Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8046,2,Mod(1,8046)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8046, 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("8046.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8046 = 2 \cdot 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8046.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: | \(64.2476334663\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 5 x^{11} - 21 x^{10} + 116 x^{9} + 106 x^{8} - 774 x^{7} - 63 x^{6} + 2013 x^{5} - 417 x^{4} + \cdots - 375 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(1.06735\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8046.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.06735 | 0.477335 | 0.238668 | − | 0.971101i | \(-0.423289\pi\) | ||||
0.238668 | + | 0.971101i | \(0.423289\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.41300 | 0.912028 | 0.456014 | − | 0.889973i | \(-0.349277\pi\) | ||||
0.456014 | + | 0.889973i | \(0.349277\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −1.06735 | −0.337527 | ||||||||
\(11\) | 2.87774 | 0.867672 | 0.433836 | − | 0.900992i | \(-0.357160\pi\) | ||||
0.433836 | + | 0.900992i | \(0.357160\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.31805 | 1.75231 | 0.876156 | − | 0.482027i | \(-0.160099\pi\) | ||||
0.876156 | + | 0.482027i | \(0.160099\pi\) | |||||||
\(14\) | −2.41300 | −0.644901 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.80297 | 1.40743 | 0.703714 | − | 0.710484i | \(-0.251524\pi\) | ||||
0.703714 | + | 0.710484i | \(0.251524\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.51725 | 0.577498 | 0.288749 | − | 0.957405i | \(-0.406761\pi\) | ||||
0.288749 | + | 0.957405i | \(0.406761\pi\) | |||||||
\(20\) | 1.06735 | 0.238668 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.87774 | −0.613537 | ||||||||
\(23\) | 4.87648 | 1.01682 | 0.508408 | − | 0.861116i | \(-0.330234\pi\) | ||||
0.508408 | + | 0.861116i | \(0.330234\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.86076 | −0.772151 | ||||||||
\(26\) | −6.31805 | −1.23907 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.41300 | 0.456014 | ||||||||
\(29\) | 5.18081 | 0.962052 | 0.481026 | − | 0.876706i | \(-0.340264\pi\) | ||||
0.481026 | + | 0.876706i | \(0.340264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.91286 | −1.42119 | −0.710596 | − | 0.703600i | \(-0.751575\pi\) | ||||
−0.710596 | + | 0.703600i | \(0.751575\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.80297 | −0.995201 | ||||||||
\(35\) | 2.57552 | 0.435343 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.64638 | −0.763860 | −0.381930 | − | 0.924191i | \(-0.624740\pi\) | ||||
−0.381930 | + | 0.924191i | \(0.624740\pi\) | |||||||
\(38\) | −2.51725 | −0.408353 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.06735 | −0.168763 | ||||||||
\(41\) | 10.6771 | 1.66749 | 0.833744 | − | 0.552152i | \(-0.186193\pi\) | ||||
0.833744 | + | 0.552152i | \(0.186193\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.1447 | 1.69955 | 0.849776 | − | 0.527144i | \(-0.176737\pi\) | ||||
0.849776 | + | 0.527144i | \(0.176737\pi\) | |||||||
\(44\) | 2.87774 | 0.433836 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.87648 | −0.718998 | ||||||||
\(47\) | 8.19941 | 1.19601 | 0.598004 | − | 0.801493i | \(-0.295961\pi\) | ||||
0.598004 | + | 0.801493i | \(0.295961\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.17744 | −0.168206 | ||||||||
\(50\) | 3.86076 | 0.545993 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6.31805 | 0.876156 | ||||||||
\(53\) | 6.76900 | 0.929794 | 0.464897 | − | 0.885365i | \(-0.346091\pi\) | ||||
0.464897 | + | 0.885365i | \(0.346091\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.07157 | 0.414170 | ||||||||
\(56\) | −2.41300 | −0.322450 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.18081 | −0.680274 | ||||||||
\(59\) | −6.78939 | −0.883903 | −0.441951 | − | 0.897039i | \(-0.645714\pi\) | ||||
−0.441951 | + | 0.897039i | \(0.645714\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.8514 | −1.51742 | −0.758711 | − | 0.651428i | \(-0.774170\pi\) | ||||
−0.758711 | + | 0.651428i | \(0.774170\pi\) | |||||||
\(62\) | 7.91286 | 1.00493 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 6.74360 | 0.836440 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12.4327 | 1.51890 | 0.759448 | − | 0.650568i | \(-0.225469\pi\) | ||||
0.759448 | + | 0.650568i | \(0.225469\pi\) | |||||||
\(68\) | 5.80297 | 0.703714 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −2.57552 | −0.307834 | ||||||||
\(71\) | 3.88117 | 0.460610 | 0.230305 | − | 0.973118i | \(-0.426028\pi\) | ||||
0.230305 | + | 0.973118i | \(0.426028\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.97024 | −0.230599 | −0.115299 | − | 0.993331i | \(-0.536783\pi\) | ||||
−0.115299 | + | 0.993331i | \(0.536783\pi\) | |||||||
\(74\) | 4.64638 | 0.540130 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.51725 | 0.288749 | ||||||||
\(77\) | 6.94399 | 0.791341 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.26625 | 0.254973 | 0.127487 | − | 0.991840i | \(-0.459309\pi\) | ||||
0.127487 | + | 0.991840i | \(0.459309\pi\) | |||||||
\(80\) | 1.06735 | 0.119334 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −10.6771 | −1.17909 | ||||||||
\(83\) | −2.68059 | −0.294233 | −0.147117 | − | 0.989119i | \(-0.546999\pi\) | ||||
−0.147117 | + | 0.989119i | \(0.546999\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.19382 | 0.671814 | ||||||||
\(86\) | −11.1447 | −1.20176 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −2.87774 | −0.306768 | ||||||||
\(89\) | −12.9074 | −1.36818 | −0.684091 | − | 0.729397i | \(-0.739801\pi\) | ||||
−0.684091 | + | 0.729397i | \(0.739801\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 15.2455 | 1.59816 | ||||||||
\(92\) | 4.87648 | 0.508408 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −8.19941 | −0.845705 | ||||||||
\(95\) | 2.68680 | 0.275660 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.69563 | 0.679839 | 0.339919 | − | 0.940455i | \(-0.389600\pi\) | ||||
0.339919 | + | 0.940455i | \(0.389600\pi\) | |||||||
\(98\) | 1.17744 | 0.118939 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.86076 | −0.386076 | ||||||||
\(101\) | −9.08647 | −0.904137 | −0.452069 | − | 0.891983i | \(-0.649314\pi\) | ||||
−0.452069 | + | 0.891983i | \(0.649314\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.3461 | −1.21650 | −0.608251 | − | 0.793745i | \(-0.708129\pi\) | ||||
−0.608251 | + | 0.793745i | \(0.708129\pi\) | |||||||
\(104\) | −6.31805 | −0.619536 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.76900 | −0.657464 | ||||||||
