Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1216,4,Mod(1,1216)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1216, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1216.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1216 = 2^{6} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1216.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: | \(71.7463225670\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 2x^{4} - 28x^{3} - 8x^{2} + 73x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 608) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-3.54663\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1216.1 |
$q$-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 | 0 | ||||||||
\(3\) | 2.55330 | 0.491382 | 0.245691 | − | 0.969348i | \(-0.420985\pi\) | ||||
0.245691 | + | 0.969348i | \(0.420985\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −7.40075 | −0.661944 | −0.330972 | − | 0.943641i | \(-0.607377\pi\) | ||||
−0.330972 | + | 0.943641i | \(0.607377\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −10.4962 | −0.566741 | −0.283371 | − | 0.959010i | \(-0.591453\pi\) | ||||
−0.283371 | + | 0.959010i | \(0.591453\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −20.4807 | −0.758543 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −48.7928 | −1.33742 | −0.668709 | − | 0.743524i | \(-0.733153\pi\) | ||||
−0.668709 | + | 0.743524i | \(0.733153\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.45376 | −0.0950194 | −0.0475097 | − | 0.998871i | \(-0.515128\pi\) | ||||
−0.0475097 | + | 0.998871i | \(0.515128\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −18.8963 | −0.325267 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −61.5346 | −0.877901 | −0.438951 | − | 0.898511i | \(-0.644650\pi\) | ||||
−0.438951 | + | 0.898511i | \(0.644650\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −19.0000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −26.7999 | −0.278487 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 34.8416 | 0.315869 | 0.157934 | − | 0.987450i | \(-0.449517\pi\) | ||||
0.157934 | + | 0.987450i | \(0.449517\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −70.2288 | −0.561831 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −121.232 | −0.864117 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 179.528 | 1.14957 | 0.574786 | − | 0.818304i | \(-0.305085\pi\) | ||||
0.574786 | + | 0.818304i | \(0.305085\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 132.845 | 0.769667 | 0.384833 | − | 0.922986i | \(-0.374259\pi\) | ||||
0.384833 | + | 0.922986i | \(0.374259\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −124.583 | −0.657184 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 77.6798 | 0.375151 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 99.3918 | 0.441619 | 0.220810 | − | 0.975317i | \(-0.429130\pi\) | ||||
0.220810 | + | 0.975317i | \(0.429130\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.3718 | −0.0466908 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 382.310 | 1.45626 | 0.728132 | − | 0.685437i | \(-0.240389\pi\) | ||||
0.728132 | + | 0.685437i | \(0.240389\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 129.659 | 0.459834 | 0.229917 | − | 0.973210i | \(-0.426154\pi\) | ||||
0.229917 | + | 0.973210i | \(0.426154\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 151.572 | 0.502113 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −488.106 | −1.51484 | −0.757420 | − | 0.652928i | \(-0.773541\pi\) | ||||
−0.757420 | + | 0.652928i | \(0.773541\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −232.830 | −0.678804 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −157.116 | −0.431385 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 129.199 | 0.334846 | 0.167423 | − | 0.985885i | \(-0.446455\pi\) | ||||
0.167423 | + | 0.985885i | \(0.446455\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 361.104 | 0.885295 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −48.5127 | −0.112731 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 479.346 | 1.05772 | 0.528861 | − | 0.848709i | \(-0.322619\pi\) | ||||
0.528861 | + | 0.848709i | \(0.322619\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 394.879 | 0.828836 | 0.414418 | − | 0.910087i | \(-0.363985\pi\) | ||||
0.414418 | + | 0.910087i | \(0.363985\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 214.969 | 0.429898 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 32.9612 | 0.0628975 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 19.8601 | 0.0362135 | 0.0181067 | − | 0.999836i | \(-0.494236\pi\) | ||||
0.0181067 | + | 0.999836i | \(0.494236\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 88.9610 | 0.155212 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 221.694 | 0.370567 | 0.185283 | − | 0.982685i | \(-0.440680\pi\) | ||||
0.185283 | + | 0.982685i | \(0.440680\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 258.902 | 0.415099 | 0.207549 | − | 0.978225i | \(-0.433451\pi\) | ||||
0.207549 | + | 0.978225i | \(0.433451\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −179.315 | −0.276074 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 512.139 | 0.757970 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 469.595 | 0.668780 | 0.334390 | − | 0.942435i | \(-0.391470\pi\) | ||||
0.334390 | + | 0.942435i | \(0.391470\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 243.436 | 0.333932 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 373.014 | 0.493296 | 0.246648 | − | 0.969105i | \(-0.420671\pi\) | ||||
0.246648 | + | 0.969105i | \(0.420671\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 455.402 | 0.581121 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 458.390 | 0.564880 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1609.29 | −1.91668 | −0.958340 | − | 0.285631i | \(-0.907797\pi\) | ||||
−0.958340 | + | 0.285631i | \(0.907797\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 46.7476 | 0.0538514 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 339.193 | 0.378201 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 140.614 | 0.151860 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1654.62 | −1.73198 | −0.865988 | − | 0.500065i | \(-0.833309\pi\) | ||||
−0.865988 | + | 0.500065i | \(0.833309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 999.310 | 1.01449 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 660.681 | 0.650893 | 0.325447 | − | 0.945560i | \(-0.394485\pi\) | ||||
0.325447 | + | 0.945560i | \(0.394485\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −99.1397 | −0.0948401 | −0.0474200 | − | 0.998875i | \(-0.515100\pi\) | ||||
