) | 33.4750 | 1.47508 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.63749 | −0.0720167 | ||||||||
\(518\) | −4.88564 | −0.214663 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.28263 | 0.231659 | ||||||||
\(521\) | 3.27223 | 0.143359 | 0.0716794 | − | 0.997428i | \(-0.477164\pi\) | ||||
0.0716794 | + | 0.997428i | \(0.477164\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.88237 | −0.344672 | −0.172336 | − | 0.985038i | \(-0.555131\pi\) | ||||
−0.172336 | + | 0.985038i | \(0.555131\pi\) | |||||||
\(524\) | −14.5868 | −0.637229 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.64979 | −0.202740 | ||||||||
\(527\) | −17.1111 | −0.745371 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12.2243 | −0.531493 | ||||||||
\(530\) | −5.75623 | −0.250035 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.60301 | −0.242693 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.18194 | 0.0943336 | ||||||||
\(536\) | 6.01289 | 0.259717 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 3.38469 | 0.145925 | ||||||||
\(539\) | −0.568530 | −0.0244883 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.2164 | 0.568218 | 0.284109 | − | 0.958792i | \(-0.408302\pi\) | ||||
0.284109 | + | 0.958792i | \(0.408302\pi\) | |||||||
\(542\) | −1.13706 | −0.0488409 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −21.6512 | −0.928286 | ||||||||
\(545\) | −2.10533 | −0.0901826 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −41.2405 | −1.76332 | −0.881658 | − | 0.471889i | \(-0.843572\pi\) | ||||
−0.881658 | + | 0.471889i | \(0.843572\pi\) | |||||||
\(548\) | 23.7518 | 1.01463 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.0826332 | −0.00352349 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.13844 | 0.133460 | ||||||||
\(554\) | 6.09415 | 0.258916 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8.56277 | −0.363142 | ||||||||
\(557\) | 25.1891 | 1.06730 | 0.533648 | − | 0.845707i | \(-0.320821\pi\) | ||||
0.533648 | + | 0.845707i | \(0.320821\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 29.1729 | 1.23388 | ||||||||
\(560\) | 20.5081 | 0.866625 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7.22296 | −0.304682 | ||||||||
\(563\) | 6.45666 | 0.272116 | 0.136058 | − | 0.990701i | \(-0.456557\pi\) | ||||
0.136058 | + | 0.990701i | \(0.456557\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.1866 | −0.428553 | ||||||||
\(566\) | 3.77782 | 0.158794 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.04102 | 0.127598 | ||||||||
\(569\) | 17.4315 | 0.730765 | 0.365383 | − | 0.930857i | \(-0.380938\pi\) | ||||
0.365383 | + | 0.930857i | \(0.380938\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.45882 | −0.0610496 | −0.0305248 | − | 0.999534i | \(-0.509718\pi\) | ||||
−0.0305248 | + | 0.999534i | \(0.509718\pi\) | |||||||
\(572\) | 1.12476 | 0.0470287 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.33981 | 0.0559226 | ||||||||
\(575\) | −6.23474 | −0.260007 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.83173 | −0.0762559 | −0.0381280 | − | 0.999273i | \(-0.512139\pi\) | ||||
−0.0381280 | + | 0.999273i | \(0.512139\pi\) | |||||||
\(578\) | −10.6408 | −0.442597 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 32.4613 | 1.34788 | ||||||||
\(581\) | −32.7518 | −1.35878 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.48727 | −0.103012 | ||||||||
\(584\) | −6.49192 | −0.268638 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −6.51927 | −0.269308 | ||||||||
\(587\) | 14.1715 | 0.584922 | 0.292461 | − | 0.956277i | \(-0.405526\pi\) | ||||
0.292461 | + | 0.956277i | \(0.405526\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −3.69905 | −0.152288 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 23.5023 | 0.965940 | ||||||||
\(593\) | 1.11436 | 0.0457613 | 0.0228806 | − | 0.999738i | \(-0.492716\pi\) | ||||
0.0228806 | + | 0.999738i | \(0.492716\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 43.9396 | 1.80135 | ||||||||
\(596\) | 4.76801 | 0.195305 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.49768 | −0.102138 | ||||||||
\(599\) | 29.9773 | 1.22484 | 0.612420 | − | 0.790533i | \(-0.290196\pi\) | ||||
