Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [513,2,Mod(1,513)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(513, 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("513.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 513 = 3^{3} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 513.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: | \(4.09632562369\) |
Analytic rank: | \(1\) |
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: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.239123\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 513.1 |
$q$-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 | \(-0.628820\pi\) | ||||
−0.393744 | + | 0.919220i | \(0.628820\pi\) | |||||||
\(6\) | 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 | \(-0.491268\pi\) | ||||
0.0274290 | + | 0.999624i | \(0.491268\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.18194 | −0.882512 | −0.441256 | − | 0.897381i | \(-0.645467\pi\) | ||||
−0.441256 | + | 0.897381i | \(0.645467\pi\) | |||||||
\(14\) | −0.760877 | −0.203353 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.66019 | 0.915047 | ||||||||
\(17\) | −7.84213 | −1.90200 | −0.950998 | − | 0.309196i | \(-0.899940\pi\) | ||||
−0.950998 | + | 0.309196i | \(0.899940\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 3.42107 | 0.764974 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.0435069 | −0.00927570 | ||||||||
\(23\) | −3.28263 | −0.684476 | −0.342238 | − | 0.939613i | \(-0.611185\pi\) | ||||
−0.342238 | + | 0.939613i | \(0.611185\pi\) | |||||||
\(24\) | 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 | \(-0.437223\pi\) | ||||
0.195944 | + | 0.980615i | \(0.437223\pi\) | |||||||
\(32\) | −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 | \(-0.676986\pi\) | ||||
−0.527808 | + | 0.849363i | \(0.676986\pi\) | |||||||
\(38\) | 0.239123 | 0.0387909 | ||||||||
\(39\) | 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 | \(-0.727918\pi\) | ||||
−0.656392 | + | 0.754420i | \(0.727918\pi\) | |||||||
\(48\) | 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 | \(-0.627377\pi\) | ||||
−0.389571 | + | 0.920996i | \(0.627377\pi\) | |||||||
\(68\) | 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 | ||||||||
\(76\) | 1.94282 | 0.222857 | ||||||||
\(77\) | 0.578933 | 0.0659756 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.986327 | −0.110970 | −0.0554852 | − | 0.998460i | \(-0.517671\pi\) | ||||
−0.0554852 | + | 0.998460i | \(0.517671\pi\) | |||||||
\(80\) | −6.44514 | −0.720589 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.421067 | 0.0464990 | ||||||||
\(83\) | 10.2930 | 1.12981 | 0.564904 | − | 0.825157i | \(-0.308913\pi\) | ||||
0.564904 | + | 0.825157i | \(0.308913\pi\) | |||||||
\(84\) | 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 | ||||||||
\(95\) | 1.76088 | 0.180662 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.784953 | 0.0796999 | 0.0398500 | − | 0.999206i | \(-0.487312\pi\) | ||||
0.0398500 | + | 0.999206i | \(0.487312\pi\) | |||||||
\(98\) | −0.747204 | −0.0754790 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.69002 | 0.369002 | ||||||||
\(101\) | 3.06758 | 0.305236 | 0.152618 | − | 0.988285i | \(-0.451230\pi\) | ||||
0.152618 | + | 0.988285i | \(0.451230\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −19.0104 | −1.87315 | −0.936575 | − | 0.350466i | \(-0.886023\pi\) | ||||
−0.936575 | + | 0.350466i | \(0.886023\pi\) | |||||||
\(104\) | −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 | \(-0.481764\pi\) | ||||
0.0572596 | + | 0.998359i | \(0.481764\pi\) | |||||||
\(110\) | 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 | \(-0.317836\pi\) | ||||