−0.0474200 | + | 0.998875i | \(0.515100\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 198.340 | 0.184342 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1584.99 | 1.43202 | 0.716011 | − | 0.698089i | \(-0.245966\pi\) | ||||
0.716011 | + | 0.698089i | \(0.245966\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 203.005 | 0.178389 | 0.0891943 | − | 0.996014i | \(-0.471571\pi\) | ||||
0.0891943 | + | 0.996014i | \(0.471571\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 253.777 | 0.217004 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1849.28 | −1.53952 | −0.769761 | − | 0.638332i | \(-0.779625\pi\) | ||||
−0.769761 | + | 0.638332i | \(0.779625\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −257.854 | −0.209087 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 91.2161 | 0.0720763 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 645.879 | 0.497543 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1049.74 | 0.788687 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 976.151 | 0.715582 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1444.84 | 1.03384 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1739.70 | −1.21554 | −0.607769 | − | 0.794114i | \(-0.707935\pi\) | ||||
−0.607769 | + | 0.794114i | \(0.707935\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 331.059 | 0.225954 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1490.46 | 0.994060 | 0.497030 | − | 0.867733i | \(-0.334424\pi\) | ||||
0.497030 | + | 0.867733i | \(0.334424\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 199.428 | 0.130019 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 897.210 | 0.571997 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 866.483 | 0.540355 | 0.270178 | − | 0.962810i | \(-0.412918\pi\) | ||||
0.270178 | + | 0.962810i | \(0.412918\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −498.851 | −0.304403 | −0.152202 | − | 0.988349i | \(-0.548636\pi\) | ||||
−0.152202 | + | 0.988349i | \(0.548636\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1246.28 | −0.744366 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 217.312 | 0.127081 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1328.65 | −0.760952 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −594.484 | −0.333552 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −696.388 | −0.382888 | −0.191444 | − | 0.981504i | \(-0.561317\pi\) | ||||
−0.191444 | + | 0.981504i | \(0.561317\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2834.12 | 1.52740 | 0.763699 | − | 0.645573i | \(-0.223381\pi\) | ||||
0.763699 | + | 0.645573i | \(0.223381\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1260.27 | 0.665926 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −983.153 | −0.509476 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2337.71 | −1.18834 | −0.594172 | − | 0.804338i | \(-0.702520\pi\) | ||||
−0.594172 | + | 0.804338i | \(0.702520\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 329.883 | 0.164537 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −365.704 | −0.179016 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −649.785 | −0.312240 | −0.156120 | − | 0.987738i | \(-0.549899\pi\) | ||||
−0.156120 | + | 0.987738i | \(0.549899\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 922.006 | 0.435018 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3101.68 | 1.43722 | 0.718609 | − | 0.695415i | \(-0.244779\pi\) | ||||
0.718609 | + | 0.695415i | \(0.244779\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2177.16 | −0.990971 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 389.133 | 0.174022 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 226.436 | 0.0995123 | 0.0497561 | − | 0.998761i | \(-0.484156\pi\) | ||||
0.0497561 | + | 0.998761i | \(0.484156\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 737.135 | 0.318413 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1223.91 | 0.519746 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2519.69 | 1.05213 | 0.526063 | − | 0.850446i | \(-0.323668\pi\) | ||||
0.526063 | + | 0.850446i | \(0.323668\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1012.54 | 0.415809 | 0.207904 | − | 0.978149i | \(-0.433336\pi\) | ||||
0.207904 | + | 0.978149i | \(0.433336\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1008.24 | 0.407276 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −735.575 | −0.292327 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3002.45 | 1.17412 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1272.48 | 0.489731 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1941.43 | 0.735480 | 0.367740 | − | 0.929929i | \(-0.380132\pi\) | ||||
0.367740 | + | 0.929929i | \(0.380132\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2069.72 | 0.771926 | 0.385963 | − | 0.922514i | \(-0.373869\pi\) | ||||
0.385963 | + | 0.922514i | \(0.373869\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 84.1598 | 0.0309067 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4208.36 | −1.52200 | −0.760998 | − | 0.648754i | \(-0.775290\pi\) | ||||
−0.760998 | + | 0.648754i | \(0.775290\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −267.700 | −0.0953604 | −0.0476802 | − | 0.998863i | \(-0.515183\pi\) | ||||
−0.0476802 | + | 0.998863i | \(0.515183\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 50.7089 | 0.0177947 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1884.37 | −0.651510 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2829.38 | −0.963964 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −713.579 | −0.239600 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 927.064 | 0.306825 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1259.32 | −0.410876 | −0.205438 | − | 0.978670i | \(-0.565862\pi\) | ||||
−0.205438 | + | 0.978670i | \(0.565862\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 566.051 | 0.182090 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −959.578 | −0.304384 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1394.37 | −0.436202 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 661.054 | 0.203972 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 274.060 | 0.0834176 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3639.90 | −1.09303 | −0.546516 | − | 0.837449i | \(-0.684046\pi\) | ||||
−0.546516 | + | 0.837449i | \(0.684046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1438.33 | 0.426173 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1873.77 | 0.547870 | 0.273935 | − | 0.961748i | \(-0.411675\pi\) | ||||