\(107\) | −4.76521 | −0.460670 | −0.230335 | − | 0.973111i | \(-0.573982\pi\) | ||||
−0.230335 | + | 0.973111i | \(0.573982\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.74157 | −0.549943 | −0.274971 | − | 0.961452i | \(-0.588668\pi\) | ||||
−0.274971 | + | 0.961452i | \(0.588668\pi\) | |||||||
\(110\) | −3.07157 | −0.292863 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.41300 | 0.228007 | ||||||||
\(113\) | 13.1555 | 1.23756 | 0.618781 | − | 0.785563i | \(-0.287627\pi\) | ||||
0.618781 | + | 0.785563i | \(0.287627\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.20493 | 0.485362 | ||||||||
\(116\) | 5.18081 | 0.481026 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.78939 | 0.625014 | ||||||||
\(119\) | 14.0026 | 1.28361 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.71860 | −0.247145 | ||||||||
\(122\) | 11.8514 | 1.07298 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −7.91286 | −0.710596 | ||||||||
\(125\) | −9.45756 | −0.845910 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.03628 | 0.269426 | 0.134713 | − | 0.990885i | \(-0.456989\pi\) | ||||
0.134713 | + | 0.990885i | \(0.456989\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −6.74360 | −0.591453 | ||||||||
\(131\) | −20.9274 | −1.82843 | −0.914217 | − | 0.405226i | \(-0.867193\pi\) | ||||
−0.914217 | + | 0.405226i | \(0.867193\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.07413 | 0.526694 | ||||||||
\(134\) | −12.4327 | −1.07402 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.80297 | −0.497601 | ||||||||
\(137\) | −5.40932 | −0.462150 | −0.231075 | − | 0.972936i | \(-0.574224\pi\) | ||||
−0.231075 | + | 0.972936i | \(0.574224\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.5243 | −0.977475 | −0.488738 | − | 0.872431i | \(-0.662542\pi\) | ||||
−0.488738 | + | 0.872431i | \(0.662542\pi\) | |||||||
\(140\) | 2.57552 | 0.217671 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.88117 | −0.325701 | ||||||||
\(143\) | 18.1817 | 1.52043 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.52976 | 0.459221 | ||||||||
\(146\) | 1.97024 | 0.163058 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −4.64638 | −0.381930 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.4343 | −1.50016 | −0.750080 | − | 0.661347i | \(-0.769985\pi\) | ||||
−0.750080 | + | 0.661347i | \(0.769985\pi\) | |||||||
\(152\) | −2.51725 | −0.204176 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −6.94399 | −0.559562 | ||||||||
\(155\) | −8.44582 | −0.678385 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −18.8174 | −1.50179 | −0.750896 | − | 0.660421i | \(-0.770378\pi\) | ||||
−0.750896 | + | 0.660421i | \(0.770378\pi\) | |||||||
\(158\) | −2.26625 | −0.180293 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.06735 | −0.0843817 | ||||||||
\(161\) | 11.7669 | 0.927365 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.6680 | −1.46219 | −0.731097 | − | 0.682273i | \(-0.760991\pi\) | ||||
−0.731097 | + | 0.682273i | \(0.760991\pi\) | |||||||
\(164\) | 10.6771 | 0.833744 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.68059 | 0.208054 | ||||||||
\(167\) | −10.7650 | −0.833017 | −0.416509 | − | 0.909132i | \(-0.636746\pi\) | ||||
−0.416509 | + | 0.909132i | \(0.636746\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 26.9178 | 2.07060 | ||||||||
\(170\) | −6.19382 | −0.475045 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 11.1447 | 0.849776 | ||||||||
\(173\) | −14.3128 | −1.08818 | −0.544092 | − | 0.839025i | \(-0.683126\pi\) | ||||
−0.544092 | + | 0.839025i | \(0.683126\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −9.31600 | −0.704223 | ||||||||
\(176\) | 2.87774 | 0.216918 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 12.9074 | 0.967451 | ||||||||
\(179\) | −14.8159 | −1.10739 | −0.553696 | − | 0.832719i | \(-0.686783\pi\) | ||||
−0.553696 | + | 0.832719i | \(0.686783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.4854 | 0.928030 | 0.464015 | − | 0.885827i | \(-0.346408\pi\) | ||||
0.464015 | + | 0.885827i | \(0.346408\pi\) | |||||||
\(182\) | −15.2455 | −1.13007 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.87648 | −0.359499 | ||||||||
\(185\) | −4.95933 | −0.364617 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 16.6995 | 1.22119 | ||||||||
\(188\) | 8.19941 | 0.598004 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.68680 | −0.194921 | ||||||||
\(191\) | 0.208714 | 0.0151020 | 0.00755100 | − | 0.999971i | \(-0.497596\pi\) | ||||
0.00755100 | + | 0.999971i | \(0.497596\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 20.4582 | 1.47261 | 0.736307 | − | 0.676648i | \(-0.236568\pi\) | ||||
0.736307 | + | 0.676648i | \(0.236568\pi\) | |||||||
\(194\) | −6.69563 | −0.480718 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.17744 | −0.0841028 | ||||||||
\(197\) | 24.9769 | 1.77953 | 0.889765 | − | 0.456419i | \(-0.150868\pi\) | ||||
0.889765 | + | 0.456419i | \(0.150868\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.3928 | −1.30383 | −0.651916 | − | 0.758291i | \(-0.726035\pi\) | ||||
−0.651916 | + | 0.758291i | \(0.726035\pi\) | |||||||
\(200\) | 3.86076 | 0.272997 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 9.08647 | 0.639322 | ||||||||
\(203\) | 12.5013 | 0.877418 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.3963 | 0.795950 | ||||||||
\(206\) | 12.3461 | 0.860197 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 6.31805 | 0.438078 | ||||||||
\(209\) | 7.24401 | 0.501079 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5.11885 | −0.352396 | −0.176198 | − | 0.984355i | \(-0.556380\pi\) | ||||
−0.176198 | + | 0.984355i | \(0.556380\pi\) | |||||||
\(212\) | 6.76900 | 0.464897 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.76521 | 0.325743 | ||||||||
\(215\) | 11.8953 | 0.811256 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −19.0937 | −1.29617 | ||||||||
\(218\) | 5.74157 | 0.388868 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 3.07157 | 0.207085 | ||||||||
\(221\) | 36.6635 | 2.46625 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.0494 | −1.61047 | −0.805233 | − | 0.592958i | \(-0.797960\pi\) | ||||
−0.805233 | + | 0.592958i | \(0.797960\pi\) | |||||||
\(224\) | −2.41300 | −0.161225 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −13.1555 | −0.875089 | ||||||||
\(227\) | 16.4469 | 1.09162 | 0.545809 | − | 0.837910i | \(-0.316223\pi\) | ||||
0.545809 | + | 0.837910i | \(0.316223\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.67491 | 0.242845 | 0.121423 | − | 0.992601i | \(-0.461254\pi\) | ||||
0.121423 | + | 0.992601i | \(0.461254\pi\) | |||||||
\(230\) | −5.20493 | −0.343203 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.18081 | −0.340137 | ||||||||