0.612420 | + | 0.790533i | \(0.290196\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.36062 | −0.0962916 | −0.0481458 | − | 0.998840i | \(-0.515331\pi\) | ||||
−0.0481458 | + | 0.998840i | \(0.515331\pi\) | |||||||
\(602\) | −6.97592 | −0.284317 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 37.9097 | 1.54252 | ||||||||
\(605\) | −19.3114 | −0.785118 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 34.4224 | 1.39716 | 0.698582 | − | 0.715530i | \(-0.253815\pi\) | ||||
0.698582 | + | 0.715530i | \(0.253815\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.296303 | 0.0119970 | ||||||||
\(611\) | 28.6375 | 1.15855 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.1144 | −0.650853 | −0.325426 | − | 0.945567i | \(-0.605508\pi\) | ||||
−0.325426 | + | 0.945567i | \(0.605508\pi\) | |||||||
\(614\) | 7.06045 | 0.284937 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −0.545830 | −0.0219921 | ||||||||
\(617\) | 24.4451 | 0.984124 | 0.492062 | − | 0.870560i | \(-0.336243\pi\) | ||||
0.492062 | + | 0.870560i | \(0.336243\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.8720 | 1.03988 | 0.519941 | − | 0.854202i | \(-0.325954\pi\) | ||||
0.519941 | + | 0.854202i | \(0.325954\pi\) | |||||||
\(620\) | 7.46457 | 0.299784 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.26896 | −0.171170 | ||||||||
\(623\) | −24.1488 | −0.967503 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −11.8960 | −0.475842 | ||||||||
\(626\) | 0.710831 | 0.0284105 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 30.1119 | 1.20159 | ||||||||
\(629\) | 50.3549 | 2.00778 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7.74393 | −0.308281 | −0.154141 | − | 0.988049i | \(-0.549261\pi\) | ||||
−0.154141 | + | 0.988049i | \(0.549261\pi\) | |||||||
\(632\) | 0.929929 | 0.0369906 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.10396 | 0.162989 | ||||||||
\(635\) | −21.4933 | −0.852935 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.94282 | 0.393949 | ||||||||
\(638\) | −0.412822 | −0.0163438 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.5275 | 0.495193 | ||||||||
\(641\) | −1.14419 | −0.0451929 | −0.0225965 | − | 0.999745i | \(-0.507193\pi\) | ||||
−0.0225965 | + | 0.999745i | \(0.507193\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −24.0572 | −0.948723 | −0.474361 | − | 0.880330i | \(-0.657321\pi\) | ||||
−0.474361 | + | 0.880330i | \(0.657321\pi\) | |||||||
\(644\) | −20.2930 | −0.799658 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.47360 | 0.136561 | 0.0682807 | − | 0.997666i | \(-0.478249\pi\) | ||||
0.0682807 | + | 0.997666i | \(0.478249\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.59836 | −0.0627413 | ||||||||
\(650\) | 1.44514 | 0.0566832 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −25.7212 | −1.00732 | ||||||||
\(653\) | −13.1923 | −0.516256 | −0.258128 | − | 0.966111i | \(-0.583106\pi\) | ||||
−0.258128 | + | 0.966111i | \(0.583106\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 13.2208 | 0.516580 | ||||||||
\(656\) | −6.44514 | −0.251641 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −6.84789 | −0.266959 | ||||||||
\(659\) | −2.42682 | −0.0945356 | −0.0472678 | − | 0.998882i | \(-0.515051\pi\) | ||||
−0.0472678 | + | 0.998882i | \(0.515051\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.32038 | 0.362521 | 0.181260 | − | 0.983435i | \(-0.441982\pi\) | ||||
0.181260 | + | 0.983435i | \(0.441982\pi\) | |||||||
\(662\) | 5.73104 | 0.222743 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −9.70448 | −0.376607 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.1477 | −1.20604 | ||||||||
\(668\) | 6.24626 | 0.241675 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2.68538 | −0.103745 | ||||||||
\(671\) | 0.128033 | 0.00494266 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −35.0826 | −1.35234 | −0.676168 | − | 0.736747i | \(-0.736361\pi\) | ||||
−0.676168 | + | 0.736747i | \(0.736361\pi\) | |||||||
\(674\) | −1.80249 | −0.0694293 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 5.58607 | 0.214849 | ||||||||
\(677\) | −16.2416 | −0.624216 | −0.312108 | − | 0.950047i | \(-0.601035\pi\) | ||||