0.273935 | + | 0.961748i | \(0.411675\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4120.43 | −1.18902 | −0.594510 | − | 0.804088i | \(-0.702654\pi\) | ||||
−0.594510 | + | 0.804088i | \(0.702654\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1307.64 | 0.372453 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 562.027 | 0.158024 | 0.0790121 | − | 0.996874i | \(-0.474823\pi\) | ||||
0.0790121 | + | 0.996874i | \(0.474823\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3612.35 | 1.00274 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1199.02 | 0.328627 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4754.65 | 1.28683 | 0.643415 | − | 0.765517i | \(-0.277517\pi\) | ||||
0.643415 | + | 0.765517i | \(0.277517\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 806.451 | 0.215552 | 0.107776 | − | 0.994175i | \(-0.465627\pi\) | ||||
0.107776 | + | 0.994175i | \(0.465627\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 3894.84 | 1.02821 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1723.12 | 0.449330 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 84.6215 | 0.0217989 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 952.415 | 0.242397 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2484.87 | −0.624876 | −0.312438 | − | 0.949938i | \(-0.601146\pi\) | ||||
−0.312438 | + | 0.949938i | \(0.601146\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1700.02 | −0.422448 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1162.78 | 0.285553 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 3530.59 | 0.856933 | 0.428467 | − | 0.903558i | \(-0.359054\pi\) | ||||
0.428467 | + | 0.903558i | \(0.359054\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1043.24 | −0.250284 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3676.86 | −0.872001 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3025.99 | −0.709470 | −0.354735 | − | 0.934967i | \(-0.615429\pi\) | ||||
−0.354735 | + | 0.934967i | \(0.615429\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −956.169 | −0.221649 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −4109.00 | −0.941822 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3179.99 | −0.720772 | −0.360386 | − | 0.932803i | \(-0.617355\pi\) | ||||
−0.360386 | + | 0.932803i | \(0.617355\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5796.15 | 1.29923 | 0.649614 | − | 0.760264i | \(-0.274931\pi\) | ||||
0.649614 | + | 0.760264i | \(0.274931\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 119.360 | 0.0264616 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 3426.66 | 0.751402 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5143.01 | 1.11557 | 0.557786 | − | 0.829984i | \(-0.311651\pi\) | ||||
0.557786 | + | 0.829984i | \(0.311651\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2720.75 | −0.583826 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2121.08 | 0.450296 | 0.225148 | − | 0.974325i | \(-0.427713\pi\) | ||||
0.225148 | + | 0.974325i | \(0.427713\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5446.02 | 1.14393 | 0.571965 | − | 0.820278i | \(-0.306181\pi\) | ||||
0.571965 | + | 0.820278i | \(0.306181\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 359.030 | 0.0746215 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4012.80 | −0.825324 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1126.50 | −0.229289 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4224.75 | −0.851062 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6125.16 | −1.22128 | −0.610641 | − | 0.791908i | \(-0.709088\pi\) | ||||
−0.610641 | + | 0.791908i | \(0.709088\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3547.53 | −0.700152 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5915.27 | 1.15569 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −155.176 | −0.0300136 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1360.93 | −0.260607 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1686.92 | 0.319837 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2922.40 | −0.548643 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1263.62 | −0.234914 | −0.117457 | − | 0.993078i | \(-0.537474\pi\) | ||||
−0.117457 | + | 0.993078i | \(0.537474\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −253.133 | −0.0466027 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4954.26 | 0.903313 | 0.451657 | − | 0.892192i | \(-0.350833\pi\) | ||||
0.451657 | + | 0.892192i | \(0.350833\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4740.07 | 0.855989 | 0.427995 | − | 0.903781i | \(-0.359220\pi\) | ||||
0.427995 | + | 0.903781i | \(0.359220\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1590.93 | −0.284568 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4986.86 | 0.883564 | 0.441782 | − | 0.897122i | \(-0.354346\pi\) | ||||
0.441782 | + | 0.897122i | \(0.354346\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8759.71 | −1.53746 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4046.94 | 0.703671 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1169.16 | 0.201404 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 312.783 | 0.0533848 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 518.332 | 0.0876570 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5123.25 | 0.858523 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4783.52 | 0.794339 | 0.397169 | − | 0.917745i | \(-0.369993\pi\) | ||||
0.397169 | + | 0.917745i | \(0.369993\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2035.61 | −0.334987 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −146.980 | −0.0239713 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 5653.91 | 0.913912 | 0.456956 | − | 0.889489i | \(-0.348940\pi\) | ||||
0.456956 | + | 0.889489i | \(0.348940\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4721.77 | −0.756494 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −6481.88 | −1.02937 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6044.02 | 0.951448 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −658.378 | −0.102742 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 12278.2 | 1.89951 | 0.949753 | − | 0.312999i | \(-0.101334\pi\) | ||||
0.949753 | + | 0.312999i | \(0.101334\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12930.5 | 1.98324 | 0.991621 | − | 0.129180i | \(-0.0412346\pi\) | ||||
0.991621 | + | 0.129180i | \(0.0412346\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 539.940 | 0.0821079 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1583.46 | 0.238751 | 0.119375 | − | 0.992849i | \(-0.461911\pi\) | ||||