\(233\) | −1.22524 | −0.0802679 | −0.0401340 | − | 0.999194i | \(-0.512778\pi\) | ||||
−0.0401340 | + | 0.999194i | \(0.512778\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.75167 | 0.570896 | ||||||||
\(236\) | −6.78939 | −0.441951 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −14.0026 | −0.907651 | ||||||||
\(239\) | −19.6354 | −1.27011 | −0.635055 | − | 0.772467i | \(-0.719022\pi\) | ||||
−0.635055 | + | 0.772467i | \(0.719022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.6153 | −1.39237 | −0.696183 | − | 0.717865i | \(-0.745120\pi\) | ||||
−0.696183 | + | 0.717865i | \(0.745120\pi\) | |||||||
\(242\) | 2.71860 | 0.174758 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.8514 | −0.758711 | ||||||||
\(245\) | −1.25674 | −0.0802904 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.9041 | 1.01196 | ||||||||
\(248\) | 7.91286 | 0.502467 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.45756 | 0.598149 | ||||||||
\(251\) | 22.9313 | 1.44741 | 0.723704 | − | 0.690110i | \(-0.242438\pi\) | ||||
0.723704 | + | 0.690110i | \(0.242438\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 14.0333 | 0.882263 | ||||||||
\(254\) | −3.03628 | −0.190513 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −13.7438 | −0.857313 | −0.428656 | − | 0.903468i | \(-0.641013\pi\) | ||||
−0.428656 | + | 0.903468i | \(0.641013\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.2117 | −0.696661 | ||||||||
\(260\) | 6.74360 | 0.418220 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 20.9274 | 1.29290 | ||||||||
\(263\) | 3.02740 | 0.186678 | 0.0933388 | − | 0.995634i | \(-0.470246\pi\) | ||||
0.0933388 | + | 0.995634i | \(0.470246\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.22492 | 0.443823 | ||||||||
\(266\) | −6.07413 | −0.372429 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 12.4327 | 0.759448 | ||||||||
\(269\) | −30.7276 | −1.87350 | −0.936748 | − | 0.350005i | \(-0.886180\pi\) | ||||
−0.936748 | + | 0.350005i | \(0.886180\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −12.7435 | −0.774111 | −0.387056 | − | 0.922056i | \(-0.626508\pi\) | ||||
−0.387056 | + | 0.922056i | \(0.626508\pi\) | |||||||
\(272\) | 5.80297 | 0.351857 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.40932 | 0.326789 | ||||||||
\(275\) | −11.1103 | −0.669974 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0878 | 0.606117 | 0.303059 | − | 0.952972i | \(-0.401992\pi\) | ||||
0.303059 | + | 0.952972i | \(0.401992\pi\) | |||||||
\(278\) | 11.5243 | 0.691179 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.57552 | −0.153917 | ||||||||
\(281\) | 20.1407 | 1.20149 | 0.600746 | − | 0.799440i | \(-0.294870\pi\) | ||||
0.600746 | + | 0.799440i | \(0.294870\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.42116 | −0.560030 | −0.280015 | − | 0.959996i | \(-0.590339\pi\) | ||||
−0.280015 | + | 0.959996i | \(0.590339\pi\) | |||||||
\(284\) | 3.88117 | 0.230305 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −18.1817 | −1.07511 | ||||||||
\(287\) | 25.7639 | 1.52079 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.6745 | 0.980852 | ||||||||
\(290\) | −5.52976 | −0.324718 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.97024 | −0.115299 | ||||||||
\(293\) | −9.52070 | −0.556205 | −0.278103 | − | 0.960551i | \(-0.589706\pi\) | ||||
−0.278103 | + | 0.960551i | \(0.589706\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −7.24668 | −0.421918 | ||||||||
\(296\) | 4.64638 | 0.270065 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.00000 | −0.0579284 | ||||||||
\(299\) | 30.8099 | 1.78178 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.8922 | 1.55004 | ||||||||
\(302\) | 18.4343 | 1.06077 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.51725 | 0.144374 | ||||||||
\(305\) | −12.6497 | −0.724318 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.01472 | 0.229132 | 0.114566 | − | 0.993416i | \(-0.463452\pi\) | ||||
0.114566 | + | 0.993416i | \(0.463452\pi\) | |||||||
\(308\) | 6.94399 | 0.395670 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 8.44582 | 0.479690 | ||||||||
\(311\) | 12.5289 | 0.710450 | 0.355225 | − | 0.934781i | \(-0.384404\pi\) | ||||
0.355225 | + | 0.934781i | \(0.384404\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −17.9628 | −1.01532 | −0.507660 | − | 0.861558i | \(-0.669489\pi\) | ||||
−0.507660 | + | 0.861558i | \(0.669489\pi\) | |||||||
\(314\) | 18.8174 | 1.06193 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.26625 | 0.127487 | ||||||||
\(317\) | −0.635891 | −0.0357152 | −0.0178576 | − | 0.999841i | \(-0.505685\pi\) | ||||
−0.0178576 | + | 0.999841i | \(0.505685\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 14.9090 | 0.834746 | ||||||||
\(320\) | 1.06735 | 0.0596669 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −11.7669 | −0.655746 | ||||||||
\(323\) | 14.6076 | 0.812786 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −24.3925 | −1.35305 | ||||||||
\(326\) | 18.6680 | 1.03393 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −10.6771 | −0.589546 | ||||||||
\(329\) | 19.7852 | 1.09079 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.11325 | −0.171120 | −0.0855599 | − | 0.996333i | \(-0.527268\pi\) | ||||
−0.0855599 | + | 0.996333i | \(0.527268\pi\) | |||||||
\(332\) | −2.68059 | −0.147117 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.7650 | 0.589032 | ||||||||
\(335\) | 13.2701 | 0.725022 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −33.9883 | −1.85146 | −0.925731 | − | 0.378182i | \(-0.876549\pi\) | ||||
−0.925731 | + | 0.378182i | \(0.876549\pi\) | |||||||
\(338\) | −26.9178 | −1.46413 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.19382 | 0.335907 | ||||||||
\(341\) | −22.7712 | −1.23313 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −19.7321 | −1.06544 | ||||||||
\(344\) | −11.1447 | −0.600882 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.3128 | 0.769463 | ||||||||
\(347\) | −25.5691 | −1.37262 | −0.686309 | − | 0.727310i | \(-0.740770\pi\) | ||||
−0.686309 | + | 0.727310i | \(0.740770\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.64078 | −0.355473 | −0.177736 | − | 0.984078i | \(-0.556877\pi\) | ||||
−0.177736 | + | 0.984078i | \(0.556877\pi\) | |||||||
\(350\) | 9.31600 | 0.497961 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.87774 | −0.153384 | ||||||||
\(353\) | −4.63793 | −0.246852 | −0.123426 | − | 0.992354i | \(-0.539388\pi\) | ||||
−0.123426 | + | 0.992354i | \(0.539388\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.14258 | 0.219866 | ||||||||
\(356\) | −12.9074 | −0.684091 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14.8159 | 0.783045 | ||||||||