−0.312108 | + | 0.950047i | \(0.601035\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.49768 | −0.0958520 | ||||||||
\(680\) | 13.0194 | 0.499272 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.0949296 | −0.00363504 | ||||||||
\(683\) | 33.1672 | 1.26911 | 0.634553 | − | 0.772879i | \(-0.281184\pi\) | ||||
0.634553 | + | 0.772879i | \(0.281184\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −21.5275 | −0.822524 | ||||||||
\(686\) | 2.94858 | 0.112577 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 33.5576 | 1.27937 | ||||||||
\(689\) | 43.4991 | 1.65718 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.9773 | −0.607805 | −0.303903 | − | 0.952703i | \(-0.598290\pi\) | ||||
−0.303903 | + | 0.952703i | \(0.598290\pi\) | |||||||
\(692\) | −21.3445 | −0.811394 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −1.86235 | −0.0706937 | ||||||||
\(695\) | 7.76088 | 0.294387 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.8090 | −0.523054 | ||||||||
\(698\) | 3.82924 | 0.144939 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 11.7414 | 0.443785 | ||||||||
\(701\) | 50.1398 | 1.89375 | 0.946877 | − | 0.321595i | \(-0.104219\pi\) | ||||
0.946877 | + | 0.321595i | \(0.104219\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.21178 | 0.0456706 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5.21505 | −0.196271 | ||||||||
\(707\) | −9.76088 | −0.367096 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −40.2873 | −1.51302 | −0.756510 | − | 0.653982i | \(-0.773097\pi\) | ||||
−0.756510 | + | 0.653982i | \(0.773097\pi\) | |||||||
\(710\) | −1.35813 | −0.0509697 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −7.15538 | −0.268159 | ||||||||
\(713\) | −7.16251 | −0.268238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.01943 | −0.0381245 | ||||||||
\(716\) | 7.02656 | 0.262595 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −3.34635 | −0.124885 | ||||||||
\(719\) | 6.19562 | 0.231058 | 0.115529 | − | 0.993304i | \(-0.463144\pi\) | ||||
0.115529 | + | 0.993304i | \(0.463144\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 60.4900 | 2.25277 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6.57318 | 0.244290 | ||||||||
\(725\) | 18.0219 | 0.669317 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 38.1157 | 1.41363 | 0.706817 | − | 0.707396i | \(-0.250130\pi\) | ||||
0.706817 | + | 0.707396i | \(0.250130\pi\) | |||||||
\(728\) | 9.54583 | 0.353792 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.89931 | 0.107308 | ||||||||
\(731\) | 71.8988 | 2.65927 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 23.6602 | 0.873909 | 0.436955 | − | 0.899484i | \(-0.356057\pi\) | ||||
0.436955 | + | 0.899484i | \(0.356057\pi\) | |||||||
\(734\) | 6.84678 | 0.252719 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9.06294 | −0.334064 | ||||||||
\(737\) | −1.16035 | −0.0427422 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.02735 | −0.0377915 | −0.0188958 | − | 0.999821i | \(-0.506015\pi\) | ||||
−0.0188958 | + | 0.999821i | \(0.506015\pi\) | |||||||
\(740\) | −21.9669 | −0.807519 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.4016 | −0.381856 | ||||||||
\(743\) | 1.74720 | 0.0640987 | 0.0320493 | − | 0.999486i | \(-0.489797\pi\) | ||||
0.0320493 | + | 0.999486i | \(0.489797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.32149 | −0.158327 | ||||||||
\(746\) | −4.11763 | −0.150757 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.77206 | 0.101357 | ||||||||
\(749\) | 3.94282 | 0.144068 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.9636 | −0.947426 | −0.473713 | − | 0.880679i | \(-0.657087\pi\) | ||||
−0.473713 | + | 0.880679i | \(0.657087\pi\) | |||||||
\(752\) | 32.9417 | 1.20126 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.21969 | 0.262926 | ||||||||
\(755\) | −34.3595 | −1.25047 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 27.3789 | 0.995104 | 0.497552 | − | 0.867434i | \(-0.334232\pi\) | ||||
0.497552 | + | 0.867434i | \(0.334232\pi\) | |||||||
\(758\) | 2.15460 | 0.0782585 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 34.9748 | 1.26784 | 0.633918 | − | 0.773400i | \(-0.281446\pi\) | ||||