0.119375 | + | 0.992849i | \(0.461911\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1640.70 | −0.245294 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1649.12 | 0.244484 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8248.96 | 1.21271 | 0.606355 | − | 0.795194i | \(-0.292631\pi\) | ||||
0.606355 | + | 0.795194i | \(0.292631\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2680.30 | 0.387547 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1916.07 | −0.274772 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1330.75 | −0.189277 | −0.0946387 | − | 0.995512i | \(-0.530170\pi\) | ||||
−0.0946387 | + | 0.995512i | \(0.530170\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −7829.97 | −1.10464 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1356.10 | −0.189771 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 262.288 | 0.0364095 | 0.0182048 | − | 0.999834i | \(-0.494205\pi\) | ||||
0.0182048 | + | 0.999834i | \(0.494205\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3689.11 | 0.508013 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −799.577 | −0.109232 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −808.151 | −0.109530 | −0.0547651 | − | 0.998499i | \(-0.517441\pi\) | ||||
−0.0547651 | + | 0.998499i | \(0.517441\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4441.97 | −0.597294 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1379.74 | 0.184076 | 0.0920382 | − | 0.995755i | \(-0.470662\pi\) | ||||
0.0920382 | + | 0.995755i | \(0.470662\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3790.22 | −0.501733 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2655.51 | −0.348804 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −15154.6 | −1.97524 | −0.987618 | − | 0.156880i | \(-0.949856\pi\) | ||||
−0.987618 | + | 0.156880i | \(0.949856\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2143.96 | −0.277301 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3805.58 | 0.488463 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3475.36 | −0.442695 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3851.15 | 0.486861 | 0.243431 | − | 0.969918i | \(-0.421727\pi\) | ||||
0.243431 | + | 0.969918i | \(0.421727\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 509.198 | 0.0638892 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 539.933 | 0.0672394 | 0.0336197 | − | 0.999435i | \(-0.489297\pi\) | ||||
0.0336197 | + | 0.999435i | \(0.489297\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −591.660 | −0.0731332 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1801.61 | −0.221044 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4849.61 | −0.590630 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −8778.60 | −1.06130 | −0.530652 | − | 0.847590i | \(-0.678053\pi\) | ||||
−0.530652 | + | 0.847590i | \(0.678053\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2212.39 | 0.265521 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −5031.31 | −0.599455 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2760.58 | −0.326534 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1273.72 | −0.149578 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13534.2 | −1.57802 | −0.789010 | − | 0.614380i | \(-0.789406\pi\) | ||||
−0.789010 | + | 0.614380i | \(0.789406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4055.19 | 0.469448 | 0.234724 | − | 0.972062i | \(-0.424581\pi\) | ||||
0.234724 | + | 0.972062i | \(0.424581\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9996.73 | 1.14907 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4321.50 | 0.493232 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4144.72 | −0.469736 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 554.862 | 0.0624452 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −14601.5 | −1.63186 | −0.815929 | − | 0.578153i | \(-0.803774\pi\) | ||||
−0.815929 | + | 0.578153i | \(0.803774\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3546.74 | −0.393638 | −0.196819 | − | 0.980440i | \(-0.563061\pi\) | ||||
−0.196819 | + | 0.980440i | \(0.563061\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3392.43 | −0.373918 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −661.990 | −0.0724652 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4947.47 | −0.537881 | −0.268941 | − | 0.963157i | \(-0.586674\pi\) | ||||
−0.268941 | + | 0.963157i | \(0.586674\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4768.51 | 0.514903 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3858.07 | 0.413776 | 0.206888 | − | 0.978365i | \(-0.433666\pi\) | ||||
0.206888 | + | 0.978365i | \(0.433666\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11910.0 | 1.26873 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −1778.08 | −0.188144 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5045.14 | −0.530278 | −0.265139 | − | 0.964210i | \(-0.585418\pi\) | ||||
−0.265139 | + | 0.964210i | \(0.585418\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −18654.0 | −1.94763 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7236.34 | 0.750536 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −345.967 | −0.0356466 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8779.52 | −0.898662 | −0.449331 | − | 0.893365i | \(-0.648338\pi\) | ||||
−0.449331 | + | 0.893365i | \(0.648338\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7459.97 | 0.758610 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16829.5 | 1.70028 | 0.850138 | − | 0.526561i | \(-0.176519\pi\) | ||||
0.850138 | + | 0.526561i | \(0.176519\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6166.41 | −0.618957 | −0.309479 | − | 0.950906i | \(-0.600155\pi\) | ||||
−0.309479 | + | 0.950906i | \(0.600155\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −2510.28 | −0.250347 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2117.84 | −0.209854 | −0.104927 | − | 0.994480i | \(-0.533461\pi\) | ||||
−0.104927 | + | 0.994480i | \(0.533461\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −208.456 | −0.0205237 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −5968.88 | −0.583931 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6326.45 | −0.614991 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1334.35 | 0.128893 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2646.08 | −0.253995 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3832.94 | −0.365619 | −0.182809 | − | 0.983148i | \(-0.558519\pi\) | ||||