\(359\) | −14.7744 | −0.779761 | −0.389881 | − | 0.920865i | \(-0.627484\pi\) | ||||
−0.389881 | + | 0.920865i | \(0.627484\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.6634 | −0.666496 | ||||||||
\(362\) | −12.4854 | −0.656216 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15.2455 | 0.799079 | ||||||||
\(365\) | −2.10294 | −0.110073 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6.92697 | 0.361585 | 0.180792 | − | 0.983521i | \(-0.442134\pi\) | ||||
0.180792 | + | 0.983521i | \(0.442134\pi\) | |||||||
\(368\) | 4.87648 | 0.254204 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.95933 | 0.257823 | ||||||||
\(371\) | 16.3336 | 0.847998 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.15412 | 0.370426 | 0.185213 | − | 0.982698i | \(-0.440702\pi\) | ||||
0.185213 | + | 0.982698i | \(0.440702\pi\) | |||||||
\(374\) | −16.6995 | −0.863508 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −8.19941 | −0.422853 | ||||||||
\(377\) | 32.7326 | 1.68582 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 25.6854 | 1.31937 | 0.659684 | − | 0.751543i | \(-0.270690\pi\) | ||||
0.659684 | + | 0.751543i | \(0.270690\pi\) | |||||||
\(380\) | 2.68680 | 0.137830 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.208714 | −0.0106787 | ||||||||
\(383\) | −23.5765 | −1.20471 | −0.602353 | − | 0.798230i | \(-0.705770\pi\) | ||||
−0.602353 | + | 0.798230i | \(0.705770\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.41169 | 0.377735 | ||||||||
\(386\) | −20.4582 | −1.04130 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.69563 | 0.339919 | ||||||||
\(389\) | 16.7592 | 0.849724 | 0.424862 | − | 0.905258i | \(-0.360323\pi\) | ||||
0.424862 | + | 0.905258i | \(0.360323\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 28.2981 | 1.43110 | ||||||||
\(392\) | 1.17744 | 0.0594697 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −24.9769 | −1.25832 | ||||||||
\(395\) | 2.41889 | 0.121708 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.12235 | −0.257083 | −0.128542 | − | 0.991704i | \(-0.541030\pi\) | ||||
−0.128542 | + | 0.991704i | \(0.541030\pi\) | |||||||
\(398\) | 18.3928 | 0.921949 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.86076 | −0.193038 | ||||||||
\(401\) | −19.0659 | −0.952106 | −0.476053 | − | 0.879417i | \(-0.657933\pi\) | ||||
−0.476053 | + | 0.879417i | \(0.657933\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −49.9939 | −2.49037 | ||||||||
\(404\) | −9.08647 | −0.452069 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.5013 | −0.620428 | ||||||||
\(407\) | −13.3711 | −0.662780 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 15.0451 | 0.743933 | 0.371966 | − | 0.928246i | \(-0.378684\pi\) | ||||
0.371966 | + | 0.928246i | \(0.378684\pi\) | |||||||
\(410\) | −11.3963 | −0.562822 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −12.3461 | −0.608251 | ||||||||
\(413\) | −16.3828 | −0.806144 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.86114 | −0.140448 | ||||||||
\(416\) | −6.31805 | −0.309768 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −7.24401 | −0.354316 | ||||||||
\(419\) | −12.6427 | −0.617637 | −0.308818 | − | 0.951121i | \(-0.599934\pi\) | ||||
−0.308818 | + | 0.951121i | \(0.599934\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.70185 | −0.424102 | −0.212051 | − | 0.977259i | \(-0.568014\pi\) | ||||
−0.212051 | + | 0.977259i | \(0.568014\pi\) | |||||||
\(422\) | 5.11885 | 0.249182 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.76900 | −0.328732 | ||||||||
\(425\) | −22.4039 | −1.08675 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.5975 | −1.38393 | ||||||||
\(428\) | −4.76521 | −0.230335 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −11.8953 | −0.573644 | ||||||||
\(431\) | 13.9905 | 0.673897 | 0.336948 | − | 0.941523i | \(-0.390605\pi\) | ||||
0.336948 | + | 0.941523i | \(0.390605\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.4355 | 1.12624 | 0.563120 | − | 0.826375i | \(-0.309601\pi\) | ||||
0.563120 | + | 0.826375i | \(0.309601\pi\) | |||||||
\(434\) | 19.0937 | 0.916528 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.74157 | −0.274971 | ||||||||
\(437\) | 12.2753 | 0.587209 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.3808 | −0.829540 | −0.414770 | − | 0.909926i | \(-0.636138\pi\) | ||||
−0.414770 | + | 0.909926i | \(0.636138\pi\) | |||||||
\(440\) | −3.07157 | −0.146431 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −36.6635 | −1.74390 | ||||||||
\(443\) | 14.3666 | 0.682579 | 0.341290 | − | 0.939958i | \(-0.389136\pi\) | ||||
0.341290 | + | 0.939958i | \(0.389136\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −13.7768 | −0.653081 | ||||||||
\(446\) | 24.0494 | 1.13877 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.41300 | 0.114003 | ||||||||
\(449\) | −4.35069 | −0.205322 | −0.102661 | − | 0.994716i | \(-0.532736\pi\) | ||||
−0.102661 | + | 0.994716i | \(0.532736\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.7260 | 1.44683 | ||||||||
\(452\) | 13.1555 | 0.618781 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −16.4469 | −0.771890 | ||||||||
\(455\) | 16.2723 | 0.762857 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −28.9116 | −1.35243 | −0.676214 | − | 0.736705i | \(-0.736380\pi\) | ||||
−0.676214 | + | 0.736705i | \(0.736380\pi\) | |||||||
\(458\) | −3.67491 | −0.171717 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 5.20493 | 0.242681 | ||||||||
\(461\) | −3.48477 | −0.162302 | −0.0811509 | − | 0.996702i | \(-0.525860\pi\) | ||||
−0.0811509 | + | 0.996702i | \(0.525860\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3353 | −0.805640 | −0.402820 | − | 0.915279i | \(-0.631970\pi\) | ||||
−0.402820 | + | 0.915279i | \(0.631970\pi\) | |||||||
\(464\) | 5.18081 | 0.240513 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.22524 | 0.0567580 | ||||||||
\(467\) | 21.8269 | 1.01003 | 0.505013 | − | 0.863111i | \(-0.331488\pi\) | ||||
0.505013 | + | 0.863111i | \(0.331488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.0001 | 1.38527 | ||||||||
\(470\) | −8.75167 | −0.403685 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.78939 | 0.312507 | ||||||||
\(473\) | 32.0716 | 1.47465 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9.71850 | −0.445916 | ||||||||
\(476\) | 14.0026 | 0.641806 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 19.6354 | 0.898103 | ||||||||
\(479\) | −32.2298 | −1.47262 | −0.736308 | − | 0.676647i | \(-0.763433\pi\) | ||||
−0.736308 | + | 0.676647i | \(0.763433\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −29.3561 | −1.33852 | ||||||||
\(482\) | 21.6153 | 0.984551 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.71860 | −0.123573 | ||||||||