0.541555 | + | 0.840666i | \(0.317836\pi\) | |||||||
\(128\) | 7.11436 | 0.628827 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.33981 | −0.117509 | ||||||||
\(131\) | −7.50808 | −0.655984 | −0.327992 | − | 0.944680i | \(-0.606372\pi\) | ||||
−0.327992 | + | 0.944680i | \(0.606372\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.18194 | −0.275909 | ||||||||
\(134\) | 1.52502 | 0.131742 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.39372 | −0.634006 | ||||||||
\(137\) | 12.2255 | 1.04449 | 0.522245 | − | 0.852795i | \(-0.325095\pi\) | ||||
0.522245 | + | 0.852795i | \(0.325095\pi\) | |||||||
\(138\) | 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 | \(-0.467947\pi\) | ||||
0.100527 | + | 0.994934i | \(0.467947\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 19.5127 | 1.58792 | 0.793962 | − | 0.607968i | \(-0.208015\pi\) | ||||
0.793962 | + | 0.607968i | \(0.208015\pi\) | |||||||
\(152\) | −0.942820 | −0.0764728 | ||||||||
\(153\) | 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 | \(-0.459869\pi\) | ||||
0.125740 | + | 0.992063i | \(0.459869\pi\) | |||||||
\(182\) | 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 | ||||||||
\(190\) | −0.421067 | −0.0305474 | ||||||||
\(191\) | 11.1111 | 0.803970 | 0.401985 | − | 0.915646i | \(-0.368320\pi\) | ||||
0.401985 | + | 0.915646i | \(0.368320\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.54583 | 0.543161 | 0.271580 | − | 0.962416i | \(-0.412454\pi\) | ||||
0.271580 | + | 0.962416i | \(0.412454\pi\) | |||||||
\(194\) | −0.187701 | −0.0134761 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.07085 | −0.433632 | ||||||||
\(197\) | 12.4016 | 0.883580 | 0.441790 | − | 0.897118i | \(-0.354344\pi\) | ||||
0.441790 | + | 0.897118i | \(0.354344\pi\) | |||||||
\(198\) | 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 | ||||||||
\(209\) | −0.181943 | −0.0125853 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.7576 | −0.809427 | −0.404714 | − | 0.914444i | \(-0.632629\pi\) | ||||
−0.404714 | + | 0.914444i | \(0.632629\pi\) | |||||||
\(212\) | −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 | \(-0.389145\pi\) | ||||
0.341265 | + | 0.939967i | \(0.389145\pi\) | |||||||
\(224\) | −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 | \(-0.856414\pi\) | ||||
−0.899973 | + | 0.435946i | \(0.856414\pi\) | |||||||
\(234\) | 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 | \(-0.703775\pi\) | ||||
−0.597337 | + | 0.801990i | \(0.703775\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.1248 | −1.23193 | −0.615967 | − | 0.787772i | \(-0.711235\pi\) | ||||
−0.615967 | + | 0.787772i | \(0.711235\pi\) | |||||||
\(242\) | 2.62244 | 0.168577 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.36716 | 0.0875232 | ||||||||
\(245\) | −5.50232 | −0.351531 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.18194 | 0.202462 | ||||||||
\(248\) | 2.05718 | 0.130631 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2.90507 | −0.183733 | ||||||||
\(251\) | 19.7472 | 1.24643 | 0.623216 | − | 0.782050i | \(-0.285826\pi\) | ||||
0.623216 | + | 0.782050i | \(0.285826\pi\) | |||||||
\(252\) | 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 | \(-0.704642\pi\) | ||||
−0.599519 | + | 0.800360i | \(0.704642\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −24.0722 | −1.47875 | ||||||||
\(266\) | 0.760877 | 0.0466523 | ||||||||
\(267\) | 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 | ||||||||
\(304\) | −3.66019 | −0.209926 | ||||||||
\(305\) | 1.23912 | 0.0709520 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 29.5264 | 1.68516 | 0.842580 | − | 0.538571i | \(-0.181036\pi\) | ||||
0.842580 | + | 0.538571i | \(0.181036\pi\) | |||||||