−0.182809 | + | 0.983148i | \(0.558519\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −442.668 | −0.0419624 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −933.752 | −0.0879652 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12245.5 | 1.14647 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3080.97 | 0.286678 | 0.143339 | − | 0.989674i | \(-0.454216\pi\) | ||||
0.143339 | + | 0.989674i | \(0.454216\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1659.10 | −0.153429 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9947.19 | 0.914278 | 0.457139 | − | 0.889395i | \(-0.348874\pi\) | ||||
0.457139 | + | 0.889395i | \(0.348874\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −11047.2 | −1.00921 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7395.65 | −0.671535 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2326.94 | −0.210015 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13670.7 | −1.22642 | −0.613211 | − | 0.789919i | \(-0.710122\pi\) | ||||
−0.613211 | + | 0.789919i | \(0.710122\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7919.51 | 0.706223 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2851.63 | 0.252779 | 0.126390 | − | 0.991981i | \(-0.459661\pi\) | ||||
0.126390 | + | 0.991981i | \(0.459661\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4889.54 | −0.430855 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5558.95 | −0.486946 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2228.47 | −0.194057 | −0.0970286 | − | 0.995282i | \(-0.530934\pi\) | ||||
−0.0970286 | + | 0.995282i | \(0.530934\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2717.49 | −0.235254 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2303.41 | 0.198242 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 733.709 | 0.0627788 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 23816.1 | 2.02597 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 578.159 | 0.0488986 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −12531.3 | −1.05375 | −0.526877 | − | 0.849942i | \(-0.676637\pi\) | ||||
−0.526877 | + | 0.849942i | \(0.676637\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −11402.8 | −0.953362 | −0.476681 | − | 0.879076i | \(-0.658160\pi\) | ||||
−0.476681 | + | 0.879076i | \(0.658160\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1882.13 | 0.156462 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8174.56 | −0.675691 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10953.1 | −0.900227 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9817.34 | −0.802328 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1702.72 | −0.138373 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11730.1 | −0.947918 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 6433.52 | 0.516996 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 11360.4 | 0.907845 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1217.02 | 0.0967171 | 0.0483585 | − | 0.998830i | \(-0.484601\pi\) | ||||
0.0483585 | + | 0.998830i | \(0.484601\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2585.31 | 0.204321 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1502.39 | −0.118083 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −13940.4 | −1.08967 | −0.544833 | − | 0.838545i | \(-0.683407\pi\) | ||||
−0.544833 | + | 0.838545i | \(0.683407\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8087.38 | −0.628708 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3411.04 | −0.263730 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4928.97 | −0.379025 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −1878.14 | −0.143644 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10002.4 | −0.760889 | −0.380445 | − | 0.924804i | \(-0.624229\pi\) | ||||
−0.380445 | + | 0.924804i | \(0.624229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −577.473 | −0.0436932 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7666.14 | 0.576942 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8869.58 | −0.663958 | −0.331979 | − | 0.943287i | \(-0.607716\pi\) | ||||
−0.331979 | + | 0.943287i | \(0.607716\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13686.1 | 1.01908 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2555.15 | −0.189253 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 8649.42 | 0.637263 | 0.318631 | − | 0.947879i | \(-0.396777\pi\) | ||||
0.318631 | + | 0.947879i | \(0.396777\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6544.85 | 0.479673 | 0.239837 | − | 0.970813i | \(-0.422906\pi\) | ||||
0.239837 | + | 0.970813i | \(0.422906\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4957.04 | 0.361402 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2446.88 | −0.177465 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 4202.01 | 0.303175 | 0.151587 | − | 0.988444i | \(-0.451561\pi\) | ||||
0.151587 | + | 0.988444i | \(0.451561\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5284.61 | 0.379311 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3915.23 | −0.279571 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6303.98 | −0.447829 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −675.068 | −0.0477105 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −21992.1 | −1.54635 | −0.773177 | − | 0.634190i | \(-0.781334\pi\) | ||||
−0.773177 | + | 0.634190i | \(0.781334\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2524.05 | −0.176574 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10745.2 | −0.747882 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −1596.92 | −0.110586 | −0.0552932 | − | 0.998470i | \(-0.517609\pi\) | ||||
−0.0552932 | + | 0.998470i | \(0.517609\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −4779.99 | −0.329345 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −683.517 | −0.0468584 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9965.77 | 0.679783 | 0.339892 | − | 0.940465i | \(-0.389610\pi\) | ||||
0.339892 | + | 0.940465i | \(0.389610\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12790.5 | −0.868110 | −0.434055 | − | 0.900886i | \(-0.642918\pi\) | ||||
−0.434055 | + | 0.900886i | \(0.642918\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −406.749 | −0.0274695 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −7768.88 | −0.522066 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −25391.9 | −1.69790 | −0.848949 | − | 0.528474i | \(-0.822764\pi\) | ||||
−0.848949 | + | 0.528474i | \(0.822764\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4811.35 | −0.320141 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2173.91 | 0.143939 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9439.11 | 0.621929 | 0.310964 | − | 0.950422i | \(-0.399348\pi\) | ||||