\(485\) | 7.14661 | 0.324511 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 36.3486 | 1.64711 | 0.823556 | − | 0.567235i | \(-0.191987\pi\) | ||||
0.823556 | + | 0.567235i | \(0.191987\pi\) | |||||||
\(488\) | 11.8514 | 0.536489 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1.25674 | 0.0567739 | ||||||||
\(491\) | −6.27108 | −0.283010 | −0.141505 | − | 0.989938i | \(-0.545194\pi\) | ||||
−0.141505 | + | 0.989938i | \(0.545194\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.0641 | 1.35402 | ||||||||
\(494\) | −15.9041 | −0.715561 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.91286 | −0.355298 | ||||||||
\(497\) | 9.36526 | 0.420089 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 31.2490 | 1.39890 | 0.699449 | − | 0.714683i | \(-0.253429\pi\) | ||||
0.699449 | + | 0.714683i | \(0.253429\pi\) | |||||||
\(500\) | −9.45756 | −0.422955 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −22.9313 | −1.02347 | ||||||||
\(503\) | 7.83456 | 0.349326 | 0.174663 | − | 0.984628i | \(-0.444116\pi\) | ||||
0.174663 | + | 0.984628i | \(0.444116\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.69847 | −0.431576 | ||||||||
\(506\) | −14.0333 | −0.623854 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.03628 | 0.134713 | ||||||||
\(509\) | −13.6569 | −0.605331 | −0.302665 | − | 0.953097i | \(-0.597876\pi\) | ||||
−0.302665 | + | 0.953097i | \(0.597876\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.75418 | −0.210312 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13.7438 | 0.606212 | ||||||||
\(515\) | −13.1777 | −0.580679 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23.5958 | 1.03774 | ||||||||
\(518\) | 11.2117 | 0.492614 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.74360 | −0.295726 | ||||||||
\(521\) | 21.5222 | 0.942903 | 0.471452 | − | 0.881892i | \(-0.343730\pi\) | ||||
0.471452 | + | 0.881892i | \(0.343730\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.3077 | 0.756815 | 0.378407 | − | 0.925639i | \(-0.376472\pi\) | ||||
0.378407 | + | 0.925639i | \(0.376472\pi\) | |||||||
\(524\) | −20.9274 | −0.914217 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.02740 | −0.132001 | ||||||||
\(527\) | −45.9181 | −2.00022 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.780061 | 0.0339157 | ||||||||
\(530\) | −7.22492 | −0.313831 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 6.07413 | 0.263347 | ||||||||
\(533\) | 67.4587 | 2.92196 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.08617 | −0.219894 | ||||||||
\(536\) | −12.4327 | −0.537011 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 30.7276 | 1.32476 | ||||||||
\(539\) | −3.38837 | −0.145947 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 34.3916 | 1.47861 | 0.739306 | − | 0.673370i | \(-0.235154\pi\) | ||||
0.739306 | + | 0.673370i | \(0.235154\pi\) | |||||||
\(542\) | 12.7435 | 0.547379 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.80297 | −0.248800 | ||||||||
\(545\) | −6.12829 | −0.262507 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.48789 | −0.0636177 | −0.0318089 | − | 0.999494i | \(-0.510127\pi\) | ||||
−0.0318089 | + | 0.999494i | \(0.510127\pi\) | |||||||
\(548\) | −5.40932 | −0.231075 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 11.1103 | 0.473743 | ||||||||
\(551\) | 13.0414 | 0.555583 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.46846 | 0.232543 | ||||||||
\(554\) | −10.0878 | −0.428590 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.5243 | −0.488738 | ||||||||
\(557\) | 27.4929 | 1.16491 | 0.582457 | − | 0.812862i | \(-0.302092\pi\) | ||||
0.582457 | + | 0.812862i | \(0.302092\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 70.4128 | 2.97815 | ||||||||
\(560\) | 2.57552 | 0.108836 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −20.1407 | −0.849584 | ||||||||
\(563\) | −1.46719 | −0.0618345 | −0.0309173 | − | 0.999522i | \(-0.509843\pi\) | ||||
−0.0309173 | + | 0.999522i | \(0.509843\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.0415 | 0.590732 | ||||||||
\(566\) | 9.42116 | 0.396001 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −3.88117 | −0.162850 | ||||||||
\(569\) | −34.4730 | −1.44518 | −0.722592 | − | 0.691274i | \(-0.757050\pi\) | ||||
−0.722592 | + | 0.691274i | \(0.757050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.4755 | 1.94494 | 0.972470 | − | 0.233028i | \(-0.0748633\pi\) | ||||
0.972470 | + | 0.233028i | \(0.0748633\pi\) | |||||||
\(572\) | 18.1817 | 0.760216 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −25.7639 | −1.07536 | ||||||||
\(575\) | −18.8269 | −0.785136 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 11.1971 | 0.466140 | 0.233070 | − | 0.972460i | \(-0.425123\pi\) | ||||
0.233070 | + | 0.972460i | \(0.425123\pi\) | |||||||
\(578\) | −16.6745 | −0.693567 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.52976 | 0.229611 | ||||||||
\(581\) | −6.46826 | −0.268349 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 19.4795 | 0.806756 | ||||||||
\(584\) | 1.97024 | 0.0815289 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.52070 | 0.393296 | ||||||||
\(587\) | 13.7039 | 0.565622 | 0.282811 | − | 0.959176i | \(-0.408733\pi\) | ||||
0.282811 | + | 0.959176i | \(0.408733\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19.9187 | −0.820735 | ||||||||
\(590\) | 7.24668 | 0.298341 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.64638 | −0.190965 | ||||||||
\(593\) | 45.7421 | 1.87840 | 0.939201 | − | 0.343367i | \(-0.111568\pi\) | ||||
0.939201 | + | 0.343367i | \(0.111568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.9457 | 0.612713 | ||||||||
\(596\) | 1.00000 | 0.0409616 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −30.8099 | −1.25991 | ||||||||
\(599\) | 27.8465 | 1.13778 | 0.568889 | − | 0.822414i | \(-0.307373\pi\) | ||||
0.568889 | + | 0.822414i | \(0.307373\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.82327 | −0.319118 | −0.159559 | − | 0.987188i | \(-0.551007\pi\) | ||||
−0.159559 | + | 0.987188i | \(0.551007\pi\) | |||||||
\(602\) | −26.8922 | −1.09604 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −18.4343 | −0.750080 | ||||||||
\(605\) | −2.90171 | −0.117971 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.46791 | −0.303113 | −0.151557 | − | 0.988449i | \(-0.548429\pi\) | ||||
−0.151557 | + | 0.988449i | \(0.548429\pi\) | |||||||
\(608\) | −2.51725 | −0.102088 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.6497 | 0.512170 | ||||||||
\(611\) | 51.8043 | 2.09578 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.6402 | 1.07599 | 0.537993 | − | 0.842949i | \(-0.319183\pi\) | ||||
0.537993 | + | 0.842949i | \(0.319183\pi\) | |||||||