0.633918 | + | 0.773400i | \(0.281446\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.80438 | −0.137728 | ||||||||
\(764\) | 21.5868 | 0.780985 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.86948 | 0.175941 | ||||||||
\(767\) | 27.9532 | 1.00933 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −30.7817 | −1.11002 | −0.555008 | − | 0.831845i | \(-0.687285\pi\) | ||||
−0.555008 | + | 0.831845i | \(0.687285\pi\) | |||||||
\(770\) | 0.243770 | 0.00878484 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.6602 | 0.527632 | ||||||||
\(773\) | −25.2553 | −0.908369 | −0.454185 | − | 0.890908i | \(-0.650069\pi\) | ||||
−0.454185 | + | 0.890908i | \(0.650069\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.14419 | 0.148864 | ||||||||
\(776\) | −0.740070 | −0.0265670 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.42296 | 0.0868673 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.586849 | −0.0209991 | ||||||||
\(782\) | −6.15571 | −0.220128 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 11.4372 | 0.408472 | ||||||||
\(785\) | −27.2919 | −0.974090 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12.2301 | −0.435956 | −0.217978 | − | 0.975954i | \(-0.569946\pi\) | ||||
−0.217978 | + | 0.975954i | \(0.569946\pi\) | |||||||
\(788\) | 24.0941 | 0.858318 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.415309 | −0.0147760 | ||||||||
\(791\) | −18.4074 | −0.654492 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.23912 | −0.0795136 | ||||||||
\(794\) | −7.25142 | −0.257343 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 36.7116 | 1.30121 | ||||||||
\(797\) | −48.6616 | −1.72368 | −0.861841 | − | 0.507179i | \(-0.830688\pi\) | ||||
−0.861841 | + | 0.507179i | \(0.830688\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 70.5792 | 2.49691 | ||||||||
\(800\) | 5.24377 | 0.185395 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.55375 | −0.266732 | ||||||||
\(803\) | 1.25280 | 0.0442102 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.3926 | 0.648254 | ||||||||
\(806\) | 1.66019 | 0.0584777 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −2.89218 | −0.101747 | ||||||||
\(809\) | −30.8389 | −1.08424 | −0.542118 | − | 0.840302i | \(-0.682378\pi\) | ||||
−0.542118 | + | 0.840302i | \(0.682378\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.9877 | 0.772093 | 0.386046 | − | 0.922479i | \(-0.373840\pi\) | ||||
0.386046 | + | 0.922479i | \(0.373840\pi\) | |||||||
\(812\) | 58.6583 | 2.05850 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.279361 | 0.00979158 | ||||||||
\(815\) | 23.3125 | 0.816600 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 7.80000 | 0.272721 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 6.02408 | 0.210370 | ||||||||
\(821\) | 28.7680 | 1.00401 | 0.502005 | − | 0.864865i | \(-0.332596\pi\) | ||||
0.502005 | + | 0.864865i | \(0.332596\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.6224 | −0.509706 | −0.254853 | − | 0.966980i | \(-0.582027\pi\) | ||||
−0.254853 | + | 0.966980i | \(0.582027\pi\) | |||||||
\(824\) | 17.9234 | 0.624391 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.68427 | −0.232575 | ||||||||
\(827\) | 19.9097 | 0.692329 | 0.346164 | − | 0.938174i | \(-0.387484\pi\) | ||||
0.346164 | + | 0.938174i | \(0.387484\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 52.2725 | 1.81550 | 0.907749 | − | 0.419513i | \(-0.137799\pi\) | ||||
0.907749 | + | 0.419513i | \(0.137799\pi\) | |||||||
\(830\) | 4.33405 | 0.150437 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −21.1923 | −0.734712 | ||||||||
\(833\) | 24.5048 | 0.849041 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.66130 | −0.195917 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.46457 | 0.223315 | ||||||||
\(839\) | −35.3905 | −1.22181 | −0.610907 | − | 0.791702i | \(-0.709195\pi\) | ||||
−0.610907 | + | 0.791702i | \(0.709195\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 61.0345 | 2.10464 | ||||||||
\(842\) | −7.99424 | −0.275500 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22.8429 | −0.786286 | ||||||||