0.310964 | + | 0.950422i | \(0.399348\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7224.26 | −0.473675 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 3247.93 | 0.211923 | 0.105962 | − | 0.994370i | \(-0.466208\pi\) | ||||
0.105962 | + | 0.994370i | \(0.466208\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2781.32 | −0.180599 | −0.0902995 | − | 0.995915i | \(-0.528782\pi\) | ||||
−0.0902995 | + | 0.995915i | \(0.528782\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4223.93 | −0.272947 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 16891.4 | 1.08626 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1914.31 | −0.122516 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2367.07 | 0.150768 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6116.03 | −0.387698 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 877.112 | 0.0553364 | 0.0276682 | − | 0.999617i | \(-0.491192\pi\) | ||||
0.0276682 | + | 0.999617i | \(0.491192\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −3215.41 | −0.201897 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 12875.1 | 0.804618 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1036.97 | 0.0644996 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4540.44 | −0.281091 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 18518.8 | 1.14111 | 0.570554 | − | 0.821260i | \(-0.306728\pi\) | ||||
0.570554 | + | 0.821260i | \(0.306728\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13493.0 | 0.827548 | 0.413774 | − | 0.910380i | \(-0.364210\pi\) | ||||
0.413774 | + | 0.910380i | \(0.364210\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2450.09 | −0.149569 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9832.93 | 0.597485 | 0.298742 | − | 0.954334i | \(-0.403433\pi\) | ||||
0.298742 | + | 0.954334i | \(0.403433\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23388.7 | −1.41462 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3560.23 | −0.214342 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4752.63 | −0.284816 | −0.142408 | − | 0.989808i | \(-0.545485\pi\) | ||||
−0.142408 | + | 0.989808i | \(0.545485\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11030.5 | −0.658012 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5302.49 | −0.314870 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −2061.33 | −0.121848 | −0.0609242 | − | 0.998142i | \(-0.519405\pi\) | ||||
−0.0609242 | + | 0.998142i | \(0.519405\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2408.74 | 0.141739 | 0.0708693 | − | 0.997486i | \(-0.477423\pi\) | ||||
0.0708693 | + | 0.997486i | \(0.477423\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 699.758 | 0.0409900 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1475.92 | −0.0860655 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6255.06 | 0.363114 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −9293.76 | −0.537096 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19267.2 | −1.10850 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22916.0 | −1.31255 | −0.656275 | − | 0.754522i | \(-0.727869\pi\) | ||||
−0.656275 | + | 0.754522i | \(0.727869\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8514.00 | 0.485487 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11902.9 | 0.675724 | 0.337862 | − | 0.941196i | \(-0.390296\pi\) | ||||
0.337862 | + | 0.941196i | \(0.390296\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17367.3 | 0.981582 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4784.29 | 0.269214 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 25810.3 | 1.44598 | 0.722989 | − | 0.690860i | \(-0.242768\pi\) | ||||
0.722989 | + | 0.690860i | \(0.242768\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6412.63 | −0.357685 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −10520.7 | −0.584264 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −575.421 | −0.0318168 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1966.02 | −0.108236 | −0.0541180 | − | 0.998535i | \(-0.517235\pi\) | ||||
−0.0541180 | + | 0.998535i | \(0.517235\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −10489.0 | −0.574953 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3691.88 | 0.201498 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −23525.3 | −1.27846 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1435.02 | 0.0776503 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −29611.2 | −1.59543 | −0.797717 | − | 0.603032i | \(-0.793959\pi\) | ||||
−0.797717 | + | 0.603032i | \(0.793959\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1888.44 | −0.101314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 9223.40 | 0.492728 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6934.64 | −0.368888 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 27618.7 | 1.46297 | 0.731483 | − | 0.681860i | \(-0.238829\pi\) | ||||
0.731483 | + | 0.681860i | \(0.238829\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −9617.63 | −0.507299 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 4628.53 | 0.243113 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1608.27 | −0.0841202 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 12140.0 | 0.632326 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 32303.4 | 1.67554 | 0.837770 | − | 0.546023i | \(-0.183859\pi\) | ||||
0.837770 | + | 0.546023i | \(0.183859\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1040.59 | 0.0537498 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2059.11 | 0.105919 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12608.1 | −0.645865 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 30854.5 | 1.57405 | 0.787023 | − | 0.616924i | \(-0.211621\pi\) | ||||
0.787023 | + | 0.616924i | \(0.211621\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3371.90 | 0.171310 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7978.54 | −0.403689 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 22692.4 | 1.14347 | 0.571735 | − | 0.820438i | \(-0.306271\pi\) | ||||
0.571735 | + | 0.820438i | \(0.306271\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4399.63 | 0.220793 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −969.033 | −0.0484325 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −34965.3 | −1.74048 | −0.870242 | − | 0.492624i | \(-0.836038\pi\) | ||||
−0.870242 | + | 0.492624i | \(0.836038\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 216.064 | 0.0107116 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18699.8 | 0.923325 | 0.461663 | − | 0.887056i | \(-0.347253\pi\) | ||||