\(614\) | −4.01472 | −0.162021 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −6.94399 | −0.279781 | ||||||||
\(617\) | −16.0512 | −0.646198 | −0.323099 | − | 0.946365i | \(-0.604725\pi\) | ||||
−0.323099 | + | 0.946365i | \(0.604725\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.0240 | −1.68909 | −0.844544 | − | 0.535487i | \(-0.820128\pi\) | ||||
−0.844544 | + | 0.535487i | \(0.820128\pi\) | |||||||
\(620\) | −8.44582 | −0.339192 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −12.5289 | −0.502364 | ||||||||
\(623\) | −31.1455 | −1.24782 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 9.20922 | 0.368369 | ||||||||
\(626\) | 17.9628 | 0.717939 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −18.8174 | −0.750896 | ||||||||
\(629\) | −26.9628 | −1.07508 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −23.5755 | −0.938524 | −0.469262 | − | 0.883059i | \(-0.655480\pi\) | ||||
−0.469262 | + | 0.883059i | \(0.655480\pi\) | |||||||
\(632\) | −2.26625 | −0.0901467 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.635891 | 0.0252545 | ||||||||
\(635\) | 3.24079 | 0.128607 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.43912 | −0.294749 | ||||||||
\(638\) | −14.9090 | −0.590254 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.06735 | −0.0421909 | ||||||||
\(641\) | −11.1542 | −0.440564 | −0.220282 | − | 0.975436i | \(-0.570698\pi\) | ||||
−0.220282 | + | 0.975436i | \(0.570698\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.17816 | 0.322515 | 0.161258 | − | 0.986912i | \(-0.448445\pi\) | ||||
0.161258 | + | 0.986912i | \(0.448445\pi\) | |||||||
\(644\) | 11.7669 | 0.463682 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −14.6076 | −0.574726 | ||||||||
\(647\) | −2.23055 | −0.0876921 | −0.0438461 | − | 0.999038i | \(-0.513961\pi\) | ||||
−0.0438461 | + | 0.999038i | \(0.513961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −19.5381 | −0.766938 | ||||||||
\(650\) | 24.3925 | 0.956751 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.6680 | −0.731097 | ||||||||
\(653\) | 13.8175 | 0.540721 | 0.270361 | − | 0.962759i | \(-0.412857\pi\) | ||||
0.270361 | + | 0.962759i | \(0.412857\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.3369 | −0.872775 | ||||||||
\(656\) | 10.6771 | 0.416872 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −19.7852 | −0.771306 | ||||||||
\(659\) | −17.9428 | −0.698951 | −0.349475 | − | 0.936946i | \(-0.613640\pi\) | ||||
−0.349475 | + | 0.936946i | \(0.613640\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.74759 | 0.262451 | 0.131225 | − | 0.991353i | \(-0.458109\pi\) | ||||
0.131225 | + | 0.991353i | \(0.458109\pi\) | |||||||
\(662\) | 3.11325 | 0.121000 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.68059 | 0.104027 | ||||||||
\(665\) | 6.48324 | 0.251409 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 25.2641 | 0.978230 | ||||||||
\(668\) | −10.7650 | −0.416509 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −13.2701 | −0.512668 | ||||||||
\(671\) | −34.1054 | −1.31662 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.2188 | 1.12630 | 0.563152 | − | 0.826353i | \(-0.309589\pi\) | ||||
0.563152 | + | 0.826353i | \(0.309589\pi\) | |||||||
\(674\) | 33.9883 | 1.30918 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 26.9178 | 1.03530 | ||||||||
\(677\) | −41.1604 | −1.58192 | −0.790961 | − | 0.611866i | \(-0.790419\pi\) | ||||
−0.790961 | + | 0.611866i | \(0.790419\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 16.1566 | 0.620032 | ||||||||
\(680\) | −6.19382 | −0.237522 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.7712 | 0.871953 | ||||||||
\(683\) | 25.1460 | 0.962184 | 0.481092 | − | 0.876670i | \(-0.340240\pi\) | ||||
0.481092 | + | 0.876670i | \(0.340240\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.77366 | −0.220600 | ||||||||
\(686\) | 19.7321 | 0.753377 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 11.1447 | 0.424888 | ||||||||
\(689\) | 42.7669 | 1.62929 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.33945 | 0.355290 | 0.177645 | − | 0.984095i | \(-0.443152\pi\) | ||||
0.177645 | + | 0.984095i | \(0.443152\pi\) | |||||||
\(692\) | −14.3128 | −0.544092 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 25.5691 | 0.970588 | ||||||||
\(695\) | −12.3005 | −0.466583 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 61.9591 | 2.34687 | ||||||||
\(698\) | 6.64078 | 0.251357 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −9.31600 | −0.352112 | ||||||||
\(701\) | 20.7946 | 0.785400 | 0.392700 | − | 0.919667i | \(-0.371541\pi\) | ||||
0.392700 | + | 0.919667i | \(0.371541\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11.6961 | −0.441127 | ||||||||
\(704\) | 2.87774 | 0.108459 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.63793 | 0.174551 | ||||||||
\(707\) | −21.9256 | −0.824598 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −34.3030 | −1.28828 | −0.644139 | − | 0.764909i | \(-0.722784\pi\) | ||||
−0.644139 | + | 0.764909i | \(0.722784\pi\) | |||||||
\(710\) | −4.14258 | −0.155468 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 12.9074 | 0.483725 | ||||||||
\(713\) | −38.5869 | −1.44509 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 19.4063 | 0.725756 | ||||||||
\(716\) | −14.8159 | −0.553696 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 14.7744 | 0.551374 | ||||||||
\(719\) | 42.1754 | 1.57288 | 0.786438 | − | 0.617670i | \(-0.211923\pi\) | ||||
0.786438 | + | 0.617670i | \(0.211923\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −29.7912 | −1.10948 | ||||||||
\(722\) | 12.6634 | 0.471284 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.4854 | 0.464015 | ||||||||
\(725\) | −20.0018 | −0.742850 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −30.1726 | −1.11904 | −0.559520 | − | 0.828817i | \(-0.689015\pi\) | ||||
−0.559520 | + | 0.828817i | \(0.689015\pi\) | |||||||
\(728\) | −15.2455 | −0.565034 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.10294 | 0.0778332 | ||||||||
\(731\) | 64.6724 | 2.39200 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.2752 | 0.785816 | 0.392908 | − | 0.919578i | \(-0.371469\pi\) | ||||
0.392908 | + | 0.919578i | \(0.371469\pi\) | |||||||
\(734\) | −6.92697 | −0.255679 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.87648 | −0.179749 | ||||||||
\(737\) | 35.7781 | 1.31790 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −27.0373 | −0.994583 | −0.497292 | − | 0.867583i | \(-0.665672\pi\) | ||||
−0.497292 | + | 0.867583i | \(0.665672\pi\) | |||||||
\(740\) | −4.95933 | −0.182309 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −16.3336 | −0.599625 | ||||||||