\(845\) | −5.06294 | −0.174170 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −34.8960 | −1.19904 | ||||||||
\(848\) | 50.0370 | 1.71828 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.56166 | 0.122164 | ||||||||
\(851\) | 21.0780 | 0.722544 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.31711 | −0.216294 | −0.108147 | − | 0.994135i | \(-0.534492\pi\) | ||||
−0.108147 | + | 0.994135i | \(0.534492\pi\) | |||||||
\(854\) | 0.535426 | 0.0183219 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.16827 | 0.0399307 | ||||||||
\(857\) | −20.3218 | −0.694178 | −0.347089 | − | 0.937832i | \(-0.612830\pi\) | ||||
−0.347089 | + | 0.937832i | \(0.612830\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −18.5516 | −0.632972 | −0.316486 | − | 0.948597i | \(-0.602503\pi\) | ||||
−0.316486 | + | 0.948597i | \(0.602503\pi\) | |||||||
\(860\) | −31.3653 | −1.06955 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.89715 | −0.0986775 | ||||||||
\(863\) | −14.5814 | −0.496357 | −0.248179 | − | 0.968714i | \(-0.579832\pi\) | ||||
−0.248179 | + | 0.968714i | \(0.579832\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.3456 | 0.657769 | ||||||||
\(866\) | −4.32862 | −0.147093 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 13.4887 | 0.457835 | ||||||||
\(869\) | −0.179456 | −0.00608761 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20.2930 | 0.687603 | ||||||||
\(872\) | −1.12725 | −0.0381735 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.6569 | −1.30684 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.3639 | 0.653872 | 0.326936 | − | 0.945046i | \(-0.393984\pi\) | ||||
0.326936 | + | 0.945046i | \(0.393984\pi\) | |||||||
\(878\) | −3.16827 | −0.106924 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.17265 | −0.0395301 | ||||||||
\(881\) | −19.3138 | −0.650700 | −0.325350 | − | 0.945594i | \(-0.605482\pi\) | ||||
−0.325350 | + | 0.945594i | \(0.605482\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.5757 | −0.557816 | −0.278908 | − | 0.960318i | \(-0.589972\pi\) | ||||
−0.278908 | + | 0.960318i | \(0.589972\pi\) | |||||||
\(884\) | −48.4796 | −1.63055 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.09991 | −0.305717 | ||||||||
\(887\) | −22.2391 | −0.746717 | −0.373358 | − | 0.927687i | \(-0.621794\pi\) | ||||
−0.373358 | + | 0.927687i | \(0.621794\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.8389 | −1.30261 | ||||||||
\(890\) | 3.19562 | 0.107117 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 19.8019 | 0.663017 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.36853 | −0.212877 | ||||||||
\(896\) | 22.6375 | 0.756265 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −7.91109 | −0.263997 | ||||||||
\(899\) | 20.7037 | 0.690507 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 107.207 | 3.57157 | ||||||||
\(902\) | −0.0766103 | −0.00255084 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.45417 | −0.181403 | ||||||||
\(905\) | −5.95760 | −0.198037 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.1067 | 1.03288 | 0.516441 | − | 0.856323i | \(-0.327257\pi\) | ||||
0.516441 | + | 0.856323i | \(0.327257\pi\) | |||||||
\(908\) | 44.1294 | 1.46449 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.26320 | −0.141324 | ||||||||
\(911\) | 30.2085 | 1.00085 | 0.500426 | − | 0.865779i | \(-0.333177\pi\) | ||||
0.500426 | + | 0.865779i | \(0.333177\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.87275 | 0.0619789 | ||||||||
\(914\) | 5.48727 | 0.181503 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −26.9975 | −0.892023 | ||||||||
\(917\) | 23.8903 | 0.788927 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 33.7141 | 1.11213 | 0.556063 | − | 0.831140i | \(-0.312311\pi\) | ||||
0.556063 | + | 0.831140i | \(0.312311\pi\) | |||||||
\(920\) | 5.44979 | 0.179674 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.75512 | −0.0578018 | ||||||||
\(923\) | 10.2632 | 0.337817 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −12.1956 | −0.400989 | ||||||||
\(926\) | 4.47111 | 0.146930 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 26.1970 | 0.859958 | ||||||||