\(308\) | −1.12476 | −0.0640893 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.918743 | 0.0521811 | ||||||||
\(311\) | −17.8525 | −1.01232 | −0.506162 | − | 0.862438i | \(-0.668936\pi\) | ||||
−0.506162 | + | 0.862438i | \(0.668936\pi\) | |||||||
\(312\) | 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 | ||||||||
\(323\) | 7.84213 | 0.436348 | ||||||||
\(324\) | 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 | \(-0.271119\pi\) | ||||
0.658670 | + | 0.752432i | \(0.271119\pi\) | |||||||
\(332\) | −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 | \(-0.565820\pi\) | ||||
−0.205308 | + | 0.978697i | \(0.565820\pi\) | |||||||
\(338\) | 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 | \(-0.567036\pi\) | ||||
−0.209047 | + | 0.977906i | \(0.567036\pi\) | |||||||
\(348\) | 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 | \(-0.697099\pi\) | ||||
−0.580389 | + | 0.814340i | \(0.697099\pi\) | |||||||
\(354\) | 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 | \(-0.620400\pi\) | ||||
−0.369294 | + | 0.929313i | \(0.620400\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −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 | \(-0.647081\pi\) | ||||
−0.445801 | + | 0.895132i | \(0.647081\pi\) | |||||||
\(374\) | 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 | \(-0.425664\pi\) | ||||
0.231417 | + | 0.972855i | \(0.425664\pi\) | |||||||
\(380\) | −3.42107 | −0.175497 | ||||||||
\(381\) | 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 | \(-0.417308\pi\) | ||||
0.256874 | + | 0.966445i | \(0.417308\pi\) | |||||||
\(390\) | 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 | \(-0.201382\pi\) | ||||
0.806457 | + | 0.591293i | \(0.201382\pi\) | |||||||
\(410\) | −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 | ||||||||
\(418\) | 0.0435069 | 0.00212799 | ||||||||
\(419\) | 27.0345 | 1.32072 | 0.660360 | − | 0.750949i | \(-0.270404\pi\) | ||||
0.660360 | + | 0.750949i | \(0.270404\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −33.4315 | −1.62935 | −0.814675 | − | 0.579918i | \(-0.803085\pi\) | ||||
−0.814675 | + | 0.579918i | \(0.803085\pi\) | |||||||
\(422\) | 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 | \(-0.643239\pi\) | ||||
−0.434965 | + | 0.900447i | \(0.643239\pi\) | |||||||
\(434\) | −1.66019 | −0.0796917 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.32287 | −0.111245 | ||||||||
\(437\) | 3.28263 | 0.157029 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −13.2495 | −0.632365 | −0.316183 | − | 0.948698i | \(-0.602401\pi\) | ||||
−0.316183 | + | 0.948698i | \(0.602401\pi\) | |||||||
\(440\) | −0.302060 | −0.0144002 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.96690 | −0.283816 | ||||||||
\(443\) | −38.0553 | −1.80806 | −0.904031 | − | 0.427468i | \(-0.859406\pi\) | ||||
−0.904031 | + | 0.427468i | \(0.859406\pi\) | |||||||
\(444\) | 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 | \(-0.554675\pi\) | ||||
−0.170925 | + | 0.985284i | \(0.554675\pi\) | |||||||
\(462\) | 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 | \(-0.678680\pi\) | ||||
−0.532322 | + | 0.846542i | \(0.678680\pi\) | |||||||
\(468\) | 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 | ||||||||
\(475\) | 1.89931 | 0.0871465 | ||||||||
\(476\) | 48.4796 | 2.22206 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.41642 | 0.202002 | ||||||||
\(479\) | 20.0482 | 0.916023 | 0.458012 | − | 0.888946i | \(-0.348562\pi\) | ||||
0.458012 | + | 0.888946i | \(0.348562\pi\) | |||||||
\(480\) | 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 | \(-0.474946\pi\) | ||||
0.0786278 | + | 0.996904i | \(0.474946\pi\) | |||||||