0.461663 | + | 0.887056i | \(0.347253\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5153.79 | 0.253450 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −7639.57 | −0.374187 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −16636.3 | −0.811586 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20650.7 | −1.00340 | −0.501700 | − | 0.865041i | \(-0.667292\pi\) | ||||
−0.501700 | + | 0.865041i | \(0.667292\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −6344.62 | −0.307053 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −20974.6 | −1.01105 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −33118.8 | −1.59012 | −0.795062 | − | 0.606528i | \(-0.792562\pi\) | ||||
−0.795062 | + | 0.606528i | \(0.792562\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4340.66 | −0.207584 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16513.6 | 0.786618 | 0.393309 | − | 0.919406i | \(-0.371330\pi\) | ||||
0.393309 | + | 0.919406i | \(0.371330\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2130.78 | −0.101100 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9326.94 | −0.440806 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2134.90 | −0.100504 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 16599.5 | 0.778406 | 0.389203 | − | 0.921152i | \(-0.372750\pi\) | ||||
0.389203 | + | 0.921152i | \(0.372750\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9014.64 | 0.421082 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22940.9 | 1.06743 | 0.533717 | − | 0.845663i | \(-0.320795\pi\) | ||||
0.533717 | + | 0.845663i | \(0.320795\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −9329.55 | −0.432422 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2663.69 | −0.122985 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7263.89 | −0.334090 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10817.1 | −0.495603 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −21764.6 | −0.993365 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17300.8 | 0.786616 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 15086.1 | 0.683304 | 0.341652 | − | 0.939826i | \(-0.389014\pi\) | ||||
0.341652 | + | 0.939826i | \(0.389014\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7726.25 | −0.348621 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 19410.4 | 0.872511 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1758.70 | −0.0787555 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −2441.38 | −0.108914 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 36309.4 | 1.61373 | 0.806867 | − | 0.590733i | \(-0.201161\pi\) | ||||
0.806867 | + | 0.590733i | \(0.201161\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30035.4 | 1.32988 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 32959.4 | 1.45388 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12632.6 | −0.555161 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2706.49 | 0.118498 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8119.47 | −0.354175 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 32700.4 | 1.42112 | 0.710560 | − | 0.703637i | \(-0.248442\pi\) | ||||
0.710560 | + | 0.703637i | \(0.248442\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6484.51 | 0.280767 | 0.140383 | − | 0.990097i | \(-0.455166\pi\) | ||||
0.140383 | + | 0.990097i | \(0.455166\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14799.3 | 0.638418 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 4808.90 | 0.206685 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2463.53 | −0.105493 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −957.422 | −0.0408486 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8864.19 | 0.376812 | 0.188406 | − | 0.982091i | \(-0.439668\pi\) | ||||
0.188406 | + | 0.982091i | \(0.439668\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 24083.4 | 1.02004 | 0.510022 | − | 0.860161i | \(-0.329637\pi\) | ||||
0.510022 | + | 0.860161i | \(0.329637\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8749.29 | 0.369226 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35052.0 | 1.47385 | 0.736927 | − | 0.675972i | \(-0.236276\pi\) | ||||
0.736927 | + | 0.675972i | \(0.236276\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1914.79 | −0.0802214 | −0.0401107 | − | 0.999195i | \(-0.512771\pi\) | ||||
−0.0401107 | + | 0.999195i | \(0.512771\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13131.6 | 0.548173 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 14327.1 | 0.595923 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −22954.8 | −0.951357 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −16105.1 | −0.665082 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −19785.9 | −0.814164 | −0.407082 | − | 0.913392i | \(-0.633454\pi\) | ||||
−0.407082 | + | 0.913392i | \(0.633454\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7841.48 | 0.321517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5415.75 | 0.221267 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 16112.7 | 0.655967 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11018.3 | −0.446981 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13905.3 | 0.562107 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3462.97 | 0.139494 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 287.455 | 0.0115384 | 0.00576920 | − | 0.999983i | \(-0.498164\pi\) | ||||
0.00576920 | + | 0.999983i | \(0.498164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2879.88 | −0.115193 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2352.88 | 0.0937839 | 0.0468919 | − | 0.998900i | \(-0.485068\pi\) | ||||
0.0468919 | + | 0.998900i | \(0.485068\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 29976.3 | 1.19066 | 0.595331 | − | 0.803480i | \(-0.297021\pi\) | ||||
0.595331 | + | 0.803480i | \(0.297021\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −10245.9 | −0.405550 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28858.3 | −1.13829 | −0.569147 | − | 0.822236i | \(-0.692726\pi\) | ||||
−0.569147 | + | 0.822236i | \(0.692726\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1675.80 | −0.0658715 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2876.28 | −0.112669 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −22912.9 | −0.894438 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −88.4524 | −0.00344098 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 33887.8 | 1.31378 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −15165.3 | −0.585922 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −45124.0 | −1.73743 | −0.868716 | − | 0.495310i | \(-0.835054\pi\) | ||||