\(743\) | 14.0456 | 0.515281 | 0.257641 | − | 0.966241i | \(-0.417055\pi\) | ||||
0.257641 | + | 0.966241i | \(0.417055\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.06735 | 0.0391048 | ||||||||
\(746\) | −7.15412 | −0.261931 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 16.6995 | 0.610593 | ||||||||
\(749\) | −11.4984 | −0.420144 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.1905 | 1.28412 | 0.642060 | − | 0.766655i | \(-0.278080\pi\) | ||||
0.642060 | + | 0.766655i | \(0.278080\pi\) | |||||||
\(752\) | 8.19941 | 0.299002 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −32.7326 | −1.19205 | ||||||||
\(755\) | −19.6759 | −0.716079 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 12.0391 | 0.437567 | 0.218783 | − | 0.975773i | \(-0.429791\pi\) | ||||
0.218783 | + | 0.975773i | \(0.429791\pi\) | |||||||
\(758\) | −25.6854 | −0.932935 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.68680 | −0.0974605 | ||||||||
\(761\) | −45.8827 | −1.66325 | −0.831623 | − | 0.555341i | \(-0.812588\pi\) | ||||
−0.831623 | + | 0.555341i | \(0.812588\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −13.8544 | −0.501563 | ||||||||
\(764\) | 0.208714 | 0.00755100 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 23.5765 | 0.851855 | ||||||||
\(767\) | −42.8957 | −1.54887 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.55195 | −0.200208 | −0.100104 | − | 0.994977i | \(-0.531918\pi\) | ||||
−0.100104 | + | 0.994977i | \(0.531918\pi\) | |||||||
\(770\) | −7.41169 | −0.267099 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 20.4582 | 0.736307 | ||||||||
\(773\) | 10.5156 | 0.378219 | 0.189110 | − | 0.981956i | \(-0.439440\pi\) | ||||
0.189110 | + | 0.981956i | \(0.439440\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 30.5496 | 1.09738 | ||||||||
\(776\) | −6.69563 | −0.240359 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.7592 | −0.600846 | ||||||||
\(779\) | 26.8770 | 0.962970 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.1690 | 0.399659 | ||||||||
\(782\) | −28.2981 | −1.01194 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.17744 | −0.0420514 | ||||||||
\(785\) | −20.0848 | −0.716858 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.3725 | −1.40348 | −0.701739 | − | 0.712434i | \(-0.747593\pi\) | ||||
−0.701739 | + | 0.712434i | \(0.747593\pi\) | |||||||
\(788\) | 24.9769 | 0.889765 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2.41889 | −0.0860604 | ||||||||
\(791\) | 31.7441 | 1.12869 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −74.8780 | −2.65900 | ||||||||
\(794\) | 5.12235 | 0.181785 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −18.3928 | −0.651916 | ||||||||
\(797\) | 19.0023 | 0.673097 | 0.336549 | − | 0.941666i | \(-0.390740\pi\) | ||||
0.336549 | + | 0.941666i | \(0.390740\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 47.5810 | 1.68329 | ||||||||
\(800\) | 3.86076 | 0.136498 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19.0659 | 0.673241 | ||||||||
\(803\) | −5.66983 | −0.200084 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.5595 | 0.442664 | ||||||||
\(806\) | 49.9939 | 1.76096 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 9.08647 | 0.319661 | ||||||||
\(809\) | 8.93922 | 0.314286 | 0.157143 | − | 0.987576i | \(-0.449772\pi\) | ||||
0.157143 | + | 0.987576i | \(0.449772\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5.23231 | 0.183731 | 0.0918657 | − | 0.995771i | \(-0.470717\pi\) | ||||
0.0918657 | + | 0.995771i | \(0.470717\pi\) | |||||||
\(812\) | 12.5013 | 0.438709 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 13.3711 | 0.468656 | ||||||||
\(815\) | −19.9254 | −0.697957 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 28.0541 | 0.981487 | ||||||||
\(818\) | −15.0451 | −0.526040 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.3963 | 0.397975 | ||||||||
\(821\) | 38.6144 | 1.34765 | 0.673826 | − | 0.738890i | \(-0.264650\pi\) | ||||
0.673826 | + | 0.738890i | \(0.264650\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −54.1702 | −1.88825 | −0.944127 | − | 0.329583i | \(-0.893092\pi\) | ||||
−0.944127 | + | 0.329583i | \(0.893092\pi\) | |||||||
\(824\) | 12.3461 | 0.430098 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.3828 | 0.570030 | ||||||||
\(827\) | −29.8399 | −1.03764 | −0.518818 | − | 0.854885i | \(-0.673628\pi\) | ||||
−0.518818 | + | 0.854885i | \(0.673628\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 29.4296 | 1.02213 | 0.511067 | − | 0.859541i | \(-0.329251\pi\) | ||||
0.511067 | + | 0.859541i | \(0.329251\pi\) | |||||||
\(830\) | 2.86114 | 0.0993116 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 6.31805 | 0.219039 | ||||||||
\(833\) | −6.83265 | −0.236737 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.4900 | −0.397628 | ||||||||
\(836\) | 7.24401 | 0.250539 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 12.6427 | 0.436735 | ||||||||
\(839\) | 6.91988 | 0.238901 | 0.119450 | − | 0.992840i | \(-0.461887\pi\) | ||||
0.119450 | + | 0.992840i | \(0.461887\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.15922 | −0.0744558 | ||||||||
\(842\) | 8.70185 | 0.299885 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.11885 | −0.176198 | ||||||||
\(845\) | 28.7308 | 0.988370 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.55997 | −0.225403 | ||||||||
\(848\) | 6.76900 | 0.232449 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 22.4039 | 0.768446 | ||||||||
\(851\) | −22.6580 | −0.776705 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.8776 | −1.05723 | −0.528614 | − | 0.848862i | \(-0.677288\pi\) | ||||
−0.528614 | + | 0.848862i | \(0.677288\pi\) | |||||||
\(854\) | 28.5975 | 0.978586 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.76521 | 0.162872 | ||||||||
\(857\) | 24.3599 | 0.832119 | 0.416059 | − | 0.909337i | \(-0.363411\pi\) | ||||
0.416059 | + | 0.909337i | \(0.363411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 46.2628 | 1.57847 | 0.789233 | − | 0.614093i | \(-0.210478\pi\) | ||||
0.789233 | + | 0.614093i | \(0.210478\pi\) | |||||||
\(860\) | 11.8953 | 0.405628 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −13.9905 | −0.476517 | ||||||||
\(863\) | 51.5003 | 1.75309 | 0.876546 | − | 0.481318i | \(-0.159842\pi\) | ||||
0.876546 | + | 0.481318i | \(0.159842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −15.2769 | −0.519429 | ||||||||
\(866\) | −23.4355 | −0.796371 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −19.0937 | −0.648083 | ||||||||
\(869\) | 6.52169 | 0.221233 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 78.5504 | 2.66158 | ||||||||
\(872\) | 5.74157 | 0.194434 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −12.2753 | −0.415220 | ||||||||