\(488\) | −0.663459 | −0.0300334 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.31573 | 0.0594388 | ||||||||
\(491\) | 26.7278 | 1.20621 | 0.603104 | − | 0.797663i | \(-0.293930\pi\) | ||||
0.603104 | + | 0.797663i | \(0.293930\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 74.4113 | 3.35131 | ||||||||
\(494\) | −0.760877 | −0.0342335 | ||||||||
\(495\) | 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 | \(-0.669084\pi\) | ||||
−0.506562 | + | 0.862203i | \(0.669084\pi\) | |||||||
\(504\) | 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 | \(-0.444869\pi\) | ||||
0.172336 | + | 0.985038i | \(0.444869\pi\) | |||||||
\(524\) | 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 | ||||||||
\(532\) | 6.18194 | 0.268021 | ||||||||
\(533\) | 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 | \(-0.156428\pi\) | ||||
0.881658 | + | 0.471889i | \(0.156428\pi\) | |||||||
\(548\) | −23.7518 | −1.01463 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.0826332 | 0.00352349 | ||||||||
\(551\) | 9.48865 | 0.404230 | ||||||||
\(552\) | 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 | \(-0.679179\pi\) | ||||
−0.533648 | + | 0.845707i | \(0.679179\pi\) | |||||||
\(558\) | 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 | \(-0.594474\pi\) | ||||
−0.292461 | + | 0.956277i | \(0.594474\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.18194 | −0.0899054 | ||||||||
\(590\) | 3.69905 | 0.152288 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −23.5023 | −0.965940 | ||||||||
\(593\) | −1.11436 | −0.0457613 | −0.0228806 | − | 0.999738i | \(-0.507284\pi\) | ||||
−0.0228806 | + | 0.999738i | \(0.507284\pi\) | |||||||
\(594\) | 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 | \(-0.484669\pi\) | ||||
0.0481458 | + | 0.998840i | \(0.484669\pi\) | |||||||
\(602\) | −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 | \(-0.746185\pi\) | ||||
−0.698582 | + | 0.715530i | \(0.746185\pi\) | |||||||
\(608\) | 2.76088 | 0.111968 | ||||||||
\(609\) | 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 | \(-0.663757\pi\) | ||||
−0.492062 | + | 0.870560i | \(0.663757\pi\) | |||||||
\(618\) | 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 | ||||||||
\(646\) | −1.87524 | −0.0737802 | ||||||||
\(647\) | −3.47360 | −0.136561 | −0.0682807 | − | 0.997666i | \(-0.521751\pi\) | ||||
−0.0682807 | + | 0.997666i | \(0.521751\pi\) | |||||||
\(648\) | 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 | \(-0.416894\pi\) | ||||
0.258128 | + | 0.966111i | \(0.416894\pi\) | |||||||
\(654\) | 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 | \(-0.558018\pi\) | ||||
−0.181260 | + | 0.983435i | \(0.558018\pi\) | |||||||
\(662\) | −5.73104 | −0.222743 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 9.70448 | 0.376607 | ||||||||
\(665\) | 5.60301 | 0.217275 | ||||||||
\(666\) | 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 | \(-0.263639\pi\) | ||||
0.676168 | + | 0.736747i | \(0.263639\pi\) | |||||||
\(674\) | 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 | \(-0.895781\pi\) | ||||
−0.946877 | + | 0.321595i | \(0.895781\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 6.42107 | 0.242175 | ||||||||
\(704\) | −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 | \(-0.536856\pi\) | ||||
−0.115529 | + | 0.993304i | \(0.536856\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −60.4900 | −2.25277 | ||||||||
\(722\) | −0.239123 | −0.00889925 | ||||||||
\(723\) | 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 | \(-0.342913\pi\) | ||||
0.473713 | + | 0.880679i | \(0.342913\pi\) | |||||||
\(752\) | −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 | ||||||||
\(760\) | 1.66019 | 0.0602214 | ||||||||