\(929\) | −14.7921 | −0.485313 | −0.242656 | − | 0.970112i | \(-0.578019\pi\) | ||||
−0.242656 | + | 0.970112i | \(0.578019\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −53.3789 | −1.74849 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.50154 | −0.180016 | ||||||||
\(935\) | −2.51246 | −0.0821663 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.7083 | 1.32988 | 0.664942 | − | 0.746895i | \(-0.268456\pi\) | ||||
0.664942 | + | 0.746895i | \(0.268456\pi\) | |||||||
\(938\) | −4.85254 | −0.158441 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −30.7896 | −1.00425 | ||||||||
\(941\) | −40.4009 | −1.31703 | −0.658515 | − | 0.752568i | \(-0.728815\pi\) | ||||
−0.658515 | + | 0.752568i | \(0.728815\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.78031 | −0.188233 | ||||||||
\(944\) | 32.1546 | 1.04654 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.398883 | 0.0129688 | ||||||||
\(947\) | −32.5770 | −1.05861 | −0.529306 | − | 0.848431i | \(-0.677548\pi\) | ||||
−0.529306 | + | 0.848431i | \(0.677548\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −21.9097 | −0.711219 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 23.5264 | 0.762495 | ||||||||
\(953\) | 3.62571 | 0.117448 | 0.0587241 | − | 0.998274i | \(-0.481297\pi\) | ||||
0.0587241 | + | 0.998274i | \(0.481297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −19.5653 | −0.633117 | ||||||||
\(956\) | −35.8824 | −1.16052 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.79398 | 0.154886 | ||||||||
\(959\) | −38.9007 | −1.25617 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.2391 | −0.846423 | ||||||||
\(962\) | −4.88564 | −0.157519 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −37.1560 | −1.19671 | ||||||||
\(965\) | −13.2873 | −0.427733 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.6375 | 0.663657 | 0.331828 | − | 0.943340i | \(-0.392334\pi\) | ||||
0.331828 | + | 0.943340i | \(0.392334\pi\) | |||||||
\(968\) | −10.3398 | −0.332334 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.330518 | 0.0106123 | ||||||||
\(971\) | 12.4692 | 0.400156 | 0.200078 | − | 0.979780i | \(-0.435880\pi\) | ||||
0.200078 | + | 0.979780i | \(0.435880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.0241 | 0.449591 | ||||||||
\(974\) | 0.829837 | 0.0265897 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.57566 | −0.0824450 | ||||||||
\(977\) | 35.9007 | 1.14856 | 0.574282 | − | 0.818657i | \(-0.305281\pi\) | ||||
0.574282 | + | 0.818657i | \(0.305281\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.38083 | 0.0441315 | ||||||||
\(980\) | −10.6900 | −0.341480 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.39123 | 0.203952 | ||||||||
\(983\) | −46.8993 | −1.49586 | −0.747928 | − | 0.663780i | \(-0.768951\pi\) | ||||
−0.747928 | + | 0.663780i | \(0.768951\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.8378 | −0.695809 | ||||||||
\(986\) | 17.7935 | 0.566659 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.0960 | 0.956998 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −57.9467 | −1.84074 | −0.920369 | − | 0.391052i | \(-0.872111\pi\) | ||||
−0.920369 | + | 0.391052i | \(0.872111\pi\) | |||||||
\(992\) | 6.02408 | 0.191265 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.45417 | −0.0778415 | ||||||||
\(995\) | −33.2736 | −1.05484 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 41.2646 | 1.30686 | 0.653431 | − | 0.756986i | \(-0.273329\pi\) | ||||
0.653431 | + | 0.756986i | \(0.273329\pi\) | |||||||
\(998\) | 5.14884 | 0.162984 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 9747.2.a.x.1.2 | 3 | ||
3.2 | odd | 2 | 9747.2.a.ba.1.2 | 3 | |||
19.18 | odd | 2 | 513.2.a.f.1.2 | yes | 3 | ||
57.56 | even | 2 | 513.2.a.e.1.2 | ✓ | 3 | ||
76.75 | even | 2 | 8208.2.a.bp.1.2 | 3 | |||
228.227 | odd | 2 | 8208.2.a.bf.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
513.2.a.e.1.2 | ✓ | 3 | 57.56 | even | 2 | ||
513.2.a.f.1.2 | yes | 3 | 19.18 | odd | 2 | ||
8208.2.a.bf.1.2 | 3 | 228.227 | odd | 2 | |||
8208.2.a.bp.1.2 | 3 | 76.75 | even | 2 | |||
9747.2.a.x.1.2 | 3 | 1.1 | even | 1 | trivial | ||
9747.2.a.ba.1.2 | 3 | 3.2 | odd | 2 |