\(875\) | −22.8211 | −0.771493 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −6.71660 | −0.226803 | −0.113402 | − | 0.993549i | \(-0.536175\pi\) | ||||
−0.113402 | + | 0.993549i | \(0.536175\pi\) | |||||||
\(878\) | 17.3808 | 0.586574 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.07157 | 0.103543 | ||||||||
\(881\) | 15.0720 | 0.507789 | 0.253894 | − | 0.967232i | \(-0.418288\pi\) | ||||
0.253894 | + | 0.967232i | \(0.418288\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.56028 | −0.0525077 | −0.0262539 | − | 0.999655i | \(-0.508358\pi\) | ||||
−0.0262539 | + | 0.999655i | \(0.508358\pi\) | |||||||
\(884\) | 36.6635 | 1.23313 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −14.3666 | −0.482656 | ||||||||
\(887\) | −3.52972 | −0.118517 | −0.0592583 | − | 0.998243i | \(-0.518874\pi\) | ||||
−0.0592583 | + | 0.998243i | \(0.518874\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.32654 | 0.245724 | ||||||||
\(890\) | 13.7768 | 0.461798 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −24.0494 | −0.805233 | ||||||||
\(893\) | 20.6400 | 0.690692 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.8138 | −0.528597 | ||||||||
\(896\) | −2.41300 | −0.0806126 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.35069 | 0.145184 | ||||||||
\(899\) | −40.9950 | −1.36726 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.2803 | 1.30862 | ||||||||
\(902\) | −30.7260 | −1.02306 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.1555 | −0.437544 | ||||||||
\(905\) | 13.3263 | 0.442981 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.131286 | 0.00435928 | 0.00217964 | − | 0.999998i | \(-0.499306\pi\) | ||||
0.00217964 | + | 0.999998i | \(0.499306\pi\) | |||||||
\(908\) | 16.4469 | 0.545809 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −16.2723 | −0.539421 | ||||||||
\(911\) | −0.346696 | −0.0114866 | −0.00574328 | − | 0.999984i | \(-0.501828\pi\) | ||||
−0.00574328 | + | 0.999984i | \(0.501828\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.71405 | −0.255298 | ||||||||
\(914\) | 28.9116 | 0.956311 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.67491 | 0.121423 | ||||||||
\(917\) | −50.4977 | −1.66758 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 52.9227 | 1.74576 | 0.872880 | − | 0.487935i | \(-0.162250\pi\) | ||||
0.872880 | + | 0.487935i | \(0.162250\pi\) | |||||||
\(920\) | −5.20493 | −0.171601 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.48477 | 0.114765 | ||||||||
\(923\) | 24.5215 | 0.807133 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 17.9385 | 0.589815 | ||||||||
\(926\) | 17.3353 | 0.569673 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −5.18081 | −0.170068 | ||||||||
\(929\) | −29.1343 | −0.955864 | −0.477932 | − | 0.878397i | \(-0.658613\pi\) | ||||
−0.477932 | + | 0.878397i | \(0.658613\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.96391 | −0.0971383 | ||||||||
\(932\) | −1.22524 | −0.0401340 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −21.8269 | −0.714197 | ||||||||
\(935\) | 17.8242 | 0.582915 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 55.7638 | 1.82172 | 0.910862 | − | 0.412711i | \(-0.135418\pi\) | ||||
0.910862 | + | 0.412711i | \(0.135418\pi\) | |||||||
\(938\) | −30.0001 | −0.979537 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 8.75167 | 0.285448 | ||||||||
\(941\) | −43.0006 | −1.40178 | −0.700889 | − | 0.713270i | \(-0.747213\pi\) | ||||
−0.700889 | + | 0.713270i | \(0.747213\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52.0668 | 1.69553 | ||||||||
\(944\) | −6.78939 | −0.220976 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −32.0716 | −1.04274 | ||||||||
\(947\) | −7.81340 | −0.253901 | −0.126951 | − | 0.991909i | \(-0.540519\pi\) | ||||
−0.126951 | + | 0.991909i | \(0.540519\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.4481 | −0.404081 | ||||||||
\(950\) | 9.71850 | 0.315310 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −14.0026 | −0.453826 | ||||||||
\(953\) | −17.0448 | −0.552135 | −0.276067 | − | 0.961138i | \(-0.589031\pi\) | ||||
−0.276067 | + | 0.961138i | \(0.589031\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.222771 | 0.00720871 | ||||||||
\(956\) | −19.6354 | −0.635055 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 32.2298 | 1.04130 | ||||||||
\(959\) | −13.0527 | −0.421493 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.6134 | 1.01979 | ||||||||
\(962\) | 29.3561 | 0.946477 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.6153 | −0.696183 | ||||||||
\(965\) | 21.8361 | 0.702930 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 30.5292 | 0.981753 | 0.490876 | − | 0.871229i | \(-0.336677\pi\) | ||||
0.490876 | + | 0.871229i | \(0.336677\pi\) | |||||||
\(968\) | 2.71860 | 0.0873791 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.14661 | −0.229464 | ||||||||
\(971\) | −41.4714 | −1.33088 | −0.665440 | − | 0.746451i | \(-0.731756\pi\) | ||||
−0.665440 | + | 0.746451i | \(0.731756\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −27.8080 | −0.891485 | ||||||||
\(974\) | −36.3486 | −1.16468 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −11.8514 | −0.379355 | ||||||||
\(977\) | 56.3272 | 1.80207 | 0.901033 | − | 0.433750i | \(-0.142810\pi\) | ||||
0.901033 | + | 0.433750i | \(0.142810\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.1442 | −1.18713 | ||||||||
\(980\) | −1.25674 | −0.0401452 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 6.27108 | 0.200118 | ||||||||
\(983\) | 43.9298 | 1.40114 | 0.700571 | − | 0.713583i | \(-0.252929\pi\) | ||||
0.700571 | + | 0.713583i | \(0.252929\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.6592 | 0.849432 | ||||||||
\(986\) | −30.0641 | −0.957436 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 15.9041 | 0.505978 | ||||||||
\(989\) | 54.3469 | 1.72813 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −39.1494 | −1.24362 | −0.621810 | − | 0.783168i | \(-0.713602\pi\) | ||||
−0.621810 | + | 0.783168i | \(0.713602\pi\) | |||||||
\(992\) | 7.91286 | 0.251234 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −9.36526 | −0.297048 | ||||||||
\(995\) | −19.6316 | −0.622365 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.2386 | −0.957666 | −0.478833 | − | 0.877906i | \(-0.658940\pi\) | ||||
−0.478833 | + | 0.877906i | \(0.658940\pi\) | |||||||
\(998\) | −31.2490 | −0.989170 | ||||||||
\(999\) | 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 | 8046.2.a.l.1.7 | ✓ | 12 | |
3.2 | odd | 2 | 8046.2.a.m.1.6 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8046.2.a.l.1.7 | ✓ | 12 | 1.1 | even | 1 | trivial | |
8046.2.a.m.1.6 | yes | 12 | 3.2 | odd | 2 |