\(761\) | −34.9748 | −1.26784 | −0.633918 | − | 0.773400i | \(-0.718554\pi\) | ||||
−0.633918 | + | 0.773400i | \(0.718554\pi\) | |||||||
\(762\) | 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 | ||||||||
\(779\) | 1.76088 | 0.0630900 | ||||||||
\(780\) | 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 | \(-0.430054\pi\) | ||||
0.217978 | + | 0.975954i | \(0.430054\pi\) | |||||||
\(788\) | −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 | \(-0.317622\pi\) | ||||
0.542118 | + | 0.840302i | \(0.317622\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.9877 | −0.772093 | −0.386046 | − | 0.922479i | \(-0.626160\pi\) | ||||
−0.386046 | + | 0.922479i | \(0.626160\pi\) | |||||||
\(812\) | 58.6583 | 2.05850 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.279361 | 0.00979158 | ||||||||
\(815\) | −23.3125 | −0.816600 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −9.16827 | −0.320757 | ||||||||
\(818\) | −7.80000 | −0.272721 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.02408 | −0.210370 | ||||||||
\(821\) | −28.7680 | −1.00401 | −0.502005 | − | 0.864865i | \(-0.667404\pi\) | ||||
−0.502005 | + | 0.864865i | \(0.667404\pi\) | |||||||
\(822\) | 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 | \(-0.862201\pi\) | ||||
−0.907749 | + | 0.419513i | \(0.862201\pi\) | |||||||
\(830\) | 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 | ||||||||
\(836\) | 0.353483 | 0.0122255 | ||||||||
\(837\) | 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 | ||||||||
\(874\) | −0.784953 | −0.0265514 | ||||||||
\(875\) | 38.6569 | 1.30684 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −19.3639 | −0.653872 | −0.326936 | − | 0.945046i | \(-0.606016\pi\) | ||||
−0.326936 | + | 0.945046i | \(0.606016\pi\) | |||||||
\(878\) | 3.16827 | 0.106924 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.17265 | −0.0395301 | ||||||||
\(881\) | 19.3138 | 0.650700 | 0.325350 | − | 0.945594i | \(-0.394518\pi\) | ||||
0.325350 | + | 0.945594i | \(0.394518\pi\) | |||||||
\(882\) | 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 | ||||||||
\(893\) | 9.00000 | 0.301174 | ||||||||
\(894\) | 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 | \(-0.672743\pi\) | ||||
−0.516441 | + | 0.856323i | \(0.672743\pi\) | |||||||
\(908\) | 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 | \(-0.421981\pi\) | ||||
0.242656 | + | 0.970112i | \(0.421981\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.12476 | −0.102410 | ||||||||
\(932\) | 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 | \(-0.322452\pi\) | ||||
0.529306 | + | 0.848431i | \(0.322452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 21.9097 | 0.711219 | ||||||||
\(950\) | −0.454170 | −0.0147352 | ||||||||
\(951\) | 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 | ||||||||
\(988\) | −6.18194 | −0.196674 | ||||||||
\(989\) | −30.0960 | −0.956998 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 57.9467 | 1.84074 | 0.920369 | − | 0.391052i | \(-0.127889\pi\) | ||||
0.920369 | + | 0.391052i | \(0.127889\pi\) | |||||||
\(992\) | −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 | 513.2.a.e.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 513.2.a.f.1.2 | yes | 3 | ||
4.3 | odd | 2 | 8208.2.a.bf.1.2 | 3 | |||
12.11 | even | 2 | 8208.2.a.bp.1.2 | 3 | |||
19.18 | odd | 2 | 9747.2.a.ba.1.2 | 3 | |||
57.56 | even | 2 | 9747.2.a.x.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
513.2.a.e.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
513.2.a.f.1.2 | yes | 3 | 3.2 | odd | 2 | ||
8208.2.a.bf.1.2 | 3 | 4.3 | odd | 2 | |||
8208.2.a.bp.1.2 | 3 | 12.11 | even | 2 | |||
9747.2.a.x.1.2 | 3 | 57.56 | even | 2 | |||
9747.2.a.ba.1.2 | 3 | 19.18 | odd | 2 |