−0.868716 | + | 0.495310i | \(0.835054\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15639.4 | −0.600116 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 46543.5 | 1.77990 | 0.889949 | − | 0.456060i | \(-0.150740\pi\) | ||||
0.889949 | + | 0.456060i | \(0.150740\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −10533.3 | −0.401442 | −0.200721 | − | 0.979648i | \(-0.564329\pi\) | ||||
−0.200721 | + | 0.979648i | \(0.564329\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −9057.89 | −0.344042 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28070.3 | 1.06258 | 0.531289 | − | 0.847191i | \(-0.321708\pi\) | ||||
0.531289 | + | 0.847191i | \(0.321708\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 18260.2 | 0.688896 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11877.9 | −0.446606 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9274.01 | 0.347528 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −18647.6 | −0.696448 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −396.211 | −0.0147482 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 23849.5 | 0.884788 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7950.19 | −0.293962 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3474.86 | −0.128058 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7493.55 | −0.275242 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 26589.1 | 0.973404 | 0.486702 | − | 0.873568i | \(-0.338200\pi\) | ||||
0.486702 | + | 0.873568i | \(0.338200\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13531.2 | −0.493731 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −32296.8 | −1.17458 | −0.587290 | − | 0.809377i | \(-0.699805\pi\) | ||||
−0.587290 | + | 0.809377i | \(0.699805\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18200.4 | −0.659743 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7461.76 | −0.269593 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −15644.1 | −0.563375 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35127.6 | 1.26089 | 0.630443 | − | 0.776236i | \(-0.282873\pi\) | ||||
0.630443 | + | 0.776236i | \(0.282873\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3226.40 | −0.115433 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −987.373 | −0.0352110 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6980.17 | −0.248115 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2030.45 | 0.0719403 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −14258.8 | −0.503570 | −0.251785 | − | 0.967783i | \(-0.581018\pi\) | ||||
−0.251785 | + | 0.967783i | \(0.581018\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4423.77 | 0.155728 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 12649.7 | 0.443872 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −22220.4 | −0.777202 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −40641.2 | −1.41696 | −0.708479 | − | 0.705732i | \(-0.750618\pi\) | ||||
−0.708479 | + | 0.705732i | \(0.750618\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12102.8 | 0.420618 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 22364.8 | 0.774782 | 0.387391 | − | 0.921915i | \(-0.373376\pi\) | ||||
0.387391 | + | 0.921915i | \(0.373376\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13320.3 | 0.459988 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9417.30 | −0.324174 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27719.2 | 0.951166 | 0.475583 | − | 0.879671i | \(-0.342237\pi\) | ||||
0.475583 | + | 0.879671i | \(0.342237\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1153.09 | −0.0394424 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 12732.9 | 0.434168 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −709.901 | −0.0241300 | −0.0120650 | − | 0.999927i | \(-0.503841\pi\) | ||||
−0.0120650 | + | 0.999927i | \(0.503841\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14368.0 | −0.486846 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −22366.1 | −0.755480 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9094.78 | −0.306242 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12143.2 | −0.407613 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −32461.6 | −1.08625 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −15317.5 | −0.510972 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2175.29 | 0.0723400 | 0.0361700 | − | 0.999346i | \(-0.488484\pi\) | ||||
0.0361700 | + | 0.999346i | \(0.488484\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2985.20 | 0.0989666 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13964.7 | 0.461533 | 0.230766 | − | 0.973009i | \(-0.425877\pi\) | ||||
0.230766 | + | 0.973009i | \(0.425877\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5236.04 | 0.172518 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 798.627 | 0.0262323 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8452.26 | −0.276778 | −0.138389 | − | 0.990378i | \(-0.544192\pi\) | ||||
−0.138389 | + | 0.990378i | \(0.544192\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 78521.9 | 2.56340 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4157.68 | −0.135316 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 55328.2 | 1.79521 | 0.897607 | − | 0.440798i | \(-0.145304\pi\) | ||||
0.897607 | + | 0.440798i | \(0.145304\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 31145.0 | 1.00748 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13081.2 | 0.421863 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 4517.54 | 0.145247 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 33520.4 | 1.07448 | 0.537240 | − | 0.843429i | \(-0.319467\pi\) | ||||
0.537240 | + | 0.843429i | \(0.319467\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12213.8 | 0.390324 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1981.18 | 0.0631232 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36267.7 | 1.15206 | 0.576032 | − | 0.817427i | \(-0.304600\pi\) | ||||
0.576032 | + | 0.817427i | \(0.304600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −12049.5 | −0.381611 |
(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 | 1216.4.a.bd.1.3 | 5 | ||
4.3 | odd | 2 | 1216.4.a.y.1.3 | 5 | |||
8.3 | odd | 2 | 608.4.a.h.1.3 | yes | 5 | ||
8.5 | even | 2 | 608.4.a.e.1.3 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
608.4.a.e.1.3 | ✓ | 5 | 8.5 | even | 2 | ||
608.4.a.h.1.3 | yes | 5 | 8.3 | odd | 2 | ||
1216.4.a.y.1.3 | 5 | 4.3 | odd | 2 | |||
1216.4.a.bd.1.3 | 5 | 1.1 | even | 1 | trivial |